diff --git a/lib/Slic3r.pm b/lib/Slic3r.pm
index 0c6c81bb57..46627311ff 100644
--- a/lib/Slic3r.pm
+++ b/lib/Slic3r.pm
@@ -167,6 +167,7 @@ sub thread_cleanup {
     *Slic3r::GUI::PresetHints::DESTROY      = sub {};
     *Slic3r::GUI::TabIface::DESTROY         = sub {};
     *Slic3r::OctoPrint::DESTROY             = sub {};
+    *Slic3r::Duet::DESTROY                  = sub {};
     *Slic3r::PresetUpdater::DESTROY         = sub {};
     return undef;  # this prevents a "Scalars leaked" warning
 }
diff --git a/lib/Slic3r/GUI/MainFrame.pm b/lib/Slic3r/GUI/MainFrame.pm
index ac62d63379..315bf2f451 100644
--- a/lib/Slic3r/GUI/MainFrame.pm
+++ b/lib/Slic3r/GUI/MainFrame.pm
@@ -26,6 +26,14 @@ our $appController;
 our $VALUE_CHANGE_EVENT    = Wx::NewEventType;
 # 2) To inform about a preset selection change or a "modified" status change.
 our $PRESETS_CHANGED_EVENT = Wx::NewEventType;
+# 3) To inform about a change of object selection
+our $OBJECT_SELECTION_CHANGED_EVENT = Wx::NewEventType;
+# 4) To inform about a change of object settings
+our $OBJECT_SETTINGS_CHANGED_EVENT = Wx::NewEventType;
+# 5) To inform about a remove of object 
+our $OBJECT_REMOVE_EVENT = Wx::NewEventType;
+# 6) To inform about a update of the scene 
+our $UPDATE_SCENE_EVENT = Wx::NewEventType;
 
 sub new {
     my ($class, %params) = @_;
@@ -123,6 +131,8 @@ sub new {
 
     $self->update_ui_from_settings;
 
+    Slic3r::GUI::update_mode();
+
     return $self;
 }
 
@@ -142,7 +152,12 @@ sub _init_tabpanel {
     });
     
     if (!$self->{no_plater}) {
-        $panel->AddPage($self->{plater} = Slic3r::GUI::Plater->new($panel), L("Plater"));
+        $panel->AddPage($self->{plater} = Slic3r::GUI::Plater->new($panel,
+            event_object_selection_changed   => $OBJECT_SELECTION_CHANGED_EVENT,
+            event_object_settings_changed    => $OBJECT_SETTINGS_CHANGED_EVENT,
+            event_remove_object              => $OBJECT_REMOVE_EVENT,
+            event_update_scene               => $UPDATE_SCENE_EVENT,
+            ), L("Plater"));
         if (!$self->{no_controller}) {
             $panel->AddPage($self->{controller} = Slic3r::GUI::Controller->new($panel), L("Controller"));
         }
@@ -163,6 +178,10 @@ sub _init_tabpanel {
                 my $value = $event->GetInt();
                 $self->{plater}->on_extruders_change($value);
             }
+            if ($opt_key eq 'printer_technology'){
+                my $value = $event->GetInt();# 0 ~ "ptFFF"; 1 ~ "ptSLA"
+                $self->{plater}->show_preset_comboboxes($value);
+            }
         }
         # don't save while loading for the first time
         $self->config->save($Slic3r::GUI::autosave) if $Slic3r::GUI::autosave && $self->{loaded};        
@@ -175,7 +194,7 @@ sub _init_tabpanel {
 
         my $tab = Slic3r::GUI::get_preset_tab($tab_name);
         if ($self->{plater}) {
-            # Update preset combo boxes (Print settings, Filament, Printer) from their respective tabs.
+            # Update preset combo boxes (Print settings, Filament, Material, Printer) from their respective tabs.
             my $presets = $tab->get_presets;
             if (defined $presets){
                 my $reload_dependent_tabs = $tab->get_dependent_tabs;
@@ -183,7 +202,7 @@ sub _init_tabpanel {
                 $self->{plater}->{"selected_item_$tab_name"} = $tab->get_selected_preset_item;
                 if ($tab_name eq 'printer') {
                     # Printer selected at the Printer tab, update "compatible" marks at the print and filament selectors.
-                    for my $tab_name_other (qw(print filament)) {
+                    for my $tab_name_other (qw(print filament sla_material)) {
                         # If the printer tells us that the print or filament preset has been switched or invalidated,
                         # refresh the print or filament tab page. Otherwise just refresh the combo box.
                         my $update_action = ($reload_dependent_tabs && (first { $_ eq $tab_name_other } (@{$reload_dependent_tabs}))) 
@@ -197,9 +216,43 @@ sub _init_tabpanel {
             }
         }
     });
+
+    # The following event is emited by the C++ Tab implementation on object selection change.
+    EVT_COMMAND($self, -1, $OBJECT_SELECTION_CHANGED_EVENT, sub {
+        my ($self, $event) = @_;
+        my $obj_idx = $event->GetId;
+        my $child = $event->GetInt == 1 ? 1 : undef;
+
+        $self->{plater}->select_object($obj_idx < 0 ? undef: $obj_idx, $child);
+        $self->{plater}->item_changed_selection($obj_idx);
+    });
+
+    # The following event is emited by the C++ GUI implementation on object settings change.
+    EVT_COMMAND($self, -1, $OBJECT_SETTINGS_CHANGED_EVENT, sub {
+        my ($self, $event) = @_;
+
+        my $line = $event->GetString;
+        my ($obj_idx, $parts_changed, $part_settings_changed) = split('',$line);
+
+        $self->{plater}->changed_object_settings($obj_idx, $parts_changed, $part_settings_changed);
+    });
+
+    # The following event is emited by the C++ GUI implementation on object remove.
+    EVT_COMMAND($self, -1, $OBJECT_REMOVE_EVENT, sub {
+        my ($self, $event) = @_;
+        $self->{plater}->remove();
+    });
+
+    # The following event is emited by the C++ GUI implementation on extruder change for object.
+    EVT_COMMAND($self, -1, $UPDATE_SCENE_EVENT, sub {
+        my ($self, $event) = @_;
+        $self->{plater}->update();
+    });
+        
+
     Slic3r::GUI::create_preset_tabs($self->{no_controller}, $VALUE_CHANGE_EVENT, $PRESETS_CHANGED_EVENT);
     $self->{options_tabs} = {};
-    for my $tab_name (qw(print filament printer)) {
+    for my $tab_name (qw(print filament sla_material printer)) {
         $self->{options_tabs}{$tab_name} = Slic3r::GUI::get_preset_tab("$tab_name");
     }
     
@@ -211,8 +264,14 @@ sub _init_tabpanel {
         # load initial config
         my $full_config = wxTheApp->{preset_bundle}->full_config;
         $self->{plater}->on_config_change($full_config);
+
         # Show a correct number of filament fields.
-        $self->{plater}->on_extruders_change(int(@{$full_config->nozzle_diameter}));
+        if (defined $full_config->nozzle_diameter){ # nozzle_diameter is undefined when SLA printer is selected
+            $self->{plater}->on_extruders_change(int(@{$full_config->nozzle_diameter}));
+        }
+
+        # Show correct preset comboboxes according to the printer_technology
+        $self->{plater}->show_preset_comboboxes(($full_config->printer_technology eq "FFF") ? 0 : 1);
     }
 }
 
diff --git a/lib/Slic3r/GUI/Plater.pm b/lib/Slic3r/GUI/Plater.pm
index a0eef72fea..3e0ecf5eb7 100644
--- a/lib/Slic3r/GUI/Plater.pm
+++ b/lib/Slic3r/GUI/Plater.pm
@@ -49,14 +49,21 @@ my $PreventListEvents = 0;
 our $appController;
 
 sub new {
-    my ($class, $parent) = @_;
+    my ($class, $parent, %params) = @_;
     my $self = $class->SUPER::new($parent, -1, wxDefaultPosition, wxDefaultSize, wxTAB_TRAVERSAL);
     $self->{config} = Slic3r::Config::new_from_defaults_keys([qw(
         bed_shape complete_objects extruder_clearance_radius skirts skirt_distance brim_width variable_layer_height
-        serial_port serial_speed octoprint_host octoprint_apikey octoprint_cafile
+        serial_port serial_speed host_type print_host printhost_apikey printhost_cafile
         nozzle_diameter single_extruder_multi_material wipe_tower wipe_tower_x wipe_tower_y wipe_tower_width
 	wipe_tower_rotation_angle extruder_colour filament_colour max_print_height printer_model
     )]);
+
+    # store input params
+    $self->{event_object_selection_changed} = $params{event_object_selection_changed};
+    $self->{event_object_settings_changed} = $params{event_object_settings_changed};
+    $self->{event_remove_object} = $params{event_remove_object};
+    $self->{event_update_scene} = $params{event_update_scene};
+
     # C++ Slic3r::Model with Perl extensions in Slic3r/Model.pm
     $self->{model} = Slic3r::Model->new;
     # C++ Slic3r::Print with Perl extensions in Slic3r/Print.pm
@@ -74,7 +81,7 @@ sub new {
     });
     
     # Initialize preview notebook
-    $self->{preview_notebook} = Wx::Notebook->new($self, -1, wxDefaultPosition, [335,335], wxNB_BOTTOM);
+    $self->{preview_notebook} = Wx::Notebook->new($self, -1, wxDefaultPosition, [-1,335], wxNB_BOTTOM);
     
     # Initialize handlers for canvases
     my $on_select_object = sub {
@@ -128,7 +135,9 @@ sub new {
         }
         $_->set_scaling_factor($scale) for @{ $model_object->instances };
         
-        $self->{list}->SetItem($obj_idx, 2, ($model_object->instances->[0]->scaling_factor * 100) . "%");
+        # Set object scale on c++ side
+        Slic3r::GUI::set_object_scale($obj_idx, $model_object->instances->[0]->scaling_factor * 100); 
+
 #        $object->transform_thumbnail($self->{model}, $obj_idx);
     
         #update print and start background processing
@@ -159,7 +168,49 @@ sub new {
             }
         }
     };
+
+    # callbacks for toolbar
+    my $on_action_add = sub {
+        $self->add;
+    };
+
+    my $on_action_delete = sub {
+        $self->remove();
+    };
+
+    my $on_action_deleteall = sub {
+        $self->reset;
+    };
+
+    my $on_action_arrange = sub {
+        $self->arrange;
+    };
+
+    my $on_action_more = sub {
+        $self->increase;
+    };
+
+    my $on_action_fewer = sub {
+        $self->decrease;
+    };
+
+    my $on_action_split = sub {
+        $self->split_object;
+    };
     
+    my $on_action_cut = sub {
+        $self->object_cut_dialog;
+    };
+
+    my $on_action_settings = sub {
+        $self->object_settings_dialog;
+    };
+    
+    my $on_action_layersediting = sub {
+        my $state = Slic3r::GUI::_3DScene::is_toolbar_item_pressed($self->{canvas3D}, "layersediting");
+        $self->on_layer_editing_toggled($state);
+    };
+        
     # Initialize 3D plater
     if ($Slic3r::GUI::have_OpenGL) {
         $self->{canvas3D} = Slic3r::GUI::Plater::3D->new($self->{preview_notebook}, $self->{objects}, $self->{model}, $self->{print}, $self->{config});
@@ -179,7 +230,18 @@ sub new {
         Slic3r::GUI::_3DScene::register_on_gizmo_scale_uniformly_callback($self->{canvas3D}, $on_gizmo_scale_uniformly);
         Slic3r::GUI::_3DScene::register_on_gizmo_rotate_callback($self->{canvas3D}, $on_gizmo_rotate);
         Slic3r::GUI::_3DScene::register_on_update_geometry_info_callback($self->{canvas3D}, $on_update_geometry_info);
+        Slic3r::GUI::_3DScene::register_action_add_callback($self->{canvas3D}, $on_action_add);
+        Slic3r::GUI::_3DScene::register_action_delete_callback($self->{canvas3D}, $on_action_delete);
+        Slic3r::GUI::_3DScene::register_action_deleteall_callback($self->{canvas3D}, $on_action_deleteall);
+        Slic3r::GUI::_3DScene::register_action_arrange_callback($self->{canvas3D}, $on_action_arrange);
+        Slic3r::GUI::_3DScene::register_action_more_callback($self->{canvas3D}, $on_action_more);
+        Slic3r::GUI::_3DScene::register_action_fewer_callback($self->{canvas3D}, $on_action_fewer);
+        Slic3r::GUI::_3DScene::register_action_split_callback($self->{canvas3D}, $on_action_split);
+        Slic3r::GUI::_3DScene::register_action_cut_callback($self->{canvas3D}, $on_action_cut);
+        Slic3r::GUI::_3DScene::register_action_settings_callback($self->{canvas3D}, $on_action_settings);
+        Slic3r::GUI::_3DScene::register_action_layersediting_callback($self->{canvas3D}, $on_action_layersediting);
         Slic3r::GUI::_3DScene::enable_gizmos($self->{canvas3D}, 1);
+        Slic3r::GUI::_3DScene::enable_toolbar($self->{canvas3D}, 1);
         Slic3r::GUI::_3DScene::enable_shader($self->{canvas3D}, 1);
         Slic3r::GUI::_3DScene::enable_force_zoom_to_bed($self->{canvas3D}, 1);
 
@@ -248,83 +310,58 @@ sub new {
         }
     });
     
-    # toolbar for object manipulation
-    if (!&Wx::wxMSW) {
-        Wx::ToolTip::Enable(1);
-        $self->{htoolbar} = Wx::ToolBar->new($self, -1, wxDefaultPosition, wxDefaultSize, wxTB_HORIZONTAL | wxTB_TEXT | wxBORDER_SIMPLE | wxTAB_TRAVERSAL);
-        $self->{htoolbar}->AddTool(TB_ADD, L("Add…"), Wx::Bitmap->new(Slic3r::var("brick_add.png"), wxBITMAP_TYPE_PNG), '');
-        $self->{htoolbar}->AddTool(TB_REMOVE, L("Delete"), Wx::Bitmap->new(Slic3r::var("brick_delete.png"), wxBITMAP_TYPE_PNG), '');
-        $self->{htoolbar}->AddTool(TB_RESET, L("Delete All"), Wx::Bitmap->new(Slic3r::var("cross.png"), wxBITMAP_TYPE_PNG), '');
-        $self->{htoolbar}->AddTool(TB_ARRANGE, L("Arrange"), Wx::Bitmap->new(Slic3r::var("bricks.png"), wxBITMAP_TYPE_PNG), '');
-        $self->{htoolbar}->AddSeparator;
-        $self->{htoolbar}->AddTool(TB_MORE, L("More"), Wx::Bitmap->new(Slic3r::var("add.png"), wxBITMAP_TYPE_PNG), '');
-        $self->{htoolbar}->AddTool(TB_FEWER, L("Fewer"), Wx::Bitmap->new(Slic3r::var("delete.png"), wxBITMAP_TYPE_PNG), '');
-        $self->{htoolbar}->AddSeparator;
-        $self->{htoolbar}->AddTool(TB_45CCW, L("45° ccw"), Wx::Bitmap->new(Slic3r::var("arrow_rotate_anticlockwise.png"), wxBITMAP_TYPE_PNG), '');
-        $self->{htoolbar}->AddTool(TB_45CW, L("45° cw"), Wx::Bitmap->new(Slic3r::var("arrow_rotate_clockwise.png"), wxBITMAP_TYPE_PNG), '');
-        $self->{htoolbar}->AddTool(TB_SCALE, L("Scale…"), Wx::Bitmap->new(Slic3r::var("arrow_out.png"), wxBITMAP_TYPE_PNG), '');
-        $self->{htoolbar}->AddTool(TB_SPLIT, L("Split"), Wx::Bitmap->new(Slic3r::var("shape_ungroup.png"), wxBITMAP_TYPE_PNG), '');
-        $self->{htoolbar}->AddTool(TB_CUT, L("Cut…"), Wx::Bitmap->new(Slic3r::var("package.png"), wxBITMAP_TYPE_PNG), '');
-        $self->{htoolbar}->AddSeparator;
-        $self->{htoolbar}->AddTool(TB_SETTINGS, L("Settings…"), Wx::Bitmap->new(Slic3r::var("cog.png"), wxBITMAP_TYPE_PNG), '');
-        $self->{htoolbar}->AddTool(TB_LAYER_EDITING, L('Layer Editing'), Wx::Bitmap->new(Slic3r::var("variable_layer_height.png"), wxBITMAP_TYPE_PNG), wxNullBitmap, 1, 0, 'Layer Editing');
-    } else {
-        my %tbar_buttons = (
-            add             => L("Add…"),
-            remove          => L("Delete"),
-            reset           => L("Delete All"),
-            arrange         => L("Arrange"),
-            increase        => "",
-            decrease        => "",
-            rotate45ccw     => "",
-            rotate45cw      => "",
-            changescale     => L("Scale…"),
-            split           => L("Split"),
-            cut             => L("Cut…"),
-            settings        => L("Settings…"),
-            layer_editing   => L("Layer editing"),
-        );
-        $self->{btoolbar} = Wx::BoxSizer->new(wxHORIZONTAL);
-        for (qw(add remove reset arrange increase decrease rotate45ccw rotate45cw changescale split cut settings)) {
-            $self->{"btn_$_"} = Wx::Button->new($self, -1, $tbar_buttons{$_}, wxDefaultPosition, wxDefaultSize, wxBU_EXACTFIT);
-            $self->{btoolbar}->Add($self->{"btn_$_"});
-        }
-        $self->{"btn_layer_editing"} = Wx::ToggleButton->new($self, -1, $tbar_buttons{'layer_editing'}, wxDefaultPosition, wxDefaultSize, wxBU_EXACTFIT);
-        $self->{btoolbar}->Add($self->{"btn_layer_editing"});
-    }
+#    # toolbar for object manipulation
+#    if (!&Wx::wxMSW) {
+#        Wx::ToolTip::Enable(1);
+#        $self->{htoolbar} = Wx::ToolBar->new($self, -1, wxDefaultPosition, wxDefaultSize, wxTB_HORIZONTAL | wxTB_TEXT | wxBORDER_SIMPLE | wxTAB_TRAVERSAL);
+#        $self->{htoolbar}->AddTool(TB_ADD, L("Add…"), Wx::Bitmap->new(Slic3r::var("brick_add.png"), wxBITMAP_TYPE_PNG), '');
+#        $self->{htoolbar}->AddTool(TB_REMOVE, L("Delete"), Wx::Bitmap->new(Slic3r::var("brick_delete.png"), wxBITMAP_TYPE_PNG), '');
+#        $self->{htoolbar}->AddTool(TB_RESET, L("Delete All"), Wx::Bitmap->new(Slic3r::var("cross.png"), wxBITMAP_TYPE_PNG), '');
+#        $self->{htoolbar}->AddTool(TB_ARRANGE, L("Arrange"), Wx::Bitmap->new(Slic3r::var("bricks.png"), wxBITMAP_TYPE_PNG), '');
+#        $self->{htoolbar}->AddSeparator;
+#        $self->{htoolbar}->AddTool(TB_MORE, L("More"), Wx::Bitmap->new(Slic3r::var("add.png"), wxBITMAP_TYPE_PNG), '');
+#        $self->{htoolbar}->AddTool(TB_FEWER, L("Fewer"), Wx::Bitmap->new(Slic3r::var("delete.png"), wxBITMAP_TYPE_PNG), '');
+#        $self->{htoolbar}->AddSeparator;
+#        $self->{htoolbar}->AddTool(TB_45CCW, L("45° ccw"), Wx::Bitmap->new(Slic3r::var("arrow_rotate_anticlockwise.png"), wxBITMAP_TYPE_PNG), '');
+#        $self->{htoolbar}->AddTool(TB_45CW, L("45° cw"), Wx::Bitmap->new(Slic3r::var("arrow_rotate_clockwise.png"), wxBITMAP_TYPE_PNG), '');
+#        $self->{htoolbar}->AddTool(TB_SCALE, L("Scale…"), Wx::Bitmap->new(Slic3r::var("arrow_out.png"), wxBITMAP_TYPE_PNG), '');
+#        $self->{htoolbar}->AddTool(TB_SPLIT, L("Split"), Wx::Bitmap->new(Slic3r::var("shape_ungroup.png"), wxBITMAP_TYPE_PNG), '');
+#        $self->{htoolbar}->AddTool(TB_CUT, L("Cut…"), Wx::Bitmap->new(Slic3r::var("package.png"), wxBITMAP_TYPE_PNG), '');
+#        $self->{htoolbar}->AddSeparator;
+#        $self->{htoolbar}->AddTool(TB_SETTINGS, L("Settings…"), Wx::Bitmap->new(Slic3r::var("cog.png"), wxBITMAP_TYPE_PNG), '');
+#        $self->{htoolbar}->AddTool(TB_LAYER_EDITING, L('Layer Editing'), Wx::Bitmap->new(Slic3r::var("variable_layer_height.png"), wxBITMAP_TYPE_PNG), wxNullBitmap, 1, 0, 'Layer Editing');
+#    } else {
+#        my %tbar_buttons = (
+#            add             => L("Add…"),
+#            remove          => L("Delete"),
+#            reset           => L("Delete All"),
+#            arrange         => L("Arrange"),
+#            increase        => "",
+#            decrease        => "",
+#            rotate45ccw     => "",
+#            rotate45cw      => "",
+#            changescale     => L("Scale…"),
+#            split           => L("Split"),
+#            cut             => L("Cut…"),
+#            settings        => L("Settings…"),
+#            layer_editing   => L("Layer editing"),
+#        );
+#        $self->{btoolbar} = Wx::BoxSizer->new(wxHORIZONTAL);
+#        for (qw(add remove reset arrange increase decrease rotate45ccw rotate45cw changescale split cut settings)) {
+#            $self->{"btn_$_"} = Wx::Button->new($self, -1, $tbar_buttons{$_}, wxDefaultPosition, wxDefaultSize, wxBU_EXACTFIT);
+#            $self->{btoolbar}->Add($self->{"btn_$_"});
+#        }
+#        $self->{"btn_layer_editing"} = Wx::ToggleButton->new($self, -1, $tbar_buttons{'layer_editing'}, wxDefaultPosition, wxDefaultSize, wxBU_EXACTFIT);
+#        $self->{btoolbar}->Add($self->{"btn_layer_editing"});
+#    }
 
     ### Panel for right column
-    $self->{right_panel} = Wx::Panel->new($self, -1, wxDefaultPosition, wxDefaultSize, wxTAB_TRAVERSAL);
-    
-    ### Scrolled Window for info boxes
-    my $scrolled_window_sizer = $self->{scrolled_window_sizer} = Wx::BoxSizer->new(wxVERTICAL);
-    $scrolled_window_sizer->SetMinSize([310, -1]);
-    my $scrolled_window_panel = $self->{scrolled_window_panel} = Wx::ScrolledWindow->new($self->{right_panel}, -1, wxDefaultPosition, wxDefaultSize, wxTAB_TRAVERSAL);
-    $scrolled_window_panel->SetSizer($scrolled_window_sizer);
-    $scrolled_window_panel->SetScrollbars(1, 1, 1, 1);    
-
-    $self->{list} = Wx::ListView->new($scrolled_window_panel, -1, wxDefaultPosition, wxDefaultSize,
-        wxLC_SINGLE_SEL | wxLC_REPORT | wxBORDER_SUNKEN | wxTAB_TRAVERSAL | wxWANTS_CHARS );
-    $self->{list}->InsertColumn(0, L("Name"), wxLIST_FORMAT_LEFT, 145);
-    $self->{list}->InsertColumn(1, L("Copies"), wxLIST_FORMAT_CENTER, 45);
-    $self->{list}->InsertColumn(2, L("Scale"), wxLIST_FORMAT_CENTER, wxLIST_AUTOSIZE_USEHEADER);
-    EVT_LIST_ITEM_SELECTED($self, $self->{list}, \&list_item_selected);
-    EVT_LIST_ITEM_DESELECTED($self, $self->{list}, \&list_item_deselected);
-    EVT_LIST_ITEM_ACTIVATED($self, $self->{list}, \&list_item_activated);
-    EVT_KEY_DOWN($self->{list}, sub {
-        my ($list, $event) = @_;
-        if ($event->GetKeyCode == WXK_TAB) {
-            $list->Navigate($event->ShiftDown ? &Wx::wxNavigateBackward : &Wx::wxNavigateForward);
-        } elsif ($event->GetKeyCode == WXK_DELETE ||
-                ($event->GetKeyCode == WXK_BACK && &Wx::wxMAC) ) {
-            $self->remove;
-        } else {
-            $event->Skip;
-        }
-    });
+#    $self->{right_panel} = Wx::Panel->new($self, -1, wxDefaultPosition, wxDefaultSize, wxTAB_TRAVERSAL);
+    $self->{right_panel} = Wx::ScrolledWindow->new($self, -1, wxDefaultPosition, wxDefaultSize, wxTAB_TRAVERSAL);
+    $self->{right_panel}->SetScrollbars(0, 1, 1, 1);
     
     # right pane buttons
-    $self->{btn_export_gcode} = Wx::Button->new($self->{right_panel}, -1, L("Export G-code…"), wxDefaultPosition, [-1, 30], wxBU_LEFT);
+    $self->{btn_export_gcode} = Wx::Button->new($self->{right_panel}, -1, L("Export G-code…"), wxDefaultPosition, [-1, 30], wxNO_BORDER);#, wxBU_LEFT);
     $self->{btn_reslice} = Wx::Button->new($self->{right_panel}, -1, L("Slice now"), wxDefaultPosition, [-1, 30], wxBU_LEFT);
     $self->{btn_print} = Wx::Button->new($self->{right_panel}, -1, L("Print…"), wxDefaultPosition, [-1, 30], wxBU_LEFT);
     $self->{btn_send_gcode} = Wx::Button->new($self->{right_panel}, -1, L("Send to printer"), wxDefaultPosition, [-1, 30], wxBU_LEFT);
@@ -334,25 +371,12 @@ sub new {
     $self->{btn_print}->Hide;
     $self->{btn_send_gcode}->Hide;
     
+#       export_gcode    cog_go.png
     my %icons = qw(
-        add             brick_add.png
-        remove          brick_delete.png
-        reset           cross.png
-        arrange         bricks.png
-        export_gcode    cog_go.png
         print           arrow_up.png
         send_gcode      arrow_up.png
         reslice         reslice.png
         export_stl      brick_go.png
-        
-        increase        add.png
-        decrease        delete.png
-        rotate45cw      arrow_rotate_clockwise.png
-        rotate45ccw     arrow_rotate_anticlockwise.png
-        changescale     arrow_out.png
-        split           shape_ungroup.png
-        cut             package.png
-        settings        cog.png
     );
     for (grep $self->{"btn_$_"}, keys %icons) {
         $self->{"btn_$_"}->SetBitmap(Wx::Bitmap->new(Slic3r::var($icons{$_}), wxBITMAP_TYPE_PNG));
@@ -371,44 +395,45 @@ sub new {
     EVT_BUTTON($self, $self->{btn_reslice}, \&reslice);
     EVT_BUTTON($self, $self->{btn_export_stl}, \&export_stl);
     
-    if ($self->{htoolbar}) {
-        EVT_TOOL($self, TB_ADD, sub { $self->add; });
-        EVT_TOOL($self, TB_REMOVE, sub { $self->remove() }); # explicitly pass no argument to remove
-        EVT_TOOL($self, TB_RESET, sub { $self->reset; });
-        EVT_TOOL($self, TB_ARRANGE, sub { $self->arrange; });
-        EVT_TOOL($self, TB_MORE, sub { $self->increase; });
-        EVT_TOOL($self, TB_FEWER, sub { $self->decrease; });
-        EVT_TOOL($self, TB_45CW, sub { $_[0]->rotate(-45, Z, 'relative') });
-        EVT_TOOL($self, TB_45CCW, sub { $_[0]->rotate(45, Z, 'relative') });
-        EVT_TOOL($self, TB_SCALE, sub { $self->changescale(undef); });
-        EVT_TOOL($self, TB_SPLIT, sub { $self->split_object; });
-        EVT_TOOL($self, TB_CUT, sub { $_[0]->object_cut_dialog });
-        EVT_TOOL($self, TB_SETTINGS, sub { $_[0]->object_settings_dialog });
-        EVT_TOOL($self, TB_LAYER_EDITING, sub {
-            my $state = Slic3r::GUI::_3DScene::is_layers_editing_enabled($self->{canvas3D});
-            $self->{htoolbar}->ToggleTool(TB_LAYER_EDITING, ! $state);
-            $self->on_layer_editing_toggled(! $state);
-        });
-    } else {
-        EVT_BUTTON($self, $self->{btn_add}, sub { $self->add; });
-        EVT_BUTTON($self, $self->{btn_remove}, sub { $self->remove() }); # explicitly pass no argument to remove
-        EVT_BUTTON($self, $self->{btn_reset}, sub { $self->reset; });
-        EVT_BUTTON($self, $self->{btn_arrange}, sub { $self->arrange; });
-        EVT_BUTTON($self, $self->{btn_increase}, sub { $self->increase; });
-        EVT_BUTTON($self, $self->{btn_decrease}, sub { $self->decrease; });
-        EVT_BUTTON($self, $self->{btn_rotate45cw}, sub { $_[0]->rotate(-45, Z, 'relative') });
-        EVT_BUTTON($self, $self->{btn_rotate45ccw}, sub { $_[0]->rotate(45, Z, 'relative') });
-        EVT_BUTTON($self, $self->{btn_changescale}, sub { $self->changescale(undef); });
-        EVT_BUTTON($self, $self->{btn_split}, sub { $self->split_object; });
-        EVT_BUTTON($self, $self->{btn_cut}, sub { $_[0]->object_cut_dialog });
-        EVT_BUTTON($self, $self->{btn_settings}, sub { $_[0]->object_settings_dialog });
-        EVT_TOGGLEBUTTON($self, $self->{btn_layer_editing}, sub { $self->on_layer_editing_toggled($self->{btn_layer_editing}->GetValue); });
-    }
+#    if ($self->{htoolbar}) {
+#        EVT_TOOL($self, TB_ADD, sub { $self->add; });
+#        EVT_TOOL($self, TB_REMOVE, sub { $self->remove() }); # explicitly pass no argument to remove
+#        EVT_TOOL($self, TB_RESET, sub { $self->reset; });
+#        EVT_TOOL($self, TB_ARRANGE, sub { $self->arrange; });
+#        EVT_TOOL($self, TB_MORE, sub { $self->increase; });
+#        EVT_TOOL($self, TB_FEWER, sub { $self->decrease; });
+#        EVT_TOOL($self, TB_45CW, sub { $_[0]->rotate(-45, Z, 'relative') });
+#        EVT_TOOL($self, TB_45CCW, sub { $_[0]->rotate(45, Z, 'relative') });
+#        EVT_TOOL($self, TB_SCALE, sub { $self->changescale(undef); });
+#        EVT_TOOL($self, TB_SPLIT, sub { $self->split_object; });
+#        EVT_TOOL($self, TB_CUT, sub { $_[0]->object_cut_dialog });
+#        EVT_TOOL($self, TB_SETTINGS, sub { $_[0]->object_settings_dialog });
+#        EVT_TOOL($self, TB_LAYER_EDITING, sub {
+#            my $state = Slic3r::GUI::_3DScene::is_layers_editing_enabled($self->{canvas3D});
+#            $self->{htoolbar}->ToggleTool(TB_LAYER_EDITING, ! $state);
+#            $self->on_layer_editing_toggled(! $state);
+#        });
+#    } else {
+#        EVT_BUTTON($self, $self->{btn_add}, sub { $self->add; });
+#        EVT_BUTTON($self, $self->{btn_remove}, sub { $self->remove() }); # explicitly pass no argument to remove
+#        EVT_BUTTON($self, $self->{btn_remove}, sub { Slic3r::GUI::remove_obj() }); # explicitly pass no argument to remove
+#        EVT_BUTTON($self, $self->{btn_reset}, sub { $self->reset; });
+#        EVT_BUTTON($self, $self->{btn_arrange}, sub { $self->arrange; });
+#        EVT_BUTTON($self, $self->{btn_increase}, sub { $self->increase; });
+#        EVT_BUTTON($self, $self->{btn_decrease}, sub { $self->decrease; });
+#        EVT_BUTTON($self, $self->{btn_rotate45cw}, sub { $_[0]->rotate(-45, Z, 'relative') });
+#        EVT_BUTTON($self, $self->{btn_rotate45ccw}, sub { $_[0]->rotate(45, Z, 'relative') });
+#        EVT_BUTTON($self, $self->{btn_changescale}, sub { $self->changescale(undef); });
+#        EVT_BUTTON($self, $self->{btn_split}, sub { $self->split_object; });
+#        EVT_BUTTON($self, $self->{btn_cut}, sub { $_[0]->object_cut_dialog });
+#        EVT_BUTTON($self, $self->{btn_settings}, sub { $_[0]->object_settings_dialog });
+#        EVT_TOGGLEBUTTON($self, $self->{btn_layer_editing}, sub { $self->on_layer_editing_toggled($self->{btn_layer_editing}->GetValue); });
+#    }
     
     $_->SetDropTarget(Slic3r::GUI::Plater::DropTarget->new($self))
         for grep defined($_),
             $self, $self->{canvas3D}, $self->{preview3D}, $self->{list};
-#            $self, $self->{canvas}, $self->{canvas3D}, $self->{preview3D}, $self->{list};
+#            $self, $self->{canvas}, $self->{canvas3D}, $self->{preview3D};
     
     EVT_COMMAND($self, -1, $PROGRESS_BAR_EVENT, sub {
         my ($self, $event) = @_;
@@ -452,20 +477,21 @@ sub new {
     {
         my $presets;
         {
-            $presets = $self->{presets_sizer} = Wx::FlexGridSizer->new(3, 2, 1, 2);
+            $presets = $self->{presets_sizer} = Wx::FlexGridSizer->new(4, 2, 1, 2);
             $presets->AddGrowableCol(1, 1);
             $presets->SetFlexibleDirection(wxHORIZONTAL);
             my %group_labels = (
                 print       => L('Print settings'),
                 filament    => L('Filament'),
+                sla_material=> L('SLA material'),
                 printer     => L('Printer'),
             );
-            # UI Combo boxes for a print, multiple filaments, and a printer.
+            # UI Combo boxes for a print, multiple filaments, SLA material and a printer.
             # Initially a single filament combo box is created, but the number of combo boxes for the filament selection may increase,
             # once a printer preset with multiple extruders is activated.
             # $self->{preset_choosers}{$group}[$idx]
             $self->{preset_choosers} = {};
-            for my $group (qw(print filament printer)) {
+            for my $group (qw(print filament sla_material printer)) {
                 my $text = Wx::StaticText->new($self->{right_panel}, -1, "$group_labels{$group}:", wxDefaultPosition, wxDefaultSize, wxALIGN_RIGHT);
                 $text->SetFont($Slic3r::GUI::small_font);
                 my $choice = Wx::BitmapComboBox->new($self->{right_panel}, -1, "", wxDefaultPosition, wxDefaultSize, [], wxCB_READONLY);
@@ -486,15 +512,32 @@ sub new {
             $presets->Layout;
         }
 
-        my $frequently_changed_parameters_sizer = Wx::BoxSizer->new(wxHORIZONTAL);
+        my $frequently_changed_parameters_sizer = $self->{frequently_changed_parameters_sizer} = Wx::BoxSizer->new(wxVERTICAL);
         Slic3r::GUI::add_frequently_changed_parameters($self->{right_panel}, $frequently_changed_parameters_sizer, $presets);
 
+        my $expert_mode_part_sizer = Wx::BoxSizer->new(wxVERTICAL);
+        Slic3r::GUI::add_expert_mode_part(  $self->{right_panel}, $expert_mode_part_sizer, 
+                                            $self->{model},
+                                            $self->{event_object_selection_changed},
+                                            $self->{event_object_settings_changed},
+                                            $self->{event_remove_object},
+                                            $self->{event_update_scene});
+#        if ($expert_mode_part_sizer->IsShown(2)==1) 
+#        { 
+#           $expert_mode_part_sizer->Layout;
+#            $expert_mode_part_sizer->Show(2, 0); # ? Why doesn't work
+#            $self->{right_panel}->Layout;
+#       }
+
         my $object_info_sizer;
         {
-            my $box = Wx::StaticBox->new($scrolled_window_panel, -1, L("Info"));
+#            my $box = Wx::StaticBox->new($scrolled_window_panel, -1, L("Info"));
+            my $box = Wx::StaticBox->new($self->{right_panel}, -1, L("Info"));
+            $box->SetFont($Slic3r::GUI::small_bold_font);
             $object_info_sizer = Wx::StaticBoxSizer->new($box, wxVERTICAL);
             $object_info_sizer->SetMinSize([300,-1]);
-            my $grid_sizer = Wx::FlexGridSizer->new(3, 4, 5, 5);
+            #!my $grid_sizer = Wx::FlexGridSizer->new(3, 4, 5, 5);
+            my $grid_sizer = Wx::FlexGridSizer->new(2, 4, 5, 5);
             $grid_sizer->SetFlexibleDirection(wxHORIZONTAL);
             $grid_sizer->AddGrowableCol(1, 1);
             $grid_sizer->AddGrowableCol(3, 1);
@@ -509,28 +552,45 @@ sub new {
             );
             while (my $field = shift @info) {
                 my $label = shift @info;
-                my $text = Wx::StaticText->new($scrolled_window_panel, -1, "$label:", wxDefaultPosition, wxDefaultSize, wxALIGN_LEFT);
+#                my $text = Wx::StaticText->new($scrolled_window_panel, -1, "$label:", wxDefaultPosition, wxDefaultSize, wxALIGN_LEFT);
+                my $text = Wx::StaticText->new($self->{right_panel}, -1, "$label:", wxDefaultPosition, wxDefaultSize, wxALIGN_LEFT);
                 $text->SetFont($Slic3r::GUI::small_font);
-                $grid_sizer->Add($text, 0);
+                #!$grid_sizer->Add($text, 0);
                 
-                $self->{"object_info_$field"} = Wx::StaticText->new($scrolled_window_panel, -1, "", wxDefaultPosition, wxDefaultSize, wxALIGN_LEFT);
+#                $self->{"object_info_$field"} = Wx::StaticText->new($scrolled_window_panel, -1, "", wxDefaultPosition, wxDefaultSize, wxALIGN_LEFT);
+                $self->{"object_info_$field"} = Wx::StaticText->new($self->{right_panel}, -1, "", wxDefaultPosition, wxDefaultSize, wxALIGN_LEFT);
                 $self->{"object_info_$field"}->SetFont($Slic3r::GUI::small_font);
                 if ($field eq 'manifold') {
-                    $self->{object_info_manifold_warning_icon} = Wx::StaticBitmap->new($scrolled_window_panel, -1, Wx::Bitmap->new(Slic3r::var("error.png"), wxBITMAP_TYPE_PNG));
-                    $self->{object_info_manifold_warning_icon}->Hide;
+#                    $self->{object_info_manifold_warning_icon} = Wx::StaticBitmap->new($scrolled_window_panel, -1, Wx::Bitmap->new(Slic3r::var("error.png"), wxBITMAP_TYPE_PNG));
+                    $self->{object_info_manifold_warning_icon} = Wx::StaticBitmap->new($self->{right_panel}, -1, Wx::Bitmap->new(Slic3r::var("error.png"), wxBITMAP_TYPE_PNG));
+                    #$self->{object_info_manifold_warning_icon}->Hide;
+                    $self->{"object_info_manifold_warning_icon_show"} = sub {
+                        if ($self->{object_info_manifold_warning_icon}->IsShown() != $_[0]) {
+                            Slic3r::GUI::set_show_manifold_warning_icon($_[0]);
+                            my $mode = wxTheApp->{app_config}->get("view_mode");
+                            return if ($mode eq "" || $mode eq "simple");
+                            $self->{object_info_manifold_warning_icon}->Show($_[0]); 
+                            $self->Layout
+                        }
+                    };
+                    $self->{"object_info_manifold_warning_icon_show"}->(0);
                     
                     my $h_sizer = Wx::BoxSizer->new(wxHORIZONTAL);
-                    $h_sizer->Add($self->{object_info_manifold_warning_icon}, 0);
-                    $h_sizer->Add($self->{"object_info_$field"}, 0);
-                    $grid_sizer->Add($h_sizer, 0, wxEXPAND);
+                    $h_sizer->Add($text, 0);
+                    $h_sizer->Add($self->{object_info_manifold_warning_icon}, 0, wxLEFT, 2);
+                    $h_sizer->Add($self->{"object_info_$field"}, 0, wxLEFT, 2);
+                    #!$grid_sizer->Add($h_sizer, 0, wxEXPAND);
+                    $object_info_sizer->Add($h_sizer, 0, wxEXPAND|wxTOP, 4);
                 } else {
+                    $grid_sizer->Add($text, 0);
                     $grid_sizer->Add($self->{"object_info_$field"}, 0);
                 }
             }
         }
 
         my $print_info_sizer = $self->{print_info_sizer} = Wx::StaticBoxSizer->new(
-                Wx::StaticBox->new($scrolled_window_panel, -1, L("Sliced Info")), wxVERTICAL);
+#                Wx::StaticBox->new($scrolled_window_panel, -1, L("Sliced Info")), wxVERTICAL);
+                Wx::StaticBox->new($self->{right_panel}, -1, L("Sliced Info")), wxVERTICAL);
         $print_info_sizer->SetMinSize([300,-1]);
         
         my $buttons_sizer = Wx::BoxSizer->new(wxHORIZONTAL);
@@ -540,34 +600,53 @@ sub new {
         $buttons_sizer->Add($self->{btn_reslice}, 0, wxALIGN_RIGHT, 0);
         $buttons_sizer->Add($self->{btn_print}, 0, wxALIGN_RIGHT, 0);
         $buttons_sizer->Add($self->{btn_send_gcode}, 0, wxALIGN_RIGHT, 0);
-        $buttons_sizer->Add($self->{btn_export_gcode}, 0, wxALIGN_RIGHT, 0);
         
-        $scrolled_window_sizer->Add($self->{list}, 1, wxEXPAND, 5);
-        $scrolled_window_sizer->Add($object_info_sizer, 0, wxEXPAND, 0);
-        $scrolled_window_sizer->Add($print_info_sizer, 0, wxEXPAND, 0);
+#        $scrolled_window_sizer->Add($self->{list}, 1, wxEXPAND, 5);
+#        $scrolled_window_sizer->Add($object_info_sizer, 0, wxEXPAND, 0);
+#        $scrolled_window_sizer->Add($print_info_sizer, 0, wxEXPAND, 0);
+        #$buttons_sizer->Add($self->{btn_export_gcode}, 0, wxALIGN_RIGHT, 0);
+
+        ### Sizer for info boxes
+        my $info_sizer = $self->{info_sizer} = Wx::BoxSizer->new(wxVERTICAL);
+        $info_sizer->SetMinSize([318, -1]);        
+        $info_sizer->Add($object_info_sizer, 0, wxEXPAND | wxBOTTOM, 5);
+        $info_sizer->Add($print_info_sizer, 0, wxEXPAND | wxBOTTOM, 5);
 
         my $right_sizer = Wx::BoxSizer->new(wxVERTICAL);
-        $right_sizer->SetMinSize([320,-1]);
+        $self->{right_panel}->SetSizer($right_sizer);
+        $right_sizer->SetMinSize([320, -1]);
         $right_sizer->Add($presets, 0, wxEXPAND | wxTOP, 10) if defined $presets;
-        $right_sizer->Add($frequently_changed_parameters_sizer, 0, wxEXPAND | wxTOP, 0) if defined $frequently_changed_parameters_sizer;
-        $right_sizer->Add($buttons_sizer, 0, wxEXPAND | wxBOTTOM, 5);
-        $right_sizer->Add($scrolled_window_panel, 1, wxEXPAND | wxALL, 1);
+        $right_sizer->Add($frequently_changed_parameters_sizer, 1, wxEXPAND | wxTOP, 0) if defined $frequently_changed_parameters_sizer;
+        $right_sizer->Add($expert_mode_part_sizer, 0, wxEXPAND | wxTOP, 10) if defined $expert_mode_part_sizer;
+        $right_sizer->Add($buttons_sizer, 0, wxEXPAND | wxBOTTOM | wxTOP, 10);
+        $right_sizer->Add($info_sizer, 0, wxEXPAND | wxLEFT, 20);
         # Show the box initially, let it be shown after the slicing is finished.
         $self->print_info_box_show(0);
-
-        $self->{right_panel}->SetSizer($right_sizer);
+        $right_sizer->Add($self->{btn_export_gcode}, 0, wxEXPAND | wxLEFT | wxTOP | wxBOTTOM, 20);
 
         my $hsizer = Wx::BoxSizer->new(wxHORIZONTAL);
         $hsizer->Add($self->{preview_notebook}, 1, wxEXPAND | wxTOP, 1);
         $hsizer->Add($self->{right_panel}, 0, wxEXPAND | wxLEFT | wxRIGHT, 3);
-        
+
         my $sizer = Wx::BoxSizer->new(wxVERTICAL);
-        $sizer->Add($self->{htoolbar}, 0, wxEXPAND, 0) if $self->{htoolbar};
-        $sizer->Add($self->{btoolbar}, 0, wxEXPAND, 0) if $self->{btoolbar};
+#        $sizer->Add($self->{htoolbar}, 0, wxEXPAND, 0) if $self->{htoolbar};
+#        $sizer->Add($self->{btoolbar}, 0, wxEXPAND, 0) if $self->{btoolbar};
         $sizer->Add($hsizer, 1, wxEXPAND, 0);
         
         $sizer->SetSizeHints($self);
         $self->SetSizer($sizer);
+
+        # Send sizers/buttons to C++
+        Slic3r::GUI::set_objects_from_perl( $self->{right_panel},
+                                $frequently_changed_parameters_sizer,
+                                $expert_mode_part_sizer,
+                                $info_sizer,
+                                $self->{btn_export_gcode},
+                                $self->{btn_export_stl},
+                                $self->{btn_reslice},
+                                $self->{btn_print},
+                                $self->{btn_send_gcode},
+                                $self->{object_info_manifold_warning_icon} );
     }
 
     # Last correct selected item for each preset
@@ -578,6 +657,7 @@ sub new {
     }
 
     $self->update_ui_from_settings();
+    $self->Layout;
     
     return $self;
 }
@@ -629,13 +709,14 @@ sub on_layer_editing_toggled {
     Slic3r::GUI::_3DScene::enable_layers_editing($self->{canvas3D}, $new_state);
     if ($new_state && ! Slic3r::GUI::_3DScene::is_layers_editing_enabled($self->{canvas3D})) {
         # Initialization of the OpenGL shaders failed. Disable the tool.
-        if ($self->{htoolbar}) {
-            $self->{htoolbar}->EnableTool(TB_LAYER_EDITING, 0);
-            $self->{htoolbar}->ToggleTool(TB_LAYER_EDITING, 0);
-        } else {
-            $self->{"btn_layer_editing"}->Disable;
-            $self->{"btn_layer_editing"}->SetValue(0);
-        }
+#        if ($self->{htoolbar}) {
+#            $self->{htoolbar}->EnableTool(TB_LAYER_EDITING, 0);
+#            $self->{htoolbar}->ToggleTool(TB_LAYER_EDITING, 0);
+#        } else {
+#            $self->{"btn_layer_editing"}->Disable;
+#            $self->{"btn_layer_editing"}->SetValue(0);
+#        }
+        Slic3r::GUI::_3DScene::enable_toolbar_item($self->{canvas3D}, "layersediting", 0);
     }
     $self->{canvas3D}->Refresh;
     $self->{canvas3D}->Update;
@@ -657,16 +738,17 @@ sub update_ui_from_settings
     }
 }
 
-# Update preset combo boxes (Print settings, Filament, Printer) from their respective tabs.
+# Update preset combo boxes (Print settings, Filament, Material, Printer) from their respective tabs.
 # Called by 
 #       Slic3r::GUI::Tab::Print::_on_presets_changed
 #       Slic3r::GUI::Tab::Filament::_on_presets_changed
+#       Slic3r::GUI::Tab::Material::_on_presets_changed
 #       Slic3r::GUI::Tab::Printer::_on_presets_changed
 # when the presets are loaded or the user selects another preset.
 # For Print settings and Printer, synchronize the selection index with their tabs.
 # For Filament, synchronize the selection index for a single extruder printer only, otherwise keep the selection.
 sub update_presets {
-    # $group: one of qw(print filament printer)
+    # $group: one of qw(print filament sla_material printer)
     # $presets: PresetCollection
     my ($self, $group, $presets) = @_;
     my @choosers = @{$self->{preset_choosers}{$group}};
@@ -682,6 +764,8 @@ sub update_presets {
         }
     } elsif ($group eq 'print') {
         wxTheApp->{preset_bundle}->print->update_platter_ui($choosers[0]);
+    } elsif ($group eq 'sla_material') {
+        wxTheApp->{preset_bundle}->sla_material->update_platter_ui($choosers[0]);
     } elsif ($group eq 'printer') {
         # Update the print choosers to only contain the compatible presets, update the dirty flags.
         wxTheApp->{preset_bundle}->print->update_platter_ui($self->{preset_choosers}{print}->[0]);
@@ -848,12 +932,10 @@ sub load_model_objects {
     foreach my $obj_idx (@obj_idx) {
         my $object = $self->{objects}[$obj_idx];
         my $model_object = $self->{model}->objects->[$obj_idx];
-        $self->{list}->InsertStringItem($obj_idx, $object->name);
-        $self->{list}->SetItemFont($obj_idx, Wx::Font->new(10, wxDEFAULT, wxNORMAL, wxNORMAL))
-            if $self->{list}->can('SetItemFont');  # legacy code for wxPerl < 0.9918 not supporting SetItemFont()
+
+        # Add object to list on c++ side
+        Slic3r::GUI::add_object_to_list($object->name, $model_object);
     
-        $self->{list}->SetItem($obj_idx, 1, $model_object->instances_count);
-        $self->{list}->SetItem($obj_idx, 2, ($model_object->instances->[0]->scaling_factor * 100) . "%");
 
 #        $self->reset_thumbnail($obj_idx);
     }
@@ -863,8 +945,6 @@ sub load_model_objects {
     # zoom to objects
     Slic3r::GUI::_3DScene::zoom_to_volumes($self->{canvas3D}) if $self->{canvas3D};
     
-    $self->{list}->Update;
-    $self->{list}->Select($obj_idx[-1], 1);
     $self->object_list_changed;
     
     $self->schedule_background_process;
@@ -899,7 +979,8 @@ sub remove {
     splice @{$self->{objects}}, $obj_idx, 1;
     $self->{model}->delete_object($obj_idx);
     $self->{print}->delete_object($obj_idx);
-    $self->{list}->DeleteItem($obj_idx);
+    # Delete object from list on c++ side
+    Slic3r::GUI::delete_object_from_list();
     $self->object_list_changed;
     
     $self->select_object(undef);
@@ -919,7 +1000,8 @@ sub reset {
     @{$self->{objects}} = ();
     $self->{model}->clear_objects;
     $self->{print}->clear_objects;
-    $self->{list}->DeleteAllItems;
+    # Delete all objects from list on c++ side
+    Slic3r::GUI::delete_all_objects_from_list();
     $self->object_list_changed;
     
     $self->select_object(undef);
@@ -941,7 +1023,8 @@ sub increase {
         );
         $self->{print}->objects->[$obj_idx]->add_copy($instance->offset);
     }
-    $self->{list}->SetItem($obj_idx, 1, $model_object->instances_count);
+    # Set conut of object on c++ side
+    Slic3r::GUI::set_object_count($obj_idx, $model_object->instances_count);
     
     # only autoarrange if user has autocentering enabled
     $self->stop_background_process;
@@ -950,6 +1033,8 @@ sub increase {
     } else {
         $self->update;
     }
+
+    $self->selection_changed;  # refresh info (size, volume etc.)
     $self->schedule_background_process;
 }
 
@@ -967,7 +1052,8 @@ sub decrease {
             $model_object->delete_last_instance;
             $self->{print}->objects->[$obj_idx]->delete_last_copy;
         }
-        $self->{list}->SetItem($obj_idx, 1, $model_object->instances_count);
+        # Set conut of object on c++ side
+        Slic3r::GUI::set_object_count($obj_idx, $model_object->instances_count);
     } elsif (defined $copies_asked) {
         # The "decrease" came from the "set number of copies" dialog.
         $self->remove;
@@ -976,11 +1062,7 @@ sub decrease {
         $self->resume_background_process;
         return;
     }
-    
-    if ($self->{objects}[$obj_idx]) {
-        $self->{list}->Select($obj_idx, 0);
-        $self->{list}->Select($obj_idx, 1);
-    }
+
     $self->update;
     $self->schedule_background_process;
 }
@@ -1078,6 +1160,7 @@ sub rotate {
 #        $model_object->center_around_origin;
 #        $self->reset_thumbnail($obj_idx);
     }
+    Slic3r::GUI::update_rotation_value(deg2rad($angle), $axis == X ? "x" : ($axis == Y ? "y" : "z"));
     
     # update print and start background processing
     $self->{print}->add_model_object($model_object, $obj_idx);
@@ -1126,8 +1209,7 @@ sub changescale {
     my $model_object = $self->{model}->objects->[$obj_idx];
     my $model_instance = $model_object->instances->[0];
     
-    my $object_size = $model_object->bounding_box->size;
-    my $bed_size = Slic3r::Polygon->new_scale(@{$self->{config}->bed_shape})->bounding_box->size;
+    my $object_size = $model_object->instance_bounding_box(0)->size;
     
     if (defined $axis) {
         my $axis_name = $axis == X ? 'X' : $axis == Y ? 'Y' : 'Z';
@@ -1135,7 +1217,7 @@ sub changescale {
         if ($tosize) {
             my $cursize = $object_size->[$axis];
             my $newsize = $self->_get_number_from_user(
-                sprintf(L('Enter the new size for the selected object (print bed: %smm):'), unscale($bed_size->[$axis])), 
+                L('Enter the new size for the selected object:'), 
                 L("Scale along ").$axis_name, L('Invalid scaling value entered'), $cursize, 1);
             return if $newsize eq '';
             $scale = $newsize / $cursize * 100;
@@ -1169,8 +1251,9 @@ sub changescale {
             $scale = $self->_get_number_from_user(L('Enter the scale % for the selected object:'), L('Scale'), L('Invalid scaling value entered'), $model_instance->scaling_factor*100, 1);
             return if ! defined($scale) || $scale eq '';
         }
-    
-        $self->{list}->SetItem($obj_idx, 2, "$scale%");
+
+        # Set object scale on c++ side
+        Slic3r::GUI::set_object_scale($obj_idx, $scale);
         $scale /= 100;  # turn percent into factor
         
         my $variation = $scale / $model_instance->scaling_factor;
@@ -1291,7 +1374,9 @@ sub async_apply_config {
 
         # We also need to reload 3D scene because of the wipe tower preview box
         if ($self->{config}->wipe_tower) {
-	       Slic3r::GUI::_3DScene::reload_scene($self->{canvas3D}, 1) if $self->{canvas3D}
+            my $selections = $self->collect_selections;
+            Slic3r::GUI::_3DScene::set_objects_selections($self->{canvas3D}, \@$selections);
+	        Slic3r::GUI::_3DScene::reload_scene($self->{canvas3D}, 1) if $self->{canvas3D}
         }
     }
 }
@@ -1507,6 +1592,8 @@ sub on_process_completed {
     $self->{preview3D}->reload_print if $self->{preview3D};
 
     # in case this was MM print, wipe tower bounding box on 3D tab might need redrawing with exact depth:
+    my $selections = $self->collect_selections;
+    Slic3r::GUI::_3DScene::set_objects_selections($self->{canvas3D}, \@$selections);
     Slic3r::GUI::_3DScene::reload_scene($self->{canvas3D}, 1);
     
     # if we have an export filename, start a new thread for exporting G-code
@@ -1569,7 +1656,7 @@ sub on_export_completed {
             $message = L("File added to print queue");
             $do_print = 1;
         } elsif ($self->{send_gcode_file}) {
-            $message = L("Sending G-code file to the OctoPrint server...");
+            $message = L("Sending G-code file to the Printer Host ...");
             $send_gcode = 1;
         } else {
             $message = L("G-code file exported to ") . $self->{export_gcode_output_file};
@@ -1585,9 +1672,10 @@ sub on_export_completed {
 
     # Send $self->{send_gcode_file} to OctoPrint.
     if ($send_gcode) {
-        my $op = Slic3r::OctoPrint->new($self->{config});
-        if ($op->send_gcode($self->{send_gcode_file})) {
-            $self->statusbar->SetStatusText(L("OctoPrint upload finished."));
+        my $host = Slic3r::PrintHost::get_print_host($self->{config});
+
+        if ($host->send_gcode($self->{send_gcode_file})) {
+            $self->statusbar->SetStatusText(L("Upload to host finished."));
         } else {
             $self->statusbar->SetStatusText("");
         }
@@ -1608,9 +1696,15 @@ sub on_export_completed {
 # Fill in the "Sliced info" box with the result of the G-code generator.
 sub print_info_box_show {
     my ($self, $show) = @_;
-    my $scrolled_window_panel = $self->{scrolled_window_panel}; 
-    my $scrolled_window_sizer = $self->{scrolled_window_sizer};
-    return if (!$show && ($scrolled_window_sizer->IsShown(2) == $show));
+#    my $scrolled_window_panel = $self->{scrolled_window_panel}; 
+#    my $scrolled_window_sizer = $self->{scrolled_window_sizer};
+#    return if (!$show && ($scrolled_window_sizer->IsShown(2) == $show));
+    my $panel = $self->{right_panel};
+    my $sizer = $self->{info_sizer};
+    return if (!$sizer || !$show && ($sizer->IsShown(1) == $show));
+
+    Slic3r::GUI::set_show_print_info($show);
+    return if (wxTheApp->{app_config}->get("view_mode") eq "simple");
 
     if ($show) {
         my $print_info_sizer = $self->{print_info_sizer};
@@ -1637,17 +1731,23 @@ sub print_info_box_show {
         while ( my $label = shift @info) {
             my $value = shift @info;
             next if $value eq "N/A";
-            my $text = Wx::StaticText->new($scrolled_window_panel, -1, "$label:", wxDefaultPosition, wxDefaultSize, wxALIGN_RIGHT);
+#            my $text = Wx::StaticText->new($scrolled_window_panel, -1, "$label:", wxDefaultPosition, wxDefaultSize, wxALIGN_RIGHT);
+            my $text = Wx::StaticText->new($panel, -1, "$label:", wxDefaultPosition, wxDefaultSize, wxALIGN_RIGHT);
             $text->SetFont($Slic3r::GUI::small_font);
             $grid_sizer->Add($text, 0);            
-            my $field = Wx::StaticText->new($scrolled_window_panel, -1, $value, wxDefaultPosition, wxDefaultSize, wxALIGN_LEFT);
+#            my $field = Wx::StaticText->new($scrolled_window_panel, -1, $value, wxDefaultPosition, wxDefaultSize, wxALIGN_LEFT);
+            my $field = Wx::StaticText->new($panel, -1, $value, wxDefaultPosition, wxDefaultSize, wxALIGN_LEFT);
             $field->SetFont($Slic3r::GUI::small_font);
             $grid_sizer->Add($field, 0);
         }
     }
 
-    $scrolled_window_sizer->Show(2, $show);
-    $scrolled_window_panel->Layout;
+#    $scrolled_window_sizer->Show(2, $show);
+#    $scrolled_window_panel->Layout;
+    $sizer->Show(1, $show);
+
+    $self->Layout;
+    $panel->Refresh;
 }
 
 sub do_print {
@@ -1856,6 +1956,24 @@ sub update {
     $self->{preview3D}->reload_print if $self->{preview3D};
 }
 
+# When a printer technology is changed, the UI needs to be updated to show/hide needed preset combo boxes.
+sub show_preset_comboboxes{
+    my ($self, $showSLA) = @_; #if showSLA is oposite value to "ptFFF"
+
+    my $choices = $self->{preset_choosers}{filament};    
+    my $print_filament_ctrls_cnt = 2 + 2 * ($#$choices+1);
+
+    foreach (0..$print_filament_ctrls_cnt-1){
+        $self->{presets_sizer}->Show($_, !$showSLA);
+    }
+    $self->{presets_sizer}->Show($print_filament_ctrls_cnt  , $showSLA);
+    $self->{presets_sizer}->Show($print_filament_ctrls_cnt+1, $showSLA);
+
+    $self->{frequently_changed_parameters_sizer}->Show(0,!$showSLA);
+
+    $self->Layout;
+}
+
 # When a number of extruders changes, the UI needs to be updated to show a single filament selection combo box per extruder.
 # Also the wxTheApp->{preset_bundle}->filament_presets needs to be resized accordingly
 # and some reasonable default has to be selected for the additional extruders.
@@ -1914,28 +2032,30 @@ sub on_config_change {
         } elsif ($opt_key eq 'serial_port') {
             $self->{btn_print}->Show($config->get('serial_port'));
             $self->Layout;
-        } elsif ($opt_key eq 'octoprint_host') {
-            $self->{btn_send_gcode}->Show($config->get('octoprint_host'));
+        } elsif ($opt_key eq 'print_host') {
+            $self->{btn_send_gcode}->Show($config->get('print_host'));
             $self->Layout;
         } elsif ($opt_key eq 'variable_layer_height') {
             if ($config->get('variable_layer_height') != 1) {
-                if ($self->{htoolbar}) {
-                    $self->{htoolbar}->EnableTool(TB_LAYER_EDITING, 0);
-                    $self->{htoolbar}->ToggleTool(TB_LAYER_EDITING, 0);
-                } else {
-                    $self->{"btn_layer_editing"}->Disable;
-                    $self->{"btn_layer_editing"}->SetValue(0);
-                }
+#                if ($self->{htoolbar}) {
+#                    $self->{htoolbar}->EnableTool(TB_LAYER_EDITING, 0);
+#                    $self->{htoolbar}->ToggleTool(TB_LAYER_EDITING, 0);
+#                } else {
+#                    $self->{"btn_layer_editing"}->Disable;
+#                    $self->{"btn_layer_editing"}->SetValue(0);
+#                }
+                Slic3r::GUI::_3DScene::enable_toolbar_item($self->{canvas3D}, "layersediting", 0);
                 Slic3r::GUI::_3DScene::enable_layers_editing($self->{canvas3D}, 0);
                 $self->{canvas3D}->Refresh;
                 $self->{canvas3D}->Update;
             } elsif (Slic3r::GUI::_3DScene::is_layers_editing_allowed($self->{canvas3D})) {
                 # Want to allow the layer editing, but do it only if the OpenGL supports it.
-                if ($self->{htoolbar}) {
-                    $self->{htoolbar}->EnableTool(TB_LAYER_EDITING, 1);
-                } else {
-                    $self->{"btn_layer_editing"}->Enable;
-                }
+#                if ($self->{htoolbar}) {
+#                    $self->{htoolbar}->EnableTool(TB_LAYER_EDITING, 1);
+#                } else {
+#                    $self->{"btn_layer_editing"}->Enable;
+#                }
+                Slic3r::GUI::_3DScene::enable_toolbar_item($self->{canvas3D}, "layersediting", 1);
             }
         } elsif ($opt_key eq 'extruder_colour') {
             $update_scheduled = 1;
@@ -1959,32 +2079,18 @@ sub on_config_change {
     $self->schedule_background_process;
 }
 
-sub list_item_deselected {
-    my ($self, $event) = @_;
-    return if $PreventListEvents;
-    $self->{_lecursor} = Wx::BusyCursor->new();
-    if ($self->{list}->GetFirstSelected == -1) {
-        $self->select_object(undef);
-#        $self->{canvas}->Refresh;
-        Slic3r::GUI::_3DScene::deselect_volumes($self->{canvas3D}) if $self->{canvas3D};
-        Slic3r::GUI::_3DScene::render($self->{canvas3D}) if $self->{canvas3D};
-    }
-    undef $self->{_lecursor};
-}
+sub item_changed_selection{
+    my ($self, $obj_idx) = @_;
 
-sub list_item_selected {
-    my ($self, $event) = @_;
-    return if $PreventListEvents;
-    $self->{_lecursor} = Wx::BusyCursor->new();
-    my $obj_idx = $event->GetIndex;
-    $self->select_object($obj_idx);
 #    $self->{canvas}->Refresh;
     if ($self->{canvas3D}) {
-        my $selections = $self->collect_selections;
-        Slic3r::GUI::_3DScene::update_volumes_selection($self->{canvas3D}, \@$selections);
+        Slic3r::GUI::_3DScene::deselect_volumes($self->{canvas3D});
+        if ($obj_idx >= 0){
+            my $selections = $self->collect_selections;
+            Slic3r::GUI::_3DScene::update_volumes_selection($self->{canvas3D}, \@$selections);
+        }
         Slic3r::GUI::_3DScene::render($self->{canvas3D});
     }
-    undef $self->{_lecursor};
 }
 
 sub collect_selections {
@@ -1996,6 +2102,7 @@ sub collect_selections {
     return $selections;
 }
 
+# doesn't used now
 sub list_item_activated {
     my ($self, $event, $obj_idx) = @_;
     
@@ -2096,6 +2203,31 @@ sub object_settings_dialog {
     }
 }
 
+sub changed_object_settings {
+    my ($self, $obj_idx, $parts_changed, $part_settings_changed) = @_;
+    
+    # update thumbnail since parts may have changed
+    if ($parts_changed) {
+        # recenter and re-align to Z = 0
+        my $model_object = $self->{model}->objects->[$obj_idx];
+        $model_object->center_around_origin;
+        $self->reset_thumbnail($obj_idx);
+    }
+    
+    # update print
+    if ($parts_changed || $part_settings_changed) {
+        $self->stop_background_process;
+        $self->{print}->reload_object($obj_idx);
+        $self->schedule_background_process;
+        $self->{canvas}->reload_scene if $self->{canvas};
+        my $selections = $self->collect_selections;
+        Slic3r::GUI::_3DScene::set_objects_selections($self->{canvas3D}, \@$selections);
+        Slic3r::GUI::_3DScene::reload_scene($self->{canvas3D}, 0);
+    } else {
+        $self->resume_background_process;
+    }
+}
+
 # Called to update various buttons depending on whether there are any objects or
 # whether background processing (export of a G-code, sending to Octoprint, forced background re-slicing) is active.
 sub object_list_changed {
@@ -2103,20 +2235,21 @@ sub object_list_changed {
         
     # Enable/disable buttons depending on whether there are any objects on the platter.
     my $have_objects = @{$self->{objects}} ? 1 : 0;
-    my $variable_layer_height_allowed = $self->{config}->variable_layer_height && Slic3r::GUI::_3DScene::is_layers_editing_allowed($self->{canvas3D});
-    if ($self->{htoolbar}) {
-        # On OSX or Linux
-        $self->{htoolbar}->EnableTool($_, $have_objects)
-            for (TB_RESET, TB_ARRANGE, TB_LAYER_EDITING);
-        $self->{htoolbar}->EnableTool(TB_LAYER_EDITING, 0) if (! $variable_layer_height_allowed);
-    } else {
-        # On MSW
-        my $method = $have_objects ? 'Enable' : 'Disable';
-        $self->{"btn_$_"}->$method
-            for grep $self->{"btn_$_"}, qw(reset arrange reslice export_gcode export_stl print send_gcode layer_editing);
-        $self->{"btn_layer_editing"}->Disable if (! $variable_layer_height_allowed);
-    }
+#    if ($self->{htoolbar}) {
+#        # On OSX or Linux
+#        $self->{htoolbar}->EnableTool($_, $have_objects)
+#            for (TB_RESET, TB_ARRANGE);
+#    } else {
+#        # On MSW
+#        my $method = $have_objects ? 'Enable' : 'Disable';
+#        $self->{"btn_$_"}->$method
+#            for grep $self->{"btn_$_"}, qw(reset arrange reslice export_gcode export_stl print send_gcode);
+#    }
 
+    for my $toolbar_item (qw(deleteall arrange)) {
+        Slic3r::GUI::_3DScene::enable_toolbar_item($self->{canvas3D}, $toolbar_item, $have_objects);
+    }
+    
     my $export_in_progress = $self->{export_gcode_output_file} || $self->{send_gcode_file};
     my $model_fits = $self->{canvas3D} ? Slic3r::GUI::_3DScene::check_volumes_outside_state($self->{canvas3D}, $self->{config}) : 1;
     # $model_fits == 1 -> ModelInstance::PVS_Partly_Outside
@@ -2130,17 +2263,56 @@ sub selection_changed {
     my ($self) = @_;
     my ($obj_idx, $object) = $self->selected_object;
     my $have_sel = defined $obj_idx;
+    my $layers_height_allowed = $self->{config}->variable_layer_height && Slic3r::GUI::_3DScene::is_layers_editing_allowed($self->{canvas3D}) && $have_sel;
 
     $self->{right_panel}->Freeze;
-    if ($self->{htoolbar}) {
-        # On OSX or Linux
-        $self->{htoolbar}->EnableTool($_, $have_sel)
-            for (TB_REMOVE, TB_MORE, TB_FEWER, TB_45CW, TB_45CCW, TB_SCALE, TB_SPLIT, TB_CUT, TB_SETTINGS);
-    } else {
-        # On MSW
-        my $method = $have_sel ? 'Enable' : 'Disable';
-        $self->{"btn_$_"}->$method
-            for grep $self->{"btn_$_"}, qw(remove increase decrease rotate45cw rotate45ccw changescale split cut settings);
+#    if ($self->{htoolbar}) {
+#        # On OSX or Linux
+#        $self->{htoolbar}->EnableTool($_, $have_sel)
+#            for (TB_REMOVE, TB_MORE, TB_45CW, TB_45CCW, TB_SCALE, TB_SPLIT, TB_CUT, TB_SETTINGS);
+#
+#        $self->{htoolbar}->EnableTool(TB_LAYER_EDITING, $layers_height_allowed);
+#
+#        if ($have_sel) {
+#            my $model_object = $self->{model}->objects->[$obj_idx];
+#            $self->{htoolbar}->EnableTool(TB_FEWER, $model_object->instances_count > 1);
+#        } else {
+#            $self->{htoolbar}->EnableTool(TB_FEWER, 0);
+#        }
+#            
+#    } else {
+#        # On MSW
+#        my $method = $have_sel ? 'Enable' : 'Disable';
+#        $self->{"btn_$_"}->$method
+#            for grep $self->{"btn_$_"}, qw(remove increase rotate45cw rotate45ccw changescale split cut settings);
+#
+#        if ($layers_height_allowed) {
+#            $self->{"btn_layer_editing"}->Enable;
+#        } else {
+#            $self->{"btn_layer_editing"}->Disable;
+#        }
+#
+#        if ($have_sel) {
+#            my $model_object = $self->{model}->objects->[$obj_idx];
+#            if ($model_object->instances_count > 1) {
+#                $self->{"btn_decrease"}->Enable;
+#            } else {
+#                $self->{"btn_decrease"}->Disable;
+#            }            
+#        } else {
+#            $self->{"btn_decrease"}->Disable;
+#        }
+#    }
+
+    for my $toolbar_item (qw(delete more fewer split cut settings)) {
+        Slic3r::GUI::_3DScene::enable_toolbar_item($self->{canvas3D}, $toolbar_item, $have_sel);
+    }
+    
+    Slic3r::GUI::_3DScene::enable_toolbar_item($self->{canvas3D}, "layersediting", $layers_height_allowed);
+    
+    if ($have_sel) {
+        my $model_object = $self->{model}->objects->[$obj_idx];
+        Slic3r::GUI::_3DScene::enable_toolbar_item($self->{canvas3D}, "fewer", $model_object->instances_count > 1);
     }
     
     if ($self->{object_info_size}) { # have we already loaded the info pane?
@@ -2157,7 +2329,8 @@ sub selection_changed {
                 $self->{object_info_facets}->SetLabel(sprintf(L('%d (%d shells)'), $model_object->facets_count, $stats->{number_of_parts}));
                 if (my $errors = sum(@$stats{qw(degenerate_facets edges_fixed facets_removed facets_added facets_reversed backwards_edges)})) {
                     $self->{object_info_manifold}->SetLabel(sprintf(L("Auto-repaired (%d errors)"), $errors));
-                    $self->{object_info_manifold_warning_icon}->Show;
+                    #$self->{object_info_manifold_warning_icon}->Show;
+                    $self->{"object_info_manifold_warning_icon_show"}->(1);
                     
                     # we don't show normals_fixed because we never provide normals
 	                # to admesh, so it generates normals for all facets
@@ -2167,7 +2340,8 @@ sub selection_changed {
                     $self->{object_info_manifold_warning_icon}->SetToolTipString($message);
                 } else {
                     $self->{object_info_manifold}->SetLabel(L("Yes"));
-                    $self->{object_info_manifold_warning_icon}->Hide;
+                    #$self->{object_info_manifold_warning_icon}->Hide;
+                    $self->{"object_info_manifold_warning_icon_show"}->(0);
                     $self->{object_info_manifold}->SetToolTipString("");
                     $self->{object_info_manifold_warning_icon}->SetToolTipString("");
                 }
@@ -2176,7 +2350,8 @@ sub selection_changed {
             }
         } else {
             $self->{"object_info_$_"}->SetLabel("") for qw(size volume facets materials manifold);
-            $self->{object_info_manifold_warning_icon}->Hide;
+            #$self->{object_info_manifold_warning_icon}->Hide;
+            $self->{"object_info_manifold_warning_icon_show"}->(0);
             $self->{object_info_manifold}->SetToolTipString("");
             $self->{object_info_manifold_warning_icon}->SetToolTipString("");
         }
@@ -2189,26 +2364,21 @@ sub selection_changed {
 }
 
 sub select_object {
-    my ($self, $obj_idx) = @_;
+    my ($self, $obj_idx, $child) = @_;
 
     # remove current selection
     foreach my $o (0..$#{$self->{objects}}) {
-        $PreventListEvents = 1;
         $self->{objects}->[$o]->selected(0);
-        $self->{list}->Select($o, 0);
-        $PreventListEvents = 0;
     }
-    
+
     if (defined $obj_idx) {
         $self->{objects}->[$obj_idx]->selected(1);
-        # We use this flag to avoid circular event handling
-        # Select() happens to fire a wxEVT_LIST_ITEM_SELECTED on Windows, 
-        # whose event handler calls this method again and again and again
-        $PreventListEvents = 1;
-        $self->{list}->Select($obj_idx, 1);
-        $PreventListEvents = 0;
+        # Select current object in the list on c++ side, if item isn't child
+        if (!defined $child){
+            Slic3r::GUI::select_current_object($obj_idx);}
     } else {
-        # TODO: deselect all in list
+        # Unselect all objects in the list on c++ side
+        Slic3r::GUI::unselect_objects();
     }
     $self->selection_changed(1);
 }
diff --git a/lib/Slic3r/GUI/Plater/ObjectPartsPanel.pm b/lib/Slic3r/GUI/Plater/ObjectPartsPanel.pm
index a20a241f79..783c1a9f5b 100644
--- a/lib/Slic3r/GUI/Plater/ObjectPartsPanel.pm
+++ b/lib/Slic3r/GUI/Plater/ObjectPartsPanel.pm
@@ -157,7 +157,7 @@ sub new {
             my ($volume_idx) = @_;
             $self->reload_tree($volume_idx);
         });
-        Slic3r::GUI::_3DScene::load_model_object($canvas, $self->{model_object}, 0, [0]);
+        Slic3r::GUI::_3DScene::load_model_object($canvas, $self->{model_object}, 0, [0]);        
         Slic3r::GUI::_3DScene::set_auto_bed_shape($canvas);
         Slic3r::GUI::_3DScene::set_axes_length($canvas, 2.0 * max(@{ Slic3r::GUI::_3DScene::get_volumes_bounding_box($canvas)->size }));
         $canvas->SetSize([500,700]);
@@ -377,7 +377,8 @@ sub on_btn_load {
             }
         }
     }
-    
+
+    $self->{model_object}->center_around_origin if $self->{parts_changed};
     $self->_parts_changed;
 }
 
@@ -479,7 +480,8 @@ sub on_btn_delete {
         $self->{model_object}->delete_volume($itemData->{volume_id});
         $self->{parts_changed} = 1;
     }
-    
+
+    $self->{model_object}->center_around_origin if $self->{parts_changed};
     $self->_parts_changed;
 }
 
diff --git a/resources/icons/add_object.png b/resources/icons/add_object.png
new file mode 100644
index 0000000000..ffc958edc4
Binary files /dev/null and b/resources/icons/add_object.png differ
diff --git a/resources/icons/bed/mk2_top.png b/resources/icons/bed/mk2_top.png
index cab4b966f8..e93430b098 100644
Binary files a/resources/icons/bed/mk2_top.png and b/resources/icons/bed/mk2_top.png differ
diff --git a/resources/icons/bed/mk3_top.png b/resources/icons/bed/mk3_top.png
index b44007ad44..9674484979 100644
Binary files a/resources/icons/bed/mk3_top.png and b/resources/icons/bed/mk3_top.png differ
diff --git a/resources/icons/colorchange_add_off.png b/resources/icons/colorchange_add_off.png
new file mode 100644
index 0000000000..6ddeccbe0a
Binary files /dev/null and b/resources/icons/colorchange_add_off.png differ
diff --git a/resources/icons/colorchange_add_on.png b/resources/icons/colorchange_add_on.png
new file mode 100644
index 0000000000..cc800b81e8
Binary files /dev/null and b/resources/icons/colorchange_add_on.png differ
diff --git a/resources/icons/colorchange_delete_off.png b/resources/icons/colorchange_delete_off.png
new file mode 100644
index 0000000000..c16655271a
Binary files /dev/null and b/resources/icons/colorchange_delete_off.png differ
diff --git a/resources/icons/colorchange_delete_on.png b/resources/icons/colorchange_delete_on.png
new file mode 100644
index 0000000000..8f27ce9fe6
Binary files /dev/null and b/resources/icons/colorchange_delete_on.png differ
diff --git a/resources/icons/disclosure_triangle_close.png b/resources/icons/disclosure_triangle_close.png
new file mode 100644
index 0000000000..0660422c7f
Binary files /dev/null and b/resources/icons/disclosure_triangle_close.png differ
diff --git a/resources/icons/disclosure_triangle_open.png b/resources/icons/disclosure_triangle_open.png
new file mode 100644
index 0000000000..81112f2a26
Binary files /dev/null and b/resources/icons/disclosure_triangle_open.png differ
diff --git a/resources/icons/down_half_circle.png b/resources/icons/down_half_circle.png
new file mode 100644
index 0000000000..84aba5c3cd
Binary files /dev/null and b/resources/icons/down_half_circle.png differ
diff --git a/resources/icons/erase.png b/resources/icons/erase.png
new file mode 100644
index 0000000000..4c4cfd755c
Binary files /dev/null and b/resources/icons/erase.png differ
diff --git a/resources/icons/exclamation_mark_.png b/resources/icons/exclamation_mark_.png
new file mode 100644
index 0000000000..5fe7c13556
Binary files /dev/null and b/resources/icons/exclamation_mark_.png differ
diff --git a/resources/icons/lambda.png b/resources/icons/lambda.png
new file mode 100644
index 0000000000..3be73b1424
Binary files /dev/null and b/resources/icons/lambda.png differ
diff --git a/resources/icons/lambda_.png b/resources/icons/lambda_.png
new file mode 100644
index 0000000000..8e9d2b0ea2
Binary files /dev/null and b/resources/icons/lambda_.png differ
diff --git a/resources/icons/left_half_circle.png b/resources/icons/left_half_circle.png
new file mode 100644
index 0000000000..c1e8d3a9c9
Binary files /dev/null and b/resources/icons/left_half_circle.png differ
diff --git a/resources/icons/object.png b/resources/icons/object.png
new file mode 100644
index 0000000000..c85cbaf2fa
Binary files /dev/null and b/resources/icons/object.png differ
diff --git a/resources/icons/one_layer_lock_off.png b/resources/icons/one_layer_lock_off.png
new file mode 100644
index 0000000000..7dc8b06118
Binary files /dev/null and b/resources/icons/one_layer_lock_off.png differ
diff --git a/resources/icons/one_layer_lock_on.png b/resources/icons/one_layer_lock_on.png
new file mode 100644
index 0000000000..41b7ff173f
Binary files /dev/null and b/resources/icons/one_layer_lock_on.png differ
diff --git a/resources/icons/one_layer_unlock_off.png b/resources/icons/one_layer_unlock_off.png
new file mode 100644
index 0000000000..c3931f8b9d
Binary files /dev/null and b/resources/icons/one_layer_unlock_off.png differ
diff --git a/resources/icons/one_layer_unlock_on.png b/resources/icons/one_layer_unlock_on.png
new file mode 100644
index 0000000000..99e0db5c26
Binary files /dev/null and b/resources/icons/one_layer_unlock_on.png differ
diff --git a/resources/icons/right_half_circle.png b/resources/icons/right_half_circle.png
new file mode 100644
index 0000000000..9f182b0b42
Binary files /dev/null and b/resources/icons/right_half_circle.png differ
diff --git a/resources/icons/split.png b/resources/icons/split.png
new file mode 100644
index 0000000000..c5680ab916
Binary files /dev/null and b/resources/icons/split.png differ
diff --git a/resources/icons/toolbar.png b/resources/icons/toolbar.png
new file mode 100644
index 0000000000..ce954143db
Binary files /dev/null and b/resources/icons/toolbar.png differ
diff --git a/resources/icons/up_half_circle.png b/resources/icons/up_half_circle.png
new file mode 100644
index 0000000000..9eea07fda7
Binary files /dev/null and b/resources/icons/up_half_circle.png differ
diff --git a/xs/CMakeLists.txt b/xs/CMakeLists.txt
index 1953a9e299..737bc4b5ec 100644
--- a/xs/CMakeLists.txt
+++ b/xs/CMakeLists.txt
@@ -204,9 +204,11 @@ add_library(libslic3r_gui STATIC
     ${LIBDIR}/slic3r/GUI/GLCanvas3DManager.hpp
     ${LIBDIR}/slic3r/GUI/GLCanvas3DManager.cpp
     ${LIBDIR}/slic3r/GUI/GLGizmo.hpp
-    ${LIBDIR}/slic3r/GUI/GLGizmo.cpp    
+    ${LIBDIR}/slic3r/GUI/GLGizmo.cpp
     ${LIBDIR}/slic3r/GUI/GLTexture.hpp
-    ${LIBDIR}/slic3r/GUI/GLTexture.cpp    
+    ${LIBDIR}/slic3r/GUI/GLTexture.cpp
+    ${LIBDIR}/slic3r/GUI/GLToolbar.hpp
+    ${LIBDIR}/slic3r/GUI/GLToolbar.cpp
     ${LIBDIR}/slic3r/GUI/Preferences.cpp
     ${LIBDIR}/slic3r/GUI/Preferences.hpp
     ${LIBDIR}/slic3r/GUI/Preset.cpp
@@ -217,6 +219,10 @@ add_library(libslic3r_gui STATIC
     ${LIBDIR}/slic3r/GUI/PresetHints.hpp
     ${LIBDIR}/slic3r/GUI/GUI.cpp
     ${LIBDIR}/slic3r/GUI/GUI.hpp
+    ${LIBDIR}/slic3r/GUI/GUI_ObjectParts.cpp
+    ${LIBDIR}/slic3r/GUI/GUI_ObjectParts.hpp
+    ${LIBDIR}/slic3r/GUI/LambdaObjectDialog.cpp
+    ${LIBDIR}/slic3r/GUI/LambdaObjectDialog.hpp
     ${LIBDIR}/slic3r/GUI/Tab.cpp
     ${LIBDIR}/slic3r/GUI/Tab.hpp
     ${LIBDIR}/slic3r/GUI/TabIface.cpp
@@ -259,8 +265,14 @@ add_library(libslic3r_gui STATIC
     ${LIBDIR}/slic3r/Utils/Http.hpp
     ${LIBDIR}/slic3r/Utils/FixModelByWin10.cpp
     ${LIBDIR}/slic3r/Utils/FixModelByWin10.hpp
+    ${LIBDIR}/slic3r/Utils/PrintHostSendDialog.cpp
+    ${LIBDIR}/slic3r/Utils/PrintHostSendDialog.hpp
     ${LIBDIR}/slic3r/Utils/OctoPrint.cpp
     ${LIBDIR}/slic3r/Utils/OctoPrint.hpp
+    ${LIBDIR}/slic3r/Utils/Duet.cpp
+    ${LIBDIR}/slic3r/Utils/Duet.hpp
+    ${LIBDIR}/slic3r/Utils/PrintHost.cpp
+    ${LIBDIR}/slic3r/Utils/PrintHost.hpp
     ${LIBDIR}/slic3r/Utils/Bonjour.cpp
     ${LIBDIR}/slic3r/Utils/Bonjour.hpp
     ${LIBDIR}/slic3r/Utils/PresetUpdater.cpp
@@ -464,7 +476,7 @@ set(XS_XSP_FILES
     ${XSP_DIR}/Surface.xsp
     ${XSP_DIR}/SurfaceCollection.xsp
     ${XSP_DIR}/TriangleMesh.xsp
-    ${XSP_DIR}/Utils_OctoPrint.xsp
+    ${XSP_DIR}/Utils_PrintHost.xsp
     ${XSP_DIR}/Utils_PresetUpdater.xsp
     ${XSP_DIR}/AppController.xsp
     ${XSP_DIR}/XS.xsp
@@ -513,7 +525,7 @@ if(APPLE)
     # Ignore undefined symbols of the perl interpreter, they will be found in the caller image.
     target_link_libraries(XS "-undefined dynamic_lookup")
 endif()
-target_link_libraries(XS libslic3r libslic3r_gui admesh miniz clipper nowide polypartition poly2tri semver avrdude)
+target_link_libraries(XS libslic3r libslic3r_gui admesh miniz clipper nowide polypartition poly2tri semver avrdude qhull)
 if(SLIC3R_PROFILE)
     target_link_libraries(XS Shiny)
 endif()
@@ -602,6 +614,10 @@ endif()
 
 add_subdirectory(src/avrdude)
 
+add_subdirectory(src/qhull)
+include_directories(${LIBDIR}/qhull/src)
+message(STATUS ${LIBDIR}/qhull/src)
+
 ## REQUIRED packages
 
 # Find and configure boost
diff --git a/xs/lib/Slic3r/XS.pm b/xs/lib/Slic3r/XS.pm
index a4847fb45e..391b06dac6 100644
--- a/xs/lib/Slic3r/XS.pm
+++ b/xs/lib/Slic3r/XS.pm
@@ -33,16 +33,6 @@ use overload
     '@{}' => sub { $_[0]->arrayref },
     'fallback' => 1;
 
-package Slic3r::Point3;
-use overload
-    '@{}' => sub { [ $_[0]->x, $_[0]->y, $_[0]->z ] },  #,
-    'fallback' => 1;
-
-sub pp {
-    my ($self) = @_;
-    return [ @$self ];
-}
-
 package Slic3r::Pointf;
 use overload
     '@{}' => sub { $_[0]->arrayref },
diff --git a/xs/src/admesh/connect.cpp b/xs/src/admesh/connect.cpp
index e9129d0079..da5b667209 100644
--- a/xs/src/admesh/connect.cpp
+++ b/xs/src/admesh/connect.cpp
@@ -25,11 +25,11 @@
 #include <string.h>
 #include <math.h>
 
+#include <boost/detail/endian.hpp>
+
 #include "stl.h"
 
 
-static void stl_match_neighbors_exact(stl_file *stl,
-                                      stl_hash_edge *edge_a, stl_hash_edge *edge_b);
 static void stl_match_neighbors_nearby(stl_file *stl,
                                        stl_hash_edge *edge_a, stl_hash_edge *edge_b);
 static void stl_record_neighbors(stl_file *stl,
@@ -43,7 +43,6 @@ static int stl_load_edge_nearby(stl_file *stl, stl_hash_edge *edge,
 static void insert_hash_edge(stl_file *stl, stl_hash_edge edge,
                              void (*match_neighbors)(stl_file *stl,
                                  stl_hash_edge *edge_a, stl_hash_edge *edge_b));
-static int stl_get_hash_for_edge(int M, stl_hash_edge *edge);
 static int stl_compare_function(stl_hash_edge *edge_a, stl_hash_edge *edge_b);
 static void stl_free_edges(stl_file *stl);
 static void stl_remove_facet(stl_file *stl, int facet_number);
@@ -82,37 +81,20 @@ stl_check_facets_exact(stl_file *stl) {
 
   for(i = 0; i < stl->stats.number_of_facets; i++) {
     facet = stl->facet_start[i];
-    // Positive and negative zeros are possible in the floats, which are considered equal by the FP unit.
-    // When using a memcmp on raw floats, those numbers report to be different.
-    // Unify all +0 and -0 to +0 to make the floats equal under memcmp.
-    {
-      uint32_t *f = (uint32_t*)&facet;
-      for (int j = 0; j < 12; ++ j, ++ f) // 3x vertex + normal: 4x3 = 12 floats
-        if (*f == 0x80000000)
-            // Negative zero, switch to positive zero.
-            *f = 0;
-    }
-
-    /* If any two of the three vertices are found to be exactally the same, call them degenerate and remove the facet. */
-    if(   !memcmp(&facet.vertex[0], &facet.vertex[1],
-                  sizeof(stl_vertex))
-          || !memcmp(&facet.vertex[1], &facet.vertex[2],
-                     sizeof(stl_vertex))
-          || !memcmp(&facet.vertex[0], &facet.vertex[2],
-                     sizeof(stl_vertex))) {
+    // If any two of the three vertices are found to be exactally the same, call them degenerate and remove the facet.
+    if (facet.vertex[0] == facet.vertex[1] ||
+        facet.vertex[1] == facet.vertex[2] ||
+        facet.vertex[0] == facet.vertex[2]) {
       stl->stats.degenerate_facets += 1;
       stl_remove_facet(stl, i);
-      i--;
+      -- i;
       continue;
-
     }
     for(j = 0; j < 3; j++) {
       edge.facet_number = i;
       edge.which_edge = j;
-      stl_load_edge_exact(stl, &edge, &facet.vertex[j],
-                          &facet.vertex[(j + 1) % 3]);
-
-      insert_hash_edge(stl, edge, stl_match_neighbors_exact);
+      stl_load_edge_exact(stl, &edge, &facet.vertex[j], &facet.vertex[(j + 1) % 3]);
+      insert_hash_edge(stl, edge, stl_record_neighbors);
     }
   }
   stl_free_edges(stl);
@@ -131,28 +113,33 @@ stl_load_edge_exact(stl_file *stl, stl_hash_edge *edge,
   if (stl->error) return;
 
   {
-    float diff_x = ABS(a->x - b->x);
-    float diff_y = ABS(a->y - b->y);
-    float diff_z = ABS(a->z - b->z);
-    float max_diff = STL_MAX(diff_x, diff_y);
-    max_diff = STL_MAX(diff_z, max_diff);
-    stl->stats.shortest_edge = STL_MIN(max_diff, stl->stats.shortest_edge);
+    stl_vertex diff = (*a - *b).cwiseAbs();
+    float max_diff = std::max(diff(0), std::max(diff(1), diff(2)));
+    stl->stats.shortest_edge = std::min(max_diff, stl->stats.shortest_edge);
   }
 
   // Ensure identical vertex ordering of equal edges.
   // This method is numerically robust.
-  if ((a->x != b->x) ? 
-        (a->x < b->x) : 
-        ((a->y != b->y) ? 
-            (a->y < b->y) : 
-            (a->z < b->z))) {
-    memcpy(&edge->key[0], a, sizeof(stl_vertex));
-    memcpy(&edge->key[3], b, sizeof(stl_vertex));
+  if (stl_vertex_lower(*a, *b)) {
   } else {
-    memcpy(&edge->key[0], b, sizeof(stl_vertex));
-    memcpy(&edge->key[3], a, sizeof(stl_vertex));
+    std::swap(a, b);
     edge->which_edge += 3; /* this edge is loaded backwards */
   }
+  memcpy(&edge->key[0],                  a->data(), sizeof(stl_vertex));
+  memcpy(&edge->key[sizeof(stl_vertex)], b->data(), sizeof(stl_vertex));
+  // Switch negative zeros to positive zeros, so memcmp will consider them to be equal.
+  for (size_t i = 0; i < 6; ++ i) {
+    unsigned char *p = edge->key + i * 4;
+#ifdef BOOST_LITTLE_ENDIAN
+    if (p[0] == 0 && p[1] == 0 && p[2] == 0 && p[3] == 0x80)
+      // Negative zero, switch to positive zero.
+      p[3] = 0;
+#else /* BOOST_LITTLE_ENDIAN */
+    if (p[0] == 0x80 && p[1] == 0 && p[2] == 0 && p[3] == 0)
+      // Negative zero, switch to positive zero.
+      p[0] = 0;
+#endif /* BOOST_LITTLE_ENDIAN */
+  }
 }
 
 static void
@@ -188,21 +175,17 @@ stl_initialize_facet_check_exact(stl_file *stl) {
   }
 }
 
-static void
-insert_hash_edge(stl_file *stl, stl_hash_edge edge,
+static void insert_hash_edge(stl_file *stl, stl_hash_edge edge,
                  void (*match_neighbors)(stl_file *stl,
-                     stl_hash_edge *edge_a, stl_hash_edge *edge_b)) {
-  stl_hash_edge *link;
-  stl_hash_edge *new_edge;
-  stl_hash_edge *temp;
-  int            chain_number;
-
+                     stl_hash_edge *edge_a, stl_hash_edge *edge_b))
+{
   if (stl->error) return;
 
-  chain_number = stl_get_hash_for_edge(stl->M, &edge);
-
-  link = stl->heads[chain_number];
+  int            chain_number = edge.hash(stl->M);
+  stl_hash_edge *link = stl->heads[chain_number];
 
+  stl_hash_edge *new_edge;
+  stl_hash_edge *temp;
   if(link == stl->tail) {
     /* This list doesn't have any edges currently in it.  Add this one. */
     new_edge = (stl_hash_edge*)malloc(sizeof(stl_hash_edge));
@@ -252,30 +235,17 @@ insert_hash_edge(stl_file *stl, stl_hash_edge edge,
   }
 }
 
-
-static int
-stl_get_hash_for_edge(int M, stl_hash_edge *edge) {
-  return ((edge->key[0] / 23 + edge->key[1] / 19 + edge->key[2] / 17
-           + edge->key[3] /13  + edge->key[4] / 11 + edge->key[5] / 7 ) % M);
+// Return 1 if the edges are not matched.
+static inline int stl_compare_function(stl_hash_edge *edge_a, stl_hash_edge *edge_b)
+{
+    // Don't match edges of the same facet
+    return (edge_a->facet_number == edge_b->facet_number) || (*edge_a != *edge_b);
 }
 
-static int
-stl_compare_function(stl_hash_edge *edge_a, stl_hash_edge *edge_b) {
-  if(edge_a->facet_number == edge_b->facet_number) {
-    return 1;			/* Don't match edges of the same facet */
-  } else {
-    return memcmp(edge_a, edge_b, SIZEOF_EDGE_SORT);
-  }
-}
-
-void
-stl_check_facets_nearby(stl_file *stl, float tolerance) {
-  stl_hash_edge  edge[3];
-  stl_facet      facet;
-  int            i;
-  int            j;
-
-  if (stl->error) return;
+void stl_check_facets_nearby(stl_file *stl, float tolerance)
+{
+  if (stl->error)
+    return;
 
   if(   (stl->stats.connected_facets_1_edge == stl->stats.number_of_facets)
         && (stl->stats.connected_facets_2_edge == stl->stats.number_of_facets)
@@ -286,27 +256,19 @@ stl_check_facets_nearby(stl_file *stl, float tolerance) {
 
   stl_initialize_facet_check_nearby(stl);
 
-  for(i = 0; i < stl->stats.number_of_facets; i++) {
-    facet = stl->facet_start[i];
-    // Positive and negative zeros are possible in the floats, which are considered equal by the FP unit.
-    // When using a memcmp on raw floats, those numbers report to be different.
-    // Unify all +0 and -0 to +0 to make the floats equal under memcmp.
-    {
-      uint32_t *f = (uint32_t*)&facet;
-      for (int j = 0; j < 12; ++ j, ++ f) // 3x vertex + normal: 4x3 = 12 floats
-        if (*f == 0x80000000)
-            // Negative zero, switch to positive zero.
-            *f = 0;
-    }
-    for(j = 0; j < 3; j++) {
+  for (int i = 0; i < stl->stats.number_of_facets; ++ i) {
+    //FIXME is the copy necessary?
+    stl_facet facet = stl->facet_start[i];
+    for (int j = 0; j < 3; j++) {
       if(stl->neighbors_start[i].neighbor[j] == -1) {
-        edge[j].facet_number = i;
-        edge[j].which_edge = j;
-        if(stl_load_edge_nearby(stl, &edge[j], &facet.vertex[j],
+        stl_hash_edge edge;
+        edge.facet_number = i;
+        edge.which_edge = j;
+        if(stl_load_edge_nearby(stl, &edge, &facet.vertex[j],
                                 &facet.vertex[(j + 1) % 3],
                                 tolerance)) {
           /* only insert edges that have different keys */
-          insert_hash_edge(stl, edge[j], stl_match_neighbors_nearby);
+          insert_hash_edge(stl, edge, stl_match_neighbors_nearby);
         }
       }
     }
@@ -315,27 +277,17 @@ stl_check_facets_nearby(stl_file *stl, float tolerance) {
   stl_free_edges(stl);
 }
 
-static int
-stl_load_edge_nearby(stl_file *stl, stl_hash_edge *edge,
-                     stl_vertex *a, stl_vertex *b, float tolerance) {
+static int stl_load_edge_nearby(stl_file *stl, stl_hash_edge *edge, stl_vertex *a, stl_vertex *b, float tolerance)
+{
   // Index of a grid cell spaced by tolerance.
-  uint32_t vertex1[3] = {
-    (uint32_t)((a->x - stl->stats.min.x) / tolerance),
-    (uint32_t)((a->y - stl->stats.min.y) / tolerance),
-    (uint32_t)((a->z - stl->stats.min.z) / tolerance)
-  };
-  uint32_t vertex2[3] = {
-    (uint32_t)((b->x - stl->stats.min.x) / tolerance),
-    (uint32_t)((b->y - stl->stats.min.y) / tolerance),
-    (uint32_t)((b->z - stl->stats.min.z) / tolerance)
-  };
+  typedef Eigen::Matrix<int32_t,  3, 1, Eigen::DontAlign> Vec3i;
+  Vec3i vertex1 = (*a / tolerance).cast<int32_t>();
+  Vec3i vertex2 = (*b / tolerance).cast<int32_t>();
+  static_assert(sizeof(Vec3i) == 12, "size of Vec3i incorrect");
 
-  if(   (vertex1[0] == vertex2[0])
-        && (vertex1[1] == vertex2[1])
-        && (vertex1[2] == vertex2[2])) {
-    /* Both vertices hash to the same value */
+  if (vertex1 == vertex2)
+    // Both vertices hash to the same value
     return 0;
-  }
 
   // Ensure identical vertex ordering of edges, which vertices land into equal grid cells.
   // This method is numerically robust.
@@ -344,30 +296,27 @@ stl_load_edge_nearby(stl_file *stl, stl_hash_edge *edge,
         ((vertex1[1] != vertex2[1]) ? 
             (vertex1[1] < vertex2[1]) : 
             (vertex1[2] < vertex2[2]))) {
-    memcpy(&edge->key[0], vertex1, sizeof(stl_vertex));
-    memcpy(&edge->key[3], vertex2, sizeof(stl_vertex));
+    memcpy(&edge->key[0],                  vertex1.data(), sizeof(stl_vertex));
+    memcpy(&edge->key[sizeof(stl_vertex)], vertex2.data(), sizeof(stl_vertex));
   } else {
-    memcpy(&edge->key[0], vertex2, sizeof(stl_vertex));
-    memcpy(&edge->key[3], vertex1, sizeof(stl_vertex));
+    memcpy(&edge->key[0],                  vertex2.data(), sizeof(stl_vertex));
+    memcpy(&edge->key[sizeof(stl_vertex)], vertex1.data(), sizeof(stl_vertex));
     edge->which_edge += 3; /* this edge is loaded backwards */
   }
   return 1;
 }
 
-static void
-stl_free_edges(stl_file *stl) {
-  int i;
-  stl_hash_edge *temp;
-
-  if (stl->error) return;
+static void stl_free_edges(stl_file *stl)
+{
+  if (stl->error)
+    return;
 
   if(stl->stats.malloced != stl->stats.freed) {
-    for(i = 0; i < stl->M; i++) {
-      for(temp = stl->heads[i]; stl->heads[i] != stl->tail;
-          temp = stl->heads[i]) {
+    for (int i = 0; i < stl->M; i++) {
+      for (stl_hash_edge *temp = stl->heads[i]; stl->heads[i] != stl->tail; temp = stl->heads[i]) {
         stl->heads[i] = stl->heads[i]->next;
         free(temp);
-        stl->stats.freed++;
+        ++ stl->stats.freed;
       }
     }
   }
@@ -375,8 +324,8 @@ stl_free_edges(stl_file *stl) {
   free(stl->tail);
 }
 
-static void
-stl_initialize_facet_check_nearby(stl_file *stl) {
+static void stl_initialize_facet_check_nearby(stl_file *stl)
+{
   int i;
 
   if (stl->error) return;
@@ -467,16 +416,8 @@ stl_record_neighbors(stl_file *stl,
   }
 }
 
-static void
-stl_match_neighbors_exact(stl_file *stl,
-                          stl_hash_edge *edge_a, stl_hash_edge *edge_b) {
-  if (stl->error) return;
-  stl_record_neighbors(stl, edge_a, edge_b);
-}
-
-static void
-stl_match_neighbors_nearby(stl_file *stl,
-                           stl_hash_edge *edge_a, stl_hash_edge *edge_b) {
+static void stl_match_neighbors_nearby(stl_file *stl, stl_hash_edge *edge_a, stl_hash_edge *edge_b)
+{
   int facet1;
   int facet2;
   int vertex1;
@@ -517,9 +458,7 @@ stl_match_neighbors_nearby(stl_file *stl,
 }
 
 
-static void
-stl_change_vertices(stl_file *stl, int facet_num, int vnot,
-                    stl_vertex new_vertex) {
+static void stl_change_vertices(stl_file *stl, int facet_num, int vnot, stl_vertex new_vertex) {
   int first_facet;
   int direction;
   int next_edge;
@@ -551,30 +490,30 @@ stl_change_vertices(stl_file *stl, int facet_num, int vnot,
       }
     }
 #if 0
-    if (stl->facet_start[facet_num].vertex[pivot_vertex].x == new_vertex.x &&
-        stl->facet_start[facet_num].vertex[pivot_vertex].y == new_vertex.y &&
-        stl->facet_start[facet_num].vertex[pivot_vertex].z == new_vertex.z)
+    if (stl->facet_start[facet_num].vertex[pivot_vertex](0) == new_vertex(0) &&
+        stl->facet_start[facet_num].vertex[pivot_vertex](1) == new_vertex(1) &&
+        stl->facet_start[facet_num].vertex[pivot_vertex](2) == new_vertex(2))
       printf("Changing vertex %f,%f,%f: Same !!!\r\n", 
-        new_vertex.x, new_vertex.y, new_vertex.z);
+        new_vertex(0), new_vertex(1), new_vertex(2));
     else {
-      if (stl->facet_start[facet_num].vertex[pivot_vertex].x != new_vertex.x)
+      if (stl->facet_start[facet_num].vertex[pivot_vertex](0) != new_vertex(0))
         printf("Changing coordinate x, vertex %e (0x%08x) to %e(0x%08x)\r\n", 
-          stl->facet_start[facet_num].vertex[pivot_vertex].x,
-          *reinterpret_cast<const int*>(&stl->facet_start[facet_num].vertex[pivot_vertex].x),
-          new_vertex.x,
-          *reinterpret_cast<const int*>(&new_vertex.x));
-      if (stl->facet_start[facet_num].vertex[pivot_vertex].y != new_vertex.y)
+          stl->facet_start[facet_num].vertex[pivot_vertex](0),
+          *reinterpret_cast<const int*>(&stl->facet_start[facet_num].vertex[pivot_vertex](0)),
+          new_vertex(0),
+          *reinterpret_cast<const int*>(&new_vertex(0)));
+      if (stl->facet_start[facet_num].vertex[pivot_vertex](1) != new_vertex(1))
         printf("Changing coordinate x, vertex %e (0x%08x) to %e(0x%08x)\r\n", 
-          stl->facet_start[facet_num].vertex[pivot_vertex].y,
-          *reinterpret_cast<const int*>(&stl->facet_start[facet_num].vertex[pivot_vertex].y),
-          new_vertex.y,
-          *reinterpret_cast<const int*>(&new_vertex.y));
-      if (stl->facet_start[facet_num].vertex[pivot_vertex].z != new_vertex.z)
+          stl->facet_start[facet_num].vertex[pivot_vertex](1),
+          *reinterpret_cast<const int*>(&stl->facet_start[facet_num].vertex[pivot_vertex](1)),
+          new_vertex(1),
+          *reinterpret_cast<const int*>(&new_vertex(1)));
+      if (stl->facet_start[facet_num].vertex[pivot_vertex](2) != new_vertex(2))
         printf("Changing coordinate x, vertex %e (0x%08x) to %e(0x%08x)\r\n", 
-          stl->facet_start[facet_num].vertex[pivot_vertex].z,
-          *reinterpret_cast<const int*>(&stl->facet_start[facet_num].vertex[pivot_vertex].z),
-          new_vertex.z,
-          *reinterpret_cast<const int*>(&new_vertex.z));
+          stl->facet_start[facet_num].vertex[pivot_vertex](2),
+          *reinterpret_cast<const int*>(&stl->facet_start[facet_num].vertex[pivot_vertex](2)),
+          new_vertex(2),
+          *reinterpret_cast<const int*>(&new_vertex(2)));
     }
 #endif
     stl->facet_start[facet_num].vertex[pivot_vertex] = new_vertex;
@@ -595,7 +534,6 @@ Try using a smaller tolerance or don't do a nearby check\n");
   }
 }
 
-
 static void
 stl_which_vertices_to_change(stl_file *stl, stl_hash_edge *edge_a,
                              stl_hash_edge *edge_b, int *facet1, int *vertex1,
@@ -622,11 +560,10 @@ stl_which_vertices_to_change(stl_file *stl, stl_hash_edge *edge_a,
     v1b = (edge_b->which_edge + 1) % 3;
   }
 
-  /* Of the first pair, which vertex, if any, should be changed */
-  if(!memcmp(&stl->facet_start[edge_a->facet_number].vertex[v1a],
-             &stl->facet_start[edge_b->facet_number].vertex[v1b],
-             sizeof(stl_vertex))) {
-    /* These facets are already equal.  No need to change. */
+  // Of the first pair, which vertex, if any, should be changed
+  if(stl->facet_start[edge_a->facet_number].vertex[v1a] == 
+     stl->facet_start[edge_b->facet_number].vertex[v1b]) {
+    // These facets are already equal.  No need to change.
     *facet1 = -1;
   } else {
     if(   (stl->neighbors_start[edge_a->facet_number].neighbor[v1a] == -1)
@@ -644,10 +581,9 @@ stl_which_vertices_to_change(stl_file *stl, stl_hash_edge *edge_a,
   }
 
   /* Of the second pair, which vertex, if any, should be changed */
-  if(!memcmp(&stl->facet_start[edge_a->facet_number].vertex[v2a],
-             &stl->facet_start[edge_b->facet_number].vertex[v2b],
-             sizeof(stl_vertex))) {
-    /* These facets are already equal.  No need to change. */
+  if(stl->facet_start[edge_a->facet_number].vertex[v2a] == 
+     stl->facet_start[edge_b->facet_number].vertex[v2b]) {
+    // These facets are already equal.  No need to change.
     *facet2 = -1;
   } else {
     if(   (stl->neighbors_start[edge_a->facet_number].neighbor[v2a] == -1)
@@ -718,40 +654,35 @@ in stl_remove_facet: neighbor = %d numfacets = %d this is wrong\n",
   }
 }
 
-void
-stl_remove_unconnected_facets(stl_file *stl) {
+void stl_remove_unconnected_facets(stl_file *stl)
+{
   /* A couple of things need to be done here.  One is to remove any */
   /* completely unconnected facets (0 edges connected) since these are */
   /* useless and could be completely wrong.   The second thing that needs to */
   /* be done is to remove any degenerate facets that were created during */
   /* stl_check_facets_nearby(). */
+  if (stl->error)
+    return;
 
-  int i;
-
-  if (stl->error) return;
-
-  /* remove degenerate facets */
-  for(i = 0; i < stl->stats.number_of_facets; i++) {
-    if(   !memcmp(&stl->facet_start[i].vertex[0],
-                  &stl->facet_start[i].vertex[1], sizeof(stl_vertex))
-          || !memcmp(&stl->facet_start[i].vertex[1],
-                     &stl->facet_start[i].vertex[2], sizeof(stl_vertex))
-          || !memcmp(&stl->facet_start[i].vertex[0],
-                     &stl->facet_start[i].vertex[2], sizeof(stl_vertex))) {
+  // remove degenerate facets
+  for (int i = 0; i < stl->stats.number_of_facets; ++ i) {
+    if(stl->facet_start[i].vertex[0] == stl->facet_start[i].vertex[1] ||
+       stl->facet_start[i].vertex[0] == stl->facet_start[i].vertex[2] ||
+       stl->facet_start[i].vertex[1] == stl->facet_start[i].vertex[2]) {
       stl_remove_degenerate(stl, i);
       i--;
     }
   }
 
   if(stl->stats.connected_facets_1_edge < stl->stats.number_of_facets) {
-    /* remove completely unconnected facets */
-    for(i = 0; i < stl->stats.number_of_facets; i++) {
-      if(   (stl->neighbors_start[i].neighbor[0] == -1)
-            && (stl->neighbors_start[i].neighbor[1] == -1)
-            && (stl->neighbors_start[i].neighbor[2] == -1)) {
-        /* This facet is completely unconnected.  Remove it. */
+    // remove completely unconnected facets
+    for (int i = 0; i < stl->stats.number_of_facets; i++) {
+      if (stl->neighbors_start[i].neighbor[0] == -1 &&
+          stl->neighbors_start[i].neighbor[1] == -1 &&
+          stl->neighbors_start[i].neighbor[2] == -1) {
+        // This facet is completely unconnected.  Remove it.
         stl_remove_facet(stl, i);
-        i--;
+        -- i;
       }
     }
   }
@@ -771,30 +702,24 @@ stl_remove_degenerate(stl_file *stl, int facet) {
 
   if (stl->error) return;
 
-  if(   !memcmp(&stl->facet_start[facet].vertex[0],
-                &stl->facet_start[facet].vertex[1], sizeof(stl_vertex))
-        && !memcmp(&stl->facet_start[facet].vertex[1],
-                   &stl->facet_start[facet].vertex[2], sizeof(stl_vertex))) {
+  if (stl->facet_start[facet].vertex[0] == stl->facet_start[facet].vertex[1] &&
+      stl->facet_start[facet].vertex[1] == stl->facet_start[facet].vertex[2]) {
     /* all 3 vertices are equal.  Just remove the facet.  I don't think*/
     /* this is really possible, but just in case... */
     printf("removing a facet in stl_remove_degenerate\n");
-
     stl_remove_facet(stl, facet);
     return;
   }
 
-  if(!memcmp(&stl->facet_start[facet].vertex[0],
-             &stl->facet_start[facet].vertex[1], sizeof(stl_vertex))) {
+  if (stl->facet_start[facet].vertex[0] == stl->facet_start[facet].vertex[1]) {
     edge1 = 1;
     edge2 = 2;
     edge3 = 0;
-  } else if(!memcmp(&stl->facet_start[facet].vertex[1],
-                    &stl->facet_start[facet].vertex[2], sizeof(stl_vertex))) {
+  } else if (stl->facet_start[facet].vertex[1] == stl->facet_start[facet].vertex[2]) {
     edge1 = 0;
     edge2 = 2;
     edge3 = 1;
-  } else if(!memcmp(&stl->facet_start[facet].vertex[2],
-                    &stl->facet_start[facet].vertex[0], sizeof(stl_vertex))) {
+  } else if (stl->facet_start[facet].vertex[2] == stl->facet_start[facet].vertex[0]) {
     edge1 = 0;
     edge2 = 1;
     edge3 = 2;
@@ -883,7 +808,7 @@ stl_fill_holes(stl_file *stl) {
       stl_load_edge_exact(stl, &edge, &facet.vertex[j],
                           &facet.vertex[(j + 1) % 3]);
 
-      insert_hash_edge(stl, edge, stl_match_neighbors_exact);
+      insert_hash_edge(stl, edge, stl_record_neighbors);
     }
   }
 
@@ -939,7 +864,7 @@ stl_fill_holes(stl_file *stl) {
             stl_load_edge_exact(stl, &edge, &new_facet.vertex[k],
                                 &new_facet.vertex[(k + 1) % 3]);
 
-            insert_hash_edge(stl, edge, stl_match_neighbors_exact);
+            insert_hash_edge(stl, edge, stl_record_neighbors);
           }
           break;
         } else {
@@ -977,9 +902,7 @@ stl_add_facet(stl_file *stl, stl_facet *new_facet) {
   stl->facet_start[stl->stats.number_of_facets] = *new_facet;
 
   /* note that the normal vector is not set here, just initialized to 0 */
-  stl->facet_start[stl->stats.number_of_facets].normal.x = 0.0;
-  stl->facet_start[stl->stats.number_of_facets].normal.y = 0.0;
-  stl->facet_start[stl->stats.number_of_facets].normal.z = 0.0;
+  stl->facet_start[stl->stats.number_of_facets].normal = stl_normal::Zero();
 
   stl->neighbors_start[stl->stats.number_of_facets].neighbor[0] = -1;
   stl->neighbors_start[stl->stats.number_of_facets].neighbor[1] = -1;
diff --git a/xs/src/admesh/normals.cpp b/xs/src/admesh/normals.cpp
index b7cf9a8ab7..a8faa44bd2 100644
--- a/xs/src/admesh/normals.cpp
+++ b/xs/src/admesh/normals.cpp
@@ -27,12 +27,6 @@
 
 #include "stl.h"
 
-static void stl_reverse_vector(float v[]) {
-  v[0] *= -1;
-  v[1] *= -1;
-  v[2] *= -1;
-}
-
 static int stl_check_normal_vector(stl_file *stl, int facet_num, int normal_fix_flag);
 
 static void
@@ -228,102 +222,52 @@ static int stl_check_normal_vector(stl_file *stl, int facet_num, int normal_fix_
   /* Returns 2 if the normal is not within tolerance and backwards */
   /* Returns 4 if the status is unknown. */
 
-  float normal[3];
-  float test_norm[3];
   stl_facet *facet;
 
   facet = &stl->facet_start[facet_num];
 
+  stl_normal normal;
   stl_calculate_normal(normal, facet);
   stl_normalize_vector(normal);
+  stl_normal normal_dif = (normal - facet->normal).cwiseAbs();
 
-  if(   (ABS(normal[0] - facet->normal.x) < 0.001)
-        && (ABS(normal[1] - facet->normal.y) < 0.001)
-        && (ABS(normal[2] - facet->normal.z) < 0.001)) {
+  const float eps = 0.001f;
+  if (normal_dif(0) < eps && normal_dif(1) < eps && normal_dif(2) < eps) {
     /* It is not really necessary to change the values here */
     /* but just for consistency, I will. */
-    facet->normal.x = normal[0];
-    facet->normal.y = normal[1];
-    facet->normal.z = normal[2];
+    facet->normal = normal;
     return 0;
   }
 
-  test_norm[0] = facet->normal.x;
-  test_norm[1] = facet->normal.y;
-  test_norm[2] = facet->normal.z;
-
+  stl_normal test_norm = facet->normal;
   stl_normalize_vector(test_norm);
-  if(   (ABS(normal[0] - test_norm[0]) < 0.001)
-        && (ABS(normal[1] - test_norm[1]) < 0.001)
-        && (ABS(normal[2] - test_norm[2]) < 0.001)) {
+  normal_dif = (normal - test_norm).cwiseAbs();
+  if (normal_dif(0) < eps && normal_dif(1) < eps && normal_dif(2) < eps) {
     if(normal_fix_flag) {
-      facet->normal.x = normal[0];
-      facet->normal.y = normal[1];
-      facet->normal.z = normal[2];
+      facet->normal = normal;
       stl->stats.normals_fixed += 1;
     }
     return 1;
   }
 
-  stl_reverse_vector(test_norm);
-  if(   (ABS(normal[0] - test_norm[0]) < 0.001)
-        && (ABS(normal[1] - test_norm[1]) < 0.001)
-        && (ABS(normal[2] - test_norm[2]) < 0.001)) {
-    /* Facet is backwards. */
+  test_norm *= -1.f;
+  normal_dif = (normal - test_norm).cwiseAbs();
+  if (normal_dif(0) < eps && normal_dif(1) < eps && normal_dif(2) < eps) {
+    // Facet is backwards.
     if(normal_fix_flag) {
-      facet->normal.x = normal[0];
-      facet->normal.y = normal[1];
-      facet->normal.z = normal[2];
+      facet->normal = normal;
       stl->stats.normals_fixed += 1;
     }
     return 2;
   }
   if(normal_fix_flag) {
-    facet->normal.x = normal[0];
-    facet->normal.y = normal[1];
-    facet->normal.z = normal[2];
+    facet->normal = normal;
     stl->stats.normals_fixed += 1;
   }
   return 4;
 }
 
-void stl_calculate_normal(float normal[], stl_facet *facet) {
-  float v1[3] = {
-    facet->vertex[1].x - facet->vertex[0].x,
-    facet->vertex[1].y - facet->vertex[0].y,
-    facet->vertex[1].z - facet->vertex[0].z
-  };
-  float v2[3] = {
-    facet->vertex[2].x - facet->vertex[0].x,
-    facet->vertex[2].y - facet->vertex[0].y,
-    facet->vertex[2].z - facet->vertex[0].z
-  };
-  normal[0] = (float)((double)v1[1] * (double)v2[2]) - ((double)v1[2] * (double)v2[1]);
-  normal[1] = (float)((double)v1[2] * (double)v2[0]) - ((double)v1[0] * (double)v2[2]);
-  normal[2] = (float)((double)v1[0] * (double)v2[1]) - ((double)v1[1] * (double)v2[0]);
-}
-
-void stl_normalize_vector(float v[]) {
-  double length;
-  double factor;
-  float min_normal_length;
-
-  length = sqrt((double)v[0] * (double)v[0] + (double)v[1] * (double)v[1] + (double)v[2] * (double)v[2]);
-  min_normal_length = 0.000000000001;
-  if(length < min_normal_length) {
-    v[0] = 0.0;
-    v[1] = 0.0;
-    v[2] = 0.0;
-    return;
-  }
-  factor = 1.0 / length;
-  v[0] *= factor;
-  v[1] *= factor;
-  v[2] *= factor;
-}
-
-void
-stl_fix_normal_values(stl_file *stl) {
+void stl_fix_normal_values(stl_file *stl) {
   int i;
 
   if (stl->error) return;
@@ -333,20 +277,16 @@ stl_fix_normal_values(stl_file *stl) {
   }
 }
 
-void
-stl_reverse_all_facets(stl_file *stl) {
-  int i;
-  float normal[3];
+void stl_reverse_all_facets(stl_file *stl)
+{
+  if (stl->error)
+  	return;
 
-  if (stl->error) return;
-
-  for(i = 0; i < stl->stats.number_of_facets; i++) {
+  stl_normal normal;
+  for(int i = 0; i < stl->stats.number_of_facets; i++) {
     stl_reverse_facet(stl, i);
     stl_calculate_normal(normal, &stl->facet_start[i]);
     stl_normalize_vector(normal);
-    stl->facet_start[i].normal.x = normal[0];
-    stl->facet_start[i].normal.y = normal[1];
-    stl->facet_start[i].normal.z = normal[2];
+    stl->facet_start[i].normal = normal;
   }
 }
-
diff --git a/xs/src/admesh/shared.cpp b/xs/src/admesh/shared.cpp
index 8080f3574e..91bb82e006 100644
--- a/xs/src/admesh/shared.cpp
+++ b/xs/src/admesh/shared.cpp
@@ -169,7 +169,7 @@ stl_write_off(stl_file *stl, char *file) {
 
   for(i = 0; i < stl->stats.shared_vertices; i++) {
     fprintf(fp, "\t%f %f %f\n",
-            stl->v_shared[i].x, stl->v_shared[i].y, stl->v_shared[i].z);
+            stl->v_shared[i](0), stl->v_shared[i](1), stl->v_shared[i](2));
   }
   for(i = 0; i < stl->stats.number_of_facets; i++) {
     fprintf(fp, "\t3 %d %d %d\n", stl->v_indices[i].vertex[0],
@@ -216,10 +216,10 @@ stl_write_vrml(stl_file *stl, char *file) {
 
   for(i = 0; i < (stl->stats.shared_vertices - 1); i++) {
     fprintf(fp, "\t\t\t\t%f %f %f,\n",
-            stl->v_shared[i].x, stl->v_shared[i].y, stl->v_shared[i].z);
+            stl->v_shared[i](0), stl->v_shared[i](1), stl->v_shared[i](2));
   }
   fprintf(fp, "\t\t\t\t%f %f %f]\n",
-          stl->v_shared[i].x, stl->v_shared[i].y, stl->v_shared[i].z);
+          stl->v_shared[i](0), stl->v_shared[i](1), stl->v_shared[i](2));
   fprintf(fp, "\t\t}\n");
   fprintf(fp, "\t\tDEF STLTriangles IndexedFaceSet {\n");
   fprintf(fp, "\t\t\tcoordIndex [\n");
@@ -254,7 +254,7 @@ void stl_write_obj (stl_file *stl, char *file) {
   }
 
   for (i = 0; i < stl->stats.shared_vertices; i++) {
-    fprintf(fp, "v %f %f %f\n", stl->v_shared[i].x, stl->v_shared[i].y, stl->v_shared[i].z);
+    fprintf(fp, "v %f %f %f\n", stl->v_shared[i](0), stl->v_shared[i](1), stl->v_shared[i](2));
   }
   for (i = 0; i < stl->stats.number_of_facets; i++) {
     fprintf(fp, "f %d %d %d\n", stl->v_indices[i].vertex[0]+1, stl->v_indices[i].vertex[1]+1, stl->v_indices[i].vertex[2]+1);
diff --git a/xs/src/admesh/stl.h b/xs/src/admesh/stl.h
index dc0f7ae195..5f7a3c5c14 100644
--- a/xs/src/admesh/stl.h
+++ b/xs/src/admesh/stl.h
@@ -27,9 +27,7 @@
 #include <stdint.h>
 #include <stddef.h>
 
-#define STL_MAX(A,B) ((A)>(B)? (A):(B))
-#define STL_MIN(A,B) ((A)<(B)? (A):(B))
-#define ABS(X)  ((X) < 0 ? -(X) : (X))
+#include <Eigen/Geometry> 
 
 // Size of the binary STL header, free form.
 #define LABEL_SIZE             80
@@ -39,31 +37,16 @@
 #define HEADER_SIZE            84
 #define STL_MIN_FILE_SIZE      284
 #define ASCII_LINES_PER_FACET  7
-// Comparing an edge by memcmp, 2x3x4 bytes = 24
-#define SIZEOF_EDGE_SORT       24
-
-typedef struct {
-  float x;
-  float y;
-  float z;
-} stl_vertex;
 
+typedef Eigen::Matrix<float, 3, 1, Eigen::DontAlign> stl_vertex;
+typedef Eigen::Matrix<float, 3, 1, Eigen::DontAlign> stl_normal;
 static_assert(sizeof(stl_vertex) == 12, "size of stl_vertex incorrect");
-
-typedef struct {
-  float x;
-  float y;
-  float z;
-} stl_normal;
-
 static_assert(sizeof(stl_normal) == 12, "size of stl_normal incorrect");
 
-typedef char stl_extra[2];
-
 typedef struct {
   stl_normal normal;
   stl_vertex vertex[3];
-  stl_extra  extra;
+  char       extra[2];
 } stl_facet;
 #define SIZEOF_STL_FACET       50
 
@@ -81,8 +64,12 @@ typedef struct {
 } stl_edge;
 
 typedef struct stl_hash_edge {
-  // Key of a hash edge: 2x binary copy of a floating point vertex.
-  uint32_t       key[6];
+  // Key of a hash edge: sorted vertices of the edge.
+  unsigned char key[2 * sizeof(stl_vertex)];
+  // Compare two keys.
+  bool operator==(const stl_hash_edge &rhs) { return memcmp(key, rhs.key, sizeof(key)) == 0; }
+  bool operator!=(const stl_hash_edge &rhs) { return ! (*this == rhs); }
+  int  hash(int M) const { return ((key[0] / 23 + key[1] / 19 + key[2] / 17 + key[3] /13  + key[4] / 11 + key[5] / 7 ) % M); }
   // Index of a facet owning this edge.
   int            facet_number;
   // Index of this edge inside the facet with an index of facet_number.
@@ -91,8 +78,6 @@ typedef struct stl_hash_edge {
   struct stl_hash_edge  *next;
 } stl_hash_edge;
 
-static_assert(offsetof(stl_hash_edge, facet_number) == SIZEOF_EDGE_SORT, "size of stl_hash_edge.key incorrect");
-
 typedef struct {
   // Index of a neighbor facet.
   int   neighbor[3];
@@ -179,8 +164,8 @@ extern void stl_fix_normal_values(stl_file *stl);
 extern void stl_reverse_all_facets(stl_file *stl);
 extern void stl_translate(stl_file *stl, float x, float y, float z);
 extern void stl_translate_relative(stl_file *stl, float x, float y, float z);
-extern void stl_scale_versor(stl_file *stl, float versor[3]);
-extern void stl_scale(stl_file *stl, float factor);
+extern void stl_scale_versor(stl_file *stl, const stl_vertex &versor);
+inline void stl_scale(stl_file *stl, float factor) { stl_scale_versor(stl, stl_vertex(factor, factor, factor)); }
 extern void stl_rotate_x(stl_file *stl, float angle);
 extern void stl_rotate_y(stl_file *stl, float angle);
 extern void stl_rotate_z(stl_file *stl, float angle);
@@ -195,8 +180,20 @@ extern void stl_write_obj(stl_file *stl, char *file);
 extern void stl_write_off(stl_file *stl, char *file);
 extern void stl_write_dxf(stl_file *stl, char *file, char *label);
 extern void stl_write_vrml(stl_file *stl, char *file);
-extern void stl_calculate_normal(float normal[], stl_facet *facet);
-extern void stl_normalize_vector(float v[]);
+inline void stl_calculate_normal(stl_normal &normal, stl_facet *facet) {
+  normal = (facet->vertex[1] - facet->vertex[0]).cross(facet->vertex[2] - facet->vertex[0]);
+}
+inline void stl_normalize_vector(stl_normal &normal) {
+  double length = normal.cast<double>().norm();
+  if (length < 0.000000000001)
+    normal = stl_normal::Zero();
+  else
+    normal *= (1.0 / length);
+}
+inline bool stl_vertex_lower(const stl_vertex &a, const stl_vertex &b) {
+  return (a(0) != b(0)) ? (a(0) < b(0)) :
+        ((a(1) != b(1)) ? (a(1) < b(1)) : (a(2) < b(2)));
+}
 extern void stl_calculate_volume(stl_file *stl);
 
 extern void stl_repair(stl_file *stl, int fixall_flag, int exact_flag, int tolerance_flag, float tolerance, int increment_flag, float increment, int nearby_flag, int iterations, int remove_unconnected_flag, int fill_holes_flag, int normal_directions_flag, int normal_values_flag, int reverse_all_flag, int verbose_flag);
@@ -204,8 +201,8 @@ extern void stl_repair(stl_file *stl, int fixall_flag, int exact_flag, int toler
 extern void stl_initialize(stl_file *stl);
 extern void stl_count_facets(stl_file *stl, const char *file);
 extern void stl_allocate(stl_file *stl);
-extern void stl_read(stl_file *stl, int first_facet, int first);
-extern void stl_facet_stats(stl_file *stl, stl_facet facet, int first);
+extern void stl_read(stl_file *stl, int first_facet, bool first);
+extern void stl_facet_stats(stl_file *stl, stl_facet facet, bool &first);
 extern void stl_reallocate(stl_file *stl);
 extern void stl_add_facet(stl_file *stl, stl_facet *new_facet);
 extern void stl_get_size(stl_file *stl);
diff --git a/xs/src/admesh/stl_io.cpp b/xs/src/admesh/stl_io.cpp
index 1603981fcb..81e29d2860 100644
--- a/xs/src/admesh/stl_io.cpp
+++ b/xs/src/admesh/stl_io.cpp
@@ -44,9 +44,9 @@ stl_print_edges(stl_file *stl, FILE *file) {
   for(i = 0; i < edges_allocated; i++) {
     fprintf(file, "%d, %f, %f, %f, %f, %f, %f\n",
             stl->edge_start[i].facet_number,
-            stl->edge_start[i].p1.x, stl->edge_start[i].p1.y,
-            stl->edge_start[i].p1.z, stl->edge_start[i].p2.x,
-            stl->edge_start[i].p2.y, stl->edge_start[i].p2.z);
+            stl->edge_start[i].p1(0), stl->edge_start[i].p1(1),
+            stl->edge_start[i].p1(2), stl->edge_start[i].p2(0),
+            stl->edge_start[i].p2(1), stl->edge_start[i].p2(2));
   }
 }
 
@@ -75,11 +75,11 @@ File type          : ASCII STL file\n");
 Header             : %s\n", stl->stats.header);
   fprintf(file, "============== Size ==============\n");
   fprintf(file, "Min X = % f, Max X = % f\n",
-          stl->stats.min.x, stl->stats.max.x);
+          stl->stats.min(0), stl->stats.max(0));
   fprintf(file, "Min Y = % f, Max Y = % f\n",
-          stl->stats.min.y, stl->stats.max.y);
+          stl->stats.min(1), stl->stats.max(1));
   fprintf(file, "Min Z = % f, Max Z = % f\n",
-          stl->stats.min.z, stl->stats.max.z);
+          stl->stats.min(2), stl->stats.max(2));
 
   fprintf(file, "\
 ========= Facet Status ========== Original ============ Final ====\n");
@@ -149,18 +149,18 @@ stl_write_ascii(stl_file *stl, const char *file, const char *label) {
 
   for(i = 0; i < stl->stats.number_of_facets; i++) {
     fprintf(fp, "  facet normal % .8E % .8E % .8E\n",
-            stl->facet_start[i].normal.x, stl->facet_start[i].normal.y,
-            stl->facet_start[i].normal.z);
+            stl->facet_start[i].normal(0), stl->facet_start[i].normal(1),
+            stl->facet_start[i].normal(2));
     fprintf(fp, "    outer loop\n");
     fprintf(fp, "      vertex % .8E % .8E % .8E\n",
-            stl->facet_start[i].vertex[0].x, stl->facet_start[i].vertex[0].y,
-            stl->facet_start[i].vertex[0].z);
+            stl->facet_start[i].vertex[0](0), stl->facet_start[i].vertex[0](1),
+            stl->facet_start[i].vertex[0](2));
     fprintf(fp, "      vertex % .8E % .8E % .8E\n",
-            stl->facet_start[i].vertex[1].x, stl->facet_start[i].vertex[1].y,
-            stl->facet_start[i].vertex[1].z);
+            stl->facet_start[i].vertex[1](0), stl->facet_start[i].vertex[1](1),
+            stl->facet_start[i].vertex[1](2));
     fprintf(fp, "      vertex % .8E % .8E % .8E\n",
-            stl->facet_start[i].vertex[2].x, stl->facet_start[i].vertex[2].y,
-            stl->facet_start[i].vertex[2].z);
+            stl->facet_start[i].vertex[2](0), stl->facet_start[i].vertex[2](1),
+            stl->facet_start[i].vertex[2](2));
     fprintf(fp, "    endloop\n");
     fprintf(fp, "  endfacet\n");
   }
@@ -264,9 +264,9 @@ void
 stl_write_vertex(stl_file *stl, int facet, int vertex) {
   if (stl->error) return;
   printf("  vertex %d/%d % .8E % .8E % .8E\n", vertex, facet,
-         stl->facet_start[facet].vertex[vertex].x,
-         stl->facet_start[facet].vertex[vertex].y,
-         stl->facet_start[facet].vertex[vertex].z);
+         stl->facet_start[facet].vertex[vertex](0),
+         stl->facet_start[facet].vertex[vertex](1),
+         stl->facet_start[facet].vertex[vertex](2));
 }
 
 void
@@ -309,10 +309,10 @@ stl_write_quad_object(stl_file *stl, char *file) {
   int       i;
   int       j;
   char      *error_msg;
-  stl_vertex connect_color;
-  stl_vertex uncon_1_color;
-  stl_vertex uncon_2_color;
-  stl_vertex uncon_3_color;
+  stl_vertex connect_color = stl_vertex::Zero();
+  stl_vertex uncon_1_color = stl_vertex::Zero();
+  stl_vertex uncon_2_color = stl_vertex::Zero();
+  stl_vertex uncon_3_color = stl_vertex::Zero();
   stl_vertex color;
 
   if (stl->error) return;
@@ -330,19 +330,6 @@ stl_write_quad_object(stl_file *stl, char *file) {
     return;
   }
 
-  connect_color.x = 0.0;
-  connect_color.y = 0.0;
-  connect_color.z = 1.0;
-  uncon_1_color.x = 0.0;
-  uncon_1_color.y = 1.0;
-  uncon_1_color.z = 0.0;
-  uncon_2_color.x = 1.0;
-  uncon_2_color.y = 1.0;
-  uncon_2_color.z = 1.0;
-  uncon_3_color.x = 1.0;
-  uncon_3_color.y = 0.0;
-  uncon_3_color.z = 0.0;
-
   fprintf(fp, "CQUAD\n");
   for(i = 0; i < stl->stats.number_of_facets; i++) {
     j = ((stl->neighbors_start[i].neighbor[0] == -1) +
@@ -358,21 +345,21 @@ stl_write_quad_object(stl_file *stl, char *file) {
       color = uncon_3_color;
     }
     fprintf(fp, "%f %f %f    %1.1f %1.1f %1.1f 1\n",
-            stl->facet_start[i].vertex[0].x,
-            stl->facet_start[i].vertex[0].y,
-            stl->facet_start[i].vertex[0].z, color.x, color.y, color.z);
+            stl->facet_start[i].vertex[0](0),
+            stl->facet_start[i].vertex[0](1),
+            stl->facet_start[i].vertex[0](2), color(0), color(1), color(2));
     fprintf(fp, "%f %f %f    %1.1f %1.1f %1.1f 1\n",
-            stl->facet_start[i].vertex[1].x,
-            stl->facet_start[i].vertex[1].y,
-            stl->facet_start[i].vertex[1].z, color.x, color.y, color.z);
+            stl->facet_start[i].vertex[1](0),
+            stl->facet_start[i].vertex[1](1),
+            stl->facet_start[i].vertex[1](2), color(0), color(1), color(2));
     fprintf(fp, "%f %f %f    %1.1f %1.1f %1.1f 1\n",
-            stl->facet_start[i].vertex[2].x,
-            stl->facet_start[i].vertex[2].y,
-            stl->facet_start[i].vertex[2].z, color.x, color.y, color.z);
+            stl->facet_start[i].vertex[2](0),
+            stl->facet_start[i].vertex[2](1),
+            stl->facet_start[i].vertex[2](2), color(0), color(1), color(2));
     fprintf(fp, "%f %f %f    %1.1f %1.1f %1.1f 1\n",
-            stl->facet_start[i].vertex[2].x,
-            stl->facet_start[i].vertex[2].y,
-            stl->facet_start[i].vertex[2].z, color.x, color.y, color.z);
+            stl->facet_start[i].vertex[2](0),
+            stl->facet_start[i].vertex[2](1),
+            stl->facet_start[i].vertex[2](2), color(0), color(1), color(2));
   }
   fclose(fp);
 }
@@ -409,17 +396,17 @@ stl_write_dxf(stl_file *stl, char *file, char *label) {
   for(i = 0; i < stl->stats.number_of_facets; i++) {
     fprintf(fp, "0\n3DFACE\n8\n0\n");
     fprintf(fp, "10\n%f\n20\n%f\n30\n%f\n",
-            stl->facet_start[i].vertex[0].x, stl->facet_start[i].vertex[0].y,
-            stl->facet_start[i].vertex[0].z);
+            stl->facet_start[i].vertex[0](0), stl->facet_start[i].vertex[0](1),
+            stl->facet_start[i].vertex[0](2));
     fprintf(fp, "11\n%f\n21\n%f\n31\n%f\n",
-            stl->facet_start[i].vertex[1].x, stl->facet_start[i].vertex[1].y,
-            stl->facet_start[i].vertex[1].z);
+            stl->facet_start[i].vertex[1](0), stl->facet_start[i].vertex[1](1),
+            stl->facet_start[i].vertex[1](2));
     fprintf(fp, "12\n%f\n22\n%f\n32\n%f\n",
-            stl->facet_start[i].vertex[2].x, stl->facet_start[i].vertex[2].y,
-            stl->facet_start[i].vertex[2].z);
+            stl->facet_start[i].vertex[2](0), stl->facet_start[i].vertex[2](1),
+            stl->facet_start[i].vertex[2](2));
     fprintf(fp, "13\n%f\n23\n%f\n33\n%f\n",
-            stl->facet_start[i].vertex[2].x, stl->facet_start[i].vertex[2].y,
-            stl->facet_start[i].vertex[2].z);
+            stl->facet_start[i].vertex[2](0), stl->facet_start[i].vertex[2](1),
+            stl->facet_start[i].vertex[2](2));
   }
 
   fprintf(fp, "0\nENDSEC\n0\nEOF\n");
diff --git a/xs/src/admesh/stlinit.cpp b/xs/src/admesh/stlinit.cpp
index e572ce9303..47a37f0a54 100644
--- a/xs/src/admesh/stlinit.cpp
+++ b/xs/src/admesh/stlinit.cpp
@@ -40,7 +40,7 @@ stl_open(stl_file *stl, const char *file) {
   stl_initialize(stl);
   stl_count_facets(stl, file);
   stl_allocate(stl);
-  stl_read(stl, 0, 1);
+  stl_read(stl, 0, true);
   if (!stl->error) fclose(stl->fp);
 }
 
@@ -227,7 +227,7 @@ stl_open_merge(stl_file *stl, char *file_to_merge) {
      Start at num_facets_so_far, the index to the first unused facet.  Also say
      that this isn't our first time so we should augment stats like min and max
      instead of erasing them. */
-  stl_read(stl, num_facets_so_far, 0);
+  stl_read(stl, num_facets_so_far, false);
 
   /* Restore the stl information we overwrote (for stl_read) so that it still accurately
      reflects the subject part: */
@@ -255,8 +255,7 @@ stl_reallocate(stl_file *stl) {
 /* Reads the contents of the file pointed to by stl->fp into the stl structure,
    starting at facet first_facet.  The second argument says if it's our first
    time running this for the stl and therefore we should reset our max and min stats. */
-void
-stl_read(stl_file *stl, int first_facet, int first) {
+void stl_read(stl_file *stl, int first_facet, bool first) {
   stl_facet facet;
   int   i;
 
@@ -294,11 +293,11 @@ stl_read(stl_file *stl, int first_facet, int first) {
       assert(res_normal == 3);
       int res_outer_loop = fscanf(stl->fp, " outer loop");
       assert(res_outer_loop == 0);
-      int res_vertex1    = fscanf(stl->fp, " vertex %f %f %f", &facet.vertex[0].x, &facet.vertex[0].y, &facet.vertex[0].z);
+      int res_vertex1    = fscanf(stl->fp, " vertex %f %f %f", &facet.vertex[0](0), &facet.vertex[0](1), &facet.vertex[0](2));
       assert(res_vertex1 == 3);
-      int res_vertex2    = fscanf(stl->fp, " vertex %f %f %f", &facet.vertex[1].x, &facet.vertex[1].y, &facet.vertex[1].z);
+      int res_vertex2    = fscanf(stl->fp, " vertex %f %f %f", &facet.vertex[1](0), &facet.vertex[1](1), &facet.vertex[1](2));
       assert(res_vertex2 == 3);
-      int res_vertex3    = fscanf(stl->fp, " vertex %f %f %f", &facet.vertex[2].x, &facet.vertex[2].y, &facet.vertex[2].z);
+      int res_vertex3    = fscanf(stl->fp, " vertex %f %f %f", &facet.vertex[2](0), &facet.vertex[2](1), &facet.vertex[2](2));
       assert(res_vertex3 == 3);
       int res_endloop    = fscanf(stl->fp, " endloop");
       assert(res_endloop == 0);
@@ -311,9 +310,9 @@ stl_read(stl_file *stl, int first_facet, int first) {
       }
 
       // The facet normal has been parsed as a single string as to workaround for not a numbers in the normal definition.
-	  if (sscanf(normal_buf[0], "%f", &facet.normal.x) != 1 ||
-		  sscanf(normal_buf[1], "%f", &facet.normal.y) != 1 ||
-		  sscanf(normal_buf[2], "%f", &facet.normal.z) != 1) {
+	  if (sscanf(normal_buf[0], "%f", &facet.normal(0)) != 1 ||
+		  sscanf(normal_buf[1], "%f", &facet.normal(1)) != 1 ||
+		  sscanf(normal_buf[2], "%f", &facet.normal(2)) != 1) {
 		  // Normal was mangled. Maybe denormals or "not a number" were stored?
 		  // Just reset the normal and silently ignore it.
 		  memset(&facet.normal, 0, sizeof(facet.normal));
@@ -326,104 +325,45 @@ stl_read(stl_file *stl, int first_facet, int first) {
       // It may be worth to round these numbers to zero during loading to reduce the number of errors reported
       // during the STL import.
       for (size_t j = 0; j < 3; ++ j) {
-        if (facet.vertex[j].x > -1e-12f && facet.vertex[j].x < 1e-12f)
-            printf("stl_read: facet %d.x = %e\r\n", j, facet.vertex[j].x);
-        if (facet.vertex[j].y > -1e-12f && facet.vertex[j].y < 1e-12f)
-            printf("stl_read: facet %d.y = %e\r\n", j, facet.vertex[j].y);
-        if (facet.vertex[j].z > -1e-12f && facet.vertex[j].z < 1e-12f)
-            printf("stl_read: facet %d.z = %e\r\n", j, facet.vertex[j].z);
+        if (facet.vertex[j](0) > -1e-12f && facet.vertex[j](0) < 1e-12f)
+            printf("stl_read: facet %d(0) = %e\r\n", j, facet.vertex[j](0));
+        if (facet.vertex[j](1) > -1e-12f && facet.vertex[j](1) < 1e-12f)
+            printf("stl_read: facet %d(1) = %e\r\n", j, facet.vertex[j](1));
+        if (facet.vertex[j](2) > -1e-12f && facet.vertex[j](2) < 1e-12f)
+            printf("stl_read: facet %d(2) = %e\r\n", j, facet.vertex[j](2));
       }
 #endif
 
-#if 1
-    {
-      // Positive and negative zeros are possible in the floats, which are considered equal by the FP unit.
-      // When using a memcmp on raw floats, those numbers report to be different.
-      // Unify all +0 and -0 to +0 to make the floats equal under memcmp.
-      uint32_t *f = (uint32_t*)&facet;
-      for (int j = 0; j < 12; ++ j, ++ f) // 3x vertex + normal: 4x3 = 12 floats
-        if (*f == 0x80000000)
-          // Negative zero, switch to positive zero.
-          *f = 0;
-    }
-#else
-    {
-      // Due to the nature of the floating point numbers, close to zero values may be represented with singificantly higher precision 
-      // than the rest of the vertices. Round them to zero.
-      float *f = (float*)&facet;
-      for (int j = 0; j < 12; ++ j, ++ f) // 3x vertex + normal: 4x3 = 12 floats
-        if (*f > -1e-12f && *f < 1e-12f)
-          // Negative zero, switch to positive zero.
-          *f = 0;
-    }
-#endif
     /* Write the facet into memory. */
-    memcpy(stl->facet_start+i, &facet, SIZEOF_STL_FACET);
+    stl->facet_start[i] = facet;
     stl_facet_stats(stl, facet, first);
-    first = 0;
   }
-  stl->stats.size.x = stl->stats.max.x - stl->stats.min.x;
-  stl->stats.size.y = stl->stats.max.y - stl->stats.min.y;
-  stl->stats.size.z = stl->stats.max.z - stl->stats.min.z;
-  stl->stats.bounding_diameter = sqrt(
-                                   stl->stats.size.x * stl->stats.size.x +
-                                   stl->stats.size.y * stl->stats.size.y +
-                                   stl->stats.size.z * stl->stats.size.z
-                                 );
+  stl->stats.size = stl->stats.max - stl->stats.min;
+  stl->stats.bounding_diameter = stl->stats.size.norm();
 }
 
-void
-stl_facet_stats(stl_file *stl, stl_facet facet, int first) {
-  float diff_x;
-  float diff_y;
-  float diff_z;
-  float max_diff;
+void stl_facet_stats(stl_file *stl, stl_facet facet, bool &first)
+{
+  if (stl->error)
+  	return;
 
-  if (stl->error) return;
+  // While we are going through all of the facets, let's find the
+  // maximum and minimum values for x, y, and z
 
-  /* while we are going through all of the facets, let's find the  */
-  /* maximum and minimum values for x, y, and z  */
-
-  /* Initialize the max and min values the first time through*/
   if (first) {
-    stl->stats.max.x = facet.vertex[0].x;
-    stl->stats.min.x = facet.vertex[0].x;
-    stl->stats.max.y = facet.vertex[0].y;
-    stl->stats.min.y = facet.vertex[0].y;
-    stl->stats.max.z = facet.vertex[0].z;
-    stl->stats.min.z = facet.vertex[0].z;
-
-    diff_x = ABS(facet.vertex[0].x - facet.vertex[1].x);
-    diff_y = ABS(facet.vertex[0].y - facet.vertex[1].y);
-    diff_z = ABS(facet.vertex[0].z - facet.vertex[1].z);
-    max_diff = STL_MAX(diff_x, diff_y);
-    max_diff = STL_MAX(diff_z, max_diff);
-    stl->stats.shortest_edge = max_diff;
-
-    first = 0;
+	// Initialize the max and min values the first time through
+    stl->stats.min = facet.vertex[0];
+    stl->stats.max = facet.vertex[0];
+    stl_vertex diff = (facet.vertex[1] - facet.vertex[0]).cwiseAbs();
+    stl->stats.shortest_edge = std::max(diff(0), std::max(diff(1), diff(2)));
+    first = false;
   }
 
-  /* now find the max and min values */
-  stl->stats.max.x = STL_MAX(stl->stats.max.x, facet.vertex[0].x);
-  stl->stats.min.x = STL_MIN(stl->stats.min.x, facet.vertex[0].x);
-  stl->stats.max.y = STL_MAX(stl->stats.max.y, facet.vertex[0].y);
-  stl->stats.min.y = STL_MIN(stl->stats.min.y, facet.vertex[0].y);
-  stl->stats.max.z = STL_MAX(stl->stats.max.z, facet.vertex[0].z);
-  stl->stats.min.z = STL_MIN(stl->stats.min.z, facet.vertex[0].z);
-
-  stl->stats.max.x = STL_MAX(stl->stats.max.x, facet.vertex[1].x);
-  stl->stats.min.x = STL_MIN(stl->stats.min.x, facet.vertex[1].x);
-  stl->stats.max.y = STL_MAX(stl->stats.max.y, facet.vertex[1].y);
-  stl->stats.min.y = STL_MIN(stl->stats.min.y, facet.vertex[1].y);
-  stl->stats.max.z = STL_MAX(stl->stats.max.z, facet.vertex[1].z);
-  stl->stats.min.z = STL_MIN(stl->stats.min.z, facet.vertex[1].z);
-
-  stl->stats.max.x = STL_MAX(stl->stats.max.x, facet.vertex[2].x);
-  stl->stats.min.x = STL_MIN(stl->stats.min.x, facet.vertex[2].x);
-  stl->stats.max.y = STL_MAX(stl->stats.max.y, facet.vertex[2].y);
-  stl->stats.min.y = STL_MIN(stl->stats.min.y, facet.vertex[2].y);
-  stl->stats.max.z = STL_MAX(stl->stats.max.z, facet.vertex[2].z);
-  stl->stats.min.z = STL_MIN(stl->stats.min.z, facet.vertex[2].z);
+  // Now find the max and min values.
+  for (size_t i = 0; i < 3; ++ i) {
+  	stl->stats.min = stl->stats.min.cwiseMin(facet.vertex[i]);
+  	stl->stats.max = stl->stats.max.cwiseMax(facet.vertex[i]);
+  }
 }
 
 void
diff --git a/xs/src/admesh/util.cpp b/xs/src/admesh/util.cpp
index f3bf59b56e..fba1ee76bf 100644
--- a/xs/src/admesh/util.cpp
+++ b/xs/src/admesh/util.cpp
@@ -62,7 +62,7 @@ stl_verify_neighbors(stl_file *stl) {
         edge_b.p1 = stl->facet_start[neighbor].vertex[(vnot + 1) % 3];
         edge_b.p2 = stl->facet_start[neighbor].vertex[(vnot + 2) % 3];
       }
-      if(memcmp(&edge_a, &edge_b, SIZEOF_EDGE_SORT) != 0) {
+      if (edge_a.p1 != edge_b.p1 || edge_a.p2 != edge_b.p2) {
         /* These edges should match but they don't.  Print results. */
         printf("edge %d of facet %d doesn't match edge %d of facet %d\n",
                j, i, vnot + 1, neighbor);
@@ -73,114 +73,67 @@ stl_verify_neighbors(stl_file *stl) {
   }
 }
 
-void
-stl_translate(stl_file *stl, float x, float y, float z) {
-  int i;
-  int j;
-
-  if (stl->error) return;
-
-  for(i = 0; i < stl->stats.number_of_facets; i++) {
-    for(j = 0; j < 3; j++) {
-      stl->facet_start[i].vertex[j].x -= (stl->stats.min.x - x);
-      stl->facet_start[i].vertex[j].y -= (stl->stats.min.y - y);
-      stl->facet_start[i].vertex[j].z -= (stl->stats.min.z - z);
-    }
-  }
-  stl->stats.max.x -= (stl->stats.min.x - x);
-  stl->stats.max.y -= (stl->stats.min.y - y);
-  stl->stats.max.z -= (stl->stats.min.z - z);
-  stl->stats.min.x = x;
-  stl->stats.min.y = y;
-  stl->stats.min.z = z;
+void stl_translate(stl_file *stl, float x, float y, float z)
+{
+  if (stl->error)
+  	return;
 
+  stl_vertex new_min(x, y, z);
+  stl_vertex shift = new_min - stl->stats.min;
+  for (int i = 0; i < stl->stats.number_of_facets; ++ i)
+    for (int j = 0; j < 3; ++ j)
+      stl->facet_start[i].vertex[j] += shift;
+  stl->stats.min = new_min;
+  stl->stats.max += shift;
   stl_invalidate_shared_vertices(stl);
 }
 
 /* Translates the stl by x,y,z, relatively from wherever it is currently */
-void
-stl_translate_relative(stl_file *stl, float x, float y, float z) {
-  int i;
-  int j;
-
-  if (stl->error) return;
-
-  for(i = 0; i < stl->stats.number_of_facets; i++) {
-    for(j = 0; j < 3; j++) {
-      stl->facet_start[i].vertex[j].x += x;
-      stl->facet_start[i].vertex[j].y += y;
-      stl->facet_start[i].vertex[j].z += z;
-    }
-  }
-  stl->stats.min.x += x;
-  stl->stats.min.y += y;
-  stl->stats.min.z += z;
-  stl->stats.max.x += x;
-  stl->stats.max.y += y;
-  stl->stats.max.z += z;
+void stl_translate_relative(stl_file *stl, float x, float y, float z)
+{
+  if (stl->error)
+  	return;
 
+  stl_vertex shift(x, y, z);
+  for (int i = 0; i < stl->stats.number_of_facets; ++ i)
+    for (int j = 0; j < 3; ++ j)
+      stl->facet_start[i].vertex[j] += shift;
+  stl->stats.min += shift;
+  stl->stats.max += shift;
   stl_invalidate_shared_vertices(stl);
 }
 
-void
-stl_scale_versor(stl_file *stl, float versor[3]) {
-  int i;
-  int j;
-
-  if (stl->error) return;
-
-  /* scale extents */
-  stl->stats.min.x *= versor[0];
-  stl->stats.min.y *= versor[1];
-  stl->stats.min.z *= versor[2];
-  stl->stats.max.x *= versor[0];
-  stl->stats.max.y *= versor[1];
-  stl->stats.max.z *= versor[2];
-
-  /* scale size */
-  stl->stats.size.x *= versor[0];
-  stl->stats.size.y *= versor[1];
-  stl->stats.size.z *= versor[2];
-
-  /* scale volume */
-  if (stl->stats.volume > 0.0) {
-    stl->stats.volume *= (versor[0] * versor[1] * versor[2]);
-  }
-
-  for(i = 0; i < stl->stats.number_of_facets; i++) {
-    for(j = 0; j < 3; j++) {
-      stl->facet_start[i].vertex[j].x *= versor[0];
-      stl->facet_start[i].vertex[j].y *= versor[1];
-      stl->facet_start[i].vertex[j].z *= versor[2];
-    }
-  }
+void stl_scale_versor(stl_file *stl, const stl_vertex &versor)
+{
+  if (stl->error)
+  	return;
 
+  // Scale extents.
+  auto s = versor.array();
+  stl->stats.min.array() *= s;
+  stl->stats.max.array() *= s;
+  // Scale size.
+  stl->stats.size.array() *= s;
+  // Scale volume.
+  if (stl->stats.volume > 0.0)
+    stl->stats.volume *= versor(0) * versor(1) * versor(2);
+  // Scale the mesh.
+  for (int i = 0; i < stl->stats.number_of_facets; ++ i)
+    for (int j = 0; j < 3; ++ j)
+      stl->facet_start[i].vertex[j].array() *= s;
   stl_invalidate_shared_vertices(stl);
 }
 
-void
-stl_scale(stl_file *stl, float factor) {
-  float versor[3];
-
-  if (stl->error) return;
-
-  versor[0] = factor;
-  versor[1] = factor;
-  versor[2] = factor;
-  stl_scale_versor(stl, versor);
-}
-
-static void calculate_normals(stl_file *stl) {
-  float normal[3];
-
-  if (stl->error) return;
+static void calculate_normals(stl_file *stl) 
+{
+  if (stl->error)
+  	return;
 
+  stl_normal normal;
   for(uint32_t i = 0; i < stl->stats.number_of_facets; i++) {
     stl_calculate_normal(normal, &stl->facet_start[i]);
     stl_normalize_vector(normal);
-    stl->facet_start[i].normal.x = normal[0];
-    stl->facet_start[i].normal.y = normal[1];
-    stl->facet_start[i].normal.z = normal[2];
+    stl->facet_start[i].normal = normal;
   }
 }
 
@@ -193,9 +146,9 @@ void stl_transform(stl_file *stl, float *trafo3x4) {
     for (i_vertex = 0; i_vertex < 3; ++ i_vertex) {
       stl_vertex &v_dst = vertices[i_vertex];
       stl_vertex  v_src = v_dst;
-      v_dst.x = trafo3x4[0] * v_src.x + trafo3x4[1] * v_src.y + trafo3x4[2]  * v_src.z + trafo3x4[3];
-      v_dst.y = trafo3x4[4] * v_src.x + trafo3x4[5] * v_src.y + trafo3x4[6]  * v_src.z + trafo3x4[7];
-      v_dst.z = trafo3x4[8] * v_src.x + trafo3x4[9] * v_src.y + trafo3x4[10] * v_src.z + trafo3x4[11];
+      v_dst(0) = trafo3x4[0] * v_src(0) + trafo3x4[1] * v_src(1) + trafo3x4[2]  * v_src(2) + trafo3x4[3];
+      v_dst(1) = trafo3x4[4] * v_src(0) + trafo3x4[5] * v_src(1) + trafo3x4[6]  * v_src(2) + trafo3x4[7];
+      v_dst(2) = trafo3x4[8] * v_src(0) + trafo3x4[9] * v_src(1) + trafo3x4[10] * v_src(2) + trafo3x4[11];
     }
   }
   stl_get_size(stl);
@@ -214,8 +167,8 @@ stl_rotate_x(stl_file *stl, float angle) {
 
   for(i = 0; i < stl->stats.number_of_facets; i++) {
     for(j = 0; j < 3; j++) {
-      stl_rotate(&stl->facet_start[i].vertex[j].y,
-                 &stl->facet_start[i].vertex[j].z, c, s);
+      stl_rotate(&stl->facet_start[i].vertex[j](1),
+                 &stl->facet_start[i].vertex[j](2), c, s);
     }
   }
   stl_get_size(stl);
@@ -234,8 +187,8 @@ stl_rotate_y(stl_file *stl, float angle) {
 
   for(i = 0; i < stl->stats.number_of_facets; i++) {
     for(j = 0; j < 3; j++) {
-      stl_rotate(&stl->facet_start[i].vertex[j].z,
-                 &stl->facet_start[i].vertex[j].x, c, s);
+      stl_rotate(&stl->facet_start[i].vertex[j](2),
+                 &stl->facet_start[i].vertex[j](0), c, s);
     }
   }
   stl_get_size(stl);
@@ -254,8 +207,8 @@ stl_rotate_z(stl_file *stl, float angle) {
 
   for(i = 0; i < stl->stats.number_of_facets; i++) {
     for(j = 0; j < 3; j++) {
-      stl_rotate(&stl->facet_start[i].vertex[j].x,
-                 &stl->facet_start[i].vertex[j].y, c, s);
+      stl_rotate(&stl->facet_start[i].vertex[j](0),
+                 &stl->facet_start[i].vertex[j](1), c, s);
     }
   }
   stl_get_size(stl);
@@ -272,142 +225,98 @@ stl_rotate(float *x, float *y, const double c, const double s) {
   *y = float(s * xold + c * yold);
 }
 
-extern void
-stl_get_size(stl_file *stl) {
-  int i;
-  int j;
-
-  if (stl->error) return;
-  if (stl->stats.number_of_facets == 0) return;
-
-  stl->stats.min.x = stl->facet_start[0].vertex[0].x;
-  stl->stats.min.y = stl->facet_start[0].vertex[0].y;
-  stl->stats.min.z = stl->facet_start[0].vertex[0].z;
-  stl->stats.max.x = stl->facet_start[0].vertex[0].x;
-  stl->stats.max.y = stl->facet_start[0].vertex[0].y;
-  stl->stats.max.z = stl->facet_start[0].vertex[0].z;
-
-  for(i = 0; i < stl->stats.number_of_facets; i++) {
-    for(j = 0; j < 3; j++) {
-      stl->stats.min.x = STL_MIN(stl->stats.min.x,
-                                 stl->facet_start[i].vertex[j].x);
-      stl->stats.min.y = STL_MIN(stl->stats.min.y,
-                                 stl->facet_start[i].vertex[j].y);
-      stl->stats.min.z = STL_MIN(stl->stats.min.z,
-                                 stl->facet_start[i].vertex[j].z);
-      stl->stats.max.x = STL_MAX(stl->stats.max.x,
-                                 stl->facet_start[i].vertex[j].x);
-      stl->stats.max.y = STL_MAX(stl->stats.max.y,
-                                 stl->facet_start[i].vertex[j].y);
-      stl->stats.max.z = STL_MAX(stl->stats.max.z,
-                                 stl->facet_start[i].vertex[j].z);
+void stl_get_size(stl_file *stl)
+{
+  if (stl->error || stl->stats.number_of_facets == 0)
+  	return;
+  stl->stats.min = stl->facet_start[0].vertex[0];
+  stl->stats.max = stl->stats.min;
+  for (int i = 0; i < stl->stats.number_of_facets; ++ i) {
+  	const stl_facet &face = stl->facet_start[i];
+    for (int j = 0; j < 3; ++ j) {
+      stl->stats.min = stl->stats.min.cwiseMin(face.vertex[j]);
+      stl->stats.max = stl->stats.max.cwiseMax(face.vertex[j]);
     }
   }
-  stl->stats.size.x = stl->stats.max.x - stl->stats.min.x;
-  stl->stats.size.y = stl->stats.max.y - stl->stats.min.y;
-  stl->stats.size.z = stl->stats.max.z - stl->stats.min.z;
-  stl->stats.bounding_diameter = sqrt(
-                                   stl->stats.size.x * stl->stats.size.x +
-                                   stl->stats.size.y * stl->stats.size.y +
-                                   stl->stats.size.z * stl->stats.size.z
-                                 );
+  stl->stats.size = stl->stats.max - stl->stats.min;
+  stl->stats.bounding_diameter = stl->stats.size.norm();
 }
 
-void
-stl_mirror_xy(stl_file *stl) {
-  int i;
-  int j;
-  float temp_size;
+void stl_mirror_xy(stl_file *stl)
+{
+  if (stl->error) 
+  	return;
 
-  if (stl->error) return;
-
-  for(i = 0; i < stl->stats.number_of_facets; i++) {
-    for(j = 0; j < 3; j++) {
-      stl->facet_start[i].vertex[j].z *= -1.0;
+  for(int i = 0; i < stl->stats.number_of_facets; i++) {
+    for(int j = 0; j < 3; j++) {
+      stl->facet_start[i].vertex[j](2) *= -1.0;
     }
   }
-  temp_size = stl->stats.min.z;
-  stl->stats.min.z = stl->stats.max.z;
-  stl->stats.max.z = temp_size;
-  stl->stats.min.z *= -1.0;
-  stl->stats.max.z *= -1.0;
+  float temp_size = stl->stats.min(2);
+  stl->stats.min(2) = stl->stats.max(2);
+  stl->stats.max(2) = temp_size;
+  stl->stats.min(2) *= -1.0;
+  stl->stats.max(2) *= -1.0;
   stl_reverse_all_facets(stl);
   stl->stats.facets_reversed -= stl->stats.number_of_facets;  /* for not altering stats */
 }
 
-void
-stl_mirror_yz(stl_file *stl) {
-  int i;
-  int j;
-  float temp_size;
-
+void stl_mirror_yz(stl_file *stl)
+{
   if (stl->error) return;
 
-  for(i = 0; i < stl->stats.number_of_facets; i++) {
-    for(j = 0; j < 3; j++) {
-      stl->facet_start[i].vertex[j].x *= -1.0;
+  for (int i = 0; i < stl->stats.number_of_facets; i++) {
+    for (int j = 0; j < 3; j++) {
+      stl->facet_start[i].vertex[j](0) *= -1.0;
     }
   }
-  temp_size = stl->stats.min.x;
-  stl->stats.min.x = stl->stats.max.x;
-  stl->stats.max.x = temp_size;
-  stl->stats.min.x *= -1.0;
-  stl->stats.max.x *= -1.0;
+  float temp_size = stl->stats.min(0);
+  stl->stats.min(0) = stl->stats.max(0);
+  stl->stats.max(0) = temp_size;
+  stl->stats.min(0) *= -1.0;
+  stl->stats.max(0) *= -1.0;
   stl_reverse_all_facets(stl);
   stl->stats.facets_reversed -= stl->stats.number_of_facets;  /* for not altering stats */
 }
 
-void
-stl_mirror_xz(stl_file *stl) {
-  int i;
-  int j;
-  float temp_size;
+void stl_mirror_xz(stl_file *stl)
+{
+  if (stl->error)
+  	return;
 
-  if (stl->error) return;
-
-  for(i = 0; i < stl->stats.number_of_facets; i++) {
-    for(j = 0; j < 3; j++) {
-      stl->facet_start[i].vertex[j].y *= -1.0;
+  for (int i = 0; i < stl->stats.number_of_facets; i++) {
+    for (int j = 0; j < 3; j++) {
+      stl->facet_start[i].vertex[j](1) *= -1.0;
     }
   }
-  temp_size = stl->stats.min.y;
-  stl->stats.min.y = stl->stats.max.y;
-  stl->stats.max.y = temp_size;
-  stl->stats.min.y *= -1.0;
-  stl->stats.max.y *= -1.0;
+  float temp_size = stl->stats.min(1);
+  stl->stats.min(1) = stl->stats.max(1);
+  stl->stats.max(1) = temp_size;
+  stl->stats.min(1) *= -1.0;
+  stl->stats.max(1) *= -1.0;
   stl_reverse_all_facets(stl);
   stl->stats.facets_reversed -= stl->stats.number_of_facets;  /* for not altering stats */
 }
 
-static float get_volume(stl_file *stl) {
-  stl_vertex p0;
-  stl_vertex p;
-  stl_normal n;
-  float height;
-  float area;
-  float volume = 0.0;
+static float get_volume(stl_file *stl)
+{
+  if (stl->error)
+  	return 0;
 
-  if (stl->error) return 0;
-
-  /* Choose a point, any point as the reference */
-  p0.x = stl->facet_start[0].vertex[0].x;
-  p0.y = stl->facet_start[0].vertex[0].y;
-  p0.z = stl->facet_start[0].vertex[0].z;
-
-  for(uint32_t i = 0; i < stl->stats.number_of_facets; i++) {
-    p.x = stl->facet_start[i].vertex[0].x - p0.x;
-    p.y = stl->facet_start[i].vertex[0].y - p0.y;
-    p.z = stl->facet_start[i].vertex[0].z - p0.z;
-    /* Do dot product to get distance from point to plane */
-    n = stl->facet_start[i].normal;
-    height = (n.x * p.x) + (n.y * p.y) + (n.z * p.z);
-    area = get_area(&stl->facet_start[i]);
+  // Choose a point, any point as the reference.
+  stl_vertex p0 = stl->facet_start[0].vertex[0];
+  float volume = 0.f;
+  for(uint32_t i = 0; i < stl->stats.number_of_facets; ++ i) {
+    // Do dot product to get distance from point to plane.
+    float height = stl->facet_start[i].normal.dot(stl->facet_start[i].vertex[0] - p0);
+    float area   = get_area(&stl->facet_start[i]);
     volume += (area * height) / 3.0f;
   }
   return volume;
 }
 
-void stl_calculate_volume(stl_file *stl) {
+void stl_calculate_volume(stl_file *stl)
+{
   if (stl->error) return;
   stl->stats.volume = get_volume(stl);
   if(stl->stats.volume < 0.0) {
@@ -416,35 +325,32 @@ void stl_calculate_volume(stl_file *stl) {
   }
 }
 
-static float get_area(stl_facet *facet) {
-  double cross[3][3];
-  float sum[3];
-  float n[3];
-  float area;
-  int i;
-
+static float get_area(stl_facet *facet)
+{
   /* cast to double before calculating cross product because large coordinates
      can result in overflowing product
     (bad area is responsible for bad volume and bad facets reversal) */
-  for(i = 0; i < 3; i++) {
-    cross[i][0]=(((double)facet->vertex[i].y * (double)facet->vertex[(i + 1) % 3].z) -
-                 ((double)facet->vertex[i].z * (double)facet->vertex[(i + 1) % 3].y));
-    cross[i][1]=(((double)facet->vertex[i].z * (double)facet->vertex[(i + 1) % 3].x) -
-                 ((double)facet->vertex[i].x * (double)facet->vertex[(i + 1) % 3].z));
-    cross[i][2]=(((double)facet->vertex[i].x * (double)facet->vertex[(i + 1) % 3].y) -
-                 ((double)facet->vertex[i].y * (double)facet->vertex[(i + 1) % 3].x));
+  double cross[3][3];
+  for (int i = 0; i < 3; i++) {
+    cross[i][0]=(((double)facet->vertex[i](1) * (double)facet->vertex[(i + 1) % 3](2)) -
+                 ((double)facet->vertex[i](2) * (double)facet->vertex[(i + 1) % 3](1)));
+    cross[i][1]=(((double)facet->vertex[i](2) * (double)facet->vertex[(i + 1) % 3](0)) -
+                 ((double)facet->vertex[i](0) * (double)facet->vertex[(i + 1) % 3](2)));
+    cross[i][2]=(((double)facet->vertex[i](0) * (double)facet->vertex[(i + 1) % 3](1)) -
+                 ((double)facet->vertex[i](1) * (double)facet->vertex[(i + 1) % 3](0)));
   }
 
-  sum[0] = cross[0][0] + cross[1][0] + cross[2][0];
-  sum[1] = cross[0][1] + cross[1][1] + cross[2][1];
-  sum[2] = cross[0][2] + cross[1][2] + cross[2][2];
+  stl_normal sum;
+  sum(0) = cross[0][0] + cross[1][0] + cross[2][0];
+  sum(1) = cross[0][1] + cross[1][1] + cross[2][1];
+  sum(2) = cross[0][2] + cross[1][2] + cross[2][2];
 
-  /* This should already be done.  But just in case, let's do it again */
+  // This should already be done.  But just in case, let's do it again.
+  //FIXME this is questionable. the "sum" normal should be accurate, while the normal "n" may be calculated with a low accuracy.
+  stl_normal n;
   stl_calculate_normal(n, facet);
   stl_normalize_vector(n);
-
-  area = 0.5 * (n[0] * sum[0] + n[1] * sum[1] + n[2] * sum[2]);
-  return area;
+  return 0.5f * n.dot(sum);
 }
 
 void stl_repair(stl_file *stl,
diff --git a/xs/src/libslic3r/BoundingBox.cpp b/xs/src/libslic3r/BoundingBox.cpp
index 68136b9160..d3cca7ff24 100644
--- a/xs/src/libslic3r/BoundingBox.cpp
+++ b/xs/src/libslic3r/BoundingBox.cpp
@@ -7,9 +7,9 @@
 namespace Slic3r {
 
 template BoundingBoxBase<Point>::BoundingBoxBase(const std::vector<Point> &points);
-template BoundingBoxBase<Pointf>::BoundingBoxBase(const std::vector<Pointf> &points);
+template BoundingBoxBase<Vec2d>::BoundingBoxBase(const std::vector<Vec2d> &points);
 
-template BoundingBox3Base<Pointf3>::BoundingBox3Base(const std::vector<Pointf3> &points);
+template BoundingBox3Base<Vec3d>::BoundingBox3Base(const std::vector<Vec3d> &points);
 
 BoundingBox::BoundingBox(const Lines &lines)
 {
@@ -22,8 +22,7 @@ BoundingBox::BoundingBox(const Lines &lines)
     *this = BoundingBox(points);
 }
 
-void
-BoundingBox::polygon(Polygon* polygon) const
+void BoundingBox::polygon(Polygon* polygon) const
 {
     polygon->points.clear();
     polygon->points.resize(4);
@@ -37,8 +36,7 @@ BoundingBox::polygon(Polygon* polygon) const
     polygon->points[3](1) = this->max(1);
 }
 
-Polygon
-BoundingBox::polygon() const
+Polygon BoundingBox::polygon() const
 {
     Polygon p;
     this->polygon(&p);
@@ -72,24 +70,23 @@ BoundingBoxBase<PointClass>::scale(double factor)
     this->max *= factor;
 }
 template void BoundingBoxBase<Point>::scale(double factor);
-template void BoundingBoxBase<Pointf>::scale(double factor);
-template void BoundingBoxBase<Pointf3>::scale(double factor);
+template void BoundingBoxBase<Vec2d>::scale(double factor);
+template void BoundingBoxBase<Vec3d>::scale(double factor);
 
 template <class PointClass> void
 BoundingBoxBase<PointClass>::merge(const PointClass &point)
 {
     if (this->defined) {
-        this->min(0) = std::min(point(0), this->min(0));
-        this->min(1) = std::min(point(1), this->min(1));
-        this->max(0) = std::max(point(0), this->max(0));
-        this->max(1) = std::max(point(1), this->max(1));
+        this->min = this->min.cwiseMin(point);
+        this->max = this->max.cwiseMax(point);
     } else {
-        this->min = this->max = point;
+        this->min = point;
+        this->max = point;
         this->defined = true;
     }
 }
 template void BoundingBoxBase<Point>::merge(const Point &point);
-template void BoundingBoxBase<Pointf>::merge(const Pointf &point);
+template void BoundingBoxBase<Vec2d>::merge(const Vec2d &point);
 
 template <class PointClass> void
 BoundingBoxBase<PointClass>::merge(const std::vector<PointClass> &points)
@@ -97,7 +94,7 @@ BoundingBoxBase<PointClass>::merge(const std::vector<PointClass> &points)
     this->merge(BoundingBoxBase(points));
 }
 template void BoundingBoxBase<Point>::merge(const Points &points);
-template void BoundingBoxBase<Pointf>::merge(const Pointfs &points);
+template void BoundingBoxBase<Vec2d>::merge(const Pointfs &points);
 
 template <class PointClass> void
 BoundingBoxBase<PointClass>::merge(const BoundingBoxBase<PointClass> &bb)
@@ -105,10 +102,8 @@ BoundingBoxBase<PointClass>::merge(const BoundingBoxBase<PointClass> &bb)
     assert(bb.defined || bb.min(0) >= bb.max(0) || bb.min(1) >= bb.max(1));
     if (bb.defined) {
         if (this->defined) {
-            this->min(0) = std::min(bb.min(0), this->min(0));
-            this->min(1) = std::min(bb.min(1), this->min(1));
-            this->max(0) = std::max(bb.max(0), this->max(0));
-            this->max(1) = std::max(bb.max(1), this->max(1));
+            this->min = this->min.cwiseMin(bb.min);
+            this->max = this->max.cwiseMax(bb.max);
         } else {
             this->min = bb.min;
             this->max = bb.max;
@@ -117,25 +112,28 @@ BoundingBoxBase<PointClass>::merge(const BoundingBoxBase<PointClass> &bb)
     }
 }
 template void BoundingBoxBase<Point>::merge(const BoundingBoxBase<Point> &bb);
-template void BoundingBoxBase<Pointf>::merge(const BoundingBoxBase<Pointf> &bb);
+template void BoundingBoxBase<Vec2d>::merge(const BoundingBoxBase<Vec2d> &bb);
 
 template <class PointClass> void
 BoundingBox3Base<PointClass>::merge(const PointClass &point)
 {
     if (this->defined) {
-        this->min(2) = std::min(point(2), this->min(2));
-        this->max(2) = std::max(point(2), this->max(2));
+        this->min = this->min.cwiseMin(point);
+        this->max = this->max.cwiseMax(point);
+    } else {
+        this->min = point;
+        this->max = point;
+        this->defined = true;
     }
-    BoundingBoxBase<PointClass>::merge(point);
 }
-template void BoundingBox3Base<Pointf3>::merge(const Pointf3 &point);
+template void BoundingBox3Base<Vec3d>::merge(const Vec3d &point);
 
 template <class PointClass> void
 BoundingBox3Base<PointClass>::merge(const std::vector<PointClass> &points)
 {
     this->merge(BoundingBox3Base(points));
 }
-template void BoundingBox3Base<Pointf3>::merge(const Pointf3s &points);
+template void BoundingBox3Base<Vec3d>::merge(const Pointf3s &points);
 
 template <class PointClass> void
 BoundingBox3Base<PointClass>::merge(const BoundingBox3Base<PointClass> &bb)
@@ -143,13 +141,16 @@ BoundingBox3Base<PointClass>::merge(const BoundingBox3Base<PointClass> &bb)
     assert(bb.defined || bb.min(0) >= bb.max(0) || bb.min(1) >= bb.max(1) || bb.min(2) >= bb.max(2));
     if (bb.defined) {
         if (this->defined) {
-            this->min(2) = std::min(bb.min(2), this->min(2));
-            this->max(2) = std::max(bb.max(2), this->max(2));
+            this->min = this->min.cwiseMin(bb.min);
+            this->max = this->max.cwiseMax(bb.max);
+        } else {
+            this->min = bb.min;
+            this->max = bb.max;
+            this->defined = true;
         }
-        BoundingBoxBase<PointClass>::merge(bb);
     }
 }
-template void BoundingBox3Base<Pointf3>::merge(const BoundingBox3Base<Pointf3> &bb);
+template void BoundingBox3Base<Vec3d>::merge(const BoundingBox3Base<Vec3d> &bb);
 
 template <class PointClass> PointClass
 BoundingBoxBase<PointClass>::size() const
@@ -157,14 +158,14 @@ BoundingBoxBase<PointClass>::size() const
     return PointClass(this->max(0) - this->min(0), this->max(1) - this->min(1));
 }
 template Point BoundingBoxBase<Point>::size() const;
-template Pointf BoundingBoxBase<Pointf>::size() const;
+template Vec2d BoundingBoxBase<Vec2d>::size() const;
 
 template <class PointClass> PointClass
 BoundingBox3Base<PointClass>::size() const
 {
     return PointClass(this->max(0) - this->min(0), this->max(1) - this->min(1), this->max(2) - this->min(2));
 }
-template Pointf3 BoundingBox3Base<Pointf3>::size() const;
+template Vec3d BoundingBox3Base<Vec3d>::size() const;
 
 template <class PointClass> double BoundingBoxBase<PointClass>::radius() const
 {
@@ -174,7 +175,7 @@ template <class PointClass> double BoundingBoxBase<PointClass>::radius() const
     return 0.5 * sqrt(x*x+y*y);
 }
 template double BoundingBoxBase<Point>::radius() const;
-template double BoundingBoxBase<Pointf>::radius() const;
+template double BoundingBoxBase<Vec2d>::radius() const;
 
 template <class PointClass> double BoundingBox3Base<PointClass>::radius() const
 {
@@ -183,7 +184,7 @@ template <class PointClass> double BoundingBox3Base<PointClass>::radius() const
     double z = this->max(2) - this->min(2);
     return 0.5 * sqrt(x*x+y*y+z*z);
 }
-template double BoundingBox3Base<Pointf3>::radius() const;
+template double BoundingBox3Base<Vec3d>::radius() const;
 
 template <class PointClass> void
 BoundingBoxBase<PointClass>::offset(coordf_t delta)
@@ -193,7 +194,7 @@ BoundingBoxBase<PointClass>::offset(coordf_t delta)
     this->max += v;
 }
 template void BoundingBoxBase<Point>::offset(coordf_t delta);
-template void BoundingBoxBase<Pointf>::offset(coordf_t delta);
+template void BoundingBoxBase<Vec2d>::offset(coordf_t delta);
 
 template <class PointClass> void
 BoundingBox3Base<PointClass>::offset(coordf_t delta)
@@ -202,29 +203,22 @@ BoundingBox3Base<PointClass>::offset(coordf_t delta)
     this->min -= v;
     this->max += v;
 }
-template void BoundingBox3Base<Pointf3>::offset(coordf_t delta);
+template void BoundingBox3Base<Vec3d>::offset(coordf_t delta);
 
 template <class PointClass> PointClass
 BoundingBoxBase<PointClass>::center() const
 {
-    return PointClass(
-        (this->max(0) + this->min(0))/2,
-        (this->max(1) + this->min(1))/2
-    );
+    return (this->min + this->max) / 2;
 }
 template Point BoundingBoxBase<Point>::center() const;
-template Pointf BoundingBoxBase<Pointf>::center() const;
+template Vec2d BoundingBoxBase<Vec2d>::center() const;
 
 template <class PointClass> PointClass
 BoundingBox3Base<PointClass>::center() const
 {
-    return PointClass(
-        (this->max(0) + this->min(0))/2,
-        (this->max(1) + this->min(1))/2,
-        (this->max(2) + this->min(2))/2
-    );
+    return (this->min + this->max) / 2;
 }
-template Pointf3 BoundingBox3Base<Pointf3>::center() const;
+template Vec3d BoundingBox3Base<Vec3d>::center() const;
 
 template <class PointClass> coordf_t
 BoundingBox3Base<PointClass>::max_size() const
@@ -232,7 +226,7 @@ BoundingBox3Base<PointClass>::max_size() const
     PointClass s = size();
     return std::max(s(0), std::max(s(1), s(2)));
 }
-template coordf_t BoundingBox3Base<Pointf3>::max_size() const;
+template coordf_t BoundingBox3Base<Vec3d>::max_size() const;
 
 // Align a coordinate to a grid. The coordinate may be negative,
 // the aligned value will never be bigger than the original one.
@@ -255,39 +249,35 @@ void BoundingBox::align_to_grid(const coord_t cell_size)
     }
 }
 
-BoundingBoxf3 BoundingBoxf3::transformed(const Transform3f& matrix) const
+BoundingBoxf3 BoundingBoxf3::transformed(const Transform3d& matrix) const
 {
-    Eigen::Matrix<float, 3, 8, Eigen::DontAlign> vertices;
+    typedef Eigen::Matrix<double, 3, 8, Eigen::DontAlign> Vertices;
 
-    vertices(0, 0) = (float)min(0); vertices(1, 0) = (float)min(1); vertices(2, 0) = (float)min(2);
-    vertices(0, 1) = (float)max(0); vertices(1, 1) = (float)min(1); vertices(2, 1) = (float)min(2);
-    vertices(0, 2) = (float)max(0); vertices(1, 2) = (float)max(1); vertices(2, 2) = (float)min(2);
-    vertices(0, 3) = (float)min(0); vertices(1, 3) = (float)max(1); vertices(2, 3) = (float)min(2);
-    vertices(0, 4) = (float)min(0); vertices(1, 4) = (float)min(1); vertices(2, 4) = (float)max(2);
-    vertices(0, 5) = (float)max(0); vertices(1, 5) = (float)min(1); vertices(2, 5) = (float)max(2);
-    vertices(0, 6) = (float)max(0); vertices(1, 6) = (float)max(1); vertices(2, 6) = (float)max(2);
-    vertices(0, 7) = (float)min(0); vertices(1, 7) = (float)max(1); vertices(2, 7) = (float)max(2);
+    Vertices src_vertices;
+    src_vertices(0, 0) = min(0); src_vertices(1, 0) = min(1); src_vertices(2, 0) = min(2);
+    src_vertices(0, 1) = max(0); src_vertices(1, 1) = min(1); src_vertices(2, 1) = min(2);
+    src_vertices(0, 2) = max(0); src_vertices(1, 2) = max(1); src_vertices(2, 2) = min(2);
+    src_vertices(0, 3) = min(0); src_vertices(1, 3) = max(1); src_vertices(2, 3) = min(2);
+    src_vertices(0, 4) = min(0); src_vertices(1, 4) = min(1); src_vertices(2, 4) = max(2);
+    src_vertices(0, 5) = max(0); src_vertices(1, 5) = min(1); src_vertices(2, 5) = max(2);
+    src_vertices(0, 6) = max(0); src_vertices(1, 6) = max(1); src_vertices(2, 6) = max(2);
+    src_vertices(0, 7) = min(0); src_vertices(1, 7) = max(1); src_vertices(2, 7) = max(2);
 
-    Eigen::Matrix<float, 3, 8, Eigen::DontAlign> transf_vertices = matrix * vertices.colwise().homogeneous();
+    Vertices dst_vertices = matrix * src_vertices.colwise().homogeneous();
 
-    float min_x = transf_vertices(0, 0);
-    float max_x = transf_vertices(0, 0);
-    float min_y = transf_vertices(1, 0);
-    float max_y = transf_vertices(1, 0);
-    float min_z = transf_vertices(2, 0);
-    float max_z = transf_vertices(2, 0);
+    Vec3d v_min(dst_vertices(0, 0), dst_vertices(1, 0), dst_vertices(2, 0));
+    Vec3d v_max = v_min;
 
     for (int i = 1; i < 8; ++i)
     {
-        min_x = std::min(min_x, transf_vertices(0, i));
-        max_x = std::max(max_x, transf_vertices(0, i));
-        min_y = std::min(min_y, transf_vertices(1, i));
-        max_y = std::max(max_y, transf_vertices(1, i));
-        min_z = std::min(min_z, transf_vertices(2, i));
-        max_z = std::max(max_z, transf_vertices(2, i));
+        for (int j = 0; j < 3; ++j)
+        {
+            v_min(j) = std::min(v_min(j), dst_vertices(j, i));
+            v_max(j) = std::max(v_max(j), dst_vertices(j, i));
+        }
     }
 
-    return BoundingBoxf3(Pointf3((coordf_t)min_x, (coordf_t)min_y, (coordf_t)min_z), Pointf3((coordf_t)max_x, (coordf_t)max_y, (coordf_t)max_z));
+    return BoundingBoxf3(v_min, v_max);
 }
 
 }
diff --git a/xs/src/libslic3r/BoundingBox.hpp b/xs/src/libslic3r/BoundingBox.hpp
index d09658774f..db56c765cf 100644
--- a/xs/src/libslic3r/BoundingBox.hpp
+++ b/xs/src/libslic3r/BoundingBox.hpp
@@ -7,11 +7,6 @@
 
 namespace Slic3r {
 
-typedef Point   Size;
-typedef Point3  Size3;
-typedef Pointf  Sizef;
-typedef Pointf3 Sizef3;
-
 template <class PointClass>
 class BoundingBoxBase
 {
@@ -20,23 +15,20 @@ public:
     PointClass max;
     bool defined;
     
-    BoundingBoxBase() : defined(false) {};
+    BoundingBoxBase() : defined(false), min(PointClass::Zero()), max(PointClass::Zero()) {}
     BoundingBoxBase(const PointClass &pmin, const PointClass &pmax) : 
         min(pmin), max(pmax), defined(pmin(0) < pmax(0) && pmin(1) < pmax(1)) {}
-    BoundingBoxBase(const std::vector<PointClass>& points)
+    BoundingBoxBase(const std::vector<PointClass>& points) : min(PointClass::Zero()), max(PointClass::Zero())
     {
         if (points.empty())
             CONFESS("Empty point set supplied to BoundingBoxBase constructor");
 
         typename std::vector<PointClass>::const_iterator it = points.begin();
-        this->min(0) = this->max(0) = (*it)(0);
-        this->min(1) = this->max(1) = (*it)(1);
-        for (++it; it != points.end(); ++it)
-        {
-            this->min(0) = std::min((*it)(0), this->min(0));
-            this->min(1) = std::min((*it)(1), this->min(1));
-            this->max(0) = std::max((*it)(0), this->max(0));
-            this->max(1) = std::max((*it)(1), this->max(1));
+        this->min = *it;
+        this->max = *it;
+        for (++ it; it != points.end(); ++ it) {
+            this->min = this->min.cwiseMin(*it);
+            this->max = this->max.cwiseMax(*it);
         }
         this->defined = (this->min(0) < this->max(0)) && (this->min(1) < this->max(1));
     }
@@ -47,7 +39,7 @@ public:
     PointClass size() const;
     double radius() const;
     void translate(coordf_t x, coordf_t y) { assert(this->defined); PointClass v(x, y); this->min += v; this->max += v; }
-    void translate(const Pointf &v) { this->min += v; this->max += v; }
+    void translate(const Vec2d &v) { this->min += v; this->max += v; }
     void offset(coordf_t delta);
     PointClass center() const;
     bool contains(const PointClass &point) const {
@@ -71,19 +63,17 @@ public:
         BoundingBoxBase<PointClass>(pmin, pmax) 
         { if (pmin(2) >= pmax(2)) BoundingBoxBase<PointClass>::defined = false; }
     BoundingBox3Base(const std::vector<PointClass>& points)
-        : BoundingBoxBase<PointClass>(points)
     {
         if (points.empty())
             CONFESS("Empty point set supplied to BoundingBox3Base constructor");
-
         typename std::vector<PointClass>::const_iterator it = points.begin();
-        this->min(2) = this->max(2) = (*it)(2);
-        for (++it; it != points.end(); ++it)
-        {
-            this->min(2) = std::min((*it)(2), this->min(2));
-            this->max(2) = std::max((*it)(2), this->max(2));
+        this->min = *it;
+        this->max = *it;
+        for (++ it; it != points.end(); ++ it) {
+            this->min = this->min.cwiseMin(*it);
+            this->max = this->max.cwiseMax(*it);
         }
-        this->defined &= (this->min(2) < this->max(2));
+        this->defined = (this->min(0) < this->max(0)) && (this->min(1) < this->max(1)) && (this->min(2) < this->max(2));
     }
     void merge(const PointClass &point);
     void merge(const std::vector<PointClass> &points);
@@ -91,7 +81,7 @@ public:
     PointClass size() const;
     double radius() const;
     void translate(coordf_t x, coordf_t y, coordf_t z) { assert(this->defined); PointClass v(x, y, z); this->min += v; this->max += v; }
-    void translate(const Pointf3 &v) { this->min += v; this->max += v; }
+    void translate(const Vec3d &v) { this->min += v; this->max += v; }
     void offset(coordf_t delta);
     PointClass center() const;
     coordf_t max_size() const;
@@ -130,30 +120,30 @@ public:
     friend BoundingBox get_extents_rotated(const Points &points, double angle);
 };
 
-class BoundingBox3  : public BoundingBox3Base<Point3> 
+class BoundingBox3  : public BoundingBox3Base<Vec3crd> 
 {
 public:
-    BoundingBox3() : BoundingBox3Base<Point3>() {};
-    BoundingBox3(const Point3 &pmin, const Point3 &pmax) : BoundingBox3Base<Point3>(pmin, pmax) {};
-    BoundingBox3(const Points3& points) : BoundingBox3Base<Point3>(points) {};
+    BoundingBox3() : BoundingBox3Base<Vec3crd>() {};
+    BoundingBox3(const Vec3crd &pmin, const Vec3crd &pmax) : BoundingBox3Base<Vec3crd>(pmin, pmax) {};
+    BoundingBox3(const Points3& points) : BoundingBox3Base<Vec3crd>(points) {};
 };
 
-class BoundingBoxf : public BoundingBoxBase<Pointf> 
+class BoundingBoxf : public BoundingBoxBase<Vec2d> 
 {
 public:
-    BoundingBoxf() : BoundingBoxBase<Pointf>() {};
-    BoundingBoxf(const Pointf &pmin, const Pointf &pmax) : BoundingBoxBase<Pointf>(pmin, pmax) {};
-    BoundingBoxf(const std::vector<Pointf> &points) : BoundingBoxBase<Pointf>(points) {};
+    BoundingBoxf() : BoundingBoxBase<Vec2d>() {};
+    BoundingBoxf(const Vec2d &pmin, const Vec2d &pmax) : BoundingBoxBase<Vec2d>(pmin, pmax) {};
+    BoundingBoxf(const std::vector<Vec2d> &points) : BoundingBoxBase<Vec2d>(points) {};
 };
 
-class BoundingBoxf3 : public BoundingBox3Base<Pointf3> 
+class BoundingBoxf3 : public BoundingBox3Base<Vec3d> 
 {
 public:
-    BoundingBoxf3() : BoundingBox3Base<Pointf3>() {};
-    BoundingBoxf3(const Pointf3 &pmin, const Pointf3 &pmax) : BoundingBox3Base<Pointf3>(pmin, pmax) {};
-    BoundingBoxf3(const std::vector<Pointf3> &points) : BoundingBox3Base<Pointf3>(points) {};
+    BoundingBoxf3() : BoundingBox3Base<Vec3d>() {};
+    BoundingBoxf3(const Vec3d &pmin, const Vec3d &pmax) : BoundingBox3Base<Vec3d>(pmin, pmax) {};
+    BoundingBoxf3(const std::vector<Vec3d> &points) : BoundingBox3Base<Vec3d>(points) {};
 
-    BoundingBoxf3 transformed(const Transform3f& matrix) const;
+    BoundingBoxf3 transformed(const Transform3d& matrix) const;
 };
 
 template<typename VT>
diff --git a/xs/src/libslic3r/Config.hpp b/xs/src/libslic3r/Config.hpp
index ee9931a610..e3cd14335a 100644
--- a/xs/src/libslic3r/Config.hpp
+++ b/xs/src/libslic3r/Config.hpp
@@ -49,9 +49,9 @@ enum ConfigOptionType {
     coPercents      = coPercent + coVectorType,
     // a fraction or an absolute value
     coFloatOrPercent = 5,
-    // single 2d point. Currently not used.
+    // single 2d point (Point2f). Currently not used.
     coPoint         = 6,
-    // vector of 2d points. Currently used for the definition of the print bed and for the extruder offsets.
+    // vector of 2d points (Point2f). Currently used for the definition of the print bed and for the extruder offsets.
     coPoints        = coPoint + coVectorType,
     // single boolean value
     coBool          = 7,
@@ -622,11 +622,11 @@ public:
     }
 };
 
-class ConfigOptionPoint : public ConfigOptionSingle<Pointf>
+class ConfigOptionPoint : public ConfigOptionSingle<Vec2d>
 {
 public:
-    ConfigOptionPoint() : ConfigOptionSingle<Pointf>(Pointf(0,0)) {}
-    explicit ConfigOptionPoint(const Pointf &value) : ConfigOptionSingle<Pointf>(value) {}
+    ConfigOptionPoint() : ConfigOptionSingle<Vec2d>(Vec2d(0,0)) {}
+    explicit ConfigOptionPoint(const Vec2d &value) : ConfigOptionSingle<Vec2d>(value) {}
     
     static ConfigOptionType static_type() { return coPoint; }
     ConfigOptionType        type()  const override { return static_type(); }
@@ -652,13 +652,13 @@ public:
     }
 };
 
-class ConfigOptionPoints : public ConfigOptionVector<Pointf>
+class ConfigOptionPoints : public ConfigOptionVector<Vec2d>
 {
 public:
-    ConfigOptionPoints() : ConfigOptionVector<Pointf>() {}
-    explicit ConfigOptionPoints(size_t n, const Pointf &value) : ConfigOptionVector<Pointf>(n, value) {}
-    explicit ConfigOptionPoints(std::initializer_list<Pointf> il) : ConfigOptionVector<Pointf>(std::move(il)) {}
-    explicit ConfigOptionPoints(const std::vector<Pointf> &values) : ConfigOptionVector<Pointf>(values) {}
+    ConfigOptionPoints() : ConfigOptionVector<Vec2d>() {}
+    explicit ConfigOptionPoints(size_t n, const Vec2d &value) : ConfigOptionVector<Vec2d>(n, value) {}
+    explicit ConfigOptionPoints(std::initializer_list<Vec2d> il) : ConfigOptionVector<Vec2d>(std::move(il)) {}
+    explicit ConfigOptionPoints(const std::vector<Vec2d> &values) : ConfigOptionVector<Vec2d>(values) {}
 
     static ConfigOptionType static_type() { return coPoints; }
     ConfigOptionType        type()  const override { return static_type(); }
@@ -696,7 +696,7 @@ public:
         std::istringstream is(str);
         std::string point_str;
         while (std::getline(is, point_str, ',')) {
-            Pointf point;
+            Vec2d point(Vec2d::Zero());
             std::istringstream iss(point_str);
             std::string coord_str;
             if (std::getline(iss, coord_str, 'x')) {
@@ -821,12 +821,7 @@ public:
     bool deserialize(const std::string &str, bool append = false) override
     {
         UNUSED(append);
-        const t_config_enum_values &enum_keys_map = ConfigOptionEnum<T>::get_enum_values();
-        auto it = enum_keys_map.find(str);
-        if (it == enum_keys_map.end())
-            return false;
-        this->value = static_cast<T>(it->second);
-        return true;
+        return from_string(str, this->value);
     }
 
     static bool has(T value) 
@@ -838,7 +833,7 @@ public:
     }
 
     // Map from an enum name to an enum integer value.
-    static t_config_enum_names& get_enum_names() 
+    static const t_config_enum_names& get_enum_names() 
     {
         static t_config_enum_names names;
         if (names.empty()) {
@@ -855,7 +850,17 @@ public:
         return names;
     }
     // Map from an enum name to an enum integer value.
-    static t_config_enum_values& get_enum_values();
+    static const t_config_enum_values& get_enum_values();
+
+    static bool from_string(const std::string &str, T &value)
+    {
+        const t_config_enum_values &enum_keys_map = ConfigOptionEnum<T>::get_enum_values();
+        auto it = enum_keys_map.find(str);
+        if (it == enum_keys_map.end())
+            return false;
+        value = static_cast<T>(it->second);
+        return true;
+    }
 };
 
 // Generic enum configuration value.
@@ -900,7 +905,7 @@ public:
     // What type? bool, int, string etc.
     ConfigOptionType                    type            = coNone;
     // Default value of this option. The default value object is owned by ConfigDef, it is released in its destructor.
-    ConfigOption                       *default_value   = nullptr;
+    const ConfigOption                 *default_value   = nullptr;
 
     // Usually empty. 
     // Special values - "i_enum_open", "f_enum_open" to provide combo box for int or float selection,
@@ -958,7 +963,7 @@ public:
     std::vector<std::string>            enum_labels;
     // For enums (when type == coEnum). Maps enum_values to enums.
     // Initialized by ConfigOptionEnum<xxx>::get_enum_values()
-    t_config_enum_values               *enum_keys_map   = nullptr;
+    const t_config_enum_values         *enum_keys_map   = nullptr;
 
     bool has_enum_value(const std::string &value) const {
         for (const std::string &v : enum_values)
diff --git a/xs/src/libslic3r/ExtrusionEntity.hpp b/xs/src/libslic3r/ExtrusionEntity.hpp
index 15363e8eda..90675c04a7 100644
--- a/xs/src/libslic3r/ExtrusionEntity.hpp
+++ b/xs/src/libslic3r/ExtrusionEntity.hpp
@@ -149,7 +149,7 @@ public:
     // Minimum volumetric velocity of this extrusion entity. Used by the constant nozzle pressure algorithm.
     double min_mm3_per_mm() const { return this->mm3_per_mm; }
     Polyline as_polyline() const { return this->polyline; }
-    virtual double total_volume() const { return mm3_per_mm * unscale(length()); }
+    virtual double total_volume() const { return mm3_per_mm * unscale<double>(length()); }
 
 private:
     void _inflate_collection(const Polylines &polylines, ExtrusionEntityCollection* collection) const;
diff --git a/xs/src/libslic3r/Fill/Fill3DHoneycomb.cpp b/xs/src/libslic3r/Fill/Fill3DHoneycomb.cpp
index 16ed12fb95..6a37e4369f 100644
--- a/xs/src/libslic3r/Fill/Fill3DHoneycomb.cpp
+++ b/xs/src/libslic3r/Fill/Fill3DHoneycomb.cpp
@@ -54,7 +54,7 @@ static std::vector<coordf_t> perpendPoints(const coordf_t offset, const size_t b
 // components that are outside these limits are set to the limits.
 static inline void trim(Pointfs &pts, coordf_t minX, coordf_t minY, coordf_t maxX, coordf_t maxY)
 {
-    for (Pointf &pt : pts) {
+    for (Vec2d &pt : pts) {
         pt(0) = clamp(minX, maxX, pt(0));
         pt(1) = clamp(minY, maxY, pt(1));
     }
@@ -66,7 +66,7 @@ static inline Pointfs zip(const std::vector<coordf_t> &x, const std::vector<coor
     Pointfs out;
     out.reserve(x.size());
     for (size_t i = 0; i < x.size(); ++ i)
-        out.push_back(Pointf(x[i], y[i]));
+        out.push_back(Vec2d(x[i], y[i]));
     return out;
 }
 
diff --git a/xs/src/libslic3r/Fill/FillConcentric.cpp b/xs/src/libslic3r/Fill/FillConcentric.cpp
index d0f9510ccc..8a3a7ea89d 100644
--- a/xs/src/libslic3r/Fill/FillConcentric.cpp
+++ b/xs/src/libslic3r/Fill/FillConcentric.cpp
@@ -21,7 +21,7 @@ void FillConcentric::_fill_surface_single(
     
     if (params.density > 0.9999f && !params.dont_adjust) {
         distance = this->_adjust_solid_spacing(bounding_box.size()(0), distance);
-        this->spacing = unscale(distance);
+        this->spacing = unscale<double>(distance);
     }
 
     Polygons loops = (Polygons)expolygon;
diff --git a/xs/src/libslic3r/Fill/FillGyroid.cpp b/xs/src/libslic3r/Fill/FillGyroid.cpp
index 003893649b..d6bf03ce65 100644
--- a/xs/src/libslic3r/Fill/FillGyroid.cpp
+++ b/xs/src/libslic3r/Fill/FillGyroid.cpp
@@ -30,15 +30,15 @@ static inline double f(double x, double z_sin, double z_cos, bool vertical, bool
 }
 
 static inline Polyline make_wave(
-    const std::vector<Pointf>& one_period, double width, double height, double offset, double scaleFactor,
+    const std::vector<Vec2d>& one_period, double width, double height, double offset, double scaleFactor,
     double z_cos, double z_sin, bool vertical)
 {
-    std::vector<Pointf> points = one_period;
+    std::vector<Vec2d> points = one_period;
     double period = points.back()(0);
     points.pop_back();
     int n = points.size();
     do {
-        points.emplace_back(Pointf(points[points.size()-n](0) + period, points[points.size()-n](1)));
+        points.emplace_back(Vec2d(points[points.size()-n](0) + period, points[points.size()-n](1)));
     } while (points.back()(0) < width);
     points.back()(0) = width;
 
@@ -55,14 +55,14 @@ static inline Polyline make_wave(
     return polyline;
 }
 
-static std::vector<Pointf> make_one_period(double width, double scaleFactor, double z_cos, double z_sin, bool vertical, bool flip)
+static std::vector<Vec2d> make_one_period(double width, double scaleFactor, double z_cos, double z_sin, bool vertical, bool flip)
 {
-    std::vector<Pointf> points;
+    std::vector<Vec2d> points;
     double dx = M_PI_4; // very coarse spacing to begin with
     double limit = std::min(2*M_PI, width);
     for (double x = 0.; x < limit + EPSILON; x += dx) {  // so the last point is there too
         x = std::min(x, limit);
-        points.emplace_back(Pointf(x,f(x, z_sin,z_cos, vertical, flip)));
+        points.emplace_back(Vec2d(x,f(x, z_sin,z_cos, vertical, flip)));
     }
 
     // now we will check all internal points and in case some are too far from the line connecting its neighbours,
@@ -71,17 +71,19 @@ static std::vector<Pointf> make_one_period(double width, double scaleFactor, dou
     for (unsigned int i=1;i<points.size()-1;++i) {
         auto& lp = points[i-1]; // left point
         auto& tp = points[i];   // this point
+        Vec2d lrv = tp - lp;
         auto& rp = points[i+1]; // right point
         // calculate distance of the point to the line:
-        double dist_mm = unscale(scaleFactor * std::abs( (rp(1) - lp(1))*tp(0) + (lp(0) - rp(0))*tp(1) + (rp(0)*lp(1) - rp(1)*lp(0)) ) / std::hypot((rp(1) - lp(1)),(lp(0) - rp(0))));
-
+        double dist_mm = unscale<double>(scaleFactor) * std::abs(cross2(rp, lp) - cross2(rp - lp, tp)) / lrv.norm();
         if (dist_mm > tolerance) {                               // if the difference from straight line is more than this
             double x = 0.5f * (points[i-1](0) + points[i](0));
-            points.emplace_back(Pointf(x, f(x, z_sin, z_cos, vertical, flip)));
+            points.emplace_back(Vec2d(x, f(x, z_sin, z_cos, vertical, flip)));
             x = 0.5f * (points[i+1](0) + points[i](0));
-            points.emplace_back(Pointf(x, f(x, z_sin, z_cos, vertical, flip)));
-            std::sort(points.begin(), points.end());            // we added the points to the end, but need them all in order
-            --i;                                                // decrement i so we also check the first newly added point
+            points.emplace_back(Vec2d(x, f(x, z_sin, z_cos, vertical, flip)));
+            // we added the points to the end, but need them all in order
+            std::sort(points.begin(), points.end(), [](const Vec2d &lhs, const Vec2d &rhs){ return lhs < rhs; });
+            // decrement i so we also check the first newly added point
+            --i;
         }
     }
     return points;
@@ -107,7 +109,7 @@ static Polylines make_gyroid_waves(double gridZ, double density_adjusted, double
         std::swap(width,height);
     }
 
-    std::vector<Pointf> one_period = make_one_period(width, scaleFactor, z_cos, z_sin, vertical, flip); // creates one period of the waves, so it doesn't have to be recalculated all the time
+    std::vector<Vec2d> one_period = make_one_period(width, scaleFactor, z_cos, z_sin, vertical, flip); // creates one period of the waves, so it doesn't have to be recalculated all the time
     Polylines result;
 
     for (double y0 = lower_bound; y0 < upper_bound+EPSILON; y0 += 2*M_PI)           // creates odd polylines
diff --git a/xs/src/libslic3r/Fill/FillPlanePath.cpp b/xs/src/libslic3r/Fill/FillPlanePath.cpp
index bb7d5ac801..615cc6efed 100644
--- a/xs/src/libslic3r/Fill/FillPlanePath.cpp
+++ b/xs/src/libslic3r/Fill/FillPlanePath.cpp
@@ -86,12 +86,12 @@ Pointfs FillArchimedeanChords::_generate(coord_t min_x, coord_t min_y, coord_t m
     coordf_t r = 1;
     Pointfs out;
     //FIXME Vojtech: If used as a solid infill, there is a gap left at the center.
-    out.push_back(Pointf(0, 0));
-    out.push_back(Pointf(1, 0));
+    out.push_back(Vec2d(0, 0));
+    out.push_back(Vec2d(1, 0));
     while (r < rmax) {
         theta += 1. / r;
         r = a + b * theta;
-        out.push_back(Pointf(r * cos(theta), r * sin(theta)));
+        out.push_back(Vec2d(r * cos(theta), r * sin(theta)));
     }
     return out;
 }
@@ -162,7 +162,7 @@ Pointfs FillHilbertCurve::_generate(coord_t min_x, coord_t min_y, coord_t max_x,
     line.reserve(sz2);
     for (size_t i = 0; i < sz2; ++ i) {
         Point p = hilbert_n_to_xy(i);
-        line.push_back(Pointf(p(0) + min_x, p(1) + min_y));
+        line.push_back(Vec2d(p(0) + min_x, p(1) + min_y));
     }
     return line;
 }
@@ -175,27 +175,27 @@ Pointfs FillOctagramSpiral::_generate(coord_t min_x, coord_t min_y, coord_t max_
     coordf_t r = 0;
     coordf_t r_inc = sqrt(2.);
     Pointfs out;
-    out.push_back(Pointf(0, 0));
+    out.push_back(Vec2d(0, 0));
     while (r < rmax) {
         r += r_inc;
         coordf_t rx = r / sqrt(2.);
         coordf_t r2 = r + rx;
-        out.push_back(Pointf( r,  0.));
-        out.push_back(Pointf( r2, rx));
-        out.push_back(Pointf( rx, rx));
-        out.push_back(Pointf( rx, r2));
-        out.push_back(Pointf(0.,  r));
-        out.push_back(Pointf(-rx, r2));
-        out.push_back(Pointf(-rx, rx));
-        out.push_back(Pointf(-r2, rx));
-        out.push_back(Pointf(-r,  0.));
-        out.push_back(Pointf(-r2, -rx));
-        out.push_back(Pointf(-rx, -rx));
-        out.push_back(Pointf(-rx, -r2));
-        out.push_back(Pointf(0., -r));
-        out.push_back(Pointf( rx, -r2));
-        out.push_back(Pointf( rx, -rx));
-        out.push_back(Pointf( r2+r_inc, -rx));
+        out.push_back(Vec2d( r,  0.));
+        out.push_back(Vec2d( r2, rx));
+        out.push_back(Vec2d( rx, rx));
+        out.push_back(Vec2d( rx, r2));
+        out.push_back(Vec2d(0.,  r));
+        out.push_back(Vec2d(-rx, r2));
+        out.push_back(Vec2d(-rx, rx));
+        out.push_back(Vec2d(-r2, rx));
+        out.push_back(Vec2d(-r,  0.));
+        out.push_back(Vec2d(-r2, -rx));
+        out.push_back(Vec2d(-rx, -rx));
+        out.push_back(Vec2d(-rx, -r2));
+        out.push_back(Vec2d(0., -r));
+        out.push_back(Vec2d( rx, -r2));
+        out.push_back(Vec2d( rx, -rx));
+        out.push_back(Vec2d( r2+r_inc, -rx));
     }
     return out;
 }
diff --git a/xs/src/libslic3r/Fill/FillRectilinear.cpp b/xs/src/libslic3r/Fill/FillRectilinear.cpp
index 2209d219e4..205eb1b669 100644
--- a/xs/src/libslic3r/Fill/FillRectilinear.cpp
+++ b/xs/src/libslic3r/Fill/FillRectilinear.cpp
@@ -27,7 +27,7 @@ void FillRectilinear::_fill_surface_single(
     // define flow spacing according to requested density
     if (params.density > 0.9999f && !params.dont_adjust) {
         this->_line_spacing = this->_adjust_solid_spacing(bounding_box.size()(0), this->_line_spacing);
-        this->spacing = unscale(this->_line_spacing);
+        this->spacing = unscale<double>(this->_line_spacing);
     } else {
         // extend bounding box so that our pattern will be aligned with other layers
         // Transform the reference point to the rotated coordinate system.
diff --git a/xs/src/libslic3r/Fill/FillRectilinear2.cpp b/xs/src/libslic3r/Fill/FillRectilinear2.cpp
index f18ab0f62f..65440d0efe 100644
--- a/xs/src/libslic3r/Fill/FillRectilinear2.cpp
+++ b/xs/src/libslic3r/Fill/FillRectilinear2.cpp
@@ -792,7 +792,7 @@ bool FillRectilinear2::fill_surface_by_lines(const Surface *surface, const FillP
     // define flow spacing according to requested density
     if (params.full_infill() && !params.dont_adjust) {
         line_spacing = this->_adjust_solid_spacing(bounding_box.size()(0), line_spacing);
-        this->spacing = unscale(line_spacing);
+        this->spacing = unscale<double>(line_spacing);
     } else {
         // extend bounding box so that our pattern will be aligned with other layers
         // Transform the reference point to the rotated coordinate system.
diff --git a/xs/src/libslic3r/Fill/FillRectilinear3.cpp b/xs/src/libslic3r/Fill/FillRectilinear3.cpp
index d80bbfe6e1..8fc129eacb 100644
--- a/xs/src/libslic3r/Fill/FillRectilinear3.cpp
+++ b/xs/src/libslic3r/Fill/FillRectilinear3.cpp
@@ -217,11 +217,11 @@ Point SegmentIntersection::pos() const
     const Point   &seg_start = poly.points[(this->iSegment == 0) ? poly.points.size() - 1 : this->iSegment - 1];
     const Point   &seg_end   = poly.points[this->iSegment];
     // Point, vector of the segment.
-    const Pointf   p1(seg_start.cast<coordf_t>());
-    const Pointf   v1((seg_end - seg_start).cast<coordf_t>());
+    const Vec2d   p1(seg_start.cast<coordf_t>());
+    const Vec2d   v1((seg_end - seg_start).cast<coordf_t>());
     // Point, vector of this hatching line.
-    const Pointf   p2(line->pos.cast<coordf_t>());
-    const Pointf   v2(line->dir.cast<coordf_t>());
+    const Vec2d   p2(line->pos.cast<coordf_t>());
+    const Vec2d   v2(line->dir.cast<coordf_t>());
     // Intersect the two rays.
     double denom = v1(0) * v2(1) - v2(0) * v1(1);
     Point out;
@@ -391,7 +391,7 @@ static bool prepare_infill_hatching_segments(
         // Full infill, adjust the line spacing to fit an integer number of lines.
         out.line_spacing = Fill::_adjust_solid_spacing(bounding_box.size()(0), line_spacing);
         // Report back the adjusted line spacing.
-        fill_dir_params.spacing = float(unscale(line_spacing));
+        fill_dir_params.spacing = unscale<double>(line_spacing);
     } else {
         // Extend bounding box so that our pattern will be aligned with the other layers.
         // Transform the reference point to the rotated coordinate system.
diff --git a/xs/src/libslic3r/Format/3mf.cpp b/xs/src/libslic3r/Format/3mf.cpp
index cd6f45c704..d054604081 100644
--- a/xs/src/libslic3r/Format/3mf.cpp
+++ b/xs/src/libslic3r/Format/3mf.cpp
@@ -1485,12 +1485,13 @@ namespace Slic3r {
                 stl_facet& facet = stl.facet_start[i];
                 for (unsigned int v = 0; v < 3; ++v)
                 {
-                    ::memcpy((void*)&facet.vertex[v].x, (const void*)&geometry.vertices[geometry.triangles[src_start_id + ii + v] * 3], 3 * sizeof(float));
+                    ::memcpy(facet.vertex[v].data(), (const void*)&geometry.vertices[geometry.triangles[src_start_id + ii + v] * 3], 3 * sizeof(float));
                 }
             }
 
             stl_get_size(&stl);
             volume->mesh.repair();
+            volume->calculate_convex_hull();
 
             // apply volume's name and config data
             for (const Metadata& metadata : volume_data.metadata)
@@ -1844,9 +1845,9 @@ namespace Slic3r {
             for (int i = 0; i < stl.stats.shared_vertices; ++i)
             {
                 stream << "     <" << VERTEX_TAG << " ";
-                stream << "x=\"" << stl.v_shared[i].x << "\" ";
-                stream << "y=\"" << stl.v_shared[i].y << "\" ";
-                stream << "z=\"" << stl.v_shared[i].z << "\" />\n";
+                stream << "x=\"" << stl.v_shared[i](0) << "\" ";
+                stream << "y=\"" << stl.v_shared[i](1) << "\" ";
+                stream << "z=\"" << stl.v_shared[i](2) << "\" />\n";
             }
         }
 
diff --git a/xs/src/libslic3r/Format/AMF.cpp b/xs/src/libslic3r/Format/AMF.cpp
index 1ad0c082aa..81617ad729 100644
--- a/xs/src/libslic3r/Format/AMF.cpp
+++ b/xs/src/libslic3r/Format/AMF.cpp
@@ -402,10 +402,11 @@ void AMFParserContext::endElement(const char * /* name */)
         for (size_t i = 0; i < m_volume_facets.size();) {
             stl_facet &facet = stl.facet_start[i/3];
             for (unsigned int v = 0; v < 3; ++ v)
-                memcpy(&facet.vertex[v].x, &m_object_vertices[m_volume_facets[i ++] * 3], 3 * sizeof(float));
+                memcpy(facet.vertex[v].data(), &m_object_vertices[m_volume_facets[i ++] * 3], 3 * sizeof(float));
         }
         stl_get_size(&stl);
         m_volume->mesh.repair();
+        m_volume->calculate_convex_hull();
         m_volume_facets.clear();
         m_volume = nullptr;
         break;
@@ -760,9 +761,9 @@ bool store_amf(const char *path, Model *model, Print* print, bool export_print_c
             for (size_t i = 0; i < stl.stats.shared_vertices; ++ i) {
                 stream << "         <vertex>\n";
                 stream << "           <coordinates>\n";
-                stream << "             <x>" << stl.v_shared[i].x << "</x>\n";
-                stream << "             <y>" << stl.v_shared[i].y << "</y>\n";
-                stream << "             <z>" << stl.v_shared[i].z << "</z>\n";
+                stream << "             <x>" << stl.v_shared[i](0) << "</x>\n";
+                stream << "             <y>" << stl.v_shared[i](1) << "</y>\n";
+                stream << "             <z>" << stl.v_shared[i](2) << "</z>\n";
                 stream << "           </coordinates>\n";
                 stream << "         </vertex>\n";
             }
diff --git a/xs/src/libslic3r/Format/OBJ.cpp b/xs/src/libslic3r/Format/OBJ.cpp
index ea6b5604c4..ee5756083d 100644
--- a/xs/src/libslic3r/Format/OBJ.cpp
+++ b/xs/src/libslic3r/Format/OBJ.cpp
@@ -57,14 +57,14 @@ bool load_obj(const char *path, Model *model, const char *object_name_in)
             continue;
         stl_facet &facet = stl.facet_start[i_face ++];
         size_t     num_normals = 0;
-        stl_normal normal = { 0.f };
+        stl_normal normal(stl_normal::Zero());
         for (unsigned int v = 0; v < 3; ++ v) {
             const ObjParser::ObjVertex &vertex = data.vertices[i++];
-            memcpy(&facet.vertex[v].x, &data.coordinates[vertex.coordIdx*4], 3 * sizeof(float));
+            memcpy(facet.vertex[v].data(), &data.coordinates[vertex.coordIdx*4], 3 * sizeof(float));
             if (vertex.normalIdx != -1) {
-                normal.x += data.normals[vertex.normalIdx*3];
-                normal.y += data.normals[vertex.normalIdx*3+1];
-                normal.z += data.normals[vertex.normalIdx*3+2];
+                normal(0) += data.normals[vertex.normalIdx*3];
+                normal(1) += data.normals[vertex.normalIdx*3+1];
+                normal(2) += data.normals[vertex.normalIdx*3+2];
                 ++ num_normals;
             }
         }
@@ -74,33 +74,27 @@ bool load_obj(const char *path, Model *model, const char *object_name_in)
             facet2.vertex[0] = facet.vertex[0];
             facet2.vertex[1] = facet.vertex[2];
 			const ObjParser::ObjVertex &vertex = data.vertices[i++];
-			memcpy(&facet2.vertex[2].x, &data.coordinates[vertex.coordIdx * 4], 3 * sizeof(float));
+			memcpy(facet2.vertex[2].data(), &data.coordinates[vertex.coordIdx * 4], 3 * sizeof(float));
 			if (vertex.normalIdx != -1) {
-                normal.x += data.normals[vertex.normalIdx*3];
-                normal.y += data.normals[vertex.normalIdx*3+1];
-                normal.z += data.normals[vertex.normalIdx*3+2];
+                normal(0) += data.normals[vertex.normalIdx*3];
+                normal(1) += data.normals[vertex.normalIdx*3+1];
+                normal(2) += data.normals[vertex.normalIdx*3+2];
                 ++ num_normals;
             }
             if (num_normals == 4) {
                 // Normalize an average normal of a quad.
-                float len = sqrt(facet.normal.x*facet.normal.x + facet.normal.y*facet.normal.y + facet.normal.z*facet.normal.z);
+                float len = facet.normal.norm();
                 if (len > EPSILON) {
-                    normal.x /= len;
-                    normal.y /= len;
-                    normal.z /= len;
+                    normal /= len;
                     facet.normal = normal;
                     facet2.normal = normal;
                 }
             }
         } else if (num_normals == 3) {
             // Normalize an average normal of a triangle.
-            float len = sqrt(facet.normal.x*facet.normal.x + facet.normal.y*facet.normal.y + facet.normal.z*facet.normal.z);
-            if (len > EPSILON) {
-                normal.x /= len;
-                normal.y /= len;
-                normal.z /= len;
-                facet.normal = normal;
-            }
+            float len = facet.normal.norm();
+            if (len > EPSILON)
+                facet.normal = normal / len;
         }
 	}
     stl_get_size(&stl);
diff --git a/xs/src/libslic3r/Format/PRUS.cpp b/xs/src/libslic3r/Format/PRUS.cpp
index b817f8305e..3cf3fc075d 100644
--- a/xs/src/libslic3r/Format/PRUS.cpp
+++ b/xs/src/libslic3r/Format/PRUS.cpp
@@ -166,7 +166,7 @@ bool load_prus(const char *path, Model *model)
             float  trafo[3][4] = { 0 };
             double instance_rotation = 0.;
             double instance_scaling_factor = 1.f;
-            Pointf instance_offset(0., 0.); 
+            Vec2d instance_offset(0., 0.); 
             bool   trafo_set = false;
             unsigned int group_id     = (unsigned int)-1;
             unsigned int extruder_id  = (unsigned int)-1;
@@ -260,8 +260,8 @@ bool load_prus(const char *path, Model *model)
 							mesh.repair();
 							// Transform the model.
 							stl_transform(&stl, &trafo[0][0]);
-							if (std::abs(stl.stats.min.z) < EPSILON)
-								stl.stats.min.z = 0.;
+							if (std::abs(stl.stats.min(2)) < EPSILON)
+								stl.stats.min(2) = 0.;
 							// Add a mesh to a model.
 							if (mesh.facets_count() > 0)
                                 mesh_valid = true;
@@ -309,11 +309,11 @@ bool load_prus(const char *path, Model *model)
 						assert(res_normal == 3);
                         int res_outer_loop	= line_reader.next_line_scanf(" outer loop");
 						assert(res_outer_loop == 0);
-						int res_vertex1 = line_reader.next_line_scanf(" vertex %f %f %f", &facet.vertex[0].x, &facet.vertex[0].y, &facet.vertex[0].z);
+						int res_vertex1 = line_reader.next_line_scanf(" vertex %f %f %f", &facet.vertex[0](0), &facet.vertex[0](1), &facet.vertex[0](2));
 						assert(res_vertex1 == 3);
-						int res_vertex2 = line_reader.next_line_scanf(" vertex %f %f %f", &facet.vertex[1].x, &facet.vertex[1].y, &facet.vertex[1].z);
+						int res_vertex2 = line_reader.next_line_scanf(" vertex %f %f %f", &facet.vertex[1](0), &facet.vertex[1](1), &facet.vertex[1](2));
 						assert(res_vertex2 == 3);
-						int res_vertex3 = line_reader.next_line_scanf(" vertex %f %f %f", &facet.vertex[2].x, &facet.vertex[2].y, &facet.vertex[2].z);
+						int res_vertex3 = line_reader.next_line_scanf(" vertex %f %f %f", &facet.vertex[2](0), &facet.vertex[2](1), &facet.vertex[2](2));
 						assert(res_vertex3 == 3);
 						int res_endloop = line_reader.next_line_scanf(" endloop");
 						assert(res_endloop == 0);
@@ -324,9 +324,9 @@ bool load_prus(const char *path, Model *model)
                             break;
                         }
                         // The facet normal has been parsed as a single string as to workaround for not a numbers in the normal definition.
-                        if (sscanf(normal_buf[0], "%f", &facet.normal.x) != 1 ||
-                            sscanf(normal_buf[1], "%f", &facet.normal.y) != 1 ||
-                            sscanf(normal_buf[2], "%f", &facet.normal.z) != 1) {
+                        if (sscanf(normal_buf[0], "%f", &facet.normal(0)) != 1 ||
+                            sscanf(normal_buf[1], "%f", &facet.normal(1)) != 1 ||
+                            sscanf(normal_buf[2], "%f", &facet.normal(2)) != 1) {
                             // Normal was mangled. Maybe denormals or "not a number" were stored?
                             // Just reset the normal and silently ignore it.
                             memset(&facet.normal, 0, sizeof(facet.normal));
diff --git a/xs/src/libslic3r/GCode.cpp b/xs/src/libslic3r/GCode.cpp
index 419299135f..fa18ddf3fc 100644
--- a/xs/src/libslic3r/GCode.cpp
+++ b/xs/src/libslic3r/GCode.cpp
@@ -64,7 +64,7 @@ std::string OozePrevention::pre_toolchange(GCode &gcodegen)
     // move to the nearest standby point
     if (!this->standby_points.empty()) {
         // get current position in print coordinates
-        Pointf3 writer_pos = gcodegen.writer().get_position();
+        Vec3d writer_pos = gcodegen.writer().get_position();
         Point pos = Point::new_scale(writer_pos(0), writer_pos(1));
         
         // find standby point
@@ -74,7 +74,7 @@ std::string OozePrevention::pre_toolchange(GCode &gcodegen)
         /*  We don't call gcodegen.travel_to() because we don't need retraction (it was already
             triggered by the caller) nor avoid_crossing_perimeters and also because the coordinates
             of the destination point must not be transformed by origin nor current extruder offset.  */
-        gcode += gcodegen.writer().travel_to_xy(Pointf::new_unscale(standby_point), 
+        gcode += gcodegen.writer().travel_to_xy(unscale(standby_point), 
             "move to standby position");
     }
     
@@ -207,7 +207,7 @@ std::string WipeTowerIntegration::append_tcr(GCode &gcodegen, const WipeTower::T
         check_add_eol(gcode);
     }
     // A phony move to the end position at the wipe tower.
-    gcodegen.writer().travel_to_xy(Pointf(end_pos.x, end_pos.y));
+    gcodegen.writer().travel_to_xy(Vec2d(end_pos.x, end_pos.y));
     gcodegen.set_last_pos(wipe_tower_point_to_object_point(gcodegen, end_pos));
 
     // Prepare a future wipe.
@@ -293,7 +293,7 @@ std::string WipeTowerIntegration::prime(GCode &gcodegen)
         gcodegen.writer().toolchange(current_extruder_id);
         gcodegen.placeholder_parser().set("current_extruder", current_extruder_id);
         // A phony move to the end position at the wipe tower.
-        gcodegen.writer().travel_to_xy(Pointf(m_priming.end_pos.x, m_priming.end_pos.y));
+        gcodegen.writer().travel_to_xy(Vec2d(m_priming.end_pos.x, m_priming.end_pos.y));
         gcodegen.set_last_pos(wipe_tower_point_to_object_point(gcodegen, m_priming.end_pos));
         // Prepare a future wipe.
         gcodegen.m_wipe.path.points.clear();
@@ -783,7 +783,7 @@ void GCode::_do_export(Print &print, FILE *file, GCodePreviewData *preview_data)
             Polygon outer_skirt = Slic3r::Geometry::convex_hull(skirt_points);
             Polygons skirts;
             for (unsigned int extruder_id : print.extruders()) {
-                const Pointf &extruder_offset = print.config.extruder_offset.get_at(extruder_id);
+                const Vec2d &extruder_offset = print.config.extruder_offset.get_at(extruder_id);
                 Polygon s(outer_skirt);
                 s.translate(Point::new_scale(- extruder_offset(0), - extruder_offset(1)));
                 skirts.emplace_back(std::move(s));
@@ -831,7 +831,7 @@ void GCode::_do_export(Print &print, FILE *file, GCodePreviewData *preview_data)
                     final_extruder_id   = tool_ordering.last_extruder();
                     assert(final_extruder_id != (unsigned int)-1);
                 }
-                this->set_origin(unscale(copy(0)), unscale(copy(1)));
+                this->set_origin(unscale(copy));
                 if (finished_objects > 0) {
                     // Move to the origin position for the copy we're going to print.
                     // This happens before Z goes down to layer 0 again, so that no collision happens hopefully.
@@ -1547,7 +1547,7 @@ void GCode::process_layer(
                     if (m_last_obj_copy != this_object_copy)
                         m_avoid_crossing_perimeters.use_external_mp_once = true;
                     m_last_obj_copy = this_object_copy;
-                    this->set_origin(unscale(copy(0)), unscale(copy(1)));
+                    this->set_origin(unscale(copy));
                     if (object_by_extruder.support != nullptr && !print_wipe_extrusions) {
                         m_layer = layers[layer_id].support_layer;
                         gcode += this->extrude_support(
@@ -1632,7 +1632,7 @@ void GCode::set_extruders(const std::vector<unsigned int> &extruder_ids)
         }
 }
 
-void GCode::set_origin(const Pointf &pointf)
+void GCode::set_origin(const Vec2d &pointf)
 {    
     // if origin increases (goes towards right), last_pos decreases because it goes towards left
     const Point translate(
@@ -2618,24 +2618,21 @@ std::string GCode::set_extruder(unsigned int extruder_id)
 }
 
 // convert a model-space scaled point into G-code coordinates
-Pointf GCode::point_to_gcode(const Point &point) const
+Vec2d GCode::point_to_gcode(const Point &point) const
 {
-    Pointf extruder_offset = EXTRUDER_CONFIG(extruder_offset);
-    return Pointf(
-        unscale(point(0)) + m_origin(0) - extruder_offset(0),
-        unscale(point(1)) + m_origin(1) - extruder_offset(1));
+    Vec2d extruder_offset = EXTRUDER_CONFIG(extruder_offset);
+    return unscale(point) + m_origin - extruder_offset;
 }
 
 // convert a model-space scaled point into G-code coordinates
-Point GCode::gcode_to_point(const Pointf &point) const
+Point GCode::gcode_to_point(const Vec2d &point) const
 {
-    Pointf extruder_offset = EXTRUDER_CONFIG(extruder_offset);
+    Vec2d extruder_offset = EXTRUDER_CONFIG(extruder_offset);
     return Point(
         scale_(point(0) - m_origin(0) + extruder_offset(0)),
         scale_(point(1) - m_origin(1) + extruder_offset(1)));
 }
 
-
 // Goes through by_region std::vector and returns reference to a subvector of entities, that are to be printed
 // during infill/perimeter wiping, or normally (depends on wiping_entities parameter)
 // Returns a reference to member to avoid copying.
diff --git a/xs/src/libslic3r/GCode.hpp b/xs/src/libslic3r/GCode.hpp
index 4953c39fef..dc8a321354 100644
--- a/xs/src/libslic3r/GCode.hpp
+++ b/xs/src/libslic3r/GCode.hpp
@@ -125,6 +125,7 @@ private:
 class GCode {
 public:        
     GCode() : 
+    	m_origin(Vec2d::Zero()),
         m_enable_loop_clipping(true), 
         m_enable_cooling_markers(false), 
         m_enable_extrusion_role_markers(false), 
@@ -152,12 +153,12 @@ public:
     void            do_export(Print *print, const char *path, GCodePreviewData *preview_data = nullptr);
 
     // Exported for the helper classes (OozePrevention, Wipe) and for the Perl binding for unit tests.
-    const Pointf&   origin() const { return m_origin; }
-    void            set_origin(const Pointf &pointf);
-    void            set_origin(const coordf_t x, const coordf_t y) { this->set_origin(Pointf(x, y)); }
+    const Vec2d&   origin() const { return m_origin; }
+    void            set_origin(const Vec2d &pointf);
+    void            set_origin(const coordf_t x, const coordf_t y) { this->set_origin(Vec2d(x, y)); }
     const Point&    last_pos() const { return m_last_pos; }
-    Pointf          point_to_gcode(const Point &point) const;
-    Point           gcode_to_point(const Pointf &point) const;
+    Vec2d          point_to_gcode(const Point &point) const;
+    Point           gcode_to_point(const Vec2d &point) const;
     const FullPrintConfig &config() const { return m_config; }
     const Layer*    layer() const { return m_layer; }
     GCodeWriter&    writer() { return m_writer; }
@@ -258,7 +259,7 @@ protected:
     /* Origin of print coordinates expressed in unscaled G-code coordinates.
        This affects the input arguments supplied to the extrude*() and travel_to()
        methods. */
-    Pointf                              m_origin;
+    Vec2d                              m_origin;
     FullPrintConfig                     m_config;
     GCodeWriter                         m_writer;
     PlaceholderParser                   m_placeholder_parser;
diff --git a/xs/src/libslic3r/GCode/Analyzer.cpp b/xs/src/libslic3r/GCode/Analyzer.cpp
index 44e6e9acb9..51d5b1a067 100644
--- a/xs/src/libslic3r/GCode/Analyzer.cpp
+++ b/xs/src/libslic3r/GCode/Analyzer.cpp
@@ -14,7 +14,7 @@ static const float MMMIN_TO_MMSEC = 1.0f / 60.0f;
 static const float INCHES_TO_MM = 25.4f;
 static const float DEFAULT_FEEDRATE = 0.0f;
 static const unsigned int DEFAULT_EXTRUDER_ID = 0;
-static const Slic3r::Pointf3 DEFAULT_START_POSITION = Slic3r::Pointf3(0.0f, 0.0f, 0.0f);
+static const Slic3r::Vec3d DEFAULT_START_POSITION = Slic3r::Vec3d(0.0f, 0.0f, 0.0f);
 static const float DEFAULT_START_EXTRUSION = 0.0f;
 
 namespace Slic3r {
@@ -71,7 +71,7 @@ bool GCodeAnalyzer::Metadata::operator != (const GCodeAnalyzer::Metadata& other)
     return false;
 }
 
-GCodeAnalyzer::GCodeMove::GCodeMove(GCodeMove::EType type, ExtrusionRole extrusion_role, unsigned int extruder_id, double mm3_per_mm, float width, float height, float feedrate, const Pointf3& start_position, const Pointf3& end_position, float delta_extruder)
+GCodeAnalyzer::GCodeMove::GCodeMove(GCodeMove::EType type, ExtrusionRole extrusion_role, unsigned int extruder_id, double mm3_per_mm, float width, float height, float feedrate, const Vec3d& start_position, const Vec3d& end_position, float delta_extruder)
     : type(type)
     , data(extrusion_role, extruder_id, mm3_per_mm, width, height, feedrate)
     , start_position(start_position)
@@ -80,7 +80,7 @@ GCodeAnalyzer::GCodeMove::GCodeMove(GCodeMove::EType type, ExtrusionRole extrusi
 {
 }
 
-GCodeAnalyzer::GCodeMove::GCodeMove(GCodeMove::EType type, const GCodeAnalyzer::Metadata& data, const Pointf3& start_position, const Pointf3& end_position, float delta_extruder)
+GCodeAnalyzer::GCodeMove::GCodeMove(GCodeMove::EType type, const GCodeAnalyzer::Metadata& data, const Vec3d& start_position, const Vec3d& end_position, float delta_extruder)
     : type(type)
     , data(data)
     , start_position(start_position)
@@ -587,12 +587,12 @@ void GCodeAnalyzer::_reset_axes_position()
     ::memset((void*)m_state.position, 0, Num_Axis * sizeof(float));
 }
 
-void GCodeAnalyzer::_set_start_position(const Pointf3& position)
+void GCodeAnalyzer::_set_start_position(const Vec3d& position)
 {
     m_state.start_position = position;
 }
 
-const Pointf3& GCodeAnalyzer::_get_start_position() const
+const Vec3d& GCodeAnalyzer::_get_start_position() const
 {
     return m_state.start_position;
 }
@@ -612,9 +612,9 @@ float GCodeAnalyzer::_get_delta_extrusion() const
     return _get_axis_position(E) - m_state.start_extrusion;
 }
 
-Pointf3 GCodeAnalyzer::_get_end_position() const
+Vec3d GCodeAnalyzer::_get_end_position() const
 {
-    return Pointf3(m_state.position[X], m_state.position[Y], m_state.position[Z]);
+    return Vec3d(m_state.position[X], m_state.position[Y], m_state.position[Z]);
 }
 
 void GCodeAnalyzer::_store_move(GCodeAnalyzer::GCodeMove::EType type)
@@ -673,7 +673,7 @@ void GCodeAnalyzer::_calc_gcode_preview_extrusion_layers(GCodePreviewData& previ
     Metadata data;
     float z = FLT_MAX;
     Polyline polyline;
-    Pointf3 position(FLT_MAX, FLT_MAX, FLT_MAX);
+    Vec3d position(FLT_MAX, FLT_MAX, FLT_MAX);
     float volumetric_rate = FLT_MAX;
     GCodePreviewData::Range height_range;
     GCodePreviewData::Range width_range;
@@ -742,7 +742,7 @@ void GCodeAnalyzer::_calc_gcode_preview_travel(GCodePreviewData& preview_data)
         return;
 
     Polyline3 polyline;
-    Pointf3 position(FLT_MAX, FLT_MAX, FLT_MAX);
+    Vec3d position(FLT_MAX, FLT_MAX, FLT_MAX);
     GCodePreviewData::Travel::EType type = GCodePreviewData::Travel::Num_Types;
     GCodePreviewData::Travel::Polyline::EDirection direction = GCodePreviewData::Travel::Polyline::Num_Directions;
     float feedrate = FLT_MAX;
@@ -768,12 +768,12 @@ void GCodeAnalyzer::_calc_gcode_preview_travel(GCodePreviewData& preview_data)
             polyline = Polyline3();
 
             // add both vertices of the move
-            polyline.append(Point3(scale_(move.start_position.x()), scale_(move.start_position.y()), scale_(move.start_position.z())));
-            polyline.append(Point3(scale_(move.end_position.x()), scale_(move.end_position.y()), scale_(move.end_position.z())));
+            polyline.append(Vec3crd(scale_(move.start_position.x()), scale_(move.start_position.y()), scale_(move.start_position.z())));
+            polyline.append(Vec3crd(scale_(move.end_position.x()), scale_(move.end_position.y()), scale_(move.end_position.z())));
         }
         else
             // append end vertex of the move to current polyline
-            polyline.append(Point3(scale_(move.end_position.x()), scale_(move.end_position.y()), scale_(move.end_position.z())));
+            polyline.append(Vec3crd(scale_(move.end_position.x()), scale_(move.end_position.y()), scale_(move.end_position.z())));
 
         // update current values
         position = move.end_position;
@@ -804,7 +804,7 @@ void GCodeAnalyzer::_calc_gcode_preview_retractions(GCodePreviewData& preview_da
     for (const GCodeMove& move : retraction_moves->second)
     {
         // store position
-        Point3 position(scale_(move.start_position.x()), scale_(move.start_position.y()), scale_(move.start_position.z()));
+        Vec3crd position(scale_(move.start_position.x()), scale_(move.start_position.y()), scale_(move.start_position.z()));
         preview_data.retraction.positions.emplace_back(position, move.data.width, move.data.height);
     }
 }
@@ -818,7 +818,7 @@ void GCodeAnalyzer::_calc_gcode_preview_unretractions(GCodePreviewData& preview_
     for (const GCodeMove& move : unretraction_moves->second)
     {
         // store position
-        Point3 position(scale_(move.start_position.x()), scale_(move.start_position.y()), scale_(move.start_position.z()));
+        Vec3crd position(scale_(move.start_position.x()), scale_(move.start_position.y()), scale_(move.start_position.z()));
         preview_data.unretraction.positions.emplace_back(position, move.data.width, move.data.height);
     }
 }
diff --git a/xs/src/libslic3r/GCode/Analyzer.hpp b/xs/src/libslic3r/GCode/Analyzer.hpp
index 03dbab3383..27a49b8690 100644
--- a/xs/src/libslic3r/GCode/Analyzer.hpp
+++ b/xs/src/libslic3r/GCode/Analyzer.hpp
@@ -75,12 +75,12 @@ public:
 
         EType type;
         Metadata data;
-        Pointf3 start_position;
-        Pointf3 end_position;
+        Vec3d start_position;
+        Vec3d end_position;
         float delta_extruder;
 
-        GCodeMove(EType type, ExtrusionRole extrusion_role, unsigned int extruder_id, double mm3_per_mm, float width, float height, float feedrate, const Pointf3& start_position, const Pointf3& end_position, float delta_extruder);
-        GCodeMove(EType type, const Metadata& data, const Pointf3& start_position, const Pointf3& end_position, float delta_extruder);
+        GCodeMove(EType type, ExtrusionRole extrusion_role, unsigned int extruder_id, double mm3_per_mm, float width, float height, float feedrate, const Vec3d& start_position, const Vec3d& end_position, float delta_extruder);
+        GCodeMove(EType type, const Metadata& data, const Vec3d& start_position, const Vec3d& end_position, float delta_extruder);
     };
 
     typedef std::vector<GCodeMove> GCodeMovesList;
@@ -93,7 +93,7 @@ private:
         EPositioningType global_positioning_type;
         EPositioningType e_local_positioning_type;
         Metadata data;
-        Pointf3 start_position;
+        Vec3d start_position = Vec3d::Zero();
         float start_extrusion;
         float position[Num_Axis];
     };
@@ -206,15 +206,15 @@ private:
     // Sets axes position to zero
     void _reset_axes_position();
 
-    void _set_start_position(const Pointf3& position);
-    const Pointf3& _get_start_position() const;
+    void _set_start_position(const Vec3d& position);
+    const Vec3d& _get_start_position() const;
 
     void _set_start_extrusion(float extrusion);
     float _get_start_extrusion() const;
     float _get_delta_extrusion() const;
 
     // Returns current xyz position (from m_state.position[])
-    Pointf3 _get_end_position() const;
+    Vec3d _get_end_position() const;
 
     // Adds a new move with the given data
     void _store_move(GCodeMove::EType type);
diff --git a/xs/src/libslic3r/GCode/CoolingBuffer.cpp b/xs/src/libslic3r/GCode/CoolingBuffer.cpp
index 0f361b250d..40ccc7b09f 100644
--- a/xs/src/libslic3r/GCode/CoolingBuffer.cpp
+++ b/xs/src/libslic3r/GCode/CoolingBuffer.cpp
@@ -23,7 +23,7 @@ CoolingBuffer::CoolingBuffer(GCode &gcodegen) : m_gcodegen(gcodegen), m_current_
 void CoolingBuffer::reset()
 {
     m_current_pos.assign(5, 0.f);
-    Pointf3 pos = m_gcodegen.writer().get_position();
+    Vec3d pos = m_gcodegen.writer().get_position();
     m_current_pos[0] = float(pos(0));
     m_current_pos[1] = float(pos(1));
     m_current_pos[2] = float(pos(2));
diff --git a/xs/src/libslic3r/GCode/PreviewData.cpp b/xs/src/libslic3r/GCode/PreviewData.cpp
index 3833bca06c..9cf9716e0a 100644
--- a/xs/src/libslic3r/GCode/PreviewData.cpp
+++ b/xs/src/libslic3r/GCode/PreviewData.cpp
@@ -226,7 +226,7 @@ void GCodePreviewData::Travel::set_default()
 
 const GCodePreviewData::Color GCodePreviewData::Retraction::Default_Color = GCodePreviewData::Color(1.0f, 1.0f, 1.0f, 1.0f);
 
-GCodePreviewData::Retraction::Position::Position(const Point3& position, float width, float height)
+GCodePreviewData::Retraction::Position::Position(const Vec3crd& position, float width, float height)
     : position(position)
     , width(width)
     , height(height)
diff --git a/xs/src/libslic3r/GCode/PreviewData.hpp b/xs/src/libslic3r/GCode/PreviewData.hpp
index ea8ca6d58a..ab74993f55 100644
--- a/xs/src/libslic3r/GCode/PreviewData.hpp
+++ b/xs/src/libslic3r/GCode/PreviewData.hpp
@@ -151,11 +151,11 @@ public:
 
         struct Position
         {
-            Point3 position;
+            Vec3crd position;
             float width;
             float height;
 
-            Position(const Point3& position, float width, float height);
+            Position(const Vec3crd& position, float width, float height);
         };
 
         typedef std::vector<Position> PositionsList;
diff --git a/xs/src/libslic3r/GCode/PrintExtents.cpp b/xs/src/libslic3r/GCode/PrintExtents.cpp
index e1d4e257f6..2ed6077696 100644
--- a/xs/src/libslic3r/GCode/PrintExtents.cpp
+++ b/xs/src/libslic3r/GCode/PrintExtents.cpp
@@ -32,8 +32,8 @@ static inline BoundingBoxf extrusionentity_extents(const ExtrusionPath &extrusio
     BoundingBox bbox = extrusion_polyline_extents(extrusion_path.polyline, scale_(0.5 * extrusion_path.width));
     BoundingBoxf bboxf;
     if (! empty(bbox)) {
-        bboxf.min = Pointf::new_unscale(bbox.min);
-        bboxf.max = Pointf::new_unscale(bbox.max);
+        bboxf.min = unscale(bbox.min);
+        bboxf.max = unscale(bbox.max);
 		bboxf.defined = true;
     }
     return bboxf;
@@ -46,8 +46,8 @@ static inline BoundingBoxf extrusionentity_extents(const ExtrusionLoop &extrusio
         bbox.merge(extrusion_polyline_extents(extrusion_path.polyline, scale_(0.5 * extrusion_path.width)));
     BoundingBoxf bboxf;
     if (! empty(bbox)) {
-        bboxf.min = Pointf::new_unscale(bbox.min);
-        bboxf.max = Pointf::new_unscale(bbox.max);
+        bboxf.min = unscale(bbox.min);
+        bboxf.max = unscale(bbox.max);
 		bboxf.defined = true;
 	}
     return bboxf;
@@ -60,8 +60,8 @@ static inline BoundingBoxf extrusionentity_extents(const ExtrusionMultiPath &ext
         bbox.merge(extrusion_polyline_extents(extrusion_path.polyline, scale_(0.5 * extrusion_path.width)));
     BoundingBoxf bboxf;
     if (! empty(bbox)) {
-        bboxf.min = Pointf::new_unscale(bbox.min);
-        bboxf.max = Pointf::new_unscale(bbox.max);
+        bboxf.min = unscale(bbox.min);
+        bboxf.max = unscale(bbox.max);
 		bboxf.defined = true;
 	}
     return bboxf;
@@ -123,7 +123,7 @@ BoundingBoxf get_print_object_extrusions_extents(const PrintObject &print_object
                 bbox_this.merge(extrusionentity_extents(extrusion_entity));
         for (const Point &offset : print_object._shifted_copies) {
             BoundingBoxf bbox_translated(bbox_this);
-            bbox_translated.translate(Pointf::new_unscale(offset));
+            bbox_translated.translate(unscale(offset));
             bbox.merge(bbox_translated);
         }
     }
@@ -136,8 +136,9 @@ BoundingBoxf get_wipe_tower_extrusions_extents(const Print &print, const coordf_
 {
     // Wipe tower extrusions are saved as if the tower was at the origin with no rotation
     // We need to get position and angle of the wipe tower to transform them to actual position.
-    Pointf wipe_tower_pos(print.config.wipe_tower_x.value, print.config.wipe_tower_y.value);
-    float wipe_tower_angle = print.config.wipe_tower_rotation_angle.value;
+    Transform2d trafo =
+        Eigen::Translation2d(print.config.wipe_tower_x.value, print.config.wipe_tower_y.value) *
+        Eigen::Rotation2Dd(print.config.wipe_tower_rotation_angle.value);
 
     BoundingBoxf bbox;
     for (const std::vector<WipeTower::ToolChangeResult> &tool_changes : print.m_wipe_tower_tool_changes) {
@@ -147,19 +148,11 @@ BoundingBoxf get_wipe_tower_extrusions_extents(const Print &print, const coordf_
             for (size_t i = 1; i < tcr.extrusions.size(); ++ i) {
                 const WipeTower::Extrusion &e = tcr.extrusions[i];
                 if (e.width > 0) {
-                    Pointf  p1((&e - 1)->pos.x, (&e - 1)->pos.y);
-                    Pointf  p2(e.pos.x, e.pos.y);
-                    p1.rotate(wipe_tower_angle);
-                    p1 += wipe_tower_pos;
-                    p2.rotate(wipe_tower_angle);
-                    p2 += wipe_tower_pos;
-
-                    bbox.merge(p1);
-                    coordf_t radius = 0.5 * e.width;
-                    bbox.min(0) = std::min(bbox.min(0), std::min(p1(0), p2(0)) - radius);
-                    bbox.min(1) = std::min(bbox.min(1), std::min(p1(1), p2(1)) - radius);
-                    bbox.max(0) = std::max(bbox.max(0), std::max(p1(0), p2(0)) + radius);
-                    bbox.max(1) = std::max(bbox.max(1), std::max(p1(1), p2(1)) + radius);
+                    Vec2d delta = 0.5 * Vec2d(e.width, e.width);
+                    Vec2d p1 = trafo * Vec2d((&e - 1)->pos.x, (&e - 1)->pos.y);
+                    Vec2d p2 = trafo * Vec2d(e.pos.x, e.pos.y);
+                    bbox.merge(p1.cwiseMin(p2) - delta);
+                    bbox.merge(p1.cwiseMax(p2) + delta);
                 }
             }
         }
@@ -176,8 +169,8 @@ BoundingBoxf get_wipe_tower_priming_extrusions_extents(const Print &print)
         for (size_t i = 1; i < tcr.extrusions.size(); ++ i) {
             const WipeTower::Extrusion &e = tcr.extrusions[i];
             if (e.width > 0) {
-                Pointf  p1((&e - 1)->pos.x, (&e - 1)->pos.y);
-                Pointf  p2(e.pos.x, e.pos.y);
+                Vec2d  p1((&e - 1)->pos.x, (&e - 1)->pos.y);
+                Vec2d  p2(e.pos.x, e.pos.y);
                 bbox.merge(p1);
                 coordf_t radius = 0.5 * e.width;
                 bbox.min(0) = std::min(bbox.min(0), std::min(p1(0), p2(0)) - radius);
diff --git a/xs/src/libslic3r/GCodeWriter.cpp b/xs/src/libslic3r/GCodeWriter.cpp
index cefbdad2e2..6ef17f4f41 100644
--- a/xs/src/libslic3r/GCodeWriter.cpp
+++ b/xs/src/libslic3r/GCodeWriter.cpp
@@ -276,7 +276,7 @@ std::string GCodeWriter::set_speed(double F, const std::string &comment, const s
     return gcode.str();
 }
 
-std::string GCodeWriter::travel_to_xy(const Pointf &point, const std::string &comment)
+std::string GCodeWriter::travel_to_xy(const Vec2d &point, const std::string &comment)
 {
     m_pos(0) = point(0);
     m_pos(1) = point(1);
@@ -290,7 +290,7 @@ std::string GCodeWriter::travel_to_xy(const Pointf &point, const std::string &co
     return gcode.str();
 }
 
-std::string GCodeWriter::travel_to_xyz(const Pointf3 &point, const std::string &comment)
+std::string GCodeWriter::travel_to_xyz(const Vec3d &point, const std::string &comment)
 {
     /*  If target Z is lower than current Z but higher than nominal Z we
         don't perform the Z move but we only move in the XY plane and
@@ -299,7 +299,7 @@ std::string GCodeWriter::travel_to_xyz(const Pointf3 &point, const std::string &
     if (!this->will_move_z(point(2))) {
         double nominal_z = m_pos(2) - m_lifted;
         m_lifted = m_lifted - (point(2) - nominal_z);
-        return this->travel_to_xy(point.xy());
+        return this->travel_to_xy(to_2d(point));
     }
     
     /*  In all the other cases, we perform an actual XYZ move and cancel
@@ -358,7 +358,7 @@ bool GCodeWriter::will_move_z(double z) const
     return true;
 }
 
-std::string GCodeWriter::extrude_to_xy(const Pointf &point, double dE, const std::string &comment)
+std::string GCodeWriter::extrude_to_xy(const Vec2d &point, double dE, const std::string &comment)
 {
     m_pos(0) = point(0);
     m_pos(1) = point(1);
@@ -373,7 +373,7 @@ std::string GCodeWriter::extrude_to_xy(const Pointf &point, double dE, const std
     return gcode.str();
 }
 
-std::string GCodeWriter::extrude_to_xyz(const Pointf3 &point, double dE, const std::string &comment)
+std::string GCodeWriter::extrude_to_xyz(const Vec3d &point, double dE, const std::string &comment)
 {
     m_pos = point;
     m_lifted = 0;
diff --git a/xs/src/libslic3r/GCodeWriter.hpp b/xs/src/libslic3r/GCodeWriter.hpp
index f706b87689..664b0e3a1d 100644
--- a/xs/src/libslic3r/GCodeWriter.hpp
+++ b/xs/src/libslic3r/GCodeWriter.hpp
@@ -55,18 +55,18 @@ public:
     std::string toolchange_prefix() const;
     std::string toolchange(unsigned int extruder_id);
     std::string set_speed(double F, const std::string &comment = std::string(), const std::string &cooling_marker = std::string()) const;
-    std::string travel_to_xy(const Pointf &point, const std::string &comment = std::string());
-    std::string travel_to_xyz(const Pointf3 &point, const std::string &comment = std::string());
+    std::string travel_to_xy(const Vec2d &point, const std::string &comment = std::string());
+    std::string travel_to_xyz(const Vec3d &point, const std::string &comment = std::string());
     std::string travel_to_z(double z, const std::string &comment = std::string());
     bool        will_move_z(double z) const;
-    std::string extrude_to_xy(const Pointf &point, double dE, const std::string &comment = std::string());
-    std::string extrude_to_xyz(const Pointf3 &point, double dE, const std::string &comment = std::string());
+    std::string extrude_to_xy(const Vec2d &point, double dE, const std::string &comment = std::string());
+    std::string extrude_to_xyz(const Vec3d &point, double dE, const std::string &comment = std::string());
     std::string retract(bool before_wipe = false);
     std::string retract_for_toolchange(bool before_wipe = false);
     std::string unretract();
     std::string lift();
     std::string unlift();
-    Pointf3     get_position() const { return m_pos; }
+    Vec3d       get_position() const { return m_pos; }
 
 private:
     std::vector<Extruder>    m_extruders;
@@ -81,7 +81,7 @@ private:
     unsigned int    m_last_bed_temperature;
     bool            m_last_bed_temperature_reached;
     double          m_lifted;
-    Pointf3         m_pos;
+    Vec3d           m_pos = Vec3d::Zero();
 
     std::string _travel_to_z(double z, const std::string &comment);
     std::string _retract(double length, double restart_extra, const std::string &comment);
diff --git a/xs/src/libslic3r/Geometry.cpp b/xs/src/libslic3r/Geometry.cpp
index b4813be14a..c978d46b61 100644
--- a/xs/src/libslic3r/Geometry.cpp
+++ b/xs/src/libslic3r/Geometry.cpp
@@ -345,7 +345,7 @@ linint(double value, double oldmin, double oldmax, double newmin, double newmax)
 // If the points have the same weight, sort them lexicographically by their positions.
 struct ArrangeItem {
     ArrangeItem() {}
-    Pointf    pos;
+    Vec2d    pos;
     coordf_t  weight;
     bool operator<(const ArrangeItem &other) const {
         return weight < other.weight ||
@@ -353,17 +353,17 @@ struct ArrangeItem {
     }
 };
 
-Pointfs arrange(size_t num_parts, const Pointf &part_size, coordf_t gap, const BoundingBoxf* bed_bounding_box)
+Pointfs arrange(size_t num_parts, const Vec2d &part_size, coordf_t gap, const BoundingBoxf* bed_bounding_box)
 {
     // Use actual part size (the largest) plus separation distance (half on each side) in spacing algorithm.
-    const Pointf       cell_size(part_size(0) + gap, part_size(1) + gap);
+    const Vec2d       cell_size(part_size(0) + gap, part_size(1) + gap);
 
     const BoundingBoxf bed_bbox = (bed_bounding_box != NULL && bed_bounding_box->defined) ? 
         *bed_bounding_box :
         // Bogus bed size, large enough not to trigger the unsufficient bed size error.
         BoundingBoxf(
-            Pointf(0, 0),
-            Pointf(cell_size(0) * num_parts, cell_size(1) * num_parts));
+            Vec2d(0, 0),
+            Vec2d(cell_size(0) * num_parts, cell_size(1) * num_parts));
 
     // This is how many cells we have available into which to put parts.
     size_t cellw = size_t(floor((bed_bbox.size()(0) + gap) / cell_size(0)));
@@ -372,8 +372,8 @@ Pointfs arrange(size_t num_parts, const Pointf &part_size, coordf_t gap, const B
         CONFESS(PRINTF_ZU " parts won't fit in your print area!\n", num_parts);
     
     // Get a bounding box of cellw x cellh cells, centered at the center of the bed.
-    Pointf       cells_size(cellw * cell_size(0) - gap, cellh * cell_size(1) - gap);
-    Pointf       cells_offset(bed_bbox.center() - 0.5 * cells_size);
+    Vec2d       cells_size(cellw * cell_size(0) - gap, cellh * cell_size(1) - gap);
+    Vec2d       cells_offset(bed_bbox.center() - 0.5 * cells_size);
     BoundingBoxf cells_bb(cells_offset, cells_size + cells_offset);
     
     // List of cells, sorted by distance from center.
@@ -405,35 +405,35 @@ Pointfs arrange(size_t num_parts, const Pointf &part_size, coordf_t gap, const B
     Pointfs positions;
     positions.reserve(num_parts);
     for (std::vector<ArrangeItem>::const_iterator it = cellsorder.begin(); it != cellsorder.end(); ++ it)
-        positions.push_back(Pointf(it->pos(0) - 0.5 * part_size(0), it->pos(1) - 0.5 * part_size(1)));
+        positions.push_back(Vec2d(it->pos(0) - 0.5 * part_size(0), it->pos(1) - 0.5 * part_size(1)));
     return positions;
 }
 #else
 class ArrangeItem {
-    public:
-    Pointf pos;
+public:
+    Vec2d pos = Vec2d::Zero();
     size_t index_x, index_y;
     coordf_t dist;
 };
 class ArrangeItemIndex {
-    public:
+public:
     coordf_t index;
     ArrangeItem item;
     ArrangeItemIndex(coordf_t _index, ArrangeItem _item) : index(_index), item(_item) {};
 };
 
 bool
-arrange(size_t total_parts, const Pointf &part_size, coordf_t dist, const BoundingBoxf* bb, Pointfs &positions)
+arrange(size_t total_parts, const Vec2d &part_size, coordf_t dist, const BoundingBoxf* bb, Pointfs &positions)
 {
     positions.clear();
 
-    Pointf part = part_size;
+    Vec2d part = part_size;
 
     // use actual part size (the largest) plus separation distance (half on each side) in spacing algorithm
     part(0) += dist;
     part(1) += dist;
     
-    Pointf area;
+    Vec2d area(Vec2d::Zero());
     if (bb != NULL && bb->defined) {
         area = bb->size();
     } else {
@@ -449,11 +449,11 @@ arrange(size_t total_parts, const Pointf &part_size, coordf_t dist, const Boundi
         return false;
     
     // total space used by cells
-    Pointf cells(cellw * part(0), cellh * part(1));
+    Vec2d cells(cellw * part(0), cellh * part(1));
     
     // bounding box of total space used by cells
     BoundingBoxf cells_bb;
-    cells_bb.merge(Pointf(0,0)); // min
+    cells_bb.merge(Vec2d(0,0)); // min
     cells_bb.merge(cells);  // max
     
     // center bounding box to area
@@ -533,7 +533,7 @@ arrange(size_t total_parts, const Pointf &part_size, coordf_t dist, const Boundi
         coordf_t cx = c.item.index_x - lx;
         coordf_t cy = c.item.index_y - ty;
         
-        positions.push_back(Pointf(cx * part(0), cy * part(1)));
+        positions.push_back(Vec2d(cx * part(0), cy * part(1)));
     }
     
     if (bb != NULL && bb->defined) {
diff --git a/xs/src/libslic3r/Geometry.hpp b/xs/src/libslic3r/Geometry.hpp
index 95c13fcdb0..1945340077 100644
--- a/xs/src/libslic3r/Geometry.hpp
+++ b/xs/src/libslic3r/Geometry.hpp
@@ -66,7 +66,7 @@ static inline bool is_ccw(const Polygon &poly)
     return o == ORIENTATION_CCW;
 }
 
-inline bool ray_ray_intersection(const Pointf &p1, const Vectorf &v1, const Pointf &p2, const Vectorf &v2, Pointf &res)
+inline bool ray_ray_intersection(const Vec2d &p1, const Vec2d &v1, const Vec2d &p2, const Vec2d &v2, Vec2d &res)
 {
     double denom = v1(0) * v2(1) - v2(0) * v1(1);
     if (std::abs(denom) < EPSILON)
@@ -77,7 +77,7 @@ inline bool ray_ray_intersection(const Pointf &p1, const Vectorf &v1, const Poin
     return true;
 }
 
-inline bool segment_segment_intersection(const Pointf &p1, const Vectorf &v1, const Pointf &p2, const Vectorf &v2, Pointf &res)
+inline bool segment_segment_intersection(const Vec2d &p1, const Vec2d &v1, const Vec2d &p2, const Vec2d &v2, Vec2d &res)
 {
     double denom = v1(0) * v2(1) - v2(0) * v1(1);
     if (std::abs(denom) < EPSILON)
@@ -123,7 +123,7 @@ void simplify_polygons(const Polygons &polygons, double tolerance, Polygons* ret
 double linint(double value, double oldmin, double oldmax, double newmin, double newmax);
 bool arrange(
     // input
-    size_t num_parts, const Pointf &part_size, coordf_t gap, const BoundingBoxf* bed_bounding_box, 
+    size_t num_parts, const Vec2d &part_size, coordf_t gap, const BoundingBoxf* bed_bounding_box, 
     // output
     Pointfs &positions);
 
diff --git a/xs/src/libslic3r/Line.cpp b/xs/src/libslic3r/Line.cpp
index 93e888efa9..a29e4ce4ee 100644
--- a/xs/src/libslic3r/Line.cpp
+++ b/xs/src/libslic3r/Line.cpp
@@ -97,11 +97,11 @@ bool Line::intersection(const Line &l2, Point *intersection) const
     return false;  // not intersecting
 }
 
-Pointf3 Linef3::intersect_plane(double z) const
+Vec3d Linef3::intersect_plane(double z) const
 {
     auto   v = (this->b - this->a).cast<double>();
     double t = (z - this->a(2)) / v(2);
-    return Pointf3(this->a(0) + v(0) * t, this->a(1) + v(1) * t, z);
+    return Vec3d(this->a(0) + v(0) * t, this->a(1) + v(1) * t, z);
 }
 
 }
diff --git a/xs/src/libslic3r/Line.hpp b/xs/src/libslic3r/Line.hpp
index 39c2e1ff1d..5b77a4b612 100644
--- a/xs/src/libslic3r/Line.hpp
+++ b/xs/src/libslic3r/Line.hpp
@@ -19,7 +19,7 @@ class Line
 {
 public:
     Line() {}
-    explicit Line(Point _a, Point _b): a(_a), b(_b) {}
+    Line(const Point& _a, const Point& _b) : a(_a), b(_b) {}
     explicit operator Lines() const { Lines lines; lines.emplace_back(*this); return lines; }
     void   scale(double factor) { this->a *= factor; this->b *= factor; }
     void   translate(double x, double y) { Vector v(x, y); this->a += v; this->b += v; }
@@ -49,45 +49,49 @@ class ThickLine : public Line
 {
 public:
     ThickLine() : a_width(0), b_width(0) {}
-    ThickLine(Point a, Point b) : Line(a, b), a_width(0), b_width(0) {}
-    ThickLine(Point a, Point b, double wa, double wb) : Line(a, b), a_width(wa), b_width(wb) {}
+    ThickLine(const Point& a, const Point& b) : Line(a, b), a_width(0), b_width(0) {}
+    ThickLine(const Point& a, const Point& b, double wa, double wb) : Line(a, b), a_width(wa), b_width(wb) {}
 
-    coordf_t a_width, b_width;    
+    double a_width, b_width;
 };
 
 class Line3
 {
 public:
-    Line3() {}
-    Line3(const Point3& _a, const Point3& _b) : a(_a), b(_b) {}
+    Line3() : a(Vec3crd::Zero()), b(Vec3crd::Zero()) {}
+    Line3(const Vec3crd& _a, const Vec3crd& _b) : a(_a), b(_b) {}
 
     double  length() const { return (this->a - this->b).cast<double>().norm(); }
-    Vector3 vector() const { return this->b - this->a; }
+    Vec3crd vector() const { return this->b - this->a; }
 
-    Point3 a;
-    Point3 b;
+    Vec3crd a;
+    Vec3crd b;
 };
 
 class Linef
 {
 public:
-    Linef() {}
-    explicit Linef(Pointf _a, Pointf _b): a(_a), b(_b) {}
+    Linef() : a(Vec2d::Zero()), b(Vec2d::Zero()) {}
+    Linef(const Vec2d& _a, const Vec2d& _b) : a(_a), b(_b) {}
 
-    Pointf a;
-    Pointf b;
+    Vec2d a;
+    Vec2d b;
 };
 
 class Linef3
 {
 public:
-    Linef3() {}
-    explicit Linef3(Pointf3 _a, Pointf3 _b): a(_a), b(_b) {}
-    Pointf3 intersect_plane(double z) const;
-    void    scale(double factor) { this->a *= factor; this->b *= factor; }
+    Linef3() : a(Vec3d::Zero()), b(Vec3d::Zero()) {}
+    Linef3(const Vec3d& _a, const Vec3d& _b) : a(_a), b(_b) {}
 
-    Pointf3 a;
-    Pointf3 b;
+    Vec3d   intersect_plane(double z) const;
+    void    scale(double factor) { this->a *= factor; this->b *= factor; }
+    Vec3d   vector() const { return this->b - this->a; }
+    Vec3d   unit_vector() const { return (length() == 0.0) ? Vec3d::Zero() : vector().normalized(); }
+    double  length() const { return vector().norm(); }
+
+    Vec3d a;
+    Vec3d b;
 };
 
 } // namespace Slic3r
diff --git a/xs/src/libslic3r/Model.cpp b/xs/src/libslic3r/Model.cpp
index c5b8ad8dfe..d046a8ef28 100644
--- a/xs/src/libslic3r/Model.cpp
+++ b/xs/src/libslic3r/Model.cpp
@@ -235,15 +235,7 @@ BoundingBoxf3 Model::bounding_box() const
     return bb;
 }
 
-BoundingBoxf3 Model::transformed_bounding_box() const
-{
-    BoundingBoxf3 bb;
-    for (const ModelObject* obj : this->objects)
-        bb.merge(obj->tight_bounding_box(false));
-    return bb;
-}
-
-void Model::center_instances_around_point(const Pointf &point)
+void Model::center_instances_around_point(const Vec2d &point)
 {
 //    BoundingBoxf3 bb = this->bounding_box();
     BoundingBoxf3 bb;
@@ -251,7 +243,7 @@ void Model::center_instances_around_point(const Pointf &point)
         for (size_t i = 0; i < o->instances.size(); ++ i)
             bb.merge(o->instance_bounding_box(i, false));
 
-    Pointf shift = point - 0.5 * bb.size().xy() - bb.min.xy();
+    Vec2d shift = point - 0.5 * to_2d(bb.size()) - to_2d(bb.min);
     for (ModelObject *o : this->objects) {
         for (ModelInstance *i : o->instances)
             i->offset += shift;
@@ -309,8 +301,8 @@ bool Model::arrange_objects(coordf_t dist, const BoundingBoxf* bb)
         for (size_t i = 0; i < o->instances.size(); ++ i) {
             // an accurate snug bounding box around the transformed mesh.
             BoundingBoxf3 bbox(o->instance_bounding_box(i, true));
-            instance_sizes.push_back(bbox.size().xy());
-            instance_centers.push_back(bbox.center().xy());
+            instance_sizes.emplace_back(to_2d(bbox.size()));
+            instance_centers.emplace_back(to_2d(bbox.center()));
         }
 
     Pointfs positions;
@@ -332,7 +324,7 @@ bool Model::arrange_objects(coordf_t dist, const BoundingBoxf* bb)
 // Duplicate the entire model preserving instance relative positions.
 void Model::duplicate(size_t copies_num, coordf_t dist, const BoundingBoxf* bb)
 {
-    Pointfs model_sizes(copies_num-1, this->bounding_box().size().xy());
+    Pointfs model_sizes(copies_num-1, to_2d(this->bounding_box().size()));
     Pointfs positions;
     if (! _arrange(model_sizes, dist, bb, positions))
         CONFESS("Cannot duplicate part as the resulting objects would not fit on the print bed.\n");
@@ -343,7 +335,7 @@ void Model::duplicate(size_t copies_num, coordf_t dist, const BoundingBoxf* bb)
         // make a copy of the pointers in order to avoid recursion when appending their copies
         ModelInstancePtrs instances = o->instances;
         for (const ModelInstance *i : instances) {
-            for (const Pointf &pos : positions) {
+            for (const Vec2d &pos : positions) {
                 ModelInstance *instance = o->add_instance(*i);
                 instance->offset += pos;
             }
@@ -375,7 +367,7 @@ void Model::duplicate_objects_grid(size_t x, size_t y, coordf_t dist)
     ModelObject* object = this->objects.front();
     object->clear_instances();
 
-    Sizef3 size = object->bounding_box().size();
+    Vec3d size = object->bounding_box().size();
 
     for (size_t x_copy = 1; x_copy <= x; ++x_copy) {
         for (size_t y_copy = 1; y_copy <= y; ++y_copy) {
@@ -621,54 +613,6 @@ const BoundingBoxf3& ModelObject::bounding_box() const
     return m_bounding_box;
 }
 
-BoundingBoxf3 ModelObject::tight_bounding_box(bool include_modifiers) const
-{
-    BoundingBoxf3 bb;
-
-    for (const ModelVolume* vol : this->volumes)
-    {
-        if (include_modifiers || !vol->modifier)
-        {
-            for (const ModelInstance* inst : this->instances)
-            {
-                double c = cos(inst->rotation);
-                double s = sin(inst->rotation);
-
-                for (int f = 0; f < vol->mesh.stl.stats.number_of_facets; ++f)
-                {
-                    const stl_facet& facet = vol->mesh.stl.facet_start[f];
-
-                    for (int i = 0; i < 3; ++i)
-                    {
-                        // original point
-                        const stl_vertex& v = facet.vertex[i];
-                        Pointf3 p((double)v.x, (double)v.y, (double)v.z);
-
-                        // scale
-                        p(0) *= inst->scaling_factor;
-                        p(1) *= inst->scaling_factor;
-                        p(2) *= inst->scaling_factor;
-
-                        // rotate Z
-                        double x = p(0);
-                        double y = p(1);
-                        p(0) = c * x - s * y;
-                        p(1) = s * x + c * y;
-
-                        // translate
-                        p(0) += inst->offset(0);
-                        p(1) += inst->offset(1);
-
-                        bb.merge(p);
-                    }
-                }
-            }
-        }
-    }
-
-    return bb;
-}
-
 // A mesh containing all transformed instances of this object.
 TriangleMesh ModelObject::mesh() const
 {
@@ -726,24 +670,22 @@ void ModelObject::center_around_origin()
         if (! v->modifier)
 			bb.merge(v->mesh.bounding_box());
     
-    // first align to origin on XYZ
-    Vectorf3 vector(-bb.min(0), -bb.min(1), -bb.min(2));
+    // First align to origin on XYZ, then center it on XY.
+    Vec3d size = bb.size();
+    size(2) = 0.;
+    Vec3d shift3 = - bb.min - 0.5 * size;
+    // Unaligned vector, for the Rotation2D to work on Visual Studio 2013.
+    Eigen::Vector2d shift2 = to_2d(shift3);
     
-    // then center it on XY
-    Sizef3 size = bb.size();
-    vector(0) -= size(0)/2;
-    vector(1) -= size(1)/2;
-    
-    this->translate(vector);
-    this->origin_translation += vector;
+    this->translate(shift3);
+    this->origin_translation += shift3;
     
     if (!this->instances.empty()) {
         for (ModelInstance *i : this->instances) {
             // apply rotation and scaling to vector as well before translating instance,
             // in order to leave final position unaltered
-            Vectorf v = - vector.xy();
-            v.rotate(i->rotation);
-            i->offset += v * i->scaling_factor;
+            Eigen::Rotation2Dd rot(i->rotation);
+            i->offset -= rot * shift2 * i->scaling_factor;
         }
         this->invalidate_bounding_box();
     }
@@ -752,39 +694,38 @@ void ModelObject::center_around_origin()
 void ModelObject::translate(coordf_t x, coordf_t y, coordf_t z)
 {
     for (ModelVolume *v : this->volumes)
+    {
         v->mesh.translate(float(x), float(y), float(z));
-    if (m_bounding_box_valid) 
+        v->m_convex_hull.translate(float(x), float(y), float(z));
+    }
+
+    if (m_bounding_box_valid)
         m_bounding_box.translate(x, y, z);
 }
 
-void ModelObject::scale(const Pointf3 &versor)
+void ModelObject::scale(const Vec3d &versor)
 {
     for (ModelVolume *v : this->volumes)
+    {
         v->mesh.scale(versor);
+        v->m_convex_hull.scale(versor);
+    }
     // reset origin translation since it doesn't make sense anymore
-    this->origin_translation = Pointf3(0,0,0);
+    this->origin_translation = Vec3d::Zero();
     this->invalidate_bounding_box();
 }
 
 void ModelObject::rotate(float angle, const Axis &axis)
 {
-    float min_z = FLT_MAX;
     for (ModelVolume *v : this->volumes)
     {
         v->mesh.rotate(angle, axis);
-        min_z = std::min(min_z, v->mesh.stl.stats.min.z);
+        v->m_convex_hull.rotate(angle, axis);
     }
 
-    if (min_z != 0.0f)
-    {
-        // translate the object so that its minimum z lays on the bed
-        for (ModelVolume *v : this->volumes)
-        {
-            v->mesh.translate(0.0f, 0.0f, -min_z);
-        }
-    }
+    center_around_origin();
 
-    this->origin_translation = Pointf3(0, 0, 0);
+    this->origin_translation = Vec3d::Zero();
     this->invalidate_bounding_box();
 }
 
@@ -796,17 +737,22 @@ void ModelObject::transform(const float* matrix3x4)
     for (ModelVolume* v : volumes)
     {
         v->mesh.transform(matrix3x4);
+        v->m_convex_hull.transform(matrix3x4);
     }
 
-    origin_translation = Pointf3(0.0, 0.0, 0.0);
-    invalidate_bounding_box();
+    this->origin_translation = Vec3d::Zero();
+    this->invalidate_bounding_box();
 }
 
 void ModelObject::mirror(const Axis &axis)
 {
     for (ModelVolume *v : this->volumes)
+    {
         v->mesh.mirror(axis);
-    this->origin_translation = Pointf3(0,0,0);
+        v->m_convex_hull.mirror(axis);
+    }
+
+    this->origin_translation = Vec3d::Zero();
     this->invalidate_bounding_box();
 }
 
@@ -910,45 +856,18 @@ void ModelObject::split(ModelObjectPtrs* new_objects)
 
 void ModelObject::check_instances_print_volume_state(const BoundingBoxf3& print_volume)
 {
-    for (ModelVolume* vol : this->volumes)
+    for (const ModelVolume* vol : this->volumes)
     {
         if (!vol->modifier)
         {
             for (ModelInstance* inst : this->instances)
             {
-                BoundingBoxf3 bb;
+                Transform3d m = Transform3d::Identity();
+                m.translate(Vec3d(inst->offset(0), inst->offset(1), 0.0));
+                m.rotate(Eigen::AngleAxisd(inst->rotation, Vec3d::UnitZ()));
+                m.scale(inst->scaling_factor);
 
-                double c = cos(inst->rotation);
-                double s = sin(inst->rotation);
-
-                for (int f = 0; f < vol->mesh.stl.stats.number_of_facets; ++f)
-                {
-                    const stl_facet& facet = vol->mesh.stl.facet_start[f];
-
-                    for (int i = 0; i < 3; ++i)
-                    {
-                        // original point
-                        const stl_vertex& v = facet.vertex[i];
-                        Pointf3 p((double)v.x, (double)v.y, (double)v.z);
-
-                        // scale
-                        p(0) *= inst->scaling_factor;
-                        p(1) *= inst->scaling_factor;
-                        p(2) *= inst->scaling_factor;
-
-                        // rotate Z
-                        double x = p(0);
-                        double y = p(1);
-                        p(0) = c * x - s * y;
-                        p(1) = s * x + c * y;
-
-                        // translate
-                        p(0) += inst->offset(0);
-                        p(1) += inst->offset(1);
-
-                        bb.merge(p);
-                    }
-                }
+                BoundingBoxf3 bb = vol->get_convex_hull().transformed_bounding_box(m);
 
                 if (print_volume.contains(bb))
                     inst->print_volume_state = ModelInstance::PVS_Inside;
@@ -970,7 +889,7 @@ void ModelObject::print_info() const
     TriangleMesh mesh = this->raw_mesh();
     mesh.check_topology();
     BoundingBoxf3 bb = mesh.bounding_box();
-    Sizef3 size = bb.size();
+    Vec3d size = bb.size();
     cout << "size_x = " << size(0) << endl;
     cout << "size_y = " << size(1) << endl;
     cout << "size_z = " << size(2) << endl;
@@ -1031,6 +950,16 @@ ModelMaterial* ModelVolume::assign_unique_material()
     return model->add_material(this->_material_id);
 }
 
+void ModelVolume::calculate_convex_hull()
+{
+    m_convex_hull = mesh.convex_hull_3d();
+}
+
+const TriangleMesh& ModelVolume::get_convex_hull() const
+{
+    return m_convex_hull;
+}
+
 // Split this volume, append the result to the object owning this volume.
 // Return the number of volumes created from this one.
 // This is useful to assign different materials to different volumes of an object.
@@ -1082,30 +1011,20 @@ BoundingBoxf3 ModelInstance::transform_mesh_bounding_box(const TriangleMesh* mes
     for (int i = 0; i < mesh->stl.stats.number_of_facets; ++ i) {
         const stl_facet &facet = mesh->stl.facet_start[i];
         for (int j = 0; j < 3; ++ j) {
-            stl_vertex v = facet.vertex[j];
-            double xold = v.x;
-            double yold = v.y;
-            v.x = float(c * xold - s * yold);
-            v.y = float(s * xold + c * yold);
-            bbox.merge(Pointf3(v.x, v.y, v.z));
+            const stl_vertex &v = facet.vertex[j];
+			bbox.merge(Vec3d(c * v(0) - s * v(1), s * v(0) + c * v(1), v(2)));
         }
     }
     if (! empty(bbox)) {
         // Scale the bounding box uniformly.
         if (std::abs(this->scaling_factor - 1.) > EPSILON) {
-            bbox.min(0) *= float(this->scaling_factor);
-            bbox.min(1) *= float(this->scaling_factor);
-            bbox.min(2) *= float(this->scaling_factor);
-            bbox.max(0) *= float(this->scaling_factor);
-            bbox.max(1) *= float(this->scaling_factor);
-            bbox.max(2) *= float(this->scaling_factor);
+            bbox.min *= this->scaling_factor;
+			bbox.max *= this->scaling_factor;
         }
         // Translate the bounding box.
         if (! dont_translate) {
-            bbox.min(0) += float(this->offset(0));
-            bbox.min(1) += float(this->offset(1));
-            bbox.max(0) += float(this->offset(0));
-            bbox.max(1) += float(this->offset(1));
+            Eigen::Map<Vec2d>(bbox.min.data()) += this->offset;
+            Eigen::Map<Vec2d>(bbox.max.data()) += this->offset;
         }
     }
     return bbox;
@@ -1113,10 +1032,11 @@ BoundingBoxf3 ModelInstance::transform_mesh_bounding_box(const TriangleMesh* mes
 
 BoundingBoxf3 ModelInstance::transform_bounding_box(const BoundingBoxf3 &bbox, bool dont_translate) const
 {
-    auto matrix = Transform3f::Identity();
+    Transform3d matrix = Transform3d::Identity();
     if (!dont_translate)
-        matrix.translate(Vec3f((float)offset(0), (float)offset(1), 0.0f));
-    matrix.rotate(Eigen::AngleAxisf(rotation, Vec3f::UnitZ()));
+        matrix.translate(Vec3d(offset(0), offset(1), 0.0));
+
+    matrix.rotate(Eigen::AngleAxisd(rotation, Vec3d::UnitZ()));
     matrix.scale(scaling_factor);
     return bbox.transformed(matrix);
 }
diff --git a/xs/src/libslic3r/Model.hpp b/xs/src/libslic3r/Model.hpp
index 8dcfff024e..468e6f8337 100644
--- a/xs/src/libslic3r/Model.hpp
+++ b/xs/src/libslic3r/Model.hpp
@@ -84,7 +84,7 @@ public:
         center_around_origin() method. Callers might want to apply the same translation
         to new volumes before adding them to this object in order to preserve alignment
         when user expects that. */
-    Pointf3                 origin_translation;
+    Vec3d                   origin_translation;
     
     Model* get_model() const { return m_model; };
     
@@ -105,9 +105,6 @@ public:
     // This bounding box is being cached.
     const BoundingBoxf3& bounding_box() const;
     void invalidate_bounding_box() { m_bounding_box_valid = false; }
-    // Returns a snug bounding box of the transformed instances.
-    // This bounding box is not being cached.
-    BoundingBoxf3 tight_bounding_box(bool include_modifiers) const;
 
     // A mesh containing all transformed instances of this object.
     TriangleMesh mesh() const;
@@ -120,9 +117,9 @@ public:
     // A snug bounding box around the transformed non-modifier object volumes.
     BoundingBoxf3 instance_bounding_box(size_t instance_idx, bool dont_translate = false) const;
     void center_around_origin();
-    void translate(const Vectorf3 &vector) { this->translate(vector(0), vector(1), vector(2)); }
+    void translate(const Vec3d &vector) { this->translate(vector(0), vector(1), vector(2)); }
     void translate(coordf_t x, coordf_t y, coordf_t z);
-    void scale(const Pointf3 &versor);
+    void scale(const Vec3d &versor);
     void rotate(float angle, const Axis &axis);
     void transform(const float* matrix3x4);
     void mirror(const Axis &axis);
@@ -138,7 +135,7 @@ public:
     void print_info() const;
     
 private:        
-    ModelObject(Model *model) : layer_height_profile_valid(false), m_model(model), m_bounding_box_valid(false) {}
+    ModelObject(Model *model) : layer_height_profile_valid(false), m_model(model), origin_translation(Vec3d::Zero()), m_bounding_box_valid(false) {}
     ModelObject(Model *model, const ModelObject &other, bool copy_volumes = true);
     ModelObject& operator= (ModelObject other);
     void swap(ModelObject &other);
@@ -157,6 +154,10 @@ private:
 class ModelVolume
 {
     friend class ModelObject;
+
+    // The convex hull of this model's mesh.
+    TriangleMesh m_convex_hull;
+
 public:
     std::string name;
     // The triangular model.
@@ -180,19 +181,32 @@ public:
 
     ModelMaterial* assign_unique_material();
     
+    void calculate_convex_hull();
+    const TriangleMesh& get_convex_hull() const;
+
 private:
     // Parent object owning this ModelVolume.
     ModelObject* object;
     t_model_material_id _material_id;
     
-    ModelVolume(ModelObject *object, const TriangleMesh &mesh) : mesh(mesh), modifier(false), object(object) {}
-    ModelVolume(ModelObject *object, TriangleMesh &&mesh) : mesh(std::move(mesh)), modifier(false), object(object) {}
-    ModelVolume(ModelObject *object, const ModelVolume &other) : 
-        name(other.name), mesh(other.mesh), config(other.config), modifier(other.modifier), object(object)
-        { this->material_id(other.material_id()); }
-    ModelVolume(ModelObject *object, const ModelVolume &other, const TriangleMesh &&mesh) : 
+    ModelVolume(ModelObject *object, const TriangleMesh &mesh) : mesh(mesh), modifier(false), object(object)
+    {
+        if (mesh.stl.stats.number_of_facets > 1)
+            calculate_convex_hull();
+    }
+    ModelVolume(ModelObject *object, TriangleMesh &&mesh, TriangleMesh &&convex_hull) : mesh(std::move(mesh)), m_convex_hull(std::move(convex_hull)), modifier(false), object(object) {}
+    ModelVolume(ModelObject *object, const ModelVolume &other) :
+        name(other.name), mesh(other.mesh), m_convex_hull(other.m_convex_hull), config(other.config), modifier(other.modifier), object(object)
+    {
+        this->material_id(other.material_id());
+    }
+    ModelVolume(ModelObject *object, const ModelVolume &other, const TriangleMesh &&mesh) :
         name(other.name), mesh(std::move(mesh)), config(other.config), modifier(other.modifier), object(object)
-        { this->material_id(other.material_id()); }
+    {
+        this->material_id(other.material_id());
+        if (mesh.stl.stats.number_of_facets > 1)
+            calculate_convex_hull();
+    }
 };
 
 // A single instance of a ModelObject.
@@ -213,7 +227,7 @@ public:
 //    Transform3d     transform;
     double rotation;            // Rotation around the Z axis, in radians around mesh center point
     double scaling_factor;
-    Pointf offset;              // in unscaled coordinates
+    Vec2d offset;              // in unscaled coordinates
     
     // flag showing the position of this instance with respect to the print volume (set by Print::validate() using ModelObject::check_instances_print_volume_state())
     EPrintVolumeState print_volume_state;
@@ -235,7 +249,7 @@ private:
     // Parent object, owning this instance.
     ModelObject* object;
 
-    ModelInstance(ModelObject *object) : rotation(0), scaling_factor(1), object(object), print_volume_state(PVS_Inside) {}
+    ModelInstance(ModelObject *object) : rotation(0), scaling_factor(1), offset(Vec2d::Zero()), object(object), print_volume_state(PVS_Inside) {}
     ModelInstance(ModelObject *object, const ModelInstance &other) :
         rotation(other.rotation), scaling_factor(other.scaling_factor), offset(other.offset), object(object), print_volume_state(PVS_Inside) {}
 };
@@ -286,9 +300,7 @@ public:
     bool add_default_instances();
     // Returns approximate axis aligned bounding box of this model
     BoundingBoxf3 bounding_box() const;
-    // Returns tight axis aligned bounding box of this model
-    BoundingBoxf3 transformed_bounding_box() const;
-    void center_instances_around_point(const Pointf &point);
+    void center_instances_around_point(const Vec2d &point);
     void translate(coordf_t x, coordf_t y, coordf_t z) { for (ModelObject *o : this->objects) o->translate(x, y, z); }
     TriangleMesh mesh() const;
     bool arrange_objects(coordf_t dist, const BoundingBoxf* bb = NULL);
diff --git a/xs/src/libslic3r/ModelArrange.hpp b/xs/src/libslic3r/ModelArrange.hpp
index 67825248a8..db18e67318 100644
--- a/xs/src/libslic3r/ModelArrange.hpp
+++ b/xs/src/libslic3r/ModelArrange.hpp
@@ -468,7 +468,7 @@ void applyResult(
         // appropriately
         auto off = item.translation();
         Radians rot = item.rotation();
-        Pointf foff(off.X*SCALING_FACTOR + batch_offset,
+        Vec2d foff(off.X*SCALING_FACTOR + batch_offset,
                     off.Y*SCALING_FACTOR);
 
         // write the tranformation data into the model instance
diff --git a/xs/src/libslic3r/MultiPoint.cpp b/xs/src/libslic3r/MultiPoint.cpp
index 0be95fd556..f44897a046 100644
--- a/xs/src/libslic3r/MultiPoint.cpp
+++ b/xs/src/libslic3r/MultiPoint.cpp
@@ -196,7 +196,7 @@ MultiPoint::_douglas_peucker(const Points &points, const double tolerance)
 
 void MultiPoint3::translate(double x, double y)
 {
-    for (Point3 &p : points) {
+    for (Vec3crd &p : points) {
         p(0) += x;
         p(1) += y;
     }
diff --git a/xs/src/libslic3r/MultiPoint.hpp b/xs/src/libslic3r/MultiPoint.hpp
index c5d35050d5..1fef4083b7 100644
--- a/xs/src/libslic3r/MultiPoint.hpp
+++ b/xs/src/libslic3r/MultiPoint.hpp
@@ -85,7 +85,7 @@ class MultiPoint3
 public:
     Points3 points;
 
-    void append(const Point3& point) { this->points.push_back(point); }
+    void append(const Vec3crd& point) { this->points.push_back(point); }
 
     void translate(double x, double y);
     void translate(const Point& vector);
diff --git a/xs/src/libslic3r/PerimeterGenerator.cpp b/xs/src/libslic3r/PerimeterGenerator.cpp
index 8e7b33cc8b..de8aeeb2ab 100644
--- a/xs/src/libslic3r/PerimeterGenerator.cpp
+++ b/xs/src/libslic3r/PerimeterGenerator.cpp
@@ -243,7 +243,7 @@ void PerimeterGenerator::process()
                 perimeter_spacing / 2;
         // only apply infill overlap if we actually have one perimeter
         if (inset > 0)
-            inset -= scale_(this->config->get_abs_value("infill_overlap", unscale(inset + solid_infill_spacing / 2)));
+            inset -= scale_(this->config->get_abs_value("infill_overlap", unscale<double>(inset + solid_infill_spacing / 2)));
         // simplify infill contours according to resolution
         Polygons pp;
         for (ExPolygon &ex : last)
@@ -420,7 +420,7 @@ static inline ExtrusionPaths thick_polyline_to_extrusion_paths(const ThickPolyli
             path.polyline.append(line.b);
             // Convert from spacing to extrusion width based on the extrusion model
             // of a square extrusion ended with semi circles.
-            flow.width = unscale(w) + flow.height * (1. - 0.25 * PI);
+            flow.width = unscale<float>(w) + flow.height * (1. - 0.25 * PI);
             #ifdef SLIC3R_DEBUG
             printf("  filling %f gap\n", flow.width);
             #endif
diff --git a/xs/src/libslic3r/Point.cpp b/xs/src/libslic3r/Point.cpp
index 10578641e0..ec6c28fe86 100644
--- a/xs/src/libslic3r/Point.cpp
+++ b/xs/src/libslic3r/Point.cpp
@@ -148,33 +148,11 @@ Point Point::projection_onto(const Line &line) const
     return ((line.a - *this).cast<double>().squaredNorm() < (line.b - *this).cast<double>().squaredNorm()) ? line.a : line.b;
 }
 
-std::ostream& operator<<(std::ostream &stm, const Pointf &pointf)
+std::ostream& operator<<(std::ostream &stm, const Vec2d &pointf)
 {
     return stm << pointf(0) << "," << pointf(1);
 }
 
-void Pointf::rotate(double angle)
-{
-    double cur_x = (*this)(0);
-    double cur_y = (*this)(1);
-    double s     = ::sin(angle);
-    double c     = ::cos(angle);
-    (*this)(0) = c * cur_x - s * cur_y;
-    (*this)(1) = c * cur_y + s * cur_x;
-}
-
-void Pointf::rotate(double angle, const Pointf &center)
-{
-    double cur_x = (*this)(0);
-    double cur_y = (*this)(1);
-    double s     = ::sin(angle);
-    double c     = ::cos(angle);
-    double dx    = cur_x - center(0);
-    double dy    = cur_y - center(1);
-    (*this)(0) = center(0) + c * dx - s * dy;
-    (*this)(1) = center(1) + c * dy + s * dx;
-}
-
 namespace int128 {
 
 int orient(const Vec2crd &p1, const Vec2crd &p2, const Vec2crd &p3)
diff --git a/xs/src/libslic3r/Point.hpp b/xs/src/libslic3r/Point.hpp
index 3119511750..b969b98390 100644
--- a/xs/src/libslic3r/Point.hpp
+++ b/xs/src/libslic3r/Point.hpp
@@ -16,19 +16,7 @@ namespace Slic3r {
 class Line;
 class MultiPoint;
 class Point;
-class Point3;
-class Pointf;
-class Pointf3;
-typedef Point                       Vector;
-typedef Point3                      Vector3;
-typedef Pointf                      Vectorf;
-typedef Pointf3                     Vectorf3;
-typedef std::vector<Point>          Points;
-typedef std::vector<Point*>         PointPtrs;
-typedef std::vector<const Point*>   PointConstPtrs;
-typedef std::vector<Point3>         Points3;
-typedef std::vector<Pointf>         Pointfs;
-typedef std::vector<Pointf3>        Pointf3s;
+typedef Point Vector;
 
 // Eigen types, to replace the Slic3r's own types in the future.
 // Vector types with a fixed point coordinate base type.
@@ -43,16 +31,37 @@ typedef Eigen::Matrix<float,    3, 1, Eigen::DontAlign> Vec3f;
 typedef Eigen::Matrix<double,   2, 1, Eigen::DontAlign> Vec2d;
 typedef Eigen::Matrix<double,   3, 1, Eigen::DontAlign> Vec3d;
 
+typedef std::vector<Point>                              Points;
+typedef std::vector<Point*>                             PointPtrs;
+typedef std::vector<const Point*>                       PointConstPtrs;
+typedef std::vector<Vec3crd>                            Points3;
+typedef std::vector<Vec2d>                              Pointfs;
+typedef std::vector<Vec3d>                              Pointf3s;
+
 typedef Eigen::Transform<float,  2, Eigen::Affine, Eigen::DontAlign> Transform2f;
 typedef Eigen::Transform<double, 2, Eigen::Affine, Eigen::DontAlign> Transform2d;
 typedef Eigen::Transform<float,  3, Eigen::Affine, Eigen::DontAlign> Transform3f;
 typedef Eigen::Transform<double, 3, Eigen::Affine, Eigen::DontAlign> Transform3d;
 
+inline bool operator<(const Vec2d &lhs, const Vec2d &rhs) { return lhs(0) < rhs(0) || (lhs(0) == rhs(0) && lhs(1) < rhs(1)); }
+
 inline int64_t cross2(const Vec2i64 &v1, const Vec2i64 &v2) { return v1(0) * v2(1) - v1(1) * v2(0); }
 inline coord_t cross2(const Vec2crd &v1, const Vec2crd &v2) { return v1(0) * v2(1) - v1(1) * v2(0); }
 inline float   cross2(const Vec2f   &v1, const Vec2f   &v2) { return v1(0) * v2(1) - v1(1) * v2(0); }
 inline double  cross2(const Vec2d   &v1, const Vec2d   &v2) { return v1(0) * v2(1) - v1(1) * v2(0); }
 
+inline Vec2crd to_2d(const Vec3crd &pt3) { return Vec2crd(pt3(0), pt3(1)); }
+inline Vec2i64 to_2d(const Vec3i64 &pt3) { return Vec2i64(pt3(0), pt3(1)); }
+inline Vec2f   to_2d(const Vec3f   &pt3) { return Vec2f  (pt3(0), pt3(1)); }
+inline Vec2d   to_2d(const Vec3d   &pt3) { return Vec2d  (pt3(0), pt3(1)); }
+
+inline Vec2d   unscale(coord_t x, coord_t y) { return Vec2d(unscale<double>(x), unscale<double>(y)); }
+inline Vec2d   unscale(const Vec2crd &pt) { return Vec2d(unscale<double>(pt(0)), unscale<double>(pt(1))); }
+inline Vec2d   unscale(const Vec2d   &pt) { return Vec2d(unscale<double>(pt(0)), unscale<double>(pt(1))); }
+inline Vec3d   unscale(coord_t x, coord_t y, coord_t z) { return Vec3d(unscale<double>(x), unscale<double>(y), unscale<double>(z)); }
+inline Vec3d   unscale(const Vec3crd &pt) { return Vec3d(unscale<double>(pt(0)), unscale<double>(pt(1)), unscale<double>(pt(2))); }
+inline Vec3d   unscale(const Vec3d   &pt) { return Vec3d(unscale<double>(pt(0)), unscale<double>(pt(1)), unscale<double>(pt(2))); }
+
 inline std::string to_string(const Vec2crd &pt) { return std::string("[") + std::to_string(pt(0)) + ", " + std::to_string(pt(1)) + "]"; }
 inline std::string to_string(const Vec2d   &pt) { return std::string("[") + std::to_string(pt(0)) + ", " + std::to_string(pt(1)) + "]"; }
 inline std::string to_string(const Vec3crd &pt) { return std::string("[") + std::to_string(pt(0)) + ", " + std::to_string(pt(1)) + ", " + std::to_string(pt(2)) + "]"; }
@@ -210,81 +219,7 @@ private:
     coord_t  m_grid_log2;
 };
 
-class Point3 : public Vec3crd
-{
-public:
-    typedef coord_t coord_type;
-
-    explicit Point3() { (*this)(0) = (*this)(1) = (*this)(2) = 0; }
-    explicit Point3(coord_t x, coord_t y, coord_t z) { (*this)(0) = x; (*this)(1) = y; (*this)(2) = z; }
-    // This constructor allows you to construct Point3 from Eigen expressions
-    template<typename OtherDerived>
-    Point3(const Eigen::MatrixBase<OtherDerived> &other) : Vec3crd(other) {}
-    static Point3 new_scale(coordf_t x, coordf_t y, coordf_t z) { return Point3(coord_t(scale_(x)), coord_t(scale_(y)), coord_t(scale_(z))); }
-
-    // This method allows you to assign Eigen expressions to MyVectorType
-    template<typename OtherDerived>
-    Point3& operator=(const Eigen::MatrixBase<OtherDerived> &other)
-    {
-        this->Vec3crd::operator=(other);
-        return *this;
-    }
-
-    Point xy() const { return Point((*this)(0), (*this)(1)); }
-};
-
-std::ostream& operator<<(std::ostream &stm, const Pointf &pointf);
-
-class Pointf : public Vec2d
-{
-public:
-    typedef coordf_t coord_type;
-
-    explicit Pointf() { (*this)(0) = (*this)(1) = 0.; }
-    explicit Pointf(coordf_t x, coordf_t y) { (*this)(0) = x; (*this)(1) = y; }
-    // This constructor allows you to construct Pointf from Eigen expressions
-    template<typename OtherDerived>
-    Pointf(const Eigen::MatrixBase<OtherDerived> &other) : Vec2d(other) {}
-    static Pointf new_unscale(coord_t x, coord_t y) { return Pointf(unscale(x), unscale(y)); }
-    static Pointf new_unscale(const Point &p) { return Pointf(unscale(p(0)), unscale(p(1))); }
-
-    // This method allows you to assign Eigen expressions to MyVectorType
-    template<typename OtherDerived>
-    Pointf& operator=(const Eigen::MatrixBase<OtherDerived> &other)
-    {
-        this->Vec2d::operator=(other);
-        return *this;
-    }
-
-    void    rotate(double angle);
-    void    rotate(double angle, const Pointf &center);
-
-    bool operator< (const Pointf& rhs) const { return (*this)(0) < rhs(0) || ((*this)(0) == rhs(0) && (*this)(1) < rhs(1)); }
-};
-
-class Pointf3 : public Vec3d
-{
-public:
-    typedef coordf_t coord_type;
-
-    explicit Pointf3() { (*this)(0) = (*this)(1) = (*this)(2) = 0.; }
-    explicit Pointf3(coordf_t x, coordf_t y, coordf_t z) { (*this)(0) = x; (*this)(1) = y; (*this)(2) = z; }
-    // This constructor allows you to construct Pointf from Eigen expressions
-    template<typename OtherDerived>
-    Pointf3(const Eigen::MatrixBase<OtherDerived> &other) : Vec3d(other) {}
-    static Pointf3 new_unscale(coord_t x, coord_t y, coord_t z) { return Pointf3(unscale(x), unscale(y), unscale(z)); }
-    static Pointf3 new_unscale(const Point3& p) { return Pointf3(unscale(p(0)), unscale(p(1)), unscale(p(2))); }
-
-    // This method allows you to assign Eigen expressions to MyVectorType
-    template<typename OtherDerived>
-    Pointf3& operator=(const Eigen::MatrixBase<OtherDerived> &other)
-    {
-        this->Vec3d::operator=(other);
-        return *this;
-    }
-
-    Pointf xy() const { return Pointf((*this)(0), (*this)(1)); }
-};
+std::ostream& operator<<(std::ostream &stm, const Vec2d &pointf);
 
 } // namespace Slic3r
 
diff --git a/xs/src/libslic3r/Polygon.cpp b/xs/src/libslic3r/Polygon.cpp
index f9c82d198a..14248d84ff 100644
--- a/xs/src/libslic3r/Polygon.cpp
+++ b/xs/src/libslic3r/Polygon.cpp
@@ -297,10 +297,10 @@ Point Polygon::point_projection(const Point &point) const
                 dmin = d;
                 proj = pt1;
             }
-            Pointf v1(coordf_t(pt1(0) - pt0(0)), coordf_t(pt1(1) - pt0(1)));
+            Vec2d v1(coordf_t(pt1(0) - pt0(0)), coordf_t(pt1(1) - pt0(1)));
             coordf_t div = v1.squaredNorm();
             if (div > 0.) {
-                Pointf v2(coordf_t(point(0) - pt0(0)), coordf_t(point(1) - pt0(1)));
+                Vec2d v2(coordf_t(point(0) - pt0(0)), coordf_t(point(1) - pt0(1)));
                 coordf_t t = v1.dot(v2) / div;
                 if (t > 0. && t < 1.) {
                     Point foot(coord_t(floor(coordf_t(pt0(0)) + t * v1(0) + 0.5)), coord_t(floor(coordf_t(pt0(1)) + t * v1(1) + 0.5)));
diff --git a/xs/src/libslic3r/Polygon.hpp b/xs/src/libslic3r/Polygon.hpp
index 0091846206..54909352ce 100644
--- a/xs/src/libslic3r/Polygon.hpp
+++ b/xs/src/libslic3r/Polygon.hpp
@@ -24,11 +24,12 @@ public:
     explicit Polygon(const Points &points): MultiPoint(points) {}
     Polygon(const Polygon &other) : MultiPoint(other.points) {}
     Polygon(Polygon &&other) : MultiPoint(std::move(other.points)) {}
-	static Polygon new_scale(std::vector<Pointf> points) { 
-		Points int_points;
-		for (auto pt : points)
-			int_points.push_back(Point::new_scale(pt(0), pt(1)));
-		return Polygon(int_points);
+	static Polygon new_scale(const std::vector<Vec2d> &points) { 
+        Polygon pgn;
+        pgn.points.reserve(points.size());
+        for (const Vec2d &pt : points)
+            pgn.points.emplace_back(Point::new_scale(pt(0), pt(1)));
+		return pgn;
 	}
     Polygon& operator=(const Polygon &other) { points = other.points; return *this; }
     Polygon& operator=(Polygon &&other) { points = std::move(other.points); return *this; }
diff --git a/xs/src/libslic3r/Polyline.hpp b/xs/src/libslic3r/Polyline.hpp
index edd27aaf68..0c934e0748 100644
--- a/xs/src/libslic3r/Polyline.hpp
+++ b/xs/src/libslic3r/Polyline.hpp
@@ -23,12 +23,11 @@ public:
     explicit Polyline(const Point &p1, const Point &p2) { points.reserve(2); points.emplace_back(p1); points.emplace_back(p2); }
     Polyline& operator=(const Polyline &other) { points = other.points; return *this; }
     Polyline& operator=(Polyline &&other) { points = std::move(other.points); return *this; }
-	static Polyline new_scale(std::vector<Pointf> points) {
+	static Polyline new_scale(const std::vector<Vec2d> &points) {
 		Polyline pl;
-		Points int_points;
-		for (auto pt : points)
-			int_points.push_back(Point::new_scale(pt(0), pt(1)));
-		pl.append(int_points);
+		pl.points.reserve(points.size());
+		for (const Vec2d &pt : points)
+			pl.points.emplace_back(Point::new_scale(pt(0), pt(1)));
 		return pl;
     }
     
diff --git a/xs/src/libslic3r/Print.cpp b/xs/src/libslic3r/Print.cpp
index c3f834e33c..9d44cd31e4 100644
--- a/xs/src/libslic3r/Print.cpp
+++ b/xs/src/libslic3r/Print.cpp
@@ -540,7 +540,7 @@ bool Print::has_skirt() const
 std::string Print::validate() const
 {
     BoundingBox bed_box_2D = get_extents(Polygon::new_scale(config.bed_shape.values));
-    BoundingBoxf3 print_volume(Pointf3(unscale(bed_box_2D.min(0)), unscale(bed_box_2D.min(1)), 0.0), Pointf3(unscale(bed_box_2D.max(0)), unscale(bed_box_2D.max(1)), config.max_print_height));
+	BoundingBoxf3 print_volume(unscale(bed_box_2D.min(0), bed_box_2D.min(1), 0.0), unscale(bed_box_2D.max(0), bed_box_2D.max(1), scale_(config.max_print_height)));
     // Allow the objects to protrude below the print bed, only the part of the object above the print bed will be sliced.
     print_volume.min(2) = -1e10;
     unsigned int printable_count = 0;
@@ -728,7 +728,7 @@ BoundingBox Print::bounding_box() const
     for (const PrintObject *object : this->objects)
         for (Point copy : object->_shifted_copies) {
             bb.merge(copy);
-            copy += object->size.xy();
+            copy += to_2d(object->size);
             bb.merge(copy);
         }
     return bb;
@@ -971,7 +971,7 @@ void Print::_make_skirt()
         this->skirt.append(eloop);
         if (this->config.min_skirt_length.value > 0) {
             // The skirt length is limited. Sum the total amount of filament length extruded, in mm.
-            extruded_length[extruder_idx] += unscale(loop.length()) * extruders_e_per_mm[extruder_idx];
+            extruded_length[extruder_idx] += unscale<double>(loop.length()) * extruders_e_per_mm[extruder_idx];
             if (extruded_length[extruder_idx] < this->config.min_skirt_length.value) {
                 // Not extruded enough yet with the current extruder. Add another loop.
                 if (i == 1)
diff --git a/xs/src/libslic3r/Print.hpp b/xs/src/libslic3r/Print.hpp
index a9e54933a5..61e77b5720 100644
--- a/xs/src/libslic3r/Print.hpp
+++ b/xs/src/libslic3r/Print.hpp
@@ -118,7 +118,7 @@ public:
     // so that next call to make_perimeters() performs a union() before computing loops
     bool typed_slices;
 
-    Point3 size;           // XYZ in scaled coordinates
+    Vec3crd size;           // XYZ in scaled coordinates
 
     // scaled coordinates to add to copies (to compensate for the alignment
     // operated when creating the object but still preserving a coherent API
@@ -138,13 +138,13 @@ public:
     const ModelObject*  model_object() const    { return this->_model_object; }
 
     const Points& copies() const { return this->_copies; }
-    bool add_copy(const Pointf &point);
+    bool add_copy(const Vec2d &point);
     bool delete_last_copy();
     bool delete_all_copies() { return this->set_copies(Points()); }
     bool set_copies(const Points &points);
     bool reload_model_instances();
     // since the object is aligned to origin, bounding box coincides with size
-    BoundingBox bounding_box() const { return BoundingBox(Point(0,0), this->size.xy()); }
+    BoundingBox bounding_box() const { return BoundingBox(Point(0,0), to_2d(this->size)); }
 
     // adds region_id, too, if necessary
     void add_region_volume(unsigned int region_id, int volume_id) {
diff --git a/xs/src/libslic3r/PrintConfig.cpp b/xs/src/libslic3r/PrintConfig.cpp
index eadba6f41d..6445b2cd6d 100644
--- a/xs/src/libslic3r/PrintConfig.cpp
+++ b/xs/src/libslic3r/PrintConfig.cpp
@@ -17,9 +17,51 @@ namespace Slic3r {
 #define L(s) Slic3r::I18N::translate(s)
 
 PrintConfigDef::PrintConfigDef()
+{
+    this->init_common_params();
+    this->init_fff_params();
+    this->init_sla_params();
+}
+
+void PrintConfigDef::init_common_params()
 {
     t_optiondef_map &Options = this->options;
+    ConfigOptionDef* def;
+
+    def = this->add("printer_technology", coEnum);
+    def->label = L("Printer technology");
+    def->tooltip = L("Printer technology");
+    def->cli = "printer-technology=s";
+    def->enum_keys_map = &ConfigOptionEnum<PrinterTechnology>::get_enum_values();
+    def->enum_values.push_back("FFF");
+    def->enum_values.push_back("SLA");
+    def->default_value = new ConfigOptionEnum<PrinterTechnology>(ptFFF);
+
+    def = this->add("bed_shape", coPoints);
+    def->label = L("Bed shape");
+    def->default_value = new ConfigOptionPoints{ Vec2d(0, 0), Vec2d(200, 0), Vec2d(200, 200), Vec2d(0, 200) };
     
+    def = this->add("layer_height", coFloat);
+    def->label = L("Layer height");
+    def->category = L("Layers and Perimeters");
+    def->tooltip = L("This setting controls the height (and thus the total number) of the slices/layers. "
+                   "Thinner layers give better accuracy but take more time to print.");
+    def->sidetext = L("mm");
+    def->cli = "layer-height=f";
+    def->min = 0;
+    def->default_value = new ConfigOptionFloat(0.3);
+
+    def = this->add("max_print_height", coFloat);
+    def->label = L("Max print height");
+    def->tooltip = L("Set this to the maximum height that can be reached by your extruder while printing.");
+    def->sidetext = L("mm");
+    def->cli = "max-print-height=f";
+    def->default_value = new ConfigOptionFloat(200.0);
+}
+
+void PrintConfigDef::init_fff_params()
+{
+    t_optiondef_map &Options = this->options;
     ConfigOptionDef* def;
 
     // Maximum extruder temperature, bumped to 1500 to support printing of glass.
@@ -33,10 +75,6 @@ PrintConfigDef::PrintConfigDef()
     def->cli = "avoid-crossing-perimeters!";
     def->default_value = new ConfigOptionBool(false);
 
-    def = this->add("bed_shape", coPoints);
-	def->label = L("Bed shape");
-    def->default_value = new ConfigOptionPoints { Pointf(0,0), Pointf(200,0), Pointf(200,200), Pointf(0,200) };
-    
     def = this->add("bed_temperature", coInts);
     def->label = L("Other layers");
     def->tooltip = L("Bed temperature for layers after the first one. "
@@ -392,7 +430,7 @@ PrintConfigDef::PrintConfigDef()
                    "from the XY coordinate).");
     def->sidetext = L("mm");
     def->cli = "extruder-offset=s@";
-    def->default_value = new ConfigOptionPoints { Pointf(0,0) };
+    def->default_value = new ConfigOptionPoints { Vec2d(0,0) };
 
     def = this->add("extrusion_axis", coString);
     def->label = L("Extrusion axis");
@@ -906,16 +944,6 @@ PrintConfigDef::PrintConfigDef()
     def->height = 50;
     def->default_value = new ConfigOptionString("");
 
-    def = this->add("layer_height", coFloat);
-    def->label = L("Layer height");
-    def->category = L("Layers and Perimeters");
-    def->tooltip = L("This setting controls the height (and thus the total number) of the slices/layers. "
-                   "Thinner layers give better accuracy but take more time to print.");
-    def->sidetext = L("mm");
-    def->cli = "layer-height=f";
-    def->min = 0;
-    def->default_value = new ConfigOptionFloat(0.3);
-
     def = this->add("remaining_times", coBool);
     def->label = L("Supports remaining times");
     def->tooltip = L("Emit M73 P[percent printed] R[remaining time in minutes] at 1 minute"
@@ -1036,13 +1064,6 @@ PrintConfigDef::PrintConfigDef()
     def->min = 0;
     def->default_value = new ConfigOptionFloats { 0. };
 
-    def = this->add("max_print_height", coFloat);
-    def->label = L("Max print height");
-    def->tooltip = L("Set this to the maximum height that can be reached by your extruder while printing.");
-    def->sidetext = L("mm");
-    def->cli = "max-print-height=f";
-    def->default_value = new ConfigOptionFloat(200.0);
-
     def = this->add("max_print_speed", coFloat);
     def->label = L("Max print speed");
     def->tooltip = L("When setting other speed settings to 0 Slic3r will autocalculate the optimal speed "
@@ -1137,25 +1158,37 @@ PrintConfigDef::PrintConfigDef()
     def->cli = "nozzle-diameter=f@";
     def->default_value = new ConfigOptionFloats { 0.5 };
 
-    def = this->add("octoprint_apikey", coString);
-    def->label = L("API Key");
-    def->tooltip = L("Slic3r can upload G-code files to OctoPrint. This field should contain "
-                   "the API Key required for authentication.");
-    def->cli = "octoprint-apikey=s";
+    def = this->add("host_type", coEnum);
+    def->label = L("Host Type");
+    def->tooltip = L("Slic3r can upload G-code files to a printer host. This field must contain "
+                   "the kind of the host.");
+    def->cli = "host-type=s";
+    def->enum_keys_map = &ConfigOptionEnum<PrintHostType>::get_enum_values();
+    def->enum_values.push_back("octoprint");
+    def->enum_values.push_back("duet");
+    def->enum_labels.push_back("OctoPrint");
+    def->enum_labels.push_back("Duet");
+    def->default_value = new ConfigOptionEnum<PrintHostType>(htOctoPrint);
+
+    def = this->add("printhost_apikey", coString);
+    def->label = L("API Key / Password");
+    def->tooltip = L("Slic3r can upload G-code files to a printer host. This field should contain "
+                   "the API Key or the password required for authentication.");
+    def->cli = "printhost-apikey=s";
     def->default_value = new ConfigOptionString("");
     
-    def = this->add("octoprint_cafile", coString);
+    def = this->add("printhost_cafile", coString);
     def->label = "HTTPS CA file";
     def->tooltip = "Custom CA certificate file can be specified for HTTPS OctoPrint connections, in crt/pem format. "
                    "If left blank, the default OS CA certificate repository is used.";
-    def->cli = "octoprint-cafile=s";
+    def->cli = "printhost-cafile=s";
     def->default_value = new ConfigOptionString("");
 
-    def = this->add("octoprint_host", coString);
+    def = this->add("print_host", coString);
     def->label = L("Hostname, IP or URL");
-    def->tooltip = L("Slic3r can upload G-code files to OctoPrint. This field should contain "
-                   "the hostname, IP address or URL of the OctoPrint instance.");
-    def->cli = "octoprint-host=s";
+    def->tooltip = L("Slic3r can upload G-code files to a printer host. This field should contain "
+                   "the hostname, IP address or URL of the printer host instance.");
+    def->cli = "print-host=s";
     def->default_value = new ConfigOptionString("");
 
     def = this->add("only_retract_when_crossing_perimeters", coBool);
@@ -2121,6 +2154,103 @@ PrintConfigDef::PrintConfigDef()
     def->default_value = new ConfigOptionFloat(35.);
 }
 
+void PrintConfigDef::init_sla_params()
+{
+    t_optiondef_map &Options = this->options;    
+    ConfigOptionDef* def;
+
+    // SLA Printer settings
+    def = this->add("display_width", coFloat);
+    def->label = L("Display width");
+    def->tooltip = L("Width of the display");
+    def->cli = "display-width=f";
+    def->min = 1;
+    def->default_value = new ConfigOptionFloat(150.);
+
+    def = this->add("display_height", coFloat);
+    def->label = L("Display height");
+    def->tooltip = L("Height of the display");
+    def->cli = "display-height=f";
+    def->min = 1;
+    def->default_value = new ConfigOptionFloat(100.);
+
+    def = this->add("display_pixels_x", coInt);
+    def->full_label = L("Number of pixels in");
+    def->label = ("X");
+    def->tooltip = L("Number of pixels in X");
+    def->cli = "display-pixels-x=i";
+    def->min = 100;
+    def->default_value = new ConfigOptionInt(2000);
+
+    def = this->add("display_pixels_y", coInt);
+    def->label = ("Y");
+    def->tooltip = L("Number of pixels in Y");
+    def->cli = "display-pixels-y=i";
+    def->min = 100;
+    def->default_value = new ConfigOptionInt(1000);
+
+    def = this->add("printer_correction", coFloats);
+    def->full_label = L("Printer scaling correction");
+    def->tooltip  = L("Printer scaling correction");
+    def->min = 0;
+    def->default_value = new ConfigOptionFloats( { 1., 1., 1. } );
+
+    // SLA Material settings.
+    def = this->add("initial_layer_height", coFloat);
+    def->label = L("Initial layer height");
+    def->tooltip = L("Initial layer height");
+    def->sidetext = L("mm");
+    def->cli = "initial-layer-height=f";
+    def->min = 0;
+    def->default_value = new ConfigOptionFloat(0.3);
+
+    def = this->add("exposure_time", coFloat);
+    def->label = L("Exposure time");
+    def->tooltip = L("Exposure time");
+    def->sidetext = L("s");
+    def->cli = "exposure-time=f";
+    def->min = 0;
+    def->default_value = new ConfigOptionFloat(10);
+
+    def = this->add("initial_exposure_time", coFloat);
+    def->label = L("Initial exposure time");
+    def->tooltip = L("Initial exposure time");
+    def->sidetext = L("s");
+    def->cli = "initial-exposure-time=f";
+    def->min = 0;
+    def->default_value = new ConfigOptionFloat(15);
+
+    def = this->add("material_correction_printing", coFloats);
+    def->full_label = L("Correction for expansion when printing");
+    def->tooltip  = L("Correction for expansion when printing");
+    def->min = 0;
+    def->default_value = new ConfigOptionFloats( { 1. , 1., 1. } );
+
+    def = this->add("material_correction_curing", coFloats);
+    def->full_label = L("Correction for expansion after curing");
+    def->tooltip  = L("Correction for expansion after curing");
+    def->min = 0;
+    def->default_value = new ConfigOptionFloats( { 1. , 1., 1. } );
+
+    def = this->add("material_notes", coString);
+    def->label = L("SLA print material notes");
+    def->tooltip = L("You can put your notes regarding the SLA print material here.");
+    def->cli = "material-notes=s";
+    def->multiline = true;
+    def->full_width = true;
+    def->height = 130;
+    def->default_value = new ConfigOptionString("");
+
+    def = this->add("default_sla_material_profile", coString);
+    def->label = L("Default SLA material profile");
+    def->tooltip = L("Default print profile associated with the current printer profile. "
+                   "On selection of the current printer profile, this print profile will be activated.");
+    def->default_value = new ConfigOptionString();
+
+    def = this->add("sla_material_settings_id", coString);
+    def->default_value = new ConfigOptionString("");
+}
+
 void PrintConfigDef::handle_legacy(t_config_option_key &opt_key, std::string &value)
 {
     // handle legacy options
@@ -2153,10 +2283,6 @@ void PrintConfigDef::handle_legacy(t_config_option_key &opt_key, std::string &va
         std::ostringstream oss;
         oss << "0x0," << p.value(0) << "x0," << p.value(0) << "x" << p.value(1) << ",0x" << p.value(1);
         value = oss.str();
-// Maybe one day we will rename octoprint_host to print_host as it has been done in the upstream Slic3r.
-// Commenting this out fixes github issue #869 for now.
-//    } else if (opt_key == "octoprint_host" && !value.empty()) {
-//        opt_key = "print_host";
     } else if ((opt_key == "perimeter_acceleration" && value == "25")
         || (opt_key == "infill_acceleration" && value == "50")) {
         /*  For historical reasons, the world's full of configs having these very low values;
@@ -2167,6 +2293,12 @@ void PrintConfigDef::handle_legacy(t_config_option_key &opt_key, std::string &va
     } else if (opt_key == "support_material_pattern" && value == "pillars") {
         // Slic3r PE does not support the pillars. They never worked well.
         value = "rectilinear";
+    } else if (opt_key == "octoprint_host") {
+        opt_key = "print_host";
+    } else if (opt_key == "octoprint_cafile") {
+        opt_key = "printhost_cafile";
+    } else if (opt_key == "octoprint_apikey") {
+        opt_key = "printhost_apikey";
     }
     
     // Ignore the following obsolete configuration keys:
@@ -2176,9 +2308,6 @@ void PrintConfigDef::handle_legacy(t_config_option_key &opt_key, std::string &va
         "standby_temperature", "scale", "rotate", "duplicate", "duplicate_grid",
         "start_perimeters_at_concave_points", "start_perimeters_at_non_overhang", "randomize_start", 
         "seal_position", "vibration_limit", "bed_size", 
-        // Maybe one day we will rename octoprint_host to print_host as it has been done in the upstream Slic3r.
-        // Commenting this out fixes github issue #869 for now.
-        // "octoprint_host",
         "print_center", "g0", "threads", "pressure_advance", "wipe_tower_per_color_wipe"
     };
 
@@ -2188,7 +2317,6 @@ void PrintConfigDef::handle_legacy(t_config_option_key &opt_key, std::string &va
     }
     
     if (! print_config_def.has(opt_key)) {
-        //printf("Unknown option %s\n", opt_key.c_str());
         opt_key = "";
         return;
     }
@@ -2446,4 +2574,8 @@ StaticPrintConfig::StaticCache<class Slic3r::PrintConfig>       PrintConfig::s_c
 StaticPrintConfig::StaticCache<class Slic3r::HostConfig>        HostConfig::s_cache_HostConfig;
 StaticPrintConfig::StaticCache<class Slic3r::FullPrintConfig>   FullPrintConfig::s_cache_FullPrintConfig;
 
+StaticPrintConfig::StaticCache<class Slic3r::SLAMaterialConfig>  SLAMaterialConfig::s_cache_SLAMaterialConfig;
+StaticPrintConfig::StaticCache<class Slic3r::SLAPrinterConfig>   SLAPrinterConfig::s_cache_SLAPrinterConfig;
+StaticPrintConfig::StaticCache<class Slic3r::SLAFullPrintConfig> SLAFullPrintConfig::s_cache_SLAFullPrintConfig;
+
 }
diff --git a/xs/src/libslic3r/PrintConfig.hpp b/xs/src/libslic3r/PrintConfig.hpp
index 074a0e6119..7845c138e0 100644
--- a/xs/src/libslic3r/PrintConfig.hpp
+++ b/xs/src/libslic3r/PrintConfig.hpp
@@ -22,11 +22,23 @@
 
 namespace Slic3r {
 
+enum PrinterTechnology
+{
+    // Fused Filament Fabrication
+    ptFFF,
+    // Stereolitography
+    ptSLA,
+};
+
 enum GCodeFlavor {
     gcfRepRap, gcfRepetier, gcfTeacup, gcfMakerWare, gcfMarlin, gcfSailfish, gcfMach3, gcfMachinekit, 
     gcfSmoothie, gcfNoExtrusion,
 };
 
+enum PrintHostType {
+    htOctoPrint, htDuet,
+};
+
 enum InfillPattern {
     ipRectilinear, ipGrid, ipTriangles, ipStars, ipCubic, ipLine, ipConcentric, ipHoneycomb, ip3DHoneycomb,
     ipGyroid, ipHilbertCurve, ipArchimedeanChords, ipOctagramSpiral,
@@ -44,7 +56,16 @@ enum FilamentType {
     ftPLA, ftABS, ftPET, ftHIPS, ftFLEX, ftSCAFF, ftEDGE, ftNGEN, ftPVA
 };
 
-template<> inline t_config_enum_values& ConfigOptionEnum<GCodeFlavor>::get_enum_values() {
+template<> inline const t_config_enum_values& ConfigOptionEnum<PrinterTechnology>::get_enum_values() {
+    static t_config_enum_values keys_map;
+    if (keys_map.empty()) {
+        keys_map["FFF"]             = ptFFF;
+        keys_map["SLA"]             = ptSLA;
+    }
+    return keys_map;
+}
+
+template<> inline const t_config_enum_values& ConfigOptionEnum<GCodeFlavor>::get_enum_values() {
     static t_config_enum_values keys_map;
     if (keys_map.empty()) {
         keys_map["reprap"]          = gcfRepRap;
@@ -61,7 +82,16 @@ template<> inline t_config_enum_values& ConfigOptionEnum<GCodeFlavor>::get_enum_
     return keys_map;
 }
 
-template<> inline t_config_enum_values& ConfigOptionEnum<InfillPattern>::get_enum_values() {
+template<> inline const t_config_enum_values& ConfigOptionEnum<PrintHostType>::get_enum_values() {
+    static t_config_enum_values keys_map;
+    if (keys_map.empty()) {
+        keys_map["octoprint"]       = htOctoPrint;
+        keys_map["duet"]            = htDuet;
+    }
+    return keys_map;
+}
+
+template<> inline const t_config_enum_values& ConfigOptionEnum<InfillPattern>::get_enum_values() {
     static t_config_enum_values keys_map;
     if (keys_map.empty()) {
         keys_map["rectilinear"]         = ipRectilinear;
@@ -81,7 +111,7 @@ template<> inline t_config_enum_values& ConfigOptionEnum<InfillPattern>::get_enu
     return keys_map;
 }
 
-template<> inline t_config_enum_values& ConfigOptionEnum<SupportMaterialPattern>::get_enum_values() {
+template<> inline const t_config_enum_values& ConfigOptionEnum<SupportMaterialPattern>::get_enum_values() {
     static t_config_enum_values keys_map;
     if (keys_map.empty()) {
         keys_map["rectilinear"]         = smpRectilinear;
@@ -91,7 +121,7 @@ template<> inline t_config_enum_values& ConfigOptionEnum<SupportMaterialPattern>
     return keys_map;
 }
 
-template<> inline t_config_enum_values& ConfigOptionEnum<SeamPosition>::get_enum_values() {
+template<> inline const t_config_enum_values& ConfigOptionEnum<SeamPosition>::get_enum_values() {
     static t_config_enum_values keys_map;
     if (keys_map.empty()) {
         keys_map["random"]              = spRandom;
@@ -102,7 +132,7 @@ template<> inline t_config_enum_values& ConfigOptionEnum<SeamPosition>::get_enum
     return keys_map;
 }
 
-template<> inline t_config_enum_values& ConfigOptionEnum<FilamentType>::get_enum_values() {
+template<> inline const t_config_enum_values& ConfigOptionEnum<FilamentType>::get_enum_values() {
     static t_config_enum_values keys_map;
     if (keys_map.empty()) {
         keys_map["PLA"]             = ftPLA;
@@ -126,6 +156,11 @@ public:
     PrintConfigDef();
 
     static void handle_legacy(t_config_option_key &opt_key, std::string &value);
+
+private:
+    void init_common_params();
+    void init_fff_params();
+    void init_sla_params();
 };
 
 // The one and only global definition of SLic3r configuration options.
@@ -801,18 +836,20 @@ class HostConfig : public StaticPrintConfig
 {
     STATIC_PRINT_CONFIG_CACHE(HostConfig)
 public:
-    ConfigOptionString              octoprint_host;
-    ConfigOptionString              octoprint_apikey;
-    ConfigOptionString              octoprint_cafile;
+    ConfigOptionEnum<PrintHostType> host_type;
+    ConfigOptionString              print_host;
+    ConfigOptionString              printhost_apikey;
+    ConfigOptionString              printhost_cafile;
     ConfigOptionString              serial_port;
     ConfigOptionInt                 serial_speed;
     
 protected:
     void initialize(StaticCacheBase &cache, const char *base_ptr)
     {
-        OPT_PTR(octoprint_host);
-        OPT_PTR(octoprint_apikey);
-        OPT_PTR(octoprint_cafile);
+        OPT_PTR(host_type);
+        OPT_PTR(print_host);
+        OPT_PTR(printhost_apikey);
+        OPT_PTR(printhost_cafile);
         OPT_PTR(serial_port);
         OPT_PTR(serial_speed);
     }
@@ -844,6 +881,73 @@ protected:
     }
 };
 
+class SLAMaterialConfig : public StaticPrintConfig
+{
+    STATIC_PRINT_CONFIG_CACHE(SLAMaterialConfig)
+public:
+    ConfigOptionFloat                       layer_height;
+    ConfigOptionFloat                       initial_layer_height;
+    ConfigOptionFloat                       exposure_time;
+    ConfigOptionFloat                       initial_exposure_time;
+    ConfigOptionFloats                      material_correction_printing;
+    ConfigOptionFloats                      material_correction_curing;
+protected:
+    void initialize(StaticCacheBase &cache, const char *base_ptr)
+    {
+        OPT_PTR(layer_height);
+        OPT_PTR(initial_layer_height);
+        OPT_PTR(exposure_time);
+        OPT_PTR(initial_exposure_time);
+        OPT_PTR(material_correction_printing);
+        OPT_PTR(material_correction_curing);
+    }
+};
+
+class SLAPrinterConfig : public StaticPrintConfig
+{
+    STATIC_PRINT_CONFIG_CACHE(SLAPrinterConfig)
+public:
+    ConfigOptionEnum<PrinterTechnology>     printer_technology;
+    ConfigOptionPoints                      bed_shape;
+    ConfigOptionFloat                       max_print_height;
+    ConfigOptionFloat                       display_width;
+    ConfigOptionFloat                       display_height;
+    ConfigOptionInt                         display_pixels_x;
+    ConfigOptionInt                         display_pixels_y;
+    ConfigOptionFloats                      printer_correction;
+protected:
+    void initialize(StaticCacheBase &cache, const char *base_ptr)
+    {
+        OPT_PTR(printer_technology);
+        OPT_PTR(bed_shape);
+        OPT_PTR(max_print_height);
+        OPT_PTR(display_width);
+        OPT_PTR(display_height);
+        OPT_PTR(display_pixels_x);
+        OPT_PTR(display_pixels_y);
+        OPT_PTR(printer_correction);
+    }
+};
+
+class SLAFullPrintConfig : public SLAPrinterConfig, public SLAMaterialConfig
+{
+    STATIC_PRINT_CONFIG_CACHE_DERIVED(SLAFullPrintConfig)
+    SLAFullPrintConfig() : SLAPrinterConfig(0), SLAMaterialConfig(0) { initialize_cache(); *this = s_cache_SLAFullPrintConfig.defaults(); }
+
+public:
+    // Validate the SLAFullPrintConfig. Returns an empty string on success, otherwise an error message is returned.
+//    std::string                 validate();
+
+protected:
+    // Protected constructor to be called to initialize ConfigCache::m_default.
+    SLAFullPrintConfig(int) : SLAPrinterConfig(0), SLAMaterialConfig(0) {}
+    void initialize(StaticCacheBase &cache, const char *base_ptr)
+    {
+        this->SLAPrinterConfig ::initialize(cache, base_ptr);
+        this->SLAMaterialConfig::initialize(cache, base_ptr);
+    }
+};
+
 #undef STATIC_PRINT_CONFIG_CACHE
 #undef STATIC_PRINT_CONFIG_CACHE_BASE
 #undef STATIC_PRINT_CONFIG_CACHE_DERIVED
diff --git a/xs/src/libslic3r/PrintObject.cpp b/xs/src/libslic3r/PrintObject.cpp
index 8df7111963..d03b994168 100644
--- a/xs/src/libslic3r/PrintObject.cpp
+++ b/xs/src/libslic3r/PrintObject.cpp
@@ -38,6 +38,7 @@ PrintObject::PrintObject(Print* print, ModelObject* model_object, const Bounding
     typed_slices(false),
     _print(print),
     _model_object(model_object),
+    size(Vec3crd::Zero()),
     layer_height_profile_valid(false)
 {
     // Compute the translation to be applied to our meshes so that we work with smaller coordinates
@@ -50,8 +51,7 @@ PrintObject::PrintObject(Print* print, ModelObject* model_object, const Bounding
         // (copies are expressed in G-code coordinates and this translation is not publicly exposed).
         this->_copies_shift = Point::new_scale(modobj_bbox.min(0), modobj_bbox.min(1));
         // Scale the object size and store it
-        Pointf3 size = modobj_bbox.size();
-        this->size = Point3::new_scale(size(0), size(1), size(2));
+        this->size = (modobj_bbox.size() * (1. / SCALING_FACTOR)).cast<coord_t>();
     }
     
     this->reload_model_instances();
@@ -59,7 +59,7 @@ PrintObject::PrintObject(Print* print, ModelObject* model_object, const Bounding
     this->layer_height_profile = model_object->layer_height_profile;
 }
 
-bool PrintObject::add_copy(const Pointf &point)
+bool PrintObject::add_copy(const Vec2d &point)
 {
     Points points = this->_copies;
     points.push_back(Point::new_scale(point(0), point(1)));
@@ -1121,7 +1121,7 @@ SlicingParameters PrintObject::slicing_parameters() const
 {
     return SlicingParameters::create_from_config(
         this->print()->config, this->config, 
-        unscale(this->size(2)), this->print()->object_extruders());
+        unscale<double>(this->size(2)), this->print()->object_extruders());
 }
 
 bool PrintObject::update_layer_height_profile(std::vector<coordf_t> &layer_height_profile) const
@@ -1335,7 +1335,7 @@ std::vector<ExPolygons> PrintObject::_slice_region(size_t region_id, const std::
                 // consider the first one
                 this->model_object()->instances.front()->transform_mesh(&mesh, true);
                 // align mesh to Z = 0 (it should be already aligned actually) and apply XY shift
-                mesh.translate(- float(unscale(this->_copies_shift(0))), - float(unscale(this->_copies_shift(1))), -float(this->model_object()->bounding_box().min(2)));
+                mesh.translate(- unscale<float>(this->_copies_shift(0)), - unscale<float>(this->_copies_shift(1)), - float(this->model_object()->bounding_box().min(2)));
                 // perform actual slicing
                 TriangleMeshSlicer mslicer(&mesh);
                 mslicer.slice(z, &layers);
diff --git a/xs/src/libslic3r/SVG.cpp b/xs/src/libslic3r/SVG.cpp
index d3a0eed36b..03f55802ef 100644
--- a/xs/src/libslic3r/SVG.cpp
+++ b/xs/src/libslic3r/SVG.cpp
@@ -3,7 +3,7 @@
 
 #include <boost/nowide/cstdio.hpp>
 
-#define COORD(x) ((float)unscale((x))*10)
+#define COORD(x) (unscale<float>((x))*10)
 
 namespace Slic3r {
 
@@ -58,8 +58,8 @@ SVG::draw(const Line &line, std::string stroke, coordf_t stroke_width)
 
 void SVG::draw(const ThickLine &line, const std::string &fill, const std::string &stroke, coordf_t stroke_width)
 {
-    Pointf dir(line.b(0)-line.a(0), line.b(1)-line.a(1));
-    Pointf perp(-dir(1), dir(0));
+    Vec2d dir(line.b(0)-line.a(0), line.b(1)-line.a(1));
+    Vec2d perp(-dir(1), dir(0));
     coordf_t len = sqrt(perp(0)*perp(0) + perp(1)*perp(1));
     coordf_t da  = coordf_t(0.5)*line.a_width/len;
     coordf_t db  = coordf_t(0.5)*line.b_width/len;
diff --git a/xs/src/libslic3r/Slicing.cpp b/xs/src/libslic3r/Slicing.cpp
index d745a803c0..1bc38502b5 100644
--- a/xs/src/libslic3r/Slicing.cpp
+++ b/xs/src/libslic3r/Slicing.cpp
@@ -561,15 +561,15 @@ int generate_layer_height_texture(
 	void *data, int rows, int cols, bool level_of_detail_2nd_level)
 {
 // https://github.com/aschn/gnuplot-colorbrewer
-    std::vector<Point3> palette_raw;
-    palette_raw.push_back(Point3(0x01A, 0x098, 0x050));
-    palette_raw.push_back(Point3(0x066, 0x0BD, 0x063));
-    palette_raw.push_back(Point3(0x0A6, 0x0D9, 0x06A));
-    palette_raw.push_back(Point3(0x0D9, 0x0F1, 0x0EB));
-    palette_raw.push_back(Point3(0x0FE, 0x0E6, 0x0EB));
-    palette_raw.push_back(Point3(0x0FD, 0x0AE, 0x061));
-    palette_raw.push_back(Point3(0x0F4, 0x06D, 0x043));
-    palette_raw.push_back(Point3(0x0D7, 0x030, 0x027));
+    std::vector<Vec3crd> palette_raw;
+    palette_raw.push_back(Vec3crd(0x01A, 0x098, 0x050));
+    palette_raw.push_back(Vec3crd(0x066, 0x0BD, 0x063));
+    palette_raw.push_back(Vec3crd(0x0A6, 0x0D9, 0x06A));
+    palette_raw.push_back(Vec3crd(0x0D9, 0x0F1, 0x0EB));
+    palette_raw.push_back(Vec3crd(0x0FE, 0x0E6, 0x0EB));
+    palette_raw.push_back(Vec3crd(0x0FD, 0x0AE, 0x061));
+    palette_raw.push_back(Vec3crd(0x0F4, 0x06D, 0x043));
+    palette_raw.push_back(Vec3crd(0x0D7, 0x030, 0x027));
 
     // Clear the main texture and the 2nd LOD level.
 //	memset(data, 0, rows * cols * (level_of_detail_2nd_level ? 5 : 4));
@@ -600,14 +600,14 @@ int generate_layer_height_texture(
             int idx1 = clamp(0, int(palette_raw.size() - 1), int(floor(idxf)));
             int idx2 = std::min(int(palette_raw.size() - 1), idx1 + 1);
 			coordf_t t = idxf - coordf_t(idx1);
-            const Point3 &color1 = palette_raw[idx1];
-            const Point3 &color2 = palette_raw[idx2];
+            const Vec3crd &color1 = palette_raw[idx1];
+            const Vec3crd &color2 = palette_raw[idx2];
             coordf_t z = cell_to_z * coordf_t(cell);
 			assert(z >= lo && z <= hi);
             // Intensity profile to visualize the layers.
             coordf_t intensity = cos(M_PI * 0.7 * (mid - z) / h);
             // Color mapping from layer height to RGB.
-            Pointf3 color(
+            Vec3d color(
                 intensity * lerp(coordf_t(color1(0)), coordf_t(color2(0)), t), 
                 intensity * lerp(coordf_t(color1(1)), coordf_t(color2(1)), t),
                 intensity * lerp(coordf_t(color1(2)), coordf_t(color2(2)), t));
@@ -636,10 +636,10 @@ int generate_layer_height_texture(
                 int idx1 = clamp(0, int(palette_raw.size() - 1), int(floor(idxf)));
                 int idx2 = std::min(int(palette_raw.size() - 1), idx1 + 1);
     			coordf_t t = idxf - coordf_t(idx1);
-                const Point3 &color1 = palette_raw[idx1];
-                const Point3 &color2 = palette_raw[idx2];
+                const Vec3crd &color1 = palette_raw[idx1];
+                const Vec3crd &color2 = palette_raw[idx2];
                 // Color mapping from layer height to RGB.
-                Pointf3 color(
+                Vec3d color(
                     lerp(coordf_t(color1(0)), coordf_t(color2(0)), t), 
                     lerp(coordf_t(color1(1)), coordf_t(color2(1)), t),
                     lerp(coordf_t(color1(2)), coordf_t(color2(2)), t));
diff --git a/xs/src/libslic3r/SlicingAdaptive.cpp b/xs/src/libslic3r/SlicingAdaptive.cpp
index ff0da76365..2ef4aec8c6 100644
--- a/xs/src/libslic3r/SlicingAdaptive.cpp
+++ b/xs/src/libslic3r/SlicingAdaptive.cpp
@@ -15,8 +15,8 @@ void SlicingAdaptive::clear()
 std::pair<float, float> face_z_span(const stl_facet *f)
 {
 	return std::pair<float, float>(
-		std::min(std::min(f->vertex[0].z, f->vertex[1].z), f->vertex[2].z),
-		std::max(std::max(f->vertex[0].z, f->vertex[1].z), f->vertex[2].z));
+		std::min(std::min(f->vertex[0](2), f->vertex[1](2)), f->vertex[2](2)),
+		std::max(std::max(f->vertex[0](2), f->vertex[1](2)), f->vertex[2](2)));
 }
 
 void SlicingAdaptive::prepare()
@@ -40,7 +40,7 @@ void SlicingAdaptive::prepare()
 	// 3) Generate Z components of the facet normals.
 	m_face_normal_z.assign(m_faces.size(), 0.f);
     for (size_t iface = 0; iface < m_faces.size(); ++ iface)
-    	m_face_normal_z[iface] = m_faces[iface]->normal.z;
+    	m_face_normal_z[iface] = m_faces[iface]->normal(2);
 }
 
 float SlicingAdaptive::cusp_height(float z, float cusp_value, int &current_facet)
diff --git a/xs/src/libslic3r/SupportMaterial.cpp b/xs/src/libslic3r/SupportMaterial.cpp
index 98f41a6639..4b7e789764 100644
--- a/xs/src/libslic3r/SupportMaterial.cpp
+++ b/xs/src/libslic3r/SupportMaterial.cpp
@@ -2057,8 +2057,8 @@ void LoopInterfaceProcessor::generate(MyLayerExtruded &top_contact_layer, const
                         const Point &p1 = *(it-1);
                         const Point &p2 = *it;
                         // Intersection of a ray (p1, p2) with a circle placed at center_last, with radius of circle_distance.
-                        const Pointf v_seg(coordf_t(p2(0)) - coordf_t(p1(0)), coordf_t(p2(1)) - coordf_t(p1(1)));
-                        const Pointf v_cntr(coordf_t(p1(0) - center_last(0)), coordf_t(p1(1) - center_last(1)));
+                        const Vec2d v_seg(coordf_t(p2(0)) - coordf_t(p1(0)), coordf_t(p2(1)) - coordf_t(p1(1)));
+                        const Vec2d v_cntr(coordf_t(p1(0) - center_last(0)), coordf_t(p1(1) - center_last(1)));
                         coordf_t a = v_seg.squaredNorm();
                         coordf_t b = 2. * v_seg.dot(v_cntr);
                         coordf_t c = v_cntr.squaredNorm() - circle_distance * circle_distance;
diff --git a/xs/src/libslic3r/TriangleMesh.cpp b/xs/src/libslic3r/TriangleMesh.cpp
index 03d05beb2c..8c432c8671 100644
--- a/xs/src/libslic3r/TriangleMesh.cpp
+++ b/xs/src/libslic3r/TriangleMesh.cpp
@@ -1,6 +1,9 @@
 #include "TriangleMesh.hpp"
 #include "ClipperUtils.hpp"
 #include "Geometry.hpp"
+#include "qhull/src/libqhullcpp/Qhull.h"
+#include "qhull/src/libqhullcpp/QhullFacetList.h"
+#include "qhull/src/libqhullcpp/QhullVertexSet.h"
 #include <cmath>
 #include <deque>
 #include <queue>
@@ -15,6 +18,8 @@
 
 #include <tbb/parallel_for.h>
 
+#include <Eigen/Dense>
+
 #if 0
     #define DEBUG
     #define _DEBUG
@@ -30,13 +35,7 @@
 
 namespace Slic3r {
 
-TriangleMesh::TriangleMesh()
-    : repaired(false)
-{
-    stl_initialize(&this->stl);
-}
-
-TriangleMesh::TriangleMesh(const Pointf3s &points, const std::vector<Point3>& facets )
+TriangleMesh::TriangleMesh(const Pointf3s &points, const std::vector<Vec3crd>& facets )
     : repaired(false)
 {
     stl_initialize(&this->stl);
@@ -51,51 +50,22 @@ TriangleMesh::TriangleMesh(const Pointf3s &points, const std::vector<Point3>& fa
 
     for (int i = 0; i < stl.stats.number_of_facets; i++) {
         stl_facet facet;
-
-        const Pointf3& ref_f1 = points[facets[i](0)];
-        facet.vertex[0].x = ref_f1(0);
-        facet.vertex[0].y = ref_f1(1);
-        facet.vertex[0].z = ref_f1(2);
-
-        const Pointf3& ref_f2 = points[facets[i](1)];
-        facet.vertex[1].x = ref_f2(0);
-        facet.vertex[1].y = ref_f2(1);
-        facet.vertex[1].z = ref_f2(2);
-
-        const Pointf3& ref_f3 = points[facets[i](2)];
-        facet.vertex[2].x = ref_f3(0);
-        facet.vertex[2].y = ref_f3(1);
-        facet.vertex[2].z = ref_f3(2);
-        
+        facet.vertex[0] = points[facets[i](0)].cast<float>();
+        facet.vertex[1] = points[facets[i](1)].cast<float>();
+        facet.vertex[2] = points[facets[i](2)].cast<float>();
         facet.extra[0] = 0;
         facet.extra[1] = 0;
 
-        float normal[3];
+        stl_normal normal;
         stl_calculate_normal(normal, &facet);
         stl_normalize_vector(normal);
-        facet.normal.x = normal[0];
-        facet.normal.y = normal[1];
-        facet.normal.z = normal[2];
+        facet.normal = normal;
 
         stl.facet_start[i] = facet;
     }
     stl_get_size(&stl);
 }
 
-TriangleMesh::TriangleMesh(const TriangleMesh &other) :
-    repaired(false)
-{
-    stl_initialize(&this->stl);
-    *this = other;
-}
-
-TriangleMesh::TriangleMesh(TriangleMesh &&other) : 
-    repaired(false)
-{
-    stl_initialize(&this->stl);
-    this->swap(other);
-}
-
 TriangleMesh& TriangleMesh::operator=(const TriangleMesh &other)
 {
     stl_close(&this->stl);
@@ -123,42 +93,8 @@ TriangleMesh& TriangleMesh::operator=(const TriangleMesh &other)
     return *this;
 }
 
-TriangleMesh& TriangleMesh::operator=(TriangleMesh &&other)
+void TriangleMesh::repair()
 {
-    this->swap(other);
-    return *this;
-}
-
-void
-TriangleMesh::swap(TriangleMesh &other)
-{
-    std::swap(this->stl,      other.stl);
-    std::swap(this->repaired, other.repaired);
-}
-
-TriangleMesh::~TriangleMesh() {
-    stl_close(&this->stl);
-}
-
-void
-TriangleMesh::ReadSTLFile(const char* input_file) {
-    stl_open(&stl, input_file);
-}
-
-void
-TriangleMesh::write_ascii(const char* output_file)
-{
-    stl_write_ascii(&this->stl, output_file, "");
-}
-
-void
-TriangleMesh::write_binary(const char* output_file)
-{
-    stl_write_binary(&this->stl, output_file, "");
-}
-
-void
-TriangleMesh::repair() {
     if (this->repaired) return;
     
     // admesh fails when repairing empty meshes
@@ -255,13 +191,7 @@ void TriangleMesh::check_topology()
     }
 }
 
-bool TriangleMesh::is_manifold() const
-{
-    return this->stl.stats.connected_facets_3_edge == this->stl.stats.number_of_facets;
-}
-
-void
-TriangleMesh::reset_repair_stats() {
+void TriangleMesh::reset_repair_stats() {
     this->stl.stats.degenerate_facets   = 0;
     this->stl.stats.edges_fixed         = 0;
     this->stl.stats.facets_removed      = 0;
@@ -271,8 +201,7 @@ TriangleMesh::reset_repair_stats() {
     this->stl.stats.normals_fixed       = 0;
 }
 
-bool
-TriangleMesh::needed_repair() const
+bool TriangleMesh::needed_repair() const
 {
     return this->stl.stats.degenerate_facets    > 0
         || this->stl.stats.edges_fixed          > 0
@@ -282,14 +211,8 @@ TriangleMesh::needed_repair() const
         || this->stl.stats.backwards_edges      > 0;
 }
 
-size_t
-TriangleMesh::facets_count() const
+void TriangleMesh::WriteOBJFile(char* output_file)
 {
-    return this->stl.stats.number_of_facets;
-}
-
-void
-TriangleMesh::WriteOBJFile(char* output_file) {
     stl_generate_shared_vertices(&stl);
     stl_write_obj(&stl, output_file);
 }
@@ -300,13 +223,9 @@ void TriangleMesh::scale(float factor)
     stl_invalidate_shared_vertices(&this->stl);
 }
 
-void TriangleMesh::scale(const Pointf3 &versor)
+void TriangleMesh::scale(const Vec3d &versor)
 {
-    float fversor[3];
-    fversor[0] = versor(0);
-    fversor[1] = versor(1);
-    fversor[2] = versor(2);
-    stl_scale_versor(&this->stl, fversor);
+    stl_scale_versor(&this->stl, versor.cast<float>());
     stl_invalidate_shared_vertices(&this->stl);
 }
 
@@ -336,21 +255,6 @@ void TriangleMesh::rotate(float angle, const Axis &axis)
     stl_invalidate_shared_vertices(&this->stl);
 }
 
-void TriangleMesh::rotate_x(float angle)
-{
-    this->rotate(angle, X);
-}
-
-void TriangleMesh::rotate_y(float angle)
-{
-    this->rotate(angle, Y);
-}
-
-void TriangleMesh::rotate_z(float angle)
-{
-    this->rotate(angle, Z);
-}
-
 void TriangleMesh::mirror(const Axis &axis)
 {
     if (axis == X) {
@@ -363,21 +267,6 @@ void TriangleMesh::mirror(const Axis &axis)
     stl_invalidate_shared_vertices(&this->stl);
 }
 
-void TriangleMesh::mirror_x()
-{
-    this->mirror(X);
-}
-
-void TriangleMesh::mirror_y()
-{
-    this->mirror(Y);
-}
-
-void TriangleMesh::mirror_z()
-{
-    this->mirror(Z);
-}
-
 void TriangleMesh::transform(const float* matrix3x4)
 {
     if (matrix3x4 == nullptr)
@@ -390,10 +279,9 @@ void TriangleMesh::transform(const float* matrix3x4)
 void TriangleMesh::align_to_origin()
 {
     this->translate(
-        -(this->stl.stats.min.x),
-        -(this->stl.stats.min.y),
-        -(this->stl.stats.min.z)
-    );
+        - this->stl.stats.min(0),
+        - this->stl.stats.min(1),
+        - this->stl.stats.min(2));
 }
 
 void TriangleMesh::rotate(double angle, Point* center)
@@ -476,14 +364,14 @@ size_t TriangleMesh::number_of_patches() const
     return num_bodies;
 }
 
-TriangleMeshPtrs
-TriangleMesh::split() const
+TriangleMeshPtrs TriangleMesh::split() const
 {
-    TriangleMeshPtrs meshes;
-    std::set<int> seen_facets;
+    TriangleMeshPtrs            meshes;
+    std::vector<unsigned char>  facet_visited(this->stl.stats.number_of_facets, false);
     
     // we need neighbors
-    if (!this->repaired) CONFESS("split() requires repair()");
+    if (!this->repaired)
+        CONFESS("split() requires repair()");
     
     // loop while we have remaining facets
     for (;;) {
@@ -491,25 +379,26 @@ TriangleMesh::split() const
         std::queue<int> facet_queue;
         std::deque<int> facets;
         for (int facet_idx = 0; facet_idx < this->stl.stats.number_of_facets; facet_idx++) {
-            if (seen_facets.find(facet_idx) == seen_facets.end()) {
+            if (! facet_visited[facet_idx]) {
                 // if facet was not seen put it into queue and start searching
                 facet_queue.push(facet_idx);
                 break;
             }
         }
-        if (facet_queue.empty()) break;
-        
-        while (!facet_queue.empty()) {
+        if (facet_queue.empty())
+            break;
+
+        while (! facet_queue.empty()) {
             int facet_idx = facet_queue.front();
             facet_queue.pop();
-            if (seen_facets.find(facet_idx) != seen_facets.end()) continue;
-            facets.emplace_back(facet_idx);
-            for (int j = 0; j <= 2; j++) {
-                facet_queue.push(this->stl.neighbors_start[facet_idx].neighbor[j]);
+            if (! facet_visited[facet_idx]) {
+                facets.emplace_back(facet_idx);
+                for (int j = 0; j < 3; ++ j)
+                    facet_queue.push(this->stl.neighbors_start[facet_idx].neighbor[j]);
+                facet_visited[facet_idx] = true;
             }
-            seen_facets.insert(facet_idx);
         }
-        
+
         TriangleMesh* mesh = new TriangleMesh;
         meshes.emplace_back(mesh);
         mesh->stl.stats.type = inmemory;
@@ -518,19 +407,17 @@ TriangleMesh::split() const
         stl_clear_error(&mesh->stl);
         stl_allocate(&mesh->stl);
         
-        int first = 1;
-        for (std::deque<int>::const_iterator facet = facets.begin(); facet != facets.end(); ++facet) {
+        bool first = true;
+        for (std::deque<int>::const_iterator facet = facets.begin(); facet != facets.end(); ++ facet) {
             mesh->stl.facet_start[facet - facets.begin()] = this->stl.facet_start[*facet];
             stl_facet_stats(&mesh->stl, this->stl.facet_start[*facet], first);
-            first = 0;
         }
     }
     
     return meshes;
 }
 
-void
-TriangleMesh::merge(const TriangleMesh &mesh)
+void TriangleMesh::merge(const TriangleMesh &mesh)
 {
     // reset stats and metadata
     int number_of_facets = this->stl.stats.number_of_facets;
@@ -561,9 +448,9 @@ ExPolygons TriangleMesh::horizontal_projection() const
         stl_facet* facet = &this->stl.facet_start[i];
         Polygon p;
         p.points.resize(3);
-        p.points[0] = Point::new_scale(facet->vertex[0].x, facet->vertex[0].y);
-        p.points[1] = Point::new_scale(facet->vertex[1].x, facet->vertex[1].y);
-        p.points[2] = Point::new_scale(facet->vertex[2].x, facet->vertex[2].y);
+        p.points[0] = Point::new_scale(facet->vertex[0](0), facet->vertex[0](1));
+        p.points[1] = Point::new_scale(facet->vertex[1](0), facet->vertex[1](1));
+        p.points[2] = Point::new_scale(facet->vertex[2](0), facet->vertex[2](1));
         p.make_counter_clockwise();  // do this after scaling, as winding order might change while doing that
         pp.emplace_back(p);
     }
@@ -578,28 +465,142 @@ Polygon TriangleMesh::convex_hull()
     Points pp;
     pp.reserve(this->stl.stats.shared_vertices);
     for (int i = 0; i < this->stl.stats.shared_vertices; ++ i) {
-        stl_vertex* v = &this->stl.v_shared[i];
-        pp.emplace_back(Point::new_scale(v->x, v->y));
+        const stl_vertex &v = this->stl.v_shared[i];
+        pp.emplace_back(Point::new_scale(v(0), v(1)));
     }
     return Slic3r::Geometry::convex_hull(pp);
 }
 
-BoundingBoxf3
-TriangleMesh::bounding_box() const
+BoundingBoxf3 TriangleMesh::bounding_box() const
 {
     BoundingBoxf3 bb;
     bb.defined = true;
-    bb.min(0) = this->stl.stats.min.x;
-    bb.min(1) = this->stl.stats.min.y;
-    bb.min(2) = this->stl.stats.min.z;
-    bb.max(0) = this->stl.stats.max.x;
-    bb.max(1) = this->stl.stats.max.y;
-    bb.max(2) = this->stl.stats.max.z;
+    bb.min = this->stl.stats.min.cast<double>();
+    bb.max = this->stl.stats.max.cast<double>();
     return bb;
 }
 
-void
-TriangleMesh::require_shared_vertices()
+BoundingBoxf3 TriangleMesh::transformed_bounding_box(const Transform3d& t) const
+{
+    bool has_shared = (stl.v_shared != nullptr);
+    if (!has_shared)
+        stl_generate_shared_vertices(&stl);
+
+    unsigned int vertices_count = (stl.stats.shared_vertices > 0) ? (unsigned int)stl.stats.shared_vertices : 3 * (unsigned int)stl.stats.number_of_facets;
+
+    if (vertices_count == 0)
+        return BoundingBoxf3();
+
+    Eigen::MatrixXd src_vertices(3, vertices_count);
+
+    if (stl.stats.shared_vertices > 0)
+    {
+        stl_vertex* vertex_ptr = stl.v_shared;
+        for (int i = 0; i < stl.stats.shared_vertices; ++i)
+        {
+            src_vertices(0, i) = (double)(*vertex_ptr)(0);
+            src_vertices(1, i) = (double)(*vertex_ptr)(1);
+            src_vertices(2, i) = (double)(*vertex_ptr)(2);
+            vertex_ptr += 1;
+        }
+    }
+    else
+    {
+        stl_facet* facet_ptr = stl.facet_start;
+        unsigned int v_id = 0;
+        while (facet_ptr < stl.facet_start + stl.stats.number_of_facets)
+        {
+            for (int i = 0; i < 3; ++i)
+            {
+                src_vertices(0, v_id) = (double)facet_ptr->vertex[i](0);
+                src_vertices(1, v_id) = (double)facet_ptr->vertex[i](1);
+                src_vertices(2, v_id) = (double)facet_ptr->vertex[i](2);
+            }
+            facet_ptr += 1;
+            ++v_id;
+        }
+    }
+
+    if (!has_shared && (stl.stats.shared_vertices > 0))
+        stl_invalidate_shared_vertices(&stl);
+
+    Eigen::MatrixXd dst_vertices(3, vertices_count);
+    dst_vertices = t * src_vertices.colwise().homogeneous();
+
+    Vec3d v_min(dst_vertices(0, 0), dst_vertices(1, 0), dst_vertices(2, 0));
+    Vec3d v_max = v_min;
+
+    for (int i = 1; i < vertices_count; ++i)
+    {
+        for (int j = 0; j < 3; ++j)
+        {
+            v_min(j) = std::min(v_min(j), dst_vertices(j, i));
+            v_max(j) = std::max(v_max(j), dst_vertices(j, i));
+        }
+    }
+
+    return BoundingBoxf3(v_min, v_max);
+}
+
+TriangleMesh TriangleMesh::convex_hull_3d() const
+{
+    // Helper struct for qhull:
+    struct PointForQHull{
+        PointForQHull(float x_p, float y_p, float z_p) : x((realT)x_p), y((realT)y_p), z((realT)z_p) {}
+        realT x, y, z;
+    };
+    std::vector<PointForQHull> src_vertices;
+
+    // We will now fill the vector with input points for computation:
+    stl_facet* facet_ptr = stl.facet_start;
+    while (facet_ptr < stl.facet_start + stl.stats.number_of_facets)
+    {
+        for (int i = 0; i < 3; ++i)
+        {
+            const stl_vertex& v = facet_ptr->vertex[i];
+            src_vertices.emplace_back(v(0), v(1), v(2));
+        }
+
+        facet_ptr += 1;
+    }
+
+    // The qhull call:
+    orgQhull::Qhull qhull;
+    qhull.disableOutputStream(); // we want qhull to be quiet
+    try
+    {
+        qhull.runQhull("", 3, (int)src_vertices.size(), (const realT*)(src_vertices.data()), "Qt");
+    }
+    catch (...)
+    {
+        std::cout << "Unable to create convex hull" << std::endl;
+        return TriangleMesh();
+    }
+
+    // Let's collect results:
+    Pointf3s dst_vertices;
+    std::vector<Vec3crd> facets;
+    auto facet_list = qhull.facetList().toStdVector();
+    for (const orgQhull::QhullFacet& facet : facet_list)
+    {   // iterate through facets
+        orgQhull::QhullVertexSet vertices = facet.vertices();
+        for (int i = 0; i < 3; ++i)
+        {   // iterate through facet's vertices
+
+            orgQhull::QhullPoint p = vertices[i].point();
+            const float* coords = p.coordinates();
+            dst_vertices.emplace_back(coords[0], coords[1], coords[2]);
+        }
+        unsigned int size = (unsigned int)dst_vertices.size();
+        facets.emplace_back(size - 3, size - 2, size - 1);
+    }
+
+    TriangleMesh output_mesh(dst_vertices, facets);
+    output_mesh.repair();
+    return output_mesh;
+}
+
+void TriangleMesh::require_shared_vertices()
 {
     BOOST_LOG_TRIVIAL(trace) << "TriangleMeshSlicer::require_shared_vertices - start";
     if (!this->repaired) 
@@ -619,11 +620,8 @@ TriangleMeshSlicer::TriangleMeshSlicer(TriangleMesh* _mesh) :
     facets_edges.assign(_mesh->stl.stats.number_of_facets * 3, -1);
     v_scaled_shared.assign(_mesh->stl.v_shared, _mesh->stl.v_shared + _mesh->stl.stats.shared_vertices);
     // Scale the copied vertices.
-    for (int i = 0; i < this->mesh->stl.stats.shared_vertices; ++ i) {
-        this->v_scaled_shared[i].x /= float(SCALING_FACTOR);
-        this->v_scaled_shared[i].y /= float(SCALING_FACTOR);
-        this->v_scaled_shared[i].z /= float(SCALING_FACTOR);
-    }
+    for (int i = 0; i < this->mesh->stl.stats.shared_vertices; ++ i)
+        this->v_scaled_shared[i] *= float(1. / SCALING_FACTOR);
 
     // Create a mapping from triangle edge into face.
     struct EdgeToFace {
@@ -697,8 +695,7 @@ TriangleMeshSlicer::TriangleMeshSlicer(TriangleMesh* _mesh) :
     }
 }
 
-void
-TriangleMeshSlicer::slice(const std::vector<float> &z, std::vector<Polygons>* layers) const
+void TriangleMeshSlicer::slice(const std::vector<float> &z, std::vector<Polygons>* layers) const
 {
     BOOST_LOG_TRIVIAL(debug) << "TriangleMeshSlicer::slice";
 
@@ -779,14 +776,14 @@ void TriangleMeshSlicer::_slice_do(size_t facet_idx, std::vector<IntersectionLin
     const stl_facet &facet = this->mesh->stl.facet_start[facet_idx];
     
     // find facet extents
-    const float min_z = fminf(facet.vertex[0].z, fminf(facet.vertex[1].z, facet.vertex[2].z));
-    const float max_z = fmaxf(facet.vertex[0].z, fmaxf(facet.vertex[1].z, facet.vertex[2].z));
+    const float min_z = fminf(facet.vertex[0](2), fminf(facet.vertex[1](2), facet.vertex[2](2)));
+    const float max_z = fmaxf(facet.vertex[0](2), fmaxf(facet.vertex[1](2), facet.vertex[2](2)));
     
     #ifdef SLIC3R_DEBUG
     printf("\n==> FACET %d (%f,%f,%f - %f,%f,%f - %f,%f,%f):\n", facet_idx,
-        facet.vertex[0].x, facet.vertex[0].y, facet.vertex[0].z,
-        facet.vertex[1].x, facet.vertex[1].y, facet.vertex[1].z,
-        facet.vertex[2].x, facet.vertex[2].y, facet.vertex[2].z);
+        facet.vertex[0].x, facet.vertex[0].y, facet.vertex[0](2),
+        facet.vertex[1].x, facet.vertex[1].y, facet.vertex[1](2),
+        facet.vertex[2].x, facet.vertex[2].y, facet.vertex[2](2));
     printf("z: min = %.2f, max = %.2f\n", min_z, max_z);
     #endif
     
@@ -806,18 +803,18 @@ void TriangleMeshSlicer::_slice_do(size_t facet_idx, std::vector<IntersectionLin
             if (il.edge_type == feHorizontal) {
                 // Insert all three edges of the face.
                 const int *vertices = this->mesh->stl.v_indices[facet_idx].vertex;
-                const bool reverse  = this->mesh->stl.facet_start[facet_idx].normal.z < 0;
+                const bool reverse  = this->mesh->stl.facet_start[facet_idx].normal(2) < 0;
                 for (int j = 0; j < 3; ++ j) {
                     int               a_id     = vertices[j % 3];
                     int               b_id     = vertices[(j+1) % 3];
                     if (reverse)
                         std::swap(a_id, b_id);
-                    const stl_vertex *a = &this->v_scaled_shared[a_id];
-                    const stl_vertex *b = &this->v_scaled_shared[b_id];
-                    il.a(0)    = a->x;
-                    il.a(1)    = a->y;
-                    il.b(0)    = b->x;
-                    il.b(1)    = b->y;
+                    const stl_vertex &a = this->v_scaled_shared[a_id];
+                    const stl_vertex &b = this->v_scaled_shared[b_id];
+                    il.a(0)    = a(0);
+                    il.a(1)    = a(1);
+                    il.b(0)    = b(0);
+                    il.b(1)    = b(1);
                     il.a_id   = a_id;
                     il.b_id   = b_id;
                     (*lines)[layer_idx].emplace_back(il);
@@ -863,66 +860,63 @@ bool TriangleMeshSlicer::slice_facet(
     // Reorder vertices so that the first one is the one with lowest Z.
     // This is needed to get all intersection lines in a consistent order
     // (external on the right of the line)
-    int i = (facet.vertex[1].z == min_z) ? 1 : ((facet.vertex[2].z == min_z) ? 2 : 0);
+    int i = (facet.vertex[1](2) == min_z) ? 1 : ((facet.vertex[2](2) == min_z) ? 2 : 0);
     for (int j = i; j - i < 3; ++ j) {  // loop through facet edges
         int               edge_id  = this->facets_edges[facet_idx * 3 + (j % 3)];
         const int        *vertices = this->mesh->stl.v_indices[facet_idx].vertex;
         int               a_id     = vertices[j % 3];
         int               b_id     = vertices[(j+1) % 3];
-        const stl_vertex *a = &this->v_scaled_shared[a_id];
-        const stl_vertex *b = &this->v_scaled_shared[b_id];
+        const stl_vertex &a = this->v_scaled_shared[a_id];
+        const stl_vertex &b = this->v_scaled_shared[b_id];
         
         // Is edge or face aligned with the cutting plane?
-        if (a->z == slice_z && b->z == slice_z) {
+        if (a(2) == slice_z && b(2) == slice_z) {
             // Edge is horizontal and belongs to the current layer.
             const stl_vertex &v0 = this->v_scaled_shared[vertices[0]];
             const stl_vertex &v1 = this->v_scaled_shared[vertices[1]];
             const stl_vertex &v2 = this->v_scaled_shared[vertices[2]];
+            bool              swap = false;
             if (min_z == max_z) {
                 // All three vertices are aligned with slice_z.
                 line_out->edge_type = feHorizontal;
-                if (this->mesh->stl.facet_start[facet_idx].normal.z < 0) {
+                if (this->mesh->stl.facet_start[facet_idx].normal(2) < 0) {
                     // If normal points downwards this is a bottom horizontal facet so we reverse its point order.
-                    std::swap(a, b);
-                    std::swap(a_id, b_id);
+                    swap = true;
                 }
-            } else if (v0.z < slice_z || v1.z < slice_z || v2.z < slice_z) {
+            } else if (v0(2) < slice_z || v1(2) < slice_z || v2(2) < slice_z) {
                 // Two vertices are aligned with the cutting plane, the third vertex is below the cutting plane.
                 line_out->edge_type = feTop;
-                std::swap(a, b);
-                std::swap(a_id, b_id);
+                swap = true;
             } else {
                 // Two vertices are aligned with the cutting plane, the third vertex is above the cutting plane.
                 line_out->edge_type = feBottom;
             }
-            line_out->a(0)  = a->x;
-            line_out->a(1)  = a->y;
-            line_out->b(0)  = b->x;
-            line_out->b(1)  = b->y;
-            line_out->a_id   = a_id;
-            line_out->b_id   = b_id;
+            line_out->a = to_2d(swap ? b : a).cast<coord_t>();
+            line_out->b = to_2d(swap ? a : b).cast<coord_t>();
+            line_out->a_id = swap ? b_id : a_id;
+            line_out->b_id = swap ? a_id : b_id;
             return true;
         }
 
-        if (a->z == slice_z) {
+        if (a(2) == slice_z) {
             // Only point a alings with the cutting plane.
             points_on_layer[num_points_on_layer ++] = num_points;
             IntersectionPoint &point = points[num_points ++];
-            point(0)       = a->x;
-            point(1)       = a->y;
+            point(0)       = a(0);
+            point(1)       = a(1);
             point.point_id  = a_id;
-        } else if (b->z == slice_z) {
+        } else if (b(2) == slice_z) {
             // Only point b alings with the cutting plane.
             points_on_layer[num_points_on_layer ++] = num_points;
             IntersectionPoint &point = points[num_points ++];
-            point(0)       = b->x;
-            point(1)       = b->y;
+            point(0)       = b(0);
+            point(1)       = b(1);
             point.point_id  = b_id;
-        } else if ((a->z < slice_z && b->z > slice_z) || (b->z < slice_z && a->z > slice_z)) {
+        } else if ((a(2) < slice_z && b(2) > slice_z) || (b(2) < slice_z && a(2) > slice_z)) {
             // A general case. The face edge intersects the cutting plane. Calculate the intersection point.
             IntersectionPoint &point = points[num_points ++];
-            point(0)       = b->x + (a->x - b->x) * (slice_z - b->z) / (a->z - b->z);
-            point(1)       = b->y + (a->y - b->y) * (slice_z - b->z) / (a->z - b->z);
+            point(0)       = b(0) + (a(0) - b(0)) * (slice_z - b(2)) / (a(2) - b(2));
+            point(1)       = b(1) + (a(1) - b(1)) * (slice_z - b(2)) / (a(2) - b(2));
             point.edge_id   = edge_id;
         }
     }
@@ -1389,8 +1383,8 @@ void TriangleMeshSlicer::cut(float z, TriangleMesh* upper, TriangleMesh* lower)
         stl_facet* facet = &this->mesh->stl.facet_start[facet_idx];
         
         // find facet extents
-        float min_z = std::min(facet->vertex[0].z, std::min(facet->vertex[1].z, facet->vertex[2].z));
-        float max_z = std::max(facet->vertex[0].z, std::max(facet->vertex[1].z, facet->vertex[2].z));
+        float min_z = std::min(facet->vertex[0](2), std::min(facet->vertex[1](2), facet->vertex[2](2)));
+        float max_z = std::max(facet->vertex[0](2), std::max(facet->vertex[1](2), facet->vertex[2](2)));
         
         // intersect facet with cutting plane
         IntersectionLine line;
@@ -1417,47 +1411,47 @@ void TriangleMeshSlicer::cut(float z, TriangleMesh* upper, TriangleMesh* lower)
 
             // look for the vertex on whose side of the slicing plane there are no other vertices
             int isolated_vertex;
-            if ( (facet->vertex[0].z > z) == (facet->vertex[1].z > z) ) {
+            if ( (facet->vertex[0](2) > z) == (facet->vertex[1](2) > z) ) {
                 isolated_vertex = 2;
-            } else if ( (facet->vertex[1].z > z) == (facet->vertex[2].z > z) ) {
+            } else if ( (facet->vertex[1](2) > z) == (facet->vertex[2](2) > z) ) {
                 isolated_vertex = 0;
             } else {
                 isolated_vertex = 1;
             }
             
             // get vertices starting from the isolated one
-            stl_vertex* v0 = &facet->vertex[isolated_vertex];
-            stl_vertex* v1 = &facet->vertex[(isolated_vertex+1) % 3];
-            stl_vertex* v2 = &facet->vertex[(isolated_vertex+2) % 3];
+            const stl_vertex &v0 = facet->vertex[isolated_vertex];
+            const stl_vertex &v1 = facet->vertex[(isolated_vertex+1) % 3];
+            const stl_vertex &v2 = facet->vertex[(isolated_vertex+2) % 3];
             
             // intersect v0-v1 and v2-v0 with cutting plane and make new vertices
             stl_vertex v0v1, v2v0;
-            v0v1.x = v1->x + (v0->x - v1->x) * (z - v1->z) / (v0->z - v1->z);
-            v0v1.y = v1->y + (v0->y - v1->y) * (z - v1->z) / (v0->z - v1->z);
-            v0v1.z = z;
-            v2v0.x = v2->x + (v0->x - v2->x) * (z - v2->z) / (v0->z - v2->z);
-            v2v0.y = v2->y + (v0->y - v2->y) * (z - v2->z) / (v0->z - v2->z);
-            v2v0.z = z;
+            v0v1(0) = v1(0) + (v0(0) - v1(0)) * (z - v1(2)) / (v0(2) - v1(2));
+            v0v1(1) = v1(1) + (v0(1) - v1(1)) * (z - v1(2)) / (v0(2) - v1(2));
+            v0v1(2) = z;
+            v2v0(0) = v2(0) + (v0(0) - v2(0)) * (z - v2(2)) / (v0(2) - v2(2));
+            v2v0(1) = v2(1) + (v0(1) - v2(1)) * (z - v2(2)) / (v0(2) - v2(2));
+            v2v0(2) = z;
             
             // build the triangular facet
             stl_facet triangle;
             triangle.normal = facet->normal;
-            triangle.vertex[0] = *v0;
+            triangle.vertex[0] = v0;
             triangle.vertex[1] = v0v1;
             triangle.vertex[2] = v2v0;
             
             // build the facets forming a quadrilateral on the other side
             stl_facet quadrilateral[2];
             quadrilateral[0].normal = facet->normal;
-            quadrilateral[0].vertex[0] = *v1;
-            quadrilateral[0].vertex[1] = *v2;
+            quadrilateral[0].vertex[0] = v1;
+            quadrilateral[0].vertex[1] = v2;
             quadrilateral[0].vertex[2] = v0v1;
             quadrilateral[1].normal = facet->normal;
-            quadrilateral[1].vertex[0] = *v2;
+            quadrilateral[1].vertex[0] = v2;
             quadrilateral[1].vertex[1] = v2v0;
             quadrilateral[1].vertex[2] = v0v1;
             
-            if (v0->z > z) {
+            if (v0(2) > z) {
                 if (upper != NULL) stl_add_facet(&upper->stl, &triangle);
                 if (lower != NULL) {
                     stl_add_facet(&lower->stl, &quadrilateral[0]);
@@ -1489,13 +1483,11 @@ void TriangleMeshSlicer::cut(float z, TriangleMesh* upper, TriangleMesh* lower)
             Polygon p = *polygon;
             p.reverse();
             stl_facet facet;
-            facet.normal.x = 0;
-            facet.normal.y = 0;
-            facet.normal.z = -1;
+            facet.normal = stl_normal(0, 0, -1.f);
             for (size_t i = 0; i <= 2; ++i) {
-                facet.vertex[i].x = unscale(p.points[i](0));
-                facet.vertex[i].y = unscale(p.points[i](1));
-                facet.vertex[i].z = z;
+                facet.vertex[i](0) = unscale<float>(p.points[i](0));
+                facet.vertex[i](1) = unscale<float>(p.points[i](1));
+                facet.vertex[i](2) = z;
             }
             stl_add_facet(&upper->stl, &facet);
         }
@@ -1515,13 +1507,11 @@ void TriangleMeshSlicer::cut(float z, TriangleMesh* upper, TriangleMesh* lower)
         // convert triangles to facets and append them to mesh
         for (Polygons::const_iterator polygon = triangles.begin(); polygon != triangles.end(); ++polygon) {
             stl_facet facet;
-            facet.normal.x = 0;
-            facet.normal.y = 0;
-            facet.normal.z = 1;
+            facet.normal = stl_normal(0, 0, 1.f);
             for (size_t i = 0; i <= 2; ++i) {
-                facet.vertex[i].x = unscale(polygon->points[i](0));
-                facet.vertex[i].y = unscale(polygon->points[i](1));
-                facet.vertex[i].z = z;
+                facet.vertex[i](0) = unscale<float>(polygon->points[i](0));
+                facet.vertex[i](1) = unscale<float>(polygon->points[i](1));
+                facet.vertex[i](2) = z;
             }
             stl_add_facet(&lower->stl, &facet);
         }
@@ -1534,19 +1524,19 @@ void TriangleMeshSlicer::cut(float z, TriangleMesh* upper, TriangleMesh* lower)
 
 // Generate the vertex list for a cube solid of arbitrary size in X/Y/Z.
 TriangleMesh make_cube(double x, double y, double z) {
-    Pointf3 pv[8] = { 
-        Pointf3(x, y, 0), Pointf3(x, 0, 0), Pointf3(0, 0, 0), 
-        Pointf3(0, y, 0), Pointf3(x, y, z), Pointf3(0, y, z), 
-        Pointf3(0, 0, z), Pointf3(x, 0, z) 
+    Vec3d pv[8] = { 
+        Vec3d(x, y, 0), Vec3d(x, 0, 0), Vec3d(0, 0, 0), 
+        Vec3d(0, y, 0), Vec3d(x, y, z), Vec3d(0, y, z), 
+        Vec3d(0, 0, z), Vec3d(x, 0, z) 
     };
-    Point3 fv[12] = { 
-        Point3(0, 1, 2), Point3(0, 2, 3), Point3(4, 5, 6), 
-        Point3(4, 6, 7), Point3(0, 4, 7), Point3(0, 7, 1), 
-        Point3(1, 7, 6), Point3(1, 6, 2), Point3(2, 6, 5), 
-        Point3(2, 5, 3), Point3(4, 0, 3), Point3(4, 3, 5) 
+    Vec3crd fv[12] = { 
+        Vec3crd(0, 1, 2), Vec3crd(0, 2, 3), Vec3crd(4, 5, 6), 
+        Vec3crd(4, 6, 7), Vec3crd(0, 4, 7), Vec3crd(0, 7, 1), 
+        Vec3crd(1, 7, 6), Vec3crd(1, 6, 2), Vec3crd(2, 6, 5), 
+        Vec3crd(2, 5, 3), Vec3crd(4, 0, 3), Vec3crd(4, 3, 5) 
     };
 
-    std::vector<Point3> facets(&fv[0], &fv[0]+12);
+    std::vector<Vec3crd> facets(&fv[0], &fv[0]+12);
     Pointf3s vertices(&pv[0], &pv[0]+8);
 
     TriangleMesh mesh(vertices ,facets);
@@ -1558,11 +1548,11 @@ TriangleMesh make_cube(double x, double y, double z) {
 // Default is 360 sides, angle fa is in radians.
 TriangleMesh make_cylinder(double r, double h, double fa) {
     Pointf3s vertices;
-    std::vector<Point3> facets;
+    std::vector<Vec3crd> facets;
 
     // 2 special vertices, top and bottom center, rest are relative to this
-    vertices.emplace_back(Pointf3(0.0, 0.0, 0.0));
-    vertices.emplace_back(Pointf3(0.0, 0.0, h));
+    vertices.emplace_back(Vec3d(0.0, 0.0, 0.0));
+    vertices.emplace_back(Vec3d(0.0, 0.0, h));
 
     // adjust via rounding to get an even multiple for any provided angle.
     double angle = (2*PI / floor(2*PI / fa));
@@ -1572,24 +1562,23 @@ TriangleMesh make_cylinder(double r, double h, double fa) {
     // top and bottom.
     // Special case: Last line shares 2 vertices with the first line.
     unsigned id = vertices.size() - 1;
-    vertices.emplace_back(Pointf3(sin(0) * r , cos(0) * r, 0));
-    vertices.emplace_back(Pointf3(sin(0) * r , cos(0) * r, h));
+    vertices.emplace_back(Vec3d(sin(0) * r , cos(0) * r, 0));
+    vertices.emplace_back(Vec3d(sin(0) * r , cos(0) * r, h));
     for (double i = 0; i < 2*PI; i+=angle) {
-        Pointf p(0, r);
-        p.rotate(i);
-        vertices.emplace_back(Pointf3(p(0), p(1), 0.));
-        vertices.emplace_back(Pointf3(p(0), p(1), h));
+        Vec2d p = Eigen::Rotation2Dd(i) * Eigen::Vector2d(0, r);
+        vertices.emplace_back(Vec3d(p(0), p(1), 0.));
+        vertices.emplace_back(Vec3d(p(0), p(1), h));
         id = vertices.size() - 1;
-        facets.emplace_back(Point3( 0, id - 1, id - 3)); // top
-        facets.emplace_back(Point3(id,      1, id - 2)); // bottom
-        facets.emplace_back(Point3(id, id - 2, id - 3)); // upper-right of side
-        facets.emplace_back(Point3(id, id - 3, id - 1)); // bottom-left of side
+        facets.emplace_back(Vec3crd( 0, id - 1, id - 3)); // top
+        facets.emplace_back(Vec3crd(id,      1, id - 2)); // bottom
+        facets.emplace_back(Vec3crd(id, id - 2, id - 3)); // upper-right of side
+        facets.emplace_back(Vec3crd(id, id - 3, id - 1)); // bottom-left of side
     }
     // Connect the last set of vertices with the first.
-    facets.emplace_back(Point3( 2, 0, id - 1));
-    facets.emplace_back(Point3( 1, 3,     id));
-    facets.emplace_back(Point3(id, 3,      2));
-    facets.emplace_back(Point3(id, 2, id - 1));
+    facets.emplace_back(Vec3crd( 2, 0, id - 1));
+    facets.emplace_back(Vec3crd( 1, 3,     id));
+    facets.emplace_back(Vec3crd(id, 3,      2));
+    facets.emplace_back(Vec3crd(id, 2, id - 1));
     
     TriangleMesh mesh(vertices, facets);
     return mesh;
@@ -1600,7 +1589,7 @@ TriangleMesh make_cylinder(double r, double h, double fa) {
 // Default angle is 1 degree.
 TriangleMesh make_sphere(double rho, double fa) {
     Pointf3s vertices;
-    std::vector<Point3> facets;
+    std::vector<Vec3crd> facets;
 
     // Algorithm: 
     // Add points one-by-one to the sphere grid and form facets using relative coordinates.
@@ -1619,17 +1608,16 @@ TriangleMesh make_sphere(double rho, double fa) {
 
     // special case: first ring connects to 0,0,0
     // insert and form facets.
-    vertices.emplace_back(Pointf3(0.0, 0.0, -rho));
+    vertices.emplace_back(Vec3d(0.0, 0.0, -rho));
     size_t id = vertices.size();
     for (size_t i = 0; i < ring.size(); i++) {
         // Fixed scaling 
         const double z = -rho + increment*rho*2.0;
         // radius of the circle for this step.
         const double r = sqrt(abs(rho*rho - z*z));
-        Pointf b(0, r);
-        b.rotate(ring[i]);
-        vertices.emplace_back(Pointf3(b(0), b(1), z));
-        facets.emplace_back((i == 0) ? Point3(1, 0, ring.size()) : Point3(id, 0, id - 1));
+        Vec2d b = Eigen::Rotation2Dd(ring[i]) * Eigen::Vector2d(0, r);
+        vertices.emplace_back(Vec3d(b(0), b(1), z));
+        facets.emplace_back((i == 0) ? Vec3crd(1, 0, ring.size()) : Vec3crd(id, 0, id - 1));
         ++ id;
     }
 
@@ -1639,16 +1627,15 @@ TriangleMesh make_sphere(double rho, double fa) {
         const double r = sqrt(abs(rho*rho - z*z));
 
         for (size_t i = 0; i < ring.size(); i++) {
-            Pointf b(0, r);
-            b.rotate(ring[i]); 
-            vertices.emplace_back(Pointf3(b(0), b(1), z));
+            Vec2d b = Eigen::Rotation2Dd(ring[i]) * Eigen::Vector2d(0, r);
+            vertices.emplace_back(Vec3d(b(0), b(1), z));
             if (i == 0) {
                 // wrap around
-                facets.emplace_back(Point3(id + ring.size() - 1 , id, id - 1)); 
-                facets.emplace_back(Point3(id, id - ring.size(),  id - 1)); 
+                facets.emplace_back(Vec3crd(id + ring.size() - 1 , id, id - 1)); 
+                facets.emplace_back(Vec3crd(id, id - ring.size(),  id - 1)); 
             } else {
-                facets.emplace_back(Point3(id , id - ring.size(), (id - 1) - ring.size())); 
-                facets.emplace_back(Point3(id, id - 1 - ring.size() ,  id - 1)); 
+                facets.emplace_back(Vec3crd(id , id - ring.size(), (id - 1) - ring.size())); 
+                facets.emplace_back(Vec3crd(id, id - 1 - ring.size() ,  id - 1)); 
             }
             id++;
         } 
@@ -1657,13 +1644,13 @@ TriangleMesh make_sphere(double rho, double fa) {
 
     // special case: last ring connects to 0,0,rho*2.0
     // only form facets.
-    vertices.emplace_back(Pointf3(0.0, 0.0, rho));
+    vertices.emplace_back(Vec3d(0.0, 0.0, rho));
     for (size_t i = 0; i < ring.size(); i++) {
         if (i == 0) {
             // third vertex is on the other side of the ring.
-            facets.emplace_back(Point3(id, id - ring.size(),  id - 1));
+            facets.emplace_back(Vec3crd(id, id - ring.size(),  id - 1));
         } else {
-            facets.emplace_back(Point3(id, id - ring.size() + i,  id - ring.size() + (i - 1)));
+            facets.emplace_back(Vec3crd(id, id - ring.size() + i,  id - ring.size() + (i - 1)));
         }
     }
     id++;
diff --git a/xs/src/libslic3r/TriangleMesh.hpp b/xs/src/libslic3r/TriangleMesh.hpp
index c700784a51..e4d377a9d0 100644
--- a/xs/src/libslic3r/TriangleMesh.hpp
+++ b/xs/src/libslic3r/TriangleMesh.hpp
@@ -20,33 +20,33 @@ typedef std::vector<TriangleMesh*> TriangleMeshPtrs;
 class TriangleMesh
 {
 public:
-    TriangleMesh();
-    TriangleMesh(const Pointf3s &points, const std::vector<Point3> &facets);
-    TriangleMesh(const TriangleMesh &other);
-    TriangleMesh(TriangleMesh &&other);
+    TriangleMesh() : repaired(false) { stl_initialize(&this->stl); }
+    TriangleMesh(const Pointf3s &points, const std::vector<Vec3crd> &facets);
+    TriangleMesh(const TriangleMesh &other) : repaired(false) { stl_initialize(&this->stl); *this = other; }
+    TriangleMesh(TriangleMesh &&other) : repaired(false) { stl_initialize(&this->stl); this->swap(other); }
+    ~TriangleMesh() { stl_close(&this->stl); }
     TriangleMesh& operator=(const TriangleMesh &other);
-    TriangleMesh& operator=(TriangleMesh &&other);
-    void swap(TriangleMesh &other);
-    ~TriangleMesh();
-    void ReadSTLFile(const char* input_file);
-    void write_ascii(const char* output_file);
-    void write_binary(const char* output_file);
+    TriangleMesh& operator=(TriangleMesh &&other) { this->swap(other); return *this; }
+    void swap(TriangleMesh &other) { std::swap(this->stl, other.stl); std::swap(this->repaired, other.repaired); }
+    void ReadSTLFile(const char* input_file) { stl_open(&stl, input_file); }
+    void write_ascii(const char* output_file) { stl_write_ascii(&this->stl, output_file, ""); }
+    void write_binary(const char* output_file) { stl_write_binary(&this->stl, output_file, ""); }
     void repair();
     float volume();
     void check_topology();
-    bool is_manifold() const;
+    bool is_manifold() const { return this->stl.stats.connected_facets_3_edge == this->stl.stats.number_of_facets; }
     void WriteOBJFile(char* output_file);
     void scale(float factor);
-    void scale(const Pointf3 &versor);
+    void scale(const Vec3d &versor);
     void translate(float x, float y, float z);
     void rotate(float angle, const Axis &axis);
-    void rotate_x(float angle);
-    void rotate_y(float angle);
-    void rotate_z(float angle);
+    void rotate_x(float angle) { this->rotate(angle, X); }
+    void rotate_y(float angle) { this->rotate(angle, Y); }
+    void rotate_z(float angle) { this->rotate(angle, Z); }
     void mirror(const Axis &axis);
-    void mirror_x();
-    void mirror_y();
-    void mirror_z();
+    void mirror_x() { this->mirror(X); }
+    void mirror_y() { this->mirror(Y); }
+    void mirror_z() { this->mirror(Z); }
     void transform(const float* matrix3x4);
     void align_to_origin();
     void rotate(double angle, Point* center);
@@ -55,9 +55,13 @@ public:
     ExPolygons horizontal_projection() const;
     Polygon convex_hull();
     BoundingBoxf3 bounding_box() const;
+    // Returns the bbox of this TriangleMesh transformed by the given transformation
+    BoundingBoxf3 transformed_bounding_box(const Transform3d& t) const;
+    // Returns the convex hull of this TriangleMesh
+    TriangleMesh convex_hull_3d() const;
     void reset_repair_stats();
     bool needed_repair() const;
-    size_t facets_count() const;
+    size_t facets_count() const { return this->stl.stats.number_of_facets; }
 
     // Returns true, if there are two and more connected patches in the mesh.
     // Returns false, if one or zero connected patch is in the mesh.
@@ -66,7 +70,7 @@ public:
     // Count disconnected triangle patches.
     size_t number_of_patches() const;
 
-    stl_file stl;
+    mutable stl_file stl;
     bool repaired;
     
 private:
diff --git a/xs/src/libslic3r/libslic3r.h b/xs/src/libslic3r/libslic3r.h
index 862ce2e516..6fea64cd12 100644
--- a/xs/src/libslic3r/libslic3r.h
+++ b/xs/src/libslic3r/libslic3r.h
@@ -45,7 +45,6 @@ typedef double  coordf_t;
 //FIXME Better to use an inline function with an explicit return type.
 //inline coord_t scale_(coordf_t v) { return coord_t(floor(v / SCALING_FACTOR + 0.5f)); }
 #define scale_(val) ((val) / SCALING_FACTOR)
-#define unscale(val) ((val) * SCALING_FACTOR)
 #define SCALED_EPSILON scale_(EPSILON)
 /* Implementation of CONFESS("foo"): */
 #ifdef _MSC_VER
@@ -102,6 +101,9 @@ inline std::string debug_out_path(const char *name, ...)
 
 namespace Slic3r {
 
+template<typename T, typename Q>
+inline T unscale(Q v) { return T(v) * T(SCALING_FACTOR); }
+
 enum Axis { X=0, Y, Z, E, F, NUM_AXES };
 
 template <class T>
diff --git a/xs/src/perlglue.cpp b/xs/src/perlglue.cpp
index dbaf35ae47..5e09187551 100644
--- a/xs/src/perlglue.cpp
+++ b/xs/src/perlglue.cpp
@@ -41,9 +41,8 @@ REGISTER_CLASS(BoundingBoxf, "Geometry::BoundingBoxf");
 REGISTER_CLASS(BoundingBoxf3, "Geometry::BoundingBoxf3");
 REGISTER_CLASS(BridgeDetector, "BridgeDetector");
 REGISTER_CLASS(Point, "Point");
-REGISTER_CLASS(Point3, "Point3");
-REGISTER_CLASS(Pointf, "Pointf");
-REGISTER_CLASS(Pointf3, "Pointf3");
+__REGISTER_CLASS(Vec2d, "Pointf");
+__REGISTER_CLASS(Vec3d, "Pointf3");
 REGISTER_CLASS(DynamicPrintConfig, "Config");
 REGISTER_CLASS(StaticPrintConfig, "Config::Static");
 REGISTER_CLASS(PrintObjectConfig, "Config::PrintObject");
@@ -64,9 +63,9 @@ REGISTER_CLASS(PresetCollection, "GUI::PresetCollection");
 REGISTER_CLASS(PresetBundle, "GUI::PresetBundle");
 REGISTER_CLASS(TabIface, "GUI::Tab");
 REGISTER_CLASS(PresetUpdater, "PresetUpdater");
-REGISTER_CLASS(OctoPrint, "OctoPrint");
 REGISTER_CLASS(AppController, "AppController");
 REGISTER_CLASS(PrintController, "PrintController");
+REGISTER_CLASS(PrintHost, "PrintHost");
 
 SV* ConfigBase__as_hash(ConfigBase* THIS)
 {
@@ -133,7 +132,7 @@ SV* ConfigOption_to_SV(const ConfigOption &opt, const ConfigOptionDef &def)
         auto optv = static_cast<const ConfigOptionPoints*>(&opt);
         AV* av = newAV();
         av_fill(av, optv->values.size()-1);
-        for (const Pointf &v : optv->values)
+        for (const Vec2d &v : optv->values)
             av_store(av, &v - optv->values.data(), perl_to_SV_clone_ref(v));
         return newRV_noinc((SV*)av);
     }
@@ -263,14 +262,14 @@ bool ConfigBase__set(ConfigBase* THIS, const t_config_option_key &opt_key, SV* v
         return from_SV_check(value, &static_cast<ConfigOptionPoint*>(opt)->value);
     case coPoints:
     {
-        std::vector<Pointf> &values = static_cast<ConfigOptionPoints*>(opt)->values;
+        std::vector<Vec2d> &values = static_cast<ConfigOptionPoints*>(opt)->values;
         AV* av = (AV*)SvRV(value);
         const size_t len = av_len(av)+1;
         values.clear();
         values.reserve(len);
         for (size_t i = 0; i < len; i++) {
             SV** elem = av_fetch(av, i, 0);
-            Pointf point;
+            Vec2d point(Vec2d::Zero());
             if (elem == NULL || !from_SV_check(*elem, &point)) return false;
             values.emplace_back(point);
         }
@@ -509,7 +508,7 @@ void from_SV_check(SV* point_sv, Point* point)
     }
 }
 
-SV* to_SV_pureperl(const Pointf* point)
+SV* to_SV_pureperl(const Vec2d* point)
 {
     AV* av = newAV();
     av_fill(av, 1);
@@ -518,23 +517,23 @@ SV* to_SV_pureperl(const Pointf* point)
     return newRV_noinc((SV*)av);
 }
 
-bool from_SV(SV* point_sv, Pointf* point)
+bool from_SV(SV* point_sv, Vec2d* point)
 {
     AV* point_av = (AV*)SvRV(point_sv);
     SV* sv_x = *av_fetch(point_av, 0, 0);
     SV* sv_y = *av_fetch(point_av, 1, 0);
     if (!looks_like_number(sv_x) || !looks_like_number(sv_y)) return false;
     
-    *point = Pointf(SvNV(sv_x), SvNV(sv_y));
+    *point = Vec2d(SvNV(sv_x), SvNV(sv_y));
     return true;
 }
 
-bool from_SV_check(SV* point_sv, Pointf* point)
+bool from_SV_check(SV* point_sv, Vec2d* point)
 {
     if (sv_isobject(point_sv) && (SvTYPE(SvRV(point_sv)) == SVt_PVMG)) {
         if (!sv_isa(point_sv, perl_class_name(point)) && !sv_isa(point_sv, perl_class_name_ref(point)))
             CONFESS("Not a valid %s object (got %s)", perl_class_name(point), HvNAME(SvSTASH(SvRV(point_sv))));
-        *point = *(Pointf*)SvIV((SV*)SvRV( point_sv ));
+        *point = *(Vec2d*)SvIV((SV*)SvRV( point_sv ));
         return true;
     } else {
         return from_SV(point_sv, point);
diff --git a/xs/src/qhull/Announce.txt b/xs/src/qhull/Announce.txt
new file mode 100644
index 0000000000..635cff1afb
--- /dev/null
+++ b/xs/src/qhull/Announce.txt
@@ -0,0 +1,47 @@
+
+ Qhull 2015.2  2016/01/18
+
+        http://www.qhull.org
+        git@github.com:qhull/qhull.git
+        http://www.geomview.org
+
+Qhull computes convex hulls, Delaunay triangulations, Voronoi diagrams,
+furthest-site Voronoi diagrams, and halfspace intersections about a point.
+It runs in 2-d, 3-d, 4-d, or higher.  It implements the Quickhull algorithm
+for computing convex hulls.   Qhull handles round-off errors from floating
+point arithmetic.  It can approximate a convex hull.
+
+The program includes options for hull volume, facet area, partial hulls,
+input transformations, randomization, tracing, multiple output formats, and
+execution statistics.  The program can be called from within your application.
+You can view the results in 2-d, 3-d and 4-d with Geomview.
+
+To download Qhull:
+        http://www.qhull.org/download
+        git@github.com:qhull/qhull.git
+ 
+Download qhull-96.ps for:
+
+        Barber, C. B., D.P. Dobkin, and H.T. Huhdanpaa, "The
+        Quickhull Algorithm for Convex Hulls," ACM Trans. on
+        Mathematical Software, 22(4):469-483, Dec. 1996.
+        http://www.acm.org/pubs/citations/journals/toms/1996-22-4/p469-barber/
+        http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.117.405
+
+Abstract:
+
+The convex hull of a set of points is the smallest convex set that contains
+the points.  This article presents a practical convex hull algorithm that
+combines the two-dimensional Quickhull Algorithm with  the general dimension
+Beneath-Beyond Algorithm.  It is similar to the randomized, incremental
+algorithms for convex hull and Delaunay triangulation.  We provide empirical
+evidence that the algorithm runs faster when the input contains non-extreme
+points, and that it uses less memory.
+
+Computational geometry algorithms have traditionally assumed that input sets
+are well behaved.  When an algorithm is implemented with floating point
+arithmetic, this assumption can lead to serious errors.  We briefly describe
+a solution to this problem when computing the convex hull in two, three, or
+four dimensions.  The output is a set of "thick" facets that contain all
+possible exact convex hulls of the input.   A variation is effective in five
+or more dimensions.
diff --git a/xs/src/qhull/CMakeLists.txt b/xs/src/qhull/CMakeLists.txt
new file mode 100644
index 0000000000..d798b018fa
--- /dev/null
+++ b/xs/src/qhull/CMakeLists.txt
@@ -0,0 +1,128 @@
+
+# This CMake file is written specifically to integrate qhull library with Slic3rPE
+# (see https://github.com/prusa3d/Slic3r for more information about the project)
+#
+# Only original libraries qhullstatic_r and qhullcpp are included.
+# They are built as a single statically linked library.
+#
+# Created by modification of the original qhull CMakeLists.
+# Lukas Matena (25.7.2018), lukasmatena@seznam.cz
+
+
+project(qhull)
+cmake_minimum_required(VERSION 2.6)
+
+# Define qhull_VERSION in CMakeLists.txt, Makefile, qhull-exports.def, qhull_p-exports.def, qhull_r-exports.def, qhull-warn.pri
+set(qhull_VERSION2 "2015.2 2016/01/18")  # not used, See global.c, global_r.c, rbox.c, rbox_r.c
+set(qhull_VERSION     "7.2.0")  # Advance every release
+
+#include(CMakeModules/CheckLFS.cmake)
+#option(WITH_LFS "Enable Large File Support" ON)
+#check_lfs(WITH_LFS)
+
+
+message(STATUS "qhull Version: ${qhull_VERSION} (static linking)")
+
+
+set(libqhull_HEADERS
+    # reentrant qhull HEADERS:
+        src/libqhull_r/libqhull_r.h
+        src/libqhull_r/geom_r.h
+        src/libqhull_r/io_r.h
+        src/libqhull_r/mem_r.h
+        src/libqhull_r/merge_r.h
+        src/libqhull_r/poly_r.h
+        src/libqhull_r/qhull_ra.h
+        src/libqhull_r/qset_r.h
+        src/libqhull_r/random_r.h
+        src/libqhull_r/stat_r.h
+        src/libqhull_r/user_r.h
+
+    # C++ interface to reentrant Qhull HEADERS:
+        src/libqhullcpp/Coordinates.h
+        src/libqhullcpp/functionObjects.h
+        src/libqhullcpp/PointCoordinates.h
+        src/libqhullcpp/Qhull.h
+        src/libqhullcpp/QhullError.h
+        src/libqhullcpp/QhullFacet.h
+        src/libqhullcpp/QhullFacetList.h
+        src/libqhullcpp/QhullFacetSet.h
+        src/libqhullcpp/QhullHyperplane.h
+        src/libqhullcpp/QhullIterator.h
+        src/libqhullcpp/QhullLinkedList.h
+        src/libqhullcpp/QhullPoint.h
+        src/libqhullcpp/QhullPoints.h
+        src/libqhullcpp/QhullPointSet.h
+        src/libqhullcpp/QhullQh.h
+        src/libqhullcpp/QhullRidge.h
+        src/libqhullcpp/QhullSet.h
+        src/libqhullcpp/QhullSets.h
+        src/libqhullcpp/QhullStat.h
+        src/libqhullcpp/QhullVertex.h
+        src/libqhullcpp/QhullVertexSet.h
+        src/libqhullcpp/RboxPoints.h
+        src/libqhullcpp/RoadError.h
+        src/libqhullcpp/RoadLogEvent.h
+        src/qhulltest/RoadTest.h
+)
+
+set(libqhull_SOURCES
+    # reentrant qhull SOURCES:
+        src/libqhull_r/global_r.c
+        src/libqhull_r/stat_r.c
+        src/libqhull_r/geom2_r.c
+        src/libqhull_r/poly2_r.c
+        src/libqhull_r/merge_r.c
+        src/libqhull_r/libqhull_r.c
+        src/libqhull_r/geom_r.c
+        src/libqhull_r/poly_r.c
+        src/libqhull_r/qset_r.c
+        src/libqhull_r/mem_r.c
+        src/libqhull_r/random_r.c
+        src/libqhull_r/usermem_r.c
+        src/libqhull_r/userprintf_r.c
+        src/libqhull_r/io_r.c
+        src/libqhull_r/user_r.c
+        src/libqhull_r/rboxlib_r.c
+        src/libqhull_r/userprintf_rbox_r.c
+
+    # C++ interface to reentrant Qhull SOURCES:
+        src/libqhullcpp/Coordinates.cpp
+        src/libqhullcpp/PointCoordinates.cpp
+        src/libqhullcpp/Qhull.cpp
+        src/libqhullcpp/QhullFacet.cpp
+        src/libqhullcpp/QhullFacetList.cpp
+        src/libqhullcpp/QhullFacetSet.cpp
+        src/libqhullcpp/QhullHyperplane.cpp
+        src/libqhullcpp/QhullPoint.cpp
+        src/libqhullcpp/QhullPointSet.cpp
+        src/libqhullcpp/QhullPoints.cpp
+        src/libqhullcpp/QhullQh.cpp
+        src/libqhullcpp/QhullRidge.cpp
+        src/libqhullcpp/QhullSet.cpp
+        src/libqhullcpp/QhullStat.cpp
+        src/libqhullcpp/QhullVertex.cpp
+        src/libqhullcpp/QhullVertexSet.cpp
+        src/libqhullcpp/RboxPoints.cpp
+        src/libqhullcpp/RoadError.cpp
+        src/libqhullcpp/RoadLogEvent.cpp
+
+    # headers for both (libqhullr and libqhullcpp:
+        ${libqhull_HEADERS}
+)
+
+
+##################################################
+# combined library (reentrant qhull and qhullcpp) for Slic3r:
+set(qhull_STATIC qhull)
+add_library(${qhull_STATIC} STATIC ${libqhull_SOURCES})
+set_target_properties(${qhull_STATIC} PROPERTIES
+    VERSION ${qhull_VERSION})
+
+if(UNIX)
+    target_link_libraries(${qhull_STATIC} m)
+endif(UNIX)
+##################################################
+
+# LIBDIR is defined in the main xs CMake file:
+target_include_directories(${qhull_STATIC} PRIVATE ${LIBDIR}/qhull/src)
diff --git a/xs/src/qhull/COPYING.txt b/xs/src/qhull/COPYING.txt
new file mode 100644
index 0000000000..2895ec6a32
--- /dev/null
+++ b/xs/src/qhull/COPYING.txt
@@ -0,0 +1,38 @@
+                    Qhull, Copyright (c) 1993-2015
+                    
+                            C.B. Barber
+                           Arlington, MA 
+                          
+                               and
+
+       The National Science and Technology Research Center for
+        Computation and Visualization of Geometric Structures
+                        (The Geometry Center)
+                       University of Minnesota
+
+                       email: qhull@qhull.org
+
+This software includes Qhull from C.B. Barber and The Geometry Center.  
+Qhull is copyrighted as noted above.  Qhull is free software and may 
+be obtained via http from www.qhull.org.  It may be freely copied, modified, 
+and redistributed under the following conditions:
+
+1. All copyright notices must remain intact in all files.
+
+2. A copy of this text file must be distributed along with any copies 
+   of Qhull that you redistribute; this includes copies that you have 
+   modified, or copies of programs or other software products that 
+   include Qhull.
+
+3. If you modify Qhull, you must include a notice giving the
+   name of the person performing the modification, the date of
+   modification, and the reason for such modification.
+
+4. When distributing modified versions of Qhull, or other software 
+   products that include Qhull, you must provide notice that the original 
+   source code may be obtained as noted above.
+
+5. There is no warranty or other guarantee of fitness for Qhull, it is 
+   provided solely "as is".  Bug reports or fixes may be sent to 
+   qhull_bug@qhull.org; the authors may or may not act on them as 
+   they desire.
diff --git a/xs/src/qhull/README.txt b/xs/src/qhull/README.txt
new file mode 100644
index 0000000000..f4c7a3b220
--- /dev/null
+++ b/xs/src/qhull/README.txt
@@ -0,0 +1,623 @@
+This distribution of qhull library is only meant for interfacing qhull with Slic3rPE
+(https://github.com/prusa3d/Slic3r).
+
+The qhull source file was acquired from https://github.com/qhull/qhull at revision
+f0bd8ceeb84b554d7cdde9bbfae7d3351270478c.
+
+No changes to the qhull library were made, except for
+- setting REALfloat=1 in user_r.h to enforce calculations in floats
+- modifying CMakeLists.txt (the original was renamed to origCMakeLists.txt)
+
+Many thanks to C. Bradford Barber and all contributors.
+
+Lukas Matena (lukasmatena@seznam.cz)
+25.7.2018
+
+
+See original contents of the README file below.
+
+======================================================================================
+======================================================================================
+======================================================================================
+
+
+Name
+
+      qhull, rbox         2015.2       2016/01/18
+  
+Convex hull, Delaunay triangulation, Voronoi diagrams, Halfspace intersection
+ 
+      Documentation:
+        html/index.htm
+        <http://www.qhull.org/html>
+
+      Available from:
+        <http://www.qhull.org>
+        <http://www.qhull.org/download>
+        <http://github.com/qhull/qhull> (git@github.com:qhull/qhull.git)
+ 
+      News and a paper:
+        <http://www.qhull.org/news>
+        <http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.117.405>
+
+     Version 1 (simplicial only):
+        <http://www.qhull.org/download/qhull-1.0.tar.gz>
+       
+Purpose
+
+  Qhull is a general dimension convex hull program that reads a set 
+  of points from stdin, and outputs the smallest convex set that contains 
+  the points to stdout.  It also generates Delaunay triangulations, Voronoi 
+  diagrams, furthest-site Voronoi diagrams, and halfspace intersections
+  about a point.
+
+  Rbox is a useful tool in generating input for Qhull; it generates 
+  hypercubes, diamonds, cones, circles, simplices, spirals, 
+  lattices, and random points.
+  
+  Qhull produces graphical output for Geomview.  This helps with
+  understanding the output. <http://www.geomview.org>
+
+Environment requirements
+
+  Qhull and rbox should run on all 32-bit and 64-bit computers.  Use
+  an ANSI C or C++ compiler to compile the program.  The software is 
+  self-contained.  It comes with examples and test scripts.
+  
+  Qhull's C++ interface uses the STL.  The C++ test program uses QTestLib 
+  from the Qt Framework.  Qhull's C++ interface may change without 
+  notice.  Eventually, it will move into the qhull shared library.
+  
+  Qhull is copyrighted software.  Please read COPYING.txt and REGISTER.txt
+  before using or distributing Qhull.
+
+To cite Qhull, please use
+
+  Barber, C.B., Dobkin, D.P., and Huhdanpaa, H.T., "The Quickhull 
+  algorithm for convex hulls," ACM Trans. on Mathematical Software,
+  22(4):469-483, Dec 1996, http://www.qhull.org.
+
+To modify Qhull, particularly the C++ interface
+
+  Qhull is on GitHub 
+     (http://github.com/qhull/qhull, git@github.com:qhull/qhull.git)
+  
+  For internal documentation, see html/qh-code.htm
+
+To install Qhull
+
+  Qhull is precompiled for Windows 32-bit, otherwise it needs compilation.
+  
+  Qhull includes Makefiles for gcc and other targets, CMakeLists.txt for CMake,
+  .sln/.vcproj/.vcxproj files for Microsoft Visual Studio, and .pro files 
+  for Qt Creator.  It compiles under Windows with mingw.
+  
+  Install and build instructions follow.  
+  
+  See the end of this document for a list of distributed files.
+
+-----------------
+Installing Qhull on Windows 10, 8, 7 (32- or 64-bit), Windows XP, and Windows NT
+
+  The zip file contains rbox.exe, qhull.exe, qconvex.exe, qdelaunay.exe, 
+  qhalf.exe, qvoronoi.exe, testqset.exe, user_eg*.exe, documentation files, 
+  and source files.  Qhull.exe and user-eg3.exe are compiled with the reentrant 
+  library while the other executables use the non-reentrant library.
+  
+  To install Qhull:
+  - Unzip the files into a directory (e.g., named 'qhull')
+  - Click on QHULL-GO or open a command window into Qhull's bin directory.
+  - Test with 'rbox D4 | qhull'
+    
+  To uninstall Qhull
+  - Delete the qhull directory
+  
+  To learn about Qhull:
+  - Execute 'qconvex' for a synopsis and examples.
+  - Execute 'rbox 10 | qconvex' to compute the convex hull of 10 random points.
+  - Execute 'rbox 10 | qconvex i TO file' to write results to 'file'.
+  - Browse the documentation: qhull\html\index.htm
+  - If an error occurs, Windows sends the error to stdout instead of stderr.
+    Use 'TO xxx' to send normal output to xxx
+
+  To improve the command window
+  - Double-click the window bar to increase the size of the window
+  - Right-click the window bar
+  - Select Properties
+  - Check QuickEdit Mode
+    Select text with right-click or Enter
+    Paste text with right-click
+  - Change Font to Lucinda Console
+  - Change Layout to Screen Buffer Height 999, Window Size Height 55
+  - Change Colors to Screen Background White, Screen Text Black
+  - Click OK
+  - Select 'Modify shortcut that started this window', then OK
+
+  If you use qhull a lot, install a bash shell such as
+    MSYS (www.mingw.org/wiki/msys), Road Bash (www.qhull.org/bash), 
+    or Cygwin (www.cygwin.com).
+
+-----------------
+Installing Qhull on Unix with gcc
+
+  To build Qhull, static libraries, shared library, and C++ interface
+  - Download and extract Qhull (either GitHub, .tgz file, or .zip file)
+  - make
+  - export LD_LIBRARY_PATH=$PWD/lib:$LD_LIBRARY_PATH
+
+  The Makefiles may be edited for other compilers.
+  If 'testqset' exits with an error, qhull is broken
+  
+  A simple Makefile for Qhull is in src/libqhull and src/libqhull_r.
+  To build the Qhull executables and libqhullstatic
+  - Extract Qhull from qhull...tgz or qhull...zip
+  - cd src/libqhull_r  # cd src/libqhull 
+  - make
+
+  
+-----------------
+Installing Qhull with CMake 2.6 or later
+
+  See CMakeLists.txt for examples and further build instructions
+  
+  To build Qhull, static libraries, shared library, and C++ interface
+  - Download and extract Qhull (either GitHub, .tgz file, or .zip file)
+  - cd build
+  - cmake --help  # List build generators
+  - make -G "<generator>" .. && cmake ..  
+  - cmake ..
+  - make
+  - make install
+
+  The ".." is important.  It refers to the parent directory (i.e., qhull/)
+
+  On Windows, CMake installs to C:/Program Files/qhull.  64-bit generators
+  have a "Win64" tag.
+  
+  If creating a qhull package, please include a pkg-config file based on build/qhull*.pc.in
+
+  If cmake fails with "No CMAKE_C_COMPILER could be found"
+  - cmake was not able to find the build environment specified by -G "..."
+  
+-----------------
+Installing Qhull with Qt
+
+  To build Qhull, including its C++ test (qhulltest)
+  - Download and extract Qhull (either GitHub, .tgz file, or .zip file)
+  - Load src/qhull-all.pro into QtCreator
+  - Build
+
+-------------------
+Working with Qhull's C++ interface
+
+  See html/qh-code.htm#cpp for calling Qhull from C++ programs
+  
+  See html/qh-code.htm#reentrant for converting from Qhull-2012
+
+  Examples of using the C++ interface
+    user_eg3_r.cpp
+    qhulltest/*_test.cpp
+
+  Qhull's C++ interface is likely to change.  Stay current with GitHub.
+
+  To clone Qhull's next branch from http://github.com/qhull/qhull
+    git init
+    git clone git@github.com:qhull/qhull.git
+    cd qhull
+    git checkout next
+    ...
+    git pull origin next
+    
+  Compile qhullcpp and libqhullstatic_r with the same compiler.  Both libraries
+  use the C routines setjmp() and longjmp() for error handling.  They must 
+  be compiled with the same compiler.
+  
+-------------------
+Calling Qhull from C programs
+
+  See html/qh-code.htm#library for calling Qhull from C programs
+
+  See html/qh-code.htm#reentrant for converting from Qhull-2012
+
+  Warning: You will need to understand Qhull's data structures and read the 
+  code.  Most users will find it easier to call Qhull as an external command.
+
+  The new, reentrant 'C' code (src/libqhull_r), passes a pointer to qhT 
+  to most Qhull routines.  This allows multiple instances of Qhull to run 
+  at the same time.  It simplifies the C++ interface.
+
+  The non-reentrant 'C' code (src/libqhull) looks unusual.  It refers to 
+  Qhull's global data structure, qhT, through a 'qh' macro (e.g., 'qh ferr'). 
+  This allows the same code to use static memory or heap memory. 
+  If qh_QHpointer is defined, qh_qh is a pointer to an allocated qhT; 
+  otherwise qh_qh is a global static data structure of type qhT.
+
+------------------
+Compiling Qhull with Microsoft Visual C++
+
+  To compile 32-bit Qhull with Microsoft Visual C++ 2010 and later
+  - Download and extract Qhull (either GitHub, .tgz file, or .zip file)
+  - Load solution build/qhull-32.sln 
+  - Build target 'Win32'
+  - Project qhulltest requires Qt for DevStudio (http://www.qt.io)
+    Set the QTDIR environment variable to your Qt directory (e.g., c:/qt/5.2.0/5.2.0/msvc2012)
+    If QTDIR is incorrect, precompile will fail with 'Can not locate the file specified'
+
+  To compile 64-bit Qhull with Microsoft Visual C++ 2010 and later
+  - 64-bit Qhull has larger data structures due to 64-bit pointers
+  - Download and extract Qhull (either GitHub, .tgz file, or .zip file)
+  - Load solution build/qhull-64.sln 
+  - Build target 'Win32'
+  - Project qhulltest requires Qt for DevStudio (http://www.qt.io)
+    Set the QTDIR environment variable to your Qt directory (e.g., c:/qt/5.2.0/5.2.0/msvc2012_64)
+    If QTDIR is incorrect, precompile will fail with 'Can not locate the file specified'
+  
+  To compile Qhull with Microsoft Visual C++ 2005 (vcproj files)
+  - Download and extract Qhull (either GitHub, .tgz file, or .zip file)
+  - Load solution build/qhull.sln 
+  - Build target 'win32' (not 'x64')
+  - Project qhulltest requires Qt for DevStudio (http://www.qt.io)
+    Set the QTDIR environment variable to your Qt directory (e.g., c:/qt/4.7.4)
+    If QTDIR is incorrect, precompile will fail with 'Can not locate the file specified'
+  
+-----------------
+Compiling Qhull with Qt Creator
+
+  Qt (http://www.qt.io) is a C++ framework for Windows, Linux, and Macintosh
+
+  Qhull uses QTestLib to test qhull's C++ interface (see src/qhulltest/)
+  
+  To compile Qhull with Qt Creator
+  - Download and extract Qhull (either GitHub, .tgz file, or .zip file)
+  - Download the Qt SDK
+  - Start Qt Creator
+  - Load src/qhull-all.pro
+  - Build
+
+-----------------
+Compiling Qhull with mingw on Windows
+
+  To compile Qhull with MINGW
+  - Download and extract Qhull (either GitHub, .tgz file, or .zip file)
+  - Install Road Bash (http://www.qhull.org/bash)
+    or install MSYS (http://www.mingw.org/wiki/msys)
+  - Install MINGW-w64 (http://sourceforge.net/projects/mingw-w64).  
+    Mingw is included with Qt SDK.  
+  - make
+  
+-----------------
+Compiling Qhull with cygwin on Windows
+
+  To compile Qhull with cygwin
+  - Download and extract Qhull (either GitHub, .tgz file, or .zip file)
+  - Install cygwin (http://www.cygwin.com)
+  - Include packages for gcc, make, ar, and ln
+  - make
+
+-----------------
+Compiling from Makfile without gcc
+
+  The file, qhull-src.tgz, contains documentation and source files for
+  qhull and rbox.  
+  
+  To unpack the tgz file
+  - tar zxf qhull-src.tgz
+  - cd qhull
+  - Use qhull/Makefile
+   Simpler Makefiles are qhull/src/libqhull/Makefile and qhull/src/libqhull_r/Makefile
+  
+  Compiling qhull and rbox with Makefile
+  - in Makefile, check the CC, CCOPTS1, PRINTMAN, and PRINTC defines
+      - the defaults are gcc and enscript
+      - CCOPTS1 should include the ANSI flag.  It defines __STDC__
+  - in user.h, check the definitions of qh_SECticks and qh_CPUclock.
+      - use '#define qh_CLOCKtype 2' for timing runs longer than 1 hour
+  - type: make 
+      - this builds: qhull qconvex qdelaunay qhalf qvoronoi rbox libqhull.a libqhull_r.a
+  - type: make doc
+      - this prints the man page
+      - See also qhull/html/index.htm
+  - if your compiler reports many errors, it is probably not a ANSI C compiler
+      - you will need to set the -ansi switch or find another compiler
+  - if your compiler warns about missing prototypes for fprintf() etc.
+      - this is ok, your compiler should have these in stdio.h
+  - if your compiler warns about missing prototypes for memset() etc.
+      - include memory.h in qhull_a.h
+  - if your compiler reports "global.c: storage size of 'qh_qh' isn't known"
+      - delete the initializer "={0}" in global.c, stat.c and mem.c
+  - if your compiler warns about "stat.c: improper initializer"
+      - this is ok, the initializer is not used
+  - if you have trouble building libqhull.a with 'ar'
+      - try 'make -f Makefile.txt qhullx' 
+  - if the code compiles, the qhull test case will automatically execute
+  - if an error occurs, there's an incompatibility between machines
+      - If you can, try a different compiler 
+      - You can turn off the Qhull memory manager with qh_NOmem in mem.h
+      - You can turn off compiler optimization (-O2 in Makefile)
+      - If you find the source of the problem, please let us know
+  - to install the programs and their man pages:
+      - define MANDIR and BINDIR
+      - type 'make install'
+
+  - if you have Geomview (www.geomview.org)
+       - try  'rbox 100 | qconvex G >a' and load 'a' into Geomview
+       - run 'q_eg' for Geomview examples of Qhull output (see qh-eg.htm)
+
+------------------
+Compiling on other machines and compilers
+
+  Qhull may compile with Borland C++ 5.0 bcc32.  A Makefile is included.
+  Execute 'cd src/libqhull; make -f Mborland'.  If you use the Borland IDE, set
+  the ANSI option in Options:Project:Compiler:Source:Language-compliance.
+  
+  Qhull may compile with Borland C++ 4.02 for Win32 and DOS Power Pack.  
+  Use 'cd src/libqhull; make -f Mborland -D_DPMI'.  Qhull 1.0 compiles with 
+  Borland C++ 4.02.  For rbox 1.0, use "bcc32 -WX -w- -O2-e -erbox -lc rbox.c".  
+  Use the same options for Qhull 1.0. [D. Zwick]
+  
+  If you have troubles with the memory manager, you can turn it off by
+  defining qh_NOmem in mem.h.
+
+-----------------
+Distributed files
+
+  README.txt           // Instructions for installing Qhull 
+  REGISTER.txt         // Qhull registration 
+  COPYING.txt          // Copyright notice 
+  QHULL-GO.lnk         // Windows icon for eg/qhull-go.bat
+  Announce.txt         // Announcement 
+  CMakeLists.txt       // CMake build file (2.6 or later)
+  CMakeModules/CheckLFS.cmake // enables Large File Support in cmake
+  File_id.diz          // Package descriptor
+  index.htm            // Home page 
+  Makefile             // Makefile for gcc and other compilers
+  qhull*.md5sum        // md5sum for all files
+
+  bin/*                // Qhull executables and dll (.zip only)
+  build/qhull*.pc.in   // pkg-config templates for qhull_r, qhull, and qhull_p
+  build/qhull-32.sln   // 32-bit DevStudio solution and project files (2010 and later)
+  build/*-32.vcxproj
+  build/qhull-64.sln   // 64-bit DevStudio solution and project files (2010 and later)
+  build/*-64.vcxproj
+  build/qhull.sln      // DevStudio solution and project files (2005 and 2009)
+  build/*.vcproj
+  eg/*                 // Test scripts and geomview files from q_eg
+  html/index.htm       // Manual
+  html/qh-faq.htm      // Frequently asked questions
+  html/qh-get.htm      // Download page
+  html/qhull-cpp.xml   // C++ style notes as a Road FAQ (www.qhull.org/road)
+  src/Changes.txt      // Change history for Qhull and rbox 
+  src/qhull-all.pro    // Qt project
+
+eg/ 
+  q_eg                 // shell script for Geomview examples (eg.01.cube)
+  q_egtest             // shell script for Geomview test examples
+  q_test               // shell script to test qhull
+  q_test-ok.txt        // output from q_test
+  qhulltest-ok.txt     // output from qhulltest (Qt only)
+  make-vcproj.sh       // bash shell script to create vcproj and vcxprog files
+  qhull-zip.sh	       // bash shell script for distribution files
+
+rbox consists of (bin, html):
+  rbox.exe             // Win32 executable (.zip only) 
+  rbox.htm             // html manual 
+  rbox.man             // Unix man page 
+  rbox.txt
+
+qhull consists of (bin, html):
+  qconvex.exe          // Win32 executables and dlls (.zip download only) 
+  qhull.exe            // Built with the reentrant library (about 2% slower)
+  qdelaunay.exe
+  qhalf.exe
+  qvoronoi.exe
+  qhull_r.dll
+  qhull-go.bat         // command window
+  qconvex.htm          // html manual
+  qdelaun.htm
+  qdelau_f.htm        
+  qhalf.htm
+  qvoronoi.htm
+  qvoron_f.htm
+  qh-eg.htm
+  qh-code.htm
+  qh-impre.htm
+  index.htm
+  qh-opt*.htm
+  qh-quick.htm
+  qh--*.gif            // images for manual
+  normal_voronoi_knauss_oesterle.jpg
+  qhull.man            // Unix man page 
+  qhull.txt
+
+bin/
+  msvcr80.dll          // Visual C++ redistributable file (.zip download only)
+
+src/
+  qhull/unix.c         // Qhull and rbox applications using non-reentrant libqhullstatic.a
+  rbox/rbox.c
+  qconvex/qconvex.c    
+  qhalf/qhalf.c
+  qdelaunay/qdelaunay.c
+  qvoronoi/qvoronoi.c
+
+  qhull/unix_r.c        // Qhull and rbox applications using reentrant libqhullstatic_r.a
+  rbox/rbox_r.c
+  qconvex/qconvex_r.c   // Qhull applications built with reentrant libqhull_r/Makefile  
+  qhalf/qhalf_r.c
+  qdelaunay/qdelaun_r.c
+  qvoronoi/qvoronoi_r.c
+
+  user_eg/user_eg_r.c     // example of using qhull_r.dll from a user program
+  user_eg2/user_eg2_r.c   // example of using libqhullstatic_r.a from a user program
+  user_eg3/user_eg3_r.cpp // example of Qhull's C++ interface libqhullcpp with libqhullstatic_r.a
+  qhulltest/qhulltest.cpp // Test of Qhull's C++ interface using Qt's QTestLib
+  qhull-*.pri             // Include files for Qt projects
+  testqset_r/testqset_r.c  // Test of reentrant qset_r.c and mem_r.c
+  testqset/testqset.c     // Test of non-rentrant qset.c and mem.c
+
+
+src/libqhull
+  libqhull.pro         // Qt project for non-rentrant, shared library (qhull.dll)
+  index.htm            // design documentation for libqhull
+  qh-*.htm
+  qhull-exports.def    // Export Definition file for Visual C++
+  Makefile             // Simple gcc Makefile for qhull and libqhullstatic.a
+  Mborland             // Makefile for Borland C++ 5.0
+
+  libqhull.h           // header file for qhull
+  user.h               // header file of user definable constants 
+  libqhull.c           // Quickhull algorithm with partitioning
+  user.c               // user re-definable functions 
+  usermem.c
+  userprintf.c
+  userprintf_rbox.c
+
+  qhull_a.h            // include files for libqhull/*.c 
+  geom.c               // geometric routines 
+  geom2.c
+  geom.h     
+  global.c             // global variables 
+  io.c                 // input-output routines 
+  io.h   
+  mem.c                // memory routines, this is stand-alone code 
+  mem.h
+  merge.c              // merging of non-convex facets 
+  merge.h
+  poly.c               // polyhedron routines 
+  poly2.c
+  poly.h 
+  qset.c               // set routines, this only depends on mem.c 
+  qset.h
+  random.c             // utilities w/ Park & Miller's random number generator
+  random.h
+  rboxlib.c            // point set generator for rbox
+  stat.c               // statistics 
+  stat.h
+
+src/libqhull_r
+  libqhull_r.pro       // Qt project for rentrant, shared library (qhull_r.dll)
+  index.htm            // design documentation for libqhull_r
+  qh-*_r.htm
+  qhull-exports_r.def  // Export Definition file for Visual C++
+  Makefile             // Simple gcc Makefile for qhull and libqhullstatic.a
+
+  libqhull_r.h          // header file for qhull
+  user_r.h              // header file of user definable constants 
+  libqhull_r.c          // Quickhull algorithm wi_r.hpartitioning
+  user_r.c              // user re-definable functions 
+  usermem.c
+  userprintf.c
+  userprintf_rbox.c
+  qhull_ra.h            // include files for libqhull/*_r.c
+  geom_r.c              // geometric routines 
+  geom2.c
+  geom_r.h    
+  global_r.c            // global variables 
+  io_r.c                // input-output routines 
+  io_r.h  
+  mem_r.c               // memory routines, this is stand-alone code 
+  mem.h
+  merge_r.c             // merging of non-convex facets 
+  merge.h
+  poly_r.c              // polyhedron routines 
+  poly2.c
+  poly_r.h
+  qset_r.c              // set routines, this only depends on mem_r.c
+  qset.h
+  random_r.c            // utilities w/ Park & Miller's random number generator
+  random.h
+  rboxlib_r.c           // point set generator for rbox
+  stat_r.c              // statistics 
+  stat.h
+
+src/libqhullcpp/
+  libqhullcpp.pro      // Qt project for renentrant, static C++ library     
+  Qhull.cpp            // Calls libqhull_r.c from C++
+  Qhull.h
+  qt-qhull.cpp         // Supporting methods for Qt
+    
+  Coordinates.cpp      // input classes
+  Coordinates.h
+
+  PointCoordinates.cpp
+  PointCoordinates.h
+  RboxPoints.cpp       // call rboxlib.c from C++
+  RboxPoints.h
+
+  QhullFacet.cpp       // data structure classes
+  QhullFacet.h
+  QhullHyperplane.cpp
+  QhullHyperplane.h
+  QhullPoint.cpp
+  QhullPoint.h
+  QhullQh.cpp
+  QhullRidge.cpp
+  QhullRidge.h
+  QhullVertex.cpp
+  QhullVertex.h
+  
+  QhullFacetList.cpp   // collection classes
+  QhullFacetList.h
+  QhullFacetSet.cpp
+  QhullFacetSet.h
+  QhullIterator.h
+  QhullLinkedList.h
+  QhullPoints.cpp
+  QhullPoints.h
+  QhullPointSet.cpp
+  QhullPointSet.h
+  QhullSet.cpp
+  QhullSet.h
+  QhullSets.h
+  QhullVertexSet.cpp
+  QhullVertexSet.h
+
+  functionObjects.h    // supporting classes
+  QhullError.cpp
+  QhullError.h
+  QhullQh.cpp
+  QhullQh.h
+  QhullStat.cpp
+  QhullStat.h
+  RoadError.cpp        // Supporting base classes
+  RoadError.h
+  RoadLogEvent.cpp
+  RoadLogEvent.h
+  usermem_r-cpp.cpp    // Optional override for qh_exit() to throw an error
+
+src/libqhullstatic/
+  libqhullstatic.pro   // Qt project for non-reentrant, static library     
+     
+src/libqhullstatic_r/
+  libqhullstatic_r.pro // Qt project for reentrant, static library     
+     
+src/qhulltest/
+  qhulltest.pro        // Qt project for test of C++ interface     
+  Coordinates_test.cpp // Test of each class
+  PointCoordinates_test.cpp
+  Qhull_test.cpp
+  QhullFacet_test.cpp
+  QhullFacetList_test.cpp
+  QhullFacetSet_test.cpp
+  QhullHyperplane_test.cpp
+  QhullLinkedList_test.cpp
+  QhullPoint_test.cpp
+  QhullPoints_test.cpp
+  QhullPointSet_test.cpp
+  QhullRidge_test.cpp
+  QhullSet_test.cpp
+  QhullVertex_test.cpp
+  QhullVertexSet_test.cpp
+  RboxPoints_test.cpp
+  RoadTest.cpp         // Run multiple test files with QTestLib
+  RoadTest.h
+
+-----------------
+Authors:
+
+  C. Bradford Barber                  Hannu Huhdanpaa (Version 1.0)
+  bradb@shore.net                     hannu@qhull.org
+  
+  Qhull 1.0 and 2.0 were developed under NSF grants NSF/DMS-8920161 
+  and NSF-CCR-91-15793 750-7504 at the Geometry Center and Harvard 
+  University.  If you find Qhull useful, please let us know.
diff --git a/xs/src/qhull/REGISTER.txt b/xs/src/qhull/REGISTER.txt
new file mode 100644
index 0000000000..16ccb1a58d
--- /dev/null
+++ b/xs/src/qhull/REGISTER.txt
@@ -0,0 +1,32 @@
+Dear Qhull User
+
+We would like to find out how you are using our software.  Think of
+Qhull as a new kind of shareware: you share your science and successes 
+with us, and we share our software and support with you. 
+
+If you use Qhull, please send us a note telling
+us what you are doing with it.
+
+We need to know:
+
+  (1) What you are working on - an abstract of your work would be
+      fine.
+
+  (2) How Qhull has helped you, for example, by increasing your 
+      productivity or allowing you to do things you could not do
+      before.  If Qhull had a direct bearing on your work, please 
+      tell us about this.
+
+We encourage you to cite Qhull in your publications.  
+
+To cite Qhull, please use
+
+        Barber, C.B., Dobkin, D.P., and Huhdanpaa, H.T., "The Quickhull 
+        algorithm for convex hulls," ACM Trans. on Mathematical Software,
+        22(4):469-483, Dec 1996, http://www.qhull.org.
+
+Please send e-mail to
+
+    bradb@shore.net
+
+Thank you!
diff --git a/xs/src/qhull/html/index.htm b/xs/src/qhull/html/index.htm
new file mode 100644
index 0000000000..ca4789b47f
--- /dev/null
+++ b/xs/src/qhull/html/index.htm
@@ -0,0 +1,935 @@
+<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN">
+<html>
+
+<head>
+<meta http-equiv="Content-Type"
+content="text/html; charset=iso-8859-1">
+<meta name="GENERATOR" content="Microsoft FrontPage 2.0">
+<title>Qhull manual</title>
+<!-- Navigation links
+NOTE -- verify all links by 'grep href=' 'grep name=' add # 'sort /+7'
+        index.htm
+-->
+</head>
+
+<body>
+
+<p><a name="TOP"><b>Up:</b></a> <a
+href="http://www.qhull.org">Home page</a> for Qhull<br>
+<b>Up:</b><a
+href="http://www.qhull.org/news">News</a> about Qhull<br>
+<b>Up:</b> <a href="http://www.qhull.org/html/qh-faq.htm">FAQ</a> about Qhull<br>
+<b>To:</b> <a href="#TOC">Qhull manual: Table of Contents</a>
+(please wait while loading) <br>
+<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
+&#149; <a href="qh-quick.htm#options">Options</a>
+&#149; <a href="qh-opto.htm#output">Output</a>
+&#149; <a href="qh-optf.htm#format">Formats</a>
+&#149; <a href="qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="qh-optp.htm#print">Print</a>
+&#149; <a href="qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="qh-optc.htm#prec">Precision</a>
+&#149; <a href="qh-optt.htm#trace">Trace</a>
+&#149; <a href="../src/libqhull_r/index.htm">Functions</a><br>
+
+<hr>
+<!-- Main text of document -->
+<h1><a
+href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/fixed.html"><img
+src="qh--rand.gif" alt="[random-fixed]" align="middle"
+width="100" height="100"></a> Qhull manual </h1>
+
+<p>Qhull is a general dimension code for computing convex hulls,
+Delaunay triangulations, halfspace intersections about a point, Voronoi
+diagrams, furthest-site Delaunay triangulations, and
+furthest-site Voronoi diagrams.  These structures have
+applications in science, engineering, statistics, and
+mathematics. See <a
+href="http://www.cs.mcgill.ca/~fukuda/soft/polyfaq/polyfaq.html">Fukuda's
+introduction</a> to convex hulls, Delaunay triangulations,
+Voronoi diagrams, and linear programming. For a detailed
+introduction, see O'Rourke [<a href="#orou94">'94</a>], <i>Computational
+Geometry in C</i>.
+</p>
+
+<p>There are six programs.  Except for rbox, they use
+the same code.  Each program includes instructions and examples.
+<blockquote>
+<ul>
+<li><a href="qconvex.htm">qconvex</a> -- convex hulls
+<li><a href="qdelaun.htm">qdelaunay</a> -- Delaunay triangulations and
+ furthest-site Delaunay triangulations
+<li><a href="qhalf.htm">qhalf</a> -- halfspace intersections about a point
+<li><a href="qhull.htm">qhull</a> -- all structures with additional options
+<li><a href="qvoronoi.htm">qvoronoi</a> -- Voronoi diagrams and
+  furthest-site Voronoi diagrams
+<li><a href="rbox.htm">rbox</a> -- generate point distributions for qhull
+</ul>
+</blockquote>
+
+<p>Qhull implements the Quickhull algorithm for computing the
+convex hull. Qhull includes options
+for hull volume, facet area, multiple output formats, and
+graphical output. It can approximate a convex hull. </p>
+
+<p>Qhull handles roundoff errors from floating point
+arithmetic.  It generates a convex hull with "thick" facets.
+A facet's outer plane is clearly above all of the points;
+its inner plane is clearly below the facet's vertices.  Any
+exact convex hull must lie between the inner and outer plane.
+
+<p>Qhull uses merged facets, triangulated output, or joggled
+input.  Triangulated output triangulates non-simplicial, merged
+facets.  Joggled input also
+guarantees simplicial output, but it
+is less accurate than merged facets.  For merged facets, Qhull
+reports the maximum outer and inner plane.
+
+<p><i>Brad Barber, Arlington, MA</i></p>
+
+<p><b>Copyright &copy; 1995-2015 C.B. Barber</b></p>
+
+<hr>
+
+<h2><a href="#TOP">&#187;</a><a name="TOC">Qhull manual: Table of
+Contents </a></h2>
+
+<ul>
+    <li><a href="#when">When</a> to use Qhull
+             <ul>
+         <li><a href="http://www.qhull.org/news">News</a> for Qhull
+         with new features and reported bugs.
+        <li><a href="http://www.qhull.org">Home</a> for Qhull with additional URLs
+                (<a href=index.htm>local copy</a>)
+                <li><a href="http://www.qhull.org/html/qh-faq.htm">FAQ</a> for Qhull (<a href="qh-faq.htm">local copy</a>)
+                <li><a href="http://www.qhull.org/download">Download</a> Qhull (<a href=qh-get.htm>local copy</a>)
+                <li><a href="qh-quick.htm#programs">Quick</a> reference for Qhull and its <a href="qh-quick.htm#options">options</a>
+      <p>
+        <li><a href="../COPYING.txt">COPYING.txt</a> - copyright notice<br>
+        <li><a href="../REGISTER.txt">REGISTER.txt</a> - registration<br>
+        <li><a href="../README.txt">README.txt</a> - installation
+        instructions<br>
+        <li><a href="../src/Changes.txt">Changes.txt</a> - change history <br>
+        <li><a href="qhull.txt">qhull.txt</a> - Unix manual page
+             </ul>
+        <p>
+    <li><a href="#description">Description</a> of Qhull
+             <ul>
+            <li><a href="#definition">de</a>finition &#149; <a
+                href="#input">in</a>put &#149; <a href="#output">ou</a>tput
+                &#149; <a href="#algorithm">al</a>gorithm &#149; <a
+                href="#structure">da</a>ta structure </li>
+            <li><a href="qh-impre.htm">Imprecision</a> in Qhull</li>
+            <li><a href="qh-impre.htm#joggle">Merged facets</a> or joggled input
+            <li><a href="qh-eg.htm">Examples</a> of Qhull</li>
+        </ul>
+        <p>
+   <li><a href=qh-quick.htm#programs>Qhull programs</a>, with instructions and examples
+        <ul>
+        <li><a href="qconvex.htm">qconvex</a> -- convex hulls
+        <li><a href="qdelaun.htm">qdelaunay</a> -- Delaunay triangulations and
+         furthest-site Delaunay triangulations
+        <li><a href="qhalf.htm">qhalf</a> -- halfspace intersections about a point
+        <li><a href="qhull.htm">qhull</a> -- all structures with additional options
+        <li><a href="qvoronoi.htm">qvoronoi</a> -- Voronoi diagrams and
+          furthest-site Voronoi diagrams
+        <li><a href="rbox.htm">rbox</a> -- generate point distributions for qhull
+        </ul>
+        <p>
+    <li><a href="qh-quick.htm#options">Qhull options</a><ul>
+            <li><a href="qh-opto.htm#output">Output</a> formats</li>
+            <li><a href="qh-optf.htm#format">Additional</a> I/O
+                formats</li>
+            <li><a href="qh-optg.htm#geomview">Geomview</a>
+                output options</li>
+            <li><a href="qh-optp.htm#print">Print</a> options</li>
+            <li><a href="qh-optq.htm#qhull">Qhull</a> control
+                options</li>
+            <li><a href="qh-optc.htm#prec">Precision</a> options</li>
+            <li><a href="qh-optt.htm#trace">Trace</a> options</li>
+        </ul>
+    </li>
+        <p>
+    <li><a href="#geomview">Geomview</a>, Qhull's graphical viewer</li>
+        <ul>
+          <li><a href="#geomview-install">Installing Geomview</a></li>
+          <li><a href="#geomview-use">Using Geomview</a></li>
+          <li><a href="#geomview-win">Building Geomview for Windows</a></li>
+        </ul>
+        <p>
+    <li><a href="qh-code.htm">Qhull internals</a><ul>
+            <li><a href="qh-code.htm#reentrant">Reentrant</a> Qhull</li>
+            <li><a href="qh-code.htm#convert">How to convert</a> code to reentrant Qhull</li>
+            <li><a href="qh-code.htm#64bit">Qhull</a> on 64-bit computers</li>
+            <li><a href="qh-code.htm#cpp">Calling</a> Qhull
+                from C++ programs</li>
+            <li><a href="qh-code.htm#library">Calling</a> Qhull
+                from C programs</li>
+            <li><a href="qh-code.htm#performance">Performance</a>
+                of Qhull</li>
+            <li><a href="qh-code.htm#enhance">Enhancements</a> to
+                Qhull</li>
+            <li><a href="../src/libqhull_r/index.htm">Reentrant</a> Qhull functions, macros, and
+                data structures </li>
+            <li><a href="../src/libqhull/index.htm">Qhull</a> functions, macros, and
+                data structures </li>
+        </ul>
+    </li>
+        <p>
+    <li>Related URLs
+         <ul>
+
+        <li><a href="news:comp.graphics.algorithms">Newsgroup</a>:
+        comp.graphics.algorithms
+        <li><a
+        href="http://www.faqs.org/faqs/graphics/algorithms-faq/">FAQ</a> for computer graphics algorithms and
+                Exaflop's <a href="http://exaflop.org/docs/cgafaq/cga6.html">geometric</a> structures.
+    <li>Amenta's <a href="http://www.geom.uiuc.edu/software/cglist">Directory
+        of Computational Geometry Software </a></li>
+    <li>Erickson's <a
+        href="http://compgeom.cs.uiuc.edu/~jeffe/compgeom/code.html">Computational
+        Geometry Software</a> </li>
+        <li>Fukuda's <a
+                href="http://www.cs.mcgill.ca/~fukuda/soft/polyfaq/polyfaq.html">
+                introduction</a> to convex hulls, Delaunay triangulations,
+                Voronoi diagrams, and linear programming.
+    <li>Stony Brook's <a
+        href="http://www.cs.sunysb.edu/~algorith/major_section/1.6.shtml">Algorithm Repository</a> on computational geometry.
+    </li>
+     </ul>
+        <p>
+    <li><a href="#bugs">What to do</a> if something goes wrong</li>
+    <li><a href="#email">Email</a></li>
+    <li><a href="#authors">Authors</a></li>
+    <li><a href="#ref">References</a></li>
+    <li><a href="#acknowledge">Acknowledgments</a></li>
+</ul>
+<h2><a href="#TOC">&#187;</a><a name="when">When to use Qhull</a></h2>
+<blockquote>
+
+<p>Qhull constructs convex hulls, Delaunay triangulations,
+halfspace intersections about a point, Voronoi diagrams, furthest-site Delaunay
+triangulations, and furthest-site Voronoi diagrams.</p>
+
+<p>For convex hulls and halfspace intersections, Qhull may be used
+for 2-d upto 8-d.  For Voronoi diagrams and Delaunay triangulations, Qhull may be
+used for 2-d upto 7-d.  In higher dimensions, the size of the output
+grows rapidly and Qhull does not work well with virtual memory.
+If <i>n</i> is the size of
+the input and <i>d</i> is the dimension (d>=3), the size of the output
+and execution time
+grows by <i>n^(floor(d/2)</i>
+[see <a href=qh-code.htm#performance>Performance</a>].  For example, do
+not try to build a 16-d convex hull of 1000 points.  It will
+have on the order of 1,000,000,000,000,000,000,000,000 facets.
+
+<p>On a 600 MHz Pentium 3, Qhull computes the 2-d convex hull of
+300,000 cocircular points in 11 seconds.  It computes the
+2-d Delaunay triangulation and 3-d convex hull of 120,000 points
+in 12 seconds.  It computes the
+3-d Delaunay triangulation and 4-d convex hull of 40,000 points
+in 18 seconds.  It computes the
+4-d Delaunay triangulation and 5-d convex hull of 6,000 points
+in 12 seconds.  It computes the
+5-d Delaunay triangulation and 6-d convex hull of 1,000 points
+in 12 seconds.  It computes the
+6-d Delaunay triangulation and 7-d convex hull of 300 points
+in 15 seconds.  It computes the
+7-d Delaunay triangulation and 8-d convex hull of 120 points
+in 15 seconds.  It computes the
+8-d Delaunay triangulation and 9-d convex hull of 70 points
+in 15 seconds.  It computes the
+9-d Delaunay triangulation and 10-d convex hull of 50 points
+in 17 seconds.  The 10-d convex hull of 50 points has about 90,000 facets.
+
+<!-- duplicated in index.htm and html/index.htm -->
+<p>Qhull does <i>not</i> support constrained Delaunay
+triangulations, triangulation of non-convex surfaces, mesh
+generation of non-convex objects, or medium-sized inputs in 9-D
+and higher. </p>
+
+<p>This is a big package with many options. It is one of the
+fastest available. It is the only 3-d code that handles precision
+problems due to floating point arithmetic. For example, it
+implements the identity function for extreme points (see <a
+href="qh-impre.htm">Imprecision in Qhull</a>). </p>
+
+<p>[2016] A newly discovered, bad case for Qhull is multiple, nearly incident points within a 10^-13 ball of 3-d and higher
+Delaunay triangulations (input sites in the unit cube).  Nearly incident points within substantially
+smaller or larger balls are OK.  Error QH6271 is reported if a problem occurs. A future release of Qhull
+will handle this case.  For more information, see "Nearly coincident points on an edge" in <a href="../html/qh-impre.htm#limit">Limitations of merged facets</a>
+
+<p>If you need a short code for convex hull, Delaunay
+triangulation, or Voronoi volumes consider Clarkson's <a
+href="http://www.netlib.org/voronoi/hull.html">hull
+program</a>. If you need 2-d Delaunay triangulations consider
+Shewchuk's <a href="http://www.cs.cmu.edu/~quake/triangle.html">triangle
+program</a>. It is much faster than Qhull and it allows
+constraints. Both programs use exact arithmetic. They are in <a
+href="http://www.netlib.org/voronoi/">http://www.netlib.org/voronoi/</a>.
+
+<p>If your input is in general position (i.e., no coplanar or colinear points),
+<li><a href="https://github.com/tomilov/quickhull/blob/master/include/quickhull.hpp">Tomilov's quickhull.hpp</a> (<a href"http://habrahabr.ru/post/245221/"documentation-ru</a/>)
+or Qhull <a
+href="http://www.qhull.org/download">version
+1.0</a> may meet your needs. Both programs detect precision problems,
+but do not handle them.</p>
+
+<p><a href=http://www.cgal.org>CGAL</a> is a library of efficient and reliable
+geometric algorithms.  It uses C++ templates and the Boost library to produce dimension-specific
+code.  This allows more efficient use of memory than Qhull's general-dimension
+code.  CGAL simulates arbitrary precision while Qhull handles round-off error
+with thick facets.  Compare the two approaches with <a href="http://doc.cgal.org/latest/Manual/devman_robustness.html">Robustness Issues in CGAL</a>,
+and <a href+"qh-impre.htm">Imprecision in Qhull</a>.
+
+
+<p><a href=http://www.algorithmic-solutions.com/enleda.htm>Leda</a> is a
+library for writing computational
+geometry programs and other combinatorial algorithms.  It
+includes routines for computing 3-d convex
+hulls, 2-d Delaunay triangulations, and 3-d Delaunay triangulations.
+It provides rational arithmetic and graphical output.  It runs on most
+platforms.
+
+<p>If your problem is in high dimensions with a few,
+non-simplicial facets, try Fukuda's <a
+href="http://www.cs.mcgill.ca/~fukuda/soft/cdd_home/cdd.html">cdd</a>.
+It is much faster than Qhull for these distributions. </p>
+
+<p>Custom software for 2-d and 3-d convex hulls may be faster
+than Qhull.  Custom software should use less memory.  Qhull uses
+general-dimension data structures and code.   The data structures
+support non-simplicial facets.</p>
+
+<p>Qhull is not suitable for mesh generation or triangulation of
+arbitrary surfaces. You may use Qhull if the surface is convex or
+completely visible from an interior point (e.g., a star-shaped
+polyhedron). First, project each site to a sphere that is
+centered at the interior point. Then, compute the convex hull of
+the projected sites. The facets of the convex hull correspond to
+a triangulation of the surface. For mesh generation of arbitrary
+surfaces, see <a
+href="http://www.robertschneiders.de/meshgeneration/meshgeneration.html">Schneiders'
+Finite Element Mesh Generation</a>.</p>
+
+<p>Qhull is not suitable for constrained Delaunay triangulations.
+With a lot of work, you can write a program that uses Qhull to
+add constraints by adding additional points to the triangulation.</p>
+
+<p>Qhull is not suitable for the subdivision of arbitrary
+objects. Use <tt>qdelaunay</tt> to subdivide a convex object.</p>
+
+</blockquote>
+<h2><a href="#TOC">&#187;</a><a name="description">Description of
+Qhull </a></h2>
+<blockquote>
+
+<h3><a href="#TOC">&#187;</a><a name="definition">definition</a></h3>
+<blockquote>
+
+<p>The <i>convex hull</i> of a point set <i>P</i> is the smallest
+convex set that contains <i>P</i>. If <i>P</i> is finite, the
+convex hull defines a matrix <i>A</i> and a vector <i>b</i> such
+that for all <i>x</i> in <i>P</i>, <i>Ax+b &lt;= [0,...]</i>. </p>
+
+<p>Qhull computes the convex hull in 2-d, 3-d, 4-d, and higher
+dimensions. Qhull represents a convex hull as a list of facets.
+Each facet has a set of vertices, a set of neighboring facets,
+and a halfspace. A halfspace is defined by a unit normal and an
+offset (i.e., a row of <i>A</i> and an element of <i>b</i>). </p>
+
+<p>Qhull accounts for round-off error. It returns
+&quot;thick&quot; facets defined by two parallel hyperplanes. The
+outer planes contain all input points. The inner planes exclude
+all output vertices. See <a href="qh-impre.htm#imprecise">Imprecise
+convex hulls</a>.</p>
+
+<p>Qhull may be used for the Delaunay triangulation or the
+Voronoi diagram of a set of points. It may be used for the
+intersection of halfspaces. </p>
+
+</blockquote>
+<h3><a href="#TOC">&#187;</a><a name="input">input format</a></h3>
+<blockquote>
+
+<p>The input data on <tt>stdin</tt> consists of:</p>
+
+<ul>
+    <li>first line contains the dimension</li>
+    <li>second line contains the number of input points</li>
+    <li>remaining lines contain point coordinates</li>
+</ul>
+
+<p>For example: </p>
+
+<pre>
+    3  #sample 3-d input
+    5
+    0.4 -0.5 1.0
+    1000 -1e-5 -100
+    0.3 0.2 0.1
+    1.0 1.0 1.0
+    0 0 0
+</pre>
+
+<p>Input may be entered by hand. End the input with a control-D
+(^D) character. </p>
+
+<p>To input data from a file, use I/O redirection or '<a
+href="qh-optt.htm#TI">TI file</a>'.  The filename may not
+include spaces or quotes.</p>
+
+<p>A comment starts with a non-numeric character and continues to
+the end of line. The first comment is reported in summaries and
+statistics. With multiple <tt>qhull</tt> commands, use option '<a
+href="qh-optf.htm#FQ">FQ</a>' to place a comment in the output.</p>
+
+<p>The dimension and number of points can be reversed. Comments
+and line breaks are ignored. Error reporting is better if there
+is one point per line.</p>
+
+</blockquote>
+<h3><a href="#TOC">&#187;</a><a name="option">option format</a></h3>
+<blockquote>
+
+<p>Use options to specify the output formats and control
+Qhull.  The <tt>qhull</tt> program takes all options.  The
+other programs use a subset of the options.  They disallow
+experimental and inappropriate options.
+
+<blockquote>
+<ul>
+<li>
+qconvex == qhull
+<li>
+qdelaunay == qhull d Qbb
+<li>
+qhalf == qhull H
+<li>
+qvoronoi == qhull v Qbb
+</ul>
+</blockquote>
+
+<p>Single letters are used for output formats and precision
+constants. The other options are grouped into menus for formats
+('<a href="qh-optf.htm#format">F</a>'), Geomview ('<a
+href="qh-optg.htm#geomview">G </a>'), printing ('<a
+href="qh-optp.htm#print">P</a>'), Qhull control ('<a
+href="qh-optq.htm#qhull">Q </a>'), and tracing ('<a
+href="qh-optt.htm#trace">T</a>'). The menu options may be listed
+together (e.g., 'GrD3' for 'Gr' and 'GD3'). Options may be in any
+order. Capitalized options take a numeric argument (except for '<a
+href="qh-optp.htm#PG">PG</a>' and '<a href="qh-optf.htm#format">F</a>'
+options). Use option '<a href="qh-optf.htm#FO">FO</a>' to print
+the selected options.</p>
+
+<p>Qhull uses zero-relative indexing. If there are <i>n</i>
+points, the index of the first point is <i>0</i> and the index of
+the last point is <i>n-1</i>.</p>
+
+<p>The default options are:</p>
+
+<ul>
+    <li>summary output ('<a href="qh-opto.htm#s">s</a>') </li>
+    <li>merged facets ('<a href="qh-optc.htm#C0">C-0</a>' in 2-d,
+        3-d, 4-d; '<a href="qh-optq.htm#Qx">Qx</a>' in 5-d and
+        up)</li>
+</ul>
+
+<p>Except for bounding box
+('<a href="qh-optq.htm#Qbk">Qbk:n</a>', etc.), drop facets
+('<a href="qh-optp.htm#Pdk">Pdk:n</a>', etc.), and
+Qhull command ('<a href="qh-optf.htm#FQ">FQ</a>'), only the last
+occurence of an option counts.
+Bounding box and drop facets may be repeated for each dimension.
+Option 'FQ' may be repeated any number of times.
+
+<p>The Unix <tt>tcsh</tt> and <tt>ksh </tt>shells make it easy to
+try out different options. In Windows 95, use a command window with <tt>doskey</tt>
+and a window scroller (e.g., <tt>peruse</tt>). </p>
+
+</blockquote>
+<h3><a href="#TOC">&#187;</a><a name="output">output format</a></h3>
+<blockquote>
+
+<p>To write the results to a file, use I/O redirection or '<a
+href="qh-optt.htm#TO">TO file</a>'. Windows 95 users should use
+'TO file' or the console.  If a filename is surrounded by single quotes,
+it may include spaces.
+</p>
+
+<p>The default output option is a short summary ('<a
+href="qh-opto.htm#s">s</a>') to <tt>stdout</tt>. There are many
+others (see <a href="qh-opto.htm">output</a> and <a
+href="qh-optf.htm">formats</a>). You can list vertex incidences,
+vertices and facets, vertex coordinates, or facet normals. You
+can view Qhull objects with Geomview, Mathematica, or Maple. You can
+print the internal data structures. You can call Qhull from your
+application (see <a href="qh-code.htm#library">Qhull library</a>).</p>
+
+<p>For example, 'qhull <a href="qh-opto.htm#o">o</a>' lists the
+vertices and facets of the convex hull. </p>
+
+<p>Error messages and additional summaries ('<a
+href="qh-opto.htm#s">s</a>') go to <tt>stderr</tt>. Unless
+redirected, <tt>stderr</tt> is the console.</p>
+
+</blockquote>
+<h3><a href="#TOC">&#187;</a><a name="algorithm">algorithm</a></h3>
+<blockquote>
+
+<p>Qhull implements the Quickhull algorithm for convex hull
+[Barber et al. <a href="#bar-dob96">'96</a>]. This algorithm
+combines the 2-d Quickhull algorithm with the <em>n</em>-d
+beneath-beyond algorithm [c.f., Preparata &amp; Shamos <a
+href="#pre-sha85">'85</a>]. It is similar to the randomized
+algorithms of Clarkson and others [Clarkson &amp; Shor <a
+href="#cla-sho89">'89</a>; Clarkson et al. <a href="#cla-meh93">'93</a>;
+Mulmuley <a href="#mulm94">'94</a>]. For a demonstration, see <a
+href="qh-eg.htm#how">How Qhull adds a point</a>. The main
+advantages of Quickhull are output sensitive performance (in
+terms of the number of extreme points), reduced space
+requirements, and floating-point error handling. </p>
+
+</blockquote>
+<h3><a href="#TOC">&#187;</a><a name="structure">data structures</a></h3>
+<blockquote>
+
+<p>Qhull produces the following data structures for dimension <i>d</i>:
+</p>
+
+<ul>
+    <li>A <em>coordinate</em> is a real number in floating point
+        format. </li>
+    <li>A <em>point</em> is an array of <i>d</i> coordinates.
+        With option '<a href="qh-optq.htm#QJn">QJ</a>', the
+        coordinates are joggled by a small amount. </li>
+    <li>A <em>vertex</em> is an input point. </li>
+    <li>A <em>hyperplane</em> is <i>d</i> normal coefficients and
+        an offset. The length of the normal is one. The
+        hyperplane defines a halfspace. If <i>V</i> is a normal, <i>b</i>
+        is an offset, and <i>x</i> is a point inside the convex
+        hull, then <i>Vx+b &lt;0</i>.</li>
+    <li>An <em>outer plane</em> is a positive
+        offset from a hyperplane. When Qhull is done, all points
+        will be below all outer planes.</li>
+    <li>An <em>inner plane</em> is a negative
+        offset from a hyperplane. When Qhull is done, all
+        vertices will be above the corresponding inner planes.</li>
+    <li>An <em>orientation</em> is either 'top' or 'bottom'. It is the
+        topological equivalent of a hyperplane's geometric
+        orientation. </li>
+    <li>A <em>simplicial facet</em> is a set of
+        <i>d</i> neighboring facets, a set of <i>d</i> vertices, a
+        hyperplane equation, an inner plane, an outer plane, and
+        an orientation. For example in 3-d, a simplicial facet is
+        a triangle. </li>
+    <li>A <em>centrum</em> is a point on a facet's hyperplane. A
+        centrum is the average of a facet's vertices. Neighboring
+        facets are <em>convex</em> if each centrum is below the
+        neighbor facet's hyperplane. </li>
+    <li>A <em>ridge</em> is a set of <i>d-1</i> vertices, two
+        neighboring facets, and an orientation. For example in
+        3-d, a ridge is a line segment. </li>
+    <li>A <em>non-simplicial facet</em> is a set of ridges, a
+        hyperplane equation, a centrum, an outer plane, and an
+        inner plane. The ridges determine a set of neighboring
+        facets, a set of vertices, and an orientation. Qhull
+        produces a non-simplicial facet when it merges two facets
+        together. For example, a cube has six non-simplicial
+        facets. </li>
+</ul>
+
+<p>For examples, use option '<a href="qh-opto.htm#f">f</a>'. See <a
+href="../src/libqhull/qh-poly.htm">polyhedron operations</a> for further
+design documentation. </p>
+
+</blockquote>
+<h3><a href="#TOC">&#187;</a>Imprecision in Qhull</h3>
+<blockquote>
+
+<p>See <a href="qh-impre.htm">Imprecision in Qhull</a> and <a href="qh-impre.htm#joggle">Merged facets or joggled input</a></p>
+
+</blockquote>
+<h3><a href="#TOC">&#187;</a>Examples of Qhull</h3>
+<blockquote>
+
+<p>See <a href="qh-eg.htm">Examples of Qhull</a>.  Most of these examples require <a href="#geomview">Geomview</a>.
+Some of the examples have <a
+href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/welcome.html">pictures
+</a>.</p>
+
+</blockquote>
+</blockquote>
+<h2><a href="#TOC">&#187;</a>Options for using Qhull </h2>
+<blockquote>
+
+<p>See <a href="qh-quick.htm#options">Options</a>.</p>
+
+</blockquote>
+<h2><a href="#TOC">&#187;</a>Qhull internals </h2>
+<blockquote>
+
+<p>See <a href="qh-code.htm">Internals</a>.</p>
+
+</blockquote>
+<h2><a href="#TOC">&#187;</a><a name="geomview">Geomview, Qhull's
+graphical viewer</a></h2>
+<blockquote>
+
+<p><a href="http://www.geomview.org">Geomview</a>
+is an interactive geometry viewing program.
+Geomview provides a good visualization of Qhull's 2-d and 3-d results.
+
+<p>Qhull includes <a href="qh-eg.htm">Examples of Qhull</a> that may be viewed with Geomview.
+
+<p>Geomview can help visulalize a 3-d Delaunay triangulation or the surface of a 4-d convex hull,
+Use option '<a href="qh-optq.htm#QVn">QVn</a>' to select the 3-D facets adjacent to a vertex.
+
+<p>You may use Geomview to create movies that animate your objects (c.f., <a href="http://www.geomview.org/FAQ/answers.shtml#mpeg">How can I create a video animation?</a>).
+Geomview helped create the <a href="http://www.geom.uiuc.edu/video/">mathematical videos</a> "Not Knot", "Outside In", and "The Shape of Space" from the Geometry Center.
+
+
+<h3><a href="#TOC">&#187;</a><a name="geomview-install">Installing Geomview</a></h3>
+<blockquote>
+
+<p>Geomview is an <a href=http://sourceforge.net/projects/geomview>open source project</a>
+under SourceForge.
+
+<p>
+For build instructions see
+<a href="http://www.geomview.org/download/">Downloading Geomview</a>.
+Geomview builds under Linux, Unix, Macintosh OS X, and Windows.
+
+<p>Geomview has <a href="https://packages.debian.org/search?keywords=geomview">installable packages</a> for Debian and Ubuntu.
+The OS X build needs Xcode, an X11 SDK, and Lesstif or Motif.
+The Windows build uses Cygwin (see <a href="#geomview-win">Building Geomview</a> below for instructions).
+
+<p>If using Xforms (e.g., for Geomview's <a href="http://www.geomview.org/docs/html/Modules.html">External Modules</a>), install the 'libXpm-devel' package from cygwin and move the xforms directory into your geomview directory, e.g.,<br><tt>mv xforms-1.2.4 geomview-1.9.5/xforms</tt>
+
+<p>Geomview's <a href="http://www.geom.uiuc.edu/software/geomview/docs/NDview/manpagehelp.html">ndview<a/> provides multiple views into 4-d and higher objects.
+This module is out-of-date (<a href="http://sourceforge.net/p/geomview/mailman/message/2004152/">geomview-users: 4dview</a>).
+Download NDview-sgi.tar.Z at <a href="ftp://www.geom.uiuc.edu/pub/software/geomview/newpieces/sgi">newpieces</a> and 4dview at <a href="https://stuff.mit.edu/afs/sipb/project/3d/arch/sgi_62/lib/Geomview/modules/">Geomview/modules</a>.
+
+</blockquote>
+<h3><a href="#TOC">&#187;</a><a name="geomview-use">Using Geomview</a></h3>
+<blockquote>
+
+<p>Use Geomview to view <a href="qh-eg.htm">Examples of Qhull</a>.   You can spin the convex hull, fly a camera through its facets,
+and see how Qhull produces thick facets in response to round-off error.
+
+<p>Follow these instructions to view 'eg,01.cube' from Examples of Qhull
+<ol>
+<li>Launch an XTerm command shell
+<ul>
+<li>If needed, start the X terminal server, Use 'xinit' or 'startx' in /usr/X11R6/bin<br><tt>xinit -- -multiwindow -clipboard</tt><br><tt>startx</tt>
+<li>Start an XTerm command shell.  In Windows, click the Cygwin/bash icon on your desktop.
+<li>Set the DISPLAY variable, e.g.,<br><tt>export DISPLAY=:0</tt><br><tt>export DISPLAY=:0 >>~/.bashenv</tt>
+</ul>
+<li>Use Qhull's <a href="qh-optg.htm">Geomview options</a> to create a geomview object
+<ul>
+<li><tt>rbox c D3 | qconvex G >eg.01.cube</tt>
+<li>On windows, convert the output to Unix text format with 'd2u'<br><tt>rbox c D3 | qconvex G | d2u >eg.01.cube</tt><br><tt>d2u eg.*</tt>
+</ul>
+<li>Run Geomview
+<ul>
+<li>Start Geomview with your example<br><tt>./geomview eg.01.cube</tt>
+<li>Follow the instructions in <a href="http://www.geomview.org/docs/html/Tutorial.html">Gemoview Tutorial</a>
+<li>Geomview creates the <i>Geomview control panel</i> with Targets and External Module, the <i>Geomview toolbar</i> with buttons for controlling Geomview, and the <i>Geomview camera window</i> showing a cube.
+<li>Clear the camera window by selecting your object in the Targets list and 'Edit > Delete' or 'dd'
+<li>Load the <i>Geomview files panel</i>.  Select 'Open' in the 'File' menu.
+<li>Set 'Filter' in the files panel to your example directory followed by '/*' (e.g., '/usr/local/qhull-2015.2/eg/*')
+<li>Click 'Filter' in the files panel to view your examples in the 'Files' list.
+<li>Load another example into the camera window by selecting it and clicking 'OK'.
+<li>Review the instructions for <a href="http://www.geomview.org/docs/html/Interaction.html">Interacting with Geomview</a>
+<li>When viewing multiple objects at once, you may want to turn off normalization.  In the 'Inspect > Apperance' control panel, set 'Normalize' to 'None'.
+</ul>
+</ol>
+
+<p>Geomview defines GCL (a textual API for controlling Geomview) and OOGL (a textual file format for defining objects).
+<ul>
+<li>To control Geomview, you may use any program that reads and writes from stdin and stdout.  For example, it could report Qhull's information about a vertex identified by a double-click 'pick' event.
+<li><a href="http://www.geomview.org/docs/html/GCL.html">GCL</a> command language for controlling Geomview
+<li><a href="http://www.geomview.org/docs/html/OOGL-File-Formats.html">OOGL</a> file format for defining objects (<a href="http://www.geomview.org/docs/oogltour.html">tutorial</a>).
+<li><a href="http://www.geomview.org/docs/html/Modules.html">External Modules</a> for interacting with Geomview via GCL
+<li>Interact with your objects via <a href="http://www.geomview.org/docs/html/pick.html">pick</a> commands in response to right-mouse double clicks.  Enable pick events with the <a href="http://www.geomview.org/docs/html/interest.html">interest</a> command.
+</ul>
+
+</blockquote>
+<h3><a href="#TOC">&#187;</a><a name="geomview-win">Building Geomview for Windows</a></h3>
+<blockquote>
+
+<p>Compile Geomview under Cygwin.  For detailed instructions, see
+<a href="http://www.ee.surrey.ac.uk/Personal/L.Wood/software/SaVi/building-under-Windows/"
+>Building Savi and Geomview under Windows</a>.  These instructions are somewhat out-of-date.  Updated
+instructions follow.
+
+<p>How to compile Geomview under 32-bit Cygwin (October 2015)</p>
+<ol>
+<li><b>Note:</b> L. Wood has run into multiple issues with Geomview on Cygwin.  He recommends Virtualbox/Ubuntu
+and a one-click install of geomview via the Ubuntu package.  See his Savi/Geomview link above.
+<li>Install 32-bit <a href="http://cygwin.com/">Cygwin</a> as follows.
+For additional guidance, see Cygwin's <a href="https://cygwin.com/install.html">Installing and Updating Cygwin Packages</a>
+and <a href="http://www.qhull.org/road/road-faq/xml/cmdline.xml#setup-cygwin">Setup cygwin</a>.
+<ul>
+<li>Launch the cygwin installer.
+<li>Select a mirror from <a href="http://cygwin.com/mirrors.html">Cygwin mirrors</a> (e.g., http://mirrors.kernel.org/sourceware/cygwin/ in California).
+<li>Select the packages to install.  Besides the cygwin packages listed in the Savi/Windows instructions consider adding
+<ul>
+<li><b>Default</b> -- libXm-devel (required for /usr/include/Xm/Xm.h)
+<li><b>Devel</b> -- bashdb, gcc-core (in place of gcc), gdb
+<li><b>Lib</b> -- libGL-devel, libGLU1 (required, obsolete), libGLU-devel (required, obsolete), libjpeg-devel(XForms), libXext-devel (required), libXpm-devel (Xforms)
+libGL and lib
+<li><b>Math</b> -- bc
+<li><b>Net</b> -- autossh, inetutils, openssh
+<li><b>System</b> -- chere
+<li><b>Utils</b> -- dos2unix (required for qhull), keychain
+<li>If installing perl, ActiveState Perl may be a better choice than cygwin's perl.  Perl is not used by Geomview or Qhull.
+<li><a href="https://cygwin.com/cgi-bin2/package-grep.cgi">Cygwin Package Search</a> -- Search for cygwin programs and packages
+</ul>
+<li>Click 'Next' to download and install the packages.
+<li>If the download is incomplete, try again.
+<li>If you try again after a successful install, cygwin will uninstall and reinstall all modules..
+<li>Click on the 'Cywin Terminal' icon on the Desktop.  It sets up a user directory in /home from /etc/skel/...
+<li>Mount your disk drives<br>mount c: /c # Ignore the warning /c does not exist
+</ul>
+<li>Consider installing the <a href="http://www.qhull.org/bash/doc/road-bash.html">Road Bash</a> scripts (/etc/road-*) from <a href="http://www.qhull.org/road/">Road</a>.
+They define aliases and functions for Unix command shells (Unix, Linux, Mac OS X, Windows),
+<ul>
+<li>Download Road Bash and unzip the downloaded file
+<li>Copy .../bash/etc/road-* to the Cywin /etc directory (by default, C:\cygwin\etc).
+<li>Using the cygwin terminal, convert the road scripts to Unix format<br>d2u /etc/road-*
+<li>Try it<br>source /etc/road-home.bashrc
+<li>Install it<br>cp /etc/road-home.bashrc ~/.bashrc
+</ul>
+<li>Launch the X terminal server from '<tt>Start > All programs > Cygwin-X > Xwin Server</tt>'.  Alternatively, run 'startx'
+<li>Launch an XTerm shell
+<ul>
+<li>Right click the Cywin icon on the system tray in the Windows taskbar.
+<li>Select '<tt>System Tools > XTerm</tt>'
+</ul>
+<li>Download and extract Geomview -- <a href="http://www.geomview.org/download/">Downloading Geomview</a>
+<li>Compile Geomview
+<ul>
+<li>./configure
+<li>make
+</ul>
+<li>If './configure' fails, check 'config.log' at the failing step.  Look carefully for missing libraries, etc.  The <a href="http://www.geomview.org/FAQ/answers.shtml">Geomview FAQ</a> contains suggestions (e.g., "configure claims it can't find OpenGl").
+<li>If 'make' fails, read the output carefully for error messages.  Usually it is a missing include file or package.  Locate and install the missing cygwin packages
+(<a href="https://cygwin.com/cgi-bin2/package-grep.cgi">Cygwin Package Search</a>).
+</ol>
+
+</blockquote>
+</blockquote>
+<h2><a href="#TOC">&#187;</a><a name="bugs">What to do if something
+goes wrong</a></h2>
+<blockquote>
+
+<p>Please report bugs to <a href=mailto:qhull_bug@qhull.org>qhull_bug@qhull.org</a>
+</a>. Please report if Qhull crashes. Please report if Qhull
+generates an &quot;internal error&quot;. Please report if Qhull
+produces a poor approximate hull in 2-d, 3-d or 4-d. Please
+report documentation errors. Please report missing or incorrect
+links.</p>
+
+<p>If you do not understand something, try a small example. The <a
+href="rbox.htm">rbox</a> program is an easy way to generate
+test cases. The <a href="#geomview">Geomview</a> program helps to
+visualize the output from Qhull.</p>
+
+<p>If Qhull does not compile, it is due to an incompatibility
+between your system and ours. The first thing to check is that
+your compiler is ANSI standard. Qhull produces a compiler error
+if __STDC__ is not defined. You may need to set a flag (e.g.,
+'-A' or '-ansi').</p>
+
+<p>If Qhull compiles but crashes on the test case (rbox D4),
+there's still incompatibility between your system and ours.
+Sometimes it is due to memory management. This can be turned off
+with qh_NOmem in mem.h. Please let us know if you figure out how
+to fix these problems. </p>
+
+<p>If you doubt the output from Qhull, add option '<a
+href="qh-optt.htm#Tv">Tv</a>'. It checks that every point is
+inside the outer planes of the convex hull. It checks that every
+facet is convex with its neighbors. It checks the topology of the
+convex hull.</p>
+
+<p>Qhull should work on all inputs. It may report precision
+errors if you turn off merged facets with option '<a
+href="qh-optq.htm#Q0">Q0</a>'. This can get as bad as facets with
+flipped orientation or two facets with the same vertices. You'll
+get a long help message if you run into such a case. They are
+easy to generate with <tt>rbox</tt>.</p>
+
+<p>If you do find a problem, try to simplify it before reporting
+the error. Try different size inputs to locate the smallest one
+that causes an error. You're welcome to hunt through the code
+using the execution trace ('<a href="qh-optt.htm#Tn">T4</a>') as
+a guide. This is especially true if you're incorporating Qhull
+into your own program. </p>
+
+<p>When you report an error, please attach a data set to the end
+of your message. Include the options that you used with Qhull,
+the results of option '<a href="qh-optf.htm#FO">FO</a>', and any
+messages generated by Qhull. This allows me to see the error for
+myself. Qhull is maintained part-time. </p>
+
+</blockquote>
+<h2><a href="#TOC">&#187;</a><a name="email">Email</a></h2>
+<blockquote>
+
+<p>Please send correspondence to Brad Barber at <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
+and report bugs to <a href=mailto:qhull_bug@qhull.org>qhull_bug@qhull.org</a>
+</a>. Let me know how you use Qhull. If you mention it in a
+paper, please send a reference and abstract.</p>
+
+<p>If you would like to get Qhull announcements (e.g., a new
+version) and news (any bugs that get fixed, etc.), let us know
+and we will add you to our mailing list. For Internet news about geometric algorithms
+and convex hulls, look at comp.graphics.algorithms and
+sci.math.num-analysis. For Qhull news look at <a
+href="http://www.qhull.org/news">qhull-news.html</a>.</p>
+
+</blockquote>
+<h2><a href="#TOC">&#187;</a><a name="authors">Authors</a></h2>
+<blockquote>
+
+<pre>
+   C. Bradford Barber                    Hannu Huhdanpaa
+   bradb@shore.net                       hannu@qhull.org
+</pre>
+
+</blockquote>
+<h2><a href="#TOC">&#187;</a><a name="acknowledge">Acknowledgments</a></h2>
+<blockquote>
+
+<p>A special thanks to David Dobkin for his guidance. A special
+thanks to Albert Marden, Victor Milenkovic, the Geometry Center,
+and Harvard University for supporting this work.</p>
+
+<p>A special thanks to Mark Phillips, Robert Miner, and Stuart Levy for running the Geometry
+ Center web site long after the Geometry Center closed.
+ Stuart moved the web site to the University of Illinois at Champaign-Urbana.
+Mark and Robert are founders of <a href=http://www.geomtech.com>Geometry Technologies</a>.
+Mark, Stuart, and Tamara Munzner are the original authors of <a href=http://www.geomview.org>Geomview</a>.
+
+<p>A special thanks to <a href="http://www.endocardial.com/">Endocardial
+Solutions, Inc.</a> of St. Paul, Minnesota for their support of the
+internal documentation (<a href=../src/libqhull/index.htm>src/libqhull/index.htm</a>). They use Qhull to build 3-d models of
+heart chambers.</p>
+
+<p>Qhull 1.0 and 2.0 were developed under National Science Foundation
+grants NSF/DMS-8920161 and NSF-CCR-91-15793 750-7504. If you find
+it useful, please let us know.</p>
+
+<p>The Geometry Center was supported by grant DMS-8920161 from the
+National Science Foundation, by grant DOE/DE-FG02-92ER25137 from
+the Department of Energy, by the University of Minnesota, and by
+Minnesota Technology, Inc.</p>
+
+</blockquote>
+<h2><a href="#TOC">&#187;</a><a name="ref">References</a></h2>
+<blockquote>
+
+<p><a name="aure91">Aurenhammer</a>, F., &quot;Voronoi diagrams
+-- A survey of a fundamental geometric data structure,&quot; <i>ACM
+Computing Surveys</i>, 1991, 23:345-405. </p>
+
+<p><a name="bar-dob96">Barber</a>, C. B., D.P. Dobkin, and H.T.
+Huhdanpaa, &quot;The Quickhull Algorithm for Convex Hulls,&quot; <i>ACM
+Transactions on Mathematical Software</i>, 22(4):469-483, Dec 1996, www.qhull.org
+[<a
+href="http://portal.acm.org/citation.cfm?doid=235815.235821">http://portal.acm.org</a>;
+<a href="http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.117.405">http://citeseerx.ist.psu.edu</a>].
+</p>
+
+<p><a name="cla-sho89">Clarkson</a>, K.L. and P.W. Shor,
+&quot;Applications of random sampling in computational geometry,
+II&quot;, <i>Discrete Computational Geometry</i>, 4:387-421, 1989</p>
+
+<p><a name="cla-meh93">Clarkson</a>, K.L., K. Mehlhorn, and R.
+Seidel, &quot;Four results on randomized incremental
+construction,&quot; <em>Computational Geometry: Theory and
+Applications</em>, vol. 3, p. 185-211, 1993.</p>
+
+<p><a name="devi01">Devillers</a>, et. al.,
+"Walking in a triangulation," <i>ACM Symposium on
+Computational Geometry</i>, June 3-5,2001, Medford MA.
+
+<p><a name="dob-kir90">Dobkin</a>, D.P. and D.G. Kirkpatrick,
+&quot;Determining the separation of preprocessed polyhedra--a
+unified approach,&quot; in <i>Proc. 17th Inter. Colloq. Automata
+Lang. Program.</i>, in <i>Lecture Notes in Computer Science</i>,
+Springer-Verlag, 443:400-413, 1990. </p>
+
+<p><a name="edel01">Edelsbrunner</a>, H, <i>Geometry and Topology for Mesh Generation</i>,
+Cambridge University Press, 2001.
+
+<p><a name=gart99>Gartner, B.</a>, "Fast and robust smallest enclosing balls", <i>Algorithms - ESA '99</i>, LNCS 1643.
+
+<p><a name=golub83>Golub, G.H. and van Loan, C.F.</a>, <i>Matric Computations</i>, Baltimore, Maryland, USA: John Hopkins Press, 1983
+
+<p><a name="fort93">Fortune, S.</a>, &quot;Computational
+geometry,&quot; in R. Martin, editor, <i>Directions in Geometric
+Computation</i>, Information Geometers, 47 Stockers Avenue,
+Winchester, SO22 5LB, UK, ISBN 1-874728-02-X, 1993.</p>
+
+<p><a name="mile93">Milenkovic, V.</a>, &quot;Robust polygon
+modeling,&quot; Computer-Aided Design, vol. 25, p. 546-566,
+September 1993. </p>
+
+<p><a name="muck96">Mucke</a>, E.P., I. Saias, B. Zhu, <i>Fast
+randomized point location without preprocessing in Two- and
+Three-dimensional Delaunay Triangulations</i>, ACM Symposium on
+Computational Geometry, p. 274-283, 1996 [<a
+href="http://www.geom.uiuc.edu/software/cglist/GeomDir/">GeomDir</a>].
+</p>
+
+<p><a name="mulm94">Mulmuley</a>, K., <i>Computational Geometry,
+An Introduction Through Randomized Algorithms</i>, Prentice-Hall,
+NJ, 1994.</p>
+
+<p><a name="orou94">O'Rourke</a>, J., <i>Computational Geometry
+in C</i>, Cambridge University Press, 1994.</p>
+
+<p><a name="pre-sha85">Preparata</a>, F. and M. Shamos, <i>Computational
+Geometry</i>, Springer-Verlag, New York, 1985.</p>
+
+</blockquote>
+<!-- Navigation links -->
+<hr>
+
+<p><b>Up:</b> <a
+href="http://www.qhull.org">Home page</a> for Qhull<br>
+<b>Up:</b><a
+href="http://www.qhull.org/news">News</a> about Qhull<br>
+<b>Up:</b> <a href="http://www.qhull.org/html/qh-faq.htm">FAQ</a> about Qhull<br>
+<b>To:</b> <a href="#TOC">Qhull manual</a>: Table of Contents<br>
+<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
+&#149; <a href="qh-quick.htm#options">Options</a>
+&#149; <a href="qh-opto.htm#output">Output</a>
+&#149; <a href="qh-optf.htm#format">Formats</a>
+&#149; <a href="qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="qh-optp.htm#print">Print</a>
+&#149; <a href="qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="qh-optc.htm#prec">Precision</a>
+&#149; <a href="qh-optt.htm#trace">Trace</a>
+&#149; <a href="../src/libqhull_r/index.htm">Functions</a><br>
+<b>Dn:</b> <a href="qh-impre.htm">Imprecision in Qhull</a><br>
+<b>Dn:</b> <a href="qh-eg.htm">Description of Qhull examples</a><br>
+<b>Dn:</b> <a href="qh-code.htm">Qhull internals</a><br>
+<b>Dn:</b> <a href="../src/libqhull/index.htm">Qhull functions, macros, and data
+structures</a>
+<!-- GC common information -->
+<hr>
+
+<p><a href="http://www.geom.uiuc.edu/"><img src="qh--geom.gif"
+align="middle" width="40" height="40"></a><i>The Geometry Center
+Home Page </i></p>
+
+<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
+</a><br>
+Created: Sept. 25, 1995 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
+</body>
+</html>
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+<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN">
+<html>
+
+<head>
+<title>qconvex -- convex hull</title>
+</head>
+
+<body>
+<!-- Navigation links -->
+<a name="TOP"><b>Up</b></a><b>:</b>
+<a href="http://www.qhull.org">Home page</a> for Qhull<br>
+<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a> -- Table of Contents<br>
+<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
+&#149; <a href="qh-quick.htm#options">Options</a>
+&#149; <a href="qh-opto.htm#output">Output</a>
+&#149; <a href="qh-optf.htm#format">Formats</a>
+&#149; <a href="qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="qh-optp.htm#print">Print</a>
+&#149; <a href="qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="qh-optc.htm#prec">Precision</a>
+&#149; <a href="qh-optt.htm#trace">Trace</a>
+&#149; <a href="../src/libqhull_r/index.htm">Functions</a><br>
+<b>To:</b> <a href="#synopsis">sy</a>nopsis
+&#149; <a href="#input">in</a>put &#149; <a href="#outputs">ou</a>tputs
+&#149; <a href="#controls">co</a>ntrols &#149; <a href="#graphics">gr</a>aphics
+&#149; <a href="#notes">no</a>tes &#149; <a href="#conventions">co</a>nventions
+&#149; <a href="#options">op</a>tions
+<hr>
+<!-- Main text of document -->
+<h1><a
+href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/cone.html"><img
+src="qh--cone.gif" alt="[cone]" align="middle" width="100"
+height="100"></a>qconvex -- convex hull</h1>
+
+<p>The convex hull of a set of points is the smallest convex set
+containing the points. See the detailed introduction by O'Rourke
+[<a href="index.htm#orou94">'94</a>]. See <a
+href="index.htm#description">Description of Qhull</a> and <a
+href="qh-eg.htm#how">How Qhull adds a point</a>.</p>
+
+<blockquote>
+<dl>
+    <dt><b>Example:</b> rbox 10 D3 | qconvex <a
+        href="qh-opto.htm#s">s</a> <a href="qh-opto.htm#o">o</a> <a
+        href="qh-optt.htm#TO">TO result</a></dt>
+    <dd>Compute the 3-d convex hull of 10 random points. Write a
+        summary to the console and the points and facets to
+        'result'.</dd>
+
+        <dt>&nbsp;</dt>
+            <dt><b>Example:</b> rbox c | qconvex <a
+                href="qh-opto.htm#n">n</a></dt>
+            <dd>Print the normals for each facet of a cube.</dd>
+            <dt>&nbsp;</dt>
+            <dt><b>Example:</b> rbox c | qconvex <a
+                href="qh-opto.htm#i">i</a> <a href="qh-optq.htm#Qt">Qt</a></dt>
+            <dd>Print the triangulated facets of a cube.</dd>
+            <dt>&nbsp;</dt>
+            <dt><b>Example:</b> rbox y 500 W0 | qconvex</dt>
+            <dd>Compute the convex hull of a simplex with 500
+                points on its surface.</dd>
+            <dt>&nbsp;</dt>
+            <dt><b>Example:</b> rbox x W1e-12 1000 | qconvex
+            <a href="qh-optq.htm#QR">QR0</a></dt>
+        <dd>Compute the convex hull of 1000 points near the
+                    surface of a randomly rotated simplex.  Report
+                        the maximum thickness of a facet.</dd>
+            <dt>&nbsp;</dt>
+       <dt><b>Example:</b> rbox 1000 s | qconvex <a
+            href="qh-opto.htm#s">s</a> <a
+            href="qh-optf.htm#FA">FA</a> </dt>
+        <dd>Compute the convex hull of 1000 cospherical
+            points. Verify the results and print a summary
+            with the total area and volume.</dd>
+        <dt>&nbsp;</dt>
+            <dt><b>Example:</b> rbox d D12 | qconvex <a
+                href="qh-optq.htm#QRn">QR0</a> <a
+                href="qh-optf.htm#FA">FA</a></dt>
+            <dd>Compute the convex hull of a 12-d diamond.
+                Randomly rotate the input. Note the large number
+                of facets and the small volume.</dd>
+            <dt>&nbsp;</dt>
+            <dt><b>Example:</b> rbox c D7 | qconvex <a
+                href="qh-optf.htm#FA">FA</a> <a
+                href="qh-optt.htm#TFn">TF1000</a></dt>
+            <dd>Compute the convex hull of the 7-d hypercube.
+                Report on progress every 1000 facets. Computing
+                the convex hull of the 9-d hypercube takes too
+                much time and space. </dd>
+            <dt>&nbsp;</dt>
+        <dt><b>Example:</b> rbox c d D2 | qconvex <a
+            href="qh-optq.htm#Qc">Qc</a> <a
+            href="qh-opto.htm#s">s</a> <a
+            href="qh-opto.htm#f">f</a> <a
+            href="qh-optf.htm#Fx">Fx</a> | more</dt>
+        <dd>Dump all fields of all facets for a square and a
+            diamond. Also print a summary and a list of
+            vertices. Note the coplanar points.</dd>
+        <dt>&nbsp;</dt>
+</dl>
+</blockquote>
+
+<p>Except for rbox, all of the qhull programs compute a convex hull.
+
+<p>By default, Qhull merges coplanar facets.  For example, the convex
+hull of a cube's vertices has six facets.
+
+<p>If you use '<a href="qh-optq.htm#Qt">Qt</a>' (triangulated output),
+all facets will be simplicial (e.g., triangles in 2-d).  For the cube
+example, it will have 12 facets.  Some facets may be
+degenerate and have zero area.
+
+<p>If you use '<a href="qh-optq.htm#QJn">QJ</a>' (joggled input),
+all facets will be simplicial.  The corresponding vertices will be
+slightly perturbed and identical points will be joggled apart.
+Joggled input is less accurate that triangulated
+output.See <a
+href="qh-impre.htm#joggle">Merged facets or joggled input</a>. </p>
+
+<p>The output for 4-d convex hulls may be confusing if the convex
+hull contains non-simplicial facets (e.g., a hypercube). See
+<a href=qh-faq.htm#extra>Why
+are there extra points in a 4-d or higher convex hull?</a><br>
+</p>
+</p>
+
+<p>The 'qconvex' program is equivalent to
+'<a href=qhull.htm#outputs>qhull</a>' in 2-d to 4-d, and
+'<a href=qhull.htm#outputs>qhull</a> <a href=qh-optq.htm#Qx>Qx</a>'
+in 5-d and higher.  It disables the following Qhull
+<a href=qh-quick.htm#options>options</a>: <i>d v H Qbb Qf Qg Qm
+Qr Qu Qv Qx Qz TR E V Fp Gt Q0,etc</i>.
+
+<p><b>Copyright &copy; 1995-2015 C.B. Barber</b></p>
+
+<hr>
+
+<h3><a href="#TOP">&#187;</a><a name="synopsis">qconvex synopsis</a></h3>
+<pre>
+qconvex- compute the convex hull.
+    input (stdin): dimension, number of points, point coordinates
+    comments start with a non-numeric character
+
+options (qconvex.htm):
+    Qt   - triangulated output
+    QJ   - joggle input instead of merging facets
+    Tv   - verify result: structure, convexity, and point inclusion
+    .    - concise list of all options
+    -    - one-line description of all options
+
+output options (subset):
+    s    - summary of results (default)
+    i    - vertices incident to each facet
+    n    - normals with offsets
+    p    - vertex coordinates (includes coplanar points if 'Qc')
+    Fx   - extreme points (convex hull vertices)
+    FA   - compute total area and volume
+    o    - OFF format (dim, n, points, facets)
+    G    - Geomview output (2-d, 3-d, and 4-d)
+    m    - Mathematica output (2-d and 3-d)
+    QVn  - print facets that include point n, -n if not
+    TO file- output results to file, may be enclosed in single quotes
+
+examples:
+    rbox c D2 | qconvex s n                    rbox c D2 | qconvex i
+    rbox c D2 | qconvex o                      rbox 1000 s | qconvex s Tv FA
+    rbox c d D2 | qconvex s Qc Fx              rbox y 1000 W0 | qconvex s n
+    rbox y 1000 W0 | qconvex s QJ              rbox d G1 D12 | qconvex QR0 FA Pp
+    rbox c D7 | qconvex FA TF1000
+</pre>
+
+<h3><a href="#TOP">&#187;</a><a name="input">qconvex
+input</a></h3>
+<blockquote>
+
+<p>The input data on <tt>stdin</tt> consists of:</p>
+<ul>
+    <li>dimension
+    <li>number of points</li>
+    <li>point coordinates</li>
+</ul>
+
+<p>Use I/O redirection (e.g., qconvex &lt; data.txt), a pipe (e.g., rbox 10 | qconvex),
+or the '<a href=qh-optt.htm#TI>TI</a>' option (e.g., qconvex TI data.txt).
+
+<p>Comments start with a non-numeric character.  Error reporting is
+simpler if there is one point per line.  Dimension
+and number of points may be reversed.
+
+<p>Here is the input for computing the convex
+hull of the unit cube.  The output is the normals, one
+per facet.</p>
+
+<blockquote>
+    <p>rbox c &gt; data </p>
+    <pre>
+3 RBOX c
+8
+  -0.5   -0.5   -0.5
+  -0.5   -0.5    0.5
+  -0.5    0.5   -0.5
+  -0.5    0.5    0.5
+   0.5   -0.5   -0.5
+   0.5   -0.5    0.5
+   0.5    0.5   -0.5
+   0.5    0.5    0.5
+</pre>
+    <p>qconvex s n &lt; data</p>
+    <pre>
+
+Convex hull of 8 points in 3-d:
+
+  Number of vertices: 8
+  Number of facets: 6
+  Number of non-simplicial facets: 6
+
+Statistics for: RBOX c | QCONVEX s n
+
+  Number of points processed: 8
+  Number of hyperplanes created: 11
+  Number of distance tests for qhull: 35
+  Number of merged facets: 6
+  Number of distance tests for merging: 84
+  CPU seconds to compute hull (after input): 0.081
+
+4
+6
+     0      0     -1   -0.5
+     0     -1      0   -0.5
+     1      0      0   -0.5
+    -1      0      0   -0.5
+     0      1      0   -0.5
+     0      0      1   -0.5
+</pre>
+</blockquote>
+
+</blockquote>
+<h3><a href="#TOP">&#187;</a><a name="outputs">qconvex outputs</a></h3>
+<blockquote>
+
+<p>These options control the output of qconvex. They may be used
+individually or together.</p>
+<blockquote>
+<dl compact>
+    <dt>&nbsp;</dt>
+    <dd><b>Vertices</b></dd>
+    <dt><a href="qh-optf.htm#Fx">Fx</a></dt>
+    <dd>list extreme points (i.e., vertices).  The first line is the number of
+        extreme points.  Each point is listed, one per line.  The cube example
+        has eight vertices.</dd>
+    <dt><a href="qh-optf.htm#Fv">Fv</a></dt>
+    <dd>list vertices for each facet.  The first line is the number of facets.
+        Each remaining line starts with the number of vertices.  For the cube example,
+        each facet has four vertices.</dd>
+    <dt><a href="qh-opto.htm#i">i</a></dt>
+    <dd>list vertices for each facet.  The first line is the number of facets.  The
+        remaining lines list the vertices for each facet.  In 4-d and
+        higher, triangulate non-simplicial facets by adding an extra point.</dd>
+    <dt>&nbsp;</dt>
+    <dt>&nbsp;</dt>
+    <dd><b>Coordinates</b></dd>
+    <dt><a href="qh-opto.htm#o">o</a></dt>
+    <dd>print vertices and facets of the convex hull in OFF format.  The
+           first line is the dimension.  The second line is the number of
+           vertices, facets, and ridges.  The vertex
+           coordinates are next, followed by the facets.  Each facet starts with
+           the number of vertices.  The cube example has four vertices per facet.</dd>
+    <dt><a href="qh-optf.htm#Ft">Ft</a></dt>
+    <dd>print a triangulation of the convex hull in OFF format.  The first line
+        is the dimension.  The second line is the number of vertices and added points,
+        followed by the number of facets and the number of ridges.
+    The vertex coordinates are next, followed by the centrum coordinates.  There is
+        one centrum for each non-simplicial facet.
+        The cube example has six centrums, one per square.
+    Each facet starts with the number of vertices or centrums.
+        In the cube example, each facet uses two vertices and one centrum.</dd>
+    <dt><a href="qh-opto.htm#p">p</a></dt>
+    <dd>print vertex coordinates.  The first line is the dimension and the second
+        line is the number of vertices.  The following lines are the coordinates of each
+        vertex.  The cube example has eight vertices.</dd>
+    <dt><a href="qh-optq.htm#Qc">Qc</a> <a href="qh-opto.htm#p">p</a></dt>
+    <dd>print coordinates of vertices and coplanar points.  The first line is the dimension.
+        The second line is the number of vertices and coplanar points.  The coordinates
+        are next, one line per point.  Use '<a href="qh-optq.htm#Qc">Qc</a> <a href="qh-optq.htm#Qi">Qi</a> p'
+        to print the coordinates of all points.</dd>
+    <dt>&nbsp;</dt>
+    <dt>&nbsp;</dt>
+    <dd><b>Facets</b></dd>
+    <dt><a href="qh-optf.htm#Fn">Fn</a></dt>
+    <dd>list neighboring facets for each facet.  The first line is the
+        number of facets.  Each remaining line starts with the number of
+        neighboring facets.  The cube example has four neighbors per facet.</dd>
+    <dt><a href="qh-optf.htm#FN">FN</a></dt>
+    <dd>list neighboring facets for each point.  The first line is the
+        total number of points.  Each remaining line starts with the number of
+        neighboring facets.  Each vertex of the cube example has three neighboring
+        facets.  Use '<a href="qh-optq.htm#Qc">Qc</a> <a href="qh-optq.htm#Qi">Qi</a> FN'
+        to include coplanar and interior points. </dd>
+    <dt><a href="qh-optf.htm#Fa">Fa</a></dt>
+    <dd>print area for each facet.  The first line is the number of facets.
+        Facet area follows, one line per facet.  For the cube example, each facet has area one.</dd>
+    <dt><a href="qh-optf.htm#FI">FI</a></dt>
+    <dd>list facet IDs.  The first line is the number of
+        facets.  The IDs follow, one per line.</dd>
+
+    <dt>&nbsp;</dt>
+    <dt>&nbsp;</dt>
+    <dd><b>Coplanar and interior points</b></dd>
+    <dt><a href="qh-optf.htm#Fc">Fc</a></dt>
+    <dd>list coplanar points for each facet.  The first line is the number
+        of facets.  The remaining lines start with the number of coplanar points.
+        A coplanar point is assigned to one facet.</dd>
+    <dt><a href="qh-optq.htm#Qi">Qi</a> <a href="qh-optf.htm#Fc">Fc</a></dt>
+    <dd>list interior points for each facet.  The first line is the number
+        of facets.  The remaining lines start with the number of interior points.
+        A coplanar point is assigned to one facet.</dd>
+    <dt><a href="qh-optf.htm#FP">FP</a></dt>
+    <dd>print distance to nearest vertex for coplanar points.  The first line is the
+        number of coplanar points.  Each remaining line starts with the point ID of
+        a vertex, followed by the point ID of a coplanar point, its facet, and distance.
+        Use '<a href="qh-optq.htm#Qc">Qc</a> <a href="qh-optq.htm#Qi">Qi</a>
+        <a href="qh-optf.htm#FP">FP</a>' for coplanar and interior points.</dd>
+
+    <dt>&nbsp;</dt>
+    <dt>&nbsp;</dt>
+    <dd><b>Hyperplanes</b></dd>
+    <dt><a href="qh-opto.htm#n">n</a></dt>
+    <dd>print hyperplane for each facet.  The first line is the dimension.  The
+        second line is the number of facets.  Each remaining line is the hyperplane's
+        coefficients followed by its offset.</dd>
+    <dt><a href="qh-optf.htm#Fo">Fo</a></dt>
+    <dd>print outer plane for each facet.  The output plane is above all points.
+         The first line is the dimension.  The
+        second line is the number of facets.  Each remaining line is the outer plane's
+        coefficients followed by its offset.</dd>
+    <dt><a href="qh-optf.htm#Fi">Fi</a></dt>
+    <dd>print inner plane for each facet.  The inner plane of a facet is
+        below its vertices.
+         The first line is the dimension.  The
+        second line is the number of facets.  Each remaining line is the inner plane's
+        coefficients followed by its offset.</dd>
+
+    <dt>&nbsp;</dt>
+    <dt>&nbsp;</dt>
+    <dd><b>General</b></dd>
+    <dt><a href="qh-opto.htm#s">s</a></dt>
+    <dd>print summary for the convex hull. Use '<a
+        href="qh-optf.htm#Fs">Fs</a>' and '<a
+        href="qh-optf.htm#FS">FS</a>' if you need numeric data.</dd>
+    <dt><a href="qh-optf.htm#FA">FA</a></dt>
+    <dd>compute total area and volume for '<a
+        href="qh-opto.htm#s">s</a>' and '<a href="qh-optf.htm#FS">FS</a>'</dd>
+    <dt><a href="qh-opto.htm#m">m</a></dt>
+    <dd>Mathematica output for the convex hull in 2-d or 3-d.</dd>
+    <dt><a href="qh-optf.htm#FM">FM</a></dt>
+    <dd>Maple output for the convex hull in 2-d or 3-d.</dd>
+    <dt><a href="qh-optg.htm#G">G</a></dt>
+    <dd>Geomview output for the convex hull in 2-d, 3-d, or 4-d.</dd>
+
+    <dt>&nbsp;</dt>
+    <dt>&nbsp;</dt>
+    <dd><b>Scaling and rotation</b></dd>
+    <dt><a href="qh-optq.htm#Qbk">Qbk:n</a></dt>
+    <dd>scale k'th coordinate to lower bound.</dd>
+    <dt><a href="qh-optq.htm#QBk">QBk:n</a></dt>
+    <dd>scale k'th coordinate to upper bound.</dd>
+    <dt><a href="qh-optq.htm#QbB">QbB</a></dt>
+    <dd>scale input to unit cube centered at the origin.</dd>
+    <dt><a href="qh-optq.htm#QRn">QRn</a></dt>
+    <dd>randomly rotate the input with a random seed of n.  If n=0, the
+        seed is the time.  If n=-1, use time for the random seed, but do
+        not rotate the input.</dd>
+    <dt><a href="qh-optq.htm#Qb0">Qbk:0Bk:0</a></dt>
+    <dd>remove k'th coordinate from input.  This computes the
+        convex hull in one lower dimension.</dd>
+</dl>
+</blockquote>
+
+</blockquote>
+<h3><a href="#TOP">&#187;</a><a name="controls">qconvex controls</a></h3>
+<blockquote>
+
+<p>These options provide additional control:</p>
+
+<blockquote>
+<dl compact>
+    <dt><a href="qh-optq.htm#Qt">Qt</a></dt>
+    <dd>triangulated output.  Qhull triangulates non-simplicial facets.  It may produce
+     degenerate facets of zero area.</dd>
+    <dt><a href="qh-optq.htm#QJn">QJ</a></dt>
+    <dd>joggle the input instead of merging facets.  This guarantees simplicial facets
+        (e.g., triangles in 3-d).  It is less accurate than triangulated output ('Qt').</dd>
+    <dt><a href="qh-optq.htm#Qc">Qc</a></dt>
+    <dd>keep coplanar points</dd>
+    <dt><a href="qh-optq.htm#Qi">Qi</a></dt>
+    <dd>keep interior points</dd>
+    <dt><a href="qh-opto.htm#f">f </a></dt>
+    <dd>facet dump.  Print the data structure for each facet.</dd>
+    <dt><a href="qh-optq.htm#QVn">QVn</a></dt>
+    <dd>select facets containing point <em>n</em> as a vertex,</dd>
+    <dt><a href="qh-optq.htm#QGn">QGn</a></dt>
+    <dd>select facets that are visible from point <em>n</em>
+        (marked 'good').  Use <em>-n</em> for the remainder.</dd>
+    <dt><a href="qh-optp.htm#PDk">PDk:0</a></dt>
+    <dd>select facets with a negative coordinate for dimension <i>k</i></dd>
+    <dt><a href="qh-optt.htm#TFn">TFn</a></dt>
+    <dd>report progress after constructing <em>n</em> facets</dd>
+    <dt><a href="qh-optt.htm#Tv">Tv</a></dt>
+    <dd>verify result</dd>
+    <dt><a href="qh-optt.htm#TO">TI file</a></dt>
+    <dd>input data from file.  The filename may not use spaces or quotes.</dd>
+    <dt><a href="qh-optt.htm#TO">TO file</a></dt>
+    <dd>output results to file.  Use single quotes if the filename
+        contains spaces (e.g., <tt>TO 'file with spaces.txt'</tt></dd>
+    <dt><a href="qh-optq.htm#Qs">Qs</a></dt>
+    <dd>search all points for the initial simplex.  If Qhull can
+        not construct an initial simplex, it reports a
+descriptive message. Usually, the point set is degenerate and one
+or more dimensions should be removed ('<a href="qh-optq.htm#Qb0">Qbk:0Bk:0</a>').
+If not, use option 'Qs'. It performs an exhaustive search for the
+best initial simplex. This is expensive is high dimensions.</dd>
+</dl>
+</blockquote>
+
+</blockquote>
+<h3><a href="#TOP">&#187;</a><a name="graphics">qconvex graphics</a></h3>
+<blockquote>
+
+<p>Display 2-d, 3-d, and 4-d convex hulls with Geomview ('<a
+href="qh-optg.htm#G">G</a>').</p>
+
+<p>Display 2-d and 3-d convex hulls with Mathematica ('<a
+href="qh-opto.htm#m">m</a>').</p>
+
+<p>To view 4-d convex hulls in 3-d, use '<a
+href="qh-optp.htm#Pdk">Pd0d1d2d3</a>' to select the positive
+octant and '<a href="qh-optg.htm#GDn">GrD2</a>' to drop dimension
+2. </p>
+
+</blockquote>
+<h3><a href="#TOP">&#187;</a><a name="notes">qconvex notes</a></h3>
+<blockquote>
+
+<p>Qhull always computes a convex hull.  The
+convex hull may be used for other geometric structures. The
+general technique is to transform the structure into an
+equivalent convex hull problem. For example, the Delaunay
+triangulation is equivalent to the convex hull of the input sites
+after lifting the points to a paraboloid.</p>
+
+</blockquote>
+<h3><a href="#TOP">&#187;</a><a name="conventions">qconvex
+conventions</a></h3>
+<blockquote>
+
+<p>The following terminology is used for convex hulls in Qhull.
+See <a href="index.htm#structure">Qhull's data structures</a>.</p>
+
+<ul>
+    <li><em>point</em> - <em>d</em> coordinates</li>
+    <li><em>vertex</em> - extreme point of the input set</li>
+    <li><em>ridge</em> - <i>d-1</i> vertices between two
+        neighboring facets</li>
+    <li><em>hyperplane</em> - halfspace defined by a unit normal
+        and offset</li>
+    <li><em>coplanar point</em> - a nearly incident point to a
+        hyperplane</li>
+    <li><em>centrum</em> - a point on the hyperplane for testing
+        convexity</li>
+    <li><em>facet</em> - a facet with vertices, ridges, coplanar
+        points, neighboring facets, and hyperplane</li>
+    <li><em>simplicial facet</em> - a facet with <em>d</em>
+        vertices, <em>d</em> ridges, and <em>d</em> neighbors</li>
+    <li><em>non-simplicial facet</em> - a facet with more than <em>d</em>
+        vertices</li>
+    <li><em>good facet</em> - a facet selected by '<a
+        href="qh-optq.htm#QVn">QVn</a>', etc.</li>
+</ul>
+</blockquote>
+<h3><a href="#TOP">&#187;</a><a name="options">qconvex options</a></h3>
+
+<pre>
+qconvex- compute the convex hull
+    http://www.qhull.org
+
+input (stdin):
+    first lines: dimension and number of points (or vice-versa).
+    other lines: point coordinates, best if one point per line
+    comments:    start with a non-numeric character
+
+options:
+    Qt   - triangulated output
+    QJ   - joggle input instead of merging facets
+    Qc   - keep coplanar points with nearest facet
+    Qi   - keep interior points with nearest facet
+
+Qhull control options:
+    Qbk:n   - scale coord k so that low bound is n
+      QBk:n - scale coord k so that upper bound is n (QBk is 0.5)
+    QbB  - scale input to unit cube centered at the origin
+    Qbk:0Bk:0 - remove k-th coordinate from input
+    QJn  - randomly joggle input in range [-n,n]
+    QRn  - random rotation (n=seed, n=0 time, n=-1 time/no rotate)
+    Qs   - search all points for the initial simplex
+    QGn  - good facet if visible from point n, -n for not visible
+    QVn  - good facet if it includes point n, -n if not
+
+Trace options:
+    T4   - trace at level n, 4=all, 5=mem/gauss, -1= events
+    Tc   - check frequently during execution
+    Ts   - print statistics
+    Tv   - verify result: structure, convexity, and point inclusion
+    Tz   - send all output to stdout
+    TFn  - report summary when n or more facets created
+    TI file - input data from file, no spaces or single quotes
+    TO file - output results to file, may be enclosed in single quotes
+    TPn  - turn on tracing when point n added to hull
+     TMn - turn on tracing at merge n
+     TWn - trace merge facets when width > n
+    TVn  - stop qhull after adding point n, -n for before (see TCn)
+     TCn - stop qhull after building cone for point n (see TVn)
+
+Precision options:
+    Cn   - radius of centrum (roundoff added).  Merge facets if non-convex
+     An  - cosine of maximum angle.  Merge facets if cosine > n or non-convex
+           C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge
+    Rn   - randomly perturb computations by a factor of [1-n,1+n]
+    Un   - max distance below plane for a new, coplanar point
+    Wn   - min facet width for outside point (before roundoff)
+
+Output formats (may be combined; if none, produces a summary to stdout):
+    f    - facet dump
+    G    - Geomview output (see below)
+    i    - vertices incident to each facet
+    m    - Mathematica output (2-d and 3-d)
+    n    - normals with offsets
+    o    - OFF file format (dim, points and facets; Voronoi regions)
+    p    - point coordinates
+    s    - summary (stderr)
+
+More formats:
+    Fa   - area for each facet
+    FA   - compute total area and volume for option 's'
+    Fc   - count plus coplanar points for each facet
+           use 'Qc' (default) for coplanar and 'Qi' for interior
+    FC   - centrum for each facet
+    Fd   - use cdd format for input (homogeneous with offset first)
+    FD   - use cdd format for numeric output (offset first)
+    FF   - facet dump without ridges
+    Fi   - inner plane for each facet
+    FI   - ID for each facet
+    Fm   - merge count for each facet (511 max)
+    FM   - Maple output (2-d and 3-d)
+    Fn   - count plus neighboring facets for each facet
+    FN   - count plus neighboring facets for each point
+    Fo   - outer plane (or max_outside) for each facet
+    FO   - options and precision constants
+    FP   - nearest vertex for each coplanar point
+    FQ   - command used for qconvex
+    Fs   - summary: #int (8), dimension, #points, tot vertices, tot facets,
+                      for output: #vertices, #facets,
+                                  #coplanar points, #non-simplicial facets
+                    #real (2), max outer plane, min vertex
+    FS   - sizes:   #int (0)
+                    #real(2) tot area, tot volume
+    Ft   - triangulation with centrums for non-simplicial facets (OFF format)
+    Fv   - count plus vertices for each facet
+    FV   - average of vertices (a feasible point for 'H')
+    Fx   - extreme points (in order for 2-d)
+
+Geomview output (2-d, 3-d, and 4-d)
+    Ga   - all points as dots
+     Gp  -  coplanar points and vertices as radii
+     Gv  -  vertices as spheres
+    Gi   - inner planes only
+     Gn  -  no planes
+     Go  -  outer planes only
+    Gc   - centrums
+    Gh   - hyperplane intersections
+    Gr   - ridges
+    GDn  - drop dimension n in 3-d and 4-d output
+
+Print options:
+    PAn  - keep n largest facets by area
+    Pdk:n - drop facet if normal[k] &lt;= n (default 0.0)
+    PDk:n - drop facet if normal[k] >= n
+    Pg   - print good facets (needs 'QGn' or 'QVn')
+    PFn  - keep facets whose area is at least n
+    PG   - print neighbors of good facets
+    PMn  - keep n facets with most merges
+    Po   - force output.  If error, output neighborhood of facet
+    Pp   - do not report precision problems
+
+    .    - list of all options
+    -    - one line descriptions of all options
+
+</pre>
+
+<!-- Navigation links -->
+<hr>
+
+<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
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+<b>To:</b> <a href="#synopsis">sy</a>nopsis
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+&#149; <a href="#notes">no</a>tes &#149; <a href="#conventions">co</a>nventions
+&#149; <a href="#options">op</a>tions
+<!-- GC common information -->
+<hr>
+
+<p><a href="http://www.geom.uiuc.edu/"><img src="qh--geom.gif"
+align="middle" width="40" height="40"></a><i>The Geometry Center
+Home Page </i></p>
+
+<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
+</a><br>
+Created: Sept. 25, 1995 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
+</body>
+</html>
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@@ -0,0 +1,416 @@
+<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN">
+<html>
+
+<head>
+<title>qdelaunay Qu -- furthest-site Delaunay triangulation</title>
+</head>
+
+<body>
+<!-- Navigation links -->
+<a name="TOP"><b>Up</b></a><b>:</b>
+<a href="http://www.qhull.org">Home page</a> for Qhull<br>
+<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
+<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
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+&#149; <a href="qh-optf.htm#format">Formats</a>
+&#149; <a href="qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="qh-optp.htm#print">Print</a>
+&#149; <a href="qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="qh-optc.htm#prec">Precision</a>
+&#149; <a href="qh-optt.htm#trace">Trace</a>
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+<b>To:</b> <a href="#synopsis">sy</a>nopsis
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+&#149; <a href="#controls">co</a>ntrols &#149; <a href="#graphics">gr</a>aphics
+&#149; <a href="#notes">no</a>tes &#149; <a href="#conventions">co</a>nventions
+&#149; <a href="#options">op</a>tions
+
+<hr>
+<!-- Main text of document -->
+<h1><a
+href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/delaunay.html"><img
+src="qh--dt.gif" alt="[delaunay]" align="middle" width="100"
+height="100"></a>qdelaunay Qu -- furthest-site Delaunay triangulation</h1>
+
+<p>The furthest-site Delaunay triangulation corresponds to the upper facets of the <a href="qdelaun.htm">Delaunay construction</a>.
+Its vertices are the
+extreme points of the input sites.
+It is the dual of the <a
+href="qvoron_f.htm">furthest-site Voronoi diagram</a>.
+
+<blockquote>
+<dl>
+    <dt><b>Example:</b> rbox 10 D2 | qdelaunay <a
+        href="qh-optq.htm#Qu">Qu</a> <a
+        href="qh-optq.htm#Qt">Qt</a> <a href="qh-opto.htm#s">s</a>
+        <a href="qh-opto.htm#i">i</a> <a href="qh-optt.htm#TO">TO
+        result</a></dt>
+    <dd>Compute the 2-d, furthest-site Delaunay triangulation of 10 random
+        points. Triangulate the output.
+        Write a summary to the console and the regions to
+        'result'.</dd>
+    <dt>&nbsp;</dt>
+    <dt><b>Example:</b> rbox 10 D2 | qdelaunay <a
+        href="qh-optq.htm#Qu">Qu</a> <a
+        href="qh-optq.htm#QJn">QJ</a> <a href="qh-opto.htm#s">s</a>
+        <a href="qh-opto.htm#i">i</a> <a href="qh-optt.htm#TO">TO
+        result</a></dt>
+    <dd>Compute the 2-d, furthest-site Delaunay triangulation of 10 random
+        points. Joggle the input to guarantee triangular output.
+        Write a summary to the console and the regions to
+        'result'.</dd>
+    <dt>&nbsp;</dt>
+    <dt><b>Example:</b> rbox r y c G1 D2 | qdelaunay <a
+        href="qh-optq.htm#Qu">Qu</a> <a href="qh-opto.htm#s">s</a>
+        <a href="qh-optf.htm#Fv">Fv</a> <a href="qh-optt.htm#TO">TO
+        result</a></dt>
+    <dd>Compute the 2-d, furthest-site Delaunay triangulation of a triangle inside
+                a square.
+        Write a summary to the console and unoriented regions to 'result'.
+        Merge regions for cocircular input sites (e.g., the square).
+                The square is the only furthest-site
+        Delaunay region.</dd>
+</dl>
+</blockquote>
+
+<p>As with the Delaunay triangulation, Qhull computes the
+furthest-site Delaunay triangulation by lifting the input sites to a
+paraboloid. The lower facets correspond to the Delaunay
+triangulation while the upper facets correspond to the
+furthest-site triangulation. Neither triangulation includes
+&quot;vertical&quot; facets (i.e., facets whose last hyperplane
+coefficient is nearly zero). Vertical facets correspond to input
+sites that are coplanar to the convex hull of the input. An
+example is points on the boundary of a lattice.</p>
+
+<p>By default, qdelaunay merges cocircular and cospherical regions.
+For example, the furthest-site Delaunay triangulation of a square inside a diamond
+('rbox D2 c d G4 | qdelaunay Qu') consists of one region (the diamond).
+
+<p>If you use '<a href="qh-optq.htm#Qt">Qt</a>' (triangulated output),
+all furthest-site Delaunay regions will be simplicial (e.g., triangles in 2-d).
+Some regions may be
+degenerate and have zero area.
+
+<p>If you use '<a href="qh-optq.htm#QJn">QJ</a>' (joggled input), all furthest-site
+Delaunay regions
+will be simplicial (e.g., triangles in 2-d).  Joggled input
+is less accurate than triangulated output ('Qt').  See <a
+href="qh-impre.htm#joggle">Merged facets or joggled input</a>. </p>
+
+<p>The output for 3-d, furthest-site Delaunay triangulations may be confusing if the
+input contains cospherical data. See the FAQ item
+<a href=qh-faq.htm#extra>Why
+are there extra points in a 4-d or higher convex hull?</a>
+Avoid these problems with triangulated output ('<a href="qh-optq.htm#Qt">Qt</a>') or
+joggled input ('<a href="qh-optq.htm#QJn">QJ</a>').
+</p>
+
+<p>The 'qdelaunay' program is equivalent to
+'<a href=qhull.htm#outputs>qhull d</a> <a href=qh-optq.htm#Qbb>Qbb</a>' in 2-d to 3-d, and
+'<a href=qhull.htm#outputs>qhull d</a> <a href=qh-optq.htm#Qbb>Qbb</a> <a href=qh-optq.htm#Qx>Qx</a>'
+in 4-d and higher.  It disables the following Qhull
+<a href=qh-quick.htm#options>options</a>: <i>d n v H U Qb QB Qc Qf Qg Qi
+Qm Qr QR Qv Qx TR E V FC Fi Fo Fp FV Q0,etc</i>.
+
+
+<p><b>Copyright &copy; 1995-2015 C.B. Barber</b></p>
+
+<hr>
+
+<h3><a href="#TOP">&#187;</a><a name="synopsis">furthest-site qdelaunay synopsis</a></h3>
+<blockquote>
+
+See <a href="qdelaun.htm#synopsis">qdelaunay synopsis</a>.  The same
+program is used for both constructions.  Use option '<a href="qh-optq.htm#Qu">Qu</a>'
+for furthest-site Delaunay triangulations.
+
+</blockquote>
+<h3><a href="#TOP">&#187;</a><a name="input">furthest-site qdelaunay
+input</a></h3>
+
+<blockquote>
+<p>The input data on <tt>stdin</tt> consists of:</p>
+<ul>
+    <li>dimension
+    <li>number of points</li>
+    <li>point coordinates</li>
+</ul>
+
+<p>Use I/O redirection (e.g., qdelaunay Qu &lt; data.txt), a pipe (e.g., rbox 10 | qdelaunay Qu),
+or the '<a href=qh-optt.htm#TI>TI</a>' option (e.g., qdelaunay Qu TI data.txt).
+
+<p>For example, this is a square containing four random points.
+Its furthest-site Delaunay
+triangulation contains one square.
+<p>
+<blockquote>
+<tt>rbox c 4 D2 &gt; data</tt>
+<blockquote><pre>
+2 RBOX c 4 D2
+8
+-0.4999921736307369 -0.3684622117955817
+0.2556053225468894 -0.0413498678629751
+0.0327672376602583 -0.2810408135699488
+-0.452955383763607 0.17886471718444
+  -0.5   -0.5
+  -0.5    0.5
+   0.5   -0.5
+   0.5    0.5
+</pre></blockquote>
+
+<p><tt>qdelaunay Qu i &lt; data</tt>
+<blockquote><pre>
+
+Furthest-site Delaunay triangulation by the convex hull of 8 points in 3-d:
+
+  Number of input sites: 8
+  Number of Delaunay regions: 1
+  Number of non-simplicial Delaunay regions: 1
+
+Statistics for: RBOX c 4 D2 | QDELAUNAY s Qu i
+
+  Number of points processed: 8
+  Number of hyperplanes created: 20
+  Number of facets in hull: 11
+  Number of distance tests for qhull: 34
+  Number of merged facets: 1
+  Number of distance tests for merging: 107
+  CPU seconds to compute hull (after input): 0.02
+
+1
+7 6 4 5
+</pre></blockquote>
+</blockquote>
+
+</blockquote>
+<h3><a href="#TOP">&#187;</a><a name="outputs">furthest-site qdelaunay
+outputs</a></h3>
+<blockquote>
+
+<p>These options control the output of furthest-site Delaunay triangulations:</p>
+<blockquote>
+
+<dl compact>
+    <dd><b>furthest-site Delaunay regions</b></dd>
+    <dt><a href="qh-opto.htm#i">i</a></dt>
+    <dd>list input sites for each furthest-site Delaunay region. The first line is the number of regions.  The
+        remaining lines list the input sites for each region.  The regions are
+                oriented.  In 3-d and
+        higher, report cospherical sites by adding extra points.  For the points-in-square example,
+        the square is the only furthest-site Delaunay region.</dd>
+    <dt><a href="qh-optf.htm#Fv">Fv</a></dt>
+    <dd>list input sites for each furthest-site Delaunay region.  The first line is the number of regions.
+        Each remaining line starts with the number of input sites.  The regions
+        are unoriented.  For the points-in-square example,
+        the square is the only furthest-site Delaunay region.</dd>
+    <dt><a href="qh-optf.htm#Ft">Ft</a></dt>
+    <dd>print a triangulation of the furthest-site Delaunay regions in OFF format.  The first line
+        is the dimension.  The second line is the number of input sites and added points,
+        followed by the number of simplices and the number of ridges.
+    The input coordinates are next, followed by the centrum coordinates.  There is
+        one centrum for each non-simplicial furthest-site Delaunay region.  Each remaining line starts
+        with dimension+1.  The
+        simplices are oriented.
+        For the points-in-square example, the square has a centrum at the
+        origin.  It splits the square into four triangular regions.</dd>
+    <dt><a href="qh-optf.htm#Fn">Fn</a></dt>
+    <dd>list neighboring regions for each furthest-site Delaunay region.  The first line is the
+        number of regions.  Each remaining line starts with the number of
+        neighboring regions.  Negative indices (e.g., <em>-1</em>) indicate regions
+        outside of the furthest-site Delaunay triangulation.
+        For the points-in-square example, the four neighboring regions
+        are outside of the triangulation.  They belong to the regular
+        Delaunay triangulation.</dd>
+    <dt><a href="qh-optf.htm#FN">FN</a></dt>
+    <dd>list the furthest-site Delaunay regions for each input site.  The first line is the
+        total number of input sites.  Each remaining line starts with the number of
+        furthest-site Delaunay regions.  Negative indices (e.g., <em>-1</em>) indicate regions
+        outside of the furthest-site Delaunay triangulation.
+        For the points-in-square example, the four random points belong to no region
+        while the square's vertices belong to region <em>0</em> and three
+        regions outside of the furthest-site Delaunay triangulation.</dd>
+    <dt><a href="qh-optf.htm#Fa">Fa</a></dt>
+    <dd>print area for each furthest-site Delaunay region. The first line is the number of regions.
+        The areas follow, one line per region.  For the points-in-square example, the
+        square has unit area. </dd>
+
+    <dt>&nbsp;</dt>
+    <dt>&nbsp;</dt>
+    <dd><b>Input sites</b></dd>
+    <dt><a href="qh-optf.htm#Fx">Fx</a></dt>
+    <dd>list extreme points of the input sites.  These points are vertices of the furthest-point
+        Delaunay triangulation.  They are on the
+        boundary of the convex hull.   The first line is the number of
+        extreme points.  Each point is listed, one per line.  The points-in-square example
+        has four extreme points.</dd>
+    <dt>&nbsp;</dt>
+    <dt>&nbsp;</dt>
+    <dd><b>General</b></dd>
+    <dt><a href="qh-optf.htm#FA">FA</a></dt>
+    <dd>compute total area for '<a href="qh-opto.htm#s">s</a>'
+        and '<a href="qh-optf.htm#FS">FS</a>'.  This is the
+                same as the area of the convex hull.</dd>
+    <dt><a href="qh-opto.htm#o">o</a></dt>
+    <dd>print upper facets of the corresponding convex hull (a
+        paraboloid)</dd>
+    <dt><a href="qh-opto.htm#m">m</a></dt>
+    <dd>Mathematica output for the upper facets of the paraboloid (2-d triangulations).</dd>
+    <dt><a href="qh-optf.htm#FM">FM</a></dt>
+    <dd>Maple output for the upper facets of the paraboloid (2-d triangulations).</dd>
+    <dt><a href="qh-optg.htm#G">G</a></dt>
+    <dd>Geomview output for the paraboloid (2-d or 3-d triangulations).</dd>
+    <dt><a href="qh-opto.htm#s">s</a></dt>
+    <dd>print summary for the furthest-site Delaunay triangulation. Use '<a
+        href="qh-optf.htm#Fs">Fs</a>' and '<a
+        href="qh-optf.htm#FS">FS</a>' for numeric data.</dd>
+</dl>
+</blockquote>
+
+</blockquote>
+<h3><a href="#TOP">&#187;</a><a name="controls">furthest-site qdelaunay
+controls</a></h3>
+<blockquote>
+
+<p>These options provide additional control:</p>
+<blockquote>
+
+<dl compact>
+   <dt><a href="qh-optq.htm#Qu">Qu</a></dt>
+    <dd>must be used for furthest-site Delaunay triangulation.</dd>
+    <dt><a href="qh-optq.htm#Qt">Qt</a></dt>
+    <dd>triangulated output.  Qhull triangulates non-simplicial facets.  It may produce
+     degenerate facets of zero area.</dd>
+   <dt><a href="qh-optq.htm#QJn">QJ</a></dt>
+    <dd>joggle the input to avoid cospherical and coincident
+        sites.    It is less accurate than triangulated output ('Qt').</dd>
+    <dt><a href="qh-optq.htm#QVn">QVn</a></dt>
+    <dd>select facets adjacent to input site <em>n</em> (marked
+        'good').</dd>
+    <dt><a href="qh-optt.htm#Tv">Tv</a></dt>
+    <dd>verify result.</dd>
+    <dt><a href="qh-optt.htm#TO">TI file</a></dt>
+    <dd>input data from file.  The filename may not use spaces or quotes.</dd>
+    <dt><a href="qh-optt.htm#TO">TO file</a></dt>
+    <dd>output results to file.  Use single quotes if the filename
+        contains spaces (e.g., <tt>TO 'file with spaces.txt'</tt></dd>
+    <dt><a href="qh-optt.htm#TFn">TFn</a></dt>
+    <dd>report progress after constructing <em>n</em> facets</dd>
+    <dt><a href="qh-optp.htm#PDk">PDk:1</a></dt>
+    <dd>include upper and lower facets in the output.  Set <em>k</em>
+        to the last dimension (e.g., 'PD2:1' for 2-d inputs). </dd>
+    <dt><a href="qh-opto.htm#f">f</a></dt>
+    <dd>facet dump.  Print the data structure for each facet (i.e., furthest-site Delaunay region).</dd>
+</dl>
+</blockquote>
+
+</blockquote>
+<h3><a href="#TOP">&#187;</a><a name="graphics">furthest-site qdelaunay
+graphics</a></h3>
+<blockquote>
+
+See <a href="qdelaun.htm#graphics">Delaunay graphics</a>.
+They are the same except for Mathematica and Maple output.
+
+</blockquote>
+<h3><a href="#TOP">&#187;</a><a name="notes">furthest-site
+qdelaunay notes</a></h3>
+<blockquote>
+
+<p>The furthest-site Delaunay triangulation does not
+record coincident input sites.  Use <tt>qdelaunay</tt> instead.
+
+<p><tt>qdelaunay Qu</tt> does not work for purely cocircular
+or cospherical points (e.g., rbox c | qdelaunay Qu).  Instead,
+use <tt>qdelaunay Qz</tt> -- when all points are vertices of the convex
+hull of the input sites, the Delaunay triangulation is the same
+as the furthest-site Delaunay triangulation.
+
+<p>A non-simplicial, furthest-site Delaunay region indicates nearly cocircular or
+cospherical input sites. To avoid non-simplicial regions triangulate
+the output ('<a href="qh-optq.htm#Qt">Qt</a>') or joggle
+the input ('<a href="qh-optq.htm#QJn">QJ</a>').  Joggled input
+is less accurate than triangulated output.
+You may also triangulate
+non-simplicial regions with option '<a
+href="qh-optf.htm#Ft">Ft</a>'. It adds
+the centrum to non-simplicial regions. Alternatively, use an <a
+href="qh-impre.htm#exact">exact arithmetic code</a>.</p>
+
+<p>Furthest-site Delaunay triangulations do not include facets that are
+coplanar with the convex hull of the input sites.  A facet is
+coplanar if the last coefficient of its normal is
+nearly zero (see <a href="../src/libqhull/user.h#ZEROdelaunay">qh_ZEROdelaunay</a>).
+
+</blockquote>
+<h3><a href="#TOP">&#187;</a><a name="conventions">furthest-site qdelaunay conventions</a></h3>
+<blockquote>
+
+<p>The following terminology is used for furthest-site Delaunay
+triangulations in Qhull. The underlying structure is the upper
+facets of a convex hull in one higher dimension. See <a
+href="qconvex.htm#conventions">convex hull conventions</a>, <a
+href="qdelaun.htm#conventions">Delaunay conventions</a>,
+and <a href="index.htm#structure">Qhull's data structures</a></p>
+<blockquote>
+<ul>
+    <li><em>input site</em> - a point in the input (one dimension
+        lower than a point on the convex hull)</li>
+    <li><em>point</em> - <i>d+1</i> coordinates. The last
+        coordinate is the sum of the squares of the input site's
+        coordinates</li>
+    <li><em>vertex</em> - a point on the paraboloid. It
+        corresponds to a unique input site. </li>
+    <li><em>furthest-site Delaunay facet</em> - an upper facet of the
+        paraboloid. The last coefficient of its normal is
+                clearly positive.</li>
+    <li><em>furthest-site Delaunay region</em> - a furthest-site Delaunay
+            facet projected to the input sites</li>
+    <li><em>non-simplicial facet</em> - more than <em>d</em>
+        points are cocircular or cospherical</li>
+    <li><em>good facet</em> - a furthest-site Delaunay facet with optional
+        restrictions by '<a href="qh-optq.htm#QVn">QVn</a>', etc.</li>
+</ul>
+</blockquote>
+</blockquote>
+<h3><a href="#TOP">&#187;</a><a name="options">furthest-site qdelaunay options</a></h3>
+<blockquote>
+
+See <a href="qdelaun.htm#options">qdelaunay options</a>.    The same
+program is used for both constructions.  Use option '<a href="qh-optq.htm#Qu">Qu</a>'
+for furthest-site Delaunay triangulations.
+
+</blockquote>
+<!-- Navigation links -->
+<hr>
+
+<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
+<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
+<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
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+<b>To:</b> <a href="#synopsis">sy</a>nopsis
+&#149; <a href="#input">in</a>put &#149; <a href="#outputs">ou</a>tputs
+&#149; <a href="#controls">co</a>ntrols &#149; <a href="#graphics">gr</a>aphics
+&#149; <a href="#notes">no</a>tes &#149; <a href="#conventions">co</a>nventions
+&#149; <a href="#options">op</a>tions
+<!-- GC common information -->
+<hr>
+
+<p><a href="http://www.geom.uiuc.edu/"><img src="qh--geom.gif"
+align="middle" width="40" height="40"></a><i>The Geometry Center
+Home Page </i></p>
+
+<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
+</a><br>
+Created: Sept. 25, 1995 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
+</body>
+</html>
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+<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN">
+<html>
+
+<head>
+<title>qdelaunay -- Delaunay triangulation</title>
+</head>
+
+<body>
+<!-- Navigation links -->
+<a name="TOP"><b>Up</b></a><b>:</b>
+<a href="http://www.qhull.org">Home page</a> for Qhull<br>
+<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
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+&#149; <a href="qh-optp.htm#print">Print</a>
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+<b>To:</b> <a href="#synopsis">sy</a>nopsis
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+&#149; <a href="#notes">no</a>tes &#149; <a href="#conventions">co</a>nventions
+&#149; <a href="#options">op</a>tions
+
+<hr>
+<!-- Main text of document -->
+<h1><a
+href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/delaunay.html"><img
+src="qh--dt.gif" alt="[delaunay]" align="middle" width="100"
+height="100"></a>qdelaunay -- Delaunay triangulation</h1>
+
+<p>The Delaunay triangulation is the triangulation with empty
+circumspheres. It has many useful properties and applications.
+See the survey article by Aurenhammer [<a
+href="index.htm#aure91">'91</a>] and the detailed introduction
+by O'Rourke [<a href="index.htm#orou94">'94</a>]. </p>
+
+<blockquote>
+<dl>
+    <dt><b>Example:</b> rbox r y c G0.1 D2 | qdelaunay <a href="qh-opto.htm#s">s</a>
+        <a href="qh-optf.htm#Fv">Fv</a> <a href="qh-optt.htm#TO">TO
+        result</a></dt>
+    <dd>Compute the 2-d Delaunay triangulation of a triangle and
+        a small square.
+        Write a summary to the console and unoriented regions to 'result'.
+        Merge regions for cocircular input sites (i.e., the
+        square).</dd>
+    <dt>&nbsp;</dt>
+    <dt><b>Example:</b> rbox r y c G0.1 D2 | qdelaunay <a href="qh-opto.htm#s">s</a>
+        <a href="qh-optf.htm#Fv">Fv</a> <a href="qh-optq.htm#Qt">Qt</a></dt>
+    <dd>Compute the 2-d Delaunay triangulation of a triangle and
+        a small square. Write a summary and unoriented
+        regions to the console.  Produce triangulated output.</dd>
+    <dt>&nbsp;</dt>
+    <dt><b>Example:</b> rbox 10 D2 | qdelaunay <a
+        href="qh-optq.htm#QJn">QJ</a> <a href="qh-opto.htm#s">s</a>
+        <a href="qh-opto.htm#i">i</a> <a href="qh-optt.htm#TO">TO
+        result</a></dt>
+    <dd>Compute the 2-d Delaunay triangulation of 10 random
+        points. Joggle the input to guarantee triangular output.
+        Write a summary to the console and the regions to
+        'result'.</dd>
+</dl>
+</blockquote>
+
+<p>Qhull computes the Delaunay triangulation by computing a
+convex hull. It lifts the input sites to a paraboloid by adding
+the sum of the squares of the coordinates. It scales the height
+of the paraboloid to improve numeric precision ('<a href=qh-optq.htm#Qbb>Qbb</a>').
+It computes the convex
+hull of the lifted sites, and projects the lower convex hull to
+the input.
+
+<p>Each region of the Delaunay triangulation
+corresponds to a facet of the lower half of the convex hull.
+Facets of the upper half of the convex hull correspond to the <a
+href="qdelau_f.htm">furthest-site Delaunay triangulation</a>.
+See the examples, <a href="qh-eg.htm#delaunay">Delaunay and
+Voronoi diagrams</a>.</p>
+
+<p>See <a href="http://www.qhull.org/html/qh-faq.htm#TOC">Qhull FAQ</a> - Delaunay and
+Voronoi diagram questions.</p>
+
+<p>By default, qdelaunay merges cocircular and cospherical regions.
+For example, the Delaunay triangulation of a square inside a diamond
+('rbox D2 c d G4 | qdelaunay') contains one region for the square.
+
+<p>Use option '<a href="qh-optq.htm#Qz">Qz</a>' if the input is circular, cospherical, or
+nearly so.  It improves precision by adding a point "at infinity," above the corresponding paraboloid.
+
+<p>If you use '<a href="qh-optq.htm#Qt">Qt</a>' (triangulated output),
+all Delaunay regions will be simplicial (e.g., triangles in 2-d).
+Some regions may be
+degenerate and have zero area.  Triangulated output identifies coincident
+points.
+
+<p>If you use '<a href="qh-optq.htm#QJn">QJ</a>' (joggled input), all Delaunay regions
+will be simplicial (e.g., triangles in 2-d).  Coincident points will
+create small regions since the points are joggled apart.  Joggled input
+is less accurate than triangulated output ('Qt').  See <a
+href="qh-impre.htm#joggle">Merged facets or joggled input</a>. </p>
+
+<p>The output for 3-d Delaunay triangulations may be confusing if the
+input contains cospherical data.  See the FAQ item
+<a href=qh-faq.htm#extra>Why
+are there extra points in a 4-d or higher convex hull?</a>
+Avoid these problems with triangulated output ('<a href="qh-optq.htm#Qt">Qt</a>') or
+joggled input ('<a href="qh-optq.htm#QJn">QJ</a>').
+</p>
+
+<p>The 'qdelaunay' program is equivalent to
+'<a href=qhull.htm#outputs>qhull d</a> <a href=qh-optq.htm#Qbb>Qbb</a>' in 2-d to 3-d, and
+'<a href=qhull.htm#outputs>qhull d</a> <a href=qh-optq.htm#Qbb>Qbb</a> <a href=qh-optq.htm#Qx>Qx</a>'
+in 4-d and higher.  It disables the following Qhull
+<a href=qh-quick.htm#options>options</a>: <i>d n v H U Qb QB Qc Qf Qg Qi
+Qm Qr QR Qv Qx TR E V FC Fi Fo Fp Ft FV Q0,etc</i>.
+
+
+<p><b>Copyright &copy; 1995-2015 C.B. Barber</b></p>
+
+<hr>
+
+<h3><a href="#TOP">&#187;</a><a name="synopsis">qdelaunay synopsis</a></h3>
+
+<pre>
+qdelaunay- compute the Delaunay triangulation.
+    input (stdin): dimension, number of points, point coordinates
+    comments start with a non-numeric character
+
+options (qdelaun.htm):
+    Qt   - triangulated output
+    QJ   - joggle input instead of merging facets
+    Qu   - furthest-site Delaunay triangulation
+    Tv   - verify result: structure, convexity, and in-circle test
+    .    - concise list of all options
+    -    - one-line description of all options
+
+output options (subset):
+    s    - summary of results (default)
+    i    - vertices incident to each Delaunay region
+    Fx   - extreme points (vertices of the convex hull)
+    o    - OFF format (shows the points lifted to a paraboloid)
+    G    - Geomview output (2-d and 3-d points lifted to a paraboloid)
+    m    - Mathematica output (2-d inputs lifted to a paraboloid)
+    QVn  - print Delaunay regions that include point n, -n if not
+    TO file- output results to file, may be enclosed in single quotes
+
+examples:
+    rbox c P0 D2 | qdelaunay s o          rbox c P0 D2 | qdelaunay i
+    rbox c P0 D3 | qdelaunay Fv Qt        rbox c P0 D2 | qdelaunay s Qu Fv
+    rbox c G1 d D2 | qdelaunay s i        rbox c G1 d D2 | qdelaunay s i Qt
+    rbox M3,4 z 100 D2 | qdelaunay s      rbox M3,4 z 100 D2 | qdelaunay s Qt
+</pre>
+
+
+<h3><a href="#TOP">&#187;</a><a name="input">qdelaunay
+input</a></h3>
+
+<blockquote>
+<p>The input data on <tt>stdin</tt> consists of:</p>
+<ul>
+    <li>dimension
+    <li>number of points</li>
+    <li>point coordinates</li>
+</ul>
+
+<p>Use I/O redirection (e.g., qdelaunay &lt; data.txt), a pipe (e.g., rbox 10 | qdelaunay),
+or the '<a href=qh-optt.htm#TI>TI</a>' option (e.g., qdelaunay TI data.txt).
+
+<p>For example, this is four cocircular points inside a square.  Its Delaunay
+triangulation contains 8 triangles and one four-sided
+figure.
+<p>
+<blockquote>
+<tt>rbox s 4 W0 c G1 D2 &gt; data</tt>
+<blockquote><pre>
+2 RBOX s 4 W0 c D2
+8
+-0.4941988586954018 -0.07594397977563715
+-0.06448037284989526 0.4958248496365813
+0.4911154367094632 0.09383830681375946
+-0.348353580869097 -0.3586778257652367
+    -1     -1
+    -1      1
+     1     -1
+     1      1
+</pre></blockquote>
+
+<p><tt>qdelaunay s i &lt; data</tt>
+<blockquote><pre>
+
+Delaunay triangulation by the convex hull of 8 points in 3-d
+
+  Number of input sites: 8
+  Number of Delaunay regions: 9
+  Number of non-simplicial Delaunay regions: 1
+
+Statistics for: RBOX s 4 W0 c D2 | QDELAUNAY s i
+
+  Number of points processed: 8
+  Number of hyperplanes created: 18
+  Number of facets in hull: 10
+  Number of distance tests for qhull: 33
+  Number of merged facets: 2
+  Number of distance tests for merging: 102
+  CPU seconds to compute hull (after input): 0.028
+
+9
+1 7 5
+6 3 4
+2 3 6
+7 2 6
+2 7 1
+0 5 4
+3 0 4
+0 1 5
+1 0 3 2
+</pre></blockquote>
+</blockquote>
+
+</blockquote>
+<h3><a href="#TOP">&#187;</a><a name="outputs">qdelaunay
+outputs</a></h3>
+<blockquote>
+
+<p>These options control the output of Delaunay triangulations:</p>
+<blockquote>
+
+<dl compact>
+    <dd><b>Delaunay regions</b></dd>
+    <dt><a href="qh-opto.htm#i">i</a></dt>
+    <dd>list input sites for each Delaunay region. The first line is the number of regions.  The
+        remaining lines list the input sites for each region.  The regions are
+                oriented.  In 3-d and
+        higher, report cospherical sites by adding extra points.  Use triangulated
+        output ('<a href="qh-optq.htm#Qt">Qt</a>') to avoid non-simpicial regions.  For the circle-in-square example,
+        eight Delaunay regions are triangular and the ninth has four input sites.</dd>
+    <dt><a href="qh-optf.htm#Fv">Fv</a></dt>
+    <dd>list input sites for each Delaunay region.  The first line is the number of regions.
+        Each remaining line starts with the number of input sites.  The regions
+        are unoriented.  For the circle-in-square example,
+        eight Delaunay regions are triangular and the ninth has four input sites.</dd>
+    <dt><a href="qh-optf.htm#Fn">Fn</a></dt>
+    <dd>list neighboring regions for each Delaunay region.  The first line is the
+        number of regions.  Each remaining line starts with the number of
+        neighboring regions.  Negative indices (e.g., <em>-1</em>) indicate regions
+        outside of the Delaunay triangulation.
+        For the circle-in-square example, the four regions on the square are neighbors to
+        the region-at-infinity.</dd>
+    <dt><a href="qh-optf.htm#FN">FN</a></dt>
+    <dd>list the Delaunay regions for each input site.  The first line is the
+        total number of input sites.  Each remaining line starts with the number of
+        Delaunay regions.  Negative indices (e.g., <em>-1</em>) indicate regions
+        outside of the Delaunay triangulation.
+        For the circle-in-square example, each point on the circle belongs to four
+        Delaunay regions.  Use '<a href="qh-optq.htm#Qc">Qc</a> FN'
+        to include coincident input sites and deleted vertices. </dd>
+    <dt><a href="qh-optf.htm#Fa">Fa</a></dt>
+    <dd>print area for each Delaunay region. The first line is the number of regions.
+        The areas follow, one line per region.  For the circle-in-square example, the
+        cocircular region has area 0.4. </dd>
+    <dt>&nbsp;</dt>
+    <dt>&nbsp;</dt>
+    <dd><b>Input sites</b></dd>
+    <dt><a href="qh-optf.htm#Fc">Fc</a></dt>
+    <dd>list coincident input sites for each Delaunay region.
+        The first line is the number of regions.  The remaining lines start with
+        the number of coincident sites and deleted vertices.  Deleted vertices
+        indicate highly degenerate input (see'<a href="qh-optf.htm#Fs">Fs</a>').
+        A coincident site is assigned to one Delaunay
+        region.  Do not use '<a href="qh-optq.htm#QJn">QJ</a>' with 'Fc'; the joggle will separate
+        coincident sites.</dd>
+    <dt><a href="qh-optf.htm#FP">FP</a></dt>
+    <dd>print coincident input sites with distance to
+        nearest site (i.e., vertex). The first line is the
+        number of coincident sites.  Each remaining line starts with the point ID of
+        an input site, followed by the point ID of a coincident point, its region, and distance.
+        Includes deleted vertices which
+        indicate highly degenerate input (see'<a href="qh-optf.htm#Fs">Fs</a>').
+        Do not use '<a href="qh-optq.htm#QJn">QJ</a>' with 'FP'; the joggle will separate
+        coincident sites.</dd>
+    <dt><a href="qh-optf.htm#Fx">Fx</a></dt>
+    <dd>list extreme points of the input sites.  These points are on the
+        boundary of the convex hull.   The first line is the number of
+        extreme points.  Each point is listed, one per line.  The circle-in-square example
+        has four extreme points.</dd>
+    <dt>&nbsp;</dt>
+    <dt>&nbsp;</dt>
+    <dd><b>General</b></dd>
+    <dt><a href="qh-optf.htm#FA">FA</a></dt>
+    <dd>compute total area for '<a href="qh-opto.htm#s">s</a>'
+        and '<a href="qh-optf.htm#FS">FS</a>'</dd>
+    <dt><a href="qh-opto.htm#o">o</a></dt>
+    <dd>print lower facets of the corresponding convex hull (a
+        paraboloid)</dd>
+    <dt><a href="qh-opto.htm#m">m</a></dt>
+    <dd>Mathematica output for the lower facets of the paraboloid (2-d triangulations).</dd>
+    <dt><a href="qh-optf.htm#FM">FM</a></dt>
+    <dd>Maple output for the lower facets of the paraboloid (2-d triangulations).</dd>
+    <dt><a href="qh-optg.htm#G">G</a></dt>
+    <dd>Geomview output for the paraboloid (2-d or 3-d triangulations).</dd>
+    <dt><a href="qh-opto.htm#s">s</a></dt>
+    <dd>print summary for the Delaunay triangulation. Use '<a
+        href="qh-optf.htm#Fs">Fs</a>' and '<a
+        href="qh-optf.htm#FS">FS</a>' for numeric data.</dd>
+</dl>
+</blockquote>
+
+</blockquote>
+<h3><a href="#TOP">&#187;</a><a name="controls">qdelaunay
+controls</a></h3>
+<blockquote>
+
+<p>These options provide additional control:</p>
+<blockquote>
+
+<dl compact>
+   <dt><a href="qh-optq.htm#Qt">Qt</a></dt>
+    <dd>triangulated output.  Qhull triangulates non-simplicial facets.  It may produce
+degenerate facets of zero area.</dd>
+   <dt><a href="qh-optq.htm#QJn">QJ</a></dt>
+    <dd>joggle the input to avoid cospherical and coincident
+        sites.    It is less accurate than triangulated output ('Qt').</dd>
+   <dt><a href="qh-optq.htm#Qu">Qu</a></dt>
+    <dd>compute the <a href="qdelau_f.htm">furthest-site Delaunay triangulation</a>.</dd>
+     <dt><a href="qh-optq.htm#Qz">Qz</a></dt>
+    <dd>add a point above the paraboloid to reduce precision
+        errors. Use it for nearly cocircular/cospherical input
+        (e.g., 'rbox c | qdelaunay Qz'). The point is printed for
+        options '<a href="qh-optf.htm#Ft">Ft</a>' and '<a
+        href="qh-opto.htm#o">o</a>'.</dd>
+    <dt><a href="qh-optq.htm#QVn">QVn</a></dt>
+    <dd>select facets adjacent to input site <em>n</em> (marked
+        'good').</dd>
+    <dt><a href="qh-optt.htm#Tv">Tv</a></dt>
+    <dd>verify result.</dd>
+    <dt><a href="qh-optt.htm#TO">TI file</a></dt>
+    <dd>input data from file.  The filename may not use spaces or quotes.</dd>
+    <dt><a href="qh-optt.htm#TO">TO file</a></dt>
+    <dd>output results to file.  Use single quotes if the filename
+        contains spaces (e.g., <tt>TO 'file with spaces.txt'</tt></dd>
+    <dt><a href="qh-optt.htm#TFn">TFn</a></dt>
+    <dd>report progress after constructing <em>n</em> facets</dd>
+    <dt><a href="qh-optp.htm#PDk">PDk:1</a></dt>
+    <dd>include upper and lower facets in the output.  Set <em>k</em>
+        to the last dimension (e.g., 'PD2:1' for 2-d inputs). </dd>
+    <dt><a href="qh-opto.htm#f">f</a></dt>
+    <dd>facet dump.  Print the data structure for each facet (i.e., Delaunay region).</dd>
+</dl>
+</blockquote>
+
+</blockquote>
+<h3><a href="#TOP">&#187;</a><a name="graphics">qdelaunay
+graphics</a></h3>
+<blockquote>
+
+<p>For 2-d and 3-d Delaunay triangulations, Geomview ('qdelaunay <a
+href="qh-optg.htm#G">G</a>') displays the corresponding convex
+hull (a paraboloid). </p>
+
+<p>To view a 2-d Delaunay triangulation, use 'qdelaunay <a
+href="qh-optg.htm#GDn">GrD2</a>' to drop the last dimension. This
+is the same as viewing the hull without perspective (see
+Geomview's 'cameras' menu). </p>
+
+<p>To view a 3-d Delaunay triangulation, use 'qdelaunay <a
+href="qh-optg.htm#GDn">GrD3</a>' to drop the last dimension. You
+may see extra edges. These are interior edges that Geomview moves
+towards the viewer (see 'lines closer' in Geomview's camera
+options). Use option '<a href="qh-optg.htm#Gt">Gt</a>' to make
+the outer ridges transparent in 3-d. See <a
+href="qh-eg.htm#delaunay">Delaunay and Voronoi examples</a>.</p>
+
+<p>For 2-d Delaunay triangulations, Mathematica ('<a
+href="qh-opto.htm#m">m</a>') and Maple ('<a
+href="qh-optf.htm#FM">FM</a>') output displays the lower facets of the corresponding convex
+hull (a paraboloid). </p>
+
+<p>For 2-d, furthest-site Delaunay triangulations, Maple and Mathematica output ('<a
+href="qh-optq.htm#Qu">Qu</a> <a
+href="qh-opto.htm#m">m</a>') displays the upper facets of the corresponding convex
+hull (a paraboloid). </p>
+
+</blockquote>
+<h3><a href="#TOP">&#187;</a><a name="notes">qdelaunay
+notes</a></h3>
+<blockquote>
+
+<p>You can simplify the Delaunay triangulation by enclosing the input
+sites in a large square or cube.  This is particularly recommended
+for cocircular or cospherical input data.
+
+<p>A non-simplicial Delaunay region indicates nearly cocircular or
+cospherical input sites. To avoid non-simplicial regions either triangulate
+the output ('<a href="qh-optq.htm#Qt">Qt</a>') or joggle
+the input ('<a href="qh-optq.htm#QJn">QJ</a>').  Triangulated output
+is more accurate than joggled input.  Alternatively, use an <a
+href="qh-impre.htm#exact">exact arithmetic code</a>.</p>
+
+<p>Delaunay triangulations do not include facets that are
+coplanar with the convex hull of the input sites.  A facet is
+coplanar if the last coefficient of its normal is
+nearly zero (see <a href="../src/libqhull/user.h#ZEROdelaunay">qh_ZEROdelaunay</a>).
+
+<p>See <a href=qh-impre.htm#delaunay>Imprecision issues :: Delaunay triangulations</a>
+for a discussion of precision issues.  Deleted vertices indicate
+highly degenerate input.  They are listed in the summary output and
+option '<a href="qh-optf.htm#Fs">Fs</a>'.</p>
+
+<p>To compute the Delaunay triangulation of points on a sphere,
+compute their convex hull. If the sphere is the unit sphere at
+the origin, the facet normals are the Voronoi vertices of the
+input. The points may be restricted to a hemisphere. [S. Fortune]
+</p>
+
+<p>The 3-d Delaunay triangulation of regular points on a half
+spiral (e.g., 'rbox 100 l | qdelaunay') has quadratic size, while the Delaunay triangulation
+of random 3-d points is
+approximately linear for reasonably sized point sets.
+
+<p>With the <a href="qh-code.htm#library">Qhull library</a>, you
+can use <tt>qh_findbestfacet</tt> in <tt>poly2.c</tt> to locate the facet
+that contains a point. You should first lift the point to the
+paraboloid (i.e., the last coordinate is the sum of the squares
+of the point's coordinates -- <tt>qh_setdelaunay</tt>). Do not use options
+'<a href="qh-optq.htm#Qbb">Qbb</a>', '<a href="qh-optq.htm#QbB">QbB</a>',
+'<a href="qh-optq.htm#Qbk">Qbk:n</a>', or '<a
+href="qh-optq.htm#QBk">QBk:n</a>' since these scale the last
+coordinate. </p>
+
+<p>If a point is interior to the convex hull of the input set, it
+is interior to the adjacent vertices of the Delaunay
+triangulation. This is demonstrated by the following pipe for
+point 0:
+
+<pre>
+    qdelaunay &lt;data s FQ QV0 p | qconvex s Qb3:0B3:0 p
+</pre>
+
+<p>The first call to qdelaunay returns the neighboring points of
+point 0 in the Delaunay triangulation. The second call to qconvex
+returns the vertices of the convex hull of these points (after
+dropping the lifted coordinate). If point 0 is interior to the
+original point set, it is interior to the reduced point set. </p>
+
+</blockquote>
+<h3><a href="#TOP">&#187;</a><a name="conventions">qdelaunay conventions</a></h3>
+<blockquote>
+
+<p>The following terminology is used for Delaunay triangulations
+in Qhull for dimension <i>d</i>. The underlying structure is the
+lower facets of a convex hull in dimension <i>d+1</i>. For
+further information, see <a href="index.htm#structure">data
+structures</a> and <a href="qconvex.htm#conventions">convex hull
+conventions</a>.</p>
+<blockquote>
+<ul>
+    <li><em>input site</em> - a point in the input (one dimension
+        lower than a point on the convex hull)</li>
+    <li><em>point</em> - a point has <i>d+1</i> coordinates. The
+        last coordinate is the sum of the squares of the input
+        site's coordinates</li>
+    <li><em>coplanar point</em> - a <em>coincident</em>
+        input site or a deleted vertex.  Deleted vertices
+        indicate highly degenerate input.</li>
+    <li><em>vertex</em> - a point on the paraboloid. It
+        corresponds to a unique input site. </li>
+    <li><em>point-at-infinity</em> - a point added above the
+        paraboloid by option '<a href="qh-optq.htm#Qz">Qz</a>'</li>
+    <li><em>lower facet</em> - a facet corresponding to a
+        Delaunay region. The last coefficient of its normal is
+        clearly negative.</li>
+    <li><em>upper facet</em> - a facet corresponding to a
+        furthest-site Delaunay region. The last coefficient of
+        its normal is clearly positive. </li>
+    <li><em>Delaunay region</em> - a
+        lower facet projected to the input sites</li>
+    <li><em>upper Delaunay region</em> - an upper facet projected
+        to the input sites</li>
+    <li><em>non-simplicial facet</em> - more than <em>d</em>
+        input sites are cocircular or cospherical</li>
+    <li><em>good facet</em> - a Delaunay region with optional
+        restrictions by '<a href="qh-optq.htm#QVn">QVn</a>', etc.</li>
+</ul>
+</blockquote>
+</blockquote>
+<h3><a href="#TOP">&#187;</a><a name="options">qdelaunay options</a></h3>
+
+<pre>
+qdelaunay- compute the Delaunay triangulation
+    http://www.qhull.org
+
+input (stdin):
+    first lines: dimension and number of points (or vice-versa).
+    other lines: point coordinates, best if one point per line
+    comments:    start with a non-numeric character
+
+options:
+    Qt   - triangulated output
+    QJ   - joggle input instead of merging facets
+    Qu   - compute furthest-site Delaunay triangulation
+
+Qhull control options:
+    QJn  - randomly joggle input in range [-n,n]
+    Qs   - search all points for the initial simplex
+    Qz   - add point-at-infinity to Delaunay triangulation
+    QGn  - print Delaunay region if visible from point n, -n if not
+    QVn  - print Delaunay regions that include point n, -n if not
+
+Trace options:
+    T4   - trace at level n, 4=all, 5=mem/gauss, -1= events
+    Tc   - check frequently during execution
+    Ts   - print statistics
+    Tv   - verify result: structure, convexity, and in-circle test
+    Tz   - send all output to stdout
+    TFn  - report summary when n or more facets created
+    TI file - input data from file, no spaces or single quotes
+    TO file - output results to file, may be enclosed in single quotes
+    TPn  - turn on tracing when point n added to hull
+     TMn - turn on tracing at merge n
+     TWn - trace merge facets when width > n
+    TVn  - stop qhull after adding point n, -n for before (see TCn)
+     TCn - stop qhull after building cone for point n (see TVn)
+
+Precision options:
+    Cn   - radius of centrum (roundoff added).  Merge facets if non-convex
+     An  - cosine of maximum angle.  Merge facets if cosine > n or non-convex
+           C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge
+    Rn   - randomly perturb computations by a factor of [1-n,1+n]
+    Wn   - min facet width for outside point (before roundoff)
+
+Output formats (may be combined; if none, produces a summary to stdout):
+    f    - facet dump
+    G    - Geomview output (see below)
+    i    - vertices incident to each Delaunay region
+    m    - Mathematica output (2-d only, lifted to a paraboloid)
+    o    - OFF format (dim, points, and facets as a paraboloid)
+    p    - point coordinates (lifted to a paraboloid)
+    s    - summary (stderr)
+
+More formats:
+    Fa   - area for each Delaunay region
+    FA   - compute total area for option 's'
+    Fc   - count plus coincident points for each Delaunay region
+    Fd   - use cdd format for input (homogeneous with offset first)
+    FD   - use cdd format for numeric output (offset first)
+    FF   - facet dump without ridges
+    FI   - ID of each Delaunay region
+    Fm   - merge count for each Delaunay region (511 max)
+    FM   - Maple output (2-d only, lifted to a paraboloid)
+    Fn   - count plus neighboring region for each Delaunay region
+    FN   - count plus neighboring region for each point
+    FO   - options and precision constants
+    FP   - nearest point and distance for each coincident point
+    FQ   - command used for qdelaunay
+    Fs   - summary: #int (8), dimension, #points, tot vertices, tot facets,
+                    for output: #vertices, #Delaunay regions,
+                                #coincident points, #non-simplicial regions
+                    #real (2), max outer plane, min vertex
+    FS   - sizes:   #int (0)
+                    #real (2), tot area, 0
+    Fv   - count plus vertices for each Delaunay region
+    Fx   - extreme points of Delaunay triangulation (on convex hull)
+
+Geomview options (2-d and 3-d)
+    Ga   - all points as dots
+     Gp  -  coplanar points and vertices as radii
+     Gv  -  vertices as spheres
+    Gi   - inner planes only
+     Gn  -  no planes
+     Go  -  outer planes only
+    Gc     - centrums
+    Gh   - hyperplane intersections
+    Gr   - ridges
+    GDn  - drop dimension n in 3-d and 4-d output
+    Gt   - transparent outer ridges to view 3-d Delaunay
+
+Print options:
+    PAn  - keep n largest Delaunay regions by area
+    Pdk:n - drop facet if normal[k] &lt;= n (default 0.0)
+    PDk:n - drop facet if normal[k] >= n
+    Pg   - print good Delaunay regions (needs 'QGn' or 'QVn')
+    PFn  - keep Delaunay regions whose area is at least n
+    PG   - print neighbors of good regions (needs 'QGn' or 'QVn')
+    PMn  - keep n Delaunay regions with most merges
+    Po   - force output.  If error, output neighborhood of facet
+    Pp   - do not report precision problems
+
+    .    - list of all options
+    -    - one line descriptions of all options
+</pre>
+
+<!-- Navigation links -->
+<hr>
+
+<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
+<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
+<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
+&#149; <a href="qh-quick.htm#options">Options</a>
+&#149; <a href="qh-opto.htm#output">Output</a>
+&#149; <a href="qh-optf.htm#format">Formats</a>
+&#149; <a href="qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="qh-optp.htm#print">Print</a>
+&#149; <a href="qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="qh-optc.htm#prec">Precision</a>
+&#149; <a href="qh-optt.htm#trace">Trace</a>
+&#149; <a href="../src/libqhull_r/index.htm">Functions</a><br>
+<b>To:</b> <a href="#synopsis">sy</a>nopsis
+&#149; <a href="#input">in</a>put &#149; <a href="#outputs">ou</a>tputs
+&#149; <a href="#controls">co</a>ntrols &#149; <a href="#graphics">gr</a>aphics
+&#149; <a href="#notes">no</a>tes &#149; <a href="#conventions">co</a>nventions
+&#149; <a href="#options">op</a>tions
+<!-- GC common information -->
+<hr>
+
+<p><a href="http://www.geom.uiuc.edu/"><img src="qh--geom.gif"
+align="middle" width="40" height="40"></a><i>The Geometry Center
+Home Page </i></p>
+
+<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
+</a><br>
+Created: Sept. 25, 1995 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
+</body>
+</html>
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+<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN">
+<html>
+
+<head>
+<title>Qhull code</title>
+<!-- Navigation links -->
+</head>
+
+<body>
+
+<p><a name="TOP"><b>Up:</b></a> <a
+href="http://www.qhull.org">Home page for Qhull</a>
+<br>
+<b>Up:</b> <a href="index.htm#TOC">Qhull manual: Table of
+Contents</a><br>
+<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
+&#149; <a href="qh-quick.htm#options">Options</a>
+&#149; <a href="qh-opto.htm#output">Output</a>
+&#149; <a href="qh-optf.htm#format">Formats</a>
+&#149; <a href="qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="qh-optp.htm#print">Print</a>
+&#149; <a href="qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="qh-optc.htm#prec">Precision</a>
+&#149; <a href="qh-optt.htm#trace">Trace</a>
+&#149; <a href="../src/libqhull_r/index.htm">Functions</a><br>
+<b>To:</b> <a href="#TOC">Qhull code</a>: Table of Contents
+(please wait while loading) <br>
+<b>Dn:</b> <a href="../src/libqhull_r/index.htm">Qhull functions</a>, macros, and data
+structures
+</p>
+
+<hr>
+<!-- Main text of document -->
+<h1><a
+href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/4dcube.html"><img
+src="qh--4d.gif" alt="[4-d cube]" align="middle" width="100"
+height="100"></a> Qhull code</h1>
+
+<p>This section discusses the code for Qhull. </p>
+
+<p><b>Copyright &copy; 1995-2015 C.B. Barber</b></p>
+
+<hr>
+
+<h2><a href="#TOP">&#187;</a><a name="TOC">Qhull code: Table of
+Contents </a></h2>
+
+<ul>
+    <li><a href="#reentrant">Reentrant</a> Qhull
+    <li><a href="#convert">How to convert</a> code to reentrant Qhull
+    <li><a href="#64bit">Qhull</a> on 64-bit computers
+    <li><a href="#cpp">Calling</a> Qhull from C++ programs
+    <ul>
+        <li><a href="#questions-cpp">Cpp questions for Qhull</a></li>
+        <li><a href="#coordinate-cpp">CoordinateIterator</a></li>
+        <li><a href="#qhull-cpp">Qhull</a></li>
+        <li><a href="#error-cpp">QhullError</a></li>
+        <li><a href="#facet-cpp">QhullFacet</a></li>
+        <li><a href="#facetlist-cpp">QhullFacetList</a></li>
+        <li><a href="#facetset-cpp">QhullFacetSet</a></li>
+        <li><a href="#iterator-cpp">QhullIterator</a></li>
+        <li><a href="#linkedlist-cpp">QhullLinkedList</a></li>
+        <li><a href="#point-cpp">QhullPoint</a></li>
+        <li><a href="#qh-cpp">QhullQh</a></li>
+        <li><a href="#pointset-cpp">QhullPointSet</a></li>
+        <li><a href="#ridge-cpp">QhullRidge</a></li>
+        <li><a href="#ridgeset-cpp">QhullRidgeSet</a></li>
+        <li><a href="#set-cpp">QhullSet</a></li>
+        <li><a href="#vertex-cpp">QhullVertex</a></li>
+        <li><a href="#vertexlist-cpp">QhullVertexList</a></li>
+        <li><a href="#vertexset-cpp">QhullVertexSet</a></li>
+        <li><a href="#rbox-cpp">RboxPoints</a></li>
+    </ul>
+    <li><a href="#library">Calling</a> Qhull from C programs
+    <ul>
+            <li><a href="#exit">How to avoid</a> exit(), fprintf(), stderr, and stdout</li>
+            <li><a href="#constrained">Constrained Delaunay</a>
+                triangulation</li>
+            <li><a href="#dids">Delaunay triangulations</a> and point indices</li>
+            <li><a href="#findfacet">Locate facet</a> with
+                qh_findbestfacet()</li>
+            <li><a href="#inc">On-line construction</a> with
+                qh_addpoint()</li>
+            <li><a href="#mem">Sets and quick memory</a> allocation</li>
+        <li><a href="#tricoplanar">Tricoplanar facets</a> and option 'Qt'</li>
+            <li><a href="#vneighbor">Vertex neighbors</a> of a vertex</li>
+            <li><a href="#vertices">Voronoi vertices</a> of a region</li>
+            <li><a href="#ridge">Voronoi vertices</a> of a ridge</li>
+        </ul>
+    </li>
+    <li><a href="#performance">Performance</a> of Qhull</li>
+    <li><a href="#enhance">Enhancements</a> to Qhull</li>
+    <li><a href="../src/libqhull_r/index.htm">Qhull</a> functions, macros, and data
+        structures </li>
+</ul>
+
+<hr>
+
+<h2><a href="#TOC">&#187;</a><a name="reentrant">Reentrant Qhull</a></h2>
+
+<p>Qhull-2015 introduces reentrant Qhull (libqhull_r).   Reentrant Qhull uses a qhT* argument instead of global data structures.
+The qhT* pointer is the first argument to most Qhull routines.  It allows multiple instances of Qhull to run at the same time.
+It simplifies the C++ interface to Qhull.
+
+<p>New code should be written with libqhull_r.   Existing users of libqhull should consider converting to libqhull_r.
+Although libqhull will be supported indefinitely, improvements may not be implemented.
+Reentrant qhull is 1-2% slower than non-reentrant qhull.
+
+<p><b>Note:</b> Reentrant Qhull is <i>not</i> thread safe.   Do not invoke Qhull routines with the same qhT* pointer from multiple threads.
+
+<h2><a href="#TOC">&#187;</a><a name="convert">How to convert</a> code to reentrant Qhull</h2>
+
+<p>C++ users need to convert to libqhull_r.
+The new C++ interface does a better, but not perfect, job of hiding Qhull's C data structures.
+The previous C++ interface was unusual due to Qhull's global data structures.
+
+<p>All other users should consider converting to libqhull_r.   The conversion is straight forward.
+The original conversion of libqhull to libqhull_r required thousands of changes, mostly global
+search and replace.  The first run of Qhull (unix_r.c) produced the same
+output, and nearly the same log files, as the original (unix.c).
+
+<p>Suggestions to help with conversion.
+<ul>
+<li>Compare qconvex_r.c with qconvex.c.   Define a qhT object and a pointer it.  The qhT* pointer is the first argument to most Qhull functions.
+Clear <tt>qh_qh-&lt;NOerrext</tt> before calling qh_initflags().  Invoke QHULL_LIB_CHECK to check for a compatible Qhull library.
+<li>Compare user_eg2_r.c with user_eg2.c
+<li>Compare user_eg_r.c with user_eg.c.   If you use qhT before invoking qh_init_A, call qh_zero() to clear the qhT object.
+user_eg_r.c includes multiple Qhull runs.
+<li>Review user_eg3_r.cpp.  As with the other programs, invoke QHULL_LIB_CHECK.
+Simple C++ programs should compile as is.
+<li>Compare QhullFacet.cpp with the same file in Qhull-2012.1.  UsingLibQhull was replaced with the macro QH_TRY_() and '<tt>qh_qh-&lt;NOerrext= true</tt>'.
+<li>For detailed notes on libqhull_r, see "libqhull_r (reentrant Qhull)" and "Source code changes for libqhull_r" in <a href="../src/Changes.txt">Changes.txt</a>.
+<li>For detailed notes on libqhullcpp, see "C++ interface" and following sections in <a href="../src/Changes.txt">Changes.txt</a>.
+<li>For regexps and conversion notes, see <a href="http://www.qhull.org/html/README_r.txt">README_r.txt</a> (unedited).
+</ul>
+
+<h2><a href="#TOC">&#187;</a><a name="64bit">Qhull on 64-bit computers</a></h2>
+
+<p>Qhull compiles for 64-bit hosts.  Since the size of a pointer on a 64-bit host is double the size on a 32-bit host,
+memory consumption increases about 50% for simplicial facets and up-to 100% for non-simplicial facets.
+
+<p>You can check memory consumption with option <a href="qh-optt.htm#Ts">Ts</a>.   It includes the size of
+each data structure:
+<ul>
+<li>32-bit -- merge 24 ridge 20 vertex 28 facet 88 normal 24 ridge vertices 16 facet vertices or neighbors 20
+<li>64-bit -- merge 32 ridge 32 vertex 48 facet 120 normal 32 ridge vertices 40 facet vertices or neighbors 48
+</ul>
+
+<p>For Qhull 2015, the maximum identifier for ridges, vertices, and facets was increased
+from 24-bits to 32-bits.  This allows for larger convex hulls, but may increase the size of
+the corresponding data structures.  The sizes for Qhull 2012.1 were
+<ul>
+<li>32-bit -- merge 24 ridge 16 vertex 24 facet 88
+<li>64-bit -- merge 32 ridge 32 vertex 40 facet 120
+</ul>
+
+<h2><a href="#TOC">&#187;</a><a name="cpp">Calling Qhull from
+C++ programs</a></h2>
+
+<p>Qhull 2015 uses reentrant Qhull for its C++ interface.  If you used
+the C++ interface from qhull 2012.1, you may need to adjust how you initialize and use
+the Qhull classes.   See <a href="#convert">How to convert code to reentrant Qhull</a>.
+
+<p>
+Qhull's C++ interface allows you to explore the results of running Qhull.
+It provides access to Qhull's data structures.
+Most of the classes derive from the corresponding qhull data structure.
+For example, <a href="#facet-cpp">QhullFacet</a> is an instance of Qhull's <a href="../src/libqhull_r/libqhull_r.h#facetT">facetT</a>.
+</p>
+
+<p>You can retain most of the data in Qhull and use the C++ interface to explore its results.
+Each object contains a reference the Qhull's data structure (via QhullQh), making the C++ representation less memory efficient.
+</p>
+
+<p>Besides using the C++ interface, you can also use libqhull_r directly.  For example,
+the FOREACHfacet_(...) macro will visit each facet in turn.
+</p>
+
+<p>The C++ interface to Qhull is incomplete. You may need to extend the interface.
+If so, you will need to understand Qhull's data structures and read the code.
+
+Example (c.f., <code>user_eg3 eg-100</code>).   It prints the facets generated by Qhull.
+
+<pre>
+    RboxPoints rbox;
+    rbox.appendRandomPoints("100");
+    Qhull qhull;
+    qhull.runQhull("", rbox);
+    QhullFacetList facets(qhull);
+    cout<< facets;
+</pre>
+
+<p>
+The C++ iterface for RboxPoints redefines the fprintf() calls
+in rboxlib.c.   Instead of writing its output to stdout, RboxPoints appends
+the output to a std::vector.
+The same technique may be used for calling Qhull from C++.
+</p>
+<ul><li>
+Run Qhull with option '<a href="qh-optt.htm#Ta">Ta</a>' to annotate the
+output with qh_fprintf() identifiers.
+</li><li>
+Redefine qh_fprintf() for these identifiers.
+</li><li>
+See RboxPoints.cpp for an example.
+</li></ul>
+<p>
+Since the C++ interface uses reentrant Qhull, multiple threads may run Qhull at the same time.   Each thread is
+one run of Qhull.
+</p>
+
+<p>
+Do <i>not</i> have two threads accessing the same Qhull instance.  Qhull is not thread-safe.
+</p>
+
+<h3><a href="#TOC">&#187;</a><a name="coordinate-cpp">CoordinateIterator</a></h3>
+<p>
+A CoordinateIterator or ConstCoordinateIterator [RboxPoints.cpp] is a <code>std::vector&lt;realT>::iterator</code> for Rbox and Qhull coordinates.
+It is the result type of <a href="#rbox-cpp">RboxPoints</a>.coordinates().
+</p>
+
+<p>Qhull does not use CoordinateIterator for its data structures.  A point in Qhull is an array of reals instead of a std::vector.
+See <a href="#point-cpp">QhullPoint</a>.
+</p>
+
+<h3><a href="#TOC">&#187;</a><a name="qhull-cpp">Qhull</a></h3>
+<p>
+Qhull is the top-level class for running Qhull.
+It initializes Qhull, runs the computation, and records errors.
+It provides access to the global data structure <a href="#qh-cpp">QhullQh</a>,
+Qhull's <a href="#facet-cpp">facets</a>, and <a href="#vertex-cpp">vertices</a>.
+</p>
+
+<h3><a href="#TOC">&#187;</a><a name="error-cpp">QhullError</a></h3>
+<p>
+QhullError is derived from <code>std::exception</code>.  It reports errors from Qhull and captures the output to stderr.
+</p>
+
+<p>
+If error handling is not set up, Qhull exits with a code from 1 to 5.  The codes are defined by
+qh_ERR* in libqhull_r.h.  The exit is via qh_exit() in usermem_r.c.
+The C++ interface does not report the
+captured output in QhullError.  Call Qhull::setErrorStream to send output to cerr instead.
+</p>
+
+<h3><a href="#TOC">&#187;</a><a name="facet-cpp">QhullFacet</a></h3>
+<p>
+A QhullFacet is a facet of the convex hull, a region of the Delaunay triangulation, a vertex of a Voronoi diagram,
+or an intersection of the halfspace intersection about a point.
+A QhullFacet has a set of <a href="#vertex-cpp">QhullVertex</a>, a set of <a href="#ridge-cpp">QhullRidge</a>, and
+a set of neighboring QhullFacets.
+</p>
+
+<h3><a href="#TOC">&#187;</a><a name="facetlist-cpp">QhullFacetList</a></h3>
+<p>
+A QhullFacetList is a linked list of <a href="#facet-cpp">QhullFacet</a>.  The result of <code>Qhull.runQhull</code> is a QhullFacetList stored
+in <a href="#qh-cpp">QhullQh</a>.
+</p>
+
+<h3><a href="#TOC">&#187;</a><a name="facetset-cpp">QhullFacetSet</a></h3>
+<p>
+A QhullFacetSet is a <a href="#set-cpp">QhullSet</a> of <a href="#facet-cpp">QhullFacet</a>.  QhullFacetSet may be ordered or unordered.  The neighboring facets of a QhullFacet is a QhullFacetSet.
+The neighbors of a <a href="#facet-cpp">QhullFacet</a> is a QhullFacetSet.
+The neighbors are ordered for simplicial facets, matching the opposite vertex of the facet.
+</p>
+
+<h3><a href="#TOC">&#187;</a><a name="iterator-cpp">QhullIterator</a></h3>
+<p>
+QhullIterator contains macros for defining Java-style iterator templates from a STL-style iterator template.
+</p>
+
+<h3><a href="#TOC">&#187;</a><a name="linkedlist-cpp">QhullLinkedList</a></h3>
+<p>
+A QhullLinkedLIst is a template for linked lists with next and previous pointers.
+<a href="#facetlist-cpp">QhullFacetList</a> and <a href="#facetlist-cpp">QhullVertexList</a> are QhullLinkedLists.
+</p>
+
+<h3><a href="#TOC">&#187;</a><a name="point-cpp">QhullPoint</a></h3>
+<p>
+A QhullPoint is an array of point coordinates, typically doubles.  The length of the array is <a href="#qh-cpp">QhullQh</a>.hull_dim.
+The identifier of a QhullPoint is its 0-based index from QhullQh.first_point followed by QhullQh.other_points.
+</p>
+
+<h3><a href="#TOC">&#187;</a><a name="pointset-cpp">QhullPointSet</a></h3>
+<p>
+A QhullPointSet is a <a href="#set-cpp">QhullSet</a> of <a href="#point-cpp">QhullPoint</a>.  The QhullPointSet of a <a href="#facet-cpp">QhullFacet</a> is its coplanar points.
+</p>
+
+<h3><a href="#TOC">&#187;</a><a name="qh-cpp">QhullQh</a></h3>
+<p>
+QhullQh is the root of Qhull's data structure.
+It contains initialized constants, sets, buffers, and variables.
+It contains an array and a set of <a href="#point-cpp">QhullPoint</a>,
+a list of <a href="#facet-cpp">QhullFacet</a>, and a list of <a href="#vertex-cpp">QhullVertex</a>.
+The points are the input to Qhull.  The facets and vertices are the result of running Qhull.
+</p>
+
+<p>
+Qhull's functions access QhullQh through the global variable, <code>qh_qh</code>.
+The global data structures, qh_stat and qh_mem, record statistics and manage memory respectively.
+</p>
+
+<h3><a href="#TOC">&#187;</a><a name="ridge-cpp">QhullRidge</a></h3>
+
+<p>
+A QhullRidge represents the edge between two <a href="#facet-cpp">QhullFacet</a>'s.
+It is always simplicial with qh.hull_dim-1 <a href="#vertex-cpp">QhullVertex</a>)'s.
+</p>
+
+<h3><a href="#TOC">&#187;</a><a name="ridgeset-cpp">QhullRidgeSet</a></h3>
+
+<p>
+A QhullRidgeSet is a <a href="#set-cpp">QhullSet</a> of <a href="#ridge-cpp">QhullRidge</a>.  Each <a href="#facet-cpp">QhullFacet</a> contains a QhullRidgeSet.
+</p>
+
+<h3><a href="#TOC">&#187;</a><a name="set-cpp">QhullSet</a></h3>
+
+<p>
+A QhullSet is a set of pointers to objects.  QhullSets may be ordered or unordered.  They are the core data structure for Qhull.
+</p>
+
+<h3><a href="#TOC">&#187;</a><a name="vertex-cpp">QhullVertex</a></h3>
+
+<p>
+A QhullVertex is a vertex of the convex hull.  A simplicial <a href="#facet-cpp">QhullFacet</a> has qh.hull_dim-1 vertices.  A QhullVertex contains a <a href="#point-cpp">QhullPoint</a>.
+It may list its neighboring <a href="#facet-cpp">QhullFacet</a>'s.
+</p>
+
+<h3><a href="#TOC">&#187;</a><a name="vertexlist-cpp">QhullVertexList</a></h3>
+
+<p>
+A QhullVertexList is a <a href="#linkedlist-cpp">QhullLinkedList</a> of <a href="#vertex-cpp">QhullVertex</a>.
+The global data structure, <a href="#qh-cpp">QhullQh</a> contains a QhullVertexList of all
+the vertices.
+</p>
+
+<h3><a href="#TOC">&#187;</a><a name="vertexset-cpp">QhullVertexSet</a></h3>
+
+<p>
+A QhullVertexSet is a <a href="#set-cpp">QhullSet</a> of <a href="#vertex-cpp">QhullVertex</a>.
+The QhullVertexSet of a <a href="#facet-cpp">QhullFacet</a> is the vertices of the facet.  It is
+ordered for simplicial facets and unordered for non-simplicial facets.
+</p>
+
+<h3><a href="#TOC">&#187;</a><a name="rbox-cpp">RboxPoints</a></h3>
+
+<p>
+RboxPoints is a std::vector of point coordinates (<a href="#point-cpp">QhullPoint</a>).
+It's iterator is <a href="#coordinate-cpp">CoordinateIterator</a>.
+</p>
+<p>
+<code>RboxPoints.appendRandomPoints()</code> appends points from a variety of distributions such as uniformly distributed within a cube and random points on a sphere.
+It can also append a cube's vertices or specific points.
+</p>
+
+<h3><a href="#TOC">&#187;</a><a name="questions-cpp">Cpp questions for Qhull</a></h3>
+
+Developing C++ code requires many conventions, idioms, and technical details.
+The following questions have either
+mystified the author or do not have a clear answer.  See also
+<a href="http://www.qhull.org/road/road-faq/xml/cpp-guideline.xml">C++ and Perl Guidelines</a>.
+and FIXUP notes in the code.
+Please add notes to <a href="http://github.com/qhull/qhull/wiki">Qhull Wiki</a>.
+
+<ul>
+<li>FIXUP QH11028 Should return reference, but get reference to temporary
+<pre>iterator Coordinates::operator++() { return iterator(++i); }</pre>
+<li>size() as size_t, size_type, or int
+<li>Should all containers have a reserve()?
+<li>Qhull.feasiblePoint interface
+<li>How to avoid copy constructor while logging, maybeThrowQhullMessage()
+<li>How to configure Qhull output.  Trace and results should go to stdout/stderr
+<li>Qhull and RboxPoints messaging.  e.g., ~Qhull, hasQhullMessage().  Rename them as QhullErrorMessage?
+<li>How to add additional output to an error message, e.g., qh_setprint
+<li>Is idx the best name for an index?  It's rather cryptic, but BSD strings.h defines index().
+<li>Qhull::feasiblePoint Qhull::useOutputStream as field or getter?
+<li>Define virtual functions for user customization of Qhull (e.g., qh_fprintf, qh_memfree,etc.)
+<li>Figure out RoadError::global_log.  clearQhullMessage currently clearGlobalLog
+<li>Should the false QhullFacet be NULL or empty?  e.g., QhullFacet::tricoplanarOwner() and QhullFacetSet::end()
+<li>Should output format for floats be predefined (qh_REAL_1, 2.2g, 10.7g) or as currently set for stream
+<li>Should cout << !point.defined() be blank or 'undefined'
+<li>Infinite point as !defined()
+<li>qlist and qlinkedlist define pointer, reference, size_type, difference_type, const_pointer, const_reference for the class but not for iterator and const_iterator
+      vector.h -- <pre>reference operator[](difference_type _Off) const</pre>
+<li>When forwarding an implementation is base() an approriate name (e.g., Coordinates::iterator::base() as std::vector<coordT>::iterator).
+<li>When forwarding an implementation, does not work "returning address of temporary"
+<li>Also --, +=, and -=
+       <pre>iterator       &operator++() { return iterator(i++); }</pre>
+<li>if vector<coordT> inheritance is bad, is QhullVertexSet OK?
+<li>Should QhullPointSet define pointer and reference data types?
+</ul>
+
+<h2><a href="#TOC">&#187;</a><a name="library">Calling Qhull from
+C programs</a></h2>
+
+<p><b>Warning:</b> Qhull was not designed for calling from C
+programs.  You may find the <a href="#cpp">C++ interface</a> easier to use.
+You will need to understand the data structures and read the code.
+Most users will find it easier to call Qhull as an external
+command.
+
+<p>For examples of calling Qhull, see GNU Octave's
+<a href=http://www.gnu.org/software/octave/doc/interpreter/Geometry.html>computational geometry code</a>,
+and Qhull's
+<a href=../src/user_eg/user_eg_r.c>user_eg_r.c</a>,
+<a href=../src/user_eg2/user_eg2_r.c>user_eg2_r.c</a>, and
+<a href=../src/libqhull_r/user_r.c>user_r.c</a>.  To see how Qhull calls its library, read
+<a href=../src/qhull/unix_r.c>unix_r.c</a>,
+<a href=../src/qconvex/qconvex.c>qconvex.c</a>,
+<a href=../src/qdelaunay/qdelaun.c>qdelaun.c</a>,
+<a href=../src/qhalf/qhalf.c>qhalf.c</a>, and
+<a href=../src/qvoronoi/qvoronoi.c>qvoronoi.c</a>.  The '*_r.c' files are reentrant, otherwise they are non-reentrant.
+Either version may be used.  New code should use reentrant Qhull.
+
+<p>See <a href="../src/libqhull_r/index.htm">Reentrant Qhull functions, macros, and data
+structures</a> for internal documentation of Qhull. The
+documentation provides an overview and index. To use the library
+you will need to read and understand the code. For most users, it
+is better to write data to a file, call the qhull program, and
+read the results from the output file.</p>
+
+<p>If you use non-reentrant Qhull, be aware of the macros &quot;qh&quot;
+and &quot;qhstat&quot;, e.g., &quot;qh hull_dim&quot;. They are
+defined in <tt>libqhull.h</tt>. They allow the global data
+structures to be pre-allocated (faster access) or dynamically
+allocated (allows multiple copies). </p>
+
+<p>Qhull's <tt>Makefile</tt> produces a library, <tt>libqhull_r.a</tt>,
+for inclusion in your programs. First review <tt>libqhull_r.h</tt>.
+This defines the data structures used by Qhull and provides
+prototypes for the top-level functions.
+Most users will only need libqhull_r.h in their programs. For
+example, the Qhull program is defined with <tt>libqhull_r.h</tt> and <tt>unix_r.c</tt>.
+To access all functions, use <tt>qhull_ra.h</tt>. Include the file
+with &quot;<tt>#include &lt;libqhull_r/qhull_ra.h&gt;</tt>&quot;. This
+avoids potential name conflicts.</p>
+
+<p>If you use the Qhull library, you are on your own as far as
+bugs go. Start with small examples for which you know the output.
+If you get a bug, try to duplicate it with the Qhull program. The
+'<a href="qh-optt.htm#Tc">Tc</a>' option will catch many problems
+as they occur. When an error occurs, use '<a
+href="qh-optt.htm#Tn">T4</a> <a href="qh-optt.htm#TPn">TPn</a>'
+to trace from the last point added to the hull. Compare your
+trace with the trace output from the Qhull program.</p>
+
+<p>Errors in the Qhull library are more likely than errors in the
+Qhull program. These are usually due to feature interactions that
+do not occur in the Qhull program. Please report all errors that
+you find in the Qhull library. Please include suggestions for
+improvement. </p>
+
+<h3><a href="#TOC">&#187;</a><a name="exit">How to avoid exit(), fprintf(), stderr, and stdout</a></h3>
+
+<p>Qhull sends output to qh.fout and errors, log messages, and summaries to qh.ferr.  qh.fout is normally
+stdout and qh.ferr is stderr.  qh.fout may be redefined by option '<a
+href="qh-optt.htm#TO">TO</a>' or the caller.  qh.ferr may be redirected to qh.fout by option  '<a
+href="qh-optt.htm#Tz">Tz</a>'.</p>
+
+<p>Qhull does not use stderr, stdout, fprintf(), or exit() directly.</p>
+
+<p>Qhull reports errors via qh_errexit() by writting a message to qh.ferr and invoking longjmp().
+This returns the caller to the corresponding setjmp() (c.f., QH_TRY_ in QhullQh.h).  If
+qh_errexit() is not available, Qhull functions call qh_exit().   qh_exit() normally calls exit(),
+but may be redefined by the user.  An example is
+libqhullcpp/usermem_r-cpp.cpp.   It redefines qh_exit() as a 'throw'.</p>
+
+<p>If qh_meminit() or qh_new_qhull() is called with ferr==NULL, then they set ferr to stderr.
+Otherwise the Qhull libraries use qh->ferr and qh->qhmem.ferr for error output.</p>
+
+<p>If an error occurs before qh->ferr is initialized, Qhull invokes qh_fprintf_stderr().  The user
+may redefine this function along with qh_exit(), qh_malloc(), and qh_free().
+
+<p>The Qhull libraries write output via qh_fprintf() [userprintf_r.c].  Otherwise, the Qhull
+libraries do not use stdout, fprintf(), or printf().  Like qh_exit(), the user may redefine
+qh_fprintf().</p>
+
+<h3><a href="#TOC">&#187;</a><a name="mem">sets and quick memory
+allocation</a></h3>
+
+<p>You can use <tt>mem_r.c</tt> and <tt>qset_r.c</tt> individually. <tt>Mem_r.c
+</tt>implements quick-fit memory allocation. It is faster than
+malloc/free in applications that allocate and deallocate lots of
+memory. </p>
+
+<p><tt>Qset_r.c</tt> implements sets and related collections. It's
+the inner loop of Qhull, so speed is more important than
+abstraction. Set iteration is particularly fast. <tt>qset_r.c</tt>
+just includes the functions needed for Qhull. </p>
+
+<h3><a href="#TOC">&#187;</a><a name="dids">Delaunay triangulations
+and point indices</a></h3>
+
+<p>Here some unchecked code to print the point indices of each
+Delaunay triangle. Use option 'QJ' if you want to avoid
+non-simplicial facets. Note that upper Delaunay regions are
+skipped. These facets correspond to the furthest-site Delaunay
+triangulation. </p>
+
+<blockquote>
+    <pre>
+  facetT *facet;
+  vertexT *vertex, **vertexp;
+
+  FORALLfacets {
+    if (!facet-&gt;upperdelaunay) {
+      printf (&quot;%d&quot;, qh_setsize (facet-&gt;vertices);
+      FOREACHvertex_(facet-&gt;vertices)
+        printf (&quot; %d&quot;, qh_pointid (vertex-&gt;point));
+      printf (&quot;\n&quot;);
+    }
+  }
+
+</pre>
+</blockquote>
+
+<h3><a href="#TOC">&#187;</a><a name="findfacet">locate a facet with
+qh_findbestfacet()</a></h3>
+
+<p>The routine qh_findbestfacet in <tt>poly2_r.c</tt> is
+particularly useful. It uses a directed search to locate the
+facet that is furthest below a point. For Delaunay
+triangulations, this facet is the Delaunay triangle that contains
+the lifted point. For convex hulls, the distance of a point to
+the convex hull is either the distance to this facet or the
+distance to a subface of the facet.</p>
+
+<blockquote>
+<p><b>Warning:</b> If triangulated output ('<a href=qh-optq.htm#Qt>Qt</a>') and
+the best facet is triangulated, qh_findbestfacet() returns one of
+the corresponding 'tricoplanar' facets.  The actual best facet may be a different
+tricoplanar facet.
+<p>
+See qh_nearvertex() in poly2.c for sample code to visit each
+tricoplanar facet.  To identify the correct tricoplanar facet,
+see Devillers, et. al., [<a href="index.htm#devi01">'01</a>]
+and Mucke, et al [<a href="index.htm#muck96">'96</a>].  If you
+implement this test in general dimension, please notify
+<a href="mailto:qhull@qhull.org">qhull@qhull.org</a>.
+</blockquote>
+
+<p>qh_findbestfacet performs an exhaustive search if its directed
+search returns a facet that is above the point. This occurs when
+the point is inside the hull or if the curvature of the convex
+hull is less than the curvature of a sphere centered at the point
+(e.g., a point near a lens-shaped convex hull). When the later
+occurs, the distance function is bimodal and a directed search
+may return a facet on the far side of the convex hull. </p>
+
+<p>Algorithms that retain the previously constructed hulls
+usually avoid an exhaustive search for the best facet. You may
+use a hierarchical decomposition of the convex hull [Dobkin and
+Kirkpatrick <a href="index.htm#dob-kir90">'90</a>]. </p>
+
+<p>To use qh_findbestfacet with Delaunay triangulations, lift the
+point to a paraboloid by summing the squares of its coordinates
+(see qh_setdelaunay in geom2_r.c). Do not scale the input with
+options 'Qbk', 'QBk', 'QbB' or 'Qbb'. See Mucke, et al [<a
+href="index.htm#muck96">'96</a>] for a good point location
+algorithm.</p>
+
+<p>The intersection of a ray with the convex hull may be found by
+locating the facet closest to a distant point on the ray.
+Intersecting the ray with the facet's hyperplane gives a new
+point to test. </p>
+
+<h3><a href="#TOC">&#187;</a><a name="inc">on-line construction with
+qh_addpoint()</a></h3>
+
+<p>The Qhull library may be used for the on-line construction of
+convex hulls, Delaunay triangulations, and halfspace
+intersections about a point. It may be slower than implementations that retain
+intermediate convex hulls (e.g., Clarkson's <a
+href="http://www.netlib.org/voronoi/hull.html">hull
+program</a>). These implementations always use a directed search.
+For the on-line construction of convex hulls and halfspace
+intersections, Qhull may use an exhaustive search
+(qh_findbestfacet). </p>
+
+<p>You may use qh_findbestfacet and qh_addpoint (<tt>libqhull.c</tt>) to add a point to
+a convex hull. Do not modify the point's coordinates since
+qh_addpoint does not make a copy of the coordinates. For Delaunay
+triangulations, you need to lift the point to a paraboloid by
+summing the squares of the coordinates (see qh_setdelaunay in
+geom2.c). Do not scale the input with options 'Qbk', 'QBk', 'QbB'
+or 'Qbb'. Do not deallocate the point's coordinates. You need to
+provide a facet that is below the point (<a href="#findfacet">qh_findbestfacet</a>).
+</p>
+
+<p>You can not delete points. Another limitation is that Qhull
+uses the initial set of points to determine the maximum roundoff
+error (via the upper and lower bounds for each coordinate). </p>
+
+<p>For many applications, it is better to rebuild the hull from
+scratch for each new point. This is especially true if the point
+set is small or if many points are added at a time.</p>
+
+<p>Calling qh_addpoint from your program may be slower than
+recomputing the convex hull with qh_qhull. This is especially
+true if the added points are not appended to the qh first_point
+array. In this case, Qhull must search a set to determine a
+point's ID. [R. Weber] </p>
+
+<p>See user_eg.c for examples of the on-line construction of
+convex hulls, Delaunay triangulations, and halfspace
+intersections. The outline is: </p>
+
+<blockquote>
+    <pre>
+initialize qhull with an initial set of points
+qh_qhull();
+
+for each additional point p
+   append p to the end of the point array or allocate p separately
+   lift p to the paraboloid by calling qh_setdelaunay
+   facet= qh_findbestfacet (p, !qh_ALL, &amp;bestdist, &amp;isoutside);
+   if (isoutside)
+      if (!qh_addpoint (point, facet, False))
+         break;  /* user requested an early exit with 'TVn' or 'TCn' */
+
+call qh_check_maxout() to compute outer planes
+terminate qhull</pre>
+</blockquote>
+
+<h3><a href="#TOC">&#187;</a><a name="constrained">Constrained
+Delaunay triangulation </a></h3>
+
+<p>With a fair amount of work, Qhull is suitable for constrained
+Delaunay triangulation. See Shewchuk, ACM Symposium on
+Computational Geometry, Minneapolis 1998.</p>
+
+<p>Here's a quick way to add a constraint to a Delaunay
+triangulation: subdivide the constraint into pieces shorter than
+the minimum feature separation. You will need an independent
+check of the constraint in the output since the minimum feature
+separation may be incorrect. [H. Geron] </p>
+
+<h3><a href="#TOC">&#187;</a><a name="tricoplanar">Tricoplanar facets and option 'Qt'</h3>
+
+<p>Option '<a href=qh-optq.htm#Qt>Qt</a>' triangulates non-simplicial
+facets (e.g., a square facet in 3-d or a cubical facet in 4-d).
+All facets share the same apex (i.e., the first vertex in facet->vertices).
+For each triangulated facet, Qhull
+sets facet->tricoplanar true and copies facet->center, facet->normal, facet->offset, and facet->maxoutside.  One of
+the facets owns facet->normal; its facet->keepcentrum is true.
+If facet->isarea is false, facet->triowner points to the owning
+facet.
+
+<p>Qhull sets facet->degenerate if the facet's vertices belong
+to the same ridge of the non-simplicial facet.
+
+<p>To visit each tricoplanar facet of a non-simplicial facet,
+either visit all neighbors of the apex or recursively visit
+all neighbors of a tricoplanar facet.  The tricoplanar facets
+will have the same facet->center.</p>
+
+<p>See <a href=../src/libqhull_r/io_r.c#detvridge>qh_detvridge</a> for an example of ignoring tricoplanar facets.</p>
+
+<h3><a href="#TOC">&#187;</a><a name="vertices">Voronoi vertices of a
+region</a></h3>
+
+<p>The following code iterates over all Voronoi vertices for each
+Voronoi region. Qhull computes Voronoi vertices from the convex
+hull that corresponds to a Delaunay triangulation. An input site
+corresponds to a vertex of the convex hull and a Voronoi vertex
+corresponds to an adjacent facet. A facet is
+&quot;upperdelaunay&quot; if it corresponds to a Voronoi vertex
+&quot;at-infinity&quot;. Qhull uses qh_printvoronoi in <tt>io.c</tt>
+for '<a href=qvoronoi.htm>qvoronoi</a> <a href="qh-opto.htm#o">o'</a> </p>
+
+<blockquote>
+    <pre>
+/* please review this code for correctness */
+qh_setvoronoi_all();
+FORALLvertices {
+   site_id = qh_pointid (vertex-&gt;point);
+   if (qh hull_dim == 3)
+      qh_order_vertexneighbors(vertex);
+   infinity_seen = 0;
+   FOREACHneighbor_(vertex) {
+      if (neighbor-&gt;upperdelaunay) {
+        if (!infinity_seen) {
+          infinity_seen = 1;
+          ... process a Voronoi vertex &quot;at infinity&quot; ...
+        }
+      }else {
+        voronoi_vertex = neighbor-&gt;center;
+        ... your code goes here ...
+      }
+   }
+}
+</pre>
+</blockquote>
+
+<h3><a href="#TOC">&#187;</a><a name="ridge">Voronoi vertices of a
+ridge</a></h3>
+
+<p>Qhull uses qh_printvdiagram() in io.c to print the ridges of a
+Voronoi diagram for option '<a href="qh-optf.htm#Fv2">Fv</a>'.
+The helper function qh_eachvoronoi() does the real work. It calls
+the callback 'printvridge' for each ridge of the Voronoi diagram.
+</p>
+
+<p>You may call qh_printvdiagram2(), qh_eachvoronoi(), or
+qh_eachvoronoi_all() with your own function. If you do not need
+the total number of ridges, you can skip the first call to
+qh_printvdiagram2(). See qh_printvridge() and qh_printvnorm() in
+io.c for examples. </p>
+
+<h3><a href="#TOC">&#187;</a><a name="vneighbor">vertex neighbors of
+a vertex</a></h3>
+
+<p>To visit all of the vertices that share an edge with a vertex:
+</p>
+
+<ul>
+    <li>Generate neighbors for each vertex with
+        qh_vertexneighbors in <tt>poly2.c</tt>. </li>
+    <li>For simplicial facets, visit the vertices of each
+        neighbor </li>
+    <li>For non-simplicial facets, <ul>
+            <li>Generate ridges for neighbors with qh_makeridges
+                in <tt>merge.c</tt>. </li>
+            <li>Generate ridges for a vertex with qh_vertexridges
+                in <tt>merge.c</tt>. </li>
+            <li>Visit the vertices of these ridges. </li>
+        </ul>
+    </li>
+</ul>
+
+<p>For non-simplicial facets, the ridges form a simplicial
+decomposition of the (d-2)-faces between each pair of facets --
+if you need 1-faces, you probably need to generate the full face
+graph of the convex hull. </p>
+
+<h2><a href="#TOC">&#187;</a><a name="performance">Performance of
+Qhull </a></h2>
+
+<p>Empirically, Qhull's performance is balanced in the sense that
+the average case happens on average. This may always be true if
+the precision of the input is limited to at most <i>O(log n)</i>
+bits. Empirically, the maximum number of vertices occurs at the
+end of constructing the hull. </p>
+
+<p>Let <i>n</i> be the number of input points, <i>v</i> be the
+number of output vertices, and <i>f_v </i>be the maximum number
+of facets for a convex hull of <i>v</i> vertices. If both
+conditions hold, Qhull runs in <i>O(n log v)</i> in 2-d and 3-d
+and <i>O(n f_v/v)</i> otherwise. The function <i>f_v</i>
+increases rapidly with dimension. It is <em>O(v^floor(d/2) /
+floor(d/2)!)</em>.</p>
+
+<p>The time complexity for merging is unknown. Options '<a
+href="qh-optc.htm#C0">C-0</a>' and '<a href="qh-optq.htm#Qx">Qx</a>'
+(defaults) handle precision problems due to floating-point
+arithmetic. They are optimized for simplicial outputs. </p>
+
+<p>When running large data sets, you should monitor Qhull's
+performance with the '<a href="qh-optt.htm#TFn">TFn</a>' option.
+The time per facet is approximately constant. In high-d with many
+merged facets, the size of the ridge sets grows rapidly. For
+example the product of 8-d simplices contains 18 facets and
+500,000 ridges. This will increase the time needed per facet. </p>
+
+<p>As dimension increases, the number of facets and ridges in a
+convex hull grows rapidly for the same number of vertices. For
+example, the convex hull of 300 cospherical points in 6-d has
+30,000 facets. </p>
+
+<p>If Qhull appears to stop processing facets, check the memory
+usage of Qhull. If more than 5-10% of Qhull is in virtual memory,
+its performance will degrade rapidly. </p>
+
+<p>When building hulls in 20-d and higher, you can follow the
+progress of Qhull with option '<a href="qh-optt.htm#Tn">T1</a>'.
+It reports each major event in processing a point. </p>
+
+<p>To reduce memory requirements, recompile Qhull for
+single-precision reals (REALfloat in <tt>user.h</tt>).
+Single-precision does not work with joggle ('<a
+href="qh-optq.htm#QJn">QJ</a>'). Check qh_MEMalign in <tt>user.h</tt>
+and the match between free list sizes and data structure sizes
+(see the end of the statistics report from '<a
+href="qh-optt.htm#Ts">Ts</a>'). If free list sizes do not match,
+you may be able to use a smaller qh_MEMalign. Setting
+qh_COMPUTEfurthest saves a small amount of memory, as does
+clearing qh_MAXoutside (both in <tt>user.h</tt>).</p>
+
+<p>Shewchuk is working on a 3-d version of his triangle
+program.  It is optimized for 3-d simplicial Delaunay triangulation
+and uses less memory than Qhull.</p>
+
+<p>To reduce the size of the Qhull executable, consider
+qh_NOtrace and qh_KEEPstatistics 0 in <tt>user.h</tt>. By
+changing <tt>user.c </tt>you can also remove the input/output
+code in <tt>io.c</tt>. If you don't need facet merging, then
+version 1.01 of Qhull is much smaller. It contains some bugs that
+prevent Qhull from initializing in simple test cases. It is
+slower in high dimensions.</p>
+
+<p>The precision options, '<a href="qh-optc.htm#Vn">Vn</a>', '<a
+href="qh-optc.htm#Wn">Wn</a>', '<a href="qh-optc.htm#Un">Un</a>'.
+'<a href="qh-optc.htm#An">A-n</a>', '<a href="qh-optc.htm#Cn">C-n</a>',
+'<a href="qh-optc.htm#An2">An</a>', '<a href="qh-optc.htm#Cn2">Cn</a>',
+and '<a href="qh-optq.htm#Qx">Qx</a>', may have large effects on
+Qhull performance. You will need to experiment to find the best
+combination for your application. </p>
+
+<p>The verify option ('<a href="qh-optt.htm#Tv">Tv</a>') checks
+every point after the hull is complete. If facet merging is used,
+it checks that every point is inside every facet. This can take a
+very long time if there are many points and many facets. You can
+interrupt the verify without losing your output. If facet merging
+is not used and there are many points and facets, Qhull uses a
+directed search instead of an exhaustive search. This should be
+fast enough for most point sets. Directed search is not used for
+facet merging because directed search was already used for
+updating the facets' outer planes.</p>
+
+<p>The check-frequently option ('<a href="qh-optt.htm#Tc">Tc</a>')
+becomes expensive as the dimension increases. The verify option
+('<a href="qh-optt.htm#Tv">Tv</a>') performs many of the same
+checks before outputting the results.</p>
+
+<p>Options '<a href="qh-optq.htm#Q0">Q0</a>' (no pre-merging), '<a
+href="qh-optq.htm#Q3">Q3</a>' (no checks for redundant vertices),
+'<a href="qh-optq.htm#Q5">Q5</a>' (no updates for outer planes),
+and '<a href="qh-optq.htm#Q8">Q8</a>' (no near-interior points)
+increase Qhull's speed. The corresponding operations may not be
+needed in your application.</p>
+
+<p>In 2-d and 3-d, a partial hull may be faster to produce.
+Option '<a href="qh-optq.htm#QGn">QgGn</a>' only builds facets
+visible to point n. Option '<a href="qh-optq.htm#QVn">QgVn</a>'
+only builds facets that contain point n. In higher-dimensions,
+this does not reduce the number of facets.</p>
+
+<p><tt>User.h</tt> includes a number of performance-related
+constants. Changes may improve Qhull performance on your data
+sets. To understand their effect on performance, you will need to
+read the corresponding code. </p>
+
+<p>GNU <tt>gprof</tt> reports that the dominate cost for 3-d
+convex hull of cosperical points is qh_distplane(), mainly called
+from qh_findbestnew().  The dominate cost for 3-d Delaunay triangulation
+is creating new facets in qh_addpoint(), while qh_distplane() remains
+the most expensive function.
+
+</p>
+<h2><a href="#TOC">&#187;</a><a name="enhance">Enhancements to Qhull </a></h2>
+
+<p>There are many ways in which Qhull can be improved. </p>
+
+<pre>
+[Jan 2016] Suggestions
+------------
+To do for a future verson of Qhull
+ - Add a post-merge pass for Delaunay slivers.  Merge into a neighbor with a circumsphere that includes the opposite point. [M. Treacy]
+ - Add a merge pass before cone creation to remove duplicate subridges between horizon facets
+ - Option to add a bounding box for Delaunay triangulations, e,g., nearly coincident points
+ - Report error when rbox Cn,r,m does not produce points (e.g., 'r' distributions)
+ - Rescale output to match 'QbB' on input [J. Metz, 1/30/2014 12:21p]
+ - Run through valgrind
+ - Notes to compgeom on conformant triangulation and Voronoi volume
+ - Git: Create signed tags for Qhull versions
+ - Implement weighted Delaunay triangulation and weighted Voronoi diagram [A. Liebscher]
+   e.g., Sugihara, "Three-dimensional convex hull as a fruitful source of diagrams," Theoretical Computer Science, 2000, 235:325-337
+ - testqset: test qh_setdelnth and move-to-front
+ - Makefile: Re-review gcc/g++ warnings.  OK in 2011.
+ - Break up -Wextra into its components or figure out how to override -Wunused-but-set-variable
+   unused-but-set-variable is reporting incorrectly.  All instances are annotated.
+ - CMakelists.txt:  Why are files duplicated for cmake build
+ - CMakeLists.txt: configure the 'ctest' target
+ - The size of maxpoints in qh_maxsimplex should be d+3 unique points to help avoid QH6154
+
+ - Can countT be defined as 'int', 'unsigned int', or 64-bit int?
+   countT is currently defined as 'int' in qset_r.h
+   Vertex ID and ridge ID perhaps should be countT, They are currently 'unsigned'
+   Check use of 'int' vs. countT in all cpp code
+   Check use of 'int' vs. countT in all c code
+   qset_r.h defines countT -- duplicates code in user_r.h -- need to add to qset.h/user.h
+   countT -1 used as a flag in Coordinates.mid(), QhullFacet->id()
+   Also QhullPoints indexOf and lastIndexOf
+   Also QhullPointSet indexOf and lastIndexOf
+   Coordinates.indexOf assumes countT is signed (from end)
+   Coordinates.lastIndexOf assumes countT is signed (from end)
+   All error messages with countT are wrong, convert to int?
+   RboxPoints.qh_fprintf_rbox, etc. message 9393 assumes countT but may be int, va_arg(args, countT);  Need to split
+
+------------
+To do for a furture version of the C++ interface
+ - Fix C++ memory leak in user_eg3 [M. Sandim]
+ - Document C++ using Doxygen conventions (//! and //!<)
+ - Should Qhull manage the output formats for doubles?  QH11010 user_r.h defines qh_REAL_1 as %6.8g
+ - Allocate memory for QhullSet using Qhull.qhmem.  Create default constructors for QhullVertexSet etc.  Also mid() etc.
+ - Add interior point for automatic translation?
+ - Add hasNext() to all next() iterators (e.g., QhullVertex)
+ - Add defineAs() to each object
+ - Write a program with concurrent Qhull
+ - Write QhullStat and QhullStat_test
+ - Add QList and vector instance of facetT*, etc.
+ - Generalize QhullPointSetIterator
+ - qh-code.htm: Document changes to C++ interface.
+      Organize C++ documentation into collection classes, etc.
+ - Review all C++ classes and C++ tests
+ - QhullVertexSet uses QhullSetBase::referenceSetT() to free it's memory.   Probably needed elsewhere
+ - The Boost Graph Library provides C++ classes for graph data structures. It may help
+   enhance Qhull's C++ interface [Dr. Dobb's 9/00 p. 29-38; OOPSLA '99 p. 399-414].
+
+[Jan 2010] Suggestions
+ - Generate vcproj from qtpro files
+   cd qtpro && qmake -spec win32-msvc2005 -tp vc -recursive
+   sed -i 's/C\:\/bash\/local\/qhull\/qtpro\///' qhull-all.sln
+   Change qhullcpp to libqhull.dll
+   Allow both builds on same host (keep /tmp separate)
+ - Make distribution -- remove tmp, news, .git, leftovers from project, change CRLF
+     search for 2010.1, Dates
+     qhulltest --all added to output
+     Add md5sum
+     Add test of user_eg3, etc.
+ - C++ class for access to statistics, accumulate vs. add
+ - Add dialog box to RoadError-- a virtual function?
+ - Option 'Gt' does not make visible all facets of the mesh example, rbox 32 M1,0,1 | qhull d Gt
+ - Option to select bounded Voronoi regions [A. Uzunovic]
+ - Merge small volume boundary cells into unbounded regions [Dominik Szczerba]
+ - Postmerge with merge options
+ - Add const to C code
+ - Add modify operators and MutablePointCoordinateIterator to PointCoordinates
+ - Add Qtest::toString() functions for QhullPoint and others.  QByteArray and qstrdup()
+ - Fix option Qt for conformant triangulations of merged facets
+ - Investigate flipped facet -- rbox 100 s D3 t1263080158 | qhull R1e-3 Tcv Qc
+ - Add doc comments to c++ code
+ - Measure performance of Qhull, seconds per point by dimension
+ - Report potential wraparound of 64-bit ints -- e.g., a large set or points
+
+Documentation
+- Qhull::addPoint().  Problems with qh_findbestfacet and otherpoints see
+   qh-code.htm#inc on-line construction with qh_addpoint()
+- How to handle 64-bit possible loss of data.  WARN64, ptr_intT, size_t/int
+- Show custom of qh_fprintf
+- grep 'qh_mem ' x | sort | awk '{ print $2; }' | uniq -c | grep -vE ' (2|4|6|8|10|12|14|16|20|64|162)[^0-9]'
+- qtpro/qhulltest contains .pro and Makefile.  Remove Makefiles by setting shadow directory to ../../tmp/projectname
+- Rules for use of qh_qh and multi processes
+    UsingQhull
+    errorIfAnotherUser
+    ~QhullPoints() needs ownership of qh_qh
+    Does !qh_pointer work?
+    When is qh_qh required?  Minimize the time.
+   qhmem, qhstat.ferr
+   qhull_inuse==1 when qhull globals active [not useful?]
+   rbox_inuse==1 when rbox globals active
+   - Multithreaded -- call largest dimension for infinityPoint() and origin()
+ - Better documentation for qhmem totshort, freesize, etc.
+ - how to change .h, .c, and .cpp to text/html.  OK in Opera
+ - QhullVertex.dimension() is not quite correct, epensive
+ - Check globalAngleEpsilon
+ - Deprecate save_qhull()
+
+[Dec 2003] Here is a partial list:
+ - fix finddelaunay() in user_eg.c for tricoplanar facets
+ - write a BGL, C++ interface to Qhull
+     http://www.boost.org/libs/graph/doc/table_of_contents.html
+ - change qh_save_qhull to swap the qhT structure instead of using pointers
+ - change error handling and tracing to be independent of 'qh ferr'
+ - determine the maximum width for a given set of parameters
+ - prove that directed search locates all coplanar facets
+ - in high-d merging, can a loop of facets become disconnected?
+ - find a way to improve inner hulls in 5-d and higher
+ - determine the best policy for facet visibility ('<a href="qh-optc.htm#Vn">Vn</a>')
+ - determine the limitations of '<a href="qh-optq.htm#Qg">Qg</a>'
+
+Precision improvements:
+ - For 'Qt', resolve cross-linked, butterfly ridges.
+     May allow retriangulation in qh_addpoint().
+ - for Delaunay triangulations ('d' or 'v') under joggled input ('QJ'),
+     remove vertical facets whose lowest vertex may be coplanar with convex hull
+ - review use of 'Qbb' with 'd QJ'.  Is MAXabs_coord better than MAXwidth?
+ - check Sugihara and Iri's better in-sphere test [Canadian
+     Conf. on Comp. Geo., 1989; Univ. of Tokyo RMI 89-05]
+ - replace centrum with center of mass and facet area
+ - handle numeric overflow in qh_normalize and elsewhere
+ - merge flipped facets into non-flipped neighbors.
+     currently they merge into best neighbor (appears ok)
+ - determine min norm for Cramer's rule (qh_sethyperplane_det).  It looks high.
+ - improve facet width for very narrow distributions
+
+New features:
+ - implement Matlab's tsearch() using Qhull
+ - compute volume of Voronoi regions.  You need to determine the dual face
+   graph in all dimensions [see Clarkson's hull program]
+ - compute alpha shapes [see Clarkson's hull program]
+ - implement deletion of Delaunay vertices
+      see Devillers, ACM Symposium on Computational Geometry, Minneapolis 1999.
+ - compute largest empty circle [see O'Rourke, chapter 5.5.3] [Hase]
+ - list redundant (i.e., coincident) vertices [Spitz]
+ - implement Mucke, et al, ['96] for point location in Delaunay triangulations
+ - implement convex hull of moving points
+ - implement constrained Delaunay diagrams
+      see Shewchuk, ACM Symposium on Computational Geometry, Minneapolis 1998.
+ - estimate outer volume of hull
+ - automatically determine lower dimensional hulls
+ - allow &quot;color&quot; data for input points
+      need to insert a coordinate for Delaunay triangulations
+
+Input/output improvements:
+ - Support the VTK Visualization Toolkit, http://www.kitware.com/vtk.html
+ - generate output data array for Qhull library [Gautier]
+ - need improved DOS window with screen fonts, scrollbar, cut/paste
+ - generate Geomview output for Voronoi ridges and unbounded rays
+ - generate Geomview output for halfspace intersection
+ - generate Geomview display of furthest-site Voronoi diagram
+ - use '<a href="qh-optg.htm#GDn">GDn</a>' to view 5-d facets in 4-d
+ - convert Geomview output for other 3-d viewers
+ - add interactive output option to avoid recomputing a hull
+ - orient vertex neighbors for '<a href="qh-optf.htm#Fv">Fv</a>' in 3-d and 2-d
+ - track total number of ridges for summary and logging
+
+Performance improvements:
+ - optimize Qhull for 2-d Delaunay triangulations
+ -   use O'Rourke's <a href="index.htm#orou94">'94</a> vertex-&gt;duplicate_edge
+ -   add bucketing
+ -   better to specialize all of the code (ca. 2-3x faster w/o merging)
+ - use updated LU decomposition to speed up hyperplane construction
+ -        [Gill et al. 1974, Math. Comp. 28:505-35]
+ - construct hyperplanes from the corresponding horizon/visible facets
+ - for merging in high d, do not use vertex-&gt;neighbors
+
+</pre>
+
+<p>Please let us know about your applications and improvements. </p>
+<!-- Navigation links -->
+<hr>
+
+<p><b>Up:</b> <a href="http://www.qhull.org">Home
+page for Qhull</a> <br>
+<b>Up:</b> <a href="index.htm#TOC">Qhull manual: Table of
+Contents</a><br>
+<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
+&#149; <a href="qh-quick.htm#options">Options</a>
+&#149; <a href="qh-opto.htm#output">Output</a>
+&#149; <a href="qh-optf.htm#format">Formats</a>
+&#149; <a href="qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="qh-optp.htm#print">Print</a>
+&#149; <a href="qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="qh-optc.htm#prec">Precision</a>
+&#149; <a href="qh-optt.htm#trace">Trace</a>
+&#149; <a href="../src/libqhull_r/index.htm">Functions</a><br>
+<b>To:</b> <a href="#TOC">Qhull code</a>: Table of Contents <br>
+<b>Dn:</b> <a href="../src/libqhull_r/index.htm">Qhull functions</a>, macros, and data
+structures <!-- GC common information -->
+
+<hr>
+
+<p><a href="http://www.geom.uiuc.edu/"><img src="qh--geom.gif"
+align="middle" width="40" height="40"></a><i>The Geometry Center
+Home Page </i></p>
+
+<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
+</a><br>
+Created: Sept. 25, 1995 --- <!-- hhmts start --> Last modified: see changes.txt <!-- hhmts end --> </p>
+</body>
+</html>
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new file mode 100644
index 0000000000..a08f0d13f4
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@@ -0,0 +1,693 @@
+<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN">
+<html>
+
+<head>
+<title>Examples of Qhull</title>
+</head>
+
+<body>
+<!-- Navigation links -->
+<p><a name="TOP"><b>Up:</b></a> <a href="http://www.qhull.org">Home
+page</a> for Qhull <br>
+<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
+<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
+&#149; <a href="qh-quick.htm#options">Options</a>
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+&#149; <a href="qh-optf.htm#format">Formats</a>
+&#149; <a href="qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="qh-optp.htm#print">Print</a>
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+<b>To: </b><a href="#TOC">Qhull examples: Table of Contents</a> (please wait
+while loading)<br>
+
+<hr>
+<!-- Main text of document -->
+<h1><a
+href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/half.html"><img
+src="qh--half.gif" alt="[halfspace]" align="middle" width="100"
+height="100"></a> Examples of Qhull</h1>
+
+<p>This section of the Qhull manual will introduce you to Qhull
+and its options. Each example is a file for viewing with <a
+href="index.htm#geomview">Geomview</a>.  You will need to
+use a Unix computer with a copy of Geomview.
+<p>
+If you are not running Unix, you can view <a
+href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/welcome.html">pictures</a>
+for some of the examples.  To understand Qhull without Geomview, try the
+examples in <a href="qh-quick.htm#programs">Programs</a> and
+<a href="qh-quick.htm#programs">Programs/input</a>.  You can also try small
+examples that you compute by hand.  Use <a href="rbox.htm">rbox</a>
+to generate examples.
+<p>
+To generate the Geomview examples, execute the shell script <tt>eg/q_eg</tt>.
+It uses <tt>rbox</tt>.  The shell script <tt>eg/q_egtest</tt> generates
+test examples, and <tt>eg/q_test</tt> exercises the code. If you
+find yourself viewing the inside of a 3-d example, use Geomview's
+normalization option on the 'obscure' menu.</p>
+
+<p><b>Copyright &copy; 1995-2015 C.B. Barber</b></p>
+
+<hr>
+
+<h2><a href="#TOP">&#187;</a><a name="TOC">Qhull examples: Table of
+Contents </a></h2>
+
+<ul>
+    <li><a href="#2d">2-d and 3-d examples</a></li>
+    <li><a href="#how">How Qhull adds a point</a></li>
+    <li><a href="#joggle">Triangulated output or joggled input</a></li>
+    <li><a href="#delaunay">Delaunay and Voronoi diagrams</a></li>
+    <li><a href="#merge">Facet merging for imprecision</a></li>
+    <li><a href="#4d">4-d objects</a></li>
+    <li><a href="#half">Halfspace intersections</a></li>
+</ul>
+
+<hr>
+<ul>
+    <li><a href="#TOC">&#187;</a><a name="2d">2-d and 3-d examples</a><ul>
+            <li><a href="#01">eg.01.cube</a></li>
+            <li><a href="#02">eg.02.diamond.cube</a></li>
+            <li><a href="#03">eg.03.sphere</a></li>
+            <li><a href="#04">eg.04.circle</a></li>
+            <li><a href="#05">eg.05.spiral</a></li>
+            <li><a href="#06">eg.06.merge.square</a></li>
+            <li><a href="#07">eg.07.box</a></li>
+            <li><a href="#08a">eg.08a.cube.sphere</a></li>
+            <li><a href="#08b">eg.08b.diamond.sphere</a></li>
+            <li><a href="#09">eg.09.lens</a></li>
+        </ul>
+    </li>
+    <li><a href="#TOC">&#187;</a><a name="how">How Qhull adds a point</a><ul>
+            <li><a href="#10a">eg.10a.sphere.visible</a></li>
+            <li><a href="#10b">eg.10b.sphere.beyond</a></li>
+            <li><a href="#10c">eg.10c.sphere.horizon</a></li>
+            <li><a href="#10d">eg.10d.sphere.cone</a></li>
+            <li><a href="#10e">eg.10e.sphere.new</a></li>
+            <li><a href="#14">eg.14.sphere.corner</a></li>
+        </ul>
+    </li>
+    <li><a href="#TOC">&#187;</a> <a name="joggle">Triangulated output or joggled input</a>
+        <ul>
+            <li><a href="#15a">eg.15a.surface</a></li>
+            <li><a href="#15b">eg.15b.triangle</a></li>
+            <li><a href="#15c">eg.15c.joggle</a></li>
+        </ul>
+    <li><a href="#TOC">&#187;</a><a name="delaunay"> Delaunay and
+        Voronoi diagrams</a><ul>
+            <li><a href="#17a">eg.17a.delaunay.2</a></li>
+            <li><a href="#17b">eg.17b.delaunay.2i</a></li>
+            <li><a href="#17c">eg.17c.delaunay.2-3</a></li>
+            <li><a href="#17d">eg.17d.voronoi.2</a></li>
+            <li><a href="#17e">eg.17e.voronoi.2i</a></li>
+            <li><a href="#17f">eg.17f.delaunay.3</a></li>
+            <li><a href="#18a">eg.18a.furthest.2-3</a></li>
+            <li><a href="#18b">eg.18b.furthest-up.2-3</a></li>
+            <li><a href="#18c">eg.18c.furthest.2</a></li>
+            <li><a href="#19">eg.19.voronoi.region.3</a></li>
+        </ul>
+    </li>
+    <li><a href="#TOC">&#187;</a><a name="merge">Facet merging for
+        imprecision </a><ul>
+            <li><a href="#20">eg.20.cone</a></li>
+            <li><a href="#21a">eg.21a.roundoff.errors</a></li>
+            <li><a href="#21b">eg.21b.roundoff.fixed</a></li>
+            <li><a href="#22a">eg.22a.merge.sphere.01</a></li>
+            <li><a href="#22b">eg.22b.merge.sphere.-01</a></li>
+            <li><a href="#22c">eg.22c.merge.sphere.05</a></li>
+            <li><a href="#22d">eg.22d.merge.sphere.-05</a></li>
+            <li><a href="#23">eg.23.merge.cube</a></li>
+        </ul>
+    </li>
+    <li><a href="#TOC">&#187;</a><a name="4d">4-d objects</a><ul>
+            <li><a href="#24">eg.24.merge.cube.4d-in-3d</a></li>
+            <li><a href="#30">eg.30.4d.merge.cube</a></li>
+            <li><a href="#31">eg.31.4d.delaunay</a></li>
+            <li><a href="#32">eg.32.4d.octant</a></li>
+        </ul>
+    </li>
+    <li><a href="#TOC">&#187;</a><a name="half">Halfspace
+        intersections</a><ul>
+            <li><a href="#33a">eg.33a.cone</a></li>
+            <li><a href="#33b">eg.33b.cone.dual</a></li>
+            <li><a href="#33c">eg.33c.cone.halfspace</a></li>
+        </ul>
+    </li>
+</ul>
+
+<hr>
+
+<h2><a href="#TOC">&#187;</a>2-d and 3-d examples</h2>
+
+<h3><a href="#2d">&#187;</a><a name="01">rbox c D3 | qconvex G
+&gt;eg.01.cube </a></h3>
+
+<p>The first example is a cube in 3-d. The color of each facet
+indicates its normal. For example, normal [0,0,1] along the Z
+axis is (r=0.5, g=0.5, b=1.0). With the 'Dn' option in <tt>rbox</tt>,
+you can generate hypercubes in any dimension. Above 7-d the
+number of intermediate facets grows rapidly. Use '<a
+href="qh-optt.htm#TFn">TFn</a>' to track qconvex's progress. Note
+that each facet is a square that qconvex merged from coplanar
+triangles.</p>
+
+<h3><a href="#2d">&#187;</a><a name="02">rbox c d G3.0 | qconvex G
+&gt;eg.02.diamond.cube </a></h3>
+
+<p>The second example is a cube plus a diamond ('d') scaled by <tt>rbox</tt>'s
+'G' option. In higher dimensions, diamonds are much simpler than
+hypercubes. </p>
+
+<h3><a href="#2d">&#187;</a><a name="03">rbox s 100 D3 | qconvex G
+&gt;eg.03.sphere </a></h3>
+
+<p>The <tt>rbox s</tt> option generates random points and
+projects them to the d-sphere. All points should be on the convex
+hull. Notice that random points look more clustered than you
+might expect. You can get a smoother distribution by merging
+facets and printing the vertices, e.g.,<i> rbox 1000 s | qconvex
+A-0.95 p | qconvex G &gt;eg.99</i>.</p>
+
+<h3><a href="#2d">&#187;</a><a name="04">rbox s 100 D2 | qconvex G
+&gt;eg.04.circle </a></h3>
+
+<p>In 2-d, there are many ways to generate a convex hull. One of
+the earliest algorithms, and one of the fastest, is the 2-d
+Quickhull algorithm [c.f., Preparata &amp; Shamos <a
+href="index.htm#pre-sha85">'85</a>]. It was the model for
+Qhull.</p>
+
+<h3><a href="#2d">&#187;</a><a name="05">rbox 10 l | qconvex G
+&gt;eg.05.spiral </a></h3>
+
+<p>One rotation of a spiral.</p>
+
+<h3><a href="#2d">&#187;</a><a name="06">rbox 1000 D2 | qconvex C-0.03
+Qc Gapcv &gt;eg.06.merge.square</a></h3>
+
+<p>This demonstrates how Qhull handles precision errors. Option '<a
+href="qh-optc.htm#Cn">C-0.03</a>' requires a clearly convex angle
+between adjacent facets. Otherwise, Qhull merges the facets. </p>
+
+<p>This is the convex hull of random points in a square. The
+facets have thickness because they must be outside all points and
+must include their vertices. The colored lines represent the
+original points and the spheres represent the vertices. Floating
+in the middle of each facet is the centrum. Each centrum is at
+least 0.03 below the planes of its neighbors. This guarantees
+that the facets are convex.</p>
+
+<h3><a href="#2d">&#187;</a><a name="07">rbox 1000 D3 | qconvex G
+&gt;eg.07.box </a></h3>
+
+<p>Here's the same distribution but in 3-d with Qhull handling
+machine roundoff errors. Note the large number of facets. </p>
+
+<h3><a href="#2d">&#187;</a><a name="08a">rbox c G0.4 s 500 | qconvex G
+&gt;eg.08a.cube.sphere </a></h3>
+
+<p>The sphere is just barely poking out of the cube. Try the same
+distribution with randomization turned on ('<a
+href="qh-optq.htm#Qr">Qr</a>'). This turns Qhull into a
+randomized incremental algorithm. To compare Qhull and
+randomization, look at the number of hyperplanes created and the
+number of points partitioned. Don't compare CPU times since Qhull's
+implementation of randomization is inefficient. The number of
+hyperplanes and partitionings indicate the dominant costs for
+Qhull. With randomization, you'll notice that the number of
+facets created is larger than before. This is especially true as
+you increase the number of points. It is because the randomized
+algorithm builds most of the sphere before it adds the cube's
+vertices.</p>
+
+<h3><a href="#2d">&#187;</a><a name="08b">rbox d G0.6 s 500 | qconvex G
+&gt;eg.08b.diamond.sphere </a></h3>
+
+<p>This is a combination of the diamond distribution and the
+sphere.</p>
+
+<h3><a href="#2d">&#187;</a><a name="09">rbox 100 L3 G0.5 s | qconvex
+G &gt;eg.09.lens </a></h3>
+
+<p>Each half of the lens distribution lies on a sphere of radius
+three. A directed search for the furthest facet below a point
+(e.g., qh_findbest in <tt>geom.c</tt>) may fail if started from
+an arbitrary facet. For example, if the first facet is on the
+opposite side of the lens, a directed search will report that the
+point is inside the convex hull even though it is outside. This
+problem occurs whenever the curvature of the convex hull is less
+than a sphere centered at the test point. </p>
+
+<p>To prevent this problem, Qhull does not use directed search
+all the time. When Qhull processes a point on the edge of the
+lens, it partitions the remaining points with an exhaustive
+search instead of a directed search (see qh_findbestnew in <tt>geom2.c</tt>).
+</p>
+
+<h2><a href="#TOC">&#187;</a>How Qhull adds a point</h2>
+
+<h3><a href="#how">&#187;</a><a name="10a">rbox 100 s P0.5,0.5,0.5 |
+qconvex Ga QG0 &gt;eg.10a.sphere.visible</a></h3>
+
+<p>The next 4 examples show how Qhull adds a point. The point
+[0.5,0.5,0.5] is at one corner of the bounding box. Qhull adds a
+point using the beneath-beyond algorithm. First Qhull finds all
+of the facets that are visible from the point. Qhull will replace
+these facets with new facets.</p>
+
+<h3><a href="#how">&#187;</a><a name="10b">rbox 100 s
+P0.5,0.5,0.5|qconvex Ga QG-0 &gt;eg.10b.sphere.beyond </a></h3>
+
+<p>These are the facets that are not visible from the point.
+Qhull will keep these facets.</p>
+
+<h3><a href="#how">&#187;</a><a name="10c">rbox 100 s P0.5,0.5,0.5 |
+qconvex PG Ga QG0 &gt;eg.10c.sphere.horizon </a></h3>
+
+<p>These facets are the horizon facets; they border the visible
+facets. The inside edges are the horizon ridges. Each horizon
+ridge will form the base for a new facet.</p>
+
+<h3><a href="#how">&#187;</a><a name="10d">rbox 100 s P0.5,0.5,0.5 |
+qconvex Ga QV0 PgG &gt;eg.10d.sphere.cone </a></h3>
+
+<p>This is the cone of points from the new point to the horizon
+facets.  Try combining this image with <tt>eg.10c.sphere.horizon</tt>
+and <tt>eg.10a.sphere.visible</tt>.
+</p>
+
+<h3><a href="#how">&#187;</a><a name="10e">rbox 100 s P0.5,0.5,0.5 |
+qconvex Ga &gt;eg.10e.sphere.new</a></h3>
+
+<p>This is the convex hull after [0.5,0.5,0.5] has been added.
+Note that in actual practice, the above sequence would never
+happen. Unlike the randomized algorithms, Qhull always processes
+a point that is furthest in an outside set. A point like
+[0.5,0.5,0.5] would be one of the first points processed.</p>
+
+<h3><a href="#how">&#187;</a><a name="14">rbox 100 s P0.5,0.5,0.5 |
+qhull Ga QV0g Q0 &gt;eg.14.sphere.corner</a></h3>
+
+<p>The '<a href="qh-optq.htm#QVn">QVn</a>', '<a
+href="qh-optq.htm#QGn">QGn </a>' and '<a href="qh-optp.htm#Pdk">Pdk</a>'
+options define good facets for Qhull. In this case '<a
+href="qh-optq.htm#QVn">QV0</a>' defines the 0'th point
+[0.5,0.5,0.5] as the good vertex, and '<a href="qh-optq.htm#Qg">Qg</a>'
+tells Qhull to only build facets that might be part of a good
+facet. This technique reduces output size in low dimensions. It
+does not work with facet merging.</p>
+
+<h2><a href="#TOC">&#187;</a>Triangulated output or joggled input</h2>
+
+<h3><a href="#joggle">&#187;</a><a name="15a">rbox 500 W0 | qconvex QR0 Qc Gvp &gt;eg.15a.surface</a></h3>
+
+<p>This is the convex hull of 500 points on the surface of
+a cube.  Note the large, non-simplicial facet for each face.
+Qhull merges non-convex facets.
+
+<p>If the facets were not merged, Qhull
+would report precision problems.  For example, turn off facet merging
+with option '<a href="qh-optq.htm#Q0">Q0</a>'.  Qhull may report concave
+facets, flipped facets, or other precision errors:
+<blockquote>
+rbox 500 W0 | qhull QR0 Q0
+</blockquote>
+
+<p>
+<h3><a href="#joggle">&#187;</a><a name="15b">rbox 500 W0 | qconvex QR0 Qt Qc Gvp &gt;eg.15b.triangle</a></h3>
+
+<p>Like the previous examples, this is the convex hull of 500 points on the
+surface of a cube.  Option '<a href="qh-optq.htm#Qt">Qt</a>' triangulates the
+non-simplicial facets.  Triangulated output is
+particularly helpful for Delaunay triangulations.
+
+<p>
+<h3><a href="#joggle">&#187;</a><a name="15c">rbox 500 W0 | qconvex QR0 QJ5e-2 Qc Gvp &gt;eg.15c.joggle</a></h3>
+
+<p>This is the convex hull of 500 joggled points on the surface of
+a cube.  The option '<a href="qh-optq.htm#QJn">QJ5e-2</a>'
+sets a very large joggle to make the effect visible.  Notice
+that all of the facets are triangles.  If you rotate the cube,
+you'll see red-yellow lines for coplanar points.
+<p>
+With option '<a href="qh-optq.htm#QJn">QJ</a>', Qhull joggles the
+input to avoid precision problems.  It adds a small random number
+to each input coordinate.  If a precision
+error occurs, it increases the joggle and tries again.  It repeats
+this process until no precision problems occur.
+<p>
+Joggled input is a simple solution to precision problems in
+computational geometry.  Qhull can also merge facets to handle
+precision problems.  See <a href="qh-impre.htm#joggle">Merged facets or joggled input</a>.
+
+<h2><a href="#TOC">&#187;</a>Delaunay and Voronoi diagrams</h2>
+
+<h3><a href="#delaunay">&#187;</a><a name="17a">qdelaunay Qt
+&lt;eg.data.17 GnraD2 &gt;eg.17a.delaunay.2</a></h3>
+
+<p>
+The input file, <tt>eg.data.17</tt>, consists of a square, 15 random
+points within the outside half of the square, and 6 co-circular
+points centered on the square.
+
+<p>The Delaunay triangulation is the triangulation with empty
+circumcircles.  The input for this example is unusual because it
+includes six co-circular points.  Every triangular subset of these
+points has the same circumcircle.  Option '<a href="qh-optq.htm#Qt">Qt</a>'
+triangulates the co-circular facet.</p>
+
+<h3><a href="#delaunay">&#187;</a><a name="17b">qdelaunay &lt;eg.data.17
+GnraD2 &gt;eg.17b.delaunay.2i</a></h3>
+
+<p>This is the same example without triangulated output ('<a href="qh-optq.htm#Qt">Qt</a>').  qdelaunay
+merges the non-unique Delaunay triangles into a hexagon.</p>
+
+<h3><a href="#delaunay">&#187;</a><a name="17c">qdelaunay &lt;eg.data.17
+Ga &gt;eg.17c.delaunay.2-3 </a></h3>
+
+<p>This is how Qhull generated both diagrams. Use Geomview's
+'obscure' menu to turn off normalization, and Geomview's
+'cameras' menu to turn off perspective. Then load this <a
+href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/delaunay.html">object</a>
+with one of the previous diagrams.</p>
+
+<p>The points are lifted to a paraboloid by summing the squares
+of each coordinate. These are the light blue points. Then the
+convex hull is taken. That's what you see here. If you look up
+the Z-axis, you'll see that points and edges coincide.</p>
+
+<h3><a href="#delaunay">&#187;</a><a name="17d">qvoronoi QJ
+&lt;eg.data.17 Gna &gt;eg.17d.voronoi.2</a></h3>
+
+<p>The Voronoi diagram is the dual of the Delaunay triangulation.
+Here you see the original sites and the Voronoi vertices.
+Notice the each
+vertex is equidistant from three sites. The edges indicate the
+Voronoi region for a site. Qhull does not draw the unbounded
+edges. Instead, it draws extra edges to close the unbounded
+Voronoi regions. You may find it helpful to enclose the input
+points in a square.  You can compute the unbounded
+rays from option '<a href="qh-optf.htm#Fo2">Fo</a>'.
+</p>
+
+<p>Instead
+of triangulated output ('<a href="qh-optq.htm#Qt">Qt</a>'), this
+example uses joggled input ('<a href="qh-optq.htm#QJn">QJ</a>').
+Normally, you should use neither 'QJ' nor 'Qt' for Voronoi diagrams.
+
+<h3><a href="#delaunay">&#187;</a><a name="17e">qvoronoi &lt;eg.data.17
+Gna &gt;eg.17e.voronoi.2i </a></h3>
+
+<p>This looks the same as the previous diagrams, but take a look
+at the data.  Run 'qvoronoi p &lt;eg/eg.data.17'.  This prints
+the Voronoi vertices.
+
+<p>With 'QJ', there are four nearly identical Voronoi vertices
+within 10^-11 of the origin.  Option 'QJ' joggled the input.  After the joggle,
+the cocircular
+input sites are no longer cocircular.  The corresponding Voronoi vertices are
+similar but not identical.
+
+<p>This example does not use options 'Qt' or 'QJ'.  The cocircular
+input sites define one Voronoi vertex near the origin. </p>
+
+<p>Option 'Qt' would triangulate the corresponding Delaunay region into
+four triangles.  Each triangle is assigned the same Voronoi vertex.</p>
+
+<h3><a href="#delaunay">&#187;</a><a name="17f"> rbox c G0.1 d |
+qdelaunay Gt Qz &lt;eg.17f.delaunay.3 </a></h3>
+
+<p>This is the 3-d Delaunay triangulation of a small cube inside
+a prism. Since the outside ridges are transparent, it shows the
+interior of the outermost facets. If you slice open the
+triangulation with Geomview's ginsu, you will see that the innermost
+facet is a cube. Note the use of '<a href="qh-optq.htm#Qz">Qz</a>'
+to add a point &quot;at infinity&quot;. This avoids a degenerate
+input due to cospherical points.</p>
+
+<h3><a href="#delaunay">&#187;</a><a name="18a">rbox 10 D2 d | qdelaunay
+Qu G &gt;eg.18a.furthest.2-3 </a></h3>
+
+<p>The furthest-site Voronoi diagram contains Voronoi regions for
+points that are <i>furthest </i>from an input site. It is the
+dual of the furthest-site Delaunay triangulation. You can
+determine the furthest-site Delaunay triangulation from the
+convex hull of the lifted points (<a href="#17c">eg.17c.delaunay.2-3</a>).
+The upper convex hull (blue) generates the furthest-site Delaunay
+triangulation. </p>
+
+<h3><a href="#delaunay">&#187;</a><a name="18b">rbox 10 D2 d | qdelaunay
+Qu Pd2 G &gt;eg.18b.furthest-up.2-3</a></h3>
+
+<p>This is the upper convex hull of the preceding example. The
+furthest-site Delaunay triangulation is the projection of the
+upper convex hull back to the input points. The furthest-site
+Voronoi vertices are the circumcenters of the furthest-site
+Delaunay triangles. </p>
+
+<h3><a href="#delaunay">&#187;</a><a name="18c">rbox 10 D2 d | qvoronoi
+Qu Gv &gt;eg.18c.furthest.2</a></h3>
+
+<p>This shows an incomplete furthest-site Voronoi diagram. It
+only shows regions with more than two vertices. The regions are
+artificially truncated. The actual regions are unbounded. You can
+print the regions' vertices with 'qvoronoi Qu <a
+href="qh-opto.htm#o">o</a>'. </p>
+
+<p>Use Geomview's 'obscure' menu to turn off normalization, and
+Geomview's 'cameras' menu to turn off perspective. Then load this
+with the upper convex hull.</p>
+
+<h3><a href="#delaunay">&#187;</a><a name="19">rbox 10 D3 | qvoronoi QV5
+p | qconvex G &gt;eg.19.voronoi.region.3 </a></h3>
+
+<p>This shows the Voronoi region for input site 5 of a 3-d
+Voronoi diagram.</p>
+
+<h2><a href="#TOC">&#187;</a>Facet merging for imprecision</h2>
+
+<h3><a href="#merge">&#187;</a><a name="20">rbox r s 20 Z1 G0.2 |
+qconvex G &gt;eg.20.cone </a></h3>
+
+<p>There are two things unusual about this <a
+href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/cone.html">cone</a>.
+One is the large flat disk at one end and the other is the
+rectangles about the middle. That's how the points were
+generated, and if those points were exact, this is the correct
+hull. But <tt>rbox</tt> used floating point arithmetic to
+generate the data. So the precise convex hull should have been
+triangles instead of rectangles. By requiring convexity, Qhull
+has recovered the original design.</p>
+
+<h3><a href="#merge">&#187;</a><a name="21a">rbox 200 s | qhull Q0
+R0.01 Gav Po &gt;eg.21a.roundoff.errors </a></h3>
+
+<p>This is the convex hull of 200 cospherical points with
+precision errors ignored ('<a href="qh-optq.htm#Q0">Q0</a>'). To
+demonstrate the effect of roundoff error, we've added a random
+perturbation ('<a href="qh-optc.htm#Rn">R0.01</a>') to every
+distance and hyperplane calculation. Qhull, like all other convex
+hull algorithms with floating point arithmetic, makes
+inconsistent decisions and generates wildly wrong results. In
+this case, one or more facets are flipped over. These facets have
+the wrong color. You can also turn on 'normals' in Geomview's
+appearances menu and turn off 'facing normals'. There should be
+some white lines pointing in the wrong direction. These
+correspond to flipped facets. </p>
+
+<p>Different machines may not produce this picture. If your
+machine generated a long error message, decrease the number of
+points or the random perturbation ('<a href="qh-optc.htm#Rn">R0.01</a>').
+If it did not report flipped facets, increase the number of
+points or perturbation.</p>
+
+<h3><a href="#merge">&#187;</a><a name="21b">rbox 200 s | qconvex Qc
+R0.01 Gpav &gt;eg.21b.roundoff.fixed </a></h3>
+
+<p>Qhull handles the random perturbations and returns an
+imprecise <a
+href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/fixed.html">sphere</a>.
+In this case, the output is a weak approximation to the points.
+This is because a random perturbation of '<a
+href="qh-optc.htm#Rn">R0.01 </a>' is equivalent to losing all but
+1.8 digits of precision. The outer planes float above the points
+because Qhull needs to allow for the maximum roundoff error. </p>
+<p>
+If you start with a smaller random perturbation, you
+can use joggle ('<a href="qh-optq.htm#QJn">QJn</a>') to avoid
+precision problems.  You need to set <i>n</i> significantly
+larger than the random perturbation.  For example, try
+'rbox 200 s | qconvex Qc R1e-4 QJ1e-1'.
+
+<h3><a href="#merge">&#187;</a><a name="22a">rbox 1000 s| qconvex C0.01
+Qc Gcrp &gt;eg.22a.merge.sphere.01</a></h3>
+
+<h3><a href="#merge">&#187;</a><a name="22b">rbox 1000 s| qconvex
+C-0.01 Qc Gcrp &gt;eg.22b.merge.sphere.-01</a></h3>
+
+<h3><a href="#merge">&#187;</a><a name="22c">rbox 1000 s| qconvex C0.05
+Qc Gcrpv &gt;eg.22c.merge.sphere.05</a></h3>
+
+<h3><a href="#merge">&#187;</a><a name="22d">rbox 1000 s| qconvex
+C-0.05 Qc Gcrpv &gt;eg.22d.merge.sphere.-05</a></h3>
+
+<p>The next four examples compare post-merging and pre-merging ('<a
+href="qh-optc.htm#Cn2">Cn</a>' vs. '<a href="qh-optc.htm#Cn">C-n</a>').
+Qhull uses '-' as a flag to indicate pre-merging.</p>
+
+<p>Post-merging happens after the convex hull is built. During
+post-merging, Qhull repeatedly merges an independent set of
+non-convex facets. For a given set of parameters, the result is
+about as good as one can hope for.</p>
+
+<p>Pre-merging does the same thing as post-merging, except that
+it happens after adding each point to the convex hull. With
+pre-merging, Qhull guarantees a convex hull, but the facets are
+wider than those from post-merging. If a pre-merge option is not
+specified, Qhull handles machine round-off errors.</p>
+
+<p>You may see coplanar points appearing slightly outside
+the facets of the last example.  This is becomes Geomview moves
+line segments forward toward the viewer.  You can avoid the
+effect by setting 'lines closer' to '0' in Geomview's camera menu.
+
+<h3><a href="#merge">&#187;</a><a name="23">rbox 1000 | qconvex s
+Gcprvah C0.1 Qc &gt;eg.23.merge.cube</a></h3>
+
+<p>Here's the 3-d imprecise cube with all of the Geomview
+options. There's spheres for the vertices, radii for the coplanar
+points, dots for the interior points, hyperplane intersections,
+centrums, and inner and outer planes.  The radii are shorter than
+the spheres because this uses post-merging ('<a href="qh-optc.htm#Cn2">C0.1</a>')
+instead of pre-merging.
+
+<h2><a href="#TOC">&#187;</a>4-d objects</h2>
+
+<p>With Qhull and Geomview you can develop an intuitive sense of
+4-d surfaces. When you get into trouble, think of viewing the
+surface of a 3-d sphere in a 2-d plane.</p>
+
+<h3><a href="#4d">&#187;</a><a name="24">rbox 5000 D4 | qconvex s GD0v
+Pd0:0.5 C-0.02 C0.1 &gt;eg.24.merge.cube.4d-in-3d</a></h3>
+
+<p>Here's one facet of the imprecise cube in 4-d. It's projected
+into 3-d (the '<a href="qh-optg.htm#GDn">GDn</a>' option drops
+dimension n). Each ridge consists of two triangles between this
+facet and the neighboring facet. In this case, Geomview displays
+the topological ridges, i.e., as triangles between three
+vertices. That is why the cube looks lopsided.</p>
+
+<h3><a href="#4d">&#187;</a><a name="30">rbox 5000 D4 | qconvex s
+C-0.02 C0.1 Gh &gt;eg.30.4d.merge.cube </a></h3>
+
+<p><a
+href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/4dcube.html">Here</a>
+is the equivalent in 4-d of the imprecise <a href="#06">square</a>
+and imprecise <a href="#23">cube</a>. It's the imprecise convex
+hull of 5000 random points in a hypercube. It's a full 4-d object
+so Geomview's <tt>ginsu </tt>does not work. If you view it in
+Geomview, you'll be inside the hypercube. To view 4-d objects
+directly, either load the <tt>4dview</tt> module or the <tt>ndview
+</tt>module. For <tt>4dview</tt>, you must have started Geomview
+in the same directory as the object. For <tt>ndview</tt>,
+initialize a set of windows with the prefab menu, and load the
+object through Geomview. The <tt>4dview</tt> module includes an
+option for slicing along any hyperplane. If you do this in the x,
+y, or z plane, you'll see the inside of a hypercube.</p>
+
+<p>The '<a href="qh-optg.htm#Gh">Gh</a>' option prints the
+geometric intersections between adjacent facets. Note the strong
+convexity constraint for post-merging ('<a href="qh-optc.htm#Cn2">C0.1</a>').
+It deletes the small facets.</p>
+
+<h3><a href="#4d">&#187;</a><a name="31">rbox 20 D3 | qdelaunay G
+&gt;eg.31.4d.delaunay </a></h3>
+
+<p>The Delaunay triangulation of 3-d sites corresponds to a 4-d
+convex hull. You can't see 4-d directly but each facet is a 3-d
+object that you can project to 3-d. This is exactly the same as
+projecting a 2-d facet of a soccer ball onto a plane.</p>
+
+<p>Here we see all of the facets together. You can use Geomview's
+<tt>ndview</tt> to look at the object from several directions.
+Try turning on edges in the appearance menu. You'll notice that
+some edges seem to disappear. That's because the object is
+actually two sets of overlapping facets.</p>
+
+<p>You can slice the object apart using Geomview's <tt>4dview</tt>.
+With <tt>4dview</tt>, try slicing along the w axis to get a
+single set of facets and then slice along the x axis to look
+inside. Another interesting picture is to slice away the equator
+in the w dimension.</p>
+
+<h3><a href="#4d">&#187;</a><a name="32">rbox 30 s D4 | qconvex s G
+Pd0d1d2D3</a></h3>
+
+<p>This is the positive octant of the convex hull of 30 4-d
+points. When looking at 4-d, it's easier to look at just a few
+facets at once. If you picked a facet that was directly above
+you, then that facet looks exactly the same in 3-d as it looks in
+4-d. If you pick several facets, then you need to imagine that
+the space of a facet is rotated relative to its neighbors. Try
+Geomview's <tt>ndview</tt> on this example.</p>
+
+<h2><a href="#TOC">&#187;</a>Halfspace intersections</h2>
+
+<h3><a href="#half">&#187;</a><a name="33a">rbox 10 r s Z1 G0.3 |
+qconvex G &gt;eg.33a.cone </a></h3>
+
+<h3><a href="#half">&#187;</a><a name="33b">rbox 10 r s Z1 G0.3 |
+qconvex FV n | qhalf G &gt;eg.33b.cone.dual</a></h3>
+
+<h3><a href="#half">&#187;</a><a name="33c">rbox 10 r s Z1 G0.3 |
+qconvex FV n | qhalf Fp | qconvex G &gt;eg.33c.cone.halfspace</a></h3>
+
+<p>These examples illustrate halfspace intersection. The first
+picture is the convex hull of two 20-gons plus an apex. The
+second picture is the dual of the first. Try loading <a
+href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/half.html">both</a>
+at once. Each vertex of the second picture corresponds to a facet
+or halfspace of the first. The vertices with four edges
+correspond to a facet with four neighbors. Similarly the facets
+correspond to vertices. A facet's normal coefficients divided by
+its negative offset is the vertice's coordinates. The coordinates
+are the intersection of the original halfspaces. </p>
+
+<p>The third picture shows how Qhull can go back and forth
+between equivalent representations. It starts with a cone,
+generates the halfspaces that define each facet of the cone, and
+then intersects these halfspaces. Except for roundoff error, the
+third picture is a duplicate of the first. </p>
+<!-- Navigation links -->
+<hr>
+
+<p><b>Up:</b> <a href="http://www.qhull.org">Home
+page for Qhull</a> <br>
+<b>Up:</b> <a href="index.htm#TOC">Qhull manual: Table of Contents</a><br>
+<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
+&#149; <a href="qh-quick.htm#options">Options</a>
+&#149; <a href="qh-opto.htm#output">Output</a>
+&#149; <a href="qh-optf.htm#format">Formats</a>
+&#149; <a href="qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="qh-optp.htm#print">Print</a>
+&#149; <a href="qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="qh-optc.htm#prec">Precision</a>
+&#149; <a href="qh-optt.htm#trace">Trace</a>
+&#149; <a href="../src/libqhull_r/index.htm">Functions</a><br>
+<b>To: </b><a href="#TOC">Qhull examples: Table of Contents</a> (please wait
+while loading)<br>
+<!-- GC common information -->
+<hr>
+
+<p><a href="http://www.geom.uiuc.edu/"><img src="qh--geom.gif"
+align="middle" width="40" height="40"></a><i>The Geometry Center
+Home Page </i></p>
+
+<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
+</a><br>
+Created: Sept. 25, 1995 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
+</body>
+</html>
diff --git a/xs/src/qhull/html/qh-faq.htm b/xs/src/qhull/html/qh-faq.htm
new file mode 100644
index 0000000000..feda544a75
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+++ b/xs/src/qhull/html/qh-faq.htm
@@ -0,0 +1,1547 @@
+<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN">
+<html>
+
+<head>
+<meta http-equiv="Content-Type"
+content="text/html; charset=iso-8859-1">
+<meta name="GENERATOR" content="Microsoft FrontPage 2.0">
+<title>Qhull FAQ</title>
+<!-- Navigation links
+NOTE -- verify all links by 'grep href=' 'grep name=' add # 'sort /+7'
+<base href> does not work since #TOC is relative to base instead of doc
+-->
+</head>
+
+<body>
+
+<p><a name="TOP"><b>Up:</b></a> <a
+ href="http://www.qhull.org">Home page</a> for Qhull
+(http://www.qhull.org)<br>
+<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
+<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
+&#149; <a href="qh-quick.htm#options">Options</a>
+&#149; <a href="qh-opto.htm#output">Output</a>
+&#149; <a href="qh-optf.htm#format">Formats</a>
+&#149; <a href="qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="qh-optp.htm#print">Print</a>
+&#149; <a href="qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="qh-optc.htm#prec">Precision</a>
+&#149; <a href="qh-optt.htm#trace">Trace</a>
+&#149; <a href="../src/libqhull_r/index.htm">Functions</a><br>
+<b>To:</b> <a href="#TOC">FAQ: Table of Contents</a> (please
+wait while loading) <br>
+
+<hr>
+<!-- Main text of document -->
+<h1><a
+ href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/4dcube.html"><IMG
+ align=middle alt ="[4-d cube]"
+ height=100 src="qh--4d.gif" width=100 ></a> Frequently Asked Questions about Qhull</h1><!--
+<p><i>This is the most recent FAQ. It was updated Sept. 13, 1999.</i>
+-->
+<p>If your question does not appear here, see: </p>
+
+<ul>
+    <li><a href="http://www.qhull.org/news">News</a> about Qhull
+    <li><a href="index.htm#TOC">Qhull manual:</a> table of contents
+    <li><a href="../README.txt">Installation</a> instructions for Qhull and rbox
+
+    <li><a href="mailto:qhull@qhull.org">Send e-mail</a> to
+  qhull@qhull.org
+    <li><a href="mailto:qhull_bug@qhull.org">Report bugs</a>
+        to qhull_bug@qhull.org </li>
+</ul>
+
+<p>Qhull is a general dimension code for computing convex hulls,
+Delaunay triangulations, halfspace intersections about a point,
+Voronoi diagrams, furthest-site Delaunay triangulations, and
+furthest-site Voronoi diagrams. These structures have
+applications in science, engineering, statistics, and
+mathematics. For a detailed introduction, see O'Rourke [<a
+ href="index.htm#orou94" >'94</a>], <i>Computational Geometry in C</i>.
+</p>
+
+<p>There are separate programs for each application of
+Qhull.  These programs disable experimental and inappropriate
+options.  If you prefer, you may use Qhull directly.  All programs
+run the same code.
+
+<p>Version 3.1 added triangulated output ('<a href="qh-optq.htm#Qt">Qt</a>').
+It should be used for Delaunay triangulations instead of
+using joggled input ('<a href="qh-optq.htm#QJn">QJ</a>').
+
+<p><i>Brad Barber, Arlington MA,
+2010/01/09 <!--
+--> </i></p>
+
+<p><b>Copyright &copy; 1998-2015 C.B. Barber</b></p>
+
+<hr>
+
+<h2><a href="#TOP">&#187;</a><a name="TOC">FAQ: Table of Contents </a></h2>
+
+<p>Within each category, the most recently asked questions are
+first.
+<ul>
+    <li>Startup questions <ul>
+            <li><a href="#console">How</a> do I run Qhull from Windows?
+            <li><a href="#input">How</a> do I enter points for Qhull?
+            <li><a href="#learn">How</a> do I learn to use Qhull?</li>
+        </ul>
+    <li>Convex hull questions<ul>
+        <li><a href="#area">How</a> do I report just the area and volume of a
+    convex hull?
+        <li><a href="#extra">Why</a> are there extra points in a 4-d or higher
+    convex hull?
+        <li><a href="#dup">How</a> do I report duplicate
+            vertices? </li>
+        </ul>
+    <li>Delaunay triangulation questions<ul>
+                <li><a href="#flat">How</a> do I get rid of nearly flat Delaunay
+    triangles?
+                <li><a href="#vclosest">How</a> do I find the Delaunay triangle or Voronoi
+    region that is closest to a point?
+
+                <li><a href="#mesh">How</a> do I compute the Delaunay triangulation of a
+    non-convex object?
+
+                <li><a href="#mesh">How</a> do I mesh a volume from a set of triangulated
+    surface points?
+
+                        <li><a href="#constrained">Can</a> Qhull produce a triangular mesh for an
+    object?
+
+                <li><a href="#dridges">For</a> 3-d Delaunay triangulations, how do I
+    report the triangles of each tetrahedron?
+
+        <li><a href="#3dd">How</a> do I construct a 3-d Delaunay triangulation?
+        <li><a href="#2d">How</a> do I get the triangles for a 2-d Delaunay
+    triangulation and the vertices of its Voronoi diagram?
+        <li><a href="#big">Can </a>Qhull triangulate a
+            hundred 16-d points?</li>
+        </ul>
+
+    <li>Voronoi diagram questions<ul>
+        <li>See also "Delaunay diagram questions".  Qhull computes the Voronoi diagram from the Delaunay triagulation.
+        <li><a href="#volume">How</a> do I compute the volume of a Voronoi region?
+        <li><a href="#maxsphere">How</a> do I get the radii of the empty
+                spheres for each Voronoi vertex?
+
+                <li><a href="#square">What</a> is the Voronoi diagram of a square?
+
+        <li><a href="#vsphere">How</a> do I construct the Voronoi diagram of
+    cospherical points?
+        <li><a href="#rays">Can</a> Qhull compute the unbounded rays of the
+    Voronoi diagram?
+        </ul>
+    <li>Approximation questions<ul>
+        <li><a href="#simplex">How</a> do I approximate data
+            with a simplex?</li>
+        </ul>
+    <li>Halfspace questions<ul>
+        <li><a href="#halfspace">How</a> do I compute the
+                        intersection of halfspaces with Qhull?</li>
+        </ul>
+    <li><a name="library">Qhull library</a> questions<ul>
+        <li><a href="#math">Is</a> Qhull available for Mathematica, Matlab, or
+    Maple?
+
+        <li><a href="#ridges">Why</a> are there too few ridges?
+        <li><a href="#call">Can</a> Qhull use coordinates without placing them in
+    a data file?
+        <li><a href="#size">How</a> large are Qhull's data structures?
+        <li><a href="#inc">Can</a> Qhull construct convex hulls and Delaunay
+    triangulations one point at a time?
+        <li><a href="#ridges2">How</a> do I visit the ridges of a Delaunay
+    triangulation?
+        <li><a href="#listd">How</a> do I visit the Delaunay facets?
+    <LI><a
+    href="#outside">When</a> is a point outside or inside a facet?
+        <li><a href="#closest">How</a> do I find the facet that is closest to a
+    point?
+        <li><a href="#vclosest">How</a> do I find the Delaunay triangle or Voronoi
+    region that is closest to a point?
+        <li><a href="#vertices">How</a> do I list the vertices?
+        <li><a href="#test">How</a> do I test code that uses the Qhull library?
+        <li><a href="#orient">When</a> I compute a plane
+            equation from a facet, I sometimes get an
+            outward-pointing normal and sometimes an
+            inward-pointing normal</li>
+        </ul>
+    </li>
+</ul>
+
+<hr>
+
+<h2><a href="#TOC">&#187;</a><a name="startup">Startup</a> questions</h2>
+
+<h4><a href="#TOC">&#187;</a><a name="console">How</a> do I run Qhull
+from Windows?</h4><blockquote>
+
+<p>Qhull is a console program. You will first need a command window
+(i.e., a "command prompt"). You can double click on
+'eg\Qhull-go.bat'. </p>
+
+<blockquote><ul>
+    <li>Type 'qconvex', 'qdelaunay', 'qhalf', 'qvoronoi,
+      'qhull', and 'rbox' for a synopsis of each program.
+
+    <li>Type 'rbox c D2 | qconvex s i' to compute the
+      convex hull of a square.
+
+    <li>Type 'rbox c D2 | qconvex s i TO results.txt' to
+      write the results to the file 'results.txt'. A summary is still printed on
+      the the console.
+
+    <li>Type 'rbox c D2' to see the input format for
+      qconvex.
+
+    <li>Type 'qconvex &lt; data.txt s i TO results.txt' to
+      read input data from 'data.txt'.
+
+    <li>If you want to enter data by hand, type 'qconvex s i TO
+        results.txt' to read input data from the console. Type in
+        the numbers and end with a ctrl-D. </li>
+</ul></blockquote>
+
+</blockquote><h4><a href="#TOC">&#187;</a><a name="input">How</a> do I enter
+points for Qhull?</h4><blockquote>
+
+<p>Qhull takes its data from standard input. For example, create
+a file named 'data.txt' with the following contents: </p>
+
+<blockquote>
+    <pre>
+2  #sample 2-d input
+5  #number of points
+1 2  #coordinates of points
+-1.1 3
+3 2.2
+4 5
+-10 -10
+</pre>
+</blockquote>
+
+<p>Then call qconvex with 'qconvex &lt; data.txt'. It will print a
+summary of the convex hull. Use 'qconvex &lt; data.txt o' to print
+the vertices and edges. See also <a href="index.htm#input">input
+format</a>. </p>
+
+<p>You can generate sample data with rbox, e.g., 'rbox 10'
+generates 10 random points in 3-d. Use a pipe ('|') to run rbox
+and qhull together, e.g., </p>
+
+<blockquote>
+    <p>rbox c | qconvex o </p>
+</blockquote>
+
+<p>computes the convex hull of a cube. </p>
+
+</blockquote><h4><a href="#TOC">&#187;</a><a name="learn">How</a> do I learn to
+use Qhull?</h4><blockquote>
+
+<p>First read: </p>
+
+<ul>
+    <li><a href="index.htm">Introduction</a> to Qhull
+    <li><a href="index.htm#when">When</a> to use Qhull
+    <li><a href="qconvex.htm">qconvex</a> -- convex hull
+    <li><a href="qdelaun.htm">qdelaunay</a> -- Delaunay triangulation
+    <li><a href="qhalf.htm">qhalf</a> -- half-space intersection about a point
+
+    <li><a href="qvoronoi.htm">qvoronoi</a> -- Voronoi diagram
+    <li><a href="rbox.htm">Rbox</a>, for sample inputs
+    <li><a href="qh-eg.htm">Examples</a> of Qhull</li>
+</ul>
+
+<p>Look at Qhull's on-line documentation: </p>
+
+<ul>
+    <li>'qconvex' gives a synopsis of qconvex and its options
+
+    <li>'rbox' lists all of the options for generating point
+    sets
+    <li>'qconvex - | more' lists the options for qconvex
+    <li>'qconvex .' gives a concise list of options
+    <li>'qdelaunay', 'qhalf', 'qvoronoi', and 'qhull' also have a synopsis and option list</li>
+</ul>
+
+<p>Then try out the Qhull programs on small examples. </p>
+
+<ul>
+    <li>'rbox c' lists the vertices of a cube
+    <li>'rbox c | qconvex' is the convex hull of a cube
+    <li>'rbox c | qconvex o' lists the vertices and facets of
+    a cube
+    <li>'rbox c | qconvex Qt o' triangulates the cube
+    <li>'rbox c | qconvex QJ o' joggles the input and
+    triangulates the cube
+    <li>'rbox c D2 | qconvex' generates the convex hull of a
+    square
+    <li>'rbox c D4 | qconvex' generates the convex hull of a
+    hypercube
+    <li>'rbox 6 s D2 | qconvex p Fx' lists 6 random points in
+    a circle and lists the vertices of their convex hull in order
+    <li>'rbox c D2 c G2 | qdelaunay' computes the Delaunay
+    triangulation of two embedded squares. It merges the cospherical facets.
+    <li>'rbox c D2 c G2 | qdelaunay Qt' computes the Delaunay
+    triangulation of two embedded squares. It triangulates the cospherical facets.
+    <li>'rbox c D2 c G2 | qvoronoi o' computes the
+    corresponding Voronoi vertices and regions.
+    <li>'rbox c D2 c G2 | qvoronio Fv' shows the Voronoi diagram
+        for the previous example. Each line is one edge of the
+        diagram. The first number is 4, the next two numbers list
+        a pair of input sites, and the last two numbers list the
+        corresponding pair of Voronoi vertices. </li>
+</ul>
+
+<p>Install <a href="http://www.geomview.org">Geomview</a>
+if you are running SGI Irix, Solaris, SunOS, Linux, HP, IBM
+RS/6000, DEC Alpha, or Next. You can then visualize the output of
+Qhull. Qhull comes with Geomview <a href="qh-eg.htm">examples</a>.
+</p>
+
+<p>Then try Qhull with a small example of your application. Work
+out the results by hand. Then experiment with Qhull's options to
+find the ones that you need. </p>
+
+<p>You will need to decide how Qhull should handle precision
+problems. It can triangulate the output ('<a
+ href="qh-optq.htm#Qt" >Qt</a>'), joggle the input ('<a
+ href="qh-optq.htm#QJn" >QJ</a>'), or merge facets (the default). </p>
+
+<ul>
+    <li>With joggle, Qhull produces simplicial (i.e.,
+    triangular) output by joggling the input.  After joggle,
+    no points are cocircular or cospherical.
+    <li>With facet merging, Qhull produces a better
+    approximation and does not modify the input.
+    <li>With triangulated output, Qhull merges facets and triangulates
+    the result.</li>
+    <li>See <a href="qh-impre.htm#joggle">Merged facets or joggled input</a>. </li>
+</ul>
+
+</blockquote>
+<h2><a href="#TOC">&#187;</a><a name="convex">Convex hull questions</a></h2>
+
+<h4><a href="#TOC">&#187;</a><a name="area">How</a> do I report just the area
+                        and volume of a convex hull?</h4><blockquote>
+
+Use option 'FS'.  For example,
+
+<blockquote><pre>
+C:\qhull>rbox 10 | qconvex FS
+0
+2 2.192915621644613 0.2027867899638665
+
+C:\qhull>rbox 10 | qconvex FA
+
+Convex hull of 10 points in 3-d:
+
+  Number of vertices: 10
+  Number of facets: 16
+
+Statistics for: RBOX 10 | QCONVEX FA
+
+  Number of points processed: 10
+  Number of hyperplanes created: 28
+  Number of distance tests for qhull: 44
+  CPU seconds to compute hull (after input):  0
+  Total facet area:   2.1929156
+  Total volume:       0.20278679
+</pre></blockquote>
+
+</blockquote><h4><a href="#TOC">&#187;</a><a name="extra">Why</a> are there extra
+points in a 4-d or higher convex hull?</h4><blockquote>
+
+<p>You may see extra points if you use options '<a
+ href="qh-opto.htm#i" >i</a>' or '<a href="qh-optf.htm#Ft">Ft</a>'
+ without using triangulated output ('<a href="qh-optq.htm#Qt">Qt</a>').
+The extra points occur when a facet is non-simplicial (i.e., a
+facet with more than <i>d</i> vertices). For example, Qhull
+reports the following for one facet of the convex hull of a hypercube.
+Option 'Pd0:0.5' returns the facet along the positive-x axis: </p>
+
+<blockquote>
+    <pre>
+rbox c D4 | qconvex i Pd0:0.5
+12
+17 13 14 15
+17 13 12 14
+17 11 13 15
+17 14 11 15
+17 10 11 14
+17 14 12 8
+17 12 13 8
+17 10 14 8
+17 11 10 8
+17 13 9 8
+17 9 11 8
+17 11 9 13
+</pre>
+</blockquote>
+
+<p>The 4-d hypercube has 16 vertices; so point "17" was
+added by qconvex. Qhull adds the point in order to report a
+simplicial decomposition of the facet. The point corresponds to
+the "centrum" which Qhull computes to test for
+convexity. </p>
+
+<p>Triangulate the output ('<a href="qh-optq.htm#Qt">Qt</a>') to avoid the extra points.
+Since the hypercube is 4-d, each simplicial facet is a tetrahedron.
+<blockquote>
+<pre>
+C:\qhull3.1>rbox c D4 | qconvex i Pd0:0.5 Qt
+9
+9 13 14 15
+12 9 13 14
+9 11 13 15
+11 9 14 15
+9 10 11 14
+12 9 14 8
+9 12 13 8
+9 10 14 8
+10 9 11 8
+</pre>
+</blockquote>
+
+<p>Use the '<a href="qh-optf.htm#Fv">Fv</a>' option to print the
+vertices of simplicial and non-simplicial facets. For example,
+here is the same hypercube facet with option 'Fv' instead of 'i':
+</p>
+
+<blockquote>
+    <pre>
+C:\qhull&gt;rbox c D4 | qconvex Pd0:0.5 Fv
+1
+8 9 10 12 11 13 14 15 8
+</pre>
+</blockquote>
+
+<p>The coordinates of the extra point are printed with the '<A
+ href="qh-optf.htm#Ft" >Ft</a>' option. </p>
+
+<blockquote>
+    <pre>
+rbox c D4 | qconvex Pd0:0.5 Ft
+4
+17 12 3
+  -0.5   -0.5   -0.5   -0.5
+  -0.5   -0.5   -0.5    0.5
+  -0.5   -0.5    0.5   -0.5
+  -0.5   -0.5    0.5    0.5
+  -0.5    0.5   -0.5   -0.5
+  -0.5    0.5   -0.5    0.5
+  -0.5    0.5    0.5   -0.5
+  -0.5    0.5    0.5    0.5
+   0.5   -0.5   -0.5   -0.5
+   0.5   -0.5   -0.5    0.5
+   0.5   -0.5    0.5   -0.5
+   0.5   -0.5    0.5    0.5
+   0.5    0.5   -0.5   -0.5
+   0.5    0.5   -0.5    0.5
+   0.5    0.5    0.5   -0.5
+   0.5    0.5    0.5    0.5
+   0.5      0      0      0
+4 16 13 14 15
+4 16 13 12 14
+4 16 11 13 15
+4 16 14 11 15
+4 16 10 11 14
+4 16 14 12 8
+4 16 12 13 8
+4 16 10 14 8
+4 16 11 10 8
+4 16 13 9 8
+4 16 9 11 8
+4 16 11 9 13
+</pre>
+</blockquote>
+
+</blockquote><h4><a href="#TOC">&#187;</a><a name="dup">How</a> do I report
+duplicate vertices?</h4><blockquote>
+
+<p>There's no direct way. You can use option
+'<a href="qh-optf.htm#FP">FP</a>' to
+report the distance to the nearest vertex for coplanar input
+points. Select the minimum distance for a duplicated vertex, and
+locate all input sites less than this distance. </p>
+
+<p>For Delaunay triangulations, all coplanar points are nearly
+incident to a vertex. If you want a report of coincident input
+sites, do not use option '<a href="qh-optq.htm#QJn">QJ</a>'. By
+adding a small random quantity to each input coordinate, it
+prevents coincident input sites. </p>
+
+</blockquote>
+<h2><a href="#TOC">&#187;</a><a name="delaunay">Delaunay triangulation questions</a></h2>
+
+<h4><a href="#TOC">&#187;</a><a name="flat">How</a> do I get rid of
+nearly flat Delaunay triangles?</h4><blockquote>
+
+<p>Nearly flat triangles occur when boundary points are nearly
+collinear or coplanar.  They also occur for nearly coincident
+points.  Both events can easily occur when using joggle.  For example
+(rbox 10 W0 D2 | qdelaunay QJ Fa) lists the areas of the Delaunay
+triangles of 10 points on the boundary of a square.  Some of
+these triangles are nearly flat.  This occurs when one point
+is joggled inside of two other points.  In this case, nearly flat
+triangles do not occur with triangulated output (rbox 10 W0 D2 | qdelaunay Qt Fa).
+
+
+<p>Another example, (rbox c P0 P0 D2 | qdelaunay QJ Fa), computes the
+areas of the Delaunay triangles for the unit square and two
+instances of the origin.  Four of the triangles have an area
+of 0.25 while two have an area of 2.0e-11.  The later are due to
+the duplicated origin.  With triangulated output (rbox c P0 P0 D2 | qdelaunay Qt Fa)
+there are four triangles of equal area.
+
+<p>Nearly flat triangles also occur without using joggle.  For
+example, (rbox c P0 P0,0.4999999999 | qdelaunay Fa), computes
+the areas of the Delaunay triangles for the unit square,
+a nearly collinear point, and the origin.  One triangle has an
+area of 3.3e-11.
+
+<p>Unfortunately, none of Qhull's merging options remove nearly
+flat Delaunay triangles due to nearly collinear or coplanar boundary
+points.
+The merging options concern the empty circumsphere
+property of Delaunay triangles.  This is independent of the area of
+the Delaunay triangles.  Qhull does handle nearly coincident points.
+
+<p>If you are calling Qhull from a program, you can merge slivers into an adjacent facet.
+In d dimensions with simplicial facets (e.g., from 'Qt'), each facet has
+d+1 neighbors.  Each neighbor shares d vertices of the facet's d+1 vertices.  Let the
+other vertex be the <i>opposite</i> vertex.  For each neighboring facet, if its circumsphere
+includes the opposite.vertex, the two facets can be merged. [M. Treacy]
+
+<p>You can handle collinear or coplanar boundary points by
+enclosing the points in a box.  For example,
+(rbox c P0 P0,0.4999999999 c G1 | qdelaunay Fa), surrounds the
+previous points with [(1,1), (1,-1), (-1,-1), (-1, 1)].
+Its Delaunay triangulation does not include a
+nearly flat triangle.  The box also simplifies the graphical
+output from Qhull.
+
+<p>Without joggle, Qhull lists coincident points as "coplanar"
+points.  For example, (rbox c P0 P0 D2 | qdelaunay Fa), ignores
+the duplicated origin and lists four triangles of size 0.25.
+Use 'Fc' to list the coincident points (e.g.,
+rbox c P0 P0 D2 | qdelaunay Fc).
+
+<p>There is no easy way to determine coincident points with joggle.
+Joggle removes all coincident, cocircular, and cospherical points
+before running Qhull.  Instead use facet merging (the default)
+or triangulated output ('<a href="qh-optq.htm#Qt">Qt</a>').
+
+</blockquote><h4><a href="#TOC">&#187;</a><a name="mesh">How</a> do I compute
+the Delaunay triangulation of a non-convex object?</h4><blockquote>
+
+<p>A similar question is
+"How do I mesh a volume from a set of triangulated surface points?"
+
+<p>This is an instance of the constrained Delaunay Triangulation
+problem.  Qhull does not handle constraints.  The boundary of the
+Delaunay triangulation is always convex.  But if the input set
+contains enough points, the triangulation will include the
+boundary.  The number of points needed depends on the input.
+
+<p>Shewchuk has developed a theory of constrained Delaunay triangulations.
+See his
+<a href="http://www.cs.cmu.edu/~jrs/jrspapers.html#cdt">paper</a> at the
+1998 Computational Geometry Conference.  Using these ideas, constraints
+could be added to Qhull.  They would have many applications.
+
+<p>There is a large literature on mesh generation and many commercial
+offerings.  For pointers see
+<a href="http://www.imr.sandia.gov/papers/topics.html">Owen's International Meshing Roundtable</a>
+and <a href="http://www.robertschneiders.de/meshgeneration/meshgeneration.html">Schneiders'
+Finite Element Mesh Generation page</a>.</p>
+
+</blockquote><h4><a href="#TOC">&#187;</a><a name="constrained">Can</a> Qhull
+produce a triangular mesh for an object?</h4><blockquote>
+
+<p>Yes for convex objects, no for non-convex objects. For
+non-convex objects, it triangulates the concavities. Unless the
+object has many points on its surface, triangles may cross the
+surface. </p>
+
+</blockquote><h4><a href="#TOC">&#187;</a><a name="dridges">For</a> 3-d Delaunay
+triangulations, how do I report the triangles of each
+tetrahedron?</h4><blockquote>
+
+<p>For points in general position, a 3-d Delaunay triangulation
+generates tetrahedron. Each face of a tetrahedron is a triangle.
+For example, the 3-d Delaunay triangulation of random points on
+the surface of a cube, is a cellular structure of tetrahedron. </p>
+
+<p>Use triangulated output ('qdelaunay Qt i') or joggled input ('qdelaunay QJ i')
+to generate the Delaunay triangulation.
+Option 'i' reports each tetrahedron. The triangles are
+every combination of 3 vertices. Each triangle is a
+"ridge" of the Delaunay triangulation. </p>
+
+<p>For example, </p>
+
+<pre>
+        rbox 10 | qdelaunay Qt i
+        14
+        9 5 8 7
+        0 9 8 7
+        5 3 8 7
+        3 0 8 7
+        5 4 8 1
+        4 6 8 1
+        2 9 5 8
+        4 2 5 8
+        4 2 9 5
+        6 2 4 8
+        9 2 0 8
+        2 6 0 8
+        2 4 9 1
+        2 6 4 1
+</pre>
+
+<p>is the Delaunay triangulation of 10 random points. Ridge 9-5-8
+occurs twice. Once for tetrahedron 9 5 8 7 and the other for
+tetrahedron 2 9 5 8. </p>
+
+<p>You can also use the Qhull library to generate the triangles.
+See "<a href="#ridges2">How</a> do I visit the ridges of a
+Delaunay triangulation?"</p>
+
+</blockquote><h4><a href="#TOC">&#187;</a><a name="3dd">How</a> do I construct a
+3-d Delaunay triangulation?</h4><blockquote>
+
+<p>For 3-d Delaunay triangulations with cospherical input sites,
+use triangulated output ('<a href="qh-optq.htm#Qt">Qt</a>') or
+joggled input  ('<a href="qh-optq.htm#QJn">QJ</a>').  Otherwise
+option 'i' will
+triangulate non-simplicial facets by adding a point to the facet.
+
+<p>If you want non-simplicial output for cospherical sites, use
+option
+'<a href="qh-optf.htm#Fv">Fv</a>' or '<a href="qh-opto.htm#o">o</a>'.
+For option 'o', ignore the last coordinate. It is the lifted
+coordinate for the corresponding convex hull in 4-d.
+
+<p>The following example is a cube
+inside a tetrahedron. The 8-vertex facet is the cube. Ignore the
+last coordinates. </p>
+
+<blockquote>
+    <pre>
+C:\qhull&gt;rbox r y c G0.1 | qdelaunay Fv
+4
+12 20 44
+   0.5      0      0 0.3055555555555555
+   0    0.5      0 0.3055555555555555
+   0      0    0.5 0.3055555555555555
+  -0.5   -0.5   -0.5 0.9999999999999999
+  -0.1   -0.1   -0.1 -6.938893903907228e-018
+  -0.1   -0.1    0.1 -6.938893903907228e-018
+  -0.1    0.1   -0.1 -6.938893903907228e-018
+  -0.1    0.1    0.1 -6.938893903907228e-018
+   0.1   -0.1   -0.1 -6.938893903907228e-018
+   0.1   -0.1    0.1 -6.938893903907228e-018
+   0.1    0.1   -0.1 -6.938893903907228e-018
+   0.1    0.1    0.1 -6.938893903907228e-018
+4 2 11 1 0
+4 10 1 0 3
+4 11 10 1 0
+4 2 9 0 3
+4 9 11 2 0
+4 7 2 1 3
+4 11 7 2 1
+4 8 10 0 3
+4 9 8 0 3
+5 8 9 10 11 0
+4 10 6 1 3
+4 6 7 1 3
+5 6 8 10 4 3
+5 6 7 10 11 1
+4 5 9 2 3
+4 7 5 2 3
+5 5 8 9 4 3
+5 5 6 7 4 3
+8 5 6 8 7 9 10 11 4
+5 5 7 9 11 2
+</pre>
+</blockquote>
+
+<p>If you want simplicial output use options
+'<a href="qh-optq.htm#Qt">Qt</a> <A
+ href="qh-optf.htm#Ft" >i</a>' or
+'<a href="qh-optq.htm#QJn">QJ</a> <A
+ href="qh-optf.htm#Ft" >i</a>', e.g.,
+</p>
+
+<blockquote>
+    <pre>
+rbox r y c G0.1 | qdelaunay Qt i
+31
+2 11 1 0
+11 10 1 0
+9 11 2 0
+11 7 2 1
+8 10 0 3
+9 8 0 3
+10 6 1 3
+6 7 1 3
+5 9 2 3
+7 5 2 3
+9 8 10 11
+8 10 11 0
+9 8 11 0
+6 8 10 4
+8 6 10 3
+6 8 4 3
+6 7 10 11
+10 6 11 1
+6 7 11 1
+8 5 4 3
+5 8 9 3
+5 6 4 3
+6 5 7 3
+5 9 10 11
+8 5 9 10
+7 5 10 11
+5 6 7 10
+8 5 10 4
+5 6 10 4
+5 9 11 2
+7 5 11 2
+</pre>
+</blockquote>
+
+</blockquote><h4><a href="#TOC">&#187;</a><a name="2d">How</a> do I get the
+triangles for a 2-d Delaunay triangulation and the vertices of
+its Voronoi diagram?</h4><blockquote>
+
+<p>To compute the Delaunay triangles indexed by the indices of
+the input sites, use </p>
+
+<blockquote>
+    <p>rbox 10 D2 | qdelaunay Qt i </p>
+</blockquote>
+
+<p>To compute the Voronoi vertices and the Voronoi region for
+each input site, use </p>
+
+<blockquote>
+    <p>rbox 10 D2 | qvoronoi o </p>
+</blockquote>
+
+<p>To compute each edge ("ridge") of the Voronoi
+diagram for each pair of adjacent input sites, use</p>
+
+<blockquote>
+    <p>rbox 10 D2 | qvoronoi Fv </p>
+</blockquote>
+
+<p>To compute the area and volume of the Voronoi region for input site 5 (site 0 is the first one),
+use </p>
+
+<blockquote>
+    <p>rbox 10 D2 | qvoronoi QV5 p | qconvex s FS </p>
+</blockquote>
+
+<p>To compute the lines ("hyperplanes") that define the
+Voronoi region for input site 5, use </p>
+
+<blockquote>
+    <p>rbox 10 D2 | qvoronoi QV5 p | qconvex n </p>
+</blockquote>
+or
+<blockquote>
+    <p>rbox 10 D2 | qvoronoi QV5 Fi Fo</p>
+</blockquote>
+
+<p>To list the extreme points of the input sites use </p>
+
+<blockquote>
+    <p>rbox 10 D2 | qdelaunay Fx </p>
+</blockquote>
+
+<p>You will get the same point ids with </p>
+
+<blockquote>
+    <p>rbox 10 D2 | qconvex Fx </p>
+</blockquote>
+
+</blockquote><h4><a href="#TOC">&#187;</a><a name="big">Can </a>Qhull triangulate
+a hundred 16-d points?</h4><blockquote>
+
+<p>No. This is an immense structure. A triangulation of 19, 16-d
+points has 43 simplices. If you add one point at a time, the
+triangulation increased as follows: 43, 189, 523, 1289, 2830,
+6071, 11410, 20487. The last triangulation for 26 points used 13
+megabytes of memory. When Qhull uses virtual memory, it becomes
+too slow to use. </p>
+
+</blockquote>
+<h2><a href="#TOC">&#187;</a><a name="voronoi">Voronoi
+diagram questions</a></h2>
+
+<h4><a href="#TOC">&#187;</a><a name="volume">How</a> do I compute the volume of a Voronoi region?</h4><blockquote>
+
+<p>For each Voronoi region, compute the convex hull of the region's Voronoi vertices.  The volume of each convex hull is the volume
+of the corresponding Vornoi region.</p>
+
+<p>For example, to compute the volume of the bounded Voronoi region about [0,0,0]: output the origin's Voronoi vertices and
+compute the volume of their convex hull.  The last number from option '<a href="qh-optf.htm#FS">FS</a>' is the volume.</p>
+<blockquote><pre>
+rbox P0 10 | qvoronoi QV0 p | qhull FS
+0
+2 1.448134756744281 0.1067973560800857
+</pre></blockquote>
+
+<p>For another example, see <a href="#2d">How</a> do I get the triangles for a 2-d Delaunay
+    triangulation and the vertices of its Voronoi diagram?</p>
+
+<p>This approach is slow if you are using the command line.  A faster approcach is to call Qhull from
+a program.  The fastest method is Clarkson's <a href="http://www.netlib.org/voronoi/hull.html">hull</a> program.
+It computes the volume for all Voronoi regions.</p>
+
+<p>An unbounded Voronoi region does not have a volume.</p>
+
+</blockquote><h4><a href="#TOC">&#187;</a><a name="maxsphere">How</a> do I get the radii of the empty
+                spheres for each Voronoi vertex?</h4><blockquote>
+
+Use option '<a href="qh-optf.htm#Fi">Fi</a>' to list each bisector (i.e. Delaunay ridge).  Then compute the
+minimum distance for each Voronoi vertex.
+
+<p>There's other ways to get the same information.   Let me know if you
+find a better method.
+
+</blockquote><h4><a href="#TOC">&#187;</a><a name="square">What</a> is the Voronoi diagram
+                            of a square?</h4><blockquote>
+
+<p>
+Consider a square,
+<blockquote><pre>
+C:\qhull&gt;rbox c D2
+2 RBOX c D2
+4
+  -0.5   -0.5
+  -0.5    0.5
+   0.5   -0.5
+   0.5    0.5
+</pre></blockquote>
+
+<p>There's two ways to compute the Voronoi diagram: with facet merging
+or with joggle.  With facet merging, the
+result is:
+
+<blockquote><pre>
+C:\qhull&gt;rbox c D2 | qvoronoi Qz
+
+Voronoi diagram by the convex hull of 5 points in 3-d:
+
+  Number of Voronoi regions and at-infinity: 5
+  Number of Voronoi vertices: 1
+  Number of facets in hull: 5
+
+Statistics for: RBOX c D2 | QVORONOI Qz
+
+  Number of points processed: 5
+  Number of hyperplanes created: 7
+  Number of distance tests for qhull: 8
+  Number of merged facets: 1
+  Number of distance tests for merging: 29
+  CPU seconds to compute hull (after input):  0
+
+C:\qhull&gt;rbox c D2 | qvoronoi Qz o
+2
+2 5 1
+-10.101 -10.101
+     0      0
+2 0 1
+2 0 1
+2 0 1
+2 0 1
+0
+
+C:\qhull&gt;rbox c D2 | qvoronoi Qz Fv
+4
+4 0 1 0 1
+4 0 2 0 1
+4 1 3 0 1
+4 2 3 0 1
+</pre></blockquote>
+
+<p>There is one Voronoi vertex at the origin and rays from the origin
+along each of the coordinate axes.
+The last line '4 2 3 0 1' means that there is
+a ray that bisects input points #2 and #3 from infinity (vertex 0) to
+the origin (vertex 1).
+Option 'Qz' adds an artificial point since the input is cocircular.
+Coordinates -10.101 indicate the
+vertex at infinity.
+
+<p>With triangulated output, the Voronoi vertex is
+duplicated:
+
+<blockquote><pre>
+C:\qhull3.1>rbox c D2 | qvoronoi Qt Qz
+
+Voronoi diagram by the convex hull of 5 points in 3-d:
+
+  Number of Voronoi regions and at-infinity: 5
+  Number of Voronoi vertices: 2
+  Number of triangulated facets: 1
+
+Statistics for: RBOX c D2 | QVORONOI Qt Qz
+
+  Number of points processed: 5
+  Number of hyperplanes created: 7
+  Number of facets in hull: 6
+  Number of distance tests for qhull: 8
+  Number of distance tests for merging: 33
+  Number of distance tests for checking: 30
+  Number of merged facets: 1
+  CPU seconds to compute hull (after input): 0.05
+
+C:\qhull3.1>rbox c D2 | qvoronoi Qt Qz o
+2
+3 5 1
+-10.101 -10.101
+     0      0
+     0      0
+3 2 0 1
+2 1 0
+2 2 0
+3 2 0 1
+0
+
+C:\qhull3.1>rbox c D2 | qvoronoi Qt Qz Fv
+4
+4 0 2 0 2
+4 0 1 0 1
+4 1 3 0 1
+4 2 3 0 2
+</pre></blockquote>
+
+
+<p>With joggle, the input is no longer cocircular and the Voronoi vertex is
+split into two:
+
+<blockquote><pre>
+C:\qhull&gt;rbox c D2 | qvoronoi Qt Qz
+
+C:\qhull&gt;rbox c D2 | qvoronoi QJ o
+2
+3 4 1
+-10.101 -10.101
+-4.71511718558304e-012 -1.775812830118184e-011
+9.020340030474472e-012 -4.02267108512433e-012
+2 0 1
+3 2 1 0
+3 2 0 1
+2 2 0
+
+C:\qhull&gt;rbox c D2 | qvoronoi QJ Fv
+5
+4 0 2 0 1
+4 0 1 0 1
+4 1 2 1 2
+4 1 3 0 2
+4 2 3 0 2
+</pre></blockquote>
+
+<p>Note that the Voronoi diagram includes the same rays as
+  before plus a short edge between the two vertices.</p>
+
+
+</blockquote><h4><a href="#TOC">&#187;</a><a name="vsphere">How</a> do I construct
+the Voronoi diagram of cospherical points?</h4><blockquote>
+
+<p>Three-d terrain data can be approximated with cospherical
+points. The Delaunay triangulation of cospherical points is the
+same as their convex hull. If the points lie on the unit sphere,
+the facet normals are the Voronoi vertices [via S. Fortune]. </p>
+
+<p>For example, consider the points {[1,0,0], [-1,0,0], [0,1,0],
+...}. Their convex hull is: </p>
+
+<pre>
+rbox d G1 | qconvex o
+3
+6 8 12
+     0      0     -1
+     0      0      1
+     0     -1      0
+     0      1      0
+    -1      0      0
+     1      0      0
+3 3 1 4
+3 1 3 5
+3 0 3 4
+3 3 0 5
+3 2 1 5
+3 1 2 4
+3 2 0 4
+3 0 2 5
+</pre>
+
+<p>The facet normals are: </p>
+
+<pre>
+rbox d G1 | qconvex n
+4
+8
+-0.5773502691896258  0.5773502691896258  0.5773502691896258 -0.5773502691896258
+ 0.5773502691896258  0.5773502691896258  0.5773502691896258 -0.5773502691896258
+-0.5773502691896258  0.5773502691896258 -0.5773502691896258 -0.5773502691896258
+ 0.5773502691896258  0.5773502691896258 -0.5773502691896258 -0.5773502691896258
+ 0.5773502691896258 -0.5773502691896258  0.5773502691896258 -0.5773502691896258
+-0.5773502691896258 -0.5773502691896258  0.5773502691896258 -0.5773502691896258
+-0.5773502691896258 -0.5773502691896258 -0.5773502691896258 -0.5773502691896258
+ 0.5773502691896258 -0.5773502691896258 -0.5773502691896258 -0.5773502691896258
+</pre>
+
+<p>If you drop the offset from each line (the last number), each
+line is the Voronoi vertex for the corresponding facet. The
+neighboring facets for each point define the Voronoi region for
+each point. For example: </p>
+
+<pre>
+rbox d G1 | qconvex FN
+6
+4 7 3 2 6
+4 5 0 1 4
+4 7 4 5 6
+4 3 1 0 2
+4 6 2 0 5
+4 7 3 1 4
+</pre>
+
+<p>The Voronoi vertices {7, 3, 2, 6} define the Voronoi region
+for point 0. Point 0 is [0,0,-1]. Its Voronoi vertices are </p>
+
+<pre>
+-0.5773502691896258  0.5773502691896258 -0.5773502691896258
+ 0.5773502691896258  0.5773502691896258 -0.5773502691896258
+-0.5773502691896258 -0.5773502691896258 -0.5773502691896258
+ 0.5773502691896258 -0.5773502691896258 -0.5773502691896258
+</pre>
+
+<p>In this case, the Voronoi vertices are oriented, but in
+general they are unordered. </p>
+
+<p>By taking the dual of the Delaunay triangulation, you can
+construct the Voronoi diagram. For cospherical points, the convex
+hull vertices for each facet, define the input sites for each
+Voronoi vertex. In 3-d, the input sites are oriented. For
+example: </p>
+
+<pre>
+rbox d G1 | qconvex i
+8
+3 1 4
+1 3 5
+0 3 4
+3 0 5
+2 1 5
+1 2 4
+2 0 4
+0 2 5
+</pre>
+
+<p>The convex hull vertices for facet 0 are {3, 1, 4}. So Voronoi
+vertex 0 (i.e., [-0.577, 0.577, 0.577]) is the Voronoi vertex for
+input sites {3, 1, 4} (i.e., {[0,1,0], [0,0,1], [-1,0,0]}). </p>
+
+</blockquote><h4><a href="#TOC">&#187;</a><a name="rays">Can</a> Qhull compute the
+unbounded rays of the Voronoi diagram?</h4><blockquote>
+
+<p>Use '<a href="qh-optf.htm#Fo2">Fo</a>' to compute the separating
+hyperplanes for unbounded Voronoi regions. The corresponding ray
+goes to infinity from the Voronoi vertices. If you enclose the
+input sites in a large enough box, the outermost bounded regions
+will represent the unbounded regions of the original points. </p>
+
+<p>If you do not box the input sites, you can identify the
+unbounded regions. They list '0' as a vertex. Vertex 0 represents
+"infinity". Each unbounded ray includes vertex 0 in
+option '<a href="qh-optf.htm#Fv2">Fv</a>. See <A
+ href="qvoronoi.htm#graphics" >Voronoi graphics</a> and <A
+ href="qvoronoi.htm#notes" >Voronoi notes</a>. </p>
+
+</blockquote>
+<h2><a href="#TOC">&#187;</a>Approximation questions</h2>
+
+<h4><a href="#TOC">&#187;</a><a name="simplex">How</a> do I
+approximate data with a simplex</h4><blockquote>
+
+<p>Qhull may be used to help select a simplex that approximates a
+data set. It will take experimentation. Geomview will help to
+visualize the results. This task may be difficult to do in 5-d
+and higher. Use rbox options 'x' and 'y' to produce random
+distributions within a simplex. Your methods work if you can
+recover the simplex. </p>
+
+<p>Use Qhull's precision options to get a first approximation to
+the hull, say with 10 to 50 facets. For example, try 'C0.05' to
+remove small facets after constructing the hull. Use 'W0.05' to
+ignore points within 0.05 of a facet. Use 'PA5' to print the five
+largest facets by area. </p>
+
+<p>Then use other methods to fit a simplex to this data. Remove
+outlying vertices with few nearby points. Look for large facets
+in different quadrants. You can use option 'Pd0d1d2' to print all
+the facets in a quadrant. </p>
+
+<p>In 4-d and higher, use the outer planes (option 'Fo' or
+'facet-&gt;maxoutside') since the hyperplane of an approximate
+facet may be below many of the input points. </p>
+
+<p>For example, consider fitting a cube to 1000 uniformly random
+points in the unit cube. In this case, the first try was good: </p>
+
+<blockquote>
+    <pre>
+rbox 1000 | qconvex W0.05 C0.05 PA6 Fo
+4
+6
+0.35715408374381 0.08706467018177928 -0.9299788727015564 -0.5985514741284483
+0.995841591359023 -0.02512604712761577 0.08756829720435189 -0.5258834069202866
+0.02448099521570909 -0.02685210459017302 0.9993396046151313 -0.5158104982631999
+-0.9990223929415094 -0.01261133513150079 0.04236994958247349 -0.509218270408407
+-0.0128069014364698 -0.9998380680115362 0.01264203427283151 -0.5002512653670584
+0.01120895057872914 0.01803671994177704 -0.9997744926535512 -0.5056824072956361
+</pre>
+</blockquote>
+
+</blockquote>
+<h2><a href="#TOC">&#187;</a>Halfspace questions</h2>
+
+<h4><a href="#TOC">&#187;</a><a name="halfspace">How</a> do I compute the
+                            intersection of halfspaces with Qhull?</h4><blockquote>
+
+<p>Qhull computes the halfspace intersection about a point.  The
+point must be inside all of the halfspaces.  Given a point, a
+duality turns a halfspace intersection problem into a convex
+hull problem.
+
+<p>Use linear programming if you
+do not know a point in the interior of the halfspaces.
+See the <a href="qhalf.htm#notes">notes</a> for qhalf. You will need
+  a linear programming code. This may require a fair amount of work to
+  implement.</p>
+
+
+
+</blockquote>
+<h2><a href="#TOC">&#187;</a><a name="library">Qhull library
+questions</a></h2>
+
+<h4><a href="#TOC">&#187;</a><a name="math">Is</a> Qhull available for Mathematica, Matlab, or Maple?</h4><blockquote>
+
+<p><b>MATLAB</b>
+
+<p>Z. You of <a href="http://www.mathworks.com">MathWorks</a> added qhull to MATLAB 6.
+See functions <a href="http://www.mathworks.com/help/techdoc/ref/convhulln.html"
+ >convhulln</a>,
+        <a href="http://www.mathworks.com/help/techdoc/ref/delaunayn.html"
+ >delaunayn</a>,
+        <a href="http://www.mathworks.com/help/techdoc/ref/griddata3.html"
+ >griddata3</a>,
+        <a href="http://www.mathworks.com/help/techdoc/ref/griddatan.html"
+ >griddatan</a>,
+        <a href="http://www.mathworks.com/help/techdoc/ref/tsearch.html"
+ >tsearch</a>,
+        <a href="http://www.mathworks.com/help/techdoc/ref/tsearchn.html"
+ >tsearchn</a>, and
+    <a href="http://www.mathworks.com/help/techdoc/ref/voronoin.html"
+ >voronoin</a>.  V. Brumberg update MATLAB R14 for Qhull 2003.1 and triangulated output.
+
+<p>Engwirda wrote <a href="http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objectId=10307&objectType=file">mesh2d</a> for unstructured mesh generation in MATLAB.
+It is based on the iterative method of Persson and generally results in better quality meshes than delaunay refinement.
+
+
+<p><b>Mathematica and Maple</b>
+
+<p>See <a href="http://library.wolfram.com/infocenter/MathSource/1160/"
+ >qh-math</a>
+for a Delaunay interface to Mathematica.  It includes projects for CodeWarrior
+on the Macintosh and Visual C++ on Win32 PCs.
+
+<p>See  Mathematica ('<a
+href="qh-opto.htm#m">m</a>') and Maple ('<a
+href="qh-optf.htm#FM">FM</a>') output options.
+
+<p></p>
+</blockquote><h4><a href="#TOC">&#187;</a><a name="ridges">Why</a> are there too few ridges?</h4><blockquote>
+
+The following sample code may produce fewer ridges than expected:
+
+<blockquote><pre>
+  facetT *facetp;
+  ridgeT *ridge, **ridgep;
+
+  FORALLfacets {
+    printf("facet f%d\n", facet->id);
+    FOREACHridge_(facet->ridges) {
+      printf("   ridge r%d between f%d and f%d\n", ridge->id, ridge->top->id, ridge->bottom->id);
+    }
+  }
+</pre></blockquote>
+
+<p>  Qhull does not create ridges for  simplicial facets.
+Instead it computes ridges from  facet-&gt;neighbors. To make ridges for a
+simplicial facet, use qh_makeridges() in  merge.c. Usefacet-&gt;visit_id to visit
+each ridge once (instead of twice).  For example,
+
+<blockquote><pre>
+  facetT *facet, *neighbor;
+  ridgeT *ridge, **ridgep;
+
+  qh visit_id++;
+  FORALLfacets {
+    printf("facet f%d\n", facet->id);
+    qh_makeridges(facet);
+    facet->visitId= qh visit_id;
+    FOREACHridge_(facet->ridges) {
+        neighbor= otherfacet_(ridge, visible);
+        if (neighbor->visitid != qh visit_id)
+            printf("   ridge r%d between f%d and f%d\n", ridge->id, ridge->top->id, ridge->bottom->id);
+    }
+  }
+</pre></blockquote>
+
+</blockquote><h4><a href="#TOC">&#187;</a><a name="call">Can</a> Qhull use coordinates without placing
+                        them in a data file?</h4><blockquote>
+
+<p>You may call Qhull from a program.  Please use the reentrant Qhull library (libqhullstatic_r.a, libqhull_r.so, or qhull_r.dll).
+
+See user_eg.c and "Qhull-template" in user_r.c for examples..
+
+See <a href="qh-code.htm">Qhull internals</a> for an introduction to Qhull's reentrant library and its C++ interface.
+
+<p>Hint: Start with a small example for which you know the
+  answer.</p>
+
+</blockquote><h4><a href="#TOC">&#187;</a><a name="size">How</a> large are Qhull's data structures?</h4><blockquote>
+
+<p>Qhull uses a general-dimension data structure.
+The size depends on the dimension.  Use option 'Ts' to print
+out the memory statistics [e.g., 'rbox D2 10 | qconvex Ts'].
+
+
+</blockquote><h4><a href="#TOC">&#187;</a><a name="inc">Can</a> Qhull construct
+convex hulls and Delaunay triangulations one point at a time?</h4><blockquote>
+
+<p>The Qhull library may be used to construct convex hulls and
+Delaunay triangulations one point at a time. It may not be used
+for deleting points or moving points. </p>
+
+<p>Qhull is designed for batch processing. Neither Clarkson's
+randomized incremental algorithm nor Qhull are designed for
+on-line operation. For many applications, it is better to
+reconstruct the convex hull or Delaunay triangulation from
+scratch for each new point. </p>
+
+<p>With random point sets and on-line processing, Clarkson's
+algorithm should run faster than Qhull. Clarkson uses the
+intermediate facets to reject new, interior points, while Qhull,
+when used on-line, visits every facet to reject such points. If
+used on-line for n points, Clarkson may take O(n) times as much
+memory as the average off-line case, while Qhull's space
+requirement does not change. </p>
+
+<p>If you triangulate the output before adding all the points
+(option 'Qt' and procedure qh_triangulate), you must set
+option '<a href="qh-optq.htm#Q11">Q11</a>'.  It duplicates the
+normals of triangulated facets and recomputes the centrums.
+This should be avoided for regular use since triangulated facets
+are not clearly convex with their neighbors.  It appears to
+work most of the time, but fails for cases that Qhull normally
+handles well [see the test call to qh_triangulate in qh_addpoint].
+
+</blockquote><h4><a href="#TOC">&#187;</a><a name="ridges2">How</a> do I visit the
+ridges of a Delaunay triangulation?</h4><blockquote>
+
+<p>To visit the ridges of a Delaunay triangulation, visit each
+facet. Each ridge will appear twice since it belongs to two
+facets. In pseudo-code: </p>
+
+<pre>
+    for each facet of the triangulation
+        if the facet is Delaunay (i.e., part of the lower convex hull)
+            for each ridge of the facet
+                if the ridge's neighboring facet has not been visited
+                    ... process a ridge of the Delaunay triangulation ...
+</pre>
+
+<p>In undebugged, C code: </p>
+
+<pre>
+    qh visit_id++;
+    FORALLfacets_(facetlist)
+        if (!facet-&gt;upperdelaunay) {
+            facet-&gt;visitid= qh visit_id;
+            qh_makeridges(facet);
+            FOREACHridge_(facet-&gt;ridges) {
+                neighbor= otherfacet_(ridge, facet);
+                if (neighbor-&gt;visitid != qh visit_id) {
+                    /* Print ridge here with facet-id and neighbor-id */
+                    /*fprintf(fp, "f%d\tf%d\t",facet-&gt;id,neighbor-&gt;ID);*/
+                    FOREACHvertex_(ridge-&gt;vertices)
+                        fprintf(fp,"%d ",qh_pointid (vertex-&gt;point) );
+                    qh_printfacetNvertex_simplicial (fp, facet, format);
+                    fprintf(fp," ");
+                    if(neighbor-&gt;upperdelaunay)
+                        fprintf(fp," -1 -1 -1 -1 ");
+                    else
+                        qh_printfacetNvertex_simplicial (fp, neighbor, format);
+                    fprintf(fp,"\n");
+                }
+            }
+        }
+    }
+</pre>
+
+<p>Qhull should be redesigned as a class library, or at least as
+an API. It currently provides everything needed, but the
+programmer has to do a lot of work. Hopefully someone will write
+C++ wrapper classes or a Python module for Qhull. </p>
+
+</blockquote><h4><a href="#TOC">&#187;</a><a name="listd">How</a> do I visit the
+Delaunay regions?</h4><blockquote>
+
+<p>Qhull constructs a Delaunay triangulation by lifting the
+input sites to a paraboloid. The Delaunay triangulation
+corresponds to the lower convex hull of the lifted points. To
+visit each facet of the lower convex hull, use: </p>
+
+<pre>
+    facetT *facet;
+
+    ...
+    FORALLfacets {
+        if (!facet-&gt;upperdelaunay) {
+            ... only facets for Delaunay regions ...
+        }
+    }
+</pre>
+
+</blockquote><h4><a href="#TOC">&#187;</a><a name="outside">When</a> is a point
+outside or inside a facet?</h4><blockquote>
+
+<p>A point is outside of a facet if it is clearly outside the
+facet's outer plane. The outer plane is defined by an offset
+(facet-&gt;maxoutside) from the facet's hyperplane. </p>
+
+<pre>
+    facetT *facet;
+    pointT *point;
+    realT dist;
+
+    ...
+    qh_distplane(point, facet, &amp;dist);
+    if (dist &gt; facet-&gt;maxoutside + 2 * qh DISTround) {
+        /* point is clearly outside of facet */
+    }
+</pre>
+
+<p>A point is inside of a facet if it is clearly inside the
+facet's inner plane. The inner plane is computed as the maximum
+distance of a vertex to the facet. It may be computed for an
+individual facet, or you may use the maximum over all facets. For
+example: </p>
+
+<pre>
+    facetT *facet;
+    pointT *point;
+    realT dist;
+
+    ...
+    qh_distplane(point, facet, &amp;dist);
+    if (dist &lt; qh min_vertex - 2 * qh DISTround) {
+        /* point is clearly inside of facet */
+    }
+</pre>
+
+<p>Both tests include two qh.DISTrounds because the computation
+of the furthest point from a facet may be off by qh.DISTround and
+the computation of the current distance to the facet may be off
+by qh.DISTround. </p>
+
+</blockquote><h4><a href="#TOC">&#187;</a><a name="closest">How</a> do I find the
+facet that is closest to a point?</h4><blockquote>
+
+<p>Use qh_findbestfacet(). For example, </p>
+
+<pre>
+    coordT point[ DIM ];
+    boolT isoutside;
+    realT bestdist;
+    facetT *facet;
+
+    ... set coordinates for point ...
+
+    facet= qh_findbestfacet (point, qh_ALL, &amp;bestdist, &amp;isoutside);
+
+    /* 'facet' is the closest facet to 'point' */
+</pre>
+
+<p>qh_findbestfacet() performs a directed search for the facet
+furthest below the point. If the point lies inside this facet,
+qh_findbestfacet() performs an exhaustive search of all facets.
+An exhaustive search may be needed because a facet on the far
+side of a lens-shaped distribution may be closer to a point than
+all of the facet's neighbors. The exhaustive search may be
+skipped for spherical distributions. </p>
+
+<p>Also see, "<a href="#vclosest">How</a> do I find the
+Delaunay triangle that is closest to a
+point?" </p>
+
+</blockquote><h4><a href="#TOC">&#187;</a><a name="vclosest">How</a> do I find the
+Delaunay triangle or Voronoi region that is closest to a point?</h4><blockquote>
+
+<p>A Delaunay triangulation subdivides the plane, or in general
+dimension, subdivides space.  Given a point, how do you determine
+the subdivision containing the point?  Or, given a set of points,
+how do you determine the subdivision containing each point of the set?
+Efficiency is important -- an exhaustive search of the subdivision
+is too slow.
+
+<p>First compute the Delaunay triangle with qh_new_qhull() in user_r.c or Qhull::runQhull().
+Lift the point to the paraboloid by summing the squares of the
+coordinates. Use qh_findbestfacet() [poly2.c] to find the closest Delaunay
+triangle. Determine the closest vertex to find the corresponding
+Voronoi region.  Do not use options
+'<a href="qh-optq.htm#Qbb">Qbb</a>', '<a href="qh-optq.htm#QbB">QbB</a>',
+'<a href="qh-optq.htm#Qbk">Qbk:n</a>', or '<A
+ href="qh-optq.htm#QBk" >QBk:n</a>' since these scale the last
+coordinate.  Optimizations of qh_findbestfacet() should
+be possible for Delaunay triangulations.</p>
+
+<p>You first need to lift the point to the paraboloid (i.e., the
+last coordinate is the sum of the squares of the point's coordinates).
+The
+routine, qh_setdelaunay() [geom2.c], lifts an array of points to the
+paraboloid. The following excerpt is from findclosest() in
+user_eg.c. </p>
+
+<pre>
+    coordT point[ DIM + 1];  /* one extra coordinate for lifting the point */
+    boolT isoutside;
+    realT bestdist;
+    facetT *facet;
+
+    ... set coordinates for point[] ...
+
+    qh_setdelaunay (DIM+1, 1, point);
+    facet= qh_findbestfacet (point, qh_ALL, &amp;bestdist, &amp;isoutside);
+    /* 'facet' is the closest Delaunay triangle to 'point' */
+</pre>
+
+<p>The returned facet either contains the point or it is the
+closest Delaunay triangle along the convex hull of the input set.
+
+<p>Point location is an active research area in Computational
+Geometry.  For a practical approach, see Mucke, et al, "Fast randomized
+point location without preprocessing in two- and
+three-dimensional Delaunay triangulations," <i>Computational
+Geometry '96</i>, p. 274-283, May 1996.
+For an introduction to planar point location see [O'Rourke '93].
+Also see, "<A
+ href="#closest" >How</a> do I find the facet that is closest to a
+point?" </p>
+
+<p>To locate the closest Voronoi region, determine the closest
+vertex of the closest Delaunay triangle. </p>
+
+<pre>
+    realT dist, bestdist= REALmax;
+        vertexT *bestvertex= NULL, *vertex, **vertexp;
+
+    /* 'facet' is the closest Delaunay triangle to 'point' */
+
+    FOREACHvertex_( facet-&gt;vertices ) {
+        dist= qh_pointdist( point, vertex-&gt;point, DIM );
+        if (dist &lt; bestdist) {
+            bestdist= dist;
+            bestvertex= vertex;
+        }
+    }
+    /* 'bestvertex' represents the Voronoi region closest to 'point'.  The corresponding
+       input site is 'bestvertex-&gt;point' */
+</pre>
+
+</blockquote><h4><a href="#TOC">&#187;</a><a name="vertices">How</a> do I list the
+vertices?</h4><blockquote>
+
+<p>To list the vertices (i.e., extreme points) of the convex hull
+use </p>
+
+<blockquote>
+    <pre>
+    vertexT *vertex;
+
+    FORALLvertices {
+      ...
+      // vertex-&gt;point is the coordinates of the vertex
+      // qh_pointid(vertex-&gt;point) is the point ID of the vertex
+      ...
+    }
+    </pre>
+</blockquote>
+
+</blockquote><h4><a href="#TOC">&#187;</a><a name="test">How</a> do I test code
+that uses the Qhull library?</h4><blockquote>
+
+<p>Compare the output from your program with the output from the
+Qhull program. Use option 'T1' or 'T4' to trace what Qhull is
+doing. Prepare a <i>small</i> example for which you know the
+output. Run the example through the Qhull program and your code.
+Compare the trace outputs. If you do everything right, the two
+trace outputs should be almost the same. The trace output will
+also guide you to the functions that you need to review. </p>
+
+</blockquote><h4><a href="#TOC">&#187;</a><a name="orient">When</a> I compute a
+plane equation from a facet, I sometimes get an outward-pointing
+normal and sometimes an inward-pointing normal</h4><blockquote>
+
+<p>Qhull orients simplicial facets, and prints oriented output
+for 'i', 'Ft', and other options. The orientation depends on <i>both</i>
+the vertex order and the flag facet-&gt;toporient.</p>
+
+<p>Qhull does not orient
+  non-simplicial facets. Instead it orients the facet's ridges. These are
+  printed with the 'Qt' and 'Ft' option. The facet's hyperplane is oriented.  </p>
+
+</blockquote>
+<hr><!-- Navigation links -->
+
+<p><a><b>Up:</b> </a><a
+ href="http://www.qhull.org">Home page for Qhull</a><br>
+<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents <br>
+<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
+&#149; <a href="qh-quick.htm#options">Options</a>
+&#149; <a href="qh-opto.htm#output">Output</a>
+&#149; <a href="qh-optf.htm#format">Formats</a>
+&#149; <a href="qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="qh-optp.htm#print">Print</a>
+&#149; <a href="qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="qh-optc.htm#prec">Precision</a>
+&#149; <a href="qh-optt.htm#trace">Trace</a>
+&#149; <a href="../src/libqhull_r/index.htm">Functions</a><br>
+<b>To:</b> <a href="#TOC">FAQ: Table of Contents</a><br><!-- GC common information -->
+
+<hr>
+
+<p><a href="http://www.geom.uiuc.edu/"><IMG align=middle
+ height=40 src="qh--geom.gif" width=40 ></a><i>The Geometry Center
+Home Page </i></p>
+
+<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
+</a><br>
+Created:
+Sept. 25, 1995 --- <!-- hhmts start -->Last modified: see top
+<!-- hhmts end --> </p>
+</body>
+</html>
diff --git a/xs/src/qhull/html/qh-get.htm b/xs/src/qhull/html/qh-get.htm
new file mode 100644
index 0000000000..c39ed22564
--- /dev/null
+++ b/xs/src/qhull/html/qh-get.htm
@@ -0,0 +1,106 @@
+<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN">
+<html>
+
+<head>
+<title>Qhull Downloads</title>
+</head>
+
+<body>
+<!-- Navigation links -->
+<p><b>Up:</b> <a href="http://www.qhull.org"><i>Qhull Home Page</i></a><br>
+</p>
+
+<hr>
+
+<h1><a
+href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/cone.html"><img
+src="../html/qh--cone.gif" alt="[CONE]" align="middle"
+width="100" height="100"></a> Qhull Downloads</h1>
+
+<ul>
+    <li><a href="http://www.qhull.org">Qhull Home Page</a> <p>Qhull
+        computes the convex hull, Delaunay triangulation, Voronoi diagram, halfspace
+        intersection about a point, furthest-site Delaunay
+        triangulation, and furthest-site Voronoi diagram. It
+        runs in 2-d, 3-d, 4-d, and higher dimensions. It
+        implements the Quickhull algorithm for computing the
+        convex hull. Qhull handles roundoff errors from floating
+        point arithmetic. It can approximate a convex hull. </p>
+
+        <p>Visit <a href="http://www.qhull.org/news">Qhull News</a>
+        for news, bug reports, change history, and users.
+        If you use Qhull 2003.1 or 2009.1, please upgrade to 2015.2 or apply
+        <a href="http://www.qhull.org/download/poly.c-qh_gethash.patch">poly.c-qh_gethash.patch</a>.</p>
+        </li>
+    <li><a
+        href="http://www.qhull.org/download/qhull-2015.2.zip">Download:
+        Qhull 2015.2 for Windows 10, 8, 7, XP, and NT</a> (2.6 MB,
+        <a href="http://www.qhull.org/README.txt">readme</a>,
+        <a href="http://www.qhull.org/download/qhull-2015.2.md5sum">md5sum</a>,
+        <a href="http://www.qhull.org/download/qhull-2015.2.zip.md5sum">contents</a>)
+        <p>Type: console programs for Windows (32- or 64-bit)</p>
+        <p>Includes 32-bit executables, documentation, and sources files. It runs in a
+        command window.  Qhull may be compiled for 64-bits.</p>
+    </li>
+    <li><a href="http://github.com/qhull/qhull/wiki">GitHub Qhull</a> (git@github.com:qhull/qhull.git)
+        <p>Type: git repository for Qhull.  See recent <a href="https://github.com/qhull/qhull/blob/master/src/Changes.txt">Changes.txt</a></p>
+        <p>Includes documentation, source files, C++ interface, and test programs.  It builds with gcc, mingw,
+        CMake, DevStudio, and Qt Creator.
+       </p>
+    </li>
+    <li><a href="http://www.qhull.org/download/qhull-2015-src-7.2.0.tgz">Download: Qhull 2015.2 for Unix</a> (1.0 MB,
+        <a href="http://www.qhull.org/README.txt">readme</a>,
+        <a href="http://www.qhull.org/download/qhull-2015.2.md5sum">md5sum</a>,
+        <a href="http://www.qhull.org/download/qhull-2015-src-7.2.0.tgz.md5sum">contents</a>)
+        <p>Type: C/C++ source code for 32-bit and 64-bit architectures.  See <a href="http://www.qhull.org/src/Changes.txt">Changes.txt</a></p>
+        <p>Includes documentation, source files, Makefiles, CMakeLists.txt, DevStudio projects, and Qt projects.
+            Includes preliminary C++ support.</p>
+        <p>Download and search sites for pre-built packages include
+           <ul>
+           <li><a href="https://launchpad.net/ubuntu/+source/qhull">https://launchpad.net/ubuntu/+source/qhull</a>
+           <li><a href="http://software.opensuse.org/download.html?project=openSUSE%3AFactory&package=qhull">http://software.opensuse.org/download.html?project=openSUSE%3AFactory&package=qhull</a>
+           <li><a href="https://www.archlinux.org/packages/extra/i686/qhull/">https://www.archlinux.org/packages/extra/i686/qhull/</a>
+           <li><a href="http://rpmfind.net/linux/rpm2html/search.php?query=qhull">http://rpmfind.net/linux/rpm2html/search.php?query=qhull</a>
+           <li><a href="http://rpm.pbone.net/index.php3/stat/3/srodzaj/1/search/qhull">http://rpm.pbone.net/index.php3/stat/3/srodzaj/1/search/qhull</a>
+         </ul></p>
+    </li>
+
+    <li><a
+        href="http://dl.acm.org/author_page.cfm?id=81100129162">Download:
+        Article about Qhull</a> (307K)
+        <p>Type: PDF on ACM Digital Library (from this page only)</p>
+        <p>Barber, C.B., Dobkin, D.P., and Huhdanpaa, H.T.,
+        &quot;The Quickhull algorithm for convex hulls,&quot; <i>ACM
+        Transactions on Mathematical Software</i>, 22(4):469-483, Dec 1996 [<a
+        href="http://portal.acm.org/citation.cfm?doid=235815.235821">abstract</a>].</p>
+    </li>
+
+    <li><a
+        href="http://www.qhull.org/download/qhull-1.0.tar.gz">Download:
+        Qhull version 1.0</a> (92K) <p>Type: C source code for
+        32-bit architectures </p>
+        <p>Version 1.0 is a fifth the size of version 2.4. It
+        computes convex hulls and Delaunay triangulations. If a
+        precision error occurs, it stops with an error message.
+        It reports an initialization error for inputs made with
+        0/1 coordinates. </p>
+        <p>Version 1.0 compiles on a PC with Borland C++ 4.02 for
+        Win32 and DOS Power Pack. The options for rbox are
+        &quot;bcc32 -WX -w- -O2-e -erbox -lc rbox.c&quot;. The
+        options for qhull are the same. [D. Zwick] </p>
+    </li>
+</ul>
+<!-- Navigation links -->
+<hr>
+
+<p><b>Up:</b> <a href="http://www.qhull.org"><i>Qhull Home Page</i></a><br>
+<!-- GC common information --></p>
+
+<hr>
+
+<p><a href="http://www.geom.uiuc.edu/"><img src="../html/qh--geom.gif" alt="[HOME]"
+align="middle"></a> <i>The Geometry Center Home Page</i> </p>
+
+<p>Comments to: <a href="mailto:qhull@qhull.org">qhull@qhull.org</a><br>
+</body>
+</html>
diff --git a/xs/src/qhull/html/qh-impre.htm b/xs/src/qhull/html/qh-impre.htm
new file mode 100644
index 0000000000..cfbe0acb82
--- /dev/null
+++ b/xs/src/qhull/html/qh-impre.htm
@@ -0,0 +1,826 @@
+<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN">
+<html>
+
+<head>
+<title>Imprecision in Qhull</title>
+</head>
+
+<body>
+<!-- Navigation links -->
+<p><a name="TOP"><b>Up:</b></a> <a href="http://www.qhull.org">Home
+page</a> for Qhull <br>
+<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of
+Contents<br>
+<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
+&#149; <a href="qh-quick.htm#options">Options</a>
+&#149; <a href="qh-opto.htm#output">Output</a>
+&#149; <a href="qh-optf.htm#format">Formats</a>
+&#149; <a href="qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="qh-optp.htm#print">Print</a>
+&#149; <a href="qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="qh-optc.htm#prec">Precision</a>
+&#149; <a href="qh-optt.htm#trace">Trace</a>
+&#149; <a href="../src/libqhull_r/index.htm">Functions</a><br>
+<b>To: </b><a href="#TOC">Qhull imprecision</a>: Table of Contents
+(please wait while loading)
+
+<hr>
+<!-- Main text of document -->
+<h1><a
+href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/4dcube.html"><img
+src="qh--4d.gif" alt="[4-d cube]" align="middle" width="100"
+height="100"></a> Imprecision in Qhull</h1>
+
+<p>This section of the Qhull manual discusses the problems caused
+by coplanar points and why Qhull uses options '<a
+href="qh-optc.htm#C0">C-0</a>' or '<a href="qh-optq.htm#Qx">Qx</a>'
+by default. If you ignore precision issues with option '<a
+href="qh-optq.htm#Q0">Q0</a>', the output from Qhull can be
+arbitrarily bad. Qhull avoids precision problems if you merge facets (the default) or joggle
+the input ('<a
+href="qh-optq.htm#QJn">QJ</a>'). </p>
+
+<p>Use option '<a href="qh-optt.htm#Tv">Tv</a>' to verify the
+output from Qhull. It verifies that adjacent facets are clearly
+convex. It verifies that all points are on or below all facets. </p>
+
+<p>Qhull automatically tests for convexity if it detects
+precision errors while constructing the hull. </p>
+
+<p><b>Copyright &copy; 1995-2015 C.B. Barber</b></p>
+
+<hr>
+
+<h2><a href="#TOP">&#187;</a><a name="TOC">Qhull
+imprecision: Table of Contents </a></h2>
+
+<ul>
+    <li><a href="#prec">Precision problems</a></li>
+    <li><a href="#joggle">Merged facets or joggled input</a></li>
+    <li><a href="#delaunay">Delaunay triangulations</a></li>
+    <li><a href="#halfspace">Halfspace intersection/a></li>
+    <li><a href="#imprecise">Merged facets</a></li>
+    <li><a href="#how">How Qhull merges facets</a></li>
+    <li><a href="#limit">Limitations of merged facets</a></li>
+    <li><a href="#injoggle">Joggled input</a></li>
+    <li><a href="#exact">Exact arithmetic</a></li>
+    <li><a href="#approximate">Approximating a convex hull</a></li>
+</ul>
+
+<hr>
+
+<h2><a href="#TOC">&#187;</a><a name="prec">Precision problems</a></h2>
+
+<p>Since Qhull uses floating point arithmetic, roundoff error
+occurs with each calculation. This causes problems for
+geometric algorithms. Other floating point codes for convex
+hulls, Delaunay triangulations, and Voronoi diagrams also suffer
+from these problems.  Qhull handles most of them.</p>
+
+<p>There are several kinds of precision errors:</p>
+
+<ul>
+    <li>Representation error occurs when there are not enough
+        digits to represent a number, e.g., 1/3.</li>
+    <li>Measurement error occurs when the input coordinates are
+        from measurements. </li>
+    <li>Roundoff error occurs when a calculation is rounded to a
+        fixed number of digits, e.g., a floating point
+        calculation.</li>
+    <li>Approximation error occurs when the user wants an
+        approximate result because the exact result contains too
+        much detail.</li>
+</ul>
+
+<p>Under imprecision, calculations may return erroneous results.
+For example, roundoff error can turn a small, positive number
+into a small, negative number. See Milenkovic [<a
+href="index.htm#mile93">'93</a>] for a discussion of <em>strict
+robust geometry</em>. Qhull does not meet Milenkovic's criterion
+for accuracy. Qhull's error bound is empirical instead of
+theoretical.</p>
+
+<p>Qhull 1.0 checked for precision errors but did not handle
+them. The output could contain concave facets, facets with
+inverted orientation (&quot;flipped&quot; facets), more than two
+facets adjacent to a ridge, and two facets with exactly the same
+set of vertices.</p>
+
+<p>Qhull 2.4 and later automatically handles errors due to
+machine round-off. Option '<a href="qh-optc.htm#C0">C-0</a>' or '<a
+href="qh-optq.htm#Qx">Qx</a>' is set by default. In 5-d and
+higher, the output is clearly convex but an input point could be
+outside of the hull. This may be corrected by using option '<a
+href="qh-optc.htm#C0">C-0</a>', but then the output may contain
+wide facets.</p>
+
+<p>Qhull 2.5 and later provides option '<a href="qh-optq.htm#QJn">QJ</a>'
+to joggled input. Each input coordinate is modified by a
+small, random quantity. If a precision error occurs, a larger
+modification is tried. When no precision errors occur, Qhull is
+done. </p>
+
+<p>Qhull 3.1 and later provides option '<a href="qh-optq.htm#Qt">Qt</a>'
+for triangulated output.  This removes the need for
+joggled input ('<a href="qh-optq.htm#QJn">QJ</a>').
+Non-simplicial facets are triangulated.
+The facets may have zero area.
+Triangulated output is particularly useful for Delaunay triangulations.</p>
+
+<p>By handling round-off errors, Qhull can provide a variety of
+output formats. For example, it can return the halfspace that
+defines each facet ('<a href="qh-opto.htm#n">n</a>'). The
+halfspaces include roundoff error. If the halfspaces were exact,
+their intersection would return the original extreme points. With
+imprecise halfspaces and exact arithmetic, nearly incident points
+may be returned for an original extreme point. By handling
+roundoff error, Qhull returns one intersection point for each of
+the original extreme points. Qhull may split or merge an extreme
+point, but this appears to be unlikely.</p>
+
+<p>The following pipe implements the identity function for
+extreme points (with roundoff):
+<blockquote>
+    qconvex <a href="qh-optf.htm#FV">FV</a> <a
+    href="qh-opto.htm#n">n</a> | qhalf <a href="qh-optf.htm#Fp">Fp</a>
+</blockquote>
+
+<p>Bernd Gartner published his
+<a href=http://www.inf.ethz.ch/personal/gaertner/miniball.html>Miniball</a>
+algorithm ["Fast and robust smallest enclosing balls", <i>Algorithms - ESA '99</i>, LNCS 1643].
+It uses floating point arithmetic and a carefully designed primitive operation.
+It is practical to 20-D or higher, and identifies at least two points on the
+convex hull of the input set.  Like Qhull, it is an incremental algorithm that
+processes points furthest from the intermediate result and ignores
+points that are close to the intermediate result.
+
+<h2><a href="#TOC">&#187;</a><a name="joggle">Merged facets or joggled input</a></h2>
+
+<p>This section discusses the choice between merged facets and joggled input.
+By default, Qhull uses merged facets to handle
+precision problems. With option '<a href="qh-optq.htm#QJn">QJ</a>',
+the input is joggled. See <a href="qh-eg.htm#joggle">examples</a>
+of joggled input and triangulated output.
+<ul>
+<li>Use merged facets (the default)
+when you want non-simplicial output (e.g., the faces of a cube).
+<li>Use merged facets and triangulated output ('<a href="qh-optq.htm#Qt">Qt</a>') when
+you want simplicial output and coplanar facets (e.g., triangles for a Delaunay triangulation).
+<li>Use joggled input ('<a href="qh-optq.htm#QJn">QJ</a>') when you need clearly-convex,
+simplicial output.
+</ul>
+
+<p>The choice between merged facets and joggled input depends on
+the application. Both run about the same speed. Joggled input may
+be faster if the initial joggle is sufficiently large to avoid
+precision errors.
+
+<p>Most applications should used merged facets
+with triangulated output. </p>
+
+<p>Use merged facets (the
+default, '<a href="qh-optc.htm#C0">C-0</a>')
+or triangulated output ('<a href="qh-optq.htm#Qt">Qt</a>') if </p>
+
+<ul>
+    <li>Your application supports non-simplicial facets, or
+    it allows degenerate, simplicial facets (option '<a href="qh-optq.htm#Qt">Qt</a>'). </li>
+    <li>You do not want the input modified. </li>
+    <li>You want to set additional options for approximating the
+        hull. </li>
+    <li>You use single precision arithmetic (<a href="../src/libqhull/user.h#realT">realT</a>).
+    </li>
+</ul>
+
+<p>Use joggled input ('<a href="qh-optq.htm#QJn">QJ</a>') if </p>
+
+<ul>
+    <li>Your application needs clearly convex, simplicial output</li>
+    <li>Your application supports perturbed input points and narrow triangles.</li>
+    <li>Seven significant digits is sufficient accuracy.</li>
+</ul>
+
+<p>You may use both techniques or combine joggle with
+post-merging ('<a href="qh-optc.htm#Cn2">Cn</a>'). </p>
+
+<p>Other researchers have used techniques similar to joggled
+input. Sullivan and Beichel [ref?] randomly perturb the input
+before computing the Delaunay triangulation. Corkum and Wyllie
+[news://comp.graphics, 1990] randomly rotate a polytope before
+testing point inclusion. Edelsbrunner and Mucke [Symp. Comp.
+Geo., 1988] and Yap [J. Comp. Sys. Sci., 1990] symbolically
+perturb the input to remove singularities. </p>
+
+<p>Merged facets ('<a href="qh-optc.htm#C0">C-0</a>') handles
+precision problems directly. If a precision problem occurs, Qhull
+merges one of the offending facets into one of its neighbors.
+Since all precision problems in Qhull are associated with one or
+more facets, Qhull will either fix the problem or attempt to merge the
+last remaining facets. </p>
+
+<h2><a href="#TOC">&#187;</a><a name="delaunay">Delaunay
+triangulations </a></h2>
+
+<p>Programs that use Delaunay triangulations traditionally assume
+a triangulated input. By default, <a href=qdelaun.htm>qdelaunay</a>
+merges regions with cocircular or cospherical input sites.
+If you want a simplicial triangulation
+use triangulated output ('<a href="qh-optq.htm#Qt">Qt</a>') or joggled
+input ('<a href="qh-optq.htm#QJn">QJ</a>').
+
+<p>For Delaunay triangulations, triangulated
+output should produce good results.  All points are within roundoff error of
+a paraboloid.  If two points are nearly incident, one will be a
+coplanar point.  So all points are clearly separated and convex.
+If qhull reports deleted vertices, the triangulation
+may contain serious precision faults.  Deleted vertices are reported
+in the summary ('<a href="qh-opto.htm#s">s</a>', '<a href="qh-optf.htm#Fs">Fs</a>'</p>
+
+<p>You should use option '<a href="qh-optq.htm#Qbb">Qbb</a>' with Delaunay
+triangulations. It scales the last coordinate and may reduce
+roundoff error. It is automatically set for <a href=qdelaun.htm>qdelaunay</a>,
+<a href=qvoronoi.htm>qvoronoi</a>, and option '<a
+href="qh-optq.htm#QJn">QJ</a>'.</p>
+
+<p>Edelsbrunner, H, <i>Geometry and Topology for Mesh Generation</i>, Cambridge University Press, 2001.
+Good mathematical treatise on Delaunay triangulation and mesh generation for 2-d
+and 3-d surfaces.  The chapter on surface simplification is
+particularly interesting.  It is similar to facet merging in Qhull.
+
+<p>Veron and Leon published an algorithm for shape preserving polyhedral
+simplification with bounded error [<i>Computers and Graphics</i>, 22.5:565-585, 1998].
+It remove nodes using front propagation and multiple remeshing.
+
+<h2><a href="#TOC">&#187;</a><a name="halfspace">Halfspace intersection</a></h2>
+
+<p>
+The identity pipe for Qhull reveals some precision questions for
+halfspace intersections.  The identity pipe creates the convex hull of
+a set of points and intersects the facets' hyperplanes.  It should return the input
+points, but narrow distributions may drop points while offset distributions may add
+points.  It may be better to normalize the input set about the origin.
+For example, compare the first results with the later two results:  [T. Abraham]
+<blockquote>
+     rbox 100 s t | tee r | qconvex FV n | qhalf Fp | cat - r | /bin/sort -n | tail
+<br>
+     rbox 100 L1e5 t | tee r | qconvex FV n | qhalf Fp | cat - r | /bin/sort -n | tail
+<br>
+     rbox 100 s O10 t | tee r | qconvex FV n | qhalf Fp | cat - r | /bin/sort -n | tail
+</blockquote>
+
+
+<h2><a href="#TOC">&#187;</a><a name="imprecise">Merged facets </a></h2>
+
+<p>Qhull detects precision
+problems when computing distances. A precision problem occurs if
+the distance computation is less than the maximum roundoff error.
+Qhull treats the result of a hyperplane computation as if it
+were exact.</p>
+
+<p>Qhull handles precision problems by merging non-convex facets.
+The result of merging two facets is a thick facet defined by an <i>inner
+plane</i> and an <i>outer plane</i>. The inner and outer planes
+are offsets from the facet's hyperplane. The inner plane is
+clearly below the facet's vertices. At the end of Qhull, the
+outer planes are clearly above all input points. Any exact convex
+hull must lie between the inner and outer planes.</p>
+
+<p>Qhull tests for convexity by computing a point for each facet.
+This point is called the facet's <i>centrum</i>. It is the
+arithmetic center of the facet's vertices projected to the
+facet's hyperplane. For simplicial facets with <em>d</em>
+vertices, the centrum is equivalent to the centroid or center of
+gravity. </p>
+
+<p>Two neighboring facets are convex if each centrum is clearly
+below the other hyperplane. The '<a href="qh-optc.htm#Cn2">Cn</a>'
+or '<a href="qh-optc.htm#Cn">C-n</a>' options sets the centrum's
+radius to <i>n </i>. A centrum is clearly below a hyperplane if
+the computed distance from the centrum to the hyperplane is
+greater than the centrum's radius plus two maximum roundoff
+errors. Two are required because the centrum can be the maximum
+roundoff error above its hyperplane and the distance computation
+can be high by the maximum roundoff error.</p>
+
+<p>With the '<a href="qh-optc.htm#Cn">C-n</a>' or '<a
+href="qh-optc.htm#An">A-n </a>' options, Qhull merges non-convex
+facets while constructing the hull. The remaining facets are
+clearly convex. With the '<a href="qh-optq.htm#Qx">Qx </a>'
+option, Qhull merges coplanar facets after constructing the hull.
+While constructing the hull, it merges coplanar horizon facets,
+flipped facets, concave facets and duplicated ridges. With '<a
+href="qh-optq.htm#Qx">Qx</a>', coplanar points may be missed, but
+it appears to be unlikely.</p>
+
+<p>If the user sets the '<a href="qh-optc.htm#An2">An</a>' or '<a
+href="qh-optc.htm#An">A-n</a>' option, then all neighboring
+facets are clearly convex and the maximum (exact) cosine of an
+angle is <i>n</i>.</p>
+
+<p>If '<a href="qh-optc.htm#C0">C-0</a>' or '<a
+href="qh-optq.htm#Qx">Qx</a>' is used without other precision
+options (default), Qhull tests vertices instead of centrums for
+adjacent simplices. In 3-d, if simplex <i>abc</i> is adjacent to
+simplex <i>bcd</i>, Qhull tests that vertex <i>a</i> is clearly
+below simplex <i>bcd </i>, and vertex <i>d</i> is clearly below
+simplex <i>abc</i>. When building the hull, Qhull tests vertices
+if the horizon is simplicial and no merges occur. </p>
+
+<h2><a href="#TOC">&#187;</a><a name="how">How Qhull merges facets</a></h2>
+
+<p>If two facets are not clearly convex, then Qhull removes one
+or the other facet by merging the facet into a neighbor. It
+selects the merge which minimizes the distance from the
+neighboring hyperplane to the facet's vertices. Qhull also
+performs merges when a facet has fewer than <i>d</i> neighbors (called a
+degenerate facet), when a facet's vertices are included in a
+neighboring facet's vertices (called a redundant facet), when a
+facet's orientation is flipped, or when a ridge occurs between
+more than two facets.</p>
+
+<p>Qhull performs merges in a series of passes sorted by merge
+angle. Each pass merges those facets which haven't already been
+merged in that pass. After a pass, Qhull checks for redundant
+vertices. For example, if a vertex has only two neighbors in 3-d,
+the vertex is redundant and Qhull merges it into an adjacent
+vertex.</p>
+
+<p>Merging two simplicial facets creates a non-simplicial facet
+of <em>d+1</em> vertices. Additional merges create larger facets.
+When merging facet A into facet B, Qhull retains facet B's
+hyperplane. It merges the vertices, neighbors, and ridges of both
+facets. It recomputes the centrum if a wide merge has not
+occurred (qh_WIDEcoplanar) and the number of extra vertices is
+smaller than a constant (qh_MAXnewcentrum).</p>
+
+
+<h2><a href="#TOC">&#187;</a><a name="limit">Limitations of merged
+facets</a></h2>
+
+<ul>
+<li><b>Uneven dimensions</b> --
+If one coordinate has a larger absolute value than other
+coordinates, it may dominate the effect of roundoff errors on
+distance computations. You may use option '<a
+href="qh-optq.htm#QbB">QbB</a>' to scale points to the unit cube.
+For Delaunay triangulations and Voronoi diagrams, <a href=qdelaun.htm>qdelaunay</a>
+and <a href=qvoronoi.htm>qvoronoi</a> always set
+option '<a href="qh-optq.htm#Qbb">Qbb</a>'.  It scales the last
+coordinate to [0,m] where <i>m</i> is the maximum width of the
+other coordinates.  Option '<a href="qh-optq.htm#Qbb">Qbb</a>' is
+needed for Delaunay triangulations of integer coordinates
+and nearly cocircular points.
+
+<p>For example, compare
+<pre>
+        rbox 1000 W0 t | qconvex Qb2:-1e-14B2:1e-14
+</pre>
+with
+<pre>
+        rbox 1000 W0 t | qconvex
+</pre>
+The distributions are the same but the first is compressed to a 2e-14 slab.
+<p>
+<li><b>Post-merging of coplanar facets</b> -- In 5-d and higher, option '<a href="qh-optq.htm#Qx">Qx</a>'
+(default) delays merging of coplanar facets until post-merging.
+This may allow &quot;dents&quot; to occur in the intermediate
+convex hulls. A point may be poorly partitioned and force a poor
+approximation. See option '<a href="qh-optq.htm#Qx">Qx</a>' for
+further discussion.</p>
+
+<p>This is difficult to produce in 5-d and higher.  Option '<a href="qh-optq.htm#Q6">Q6</a>' turns off merging of concave
+facets.  This is similar to 'Qx'.  It may lead to serious precision errors,
+for example,
+<pre>
+        rbox 10000 W1e-13  | qhull Q6  Tv
+</pre>
+
+<p>
+<li><b>Maximum facet width</b> --
+Qhull reports the maximum outer plane and inner planes (if
+more than roundoff error apart). There is no upper bound
+for either figure. This is an area for further research. Qhull
+does a good job of post-merging in all dimensions. Qhull does a
+good job of pre-merging in 2-d, 3-d, and 4-d. With the '<a
+href="qh-optq.htm#Qx">Qx</a>' option, it does a good job in
+higher dimensions. In 5-d and higher, Qhull does poorly at
+detecting redundant vertices. </p>
+
+<p>In the summary ('<a href="qh-opto.htm#s">s</a>'), look at the
+ratio between the maximum facet width and the maximum width of a
+single merge, e.g., &quot;(3.4x)&quot;. Qhull usually reports a
+ratio of four or lower in 3-d and six or lower in 4-d. If it
+reports a ratio greater than 10, this may indicate an
+implementation error.  Narrow distributions (see following) may
+produce wide facets.
+
+<p>For example, if special processing for narrow distributions is
+turned off ('<a href="qh-optq.htm#Q10">Q10</a>'), qhull may produce
+a wide facet:</p>
+<pre>
+         rbox 1000 L100000 s G1e-16 t1002074964 | qhull Tv Q10
+</pre>
+
+<p>
+<li><b>Narrow distribution</b> -- In 3-d, a narrow distribution may result in a poor
+approximation. For example, if you do not use qdelaunay nor option
+'<a href="qh-optq.htm#Qbb">Qbb</a>', the furthest-site
+Delaunay triangulation of nearly cocircular points may produce a poor
+approximation:
+<pre>
+         rbox s 5000 W1e-13 D2 t1002151341 | qhull d Qt
+         rbox 1000 s W1e-13 t1002231672 | qhull d Tv
+</pre>
+
+<p>During
+construction of the hull, a point may be above two
+facets with opposite orientations that span the input
+set.  Even though the point may be nearly coplanar with both
+facets, and can be distant from the precise convex
+hull of the input sites.  Additional facets leave the point distant from
+a facet.  To fix this problem, add option '<a href="qh-optq.htm#Qbb">Qbb</a>'
+(it scales the last coordinate).  Option '<a href="qh-optq.htm#Qbb">Qbb</a>'
+is automatically set for <a href=qdelaun.htm>qdelaunay</a> and <a href=qvoronoi.htm>qvoronoi</a>.
+
+<p>Qhull generates a warning if the initial simplex is narrow.
+For narrow distributions, Qhull changes how it processes coplanar
+points -- it does not make a point coplanar until the hull is
+finished.
+Use option '<a href="qh-optq.htm#Q10">Q10</a>' to try Qhull without
+special processing for narrow distributions.
+For example, special processing is needed for:
+<pre>
+         rbox 1000 L100000 s G1e-16 t1002074964 | qhull Tv Q10
+</pre>
+
+<p>You may turn off the warning message by reducing
+qh_WARNnarrow in <tt>user.h</tt> or by setting option
+'<a href="qh-optp.htm#Pp">Pp</a>'. </p>
+
+<p>Similar problems occur for distributions with a large flat facet surrounded
+with many small facet at a sharp angle to the large facet.
+Qhull 3.1 fixes most of these problems, but a poor approximation can occur.
+A point may be left outside of the convex hull ('<a href="qh-optt.htm#Tv">Tv</a>').
+Examples include
+the furthest-site Delaunay triangulation of nearly cocircular points plus the origin, and the convex hull of a cone of nearly cocircular points. The width of the band is 10^-13.
+<pre>
+        rbox s 1000 W1e-13 P0 D2 t996799242 | qhull d Tv
+        rbox 1000 s Z1 G1e-13 t1002152123 | qhull Tv
+        rbox 1000 s Z1 G1e-13 t1002231668 | qhull Tv
+</pre>
+
+<p>
+<li><b>Quadratic running time</b> -- If the output contains large, non-simplicial
+facets, the running time for Qhull may be quadratic in the size of the triangulated
+output.   For example, <tt>rbox 1000 s W1e-13 c G2 | qhull d</tt> is 4 times
+faster for 500 points.  The convex hull contains two large nearly spherical facets and
+many nearly coplanar facets.  Each new point retriangulates the spherical facet and repartitions the remaining points into all of the nearly coplanar facets.
+In this case, quadratic running time is avoided if you use qdelaunay,
+add option '<a href="qh-optq.htm#Qbb">Qbb</a>',
+or add the origin ('P0') to the input.
+<p>
+<li><b>Nearly coincident points within 1e-13</b> --
+Multiple, nearly coincident points within a 1e-13 ball of points in the unit cube
+may lead to wide facets or quadratic running time.
+For example, the convex hull a 1000 coincident, cospherical points in 4-D,
+or the 3-D Delaunay triangulation of nearly coincident points, may lead to very
+wide facets (e.g., 2267021951.3x).
+
+<p>For Delaunay triangulations, the problem typically occurs for extreme points of the input
+set (i.e., on the edge between the upper and lower convex hull).  After multiple facet merges, four
+facets may share the same, duplicate ridge and must be merged.
+Some of these facets may be long and narrow, leading to a very wide merged facet.
+If so, error QH6271 is reported.  It may be overriden with option '<a href="qh-optq.htm#Q12">Q12</a>'.
+
+<p>Duplicate ridges occur when the horizon facets for a new point is "pinched".
+In a duplicate ridge, a subridge (e.g., a line segment in 3-d) is shared by two horizon facets.
+At least two of its vertices are nearly coincident.  It is easy to generate coincident points with
+option 'Cn,r,m' of rbox.  It generates n points within an r ball for each of m input sites.  For example,
+every point of the following  distributions has a nearly coincident point within a 1e-13 ball.
+Substantially smaller or larger balls do not lead to pinched horizons.
+<pre>
+        rbox 1000 C1,1e-13 D4 s t | qhull
+        rbox 75 C1,1e-13 t | qhull d
+</pre>
+For Delaunay triangulations, a bounding box may alleviate this error (e.g.,  <tt>rbox 500 C1,1E-13 t c G1 | qhull d</tt>).
+A later release of qhull will avoid pinched horizons by merging duplicate subridges.  A subridge is
+merged by merging adjacent vertices.
+<p>
+<li><b>Facet with zero-area</b> --
+It is possible for a zero-area facet to be convex with its
+neighbors. This can occur if the hyperplanes of neighboring
+facets are above the facet's centrum, and the facet's hyperplane
+is above the neighboring centrums. Qhull computes the facet's
+hyperplane so that it passes through the facet's vertices. The
+vertices can be collinear. </p>
+
+<p>
+<li><b>No more facets</b> -- Qhull reports an error if there are <em>d+1</em> facets left
+and two of the facets are not clearly convex. This typically
+occurs when the convexity constraints are too strong or the input
+points are degenerate. The former is more likely in 5-d and
+higher -- especially with option '<a href="qh-optc.htm#Cn">C-n</a>'.</p>
+
+<p>
+<li><b>Deleted cone</b> -- Lots of merging can end up deleting all
+of the new facets for a point.  This is a rare event that has
+only been seen while debugging the code.
+
+<p>
+<li><b>Triangulated output leads to precision problems</b> -- With sufficient
+merging, the ridges of a non-simplicial facet may have serious topological
+and geometric problems.  A ridge may be between more than two
+neighboring facets.  If so, their triangulation ('<a href="qh-optq.htm#Qt">Qt</a>')
+will fail since two facets have the same vertex set.  Furthermore,
+a triangulated facet may have flipped orientation compared to its
+neighbors.</li>
+
+<p>The triangulation process detects degenerate facets with
+only two neighbors.  These are marked degenerate.  They have
+zero area.
+
+<p>
+<li><b>Coplanar points</b> --
+Option '<a href="qh-optq.htm#Qc">Qc</a>' is determined by
+qh_check_maxout() after constructing the hull. Qhull needs to
+retain all possible coplanar points in the facets' coplanar sets.
+This depends on qh_RATIOnearInside in <tt>user.h.</tt>
+Furthermore, the cutoff for a coplanar point is arbitrarily set
+at the minimum vertex. If coplanar points are important to your
+application, remove the interior points by hand (set '<a
+href="qh-optq.htm#Qc">Qc</a> <a href="qh-optq.htm#Qi">Qi</a>') or
+make qh_RATIOnearInside sufficiently large.</p>
+
+<p>
+<li><b>Maximum roundoff error</b> -- Qhull computes the maximum roundoff error from the maximum
+coordinates of the point set. Usually the maximum roundoff error
+is a reasonable choice for all distance computations. The maximum
+roundoff error could be computed separately for each point or for
+each distance computation. This is expensive and it conflicts
+with option '<a href="qh-optc.htm#Cn">C-n</a>'.
+
+<p>
+<li><b>All flipped or upper Delaunay</b> -- When a lot of merging occurs for
+Delaunay triangulations, a new point may lead to no good facets.  For example,
+try a strong convexity constraint:
+<pre>
+        rbox 1000 s t993602376 | qdelaunay C-1e-3
+</pre>
+
+</ul>
+
+<h2><a href="#TOC">&#187;</a><a name="injoggle">Joggled input</a></h2>
+
+<p>Joggled input is a simple work-around for precision problems
+in computational geometry [&quot;joggle: to shake or jar
+slightly,&quot; Amer. Heritage Dictionary].  Other names are
+<i>jostled input</i> or <i>random perturbation</i>.
+Qhull joggles the
+input by modifying each coordinate by a small random quantity. If
+a precision problem occurs, Qhull joggles the input with a larger
+quantity and the algorithm is restarted. This process continues
+until no precision problems occur. Unless all inputs incur
+precision problems, Qhull will terminate. Qhull adjusts the inner
+and outer planes to account for the joggled input. </p>
+
+<p>Neither joggle nor merged facets has an upper bound for the width of the output
+facets, but both methods work well in practice. Joggled input is
+easier to justify. Precision errors occur when the points are
+nearly singular. For example, four points may be coplanar or
+three points may be collinear. Consider a line and an incident
+point. A precision error occurs if the point is within some
+epsilon of the line. Now joggle the point away from the line by a
+small, uniformly distributed, random quantity. If the point is
+changed by more than epsilon, the precision error is avoided. The
+probability of this event depends on the maximum joggle. Once the
+maximum joggle is larger than epsilon, doubling the maximum
+joggle will halve the probability of a precision error. </p>
+
+<p>With actual data, an analysis would need to account for each
+point changing independently and other computations. It is easier
+to determine the probabilities empirically ('<a href="qh-optt.htm#TRn">TRn</a>') . For example, consider
+computing the convex hull of the unit cube centered on the
+origin. The arithmetic has 16 significant decimal digits. </p>
+
+<blockquote>
+    <p><b>Convex hull of unit cube</b> </p>
+    <table border="1">
+        <tr>
+            <th align="left">joggle</th>
+            <th align="right">error prob. </th>
+        </tr>
+        <tr>
+            <td align="right">1.0e-15</td>
+            <td align="center">0.983 </td>
+        </tr>
+        <tr>
+            <td align="right">2.0e-15</td>
+            <td align="center">0.830 </td>
+        </tr>
+        <tr>
+            <td align="right">4.0e-15</td>
+            <td align="center">0.561 </td>
+        </tr>
+        <tr>
+            <td align="right">8.0e-15</td>
+            <td align="center">0.325 </td>
+        </tr>
+        <tr>
+            <td align="right">1.6e-14</td>
+            <td align="center">0.185 </td>
+        </tr>
+        <tr>
+            <td align="right">3.2e-14</td>
+            <td align="center">0.099 </td>
+        </tr>
+        <tr>
+            <td align="right">6.4e-14</td>
+            <td align="center">0.051 </td>
+        </tr>
+        <tr>
+            <td align="right">1.3e-13</td>
+            <td align="center">0.025 </td>
+        </tr>
+        <tr>
+            <td align="right">2.6e-13</td>
+            <td align="center">0.010 </td>
+        </tr>
+        <tr>
+            <td align="right">5.1e-13</td>
+            <td align="center">0.004 </td>
+        </tr>
+        <tr>
+            <td align="right">1.0e-12</td>
+            <td align="center">0.002 </td>
+        </tr>
+        <tr>
+            <td align="right">2.0e-12</td>
+            <td align="center">0.001 </td>
+        </tr>
+    </table>
+</blockquote>
+
+<p>A larger joggle is needed for multiple points. Since the
+number of potential singularities increases, the probability of
+one or more precision errors increases. Here is an example. </p>
+
+<blockquote>
+    <p><b>Convex hull of 1000 points on unit cube</b> </p>
+    <table border="1">
+        <tr>
+            <th align="left">joggle</th>
+            <th align="right">error prob. </th>
+        </tr>
+        <tr>
+            <td align="right">1.0e-12</td>
+            <td align="center">0.870 </td>
+        </tr>
+        <tr>
+            <td align="right">2.0e-12</td>
+            <td align="center">0.700 </td>
+        </tr>
+        <tr>
+            <td align="right">4.0e-12</td>
+            <td align="center">0.450 </td>
+        </tr>
+        <tr>
+            <td align="right">8.0e-12</td>
+            <td align="center">0.250 </td>
+        </tr>
+        <tr>
+            <td align="right">1.6e-11</td>
+            <td align="center">0.110 </td>
+        </tr>
+        <tr>
+            <td align="right">3.2e-11</td>
+            <td align="center">0.065 </td>
+        </tr>
+        <tr>
+            <td align="right">6.4e-11</td>
+            <td align="center">0.030 </td>
+        </tr>
+        <tr>
+            <td align="right">1.3e-10</td>
+            <td align="center">0.010 </td>
+        </tr>
+        <tr>
+            <td align="right">2.6e-10</td>
+            <td align="center">0.008 </td>
+        </tr>
+        <tr>
+            <td align="right">5.1e-09</td>
+            <td align="center">0.003 </td>
+        </tr>
+    </table>
+</blockquote>
+
+<p>Other distributions behave similarly. No distribution should
+behave significantly worse. In Euclidean space, the probability
+measure of all singularities is zero. With floating point
+numbers, the probability of a singularity is non-zero. With
+sufficient digits, the probability of a singularity is extremely
+small for random data. For a sufficiently large joggle, all data
+is nearly random data. </p>
+
+<p>Qhull uses an initial joggle of 30,000 times the maximum
+roundoff error for a distance computation. This avoids most
+potential singularities. If a failure occurs, Qhull retries at
+the initial joggle (in case bad luck occurred). If it occurs
+again, Qhull increases the joggle by ten-fold and tries again.
+This process repeats until the joggle is a hundredth of the width
+of the input points. Qhull reports an error after 100 attempts.
+This should never happen with double-precision arithmetic. Once
+the probability of success is non-zero, the probability of
+success increases about ten-fold at each iteration. The
+probability of repeated failures becomes extremely small. </p>
+
+<p>Merged facets produces a significantly better approximation.
+Empirically, the maximum separation between inner and outer
+facets is about 30 times the maximum roundoff error for a
+distance computation. This is about 2,000 times better than
+joggled input. Most applications though will not notice the
+difference. </p>
+
+<h2><a href="#TOC">&#187;</a><a name="exact">Exact arithmetic</a></h2>
+
+<p>Exact arithmetic may be used instead of floating point.
+Singularities such as coplanar points can either be handled
+directly or the input can be symbolically perturbed. Using exact
+arithmetic is slower than using floating point arithmetic and the
+output may take more space. Chaining a sequence of operations
+increases the time and space required. Some operations are
+difficult to do.</p>
+
+<p>Clarkson's <a
+href="http://www.netlib.org/voronoi/hull.html">hull
+program</a> and Shewchuk's <a
+href="http://www.cs.cmu.edu/~quake/triangle.html">triangle
+program</a> are practical implementations of exact arithmetic.</p>
+
+<p>Clarkson limits the input precision to about fifteen digits.
+This reduces the number of nearly singular computations. When a
+determinant is nearly singular, he uses exact arithmetic to
+compute a precise result.</p>
+
+<h2><a href="#TOC">&#187;</a><a name="approximate">Approximating a
+convex hull</a></h2>
+
+<p>Qhull may be used for approximating a convex hull. This is
+particularly valuable in 5-d and higher where hulls can be
+immense. You can use '<a href="qh-optq.htm#Qx">Qx</a> <a
+href="qh-optc.htm#Cn">C-n</a>' to merge facets as the hull is
+being constructed. Then use '<a href="qh-optc.htm#Cn2">Cn</a>'
+and/or '<a href="qh-optc.htm#An2">An</a>' to merge small facets
+during post-processing. You can print the <i>n</i> largest facets
+with option '<a href="qh-optp.htm#PAn">PAn</a>'. You can print
+facets whose area is at least <i>n</i> with option '<a
+href="qh-optp.htm#PFn">PFn</a>'. You can output the outer planes
+and an interior point with '<a href="qh-optf.htm#FV">FV</a> <a
+href="qh-optf.htm#Fo">Fo</a>' and then compute their intersection
+with 'qhalf'. </p>
+
+<p>To approximate a convex hull in 6-d and higher, use
+post-merging with '<a href="qh-optc.htm#Wn">Wn</a>' (e.g., qhull
+W1e-1 C1e-2 TF2000). Pre-merging with a convexity constraint
+(e.g., qhull Qx C-1e-2) often produces a poor approximation or
+terminates with a simplex. Option '<a href="qh-optq.htm#QbB">QbB</a>'
+may help to spread out the data.</p>
+
+<p>You will need to experiment to determine a satisfactory set of
+options. Use <a href="rbox.htm">rbox</a> to generate test sets
+quickly and <a href="index.htm#geomview">Geomview</a> to view
+the results. You will probably want to write your own driver for
+Qhull using the Qhull library. For example, you could select the
+largest facet in each quadrant.</p>
+
+<!-- Navigation links -->
+<hr>
+
+<p><b>Up:</b> <a href="http://www.qhull.org">Home
+page</a> for Qhull <br>
+<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of
+Contents<br>
+<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
+&#149; <a href="qh-quick.htm#options">Options</a>
+&#149; <a href="qh-opto.htm#output">Output</a>
+&#149; <a href="qh-optf.htm#format">Formats</a>
+&#149; <a href="qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="qh-optp.htm#print">Print</a>
+&#149; <a href="qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="qh-optc.htm#prec">Precision</a>
+&#149; <a href="qh-optt.htm#trace">Trace</a>
+&#149; <a href="../src/libqhull_r/index.htm">Functions</a><br>
+<b>To:</b> <a href="#TOC">Qhull imprecision: Table of Contents</a>
+
+<!-- GC common information -->
+<hr>
+
+<p><a href="http://www.geom.uiuc.edu/"><img src="qh--geom.gif"
+align="middle" width="40" height="40"></a><i>The Geometry Center
+Home Page </i></p>
+
+<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
+</a><br>
+Created: Sept. 25, 1995 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
+</body>
+</html>
diff --git a/xs/src/qhull/html/qh-optc.htm b/xs/src/qhull/html/qh-optc.htm
new file mode 100644
index 0000000000..87308180d7
--- /dev/null
+++ b/xs/src/qhull/html/qh-optc.htm
@@ -0,0 +1,292 @@
+<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN">
+<html>
+
+<head>
+<title>Qhull precision options</title>
+</head>
+
+<body>
+<!-- Navigation links -->
+<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
+<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
+<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
+&#149; <a href="qh-quick.htm#options">Options</a>
+&#149; <a href="qh-opto.htm#output">Output</a>
+&#149; <a href="qh-optf.htm#format">Formats</a>
+&#149; <a href="qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="qh-optp.htm#print">Print</a>
+&#149; <a href="qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="qh-optc.htm#prec">Precision</a>
+&#149; <a href="qh-optt.htm#trace">Trace</a>
+&#149; <a href="../src/libqhull_r/index.htm">Functions</a></p>
+
+<hr>
+<!-- Main text of document -->
+<h1><a
+href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/delaunay.html"><img
+src="qh--dt.gif" alt="[delaunay]" align="middle" width="100"
+height="100"></a> Qhull precision options</h1>
+
+This section lists the precision options for Qhull. These options are
+indicated by an upper-case letter followed by a number.
+
+<p><b>Copyright &copy; 1995-2015 C.B. Barber</b></p>
+
+<hr>
+
+<p><a href="index.htm#TOC">&#187;</a> <a href="qh-quick.htm#programs">Programs</a>
+<a name="prec">&#149;</a> <a href="qh-quick.htm#options">Options</a>
+&#149; <a href="qh-opto.htm#output">Output</a>
+&#149; <a href="qh-optf.htm#format">Formats</a>
+&#149; <a href="qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="qh-optp.htm#print">Print</a>
+&#149; <a href="qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="qh-optc.htm#prec">Precision</a>
+&#149; <a href="qh-optt.htm#trace">Trace</a>
+&#149; <a href="../src/libqhull_r/index.htm">Functions</a></p>
+
+<h2>Precision options</h2>
+
+<p>Most users will not need to set these options. They are best
+used for <a href="qh-impre.htm#approximate">approximating</a> a
+convex hull. They may also be used for testing Qhull's handling
+of precision errors.</p>
+
+<p>By default, Qhull uses options '<a href="#C0">C-0</a>' for
+2-d, 3-d and 4-d, and '<a href="qh-optq.htm#Qx">Qx</a>' for 5-d
+and higher. These options use facet merging to handle precision
+errors.  You may also use joggled input '<a href="qh-optq.htm#QJn">QJ</a>'
+to avoid precision problems.
+For more information see <a
+href="qh-impre.htm">Imprecision in Qhull</a>.</p>
+
+<dl compact>
+    <dt>&nbsp;</dt>
+    <dd><b>General</b></dd>
+    <dt><a href="#Cn2">Cn</a></dt>
+    <dd>centrum radius for post-merging</dd>
+    <dt><a href="#Cn">C-n</a></dt>
+    <dd>centrum radius for pre-merging</dd>
+    <dt><a href="#An2">An</a></dt>
+    <dd>cosine of maximum angle for post-merging</dd>
+    <dt><a href="#An">A-n</a></dt>
+    <dd>cosine of maximum angle for pre-merging</dd>
+    <dt><a href="qh-optq.htm#Qx">Qx</a></dt>
+    <dd>exact pre-merges (allows coplanar facets)</dd>
+    <dt><a href="#C0">C-0</a></dt>
+    <dd>handle all precision errors</dd>
+    <dt><a href="#Wn">Wn</a></dt>
+    <dd>min distance above plane for outside points</dd>
+</dl>
+
+<dl compact>
+    <dt>&nbsp;</dt>
+    <dd><b>Experimental</b></dd>
+    <dt><a href="#Un">Un</a></dt>
+    <dd>max distance below plane for a new, coplanar point</dd>
+    <dt><a href="#En">En</a></dt>
+    <dd>max roundoff error for distance computation</dd>
+    <dt><a href="#Vn">Vn</a></dt>
+    <dd>min distance above plane for a visible facet</dd>
+    <dt><a href="#Rn">Rn</a></dt>
+    <dd>randomly perturb computations by a factor of [1-n,1+n]</dd>
+</dl>
+
+<dl compact>
+</dl>
+
+<hr>
+
+<h3><a href="#prec">&#187;</a><a name="An">A-n - cosine of maximum
+angle for pre-merging.</a></h3>
+
+<p>Pre-merging occurs while Qhull constructs the hull. It is
+indicated by '<a href="#Cn">C-n</a>', 'A-n', or '<a
+href="qh-optq.htm#Qx">Qx</a>'.</p>
+
+<p>If the angle between a pair of facet normals is greater than <i>n</i>,
+Qhull merges one of the facets into a neighbor. It selects the
+facet that is closest to a neighboring facet.</p>
+
+<p>For example, option 'A-0.99' merges facets during the
+construction of the hull. If the cosine of the angle between
+facets is greater than 0.99, one or the other facet is merged.
+Qhull accounts for the maximum roundoff error.</p>
+
+<p>If 'A-n' is set without '<a href="#Cn">C-n</a>', then '<a
+href="#C0">C-0</a>' is automatically set. </p>
+
+<p>In 5-d and higher, you should set '<a href="qh-optq.htm#Qx">Qx</a>'
+along with 'A-n'. It skips merges of coplanar facets until after
+the hull is constructed and before '<a href="#An2">An</a>' and '<a
+href="#Cn2">Cn</a>' are checked. </p>
+
+<h3><a href="#prec">&#187;</a><a name="An2">An - cosine of maximum angle for
+post-merging.</a></h3>
+
+<p>Post merging occurs after the hull is constructed. For
+example, option 'A0.99' merges a facet if the cosine of the angle
+between facets is greater than 0.99. Qhull accounts for the
+maximum roundoff error.</p>
+
+<p>If 'An' is set without '<a href="#Cn2">Cn</a>', then '<a
+href="#Cn2">C0</a>' is automatically set. </p>
+
+<h3><a href="#prec">&#187;</a><a name="C0">C-0 - handle all precision
+errors </a></h3>
+
+<p>Qhull handles precision errors by merging facets. The 'C-0'
+option handles all precision errors in 2-d, 3-d, and 4-d. It is
+set by default. It may be used in higher dimensions, but
+sometimes the facet width grows rapidly. It is usually better to
+use '<a href="qh-optq.htm#Qx">Qx</a>' in 5-d and higher.
+Use '<a href="qh-optq.htm#QJn">QJ</a>' to joggle the input
+instead of merging facets.
+Use '<a
+href="qh-optq.htm#Q0">Q0</a>' to turn both options off.</p>
+
+<p>Qhull optimizes 'C-0' (&quot;_zero-centrum&quot;) by testing
+vertices instead of centrums for adjacent simplices. This may be
+slower in higher dimensions if merges decrease the number of
+processed points. The optimization may be turned off by setting a
+small value such as 'C-1e-30'. See <a href="qh-impre.htm">How
+Qhull handles imprecision</a>.</p>
+
+<h3><a href="#prec">&#187;</a><a name="Cn">C-n - centrum radius for
+pre-merging</a></h3>
+
+<p>Pre-merging occurs while Qhull constructs the hull. It is
+indicated by 'C-n', '<a href="#An">A-n</a>', or '<a
+href="qh-optq.htm#Qx">Qx</a>'.</p>
+
+<p>The <i>centrum</i> of a facet is a point on the facet for
+testing facet convexity. It is the average of the vertices
+projected to the facet's hyperplane. Two adjacent facets are
+convex if each centrum is clearly below the other facet. </p>
+
+<p>If adjacent facets are non-convex, one of the facets is merged
+into a neighboring facet. Qhull merges the facet that is closest
+to a neighboring facet. </p>
+
+<p>For option 'C-n', <i>n</i> is the centrum radius. For example,
+'C-0.001' merges facets whenever the centrum is less than 0.001
+from a neighboring hyperplane. Qhull accounts for roundoff error
+when testing the centrum.</p>
+
+<p>In 5-d and higher, you should set '<a href="qh-optq.htm#Qx">Qx</a>'
+along with 'C-n'. It skips merges of coplanar facets until after
+the hull is constructed and before '<a href="#An2">An</a>' and '<a
+href="#Cn2">Cn</a>' are checked. </p>
+
+<h3><a href="#prec">&#187;</a><a name="Cn2">Cn - centrum radius for
+post-merging</a></h3>
+
+<p>Post-merging occurs after Qhull constructs the hull. It is
+indicated by '<a href="#Cn2">Cn</a>' or '<a href="#An2">An</a>'. </p>
+
+<p>For option '<a href="#Cn2">Cn</a>', <i>n</i> is the centrum
+radius. For example, 'C0.001' merges facets when the centrum is
+less than 0.001 from a neighboring hyperplane. Qhull accounts for
+roundoff error when testing the centrum.</p>
+
+<p>Both pre-merging and post-merging may be defined. If only
+post-merging is used ('<a href="qh-optq.htm#Q0">Q0</a>' with
+'Cn'), Qhull may fail to produce a hull due to precision errors
+during the hull's construction.</p>
+
+<h3><a href="#prec">&#187;</a><a name="En">En - max roundoff error
+for distance computations</a></h3>
+
+<p>This allows the user to change the maximum roundoff error
+computed by Qhull. The value computed by Qhull may be overly
+pessimistic. If 'En' is set too small, then the output may not be
+convex. The statistic &quot;max. distance of a new vertex to a
+facet&quot; (from option '<a href="qh-optt.htm#Ts">Ts</a>') is a
+reasonable upper bound for the actual roundoff error. </p>
+
+<h3><a href="#prec">&#187;</a><a name="Rn">Rn - randomly perturb
+computations </a></h3>
+
+<p>This option perturbs every distance, hyperplane, and angle
+computation by up to <i>(+/- n * max_coord)</i>. It simulates the
+effect of roundoff errors. Unless '<a href="#En">En</a>' is
+explicitly set, it is adjusted for 'Rn'. The command 'qhull Rn'
+will generate a convex hull despite the perturbations. See the <a
+href="qh-eg.htm#merge">Examples </a>section for an example.</p>
+
+<p>Options 'Rn C-n' have the effect of '<a href="#Wn">W2n</a>'
+and '<a href="#Cn">C-2n</a>'. To use time as the random number
+seed, use option '<a href="qh-optq.htm#QRn">QR-1</a>'.</p>
+
+<h3><a href="#prec">&#187;</a><a name="Un">Un - max distance for a
+new, coplanar point </a></h3>
+
+<p>This allows the user to set coplanarity. When pre-merging ('<a
+href="#Cn">C-n </a>', '<a href="#An">A-n</a>' or '<a
+href="qh-optq.htm#Qx">Qx</a>'), Qhull merges a new point into any
+coplanar facets. The default value for 'Un' is '<a href="#Vn">Vn</a>'.</p>
+
+<h3><a href="#prec">&#187;</a><a name="Vn">Vn - min distance for a
+visible facet </a></h3>
+
+<p>This allows the user to set facet visibility. When adding a
+point to the convex hull, Qhull determines all facets that are
+visible from the point. A facet is visible if the distance from
+the point to the facet is greater than 'Vn'.</p>
+
+<p>Without merging, the default value for 'Vn' is the roundoff
+error ('<a href="#En">En</a>'). With merging, the default value
+is the pre-merge centrum ('<a href="#Cn">C-n</a>') in 2-d or 3-d,
+or three times that in other dimensions. If the outside width is
+specified with option '<a href="#Wn">Wn </a>', the maximum,
+default value for 'Vn' is '<a href="#Wn">Wn</a>'.</p>
+
+<p>Qhull warns if 'Vn' is greater than '<a href="#Wn">Wn</a>' and
+furthest outside ('<a href="qh-optq.htm#Qf">Qf</a>') is not
+selected; this combination usually results in flipped facets
+(i.e., reversed normals).</p>
+
+<h3><a href="#prec">&#187;</a><a name="Wn">Wn - min distance above
+plane for outside points</a></h3>
+
+<p>Points are added to the convex hull only if they are clearly
+outside of a facet. A point is outside of a facet if its distance
+to the facet is greater than 'Wn'. Without pre-merging, the
+default value for 'Wn' is '<a href="#En">En </a>'. If the user
+specifies pre-merging and does not set 'Wn', than 'Wn' is set to
+the maximum of '<a href="#Cn">C-n</a>' and <i>maxcoord*(1 - </i><a
+href="#An"><i>A-n</i></a><i>)</i>.</p>
+
+<p>This option is good for <a href="qh-impre.htm#approximate">approximating</a>
+a convex hull.</p>
+
+<p>Options '<a href="qh-optq.htm#Qc">Qc</a>' and '<a
+href="qh-optq.htm#Qi">Qi</a>' use the minimum vertex to
+distinguish coplanar points from interior points.</p>
+<!-- Navigation links -->
+<hr>
+
+<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
+<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
+<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
+&#149; <a href="qh-quick.htm#options">Options</a>
+&#149; <a href="qh-opto.htm#output">Output</a>
+&#149; <a href="qh-optf.htm#format">Formats</a>
+&#149; <a href="qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="qh-optp.htm#print">Print</a>
+&#149; <a href="qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="qh-optc.htm#prec">Precision</a>
+&#149; <a href="qh-optt.htm#trace">Trace</a>
+&#149; <a href="../src/libqhull_r/index.htm">Functions</a></p>
+<!-- GC common information -->
+<hr>
+
+<p><a href="http://www.geom.uiuc.edu/"><img src="qh--geom.gif"
+align="middle" width="40" height="40"></a><i>The Geometry Center
+Home Page </i></p>
+
+<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
+</a><br>
+Created: Sept. 25, 1995 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
+</body>
+</html>
diff --git a/xs/src/qhull/html/qh-optf.htm b/xs/src/qhull/html/qh-optf.htm
new file mode 100644
index 0000000000..3c7a2b1db2
--- /dev/null
+++ b/xs/src/qhull/html/qh-optf.htm
@@ -0,0 +1,736 @@
+<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN">
+<html>
+
+<head>
+<title>Qhull format options (F)</title>
+</head>
+
+<body><!-- Navigation links -->
+<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
+<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
+<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
+&#149; <a href="qh-quick.htm#options">Options</a>
+&#149; <a href="qh-opto.htm#output">Output</a>
+&#149; <a href="qh-optf.htm#format">Formats</a>
+&#149; <a href="qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="qh-optp.htm#print">Print</a>
+&#149; <a href="qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="qh-optc.htm#prec">Precision</a>
+&#149; <a href="qh-optt.htm#trace">Trace</a>
+&#149; <a href="../src/libqhull_r/index.htm">Functions</a></p>
+<hr>
+<!-- Main text of document -->
+<h1><a
+ href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/delaunay.html"><IMG
+ align=middle alt=[delaunay] height=100
+ src="qh--dt.gif" width=100 ></a> Qhull format options (F)</h1>
+
+<p>This section lists the format options for Qhull. These options
+are indicated by 'F' followed by a letter. See <A
+ href="qh-opto.htm#output" >Output</a>, <a href="qh-optp.htm#print">Print</a>,
+and <a href="qh-optg.htm#geomview">Geomview</a> for other output
+options. </p>
+
+<p><b>Copyright &copy; 1995-2015 C.B. Barber</b></p>
+
+<hr>
+
+<p><a href="index.htm#TOC">&#187;</a> <a href="qh-quick.htm#programs">Programs</a>
+<a name="format">&#149;</a> <a href="qh-quick.htm#options">Options</a>
+&#149; <a href="qh-opto.htm#output">Output</a>
+&#149; <a href="qh-optf.htm#format">Formats</a>
+&#149; <a href="qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="qh-optp.htm#print">Print</a>
+&#149; <a href="qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="qh-optc.htm#prec">Precision</a>
+&#149; <a href="qh-optt.htm#trace">Trace</a>
+&#149; <a href="../src/libqhull_r/index.htm">Functions</a></p>
+
+<h2>Additional input &amp; output formats</h2>
+
+<p>These options allow for automatic processing of Qhull output.
+Options '<a href="qh-opto.htm#i">i</a>', '<a href="qh-opto.htm#o">o</a>',
+'<a href="qh-opto.htm#n">n</a>', and '<a href="qh-opto.htm#p">p</a>'
+may also be used.</p>
+
+<dl compact>
+    <dt>
+    <dd><b>Summary and control</b>
+    <dt><a href="#FA">FA</a>
+    <dd>compute total area and volume for option '<A
+        href="qh-opto.htm#s">s</a>'
+
+    <dt><a href="#FV">FV</a>
+    <dd>print average vertex (interior point for '<A
+        href="qhalf.htm">qhalf</a>')
+    <dt><a href="#FQ">FQ</a>
+    <dd>print command for qhull and input
+    <dt><a href="#FO">FO</a>
+    <dd>print options to stderr or stdout
+    <dt><a href="#FS">FS</a>
+    <dd>print sizes: total area and volume
+    <dt><a href="#Fs">Fs</a>
+    <dd>print summary: dim, #points, total vertices and
+  facets, #vertices, #facets, max outer and inner plane
+    <dt><a href="#Fd">Fd</a>
+    <dd>use  format for input (offset first)
+    <dt><a href="#FD">FD</a>
+    <dd>use cdd format for normals (offset first)
+    <dt><a href="#FM">FM</a>
+    <dd>print Maple output (2-d and 3-d)
+    <dt>
+    <dt>
+    <dd><b>Facets, points, and vertices</b>
+    <dt><a href="#Fa">Fa</a>
+    <dd>print area for each facet
+    <dt><a href="#FC">FC</a>
+    <dd>print centrum for each facet
+    <dt><a href="#Fc">Fc</a>
+    <dd>print coplanar points for each facet
+    <dt><a href="#Fx">Fx</a>
+    <dd>print extreme points (i.e., vertices) of convex hull.
+
+    <dt><a href="#FF">FF</a>
+    <dd>print facets w/o ridges
+    <dt><a href="#FI">FI</a>
+    <dd>print ID for each facet
+    <dt><a href="#Fi">Fi</a>
+    <dd>print inner planes for each facet
+    <dt><a href="#Fm">Fm</a>
+    <dd>print merge count for each facet (511 max)
+    <dt><a href="#FP">FP</a>
+    <dd>print nearest vertex for coplanar points
+    <dt><a href="#Fn">Fn</a>
+    <dd>print neighboring facets for each facet
+    <dt><a href="#FN">FN</a>
+    <dd>print neighboring facets for each point
+    <dt><a href="#Fo">Fo</a>
+    <dd>print outer planes for each facet
+    <dt><a href="#Ft">Ft</a>
+    <dd>print triangulation with added points
+    <dt><a href="#Fv">Fv</a>
+    <dd>print vertices for each facet
+    <dt>
+    <dt>
+    <dd><b>Delaunay, Voronoi, and halfspace</b>
+    <dt><a href="#Fx">Fx</a>
+    <dd>print extreme input sites of Delaunay triangulation
+  or Voronoi diagram.
+    <dt><a href="#Fp">Fp</a>
+    <dd>print points at halfspace intersections
+    <dt><a href="#Fi2">Fi</a>
+    <dd>print separating hyperplanes for inner, bounded
+  Voronoi regions
+    <dt><a href="#Fo2">Fo</a>
+    <dd>print separating hyperplanes for outer, unbounded
+  Voronoi regions
+    <dt><a href="#Fv2">Fv</a>
+    <dd>print Voronoi diagram as ridges for each input pair
+    <dt><a href="#FC">FC</a>
+    <dd>print Voronoi vertex ("center") for each facet</dd>
+</dl>
+
+<hr>
+
+<h3><a href="#format">&#187;</a><a name="Fa">Fa - print area for each
+facet </a></h3>
+
+<p>The first line is the number of facets. The remaining lines
+are the area for each facet, one facet per line. See '<A
+ href="#FA" >FA</a>' and '<a href="#FS">FS</a>' for computing the total area and volume.</p>
+
+<p>Use '<a href="qh-optp.htm#PAn">PAn</a>' for printing the n
+largest facets. Use option '<a href="qh-optp.htm#PFn">PFn</a>'
+for printing facets larger than <i>n</i>.</p>
+
+<p>For Delaunay triangulations, the area is the area of each
+Delaunay triangle. For Voronoi vertices, the area is the area of
+the dual facet to each vertex. </p>
+
+<p>Qhull uses the centrum and ridges to triangulate
+non-simplicial facets. The area for non-simplicial facets is the
+sum of the areas for each triangle. It is an approximation of the
+actual area. The ridge's vertices are projected to the facet's
+hyperplane. If a vertex is far below a facet (qh_WIDEcoplanar in <tt>user.h</tt>),
+the corresponding triangles are ignored.</p>
+
+<p>For non-simplicial facets, vertices are often below the
+facet's hyperplane. If so, the approximation is less than the
+actual value and it may be significantly less. </p>
+
+<h3><a href="#format">&#187;</a><a name="FA">FA - compute total area
+and volume for option 's' </a></h3>
+
+<p>With option 'FA', Qhull includes the total area and volume in
+the summary ('<a href="qh-opto.htm#s">s</a>').  Option '<a href="#FS">FS</a>' also includes the total area and volume.
+If facets are
+merged, the area and volume are approximations. Option 'FA' is
+automatically set for options '<a href="#Fa">Fa</a>', '<A
+ href="qh-optp.htm#PAn" >PAn</a>', and '<a href="qh-optp.htm#PFn">PFn</a>'.
+</p>
+
+<p>With '<a href="qdelaun.htm">qdelaunay</a> <A
+ href="qh-opto.htm#s" >s</a> FA', Qhull computes the total area of
+the Delaunay triangulation. This equals the volume of the convex
+hull of the data points. With options '<a href="qdelau_f.htm">qdelaunay Qu</a>
+<a href="qh-opto.htm#s">s</a> FA', Qhull computes the
+total area of the furthest-site Delaunay triangulation. This
+equals of the total area of the Delaunay triangulation. </p>
+
+<p>See '<a href="#Fa">Fa</a>' for further details.  Option '<a href="#FS">FS</a>' also computes the total area and volume.</p>
+
+<h3><a href="#format">&#187;</a><a name="Fc">Fc - print coplanar
+points for each facet </a></h3>
+
+<p>The output starts with the number of facets. Then each facet
+is printed one per line. Each line is the number of coplanar
+points followed by the point ids. </p>
+
+<p>By default, option 'Fc' reports coplanar points
+('<a href="qh-optq.htm#Qc">Qc</a>').  You may also use
+option '<a href="qh-optq.htm#Qi">Qi</a>'. Options 'Qi Fc' prints
+interior points while 'Qci Fc' prints both coplanar and interior
+points.
+
+<p>Each coplanar point or interior point is assigned to the
+facet it is furthest above (resp., least below). </p>
+
+<p>Use 'Qc <a href="qh-opto.htm#p">p</a>' to print vertex and
+coplanar point coordinates. Use '<a href="qh-optf.htm#Fv">Fv</a>'
+to print vertices. </p>
+
+<h3><a href="#format">&#187;</a><a name="FC">FC - print centrum or
+Voronoi vertex for each facet </a></h3>
+
+<p>The output starts with the dimension followed by the number of
+facets. Then each facet centrum is printed, one per line. For
+<a href="qvoronoi.htm">qvoronoi</a>, Voronoi vertices are
+printed instead. </p>
+
+<h3><a href="#format">&#187;</a><a name="Fd">Fd - use cdd format for
+input </a></h3>
+
+<p>The input starts with comments. The first comment is reported
+in the summary. Data starts after a "begin" line. The
+next line is the number of points followed by the dimension plus
+one and "real" or "integer". Then the points
+are listed with a leading "1" or "1.0". The
+data ends with an "end" line.</p>
+
+<p>For halfspaces ('<a href="qhalf.htm">qhalf</a> Fd'),
+the input format is the same. Each halfspace starts with its
+offset. The signs of the offset and coefficients are the
+opposite of Qhull's
+convention. The first two lines of the input may be an interior
+point in '<a href="#FV">FV</a>' format.</p>
+
+<h3><a href="#format">&#187;</a><a name="FD">FD - use cdd format for
+normals </a></h3>
+
+<p>Option 'FD' prints normals ('<a href="qh-opto.htm#n">n</a>', '<A
+ href="#Fo" >Fo</a>', '<a href="#Fi">Fi</a>') or points ('<A
+ href="qh-opto.htm#p" >p</a>') in cdd format. The first line is the
+command line that invoked Qhull. Data starts with a
+"begin" line. The next line is the number of normals or
+points followed by the dimension plus one and "real".
+Then the normals or points are listed with the offset before the
+coefficients. The offset for points is 1.0. For normals,
+the offset and coefficients use the opposite sign from Qhull.
+The data ends with an "end" line.</p>
+
+<h3><a href="#format">&#187;</a><a name="FF">FF - print facets w/o
+ridges </a></h3>
+
+<p>Option 'FF' prints all fields of all facets (as in '<A
+ href="qh-opto.htm#f" >f</a>') without printing the ridges. This is
+useful in higher dimensions where a facet may have many ridges.
+For simplicial facets, options 'FF' and '<a href="qh-opto.htm#f">f
+</a>' are equivalent.</p>
+
+<h3><a href="#format">&#187;</a><a name="Fi">Fi - print inner planes
+for each facet </a></h3>
+
+<p>The first line is the dimension plus one. The second line is
+the number of facets. The remainder is one inner plane per line.
+The format is the same as option '<a href="qh-opto.htm#n">n</a>'.</p>
+
+<p>The inner plane is a plane that is below the facet's vertices.
+It is an offset from the facet's hyperplane. It includes a
+roundoff error for computing the vertex distance.</p>
+
+<p>Note that the inner planes for Geomview output ('<A
+ href="qh-optg.htm#Gi" >Gi</a>') include an additional offset for
+vertex visualization and roundoff error. </p>
+
+<h3><a href="#format">&#187;</a><a name="Fi2">Fi - print separating
+hyperplanes for inner, bounded Voronoi regions</a></h3>
+
+<p>With <a href="qvoronoi.htm" >qvoronoi</a>, 'Fi' prints the
+separating hyperplanes for inner, bounded regions of the Voronoi
+diagram. The first line is the number of ridges. Then each
+hyperplane is printed, one per line. A line starts with the
+number of indices and floats. The first pair of indices indicates
+an adjacent pair of input sites. The next <i>d</i> floats are the
+normalized coefficients for the hyperplane, and the last float is
+the offset. The hyperplane is oriented toward '<A
+ href="qh-optq.htm#QVn" >QVn</a>' (if defined), or the first input
+site of the pair. </p>
+
+<p>Use '<a href="qh-optf.htm#Fo2">Fo</a>' for unbounded regions,
+and '<a href="qh-optf.htm#Fv2">Fv</a>' for the corresponding
+Voronoi vertices. </p>
+
+<p>Use '<a href="qh-optt.htm#Tv">Tv</a>' to verify that the
+hyperplanes are perpendicular bisectors. It will list relevant
+statistics to stderr. The hyperplane is a perpendicular bisector
+if the midpoint of the input sites lies on the plane, all Voronoi
+vertices in the ridge lie on the plane, and the angle between the
+input sites and the plane is ninety degrees. This is true if all
+statistics are zero. Roundoff and computation errors make these
+non-zero. The deviations appear to be largest when the
+corresponding Delaunay triangles are large and thin; for example,
+the Voronoi diagram of nearly cospherical points. </p>
+
+<h3><a href="#format">&#187;</a><a name="FI">FI - print ID for each
+facet </a></h3>
+
+<p>Print facet identifiers. These are used internally and listed
+with options '<a href="qh-opto.htm#f">f</a>' and '<a href="#FF">FF</a>'.
+Options '<a href="#Fn">Fn </a>' and '<a href="#FN">FN</a>' use
+facet identifiers for negative indices. </p>
+
+<h3><a href="#format">&#187;</a><a name="Fm">Fm - print merge count
+for each facet </a></h3>
+
+<p>The first line is the number of facets. The remainder is the
+number of merges for each facet, one per line. At most 511 merges
+are reported for a facet. See '<a href="qh-optp.htm#PMn">PMn</a>'
+for printing the facets with the most merges. </p>
+
+<h3><a href="#format">&#187;</a><a name="FM">FM - print Maple
+output </a></h3>
+
+<p>Qhull writes a Maple file for 2-d and 3-d convex hulls,
+2-d and 3-d halfspace intersections,
+and 2-d Delaunay triangulations. Qhull produces a 2-d
+or 3-d plot.
+
+<p><i>Warning</i>: This option has not been tested in Maple.
+
+<p>[From T. K. Abraham with help from M. R. Feinberg and N. Platinova.]
+The following steps apply while working within the
+Maple worksheet environment :
+<ol>
+<li>Generate the data and store it as an array . For example, in 3-d, data generated
+in Maple is of the form : x[i],y[i],z[i]
+<p>
+<li>Create a single variable and assign the entire array of data points to this variable.
+Use the "seq" command within square brackets as shown in the following example.
+(The square brackets are essential for the rest of the steps to work.)
+<p>
+>data:=[seq([x[i],y[i],z[i]],i=1..n)]:# here n is the number of data points
+
+<li>Next we need to write the data to a file to be read by qhull. Before
+writing the data to a file, make sure that the qhull executable files and
+the data file lie in   the same subdirectory. If the executable files are
+stored in the "C:\qhull3.1\" subdirectory, then save the file in the same
+subdirectory, say "C:\qhull3.1\datafile.txt". For the sake of integrity of
+the data file , it is best to first ensure that the data file does not
+exist before writing into the data file. This can be done by running a
+delete command first . To write the data to the file, use the "writedata"
+and the "writedata[APPEND]" commands as illustrated in the following example :
+<p>
+>system("del c:\\qhull3.1\\datafile.txt");#To erase any previous versions of the file
+<br>>writedata("c:\\qhull3.1\\datafile.txt ",[3, nops(data)]);#writing in qhull format
+<br>>writedata[APPEND]("c:\\ qhull3.1\\datafile.txt ",   data);#writing the data points
+<li>
+Use the 'FM' option to produce Maple output.  Store the output as a ".mpl" file.
+For example, using the file we created above, we type the following (in DOS environment)
+<p>
+qconvex s FM &lt;datafile.txt >dataplot.mpl
+
+<li>
+To read 3-d output in Maple, we use the 'read'  command followed by
+a 'display3d' command.  For example (in Maple environment):
+<p>
+>with (plots):
+<br>>read `c:\\qhull3.1\\dataplot.mpl`:#IMPORTANT - Note that the punctuation mark used is ' and NOT '. The correct punctuation   mark is the one next to the key for "1" (not the punctuation mark near the enter key)
+<br>> qhullplot:=%:
+<br>> display3d(qhullplot);
+</ol>
+
+<p>For Delaunay triangulation orthogonal projection is better.
+
+<p>For halfspace intersections, Qhull produces the dual
+convex hull.
+
+<p>See <a href="qh-faq.htm#math">Is Qhull available for Maple?</a>
+for other URLs.
+
+<h3><a href="#format">&#187;</a><a name="Fn">Fn - print neighboring
+facets for each facet </a></h3>
+
+<p>The output starts with the number of facets. Then each facet
+is printed one per line. Each line is the number of neighbors
+followed by an index for each neighbor. The indices match the
+other facet output formats.</p>
+
+<p>For simplicial facets, each neighbor is opposite
+the corresponding vertex (option '<a href="#Fv">Fv</a>').
+Do not compare to option '<a href="qh-opto.htm#i">i</a>'.  Option 'i'
+orients facets by reversing the order of two vertices.  For non-simplicial facets,
+the neighbors are unordered.
+
+<p>A negative index indicates an unprinted facet due to printing
+only good facets ('<a href="qh-optp.htm#Pg">Pg</a>', <a href="qdelaun.htm" >qdelaunay</a>,
+<a href="qvoronoi.htm" >qvoronoi</a>). It
+is the negation of the facet's ID (option '<a href="#FI">FI</a>').
+For example, negative indices are used for facets "at
+infinity" in the Delaunay triangulation.</p>
+
+<h3><a href="#format">&#187;</a><a name="FN">FN - print neighboring
+facets for each point </a></h3>
+
+<p>The first line is the number of points. Then each point is
+printed, one per line. For unassigned points (either interior or
+coplanar), the line is "0". For assigned coplanar
+points ('<a href="qh-optq.htm#Qc">Qc</a>'), the line is
+"1" followed by the index of the facet that is furthest
+below the point. For assigned interior points ('<A
+ href="qh-optq.htm#Qi" >Qi</a>'), the line is "1"
+followed by the index of the facet that is least above the point.
+For vertices that do not belong to good facet, the line is
+"0"</p>
+
+<p>For vertices of good facets, the line is the number of
+neighboring facets followed by the facet indices. The indices
+correspond to the other '<a href="#format">F</a>' formats. In 4-d
+and higher, the facets are sorted by index. In 3-d, the facets
+are in adjacency order (not oriented).</p>
+
+<p>A negative index indicates an unprinted facet due to printing
+only good facets (<a href="qdelaun.htm" >qdelaunay</a>,
+<a href="qvoronoi.htm" >qvoronoi</a>, '<a href="qh-optp.htm#Pdk">Pdk</a>',
+'<a href="qh-optp.htm#Pg">Pg</a>'). It is the negation of the
+facet's ID ('<a href="#FI"> FI</a>'). For example, negative
+indices are used for facets "at infinity" in the
+Delaunay triangulation.</p>
+
+<p>For Voronoi vertices, option 'FN' lists the vertices of the
+Voronoi region for each input site. Option 'FN' lists the regions
+in site ID order. Option 'FN' corresponds to the second half of
+option '<a href="qh-opto.htm#o">o</a>'. To convert from 'FN' to '<A
+ href="qh-opto.htm#o" >o</a>', replace negative indices with zero
+and increment non-negative indices by one. </p>
+
+<p>If you are using the <a href="qh-code.htm#library">Qhull
+library</a> or <a href="qh-code.htm#cpp">C++ interface</a>, option 'FN' has the side effect of reordering the
+neighbors for a vertex </p>
+
+<h3><a href="#format">&#187;</a><a name="Fo">Fo - print outer planes
+for each facet </a></h3>
+
+<p>The first line is the dimension plus one. The second line is
+the number of facets. The remainder is one outer plane per line.
+The format is the same as option '<a href="qh-opto.htm#n">n</a>'.</p>
+
+<p>The outer plane is a plane that is above all points. It is an
+offset from the facet's hyperplane. It includes a roundoff error
+for computing the point distance. When testing the outer plane
+(e.g., '<a href="qh-optt.htm#Tv">Tv</a>'), another roundoff error
+should be added for the tested point.</p>
+
+<p>If outer planes are not checked ('<a href="qh-optq.htm#Q5">Q5</a>')
+or not computed (!qh_MAXoutside), the maximum, computed outside
+distance is used instead. This can be much larger than the actual
+outer planes.</p>
+
+<p>Note that the outer planes for Geomview output ('<A
+ href="qh-optg.htm#G" >G</a>') include an additional offset for
+vertex/point visualization, 'lines closer,' and roundoff error.</p>
+
+<h3><a href="#format">&#187;</a><a name="Fo2">Fo - print separating
+hyperplanes for outer, unbounded Voronoi regions</a></h3>
+
+<p>With <a href="qvoronoi.htm" >qvoronoi</a>, 'Fo' prints the
+separating hyperplanes for outer, unbounded regions of the
+Voronoi diagram. The first line is the number of ridges. Then
+each hyperplane is printed, one per line. A line starts with the
+number of indices and floats. The first pair of indices indicates
+an adjacent pair of input sites. The next <i>d</i> floats are the
+normalized coefficients for the hyperplane, and the last float is
+the offset. The hyperplane is oriented toward '<A
+ href="qh-optq.htm#QVn" >QVn</a>' (if defined), or the first input
+site of the pair. </p>
+
+<p>Option 'Fo' gives the hyperplanes for the unbounded rays of
+the unbounded regions of the Voronoi diagram. Each hyperplane
+goes through the midpoint of the corresponding input sites. The
+rays are directed away from the input sites. </p>
+
+<p>Use '<a href="qh-optf.htm#Fi2">Fi</a>' for bounded regions,
+and '<a href="qh-optf.htm#Fv2">Fv</a>' for the corresponding
+Voronoi vertices. Use '<a href="qh-optt.htm#Tv">Tv</a>' to verify
+that the corresponding Voronoi vertices lie on the hyperplane. </p>
+
+<h3><a href="#format">&#187;</a><a name="FO">FO - print list of
+selected options </a></h3>
+
+<p>Lists selected options and default values to stderr.
+Additional 'FO's are printed to stdout. </p>
+
+<h3><a href="#format">&#187;</a><a name="Fp">Fp - print points at
+halfspace intersections</a></h3>
+
+<p>The first line is the number of intersection points. The
+remainder is one intersection point per line. A intersection
+point is the intersection of <i>d</i> or more halfspaces from
+'<a href="qhalf.htm">qhalf</a>'. It corresponds to a
+facet of the dual polytope. The "infinity" point
+[-10.101,-10.101,...] indicates an unbounded intersection.</p>
+
+<p>If [x,y,z] are the dual facet's normal coefficients and <i>b&lt;0</i>
+is its offset, the halfspace intersection occurs at
+[x/-b,y/-b,z/-b] plus the interior point. If <i>b&gt;=0</i>, the
+halfspace intersection is unbounded. </p>
+
+<h3><a href="#format">&#187;</a><a name="FP">FP - print nearest
+vertex for coplanar points </a></h3>
+
+<p>The output starts with the number of coplanar points. Then
+each coplanar point is printed one per line. Each line is the
+point ID of the closest vertex, the point ID of the coplanar
+point, the corresponding facet ID, and the distance. Sort the
+lines to list the coplanar points nearest to each vertex. </p>
+
+<p>Use options '<a href="qh-optq.htm#Qc">Qc</a>' and/or '<A
+ href="qh-optq.htm#Qi" >Qi</a>' with 'FP'. Options 'Qc FP' prints
+coplanar points while 'Qci FP' prints coplanar and interior
+points.  Option 'Qc' is automatically selected if 'Qi' is not
+selected.
+
+<p>For Delaunay triangulations (<a href="qdelaun.htm" >qdelaunay</a>
+or <a href="qvoronoi.htm" >qvoronoi</a>), a coplanar point is nearly
+incident to a vertex. The distance is the distance in the
+original point set.</p>
+
+<p>If imprecision problems are severe, Qhull will delete input
+sites when constructing the Delaunay triangulation.  Option 'FP' will
+list these points along with coincident points.</p>
+
+<p>If there are many coplanar or coincident points and non-simplicial
+facets are triangulated ('<a href="qh-optq.htm#Qt">Qt</a>'), option
+'FP' may be inefficient.  It redetermines the original vertex set
+for each coplanar point.</p>
+
+<h3><a href="#format">&#187;</a><a name="FQ">FQ - print command for
+qhull and input </a></h3>
+
+<p>Prints qhull and input command, e.g., "rbox 10 s | qhull
+FQ".   Option 'FQ' may be repeated multiple times.</p>
+
+<h3><a href="#format">&#187;</a><a name="Fs">Fs - print summary</a></h3>
+
+<p>The first line consists of number of integers ("10")
+followed by the:
+<ul>
+<li>dimension
+<li>number of points
+<li>number of vertices
+<li>number of facets
+<li>number of vertices selected for output
+<li>number of facets selected for output
+<li>number of coplanar points for selected facets
+<li>number of nonsimplicial or merged facets selected for
+  output
+<LI>number of deleted vertices</LI>
+<LI>number of triangulated facets ('<a href="qh-optq.htm#Qt">Qt</a>')</LI>
+</ul>
+
+<p>The second line consists of the number of reals
+("2") followed by the:
+<ul>
+<li>maximum offset to an outer plane
+<li>minimum offset to an inner plane.</li>
+</ul>
+Roundoff and joggle are included.
+<P></P>
+
+<p>For Delaunay triangulations and Voronoi diagrams, the
+number of deleted vertices should be zero. If greater than zero, then the
+input is highly degenerate and coplanar points are not necessarily coincident
+points.  For example, <tt>'RBOX 1000 s W1e-13 t995138628 | QHULL d Qbb'</tt> reports
+deleted vertices; the input is nearly cospherical.</p>
+
+<P>Later versions of Qhull may produce additional integers or reals.</P>
+
+<h3><a href="#format">&#187;</a><a name="FS">FS - print sizes</a></h3>
+
+<p>The first line consists of the number of integers
+("0"). The second line consists of the number of reals
+("2"), followed by the total facet area, and the total
+volume. Later versions of Qhull may produce additional integers
+or reals.</p>
+
+<p>The total volume measures the volume of the intersection of
+the halfspaces defined by each facet. It is computed from the
+facet area. Both area and volume are approximations for
+non-simplicial facets. See option '<a href="#Fa">Fa </a>' for
+further notes. Option '<a href="#FA">FA </a>' also computes the total area and volume. </p>
+
+<h3><a href="#format">&#187;</a><a name="Ft">Ft - print triangulation</a></h3>
+
+<p>Prints a triangulation with added points for non-simplicial
+facets. The output is </p>
+
+<ul>
+    <li>The first line is the dimension
+    <li>The second line is the number of points, the number
+  of facets, and the number of ridges.
+    <li>All of the input points follow, one per line.
+    <li>The centrums follow, one per non-simplicial facet
+    <li>Then the facets follow as a list of point indices
+        preceded by the number of points. The simplices are
+        oriented. </li>
+</ul>
+
+<p>For convex hulls with simplicial facets, the output is the
+same as option '<a href="qh-opto.htm#o">o</a>'.</p>
+
+<p>The added points are the centrums of the non-simplicial
+facets. Except for large facets, the centrum is the average
+vertex coordinate projected to the facet's hyperplane. Large
+facets may use an old centrum to avoid recomputing the centrum
+after each merge. In either case, the centrum is clearly below
+neighboring facets. See <a href="qh-impre.htm">Precision issues</a>.
+</p>
+
+<p>The new simplices will not be clearly convex with their
+neighbors and they will not satisfy the Delaunay property. They
+may even have a flipped orientation. Use triangulated input ('<A
+ href="qh-optq.htm#Qt">Qt</a>') for Delaunay triangulations.
+
+<p>For Delaunay triangulations with simplicial facets, the output is the
+same as option '<a href="qh-opto.htm#o">o</a>' without the lifted
+coordinate.  Since 'Ft' is invalid for merged Delaunay facets, option
+'Ft' is not available for qdelaunay or qvoronoi.  It may be used with
+joggled input ('<a  href="qh-optq.htm#QJn" >QJ</a>') or triangulated output ('<A
+ href="qh-optq.htm#Qt" >Qt</a>'), for example, rbox 10 c G 0.01 | qhull d QJ Ft</p>
+
+<p>If you add a point-at-infinity with '<a href="qh-optq.htm#Qz">Qz</a>',
+it is printed after the input sites and before any centrums. It
+will not be used in a Delaunay facet.</p>
+
+<h3><a href="#format">&#187;</a><a name="Fv">Fv - print vertices for
+each facet</a></h3>
+
+<p>The first line is the number of facets. Then each facet is
+printed, one per line. Each line is the number of vertices
+followed by the corresponding point ids. Vertices are listed in
+the order they were added to the hull (the last one added is the
+first listed).
+</p>
+<p>Option '<a href="qh-opto.htm#i">i</a>' also lists the vertices,
+but it orients facets by reversing the order of two
+vertices.  Option 'i' triangulates non-simplicial, 4-d and higher facets by
+adding vertices for the centrums.
+</p>
+
+<h3><a href="#format">&#187;</a><a name="Fv2">Fv - print Voronoi
+diagram</a></h3>
+
+<p>With <a href="qvoronoi.htm" >qvoronoi</a>, 'Fv' prints the
+Voronoi diagram or furthest-site Voronoi diagram. The first line
+is the number of ridges. Then each ridge is printed, one per
+line. The first number is the count of indices. The second pair
+of indices indicates a pair of input sites. The remaining indices
+list the corresponding ridge of Voronoi vertices. Vertex 0 is the
+vertex-at-infinity. It indicates an unbounded ray. </p>
+
+<p>All vertices of a ridge are coplanar. If the ridge is
+unbounded, add the midpoint of the pair of input sites. The
+unbounded ray is directed from the Voronoi vertices to infinity. </p>
+
+<p>Use '<a href="qh-optf.htm#Fo2">Fo</a>' for separating
+hyperplanes of outer, unbounded regions. Use '<A
+ href="qh-optf.htm#Fi2" >Fi</a>' for separating hyperplanes of
+inner, bounded regions. </p>
+
+<p>Option 'Fv' does not list ridges that require more than one
+midpoint. For example, the Voronoi diagram of cospherical points
+lists zero ridges (e.g., 'rbox 10 s | qvoronoi Fv Qz').
+Other examples are the Voronoi diagrams of a rectangular mesh
+(e.g., 'rbox 27 M1,0 | qvoronoi Fv') or a point set with
+a rectangular corner (e.g.,
+'rbox P4,4,4 P4,2,4 P2,4,4 P4,4,2 10 | qvoronoi Fv').
+Both cases miss unbounded rays at the corners.
+To determine these ridges, surround the points with a
+large cube (e.g., 'rbox 10 s c G2.0 | qvoronoi Fv Qz').
+The cube needs to be large enough to bound all Voronoi regions of the original point set.
+Please report any other cases that are missed. If you
+can formally describe these cases or
+write code to handle them, please send email to <A
+ href="mailto:qhull@qhull.org" >qhull@qhull.org</a>. </p>
+
+<h3><a href="#format">&#187;</a><a name="FV">FV - print average
+vertex </a></h3>
+
+<p>The average vertex is the average of all vertex coordinates.
+It is an interior point for halfspace intersection. The first
+line is the dimension and "1"; the second line is the
+coordinates. For example,</p>
+
+<blockquote>
+    <p>qconvex FV <A
+    href="qh-opto.htm#n">n</a> | qhalf <a href="#Fp">Fp</a></p>
+</blockquote>
+
+<p>prints the extreme points of the original point set (roundoff
+included). </p>
+
+<h3><a href="#format">&#187;</a><a name="Fx">Fx - print extreme
+points (vertices) of convex hulls and Delaunay triangulations</a></h3>
+
+<p>The first line is the number of points. The following lines
+give the index of the corresponding points. The first point is
+'0'. </p>
+
+<p>In 2-d, the extreme points (vertices) are listed in
+counterclockwise order (by qh_ORIENTclock in user.h). </p>
+
+<p>In 3-d and higher convex hulls, the extreme points (vertices)
+are sorted by index. This is the same order as option '<A
+ href="qh-opto.htm#p" >p</a>' when it doesn't include coplanar or
+interior points. </p>
+
+<p>For Delaunay triangulations, 'Fx' lists the extreme
+points of the input sites (i.e., the vertices of their convex hull). The points
+are unordered. <!-- Navigation links --> </p>
+
+<hr>
+
+<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
+<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
+<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
+&#149; <a href="qh-quick.htm#options">Options</a>
+&#149; <a href="qh-opto.htm#output">Output</a>
+&#149; <a href="qh-optf.htm#format">Formats</a>
+&#149; <a href="qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="qh-optp.htm#print">Print</a>
+&#149; <a href="qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="qh-optc.htm#prec">Precision</a>
+&#149; <a href="qh-optt.htm#trace">Trace</a>
+&#149; <a href="../src/libqhull_r/index.htm">Functions</a></p><!-- GC common information -->
+<hr>
+
+<p><a href="http://www.geom.uiuc.edu/"><IMG align=middle
+ height=40 src="qh--geom.gif" width=40 ></a><i>The Geometry Center
+Home Page </i></p>
+
+<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
+</a><br>
+Created:
+Sept. 25, 1995 --- <!-- hhmts start -->Last modified: see top
+<!-- hhmts end --> </p>
+</body>
+</html>
diff --git a/xs/src/qhull/html/qh-optg.htm b/xs/src/qhull/html/qh-optg.htm
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+<html>
+
+<head>
+<title>Qhull Geomview options (G)</title>
+</head>
+
+<body>
+<!-- Navigation links -->
+
+<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
+<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
+<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
+&#149; <a href="qh-quick.htm#options">Options</a>
+&#149; <a href="qh-opto.htm#output">Output</a>
+&#149; <a href="qh-optf.htm#format">Formats</a>
+&#149; <a href="qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="qh-optp.htm#print">Print</a>
+&#149; <a href="qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="qh-optc.htm#prec">Precision</a>
+&#149; <a href="qh-optt.htm#trace">Trace</a>
+&#149; <a href="../src/libqhull_r/index.htm">Functions</a></p>
+
+<hr>
+<!-- Main text of document -->
+
+<h1><a
+href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/delaunay.html"><img
+src="qh--dt.gif" alt="[delaunay]" align="middle" width="100"
+height="100"></a> Qhull Geomview options (G)</h1>
+
+This section lists the Geomview options for Qhull. These options are
+indicated by 'G' followed by a letter.  See
+<a href="qh-opto.htm#output">Output</a>, <a href="qh-optp.htm#print">Print</a>,
+and <a href="qh-optf.htm#format">Format</a> for other output options.
+
+
+<p><b>Copyright &copy; 1995-2015 C.B. Barber</b></p>
+
+<hr>
+
+<p><a href="index.htm#TOC">&#187;</a> <a href="qh-quick.htm#programs">Programs</a>
+<a name="geomview">&#149;</a> <a href="qh-quick.htm#options">Options</a>
+&#149; <a href="qh-opto.htm#output">Output</a>
+&#149; <a href="qh-optf.htm#format">Formats</a>
+&#149; <a href="qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="qh-optp.htm#print">Print</a>
+&#149; <a href="qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="qh-optc.htm#prec">Precision</a>
+&#149; <a href="qh-optt.htm#trace">Trace</a>
+&#149; <a href="../src/libqhull_r/index.htm">Functions</a></p>
+
+<h2>Geomview output options</h2>
+
+<p><a href="http://www.geomview.org">Geomview</a> is the graphical
+viewer for visualizing Qhull output in 2-d, 3-d and 4-d.</p>
+
+<p>Geomview displays each facet of the convex hull. The color of
+a facet is determined by the coefficients of the facet's normal
+equation. For imprecise hulls, Geomview displays the inner and
+outer hull. Geomview can also display points, ridges, vertices,
+coplanar points, and facet intersections. </p>
+
+<p>For 2-d Delaunay triangulations, Geomview displays the
+corresponding paraboloid.  Geomview displays the 2-d Voronoi
+diagram. For halfspace intersections, it displays the
+dual convex hull. </p>
+
+<dl compact>
+    <dt>&nbsp;</dt>
+    <dd><b>General</b></dd>
+    <dt><a href="#G">G</a></dt>
+    <dd>display Geomview output</dd>
+    <dt><a href="#Gt">Gt</a></dt>
+    <dd>display transparent 3-d Delaunay triangulation</dd>
+    <dt><a href="#GDn">GDn</a></dt>
+    <dd>drop dimension n in 3-d and 4-d output </dd>
+
+    <dt>&nbsp;</dt>
+    <dt>&nbsp;</dt>
+    <dd><b>Specific</b></dd>
+    <dt><a href="#Ga">Ga</a></dt>
+    <dd>display all points as dots</dd>
+    <dt><a href="#Gc">Gc</a></dt>
+    <dd>display centrums (2-d, 3-d)</dd>
+    <dt><a href="#Gp">Gp</a></dt>
+    <dd>display coplanar points and vertices as radii</dd>
+    <dt><a href="#Gh">Gh</a></dt>
+    <dd>display hyperplane intersections</dd>
+    <dt><a href="#Gi">Gi</a></dt>
+    <dd>display inner planes only (2-d, 3-d)</dd>
+    <dt><a href="#Go">Go</a></dt>
+    <dd>display outer planes only (2-d, 3-d)</dd>
+    <dt><a href="#Gr">Gr</a></dt>
+    <dd>display ridges (3-d)</dd>
+    <dt><a href="#Gv">Gv</a></dt>
+    <dd>display vertices as spheres</dd>
+    <dt><a href="#Gn">Gn</a></dt>
+    <dd>do not display planes</dd>
+
+</dl>
+
+<hr>
+
+<h3><a href="#geomview">&#187;</a><a name="G">G - produce output for
+viewing with Geomview</a></h3>
+
+<p>By default, option 'G' displays edges in 2-d, outer planes in
+3-d, and ridges in 4-d.</p>
+
+<p>A ridge can be explicit or implicit. An explicit ridge is a <i>(d-1)</i>-dimensional
+simplex between two facets. In 4-d, the explicit ridges are
+triangles. An implicit ridge is the topological intersection of
+two neighboring facets. It is the union of explicit ridges.</p>
+
+<p>For non-simplicial 4-d facets, the explicit ridges can be
+quite complex. When displaying a ridge in 4-d, Qhull projects the
+ridge's vertices to one of its facets' hyperplanes. Use '<a
+href="#Gh">Gh</a>' to project ridges to the intersection of both
+hyperplanes. This usually results in a cleaner display. </p>
+
+<p>For 2-d Delaunay triangulations, Geomview displays the
+corresponding paraboloid.  Geomview displays the 2-d Voronoi
+diagram. For halfspace intersections, it displays the
+dual convex hull.
+
+<h3><a href="#geomview">&#187;</a><a name="Ga">Ga - display all
+points as dots </a></h3>
+
+<p>Each input point is displayed as a green dot.</p>
+
+<h3><a href="#geomview">&#187;</a><a name="Gc">Gc - display centrums
+(3-d) </a></h3>
+
+<p>The centrum is defined by a green radius sitting on a blue
+plane. The plane corresponds to the facet's hyperplane. If you
+sight along a facet's hyperplane, you will see that all
+neighboring centrums are below the facet. The radius is defined
+by '<a href="qh-optc.htm#Cn">C-n</a>' or '<a
+href="qh-optc.htm#Cn2">Cn</a>'.</p>
+
+<h3><a href="#geomview">&#187;</a><a name="GDn">GDn - drop dimension
+n in 3-d and 4-d output </a></h3>
+
+<p>The result is a 2-d or 3-d object. In 4-d, this corresponds to
+viewing the 4-d object from the nth axis without perspective.
+It's best to view 4-d objects in pieces. Use the '<a
+href="qh-optp.htm#Pdk">Pdk</a>' '<a href="qh-optp.htm#Pg">Pg</a>'
+'<a href="qh-optp.htm#PG">PG</a>' '<a href="qh-optq.htm#QGn">QGn</a>'
+and '<a href="qh-optq.htm#QVn">QVn</a>' options to select a few
+facets. If one of the facets is perpendicular to an axis, then
+projecting along that axis will show the facet exactly as it is
+in 4-d. If you generate many facets, use Geomview's <tt>ginsu</tt>
+module to view the interior</p>
+
+<p>To view multiple 4-d dimensions at once, output the object
+without 'GDn' and read it with Geomview's <tt>ndview</tt>. As you
+rotate the object in one set of dimensions, you can see how it
+changes in other sets of dimensions.</p>
+
+<p>For additional control over 4-d objects, output the object
+without 'GDn' and read it with Geomview's <tt>4dview</tt>. You
+can slice the object along any 4-d plane. You can also flip the
+halfspace that's deleted when slicing. By combining these
+features, you can get some interesting cross sections.</p>
+
+<h3><a href="#geomview">&#187;</a><a name="Gh">Gh - display
+hyperplane intersections (3-d, 4-d)</a></h3>
+
+<p>In 3-d, the intersection is a black line. It lies on two
+neighboring hyperplanes, c.f., the blue squares associated with
+centrums ('<a href="#Gc">Gc </a>'). In 4-d, the ridges are
+projected to the intersection of both hyperplanes. If you turn on
+edges (Geomview's 'appearances' menu), each triangle corresponds
+to one ridge. The ridges may overlap each other.</p>
+
+<h3><a href="#geomview">&#187;</a><a name="Gi">Gi - display inner
+planes only (2-d, 3-d)</a></h3>
+
+<p>The inner plane of a facet is below all of its vertices. It is
+parallel to the facet's hyperplane. The inner plane's color is
+the opposite of the outer plane's color, i.e., <i>[1-r,1-g,1-b] </i>.
+Its edges are determined by the vertices.</p>
+
+<h3><a href="#geomview">&#187;</a><a name="Gn">Gn - do not display
+planes </a></h3>
+
+<p>By default, Geomview displays the precise plane (no merging)
+or both inner and output planes (if merging). If merging,
+Geomview does not display the inner plane if the the difference
+between inner and outer is too small.</p>
+
+<h3><a href="#geomview">&#187;</a><a name="Go">Go - display outer
+planes only (2-d, 3-d)</a></h3>
+
+<p>The outer plane of a facet is above all input points. It is
+parallel to the facet's hyperplane. Its color is determined by
+the facet's normal, and its edges are determined by the vertices.</p>
+
+<h3><a href="#geomview">&#187;</a><a name="Gp">Gp - display coplanar
+points and vertices as radii </a></h3>
+
+<p>Coplanar points ('<a href="qh-optq.htm#Qc">Qc</a>'), interior
+points ('<a href="qh-optq.htm#Qi">Qi</a>'), outside points ('<a
+href="qh-optt.htm#TCn">TCn</a>' or '<a href="qh-optt.htm#TVn">TVn</a>'),
+and vertices are displayed as red and yellow radii. The radii are
+perpendicular to the corresponding facet. Vertices are aligned
+with an interior point. The radii define a ball which corresponds
+to the imprecision of the point. The imprecision is the maximum
+of the roundoff error, the centrum radius, and <i>maxcoord * (1 -
+</i><a href="qh-optc.htm#An"><i>A-n</i></a><i>)</i>. It is at
+least 1/20'th of the maximum coordinate, and ignores post merging
+if pre-merging is done.</p>
+
+<p>If '<a href="qh-optg.htm#Gv">Gv</a>' (print vertices as
+spheres) is also selected, option 'Gp' displays coplanar
+points as radii.  Select options <a href="qh-optq.htm#Qc">Qc</a>'
+and/or '<a href="qh-optq.htm#Qi">Qi</a>'. Options 'Qc Gpv' displays
+coplanar points while 'Qci Gpv' displays coplanar and interior
+points.  Option 'Qc' is automatically selected if 'Qi' is not
+selected with options 'Gpv'.
+
+<h3><a href="#geomview">&#187;</a><a name="Gr">Gr - display ridges
+(3-d) </a></h3>
+
+<p>A ridge connects the two vertices that are shared by
+neighboring facets. It is displayed in green. A ridge is the
+topological edge between two facets while the hyperplane
+intersection is the geometric edge between two facets. Ridges are
+always displayed in 4-d.</p>
+
+<h3><a href="#geomview">&#187;</a><a name="Gt">Gt - transparent 3-d
+Delaunay </a></h3>
+
+<p>A 3-d Delaunay triangulation looks like a convex hull with
+interior facets. Option 'Gt' removes the outside ridges to reveal
+the outermost facets. It automatically sets options '<a
+href="#Gr">Gr</a>' and '<a href="#GDn">GDn</a>'. See example <a
+href="qh-eg.htm#17f">eg.17f.delaunay.3</a>.</p>
+
+<h3><a href="#geomview">&#187;</a><a name="Gv">Gv - display vertices
+as spheres (2-d, 3-d)</a></h3>
+
+<p>The radius of the sphere corresponds to the imprecision of the
+data. See '<a href="#Gp">Gp</a>' for determining the radius.</p>
+
+<!-- Navigation links -->
+
+<hr>
+
+<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
+<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
+<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
+&#149; <a href="qh-quick.htm#options">Options</a>
+&#149; <a href="qh-opto.htm#output">Output</a>
+&#149; <a href="qh-optf.htm#format">Formats</a>
+&#149; <a href="qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="qh-optp.htm#print">Print</a>
+&#149; <a href="qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="qh-optc.htm#prec">Precision</a>
+&#149; <a href="qh-optt.htm#trace">Trace</a>
+&#149; <a href="../src/libqhull_r/index.htm">Functions</a></p>
+<!-- GC common information -->
+
+<hr>
+
+<p><a href="http://www.geom.uiuc.edu/"><img src="qh--geom.gif"
+align="middle" width="40" height="40"></a><i>The Geometry Center
+Home Page </i></p>
+
+<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
+</a><br>
+Created: Sept. 25, 1995 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
+</body>
+</html>
diff --git a/xs/src/qhull/html/qh-opto.htm b/xs/src/qhull/html/qh-opto.htm
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@@ -0,0 +1,353 @@
+<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN">
+<html>
+
+<head>
+<title>Qhull output options</title>
+</head>
+
+<body>
+<!-- Navigation links -->
+<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
+<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
+<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
+&#149; <a href="qh-quick.htm#options">Options</a>
+&#149; <a href="qh-opto.htm#output">Output</a>
+&#149; <a href="qh-optf.htm#format">Formats</a>
+&#149; <a href="qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="qh-optp.htm#print">Print</a>
+&#149; <a href="qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="qh-optc.htm#prec">Precision</a>
+&#149; <a href="qh-optt.htm#trace">Trace</a>
+&#149; <a href="../src/libqhull_r/index.htm">Functions</a></p>
+
+<hr>
+<!-- Main text of document -->
+<h1><a
+href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/delaunay.html"><img
+src="qh--dt.gif" alt="[delaunay]" align="middle" width="100"
+height="100"></a> Qhull output options</h1>
+
+<p>This section lists the output options for Qhull. These options
+are indicated by lower case characters. See <a
+href="qh-optf.htm#format">Formats</a>, <a
+href="qh-optp.htm#print">Print</a>, and <a
+href="qh-optg.htm#geomview">Geomview</a> for other output
+options. </p>
+
+<p><b>Copyright &copy; 1995-2015 C.B. Barber</b></p>
+
+<hr>
+
+<p><a href="index.htm#TOC">&#187;</a> <a href="qh-quick.htm#programs">Programs</a>
+<a name="output">&#149;</a> <a href="qh-quick.htm#options">Options</a>
+&#149; <a href="qh-opto.htm#output">Output</a>
+&#149; <a href="qh-optf.htm#format">Formats</a>
+&#149; <a href="qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="qh-optp.htm#print">Print</a>
+&#149; <a href="qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="qh-optc.htm#prec">Precision</a>
+&#149; <a href="qh-optt.htm#trace">Trace</a>
+&#149; <a href="../src/libqhull_r/index.htm">Functions</a></p>
+
+<h2>Output options</h2>
+
+<p>Qhull prints its output to standard out. All output is printed
+text. The default output is a summary (option '<a href="#s">s</a>').
+Other outputs may be specified as follows. </p>
+
+<dl compact>
+    <dt><a href="#f">f</a></dt>
+    <dd>print all fields of all facets</dd>
+    <dt><a href="#n">n</a></dt>
+    <dd>print hyperplane normals with offsets</dd>
+    <dt><a href="#m">m</a></dt>
+    <dd>print Mathematica output (2-d and 3-d)</dd>
+    <dt><a href="#o">o</a></dt>
+    <dd>print OFF file format (dim, points and facets)</dd>
+    <dt><a href="#s">s</a></dt>
+    <dd>print summary to stderr</dd>
+    <dt><a href="#p">p</a></dt>
+    <dd>print vertex and point coordinates</dd>
+    <dt><a href="#i">i</a></dt>
+    <dd>print vertices incident to each facet </dd>
+    <dt>&nbsp;</dt>
+    <dt>&nbsp;</dt>
+    <dd><b>Related options</b></dd>
+    <dt><a href="qh-optf.htm#format">F</a></dt>
+    <dd>additional input/output formats</dd>
+    <dt><a href="qh-optg.htm#geomview">G</a></dt>
+    <dd>Geomview output</dd>
+    <dt><a href="qh-optp.htm#print">P</a></dt>
+    <dd>Print options</dd>
+    <dt><a href="qh-optf.htm#Ft">Ft</a></dt>
+    <dd>print triangulation with added points</dd>
+    <dt>&nbsp;</dt>
+</dl>
+
+<hr>
+
+<h3><a href="#output">&#187;</a><a name="f">f - print all fields of
+all facets </a></h3>
+
+<p>Print <a href=../src/libqhull.h#facetT>all fields</a> of all facets.
+The facet is the primary <a href=index.htm#structure>data structure</a> for
+Qhull.
+
+<p>Option 'f' is for
+debugging. Most of the fields are available via the '<a
+href="qh-optf.htm#format">F</a>' options. If you need specialized
+information from Qhull, you can use the <a
+href="qh-code.htm#library">Qhull library</a> or <a
+href="qh-code.htm#cpp">C++ interface</a>.</p>
+
+<p>Use the '<a href="qh-optf.htm#FF">FF</a>' option to print the
+facets but not the ridges. </p>
+
+<h3><a href="#output">&#187;</a><a name="i">i - print vertices
+incident to each facet </a></h3>
+
+<p>The first line is the number of facets. The remaining lines
+list the vertices for each facet, one facet per line. The indices
+are 0-relative indices of the corresponding input points. The
+facets are oriented. Option '<a href="qh-optf.htm#Fv">Fv</a>'
+displays an unoriented list of vertices with a vertex count per
+line. Options '<a href="qh-opto.htm#o">o</a>' and '<a
+href="qh-optf.htm#Ft">Ft</a>' displays coordinates for each
+vertex prior to the vertices for each facet. </p>
+
+<p>Simplicial facets (e.g., triangles in 3-d) consist of <i>d</i>
+vertices. Non-simplicial facets in 3-d consist of 4 or more
+vertices. For example, a facet of a cube consists of 4 vertices.
+Use option '<a href="qh-optq.htm#Qt">Qt</a>' to triangulate non-simplicial facets.</p>
+
+<p>For 4-d and higher convex hulls and 3-d and higher Delaunay
+triangulations, <i>d</i> vertices are listed for all facets. A
+non-simplicial facet is triangulated with its centrum and each
+ridge. The index of the centrum is higher than any input point.
+Use option '<a href="qh-optf.htm#Fv">Fv</a>' to list the vertices
+of non-simplicial facets as is. Use option '<a
+href="qh-optf.htm#Ft">Ft</a>' to print the coordinates of the
+centrums as well as those of the input points. </p>
+
+<h3><a href="#output">&#187;</a><a name="m">m - print Mathematica
+output </a></h3>
+
+<p>Qhull writes a Mathematica file for 2-d and 3-d convex hulls,
+2-d and 3-d halfspace intersections,
+and 2-d Delaunay triangulations. Qhull produces a list of
+objects that you can assign to a variable in Mathematica, for
+example: &quot;<tt>list= &lt;&lt; &lt;outputfilename&gt; </tt>&quot;.
+If the object is 2-d, it can be visualized by &quot;<tt>Show[Graphics[list]]
+</tt>&quot;. For 3-d objects the command is &quot;<tt>Show[Graphics3D[list]]
+</tt>&quot;. Now the object can be manipulated by commands of the
+form <tt>&quot;Show[%, &lt;parametername&gt; -&gt;
+&lt;newvalue&gt;]</tt>&quot;. </p>
+
+<p>For Delaunay triangulation orthogonal projection is better.
+This can be specified, for example, by &quot;<tt>BoxRatios:
+Show[%, BoxRatios -&gt; {1, 1, 1e-8}]</tt>&quot;. To see the
+meaningful side of the 3-d object used to visualize 2-d Delaunay,
+you need to change the viewpoint: &quot;<tt>Show[%, ViewPoint
+-&gt; {0, 0, -1}]</tt>&quot;. By specifying different viewpoints
+you can slowly rotate objects. </p>
+
+<p>For halfspace intersections, Qhull produces the dual
+convex hull.
+
+<p>See <a href="qh-faq.htm#math">Is Qhull available for Mathematica?</a>
+for URLs.
+
+<h3><a href="#output">&#187;</a><a name="n">n - print hyperplane
+normals with offsets </a></h3>
+
+<p>The first line is the dimension plus one. The second line is
+the number of facets. The remaining lines are the normals for
+each facet, one normal per line. The facet's offset follows its
+normal coefficients.</p>
+
+<p>The normals point outward, i.e., the convex hull satisfies <i>Ax
+&lt;= -b </i>where <i>A</i> is the matrix of coefficients and <i>b</i>
+is the vector of offsets.</p>
+
+<p>A point is <i>inside</i> or <i>below</i> a hyperplane if its distance
+to the hyperplane is negative.  A point is <i>outside</i> or <i>above</i> a hyperplane
+if its distance to the hyperplane is positive.  Otherwise a point is <i>on</i> or
+<i>coplanar to</i> the hyperplane.
+
+<p>If cdd output is specified ('<a href="qh-optf.htm#FD">FD</a>'),
+Qhull prints the command line, the keyword &quot;begin&quot;, the
+number of facets, the dimension (plus one), the keyword
+&quot;real&quot;, and the normals for each facet. The facet's
+negative offset precedes its normal coefficients (i.e., if the
+origin is an interior point, the offset is positive). Qhull ends
+the output with the keyword &quot;end&quot;. </p>
+
+<h3><a href="#output">&#187;</a><a name="o">o - print OFF file format
+</a></h3>
+
+<p>The output is: </p>
+
+<ul>
+    <li>The first line is the dimension </li>
+    <li>The second line is the number of points, the number of
+        facets, and the number of ridges. </li>
+    <li>All of the input points follow, one per line. </li>
+    <li>Then Qhull prints the vertices for each facet. Each facet
+        is on a separate line. The first number is the number of
+        vertices. The remainder is the indices of the
+        corresponding points. The vertices are oriented in 2-d,
+        3-d, and in simplicial facets. </li>
+</ul>
+
+<p>Option '<a href="qh-optf.htm#Ft">Ft</a>' prints the same
+information with added points for non-simplicial facets.</p>
+
+<p>Option '<a href="qh-opto.htm#i">i</a>' displays vertices
+without the point coordinates. Option '<a href="qh-opto.htm#p">p</a>'
+displays the point coordinates without vertex and facet information.</p>
+
+<p>In 3-d, Geomview can load the file directly if you delete the
+first line (e.g., by piping through '<tt>tail +2</tt>').</p>
+
+<p>For Voronoi diagrams (<a href=qvoronoi.htm>qvoronoi</a>), option
+'o' prints Voronoi vertices and Voronoi regions instead of input
+points and facets. The first vertex is the infinity vertex
+[-10.101, -10.101, ...]. Then, option 'o' lists the vertices in
+the Voronoi region for each input site. The regions appear in
+site ID order. In 2-d, the vertices of a Voronoi region are
+sorted by adjacency (non-oriented). In 3-d and higher, the
+Voronoi vertices are sorted by index. See the '<a
+href="qh-optf.htm#FN">FN</a>' option for listing Voronoi regions
+without listing Voronoi vertices.</p>
+
+<p>If you are using the Qhull library, options 'v o' have the
+side effect of reordering the neighbors for a vertex.</p>
+
+<h3><a href="#output">&#187;</a><a name="p">p - print vertex and
+point coordinates </a></h3>
+
+<p>The first line is the dimension. The second line is the number
+of vertices. The remaining lines are the vertices, one vertex per
+line. A vertex consists of its point coordinates</p>
+
+<p>With the '<a href="qh-optg.htm#Gc">Gc</a>' and '<a
+href="qh-optg.htm#Gi">Gi</a>' options, option 'p' also prints
+coplanar and interior points respectively.</p>
+
+<p>For <a href=qvoronoi.htm>qvoronoi</a>, it prints the
+coordinates of each Voronoi vertex.</p>
+
+<p>For <a href=qdelaun.htm>qdelaunay</a>, it prints the
+input sites as lifted to a paraboloid.  For <a href=qhalf.htm>qhalf</a>
+it prints the dual points.  For both, option 'p' is the same as the first
+section of option '<a href="qh-opto.htm#o">o</a>'.</p>
+
+<p>Use '<a href="qh-optf.htm#Fx">Fx</a>' to list the point ids of
+the extreme points (i.e., vertices). </p>
+
+<p>If a subset of the facets is selected ('<a
+href="qh-optp.htm#Pdk">Pdk</a>', '<a href="qh-optp.htm#PDk">PDk</a>',
+'<a href="qh-optp.htm#Pg">Pg</a>' options), option 'p' only
+prints vertices and points associated with those facets.</p>
+
+<p>If cdd-output format is selected ('<a href="qh-optf.htm#FD">FD</a>'),
+the first line is &quot;begin&quot;. The second line is the
+number of vertices, the dimension plus one, and &quot;real&quot;.
+The vertices follow with a leading &quot;1&quot;. Output ends
+with &quot;end&quot;. </p>
+
+<h3><a href="#output">&#187;</a><a name="s">s - print summary to
+stderr </a></h3>
+
+<p>The default output of Qhull is a summary to stderr. Options '<a
+href="qh-optf.htm#FS">FS</a>' and '<a href="qh-optf.htm#Fs">Fs</a>'
+produce the same information for programs.  <b>Note</b>: Windows 95 and 98
+treats stderr the same as stdout.  Use option '<a href="qh-optt.htm#TO">TO file</a>' to separate
+stderr and stdout.</p>
+
+<p>The summary lists the number of input points, the dimension,
+the number of vertices in the convex hull, and the number of
+facets in the convex hull. It lists the number of selected
+(&quot;good&quot;) facets for options '<a href="qh-optp.htm#Pg">Pg</a>',
+'<a href="qh-optp.htm#Pdk">Pdk</a>', <a href=qdelaun.htm>qdelaunay</a>,
+or <a href=qvoronoi.htm>qvoronoi</a> (Delaunay triangulations only
+use the lower half of a convex hull). It lists the number of
+coplanar points. For Delaunay triangulations without '<a
+href="qh-optq.htm#Qc">Qc</a>', it lists the total number of
+coplanar points. It lists the number of simplicial facets in
+the output.</p>
+
+<p>The terminology depends on the output structure. </p>
+
+<p>The summary lists these statistics:</p>
+
+<ul>
+    <li>number of points processed by Qhull </li>
+    <li>number of hyperplanes created</li>
+    <li>number of distance tests (not counting statistics,
+        summary, and checking) </li>
+    <li>number of merged facets (if any)</li>
+    <li>number of distance tests for merging (if any)</li>
+    <li>CPU seconds to compute the hull</li>
+    <li>the maximum joggle for '<a href="qh-optq.htm#QJn">QJ</a>'<br>
+        or, the probability of precision errors for '<a
+        href="qh-optq.htm#QJn">QJ</a> <a href="qh-optt.htm#TRn">TRn</a>'
+    </li>
+    <li>total area and volume (if computed, see '<a
+        href="qh-optf.htm#FS">FS</a>' '<a href="qh-optf.htm#FA">FA</a>'
+        '<a href="qh-optf.htm#Fa">Fa</a>' '<a
+        href="qh-optp.htm#PAn">PAn</a>')</li>
+    <li>max. distance of a point above a facet (if non-zero)</li>
+    <li>max. distance of a vertex below a facet (if non-zero)</li>
+</ul>
+
+<p>The statistics include intermediate hulls. For example 'rbox d
+D4 | qhull' reports merged facets even though the final hull is
+simplicial. </p>
+
+<p>Qhull starts counting CPU seconds after it has read and
+projected the input points. It stops counting before producing
+output. In the code, CPU seconds measures the execution time of
+function qhull() in <tt>libqhull.c</tt>. If the number of CPU
+seconds is clearly wrong, check qh_SECticks in <tt>user.h</tt>. </p>
+
+<p>The last two figures measure the maximum distance from a point
+or vertex to a facet. They are not printed if less than roundoff
+or if not merging. They account for roundoff error in computing
+the distance (c.f., option '<a href="qh-optc.htm#Rn">Rn</a>').
+Use '<a href="qh-optf.htm#Fs">Fs</a>' to report the maximum outer
+and inner plane. </p>
+
+<p>A number may appear in parentheses after the maximum distance
+(e.g., 2.1x). It is the ratio between the maximum distance and
+the worst-case distance due to merging two simplicial facets. It
+should be small for 2-d, 3-d, and 4-d, and for higher dimensions
+with '<a href="qh-optq.htm#Qx">Qx</a>'. It is not printed if less
+than 0.05. </p>
+<!-- Navigation links -->
+<hr>
+
+<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
+<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
+<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
+&#149; <a href="qh-quick.htm#options">Options</a>
+&#149; <a href="qh-opto.htm#output">Output</a>
+&#149; <a href="qh-optf.htm#format">Formats</a>
+&#149; <a href="qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="qh-optp.htm#print">Print</a>
+&#149; <a href="qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="qh-optc.htm#prec">Precision</a>
+&#149; <a href="qh-optt.htm#trace">Trace</a>
+&#149; <a href="../src/libqhull_r/index.htm">Functions</a></p>
+<!-- GC common information -->
+<hr>
+
+<p><a href="http://www.geom.uiuc.edu/"><img src="qh--geom.gif"
+align="middle" width="40" height="40"></a><i>The Geometry Center
+Home Page </i></p>
+
+<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
+</a><br>
+Created: Sept. 25, 1995 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
+</body>
+</html>
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new file mode 100644
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@@ -0,0 +1,253 @@
+<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN">
+<html>
+
+<head>
+<title>Qhull print options (P)</title>
+</head>
+
+<body>
+<!-- Navigation links -->
+<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
+<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
+<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
+&#149; <a href="qh-quick.htm#options">Options</a>
+&#149; <a href="qh-opto.htm#output">Output</a>
+&#149; <a href="qh-optf.htm#format">Formats</a>
+&#149; <a href="qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="qh-optp.htm#print">Print</a>
+&#149; <a href="qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="qh-optc.htm#prec">Precision</a>
+&#149; <a href="qh-optt.htm#trace">Trace</a>
+&#149; <a href="../src/libqhull_r/index.htm">Functions</a></p>
+
+<hr>
+<!-- Main text of document -->
+<h1><a
+href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/delaunay.html"><img
+src="qh--dt.gif" alt="[delaunay]" align="middle" width="100"
+height="100"></a> Qhull print options (P)</h1>
+
+This section lists the print options for Qhull. These options are
+indicated by 'P' followed by a letter.  See
+<a href="qh-opto.htm#output">Output</a>, <a href="qh-optg.htm#geomview">Geomview</a>,
+and <a href="qh-optf.htm#format">Format</a> for other output options.
+
+
+<p><b>Copyright &copy; 1995-2015 C.B. Barber</b></p>
+
+<hr>
+
+<p><a href="index.htm#TOC">&#187;</a> <a href="qh-quick.htm#programs">Programs</a>
+<a name="format">&#149;</a> <a href="qh-quick.htm#options">Options</a>
+&#149; <a href="qh-opto.htm#output">Output</a>
+&#149; <a href="qh-optf.htm#format">Formats</a>
+&#149; <a href="qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="qh-optp.htm#print">Print</a>
+&#149; <a href="qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="qh-optc.htm#prec">Precision</a>
+&#149; <a href="qh-optt.htm#trace">Trace</a>
+&#149; <a href="../src/libqhull_r/index.htm">Functions</a></p>
+
+<h2>Print options</h2>
+<blockquote>
+<dl compact>
+    <dt>&nbsp;</dt>
+    <dd><b>General</b></dd>
+    <dt><a href="#Pp">Pp</a></dt>
+    <dd>do not report precision problems </dd>
+    <dt><a href="#Po">Po</a></dt>
+    <dd>force output despite precision problems</dd>
+    <dt><a href="#Po2">Po</a></dt>
+    <dd>if error, output neighborhood of facet</dd>
+    <dt>&nbsp;</dt>
+    <dt>&nbsp;</dt>
+    <dd><b>Select</b></dd>
+    <dt><a href="#Pdk">Pdk:n</a></dt>
+    <dd>print facets with normal[k] &gt;= n (default 0.0)</dd>
+    <dt><a href="#PDk">PDk:n</a></dt>
+    <dd>print facets with normal[k] &lt;= n </dd>
+    <dt><a href="#PFn">PFn</a></dt>
+    <dd>print facets whose area is at least n</dd>
+    <dt><a href="#Pg">Pg</a></dt>
+    <dd>print good facets only (needs '<a href="qh-optq.htm#QGn">QGn</a>'
+        or '<a href="qh-optq.htm#QVn">QVn </a>')</dd>
+    <dt><a href="#PMn">PMn</a></dt>
+    <dd>print n facets with most merges</dd>
+    <dt><a href="#PAn">PAn</a></dt>
+    <dd>print n largest facets by area</dd>
+    <dt><a href="#PG">PG</a></dt>
+    <dd>print neighbors of good facets</dd>
+</dl>
+</blockquote>
+<hr>
+
+<h3><a href="#print">&#187;</a><a name="PAn">PAn - keep n largest
+facets by area</a></h3>
+
+<p>The <i>n</i> largest facets are marked good for printing. This
+may be useful for <a href="qh-impre.htm#approximate">approximating
+a hull</a>. Unless '<a href="#PG">PG</a>' is set, '<a href="#Pg">Pg</a>'
+is automatically set. </p>
+
+<h3><a href="#print">&#187;</a><a name="Pdk">Pdk:n - print facet if
+normal[k] &gt;= n </a></h3>
+
+<p>For a given output, print only those facets with <i>normal[k] &gt;= n</i>
+and <i>drop</i> the others.  For example, 'Pd0:0.5' prints facets with <i>normal[0]
+&gt;= 0.5 </i>. The default value of <i>n</i> is zero. For
+example in 3-d, 'Pd0d1d2' prints facets in the positive octant.
+<p>
+If no facets match, the closest facet is returned.</p>
+<p>
+On Windows 95, do not combine multiple options.  A 'd' is considered
+part of a number.  For example, use 'Pd0:0.5 Pd1:0.5' instead of
+'Pd0:0.5d1:0.5'.
+
+<h3><a href="#print">&#187;</a><a name="PDk">PDk:n - print facet if
+normal[k] &lt;= n</a></h3>
+
+<p>For a given output, print only those facets with <i>normal[k] &lt;= n</i>
+and <i>drop</i> the others.
+For example, 'PD0:0.5' prints facets with <i>normal[0]
+&lt;= 0.5 </i>. The default value of <i>n</i> is zero. For
+example in 3-d, 'PD0D1D2' displays facets in the negative octant.
+<p>
+If no facets match, the closest facet is returned.</p>
+
+<p>In 2-d, 'd G PD2' displays the Delaunay triangulation instead
+of the corresponding paraboloid. </p>
+
+<p>Be careful of placing 'Dk' or 'dk' immediately after a real
+number. Some compilers treat the 'D' as a double precision
+exponent. </p>
+
+<h3><a href="#print">&#187;</a><a name="PFn">PFn - keep facets whose
+area is at least n</a></h3>
+
+<p>The facets with area at least <i>n</i> are marked good for
+printing. This may be useful for <a
+href="qh-impre.htm#approximate">approximating a hull</a>. Unless
+'<a href="#PG">PG</a>' is set, '<a href="#Pg">Pg</a>' is
+automatically set. </p>
+
+<h3><a href="#print">&#187;</a><a name="Pg">Pg - print good facets </a></h3>
+
+<p>Qhull can mark facets as &quot;good&quot;. This is used to</p>
+
+<ul>
+    <li>mark the lower convex hull for Delaunay triangulations
+        and Voronoi diagrams</li>
+    <li>mark the facets that are visible from a point (the '<a
+        href="qh-optq.htm#QGn">QGn </a>' option)</li>
+    <li>mark the facets that contain a point (the '<a
+        href="qh-optq.htm#QVn">QVn</a>' option).</li>
+    <li>indicate facets with a large enough area (options '<a
+        href="#PAn">PAn</a>' and '<a href="#PFn">PFn</a>')</li>
+</ul>
+
+<p>Option '<a href="#Pg">Pg</a>' only prints good facets that
+also meet '<a href="#Pdk">Pdk</a>' and '<a href="#PDk">PDk</a>'
+options. It is automatically set for options '<a href="#PAn">PAn</a>',
+'<a href="#PFn">PFn </a>', '<a href="qh-optq.htm#QGn">QGn</a>',
+and '<a href="qh-optq.htm#QVn">QVn</a>'.</p>
+
+<h3><a href="#print">&#187;</a><a name="PG">PG - print neighbors of
+good facets</a></h3>
+
+<p>Option 'PG' can be used with or without option '<a href="#Pg">Pg</a>'
+to print the neighbors of good facets. For example, options '<a
+href="qh-optq.htm#QGn">QGn</a>' and '<a href="qh-optq.htm#QVn">QVn</a>'
+print the horizon facets for point <i>n. </i></p>
+
+<h3><a href="#print">&#187;</a><a name="PMn">PMn - keep n facets with
+most merges</a></h3>
+
+<p>The n facets with the most merges are marked good for
+printing. This may be useful for <a
+href="qh-impre.htm#approximate">approximating a hull</a>. Unless
+'<a href="#PG">PG</a>' is set, '<a href="#Pg">Pg</a>' is
+automatically set. </p>
+
+<p>Use option '<a href="qh-optf.htm#Fm">Fm</a>' to print merges
+per facet.
+
+<h3><a href="#print">&#187;</a><a name="Po">Po - force output despite
+precision problems</a></h3>
+
+<p>Use options 'Po' and '<a href="qh-optq.htm#Q0">Q0</a>' if you
+can not merge facets, triangulate the output ('<a href="qh-optq.htm#Qt">Qt</a>'),
+or joggle the input (<a href="qh-optq.htm#QJn">QJ</a>).
+
+<p>Option 'Po' can not force output when
+duplicate ridges or duplicate facets occur. It may produce
+erroneous results. For these reasons, merged facets, joggled input, or <a
+href="qh-impre.htm#exact">exact arithmetic</a> are better.</p>
+
+<p>If you need a simplicial Delaunay triangulation, use
+joggled input '<a href="qh-optq.htm#QJn">QJ</a>' or triangulated
+output '<a
+href="qh-optf.htm#Ft">Ft</a>'.
+
+<p>Option 'Po' may be used without '<a href="qh-optq.htm#Q0">Q0</a>'
+to remove some steps from Qhull or to output the neighborhood of
+an error.</p>
+
+<p>Option 'Po' may be used with option '<a href="qh-optq.htm#Q5">Q5</a>')
+to skip qh_check_maxout (i.e., do not determine the maximum outside distance).
+This can save a significant amount of time.
+
+<p>If option 'Po' is used,</p>
+
+<ul>
+    <li>most precision errors allow Qhull to continue. </li>
+    <li>verify ('<a href="qh-optt.htm#Tv">Tv</a>') does not check
+        coplanar points.</li>
+    <li>points are not partitioned into flipped facets and a
+        flipped facet is always visible to a point. This may
+        delete flipped facets from the output. </li>
+</ul>
+
+<h3><a href="#print">&#187;</a><a name="Po2">Po - if error, output
+neighborhood of facet</a></h3>
+
+<p>If an error occurs before the completion of Qhull and tracing
+is not active, 'Po' outputs a neighborhood of the erroneous
+facets (if any). It uses the current output options.</p>
+
+<p>See '<a href="qh-optp.htm#Po">Po</a>' - force output despite
+precision problems.
+
+<h3><a href="#print">&#187;</a><a name="Pp">Pp - do not report
+precision problems </a></h3>
+
+<p>With option 'Pp', Qhull does not print statistics about
+precision problems, and it removes some of the warnings.  It
+removes the narrow hull warning.</p>
+
+<!-- Navigation links -->
+<hr>
+
+<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
+<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
+<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
+&#149; <a href="qh-quick.htm#options">Options</a>
+&#149; <a href="qh-opto.htm#output">Output</a>
+&#149; <a href="qh-optf.htm#format">Formats</a>
+&#149; <a href="qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="qh-optp.htm#print">Print</a>
+&#149; <a href="qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="qh-optc.htm#prec">Precision</a>
+&#149; <a href="qh-optt.htm#trace">Trace</a>
+&#149; <a href="../src/libqhull_r/index.htm">Functions</a></p>
+<!-- GC common information -->
+<hr>
+
+<p><a href="http://www.geom.uiuc.edu/"><img src="qh--geom.gif"
+align="middle" width="40" height="40"></a><i>The Geometry Center
+Home Page </i></p>
+
+<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
+</a><br>
+Created: Sept. 25, 1995 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
+</body>
+</html>
diff --git a/xs/src/qhull/html/qh-optq.htm b/xs/src/qhull/html/qh-optq.htm
new file mode 100644
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@@ -0,0 +1,731 @@
+<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN">
+<html>
+
+<head>
+<title>Qhull control options (Q)</title>
+</head>
+
+<body>
+<!-- Navigation links -->
+<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
+<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
+<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
+&#149; <a href="qh-quick.htm#options">Options</a>
+&#149; <a href="qh-opto.htm#output">Output</a>
+&#149; <a href="qh-optf.htm#format">Formats</a>
+&#149; <a href="qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="qh-optp.htm#print">Print</a>
+&#149; <a href="qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="qh-optc.htm#prec">Precision</a>
+&#149; <a href="qh-optt.htm#trace">Trace</a>
+&#149; <a href="../src/libqhull_r/index.htm">Functions</a></p>
+
+<hr>
+<!-- Main text of document -->
+<h1><a
+href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/delaunay.html"><img
+src="qh--dt.gif" alt="[delaunay]" align="middle" width="100"
+height="100"></a> Qhull control options (Q)</h1>
+
+<p>This section lists the control options for Qhull. These
+options are indicated by 'Q' followed by a letter. </p>
+
+<p><b>Copyright &copy; 1995-2015 C.B. Barber</b></p>
+
+<hr>
+
+<p><a href="index.htm#TOC">&#187;</a> <a href="qh-quick.htm#programs">Programs</a>
+<a name="qhull">&#149;</a> <a href="qh-quick.htm#options">Options</a>
+&#149; <a href="qh-opto.htm#output">Output</a>
+&#149; <a href="qh-optf.htm#format">Formats</a>
+&#149; <a href="qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="qh-optp.htm#print">Print</a>
+&#149; <a href="qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="qh-optc.htm#prec">Precision</a>
+&#149; <a href="qh-optt.htm#trace">Trace</a>
+&#149; <a href="../src/libqhull_r/index.htm">Functions</a></p>
+
+<h2>Qhull control options</h2>
+
+<dl compact>
+    <dt>&nbsp;</dt>
+    <dd><b>General</b></dd>
+    <dt><a href="#Qu">Qu</a></dt>
+    <dd>compute upper hull for furthest-site Delaunay
+        triangulation </dd>
+    <dt><a href="#Qc">Qc</a></dt>
+    <dd>keep coplanar points with nearest facet</dd>
+    <dt><a href="#Qi">Qi</a></dt>
+    <dd>keep interior points with nearest facet</dd>
+    <dt><a href="#QJn">QJ</a></dt>
+    <dd>joggled input to avoid precision problems</dd>
+    <dt><a href="#Qt">Qt</a></dt>
+    <dd>triangulated output</dd>
+    <dt>&nbsp;</dt>
+    <dt>&nbsp;</dt>
+    <dd><b>Precision handling</b></dd>
+    <dt><a href="#Qz">Qz</a></dt>
+    <dd>add a point-at-infinity for Delaunay triangulations</dd>
+    <dt><a href="#Qx">Qx</a></dt>
+    <dd>exact pre-merges (allows coplanar facets)</dd>
+    <dt><a href="#Qs">Qs</a></dt>
+    <dd>search all points for the initial simplex</dd>
+    <dt><a href="#Qbb">Qbb</a></dt>
+    <dd>scale last coordinate to [0,m] for Delaunay</dd>
+    <dt><a href="#Qv">Qv</a></dt>
+    <dd>test vertex neighbors for convexity</dd>
+    <dt>&nbsp;</dt>
+    <dt>&nbsp;</dt>
+    <dd><b>Transform input</b></dd>
+    <dt><a href="#Qb0">Qbk:0Bk:0</a></dt>
+    <dd>drop dimension k from input</dd>
+    <dt><a href="#QRn">QRn</a></dt>
+    <dd>random rotation (n=seed, n=0 time, n=-1 time/no rotate)</dd>
+    <dt><a href="#Qbk">Qbk:n</a></dt>
+    <dd>scale coord[k] to low bound of n (default -0.5)</dd>
+    <dt><a href="#QBk">QBk:n</a></dt>
+    <dd>scale coord[k] to upper bound of n (default 0.5)</dd>
+    <dt><a href="#QbB">QbB</a></dt>
+    <dd>scale input to fit the unit cube</dd>
+    <dt>&nbsp;</dt>
+    <dt>&nbsp;</dt>
+    <dd><b>Select facets</b></dd>
+    <dt><a href="#QVn">QVn</a></dt>
+    <dd>good facet if it includes point n, -n if not</dd>
+    <dt><a href="#QGn">QGn</a></dt>
+    <dd>good facet if visible from point n, -n for not visible</dd>
+    <dt><a href="#Qg">Qg</a></dt>
+    <dd>only build good facets (needs '<a href="#QGn">QGn</a>', '<a
+        href="#QVn">QVn </a>', or '<a href="qh-optp.htm#Pdk">Pdk</a>')</dd>
+    <dt>&nbsp;</dt>
+    <dt>&nbsp;</dt>
+    <dd><b>Experimental</b></dd>
+    <dt><a href="#Q4">Q4</a></dt>
+    <dd>avoid merging old facets into new facets</dd>
+    <dt><a href="#Q5">Q5</a></dt>
+    <dd>do not correct outer planes at end of qhull</dd>
+    <dt><a href="#Q3">Q3</a></dt>
+    <dd>do not merge redundant vertices</dd>
+    <dt><a href="#Q6">Q6</a></dt>
+    <dd>do not pre-merge concave or coplanar facets</dd>
+    <dt><a href="#Q0">Q0</a></dt>
+    <dd>do not pre-merge facets with 'C-0' or 'Qx'</dd>
+    <dt><a href="#Q8">Q8</a></dt>
+    <dd>ignore near-interior points</dd>
+    <dt><a href="#Q2">Q2</a></dt>
+    <dd>merge all non-convex at once instead of independent sets</dd>
+    <dt><a href="#Qf">Qf</a></dt>
+    <dd>partition point to furthest outside facet</dd>
+    <dt><a href="#Q7">Q7</a></dt>
+    <dd>process facets depth-first instead of breadth-first</dd>
+    <dt><a href="#Q9">Q9</a></dt>
+    <dd>process furthest of furthest points</dd>
+    <dt><a href="#Q10">Q10</a></dt>
+    <dd>no special processing for narrow distributions</dd>
+    <dt><a href="#Q11">Q11</a></dt>
+    <dd>copy normals and recompute centrums for tricoplanar facets</dd>
+    <dt><a href="#Q12">Q12</a></dt>
+    <dd>do not error on wide merge due to duplicate ridge and nearly coincident points</dd>
+    <dt><a href="#Qm">Qm</a></dt>
+    <dd>process points only if they would increase the max. outer
+        plane </dd>
+    <dt><a href="#Qr">Qr</a></dt>
+    <dd>process random outside points instead of furthest one</dd>
+    <dt><a href="#Q1">Q1</a></dt>
+    <dd>sort merges by type instead of angle</dd>
+</dl>
+
+<hr>
+
+<h3><a href="#qhull">&#187;</a><a name="Qbb">Qbb - scale the last
+coordinate to [0,m] for Delaunay</a></h3>
+
+<p>After scaling with option 'Qbb', the lower bound of the last
+coordinate will be 0 and the upper bound will be the maximum
+width of the other coordinates. Scaling happens after projecting
+the points to a paraboloid and scaling other coordinates. </p>
+
+<p>Option 'Qbb' is automatically set for <a href=qdelaun.htm>qdelaunay</a>
+and <a href=qvoronoi.htm>qvoronoi</a>.  Option 'Qbb' is automatically set for joggled input '<a
+href="qh-optq.htm#QJn">QJ</a>'. </p>
+
+<p>Option 'Qbb' should be used for Delaunay triangulations with
+integer coordinates. Since the last coordinate is the sum of
+squares, it may be much larger than the other coordinates. For
+example, <tt>rbox 10000 D2 B1e8 | qhull d</tt> has precision
+problems while <tt>rbox 10000 D2 B1e8 | qhull d Qbb</tt> is OK. </p>
+
+<h3><a href="#qhull">&#187;</a><a name="QbB">QbB - scale the input to
+fit the unit cube</a></h3>
+
+<p>After scaling with option 'QbB', the lower bound will be -0.5
+and the upper bound +0.5 in all dimensions. For different bounds
+change qh_DEFAULTbox in <tt>user.h</tt> (0.5 is best for <a
+href="index.htm#geomview">Geomview</a>).</p>
+
+<p>For Delaunay and Voronoi diagrams, scaling happens after
+projection to the paraboloid. Under precise arithmetic, scaling
+does not change the topology of the convex hull. Scaling may
+reduce precision errors if coordinate values vary widely.</p>
+
+<h3><a href="#qhull">&#187;</a><a name="Qbk">Qbk:n - scale coord[k]
+to low bound</a></h3>
+
+<p>After scaling, the lower bound for dimension k of the input
+points will be n. 'Qbk' scales coord[k] to -0.5. </p>
+
+<h3><a href="#qhull">&#187;</a><a name="QBk">QBk:n - scale coord[k]
+to upper bound </a></h3>
+
+<p>After scaling, the upper bound for dimension k of the input
+points will be n. 'QBk' scales coord[k] to 0.5. </p>
+
+<h3><a href="#qhull">&#187;</a><a name="Qb0">Qbk:0Bk:0 - drop
+dimension k from the input points</a></h3>
+
+<p>Drop dimension<em> k </em>from the input points. For example,
+'Qb1:0B1:0' deletes the y-coordinate from all input points. This
+allows the user to take convex hulls of sub-dimensional objects.
+It happens before the Delaunay and Voronoi transformation.
+It happens after the halfspace transformation for both the data
+and the feasible point.</p>
+
+<h3><a href="#qhull">&#187;</a><a name="Qc">Qc - keep coplanar points
+with nearest facet </a></h3>
+
+<p>During construction of the hull, a point is coplanar if it is
+between '<a href="qh-optc.htm#Wn">Wn</a>' above and '<a
+href="qh-optc.htm#Un">Un</a>' below a facet's hyperplane. A
+different definition is used for output from Qhull. </p>
+
+<p>For output, a coplanar point is above the minimum vertex
+(i.e., above the inner plane). With joggle ('<a
+href="qh-optq.htm#QJn">QJ</a>'), a coplanar point includes points
+within one joggle of the inner plane. </p>
+
+<p>With option 'Qc', output formats '<a href="qh-opto.htm#p">p </a>',
+'<a href="qh-opto.htm#f">f</a>', '<a href="qh-optg.htm#Gp">Gp</a>',
+'<a href="qh-optf.htm#Fc">Fc</a>', '<a href="qh-optf.htm#FN">FN</a>',
+and '<a href="qh-optf.htm#FP">FP</a>' will print the coplanar
+points. With options 'Qc <a href="#Qi">Qi</a>' these outputs
+include the interior points.</p>
+
+<p>For Delaunay triangulations (<a href=qdelaun.htm>qdelaunay</a>
+or <a href=qvoronoi.htm>qvoronoi</a>), a coplanar point is a point
+that is nearly incident to a vertex. All input points are either
+vertices of the triangulation or coplanar.</p>
+
+<p>Qhull stores coplanar points with a facet. While constructing
+the hull, it retains all points within qh_RATIOnearInside
+(user.h) of a facet. In qh_check_maxout(), it uses these points
+to determine the outer plane for each facet. With option 'Qc',
+qh_check_maxout() retains points above the minimum vertex for the
+hull. Other points are removed. If qh_RATIOnearInside is wrong or
+if options '<a href="#Q5">Q5</a> <a href="#Q8">Q8</a>' are set, a
+coplanar point may be missed in the output (see <a
+href="qh-impre.htm#limit">Qhull limitations</a>).</p>
+
+<h3><a href="#qhull">&#187;</a><a name="Qf">Qf - partition point to
+furthest outside facet </a></h3>
+
+<p>After adding a new point to the convex hull, Qhull partitions
+the outside points and coplanar points of the old, visible
+facets. Without the '<a href="qh-opto.htm#f">f </a>' option and
+merging, it assigns a point to the first facet that it is outside
+('<a href="qh-optc.htm#Wn">Wn</a>'). When merging, it assigns a
+point to the first facet that is more than several times outside
+(see qh_DISToutside in user.h).</p>
+
+<p>If option 'Qf' is selected, Qhull performs a directed search
+(no merging) or an exhaustive search (merging) of new facets.
+Option 'Qf' may reduce precision errors if pre-merging does not
+occur.</p>
+
+<p>Option '<a href="#Q9">Q9</a>' processes the furthest of all
+furthest points.</p>
+
+<h3><a href="#qhull">&#187;</a><a name="Qg">Qg - only build good
+facets (needs 'QGn' 'QVn' or 'Pdk') </a></h3>
+
+<p>Qhull has several options for defining and printing good
+facets. With the '<a href="#Qg">Qg</a>' option, Qhull will only
+build those facets that it needs to determine the good facets in
+the output. This may speed up Qhull in 2-d and 3-d. It is
+useful for furthest-site Delaunay
+triangulations (<a href=qdelau_f.htm>qdelaunay Qu</a>,
+invoke with 'qhull d Qbb <a href="#Qu">Qu</a> Qg').
+It is not effective in higher
+dimensions because many facets see a given point and contain a
+given vertex. It is not guaranteed to work for all combinations.</p>
+
+<p>See '<a href="#QGn">QGn</a>', '<a href="#QVn">QVn</a>', and '<a
+href="qh-optp.htm#Pdk">Pdk</a>' for defining good facets, and '<a
+href="qh-optp.htm#Pg">Pg</a>' and '<a href="qh-optp.htm#PG">PG</a>'
+for printing good facets and their neighbors. If pre-merging ('<a
+href="qh-optc.htm#Cn">C-n</a>') is not used and there are
+coplanar facets, then 'Qg Pg' may produce a different result than
+'<a href="qh-optp.htm#Pg">Pg</a>'. </p>
+
+<h3><a href="#qhull">&#187;</a><a name="QGn">QGn - good facet if
+visible from point n, -n for not visible </a></h3>
+
+<p>With option 'QGn', a facet is good (see '<a href="#Qg">Qg</a>'
+and '<a href="qh-optp.htm#Pg">Pg</a>') if it is visible from
+point n. If <i>n &lt; 0</i>, a facet is good if it is not visible
+from point n. Point n is not added to the hull (unless '<a
+href="qh-optt.htm#TCn">TCn</a>' or '<a href="qh-optt.htm#TPn">TPn</a>').</p>
+
+<p>With <a href="rbox.htm">rbox</a>, use the 'Pn,m,r' option
+to define your point; it will be point 0 ('QG0'). </p>
+
+<h3><a href="#qhull">&#187;</a><a name="Qi">Qi - keep interior points
+with nearest facet </a></h3>
+
+<p>Normally Qhull ignores points that are clearly interior to the
+convex hull. With option 'Qi', Qhull treats interior points the
+same as coplanar points. Option 'Qi' does not retain coplanar
+points. You will probably want '<a href="#Qc">Qc </a>' as well. </p>
+
+<p>Option 'Qi' is automatically set for '<a href=qdelaun.htm>qdelaunay</a>
+<a href="#Qc">Qc</a>' and '<a href=qvoronoi.htm>qvoronoi</a>
+<a href="#Qc">Qc</a>'. If you use
+'<a href=qdelaun.htm>qdelaunay</a> Qi' or '<a href=qvoronoi.htm>qvoronoi</a>
+Qi', option '<a href="qh-opto.htm#s">s</a>' reports all nearly
+incident points while option '<a href="qh-optf.htm#Fs">Fs</a>'
+reports the number of interior points (should always be zero).</p>
+
+<p>With option 'Qi', output formats '<a href="qh-opto.htm#p">p</a>',
+'<a href="qh-opto.htm#f">f</a>','<a href="qh-optg.htm#Gp">Gp</a>',
+'<a href="qh-optf.htm#Fc">Fc</a>', '<a href="qh-optf.htm#FN">FN</a>',
+and '<a href="qh-optf.htm#FP">FP</a>' include interior points. </p>
+
+<h3><a href="#qhull">&#187;</a><a name="QJ">QJ</a> or <a name="QJn">QJn</a> - joggled
+input to avoid precision errors</a></h3>
+
+<p>Option 'QJ' or 'QJn' joggles each input coordinate by adding a
+random number in the range [-n,n]. If a precision error occurs,
+It tries again. If precision errors still occur, Qhull increases <i>n</i>
+ten-fold and tries again. The maximum value for increasing <i>n</i>
+is 0.01 times the maximum width of the input. Option 'QJ' selects
+a default value for <i>n</i>. <a href="../src/user.h#JOGGLEdefault">User.h</a>
+defines these parameters and a maximum number of retries. See <a
+href="qh-impre.htm#joggle">Merged facets or joggled input</a>. </p>
+
+<p>Users of joggled input should consider converting to
+triangulated output ('<a href="../html/qh-optq.htm#Qt">Qt</a>').  Triangulated output is
+approximately 1000 times more accurate than joggled input.
+
+<p>Option 'QJ' also sets '<a href="qh-optq.htm#Qbb">Qbb</a>' for
+Delaunay triangulations and Voronoi diagrams. It does not set
+'Qbb' if '<a href="qh-optq.htm#Qbk">Qbk:n</a>' or '<a
+href="qh-optq.htm#QBk">QBk:n</a>' are set. </p>
+
+<p>If 'QJn' is set, Qhull does not merge facets unless requested
+to. All facets are simplicial (triangular in 2-d). This may be
+important for your application.  You may also use triangulated output
+('<a href="qh-optq.htm#Qt">Qt</a>') or Option '<a href="qh-optf.htm#Ft">Ft</a>'.
+
+<p>Qhull adjusts the outer and inner planes for 'QJn' ('<a
+href="qh-optf.htm#Fs">Fs</a>'). They are increased by <i>sqrt(d)*n</i>
+to account for the maximum distance between a joggled point and
+the corresponding input point. Coplanar points ('<a
+href="qh-optq.htm#Qc">Qc</a>') require an additional <i>sqrt(d)*n</i>
+since vertices and coplanar points may be joggled in opposite
+directions. </p>
+
+<p>For Delaunay triangulations (<a href=qdelaun.htm>qdelaunay</a>), joggle
+happens before lifting the input sites to a paraboloid.  Instead of
+'QJ', you may use triangulated output ('<a
+href="qh-optq.htm#Qt">Qt</a>')</p>
+
+<p>This option is deprecated for Voronoi diagrams (<a href=qvoronoi.htm>qvoronoi</a>).
+It triangulates cospherical points, leading to duplicated Voronoi vertices.</p>
+
+<p>By default, 'QJn' uses a fixed random number seed. To use time
+as the random number seed, select '<a href="qh-optq.htm#QRn">QR-1</a>'.
+The summary ('<a href="qh-opto.htm#s">s</a>') will show the
+selected seed as 'QR-n'.
+
+<p>With 'QJn', Qhull does not error on degenerate hyperplane
+computations. Except for Delaunay and Voronoi computations, Qhull
+does not error on coplanar points. </p>
+
+<p>Use option '<a href="qh-optf.htm#FO">FO</a>' to display the
+selected options. Option 'FO' displays the joggle and the joggle
+seed. If Qhull restarts, it will redisplay the options. </p>
+
+<p>Use option '<a href="qh-optt.htm#TRn">TRn</a>' to estimate the
+probability that Qhull will fail for a given 'QJn'.
+
+<h3><a href="#qhull">&#187;</a><a name="Qm">Qm - only process points
+that increase the maximum outer plane </a></h3>
+
+<p>Qhull reports the maximum outer plane in its summary ('<a
+href="qh-opto.htm#s">s</a>'). With option 'Qm', Qhull does not
+process points that are below the current, maximum outer plane.
+This is equivalent to always adjusting '<a href="qh-optc.htm#Wn">Wn
+</a>' to the maximum distance of a coplanar point to a facet. It
+is ignored for points above the upper convex hull of a Delaunay
+triangulation. Option 'Qm' is no longer important for merging.</p>
+
+<h3><a href="#qhull">&#187;</a><a name="Qr">Qr - process random
+outside points instead of furthest ones </a></h3>
+
+<p>Normally, Qhull processes the furthest point of a facet's
+outside points. Option 'Qr' instead selects a random outside
+point for processing. This makes Qhull equivalent to the
+randomized incremental algorithms.</p>
+
+<p>The original randomization algorithm by Clarkson and Shor [<a
+href="index.htm#cla-sho89">'89</a>] used a conflict list which
+is equivalent to Qhull's outside set. Later randomized algorithms
+retained the previously constructed facets. </p>
+
+<p>To compare Qhull to the randomized algorithms with option
+'Qr', compare &quot;hyperplanes constructed&quot; and
+&quot;distance tests&quot;. Qhull does not report CPU time
+because the randomization is inefficient. </p>
+
+<h3><a href="#qhull">&#187;</a><a name="QRn">QRn - random rotation </a></h3>
+
+<p>Option 'QRn' randomly rotates the input. For Delaunay
+triangulations (<a href=qdelaun.htm>qdelaunay</a> or <a href=qvoronoi.htm>qvoronoi</a>),
+it rotates the lifted points about
+the last axis. </p>
+
+<p>If <em>n=0</em>, use time as the random number seed. If <em>n&gt;0</em>,
+use n as the random number seed. If <em>n=-1</em>, don't rotate
+but use time as the random number seed. If <em>n&lt;-1</em>,
+don't rotate but use <em>n</em> as the random number seed. </p>
+
+<h3><a href="#qhull">&#187;</a><a name="Qs">Qs - search all points
+for the initial simplex </a></h3>
+
+<p>Qhull constructs an initial simplex from <i>d+1</i> points. It
+selects points with the maximum and minimum coordinates and
+non-zero determinants. If this fails, it searches all other
+points. In 8-d and higher, Qhull selects points with the minimum
+x or maximum coordinate (see qh_initialvertices in <tt>poly2.c </tt>).
+It rejects points with nearly zero determinants. This should work
+for almost all input sets.</p>
+
+<p>If Qhull can not construct an initial simplex, it reports a
+descriptive message. Usually, the point set is degenerate and one
+or more dimensions should be removed ('<a href="#Qb0">Qbk:0Bk:0</a>').
+If not, use option 'Qs'. It performs an exhaustive search for the
+best initial simplex. This is expensive is high dimensions. </p>
+
+<h3><a href="#qhull">&#187;</a><a name="Qt">Qt - triangulated output</a></h3>
+
+<p>By default, qhull merges facets to handle precision errors.  This
+produces non-simplicial facets (e.g., the convex hull of a cube has 6 square
+facets).  Each facet is non-simplicial because it has four vertices.
+
+<p>Use option 'Qt' to triangulate all non-simplicial facets before generating
+results.  Alternatively, use joggled input ('<a href="#QJn">QJ</a>') to
+prevent non-simplical facets.  Unless '<a href="qh-optp.htm#Pp">Pp</a>' is set,
+qhull produces a warning if 'QJ' and 'Qt' are used together.
+
+<p>For Delaunay triangulations (<a href=qdelaun.htm>qdelaunay</a>), triangulation
+occurs after lifting the input sites to a paraboloid and computing the convex hull.
+</p>
+
+<p>Option 'Qt' is deprecated for Voronoi diagrams (<a href=qvoronoi.htm>qvoronoi</a>).
+It triangulates cospherical points, leading to duplicated Voronoi vertices.</p>
+
+<p>Option 'Qt' may produce degenerate facets with zero area.</p>
+
+<p>Facet area and hull volumes may differ with and without
+'Qt'.  The triangulations are different and different triangles
+may be ignored due to precision errors.
+
+<p>With sufficient merging, the ridges of a non-simplicial facet may share more than two neighboring facets. If so, their triangulation ('<a href="#Qt">Qt</a>') will fail since two facets have the same vertex set. </p>
+
+<h3><a href="#qhull">&#187;</a><a name="Qu">Qu - compute upper hull
+for furthest-site Delaunay triangulation </a></h3>
+
+<p>When computing a Delaunay triangulation (<a href=qdelaun.htm>qdelaunay</a>
+or <a href=qvoronoi.htm>qvoronoi</a>),
+Qhull computes both the the convex hull of points on a
+paraboloid. It normally prints facets of the lower hull. These
+correspond to the Delaunay triangulation. With option 'Qu', Qhull
+prints facets of the upper hull. These correspond to the <a
+href="qdelau_f.htm">furthest-site Delaunay triangulation</a>
+and the <a href="qvoron_f.htm">furthest-site Voronoi diagram</a>.</p>
+
+<p>Option 'qhull d Qbb Qu <a href="#Qg">Qg</a>' may improve the speed of option
+'Qu'. If you use the Qhull library, a faster method is 1) use
+Qhull to compute the convex hull of the input sites; 2) take the
+extreme points (vertices) of the convex hull; 3) add one interior
+point (e.g.,
+'<a href="qh-optf.htm#FV">FV</a>', the average of <em>d</em> extreme points); 4) run
+'qhull d Qbb Qu' or 'qhull v Qbb Qu' on these points.</p>
+
+<h3><a href="#qhull">&#187;</a><a name="Qv">Qv - test vertex
+neighbors for convexity </a></h3>
+
+<p>Normally, Qhull tests all facet neighbors for convexity.
+Non-neighboring facets which share a vertex may not satisfy the
+convexity constraint. This occurs when a facet undercuts the
+centrum of another facet. They should still be convex. Option
+'Qv' extends Qhull's convexity testing to all neighboring facets
+of each vertex. The extra testing occurs after the hull is
+constructed.. </p>
+
+<h3><a href="#qhull">&#187;</a><a name="QVn">QVn - good facet if it
+includes point n, -n if not </a></h3>
+
+<p>With option 'QVn', a facet is good ('<a href="#Qg">Qg</a>',
+'<a href="qh-optp.htm#Pg">Pg</a>') if one of its vertices is
+point n. If <i>n&lt;0</i>, a good facet does not include point n.
+
+<p>If options '<a href="qh-optp.htm#PG">PG</a>'
+and '<a href="#Qg">Qg</a>' are not set, option '<a href="qh-optp.htm#Pg">Pg</a>'
+(print only good)
+is automatically set.
+</p>
+
+<p>Option 'QVn' behaves oddly with options '<a href="qh-optf.htm#Fx">Fx</a>'
+and '<a href=qvoronoi.htm>qvoronoi</a> <a href="qh-optf.htm#Fv2">Fv</a>'.
+
+<p>If used with option '<a href="#Qg">Qg</a>' (only process good facets), point n is
+either in the initial simplex or it is the first
+point added to the hull. Options 'QVn Qg' require either '<a href="#QJn">QJ</a>' or
+'<a href="#Q0">Q0</a>' (no merging).</p>
+
+<h3><a href="#qhull">&#187;</a><a name="Qx">Qx - exact pre-merges
+(allows coplanar facets) </a></h3>
+
+<p>Option 'Qx' performs exact merges while building the hull.
+Option 'Qx' is set by default in 5-d and higher. Use option '<a
+href="#Q0">Q0</a>' to not use 'Qx' by default. Unless otherwise
+specified, option 'Qx' sets option '<a href="qh-optc.htm#C0">C-0</a>'.
+</p>
+
+<p>The &quot;exact&quot; merges are merging a point into a
+coplanar facet (defined by '<a href="qh-optc.htm#Vn">Vn </a>', '<a
+href="qh-optc.htm#Un">Un</a>', and '<a href="qh-optc.htm#Cn">C-n</a>'),
+merging concave facets, merging duplicate ridges, and merging
+flipped facets. Coplanar merges and angle coplanar merges ('<a
+href="qh-optc.htm#An">A-n</a>') are not performed. Concavity
+testing is delayed until a merge occurs.</p>
+
+<p>After the hull is built, all coplanar merges are performed
+(defined by '<a href="qh-optc.htm#Cn">C-n</a>' and '<a
+href="qh-optc.htm#An">A-n</a>'), then post-merges are performed
+(defined by '<a href="qh-optc.htm#Cn2">Cn</a>' and '<a
+href="qh-optc.htm#An2">An</a>'). If facet progress is logged ('<a
+href="qh-optt.htm#TFn">TFn</a>'), Qhull reports each phase and
+prints intermediate summaries and statistics ('<a
+href="qh-optt.htm#Ts">Ts</a>'). </p>
+
+<p>Without 'Qx' in 5-d and higher, options '<a
+href="qh-optc.htm#Cn">C-n</a>' and '<a href="qh-optc.htm#An">A-n</a>'
+may merge too many facets. Since redundant vertices are not
+removed effectively, facets become increasingly wide. </p>
+
+<p>Option 'Qx' may report a wide facet. With 'Qx', coplanar
+facets are not merged. This can produce a &quot;dent&quot; in an
+intermediate hull. If a point is partitioned into a dent and it
+is below the surrounding facets but above other facets, one or
+more wide facets will occur. In practice, this is unlikely. To
+observe this effect, run Qhull with option '<a href="#Q6">Q6</a>'
+which doesn't pre-merge concave facets. A concave facet makes a
+large dent in the intermediate hull.</p>
+
+<p>Option 'Qx' may set an outer plane below one of the input
+points. A coplanar point may be assigned to the wrong facet
+because of a &quot;dent&quot; in an intermediate hull. After
+constructing the hull, Qhull double checks all outer planes with
+qh_check_maxout in <tt>poly2.c </tt>. If a coplanar point is
+assigned to the wrong facet, qh_check_maxout may reach a local
+maximum instead of locating all coplanar facets. This appears to
+be unlikely.</p>
+
+<h3><a href="#qhull">&#187;</a><a name="Qz">Qz - add a
+point-at-infinity for Delaunay triangulations</a></h3>
+
+<p>Option 'Qz' adds a point above the paraboloid of lifted sites
+for a Delaunay triangulation. It allows the Delaunay
+triangulation of cospherical sites. It reduces precision errors
+for nearly cospherical sites.</p>
+
+<h3><a href="#qhull">&#187;</a><a name="Q0">Q0 - no merging with C-0
+and Qx</a></h3>
+
+<p>Turn off default merge options '<a href="qh-optc.htm#C0">C-0</a>'
+and '<a href="#Qx">Qx</a>'. </p>
+
+<p>With 'Q0' and without other pre-merge options, Qhull ignores
+precision issues while constructing the convex hull. This may
+lead to precision errors. If so, a descriptive warning is
+generated. See <a href="qh-impre.htm">Precision issues</a>.</p>
+
+<h3><a href="#qhull">&#187;</a><a name="Q1">Q1 - sort merges by type
+instead of angle </a></h3>
+
+<p>Qhull sorts the coplanar facets before picking a subset of the
+facets to merge. It merges concave and flipped facets first. Then
+it merges facets that meet at a steep angle. With 'Q1', Qhull
+sorts merges by type (coplanar, angle coplanar, concave) instead
+of by angle. This may make the facets wider. </p>
+
+<h3><a href="#qhull">&#187;</a><a name="Q2">Q2 - merge all non-convex
+at once instead of independent sets </a></h3>
+
+<p>With 'Q2', Qhull merges all facets at once instead of
+performing merges in independent sets. This may make the facets
+wider. </p>
+
+<h3><a href="#qhull">&#187;</a><a name="Q3">Q3 - do not merge
+redundant vertices </a></h3>
+
+<p>With 'Q3', Qhull does not remove redundant vertices. In 6-d
+and higher, Qhull never removes redundant vertices (since
+vertices are highly interconnected). Option 'Q3' may be faster,
+but it may result in wider facets. Its effect is easiest to see
+in 3-d and 4-d.</p>
+
+<h3><a href="#qhull">&#187;</a><a name="Q4">Q4 - avoid merging </a>old
+facets into new facets</h3>
+
+<p>With 'Q4', Qhull avoids merges of an old facet into a new
+facet. This sometimes improves facet width and sometimes makes it
+worse. </p>
+
+<h3><a href="#qhull">&#187;</a><a name="Q5">Q5 - do not correct outer
+planes at end of qhull </a></h3>
+
+<p>When merging facets or approximating a hull, Qhull tests
+coplanar points and outer planes after constructing the hull. It
+does this by performing a directed search (qh_findbest in <tt>geom.c</tt>).
+It includes points that are just inside the hull. </p>
+
+<p>With options 'Q5' or '<a href="qh-optp.htm#Po">Po</a>', Qhull
+does not test outer planes. The maximum outer plane is used
+instead. Coplanar points ('<a href="#Qc">Qc</a>') are defined by
+'<a href="qh-optc.htm#Un">Un</a>'. An input point may be outside
+of the maximum outer plane (this appears to be unlikely). An
+interior point may be above '<a href="qh-optc.htm#Un">Un</a>'
+from a hyperplane.</p>
+
+<p>Option 'Q5' may be used if outer planes are not needed. Outer
+planes are needed for options '<a href="qh-opto.htm#s">s</a>', '<a
+href="qh-optg.htm#G">G</a>', '<a href="qh-optg.htm#Go">Go </a>',
+'<a href="qh-optf.htm#Fs">Fs</a>', '<a href="qh-optf.htm#Fo">Fo</a>',
+'<a href="qh-optf.htm#FF">FF</a>', and '<a href="qh-opto.htm#f">f</a>'.</p>
+
+<h3><a href="#qhull">&#187;</a><a name="Q6">Q6 - do not pre-merge
+concave or coplanar facets </a></h3>
+
+<p>With 'Q6', Qhull does not pre-merge concave or coplanar
+facets. This demonstrates the effect of &quot;dents&quot; when
+using '<a href="#Qx">Qx</a>'. </p>
+
+<h3><a href="#qhull">&#187;</a><a name="Q7">Q7 - depth-first
+processing instead of breadth-first </a></h3>
+
+<p>With 'Q7', Qhull processes facets in depth-first order instead
+of breadth-first order. This may increase the locality of
+reference in low dimensions. If so, Qhull may be able to use
+virtual memory effectively. </p>
+
+<p>In 5-d and higher, many facets are visible from each
+unprocessed point. So each iteration may access a large
+proportion of allocated memory. This makes virtual memory
+ineffectual. Once real memory is used up, Qhull will spend most
+of its time waiting for I/O.</p>
+
+<p>Under 'Q7', Qhull runs slower and the facets may be wider. </p>
+
+<h3><a href="#qhull">&#187;</a><a name="Q8">Q8 - ignore near-interior
+points </a></h3>
+
+<p>With 'Q8' and merging, Qhull does not process interior points
+that are near to a facet (as defined by qh_RATIOnearInside in
+user.h). This avoids partitioning steps. It may miss a coplanar
+point when adjusting outer hulls in qh_check_maxout(). The best
+value for qh_RATIOnearInside is not known. Options 'Q8 <a
+href="#Qc">Qc</a>' may be sufficient. </p>
+
+<h3><a href="#qhull">&#187;</a><a name="Q9">Q9 - process furthest of
+furthest points </a></h3>
+
+<p>With 'Q9', Qhull processes the furthest point of all outside
+sets. This may reduce precision problems. The furthest point of
+all outside sets is not necessarily the furthest point from the
+convex hull.</p>
+
+<h3><a href="#qhull">&#187;</a><a name="Q10">Q10 - no special processing
+for narrow distributions</a></h3>
+
+<p>With 'Q10', Qhull does not special-case narrow distributions.
+See <a href=qh-impre.htm#limit>Limitations of merged facets</a> for
+more information.
+
+<h3><a href="#qhull">&#187;</a><a name="Q11">Q11 - copy normals and recompute
+centrums for
+tricoplanar facets</a></h3>
+
+Option '<a href="#Qt">Qt</a>' triangulates non-simplicial facets
+into "tricoplanar" facets.
+Normally tricoplanar facets share the same normal, centrum, and
+Voronoi vertex.  They can not be merged or replaced.  With
+option 'Q11', Qhull duplicates the normal and Voronoi vertex.
+It recomputes the centrum.
+
+<p>Use 'Q11' if you use the Qhull library to add points
+incrementally and call qh_triangulate() after each point.
+Otherwise, Qhull will report an error when it tries to
+merge and replace a tricoplanar facet.
+
+<p>With sufficient merging and new points, option 'Q11' may
+lead to precision problems such
+as duplicate ridges and concave facets.  For example, if qh_triangulate()
+is added to qh_addpoint(), RBOX 1000 s W1e-12 t1001813667 P0 | QHULL d Q11 Tv,
+reports an error due to a duplicate ridge.
+
+<h3><a href="#qhull">&#187;</a><a name="Q12">Q12 - do not error
+on wide merge due to duplicate ridge and nearly coincident points</a></h3>
+
+<p>In 3-d and higher Delaunay Triangulations or 4-d and higher convex hulls, multiple,
+nearly coincident points may lead to very wide facets.  An error is reported if a
+merge across a duplicate ridge would increase the facet width by 100x or more.
+
+<p>Use option 'Q12' to log a warning instead of throwing an error.
+
+<p>For Delaunay triangulations, a bounding box may alleviate this error (e.g., <tt>rbox 500 C1,1E-13 t c G1 | qhull d</tt>).
+This avoids the ill-defined edge between upper and lower convex hulls.
+The problem will be fixed in a future release of Qhull.
+
+<p>To demonstrate the problem, use rbox option 'Cn,r,m' to generate nearly coincident points.
+For more information, see "Nearly coincident points on an edge"
+in <a href="qh-impre.htm#limit"</a>Nearly coincident points on an edge</a>.
+
+<!-- Navigation links -->
+<hr>
+
+<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
+<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
+<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
+&#149; <a href="qh-quick.htm#options">Options</a>
+&#149; <a href="qh-opto.htm#output">Output</a>
+&#149; <a href="qh-optf.htm#format">Formats</a>
+&#149; <a href="qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="qh-optp.htm#print">Print</a>
+&#149; <a href="qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="qh-optc.htm#prec">Precision</a>
+&#149; <a href="qh-optt.htm#trace">Trace</a>
+&#149; <a href="../src/libqhull_r/index.htm">Functions</a></p>
+<!-- GC common information -->
+<hr>
+
+<p><a href="http://www.geom.uiuc.edu/"><img src="qh--geom.gif"
+align="middle" width="40" height="40"></a><i>The Geometry Center
+Home Page </i></p>
+
+<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
+</a><br>
+Created: Sept. 25, 1995 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
+</body>
+</html>
diff --git a/xs/src/qhull/html/qh-optt.htm b/xs/src/qhull/html/qh-optt.htm
new file mode 100644
index 0000000000..0709f58c66
--- /dev/null
+++ b/xs/src/qhull/html/qh-optt.htm
@@ -0,0 +1,278 @@
+<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN">
+<html>
+
+<head>
+<title>Qhull trace options (T)</title>
+</head>
+
+<body>
+<!-- Navigation links -->
+<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
+<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
+<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
+&#149; <a href="qh-quick.htm#options">Options</a>
+&#149; <a href="qh-opto.htm#output">Output</a>
+&#149; <a href="qh-optf.htm#format">Formats</a>
+&#149; <a href="qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="qh-optp.htm#print">Print</a>
+&#149; <a href="qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="qh-optc.htm#prec">Precision</a>
+&#149; <a href="qh-optt.htm#trace">Trace</a>
+&#149; <a href="../src/libqhull_r/index.htm">Functions</a></p>
+
+<hr>
+<!-- Main text of document -->
+<h1><a
+href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/delaunay.html"><img
+src="qh--dt.gif" alt="[delaunay]" align="middle" width="100"
+height="100"></a> Qhull trace options (T)</h1>
+
+This section lists the trace options for Qhull. These options are
+indicated by 'T' followed by a letter.
+
+<p><b>Copyright &copy; 1995-2015 C.B. Barber</b></p>
+
+<hr>
+
+<p><a href="index.htm#TOC">&#187;</a> <a href="qh-quick.htm#programs">Programs</a>
+<a name="trace">&#149;</a> <a href="qh-quick.htm#options">Options</a>
+&#149; <a href="qh-opto.htm#output">Output</a>
+&#149; <a href="qh-optf.htm#format">Formats</a>
+&#149; <a href="qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="qh-optp.htm#print">Print</a>
+&#149; <a href="qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="qh-optc.htm#prec">Precision</a>
+&#149; <a href="qh-optt.htm#trace">Trace</a>
+&#149; <a href="../src/libqhull_r/index.htm">Functions</a></p>
+
+<h2>Trace options</h2>
+
+<dl compact>
+    <dt>&nbsp;</dt>
+    <dd><b>General</b></dd>
+    <dt><a href="#Tz">Tz</a></dt>
+    <dd>output error information to stdout instead of stderr</dd>
+    <dt><a href="#TI">TI file</a></dt>
+    <dd>input data from a file</dd>
+    <dt><a href="#TO">TO file</a></dt>
+    <dd>output results to a file</dd>
+    <dt><a href="#Ts">Ts</a></dt>
+    <dd>print statistics</dd>
+    <dt><a href="#TFn">TFn</a></dt>
+    <dd>report progress whenever n or more facets created</dd>
+    <dt><a href="#TRn">TRn</a></dt>
+    <dd>rerun qhull n times</dd>
+    <dt><a href="#Tv">Tv</a></dt>
+    <dd>verify result: structure, convexity, and point inclusion</dd>
+
+    <dt>&nbsp;</dt>
+    <dt>&nbsp;</dt>
+    <dd><b>Debugging</b></dd>
+    <dt><a href="#Tc">Tc</a></dt>
+    <dd>check frequently during execution</dd>
+    <dt><a href="#TVn2">TVn</a></dt>
+    <dd>stop qhull after adding point n </dd>
+    <dt><a href="#TCn">TCn</a></dt>
+    <dd>stop qhull after building cone for point n</dd>
+    <dt><a href="#TVn">TV-n</a></dt>
+    <dd>stop qhull before adding point n</dd>
+    <dt><a href="#Tn">T4</a></dt>
+    <dd>trace at level n, 4=all, 5=mem/gauss, -1= events</dd>
+    <dt><a href="#TWn">TWn</a></dt>
+    <dd>trace merge facets when width &gt; n</dd>
+    <dt><a href="#TMn">TMn</a></dt>
+    <dd>turn on tracing at merge n</dd>
+    <dt><a href="#TPn">TPn</a></dt>
+    <dd>turn on tracing when point n added to hull</dd>
+</dl>
+
+<hr>
+
+<h3><a href="#trace">&#187;</a><a name="Tc">Tc - check frequently
+during execution </a></h3>
+
+<p>Qhull includes frequent checks of its data structures. Option
+'Tc' will catch most inconsistency errors. It is slow and should
+not be used for production runs. Option '<a href="#Tv">Tv</a>'
+performs the same checks after the hull is constructed.</p>
+
+<h3><a href="#trace">&#187;</a><a name="TCn">TCn - stop qhull after
+building cone for point n</a></h3>
+
+<p>Qhull builds a cone from the point to its horizon facets.
+Option 'TCn' stops Qhull just after building the cone. The output
+for '<a href="qh-opto.htm#f">f</a>' includes the cone and the old
+hull.'. </p>
+
+<h3><a href="#trace">&#187;</a><a name="TFn">TFn - report summary
+whenever n or more facets created </a></h3>
+
+<p>Option 'TFn' reports progress whenever more than n facets are
+created. The test occurs just before adding a new point to the
+hull. During post-merging, 'TFn' reports progress after more than
+<i>n/2</i> merges. </p>
+
+<h3><a href="#trace">&#187;</a><a name="TI">TI file - input data from file</a></h3>
+
+<p>Input data from 'file' instead of stdin.  The filename may not
+contain spaces or use single quotes.
+You may use I/O redirection
+instead (e.g., 'rbox 10 | qdelaunay >results').</P>
+
+<h3><a href="#trace">&#187;</a><a name="TMn">TMn - turn on tracing at
+merge n </a></h3>
+
+<p>Turn on tracing at n'th merge. </p>
+
+<h3><a href="#trace">&#187;</a><a name="Tn">Tn - trace at level n</a></h3>
+
+<p>Qhull includes full execution tracing. 'T-1' traces events.
+'T1' traces the overall execution of the program. 'T2' and 'T3'
+trace overall execution and geometric and topological events.
+'T4' traces the algorithm. 'T5' includes information about memory
+allocation and Gaussian elimination. 'T1' is useful for logging
+progress of Qhull in high dimensions.</p>
+
+<p>Option 'Tn' can produce large amounts of output. Use options '<a
+href="#TPn">TPn</a>', '<a href="#TWn">TWn</a>', and '<a href="#TMn">TMn</a>' to selectively
+turn on tracing. Since all errors report the last processed
+point, option '<a href="#TPn">TPn</a>' is particularly useful.</p>
+
+<p>Different executions of the same program may produce different
+traces and different results.  The reason is that Qhull uses hashing
+to match ridges of non-simplicial facets.  For performance reasons,
+the hash computation uses
+memory addresses which may change across executions.
+
+<h3><a href="#trace">&#187;</a><a name="TO">TO file - output results to file</a></h3>
+
+<p>Redirect stdout to 'file'.  The filename may be enclosed in
+single quotes.  Unix and Windows NT users may use I/O redirection
+instead (e.g., 'rbox 10 | qdelaunay >results').</P>
+<p>
+Windows95 users should always use 'TO file'.  If they use I/O redirection,
+error output is not sent to the console.  Qhull uses single quotes instead
+of double quotes because a missing double quote can
+freeze Windows95 (e.g., do not run, rbox 10 | qhull TO &quot;x)</p>
+<p>
+
+<h3><a href="#trace">&#187;</a><a name="TPn">TPn - turn on tracing
+when point n added to hull </a></h3>
+
+<p>Option 'TPn' turns on tracing when point n is added to
+the hull.  It also traces partitions of point n.  This option
+reduces the output size when tracing.  It is the normal
+method to determine the cause of a Qhull error. All Qhull errors
+report the last point added.
+
+<p>Use options 'TPn <a href="qh-optt.htm#TVn">TVn</a>' to
+trace the addition of point n to the convex hull and stop when done.</p>
+
+<p>If used with option '<a href="qh-optt.htm#TWn">TWn</a>',
+'TPn' turns off tracing after adding point n to the hull.
+Use options 'TPn TWn' to
+trace the addition of point n to the convex hull, partitions
+of point n, and wide merges.</p>
+
+<h3><a href="#trace">&#187;</a><a name="TRn">TRn - rerun qhull n times</a></h3>
+
+<p>Option 'TRn' reruns Qhull n times.  It is usually used
+with '<a href="qh-optq.htm#QJn">QJn</a>' to determine the probability
+that a given joggle will fail.  The summary
+('<a href="qh-opto.htm#s">s</a>') lists the failure
+rate and the precision errors that occurred.
+Option '<a href="#Ts">Ts</a>' will report statistics for
+all of the runs.  Trace and output options only apply to the last
+run.  An event trace, '<a href="#Tn">T-1</a>' reports events for all runs.
+
+<p>Tracing applies to the last run of Qhull.  If an error
+is reported, the options list the run number as "_run".
+To trace this run, set 'TRn' to the same value.</p>
+
+<h3><a href="#trace">&#187;</a><a name="Ts">Ts - print statistics </a></h3>
+
+<p>Option 'Ts' collects statistics and prints them to stderr. For
+Delaunay triangulations, the angle statistics are restricted to
+the lower or upper envelope.</p>
+
+<h3><a href="#trace">&#187;</a><a name="Tv">Tv - verify result:
+structure, convexity, and point inclusion </a></h3>
+
+<p>Option 'Tv' checks the topological structure, convexity, and
+point inclusion. If precision problems occurred, facet convexity
+is tested whether or not 'Tv' is selected. Option 'Tv' does not
+check point inclusion if forcing output with '<a
+href="qh-optp.htm#Po">Po</a>', or if '<a href="qh-optq.htm#Q5">Q5</a>'
+is set. </p>
+
+<p>The convex hull of a set of points is the smallest polytope
+that includes the points. Option 'Tv' tests point inclusion.
+Qhull verifies that all points are below all outer planes
+(facet-&gt;maxoutside). Point inclusion is exhaustive if merging
+or if the facet-point product is small enough; otherwise Qhull
+verifies each point with a directed search (qh_findbest). To
+force an exhaustive test when using option '<a
+href="qh-optc.htm#C0">C-0</a>' (default), use 'C-1e-30' instead. </p>
+
+<p>Point inclusion testing occurs after producing output. It
+prints a message to stderr unless option '<a
+href="qh-optp.htm#Pp">Pp</a>' is used. This allows the user to
+interrupt Qhull without changing the output. </p>
+
+<p>With '<a href=qvoronoi.htm>qvoronoi</a> <a href="qh-optf.htm#Fi2">Fi</a>'
+and '<a href=qvoronoi.htm>qvoronoi</a> <a href="qh-optf.htm#Fo2">Fo</a>',
+option 'Tv' collects statistics that verify all Voronoi vertices lie
+on the separating hyperplane, and for bounded regions, all
+separating hyperplanes are perpendicular bisectors.
+
+<h3><a href="#trace">&#187;</a><a name="TVn">TV-n - stop qhull before
+adding point n</a></h3>
+
+<p>Qhull adds one point at a time to the convex hull. See <a
+href="qh-eg.htm#how">how Qhull adds a point</a>. Option 'TV-n'
+stops Qhull just before adding a new point. Output shows the hull
+at this time.</p>
+
+<h3><a href="#trace">&#187;</a><a name="TVn2">TVn - stop qhull after
+adding point n</a></h3>
+
+<p>Option 'TVn' stops Qhull after it has added point n. Output
+shows the hull at this time.</p>
+
+<h3><a href="#trace">&#187;</a><a name="TWn">TWn - trace merge facets
+when width &gt; n </a></h3>
+
+<p>Along with TMn, this option allows the user to determine the
+cause of a wide merge.</p>
+<h3><a href="#trace">&#187;</a><a name="Tz">Tz - send all output to
+stdout </a></h3>
+
+<p>Redirect stderr to stdout. </p>
+
+<!-- Navigation links -->
+<hr>
+
+<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
+<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
+<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
+&#149; <a href="qh-quick.htm#options">Options</a>
+&#149; <a href="qh-opto.htm#output">Output</a>
+&#149; <a href="qh-optf.htm#format">Formats</a>
+&#149; <a href="qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="qh-optp.htm#print">Print</a>
+&#149; <a href="qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="qh-optc.htm#prec">Precision</a>
+&#149; <a href="qh-optt.htm#trace">Trace</a>
+&#149; <a href="../src/libqhull_r/index.htm">Functions</a></p>
+<!-- GC common information -->
+<hr>
+
+<p><a href="http://www.geom.uiuc.edu/"><img src="qh--geom.gif"
+align="middle" width="40" height="40"></a><i>The Geometry Center
+Home Page </i></p>
+
+<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
+</a><br>
+Created: Sept. 25, 1995 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
+</body>
+</html>
diff --git a/xs/src/qhull/html/qh-quick.htm b/xs/src/qhull/html/qh-quick.htm
new file mode 100644
index 0000000000..9d52e7d750
--- /dev/null
+++ b/xs/src/qhull/html/qh-quick.htm
@@ -0,0 +1,495 @@
+<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN">
+<html>
+
+<head>
+<title>Qhull quick reference</title>
+</head>
+
+<body>
+<!-- Navigation links -->
+<p><a name="TOC"><b>Up:</b></a> <a href="http://www.qhull.org">Home
+page for Qhull</a> <br>
+<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a> <br>
+<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
+&#149; <a href="qh-quick.htm#options">Options</a>
+&#149; <a href="qh-opto.htm#output">Output</a>
+&#149; <a href="qh-optf.htm#format">Formats</a>
+&#149; <a href="qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="qh-optp.htm#print">Print</a>
+&#149; <a href="qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="qh-optc.htm#prec">Precision</a>
+&#149; <a href="qh-optt.htm#trace">Trace</a>
+&#149; <a href="../src/libqhull_r/index.htm">Functions</a><br>
+<b>To:</b> <a href="qh-code.htm#TOC">Qhull internals</a><br>
+<b>To:</b> <a href="../src/libqhull/index.htm">Qhull functions</a>, macros, and data structures<br>
+<b>To:</b> <a href="../src/libqhull/index.htm#TOC">Qhull files</a><br>
+<b>To:</b> <a href="../src/libqhull/qh-geom.htm">Geom</a> &#149; <a href="../src/libqhull/qh-globa.htm">Global</a>
+&#149; <a href="../src/libqhull/qh-io.htm">Io</a> &#149; <a href="../src/libqhull/qh-mem.htm">Mem</a>
+&#149; <a href="../src/libqhull/qh-merge.htm">Merge</a> &#149; <a href="../src/libqhull/qh-poly.htm">Poly</a>
+&#149; <a href="../src/libqhull/qh-qhull.htm">Qhull</a> &#149; <a href="../src/libqhull/qh-set.htm">Set</a>
+&#149; <a href="../src/libqhull/qh-stat.htm">Stat</a> &#149; <a href="../src/libqhull/qh-user.htm">User</a>
+</p>
+
+<hr>
+<!-- Main text of document -->
+<h1><a
+href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/cone.html"><img
+src="qh--cone.gif" alt="[cone]" align="middle" width="100"
+height="100"></a> Qhull quick reference</h1>
+
+This section lists all programs and options in Qhull.
+
+<p><b>Copyright &copy; 1995-2015 C.B. Barber</b></p>
+
+<p>
+<a name="programs">&nbsp;</a>
+<hr>
+<b>Qhull programs</b>
+<p><a href="#TOC">&#187;</a> <a href="qh-quick.htm#programs">Programs</a>
+&#149; <a href="qh-quick.htm#options">Options</a>
+&#149; <a href="qh-opto.htm#output">Output</a>
+&#149; <a href="qh-optf.htm#format">Formats</a>
+&#149; <a href="qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="qh-optp.htm#print">Print</a>
+&#149; <a href="qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="qh-optc.htm#prec">Precision</a>
+&#149; <a href="qh-optt.htm#trace">Trace</a>
+&#149; <a href="../src/libqhull_r/index.htm">Functions</a></p>
+
+<dl>
+    <dt><a href="qconvex.htm">qconvex</a> -- convex hull</dt>
+    <dd><a href="qconvex.htm#synopsis">sy</a>nopsis &#149; <a
+            href="qconvex.htm#input">in</a>put &#149; <a
+        href="qconvex.htm#outputs">ou</a>tputs &#149; <a
+        href="qconvex.htm#controls">co</a>ntrols &#149; <a
+        href="qconvex.htm#graphics">gr</a>aphics &#149; <a
+        href="qconvex.htm#notes">no</a>tes &#149; <a
+        href="qconvex.htm#conventions">co</a>nventions &#149; <a
+                href="qconvex.htm#options">op</a>tions</dd>
+    <dt>&nbsp;</dt>
+    <dt><a href="qdelaun.htm">qdelaunay</a> -- Delaunay triangulation</dt>
+    <dd><a href="qdelaun.htm#synopsis">sy</a>nopsis &#149; <a
+            href="qdelaun.htm#input">in</a>put &#149; <a
+        href="qdelaun.htm#outputs">ou</a>tputs &#149; <a
+                 href="qdelaun.htm#controls">co</a>ntrols &#149; <a
+        href="qdelaun.htm#graphics">gr</a>aphics &#149; <a
+        href="qdelaun.htm#notes">no</a>tes &#149; <a
+                href="qdelaun.htm#conventions">co</a>nventions &#149; <a
+            href="qdelaun.htm#options">op</a>tions</dd>
+    <dt>&nbsp;</dt>
+    <dt><a href="qdelau_f.htm">qdelaunay Qu</a> -- furthest-site Delaunay triangulation</dt>
+    <dd><a href="qdelau_f.htm#synopsis">sy</a>nopsis &#149; <a
+            href="qdelau_f.htm#input">in</a>put &#149; <a
+        href="qdelau_f.htm#outputs">ou</a>tputs &#149; <a
+                 href="qdelau_f.htm#controls">co</a>ntrols &#149; <a
+        href="qdelau_f.htm#graphics">gr</a>aphics &#149; <a
+        href="qdelau_f.htm#notes">no</a>tes &#149; <a
+                href="qdelau_f.htm#conventions">co</a>nventions &#149; <a
+            href="qdelau_f.htm#options">op</a>tions</dd>
+    <dt>&nbsp;</dt>
+    <dt><a href="qhalf.htm">qhalf</a> -- halfspace intersection about a point</dt>
+    <dd><a href="qhalf.htm#synopsis">sy</a>nopsis &#149; <a
+            href="qhalf.htm#input">in</a>put &#149; <a
+        href="qhalf.htm#outputs">ou</a>tputs &#149; <a
+        href="qhalf.htm#controls">co</a>ntrols &#149; <a
+        href="qhalf.htm#graphics">gr</a>aphics &#149; <a
+        href="qhalf.htm#notes">no</a>tes &#149; <a
+        href="qhalf.htm#conventions">co</a>nventions &#149; <a
+                href="qhalf.htm#options">op</a>tions</dd>
+    <dt>&nbsp;</dt>
+    <dt><a href="qvoronoi.htm">qvoronoi</a> -- Voronoi diagram</dt>
+    <dd><a href="qvoronoi.htm#synopsis">sy</a>nopsis &#149; <a
+            href="qvoronoi.htm#input">in</a>put &#149; <a
+            href="qvoronoi.htm#outputs">ou</a>tputs &#149;
+        <a href="qvoronoi.htm#controls">co</a>ntrols &#149; <a
+        href="qvoronoi.htm#graphics">gr</a>aphics &#149; <a
+        href="qvoronoi.htm#notes">no</a>tes  &#149; <a
+            href="qvoronoi.htm#conventions">co</a>nventions &#149; <a
+            href="qvoronoi.htm#options">op</a>tions</dd>
+    <dt>&nbsp;</dt>
+    <dt><a href="qvoron_f.htm">qvoronoi Qu</a> -- furthest-site Voronoi diagram</dt>
+    <dd><a href="qvoron_f.htm#synopsis">sy</a>nopsis &#149; <a
+            href="qvoron_f.htm#input">in</a>put &#149; <a
+        href="qvoron_f.htm#outputs">ou</a>tputs &#149; <a
+                 href="qvoron_f.htm#controls">co</a>ntrols &#149; <a
+        href="qvoron_f.htm#graphics">gr</a>aphics &#149; <a
+        href="qvoron_f.htm#notes">no</a>tes &#149; <a
+                href="qvoron_f.htm#conventions">co</a>nventions &#149; <a
+            href="qvoron_f.htm#options">op</a>tions</dd>
+    <dt>&nbsp;</dt>
+    <dt><a href="rbox.htm">rbox</a> -- generate point distributions for qhull</dt>
+    <dd><a href="rbox.htm#synopsis">sy</a>nopsis &#149; <a
+                href="rbox.htm#outputs">ou</a>tputs &#149; <a
+        href="rbox.htm#examples">ex</a>amples &#149; <a
+        href="rbox.htm#notes">no</a>tes &#149; <a
+                href="rbox.htm#options">op</a>tions</dd>
+    <dt>&nbsp;</dt>
+    <dt><a href="qhull.htm">qhull</a> -- convex hull and related structures</dt>
+    <dd><a href="qhull.htm#synopsis">sy</a>nopsis &#149; <a
+            href="qhull.htm#input">in</a>put &#149; <a
+        href="qhull.htm#outputs">ou</a>tputs &#149; <a
+        href="qhull.htm#controls">co</a>ntrols &#149; <a
+                href="qhull.htm#options">op</a>tions</dd>
+    </dl>
+<a name="options">&nbsp;</a>
+<hr>
+<b>Qhull options</b>
+
+<p><a href="#TOC">&#187;</a> <a href="qh-quick.htm#programs">Programs</a>
+&#149; <a href="qh-quick.htm#options">Options</a>
+&#149; <a href="qh-opto.htm#output">Output</a>
+&#149; <a href="qh-optf.htm#format">Formats</a>
+&#149; <a href="qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="qh-optp.htm#print">Print</a>
+&#149; <a href="qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="qh-optc.htm#prec">Precision</a>
+&#149; <a href="qh-optt.htm#trace">Trace</a>
+&#149; <a href="../src/libqhull_r/index.htm">Functions</a></p>
+
+<p><table>
+<!-- Note: keep all lines the same for easy reorganization -->
+<tr>
+<td><nobr>'<a href=qh-optf.htm#Fa>Fa</a>'
+Farea
+</nobr></td><td><nobr>'<a href=qh-optf.htm#Fa>FA</a>'
+FArea-total
+</nobr></td><td><nobr>'<a href=qh-optf.htm#Fc>Fc</a>'
+Fcoplanars
+</nobr></td><td><nobr>'<a href=qh-optf.htm#FC>FC</a>'
+FCentrums
+
+</nobr></td></tr><tr>
+<td><nobr>'<a href=qh-optf.htm#Fd>Fd</a>'
+Fd-cdd-in
+</nobr></td><td><nobr>'<a href=qh-optf.htm#FD>FD</a>'
+FD-cdd-out
+</nobr></td><td><nobr>'<a href=qh-optf.htm#FF>FF</a>'
+FF-dump-xridge
+</nobr></td><td><nobr>'<a href=qh-optf.htm#Fi>Fi</a>'
+Finner
+
+</nobr></td></tr><tr>
+<td><nobr>'<a href=qh-optf.htm#Fi2>Fi</a>'
+Finner_bounded
+</nobr></td><td><nobr>'<a href=qh-optf.htm#FI>FI</a>'
+FIDs
+</nobr></td><td><nobr>'<a href=qh-optf.htm#Fm>Fm</a>'
+Fmerges
+</nobr></td><td><nobr>'<a href=qh-optf.htm#FM>FM</a>'
+FMaple
+
+</nobr></td></tr><tr>
+<td><nobr>'<a href=qh-optf.htm#Fn>Fn</a>'
+Fneighbors
+</nobr></td><td><nobr>'<a href=qh-optf.htm#FN>FN</a>'
+FNeigh-vertex
+</nobr></td><td><nobr>'<a href=qh-optf.htm#Fo>Fo</a>'
+Fouter
+</nobr></td><td><nobr>'<a href=qh-optf.htm#Fo2>Fo</a>'
+Fouter_unbounded
+
+</nobr></td></tr><tr>
+<td><nobr>'<a href=qh-optf.htm#FO>FO</a>'
+FOptions
+</nobr></td><td><nobr>'<a href=qh-optf.htm#Fp>Fp</a>'
+Fpoint-intersect
+</nobr></td><td><nobr>'<a href=qh-optf.htm#FP>FP</a>'
+FPoint_near
+</nobr></td><td><nobr>'<a href=qh-optf.htm#FQ>FQ</a>'
+FQhull
+
+</nobr></td></tr><tr>
+<td><nobr>'<a href=qh-optf.htm#Fs>Fs</a>'
+Fsummary
+</nobr></td><td><nobr>'<a href=qh-optf.htm#FS>FS</a>'
+FSize
+</nobr></td><td><nobr>'<a href=qh-optf.htm#Ft>Ft</a>'
+Ftriangles
+</nobr></td><td><nobr>'<a href=qh-optf.htm#Fv>Fv</a>'
+Fvertices
+
+</nobr></td></tr><tr>
+<td><nobr>'<a href=qh-optf.htm#Fv2>Fv</a>'
+Fvoronoi
+</nobr></td><td><nobr>'<a href=qh-optf.htm#FV>FV</a>'
+FVertex-ave
+</nobr></td><td><nobr>'<a href=qh-optf.htm#Fx>Fx</a>'
+Fxtremes
+</nobr></td><td colspan=2><nobr>
+<a href=qh-impre.htm#joggle>Merged facets or joggled input</a>
+
+</nobr></td></tr>
+<tr><td>&nbsp;</td></tr><tr>
+<td><nobr>'<a href=qh-optp.htm#PAn>PAn</a>'
+PArea-keep
+</nobr></td><td><nobr>'<a href=qh-optp.htm#Pdk>Pdk:n</a>'
+Pdrop_low
+</nobr></td><td><nobr>'<a href=qh-optp.htm#PDk>PDk:n</a>'
+Pdrop_high
+</nobr></td><td><nobr>'<a href=qh-optp.htm#Pg>Pg</a>'
+Pgood
+
+</nobr></td></tr><tr>
+<td><nobr>'<a href=qh-optp.htm#PFn>PFn</a>'
+PFacet_area_keep
+</nobr></td><td><nobr>'<a href=qh-optp.htm#PG>PG</a>'
+PGood_neighbors
+</nobr></td><td><nobr>'<a href=qh-optp.htm#PMn>PMn</a>'
+PMerge-keep
+</nobr></td><td><nobr>'<a href=qh-optp.htm#Po>Po</a>'
+Poutput_forced
+
+</nobr></td></tr><tr>
+<td><nobr>'<a href=qh-optp.htm#Po2>Po</a>'
+Poutput_error
+</nobr></td><td><nobr>'<a href=qh-optp.htm#Pp>Pp</a>'
+Pprecision_not
+
+</nobr></td></tr>
+<tr><td>&nbsp;</td></tr><tr>
+<td><nobr>'<a href=qhull.htm#outputs>d</a>'
+delaunay
+</nobr></td><td><nobr>'<a href=qhull.htm#outputs>v</a>'
+voronoi
+</nobr></td><td><nobr>'<a href=qh-optg.htm>G</a>'
+Geomview
+</nobr></td><td><nobr>'<a href=qhull.htm#outputs>H</a>'
+Halfspace
+
+</nobr></td></tr><tr>
+<td><nobr>'<a href=qh-opto.htm#f>f</a>'
+facet_dump
+</nobr></td><td><nobr>'<a href=qh-opto.htm#i>i</a>'
+incidences
+</nobr></td><td><nobr>'<a href=qh-opto.htm#m>m</a>'
+mathematica
+</nobr></td><td><nobr>'<a href=qh-opto.htm#n>n</a>'
+normals
+
+</nobr></td></tr><tr>
+<td><nobr>'<a href=qh-opto.htm#o>o</a>'
+OFF_format
+</nobr></td><td><nobr>'<a href=qh-opto.htm#p>p</a>'
+points
+</nobr></td><td><nobr>'<a href=qh-opto.htm#s>s</a>'
+summary
+
+</nobr></td></tr>
+<tr><td>&nbsp;</td></tr><tr>
+<td><nobr>'<a href=qh-optg.htm#Gv>Gv</a>'
+Gvertices
+</nobr></td><td><nobr>'<a href=qh-optg.htm#Gp>Gp</a>'
+Gpoints
+</nobr></td><td><nobr>'<a href=qh-optg.htm#Ga>Ga</a>'
+Gall_points
+</nobr></td><td><nobr>'<a href=qh-optg.htm#Gn>Gn</a>'
+Gno_planes
+
+</nobr></td></tr><tr>
+<td><nobr>'<a href=qh-optg.htm#Gi>Gi</a>'
+Ginner
+</nobr></td><td><nobr>'<a href=qh-optg.htm#Gc>Gc</a>'
+Gcentrums
+</nobr></td><td><nobr>'<a href=qh-optg.htm#Gh>Gh</a>'
+Ghyperplanes
+</nobr></td><td><nobr>'<a href=qh-optg.htm#Gr>Gr</a>'
+Gridges
+
+</nobr></td></tr><tr>
+<td><nobr>'<a href=qh-optg.htm#Go>Go</a>'
+Gouter
+</nobr></td><td><nobr>'<a href=qh-optg.htm#GDn>GDn</a>'
+GDrop_dim
+</nobr></td><td><nobr>'<a href=qh-optg.htm#Gt>Gt</a>'
+Gtransparent
+
+</nobr></td></tr>
+<tr><td>&nbsp;</td></tr><tr>
+<td><nobr>'<a href=qh-optt.htm#Tn>T4</a>'
+T4_trace
+</nobr></td><td><nobr>'<a href=qh-optt.htm#Tc>Tc</a>'
+Tcheck_often
+</nobr></td><td><nobr>'<a href=qh-optt.htm#Ts>Ts</a>'
+Tstatistics
+</nobr></td><td><nobr>'<a href=qh-optt.htm#Tv>Tv</a>'
+Tverify
+
+</nobr></td></tr><tr>
+<td><nobr>'<a href=qh-optt.htm#Tz>Tz</a>'
+Tz_stdout
+</nobr></td><td><nobr>'<a href=qh-optt.htm#TFn>TFn</a>'
+TFacet_log
+<td><nobr>'<a href=qh-optt.htm#TI>TI file</a>'
+TInput_file
+</nobr></td><td><nobr>'<a href=qh-optt.htm#TPn>TPn</a>'
+TPoint_trace
+
+</nobr></td></tr><tr>
+<td><nobr>'<a href=qh-optt.htm#TMn>TMn</a>'
+TMerge_trace
+</nobr></td><td><nobr>'<a href=qh-optt.htm#TO>TO file</a>'
+TOutput_file
+</nobr></td><td><nobr>'<a href=qh-optt.htm#TRn>TRn</a>'
+TRerun
+</nobr></td><td><nobr>'<a href=qh-optt.htm#TWn>TWn</a>'
+TWide_trace
+
+</nobr></td></tr><tr>
+<td><nobr>'<a href=qh-optt.htm#TVn>TV-n</a>'
+TVertex_stop_before
+</nobr></td></tr><tr>
+<td><nobr>'<a href=qh-optt.htm#TVn2>TVn</a>'
+TVertex_stop_after
+</nobr></td><td><nobr>'<a href=qh-optt.htm#TCn>TCn</a>'
+TCone_stop_after
+
+</nobr></td></tr>
+<tr><td>&nbsp;</td></tr><tr>
+<td><nobr>'<a href=qh-optc.htm#An>A-n</a>'
+Angle_max_pre
+</nobr></td><td><nobr>'<a href=qh-optc.htm#An2>An</a>'
+Angle_max_post
+</nobr></td><td><nobr>'<a href=qh-optc.htm#C0>C-0</a>'
+Centrum_roundoff
+</nobr></td><td><nobr>'<a href=qh-optc.htm#Cn>C-n</a>'
+Centrum_size_pre
+
+</nobr></td></tr><tr>
+<td><nobr>'<a href=qh-optc.htm#Cn2>Cn</a>'
+Centrum_size_post
+</nobr></td><td><nobr>'<a href=qh-optc.htm#En>En</a>'
+Error_round
+</nobr></td><td><nobr>'<a href=qh-optc.htm#Rn>Rn</a>'
+Random_dist
+</nobr></td><td><nobr>'<a href=qh-optc.htm#Vn>Vn</a>'
+Visible_min
+
+</nobr></td></tr><tr>
+<td><nobr>'<a href=qh-optc.htm#Un>Un</a>'
+Ucoplanar_max
+</nobr></td><td><nobr>'<a href=qh-optc.htm#Wn>Wn</a>'
+Wide_outside
+
+</nobr></td></tr>
+<tr><td>&nbsp;</td></tr><tr>
+<td><nobr>'<a href=qh-optq.htm#Qbk>Qbk:n</a>'
+Qbound_low
+</nobr></td><td><nobr>'<a href=qh-optq.htm#QBk>QBk:n</a>'
+QBound_high
+</nobr></td><td><nobr>'<a href=qh-optq.htm#Qb0>Qbk:0Bk:0</a>'
+Qbound_drop
+</nobr></td><td><nobr>'<a href=qh-optq.htm#QbB>QbB</a>'
+QbB-scale-box
+
+</nobr></td></tr><tr>
+<td><nobr>'<a href=qh-optq.htm#Qbb>Qbb</a>'
+Qbb-scale-last
+</nobr></td><td><nobr>'<a href=qh-optq.htm#Qc>Qc</a>'
+Qcoplanar
+</nobr></td><td><nobr>'<a href=qh-optq.htm#Qf>Qf</a>'
+Qfurthest
+</nobr></td><td><nobr>'<a href=qh-optq.htm#Qg>Qg</a>'
+Qgood_only
+
+</nobr></td></tr><tr>
+<td><nobr>'<a href=qh-optq.htm#QGn>QGn</a>'
+QGood_point
+</nobr></td><td><nobr>'<a href=qh-optq.htm#Qi>Qi</a>'
+Qinterior
+</nobr></td><td><nobr>'<a href=qh-optq.htm#Qm>Qm</a>'
+Qmax_out
+</nobr></td><td><nobr>'<a href=qh-optq.htm#QJn>QJn</a>'
+QJoggle
+
+</nobr></td></tr><tr>
+<td><nobr>'<a href=qh-optq.htm#Qr>Qr</a>'
+Qrandom
+</nobr></td><td><nobr>'<a href=qh-optq.htm#QRn>QRn</a>'
+QRotate
+</nobr></td><td><nobr>'<a href=qh-optq.htm#Qs>Qs</a>'
+Qsearch_1st
+</nobr></td><td><nobr>'<a href=qh-optq.htm#Qt>Qt</a>'
+Qtriangulate
+
+</nobr></td></tr><tr>
+<td><nobr>'<a href=qh-optq.htm#Qu>Qu</a>'
+QupperDelaunay
+</nobr><td><nobr>'<a href=qh-optq.htm#QVn>QVn</a>'
+QVertex_good
+</nobr></td><td><nobr>'<a href=qh-optq.htm#Qv>Qv</a>'
+Qvneighbors
+</nobr></td><td><nobr>'<a href=qh-optq.htm#Qx>Qx</a>'
+Qxact_merge
+
+</nobr></td></tr><tr>
+<td><nobr>'<a href=qh-optq.htm#Qz>Qz</a>'
+Qzinfinite
+
+</nobr></td></tr>
+<tr><td>&nbsp;</td></tr><tr>
+<td><nobr>'<a href=qh-optq.htm#Q0>Q0</a>'
+Q0_no_premerge
+</nobr></td><td><nobr>'<a href=qh-optq.htm#Q1>Q1</a>'
+Q1_no_angle
+</nobr></td><td><nobr>'<a href=qh-optq.htm#Q2>Q2</a>'
+Q2_no_independ
+</nobr></td><td><nobr>'<a href=qh-optq.htm#Q3>Q3</a>'
+Q3_no_redundant
+
+</nobr></td></tr><tr>
+<td><nobr>'<a href=qh-optq.htm#Q4>Q4</a>'
+Q4_no_old
+</nobr></td><td><nobr>'<a href=qh-optq.htm#Q5>Q5</a>'
+Q5_no_check_out
+</nobr></td><td><nobr>'<a href=qh-optq.htm#Q6>Q6</a>'
+Q6_no_concave
+</nobr></td><td><nobr>'<a href=qh-optq.htm#Q7>Q7</a>'
+Q7_depth_first
+
+</nobr></td></tr><tr>
+<td><nobr>'<a href=qh-optq.htm#Q8>Q8</a>'
+Q8_no_near_in
+</nobr></td><td><nobr>'<a href=qh-optq.htm#Q9>Q9</a>'
+Q9_pick_furthest
+</nobr></td><td><nobr>'<a href=qh-optq.htm#Q10>Q10</a>'
+Q10_no_narrow
+</nobr></td><td><nobr>'<a href=qh-optq.htm#Q11>Q11</a>'
+Q11_trinormals
+</td></tr></table>
+
+<!-- Navigation links -->
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+<!-- GC common information -->
+<hr>
+
+<p><a href="http://www.geom.uiuc.edu/"><img src="qh--geom.gif"
+align="middle" width="40" height="40"></a><i>The Geometry Center
+Home Page </i></p>
+
+<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
+</a><br>
+Created: Sept. 25, 1995 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
+</body>
+</html>
diff --git a/xs/src/qhull/html/qhalf.htm b/xs/src/qhull/html/qhalf.htm
new file mode 100644
index 0000000000..c87fe719ed
--- /dev/null
+++ b/xs/src/qhull/html/qhalf.htm
@@ -0,0 +1,626 @@
+<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN">
+<html>
+
+<head>
+<title>qhalf -- halfspace intersection about a point</title>
+</head>
+
+<body>
+<!-- Navigation links -->
+<p><a name="TOP"><b>Up</b></a><b>:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
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+&#149; <a href="#notes">no</a>tes &#149; <a href="#conventions">co</a>nventions
+&#149; <a href="#options">op</a>tions
+
+<hr>
+<!-- Main text of document -->
+<h1><a
+href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/half.html"><img
+src="qh--half.gif" alt="[halfspace]" align="middle" width="100"
+height="100"></a>qhalf -- halfspace intersection about a point</h1>
+
+<p>The intersection of a set of halfspaces is a polytope. The
+polytope may be unbounded. See Preparata &amp; Shamos [<a
+href="index.htm#pre-sha85">'85</a>] for a discussion. In low
+dimensions, halfspace intersection may be used for linear
+programming.
+
+<blockquote>
+<dl compact>
+    <dt><p><b>Example:</b> rbox c | qconvex <a href="qh-optf.htm#FQ">FQ</a> <a href="qh-optf.htm#FV">FV</a>
+        <a href="qh-opto.htm#n">n</a> | qhalf <a
+        href="qh-optf.htm#Fp">Fp</a></dt>
+    <dd>Print the intersection of the facets of a cube.  <tt>rbox c</tt>
+        generates the vertices of a cube.  <tt>qconvex FV n</tt> returns of average
+        of the cube's vertices (in this case, the origin) and the halfspaces
+        that define the cube.  <tt>qhalf Fp</tt> computes the intersection of
+        the halfspaces about the origin.  The intersection is the vertices
+        of the original cube.</dd>
+
+    <dt><p><b>Example:</b> rbox c d G0.55 | qconvex <a href="qh-optf.htm#FQ">FQ</a> <a href="qh-optf.htm#FV">FV</a>
+        <a href="qh-opto.htm#n">n</a> | qhalf <a
+        href="qh-optf.htm#Fp">Fp</a></dt>
+    <dd>Print the intersection of the facets of a cube and a diamond.  There
+        are 24 facets and 14 intersection points.  Four facets define each diamond
+        vertex.  Six facets define each cube vertex.
+        </dd>
+
+    <dt><p><b>Example:</b> rbox c d G0.55 | qconvex <a href="qh-optf.htm#FQ">FQ</a> <a href="qh-optf.htm#FV">FV</a>
+        <a href="qh-opto.htm#n">n</a> | qhalf <a
+        href="qh-optf.htm#Fp">Fp</a>
+                <a href="qh-optq.htm#Qt">Qt</a></dt>
+    <dd>Same as above except triangulate before computing
+        the intersection points.  Three facets define each intersection
+        point.  There are two duplicates of the diamond and four duplicates of the cube.
+        </dd>
+
+    <dt><p><b>Example:</b> rbox 10 s t10 | qconvex <a href="qh-optf.htm#FQ">FQ</a> <a href="qh-optf.htm#FV">FV</a>
+        <a href="qh-opto.htm#n">n</a> | qhalf <a
+        href="qh-optf.htm#Fp">Fp</a> <a
+        href="qh-optf.htm#Fn">Fn</a></dt>
+    <dd>Print the intersection of the facets of the convex hull of 10 cospherical points.
+        Include the intersection points and the neighboring intersections.
+        As in the previous examples, the intersection points are nearly the same as the
+        original input points.
+        </dd>
+</dl>
+</blockquote>
+
+<p>In Qhull, a <i>halfspace</i> is defined by the points on or below a hyperplane.
+The distance of each point to the hyperplane is less than or equal to zero.
+
+<p>Qhull computes a halfspace intersection by the geometric
+duality between points and halfspaces.
+See <a href="qh-eg.htm#half">halfspace examples</a>,
+<a href="#notes">qhalf notes</a>, and
+option 'p' of <a href="#outputs">qhalf outputs</a>. </p>
+
+<p>Qhalf's <a href="#outputs">outputs</a> are the intersection
+points (<a href="qh-optf.htm#Fp">Fp</a>) and
+the neighboring intersection points (<a href="qh-optf.htm#Fn">Fn</a>).
+For random inputs, halfspace
+intersections are usually defined by more than <i>d</i> halfspaces.  See the sphere example.
+
+<p>You can try triangulated output ('<a href="qh-optq.htm#Qt">Qt</a>') and joggled input ('<a href="qh-optq.htm#QJn">QJ</a>').
+It demonstrates that triangulated output is more accurate than joggled input.
+
+<p>If you use '<a href="qh-optq.htm#Qt">Qt</a>' (triangulated output), all
+halfspace intersections are simplicial (e.g., three halfspaces per
+intersection in 3-d).  In 3-d, if more than three halfspaces intersect
+at the same point, triangulated output will produce
+duplicate intersections, one for each additional halfspace.  See the third example, or
+add 'Qt' to the sphere example.</p>
+
+<p>If you use '<a href="qh-optq.htm#QJn">QJ</a>' (joggled input), all halfspace
+intersections are simplicial.  This may lead to nearly identical
+intersections.  For example, either replace 'Qt' with 'QJ' above, or add
+'QJ' to the sphere example.
+See <a
+href="qh-impre.htm#joggle">Merged facets or joggled input</a>. </p>
+
+<p>The 'qhalf' program is equivalent to
+'<a href=qhull.htm#outputs>qhull H</a>' in 2-d to 4-d, and
+'<a href=qhull.htm#outputs>qhull H</a> <a href=qh-optq.htm#Qx>Qx</a>'
+in 5-d and higher.  It disables the following Qhull
+<a href=qh-quick.htm#options>options</a>: <i>d n v Qbb QbB Qf Qg Qm
+Qr QR Qv Qx Qz TR E V Fa FA FC FD FS Ft FV Gt Q0,etc</i>.
+
+
+<p><b>Copyright &copy; 1995-2015 C.B. Barber</b></p>
+<hr>
+
+<h3><a href="#TOP">&#187;</a><a name="synopsis">qhalf synopsis</a></h3>
+<pre>
+qhalf- halfspace intersection about a point.
+    input (stdin): [dim, 1, interior point]
+                   dim+1, n
+                   halfspace coefficients + offset
+    comments start with a non-numeric character
+
+options (qhalf.htm):
+    Hn,n - specify coordinates of interior point
+    Qt   - triangulated output
+    QJ   - joggle input instead of merging facets
+    Tv   - verify result: structure, convexity, and redundancy
+    .    - concise list of all options
+    -    - one-line description of all options
+
+output options (subset):
+    s    - summary of results (default)
+    Fp   - intersection coordinates
+    Fv   - non-redundant halfspaces incident to each intersection
+    Fx   - non-redundant halfspaces
+    o    - OFF file format (dual convex hull)
+    G    - Geomview output (dual convex hull)
+    m    - Mathematica output (dual convex hull)
+    QVn  - print intersections for halfspace n, -n if not
+    TO file - output results to file, may be enclosed in single quotes
+
+examples:
+    rbox d | qconvex n | qhalf s H0,0,0 Fp
+    rbox c | qconvex FV n | qhalf s i
+    rbox c | qconvex FV n | qhalf s o
+</pre>
+
+<h3><a href="#TOP">&#187;</a><a name="input">qhalf input</a></h3>
+
+<blockquote>
+<p>The input data on <tt>stdin</tt> consists of:</p>
+<ul>
+    <li>[optional] interior point
+           <ul>
+           <li>dimension
+           <li>1
+           <li>coordinates of interior point
+           </ul>
+    <li>dimension + 1
+    <li>number of halfspaces</li>
+    <li>halfspace coefficients followed by offset</li>
+</ul>
+
+<p>Use I/O redirection (e.g., qhalf &lt; data.txt), a pipe (e.g., rbox c | qconvex FV n | qhalf),
+or the '<a href=qh-optt.htm#TI>TI</a>' option (e.g., qhalf TI data.txt).
+
+<p>Qhull needs an interior point to compute the halfspace
+intersection. An interior point is clearly inside all of the halfspaces.
+A point is <i>inside</i> a halfspace if its distance to the corresponding hyperplane is negative.
+
+<p>The interior point may be listed at the beginning of the input (as shown above).
+If not, option
+'Hn,n' defines the interior point as
+[n,n,0,...] where <em>0</em> is the default coordinate (e.g.,
+'H0' is the origin).  Use linear programming if you do not know
+the interior point (see <a href="#notes">halfspace notes</a>),</p>
+
+<p>The input to qhalf is a set of halfspaces that are defined by their hyperplanes.
+Each halfspace is defined by
+<em>d</em> coefficients followed by a signed offset. This defines
+a linear inequality. The coefficients define a vector that is
+normal to the halfspace.
+The vector may have any length. If it
+has length one, the offset is the distance from the origin to the
+halfspace's boundary.  Points in the halfspace have a negative distance to the hyperplane.
+The distance from the interior point to each
+halfspace is likewise negative.</p>
+
+<p>The halfspace format is the same as Qhull's output options '<a
+href="qh-opto.htm#n">n</a>', '<a href="qh-optf.htm#Fo">Fo</a>',
+and '<a href="qh-optf.htm#Fi">Fi</a>'. Use option '<a
+href="qh-optf.htm#Fd">Fd</a>' to use cdd format for the
+halfspaces.</p>
+
+<p>For example, here is the input for computing the intersection
+of halfplanes that form a cube.</p>
+
+<blockquote>
+    <p>rbox c | qconvex FQ FV n TO data </p>
+    <pre>
+RBOX c | QCONVEX FQ FV n
+3 1
+     0      0      0
+4
+6
+     0      0     -1   -0.5
+     0     -1      0   -0.5
+     1      0      0   -0.5
+    -1      0      0   -0.5
+     0      1      0   -0.5
+     0      0      1   -0.5
+</pre>
+    <p>qhalf s Fp &lt; data </p>
+    <pre>
+
+Halfspace intersection by the convex hull of 6 points in 3-d:
+
+  Number of halfspaces: 6
+  Number of non-redundant halfspaces: 6
+  Number of intersection points: 8
+
+Statistics for: RBOX c | QCONVEX FQ FV n | QHALF s Fp
+
+  Number of points processed: 6
+  Number of hyperplanes created: 11
+  Number of distance tests for qhull: 11
+  Number of merged facets: 1
+  Number of distance tests for merging: 45
+  CPU seconds to compute hull (after input):  0
+
+3
+3
+8
+  -0.5    0.5    0.5
+   0.5    0.5    0.5
+  -0.5    0.5   -0.5
+   0.5    0.5   -0.5
+   0.5   -0.5    0.5
+  -0.5   -0.5    0.5
+  -0.5   -0.5   -0.5
+   0.5   -0.5   -0.5
+</pre>
+</blockquote>
+
+</blockquote>
+<h3><a href="#TOP">&#187;</a><a name="outputs">qhalf outputs</a></h3>
+<blockquote>
+
+<p>The following options control the output for halfspace
+intersection.</p>
+<blockquote>
+<dl compact>
+    <dt>&nbsp;</dt>
+    <dd><b>Intersections</b></dd>
+    <dt><a href="qh-optf.htm#FN">FN</a></dt>
+    <dd>list intersection points for each non-redundant
+        halfspace.  The first line
+            is the number of non-redundant halfspaces.  Each remaining
+                lines starts with the number of intersection points.  For the cube
+                example, each halfspace has four intersection points.</dd>
+    <dt><a href="qh-optf.htm#Fn">Fn</a></dt>
+    <dd>list neighboring intersections for each intersection point.  The first line
+            is the number of intersection points.  Each remaining line
+                starts with the number of neighboring intersections.  For the cube
+                example, each intersection point has three neighboring intersections.
+                <p>
+                In 3-d, a non-simplicial intersection has more than three neighboring
+                intersections.  For random data (e.g., the sphere example), non-simplicial intersections are the norm.
+                Option '<a href="qh-optq.htm#Qt">Qt</a>' produces three
+                neighboring intersections per intersection by duplicating the intersection
+                points.  Option <a href="qh-optq.htm#QJn">QJ</a>' produces three
+                neighboring intersections per intersection by joggling the hyperplanes and
+                hence their intersections.
+             </dd>
+    <dt><a href="qh-optf.htm#Fp">Fp</a></dt>
+    <dd>print intersection coordinates.  The first line is the dimension and the
+        second line is the number of intersection points.  The following lines are the
+        coordinates of each intersection.</dd>
+    <dt><a href="qh-optf.htm#FI">FI</a></dt>
+    <dd>list intersection IDs.  The first line is the number of
+        intersections.  The IDs follow, one per line.</dd>
+    <dt>&nbsp;</dt>
+    <dt>&nbsp;</dt>
+    <dd><b>Halfspaces</b></dd>
+    <dt><a href="qh-optf.htm#Fx">Fx</a></dt>
+    <dd>list non-redundant halfspaces.  The first line is the number of
+        non-redundant halfspaces.  The other lines list one halfspace per line.
+        A halfspace is <i>non-redundant</i> if it
+        defines a facet of the intersection.  Redundant halfspaces are ignored.  For
+        the cube example, all of the halfspaces are non-redundant.
+        </dd>
+    <dt><a href="qh-optf.htm#Fv">Fv</a></dt>
+    <dd>list non-redundant halfspaces incident to each intersection point.
+        The first line is the number of
+        non-redundant halfspaces.  Each remaining line starts with the number
+        of non-redundant halfspaces.  For the
+         cube example, each intersection is incident to three halfspaces.</dd>
+    <dt><a href="qh-opto.htm#i">i</a></dt>
+    <dd>list non-redundant halfspaces incident to each intersection point.  The first
+          line is the number of intersection points.  Each remaining line
+          lists the incident, non-redundant halfspaces.  For the
+         cube example, each intersection is incident to three halfspaces.
+       </dd>
+    <dt><a href="qh-optf.htm#Fc">Fc</a></dt>
+    <dd>list coplanar halfspaces for each intersection point. The first line is
+           the number of intersection points.  Each remaining line starts with
+           the number of coplanar halfspaces.  A coplanar halfspace is listed for
+           one intersection point even though it is coplanar to multiple intersection
+           points.</dd>
+  <dt><a href="qh-optq.htm#Qc">Qi</a> <a href="qh-optf.htm#Fc">Fc</a></dt>
+    <dd>list redundant halfspaces for each intersection point.  The first line is
+           the number of intersection points.  Each remaining line starts with
+           the number of redundant halfspaces.  Use options '<a href="qh-optq.htm#Qc">Qc</a> Qi Fc' to list
+           coplanar and redundant halfspaces.</dd>
+
+    <dt>&nbsp;</dt>
+    <dt>&nbsp;</dt>
+    <dd><b>General</b></dd>
+    <dt><a href="qh-opto.htm#s">s</a></dt>
+    <dd>print summary for the halfspace intersection. Use '<a
+        href="qh-optf.htm#Fs">Fs</a>' if you need numeric data.</dd>
+    <dt><a href="qh-opto.htm#o">o</a></dt>
+    <dd>print vertices and facets of the dual convex hull.    The
+           first line is the dimension.  The second line is the number of
+           vertices, facets, and ridges.  The vertex
+           coordinates are next, followed by the facets, one per line.</dd>
+    <dt><a href="qh-opto.htm#p">p</a></dt>
+    <dd>print vertex coordinates of the dual convex hull.  Each vertex corresponds
+           to a non-redundant halfspace.  Its coordinates are the negative of the hyperplane's coefficients
+           divided by the offset plus the inner product of the coefficients and
+           the interior point (-c/(b+a.p).
+           Options 'p <a href="qh-optq.htm#Qc">Qc</a>' includes coplanar halfspaces.
+           Options 'p <a href="qh-optq.htm#Qi">Qi</a>' includes redundant halfspaces.</dd>
+    <dt><a href="qh-opto.htm#m">m</a></dt>
+    <dd>Mathematica output for the dual convex hull in 2-d or 3-d.</dd>
+    <dt><a href="qh-optf.htm#FM">FM</a></dt>
+    <dd>Maple output for the dual convex hull in 2-d or 3-d.</dd>
+    <dt><a href="qh-optg.htm#G">G</a></dt>
+    <dd>Geomview output for the dual convex hull in 2-d, 3-d, or 4-d.</dd>
+ </dl>
+</blockquote>
+
+</blockquote>
+<h3><a href="#TOP">&#187;</a><a name="controls">qhalf controls</a></h3>
+<blockquote>
+
+<p>These options provide additional control:</p>
+
+<blockquote>
+<dl compact>
+    <dt><a href="qh-optq.htm#Qt">Qt</a></dt>
+    <dd>triangulated output.  If a 3-d intersection is defined by more than
+      three hyperplanes, Qhull produces duplicate intersections -- one for
+      each extra hyperplane.</dd>
+    <dt><a href="qh-optq.htm#QJn">QJ</a></dt>
+    <dd>joggle the input instead of merging facets.  In 3-d, this guarantees that
+        each intersection is defined by three hyperplanes.</dd>
+    <dt><a href="qh-opto.htm#f">f </a></dt>
+    <dd>facet dump.  Print the data structure for each intersection (i.e.,
+        facet)</dd>
+    <dt><a href="qh-optt.htm#TFn">TFn</a></dt>
+    <dd>report summary after constructing <em>n</em>
+        intersections</dd>
+    <dt><a href="qh-optq.htm#QVn">QVn</a></dt>
+    <dd>select intersection points for halfspace <em>n</em>
+        (marked 'good')</dd>
+    <dt><a href="qh-optq.htm#QGn">QGn</a></dt>
+    <dd>select intersection points that are visible to halfspace <em>n</em>
+        (marked 'good').  Use <em>-n</em> for the remainder.</dd>
+        <dt><a href="qh-optq.htm#Qb0">Qbk:0Bk:0</a></dt>
+    <dd>remove the k-th coordinate from the input.  This computes the
+        halfspace intersection in one lower dimension.</dd>
+    <dt><a href="qh-optt.htm#Tv">Tv</a></dt>
+    <dd>verify result</dd>
+    <dt><a href="qh-optt.htm#TO">TI file</a></dt>
+    <dd>input data from file.  The filename may not use spaces or quotes.</dd>
+    <dt><a href="qh-optt.htm#TO">TO file</a></dt>
+    <dd>output results to file.  Use single quotes if the filename
+        contains spaces (e.g., <tt>TO 'file with spaces.txt'</tt></dd>
+    <dt><a href="qh-optq.htm#Qs">Qs</a></dt>
+    <dd>search all points for the initial simplex.  If Qhull can
+        not construct an initial simplex, it reports a
+descriptive message. Usually, the point set is degenerate and one
+or more dimensions should be removed ('<a href="qh-optq.htm#Qb0">Qbk:0Bk:0</a>').
+If not, use option 'Qs'. It performs an exhaustive search for the
+best initial simplex. This is expensive is high dimensions.</dd>
+</dl>
+</blockquote>
+
+
+</blockquote>
+<h3><a href="#TOP">&#187;</a><a name="graphics">qhalf graphics</a></h3>
+<blockquote>
+
+<p>To view the results with Geomview, compute the convex hull of
+the intersection points ('qhull FQ H0 Fp | qhull G'). See <a
+href="qh-eg.htm#half">Halfspace examples</a>.</p>
+
+</blockquote>
+<h3><a href="#TOP">&#187;</a><a name="notes">qhalf notes</a></h3>
+<blockquote>
+
+<p>See <a href="qh-impre.htm#halfspace">halfspace intersection</a> for precision issues related to qhalf.</p>
+
+<p>If you do not know an interior point for the halfspaces, use
+linear programming to find one. Assume, <em>n</em> halfspaces
+defined by: <em>aj*x1+bj*x2+cj*x3+dj&lt;=0, j=1..n</em>.  Perform
+the following linear program: </p>
+
+<blockquote>
+    <p>max(x5) aj*x1+bj*x2+cj*x3+dj*x4+x5&lt;=0, j=1..n</p>
+</blockquote>
+
+<p>Then, if <em>[x1,x2,x3,x4,x5]</em> is an optimal solution with
+<em>x4&gt;0</em> and <em>x5&gt;0</em> we get: </p>
+
+<blockquote>
+    <p>aj*(x1/x4)+bj*(x2/x4)+cj*(x3/x4)+dj&lt;=(-x5/x4) j=1..n and (-x5/x4)&lt;0,
+    </p>
+</blockquote>
+
+<p>and conclude that the point <em>[x1/x4,x2/x4,x3/x4]</em> is in
+the interior of all the halfspaces. Since <em>x5</em> is
+optimal, this point is &quot;way in&quot; the interior (good
+for precision errors).</p>
+
+<p>After finding an interior point, the rest of the intersection
+algorithm is from Preparata &amp; Shamos [<a
+href="index.htm#pre-sha85">'85</a>, p. 316, &quot;A simple case
+...&quot;]. Translate the halfspaces so that the interior point
+is the origin. Calculate the dual polytope. The dual polytope is
+the convex hull of the vertices dual to the original faces in
+regard to the unit sphere (i.e., halfspaces at distance <em>d</em>
+from the origin are dual to vertices at distance <em>1/d</em>).
+Then calculate the resulting polytope, which is the dual of the
+dual polytope, and translate the origin back to the interior
+point [S. Spitz, S. Teller, D. Strawn].</p>
+
+
+</blockquote>
+<h3><a href="#TOP">&#187;</a><a name="conventions">qhalf
+conventions</a></h3>
+<blockquote>
+
+<p>The following terminology is used for halfspace intersection
+in Qhull. This is the hardest structure to understand. The
+underlying structure is a convex hull with one vertex per
+non-redundant halfspace. See <a href="#conventions">convex hull
+conventions</a> and <a href="index.htm#structure">Qhull's data structures</a>.</p>
+
+<ul>
+    <li><em>interior point</em> - a point in the intersection of
+        the halfspaces. Qhull needs an interior point to compute
+        the intersection. See <a href="#input">halfspace input</a>.</li>
+    <li><em>halfspace</em> - <em>d</em> coordinates for the
+        normal and a signed offset. The distance to an interior
+        point is negative.</li>
+    <li><em>non-redundant halfspace</em> - a halfspace that
+        defines an output facet</li>
+    <li><em>vertex</em> - a dual vertex in the convex hull
+        corresponding to a non-redundant halfspace</li>
+    <li><em>coplanar point</em> - the dual point corresponding to
+        a similar halfspace</li>
+    <li><em>interior point</em> - the dual point corresponding to
+        a redundant halfspace</li>
+    <li><em>intersection point</em>- the intersection of <em>d</em>
+        or more non-redundant halfspaces</li>
+    <li><em>facet</em> - a dual facet in the convex hull
+        corresponding to an intersection point</li>
+    <li><em>non-simplicial facet</em> - more than <em>d</em>
+        halfspaces intersect at a point</li>
+    <li><em>good facet</em> - an intersection point that
+        satisfies restriction '<a href="qh-optq.htm#QVn">QVn</a>',
+        etc.</li>
+</ul>
+
+</blockquote>
+<h3><a href="#TOP">&#187;</a><a name="options">qhalf options</a></h3>
+
+<pre>
+qhalf- compute the intersection of halfspaces about a point
+    http://www.qhull.org
+
+input (stdin):
+    optional interior point: dimension, 1, coordinates
+    first lines: dimension+1 and number of halfspaces
+    other lines: halfspace coefficients followed by offset
+    comments:    start with a non-numeric character
+
+options:
+    Hn,n - specify coordinates of interior point
+    Qt   - triangulated ouput
+    QJ   - joggle input instead of merging facets
+    Qc   - keep coplanar halfspaces
+    Qi   - keep other redundant halfspaces
+
+Qhull control options:
+    QJn  - randomly joggle input in range [-n,n]
+    Qbk:0Bk:0 - remove k-th coordinate from input
+    Qs   - search all halfspaces for the initial simplex
+    QGn  - print intersection if redundant to halfspace n, -n for not
+    QVn  - print intersections for halfspace n, -n if not
+
+Trace options:
+    T4   - trace at level n, 4=all, 5=mem/gauss, -1= events
+    Tc   - check frequently during execution
+    Ts   - print statistics
+    Tv   - verify result: structure, convexity, and redundancy
+    Tz   - send all output to stdout
+    TFn  - report summary when n or more facets created
+    TI file - input data from file, no spaces or single quotes
+    TO file - output results to file, may be enclosed in single quotes
+    TPn  - turn on tracing when halfspace n added to intersection
+    TMn  - turn on tracing at merge n
+    TWn  - trace merge facets when width > n
+    TVn  - stop qhull after adding halfspace n, -n for before (see TCn)
+    TCn  - stop qhull after building cone for halfspace n (see TVn)
+
+Precision options:
+    Cn   - radius of centrum (roundoff added).  Merge facets if non-convex
+     An  - cosine of maximum angle.  Merge facets if cosine > n or non-convex
+           C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge
+    Rn   - randomly perturb computations by a factor of [1-n,1+n]
+    Un   - max distance below plane for a new, coplanar halfspace
+    Wn   - min facet width for outside halfspace (before roundoff)
+
+Output formats (may be combined; if none, produces a summary to stdout):
+    f    - facet dump
+    G    - Geomview output (dual convex hull)
+    i    - non-redundant halfspaces incident to each intersection
+    m    - Mathematica output (dual convex hull)
+    o    - OFF format (dual convex hull: dimension, points, and facets)
+    p    - vertex coordinates of dual convex hull (coplanars if 'Qc' or 'Qi')
+    s    - summary (stderr)
+
+More formats:
+    Fc   - count plus redundant halfspaces for each intersection
+         -   Qc (default) for coplanar and Qi for other redundant
+    Fd   - use cdd format for input (homogeneous with offset first)
+    FF   - facet dump without ridges
+    FI   - ID of each intersection
+    Fm   - merge count for each intersection (511 max)
+    FM   - Maple output (dual convex hull)
+    Fn   - count plus neighboring intersections for each intersection
+    FN   - count plus intersections for each non-redundant halfspace
+    FO   - options and precision constants
+    Fp   - dim, count, and intersection coordinates
+    FP   - nearest halfspace and distance for each redundant halfspace
+    FQ   - command used for qhalf
+    Fs   - summary: #int (8), dim, #halfspaces, #non-redundant, #intersections
+                      for output: #non-redundant, #intersections, #coplanar
+                                  halfspaces, #non-simplicial intersections
+                    #real (2), max outer plane, min vertex
+    Fv   - count plus non-redundant halfspaces for each intersection
+    Fx   - non-redundant halfspaces
+
+Geomview output (2-d, 3-d and 4-d; dual convex hull)
+    Ga   - all points (i.e., transformed halfspaces) as dots
+     Gp  -  coplanar points and vertices as radii
+     Gv  -  vertices (i.e., non-redundant halfspaces) as spheres
+    Gi   - inner planes (i.e., halfspace intersections) only
+     Gn  -  no planes
+     Go  -  outer planes only
+    Gc   - centrums
+    Gh   - hyperplane intersections
+    Gr   - ridges
+    GDn  - drop dimension n in 3-d and 4-d output
+
+Print options:
+    PAn  - keep n largest facets (i.e., intersections) by area
+    Pdk:n- drop facet if normal[k] &lt;= n (default 0.0)
+    PDk:n- drop facet if normal[k] >= n
+    Pg   - print good facets (needs 'QGn' or 'QVn')
+    PFn  - keep facets whose area is at least n
+    PG   - print neighbors of good facets
+    PMn  - keep n facets with most merges
+    Po   - force output.  If error, output neighborhood of facet
+    Pp   - do not report precision problems
+
+    .    - list of all options
+    -    - one line descriptions of all options
+</pre>
+
+<!-- Navigation links -->
+<hr>
+
+<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
+<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
+<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
+&#149; <a href="qh-quick.htm#options">Options</a>
+&#149; <a href="qh-opto.htm#output">Output</a>
+&#149; <a href="qh-optf.htm#format">Formats</a>
+&#149; <a href="qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="qh-optp.htm#print">Print</a>
+&#149; <a href="qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="qh-optc.htm#prec">Precision</a>
+&#149; <a href="qh-optt.htm#trace">Trace</a>
+&#149; <a href="../src/libqhull_r/index.htm">Functions</a><br>
+<b>To:</b> <a href="#synopsis">sy</a>nopsis
+&#149; <a href="#input">in</a>put &#149; <a href="#outputs">ou</a>tputs
+&#149; <a href="#controls">co</a>ntrols &#149; <a href="#graphics">gr</a>aphics
+&#149; <a href="#notes">no</a>tes &#149; <a href="#conventions">co</a>nventions
+&#149; <a href="#options">op</a>tions
+<!-- GC common information -->
+<hr>
+
+<p><a href="http://www.geom.uiuc.edu/"><img src="qh--geom.gif"
+align="middle" width="40" height="40"></a><i>The Geometry Center
+Home Page </i></p>
+
+<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
+</a><br>
+Created: Sept. 25, 1995 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
+</body>
+</html>
+
diff --git a/xs/src/qhull/html/qhull-cpp.xml b/xs/src/qhull/html/qhull-cpp.xml
new file mode 100644
index 0000000000..ae755e8266
--- /dev/null
+++ b/xs/src/qhull/html/qhull-cpp.xml
@@ -0,0 +1,214 @@
+<?xml version="1.0" encoding="utf-8"?>
+<?xml-stylesheet type="text/xsl" href="../../road-faq/xsl/road-faq.xsl"?>
+
+<rf:topic xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"  
+    xsi:schemaLocation="http://schemas.roadintranet.org/road-faq-1 /road/road-faq/xsl/road-faq.xsd"  
+   xmlns:rf="http://schemas.roadintranet.org/road-faq-1"
+ title=" C++ interface to Qhull"
+ file="qhull-cpp.xml"
+ fileid="$Id: //main/2015/qhull/html/qhull-cpp.xml#2 $$Change: 2027 $"
+ fileChange="$DateTime: 2015/11/09 23:18:11 $$Author: bbarber $">
+    <div><h4>Qhull C++  -- C++ interface to Qhull</h4></div>
+    <rf:copyright>
+        <a href="../cpp/COPYING.txt">Copyright</a> (c) 2009-2015, C.B. Barber
+    </rf:copyright>
+   <rf:section id="cpp-cpp-links" title="Useful Links for Qhull C++">
+       <div>
+           <p> This draft
+               document records some of the design decisions for Qhull C++.  Convert it to HTML by road-faq.xsl from <a href="http://www.qhull.org/road/road-faq/road-faq.html">road-faq</a>.
+               
+               Please send comments and suggestions to <a
+                   href="mailto:bradb@shore.net">bradb@shore.net</a>
+           </p>
+       </div>
+       <div class="twocol">
+           <div class="col leftcol">
+               Help
+               <ul><li>
+                </li><li>
+               </li><li>
+               </li></ul>
+           </div>
+           <div class="col rightcol">
+             <ul><li>
+             </li><li>
+             </li></ul>
+         </div>
+       </div>
+       <div>
+           . <!-- clear the two column display -->
+       </div>
+       
+   </rf:section>
+    <rf:section id="qhull-api" title="Qhull's collection classes">
+  
+         <rf:item id="collection-api" title="API for Qhull collections" date="Feb 2009" author="bbarber">
+             Qhull's collection APIs are modeled on Qt's collection API (QList, QVector, QHash) w/o QT_STRICT_ITERATORS.  They support STL and Qt programming.  
+             
+             <p>Some of Qhull's collection classes derive from STL classes.  If so, 
+             please avoid additional STL functions and operators added by inheritance.
+             These collection classes may be rewritten to derive from Qt classes instead.
+             See Road's <rf:iref item="cpp-collection-api"/>.
+	     </p>
+	     
+             
+             Qhull's collection API (where applicable).  For documentation, see Qt's QList, QMap, QListIterator, QMapIterator, QMutableListIterator, and QMutableMapIterator
+             <ul><li>
+                 STL types [list, qlinkedlist, qlist, qvector, vector] -- const_iterator, iterator
+             </li><li>
+                 STL types describing iterators [list, qlinkedlist, qlist, qvector, vector] -- const_pointer, const_reference, difference_type,
+                     pointer, reference, size_type, value_type.
+                 Pointer and reference types not defined if unavailable (not needed for &lt;algorithm&gt;)
+             </li><li>
+                 const_iterator, iterator types -- difference_type, iterator_category, pointer, reference, value_type
+             </li><li>
+                 Qt types [qlinkedlist, qlist, qvector] -- ConstIterator, Iterator, QhullclassIterator, MutableQhullclassIterator.
+                 Qt's foreach requires const_iterator.
+             </li><li>
+                 Types for sets/maps [hash_map, QHash] -- key_compare, key_type, mapped_type
+             </li><li>
+                 Constructor -- default constructor, copy constructor, assignment operator, destructor
+             </li><li>
+                 Conversion -- to/from/as corresponding C, STL, and Qt constructs.  Include toQList and toStdVector (may be filtered, e.g., QhullFacetSet).
+                               Do not define fromStdList and fromQList if container is not reference counted (i.e., acts like a value)
+             </li><li>
+                 Get/set -- configuration options for class
+             </li><li>
+                 STL-style iterator - begin, constBegin, constEnd, end, key, value, =, *, [], ->, ++, --, +, -, ==, !=, &lt;,
+                 &lt;=, &gt;, &gt;=, const_iterator(iterator), iterator COMPARE const_iterator.  
+                 An iterator is an abstraction of a pointer.  It is not aware of its container.
+             </li><li>
+                 Java-style iterator [qiterator.h] - countRemaining, findNext, findPrevious, hasNext, hasPrevious, next, peekNext, peekPrevious, previous, toBack, toFront, = Coordinates
+             </li><li>
+                 Mutable Java-style iterator adds - insert, remove, setValue, value
+             </li><li>
+                 Element access -- back, first, front, last
+             </li><li>
+                 Element access w/ index -- [], at (const&amp; only), constData, data, mid, value
+             </li><li>
+                 Read-only - (int)count, empty, isEmpty, (size_t)size.  Count() and size() may be filtered.  If so, they may be zero when !empty().
+             </li><li>
+                 Read-only for sets/maps - capacity, key, keys, reserve, resize, values
+             </li><li>
+                 Operator - ==, !=, +, +=, &lt;&lt;
+             </li><li>
+                 Read-write -- append, clear, erase, insert, move, prepend, pop_back, pop_front, push_back, push_front, removeAll, removeAt, removeFirst, removeLast, replace,
+                 swap, takeAt, takeFirst, takeLast
+             </li><li>
+                 Read-write for sets/maps -- insertMulti, squeeze, take, unite
+             </li><li>
+                 Search -- contains(const T &amp;), count(const T &amp;), indexOf, lastIndexOf
+             </li><li>
+                 Search for sets/maps -- constFind, lowerBound, upperBound
+             </li><li>
+                 Stream I/O -- stream &lt;&lt;
+             </li></ul>
+
+             STL list and vector -- For unfiltered access to each element.
+             <ul><li>
+                 <a href="http://stdcxx.apache.org/doc/stdlibug/16-3.html">Apache: Creating your own containers</a> -- requirements for STL containers.  Iterators should define the types from 'iterator_traits'.
+             </li><li>
+                 STL types -- allocator_type, const_iterator, const_pointer, const_reference, const_reverse_iterator, difference_type, iterator, iterator_category, pointer, reference, reverse_iterator, size_type, value_type
+             </li><li>
+                 STL constructors -- MyType(), MyType(count), MyType(count, value), MyType(first, last),
+                 MyType(MyType&amp;),
+             </li><li>
+                 STL getter/setters -- at (random_access only), back, begin, capacity, end, front, rbegin, rend, size, max_size
+             </li><li>
+                 STL predicates -- empty
+             </li><li>
+                 STL iterator types -- const_pointer, const_reference, difference_type, iterator_category, pointer, reference, value_type
+             </li><li>
+                 STL iterator operators -- *, -&lt;, ++, --, +=, -=, +, -, [], ==, !=, &lt;, &gt;, &gt;=, &lt;=
+             </li><li>
+                 STL operators -- =, [] (random_access only), ==, !=, &lt;, &gt;, &lt;=, &gt;=
+             </li><li>
+                 STL modifiers -- assign, clear, erase, insert, pop_back, push_back, reserve, resize, swap
+             </li><li>
+             </li></ul>
+
+             Qt Qlist  -- For unfiltered access to each element
+             <ul><li>
+             </li><li>
+                 Additional Qt types -- ConstIterator, Iterator, QListIterator, QMutableListIterator
+             </li><li>
+                 Additional Qt get/set -- constBegin, constEnd, count, first, last, value (random_access only)
+             </li><li>
+                 Additional Qt predicates -- isEmpty
+             </li><li>
+                 Additional Qt -- mid (random_access only)
+             </li><li>
+                 Additional Qt search -- contains, count(T&amp;), indexOf (random_access only), lastIndeOf (random_access only)
+             </li><li>
+                 Additional Qt modifiers -- append, insert(index,value) (random_access only), move (random_access only), pop_front, prepend, push_front, removeAll, removeAt (random_access only), removeFirst, removeLast, replace, swap by index, takeAt, takeFirst, takeLast
+             </li><li>
+                 Additional Qt operators -- +, &lt;&lt;, +=,
+                         stream &lt;&lt; and &gt;&gt;
+             </li><li>
+                 Unsupported types by Qt -- allocator_type, const_reverse_iterator, reverse_iterator
+             </li><li>
+                 Unsupported accessors by Qt -- max_size, rbegin, rend
+             </li><li>
+                 Unsupported constructors by Qt -- multi-value constructors
+             </li><li>
+                 unsupported modifiers by Qt -- assign, muli-value inserts, STL's swaps
+             </li><li>
+             </li></ul>
+
+             STL map and Qt QMap.  These use nearly the same API as list and vector classes.  They add the following.
+             <ul><li>
+               STL types -- key_compare, key_type, mapped_type
+             </li><li>
+                 STL search -- equal_range, find, lower_bound, upper_bound
+             </li><li>
+               Qt removes -- equal_range, key_compare
+             </li><li>
+                 Qt renames -- lowerBound, upperBound
+             </li><li>
+               Qt adds -- constFind, insertMulti, key, keys, take, uniqueKeys, unite, values
+             </li><li>
+                 Not applicable to map and QMap -- at, back, pop_back, pop_front, push_back, push_front, swap
+             </li><li>
+                Not applicable to QMap -- append, first, last, lastIndexOf, mid, move, prepend, removeAll, removeAt, removeFirst, removeLast, replace, squeeze, takeAt, takeFirst, takeLast
+             </li><li>
+                 Not applicable to map -- assign
+             </li></ul>
+
+             Qt QHash.  STL extensions provide similar classes, e.g., Microsoft's stdext::hash_set.  THey are nearly the same as QMap
+             <ul><li>
+             </li><li>
+             </li><li>
+               Not applicable to Qhash -- lowerBound, unite, upperBound, 
+             </li><li>
+               Qt adds -- squeeze
+             </li></ul>
+         </rf:item>
+        <rf:item id="class-api" title="API for Qhull collections" date="Feb 2009" author="bbarber">
+            <ul><li>
+                check... -- Throw error on failure
+            </li><li>
+                try... -- Return false on failure.  Do not throw errors.
+            </li><li>
+                ...Temporarily -- lifetime depends on source. e.g., toByteArrayTemporarily
+            </li><li>
+                ...p -- indicates pointer-to.
+            </li><li>
+                end... -- points to one beyond the last available
+            </li><li>
+                private functions -- No syntactic indication.  They may become public later on.
+            </li><li>
+                Error messages -- Preceed error messages with the name of the class throwing the error (e.g. "ClassName: ...").  If this is an internal error, use "ClassName inconsistent: ..."
+            </li><li>
+               parameter order -- qhRunId, dimension, coordinates, count.
+            </li><li>
+               toClass -- Convert into a Class object (makes a deep copy)
+            </li><li>
+                qRunId -- Requires Qh installed.  Some routines allow 0 for limited info (e.g., operator&lt;&lt;)
+            </li><li>
+                Disable methods in derived classes -- If the default constructor, copy constructor, or copy assignment is disabled, it should be also disabled in derived classes (better error messages).
+            </li><li>
+                Constructor order -- default constructor, other constructors, copy constructor, copy assignment, destructor
+            </li></ul>
+        </rf:item>
+    </rf:section>
+</rf:topic>
diff --git a/xs/src/qhull/html/qhull.htm b/xs/src/qhull/html/qhull.htm
new file mode 100644
index 0000000000..0a2aa75e06
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+++ b/xs/src/qhull/html/qhull.htm
@@ -0,0 +1,473 @@
+<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN">
+<html>
+
+<head>
+<title>qhull -- convex hull and related structures</title>
+</head>
+
+<body>
+<!-- Navigation links -->
+<p><b><a name="TOP">Up</a></b><b>:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
+<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
+<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
+&#149; <a href="qh-quick.htm#options">Options</a>
+&#149; <a href="qh-opto.htm#output">Output</a>
+&#149; <a href="qh-optf.htm#format">Formats</a>
+&#149; <a href="qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="qh-optp.htm#print">Print</a>
+&#149; <a href="qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="qh-optc.htm#prec">Precision</a>
+&#149; <a href="qh-optt.htm#trace">Trace</a>
+&#149; <a href="../src/libqhull_r/index.htm">Functions</a><br>
+<b>To:</b> <a href="#synopsis">sy</a>nopsis &#149; <a href="#input">in</a>put
+&#149; <a href="#outputs">ou</a>tputs &#149; <a href="#controls">co</a>ntrols
+&#149; <a href="#options">op</a>tions
+<hr>
+<!-- Main text of document -->
+<h1><a
+href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/cone.html"><img
+src="qh--cone.gif" alt="[cone]" align="middle" width="100"
+height="100"></a>qhull -- convex hull and related structures</h1>
+
+<p>The convex hull of a set of points is the smallest convex set
+containing the points.  The Delaunay triangulation and furthest-site
+Delaunay triangulation are equivalent to a convex hull in one
+higher dimension.  Halfspace intersection about a point is
+equivalent to a convex hull by polar duality.
+
+<p>The <tt>qhull</tt> program provides options to build these
+structures and to experiment with the process.  Use the
+<a href=qconvex.htm>qconvex</a>,
+<a href=qdelaun.htm>qdelaunay</a>, <a href=qhalf.htm>qhalf</a>,
+and <a href=qvoronoi.htm>qvoronoi</a> programs
+to build specific structures.  You may use <tt>qhull</tt> instead.
+It takes the same options and uses the same code.
+<blockquote>
+<dl>
+    <dt><b>Example:</b> rbox 1000 D3 | qhull
+         <a href="qh-optc.htm#Cn">C-1e-4</a>
+         <a href="qh-optf.htm#FO">FO</a>
+         <a href="qh-optt.htm#Ts">Ts</a>
+         </dt>
+    <dd>Compute the 3-d convex hull of 1000 random
+             points.
+                 Centrums must be 10^-4 below neighboring
+                 hyperplanes.  Print the options and precision constants.
+                 When done, print statistics.  These options may be
+                 used with any of the Qhull programs.</dd>
+    <dt>&nbsp;</dt>
+    <dt><b>Example:</b> rbox 1000 D3 | qhull <a href=qhull.htm#outputs>d</a>
+         <a href="qh-optq.htm#Qbb">Qbb</a>
+         <a href="qh-optc.htm#Rn">R1e-4</a>
+         <a href="qh-optq.htm#Q0">Q0</a></dt>
+    <dd>Compute the 3-d Delaunay triangulation of 1000 random
+             points.  Randomly perturb all calculations by
+                 [0.9999,1.0001].  Do not correct precision problems.
+                 This leads to serious precision errors.</dd>
+</dl>
+</blockquote>
+<p>Use the following equivalences when calling <tt>qhull</tt> in 2-d to 4-d (a 3-d
+Delaunay triangulation is a 4-d convex hull):
+<blockquote>
+<ul>
+<li>
+<a href="qconvex.htm">qconvex</a> == qhull
+<li>
+<a href=qdelaun.htm>qdelaunay</a> == qhull d <a href="qh-optq.htm#Qbb">Qbb</a>
+<li>
+<a href=qhalf.htm>qhalf</a> == qhull H
+<li>
+<a href=qvoronoi.htm>qvoronoi</a> == qhull v <a href="qh-optq.htm#Qbb">Qbb</a>
+</ul>
+</blockquote>
+
+<p>Use the following equivalences when calling <tt>qhull</tt> in 5-d and higher (a 4-d
+Delaunay triangulation is a 5-d convex hull):
+<blockquote>
+<ul>
+<li>
+<a href="qconvex.htm">qconvex</a> == qhull <a href="qh-optq.htm#Qx">Qx</a>
+<li>
+<a href=qdelaun.htm>qdelaunay</a> == qhull d <a href="qh-optq.htm#Qbb">Qbb</a> <a href="qh-optq.htm#Qx">Qx</a>
+<li>
+<a href=qhalf.htm>qhalf</a> == qhull H <a href="qh-optq.htm#Qx">Qx</a>
+<li>
+<a href=qvoronoi.htm>qvoronoi</a> == qhull v <a href="qh-optq.htm#Qbb">Qbb</a> <a href="qh-optq.htm#Qx">Qx</a>
+</ul>
+</blockquote>
+
+
+<p>By default, Qhull merges coplanar facets.  For example, the convex
+hull of a cube's vertices has six facets.
+
+<p>If you use '<a href="qh-optq.htm#Qt">Qt</a>' (triangulated output),
+all facets will be simplicial (e.g., triangles in 2-d).  For the cube
+example, it will have 12 facets.  Some facets may be
+degenerate and have zero area.
+
+<p>If you use '<a href="qh-optq.htm#QJn">QJ</a>' (joggled input),
+all facets will be simplicial.  The corresponding vertices will be
+slightly perturbed.  Joggled input is less accurate that triangulated
+output.See <a
+href="qh-impre.htm#joggle">Merged facets or joggled input</a>. </p>
+
+<p>The output for 4-d convex hulls may be confusing if the convex
+hull contains non-simplicial facets (e.g., a hypercube). See
+<a href=qh-faq.htm#extra>Why
+are there extra points in a 4-d or higher convex hull?</a><br>
+</p>
+
+<p><b>Copyright &copy; 1995-2015 C.B. Barber</b></p>
+
+<hr>
+
+<h3><a href="#TOP">&#187;</a><a name="synopsis">qhull synopsis</a></h3>
+<pre>
+qhull- compute convex hulls and related structures.
+    input (stdin): dimension, n, point coordinates
+    comments start with a non-numeric character
+    halfspace: use dim+1 and put offsets after coefficients
+
+options (qh-quick.htm):
+    d    - Delaunay triangulation by lifting points to a paraboloid
+    d Qu - furthest-site Delaunay triangulation (upper convex hull)
+    v    - Voronoi diagram as the dual of the Delaunay triangulation
+    v Qu - furthest-site Voronoi diagram
+    H1,1 - Halfspace intersection about [1,1,0,...] via polar duality
+    Qt   - triangulated output
+    QJ   - joggle input instead of merging facets
+    Tv   - verify result: structure, convexity, and point inclusion
+    .    - concise list of all options
+    -    - one-line description of all options
+
+Output options (subset):
+    s    - summary of results (default)
+    i    - vertices incident to each facet
+    n    - normals with offsets
+    p    - vertex coordinates (if 'Qc', includes coplanar points)
+           if 'v', Voronoi vertices
+    Fp   - halfspace intersections
+    Fx   - extreme points (convex hull vertices)
+    FA   - compute total area and volume
+    o    - OFF format (if 'v', outputs Voronoi regions)
+    G    - Geomview output (2-d, 3-d and 4-d)
+    m    - Mathematica output (2-d and 3-d)
+    QVn  - print facets that include point n, -n if not
+    TO file- output results to file, may be enclosed in single quotes
+
+examples:
+    rbox c d D2 | qhull Qc s f Fx | more      rbox 1000 s | qhull Tv s FA
+    rbox 10 D2 | qhull d QJ s i TO result     rbox 10 D2 | qhull v Qbb Qt p
+    rbox 10 D2 | qhull d Qu QJ m              rbox 10 D2 | qhull v Qu QJ o
+    rbox c | qhull n                          rbox c | qhull FV n | qhull H Fp
+    rbox d D12 | qhull QR0 FA                 rbox c D7 | qhull FA TF1000
+    rbox y 1000 W0 | qhull                    rbox 10 | qhull v QJ o Fv
+</pre>
+
+<h3><a href="#TOP">&#187;</a><a name="input">qhull input</a></h3>
+<blockquote>
+
+<p>The input data on <tt>stdin</tt> consists of:</p>
+<ul>
+    <li>dimension
+    <li>number of points</li>
+    <li>point coordinates</li>
+</ul>
+
+<p>Use I/O redirection (e.g., qhull &lt; data.txt), a pipe (e.g., rbox 10 | qhull),
+or the '<a href=qh-optt.htm#TI>TI</a>' option (e.g., qhull TI data.txt).
+
+<p>Comments start with a non-numeric character.  Error reporting is
+simpler if there is one point per line.  Dimension
+and number of points may be reversed.  For halfspace intersection,
+an interior point may be prepended (see <a href=qhalf.htm#input>qhalf input</a>).
+
+<p>Here is the input for computing the convex
+hull of the unit cube.  The output is the normals, one
+per facet.</p>
+
+<blockquote>
+    <p>rbox c &gt; data </p>
+    <pre>
+3 RBOX c
+8
+  -0.5   -0.5   -0.5
+  -0.5   -0.5    0.5
+  -0.5    0.5   -0.5
+  -0.5    0.5    0.5
+   0.5   -0.5   -0.5
+   0.5   -0.5    0.5
+   0.5    0.5   -0.5
+   0.5    0.5    0.5
+</pre>
+    <p>qhull s n &lt; data</p>
+    <pre>
+
+Convex hull of 8 points in 3-d:
+
+  Number of vertices: 8
+  Number of facets: 6
+  Number of non-simplicial facets: 6
+
+Statistics for: RBOX c | QHULL s n
+
+  Number of points processed: 8
+  Number of hyperplanes created: 11
+  Number of distance tests for qhull: 35
+  Number of merged facets: 6
+  Number of distance tests for merging: 84
+  CPU seconds to compute hull (after input): 0.081
+
+4
+6
+     0      0     -1   -0.5
+     0     -1      0   -0.5
+     1      0      0   -0.5
+    -1      0      0   -0.5
+     0      1      0   -0.5
+     0      0      1   -0.5
+</pre>
+</blockquote>
+
+</blockquote>
+<h3><a href="#TOP">&#187;</a><a name="outputs">qhull outputs</a></h3>
+<blockquote>
+
+<p>These options control the output of qhull. They may be used
+individually or together.</p>
+<blockquote>
+<dl compact>
+    <dt>&nbsp;</dt>
+    <dd><b>General</b></dd>
+    <dt><a>qhull</a></dt>
+    <dd>compute the convex hull of the input points.
+        See <a href=qconvex.htm>qconvex</a>.</dd>
+    <dt><a name="d">qhull d Qbb</a></dt>
+    <dd>compute the Delaunay triangulation by lifting the points
+        to a paraboloid.  Use option '<a href="qh-optq.htm#Qbb">Qbb</a>'
+        to scale the paraboloid and improve numeric precision.
+        See <a href=qdelaun.htm>qdelaunay</a>.</dd>
+    <dt><a name="v">qhull v Qbb</a></dt>
+    <dd>compute the Voronoi diagram by computing the Delaunay
+        triangulation.    Use option '<a href="qh-optq.htm#Qbb">Qbb</a>'
+        to scale the paraboloid and improve numeric precision.
+        See <a href=qvoronoi.htm>qvoronoi</a>.</dd>
+    <dt><a name="H">qhull H</a></dt>
+    <dd>compute the halfspace intersection about a point via polar
+        duality.  The point is below the hyperplane that defines the halfspace.
+        See <a href=qhalf.htm>qhalf</a>.</dd>
+</dl>
+</blockquote>
+
+<p>For a full list of output options see
+<blockquote>
+<ul>
+            <li><a href="qh-opto.htm#output">Output</a> formats</li>
+            <li><a href="qh-optf.htm#format">Additional</a> I/O
+                formats</li>
+            <li><a href="qh-optg.htm#geomview">Geomview</a>
+                output options</li>
+            <li><a href="qh-optp.htm#print">Print</a> options</li>
+</ul>
+</blockquote>
+
+</blockquote>
+<h3><a href="#TOP">&#187;</a><a name="controls">qhull controls</a></h3>
+<blockquote>
+
+<p>For a full list of control options see
+<blockquote>
+<ul>
+            <li><a href="qh-optq.htm#qhull">Qhull</a> control
+                options</li>
+            <li><a href="qh-optc.htm#prec">Precision</a> options</li>
+            <li><a href="qh-optt.htm#trace">Trace</a> options</li>
+</ul>
+</blockquote>
+
+</blockquote>
+<h3><a href="#TOP">&#187;</a><a name="options">qhull options</a></h3>
+
+<pre>
+qhull- compute convex hulls and related structures.
+    http://www.qhull.org
+
+input (stdin):
+    first lines: dimension and number of points (or vice-versa).
+    other lines: point coordinates, best if one point per line
+    comments:    start with a non-numeric character
+    halfspaces:  use dim plus one and put offset after coefficients.
+                 May be preceded by a single interior point ('H').
+
+options:
+    d    - Delaunay triangulation by lifting points to a paraboloid
+    d Qu - furthest-site Delaunay triangulation (upper convex hull)
+    v    - Voronoi diagram (dual of the Delaunay triangulation)
+    v Qu - furthest-site Voronoi diagram
+    Hn,n,... - halfspace intersection about point [n,n,0,...]
+    Qt   - triangulated output
+    QJ   - joggle input instead of merging facets
+    Qc   - keep coplanar points with nearest facet
+    Qi   - keep interior points with nearest facet
+
+Qhull control options:
+    Qbk:n   - scale coord k so that low bound is n
+      QBk:n - scale coord k so that upper bound is n (QBk is 0.5)
+    QbB  - scale input to unit cube centered at the origin
+    Qbb  - scale last coordinate to [0,m] for Delaunay triangulations
+    Qbk:0Bk:0 - remove k-th coordinate from input
+    QJn  - randomly joggle input in range [-n,n]
+    QRn  - random rotation (n=seed, n=0 time, n=-1 time/no rotate)
+    Qf   - partition point to furthest outside facet
+    Qg   - only build good facets (needs 'QGn', 'QVn', or 'PdD')
+    Qm   - only process points that would increase max_outside
+    Qr   - process random outside points instead of furthest ones
+    Qs   - search all points for the initial simplex
+    Qu   - for 'd' or 'v', compute upper hull without point at-infinity
+              returns furthest-site Delaunay triangulation
+    Qv   - test vertex neighbors for convexity
+    Qx   - exact pre-merges (skips coplanar and anglomaniacs facets)
+    Qz   - add point-at-infinity to Delaunay triangulation
+    QGn  - good facet if visible from point n, -n for not visible
+    QVn  - good facet if it includes point n, -n if not
+    Q0   - turn off default p remerge with 'C-0'/'Qx'
+    Q1     - sort merges by type instead of angle
+    Q2   - merge all non-convex at once instead of independent sets
+    Q3   - do not merge redundant vertices
+    Q4   - avoid old>new merges
+    Q5   - do not correct outer planes at end of qhull
+    Q6   - do not pre-merge concave or coplanar facets
+    Q7   - depth-first processing instead of breadth-first
+    Q8   - do not process near-inside points
+    Q9   - process furthest of furthest points
+    Q10  - no special processing for narrow distributions
+    Q11  - copy normals and recompute centrums for tricoplanar facets
+    Q12  - do not error on wide merge due to duplicate ridge and nearly coincident points
+
+Towpaths Trace options:
+    T4   - trace at level n, 4=all, 5=mem/gauss, -1= events
+    Tc   - check frequently during execution
+    Ts   - print statistics
+    Tv   - verify result: structure, convexity, and point inclusion
+    Tz   - send all output to stdout
+    TFn  - report summary when n or more facets created
+    TI file - input data from file, no spaces or single quotes
+    TO file - output results to file, may be enclosed in single quotes
+    TPn  - turn on tracing when point n added to hull
+     TMn - turn on tracing at merge n
+     TWn - trace merge facets when width > n
+    TRn  - rerun qhull n times.  Use with 'QJn'
+    TVn  - stop qhull after adding point n, -n for before (see TCn)
+     TCn - stop qhull after building cone for point n (see TVn)
+
+Precision options:
+    Cn   - radius of centrum (roundoff added).  Merge facets if non-convex
+     An  - cosine of maximum angle.  Merge facets if cosine > n or non-convex
+           C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge
+    En   - max roundoff error for distance computation
+    Rn   - randomly perturb computations by a factor of [1-n,1+n]
+    Vn   - min distance above plane for a visible facet (default 3C-n or En)
+    Un   - max distance below plane for a new, coplanar point (default Vn)
+    Wn   - min facet width for outside point (before roundoff, default 2Vn)
+
+Output formats (may be combined; if none, produces a summary to stdout):
+    f    - facet dump
+    G    - Geomview output (see below)
+    i    - vertices incident to each facet
+    m    - Mathematica output (2-d and 3-d)
+    o    - OFF format (dim, points and facets; Voronoi regions)
+    n    - normals with offsets
+    p    - vertex coordinates or Voronoi vertices (coplanar points if 'Qc')
+    s    - summary (stderr)
+
+More formats:
+    Fa   - area for each facet
+    FA   - compute total area and volume for option 's'
+    Fc   - count plus coplanar points for each facet
+           use 'Qc' (default) for coplanar and 'Qi' for interior
+    FC   - centrum or Voronoi center for each facet
+    Fd   - use cdd format for input (homogeneous with offset first)
+    FD   - use cdd format for numeric output (offset first)
+    FF   - facet dump without ridges
+    Fi   - inner plane for each facet
+           for 'v', separating hyperplanes for bounded Voronoi regions
+    FI   - ID of each facet
+    Fm   - merge count for each facet (511 max)
+    FM   - Maple output (2-d and 3-d)
+    Fn   - count plus neighboring facets for each facet
+    FN   - count plus neighboring facets for each point
+    Fo   - outer plane (or max_outside) for each facet
+           for 'v', separating hyperplanes for unbounded Voronoi regions
+    FO   - options and precision constants
+    Fp   - dim, count, and intersection coordinates (halfspace only)
+    FP   - nearest vertex and distance for each coplanar point
+    FQ   - command used for qhull
+    Fs   - summary: #int (8), dimension, #points, tot vertices, tot facets,
+                      output: #vertices, #facets, #coplanars, #nonsimplicial
+                    #real (2), max outer plane, min vertex
+    FS   - sizes:   #int (0)
+                    #real(2) tot area, tot volume
+    Ft   - triangulation with centrums for non-simplicial facets (OFF format)
+    Fv   - count plus vertices for each facet
+           for 'v', Voronoi diagram as Voronoi vertices for pairs of sites
+    FV   - average of vertices (a feasible point for 'H')
+    Fx   - extreme points (in order for 2-d)
+
+Geomview options (2-d, 3-d, and 4-d; 2-d Voronoi)
+    Ga   - all points as dots
+     Gp  -  coplanar points and vertices as radii
+     Gv  -  vertices as spheres
+    Gi   - inner planes only
+     Gn  -  no planes
+     Go  -  outer planes only
+    Gc   - centrums
+    Gh   - hyperplane intersections
+    Gr   - ridges
+    GDn  - drop dimension n in 3-d and 4-d output
+    Gt   - for 3-d 'd', transparent outer ridges
+
+Print options:
+    PAn  - keep n largest facets by area
+    Pdk:n - drop facet if normal[k] &lt;= n (default 0.0)
+    PDk:n - drop facet if normal[k] >= n
+    Pg   - print good facets (needs 'QGn' or 'QVn')
+    PFn  - keep facets whose area is at least n
+    PG   - print neighbors of good facets
+    PMn  - keep n facets with most merges
+    Po   - force output.  If error, output neighborhood of facet
+    Pp   - do not report precision problems
+
+    .    - list of all options
+    -    - one line descriptions of all options
+</pre>
+
+<!-- Navigation links -->
+<hr>
+
+<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
+<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
+<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
+&#149; <a href="qh-quick.htm#options">Options</a>
+&#149; <a href="qh-opto.htm#output">Output</a>
+&#149; <a href="qh-optf.htm#format">Formats</a>
+&#149; <a href="qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="qh-optp.htm#print">Print</a>
+&#149; <a href="qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="qh-optc.htm#prec">Precision</a>
+&#149; <a href="qh-optt.htm#trace">Trace</a>
+&#149; <a href="../src/libqhull_r/index.htm">Functions</a><br>
+<b>To:</b> <a href="#synopsis">sy</a>nopsis &#149; <a href="#input">in</a>put
+&#149; <a href="#outputs">ou</a>tputs &#149; <a href="#controls">co</a>ntrols
+&#149; <a href="#options">op</a>tions
+<!-- GC common information -->
+<hr>
+
+<p><a href="http://www.geom.uiuc.edu/"><img src="qh--geom.gif"
+align="middle" width="40" height="40"></a><i>The Geometry Center
+Home Page </i></p>
+
+<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
+</a><br>
+Created: Sept. 25, 1995 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
+</body>
+</html>
diff --git a/xs/src/qhull/html/qhull.man b/xs/src/qhull/html/qhull.man
new file mode 100644
index 0000000000..8d1dc08ace
--- /dev/null
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@@ -0,0 +1,1008 @@
+.\"  This is the Unix manual page for qhull, written in nroff, the standard
+.\"  manual formatter for Unix systems.  To format it, type
+.\"
+.\"  nroff -man qhull.man
+.\"
+.\"  This will print a formatted copy to standard output.  If you want
+.\"  to ensure that the output is plain ASCII, free of any control
+.\"  characters that nroff uses for underlining etc, pipe the output
+.\"  through "col -b":
+.\"
+.\"  nroff -man qhull.man | col -b
+.\"
+.\"  Warning: a leading quote "'" or dot "." will not format correctly
+.\"
+.TH qhull 1 "2003/12/30" "Geometry Center"
+.SH NAME
+qhull \- convex hull, Delaunay triangulation, Voronoi diagram,
+halfspace intersection about a point, hull volume, facet area
+.SH SYNOPSIS
+.nf
+qhull- compute convex hulls and related structures
+    input (stdin): dimension, #points, point coordinates
+    first comment (non-numeric) is listed in the summary
+    halfspace: use dim plus one with offsets after coefficients
+
+options (qh-quick.htm):
+    d      - Delaunay triangulation by lifting points to a paraboloid
+    v      - Voronoi diagram via the Delaunay triangulation
+    H1,1   - Halfspace intersection about [1,1,0,...]
+    d Qu   - Furthest-site Delaunay triangulation (upper convex hull)
+    v Qu   - Furthest-site Voronoi diagram
+    Qt     - triangulated output
+    QJ     - Joggle the input to avoid precision problems
+    .      - concise list of all options
+    -      - one-line description of all options
+
+Output options (subset):
+    FA     - compute total area and volume
+    Fx     - extreme points (convex hull vertices)
+    G      - Geomview output (2-d, 3-d and 4-d)
+    Fp     - halfspace intersection coordinates
+    m      - Mathematica output (2-d and 3-d)
+    n      - normals with offsets
+    o      - OFF file format (if Voronoi, outputs regions)
+    TO file- output results to file, may be enclosed in single quotes
+    f      - print all fields of all facets
+    s      - summary of results (default)
+    Tv     - verify result: structure, convexity, and point inclusion
+    p      - vertex coordinates (centers for Voronoi)
+    i      - vertices incident to each facet
+
+example:
+    rbox 1000 s | qhull Tv s FA
+.fi
+
+ - html manual:    index.htm
+ - installation:   README.txt
+ - see also:       COPYING.txt, REGISTER.txt, Changes.txt
+ - WWW:            <http://www.qhull.org>
+ - GIT:            <git@github.com:qhull/qhull.git>
+ - mirror:         <http://www6.uniovi.es/ftp/pub/mirrors/geom.umn.edu/software/ghindex.html>
+ - news:           <http://www.qhull.org/news>
+ - Geomview:       <http://www.geomview.org>
+ - news group:     <news:comp.graphics.algorithms>
+ - FAQ:            <http://www.faqs.org/faqs/graphics/algorithms-faq/>
+ - email:          qhull@qhull.org
+ - bug reports:    qhull_bug@qhull.org
+
+The sections are:
+ - INTRODUCTION
+ - DESCRIPTION, a description of Qhull
+ - IMPRECISION, how Qhull handles imprecision
+ - OPTIONS
+ -    Input and output options
+ -    Additional input/output formats
+ -    Precision options
+ -    Geomview options
+ -    Print options
+ -    Qhull options
+ -    Trace options
+ - BUGS
+ - E-MAIL
+ - SEE ALSO
+ - AUTHORS
+ - ACKNOWLEGEMENTS
+
+This man page briefly describes all Qhull options.  Please report
+any mismatches with Qhull's html manual (index.htm).
+
+.PP
+.SH INTRODUCTION
+Qhull is a general dimension code for computing convex hulls, Delaunay
+triangulations, Voronoi diagram, furthest\[hy]site Voronoi diagram,
+furthest\[hy]site Delaunay triangulations, and
+halfspace intersections about a point.  It implements the Quickhull algorithm for
+computing the convex hull.  Qhull handles round\[hy]off errors from floating
+point arithmetic.  It can approximate a convex hull.
+
+The program includes options for hull volume, facet area, partial hulls,
+input transformations, randomization, tracing, multiple output formats, and
+execution statistics.  The program can be called from within your application.
+You can view the results in 2\[hy]d, 3\[hy]d and 4\[hy]d with Geomview.
+.PP
+.SH DESCRIPTION
+.PP
+The format of input is the following: first line contains the dimension,
+second line contains the number of input points, and point coordinates follow.
+The dimension and number of points can be reversed.
+Comments and line breaks are ignored.  A comment starts with a
+non\[hy]numeric character and continues to the end of line.  The first comment
+is reported in summaries and statistics.
+Error reporting is
+better if there is one point per line.
+.PP
+The default printout option is a short summary. There are many
+other output formats.
+.PP
+Qhull implements the Quickhull algorithm for convex hull. This algorithm combines
+the 2\[hy]d Quickhull algorithm with the n\[hy]d beneath\[hy]beyond algorithm
+[c.f., Preparata & Shamos '85].
+It is similar to the randomized algorithms of Clarkson and
+others [Clarkson et al. '93].  The main
+advantages of Quickhull are output sensitive performance, reduced
+space requirements, and automatic handling of precision problems.
+.PP
+The data structure produced by Qhull consists of vertices, ridges, and facets.
+A vertex is a point of the input set.  A ridge is a set of d vertices
+and two neighboring facets.  For example in 3\[hy]d, a ridge is an edge of the
+polyhedron.  A facet is a set of ridges, a set of neighboring facets, a set
+of incident vertices, and a hyperplane equation.  For simplicial facets, the
+ridges are defined by the vertices and neighboring facets.  When Qhull
+merges two facets, it produces a non\[hy]simplicial
+facet.  A non\[hy]simplicial facet has more than d neighbors and may share more than
+one ridge with a neighbor.
+.PP
+.SH IMPRECISION
+.PP
+Since Qhull uses floating point arithmetic, roundoff error may occur for each
+calculation.  This causes  problems
+for most geometric algorithms.
+.PP
+Qhull automatically sets option 'C\-0' in 2\[hy]d, 3\[hy]d, and 4\[hy]d, or
+option 'Qx' in 5\[hy]d and higher.  These options handle precision problems
+by merging facets.  Alternatively, use option 'QJ' to joggle the
+input.
+.PP
+With 'C\-0', Qhull merges non\[hy]convex
+facets while constructing the hull. The remaining facets are
+clearly convex. With 'Qx', Qhull merges
+coplanar horizon facets, flipped facets, concave facets and
+duplicated ridges.  It merges coplanar facets after constructing
+the hull.
+With 'Qx', coplanar points may be missed, but it
+appears to be unlikely.
+.PP
+To guarantee triangular output, joggle the input with option 'QJ'.  Facet
+merging will not occur.
+.SH OPTIONS
+.PP
+To get a list of the most important options, execute 'qhull' by itself.
+To get a complete list of options,
+execute 'qhull \-'.
+To get a complete, concise list of options, execute 'qhull .'.
+
+Options can be in any order.
+Capitalized options take an argument (except 'PG' and 'F' options).
+Single letters are used for output formats and precision constants.  The
+other options are grouped into menus for other output formats ('F'),
+Geomview output ('G'),
+printing ('P'), Qhull control ('Q'), and tracing ('T').
+.TP
+Main options:
+.TP
+default
+Compute the convex hull of the input points.  Report a summary of
+the result.
+.TP
+d
+Compute the Delaunay triangulation by lifting the input points to a
+paraboloid.  The 'o' option prints the input points and facets.
+The 'QJ' option guarantees triangular output.  The 'Ft'
+option prints a triangulation.  It adds points (the centrums) to non\[hy]simplicial
+facets.
+.TP
+v
+Compute the Voronoi diagram from the Delaunay triangulation.
+The 'p' option prints the Voronoi vertices.
+The 'o' option prints the Voronoi vertices and the
+vertices in each Voronoi region.  It lists regions in
+site ID order.
+The 'Fv' option prints each ridge of the Voronoi diagram.
+The first or zero'th vertex
+indicates the infinity vertex.  Its coordinates are
+qh_INFINITE (\-10.101).  It indicates unbounded Voronoi
+regions or degenerate Delaunay triangles.
+.TP
+Hn,n,...
+Compute halfspace intersection about [n,n,0,...].
+The input is a set of halfspaces
+defined in the same format as 'n', 'Fo', and 'Fi'.
+Use 'Fp' to print the intersection points.  Use 'Fv'
+to list the intersection points for each halfspace.  The
+other output formats display the dual convex hull.
+
+The point [n,n,n,...] is a feasible point for the halfspaces, i.e.,
+a point that is inside all
+of the halfspaces (Hx+b <= 0).  The default coordinate value is 0.
+
+The input may start with a feasible point.  If so, use 'H' by itself.
+The input starts with a feasible point when the first number is the dimension,
+the second number is "1", and the coordinates complete a line.  The 'FV'
+option produces a feasible point for a convex hull.
+.TP
+d Qu
+Compute the furthest\[hy]site Delaunay triangulation from the upper
+convex hull.  The 'o' option prints the input points and facets.
+The 'QJ' option guarantees triangular otuput.  You can also use 'Ft'
+to triangulate via the centrums of non\[hy]simplicial
+facets.
+.TP
+v Qu
+Compute the furthest\[hy]site Voronoi diagram.
+The 'p' option prints the Voronoi vertices.
+The 'o' option prints the Voronoi vertices and the
+vertices in each Voronoi region.
+The 'Fv' option prints each ridge of the Voronoi diagram.
+The first or zero'th vertex
+indicates the infinity vertex at infinity.  Its coordinates are
+qh_INFINITE (\-10.101).  It indicates unbounded Voronoi regions
+and degenerate Delaunay triangles.
+.PP
+.TP
+Input/Output options:
+.TP
+f
+Print out all facets and all fields of each facet.
+.TP
+G
+Output the hull in Geomview format.  For imprecise hulls,
+Geomview displays the inner and outer hull.  Geomview can also
+display points, ridges, vertices, coplanar points, and
+facet intersections.  See below for a list of options.
+
+For Delaunay triangulations, 'G' displays the
+corresponding paraboloid.  For halfspace intersection, 'G' displays the
+dual polytope.
+.TP
+i
+Output the incident vertices for each facet.
+Qhull prints the number of facets followed by the
+vertices of each facet.  One facet is printed per line.  The numbers
+are the 0\[hy]relative indices of the corresponding input points.
+The facets
+are oriented.
+
+In 4d and higher,
+Qhull triangulates non\[hy]simplicial facets.  Each apex (the first vertex) is
+a created point that corresponds to the facet's centrum.  Its index is greater
+than the indices of the input points.  Each base
+corresponds to a simplicial ridge between two facets.
+To print the vertices without triangulation, use option 'Fv'.
+.TP
+m
+Output the hull in Mathematica format.  Qhull writes a Mathematica file for 2\[hy]d and 3\[hy]d
+convex hulls and for 2\[hy]d Delaunay triangulations.   Qhull produces a list of objects
+that you can assign to a variable in Mathematica, for example:
+"list= << <outputfilename> ". If the object is 2\[hy]d, it can be
+visualized by "Show[Graphics[list]] ". For 3\[hy]d objects the command is
+"Show[Graphics3D[list]]".
+.TP
+n
+Output the normal equation for each facet.
+Qhull prints the dimension (plus one), the number of facets,
+and the normals for each facet.  The facet's offset follows its
+normal coefficients.
+.TP
+o
+Output the facets in OFF file format.
+Qhull prints the dimension, number of points, number
+of facets, and number of ridges.  Then it prints the coordinates of
+the input points and the vertices for each facet.  Each facet is on
+a separate line.  The first number is the number of vertices.  The
+remainder are the indices of the corresponding points.  The vertices are
+oriented in 2\[hy]d, 3\[hy]d, and in simplicial facets.
+
+For 2\[hy]d Voronoi diagrams,
+the vertices are sorted by adjacency, but not oriented.  In 3\[hy]d and higher,
+the Voronoi vertices are sorted by index.
+See the 'v' option for more information.
+.TP
+p
+Output the coordinates of each vertex point.
+Qhull prints the dimension, the number of points,
+and the coordinates for each vertex.
+With the 'Gc' and 'Gi' options, it also prints coplanar
+and interior points.  For Voronoi diagrams, it prints the coordinates
+of each Voronoi vertex.
+.TP
+s
+Print a summary to stderr.  If no output options
+are specified at all, a summary goes to stdout.  The summary lists
+the number of input points, the dimension, the number of vertices
+in the convex hull, the number of facets in the convex hull, the
+number of good facets (if 'Pg'), and statistics.
+
+The last two statistics (if needed) measure the maximum distance
+from a point or vertex to a
+facet.  The number in parenthesis (e.g., 2.1x) is the ratio between the
+maximum distance and the worst\[hy]case distance due to merging
+two simplicial facets.
+.PP
+.TP
+Precision options
+.TP
+An
+Maximum angle given as a cosine.  If the angle between a pair of facet
+normals
+is greater than n, Qhull merges one of the facets into a neighbor.
+If 'n' is negative, Qhull tests angles after adding
+each point to the hull (pre\[hy]merging).
+If 'n' is positive, Qhull tests angles after
+constructing the hull (post\[hy]merging).
+Both pre\[hy] and post\[hy]merging can be defined.
+
+Option 'C0' or 'C\-0' is set if the corresponding 'Cn' or 'C\-n'
+is not set.  If 'Qx'
+is set, then 'A\-n' and 'C\-n' are checked after the hull is constructed
+and before 'An' and 'Cn' are checked.
+.TP
+Cn
+Centrum radius.
+If a centrum is less than n below a neighboring facet, Qhull merges one
+of the facets.
+If 'n' is negative or '\-0', Qhull tests and merges facets after adding
+each point to the hull.  This is called "pre\[hy]merging".  If 'n' is positive,
+Qhull tests for convexity after constructing the hull ("post\[hy]merging").
+Both pre\[hy] and post\[hy]merging can be defined.
+
+For 5\[hy]d and higher, 'Qx' should be used
+instead of 'C\-n'.  Otherwise, most or all facets may be merged
+together.
+.TP
+En
+Maximum roundoff error for distance computations.
+.TP
+Rn
+Randomly perturb distance computations up to +/\- n * max_coord.
+This option perturbs every distance, hyperplane, and angle computation.
+To use time as the random number seed, use option 'QR\-1'.
+.TP
+Vn
+Minimum distance for a facet to be visible.
+A facet is visible if the distance from the point to the
+facet is greater than 'Vn'.
+
+Without merging, the default value for 'Vn' is the round\[hy]off error ('En').
+With merging, the default value is the pre\[hy]merge centrum ('C\-n') in 2\[hy]d or
+3\[hy]d, or three times that in other dimensions.  If the outside width
+is specified ('Wn'), the maximum, default value for 'Vn' is 'Wn'.
+.TP
+Un
+Maximum distance below a facet for a point to be coplanar to the facet.  The
+default value is 'Vn'.
+.TP
+Wn
+Minimum outside width of the hull.  Points are added to the convex hull
+only if they are clearly outside of a facet.  A point is outside of a
+facet if its distance to the facet is greater than 'Wn'.  The normal
+value for 'Wn' is 'En'.  If the user specifies pre\[hy]merging and
+does not set 'Wn', than 'Wn' is set
+to the premerge 'Cn' and maxcoord*(1\-An).
+.PP
+.TP
+Additional input/output formats
+.TP
+Fa
+Print area for each facet.
+For Delaunay triangulations, the area is the area of the triangle.
+For Voronoi diagrams, the area is the area of the dual facet.
+Use 'PAn' for printing the n largest facets, and option 'PFn' for
+printing facets larger than 'n'.
+
+The area for non\[hy]simplicial facets is the sum of the
+areas for each ridge to the centrum.   Vertices far below
+the facet's hyperplane are ignored.
+The reported area may be significantly less than the actual area.
+.TP
+FA
+Compute the total area and volume for option 's'.  It is an approximation
+for non\[hy]simplicial facets (see 'Fa').
+.TP
+Fc
+Print coplanar points for each facet.  The output starts with the
+number of facets.  Then each facet is printed one per line.  Each line
+is the number of coplanar points followed by the point ids.
+Option 'Qi' includes the interior points.  Each coplanar point (interior point) is
+assigned to the facet it is furthest above (resp., least below).
+.TP
+FC
+Print centrums for each facet.  The output starts with the
+dimension followed by the number of facets.
+Then each facet centrum is printed, one per line.
+.TP
+Fd
+Read input in cdd format with homogeneous points.
+The input starts with comments.  The first comment is reported in
+the summary.
+Data starts after a "begin" line.  The next line is the number of points
+followed by the dimension+1 and "real" or "integer".  Then the points
+are listed  with a leading "1" or "1.0".  The data ends with an "end" line.
+
+For halfspaces ('Fd Hn,n,...'), the input format is the same.  Each halfspace
+starts with its offset.  The sign of the offset is the opposite of Qhull's
+convention.
+.TP
+FD
+Print normals ('n', 'Fo', 'Fi') or points ('p') in cdd format.
+The first line is the command line that invoked Qhull.
+Data starts with a "begin" line.  The next line is the number of normals or points
+followed by the dimension+1 and "real".  Then the normals or points
+are listed  with the offset before the coefficients.  The offset for points is
+1.0.  The offset for normals has the opposite sign.
+The data ends with an "end" line.
+.TP
+FF
+Print facets (as in 'f') without printing the ridges.
+.TP
+Fi
+Print inner planes for each facet.  The inner plane is below all vertices.
+.TP
+Fi
+Print separating hyperplanes for bounded, inner regions of the Voronoi
+diagram.  The first line is the number
+of ridges.  Then each hyperplane is printed, one per line.  A line starts
+with the number of indices and floats.  The first pair lists
+adjacent input
+sites, the next d floats are the normalized coefficients for the hyperplane,
+and the last float is the offset.  The hyperplane is oriented toward 'QVn'
+(if defined), or the first input site of the pair.  Use 'Tv' to
+verify that the hyperplanes are perpendicular bisectors.  Use 'Fo' for
+unbounded regions, and 'Fv' for the corresponding Voronoi vertices.
+.TP
+FI
+Print facet identifiers.
+.TP
+Fm
+Print number of merges for each facet.  At most 511 merges are reported for
+a facet.  See 'PMn' for printing the facets with the most merges.
+.TP
+FM
+Output the hull in Maple format.  Qhull writes a Maple
+file for 2\[hy]d and 3\[hy]d
+convex hulls and for 2\[hy]d Delaunay triangulations.   Qhull produces a '.mpl'
+file for displaying with display3d().
+.TP
+Fn
+Print neighbors for each facet.  The output starts with the number of facets.
+Then each facet is printed one per line.  Each line
+is the number of neighbors followed by an index for each neighbor.  The indices
+match the other facet output formats.
+
+A negative index indicates an unprinted
+facet due to printing only good facets ('Pg').  It is the negation of the facet's
+ID (option 'FI').
+For example, negative indices are used for facets
+"at infinity" in the Delaunay triangulation.
+.TP
+FN
+Print vertex neighbors or coplanar facet for each point.
+The first line is the number
+of points.  Then each point is printed, one per line.  If the
+point is coplanar, the line is "1" followed by the facet's ID.
+If the point is
+not a selected vertex, the line is "0".
+Otherwise, each line is the number of
+neighbors followed by the corresponding facet indices (see 'Fn').
+.TP
+Fo
+Print outer planes for each facet in the same format as 'n'.
+The outer plane is above all points.
+.TP
+Fo
+Print separating hyperplanes for unbounded, outer regions of the Voronoi
+diagram.  The first line is the number
+of ridges.  Then each hyperplane is printed, one per line.  A line starts
+with the number of indices and floats.  The first pair lists
+adjacent input
+sites, the next d floats are the normalized coefficients for the hyperplane,
+and the last float is the offset.  The hyperplane is oriented toward 'QVn'
+(if defined), or the first input site of the pair.  Use 'Tv' to
+verify that the hyperplanes are perpendicular bisectors.  Use 'Fi' for
+bounded regions, and 'Fv' for the corresponding Voronoi vertices.
+.TP
+FO
+List all options to stderr, including the default values.  Additional 'FO's
+are printed to stdout.
+.TP
+Fp
+Print points for halfspace intersections (option 'Hn,n,...').  Each
+intersection corresponds to a facet of the dual polytope.
+The "infinity" point [\-10.101,\-10.101,...]
+indicates an unbounded intersection.
+.TP
+FP
+For each coplanar point ('Qc') print the point ID of the nearest vertex,
+the point ID, the facet ID, and the distance.
+.TP
+FQ
+Print command used for qhull and input.
+.TP
+Fs
+Print a summary.  The first line consists of the number of integers ("8"),
+followed by the dimension, the number of points, the number of vertices,
+the number of facets, the number of vertices selected for output, the
+number of facets selected for output, the number of coplanar points selected
+for output, number of simplicial, unmerged facets in output
+
+The second line consists of the number of reals ("2"),
+followed by the maxmimum offset to an outer plane and and minimum offset to
+an inner plane.  Roundoff is included.  Later
+versions of Qhull may produce additional integers or reals.
+.TP
+FS
+Print the size of the hull.  The first line consists of the number of integers ("0").
+The second line consists of the number of reals ("2"),
+followed by the total facet area, and the total volume.
+Later
+versions of Qhull may produce additional integers or reals.
+
+The total volume measures the volume
+of the intersection of the halfspaces defined by each facet.
+Both area and volume are
+approximations for non\[hy]simplicial facets.  See option 'Fa'.
+.TP
+Ft
+Print a triangulation with added points for non\[hy]simplicial
+facets.  The first line is the dimension and the second line is the
+number of points and the number of facets.  The points follow, one
+per line, then the facets follow as a list of point indices.  With option 'Qz', the
+points include the point\[hy]at\[hy]infinity.
+.TP
+Fv
+Print vertices for each facet.  The first line is the number
+of facets.  Then each facet is printed, one per line.  Each line is
+the number of vertices followed by the corresponding point ids.  Vertices
+are listed in the order they were added to the hull (the last one is first).
+.TP
+Fv
+Print all ridges of a Voronoi diagram.  The first line is the number
+of ridges.  Then each ridge is printed, one per line.  A line starts
+with the number of indices.  The first pair lists adjacent input
+sites, the remaining indices list Voronoi vertices.  Vertex '0' indicates
+the vertex\[hy]at\[hy]infinity (i.e., an unbounded ray).  In 3\[hy]d, the vertices
+are listed in order.  See 'Fi' and 'Fo' for separating hyperplanes.
+.TP
+FV
+Print average vertex.  The average vertex is a feasible point
+for halfspace intersection.
+.TP
+Fx
+List extreme points (vertices) of the convex hull.  The first line
+is the number of points.  The other lines give the indices of the
+corresponding points.  The first point is '0'.  In 2\[hy]d, the points
+occur in counter\[hy]clockwise order; otherwise they occur in input order.
+For Delaunay triangulations, 'Fx' lists the extreme points of the
+input sites.  The points are unordered.
+.PP
+.TP
+Geomview options
+.TP
+G
+Produce a file for viewing with Geomview.  Without other options,
+Qhull displays edges in 2\[hy]d, outer planes in 3\[hy]d, and ridges in 4\[hy]d.
+A ridge can be
+explicit or implicit.  An explicit ridge is a dim\-1 dimensional simplex
+between two facets.
+In 4\[hy]d, the explicit ridges are triangles.
+When displaying a ridge in 4\[hy]d, Qhull projects the ridge's vertices to
+one of its facets' hyperplanes.
+Use 'Gh' to
+project ridges to the intersection of both hyperplanes.
+.TP
+Ga
+Display all input points as dots.
+.TP
+Gc
+Display the centrum for each facet in 3\[hy]d.  The centrum is defined by a
+green radius sitting on a blue plane.  The plane corresponds to the
+facet's hyperplane.
+The radius is defined by 'C\-n' or 'Cn'.
+.TP
+GDn
+Drop dimension n in 3\[hy]d or 4\[hy]d.  The result is a 2\[hy]d or 3\[hy]d object.
+.TP
+Gh
+Display hyperplane intersections in 3\[hy]d and 4\[hy]d.   In 3\[hy]d, the
+intersection is a black line.  It lies on two neighboring hyperplanes
+(c.f., the blue squares associated with centrums ('Gc')).  In 4\[hy]d,
+the ridges are projected to the intersection of both hyperplanes.
+.TP
+Gi
+Display inner planes in 2\[hy]d and 3\[hy]d.  The inner plane of a facet
+is below all of its vertices.  It is parallel to the facet's hyperplane.
+The inner plane's color is the opposite (1\-r,1\-g,1\-b) of the outer
+plane.  Its edges are determined by the vertices.
+.TP
+Gn
+Do not display inner or outer planes.  By default,
+Geomview displays the precise plane (no merging) or both
+inner and output planes (merging).  Under merging, Geomview does
+not display the inner plane if the
+the difference between inner and outer is too small.
+.TP
+Go
+Display outer planes in 2\[hy]d and 3\[hy]d.  The outer plane of a facet
+is above all input points.  It is parallel to the facet's hyperplane.
+Its color is determined by the facet's normal, and its
+edges are determined by the vertices.
+.TP
+Gp
+Display coplanar points and vertices as radii.  A radius defines a ball
+which corresponds to the imprecision of the point.  The imprecision is
+the maximum of the roundoff error, the centrum radius, and maxcoord *
+(1\-An).  It is at least 1/20'th of the maximum coordinate,
+and ignores post\[hy]merging if pre\[hy]merging is done.
+.TP
+Gr
+Display ridges in 3\[hy]d.  A ridge connects the two vertices that are shared
+by neighboring facets.  Ridges are always displayed in 4\[hy]d.
+.TP
+Gt
+A 3\[hy]d Delaunay triangulation looks like a convex hull with interior
+facets.  Option 'Gt' removes the outside ridges to reveal the outermost
+facets.  It automatically sets options 'Gr' and 'GDn'.
+.TP
+Gv
+Display vertices as spheres.  The radius of the sphere corresponds to
+the imprecision of the data.  See 'Gp' for determining the radius.
+.PP
+.TP
+Print options
+.TP
+PAn
+Only the n largest facets are marked good for printing.
+Unless 'PG' is set, 'Pg' is automatically set.
+.TP
+Pdk:n
+Drop facet from output if normal[k] <= n.  The option 'Pdk' uses the
+default value of 0 for n.
+.TP
+PDk:n
+Drop facet from output if normal[k] >= n.  The option 'PDk' uses the
+default value of 0 for n.
+.TP
+PFn
+Only facets with area at least 'n' are marked good for printing.
+Unless 'PG' is set, 'Pg' is automatically set.
+.TP
+Pg
+Print only good facets.  A good facet is either visible from a point
+(the 'QGn' option) or includes a point (the 'QVn' option).  It also meets the
+requirements of 'Pdk' and 'PDk' options.  Option 'Pg' is automatically
+set for options 'PAn' and 'PFn'.
+.TP
+PG
+Print neighbors of good facets.
+.TP
+PMn
+Only the n facets with the most merges are marked good for printing.
+Unless 'PG' is set, 'Pg' is automatically set.
+.TP
+Po
+Force output despite precision problems.  Verify ('Tv') does not check
+coplanar points.
+Flipped facets are reported and concave facets are counted.
+If 'Po' is used, points are not
+partitioned into flipped facets and a flipped facet is always visible
+to a point.
+Also, if an error occurs before the completion of Qhull and tracing is
+not active, 'Po' outputs a neighborhood of the erroneous facets
+(if any).
+.TP
+Pp
+Do not report precision problems.
+.PP
+.TP
+Qhull control options
+.TP
+Qbk:0Bk:0
+Drop dimension k from the input points.  This allows the user to
+take convex hulls of sub\[hy]dimensional objects.  It happens before
+the Delaunay and Voronoi transformation.
+.TP
+QbB
+Scale the input points to fit the unit cube.  After scaling, the lower
+bound will be \-0.5 and the upper bound +0.5 in all dimensions.
+For Delaunay and
+Voronoi diagrams, scaling happens after projection to the paraboloid.
+Under precise
+arithmetic, scaling does not change the topology of the convex hull.
+.TP
+Qbb
+Scale the last coordinate to [0, m] where m is the maximum absolute
+value of the other coordinates.  For Delaunay and
+Voronoi diagrams, scaling happens after projection to the paraboloid.
+It reduces roundoff error for inputs with integer coordinates.
+Under precise
+arithmetic, scaling does not change the topology of the convex hull.
+.TP
+Qbk:n
+Scale the k'th coordinate of the input points.  After scaling, the lower
+bound of the input points will be n.  'Qbk' scales to \-0.5.
+.TP
+QBk:n
+Scale the k'th coordinate of the input points.  After scaling, the upper
+bound will be n.  'QBk' scales to +0.5.
+.TP
+Qc
+Keep coplanar points with the nearest facet.  Output
+formats 'p', 'f', 'Gp', 'Fc', 'FN', and 'FP' will print the points.
+.TP
+Qf
+Partition points to the furthest outside facet.
+.TP
+Qg
+Only build good facets.  With the 'Qg' option, Qhull will only build
+those facets that it needs to determine the good facets in the output.
+See 'QGn', 'QVn', and 'PdD' for defining good facets, and 'Pg' and 'PG'
+for printing good facets and their neighbors.
+.TP
+QGn
+A facet is good (see 'Qg' and 'Pg') if it is visible from point n.  If n < 0, a facet is
+good if it is not visible from point n.  Point n is not added to the
+hull (unless 'TCn' or 'TPn').
+With rbox, use the 'Pn,m,r' option to define your point; it
+will be point 0 (QG0).
+.TP
+Qi
+Keep interior points with the nearest facet.
+Output formats 'p', 'f', 'Gp', 'FN', 'FP', and 'Fc' will print the points.
+.TP
+QJn
+Joggle each input coordinate by adding a random number in [\-n,n].  If a
+precision error occurs, then qhull increases n and tries again.  It does
+not increase n beyond a certain value, and it stops after a certain number
+of attempts [see user.h].  Option 'QJ'
+selects a default value for n.  The output will be simplicial.  For
+Delaunay triangulations, 'QJn' sets 'Qbb' to scale the last coordinate
+(not if 'Qbk:n' or 'QBk:n' is set).
+\'QJn' is deprecated for Voronoi diagrams.  See also 'Qt'.
+.TP
+Qm
+Only process points that would otherwise increase max_outside.  Other
+points are treated as coplanar or interior points.
+.TP
+Qr
+Process random outside points instead of furthest ones.  This makes
+Qhull equivalent to the randomized incremental algorithms.  CPU time
+is not reported since the randomization is inefficient.
+.TP
+QRn
+Randomly rotate the input points.  If n=0, use time as the random number seed.
+If n>0, use n as the random number seed.  If n=\-1, don't rotate but use
+time as the random number seed.  For Delaunay triangulations ('d' and 'v'),
+rotate about the last axis.
+.TP
+Qs
+Search all points for the initial simplex.
+.TP
+Qt
+Triangulated output.  Triangulate all non\[hy]simplicial facets.  
+\'Qt' is deprecated for Voronoi diagrams.  See also 'Qt'.
+.TP
+Qv
+Test vertex neighbors for convexity after post\[hy]merging.
+To use the 'Qv' option, you also need to set a merge option
+(e.g., 'Qx' or 'C\-0').
+.TP
+QVn
+A good facet (see 'Qg' and 'Pg') includes point n.  If n<0, then a good facet does not
+include point n.  The point is either in the initial simplex or it
+is the first point added to the hull.  Option 'QVn' may not be used with merging.
+.TP
+Qx
+Perform exact merges while building the hull.  The "exact" merges
+are merging a point into a coplanar facet (defined by 'Vn', 'Un',
+and 'C\-n'), merging concave facets, merging duplicate ridges, and
+merging flipped facets.  Coplanar merges and angle coplanar merges ('A\-n')
+are not performed.  Concavity testing is delayed until a merge occurs.
+
+After
+the hull is built, all coplanar merges are performed (defined by 'C\-n'
+and 'A\-n'), then post\[hy]merges are performed
+(defined by 'Cn' and 'An').
+.TP
+Qz
+Add a point "at infinity" that is above the paraboloid for Delaunay triangulations
+and Voronoi diagrams.  This reduces precision problems and allows the triangulation
+of cospherical points.
+.PP
+.TP
+Qhull experiments and speedups
+.TP
+Q0
+Turn off pre\[hy]merging as a default option.
+With 'Q0'/'Qx' and without explicit pre\[hy]merge options, Qhull
+ignores precision issues while constructing the convex hull.  This
+may lead to precision errors.  If so, a descriptive warning is
+generated.
+.TP
+Q1
+With 'Q1', Qhull sorts merges by type (coplanar, angle coplanar, concave)
+instead of by angle.
+.TP
+Q2
+With 'Q2', Qhull merges all facets at once instead of using
+independent sets of merges and then retesting.
+.TP
+Q3
+With 'Q3', Qhull does not remove redundant vertices.
+.TP
+Q4
+With 'Q4', Qhull avoids merges of an old facet into a new facet.
+.TP
+Q5
+With 'Q5', Qhull does not correct outer planes at the end.  The
+maximum outer plane is used instead.
+.TP
+Q6
+With 'Q6', Qhull does not pre\[hy]merge concave or coplanar facets.
+.TP
+Q7
+With 'Q7', Qhull processes facets in depth\[hy]first order instead of
+breadth\[hy]first order.
+.TP
+Q8
+With 'Q8' and merging, Qhull does not retain near\[hy]interior points for adjusting
+outer planes.  'Qc' will probably retain
+all points that adjust outer planes.
+.TP
+Q9
+With 'Q9', Qhull processes the furthest of all outside sets at each iteration.
+.TP
+Q10
+With 'Q10', Qhull does not use special processing for narrow distributions.
+.TP
+Q11
+With 'Q11', Qhull copies normals and recompute centrums for tricoplanar facets.
+.TP
+Q12
+With 'Q12', Qhull does not report a very wide merge due to a duplicated ridge with nearly coincident vertices
+.PP
+.TP
+Trace options
+.TP
+Tn
+Trace at level n.  Qhull includes full execution tracing.  'T\-1'
+traces events.  'T1' traces
+the overall execution of the program.  'T2' and 'T3' trace overall
+execution and geometric and topological events.  'T4' traces the
+algorithm.  'T5' includes information about memory allocation and
+Gaussian elimination.
+.TP
+Ta
+Annotate output with codes that identify the
+corresponding qh_fprintf() statement.
+.TP
+Tc
+Check frequently during execution.  This will catch most inconsistency
+errors.
+.TP
+TCn
+Stop Qhull after building the cone of new facets for point n.  The
+output for 'f' includes the cone and the old hull.
+See also 'TVn'.
+.TP
+TFn
+Report progress whenever more than n facets are created
+During post\[hy]merging, 'TFn'
+reports progress after more than n/2 merges.
+.TP
+TI file
+Input data from 'file'.  The filename may not include spaces or
+quotes.
+.TP
+TO file
+Output results to 'file'.  The name may be enclosed in single
+quotes.
+.TP
+TPn
+Turn on tracing when point n is added to the hull.  Trace
+partitions of point n.  If used with TWn, turn off
+tracing after adding point n to the hull.
+.TP
+TRn
+Rerun qhull n times.  Usually used with 'QJn' to determine the
+probability that a given joggle will fail.
+.TP
+Ts
+Collect statistics and print to stderr at the end of execution.
+.TP
+Tv
+Verify the convex hull.  This checks the topological structure, facet
+convexity, and point inclusion.
+If precision problems occurred, facet convexity is tested whether or
+not 'Tv' is selected.
+Option 'Tv' does not check point inclusion if forcing output with 'Po',
+or if 'Q5' is set.
+
+For point inclusion testing, Qhull verifies that all points are below
+all outer planes (facet\->maxoutside).  Point inclusion is exhaustive
+if merging or if the facet\[hy]point product is small enough;
+otherwise Qhull verifies each point with a directed
+search (qh_findbest).
+
+Point inclusion testing occurs after producing output.  It prints
+a message to stderr unless option 'Pp' is used.  This
+allows the user to interrupt Qhull without changing the output.
+.TP
+TVn
+Stop Qhull after adding point n.  If n < 0, stop Qhull before adding
+point n.  Output shows the hull at this time.  See also 'TCn'
+.TP
+TMn
+Turn on tracing at n'th merge.
+.TP
+TWn
+Trace merge facets when the width is greater than n.
+.TP
+Tz
+Redirect stderr to stdout.
+.PP
+.SH BUGS
+Please report bugs to Brad Barber at qhull_bug@qhull.org.
+
+If Qhull does not compile, it is due to an incompatibility between your
+system and ours.  The first thing to check is that your compiler is
+ANSI standard.  If it is, check the man page for the best options, or
+find someone to help you.  If you locate the cause of your problem,
+please send email since it might help others.
+
+If Qhull compiles but crashes on the test case (rbox D4), there's
+still incompatibility between your system and ours.  Typically it's
+been due to mem.c and memory alignment.  You can use qh_NOmem in mem.h
+to turn off memory management.  Please let us know if you figure out
+how to fix these problems.
+
+If you do find a problem, try to simplify it before reporting the
+error.  Try different size inputs to locate the smallest one that
+causes an error.  You're welcome to hunt through the code using the
+execution trace as a guide.  This is especially true if you're
+incorporating Qhull into your own program.
+
+When you do report an error, please attach a data set to the
+end of your message.  This allows us to see the error for ourselves.
+Qhull is maintained part\[hy]time.
+.PP
+.SH E\[hy]MAIL
+Please send correspondence to qhull@qhull.org and report bugs to
+qhull_bug@qhull.org.  Let us know how you use Qhull.  If you
+mention it in a paper, please send the reference and an abstract.
+
+If you would like to get Qhull announcements (e.g., a new version)
+and news (any bugs that get fixed, etc.), let us know and we will add you to
+our mailing list.  If you would like to communicate with other
+Qhull users, we will add you to the qhull_users alias.
+For Internet news about geometric algorithms and convex hulls, look at
+comp.graphics.algorithms and sci.math.num\-analysis
+
+.SH SEE ALSO
+rbox(1)
+
+Barber, C. B., D.P. Dobkin, and H.T. Huhdanpaa,
+"The Quickhull Algorithm for Convex Hulls," ACM
+Trans. on Mathematical Software, 22(4):469\[en]483, Dec. 1996.
+http://portal.acm.org/citation.cfm?doid=235815.235821
+http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.117.405
+
+Clarkson, K.L., K. Mehlhorn, and R. Seidel, "Four results on randomized
+incremental construction," Computational Geometry: Theory and Applications,
+vol. 3, p. 185\[en]211, 1993.
+
+Preparata, F. and M. Shamos, Computational
+Geometry, Springer\[hy]Verlag, New York, 1985.
+
+.PP
+.SH AUTHORS
+.nf
+  C. Bradford Barber                    Hannu Huhdanpaa
+  bradb@shore.net                       hannu@qhull.org
+
+ .fi
+
+.SH ACKNOWLEDGEMENTS
+
+A special thanks to Albert Marden, Victor Milenkovic, the Geometry Center,
+Harvard University, and Endocardial Solutions, Inc. for supporting this work.
+
+Qhull 1.0 and 2.0 were developed under National Science Foundation
+grants NSF/DMS\[hy]8920161 and NSF\[hy]CCR\[hy]91\[hy]15793 750\[hy]7504.  David Dobkin
+guided the original work at Princeton University.
+If you find it useful, please let us know.
+
+The Geometry Center is supported by grant DMS\[hy]8920161 from the National
+Science Foundation, by grant DOE/DE\[hy]FG02\[hy]92ER25137 from the Department
+of Energy, by the University of Minnesota, and by Minnesota Technology, Inc.
+
+Qhull is available from http://www.qhull.org
diff --git a/xs/src/qhull/html/qhull.txt b/xs/src/qhull/html/qhull.txt
new file mode 100644
index 0000000000..03753547e9
--- /dev/null
+++ b/xs/src/qhull/html/qhull.txt
@@ -0,0 +1,1263 @@
+
+
+
+qhull(1)                                                 qhull(1)
+
+
+NAME
+       qhull  - convex hull, Delaunay triangulation, Voronoi dia-
+       gram, halfspace intersection about a point, hull volume, facet area
+
+SYNOPSIS
+       qhull- compute convex hulls and related structures
+           input (stdin): dimension, #points, point coordinates
+           first comment (non-numeric) is listed in the summary
+           halfspace: use dim plus one with offsets after coefficients
+
+       options (qh-quick.htm):
+           d      - Delaunay triangulation by lifting points to a paraboloid
+           v      - Voronoi diagram via the Delaunay triangulation
+           H1,1   - Halfspace intersection about [1,1,0,...]
+           d Qu   - Furthest-site Delaunay triangulation (upper convex hull)
+           v Qu   - Furthest-site Voronoi diagram
+           QJ     - Joggle the input to avoid precision problems
+           .      - concise list of all options
+           -      - one-line description of all options
+
+       Output options (subset):
+           FA     - compute total area and volume
+           Fx     - extreme points (convex hull vertices)
+           G      - Geomview output (2-d, 3-d and 4-d)
+           Fp     - halfspace intersection coordinates
+           m      - Mathematica output (2-d and 3-d)
+           n      - normals with offsets
+           o      - OFF file format (if Voronoi, outputs regions)
+           TO file- output results to file, may be enclosed in single quotes
+           f      - print all fields of all facets
+           s      - summary of results (default)
+           Tv     - verify result: structure, convexity, and point inclusion
+           p      - vertex coordinates
+           i      - vertices incident to each facet
+
+       example:
+           rbox 1000 s | qhull Tv s FA
+
+        - html manual:    index.htm
+        - installation:   README.txt
+        - see also:       COPYING.txt, REGISTER.txt, Changes.txt
+        - WWW:            <http://www.qhull.org>
+        - GIT:            <git@github.com:qhull/qhull.git>
+        - mirror:         <http://www6.uniovi.es/ftp/pub/mirrors/geom.umn.edu/software/ghindex.html>
+        - news:           <http://www.qhull.org/news>
+        - Geomview:       <http://www.geomview.org>
+        - news group:     <news:comp.graphics.algorithms>
+        - FAQ:            <http://www.faqs.org/faqs/graphics/algorithms-faq/>
+        - email:          qhull@qhull.org
+        - bug reports:    qhull_bug@qhull.org
+
+
+
+
+Geometry Center              2003/12/30                 1
+
+
+
+
+
+qhull(1)                                                 qhull(1)
+
+
+       The sections are:
+        - INTRODUCTION
+        - DESCRIPTION, a description of Qhull
+        - IMPRECISION, how Qhull handles imprecision
+        - OPTIONS
+        -    Input and output options
+        -    Additional input/output formats
+        -    Precision options
+        -    Geomview options
+        -    Print options
+        -    Qhull options
+        -    Trace options
+        - BUGS
+        - E-MAIL
+        - SEE ALSO
+        - AUTHORS
+        - ACKNOWLEGEMENTS
+
+       This man page briefly describes all Qhull options.  Please
+       report  any  mismatches  with  Qhull's  html  manual  (qh-
+       man.htm).
+
+
+
+INTRODUCTION
+       Qhull  is  a  general  dimension code for computing convex
+       hulls, Delaunay triangulations, Voronoi diagram, furthest-
+       site  Voronoi  diagram,  furthest-site Delaunay triangula-
+       tions, and halfspace  intersections  about  a  point.   It
+       implements  the Quickhull algorithm for computing the con-
+       vex hull.  Qhull handles round-off  errors  from  floating
+       point arithmetic.  It can approximate a convex hull.
+
+       The  program includes options for hull volume, facet area,
+       partial hulls, input transformations, randomization, trac-
+       ing,  multiple  output  formats, and execution statistics.
+       The program can be called from  within  your  application.
+       You  can  view  the  results  in  2-d,  3-d  and  4-d with
+       Geomview.
+
+
+DESCRIPTION
+       The format of input is the following: first line  contains
+       the  dimension,  second  line contains the number of input
+       points, and point coordinates follow.  The  dimension  and
+       number  of  points  can  be  reversed.   Comments and line
+       breaks are ignored.  A comment starts with  a  non-numeric
+       character  and  continues  to  the end of line.  The first
+       comment is reported in summaries  and  statistics.   Error
+       reporting is better if there is one point per line.
+
+       The  default printout option is a short summary. There are
+       many other output formats.
+
+
+
+
+Geometry Center              2003/12/30                 2
+
+
+
+
+
+qhull(1)                                                 qhull(1)
+
+
+       Qhull implements the Quickhull algorithm for convex  hull.
+       This  algorithm  combines the 2-d Quickhull algorithm with
+       the n-d beneath-beyond algorithm [c.f., Preparata & Shamos
+       '85].   It  is  similar  to  the  randomized algorithms of
+       Clarkson and others  [Clarkson  et  al.  '93].   The  main
+       advantages  of Quickhull are output sensitive performance,
+       reduced space requirements, and automatic handling of pre-
+       cision problems.
+
+       The data structure produced by Qhull consists of vertices,
+       ridges, and facets.  A vertex is a point of the input set.
+       A ridge is a set of d vertices and two neighboring facets.
+       For example in 3-d, a ridge is an edge of the  polyhedron.
+       A facet is a set of ridges, a set of neighboring facets, a
+       set of incident vertices, and a hyperplane equation.   For
+       simplicial  facets, the ridges are defined by the vertices
+       and neighboring facets.  When Qhull merges two facets,  it
+       produces  a  non-simplicial facet.  A non-simplicial facet
+       has more than d neighbors and  may  share  more  than  one
+       ridge with a neighbor.
+
+
+IMPRECISION
+       Since Qhull uses floating point arithmetic, roundoff error
+       may occur for each calculation.  This causes  problems for
+       most geometric algorithms.
+
+       Qhull  automatically  sets  option  'C-0' in 2-d, 3-d, and
+       4-d, or option 'Qx' in 5-d and higher.  These options han-
+       dle  precision problems by merging facets.  Alternatively,
+       use option 'QJ' to joggle the input.
+
+       With 'C-0', Qhull  merges  non-convex  facets  while  con-
+       structing  the hull. The remaining facets are clearly con-
+       vex. With 'Qx',  Qhull  merges  coplanar  horizon  facets,
+       flipped  facets, concave facets and duplicated ridges.  It
+       merges coplanar facets after constructing the hull.   With
+       'Qx',  coplanar points may be missed, but it appears to be
+       unlikely.
+
+       To guarantee triangular  output,  joggle  the  input  with
+       option 'QJ'.  Facet merging will not occur.
+
+OPTIONS
+       To  get  a  list  of  the  most important options, execute
+       'qhull' by itself.  To get a  complete  list  of  options,
+       execute  'qhull  -'.   To  get a complete, concise list of
+       options, execute 'qhull .'.
+
+       Options can be in any order.  Capitalized options take  an
+       argument  (except  'PG'  and 'F' options).  Single letters
+       are used for output formats and precision constants.   The
+       other options are grouped into menus for other output for-
+       mats ('F'), Geomview output ('G'), printing  ('P'),  Qhull
+
+
+
+Geometry Center              2003/12/30                 3
+
+
+
+
+
+qhull(1)                                                 qhull(1)
+
+
+       control ('Q'), and tracing ('T').
+
+       Main options:
+
+       default
+              Compute  the  convex  hull  of  the  input  points.
+              Report a summary of the result.
+
+       d      Compute the Delaunay triangulation by  lifting  the
+              input  points  to  a  paraboloid.   The  'o' option
+              prints the  input  points  and  facets.   The  'QJ'
+              option  guarantees  triangular  output.   The  'Ft'
+              option prints a triangulation.  It adds points (the
+              centrums) to non-simplicial facets.
+
+       v      Compute  the Voronoi diagram from the Delaunay tri-
+              angulation.  The 'p' option prints the Voronoi ver-
+              tices.   The 'o' option prints the Voronoi vertices
+              and the vertices in each Voronoi region.  It  lists
+              regions  in  site id order.  The 'Fv' option prints
+              each ridge of the Voronoi diagram.   The  first  or
+              zero'th  vertex indicates the infinity vertex.  Its
+              coordinates are qh_INFINITE  (-10.101).   It  indi-
+              cates   unbounded  Voronoi  regions  or  degenerate
+              Delaunay triangles.
+
+       Hn,n,...
+              Compute halfspace intersection  about  [n,n,0,...].
+              The  input  is  a  set of halfspaces defined in the
+              same format as 'n', 'Fo', and 'Fi'.   Use  'Fp'  to
+              print  the  intersection  points.  Use 'Fv' to list
+              the intersection points for  each  halfspace.   The
+              other  output formats display the dual convex hull.
+
+              The point [n,n,n,...] is a feasible point  for  the
+              halfspaces, i.e., a point that is inside all of the
+              halfspaces (Hx+b <=  0).   The  default  coordinate
+              value is 0.
+
+              The  input may start with a feasible point.  If so,
+              use 'H' by itself.  The input starts with a  feasi-
+              ble  point  when the first number is the dimension,
+              the second number is "1", and the coordinates  com-
+              plete  a line.  The 'FV' option produces a feasible
+              point for a convex hull.
+
+       d Qu   Compute the  furthest-site  Delaunay  triangulation
+              from  the upper convex hull.  The 'o' option prints
+              the input points and facets.  The 'QJ' option guar-
+              antees triangular otuput.  You can also use facets.
+
+       v Qu   Compute the furthest-site Voronoi diagram.  The 'p'
+              option prints the Voronoi vertices.  The 'o' option
+              prints the Voronoi vertices  and  the  vertices  in
+
+
+
+Geometry Center              2003/12/30                 4
+
+
+
+
+
+qhull(1)                                                 qhull(1)
+
+
+              each  Voronoi  region.  The 'Fv' option prints each
+              ridge of the Voronoi diagram.  The first or zero'th
+              vertex  indicates  the infinity vertex at infinity.
+              Its  coordinates  are  qh_INFINITE  (-10.101).   It
+              indicates  unbounded Voronoi regions and degenerate
+              Delaunay triangles.
+
+       Qt     Triangulated output.
+
+
+       Input/Output options:
+
+       f      Print out all facets and all fields of each  facet.
+
+       G      Output  the hull in Geomview format.  For imprecise
+              hulls, Geomview displays the inner and outer  hull.
+              Geomview can also display points, ridges, vertices,
+              coplanar  points,  and  facet  intersections.   See
+              below for a list of options.
+
+              For  Delaunay triangulations, 'G' displays the cor-
+              responding paraboloid.  For halfspace intersection,
+              'G' displays the dual polytope.
+
+       i      Output the incident vertices for each facet.  Qhull
+              prints the number of facets followed  by  the  ver-
+              tices  of  each  facet.   One  facet is printed per
+              line.  The numbers are the  0-relative  indices  of
+              the  corresponding  input  points.   The facets are
+              oriented.
+
+              In 4-d and higher, Qhull  triangulates  non-simpli-
+              cial  facets.   Each  apex  (the first vertex) is a
+              created point that corresponds to the facet's  cen-
+              trum.  Its index is greater than the indices of the
+              input points.  Each base corresponds to  a  simpli-
+              cial  ridge  between two facets.  To print the ver-
+              tices without triangulation, use option 'Fv'.
+
+       m      Output  the  hull  in  Mathematica  format.   Qhull
+              writes  a  Mathematica  file for 2-d and 3-d convex
+              hulls and for 2-d Delaunay triangulations.    Qhull
+              produces a list of objects that you can assign to a
+              variable in Mathematica,  for  example:  "list=  <<
+              <outputfilename> ". If the object is 2-d, it can be
+              visualized  by  "Show[Graphics[list]]  ".  For  3-d
+              objects the command is "Show[Graphics3D[list]]".
+
+       n      Output  the  normal equation for each facet.  Qhull
+              prints the dimension  (plus  one),  the  number  of
+              facets,  and  the  normals  for  each  facet.   The
+              facet's offset follows its normal coefficients.
+
+       o      Output the facets in OFF file format.  Qhull prints
+              the  dimension, number of points, number of facets,
+              and  number  of  ridges.   Then   it   prints   the
+
+
+
+Geometry Center              2003/12/30                 5
+
+
+
+
+
+qhull(1)                                                 qhull(1)
+
+
+              coordinates  of  the  input points and the vertices
+              for each facet.  Each facet is on a separate  line.
+              The  first  number  is the number of vertices.  The
+              remainder are  the  indices  of  the  corresponding
+              points.  The vertices are oriented in 2-d, 3-d, and
+              in simplicial facets.
+
+              For 2-d Voronoi diagrams, the vertices  are  sorted
+              by adjacency, but not oriented.  In 3-d and higher,
+              the Voronoi vertices are sorted by index.  See  the
+              'v' option for more information.
+
+       p      Output the coordinates of each vertex point.  Qhull
+              prints the dimension, the number of points, and the
+              coordinates  for  each  vertex.   With the 'Gc' and
+              'Gi' options, it also prints coplanar and  interior
+              points.   For Voronoi diagrams, it prints the coor-
+              dinates of each Voronoi vertex.
+
+       s      Print a summary to stderr.  If  no  output  options
+              are  specified  at  all,  a summary goes to stdout.
+              The summary lists the number of input  points,  the
+              dimension,  the  number  of  vertices in the convex
+              hull, the number of facets in the convex hull,  the
+              number of good facets (if 'Pg'), and statistics.
+
+              The  last  two  statistics  (if needed) measure the
+              maximum distance from a point or vertex to a facet.
+              The number in parenthesis (e.g., 2.1x) is the ratio
+              between the maximum  distance  and  the  worst-case
+              distance due to merging two simplicial facets.
+
+
+       Precision options
+
+       An     Maximum  angle  given  as  a  cosine.  If the angle
+              between a pair of facet normals is greater than n, Qhull
+              merges  one  of the facets into a neighbor.  If 'n'
+              is negative, Qhull tests angles after  adding  each
+              point  to  the hull (pre-merging).  If 'n' is posi-
+              tive, Qhull tests  angles  after  constructing  the
+              hull  (post-merging).   Both  pre- and post-merging
+              can be defined.
+
+              Option 'C0' or 'C-0' is set  if  the  corresponding
+              'Cn' or 'C-n' is not set.  If 'Qx' is set, then 'A-
+              n' and 'C-n' are checked after  the  hull  is  con-
+              structed and before 'An' and 'Cn' are checked.
+
+       Cn     Centrum  radius.  If a centrum is less than n below
+              a  neighboring  facet,  Qhull  merges  one  of  the
+              facets.   If  'n'  is negative or '-0', Qhull tests
+              and merges facets after adding each  point  to  the
+              hull.   This  is  called  "pre-merging".  If 'n' is
+
+
+
+Geometry Center              2003/12/30                 6
+
+
+
+
+
+qhull(1)                                                 qhull(1)
+
+
+              positive, Qhull  tests  for  convexity  after  con-
+              structing the hull ("post-merging").  Both pre- and
+              post-merging can be defined.
+
+              For 5-d and higher, 'Qx' should be used instead  of
+              'C-n'.  Otherwise, most or all facets may be merged
+              together.
+
+       En     Maximum roundoff error for distance computations.
+
+       Rn     Randomly perturb distance computations up to +/-  n
+              *  max_coord.  This option perturbs every distance,
+              hyperplane, and angle computation.  To use time  as
+              the random number seed, use option 'QR-1'.
+
+       Vn     Minimum  distance  for  a  facet  to be visible.  A
+              facet is visible if the distance from the point  to
+              the facet is greater than 'Vn'.
+
+              Without  merging, the default value for 'Vn' is the
+              round-off error ('En').  With merging, the  default
+              value  is  the  pre-merge centrum ('C-n') in 2-d or
+              3--d, or three times that in other dimensions.   If
+              the outside width is specified ('Wn'), the maximum,
+              default value for 'Vn' is 'Wn'.
+
+       Un     Maximum distance below a facet for a  point  to  be
+              coplanar  to the facet.  The default value is 'Vn'.
+
+       Wn     Minimum outside width  of  the  hull.   Points  are
+              added  to  the convex hull only if they are clearly
+              outside of a facet.  A point is outside of a  facet
+              if  its distance to the facet is greater than 'Wn'.
+              The normal value for 'Wn' is  'En'.   If  the  user
+              specifies  pre-merging  and does not set 'Wn', than
+              'Wn'  is  set  to  the  premerge  'Cn'  and  maxco-
+              ord*(1-An).
+
+
+       Additional input/output formats
+
+       Fa     Print area for each facet.  For Delaunay triangula-
+              tions, the area is the area of the  triangle.   For
+              Voronoi  diagrams, the area is the area of the dual
+              facet.   Use  'PAn'  for  printing  the  n  largest
+              facets, and option 'PFn' for printing facets larger
+              than 'n'.
+
+              The area for non-simplicial facets is  the  sum  of
+              the areas for each ridge to the centrum.   Vertices
+              far below the facet's hyperplane are ignored.   The
+              reported  area  may  be significantly less than the
+              actual area.
+
+
+
+
+Geometry Center              2003/12/30                 7
+
+
+
+
+
+qhull(1)                                                 qhull(1)
+
+
+       FA     Compute the total area and volume for  option  's'.
+              It  is  an  approximation for non-simplicial facets
+              (see 'Fa').
+
+       Fc     Print coplanar points for each facet.   The  output
+              starts  with the number of facets.  Then each facet
+              is printed one per line.  Each line is  the  number
+              of  coplanar  points  followed  by  the  point ids.
+              Option 'Qi' includes  the  interior  points.   Each
+              coplanar  point (interior point) is assigned to the
+              facet it is furthest above (resp., least below).
+
+       FC     Print centrums for each facet.  The  output  starts
+              with  the  dimension  followed  by  the  number  of
+              facets.  Then each facet centrum  is  printed,  one
+              per line.
+
+       Fd     Read  input  in cdd format with homogeneous points.
+              The input starts with comments.  The first  comment
+              is  reported  in  the summary.  Data starts after a
+              "begin" line.  The  next  line  is  the  number  of
+              points  followed  by  the dimension+1 and "real" or
+              "integer".  Then the  points  are  listed   with  a
+              leading  "1" or "1.0".  The data ends with an "end"
+              line.
+
+              For halfspaces ('Fd Hn,n,...'), the input format is
+              the  same.   Each halfspace starts with its offset.
+              The sign of the offset is the opposite  of  Qhull's
+              convention.
+
+       FD     Print  normals ('n', 'Fo', 'Fi') or points ('p') in
+              cdd format.  The first line  is  the  command  line
+              that  invoked  Qhull.   Data  starts with a "begin"
+              line.  The next line is the number  of  normals  or
+              points  followed  by  the  dimension+1  and "real".
+              Then the normals or points  are  listed   with  the
+              offset  before  the  coefficients.   The offset for
+              points is 1.0.  The  offset  for  normals  has  the
+              opposite sign.  The data ends with an "end" line.
+
+       FF     Print  facets  (as  in  'f')  without  printing the
+              ridges.
+
+       Fi     Print inner planes for each facet.  The inner plane
+              is below all vertices.
+
+       Fi     Print  separating  hyperplanes  for  bounded, inner
+              regions of the Voronoi diagram.  The first line  is
+              the  number  of  ridges.   Then  each hyperplane is
+              printed, one per line.  A line starts with the num-
+              ber  of  indices  and floats.  The first pair lists
+              adjacent input sites, the next  d  floats  are  the
+              normalized coefficients for the hyperplane, and the
+
+
+
+Geometry Center              2003/12/30                 8
+
+
+
+
+
+qhull(1)                                                 qhull(1)
+
+
+              last float is the offset.  The hyperplane  is  ori-
+              ented  toward  verify that the hyperplanes are per-
+              pendicular  bisectors.   Use  'Fo'  for   unbounded
+              regions,  and  'Fv'  for  the corresponding Voronoi
+              vertices.
+
+       FI     Print facet identifiers.
+
+       Fm     Print number of merges for each facet.  At most 511
+              merges  are  reported  for  a facet.  See 'PMn' for
+              printing the facets with the most merges.
+
+       FM     Output  the  hull  in  Maple format.  See 'm'
+
+       Fn     Print neighbors for each facet.  The output  starts
+              with  the  number  of  facets.   Then each facet is
+              printed one per line.  Each line is the  number  of
+              neighbors  followed  by an index for each neighbor.
+              The indices match the other facet output formats.
+
+              A negative index indicates an unprinted  facet  due
+              to  printing  only  good  facets ('Pg').  It is the
+              negation of the  facet's  id  (option  'FI').   For
+              example,  negative  indices are used for facets "at
+              infinity" in the Delaunay triangulation.
+
+       FN     Print vertex neighbors or coplanar facet  for  each
+              point.   The  first  line  is the number of points.
+              Then each point is printed, one per line.   If  the
+              point  is coplanar, the line is "1" followed by the
+              facet's id.  If the point is not a selected vertex,
+              the  line is "0".  Otherwise, each line is the num-
+              ber of  neighbors  followed  by  the  corresponding
+              facet indices (see 'Fn').
+
+       Fo     Print  outer planes for each facet in the same for-
+              mat as 'n'.  The outer plane is above all points.
+
+       Fo     Print separating hyperplanes for  unbounded,  outer
+              regions  of the Voronoi diagram.  The first line is
+              the number of  ridges.   Then  each  hyperplane  is
+              printed, one per line.  A line starts with the num-
+              ber of indices and floats.  The  first  pair  lists
+              adjacent  input  sites,  the  next d floats are the
+              normalized coefficients for the hyperplane, and the
+              last  float  is the offset.  The hyperplane is ori-
+              ented toward verify that the hyperplanes  are  per-
+              pendicular   bisectors.    Use   'Fi'  for  bounded
+              regions, and 'Fv'  for  the  corresponding  Voronoi
+              vertices.
+
+       FO     List  all  options to stderr, including the default
+              values.  Additional 'FO's are printed to stdout.
+
+       Fp     Print points for  halfspace  intersections  (option
+              'Hn,n,...').   Each  intersection  corresponds to a
+
+
+
+Geometry Center              2003/12/30                 9
+
+
+
+qhull(1)                                                 qhull(1)
+
+
+              facet of the dual polytope.  The  "infinity"  point
+              [-10.101,-10.101,...]    indicates   an   unbounded
+              intersection.
+
+       FP     For each coplanar point ('Qc') print the  point  id
+              of  the nearest vertex, the point id, the facet id,
+              and the distance.
+
+       FQ     Print command used for qhull and input.
+
+       Fs     Print a summary.  The first line  consists  of  the
+              number  of  integers  ("7"), followed by the dimen-
+              sion, the number of points, the number of vertices,
+              the  number  of  facets,  the  number  of  vertices
+              selected for output, the number of facets  selected
+              for  output, the number of coplanar points selected
+              for output.
+
+              The second line consists of  the  number  of  reals
+              ("2"),  followed by the maxmimum offset to an outer
+              plane and and minimum offset  to  an  inner  plane.
+              Roundoff  is included.  Later versions of Qhull may
+              produce additional integers or reals.
+
+       FS     Print the size of the hull.  The  first  line  con-
+              sists  of the number of integers ("0").  The second
+              line consists of the number of  reals  ("2"),  fol-
+              lowed  by  the total facet area, and the total vol-
+              ume.  Later versions of  Qhull  may  produce  addi-
+              tional integers or reals.
+
+              The  total volume measures the volume of the inter-
+              section of the halfspaces defined  by  each  facet.
+              Both  area  and  volume are approximations for non-
+              simplicial facets.  See option 'Fa'.
+
+       Ft     Print a triangulation with added  points  for  non-
+              simplicial facets.  The first line is the dimension
+              and the second line is the number of points and the
+              number of facets.  The points follow, one per line,
+              then the facets follow as a list of point  indices.
+              With option points include the point-at-infinity.
+
+       Fv     Print  vertices  for each facet.  The first line is
+              the number of facets.  Then each facet is  printed,
+              one  per line.  Each line is the number of vertices
+              followed by the corresponding point ids.   Vertices
+              are listed in the order they were added to the hull
+              (the last one is first).
+
+       Fv     Print all ridges of a Voronoi diagram.   The  first
+              line  is  the number of ridges.  Then each ridge is
+              printed, one per line.  A line starts with the num-
+              ber  of  indices.   The  first  pair lists adjacent
+
+
+
+Geometry Center              2003/12/30                10
+
+
+
+
+
+qhull(1)                                                 qhull(1)
+
+
+              input sites, the  remaining  indices  list  Voronoi
+              vertices.   Vertex  '0'  indicates  the  vertex-at-
+              infinity (i.e., an unbounded  ray).   In  3-d,  the
+              vertices  are  listed  in order.  See 'Fi' and 'Fo'
+              for separating hyperplanes.
+
+       FV     Print average vertex.  The average vertex is a fea-
+              sible point for halfspace intersection.
+
+       Fx     List  extreme points (vertices) of the convex hull.
+              The first line is the number of points.  The  other
+              lines give the indices of the corresponding points.
+              The first point is '0'.  In 2-d, the  points  occur
+              in counter-clockwise order; otherwise they occur in
+              input order.   For  Delaunay  triangulations,  'Fx'
+              lists  the  extreme points of the input sites.  The
+              points are unordered.
+
+
+       Geomview options
+
+       G      Produce a file for viewing with Geomview.   Without
+              other  options,  Qhull displays edges in 2-d, outer
+              planes in 3-d, and ridges in 4-d.  A ridge  can  be
+              explicit or implicit.  An explicit ridge is a dim-1
+              dimensional simplex between two  facets.   In  4-d,
+              the explicit ridges are triangles.  When displaying
+              a ridge in 4-d, Qhull projects the ridge's vertices
+              to  one  of  its  facets' hyperplanes.  Use 'Gh' to
+              project ridges to the intersection of  both  hyper-
+              planes.
+
+       Ga     Display all input points as dots.
+
+       Gc     Display  the  centrum  for  each facet in 3-d.  The
+              centrum is defined by a green radius sitting  on  a
+              blue  plane.   The plane corresponds to the facet's
+              hyperplane.  The radius  is  defined  by  'C-n'  or
+              'Cn'.
+
+       GDn    Drop  dimension  n  in 3-d or 4-d.  The result is a
+              2-d or 3-d object.
+
+       Gh     Display hyperplane intersections in  3-d  and  4-d.
+              In  3-d, the intersection is a black line.  It lies
+              on two  neighboring  hyperplanes  (c.f.,  the  blue
+              squares  associated with centrums ('Gc')).  In 4-d,
+              the ridges are projected  to  the  intersection  of
+              both hyperplanes.
+
+       Gi     Display  inner  planes  in  2-d and 3-d.  The inner
+              plane of a facet is below all of its vertices.   It
+              is  parallel  to the facet's hyperplane.  The inner
+              plane's color is the opposite (1-r,1-g,1-b) of  the
+
+
+
+Geometry Center              2003/12/30                11
+
+
+
+
+
+qhull(1)                                                 qhull(1)
+
+
+              outer  plane.  Its edges are determined by the ver-
+              tices.
+
+       Gn     Do not display inner or outer planes.  By  default,
+              Geomview displays the precise plane (no merging) or
+              both inner  and  output  planes  (merging).   Under
+              merging,  Geomview does not display the inner plane
+              if the the difference between inner  and  outer  is
+              too small.
+
+       Go     Display  outer  planes  in  2-d and 3-d.  The outer
+              plane of a facet is above all input points.  It  is
+              parallel  to  the facet's hyperplane.  Its color is
+              determined by the facet's normal, and its edges are
+              determined by the vertices.
+
+       Gp     Display  coplanar  points and vertices as radii.  A
+              radius defines a  ball  which  corresponds  to  the
+              imprecision  of  the point.  The imprecision is the
+              maximum of the roundoff error, the centrum  radius,
+              and  maxcoord  * (1-An).  It is at least 1/20'th of
+              the maximum coordinate, and ignores post-merging if
+              pre-merging is done.
+
+       Gr     Display  ridges  in  3-d.  A ridge connects the two
+              vertices that are  shared  by  neighboring  facets.
+              Ridges are always displayed in 4-d.
+
+       Gt     A  3-d  Delaunay  triangulation looks like a convex
+              hull with interior facets.  Option 'Gt' removes the
+              outside  ridges to reveal the outermost facets.  It
+              automatically sets options 'Gr' and 'GDn'.
+
+       Gv     Display vertices as spheres.   The  radius  of  the
+              sphere  corresponds to the imprecision of the data.
+              See 'Gp' for determining the radius.
+
+
+       Print options
+
+       PAn    Only the n  largest  facets  are  marked  good  for
+              printing.   Unless  'PG'  is set, 'Pg' is automati-
+              cally set.
+
+       Pdk:n  Drop facet from output  if  normal[k]  <=  n.   The
+              option 'Pdk' uses the default value of 0 for n.
+
+       PDk:n  Drop  facet  from  output  if  normal[k] >= n.  The
+              option 'PDk' uses the default value of 0 for n.
+
+       PFn    Only facets with area at least 'n' are marked  good
+              for printing.  Unless 'PG' is set, 'Pg' is automat-
+              ically set.
+
+
+
+
+Geometry Center              2003/12/30                12
+
+
+
+
+
+qhull(1)                                                 qhull(1)
+
+
+       Pg     Print only good facets.  A  good  facet  is  either
+              visible from a point (the 'QGn' option) or includes
+              a point (the 'QVn'  option).   It  also  meets  the
+              requirements  of  'Pdk'  and 'PDk' options.  Option
+              'Pg' is automatically set  for  options  'PAn'  and
+              'PFn'.
+
+       PG     Print neighbors of good facets.
+
+       PMn    Only  the  n facets with the most merges are marked
+              good for printing.  Unless 'PG'  is  set,  'Pg'  is
+              automatically set.
+
+       Po     Force output despite precision problems.  Verify  ('Tv')  does    not check
+              coplanar points.  Flipped facets are  reported  and
+              concave  facets  are  counted.   If  'Po'  is used,
+              points are not partitioned into flipped facets  and
+              a  flipped  facet  is  always  visible  to a point.
+              Also, if an error occurs before the  completion  of
+              Qhull  and  tracing  is  not active, 'Po' outputs a
+              neighborhood of the erroneous facets (if any).
+
+       Pp     Do not report precision problems.
+
+
+       Qhull control options
+
+       Qbk:0Bk:0
+              Drop dimension  k  from  the  input  points.   This
+              allows  the user to take convex hulls of sub-dimen-
+              sional objects.  It happens before the Delaunay and
+              Voronoi transformation.
+
+       QbB    Scale the input points to fit the unit cube.  After
+              scaling, the lower bound will be -0.5 and the upper
+              bound  +0.5  in  all  dimensions.  For Delaunay and
+              Voronoi diagrams, scaling happens after  projection
+              to the paraboloid.  Under precise arithmetic, scal-
+              ing does not change  the  topology  of  the  convex
+              hull.
+
+       Qbb    Scale  the last coordinate to [0, m] where m is the
+              maximum absolute value of  the  other  coordinates.
+              For  Delaunay and Voronoi diagrams, scaling happens
+              after projection to  the  paraboloid.   It  reduces
+              roundoff error for inputs with integer coordinates.
+              Under precise arithmetic, scaling does  not  change
+              the topology of the convex hull.
+
+       Qbk:n  Scale  the  k'th  coordinate  of  the input points.
+              After scaling, the lower bound of the input  points
+              will be n.  'Qbk' scales to -0.5.
+
+
+
+Geometry Center              2003/12/30                13
+
+
+
+
+
+qhull(1)                                                 qhull(1)
+
+
+       QBk:n  Scale  the  k'th  coordinate  of  the input points.
+              After scaling, the upper bound will  be  n.   'QBk'
+              scales to +0.5.
+
+       Qc     Keep  coplanar points with the nearest facet.  Out-
+              put formats 'p', 'f', 'Gp', 'Fc',  'FN',  and  'FP'
+              will print the points.
+
+       Qf     Partition points to the furthest outside facet.
+
+       Qg     Only  build  good  facets.   With  the 'Qg' option,
+              Qhull will only build those facets that it needs to
+              determine  the  good  facets  in  the  output.  See
+              'QGn', 'QVn', and 'PdD' for defining  good  facets,
+              and  'Pg'  and  'PG'  for  printing good facets and
+              their neighbors.
+
+       QGn    A facet is good (see 'Qg' and 'Pg') if it is  visi-
+              ble  from point n.  If n < 0, a facet is good if it
+              is not visible from point n.  Point n is not  added
+              to  the  hull  (unless 'TCn' or 'TPn').  With rbox,
+              use the 'Pn,m,r' option to define  your  point;  it
+              will be point 0 (QG0).
+
+       Qi     Keep  interior points with the nearest facet.  Out-
+              put formats 'p', 'f', 'Gp', 'FN',  'FP',  and  'Fc'
+              will print the points.
+
+       QJn    Joggle  each  input  coordinate  by adding a random
+              number in [-n,n].  If  a  precision  error  occurs,
+              then  qhull  increases  n and tries again.  It does
+              not increase n beyond a certain value, and it stops
+              after  a  certain  number of attempts [see user.h].
+              Option 'QJ' selects a default  value  for  n.   The
+              output will be simplicial.  For Delaunay triangula-
+              tions, 'QJn' sets 'Qbb' to scale the  last  coordi-
+              nate (not if 'Qbk:n' or 'QBk:n' is set).  'QJn' is
+              deprecated for Voronoi diagrams.  See also 'Qt'.
+
+       Qm     Only  process  points that would otherwise increase
+              max_outside.  Other points are treated as  coplanar
+              or interior points.
+
+       Qr     Process  random  outside points instead of furthest
+              ones.  This makes Qhull equivalent to  the  random-
+              ized  incremental  algorithms.   CPU  time  is  not
+              reported since the randomization is inefficient.
+
+       QRn    Randomly rotate the input points.  If n=0, use time
+              as  the  random  number seed.  If n>0, use n as the
+              random number seed.  If n=-1, don't rotate but  use
+              time  as the random number seed.  For Delaunay tri-
+              angulations ('d' and 'v'), rotate  about  the  last
+              axis.
+
+
+
+
+Geometry Center              2003/12/30                14
+
+
+
+
+
+qhull(1)                                                 qhull(1)
+
+
+       Qs     Search all points for the initial simplex.
+
+       Qt     Triangulated output.  Triangulate non-simplicial
+              facets. 'Qt' is deprecated for Voronoi diagrams.
+              See also 'QJn'
+
+       Qv     Test  vertex  neighbors  for  convexity after post-
+              merging.  To use the 'Qv' option, you also need  to
+              set a merge option (e.g., 'Qx' or 'C-0').
+
+       QVn    A  good facet (see 'Qg' and 'Pg') includes point n.
+              If n<0, then a good facet does not include point n.
+              The point is either in the initial simplex or it is
+              the first point added to the  hull.   Option  'QVn'
+              may not be used with merging.
+
+       Qx     Perform  exact merges while building the hull.  The
+              "exact" merges are merging a point into a  coplanar
+              facet  (defined  by 'Vn', 'Un', and 'C-n'), merging
+              concave facets, merging duplicate ridges, and merg-
+              ing  flipped  facets.   Coplanar  merges  and angle
+              coplanar merges ('A-n') are not performed.  Concav-
+              ity testing is delayed until a merge occurs.
+
+              After  the  hull  is built, all coplanar merges are
+              performed (defined by 'C-n' and 'A-n'), then  post-
+              merges are performed (defined by 'Cn' and 'An').
+
+       Qz     Add  a  point  "at  infinity"  that  is  above  the
+              paraboloid for Delaunay triangulations and  Voronoi
+              diagrams.   This  reduces  precision  problems  and
+              allows the triangulation of cospherical points.
+
+
+       Qhull experiments and speedups
+
+       Q0     Turn off pre-merging as  a  default  option.   With
+              'Q0'/'Qx'  and  without explicit pre-merge options,
+              Qhull ignores precision issues  while  constructing
+              the  convex  hull.   This  may  lead  to  precision
+              errors.  If so, a descriptive warning is generated.
+
+       Q1     With  'Q1',  Qhull  sorts merges by type (coplanar,
+              angle coplanar, concave) instead of by angle.
+
+       Q2     With 'Q2', Qhull merges all facets at once  instead
+              of  using  independent  sets  of  merges  and  then
+              retesting.
+
+       Q3     With 'Q3', Qhull does  not  remove  redundant  ver-
+              tices.
+
+       Q4     With 'Q4', Qhull avoids merges of an old facet into
+              a new facet.
+
+       Q5     With 'Q5', Qhull does not correct outer  planes  at
+              the  end.  The maximum outer plane is used instead.
+
+
+
+
+Geometry Center              2003/12/30                15
+
+
+
+
+
+qhull(1)                                                 qhull(1)
+
+
+       Q6     With 'Q6', Qhull  does  not  pre-merge  concave  or
+              coplanar facets.
+
+       Q7     With  'Q7',  Qhull  processes facets in depth-first
+              order instead of breadth-first order.
+
+       Q8     With 'Q8' and merging, Qhull does not retain  near-
+              interior  points  for adjusting outer planes.  'Qc'
+              will probably retain all points that  adjust  outer
+              planes.
+
+       Q9     With 'Q9', Qhull processes the furthest of all out-
+              side sets at each iteration.
+
+       Q10    With 'Q10', Qhull does not use special processing
+              for narrow distributions.
+
+       Q11    With 'Q11', Qhull copies normals and recomputes
+              centrums for tricoplanar facets.
+
+       Q12    With 'Q12', Qhull does not report a very wide merge due 
+              to a duplicated ridge with nearly coincident vertices
+
+       Trace options
+
+       Tn     Trace at level n.  Qhull  includes  full  execution
+              tracing.   'T-1'  traces  events.   'T1' traces the
+              overall execution of the program.   'T2'  and  'T3'
+              trace overall execution and geometric and topologi-
+              cal  events.   'T4'  traces  the  algorithm.   'T5'
+              includes  information  about  memory allocation and
+              Gaussian elimination.
+
+       Ta     Annotate output with codes that identify the
+              corresponding qh_fprintf() statement.
+
+       Tc     Check frequently during execution.  This will catch
+              most inconsistency errors.
+
+       TCn    Stop  Qhull  after  building the cone of new facets
+              for point n.  The output for 'f' includes the  cone
+              and the old hull.  See also 'TVn'.
+
+       TFn    Report  progress  whenever  more  than n facets are
+              created During post-merging, 'TFn' reports progress
+              after more than n/2 merges.
+
+       TI file
+              Input data from 'file'.  The filename may not include
+                  spaces or quotes.
+
+       TO file
+              Output results to 'file'.  The name may be enclosed
+              in single quotes.
+
+       TPn    Turn on tracing when point n is added to the  hull.
+          Trace partitions of point n. If used with TWn, turn off
+          tracing after adding point n to the hull.
+
+       TRn    Rerun  qhull  n  times.  Usually used with 'QJn' to
+              determine the probability that a given joggle  will
+              fail.
+
+       Ts     Collect  statistics  and print to stderr at the end
+              of execution.
+
+       Tv     Verify the convex hull.  This checks the  topologi-
+              cal  structure,  facet  convexity, and point inclu-
+              sion.  If precision problems occurred,  facet  con-
+              vexity  is  tested whether or not 'Tv' is selected.
+              Option 'Tv'  does  not  check  point  inclusion  if
+
+
+
+Geometry Center              2003/12/30                16
+
+
+
+
+
+qhull(1)                                                 qhull(1)
+
+
+              forcing output with 'Po', or if 'Q5' is set.
+
+              For  point  inclusion  testing, Qhull verifies that
+              all points are below all outer planes  (facet->max-
+              outside).  Point inclusion is exhaustive if merging
+              or if the facet-point product is small enough; oth-
+              erwise  Qhull  verifies  each point with a directed
+              search (qh_findbest).
+
+              Point inclusion testing occurs after producing out-
+              put.   It  prints a message to stderr unless option
+              'Pp' is used.  This allows the  user  to  interrupt
+              Qhull without changing the output.
+
+       TVn    Stop  Qhull  after  adding point n.  If n < 0, stop
+              Qhull before adding point n.  Output shows the hull
+              at this time.  See also 'TCn'
+
+       TMn    Turn on tracing at n'th merge.
+
+       TWn    Trace  merge  facets when the width is greater than
+              n.
+
+       Tz     Redirect stderr to stdout.
+
+
+BUGS
+       Please    report    bugs     to     Brad     Barber     at
+       qhull_bug@qhull.org.
+
+       If Qhull does not compile, it is due to an incompatibility
+       between your system and ours.  The first thing to check is
+       that  your compiler is ANSI standard.  If it is, check the
+       man page for the best options, or  find  someone  to  help
+       you.  If you locate the cause of your problem, please send
+       email since it might help others.
+
+       If Qhull compiles but crashes on the test case (rbox  D4),
+       there's  still  incompatibility  between  your  system and
+       ours.  Typically it's been due to mem.c and memory  align-
+       ment.   You  can  use qh_NOmem in mem.h to turn off memory
+       management.  Please let us know if you figure out  how  to
+       fix these problems.
+
+       If  you  do  find  a  problem,  try  to simplify it before
+       reporting the error.  Try different size inputs to  locate
+       the  smallest one that causes an error.  You're welcome to
+       hunt through the code  using  the  execution  trace  as  a
+       guide.   This  is  especially true if you're incorporating
+       Qhull into your own program.
+
+       When you do report an error, please attach a data  set  to
+       the  end of your message.  This allows us to see the error
+       for ourselves.  Qhull is maintained part-time.
+
+
+
+Geometry Center              2003/12/30                17
+
+
+
+
+
+qhull(1)                                                 qhull(1)
+
+
+E-MAIL
+       Please  send  correspondence  to  qhull@qhull.org   and
+       report  bugs  to  qhull_bug@qhull.org.  Let us know how
+       you use Qhull.  If you mention it in a paper, please  send
+       the reference and an abstract.
+
+       If  you would like to get Qhull announcements (e.g., a new
+       version) and news (any bugs that get fixed, etc.), let  us
+       know  and  we  will  add  you to our mailing list.  If you
+       would like to communicate with other Qhull users, we  will
+       add you to the qhull_users alias.  For Internet news about
+       geometric algorithms and convex hulls, look at comp.graph-
+       ics.algorithms and sci.math.num-analysis
+
+
+SEE ALSO
+       rbox(1)
+
+       Barber,  C.  B.,  D.P.  Dobkin,  and  H.T. Huhdanpaa, "The
+       Quickhull Algorithm for Convex Hulls," ACM Trans. on Math-
+       ematical Software, 22(4):469-483, Dec. 1996.
+       http://portal.acm.org/citation.cfm?doid=235815.235821
+       http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.117.405
+
+
+       Clarkson, K.L., K. Mehlhorn, and R. Seidel, "Four  results
+       on  randomized  incremental  construction,"  Computational
+       Geometry: Theory and Applications,  vol.  3,  p.  185-211,
+       1993.
+
+       Preparata,  F.  and  M.  Shamos,  Computational  Geometry,
+       Springer-Verlag, New York, 1985.
+
+
+
+AUTHORS
+         C. Bradford Barber                    Hannu Huhdanpaa
+         bradb@shore.net                       hannu@qhull.org
+
+
+
+ACKNOWLEDGEMENTS
+       A special thanks to Albert Marden, Victor Milenkovic,  the
+       Geometry Center, Harvard University, and Endocardial Solu-
+       tions, Inc. for supporting this work.
+
+       Qhull 1.0 and 2.0 were developed under National Science Foundation
+       grants NSF/DMS-8920161 and NSF-CCR-91-15793 750-7504.  David Dobkin
+
+
+
+Geometry Center              2003/12/30                18
+
+
+
+
+
+qhull(1)                                                 qhull(1)
+
+
+       guided the original work at Princeton University.  If you find it
+       useful, please let us know.
+
+       The Geometry Center was supported by grant DMS-8920161 from the National
+       Science Foundation, by grant DOE/DE-FG02-92ER25137 from the Department
+       of Energy, by the University of Minnesota, and by Minnesota Technology, Inc.
+
+       Qhull is available from http://www.qhull.org
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+Geometry Center              2003/12/30                19
+
+
diff --git a/xs/src/qhull/html/qvoron_f.htm b/xs/src/qhull/html/qvoron_f.htm
new file mode 100644
index 0000000000..db538b5ab5
--- /dev/null
+++ b/xs/src/qhull/html/qvoron_f.htm
@@ -0,0 +1,396 @@
+<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN">
+<html>
+
+<head>
+<title>qvoronoi Qu -- furthest-site Voronoi diagram</title>
+</head>
+
+<body>
+<!-- Navigation links -->
+<a name="TOP"><b>Up</b></a><b>:</b>
+<a href="http://www.qhull.org">Home page</a> for Qhull<br>
+<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
+<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
+&#149; <a href="qh-quick.htm#options">Options</a>
+&#149; <a href="qh-opto.htm#output">Output</a>
+&#149; <a href="qh-optf.htm#format">Formats</a>
+&#149; <a href="qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="qh-optp.htm#print">Print</a>
+&#149; <a href="qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="qh-optc.htm#prec">Precision</a>
+&#149; <a href="qh-optt.htm#trace">Trace</a>
+&#149; <a href="../src/libqhull_r/index.htm">Functions</a><br>
+<b>To:</b> <a href="#synopsis">sy</a>nopsis
+&#149; <a href="#input">in</a>put &#149; <a href="#outputs">ou</a>tputs
+&#149; <a href="#controls">co</a>ntrols &#149; <a href="#graphics">gr</a>aphics
+&#149; <a href="#notes">no</a>tes &#149; <a href="#conventions">co</a>nventions
+&#149; <a href="#options">op</a>tions
+
+<hr>
+<!-- Main text of document -->
+<h1><a
+href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/delaunay.html"><img
+src="qh--dt.gif" alt="[delaunay]" align="middle" width="100"
+height="100"></a>qvoronoi Qu -- furthest-site Voronoi diagram</h1>
+
+<p>The furthest-site Voronoi diagram is the furthest-neighbor map for a set of
+points. Each region contains those points that are further
+from one input site than any other input site.  See the
+survey article by Aurenhammer [<a href="index.htm#aure91">'91</a>]
+and the brief introduction by O'Rourke [<a
+href="index.htm#orou94">'94</a>].  The furthest-site Voronoi diagram is the dual of the <a
+href="qdelau_f.htm">furthest-site Delaunay triangulation</a>.
+</p>
+
+<blockquote>
+<dl>
+    <dt><b>Example:</b> rbox 10 D2 | qvoronoi <a
+        href="qh-optq.htm#Qu">Qu</a>  <a href="qh-opto.htm#s">s</a>
+        <a href="qh-opto.htm#o">o</a> <a href="qh-optt.htm#TO">TO
+        result</a></dt>
+    <dd>Compute the 2-d, furthest-site Voronoi diagram of 10
+        random points. Write a summary to the console and the Voronoi
+        regions and vertices to 'result'. The first vertex of the
+        result indicates unbounded regions. Almost all regions
+        are unbounded.</dd>
+</dl>
+
+<dl>
+    <dt><b>Example:</b> rbox r y c G1 D2 | qvoronoi <a
+        href="qh-optq.htm#Qu">Qu</a>
+        <a href="qh-opto.htm#s">s</a>
+        <a href="qh-optf.htm#Fn">Fn</a> <a href="qh-optt.htm#TO">TO
+        result</a></dt>
+    <dd>Compute the 2-d furthest-site Voronoi diagram of a square
+        and a small triangle. Write a summary to the console and the Voronoi
+        vertices for each input site to 'result'.
+        The origin is the only furthest-site Voronoi vertex.  The
+                negative indices indicate vertices-at-infinity.</dd>
+</dl>
+</blockquote>
+
+<p>
+Qhull computes the furthest-site Voronoi diagram via the <a href="qdelau_f.htm">
+furthest-site Delaunay triangulation</a>.
+Each furthest-site Voronoi vertex is the circumcenter of an upper
+facet of the Delaunay triangulation. Each furthest-site Voronoi
+region corresponds to a vertex of the Delaunay triangulation
+(i.e., an input site).</p>
+
+<p>See <a href="http://www.qhull.org/html/qh-faq.htm#TOC">Qhull FAQ</a> - Delaunay and
+Voronoi diagram questions.</p>
+
+<p>The 'qvonoroi' program is equivalent to
+'<a href=qhull.htm#outputs>qhull v</a> <a href=qh-optq.htm#Qbb>Qbb</a>' in 2-d to 3-d, and
+'<a href=qhull.htm#outputs>qhull v</a> <a href=qh-optq.htm#Qbb>Qbb</a> <a href=qh-optq.htm#Qx>Qx</a>'
+in 4-d and higher.  It disables the following Qhull
+<a href=qh-quick.htm#options>options</a>: <i>d n m v H U Qb
+QB Qc Qf Qg Qi Qm Qr QR Qv Qx TR E V Fa FA FC Fp FS Ft FV Gt Q0,etc</i>.
+
+
+<p><b>Copyright &copy; 1995-2015 C.B. Barber</b></p>
+
+<hr>
+<h3><a href="#TOP">&#187;</a><a name="synopsis">furthest-site qvoronoi synopsis</a></h3>
+<blockquote>
+
+See <a href="qvoronoi.htm#synopsis">qvoronoi synopsis</a>.  The same
+program is used for both constructions.  Use option '<a href="qh-optq.htm#Qu">Qu</a>'
+for furthest-site Voronoi diagrams.
+
+
+</blockquote>
+<h3><a href="#TOP">&#187;</a><a name="input">furthest-site qvoronoi
+input</a></h3>
+<blockquote>
+<p>The input data on <tt>stdin</tt> consists of:</p>
+<ul>
+    <li>dimension
+    <li>number of points</li>
+    <li>point coordinates</li>
+</ul>
+
+<p>Use I/O redirection (e.g., qvoronoi Qu &lt; data.txt), a pipe (e.g., rbox 10 | qvoronoi Qu),
+or the '<a href=qh-optt.htm#TI>TI</a>' option (e.g., qvoronoi TI data.txt Qu).
+
+<p>For example, this is a square containing four random points.
+Its furthest-site Voronoi diagram has on vertex and four unbounded,
+separating hyperplanes (i.e., the coordinate axes)
+<p>
+<blockquote>
+<tt>rbox c 4 D2 &gt; data</tt>
+<blockquote><pre>
+2 RBOX c 4 D2
+8
+-0.4999921736307369 -0.3684622117955817
+0.2556053225468894 -0.0413498678629751
+0.0327672376602583 -0.2810408135699488
+-0.452955383763607 0.17886471718444
+  -0.5   -0.5
+  -0.5    0.5
+   0.5   -0.5
+   0.5    0.5
+</pre></blockquote>
+
+<p><tt>qvoronoi Qu s Fo &lt; data</tt>
+<blockquote><pre>
+
+Furthest-site Voronoi vertices by the convex hull of 8 points in 3-d:
+
+  Number of Voronoi regions: 8
+  Number of Voronoi vertices: 1
+  Number of non-simplicial Voronoi vertices: 1
+
+Statistics for: RBOX c 4 D2 | QVORONOI Qu s Fo
+
+  Number of points processed: 8
+  Number of hyperplanes created: 20
+  Number of facets in hull: 11
+  Number of distance tests for qhull: 34
+  Number of merged facets: 1
+  Number of distance tests for merging: 107
+  CPU seconds to compute hull (after input):  0
+
+4
+5 4 5      0      1      0
+5 4 6      1      0      0
+5 5 7      1      0      0
+5 6 7      0      1      0
+</pre></blockquote>
+</blockquote>
+
+</blockquote>
+<h3><a href="#TOP">&#187;</a> <a name="outputs">furthest-site qvoronoi
+outputs</a></h3>
+<blockquote>
+
+<p>These options control the output of furthest-site Voronoi diagrams.</p>
+<blockquote>
+
+<dl compact>
+    <dt>&nbsp;</dt>
+    <dd><b>furthest-site Voronoi vertices</b></dd>
+    <dt><a href="qh-opto.htm#p">p</a></dt>
+    <dd>print the coordinates of the furthest-site Voronoi vertices.  The first line
+        is the dimension.  The second line is the number of vertices.  Each
+        remaining line is a furthest-site Voronoi vertex.  The points-in-square example
+        has one furthest-site Voronoi vertex at the origin.</dd>
+    <dt><a href="qh-optf.htm#Fn">Fn</a></dt>
+    <dd>list the neighboring furthest-site Voronoi vertices for each furthest-site Voronoi
+        vertex.  The first line is the number of Voronoi vertices.  Each
+                remaining line starts with the number of neighboring vertices.  Negative indices (e.g., <em>-1</em>) indicate vertices
+        outside of the Voronoi diagram.  In the points-in-square example, the
+                Voronoi vertex at the origin has four neighbors-at-infinity.</dd>
+    <dt><a href="qh-optf.htm#FN">FN</a></dt>
+    <dd>list the furthest-site Voronoi vertices for each furthest-site Voronoi region.  The first line is
+        the number of Voronoi regions.  Each remaining line starts with the
+        number of Voronoi vertices.  Negative indices (e.g., <em>-1</em>) indicate vertices
+        outside of the Voronoi diagram.
+        In the points-in-square example, all regions share the Voronoi vertex
+        at the origin.</dd>
+
+    <dt>&nbsp;</dt>
+    <dt>&nbsp;</dt>
+    <dd><b>furthest-site Voronoi regions</b></dd>
+    <dt><a href="qh-opto.htm#o">o</a></dt>
+    <dd>print the furthest-site Voronoi regions in OFF format.  The first line is the
+        dimension.  The second line is the number of vertices, the number
+        of input sites, and "1".  The third line represents the vertex-at-infinity.
+        Its coordinates are "-10.101".  The next lines are the coordinates
+        of the furthest-site Voronoi vertices.  Each remaining line starts with the number
+        of Voronoi vertices in a Voronoi region.  In 2-d, the vertices are
+listed in adjacency order (unoriented). In 3-d and higher, the
+vertices are listed in numeric order.  In the points-in-square
+        example, each unbounded region includes the Voronoi vertex at
+        the origin.  Lines consisting of <em>0</em> indicate
+        interior input sites.  </dd>
+    <dt><a href="qh-optf.htm#Fi2">Fi</a></dt>
+    <dd>print separating hyperplanes for inner, bounded furthest-site Voronoi
+        regions.  The first number is the number of separating
+                hyperplanes.  Each remaining line starts with <i>3+dim</i>.  The
+                next two numbers are adjacent input sites.  The next <i>dim</i>
+                numbers are the coefficients of the separating hyperplane.  The
+                last number is its offset.  The are no bounded, separating hyperplanes
+                for the points-in-square example.</dd>
+    <dt><a href="qh-optf.htm#Fo2">Fo</a></dt>
+    <dd>print separating hyperplanes for outer, unbounded furthest-site Voronoi
+        regions.  The first number is the number of separating
+                hyperplanes.  Each remaining line starts with <i>3+dim</i>.  The
+                next two numbers are adjacent input sites on the convex hull.  The
+                next <i>dim</i>
+                numbers are the coefficients of the separating hyperplane.  The
+                last number is its offset.  The points-in-square example has four
+                unbounded, separating hyperplanes.</dd>
+    <dt>&nbsp;</dt>
+    <dt>&nbsp;</dt>
+    <dd><b>Input sites</b></dd>
+    <dt><a href="qh-optf.htm#Fv2">Fv</a></dt>
+    <dd>list ridges of furthest-site Voronoi vertices for pairs of input sites.  The
+        first line is the number of ridges.  Each remaining line starts with
+        two plus the number of Voronoi vertices in the ridge.  The next
+        two numbers are two adjacent input sites.  The remaining numbers list
+        the Voronoi vertices.  As with option 'o', a <em>0</em> indicates
+        the vertex-at-infinity
+        and an unbounded, separating hyperplane.
+        The perpendicular bisector (separating hyperplane)
+        of the input sites is a flat through these vertices.
+        In the points-in-square example, the ridge for each edge of the square
+        is unbounded.</dd>
+    <dt>&nbsp;</dt>
+    <dt>&nbsp;</dt>
+    <dd><b>General</b></dd>
+    <dt><a href="qh-opto.htm#s">s</a></dt>
+    <dd>print summary of the furthest-site Voronoi diagram. Use '<a
+        href="qh-optf.htm#Fs">Fs</a>' for numeric data.</dd>
+    <dt><a href="qh-opto.htm#i">i</a></dt>
+    <dd>list input sites for each <a href=qdelau_f.htm>furthest-site Delaunay region</a>.  Use option '<a href="qh-optp.htm#Pp">Pp</a>'
+        to avoid the warning.  The first line is the number of regions.  The
+        remaining lines list the input sites for each region.  The regions are
+        oriented.  In the points-in-square example, the square region has four
+        input sites.  In 3-d and higher, report cospherical sites by adding extra points.
+        </dd>
+    <dt><a href="qh-optg.htm#G">G</a></dt>
+    <dd>Geomview output for 2-d furthest-site Voronoi diagrams.</dd>
+        </dl>
+</blockquote>
+
+</blockquote>
+<h3><a href="#TOP">&#187;</a> <a name="controls">furthest-site qvoronoi
+controls</a></h3>
+<blockquote>
+
+<p>These options provide additional control:</p>
+<blockquote>
+
+<dl compact>
+   <dt><a href="qh-optq.htm#Qu">Qu</a></dt>
+    <dd>must be used.</dd>
+    <dt><a href="qh-optq.htm#QVn">QVn</a></dt>
+    <dd>select furthest-site Voronoi vertices for input site <em>n</em> </dd>
+    <dt><a href="qh-optt.htm#Tv">Tv</a></dt>
+    <dd>verify result</dd>
+    <dt><a href="qh-optt.htm#TO">TI file</a></dt>
+    <dd>input data from file.  The filename may not use spaces or quotes.</dd>
+    <dt><a href="qh-optt.htm#TO">TO file</a></dt>
+    <dd>output results to file.  Use single quotes if the filename
+        contains spaces (e.g., <tt>TO 'file with spaces.txt'</tt></dd>
+    <dt><a href="qh-optt.htm#TFn">TFn</a></dt>
+    <dd>report progress after constructing <em>n</em> facets</dd>
+    <dt><a href="qh-optp.htm#PDk">PDk:1</a></dt>
+    <dd>include upper and lower facets in the output.  Set <em>k</em>
+        to the last dimension (e.g., 'PD2:1' for 2-d inputs). </dd>
+    <dt><a href="qh-opto.htm#f">f </a></dt>
+    <dd>facet dump.  Print the data structure for each facet (i.e.,
+        furthest-site Voronoi vertex).</dd>
+</dl>
+
+</blockquote>
+</blockquote>
+<h3><a href="#TOP">&#187;</a> <a name="graphics">furthest-site qvoronoi
+graphics</a></h3>
+<blockquote>
+<p>In 2-d, Geomview output ('<a href="qh-optg.htm#G">G</a>')
+displays a furthest-site Voronoi diagram with extra edges to
+close the unbounded furthest-site Voronoi regions. All regions
+will be unbounded.  Since the points-in-box example has only
+one furthest-site Voronoi vertex, the Geomview output is one
+point.</p>
+
+<p>See the <a href="qh-eg.htm#delaunay">Delaunay and Voronoi
+examples</a> for a 2-d example. Turn off normalization (on
+Geomview's 'obscure' menu) when comparing the furthest-site
+Voronoi diagram with the corresponding Voronoi diagram. </p>
+
+</blockquote>
+<h3><a href="#TOP">&#187;</a><a name="notes">furthest-site qvoronoi
+notes</a></h3>
+<blockquote>
+
+<p>See <a href="qvoronoi.htm#notes">Voronoi notes</a>.</p>
+
+</blockquote>
+<h3><a href="#TOP">&#187;</a><a name="conventions">furthest-site qvoronoi conventions</a></h3>
+<blockquote>
+
+<p>The following terminology is used for furthest-site Voronoi
+diagrams in Qhull. The underlying structure is a furthest-site
+Delaunay triangulation from a convex hull in one higher
+dimension. Upper facets of the Delaunay triangulation correspond
+to vertices of the furthest-site Voronoi diagram. Vertices of the
+furthest-site Delaunay triangulation correspond to input sites.
+They also define regions of the furthest-site Voronoi diagram.
+All vertices are extreme points of the input sites. See <a
+href="qconvex.htm#conventions">qconvex conventions</a>, <a
+href="qdelau_f.htm#conventions">furthest-site delaunay
+conventions</a>, and <a href="index.htm#structure">Qhull's data structures</a>.</p>
+
+<ul>
+    <li><em>input site</em> - a point in the input (one dimension
+        lower than a point on the convex hull)</li>
+    <li><em>point</em> - a point has <i>d+1</i> coordinates. The
+        last coordinate is the sum of the squares of the input
+        site's coordinates</li>
+    <li><em>vertex</em> - a point on the upper facets of the
+        paraboloid. It corresponds to a unique input site. </li>
+    <li><em>furthest-site Delaunay facet</em> - an upper facet of the
+        paraboloid. The last coefficient of its normal is
+                clearly positive.</li>
+    <li><em>furthest-site Voronoi vertex</em> - the circumcenter
+        of a furthest-site Delaunay facet</li>
+    <li><em>furthest-site Voronoi region</em> - the region of
+        Euclidean space further from an input site than any other
+        input site. Qhull lists the furthest-site Voronoi
+        vertices that define each furthest-site Voronoi region.</li>
+    <li><em>furthest-site Voronoi diagram</em> - the graph of the
+        furthest-site Voronoi regions with the ridges (edges)
+        between the regions.</li>
+    <li><em>infinity vertex</em> - the Voronoi vertex for
+        unbounded furthest-site Voronoi regions in '<a
+        href="qh-opto.htm#o">o</a>' output format. Its
+        coordinates are <em>-10.101</em>.</li>
+    <li><em>good facet</em> - an furthest-site Voronoi vertex with
+        optional restrictions by '<a href="qh-optq.htm#QVn">QVn</a>',
+        etc.</li>
+</ul>
+
+</blockquote>
+<h3><a href="#TOP">&#187;</a><a name="options">furthest-site qvoronoi options</a></h3>
+<blockquote>
+
+See <a href="qvoronoi.htm#options">qvoronoi options</a>.    The same
+program is used for both constructions.  Use option '<a href="qh-optq.htm#Qu">Qu</a>'
+for furthest-site Voronoi diagrams.
+</blockquote>
+
+<!-- Navigation links -->
+<hr>
+
+<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
+<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
+<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
+&#149; <a href="qh-quick.htm#options">Options</a>
+&#149; <a href="qh-opto.htm#output">Output</a>
+&#149; <a href="qh-optf.htm#format">Formats</a>
+&#149; <a href="qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="qh-optp.htm#print">Print</a>
+&#149; <a href="qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="qh-optc.htm#prec">Precision</a>
+&#149; <a href="qh-optt.htm#trace">Trace</a>
+&#149; <a href="../src/libqhull_r/index.htm">Functions</a><br>
+<b>To:</b> <a href="#synopsis">sy</a>nopsis
+&#149; <a href="#input">in</a>put &#149; <a href="#outputs">ou</a>tputs
+&#149; <a href="#controls">co</a>ntrols &#149; <a href="#graphics">gr</a>aphics
+&#149; <a href="#notes">no</a>tes &#149; <a href="#conventions">co</a>nventions
+&#149; <a href="#options">op</a>tions
+<!-- GC common information -->
+<hr>
+
+<p><a href="http://www.geom.uiuc.edu/"><img src="qh--geom.gif"
+align="middle" width="40" height="40"></a><i>The Geometry Center
+Home Page </i></p>
+
+<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
+</a><br>
+Created: Sept. 25, 1995 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
+</body>
+</html>
diff --git a/xs/src/qhull/html/qvoronoi.htm b/xs/src/qhull/html/qvoronoi.htm
new file mode 100644
index 0000000000..6d81d48c15
--- /dev/null
+++ b/xs/src/qhull/html/qvoronoi.htm
@@ -0,0 +1,667 @@
+<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN">
+<html>
+
+<head>
+<title>qvoronoi -- Voronoi diagram</title>
+</head>
+
+<body>
+<!-- Navigation links -->
+<a name="TOP"><b>Up</b></a><b>:</b>
+<a href="http://www.qhull.org">Home page</a> for Qhull<br>
+<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
+<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
+&#149; <a href="qh-quick.htm#options">Options</a>
+&#149; <a href="qh-opto.htm#output">Output</a>
+&#149; <a href="qh-optf.htm#format">Formats</a>
+&#149; <a href="qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="qh-optp.htm#print">Print</a>
+&#149; <a href="qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="qh-optc.htm#prec">Precision</a>
+&#149; <a href="qh-optt.htm#trace">Trace</a>
+&#149; <a href="../src/libqhull_r/index.htm">Functions</a><br>
+<b>To:</b> <a href="#synopsis">sy</a>nopsis
+&#149; <a href="#input">in</a>put &#149; <a href="#outputs">ou</a>tputs
+&#149; <a href="#controls">co</a>ntrols &#149; <a href="#graphics">gr</a>aphics
+&#149; <a href="#notes">no</a>tes &#149; <a href="#conventions">co</a>nventions
+&#149; <a href="#options">op</a>tions
+
+<hr>
+<!-- Main text of document -->
+<h1><a
+href="http://www.archinect.com/gallery/displayimage.php?pos=-4658"><img
+src="normal_voronoi_knauss_oesterle.jpg" alt="[voronoi]" align="middle"
+height="100"></a>qvoronoi -- Voronoi diagram</h1>
+
+<p>The Voronoi diagram is the nearest-neighbor map for a set of
+points.  Each region contains those points that are nearer
+one input site than any other input site.  It has many useful properties and applications. See the
+survey article by Aurenhammer [<a href="index.htm#aure91">'91</a>]
+and the detailed introduction by O'Rourke [<a
+href="index.htm#orou94">'94</a>]. The Voronoi diagram is the
+dual of the <a href=qdelaun.htm>Delaunay triangulation</a>. </p>
+
+<blockquote>
+<dl>
+    <dt><b>Example:</b> rbox 10 D3 | qvoronoi <a href="qh-opto.htm#s">s</a>
+        <a href="qh-opto.htm#o">o</a> <a href="qh-optt.htm#TO">TO
+        result</a></dt>
+    <dd>Compute the 3-d Voronoi diagram of 10 random points. Write a
+        summary to the console and the Voronoi vertices and
+        regions to 'result'. The first vertex of the result
+        indicates unbounded regions.</dd>
+
+    <dt>&nbsp;</dt>
+    <dt><b>Example:</b> rbox r y c G0.1 D2 | qvoronoi
+             <a href="qh-opto.htm#s">s</a>
+        <a href="qh-opto.htm#o">o</a> <a href="qh-optt.htm#TO">TO
+        result</a></dt>
+    <dd>Compute the 2-d Voronoi diagram of a triangle and a small
+        square. Write a
+        summary to the console and Voronoi vertices and regions
+        to 'result'. Report a single Voronoi vertex for
+        cocircular input sites. The first vertex of the result
+        indicates unbounded regions. The origin is the Voronoi
+        vertex for the square.</dd>
+
+    <dt>&nbsp;</dt>
+    <dt><b>Example:</b> rbox r y c G0.1 D2 | qvoronoi <a href="qh-optf.htm#Fv2">Fv</a>
+        <a href="qh-optt.htm#TO">TO result</a></dt>
+    <dd>Compute the 2-d Voronoi diagram of a triangle and a small
+        square. Write a
+        summary to the console and the Voronoi ridges to
+        'result'. Each ridge is the perpendicular bisector of a
+        pair of input sites. Vertex &quot;0&quot; indicates
+        unbounded ridges. Vertex &quot;8&quot; is the Voronoi
+        vertex for the square.</dd>
+
+    <dt>&nbsp;</dt>
+    <dt><b>Example:</b> rbox r y c G0.1 D2 | qvoronoi <a href="qh-optf.htm#Fi2">Fi</a></dt>
+    <dd>Print the bounded, separating hyperplanes for the 2-d Voronoi diagram of a
+              triangle and a small
+        square.  Note the four hyperplanes (i.e., lines) for Voronoi vertex
+                &quot;8&quot;.  It is at the origin.
+                </dd>
+</dl>
+</blockquote>
+
+<p>Qhull computes the Voronoi diagram via the <a href="qdelaun.htm">Delaunay
+triangulation</a>. Each Voronoi
+vertex is the circumcenter of a facet of the Delaunay
+triangulation. Each Voronoi region corresponds to a vertex (i.e., input site) of the
+Delaunay triangulation. </p>
+
+<p>Qhull outputs the Voronoi vertices for each Voronoi region. With
+option '<a href="qh-optf.htm#Fv2">Fv</a>',
+it lists all ridges of the Voronoi diagram with the corresponding
+pairs of input sites. With
+options '<a href="qh-optf.htm#Fi2">Fi</a>' and '<a href="qh-optf.htm#Fo2">Fo</a>',
+it lists the bounded and unbounded separating hyperplanes.
+You can also output a single Voronoi region
+for further processing [see <a href="#graphics">graphics</a>].</p>
+
+<p>Use option '<a href="qh-optq.htm#Qz">Qz</a>' if the input is circular, cospherical, or
+nearly so.  It improves precision by adding a point "at infinity," above the corresponding paraboloid.
+
+<p>See <a href="http://www.qhull.org/html/qh-faq.htm#TOC">Qhull FAQ</a> - Delaunay and
+Voronoi diagram questions.</p>
+
+<p>The 'qvonoroi' program is equivalent to
+'<a href=qhull.htm#outputs>qhull v</a> <a href=qh-optq.htm#Qbb>Qbb</a>' in 2-d to 3-d, and
+'<a href=qhull.htm#outputs>qhull v</a> <a href=qh-optq.htm#Qbb>Qbb</a> <a href=qh-optq.htm#Qx>Qx</a>'
+in 4-d and higher.  It disables the following Qhull
+<a href=qh-quick.htm#options>options</a>: <i>d n v Qbb QbB Qf Qg Qm
+Qr QR Qv Qx Qz TR E V Fa FA FC FD FS Ft FV Gt Q0,etc</i>.
+
+<p><b>Copyright &copy; 1995-2015 C.B. Barber</b></p>
+
+<p>Voronoi image by KOOK Architecture, Silvan Oesterle and Michael Knauss.
+
+<hr>
+<h3><a href="#TOP">&#187;</a><a name="synopsis">qvoronoi synopsis</a></h3>
+
+<pre>
+qvoronoi- compute the Voronoi diagram.
+    input (stdin): dimension, number of points, point coordinates
+    comments start with a non-numeric character
+
+options (qh-voron.htm):
+    Qu   - compute furthest-site Voronoi diagram
+    Tv   - verify result: structure, convexity, and in-circle test
+    .    - concise list of all options
+    -    - one-line description of all options
+
+output options (subset):
+    s    - summary of results (default)
+    p    - Voronoi vertices
+    o    - OFF file format (dim, Voronoi vertices, and Voronoi regions)
+    FN   - count and Voronoi vertices for each Voronoi region
+    Fv   - Voronoi diagram as Voronoi vertices between adjacent input sites
+    Fi   - separating hyperplanes for bounded regions, 'Fo' for unbounded
+    G    - Geomview output (2-d only)
+    QVn  - Voronoi vertices for input point n, -n if not
+    TO file- output results to file, may be enclosed in single quotes
+
+examples:
+rbox c P0 D2 | qvoronoi s o         rbox c P0 D2 | qvoronoi Fi
+rbox c P0 D2 | qvoronoi Fo          rbox c P0 D2 | qvoronoi Fv
+rbox c P0 D2 | qvoronoi s Qu Fv     rbox c P0 D2 | qvoronoi Qu Fo
+rbox c G1 d D2 | qvoronoi s p       rbox c P0 D2 | qvoronoi s Fv QV0
+</pre>
+
+<h3><a href="#TOP">&#187;</a><a name="input">qvoronoi input</a></h3>
+<blockquote>
+The input data on <tt>stdin</tt> consists of:
+<ul>
+    <li>dimension
+    <li>number of points</li>
+    <li>point coordinates</li>
+</ul>
+
+<p>Use I/O redirection (e.g., qvoronoi &lt; data.txt), a pipe (e.g., rbox 10 | qvoronoi),
+or the '<a href=qh-optt.htm#TI>TI</a>' option (e.g., qvoronoi TI data.txt).
+
+<p>For example, this is four cocircular points inside a square.  Their Voronoi
+diagram has nine vertices and eight regions.  Notice the Voronoi vertex
+at the origin, and the Voronoi vertices (on each axis) for the four
+sides of the square.
+<p>
+<blockquote>
+<tt>rbox s 4 W0 c G1 D2 &gt; data</tt>
+<blockquote><pre>
+2 RBOX s 4 W0 c D2
+8
+-0.4941988586954018 -0.07594397977563715
+-0.06448037284989526 0.4958248496365813
+0.4911154367094632 0.09383830681375946
+-0.348353580869097 -0.3586778257652367
+    -1     -1
+    -1      1
+     1     -1
+     1      1
+</pre></blockquote>
+
+<p><tt>qvoronoi s p &lt; data</tt>
+<blockquote><pre>
+
+Voronoi diagram by the convex hull of 8 points in 3-d:
+
+  Number of Voronoi regions: 8
+  Number of Voronoi vertices: 9
+  Number of non-simplicial Voronoi vertices: 1
+
+Statistics for: RBOX s 4 W0 c D2 | QVORONOI s p
+
+  Number of points processed: 8
+  Number of hyperplanes created: 18
+  Number of facets in hull: 10
+  Number of distance tests for qhull: 33
+  Number of merged facets: 2
+  Number of distance tests for merging: 102
+  CPU seconds to compute hull (after input): 0.094
+
+2
+9
+4.217546450968612e-17 1.735507986399734
+-8.402566836762659e-17 -1.364368854147395
+0.3447488772716865 -0.6395484723719818
+1.719446929853986 2.136555906154247e-17
+0.4967882915039657 0.68662371396699
+-1.729928876283549 1.343733067524222e-17
+-0.8906163241424728 -0.4594150543829102
+-0.6656840313875723 0.5003013793414868
+-7.318364664277155e-19 -1.188217818408333e-16
+</pre></blockquote>
+</blockquote>
+
+</blockquote>
+<h3><a href="#TOP">&#187;</a> <a name="outputs">qvoronoi
+outputs</a></h3>
+<blockquote>
+
+<p>These options control the output of Voronoi diagrams.</p>
+<blockquote>
+
+<dl compact>
+    <dt>&nbsp;</dt>
+    <dd><b>Voronoi vertices</b></dd>
+    <dt><a href="qh-opto.htm#p">p</a></dt>
+    <dd>print the coordinates of the Voronoi vertices.  The first line
+        is the dimension.  The second line is the number of vertices.  Each
+        remaining line is a Voronoi vertex.</dd>
+    <dt><a href="qh-optf.htm#Fn">Fn</a></dt>
+    <dd>list the neighboring Voronoi vertices for each Voronoi
+        vertex.  The first line is the number of Voronoi vertices.  Each
+                remaining line starts with the number of neighboring vertices.
+                Negative vertices (e.g., <em>-1</em>) indicate vertices
+        outside of the Voronoi diagram.
+     In the circle-in-box example, the
+                Voronoi vertex at the origin has four neighbors.</dd>
+    <dt><a href="qh-optf.htm#FN">FN</a></dt>
+    <dd>list the Voronoi vertices for each Voronoi region.  The first line is
+        the number of Voronoi regions.  Each remaining line starts with the
+        number of Voronoi vertices.  Negative indices (e.g., <em>-1</em>) indicate vertices
+        outside of the Voronoi diagram.
+        In the circle-in-box example, the four bounded regions are defined by four
+        Voronoi vertices.</dd>
+
+    <dt>&nbsp;</dt>
+    <dt>&nbsp;</dt>
+    <dd><b>Voronoi regions</b></dd>
+    <dt><a href="qh-opto.htm#o">o</a></dt>
+    <dd>print the Voronoi regions in OFF format.  The first line is the
+        dimension.  The second line is the number of vertices, the number
+        of input sites, and "1".  The third line represents the vertex-at-infinity.
+        Its coordinates are "-10.101".  The next lines are the coordinates
+        of the Voronoi vertices.  Each remaining line starts with the number
+        of Voronoi vertices in a Voronoi region.  In 2-d, the vertices are
+listed in adjacency order (unoriented). In 3-d and higher, the
+vertices are listed in numeric order.  In the circle-in-square
+        example, each bounded region includes the Voronoi vertex at
+        the origin.  Lines consisting of <em>0</em> indicate
+        coplanar input sites or '<a href="qh-optq.htm#Qz">Qz</a>'.  </dd>
+    <dt><a href="qh-optf.htm#Fi2">Fi</a></dt>
+    <dd>print separating hyperplanes for inner, bounded Voronoi
+        regions.  The first number is the number of separating
+                hyperplanes.  Each remaining line starts with <i>3+dim</i>.  The
+                next two numbers are adjacent input sites.  The next <i>dim</i>
+                numbers are the coefficients of the separating hyperplane.  The
+                last number is its offset.  Use '<a href="qh-optt.htm#Tv">Tv</a>' to verify that the
+hyperplanes are perpendicular bisectors. It will list relevant
+statistics to stderr. </dd>
+    <dt><a href="qh-optf.htm#Fo2">Fo</a></dt>
+    <dd>print separating hyperplanes for outer, unbounded Voronoi
+        regions.  The first number is the number of separating
+                hyperplanes.  Each remaining line starts with <i>3+dim</i>.  The
+                next two numbers are adjacent input sites on the convex hull.  The
+                next <i>dim</i>
+                numbers are the coefficients of the separating hyperplane.  The
+                last number is its offset.  Use '<a href="qh-optt.htm#Tv">Tv</a>' to verify that the
+hyperplanes are perpendicular bisectors. It will list relevant
+statistics to stderr,</dd>
+    <dt>&nbsp;</dt>
+    <dt>&nbsp;</dt>
+    <dd><b>Input sites</b></dd>
+    <dt><a href="qh-optf.htm#Fv2">Fv</a></dt>
+    <dd>list ridges of Voronoi vertices for pairs of input sites.  The
+        first line is the number of ridges.  Each remaining line starts with
+        two plus the number of Voronoi vertices in the ridge.  The next
+        two numbers are two adjacent input sites.  The remaining numbers list
+        the Voronoi vertices.  As with option 'o', a <em>0</em> indicates
+        the vertex-at-infinity
+        and an unbounded, separating hyperplane.
+        The perpendicular bisector (separating hyperplane)
+        of the input sites is a flat through these vertices.
+        In the circle-in-square example, the ridge for each edge of the square
+        is unbounded.</dd>
+    <dt><a href="qh-optf.htm#Fc">Fc</a></dt>
+    <dd>list coincident input sites for each Voronoi vertex.
+        The first line is the number of vertices.  The remaining lines start with
+        the number of coincident sites and deleted vertices.  Deleted vertices
+        indicate highly degenerate input (see'<a href="qh-optf.htm#Fs">Fs</a>').
+        A coincident site is assigned to one Voronoi
+        vertex.  Do not use '<a href="qh-optq.htm#QJn">QJ</a>' with 'Fc'; the joggle will separate
+        coincident sites.</dd>
+    <dt><a href="qh-optf.htm#FP">FP</a></dt>
+    <dd>print coincident input sites with distance to
+        nearest site (i.e., vertex). The first line is the
+        number of coincident sites.  Each remaining line starts with the point ID of
+        an input site, followed by the point ID of a coincident point, its vertex, and distance.
+        Includes deleted vertices which
+        indicate highly degenerate input (see'<a href="qh-optf.htm#Fs">Fs</a>').
+        Do not use '<a href="qh-optq.htm#QJn">QJ</a>' with 'FP'; the joggle will separate
+        coincident sites.</dd>
+    <dt>&nbsp;</dt>
+    <dt>&nbsp;</dt>
+    <dd><b>General</b></dd>
+    <dt><a href="qh-opto.htm#s">s</a></dt>
+    <dd>print summary of the Voronoi diagram. Use '<a
+        href="qh-optf.htm#Fs">Fs</a>' for numeric data.</dd>
+    <dt><a href="qh-opto.htm#i">i</a></dt>
+    <dd>list input sites for each <a href=qdelaun.htm>Delaunay region</a>.  Use option '<a href="qh-optp.htm#Pp">Pp</a>'
+        to avoid the warning.  The first line is the number of regions.  The
+        remaining lines list the input sites for each region.  The regions are
+        oriented.  In the circle-in-square example, the cocircular region has four
+        edges.  In 3-d and higher, report cospherical sites by adding extra points.
+        </dd>
+    <dt><a href="qh-optg.htm#G">G</a></dt>
+    <dd>Geomview output for 2-d Voronoi diagrams.</dd>
+        </dl>
+</blockquote>
+</blockquote>
+<h3><a href="#TOP">&#187;</a> <a name="controls">qvoronoi
+controls</a></h3>
+<blockquote>
+
+<p>These options provide additional control:</p>
+<blockquote>
+
+<dl compact>
+   <dt><a href="qh-optq.htm#Qu">Qu</a></dt>
+    <dd>compute the <a href="qvoron_f.htm">furthest-site Voronoi diagram</a>.</dd>
+    <dt><a href="qh-optq.htm#QVn">QVn</a></dt>
+    <dd>select Voronoi vertices for input site <em>n</em> </dd>
+    <dt><a href="qh-optq.htm#Qz">Qz</a></dt>
+    <dd>add a point above the paraboloid to reduce precision
+        errors. Use it for nearly cocircular/cospherical input
+        (e.g., 'rbox c | qvoronoi Qz').</dd>
+    <dt><a href="qh-optt.htm#Tv">Tv</a></dt>
+    <dd>verify result</dd>
+    <dt><a href="qh-optt.htm#TO">TI file</a></dt>
+    <dd>input data from file.  The filename may not use spaces or quotes.</dd>
+    <dt><a href="qh-optt.htm#TO">TO file</a></dt>
+    <dd>output results to file.  Use single quotes if the filename
+        contains spaces (e.g., <tt>TO 'file with spaces.txt'</tt></dd>
+    <dt><a href="qh-optt.htm#TFn">TFn</a></dt>
+    <dd>report progress after constructing <em>n</em> facets</dd>
+    <dt><a href="qh-optp.htm#PDk">PDk:1</a></dt>
+    <dd>include upper and lower facets in the output.  Set <em>k</em>
+        to the last dimension (e.g., 'PD2:1' for 2-d inputs). </dd>
+    <dt><a href="qh-opto.htm#f">f </a></dt>
+    <dd>facet dump.  Print the data structure for each facet (i.e.,
+        Voronoi vertex).</dd>
+</dl>
+
+</blockquote>
+</blockquote>
+<h3><a href="#TOP">&#187;</a> <a name="graphics">qvoronoi
+graphics</a></h3>
+<blockquote>
+
+<p>In 2-d, Geomview output ('<a href="qh-optg.htm#G">G</a>')
+displays a Voronoi diagram with extra edges to close the
+unbounded Voronoi regions. To view the unbounded rays, enclose
+the input points in a square.</p>
+
+<p>You can also view <i>individual</i> Voronoi regions in 3-d. To
+view the Voronoi region for site 3 in Geomview, execute</p>
+
+<blockquote>
+    <p>qvoronoi &lt;data <a href="qh-optq.htm#QVn">QV3</a> <a
+    href="qh-opto.htm#p">p</a> | qconvex s G &gt;output</p>
+</blockquote>
+
+<p>The <tt>qvoronoi</tt> command returns the Voronoi vertices
+for input site 3.  The <tt>qconvex</tt> command computes their convex hull.
+This is the Voronoi region for input site 3.  Its
+hyperplane normals (qconvex 'n') are the same as the separating hyperplanes
+from options '<a href="qh-optf.htm#Fi">Fi</a>'
+and '<a href="qh-optf.htm#Fo">Fo</a>' (up to roundoff error).
+
+<p>See the <a href="qh-eg.htm#delaunay">Delaunay and Voronoi
+examples</a> for 2-d and 3-d examples. Turn off normalization (on
+Geomview's 'obscure' menu) when comparing the Voronoi diagram
+with the corresponding Delaunay triangulation. </p>
+
+</blockquote>
+<h3><a href="#TOP">&#187;</a><a name="notes">qvoronoi
+notes</a></h3>
+<blockquote>
+
+<p>You can simplify the Voronoi diagram by enclosing the input
+sites in a large square or cube.  This is particularly recommended
+for cocircular or cospherical input data.</p>
+
+<p>See <a href="#graphics">Voronoi graphics</a> for computing
+the convex hull of a Voronoi region. </p>
+
+<p>Voronoi diagrams do not include facets that are
+coplanar with the convex hull of the input sites.  A facet is
+coplanar if the last coefficient of its normal is
+nearly zero (see <a href="../src/user.h#ZEROdelaunay">qh_ZEROdelaunay</a>).
+
+<p>Unbounded regions can be confusing. For example, '<tt>rbox c |
+qvoronoi Qz o</tt>' produces the Voronoi regions for the vertices
+of a cube centered at the origin. All regions are unbounded. The
+output is </p>
+
+<blockquote>
+    <pre>3
+2 9 1
+-10.101 -10.101 -10.101
+     0      0      0
+2 0 1
+2 0 1
+2 0 1
+2 0 1
+2 0 1
+2 0 1
+2 0 1
+2 0 1
+0
+</pre>
+</blockquote>
+
+<p>The first line is the dimension. The second line is the number
+of vertices and the number of regions. There is one region per
+input point plus a region for the point-at-infinity added by
+option '<a href="qh-optq.htm#Qz">Qz</a>'. The next two lines
+lists the Voronoi vertices. The first vertex is the infinity
+vertex. It is indicate by the coordinates <em>-10.101</em>. The
+second vertex is the origin. The next nine lines list the
+regions. Each region lists two vertices -- the infinity vertex
+and the origin. The last line is &quot;0&quot; because no region
+is associated with the point-at-infinity. A &quot;0&quot; would
+also be listed for nearly incident input sites. </p>
+
+<p>To use option '<a href="qh-optf.htm#Fv">Fv</a>', add an
+interior point. For example, </p>
+
+<blockquote>
+    <pre>
+rbox c P0 | qvoronoi Fv
+20
+5 0 7 1 3 5
+5 0 3 1 4 5
+5 0 5 1 2 3
+5 0 1 1 2 4
+5 0 6 2 3 6
+5 0 2 2 4 6
+5 0 4 4 5 6
+5 0 8 5 3 6
+5 1 2 0 2 4
+5 1 3 0 1 4
+5 1 5 0 1 2
+5 2 4 0 4 6
+5 2 6 0 2 6
+5 3 4 0 4 5
+5 3 7 0 1 5
+5 4 8 0 6 5
+5 5 6 0 2 3
+5 5 7 0 1 3
+5 6 8 0 6 3
+5 7 8 0 3 5
+</pre>
+</blockquote>
+
+<p>The output consists of 20 ridges and each ridge lists a pair
+of input sites and a triplet of Voronoi vertices. The first eight
+ridges connect the origin ('P0'). The remainder list the edges of
+the cube. Each edge generates an unbounded ray through the
+midpoint. The corresponding separating planes ('Fo') follow each
+pair of coordinate axes. </p>
+
+<p>Options '<a href="qh-optq.htm#Qt">Qt</a>' (triangulated output)
+and '<a href="qh-optq.htm#QJn">QJ</a>' (joggled input) are deprecated.  They may produce
+unexpected results.   If you use these options, cocircular and cospherical input sites will
+produce duplicate or nearly duplicate Voronoi vertices.  See also <a
+href="qh-impre.htm#joggle">Merged facets or joggled input</a>. </p>
+
+</blockquote>
+<h3><a href="#TOP">&#187;</a><a name="conventions">qvoronoi conventions</a></h3>
+<blockquote>
+
+<p>The following terminology is used for Voronoi diagrams in
+Qhull. The underlying structure is a Delaunay triangulation from
+a convex hull in one higher dimension. Facets of the Delaunay
+triangulation correspond to vertices of the Voronoi diagram.
+Vertices of the Delaunay triangulation correspond to input sites.
+They also correspond to regions of the Voronoi diagram. See <a
+href="qconvex.htm#conventions">convex hull conventions</a>, <a
+href="qdelaun.htm#conventions">Delaunay conventions</a>, and
+<a href="index.htm#structure">Qhull's data structures</a>.</p>
+<blockquote>
+
+<ul>
+    <li><em>input site</em> - a point in the input (one dimension
+        lower than a point on the convex hull)</li>
+    <li><em>point</em> - a point has <i>d+1</i> coordinates. The
+        last coordinate is the sum of the squares of the input
+        site's coordinates</li>
+    <li><em>coplanar point</em> - a <em>nearly incident</em>
+        input site</li>
+    <li><em>vertex</em> - a point on the paraboloid. It
+        corresponds to a unique input site. </li>
+    <li><em>point-at-infinity</em> - a point added above the
+        paraboloid by option '<a href="qh-optq.htm#Qz">Qz</a>'</li>
+    <li><em>Delaunay facet</em> - a lower facet of the
+        paraboloid. The last coefficient of its normal is
+                clearly negative.</li>
+    <li><em>Voronoi vertex</em> - the circumcenter of a Delaunay
+        facet</li>
+    <li><em>Voronoi region</em> - the Voronoi vertices for an
+        input site. The region of Euclidean space nearest to an
+        input site.</li>
+    <li><em>Voronoi diagram</em> - the graph of the Voronoi
+        regions. It includes the ridges (i.e., edges) between the
+        regions.</li>
+    <li><em>vertex-at-infinity</em> - the Voronoi vertex that
+        indicates unbounded Voronoi regions in '<a
+        href="qh-opto.htm#o">o</a>' output format. Its
+        coordinates are <em>-10.101</em>.</li>
+    <li><em>good facet</em> - a Voronoi vertex with optional
+        restrictions by '<a href="qh-optq.htm#QVn">QVn</a>', etc.</li>
+</ul>
+
+</blockquote>
+</blockquote>
+<h3><a href="#TOP">&#187;</a><a name="options">qvoronoi options</a></h3>
+
+<pre>
+qvoronoi- compute the Voronoi diagram
+    http://www.qhull.org
+
+input (stdin):
+    first lines: dimension and number of points (or vice-versa).
+    other lines: point coordinates, best if one point per line
+    comments:    start with a non-numeric character
+
+options:
+    Qu   - compute furthest-site Voronoi diagram
+
+Qhull control options:
+    QJn  - randomly joggle input in range [-n,n]
+    Qs   - search all points for the initial simplex
+    Qz   - add point-at-infinity to Voronoi diagram
+    QGn  - Voronoi vertices if visible from point n, -n if not
+    QVn  - Voronoi vertices for input point n, -n if not
+
+Trace options:
+    T4   - trace at level n, 4=all, 5=mem/gauss, -1= events
+    Tc   - check frequently during execution
+    Ts   - statistics
+    Tv   - verify result: structure, convexity, and in-circle test
+    Tz   - send all output to stdout
+    TFn  - report summary when n or more facets created
+    TI file - input data from file, no spaces or single quotes
+    TO file - output results to file, may be enclosed in single quotes
+    TPn  - turn on tracing when point n added to hull
+     TMn - turn on tracing at merge n
+     TWn - trace merge facets when width > n
+    TVn  - stop qhull after adding point n, -n for before (see TCn)
+     TCn - stop qhull after building cone for point n (see TVn)
+
+Precision options:
+    Cn   - radius of centrum (roundoff added).  Merge facets if non-convex
+     An  - cosine of maximum angle.  Merge facets if cosine > n or non-convex
+           C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge
+    Rn   - randomly perturb computations by a factor of [1-n,1+n]
+    Wn   - min facet width for non-coincident point (before roundoff)
+
+Output formats (may be combined; if none, produces a summary to stdout):
+    s    - summary to stderr
+    p    - Voronoi vertices
+    o    - OFF format (dim, Voronoi vertices, and Voronoi regions)
+    i    - Delaunay regions (use 'Pp' to avoid warning)
+    f    - facet dump
+
+More formats:
+    Fc   - count plus coincident points (by Voronoi vertex)
+    Fd   - use cdd format for input (homogeneous with offset first)
+    FD   - use cdd format for output (offset first)
+    FF   - facet dump without ridges
+    Fi   - separating hyperplanes for bounded Voronoi regions
+    FI   - ID for each Voronoi vertex
+    Fm   - merge count for each Voronoi vertex (511 max)
+    Fn   - count plus neighboring Voronoi vertices for each Voronoi vertex
+    FN   - count and Voronoi vertices for each Voronoi region
+    Fo   - separating hyperplanes for unbounded Voronoi regions
+    FO   - options and precision constants
+    FP   - nearest point and distance for each coincident point
+    FQ   - command used for qvoronoi
+    Fs   - summary: #int (8), dimension, #points, tot vertices, tot facets,
+                    for output: #Voronoi regions, #Voronoi vertices,
+                                #coincident points, #non-simplicial regions
+                    #real (2), max outer plane and min vertex
+    Fv   - Voronoi diagram as Voronoi vertices between adjacent input sites
+    Fx   - extreme points of Delaunay triangulation (on convex hull)
+
+Geomview options (2-d only)
+    Ga   - all points as dots
+     Gp  -  coplanar points and vertices as radii
+     Gv  -  vertices as spheres
+    Gi   - inner planes only
+     Gn  -  no planes
+     Go  -  outer planes only
+    Gc   - centrums
+    Gh   - hyperplane intersections
+    Gr   - ridges
+    GDn  - drop dimension n in 3-d and 4-d output
+
+Print options:
+    PAn  - keep n largest Voronoi vertices by 'area'
+    Pdk:n - drop facet if normal[k] &lt;= n (default 0.0)
+    PDk:n - drop facet if normal[k] >= n
+    Pg   - print good Voronoi vertices (needs 'QGn' or 'QVn')
+    PFn  - keep Voronoi vertices whose 'area' is at least n
+    PG   - print neighbors of good Voronoi vertices
+    PMn  - keep n Voronoi vertices with most merges
+    Po   - force output.  If error, output neighborhood of facet
+    Pp   - do not report precision problems
+
+    .    - list of all options
+    -    - one line descriptions of all options
+</pre>
+
+<!-- Navigation links -->
+<hr>
+
+<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
+<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
+<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
+&#149; <a href="qh-quick.htm#options">Options</a>
+&#149; <a href="qh-opto.htm#output">Output</a>
+&#149; <a href="qh-optf.htm#format">Formats</a>
+&#149; <a href="qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="qh-optp.htm#print">Print</a>
+&#149; <a href="qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="qh-optc.htm#prec">Precision</a>
+&#149; <a href="qh-optt.htm#trace">Trace</a>
+&#149; <a href="../src/libqhull_r/index.htm">Functions</a><br>
+<b>To:</b> <a href="#synopsis">sy</a>nopsis
+&#149; <a href="#input">in</a>put &#149; <a href="#outputs">ou</a>tputs
+&#149; <a href="#controls">co</a>ntrols &#149; <a href="#graphics">gr</a>aphics
+&#149; <a href="#notes">no</a>tes &#149; <a href="#conventions">co</a>nventions
+&#149; <a href="#options">op</a>tions
+<!-- GC common information -->
+<hr>
+
+<p><a href="http://www.geom.uiuc.edu/"><img src="qh--geom.gif"
+align="middle" width="40" height="40"></a><i>The Geometry Center
+Home Page </i></p>
+
+<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
+</a><br>
+Created: Sept. 25, 1995 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
+</body>
+</html>
diff --git a/xs/src/qhull/html/rbox.htm b/xs/src/qhull/html/rbox.htm
new file mode 100644
index 0000000000..9c28face56
--- /dev/null
+++ b/xs/src/qhull/html/rbox.htm
@@ -0,0 +1,277 @@
+<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN">
+<html>
+
+<head>
+<title>rbox -- generate point distributions</title>
+</head>
+
+<body>
+<!-- Navigation links -->
+<p><b><a name="TOP">Up:</a></b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
+<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
+<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
+&#149; <a href="qh-quick.htm#options">Options</a>
+&#149; <a href="qh-opto.htm#output">Output</a>
+&#149; <a href="qh-optf.htm#format">Formats</a>
+&#149; <a href="qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="qh-optp.htm#print">Print</a>
+&#149; <a href="qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="qh-optc.htm#prec">Precision</a>
+&#149; <a href="qh-optt.htm#trace">Trace</a>
+&#149; <a href="../src/libqhull_r/index.htm">Functions</a><br>
+<b>To:</b> <a href="#synopsis">sy</a>nopsis &#149; <a href="#outputs">ou</a>tputs
+&#149; <a href="#examples">ex</a>amples &#149; <a href="#notes">no</a>tes
+&#149; <a href="#options">op</a>tions
+<hr>
+<!-- Main text of document -->
+<h1><a
+href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/cone.html"><img
+src="qh--cone.gif" alt="[CONE]" align="middle" width="100"
+height="100"></a>rbox -- generate point distributions</h1>
+
+<blockquote>
+       rbox  generates  random or regular points according to the
+       options given, and  outputs  the  points  to  stdout.  The
+       points  are  generated in a cube, unless 's', 'x', or 'y'
+           are given.
+
+</blockquote>
+<h3><a href="#TOP">&#187;</a><a name="synopsis">rbox synopsis</a></h3>
+<pre>
+rbox- generate various point distributions.  Default is random in cube.
+
+args (any order, space separated):
+  3000    number of random points in cube, lens, spiral, sphere or grid
+  D3      dimension 3-d
+  c       add a unit cube to the output ('c G2.0' sets size)
+  d       add a unit diamond to the output ('d G2.0' sets size)
+  l       generate a regular 3-d spiral
+  r       generate a regular polygon, ('r s Z1 G0.1' makes a cone)
+  s       generate cospherical points
+  x       generate random points in simplex, may use 'r' or 'Wn'
+  y       same as 'x', plus simplex
+  Cn,r,m  add n nearly coincident points within radius r of m points
+  Pn,m,r  add point [n,m,r] first, pads with 0
+
+  Ln      lens distribution of radius n.  Also 's', 'r', 'G', 'W'.
+  Mn,m,r  lattice (Mesh) rotated by [n,-m,0], [m,n,0], [0,0,r], ...
+          '27 M1,0,1' is {0,1,2} x {0,1,2} x {0,1,2}.  Try 'M3,4 z'.
+  W0.1    random distribution within 0.1 of the cube's or sphere's surface
+  Z0.5 s  random points in a 0.5 disk projected to a sphere
+  Z0.5 s G0.6 same as Z0.5 within a 0.6 gap
+
+  Bn      bounding box coordinates, default 0.5
+  h       output as homogeneous coordinates for cdd
+  n       remove command line from the first line of output
+  On      offset coordinates by n
+  t       use time as the random number seed (default is command line)
+  tn      use n as the random number seed
+  z       print integer coordinates, default 'Bn' is 1e+06
+</pre>
+
+<h3><a href="#TOP">&#187;</a><a name="outputs">rbox outputs</a></h3>
+<blockquote>
+
+The format of the output is the following: first line contains
+       the dimension and a comment, second line contains the
+           number of points, and the following lines contain the points,
+       one  point per line. Points are represented by their coordinate values.
+
+<p>For example, <tt>rbox c 10 D2</tt> generates
+<blockquote>
+<pre>
+2 RBOX c 10 D2
+14
+-0.4999921736307369 -0.3684622117955817
+0.2556053225468894 -0.0413498678629751
+0.0327672376602583 -0.2810408135699488
+-0.452955383763607 0.17886471718444
+0.1792964061529342 0.4346928963760779
+-0.1164979223315585 0.01941637230982666
+0.3309653464993139 -0.4654278894564396
+-0.4465383649305798 0.02970019358182344
+0.1711493843897706 -0.4923018137852678
+-0.1165843490665633 -0.433157762450313
+  -0.5   -0.5
+  -0.5    0.5
+   0.5   -0.5
+   0.5    0.5
+</pre>
+
+</blockquote>
+
+</blockquote>
+<h3><a href="#TOP">&#187;</a><a name="examples">rbox examples</a></h3>
+
+<pre>
+       rbox 10
+              10 random points in the unit cube centered  at  the
+              origin.
+
+       rbox 10 s D2
+              10 random points on a 2-d circle.
+
+       rbox 100 W0
+              100 random points on the surface of a cube.
+
+       rbox 1000 s D4
+              1000 random points on a 4-d sphere.
+
+       rbox c D5 O0.5
+              a 5-d hypercube with one corner at the origin.
+
+       rbox d D10
+              a 10-d diamond.
+
+       rbox x 1000 r W0
+              100 random points on the surface of a fixed simplex
+
+       rbox y D12
+              a 12-d simplex.
+
+       rbox l 10
+              10 random points along a spiral
+
+       rbox l 10 r
+              10 regular points  along  a  spiral  plus  two  end
+              points
+
+       rbox 1000 L10000 D4 s
+              1000 random points on the surface of a narrow lens.
+
+           rbox 1000 L100000 s G1e-6
+                  1000 random points near the edge of a narrow lens
+
+       rbox c G2 d G3
+              a cube with coordinates +2/-2 and  a  diamond  with
+              coordinates +3/-3.
+
+       rbox 64 M3,4 z
+              a  rotated,  {0,1,2,3} x {0,1,2,3} x {0,1,2,3} lat-
+              tice (Mesh) of integer points.
+
+       rbox P0 P0 P0 P0 P0
+              5 copies of the origin in 3-d.  Try 'rbox P0 P0  P0
+              P0 P0 | qhull QJ'.
+
+       r 100 s Z1 G0.1
+              two  cospherical  100-gons plus another cospherical
+              point.
+
+       100 s Z1
+              a cone of points.
+
+       100 s Z1e-7
+              a narrow cone of points with many precision errors.
+</pre>
+
+<h3><a href="#TOP">&#187;</a><a name="notes">rbox notes</a></h3>
+<blockquote>
+Some combinations of arguments generate odd results.
+
+</blockquote>
+<h3><a href="#TOP">&#187;</a><a name="options">rbox options</a></h3>
+
+<pre>
+       n      number of points
+
+       Dn     dimension n-d (default 3-d)
+
+       Bn     bounding box coordinates (default 0.5)
+
+       l      spiral distribution, available only in 3-d
+
+       Ln     lens  distribution  of  radius n.  May be used with
+              's', 'r', 'G', and 'W'.
+
+       Mn,m,r lattice  (Mesh)  rotated  by  {[n,-m,0],   [m,n,0],
+              [0,0,r],  ...}.   Use  'Mm,n'  for a rigid rotation
+              with r = sqrt(n^2+m^2).  'M1,0'  is  an  orthogonal
+              lattice.   For  example,  '27  M1,0'  is  {0,1,2} x
+              {0,1,2} x {0,1,2}.
+
+       s      cospherical points randomly generated in a cube and
+              projected to the unit sphere
+
+       x      simplicial  distribution.   It  is fixed for option
+              'r'.  May be used with 'W'.
+
+       y      simplicial distribution plus a simplex.   Both  'x'
+              and 'y' generate the same points.
+
+       Wn     restrict  points  to distance n of the surface of a
+              sphere or a cube
+
+       c      add a unit cube to the output
+
+       c Gm   add a cube with all combinations of +m  and  -m  to
+              the output
+
+       d      add a unit diamond to the output.
+
+       d Gm   add a diamond made of 0, +m and -m to the output
+
+       Cn,r,m add n nearly coincident points within radius r of m points
+
+       Pn,m,r add point [n,m,r] to the output first.  Pad coordi-
+              nates with 0.0.
+
+       n      Remove the command line from the first line of out-
+              put.
+
+       On     offset the data by adding n to each coordinate.
+
+       t      use  time  in  seconds  as  the  random number seed
+              (default is command line).
+
+       tn     set the random number seed to n.
+
+       z      generate integer coordinates.  Use 'Bn'  to  change
+              the  range.   The  default  is 'B1e6' for six-digit
+              coordinates.  In R^4, seven-digit coordinates  will
+              overflow hyperplane normalization.
+
+       Zn s   restrict points to a disk about the z+ axis and the
+              sphere (default Z1.0).  Includes the opposite pole.
+              'Z1e-6'  generates  degenerate  points under single
+              precision.
+
+       Zn Gm s
+              same as Zn with an empty center (default G0.5).
+
+       r s D2 generate a regular polygon
+
+       r s Z1 G0.1
+              generate a regular cone
+</pre>
+
+<!-- Navigation links -->
+<hr>
+
+<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
+<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
+<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
+&#149; <a href="qh-quick.htm#options">Options</a>
+&#149; <a href="qh-opto.htm#output">Output</a>
+&#149; <a href="qh-optf.htm#format">Formats</a>
+&#149; <a href="qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="qh-optp.htm#print">Print</a>
+&#149; <a href="qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="qh-optc.htm#prec">Precision</a>
+&#149; <a href="qh-optt.htm#trace">Trace</a>
+&#149; <a href="../src/libqhull_r/index.htm">Functions</a><br>
+<b>To:</b> <a href="#synopsis">sy</a>nopsis &#149; <a href="#outputs">ou</a>tputs
+&#149; <a href="#examples">ex</a>amples &#149; <a href="#notes">no</a>tes
+&#149; <a href="#options">op</a>tions
+<!-- GC common information -->
+<hr>
+
+<p><a href="http://www.geom.uiuc.edu/"><img src="qh--geom.gif"
+align="middle" width="40" height="40"></a><i>The Geometry Center
+Home Page </i></p>
+
+<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
+<br>
+Created: Sept. 25, 1995 --- <!-- hhmts start --> Last modified: August 12, 1998 <!-- hhmts end --> </p>
+</body>
+</html>
diff --git a/xs/src/qhull/html/rbox.man b/xs/src/qhull/html/rbox.man
new file mode 100644
index 0000000000..3ea6395e69
--- /dev/null
+++ b/xs/src/qhull/html/rbox.man
@@ -0,0 +1,176 @@
+.\"  This is the Unix manual page for rbox, written in nroff, the standard
+.\"  manual formatter for Unix systems.  To format it, type
+.\"
+.\"  nroff -man rbox.man
+.\"
+.\"  This will print a formatted copy to standard output.  If you want
+.\"  to ensure that the output is plain ascii, free of any control
+.\"  characters that nroff uses for underlining etc, pipe the output
+.\"  through "col -b":
+.\"
+.\"  nroff -man rbox.man | col -b
+.\"
+.TH rbox 1 "August 10, 1998" "Geometry Center"
+.SH NAME
+rbox \- generate point distributions for qhull
+.SH SYNOPSIS
+Command "rbox" (w/o arguments) lists the options.
+.SH DESCRIPTION
+.PP
+rbox generates random or regular points according to the options given, and 
+outputs
+the points to stdout. The points are generated in a cube, unless 's' or  'k' 
+option is
+given. The format of the output is the following: first line
+contains the dimension and a comment, 
+second line contains the number of points, and the 
+following lines contain the points, one point per line. Points are represented
+by their coordinate values.
+.SH EXAMPLES
+.TP
+rbox 10
+10 random points in the unit cube centered at the origin.
+.TP
+rbox 10 s D2
+10 random points on a 2\[hy]d circle.
+.TP
+rbox 100 W0
+100 random points on the surface of a cube.
+.TP
+rbox 1000 s D4
+1000 random points on a 4\[hy]d sphere.
+.TP
+rbox c D5 O0.5
+a 5\[hy]d hypercube with one corner at the origin.
+.TP
+rbox d D10
+a 10\[hy]d diamond.
+.TP 
+rbox x 1000 r W0
+100 random points on the surface of a fixed simplex 
+.TP
+rbox y D12
+a 12\[hy]d simplex.
+.TP
+rbox l 10
+10 random points along a spiral
+.TP
+rbox l 10 r
+10 regular points along a spiral plus two end points
+.TP
+rbox 1000 L10000 D4 s
+1000 random points on the surface of a narrow lens.
+.TP
+rbox c G2 d G3
+a cube with coordinates +2/\-2 and a diamond with coordinates +3/\-3.
+.TP
+rbox 64 M3,4 z
+a rotated, {0,1,2,3} x {0,1,2,3} x {0,1,2,3} lattice (Mesh) of integer
+points. 'rbox 64 M1,0' is orthogonal.
+.TP
+rbox P0 P0 P0 P0 P0
+5 copies of the origin in 3\-d.  Try 'rbox P0 P0 P0 P0 P0 | qhull QJ'.
+.TP
+r 100 s Z1 G0.1
+two cospherical 100\-gons plus another cospherical point.
+.TP
+100 s Z1
+a cone of points.
+.TP 
+100 s Z1e\-7
+a narrow cone of points with many precision errors.
+.SH OPTIONS
+.TP
+n
+number of points
+.TP
+Dn
+dimension n\[hy]d (default 3\[hy]d)
+.TP
+Bn
+bounding box coordinates (default 0.5)
+.TP
+l
+spiral distribution, available only in 3\[hy]d
+.TP
+Ln
+lens distribution of radius n.  May be used with 's', 'r', 'G', and 'W'.
+.TP
+Mn,m,r
+lattice (Mesh) rotated by {[n,\-m,0], [m,n,0], [0,0,r], ...}.  
+Use 'Mm,n' for a rigid rotation with r = sqrt(n^2+m^2).  'M1,0' is an 
+orthogonal lattice.  For example, '27 M1,0' is {0,1,2} x {0,1,2} x 
+{0,1,2}. '27 M3,4 z' is a rotated integer lattice.
+.TP
+s
+cospherical points randomly generated in a cube and projected to the unit sphere
+.TP
+x
+simplicial distribution.  It is fixed for option 'r'.  May be used with 'W'.
+.TP
+y
+simplicial distribution plus a simplex.  Both 'x' and 'y' generate the same points.
+.TP
+Wn
+restrict points to distance n of the surface of a sphere or a cube
+.TP
+c
+add a unit cube to the output
+.TP
+c Gm
+add a cube with all combinations of +m and \-m to the output
+.TP
+d
+add a unit diamond to the output.
+.TP
+d Gm
+add a diamond made of 0, +m and \-m to the output
+.TP
+Cn,r,m  
+add n nearly coincident points within radius r of m points
+.TP
+Pn,m,r
+add point [n,m,r] to the output first.  Pad coordinates with 0.0.
+.TP
+n
+Remove the command line from the first line of output.
+.TP
+On
+offset the data by adding n to each coordinate.
+.TP
+t
+use time in seconds as the random number seed (default is command line).
+.TP
+tn
+set the random number seed to n.
+.TP
+z
+generate integer coordinates.  Use 'Bn' to change the range.  
+The default is 'B1e6' for six\[hy]digit coordinates.  In R^4, seven\[hy]digit
+coordinates will overflow hyperplane normalization.
+.TP
+Zn s
+restrict points to a disk about the z+ axis and the sphere (default Z1.0). 
+Includes the opposite pole.  'Z1e\-6' generates degenerate points under
+single precision.
+.TP
+Zn Gm s
+same as Zn with an empty center (default G0.5). 
+.TP
+r s D2
+generate a regular polygon
+.TP
+r s Z1 G0.1
+generate a regular cone
+.SH BUGS
+Some combinations of arguments generate odd results.
+
+Report bugs to qhull_bug@qhull.org, other correspondence to qhull@qhull.org 
+.SH SEE ALSO
+qhull(1)
+.SH AUTHOR
+.nf
+C. Bradford Barber
+bradb@shore.net
+.fi
+
diff --git a/xs/src/qhull/html/rbox.txt b/xs/src/qhull/html/rbox.txt
new file mode 100644
index 0000000000..e3cf721892
--- /dev/null
+++ b/xs/src/qhull/html/rbox.txt
@@ -0,0 +1,195 @@
+
+
+
+rbox(1)                                                   rbox(1)
+
+
+NAME
+       rbox - generate point distributions for qhull
+
+SYNOPSIS
+       Command "rbox" (w/o arguments) lists the options.
+
+DESCRIPTION
+       rbox  generates random or regular points according to the
+       options given, and  outputs  the  points  to  stdout.  The
+       points  are  generated in a cube, unless 's' or given. The
+       format of the output is the following: first line contains
+       the dimension and a comment, second line contains the num-
+       ber of points, and the following lines contain the points,
+       one  point per line. Points are represented by their coor-
+       dinate values.
+
+EXAMPLES
+       rbox 10
+              10 random points in the unit cube centered  at  the
+              origin.
+
+       rbox 10 s D2
+              10 random points on a 2-d circle.
+
+       rbox 100 W0
+              100 random points on the surface of a cube.
+
+       rbox 1000 s D4
+              1000 random points on a 4-d sphere.
+
+       rbox c D5 O0.5
+              a 5-d hypercube with one corner at the origin.
+
+       rbox d D10
+              a 10-d diamond.
+
+       rbox x 1000 r W0
+              100 random points on the surface of a fixed simplex
+
+       rbox y D12
+              a 12-d simplex.
+
+       rbox l 10
+              10 random points along a spiral
+
+       rbox l 10 r
+              10 regular points  along  a  spiral  plus  two  end
+              points
+
+       rbox 1000 L10000 D4 s
+              1000 random points on the surface of a narrow lens.
+
+       rbox c G2 d G3
+              a cube with coordinates +2/-2 and  a  diamond  with
+
+
+
+Geometry Center          August 10, 1998                        1
+
+
+
+
+
+rbox(1)                                                   rbox(1)
+
+
+              coordinates +3/-3.
+
+       rbox 64 M3,4 z
+              a  rotated,  {0,1,2,3} x {0,1,2,3} x {0,1,2,3} lat-
+              tice (Mesh) of integer points.
+
+       rbox P0 P0 P0 P0 P0
+              5 copies of the origin in 3-d.  Try 'rbox P0 P0  P0
+              P0 P0 | qhull QJ'.
+
+       r 100 s Z1 G0.1
+              two  cospherical  100-gons plus another cospherical
+              point.
+
+       100 s Z1
+              a cone of points.
+
+       100 s Z1e-7
+              a narrow cone of points with many precision errors.
+
+OPTIONS
+       n      number of points
+
+       Dn     dimension n-d (default 3-d)
+
+       Bn     bounding box coordinates (default 0.5)
+
+       l      spiral distribution, available only in 3-d
+
+       Ln     lens  distribution  of  radius n.  May be used with
+              's', 'r', 'G', and 'W'.
+
+       Mn,m,r lattice  (Mesh)  rotated  by  {[n,-m,0],   [m,n,0],
+              [0,0,r],  ...}.   Use  'Mm,n'  for a rigid rotation
+              with r = sqrt(n^2+m^2).  'M1,0'  is  an  orthogonal
+              lattice.   For  example,  '27  M1,0'  is  {0,1,2} x
+              {0,1,2} x {0,1,2}.
+
+       s      cospherical points randomly generated in a cube and
+              projected to the unit sphere
+
+       x      simplicial  distribution.   It  is fixed for option
+              'r'.  May be used with 'W'.
+
+       y      simplicial distribution plus a simplex.   Both  'x'
+              and 'y' generate the same points.
+
+       Wn     restrict  points  to distance n of the surface of a
+              sphere or a cube
+
+       c      add a unit cube to the output
+
+       c Gm   add a cube with all combinations of +m  and  -m  to
+              the output
+
+
+
+Geometry Center          August 10, 1998                        2
+
+
+
+
+
+rbox(1)                                                   rbox(1)
+
+
+       d      add a unit diamond to the output.
+
+       d Gm   add a diamond made of 0, +m and -m to the output
+       
+       Cn,r,m add n nearly coincident points within radius r of m points
+
+       Pn,m,r add point [n,m,r] to the output first.  Pad coordi-
+              nates with 0.0.
+
+       n      Remove the command line from the first line of out-
+              put.
+
+       On     offset the data by adding n to each coordinate.
+
+       t      use  time  in  seconds  as  the  random number seed
+              (default is command line).
+
+       tn     set the random number seed to n.
+
+       z      generate integer coordinates.  Use 'Bn'  to  change
+              the  range.   The  default  is 'B1e6' for six-digit
+              coordinates.  In R^4, seven-digit coordinates  will
+              overflow hyperplane normalization.
+
+       Zn s   restrict points to a disk about the z+ axis and the
+              sphere (default Z1.0).  Includes the opposite pole.
+              'Z1e-6'  generates  degenerate  points under single
+              precision.
+
+       Zn Gm s
+              same as Zn with an empty center (default G0.5).
+
+       r s D2 generate a regular polygon
+
+       r s Z1 G0.1
+              generate a regular cone
+
+BUGS
+       Some combinations of arguments generate odd results.
+
+       Report bugs to  qhull_bug@qhull.org,     other  correspon-
+       dence to qhull@qhull.org
+
+SEE ALSO
+       qhull(1)
+
+AUTHOR
+       C. Bradford Barber
+       bradb@shore.net
+       
+
+
+
+
+Geometry Center          August 10, 1998                        3
+
+
diff --git a/xs/src/qhull/index.htm b/xs/src/qhull/index.htm
new file mode 100644
index 0000000000..4ea7806c93
--- /dev/null
+++ b/xs/src/qhull/index.htm
@@ -0,0 +1,284 @@
+<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN">
+<html>
+
+<head>
+<title>Qhull code for Convex Hull, Delaunay Triangulation, Voronoi Diagram, and Halfspace Intersection about a Point</title>
+</head>
+
+<body>
+<!-- Navigation links -->
+<b>URL:</b> <a href="http://www.qhull.org">http://www.qhull.org</a>
+<br><b>To:</b>
+<a href="http://www.qhull.org/news">News</a>
+&#149; <a href="http://www.qhull.org/download">Download</a>
+&#149; <a href="http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.117.405">CiteSeer</a>
+&#149; <a href=http://images.google.com/images?q=qhull&num=100>Images</a>
+&#149; <a href="html/index.htm#TOC">Manual</a>
+&#149; <a href="http://www.qhull.org/html/qh-faq.htm">FAQ</a>
+&#149; <a href="html/qh-quick.htm#programs">Programs</a>
+&#149; <a href="html/qh-quick.htm#options">Options</a>
+</p>
+
+<hr>
+<!-- Main text of document -->
+<table>
+<tr><td valign=top>
+        <h1>Qhull</h1>
+        <a
+        href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/cone.html"><img
+        src="html/qh--cone.gif" alt="[CONE]" align="middle" width="100"
+        height="100"></a>
+</td><td>
+Qhull computes the convex hull, Delaunay triangulation, Voronoi diagram,
+halfspace intersection about a point, furthest-site Delaunay
+triangulation, and furthest-site Voronoi diagram. The source code runs in
+2-d, 3-d, 4-d, and higher dimensions. Qhull implements the Quickhull
+algorithm for computing the convex hull. It handles roundoff
+errors from floating point arithmetic. It computes volumes,
+surface areas, and approximations to the convex hull.</p>
+
+<!-- duplicated in index.htm and html/index.htm -->
+<p>Qhull does <i>not</i> support triangulation of non-convex surfaces, mesh
+generation of non-convex objects, medium-sized inputs in 9-D
+and higher, alpha shapes, weighted Voronoi diagrams, Voronoi volumes, or
+constrained Delaunay triangulations,  </p>
+
+<p>Qhull 2015.2 introduces reentrant Qhull.  It allows concurrent Qhull runs and simplifies the C++ interface to Qhull.
+If you call Qhull from your program, you should use reentrant Qhull (libqhull_r) instead of qh_QHpointer (libqhull).
+If you use Qhull 2003.1. please upgrade or apply <a href="http://www.qhull.org/download/poly.c-qh_gethash.patch">poly.c-qh_gethash.patch</a>.
+</p>
+</td></tr></table>
+
+<hr>
+<form method=get action=http://www.google.com/search>
+<input type=hidden name=sitesearch value=www.qhull.org>
+<input type=hidden name=num value=100>
+<ul>
+    <li><a href="http://www.qhull.org/news">News</a> and
+        <a href="http://www.qhull.org/news/qhull-news.html#bugs">Bugs</a>
+        about Qhull 2015.2  2016/01/18</li>
+         <li><a href="http://www.qhull.org/download">Download</a> Qhull (<a href="http://www.qhull.org/src/Changes.txt">changes</a>)</li>
+        <li><a href=http://github.com/qhull/qhull/wiki>GitHub</a> C++ interface to Qhull
+        <li><a href="html/index.htm">Manual</a> for Qhull and rbox
+        <li><a href="html/index.htm#geomview">Geomview</a> for 3-D and 4-D visualization of Qhull output
+        <li><input name=as_q size=10 value="">
+                <input type="submit" value="Search">
+                www.qhull.org
+        <p>
+    <li><a href="http://www.qhull.org/news/qhull-news.html#users">How</a> is Qhull used?</li>
+        <li><a href="http://scholar.google.com/scholar?cites=13151392091060773178&as_sdt=40000005">Google Scholar</a>,
+        <a href="http://libra.msra.cn/Publication/232063/the-quickhull-algorithm-for-convex-hulls">Microsoft Academic</a>,
+        and <a href="http://citeseerx.ist.psu.edu/showciting?doi=10.1.1.117.405&sort=cite">CiteSeer</a>
+        references to Qhull
+    <li>
+    <a href=http://www.google.com/search?as_q=qhull+-debian+-cvs+-gentoo+-pool+-mirrors&num=100>Google</a> Qhull,
+         <a href="http://images.google.com/images?q=qhull&num=100">Images</a>,
+         <a href="http://www.google.com/#q=qhull&tbm=bks">Books</a>,
+         <a href="http://www.google.com/search?q=qhull&tbm=pts">Patents</a>,
+         <a href="http://groups.google.com/groups?as_q=qhull&num=100&as_scoring=d">Newsgroups</a>,
+         <a href="http://www.google.com/search?q=qhull&tbm=blg">Blogs</a>,
+        and <a href=http://www.googlism.com/who_is/q/qhull/>Who is</a> Qhull?
+
+
+        <p>
+        <li><a href=http://www.mathworks.com/>MATLAB</a> uses Qhull for their n-d computational geometry functions:
+        <a href=http://www.mathworks.com/help/techdoc/ref/convhulln.html>convhulln</a>
+        <a href=http://www.mathworks.com/help/techdoc/ref/delaunayn.html>delaunayn</a>
+        <a href=http://www.mathworks.com/help/techdoc/ref/griddatan.html>griddatan</a>
+        <a href=http://www.mathworks.com/help/techdoc/ref/voronoin.html>voronoin</a>.
+    </li>
+        <li>The <a href="http://cran.r-project.org/web/packages/geometry/geometry.pdf">geometry</a> package of <a href="http://www.r-project.org/">R</a> provides <a href="http://geometry.r-forge.r-project.org/">Qhull in R</a>.
+        <li>The <a href="http://packages.debian.org/sid/octave3.2">Debian build</a> of
+        <a href=http://www.octave.org/>GNU Octave</a> includes Qhull for <a href="http://www.gnu.org/software/octave/doc/interpreter/Geometry.html">computational geometry<a>.
+        <li><a href=http://www.wolfram.com/products/mathematica/>Mathematica</a>'s Delaunay interface <a href=http://library.wolfram.com/infocenter/MathSource/1160/>qh-math</a>
+        and <a href="http://portal.uni-freiburg.de/imteksimulation/downloads/ims">QHullInterface</a>
+     <li>The <a href="http://docs.scipy.org/doc/scipy/reference/tutorial/spatial.html">scipy.spatial</a> of <a href="http://scipy.org/">SciPy</a> is implemented with Qhull.  It includes
+     support for Delaunay triangulations,
+</ul>
+</form>
+
+<p><b>Introduction</b>
+<ul>
+    <li><a
+        href="http://www.cs.mcgill.ca/~fukuda/soft/polyfaq/polyfaq.html"
+                >Fukuda's introduction</a> to convex hulls, Delaunay
+        triangulations, Voronoi diagrams, and linear programming</li>
+    <li><a
+        href="http://www.cse.unsw.edu.au/~lambert/java/3d/hull.html"
+                >Lambert's Java</a> visualization of convex hull algorithms </li>
+        <li><a
+        href="http://www.algorithmic-solutions.info/leda_guide/geometryalgorithms.html"
+                >LEDA Guide</a> to geometry algorithms
+        <li><a
+            href="http://mathworld.wolfram.com/ComputationalGeometry.html"
+                >MathWorld's</a> Computational Geometry from Wolfram Research
+        <li><a
+                href="http://www.cs.sunysb.edu/~algorith/major_section/1.6.shtml"
+                >Skiena's</a> Computational Geometry from his <i>Algorithm Design Manual</i>.
+    <li><a
+        href="http://www.cs.sunysb.edu/~algorith/major_section/1.6.shtml"
+                >Stony Brook</a> Algorithm Repository, computational geometry</li>
+</ul>
+
+<p><b>Qhull Documentation and Support</b>
+<ul>
+   <li><a href="html/index.htm">Manual</a> for Qhull and rbox
+   <table><tr><td>
+        <ul>
+          <li><a href="html/index.htm#description">Description</a> of Qhull
+                <li><a href="html/qh-impre.htm">Imprecision</a> in Qhull
+                <li><a href="html/qh-quick.htm#programs">Programs</a> and <a href="html/qh-quick.htm#options">Options</a>
+                    quick reference
+                <li><a href="html/qconvex.htm">qconvex</a> -- convex hull
+                <li><a href="html/qdelaun.htm">qdelaunay</a> -- Delaunay triangulation
+                <li><a href="html/qvoronoi.htm">qvoronoi</a> -- Voronoi diagram
+                <li><a href="html/qhalf.htm">qhalf</a> -- halfspace intersection about a point
+                <li><a href="html/rbox.htm">rbox</a> -- generate point distributions
+        </ul></td><td><ul>
+            <li><a href="http://www.qhull.org/html/qh-faq.htm">Frequently</a> asked
+                questions about Qhull</li>
+            <li><a href="html/index.htm#geomview">Geomview</a> for visualizing Qhull
+            <li><a href="COPYING.txt">COPYING.txt</a> - copyright notice<br>
+            <li><a href="REGISTER.txt">REGISTER.txt</a> - registration<br>
+            <li><a href="README.txt">README.txt</a> - installation
+            instructions<br>
+            <li><a href="src/Changes.txt">Changes.txt</a> - change history <br>
+            <li><a href="html/qh-code.htm">Calling Qhull</a> from your program
+            <li><a href="src/libqhull_r/index.htm">Reentrant</a> Qhull functions, macros, and data structures with source
+            </ul>
+        </td></tr></table>
+    <li>Send e-mail to <a href=mailto:qhull@qhull.org>qhull@qhull.org</a> </li>
+    <li>Report bugs to <a
+        href="mailto:qhull_bug@qhull.org">qhull_bug@qhull.org</a>
+</ul>
+
+<p><b>Related URLs</b>
+<ul>
+    <li><a href="http://www.geom.uiuc.edu/software/cglist">Amenta's directory</a> of
+        computational geometry software </li>
+
+        <li><a href=http://www.boost.org/libs/graph/doc/table_of_contents.html>BGL</a>
+        Boost Graph Library provides C++ classes for graph data structures
+and algorithms,
+    <li><a
+        href="http://www.netlib.org/voronoi/hull.html">Clarkson's
+        hull </a>program with exact arithmetic for convex hulls, Delaunay triangulations,
+                Voronoi volumes, and alpha shapes. </li>
+        <li><a href="http://compgeom.cs.uiuc.edu/~jeffe/compgeom/compgeom.html">Erickson's
+            Computational</a> Geometry Pages and
+                <a href="http://compgeom.cs.uiuc.edu/~jeffe/compgeom/code.html">Software</a>
+    <li><a
+        href="http://www.cs.mcgill.ca/~fukuda/soft/cdd_home/cdd.html">Fukuda's
+        cdd</a> program for halfspace intersection and convex hulls (<a
+        href="http://www.csb.ethz.ch/tools/polco">Polco/Java</a>)</li>
+        <li><a href="http://www.inf.ethz.ch/personal/gaertner/miniball.html">Gartner's
+        Miniball</a> for fast and robust smallest enclosing balls (up to 20-d)
+
+    <li><a href=http://www.algorithmic-solutions.com/enleda.htm>Leda</a>
+and <a href=http://www.cgal.org/>CGAL</a> libraries for writing computational
+geometry programs and other combinatorial algorithms
+        <li><a href=http://www.mathtools.net/>Mathtools.net</a> of scientific and engineering
+        software
+    <li><a href="http://www.imr.sandia.gov/papers/topics.html">Owen's International Meshing</a> Roundtable
+    <li><a
+        href="http://www.robertschneiders.de/meshgeneration/meshgeneration.html">Schneiders'
+        Finite Element</a> Mesh Generation page</li>
+    <li><a href="http://www.cs.cmu.edu/~quake/triangle.html">Shewchuk's
+        triangle </a>program for 2-d Delaunay</li>
+        <li><a href=http://www.voronoi.com>Voronoi Web Site</a> for all things Voronoi
+        <li>Young's <a href="http://homepage.usask.ca/~ijm451/finite/fe_resources/">Internet Finite Element Resources</a>
+        <li><a href="http://www.uic.nnov.ru/~zny/skeleton/">Zolotykh's Skeleton</a> generates all extreme rays of a polyhedral cone using the Double Description Method</li>
+        <li><a href="https://github.com/tomilov/quickhull/blob/master/include/quickhull.hpp">Tomilov's quickhull.hpp</a> (<a href="http://habrahabr.ru/post/245221/">doc-ru</a>) implements the Quickhull algorithm for points in general position.
+</ul>
+
+<p><b>FAQs and Newsgroups</b>
+<ul>
+    <li><a
+        href="http://www.faqs.org/faqs/graphics/algorithms-faq/">FAQ</a>
+        for computer graphics algorithms
+                (Exaflop.org: <a href="http://exaflop.org/docs/cgafaq/cga6.html">geometric</a> structures)
+ </li>
+    <li><a
+        href="http://www-unix.mcs.anl.gov/otc/Guide/faq/linear-programming-faq.html">FAQ
+        </a>for linear programming </li>
+    <li><a href="news:comp.graphics.algorithms">Newsgroup</a>:
+        comp.graphics.algorithms </li>
+        <li><a href="news:comp.soft-sys.matlab">Newsgroup</a>:
+            comp.soft-sys.matlab</li>
+    <li><a href="news:sci.math.num-analysis">Newsgroup</a>:
+        sci.math.num-analysis </li>
+    <li><a href="news:sci.op-research">Newsgroup</a>:
+        sci.op-research </li>
+</ul>
+</blockquote>
+<hr>
+
+<p>The program includes options for input transformations,
+randomization, tracing, multiple output formats, and execution
+statistics. The program can be called from within your
+application. </p>
+
+<p>You can view the results in 2-d, 3-d and 4-d with <a
+href="http://www.geomview.org">Geomview</a>.   An alternative
+is <a href=http://www.vtk.org/>VTK</a>.</p>
+
+<p>For an article about Qhull, download from
+  <a href="http://dl.acm.org/authorize?89250">ACM</a> or <a
+    href="http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.117.405">CiteSeer</a>:
+</p>
+
+<blockquote>
+    <p>Barber, C.B., Dobkin, D.P., and Huhdanpaa, H.T., &quot;The
+    Quickhull algorithm for convex hulls,&quot; <i>ACM Trans. on
+    Mathematical Software</i>, 22(4):469-483, Dec 1996, http://www.qhull.org</p>
+</blockquote>
+
+<p>Abstract: </p>
+
+<blockquote>
+    <p>The convex hull of a set of points is the smallest convex
+    set that contains the points. This article presents a
+    practical convex hull algorithm that combines the
+    two-dimensional Quickhull Algorithm with the general
+    dimension Beneath-Beyond Algorithm. It is similar to the
+    randomized, incremental algorithms for convex hull and
+    Delaunay triangulation. We provide empirical evidence that
+    the algorithm runs faster when the input contains non-extreme
+    points, and that it uses less memory. </p>
+    <p>Computational geometry algorithms have traditionally
+    assumed that input sets are well behaved. When an algorithm
+    is implemented with floating point arithmetic, this
+    assumption can lead to serious errors. We briefly describe a
+    solution to this problem when computing the convex hull in
+    two, three, or four dimensions. The output is a set of
+    "thick" facets that contain all possible exact convex hulls
+    of the input. A variation is effective in five or more
+    dimensions. </p>
+</blockquote>
+<!-- Navigation links -->
+<hr>
+
+<p><b>Up:</b> <a href="http://www.geom.uiuc.edu/software/past-projects.html"><i>Past Software
+Projects of the Geometry Center</i></a> <br>
+<b>URL:</b> <a href="http://www.qhull.org">http://www.qhull.org</a>
+<br><b>To:</b>
+<a href="http://www.qhull.org/news">News</a>
+&#149; <a href="http://www.qhull.org/download">Download</a>
+&#149; <a href="http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.117.405">CiteSeer</a>
+&#149; <a href=http://images.google.com/images?q=qhull&num=100>Images</a>
+&#149; <a href="html/index.htm#TOC">Manual</a>
+&#149; <a href="http://www.qhull.org/html/qh-faq.htm">FAQ</a>
+&#149; <a href="html/qh-quick.htm#programs">Programs</a>
+&#149; <a href="html/qh-quick.htm#options">Options</a>
+<!-- GC common information --></p>
+
+<hr>
+
+<p><a href="http://www.geom.uiuc.edu/"><img src="html/qh--geom.gif" alt="[HOME]"
+align="middle"></a> <i>The Geometry Center Home Page</i> </p>
+
+<p>Comments to: <a href="mailto:qhull@qhull.org">qhull@qhull.org</a>
+<br>
+Created: May 17 1995 --- <!-- hhmts start -->
+</body>
+</html>
diff --git a/xs/src/qhull/origCMakeLists.txt b/xs/src/qhull/origCMakeLists.txt
new file mode 100644
index 0000000000..1034d1dea9
--- /dev/null
+++ b/xs/src/qhull/origCMakeLists.txt
@@ -0,0 +1,426 @@
+# CMakeLists.txt -- CMake configuration file for qhull, qhull6, and related programs
+#
+# To install CMake
+#   Download from http://www.cmake.org/download/
+#
+# To find the available targets for CMake -G "..."
+#   cmake --help
+#
+# To build with MSYS/mingw
+#   cd build && cmake -G "MSYS Makefiles" .. && cmake ..
+#   make
+#   make install
+#
+# To uninstall on unix or MSYS/mingw
+#   xargs rm <build/install_manifest.txt
+#
+# To build Qhull with Visual Studio projects, run cmake twice
+#   To install bin/doc/include/lib in the current directory
+#      mkdir -p build-cmake && cd build-cmake && cmake -G "Visual Studio 11 2012" .. && cmake -DCMAKE_INSTALL_PREFIX=.. ..
+#      mkdir -p build-cmake && cd build-cmake && cmake -G "Visual Studio 11 2012 Win64" .. && cmake -DCMAKE_INSTALL_PREFIX=.. ..
+#   To install into Program Files/qhull
+#      mkdir -p build-cmake && cd build-cmake && cmake -G "Visual Studio 11 2012" .. && cmake ..
+#      mkdir -p build-cmake && cd build-cmake && cmake -G "Visual Studio 11 2012 Win64" .. && cmake ..
+#   To build for Visual Studio 2005 and install into Program Files/qhull
+#      mkdir -p build-cmake && cd build-cmake && cmake -G "Visual Studio 8 2005" .. && cmake  ..
+#      mkdir -p build-cmake && cd build-cmake && cmake -G "Visual Studio 8 2005 Win64" .. && cmake  ..
+#   Double click build-cmake/qhull-all.sln
+#   Build INSTALL to copy files into C:/Program Files/qhull
+#
+# Additional build targets
+#   qhullp -- Same as qhull using qh_QHpointer and deprecated libqhull_p
+#   user_egp -- Same as user_eg using qh_QHpointer and deprecated libqhull_p
+#
+# Notes on Visual Studio projects
+#   You may need to copy bin/msvcr80.dll into C:/Program Files/qhull/bin
+#   If using library debug targets, please rename with '_d' (e.g., qhullstatic_d.lib)
+# 
+# Troubleshooting
+#   "No CMAKE_C_COMPILER could be found"
+#     cmake was not able to find the build environment specified (e.g., Visual Studio 11)
+# 
+# To uninstall on Windows
+#   Delete C:/Program Files/qhull
+#
+# If creating a qhull package, please include a pkg-config file based on build/qhull*.pc.in
+#
+# For qhulltest, use the Qt build (src/qhull-all.pro)
+#
+# Qhull ships with cmake-derived sln and proj files for DevStudio 8 2005
+#   See eg/make-vcproj.sh
+#   Change to relative paths
+#   Remove ZERO_CHECK, ALL_BUILD, and INSTALL projects
+#   Change targets to bin/ and lib/ directories
+#   Disable incremental linking and ilk files (LinkIncremental="1")
+#   Disable Run-Time Type Info (rtti)
+#   Remove src/libqhullcpp from most of the AdditionalIncludeDirectories
+#   Remove CMAKE_INTDIR from PreprocessorDefinitions
+#   Adjust target names and destinations (e.g., lib/libqhullstatic_rd.a)
+#  
+# $Id: //main/2015/qhull/CMakeLists.txt#8 $$Change: 2066 $
+# $DateTime: 2016/01/18 19:29:17 $$Author: bbarber $
+
+project(qhull)
+cmake_minimum_required(VERSION 2.6)
+
+# Define qhull_VERSION in CMakeLists.txt, Makefile, qhull-exports.def, qhull_p-exports.def, qhull_r-exports.def, qhull-warn.pri
+set(qhull_VERSION2 "2015.2 2016/01/18")  # not used, See global.c, global_r.c, rbox.c, rbox_r.c
+set(qhull_VERSION     "7.2.0")  # Advance every release
+
+# SOVERSION -- qhull 2003 = empty, 2009 = 5, 2010-2012 = 6, 2015 (reentrant) = 7
+set(qhull_SOVERSION 7) # For SOVERSION 
+
+include(CMakeModules/CheckLFS.cmake)
+option(WITH_LFS "Enable Large File Support" ON)
+check_lfs(WITH_LFS)
+
+if(INCLUDE_INSTALL_DIR)
+else()
+set(INCLUDE_INSTALL_DIR ${CMAKE_INSTALL_PREFIX}/include)
+endif()
+if(LIB_INSTALL_DIR)
+else()
+set(LIB_INSTALL_DIR ${CMAKE_INSTALL_PREFIX}/lib)
+endif()
+if(BIN_INSTALL_DIR)
+else()
+set(BIN_INSTALL_DIR ${CMAKE_INSTALL_PREFIX}/bin)
+endif()
+if(MAN_INSTALL_DIR)
+else()
+    if(WIN32)
+        set(MAN_INSTALL_DIR ${CMAKE_INSTALL_PREFIX}/man/man1)
+    else()
+        set(MAN_INSTALL_DIR ${CMAKE_INSTALL_PREFIX}/share/man/man1)
+    endif()
+endif()
+if(DOC_INSTALL_DIR)
+else()
+    if(WIN32)
+        set(DOC_INSTALL_DIR ${CMAKE_INSTALL_PREFIX}/doc)
+    else()
+        set(DOC_INSTALL_DIR ${CMAKE_INSTALL_PREFIX}/share/doc/qhull)
+    endif()
+endif()
+message(STATUS)
+message(STATUS "========== qhull Build Information ==========")
+message(STATUS "Build Version:                             ${qhull_VERSION}")
+message(STATUS "Install Prefix (CMAKE_INSTALL_PREFIX):     ${CMAKE_INSTALL_PREFIX}")
+message(STATUS "Binary Directory (BIN_INSTALL_DIR):        ${BIN_INSTALL_DIR}")
+message(STATUS "Library Directory (LIB_INSTALL_DIR):       ${LIB_INSTALL_DIR}")
+message(STATUS "Include Directory (INCLUDE_INSTALL_DIR):   ${INCLUDE_INSTALL_DIR}")
+message(STATUS "Documentation Directory (DOC_INSTALL_DIR): ${DOC_INSTALL_DIR}")
+message(STATUS "Man Pages Directory (MAN_INSTALL_DIR):     ${MAN_INSTALL_DIR}")
+message(STATUS "Build Type (CMAKE_BUILD_TYPE):             ${CMAKE_BUILD_TYPE}")
+message(STATUS "To override these options, add -D{OPTION_NAME}=... to the cmake command")
+message(STATUS "  Build the debug targets                  -DCMAKE_BUILD_TYPE=Debug")
+message(STATUS)
+message(STATUS "To build and install qhull, enter \"make\" and \"make install\"")
+message(STATUS "To smoketest qhull, enter \"ctest\"")
+message(STATUS)
+
+
+# ---------------------------------------
+# Define library source files and variables
+#
+# Files for individual targets are defined with the target
+# ---------------------------------------
+
+# Order libqhull object files by frequency of execution.  Small files at end.
+
+# Non-reentrant Qhull
+set(
+    libqhull_HEADERS
+        src/libqhull/libqhull.h
+        src/libqhull/geom.h
+        src/libqhull/io.h
+        src/libqhull/mem.h
+        src/libqhull/merge.h
+        src/libqhull/poly.h
+        src/libqhull/qhull_a.h
+        src/libqhull/qset.h
+        src/libqhull/random.h
+        src/libqhull/stat.h
+        src/libqhull/user.h
+)
+set(
+    libqhull_SOURCES
+        src/libqhull/global.c
+        src/libqhull/stat.c
+        src/libqhull/geom2.c
+        src/libqhull/poly2.c
+        src/libqhull/merge.c
+        src/libqhull/libqhull.c
+        src/libqhull/geom.c
+        src/libqhull/poly.c
+        src/libqhull/qset.c
+        src/libqhull/mem.c
+        src/libqhull/random.c
+        src/libqhull/usermem.c
+        src/libqhull/userprintf.c
+        src/libqhull/io.c
+        src/libqhull/user.c
+        src/libqhull/rboxlib.c
+        src/libqhull/userprintf_rbox.c
+        ${libqhull_HEADERS}
+)
+
+set(
+    libqhull_DOC
+        src/libqhull/index.htm
+        src/libqhull/qh-geom.htm
+        src/libqhull/qh-globa.htm
+        src/libqhull/qh-io.htm
+        src/libqhull/qh-mem.htm
+        src/libqhull/qh-merge.htm
+        src/libqhull/qh-poly.htm
+        src/libqhull/qh-qhull.htm
+        src/libqhull/qh-set.htm
+        src/libqhull/qh-stat.htm
+        src/libqhull/qh-user.htm    
+        src/libqhull/DEPRECATED.txt    
+)
+
+set(
+    testqset_HEADERS
+        src/libqhull/mem.h
+        src/libqhull/qset.h
+)
+set(
+    testqset_SOURCES
+        src/libqhull/qset.c
+        src/libqhull/mem.c
+        src/libqhull/usermem.c
+        src/testqset/testqset.c
+        ${testqset_HEADERS}
+)
+
+# Reeentrant Qhull
+
+set(
+    libqhullr_HEADERS
+        src/libqhull_r/libqhull_r.h
+        src/libqhull_r/geom_r.h
+        src/libqhull_r/io_r.h
+        src/libqhull_r/mem_r.h
+        src/libqhull_r/merge_r.h
+        src/libqhull_r/poly_r.h
+        src/libqhull_r/qhull_ra.h
+        src/libqhull_r/qset_r.h
+        src/libqhull_r/random_r.h
+        src/libqhull_r/stat_r.h
+        src/libqhull_r/user_r.h
+)
+set(
+    libqhullr_SOURCES
+        src/libqhull_r/global_r.c
+        src/libqhull_r/stat_r.c
+        src/libqhull_r/geom2_r.c
+        src/libqhull_r/poly2_r.c
+        src/libqhull_r/merge_r.c
+        src/libqhull_r/libqhull_r.c
+        src/libqhull_r/geom_r.c
+        src/libqhull_r/poly_r.c
+        src/libqhull_r/qset_r.c
+        src/libqhull_r/mem_r.c
+        src/libqhull_r/random_r.c
+        src/libqhull_r/usermem_r.c
+        src/libqhull_r/userprintf_r.c
+        src/libqhull_r/io_r.c
+        src/libqhull_r/user_r.c
+        src/libqhull_r/rboxlib_r.c
+        src/libqhull_r/userprintf_rbox_r.c
+        ${libqhullr_HEADERS}
+)
+
+set(
+    libqhullr_DOC
+        src/libqhull_r/index.htm
+        src/libqhull_r/qh-geom_r.htm
+        src/libqhull_r/qh-globa_r.htm
+        src/libqhull_r/qh-io_r.htm
+        src/libqhull_r/qh-mem_r.htm
+        src/libqhull_r/qh-merge_r.htm
+        src/libqhull_r/qh-poly_r.htm
+        src/libqhull_r/qh-qhull_r.htm
+        src/libqhull_r/qh-set_r.htm
+        src/libqhull_r/qh-stat_r.htm
+        src/libqhull_r/qh-user_r.htm    
+)
+
+set(
+    testqsetr_HEADERS
+        src/libqhull_r/mem_r.h
+        src/libqhull_r/qset_r.h
+)
+set(
+    testqsetr_SOURCES
+        src/libqhull_r/qset_r.c
+        src/libqhull_r/mem_r.c
+        src/libqhull_r/usermem_r.c
+        src/testqset_r/testqset_r.c
+        ${testqsetr_HEADERS}
+)
+
+# C++ interface to reentrant Qhull
+
+set(
+    libqhullcpp_HEADERS
+        src/libqhullcpp/Coordinates.h
+        src/libqhullcpp/functionObjects.h
+        src/libqhullcpp/PointCoordinates.h
+        src/libqhullcpp/Qhull.h
+        src/libqhullcpp/QhullError.h
+        src/libqhullcpp/QhullFacet.h
+        src/libqhullcpp/QhullFacetList.h
+        src/libqhullcpp/QhullFacetSet.h
+        src/libqhullcpp/QhullHyperplane.h
+        src/libqhullcpp/QhullIterator.h
+        src/libqhullcpp/QhullLinkedList.h
+        src/libqhullcpp/QhullPoint.h
+        src/libqhullcpp/QhullPoints.h
+        src/libqhullcpp/QhullPointSet.h
+        src/libqhullcpp/QhullQh.h
+        src/libqhullcpp/QhullRidge.h
+        src/libqhullcpp/QhullSet.h
+        src/libqhullcpp/QhullSets.h
+        src/libqhullcpp/QhullStat.h
+        src/libqhullcpp/QhullVertex.h
+        src/libqhullcpp/QhullVertexSet.h
+        src/libqhullcpp/RboxPoints.h
+        src/libqhullcpp/RoadError.h
+        src/libqhullcpp/RoadLogEvent.h
+        src/qhulltest/RoadTest.h
+)
+
+set(
+    libqhullcpp_SOURCES
+        src/libqhullcpp/Coordinates.cpp
+        src/libqhullcpp/PointCoordinates.cpp
+        src/libqhullcpp/Qhull.cpp
+        src/libqhullcpp/QhullFacet.cpp
+        src/libqhullcpp/QhullFacetList.cpp
+        src/libqhullcpp/QhullFacetSet.cpp
+        src/libqhullcpp/QhullHyperplane.cpp
+        src/libqhullcpp/QhullPoint.cpp
+        src/libqhullcpp/QhullPointSet.cpp
+        src/libqhullcpp/QhullPoints.cpp
+        src/libqhullcpp/QhullQh.cpp
+        src/libqhullcpp/QhullRidge.cpp
+        src/libqhullcpp/QhullSet.cpp
+        src/libqhullcpp/QhullStat.cpp
+        src/libqhullcpp/QhullVertex.cpp
+        src/libqhullcpp/QhullVertexSet.cpp
+        src/libqhullcpp/RboxPoints.cpp
+        src/libqhullcpp/RoadError.cpp
+        src/libqhullcpp/RoadLogEvent.cpp
+        ${libqhullcpp_HEADERS}
+)
+
+# Documentation files (index.htm refers to html/...)
+
+set(
+    doc_FILES
+        README.txt 
+        REGISTER.txt 
+        Announce.txt 
+        COPYING.txt 
+        index.htm
+)
+
+include_directories(${CMAKE_SOURCE_DIR}/src)
+
+if(CMAKE_BUILD_TYPE MATCHES "[dD]ebug")
+    set(qhull_CPP qhullcpp_d)
+    set(qhull_SHARED qhull_d) 
+    set(qhull_SHAREDP qhull_pd)
+    set(qhull_SHAREDR qhull_rd)
+    set(qhull_STATIC qhullstatic_d)
+    set(qhull_STATICR qhullstatic_rd)
+else()
+    set(qhull_CPP qhullcpp)
+    set(qhull_SHARED libqhull)  # Temporarily avoid name conflict with qhull executable
+    set(qhull_SHAREDP qhull_p)
+    set(qhull_SHAREDR qhull_r)
+    set(qhull_STATIC qhullstatic)
+    set(qhull_STATICR qhullstatic_r)
+endif()
+
+
+
+# ---------------------------------------
+# Define static libraries qhullstatic (non-reentrant) and qhullstatic_r (reentrant)
+# ---------------------------------------
+
+add_library(${qhull_STATIC} STATIC ${libqhull_SOURCES})
+set_target_properties(${qhull_STATIC} PROPERTIES
+    VERSION ${qhull_VERSION})
+
+add_library(${qhull_STATICR} STATIC ${libqhullr_SOURCES})
+set_target_properties(${qhull_STATICR} PROPERTIES
+    VERSION ${qhull_VERSION})
+
+if(UNIX)
+    target_link_libraries(${qhull_STATIC} m)
+    target_link_libraries(${qhull_STATICR} m)
+endif(UNIX)
+
+# ---------------------------------------
+# Define C++ static library qhullcpp
+#     Do not create libqhullcpp as a shared library.  Qhull C++ classes may change layout and size. 
+# ---------------------------------------
+
+add_library(${qhull_CPP} STATIC ${libqhullcpp_SOURCES})
+set_target_properties(${qhull_CPP} PROPERTIES
+    VERSION ${qhull_VERSION})
+
+# ---------------------------------------
+# Define qhull executables linked to qhullstatic library
+#   qhull is linked to reentrant qhull (more flexible)
+#   the others are linked to non-reentrant qhull (somewhat faster)
+# ---------------------------------------
+
+set(qhull_SOURCES       src/qhull/unix_r.c)
+set(rbox_SOURCES        src/rbox/rbox.c)
+set(qconvex_SOURCES     src/qconvex/qconvex.c)
+set(qdelaunay_SOURCES   src/qdelaunay/qdelaun.c)
+set(qvoronoi_SOURCES    src/qvoronoi/qvoronoi.c)
+set(qhalf_SOURCES       src/qhalf/qhalf.c)
+
+add_executable(qhull ${qhull_SOURCES})
+target_link_libraries(qhull ${qhull_STATICR})
+
+add_executable(rbox ${rbox_SOURCES})
+target_link_libraries(rbox ${qhull_STATIC})
+
+add_executable(qconvex ${qconvex_SOURCES})
+target_link_libraries(qconvex ${qhull_STATIC})
+
+add_executable(qdelaunay ${qdelaunay_SOURCES})
+target_link_libraries(qdelaunay ${qhull_STATIC})
+
+add_executable(qvoronoi ${qvoronoi_SOURCES})
+target_link_libraries(qvoronoi ${qhull_STATIC})
+
+add_executable(qhalf ${qhalf_SOURCES})
+target_link_libraries(qhalf ${qhull_STATIC})
+
+
+# ---------------------------------------
+# Define install
+# ---------------------------------------
+
+install(TARGETS ${qhull_TARGETS_INSTALL}
+        RUNTIME DESTINATION ${BIN_INSTALL_DIR}
+        LIBRARY DESTINATION ${LIB_INSTALL_DIR}
+        ARCHIVE DESTINATION ${LIB_INSTALL_DIR})
+
+install(FILES ${libqhull_HEADERS}    DESTINATION ${INCLUDE_INSTALL_DIR}/libqhull)
+install(FILES ${libqhull_DOC}        DESTINATION ${INCLUDE_INSTALL_DIR}/libqhull)
+install(FILES ${libqhullr_HEADERS}    DESTINATION ${INCLUDE_INSTALL_DIR}/libqhull_r)
+install(FILES ${libqhullr_DOC}        DESTINATION ${INCLUDE_INSTALL_DIR}/libqhull_r)
+install(FILES ${libqhullcpp_HEADERS} DESTINATION ${INCLUDE_INSTALL_DIR}/libqhullcpp)
+install(FILES html/qhull.man         DESTINATION ${MAN_INSTALL_DIR} RENAME qhull.1)
+install(FILES html/rbox.man          DESTINATION ${MAN_INSTALL_DIR} RENAME rbox.1)
+install(FILES ${doc_FILES}           DESTINATION ${DOC_INSTALL_DIR})
+install(DIRECTORY html/              DESTINATION ${DOC_INSTALL_DIR})
diff --git a/xs/src/qhull/src/Changes.txt b/xs/src/qhull/src/Changes.txt
new file mode 100644
index 0000000000..2dbf41e396
--- /dev/null
+++ b/xs/src/qhull/src/Changes.txt
@@ -0,0 +1,2129 @@
+$Id: //main/2015/qhull/src/Changes.txt#29 $
+
+.............This file lists all changes to qhull and rbox.....................
+
+------------
+Need help
+ - Write an incremental addPoint using bucketed inputs and facet location search (see CGAL)
+ - Compute hyperplanes in parallel (cf. qh_setfactplane)
+ - Create Voronoi volumes and topology using a parallel implementation
+ - Produce conformant triangulations for merged facets using option 'Qt' 
+ - Integrate 4dview with Geomview 1.9.5
+ - Qhull needs RPM and Debian builds (CMake's CPackRMP and CPackDeb).   
+ - Qhull needs a mirror/archive site for old and new builds
+ - Constrained delaunay triangulation via Shewchuk's algorithm (ACM Symp. Comp. Geo., 1998)
+ - More enhancements -- http://www.qhull.org/html/qh-code.htm#enhance
+ - The C++ interface needs work.  Give it a try and make it better. 
+   http://github.com/qhull/qhull/wiki
+
+Octave creates endpoints for the ridges that would extend to infinity to be able to draw the diagram [M. Voss]
+
+------
+Qhull 2016.1
+ - Move 'extern "C" {}' logic from C++ to C headers [C. Atkins, github]
+ 
+ - Explanation of clobbered warning for Qhull::runQhull and qh_new_qhull
+ - html/index.htm: Add "Nearly coincident points" to "When to use Qhull"
+ - html/index.htm: Add Tomilov's qhullhull.hpp for general position input.
+ - index.htm: Add Tomilov's qhullhull.hpp for general position input.
+ - qh-faq.htm: Add a note about merging slivers in a Delaunay triangulation [M. Treacy] 
+ 
+------------
+Qhull 2015.2 2016/01/18 (7.2.0) 
+ - Fixed memory leak in ~QhullQh [M. Sandim]
+   QhullQh.cpp: call checkAndFreeQhullMemory() in the destructor.  Otherwise memT is not freed.
+   Remove checkAndFreeQhullMemory() from Qhull.h.  It is not needed.
+   Remove calls to checkAndFreeQhullMemory in qhulltest.  It is called by ~QhullQh()
+   libqhull_r.h: Document qh_ASvornoi and facetT.center
+   qh_freeqhull: if qh_NOmem, use qh_ALL
+   qh_memalloc: short memory is freed by qh_memfreeshort unless qh_NOmem
+   qh_memstatistics (mem.c): call qh_memcheck() as done in mem_r.c
+   qh_new_qhull calls qh_memcheck
+   qh_newvertex: free vertex on error
+   qh_projectinput: Free memory allocations on error
+   qh_rboxpoints: free simplex on error
+   qh_sethalfspace_all: Fixed memory leak on error QH8032 feasible not inside halfspace
+   qh_triangulate_facet: For TRInormals ('Q11') replace qh_copypoints with qh_memalloc
+   qh_triangulate_facet: Document qh.TRInormals
+   qh_voronoi_center: Free center on error
+   qhulltest: Fixed memory leak of s_testcases by calling RoadTest::deleteTests()
+   qhulltest: The 'add_*_test' functions append the test object to RoadTest::s_testcases
+   ~RoadTest: declare virtual for Q_OBJECT, removeAll not needed
+   user_eg2: Check memory at end of each run
+   user_r.h: Add QHULL_CRTDBG for invoking Microsoft's memory leak detector
+   use _MSC_VER instead of QHULL_OS_WIN for QHULL_CRTDBG
+   Call qh_freeqhull with qh_ALL/!qh_ALL instead of 'True/False'
+   Include user_r.h with RoadError,h for QHULL_CRTDBG
+   Invoke _CrtSetDbgFlag... at beginning of program
+   Moved user_r.h/libqhull_r.h/qhull_ra.h as first include (for QHULL_CRTDBG)
+   Moved QHULL_OS_WIN from qhull_ra.h to user_r.h
+   Removed __CYGWIN__ from QHULL_OS_WIN (same as Qt's qglobal.h)
+
+ - check_dupridge: A bounding box is not sufficient to avoid dupridge errors
+ - qh_findbestneighor: Error if qh.CENTERtype is qh_ASvoronoi (i.e., no merging now)
+ - qh_printstatlevel: Remove unused parameter, 'start'
+ - QhullLinkedList::last() and back(): Return T instead of T& (T is computed)
+ 
+ - qh-code.htm: "How to convert code to reentrant Qhull"
+   Update "Nearly coincident points on an edge"
+   Add 2012 size of data structures to "Qhull on 64-bit computers"
+ - html/index.htm: Add CGAL to "When to use" 
+ - qh-optq.htm: Add documentation for option 'Q12'
+ - Move suggestions from Changes.txt to qh-code.htm#enhance
+ - user_r.h: Fixed qh-us_r.html links
+ - Fixed links in html pages
+
+ - QhullIterator and QhullLinkedList: Include <iterator> [B. Boeckel]
+ - Moved include file for each C++ source file to the top of the includes
+ - Prepend cpp includes with "libqhullcpp/"
+ - RoadLogEvent includes RoadLogEvent.h
+ - QhullIterator.h: Only QHULL_DECLARE_SEQUENTIAL_ITERATOR is used.
+ 
+ - Compared src/libqhull/* to src/libqhull_r/* and resolved differences
+ - qh_printpoint in io.c skips qh_IDnone like io_r.c
+ - qhull_p-exports.def: Added three missing exports
+ - set_r.h: Removed countT. Too many issues
+ 
+ - libqhull_r/Makefile: Add help prompts to 'make qtest'
+ - libqhull.pro: Add '../libqhull/' to sources and headers
+ - libqhull/Makefile: Fixed -I,./,,/src
+
+ - qhull-zip.sh: Add CMakeModules to tarball [C. Rosenvik]
+ - CMakeLists.txt: Add targets qhullp and user_egp for qh_QHpointer and libqhull_p
+ - Reorganized 'make help'
+ - Makefile cleanall: Delete testqset and qhulltest from bin/
+ - Fix filetype of Unix-only files
+ - Fix Unix line endings for Makefile and check in qhull-zip.sh
+ - Fix Windows line-endings and check in qhull-zip.sh
+ - qhull-zip.sh: Check for Unix text files
+
+ ------------
+Qhull 2015.1 2016/01/03 (7.1.0) 
+ - Add Rbox option 'Cn,r,m' to add nearly coincident points.  Trigger for duplicate ridges
+ - Add Qhull option 'Q12' to ignore error on wide merge due to duplicate ridge
+
+ - qh_findbestlower: Call qh_findfacet_all to fix rare "flipped or upper Delaunay" error QH6228.
+   QH6228 input provided by J. Metz.  Reported (date order): L. Fiaschi, N. Bowler, A. Liebscher, V. Vieira, N. Rhinehart, N. Vance, P. Shafer
+ - qh_check_dupridge: Check if wide merge due to duplicate ridge from nearly coincident points
+ - qh_initialhull: Fix error messages for initial simplex is flat
+ - qh_determinant: increased 2-d and 3-d nearzero by 10x due to a counter-example
+ - rbox: Add qh_outcoord() to output coordinates w/ or w/o iscdd
+ - qh_meminit (mem.c): Add call to qh_memcheck
+ - Compare libqhull/... to libqhull_r/... and resolve differences
+ - Update builds for DevStudio (qhull.sln for msdev 2005..2009, qhull-32.sln and qhull-64.sln for recent releases)
+
+ - qh-impre.htm: Add a section about precision errors for 'Nearly coincident points on an edge'
+ - html/index.htm#geomview: Document how to install, build, and use Geomview.
+ - html/index.htm: Emphasize program links and move related urls to end
+ - qhull/index.htm: Emphasize manual, geomview, and imprecision
+ - Fix documentation links in libqhull_r/index.htm
+ - Add 'Functions' link to documentation headers
+ - Change '<A>...</A>' to '<a>...</a>'
+ - libqhull_r/index.htm -- Add instructions for configuring web browsers for source links.
+ - libqhull_r/ -- Fix source links for ..._r.htm files
+
+------------
+Qhull 2015.0.7 2015/11/09 (7.0.7)
+ - Fix return type of operator-> in QhullLinkedList and other collection classes [F. Jares]
+ - Fix return types for QhullLinkedList
+ - Fix return types for QhullPoints
+ - Simplify return type for Coordinates::operator[] (same as QList) 
+ - Add const to operators for QhullSet::iterator and add documentation
+ - Coordinates.h: Fix return types for operations of iterator and const_iterator
+ - Drop use of Perforce changelist number in qhull_VERSION of CMakeLists.txt
+ - Rename the md5sum files as *.tgz.md5sum instead of *-tgz.md5sum
+ - Fix build dependency for testqset_r [asekez]
+ - rbox.c depends on Qhull due to qh_lib_check which uses qh_version2 for error messages
+ - QhullFacet_test.cpp: Annotate Qhull invocations.   Allows their repetition.
+ - QhullFacet_test.cpp: Adjust epsilon on distance tests
+ - Do not create libqhullcpp as a shared library.  Qhull C++ classes may change layout and size. 
+ - qhull-cpp.xml: Make a relative path to road-faq.xsl
+
+------------
+Qhull 2015.0.6 2015/10/20 (7.0.6.2013)
+ - In the libraries, exit() is only called from qh_exit().  qh_exit may be redefined.
+ - Add qh_fprintf_stderr to usermem.c.  May be overridden to avoid use of stderr [D. Sterratt]
+   Add usermem to testqset builds
+   Used by qh_fprintf_rbox
+ - Remove most instances of stderr/stdout from libqhull, libqhull_r, and libqhullcpp [D. Sterratt]
+   qh_fprintf_stderr may be redefined.  qh_meminit and qh_new_qhull use stderr as the default ferr
+ - qh_initflags: Use qh.fout instead of stdout for 'TO file'.  A library caller may define a different qh.fout.
+ - qh_settemppush: Call qh_fprintf() instead of fprintf() on error.
+ - Rename qh_call_qhull as "Qhull-template" from user.c.  Updated its references.
+
+ - qh-code.htm: "How to avoid</a> exit(), fprintf(), stderr, and stdout"
+ - html/index.htm: Fix table of contents for qh-code
+ - libqhull_r/index.htm: Rewrite introduction to Reentrant Qhull
+ - qh-faq.htm: Rewrite "Can Qhull use coordinates without placing  them in a data file?"
+ - qh-get.html: Link to github
+ - Remove qhull_interface.cpp from the documentation
+
+------------
+Qhull 2015.0.5 2015/10/12 (7.0.5.1995)
+- qh_new_qhull: default 'errfile' is 'stderr'.  outfile and errfile are optional [B. Pearlmutter]
+- qh_new_qhull: returns qh_ERRinput instead of exit() if qhull_cmd is not "qhull ..." [B. Pearlmutter]
+- qhalf_r.c,etc: Add clear of qh.NOerrexit
+- global.c: gcc 4.4.0 mingw32 segfault cleared by adding comment
+- usermem_r-cpp.cpp: Optional file to redefine qh_exit() as throw "QH10003.." [B. Pearlmutter]
+  qh_exit() is called by qhull_r when qh_errexit() is not available.
+
+- html/index.htm:  Add bibliographic reference to Golub & van Loan and other references [R. Gaul]
+- qhalf.htm: A halfspace is the points on or below a hyperplane [D. Strawn]
+- qh-opto.htm#n: Defined inside, outside, on, above, and below a hyperplane [D. Strawn]
+- qhalf.htm#notes: Recast the linear program using negative halfspaces (as used by Qhull) [D. Strawn]
+- qhull_a.h: Fix comment '#include "libqhull/qhull_a.h" [fe rew]
+
+- build/qhull*.pc.in: Templates for pkg-config (derived from Fedorra) [P. McMunn]
+  https://bitbucket.org/mgorny/pkg-config-spec/src/c1bf12afe0df6d95f2fe3f5e1ffb4c50f018825d/pkg-config-spec.txt?at=master&fileviewer=file-view-default
+- Makefile: Remove user_eg3.o from LIBQHULLCPP_OBJS
+- Makefile: Add .h dependencies for unix_r.o, etc.
+- libqhull/Makefile: Fix build of rbox
+- libqhull_r/Makefile: Fix build -I
+- qhull.sln/user_eg3:  Add dependency on libcpp
+- Removed bin/libqhull_r.dll (should be qhull_r.dll) 
+- Removed  build/qhulltest.vcproj (see build/qhulltest/qhulltest.vcproj)
+  
+------------
+Qhull 2015.0.4 2015/9/30 (7.0.4.1984)
+ - qh-get.htm: Unix tarball includes version number (e.g., qhull-2015-src-7.1.0.1940.tgz) [Hauptman]
+ - qglobal.c: Add qh_version2 with Unix version for "-V" option [Hauptman]
+ - build/qhull-32.sln, *-32.vcxproj: Add Visual Studio 32-bit build for 2010+
+ - build/qhull-64.sln, *-64.vcxproj: Add Visual Studio 64-bit build for 2010+ [G. Lodron]
+ - make-vcproj.sh: Restore to eg/... It is required for Visual Studio builds
+ - README.txt: updated builds and reentrant Qhull
+ - Add documentation for QHULL_LIB_CHECK
+ - qh_lib_check: Check for unknown QHULL_LIB_TYPE
+ - qh-code.htm: Add memory requirements for 32- and 64-bit
+
+------------
+Qhull 2015.0.3 2015/9/22
+ - qh_mem, qh_merge: Log before 'delete' instead of afterwards [Coverity, K. Schwehr]
+ - qh_merge: Test for NULL horizon in qh_checkzero [Coverity, K. Schwehr]
+ - qh_matchneighbor: Check for matchfacet not a neighbor of facet [Coverity, K. Schwehr]
+ - qh_triangulate: Explicit check for visible==NULL [Coverity, K. Schwehr]
+ - qh_findbestfacet (unused by qhull): Fix test of isoutside [Coverity, K. Schwehr]
+ - qh_check_maxout: Check bestfacet!=0 for logging its id [Coverity, K. Schwehr]
+ - qh_nearvertex: Check for bestvertex not found [Coverity, K. Schwehr]
+ - qh_checkfacet: Check for missing neighbors of simplicial facets [Coverity, K. Schwehr]
+ - qh_setdelnth: Check 'nth' before using it [Coverity, K. Schwehr]
+ - Annotate code for Coverity warnings (most of these protected by qh_errexit) [K. Schwehr]
+
+ - qh_printfacet3math: explicit format string (duplicates change to io.c) [B. Pearlmutter]
+ - libqhull_r.h: fix spelling error (duplicates change to libqhull.h) [B. Pearlmutter]
+ - unix_r.c: fix spelling error (duplicates change to unix.c) [B. Pearlmutter]
+ - qhull_a.h: define qhullUnused() only if defined(__cplusplus) [R. Stogner]
+ - qh_version: Use const char str[]= "string" instead of const char * str= "string" [U. Drepper, p. 27]
+ - qh_newvertex: Use UINT_MAX instead of 0xFFFFFFFF
+ - qh_newridge: Use UINT_MAX instead of 0xFFFFFFFF
+ - Reviewed FIXUP notes
+
+ - QhullRidge_test: t_foreach use 'foreach(const QhullVertex &v, vertices) 
+ - Made '#include "RoadTest.h" consistent across all C++ tests
+
+ - qh-code.htm: May also use libqhull_r (e.g., FOREACHfacet_(...))
+ - qh-get.htm: Add list of download build repositories
+
+ - Add CMakeModules/CheckLFS.cmake: Enables Large File Support [B. Pearlmutter]
+ - Makefile: Use -fpic at all times instead of -fPIC, [U. Drepper p. 15]
+
+------------
+Qhull 2015.0.2 2015/9/1
+ - global_r.c: Fixed spelling of /* duplicated in...qh_clear_outputflags */ [K. Schwehr]
+ - Replaced Gitorious with GitHub
+ - Moved 'to do' comments into Changes.txt
+
+------------
+Qhull 2015.0.1 2015/8/31
+
+ Source code changes
+ - Increased size of vertexT.id and ridgeT.id to 2^32 [H. Strandenes, C. Carson, K. Nguyen]
+   Reworded the warning message for ridgeT.id overflow.  It does not affect Qhull output
+ - Add qh_lib_check to check for a compatible Qhull library.
+   Programs should call QHULL_LIB_CHECK before calling Qhull.
+ - Include headers prefixed with libqhull/, libqhull_r/, or libqhullcpp/
+ - Renamed debugging routines dfacet/dvertex to qh_dfacet/qh_dvertex 
+ - Rewrote user_eg, user_eg2, and user_eg3 as reentrant code
+ - Renamed 'qh_rand_seed' to 'qh_last_random'.  Declare it as DATA
+ - qh_initqhull_start2 sets qh->NOerrexit on initialization
+   User must clear NOerrexit after setjmp()
+   
+ Other source code changes
+ - Define ptr_intT as 'long long' for __MINGW64__ [A. Voskov]
+ - poly_r.c: initialize horizon_skip [K. Schwehr]
+ - Removed vertexT.dim and MAX_vdim.  It is not used by reentrant Qhull.
+ - Removed qhull_inuse.  Not used by C++
+ - Removed old __MWERKS__/__POWERPC__ code that speed up SIOUX I/O
+ - Moved #include libqhull/... before system includes (e.g., <stdio.h>
+ - Comment-out _isatty declaration.  Avoids "C4273 ... inconsistent dll linkage"
+ - Add random.h/random_r.h as an include file to random.c/random_r.c 
+ - Rename rbox routines to qh_roundi/qh_out1/qh_out2n/qh_out3n 
+ - Rename dfacet and dvertex to qh_dfacet and qh_dvertex 
+ - Replace 'qhmem .zzz' with 'qhmem.zzz'
+ - Removed spaces between function name and parentheses
+ - Rename 'enum statistics' to 'enum qh_statistics'
+ - Declare rbox as DATA in qhull-exports.def and qhull_p-exports.def
+ - In comments, use 'qh.zzz' to reference qhT fields
+ - In qh_fprintf, use qhmem.ferr to report errors
+ - qh_fprintf may be called for errors in qh_initstatistics and qh_meminit
+ - qh_pointid returns qh_IDnone, qh_IDinterior, qh_IDunknown in place of -3, -2, -1 resp.
+ - getid_() returns qh_IDunknown in place of -1
+ - After qh_meminit, qhmem.ferr is non-zero (stderr is the default)
+ - Update qh_MEMalign in testqset.c to user.h (with realT and void*)
+ - Split rboxT into a header file
+ - Add rboxlib.h to libqhull_a.h
+ - Rename PI to qh_PI and extend to 30 digits
+ - Rename MAXdim to qh_MAXdim
+ - Change spacing for type annotations '*' and '&' in C++ header files
+ - Test for !rbox_output/cpp_object in qh_fprintf_rbox
+ - Remove 'inline' annotation from explicit inline declarations
+ - Column 25 formatting for iterators, etc.
+ - Use '#//!\name' for section headers
+ - QhullFacet.cpp: zinc_(Zdistio);
+ - Clear qhT.ALLOWrestart in qh_errexit
+ - Replace longjmp with qh_errexit_rbox in qh_rboxpoints
+ - Add jmpExtra after rbox_errexit to protect against compiler errors
+ - Add qh.ISqhullQh to indicate initialization by QhullQh()
+ - Add library warnings to 'rbox D4', user_eg, user_eg2, user_eg3
+ - Add headers to q_eg, q_egtest, and q_test
+ - Check that qh.NOerrexit is cleared before call to qh_initflags
+
+Qhull documentation
+ - README.txt: Added references to qh-code.htm
+ - README.txt: Added section 'Calling Qhull from C programs'
+ - qh-code.htm: Moved Performance after C++ and C interface
+ - qh-code.htm: Moved Cpp Questions to end of the C++ section
+ - qh-code.htm: Fixed documentation for 'include' path.  It should be include/libqhull
+ - qconvex.htm: Fixed documentation for 'i'.  It triangulates in 4-d and higher [ref]
+ - Clarified qhalf space documentation for the interior point [J. Santos]
+ - rbox.c: Version is same date as qh_version in global.c
+ - gobal_r.c: Version includes a '.r' suffix to indicate 'reentrant'
+
+Qhull builds
+ - Development moved to http://github.com/qhull/qhull
+   git clone git@github.com:qhull/qhull.git
+ - Exchanged make targets for testing.  
+   'make test' is a quick test of qhull programs.  
+   'make testall' is a thorough test
+ - Added 'make help' and 'make test' to libqhull and libqhull_r Makefiles
+ - CMakeLists.txt: Remove libqhull, libqhull_r, and libqhullcpp from include_directories
+ - CMakeLists.txt: Add qhull_SHAREDR for qhull_r
+ - CMakeLists.txt: Retain qhull_SHARED and qhull_SHAREDP (qh_QHpointer)
+ - CMakeLists.txt: Move qhull_SHARED and qhull_SHAREDP (qh_QHpointer) to qhull_TARGETS_OLD
+   Drop qhull_STATICP (use qhull_SHAREDP or qhull_STATIC)
+   Set SOVERSION and VERSION for shared libraries
+ - Move qhull_p-exports.def back to libqhull
+ - Switched to mingw-w64-install for gcc
+ - Improved prompts for 'make'
+ - qhull-all.pro: Remove user_eg3.cpp from OTHER_FILES
+ - libqhull.pro: Ordered object files by frequency of execution, as done before
+ - Add the folder name to C++ includes and remove libqhullcpp from INCLUDEPATH
+ - Changed CONFIG+=qtestlib to QT+=testlib
+ - Changed Makefile to gcc -O3 (was -O2)
+ - Changed libqhull/libqhull_r Makefiles to both produce rbox, qhull, ..., user_eg, and user_eg2
+ - Removed Debian 'config/...'.  It was needed for Qhull 2012.
+
+libqhull_r (reentrant Qhull)
+ - Replaced qh_qh with a parameter to each procedure [P. Klosterman]
+   No more globally defined data structures in Qhull
+   Simplified multithreading and C++ user interface
+   All functions are reentrant (Qt: "A reentrant function can ... be called simultaneously from multiple threads, but only if each invocation uses its own data.")
+   No more qh_QHpointer.
+   See user_eg3 and qhulltest
+   New libraries
+      libqhull_r -- Shared library with reentrant sources (e.g., poly_r.h and poly_r.c which replace libqhull's poly.h and poly.c)
+      libqhullstatic_r -- Static library with the same sources as libqhull_r
+      libqhullcpp -- The C++ interface using libqhullstatic_r (further notes below)
+   New executables
+      testqset_r -- Test qset_r.c (the reentrant version of qset.c
+      
+ Source code changes for libqhull_r      
+ - Add qh_zero() to initialize and zero memory for qh_new_qhull
+ - Remove qh_save_qhull(), qh_restore_qhull(), and qh.old_qhstat from global_r.c
+ - Remove qh_freeqhull2() (global_r.c)
+ - Remove qh_freestatistics() (stat_r.c)
+ - Remove qh_compare_vertexpoint (qhT is not available, unused code)
+ - Remove conditional code for __POWERPC__ from unix_r.c and rbox_r.c
+ - Move qh_last_random into qh->last_random (random_r.c)
+ - Rename sources files with a '_r' suffix.  qhull_a.h becomes qhull_ra.h
+ - Replace 'qh' macro with 'qh->'
+ - Replace global qhT with parameter-0
+ - Add qhmemT to beginning of qhT.  It may not be used standalone.
+ - Add qhstatT to end of qhT
+ - Remove qhull_inuse
+ - Change qhmem.zzz to qh->qhmem.zzz
+ - Replace qh_qhstat with qh->qhstat
+ - Remove qh_freestatistics
+ - Replace qh_last_random with qh->last_random
+ - Replace rboxT with qh->rbox_errexit, rbox_isinteger, rbox_out_offset
+ - Replace rbox.ferr/fout with qh->ferr/fout
+ - No qh for qh_exit, qh_free, qh_malloc, qh_strtod, qh_strtol, qh_stddev
+ - New qmake include files qhull-app-c_r.pri, qhull-app-shared_r.pri, qhull-libqhull-src_r.pri
+ - Replace 'int' with 'countT' and 'COUNTmax' for large counts and identifiers
+ - qhset converted to countT
+ - Removed vertexT.dim -- No longer needed by cpp 
+   Removed MAX_vdim
+ - Guarantee that qh->run_id!=0.  Old code assumed that qh_RANDOMint was 31 bits
+
+Changes to libqhullcpp
+ - Added QhullVertexSet.h to libqhullcpp.pro and libqhullpcpp.pro
+ - QhullVertexSet: error if qhsettemp_defined at copy constructor/assignment (otherwise double free)
+ - Enable QhullSet.operator=.  Copy constructor and assignment only copies pointers
+ - Changed QhullPoint.operator==() to sqrt(distanceEpsilon)
+ - Added assignment of base class QhullPoints to PointCoordinates.operator=
+ - Enable QhullPoints.operator=
+ - Rename PointCoordinates.point_comment to describe_points
+ - Add 'typename T' to definition of QhullSet<T>::value()
+
+C++ interface
+ - Reimplemented C++ interface on reentrant libqhull_r instead of libqhull
+ - Prepend include files with libqhullcpp/
+ - Replaced UsingLibQhull with QhullQh and macro QH_TRY
+   Removed UsingLibQhull.currentAngleEpsilon and related routines
+   Removed UsingLibQhull_test.cpp
+   Replaced globalDistanceEpsilon with QhullQh.distanceEpsilon
+   Replaced globalAngleEpsilon with QhullQh.angleEpsilon
+   Moved UsingQhullLib.checkQhullMemoryEmpty to QhullQh.checkAndFreeQhullMemory
+   Replaced FACTORepsilon=10 with QhullQh.factor_epsilon=1.0
+ - To avoid -Wshadow for QhullQh*, use 'qqh' for parameters and 'qh()' for methods
+ - Moved messaging from Qhull to QhullQh
+ - Add check of RboxPoints* in qh_fprintf_rbox
+ - Renamed Qhull.initializeQhull to Qhull.allocateQhullQh
+   Added qh_freeqhull(!qh_ALL) as done by unix.c and other programs
+ - Moved QhullPoints.extraCoordinatesCount into QhullPoints.cpp
+ - Replaced section tags with '#//!\name ...'
+ - Removed qhRunId from print() to ostream.
+ - Removed print() to ostream.  Use '<< qhullPoint' or '<< qhullPoint.print("message")'
+
+C++ interface for most classes
+ - Remove qhRunId
+ - Add QhullQh *qh_qh to all types
+    Pointer comparisons of facetT,etc. do not test corresponding qh_qh
+    Added to end of type for debugging information, unless wasteful alignment 
+ - Add QhullQh * to all constructors
+ - All constructors may use Qhull & instead of QhullQh *
+ - For inherited QhullQh types, change to 'protected'
+ - Renamed 'o' to 'other' except where used extensively in iterators
+ - Except for conditional code, merged the Conversion section into GetSet
+ - Removed empty().  Use isEmpty() instead
+ - Add operator= instead of keeping it private
+ - print_message=0 not allowed.  Use "" instead.
+ - Rename isDefined() to isValid() to match Qt conventions
+ 
+C++ interface by class
+ - Coordinates
+   Removed empty().  Use isEmpty() instead
+   Added append(dim, coordT*)
+   Reformated the iterators
+   Convert to countT
+ - PointCoordinates
+   Added constructors for Qhull or QhullQh* (provides access to QhullPoint.operator==)
+   Removed PointCoordinates(int pointDimension) since PointCoordinates should have a comment.  Also, it is ambiguous with PointCoordinates(QhullQh*)
+   Renamed point_comment to describe_points
+   Convert to countT
+ - Qhull
+   Remove qhull_run_i
+   Remove qh_active
+   Replace property feasiblePoint with field feasible_point and methods setFeasiblePoint/feasiblePoint
+     Returns qh.feasible_point if defined
+   Moved useOutputStream to QhullQh use_output_stream
+   Renamed useOutputStream() to hasOutputStream()
+   Replaced qhull_dimension with qh->input_dim  //! Dimension of result (qh.hull_dim or one less for Delaunay/Voronoi)
+   Removed global s_qhull_output= 0; 
+   Move qhull_status, qhull_message, error_stream, output_stream to QhullQh
+   Renamed qhullQh() to qh()
+   Added check of base address to allocateQhullQh(),  Was not needed for qhullpcpp
+ - QhullFacet
+   Constructor requires Qhull or QhullQh* pointer
+   Convert to countT
+   Dropped implicit conversion from facetT
+   Dropped runId
+   Add print("message") to replace print()
+ - QhullFacetList
+   Constructor requires Qhull or QhullQh* pointer
+   Convert to countT
+   Dropped runId
+ - QhullFacetSet
+   Removed empty().  Use isEmpty() instead
+   Constructor requires Qhull or QhullQh* pointer
+   Convert to countT
+   Dropped runId
+   Add operator=
+   Implement print("message")
+ - QhullHyperplane
+   Add hyperplaneAngle() method
+   Rewrite operator== to use hyperplaneAngle()
+   Reorganize fields to keep pointers aligned
+   Except for default constructor requires Qhull or QhullQh* pointer
+   Enable copy assignment
+   Reorganized header
+ - QhullLinkedList
+   Add operator=
+   Removed empty().  Use isEmpty() instead
+   Convert to countT
+   iterator(T) made iterator(const T &) 
+   const_iterator(T) made const_iterator(const T &) 
+   const_iterator(iterator) made const_iterator(const iterator &) 
+ - QhullPoint
+   Add constructors for Qhull or QhullQh* pointer (for id() and operator==)
+   Add defineAs(coordT*)
+   Add getBaseT() and base_type for QhullSet<QhullPoint>
+   Added checks for point_coordinates==0
+   Removed static QhullPoint::id(), use QhullPoint.id() instead
+   distance() throws an error if dimension doesn't agree or if a point is undefined
+   Convert to countT
+   If !qh_qh, operator==() requires equal coordinates
+   Use cout<<p instead of cout<<p.print()
+   Reorganized
+ - QhullPoints
+   Add constructors for Qhull and QhullQh* (for qh.hull_dim, QhullPoint::operator==)
+   Remove QhullPoints(int pointDimension) since it is ambiguous with QhullPoints(QhullQh *qqh)
+   Add operator=
+   Removed empty().  Use isEmpty() instead
+   Convert to countT
+   operator==() tests if pointers are the same.  Ituses distanceEpsilon if qh_qh is defined
+   Reorganized
+ - QhullPoints::Iterator and ConstIterator
+   Removed default constructors
+   Add constructors for Qhull and QhullQh* (for qh.hull_dim, QhullPoint::operator==)
+   Moved test of dimension from QHULL_ASSERT to operator==
+   Added QHULL_ASSERT of qh_qh
+   Convert to countT
+ - QhullPointSet
+   Constructor requires Qhull or QhullQh* instead of dimension()
+   Add operator=
+   Removed empty().  Use isEmpty() instead
+   Convert to countT
+   Always print print_message
+   Drop print().  Replace with print("")
+ - QhullQh
+   Added methods hasOutputStream(), disableOutputStream(), and enableOutputStream() (was Qhull UseOutputStream)
+   Add test of qh.NOerrexit to maybeThrowQhullMessage()
+   Add qhull_status, qhull_message, error_stream, output_stream from Qhull
+   Add factor_epsilon 
+ - QhullRidge
+   Constructor requires Qhull or QhullQh* pointer
+   Dropped implicit conversion from ridgeT
+   Converted otherFacet() to 'const &'
+   Converted nextRidge3d() to 'const &'
+   Message for '<< QhullRidge' replaces "   - " instead of preceding it
+ - QhullSet
+   Removed empty().  Use isEmpty() instead
+   Constructor requires Qhull or QhullQh* pointer
+   Convert to countT
+   Add operator=
+ - QhullVertex
+   Constructor requires Qhull or QhullQh* pointer
+   Convert to countT
+   Dropped implicit conversion from vertexT
+   Add message to '<< QhullVertex'
+ - QhullVertexSet
+   Removed empty().  Use isEmpty() instead
+   Constructor requires Qhull or QhullQh* pointer
+   Convert to countT
+ - UsingQhullLib
+   Removed
+   Replace setGlobalDistanceEpsilon with setFactorEpsilon
+   Replace globalDistanceEpsilon with distanceEpsilon
+   
+------------
+Qhull 2012.1  2012/02/18 6.3.1.1494
+ - Fix CMakeLists for libqhull with MATCHES [P. Gajdos]
+
+------------
+Qhull 2012.1  2012/02/18 6.3.1.1490
+
+Code changes
+ - Require option 'Qz' for Delaunay triangulation/Voronoi diagram 
+   of cocircular/cospherical points [D. Sheehy]
+ - qh_errexit: Do not call qh_printsummary or qh_printstats on qh_ERRinput
+ - Change error QH6227 (all degenerate) from qh_ERRinput to qh_ERRprec
+ - Change error QH6159 (ID overflow) from qh_ERRinput to qh_ERRqhull
+ - eg/q_eg, q_egtest, q_test: Run if qconvex is in $PATH [M. Atzeri]
+   
+Build changes [M. Atzeri]
+ - Install to share/doc/qhull instead of share/doc/packages/qhull
+ - On Unix systems, install to share/man/man1 instead of man/man1
+ - CMakeLists: Remove the installation of user_eg* and testqset
+ - CMakeLists: Remove VERSION from qhull executables and libraries
+ - CMakeLists: Define qhull_SOVERSION instead of qhull_MAJOR 
+ - CMakeLists: Set SOVERSION for shared libraries
+ - Rename libraries to qhull, qhull_d, qhull_p, and qhull_pd
+   libqhull6_p.vcproj is now libqhull_p.vcproj
+   mingw builds as libqhull.dll
+   cygwin builds as cygqhull-6.dll
+   linux builds as libqhull.so.6.3.1 with symbolic link as libqhull.so
+ - Developers using qhull 2011: 
+   libqhull6.so is now libqhull_p.so.  Do not use libqhull.so.
+   qhull6.dll is now qhull_p.dll.  Do not use qhull.dll. 
+ - Merged road/ into libqhullcpp/ and qhulltest/
+   Moved RoadLogEvent.* and RoadError.* to libqhullcpp
+   Moved RoadTest.* to qhulltest (requires Qt)
+   Installed RoadTest.h in libqhullcpp 
+
+Doc changes
+ - index.htm: Mathworks uses qhull for n-d
+ - qhull.htm: Fix qhull for qconvex
+ - qdelaun.htm/qvoronoi.htm: Use option 'Qz' for circular/cospherical inputs
+ - make help: Display targets
+ - Makefile: Better messaging
+
+------------
+Qhull 2012.1  2012/02/02 6.3.0.1483
+
+Bug fixes
+ - Fixed qset.c for -fno-strict-aliasing. This gcc option is no longer needed
+   (disallow two pointers of differing types to the same memory location)
+ - Fixed error in qh_setappend_set if first set full and second set empty
+ - qh_setdelnth, qh_setdelnth_sorted: fixed wording of error message
+ - qh_setcheck: error message listed size and max backwards.
+ - qh_setequal: Allow NULL set as documented
+ - qh_setindex: Allow NULL set as documented
+ - qh_settemppush: report error if NULL
+
+Code changes
+ - Add testqset: low level test of qset.c with mem.c
+ - qh_setendpointer: Implements QSet::endPointer()
+ - Assigned unique error code for qh_gethash
+
+Build changes
+ - Added qhull.dll(.so) for Octave and other Debian builds
+   The global data structure qh_qh is statically defined (no qh_QHpointer)
+   Linked user_eg2 with qhull.dll (libqhull.so) instead of qhullstatic
+   Added qh_dllimport to libqhull.h for qhull.dll with MSVC 
+   Changed qhull-app-shared.pri to use libqhull (without qh_QHpointer)
+ - Renamed libqhull6.so to libqhull6_p.so
+   Renamed qhull6.dll to qhull6_p.dll
+   The _p libraries (e.g., libqhull6_p.so) require -Dqh_QHpointer
+   Renamed qhull6.vcproj to libqhull6_p.vcproj
+   Added libqhullp/libqhullp.pro for shared library (libqhull6_p.so)
+   Added qhull-app-sharedp.pri for shared libraries with qh_QHpointer
+ - Install libqhull/*.htm files into include/libqhull
+ - Removed libqhull/qhull.h-deprecated [J. Eaton]
+ - Other changes to Makefile builds
+   Added 'make qtestall' as a smoketest of each qhull program
+   src/libqhull/Makefile: Use 'ar -rs ...' instead of ranlib
+   src/libqhull/Makefile: Fixed targets for cleanall
+ - Other changes to DevStudio builds
+   Moved pdb files for qhull libraries to lib/
+   AdditionalIncludeDirectories: Removed ../src/libqhullcpp 
+   Use build-cmake/ for the DevStudio CMake build
+ - Other changes to Qt builds
+   Renamed qhull-libsrc.pri to qhull-libqhull-src.pri
+ - Added explicit d2u conversions to qhull-zip.sh
+ - Fixed \n vs. \r\n issues for Windows source files
+
+ Draft of Debian/AutoConf build (untested)
+ - Adjusted the Makefile.am's for the new directory structure.
+ - Added testqset to bin_PROGRAMS
+ - config/bootstrap.sh copies program sources into src/libqhull
+ - Kept qh_QHpointer=0 (static global data structure, qh_qh).  It is faster.
+   Planning a new interface (qhull7?) which passes qh_qh as a parameter
+ - Added config/changelog from the 2003.1 Debian build
+ - Moved the debian/patches directory to config/
+   Optional patches to change smoketest message and turn on qh_QHpointer
+ - Deleted the debian directory.  It was the old Debian build from 2003.1
+   Rafael Laboissiere's config directory replaced this build..
+ - Deleted Make-conf.sh (also the old Debian build)
+ 
+Doc changes
+ - FAQ: Updated notes on computing volume of a Voronoi region
+ - Added direct link to ACM Digital Library for downloading the qhull paper
+ - Added link to Qhull in R
+ - qset.c: Updated notes about NULL sets
+ - qh_setappend: clarify qh_setappend for NULL newelem
+ - qh_setdellast: Fix head note
+ - Add build/README.txt
+ - Add uninstall instructions to README.txt and CMakeLists.txt
+ - Added instructions to create build/*.vcproj to CMakeLists.txt
+ - Update copyright to 2012
+ - Updated page links.  Added Google books, patents, and blogs. 
+
+-----------
+Qhull 2009.1.3 2011/12/06
+  configure: Add  -fno-strict-aliasing if $GCC,  Required for gcc 4.1+
+
+------------
+Qhull 2011.2  2011/11/29 6.2.1.1446
+
+Bug fixes
+ - qh_new_qhull: Call qh_prepare_output if !outfile [A. Aldoma]
+   No effect on qhull users since qh_prepare_output is always called.
+ - Replace Qhull-go.pif with Qhull-go.lnk for Windows 7 64-bit [lots]
+ - Error if qh_newhashtable, qh_setnew, or qh_memalloc overflows [X. Cheng]
+   For example, 'rbox 64 D32' overflows hash table for qh_matchnewfacets
+   Qhull uses 32-bit ints for identifiers, counts, and sizes. See "WARN64"
+ - q_eg, q_test: change tail +3 to tail -n +3 [N. Dubray, M. Atzeri]
+ - Qhull-go.bat: Changed 'cmd' to '%comspec%'
+
+Build changes
+ - Added src/libqhull/Makefile for simple gcc build of executables and lib
+ - qhulltest.vcproj: Replaced full path to QT with $QTDIR (e.g., c:/qt/4.7.4)
+ - Split userprintf_rbox.c from userprintf.c,  
+   Otherwise qhull brings in rboxlib and rbox brings in libqhull
+ - Makefile: qhullx target must be after LIBQHULLS_OBJS
+ - Makefile: Explicitly list rbox dependencies for qhullx target
+ - MBorland: Fixed tabs
+ - Placed $LIBQHULLS_OBJS in same order.  Frequently called ones together. 
+ - Update file lists for Make-config.sh [O. Lahaye]
+ - CMakeLists: add README.txt,etc. to DOC_INSTALL_DIR [M. Atzeri]
+ - Restored qhull.h-deprecated.  
+   qhull.h conflicts with Qhull.h on Windows systems [C. Abela]
+ - make-config.sh: Add warning that it is out-of-date
+ - Remove extra space in '#! /bin/sh' in q_eg, etc. [P. Cheeseman]
+
+Source changes
+ - libqhull.h: Added qh_True and qh_False for True/False [A. Mutzel]
+   Did not remove or replace True/False since it is used everywhere
+ - Moved error message from qh_argv_to_command to caller.  Avoids dependency.
+ - user_eg3.c: Use '10 D2' as default rbox (e.g., 'user_eg3 rbox qhull d')
+ - user.c, user_eg2.c: Add test of qh_qh as done in user_eg.c
+ - q_test: Removed duplicate test of qhull C-0.02
+
+Documentation
+ - index.html: Added ACM Authorizer link to ACM Trans. Math. Software
+ - Split Delaunay and Voronoi FAQs
+ - FAQ: How to compute the volume of a Voronoi region [C, Brinch]
+ - Add 'FS' to qconvex prompt (total area and volume) 
+ - Add clarification to 'Fv' about corner input sites [O. Can]
+ - Qhull-go.bat: Removed out-of-date advice.  Added title.
+ - qh-code.htm: Updated the discussion of multi-threading for C++ [I. Pirwani]
+ 
+Qhull 2009.1.2 2011/11/21
+ - Revert to LF line endings [P. Cheeseman]
+ - Remove out-of-date material from qhull-go.bat
+ - Replaced QHULL-GO with a lnk file
+
+Qhull 2011.1  2011/05/23 6.2.0.1385 (exe/dll files unchanged)
+ - delaunay.vcproj: Fixed qhullstatic_d.lib for debug and minrelsize builds
+ - Did not redate the distribution
+
+Qhull 2011.1  2011/05/18 6.2.0.1385 (exe/dll files unchanged)
+ - Add 'm' library to shared and static targets on Unix [A. Bouchard]
+
+Qhull 2011.1  2011/05/14 6.2.0.1383 (exe/dll files unchanged)
+ - PointCoordinates.cpp: Add #include <iterator> [R. Richter, S. Pasko]
+ - Remove deprecated libqhull/qhull.h
+   Use libqhull/libqhull.h instead.  Avoids confusion with libqhullcpp/Qhull.h
+ - Makefile: Add LIBDIR, INCDIR, and DESTDIR to install [L.H. de Mello]
+     Separate MAN install from DOC install
+     Create install directories
+     Installs headers to include/libqhull, include/libqhullcpp, include/road
+ - CMakeLists.txt: Add MAN_INSTALL_DIR for qhull.1 and rbox.1 man pages
+     Add RoadTest.h to include/road for Qt users (road_HEADERS)
+ - Renamed md5sum files to avoid two extensions
+ - qh-get.htm: Add Readme links and 2009.1 note.
+ - qh-optf.htm: Fix link
+ - index.htm: Updated Google Scholar link
+ - qhull-zip.sh: Improved error message.
+
+------------
+Qhull 2011.1  2011/04/17 6.2.0.1373
+
+Changes to deliverables
+ - qvoronoi: Deprecated 'Qt' and 'QJn'. Removed from documentation and prompts.
+   These options produced duplicate Voronoi vertices for cospherical data.
+ - Removed doskey from Qhull-go.bat.  It is incompatible with Windows 7
+ - Added 'facets' argument to user_eg3.cpp
+ - user_eg links with shared library
+ - qhulltest.cpp: Add closing prompt.
+
+Changes to build system
+ - Reorganized source directories
+ - Moved executables to bin directory
+ - Add CMake build for all targets (CMakeFiles.txt) [M. Moll assisted]
+ - Add gcc build for all targets (Makefile)
+ - Fixed location of qhull.man and rbox.man [M. Moll]
+ - Add DevStudio builds for all targets (build/*.vcproj)
+ - Added shared library (lib/qhull6.dll)
+   Added qh_QHpointer_dllimport to work around problems with MSVC
+ - Added static libraries with and without qh_QHpointer (lib/qhullstatic.lib)
+ - Added eg/make-vcproj.sh to create vcproj/sln files from cmake and qmake
+ - Document location of qh_QHpointer
+ - Use shadow build directory
+ - Made -fno-strict-aliasing conditional on gcc version
+ - Added src/qhull-app-cpp.pri, src/qhull-app-c.pri, etc. for common settings
+ - Add .gitignore with ignored files and directories.  
+ -   Use .git/info/exclude for locally excluded files.
+ - Fixed MBorland for new directory structure
+ - cleanall (Makefile): Delete 'linked' programs due to libqhull_r and libqhull/Makefile
+
+Changes to documentation
+ - qvoronoi.htm: Remove quotes from qvoronoi example
+ - qhull-cpp.xml: Add naming conventions
+ - index.htm: Add Google Scholar references
+ - qh-optf.htm: Add note about order of 'Fn' matching 'Fv' order [Q. Pan]
+ - Add patch for old builds in qh-get.htm
+ - Added C++ compiling instructions to README.txt
+ - Add instructions for fixing the DOS window
+ - Changed DOS window to command window
+ - Fixed html links
+ - qh-get.htm: Dropped the Spanish mirror site.  It was disabled.
+
+Changes to C code
+ - mem.h: Define ptr_intT as 'long long' for Microsoft Windows _win64 builds.
+   On Linux and Mac, 'long' is 64-bits on a 64-bit host
+ - Added qh_QHpointer_dllimport to work around MSVC problem
+ - qconvex.c,etc.: Define prototype for _isatty
+ - Define MSG_QHULL_ERROR in user.h
+ - Move MSG_FIXUP to 11000 and updated FIXUP QH11...
+
+Changes to test code
+ - Add note to q_test than R1e-3 may error (qh-code.htm, Enhancements)
+ - Add test for executables to q_eg, etc.
+ - Fixed Qhull-go.bat.  QHULL-GO invokes it with command.com,
+
+Changes to C++ interface
+ - QhullFacet: Added isSimplicial, isTopOrient, isTriCoplanar, isUpperDelaunay
+ - Added Qhull::defineVertexFacetNeighbors() for facetNeighbors of vertices.
+   Automatically called for facet merging and Voronoi diagrams
+   Do not print QhullVertex::facetNeighbors is !facetNeighborsDefined()
+ - Assigned FIXUP identifiers
+ - QhullError: Add copy constructor, assignment operator, and destructor
+ - Add throw() specifiers to RoadError and QhullError
+ - Renamed RoadError::defined() to RoadError::isDefined()
+ - Add #error to Qhull.h if qh_QHpointer is not defined
+
+Changes to C++ code
+ - Fixed bug reported by renangms.  Vertex output throws error QH10034
+   and defineVertexNeighbors() does not exist.
+ - Define QHULL_USES_QT for qt-qhull.cpp [renangms]
+ - Reviewed all copy constructors and copy assignments.  Updated comments.
+   Defined Qhull copy constructor and copy assignment [G. Rivet-Sabourin]
+   Disabled UsingQhullLib default constructor, copy construct, and copy assign 
+ - Merged changes from J. Obermayr in gitorious/jobermayrs-qhull:next
+ -   Fix strncat limit in rboxlib.c and global.c
+ -   Changes to CMakeLists.txt for openSUSE
+ - Fixed additional uses of strncat
+ - Fixed QhullFacet::PrintRidges to check hasNextRidge3d()
+ - Removed gcc warnings for shadowing from code (src/qhull-warn.pri)
+ - Removed semicolon after extern "C" {...}
+ - Removed experimental QhullEvent/QhullLog
+ - Use fabs() instead of abs() to avoid accidental conversions to int
+ - Fixed type of vertex->neighbors in qh_printvoronoi [no effect on results]
+ - Removed unnecessary if statement in qh_printvoronoi
+
+------------
+qhull 2010.1 2010/01/14
+- Fixed quote for #include in qhull.h [U.Hergenhahn, K.Roland]
+- Add qt-qhull.cpp with Qt conditional code
+- Add libqhullp.proj
+- Add libqhull5 to Readme, Announce, download
+- Reviewed #pragma
+- Reviewed FIXUP and assigned QH tags
+- All projects compile with warnings enabled
+- Replaced 'up' glyphs with &#187;
+- Moved cpp questions to qh-code.htm#questions-cpp 
+- Moved suggestions to qh-code.htm#enhance 
+- Moved documentation requests to qh-code.htm#enhance
+- Add md5sum file to distributions
+- Switched to DevStudio builds to avoid dependent libraries, 10% slower
+  Removed user_eg3.exe and qhullcpp.dll from Windows build 
+  Fix qhull.sln and project files for qh_QHpointer
+- Add eg/qhull-zip.sh to build qhull distribution files
+
+------------
+qhull 2010.1 2010/01/10
+- Test for NULL fp in qh_eachvoronoi [D. Szczerba]
+
+qhull 2010.1 2010/01/09
+
+Changes to build and distribution
+- Use qh_QHpointer=0 for libqhull.a, qhull, rbox, etc.
+  Use -Dqh_QHpointer for libqhullp.a, qhullcpp.dll, etc.
+  qh_QHpointer [2010, gcc] 4% time 4% space, [2003, msvc] 8% time 2% space
+- Add config/ and project/debian/ for Autoconf build [R. Laboissiere]
+  from debian branch in git and http://savannah.nongnu.org/cvs/?group=qhull
+- Add CMakeLists.txt [kwilliams]
+- Fix tabs in Makefile.txt [mschamschula]
+- Add -fno-strict-aliasing to Makefile for gcc 4.1, 4.2, and 4.3 qset segfault
+- Remove user_eg.exe and user_eg2.exe from Windows distribution
+- Order object files by frequency of execution for better locality.
+
+Changes to source
+- Remove ptr_intT from qh_matchvertices.  It was int since the beginning.
+- user.h requires <time.h> for CLOCKS_PER_SEC
+- Move ostream<<QhullFacetList from inline to compiled.
+- Removed ConvexHull/ from git.  Not used.
+
+------------
+qhull 2009.1.1 2010/01/09
+- Patch release of 2009.1.
+  qh_gethash allowed a negative result, causing overwrite or segfault
+  See git:qhull/project/patch/qhull-2003.1/poly.c-qh_gethash.patch
+  Compared results of q_test, q_eg, q_egtest with patched poly.c, qhull-2003.1
+
+------------
+qhull 2010.1 2010/01/07
+- Assign type to qh.old_qhstat and memT.tempstack [amorilia]
+- Replace tabs with spaces.
+- Fix qh_pointid in case ptr_intT is unsigned
+
+qhull 2010.1 2010/01/06
+- Fixed serious bug in qh_gethash [poly.c]
+- Documentation and build system are incomplete (see above)
+- First release of C++ interface [qh-code.htm]
+- Development moved to http://gitorious.org/qhull
+  git clone git@gitorious.org:qhull/qhull.git
+- Did not fix conformant tesselations for 'Qt'.
+  For details, see http://www.qhull.org/news#bugs of May 2007 and Dec 2006.
+- Use g++ builds for Windows distribution (10% faster than msvc2005)
+  Combined vcproj/ and qtproj/ into project/
+  vcproj will be replaced by qmake generated files
+
+------------
+qhull 2010.0.3 2010/01/05
+Fixed bugs
+- 'QJn': Fix qh.STOPcone in qh_build_withrestart().  It was not cleared.
+- qh_initqhull_outputflags [global.c]: warn about Qc only if QHULLfinished
+    otherwise set if needed
+
+qhull 2010.0.2 2010/01/04
+
+Fixed bugs
+- qh_gethash [poly.c]: fix sign conversion.
+    Previously, the result may be negative, leading to a segfault.
+    The bug is more likely with large address spaces
+    Reviewed all uses of %(modulo) for remainder with negative arguments
+- Reviewed output of q_test and compared to results from 2003.1
+
+Breaking code changes
+- Return type of qh_gethash changed from unsigned to int.  Matches 'size'
+- addhash takes a signed hash
+  qh_addhash( newelem, hashtable, hashsize, hash )
+
+Code changes
+- Test for qh_qh in qh_printf
+- Makefile.txt corrected for libqhull build [amorilia]
+- Renamed index to idx to avoid shadowing BSD strings.h [kwilliams]
+
+qhull 2010.0.1  2010/01/03
+
+New Features:
+ - Added option 'Ta' to annotate output with message codes
+
+Preliminary C++ support:
+ - C++ declarations may change without warning
+ - Preliminary documentation for Qhull's C++ interface [qh-code.htm#cpp, qhull-cpp.xml]
+ - Added user_eg3 as an example of Qhull.cpp
+ - Removed qhull_interface.cpp.  Use Qhull.cpp instead.
+   If math.h breaks '#include qhull_a.h', preceed it with '#include math.h'
+
+Changes to qhull options and results
+ - Allow 'd' and 'v' as the filename for 'TO ..' and 'TI ...' in qdelaunay [M. Jambon]
+ - 'rbox tN' requires an integer (previously allowed floats)
+ - Allow quoted filenames for 'TO ...' and 'TI ...'
+ - Prefix error messages and warnings with a message code (e.g., QH6012)
+ - Fixed rbox ignoring flags that were not separated by spaces
+ - Report all hidden options before exiting in qh_checkflags()
+ - Defined qh_OPTIONline [user.h] as max length of option line ('FO')
+ - Report error if negative arguments to rbox 'G', 'L', 'Z'
+ - Unknown rbox flag changed from a warning to an error
+ - Set error status 4 qh_ERRmem if rbox runs out of memory
+ - Removed extra spaces at end of line
+
+Breaking Code Changes:
+ - Renamed qh.coplanarset to coplanarfacetset.  Avoids conflict with facetT.coplanarset
+ - qh_restore_qhull() zeroes out qh.old_qhstat and qh.old_tempstack.  Ownership moved.
+ - Rewrote save_qhull/restore_qhull
+ - Add Ztotcheck to zzdef_ [R. Gardener]
+ - Changed qh_malloc to size_t (was unsigned long)
+ - Declare qh_PRINT instead of int [kwilliams]
+ - In qh_printafacet(), changed error output to 'qh ferr'
+
+Bug fixes to C code:
+ - Use gcc 4.4.0 or later.  gcc 4.2.1, 4.2.2, and 4.3.2 -O2 segfaults in qset.c .  gcc 4.1.1 was OK
+   See bug report http://gcc.gnu.org/ml/gcc-bugs/2007-09/msg00474.html
+ - Rewrite qh_setappend to avoid g++ 4.1, 4.2, and 4.3 strict_aliasing error.
+     Orion Poplawski (orion@cora.nwra.com)
+     http://www.rpmfind.net/linux/RPM/fedora/12/ppc/qhull-devel-2003.1-13.fc12.ppc64.html
+ - Fixed qh_findfacet_all(), "REALmin" should be "-REALmax" [L.A. Taylor].
+     Effects library users for convex hulls and halfspace intersections.
+ - qh_printfacet [io.c] Removed extra space for neighboring facets
+ - Report error if d points, Delaunay, and not Qz
+ - Fixed double-free of facet->centrum for triangulated facets
+ - Fixed mindist initialization if !testcentrum in io.c findbest_test [Ratcliff]
+ - Fixed parentheses around warning for missing 'Qc' [qh_initqhull_outputflags]
+ - Fixed rbox buffer overflow of 'command' when appending seedbuf
+ - Fixed option string for 'rbox t t999'.  Although seed was correctly set to 999,
+   a random seed was appended to the rbox comment (e.g., 'rbox t t999 t32343')
+ - Fixed upper bound of sanity check for qh_RANDOMmax in qh_initqhull_globals()
+
+Changes to C code
+ - Reordered #include from specific to general.  Move up .h for module.
+ - Removed qh.old_stat -- never used
+ - Removed qh_clearcenters from qh_freeqhull.  Duplicated by qh_delfacet
+ - qh_printcenter [io.c] removed unreachable fprintf argument
+ - qh_getarea() [geom2.c] ignored on multiple calls (qh.hasAreaVolume)
+ - qh_getarea() [geom2.c] checks facet->isarea. Set by QhullFacet.facetArea()
+ - qh_triangulate() [poly2.c] ignored on multiple calls (qh.hasTriangulation)
+ - Add statistics for vertex_visit and visit_id to buildtracing
+ - Defined scale and offset parameters for qh_randomfactor
+
+Bug fixes and changes to mem.c/mem.h
+ - Fixed qhmem.totshort (total short memory in use)
+ - Memory tracing (T5) redone for sort order by object
+ - Added full tracing for short memory allocations.
+ - Added qhmem.totfree (total short memory on freelists)
+     Increases size of qh_memalloc_ and qh_memfree_
+ - Added qhmem.totdropped (leftover freesize at end of each short buffer)
+ - Added qhmem.totunused (short size - request size)
+ - Added qhmem.totbuffer (total short memory buffer w/o links)
+ - Added memory statistics to qh_NOmem;
+ - Added qh_memtotal to track allocated memory
+ - Renamed qh_memfree parameter to 'insize' for consistency with qh_memalloc
+ - Removed qhmem.curlong.  qa_memfreeshort computes curlong from cntlong and cntfree
+ - In mem.h, changed ptr_intT to long.  qh_meminit() checks that it holds a 'void*'
+
+Fixed g++ and devstudio warnings
+ - Except for bit field conversions, compiles cleanly with
+   -Wall -Wextra -Wshadow -Wcast-qual -Wwrite-strings -Wno-sign-conversion -Wconversion
+ - Fixed warnings at VC8, level 4
+ - Fix data types to remove conversion warnings [kwilliams]
+ - Use size_t for calls to malloc,etc [kwilliams]
+   Retained int sizes for qset.h and mem.h.  Follows Qt convention
+   and is easier to work with.  int can be 64-bits if 2 billion facets
+ - Change literal strings to const char* [kwilliams]
+ - Added type casts to SETfirst and SETsecond [amorilia+alphax]
+ - getid_() returns an int [kwilliams]
+ - Add missing const annotations [kwilliams]
+ - Fixed 64-bit warnings (marked with "WARN64")
+ - Convert sizeof to (int) for int parameters
+ - In libqhull.c, added explicit casts from long to float,  Avoids warning
+ - In global.c, cast time() to int for QRandom-seed.  Avoids warning
+
+Changes to C code for C++ support
+ - Add sln, vcproj, and qtpro files for building Qhull -- add to README notes
+ - Added dim to vertexT for cpp interface. Reduced size of qh.vertex_visit
+ - qh_produce_output [io.c] may be called multiple times (C++ interface)
+ - Moved SETsizeaddr_() to qset.h for use by QhullSet.cpp
+ - Option 'Tz' sets flag qh.USEstdout for QhullPoints.cpp
+ - Added support for multiple output runs from QhullPoints.outputQhull
+ -   qh_clear_outputflags() resets the output flags
+ -   qh_initqhull_outputflags split from qh_initqhull_globals
+ - Added qh.run_id, a random identifier for this instance of Qhull (QhullPoints)
+ -   For qh.run_id, initqhull_start initializes qh_RANDOMseed to time instead of 1
+ - Extracted qh_argv_to_command (random.c) from qh_init_qhull_command and fixed a buffer overflow
+ - Moved qh_strtod/qh_strtol from global.c to random.c for use in rboxlib.c
+ - Split out random functions into random.c
+ - Added message codes to qh_fprintf().  See its definition in user.c
+ - Replaced exit, malloc, free, fprintf, and fputs with qh_malloc,...[J.W. Ratcliff]
+ - Added qh_fprintf, qh_malloc, qh_free, ph_printhelp_narrowhull to user.c
+ - Moved qh_printhelp_degenerate and qh_printhelp_singular from io.c to user.c
+ - Clear qh.ERREXITcalled at end of qh_errexit().
+
+Documentation:
+ - Fixed out-of-date CiteSeer references
+ - Renamed html/qh-in.htm to html/qh-code.htm
+ - Add reference to 'Qt' to 'i'
+ - Add reference to 'FS' to 'FA'
+ - qh-impre.htm discusses precision issues for halfspace intersection
+ - Add cross references between options 'FA' and 'FS'
+ - Added link to Wolfram Research's MathWorld site
+ - Updated Fukuda's links
+ - Changed copyright to C.B. Barber for C++, documentation, and merge.c
+ - Updated Qhull citation with page numbers.
+ - Proposed project: constructing Voronoi diagram
+ - Proposed project: computing Voronoi volumes
+ - Replaced tabs with spaces in qhull.txt and rbox.txt
+
+------------
+qhull 2009.1  2009/6/11
+
+This is a maintenance release done by Rafael Laboissiere <rafael@debian.org>.
+ - src/rbox.c (main): Avoid problems of evaluation order when
+   pre-incrementing arguments of strtod
+ - src/io.c (qh_produce_output), src/stat.c (qh_initstatistics): Use %lu
+   instead of %d in the format string for arguments of type size_t
+ - html/qhull.man, html/rbox.man: Fix several syntax, macros, and hyphen
+   problems in man pages
+ - The Autotools files have been generated with modern version of autoconf (2.63),
+   automake/aclocal (1.10.2), and libtool (2.2.6)
+ - Some character issues in the man pages are fixed
+
+------------
+qhull 2003.1  2003/12/30
+
+New Features:
+ - Add Maple output ('FM') for 2-d and 3-d convex hulls [T. Abraham]
+
+Breaking Code Changes:
+ - Annotate C code with 'const'.  An ANSI compatible compiler is required.
+
+Bug Fixes and Code Changes:
+ - Fixed qh_findbest() for upperdelaunay facets w/o better, lower neighbors
+     For library users and some qhull users [A. Cutti, E. Milloti, K. Sun]
+ - Preserved qhmem.ferr in qh_memfreeshort() for library users
+ - Removed 'static' from qh_compare... for io.h and merge.h [V. Brumberg]
+ - Split out qh_initqhull_start2() to avoid allocating qh_qh
+ - Split out qh_freeqhull2() to avoid freeing qh_qh
+ - Split out qh_produce_output2() and qh_prepare_output()
+ - qh_initstatistics() frees a previously existing qh_qhstat
+ - qh_initqhull_start2() checks that qh_initstatistics() called first
+
+Documentation:
+ - Add warning to findDelaunay() and qh_in.htm about tricoplanar facets
+ - Noted Edelsbrunner's Geometry & Topology for Mesh Generation [qh-impre.htm]
+ - Noted Gartner's Miniball algorithm [qh_impre.htm]
+ - Noted Veron and Leon's shape preserving simplification [qh_impre.htm]
+
+qhull 2003.1  2003/12/19
+
+Bug Fixes:
+ - Reversed coordinate order for qh.ATinfinity in qh_projectinput [V. Brumberg]
+   This effects:
+     Qhull library 'd' or 'v' users with 'Qz' and unequal coordinate ranges.
+     qdelaunay/qvoronoi users with 'Qbk:0Bk:0', 'Qz', and unequal coordinate ranges
+
+Changes to code:
+ - Replaced qh_VERSION with qh_version in global.c [B. Pearlmutter]
+    The previous techniques were either clumsy or caused compiler errors
+ - Removed unused variables from qh_findbest and qh_findbestnew [B. Pearlmutter]
+ - Note that qh.TESTpoints was added in 2002.1 for tsearch implementation
+
+Changes to distribution:
+ - Added Unix distribution including Debian files [R. Laboissiere]
+    The previous Unix distribution is now the source distribution
+ - Added rpm distribution [L. Mazet]
+ - Investigated generation of Win32 dll.  Need to define a C++ interface.
+
+Changes to documentation:
+ - Moved Qhull to www.qhull.org (geom.umn.edu is not available)
+ - The Geometry Center is archived at http://www.geom.uiuc.edu
+ - Reviewed introduction to each program
+    Triangulated output ('Qt') is more accurate than joggled input ('QJ')
+    qdelaunay is 'qhull d Qbb' [C. Ulbrich]
+    qvoronoi is 'qhull v Qbb'
+    Added example of non-simplicial intersection to halfspace intersections
+ - Added warning about using the Qhull library.
+ - Added qhull timings to When to use Qhull [C. Ulbrich]
+ - Reorganized the home page index and the manual index
+ - Moved qh-home.htm to index.htm
+
+Changes to examples
+ - Fixed options for eg/eg.t23.voronoi.imprecise [B. Pearlmutter]
+
+
+------------
+qhull 2002.1  2002/8/20
+
+Changes to distribution:
+ - Set up savannah.nongnu.org/projects/qhull/ [R. Laboissiere]
+ - Set up www.thesa.com as a backup
+ - Added qh-get.htm, a local copy of the download page
+ - Added Visual C++ interface to Qhull, qhull_interface.cpp [K. Erleben]
+ - Use HTTP instead of FTP for downloading Qhull
+ - Renamed qhull-1.0.sit.hqx
+
+Bug fixes:
+ - Fixed sign of coefficients for cdd halfspaces ('FD','Fd')  [T. Abraham]
+
+Changes to code:
+ - Replace qh_version with qh_VERSION in libqhull.h.
+   Allows shared libraries and single point of definition
+ - Added qh.TESTpoints for future implementation of tsearch
+
+Changes to build
+ - Makefile.txt works under cygwin
+ - Added Make-config.sh to create a Debian build [R. Laboissiere]
+ - Added .exe to Makefile.txt#clean.
+ - In README, use -fno-strict-aliasing with gcc-2.95.1 [Karas, Krishnaswami]
+ - Fixed chmod in Makefile.txt [B. Karas]
+
+Documentation updates
+ - Documented input options for each program [A. Montesinos]
+ - FAQ: "How to get the radii of the empty spheres for Voronoi vertices"
+
+URL updates:
+ - Changed official URL from locate/qhull to software/qhull
+ - Changed URLs from relative to absolute in qh-home.htm and qh-get.htm
+ - Added URL for Newsgroup: comp.soft-sys.matlab
+ - Added URL for GNU Octave
+ - Added URLs for Google and Google Groups
+ - Replaced qhull_mail.html and qhull_bug.html with mailto links.
+ - Removed URL for Computational Geometry Tribune
+ - Changed URL for locate/cglist to software/cglist
+ - Used site relative links for qh-home.htm
+
+------------
+qhull 3.1 2001/10/04
+
+New features
+ - Added option 'Qt' to triangulate non-simplicial facets
+ - Added option 'TI file' to input data from file
+ - Added option 'Q10' to prevent special processing for narrow distributions
+        e.g., RBOX 1000 L100000 s G1e-6 t1001803691 | QHULL Tv Q10
+ - Tried to compute Voronoi volumes ('Pv'). Requires dual face graph--not easy
+        See Clarkson's hull program for code.
+
+Changes to options
+ - Added numtricoplanars to 'Fs'. Number of good, triangulated facets for 'Qt'
+ - Added Zdelvertextot to 'Fs'.  If non-zero and Delaunay, input is degenerate
+ - Qhull command ('FQ') may be repeated.
+ - If 'TPn' and 'TWn' defined, trace the addition of point 'n'
+     otherwise continue tracing (previously it stopped in 4-d)
+ - Removed 'Ft' from qdelaunay.  Use 'Qt o' or 'qhull d QJ Qt' instead.
+     For non-simplicial regions, 'Ft' does not satisify the Delaunay property.
+ - If 'Po' or 'TVn', qhull checks outer planes.  Use 'Q5' to turn off.
+ - If 'T4', print facet lists and check polygon after adding each point
+
+Corrections to code
+ - rbox: allow 'c' and 'd' with 's r', meshes, etc.
+ - qh_findbest: redesigned as directed search. qh_findbesthorizon for coplanar
+      qh_findbest is faster for many distributions
+ - qh_findbestnew: redesigned to search horizon of coplanar best newfacets
+      needed for distributions with a sharp edge,
+          e.g., rbox 1000 s Z1 G1e-13 | qhull Tv
+ - qh_findbest/qh_findbestnew: search neighbors of better horizon facets
+      was needed for RBOX 1000 s Z1 G1e-13 t996564279 | qhull Tv
+      and RBOX 1000 s W1e-13 P0 t996547055 | QHULL d Qbb Qc Tv
+ - qh_findbest with noupper: could return an upperdelaunay facet if dist>qh.MINoutside.
+ - qh_findbestnew: allow facet->upperdelaunay if dist > qh.MINoutside
+ - qh_partitioncoplanar: call qh_partitionpoint if outside and perpendicular
+      for distributions with a sharp edge
+ - qh_partitionvisible: report precision error if all newfacets degenerate.
+      was needed for RBOX 1000 s W1e-13 t995138628 | QHULL d
+ - qh_createsimplex: clears qh.num_visible, may be non-zero with 'TRn QJ'
+
+Changes to prompts, warnings, and statistics
+ - For Delaunay & Voronoi, 's' reports deleted vertices due to facet merging.
+   They were incorrectly reported as nearly incident points.
+ - Warn if recompute centrum after constructing hull
+ - Simplified narrow hull warning and print all digits of cosine.
+     A narrow hull may lead to a point outside of the hull.
+ - Print total vertices deleted instead of ave. per iteration (Zdelvertextot)
+ - Improved tracing for qh_partitionpoint and qh_partitioncoplanar
+ - Added number of distance tests for checking outer planes (qh_check_maxout)
+ - Simplified "qhull precision error: Only n facets remain."
+ - Included 'TRn' in the causes of a premature exit
+
+Changes to documentation
+ - README.txt: Added quickstart instructions for Visual C++
+ - rbox: Added example of edge of narrow lens, rbox 1000 L100000 s G1e-6
+ - Added cross references between options 'o' and 'p'.
+ - qh-eg.html: added examples comparing 'Qt', 'QJ', and neither 'Qt' nor 'QJ'
+        eg.15a.surface, eg.15b.triangle, eg.17a.delaunay.2, etc.
+ - Reorganized and enhanced discussion of precision problems in qh_impre.htm
+ - Fixed spelling errors [K. Briggs]
+ - Fixed link errors, validated HTML, and spell checked [HomeSite]
+ - Removed unnecessary #TOP links
+ - Added source links to the qh-quick.htm's header and footer
+ - qh-geom.htm, qh-poly.htm: add links to Voronoi functions in io.c
+ - src/index.htm: Added how to search libqhull.h for qhull options
+ - qvoronoi.htm/qdelaun.htm: 'Fc' and 'FN' includes deleted vertices
+
+Changes to URLs
+ - Added http://www.voronoi.com and http://www.magic-software.com
+
+Changes to code
+ - qh_qhull: if 'TVn' or 'TCn' do not call qh_check_maxout and qh_nearcoplanar
+ - reviewed time profile.  Qhull is slower.  Optimized qh_findbestnew()
+ - qh_addpoint: Added warning note about avoiding a local minimum
+ - qh_checkpolygon: report qh.facet_next error if NARROWhull & dist>MINoutside
+ - qh_findbest: renamed "newfacets" parameter to "isnewfacets" since it is boolT
+ - qh_findbest/qh_findbestnew: testhorizon even if !MERGING
+        Otherwise qhull c D6 | qhull Q0 Tv assigns coplanar points
+ - qh_resetlists: add qh_RESETvisible for qh_triangulate
+ - qh_findbest: search better facets first.  Rewritten.
+ - qh_findbest: increased minminsearch, always check coplanar facets.
+        See: RBOX 1000 s Z1 G1e-13 t996564279 | QHULL Tv
+ - qh_findbestnew: report precision error for deleted cones [rare event]
+        e.g.:  RBOX 1000 s W1e-13 P0 t1001034076 | QHULL d Qbb Qc Tv
+ - qh_findbesthorizon: search horizon of qh.coplanarset.  New.
+ - qh_findbestsharp: replaced with qh_sharpnewfacets followed by qh_findbestnew
+ - qh_partitionpoint, Delaunay sites can not be inside.  Otherwise points may
+       be outside upperDelaunay facets yet not near-inside Delaunay facets
+       See: RBOX s 1000 t993602376 | QHULL C-1e-3 d  Qbb FA Tv
+ - qh_partitioncoplanar: call qh_findbest/qh_findbestnew with qh DELAUNAY
+ - qh_printlists: format long lines
+ - qh_printvertex: format long lines
+ - user.h: tightened qh_WARNnarrow and qh_MAXnarrow.  Do not see problems
+       until they are -1.0.
+ - user.h: defined qh_DISToutside, qh_SEARCHdist, and qh_USEfindbestnew
+ - qh_checkfacet: in 3-d, allow #ridges > #vertices.  Can get a vertex twice
+   in a ridge list, e.g,  RBOX 1000 s W1e-13 t995849315 D2 | QHULL d Tc Tv
+
+Changes to FAQ
+ - Recommended use of triangulated output ('Qt')
+
+Changes to distribution
+ - Recompiled in Visual C++ 5.0 with optimization (as was version 2.6)
+ - q_test: Added bad cases for Qhull and tests for new features
+
+Changes to Qhull library
+ - Added qh_triangulate() to poly2.c.  It triangulates the output.
+ - Added option 'Q11' to copy normals and recompute centrums for tricoplanar facets
+        'FP' may not print the nearest vertex for coplanar points
+        Use option 'Q11' when adding points after qh_triangulate()
+
+------------
+qhull 3.0 2001/02/11
+
+Changes to distribution
+ - added qconvex, qdelaunay, qhalf, and qvoronoi
+ - added qhull-interface.cpp on calling Qhull from C++ [K. Erleben]
+ - renamed to qhull3.0/.
+ - added eg/, html/, and src/ directories
+
+Changes to URLs
+ - MathLab6 qhull: convhulln, delaunayn, griddatan, tsearchn, vororoin [Z. You]
+ - Wolfram Research wrote a Mathematica interface for qdelaunay [Hinton]
+ - Geomview moved from www.geom.umn.edu to www.geomview.org [M. Phillips}
+ - added URLs for tcsh and cygwin to README.txt
+
+Changes to documentation
+ - reorganized table of contents and renamed qh-man.htm to index.htm
+ - wrote program documentation, dropped qh-opt.htm and qh-optv.htm
+ - added quick reference, qh-quick.htm
+ - reorganized qh-rbox.htm and renamed it to rbox.htm
+ - split up qh-c.htm for quick navigation
+
+Corrections to code
+ - fixed type of arg for error message in qh_initqhull_globals [N. Max]
+ - fixed incorrect initialization of qh MINdenom_1 for scalepoints
+ - fixed drop dim for 'H Qbk:0Bk:0'.  Added qh.feasible_point to qh_projectinput
+ - qh_WARNnarrow is angle between facet normals.  Negate for warning message.
+ -   statistics for Wangle/etc. concerns facet normals.  Reworded [E. Voth]
+ - fixed error message for 'FC v'
+ - report cospherical points if Delaunay and error in qh_scalelast()
+
+Changes to code
+ - turn on Pg if (QVn or QGn) and not (Qg or PG)
+ - turn on Qc if format option 'Fc', 'FP', or 'Gp' (removes warning)
+ - removed last good facet unless ONLYgood ('Qg').
+ - added count of non-simplicial or merged facets to 'FS'
+ - added count of non-simplicial facets to 's' (OK if #vertices==dim)
+ - added Znonsimplicial and Znowsimplicial to 'Ts'
+ - allow Mathematica output of dual polytope for halfspace intersection
+ - added qh_checkflags to globals.c for multiple front ends
+ - qh_initqhull_globals sets qh.MERGING if qh.MERGEexact
+ - removed hashentryT.  It is no longer used.
+
+Changes to prompts and warnings
+ - reorganized prompts
+ - reorganized synopsis for rbox.c
+ - print warning if 'Fc' or 'FP' with 'd QJ'.  Coincident points are unlikely.
+ - ignore warning if options 'v i Pp'.  qvoronoi users may need Delaunay tri.
+ - reworded warning if 'Pg' and 'QVn' is not a vertex.
+ - reworded warning for 'Qx Tv', qh_check_points() in poly2.c
+ - if 'Pp', turn off warning for 'Qbb' without 'd' or 'v'
+ - in qh_printsummary() of Voronoi and Delaunay, distinguish QVn, QGn, Pdn, PDn
+
+Changes to FAQ
+ - added FAQ item for nearly flat Delaunay triangles [Z. You]
+ - added FAQ item for area and volume [R. Konatham]
+ - added FAQ item for Voronoi diagram of a square [J. Yong]
+ - edited FAQ item on point location in Delaunay triangles [Z. You]
+ - added FAQ item on nearly flat Delaunay triangles [Dehghani]
+ - added FAQ item about halfspace intersection [V. Tyberghein]
+ - added FAQ item for missing ridges [M. Schmidt]
+ - added FAQ item about qh_call_qhull [R. Snyder]
+ - added FAQ item about memory statistics [Masi]
+ - added FAQ item on meshing non-convex objects
+ - added FAQ item on MATLAB and Mathematica interface
+
+------------
+qhull 2.6 1999/04/19
+ - fixed memory overwrite (no effect) in qh_initstatistics() [K. Ford]
+ - added zdoc11 to qh-stat.h#ZZdef for !qh_KEEPstatistics [K. Ford]
+ - enhanced qh_initqhull_globals() test of qh_RANDOMint and qh_RANDOMmax
+ - added debugging option to always return qh_RANDOMmax from qh_rand()
+ - fixed option 'Qr', qh_initialvertices(), to allow a broken qh_rand()
+   fixed option 'Qr', qh_nextfurthest(), to allow narrow hulls
+     Option 'Qr' simulates the random incremental algorithm for convex hulls
+ - added note that qh.num_outside includes coplanar points for narrow hulls
+ - added FAQ items for triangles/ridges of 3-d Delaunay triangulation[P. Kumar]
+ - added FAQ item about on-line processing with the Qhull library [O. Skare]
+ - changed name of option 'Error-roundoff' to 'Distance-roundoff'
+
+------------
+qhull 2.6 1998/12/30
+ - for the unbounded rays of the Voronoi diagram, use a large box [Schmidt]
+     e.g., 'rbox P4,4,4 P4,2,4 P2,4,4 P4,4,2 10 | qhull v Fv' fails for point 0
+     while 'rbox P4,4,4 P4,2,4 P2,4,4 P4,4,2 10 c G5 | qhull v Fv' is OK.
+ - fixed qh_new_qhull() to use outfile/errfile instead of stdout/stderr [Ford]
+ - clarified COPYING.txt for use in other programs [Archer]
+ - improved qh_readpoints() error message for incorrect point count.
+ - added FAQ item for closest triangle to a point [Sminchisescu & Heijting]
+ - added FAQ item for is a point outside of a facet [Beardsley]
+ - added FAQ item for visiting facets of the Delaunay triangulation [Heijting]
+ - added link to Erickson's Computational Geometry Software
+ - added link to Sharman's HTML version of the comp.graphics.algorithms FAQ
+ - added link to Owen's Meshing Research Corner
+ - added note to 'd' about quadratic size of 'rbox 100 l | qhull d' [Kumar]
+ - added 'about a point' to mentions of halfspace intersection
+ - added request to qh-code.htm to compute largest empty circle [Hase]
+ - the DOS window in Windows NT is better than the DOS window in Windows 95
+ - removed obsolete qh_findfacet() from qh-c.htm [Sminchisescu]
+
+------------
+qhull 2.6 1998/8/12
+ new and modified features
+ - rbox: added option Mn,m,r to generate a rotated lattice or mesh
+ - rbox: report error if more than one of 'l', 'x', 'L', 's', or 'M'
+
+ Qhull library changes
+ - added qh_new_qhull() to user.c for calling qhull() from a program [D. Zwick]
+   rewrote user_eg.c to use qh_new_qhull().  Added qh_QHpointer example.
+ - added qh_CLOCKtype 2 in user.h to call times() for CPU time [B. Hemkemeier]
+ - renamed set.c/set.h to avoid conflict with STL's set.h [G. van den Bergen]
+   can also use '#include <qhull/qhull_a.h>' for Qhull library
+
+ fixed errors
+ - fixed qh_init_B() to call qh_initqhull_mem() once only [D. Zwick]
+   This only effects Qhull library users of qh_QHpointer.
+ - fixed qh_mergecycle_all() to check for redundant vertices [J. Nagle]
+   e.g., 'rbox M3,4 64 | qhull Qc' should report 8 vertices & 48 coplanars
+ - fixed gmcoord initialization in qh_setfacetplane() for qh.RANDOMdist
+ - turn off qh.RANDOMdist during qh_printfacetheader()
+ - fixed error messages for unknown option flags
+
+ documentation changes
+ - added note to FAQ on the Voronoi diagram of cospherical points [H. Hase]
+ - added note to 'Qu' on furthest-site Delaunay triangulation via convex hull
+ - added note to 'QJ' about coplanar points on the convex hull of the input
+ - added note that 'o' and 'FN' list Voronoi regions in site id order [Arvind]
+ - added links to Fukuda's introduction to convex hulls, etc. [H. Hase]
+ - added .c and .h source files to web distribution and qh-c.htm [J. Sands]
+ - documented qh_ZEROdelaunay.  Delaunay and Voronoi diagrams do not include
+   facets that are coplanar with the convex hull of the input sites.
+
+ modified code
+ - replaced computed minnorm in qh_sethyperplane_det with distance test
+ - removed 'qh rand_seed' since random number generator is independent of qhull
+ - dropt 'qhull-PPC.sit.bin' from the distribution (out-of-date) [M. Harris]
+
+------------
+qhull 2.5 1998/5/4
+
+ fixed errors
+ - removed zero-area Delaunay triangles and furthest-site triangles [I. Beichl]
+   Zero-area triangles occur for points coplanar with the input's convex hull.
+ - replaced qh.MINnorm with computed minnorm in qh_sethyperplane_det [J. Nagle]
+   qh.MINnorm was incorrect for the convex hull of the "teapot" example.
+   Qhull runs 0-20% slower in 3-d and 4-d.
+ - allow 'Qg' with furthest-site Delaunay triangulation (may be faster)
+ - removed extra space in definition of FOREACHmerge_() for Alpha cc [R. LeRoy]
+ - fixed innerouter type in qh_printvdiagram2 [does not effect code, R. Adams]
+
+ documentation changes
+ - to browse qh-c.htm, set MIME type of .c and .h files to text/html
+ - added example of 3-d Delaunay triangulation to q-faq.htm
+ - added Delaunay and Voronoi examples to qh-optv.htm
+
+------------
+qhull 2.5 1998/2/4
+ - added option 'v Fi' for separating hyperplanes of bounded Voronoi regions
+ - added option 'v Fo' for separating hyperplanes of unbounded Voronoi regions
+ - option 'Pp' turns off the warning, "initial hull is narrow"
+ - fixed partial, 3-d Voronoi diagrams (i.e., 'v Fv QVn Tc')
+ - fixed missing statistics in qh_allstat* [T. Johnson]
+ - rearranged qh_printvdiagram.  Use qh_eachvoronoi to iterate Voronoi ridges.
+ - added qh_check_points to qh-math.c
+
+qhull 2.5 1998/1/28
+ - added option 'Fv' to print the Voronoi diagram
+ - added rbox option 'x' to generate random points in a simplex
+ - added rbox option 'y' to generate a simplex and random points
+ - added rbox option 'On' to offset the output
+ - add unpacking instructions to README.txt
+ - updated discussion of forced output, 'Po'
+ - sorted the options alphabetically
+ - removed __STDC__ check from libqhull.h for VisualC++
+ - moved qh_markvoronoi from qh_printvoronoi and cleared facet->seen flags
+ - added facet->seen2 flag for 'Fv'
+
+qhull 2.5 1998/1/16
+ - fixed initialization of qh.last_low on restart of 'd QJ'
+ - renamed qh_JOGGLEmax to qh_JOGGLEmaxincrease
+ - updated URL for Fukuda's cdd program
+
+qhull 2.5 1998/1/12
+
+New or modified features
+ - added option 'Fx' to print vertices by point id [G. Harris, T. McClendon]
+     in 2-d, the vertices are printed in counter-clockwise order
+     for Delaunay triangl., 'Fx' lists the extreme points of the input sites
+ - added option 'QJ' to randomly joggle input instead of merging facets
+ - added option 'TO file' to output results to a file.  Needed for Windows95.
+ - added option 'TRn' to rerun Qhull n times. Use to collect joggle statistics
+
+Corrections
+ - fixed 2-d facet orientation for 'i' and 'o' outputs
+ - for Mathematica 2.2 ('m') changed %10.8g to %16.8f [A. Zhaxybayev]
+ - fixed incorrect warning for 'QV0 Qg' in qh_initbuild [B. Wythoff]
+ - fixed unaccessible statistic if !qh_KEEPstatistics for Wnewvertexmax
+ - fixed overestimate of qh ONEmerge for point sets outside of
+     first quadrant and far from the origin
+ - fixed overestimate of 'Qbb' for point sets far from the origin
+ - fixed potential overestimate of qh DISTround under 'Qbb'
+ - fixed 'p' printing coplanar points of unselected facets
+ - fixed 'Ft' printing centrums unnecessarily in 2-d
+
+Changes to documentation
+ - wrote internal design documentation (qh-c.htm)
+ - started frequently asked questions (qh-faq.htm)
+ - added a section on joggled input to qh-impre.htm
+ -   added joggle example to qh-eg.htm (eg.15.joggle)
+ -   changed q_eg to use 'QJ' instead of 'Q0' were appropriate
+ - added an example to each of the main options
+ - added examples to rbox.htm
+ - added examples to the synopsis
+ - added a reference to Mucke, et al ['96], Fast randomized point location ...
+ - added code for printing Delaunay triangles to qh-code.htm [A. Tsui]
+ - options 'Pdk' and 'PDk' do not drop on equality
+
+Improvements to the code
+ - reviewed warning messages for Qhull options in qh_initflags
+ - added warning to 's' if premature exit from 'TCn' or 'TVn'
+ - 's' prints max distance above/below only if qh.MERGING
+ - reduced maxoutside in qh_check_bestdist/qh_check_points for 'Rn'
+ - in post-merging, rebuild centrums of large facets that become small
+ - lowered cutoff for coplanar facets for ischeckmax/qh_findbest
+ - removed qh_check_maxout for 'Wn Q0'
+ - reset tracing after 'TPn' adds point in 4-d and higher
+
+Changes for the Qhull library
+ - changed qh_setdelaunay to call qh_scalelast if used with 'Qbb' or 'QJ'
+     Delaunay callers to qh_findbestfacet, qh_addpoint, or qh_findfacet_all
+     should always use qh_setdelaunay as in user_eg.c
+ - defined qh.outside_err to check points against a given epsilon [E. Voth]
+ - added header to user_eg.c to avoid its incorporation into qhull [C. Begnis]
+ - added qh_nearcoplanar() calls to user_eg.c
+     only needed if use 'QJ'
+ - expanded __STDC__ warning message in libqhull.h [C. Begnis]
+ - renamed qh maxmaxcoord to qh MAXabs_coord
+ - replaced qh MAXlowcoord with qh MAXabs_coord
+ - random seed ('QR-n') is reset in qh_initqhull_globals after testing
+ - replaced 'FO' options "_max-coord/_min-coord" with "_max-width"/qh.MAXwidth
+
+Other changes to Qhull functions
+ - report error for !bestfacet in qh_findbest (it shouldn't happen) [H. Meuret]
+ - set newbest in qh_findbest only if bestfacet updated
+ - renamed facet parameter for qh_findbest
+ - added maxdist argument to qh_checkpoint
+ - moved 'FO' output after qh_partitionall
+ - separated qh_initbuild from qh_qhull
+ -   reinitialize globals modified by qh_buildhull
+ -   moved initialization of qh.GOODvertexp & qh.GOODpointp to qh_initbuild
+ - separated qh_nearcoplanar from qh_check_maxout
+ - separated qh_geomplanes from qh_printfacet2geom, etc.
+ - separated qh_freebuild from qh_freeqhull
+ - separated qh_outerinner from io.c to return outer and inner planes
+ - separated qh_distround and qh_detroundoff from qh_maxmin
+
+
+------------
+qhull 2.4 97/4/2
+
+New or modified features
+ - made 'C-0' and 'Qx' default options.  Use 'Q0' to not handle roundoff errors
+ - removed point-at-infinity from Delaunay/Voronoi.
+     you no longer need to use 'Qu PDk'
+ - added 'Qz' to add a point-at-infinity to Delaunay and Voronoi constructions
+ - added published version of qhull article in ACM Trans Math Software
+ - ported qhull to Windows95 under Visual C++ and Borland C++
+ - added 'Ft' for triangulation by adding the centrums of non-simplicial facets
+ - added 'Gt' to display 3-d Delaunay triangulations with a transparent hull
+ - changed definition of coplanar point in output to qh min_vertex (see 'Qc')
+     it was qh MAXcoplanar ('Un') [could make vertices non-coplanar]
+ - automatically set 'Qi' for options 'd Qc' and 'v Qc'.
+ - reworded summary ('s') for Delaunay/Voronoi/halfspace.
+     use 'Fs' and 'FS' for summary statistics.
+ - for summary 's' of Delaunay/Voronoi, display number of coplanars for facets
+     if none, display total number of coplanars (i.e., non-vertices)
+ - input comment is first non-numeric text (previously limited to header)
+ - added input warning if use 'Qbb' without 'd' or 'v'
+ - 'Q3' can not be followed with a numeric option
+
+Corrections
+ - fixed qh_partitioncoplanar() to not drop interior points if 'Qi' is used
+ - fixed 'FP d' to report distance in point set instead of paraboloid
+ - fixed qh_findbest() to search all coplanar facets for qh_check_maxout()
+
+Changes to documentation
+ - added example eg.17f.delaunay.3 to show a triangulation of cospherical sites
+ - split up qh-opt.htm into multiple pieces
+ - split off qh-code.htm for Qhull code
+ - renamed .html files to .htm for Windows95
+ - rewrote qh-optv.htm on Delaunay triangulation and Voronoi vertices
+ - added 'man' pages qhull.txt and rbox.txt.  These list all the options
+ - removed 'txt' versions of html files
+ - added note to 'PDk' about avoiding a 'd' option immediately after a float
+ - under option 'd', display the triangulation with 'GrD3', not 'GnrD3'
+
+Changes to the Qhull library
+ - added 'format' argument to qh_printfacetNvertex_nonsimplicial() in io.c
+ - removed C++ type errors [J. Stern, S. Marino]
+ -  created SETelemt, SETfirstt, etc. for specifying data types.
+ -  use SETelem,etc. for assignments.
+ -  changed setT.maxsize to 'int' to prevent type conversion warnings
+ -  changed FOREACH.. to a comma expression for better code and less warning
+ -  changed qh.vertex_visit and .visit_id to unsigned int to prevent warnings
+ - changed clock() to qh_CPUclock (user.h)
+ - qh_init_B() and qh_readpoints() do not set qh.ATinfinity for Delaunay tri.
+ - qh_setvoronoi_all() sets upper Delaunay facets if qh.UPPERdelaunay is set
+ - qh_nearvertex() returns distance in dim-1 for qh.DELAUNAY
+ - removed MSDOS path from qhull_command.  Spaces in Win95 tripped qh_setflags
+ - removed memory.h from qhull_a.h.  memset,etc. should be in strings.h
+ - split qh_prompt into pieces for Visual C++
+ - added note to qh_addpoint that coordinates can not be deallocated
+ - added Baker '89 to constrained Delaunay diagrams under Enhancements
+    please let me know if you try this
+ - added request for unbounded Voronoi rays to Enhancements
+    please let me know if you try this
+
+------------
+qhull V2.3 96/6/5
+ - fixed total area of Delaunay triangulation. [A. Enge]
+      It should ignore facets on the upper-envelope.
+ - if 'd Qu FA', the total area is summed over the upper-Delaunay triangles
+ - fixed sign of area for Delaunay triangulations.
+ - fixed cdd input format for Delaunay triangulation. [A. Enge]
+ - for cdd input, allow feasible point for halfspaces.
+ - warning if cdd output format for centrums, halfspace intersections, or OFF.
+ - print '0' for area ('Fa') if area is not computed for a facet
+ - option 'QR-n' sets random number seed to n without rotating input
+ - fixed qh_findbest() to retest coplanar and flipped facets after a restart
+ - for 'd Qu Ts' collects angle statistics for upper Delaunay facets
+
+ Changes to the Qhull library
+ - expanded user_eg.c for incremental constructions and Delaunay triangulation
+ - added discussion of incremental construction to qh_man.html#library
+ - WARNING: The default value of qh ATinfinity was changed from True to False.
+            A new flag, qh UPPERdelaunay, was defined for 'Qu'.
+         Please set qh ATinfinity if you explicitly add the point "at-infinity"
+         Please set qh ATinfinity if you explicitly call qh_projectinput.
+         Please set qh UPPERdelaunay if you explicitly cleared qh ATinfinity.
+         Other users do not need to change their code.
+   Now you can build a Delaunay triangulation without creating a point
+   "at-infinity".  This removes a potential, hard-to-understand error.
+   qh_readpoints sets qh ATinfinity for options 'd' or 'v' without 'Qu'.
+   qh_initB sets qh ATinfinity for qh PROJECTdelaunay w/o qh UPPERdelaunay.
+   qh_projectinput adds a point "at-infinity" only if qh ATinfinity is set.
+ - added qh_setdelaunay to geom2.c to project points to paraboloid
+ - added qh_findbestfacet() to poly2.c to replace qh_findfacet()
+ - removed procedure qh_findfacet().  It does not always work.
+ - removed NULL option for facet in qh_addpoint().  It does not always work.
+ - added noupper parameter to qh_findbest.
+ - added search of upperdelaunay facets to qh_findbest()
+ - allowed qh_findbest() to start with a flipped or upperdelaunay facet
+ - removed qh_nonupper() -- it is no longer needed
+ - allow space at end of options
+ - fixed qh_projectinput for furthest-site Delaunay (qh PROJECTdelaunay 'd Qu')
+ - added voids to procedure declarations with empty parameter lists
+
+------------
+qhull V2.3 96/3/25
+ - fixed missing qh_check_maxout when coplanar points and no merged facets.
+ - fixed qh_freeqhull/allmem (e.g., if qh_NOmem) [only custom code] [E. Voth]
+ - fixed qh_freeqhull to free qh interior_point [E. Voth]
+ - fixed main() to free all of memory if qh_NOmem.  Include "mem.h" [E. Voth]
+ - reset f.newcycle link in qh_mergecycle_all [E. Voth]
+ - fixed false error if 'Tc', coplanar points, and a narrow hull
+ - turn off 'Rn' when computing statistics, checking code, or tracing code
+ - removed ={0} from global.c and stat.c to reduce compiler warnings
+ - changed Makefile dependences to $(HFILES) for all but unix.o, set.o, mem.o
+ - pulled out qh_printpointid and reordered qh_pointid [E. Voth]
+ - removed some compiler warnings
+ - moved 'FO' print of options to just before qh_buildhull
+ - changed 'FO' to list difference from -1 for _narrow-hull
+
+------------
+qhull V2.2 96/2/15
+ - detect narrow initial hulls (cosine of min angle < qh_MAXnarrow in user.h).
+   Write warning if cosine < qh_WARNnarrow in user.h.  If narrow (qh NARROWhull),
+   partition coplanar points as outside points and delay coplanar test to end.
+   Needed for  RBOX 1000 L100000 s G1e-6 t995127886 | QHULL Tv
+   See 'limitations' in qh-impre.html for further discussion.
+ - corrected some confusions between 'FV' and 'Fv' in qh-opt.html
+ - fixed initialization error for small Voronoi diagrams (e.g., [0,0], [1,0], [0,1]) [J. Velez]
+  - fixed bad return from qh_mindiff in geom2.c
+ - for initial hull, first process facet with furthest outside point (qh_furthestnext)
+ - added facet->notfurthest flag for recomputing furthest point
+ - added check for __STDC__ (needs ANSI C) [E. Voth]
+ - reduced warning messages from [E. Voth].  e[1] in setT still reports a warning.
+ - added a cube to the discussion of option 'v' (Voronoi) in qh-opt.html [J. Velez]
+ - added notes about adjacent vertices to "Calling Qhull" in qh-man.html [R. Lewis & J. Velez]
+ - added note about 'lines closer' when viewing 3-d Delaunay triangulations [P. Kallberg]
+ - added option 'Q9' to always process furthest of furthest outside points.
+ - removed option 'Pp' from q_eg and qh-eg.html.
+
+------------
+qhull V2.2 95/12/28
+ - added option 'Qbb' to scale the last coordinate to [0,m] (max prev coord).
+   This reduces roundoff errors for Delaunay triangulations with integer coordinates.
+ - changed option 'Qu d' to print out the furthest-site Delaunay triangulation
+   Use options 'Qu d PD2' to compute the normal 2-d Delaunay triangulation without
+   the point at infinity.
+ - added notes to the documentation of option 'd'
+ - added notes to limitations of how Qhull handles imprecision
+ - added warning if options 'FP', 'Fc', or 'Gp' without option 'Qc' or 'Qi'
+ - added note to options 'PDk:n' and 'Pdk:n' that closest facet is returned if none match
+ - added check that 'Qbk' and 'QBk' does not invert paraboloid for 'd'
+ - added notes that qh_findfacet and qh_addpoint require lifted points for Delaunay triangulations
+ - fixed 'rbox s 5000 W1e-13 D2 | qhull d Qcu C-0 Qbb'
+ - fixed option 'QbB' (qh SCALEpoints was not set)
+ - fixed minor confusion between 'Gc' (print centrums) and 'Gp' (print points)
+ - rewrote qh_findbestnew for upper convex hull, Delaunay facets
+ - changed option name for 'Gp' from 'Gcoplanar' to 'Gpoints'
+ - changed "nearest" facet for 'Pdk' to threshold - normal
+ - reworked qh GOODclosest for 'Qg'
+ - added note that 'Qg' does not always work
+ - recorded option 'C-0' as "_zero-merge" in option 'FO'
+ - refined qh DISTround in qh_maxmin/geom2.c for Delaunay triangulations
+
+qhull V2.2 95/12/4
+ - Version 2.2 fixes an important bug in computing Delaunay triangulations
+   and convex hulls with edges sharper than ninety degrees.  The problem
+   occurs when processing a point at a sharp edge.  A directed search can
+   not be used for partitioning because one side may hide facets from the
+   other side.  The new lens-shaped distribution for rbox demonstrates the
+   problem.  For example, 'rbox 100 L3 G0.5 s | qhull Tv' fails for Version 2.1.
+   O. Schramm found the bug when computing the Delaunay triangulation of points
+   near an outside edge.
+
+   I rewrote qh_findbest and related functions.  Qh_findbest
+   uses an exhaustive test for sharp edges (qh_findbest_sharp).
+   Qh_findbest avoids the upper convex hull of Delaunay triangulations.
+
+   Options 'd' and 'v' no longer assign coplanar points to the upper convex hull.
+
+   Qh_check_maxout tests near-inside points.  It ignores fully inside points.
+   When done, it removes near-inside points from the coplanar sets.
+
+   If you use qh_addpoint or qh_findbest, please review the function headers.
+   They do not work for lens-shaped hulls for arbitrary facets.  They do work for
+   Delaunay triangulations.
+
+ Changes to options for V2.2
+ - added 'Qu' for computing the furthest-site Delaunay triangulation (upper hull)
+   and furthest-site Voronoi vertices.
+ - added 'FP' to print nearest vertex for coplanar points
+ - added coplanar count to 'Fs' and 's'
+ - added number of similar points to summary for Delaunay/Voronoi
+ - Option 'Qc' is no longer necessary when merging.
+ - 'o' format for Voronoi vertices ('v') generates "0" lines for similar points
+ - 'QRn' for Delaunay ('d' or 'v') now rotates about the Z axis (see qh_init_B).
+   Otherwise Qhull does not identify the upper hull
+ - removed option 'Qa' for "all points outside".  In V2.1 it was automatically
+   set for 'd'.  Even though it was a bad idea, it revealed the above bug.
+ - for option list ('FO'), added version, values for one-merge, maxpos, maxneg,
+   and near-inside, and flags for zero-centrum
+ - optimized 'C-0' and 'Qx'.  These options ("zero-centrum") test vertices
+   instead of centrums for adjacent simplicial facets.
+ - if 'Tv', report number of points that are not verified due to qh_findbest
+ - Option 'Q8' ignores near-inside points.
+
+ rbox 95/12/3
+ - added lens distribution ('Ln')  It may be used with 's', 'r', 'Wn', and 'Gn'
+ - removed default point count except for the test case, 'Dn'
+ - divided main() of rbox.c into sections
+
+ Documentation changes for V2.2
+ - added examples for lens distribution and furthest-site Delaunay triangulation
+   and renumbered the examples for q_eg
+ - described facet orientation in 'data structure' section [P. Soikkonen]
+ - added notes to qh-man.html/"What to do if something goes wrong"
+ - added note about using 'Tv' to verify the results [O. Schramm]
+ - expanded definition of f_r in Performance section [S. Grundmann]
+ - noted that Geomview display of a Voronoi diagram adds extra edges
+   for unbounded Voronoi cells
+ - rewrote error "convexity constraints may be too strong" [D. Newland]
+ - added limitations section to "Imprecision in Qhull"
+ - added note about zero-area facets to 'Imprecise convex hulls' in qh-impre.html
+ - added note to 'Qi' that it does not retain coplanar points
+ - added note that option 'Q5' may be used if outer planes are not needed
+ - added note to README.txt about Irix 5.1 [C. Goudeseune]
+ - added code fragment for visiting Voronoi vertices to "Calling Qhull" [M. Downes]
+ - added note about qh_addpoint() to "Calling Qhull" [M. Downes]
+
+ Errors fixed for V2.2
+ - use qh_sethyperplane_gauss if 3-d or 4-d norm is less than qh MINnorm
+ - count Zcentrumtests if qh_NOstat
+ - reversed sign convention for qh_sethyperplane_gauss
+   it was opposite to qh_sethyperplane_det
+   this effects qh_determinant and qh_detsimplex
+ - fixed error in qh_findgood_all with multiple restrictions, e.g., 'QVn Pdk'
+ - fixed call to qh_clearcenters for qh_produce_output
+ - in qh_errexit, report p0 if last furthest point
+
+ Changes for users of the Qhull library
+ - user code needs to define qh_version (see user_eg.c)
+ - merged initialization code into qh_init_A and qh_init_B [M. Mazzario]
+   old code works as before.
+   qh_initflags also sets qh qhull_command for qh_initthresholds
+   redid initialization for user_eg.c
+ - simplified user_eg.c.  It computes the convex hull of a cube.
+ - added qh_setvoronoi_all in poly2.c to compute Voronoi centers
+   added related note to call_qhull
+ - added qh_findfacet to use in place of qh_findbest
+ - added qh_nearvertex to return nearest vertex in facet to point
+ - redid notes on multiple, concurrent calls in call_qhull/user.c
+ - changed BoolT to unsigned int (prevent implicit enum conversion warnings)
+ - added upperdelaunay to facetT.  It indicates a facet of the upper convex hull.
+ - converted qhull-PPC.sit for CodeWarrior 7
+
+ Code changes for V2.2
+ - simplified calls to setjmp() for Cray J916 [Salazar & Velez]
+ - replaced fprintf(fp,string) with fputs in io.c
+ - 'qh num_coplanar' removed (too expensive and not used).
+ - added numcoplanars to qh_countfacets()
+ - added min norm to qh_normalize2().  qh_normalize() wasn't changed
+ - removed type casts from qh_point and qh_pointid [Salazar & Velez]
+ - account for roundoff error in detecting upper convex hull (qh ANGLEround).
+ - post merging uses qh_findbestnew for partitioning
+ - qh_findbestnew for qh_partitioncoplanar goes to best facet
+ - 'Qm' always processes points above the upper hull of a Delaunay triangulation
+ - GOODvertex initialized with qh_findbestnew instead of qh_findbest
+ - for 'v', qh_facetcenter returns furthest-neighbor vertex if 'Qu'
+ - added test for qh feasible_point if use 'Fp' and qh_sethalfspace_all
+ - reviewed Sugihara's algorithm for topologically robust beneath-beyond
+ - on error, report if qhull in post-merging or has completed
+ - if tracing, option 'FO' and qhull command always printed
+ - added current furthest point ("during p%d") to 'T-1' events
+ - added 'TWn' tracing for vertices of new facets (qh_setfacetplane)
+ - added 'TWn' tracing for vertices in an output facet (qh_check_maxout)
+ - reorganized split between poly/poly2.c and geom/geom2.c
+ - reordered object files in Makefile
+
+------------
+qhull V2.1 95/9/25
+ - converted qhull.man to html format, many edits
+ - referenced Shewchuk's triangle program and Schneiders' Mesh Generation page
+ - added option 'Qa' to force all points outside
+     automatically set for "precise" Delaunay or Voronoi [Salazar & Velez]
+     it is turned off by merging, 'Wn', 'Qc' or 'Qi'
+ - added coplanar points to option 'FN'
+ - moved option 'FO' to include default precision options
+ - changed default random number generator to qh_rand in geom2.c (user.h)
+
+ other code changes
+ - fixed option comment Pdrop-facets-dim-less, Qbound-dim-low, QbBound-unit-box
+ - defined ptr_intT for converting 64-bit ptrs to 'unsigned long' [D. Bremner]
+ - defined setelemT to distinguish actual size from pointers [D. Bremner]
+     use either e[...].p or e[...].i (user-level code should use set.h macros)
+ - changed %x to %p in format statements for pointers [D. Bremner]
+ - added test of REALmax,etc. to qh_maxmin [H. Poulard]
+ - added type parameter to qh_memalloc_() macro for type conversion
+ - added type conversion to qh_memalloc() calls where missing
+ - added type conversion to calls into set.c that return void*
+
+ other documentation changes:
+ - new URLs for graphics images
+ - fixed comment for facetT.neighbors in libqhull.h [P. Soikkonen]
+ - changed recommendations for precision errors in qh_printhelp_degenerate()
+ -  added recommendation for 'V0' (facet is visible if distance >= 0)
+ - added note about 'long double' to user.h [S. Grundmann]
+ - added note about zero area Delaunay triangles for the 'v' option
+ - added note about locating Delaunay triangles to option 'd' [A. Curtis]
+ - added note that coplanar vertices correspond to duplicate points for 'd'
+ - added note about option 'd' automatically setting 'PDk' (lower convex hull)
+ - added note about precision errors to option 'd' [many users]
+ - added note about qh_findbest() to the Qhull library section [L. Lai]
+ - 'make install' renames qhull.man to qhull.1 for Unix [M. Phillips]
+ - renamed README, etc. to *.txt to match WWW conventions [D. Cervone]
+
+------------
+qhull V2.1 7/10/95
+  - in 2-d, 'v o' lists the vertex at infinity in order [R. Critchlow]
+  -   it used to always list the vertex at infinity ("0") first
+  - rewrote description of 'v' option (Voronoi vertices and 2-d diagrams)
+  - added 'PFn' for printing facets whose area is at least 'n' [D. Holland]
+  - prefixed 'Q',etc. to the 'Q',etc. options in the long help prompt
+  - fixed references to 'Fv' and 'FV' options under option 'Hn,n,n'
+  - updated reference to cdd, <ftp://ifor13.ethz.ch/pub/fukuda/cdd/>
+  - in set.c, added some missing type coercions for qhmem.tempstack
+
+qhull V2.1 6/12/95
+  - replaced qhull.ps with qhull-2.ps (paper submitted to ACM TOMS)
+  - use BUFSIZ for setvbuf for Power Macintosh
+  - number of good facets printed if QVn, QGn, Pd, or PD
+  - added Makefile for Borland C++ 4.02 with Win32 [D. Zwick]
+  - added note to Enhancements section of qhull.1 about constrained
+       Delaunay triangulations [T. Rasanen]
+
+qhull V2.1 6/7/95
+  - fixed qh_facetarea_simplex() for non-simplicial facets [L. Schramm]
+  - fixed cast in qh_point and qh_pointid for 64-bit architectures
+  - fixed URL for Amenta's list of computational geometry software
+  - fixed cast in qh_meminitbuffers for qhmem.freelists
+  - added test for !qh half_space in qh readpoints
+  - clarified options for qh_printhelp_singular()
+  - discussed non-simplicial facet area under option 'Fa' in qhull.1
+
+qhull V2.1 6/3/95
+  - home page for Qhull and new descriptions for the Qhull examples
+      http://www.qhull.org
+  - changed SIOUX buffering for Power Macintosh.   It runs fast now.
+      added a project file for Metrowerk's C
+  - note in README about compiling qhull on the PC
+
+qhull V2.1 beta 5/15/95
+
+                ======= main changes ========
+  - added halfspace intersection ('Hn,n,n')
+  - facet merging is better, especially for high dimensions
+  -   added 'Qx' for exact merges of coplanar points and precision faults
+  - facet merging is faster, especially for high dimensions.
+      e.g., convex hull of the 8-d hypercube is seven times faster
+  - added 'F' output formats for printing each aspect of the convex hull
+  - format 'Fa' computes facet areas, total area, and total volume
+  - format 'FO' writes a descriptive list of selected options to stderr
+  - moved all customization options to user.h
+  - changed the default precision to 'double' since it's needed for Delaunay.
+      using 'float' is faster and takes less space (REALfloat in user.h)
+  - option 'Qm' is no longer important for facet merging
+  - removed need for 'Qs' by selecting initial simplex with pos. determinants
+  - renamed 'Qv' to 'Q7' since virtual memory does not work well for qhull
+  - Qhull is available for the Power Mac (no graphical output)
+
+                 ====== other new and modified options ===========
+  - changed default MINvisible ('Vn') to a multiple of premerge_centrum ('C-n')
+  - added 'Un' option to set width of facet for coplanar points.
+       This replaces the previous rules for determining coplanar points.
+  - changed default MINoutside ('Wn') to twice MINvisible ('Vn')
+  - Geomview output adjusts point radii for MINvisible 'Vn'
+  - the input format allows the number of points to precede the dimension
+  - options 'v' 'd' 'FAn' and 'FMn' record good facets ('Pg')
+  - added 'Fd' and 'FD' options for homogeneous coordinates in cdd format
+  -   in rbox, added 'h' flag to generate homogeneous coordinates in cdd format
+  - option 'PAn' prints out the n facets with the largest area
+  - option 'PMn' prints out the n facets with the most merges
+  - option 'Po' under tracing ('Tn') no longer tries to write erroneous facets
+  - option 'TCn' only prints the old 'visible' facets for 'f'
+  - 'TFn' reports intermediate results when post-merging
+  -   option 'Ts' with option 'TFn' prints intermediate statistics
+  - the message for 'Tv' reports if it is checking outer planes
+  - 'Tz' sends stderr output to stdout
+  - added 'Q1' to ignore angle when sorting merges (merges are worse)
+  - added 'Q2' to not perform merges in independent sets (merges are worse)
+  - added 'Q3' to not remove redundant vertices (faster)
+  - added 'Q4' to avoid merges of old facets into new facets (does worse)
+  - added 'Q5' to skip qh_check_maxout (faster, but less accurate)
+  - added 'Q6' to skip pre-merge of concave and coplanar facets
+  - added 'Qv' for testing vertex neighbors for convexity (needs merge option)
+  - added warning if mix Geomview output with other outputs ('Po' turns off)
+  - options 'o v' for 3-d and higher sort the Voronoi vertices by index
+
+                ======= documentation =======
+  - rewrote the introduction and precision sections
+  - added a section on performance
+  - added an example on halfspace intersection
+  - installed examples of Qhull in
+    <http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/>
+
+                ======= Makefile, user.h, and messages =======
+  - Makefile calls ./qhull, ./rbox, and prints short prompt for qhull
+  - added new statistics, e.g., for buildhull
+  - changed default qh_RANDOMtype to RAND_MAX with rand()
+  - added comment about numeric overflow to printhelp_singular
+  - reorganized the code to improve locality of reference
+  - option in mem.h (qh_NOmem) to turn off memory management in qhull
+  - option in user.h (qh_NOtrace) to turn off tracing in qhull
+  - option in user.h (qh_NOmerge) to turn off merging in qhull.
+  -   use this instead of redefining qh_merge_nonconvex in user.c
+  - simplified user_eg.c.  See qh_call_qhull() in user.c for the full version
+
+                ======== bug fixes ============
+  - fixed error in number of points for 'rbox 100 r' (odd distribution)
+  - fixed performance error in qh_degen_redundant_neighbors
+  - qh_partitionpoint now sets facet->maxoutside for first outside point
+  - fixed performance error in partitioning when merging a large, regular cone
+  - removed memory leak in qh_appendmergeset
+  - removed double free of qh line under errors in qh_readinput()
+  - forcing output on error ('Po') fixed for options 'n' 'o' 'i' 's'
+  - fixed optimization error on HP machines [fprintf(... *p++)]
+
+                ======== changes to libqhull.h for user code =======
+  - qh_collectstatistics and qh_printstatistics removed from libqhull.h.
+      should use qh_printallstatistics instead
+  - qh_findbest uses boolT for newfacets
+  - added qh_findbestnew for non-simplicial facets.  qh_findbest is
+    too slow in this case since it needs to look at many nearly coplanar
+    facets.
+  - renamed qh_voronoi/qh_centrum to qh_ASvoronoi, qh_AScentrum
+  - changed facet->id to 32-bits, added new flags for merging
+  - added facet->f for facet pointers while merging and for facet area
+  - added dfacet/dvertex for printing facets/vertices while debugging
+  - added qh_produce_output and qh_printsummary
+
+                ======== changes to code ==========
+  - moved qh_setfacetplane from qh_makenewfacets to qh_makenewplanes
+  - added qh_setfree2, qh_setcompact, and qh_setduplicate to set.c
+  - qh_findgooddist returns list of visible facets instead of setting global
+  - in qh_check_maxout, inside points may be added to coplanar list.
+  - qh_findbestnew used for qh_partitionall.  It is faster.
+  - in qh_findbest, changed searchdist to MINvisible+max_outside+DISTround.
+      MINvisible is the default MAXcoplanar.
+  - cleaned up list management via qh_resetlists
+  - uses facet->dupridge to indicate duplicated ridges instead of ->seen
+  - qh_buildtracing records CPU time relative to qh hulltime instead of 0
+
+                ========== changes to merging =======
+  - many performance improvements, especially in high-d.
+  - when merging, qh_findbest and qh_findbestnew stops search at qh_DISToutside
+  - vertex neighbors delayed until first merge
+  - post merges reported every TFn/2 merges
+  - vertex merging turned off in 7-d and higher (lots of work, no benefit).
+      vertex merging moved to qh_qhull_postmerging in 6-d.
+  - replaced qh min_vertex with MAXcoplanar for determining coplanarity
+  - pick closest facets to merge in duplicate ridge instead of flip/flip
+      (see qh_matchduplicates in poly2.c)
+  - optimize merge of simplex into a facet
+  - optimize merge of a "samecycle" of facets into a coplanar horizon facet
+  - cleaned up qh_forcedmerges/qh_flippedmerges and removed facet->newmerge
+  - rewrote qh_merge_degenredundant with separate queue
+  - qh_facetdegen replaced by facet->degenredun
+  - flipped neighbors no longer merged in preference to flip/non-flip pairs
+  - removed angle argument from qh_merge_degenredundant and qh_mergefacet
+       only used for tracing
+  - getmergeset_initial had extra test of neighbor->simplicial
+  - ridge->nonconvex is now set on only one ridge between non-convex facets
+  - moved centrum deletion to qh_updatetested
+  - qh_isnewmerge(facet) changed to facet->newmerge (removed NEWmerges)
+  - qh_findbestneighbor reports correct distance even if testcentrum
+  - added hull_dim factor to qh_BESTcentrum
+  - removed horizon preference in qh_merge_nonconvex (qh AVOIDold)
+  - facet->keepcentrum if qh WIDEfacet or qh_MAXnewcentrum extra vertices
+
+------------
+qhull V2.02 1/25/95
+  - rbox 'z' prints integer coordinates, use 'Bn' to change range
+  - fixed rare bug in qh_check_maxout when qh_bestfacet returns NULL
+  - fixed performance bug in findbestneighbor, should be + BESTnonconvex
+  - renamed 'notgood' flag in 'f' option to 'notG' flag (caused confusion)
+  - changed qh.hulltime to (unsigned) to prevent negative CPU times
+  - added random perturbations to qh_getangle under the 'Rn' option
+  - reviewed the documentation and enhancement list
+  - added discussion of how to intersect halfspaces using qhull
+  - replaced expression that caused incorrect code under an old version of gcc
+  - added buffer after qh.errexit in case 'jmp_buf' has the wrong size
+  - rewrote qh_printhelp_singular for lower-dimensional inputs
+  - rewrote qh_printhelp_degenerate
+  - added options for qh_RANDOMint in qhull_a.h
+  - changed time format for 'TFn' to %02d
+
+------------
+qhull V2.01 6/20/94
+  - fixed bug in qh_matchnewfacets that occured when memory alignment makes
+    facet->neighbors larger than necessary.
+  - fixed bug in computing worst-case simplicial merge of angle coplanar
+    facets (ONEmerge).  This decreases (...x) in printsummary.
+
+qhull V2.01 6/17/94
+  - added recommendation for 'Qcm' to documentation and help prompts
+  - added an input warning to qh_check_points ('Tv') if coplanars and no 'Qc'
+  - qh_partitionpoint: always counts coplanar partitions (Zcoplanarpart)
+  - rewrote qh_printhelp_degenerate to emphasize option 'C-0'
+  - For Geomview output, roundoff is not needed when printing the inner and
+    outer planes.  This improves Geomview output for the 'Rn' option.
+  - For Geomview output without coplanar points or vertices, qh_GEOMepislon
+    is not needed.  This removes the edge gap when displaying a Voronoi cell.
+  - For Geomview output 'Gp', direct vertices to the interior point
+    instead of the arithmetic center of the displayed vertices.
+
+qhull V2.01 6/11/94
+  - if pre-merge, 'Qf' is automatically set.  Otherwise an outside point may
+        be dropt by qh_findbest().  This slows down partitioning.
+  - always use 'Qc' if merging and all facet->maxoutside's must be right.
+        Otherwise distributions with many coplanar points may occassionally
+        miss a coplanar point for a facet.  This is because qh_findbest, when
+        called by qh_check_maxout, can become stuck at a local maximum if
+        the search is started at an arbitrary facet.  With 'Qc', the search
+        is started from a coplanar facet.  For example,
+                rbox 1000 W8e-6 t | qhull C-0 Tv
+        will (rarely) report that a facet->minoutside is incorrect
+  - option 'Pp' turns off "Verifying" message for 'Tv'
+  - added qh_copynonconvex to qh_renameridgevertex (fixes rare error)
+  - 'rbox tn' sets random seed to n
+  - 'rbox t' reports random seed in comment line
+  - qh_errexit reports rbox_command | qhull_command and 'QR' random seed
+  - added additional tracing to bestdist and setfacetplane
+  - in qh_checkconvex, need to test coplanar against 0 instead of -DISTround
+  - in qh_checkconvex, always test centrums if merging.  The opposite
+    vertex of a simplicial facet may be coplanar since a vertex of
+    a simplicial facet may be above the facet's hyperplane.
+  - fixed error handling in qh_checkconvex when merging
+  - in qh_printsummary, one merge ratio not printed if less than 'Wn'
+  - documented that 'Tv' verifies all facet->maxoutside
+
+qhull V2.01 6/2/94
+  - 's' prints summary to stderr
+  - multiple output formats printed in order to stdout
+  - added statistic for worst-case distance for merging simplicial facets
+        can not hope for a better "max distance above/below facet"
+        print factor for "max distance.."/"merge simplicial" in printsummary
+  - fixed error in scaling input with min/max reversed ('Qb0:1B0:-1')
+  - fixed error in scaling if project & Delaunay & scale ('d Qb0:0B1:0b2:0')
+  - user_eg.c: qh_delpoint removed since it does not always work
+  - user_eg.c now works for either convex hull or Delaunay triangulation
+  - added PROJECTdelaunay for Delaunay triangulations and Voronoi diagrams
+        with libqhull.a and user_eg.c
+  - user_eg.c: if project or scale input, need to copy points
+  - user_eg.c: default just defines main, added fprintf's for qh_errprint etc.
+  - qh_gausselim: a 0 pivot no longer zeros the rest of the array,
+          need the remaining elements for area computation
+  - qh_qhull: restore cos_max, centrum_radius at end of POSTmerging
+  - qh_checkflipped with !allerror is >=0.0 instead of >0.0
+  - removed -Wall from gcc due to unnecesssary "warning: implicit declaration"
+  - renamed 'new' variables and fields to allow compilation by g++
+  - added README notes on C++, and "size isn't known"
+  - updated manual on 'Qg' with coplanar facets and no merging ('rbox c D7')
+      'Qg Pg' and 'Pg' produce different results because of precision problems
+
+------------
+Converting from qhull 1.01 to qhull 2.00
+  - 'qhull An' is now 'qhull Wn'
+        option 'Wn Po' is faster but it doesn't check coplanars
+  - 'qhull g' is now 'qhull G', and the output formats are different
+  - 'qhull c' is now 'qhull Tc'
+  - 'qhull f' is now 'qhull Qf'
+  - 'qhull o' is now 'qhull Po'
+  - 'qhull b' is now always done
+  - qhull and rbox now use floats, change REALfloat in libqhull.h for doubles
+  - qhull 2.00 fixes several initialization errors and performanace errors
+        e.g., "singular input" on data with lots of 0 coordinates
+  - 'rbox b' is now 'rbox c G0.48'
+  - all rbox distributions are now scaled to a 0.5 box (use 'Bn' to change)
+  - rbox now adds a comment line.  This may be removed by 'rbox n'
+  - 'rbox r s Z G' no longer includes the positive pole
+  - no changes to the Macintosh version
+
+qhull V2.00 5/23/94
+  - if force output ('Po'), facet->maxoutside= 'Wn' since coplanars not updated
+        convexity checked if precision problems or verify ('Tv')
+  - if merging, new facets always checked for flipped orientation
+  - a facet is visible (findhorizon) under 'Qm' if distance > max_vertex
+  - if using 'Qm' then min. outside is max_vertex instead of max_outside
+  - default is random()/srandom() in qhull_a.h, checked in initqhull_globals
+  - created internal strtod since strtod may skip spacing after number
+  - removed lower bound (1.0) for qh maxmaxcoord
+  - divzero needs to handle 0/0 and large/small
+  - decreased size of precise vertices
+  - need to initialize qh MINdenom_1 for scalepoints
+  - added factor of qh maxmaxcoord into DISTround (needed for offset)
+  - 'Rn' perturbs distance computations by random +/-n
+  - check_points needs an extra DISTround to get from precise point to computed
+  - rewrote some of the IMPRECISION section in qhull.man
+  - added the input format to the qhull prompt
+  - moved include files to qhull_a.h since some compilers do not use float.h
+  - added qhull.1 and rbox.1 since SGI does not ship nroff
+  - reduced cutoff for printpointvect
+  - use time for qhull random seed only if QR0 or QR-1
+  - radius of vertices and coplanar points determined by pre-merge values
+
+qhull V2.00 5/12/94
+  - facet2point (io.c) used vertex0 instead of vertex1
+  - can't print visible facets after cone is attached
+  - shouldn't check output after STOPcone (TCn)
+  - statistic 'Wminvertex' and 'Wmaxoutside' only if MERGING or APPROXhull
+  - 'make doc' uses lineprinter format for paging
+  - warning if Gpv in 4-d
+
+qhull V2.b05 5/9/94
+  - decreased size of precise vertices
+  - precise facets in 2-d print hyperplanes
+  - accounted for GOODpoint in printsummary
+  - added IMPRECISION section to qhull.man
+  - 'Qg' does work in 7-d unless there's many coplanar facets
+
diff --git a/xs/src/qhull/src/libqhull/DEPRECATED.txt b/xs/src/qhull/src/libqhull/DEPRECATED.txt
new file mode 100644
index 0000000000..617275c14d
--- /dev/null
+++ b/xs/src/qhull/src/libqhull/DEPRECATED.txt
@@ -0,0 +1,29 @@
+
+qhull/src/libqhull
+
+    This directory contains the non-reentrant version of qhull, libqhull.
+    
+    New code should use the reentrant version of qhull (libqhull_r).
+    It allows multiple instances of qhull to run at the same time. On 
+    modern architectures, it is nearly as fast as libqhull.   
+    
+    Qhull programs may be built with either library.  Each program has a
+    reentrant version (e.g., qconvex_r.c) and a non-reentrant 
+    version (qconvex.c).   The programs, rbox, qconvex, qdelaunay, qhalf, 
+    and qvoronoi, are built with libqhull.  The qhull program is built 
+    with libqhull_r.
+
+    Qhull's C++ interface requires libqhull_r.  If you previously used the 
+    C++ interface, you will need to update your code.   See Changes.txt for 
+    suggestions.
+     
+    The C code in libqhull looks unusual because of the 'qh' macro.  The 'qh'
+    macro controls access to Qhull's global data structure, qhT.  If 
+    'qh_QHpointer' is defined, 'qh' is 'qh_qh->' and 'qh_qh' is defined as
+    'qhT *qh_qh', otherwise 'qh' is 'qh_qh.' and 'qh_qh' is defined as
+    'qhT qh_qh'.
+
+    libqhull will be supported indefinitely.  The qh_QHpointer variation
+    of libqhull will be not be retested each release.  It is replaced by 
+    libqhull_r.
+ 
diff --git a/xs/src/qhull/src/libqhull/Makefile b/xs/src/qhull/src/libqhull/Makefile
new file mode 100644
index 0000000000..bcad657773
--- /dev/null
+++ b/xs/src/qhull/src/libqhull/Makefile
@@ -0,0 +1,240 @@
+# Simple gcc Makefile for non-reentrant qhull and rbox (default gcc/g++)
+#
+#   make help
+#   See README.txt and ../../Makefile
+#       
+# Variables
+#   BINDIR         directory where to copy executables
+#   DESTDIR        destination directory for 'make install'
+#   DOCDIR         directory where to copy html documentation
+#   INCDIR         directory where to copy headers
+#   LIBDIR         directory where to copy libraries
+#   MANDIR         directory where to copy manual pages
+#   PRINTMAN       command for printing manual pages
+#   PRINTC         command for printing C files
+#   CC             ANSI C or C++ compiler
+#   CC_OPTS1       options used to compile .c files
+#   CC_OPTS2       options used to link .o files
+#   CC_OPTS3       options to build shared libraries
+#
+#   LIBQHULL_OBJS  .o files for linking
+#   LIBQHULL_HDRS  .h files for printing
+#   CFILES         .c files for printing
+#   DOCFILES       documentation files
+#   FILES          miscellaneous files for printing
+#   TFILES         .txt versions of html files
+#   FILES          all other files
+#   LIBQHULL_OBJS  specifies the object files of libqhullstatic_r.a
+#
+# Results
+#   rbox           Generates points sets for qhull, qconvex, etc.
+#   qhull          Computes convex hulls and related structures
+#   qconvex, qdelaunay, qhalf, qvoronoi
+#                  Specializations of qhull for each geometric structure
+#   libqhullstatic_r.a Static library for non-reentrant qhull
+#   testqset_r     Standalone test of non-reentrant qset_r.c with mem_r.c
+#   user_eg        An example of using qhull (non-reentrant)
+#   user_eg2       An example of using qhull (non-reentrant)
+#
+# Make targets
+#   make           Build results using gcc or another compiler
+#   make clean     Remove object files
+#   make cleanall  Remove generated files
+#   make doc       Print documentation
+#   make help
+#   make install   Copy qhull, rbox, qhull.1, rbox.1 to BINDIR, MANDIR
+#   make new       Rebuild qhull and rbox from source
+#   make printall  Print all files
+#   make qtest     Quick test of qset, rbox, and qhull
+#   make test      Quck test of qhull, qconvex, etc.
+#
+# Do not replace tabs with spaces.  Needed for build rules
+# Unix line endings (\n)
+# $Id: //main/2015/qhull/src/libqhull/Makefile#8 $
+
+DESTDIR = /usr/local
+BINDIR	= $(DESTDIR)/bin
+INCDIR	= $(DESTDIR)/include
+LIBDIR	= $(DESTDIR)/lib
+DOCDIR	= $(DESTDIR)/share/doc/qhull
+MANDIR	= $(DESTDIR)/share/man/man1
+
+# if you do not have enscript, try a2ps or just use lpr.  The files are text.
+PRINTMAN = enscript -2rl
+PRINTC = enscript -2r
+# PRINTMAN = lpr
+# PRINTC = lpr
+
+#for Gnu's gcc compiler, -O3 for optimization, -g for debugging, -pg for profiling
+# -fpic  needed for gcc x86_64-linux-gnu.  Not needed for mingw
+CC        = gcc
+CC_OPTS1  = -O3 -ansi -I../../src -fpic $(CC_WARNINGS)
+
+# for Sun's cc compiler, -fast or O2 for optimization, -g for debugging, -Xc for ANSI
+#CC       = cc
+#CC_OPTS1 = -Xc -v -fast -I../../src 
+
+# for Silicon Graphics cc compiler, -O2 for optimization, -g for debugging
+#CC       = cc
+#CC_OPTS1 = -ansi -O2 -I../../src 
+
+# for Next cc compiler with fat executable
+#CC       = cc
+#CC_OPTS1 = -ansi -O2 -I../../src -arch m68k -arch i386 -arch hppa
+
+# For loader, ld, 
+CC_OPTS2 = $(CC_OPTS1)
+
+# Default targets for make
+
+all: qhull_links qhull_all qtest
+
+help:
+	head -n 50 Makefile
+
+clean:
+	rm -f *.o 
+	# Delete linked files from other directories [qhull_links]
+	rm -f qconvex.c unix.c qdelaun.c qhalf.c qvoronoi.c rbox.c
+	rm -f user_eg.c user_eg2.c testqset.c
+	
+cleanall: clean
+	rm -f qconvex qdelaunay qhalf qvoronoi qhull *.exe
+	rm -f core user_eg user_eg2 testqset libqhullstatic.a
+
+doc: 
+	$(PRINTMAN) $(TXTFILES) $(DOCFILES)
+
+install:
+	mkdir -p $(BINDIR)
+	mkdir -p $(DOCDIR)
+	mkdir -p $(INCDIR)/libqhull
+	mkdir -p $(MANDIR)
+	cp -p qconvex qdelaunay qhalf qhull qvoronoi rbox $(BINDIR)
+	cp -p libqhullstatic.a $(LIBDIR)
+	cp -p ../../html/qhull.man $(MANDIR)/qhull.1
+	cp -p ../../html/rbox.man $(MANDIR)/rbox.1
+	cp -p ../../html/* $(DOCDIR)
+	cp *.h $(INCDIR)/libqhull
+
+new:	cleanall all
+
+printall: doc printh printc printf
+
+printh:
+	$(PRINTC) $(LIBQHULL_HDRS)
+
+printc:
+	$(PRINTC) $(CFILES)
+
+# LIBQHULL_OBJS_1 ordered by frequency of execution with small files at end.  Better locality.
+# Same definitions as ../../Makefile
+
+LIBQHULLS_OBJS_1= global.o stat.o geom2.o poly2.o merge.o \
+        libqhull.o geom.o poly.o qset.o mem.o random.o 
+
+LIBQHULLS_OBJS_2= $(LIBQHULLS_OBJS_1) usermem.o userprintf.o io.o user.o
+
+LIBQHULLS_OBJS= $(LIBQHULLS_OBJS_2)  rboxlib.o userprintf_rbox.o
+
+LIBQHULL_HDRS= user.h libqhull.h qhull_a.h geom.h \
+        io.h mem.h merge.h poly.h random.h \
+        qset.h stat.h
+
+# CFILES ordered alphabetically after libqhull.c 
+CFILES= ../qhull/unix.c libqhull.c geom.c geom2.c global.c io.c \
+	mem.c merge.c poly.c poly2.c random.c rboxlib.c \
+	qset.c stat.c user.c usermem.c userprintf.c \
+	../qconvex/qconvex.c ../qdelaunay/qdelaun.c ../qhalf/qhalf.c ../qvoronoi/qvoronoi.c
+
+TXTFILES= ../../Announce.txt ../../REGISTER.txt ../../COPYING.txt ../../README.txt ../Changes.txt
+DOCFILES= ../../html/rbox.txt ../../html/qhull.txt
+
+.c.o:
+	$(CC) -c $(CC_OPTS1) -o $@ $<
+
+# Work around problems with ../ in Red Hat Linux
+qhull_links:
+	# On MINSYS, 'ln -s' may create a copy instead of a symbolic link
+	[ -f qconvex.c ]    || ln -s ../qconvex/qconvex.c
+	[ -f qdelaun.c ]    || ln -s ../qdelaunay/qdelaun.c
+	[ -f qhalf.c ]	    || ln -s ../qhalf/qhalf.c
+	[ -f qvoronoi.c ]   || ln -s ../qvoronoi/qvoronoi.c
+	[ -f rbox.c ]	    || ln -s ../rbox/rbox.c
+	[ -f testqset.c ]   || ln -s ../testqset/testqset.c
+	[ -f unix.c ]	    || ln -s ../qhull/unix.c
+	[ -f user_eg.c ]    || ln -s ../user_eg/user_eg.c
+	[ -f user_eg2.c ]   || ln -s ../user_eg2/user_eg2.c
+
+# compile qhull without using bin/libqhullstatic.a
+qhull_all: qconvex.o qdelaun.o qhalf.o qvoronoi.o unix.o user_eg.o user_eg2.o rbox.o testqset.o $(LIBQHULLS_OBJS)
+	$(CC) -o qconvex $(CC_OPTS2) -lm $(LIBQHULLS_OBJS_2) qconvex.o 
+	$(CC) -o qdelaunay $(CC_OPTS2) -lm $(LIBQHULLS_OBJS_2) qdelaun.o
+	$(CC) -o qhalf $(CC_OPTS2) -lm $(LIBQHULLS_OBJS_2) qhalf.o 
+	$(CC) -o qvoronoi $(CC_OPTS2) -lm $(LIBQHULLS_OBJS_2) qvoronoi.o 
+	$(CC) -o qhull $(CC_OPTS2) -lm $(LIBQHULLS_OBJS_2) unix.o
+	$(CC) -o rbox $(CC_OPTS2) -lm $(LIBQHULLS_OBJS) rbox.o
+	$(CC) -o user_eg $(CC_OPTS2) -lm $(LIBQHULLS_OBJS_2) user_eg.o
+	$(CC) -o user_eg2 $(CC_OPTS2) -lm $(LIBQHULLS_OBJS_1) user_eg2.o  usermem.o userprintf.o io.o
+	$(CC) -o testqset $(CC_OPTS2) -lm mem.o qset.o usermem.o testqset.o
+	-ar -rs libqhullstatic.a $(LIBQHULLS_OBJS)
+	#libqhullstatic.a is not needed for qhull
+	#If 'ar -rs' fails try using 'ar -s' with 'ranlib'
+	#ranlib libqhullstatic.a
+
+qtest:
+	@echo ============================================
+	@echo == make qtest ==============================
+	@echo ============================================
+	@echo -n "== "
+	@date
+	@echo
+	@echo Testing qset.c and mem.c with testqset
+	./testqset 10000
+	@echo Run the qhull smoketest
+	./rbox D4 | ./qhull
+	@echo ============================================
+	@echo == To smoketest qhull programs
+	@echo '==     make test'
+	@echo ============================================
+	@echo
+	@echo ============================================
+	@echo == For all make targets
+	@echo '==     make help'
+	@echo ============================================
+	@echo
+
+test: qtest
+	@echo ==============================
+	@echo ========= qconvex ============
+	@echo ==============================
+	-./rbox 10 | ./qconvex Tv 
+	@echo
+	@echo ==============================
+	@echo ========= qdelaunay ==========
+	@echo ==============================
+	-./rbox 10 | ./qdelaunay Tv 
+	@echo
+	@echo ==============================
+	@echo ========= qhalf ==============
+	@echo ==============================
+	-./rbox 10 | ./qconvex FQ FV n Tv | ./qhalf Tv
+	@echo
+	@echo ==============================
+	@echo ========= qvoronoi ===========
+	@echo ==============================
+	-./rbox 10 | ./qvoronoi Tv
+	@echo
+	@echo ==============================
+	@echo ========= user_eg ============
+	@echo == w/o shared library ========
+	@echo ==============================
+	-./user_eg
+	@echo
+	@echo ==============================
+	@echo ========= user_eg2 ===========
+	@echo ==============================
+	-./user_eg2
+	@echo
+
+# end of Makefile
diff --git a/xs/src/qhull/src/libqhull/Mborland b/xs/src/qhull/src/libqhull/Mborland
new file mode 100644
index 0000000000..46d88dbd4d
--- /dev/null
+++ b/xs/src/qhull/src/libqhull/Mborland
@@ -0,0 +1,206 @@
+#########################################################################
+#  Borland C++ 4.02 for Win32 and DOS Power Pack			#
+#  Makefile for qhull and rbox					        #
+#								        #
+#       make -fMborland all       to produce qconvex, qhull, and rbox   #
+#       make -fMborland user_eg   to produce user_eg		        #
+#       make -fMborland user_eg2  to produce user_eg2		        #
+#       make -fMborland new       to rebuild qhull and rbox from source #
+#       make -fMborland clean     to remove object files		#
+#       make -fMborland cleanall  to remove all generated files	        #
+#       make -fMborland test      to test rbox and qhull		#
+#								        #
+#  Author: D. Zwick of Germany, C.B. Barber			        #
+#########################################################################
+
+CC      = bcc32    # 32 bit compiler for DOS
+		   # bcc32i - Intel's compiler
+LINKER  = $(CC)    # bcc calls tlink32 with needed options
+CFLAGS  = -w- -A -O2   
+		    # -w- no warnings, bcc doesn't handle assigns in conditions
+			# -A Ansi standard
+			# -X no auto-dependency outputs
+			# -v debugging, use CCOPTS for both 
+			# -O2 optimization   
+!if $d(_DPMI)
+LFLAGS  = -WX -w-   # -WX loads DPMI library
+!else
+LFLAGS  = -lap -lx -lc
+					# -lap 32-bit console application
+					# -lx no map file
+					# -lc case is significant 
+!endif
+
+EXERB = rbox
+EXEQH = qhull
+EXEQC = qconvex
+EXEQD = qdelaunay
+EXEQV = qvoronoi
+EXEQF = qhalf
+EXEEG = user_eg
+EXEEG2 = user_eg2
+
+TMPFILE = BCC32tmp.cfg
+
+OBJS1 =   global.obj stat.obj geom2.obj poly2.obj merge.obj
+OBJS2 =   libqhull.obj geom.obj poly.obj qset.obj mem.obj 
+OBJS3 =   random.obj usermem.obj userprintf.obj io.obj user.obj
+OBJS4 =   rboxlib.obj random.obj usermem.obj userprintf_rbox.obj
+
+HFILES1 = libqhull.h stat.h qhull_a.h user.h
+
+
+# General rules
+
+.c.obj:
+	$(CC) -c $(CFLAGS) $<
+
+# Default
+
+all:	  $(EXERB) $(EXEQH) $(EXEQC) $(EXEQD) $(EXEQV) $(EXEQF) test
+
+help:
+	@echo  USAGE:
+	@echo  "make all       to produce qhull, rbox, qconvex, qdelaun, qvoronoi, qhalf"
+	@echo  "make user_eg   to produce user_eg"
+	@echo  "make user_eg2  to produce user_eg2"
+	@echo  "make new       to rebuild qhull and rbox from source"
+	@echo  "make clean     to remove object files"
+	@echo  "make cleanall  to remove all generated file"
+	@echo  "make test      to test rbox and qhull"
+	@echo  OPTIONS (default is 32-bit console app):
+	@echo  "-D_DPMI	for C++ 4.01 and DOS Power Pack"
+
+# Executables
+
+$(EXEQH):     ..\..\bin\$(EXEQH).exe
+	@echo Made ..\..\bin\$(EXEQH).exe
+
+unix.obj: ..\qhull\unix.c 
+..\..\bin\$(EXEQH).exe: unix.obj $(OBJS1) $(OBJS2) $(OBJS3)
+	@echo unix.obj > $(TMPFILE)
+	@echo $(OBJS1) >> $(TMPFILE)
+	@echo $(OBJS2) >> $(TMPFILE)
+	@echo $(OBJS3) >> $(TMPFILE)
+	$(LINKER) -e$@ $(CFLAGS) $(LFLAGS) @$(TMPFILE)
+
+$(EXEQC):     ..\..\bin\$(EXEQC).exe
+	@echo Made ..\..\bin\$(EXEQC).exe
+
+qconvex.obj: ..\qconvex\qconvex.c
+..\..\bin\$(EXEQC).exe: qconvex.obj $(OBJS1) $(OBJS2) $(OBJS3)
+	@echo qconvex.obj > $(TMPFILE)
+	@echo $(OBJS1) >> $(TMPFILE)
+	@echo $(OBJS2) >> $(TMPFILE)
+	@echo $(OBJS3) >> $(TMPFILE)
+	$(LINKER) -e$@ $(CFLAGS) $(LFLAGS) @$(TMPFILE)
+
+$(EXEQD):     ..\..\bin\$(EXEQD).exe
+	@echo Made ..\..\bin\$(EXEQD).exe
+
+qdelaun.obj: ..\qdelaunay\qdelaun.c
+..\..\bin\$(EXEQD).exe: qdelaun.obj $(OBJS1) $(OBJS2) $(OBJS3)
+	@echo qdelaun.obj > $(TMPFILE)
+	@echo $(OBJS1) >> $(TMPFILE)
+	@echo $(OBJS2) >> $(TMPFILE)
+	@echo $(OBJS3) >> $(TMPFILE)
+	$(LINKER) -e$@ $(CFLAGS) $(LFLAGS) @$(TMPFILE)
+
+$(EXEQV):     ..\..\bin\$(EXEQV).exe
+	@echo Made ..\..\bin\$(EXEQV).exe
+
+qvoronoi.obj: ..\qvoronoi\qvoronoi.c
+..\..\bin\$(EXEQV).exe: qvoronoi.obj $(OBJS1) $(OBJS2) $(OBJS3)
+	@echo qvoronoi.obj > $(TMPFILE)
+	@echo $(OBJS1) >> $(TMPFILE)
+	@echo $(OBJS2) >> $(TMPFILE)
+	@echo $(OBJS3) >> $(TMPFILE)
+	$(LINKER) -e$@ $(CFLAGS) $(LFLAGS) @$(TMPFILE)
+
+$(EXEQF):     ..\..\bin\$(EXEQF).exe
+	@echo Made ..\..\bin\$(EXEQF).exe
+
+qhalf.obj: ..\qhalf\qhalf.c
+..\..\bin\$(EXEQF).exe:  qhalf.obj $(OBJS1) $(OBJS2) $(OBJS3)
+	@echo qhalf.obj > $(TMPFILE)
+	@echo $(OBJS1) >> $(TMPFILE)
+	@echo $(OBJS2) >> $(TMPFILE)
+	@echo $(OBJS3) >> $(TMPFILE)
+	$(LINKER) -e$@ $(CFLAGS) $(LFLAGS) @$(TMPFILE)
+
+$(EXEEG):     ..\..\bin\$(EXEEG).exe
+	@echo Made ..\..\bin\$(EXEEG).exe
+
+user_eg.obj: ..\user_eg\user_eg.c
+..\..\bin\$(EXEEG).exe: user_eg.obj $(OBJS1) $(OBJS2) $(OBJS3)
+	@echo user_eg.obj > $(TMPFILE)
+	@echo $(OBJS1) >> $(TMPFILE)
+	@echo $(OBJS2) >> $(TMPFILE)
+	@echo $(OBJS3) >> $(TMPFILE)
+	$(LINKER) -e$@ $(CFLAGS) $(LFLAGS) @$(TMPFILE)
+
+$(EXEEG2):     ..\..\bin\$(EXEEG2).exe
+	@echo Made ..\..\bin\$(EXEEG2).exe
+
+user_eg2.obj: ..\user_eg2\user_eg2.c
+..\..\bin\$(EXEEG2).exe: user_eg2.obj $(OBJS1) $(OBJS2) $(OBJS3)
+	@echo user_eg2.obj > $(TMPFILE)
+	@echo $(OBJS1) >> $(TMPFILE)
+	@echo $(OBJS2) >> $(TMPFILE)
+	@echo $(OBJS3) >> $(TMPFILE)
+	$(LINKER) -e$@ $(CFLAGS) $(LFLAGS) @$(TMPFILE)
+
+$(EXERB):     ..\..\bin\$(EXERB).exe
+	@echo Made ..\..\bin\$(EXERB).exe
+
+rbox.obj: ..\rbox\rbox.c 
+..\..\bin\$(EXERB).exe: rbox.obj $(OBJS4)
+	@echo rbox.obj > $(TMPFILE)
+	@echo $(OBJS4) >> $(TMPFILE)
+	$(LINKER) -e$@ $(CFLAGS) $(LFLAGS) @$(TMPFILE)
+
+# Test rbox and qhull
+
+test:   
+	@..\..\bin\rbox D4 > test.x
+	@..\..\bin\qhull <test.x
+	@del test.x
+
+# Clean up
+
+clean:
+	@del *.obj
+	@del $(TMPFILE) 
+
+cleanall: clean
+	@del ..\..\bin\$(EXERB).exe
+	@del ..\..\bin\$(EXEQC).exe
+	@del ..\..\bin\$(EXEQD).exe
+	@del ..\..\bin\$(EXEQF).exe
+	@del ..\..\bin\$(EXEQH).exe
+	@del ..\..\bin\$(EXEQV).exe
+	@del ..\..\bin\$(EXEEG).exe
+	@del ..\..\bin\$(EXEEG2).exe
+	@del ..\q_test.x
+	@del ..\q_test.log.1
+
+# Clean up and rebuild all
+
+new:      cleanall all
+
+# Header file dependencies
+
+libqhull.obj stat.obj user.obj global.obj usermem.obj userprintf.obj: $(HFILES1)
+random.obj:  libqhull.h random.h
+geom.obj geom2.obj:  $(HFILES1) geom.h
+poly.obj poly2.obj:  $(HFILES1) poly.h
+io.obj:     $(HFILES1) io.h
+merge.obj:  $(HFILES1) merge.h
+mem.obj:    mem.h
+qset.obj:   qset.h mem.h
+unix.obj:   libqhull.h user.h
+qconvex.obj:   libqhull.h user.h
+qdelaun.obj:   libqhull.h user.h
+qhalf.obj:   libqhull.h user.h
+qvoronoi.obj:   libqhull.h user.h
+rbox.obj:   user.h
diff --git a/xs/src/qhull/src/libqhull/geom.c b/xs/src/qhull/src/libqhull/geom.c
new file mode 100644
index 0000000000..71444f05a4
--- /dev/null
+++ b/xs/src/qhull/src/libqhull/geom.c
@@ -0,0 +1,1234 @@
+/*<html><pre>  -<a                             href="qh-geom.htm"
+  >-------------------------------</a><a name="TOP">-</a>
+
+   geom.c
+   geometric routines of qhull
+
+   see qh-geom.htm and geom.h
+
+   Copyright (c) 1993-2015 The Geometry Center.
+   $Id: //main/2015/qhull/src/libqhull/geom.c#2 $$Change: 1995 $
+   $DateTime: 2015/10/13 21:59:42 $$Author: bbarber $
+
+   infrequent code goes into geom2.c
+*/
+
+#include "qhull_a.h"
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >-------------------------------</a><a name="distplane">-</a>
+
+  qh_distplane( point, facet, dist )
+    return distance from point to facet
+
+  returns:
+    dist
+    if qh.RANDOMdist, joggles result
+
+  notes:
+    dist > 0 if point is above facet (i.e., outside)
+    does not error (for qh_sortfacets, qh_outerinner)
+
+  see:
+    qh_distnorm in geom2.c
+    qh_distplane [geom.c], QhullFacet::distance, and QhullHyperplane::distance are copies
+*/
+void qh_distplane(pointT *point, facetT *facet, realT *dist) {
+  coordT *normal= facet->normal, *coordp, randr;
+  int k;
+
+  switch (qh hull_dim){
+  case 2:
+    *dist= facet->offset + point[0] * normal[0] + point[1] * normal[1];
+    break;
+  case 3:
+    *dist= facet->offset + point[0] * normal[0] + point[1] * normal[1] + point[2] * normal[2];
+    break;
+  case 4:
+    *dist= facet->offset+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3];
+    break;
+  case 5:
+    *dist= facet->offset+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3]+point[4]*normal[4];
+    break;
+  case 6:
+    *dist= facet->offset+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3]+point[4]*normal[4]+point[5]*normal[5];
+    break;
+  case 7:
+    *dist= facet->offset+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3]+point[4]*normal[4]+point[5]*normal[5]+point[6]*normal[6];
+    break;
+  case 8:
+    *dist= facet->offset+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3]+point[4]*normal[4]+point[5]*normal[5]+point[6]*normal[6]+point[7]*normal[7];
+    break;
+  default:
+    *dist= facet->offset;
+    coordp= point;
+    for (k=qh hull_dim; k--; )
+      *dist += *coordp++ * *normal++;
+    break;
+  }
+  zinc_(Zdistplane);
+  if (!qh RANDOMdist && qh IStracing < 4)
+    return;
+  if (qh RANDOMdist) {
+    randr= qh_RANDOMint;
+    *dist += (2.0 * randr / qh_RANDOMmax - 1.0) *
+      qh RANDOMfactor * qh MAXabs_coord;
+  }
+  if (qh IStracing >= 4) {
+    qh_fprintf(qh ferr, 8001, "qh_distplane: ");
+    qh_fprintf(qh ferr, 8002, qh_REAL_1, *dist);
+    qh_fprintf(qh ferr, 8003, "from p%d to f%d\n", qh_pointid(point), facet->id);
+  }
+  return;
+} /* distplane */
+
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >-------------------------------</a><a name="findbest">-</a>
+
+  qh_findbest( point, startfacet, bestoutside, qh_ISnewfacets, qh_NOupper, dist, isoutside, numpart )
+    find facet that is furthest below a point
+    for upperDelaunay facets
+      returns facet only if !qh_NOupper and clearly above
+
+  input:
+    starts search at 'startfacet' (can not be flipped)
+    if !bestoutside(qh_ALL), stops at qh.MINoutside
+
+  returns:
+    best facet (reports error if NULL)
+    early out if isoutside defined and bestdist > qh.MINoutside
+    dist is distance to facet
+    isoutside is true if point is outside of facet
+    numpart counts the number of distance tests
+
+  see also:
+    qh_findbestnew()
+
+  notes:
+    If merging (testhorizon), searches horizon facets of coplanar best facets because
+    after qh_distplane, this and qh_partitionpoint are the most expensive in 3-d
+      avoid calls to distplane, function calls, and real number operations.
+    caller traces result
+    Optimized for outside points.   Tried recording a search set for qh_findhorizon.
+    Made code more complicated.
+
+  when called by qh_partitionvisible():
+    indicated by qh_ISnewfacets
+    qh.newfacet_list is list of simplicial, new facets
+    qh_findbestnew set if qh_sharpnewfacets returns True (to use qh_findbestnew)
+    qh.bestfacet_notsharp set if qh_sharpnewfacets returns False
+
+  when called by qh_findfacet(), qh_partitionpoint(), qh_partitioncoplanar(),
+                 qh_check_bestdist(), qh_addpoint()
+    indicated by !qh_ISnewfacets
+    returns best facet in neighborhood of given facet
+      this is best facet overall if dist > -   qh.MAXcoplanar
+        or hull has at least a "spherical" curvature
+
+  design:
+    initialize and test for early exit
+    repeat while there are better facets
+      for each neighbor of facet
+        exit if outside facet found
+        test for better facet
+    if point is inside and partitioning
+      test for new facets with a "sharp" intersection
+      if so, future calls go to qh_findbestnew()
+    test horizon facets
+*/
+facetT *qh_findbest(pointT *point, facetT *startfacet,
+                     boolT bestoutside, boolT isnewfacets, boolT noupper,
+                     realT *dist, boolT *isoutside, int *numpart) {
+  realT bestdist= -REALmax/2 /* avoid underflow */;
+  facetT *facet, *neighbor, **neighborp;
+  facetT *bestfacet= NULL, *lastfacet= NULL;
+  int oldtrace= qh IStracing;
+  unsigned int visitid= ++qh visit_id;
+  int numpartnew=0;
+  boolT testhorizon = True; /* needed if precise, e.g., rbox c D6 | qhull Q0 Tv */
+
+  zinc_(Zfindbest);
+  if (qh IStracing >= 3 || (qh TRACElevel && qh TRACEpoint >= 0 && qh TRACEpoint == qh_pointid(point))) {
+    if (qh TRACElevel > qh IStracing)
+      qh IStracing= qh TRACElevel;
+    qh_fprintf(qh ferr, 8004, "qh_findbest: point p%d starting at f%d isnewfacets? %d, unless %d exit if > %2.2g\n",
+             qh_pointid(point), startfacet->id, isnewfacets, bestoutside, qh MINoutside);
+    qh_fprintf(qh ferr, 8005, "  testhorizon? %d noupper? %d", testhorizon, noupper);
+    qh_fprintf(qh ferr, 8006, "  Last point added was p%d.", qh furthest_id);
+    qh_fprintf(qh ferr, 8007, "  Last merge was #%d.  max_outside %2.2g\n", zzval_(Ztotmerge), qh max_outside);
+  }
+  if (isoutside)
+    *isoutside= True;
+  if (!startfacet->flipped) {  /* test startfacet */
+    *numpart= 1;
+    qh_distplane(point, startfacet, dist);  /* this code is duplicated below */
+    if (!bestoutside && *dist >= qh MINoutside
+    && (!startfacet->upperdelaunay || !noupper)) {
+      bestfacet= startfacet;
+      goto LABELreturn_best;
+    }
+    bestdist= *dist;
+    if (!startfacet->upperdelaunay) {
+      bestfacet= startfacet;
+    }
+  }else
+    *numpart= 0;
+  startfacet->visitid= visitid;
+  facet= startfacet;
+  while (facet) {
+    trace4((qh ferr, 4001, "qh_findbest: neighbors of f%d, bestdist %2.2g f%d\n",
+                facet->id, bestdist, getid_(bestfacet)));
+    lastfacet= facet;
+    FOREACHneighbor_(facet) {
+      if (!neighbor->newfacet && isnewfacets)
+        continue;
+      if (neighbor->visitid == visitid)
+        continue;
+      neighbor->visitid= visitid;
+      if (!neighbor->flipped) {  /* code duplicated above */
+        (*numpart)++;
+        qh_distplane(point, neighbor, dist);
+        if (*dist > bestdist) {
+          if (!bestoutside && *dist >= qh MINoutside
+          && (!neighbor->upperdelaunay || !noupper)) {
+            bestfacet= neighbor;
+            goto LABELreturn_best;
+          }
+          if (!neighbor->upperdelaunay) {
+            bestfacet= neighbor;
+            bestdist= *dist;
+            break; /* switch to neighbor */
+          }else if (!bestfacet) {
+            bestdist= *dist;
+            break; /* switch to neighbor */
+          }
+        } /* end of *dist>bestdist */
+      } /* end of !flipped */
+    } /* end of FOREACHneighbor */
+    facet= neighbor;  /* non-NULL only if *dist>bestdist */
+  } /* end of while facet (directed search) */
+  if (isnewfacets) {
+    if (!bestfacet) {
+      bestdist= -REALmax/2;
+      bestfacet= qh_findbestnew(point, startfacet->next, &bestdist, bestoutside, isoutside, &numpartnew);
+      testhorizon= False; /* qh_findbestnew calls qh_findbesthorizon */
+    }else if (!qh findbest_notsharp && bestdist < - qh DISTround) {
+      if (qh_sharpnewfacets()) {
+        /* seldom used, qh_findbestnew will retest all facets */
+        zinc_(Zfindnewsharp);
+        bestfacet= qh_findbestnew(point, bestfacet, &bestdist, bestoutside, isoutside, &numpartnew);
+        testhorizon= False; /* qh_findbestnew calls qh_findbesthorizon */
+        qh findbestnew= True;
+      }else
+        qh findbest_notsharp= True;
+    }
+  }
+  if (!bestfacet)
+    bestfacet= qh_findbestlower(lastfacet, point, &bestdist, numpart);
+  if (testhorizon)
+    bestfacet= qh_findbesthorizon(!qh_IScheckmax, point, bestfacet, noupper, &bestdist, &numpartnew);
+  *dist= bestdist;
+  if (isoutside && bestdist < qh MINoutside)
+    *isoutside= False;
+LABELreturn_best:
+  zadd_(Zfindbesttot, *numpart);
+  zmax_(Zfindbestmax, *numpart);
+  (*numpart) += numpartnew;
+  qh IStracing= oldtrace;
+  return bestfacet;
+}  /* findbest */
+
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >-------------------------------</a><a name="findbesthorizon">-</a>
+
+  qh_findbesthorizon( qh_IScheckmax, point, startfacet, qh_NOupper, &bestdist, &numpart )
+    search coplanar and better horizon facets from startfacet/bestdist
+    ischeckmax turns off statistics and minsearch update
+    all arguments must be initialized
+  returns(ischeckmax):
+    best facet
+  returns(!ischeckmax):
+    best facet that is not upperdelaunay
+    allows upperdelaunay that is clearly outside
+  returns:
+    bestdist is distance to bestfacet
+    numpart -- updates number of distance tests
+
+  notes:
+    no early out -- use qh_findbest() or qh_findbestnew()
+    Searches coplanar or better horizon facets
+
+  when called by qh_check_maxout() (qh_IScheckmax)
+    startfacet must be closest to the point
+      Otherwise, if point is beyond and below startfacet, startfacet may be a local minimum
+      even though other facets are below the point.
+    updates facet->maxoutside for good, visited facets
+    may return NULL
+
+    searchdist is qh.max_outside + 2 * DISTround
+      + max( MINvisible('Vn'), MAXcoplanar('Un'));
+    This setting is a guess.  It must be at least max_outside + 2*DISTround
+    because a facet may have a geometric neighbor across a vertex
+
+  design:
+    for each horizon facet of coplanar best facets
+      continue if clearly inside
+      unless upperdelaunay or clearly outside
+         update best facet
+*/
+facetT *qh_findbesthorizon(boolT ischeckmax, pointT* point, facetT *startfacet, boolT noupper, realT *bestdist, int *numpart) {
+  facetT *bestfacet= startfacet;
+  realT dist;
+  facetT *neighbor, **neighborp, *facet;
+  facetT *nextfacet= NULL; /* optimize last facet of coplanarfacetset */
+  int numpartinit= *numpart, coplanarfacetset_size;
+  unsigned int visitid= ++qh visit_id;
+  boolT newbest= False; /* for tracing */
+  realT minsearch, searchdist;  /* skip facets that are too far from point */
+
+  if (!ischeckmax) {
+    zinc_(Zfindhorizon);
+  }else {
+#if qh_MAXoutside
+    if ((!qh ONLYgood || startfacet->good) && *bestdist > startfacet->maxoutside)
+      startfacet->maxoutside= *bestdist;
+#endif
+  }
+  searchdist= qh_SEARCHdist; /* multiple of qh.max_outside and precision constants */
+  minsearch= *bestdist - searchdist;
+  if (ischeckmax) {
+    /* Always check coplanar facets.  Needed for RBOX 1000 s Z1 G1e-13 t996564279 | QHULL Tv */
+    minimize_(minsearch, -searchdist);
+  }
+  coplanarfacetset_size= 0;
+  facet= startfacet;
+  while (True) {
+    trace4((qh ferr, 4002, "qh_findbesthorizon: neighbors of f%d bestdist %2.2g f%d ischeckmax? %d noupper? %d minsearch %2.2g searchdist %2.2g\n",
+                facet->id, *bestdist, getid_(bestfacet), ischeckmax, noupper,
+                minsearch, searchdist));
+    FOREACHneighbor_(facet) {
+      if (neighbor->visitid == visitid)
+        continue;
+      neighbor->visitid= visitid;
+      if (!neighbor->flipped) {
+        qh_distplane(point, neighbor, &dist);
+        (*numpart)++;
+        if (dist > *bestdist) {
+          if (!neighbor->upperdelaunay || ischeckmax || (!noupper && dist >= qh MINoutside)) {
+            bestfacet= neighbor;
+            *bestdist= dist;
+            newbest= True;
+            if (!ischeckmax) {
+              minsearch= dist - searchdist;
+              if (dist > *bestdist + searchdist) {
+                zinc_(Zfindjump);  /* everything in qh.coplanarfacetset at least searchdist below */
+                coplanarfacetset_size= 0;
+              }
+            }
+          }
+        }else if (dist < minsearch)
+          continue;  /* if ischeckmax, dist can't be positive */
+#if qh_MAXoutside
+        if (ischeckmax && dist > neighbor->maxoutside)
+          neighbor->maxoutside= dist;
+#endif
+      } /* end of !flipped */
+      if (nextfacet) {
+        if (!coplanarfacetset_size++) {
+          SETfirst_(qh coplanarfacetset)= nextfacet;
+          SETtruncate_(qh coplanarfacetset, 1);
+        }else
+          qh_setappend(&qh coplanarfacetset, nextfacet); /* Was needed for RBOX 1000 s W1e-13 P0 t996547055 | QHULL d Qbb Qc Tv
+                                                 and RBOX 1000 s Z1 G1e-13 t996564279 | qhull Tv  */
+      }
+      nextfacet= neighbor;
+    } /* end of EACHneighbor */
+    facet= nextfacet;
+    if (facet)
+      nextfacet= NULL;
+    else if (!coplanarfacetset_size)
+      break;
+    else if (!--coplanarfacetset_size) {
+      facet= SETfirstt_(qh coplanarfacetset, facetT);
+      SETtruncate_(qh coplanarfacetset, 0);
+    }else
+      facet= (facetT*)qh_setdellast(qh coplanarfacetset);
+  } /* while True, for each facet in qh.coplanarfacetset */
+  if (!ischeckmax) {
+    zadd_(Zfindhorizontot, *numpart - numpartinit);
+    zmax_(Zfindhorizonmax, *numpart - numpartinit);
+    if (newbest)
+      zinc_(Zparthorizon);
+  }
+  trace4((qh ferr, 4003, "qh_findbesthorizon: newbest? %d bestfacet f%d bestdist %2.2g\n", newbest, getid_(bestfacet), *bestdist));
+  return bestfacet;
+}  /* findbesthorizon */
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >-------------------------------</a><a name="findbestnew">-</a>
+
+  qh_findbestnew( point, startfacet, dist, isoutside, numpart )
+    find best newfacet for point
+    searches all of qh.newfacet_list starting at startfacet
+    searches horizon facets of coplanar best newfacets
+    searches all facets if startfacet == qh.facet_list
+  returns:
+    best new or horizon facet that is not upperdelaunay
+    early out if isoutside and not 'Qf'
+    dist is distance to facet
+    isoutside is true if point is outside of facet
+    numpart is number of distance tests
+
+  notes:
+    Always used for merged new facets (see qh_USEfindbestnew)
+    Avoids upperdelaunay facet unless (isoutside and outside)
+
+    Uses qh.visit_id, qh.coplanarfacetset.
+    If share visit_id with qh_findbest, coplanarfacetset is incorrect.
+
+    If merging (testhorizon), searches horizon facets of coplanar best facets because
+    a point maybe coplanar to the bestfacet, below its horizon facet,
+    and above a horizon facet of a coplanar newfacet.  For example,
+      rbox 1000 s Z1 G1e-13 | qhull
+      rbox 1000 s W1e-13 P0 t992110337 | QHULL d Qbb Qc
+
+    qh_findbestnew() used if
+       qh_sharpnewfacets -- newfacets contains a sharp angle
+       if many merges, qh_premerge found a merge, or 'Qf' (qh.findbestnew)
+
+  see also:
+    qh_partitionall() and qh_findbest()
+
+  design:
+    for each new facet starting from startfacet
+      test distance from point to facet
+      return facet if clearly outside
+      unless upperdelaunay and a lowerdelaunay exists
+         update best facet
+    test horizon facets
+*/
+facetT *qh_findbestnew(pointT *point, facetT *startfacet,
+           realT *dist, boolT bestoutside, boolT *isoutside, int *numpart) {
+  realT bestdist= -REALmax/2;
+  facetT *bestfacet= NULL, *facet;
+  int oldtrace= qh IStracing, i;
+  unsigned int visitid= ++qh visit_id;
+  realT distoutside= 0.0;
+  boolT isdistoutside; /* True if distoutside is defined */
+  boolT testhorizon = True; /* needed if precise, e.g., rbox c D6 | qhull Q0 Tv */
+
+  if (!startfacet) {
+    if (qh MERGING)
+      qh_fprintf(qh ferr, 6001, "qhull precision error (qh_findbestnew): merging has formed and deleted a cone of new facets.  Can not continue.\n");
+    else
+      qh_fprintf(qh ferr, 6002, "qhull internal error (qh_findbestnew): no new facets for point p%d\n",
+              qh furthest_id);
+    qh_errexit(qh_ERRqhull, NULL, NULL);
+  }
+  zinc_(Zfindnew);
+  if (qh BESToutside || bestoutside)
+    isdistoutside= False;
+  else {
+    isdistoutside= True;
+    distoutside= qh_DISToutside; /* multiple of qh.MINoutside & qh.max_outside, see user.h */
+  }
+  if (isoutside)
+    *isoutside= True;
+  *numpart= 0;
+  if (qh IStracing >= 3 || (qh TRACElevel && qh TRACEpoint >= 0 && qh TRACEpoint == qh_pointid(point))) {
+    if (qh TRACElevel > qh IStracing)
+      qh IStracing= qh TRACElevel;
+    qh_fprintf(qh ferr, 8008, "qh_findbestnew: point p%d facet f%d. Stop? %d if dist > %2.2g\n",
+             qh_pointid(point), startfacet->id, isdistoutside, distoutside);
+    qh_fprintf(qh ferr, 8009, "  Last point added p%d visitid %d.",  qh furthest_id, visitid);
+    qh_fprintf(qh ferr, 8010, "  Last merge was #%d.\n", zzval_(Ztotmerge));
+  }
+  /* visit all new facets starting with startfacet, maybe qh facet_list */
+  for (i=0, facet=startfacet; i < 2; i++, facet= qh newfacet_list) {
+    FORALLfacet_(facet) {
+      if (facet == startfacet && i)
+        break;
+      facet->visitid= visitid;
+      if (!facet->flipped) {
+        qh_distplane(point, facet, dist);
+        (*numpart)++;
+        if (*dist > bestdist) {
+          if (!facet->upperdelaunay || *dist >= qh MINoutside) {
+            bestfacet= facet;
+            if (isdistoutside && *dist >= distoutside)
+              goto LABELreturn_bestnew;
+            bestdist= *dist;
+          }
+        }
+      } /* end of !flipped */
+    } /* FORALLfacet from startfacet or qh newfacet_list */
+  }
+  if (testhorizon || !bestfacet) /* testhorizon is always True.  Keep the same code as qh_findbest */
+    bestfacet= qh_findbesthorizon(!qh_IScheckmax, point, bestfacet ? bestfacet : startfacet,
+                                        !qh_NOupper, &bestdist, numpart);
+  *dist= bestdist;
+  if (isoutside && *dist < qh MINoutside)
+    *isoutside= False;
+LABELreturn_bestnew:
+  zadd_(Zfindnewtot, *numpart);
+  zmax_(Zfindnewmax, *numpart);
+  trace4((qh ferr, 4004, "qh_findbestnew: bestfacet f%d bestdist %2.2g\n", getid_(bestfacet), *dist));
+  qh IStracing= oldtrace;
+  return bestfacet;
+}  /* findbestnew */
+
+/* ============ hyperplane functions -- keep code together [?] ============ */
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >-------------------------------</a><a name="backnormal">-</a>
+
+  qh_backnormal( rows, numrow, numcol, sign, normal, nearzero )
+    given an upper-triangular rows array and a sign,
+    solve for normal equation x using back substitution over rows U
+
+  returns:
+     normal= x
+
+     if will not be able to divzero() when normalized(qh.MINdenom_2 and qh.MINdenom_1_2),
+       if fails on last row
+         this means that the hyperplane intersects [0,..,1]
+         sets last coordinate of normal to sign
+       otherwise
+         sets tail of normal to [...,sign,0,...], i.e., solves for b= [0...0]
+         sets nearzero
+
+  notes:
+     assumes numrow == numcol-1
+
+     see Golub & van Loan, 1983, Eq. 4.4-9 for "Gaussian elimination with complete pivoting"
+
+     solves Ux=b where Ax=b and PA=LU
+     b= [0,...,0,sign or 0]  (sign is either -1 or +1)
+     last row of A= [0,...,0,1]
+
+     1) Ly=Pb == y=b since P only permutes the 0's of   b
+
+  design:
+    for each row from end
+      perform back substitution
+      if near zero
+        use qh_divzero for division
+        if zero divide and not last row
+          set tail of normal to 0
+*/
+void qh_backnormal(realT **rows, int numrow, int numcol, boolT sign,
+        coordT *normal, boolT *nearzero) {
+  int i, j;
+  coordT *normalp, *normal_tail, *ai, *ak;
+  realT diagonal;
+  boolT waszero;
+  int zerocol= -1;
+
+  normalp= normal + numcol - 1;
+  *normalp--= (sign ? -1.0 : 1.0);
+  for (i=numrow; i--; ) {
+    *normalp= 0.0;
+    ai= rows[i] + i + 1;
+    ak= normalp+1;
+    for (j=i+1; j < numcol; j++)
+      *normalp -= *ai++ * *ak++;
+    diagonal= (rows[i])[i];
+    if (fabs_(diagonal) > qh MINdenom_2)
+      *(normalp--) /= diagonal;
+    else {
+      waszero= False;
+      *normalp= qh_divzero(*normalp, diagonal, qh MINdenom_1_2, &waszero);
+      if (waszero) {
+        zerocol= i;
+        *(normalp--)= (sign ? -1.0 : 1.0);
+        for (normal_tail= normalp+2; normal_tail < normal + numcol; normal_tail++)
+          *normal_tail= 0.0;
+      }else
+        normalp--;
+    }
+  }
+  if (zerocol != -1) {
+    zzinc_(Zback0);
+    *nearzero= True;
+    trace4((qh ferr, 4005, "qh_backnormal: zero diagonal at column %d.\n", i));
+    qh_precision("zero diagonal on back substitution");
+  }
+} /* backnormal */
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >-------------------------------</a><a name="gausselim">-</a>
+
+  qh_gausselim( rows, numrow, numcol, sign )
+    Gaussian elimination with partial pivoting
+
+  returns:
+    rows is upper triangular (includes row exchanges)
+    flips sign for each row exchange
+    sets nearzero if pivot[k] < qh.NEARzero[k], else clears it
+
+  notes:
+    if nearzero, the determinant's sign may be incorrect.
+    assumes numrow <= numcol
+
+  design:
+    for each row
+      determine pivot and exchange rows if necessary
+      test for near zero
+      perform gaussian elimination step
+*/
+void qh_gausselim(realT **rows, int numrow, int numcol, boolT *sign, boolT *nearzero) {
+  realT *ai, *ak, *rowp, *pivotrow;
+  realT n, pivot, pivot_abs= 0.0, temp;
+  int i, j, k, pivoti, flip=0;
+
+  *nearzero= False;
+  for (k=0; k < numrow; k++) {
+    pivot_abs= fabs_((rows[k])[k]);
+    pivoti= k;
+    for (i=k+1; i < numrow; i++) {
+      if ((temp= fabs_((rows[i])[k])) > pivot_abs) {
+        pivot_abs= temp;
+        pivoti= i;
+      }
+    }
+    if (pivoti != k) {
+      rowp= rows[pivoti];
+      rows[pivoti]= rows[k];
+      rows[k]= rowp;
+      *sign ^= 1;
+      flip ^= 1;
+    }
+    if (pivot_abs <= qh NEARzero[k]) {
+      *nearzero= True;
+      if (pivot_abs == 0.0) {   /* remainder of column == 0 */
+        if (qh IStracing >= 4) {
+          qh_fprintf(qh ferr, 8011, "qh_gausselim: 0 pivot at column %d. (%2.2g < %2.2g)\n", k, pivot_abs, qh DISTround);
+          qh_printmatrix(qh ferr, "Matrix:", rows, numrow, numcol);
+        }
+        zzinc_(Zgauss0);
+        qh_precision("zero pivot for Gaussian elimination");
+        goto LABELnextcol;
+      }
+    }
+    pivotrow= rows[k] + k;
+    pivot= *pivotrow++;  /* signed value of pivot, and remainder of row */
+    for (i=k+1; i < numrow; i++) {
+      ai= rows[i] + k;
+      ak= pivotrow;
+      n= (*ai++)/pivot;   /* divzero() not needed since |pivot| >= |*ai| */
+      for (j= numcol - (k+1); j--; )
+        *ai++ -= n * *ak++;
+    }
+  LABELnextcol:
+    ;
+  }
+  wmin_(Wmindenom, pivot_abs);  /* last pivot element */
+  if (qh IStracing >= 5)
+    qh_printmatrix(qh ferr, "qh_gausselem: result", rows, numrow, numcol);
+} /* gausselim */
+
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >-------------------------------</a><a name="getangle">-</a>
+
+  qh_getangle( vect1, vect2 )
+    returns the dot product of two vectors
+    if qh.RANDOMdist, joggles result
+
+  notes:
+    the angle may be > 1.0 or < -1.0 because of roundoff errors
+
+*/
+realT qh_getangle(pointT *vect1, pointT *vect2) {
+  realT angle= 0, randr;
+  int k;
+
+  for (k=qh hull_dim; k--; )
+    angle += *vect1++ * *vect2++;
+  if (qh RANDOMdist) {
+    randr= qh_RANDOMint;
+    angle += (2.0 * randr / qh_RANDOMmax - 1.0) *
+      qh RANDOMfactor;
+  }
+  trace4((qh ferr, 4006, "qh_getangle: %2.2g\n", angle));
+  return(angle);
+} /* getangle */
+
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >-------------------------------</a><a name="getcenter">-</a>
+
+  qh_getcenter( vertices )
+    returns arithmetic center of a set of vertices as a new point
+
+  notes:
+    allocates point array for center
+*/
+pointT *qh_getcenter(setT *vertices) {
+  int k;
+  pointT *center, *coord;
+  vertexT *vertex, **vertexp;
+  int count= qh_setsize(vertices);
+
+  if (count < 2) {
+    qh_fprintf(qh ferr, 6003, "qhull internal error (qh_getcenter): not defined for %d points\n", count);
+    qh_errexit(qh_ERRqhull, NULL, NULL);
+  }
+  center= (pointT *)qh_memalloc(qh normal_size);
+  for (k=0; k < qh hull_dim; k++) {
+    coord= center+k;
+    *coord= 0.0;
+    FOREACHvertex_(vertices)
+      *coord += vertex->point[k];
+    *coord /= count;  /* count>=2 by QH6003 */
+  }
+  return(center);
+} /* getcenter */
+
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >-------------------------------</a><a name="getcentrum">-</a>
+
+  qh_getcentrum( facet )
+    returns the centrum for a facet as a new point
+
+  notes:
+    allocates the centrum
+*/
+pointT *qh_getcentrum(facetT *facet) {
+  realT dist;
+  pointT *centrum, *point;
+
+  point= qh_getcenter(facet->vertices);
+  zzinc_(Zcentrumtests);
+  qh_distplane(point, facet, &dist);
+  centrum= qh_projectpoint(point, facet, dist);
+  qh_memfree(point, qh normal_size);
+  trace4((qh ferr, 4007, "qh_getcentrum: for f%d, %d vertices dist= %2.2g\n",
+          facet->id, qh_setsize(facet->vertices), dist));
+  return centrum;
+} /* getcentrum */
+
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >-------------------------------</a><a name="getdistance">-</a>
+
+  qh_getdistance( facet, neighbor, mindist, maxdist )
+    returns the maxdist and mindist distance of any vertex from neighbor
+
+  returns:
+    the max absolute value
+
+  design:
+    for each vertex of facet that is not in neighbor
+      test the distance from vertex to neighbor
+*/
+realT qh_getdistance(facetT *facet, facetT *neighbor, realT *mindist, realT *maxdist) {
+  vertexT *vertex, **vertexp;
+  realT dist, maxd, mind;
+
+  FOREACHvertex_(facet->vertices)
+    vertex->seen= False;
+  FOREACHvertex_(neighbor->vertices)
+    vertex->seen= True;
+  mind= 0.0;
+  maxd= 0.0;
+  FOREACHvertex_(facet->vertices) {
+    if (!vertex->seen) {
+      zzinc_(Zbestdist);
+      qh_distplane(vertex->point, neighbor, &dist);
+      if (dist < mind)
+        mind= dist;
+      else if (dist > maxd)
+        maxd= dist;
+    }
+  }
+  *mindist= mind;
+  *maxdist= maxd;
+  mind= -mind;
+  if (maxd > mind)
+    return maxd;
+  else
+    return mind;
+} /* getdistance */
+
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >-------------------------------</a><a name="normalize">-</a>
+
+  qh_normalize( normal, dim, toporient )
+    normalize a vector and report if too small
+    does not use min norm
+
+  see:
+    qh_normalize2
+*/
+void qh_normalize(coordT *normal, int dim, boolT toporient) {
+  qh_normalize2( normal, dim, toporient, NULL, NULL);
+} /* normalize */
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >-------------------------------</a><a name="normalize2">-</a>
+
+  qh_normalize2( normal, dim, toporient, minnorm, ismin )
+    normalize a vector and report if too small
+    qh.MINdenom/MINdenom1 are the upper limits for divide overflow
+
+  returns:
+    normalized vector
+    flips sign if !toporient
+    if minnorm non-NULL,
+      sets ismin if normal < minnorm
+
+  notes:
+    if zero norm
+       sets all elements to sqrt(1.0/dim)
+    if divide by zero (divzero())
+       sets largest element to   +/-1
+       bumps Znearlysingular
+
+  design:
+    computes norm
+    test for minnorm
+    if not near zero
+      normalizes normal
+    else if zero norm
+      sets normal to standard value
+    else
+      uses qh_divzero to normalize
+      if nearzero
+        sets norm to direction of maximum value
+*/
+void qh_normalize2(coordT *normal, int dim, boolT toporient,
+            realT *minnorm, boolT *ismin) {
+  int k;
+  realT *colp, *maxp, norm= 0, temp, *norm1, *norm2, *norm3;
+  boolT zerodiv;
+
+  norm1= normal+1;
+  norm2= normal+2;
+  norm3= normal+3;
+  if (dim == 2)
+    norm= sqrt((*normal)*(*normal) + (*norm1)*(*norm1));
+  else if (dim == 3)
+    norm= sqrt((*normal)*(*normal) + (*norm1)*(*norm1) + (*norm2)*(*norm2));
+  else if (dim == 4) {
+    norm= sqrt((*normal)*(*normal) + (*norm1)*(*norm1) + (*norm2)*(*norm2)
+               + (*norm3)*(*norm3));
+  }else if (dim > 4) {
+    norm= (*normal)*(*normal) + (*norm1)*(*norm1) + (*norm2)*(*norm2)
+               + (*norm3)*(*norm3);
+    for (k=dim-4, colp=normal+4; k--; colp++)
+      norm += (*colp) * (*colp);
+    norm= sqrt(norm);
+  }
+  if (minnorm) {
+    if (norm < *minnorm)
+      *ismin= True;
+    else
+      *ismin= False;
+  }
+  wmin_(Wmindenom, norm);
+  if (norm > qh MINdenom) {
+    if (!toporient)
+      norm= -norm;
+    *normal /= norm;
+    *norm1 /= norm;
+    if (dim == 2)
+      ; /* all done */
+    else if (dim == 3)
+      *norm2 /= norm;
+    else if (dim == 4) {
+      *norm2 /= norm;
+      *norm3 /= norm;
+    }else if (dim >4) {
+      *norm2 /= norm;
+      *norm3 /= norm;
+      for (k=dim-4, colp=normal+4; k--; )
+        *colp++ /= norm;
+    }
+  }else if (norm == 0.0) {
+    temp= sqrt(1.0/dim);
+    for (k=dim, colp=normal; k--; )
+      *colp++ = temp;
+  }else {
+    if (!toporient)
+      norm= -norm;
+    for (k=dim, colp=normal; k--; colp++) { /* k used below */
+      temp= qh_divzero(*colp, norm, qh MINdenom_1, &zerodiv);
+      if (!zerodiv)
+        *colp= temp;
+      else {
+        maxp= qh_maxabsval(normal, dim);
+        temp= ((*maxp * norm >= 0.0) ? 1.0 : -1.0);
+        for (k=dim, colp=normal; k--; colp++)
+          *colp= 0.0;
+        *maxp= temp;
+        zzinc_(Znearlysingular);
+        trace0((qh ferr, 1, "qh_normalize: norm=%2.2g too small during p%d\n",
+               norm, qh furthest_id));
+        return;
+      }
+    }
+  }
+} /* normalize */
+
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >-------------------------------</a><a name="projectpoint">-</a>
+
+  qh_projectpoint( point, facet, dist )
+    project point onto a facet by dist
+
+  returns:
+    returns a new point
+
+  notes:
+    if dist= distplane(point,facet)
+      this projects point to hyperplane
+    assumes qh_memfree_() is valid for normal_size
+*/
+pointT *qh_projectpoint(pointT *point, facetT *facet, realT dist) {
+  pointT *newpoint, *np, *normal;
+  int normsize= qh normal_size;
+  int k;
+  void **freelistp; /* used if !qh_NOmem by qh_memalloc_() */
+
+  qh_memalloc_(normsize, freelistp, newpoint, pointT);
+  np= newpoint;
+  normal= facet->normal;
+  for (k=qh hull_dim; k--; )
+    *(np++)= *point++ - dist * *normal++;
+  return(newpoint);
+} /* projectpoint */
+
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >-------------------------------</a><a name="setfacetplane">-</a>
+
+  qh_setfacetplane( facet )
+    sets the hyperplane for a facet
+    if qh.RANDOMdist, joggles hyperplane
+
+  notes:
+    uses global buffers qh.gm_matrix and qh.gm_row
+    overwrites facet->normal if already defined
+    updates Wnewvertex if PRINTstatistics
+    sets facet->upperdelaunay if upper envelope of Delaunay triangulation
+
+  design:
+    copy vertex coordinates to qh.gm_matrix/gm_row
+    compute determinate
+    if nearzero
+      recompute determinate with gaussian elimination
+      if nearzero
+        force outside orientation by testing interior point
+*/
+void qh_setfacetplane(facetT *facet) {
+  pointT *point;
+  vertexT *vertex, **vertexp;
+  int normsize= qh normal_size;
+  int k,i, oldtrace= 0;
+  realT dist;
+  void **freelistp; /* used if !qh_NOmem by qh_memalloc_() */
+  coordT *coord, *gmcoord;
+  pointT *point0= SETfirstt_(facet->vertices, vertexT)->point;
+  boolT nearzero= False;
+
+  zzinc_(Zsetplane);
+  if (!facet->normal)
+    qh_memalloc_(normsize, freelistp, facet->normal, coordT);
+  if (facet == qh tracefacet) {
+    oldtrace= qh IStracing;
+    qh IStracing= 5;
+    qh_fprintf(qh ferr, 8012, "qh_setfacetplane: facet f%d created.\n", facet->id);
+    qh_fprintf(qh ferr, 8013, "  Last point added to hull was p%d.", qh furthest_id);
+    if (zzval_(Ztotmerge))
+      qh_fprintf(qh ferr, 8014, "  Last merge was #%d.", zzval_(Ztotmerge));
+    qh_fprintf(qh ferr, 8015, "\n\nCurrent summary is:\n");
+      qh_printsummary(qh ferr);
+  }
+  if (qh hull_dim <= 4) {
+    i= 0;
+    if (qh RANDOMdist) {
+      gmcoord= qh gm_matrix;
+      FOREACHvertex_(facet->vertices) {
+        qh gm_row[i++]= gmcoord;
+        coord= vertex->point;
+        for (k=qh hull_dim; k--; )
+          *(gmcoord++)= *coord++ * qh_randomfactor(qh RANDOMa, qh RANDOMb);
+      }
+    }else {
+      FOREACHvertex_(facet->vertices)
+       qh gm_row[i++]= vertex->point;
+    }
+    qh_sethyperplane_det(qh hull_dim, qh gm_row, point0, facet->toporient,
+                facet->normal, &facet->offset, &nearzero);
+  }
+  if (qh hull_dim > 4 || nearzero) {
+    i= 0;
+    gmcoord= qh gm_matrix;
+    FOREACHvertex_(facet->vertices) {
+      if (vertex->point != point0) {
+        qh gm_row[i++]= gmcoord;
+        coord= vertex->point;
+        point= point0;
+        for (k=qh hull_dim; k--; )
+          *(gmcoord++)= *coord++ - *point++;
+      }
+    }
+    qh gm_row[i]= gmcoord;  /* for areasimplex */
+    if (qh RANDOMdist) {
+      gmcoord= qh gm_matrix;
+      for (i=qh hull_dim-1; i--; ) {
+        for (k=qh hull_dim; k--; )
+          *(gmcoord++) *= qh_randomfactor(qh RANDOMa, qh RANDOMb);
+      }
+    }
+    qh_sethyperplane_gauss(qh hull_dim, qh gm_row, point0, facet->toporient,
+                facet->normal, &facet->offset, &nearzero);
+    if (nearzero) {
+      if (qh_orientoutside(facet)) {
+        trace0((qh ferr, 2, "qh_setfacetplane: flipped orientation after testing interior_point during p%d\n", qh furthest_id));
+      /* this is part of using Gaussian Elimination.  For example in 5-d
+           1 1 1 1 0
+           1 1 1 1 1
+           0 0 0 1 0
+           0 1 0 0 0
+           1 0 0 0 0
+           norm= 0.38 0.38 -0.76 0.38 0
+         has a determinate of 1, but g.e. after subtracting pt. 0 has
+         0's in the diagonal, even with full pivoting.  It does work
+         if you subtract pt. 4 instead. */
+      }
+    }
+  }
+  facet->upperdelaunay= False;
+  if (qh DELAUNAY) {
+    if (qh UPPERdelaunay) {     /* matches qh_triangulate_facet and qh.lower_threshold in qh_initbuild */
+      if (facet->normal[qh hull_dim -1] >= qh ANGLEround * qh_ZEROdelaunay)
+        facet->upperdelaunay= True;
+    }else {
+      if (facet->normal[qh hull_dim -1] > -qh ANGLEround * qh_ZEROdelaunay)
+        facet->upperdelaunay= True;
+    }
+  }
+  if (qh PRINTstatistics || qh IStracing || qh TRACElevel || qh JOGGLEmax < REALmax) {
+    qh old_randomdist= qh RANDOMdist;
+    qh RANDOMdist= False;
+    FOREACHvertex_(facet->vertices) {
+      if (vertex->point != point0) {
+        boolT istrace= False;
+        zinc_(Zdiststat);
+        qh_distplane(vertex->point, facet, &dist);
+        dist= fabs_(dist);
+        zinc_(Znewvertex);
+        wadd_(Wnewvertex, dist);
+        if (dist > wwval_(Wnewvertexmax)) {
+          wwval_(Wnewvertexmax)= dist;
+          if (dist > qh max_outside) {
+            qh max_outside= dist;  /* used by qh_maxouter() */
+            if (dist > qh TRACEdist)
+              istrace= True;
+          }
+        }else if (-dist > qh TRACEdist)
+          istrace= True;
+        if (istrace) {
+          qh_fprintf(qh ferr, 8016, "qh_setfacetplane: ====== vertex p%d(v%d) increases max_outside to %2.2g for new facet f%d last p%d\n",
+                qh_pointid(vertex->point), vertex->id, dist, facet->id, qh furthest_id);
+          qh_errprint("DISTANT", facet, NULL, NULL, NULL);
+        }
+      }
+    }
+    qh RANDOMdist= qh old_randomdist;
+  }
+  if (qh IStracing >= 3) {
+    qh_fprintf(qh ferr, 8017, "qh_setfacetplane: f%d offset %2.2g normal: ",
+             facet->id, facet->offset);
+    for (k=0; k < qh hull_dim; k++)
+      qh_fprintf(qh ferr, 8018, "%2.2g ", facet->normal[k]);
+    qh_fprintf(qh ferr, 8019, "\n");
+  }
+  if (facet == qh tracefacet)
+    qh IStracing= oldtrace;
+} /* setfacetplane */
+
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >-------------------------------</a><a name="sethyperplane_det">-</a>
+
+  qh_sethyperplane_det( dim, rows, point0, toporient, normal, offset, nearzero )
+    given dim X dim array indexed by rows[], one row per point,
+        toporient(flips all signs),
+        and point0 (any row)
+    set normalized hyperplane equation from oriented simplex
+
+  returns:
+    normal (normalized)
+    offset (places point0 on the hyperplane)
+    sets nearzero if hyperplane not through points
+
+  notes:
+    only defined for dim == 2..4
+    rows[] is not modified
+    solves det(P-V_0, V_n-V_0, ..., V_1-V_0)=0, i.e. every point is on hyperplane
+    see Bower & Woodworth, A programmer's geometry, Butterworths 1983.
+
+  derivation of 3-d minnorm
+    Goal: all vertices V_i within qh.one_merge of hyperplane
+    Plan: exactly translate the facet so that V_0 is the origin
+          exactly rotate the facet so that V_1 is on the x-axis and y_2=0.
+          exactly rotate the effective perturbation to only effect n_0
+             this introduces a factor of sqrt(3)
+    n_0 = ((y_2-y_0)*(z_1-z_0) - (z_2-z_0)*(y_1-y_0)) / norm
+    Let M_d be the max coordinate difference
+    Let M_a be the greater of M_d and the max abs. coordinate
+    Let u be machine roundoff and distround be max error for distance computation
+    The max error for n_0 is sqrt(3) u M_a M_d / norm.  n_1 is approx. 1 and n_2 is approx. 0
+    The max error for distance of V_1 is sqrt(3) u M_a M_d M_d / norm.  Offset=0 at origin
+    Then minnorm = 1.8 u M_a M_d M_d / qh.ONEmerge
+    Note that qh.one_merge is approx. 45.5 u M_a and norm is usually about M_d M_d
+
+  derivation of 4-d minnorm
+    same as above except rotate the facet so that V_1 on x-axis and w_2, y_3, w_3=0
+     [if two vertices fixed on x-axis, can rotate the other two in yzw.]
+    n_0 = det3_(...) = y_2 det2_(z_1, w_1, z_3, w_3) = - y_2 w_1 z_3
+     [all other terms contain at least two factors nearly zero.]
+    The max error for n_0 is sqrt(4) u M_a M_d M_d / norm
+    Then minnorm = 2 u M_a M_d M_d M_d / qh.ONEmerge
+    Note that qh.one_merge is approx. 82 u M_a and norm is usually about M_d M_d M_d
+*/
+void qh_sethyperplane_det(int dim, coordT **rows, coordT *point0,
+          boolT toporient, coordT *normal, realT *offset, boolT *nearzero) {
+  realT maxround, dist;
+  int i;
+  pointT *point;
+
+
+  if (dim == 2) {
+    normal[0]= dY(1,0);
+    normal[1]= dX(0,1);
+    qh_normalize2(normal, dim, toporient, NULL, NULL);
+    *offset= -(point0[0]*normal[0]+point0[1]*normal[1]);
+    *nearzero= False;  /* since nearzero norm => incident points */
+  }else if (dim == 3) {
+    normal[0]= det2_(dY(2,0), dZ(2,0),
+                     dY(1,0), dZ(1,0));
+    normal[1]= det2_(dX(1,0), dZ(1,0),
+                     dX(2,0), dZ(2,0));
+    normal[2]= det2_(dX(2,0), dY(2,0),
+                     dX(1,0), dY(1,0));
+    qh_normalize2(normal, dim, toporient, NULL, NULL);
+    *offset= -(point0[0]*normal[0] + point0[1]*normal[1]
+               + point0[2]*normal[2]);
+    maxround= qh DISTround;
+    for (i=dim; i--; ) {
+      point= rows[i];
+      if (point != point0) {
+        dist= *offset + (point[0]*normal[0] + point[1]*normal[1]
+               + point[2]*normal[2]);
+        if (dist > maxround || dist < -maxround) {
+          *nearzero= True;
+          break;
+        }
+      }
+    }
+  }else if (dim == 4) {
+    normal[0]= - det3_(dY(2,0), dZ(2,0), dW(2,0),
+                        dY(1,0), dZ(1,0), dW(1,0),
+                        dY(3,0), dZ(3,0), dW(3,0));
+    normal[1]=   det3_(dX(2,0), dZ(2,0), dW(2,0),
+                        dX(1,0), dZ(1,0), dW(1,0),
+                        dX(3,0), dZ(3,0), dW(3,0));
+    normal[2]= - det3_(dX(2,0), dY(2,0), dW(2,0),
+                        dX(1,0), dY(1,0), dW(1,0),
+                        dX(3,0), dY(3,0), dW(3,0));
+    normal[3]=   det3_(dX(2,0), dY(2,0), dZ(2,0),
+                        dX(1,0), dY(1,0), dZ(1,0),
+                        dX(3,0), dY(3,0), dZ(3,0));
+    qh_normalize2(normal, dim, toporient, NULL, NULL);
+    *offset= -(point0[0]*normal[0] + point0[1]*normal[1]
+               + point0[2]*normal[2] + point0[3]*normal[3]);
+    maxround= qh DISTround;
+    for (i=dim; i--; ) {
+      point= rows[i];
+      if (point != point0) {
+        dist= *offset + (point[0]*normal[0] + point[1]*normal[1]
+               + point[2]*normal[2] + point[3]*normal[3]);
+        if (dist > maxround || dist < -maxround) {
+          *nearzero= True;
+          break;
+        }
+      }
+    }
+  }
+  if (*nearzero) {
+    zzinc_(Zminnorm);
+    trace0((qh ferr, 3, "qh_sethyperplane_det: degenerate norm during p%d.\n", qh furthest_id));
+    zzinc_(Znearlysingular);
+  }
+} /* sethyperplane_det */
+
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >-------------------------------</a><a name="sethyperplane_gauss">-</a>
+
+  qh_sethyperplane_gauss( dim, rows, point0, toporient, normal, offset, nearzero )
+    given(dim-1) X dim array of rows[i]= V_{i+1} - V_0 (point0)
+    set normalized hyperplane equation from oriented simplex
+
+  returns:
+    normal (normalized)
+    offset (places point0 on the hyperplane)
+
+  notes:
+    if nearzero
+      orientation may be incorrect because of incorrect sign flips in gausselim
+    solves [V_n-V_0,...,V_1-V_0, 0 .. 0 1] * N == [0 .. 0 1]
+        or [V_n-V_0,...,V_1-V_0, 0 .. 0 1] * N == [0]
+    i.e., N is normal to the hyperplane, and the unnormalized
+        distance to [0 .. 1] is either 1 or   0
+
+  design:
+    perform gaussian elimination
+    flip sign for negative values
+    perform back substitution
+    normalize result
+    compute offset
+*/
+void qh_sethyperplane_gauss(int dim, coordT **rows, pointT *point0,
+                boolT toporient, coordT *normal, coordT *offset, boolT *nearzero) {
+  coordT *pointcoord, *normalcoef;
+  int k;
+  boolT sign= toporient, nearzero2= False;
+
+  qh_gausselim(rows, dim-1, dim, &sign, nearzero);
+  for (k=dim-1; k--; ) {
+    if ((rows[k])[k] < 0)
+      sign ^= 1;
+  }
+  if (*nearzero) {
+    zzinc_(Znearlysingular);
+    trace0((qh ferr, 4, "qh_sethyperplane_gauss: nearly singular or axis parallel hyperplane during p%d.\n", qh furthest_id));
+    qh_backnormal(rows, dim-1, dim, sign, normal, &nearzero2);
+  }else {
+    qh_backnormal(rows, dim-1, dim, sign, normal, &nearzero2);
+    if (nearzero2) {
+      zzinc_(Znearlysingular);
+      trace0((qh ferr, 5, "qh_sethyperplane_gauss: singular or axis parallel hyperplane at normalization during p%d.\n", qh furthest_id));
+    }
+  }
+  if (nearzero2)
+    *nearzero= True;
+  qh_normalize2(normal, dim, True, NULL, NULL);
+  pointcoord= point0;
+  normalcoef= normal;
+  *offset= -(*pointcoord++ * *normalcoef++);
+  for (k=dim-1; k--; )
+    *offset -= *pointcoord++ * *normalcoef++;
+} /* sethyperplane_gauss */
+
+
+
diff --git a/xs/src/qhull/src/libqhull/geom.h b/xs/src/qhull/src/libqhull/geom.h
new file mode 100644
index 0000000000..16ef48d2d7
--- /dev/null
+++ b/xs/src/qhull/src/libqhull/geom.h
@@ -0,0 +1,176 @@
+/*<html><pre>  -<a                             href="qh-geom.htm"
+  >-------------------------------</a><a name="TOP">-</a>
+
+  geom.h
+    header file for geometric routines
+
+   see qh-geom.htm and geom.c
+
+   Copyright (c) 1993-2015 The Geometry Center.
+   $Id: //main/2015/qhull/src/libqhull/geom.h#1 $$Change: 1981 $
+   $DateTime: 2015/09/28 20:26:32 $$Author: bbarber $
+*/
+
+#ifndef qhDEFgeom
+#define qhDEFgeom 1
+
+#include "libqhull.h"
+
+/* ============ -macros- ======================== */
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >--------------------------------</a><a name="fabs_">-</a>
+
+  fabs_(a)
+    returns the absolute value of a
+*/
+#define fabs_( a ) ((( a ) < 0 ) ? -( a ):( a ))
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >--------------------------------</a><a name="fmax_">-</a>
+
+  fmax_(a,b)
+    returns the maximum value of a and b
+*/
+#define fmax_( a,b )  ( ( a ) < ( b ) ? ( b ) : ( a ) )
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >--------------------------------</a><a name="fmin_">-</a>
+
+  fmin_(a,b)
+    returns the minimum value of a and b
+*/
+#define fmin_( a,b )  ( ( a ) > ( b ) ? ( b ) : ( a ) )
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >--------------------------------</a><a name="maximize_">-</a>
+
+  maximize_(maxval, val)
+    set maxval to val if val is greater than maxval
+*/
+#define maximize_( maxval, val ) { if (( maxval ) < ( val )) ( maxval )= ( val ); }
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >--------------------------------</a><a name="minimize_">-</a>
+
+  minimize_(minval, val)
+    set minval to val if val is less than minval
+*/
+#define minimize_( minval, val ) { if (( minval ) > ( val )) ( minval )= ( val ); }
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >--------------------------------</a><a name="det2_">-</a>
+
+  det2_(a1, a2,
+        b1, b2)
+
+    compute a 2-d determinate
+*/
+#define det2_( a1,a2,b1,b2 ) (( a1 )*( b2 ) - ( a2 )*( b1 ))
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >--------------------------------</a><a name="det3_">-</a>
+
+  det3_(a1, a2, a3,
+       b1, b2, b3,
+       c1, c2, c3)
+
+    compute a 3-d determinate
+*/
+#define det3_( a1,a2,a3,b1,b2,b3,c1,c2,c3 ) ( ( a1 )*det2_( b2,b3,c2,c3 ) \
+                - ( b1 )*det2_( a2,a3,c2,c3 ) + ( c1 )*det2_( a2,a3,b2,b3 ) )
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >--------------------------------</a><a name="dX">-</a>
+
+  dX( p1, p2 )
+  dY( p1, p2 )
+  dZ( p1, p2 )
+
+    given two indices into rows[],
+
+    compute the difference between X, Y, or Z coordinates
+*/
+#define dX( p1,p2 )  ( *( rows[p1] ) - *( rows[p2] ))
+#define dY( p1,p2 )  ( *( rows[p1]+1 ) - *( rows[p2]+1 ))
+#define dZ( p1,p2 )  ( *( rows[p1]+2 ) - *( rows[p2]+2 ))
+#define dW( p1,p2 )  ( *( rows[p1]+3 ) - *( rows[p2]+3 ))
+
+/*============= prototypes in alphabetical order, infrequent at end ======= */
+
+void    qh_backnormal(realT **rows, int numrow, int numcol, boolT sign, coordT *normal, boolT *nearzero);
+void    qh_distplane(pointT *point, facetT *facet, realT *dist);
+facetT *qh_findbest(pointT *point, facetT *startfacet,
+                     boolT bestoutside, boolT isnewfacets, boolT noupper,
+                     realT *dist, boolT *isoutside, int *numpart);
+facetT *qh_findbesthorizon(boolT ischeckmax, pointT *point,
+                     facetT *startfacet, boolT noupper, realT *bestdist, int *numpart);
+facetT *qh_findbestnew(pointT *point, facetT *startfacet, realT *dist,
+                     boolT bestoutside, boolT *isoutside, int *numpart);
+void    qh_gausselim(realT **rows, int numrow, int numcol, boolT *sign, boolT *nearzero);
+realT   qh_getangle(pointT *vect1, pointT *vect2);
+pointT *qh_getcenter(setT *vertices);
+pointT *qh_getcentrum(facetT *facet);
+realT   qh_getdistance(facetT *facet, facetT *neighbor, realT *mindist, realT *maxdist);
+void    qh_normalize(coordT *normal, int dim, boolT toporient);
+void    qh_normalize2(coordT *normal, int dim, boolT toporient,
+            realT *minnorm, boolT *ismin);
+pointT *qh_projectpoint(pointT *point, facetT *facet, realT dist);
+
+void    qh_setfacetplane(facetT *newfacets);
+void    qh_sethyperplane_det(int dim, coordT **rows, coordT *point0,
+              boolT toporient, coordT *normal, realT *offset, boolT *nearzero);
+void    qh_sethyperplane_gauss(int dim, coordT **rows, pointT *point0,
+             boolT toporient, coordT *normal, coordT *offset, boolT *nearzero);
+boolT   qh_sharpnewfacets(void);
+
+/*========= infrequently used code in geom2.c =============*/
+
+coordT *qh_copypoints(coordT *points, int numpoints, int dimension);
+void    qh_crossproduct(int dim, realT vecA[3], realT vecB[3], realT vecC[3]);
+realT   qh_determinant(realT **rows, int dim, boolT *nearzero);
+realT   qh_detjoggle(pointT *points, int numpoints, int dimension);
+void    qh_detroundoff(void);
+realT   qh_detsimplex(pointT *apex, setT *points, int dim, boolT *nearzero);
+realT   qh_distnorm(int dim, pointT *point, pointT *normal, realT *offsetp);
+realT   qh_distround(int dimension, realT maxabs, realT maxsumabs);
+realT   qh_divzero(realT numer, realT denom, realT mindenom1, boolT *zerodiv);
+realT   qh_facetarea(facetT *facet);
+realT   qh_facetarea_simplex(int dim, coordT *apex, setT *vertices,
+          vertexT *notvertex,  boolT toporient, coordT *normal, realT *offset);
+pointT *qh_facetcenter(setT *vertices);
+facetT *qh_findgooddist(pointT *point, facetT *facetA, realT *distp, facetT **facetlist);
+void    qh_getarea(facetT *facetlist);
+boolT   qh_gram_schmidt(int dim, realT **rows);
+boolT   qh_inthresholds(coordT *normal, realT *angle);
+void    qh_joggleinput(void);
+realT  *qh_maxabsval(realT *normal, int dim);
+setT   *qh_maxmin(pointT *points, int numpoints, int dimension);
+realT   qh_maxouter(void);
+void    qh_maxsimplex(int dim, setT *maxpoints, pointT *points, int numpoints, setT **simplex);
+realT   qh_minabsval(realT *normal, int dim);
+int     qh_mindiff(realT *vecA, realT *vecB, int dim);
+boolT   qh_orientoutside(facetT *facet);
+void    qh_outerinner(facetT *facet, realT *outerplane, realT *innerplane);
+coordT  qh_pointdist(pointT *point1, pointT *point2, int dim);
+void    qh_printmatrix(FILE *fp, const char *string, realT **rows, int numrow, int numcol);
+void    qh_printpoints(FILE *fp, const char *string, setT *points);
+void    qh_projectinput(void);
+void    qh_projectpoints(signed char *project, int n, realT *points,
+             int numpoints, int dim, realT *newpoints, int newdim);
+void    qh_rotateinput(realT **rows);
+void    qh_rotatepoints(realT *points, int numpoints, int dim, realT **rows);
+void    qh_scaleinput(void);
+void    qh_scalelast(coordT *points, int numpoints, int dim, coordT low,
+                   coordT high, coordT newhigh);
+void    qh_scalepoints(pointT *points, int numpoints, int dim,
+                realT *newlows, realT *newhighs);
+boolT   qh_sethalfspace(int dim, coordT *coords, coordT **nextp,
+              coordT *normal, coordT *offset, coordT *feasible);
+coordT *qh_sethalfspace_all(int dim, int count, coordT *halfspaces, pointT *feasible);
+pointT *qh_voronoi_center(int dim, setT *points);
+
+#endif /* qhDEFgeom */
+
+
+
diff --git a/xs/src/qhull/src/libqhull/geom2.c b/xs/src/qhull/src/libqhull/geom2.c
new file mode 100644
index 0000000000..82ec4936ef
--- /dev/null
+++ b/xs/src/qhull/src/libqhull/geom2.c
@@ -0,0 +1,2094 @@
+/*<html><pre>  -<a                             href="qh-geom.htm"
+  >-------------------------------</a><a name="TOP">-</a>
+
+
+   geom2.c
+   infrequently used geometric routines of qhull
+
+   see qh-geom.htm and geom.h
+
+   Copyright (c) 1993-2015 The Geometry Center.
+   $Id: //main/2015/qhull/src/libqhull/geom2.c#6 $$Change: 2065 $
+   $DateTime: 2016/01/18 13:51:04 $$Author: bbarber $
+
+   frequently used code goes into geom.c
+*/
+
+#include "qhull_a.h"
+
+/*================== functions in alphabetic order ============*/
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >-------------------------------</a><a name="copypoints">-</a>
+
+  qh_copypoints( points, numpoints, dimension)
+    return qh_malloc'd copy of points
+  notes:
+    qh_free the returned points to avoid a memory leak
+*/
+coordT *qh_copypoints(coordT *points, int numpoints, int dimension) {
+  int size;
+  coordT *newpoints;
+
+  size= numpoints * dimension * (int)sizeof(coordT);
+  if (!(newpoints=(coordT*)qh_malloc((size_t)size))) {
+    qh_fprintf(qh ferr, 6004, "qhull error: insufficient memory to copy %d points\n",
+        numpoints);
+    qh_errexit(qh_ERRmem, NULL, NULL);
+  }
+  memcpy((char *)newpoints, (char *)points, (size_t)size); /* newpoints!=0 by QH6004 */
+  return newpoints;
+} /* copypoints */
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >-------------------------------</a><a name="crossproduct">-</a>
+
+  qh_crossproduct( dim, vecA, vecB, vecC )
+    crossproduct of 2 dim vectors
+    C= A x B
+
+  notes:
+    from Glasner, Graphics Gems I, p. 639
+    only defined for dim==3
+*/
+void qh_crossproduct(int dim, realT vecA[3], realT vecB[3], realT vecC[3]){
+
+  if (dim == 3) {
+    vecC[0]=   det2_(vecA[1], vecA[2],
+                     vecB[1], vecB[2]);
+    vecC[1]= - det2_(vecA[0], vecA[2],
+                     vecB[0], vecB[2]);
+    vecC[2]=   det2_(vecA[0], vecA[1],
+                     vecB[0], vecB[1]);
+  }
+} /* vcross */
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >-------------------------------</a><a name="determinant">-</a>
+
+  qh_determinant( rows, dim, nearzero )
+    compute signed determinant of a square matrix
+    uses qh.NEARzero to test for degenerate matrices
+
+  returns:
+    determinant
+    overwrites rows and the matrix
+    if dim == 2 or 3
+      nearzero iff determinant < qh NEARzero[dim-1]
+      (!quite correct, not critical)
+    if dim >= 4
+      nearzero iff diagonal[k] < qh NEARzero[k]
+*/
+realT qh_determinant(realT **rows, int dim, boolT *nearzero) {
+  realT det=0;
+  int i;
+  boolT sign= False;
+
+  *nearzero= False;
+  if (dim < 2) {
+    qh_fprintf(qh ferr, 6005, "qhull internal error (qh_determinate): only implemented for dimension >= 2\n");
+    qh_errexit(qh_ERRqhull, NULL, NULL);
+  }else if (dim == 2) {
+    det= det2_(rows[0][0], rows[0][1],
+                 rows[1][0], rows[1][1]);
+    if (fabs_(det) < 10*qh NEARzero[1])  /* not really correct, what should this be? */
+      *nearzero= True;
+  }else if (dim == 3) {
+    det= det3_(rows[0][0], rows[0][1], rows[0][2],
+                 rows[1][0], rows[1][1], rows[1][2],
+                 rows[2][0], rows[2][1], rows[2][2]);
+    if (fabs_(det) < 10*qh NEARzero[2])  /* what should this be?  det 5.5e-12 was flat for qh_maxsimplex of qdelaunay 0,0 27,27 -36,36 -9,63  */
+      *nearzero= True;
+  }else {
+    qh_gausselim(rows, dim, dim, &sign, nearzero);  /* if nearzero, diagonal still ok*/
+    det= 1.0;
+    for (i=dim; i--; )
+      det *= (rows[i])[i];
+    if (sign)
+      det= -det;
+  }
+  return det;
+} /* determinant */
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >-------------------------------</a><a name="detjoggle">-</a>
+
+  qh_detjoggle( points, numpoints, dimension )
+    determine default max joggle for point array
+      as qh_distround * qh_JOGGLEdefault
+
+  returns:
+    initial value for JOGGLEmax from points and REALepsilon
+
+  notes:
+    computes DISTround since qh_maxmin not called yet
+    if qh SCALElast, last dimension will be scaled later to MAXwidth
+
+    loop duplicated from qh_maxmin
+*/
+realT qh_detjoggle(pointT *points, int numpoints, int dimension) {
+  realT abscoord, distround, joggle, maxcoord, mincoord;
+  pointT *point, *pointtemp;
+  realT maxabs= -REALmax;
+  realT sumabs= 0;
+  realT maxwidth= 0;
+  int k;
+
+  for (k=0; k < dimension; k++) {
+    if (qh SCALElast && k == dimension-1)
+      abscoord= maxwidth;
+    else if (qh DELAUNAY && k == dimension-1) /* will qh_setdelaunay() */
+      abscoord= 2 * maxabs * maxabs;  /* may be low by qh hull_dim/2 */
+    else {
+      maxcoord= -REALmax;
+      mincoord= REALmax;
+      FORALLpoint_(points, numpoints) {
+        maximize_(maxcoord, point[k]);
+        minimize_(mincoord, point[k]);
+      }
+      maximize_(maxwidth, maxcoord-mincoord);
+      abscoord= fmax_(maxcoord, -mincoord);
+    }
+    sumabs += abscoord;
+    maximize_(maxabs, abscoord);
+  } /* for k */
+  distround= qh_distround(qh hull_dim, maxabs, sumabs);
+  joggle= distround * qh_JOGGLEdefault;
+  maximize_(joggle, REALepsilon * qh_JOGGLEdefault);
+  trace2((qh ferr, 2001, "qh_detjoggle: joggle=%2.2g maxwidth=%2.2g\n", joggle, maxwidth));
+  return joggle;
+} /* detjoggle */
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >-------------------------------</a><a name="detroundoff">-</a>
+
+  qh_detroundoff()
+    determine maximum roundoff errors from
+      REALepsilon, REALmax, REALmin, qh.hull_dim, qh.MAXabs_coord,
+      qh.MAXsumcoord, qh.MAXwidth, qh.MINdenom_1
+
+    accounts for qh.SETroundoff, qh.RANDOMdist, qh MERGEexact
+      qh.premerge_cos, qh.postmerge_cos, qh.premerge_centrum,
+      qh.postmerge_centrum, qh.MINoutside,
+      qh_RATIOnearinside, qh_COPLANARratio, qh_WIDEcoplanar
+
+  returns:
+    sets qh.DISTround, etc. (see below)
+    appends precision constants to qh.qhull_options
+
+  see:
+    qh_maxmin() for qh.NEARzero
+
+  design:
+    determine qh.DISTround for distance computations
+    determine minimum denominators for qh_divzero
+    determine qh.ANGLEround for angle computations
+    adjust qh.premerge_cos,... for roundoff error
+    determine qh.ONEmerge for maximum error due to a single merge
+    determine qh.NEARinside, qh.MAXcoplanar, qh.MINvisible,
+      qh.MINoutside, qh.WIDEfacet
+    initialize qh.max_vertex and qh.minvertex
+*/
+void qh_detroundoff(void) {
+
+  qh_option("_max-width", NULL, &qh MAXwidth);
+  if (!qh SETroundoff) {
+    qh DISTround= qh_distround(qh hull_dim, qh MAXabs_coord, qh MAXsumcoord);
+    if (qh RANDOMdist)
+      qh DISTround += qh RANDOMfactor * qh MAXabs_coord;
+    qh_option("Error-roundoff", NULL, &qh DISTround);
+  }
+  qh MINdenom= qh MINdenom_1 * qh MAXabs_coord;
+  qh MINdenom_1_2= sqrt(qh MINdenom_1 * qh hull_dim) ;  /* if will be normalized */
+  qh MINdenom_2= qh MINdenom_1_2 * qh MAXabs_coord;
+                                              /* for inner product */
+  qh ANGLEround= 1.01 * qh hull_dim * REALepsilon;
+  if (qh RANDOMdist)
+    qh ANGLEround += qh RANDOMfactor;
+  if (qh premerge_cos < REALmax/2) {
+    qh premerge_cos -= qh ANGLEround;
+    if (qh RANDOMdist)
+      qh_option("Angle-premerge-with-random", NULL, &qh premerge_cos);
+  }
+  if (qh postmerge_cos < REALmax/2) {
+    qh postmerge_cos -= qh ANGLEround;
+    if (qh RANDOMdist)
+      qh_option("Angle-postmerge-with-random", NULL, &qh postmerge_cos);
+  }
+  qh premerge_centrum += 2 * qh DISTround;    /*2 for centrum and distplane()*/
+  qh postmerge_centrum += 2 * qh DISTround;
+  if (qh RANDOMdist && (qh MERGEexact || qh PREmerge))
+    qh_option("Centrum-premerge-with-random", NULL, &qh premerge_centrum);
+  if (qh RANDOMdist && qh POSTmerge)
+    qh_option("Centrum-postmerge-with-random", NULL, &qh postmerge_centrum);
+  { /* compute ONEmerge, max vertex offset for merging simplicial facets */
+    realT maxangle= 1.0, maxrho;
+
+    minimize_(maxangle, qh premerge_cos);
+    minimize_(maxangle, qh postmerge_cos);
+    /* max diameter * sin theta + DISTround for vertex to its hyperplane */
+    qh ONEmerge= sqrt((realT)qh hull_dim) * qh MAXwidth *
+      sqrt(1.0 - maxangle * maxangle) + qh DISTround;
+    maxrho= qh hull_dim * qh premerge_centrum + qh DISTround;
+    maximize_(qh ONEmerge, maxrho);
+    maxrho= qh hull_dim * qh postmerge_centrum + qh DISTround;
+    maximize_(qh ONEmerge, maxrho);
+    if (qh MERGING)
+      qh_option("_one-merge", NULL, &qh ONEmerge);
+  }
+  qh NEARinside= qh ONEmerge * qh_RATIOnearinside; /* only used if qh KEEPnearinside */
+  if (qh JOGGLEmax < REALmax/2 && (qh KEEPcoplanar || qh KEEPinside)) {
+    realT maxdist;             /* adjust qh.NEARinside for joggle */
+    qh KEEPnearinside= True;
+    maxdist= sqrt((realT)qh hull_dim) * qh JOGGLEmax + qh DISTround;
+    maxdist= 2*maxdist;        /* vertex and coplanar point can joggle in opposite directions */
+    maximize_(qh NEARinside, maxdist);  /* must agree with qh_nearcoplanar() */
+  }
+  if (qh KEEPnearinside)
+    qh_option("_near-inside", NULL, &qh NEARinside);
+  if (qh JOGGLEmax < qh DISTround) {
+    qh_fprintf(qh ferr, 6006, "qhull error: the joggle for 'QJn', %.2g, is below roundoff for distance computations, %.2g\n",
+         qh JOGGLEmax, qh DISTround);
+    qh_errexit(qh_ERRinput, NULL, NULL);
+  }
+  if (qh MINvisible > REALmax/2) {
+    if (!qh MERGING)
+      qh MINvisible= qh DISTround;
+    else if (qh hull_dim <= 3)
+      qh MINvisible= qh premerge_centrum;
+    else
+      qh MINvisible= qh_COPLANARratio * qh premerge_centrum;
+    if (qh APPROXhull && qh MINvisible > qh MINoutside)
+      qh MINvisible= qh MINoutside;
+    qh_option("Visible-distance", NULL, &qh MINvisible);
+  }
+  if (qh MAXcoplanar > REALmax/2) {
+    qh MAXcoplanar= qh MINvisible;
+    qh_option("U-coplanar-distance", NULL, &qh MAXcoplanar);
+  }
+  if (!qh APPROXhull) {             /* user may specify qh MINoutside */
+    qh MINoutside= 2 * qh MINvisible;
+    if (qh premerge_cos < REALmax/2)
+      maximize_(qh MINoutside, (1- qh premerge_cos) * qh MAXabs_coord);
+    qh_option("Width-outside", NULL, &qh MINoutside);
+  }
+  qh WIDEfacet= qh MINoutside;
+  maximize_(qh WIDEfacet, qh_WIDEcoplanar * qh MAXcoplanar);
+  maximize_(qh WIDEfacet, qh_WIDEcoplanar * qh MINvisible);
+  qh_option("_wide-facet", NULL, &qh WIDEfacet);
+  if (qh MINvisible > qh MINoutside + 3 * REALepsilon
+  && !qh BESToutside && !qh FORCEoutput)
+    qh_fprintf(qh ferr, 7001, "qhull input warning: minimum visibility V%.2g is greater than \nminimum outside W%.2g.  Flipped facets are likely.\n",
+             qh MINvisible, qh MINoutside);
+  qh max_vertex= qh DISTround;
+  qh min_vertex= -qh DISTround;
+  /* numeric constants reported in printsummary */
+} /* detroundoff */
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >-------------------------------</a><a name="detsimplex">-</a>
+
+  qh_detsimplex( apex, points, dim, nearzero )
+    compute determinant of a simplex with point apex and base points
+
+  returns:
+     signed determinant and nearzero from qh_determinant
+
+  notes:
+     uses qh.gm_matrix/qh.gm_row (assumes they're big enough)
+
+  design:
+    construct qm_matrix by subtracting apex from points
+    compute determinate
+*/
+realT qh_detsimplex(pointT *apex, setT *points, int dim, boolT *nearzero) {
+  pointT *coorda, *coordp, *gmcoord, *point, **pointp;
+  coordT **rows;
+  int k,  i=0;
+  realT det;
+
+  zinc_(Zdetsimplex);
+  gmcoord= qh gm_matrix;
+  rows= qh gm_row;
+  FOREACHpoint_(points) {
+    if (i == dim)
+      break;
+    rows[i++]= gmcoord;
+    coordp= point;
+    coorda= apex;
+    for (k=dim; k--; )
+      *(gmcoord++)= *coordp++ - *coorda++;
+  }
+  if (i < dim) {
+    qh_fprintf(qh ferr, 6007, "qhull internal error (qh_detsimplex): #points %d < dimension %d\n",
+               i, dim);
+    qh_errexit(qh_ERRqhull, NULL, NULL);
+  }
+  det= qh_determinant(rows, dim, nearzero);
+  trace2((qh ferr, 2002, "qh_detsimplex: det=%2.2g for point p%d, dim %d, nearzero? %d\n",
+          det, qh_pointid(apex), dim, *nearzero));
+  return det;
+} /* detsimplex */
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >-------------------------------</a><a name="distnorm">-</a>
+
+  qh_distnorm( dim, point, normal, offset )
+    return distance from point to hyperplane at normal/offset
+
+  returns:
+    dist
+
+  notes:
+    dist > 0 if point is outside of hyperplane
+
+  see:
+    qh_distplane in geom.c
+*/
+realT qh_distnorm(int dim, pointT *point, pointT *normal, realT *offsetp) {
+  coordT *normalp= normal, *coordp= point;
+  realT dist;
+  int k;
+
+  dist= *offsetp;
+  for (k=dim; k--; )
+    dist += *(coordp++) * *(normalp++);
+  return dist;
+} /* distnorm */
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >-------------------------------</a><a name="distround">-</a>
+
+  qh_distround(dimension, maxabs, maxsumabs )
+    compute maximum round-off error for a distance computation
+      to a normalized hyperplane
+    maxabs is the maximum absolute value of a coordinate
+    maxsumabs is the maximum possible sum of absolute coordinate values
+
+  returns:
+    max dist round for REALepsilon
+
+  notes:
+    calculate roundoff error according to Golub & van Loan, 1983, Lemma 3.2-1, "Rounding Errors"
+    use sqrt(dim) since one vector is normalized
+      or use maxsumabs since one vector is < 1
+*/
+realT qh_distround(int dimension, realT maxabs, realT maxsumabs) {
+  realT maxdistsum, maxround;
+
+  maxdistsum= sqrt((realT)dimension) * maxabs;
+  minimize_( maxdistsum, maxsumabs);
+  maxround= REALepsilon * (dimension * maxdistsum * 1.01 + maxabs);
+              /* adds maxabs for offset */
+  trace4((qh ferr, 4008, "qh_distround: %2.2g maxabs %2.2g maxsumabs %2.2g maxdistsum %2.2g\n",
+                 maxround, maxabs, maxsumabs, maxdistsum));
+  return maxround;
+} /* distround */
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >-------------------------------</a><a name="divzero">-</a>
+
+  qh_divzero( numer, denom, mindenom1, zerodiv )
+    divide by a number that's nearly zero
+    mindenom1= minimum denominator for dividing into 1.0
+
+  returns:
+    quotient
+    sets zerodiv and returns 0.0 if it would overflow
+
+  design:
+    if numer is nearly zero and abs(numer) < abs(denom)
+      return numer/denom
+    else if numer is nearly zero
+      return 0 and zerodiv
+    else if denom/numer non-zero
+      return numer/denom
+    else
+      return 0 and zerodiv
+*/
+realT qh_divzero(realT numer, realT denom, realT mindenom1, boolT *zerodiv) {
+  realT temp, numerx, denomx;
+
+
+  if (numer < mindenom1 && numer > -mindenom1) {
+    numerx= fabs_(numer);
+    denomx= fabs_(denom);
+    if (numerx < denomx) {
+      *zerodiv= False;
+      return numer/denom;
+    }else {
+      *zerodiv= True;
+      return 0.0;
+    }
+  }
+  temp= denom/numer;
+  if (temp > mindenom1 || temp < -mindenom1) {
+    *zerodiv= False;
+    return numer/denom;
+  }else {
+    *zerodiv= True;
+    return 0.0;
+  }
+} /* divzero */
+
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >-------------------------------</a><a name="facetarea">-</a>
+
+  qh_facetarea( facet )
+    return area for a facet
+
+  notes:
+    if non-simplicial,
+      uses centrum to triangulate facet and sums the projected areas.
+    if (qh DELAUNAY),
+      computes projected area instead for last coordinate
+    assumes facet->normal exists
+    projecting tricoplanar facets to the hyperplane does not appear to make a difference
+
+  design:
+    if simplicial
+      compute area
+    else
+      for each ridge
+        compute area from centrum to ridge
+    negate area if upper Delaunay facet
+*/
+realT qh_facetarea(facetT *facet) {
+  vertexT *apex;
+  pointT *centrum;
+  realT area= 0.0;
+  ridgeT *ridge, **ridgep;
+
+  if (facet->simplicial) {
+    apex= SETfirstt_(facet->vertices, vertexT);
+    area= qh_facetarea_simplex(qh hull_dim, apex->point, facet->vertices,
+                    apex, facet->toporient, facet->normal, &facet->offset);
+  }else {
+    if (qh CENTERtype == qh_AScentrum)
+      centrum= facet->center;
+    else
+      centrum= qh_getcentrum(facet);
+    FOREACHridge_(facet->ridges)
+      area += qh_facetarea_simplex(qh hull_dim, centrum, ridge->vertices,
+                 NULL, (boolT)(ridge->top == facet),  facet->normal, &facet->offset);
+    if (qh CENTERtype != qh_AScentrum)
+      qh_memfree(centrum, qh normal_size);
+  }
+  if (facet->upperdelaunay && qh DELAUNAY)
+    area= -area;  /* the normal should be [0,...,1] */
+  trace4((qh ferr, 4009, "qh_facetarea: f%d area %2.2g\n", facet->id, area));
+  return area;
+} /* facetarea */
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >-------------------------------</a><a name="facetarea_simplex">-</a>
+
+  qh_facetarea_simplex( dim, apex, vertices, notvertex, toporient, normal, offset )
+    return area for a simplex defined by
+      an apex, a base of vertices, an orientation, and a unit normal
+    if simplicial or tricoplanar facet,
+      notvertex is defined and it is skipped in vertices
+
+  returns:
+    computes area of simplex projected to plane [normal,offset]
+    returns 0 if vertex too far below plane (qh WIDEfacet)
+      vertex can't be apex of tricoplanar facet
+
+  notes:
+    if (qh DELAUNAY),
+      computes projected area instead for last coordinate
+    uses qh gm_matrix/gm_row and qh hull_dim
+    helper function for qh_facetarea
+
+  design:
+    if Notvertex
+      translate simplex to apex
+    else
+      project simplex to normal/offset
+      translate simplex to apex
+    if Delaunay
+      set last row/column to 0 with -1 on diagonal
+    else
+      set last row to Normal
+    compute determinate
+    scale and flip sign for area
+*/
+realT qh_facetarea_simplex(int dim, coordT *apex, setT *vertices,
+        vertexT *notvertex,  boolT toporient, coordT *normal, realT *offset) {
+  pointT *coorda, *coordp, *gmcoord;
+  coordT **rows, *normalp;
+  int k,  i=0;
+  realT area, dist;
+  vertexT *vertex, **vertexp;
+  boolT nearzero;
+
+  gmcoord= qh gm_matrix;
+  rows= qh gm_row;
+  FOREACHvertex_(vertices) {
+    if (vertex == notvertex)
+      continue;
+    rows[i++]= gmcoord;
+    coorda= apex;
+    coordp= vertex->point;
+    normalp= normal;
+    if (notvertex) {
+      for (k=dim; k--; )
+        *(gmcoord++)= *coordp++ - *coorda++;
+    }else {
+      dist= *offset;
+      for (k=dim; k--; )
+        dist += *coordp++ * *normalp++;
+      if (dist < -qh WIDEfacet) {
+        zinc_(Znoarea);
+        return 0.0;
+      }
+      coordp= vertex->point;
+      normalp= normal;
+      for (k=dim; k--; )
+        *(gmcoord++)= (*coordp++ - dist * *normalp++) - *coorda++;
+    }
+  }
+  if (i != dim-1) {
+    qh_fprintf(qh ferr, 6008, "qhull internal error (qh_facetarea_simplex): #points %d != dim %d -1\n",
+               i, dim);
+    qh_errexit(qh_ERRqhull, NULL, NULL);
+  }
+  rows[i]= gmcoord;
+  if (qh DELAUNAY) {
+    for (i=0; i < dim-1; i++)
+      rows[i][dim-1]= 0.0;
+    for (k=dim; k--; )
+      *(gmcoord++)= 0.0;
+    rows[dim-1][dim-1]= -1.0;
+  }else {
+    normalp= normal;
+    for (k=dim; k--; )
+      *(gmcoord++)= *normalp++;
+  }
+  zinc_(Zdetsimplex);
+  area= qh_determinant(rows, dim, &nearzero);
+  if (toporient)
+    area= -area;
+  area *= qh AREAfactor;
+  trace4((qh ferr, 4010, "qh_facetarea_simplex: area=%2.2g for point p%d, toporient %d, nearzero? %d\n",
+          area, qh_pointid(apex), toporient, nearzero));
+  return area;
+} /* facetarea_simplex */
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >-------------------------------</a><a name="facetcenter">-</a>
+
+  qh_facetcenter( vertices )
+    return Voronoi center (Voronoi vertex) for a facet's vertices
+
+  returns:
+    return temporary point equal to the center
+
+  see:
+    qh_voronoi_center()
+*/
+pointT *qh_facetcenter(setT *vertices) {
+  setT *points= qh_settemp(qh_setsize(vertices));
+  vertexT *vertex, **vertexp;
+  pointT *center;
+
+  FOREACHvertex_(vertices)
+    qh_setappend(&points, vertex->point);
+  center= qh_voronoi_center(qh hull_dim-1, points);
+  qh_settempfree(&points);
+  return center;
+} /* facetcenter */
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >-------------------------------</a><a name="findgooddist">-</a>
+
+  qh_findgooddist( point, facetA, dist, facetlist )
+    find best good facet visible for point from facetA
+    assumes facetA is visible from point
+
+  returns:
+    best facet, i.e., good facet that is furthest from point
+      distance to best facet
+      NULL if none
+
+    moves good, visible facets (and some other visible facets)
+      to end of qh facet_list
+
+  notes:
+    uses qh visit_id
+
+  design:
+    initialize bestfacet if facetA is good
+    move facetA to end of facetlist
+    for each facet on facetlist
+      for each unvisited neighbor of facet
+        move visible neighbors to end of facetlist
+        update best good neighbor
+        if no good neighbors, update best facet
+*/
+facetT *qh_findgooddist(pointT *point, facetT *facetA, realT *distp,
+               facetT **facetlist) {
+  realT bestdist= -REALmax, dist;
+  facetT *neighbor, **neighborp, *bestfacet=NULL, *facet;
+  boolT goodseen= False;
+
+  if (facetA->good) {
+    zzinc_(Zcheckpart);  /* calls from check_bestdist occur after print stats */
+    qh_distplane(point, facetA, &bestdist);
+    bestfacet= facetA;
+    goodseen= True;
+  }
+  qh_removefacet(facetA);
+  qh_appendfacet(facetA);
+  *facetlist= facetA;
+  facetA->visitid= ++qh visit_id;
+  FORALLfacet_(*facetlist) {
+    FOREACHneighbor_(facet) {
+      if (neighbor->visitid == qh visit_id)
+        continue;
+      neighbor->visitid= qh visit_id;
+      if (goodseen && !neighbor->good)
+        continue;
+      zzinc_(Zcheckpart);
+      qh_distplane(point, neighbor, &dist);
+      if (dist > 0) {
+        qh_removefacet(neighbor);
+        qh_appendfacet(neighbor);
+        if (neighbor->good) {
+          goodseen= True;
+          if (dist > bestdist) {
+            bestdist= dist;
+            bestfacet= neighbor;
+          }
+        }
+      }
+    }
+  }
+  if (bestfacet) {
+    *distp= bestdist;
+    trace2((qh ferr, 2003, "qh_findgooddist: p%d is %2.2g above good facet f%d\n",
+      qh_pointid(point), bestdist, bestfacet->id));
+    return bestfacet;
+  }
+  trace4((qh ferr, 4011, "qh_findgooddist: no good facet for p%d above f%d\n",
+      qh_pointid(point), facetA->id));
+  return NULL;
+}  /* findgooddist */
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >-------------------------------</a><a name="getarea">-</a>
+
+  qh_getarea( facetlist )
+    set area of all facets in facetlist
+    collect statistics
+    nop if hasAreaVolume
+
+  returns:
+    sets qh totarea/totvol to total area and volume of convex hull
+    for Delaunay triangulation, computes projected area of the lower or upper hull
+      ignores upper hull if qh ATinfinity
+
+  notes:
+    could compute outer volume by expanding facet area by rays from interior
+    the following attempt at perpendicular projection underestimated badly:
+      qh.totoutvol += (-dist + facet->maxoutside + qh DISTround)
+                            * area/ qh hull_dim;
+  design:
+    for each facet on facetlist
+      compute facet->area
+      update qh.totarea and qh.totvol
+*/
+void qh_getarea(facetT *facetlist) {
+  realT area;
+  realT dist;
+  facetT *facet;
+
+  if (qh hasAreaVolume)
+    return;
+  if (qh REPORTfreq)
+    qh_fprintf(qh ferr, 8020, "computing area of each facet and volume of the convex hull\n");
+  else
+    trace1((qh ferr, 1001, "qh_getarea: computing volume and area for each facet\n"));
+  qh totarea= qh totvol= 0.0;
+  FORALLfacet_(facetlist) {
+    if (!facet->normal)
+      continue;
+    if (facet->upperdelaunay && qh ATinfinity)
+      continue;
+    if (!facet->isarea) {
+      facet->f.area= qh_facetarea(facet);
+      facet->isarea= True;
+    }
+    area= facet->f.area;
+    if (qh DELAUNAY) {
+      if (facet->upperdelaunay == qh UPPERdelaunay)
+        qh totarea += area;
+    }else {
+      qh totarea += area;
+      qh_distplane(qh interior_point, facet, &dist);
+      qh totvol += -dist * area/ qh hull_dim;
+    }
+    if (qh PRINTstatistics) {
+      wadd_(Wareatot, area);
+      wmax_(Wareamax, area);
+      wmin_(Wareamin, area);
+    }
+  }
+  qh hasAreaVolume= True;
+} /* getarea */
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >-------------------------------</a><a name="gram_schmidt">-</a>
+
+  qh_gram_schmidt( dim, row )
+    implements Gram-Schmidt orthogonalization by rows
+
+  returns:
+    false if zero norm
+    overwrites rows[dim][dim]
+
+  notes:
+    see Golub & van Loan, 1983, Algorithm 6.2-2, "Modified Gram-Schmidt"
+    overflow due to small divisors not handled
+
+  design:
+    for each row
+      compute norm for row
+      if non-zero, normalize row
+      for each remaining rowA
+        compute inner product of row and rowA
+        reduce rowA by row * inner product
+*/
+boolT qh_gram_schmidt(int dim, realT **row) {
+  realT *rowi, *rowj, norm;
+  int i, j, k;
+
+  for (i=0; i < dim; i++) {
+    rowi= row[i];
+    for (norm= 0.0, k= dim; k--; rowi++)
+      norm += *rowi * *rowi;
+    norm= sqrt(norm);
+    wmin_(Wmindenom, norm);
+    if (norm == 0.0)  /* either 0 or overflow due to sqrt */
+      return False;
+    for (k=dim; k--; )
+      *(--rowi) /= norm;
+    for (j=i+1; j < dim; j++) {
+      rowj= row[j];
+      for (norm= 0.0, k=dim; k--; )
+        norm += *rowi++ * *rowj++;
+      for (k=dim; k--; )
+        *(--rowj) -= *(--rowi) * norm;
+    }
+  }
+  return True;
+} /* gram_schmidt */
+
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >-------------------------------</a><a name="inthresholds">-</a>
+
+  qh_inthresholds( normal, angle )
+    return True if normal within qh.lower_/upper_threshold
+
+  returns:
+    estimate of angle by summing of threshold diffs
+      angle may be NULL
+      smaller "angle" is better
+
+  notes:
+    invalid if qh.SPLITthresholds
+
+  see:
+    qh.lower_threshold in qh_initbuild()
+    qh_initthresholds()
+
+  design:
+    for each dimension
+      test threshold
+*/
+boolT qh_inthresholds(coordT *normal, realT *angle) {
+  boolT within= True;
+  int k;
+  realT threshold;
+
+  if (angle)
+    *angle= 0.0;
+  for (k=0; k < qh hull_dim; k++) {
+    threshold= qh lower_threshold[k];
+    if (threshold > -REALmax/2) {
+      if (normal[k] < threshold)
+        within= False;
+      if (angle) {
+        threshold -= normal[k];
+        *angle += fabs_(threshold);
+      }
+    }
+    if (qh upper_threshold[k] < REALmax/2) {
+      threshold= qh upper_threshold[k];
+      if (normal[k] > threshold)
+        within= False;
+      if (angle) {
+        threshold -= normal[k];
+        *angle += fabs_(threshold);
+      }
+    }
+  }
+  return within;
+} /* inthresholds */
+
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >-------------------------------</a><a name="joggleinput">-</a>
+
+  qh_joggleinput()
+    randomly joggle input to Qhull by qh.JOGGLEmax
+    initial input is qh.first_point/qh.num_points of qh.hull_dim
+      repeated calls use qh.input_points/qh.num_points
+
+  returns:
+    joggles points at qh.first_point/qh.num_points
+    copies data to qh.input_points/qh.input_malloc if first time
+    determines qh.JOGGLEmax if it was zero
+    if qh.DELAUNAY
+      computes the Delaunay projection of the joggled points
+
+  notes:
+    if qh.DELAUNAY, unnecessarily joggles the last coordinate
+    the initial 'QJn' may be set larger than qh_JOGGLEmaxincrease
+
+  design:
+    if qh.DELAUNAY
+      set qh.SCALElast for reduced precision errors
+    if first call
+      initialize qh.input_points to the original input points
+      if qh.JOGGLEmax == 0
+        determine default qh.JOGGLEmax
+    else
+      increase qh.JOGGLEmax according to qh.build_cnt
+    joggle the input by adding a random number in [-qh.JOGGLEmax,qh.JOGGLEmax]
+    if qh.DELAUNAY
+      sets the Delaunay projection
+*/
+void qh_joggleinput(void) {
+  int i, seed, size;
+  coordT *coordp, *inputp;
+  realT randr, randa, randb;
+
+  if (!qh input_points) { /* first call */
+    qh input_points= qh first_point;
+    qh input_malloc= qh POINTSmalloc;
+    size= qh num_points * qh hull_dim * sizeof(coordT);
+    if (!(qh first_point=(coordT*)qh_malloc((size_t)size))) {
+      qh_fprintf(qh ferr, 6009, "qhull error: insufficient memory to joggle %d points\n",
+          qh num_points);
+      qh_errexit(qh_ERRmem, NULL, NULL);
+    }
+    qh POINTSmalloc= True;
+    if (qh JOGGLEmax == 0.0) {
+      qh JOGGLEmax= qh_detjoggle(qh input_points, qh num_points, qh hull_dim);
+      qh_option("QJoggle", NULL, &qh JOGGLEmax);
+    }
+  }else {                 /* repeated call */
+    if (!qh RERUN && qh build_cnt > qh_JOGGLEretry) {
+      if (((qh build_cnt-qh_JOGGLEretry-1) % qh_JOGGLEagain) == 0) {
+        realT maxjoggle= qh MAXwidth * qh_JOGGLEmaxincrease;
+        if (qh JOGGLEmax < maxjoggle) {
+          qh JOGGLEmax *= qh_JOGGLEincrease;
+          minimize_(qh JOGGLEmax, maxjoggle);
+        }
+      }
+    }
+    qh_option("QJoggle", NULL, &qh JOGGLEmax);
+  }
+  if (qh build_cnt > 1 && qh JOGGLEmax > fmax_(qh MAXwidth/4, 0.1)) {
+      qh_fprintf(qh ferr, 6010, "qhull error: the current joggle for 'QJn', %.2g, is too large for the width\nof the input.  If possible, recompile Qhull with higher-precision reals.\n",
+                qh JOGGLEmax);
+      qh_errexit(qh_ERRqhull, NULL, NULL);
+  }
+  /* for some reason, using qh ROTATErandom and qh_RANDOMseed does not repeat the run. Use 'TRn' instead */
+  seed= qh_RANDOMint;
+  qh_option("_joggle-seed", &seed, NULL);
+  trace0((qh ferr, 6, "qh_joggleinput: joggle input by %2.2g with seed %d\n",
+    qh JOGGLEmax, seed));
+  inputp= qh input_points;
+  coordp= qh first_point;
+  randa= 2.0 * qh JOGGLEmax/qh_RANDOMmax;
+  randb= -qh JOGGLEmax;
+  size= qh num_points * qh hull_dim;
+  for (i=size; i--; ) {
+    randr= qh_RANDOMint;
+    *(coordp++)= *(inputp++) + (randr * randa + randb);
+  }
+  if (qh DELAUNAY) {
+    qh last_low= qh last_high= qh last_newhigh= REALmax;
+    qh_setdelaunay(qh hull_dim, qh num_points, qh first_point);
+  }
+} /* joggleinput */
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >-------------------------------</a><a name="maxabsval">-</a>
+
+  qh_maxabsval( normal, dim )
+    return pointer to maximum absolute value of a dim vector
+    returns NULL if dim=0
+*/
+realT *qh_maxabsval(realT *normal, int dim) {
+  realT maxval= -REALmax;
+  realT *maxp= NULL, *colp, absval;
+  int k;
+
+  for (k=dim, colp= normal; k--; colp++) {
+    absval= fabs_(*colp);
+    if (absval > maxval) {
+      maxval= absval;
+      maxp= colp;
+    }
+  }
+  return maxp;
+} /* maxabsval */
+
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >-------------------------------</a><a name="maxmin">-</a>
+
+  qh_maxmin( points, numpoints, dimension )
+    return max/min points for each dimension
+    determine max and min coordinates
+
+  returns:
+    returns a temporary set of max and min points
+      may include duplicate points. Does not include qh.GOODpoint
+    sets qh.NEARzero, qh.MAXabs_coord, qh.MAXsumcoord, qh.MAXwidth
+         qh.MAXlastcoord, qh.MINlastcoord
+    initializes qh.max_outside, qh.min_vertex, qh.WAScoplanar, qh.ZEROall_ok
+
+  notes:
+    loop duplicated in qh_detjoggle()
+
+  design:
+    initialize global precision variables
+    checks definition of REAL...
+    for each dimension
+      for each point
+        collect maximum and minimum point
+      collect maximum of maximums and minimum of minimums
+      determine qh.NEARzero for Gaussian Elimination
+*/
+setT *qh_maxmin(pointT *points, int numpoints, int dimension) {
+  int k;
+  realT maxcoord, temp;
+  pointT *minimum, *maximum, *point, *pointtemp;
+  setT *set;
+
+  qh max_outside= 0.0;
+  qh MAXabs_coord= 0.0;
+  qh MAXwidth= -REALmax;
+  qh MAXsumcoord= 0.0;
+  qh min_vertex= 0.0;
+  qh WAScoplanar= False;
+  if (qh ZEROcentrum)
+    qh ZEROall_ok= True;
+  if (REALmin < REALepsilon && REALmin < REALmax && REALmin > -REALmax
+  && REALmax > 0.0 && -REALmax < 0.0)
+    ; /* all ok */
+  else {
+    qh_fprintf(qh ferr, 6011, "qhull error: floating point constants in user.h are wrong\n\
+REALepsilon %g REALmin %g REALmax %g -REALmax %g\n",
+             REALepsilon, REALmin, REALmax, -REALmax);
+    qh_errexit(qh_ERRinput, NULL, NULL);
+  }
+  set= qh_settemp(2*dimension);
+  for (k=0; k < dimension; k++) {
+    if (points == qh GOODpointp)
+      minimum= maximum= points + dimension;
+    else
+      minimum= maximum= points;
+    FORALLpoint_(points, numpoints) {
+      if (point == qh GOODpointp)
+        continue;
+      if (maximum[k] < point[k])
+        maximum= point;
+      else if (minimum[k] > point[k])
+        minimum= point;
+    }
+    if (k == dimension-1) {
+      qh MINlastcoord= minimum[k];
+      qh MAXlastcoord= maximum[k];
+    }
+    if (qh SCALElast && k == dimension-1)
+      maxcoord= qh MAXwidth;
+    else {
+      maxcoord= fmax_(maximum[k], -minimum[k]);
+      if (qh GOODpointp) {
+        temp= fmax_(qh GOODpointp[k], -qh GOODpointp[k]);
+        maximize_(maxcoord, temp);
+      }
+      temp= maximum[k] - minimum[k];
+      maximize_(qh MAXwidth, temp);
+    }
+    maximize_(qh MAXabs_coord, maxcoord);
+    qh MAXsumcoord += maxcoord;
+    qh_setappend(&set, maximum);
+    qh_setappend(&set, minimum);
+    /* calculation of qh NEARzero is based on Golub & van Loan, 1983,
+       Eq. 4.4-13 for "Gaussian elimination with complete pivoting".
+       Golub & van Loan say that n^3 can be ignored and 10 be used in
+       place of rho */
+    qh NEARzero[k]= 80 * qh MAXsumcoord * REALepsilon;
+  }
+  if (qh IStracing >=1)
+    qh_printpoints(qh ferr, "qh_maxmin: found the max and min points(by dim):", set);
+  return(set);
+} /* maxmin */
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >-------------------------------</a><a name="maxouter">-</a>
+
+  qh_maxouter()
+    return maximum distance from facet to outer plane
+    normally this is qh.max_outside+qh.DISTround
+    does not include qh.JOGGLEmax
+
+  see:
+    qh_outerinner()
+
+  notes:
+    need to add another qh.DISTround if testing actual point with computation
+
+  for joggle:
+    qh_setfacetplane() updated qh.max_outer for Wnewvertexmax (max distance to vertex)
+    need to use Wnewvertexmax since could have a coplanar point for a high
+      facet that is replaced by a low facet
+    need to add qh.JOGGLEmax if testing input points
+*/
+realT qh_maxouter(void) {
+  realT dist;
+
+  dist= fmax_(qh max_outside, qh DISTround);
+  dist += qh DISTround;
+  trace4((qh ferr, 4012, "qh_maxouter: max distance from facet to outer plane is %2.2g max_outside is %2.2g\n", dist, qh max_outside));
+  return dist;
+} /* maxouter */
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >-------------------------------</a><a name="maxsimplex">-</a>
+
+  qh_maxsimplex( dim, maxpoints, points, numpoints, simplex )
+    determines maximum simplex for a set of points
+    starts from points already in simplex
+    skips qh.GOODpointp (assumes that it isn't in maxpoints)
+
+  returns:
+    simplex with dim+1 points
+
+  notes:
+    assumes at least pointsneeded points in points
+    maximizes determinate for x,y,z,w, etc.
+    uses maxpoints as long as determinate is clearly non-zero
+
+  design:
+    initialize simplex with at least two points
+      (find points with max or min x coordinate)
+    for each remaining dimension
+      add point that maximizes the determinate
+        (use points from maxpoints first)
+*/
+void qh_maxsimplex(int dim, setT *maxpoints, pointT *points, int numpoints, setT **simplex) {
+  pointT *point, **pointp, *pointtemp, *maxpoint, *minx=NULL, *maxx=NULL;
+  boolT nearzero, maxnearzero= False;
+  int k, sizinit;
+  realT maxdet= -REALmax, det, mincoord= REALmax, maxcoord= -REALmax;
+
+  sizinit= qh_setsize(*simplex);
+  if (sizinit < 2) {
+    if (qh_setsize(maxpoints) >= 2) {
+      FOREACHpoint_(maxpoints) {
+        if (maxcoord < point[0]) {
+          maxcoord= point[0];
+          maxx= point;
+        }
+        if (mincoord > point[0]) {
+          mincoord= point[0];
+          minx= point;
+        }
+      }
+    }else {
+      FORALLpoint_(points, numpoints) {
+        if (point == qh GOODpointp)
+          continue;
+        if (maxcoord < point[0]) {
+          maxcoord= point[0];
+          maxx= point;
+        }
+        if (mincoord > point[0]) {
+          mincoord= point[0];
+          minx= point;
+        }
+      }
+    }
+    qh_setunique(simplex, minx);
+    if (qh_setsize(*simplex) < 2)
+      qh_setunique(simplex, maxx);
+    sizinit= qh_setsize(*simplex);
+    if (sizinit < 2) {
+      qh_precision("input has same x coordinate");
+      if (zzval_(Zsetplane) > qh hull_dim+1) {
+        qh_fprintf(qh ferr, 6012, "qhull precision error (qh_maxsimplex for voronoi_center):\n%d points with the same x coordinate.\n",
+                 qh_setsize(maxpoints)+numpoints);
+        qh_errexit(qh_ERRprec, NULL, NULL);
+      }else {
+        qh_fprintf(qh ferr, 6013, "qhull input error: input is less than %d-dimensional since it has the same x coordinate\n", qh hull_dim);
+        qh_errexit(qh_ERRinput, NULL, NULL);
+      }
+    }
+  }
+  for (k=sizinit; k < dim+1; k++) {
+    maxpoint= NULL;
+    maxdet= -REALmax;
+    FOREACHpoint_(maxpoints) {
+      if (!qh_setin(*simplex, point)) {
+        det= qh_detsimplex(point, *simplex, k, &nearzero);
+        if ((det= fabs_(det)) > maxdet) {
+          maxdet= det;
+          maxpoint= point;
+          maxnearzero= nearzero;
+        }
+      }
+    }
+    if (!maxpoint || maxnearzero) {
+      zinc_(Zsearchpoints);
+      if (!maxpoint) {
+        trace0((qh ferr, 7, "qh_maxsimplex: searching all points for %d-th initial vertex.\n", k+1));
+      }else {
+        trace0((qh ferr, 8, "qh_maxsimplex: searching all points for %d-th initial vertex, better than p%d det %2.2g\n",
+                k+1, qh_pointid(maxpoint), maxdet));
+      }
+      FORALLpoint_(points, numpoints) {
+        if (point == qh GOODpointp)
+          continue;
+        if (!qh_setin(*simplex, point)) {
+          det= qh_detsimplex(point, *simplex, k, &nearzero);
+          if ((det= fabs_(det)) > maxdet) {
+            maxdet= det;
+            maxpoint= point;
+            maxnearzero= nearzero;
+          }
+        }
+      }
+    } /* !maxpoint */
+    if (!maxpoint) {
+      qh_fprintf(qh ferr, 6014, "qhull internal error (qh_maxsimplex): not enough points available\n");
+      qh_errexit(qh_ERRqhull, NULL, NULL);
+    }
+    qh_setappend(simplex, maxpoint);
+    trace1((qh ferr, 1002, "qh_maxsimplex: selected point p%d for %d`th initial vertex, det=%2.2g\n",
+            qh_pointid(maxpoint), k+1, maxdet));
+  } /* k */
+} /* maxsimplex */
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >-------------------------------</a><a name="minabsval">-</a>
+
+  qh_minabsval( normal, dim )
+    return minimum absolute value of a dim vector
+*/
+realT qh_minabsval(realT *normal, int dim) {
+  realT minval= 0;
+  realT maxval= 0;
+  realT *colp;
+  int k;
+
+  for (k=dim, colp=normal; k--; colp++) {
+    maximize_(maxval, *colp);
+    minimize_(minval, *colp);
+  }
+  return fmax_(maxval, -minval);
+} /* minabsval */
+
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >-------------------------------</a><a name="mindiff">-</a>
+
+  qh_mindif( vecA, vecB, dim )
+    return index of min abs. difference of two vectors
+*/
+int qh_mindiff(realT *vecA, realT *vecB, int dim) {
+  realT mindiff= REALmax, diff;
+  realT *vecAp= vecA, *vecBp= vecB;
+  int k, mink= 0;
+
+  for (k=0; k < dim; k++) {
+    diff= *vecAp++ - *vecBp++;
+    diff= fabs_(diff);
+    if (diff < mindiff) {
+      mindiff= diff;
+      mink= k;
+    }
+  }
+  return mink;
+} /* mindiff */
+
+
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >-------------------------------</a><a name="orientoutside">-</a>
+
+  qh_orientoutside( facet  )
+    make facet outside oriented via qh.interior_point
+
+  returns:
+    True if facet reversed orientation.
+*/
+boolT qh_orientoutside(facetT *facet) {
+  int k;
+  realT dist;
+
+  qh_distplane(qh interior_point, facet, &dist);
+  if (dist > 0) {
+    for (k=qh hull_dim; k--; )
+      facet->normal[k]= -facet->normal[k];
+    facet->offset= -facet->offset;
+    return True;
+  }
+  return False;
+} /* orientoutside */
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >-------------------------------</a><a name="outerinner">-</a>
+
+  qh_outerinner( facet, outerplane, innerplane  )
+    if facet and qh.maxoutdone (i.e., qh_check_maxout)
+      returns outer and inner plane for facet
+    else
+      returns maximum outer and inner plane
+    accounts for qh.JOGGLEmax
+
+  see:
+    qh_maxouter(), qh_check_bestdist(), qh_check_points()
+
+  notes:
+    outerplaner or innerplane may be NULL
+    facet is const
+    Does not error (QhullFacet)
+
+    includes qh.DISTround for actual points
+    adds another qh.DISTround if testing with floating point arithmetic
+*/
+void qh_outerinner(facetT *facet, realT *outerplane, realT *innerplane) {
+  realT dist, mindist;
+  vertexT *vertex, **vertexp;
+
+  if (outerplane) {
+    if (!qh_MAXoutside || !facet || !qh maxoutdone) {
+      *outerplane= qh_maxouter();       /* includes qh.DISTround */
+    }else { /* qh_MAXoutside ... */
+#if qh_MAXoutside
+      *outerplane= facet->maxoutside + qh DISTround;
+#endif
+
+    }
+    if (qh JOGGLEmax < REALmax/2)
+      *outerplane += qh JOGGLEmax * sqrt((realT)qh hull_dim);
+  }
+  if (innerplane) {
+    if (facet) {
+      mindist= REALmax;
+      FOREACHvertex_(facet->vertices) {
+        zinc_(Zdistio);
+        qh_distplane(vertex->point, facet, &dist);
+        minimize_(mindist, dist);
+      }
+      *innerplane= mindist - qh DISTround;
+    }else
+      *innerplane= qh min_vertex - qh DISTround;
+    if (qh JOGGLEmax < REALmax/2)
+      *innerplane -= qh JOGGLEmax * sqrt((realT)qh hull_dim);
+  }
+} /* outerinner */
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >-------------------------------</a><a name="pointdist">-</a>
+
+  qh_pointdist( point1, point2, dim )
+    return distance between two points
+
+  notes:
+    returns distance squared if 'dim' is negative
+*/
+coordT qh_pointdist(pointT *point1, pointT *point2, int dim) {
+  coordT dist, diff;
+  int k;
+
+  dist= 0.0;
+  for (k= (dim > 0 ? dim : -dim); k--; ) {
+    diff= *point1++ - *point2++;
+    dist += diff * diff;
+  }
+  if (dim > 0)
+    return(sqrt(dist));
+  return dist;
+} /* pointdist */
+
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >-------------------------------</a><a name="printmatrix">-</a>
+
+  qh_printmatrix( fp, string, rows, numrow, numcol )
+    print matrix to fp given by row vectors
+    print string as header
+
+  notes:
+    print a vector by qh_printmatrix(fp, "", &vect, 1, len)
+*/
+void qh_printmatrix(FILE *fp, const char *string, realT **rows, int numrow, int numcol) {
+  realT *rowp;
+  realT r; /*bug fix*/
+  int i,k;
+
+  qh_fprintf(fp, 9001, "%s\n", string);
+  for (i=0; i < numrow; i++) {
+    rowp= rows[i];
+    for (k=0; k < numcol; k++) {
+      r= *rowp++;
+      qh_fprintf(fp, 9002, "%6.3g ", r);
+    }
+    qh_fprintf(fp, 9003, "\n");
+  }
+} /* printmatrix */
+
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >-------------------------------</a><a name="printpoints">-</a>
+
+  qh_printpoints( fp, string, points )
+    print pointids to fp for a set of points
+    if string, prints string and 'p' point ids
+*/
+void qh_printpoints(FILE *fp, const char *string, setT *points) {
+  pointT *point, **pointp;
+
+  if (string) {
+    qh_fprintf(fp, 9004, "%s", string);
+    FOREACHpoint_(points)
+      qh_fprintf(fp, 9005, " p%d", qh_pointid(point));
+    qh_fprintf(fp, 9006, "\n");
+  }else {
+    FOREACHpoint_(points)
+      qh_fprintf(fp, 9007, " %d", qh_pointid(point));
+    qh_fprintf(fp, 9008, "\n");
+  }
+} /* printpoints */
+
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >-------------------------------</a><a name="projectinput">-</a>
+
+  qh_projectinput()
+    project input points using qh.lower_bound/upper_bound and qh DELAUNAY
+    if qh.lower_bound[k]=qh.upper_bound[k]= 0,
+      removes dimension k
+    if halfspace intersection
+      removes dimension k from qh.feasible_point
+    input points in qh first_point, num_points, input_dim
+
+  returns:
+    new point array in qh first_point of qh hull_dim coordinates
+    sets qh POINTSmalloc
+    if qh DELAUNAY
+      projects points to paraboloid
+      lowbound/highbound is also projected
+    if qh ATinfinity
+      adds point "at-infinity"
+    if qh POINTSmalloc
+      frees old point array
+
+  notes:
+    checks that qh.hull_dim agrees with qh.input_dim, PROJECTinput, and DELAUNAY
+
+
+  design:
+    sets project[k] to -1 (delete), 0 (keep), 1 (add for Delaunay)
+    determines newdim and newnum for qh hull_dim and qh num_points
+    projects points to newpoints
+    projects qh.lower_bound to itself
+    projects qh.upper_bound to itself
+    if qh DELAUNAY
+      if qh ATINFINITY
+        projects points to paraboloid
+        computes "infinity" point as vertex average and 10% above all points
+      else
+        uses qh_setdelaunay to project points to paraboloid
+*/
+void qh_projectinput(void) {
+  int k,i;
+  int newdim= qh input_dim, newnum= qh num_points;
+  signed char *project;
+  int projectsize= (qh input_dim+1)*sizeof(*project);
+  pointT *newpoints, *coord, *infinity;
+  realT paraboloid, maxboloid= 0;
+
+  project= (signed char*)qh_memalloc(projectsize);
+  memset((char*)project, 0, (size_t)projectsize);
+  for (k=0; k < qh input_dim; k++) {   /* skip Delaunay bound */
+    if (qh lower_bound[k] == 0 && qh upper_bound[k] == 0) {
+      project[k]= -1;
+      newdim--;
+    }
+  }
+  if (qh DELAUNAY) {
+    project[k]= 1;
+    newdim++;
+    if (qh ATinfinity)
+      newnum++;
+  }
+  if (newdim != qh hull_dim) {
+    qh_memfree(project, projectsize);
+    qh_fprintf(qh ferr, 6015, "qhull internal error (qh_projectinput): dimension after projection %d != hull_dim %d\n", newdim, qh hull_dim);
+    qh_errexit(qh_ERRqhull, NULL, NULL);
+  }
+  if (!(newpoints= qh temp_malloc= (coordT*)qh_malloc(newnum*newdim*sizeof(coordT)))){
+    qh_memfree(project, projectsize);
+    qh_fprintf(qh ferr, 6016, "qhull error: insufficient memory to project %d points\n",
+           qh num_points);
+    qh_errexit(qh_ERRmem, NULL, NULL);
+  }
+  /* qh_projectpoints throws error if mismatched dimensions */
+  qh_projectpoints(project, qh input_dim+1, qh first_point,
+                    qh num_points, qh input_dim, newpoints, newdim);
+  trace1((qh ferr, 1003, "qh_projectinput: updating lower and upper_bound\n"));
+  qh_projectpoints(project, qh input_dim+1, qh lower_bound,
+                    1, qh input_dim+1, qh lower_bound, newdim+1);
+  qh_projectpoints(project, qh input_dim+1, qh upper_bound,
+                    1, qh input_dim+1, qh upper_bound, newdim+1);
+  if (qh HALFspace) {
+    if (!qh feasible_point) {
+      qh_memfree(project, projectsize);
+      qh_fprintf(qh ferr, 6017, "qhull internal error (qh_projectinput): HALFspace defined without qh.feasible_point\n");
+      qh_errexit(qh_ERRqhull, NULL, NULL);
+    }
+    qh_projectpoints(project, qh input_dim, qh feasible_point,
+                      1, qh input_dim, qh feasible_point, newdim);
+  }
+  qh_memfree(project, projectsize);
+  if (qh POINTSmalloc)
+    qh_free(qh first_point);
+  qh first_point= newpoints;
+  qh POINTSmalloc= True;
+  qh temp_malloc= NULL;
+  if (qh DELAUNAY && qh ATinfinity) {
+    coord= qh first_point;
+    infinity= qh first_point + qh hull_dim * qh num_points;
+    for (k=qh hull_dim-1; k--; )
+      infinity[k]= 0.0;
+    for (i=qh num_points; i--; ) {
+      paraboloid= 0.0;
+      for (k=0; k < qh hull_dim-1; k++) {
+        paraboloid += *coord * *coord;
+        infinity[k] += *coord;
+        coord++;
+      }
+      *(coord++)= paraboloid;
+      maximize_(maxboloid, paraboloid);
+    }
+    /* coord == infinity */
+    for (k=qh hull_dim-1; k--; )
+      *(coord++) /= qh num_points;
+    *(coord++)= maxboloid * 1.1;
+    qh num_points++;
+    trace0((qh ferr, 9, "qh_projectinput: projected points to paraboloid for Delaunay\n"));
+  }else if (qh DELAUNAY)  /* !qh ATinfinity */
+    qh_setdelaunay( qh hull_dim, qh num_points, qh first_point);
+} /* projectinput */
+
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >-------------------------------</a><a name="projectpoints">-</a>
+
+  qh_projectpoints( project, n, points, numpoints, dim, newpoints, newdim )
+    project points/numpoints/dim to newpoints/newdim
+    if project[k] == -1
+      delete dimension k
+    if project[k] == 1
+      add dimension k by duplicating previous column
+    n is size of project
+
+  notes:
+    newpoints may be points if only adding dimension at end
+
+  design:
+    check that 'project' and 'newdim' agree
+    for each dimension
+      if project == -1
+        skip dimension
+      else
+        determine start of column in newpoints
+        determine start of column in points
+          if project == +1, duplicate previous column
+        copy dimension (column) from points to newpoints
+*/
+void qh_projectpoints(signed char *project, int n, realT *points,
+        int numpoints, int dim, realT *newpoints, int newdim) {
+  int testdim= dim, oldk=0, newk=0, i,j=0,k;
+  realT *newp, *oldp;
+
+  for (k=0; k < n; k++)
+    testdim += project[k];
+  if (testdim != newdim) {
+    qh_fprintf(qh ferr, 6018, "qhull internal error (qh_projectpoints): newdim %d should be %d after projection\n",
+      newdim, testdim);
+    qh_errexit(qh_ERRqhull, NULL, NULL);
+  }
+  for (j=0; j<n; j++) {
+    if (project[j] == -1)
+      oldk++;
+    else {
+      newp= newpoints+newk++;
+      if (project[j] == +1) {
+        if (oldk >= dim)
+          continue;
+        oldp= points+oldk;
+      }else
+        oldp= points+oldk++;
+      for (i=numpoints; i--; ) {
+        *newp= *oldp;
+        newp += newdim;
+        oldp += dim;
+      }
+    }
+    if (oldk >= dim)
+      break;
+  }
+  trace1((qh ferr, 1004, "qh_projectpoints: projected %d points from dim %d to dim %d\n",
+    numpoints, dim, newdim));
+} /* projectpoints */
+
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >-------------------------------</a><a name="rotateinput">-</a>
+
+  qh_rotateinput( rows )
+    rotate input using row matrix
+    input points given by qh first_point, num_points, hull_dim
+    assumes rows[dim] is a scratch buffer
+    if qh POINTSmalloc, overwrites input points, else mallocs a new array
+
+  returns:
+    rotated input
+    sets qh POINTSmalloc
+
+  design:
+    see qh_rotatepoints
+*/
+void qh_rotateinput(realT **rows) {
+
+  if (!qh POINTSmalloc) {
+    qh first_point= qh_copypoints(qh first_point, qh num_points, qh hull_dim);
+    qh POINTSmalloc= True;
+  }
+  qh_rotatepoints(qh first_point, qh num_points, qh hull_dim, rows);
+}  /* rotateinput */
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >-------------------------------</a><a name="rotatepoints">-</a>
+
+  qh_rotatepoints( points, numpoints, dim, row )
+    rotate numpoints points by a d-dim row matrix
+    assumes rows[dim] is a scratch buffer
+
+  returns:
+    rotated points in place
+
+  design:
+    for each point
+      for each coordinate
+        use row[dim] to compute partial inner product
+      for each coordinate
+        rotate by partial inner product
+*/
+void qh_rotatepoints(realT *points, int numpoints, int dim, realT **row) {
+  realT *point, *rowi, *coord= NULL, sum, *newval;
+  int i,j,k;
+
+  if (qh IStracing >= 1)
+    qh_printmatrix(qh ferr, "qh_rotatepoints: rotate points by", row, dim, dim);
+  for (point= points, j= numpoints; j--; point += dim) {
+    newval= row[dim];
+    for (i=0; i < dim; i++) {
+      rowi= row[i];
+      coord= point;
+      for (sum= 0.0, k= dim; k--; )
+        sum += *rowi++ * *coord++;
+      *(newval++)= sum;
+    }
+    for (k=dim; k--; )
+      *(--coord)= *(--newval);
+  }
+} /* rotatepoints */
+
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >-------------------------------</a><a name="scaleinput">-</a>
+
+  qh_scaleinput()
+    scale input points using qh low_bound/high_bound
+    input points given by qh first_point, num_points, hull_dim
+    if qh POINTSmalloc, overwrites input points, else mallocs a new array
+
+  returns:
+    scales coordinates of points to low_bound[k], high_bound[k]
+    sets qh POINTSmalloc
+
+  design:
+    see qh_scalepoints
+*/
+void qh_scaleinput(void) {
+
+  if (!qh POINTSmalloc) {
+    qh first_point= qh_copypoints(qh first_point, qh num_points, qh hull_dim);
+    qh POINTSmalloc= True;
+  }
+  qh_scalepoints(qh first_point, qh num_points, qh hull_dim,
+       qh lower_bound, qh upper_bound);
+}  /* scaleinput */
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >-------------------------------</a><a name="scalelast">-</a>
+
+  qh_scalelast( points, numpoints, dim, low, high, newhigh )
+    scale last coordinate to [0,m] for Delaunay triangulations
+    input points given by points, numpoints, dim
+
+  returns:
+    changes scale of last coordinate from [low, high] to [0, newhigh]
+    overwrites last coordinate of each point
+    saves low/high/newhigh in qh.last_low, etc. for qh_setdelaunay()
+
+  notes:
+    when called by qh_setdelaunay, low/high may not match actual data
+
+  design:
+    compute scale and shift factors
+    apply to last coordinate of each point
+*/
+void qh_scalelast(coordT *points, int numpoints, int dim, coordT low,
+                   coordT high, coordT newhigh) {
+  realT scale, shift;
+  coordT *coord;
+  int i;
+  boolT nearzero= False;
+
+  trace4((qh ferr, 4013, "qh_scalelast: scale last coordinate from [%2.2g, %2.2g] to [0,%2.2g]\n",
+    low, high, newhigh));
+  qh last_low= low;
+  qh last_high= high;
+  qh last_newhigh= newhigh;
+  scale= qh_divzero(newhigh, high - low,
+                  qh MINdenom_1, &nearzero);
+  if (nearzero) {
+    if (qh DELAUNAY)
+      qh_fprintf(qh ferr, 6019, "qhull input error: can not scale last coordinate.  Input is cocircular\n   or cospherical.   Use option 'Qz' to add a point at infinity.\n");
+    else
+      qh_fprintf(qh ferr, 6020, "qhull input error: can not scale last coordinate.  New bounds [0, %2.2g] are too wide for\nexisting bounds [%2.2g, %2.2g] (width %2.2g)\n",
+                newhigh, low, high, high-low);
+    qh_errexit(qh_ERRinput, NULL, NULL);
+  }
+  shift= - low * newhigh / (high-low);
+  coord= points + dim - 1;
+  for (i=numpoints; i--; coord += dim)
+    *coord= *coord * scale + shift;
+} /* scalelast */
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >-------------------------------</a><a name="scalepoints">-</a>
+
+  qh_scalepoints( points, numpoints, dim, newlows, newhighs )
+    scale points to new lowbound and highbound
+    retains old bound when newlow= -REALmax or newhigh= +REALmax
+
+  returns:
+    scaled points
+    overwrites old points
+
+  design:
+    for each coordinate
+      compute current low and high bound
+      compute scale and shift factors
+      scale all points
+      enforce new low and high bound for all points
+*/
+void qh_scalepoints(pointT *points, int numpoints, int dim,
+        realT *newlows, realT *newhighs) {
+  int i,k;
+  realT shift, scale, *coord, low, high, newlow, newhigh, mincoord, maxcoord;
+  boolT nearzero= False;
+
+  for (k=0; k < dim; k++) {
+    newhigh= newhighs[k];
+    newlow= newlows[k];
+    if (newhigh > REALmax/2 && newlow < -REALmax/2)
+      continue;
+    low= REALmax;
+    high= -REALmax;
+    for (i=numpoints, coord=points+k; i--; coord += dim) {
+      minimize_(low, *coord);
+      maximize_(high, *coord);
+    }
+    if (newhigh > REALmax/2)
+      newhigh= high;
+    if (newlow < -REALmax/2)
+      newlow= low;
+    if (qh DELAUNAY && k == dim-1 && newhigh < newlow) {
+      qh_fprintf(qh ferr, 6021, "qhull input error: 'Qb%d' or 'QB%d' inverts paraboloid since high bound %.2g < low bound %.2g\n",
+               k, k, newhigh, newlow);
+      qh_errexit(qh_ERRinput, NULL, NULL);
+    }
+    scale= qh_divzero(newhigh - newlow, high - low,
+                  qh MINdenom_1, &nearzero);
+    if (nearzero) {
+      qh_fprintf(qh ferr, 6022, "qhull input error: %d'th dimension's new bounds [%2.2g, %2.2g] too wide for\nexisting bounds [%2.2g, %2.2g]\n",
+              k, newlow, newhigh, low, high);
+      qh_errexit(qh_ERRinput, NULL, NULL);
+    }
+    shift= (newlow * high - low * newhigh)/(high-low);
+    coord= points+k;
+    for (i=numpoints; i--; coord += dim)
+      *coord= *coord * scale + shift;
+    coord= points+k;
+    if (newlow < newhigh) {
+      mincoord= newlow;
+      maxcoord= newhigh;
+    }else {
+      mincoord= newhigh;
+      maxcoord= newlow;
+    }
+    for (i=numpoints; i--; coord += dim) {
+      minimize_(*coord, maxcoord);  /* because of roundoff error */
+      maximize_(*coord, mincoord);
+    }
+    trace0((qh ferr, 10, "qh_scalepoints: scaled %d'th coordinate [%2.2g, %2.2g] to [%.2g, %.2g] for %d points by %2.2g and shifted %2.2g\n",
+      k, low, high, newlow, newhigh, numpoints, scale, shift));
+  }
+} /* scalepoints */
+
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >-------------------------------</a><a name="setdelaunay">-</a>
+
+  qh_setdelaunay( dim, count, points )
+    project count points to dim-d paraboloid for Delaunay triangulation
+
+    dim is one more than the dimension of the input set
+    assumes dim is at least 3 (i.e., at least a 2-d Delaunay triangulation)
+
+    points is a dim*count realT array.  The first dim-1 coordinates
+    are the coordinates of the first input point.  array[dim] is
+    the first coordinate of the second input point.  array[2*dim] is
+    the first coordinate of the third input point.
+
+    if qh.last_low defined (i.e., 'Qbb' called qh_scalelast)
+      calls qh_scalelast to scale the last coordinate the same as the other points
+
+  returns:
+    for each point
+      sets point[dim-1] to sum of squares of coordinates
+    scale points to 'Qbb' if needed
+
+  notes:
+    to project one point, use
+      qh_setdelaunay(qh hull_dim, 1, point)
+
+    Do not use options 'Qbk', 'QBk', or 'QbB' since they scale
+    the coordinates after the original projection.
+
+*/
+void qh_setdelaunay(int dim, int count, pointT *points) {
+  int i, k;
+  coordT *coordp, coord;
+  realT paraboloid;
+
+  trace0((qh ferr, 11, "qh_setdelaunay: project %d points to paraboloid for Delaunay triangulation\n", count));
+  coordp= points;
+  for (i=0; i < count; i++) {
+    coord= *coordp++;
+    paraboloid= coord*coord;
+    for (k=dim-2; k--; ) {
+      coord= *coordp++;
+      paraboloid += coord*coord;
+    }
+    *coordp++ = paraboloid;
+  }
+  if (qh last_low < REALmax/2)
+    qh_scalelast(points, count, dim, qh last_low, qh last_high, qh last_newhigh);
+} /* setdelaunay */
+
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >-------------------------------</a><a name="sethalfspace">-</a>
+
+  qh_sethalfspace( dim, coords, nextp, normal, offset, feasible )
+    set point to dual of halfspace relative to feasible point
+    halfspace is normal coefficients and offset.
+
+  returns:
+    false and prints error if feasible point is outside of hull
+    overwrites coordinates for point at dim coords
+    nextp= next point (coords)
+    does not call qh_errexit
+
+  design:
+    compute distance from feasible point to halfspace
+    divide each normal coefficient by -dist
+*/
+boolT qh_sethalfspace(int dim, coordT *coords, coordT **nextp,
+         coordT *normal, coordT *offset, coordT *feasible) {
+  coordT *normp= normal, *feasiblep= feasible, *coordp= coords;
+  realT dist;
+  realT r; /*bug fix*/
+  int k;
+  boolT zerodiv;
+
+  dist= *offset;
+  for (k=dim; k--; )
+    dist += *(normp++) * *(feasiblep++);
+  if (dist > 0)
+    goto LABELerroroutside;
+  normp= normal;
+  if (dist < -qh MINdenom) {
+    for (k=dim; k--; )
+      *(coordp++)= *(normp++) / -dist;
+  }else {
+    for (k=dim; k--; ) {
+      *(coordp++)= qh_divzero(*(normp++), -dist, qh MINdenom_1, &zerodiv);
+      if (zerodiv)
+        goto LABELerroroutside;
+    }
+  }
+  *nextp= coordp;
+  if (qh IStracing >= 4) {
+    qh_fprintf(qh ferr, 8021, "qh_sethalfspace: halfspace at offset %6.2g to point: ", *offset);
+    for (k=dim, coordp=coords; k--; ) {
+      r= *coordp++;
+      qh_fprintf(qh ferr, 8022, " %6.2g", r);
+    }
+    qh_fprintf(qh ferr, 8023, "\n");
+  }
+  return True;
+LABELerroroutside:
+  feasiblep= feasible;
+  normp= normal;
+  qh_fprintf(qh ferr, 6023, "qhull input error: feasible point is not clearly inside halfspace\nfeasible point: ");
+  for (k=dim; k--; )
+    qh_fprintf(qh ferr, 8024, qh_REAL_1, r=*(feasiblep++));
+  qh_fprintf(qh ferr, 8025, "\n     halfspace: ");
+  for (k=dim; k--; )
+    qh_fprintf(qh ferr, 8026, qh_REAL_1, r=*(normp++));
+  qh_fprintf(qh ferr, 8027, "\n     at offset: ");
+  qh_fprintf(qh ferr, 8028, qh_REAL_1, *offset);
+  qh_fprintf(qh ferr, 8029, " and distance: ");
+  qh_fprintf(qh ferr, 8030, qh_REAL_1, dist);
+  qh_fprintf(qh ferr, 8031, "\n");
+  return False;
+} /* sethalfspace */
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >-------------------------------</a><a name="sethalfspace_all">-</a>
+
+  qh_sethalfspace_all( dim, count, halfspaces, feasible )
+    generate dual for halfspace intersection with feasible point
+    array of count halfspaces
+      each halfspace is normal coefficients followed by offset
+      the origin is inside the halfspace if the offset is negative
+    feasible is a point inside all halfspaces (http://www.qhull.org/html/qhalf.htm#notes)
+
+  returns:
+    malloc'd array of count X dim-1 points
+
+  notes:
+    call before qh_init_B or qh_initqhull_globals
+    free memory when done
+    unused/untested code: please email bradb@shore.net if this works ok for you
+    if using option 'Fp', qh->feasible_point must be set (e.g., to 'feasible')
+    qh->feasible_point is a malloc'd array that is freed by qh_freebuffers.
+
+  design:
+    see qh_sethalfspace
+*/
+coordT *qh_sethalfspace_all(int dim, int count, coordT *halfspaces, pointT *feasible) {
+  int i, newdim;
+  pointT *newpoints;
+  coordT *coordp, *normalp, *offsetp;
+
+  trace0((qh ferr, 12, "qh_sethalfspace_all: compute dual for halfspace intersection\n"));
+  newdim= dim - 1;
+  if (!(newpoints=(coordT*)qh_malloc(count*newdim*sizeof(coordT)))){
+    qh_fprintf(qh ferr, 6024, "qhull error: insufficient memory to compute dual of %d halfspaces\n",
+          count);
+    qh_errexit(qh_ERRmem, NULL, NULL);
+  }
+  coordp= newpoints;
+  normalp= halfspaces;
+  for (i=0; i < count; i++) {
+    offsetp= normalp + newdim;
+    if (!qh_sethalfspace(newdim, coordp, &coordp, normalp, offsetp, feasible)) {
+      qh_free(newpoints);  /* feasible is not inside halfspace as reported by qh_sethalfspace */
+      qh_fprintf(qh ferr, 8032, "The halfspace was at index %d\n", i);
+      qh_errexit(qh_ERRinput, NULL, NULL);
+    }
+    normalp= offsetp + 1;
+  }
+  return newpoints;
+} /* sethalfspace_all */
+
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >-------------------------------</a><a name="sharpnewfacets">-</a>
+
+  qh_sharpnewfacets()
+
+  returns:
+    true if could be an acute angle (facets in different quadrants)
+
+  notes:
+    for qh_findbest
+
+  design:
+    for all facets on qh.newfacet_list
+      if two facets are in different quadrants
+        set issharp
+*/
+boolT qh_sharpnewfacets(void) {
+  facetT *facet;
+  boolT issharp = False;
+  int *quadrant, k;
+
+  quadrant= (int*)qh_memalloc(qh hull_dim * sizeof(int));
+  FORALLfacet_(qh newfacet_list) {
+    if (facet == qh newfacet_list) {
+      for (k=qh hull_dim; k--; )
+        quadrant[ k]= (facet->normal[ k] > 0);
+    }else {
+      for (k=qh hull_dim; k--; ) {
+        if (quadrant[ k] != (facet->normal[ k] > 0)) {
+          issharp= True;
+          break;
+        }
+      }
+    }
+    if (issharp)
+      break;
+  }
+  qh_memfree( quadrant, qh hull_dim * sizeof(int));
+  trace3((qh ferr, 3001, "qh_sharpnewfacets: %d\n", issharp));
+  return issharp;
+} /* sharpnewfacets */
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >-------------------------------</a><a name="voronoi_center">-</a>
+
+  qh_voronoi_center( dim, points )
+    return Voronoi center for a set of points
+    dim is the orginal dimension of the points
+    gh.gm_matrix/qh.gm_row are scratch buffers
+
+  returns:
+    center as a temporary point (qh_memalloc)
+    if non-simplicial,
+      returns center for max simplex of points
+
+  notes:
+    only called by qh_facetcenter
+    from Bowyer & Woodwark, A Programmer's Geometry, 1983, p. 65
+
+  design:
+    if non-simplicial
+      determine max simplex for points
+    translate point0 of simplex to origin
+    compute sum of squares of diagonal
+    compute determinate
+    compute Voronoi center (see Bowyer & Woodwark)
+*/
+pointT *qh_voronoi_center(int dim, setT *points) {
+  pointT *point, **pointp, *point0;
+  pointT *center= (pointT*)qh_memalloc(qh center_size);
+  setT *simplex;
+  int i, j, k, size= qh_setsize(points);
+  coordT *gmcoord;
+  realT *diffp, sum2, *sum2row, *sum2p, det, factor;
+  boolT nearzero, infinite;
+
+  if (size == dim+1)
+    simplex= points;
+  else if (size < dim+1) {
+    qh_memfree(center, qh center_size);
+    qh_fprintf(qh ferr, 6025, "qhull internal error (qh_voronoi_center):\n  need at least %d points to construct a Voronoi center\n",
+             dim+1);
+    qh_errexit(qh_ERRqhull, NULL, NULL);
+    simplex= points;  /* never executed -- avoids warning */
+  }else {
+    simplex= qh_settemp(dim+1);
+    qh_maxsimplex(dim, points, NULL, 0, &simplex);
+  }
+  point0= SETfirstt_(simplex, pointT);
+  gmcoord= qh gm_matrix;
+  for (k=0; k < dim; k++) {
+    qh gm_row[k]= gmcoord;
+    FOREACHpoint_(simplex) {
+      if (point != point0)
+        *(gmcoord++)= point[k] - point0[k];
+    }
+  }
+  sum2row= gmcoord;
+  for (i=0; i < dim; i++) {
+    sum2= 0.0;
+    for (k=0; k < dim; k++) {
+      diffp= qh gm_row[k] + i;
+      sum2 += *diffp * *diffp;
+    }
+    *(gmcoord++)= sum2;
+  }
+  det= qh_determinant(qh gm_row, dim, &nearzero);
+  factor= qh_divzero(0.5, det, qh MINdenom, &infinite);
+  if (infinite) {
+    for (k=dim; k--; )
+      center[k]= qh_INFINITE;
+    if (qh IStracing)
+      qh_printpoints(qh ferr, "qh_voronoi_center: at infinity for ", simplex);
+  }else {
+    for (i=0; i < dim; i++) {
+      gmcoord= qh gm_matrix;
+      sum2p= sum2row;
+      for (k=0; k < dim; k++) {
+        qh gm_row[k]= gmcoord;
+        if (k == i) {
+          for (j=dim; j--; )
+            *(gmcoord++)= *sum2p++;
+        }else {
+          FOREACHpoint_(simplex) {
+            if (point != point0)
+              *(gmcoord++)= point[k] - point0[k];
+          }
+        }
+      }
+      center[i]= qh_determinant(qh gm_row, dim, &nearzero)*factor + point0[i];
+    }
+#ifndef qh_NOtrace
+    if (qh IStracing >= 3) {
+      qh_fprintf(qh ferr, 8033, "qh_voronoi_center: det %2.2g factor %2.2g ", det, factor);
+      qh_printmatrix(qh ferr, "center:", &center, 1, dim);
+      if (qh IStracing >= 5) {
+        qh_printpoints(qh ferr, "points", simplex);
+        FOREACHpoint_(simplex)
+          qh_fprintf(qh ferr, 8034, "p%d dist %.2g, ", qh_pointid(point),
+                   qh_pointdist(point, center, dim));
+        qh_fprintf(qh ferr, 8035, "\n");
+      }
+    }
+#endif
+  }
+  if (simplex != points)
+    qh_settempfree(&simplex);
+  return center;
+} /* voronoi_center */
+
diff --git a/xs/src/qhull/src/libqhull/global.c b/xs/src/qhull/src/libqhull/global.c
new file mode 100644
index 0000000000..0328fea7b9
--- /dev/null
+++ b/xs/src/qhull/src/libqhull/global.c
@@ -0,0 +1,2217 @@
+
+/*<html><pre>  -<a                             href="qh-globa.htm"
+  >-------------------------------</a><a name="TOP">-</a>
+
+   global.c
+   initializes all the globals of the qhull application
+
+   see README
+
+   see libqhull.h for qh.globals and function prototypes
+
+   see qhull_a.h for internal functions
+
+   Copyright (c) 1993-2015 The Geometry Center.
+   $Id: //main/2015/qhull/src/libqhull/global.c#17 $$Change: 2066 $
+   $DateTime: 2016/01/18 19:29:17 $$Author: bbarber $
+ */
+
+#include "qhull_a.h"
+
+/*========= qh definition -- globals defined in libqhull.h =======================*/
+
+#if qh_QHpointer
+qhT *qh_qh= NULL;       /* pointer to all global variables */
+#else
+qhT qh_qh;              /* all global variables.
+                           Add "= {0}" if this causes a compiler error.
+                           Also qh_qhstat in stat.c and qhmem in mem.c.  */
+#endif
+
+/*-<a                             href  ="qh-globa.htm#TOC"
+  >--------------------------------</a><a name="qh_version">-</a>
+
+  qh_version
+    version string by year and date
+    qh_version2 for Unix users and -V
+
+    the revision increases on code changes only
+
+  notes:
+    change date:    Changes.txt, Announce.txt, index.htm, README.txt,
+                    qhull-news.html, Eudora signatures, CMakeLists.txt
+    change version: README.txt, qh-get.htm, File_id.diz, Makefile.txt, CMakeLists.txt
+    check that CmakeLists @version is the same as qh_version2
+    change year:    Copying.txt
+    check download size
+    recompile user_eg.c, rbox.c, libqhull.c, qconvex.c, qdelaun.c qvoronoi.c, qhalf.c, testqset.c
+*/
+
+const char qh_version[]= "2015.2 2016/01/18";
+const char qh_version2[]= "qhull 7.2.0 (2015.2 2016/01/18)";
+
+/*-<a                             href="qh-globa.htm#TOC"
+  >-------------------------------</a><a name="appendprint">-</a>
+
+  qh_appendprint( printFormat )
+    append printFormat to qh.PRINTout unless already defined
+*/
+void qh_appendprint(qh_PRINT format) {
+  int i;
+
+  for (i=0; i < qh_PRINTEND; i++) {
+    if (qh PRINTout[i] == format && format != qh_PRINTqhull)
+      break;
+    if (!qh PRINTout[i]) {
+      qh PRINTout[i]= format;
+      break;
+    }
+  }
+} /* appendprint */
+
+/*-<a                             href="qh-globa.htm#TOC"
+  >-------------------------------</a><a name="checkflags">-</a>
+
+  qh_checkflags( commandStr, hiddenFlags )
+    errors if commandStr contains hiddenFlags
+    hiddenFlags starts and ends with a space and is space delimited (checked)
+
+  notes:
+    ignores first word (e.g., "qconvex i")
+    use qh_strtol/strtod since strtol/strtod may or may not skip trailing spaces
+
+  see:
+    qh_initflags() initializes Qhull according to commandStr
+*/
+void qh_checkflags(char *command, char *hiddenflags) {
+  char *s= command, *t, *chkerr; /* qh_skipfilename is non-const */
+  char key, opt, prevopt;
+  char chkkey[]= "   ";
+  char chkopt[]=  "    ";
+  char chkopt2[]= "     ";
+  boolT waserr= False;
+
+  if (*hiddenflags != ' ' || hiddenflags[strlen(hiddenflags)-1] != ' ') {
+    qh_fprintf(qh ferr, 6026, "qhull error (qh_checkflags): hiddenflags must start and end with a space: \"%s\"", hiddenflags);
+    qh_errexit(qh_ERRinput, NULL, NULL);
+  }
+  if (strpbrk(hiddenflags, ",\n\r\t")) {
+    qh_fprintf(qh ferr, 6027, "qhull error (qh_checkflags): hiddenflags contains commas, newlines, or tabs: \"%s\"", hiddenflags);
+    qh_errexit(qh_ERRinput, NULL, NULL);
+  }
+  while (*s && !isspace(*s))  /* skip program name */
+    s++;
+  while (*s) {
+    while (*s && isspace(*s))
+      s++;
+    if (*s == '-')
+      s++;
+    if (!*s)
+      break;
+    key = *s++;
+    chkerr = NULL;
+    if (key == 'T' && (*s == 'I' || *s == 'O')) {  /* TI or TO 'file name' */
+      s= qh_skipfilename(++s);
+      continue;
+    }
+    chkkey[1]= key;
+    if (strstr(hiddenflags, chkkey)) {
+      chkerr= chkkey;
+    }else if (isupper(key)) {
+      opt= ' ';
+      prevopt= ' ';
+      chkopt[1]= key;
+      chkopt2[1]= key;
+      while (!chkerr && *s && !isspace(*s)) {
+        opt= *s++;
+        if (isalpha(opt)) {
+          chkopt[2]= opt;
+          if (strstr(hiddenflags, chkopt))
+            chkerr= chkopt;
+          if (prevopt != ' ') {
+            chkopt2[2]= prevopt;
+            chkopt2[3]= opt;
+            if (strstr(hiddenflags, chkopt2))
+              chkerr= chkopt2;
+          }
+        }else if (key == 'Q' && isdigit(opt) && prevopt != 'b'
+              && (prevopt == ' ' || islower(prevopt))) {
+            chkopt[2]= opt;
+            if (strstr(hiddenflags, chkopt))
+              chkerr= chkopt;
+        }else {
+          qh_strtod(s-1, &t);
+          if (s < t)
+            s= t;
+        }
+        prevopt= opt;
+      }
+    }
+    if (chkerr) {
+      *chkerr= '\'';
+      chkerr[strlen(chkerr)-1]=  '\'';
+      qh_fprintf(qh ferr, 6029, "qhull error: option %s is not used with this program.\n             It may be used with qhull.\n", chkerr);
+      waserr= True;
+    }
+  }
+  if (waserr)
+    qh_errexit(qh_ERRinput, NULL, NULL);
+} /* checkflags */
+
+/*-<a                             href="qh-globa.htm#TOC"
+  >-------------------------------</a><a name="qh_clear_outputflags">-</a>
+
+  qh_clear_outputflags()
+    Clear output flags for QhullPoints
+*/
+void qh_clear_outputflags(void) {
+  int i,k;
+
+  qh ANNOTATEoutput= False;
+  qh DOintersections= False;
+  qh DROPdim= -1;
+  qh FORCEoutput= False;
+  qh GETarea= False;
+  qh GOODpoint= 0;
+  qh GOODpointp= NULL;
+  qh GOODthreshold= False;
+  qh GOODvertex= 0;
+  qh GOODvertexp= NULL;
+  qh IStracing= 0;
+  qh KEEParea= False;
+  qh KEEPmerge= False;
+  qh KEEPminArea= REALmax;
+  qh PRINTcentrums= False;
+  qh PRINTcoplanar= False;
+  qh PRINTdots= False;
+  qh PRINTgood= False;
+  qh PRINTinner= False;
+  qh PRINTneighbors= False;
+  qh PRINTnoplanes= False;
+  qh PRINToptions1st= False;
+  qh PRINTouter= False;
+  qh PRINTprecision= True;
+  qh PRINTridges= False;
+  qh PRINTspheres= False;
+  qh PRINTstatistics= False;
+  qh PRINTsummary= False;
+  qh PRINTtransparent= False;
+  qh SPLITthresholds= False;
+  qh TRACElevel= 0;
+  qh TRInormals= False;
+  qh USEstdout= False;
+  qh VERIFYoutput= False;
+  for (k=qh input_dim+1; k--; ) {  /* duplicated in qh_initqhull_buffers and qh_clear_outputflags */
+    qh lower_threshold[k]= -REALmax;
+    qh upper_threshold[k]= REALmax;
+    qh lower_bound[k]= -REALmax;
+    qh upper_bound[k]= REALmax;
+  }
+
+  for (i=0; i < qh_PRINTEND; i++) {
+    qh PRINTout[i]= qh_PRINTnone;
+  }
+
+  if (!qh qhull_commandsiz2)
+      qh qhull_commandsiz2= (int)strlen(qh qhull_command); /* WARN64 */
+  else {
+      qh qhull_command[qh qhull_commandsiz2]= '\0';
+  }
+  if (!qh qhull_optionsiz2)
+    qh qhull_optionsiz2= (int)strlen(qh qhull_options);  /* WARN64 */
+  else {
+    qh qhull_options[qh qhull_optionsiz2]= '\0';
+    qh qhull_optionlen= qh_OPTIONline;  /* start a new line */
+  }
+} /* clear_outputflags */
+
+/*-<a                             href="qh-globa.htm#TOC"
+  >-------------------------------</a><a name="clock">-</a>
+
+  qh_clock()
+    return user CPU time in 100ths (qh_SECtick)
+    only defined for qh_CLOCKtype == 2
+
+  notes:
+    use first value to determine time 0
+    from Stevens '92 8.15
+*/
+unsigned long qh_clock(void) {
+
+#if (qh_CLOCKtype == 2)
+  struct tms time;
+  static long clktck;  /* initialized first call and never updated */
+  double ratio, cpu;
+  unsigned long ticks;
+
+  if (!clktck) {
+    if ((clktck= sysconf(_SC_CLK_TCK)) < 0) {
+      qh_fprintf(qh ferr, 6030, "qhull internal error (qh_clock): sysconf() failed.  Use qh_CLOCKtype 1 in user.h\n");
+      qh_errexit(qh_ERRqhull, NULL, NULL);
+    }
+  }
+  if (times(&time) == -1) {
+    qh_fprintf(qh ferr, 6031, "qhull internal error (qh_clock): times() failed.  Use qh_CLOCKtype 1 in user.h\n");
+    qh_errexit(qh_ERRqhull, NULL, NULL);
+  }
+  ratio= qh_SECticks / (double)clktck;
+  ticks= time.tms_utime * ratio;
+  return ticks;
+#else
+  qh_fprintf(qh ferr, 6032, "qhull internal error (qh_clock): use qh_CLOCKtype 2 in user.h\n");
+  qh_errexit(qh_ERRqhull, NULL, NULL); /* never returns */
+  return 0;
+#endif
+} /* clock */
+
+/*-<a                             href="qh-globa.htm#TOC"
+  >-------------------------------</a><a name="freebuffers">-</a>
+
+  qh_freebuffers()
+    free up global memory buffers
+
+  notes:
+    must match qh_initbuffers()
+*/
+void qh_freebuffers(void) {
+
+  trace5((qh ferr, 5001, "qh_freebuffers: freeing up global memory buffers\n"));
+  /* allocated by qh_initqhull_buffers */
+  qh_memfree(qh NEARzero, qh hull_dim * sizeof(realT));
+  qh_memfree(qh lower_threshold, (qh input_dim+1) * sizeof(realT));
+  qh_memfree(qh upper_threshold, (qh input_dim+1) * sizeof(realT));
+  qh_memfree(qh lower_bound, (qh input_dim+1) * sizeof(realT));
+  qh_memfree(qh upper_bound, (qh input_dim+1) * sizeof(realT));
+  qh_memfree(qh gm_matrix, (qh hull_dim+1) * qh hull_dim * sizeof(coordT));
+  qh_memfree(qh gm_row, (qh hull_dim+1) * sizeof(coordT *));
+  qh NEARzero= qh lower_threshold= qh upper_threshold= NULL;
+  qh lower_bound= qh upper_bound= NULL;
+  qh gm_matrix= NULL;
+  qh gm_row= NULL;
+  qh_setfree(&qh other_points);
+  qh_setfree(&qh del_vertices);
+  qh_setfree(&qh coplanarfacetset);
+  if (qh line)                /* allocated by qh_readinput, freed if no error */
+    qh_free(qh line);
+  if (qh half_space)
+    qh_free(qh half_space);
+  if (qh temp_malloc)
+    qh_free(qh temp_malloc);
+  if (qh feasible_point)      /* allocated by qh_readfeasible */
+    qh_free(qh feasible_point);
+  if (qh feasible_string)     /* allocated by qh_initflags */
+    qh_free(qh feasible_string);
+  qh line= qh feasible_string= NULL;
+  qh half_space= qh feasible_point= qh temp_malloc= NULL;
+  /* usually allocated by qh_readinput */
+  if (qh first_point && qh POINTSmalloc) {
+    qh_free(qh first_point);
+    qh first_point= NULL;
+  }
+  if (qh input_points && qh input_malloc) { /* set by qh_joggleinput */
+    qh_free(qh input_points);
+    qh input_points= NULL;
+  }
+  trace5((qh ferr, 5002, "qh_freebuffers: finished\n"));
+} /* freebuffers */
+
+
+/*-<a                             href="qh-globa.htm#TOC"
+  >-------------------------------</a><a name="freebuild">-</a>
+
+  qh_freebuild( allmem )
+    free global memory used by qh_initbuild and qh_buildhull
+    if !allmem,
+      does not free short memory (e.g., facetT, freed by qh_memfreeshort)
+
+  design:
+    free centrums
+    free each vertex
+    mark unattached ridges
+    for each facet
+      free ridges
+      free outside set, coplanar set, neighbor set, ridge set, vertex set
+      free facet
+    free hash table
+    free interior point
+    free merge set
+    free temporary sets
+*/
+void qh_freebuild(boolT allmem) {
+  facetT *facet;
+  vertexT *vertex;
+  ridgeT *ridge, **ridgep;
+  mergeT *merge, **mergep;
+
+  trace1((qh ferr, 1005, "qh_freebuild: free memory from qh_inithull and qh_buildhull\n"));
+  if (qh del_vertices)
+    qh_settruncate(qh del_vertices, 0);
+  if (allmem) {
+    while ((vertex= qh vertex_list)) {
+      if (vertex->next)
+        qh_delvertex(vertex);
+      else {
+        qh_memfree(vertex, (int)sizeof(vertexT));
+        qh newvertex_list= qh vertex_list= NULL;
+      }
+    }
+  }else if (qh VERTEXneighbors) {
+    FORALLvertices
+      qh_setfreelong(&(vertex->neighbors));
+  }
+  qh VERTEXneighbors= False;
+  qh GOODclosest= NULL;
+  if (allmem) {
+    FORALLfacets {
+      FOREACHridge_(facet->ridges)
+        ridge->seen= False;
+    }
+    FORALLfacets {
+      if (facet->visible) {
+        FOREACHridge_(facet->ridges) {
+          if (!otherfacet_(ridge, facet)->visible)
+            ridge->seen= True;  /* an unattached ridge */
+        }
+      }
+    }
+    while ((facet= qh facet_list)) {
+      FOREACHridge_(facet->ridges) {
+        if (ridge->seen) {
+          qh_setfree(&(ridge->vertices));
+          qh_memfree(ridge, (int)sizeof(ridgeT));
+        }else
+          ridge->seen= True;
+      }
+      qh_setfree(&(facet->outsideset));
+      qh_setfree(&(facet->coplanarset));
+      qh_setfree(&(facet->neighbors));
+      qh_setfree(&(facet->ridges));
+      qh_setfree(&(facet->vertices));
+      if (facet->next)
+        qh_delfacet(facet);
+      else {
+        qh_memfree(facet, (int)sizeof(facetT));
+        qh visible_list= qh newfacet_list= qh facet_list= NULL;
+      }
+    }
+  }else {
+    FORALLfacets {
+      qh_setfreelong(&(facet->outsideset));
+      qh_setfreelong(&(facet->coplanarset));
+      if (!facet->simplicial) {
+        qh_setfreelong(&(facet->neighbors));
+        qh_setfreelong(&(facet->ridges));
+        qh_setfreelong(&(facet->vertices));
+      }
+    }
+  }
+  qh_setfree(&(qh hash_table));
+  qh_memfree(qh interior_point, qh normal_size);
+  qh interior_point= NULL;
+  FOREACHmerge_(qh facet_mergeset)  /* usually empty */
+    qh_memfree(merge, (int)sizeof(mergeT));
+  qh facet_mergeset= NULL;  /* temp set */
+  qh degen_mergeset= NULL;  /* temp set */
+  qh_settempfree_all();
+} /* freebuild */
+
+/*-<a                             href="qh-globa.htm#TOC"
+  >-------------------------------</a><a name="freeqhull">-</a>
+
+  qh_freeqhull( allmem )
+    see qh_freeqhull2
+    if qh_QHpointer, frees qh_qh
+*/
+void qh_freeqhull(boolT allmem) {
+    qh_freeqhull2(allmem);
+#if qh_QHpointer
+    qh_free(qh_qh);
+    qh_qh= NULL;
+#endif
+}
+
+/*-<a                             href="qh-globa.htm#TOC"
+>-------------------------------</a><a name="freeqhull2">-</a>
+
+qh_freeqhull2( allmem )
+  free global memory and set qhT to 0
+  if !allmem,
+    does not free short memory (freed by qh_memfreeshort unless qh_NOmem)
+
+notes:
+  sets qh.NOerrexit in case caller forgets to
+  Does not throw errors
+
+see:
+  see qh_initqhull_start2()
+
+design:
+  free global and temporary memory from qh_initbuild and qh_buildhull
+  free buffers
+  free statistics
+*/
+void qh_freeqhull2(boolT allmem) {
+
+  qh NOerrexit= True;  /* no more setjmp since called at exit and ~QhullQh */
+  trace1((qh ferr, 1006, "qh_freeqhull: free global memory\n"));
+  qh_freebuild(allmem);
+  qh_freebuffers();
+  qh_freestatistics();
+#if qh_QHpointer
+  memset((char *)qh_qh, 0, sizeof(qhT));
+  /* qh_qh freed by caller, qh_freeqhull() */
+#else
+  memset((char *)&qh_qh, 0, sizeof(qhT));
+#endif
+  qh NOerrexit= True;
+} /* freeqhull2 */
+
+/*-<a                             href="qh-globa.htm#TOC"
+  >-------------------------------</a><a name="init_A">-</a>
+
+  qh_init_A( infile, outfile, errfile, argc, argv )
+    initialize memory and stdio files
+    convert input options to option string (qh.qhull_command)
+
+  notes:
+    infile may be NULL if qh_readpoints() is not called
+
+    errfile should always be defined.  It is used for reporting
+    errors.  outfile is used for output and format options.
+
+    argc/argv may be 0/NULL
+
+    called before error handling initialized
+    qh_errexit() may not be used
+*/
+void qh_init_A(FILE *infile, FILE *outfile, FILE *errfile, int argc, char *argv[]) {
+  qh_meminit(errfile);
+  qh_initqhull_start(infile, outfile, errfile);
+  qh_init_qhull_command(argc, argv);
+} /* init_A */
+
+/*-<a                             href="qh-globa.htm#TOC"
+  >-------------------------------</a><a name="init_B">-</a>
+
+  qh_init_B( points, numpoints, dim, ismalloc )
+    initialize globals for points array
+
+    points has numpoints dim-dimensional points
+      points[0] is the first coordinate of the first point
+      points[1] is the second coordinate of the first point
+      points[dim] is the first coordinate of the second point
+
+    ismalloc=True
+      Qhull will call qh_free(points) on exit or input transformation
+    ismalloc=False
+      Qhull will allocate a new point array if needed for input transformation
+
+    qh.qhull_command
+      is the option string.
+      It is defined by qh_init_B(), qh_qhull_command(), or qh_initflags
+
+  returns:
+    if qh.PROJECTinput or (qh.DELAUNAY and qh.PROJECTdelaunay)
+      projects the input to a new point array
+
+        if qh.DELAUNAY,
+          qh.hull_dim is increased by one
+        if qh.ATinfinity,
+          qh_projectinput adds point-at-infinity for Delaunay tri.
+
+    if qh.SCALEinput
+      changes the upper and lower bounds of the input, see qh_scaleinput()
+
+    if qh.ROTATEinput
+      rotates the input by a random rotation, see qh_rotateinput()
+      if qh.DELAUNAY
+        rotates about the last coordinate
+
+  notes:
+    called after points are defined
+    qh_errexit() may be used
+*/
+void qh_init_B(coordT *points, int numpoints, int dim, boolT ismalloc) {
+  qh_initqhull_globals(points, numpoints, dim, ismalloc);
+  if (qhmem.LASTsize == 0)
+    qh_initqhull_mem();
+  /* mem.c and qset.c are initialized */
+  qh_initqhull_buffers();
+  qh_initthresholds(qh qhull_command);
+  if (qh PROJECTinput || (qh DELAUNAY && qh PROJECTdelaunay))
+    qh_projectinput();
+  if (qh SCALEinput)
+    qh_scaleinput();
+  if (qh ROTATErandom >= 0) {
+    qh_randommatrix(qh gm_matrix, qh hull_dim, qh gm_row);
+    if (qh DELAUNAY) {
+      int k, lastk= qh hull_dim-1;
+      for (k=0; k < lastk; k++) {
+        qh gm_row[k][lastk]= 0.0;
+        qh gm_row[lastk][k]= 0.0;
+      }
+      qh gm_row[lastk][lastk]= 1.0;
+    }
+    qh_gram_schmidt(qh hull_dim, qh gm_row);
+    qh_rotateinput(qh gm_row);
+  }
+} /* init_B */
+
+/*-<a                             href="qh-globa.htm#TOC"
+  >-------------------------------</a><a name="init_qhull_command">-</a>
+
+  qh_init_qhull_command( argc, argv )
+    build qh.qhull_command from argc/argv
+    Calls qh_exit if qhull_command is too short
+
+  returns:
+    a space-delimited string of options (just as typed)
+
+  notes:
+    makes option string easy to input and output
+
+    argc/argv may be 0/NULL
+*/
+void qh_init_qhull_command(int argc, char *argv[]) {
+
+  if (!qh_argv_to_command(argc, argv, qh qhull_command, (int)sizeof(qh qhull_command))){
+    /* Assumes qh.ferr is defined. */
+    qh_fprintf(qh ferr, 6033, "qhull input error: more than %d characters in command line\n",
+          (int)sizeof(qh qhull_command));
+    qh_exit(qh_ERRinput);  /* error reported, can not use qh_errexit */
+  }
+} /* init_qhull_command */
+
+/*-<a                             href="qh-globa.htm#TOC"
+  >-------------------------------</a><a name="initflags">-</a>
+
+  qh_initflags( commandStr )
+    set flags and initialized constants from commandStr
+    calls qh_exit() if qh->NOerrexit
+
+  returns:
+    sets qh.qhull_command to command if needed
+
+  notes:
+    ignores first word (e.g., "qhull d")
+    use qh_strtol/strtod since strtol/strtod may or may not skip trailing spaces
+
+  see:
+    qh_initthresholds() continues processing of 'Pdn' and 'PDn'
+    'prompt' in unix.c for documentation
+
+  design:
+    for each space-delimited option group
+      if top-level option
+        check syntax
+        append appropriate option to option string
+        set appropriate global variable or append printFormat to print options
+      else
+        for each sub-option
+          check syntax
+          append appropriate option to option string
+          set appropriate global variable or append printFormat to print options
+*/
+void qh_initflags(char *command) {
+  int k, i, lastproject;
+  char *s= command, *t, *prev_s, *start, key;
+  boolT isgeom= False, wasproject;
+  realT r;
+
+  if(qh NOerrexit){/* without this comment, segfault in gcc 4.4.0 mingw32 */
+    qh_fprintf(qh ferr, 6245, "qhull initflags error: qh.NOerrexit was not cleared before calling qh_initflags().  It should be cleared after setjmp().  Exit qhull.");
+    qh_exit(6245);
+  }
+  if (command <= &qh qhull_command[0] || command > &qh qhull_command[0] + sizeof(qh qhull_command)) {
+    if (command != &qh qhull_command[0]) {
+      *qh qhull_command= '\0';
+      strncat(qh qhull_command, command, sizeof(qh qhull_command)-strlen(qh qhull_command)-1);
+    }
+    while (*s && !isspace(*s))  /* skip program name */
+      s++;
+  }
+  while (*s) {
+    while (*s && isspace(*s))
+      s++;
+    if (*s == '-')
+      s++;
+    if (!*s)
+      break;
+    prev_s= s;
+    switch (*s++) {
+    case 'd':
+      qh_option("delaunay", NULL, NULL);
+      qh DELAUNAY= True;
+      break;
+    case 'f':
+      qh_option("facets", NULL, NULL);
+      qh_appendprint(qh_PRINTfacets);
+      break;
+    case 'i':
+      qh_option("incidence", NULL, NULL);
+      qh_appendprint(qh_PRINTincidences);
+      break;
+    case 'm':
+      qh_option("mathematica", NULL, NULL);
+      qh_appendprint(qh_PRINTmathematica);
+      break;
+    case 'n':
+      qh_option("normals", NULL, NULL);
+      qh_appendprint(qh_PRINTnormals);
+      break;
+    case 'o':
+      qh_option("offFile", NULL, NULL);
+      qh_appendprint(qh_PRINToff);
+      break;
+    case 'p':
+      qh_option("points", NULL, NULL);
+      qh_appendprint(qh_PRINTpoints);
+      break;
+    case 's':
+      qh_option("summary", NULL, NULL);
+      qh PRINTsummary= True;
+      break;
+    case 'v':
+      qh_option("voronoi", NULL, NULL);
+      qh VORONOI= True;
+      qh DELAUNAY= True;
+      break;
+    case 'A':
+      if (!isdigit(*s) && *s != '.' && *s != '-')
+        qh_fprintf(qh ferr, 7002, "qhull warning: no maximum cosine angle given for option 'An'.  Ignored.\n");
+      else {
+        if (*s == '-') {
+          qh premerge_cos= -qh_strtod(s, &s);
+          qh_option("Angle-premerge-", NULL, &qh premerge_cos);
+          qh PREmerge= True;
+        }else {
+          qh postmerge_cos= qh_strtod(s, &s);
+          qh_option("Angle-postmerge", NULL, &qh postmerge_cos);
+          qh POSTmerge= True;
+        }
+        qh MERGING= True;
+      }
+      break;
+    case 'C':
+      if (!isdigit(*s) && *s != '.' && *s != '-')
+        qh_fprintf(qh ferr, 7003, "qhull warning: no centrum radius given for option 'Cn'.  Ignored.\n");
+      else {
+        if (*s == '-') {
+          qh premerge_centrum= -qh_strtod(s, &s);
+          qh_option("Centrum-premerge-", NULL, &qh premerge_centrum);
+          qh PREmerge= True;
+        }else {
+          qh postmerge_centrum= qh_strtod(s, &s);
+          qh_option("Centrum-postmerge", NULL, &qh postmerge_centrum);
+          qh POSTmerge= True;
+        }
+        qh MERGING= True;
+      }
+      break;
+    case 'E':
+      if (*s == '-')
+        qh_fprintf(qh ferr, 7004, "qhull warning: negative maximum roundoff given for option 'An'.  Ignored.\n");
+      else if (!isdigit(*s))
+        qh_fprintf(qh ferr, 7005, "qhull warning: no maximum roundoff given for option 'En'.  Ignored.\n");
+      else {
+        qh DISTround= qh_strtod(s, &s);
+        qh_option("Distance-roundoff", NULL, &qh DISTround);
+        qh SETroundoff= True;
+      }
+      break;
+    case 'H':
+      start= s;
+      qh HALFspace= True;
+      qh_strtod(s, &t);
+      while (t > s)  {
+        if (*t && !isspace(*t)) {
+          if (*t == ',')
+            t++;
+          else
+            qh_fprintf(qh ferr, 7006, "qhull warning: origin for Halfspace intersection should be 'Hn,n,n,...'\n");
+        }
+        s= t;
+        qh_strtod(s, &t);
+      }
+      if (start < t) {
+        if (!(qh feasible_string= (char*)calloc((size_t)(t-start+1), (size_t)1))) {
+          qh_fprintf(qh ferr, 6034, "qhull error: insufficient memory for 'Hn,n,n'\n");
+          qh_errexit(qh_ERRmem, NULL, NULL);
+        }
+        strncpy(qh feasible_string, start, (size_t)(t-start));
+        qh_option("Halfspace-about", NULL, NULL);
+        qh_option(qh feasible_string, NULL, NULL);
+      }else
+        qh_option("Halfspace", NULL, NULL);
+      break;
+    case 'R':
+      if (!isdigit(*s))
+        qh_fprintf(qh ferr, 7007, "qhull warning: missing random perturbation for option 'Rn'.  Ignored\n");
+      else {
+        qh RANDOMfactor= qh_strtod(s, &s);
+        qh_option("Random_perturb", NULL, &qh RANDOMfactor);
+        qh RANDOMdist= True;
+      }
+      break;
+    case 'V':
+      if (!isdigit(*s) && *s != '-')
+        qh_fprintf(qh ferr, 7008, "qhull warning: missing visible distance for option 'Vn'.  Ignored\n");
+      else {
+        qh MINvisible= qh_strtod(s, &s);
+        qh_option("Visible", NULL, &qh MINvisible);
+      }
+      break;
+    case 'U':
+      if (!isdigit(*s) && *s != '-')
+        qh_fprintf(qh ferr, 7009, "qhull warning: missing coplanar distance for option 'Un'.  Ignored\n");
+      else {
+        qh MAXcoplanar= qh_strtod(s, &s);
+        qh_option("U-coplanar", NULL, &qh MAXcoplanar);
+      }
+      break;
+    case 'W':
+      if (*s == '-')
+        qh_fprintf(qh ferr, 7010, "qhull warning: negative outside width for option 'Wn'.  Ignored.\n");
+      else if (!isdigit(*s))
+        qh_fprintf(qh ferr, 7011, "qhull warning: missing outside width for option 'Wn'.  Ignored\n");
+      else {
+        qh MINoutside= qh_strtod(s, &s);
+        qh_option("W-outside", NULL, &qh MINoutside);
+        qh APPROXhull= True;
+      }
+      break;
+    /************  sub menus ***************/
+    case 'F':
+      while (*s && !isspace(*s)) {
+        switch (*s++) {
+        case 'a':
+          qh_option("Farea", NULL, NULL);
+          qh_appendprint(qh_PRINTarea);
+          qh GETarea= True;
+          break;
+        case 'A':
+          qh_option("FArea-total", NULL, NULL);
+          qh GETarea= True;
+          break;
+        case 'c':
+          qh_option("Fcoplanars", NULL, NULL);
+          qh_appendprint(qh_PRINTcoplanars);
+          break;
+        case 'C':
+          qh_option("FCentrums", NULL, NULL);
+          qh_appendprint(qh_PRINTcentrums);
+          break;
+        case 'd':
+          qh_option("Fd-cdd-in", NULL, NULL);
+          qh CDDinput= True;
+          break;
+        case 'D':
+          qh_option("FD-cdd-out", NULL, NULL);
+          qh CDDoutput= True;
+          break;
+        case 'F':
+          qh_option("FFacets-xridge", NULL, NULL);
+          qh_appendprint(qh_PRINTfacets_xridge);
+          break;
+        case 'i':
+          qh_option("Finner", NULL, NULL);
+          qh_appendprint(qh_PRINTinner);
+          break;
+        case 'I':
+          qh_option("FIDs", NULL, NULL);
+          qh_appendprint(qh_PRINTids);
+          break;
+        case 'm':
+          qh_option("Fmerges", NULL, NULL);
+          qh_appendprint(qh_PRINTmerges);
+          break;
+        case 'M':
+          qh_option("FMaple", NULL, NULL);
+          qh_appendprint(qh_PRINTmaple);
+          break;
+        case 'n':
+          qh_option("Fneighbors", NULL, NULL);
+          qh_appendprint(qh_PRINTneighbors);
+          break;
+        case 'N':
+          qh_option("FNeighbors-vertex", NULL, NULL);
+          qh_appendprint(qh_PRINTvneighbors);
+          break;
+        case 'o':
+          qh_option("Fouter", NULL, NULL);
+          qh_appendprint(qh_PRINTouter);
+          break;
+        case 'O':
+          if (qh PRINToptions1st) {
+            qh_option("FOptions", NULL, NULL);
+            qh_appendprint(qh_PRINToptions);
+          }else
+            qh PRINToptions1st= True;
+          break;
+        case 'p':
+          qh_option("Fpoint-intersect", NULL, NULL);
+          qh_appendprint(qh_PRINTpointintersect);
+          break;
+        case 'P':
+          qh_option("FPoint-nearest", NULL, NULL);
+          qh_appendprint(qh_PRINTpointnearest);
+          break;
+        case 'Q':
+          qh_option("FQhull", NULL, NULL);
+          qh_appendprint(qh_PRINTqhull);
+          break;
+        case 's':
+          qh_option("Fsummary", NULL, NULL);
+          qh_appendprint(qh_PRINTsummary);
+          break;
+        case 'S':
+          qh_option("FSize", NULL, NULL);
+          qh_appendprint(qh_PRINTsize);
+          qh GETarea= True;
+          break;
+        case 't':
+          qh_option("Ftriangles", NULL, NULL);
+          qh_appendprint(qh_PRINTtriangles);
+          break;
+        case 'v':
+          /* option set in qh_initqhull_globals */
+          qh_appendprint(qh_PRINTvertices);
+          break;
+        case 'V':
+          qh_option("FVertex-average", NULL, NULL);
+          qh_appendprint(qh_PRINTaverage);
+          break;
+        case 'x':
+          qh_option("Fxtremes", NULL, NULL);
+          qh_appendprint(qh_PRINTextremes);
+          break;
+        default:
+          s--;
+          qh_fprintf(qh ferr, 7012, "qhull warning: unknown 'F' output option %c, rest ignored\n", (int)s[0]);
+          while (*++s && !isspace(*s));
+          break;
+        }
+      }
+      break;
+    case 'G':
+      isgeom= True;
+      qh_appendprint(qh_PRINTgeom);
+      while (*s && !isspace(*s)) {
+        switch (*s++) {
+        case 'a':
+          qh_option("Gall-points", NULL, NULL);
+          qh PRINTdots= True;
+          break;
+        case 'c':
+          qh_option("Gcentrums", NULL, NULL);
+          qh PRINTcentrums= True;
+          break;
+        case 'h':
+          qh_option("Gintersections", NULL, NULL);
+          qh DOintersections= True;
+          break;
+        case 'i':
+          qh_option("Ginner", NULL, NULL);
+          qh PRINTinner= True;
+          break;
+        case 'n':
+          qh_option("Gno-planes", NULL, NULL);
+          qh PRINTnoplanes= True;
+          break;
+        case 'o':
+          qh_option("Gouter", NULL, NULL);
+          qh PRINTouter= True;
+          break;
+        case 'p':
+          qh_option("Gpoints", NULL, NULL);
+          qh PRINTcoplanar= True;
+          break;
+        case 'r':
+          qh_option("Gridges", NULL, NULL);
+          qh PRINTridges= True;
+          break;
+        case 't':
+          qh_option("Gtransparent", NULL, NULL);
+          qh PRINTtransparent= True;
+          break;
+        case 'v':
+          qh_option("Gvertices", NULL, NULL);
+          qh PRINTspheres= True;
+          break;
+        case 'D':
+          if (!isdigit(*s))
+            qh_fprintf(qh ferr, 6035, "qhull input error: missing dimension for option 'GDn'\n");
+          else {
+            if (qh DROPdim >= 0)
+              qh_fprintf(qh ferr, 7013, "qhull warning: can only drop one dimension.  Previous 'GD%d' ignored\n",
+                   qh DROPdim);
+            qh DROPdim= qh_strtol(s, &s);
+            qh_option("GDrop-dim", &qh DROPdim, NULL);
+          }
+          break;
+        default:
+          s--;
+          qh_fprintf(qh ferr, 7014, "qhull warning: unknown 'G' print option %c, rest ignored\n", (int)s[0]);
+          while (*++s && !isspace(*s));
+          break;
+        }
+      }
+      break;
+    case 'P':
+      while (*s && !isspace(*s)) {
+        switch (*s++) {
+        case 'd': case 'D':  /* see qh_initthresholds() */
+          key= s[-1];
+          i= qh_strtol(s, &s);
+          r= 0;
+          if (*s == ':') {
+            s++;
+            r= qh_strtod(s, &s);
+          }
+          if (key == 'd')
+            qh_option("Pdrop-facets-dim-less", &i, &r);
+          else
+            qh_option("PDrop-facets-dim-more", &i, &r);
+          break;
+        case 'g':
+          qh_option("Pgood-facets", NULL, NULL);
+          qh PRINTgood= True;
+          break;
+        case 'G':
+          qh_option("PGood-facet-neighbors", NULL, NULL);
+          qh PRINTneighbors= True;
+          break;
+        case 'o':
+          qh_option("Poutput-forced", NULL, NULL);
+          qh FORCEoutput= True;
+          break;
+        case 'p':
+          qh_option("Pprecision-ignore", NULL, NULL);
+          qh PRINTprecision= False;
+          break;
+        case 'A':
+          if (!isdigit(*s))
+            qh_fprintf(qh ferr, 6036, "qhull input error: missing facet count for keep area option 'PAn'\n");
+          else {
+            qh KEEParea= qh_strtol(s, &s);
+            qh_option("PArea-keep", &qh KEEParea, NULL);
+            qh GETarea= True;
+          }
+          break;
+        case 'F':
+          if (!isdigit(*s))
+            qh_fprintf(qh ferr, 6037, "qhull input error: missing facet area for option 'PFn'\n");
+          else {
+            qh KEEPminArea= qh_strtod(s, &s);
+            qh_option("PFacet-area-keep", NULL, &qh KEEPminArea);
+            qh GETarea= True;
+          }
+          break;
+        case 'M':
+          if (!isdigit(*s))
+            qh_fprintf(qh ferr, 6038, "qhull input error: missing merge count for option 'PMn'\n");
+          else {
+            qh KEEPmerge= qh_strtol(s, &s);
+            qh_option("PMerge-keep", &qh KEEPmerge, NULL);
+          }
+          break;
+        default:
+          s--;
+          qh_fprintf(qh ferr, 7015, "qhull warning: unknown 'P' print option %c, rest ignored\n", (int)s[0]);
+          while (*++s && !isspace(*s));
+          break;
+        }
+      }
+      break;
+    case 'Q':
+      lastproject= -1;
+      while (*s && !isspace(*s)) {
+        switch (*s++) {
+        case 'b': case 'B':  /* handled by qh_initthresholds */
+          key= s[-1];
+          if (key == 'b' && *s == 'B') {
+            s++;
+            r= qh_DEFAULTbox;
+            qh SCALEinput= True;
+            qh_option("QbBound-unit-box", NULL, &r);
+            break;
+          }
+          if (key == 'b' && *s == 'b') {
+            s++;
+            qh SCALElast= True;
+            qh_option("Qbbound-last", NULL, NULL);
+            break;
+          }
+          k= qh_strtol(s, &s);
+          r= 0.0;
+          wasproject= False;
+          if (*s == ':') {
+            s++;
+            if ((r= qh_strtod(s, &s)) == 0.0) {
+              t= s;            /* need true dimension for memory allocation */
+              while (*t && !isspace(*t)) {
+                if (toupper(*t++) == 'B'
+                 && k == qh_strtol(t, &t)
+                 && *t++ == ':'
+                 && qh_strtod(t, &t) == 0.0) {
+                  qh PROJECTinput++;
+                  trace2((qh ferr, 2004, "qh_initflags: project dimension %d\n", k));
+                  qh_option("Qb-project-dim", &k, NULL);
+                  wasproject= True;
+                  lastproject= k;
+                  break;
+                }
+              }
+            }
+          }
+          if (!wasproject) {
+            if (lastproject == k && r == 0.0)
+              lastproject= -1;  /* doesn't catch all possible sequences */
+            else if (key == 'b') {
+              qh SCALEinput= True;
+              if (r == 0.0)
+                r= -qh_DEFAULTbox;
+              qh_option("Qbound-dim-low", &k, &r);
+            }else {
+              qh SCALEinput= True;
+              if (r == 0.0)
+                r= qh_DEFAULTbox;
+              qh_option("QBound-dim-high", &k, &r);
+            }
+          }
+          break;
+        case 'c':
+          qh_option("Qcoplanar-keep", NULL, NULL);
+          qh KEEPcoplanar= True;
+          break;
+        case 'f':
+          qh_option("Qfurthest-outside", NULL, NULL);
+          qh BESToutside= True;
+          break;
+        case 'g':
+          qh_option("Qgood-facets-only", NULL, NULL);
+          qh ONLYgood= True;
+          break;
+        case 'i':
+          qh_option("Qinterior-keep", NULL, NULL);
+          qh KEEPinside= True;
+          break;
+        case 'm':
+          qh_option("Qmax-outside-only", NULL, NULL);
+          qh ONLYmax= True;
+          break;
+        case 'r':
+          qh_option("Qrandom-outside", NULL, NULL);
+          qh RANDOMoutside= True;
+          break;
+        case 's':
+          qh_option("Qsearch-initial-simplex", NULL, NULL);
+          qh ALLpoints= True;
+          break;
+        case 't':
+          qh_option("Qtriangulate", NULL, NULL);
+          qh TRIangulate= True;
+          break;
+        case 'T':
+          qh_option("QTestPoints", NULL, NULL);
+          if (!isdigit(*s))
+            qh_fprintf(qh ferr, 6039, "qhull input error: missing number of test points for option 'QTn'\n");
+          else {
+            qh TESTpoints= qh_strtol(s, &s);
+            qh_option("QTestPoints", &qh TESTpoints, NULL);
+          }
+          break;
+        case 'u':
+          qh_option("QupperDelaunay", NULL, NULL);
+          qh UPPERdelaunay= True;
+          break;
+        case 'v':
+          qh_option("Qvertex-neighbors-convex", NULL, NULL);
+          qh TESTvneighbors= True;
+          break;
+        case 'x':
+          qh_option("Qxact-merge", NULL, NULL);
+          qh MERGEexact= True;
+          break;
+        case 'z':
+          qh_option("Qz-infinity-point", NULL, NULL);
+          qh ATinfinity= True;
+          break;
+        case '0':
+          qh_option("Q0-no-premerge", NULL, NULL);
+          qh NOpremerge= True;
+          break;
+        case '1':
+          if (!isdigit(*s)) {
+            qh_option("Q1-no-angle-sort", NULL, NULL);
+            qh ANGLEmerge= False;
+            break;
+          }
+          switch (*s++) {
+          case '0':
+            qh_option("Q10-no-narrow", NULL, NULL);
+            qh NOnarrow= True;
+            break;
+          case '1':
+            qh_option("Q11-trinormals Qtriangulate", NULL, NULL);
+            qh TRInormals= True;
+            qh TRIangulate= True;
+            break;
+          case '2':
+            qh_option("Q12-no-wide-dup", NULL, NULL);
+            qh NOwide= True;
+            break;
+          default:
+            s--;
+            qh_fprintf(qh ferr, 7016, "qhull warning: unknown 'Q' qhull option 1%c, rest ignored\n", (int)s[0]);
+            while (*++s && !isspace(*s));
+            break;
+          }
+          break;
+        case '2':
+          qh_option("Q2-no-merge-independent", NULL, NULL);
+          qh MERGEindependent= False;
+          goto LABELcheckdigit;
+          break; /* no warnings */
+        case '3':
+          qh_option("Q3-no-merge-vertices", NULL, NULL);
+          qh MERGEvertices= False;
+        LABELcheckdigit:
+          if (isdigit(*s))
+            qh_fprintf(qh ferr, 7017, "qhull warning: can not follow '1', '2', or '3' with a digit.  '%c' skipped.\n",
+                     *s++);
+          break;
+        case '4':
+          qh_option("Q4-avoid-old-into-new", NULL, NULL);
+          qh AVOIDold= True;
+          break;
+        case '5':
+          qh_option("Q5-no-check-outer", NULL, NULL);
+          qh SKIPcheckmax= True;
+          break;
+        case '6':
+          qh_option("Q6-no-concave-merge", NULL, NULL);
+          qh SKIPconvex= True;
+          break;
+        case '7':
+          qh_option("Q7-no-breadth-first", NULL, NULL);
+          qh VIRTUALmemory= True;
+          break;
+        case '8':
+          qh_option("Q8-no-near-inside", NULL, NULL);
+          qh NOnearinside= True;
+          break;
+        case '9':
+          qh_option("Q9-pick-furthest", NULL, NULL);
+          qh PICKfurthest= True;
+          break;
+        case 'G':
+          i= qh_strtol(s, &t);
+          if (qh GOODpoint)
+            qh_fprintf(qh ferr, 7018, "qhull warning: good point already defined for option 'QGn'.  Ignored\n");
+          else if (s == t)
+            qh_fprintf(qh ferr, 7019, "qhull warning: missing good point id for option 'QGn'.  Ignored\n");
+          else if (i < 0 || *s == '-') {
+            qh GOODpoint= i-1;
+            qh_option("QGood-if-dont-see-point", &i, NULL);
+          }else {
+            qh GOODpoint= i+1;
+            qh_option("QGood-if-see-point", &i, NULL);
+          }
+          s= t;
+          break;
+        case 'J':
+          if (!isdigit(*s) && *s != '-')
+            qh JOGGLEmax= 0.0;
+          else {
+            qh JOGGLEmax= (realT) qh_strtod(s, &s);
+            qh_option("QJoggle", NULL, &qh JOGGLEmax);
+          }
+          break;
+        case 'R':
+          if (!isdigit(*s) && *s != '-')
+            qh_fprintf(qh ferr, 7020, "qhull warning: missing random seed for option 'QRn'.  Ignored\n");
+          else {
+            qh ROTATErandom= i= qh_strtol(s, &s);
+            if (i > 0)
+              qh_option("QRotate-id", &i, NULL );
+            else if (i < -1)
+              qh_option("QRandom-seed", &i, NULL );
+          }
+          break;
+        case 'V':
+          i= qh_strtol(s, &t);
+          if (qh GOODvertex)
+            qh_fprintf(qh ferr, 7021, "qhull warning: good vertex already defined for option 'QVn'.  Ignored\n");
+          else if (s == t)
+            qh_fprintf(qh ferr, 7022, "qhull warning: no good point id given for option 'QVn'.  Ignored\n");
+          else if (i < 0) {
+            qh GOODvertex= i - 1;
+            qh_option("QV-good-facets-not-point", &i, NULL);
+          }else {
+            qh_option("QV-good-facets-point", &i, NULL);
+            qh GOODvertex= i + 1;
+          }
+          s= t;
+          break;
+        default:
+          s--;
+          qh_fprintf(qh ferr, 7023, "qhull warning: unknown 'Q' qhull option %c, rest ignored\n", (int)s[0]);
+          while (*++s && !isspace(*s));
+          break;
+        }
+      }
+      break;
+    case 'T':
+      while (*s && !isspace(*s)) {
+        if (isdigit(*s) || *s == '-')
+          qh IStracing= qh_strtol(s, &s);
+        else switch (*s++) {
+        case 'a':
+          qh_option("Tannotate-output", NULL, NULL);
+          qh ANNOTATEoutput= True;
+          break;
+        case 'c':
+          qh_option("Tcheck-frequently", NULL, NULL);
+          qh CHECKfrequently= True;
+          break;
+        case 's':
+          qh_option("Tstatistics", NULL, NULL);
+          qh PRINTstatistics= True;
+          break;
+        case 'v':
+          qh_option("Tverify", NULL, NULL);
+          qh VERIFYoutput= True;
+          break;
+        case 'z':
+          if (qh ferr == qh_FILEstderr) {
+            /* The C++ interface captures the output in qh_fprint_qhull() */
+            qh_option("Tz-stdout", NULL, NULL);
+            qh USEstdout= True;
+          }else if (!qh fout)
+            qh_fprintf(qh ferr, 7024, "qhull warning: output file undefined(stdout).  Option 'Tz' ignored.\n");
+          else {
+            qh_option("Tz-stdout", NULL, NULL);
+            qh USEstdout= True;
+            qh ferr= qh fout;
+            qhmem.ferr= qh fout;
+          }
+          break;
+        case 'C':
+          if (!isdigit(*s))
+            qh_fprintf(qh ferr, 7025, "qhull warning: missing point id for cone for trace option 'TCn'.  Ignored\n");
+          else {
+            i= qh_strtol(s, &s);
+            qh_option("TCone-stop", &i, NULL);
+            qh STOPcone= i + 1;
+          }
+          break;
+        case 'F':
+          if (!isdigit(*s))
+            qh_fprintf(qh ferr, 7026, "qhull warning: missing frequency count for trace option 'TFn'.  Ignored\n");
+          else {
+            qh REPORTfreq= qh_strtol(s, &s);
+            qh_option("TFacet-log", &qh REPORTfreq, NULL);
+            qh REPORTfreq2= qh REPORTfreq/2;  /* for tracemerging() */
+          }
+          break;
+        case 'I':
+          if (!isspace(*s))
+            qh_fprintf(qh ferr, 7027, "qhull warning: missing space between 'TI' and filename, %s\n", s);
+          while (isspace(*s))
+            s++;
+          t= qh_skipfilename(s);
+          {
+            char filename[qh_FILENAMElen];
+
+            qh_copyfilename(filename, (int)sizeof(filename), s, (int)(t-s));   /* WARN64 */
+            s= t;
+            if (!freopen(filename, "r", stdin)) {
+              qh_fprintf(qh ferr, 6041, "qhull error: could not open file \"%s\".", filename);
+              qh_errexit(qh_ERRinput, NULL, NULL);
+            }else {
+              qh_option("TInput-file", NULL, NULL);
+              qh_option(filename, NULL, NULL);
+            }
+          }
+          break;
+        case 'O':
+            if (!isspace(*s))
+                qh_fprintf(qh ferr, 7028, "qhull warning: missing space between 'TO' and filename, %s\n", s);
+            while (isspace(*s))
+                s++;
+            t= qh_skipfilename(s);
+            {
+              char filename[qh_FILENAMElen];
+
+              qh_copyfilename(filename, (int)sizeof(filename), s, (int)(t-s));  /* WARN64 */
+              s= t;
+              if (!qh fout) {
+                qh_fprintf(qh ferr, 6266, "qhull input warning: qh.fout was not set by caller.  Cannot use option 'TO' to redirect output.  Ignoring option 'TO'\n");
+              }else if (!freopen(filename, "w", qh fout)) {
+                qh_fprintf(qh ferr, 6044, "qhull error: could not open file \"%s\".", filename);
+                qh_errexit(qh_ERRinput, NULL, NULL);
+              }else {
+                qh_option("TOutput-file", NULL, NULL);
+              qh_option(filename, NULL, NULL);
+            }
+          }
+          break;
+        case 'P':
+          if (!isdigit(*s))
+            qh_fprintf(qh ferr, 7029, "qhull warning: missing point id for trace option 'TPn'.  Ignored\n");
+          else {
+            qh TRACEpoint= qh_strtol(s, &s);
+            qh_option("Trace-point", &qh TRACEpoint, NULL);
+          }
+          break;
+        case 'M':
+          if (!isdigit(*s))
+            qh_fprintf(qh ferr, 7030, "qhull warning: missing merge id for trace option 'TMn'.  Ignored\n");
+          else {
+            qh TRACEmerge= qh_strtol(s, &s);
+            qh_option("Trace-merge", &qh TRACEmerge, NULL);
+          }
+          break;
+        case 'R':
+          if (!isdigit(*s))
+            qh_fprintf(qh ferr, 7031, "qhull warning: missing rerun count for trace option 'TRn'.  Ignored\n");
+          else {
+            qh RERUN= qh_strtol(s, &s);
+            qh_option("TRerun", &qh RERUN, NULL);
+          }
+          break;
+        case 'V':
+          i= qh_strtol(s, &t);
+          if (s == t)
+            qh_fprintf(qh ferr, 7032, "qhull warning: missing furthest point id for trace option 'TVn'.  Ignored\n");
+          else if (i < 0) {
+            qh STOPpoint= i - 1;
+            qh_option("TV-stop-before-point", &i, NULL);
+          }else {
+            qh STOPpoint= i + 1;
+            qh_option("TV-stop-after-point", &i, NULL);
+          }
+          s= t;
+          break;
+        case 'W':
+          if (!isdigit(*s))
+            qh_fprintf(qh ferr, 7033, "qhull warning: missing max width for trace option 'TWn'.  Ignored\n");
+          else {
+            qh TRACEdist= (realT) qh_strtod(s, &s);
+            qh_option("TWide-trace", NULL, &qh TRACEdist);
+          }
+          break;
+        default:
+          s--;
+          qh_fprintf(qh ferr, 7034, "qhull warning: unknown 'T' trace option %c, rest ignored\n", (int)s[0]);
+          while (*++s && !isspace(*s));
+          break;
+        }
+      }
+      break;
+    default:
+      qh_fprintf(qh ferr, 7035, "qhull warning: unknown flag %c(%x)\n", (int)s[-1],
+               (int)s[-1]);
+      break;
+    }
+    if (s-1 == prev_s && *s && !isspace(*s)) {
+      qh_fprintf(qh ferr, 7036, "qhull warning: missing space after flag %c(%x); reserved for menu. Skipped.\n",
+               (int)*prev_s, (int)*prev_s);
+      while (*s && !isspace(*s))
+        s++;
+    }
+  }
+  if (qh STOPcone && qh JOGGLEmax < REALmax/2)
+    qh_fprintf(qh ferr, 7078, "qhull warning: 'TCn' (stopCone) ignored when used with 'QJn' (joggle)\n");
+  if (isgeom && !qh FORCEoutput && qh PRINTout[1])
+    qh_fprintf(qh ferr, 7037, "qhull warning: additional output formats are not compatible with Geomview\n");
+  /* set derived values in qh_initqhull_globals */
+} /* initflags */
+
+
+/*-<a                             href="qh-globa.htm#TOC"
+  >-------------------------------</a><a name="initqhull_buffers">-</a>
+
+  qh_initqhull_buffers()
+    initialize global memory buffers
+
+  notes:
+    must match qh_freebuffers()
+*/
+void qh_initqhull_buffers(void) {
+  int k;
+
+  qh TEMPsize= (qhmem.LASTsize - sizeof(setT))/SETelemsize;
+  if (qh TEMPsize <= 0 || qh TEMPsize > qhmem.LASTsize)
+    qh TEMPsize= 8;  /* e.g., if qh_NOmem */
+  qh other_points= qh_setnew(qh TEMPsize);
+  qh del_vertices= qh_setnew(qh TEMPsize);
+  qh coplanarfacetset= qh_setnew(qh TEMPsize);
+  qh NEARzero= (realT *)qh_memalloc(qh hull_dim * sizeof(realT));
+  qh lower_threshold= (realT *)qh_memalloc((qh input_dim+1) * sizeof(realT));
+  qh upper_threshold= (realT *)qh_memalloc((qh input_dim+1) * sizeof(realT));
+  qh lower_bound= (realT *)qh_memalloc((qh input_dim+1) * sizeof(realT));
+  qh upper_bound= (realT *)qh_memalloc((qh input_dim+1) * sizeof(realT));
+  for (k=qh input_dim+1; k--; ) {  /* duplicated in qh_initqhull_buffers and qh_clear_outputflags */
+    qh lower_threshold[k]= -REALmax;
+    qh upper_threshold[k]= REALmax;
+    qh lower_bound[k]= -REALmax;
+    qh upper_bound[k]= REALmax;
+  }
+  qh gm_matrix= (coordT *)qh_memalloc((qh hull_dim+1) * qh hull_dim * sizeof(coordT));
+  qh gm_row= (coordT **)qh_memalloc((qh hull_dim+1) * sizeof(coordT *));
+} /* initqhull_buffers */
+
+/*-<a                             href="qh-globa.htm#TOC"
+  >-------------------------------</a><a name="initqhull_globals">-</a>
+
+  qh_initqhull_globals( points, numpoints, dim, ismalloc )
+    initialize globals
+    if ismalloc
+      points were malloc'd and qhull should free at end
+
+  returns:
+    sets qh.first_point, num_points, input_dim, hull_dim and others
+    seeds random number generator (seed=1 if tracing)
+    modifies qh.hull_dim if ((qh.DELAUNAY and qh.PROJECTdelaunay) or qh.PROJECTinput)
+    adjust user flags as needed
+    also checks DIM3 dependencies and constants
+
+  notes:
+    do not use qh_point() since an input transformation may move them elsewhere
+
+  see:
+    qh_initqhull_start() sets default values for non-zero globals
+
+  design:
+    initialize points array from input arguments
+    test for qh.ZEROcentrum
+      (i.e., use opposite vertex instead of cetrum for convexity testing)
+    initialize qh.CENTERtype, qh.normal_size,
+      qh.center_size, qh.TRACEpoint/level,
+    initialize and test random numbers
+    qh_initqhull_outputflags() -- adjust and test output flags
+*/
+void qh_initqhull_globals(coordT *points, int numpoints, int dim, boolT ismalloc) {
+  int seed, pointsneeded, extra= 0, i, randi, k;
+  realT randr;
+  realT factorial;
+
+  time_t timedata;
+
+  trace0((qh ferr, 13, "qh_initqhull_globals: for %s | %s\n", qh rbox_command,
+      qh qhull_command));
+  qh POINTSmalloc= ismalloc;
+  qh first_point= points;
+  qh num_points= numpoints;
+  qh hull_dim= qh input_dim= dim;
+  if (!qh NOpremerge && !qh MERGEexact && !qh PREmerge && qh JOGGLEmax > REALmax/2) {
+    qh MERGING= True;
+    if (qh hull_dim <= 4) {
+      qh PREmerge= True;
+      qh_option("_pre-merge", NULL, NULL);
+    }else {
+      qh MERGEexact= True;
+      qh_option("Qxact_merge", NULL, NULL);
+    }
+  }else if (qh MERGEexact)
+    qh MERGING= True;
+  if (!qh NOpremerge && qh JOGGLEmax > REALmax/2) {
+#ifdef qh_NOmerge
+    qh JOGGLEmax= 0.0;
+#endif
+  }
+  if (qh TRIangulate && qh JOGGLEmax < REALmax/2 && qh PRINTprecision)
+    qh_fprintf(qh ferr, 7038, "qhull warning: joggle('QJ') always produces simplicial output.  Triangulated output('Qt') does nothing.\n");
+  if (qh JOGGLEmax < REALmax/2 && qh DELAUNAY && !qh SCALEinput && !qh SCALElast) {
+    qh SCALElast= True;
+    qh_option("Qbbound-last-qj", NULL, NULL);
+  }
+  if (qh MERGING && !qh POSTmerge && qh premerge_cos > REALmax/2
+  && qh premerge_centrum == 0) {
+    qh ZEROcentrum= True;
+    qh ZEROall_ok= True;
+    qh_option("_zero-centrum", NULL, NULL);
+  }
+  if (qh JOGGLEmax < REALmax/2 && REALepsilon > 2e-8 && qh PRINTprecision)
+    qh_fprintf(qh ferr, 7039, "qhull warning: real epsilon, %2.2g, is probably too large for joggle('QJn')\nRecompile with double precision reals(see user.h).\n",
+          REALepsilon);
+#ifdef qh_NOmerge
+  if (qh MERGING) {
+    qh_fprintf(qh ferr, 6045, "qhull input error: merging not installed(qh_NOmerge + 'Qx', 'Cn' or 'An')\n");
+    qh_errexit(qh_ERRinput, NULL, NULL);
+  }
+#endif
+  if (qh DELAUNAY && qh KEEPcoplanar && !qh KEEPinside) {
+    qh KEEPinside= True;
+    qh_option("Qinterior-keep", NULL, NULL);
+  }
+  if (qh DELAUNAY && qh HALFspace) {
+    qh_fprintf(qh ferr, 6046, "qhull input error: can not use Delaunay('d') or Voronoi('v') with halfspace intersection('H')\n");
+    qh_errexit(qh_ERRinput, NULL, NULL);
+  }
+  if (!qh DELAUNAY && (qh UPPERdelaunay || qh ATinfinity)) {
+    qh_fprintf(qh ferr, 6047, "qhull input error: use upper-Delaunay('Qu') or infinity-point('Qz') with Delaunay('d') or Voronoi('v')\n");
+    qh_errexit(qh_ERRinput, NULL, NULL);
+  }
+  if (qh UPPERdelaunay && qh ATinfinity) {
+    qh_fprintf(qh ferr, 6048, "qhull input error: can not use infinity-point('Qz') with upper-Delaunay('Qu')\n");
+    qh_errexit(qh_ERRinput, NULL, NULL);
+  }
+  if (qh SCALElast && !qh DELAUNAY && qh PRINTprecision)
+    qh_fprintf(qh ferr, 7040, "qhull input warning: option 'Qbb' (scale-last-coordinate) is normally used with 'd' or 'v'\n");
+  qh DOcheckmax= (!qh SKIPcheckmax && qh MERGING );
+  qh KEEPnearinside= (qh DOcheckmax && !(qh KEEPinside && qh KEEPcoplanar)
+                          && !qh NOnearinside);
+  if (qh MERGING)
+    qh CENTERtype= qh_AScentrum;
+  else if (qh VORONOI)
+    qh CENTERtype= qh_ASvoronoi;
+  if (qh TESTvneighbors && !qh MERGING) {
+    qh_fprintf(qh ferr, 6049, "qhull input error: test vertex neighbors('Qv') needs a merge option\n");
+    qh_errexit(qh_ERRinput, NULL ,NULL);
+  }
+  if (qh PROJECTinput || (qh DELAUNAY && qh PROJECTdelaunay)) {
+    qh hull_dim -= qh PROJECTinput;
+    if (qh DELAUNAY) {
+      qh hull_dim++;
+      if (qh ATinfinity)
+        extra= 1;
+    }
+  }
+  if (qh hull_dim <= 1) {
+    qh_fprintf(qh ferr, 6050, "qhull error: dimension %d must be > 1\n", qh hull_dim);
+    qh_errexit(qh_ERRinput, NULL, NULL);
+  }
+  for (k=2, factorial=1.0; k < qh hull_dim; k++)
+    factorial *= k;
+  qh AREAfactor= 1.0 / factorial;
+  trace2((qh ferr, 2005, "qh_initqhull_globals: initialize globals.  dim %d numpoints %d malloc? %d projected %d to hull_dim %d\n",
+        dim, numpoints, ismalloc, qh PROJECTinput, qh hull_dim));
+  qh normal_size= qh hull_dim * sizeof(coordT);
+  qh center_size= qh normal_size - sizeof(coordT);
+  pointsneeded= qh hull_dim+1;
+  if (qh hull_dim > qh_DIMmergeVertex) {
+    qh MERGEvertices= False;
+    qh_option("Q3-no-merge-vertices-dim-high", NULL, NULL);
+  }
+  if (qh GOODpoint)
+    pointsneeded++;
+#ifdef qh_NOtrace
+  if (qh IStracing) {
+    qh_fprintf(qh ferr, 6051, "qhull input error: tracing is not installed(qh_NOtrace in user.h)");
+    qh_errexit(qh_ERRqhull, NULL, NULL);
+  }
+#endif
+  if (qh RERUN > 1) {
+    qh TRACElastrun= qh IStracing; /* qh_build_withrestart duplicates next conditional */
+    if (qh IStracing != -1)
+      qh IStracing= 0;
+  }else if (qh TRACEpoint != qh_IDunknown || qh TRACEdist < REALmax/2 || qh TRACEmerge) {
+    qh TRACElevel= (qh IStracing? qh IStracing : 3);
+    qh IStracing= 0;
+  }
+  if (qh ROTATErandom == 0 || qh ROTATErandom == -1) {
+    seed= (int)time(&timedata);
+    if (qh ROTATErandom  == -1) {
+      seed= -seed;
+      qh_option("QRandom-seed", &seed, NULL );
+    }else
+      qh_option("QRotate-random", &seed, NULL);
+    qh ROTATErandom= seed;
+  }
+  seed= qh ROTATErandom;
+  if (seed == INT_MIN)    /* default value */
+    seed= 1;
+  else if (seed < 0)
+    seed= -seed;
+  qh_RANDOMseed_(seed);
+  randr= 0.0;
+  for (i=1000; i--; ) {
+    randi= qh_RANDOMint;
+    randr += randi;
+    if (randi > qh_RANDOMmax) {
+      qh_fprintf(qh ferr, 8036, "\
+qhull configuration error (qh_RANDOMmax in user.h):\n\
+   random integer %d > qh_RANDOMmax(%.8g)\n",
+               randi, qh_RANDOMmax);
+      qh_errexit(qh_ERRinput, NULL, NULL);
+    }
+  }
+  qh_RANDOMseed_(seed);
+  randr = randr/1000;
+  if (randr < qh_RANDOMmax * 0.1
+  || randr > qh_RANDOMmax * 0.9)
+    qh_fprintf(qh ferr, 8037, "\
+qhull configuration warning (qh_RANDOMmax in user.h):\n\
+   average of 1000 random integers (%.2g) is much different than expected (%.2g).\n\
+   Is qh_RANDOMmax (%.2g) wrong?\n",
+             randr, qh_RANDOMmax * 0.5, qh_RANDOMmax);
+  qh RANDOMa= 2.0 * qh RANDOMfactor/qh_RANDOMmax;
+  qh RANDOMb= 1.0 - qh RANDOMfactor;
+  if (qh_HASHfactor < 1.1) {
+    qh_fprintf(qh ferr, 6052, "qhull internal error (qh_initqhull_globals): qh_HASHfactor %d must be at least 1.1.  Qhull uses linear hash probing\n",
+      qh_HASHfactor);
+    qh_errexit(qh_ERRqhull, NULL, NULL);
+  }
+  if (numpoints+extra < pointsneeded) {
+    qh_fprintf(qh ferr, 6214, "qhull input error: not enough points(%d) to construct initial simplex (need %d)\n",
+            numpoints, pointsneeded);
+    qh_errexit(qh_ERRinput, NULL, NULL);
+  }
+  qh_initqhull_outputflags();
+} /* initqhull_globals */
+
+/*-<a                             href="qh-globa.htm#TOC"
+  >-------------------------------</a><a name="initqhull_mem">-</a>
+
+  qh_initqhull_mem(  )
+    initialize mem.c for qhull
+    qh.hull_dim and qh.normal_size determine some of the allocation sizes
+    if qh.MERGING,
+      includes ridgeT
+    calls qh_user_memsizes() to add up to 10 additional sizes for quick allocation
+      (see numsizes below)
+
+  returns:
+    mem.c already for qh_memalloc/qh_memfree (errors if called beforehand)
+
+  notes:
+    qh_produceoutput() prints memsizes
+
+*/
+void qh_initqhull_mem(void) {
+  int numsizes;
+  int i;
+
+  numsizes= 8+10;
+  qh_meminitbuffers(qh IStracing, qh_MEMalign, numsizes,
+                     qh_MEMbufsize,qh_MEMinitbuf);
+  qh_memsize((int)sizeof(vertexT));
+  if (qh MERGING) {
+    qh_memsize((int)sizeof(ridgeT));
+    qh_memsize((int)sizeof(mergeT));
+  }
+  qh_memsize((int)sizeof(facetT));
+  i= sizeof(setT) + (qh hull_dim - 1) * SETelemsize;  /* ridge.vertices */
+  qh_memsize(i);
+  qh_memsize(qh normal_size);        /* normal */
+  i += SETelemsize;                 /* facet.vertices, .ridges, .neighbors */
+  qh_memsize(i);
+  qh_user_memsizes();
+  qh_memsetup();
+} /* initqhull_mem */
+
+/*-<a                             href="qh-globa.htm#TOC"
+  >-------------------------------</a><a name="initqhull_outputflags">-</a>
+
+  qh_initqhull_outputflags
+    initialize flags concerned with output
+
+  returns:
+    adjust user flags as needed
+
+  see:
+    qh_clear_outputflags() resets the flags
+
+  design:
+    test for qh.PRINTgood (i.e., only print 'good' facets)
+    check for conflicting print output options
+*/
+void qh_initqhull_outputflags(void) {
+  boolT printgeom= False, printmath= False, printcoplanar= False;
+  int i;
+
+  trace3((qh ferr, 3024, "qh_initqhull_outputflags: %s\n", qh qhull_command));
+  if (!(qh PRINTgood || qh PRINTneighbors)) {
+    if (qh KEEParea || qh KEEPminArea < REALmax/2 || qh KEEPmerge || qh DELAUNAY
+        || (!qh ONLYgood && (qh GOODvertex || qh GOODpoint))) {
+      qh PRINTgood= True;
+      qh_option("Pgood", NULL, NULL);
+    }
+  }
+  if (qh PRINTtransparent) {
+    if (qh hull_dim != 4 || !qh DELAUNAY || qh VORONOI || qh DROPdim >= 0) {
+      qh_fprintf(qh ferr, 6215, "qhull input error: transparent Delaunay('Gt') needs 3-d Delaunay('d') w/o 'GDn'\n");
+      qh_errexit(qh_ERRinput, NULL, NULL);
+    }
+    qh DROPdim = 3;
+    qh PRINTridges = True;
+  }
+  for (i=qh_PRINTEND; i--; ) {
+    if (qh PRINTout[i] == qh_PRINTgeom)
+      printgeom= True;
+    else if (qh PRINTout[i] == qh_PRINTmathematica || qh PRINTout[i] == qh_PRINTmaple)
+      printmath= True;
+    else if (qh PRINTout[i] == qh_PRINTcoplanars)
+      printcoplanar= True;
+    else if (qh PRINTout[i] == qh_PRINTpointnearest)
+      printcoplanar= True;
+    else if (qh PRINTout[i] == qh_PRINTpointintersect && !qh HALFspace) {
+      qh_fprintf(qh ferr, 6053, "qhull input error: option 'Fp' is only used for \nhalfspace intersection('Hn,n,n').\n");
+      qh_errexit(qh_ERRinput, NULL, NULL);
+    }else if (qh PRINTout[i] == qh_PRINTtriangles && (qh HALFspace || qh VORONOI)) {
+      qh_fprintf(qh ferr, 6054, "qhull input error: option 'Ft' is not available for Voronoi vertices or halfspace intersection\n");
+      qh_errexit(qh_ERRinput, NULL, NULL);
+    }else if (qh PRINTout[i] == qh_PRINTcentrums && qh VORONOI) {
+      qh_fprintf(qh ferr, 6055, "qhull input error: option 'FC' is not available for Voronoi vertices('v')\n");
+      qh_errexit(qh_ERRinput, NULL, NULL);
+    }else if (qh PRINTout[i] == qh_PRINTvertices) {
+      if (qh VORONOI)
+        qh_option("Fvoronoi", NULL, NULL);
+      else
+        qh_option("Fvertices", NULL, NULL);
+    }
+  }
+  if (printcoplanar && qh DELAUNAY && qh JOGGLEmax < REALmax/2) {
+    if (qh PRINTprecision)
+      qh_fprintf(qh ferr, 7041, "qhull input warning: 'QJ' (joggle) will usually prevent coincident input sites for options 'Fc' and 'FP'\n");
+  }
+  if (printmath && (qh hull_dim > 3 || qh VORONOI)) {
+    qh_fprintf(qh ferr, 6056, "qhull input error: Mathematica and Maple output is only available for 2-d and 3-d convex hulls and 2-d Delaunay triangulations\n");
+    qh_errexit(qh_ERRinput, NULL, NULL);
+  }
+  if (printgeom) {
+    if (qh hull_dim > 4) {
+      qh_fprintf(qh ferr, 6057, "qhull input error: Geomview output is only available for 2-d, 3-d and 4-d\n");
+      qh_errexit(qh_ERRinput, NULL, NULL);
+    }
+    if (qh PRINTnoplanes && !(qh PRINTcoplanar + qh PRINTcentrums
+     + qh PRINTdots + qh PRINTspheres + qh DOintersections + qh PRINTridges)) {
+      qh_fprintf(qh ferr, 6058, "qhull input error: no output specified for Geomview\n");
+      qh_errexit(qh_ERRinput, NULL, NULL);
+    }
+    if (qh VORONOI && (qh hull_dim > 3 || qh DROPdim >= 0)) {
+      qh_fprintf(qh ferr, 6059, "qhull input error: Geomview output for Voronoi diagrams only for 2-d\n");
+      qh_errexit(qh_ERRinput, NULL, NULL);
+    }
+    /* can not warn about furthest-site Geomview output: no lower_threshold */
+    if (qh hull_dim == 4 && qh DROPdim == -1 &&
+        (qh PRINTcoplanar || qh PRINTspheres || qh PRINTcentrums)) {
+      qh_fprintf(qh ferr, 7042, "qhull input warning: coplanars, vertices, and centrums output not\n\
+available for 4-d output(ignored).  Could use 'GDn' instead.\n");
+      qh PRINTcoplanar= qh PRINTspheres= qh PRINTcentrums= False;
+    }
+  }
+  if (!qh KEEPcoplanar && !qh KEEPinside && !qh ONLYgood) {
+    if ((qh PRINTcoplanar && qh PRINTspheres) || printcoplanar) {
+      if (qh QHULLfinished) {
+        qh_fprintf(qh ferr, 7072, "qhull output warning: ignoring coplanar points, option 'Qc' was not set for the first run of qhull.\n");
+      }else {
+        qh KEEPcoplanar = True;
+        qh_option("Qcoplanar", NULL, NULL);
+      }
+    }
+  }
+  qh PRINTdim= qh hull_dim;
+  if (qh DROPdim >=0) {    /* after Geomview checks */
+    if (qh DROPdim < qh hull_dim) {
+      qh PRINTdim--;
+      if (!printgeom || qh hull_dim < 3)
+        qh_fprintf(qh ferr, 7043, "qhull input warning: drop dimension 'GD%d' is only available for 3-d/4-d Geomview\n", qh DROPdim);
+    }else
+      qh DROPdim= -1;
+  }else if (qh VORONOI) {
+    qh DROPdim= qh hull_dim-1;
+    qh PRINTdim= qh hull_dim-1;
+  }
+} /* qh_initqhull_outputflags */
+
+/*-<a                             href="qh-globa.htm#TOC"
+  >-------------------------------</a><a name="initqhull_start">-</a>
+
+  qh_initqhull_start( infile, outfile, errfile )
+    allocate memory if needed and call qh_initqhull_start2()
+*/
+void qh_initqhull_start(FILE *infile, FILE *outfile, FILE *errfile) {
+
+#if qh_QHpointer
+  if (qh_qh) {
+    qh_fprintf(errfile, 6205, "qhull error (qh_initqhull_start): qh_qh already defined.  Call qh_save_qhull() first\n");
+    qh_exit(qh_ERRqhull);  /* no error handler */
+  }
+  if (!(qh_qh= (qhT *)qh_malloc(sizeof(qhT)))) {
+    qh_fprintf(errfile, 6060, "qhull error (qh_initqhull_start): insufficient memory\n");
+    qh_exit(qh_ERRmem);  /* no error handler */
+  }
+#endif
+  qh_initstatistics();
+  qh_initqhull_start2(infile, outfile, errfile);
+} /* initqhull_start */
+
+/*-<a                             href="qh-globa.htm#TOC"
+  >-------------------------------</a><a name="initqhull_start2">-</a>
+
+  qh_initqhull_start2( infile, outfile, errfile )
+    start initialization of qhull
+    initialize statistics, stdio, default values for global variables
+    assumes qh_qh is defined
+  notes:
+    report errors elsewhere, error handling and g_qhull_output [Qhull.cpp, QhullQh()] not in initialized
+  see:
+    qh_maxmin() determines the precision constants
+    qh_freeqhull2()
+*/
+void qh_initqhull_start2(FILE *infile, FILE *outfile, FILE *errfile) {
+  time_t timedata;
+  int seed;
+
+  qh_CPUclock; /* start the clock(for qh_clock).  One-shot. */
+#if qh_QHpointer
+  memset((char *)qh_qh, 0, sizeof(qhT));   /* every field is 0, FALSE, NULL */
+#else
+  memset((char *)&qh_qh, 0, sizeof(qhT));
+#endif
+  qh ANGLEmerge= True;
+  qh DROPdim= -1;
+  qh ferr= errfile;
+  qh fin= infile;
+  qh fout= outfile;
+  qh furthest_id= qh_IDunknown;
+  qh JOGGLEmax= REALmax;
+  qh KEEPminArea = REALmax;
+  qh last_low= REALmax;
+  qh last_high= REALmax;
+  qh last_newhigh= REALmax;
+  qh max_outside= 0.0;
+  qh max_vertex= 0.0;
+  qh MAXabs_coord= 0.0;
+  qh MAXsumcoord= 0.0;
+  qh MAXwidth= -REALmax;
+  qh MERGEindependent= True;
+  qh MINdenom_1= fmax_(1.0/REALmax, REALmin); /* used by qh_scalepoints */
+  qh MINoutside= 0.0;
+  qh MINvisible= REALmax;
+  qh MAXcoplanar= REALmax;
+  qh outside_err= REALmax;
+  qh premerge_centrum= 0.0;
+  qh premerge_cos= REALmax;
+  qh PRINTprecision= True;
+  qh PRINTradius= 0.0;
+  qh postmerge_cos= REALmax;
+  qh postmerge_centrum= 0.0;
+  qh ROTATErandom= INT_MIN;
+  qh MERGEvertices= True;
+  qh totarea= 0.0;
+  qh totvol= 0.0;
+  qh TRACEdist= REALmax;
+  qh TRACEpoint= qh_IDunknown; /* recompile or use 'TPn' */
+  qh tracefacet_id= UINT_MAX;  /* recompile to trace a facet */
+  qh tracevertex_id= UINT_MAX; /* recompile to trace a vertex */
+  seed= (int)time(&timedata);
+  qh_RANDOMseed_(seed);
+  qh run_id= qh_RANDOMint;
+  if(!qh run_id)
+      qh run_id++;  /* guarantee non-zero */
+  qh_option("run-id", &qh run_id, NULL);
+  strcat(qh qhull, "qhull");
+} /* initqhull_start2 */
+
+/*-<a                             href="qh-globa.htm#TOC"
+  >-------------------------------</a><a name="initthresholds">-</a>
+
+  qh_initthresholds( commandString )
+    set thresholds for printing and scaling from commandString
+
+  returns:
+    sets qh.GOODthreshold or qh.SPLITthreshold if 'Pd0D1' used
+
+  see:
+    qh_initflags(), 'Qbk' 'QBk' 'Pdk' and 'PDk'
+    qh_inthresholds()
+
+  design:
+    for each 'Pdn' or 'PDn' option
+      check syntax
+      set qh.lower_threshold or qh.upper_threshold
+    set qh.GOODthreshold if an unbounded threshold is used
+    set qh.SPLITthreshold if a bounded threshold is used
+*/
+void qh_initthresholds(char *command) {
+  realT value;
+  int idx, maxdim, k;
+  char *s= command; /* non-const due to strtol */
+  char key;
+
+  maxdim= qh input_dim;
+  if (qh DELAUNAY && (qh PROJECTdelaunay || qh PROJECTinput))
+    maxdim++;
+  while (*s) {
+    if (*s == '-')
+      s++;
+    if (*s == 'P') {
+      s++;
+      while (*s && !isspace(key= *s++)) {
+        if (key == 'd' || key == 'D') {
+          if (!isdigit(*s)) {
+            qh_fprintf(qh ferr, 7044, "qhull warning: no dimension given for Print option '%c' at: %s.  Ignored\n",
+                    key, s-1);
+            continue;
+          }
+          idx= qh_strtol(s, &s);
+          if (idx >= qh hull_dim) {
+            qh_fprintf(qh ferr, 7045, "qhull warning: dimension %d for Print option '%c' is >= %d.  Ignored\n",
+                idx, key, qh hull_dim);
+            continue;
+          }
+          if (*s == ':') {
+            s++;
+            value= qh_strtod(s, &s);
+            if (fabs((double)value) > 1.0) {
+              qh_fprintf(qh ferr, 7046, "qhull warning: value %2.4g for Print option %c is > +1 or < -1.  Ignored\n",
+                      value, key);
+              continue;
+            }
+          }else
+            value= 0.0;
+          if (key == 'd')
+            qh lower_threshold[idx]= value;
+          else
+            qh upper_threshold[idx]= value;
+        }
+      }
+    }else if (*s == 'Q') {
+      s++;
+      while (*s && !isspace(key= *s++)) {
+        if (key == 'b' && *s == 'B') {
+          s++;
+          for (k=maxdim; k--; ) {
+            qh lower_bound[k]= -qh_DEFAULTbox;
+            qh upper_bound[k]= qh_DEFAULTbox;
+          }
+        }else if (key == 'b' && *s == 'b')
+          s++;
+        else if (key == 'b' || key == 'B') {
+          if (!isdigit(*s)) {
+            qh_fprintf(qh ferr, 7047, "qhull warning: no dimension given for Qhull option %c.  Ignored\n",
+                    key);
+            continue;
+          }
+          idx= qh_strtol(s, &s);
+          if (idx >= maxdim) {
+            qh_fprintf(qh ferr, 7048, "qhull warning: dimension %d for Qhull option %c is >= %d.  Ignored\n",
+                idx, key, maxdim);
+            continue;
+          }
+          if (*s == ':') {
+            s++;
+            value= qh_strtod(s, &s);
+          }else if (key == 'b')
+            value= -qh_DEFAULTbox;
+          else
+            value= qh_DEFAULTbox;
+          if (key == 'b')
+            qh lower_bound[idx]= value;
+          else
+            qh upper_bound[idx]= value;
+        }
+      }
+    }else {
+      while (*s && !isspace(*s))
+        s++;
+    }
+    while (isspace(*s))
+      s++;
+  }
+  for (k=qh hull_dim; k--; ) {
+    if (qh lower_threshold[k] > -REALmax/2) {
+      qh GOODthreshold= True;
+      if (qh upper_threshold[k] < REALmax/2) {
+        qh SPLITthresholds= True;
+        qh GOODthreshold= False;
+        break;
+      }
+    }else if (qh upper_threshold[k] < REALmax/2)
+      qh GOODthreshold= True;
+  }
+} /* initthresholds */
+
+/*-<a                             href="qh-globa.htm#TOC"
+  >-------------------------------</a><a name="lib_check">-</a>
+
+  qh_lib_check( qhullLibraryType, qhTsize, vertexTsize, ridgeTsize, facetTsize, setTsize, qhmemTsize )
+    Report error if library does not agree with caller
+
+  notes:
+    NOerrors -- qh_lib_check can not call qh_errexit()
+*/
+void qh_lib_check(int qhullLibraryType, int qhTsize, int vertexTsize, int ridgeTsize, int facetTsize, int setTsize, int qhmemTsize) {
+    boolT iserror= False;
+
+#if defined(_MSC_VER) && defined(_DEBUG) && defined(QHULL_CRTDBG)  /* user_r.h */
+    // _CrtSetBreakAlloc(744);  /* Break at memalloc {744}, or 'watch' _crtBreakAlloc */
+    _CrtSetDbgFlag( _CRTDBG_ALLOC_MEM_DF | _CRTDBG_DELAY_FREE_MEM_DF | _CRTDBG_LEAK_CHECK_DF | _CrtSetDbgFlag(_CRTDBG_REPORT_FLAG) );
+    _CrtSetReportMode( _CRT_ERROR, _CRTDBG_MODE_FILE | _CRTDBG_MODE_DEBUG );
+    _CrtSetReportFile( _CRT_ERROR, _CRTDBG_FILE_STDERR );
+    _CrtSetReportMode( _CRT_WARN, _CRTDBG_MODE_FILE | _CRTDBG_MODE_DEBUG );
+    _CrtSetReportFile( _CRT_WARN, _CRTDBG_FILE_STDERR );
+    _CrtSetReportMode( _CRT_ASSERT, _CRTDBG_MODE_FILE | _CRTDBG_MODE_DEBUG );
+    _CrtSetReportFile( _CRT_ASSERT, _CRTDBG_FILE_STDERR );
+#endif
+
+    if (qhullLibraryType==QHULL_NON_REENTRANT) { /* 0 */
+        if (qh_QHpointer) {
+            qh_fprintf_stderr(6246, "qh_lib_check: Incorrect qhull library called.  Caller uses a static qhT while library uses a dynamic qhT via qh_QHpointer.  Both caller and library are non-reentrant.\n");
+            iserror= True;
+        }
+    }else if (qhullLibraryType==QHULL_QH_POINTER) { /* 1 */
+        if (!qh_QHpointer) {
+            qh_fprintf_stderr(6247, "qh_lib_check: Incorrect qhull library called.  Caller uses a dynamic qhT via qh_QHpointer while library uses a static qhT.  Both caller and library are non-reentrant.\n");
+            iserror= True;
+        }
+    }else if (qhullLibraryType==QHULL_REENTRANT) { /* 2 */
+        qh_fprintf_stderr(6248, "qh_lib_check: Incorrect qhull library called.  Caller uses reentrant Qhull while library is non-reentrant\n");
+        iserror= True;
+    }else{
+        qh_fprintf_stderr(6262, "qh_lib_check: Expecting qhullLibraryType QHULL_NON_REENTRANT(0), QHULL_QH_POINTER(1), or QHULL_REENTRANT(2).  Got %d\n", qhullLibraryType);
+        iserror= True;
+    }
+    if (qhTsize != sizeof(qhT)) {
+        qh_fprintf_stderr(6249, "qh_lib_check: Incorrect qhull library called.  Size of qhT for caller is %d, but for library is %d.\n", qhTsize, sizeof(qhT));
+        iserror= True;
+    }
+    if (vertexTsize != sizeof(vertexT)) {
+        qh_fprintf_stderr(6250, "qh_lib_check: Incorrect qhull library called.  Size of vertexT for caller is %d, but for library is %d.\n", vertexTsize, sizeof(vertexT));
+        iserror= True;
+    }
+    if (ridgeTsize != sizeof(ridgeT)) {
+        qh_fprintf_stderr(6251, "qh_lib_check: Incorrect qhull library called.  Size of ridgeT for caller is %d, but for library is %d.\n", ridgeTsize, sizeof(ridgeT));
+        iserror= True;
+    }
+    if (facetTsize != sizeof(facetT)) {
+        qh_fprintf_stderr(6252, "qh_lib_check: Incorrect qhull library called.  Size of facetT for caller is %d, but for library is %d.\n", facetTsize, sizeof(facetT));
+        iserror= True;
+    }
+    if (setTsize && setTsize != sizeof(setT)) {
+        qh_fprintf_stderr(6253, "qh_lib_check: Incorrect qhull library called.  Size of setT for caller is %d, but for library is %d.\n", setTsize, sizeof(setT));
+        iserror= True;
+    }
+    if (qhmemTsize && qhmemTsize != sizeof(qhmemT)) {
+        qh_fprintf_stderr(6254, "qh_lib_check: Incorrect qhull library called.  Size of qhmemT for caller is %d, but for library is %d.\n", qhmemTsize, sizeof(qhmemT));
+        iserror= True;
+    }
+    if (iserror) {
+        if(qh_QHpointer){
+            qh_fprintf_stderr(6255, "qh_lib_check: Cannot continue.  Library '%s' uses a dynamic qhT via qh_QHpointer (e.g., qhull_p.so)\n", qh_version2);
+        }else{
+            qh_fprintf_stderr(6256, "qh_lib_check: Cannot continue.  Library '%s' uses a static qhT (e.g., libqhull.so)\n", qh_version2);
+        }
+        qh_exit(qh_ERRqhull);  /* can not use qh_errexit() */
+    }
+} /* lib_check */
+
+/*-<a                             href="qh-globa.htm#TOC"
+  >-------------------------------</a><a name="option">-</a>
+
+  qh_option( option, intVal, realVal )
+    add an option description to qh.qhull_options
+
+  notes:
+    NOerrors -- qh_option can not call qh_errexit() [qh_initqhull_start2]
+    will be printed with statistics ('Ts') and errors
+    strlen(option) < 40
+*/
+void qh_option(const char *option, int *i, realT *r) {
+  char buf[200];
+  int len, maxlen;
+
+  sprintf(buf, "  %s", option);
+  if (i)
+    sprintf(buf+strlen(buf), " %d", *i);
+  if (r)
+    sprintf(buf+strlen(buf), " %2.2g", *r);
+  len= (int)strlen(buf);  /* WARN64 */
+  qh qhull_optionlen += len;
+  maxlen= sizeof(qh qhull_options) - len -1;
+  maximize_(maxlen, 0);
+  if (qh qhull_optionlen >= qh_OPTIONline && maxlen > 0) {
+    qh qhull_optionlen= len;
+    strncat(qh qhull_options, "\n", (size_t)(maxlen--));
+  }
+  strncat(qh qhull_options, buf, (size_t)maxlen);
+} /* option */
+
+#if qh_QHpointer
+/*-<a                             href="qh-globa.htm#TOC"
+  >-------------------------------</a><a name="restore_qhull">-</a>
+
+  qh_restore_qhull( oldqh )
+    restores a previously saved qhull
+    also restores qh_qhstat and qhmem.tempstack
+    Sets *oldqh to NULL
+  notes:
+    errors if current qhull hasn't been saved or freed
+    uses qhmem for error reporting
+
+  NOTE 1998/5/11:
+    Freeing memory after qh_save_qhull and qh_restore_qhull
+    is complicated.  The procedures will be redesigned.
+
+  see:
+    qh_save_qhull(), UsingLibQhull
+*/
+void qh_restore_qhull(qhT **oldqh) {
+
+  if (*oldqh && strcmp((*oldqh)->qhull, "qhull")) {
+    qh_fprintf(qhmem.ferr, 6061, "qhull internal error (qh_restore_qhull): %p is not a qhull data structure\n",
+                  *oldqh);
+    qh_errexit(qh_ERRqhull, NULL, NULL);
+  }
+  if (qh_qh) {
+    qh_fprintf(qhmem.ferr, 6062, "qhull internal error (qh_restore_qhull): did not save or free existing qhull\n");
+    qh_errexit(qh_ERRqhull, NULL, NULL);
+  }
+  if (!*oldqh || !(*oldqh)->old_qhstat) {
+    qh_fprintf(qhmem.ferr, 6063, "qhull internal error (qh_restore_qhull): did not previously save qhull %p\n",
+                  *oldqh);
+    qh_errexit(qh_ERRqhull, NULL, NULL);
+  }
+  qh_qh= *oldqh;
+  *oldqh= NULL;
+  qh_qhstat= qh old_qhstat;
+  qhmem.tempstack= qh old_tempstack;
+  qh old_qhstat= 0;
+  qh old_tempstack= 0;
+  trace1((qh ferr, 1007, "qh_restore_qhull: restored qhull from %p\n", *oldqh));
+} /* restore_qhull */
+
+/*-<a                             href="qh-globa.htm#TOC"
+  >-------------------------------</a><a name="save_qhull">-</a>
+
+  qh_save_qhull(  )
+    saves qhull for a later qh_restore_qhull
+    also saves qh_qhstat and qhmem.tempstack
+
+  returns:
+    qh_qh=NULL
+
+  notes:
+    need to initialize qhull or call qh_restore_qhull before continuing
+
+  NOTE 1998/5/11:
+    Freeing memory after qh_save_qhull and qh_restore_qhull
+    is complicated.  The procedures will be redesigned.
+
+  see:
+    qh_restore_qhull()
+*/
+qhT *qh_save_qhull(void) {
+  qhT *oldqh;
+
+  trace1((qhmem.ferr, 1045, "qh_save_qhull: save qhull %p\n", qh_qh));
+  if (!qh_qh) {
+    qh_fprintf(qhmem.ferr, 6064, "qhull internal error (qh_save_qhull): qhull not initialized\n");
+    qh_errexit(qh_ERRqhull, NULL, NULL);
+  }
+  qh old_qhstat= qh_qhstat;
+  qh_qhstat= NULL;
+  qh old_tempstack= qhmem.tempstack;
+  qhmem.tempstack= NULL;
+  oldqh= qh_qh;
+  qh_qh= NULL;
+  return oldqh;
+} /* save_qhull */
+
+#endif
+
diff --git a/xs/src/qhull/src/libqhull/index.htm b/xs/src/qhull/src/libqhull/index.htm
new file mode 100644
index 0000000000..62b9d99701
--- /dev/null
+++ b/xs/src/qhull/src/libqhull/index.htm
@@ -0,0 +1,264 @@
+<!-- Do not edit with Front Page, it adds too many spaces -->
+<html>
+<head>
+<meta http-equiv="Content-Type"
+content="text/html; charset=iso-8859-1">
+<title>Qhull functions, macros, and data structures</title>
+</head>
+
+<body>
+<!-- Navigation links -->
+<p><a name="TOP"><b>Up:</b></a> <a
+href="http://www.qhull.org">Home page</a> for Qhull<br>
+<b>Up:</b> <a href="../../html/index.htm#TOC">Qhull manual</a>: Table of Contents <br>
+<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a>
+&#149; <a href="../../html/qh-quick.htm#options">Options</a>
+&#149; <a href="../../html/qh-opto.htm#output">Output</a>
+&#149; <a href="../../html/qh-optf.htm#format">Formats</a>
+&#149; <a href="../../html/qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="../../html/qh-optp.htm#print">Print</a>
+&#149; <a href="../../html/qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="../../html/qh-optc.htm#prec">Precision</a>
+&#149; <a href="../../html/qh-optt.htm#trace">Trace</a>
+&#149; <a href="index.htm">Functions</a><br>
+<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code</a><br>
+<b>To:</b> <a href="#TOC">Qhull files</a><br>
+<b>To:</b> <a href="qh-geom.htm">Geom</a> &#149; <a href="qh-globa.htm">Global</a>
+&#149; <a href="qh-io.htm">Io</a> &#149; <a href="qh-mem.htm">Mem</a>
+&#149; <a href="qh-merge.htm">Merge</a> &#149; <a href="qh-poly.htm">Poly</a>
+&#149; <a href="qh-qhull.htm">Qhull</a> &#149; <a href="qh-set.htm">Set</a>
+&#149; <a href="qh-stat.htm">Stat</a> &#149; <a href="qh-user.htm">User</a>
+
+<hr>
+<!-- Main text of document. -->
+
+<h1>Qhull functions, macros, and data structures</h1>
+<blockquote>
+<p>The following sections provide an overview and index to
+Qhull's functions, macros, and data structures.
+Each section starts with an introduction.
+See also <a href=../../html/qh-code.htm#library>Calling
+Qhull from C programs</a> and <a href="../../html/qh-code.htm#cpp">Calling Qhull from C++ programs</a>.</p>
+
+<p>Qhull uses the following conventions:</p>
+<blockquote>
+
+<ul>
+<li>in code, global variables start with &quot;qh &quot;
+<li>in documentation, global variables start with 'qh.'
+<li>constants start with an upper case word
+<li>important globals include an '_'
+<li>functions, macros, and constants start with &quot;qh_&quot;</li>
+<li>data types end in &quot;T&quot;</li>
+<li>macros with arguments end in &quot;_&quot;</li>
+<li>iterators are macros that use local variables</li>
+<li>iterators for sets start with &quot;FOREACH&quot;</li>
+<li>iterators for lists start with &quot;FORALL&quot;</li>
+<li>qhull options are in single quotes (e.g., 'Pdn')</li>
+<li>lists are sorted alphabetically</li>
+<li>preprocessor directives on left margin for older compilers</li>
+</ul>
+</blockquote>
+<p>
+When reading the code, please note that the
+global data structure, 'qh', is a macro.  It
+either expands to &quot;qh_qh.&quot; or to
+&quot;qh_qh-&gt;&quot;. The later is used for
+applications which run concurrent calls to qh_qhull().
+<p>
+When reading code with an editor, a search for
+'<i>&quot;function</i>'
+will locate the header of <i>qh_function</i>.  A search for '<i>* function</i>'
+will locate the tail of <i>qh_function</i>.
+
+<p>A useful starting point is <a href="libqhull.h">libqhull.h</a>.  It defines most
+of Qhull data structures and top-level functions.  Search for <i>'PFn'</i> to
+determine the corresponding constant in Qhull.  Search for <i>'Fp'</i> to
+determine the corresponding <a href="libqhull.h#qh_PRINT">qh_PRINT...</a> constant.
+Search <a href="io.c">io.c</a> to learn how the print function is implemented.</p>
+
+<p>If your web browser is configured for .c and .h files, the function, macro, and data type links
+go to the corresponding source location.  To configure your web browser for .c and .h files.
+<ul>
+<li>In the Download Preferences or Options panel, add file extensions 'c' and 'h' to mime type 'text/html'.
+<li>Opera 12.10
+<ol>
+<li>In Tools > Preferences > Advanced > Downloads
+<li>Uncheck 'Hide file types opened with Opera'
+<li>Quick find 'html'
+<li>Select 'text/html' > Edit
+<li>Add File extensions 'c,h,'
+<li>Click 'OK'
+</ol>
+<li>Internet Explorer -- Mime types are not available from 'Internet Options'.    Is there a registry key for these settings?
+<li>Firefox -- Mime types are not available from 'Preferences'.  Is there an add-on to change the file extensions for a mime type?
+<li>Chrome -- Can Chrome be configured?
+</ul>
+
+<p>
+Please report documentation and link errors
+to <a href="mailto:qhull-bug@qhull.org">qhull-bug@qhull.org</a>.
+</blockquote>
+
+<p><b>Copyright &copy; 1997-2015 C.B. Barber</b></p>
+
+<hr>
+
+<h2><a href="#TOP">&#187;</a><a name="TOC">Qhull files</a> </h2>
+<blockquote>
+
+<p>This sections lists the .c and .h files for Qhull. Please
+refer to these files for detailed information.</p>
+<blockquote>
+
+<dl>
+<dt><a href="../../Makefile"><b>Makefile</b></a><b>, </b><a href="../../CMakeLists.txt"><b>CMakeLists.txt</b></a></dt>
+<dd><tt>Makefile</tt> is preconfigured for gcc.  <tt>CMakeLists.txt</tt> supports multiple
+platforms with <a href=http://www.cmake.org/>CMake</a>.
+Qhull includes project files for Visual Studio and Qt.
+</dd>
+
+<dt>&nbsp;</dt>
+<dt><a href="libqhull.h"><b>libqhull.h</b></a> </dt>
+<dd>Include file for the Qhull library (<tt>libqhull.so</tt>, <tt>qhull.dll</tt>, <tt>libqhullstatic.a</tt>).
+Data structures are documented under <a href="qh-poly.htm">Poly</a>.
+Global variables are documented under <a href="qh-globa.htm">Global</a>.
+Other data structures and variables are documented under
+<a href="qh-qhull.htm#TOC">Qhull</a> or <a href="qh-geom.htm"><b>Geom</b></a><b>.</b></dd>
+
+<dt>&nbsp;</dt>
+<dt><a href="qh-geom.htm"><b>Geom</b></a><b>, </b>
+<a href="geom.h"><b>geom.h</b></a><b>, </b>
+<a href="geom.c"><b>geom.c</b></a><b>, </b>
+<a href="geom2.c"><b>geom2.c</b></a><b>, </b>
+<a href="random.c"><b>random.c</b></a><b>, </b>
+<a href="random.h"><b>random.h</b></a></dt>
+<dd>Geometric routines. These routines implement mathematical
+functions such as Gaussian elimination and geometric
+routines needed for Qhull. Frequently used routines are
+in <tt>geom.c</tt> while infrequent ones are in <tt>geom2.c</tt>.
+</dd>
+
+<dt>&nbsp;</dt>
+<dt><a href="qh-globa.htm"><b>Global</b></a><b>, </b>
+<a href="global.c"><b>global.c</b></a><b>, </b>
+<a href="libqhull.h"><b>libqhull.h</b></a> </dt>
+<dd>Global routines. Qhull uses a global data structure, <tt>qh</tt>,
+to store globally defined constants, lists, sets, and
+variables.
+<tt>global.c</tt> initializes and frees these
+structures. </dd>
+
+<dt>&nbsp;</dt>
+<dt><a href="qh-io.htm"><b>Io</b></a><b>, </b><a href="io.h"><b>io.h</b></a><b>,
+</b><a href="io.c"><b>io.c</b></a> </dt>
+<dd>Input and output routines. Qhull provides a wide range of
+input and output options.</dd>
+
+<dt>&nbsp;</dt>
+<dt><a href="qh-mem.htm"><b>Mem</b></a><b>, </b>
+<a href="mem.h"><b>mem.h</b></a><b>, </b>
+<a href="mem.c"><b>mem.c</b></a> </dt>
+<dd>Memory routines. Qhull provides memory allocation and
+deallocation. It uses quick-fit allocation.</dd>
+
+<dt>&nbsp;</dt>
+<dt><a href="qh-merge.htm"><b>Merge</b></a><b>, </b>
+<a href="merge.h"><b>merge.h</b></a><b>, </b>
+<a href="merge.c"><b>merge.c</b></a> </dt>
+<dd>Merge routines. Qhull handles precision problems by
+merged facets or joggled input. These routines merge simplicial facets,
+merge non-simplicial facets, merge cycles of facets, and
+rename redundant vertices.</dd>
+
+<dt>&nbsp;</dt>
+<dt><a href="qh-poly.htm"><b>Poly</b></a><b>, </b>
+<a href="poly.h"><b>poly.h</b></a><b>, </b>
+<a href="poly.c"><b>poly.c</b></a><b>, </b>
+<a href="poly2.c"><b>poly2.c</b></a><b>, </b>
+<a href="libqhull.h"><b>libqhull.h</b></a> </dt>
+<dd>Polyhedral routines. Qhull produces a polyhedron as a
+list of facets with vertices, neighbors, ridges, and
+geometric information. <tt>libqhull.h</tt> defines the main
+data structures. Frequently used routines are in <tt>poly.c</tt>
+while infrequent ones are in <tt>poly2.c</tt>.</dd>
+
+<dt>&nbsp;</dt>
+<dt><a href="qh-qhull.htm#TOC"><b>Qhull</b></a><b>, </b>
+<a href="libqhull.c"><b>libqhull.c</b></a><b>, </b>
+<a href="libqhull.h"><b>libqhull.h</b></a><b>, </b>
+<a href="qhull_a.h"><b>qhull_a.h</b></a><b>, </b>
+<a href="../qhullo/unix.c"><b>unix.c</b></a> <b>, </b>
+<a href="../qconvex/qconvex.c"><b>qconvex.c</b></a> <b>, </b>
+<a href="../qdelaunay/qdelaun.c"><b>qdelaun.c</b></a> <b>, </b>
+<a href="../qhalf/qhalf.c"><b>qhalf.c</b></a> <b>, </b>
+<a href="../qvoronoi/qvoronoi.c"><b>qvoronoi.c</b></a> </dt>
+<dd>Top-level routines. The Quickhull algorithm is
+implemented by <tt>libqhull.c</tt>. <tt>qhull_a.h</tt>
+includes all header files. </dd>
+
+<dt>&nbsp;</dt>
+<dt><a href="qh-set.htm"><b>Set</b></a><b>, </b>
+<a href="qset.h"><b>qset.h</b></a><b>, </b>
+<a href="qset.c"><b>qset.c</b></a> </dt>
+<dd>Set routines. Qhull implements its data structures as
+sets. A set is an array of pointers that is expanded as
+needed. This is a separate package that may be used in
+other applications. </dd>
+
+<dt>&nbsp;</dt>
+<dt><a href="qh-stat.htm"><b>Stat</b></a><b>, </b>
+<a href="stat.h"><b>stat.h</b></a><b>, </b>
+<a href="stat.c"><b>stat.c</b></a> </dt>
+<dd>Statistical routines. Qhull maintains statistics about
+its implementation. </dd>
+
+<dt>&nbsp;</dt>
+<dt><a href="qh-user.htm"><b>User</b></a><b>, </b>
+<a href="user.h"><b>user.h</b></a><b>, </b>
+<a href="user.c"><b>user.c</b></a><b>, </b>
+<a href="../user_eg/user_eg.c"><b>user_eg.c</b></a><b>, </b>
+<a href="../user_eg2/user_eg2.c"><b>user_eg2.c</b></a><b>, </b>
+</dt>
+<dd>User-defined routines. Qhull allows the user to configure
+the code with defined constants and specialized routines.
+</dd>
+</dl>
+</blockquote>
+
+</blockquote>
+<p><!-- Navigation links --> </p>
+<hr>
+<p><b>Up:</b>
+<a href="http://www.qhull.org">Home page for
+Qhull</a> <br>
+<b>Up:</b> <a href="../../html/index.htm#TOC">Qhull manual: Table of Contents</a> <br>
+<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a>
+&#149; <a href="../../html/qh-quick.htm#options">Options</a>
+&#149; <a href="../../html/qh-opto.htm#output">Output</a>
+&#149; <a href="../../html/qh-optf.htm#format">Formats</a>
+&#149; <a href="../../html/qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="../../html/qh-optp.htm#print">Print</a>
+&#149; <a href="../../html/qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="../../html/qh-optc.htm#prec">Precision</a>
+&#149; <a href="../../html/qh-optt.htm#trace">Trace</a>
+&#149; <a href="index.htm">Functions</a><br>
+<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code: Table of Contents</a> <br>
+<b>To:</b> <a href="#TOC">Qhull files</a><br>
+<b>To:</b> <a href="qh-geom.htm">Geom</a> &#149;
+<a href="qh-globa.htm">Global</a> &#149; <a href="qh-io.htm">Io</a>
+&#149; <a href="qh-mem.htm">Mem</a> &#149; <a href="qh-merge.htm">Merge</a>
+&#149; <a href="qh-poly.htm">Poly</a> &#149; <a href="qh-qhull.htm#TOC">Qhull</a>
+&#149; <a href="qh-set.htm">Set</a> &#149; <a href="qh-stat.htm">Stat</a>
+&#149; <a href="qh-user.htm">User</a><br>
+
+<p><!-- GC common information --> </p>
+<hr>
+<p><a href="http://www.geom.uiuc.edu/"><img
+src="../../html/qh--geom.gif" align="middle" width="40" height="40"></a><i>The
+Geometry Center Home Page </i></p>
+<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
+</a><br>
+Created: May 2, 1997 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
+</body>
+</html>
diff --git a/xs/src/qhull/src/libqhull/io.c b/xs/src/qhull/src/libqhull/io.c
new file mode 100644
index 0000000000..401987ec08
--- /dev/null
+++ b/xs/src/qhull/src/libqhull/io.c
@@ -0,0 +1,4062 @@
+/*<html><pre>  -<a                             href="qh-io.htm"
+  >-------------------------------</a><a name="TOP">-</a>
+
+   io.c
+   Input/Output routines of qhull application
+
+   see qh-io.htm and io.h
+
+   see user.c for qh_errprint and qh_printfacetlist
+
+   unix.c calls qh_readpoints and qh_produce_output
+
+   unix.c and user.c are the only callers of io.c functions
+   This allows the user to avoid loading io.o from qhull.a
+
+   Copyright (c) 1993-2015 The Geometry Center.
+   $Id: //main/2015/qhull/src/libqhull/io.c#5 $$Change: 2064 $
+   $DateTime: 2016/01/18 12:36:08 $$Author: bbarber $
+*/
+
+#include "qhull_a.h"
+
+/*========= -functions in alphabetical order after qh_produce_output()  =====*/
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="produce_output">-</a>
+
+  qh_produce_output()
+  qh_produce_output2()
+    prints out the result of qhull in desired format
+    qh_produce_output2() does not call qh_prepare_output()
+    if qh.GETarea
+      computes and prints area and volume
+    qh.PRINTout[] is an array of output formats
+
+  notes:
+    prints output in qh.PRINTout order
+*/
+void qh_produce_output(void) {
+    int tempsize= qh_setsize(qhmem.tempstack);
+
+    qh_prepare_output();
+    qh_produce_output2();
+    if (qh_setsize(qhmem.tempstack) != tempsize) {
+        qh_fprintf(qh ferr, 6206, "qhull internal error (qh_produce_output): temporary sets not empty(%d)\n",
+            qh_setsize(qhmem.tempstack));
+        qh_errexit(qh_ERRqhull, NULL, NULL);
+    }
+} /* produce_output */
+
+
+void qh_produce_output2(void) {
+  int i, tempsize= qh_setsize(qhmem.tempstack), d_1;
+
+  if (qh PRINTsummary)
+    qh_printsummary(qh ferr);
+  else if (qh PRINTout[0] == qh_PRINTnone)
+    qh_printsummary(qh fout);
+  for (i=0; i < qh_PRINTEND; i++)
+    qh_printfacets(qh fout, qh PRINTout[i], qh facet_list, NULL, !qh_ALL);
+  qh_allstatistics();
+  if (qh PRINTprecision && !qh MERGING && (qh JOGGLEmax > REALmax/2 || qh RERUN))
+    qh_printstats(qh ferr, qhstat precision, NULL);
+  if (qh VERIFYoutput && (zzval_(Zridge) > 0 || zzval_(Zridgemid) > 0))
+    qh_printstats(qh ferr, qhstat vridges, NULL);
+  if (qh PRINTstatistics) {
+    qh_printstatistics(qh ferr, "");
+    qh_memstatistics(qh ferr);
+    d_1= sizeof(setT) + (qh hull_dim - 1) * SETelemsize;
+    qh_fprintf(qh ferr, 8040, "\
+    size in bytes: merge %d ridge %d vertex %d facet %d\n\
+         normal %d ridge vertices %d facet vertices or neighbors %d\n",
+            (int)sizeof(mergeT), (int)sizeof(ridgeT),
+            (int)sizeof(vertexT), (int)sizeof(facetT),
+            qh normal_size, d_1, d_1 + SETelemsize);
+  }
+  if (qh_setsize(qhmem.tempstack) != tempsize) {
+    qh_fprintf(qh ferr, 6065, "qhull internal error (qh_produce_output2): temporary sets not empty(%d)\n",
+             qh_setsize(qhmem.tempstack));
+    qh_errexit(qh_ERRqhull, NULL, NULL);
+  }
+} /* produce_output2 */
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="dfacet">-</a>
+
+  qh_dfacet( id )
+    print facet by id, for debugging
+
+*/
+void qh_dfacet(unsigned id) {
+  facetT *facet;
+
+  FORALLfacets {
+    if (facet->id == id) {
+      qh_printfacet(qh fout, facet);
+      break;
+    }
+  }
+} /* dfacet */
+
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="dvertex">-</a>
+
+  qh_dvertex( id )
+    print vertex by id, for debugging
+*/
+void qh_dvertex(unsigned id) {
+  vertexT *vertex;
+
+  FORALLvertices {
+    if (vertex->id == id) {
+      qh_printvertex(qh fout, vertex);
+      break;
+    }
+  }
+} /* dvertex */
+
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="compare_facetarea">-</a>
+
+  qh_compare_facetarea( p1, p2 )
+    used by qsort() to order facets by area
+*/
+int qh_compare_facetarea(const void *p1, const void *p2) {
+  const facetT *a= *((facetT *const*)p1), *b= *((facetT *const*)p2);
+
+  if (!a->isarea)
+    return -1;
+  if (!b->isarea)
+    return 1;
+  if (a->f.area > b->f.area)
+    return 1;
+  else if (a->f.area == b->f.area)
+    return 0;
+  return -1;
+} /* compare_facetarea */
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="compare_facetmerge">-</a>
+
+  qh_compare_facetmerge( p1, p2 )
+    used by qsort() to order facets by number of merges
+*/
+int qh_compare_facetmerge(const void *p1, const void *p2) {
+  const facetT *a= *((facetT *const*)p1), *b= *((facetT *const*)p2);
+
+  return(a->nummerge - b->nummerge);
+} /* compare_facetvisit */
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="compare_facetvisit">-</a>
+
+  qh_compare_facetvisit( p1, p2 )
+    used by qsort() to order facets by visit id or id
+*/
+int qh_compare_facetvisit(const void *p1, const void *p2) {
+  const facetT *a= *((facetT *const*)p1), *b= *((facetT *const*)p2);
+  int i,j;
+
+  if (!(i= a->visitid))
+    i= 0 - a->id; /* do not convert to int, sign distinguishes id from visitid */
+  if (!(j= b->visitid))
+    j= 0 - b->id;
+  return(i - j);
+} /* compare_facetvisit */
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="compare_vertexpoint">-</a>
+
+  qh_compare_vertexpoint( p1, p2 )
+    used by qsort() to order vertices by point id
+
+  Not used.  Not available in libqhull_r.h since qh_pointid depends on qh
+*/
+int qh_compare_vertexpoint(const void *p1, const void *p2) {
+  const vertexT *a= *((vertexT *const*)p1), *b= *((vertexT *const*)p2);
+
+  return((qh_pointid(a->point) > qh_pointid(b->point)?1:-1));
+} /* compare_vertexpoint */
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="copyfilename">-</a>
+
+  qh_copyfilename( dest, size, source, length )
+    copy filename identified by qh_skipfilename()
+
+  notes:
+    see qh_skipfilename() for syntax
+*/
+void qh_copyfilename(char *filename, int size, const char* source, int length) {
+  char c= *source;
+
+  if (length > size + 1) {
+      qh_fprintf(qh ferr, 6040, "qhull error: filename is more than %d characters, %s\n",  size-1, source);
+      qh_errexit(qh_ERRinput, NULL, NULL);
+  }
+  strncpy(filename, source, length);
+  filename[length]= '\0';
+  if (c == '\'' || c == '"') {
+    char *s= filename + 1;
+    char *t= filename;
+    while (*s) {
+      if (*s == c) {
+          if (s[-1] == '\\')
+              t[-1]= c;
+      }else
+          *t++= *s;
+      s++;
+    }
+    *t= '\0';
+  }
+} /* copyfilename */
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="countfacets">-</a>
+
+  qh_countfacets( facetlist, facets, printall,
+          numfacets, numsimplicial, totneighbors, numridges, numcoplanar, numtricoplanars  )
+    count good facets for printing and set visitid
+    if allfacets, ignores qh_skipfacet()
+
+  notes:
+    qh_printsummary and qh_countfacets must match counts
+
+  returns:
+    numfacets, numsimplicial, total neighbors, numridges, coplanars
+    each facet with ->visitid indicating 1-relative position
+      ->visitid==0 indicates not good
+
+  notes
+    numfacets >= numsimplicial
+    if qh.NEWfacets,
+      does not count visible facets (matches qh_printafacet)
+
+  design:
+    for all facets on facetlist and in facets set
+      unless facet is skipped or visible (i.e., will be deleted)
+        mark facet->visitid
+        update counts
+*/
+void qh_countfacets(facetT *facetlist, setT *facets, boolT printall,
+    int *numfacetsp, int *numsimplicialp, int *totneighborsp, int *numridgesp, int *numcoplanarsp, int *numtricoplanarsp) {
+  facetT *facet, **facetp;
+  int numfacets= 0, numsimplicial= 0, numridges= 0, totneighbors= 0, numcoplanars= 0, numtricoplanars= 0;
+
+  FORALLfacet_(facetlist) {
+    if ((facet->visible && qh NEWfacets)
+    || (!printall && qh_skipfacet(facet)))
+      facet->visitid= 0;
+    else {
+      facet->visitid= ++numfacets;
+      totneighbors += qh_setsize(facet->neighbors);
+      if (facet->simplicial) {
+        numsimplicial++;
+        if (facet->keepcentrum && facet->tricoplanar)
+          numtricoplanars++;
+      }else
+        numridges += qh_setsize(facet->ridges);
+      if (facet->coplanarset)
+        numcoplanars += qh_setsize(facet->coplanarset);
+    }
+  }
+
+  FOREACHfacet_(facets) {
+    if ((facet->visible && qh NEWfacets)
+    || (!printall && qh_skipfacet(facet)))
+      facet->visitid= 0;
+    else {
+      facet->visitid= ++numfacets;
+      totneighbors += qh_setsize(facet->neighbors);
+      if (facet->simplicial){
+        numsimplicial++;
+        if (facet->keepcentrum && facet->tricoplanar)
+          numtricoplanars++;
+      }else
+        numridges += qh_setsize(facet->ridges);
+      if (facet->coplanarset)
+        numcoplanars += qh_setsize(facet->coplanarset);
+    }
+  }
+  qh visit_id += numfacets+1;
+  *numfacetsp= numfacets;
+  *numsimplicialp= numsimplicial;
+  *totneighborsp= totneighbors;
+  *numridgesp= numridges;
+  *numcoplanarsp= numcoplanars;
+  *numtricoplanarsp= numtricoplanars;
+} /* countfacets */
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="detvnorm">-</a>
+
+  qh_detvnorm( vertex, vertexA, centers, offset )
+    compute separating plane of the Voronoi diagram for a pair of input sites
+    centers= set of facets (i.e., Voronoi vertices)
+      facet->visitid= 0 iff vertex-at-infinity (i.e., unbounded)
+
+  assumes:
+    qh_ASvoronoi and qh_vertexneighbors() already set
+
+  returns:
+    norm
+      a pointer into qh.gm_matrix to qh.hull_dim-1 reals
+      copy the data before reusing qh.gm_matrix
+    offset
+      if 'QVn'
+        sign adjusted so that qh.GOODvertexp is inside
+      else
+        sign adjusted so that vertex is inside
+
+    qh.gm_matrix= simplex of points from centers relative to first center
+
+  notes:
+    in io.c so that code for 'v Tv' can be removed by removing io.c
+    returns pointer into qh.gm_matrix to avoid tracking of temporary memory
+
+  design:
+    determine midpoint of input sites
+    build points as the set of Voronoi vertices
+    select a simplex from points (if necessary)
+      include midpoint if the Voronoi region is unbounded
+    relocate the first vertex of the simplex to the origin
+    compute the normalized hyperplane through the simplex
+    orient the hyperplane toward 'QVn' or 'vertex'
+    if 'Tv' or 'Ts'
+      if bounded
+        test that hyperplane is the perpendicular bisector of the input sites
+      test that Voronoi vertices not in the simplex are still on the hyperplane
+    free up temporary memory
+*/
+pointT *qh_detvnorm(vertexT *vertex, vertexT *vertexA, setT *centers, realT *offsetp) {
+  facetT *facet, **facetp;
+  int  i, k, pointid, pointidA, point_i, point_n;
+  setT *simplex= NULL;
+  pointT *point, **pointp, *point0, *midpoint, *normal, *inpoint;
+  coordT *coord, *gmcoord, *normalp;
+  setT *points= qh_settemp(qh TEMPsize);
+  boolT nearzero= False;
+  boolT unbounded= False;
+  int numcenters= 0;
+  int dim= qh hull_dim - 1;
+  realT dist, offset, angle, zero= 0.0;
+
+  midpoint= qh gm_matrix + qh hull_dim * qh hull_dim;  /* last row */
+  for (k=0; k < dim; k++)
+    midpoint[k]= (vertex->point[k] + vertexA->point[k])/2;
+  FOREACHfacet_(centers) {
+    numcenters++;
+    if (!facet->visitid)
+      unbounded= True;
+    else {
+      if (!facet->center)
+        facet->center= qh_facetcenter(facet->vertices);
+      qh_setappend(&points, facet->center);
+    }
+  }
+  if (numcenters > dim) {
+    simplex= qh_settemp(qh TEMPsize);
+    qh_setappend(&simplex, vertex->point);
+    if (unbounded)
+      qh_setappend(&simplex, midpoint);
+    qh_maxsimplex(dim, points, NULL, 0, &simplex);
+    qh_setdelnth(simplex, 0);
+  }else if (numcenters == dim) {
+    if (unbounded)
+      qh_setappend(&points, midpoint);
+    simplex= points;
+  }else {
+    qh_fprintf(qh ferr, 6216, "qhull internal error (qh_detvnorm): too few points(%d) to compute separating plane\n", numcenters);
+    qh_errexit(qh_ERRqhull, NULL, NULL);
+  }
+  i= 0;
+  gmcoord= qh gm_matrix;
+  point0= SETfirstt_(simplex, pointT);
+  FOREACHpoint_(simplex) {
+    if (qh IStracing >= 4)
+      qh_printmatrix(qh ferr, "qh_detvnorm: Voronoi vertex or midpoint",
+                              &point, 1, dim);
+    if (point != point0) {
+      qh gm_row[i++]= gmcoord;
+      coord= point0;
+      for (k=dim; k--; )
+        *(gmcoord++)= *point++ - *coord++;
+    }
+  }
+  qh gm_row[i]= gmcoord;  /* does not overlap midpoint, may be used later for qh_areasimplex */
+  normal= gmcoord;
+  qh_sethyperplane_gauss(dim, qh gm_row, point0, True,
+                normal, &offset, &nearzero);
+  if (qh GOODvertexp == vertexA->point)
+    inpoint= vertexA->point;
+  else
+    inpoint= vertex->point;
+  zinc_(Zdistio);
+  dist= qh_distnorm(dim, inpoint, normal, &offset);
+  if (dist > 0) {
+    offset= -offset;
+    normalp= normal;
+    for (k=dim; k--; ) {
+      *normalp= -(*normalp);
+      normalp++;
+    }
+  }
+  if (qh VERIFYoutput || qh PRINTstatistics) {
+    pointid= qh_pointid(vertex->point);
+    pointidA= qh_pointid(vertexA->point);
+    if (!unbounded) {
+      zinc_(Zdiststat);
+      dist= qh_distnorm(dim, midpoint, normal, &offset);
+      if (dist < 0)
+        dist= -dist;
+      zzinc_(Zridgemid);
+      wwmax_(Wridgemidmax, dist);
+      wwadd_(Wridgemid, dist);
+      trace4((qh ferr, 4014, "qh_detvnorm: points %d %d midpoint dist %2.2g\n",
+                 pointid, pointidA, dist));
+      for (k=0; k < dim; k++)
+        midpoint[k]= vertexA->point[k] - vertex->point[k];  /* overwrites midpoint! */
+      qh_normalize(midpoint, dim, False);
+      angle= qh_distnorm(dim, midpoint, normal, &zero); /* qh_detangle uses dim+1 */
+      if (angle < 0.0)
+        angle= angle + 1.0;
+      else
+        angle= angle - 1.0;
+      if (angle < 0.0)
+        angle -= angle;
+      trace4((qh ferr, 4015, "qh_detvnorm: points %d %d angle %2.2g nearzero %d\n",
+                 pointid, pointidA, angle, nearzero));
+      if (nearzero) {
+        zzinc_(Zridge0);
+        wwmax_(Wridge0max, angle);
+        wwadd_(Wridge0, angle);
+      }else {
+        zzinc_(Zridgeok)
+        wwmax_(Wridgeokmax, angle);
+        wwadd_(Wridgeok, angle);
+      }
+    }
+    if (simplex != points) {
+      FOREACHpoint_i_(points) {
+        if (!qh_setin(simplex, point)) {
+          facet= SETelemt_(centers, point_i, facetT);
+          zinc_(Zdiststat);
+          dist= qh_distnorm(dim, point, normal, &offset);
+          if (dist < 0)
+            dist= -dist;
+          zzinc_(Zridge);
+          wwmax_(Wridgemax, dist);
+          wwadd_(Wridge, dist);
+          trace4((qh ferr, 4016, "qh_detvnorm: points %d %d Voronoi vertex %d dist %2.2g\n",
+                             pointid, pointidA, facet->visitid, dist));
+        }
+      }
+    }
+  }
+  *offsetp= offset;
+  if (simplex != points)
+    qh_settempfree(&simplex);
+  qh_settempfree(&points);
+  return normal;
+} /* detvnorm */
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="detvridge">-</a>
+
+  qh_detvridge( vertexA )
+    determine Voronoi ridge from 'seen' neighbors of vertexA
+    include one vertex-at-infinite if an !neighbor->visitid
+
+  returns:
+    temporary set of centers (facets, i.e., Voronoi vertices)
+    sorted by center id
+*/
+setT *qh_detvridge(vertexT *vertex) {
+  setT *centers= qh_settemp(qh TEMPsize);
+  setT *tricenters= qh_settemp(qh TEMPsize);
+  facetT *neighbor, **neighborp;
+  boolT firstinf= True;
+
+  FOREACHneighbor_(vertex) {
+    if (neighbor->seen) {
+      if (neighbor->visitid) {
+        if (!neighbor->tricoplanar || qh_setunique(&tricenters, neighbor->center))
+          qh_setappend(&centers, neighbor);
+      }else if (firstinf) {
+        firstinf= False;
+        qh_setappend(&centers, neighbor);
+      }
+    }
+  }
+  qsort(SETaddr_(centers, facetT), (size_t)qh_setsize(centers),
+             sizeof(facetT *), qh_compare_facetvisit);
+  qh_settempfree(&tricenters);
+  return centers;
+} /* detvridge */
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="detvridge3">-</a>
+
+  qh_detvridge3( atvertex, vertex )
+    determine 3-d Voronoi ridge from 'seen' neighbors of atvertex and vertex
+    include one vertex-at-infinite for !neighbor->visitid
+    assumes all facet->seen2= True
+
+  returns:
+    temporary set of centers (facets, i.e., Voronoi vertices)
+    listed in adjacency order (!oriented)
+    all facet->seen2= True
+
+  design:
+    mark all neighbors of atvertex
+    for each adjacent neighbor of both atvertex and vertex
+      if neighbor selected
+        add neighbor to set of Voronoi vertices
+*/
+setT *qh_detvridge3(vertexT *atvertex, vertexT *vertex) {
+  setT *centers= qh_settemp(qh TEMPsize);
+  setT *tricenters= qh_settemp(qh TEMPsize);
+  facetT *neighbor, **neighborp, *facet= NULL;
+  boolT firstinf= True;
+
+  FOREACHneighbor_(atvertex)
+    neighbor->seen2= False;
+  FOREACHneighbor_(vertex) {
+    if (!neighbor->seen2) {
+      facet= neighbor;
+      break;
+    }
+  }
+  while (facet) {
+    facet->seen2= True;
+    if (neighbor->seen) {
+      if (facet->visitid) {
+        if (!facet->tricoplanar || qh_setunique(&tricenters, facet->center))
+          qh_setappend(&centers, facet);
+      }else if (firstinf) {
+        firstinf= False;
+        qh_setappend(&centers, facet);
+      }
+    }
+    FOREACHneighbor_(facet) {
+      if (!neighbor->seen2) {
+        if (qh_setin(vertex->neighbors, neighbor))
+          break;
+        else
+          neighbor->seen2= True;
+      }
+    }
+    facet= neighbor;
+  }
+  if (qh CHECKfrequently) {
+    FOREACHneighbor_(vertex) {
+      if (!neighbor->seen2) {
+          qh_fprintf(qh ferr, 6217, "qhull internal error (qh_detvridge3): neighbors of vertex p%d are not connected at facet %d\n",
+                 qh_pointid(vertex->point), neighbor->id);
+        qh_errexit(qh_ERRqhull, neighbor, NULL);
+      }
+    }
+  }
+  FOREACHneighbor_(atvertex)
+    neighbor->seen2= True;
+  qh_settempfree(&tricenters);
+  return centers;
+} /* detvridge3 */
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="eachvoronoi">-</a>
+
+  qh_eachvoronoi( fp, printvridge, vertex, visitall, innerouter, inorder )
+    if visitall,
+      visit all Voronoi ridges for vertex (i.e., an input site)
+    else
+      visit all unvisited Voronoi ridges for vertex
+      all vertex->seen= False if unvisited
+    assumes
+      all facet->seen= False
+      all facet->seen2= True (for qh_detvridge3)
+      all facet->visitid == 0 if vertex_at_infinity
+                         == index of Voronoi vertex
+                         >= qh.num_facets if ignored
+    innerouter:
+      qh_RIDGEall--  both inner (bounded) and outer(unbounded) ridges
+      qh_RIDGEinner- only inner
+      qh_RIDGEouter- only outer
+
+    if inorder
+      orders vertices for 3-d Voronoi diagrams
+
+  returns:
+    number of visited ridges (does not include previously visited ridges)
+
+    if printvridge,
+      calls printvridge( fp, vertex, vertexA, centers)
+        fp== any pointer (assumes FILE*)
+        vertex,vertexA= pair of input sites that define a Voronoi ridge
+        centers= set of facets (i.e., Voronoi vertices)
+                 ->visitid == index or 0 if vertex_at_infinity
+                 ordered for 3-d Voronoi diagram
+  notes:
+    uses qh.vertex_visit
+
+  see:
+    qh_eachvoronoi_all()
+
+  design:
+    mark selected neighbors of atvertex
+    for each selected neighbor (either Voronoi vertex or vertex-at-infinity)
+      for each unvisited vertex
+        if atvertex and vertex share more than d-1 neighbors
+          bump totalcount
+          if printvridge defined
+            build the set of shared neighbors (i.e., Voronoi vertices)
+            call printvridge
+*/
+int qh_eachvoronoi(FILE *fp, printvridgeT printvridge, vertexT *atvertex, boolT visitall, qh_RIDGE innerouter, boolT inorder) {
+  boolT unbounded;
+  int count;
+  facetT *neighbor, **neighborp, *neighborA, **neighborAp;
+  setT *centers;
+  setT *tricenters= qh_settemp(qh TEMPsize);
+
+  vertexT *vertex, **vertexp;
+  boolT firstinf;
+  unsigned int numfacets= (unsigned int)qh num_facets;
+  int totridges= 0;
+
+  qh vertex_visit++;
+  atvertex->seen= True;
+  if (visitall) {
+    FORALLvertices
+      vertex->seen= False;
+  }
+  FOREACHneighbor_(atvertex) {
+    if (neighbor->visitid < numfacets)
+      neighbor->seen= True;
+  }
+  FOREACHneighbor_(atvertex) {
+    if (neighbor->seen) {
+      FOREACHvertex_(neighbor->vertices) {
+        if (vertex->visitid != qh vertex_visit && !vertex->seen) {
+          vertex->visitid= qh vertex_visit;
+          count= 0;
+          firstinf= True;
+          qh_settruncate(tricenters, 0);
+          FOREACHneighborA_(vertex) {
+            if (neighborA->seen) {
+              if (neighborA->visitid) {
+                if (!neighborA->tricoplanar || qh_setunique(&tricenters, neighborA->center))
+                  count++;
+              }else if (firstinf) {
+                count++;
+                firstinf= False;
+              }
+            }
+          }
+          if (count >= qh hull_dim - 1) {  /* e.g., 3 for 3-d Voronoi */
+            if (firstinf) {
+              if (innerouter == qh_RIDGEouter)
+                continue;
+              unbounded= False;
+            }else {
+              if (innerouter == qh_RIDGEinner)
+                continue;
+              unbounded= True;
+            }
+            totridges++;
+            trace4((qh ferr, 4017, "qh_eachvoronoi: Voronoi ridge of %d vertices between sites %d and %d\n",
+                  count, qh_pointid(atvertex->point), qh_pointid(vertex->point)));
+            if (printvridge && fp) {
+              if (inorder && qh hull_dim == 3+1) /* 3-d Voronoi diagram */
+                centers= qh_detvridge3(atvertex, vertex);
+              else
+                centers= qh_detvridge(vertex);
+              (*printvridge)(fp, atvertex, vertex, centers, unbounded);
+              qh_settempfree(&centers);
+            }
+          }
+        }
+      }
+    }
+  }
+  FOREACHneighbor_(atvertex)
+    neighbor->seen= False;
+  qh_settempfree(&tricenters);
+  return totridges;
+} /* eachvoronoi */
+
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="eachvoronoi_all">-</a>
+
+  qh_eachvoronoi_all( fp, printvridge, isUpper, innerouter, inorder )
+    visit all Voronoi ridges
+
+    innerouter:
+      see qh_eachvoronoi()
+
+    if inorder
+      orders vertices for 3-d Voronoi diagrams
+
+  returns
+    total number of ridges
+
+    if isUpper == facet->upperdelaunay  (i.e., a Vornoi vertex)
+      facet->visitid= Voronoi vertex index(same as 'o' format)
+    else
+      facet->visitid= 0
+
+    if printvridge,
+      calls printvridge( fp, vertex, vertexA, centers)
+      [see qh_eachvoronoi]
+
+  notes:
+    Not used for qhull.exe
+    same effect as qh_printvdiagram but ridges not sorted by point id
+*/
+int qh_eachvoronoi_all(FILE *fp, printvridgeT printvridge, boolT isUpper, qh_RIDGE innerouter, boolT inorder) {
+  facetT *facet;
+  vertexT *vertex;
+  int numcenters= 1;  /* vertex 0 is vertex-at-infinity */
+  int totridges= 0;
+
+  qh_clearcenters(qh_ASvoronoi);
+  qh_vertexneighbors();
+  maximize_(qh visit_id, (unsigned) qh num_facets);
+  FORALLfacets {
+    facet->visitid= 0;
+    facet->seen= False;
+    facet->seen2= True;
+  }
+  FORALLfacets {
+    if (facet->upperdelaunay == isUpper)
+      facet->visitid= numcenters++;
+  }
+  FORALLvertices
+    vertex->seen= False;
+  FORALLvertices {
+    if (qh GOODvertex > 0 && qh_pointid(vertex->point)+1 != qh GOODvertex)
+      continue;
+    totridges += qh_eachvoronoi(fp, printvridge, vertex,
+                   !qh_ALL, innerouter, inorder);
+  }
+  return totridges;
+} /* eachvoronoi_all */
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="facet2point">-</a>
+
+  qh_facet2point( facet, point0, point1, mindist )
+    return two projected temporary vertices for a 2-d facet
+    may be non-simplicial
+
+  returns:
+    point0 and point1 oriented and projected to the facet
+    returns mindist (maximum distance below plane)
+*/
+void qh_facet2point(facetT *facet, pointT **point0, pointT **point1, realT *mindist) {
+  vertexT *vertex0, *vertex1;
+  realT dist;
+
+  if (facet->toporient ^ qh_ORIENTclock) {
+    vertex0= SETfirstt_(facet->vertices, vertexT);
+    vertex1= SETsecondt_(facet->vertices, vertexT);
+  }else {
+    vertex1= SETfirstt_(facet->vertices, vertexT);
+    vertex0= SETsecondt_(facet->vertices, vertexT);
+  }
+  zadd_(Zdistio, 2);
+  qh_distplane(vertex0->point, facet, &dist);
+  *mindist= dist;
+  *point0= qh_projectpoint(vertex0->point, facet, dist);
+  qh_distplane(vertex1->point, facet, &dist);
+  minimize_(*mindist, dist);
+  *point1= qh_projectpoint(vertex1->point, facet, dist);
+} /* facet2point */
+
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="facetvertices">-</a>
+
+  qh_facetvertices( facetlist, facets, allfacets )
+    returns temporary set of vertices in a set and/or list of facets
+    if allfacets, ignores qh_skipfacet()
+
+  returns:
+    vertices with qh.vertex_visit
+
+  notes:
+    optimized for allfacets of facet_list
+
+  design:
+    if allfacets of facet_list
+      create vertex set from vertex_list
+    else
+      for each selected facet in facets or facetlist
+        append unvisited vertices to vertex set
+*/
+setT *qh_facetvertices(facetT *facetlist, setT *facets, boolT allfacets) {
+  setT *vertices;
+  facetT *facet, **facetp;
+  vertexT *vertex, **vertexp;
+
+  qh vertex_visit++;
+  if (facetlist == qh facet_list && allfacets && !facets) {
+    vertices= qh_settemp(qh num_vertices);
+    FORALLvertices {
+      vertex->visitid= qh vertex_visit;
+      qh_setappend(&vertices, vertex);
+    }
+  }else {
+    vertices= qh_settemp(qh TEMPsize);
+    FORALLfacet_(facetlist) {
+      if (!allfacets && qh_skipfacet(facet))
+        continue;
+      FOREACHvertex_(facet->vertices) {
+        if (vertex->visitid != qh vertex_visit) {
+          vertex->visitid= qh vertex_visit;
+          qh_setappend(&vertices, vertex);
+        }
+      }
+    }
+  }
+  FOREACHfacet_(facets) {
+    if (!allfacets && qh_skipfacet(facet))
+      continue;
+    FOREACHvertex_(facet->vertices) {
+      if (vertex->visitid != qh vertex_visit) {
+        vertex->visitid= qh vertex_visit;
+        qh_setappend(&vertices, vertex);
+      }
+    }
+  }
+  return vertices;
+} /* facetvertices */
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >-------------------------------</a><a name="geomplanes">-</a>
+
+  qh_geomplanes( facet, outerplane, innerplane )
+    return outer and inner planes for Geomview
+    qh.PRINTradius is size of vertices and points (includes qh.JOGGLEmax)
+
+  notes:
+    assume precise calculations in io.c with roundoff covered by qh_GEOMepsilon
+*/
+void qh_geomplanes(facetT *facet, realT *outerplane, realT *innerplane) {
+  realT radius;
+
+  if (qh MERGING || qh JOGGLEmax < REALmax/2) {
+    qh_outerinner(facet, outerplane, innerplane);
+    radius= qh PRINTradius;
+    if (qh JOGGLEmax < REALmax/2)
+      radius -= qh JOGGLEmax * sqrt((realT)qh hull_dim);  /* already accounted for in qh_outerinner() */
+    *outerplane += radius;
+    *innerplane -= radius;
+    if (qh PRINTcoplanar || qh PRINTspheres) {
+      *outerplane += qh MAXabs_coord * qh_GEOMepsilon;
+      *innerplane -= qh MAXabs_coord * qh_GEOMepsilon;
+    }
+  }else
+    *innerplane= *outerplane= 0;
+} /* geomplanes */
+
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="markkeep">-</a>
+
+  qh_markkeep( facetlist )
+    mark good facets that meet qh.KEEParea, qh.KEEPmerge, and qh.KEEPminArea
+    ignores visible facets (!part of convex hull)
+
+  returns:
+    may clear facet->good
+    recomputes qh.num_good
+
+  design:
+    get set of good facets
+    if qh.KEEParea
+      sort facets by area
+      clear facet->good for all but n largest facets
+    if qh.KEEPmerge
+      sort facets by merge count
+      clear facet->good for all but n most merged facets
+    if qh.KEEPminarea
+      clear facet->good if area too small
+    update qh.num_good
+*/
+void qh_markkeep(facetT *facetlist) {
+  facetT *facet, **facetp;
+  setT *facets= qh_settemp(qh num_facets);
+  int size, count;
+
+  trace2((qh ferr, 2006, "qh_markkeep: only keep %d largest and/or %d most merged facets and/or min area %.2g\n",
+          qh KEEParea, qh KEEPmerge, qh KEEPminArea));
+  FORALLfacet_(facetlist) {
+    if (!facet->visible && facet->good)
+      qh_setappend(&facets, facet);
+  }
+  size= qh_setsize(facets);
+  if (qh KEEParea) {
+    qsort(SETaddr_(facets, facetT), (size_t)size,
+             sizeof(facetT *), qh_compare_facetarea);
+    if ((count= size - qh KEEParea) > 0) {
+      FOREACHfacet_(facets) {
+        facet->good= False;
+        if (--count == 0)
+          break;
+      }
+    }
+  }
+  if (qh KEEPmerge) {
+    qsort(SETaddr_(facets, facetT), (size_t)size,
+             sizeof(facetT *), qh_compare_facetmerge);
+    if ((count= size - qh KEEPmerge) > 0) {
+      FOREACHfacet_(facets) {
+        facet->good= False;
+        if (--count == 0)
+          break;
+      }
+    }
+  }
+  if (qh KEEPminArea < REALmax/2) {
+    FOREACHfacet_(facets) {
+      if (!facet->isarea || facet->f.area < qh KEEPminArea)
+        facet->good= False;
+    }
+  }
+  qh_settempfree(&facets);
+  count= 0;
+  FORALLfacet_(facetlist) {
+    if (facet->good)
+      count++;
+  }
+  qh num_good= count;
+} /* markkeep */
+
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="markvoronoi">-</a>
+
+  qh_markvoronoi( facetlist, facets, printall, isLower, numcenters )
+    mark voronoi vertices for printing by site pairs
+
+  returns:
+    temporary set of vertices indexed by pointid
+    isLower set if printing lower hull (i.e., at least one facet is lower hull)
+    numcenters= total number of Voronoi vertices
+    bumps qh.printoutnum for vertex-at-infinity
+    clears all facet->seen and sets facet->seen2
+
+    if selected
+      facet->visitid= Voronoi vertex id
+    else if upper hull (or 'Qu' and lower hull)
+      facet->visitid= 0
+    else
+      facet->visitid >= qh num_facets
+
+  notes:
+    ignores qh.ATinfinity, if defined
+*/
+setT *qh_markvoronoi(facetT *facetlist, setT *facets, boolT printall, boolT *isLowerp, int *numcentersp) {
+  int numcenters=0;
+  facetT *facet, **facetp;
+  setT *vertices;
+  boolT isLower= False;
+
+  qh printoutnum++;
+  qh_clearcenters(qh_ASvoronoi);  /* in case, qh_printvdiagram2 called by user */
+  qh_vertexneighbors();
+  vertices= qh_pointvertex();
+  if (qh ATinfinity)
+    SETelem_(vertices, qh num_points-1)= NULL;
+  qh visit_id++;
+  maximize_(qh visit_id, (unsigned) qh num_facets);
+  FORALLfacet_(facetlist) {
+    if (printall || !qh_skipfacet(facet)) {
+      if (!facet->upperdelaunay) {
+        isLower= True;
+        break;
+      }
+    }
+  }
+  FOREACHfacet_(facets) {
+    if (printall || !qh_skipfacet(facet)) {
+      if (!facet->upperdelaunay) {
+        isLower= True;
+        break;
+      }
+    }
+  }
+  FORALLfacets {
+    if (facet->normal && (facet->upperdelaunay == isLower))
+      facet->visitid= 0;  /* facetlist or facets may overwrite */
+    else
+      facet->visitid= qh visit_id;
+    facet->seen= False;
+    facet->seen2= True;
+  }
+  numcenters++;  /* qh_INFINITE */
+  FORALLfacet_(facetlist) {
+    if (printall || !qh_skipfacet(facet))
+      facet->visitid= numcenters++;
+  }
+  FOREACHfacet_(facets) {
+    if (printall || !qh_skipfacet(facet))
+      facet->visitid= numcenters++;
+  }
+  *isLowerp= isLower;
+  *numcentersp= numcenters;
+  trace2((qh ferr, 2007, "qh_markvoronoi: isLower %d numcenters %d\n", isLower, numcenters));
+  return vertices;
+} /* markvoronoi */
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="order_vertexneighbors">-</a>
+
+  qh_order_vertexneighbors( vertex )
+    order facet neighbors of a 2-d or 3-d vertex by adjacency
+
+  notes:
+    does not orient the neighbors
+
+  design:
+    initialize a new neighbor set with the first facet in vertex->neighbors
+    while vertex->neighbors non-empty
+      select next neighbor in the previous facet's neighbor set
+    set vertex->neighbors to the new neighbor set
+*/
+void qh_order_vertexneighbors(vertexT *vertex) {
+  setT *newset;
+  facetT *facet, *neighbor, **neighborp;
+
+  trace4((qh ferr, 4018, "qh_order_vertexneighbors: order neighbors of v%d for 3-d\n", vertex->id));
+  newset= qh_settemp(qh_setsize(vertex->neighbors));
+  facet= (facetT*)qh_setdellast(vertex->neighbors);
+  qh_setappend(&newset, facet);
+  while (qh_setsize(vertex->neighbors)) {
+    FOREACHneighbor_(vertex) {
+      if (qh_setin(facet->neighbors, neighbor)) {
+        qh_setdel(vertex->neighbors, neighbor);
+        qh_setappend(&newset, neighbor);
+        facet= neighbor;
+        break;
+      }
+    }
+    if (!neighbor) {
+      qh_fprintf(qh ferr, 6066, "qhull internal error (qh_order_vertexneighbors): no neighbor of v%d for f%d\n",
+        vertex->id, facet->id);
+      qh_errexit(qh_ERRqhull, facet, NULL);
+    }
+  }
+  qh_setfree(&vertex->neighbors);
+  qh_settemppop();
+  vertex->neighbors= newset;
+} /* order_vertexneighbors */
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="prepare_output">-</a>
+
+  qh_prepare_output( )
+    prepare for qh_produce_output2() according to
+      qh.KEEPminArea, KEEParea, KEEPmerge, GOODvertex, GOODthreshold, GOODpoint, ONLYgood, SPLITthresholds
+    does not reset facet->good
+
+  notes
+    except for PRINTstatistics, no-op if previously called with same options
+*/
+void qh_prepare_output(void) {
+  if (qh VORONOI) {
+    qh_clearcenters(qh_ASvoronoi);  /* must be before qh_triangulate */
+    qh_vertexneighbors();
+  }
+  if (qh TRIangulate && !qh hasTriangulation) {
+    qh_triangulate();
+    if (qh VERIFYoutput && !qh CHECKfrequently)
+      qh_checkpolygon(qh facet_list);
+  }
+  qh_findgood_all(qh facet_list);
+  if (qh GETarea)
+    qh_getarea(qh facet_list);
+  if (qh KEEParea || qh KEEPmerge || qh KEEPminArea < REALmax/2)
+    qh_markkeep(qh facet_list);
+  if (qh PRINTstatistics)
+    qh_collectstatistics();
+}
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="printafacet">-</a>
+
+  qh_printafacet( fp, format, facet, printall )
+    print facet to fp in given output format (see qh.PRINTout)
+
+  returns:
+    nop if !printall and qh_skipfacet()
+    nop if visible facet and NEWfacets and format != PRINTfacets
+    must match qh_countfacets
+
+  notes
+    preserves qh.visit_id
+    facet->normal may be null if PREmerge/MERGEexact and STOPcone before merge
+
+  see
+    qh_printbegin() and qh_printend()
+
+  design:
+    test for printing facet
+    call appropriate routine for format
+    or output results directly
+*/
+void qh_printafacet(FILE *fp, qh_PRINT format, facetT *facet, boolT printall) {
+  realT color[4], offset, dist, outerplane, innerplane;
+  boolT zerodiv;
+  coordT *point, *normp, *coordp, **pointp, *feasiblep;
+  int k;
+  vertexT *vertex, **vertexp;
+  facetT *neighbor, **neighborp;
+
+  if (!printall && qh_skipfacet(facet))
+    return;
+  if (facet->visible && qh NEWfacets && format != qh_PRINTfacets)
+    return;
+  qh printoutnum++;
+  switch (format) {
+  case qh_PRINTarea:
+    if (facet->isarea) {
+      qh_fprintf(fp, 9009, qh_REAL_1, facet->f.area);
+      qh_fprintf(fp, 9010, "\n");
+    }else
+      qh_fprintf(fp, 9011, "0\n");
+    break;
+  case qh_PRINTcoplanars:
+    qh_fprintf(fp, 9012, "%d", qh_setsize(facet->coplanarset));
+    FOREACHpoint_(facet->coplanarset)
+      qh_fprintf(fp, 9013, " %d", qh_pointid(point));
+    qh_fprintf(fp, 9014, "\n");
+    break;
+  case qh_PRINTcentrums:
+    qh_printcenter(fp, format, NULL, facet);
+    break;
+  case qh_PRINTfacets:
+    qh_printfacet(fp, facet);
+    break;
+  case qh_PRINTfacets_xridge:
+    qh_printfacetheader(fp, facet);
+    break;
+  case qh_PRINTgeom:  /* either 2 , 3, or 4-d by qh_printbegin */
+    if (!facet->normal)
+      break;
+    for (k=qh hull_dim; k--; ) {
+      color[k]= (facet->normal[k]+1.0)/2.0;
+      maximize_(color[k], -1.0);
+      minimize_(color[k], +1.0);
+    }
+    qh_projectdim3(color, color);
+    if (qh PRINTdim != qh hull_dim)
+      qh_normalize2(color, 3, True, NULL, NULL);
+    if (qh hull_dim <= 2)
+      qh_printfacet2geom(fp, facet, color);
+    else if (qh hull_dim == 3) {
+      if (facet->simplicial)
+        qh_printfacet3geom_simplicial(fp, facet, color);
+      else
+        qh_printfacet3geom_nonsimplicial(fp, facet, color);
+    }else {
+      if (facet->simplicial)
+        qh_printfacet4geom_simplicial(fp, facet, color);
+      else
+        qh_printfacet4geom_nonsimplicial(fp, facet, color);
+    }
+    break;
+  case qh_PRINTids:
+    qh_fprintf(fp, 9015, "%d\n", facet->id);
+    break;
+  case qh_PRINTincidences:
+  case qh_PRINToff:
+  case qh_PRINTtriangles:
+    if (qh hull_dim == 3 && format != qh_PRINTtriangles)
+      qh_printfacet3vertex(fp, facet, format);
+    else if (facet->simplicial || qh hull_dim == 2 || format == qh_PRINToff)
+      qh_printfacetNvertex_simplicial(fp, facet, format);
+    else
+      qh_printfacetNvertex_nonsimplicial(fp, facet, qh printoutvar++, format);
+    break;
+  case qh_PRINTinner:
+    qh_outerinner(facet, NULL, &innerplane);
+    offset= facet->offset - innerplane;
+    goto LABELprintnorm;
+    break; /* prevent warning */
+  case qh_PRINTmerges:
+    qh_fprintf(fp, 9016, "%d\n", facet->nummerge);
+    break;
+  case qh_PRINTnormals:
+    offset= facet->offset;
+    goto LABELprintnorm;
+    break; /* prevent warning */
+  case qh_PRINTouter:
+    qh_outerinner(facet, &outerplane, NULL);
+    offset= facet->offset - outerplane;
+  LABELprintnorm:
+    if (!facet->normal) {
+      qh_fprintf(fp, 9017, "no normal for facet f%d\n", facet->id);
+      break;
+    }
+    if (qh CDDoutput) {
+      qh_fprintf(fp, 9018, qh_REAL_1, -offset);
+      for (k=0; k < qh hull_dim; k++)
+        qh_fprintf(fp, 9019, qh_REAL_1, -facet->normal[k]);
+    }else {
+      for (k=0; k < qh hull_dim; k++)
+        qh_fprintf(fp, 9020, qh_REAL_1, facet->normal[k]);
+      qh_fprintf(fp, 9021, qh_REAL_1, offset);
+    }
+    qh_fprintf(fp, 9022, "\n");
+    break;
+  case qh_PRINTmathematica:  /* either 2 or 3-d by qh_printbegin */
+  case qh_PRINTmaple:
+    if (qh hull_dim == 2)
+      qh_printfacet2math(fp, facet, format, qh printoutvar++);
+    else
+      qh_printfacet3math(fp, facet, format, qh printoutvar++);
+    break;
+  case qh_PRINTneighbors:
+    qh_fprintf(fp, 9023, "%d", qh_setsize(facet->neighbors));
+    FOREACHneighbor_(facet)
+      qh_fprintf(fp, 9024, " %d",
+               neighbor->visitid ? neighbor->visitid - 1: 0 - neighbor->id);
+    qh_fprintf(fp, 9025, "\n");
+    break;
+  case qh_PRINTpointintersect:
+    if (!qh feasible_point) {
+      qh_fprintf(qh ferr, 6067, "qhull input error (qh_printafacet): option 'Fp' needs qh feasible_point\n");
+      qh_errexit( qh_ERRinput, NULL, NULL);
+    }
+    if (facet->offset > 0)
+      goto LABELprintinfinite;
+    point= coordp= (coordT*)qh_memalloc(qh normal_size);
+    normp= facet->normal;
+    feasiblep= qh feasible_point;
+    if (facet->offset < -qh MINdenom) {
+      for (k=qh hull_dim; k--; )
+        *(coordp++)= (*(normp++) / - facet->offset) + *(feasiblep++);
+    }else {
+      for (k=qh hull_dim; k--; ) {
+        *(coordp++)= qh_divzero(*(normp++), facet->offset, qh MINdenom_1,
+                                 &zerodiv) + *(feasiblep++);
+        if (zerodiv) {
+          qh_memfree(point, qh normal_size);
+          goto LABELprintinfinite;
+        }
+      }
+    }
+    qh_printpoint(fp, NULL, point);
+    qh_memfree(point, qh normal_size);
+    break;
+  LABELprintinfinite:
+    for (k=qh hull_dim; k--; )
+      qh_fprintf(fp, 9026, qh_REAL_1, qh_INFINITE);
+    qh_fprintf(fp, 9027, "\n");
+    break;
+  case qh_PRINTpointnearest:
+    FOREACHpoint_(facet->coplanarset) {
+      int id, id2;
+      vertex= qh_nearvertex(facet, point, &dist);
+      id= qh_pointid(vertex->point);
+      id2= qh_pointid(point);
+      qh_fprintf(fp, 9028, "%d %d %d " qh_REAL_1 "\n", id, id2, facet->id, dist);
+    }
+    break;
+  case qh_PRINTpoints:  /* VORONOI only by qh_printbegin */
+    if (qh CDDoutput)
+      qh_fprintf(fp, 9029, "1 ");
+    qh_printcenter(fp, format, NULL, facet);
+    break;
+  case qh_PRINTvertices:
+    qh_fprintf(fp, 9030, "%d", qh_setsize(facet->vertices));
+    FOREACHvertex_(facet->vertices)
+      qh_fprintf(fp, 9031, " %d", qh_pointid(vertex->point));
+    qh_fprintf(fp, 9032, "\n");
+    break;
+  default:
+    break;
+  }
+} /* printafacet */
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="printbegin">-</a>
+
+  qh_printbegin(  )
+    prints header for all output formats
+
+  returns:
+    checks for valid format
+
+  notes:
+    uses qh.visit_id for 3/4off
+    changes qh.interior_point if printing centrums
+    qh_countfacets clears facet->visitid for non-good facets
+
+  see
+    qh_printend() and qh_printafacet()
+
+  design:
+    count facets and related statistics
+    print header for format
+*/
+void qh_printbegin(FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall) {
+  int numfacets, numsimplicial, numridges, totneighbors, numcoplanars, numtricoplanars;
+  int i, num;
+  facetT *facet, **facetp;
+  vertexT *vertex, **vertexp;
+  setT *vertices;
+  pointT *point, **pointp, *pointtemp;
+
+  qh printoutnum= 0;
+  qh_countfacets(facetlist, facets, printall, &numfacets, &numsimplicial,
+      &totneighbors, &numridges, &numcoplanars, &numtricoplanars);
+  switch (format) {
+  case qh_PRINTnone:
+    break;
+  case qh_PRINTarea:
+    qh_fprintf(fp, 9033, "%d\n", numfacets);
+    break;
+  case qh_PRINTcoplanars:
+    qh_fprintf(fp, 9034, "%d\n", numfacets);
+    break;
+  case qh_PRINTcentrums:
+    if (qh CENTERtype == qh_ASnone)
+      qh_clearcenters(qh_AScentrum);
+    qh_fprintf(fp, 9035, "%d\n%d\n", qh hull_dim, numfacets);
+    break;
+  case qh_PRINTfacets:
+  case qh_PRINTfacets_xridge:
+    if (facetlist)
+      qh_printvertexlist(fp, "Vertices and facets:\n", facetlist, facets, printall);
+    break;
+  case qh_PRINTgeom:
+    if (qh hull_dim > 4)  /* qh_initqhull_globals also checks */
+      goto LABELnoformat;
+    if (qh VORONOI && qh hull_dim > 3)  /* PRINTdim == DROPdim == hull_dim-1 */
+      goto LABELnoformat;
+    if (qh hull_dim == 2 && (qh PRINTridges || qh DOintersections))
+      qh_fprintf(qh ferr, 7049, "qhull warning: output for ridges and intersections not implemented in 2-d\n");
+    if (qh hull_dim == 4 && (qh PRINTinner || qh PRINTouter ||
+                             (qh PRINTdim == 4 && qh PRINTcentrums)))
+      qh_fprintf(qh ferr, 7050, "qhull warning: output for outer/inner planes and centrums not implemented in 4-d\n");
+    if (qh PRINTdim == 4 && (qh PRINTspheres))
+      qh_fprintf(qh ferr, 7051, "qhull warning: output for vertices not implemented in 4-d\n");
+    if (qh PRINTdim == 4 && qh DOintersections && qh PRINTnoplanes)
+      qh_fprintf(qh ferr, 7052, "qhull warning: 'Gnh' generates no output in 4-d\n");
+    if (qh PRINTdim == 2) {
+      qh_fprintf(fp, 9036, "{appearance {linewidth 3} LIST # %s | %s\n",
+              qh rbox_command, qh qhull_command);
+    }else if (qh PRINTdim == 3) {
+      qh_fprintf(fp, 9037, "{appearance {+edge -evert linewidth 2} LIST # %s | %s\n",
+              qh rbox_command, qh qhull_command);
+    }else if (qh PRINTdim == 4) {
+      qh visit_id++;
+      num= 0;
+      FORALLfacet_(facetlist)    /* get number of ridges to be printed */
+        qh_printend4geom(NULL, facet, &num, printall);
+      FOREACHfacet_(facets)
+        qh_printend4geom(NULL, facet, &num, printall);
+      qh ridgeoutnum= num;
+      qh printoutvar= 0;  /* counts number of ridges in output */
+      qh_fprintf(fp, 9038, "LIST # %s | %s\n", qh rbox_command, qh qhull_command);
+    }
+
+    if (qh PRINTdots) {
+      qh printoutnum++;
+      num= qh num_points + qh_setsize(qh other_points);
+      if (qh DELAUNAY && qh ATinfinity)
+        num--;
+      if (qh PRINTdim == 4)
+        qh_fprintf(fp, 9039, "4VECT %d %d 1\n", num, num);
+      else
+        qh_fprintf(fp, 9040, "VECT %d %d 1\n", num, num);
+
+      for (i=num; i--; ) {
+        if (i % 20 == 0)
+          qh_fprintf(fp, 9041, "\n");
+        qh_fprintf(fp, 9042, "1 ");
+      }
+      qh_fprintf(fp, 9043, "# 1 point per line\n1 ");
+      for (i=num-1; i--; ) { /* num at least 3 for D2 */
+        if (i % 20 == 0)
+          qh_fprintf(fp, 9044, "\n");
+        qh_fprintf(fp, 9045, "0 ");
+      }
+      qh_fprintf(fp, 9046, "# 1 color for all\n");
+      FORALLpoints {
+        if (!qh DELAUNAY || !qh ATinfinity || qh_pointid(point) != qh num_points-1) {
+          if (qh PRINTdim == 4)
+            qh_printpoint(fp, NULL, point);
+            else
+              qh_printpoint3(fp, point);
+        }
+      }
+      FOREACHpoint_(qh other_points) {
+        if (qh PRINTdim == 4)
+          qh_printpoint(fp, NULL, point);
+        else
+          qh_printpoint3(fp, point);
+      }
+      qh_fprintf(fp, 9047, "0 1 1 1  # color of points\n");
+    }
+
+    if (qh PRINTdim == 4  && !qh PRINTnoplanes)
+      /* 4dview loads up multiple 4OFF objects slowly */
+      qh_fprintf(fp, 9048, "4OFF %d %d 1\n", 3*qh ridgeoutnum, qh ridgeoutnum);
+    qh PRINTcradius= 2 * qh DISTround;  /* include test DISTround */
+    if (qh PREmerge) {
+      maximize_(qh PRINTcradius, qh premerge_centrum + qh DISTround);
+    }else if (qh POSTmerge)
+      maximize_(qh PRINTcradius, qh postmerge_centrum + qh DISTround);
+    qh PRINTradius= qh PRINTcradius;
+    if (qh PRINTspheres + qh PRINTcoplanar)
+      maximize_(qh PRINTradius, qh MAXabs_coord * qh_MINradius);
+    if (qh premerge_cos < REALmax/2) {
+      maximize_(qh PRINTradius, (1- qh premerge_cos) * qh MAXabs_coord);
+    }else if (!qh PREmerge && qh POSTmerge && qh postmerge_cos < REALmax/2) {
+      maximize_(qh PRINTradius, (1- qh postmerge_cos) * qh MAXabs_coord);
+    }
+    maximize_(qh PRINTradius, qh MINvisible);
+    if (qh JOGGLEmax < REALmax/2)
+      qh PRINTradius += qh JOGGLEmax * sqrt((realT)qh hull_dim);
+    if (qh PRINTdim != 4 &&
+        (qh PRINTcoplanar || qh PRINTspheres || qh PRINTcentrums)) {
+      vertices= qh_facetvertices(facetlist, facets, printall);
+      if (qh PRINTspheres && qh PRINTdim <= 3)
+        qh_printspheres(fp, vertices, qh PRINTradius);
+      if (qh PRINTcoplanar || qh PRINTcentrums) {
+        qh firstcentrum= True;
+        if (qh PRINTcoplanar&& !qh PRINTspheres) {
+          FOREACHvertex_(vertices)
+            qh_printpointvect2(fp, vertex->point, NULL, qh interior_point, qh PRINTradius);
+        }
+        FORALLfacet_(facetlist) {
+          if (!printall && qh_skipfacet(facet))
+            continue;
+          if (!facet->normal)
+            continue;
+          if (qh PRINTcentrums && qh PRINTdim <= 3)
+            qh_printcentrum(fp, facet, qh PRINTcradius);
+          if (!qh PRINTcoplanar)
+            continue;
+          FOREACHpoint_(facet->coplanarset)
+            qh_printpointvect2(fp, point, facet->normal, NULL, qh PRINTradius);
+          FOREACHpoint_(facet->outsideset)
+            qh_printpointvect2(fp, point, facet->normal, NULL, qh PRINTradius);
+        }
+        FOREACHfacet_(facets) {
+          if (!printall && qh_skipfacet(facet))
+            continue;
+          if (!facet->normal)
+            continue;
+          if (qh PRINTcentrums && qh PRINTdim <= 3)
+            qh_printcentrum(fp, facet, qh PRINTcradius);
+          if (!qh PRINTcoplanar)
+            continue;
+          FOREACHpoint_(facet->coplanarset)
+            qh_printpointvect2(fp, point, facet->normal, NULL, qh PRINTradius);
+          FOREACHpoint_(facet->outsideset)
+            qh_printpointvect2(fp, point, facet->normal, NULL, qh PRINTradius);
+        }
+      }
+      qh_settempfree(&vertices);
+    }
+    qh visit_id++; /* for printing hyperplane intersections */
+    break;
+  case qh_PRINTids:
+    qh_fprintf(fp, 9049, "%d\n", numfacets);
+    break;
+  case qh_PRINTincidences:
+    if (qh VORONOI && qh PRINTprecision)
+      qh_fprintf(qh ferr, 7053, "qhull warning: writing Delaunay.  Use 'p' or 'o' for Voronoi centers\n");
+    qh printoutvar= qh vertex_id;  /* centrum id for non-simplicial facets */
+    if (qh hull_dim <= 3)
+      qh_fprintf(fp, 9050, "%d\n", numfacets);
+    else
+      qh_fprintf(fp, 9051, "%d\n", numsimplicial+numridges);
+    break;
+  case qh_PRINTinner:
+  case qh_PRINTnormals:
+  case qh_PRINTouter:
+    if (qh CDDoutput)
+      qh_fprintf(fp, 9052, "%s | %s\nbegin\n    %d %d real\n", qh rbox_command,
+            qh qhull_command, numfacets, qh hull_dim+1);
+    else
+      qh_fprintf(fp, 9053, "%d\n%d\n", qh hull_dim+1, numfacets);
+    break;
+  case qh_PRINTmathematica:
+  case qh_PRINTmaple:
+    if (qh hull_dim > 3)  /* qh_initbuffers also checks */
+      goto LABELnoformat;
+    if (qh VORONOI)
+      qh_fprintf(qh ferr, 7054, "qhull warning: output is the Delaunay triangulation\n");
+    if (format == qh_PRINTmaple) {
+      if (qh hull_dim == 2)
+        qh_fprintf(fp, 9054, "PLOT(CURVES(\n");
+      else
+        qh_fprintf(fp, 9055, "PLOT3D(POLYGONS(\n");
+    }else
+      qh_fprintf(fp, 9056, "{\n");
+    qh printoutvar= 0;   /* counts number of facets for notfirst */
+    break;
+  case qh_PRINTmerges:
+    qh_fprintf(fp, 9057, "%d\n", numfacets);
+    break;
+  case qh_PRINTpointintersect:
+    qh_fprintf(fp, 9058, "%d\n%d\n", qh hull_dim, numfacets);
+    break;
+  case qh_PRINTneighbors:
+    qh_fprintf(fp, 9059, "%d\n", numfacets);
+    break;
+  case qh_PRINToff:
+  case qh_PRINTtriangles:
+    if (qh VORONOI)
+      goto LABELnoformat;
+    num = qh hull_dim;
+    if (format == qh_PRINToff || qh hull_dim == 2)
+      qh_fprintf(fp, 9060, "%d\n%d %d %d\n", num,
+        qh num_points+qh_setsize(qh other_points), numfacets, totneighbors/2);
+    else { /* qh_PRINTtriangles */
+      qh printoutvar= qh num_points+qh_setsize(qh other_points); /* first centrum */
+      if (qh DELAUNAY)
+        num--;  /* drop last dimension */
+      qh_fprintf(fp, 9061, "%d\n%d %d %d\n", num, qh printoutvar
+        + numfacets - numsimplicial, numsimplicial + numridges, totneighbors/2);
+    }
+    FORALLpoints
+      qh_printpointid(qh fout, NULL, num, point, qh_IDunknown);
+    FOREACHpoint_(qh other_points)
+      qh_printpointid(qh fout, NULL, num, point, qh_IDunknown);
+    if (format == qh_PRINTtriangles && qh hull_dim > 2) {
+      FORALLfacets {
+        if (!facet->simplicial && facet->visitid)
+          qh_printcenter(qh fout, format, NULL, facet);
+      }
+    }
+    break;
+  case qh_PRINTpointnearest:
+    qh_fprintf(fp, 9062, "%d\n", numcoplanars);
+    break;
+  case qh_PRINTpoints:
+    if (!qh VORONOI)
+      goto LABELnoformat;
+    if (qh CDDoutput)
+      qh_fprintf(fp, 9063, "%s | %s\nbegin\n%d %d real\n", qh rbox_command,
+           qh qhull_command, numfacets, qh hull_dim);
+    else
+      qh_fprintf(fp, 9064, "%d\n%d\n", qh hull_dim-1, numfacets);
+    break;
+  case qh_PRINTvertices:
+    qh_fprintf(fp, 9065, "%d\n", numfacets);
+    break;
+  case qh_PRINTsummary:
+  default:
+  LABELnoformat:
+    qh_fprintf(qh ferr, 6068, "qhull internal error (qh_printbegin): can not use this format for dimension %d\n",
+         qh hull_dim);
+    qh_errexit(qh_ERRqhull, NULL, NULL);
+  }
+} /* printbegin */
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="printcenter">-</a>
+
+  qh_printcenter( fp, string, facet )
+    print facet->center as centrum or Voronoi center
+    string may be NULL.  Don't include '%' codes.
+    nop if qh CENTERtype neither CENTERvoronoi nor CENTERcentrum
+    if upper envelope of Delaunay triangulation and point at-infinity
+      prints qh_INFINITE instead;
+
+  notes:
+    defines facet->center if needed
+    if format=PRINTgeom, adds a 0 if would otherwise be 2-d
+    Same as QhullFacet::printCenter
+*/
+void qh_printcenter(FILE *fp, qh_PRINT format, const char *string, facetT *facet) {
+  int k, num;
+
+  if (qh CENTERtype != qh_ASvoronoi && qh CENTERtype != qh_AScentrum)
+    return;
+  if (string)
+    qh_fprintf(fp, 9066, string);
+  if (qh CENTERtype == qh_ASvoronoi) {
+    num= qh hull_dim-1;
+    if (!facet->normal || !facet->upperdelaunay || !qh ATinfinity) {
+      if (!facet->center)
+        facet->center= qh_facetcenter(facet->vertices);
+      for (k=0; k < num; k++)
+        qh_fprintf(fp, 9067, qh_REAL_1, facet->center[k]);
+    }else {
+      for (k=0; k < num; k++)
+        qh_fprintf(fp, 9068, qh_REAL_1, qh_INFINITE);
+    }
+  }else /* qh.CENTERtype == qh_AScentrum */ {
+    num= qh hull_dim;
+    if (format == qh_PRINTtriangles && qh DELAUNAY)
+      num--;
+    if (!facet->center)
+      facet->center= qh_getcentrum(facet);
+    for (k=0; k < num; k++)
+      qh_fprintf(fp, 9069, qh_REAL_1, facet->center[k]);
+  }
+  if (format == qh_PRINTgeom && num == 2)
+    qh_fprintf(fp, 9070, " 0\n");
+  else
+    qh_fprintf(fp, 9071, "\n");
+} /* printcenter */
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="printcentrum">-</a>
+
+  qh_printcentrum( fp, facet, radius )
+    print centrum for a facet in OOGL format
+    radius defines size of centrum
+    2-d or 3-d only
+
+  returns:
+    defines facet->center if needed
+*/
+void qh_printcentrum(FILE *fp, facetT *facet, realT radius) {
+  pointT *centrum, *projpt;
+  boolT tempcentrum= False;
+  realT xaxis[4], yaxis[4], normal[4], dist;
+  realT green[3]={0, 1, 0};
+  vertexT *apex;
+  int k;
+
+  if (qh CENTERtype == qh_AScentrum) {
+    if (!facet->center)
+      facet->center= qh_getcentrum(facet);
+    centrum= facet->center;
+  }else {
+    centrum= qh_getcentrum(facet);
+    tempcentrum= True;
+  }
+  qh_fprintf(fp, 9072, "{appearance {-normal -edge normscale 0} ");
+  if (qh firstcentrum) {
+    qh firstcentrum= False;
+    qh_fprintf(fp, 9073, "{INST geom { define centrum CQUAD  # f%d\n\
+-0.3 -0.3 0.0001     0 0 1 1\n\
+ 0.3 -0.3 0.0001     0 0 1 1\n\
+ 0.3  0.3 0.0001     0 0 1 1\n\
+-0.3  0.3 0.0001     0 0 1 1 } transform { \n", facet->id);
+  }else
+    qh_fprintf(fp, 9074, "{INST geom { : centrum } transform { # f%d\n", facet->id);
+  apex= SETfirstt_(facet->vertices, vertexT);
+  qh_distplane(apex->point, facet, &dist);
+  projpt= qh_projectpoint(apex->point, facet, dist);
+  for (k=qh hull_dim; k--; ) {
+    xaxis[k]= projpt[k] - centrum[k];
+    normal[k]= facet->normal[k];
+  }
+  if (qh hull_dim == 2) {
+    xaxis[2]= 0;
+    normal[2]= 0;
+  }else if (qh hull_dim == 4) {
+    qh_projectdim3(xaxis, xaxis);
+    qh_projectdim3(normal, normal);
+    qh_normalize2(normal, qh PRINTdim, True, NULL, NULL);
+  }
+  qh_crossproduct(3, xaxis, normal, yaxis);
+  qh_fprintf(fp, 9075, "%8.4g %8.4g %8.4g 0\n", xaxis[0], xaxis[1], xaxis[2]);
+  qh_fprintf(fp, 9076, "%8.4g %8.4g %8.4g 0\n", yaxis[0], yaxis[1], yaxis[2]);
+  qh_fprintf(fp, 9077, "%8.4g %8.4g %8.4g 0\n", normal[0], normal[1], normal[2]);
+  qh_printpoint3(fp, centrum);
+  qh_fprintf(fp, 9078, "1 }}}\n");
+  qh_memfree(projpt, qh normal_size);
+  qh_printpointvect(fp, centrum, facet->normal, NULL, radius, green);
+  if (tempcentrum)
+    qh_memfree(centrum, qh normal_size);
+} /* printcentrum */
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="printend">-</a>
+
+  qh_printend( fp, format )
+    prints trailer for all output formats
+
+  see:
+    qh_printbegin() and qh_printafacet()
+
+*/
+void qh_printend(FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall) {
+  int num;
+  facetT *facet, **facetp;
+
+  if (!qh printoutnum)
+    qh_fprintf(qh ferr, 7055, "qhull warning: no facets printed\n");
+  switch (format) {
+  case qh_PRINTgeom:
+    if (qh hull_dim == 4 && qh DROPdim < 0  && !qh PRINTnoplanes) {
+      qh visit_id++;
+      num= 0;
+      FORALLfacet_(facetlist)
+        qh_printend4geom(fp, facet,&num, printall);
+      FOREACHfacet_(facets)
+        qh_printend4geom(fp, facet, &num, printall);
+      if (num != qh ridgeoutnum || qh printoutvar != qh ridgeoutnum) {
+        qh_fprintf(qh ferr, 6069, "qhull internal error (qh_printend): number of ridges %d != number printed %d and at end %d\n", qh ridgeoutnum, qh printoutvar, num);
+        qh_errexit(qh_ERRqhull, NULL, NULL);
+      }
+    }else
+      qh_fprintf(fp, 9079, "}\n");
+    break;
+  case qh_PRINTinner:
+  case qh_PRINTnormals:
+  case qh_PRINTouter:
+    if (qh CDDoutput)
+      qh_fprintf(fp, 9080, "end\n");
+    break;
+  case qh_PRINTmaple:
+    qh_fprintf(fp, 9081, "));\n");
+    break;
+  case qh_PRINTmathematica:
+    qh_fprintf(fp, 9082, "}\n");
+    break;
+  case qh_PRINTpoints:
+    if (qh CDDoutput)
+      qh_fprintf(fp, 9083, "end\n");
+    break;
+  default:
+    break;
+  }
+} /* printend */
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="printend4geom">-</a>
+
+  qh_printend4geom( fp, facet, numridges, printall )
+    helper function for qh_printbegin/printend
+
+  returns:
+    number of printed ridges
+
+  notes:
+    just counts printed ridges if fp=NULL
+    uses facet->visitid
+    must agree with qh_printfacet4geom...
+
+  design:
+    computes color for facet from its normal
+    prints each ridge of facet
+*/
+void qh_printend4geom(FILE *fp, facetT *facet, int *nump, boolT printall) {
+  realT color[3];
+  int i, num= *nump;
+  facetT *neighbor, **neighborp;
+  ridgeT *ridge, **ridgep;
+
+  if (!printall && qh_skipfacet(facet))
+    return;
+  if (qh PRINTnoplanes || (facet->visible && qh NEWfacets))
+    return;
+  if (!facet->normal)
+    return;
+  if (fp) {
+    for (i=0; i < 3; i++) {
+      color[i]= (facet->normal[i]+1.0)/2.0;
+      maximize_(color[i], -1.0);
+      minimize_(color[i], +1.0);
+    }
+  }
+  facet->visitid= qh visit_id;
+  if (facet->simplicial) {
+    FOREACHneighbor_(facet) {
+      if (neighbor->visitid != qh visit_id) {
+        if (fp)
+          qh_fprintf(fp, 9084, "3 %d %d %d %8.4g %8.4g %8.4g 1 # f%d f%d\n",
+                 3*num, 3*num+1, 3*num+2, color[0], color[1], color[2],
+                 facet->id, neighbor->id);
+        num++;
+      }
+    }
+  }else {
+    FOREACHridge_(facet->ridges) {
+      neighbor= otherfacet_(ridge, facet);
+      if (neighbor->visitid != qh visit_id) {
+        if (fp)
+          qh_fprintf(fp, 9085, "3 %d %d %d %8.4g %8.4g %8.4g 1 #r%d f%d f%d\n",
+                 3*num, 3*num+1, 3*num+2, color[0], color[1], color[2],
+                 ridge->id, facet->id, neighbor->id);
+        num++;
+      }
+    }
+  }
+  *nump= num;
+} /* printend4geom */
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="printextremes">-</a>
+
+  qh_printextremes( fp, facetlist, facets, printall )
+    print extreme points for convex hulls or halfspace intersections
+
+  notes:
+    #points, followed by ids, one per line
+
+    sorted by id
+    same order as qh_printpoints_out if no coplanar/interior points
+*/
+void qh_printextremes(FILE *fp, facetT *facetlist, setT *facets, boolT printall) {
+  setT *vertices, *points;
+  pointT *point;
+  vertexT *vertex, **vertexp;
+  int id;
+  int numpoints=0, point_i, point_n;
+  int allpoints= qh num_points + qh_setsize(qh other_points);
+
+  points= qh_settemp(allpoints);
+  qh_setzero(points, 0, allpoints);
+  vertices= qh_facetvertices(facetlist, facets, printall);
+  FOREACHvertex_(vertices) {
+    id= qh_pointid(vertex->point);
+    if (id >= 0) {
+      SETelem_(points, id)= vertex->point;
+      numpoints++;
+    }
+  }
+  qh_settempfree(&vertices);
+  qh_fprintf(fp, 9086, "%d\n", numpoints);
+  FOREACHpoint_i_(points) {
+    if (point)
+      qh_fprintf(fp, 9087, "%d\n", point_i);
+  }
+  qh_settempfree(&points);
+} /* printextremes */
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="printextremes_2d">-</a>
+
+  qh_printextremes_2d( fp, facetlist, facets, printall )
+    prints point ids for facets in qh_ORIENTclock order
+
+  notes:
+    #points, followed by ids, one per line
+    if facetlist/facets are disjoint than the output includes skips
+    errors if facets form a loop
+    does not print coplanar points
+*/
+void qh_printextremes_2d(FILE *fp, facetT *facetlist, setT *facets, boolT printall) {
+  int numfacets, numridges, totneighbors, numcoplanars, numsimplicial, numtricoplanars;
+  setT *vertices;
+  facetT *facet, *startfacet, *nextfacet;
+  vertexT *vertexA, *vertexB;
+
+  qh_countfacets(facetlist, facets, printall, &numfacets, &numsimplicial,
+      &totneighbors, &numridges, &numcoplanars, &numtricoplanars); /* marks qh visit_id */
+  vertices= qh_facetvertices(facetlist, facets, printall);
+  qh_fprintf(fp, 9088, "%d\n", qh_setsize(vertices));
+  qh_settempfree(&vertices);
+  if (!numfacets)
+    return;
+  facet= startfacet= facetlist ? facetlist : SETfirstt_(facets, facetT);
+  qh vertex_visit++;
+  qh visit_id++;
+  do {
+    if (facet->toporient ^ qh_ORIENTclock) {
+      vertexA= SETfirstt_(facet->vertices, vertexT);
+      vertexB= SETsecondt_(facet->vertices, vertexT);
+      nextfacet= SETfirstt_(facet->neighbors, facetT);
+    }else {
+      vertexA= SETsecondt_(facet->vertices, vertexT);
+      vertexB= SETfirstt_(facet->vertices, vertexT);
+      nextfacet= SETsecondt_(facet->neighbors, facetT);
+    }
+    if (facet->visitid == qh visit_id) {
+      qh_fprintf(qh ferr, 6218, "Qhull internal error (qh_printextremes_2d): loop in facet list.  facet %d nextfacet %d\n",
+                 facet->id, nextfacet->id);
+      qh_errexit2(qh_ERRqhull, facet, nextfacet);
+    }
+    if (facet->visitid) {
+      if (vertexA->visitid != qh vertex_visit) {
+        vertexA->visitid= qh vertex_visit;
+        qh_fprintf(fp, 9089, "%d\n", qh_pointid(vertexA->point));
+      }
+      if (vertexB->visitid != qh vertex_visit) {
+        vertexB->visitid= qh vertex_visit;
+        qh_fprintf(fp, 9090, "%d\n", qh_pointid(vertexB->point));
+      }
+    }
+    facet->visitid= qh visit_id;
+    facet= nextfacet;
+  }while (facet && facet != startfacet);
+} /* printextremes_2d */
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="printextremes_d">-</a>
+
+  qh_printextremes_d( fp, facetlist, facets, printall )
+    print extreme points of input sites for Delaunay triangulations
+
+  notes:
+    #points, followed by ids, one per line
+
+    unordered
+*/
+void qh_printextremes_d(FILE *fp, facetT *facetlist, setT *facets, boolT printall) {
+  setT *vertices;
+  vertexT *vertex, **vertexp;
+  boolT upperseen, lowerseen;
+  facetT *neighbor, **neighborp;
+  int numpoints=0;
+
+  vertices= qh_facetvertices(facetlist, facets, printall);
+  qh_vertexneighbors();
+  FOREACHvertex_(vertices) {
+    upperseen= lowerseen= False;
+    FOREACHneighbor_(vertex) {
+      if (neighbor->upperdelaunay)
+        upperseen= True;
+      else
+        lowerseen= True;
+    }
+    if (upperseen && lowerseen) {
+      vertex->seen= True;
+      numpoints++;
+    }else
+      vertex->seen= False;
+  }
+  qh_fprintf(fp, 9091, "%d\n", numpoints);
+  FOREACHvertex_(vertices) {
+    if (vertex->seen)
+      qh_fprintf(fp, 9092, "%d\n", qh_pointid(vertex->point));
+  }
+  qh_settempfree(&vertices);
+} /* printextremes_d */
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="printfacet">-</a>
+
+  qh_printfacet( fp, facet )
+    prints all fields of a facet to fp
+
+  notes:
+    ridges printed in neighbor order
+*/
+void qh_printfacet(FILE *fp, facetT *facet) {
+
+  qh_printfacetheader(fp, facet);
+  if (facet->ridges)
+    qh_printfacetridges(fp, facet);
+} /* printfacet */
+
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="printfacet2geom">-</a>
+
+  qh_printfacet2geom( fp, facet, color )
+    print facet as part of a 2-d VECT for Geomview
+
+    notes:
+      assume precise calculations in io.c with roundoff covered by qh_GEOMepsilon
+      mindist is calculated within io.c.  maxoutside is calculated elsewhere
+      so a DISTround error may have occurred.
+*/
+void qh_printfacet2geom(FILE *fp, facetT *facet, realT color[3]) {
+  pointT *point0, *point1;
+  realT mindist, innerplane, outerplane;
+  int k;
+
+  qh_facet2point(facet, &point0, &point1, &mindist);
+  qh_geomplanes(facet, &outerplane, &innerplane);
+  if (qh PRINTouter || (!qh PRINTnoplanes && !qh PRINTinner))
+    qh_printfacet2geom_points(fp, point0, point1, facet, outerplane, color);
+  if (qh PRINTinner || (!qh PRINTnoplanes && !qh PRINTouter &&
+                outerplane - innerplane > 2 * qh MAXabs_coord * qh_GEOMepsilon)) {
+    for (k=3; k--; )
+      color[k]= 1.0 - color[k];
+    qh_printfacet2geom_points(fp, point0, point1, facet, innerplane, color);
+  }
+  qh_memfree(point1, qh normal_size);
+  qh_memfree(point0, qh normal_size);
+} /* printfacet2geom */
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="printfacet2geom_points">-</a>
+
+  qh_printfacet2geom_points( fp, point1, point2, facet, offset, color )
+    prints a 2-d facet as a VECT with 2 points at some offset.
+    The points are on the facet's plane.
+*/
+void qh_printfacet2geom_points(FILE *fp, pointT *point1, pointT *point2,
+                               facetT *facet, realT offset, realT color[3]) {
+  pointT *p1= point1, *p2= point2;
+
+  qh_fprintf(fp, 9093, "VECT 1 2 1 2 1 # f%d\n", facet->id);
+  if (offset != 0.0) {
+    p1= qh_projectpoint(p1, facet, -offset);
+    p2= qh_projectpoint(p2, facet, -offset);
+  }
+  qh_fprintf(fp, 9094, "%8.4g %8.4g %8.4g\n%8.4g %8.4g %8.4g\n",
+           p1[0], p1[1], 0.0, p2[0], p2[1], 0.0);
+  if (offset != 0.0) {
+    qh_memfree(p1, qh normal_size);
+    qh_memfree(p2, qh normal_size);
+  }
+  qh_fprintf(fp, 9095, "%8.4g %8.4g %8.4g 1.0\n", color[0], color[1], color[2]);
+} /* printfacet2geom_points */
+
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="printfacet2math">-</a>
+
+  qh_printfacet2math( fp, facet, format, notfirst )
+    print 2-d Maple or Mathematica output for a facet
+    may be non-simplicial
+
+  notes:
+    use %16.8f since Mathematica 2.2 does not handle exponential format
+    see qh_printfacet3math
+*/
+void qh_printfacet2math(FILE *fp, facetT *facet, qh_PRINT format, int notfirst) {
+  pointT *point0, *point1;
+  realT mindist;
+  const char *pointfmt;
+
+  qh_facet2point(facet, &point0, &point1, &mindist);
+  if (notfirst)
+    qh_fprintf(fp, 9096, ",");
+  if (format == qh_PRINTmaple)
+    pointfmt= "[[%16.8f, %16.8f], [%16.8f, %16.8f]]\n";
+  else
+    pointfmt= "Line[{{%16.8f, %16.8f}, {%16.8f, %16.8f}}]\n";
+  qh_fprintf(fp, 9097, pointfmt, point0[0], point0[1], point1[0], point1[1]);
+  qh_memfree(point1, qh normal_size);
+  qh_memfree(point0, qh normal_size);
+} /* printfacet2math */
+
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="printfacet3geom_nonsimplicial">-</a>
+
+  qh_printfacet3geom_nonsimplicial( fp, facet, color )
+    print Geomview OFF for a 3-d nonsimplicial facet.
+    if DOintersections, prints ridges to unvisited neighbors(qh visit_id)
+
+  notes
+    uses facet->visitid for intersections and ridges
+*/
+void qh_printfacet3geom_nonsimplicial(FILE *fp, facetT *facet, realT color[3]) {
+  ridgeT *ridge, **ridgep;
+  setT *projectedpoints, *vertices;
+  vertexT *vertex, **vertexp, *vertexA, *vertexB;
+  pointT *projpt, *point, **pointp;
+  facetT *neighbor;
+  realT dist, outerplane, innerplane;
+  int cntvertices, k;
+  realT black[3]={0, 0, 0}, green[3]={0, 1, 0};
+
+  qh_geomplanes(facet, &outerplane, &innerplane);
+  vertices= qh_facet3vertex(facet); /* oriented */
+  cntvertices= qh_setsize(vertices);
+  projectedpoints= qh_settemp(cntvertices);
+  FOREACHvertex_(vertices) {
+    zinc_(Zdistio);
+    qh_distplane(vertex->point, facet, &dist);
+    projpt= qh_projectpoint(vertex->point, facet, dist);
+    qh_setappend(&projectedpoints, projpt);
+  }
+  if (qh PRINTouter || (!qh PRINTnoplanes && !qh PRINTinner))
+    qh_printfacet3geom_points(fp, projectedpoints, facet, outerplane, color);
+  if (qh PRINTinner || (!qh PRINTnoplanes && !qh PRINTouter &&
+                outerplane - innerplane > 2 * qh MAXabs_coord * qh_GEOMepsilon)) {
+    for (k=3; k--; )
+      color[k]= 1.0 - color[k];
+    qh_printfacet3geom_points(fp, projectedpoints, facet, innerplane, color);
+  }
+  FOREACHpoint_(projectedpoints)
+    qh_memfree(point, qh normal_size);
+  qh_settempfree(&projectedpoints);
+  qh_settempfree(&vertices);
+  if ((qh DOintersections || qh PRINTridges)
+  && (!facet->visible || !qh NEWfacets)) {
+    facet->visitid= qh visit_id;
+    FOREACHridge_(facet->ridges) {
+      neighbor= otherfacet_(ridge, facet);
+      if (neighbor->visitid != qh visit_id) {
+        if (qh DOintersections)
+          qh_printhyperplaneintersection(fp, facet, neighbor, ridge->vertices, black);
+        if (qh PRINTridges) {
+          vertexA= SETfirstt_(ridge->vertices, vertexT);
+          vertexB= SETsecondt_(ridge->vertices, vertexT);
+          qh_printline3geom(fp, vertexA->point, vertexB->point, green);
+        }
+      }
+    }
+  }
+} /* printfacet3geom_nonsimplicial */
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="printfacet3geom_points">-</a>
+
+  qh_printfacet3geom_points( fp, points, facet, offset )
+    prints a 3-d facet as OFF Geomview object.
+    offset is relative to the facet's hyperplane
+    Facet is determined as a list of points
+*/
+void qh_printfacet3geom_points(FILE *fp, setT *points, facetT *facet, realT offset, realT color[3]) {
+  int k, n= qh_setsize(points), i;
+  pointT *point, **pointp;
+  setT *printpoints;
+
+  qh_fprintf(fp, 9098, "{ OFF %d 1 1 # f%d\n", n, facet->id);
+  if (offset != 0.0) {
+    printpoints= qh_settemp(n);
+    FOREACHpoint_(points)
+      qh_setappend(&printpoints, qh_projectpoint(point, facet, -offset));
+  }else
+    printpoints= points;
+  FOREACHpoint_(printpoints) {
+    for (k=0; k < qh hull_dim; k++) {
+      if (k == qh DROPdim)
+        qh_fprintf(fp, 9099, "0 ");
+      else
+        qh_fprintf(fp, 9100, "%8.4g ", point[k]);
+    }
+    if (printpoints != points)
+      qh_memfree(point, qh normal_size);
+    qh_fprintf(fp, 9101, "\n");
+  }
+  if (printpoints != points)
+    qh_settempfree(&printpoints);
+  qh_fprintf(fp, 9102, "%d ", n);
+  for (i=0; i < n; i++)
+    qh_fprintf(fp, 9103, "%d ", i);
+  qh_fprintf(fp, 9104, "%8.4g %8.4g %8.4g 1.0 }\n", color[0], color[1], color[2]);
+} /* printfacet3geom_points */
+
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="printfacet3geom_simplicial">-</a>
+
+  qh_printfacet3geom_simplicial(  )
+    print Geomview OFF for a 3-d simplicial facet.
+
+  notes:
+    may flip color
+    uses facet->visitid for intersections and ridges
+
+    assume precise calculations in io.c with roundoff covered by qh_GEOMepsilon
+    innerplane may be off by qh DISTround.  Maxoutside is calculated elsewhere
+    so a DISTround error may have occurred.
+*/
+void qh_printfacet3geom_simplicial(FILE *fp, facetT *facet, realT color[3]) {
+  setT *points, *vertices;
+  vertexT *vertex, **vertexp, *vertexA, *vertexB;
+  facetT *neighbor, **neighborp;
+  realT outerplane, innerplane;
+  realT black[3]={0, 0, 0}, green[3]={0, 1, 0};
+  int k;
+
+  qh_geomplanes(facet, &outerplane, &innerplane);
+  vertices= qh_facet3vertex(facet);
+  points= qh_settemp(qh TEMPsize);
+  FOREACHvertex_(vertices)
+    qh_setappend(&points, vertex->point);
+  if (qh PRINTouter || (!qh PRINTnoplanes && !qh PRINTinner))
+    qh_printfacet3geom_points(fp, points, facet, outerplane, color);
+  if (qh PRINTinner || (!qh PRINTnoplanes && !qh PRINTouter &&
+              outerplane - innerplane > 2 * qh MAXabs_coord * qh_GEOMepsilon)) {
+    for (k=3; k--; )
+      color[k]= 1.0 - color[k];
+    qh_printfacet3geom_points(fp, points, facet, innerplane, color);
+  }
+  qh_settempfree(&points);
+  qh_settempfree(&vertices);
+  if ((qh DOintersections || qh PRINTridges)
+  && (!facet->visible || !qh NEWfacets)) {
+    facet->visitid= qh visit_id;
+    FOREACHneighbor_(facet) {
+      if (neighbor->visitid != qh visit_id) {
+        vertices= qh_setnew_delnthsorted(facet->vertices, qh hull_dim,
+                          SETindex_(facet->neighbors, neighbor), 0);
+        if (qh DOintersections)
+           qh_printhyperplaneintersection(fp, facet, neighbor, vertices, black);
+        if (qh PRINTridges) {
+          vertexA= SETfirstt_(vertices, vertexT);
+          vertexB= SETsecondt_(vertices, vertexT);
+          qh_printline3geom(fp, vertexA->point, vertexB->point, green);
+        }
+        qh_setfree(&vertices);
+      }
+    }
+  }
+} /* printfacet3geom_simplicial */
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="printfacet3math">-</a>
+
+  qh_printfacet3math( fp, facet, notfirst )
+    print 3-d Maple or Mathematica output for a facet
+
+  notes:
+    may be non-simplicial
+    use %16.8f since Mathematica 2.2 does not handle exponential format
+    see qh_printfacet2math
+*/
+void qh_printfacet3math(FILE *fp, facetT *facet, qh_PRINT format, int notfirst) {
+  vertexT *vertex, **vertexp;
+  setT *points, *vertices;
+  pointT *point, **pointp;
+  boolT firstpoint= True;
+  realT dist;
+  const char *pointfmt, *endfmt;
+
+  if (notfirst)
+    qh_fprintf(fp, 9105, ",\n");
+  vertices= qh_facet3vertex(facet);
+  points= qh_settemp(qh_setsize(vertices));
+  FOREACHvertex_(vertices) {
+    zinc_(Zdistio);
+    qh_distplane(vertex->point, facet, &dist);
+    point= qh_projectpoint(vertex->point, facet, dist);
+    qh_setappend(&points, point);
+  }
+  if (format == qh_PRINTmaple) {
+    qh_fprintf(fp, 9106, "[");
+    pointfmt= "[%16.8f, %16.8f, %16.8f]";
+    endfmt= "]";
+  }else {
+    qh_fprintf(fp, 9107, "Polygon[{");
+    pointfmt= "{%16.8f, %16.8f, %16.8f}";
+    endfmt= "}]";
+  }
+  FOREACHpoint_(points) {
+    if (firstpoint)
+      firstpoint= False;
+    else
+      qh_fprintf(fp, 9108, ",\n");
+    qh_fprintf(fp, 9109, pointfmt, point[0], point[1], point[2]);
+  }
+  FOREACHpoint_(points)
+    qh_memfree(point, qh normal_size);
+  qh_settempfree(&points);
+  qh_settempfree(&vertices);
+  qh_fprintf(fp, 9110, "%s", endfmt);
+} /* printfacet3math */
+
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="printfacet3vertex">-</a>
+
+  qh_printfacet3vertex( fp, facet, format )
+    print vertices in a 3-d facet as point ids
+
+  notes:
+    prints number of vertices first if format == qh_PRINToff
+    the facet may be non-simplicial
+*/
+void qh_printfacet3vertex(FILE *fp, facetT *facet, qh_PRINT format) {
+  vertexT *vertex, **vertexp;
+  setT *vertices;
+
+  vertices= qh_facet3vertex(facet);
+  if (format == qh_PRINToff)
+    qh_fprintf(fp, 9111, "%d ", qh_setsize(vertices));
+  FOREACHvertex_(vertices)
+    qh_fprintf(fp, 9112, "%d ", qh_pointid(vertex->point));
+  qh_fprintf(fp, 9113, "\n");
+  qh_settempfree(&vertices);
+} /* printfacet3vertex */
+
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="printfacet4geom_nonsimplicial">-</a>
+
+  qh_printfacet4geom_nonsimplicial(  )
+    print Geomview 4OFF file for a 4d nonsimplicial facet
+    prints all ridges to unvisited neighbors (qh.visit_id)
+    if qh.DROPdim
+      prints in OFF format
+
+  notes:
+    must agree with printend4geom()
+*/
+void qh_printfacet4geom_nonsimplicial(FILE *fp, facetT *facet, realT color[3]) {
+  facetT *neighbor;
+  ridgeT *ridge, **ridgep;
+  vertexT *vertex, **vertexp;
+  pointT *point;
+  int k;
+  realT dist;
+
+  facet->visitid= qh visit_id;
+  if (qh PRINTnoplanes || (facet->visible && qh NEWfacets))
+    return;
+  FOREACHridge_(facet->ridges) {
+    neighbor= otherfacet_(ridge, facet);
+    if (neighbor->visitid == qh visit_id)
+      continue;
+    if (qh PRINTtransparent && !neighbor->good)
+      continue;
+    if (qh DOintersections)
+      qh_printhyperplaneintersection(fp, facet, neighbor, ridge->vertices, color);
+    else {
+      if (qh DROPdim >= 0)
+        qh_fprintf(fp, 9114, "OFF 3 1 1 # f%d\n", facet->id);
+      else {
+        qh printoutvar++;
+        qh_fprintf(fp, 9115, "# r%d between f%d f%d\n", ridge->id, facet->id, neighbor->id);
+      }
+      FOREACHvertex_(ridge->vertices) {
+        zinc_(Zdistio);
+        qh_distplane(vertex->point,facet, &dist);
+        point=qh_projectpoint(vertex->point,facet, dist);
+        for (k=0; k < qh hull_dim; k++) {
+          if (k != qh DROPdim)
+            qh_fprintf(fp, 9116, "%8.4g ", point[k]);
+        }
+        qh_fprintf(fp, 9117, "\n");
+        qh_memfree(point, qh normal_size);
+      }
+      if (qh DROPdim >= 0)
+        qh_fprintf(fp, 9118, "3 0 1 2 %8.4g %8.4g %8.4g\n", color[0], color[1], color[2]);
+    }
+  }
+} /* printfacet4geom_nonsimplicial */
+
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="printfacet4geom_simplicial">-</a>
+
+  qh_printfacet4geom_simplicial( fp, facet, color )
+    print Geomview 4OFF file for a 4d simplicial facet
+    prints triangles for unvisited neighbors (qh.visit_id)
+
+  notes:
+    must agree with printend4geom()
+*/
+void qh_printfacet4geom_simplicial(FILE *fp, facetT *facet, realT color[3]) {
+  setT *vertices;
+  facetT *neighbor, **neighborp;
+  vertexT *vertex, **vertexp;
+  int k;
+
+  facet->visitid= qh visit_id;
+  if (qh PRINTnoplanes || (facet->visible && qh NEWfacets))
+    return;
+  FOREACHneighbor_(facet) {
+    if (neighbor->visitid == qh visit_id)
+      continue;
+    if (qh PRINTtransparent && !neighbor->good)
+      continue;
+    vertices= qh_setnew_delnthsorted(facet->vertices, qh hull_dim,
+                          SETindex_(facet->neighbors, neighbor), 0);
+    if (qh DOintersections)
+      qh_printhyperplaneintersection(fp, facet, neighbor, vertices, color);
+    else {
+      if (qh DROPdim >= 0)
+        qh_fprintf(fp, 9119, "OFF 3 1 1 # ridge between f%d f%d\n",
+                facet->id, neighbor->id);
+      else {
+        qh printoutvar++;
+        qh_fprintf(fp, 9120, "# ridge between f%d f%d\n", facet->id, neighbor->id);
+      }
+      FOREACHvertex_(vertices) {
+        for (k=0; k < qh hull_dim; k++) {
+          if (k != qh DROPdim)
+            qh_fprintf(fp, 9121, "%8.4g ", vertex->point[k]);
+        }
+        qh_fprintf(fp, 9122, "\n");
+      }
+      if (qh DROPdim >= 0)
+        qh_fprintf(fp, 9123, "3 0 1 2 %8.4g %8.4g %8.4g\n", color[0], color[1], color[2]);
+    }
+    qh_setfree(&vertices);
+  }
+} /* printfacet4geom_simplicial */
+
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="printfacetNvertex_nonsimplicial">-</a>
+
+  qh_printfacetNvertex_nonsimplicial( fp, facet, id, format )
+    print vertices for an N-d non-simplicial facet
+    triangulates each ridge to the id
+*/
+void qh_printfacetNvertex_nonsimplicial(FILE *fp, facetT *facet, int id, qh_PRINT format) {
+  vertexT *vertex, **vertexp;
+  ridgeT *ridge, **ridgep;
+
+  if (facet->visible && qh NEWfacets)
+    return;
+  FOREACHridge_(facet->ridges) {
+    if (format == qh_PRINTtriangles)
+      qh_fprintf(fp, 9124, "%d ", qh hull_dim);
+    qh_fprintf(fp, 9125, "%d ", id);
+    if ((ridge->top == facet) ^ qh_ORIENTclock) {
+      FOREACHvertex_(ridge->vertices)
+        qh_fprintf(fp, 9126, "%d ", qh_pointid(vertex->point));
+    }else {
+      FOREACHvertexreverse12_(ridge->vertices)
+        qh_fprintf(fp, 9127, "%d ", qh_pointid(vertex->point));
+    }
+    qh_fprintf(fp, 9128, "\n");
+  }
+} /* printfacetNvertex_nonsimplicial */
+
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="printfacetNvertex_simplicial">-</a>
+
+  qh_printfacetNvertex_simplicial( fp, facet, format )
+    print vertices for an N-d simplicial facet
+    prints vertices for non-simplicial facets
+      2-d facets (orientation preserved by qh_mergefacet2d)
+      PRINToff ('o') for 4-d and higher
+*/
+void qh_printfacetNvertex_simplicial(FILE *fp, facetT *facet, qh_PRINT format) {
+  vertexT *vertex, **vertexp;
+
+  if (format == qh_PRINToff || format == qh_PRINTtriangles)
+    qh_fprintf(fp, 9129, "%d ", qh_setsize(facet->vertices));
+  if ((facet->toporient ^ qh_ORIENTclock)
+  || (qh hull_dim > 2 && !facet->simplicial)) {
+    FOREACHvertex_(facet->vertices)
+      qh_fprintf(fp, 9130, "%d ", qh_pointid(vertex->point));
+  }else {
+    FOREACHvertexreverse12_(facet->vertices)
+      qh_fprintf(fp, 9131, "%d ", qh_pointid(vertex->point));
+  }
+  qh_fprintf(fp, 9132, "\n");
+} /* printfacetNvertex_simplicial */
+
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="printfacetheader">-</a>
+
+  qh_printfacetheader( fp, facet )
+    prints header fields of a facet to fp
+
+  notes:
+    for 'f' output and debugging
+    Same as QhullFacet::printHeader()
+*/
+void qh_printfacetheader(FILE *fp, facetT *facet) {
+  pointT *point, **pointp, *furthest;
+  facetT *neighbor, **neighborp;
+  realT dist;
+
+  if (facet == qh_MERGEridge) {
+    qh_fprintf(fp, 9133, " MERGEridge\n");
+    return;
+  }else if (facet == qh_DUPLICATEridge) {
+    qh_fprintf(fp, 9134, " DUPLICATEridge\n");
+    return;
+  }else if (!facet) {
+    qh_fprintf(fp, 9135, " NULLfacet\n");
+    return;
+  }
+  qh old_randomdist= qh RANDOMdist;
+  qh RANDOMdist= False;
+  qh_fprintf(fp, 9136, "- f%d\n", facet->id);
+  qh_fprintf(fp, 9137, "    - flags:");
+  if (facet->toporient)
+    qh_fprintf(fp, 9138, " top");
+  else
+    qh_fprintf(fp, 9139, " bottom");
+  if (facet->simplicial)
+    qh_fprintf(fp, 9140, " simplicial");
+  if (facet->tricoplanar)
+    qh_fprintf(fp, 9141, " tricoplanar");
+  if (facet->upperdelaunay)
+    qh_fprintf(fp, 9142, " upperDelaunay");
+  if (facet->visible)
+    qh_fprintf(fp, 9143, " visible");
+  if (facet->newfacet)
+    qh_fprintf(fp, 9144, " new");
+  if (facet->tested)
+    qh_fprintf(fp, 9145, " tested");
+  if (!facet->good)
+    qh_fprintf(fp, 9146, " notG");
+  if (facet->seen)
+    qh_fprintf(fp, 9147, " seen");
+  if (facet->coplanar)
+    qh_fprintf(fp, 9148, " coplanar");
+  if (facet->mergehorizon)
+    qh_fprintf(fp, 9149, " mergehorizon");
+  if (facet->keepcentrum)
+    qh_fprintf(fp, 9150, " keepcentrum");
+  if (facet->dupridge)
+    qh_fprintf(fp, 9151, " dupridge");
+  if (facet->mergeridge && !facet->mergeridge2)
+    qh_fprintf(fp, 9152, " mergeridge1");
+  if (facet->mergeridge2)
+    qh_fprintf(fp, 9153, " mergeridge2");
+  if (facet->newmerge)
+    qh_fprintf(fp, 9154, " newmerge");
+  if (facet->flipped)
+    qh_fprintf(fp, 9155, " flipped");
+  if (facet->notfurthest)
+    qh_fprintf(fp, 9156, " notfurthest");
+  if (facet->degenerate)
+    qh_fprintf(fp, 9157, " degenerate");
+  if (facet->redundant)
+    qh_fprintf(fp, 9158, " redundant");
+  qh_fprintf(fp, 9159, "\n");
+  if (facet->isarea)
+    qh_fprintf(fp, 9160, "    - area: %2.2g\n", facet->f.area);
+  else if (qh NEWfacets && facet->visible && facet->f.replace)
+    qh_fprintf(fp, 9161, "    - replacement: f%d\n", facet->f.replace->id);
+  else if (facet->newfacet) {
+    if (facet->f.samecycle && facet->f.samecycle != facet)
+      qh_fprintf(fp, 9162, "    - shares same visible/horizon as f%d\n", facet->f.samecycle->id);
+  }else if (facet->tricoplanar /* !isarea */) {
+    if (facet->f.triowner)
+      qh_fprintf(fp, 9163, "    - owner of normal & centrum is facet f%d\n", facet->f.triowner->id);
+  }else if (facet->f.newcycle)
+    qh_fprintf(fp, 9164, "    - was horizon to f%d\n", facet->f.newcycle->id);
+  if (facet->nummerge)
+    qh_fprintf(fp, 9165, "    - merges: %d\n", facet->nummerge);
+  qh_printpointid(fp, "    - normal: ", qh hull_dim, facet->normal, qh_IDunknown);
+  qh_fprintf(fp, 9166, "    - offset: %10.7g\n", facet->offset);
+  if (qh CENTERtype == qh_ASvoronoi || facet->center)
+    qh_printcenter(fp, qh_PRINTfacets, "    - center: ", facet);
+#if qh_MAXoutside
+  if (facet->maxoutside > qh DISTround)
+    qh_fprintf(fp, 9167, "    - maxoutside: %10.7g\n", facet->maxoutside);
+#endif
+  if (!SETempty_(facet->outsideset)) {
+    furthest= (pointT*)qh_setlast(facet->outsideset);
+    if (qh_setsize(facet->outsideset) < 6) {
+      qh_fprintf(fp, 9168, "    - outside set(furthest p%d):\n", qh_pointid(furthest));
+      FOREACHpoint_(facet->outsideset)
+        qh_printpoint(fp, "     ", point);
+    }else if (qh_setsize(facet->outsideset) < 21) {
+      qh_printpoints(fp, "    - outside set:", facet->outsideset);
+    }else {
+      qh_fprintf(fp, 9169, "    - outside set:  %d points.", qh_setsize(facet->outsideset));
+      qh_printpoint(fp, "  Furthest", furthest);
+    }
+#if !qh_COMPUTEfurthest
+    qh_fprintf(fp, 9170, "    - furthest distance= %2.2g\n", facet->furthestdist);
+#endif
+  }
+  if (!SETempty_(facet->coplanarset)) {
+    furthest= (pointT*)qh_setlast(facet->coplanarset);
+    if (qh_setsize(facet->coplanarset) < 6) {
+      qh_fprintf(fp, 9171, "    - coplanar set(furthest p%d):\n", qh_pointid(furthest));
+      FOREACHpoint_(facet->coplanarset)
+        qh_printpoint(fp, "     ", point);
+    }else if (qh_setsize(facet->coplanarset) < 21) {
+      qh_printpoints(fp, "    - coplanar set:", facet->coplanarset);
+    }else {
+      qh_fprintf(fp, 9172, "    - coplanar set:  %d points.", qh_setsize(facet->coplanarset));
+      qh_printpoint(fp, "  Furthest", furthest);
+    }
+    zinc_(Zdistio);
+    qh_distplane(furthest, facet, &dist);
+    qh_fprintf(fp, 9173, "      furthest distance= %2.2g\n", dist);
+  }
+  qh_printvertices(fp, "    - vertices:", facet->vertices);
+  qh_fprintf(fp, 9174, "    - neighboring facets:");
+  FOREACHneighbor_(facet) {
+    if (neighbor == qh_MERGEridge)
+      qh_fprintf(fp, 9175, " MERGE");
+    else if (neighbor == qh_DUPLICATEridge)
+      qh_fprintf(fp, 9176, " DUP");
+    else
+      qh_fprintf(fp, 9177, " f%d", neighbor->id);
+  }
+  qh_fprintf(fp, 9178, "\n");
+  qh RANDOMdist= qh old_randomdist;
+} /* printfacetheader */
+
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="printfacetridges">-</a>
+
+  qh_printfacetridges( fp, facet )
+    prints ridges of a facet to fp
+
+  notes:
+    ridges printed in neighbor order
+    assumes the ridges exist
+    for 'f' output
+    same as QhullFacet::printRidges
+*/
+void qh_printfacetridges(FILE *fp, facetT *facet) {
+  facetT *neighbor, **neighborp;
+  ridgeT *ridge, **ridgep;
+  int numridges= 0;
+
+
+  if (facet->visible && qh NEWfacets) {
+    qh_fprintf(fp, 9179, "    - ridges(ids may be garbage):");
+    FOREACHridge_(facet->ridges)
+      qh_fprintf(fp, 9180, " r%d", ridge->id);
+    qh_fprintf(fp, 9181, "\n");
+  }else {
+    qh_fprintf(fp, 9182, "    - ridges:\n");
+    FOREACHridge_(facet->ridges)
+      ridge->seen= False;
+    if (qh hull_dim == 3) {
+      ridge= SETfirstt_(facet->ridges, ridgeT);
+      while (ridge && !ridge->seen) {
+        ridge->seen= True;
+        qh_printridge(fp, ridge);
+        numridges++;
+        ridge= qh_nextridge3d(ridge, facet, NULL);
+        }
+    }else {
+      FOREACHneighbor_(facet) {
+        FOREACHridge_(facet->ridges) {
+          if (otherfacet_(ridge,facet) == neighbor) {
+            ridge->seen= True;
+            qh_printridge(fp, ridge);
+            numridges++;
+          }
+        }
+      }
+    }
+    if (numridges != qh_setsize(facet->ridges)) {
+      qh_fprintf(fp, 9183, "     - all ridges:");
+      FOREACHridge_(facet->ridges)
+        qh_fprintf(fp, 9184, " r%d", ridge->id);
+        qh_fprintf(fp, 9185, "\n");
+    }
+    FOREACHridge_(facet->ridges) {
+      if (!ridge->seen)
+        qh_printridge(fp, ridge);
+    }
+  }
+} /* printfacetridges */
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="printfacets">-</a>
+
+  qh_printfacets( fp, format, facetlist, facets, printall )
+    prints facetlist and/or facet set in output format
+
+  notes:
+    also used for specialized formats ('FO' and summary)
+    turns off 'Rn' option since want actual numbers
+*/
+void qh_printfacets(FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall) {
+  int numfacets, numsimplicial, numridges, totneighbors, numcoplanars, numtricoplanars;
+  facetT *facet, **facetp;
+  setT *vertices;
+  coordT *center;
+  realT outerplane, innerplane;
+
+  qh old_randomdist= qh RANDOMdist;
+  qh RANDOMdist= False;
+  if (qh CDDoutput && (format == qh_PRINTcentrums || format == qh_PRINTpointintersect || format == qh_PRINToff))
+    qh_fprintf(qh ferr, 7056, "qhull warning: CDD format is not available for centrums, halfspace\nintersections, and OFF file format.\n");
+  if (format == qh_PRINTnone)
+    ; /* print nothing */
+  else if (format == qh_PRINTaverage) {
+    vertices= qh_facetvertices(facetlist, facets, printall);
+    center= qh_getcenter(vertices);
+    qh_fprintf(fp, 9186, "%d 1\n", qh hull_dim);
+    qh_printpointid(fp, NULL, qh hull_dim, center, qh_IDunknown);
+    qh_memfree(center, qh normal_size);
+    qh_settempfree(&vertices);
+  }else if (format == qh_PRINTextremes) {
+    if (qh DELAUNAY)
+      qh_printextremes_d(fp, facetlist, facets, printall);
+    else if (qh hull_dim == 2)
+      qh_printextremes_2d(fp, facetlist, facets, printall);
+    else
+      qh_printextremes(fp, facetlist, facets, printall);
+  }else if (format == qh_PRINToptions)
+    qh_fprintf(fp, 9187, "Options selected for Qhull %s:\n%s\n", qh_version, qh qhull_options);
+  else if (format == qh_PRINTpoints && !qh VORONOI)
+    qh_printpoints_out(fp, facetlist, facets, printall);
+  else if (format == qh_PRINTqhull)
+    qh_fprintf(fp, 9188, "%s | %s\n", qh rbox_command, qh qhull_command);
+  else if (format == qh_PRINTsize) {
+    qh_fprintf(fp, 9189, "0\n2 ");
+    qh_fprintf(fp, 9190, qh_REAL_1, qh totarea);
+    qh_fprintf(fp, 9191, qh_REAL_1, qh totvol);
+    qh_fprintf(fp, 9192, "\n");
+  }else if (format == qh_PRINTsummary) {
+    qh_countfacets(facetlist, facets, printall, &numfacets, &numsimplicial,
+      &totneighbors, &numridges, &numcoplanars, &numtricoplanars);
+    vertices= qh_facetvertices(facetlist, facets, printall);
+    qh_fprintf(fp, 9193, "10 %d %d %d %d %d %d %d %d %d %d\n2 ", qh hull_dim,
+                qh num_points + qh_setsize(qh other_points),
+                qh num_vertices, qh num_facets - qh num_visible,
+                qh_setsize(vertices), numfacets, numcoplanars,
+                numfacets - numsimplicial, zzval_(Zdelvertextot),
+                numtricoplanars);
+    qh_settempfree(&vertices);
+    qh_outerinner(NULL, &outerplane, &innerplane);
+    qh_fprintf(fp, 9194, qh_REAL_2n, outerplane, innerplane);
+  }else if (format == qh_PRINTvneighbors)
+    qh_printvneighbors(fp, facetlist, facets, printall);
+  else if (qh VORONOI && format == qh_PRINToff)
+    qh_printvoronoi(fp, format, facetlist, facets, printall);
+  else if (qh VORONOI && format == qh_PRINTgeom) {
+    qh_printbegin(fp, format, facetlist, facets, printall);
+    qh_printvoronoi(fp, format, facetlist, facets, printall);
+    qh_printend(fp, format, facetlist, facets, printall);
+  }else if (qh VORONOI
+  && (format == qh_PRINTvertices || format == qh_PRINTinner || format == qh_PRINTouter))
+    qh_printvdiagram(fp, format, facetlist, facets, printall);
+  else {
+    qh_printbegin(fp, format, facetlist, facets, printall);
+    FORALLfacet_(facetlist)
+      qh_printafacet(fp, format, facet, printall);
+    FOREACHfacet_(facets)
+      qh_printafacet(fp, format, facet, printall);
+    qh_printend(fp, format, facetlist, facets, printall);
+  }
+  qh RANDOMdist= qh old_randomdist;
+} /* printfacets */
+
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="printhyperplaneintersection">-</a>
+
+  qh_printhyperplaneintersection( fp, facet1, facet2, vertices, color )
+    print Geomview OFF or 4OFF for the intersection of two hyperplanes in 3-d or 4-d
+*/
+void qh_printhyperplaneintersection(FILE *fp, facetT *facet1, facetT *facet2,
+                   setT *vertices, realT color[3]) {
+  realT costheta, denominator, dist1, dist2, s, t, mindenom, p[4];
+  vertexT *vertex, **vertexp;
+  int i, k;
+  boolT nearzero1, nearzero2;
+
+  costheta= qh_getangle(facet1->normal, facet2->normal);
+  denominator= 1 - costheta * costheta;
+  i= qh_setsize(vertices);
+  if (qh hull_dim == 3)
+    qh_fprintf(fp, 9195, "VECT 1 %d 1 %d 1 ", i, i);
+  else if (qh hull_dim == 4 && qh DROPdim >= 0)
+    qh_fprintf(fp, 9196, "OFF 3 1 1 ");
+  else
+    qh printoutvar++;
+  qh_fprintf(fp, 9197, "# intersect f%d f%d\n", facet1->id, facet2->id);
+  mindenom= 1 / (10.0 * qh MAXabs_coord);
+  FOREACHvertex_(vertices) {
+    zadd_(Zdistio, 2);
+    qh_distplane(vertex->point, facet1, &dist1);
+    qh_distplane(vertex->point, facet2, &dist2);
+    s= qh_divzero(-dist1 + costheta * dist2, denominator,mindenom,&nearzero1);
+    t= qh_divzero(-dist2 + costheta * dist1, denominator,mindenom,&nearzero2);
+    if (nearzero1 || nearzero2)
+      s= t= 0.0;
+    for (k=qh hull_dim; k--; )
+      p[k]= vertex->point[k] + facet1->normal[k] * s + facet2->normal[k] * t;
+    if (qh PRINTdim <= 3) {
+      qh_projectdim3(p, p);
+      qh_fprintf(fp, 9198, "%8.4g %8.4g %8.4g # ", p[0], p[1], p[2]);
+    }else
+      qh_fprintf(fp, 9199, "%8.4g %8.4g %8.4g %8.4g # ", p[0], p[1], p[2], p[3]);
+    if (nearzero1+nearzero2)
+      qh_fprintf(fp, 9200, "p%d(coplanar facets)\n", qh_pointid(vertex->point));
+    else
+      qh_fprintf(fp, 9201, "projected p%d\n", qh_pointid(vertex->point));
+  }
+  if (qh hull_dim == 3)
+    qh_fprintf(fp, 9202, "%8.4g %8.4g %8.4g 1.0\n", color[0], color[1], color[2]);
+  else if (qh hull_dim == 4 && qh DROPdim >= 0)
+    qh_fprintf(fp, 9203, "3 0 1 2 %8.4g %8.4g %8.4g 1.0\n", color[0], color[1], color[2]);
+} /* printhyperplaneintersection */
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="printline3geom">-</a>
+
+  qh_printline3geom( fp, pointA, pointB, color )
+    prints a line as a VECT
+    prints 0's for qh.DROPdim
+
+  notes:
+    if pointA == pointB,
+      it's a 1 point VECT
+*/
+void qh_printline3geom(FILE *fp, pointT *pointA, pointT *pointB, realT color[3]) {
+  int k;
+  realT pA[4], pB[4];
+
+  qh_projectdim3(pointA, pA);
+  qh_projectdim3(pointB, pB);
+  if ((fabs(pA[0] - pB[0]) > 1e-3) ||
+      (fabs(pA[1] - pB[1]) > 1e-3) ||
+      (fabs(pA[2] - pB[2]) > 1e-3)) {
+    qh_fprintf(fp, 9204, "VECT 1 2 1 2 1\n");
+    for (k=0; k < 3; k++)
+       qh_fprintf(fp, 9205, "%8.4g ", pB[k]);
+    qh_fprintf(fp, 9206, " # p%d\n", qh_pointid(pointB));
+  }else
+    qh_fprintf(fp, 9207, "VECT 1 1 1 1 1\n");
+  for (k=0; k < 3; k++)
+    qh_fprintf(fp, 9208, "%8.4g ", pA[k]);
+  qh_fprintf(fp, 9209, " # p%d\n", qh_pointid(pointA));
+  qh_fprintf(fp, 9210, "%8.4g %8.4g %8.4g 1\n", color[0], color[1], color[2]);
+}
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="printneighborhood">-</a>
+
+  qh_printneighborhood( fp, format, facetA, facetB, printall )
+    print neighborhood of one or two facets
+
+  notes:
+    calls qh_findgood_all()
+    bumps qh.visit_id
+*/
+void qh_printneighborhood(FILE *fp, qh_PRINT format, facetT *facetA, facetT *facetB, boolT printall) {
+  facetT *neighbor, **neighborp, *facet;
+  setT *facets;
+
+  if (format == qh_PRINTnone)
+    return;
+  qh_findgood_all(qh facet_list);
+  if (facetA == facetB)
+    facetB= NULL;
+  facets= qh_settemp(2*(qh_setsize(facetA->neighbors)+1));
+  qh visit_id++;
+  for (facet= facetA; facet; facet= ((facet == facetA) ? facetB : NULL)) {
+    if (facet->visitid != qh visit_id) {
+      facet->visitid= qh visit_id;
+      qh_setappend(&facets, facet);
+    }
+    FOREACHneighbor_(facet) {
+      if (neighbor->visitid == qh visit_id)
+        continue;
+      neighbor->visitid= qh visit_id;
+      if (printall || !qh_skipfacet(neighbor))
+        qh_setappend(&facets, neighbor);
+    }
+  }
+  qh_printfacets(fp, format, NULL, facets, printall);
+  qh_settempfree(&facets);
+} /* printneighborhood */
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="printpoint">-</a>
+
+  qh_printpoint( fp, string, point )
+  qh_printpointid( fp, string, dim, point, id )
+    prints the coordinates of a point
+
+  returns:
+    if string is defined
+      prints 'string p%d'.  Skips p%d if id=qh_IDunknown(-1) or qh_IDnone(-3)
+
+  notes:
+    nop if point is NULL
+    Same as QhullPoint's printPoint
+*/
+void qh_printpoint(FILE *fp, const char *string, pointT *point) {
+  int id= qh_pointid( point);
+
+  qh_printpointid( fp, string, qh hull_dim, point, id);
+} /* printpoint */
+
+void qh_printpointid(FILE *fp, const char *string, int dim, pointT *point, int id) {
+  int k;
+  realT r; /*bug fix*/
+
+  if (!point)
+    return;
+  if (string) {
+    qh_fprintf(fp, 9211, "%s", string);
+    if (id != qh_IDunknown && id != qh_IDnone)
+      qh_fprintf(fp, 9212, " p%d: ", id);
+  }
+  for (k=dim; k--; ) {
+    r= *point++;
+    if (string)
+      qh_fprintf(fp, 9213, " %8.4g", r);
+    else
+      qh_fprintf(fp, 9214, qh_REAL_1, r);
+  }
+  qh_fprintf(fp, 9215, "\n");
+} /* printpointid */
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="printpoint3">-</a>
+
+  qh_printpoint3( fp, point )
+    prints 2-d, 3-d, or 4-d point as Geomview 3-d coordinates
+*/
+void qh_printpoint3(FILE *fp, pointT *point) {
+  int k;
+  realT p[4];
+
+  qh_projectdim3(point, p);
+  for (k=0; k < 3; k++)
+    qh_fprintf(fp, 9216, "%8.4g ", p[k]);
+  qh_fprintf(fp, 9217, " # p%d\n", qh_pointid(point));
+} /* printpoint3 */
+
+/*----------------------------------------
+-printpoints- print pointids for a set of points starting at index
+   see geom.c
+*/
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="printpoints_out">-</a>
+
+  qh_printpoints_out( fp, facetlist, facets, printall )
+    prints vertices, coplanar/inside points, for facets by their point coordinates
+    allows qh.CDDoutput
+
+  notes:
+    same format as qhull input
+    if no coplanar/interior points,
+      same order as qh_printextremes
+*/
+void qh_printpoints_out(FILE *fp, facetT *facetlist, setT *facets, boolT printall) {
+  int allpoints= qh num_points + qh_setsize(qh other_points);
+  int numpoints=0, point_i, point_n;
+  setT *vertices, *points;
+  facetT *facet, **facetp;
+  pointT *point, **pointp;
+  vertexT *vertex, **vertexp;
+  int id;
+
+  points= qh_settemp(allpoints);
+  qh_setzero(points, 0, allpoints);
+  vertices= qh_facetvertices(facetlist, facets, printall);
+  FOREACHvertex_(vertices) {
+    id= qh_pointid(vertex->point);
+    if (id >= 0)
+      SETelem_(points, id)= vertex->point;
+  }
+  if (qh KEEPinside || qh KEEPcoplanar || qh KEEPnearinside) {
+    FORALLfacet_(facetlist) {
+      if (!printall && qh_skipfacet(facet))
+        continue;
+      FOREACHpoint_(facet->coplanarset) {
+        id= qh_pointid(point);
+        if (id >= 0)
+          SETelem_(points, id)= point;
+      }
+    }
+    FOREACHfacet_(facets) {
+      if (!printall && qh_skipfacet(facet))
+        continue;
+      FOREACHpoint_(facet->coplanarset) {
+        id= qh_pointid(point);
+        if (id >= 0)
+          SETelem_(points, id)= point;
+      }
+    }
+  }
+  qh_settempfree(&vertices);
+  FOREACHpoint_i_(points) {
+    if (point)
+      numpoints++;
+  }
+  if (qh CDDoutput)
+    qh_fprintf(fp, 9218, "%s | %s\nbegin\n%d %d real\n", qh rbox_command,
+             qh qhull_command, numpoints, qh hull_dim + 1);
+  else
+    qh_fprintf(fp, 9219, "%d\n%d\n", qh hull_dim, numpoints);
+  FOREACHpoint_i_(points) {
+    if (point) {
+      if (qh CDDoutput)
+        qh_fprintf(fp, 9220, "1 ");
+      qh_printpoint(fp, NULL, point);
+    }
+  }
+  if (qh CDDoutput)
+    qh_fprintf(fp, 9221, "end\n");
+  qh_settempfree(&points);
+} /* printpoints_out */
+
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="printpointvect">-</a>
+
+  qh_printpointvect( fp, point, normal, center, radius, color )
+    prints a 2-d, 3-d, or 4-d point as 3-d VECT's relative to normal or to center point
+*/
+void qh_printpointvect(FILE *fp, pointT *point, coordT *normal, pointT *center, realT radius, realT color[3]) {
+  realT diff[4], pointA[4];
+  int k;
+
+  for (k=qh hull_dim; k--; ) {
+    if (center)
+      diff[k]= point[k]-center[k];
+    else if (normal)
+      diff[k]= normal[k];
+    else
+      diff[k]= 0;
+  }
+  if (center)
+    qh_normalize2(diff, qh hull_dim, True, NULL, NULL);
+  for (k=qh hull_dim; k--; )
+    pointA[k]= point[k]+diff[k] * radius;
+  qh_printline3geom(fp, point, pointA, color);
+} /* printpointvect */
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="printpointvect2">-</a>
+
+  qh_printpointvect2( fp, point, normal, center, radius )
+    prints a 2-d, 3-d, or 4-d point as 2 3-d VECT's for an imprecise point
+*/
+void qh_printpointvect2(FILE *fp, pointT *point, coordT *normal, pointT *center, realT radius) {
+  realT red[3]={1, 0, 0}, yellow[3]={1, 1, 0};
+
+  qh_printpointvect(fp, point, normal, center, radius, red);
+  qh_printpointvect(fp, point, normal, center, -radius, yellow);
+} /* printpointvect2 */
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="printridge">-</a>
+
+  qh_printridge( fp, ridge )
+    prints the information in a ridge
+
+  notes:
+    for qh_printfacetridges()
+    same as operator<< [QhullRidge.cpp]
+*/
+void qh_printridge(FILE *fp, ridgeT *ridge) {
+
+  qh_fprintf(fp, 9222, "     - r%d", ridge->id);
+  if (ridge->tested)
+    qh_fprintf(fp, 9223, " tested");
+  if (ridge->nonconvex)
+    qh_fprintf(fp, 9224, " nonconvex");
+  qh_fprintf(fp, 9225, "\n");
+  qh_printvertices(fp, "           vertices:", ridge->vertices);
+  if (ridge->top && ridge->bottom)
+    qh_fprintf(fp, 9226, "           between f%d and f%d\n",
+            ridge->top->id, ridge->bottom->id);
+} /* printridge */
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="printspheres">-</a>
+
+  qh_printspheres( fp, vertices, radius )
+    prints 3-d vertices as OFF spheres
+
+  notes:
+    inflated octahedron from Stuart Levy earth/mksphere2
+*/
+void qh_printspheres(FILE *fp, setT *vertices, realT radius) {
+  vertexT *vertex, **vertexp;
+
+  qh printoutnum++;
+  qh_fprintf(fp, 9227, "{appearance {-edge -normal normscale 0} {\n\
+INST geom {define vsphere OFF\n\
+18 32 48\n\
+\n\
+0 0 1\n\
+1 0 0\n\
+0 1 0\n\
+-1 0 0\n\
+0 -1 0\n\
+0 0 -1\n\
+0.707107 0 0.707107\n\
+0 -0.707107 0.707107\n\
+0.707107 -0.707107 0\n\
+-0.707107 0 0.707107\n\
+-0.707107 -0.707107 0\n\
+0 0.707107 0.707107\n\
+-0.707107 0.707107 0\n\
+0.707107 0.707107 0\n\
+0.707107 0 -0.707107\n\
+0 0.707107 -0.707107\n\
+-0.707107 0 -0.707107\n\
+0 -0.707107 -0.707107\n\
+\n\
+3 0 6 11\n\
+3 0 7 6 \n\
+3 0 9 7 \n\
+3 0 11 9\n\
+3 1 6 8 \n\
+3 1 8 14\n\
+3 1 13 6\n\
+3 1 14 13\n\
+3 2 11 13\n\
+3 2 12 11\n\
+3 2 13 15\n\
+3 2 15 12\n\
+3 3 9 12\n\
+3 3 10 9\n\
+3 3 12 16\n\
+3 3 16 10\n\
+3 4 7 10\n\
+3 4 8 7\n\
+3 4 10 17\n\
+3 4 17 8\n\
+3 5 14 17\n\
+3 5 15 14\n\
+3 5 16 15\n\
+3 5 17 16\n\
+3 6 13 11\n\
+3 7 8 6\n\
+3 9 10 7\n\
+3 11 12 9\n\
+3 14 8 17\n\
+3 15 13 14\n\
+3 16 12 15\n\
+3 17 10 16\n} transforms { TLIST\n");
+  FOREACHvertex_(vertices) {
+    qh_fprintf(fp, 9228, "%8.4g 0 0 0 # v%d\n 0 %8.4g 0 0\n0 0 %8.4g 0\n",
+      radius, vertex->id, radius, radius);
+    qh_printpoint3(fp, vertex->point);
+    qh_fprintf(fp, 9229, "1\n");
+  }
+  qh_fprintf(fp, 9230, "}}}\n");
+} /* printspheres */
+
+
+/*----------------------------------------------
+-printsummary-
+                see libqhull.c
+*/
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="printvdiagram">-</a>
+
+  qh_printvdiagram( fp, format, facetlist, facets, printall )
+    print voronoi diagram
+      # of pairs of input sites
+      #indices site1 site2 vertex1 ...
+
+    sites indexed by input point id
+      point 0 is the first input point
+    vertices indexed by 'o' and 'p' order
+      vertex 0 is the 'vertex-at-infinity'
+      vertex 1 is the first Voronoi vertex
+
+  see:
+    qh_printvoronoi()
+    qh_eachvoronoi_all()
+
+  notes:
+    if all facets are upperdelaunay,
+      prints upper hull (furthest-site Voronoi diagram)
+*/
+void qh_printvdiagram(FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall) {
+  setT *vertices;
+  int totcount, numcenters;
+  boolT isLower;
+  qh_RIDGE innerouter= qh_RIDGEall;
+  printvridgeT printvridge= NULL;
+
+  if (format == qh_PRINTvertices) {
+    innerouter= qh_RIDGEall;
+    printvridge= qh_printvridge;
+  }else if (format == qh_PRINTinner) {
+    innerouter= qh_RIDGEinner;
+    printvridge= qh_printvnorm;
+  }else if (format == qh_PRINTouter) {
+    innerouter= qh_RIDGEouter;
+    printvridge= qh_printvnorm;
+  }else {
+    qh_fprintf(qh ferr, 6219, "Qhull internal error (qh_printvdiagram): unknown print format %d.\n", format);
+    qh_errexit(qh_ERRinput, NULL, NULL);
+  }
+  vertices= qh_markvoronoi(facetlist, facets, printall, &isLower, &numcenters);
+  totcount= qh_printvdiagram2(NULL, NULL, vertices, innerouter, False);
+  qh_fprintf(fp, 9231, "%d\n", totcount);
+  totcount= qh_printvdiagram2(fp, printvridge, vertices, innerouter, True /* inorder*/);
+  qh_settempfree(&vertices);
+#if 0  /* for testing qh_eachvoronoi_all */
+  qh_fprintf(fp, 9232, "\n");
+  totcount= qh_eachvoronoi_all(fp, printvridge, qh UPPERdelaunay, innerouter, True /* inorder*/);
+  qh_fprintf(fp, 9233, "%d\n", totcount);
+#endif
+} /* printvdiagram */
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="printvdiagram2">-</a>
+
+  qh_printvdiagram2( fp, printvridge, vertices, innerouter, inorder )
+    visit all pairs of input sites (vertices) for selected Voronoi vertices
+    vertices may include NULLs
+
+  innerouter:
+    qh_RIDGEall   print inner ridges(bounded) and outer ridges(unbounded)
+    qh_RIDGEinner print only inner ridges
+    qh_RIDGEouter print only outer ridges
+
+  inorder:
+    print 3-d Voronoi vertices in order
+
+  assumes:
+    qh_markvoronoi marked facet->visitid for Voronoi vertices
+    all facet->seen= False
+    all facet->seen2= True
+
+  returns:
+    total number of Voronoi ridges
+    if printvridge,
+      calls printvridge( fp, vertex, vertexA, centers) for each ridge
+      [see qh_eachvoronoi()]
+
+  see:
+    qh_eachvoronoi_all()
+*/
+int qh_printvdiagram2(FILE *fp, printvridgeT printvridge, setT *vertices, qh_RIDGE innerouter, boolT inorder) {
+  int totcount= 0;
+  int vertex_i, vertex_n;
+  vertexT *vertex;
+
+  FORALLvertices
+    vertex->seen= False;
+  FOREACHvertex_i_(vertices) {
+    if (vertex) {
+      if (qh GOODvertex > 0 && qh_pointid(vertex->point)+1 != qh GOODvertex)
+        continue;
+      totcount += qh_eachvoronoi(fp, printvridge, vertex, !qh_ALL, innerouter, inorder);
+    }
+  }
+  return totcount;
+} /* printvdiagram2 */
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="printvertex">-</a>
+
+  qh_printvertex( fp, vertex )
+    prints the information in a vertex
+    Duplicated as operator<< [QhullVertex.cpp]
+*/
+void qh_printvertex(FILE *fp, vertexT *vertex) {
+  pointT *point;
+  int k, count= 0;
+  facetT *neighbor, **neighborp;
+  realT r; /*bug fix*/
+
+  if (!vertex) {
+    qh_fprintf(fp, 9234, "  NULLvertex\n");
+    return;
+  }
+  qh_fprintf(fp, 9235, "- p%d(v%d):", qh_pointid(vertex->point), vertex->id);
+  point= vertex->point;
+  if (point) {
+    for (k=qh hull_dim; k--; ) {
+      r= *point++;
+      qh_fprintf(fp, 9236, " %5.2g", r);
+    }
+  }
+  if (vertex->deleted)
+    qh_fprintf(fp, 9237, " deleted");
+  if (vertex->delridge)
+    qh_fprintf(fp, 9238, " ridgedeleted");
+  qh_fprintf(fp, 9239, "\n");
+  if (vertex->neighbors) {
+    qh_fprintf(fp, 9240, "  neighbors:");
+    FOREACHneighbor_(vertex) {
+      if (++count % 100 == 0)
+        qh_fprintf(fp, 9241, "\n     ");
+      qh_fprintf(fp, 9242, " f%d", neighbor->id);
+    }
+    qh_fprintf(fp, 9243, "\n");
+  }
+} /* printvertex */
+
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="printvertexlist">-</a>
+
+  qh_printvertexlist( fp, string, facetlist, facets, printall )
+    prints vertices used by a facetlist or facet set
+    tests qh_skipfacet() if !printall
+*/
+void qh_printvertexlist(FILE *fp, const char* string, facetT *facetlist,
+                         setT *facets, boolT printall) {
+  vertexT *vertex, **vertexp;
+  setT *vertices;
+
+  vertices= qh_facetvertices(facetlist, facets, printall);
+  qh_fprintf(fp, 9244, "%s", string);
+  FOREACHvertex_(vertices)
+    qh_printvertex(fp, vertex);
+  qh_settempfree(&vertices);
+} /* printvertexlist */
+
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="printvertices">-</a>
+
+  qh_printvertices( fp, string, vertices )
+    prints vertices in a set
+    duplicated as printVertexSet [QhullVertex.cpp]
+*/
+void qh_printvertices(FILE *fp, const char* string, setT *vertices) {
+  vertexT *vertex, **vertexp;
+
+  qh_fprintf(fp, 9245, "%s", string);
+  FOREACHvertex_(vertices)
+    qh_fprintf(fp, 9246, " p%d(v%d)", qh_pointid(vertex->point), vertex->id);
+  qh_fprintf(fp, 9247, "\n");
+} /* printvertices */
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="printvneighbors">-</a>
+
+  qh_printvneighbors( fp, facetlist, facets, printall )
+    print vertex neighbors of vertices in facetlist and facets ('FN')
+
+  notes:
+    qh_countfacets clears facet->visitid for non-printed facets
+
+  design:
+    collect facet count and related statistics
+    if necessary, build neighbor sets for each vertex
+    collect vertices in facetlist and facets
+    build a point array for point->vertex and point->coplanar facet
+    for each point
+      list vertex neighbors or coplanar facet
+*/
+void qh_printvneighbors(FILE *fp, facetT* facetlist, setT *facets, boolT printall) {
+  int numfacets, numsimplicial, numridges, totneighbors, numneighbors, numcoplanars, numtricoplanars;
+  setT *vertices, *vertex_points, *coplanar_points;
+  int numpoints= qh num_points + qh_setsize(qh other_points);
+  vertexT *vertex, **vertexp;
+  int vertex_i, vertex_n;
+  facetT *facet, **facetp, *neighbor, **neighborp;
+  pointT *point, **pointp;
+
+  qh_countfacets(facetlist, facets, printall, &numfacets, &numsimplicial,
+      &totneighbors, &numridges, &numcoplanars, &numtricoplanars);  /* sets facet->visitid */
+  qh_fprintf(fp, 9248, "%d\n", numpoints);
+  qh_vertexneighbors();
+  vertices= qh_facetvertices(facetlist, facets, printall);
+  vertex_points= qh_settemp(numpoints);
+  coplanar_points= qh_settemp(numpoints);
+  qh_setzero(vertex_points, 0, numpoints);
+  qh_setzero(coplanar_points, 0, numpoints);
+  FOREACHvertex_(vertices)
+    qh_point_add(vertex_points, vertex->point, vertex);
+  FORALLfacet_(facetlist) {
+    FOREACHpoint_(facet->coplanarset)
+      qh_point_add(coplanar_points, point, facet);
+  }
+  FOREACHfacet_(facets) {
+    FOREACHpoint_(facet->coplanarset)
+      qh_point_add(coplanar_points, point, facet);
+  }
+  FOREACHvertex_i_(vertex_points) {
+    if (vertex) {
+      numneighbors= qh_setsize(vertex->neighbors);
+      qh_fprintf(fp, 9249, "%d", numneighbors);
+      if (qh hull_dim == 3)
+        qh_order_vertexneighbors(vertex);
+      else if (qh hull_dim >= 4)
+        qsort(SETaddr_(vertex->neighbors, facetT), (size_t)numneighbors,
+             sizeof(facetT *), qh_compare_facetvisit);
+      FOREACHneighbor_(vertex)
+        qh_fprintf(fp, 9250, " %d",
+                 neighbor->visitid ? neighbor->visitid - 1 : 0 - neighbor->id);
+      qh_fprintf(fp, 9251, "\n");
+    }else if ((facet= SETelemt_(coplanar_points, vertex_i, facetT)))
+      qh_fprintf(fp, 9252, "1 %d\n",
+                  facet->visitid ? facet->visitid - 1 : 0 - facet->id);
+    else
+      qh_fprintf(fp, 9253, "0\n");
+  }
+  qh_settempfree(&coplanar_points);
+  qh_settempfree(&vertex_points);
+  qh_settempfree(&vertices);
+} /* printvneighbors */
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="printvoronoi">-</a>
+
+  qh_printvoronoi( fp, format, facetlist, facets, printall )
+    print voronoi diagram in 'o' or 'G' format
+    for 'o' format
+      prints voronoi centers for each facet and for infinity
+      for each vertex, lists ids of printed facets or infinity
+      assumes facetlist and facets are disjoint
+    for 'G' format
+      prints an OFF object
+      adds a 0 coordinate to center
+      prints infinity but does not list in vertices
+
+  see:
+    qh_printvdiagram()
+
+  notes:
+    if 'o',
+      prints a line for each point except "at-infinity"
+    if all facets are upperdelaunay,
+      reverses lower and upper hull
+*/
+void qh_printvoronoi(FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall) {
+  int k, numcenters, numvertices= 0, numneighbors, numinf, vid=1, vertex_i, vertex_n;
+  facetT *facet, **facetp, *neighbor, **neighborp;
+  setT *vertices;
+  vertexT *vertex;
+  boolT isLower;
+  unsigned int numfacets= (unsigned int) qh num_facets;
+
+  vertices= qh_markvoronoi(facetlist, facets, printall, &isLower, &numcenters);
+  FOREACHvertex_i_(vertices) {
+    if (vertex) {
+      numvertices++;
+      numneighbors = numinf = 0;
+      FOREACHneighbor_(vertex) {
+        if (neighbor->visitid == 0)
+          numinf= 1;
+        else if (neighbor->visitid < numfacets)
+          numneighbors++;
+      }
+      if (numinf && !numneighbors) {
+        SETelem_(vertices, vertex_i)= NULL;
+        numvertices--;
+      }
+    }
+  }
+  if (format == qh_PRINTgeom)
+    qh_fprintf(fp, 9254, "{appearance {+edge -face} OFF %d %d 1 # Voronoi centers and cells\n",
+                numcenters, numvertices);
+  else
+    qh_fprintf(fp, 9255, "%d\n%d %d 1\n", qh hull_dim-1, numcenters, qh_setsize(vertices));
+  if (format == qh_PRINTgeom) {
+    for (k=qh hull_dim-1; k--; )
+      qh_fprintf(fp, 9256, qh_REAL_1, 0.0);
+    qh_fprintf(fp, 9257, " 0 # infinity not used\n");
+  }else {
+    for (k=qh hull_dim-1; k--; )
+      qh_fprintf(fp, 9258, qh_REAL_1, qh_INFINITE);
+    qh_fprintf(fp, 9259, "\n");
+  }
+  FORALLfacet_(facetlist) {
+    if (facet->visitid && facet->visitid < numfacets) {
+      if (format == qh_PRINTgeom)
+        qh_fprintf(fp, 9260, "# %d f%d\n", vid++, facet->id);
+      qh_printcenter(fp, format, NULL, facet);
+    }
+  }
+  FOREACHfacet_(facets) {
+    if (facet->visitid && facet->visitid < numfacets) {
+      if (format == qh_PRINTgeom)
+        qh_fprintf(fp, 9261, "# %d f%d\n", vid++, facet->id);
+      qh_printcenter(fp, format, NULL, facet);
+    }
+  }
+  FOREACHvertex_i_(vertices) {
+    numneighbors= 0;
+    numinf=0;
+    if (vertex) {
+      if (qh hull_dim == 3)
+        qh_order_vertexneighbors(vertex);
+      else if (qh hull_dim >= 4)
+        qsort(SETaddr_(vertex->neighbors, facetT),
+             (size_t)qh_setsize(vertex->neighbors),
+             sizeof(facetT *), qh_compare_facetvisit);
+      FOREACHneighbor_(vertex) {
+        if (neighbor->visitid == 0)
+          numinf= 1;
+        else if (neighbor->visitid < numfacets)
+          numneighbors++;
+      }
+    }
+    if (format == qh_PRINTgeom) {
+      if (vertex) {
+        qh_fprintf(fp, 9262, "%d", numneighbors);
+        FOREACHneighbor_(vertex) {
+          if (neighbor->visitid && neighbor->visitid < numfacets)
+            qh_fprintf(fp, 9263, " %d", neighbor->visitid);
+        }
+        qh_fprintf(fp, 9264, " # p%d(v%d)\n", vertex_i, vertex->id);
+      }else
+        qh_fprintf(fp, 9265, " # p%d is coplanar or isolated\n", vertex_i);
+    }else {
+      if (numinf)
+        numneighbors++;
+      qh_fprintf(fp, 9266, "%d", numneighbors);
+      if (vertex) {
+        FOREACHneighbor_(vertex) {
+          if (neighbor->visitid == 0) {
+            if (numinf) {
+              numinf= 0;
+              qh_fprintf(fp, 9267, " %d", neighbor->visitid);
+            }
+          }else if (neighbor->visitid < numfacets)
+            qh_fprintf(fp, 9268, " %d", neighbor->visitid);
+        }
+      }
+      qh_fprintf(fp, 9269, "\n");
+    }
+  }
+  if (format == qh_PRINTgeom)
+    qh_fprintf(fp, 9270, "}\n");
+  qh_settempfree(&vertices);
+} /* printvoronoi */
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="printvnorm">-</a>
+
+  qh_printvnorm( fp, vertex, vertexA, centers, unbounded )
+    print one separating plane of the Voronoi diagram for a pair of input sites
+    unbounded==True if centers includes vertex-at-infinity
+
+  assumes:
+    qh_ASvoronoi and qh_vertexneighbors() already set
+
+  note:
+    parameter unbounded is UNUSED by this callback
+
+  see:
+    qh_printvdiagram()
+    qh_eachvoronoi()
+*/
+void qh_printvnorm(FILE *fp, vertexT *vertex, vertexT *vertexA, setT *centers, boolT unbounded) {
+  pointT *normal;
+  realT offset;
+  int k;
+  QHULL_UNUSED(unbounded);
+
+  normal= qh_detvnorm(vertex, vertexA, centers, &offset);
+  qh_fprintf(fp, 9271, "%d %d %d ",
+      2+qh hull_dim, qh_pointid(vertex->point), qh_pointid(vertexA->point));
+  for (k=0; k< qh hull_dim-1; k++)
+    qh_fprintf(fp, 9272, qh_REAL_1, normal[k]);
+  qh_fprintf(fp, 9273, qh_REAL_1, offset);
+  qh_fprintf(fp, 9274, "\n");
+} /* printvnorm */
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="printvridge">-</a>
+
+  qh_printvridge( fp, vertex, vertexA, centers, unbounded )
+    print one ridge of the Voronoi diagram for a pair of input sites
+    unbounded==True if centers includes vertex-at-infinity
+
+  see:
+    qh_printvdiagram()
+
+  notes:
+    the user may use a different function
+    parameter unbounded is UNUSED
+*/
+void qh_printvridge(FILE *fp, vertexT *vertex, vertexT *vertexA, setT *centers, boolT unbounded) {
+  facetT *facet, **facetp;
+  QHULL_UNUSED(unbounded);
+
+  qh_fprintf(fp, 9275, "%d %d %d", qh_setsize(centers)+2,
+       qh_pointid(vertex->point), qh_pointid(vertexA->point));
+  FOREACHfacet_(centers)
+    qh_fprintf(fp, 9276, " %d", facet->visitid);
+  qh_fprintf(fp, 9277, "\n");
+} /* printvridge */
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="projectdim3">-</a>
+
+  qh_projectdim3( source, destination )
+    project 2-d 3-d or 4-d point to a 3-d point
+    uses qh.DROPdim and qh.hull_dim
+    source and destination may be the same
+
+  notes:
+    allocate 4 elements to destination just in case
+*/
+void qh_projectdim3(pointT *source, pointT *destination) {
+  int i,k;
+
+  for (k=0, i=0; k < qh hull_dim; k++) {
+    if (qh hull_dim == 4) {
+      if (k != qh DROPdim)
+        destination[i++]= source[k];
+    }else if (k == qh DROPdim)
+      destination[i++]= 0;
+    else
+      destination[i++]= source[k];
+  }
+  while (i < 3)
+    destination[i++]= 0.0;
+} /* projectdim3 */
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="readfeasible">-</a>
+
+  qh_readfeasible( dim, curline )
+    read feasible point from current line and qh.fin
+
+  returns:
+    number of lines read from qh.fin
+    sets qh.feasible_point with malloc'd coordinates
+
+  notes:
+    checks for qh.HALFspace
+    assumes dim > 1
+
+  see:
+    qh_setfeasible
+*/
+int qh_readfeasible(int dim, const char *curline) {
+  boolT isfirst= True;
+  int linecount= 0, tokcount= 0;
+  const char *s;
+  char *t, firstline[qh_MAXfirst+1];
+  coordT *coords, value;
+
+  if (!qh HALFspace) {
+    qh_fprintf(qh ferr, 6070, "qhull input error: feasible point(dim 1 coords) is only valid for halfspace intersection\n");
+    qh_errexit(qh_ERRinput, NULL, NULL);
+  }
+  if (qh feasible_string)
+    qh_fprintf(qh ferr, 7057, "qhull input warning: feasible point(dim 1 coords) overrides 'Hn,n,n' feasible point for halfspace intersection\n");
+  if (!(qh feasible_point= (coordT*)qh_malloc(dim* sizeof(coordT)))) {
+    qh_fprintf(qh ferr, 6071, "qhull error: insufficient memory for feasible point\n");
+    qh_errexit(qh_ERRmem, NULL, NULL);
+  }
+  coords= qh feasible_point;
+  while ((s= (isfirst ?  curline : fgets(firstline, qh_MAXfirst, qh fin)))) {
+    if (isfirst)
+      isfirst= False;
+    else
+      linecount++;
+    while (*s) {
+      while (isspace(*s))
+        s++;
+      value= qh_strtod(s, &t);
+      if (s == t)
+        break;
+      s= t;
+      *(coords++)= value;
+      if (++tokcount == dim) {
+        while (isspace(*s))
+          s++;
+        qh_strtod(s, &t);
+        if (s != t) {
+          qh_fprintf(qh ferr, 6072, "qhull input error: coordinates for feasible point do not finish out the line: %s\n",
+               s);
+          qh_errexit(qh_ERRinput, NULL, NULL);
+        }
+        return linecount;
+      }
+    }
+  }
+  qh_fprintf(qh ferr, 6073, "qhull input error: only %d coordinates.  Could not read %d-d feasible point.\n",
+           tokcount, dim);
+  qh_errexit(qh_ERRinput, NULL, NULL);
+  return 0;
+} /* readfeasible */
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="readpoints">-</a>
+
+  qh_readpoints( numpoints, dimension, ismalloc )
+    read points from qh.fin into qh.first_point, qh.num_points
+    qh.fin is lines of coordinates, one per vertex, first line number of points
+    if 'rbox D4',
+      gives message
+    if qh.ATinfinity,
+      adds point-at-infinity for Delaunay triangulations
+
+  returns:
+    number of points, array of point coordinates, dimension, ismalloc True
+    if qh.DELAUNAY & !qh.PROJECTinput, projects points to paraboloid
+        and clears qh.PROJECTdelaunay
+    if qh.HALFspace, reads optional feasible point, reads halfspaces,
+        converts to dual.
+
+  for feasible point in "cdd format" in 3-d:
+    3 1
+    coordinates
+    comments
+    begin
+    n 4 real/integer
+    ...
+    end
+
+  notes:
+    dimension will change in qh_initqhull_globals if qh.PROJECTinput
+    uses malloc() since qh_mem not initialized
+    FIXUP QH11012: qh_readpoints needs rewriting, too long
+*/
+coordT *qh_readpoints(int *numpoints, int *dimension, boolT *ismalloc) {
+  coordT *points, *coords, *infinity= NULL;
+  realT paraboloid, maxboloid= -REALmax, value;
+  realT *coordp= NULL, *offsetp= NULL, *normalp= NULL;
+  char *s= 0, *t, firstline[qh_MAXfirst+1];
+  int diminput=0, numinput=0, dimfeasible= 0, newnum, k, tempi;
+  int firsttext=0, firstshort=0, firstlong=0, firstpoint=0;
+  int tokcount= 0, linecount=0, maxcount, coordcount=0;
+  boolT islong, isfirst= True, wasbegin= False;
+  boolT isdelaunay= qh DELAUNAY && !qh PROJECTinput;
+
+  if (qh CDDinput) {
+    while ((s= fgets(firstline, qh_MAXfirst, qh fin))) {
+      linecount++;
+      if (qh HALFspace && linecount == 1 && isdigit(*s)) {
+        dimfeasible= qh_strtol(s, &s);
+        while (isspace(*s))
+          s++;
+        if (qh_strtol(s, &s) == 1)
+          linecount += qh_readfeasible(dimfeasible, s);
+        else
+          dimfeasible= 0;
+      }else if (!memcmp(firstline, "begin", (size_t)5) || !memcmp(firstline, "BEGIN", (size_t)5))
+        break;
+      else if (!*qh rbox_command)
+        strncat(qh rbox_command, s, sizeof(qh rbox_command)-1);
+    }
+    if (!s) {
+      qh_fprintf(qh ferr, 6074, "qhull input error: missing \"begin\" for cdd-formated input\n");
+      qh_errexit(qh_ERRinput, NULL, NULL);
+    }
+  }
+  while (!numinput && (s= fgets(firstline, qh_MAXfirst, qh fin))) {
+    linecount++;
+    if (!memcmp(s, "begin", (size_t)5) || !memcmp(s, "BEGIN", (size_t)5))
+      wasbegin= True;
+    while (*s) {
+      while (isspace(*s))
+        s++;
+      if (!*s)
+        break;
+      if (!isdigit(*s)) {
+        if (!*qh rbox_command) {
+          strncat(qh rbox_command, s, sizeof(qh rbox_command)-1);
+          firsttext= linecount;
+        }
+        break;
+      }
+      if (!diminput)
+        diminput= qh_strtol(s, &s);
+      else {
+        numinput= qh_strtol(s, &s);
+        if (numinput == 1 && diminput >= 2 && qh HALFspace && !qh CDDinput) {
+          linecount += qh_readfeasible(diminput, s); /* checks if ok */
+          dimfeasible= diminput;
+          diminput= numinput= 0;
+        }else
+          break;
+      }
+    }
+  }
+  if (!s) {
+    qh_fprintf(qh ferr, 6075, "qhull input error: short input file.  Did not find dimension and number of points\n");
+    qh_errexit(qh_ERRinput, NULL, NULL);
+  }
+  if (diminput > numinput) {
+    tempi= diminput;    /* exchange dim and n, e.g., for cdd input format */
+    diminput= numinput;
+    numinput= tempi;
+  }
+  if (diminput < 2) {
+    qh_fprintf(qh ferr, 6220,"qhull input error: dimension %d(first number) should be at least 2\n",
+            diminput);
+    qh_errexit(qh_ERRinput, NULL, NULL);
+  }
+  if (isdelaunay) {
+    qh PROJECTdelaunay= False;
+    if (qh CDDinput)
+      *dimension= diminput;
+    else
+      *dimension= diminput+1;
+    *numpoints= numinput;
+    if (qh ATinfinity)
+      (*numpoints)++;
+  }else if (qh HALFspace) {
+    *dimension= diminput - 1;
+    *numpoints= numinput;
+    if (diminput < 3) {
+      qh_fprintf(qh ferr, 6221,"qhull input error: dimension %d(first number, includes offset) should be at least 3 for halfspaces\n",
+            diminput);
+      qh_errexit(qh_ERRinput, NULL, NULL);
+    }
+    if (dimfeasible) {
+      if (dimfeasible != *dimension) {
+        qh_fprintf(qh ferr, 6222,"qhull input error: dimension %d of feasible point is not one less than dimension %d for halfspaces\n",
+          dimfeasible, diminput);
+        qh_errexit(qh_ERRinput, NULL, NULL);
+      }
+    }else
+      qh_setfeasible(*dimension);
+  }else {
+    if (qh CDDinput)
+      *dimension= diminput-1;
+    else
+      *dimension= diminput;
+    *numpoints= numinput;
+  }
+  qh normal_size= *dimension * sizeof(coordT); /* for tracing with qh_printpoint */
+  if (qh HALFspace) {
+    qh half_space= coordp= (coordT*)qh_malloc(qh normal_size + sizeof(coordT));
+    if (qh CDDinput) {
+      offsetp= qh half_space;
+      normalp= offsetp + 1;
+    }else {
+      normalp= qh half_space;
+      offsetp= normalp + *dimension;
+    }
+  }
+  qh maxline= diminput * (qh_REALdigits + 5);
+  maximize_(qh maxline, 500);
+  qh line= (char*)qh_malloc((qh maxline+1) * sizeof(char));
+  *ismalloc= True;  /* use malloc since memory not setup */
+  coords= points= qh temp_malloc=  /* numinput and diminput >=2 by QH6220 */
+        (coordT*)qh_malloc((*numpoints)*(*dimension)*sizeof(coordT));
+  if (!coords || !qh line || (qh HALFspace && !qh half_space)) {
+    qh_fprintf(qh ferr, 6076, "qhull error: insufficient memory to read %d points\n",
+            numinput);
+    qh_errexit(qh_ERRmem, NULL, NULL);
+  }
+  if (isdelaunay && qh ATinfinity) {
+    infinity= points + numinput * (*dimension);
+    for (k= (*dimension) - 1; k--; )
+      infinity[k]= 0.0;
+  }
+  maxcount= numinput * diminput;
+  paraboloid= 0.0;
+  while ((s= (isfirst ?  s : fgets(qh line, qh maxline, qh fin)))) {
+    if (!isfirst) {
+      linecount++;
+      if (*s == 'e' || *s == 'E') {
+        if (!memcmp(s, "end", (size_t)3) || !memcmp(s, "END", (size_t)3)) {
+          if (qh CDDinput )
+            break;
+          else if (wasbegin)
+            qh_fprintf(qh ferr, 7058, "qhull input warning: the input appears to be in cdd format.  If so, use 'Fd'\n");
+        }
+      }
+    }
+    islong= False;
+    while (*s) {
+      while (isspace(*s))
+        s++;
+      value= qh_strtod(s, &t);
+      if (s == t) {
+        if (!*qh rbox_command)
+         strncat(qh rbox_command, s, sizeof(qh rbox_command)-1);
+        if (*s && !firsttext)
+          firsttext= linecount;
+        if (!islong && !firstshort && coordcount)
+          firstshort= linecount;
+        break;
+      }
+      if (!firstpoint)
+        firstpoint= linecount;
+      s= t;
+      if (++tokcount > maxcount)
+        continue;
+      if (qh HALFspace) {
+        if (qh CDDinput)
+          *(coordp++)= -value; /* both coefficients and offset */
+        else
+          *(coordp++)= value;
+      }else {
+        *(coords++)= value;
+        if (qh CDDinput && !coordcount) {
+          if (value != 1.0) {
+            qh_fprintf(qh ferr, 6077, "qhull input error: for cdd format, point at line %d does not start with '1'\n",
+                   linecount);
+            qh_errexit(qh_ERRinput, NULL, NULL);
+          }
+          coords--;
+        }else if (isdelaunay) {
+          paraboloid += value * value;
+          if (qh ATinfinity) {
+            if (qh CDDinput)
+              infinity[coordcount-1] += value;
+            else
+              infinity[coordcount] += value;
+          }
+        }
+      }
+      if (++coordcount == diminput) {
+        coordcount= 0;
+        if (isdelaunay) {
+          *(coords++)= paraboloid;
+          maximize_(maxboloid, paraboloid);
+          paraboloid= 0.0;
+        }else if (qh HALFspace) {
+          if (!qh_sethalfspace(*dimension, coords, &coords, normalp, offsetp, qh feasible_point)) {
+            qh_fprintf(qh ferr, 8048, "The halfspace was on line %d\n", linecount);
+            if (wasbegin)
+              qh_fprintf(qh ferr, 8049, "The input appears to be in cdd format.  If so, you should use option 'Fd'\n");
+            qh_errexit(qh_ERRinput, NULL, NULL);
+          }
+          coordp= qh half_space;
+        }
+        while (isspace(*s))
+          s++;
+        if (*s) {
+          islong= True;
+          if (!firstlong)
+            firstlong= linecount;
+        }
+      }
+    }
+    if (!islong && !firstshort && coordcount)
+      firstshort= linecount;
+    if (!isfirst && s - qh line >= qh maxline) {
+      qh_fprintf(qh ferr, 6078, "qhull input error: line %d contained more than %d characters\n",
+              linecount, (int) (s - qh line));   /* WARN64 */
+      qh_errexit(qh_ERRinput, NULL, NULL);
+    }
+    isfirst= False;
+  }
+  if (tokcount != maxcount) {
+    newnum= fmin_(numinput, tokcount/diminput);
+    qh_fprintf(qh ferr, 7073,"\
+qhull warning: instead of %d %d-dimensional points, input contains\n\
+%d points and %d extra coordinates.  Line %d is the first\npoint",
+       numinput, diminput, tokcount/diminput, tokcount % diminput, firstpoint);
+    if (firsttext)
+      qh_fprintf(qh ferr, 8051, ", line %d is the first comment", firsttext);
+    if (firstshort)
+      qh_fprintf(qh ferr, 8052, ", line %d is the first short\nline", firstshort);
+    if (firstlong)
+      qh_fprintf(qh ferr, 8053, ", line %d is the first long line", firstlong);
+    qh_fprintf(qh ferr, 8054, ".  Continue with %d points.\n", newnum);
+    numinput= newnum;
+    if (isdelaunay && qh ATinfinity) {
+      for (k= tokcount % diminput; k--; )
+        infinity[k] -= *(--coords);
+      *numpoints= newnum+1;
+    }else {
+      coords -= tokcount % diminput;
+      *numpoints= newnum;
+    }
+  }
+  if (isdelaunay && qh ATinfinity) {
+    for (k= (*dimension) -1; k--; )
+      infinity[k] /= numinput;
+    if (coords == infinity)
+      coords += (*dimension) -1;
+    else {
+      for (k=0; k < (*dimension) -1; k++)
+        *(coords++)= infinity[k];
+    }
+    *(coords++)= maxboloid * 1.1;
+  }
+  if (qh rbox_command[0]) {
+    qh rbox_command[strlen(qh rbox_command)-1]= '\0';
+    if (!strcmp(qh rbox_command, "./rbox D4"))
+      qh_fprintf(qh ferr, 8055, "\n\
+This is the qhull test case.  If any errors or core dumps occur,\n\
+recompile qhull with 'make new'.  If errors still occur, there is\n\
+an incompatibility.  You should try a different compiler.  You can also\n\
+change the choices in user.h.  If you discover the source of the problem,\n\
+please send mail to qhull_bug@qhull.org.\n\
+\n\
+Type 'qhull' for a short list of options.\n");
+  }
+  qh_free(qh line);
+  qh line= NULL;
+  if (qh half_space) {
+    qh_free(qh half_space);
+    qh half_space= NULL;
+  }
+  qh temp_malloc= NULL;
+  trace1((qh ferr, 1008,"qh_readpoints: read in %d %d-dimensional points\n",
+          numinput, diminput));
+  return(points);
+} /* readpoints */
+
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="setfeasible">-</a>
+
+  qh_setfeasible( dim )
+    set qh.feasible_point from qh.feasible_string in "n,n,n" or "n n n" format
+
+  notes:
+    "n,n,n" already checked by qh_initflags()
+    see qh_readfeasible()
+    called only once from qh_new_qhull, otherwise leaks memory
+*/
+void qh_setfeasible(int dim) {
+  int tokcount= 0;
+  char *s;
+  coordT *coords, value;
+
+  if (!(s= qh feasible_string)) {
+    qh_fprintf(qh ferr, 6223, "\
+qhull input error: halfspace intersection needs a feasible point.\n\
+Either prepend the input with 1 point or use 'Hn,n,n'.  See manual.\n");
+    qh_errexit(qh_ERRinput, NULL, NULL);
+  }
+  if (!(qh feasible_point= (pointT*)qh_malloc(dim * sizeof(coordT)))) {
+    qh_fprintf(qh ferr, 6079, "qhull error: insufficient memory for 'Hn,n,n'\n");
+    qh_errexit(qh_ERRmem, NULL, NULL);
+  }
+  coords= qh feasible_point;
+  while (*s) {
+    value= qh_strtod(s, &s);
+    if (++tokcount > dim) {
+      qh_fprintf(qh ferr, 7059, "qhull input warning: more coordinates for 'H%s' than dimension %d\n",
+          qh feasible_string, dim);
+      break;
+    }
+    *(coords++)= value;
+    if (*s)
+      s++;
+  }
+  while (++tokcount <= dim)
+    *(coords++)= 0.0;
+} /* setfeasible */
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="skipfacet">-</a>
+
+  qh_skipfacet( facet )
+    returns 'True' if this facet is not to be printed
+
+  notes:
+    based on the user provided slice thresholds and 'good' specifications
+*/
+boolT qh_skipfacet(facetT *facet) {
+  facetT *neighbor, **neighborp;
+
+  if (qh PRINTneighbors) {
+    if (facet->good)
+      return !qh PRINTgood;
+    FOREACHneighbor_(facet) {
+      if (neighbor->good)
+        return False;
+    }
+    return True;
+  }else if (qh PRINTgood)
+    return !facet->good;
+  else if (!facet->normal)
+    return True;
+  return(!qh_inthresholds(facet->normal, NULL));
+} /* skipfacet */
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="skipfilename">-</a>
+
+  qh_skipfilename( string )
+    returns pointer to character after filename
+
+  notes:
+    skips leading spaces
+    ends with spacing or eol
+    if starts with ' or " ends with the same, skipping \' or \"
+    For qhull, qh_argv_to_command() only uses double quotes
+*/
+char *qh_skipfilename(char *filename) {
+  char *s= filename;  /* non-const due to return */
+  char c;
+
+  while (*s && isspace(*s))
+    s++;
+  c= *s++;
+  if (c == '\0') {
+    qh_fprintf(qh ferr, 6204, "qhull input error: filename expected, none found.\n");
+    qh_errexit(qh_ERRinput, NULL, NULL);
+  }
+  if (c == '\'' || c == '"') {
+    while (*s !=c || s[-1] == '\\') {
+      if (!*s) {
+        qh_fprintf(qh ferr, 6203, "qhull input error: missing quote after filename -- %s\n", filename);
+        qh_errexit(qh_ERRinput, NULL, NULL);
+      }
+      s++;
+    }
+    s++;
+  }
+  else while (*s && !isspace(*s))
+      s++;
+  return s;
+} /* skipfilename */
+
diff --git a/xs/src/qhull/src/libqhull/io.h b/xs/src/qhull/src/libqhull/io.h
new file mode 100644
index 0000000000..eca0369d30
--- /dev/null
+++ b/xs/src/qhull/src/libqhull/io.h
@@ -0,0 +1,159 @@
+/*<html><pre>  -<a                             href="qh-io.htm"
+  >-------------------------------</a><a name="TOP">-</a>
+
+   io.h
+   declarations of Input/Output functions
+
+   see README, libqhull.h and io.c
+
+   Copyright (c) 1993-2015 The Geometry Center.
+   $Id: //main/2015/qhull/src/libqhull/io.h#1 $$Change: 1981 $
+   $DateTime: 2015/09/28 20:26:32 $$Author: bbarber $
+*/
+
+#ifndef qhDEFio
+#define qhDEFio 1
+
+#include "libqhull.h"
+
+/*============ constants and flags ==================*/
+
+/*-<a                             href="qh-io.htm#TOC"
+  >--------------------------------</a><a name="qh_MAXfirst">-</a>
+
+  qh_MAXfirst
+    maximum length of first two lines of stdin
+*/
+#define qh_MAXfirst  200
+
+/*-<a                             href="qh-io.htm#TOC"
+  >--------------------------------</a><a name="qh_MINradius">-</a>
+
+  qh_MINradius
+    min radius for Gp and Gv, fraction of maxcoord
+*/
+#define qh_MINradius 0.02
+
+/*-<a                             href="qh-io.htm#TOC"
+  >--------------------------------</a><a name="qh_GEOMepsilon">-</a>
+
+  qh_GEOMepsilon
+    adjust outer planes for 'lines closer' and geomview roundoff.
+    This prevents bleed through.
+*/
+#define qh_GEOMepsilon 2e-3
+
+/*-<a                             href="qh-io.htm#TOC"
+  >--------------------------------</a><a name="qh_WHITESPACE">-</a>
+
+  qh_WHITESPACE
+    possible values of white space
+*/
+#define qh_WHITESPACE " \n\t\v\r\f"
+
+
+/*-<a                             href="qh-io.htm#TOC"
+  >--------------------------------</a><a name="RIDGE">-</a>
+
+  qh_RIDGE
+    to select which ridges to print in qh_eachvoronoi
+*/
+typedef enum
+{
+    qh_RIDGEall = 0, qh_RIDGEinner, qh_RIDGEouter
+}
+qh_RIDGE;
+
+/*-<a                             href="qh-io.htm#TOC"
+  >--------------------------------</a><a name="printvridgeT">-</a>
+
+  printvridgeT
+    prints results of qh_printvdiagram
+
+  see:
+    <a href="io.c#printvridge">qh_printvridge</a> for an example
+*/
+typedef void (*printvridgeT)(FILE *fp, vertexT *vertex, vertexT *vertexA, setT *centers, boolT unbounded);
+
+/*============== -prototypes in alphabetical order =========*/
+
+void    qh_dfacet(unsigned id);
+void    qh_dvertex(unsigned id);
+int     qh_compare_facetarea(const void *p1, const void *p2);
+int     qh_compare_facetmerge(const void *p1, const void *p2);
+int     qh_compare_facetvisit(const void *p1, const void *p2);
+int     qh_compare_vertexpoint(const void *p1, const void *p2); /* not used, not in libqhull_r.h */
+void    qh_copyfilename(char *filename, int size, const char* source, int length);
+void    qh_countfacets(facetT *facetlist, setT *facets, boolT printall,
+              int *numfacetsp, int *numsimplicialp, int *totneighborsp,
+              int *numridgesp, int *numcoplanarsp, int *numnumtricoplanarsp);
+pointT *qh_detvnorm(vertexT *vertex, vertexT *vertexA, setT *centers, realT *offsetp);
+setT   *qh_detvridge(vertexT *vertex);
+setT   *qh_detvridge3(vertexT *atvertex, vertexT *vertex);
+int     qh_eachvoronoi(FILE *fp, printvridgeT printvridge, vertexT *atvertex, boolT visitall, qh_RIDGE innerouter, boolT inorder);
+int     qh_eachvoronoi_all(FILE *fp, printvridgeT printvridge, boolT isUpper, qh_RIDGE innerouter, boolT inorder);
+void    qh_facet2point(facetT *facet, pointT **point0, pointT **point1, realT *mindist);
+setT   *qh_facetvertices(facetT *facetlist, setT *facets, boolT allfacets);
+void    qh_geomplanes(facetT *facet, realT *outerplane, realT *innerplane);
+void    qh_markkeep(facetT *facetlist);
+setT   *qh_markvoronoi(facetT *facetlist, setT *facets, boolT printall, boolT *isLowerp, int *numcentersp);
+void    qh_order_vertexneighbors(vertexT *vertex);
+void    qh_prepare_output(void);
+void    qh_printafacet(FILE *fp, qh_PRINT format, facetT *facet, boolT printall);
+void    qh_printbegin(FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall);
+void    qh_printcenter(FILE *fp, qh_PRINT format, const char *string, facetT *facet);
+void    qh_printcentrum(FILE *fp, facetT *facet, realT radius);
+void    qh_printend(FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall);
+void    qh_printend4geom(FILE *fp, facetT *facet, int *num, boolT printall);
+void    qh_printextremes(FILE *fp, facetT *facetlist, setT *facets, boolT printall);
+void    qh_printextremes_2d(FILE *fp, facetT *facetlist, setT *facets, boolT printall);
+void    qh_printextremes_d(FILE *fp, facetT *facetlist, setT *facets, boolT printall);
+void    qh_printfacet(FILE *fp, facetT *facet);
+void    qh_printfacet2math(FILE *fp, facetT *facet, qh_PRINT format, int notfirst);
+void    qh_printfacet2geom(FILE *fp, facetT *facet, realT color[3]);
+void    qh_printfacet2geom_points(FILE *fp, pointT *point1, pointT *point2,
+                               facetT *facet, realT offset, realT color[3]);
+void    qh_printfacet3math(FILE *fp, facetT *facet, qh_PRINT format, int notfirst);
+void    qh_printfacet3geom_nonsimplicial(FILE *fp, facetT *facet, realT color[3]);
+void    qh_printfacet3geom_points(FILE *fp, setT *points, facetT *facet, realT offset, realT color[3]);
+void    qh_printfacet3geom_simplicial(FILE *fp, facetT *facet, realT color[3]);
+void    qh_printfacet3vertex(FILE *fp, facetT *facet, qh_PRINT format);
+void    qh_printfacet4geom_nonsimplicial(FILE *fp, facetT *facet, realT color[3]);
+void    qh_printfacet4geom_simplicial(FILE *fp, facetT *facet, realT color[3]);
+void    qh_printfacetNvertex_nonsimplicial(FILE *fp, facetT *facet, int id, qh_PRINT format);
+void    qh_printfacetNvertex_simplicial(FILE *fp, facetT *facet, qh_PRINT format);
+void    qh_printfacetheader(FILE *fp, facetT *facet);
+void    qh_printfacetridges(FILE *fp, facetT *facet);
+void    qh_printfacets(FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall);
+void    qh_printhyperplaneintersection(FILE *fp, facetT *facet1, facetT *facet2,
+                   setT *vertices, realT color[3]);
+void    qh_printneighborhood(FILE *fp, qh_PRINT format, facetT *facetA, facetT *facetB, boolT printall);
+void    qh_printline3geom(FILE *fp, pointT *pointA, pointT *pointB, realT color[3]);
+void    qh_printpoint(FILE *fp, const char *string, pointT *point);
+void    qh_printpointid(FILE *fp, const char *string, int dim, pointT *point, int id);
+void    qh_printpoint3(FILE *fp, pointT *point);
+void    qh_printpoints_out(FILE *fp, facetT *facetlist, setT *facets, boolT printall);
+void    qh_printpointvect(FILE *fp, pointT *point, coordT *normal, pointT *center, realT radius, realT color[3]);
+void    qh_printpointvect2(FILE *fp, pointT *point, coordT *normal, pointT *center, realT radius);
+void    qh_printridge(FILE *fp, ridgeT *ridge);
+void    qh_printspheres(FILE *fp, setT *vertices, realT radius);
+void    qh_printvdiagram(FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall);
+int     qh_printvdiagram2(FILE *fp, printvridgeT printvridge, setT *vertices, qh_RIDGE innerouter, boolT inorder);
+void    qh_printvertex(FILE *fp, vertexT *vertex);
+void    qh_printvertexlist(FILE *fp, const char* string, facetT *facetlist,
+                         setT *facets, boolT printall);
+void    qh_printvertices(FILE *fp, const char* string, setT *vertices);
+void    qh_printvneighbors(FILE *fp, facetT* facetlist, setT *facets, boolT printall);
+void    qh_printvoronoi(FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall);
+void    qh_printvnorm(FILE *fp, vertexT *vertex, vertexT *vertexA, setT *centers, boolT unbounded);
+void    qh_printvridge(FILE *fp, vertexT *vertex, vertexT *vertexA, setT *centers, boolT unbounded);
+void    qh_produce_output(void);
+void    qh_produce_output2(void);
+void    qh_projectdim3(pointT *source, pointT *destination);
+int     qh_readfeasible(int dim, const char *curline);
+coordT *qh_readpoints(int *numpoints, int *dimension, boolT *ismalloc);
+void    qh_setfeasible(int dim);
+boolT   qh_skipfacet(facetT *facet);
+char   *qh_skipfilename(char *filename);
+
+#endif /* qhDEFio */
diff --git a/xs/src/qhull/src/libqhull/libqhull.c b/xs/src/qhull/src/libqhull/libqhull.c
new file mode 100644
index 0000000000..7696a8a9fe
--- /dev/null
+++ b/xs/src/qhull/src/libqhull/libqhull.c
@@ -0,0 +1,1403 @@
+/*<html><pre>  -<a                             href="qh-qhull.htm"
+  >-------------------------------</a><a name="TOP">-</a>
+
+   libqhull.c
+   Quickhull algorithm for convex hulls
+
+   qhull() and top-level routines
+
+   see qh-qhull.htm, libqhull.h, unix.c
+
+   see qhull_a.h for internal functions
+
+   Copyright (c) 1993-2015 The Geometry Center.
+   $Id: //main/2015/qhull/src/libqhull/libqhull.c#3 $$Change: 2047 $
+   $DateTime: 2016/01/04 22:03:18 $$Author: bbarber $
+*/
+
+#include "qhull_a.h"
+
+/*============= functions in alphabetic order after qhull() =======*/
+
+/*-<a                             href="qh-qhull.htm#TOC"
+  >-------------------------------</a><a name="qhull">-</a>
+
+  qh_qhull()
+    compute DIM3 convex hull of qh.num_points starting at qh.first_point
+    qh contains all global options and variables
+
+  returns:
+    returns polyhedron
+      qh.facet_list, qh.num_facets, qh.vertex_list, qh.num_vertices,
+
+    returns global variables
+      qh.hulltime, qh.max_outside, qh.interior_point, qh.max_vertex, qh.min_vertex
+
+    returns precision constants
+      qh.ANGLEround, centrum_radius, cos_max, DISTround, MAXabs_coord, ONEmerge
+
+  notes:
+    unless needed for output
+      qh.max_vertex and qh.min_vertex are max/min due to merges
+
+  see:
+    to add individual points to either qh.num_points
+      use qh_addpoint()
+
+    if qh.GETarea
+      qh_produceoutput() returns qh.totarea and qh.totvol via qh_getarea()
+
+  design:
+    record starting time
+    initialize hull and partition points
+    build convex hull
+    unless early termination
+      update facet->maxoutside for vertices, coplanar, and near-inside points
+    error if temporary sets exist
+    record end time
+*/
+
+void qh_qhull(void) {
+  int numoutside;
+
+  qh hulltime= qh_CPUclock;
+  if (qh RERUN || qh JOGGLEmax < REALmax/2)
+    qh_build_withrestart();
+  else {
+    qh_initbuild();
+    qh_buildhull();
+  }
+  if (!qh STOPpoint && !qh STOPcone) {
+    if (qh ZEROall_ok && !qh TESTvneighbors && qh MERGEexact)
+      qh_checkzero( qh_ALL);
+    if (qh ZEROall_ok && !qh TESTvneighbors && !qh WAScoplanar) {
+      trace2((qh ferr, 2055, "qh_qhull: all facets are clearly convex and no coplanar points.  Post-merging and check of maxout not needed.\n"));
+      qh DOcheckmax= False;
+    }else {
+      if (qh MERGEexact || (qh hull_dim > qh_DIMreduceBuild && qh PREmerge))
+        qh_postmerge("First post-merge", qh premerge_centrum, qh premerge_cos,
+             (qh POSTmerge ? False : qh TESTvneighbors));
+      else if (!qh POSTmerge && qh TESTvneighbors)
+        qh_postmerge("For testing vertex neighbors", qh premerge_centrum,
+             qh premerge_cos, True);
+      if (qh POSTmerge)
+        qh_postmerge("For post-merging", qh postmerge_centrum,
+             qh postmerge_cos, qh TESTvneighbors);
+      if (qh visible_list == qh facet_list) { /* i.e., merging done */
+        qh findbestnew= True;
+        qh_partitionvisible(/*qh.visible_list*/ !qh_ALL, &numoutside);
+        qh findbestnew= False;
+        qh_deletevisible(/*qh.visible_list*/);
+        qh_resetlists(False, qh_RESETvisible /*qh.visible_list newvertex_list newfacet_list */);
+      }
+    }
+    if (qh DOcheckmax){
+      if (qh REPORTfreq) {
+        qh_buildtracing(NULL, NULL);
+        qh_fprintf(qh ferr, 8115, "\nTesting all coplanar points.\n");
+      }
+      qh_check_maxout();
+    }
+    if (qh KEEPnearinside && !qh maxoutdone)
+      qh_nearcoplanar();
+  }
+  if (qh_setsize(qhmem.tempstack) != 0) {
+    qh_fprintf(qh ferr, 6164, "qhull internal error (qh_qhull): temporary sets not empty(%d)\n",
+             qh_setsize(qhmem.tempstack));
+    qh_errexit(qh_ERRqhull, NULL, NULL);
+  }
+  qh hulltime= qh_CPUclock - qh hulltime;
+  qh QHULLfinished= True;
+  trace1((qh ferr, 1036, "Qhull: algorithm completed\n"));
+} /* qhull */
+
+/*-<a                             href="qh-qhull.htm#TOC"
+  >-------------------------------</a><a name="addpoint">-</a>
+
+  qh_addpoint( furthest, facet, checkdist )
+    add point (usually furthest point) above facet to hull
+    if checkdist,
+      check that point is above facet.
+      if point is not outside of the hull, uses qh_partitioncoplanar()
+      assumes that facet is defined by qh_findbestfacet()
+    else if facet specified,
+      assumes that point is above facet (major damage if below)
+    for Delaunay triangulations,
+      Use qh_setdelaunay() to lift point to paraboloid and scale by 'Qbb' if needed
+      Do not use options 'Qbk', 'QBk', or 'QbB' since they scale the coordinates.
+
+  returns:
+    returns False if user requested an early termination
+     qh.visible_list, newfacet_list, delvertex_list, NEWfacets may be defined
+    updates qh.facet_list, qh.num_facets, qh.vertex_list, qh.num_vertices
+    clear qh.maxoutdone (will need to call qh_check_maxout() for facet->maxoutside)
+    if unknown point, adds a pointer to qh.other_points
+      do not deallocate the point's coordinates
+
+  notes:
+    assumes point is near its best facet and not at a local minimum of a lens
+      distributions.  Use qh_findbestfacet to avoid this case.
+    uses qh.visible_list, qh.newfacet_list, qh.delvertex_list, qh.NEWfacets
+
+  see also:
+    qh_triangulate() -- triangulate non-simplicial facets
+
+  design:
+    add point to other_points if needed
+    if checkdist
+      if point not above facet
+        partition coplanar point
+        exit
+    exit if pre STOPpoint requested
+    find horizon and visible facets for point
+    make new facets for point to horizon
+    make hyperplanes for point
+    compute balance statistics
+    match neighboring new facets
+    update vertex neighbors and delete interior vertices
+    exit if STOPcone requested
+    merge non-convex new facets
+    if merge found, many merges, or 'Qf'
+       use qh_findbestnew() instead of qh_findbest()
+    partition outside points from visible facets
+    delete visible facets
+    check polyhedron if requested
+    exit if post STOPpoint requested
+    reset working lists of facets and vertices
+*/
+boolT qh_addpoint(pointT *furthest, facetT *facet, boolT checkdist) {
+  int goodvisible, goodhorizon;
+  vertexT *vertex;
+  facetT *newfacet;
+  realT dist, newbalance, pbalance;
+  boolT isoutside= False;
+  int numpart, numpoints, numnew, firstnew;
+
+  qh maxoutdone= False;
+  if (qh_pointid(furthest) == qh_IDunknown)
+    qh_setappend(&qh other_points, furthest);
+  if (!facet) {
+    qh_fprintf(qh ferr, 6213, "qhull internal error (qh_addpoint): NULL facet.  Need to call qh_findbestfacet first\n");
+    qh_errexit(qh_ERRqhull, NULL, NULL);
+  }
+  if (checkdist) {
+    facet= qh_findbest(furthest, facet, !qh_ALL, !qh_ISnewfacets, !qh_NOupper,
+                        &dist, &isoutside, &numpart);
+    zzadd_(Zpartition, numpart);
+    if (!isoutside) {
+      zinc_(Znotmax);  /* last point of outsideset is no longer furthest. */
+      facet->notfurthest= True;
+      qh_partitioncoplanar(furthest, facet, &dist);
+      return True;
+    }
+  }
+  qh_buildtracing(furthest, facet);
+  if (qh STOPpoint < 0 && qh furthest_id == -qh STOPpoint-1) {
+    facet->notfurthest= True;
+    return False;
+  }
+  qh_findhorizon(furthest, facet, &goodvisible, &goodhorizon);
+  if (qh ONLYgood && !(goodvisible+goodhorizon) && !qh GOODclosest) {
+    zinc_(Znotgood);
+    facet->notfurthest= True;
+    /* last point of outsideset is no longer furthest.  This is ok
+       since all points of the outside are likely to be bad */
+    qh_resetlists(False, qh_RESETvisible /*qh.visible_list newvertex_list newfacet_list */);
+    return True;
+  }
+  zzinc_(Zprocessed);
+  firstnew= qh facet_id;
+  vertex= qh_makenewfacets(furthest /*visible_list, attaches if !ONLYgood */);
+  qh_makenewplanes(/* newfacet_list */);
+  numnew= qh facet_id - firstnew;
+  newbalance= numnew - (realT) (qh num_facets-qh num_visible)
+                         * qh hull_dim/qh num_vertices;
+  wadd_(Wnewbalance, newbalance);
+  wadd_(Wnewbalance2, newbalance * newbalance);
+  if (qh ONLYgood
+  && !qh_findgood(qh newfacet_list, goodhorizon) && !qh GOODclosest) {
+    FORALLnew_facets
+      qh_delfacet(newfacet);
+    qh_delvertex(vertex);
+    qh_resetlists(True, qh_RESETvisible /*qh.visible_list newvertex_list newfacet_list */);
+    zinc_(Znotgoodnew);
+    facet->notfurthest= True;
+    return True;
+  }
+  if (qh ONLYgood)
+    qh_attachnewfacets(/*visible_list*/);
+  qh_matchnewfacets();
+  qh_updatevertices();
+  if (qh STOPcone && qh furthest_id == qh STOPcone-1) {
+    facet->notfurthest= True;
+    return False;  /* visible_list etc. still defined */
+  }
+  qh findbestnew= False;
+  if (qh PREmerge || qh MERGEexact) {
+    qh_premerge(vertex, qh premerge_centrum, qh premerge_cos);
+    if (qh_USEfindbestnew)
+      qh findbestnew= True;
+    else {
+      FORALLnew_facets {
+        if (!newfacet->simplicial) {
+          qh findbestnew= True;  /* use qh_findbestnew instead of qh_findbest*/
+          break;
+        }
+      }
+    }
+  }else if (qh BESToutside)
+    qh findbestnew= True;
+  qh_partitionvisible(/*qh.visible_list*/ !qh_ALL, &numpoints);
+  qh findbestnew= False;
+  qh findbest_notsharp= False;
+  zinc_(Zpbalance);
+  pbalance= numpoints - (realT) qh hull_dim /* assumes all points extreme */
+                * (qh num_points - qh num_vertices)/qh num_vertices;
+  wadd_(Wpbalance, pbalance);
+  wadd_(Wpbalance2, pbalance * pbalance);
+  qh_deletevisible(/*qh.visible_list*/);
+  zmax_(Zmaxvertex, qh num_vertices);
+  qh NEWfacets= False;
+  if (qh IStracing >= 4) {
+    if (qh num_facets < 2000)
+      qh_printlists();
+    qh_printfacetlist(qh newfacet_list, NULL, True);
+    qh_checkpolygon(qh facet_list);
+  }else if (qh CHECKfrequently) {
+    if (qh num_facets < 50)
+      qh_checkpolygon(qh facet_list);
+    else
+      qh_checkpolygon(qh newfacet_list);
+  }
+  if (qh STOPpoint > 0 && qh furthest_id == qh STOPpoint-1)
+    return False;
+  qh_resetlists(True, qh_RESETvisible /*qh.visible_list newvertex_list newfacet_list */);
+  /* qh_triangulate(); to test qh.TRInormals */
+  trace2((qh ferr, 2056, "qh_addpoint: added p%d new facets %d new balance %2.2g point balance %2.2g\n",
+    qh_pointid(furthest), numnew, newbalance, pbalance));
+  return True;
+} /* addpoint */
+
+/*-<a                             href="qh-qhull.htm#TOC"
+  >-------------------------------</a><a name="build_withrestart">-</a>
+
+  qh_build_withrestart()
+    allow restarts due to qh.JOGGLEmax while calling qh_buildhull()
+       qh_errexit always undoes qh_build_withrestart()
+    qh.FIRSTpoint/qh.NUMpoints is point array
+        it may be moved by qh_joggleinput()
+*/
+void qh_build_withrestart(void) {
+  int restart;
+
+  qh ALLOWrestart= True;
+  while (True) {
+    restart= setjmp(qh restartexit); /* simple statement for CRAY J916 */
+    if (restart) {       /* only from qh_precision() */
+      zzinc_(Zretry);
+      wmax_(Wretrymax, qh JOGGLEmax);
+      /* QH7078 warns about using 'TCn' with 'QJn' */
+      qh STOPcone= qh_IDunknown; /* if break from joggle, prevents normal output */
+    }
+    if (!qh RERUN && qh JOGGLEmax < REALmax/2) {
+      if (qh build_cnt > qh_JOGGLEmaxretry) {
+        qh_fprintf(qh ferr, 6229, "qhull precision error: %d attempts to construct a convex hull\n\
+        with joggled input.  Increase joggle above 'QJ%2.2g'\n\
+        or modify qh_JOGGLE... parameters in user.h\n",
+           qh build_cnt, qh JOGGLEmax);
+        qh_errexit(qh_ERRqhull, NULL, NULL);
+      }
+      if (qh build_cnt && !restart)
+        break;
+    }else if (qh build_cnt && qh build_cnt >= qh RERUN)
+      break;
+    qh STOPcone= 0;
+    qh_freebuild(True);  /* first call is a nop */
+    qh build_cnt++;
+    if (!qh qhull_optionsiz)
+      qh qhull_optionsiz= (int)strlen(qh qhull_options);   /* WARN64 */
+    else {
+      qh qhull_options [qh qhull_optionsiz]= '\0';
+      qh qhull_optionlen= qh_OPTIONline;  /* starts a new line */
+    }
+    qh_option("_run", &qh build_cnt, NULL);
+    if (qh build_cnt == qh RERUN) {
+      qh IStracing= qh TRACElastrun;  /* duplicated from qh_initqhull_globals */
+      if (qh TRACEpoint != qh_IDunknown || qh TRACEdist < REALmax/2 || qh TRACEmerge) {
+        qh TRACElevel= (qh IStracing? qh IStracing : 3);
+        qh IStracing= 0;
+      }
+      qhmem.IStracing= qh IStracing;
+    }
+    if (qh JOGGLEmax < REALmax/2)
+      qh_joggleinput();
+    qh_initbuild();
+    qh_buildhull();
+    if (qh JOGGLEmax < REALmax/2 && !qh MERGING)
+      qh_checkconvex(qh facet_list, qh_ALGORITHMfault);
+  }
+  qh ALLOWrestart= False;
+} /* qh_build_withrestart */
+
+/*-<a                             href="qh-qhull.htm#TOC"
+  >-------------------------------</a><a name="buildhull">-</a>
+
+  qh_buildhull()
+    construct a convex hull by adding outside points one at a time
+
+  returns:
+
+  notes:
+    may be called multiple times
+    checks facet and vertex lists for incorrect flags
+    to recover from STOPcone, call qh_deletevisible and qh_resetlists
+
+  design:
+    check visible facet and newfacet flags
+    check newlist vertex flags and qh.STOPcone/STOPpoint
+    for each facet with a furthest outside point
+      add point to facet
+      exit if qh.STOPcone or qh.STOPpoint requested
+    if qh.NARROWhull for initial simplex
+      partition remaining outside points to coplanar sets
+*/
+void qh_buildhull(void) {
+  facetT *facet;
+  pointT *furthest;
+  vertexT *vertex;
+  int id;
+
+  trace1((qh ferr, 1037, "qh_buildhull: start build hull\n"));
+  FORALLfacets {
+    if (facet->visible || facet->newfacet) {
+      qh_fprintf(qh ferr, 6165, "qhull internal error (qh_buildhull): visible or new facet f%d in facet list\n",
+                   facet->id);
+      qh_errexit(qh_ERRqhull, facet, NULL);
+    }
+  }
+  FORALLvertices {
+    if (vertex->newlist) {
+      qh_fprintf(qh ferr, 6166, "qhull internal error (qh_buildhull): new vertex f%d in vertex list\n",
+                   vertex->id);
+      qh_errprint("ERRONEOUS", NULL, NULL, NULL, vertex);
+      qh_errexit(qh_ERRqhull, NULL, NULL);
+    }
+    id= qh_pointid(vertex->point);
+    if ((qh STOPpoint>0 && id == qh STOPpoint-1) ||
+        (qh STOPpoint<0 && id == -qh STOPpoint-1) ||
+        (qh STOPcone>0 && id == qh STOPcone-1)) {
+      trace1((qh ferr, 1038,"qh_buildhull: stop point or cone P%d in initial hull\n", id));
+      return;
+    }
+  }
+  qh facet_next= qh facet_list;      /* advance facet when processed */
+  while ((furthest= qh_nextfurthest(&facet))) {
+    qh num_outside--;  /* if ONLYmax, furthest may not be outside */
+    if (!qh_addpoint(furthest, facet, qh ONLYmax))
+      break;
+  }
+  if (qh NARROWhull) /* move points from outsideset to coplanarset */
+    qh_outcoplanar( /* facet_list */ );
+  if (qh num_outside && !furthest) {
+    qh_fprintf(qh ferr, 6167, "qhull internal error (qh_buildhull): %d outside points were never processed.\n", qh num_outside);
+    qh_errexit(qh_ERRqhull, NULL, NULL);
+  }
+  trace1((qh ferr, 1039, "qh_buildhull: completed the hull construction\n"));
+} /* buildhull */
+
+
+/*-<a                             href="qh-qhull.htm#TOC"
+  >-------------------------------</a><a name="buildtracing">-</a>
+
+  qh_buildtracing( furthest, facet )
+    trace an iteration of qh_buildhull() for furthest point and facet
+    if !furthest, prints progress message
+
+  returns:
+    tracks progress with qh.lastreport
+    updates qh.furthest_id (-3 if furthest is NULL)
+    also resets visit_id, vertext_visit on wrap around
+
+  see:
+    qh_tracemerging()
+
+  design:
+    if !furthest
+      print progress message
+      exit
+    if 'TFn' iteration
+      print progress message
+    else if tracing
+      trace furthest point and facet
+    reset qh.visit_id and qh.vertex_visit if overflow may occur
+    set qh.furthest_id for tracing
+*/
+void qh_buildtracing(pointT *furthest, facetT *facet) {
+  realT dist= 0;
+  float cpu;
+  int total, furthestid;
+  time_t timedata;
+  struct tm *tp;
+  vertexT *vertex;
+
+  qh old_randomdist= qh RANDOMdist;
+  qh RANDOMdist= False;
+  if (!furthest) {
+    time(&timedata);
+    tp= localtime(&timedata);
+    cpu= (float)qh_CPUclock - (float)qh hulltime;
+    cpu /= (float)qh_SECticks;
+    total= zzval_(Ztotmerge) - zzval_(Zcyclehorizon) + zzval_(Zcyclefacettot);
+    qh_fprintf(qh ferr, 8118, "\n\
+At %02d:%02d:%02d & %2.5g CPU secs, qhull has created %d facets and merged %d.\n\
+ The current hull contains %d facets and %d vertices.  Last point was p%d\n",
+      tp->tm_hour, tp->tm_min, tp->tm_sec, cpu, qh facet_id -1,
+      total, qh num_facets, qh num_vertices, qh furthest_id);
+    return;
+  }
+  furthestid= qh_pointid(furthest);
+  if (qh TRACEpoint == furthestid) {
+    qh IStracing= qh TRACElevel;
+    qhmem.IStracing= qh TRACElevel;
+  }else if (qh TRACEpoint != qh_IDunknown && qh TRACEdist < REALmax/2) {
+    qh IStracing= 0;
+    qhmem.IStracing= 0;
+  }
+  if (qh REPORTfreq && (qh facet_id-1 > qh lastreport+qh REPORTfreq)) {
+    qh lastreport= qh facet_id-1;
+    time(&timedata);
+    tp= localtime(&timedata);
+    cpu= (float)qh_CPUclock - (float)qh hulltime;
+    cpu /= (float)qh_SECticks;
+    total= zzval_(Ztotmerge) - zzval_(Zcyclehorizon) + zzval_(Zcyclefacettot);
+    zinc_(Zdistio);
+    qh_distplane(furthest, facet, &dist);
+    qh_fprintf(qh ferr, 8119, "\n\
+At %02d:%02d:%02d & %2.5g CPU secs, qhull has created %d facets and merged %d.\n\
+ The current hull contains %d facets and %d vertices.  There are %d\n\
+ outside points.  Next is point p%d(v%d), %2.2g above f%d.\n",
+      tp->tm_hour, tp->tm_min, tp->tm_sec, cpu, qh facet_id -1,
+      total, qh num_facets, qh num_vertices, qh num_outside+1,
+      furthestid, qh vertex_id, dist, getid_(facet));
+  }else if (qh IStracing >=1) {
+    cpu= (float)qh_CPUclock - (float)qh hulltime;
+    cpu /= (float)qh_SECticks;
+    qh_distplane(furthest, facet, &dist);
+    qh_fprintf(qh ferr, 8120, "qh_addpoint: add p%d(v%d) to hull of %d facets(%2.2g above f%d) and %d outside at %4.4g CPU secs.  Previous was p%d.\n",
+      furthestid, qh vertex_id, qh num_facets, dist,
+      getid_(facet), qh num_outside+1, cpu, qh furthest_id);
+  }
+  zmax_(Zvisit2max, (int)qh visit_id/2);
+  if (qh visit_id > (unsigned) INT_MAX) { /* 31 bits */
+    zinc_(Zvisit);
+    qh visit_id= 0;
+    FORALLfacets
+      facet->visitid= 0;
+  }
+  zmax_(Zvvisit2max, (int)qh vertex_visit/2);
+  if (qh vertex_visit > (unsigned) INT_MAX) { /* 31 bits */
+    zinc_(Zvvisit);
+    qh vertex_visit= 0;
+    FORALLvertices
+      vertex->visitid= 0;
+  }
+  qh furthest_id= furthestid;
+  qh RANDOMdist= qh old_randomdist;
+} /* buildtracing */
+
+/*-<a                             href="qh-qhull.htm#TOC"
+  >-------------------------------</a><a name="errexit2">-</a>
+
+  qh_errexit2( exitcode, facet, otherfacet )
+    return exitcode to system after an error
+    report two facets
+
+  returns:
+    assumes exitcode non-zero
+
+  see:
+    normally use qh_errexit() in user.c(reports a facet and a ridge)
+*/
+void qh_errexit2(int exitcode, facetT *facet, facetT *otherfacet) {
+
+  qh_errprint("ERRONEOUS", facet, otherfacet, NULL, NULL);
+  qh_errexit(exitcode, NULL, NULL);
+} /* errexit2 */
+
+
+/*-<a                             href="qh-qhull.htm#TOC"
+  >-------------------------------</a><a name="findhorizon">-</a>
+
+  qh_findhorizon( point, facet, goodvisible, goodhorizon )
+    given a visible facet, find the point's horizon and visible facets
+    for all facets, !facet-visible
+
+  returns:
+    returns qh.visible_list/num_visible with all visible facets
+      marks visible facets with ->visible
+    updates count of good visible and good horizon facets
+    updates qh.max_outside, qh.max_vertex, facet->maxoutside
+
+  see:
+    similar to qh_delpoint()
+
+  design:
+    move facet to qh.visible_list at end of qh.facet_list
+    for all visible facets
+     for each unvisited neighbor of a visible facet
+       compute distance of point to neighbor
+       if point above neighbor
+         move neighbor to end of qh.visible_list
+       else if point is coplanar with neighbor
+         update qh.max_outside, qh.max_vertex, neighbor->maxoutside
+         mark neighbor coplanar (will create a samecycle later)
+         update horizon statistics
+*/
+void qh_findhorizon(pointT *point, facetT *facet, int *goodvisible, int *goodhorizon) {
+  facetT *neighbor, **neighborp, *visible;
+  int numhorizon= 0, coplanar= 0;
+  realT dist;
+
+  trace1((qh ferr, 1040,"qh_findhorizon: find horizon for point p%d facet f%d\n",qh_pointid(point),facet->id));
+  *goodvisible= *goodhorizon= 0;
+  zinc_(Ztotvisible);
+  qh_removefacet(facet);  /* visible_list at end of qh facet_list */
+  qh_appendfacet(facet);
+  qh num_visible= 1;
+  if (facet->good)
+    (*goodvisible)++;
+  qh visible_list= facet;
+  facet->visible= True;
+  facet->f.replace= NULL;
+  if (qh IStracing >=4)
+    qh_errprint("visible", facet, NULL, NULL, NULL);
+  qh visit_id++;
+  FORALLvisible_facets {
+    if (visible->tricoplanar && !qh TRInormals) {
+      qh_fprintf(qh ferr, 6230, "Qhull internal error (qh_findhorizon): does not work for tricoplanar facets.  Use option 'Q11'\n");
+      qh_errexit(qh_ERRqhull, visible, NULL);
+    }
+    visible->visitid= qh visit_id;
+    FOREACHneighbor_(visible) {
+      if (neighbor->visitid == qh visit_id)
+        continue;
+      neighbor->visitid= qh visit_id;
+      zzinc_(Znumvisibility);
+      qh_distplane(point, neighbor, &dist);
+      if (dist > qh MINvisible) {
+        zinc_(Ztotvisible);
+        qh_removefacet(neighbor);  /* append to end of qh visible_list */
+        qh_appendfacet(neighbor);
+        neighbor->visible= True;
+        neighbor->f.replace= NULL;
+        qh num_visible++;
+        if (neighbor->good)
+          (*goodvisible)++;
+        if (qh IStracing >=4)
+          qh_errprint("visible", neighbor, NULL, NULL, NULL);
+      }else {
+        if (dist > - qh MAXcoplanar) {
+          neighbor->coplanar= True;
+          zzinc_(Zcoplanarhorizon);
+          qh_precision("coplanar horizon");
+          coplanar++;
+          if (qh MERGING) {
+            if (dist > 0) {
+              maximize_(qh max_outside, dist);
+              maximize_(qh max_vertex, dist);
+#if qh_MAXoutside
+              maximize_(neighbor->maxoutside, dist);
+#endif
+            }else
+              minimize_(qh min_vertex, dist);  /* due to merge later */
+          }
+          trace2((qh ferr, 2057, "qh_findhorizon: point p%d is coplanar to horizon f%d, dist=%2.7g < qh MINvisible(%2.7g)\n",
+              qh_pointid(point), neighbor->id, dist, qh MINvisible));
+        }else
+          neighbor->coplanar= False;
+        zinc_(Ztothorizon);
+        numhorizon++;
+        if (neighbor->good)
+          (*goodhorizon)++;
+        if (qh IStracing >=4)
+          qh_errprint("horizon", neighbor, NULL, NULL, NULL);
+      }
+    }
+  }
+  if (!numhorizon) {
+    qh_precision("empty horizon");
+    qh_fprintf(qh ferr, 6168, "qhull precision error (qh_findhorizon): empty horizon\n\
+QhullPoint p%d was above all facets.\n", qh_pointid(point));
+    qh_printfacetlist(qh facet_list, NULL, True);
+    qh_errexit(qh_ERRprec, NULL, NULL);
+  }
+  trace1((qh ferr, 1041, "qh_findhorizon: %d horizon facets(good %d), %d visible(good %d), %d coplanar\n",
+       numhorizon, *goodhorizon, qh num_visible, *goodvisible, coplanar));
+  if (qh IStracing >= 4 && qh num_facets < 50)
+    qh_printlists();
+} /* findhorizon */
+
+/*-<a                             href="qh-qhull.htm#TOC"
+  >-------------------------------</a><a name="nextfurthest">-</a>
+
+  qh_nextfurthest( visible )
+    returns next furthest point and visible facet for qh_addpoint()
+    starts search at qh.facet_next
+
+  returns:
+    removes furthest point from outside set
+    NULL if none available
+    advances qh.facet_next over facets with empty outside sets
+
+  design:
+    for each facet from qh.facet_next
+      if empty outside set
+        advance qh.facet_next
+      else if qh.NARROWhull
+        determine furthest outside point
+        if furthest point is not outside
+          advance qh.facet_next(point will be coplanar)
+    remove furthest point from outside set
+*/
+pointT *qh_nextfurthest(facetT **visible) {
+  facetT *facet;
+  int size, idx;
+  realT randr, dist;
+  pointT *furthest;
+
+  while ((facet= qh facet_next) != qh facet_tail) {
+    if (!facet->outsideset) {
+      qh facet_next= facet->next;
+      continue;
+    }
+    SETreturnsize_(facet->outsideset, size);
+    if (!size) {
+      qh_setfree(&facet->outsideset);
+      qh facet_next= facet->next;
+      continue;
+    }
+    if (qh NARROWhull) {
+      if (facet->notfurthest)
+        qh_furthestout(facet);
+      furthest= (pointT*)qh_setlast(facet->outsideset);
+#if qh_COMPUTEfurthest
+      qh_distplane(furthest, facet, &dist);
+      zinc_(Zcomputefurthest);
+#else
+      dist= facet->furthestdist;
+#endif
+      if (dist < qh MINoutside) { /* remainder of outside set is coplanar for qh_outcoplanar */
+        qh facet_next= facet->next;
+        continue;
+      }
+    }
+    if (!qh RANDOMoutside && !qh VIRTUALmemory) {
+      if (qh PICKfurthest) {
+        qh_furthestnext(/* qh.facet_list */);
+        facet= qh facet_next;
+      }
+      *visible= facet;
+      return((pointT*)qh_setdellast(facet->outsideset));
+    }
+    if (qh RANDOMoutside) {
+      int outcoplanar = 0;
+      if (qh NARROWhull) {
+        FORALLfacets {
+          if (facet == qh facet_next)
+            break;
+          if (facet->outsideset)
+            outcoplanar += qh_setsize( facet->outsideset);
+        }
+      }
+      randr= qh_RANDOMint;
+      randr= randr/(qh_RANDOMmax+1);
+      idx= (int)floor((qh num_outside - outcoplanar) * randr);
+      FORALLfacet_(qh facet_next) {
+        if (facet->outsideset) {
+          SETreturnsize_(facet->outsideset, size);
+          if (!size)
+            qh_setfree(&facet->outsideset);
+          else if (size > idx) {
+            *visible= facet;
+            return((pointT*)qh_setdelnth(facet->outsideset, idx));
+          }else
+            idx -= size;
+        }
+      }
+      qh_fprintf(qh ferr, 6169, "qhull internal error (qh_nextfurthest): num_outside %d is too low\nby at least %d, or a random real %g >= 1.0\n",
+              qh num_outside, idx+1, randr);
+      qh_errexit(qh_ERRqhull, NULL, NULL);
+    }else { /* VIRTUALmemory */
+      facet= qh facet_tail->previous;
+      if (!(furthest= (pointT*)qh_setdellast(facet->outsideset))) {
+        if (facet->outsideset)
+          qh_setfree(&facet->outsideset);
+        qh_removefacet(facet);
+        qh_prependfacet(facet, &qh facet_list);
+        continue;
+      }
+      *visible= facet;
+      return furthest;
+    }
+  }
+  return NULL;
+} /* nextfurthest */
+
+/*-<a                             href="qh-qhull.htm#TOC"
+  >-------------------------------</a><a name="partitionall">-</a>
+
+  qh_partitionall( vertices, points, numpoints )
+    partitions all points in points/numpoints to the outsidesets of facets
+    vertices= vertices in qh.facet_list(!partitioned)
+
+  returns:
+    builds facet->outsideset
+    does not partition qh.GOODpoint
+    if qh.ONLYgood && !qh.MERGING,
+      does not partition qh.GOODvertex
+
+  notes:
+    faster if qh.facet_list sorted by anticipated size of outside set
+
+  design:
+    initialize pointset with all points
+    remove vertices from pointset
+    remove qh.GOODpointp from pointset (unless it's qh.STOPcone or qh.STOPpoint)
+    for all facets
+      for all remaining points in pointset
+        compute distance from point to facet
+        if point is outside facet
+          remove point from pointset (by not reappending)
+          update bestpoint
+          append point or old bestpoint to facet's outside set
+      append bestpoint to facet's outside set (furthest)
+    for all points remaining in pointset
+      partition point into facets' outside sets and coplanar sets
+*/
+void qh_partitionall(setT *vertices, pointT *points, int numpoints){
+  setT *pointset;
+  vertexT *vertex, **vertexp;
+  pointT *point, **pointp, *bestpoint;
+  int size, point_i, point_n, point_end, remaining, i, id;
+  facetT *facet;
+  realT bestdist= -REALmax, dist, distoutside;
+
+  trace1((qh ferr, 1042, "qh_partitionall: partition all points into outside sets\n"));
+  pointset= qh_settemp(numpoints);
+  qh num_outside= 0;
+  pointp= SETaddr_(pointset, pointT);
+  for (i=numpoints, point= points; i--; point += qh hull_dim)
+    *(pointp++)= point;
+  qh_settruncate(pointset, numpoints);
+  FOREACHvertex_(vertices) {
+    if ((id= qh_pointid(vertex->point)) >= 0)
+      SETelem_(pointset, id)= NULL;
+  }
+  id= qh_pointid(qh GOODpointp);
+  if (id >=0 && qh STOPcone-1 != id && -qh STOPpoint-1 != id)
+    SETelem_(pointset, id)= NULL;
+  if (qh GOODvertexp && qh ONLYgood && !qh MERGING) { /* matches qhull()*/
+    if ((id= qh_pointid(qh GOODvertexp)) >= 0)
+      SETelem_(pointset, id)= NULL;
+  }
+  if (!qh BESToutside) {  /* matches conditional for qh_partitionpoint below */
+    distoutside= qh_DISToutside; /* multiple of qh.MINoutside & qh.max_outside, see user.h */
+    zval_(Ztotpartition)= qh num_points - qh hull_dim - 1; /*misses GOOD... */
+    remaining= qh num_facets;
+    point_end= numpoints;
+    FORALLfacets {
+      size= point_end/(remaining--) + 100;
+      facet->outsideset= qh_setnew(size);
+      bestpoint= NULL;
+      point_end= 0;
+      FOREACHpoint_i_(pointset) {
+        if (point) {
+          zzinc_(Zpartitionall);
+          qh_distplane(point, facet, &dist);
+          if (dist < distoutside)
+            SETelem_(pointset, point_end++)= point;
+          else {
+            qh num_outside++;
+            if (!bestpoint) {
+              bestpoint= point;
+              bestdist= dist;
+            }else if (dist > bestdist) {
+              qh_setappend(&facet->outsideset, bestpoint);
+              bestpoint= point;
+              bestdist= dist;
+            }else
+              qh_setappend(&facet->outsideset, point);
+          }
+        }
+      }
+      if (bestpoint) {
+        qh_setappend(&facet->outsideset, bestpoint);
+#if !qh_COMPUTEfurthest
+        facet->furthestdist= bestdist;
+#endif
+      }else
+        qh_setfree(&facet->outsideset);
+      qh_settruncate(pointset, point_end);
+    }
+  }
+  /* if !qh BESToutside, pointset contains points not assigned to outsideset */
+  if (qh BESToutside || qh MERGING || qh KEEPcoplanar || qh KEEPinside) {
+    qh findbestnew= True;
+    FOREACHpoint_i_(pointset) {
+      if (point)
+        qh_partitionpoint(point, qh facet_list);
+    }
+    qh findbestnew= False;
+  }
+  zzadd_(Zpartitionall, zzval_(Zpartition));
+  zzval_(Zpartition)= 0;
+  qh_settempfree(&pointset);
+  if (qh IStracing >= 4)
+    qh_printfacetlist(qh facet_list, NULL, True);
+} /* partitionall */
+
+
+/*-<a                             href="qh-qhull.htm#TOC"
+  >-------------------------------</a><a name="partitioncoplanar">-</a>
+
+  qh_partitioncoplanar( point, facet, dist )
+    partition coplanar point to a facet
+    dist is distance from point to facet
+    if dist NULL,
+      searches for bestfacet and does nothing if inside
+    if qh.findbestnew set,
+      searches new facets instead of using qh_findbest()
+
+  returns:
+    qh.max_ouside updated
+    if qh.KEEPcoplanar or qh.KEEPinside
+      point assigned to best coplanarset
+
+  notes:
+    facet->maxoutside is updated at end by qh_check_maxout
+
+  design:
+    if dist undefined
+      find best facet for point
+      if point sufficiently below facet (depends on qh.NEARinside and qh.KEEPinside)
+        exit
+    if keeping coplanar/nearinside/inside points
+      if point is above furthest coplanar point
+        append point to coplanar set (it is the new furthest)
+        update qh.max_outside
+      else
+        append point one before end of coplanar set
+    else if point is clearly outside of qh.max_outside and bestfacet->coplanarset
+    and bestfacet is more than perpendicular to facet
+      repartition the point using qh_findbest() -- it may be put on an outsideset
+    else
+      update qh.max_outside
+*/
+void qh_partitioncoplanar(pointT *point, facetT *facet, realT *dist) {
+  facetT *bestfacet;
+  pointT *oldfurthest;
+  realT bestdist, dist2= 0, angle;
+  int numpart= 0, oldfindbest;
+  boolT isoutside;
+
+  qh WAScoplanar= True;
+  if (!dist) {
+    if (qh findbestnew)
+      bestfacet= qh_findbestnew(point, facet, &bestdist, qh_ALL, &isoutside, &numpart);
+    else
+      bestfacet= qh_findbest(point, facet, qh_ALL, !qh_ISnewfacets, qh DELAUNAY,
+                          &bestdist, &isoutside, &numpart);
+    zinc_(Ztotpartcoplanar);
+    zzadd_(Zpartcoplanar, numpart);
+    if (!qh DELAUNAY && !qh KEEPinside) { /*  for 'd', bestdist skips upperDelaunay facets */
+      if (qh KEEPnearinside) {
+        if (bestdist < -qh NEARinside) {
+          zinc_(Zcoplanarinside);
+          trace4((qh ferr, 4062, "qh_partitioncoplanar: point p%d is more than near-inside facet f%d dist %2.2g findbestnew %d\n",
+                  qh_pointid(point), bestfacet->id, bestdist, qh findbestnew));
+          return;
+        }
+      }else if (bestdist < -qh MAXcoplanar) {
+          trace4((qh ferr, 4063, "qh_partitioncoplanar: point p%d is inside facet f%d dist %2.2g findbestnew %d\n",
+                  qh_pointid(point), bestfacet->id, bestdist, qh findbestnew));
+        zinc_(Zcoplanarinside);
+        return;
+      }
+    }
+  }else {
+    bestfacet= facet;
+    bestdist= *dist;
+  }
+  if (bestdist > qh max_outside) {
+    if (!dist && facet != bestfacet) {
+      zinc_(Zpartangle);
+      angle= qh_getangle(facet->normal, bestfacet->normal);
+      if (angle < 0) {
+        /* typically due to deleted vertex and coplanar facets, e.g.,
+             RBOX 1000 s Z1 G1e-13 t1001185205 | QHULL Tv */
+        zinc_(Zpartflip);
+        trace2((qh ferr, 2058, "qh_partitioncoplanar: repartition point p%d from f%d.  It is above flipped facet f%d dist %2.2g\n",
+                qh_pointid(point), facet->id, bestfacet->id, bestdist));
+        oldfindbest= qh findbestnew;
+        qh findbestnew= False;
+        qh_partitionpoint(point, bestfacet);
+        qh findbestnew= oldfindbest;
+        return;
+      }
+    }
+    qh max_outside= bestdist;
+    if (bestdist > qh TRACEdist) {
+      qh_fprintf(qh ferr, 8122, "qh_partitioncoplanar: ====== p%d from f%d increases max_outside to %2.2g of f%d last p%d\n",
+                     qh_pointid(point), facet->id, bestdist, bestfacet->id, qh furthest_id);
+      qh_errprint("DISTANT", facet, bestfacet, NULL, NULL);
+    }
+  }
+  if (qh KEEPcoplanar + qh KEEPinside + qh KEEPnearinside) {
+    oldfurthest= (pointT*)qh_setlast(bestfacet->coplanarset);
+    if (oldfurthest) {
+      zinc_(Zcomputefurthest);
+      qh_distplane(oldfurthest, bestfacet, &dist2);
+    }
+    if (!oldfurthest || dist2 < bestdist)
+      qh_setappend(&bestfacet->coplanarset, point);
+    else
+      qh_setappend2ndlast(&bestfacet->coplanarset, point);
+  }
+  trace4((qh ferr, 4064, "qh_partitioncoplanar: point p%d is coplanar with facet f%d(or inside) dist %2.2g\n",
+          qh_pointid(point), bestfacet->id, bestdist));
+} /* partitioncoplanar */
+
+/*-<a                             href="qh-qhull.htm#TOC"
+  >-------------------------------</a><a name="partitionpoint">-</a>
+
+  qh_partitionpoint( point, facet )
+    assigns point to an outside set, coplanar set, or inside set (i.e., dropt)
+    if qh.findbestnew
+      uses qh_findbestnew() to search all new facets
+    else
+      uses qh_findbest()
+
+  notes:
+    after qh_distplane(), this and qh_findbest() are most expensive in 3-d
+
+  design:
+    find best facet for point
+      (either exhaustive search of new facets or directed search from facet)
+    if qh.NARROWhull
+      retain coplanar and nearinside points as outside points
+    if point is outside bestfacet
+      if point above furthest point for bestfacet
+        append point to outside set (it becomes the new furthest)
+        if outside set was empty
+          move bestfacet to end of qh.facet_list (i.e., after qh.facet_next)
+        update bestfacet->furthestdist
+      else
+        append point one before end of outside set
+    else if point is coplanar to bestfacet
+      if keeping coplanar points or need to update qh.max_outside
+        partition coplanar point into bestfacet
+    else if near-inside point
+      partition as coplanar point into bestfacet
+    else is an inside point
+      if keeping inside points
+        partition as coplanar point into bestfacet
+*/
+void qh_partitionpoint(pointT *point, facetT *facet) {
+  realT bestdist;
+  boolT isoutside;
+  facetT *bestfacet;
+  int numpart;
+#if qh_COMPUTEfurthest
+  realT dist;
+#endif
+
+  if (qh findbestnew)
+    bestfacet= qh_findbestnew(point, facet, &bestdist, qh BESToutside, &isoutside, &numpart);
+  else
+    bestfacet= qh_findbest(point, facet, qh BESToutside, qh_ISnewfacets, !qh_NOupper,
+                          &bestdist, &isoutside, &numpart);
+  zinc_(Ztotpartition);
+  zzadd_(Zpartition, numpart);
+  if (qh NARROWhull) {
+    if (qh DELAUNAY && !isoutside && bestdist >= -qh MAXcoplanar)
+      qh_precision("nearly incident point(narrow hull)");
+    if (qh KEEPnearinside) {
+      if (bestdist >= -qh NEARinside)
+        isoutside= True;
+    }else if (bestdist >= -qh MAXcoplanar)
+      isoutside= True;
+  }
+
+  if (isoutside) {
+    if (!bestfacet->outsideset
+    || !qh_setlast(bestfacet->outsideset)) {
+      qh_setappend(&(bestfacet->outsideset), point);
+      if (!bestfacet->newfacet) {
+        qh_removefacet(bestfacet);  /* make sure it's after qh facet_next */
+        qh_appendfacet(bestfacet);
+      }
+#if !qh_COMPUTEfurthest
+      bestfacet->furthestdist= bestdist;
+#endif
+    }else {
+#if qh_COMPUTEfurthest
+      zinc_(Zcomputefurthest);
+      qh_distplane(oldfurthest, bestfacet, &dist);
+      if (dist < bestdist)
+        qh_setappend(&(bestfacet->outsideset), point);
+      else
+        qh_setappend2ndlast(&(bestfacet->outsideset), point);
+#else
+      if (bestfacet->furthestdist < bestdist) {
+        qh_setappend(&(bestfacet->outsideset), point);
+        bestfacet->furthestdist= bestdist;
+      }else
+        qh_setappend2ndlast(&(bestfacet->outsideset), point);
+#endif
+    }
+    qh num_outside++;
+    trace4((qh ferr, 4065, "qh_partitionpoint: point p%d is outside facet f%d new? %d (or narrowhull)\n",
+          qh_pointid(point), bestfacet->id, bestfacet->newfacet));
+  }else if (qh DELAUNAY || bestdist >= -qh MAXcoplanar) { /* for 'd', bestdist skips upperDelaunay facets */
+    zzinc_(Zcoplanarpart);
+    if (qh DELAUNAY)
+      qh_precision("nearly incident point");
+    if ((qh KEEPcoplanar + qh KEEPnearinside) || bestdist > qh max_outside)
+      qh_partitioncoplanar(point, bestfacet, &bestdist);
+    else {
+      trace4((qh ferr, 4066, "qh_partitionpoint: point p%d is coplanar to facet f%d (dropped)\n",
+          qh_pointid(point), bestfacet->id));
+    }
+  }else if (qh KEEPnearinside && bestdist > -qh NEARinside) {
+    zinc_(Zpartnear);
+    qh_partitioncoplanar(point, bestfacet, &bestdist);
+  }else {
+    zinc_(Zpartinside);
+    trace4((qh ferr, 4067, "qh_partitionpoint: point p%d is inside all facets, closest to f%d dist %2.2g\n",
+          qh_pointid(point), bestfacet->id, bestdist));
+    if (qh KEEPinside)
+      qh_partitioncoplanar(point, bestfacet, &bestdist);
+  }
+} /* partitionpoint */
+
+/*-<a                             href="qh-qhull.htm#TOC"
+  >-------------------------------</a><a name="partitionvisible">-</a>
+
+  qh_partitionvisible( allpoints, numoutside )
+    partitions points in visible facets to qh.newfacet_list
+    qh.visible_list= visible facets
+    for visible facets
+      1st neighbor (if any) points to a horizon facet or a new facet
+    if allpoints(!used),
+      repartitions coplanar points
+
+  returns:
+    updates outside sets and coplanar sets of qh.newfacet_list
+    updates qh.num_outside (count of outside points)
+
+  notes:
+    qh.findbest_notsharp should be clear (extra work if set)
+
+  design:
+    for all visible facets with outside set or coplanar set
+      select a newfacet for visible facet
+      if outside set
+        partition outside set into new facets
+      if coplanar set and keeping coplanar/near-inside/inside points
+        if allpoints
+          partition coplanar set into new facets, may be assigned outside
+        else
+          partition coplanar set into coplanar sets of new facets
+    for each deleted vertex
+      if allpoints
+        partition vertex into new facets, may be assigned outside
+      else
+        partition vertex into coplanar sets of new facets
+*/
+void qh_partitionvisible(/*qh.visible_list*/ boolT allpoints, int *numoutside) {
+  facetT *visible, *newfacet;
+  pointT *point, **pointp;
+  int coplanar=0, size;
+  unsigned count;
+  vertexT *vertex, **vertexp;
+
+  if (qh ONLYmax)
+    maximize_(qh MINoutside, qh max_vertex);
+  *numoutside= 0;
+  FORALLvisible_facets {
+    if (!visible->outsideset && !visible->coplanarset)
+      continue;
+    newfacet= visible->f.replace;
+    count= 0;
+    while (newfacet && newfacet->visible) {
+      newfacet= newfacet->f.replace;
+      if (count++ > qh facet_id)
+        qh_infiniteloop(visible);
+    }
+    if (!newfacet)
+      newfacet= qh newfacet_list;
+    if (newfacet == qh facet_tail) {
+      qh_fprintf(qh ferr, 6170, "qhull precision error (qh_partitionvisible): all new facets deleted as\n        degenerate facets. Can not continue.\n");
+      qh_errexit(qh_ERRprec, NULL, NULL);
+    }
+    if (visible->outsideset) {
+      size= qh_setsize(visible->outsideset);
+      *numoutside += size;
+      qh num_outside -= size;
+      FOREACHpoint_(visible->outsideset)
+        qh_partitionpoint(point, newfacet);
+    }
+    if (visible->coplanarset && (qh KEEPcoplanar + qh KEEPinside + qh KEEPnearinside)) {
+      size= qh_setsize(visible->coplanarset);
+      coplanar += size;
+      FOREACHpoint_(visible->coplanarset) {
+        if (allpoints) /* not used */
+          qh_partitionpoint(point, newfacet);
+        else
+          qh_partitioncoplanar(point, newfacet, NULL);
+      }
+    }
+  }
+  FOREACHvertex_(qh del_vertices) {
+    if (vertex->point) {
+      if (allpoints) /* not used */
+        qh_partitionpoint(vertex->point, qh newfacet_list);
+      else
+        qh_partitioncoplanar(vertex->point, qh newfacet_list, NULL);
+    }
+  }
+  trace1((qh ferr, 1043,"qh_partitionvisible: partitioned %d points from outsidesets and %d points from coplanarsets\n", *numoutside, coplanar));
+} /* partitionvisible */
+
+
+
+/*-<a                             href="qh-qhull.htm#TOC"
+  >-------------------------------</a><a name="precision">-</a>
+
+  qh_precision( reason )
+    restart on precision errors if not merging and if 'QJn'
+*/
+void qh_precision(const char *reason) {
+
+  if (qh ALLOWrestart && !qh PREmerge && !qh MERGEexact) {
+    if (qh JOGGLEmax < REALmax/2) {
+      trace0((qh ferr, 26, "qh_precision: qhull restart because of %s\n", reason));
+      /* May be called repeatedly if qh->ALLOWrestart */
+      longjmp(qh restartexit, qh_ERRprec);
+    }
+  }
+} /* qh_precision */
+
+/*-<a                             href="qh-qhull.htm#TOC"
+  >-------------------------------</a><a name="printsummary">-</a>
+
+  qh_printsummary( fp )
+    prints summary to fp
+
+  notes:
+    not in io.c so that user_eg.c can prevent io.c from loading
+    qh_printsummary and qh_countfacets must match counts
+
+  design:
+    determine number of points, vertices, and coplanar points
+    print summary
+*/
+void qh_printsummary(FILE *fp) {
+  realT ratio, outerplane, innerplane;
+  float cpu;
+  int size, id, nummerged, numvertices, numcoplanars= 0, nonsimplicial=0;
+  int goodused;
+  facetT *facet;
+  const char *s;
+  int numdel= zzval_(Zdelvertextot);
+  int numtricoplanars= 0;
+
+  size= qh num_points + qh_setsize(qh other_points);
+  numvertices= qh num_vertices - qh_setsize(qh del_vertices);
+  id= qh_pointid(qh GOODpointp);
+  FORALLfacets {
+    if (facet->coplanarset)
+      numcoplanars += qh_setsize( facet->coplanarset);
+    if (facet->good) {
+      if (facet->simplicial) {
+        if (facet->keepcentrum && facet->tricoplanar)
+          numtricoplanars++;
+      }else if (qh_setsize(facet->vertices) != qh hull_dim)
+        nonsimplicial++;
+    }
+  }
+  if (id >=0 && qh STOPcone-1 != id && -qh STOPpoint-1 != id)
+    size--;
+  if (qh STOPcone || qh STOPpoint)
+      qh_fprintf(fp, 9288, "\nAt a premature exit due to 'TVn', 'TCn', 'TRn', or precision error with 'QJn'.");
+  if (qh UPPERdelaunay)
+    goodused= qh GOODvertex + qh GOODpoint + qh SPLITthresholds;
+  else if (qh DELAUNAY)
+    goodused= qh GOODvertex + qh GOODpoint + qh GOODthreshold;
+  else
+    goodused= qh num_good;
+  nummerged= zzval_(Ztotmerge) - zzval_(Zcyclehorizon) + zzval_(Zcyclefacettot);
+  if (qh VORONOI) {
+    if (qh UPPERdelaunay)
+      qh_fprintf(fp, 9289, "\n\
+Furthest-site Voronoi vertices by the convex hull of %d points in %d-d:\n\n", size, qh hull_dim);
+    else
+      qh_fprintf(fp, 9290, "\n\
+Voronoi diagram by the convex hull of %d points in %d-d:\n\n", size, qh hull_dim);
+    qh_fprintf(fp, 9291, "  Number of Voronoi regions%s: %d\n",
+              qh ATinfinity ? " and at-infinity" : "", numvertices);
+    if (numdel)
+      qh_fprintf(fp, 9292, "  Total number of deleted points due to merging: %d\n", numdel);
+    if (numcoplanars - numdel > 0)
+      qh_fprintf(fp, 9293, "  Number of nearly incident points: %d\n", numcoplanars - numdel);
+    else if (size - numvertices - numdel > 0)
+      qh_fprintf(fp, 9294, "  Total number of nearly incident points: %d\n", size - numvertices - numdel);
+    qh_fprintf(fp, 9295, "  Number of%s Voronoi vertices: %d\n",
+              goodused ? " 'good'" : "", qh num_good);
+    if (nonsimplicial)
+      qh_fprintf(fp, 9296, "  Number of%s non-simplicial Voronoi vertices: %d\n",
+              goodused ? " 'good'" : "", nonsimplicial);
+  }else if (qh DELAUNAY) {
+    if (qh UPPERdelaunay)
+      qh_fprintf(fp, 9297, "\n\
+Furthest-site Delaunay triangulation by the convex hull of %d points in %d-d:\n\n", size, qh hull_dim);
+    else
+      qh_fprintf(fp, 9298, "\n\
+Delaunay triangulation by the convex hull of %d points in %d-d:\n\n", size, qh hull_dim);
+    qh_fprintf(fp, 9299, "  Number of input sites%s: %d\n",
+              qh ATinfinity ? " and at-infinity" : "", numvertices);
+    if (numdel)
+      qh_fprintf(fp, 9300, "  Total number of deleted points due to merging: %d\n", numdel);
+    if (numcoplanars - numdel > 0)
+      qh_fprintf(fp, 9301, "  Number of nearly incident points: %d\n", numcoplanars - numdel);
+    else if (size - numvertices - numdel > 0)
+      qh_fprintf(fp, 9302, "  Total number of nearly incident points: %d\n", size - numvertices - numdel);
+    qh_fprintf(fp, 9303, "  Number of%s Delaunay regions: %d\n",
+              goodused ? " 'good'" : "", qh num_good);
+    if (nonsimplicial)
+      qh_fprintf(fp, 9304, "  Number of%s non-simplicial Delaunay regions: %d\n",
+              goodused ? " 'good'" : "", nonsimplicial);
+  }else if (qh HALFspace) {
+    qh_fprintf(fp, 9305, "\n\
+Halfspace intersection by the convex hull of %d points in %d-d:\n\n", size, qh hull_dim);
+    qh_fprintf(fp, 9306, "  Number of halfspaces: %d\n", size);
+    qh_fprintf(fp, 9307, "  Number of non-redundant halfspaces: %d\n", numvertices);
+    if (numcoplanars) {
+      if (qh KEEPinside && qh KEEPcoplanar)
+        s= "similar and redundant";
+      else if (qh KEEPinside)
+        s= "redundant";
+      else
+        s= "similar";
+      qh_fprintf(fp, 9308, "  Number of %s halfspaces: %d\n", s, numcoplanars);
+    }
+    qh_fprintf(fp, 9309, "  Number of intersection points: %d\n", qh num_facets - qh num_visible);
+    if (goodused)
+      qh_fprintf(fp, 9310, "  Number of 'good' intersection points: %d\n", qh num_good);
+    if (nonsimplicial)
+      qh_fprintf(fp, 9311, "  Number of%s non-simplicial intersection points: %d\n",
+              goodused ? " 'good'" : "", nonsimplicial);
+  }else {
+    qh_fprintf(fp, 9312, "\n\
+Convex hull of %d points in %d-d:\n\n", size, qh hull_dim);
+    qh_fprintf(fp, 9313, "  Number of vertices: %d\n", numvertices);
+    if (numcoplanars) {
+      if (qh KEEPinside && qh KEEPcoplanar)
+        s= "coplanar and interior";
+      else if (qh KEEPinside)
+        s= "interior";
+      else
+        s= "coplanar";
+      qh_fprintf(fp, 9314, "  Number of %s points: %d\n", s, numcoplanars);
+    }
+    qh_fprintf(fp, 9315, "  Number of facets: %d\n", qh num_facets - qh num_visible);
+    if (goodused)
+      qh_fprintf(fp, 9316, "  Number of 'good' facets: %d\n", qh num_good);
+    if (nonsimplicial)
+      qh_fprintf(fp, 9317, "  Number of%s non-simplicial facets: %d\n",
+              goodused ? " 'good'" : "", nonsimplicial);
+  }
+  if (numtricoplanars)
+      qh_fprintf(fp, 9318, "  Number of triangulated facets: %d\n", numtricoplanars);
+  qh_fprintf(fp, 9319, "\nStatistics for: %s | %s",
+                      qh rbox_command, qh qhull_command);
+  if (qh ROTATErandom != INT_MIN)
+    qh_fprintf(fp, 9320, " QR%d\n\n", qh ROTATErandom);
+  else
+    qh_fprintf(fp, 9321, "\n\n");
+  qh_fprintf(fp, 9322, "  Number of points processed: %d\n", zzval_(Zprocessed));
+  qh_fprintf(fp, 9323, "  Number of hyperplanes created: %d\n", zzval_(Zsetplane));
+  if (qh DELAUNAY)
+    qh_fprintf(fp, 9324, "  Number of facets in hull: %d\n", qh num_facets - qh num_visible);
+  qh_fprintf(fp, 9325, "  Number of distance tests for qhull: %d\n", zzval_(Zpartition)+
+      zzval_(Zpartitionall)+zzval_(Znumvisibility)+zzval_(Zpartcoplanar));
+#if 0  /* NOTE: must print before printstatistics() */
+  {realT stddev, ave;
+  qh_fprintf(fp, 9326, "  average new facet balance: %2.2g\n",
+          wval_(Wnewbalance)/zval_(Zprocessed));
+  stddev= qh_stddev(zval_(Zprocessed), wval_(Wnewbalance),
+                                 wval_(Wnewbalance2), &ave);
+  qh_fprintf(fp, 9327, "  new facet standard deviation: %2.2g\n", stddev);
+  qh_fprintf(fp, 9328, "  average partition balance: %2.2g\n",
+          wval_(Wpbalance)/zval_(Zpbalance));
+  stddev= qh_stddev(zval_(Zpbalance), wval_(Wpbalance),
+                                 wval_(Wpbalance2), &ave);
+  qh_fprintf(fp, 9329, "  partition standard deviation: %2.2g\n", stddev);
+  }
+#endif
+  if (nummerged) {
+    qh_fprintf(fp, 9330,"  Number of distance tests for merging: %d\n",zzval_(Zbestdist)+
+          zzval_(Zcentrumtests)+zzval_(Zdistconvex)+zzval_(Zdistcheck)+
+          zzval_(Zdistzero));
+    qh_fprintf(fp, 9331,"  Number of distance tests for checking: %d\n",zzval_(Zcheckpart));
+    qh_fprintf(fp, 9332,"  Number of merged facets: %d\n", nummerged);
+  }
+  if (!qh RANDOMoutside && qh QHULLfinished) {
+    cpu= (float)qh hulltime;
+    cpu /= (float)qh_SECticks;
+    wval_(Wcpu)= cpu;
+    qh_fprintf(fp, 9333, "  CPU seconds to compute hull (after input): %2.4g\n", cpu);
+  }
+  if (qh RERUN) {
+    if (!qh PREmerge && !qh MERGEexact)
+      qh_fprintf(fp, 9334, "  Percentage of runs with precision errors: %4.1f\n",
+           zzval_(Zretry)*100.0/qh build_cnt);  /* careful of order */
+  }else if (qh JOGGLEmax < REALmax/2) {
+    if (zzval_(Zretry))
+      qh_fprintf(fp, 9335, "  After %d retries, input joggled by: %2.2g\n",
+         zzval_(Zretry), qh JOGGLEmax);
+    else
+      qh_fprintf(fp, 9336, "  Input joggled by: %2.2g\n", qh JOGGLEmax);
+  }
+  if (qh totarea != 0.0)
+    qh_fprintf(fp, 9337, "  %s facet area:   %2.8g\n",
+            zzval_(Ztotmerge) ? "Approximate" : "Total", qh totarea);
+  if (qh totvol != 0.0)
+    qh_fprintf(fp, 9338, "  %s volume:       %2.8g\n",
+            zzval_(Ztotmerge) ? "Approximate" : "Total", qh totvol);
+  if (qh MERGING) {
+    qh_outerinner(NULL, &outerplane, &innerplane);
+    if (outerplane > 2 * qh DISTround) {
+      qh_fprintf(fp, 9339, "  Maximum distance of %spoint above facet: %2.2g",
+            (qh QHULLfinished ? "" : "merged "), outerplane);
+      ratio= outerplane/(qh ONEmerge + qh DISTround);
+      /* don't report ratio if MINoutside is large */
+      if (ratio > 0.05 && 2* qh ONEmerge > qh MINoutside && qh JOGGLEmax > REALmax/2)
+        qh_fprintf(fp, 9340, " (%.1fx)\n", ratio);
+      else
+        qh_fprintf(fp, 9341, "\n");
+    }
+    if (innerplane < -2 * qh DISTround) {
+      qh_fprintf(fp, 9342, "  Maximum distance of %svertex below facet: %2.2g",
+            (qh QHULLfinished ? "" : "merged "), innerplane);
+      ratio= -innerplane/(qh ONEmerge+qh DISTround);
+      if (ratio > 0.05 && qh JOGGLEmax > REALmax/2)
+        qh_fprintf(fp, 9343, " (%.1fx)\n", ratio);
+      else
+        qh_fprintf(fp, 9344, "\n");
+    }
+  }
+  qh_fprintf(fp, 9345, "\n");
+} /* printsummary */
+
+
diff --git a/xs/src/qhull/src/libqhull/libqhull.h b/xs/src/qhull/src/libqhull/libqhull.h
new file mode 100644
index 0000000000..677085808d
--- /dev/null
+++ b/xs/src/qhull/src/libqhull/libqhull.h
@@ -0,0 +1,1140 @@
+/*<html><pre>  -<a                             href="qh-qhull.htm"
+  >-------------------------------</a><a name="TOP">-</a>
+
+   libqhull.h
+   user-level header file for using qhull.a library
+
+   see qh-qhull.htm, qhull_a.h
+
+   Copyright (c) 1993-2015 The Geometry Center.
+   $Id: //main/2015/qhull/src/libqhull/libqhull.h#7 $$Change: 2066 $
+   $DateTime: 2016/01/18 19:29:17 $$Author: bbarber $
+
+   NOTE: access to qh_qh is via the 'qh' macro.  This allows
+   qh_qh to be either a pointer or a structure.  An example
+   of using qh is "qh.DROPdim" which accesses the DROPdim
+   field of qh_qh.  Similarly, access to qh_qhstat is via
+   the 'qhstat' macro.
+
+   includes function prototypes for libqhull.c, geom.c, global.c, io.c, user.c
+
+   use mem.h for mem.c
+   use qset.h for qset.c
+
+   see unix.c for an example of using libqhull.h
+
+   recompile qhull if you change this file
+*/
+
+#ifndef qhDEFlibqhull
+#define qhDEFlibqhull 1
+
+/*=========================== -included files ==============*/
+
+/* user_r.h first for QHULL_CRTDBG */
+#include "user.h"      /* user definable constants (e.g., qh_QHpointer) */
+
+#include "mem.h"   /* Needed qhT in libqhull_r.h.  Here for compatibility */
+#include "qset.h"   /* Needed for QHULL_LIB_CHECK */
+/* include stat_r.h after defining boolT.  Needed for qhT in libqhull_r.h.  Here for compatibility and statT */
+
+#include <setjmp.h>
+#include <float.h>
+#include <time.h>
+#include <stdio.h>
+
+#if __MWERKS__ && __POWERPC__
+#include  <SIOUX.h>
+#include  <Files.h>
+#include        <Desk.h>
+#endif
+
+#ifndef __STDC__
+#ifndef __cplusplus
+#if     !_MSC_VER
+#error  Neither __STDC__ nor __cplusplus is defined.  Please use strict ANSI C or C++ to compile
+#error  Qhull.  You may need to turn off compiler extensions in your project configuration.  If
+#error  your compiler is a standard C compiler, you can delete this warning from libqhull.h
+#endif
+#endif
+#endif
+
+/*============ constants and basic types ====================*/
+
+extern const char qh_version[]; /* defined in global.c */
+extern const char qh_version2[]; /* defined in global.c */
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >--------------------------------</a><a name="coordT">-</a>
+
+  coordT
+    coordinates and coefficients are stored as realT (i.e., double)
+
+  notes:
+    Qhull works well if realT is 'float'.  If so joggle (QJ) is not effective.
+
+    Could use 'float' for data and 'double' for calculations (realT vs. coordT)
+      This requires many type casts, and adjusted error bounds.
+      Also C compilers may do expressions in double anyway.
+*/
+#define coordT realT
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >--------------------------------</a><a name="pointT">-</a>
+
+  pointT
+    a point is an array of coordinates, usually qh.hull_dim
+    qh_pointid returns
+      qh_IDnone if point==0 or qh is undefined
+      qh_IDinterior for qh.interior_point
+      qh_IDunknown if point is neither in qh.first_point... nor qh.other_points
+
+  notes:
+    qh.STOPcone and qh.STOPpoint assume that qh_IDunknown==-1 (other negative numbers indicate points)
+    qh_IDunknown is also returned by getid_() for unknown facet, ridge, or vertex
+*/
+#define pointT coordT
+typedef enum
+{
+    qh_IDnone = -3, qh_IDinterior = -2, qh_IDunknown = -1
+}
+qh_pointT;
+
+/*-<a                             href="qh-qhull.htm#TOC"
+  >--------------------------------</a><a name="flagT">-</a>
+
+  flagT
+    Boolean flag as a bit
+*/
+#define flagT unsigned int
+
+/*-<a                             href="qh-qhull.htm#TOC"
+  >--------------------------------</a><a name="boolT">-</a>
+
+  boolT
+    boolean value, either True or False
+
+  notes:
+    needed for portability
+    Use qh_False/qh_True as synonyms
+*/
+#define boolT unsigned int
+#ifdef False
+#undef False
+#endif
+#ifdef True
+#undef True
+#endif
+#define False 0
+#define True 1
+#define qh_False 0
+#define qh_True 1
+
+#include "stat.h"  /* after define of boolT */
+
+/*-<a                             href="qh-qhull.htm#TOC"
+  >--------------------------------</a><a name="CENTERtype">-</a>
+
+  qh_CENTER
+    to distinguish facet->center
+*/
+typedef enum
+{
+    qh_ASnone = 0,   /* If not MERGING and not VORONOI */
+    qh_ASvoronoi,    /* Set by qh_clearcenters on qh_prepare_output, or if not MERGING and VORONOI */
+    qh_AScentrum     /* If MERGING (assumed during merging) */
+}
+qh_CENTER;
+
+/*-<a                             href="qh-qhull.htm#TOC"
+  >--------------------------------</a><a name="qh_PRINT">-</a>
+
+  qh_PRINT
+    output formats for printing (qh.PRINTout).
+    'Fa' 'FV' 'Fc' 'FC'
+
+
+   notes:
+   some of these names are similar to qhT names.  The similar names are only
+   used in switch statements in qh_printbegin() etc.
+*/
+typedef enum {qh_PRINTnone= 0,
+  qh_PRINTarea, qh_PRINTaverage,           /* 'Fa' 'FV' 'Fc' 'FC' */
+  qh_PRINTcoplanars, qh_PRINTcentrums,
+  qh_PRINTfacets, qh_PRINTfacets_xridge,   /* 'f' 'FF' 'G' 'FI' 'Fi' 'Fn' */
+  qh_PRINTgeom, qh_PRINTids, qh_PRINTinner, qh_PRINTneighbors,
+  qh_PRINTnormals, qh_PRINTouter, qh_PRINTmaple, /* 'n' 'Fo' 'i' 'm' 'Fm' 'FM', 'o' */
+  qh_PRINTincidences, qh_PRINTmathematica, qh_PRINTmerges, qh_PRINToff,
+  qh_PRINToptions, qh_PRINTpointintersect, /* 'FO' 'Fp' 'FP' 'p' 'FQ' 'FS' */
+  qh_PRINTpointnearest, qh_PRINTpoints, qh_PRINTqhull, qh_PRINTsize,
+  qh_PRINTsummary, qh_PRINTtriangles,      /* 'Fs' 'Ft' 'Fv' 'FN' 'Fx' */
+  qh_PRINTvertices, qh_PRINTvneighbors, qh_PRINTextremes,
+  qh_PRINTEND} qh_PRINT;
+
+/*-<a                             href="qh-qhull.htm#TOC"
+  >--------------------------------</a><a name="qh_ALL">-</a>
+
+  qh_ALL
+    argument flag for selecting everything
+*/
+#define qh_ALL      True
+#define qh_NOupper  True     /* argument for qh_findbest */
+#define qh_IScheckmax  True     /* argument for qh_findbesthorizon */
+#define qh_ISnewfacets  True     /* argument for qh_findbest */
+#define qh_RESETvisible  True     /* argument for qh_resetlists */
+
+/*-<a                             href="qh-qhull.htm#TOC"
+  >--------------------------------</a><a name="qh_ERR">-</a>
+
+  qh_ERR
+    Qhull exit codes, for indicating errors
+    See: MSG_ERROR and MSG_WARNING [user.h]
+*/
+#define qh_ERRnone  0    /* no error occurred during qhull */
+#define qh_ERRinput 1    /* input inconsistency */
+#define qh_ERRsingular 2 /* singular input data */
+#define qh_ERRprec  3    /* precision error */
+#define qh_ERRmem   4    /* insufficient memory, matches mem.h */
+#define qh_ERRqhull 5    /* internal error detected, matches mem.h */
+
+/*-<a                             href="qh-qhull.htm#TOC"
+>--------------------------------</a><a name="qh_FILEstderr">-</a>
+
+qh_FILEstderr
+Fake stderr to distinguish error output from normal output
+For C++ interface.  Must redefine qh_fprintf_qhull
+*/
+#define qh_FILEstderr ((FILE*)1)
+
+/* ============ -structures- ====================
+   each of the following structures is defined by a typedef
+   all realT and coordT fields occur at the beginning of a structure
+        (otherwise space may be wasted due to alignment)
+   define all flags together and pack into 32-bit number
+   DEFsetT is likewise defined in
+   mem.h and qset.h
+*/
+
+typedef struct vertexT vertexT;
+typedef struct ridgeT ridgeT;
+typedef struct facetT facetT;
+#ifndef DEFsetT
+#define DEFsetT 1
+typedef struct setT setT;          /* defined in qset.h */
+#endif
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >--------------------------------</a><a name="facetT">-</a>
+
+  facetT
+    defines a facet
+
+  notes:
+   qhull() generates the hull as a list of facets.
+
+  topological information:
+    f.previous,next     doubly-linked list of facets
+    f.vertices          set of vertices
+    f.ridges            set of ridges
+    f.neighbors         set of neighbors
+    f.toporient         True if facet has top-orientation (else bottom)
+
+  geometric information:
+    f.offset,normal     hyperplane equation
+    f.maxoutside        offset to outer plane -- all points inside
+    f.center            centrum for testing convexity
+    f.simplicial        True if facet is simplicial
+    f.flipped           True if facet does not include qh.interior_point
+
+  for constructing hull:
+    f.visible           True if facet on list of visible facets (will be deleted)
+    f.newfacet          True if facet on list of newly created facets
+    f.coplanarset       set of points coplanar with this facet
+                        (includes near-inside points for later testing)
+    f.outsideset        set of points outside of this facet
+    f.furthestdist      distance to furthest point of outside set
+    f.visitid           marks visited facets during a loop
+    f.replace           replacement facet for to-be-deleted, visible facets
+    f.samecycle,newcycle cycle of facets for merging into horizon facet
+
+  see below for other flags and fields
+*/
+struct facetT {
+#if !qh_COMPUTEfurthest
+  coordT   furthestdist;/* distance to furthest point of outsideset */
+#endif
+#if qh_MAXoutside
+  coordT   maxoutside;  /* max computed distance of point to facet
+                        Before QHULLfinished this is an approximation
+                        since maxdist not always set for mergefacet
+                        Actual outer plane is +DISTround and
+                        computed outer plane is +2*DISTround */
+#endif
+  coordT   offset;      /* exact offset of hyperplane from origin */
+  coordT  *normal;      /* normal of hyperplane, hull_dim coefficients */
+                        /*   if tricoplanar, shared with a neighbor */
+  union {               /* in order of testing */
+   realT   area;        /* area of facet, only in io.c if  ->isarea */
+   facetT *replace;     /*  replacement facet if ->visible and NEWfacets
+                             is NULL only if qh_mergedegen_redundant or interior */
+   facetT *samecycle;   /*  cycle of facets from the same visible/horizon intersection,
+                             if ->newfacet */
+   facetT *newcycle;    /*  in horizon facet, current samecycle of new facets */
+   facetT *trivisible;  /* visible facet for ->tricoplanar facets during qh_triangulate() */
+   facetT *triowner;    /* owner facet for ->tricoplanar, !isarea facets w/ ->keepcentrum */
+  }f;
+  coordT  *center;      /* set according to qh.CENTERtype */
+                        /*   qh_ASnone:    no center (not MERGING) */
+                        /*   qh_AScentrum: centrum for testing convexity (qh_getcentrum) */
+                        /*                 assumed qh_AScentrum while merging */
+                        /*   qh_ASvoronoi: Voronoi center (qh_facetcenter) */
+                        /* after constructing the hull, it may be changed (qh_clearcenter) */
+                        /* if tricoplanar and !keepcentrum, shared with a neighbor */
+  facetT  *previous;    /* previous facet in the facet_list */
+  facetT  *next;        /* next facet in the facet_list */
+  setT    *vertices;    /* vertices for this facet, inverse sorted by ID
+                           if simplicial, 1st vertex was apex/furthest */
+  setT    *ridges;      /* explicit ridges for nonsimplicial facets.
+                           for simplicial facets, neighbors define the ridges */
+  setT    *neighbors;   /* neighbors of the facet.  If simplicial, the kth
+                           neighbor is opposite the kth vertex, and the first
+                           neighbor is the horizon facet for the first vertex*/
+  setT    *outsideset;  /* set of points outside this facet
+                           if non-empty, last point is furthest
+                           if NARROWhull, includes coplanars for partitioning*/
+  setT    *coplanarset; /* set of points coplanar with this facet
+                           > qh.min_vertex and <= facet->max_outside
+                           a point is assigned to the furthest facet
+                           if non-empty, last point is furthest away */
+  unsigned visitid;     /* visit_id, for visiting all neighbors,
+                           all uses are independent */
+  unsigned id;          /* unique identifier from qh.facet_id */
+  unsigned nummerge:9;  /* number of merges */
+#define qh_MAXnummerge 511 /*     2^9-1, 32 flags total, see "flags:" in io.c */
+  flagT    tricoplanar:1; /* True if TRIangulate and simplicial and coplanar with a neighbor */
+                          /*   all tricoplanars share the same apex */
+                          /*   all tricoplanars share the same ->center, ->normal, ->offset, ->maxoutside */
+                          /*     ->keepcentrum is true for the owner.  It has the ->coplanareset */
+                          /*   if ->degenerate, does not span facet (one logical ridge) */
+                          /*   during qh_triangulate, f.trivisible points to original facet */
+  flagT    newfacet:1;  /* True if facet on qh.newfacet_list (new or merged) */
+  flagT    visible:1;   /* True if visible facet (will be deleted) */
+  flagT    toporient:1; /* True if created with top orientation
+                           after merging, use ridge orientation */
+  flagT    simplicial:1;/* True if simplicial facet, ->ridges may be implicit */
+  flagT    seen:1;      /* used to perform operations only once, like visitid */
+  flagT    seen2:1;     /* used to perform operations only once, like visitid */
+  flagT    flipped:1;   /* True if facet is flipped */
+  flagT    upperdelaunay:1; /* True if facet is upper envelope of Delaunay triangulation */
+  flagT    notfurthest:1; /* True if last point of outsideset is not furthest*/
+
+/*-------- flags primarily for output ---------*/
+  flagT    good:1;      /* True if a facet marked good for output */
+  flagT    isarea:1;    /* True if facet->f.area is defined */
+
+/*-------- flags for merging ------------------*/
+  flagT    dupridge:1;  /* True if duplicate ridge in facet */
+  flagT    mergeridge:1; /* True if facet or neighbor contains a qh_MERGEridge
+                            ->normal defined (also defined for mergeridge2) */
+  flagT    mergeridge2:1; /* True if neighbor contains a qh_MERGEridge (mark_dupridges */
+  flagT    coplanar:1;  /* True if horizon facet is coplanar at last use */
+  flagT     mergehorizon:1; /* True if will merge into horizon (->coplanar) */
+  flagT     cycledone:1;/* True if mergecycle_all already done */
+  flagT    tested:1;    /* True if facet convexity has been tested (false after merge */
+  flagT    keepcentrum:1; /* True if keep old centrum after a merge, or marks owner for ->tricoplanar */
+  flagT    newmerge:1;  /* True if facet is newly merged for reducevertices */
+  flagT    degenerate:1; /* True if facet is degenerate (degen_mergeset or ->tricoplanar) */
+  flagT    redundant:1;  /* True if facet is redundant (degen_mergeset) */
+};
+
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >--------------------------------</a><a name="ridgeT">-</a>
+
+  ridgeT
+    defines a ridge
+
+  notes:
+  a ridge is hull_dim-1 simplex between two neighboring facets.  If the
+  facets are non-simplicial, there may be more than one ridge between
+  two facets.  E.G. a 4-d hypercube has two triangles between each pair
+  of neighboring facets.
+
+  topological information:
+    vertices            a set of vertices
+    top,bottom          neighboring facets with orientation
+
+  geometric information:
+    tested              True if ridge is clearly convex
+    nonconvex           True if ridge is non-convex
+*/
+struct ridgeT {
+  setT    *vertices;    /* vertices belonging to this ridge, inverse sorted by ID
+                           NULL if a degen ridge (matchsame) */
+  facetT  *top;         /* top facet this ridge is part of */
+  facetT  *bottom;      /* bottom facet this ridge is part of */
+  unsigned id;          /* unique identifier.  Same size as vertex_id and ridge_id */
+  flagT    seen:1;      /* used to perform operations only once */
+  flagT    tested:1;    /* True when ridge is tested for convexity */
+  flagT    nonconvex:1; /* True if getmergeset detected a non-convex neighbor
+                           only one ridge between neighbors may have nonconvex */
+};
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >--------------------------------</a><a name="vertexT">-</a>
+
+  vertexT
+     defines a vertex
+
+  topological information:
+    next,previous       doubly-linked list of all vertices
+    neighbors           set of adjacent facets (only if qh.VERTEXneighbors)
+
+  geometric information:
+    point               array of DIM3 coordinates
+*/
+struct vertexT {
+  vertexT *next;        /* next vertex in vertex_list */
+  vertexT *previous;    /* previous vertex in vertex_list */
+  pointT  *point;       /* hull_dim coordinates (coordT) */
+  setT    *neighbors;   /* neighboring facets of vertex, qh_vertexneighbors()
+                           inits in io.c or after first merge */
+  unsigned id;          /* unique identifier.  Same size as qh.vertex_id and qh.ridge_id */
+  unsigned visitid;     /* for use with qh.vertex_visit, size must match */
+  flagT    seen:1;      /* used to perform operations only once */
+  flagT    seen2:1;     /* another seen flag */
+  flagT    delridge:1;  /* vertex was part of a deleted ridge */
+  flagT    deleted:1;   /* true if vertex on qh.del_vertices */
+  flagT    newlist:1;   /* true if vertex on qh.newvertex_list */
+};
+
+/*======= -global variables -qh ============================*/
+
+/*-<a                             href="qh-globa.htm#TOC"
+  >--------------------------------</a><a name="qh">-</a>
+
+  qh
+   all global variables for qhull are in qh, qhmem, and qhstat
+
+  notes:
+   qhmem is defined in mem.h, qhstat is defined in stat.h, qhrbox is defined in rboxpoints.h
+   Access to qh_qh is via the "qh" macro.  See qh_QHpointer in user.h
+
+   All global variables for qhull are in qh, qhmem, and qhstat
+   qh must be unique for each instance of qhull
+   qhstat may be shared between qhull instances.
+   qhmem may be shared across multiple instances of Qhull.
+   Rbox uses global variables rbox_inuse and rbox, but does not persist data across calls.
+
+   Qhull is not multi-threaded.  Global state could be stored in thread-local storage.
+
+   QHULL_LIB_CHECK checks that a program and the corresponding
+   qhull library were built with the same type of header files.
+*/
+
+typedef struct qhT qhT;
+
+#define QHULL_NON_REENTRANT 0
+#define QHULL_QH_POINTER 1
+#define QHULL_REENTRANT 2
+
+#if qh_QHpointer_dllimport
+#define qh qh_qh->
+__declspec(dllimport) extern qhT *qh_qh;     /* allocated in global.c */
+#define QHULL_LIB_TYPE QHULL_QH_POINTER
+
+#elif qh_QHpointer
+#define qh qh_qh->
+extern qhT *qh_qh;     /* allocated in global.c */
+#define QHULL_LIB_TYPE QHULL_QH_POINTER
+
+#elif qh_dllimport
+#define qh qh_qh.
+__declspec(dllimport) extern qhT qh_qh;      /* allocated in global.c */
+#define QHULL_LIB_TYPE QHULL_NON_REENTRANT
+
+#else
+#define qh qh_qh.
+extern qhT qh_qh;
+#define QHULL_LIB_TYPE QHULL_NON_REENTRANT
+#endif
+
+#define QHULL_LIB_CHECK qh_lib_check(QHULL_LIB_TYPE, sizeof(qhT), sizeof(vertexT), sizeof(ridgeT), sizeof(facetT), sizeof(setT), sizeof(qhmemT));
+#define QHULL_LIB_CHECK_RBOX qh_lib_check(QHULL_LIB_TYPE, sizeof(qhT), sizeof(vertexT), sizeof(ridgeT), sizeof(facetT), 0, 0);
+
+struct qhT {
+
+/*-<a                             href="qh-globa.htm#TOC"
+  >--------------------------------</a><a name="qh-const">-</a>
+
+  qh constants
+    configuration flags and constants for Qhull
+
+  notes:
+    The user configures Qhull by defining flags.  They are
+    copied into qh by qh_setflags().  qh-quick.htm#options defines the flags.
+*/
+  boolT ALLpoints;        /* true 'Qs' if search all points for initial simplex */
+  boolT ANGLEmerge;       /* true 'Qa' if sort potential merges by angle */
+  boolT APPROXhull;       /* true 'Wn' if MINoutside set */
+  realT   MINoutside;     /*   'Wn' min. distance for an outside point */
+  boolT ANNOTATEoutput;   /* true 'Ta' if annotate output with message codes */
+  boolT ATinfinity;       /* true 'Qz' if point num_points-1 is "at-infinity"
+                             for improving precision in Delaunay triangulations */
+  boolT AVOIDold;         /* true 'Q4' if avoid old->new merges */
+  boolT BESToutside;      /* true 'Qf' if partition points into best outsideset */
+  boolT CDDinput;         /* true 'Pc' if input uses CDD format (1.0/offset first) */
+  boolT CDDoutput;        /* true 'PC' if print normals in CDD format (offset first) */
+  boolT CHECKfrequently;  /* true 'Tc' if checking frequently */
+  realT premerge_cos;     /*   'A-n'   cos_max when pre merging */
+  realT postmerge_cos;    /*   'An'    cos_max when post merging */
+  boolT DELAUNAY;         /* true 'd' if computing DELAUNAY triangulation */
+  boolT DOintersections;  /* true 'Gh' if print hyperplane intersections */
+  int   DROPdim;          /* drops dim 'GDn' for 4-d -> 3-d output */
+  boolT FORCEoutput;      /* true 'Po' if forcing output despite degeneracies */
+  int   GOODpoint;        /* 1+n for 'QGn', good facet if visible/not(-) from point n*/
+  pointT *GOODpointp;     /*   the actual point */
+  boolT GOODthreshold;    /* true if qh.lower_threshold/upper_threshold defined
+                             false if qh.SPLITthreshold */
+  int   GOODvertex;       /* 1+n, good facet if vertex for point n */
+  pointT *GOODvertexp;     /*   the actual point */
+  boolT HALFspace;        /* true 'Hn,n,n' if halfspace intersection */
+  boolT ISqhullQh;        /* Set by Qhull.cpp on initialization */
+  int   IStracing;        /* trace execution, 0=none, 1=least, 4=most, -1=events */
+  int   KEEParea;         /* 'PAn' number of largest facets to keep */
+  boolT KEEPcoplanar;     /* true 'Qc' if keeping nearest facet for coplanar points */
+  boolT KEEPinside;       /* true 'Qi' if keeping nearest facet for inside points
+                              set automatically if 'd Qc' */
+  int   KEEPmerge;        /* 'PMn' number of facets to keep with most merges */
+  realT KEEPminArea;      /* 'PFn' minimum facet area to keep */
+  realT MAXcoplanar;      /* 'Un' max distance below a facet to be coplanar*/
+  boolT MERGEexact;       /* true 'Qx' if exact merges (coplanar, degen, dupridge, flipped) */
+  boolT MERGEindependent; /* true 'Q2' if merging independent sets */
+  boolT MERGING;          /* true if exact-, pre- or post-merging, with angle and centrum tests */
+  realT   premerge_centrum;  /*   'C-n' centrum_radius when pre merging.  Default is round-off */
+  realT   postmerge_centrum; /*   'Cn' centrum_radius when post merging.  Default is round-off */
+  boolT MERGEvertices;    /* true 'Q3' if merging redundant vertices */
+  realT MINvisible;       /* 'Vn' min. distance for a facet to be visible */
+  boolT NOnarrow;         /* true 'Q10' if no special processing for narrow distributions */
+  boolT NOnearinside;     /* true 'Q8' if ignore near-inside points when partitioning */
+  boolT NOpremerge;       /* true 'Q0' if no defaults for C-0 or Qx */
+  boolT NOwide;           /* true 'Q12' if no error on wide merge due to duplicate ridge */
+  boolT ONLYgood;         /* true 'Qg' if process points with good visible or horizon facets */
+  boolT ONLYmax;          /* true 'Qm' if only process points that increase max_outside */
+  boolT PICKfurthest;     /* true 'Q9' if process furthest of furthest points*/
+  boolT POSTmerge;        /* true if merging after buildhull (Cn or An) */
+  boolT PREmerge;         /* true if merging during buildhull (C-n or A-n) */
+                        /* NOTE: some of these names are similar to qh_PRINT names */
+  boolT PRINTcentrums;    /* true 'Gc' if printing centrums */
+  boolT PRINTcoplanar;    /* true 'Gp' if printing coplanar points */
+  int   PRINTdim;         /* print dimension for Geomview output */
+  boolT PRINTdots;        /* true 'Ga' if printing all points as dots */
+  boolT PRINTgood;        /* true 'Pg' if printing good facets */
+  boolT PRINTinner;       /* true 'Gi' if printing inner planes */
+  boolT PRINTneighbors;   /* true 'PG' if printing neighbors of good facets */
+  boolT PRINTnoplanes;    /* true 'Gn' if printing no planes */
+  boolT PRINToptions1st;  /* true 'FO' if printing options to stderr */
+  boolT PRINTouter;       /* true 'Go' if printing outer planes */
+  boolT PRINTprecision;   /* false 'Pp' if not reporting precision problems */
+  qh_PRINT PRINTout[qh_PRINTEND]; /* list of output formats to print */
+  boolT PRINTridges;      /* true 'Gr' if print ridges */
+  boolT PRINTspheres;     /* true 'Gv' if print vertices as spheres */
+  boolT PRINTstatistics;  /* true 'Ts' if printing statistics to stderr */
+  boolT PRINTsummary;     /* true 's' if printing summary to stderr */
+  boolT PRINTtransparent; /* true 'Gt' if print transparent outer ridges */
+  boolT PROJECTdelaunay;  /* true if DELAUNAY, no readpoints() and
+                             need projectinput() for Delaunay in qh_init_B */
+  int   PROJECTinput;     /* number of projected dimensions 'bn:0Bn:0' */
+  boolT QUICKhelp;        /* true if quick help message for degen input */
+  boolT RANDOMdist;       /* true if randomly change distplane and setfacetplane */
+  realT RANDOMfactor;     /*    maximum random perturbation */
+  realT RANDOMa;          /*    qh_randomfactor is randr * RANDOMa + RANDOMb */
+  realT RANDOMb;
+  boolT RANDOMoutside;    /* true if select a random outside point */
+  int   REPORTfreq;       /* buildtracing reports every n facets */
+  int   REPORTfreq2;      /* tracemerging reports every REPORTfreq/2 facets */
+  int   RERUN;            /* 'TRn' rerun qhull n times (qh.build_cnt) */
+  int   ROTATErandom;     /* 'QRn' seed, 0 time, >= rotate input */
+  boolT SCALEinput;       /* true 'Qbk' if scaling input */
+  boolT SCALElast;        /* true 'Qbb' if scale last coord to max prev coord */
+  boolT SETroundoff;      /* true 'E' if qh.DISTround is predefined */
+  boolT SKIPcheckmax;     /* true 'Q5' if skip qh_check_maxout */
+  boolT SKIPconvex;       /* true 'Q6' if skip convexity testing during pre-merge */
+  boolT SPLITthresholds;  /* true if upper_/lower_threshold defines a region
+                               used only for printing (!for qh.ONLYgood) */
+  int   STOPcone;         /* 'TCn' 1+n for stopping after cone for point n */
+                          /*       also used by qh_build_withresart for err exit*/
+  int   STOPpoint;        /* 'TVn' 'TV-n' 1+n for stopping after/before(-)
+                                        adding point n */
+  int   TESTpoints;       /* 'QTn' num of test points after qh.num_points.  Test points always coplanar. */
+  boolT TESTvneighbors;   /*  true 'Qv' if test vertex neighbors at end */
+  int   TRACElevel;       /* 'Tn' conditional IStracing level */
+  int   TRACElastrun;     /*  qh.TRACElevel applies to last qh.RERUN */
+  int   TRACEpoint;       /* 'TPn' start tracing when point n is a vertex */
+  realT TRACEdist;        /* 'TWn' start tracing when merge distance too big */
+  int   TRACEmerge;       /* 'TMn' start tracing before this merge */
+  boolT TRIangulate;      /* true 'Qt' if triangulate non-simplicial facets */
+  boolT TRInormals;       /* true 'Q11' if triangulate duplicates ->normal and ->center (sets Qt) */
+  boolT UPPERdelaunay;    /* true 'Qu' if computing furthest-site Delaunay */
+  boolT USEstdout;        /* true 'Tz' if using stdout instead of stderr */
+  boolT VERIFYoutput;     /* true 'Tv' if verify output at end of qhull */
+  boolT VIRTUALmemory;    /* true 'Q7' if depth-first processing in buildhull */
+  boolT VORONOI;          /* true 'v' if computing Voronoi diagram */
+
+  /*--------input constants ---------*/
+  realT AREAfactor;       /* 1/(hull_dim-1)! for converting det's to area */
+  boolT DOcheckmax;       /* true if calling qh_check_maxout (qh_initqhull_globals) */
+  char  *feasible_string;  /* feasible point 'Hn,n,n' for halfspace intersection */
+  coordT *feasible_point;  /*    as coordinates, both malloc'd */
+  boolT GETarea;          /* true 'Fa', 'FA', 'FS', 'PAn', 'PFn' if compute facet area/Voronoi volume in io.c */
+  boolT KEEPnearinside;   /* true if near-inside points in coplanarset */
+  int   hull_dim;         /* dimension of hull, set by initbuffers */
+  int   input_dim;        /* dimension of input, set by initbuffers */
+  int   num_points;       /* number of input points */
+  pointT *first_point;    /* array of input points, see POINTSmalloc */
+  boolT POINTSmalloc;     /*   true if qh.first_point/num_points allocated */
+  pointT *input_points;   /* copy of original qh.first_point for input points for qh_joggleinput */
+  boolT input_malloc;     /* true if qh.input_points malloc'd */
+  char  qhull_command[256];/* command line that invoked this program */
+  int   qhull_commandsiz2; /*    size of qhull_command at qh_clear_outputflags */
+  char  rbox_command[256]; /* command line that produced the input points */
+  char  qhull_options[512];/* descriptive list of options */
+  int   qhull_optionlen;  /*    length of last line */
+  int   qhull_optionsiz;  /*    size of qhull_options at qh_build_withrestart */
+  int   qhull_optionsiz2; /*    size of qhull_options at qh_clear_outputflags */
+  int   run_id;           /* non-zero, random identifier for this instance of qhull */
+  boolT VERTEXneighbors;  /* true if maintaining vertex neighbors */
+  boolT ZEROcentrum;      /* true if 'C-0' or 'C-0 Qx'.  sets ZEROall_ok */
+  realT *upper_threshold; /* don't print if facet->normal[k]>=upper_threshold[k]
+                             must set either GOODthreshold or SPLITthreshold
+                             if Delaunay, default is 0.0 for upper envelope */
+  realT *lower_threshold; /* don't print if facet->normal[k] <=lower_threshold[k] */
+  realT *upper_bound;     /* scale point[k] to new upper bound */
+  realT *lower_bound;     /* scale point[k] to new lower bound
+                             project if both upper_ and lower_bound == 0 */
+
+/*-<a                             href="qh-globa.htm#TOC"
+  >--------------------------------</a><a name="qh-prec">-</a>
+
+  qh precision constants
+    precision constants for Qhull
+
+  notes:
+    qh_detroundoff() computes the maximum roundoff error for distance
+    and other computations.  It also sets default values for the
+    qh constants above.
+*/
+  realT ANGLEround;       /* max round off error for angles */
+  realT centrum_radius;   /* max centrum radius for convexity (roundoff added) */
+  realT cos_max;          /* max cosine for convexity (roundoff added) */
+  realT DISTround;        /* max round off error for distances, 'E' overrides qh_distround() */
+  realT MAXabs_coord;     /* max absolute coordinate */
+  realT MAXlastcoord;     /* max last coordinate for qh_scalelast */
+  realT MAXsumcoord;      /* max sum of coordinates */
+  realT MAXwidth;         /* max rectilinear width of point coordinates */
+  realT MINdenom_1;       /* min. abs. value for 1/x */
+  realT MINdenom;         /*    use divzero if denominator < MINdenom */
+  realT MINdenom_1_2;     /* min. abs. val for 1/x that allows normalization */
+  realT MINdenom_2;       /*    use divzero if denominator < MINdenom_2 */
+  realT MINlastcoord;     /* min. last coordinate for qh_scalelast */
+  boolT NARROWhull;       /* set in qh_initialhull if angle < qh_MAXnarrow */
+  realT *NEARzero;        /* hull_dim array for near zero in gausselim */
+  realT NEARinside;       /* keep points for qh_check_maxout if close to facet */
+  realT ONEmerge;         /* max distance for merging simplicial facets */
+  realT outside_err;      /* application's epsilon for coplanar points
+                             qh_check_bestdist() qh_check_points() reports error if point outside */
+  realT WIDEfacet;        /* size of wide facet for skipping ridge in
+                             area computation and locking centrum */
+
+/*-<a                             href="qh-globa.htm#TOC"
+  >--------------------------------</a><a name="qh-codetern">-</a>
+
+  qh internal constants
+    internal constants for Qhull
+*/
+  char qhull[sizeof("qhull")]; /* "qhull" for checking ownership while debugging */
+  jmp_buf errexit;        /* exit label for qh_errexit, defined by setjmp() and NOerrexit */
+  char jmpXtra[40];       /* extra bytes in case jmp_buf is defined wrong by compiler */
+  jmp_buf restartexit;    /* restart label for qh_errexit, defined by setjmp() and ALLOWrestart */
+  char jmpXtra2[40];      /* extra bytes in case jmp_buf is defined wrong by compiler*/
+  FILE *fin;              /* pointer to input file, init by qh_initqhull_start2 */
+  FILE *fout;             /* pointer to output file */
+  FILE *ferr;             /* pointer to error file */
+  pointT *interior_point; /* center point of the initial simplex*/
+  int normal_size;     /* size in bytes for facet normals and point coords*/
+  int center_size;     /* size in bytes for Voronoi centers */
+  int   TEMPsize;         /* size for small, temporary sets (in quick mem) */
+
+/*-<a                             href="qh-globa.htm#TOC"
+  >--------------------------------</a><a name="qh-lists">-</a>
+
+  qh facet and vertex lists
+    defines lists of facets, new facets, visible facets, vertices, and
+    new vertices.  Includes counts, next ids, and trace ids.
+  see:
+    qh_resetlists()
+*/
+  facetT *facet_list;     /* first facet */
+  facetT  *facet_tail;     /* end of facet_list (dummy facet) */
+  facetT *facet_next;     /* next facet for buildhull()
+                             previous facets do not have outside sets
+                             NARROWhull: previous facets may have coplanar outside sets for qh_outcoplanar */
+  facetT *newfacet_list;  /* list of new facets to end of facet_list */
+  facetT *visible_list;   /* list of visible facets preceding newfacet_list,
+                             facet->visible set */
+  int       num_visible;  /* current number of visible facets */
+  unsigned tracefacet_id;  /* set at init, then can print whenever */
+  facetT *tracefacet;     /*   set in newfacet/mergefacet, undone in delfacet*/
+  unsigned tracevertex_id;  /* set at buildtracing, can print whenever */
+  vertexT *tracevertex;     /*   set in newvertex, undone in delvertex*/
+  vertexT *vertex_list;     /* list of all vertices, to vertex_tail */
+  vertexT  *vertex_tail;    /*      end of vertex_list (dummy vertex) */
+  vertexT *newvertex_list; /* list of vertices in newfacet_list, to vertex_tail
+                             all vertices have 'newlist' set */
+  int   num_facets;       /* number of facets in facet_list
+                             includes visible faces (num_visible) */
+  int   num_vertices;     /* number of vertices in facet_list */
+  int   num_outside;      /* number of points in outsidesets (for tracing and RANDOMoutside)
+                               includes coplanar outsideset points for NARROWhull/qh_outcoplanar() */
+  int   num_good;         /* number of good facets (after findgood_all) */
+  unsigned facet_id;      /* ID of next, new facet from newfacet() */
+  unsigned ridge_id;      /* ID of next, new ridge from newridge() */
+  unsigned vertex_id;     /* ID of next, new vertex from newvertex() */
+
+/*-<a                             href="qh-globa.htm#TOC"
+  >--------------------------------</a><a name="qh-var">-</a>
+
+  qh global variables
+    defines minimum and maximum distances, next visit ids, several flags,
+    and other global variables.
+    initialize in qh_initbuild or qh_maxmin if used in qh_buildhull
+*/
+  unsigned long hulltime; /* ignore time to set up input and randomize */
+                          /*   use unsigned to avoid wrap-around errors */
+  boolT ALLOWrestart;     /* true if qh_precision can use qh.restartexit */
+  int   build_cnt;        /* number of calls to qh_initbuild */
+  qh_CENTER CENTERtype;   /* current type of facet->center, qh_CENTER */
+  int   furthest_id;      /* pointid of furthest point, for tracing */
+  facetT *GOODclosest;    /* closest facet to GOODthreshold in qh_findgood */
+  boolT hasAreaVolume;    /* true if totarea, totvol was defined by qh_getarea */
+  boolT hasTriangulation; /* true if triangulation created by qh_triangulate */
+  realT JOGGLEmax;        /* set 'QJn' if randomly joggle input */
+  boolT maxoutdone;       /* set qh_check_maxout(), cleared by qh_addpoint() */
+  realT max_outside;      /* maximum distance from a point to a facet,
+                               before roundoff, not simplicial vertices
+                               actual outer plane is +DISTround and
+                               computed outer plane is +2*DISTround */
+  realT max_vertex;       /* maximum distance (>0) from vertex to a facet,
+                               before roundoff, due to a merge */
+  realT min_vertex;       /* minimum distance (<0) from vertex to a facet,
+                               before roundoff, due to a merge
+                               if qh.JOGGLEmax, qh_makenewplanes sets it
+                               recomputed if qh.DOcheckmax, default -qh.DISTround */
+  boolT NEWfacets;        /* true while visible facets invalid due to new or merge
+                              from makecone/attachnewfacets to deletevisible */
+  boolT findbestnew;      /* true if partitioning calls qh_findbestnew */
+  boolT findbest_notsharp; /* true if new facets are at least 90 degrees */
+  boolT NOerrexit;        /* true if qh.errexit is not available, cleared after setjmp */
+  realT PRINTcradius;     /* radius for printing centrums */
+  realT PRINTradius;      /* radius for printing vertex spheres and points */
+  boolT POSTmerging;      /* true when post merging */
+  int   printoutvar;      /* temporary variable for qh_printbegin, etc. */
+  int   printoutnum;      /* number of facets printed */
+  boolT QHULLfinished;    /* True after qhull() is finished */
+  realT totarea;          /* 'FA': total facet area computed by qh_getarea, hasAreaVolume */
+  realT totvol;           /* 'FA': total volume computed by qh_getarea, hasAreaVolume */
+  unsigned int visit_id;  /* unique ID for searching neighborhoods, */
+  unsigned int vertex_visit; /* unique ID for searching vertices, reset with qh_buildtracing */
+  boolT ZEROall_ok;       /* True if qh_checkzero always succeeds */
+  boolT WAScoplanar;      /* True if qh_partitioncoplanar (qh_check_maxout) */
+
+/*-<a                             href="qh-globa.htm#TOC"
+  >--------------------------------</a><a name="qh-set">-</a>
+
+  qh global sets
+    defines sets for merging, initial simplex, hashing, extra input points,
+    and deleted vertices
+*/
+  setT *facet_mergeset;   /* temporary set of merges to be done */
+  setT *degen_mergeset;   /* temporary set of degenerate and redundant merges */
+  setT *hash_table;       /* hash table for matching ridges in qh_matchfacets
+                             size is setsize() */
+  setT *other_points;     /* additional points */
+  setT *del_vertices;     /* vertices to partition and delete with visible
+                             facets.  Have deleted set for checkfacet */
+
+/*-<a                             href="qh-globa.htm#TOC"
+  >--------------------------------</a><a name="qh-buf">-</a>
+
+  qh global buffers
+    defines buffers for maxtrix operations, input, and error messages
+*/
+  coordT *gm_matrix;      /* (dim+1)Xdim matrix for geom.c */
+  coordT **gm_row;        /* array of gm_matrix rows */
+  char* line;             /* malloc'd input line of maxline+1 chars */
+  int maxline;
+  coordT *half_space;     /* malloc'd input array for halfspace (qh normal_size+coordT) */
+  coordT *temp_malloc;    /* malloc'd input array for points */
+
+/*-<a                             href="qh-globa.htm#TOC"
+  >--------------------------------</a><a name="qh-static">-</a>
+
+  qh static variables
+    defines static variables for individual functions
+
+  notes:
+    do not use 'static' within a function.  Multiple instances of qhull
+    may exist.
+
+    do not assume zero initialization, 'QPn' may cause a restart
+*/
+  boolT ERREXITcalled;    /* true during qh_errexit (prevents duplicate calls */
+  boolT firstcentrum;     /* for qh_printcentrum */
+  boolT old_randomdist;   /* save RANDOMdist flag during io, tracing, or statistics */
+  setT *coplanarfacetset;  /* set of coplanar facets for searching qh_findbesthorizon() */
+  realT last_low;         /* qh_scalelast parameters for qh_setdelaunay */
+  realT last_high;
+  realT last_newhigh;
+  unsigned lastreport;    /* for qh_buildtracing */
+  int mergereport;        /* for qh_tracemerging */
+  qhstatT *old_qhstat;    /* for saving qh_qhstat in save_qhull() and UsingLibQhull.  Free with qh_free() */
+  setT *old_tempstack;    /* for saving qhmem.tempstack in save_qhull */
+  int   ridgeoutnum;      /* number of ridges for 4OFF output (qh_printbegin,etc) */
+};
+
+/*=========== -macros- =========================*/
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >--------------------------------</a><a name="otherfacet_">-</a>
+
+  otherfacet_(ridge, facet)
+    return neighboring facet for a ridge in facet
+*/
+#define otherfacet_(ridge, facet) \
+                        (((ridge)->top == (facet)) ? (ridge)->bottom : (ridge)->top)
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >--------------------------------</a><a name="getid_">-</a>
+
+  getid_(p)
+    return int ID for facet, ridge, or vertex
+    return qh_IDunknown(-1) if NULL
+*/
+#define getid_(p)       ((p) ? (int)((p)->id) : qh_IDunknown)
+
+/*============== FORALL macros ===================*/
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >--------------------------------</a><a name="FORALLfacets">-</a>
+
+  FORALLfacets { ... }
+    assign 'facet' to each facet in qh.facet_list
+
+  notes:
+    uses 'facetT *facet;'
+    assumes last facet is a sentinel
+
+  see:
+    FORALLfacet_( facetlist )
+*/
+#define FORALLfacets for (facet=qh facet_list;facet && facet->next;facet=facet->next)
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >--------------------------------</a><a name="FORALLpoints">-</a>
+
+  FORALLpoints { ... }
+    assign 'point' to each point in qh.first_point, qh.num_points
+
+  declare:
+    coordT *point, *pointtemp;
+*/
+#define FORALLpoints FORALLpoint_(qh first_point, qh num_points)
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >--------------------------------</a><a name="FORALLpoint_">-</a>
+
+  FORALLpoint_( points, num) { ... }
+    assign 'point' to each point in points array of num points
+
+  declare:
+    coordT *point, *pointtemp;
+*/
+#define FORALLpoint_(points, num) for (point= (points), \
+      pointtemp= (points)+qh hull_dim*(num); point < pointtemp; point += qh hull_dim)
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >--------------------------------</a><a name="FORALLvertices">-</a>
+
+  FORALLvertices { ... }
+    assign 'vertex' to each vertex in qh.vertex_list
+
+  declare:
+    vertexT *vertex;
+
+  notes:
+    assumes qh.vertex_list terminated with a sentinel
+*/
+#define FORALLvertices for (vertex=qh vertex_list;vertex && vertex->next;vertex= vertex->next)
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >--------------------------------</a><a name="FOREACHfacet_">-</a>
+
+  FOREACHfacet_( facets ) { ... }
+    assign 'facet' to each facet in facets
+
+  declare:
+    facetT *facet, **facetp;
+
+  see:
+    <a href="qset.h#FOREACHsetelement_">FOREACHsetelement_</a>
+*/
+#define FOREACHfacet_(facets)    FOREACHsetelement_(facetT, facets, facet)
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >--------------------------------</a><a name="FOREACHneighbor_">-</a>
+
+  FOREACHneighbor_( facet ) { ... }
+    assign 'neighbor' to each neighbor in facet->neighbors
+
+  FOREACHneighbor_( vertex ) { ... }
+    assign 'neighbor' to each neighbor in vertex->neighbors
+
+  declare:
+    facetT *neighbor, **neighborp;
+
+  see:
+    <a href="qset.h#FOREACHsetelement_">FOREACHsetelement_</a>
+*/
+#define FOREACHneighbor_(facet)  FOREACHsetelement_(facetT, facet->neighbors, neighbor)
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >--------------------------------</a><a name="FOREACHpoint_">-</a>
+
+  FOREACHpoint_( points ) { ... }
+    assign 'point' to each point in points set
+
+  declare:
+    pointT *point, **pointp;
+
+  see:
+    <a href="qset.h#FOREACHsetelement_">FOREACHsetelement_</a>
+*/
+#define FOREACHpoint_(points)    FOREACHsetelement_(pointT, points, point)
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >--------------------------------</a><a name="FOREACHridge_">-</a>
+
+  FOREACHridge_( ridges ) { ... }
+    assign 'ridge' to each ridge in ridges set
+
+  declare:
+    ridgeT *ridge, **ridgep;
+
+  see:
+    <a href="qset.h#FOREACHsetelement_">FOREACHsetelement_</a>
+*/
+#define FOREACHridge_(ridges)    FOREACHsetelement_(ridgeT, ridges, ridge)
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >--------------------------------</a><a name="FOREACHvertex_">-</a>
+
+  FOREACHvertex_( vertices ) { ... }
+    assign 'vertex' to each vertex in vertices set
+
+  declare:
+    vertexT *vertex, **vertexp;
+
+  see:
+    <a href="qset.h#FOREACHsetelement_">FOREACHsetelement_</a>
+*/
+#define FOREACHvertex_(vertices) FOREACHsetelement_(vertexT, vertices,vertex)
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >--------------------------------</a><a name="FOREACHfacet_i_">-</a>
+
+  FOREACHfacet_i_( facets ) { ... }
+    assign 'facet' and 'facet_i' for each facet in facets set
+
+  declare:
+    facetT *facet;
+    int     facet_n, facet_i;
+
+  see:
+    <a href="qset.h#FOREACHsetelement_i_">FOREACHsetelement_i_</a>
+*/
+#define FOREACHfacet_i_(facets)    FOREACHsetelement_i_(facetT, facets, facet)
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >--------------------------------</a><a name="FOREACHneighbor_i_">-</a>
+
+  FOREACHneighbor_i_( facet ) { ... }
+    assign 'neighbor' and 'neighbor_i' for each neighbor in facet->neighbors
+
+  FOREACHneighbor_i_( vertex ) { ... }
+    assign 'neighbor' and 'neighbor_i' for each neighbor in vertex->neighbors
+
+  declare:
+    facetT *neighbor;
+    int     neighbor_n, neighbor_i;
+
+  see:
+    <a href="qset.h#FOREACHsetelement_i_">FOREACHsetelement_i_</a>
+*/
+#define FOREACHneighbor_i_(facet)  FOREACHsetelement_i_(facetT, facet->neighbors, neighbor)
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >--------------------------------</a><a name="FOREACHpoint_i_">-</a>
+
+  FOREACHpoint_i_( points ) { ... }
+    assign 'point' and 'point_i' for each point in points set
+
+  declare:
+    pointT *point;
+    int     point_n, point_i;
+
+  see:
+    <a href="qset.h#FOREACHsetelement_i_">FOREACHsetelement_i_</a>
+*/
+#define FOREACHpoint_i_(points)    FOREACHsetelement_i_(pointT, points, point)
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >--------------------------------</a><a name="FOREACHridge_i_">-</a>
+
+  FOREACHridge_i_( ridges ) { ... }
+    assign 'ridge' and 'ridge_i' for each ridge in ridges set
+
+  declare:
+    ridgeT *ridge;
+    int     ridge_n, ridge_i;
+
+  see:
+    <a href="qset.h#FOREACHsetelement_i_">FOREACHsetelement_i_</a>
+*/
+#define FOREACHridge_i_(ridges)    FOREACHsetelement_i_(ridgeT, ridges, ridge)
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >--------------------------------</a><a name="FOREACHvertex_i_">-</a>
+
+  FOREACHvertex_i_( vertices ) { ... }
+    assign 'vertex' and 'vertex_i' for each vertex in vertices set
+
+  declare:
+    vertexT *vertex;
+    int     vertex_n, vertex_i;
+
+  see:
+    <a href="qset.h#FOREACHsetelement_i_">FOREACHsetelement_i_</a>
+*/
+#define FOREACHvertex_i_(vertices) FOREACHsetelement_i_(vertexT, vertices,vertex)
+
+/********* -libqhull.c prototypes (duplicated from qhull_a.h) **********************/
+
+void    qh_qhull(void);
+boolT   qh_addpoint(pointT *furthest, facetT *facet, boolT checkdist);
+void    qh_printsummary(FILE *fp);
+
+/********* -user.c prototypes (alphabetical) **********************/
+
+void    qh_errexit(int exitcode, facetT *facet, ridgeT *ridge);
+void    qh_errprint(const char* string, facetT *atfacet, facetT *otherfacet, ridgeT *atridge, vertexT *atvertex);
+int     qh_new_qhull(int dim, int numpoints, coordT *points, boolT ismalloc,
+                char *qhull_cmd, FILE *outfile, FILE *errfile);
+void    qh_printfacetlist(facetT *facetlist, setT *facets, boolT printall);
+void    qh_printhelp_degenerate(FILE *fp);
+void    qh_printhelp_narrowhull(FILE *fp, realT minangle);
+void    qh_printhelp_singular(FILE *fp);
+void    qh_user_memsizes(void);
+
+/********* -usermem.c prototypes (alphabetical) **********************/
+void    qh_exit(int exitcode);
+void    qh_fprintf_stderr(int msgcode, const char *fmt, ... );
+void    qh_free(void *mem);
+void   *qh_malloc(size_t size);
+
+/********* -userprintf.c and userprintf_rbox.c prototypes **********************/
+void    qh_fprintf(FILE *fp, int msgcode, const char *fmt, ... );
+void    qh_fprintf_rbox(FILE *fp, int msgcode, const char *fmt, ... );
+
+/***** -geom.c/geom2.c/random.c prototypes (duplicated from geom.h, random.h) ****************/
+
+facetT *qh_findbest(pointT *point, facetT *startfacet,
+                     boolT bestoutside, boolT newfacets, boolT noupper,
+                     realT *dist, boolT *isoutside, int *numpart);
+facetT *qh_findbestnew(pointT *point, facetT *startfacet,
+                     realT *dist, boolT bestoutside, boolT *isoutside, int *numpart);
+boolT   qh_gram_schmidt(int dim, realT **rows);
+void    qh_outerinner(facetT *facet, realT *outerplane, realT *innerplane);
+void    qh_printsummary(FILE *fp);
+void    qh_projectinput(void);
+void    qh_randommatrix(realT *buffer, int dim, realT **row);
+void    qh_rotateinput(realT **rows);
+void    qh_scaleinput(void);
+void    qh_setdelaunay(int dim, int count, pointT *points);
+coordT  *qh_sethalfspace_all(int dim, int count, coordT *halfspaces, pointT *feasible);
+
+/***** -global.c prototypes (alphabetical) ***********************/
+
+unsigned long qh_clock(void);
+void    qh_checkflags(char *command, char *hiddenflags);
+void    qh_clear_outputflags(void);
+void    qh_freebuffers(void);
+void    qh_freeqhull(boolT allmem);
+void    qh_freeqhull2(boolT allmem);
+void    qh_init_A(FILE *infile, FILE *outfile, FILE *errfile, int argc, char *argv[]);
+void    qh_init_B(coordT *points, int numpoints, int dim, boolT ismalloc);
+void    qh_init_qhull_command(int argc, char *argv[]);
+void    qh_initbuffers(coordT *points, int numpoints, int dim, boolT ismalloc);
+void    qh_initflags(char *command);
+void    qh_initqhull_buffers(void);
+void    qh_initqhull_globals(coordT *points, int numpoints, int dim, boolT ismalloc);
+void    qh_initqhull_mem(void);
+void    qh_initqhull_outputflags(void);
+void    qh_initqhull_start(FILE *infile, FILE *outfile, FILE *errfile);
+void    qh_initqhull_start2(FILE *infile, FILE *outfile, FILE *errfile);
+void    qh_initthresholds(char *command);
+void    qh_lib_check(int qhullLibraryType, int qhTsize, int vertexTsize, int ridgeTsize, int facetTsize, int setTsize, int qhmemTsize);
+void    qh_option(const char *option, int *i, realT *r);
+#if qh_QHpointer
+void    qh_restore_qhull(qhT **oldqh);
+qhT    *qh_save_qhull(void);
+#endif
+
+/***** -io.c prototypes (duplicated from io.h) ***********************/
+
+void    qh_dfacet(unsigned id);
+void    qh_dvertex(unsigned id);
+void    qh_printneighborhood(FILE *fp, qh_PRINT format, facetT *facetA, facetT *facetB, boolT printall);
+void    qh_produce_output(void);
+coordT *qh_readpoints(int *numpoints, int *dimension, boolT *ismalloc);
+
+
+/********* -mem.c prototypes (duplicated from mem.h) **********************/
+
+void qh_meminit(FILE *ferr);
+void qh_memfreeshort(int *curlong, int *totlong);
+
+/********* -poly.c/poly2.c prototypes (duplicated from poly.h) **********************/
+
+void    qh_check_output(void);
+void    qh_check_points(void);
+setT   *qh_facetvertices(facetT *facetlist, setT *facets, boolT allfacets);
+facetT *qh_findbestfacet(pointT *point, boolT bestoutside,
+           realT *bestdist, boolT *isoutside);
+vertexT *qh_nearvertex(facetT *facet, pointT *point, realT *bestdistp);
+pointT *qh_point(int id);
+setT   *qh_pointfacet(void /*qh.facet_list*/);
+int     qh_pointid(pointT *point);
+setT   *qh_pointvertex(void /*qh.facet_list*/);
+void    qh_setvoronoi_all(void);
+void    qh_triangulate(void /*qh.facet_list*/);
+
+/********* -rboxlib.c prototypes **********************/
+int     qh_rboxpoints(FILE* fout, FILE* ferr, char* rbox_command);
+void    qh_errexit_rbox(int exitcode);
+
+/********* -stat.c prototypes (duplicated from stat.h) **********************/
+
+void    qh_collectstatistics(void);
+void    qh_printallstatistics(FILE *fp, const char *string);
+
+#endif /* qhDEFlibqhull */
diff --git a/xs/src/qhull/src/libqhull/libqhull.pro b/xs/src/qhull/src/libqhull/libqhull.pro
new file mode 100644
index 0000000000..18005da59d
--- /dev/null
+++ b/xs/src/qhull/src/libqhull/libqhull.pro
@@ -0,0 +1,67 @@
+# -------------------------------------------------
+# libqhull.pro -- Qt project for Qhull shared library
+# -------------------------------------------------
+
+include(../qhull-warn.pri)
+
+DESTDIR = ../../lib
+DLLDESTDIR = ../../bin
+TEMPLATE = lib
+CONFIG += shared warn_on
+CONFIG -= qt
+
+build_pass:CONFIG(debug, debug|release):{
+    TARGET = qhull_d
+    OBJECTS_DIR = Debug
+}else:build_pass:CONFIG(release, debug|release):{
+    TARGET = qhull
+    OBJECTS_DIR = Release
+}
+win32-msvc* : QMAKE_LFLAGS += /INCREMENTAL:NO
+
+win32-msvc* : DEF_FILE += ../../src/libqhull/qhull-exports.def
+
+# Order object files by frequency of execution.  Small files at end.
+
+# libqhull/libqhull.pro and ../qhull-libqhull-src.pri have the same SOURCES and HEADERS
+SOURCES += ../libqhull/global.c
+SOURCES += ../libqhull/stat.c
+SOURCES += ../libqhull/geom2.c
+SOURCES += ../libqhull/poly2.c
+SOURCES += ../libqhull/merge.c
+SOURCES += ../libqhull/libqhull.c
+SOURCES += ../libqhull/geom.c
+SOURCES += ../libqhull/poly.c
+SOURCES += ../libqhull/qset.c
+SOURCES += ../libqhull/mem.c
+SOURCES += ../libqhull/random.c
+SOURCES += ../libqhull/usermem.c
+SOURCES += ../libqhull/userprintf.c
+SOURCES += ../libqhull/io.c
+SOURCES += ../libqhull/user.c
+SOURCES += ../libqhull/rboxlib.c
+SOURCES += ../libqhull/userprintf_rbox.c
+
+HEADERS += ../libqhull/geom.h
+HEADERS += ../libqhull/io.h
+HEADERS += ../libqhull/libqhull.h
+HEADERS += ../libqhull/mem.h
+HEADERS += ../libqhull/merge.h
+HEADERS += ../libqhull/poly.h
+HEADERS += ../libqhull/random.h
+HEADERS += ../libqhull/qhull_a.h
+HEADERS += ../libqhull/qset.h
+HEADERS += ../libqhull/stat.h
+HEADERS += ../libqhull/user.h
+
+OTHER_FILES += Mborland
+OTHER_FILES += qh-geom.htm
+OTHER_FILES += qh-globa.htm
+OTHER_FILES += qh-io.htm
+OTHER_FILES += qh-mem.htm
+OTHER_FILES += qh-merge.htm
+OTHER_FILES += qh-poly.htm
+OTHER_FILES += qh-qhull.htm
+OTHER_FILES += qh-set.htm
+OTHER_FILES += qh-stat.htm
+OTHER_FILES += qh-user.htm
diff --git a/xs/src/qhull/src/libqhull/mem.c b/xs/src/qhull/src/libqhull/mem.c
new file mode 100644
index 0000000000..db72bb4e19
--- /dev/null
+++ b/xs/src/qhull/src/libqhull/mem.c
@@ -0,0 +1,576 @@
+/*<html><pre>  -<a                             href="qh-mem.htm"
+  >-------------------------------</a><a name="TOP">-</a>
+
+  mem.c
+    memory management routines for qhull
+
+  This is a standalone program.
+
+  To initialize memory:
+
+    qh_meminit(stderr);
+    qh_meminitbuffers(qh IStracing, qh_MEMalign, 7, qh_MEMbufsize,qh_MEMinitbuf);
+    qh_memsize((int)sizeof(facetT));
+    qh_memsize((int)sizeof(facetT));
+    ...
+    qh_memsetup();
+
+  To free up all memory buffers:
+    qh_memfreeshort(&curlong, &totlong);
+
+  if qh_NOmem,
+    malloc/free is used instead of mem.c
+
+  notes:
+    uses Quickfit algorithm (freelists for commonly allocated sizes)
+    assumes small sizes for freelists (it discards the tail of memory buffers)
+
+  see:
+    qh-mem.htm and mem.h
+    global.c (qh_initbuffers) for an example of using mem.c
+
+  Copyright (c) 1993-2015 The Geometry Center.
+  $Id: //main/2015/qhull/src/libqhull/mem.c#7 $$Change: 2065 $
+  $DateTime: 2016/01/18 13:51:04 $$Author: bbarber $
+*/
+
+#include "user.h"  /* for QHULL_CRTDBG */
+#include "mem.h"
+#include <string.h>
+#include <stdio.h>
+#include <stdlib.h>
+
+#ifndef qhDEFlibqhull
+typedef struct ridgeT ridgeT;
+typedef struct facetT facetT;
+#ifdef _MSC_VER  /* Microsoft Visual C++ -- warning level 4 */
+#pragma warning( disable : 4127)  /* conditional expression is constant */
+#pragma warning( disable : 4706)  /* assignment within conditional function */
+#endif
+void    qh_errexit(int exitcode, facetT *, ridgeT *);
+void    qh_exit(int exitcode);
+void    qh_fprintf(FILE *fp, int msgcode, const char *fmt, ... );
+void    qh_fprintf_stderr(int msgcode, const char *fmt, ... );
+void    qh_free(void *mem);
+void   *qh_malloc(size_t size);
+#endif
+
+/*============ -global data structure ==============
+    see mem.h for definition
+*/
+
+qhmemT qhmem= {0,0,0,0,0,0,0,0,0,0,0,
+               0,0,0,0,0,0,0,0,0,0,0,
+               0,0,0,0,0,0,0};     /* remove "= {0}" if this causes a compiler error */
+
+#ifndef qh_NOmem
+
+/*============= internal functions ==============*/
+
+static int qh_intcompare(const void *i, const void *j);
+
+/*========== functions in alphabetical order ======== */
+
+/*-<a                             href="qh-mem.htm#TOC"
+  >-------------------------------</a><a name="intcompare">-</a>
+
+  qh_intcompare( i, j )
+    used by qsort and bsearch to compare two integers
+*/
+static int qh_intcompare(const void *i, const void *j) {
+  return(*((const int *)i) - *((const int *)j));
+} /* intcompare */
+
+
+/*-<a                             href="qh-mem.htm#TOC"
+  >--------------------------------</a><a name="memalloc">-</a>
+
+  qh_memalloc( insize )
+    returns object of insize bytes
+    qhmem is the global memory structure
+
+  returns:
+    pointer to allocated memory
+    errors if insufficient memory
+
+  notes:
+    use explicit type conversion to avoid type warnings on some compilers
+    actual object may be larger than insize
+    use qh_memalloc_() for inline code for quick allocations
+    logs allocations if 'T5'
+    caller is responsible for freeing the memory.
+    short memory is freed on shutdown by qh_memfreeshort unless qh_NOmem
+
+  design:
+    if size < qhmem.LASTsize
+      if qhmem.freelists[size] non-empty
+        return first object on freelist
+      else
+        round up request to size of qhmem.freelists[size]
+        allocate new allocation buffer if necessary
+        allocate object from allocation buffer
+    else
+      allocate object with qh_malloc() in user.c
+*/
+void *qh_memalloc(int insize) {
+  void **freelistp, *newbuffer;
+  int idx, size, n;
+  int outsize, bufsize;
+  void *object;
+
+  if (insize<0) {
+      qh_fprintf(qhmem.ferr, 6235, "qhull error (qh_memalloc): negative request size (%d).  Did int overflow due to high-D?\n", insize); /* WARN64 */
+      qh_errexit(qhmem_ERRmem, NULL, NULL);
+  }
+  if (insize>=0 && insize <= qhmem.LASTsize) {
+    idx= qhmem.indextable[insize];
+    outsize= qhmem.sizetable[idx];
+    qhmem.totshort += outsize;
+    freelistp= qhmem.freelists+idx;
+    if ((object= *freelistp)) {
+      qhmem.cntquick++;
+      qhmem.totfree -= outsize;
+      *freelistp= *((void **)*freelistp);  /* replace freelist with next object */
+#ifdef qh_TRACEshort
+      n= qhmem.cntshort+qhmem.cntquick+qhmem.freeshort;
+      if (qhmem.IStracing >= 5)
+          qh_fprintf(qhmem.ferr, 8141, "qh_mem %p n %8d alloc quick: %d bytes (tot %d cnt %d)\n", object, n, outsize, qhmem.totshort, qhmem.cntshort+qhmem.cntquick-qhmem.freeshort);
+#endif
+      return(object);
+    }else {
+      qhmem.cntshort++;
+      if (outsize > qhmem.freesize) {
+        qhmem.totdropped += qhmem.freesize;
+        if (!qhmem.curbuffer)
+          bufsize= qhmem.BUFinit;
+        else
+          bufsize= qhmem.BUFsize;
+        if (!(newbuffer= qh_malloc((size_t)bufsize))) {
+          qh_fprintf(qhmem.ferr, 6080, "qhull error (qh_memalloc): insufficient memory to allocate short memory buffer (%d bytes)\n", bufsize);
+          qh_errexit(qhmem_ERRmem, NULL, NULL);
+        }
+        *((void **)newbuffer)= qhmem.curbuffer;  /* prepend newbuffer to curbuffer
+                                                    list.  newbuffer!=0 by QH6080 */
+        qhmem.curbuffer= newbuffer;
+        size= (sizeof(void **) + qhmem.ALIGNmask) & ~qhmem.ALIGNmask;
+        qhmem.freemem= (void *)((char *)newbuffer+size);
+        qhmem.freesize= bufsize - size;
+        qhmem.totbuffer += bufsize - size; /* easier to check */
+        /* Periodically test totbuffer.  It matches at beginning and exit of every call */
+        n = qhmem.totshort + qhmem.totfree + qhmem.totdropped + qhmem.freesize - outsize;
+        if (qhmem.totbuffer != n) {
+            qh_fprintf(qhmem.ferr, 6212, "qh_memalloc internal error: short totbuffer %d != totshort+totfree... %d\n", qhmem.totbuffer, n);
+            qh_errexit(qhmem_ERRmem, NULL, NULL);
+        }
+      }
+      object= qhmem.freemem;
+      qhmem.freemem= (void *)((char *)qhmem.freemem + outsize);
+      qhmem.freesize -= outsize;
+      qhmem.totunused += outsize - insize;
+#ifdef qh_TRACEshort
+      n= qhmem.cntshort+qhmem.cntquick+qhmem.freeshort;
+      if (qhmem.IStracing >= 5)
+          qh_fprintf(qhmem.ferr, 8140, "qh_mem %p n %8d alloc short: %d bytes (tot %d cnt %d)\n", object, n, outsize, qhmem.totshort, qhmem.cntshort+qhmem.cntquick-qhmem.freeshort);
+#endif
+      return object;
+    }
+  }else {                     /* long allocation */
+    if (!qhmem.indextable) {
+      qh_fprintf(qhmem.ferr, 6081, "qhull internal error (qh_memalloc): qhmem has not been initialized.\n");
+      qh_errexit(qhmem_ERRqhull, NULL, NULL);
+    }
+    outsize= insize;
+    qhmem.cntlong++;
+    qhmem.totlong += outsize;
+    if (qhmem.maxlong < qhmem.totlong)
+      qhmem.maxlong= qhmem.totlong;
+    if (!(object= qh_malloc((size_t)outsize))) {
+      qh_fprintf(qhmem.ferr, 6082, "qhull error (qh_memalloc): insufficient memory to allocate %d bytes\n", outsize);
+      qh_errexit(qhmem_ERRmem, NULL, NULL);
+    }
+    if (qhmem.IStracing >= 5)
+      qh_fprintf(qhmem.ferr, 8057, "qh_mem %p n %8d alloc long: %d bytes (tot %d cnt %d)\n", object, qhmem.cntlong+qhmem.freelong, outsize, qhmem.totlong, qhmem.cntlong-qhmem.freelong);
+  }
+  return(object);
+} /* memalloc */
+
+
+/*-<a                             href="qh-mem.htm#TOC"
+  >--------------------------------</a><a name="memcheck">-</a>
+
+  qh_memcheck( )
+*/
+void qh_memcheck(void) {
+  int i, count, totfree= 0;
+  void *object;
+
+  if (qhmem.ferr == 0 || qhmem.IStracing < 0 || qhmem.IStracing > 10 || (((qhmem.ALIGNmask+1) & qhmem.ALIGNmask) != 0)) {
+    qh_fprintf_stderr(6244, "qh_memcheck error: either qhmem is overwritten or qhmem is not initialized.  Call qh_meminit() or qh_new_qhull() before calling qh_mem routines.  ferr 0x%x IsTracing %d ALIGNmask 0x%x", qhmem.ferr, qhmem.IStracing, qhmem.ALIGNmask);
+    qh_exit(qhmem_ERRqhull);  /* can not use qh_errexit() */
+  }
+  if (qhmem.IStracing != 0)
+    qh_fprintf(qhmem.ferr, 8143, "qh_memcheck: check size of freelists on qhmem\nqh_memcheck: A segmentation fault indicates an overwrite of qhmem\n");
+  for (i=0; i < qhmem.TABLEsize; i++) {
+    count=0;
+    for (object= qhmem.freelists[i]; object; object= *((void **)object))
+      count++;
+    totfree += qhmem.sizetable[i] * count;
+  }
+  if (totfree != qhmem.totfree) {
+    qh_fprintf(qhmem.ferr, 6211, "Qhull internal error (qh_memcheck): totfree %d not equal to freelist total %d\n", qhmem.totfree, totfree);
+    qh_errexit(qhmem_ERRqhull, NULL, NULL);
+  }
+  if (qhmem.IStracing != 0)
+    qh_fprintf(qhmem.ferr, 8144, "qh_memcheck: total size of freelists totfree is the same as qhmem.totfree\n", totfree);
+} /* memcheck */
+
+/*-<a                             href="qh-mem.htm#TOC"
+  >--------------------------------</a><a name="memfree">-</a>
+
+  qh_memfree( object, insize )
+    free up an object of size bytes
+    size is insize from qh_memalloc
+
+  notes:
+    object may be NULL
+    type checking warns if using (void **)object
+    use qh_memfree_() for quick free's of small objects
+
+  design:
+    if size <= qhmem.LASTsize
+      append object to corresponding freelist
+    else
+      call qh_free(object)
+*/
+void qh_memfree(void *object, int insize) {
+  void **freelistp;
+  int idx, outsize;
+
+  if (!object)
+    return;
+  if (insize <= qhmem.LASTsize) {
+    qhmem.freeshort++;
+    idx= qhmem.indextable[insize];
+    outsize= qhmem.sizetable[idx];
+    qhmem.totfree += outsize;
+    qhmem.totshort -= outsize;
+    freelistp= qhmem.freelists + idx;
+    *((void **)object)= *freelistp;
+    *freelistp= object;
+#ifdef qh_TRACEshort
+    idx= qhmem.cntshort+qhmem.cntquick+qhmem.freeshort;
+    if (qhmem.IStracing >= 5)
+        qh_fprintf(qhmem.ferr, 8142, "qh_mem %p n %8d free short: %d bytes (tot %d cnt %d)\n", object, idx, outsize, qhmem.totshort, qhmem.cntshort+qhmem.cntquick-qhmem.freeshort);
+#endif
+  }else {
+    qhmem.freelong++;
+    qhmem.totlong -= insize;
+    if (qhmem.IStracing >= 5)
+      qh_fprintf(qhmem.ferr, 8058, "qh_mem %p n %8d free long: %d bytes (tot %d cnt %d)\n", object, qhmem.cntlong+qhmem.freelong, insize, qhmem.totlong, qhmem.cntlong-qhmem.freelong);
+    qh_free(object);
+  }
+} /* memfree */
+
+
+/*-<a                             href="qh-mem.htm#TOC"
+  >-------------------------------</a><a name="memfreeshort">-</a>
+
+  qh_memfreeshort( curlong, totlong )
+    frees up all short and qhmem memory allocations
+
+  returns:
+    number and size of current long allocations
+
+  see:
+    qh_freeqhull(allMem)
+    qh_memtotal(curlong, totlong, curshort, totshort, maxlong, totbuffer);
+*/
+void qh_memfreeshort(int *curlong, int *totlong) {
+  void *buffer, *nextbuffer;
+  FILE *ferr;
+
+  *curlong= qhmem.cntlong - qhmem.freelong;
+  *totlong= qhmem.totlong;
+  for (buffer= qhmem.curbuffer; buffer; buffer= nextbuffer) {
+    nextbuffer= *((void **) buffer);
+    qh_free(buffer);
+  }
+  qhmem.curbuffer= NULL;
+  if (qhmem.LASTsize) {
+    qh_free(qhmem.indextable);
+    qh_free(qhmem.freelists);
+    qh_free(qhmem.sizetable);
+  }
+  ferr= qhmem.ferr;
+  memset((char *)&qhmem, 0, sizeof(qhmem));  /* every field is 0, FALSE, NULL */
+  qhmem.ferr= ferr;
+} /* memfreeshort */
+
+
+/*-<a                             href="qh-mem.htm#TOC"
+  >--------------------------------</a><a name="meminit">-</a>
+
+  qh_meminit( ferr )
+    initialize qhmem and test sizeof( void*)
+    Does not throw errors.  qh_exit on failure
+*/
+void qh_meminit(FILE *ferr) {
+
+  memset((char *)&qhmem, 0, sizeof(qhmem));  /* every field is 0, FALSE, NULL */
+  if (ferr)
+    qhmem.ferr= ferr;
+  else
+    qhmem.ferr= stderr;
+  if (sizeof(void*) < sizeof(int)) {
+    qh_fprintf(qhmem.ferr, 6083, "qhull internal error (qh_meminit): sizeof(void*) %d < sizeof(int) %d.  qset.c will not work\n", (int)sizeof(void*), (int)sizeof(int));
+    qh_exit(qhmem_ERRqhull);  /* can not use qh_errexit() */
+  }
+  if (sizeof(void*) > sizeof(ptr_intT)) {
+      qh_fprintf(qhmem.ferr, 6084, "qhull internal error (qh_meminit): sizeof(void*) %d > sizeof(ptr_intT) %d. Change ptr_intT in mem.h to 'long long'\n", (int)sizeof(void*), (int)sizeof(ptr_intT));
+      qh_exit(qhmem_ERRqhull);  /* can not use qh_errexit() */
+  }
+  qh_memcheck();
+} /* meminit */
+
+/*-<a                             href="qh-mem.htm#TOC"
+  >-------------------------------</a><a name="meminitbuffers">-</a>
+
+  qh_meminitbuffers( tracelevel, alignment, numsizes, bufsize, bufinit )
+    initialize qhmem
+    if tracelevel >= 5, trace memory allocations
+    alignment= desired address alignment for memory allocations
+    numsizes= number of freelists
+    bufsize=  size of additional memory buffers for short allocations
+    bufinit=  size of initial memory buffer for short allocations
+*/
+void qh_meminitbuffers(int tracelevel, int alignment, int numsizes, int bufsize, int bufinit) {
+
+  qhmem.IStracing= tracelevel;
+  qhmem.NUMsizes= numsizes;
+  qhmem.BUFsize= bufsize;
+  qhmem.BUFinit= bufinit;
+  qhmem.ALIGNmask= alignment-1;
+  if (qhmem.ALIGNmask & ~qhmem.ALIGNmask) {
+    qh_fprintf(qhmem.ferr, 6085, "qhull internal error (qh_meminit): memory alignment %d is not a power of 2\n", alignment);
+    qh_errexit(qhmem_ERRqhull, NULL, NULL);
+  }
+  qhmem.sizetable= (int *) calloc((size_t)numsizes, sizeof(int));
+  qhmem.freelists= (void **) calloc((size_t)numsizes, sizeof(void *));
+  if (!qhmem.sizetable || !qhmem.freelists) {
+    qh_fprintf(qhmem.ferr, 6086, "qhull error (qh_meminit): insufficient memory\n");
+    qh_errexit(qhmem_ERRmem, NULL, NULL);
+  }
+  if (qhmem.IStracing >= 1)
+    qh_fprintf(qhmem.ferr, 8059, "qh_meminitbuffers: memory initialized with alignment %d\n", alignment);
+} /* meminitbuffers */
+
+/*-<a                             href="qh-mem.htm#TOC"
+  >-------------------------------</a><a name="memsetup">-</a>
+
+  qh_memsetup()
+    set up memory after running memsize()
+*/
+void qh_memsetup(void) {
+  int k,i;
+
+  qsort(qhmem.sizetable, (size_t)qhmem.TABLEsize, sizeof(int), qh_intcompare);
+  qhmem.LASTsize= qhmem.sizetable[qhmem.TABLEsize-1];
+  if (qhmem.LASTsize >= qhmem.BUFsize || qhmem.LASTsize >= qhmem.BUFinit) {
+    qh_fprintf(qhmem.ferr, 6087, "qhull error (qh_memsetup): largest mem size %d is >= buffer size %d or initial buffer size %d\n",
+            qhmem.LASTsize, qhmem.BUFsize, qhmem.BUFinit);
+    qh_errexit(qhmem_ERRmem, NULL, NULL);
+  }
+  if (!(qhmem.indextable= (int *)qh_malloc((qhmem.LASTsize+1) * sizeof(int)))) {
+    qh_fprintf(qhmem.ferr, 6088, "qhull error (qh_memsetup): insufficient memory\n");
+    qh_errexit(qhmem_ERRmem, NULL, NULL);
+  }
+  for (k=qhmem.LASTsize+1; k--; )
+    qhmem.indextable[k]= k;
+  i= 0;
+  for (k=0; k <= qhmem.LASTsize; k++) {
+    if (qhmem.indextable[k] <= qhmem.sizetable[i])
+      qhmem.indextable[k]= i;
+    else
+      qhmem.indextable[k]= ++i;
+  }
+} /* memsetup */
+
+/*-<a                             href="qh-mem.htm#TOC"
+  >-------------------------------</a><a name="memsize">-</a>
+
+  qh_memsize( size )
+    define a free list for this size
+*/
+void qh_memsize(int size) {
+  int k;
+
+  if (qhmem.LASTsize) {
+    qh_fprintf(qhmem.ferr, 6089, "qhull error (qh_memsize): called after qhmem_setup\n");
+    qh_errexit(qhmem_ERRqhull, NULL, NULL);
+  }
+  size= (size + qhmem.ALIGNmask) & ~qhmem.ALIGNmask;
+  for (k=qhmem.TABLEsize; k--; ) {
+    if (qhmem.sizetable[k] == size)
+      return;
+  }
+  if (qhmem.TABLEsize < qhmem.NUMsizes)
+    qhmem.sizetable[qhmem.TABLEsize++]= size;
+  else
+    qh_fprintf(qhmem.ferr, 7060, "qhull warning (memsize): free list table has room for only %d sizes\n", qhmem.NUMsizes);
+} /* memsize */
+
+
+/*-<a                             href="qh-mem.htm#TOC"
+  >-------------------------------</a><a name="memstatistics">-</a>
+
+  qh_memstatistics( fp )
+    print out memory statistics
+
+    Verifies that qhmem.totfree == sum of freelists
+*/
+void qh_memstatistics(FILE *fp) {
+  int i;
+  int count;
+  void *object;
+
+  qh_memcheck();
+  qh_fprintf(fp, 9278, "\nmemory statistics:\n\
+%7d quick allocations\n\
+%7d short allocations\n\
+%7d long allocations\n\
+%7d short frees\n\
+%7d long frees\n\
+%7d bytes of short memory in use\n\
+%7d bytes of short memory in freelists\n\
+%7d bytes of dropped short memory\n\
+%7d bytes of unused short memory (estimated)\n\
+%7d bytes of long memory allocated (max, except for input)\n\
+%7d bytes of long memory in use (in %d pieces)\n\
+%7d bytes of short memory buffers (minus links)\n\
+%7d bytes per short memory buffer (initially %d bytes)\n",
+           qhmem.cntquick, qhmem.cntshort, qhmem.cntlong,
+           qhmem.freeshort, qhmem.freelong,
+           qhmem.totshort, qhmem.totfree,
+           qhmem.totdropped + qhmem.freesize, qhmem.totunused,
+           qhmem.maxlong, qhmem.totlong, qhmem.cntlong - qhmem.freelong,
+           qhmem.totbuffer, qhmem.BUFsize, qhmem.BUFinit);
+  if (qhmem.cntlarger) {
+    qh_fprintf(fp, 9279, "%7d calls to qh_setlarger\n%7.2g     average copy size\n",
+           qhmem.cntlarger, ((float)qhmem.totlarger)/(float)qhmem.cntlarger);
+    qh_fprintf(fp, 9280, "  freelists(bytes->count):");
+  }
+  for (i=0; i < qhmem.TABLEsize; i++) {
+    count=0;
+    for (object= qhmem.freelists[i]; object; object= *((void **)object))
+      count++;
+    qh_fprintf(fp, 9281, " %d->%d", qhmem.sizetable[i], count);
+  }
+  qh_fprintf(fp, 9282, "\n\n");
+} /* memstatistics */
+
+
+/*-<a                             href="qh-mem.htm#TOC"
+  >-------------------------------</a><a name="NOmem">-</a>
+
+  qh_NOmem
+    turn off quick-fit memory allocation
+
+  notes:
+    uses qh_malloc() and qh_free() instead
+*/
+#else /* qh_NOmem */
+
+void *qh_memalloc(int insize) {
+  void *object;
+
+  if (!(object= qh_malloc((size_t)insize))) {
+    qh_fprintf(qhmem.ferr, 6090, "qhull error (qh_memalloc): insufficient memory\n");
+    qh_errexit(qhmem_ERRmem, NULL, NULL);
+  }
+  qhmem.cntlong++;
+  qhmem.totlong += insize;
+  if (qhmem.maxlong < qhmem.totlong)
+      qhmem.maxlong= qhmem.totlong;
+  if (qhmem.IStracing >= 5)
+    qh_fprintf(qhmem.ferr, 8060, "qh_mem %p n %8d alloc long: %d bytes (tot %d cnt %d)\n", object, qhmem.cntlong+qhmem.freelong, insize, qhmem.totlong, qhmem.cntlong-qhmem.freelong);
+  return object;
+}
+
+void qh_memfree(void *object, int insize) {
+
+  if (!object)
+    return;
+  qh_free(object);
+  qhmem.freelong++;
+  qhmem.totlong -= insize;
+  if (qhmem.IStracing >= 5)
+    qh_fprintf(qhmem.ferr, 8061, "qh_mem %p n %8d free long: %d bytes (tot %d cnt %d)\n", object, qhmem.cntlong+qhmem.freelong, insize, qhmem.totlong, qhmem.cntlong-qhmem.freelong);
+}
+
+void qh_memfreeshort(int *curlong, int *totlong) {
+  *totlong= qhmem.totlong;
+  *curlong= qhmem.cntlong - qhmem.freelong;
+  memset((char *)&qhmem, 0, sizeof(qhmem));  /* every field is 0, FALSE, NULL */
+}
+
+void qh_meminit(FILE *ferr) {
+
+  memset((char *)&qhmem, 0, sizeof(qhmem));  /* every field is 0, FALSE, NULL */
+  if (ferr)
+      qhmem.ferr= ferr;
+  else
+      qhmem.ferr= stderr;
+  if (sizeof(void*) < sizeof(int)) {
+    qh_fprintf(qhmem.ferr, 6091, "qhull internal error (qh_meminit): sizeof(void*) %d < sizeof(int) %d.  qset.c will not work\n", (int)sizeof(void*), (int)sizeof(int));
+    qh_errexit(qhmem_ERRqhull, NULL, NULL);
+  }
+}
+
+void qh_meminitbuffers(int tracelevel, int alignment, int numsizes, int bufsize, int bufinit) {
+
+  qhmem.IStracing= tracelevel;
+}
+
+void qh_memsetup(void) {
+
+}
+
+void qh_memsize(int size) {
+
+}
+
+void qh_memstatistics(FILE *fp) {
+
+  qh_fprintf(fp, 9409, "\nmemory statistics:\n\
+%7d long allocations\n\
+%7d long frees\n\
+%7d bytes of long memory allocated (max, except for input)\n\
+%7d bytes of long memory in use (in %d pieces)\n",
+           qhmem.cntlong,
+           qhmem.freelong,
+           qhmem.maxlong, qhmem.totlong, qhmem.cntlong - qhmem.freelong);
+}
+
+#endif /* qh_NOmem */
+
+/*-<a                             href="qh-mem.htm#TOC"
+>-------------------------------</a><a name="memtotlong">-</a>
+
+  qh_memtotal( totlong, curlong, totshort, curshort, maxlong, totbuffer )
+    Return the total, allocated long and short memory
+
+  returns:
+    Returns the total current bytes of long and short allocations
+    Returns the current count of long and short allocations
+    Returns the maximum long memory and total short buffer (minus one link per buffer)
+    Does not error (UsingLibQhull.cpp)
+*/
+void qh_memtotal(int *totlong, int *curlong, int *totshort, int *curshort, int *maxlong, int *totbuffer) {
+    *totlong= qhmem.totlong;
+    *curlong= qhmem.cntlong - qhmem.freelong;
+    *totshort= qhmem.totshort;
+    *curshort= qhmem.cntshort + qhmem.cntquick - qhmem.freeshort;
+    *maxlong= qhmem.maxlong;
+    *totbuffer= qhmem.totbuffer;
+} /* memtotlong */
+
diff --git a/xs/src/qhull/src/libqhull/mem.h b/xs/src/qhull/src/libqhull/mem.h
new file mode 100644
index 0000000000..453f319df3
--- /dev/null
+++ b/xs/src/qhull/src/libqhull/mem.h
@@ -0,0 +1,222 @@
+/*<html><pre>  -<a                             href="qh-mem.htm"
+  >-------------------------------</a><a name="TOP">-</a>
+
+   mem.h
+     prototypes for memory management functions
+
+   see qh-mem.htm, mem.c and qset.h
+
+   for error handling, writes message and calls
+     qh_errexit(qhmem_ERRmem, NULL, NULL) if insufficient memory
+       and
+     qh_errexit(qhmem_ERRqhull, NULL, NULL) otherwise
+
+   Copyright (c) 1993-2015 The Geometry Center.
+   $Id: //main/2015/qhull/src/libqhull/mem.h#2 $$Change: 2062 $
+   $DateTime: 2016/01/17 13:13:18 $$Author: bbarber $
+*/
+
+#ifndef qhDEFmem
+#define qhDEFmem 1
+
+#include <stdio.h>
+
+/*-<a                             href="qh-mem.htm#TOC"
+  >-------------------------------</a><a name="NOmem">-</a>
+
+  qh_NOmem
+    turn off quick-fit memory allocation
+
+  notes:
+    mem.c implements Quickfit memory allocation for about 20% time
+    savings.  If it fails on your machine, try to locate the
+    problem, and send the answer to qhull@qhull.org.  If this can
+    not be done, define qh_NOmem to use malloc/free instead.
+
+   #define qh_NOmem
+*/
+
+/*-<a                             href="qh-mem.htm#TOC"
+>-------------------------------</a><a name="TRACEshort">-</a>
+
+qh_TRACEshort
+Trace short and quick memory allocations at T5
+
+*/
+#define qh_TRACEshort
+
+/*-------------------------------------------
+    to avoid bus errors, memory allocation must consider alignment requirements.
+    malloc() automatically takes care of alignment.   Since mem.c manages
+    its own memory, we need to explicitly specify alignment in
+    qh_meminitbuffers().
+
+    A safe choice is sizeof(double).  sizeof(float) may be used if doubles
+    do not occur in data structures and pointers are the same size.  Be careful
+    of machines (e.g., DEC Alpha) with large pointers.  If gcc is available,
+    use __alignof__(double) or fmax_(__alignof__(float), __alignof__(void *)).
+
+   see <a href="user.h#MEMalign">qh_MEMalign</a> in user.h for qhull's alignment
+*/
+
+#define qhmem_ERRmem 4    /* matches qh_ERRmem in libqhull.h */
+#define qhmem_ERRqhull 5  /* matches qh_ERRqhull in libqhull.h */
+
+/*-<a                             href="qh-mem.htm#TOC"
+  >--------------------------------</a><a name="ptr_intT">-</a>
+
+  ptr_intT
+    for casting a void * to an integer-type that holds a pointer
+    Used for integer expressions (e.g., computing qh_gethash() in poly.c)
+
+  notes:
+    WARN64 -- these notes indicate 64-bit issues
+    On 64-bit machines, a pointer may be larger than an 'int'.
+    qh_meminit()/mem.c checks that 'ptr_intT' holds a 'void*'
+    ptr_intT is typically a signed value, but not necessarily so
+    size_t is typically unsigned, but should match the parameter type
+    Qhull uses int instead of size_t except for system calls such as malloc, qsort, qh_malloc, etc.
+    This matches Qt convention and is easier to work with.
+*/
+#if (defined(__MINGW64__)) && defined(_WIN64)
+typedef long long ptr_intT;
+#elif (_MSC_VER) && defined(_WIN64)
+typedef long long ptr_intT;
+#else
+typedef long ptr_intT;
+#endif
+
+/*-<a                             href="qh-mem.htm#TOC"
+  >--------------------------------</a><a name="qhmemT">-</a>
+
+  qhmemT
+    global memory structure for mem.c
+
+ notes:
+   users should ignore qhmem except for writing extensions
+   qhmem is allocated in mem.c
+
+   qhmem could be swapable like qh and qhstat, but then
+   multiple qh's and qhmem's would need to keep in synch.
+   A swapable qhmem would also waste memory buffers.  As long
+   as memory operations are atomic, there is no problem with
+   multiple qh structures being active at the same time.
+   If you need separate address spaces, you can swap the
+   contents of qhmem.
+*/
+typedef struct qhmemT qhmemT;
+extern qhmemT qhmem;
+
+#ifndef DEFsetT
+#define DEFsetT 1
+typedef struct setT setT;          /* defined in qset.h */
+#endif
+
+/* Update qhmem in mem.c if add or remove fields */
+struct qhmemT {               /* global memory management variables */
+  int      BUFsize;           /* size of memory allocation buffer */
+  int      BUFinit;           /* initial size of memory allocation buffer */
+  int      TABLEsize;         /* actual number of sizes in free list table */
+  int      NUMsizes;          /* maximum number of sizes in free list table */
+  int      LASTsize;          /* last size in free list table */
+  int      ALIGNmask;         /* worst-case alignment, must be 2^n-1 */
+  void   **freelists;          /* free list table, linked by offset 0 */
+  int     *sizetable;         /* size of each freelist */
+  int     *indextable;        /* size->index table */
+  void    *curbuffer;         /* current buffer, linked by offset 0 */
+  void    *freemem;           /*   free memory in curbuffer */
+  int      freesize;          /*   size of freemem in bytes */
+  setT    *tempstack;         /* stack of temporary memory, managed by users */
+  FILE    *ferr;              /* file for reporting errors when 'qh' may be undefined */
+  int      IStracing;         /* =5 if tracing memory allocations */
+  int      cntquick;          /* count of quick allocations */
+                              /* Note: removing statistics doesn't effect speed */
+  int      cntshort;          /* count of short allocations */
+  int      cntlong;           /* count of long allocations */
+  int      freeshort;         /* count of short memfrees */
+  int      freelong;          /* count of long memfrees */
+  int      totbuffer;         /* total short memory buffers minus buffer links */
+  int      totdropped;        /* total dropped memory at end of short memory buffers (e.g., freesize) */
+  int      totfree;           /* total size of free, short memory on freelists */
+  int      totlong;           /* total size of long memory in use */
+  int      maxlong;           /*   maximum totlong */
+  int      totshort;          /* total size of short memory in use */
+  int      totunused;         /* total unused short memory (estimated, short size - request size of first allocations) */
+  int      cntlarger;         /* count of setlarger's */
+  int      totlarger;         /* total copied by setlarger */
+};
+
+
+/*==================== -macros ====================*/
+
+/*-<a                             href="qh-mem.htm#TOC"
+  >--------------------------------</a><a name="memalloc_">-</a>
+
+  qh_memalloc_(insize, freelistp, object, type)
+    returns object of size bytes
+        assumes size<=qhmem.LASTsize and void **freelistp is a temp
+*/
+
+#if defined qh_NOmem
+#define qh_memalloc_(insize, freelistp, object, type) {\
+  object= (type*)qh_memalloc(insize); }
+#elif defined qh_TRACEshort
+#define qh_memalloc_(insize, freelistp, object, type) {\
+    freelistp= NULL; /* Avoid warnings */ \
+    object= (type*)qh_memalloc(insize); }
+#else /* !qh_NOmem */
+
+#define qh_memalloc_(insize, freelistp, object, type) {\
+  freelistp= qhmem.freelists + qhmem.indextable[insize];\
+  if ((object= (type*)*freelistp)) {\
+    qhmem.totshort += qhmem.sizetable[qhmem.indextable[insize]]; \
+    qhmem.totfree -= qhmem.sizetable[qhmem.indextable[insize]]; \
+    qhmem.cntquick++;  \
+    *freelistp= *((void **)*freelistp);\
+  }else object= (type*)qh_memalloc(insize);}
+#endif
+
+/*-<a                             href="qh-mem.htm#TOC"
+  >--------------------------------</a><a name="memfree_">-</a>
+
+  qh_memfree_(object, insize, freelistp)
+    free up an object
+
+  notes:
+    object may be NULL
+    assumes size<=qhmem.LASTsize and void **freelistp is a temp
+*/
+#if defined qh_NOmem
+#define qh_memfree_(object, insize, freelistp) {\
+  qh_memfree(object, insize); }
+#elif defined qh_TRACEshort
+#define qh_memfree_(object, insize, freelistp) {\
+    freelistp= NULL; /* Avoid warnings */ \
+    qh_memfree(object, insize); }
+#else /* !qh_NOmem */
+
+#define qh_memfree_(object, insize, freelistp) {\
+  if (object) { \
+    qhmem.freeshort++;\
+    freelistp= qhmem.freelists + qhmem.indextable[insize];\
+    qhmem.totshort -= qhmem.sizetable[qhmem.indextable[insize]]; \
+    qhmem.totfree += qhmem.sizetable[qhmem.indextable[insize]]; \
+    *((void **)object)= *freelistp;\
+    *freelistp= object;}}
+#endif
+
+/*=============== prototypes in alphabetical order ============*/
+
+void *qh_memalloc(int insize);
+void qh_memcheck(void);
+void qh_memfree(void *object, int insize);
+void qh_memfreeshort(int *curlong, int *totlong);
+void qh_meminit(FILE *ferr);
+void qh_meminitbuffers(int tracelevel, int alignment, int numsizes,
+                        int bufsize, int bufinit);
+void qh_memsetup(void);
+void qh_memsize(int size);
+void qh_memstatistics(FILE *fp);
+void qh_memtotal(int *totlong, int *curlong, int *totshort, int *curshort, int *maxlong, int *totbuffer);
+
+#endif /* qhDEFmem */
diff --git a/xs/src/qhull/src/libqhull/merge.c b/xs/src/qhull/src/libqhull/merge.c
new file mode 100644
index 0000000000..22104dc031
--- /dev/null
+++ b/xs/src/qhull/src/libqhull/merge.c
@@ -0,0 +1,3628 @@
+/*<html><pre>  -<a                             href="qh-merge.htm#TOC"
+  >-------------------------------</a><a name="TOP">-</a>
+
+   merge.c
+   merges non-convex facets
+
+   see qh-merge.htm and merge.h
+
+   other modules call qh_premerge() and qh_postmerge()
+
+   the user may call qh_postmerge() to perform additional merges.
+
+   To remove deleted facets and vertices (qhull() in libqhull.c):
+     qh_partitionvisible(!qh_ALL, &numoutside);  // visible_list, newfacet_list
+     qh_deletevisible();         // qh.visible_list
+     qh_resetlists(False, qh_RESETvisible);       // qh.visible_list newvertex_list newfacet_list
+
+   assumes qh.CENTERtype= centrum
+
+   merges occur in qh_mergefacet and in qh_mergecycle
+   vertex->neighbors not set until the first merge occurs
+
+   Copyright (c) 1993-2015 C.B. Barber.
+   $Id: //main/2015/qhull/src/libqhull/merge.c#4 $$Change: 2064 $
+   $DateTime: 2016/01/18 12:36:08 $$Author: bbarber $
+*/
+
+#include "qhull_a.h"
+
+#ifndef qh_NOmerge
+
+/*===== functions(alphabetical after premerge and postmerge) ======*/
+
+/*-<a                             href="qh-merge.htm#TOC"
+  >-------------------------------</a><a name="premerge">-</a>
+
+  qh_premerge( apex, maxcentrum )
+    pre-merge nonconvex facets in qh.newfacet_list for apex
+    maxcentrum defines coplanar and concave (qh_test_appendmerge)
+
+  returns:
+    deleted facets added to qh.visible_list with facet->visible set
+
+  notes:
+    uses globals, qh.MERGEexact, qh.PREmerge
+
+  design:
+    mark duplicate ridges in qh.newfacet_list
+    merge facet cycles in qh.newfacet_list
+    merge duplicate ridges and concave facets in qh.newfacet_list
+    check merged facet cycles for degenerate and redundant facets
+    merge degenerate and redundant facets
+    collect coplanar and concave facets
+    merge concave, coplanar, degenerate, and redundant facets
+*/
+void qh_premerge(vertexT *apex, realT maxcentrum, realT maxangle) {
+  boolT othermerge= False;
+  facetT *newfacet;
+
+  if (qh ZEROcentrum && qh_checkzero(!qh_ALL))
+    return;
+  trace2((qh ferr, 2008, "qh_premerge: premerge centrum %2.2g angle %2.2g for apex v%d facetlist f%d\n",
+            maxcentrum, maxangle, apex->id, getid_(qh newfacet_list)));
+  if (qh IStracing >= 4 && qh num_facets < 50)
+    qh_printlists();
+  qh centrum_radius= maxcentrum;
+  qh cos_max= maxangle;
+  qh degen_mergeset= qh_settemp(qh TEMPsize);
+  qh facet_mergeset= qh_settemp(qh TEMPsize);
+  if (qh hull_dim >=3) {
+    qh_mark_dupridges(qh newfacet_list); /* facet_mergeset */
+    qh_mergecycle_all(qh newfacet_list, &othermerge);
+    qh_forcedmerges(&othermerge /* qh.facet_mergeset */);
+    FORALLnew_facets {  /* test samecycle merges */
+      if (!newfacet->simplicial && !newfacet->mergeridge)
+        qh_degen_redundant_neighbors(newfacet, NULL);
+    }
+    if (qh_merge_degenredundant())
+      othermerge= True;
+  }else /* qh.hull_dim == 2 */
+    qh_mergecycle_all(qh newfacet_list, &othermerge);
+  qh_flippedmerges(qh newfacet_list, &othermerge);
+  if (!qh MERGEexact || zzval_(Ztotmerge)) {
+    zinc_(Zpremergetot);
+    qh POSTmerging= False;
+    qh_getmergeset_initial(qh newfacet_list);
+    qh_all_merges(othermerge, False);
+  }
+  qh_settempfree(&qh facet_mergeset);
+  qh_settempfree(&qh degen_mergeset);
+} /* premerge */
+
+/*-<a                             href="qh-merge.htm#TOC"
+  >-------------------------------</a><a name="postmerge">-</a>
+
+  qh_postmerge( reason, maxcentrum, maxangle, vneighbors )
+    post-merge nonconvex facets as defined by maxcentrum and maxangle
+    'reason' is for reporting progress
+    if vneighbors,
+      calls qh_test_vneighbors at end of qh_all_merge
+    if firstmerge,
+      calls qh_reducevertices before qh_getmergeset
+
+  returns:
+    if first call (qh.visible_list != qh.facet_list),
+      builds qh.facet_newlist, qh.newvertex_list
+    deleted facets added to qh.visible_list with facet->visible
+    qh.visible_list == qh.facet_list
+
+  notes:
+
+
+  design:
+    if first call
+      set qh.visible_list and qh.newfacet_list to qh.facet_list
+      add all facets to qh.newfacet_list
+      mark non-simplicial facets, facet->newmerge
+      set qh.newvertext_list to qh.vertex_list
+      add all vertices to qh.newvertex_list
+      if a pre-merge occured
+        set vertex->delridge {will retest the ridge}
+        if qh.MERGEexact
+          call qh_reducevertices()
+      if no pre-merging
+        merge flipped facets
+    determine non-convex facets
+    merge all non-convex facets
+*/
+void qh_postmerge(const char *reason, realT maxcentrum, realT maxangle,
+                      boolT vneighbors) {
+  facetT *newfacet;
+  boolT othermerges= False;
+  vertexT *vertex;
+
+  if (qh REPORTfreq || qh IStracing) {
+    qh_buildtracing(NULL, NULL);
+    qh_printsummary(qh ferr);
+    if (qh PRINTstatistics)
+      qh_printallstatistics(qh ferr, "reason");
+    qh_fprintf(qh ferr, 8062, "\n%s with 'C%.2g' and 'A%.2g'\n",
+        reason, maxcentrum, maxangle);
+  }
+  trace2((qh ferr, 2009, "qh_postmerge: postmerge.  test vneighbors? %d\n",
+            vneighbors));
+  qh centrum_radius= maxcentrum;
+  qh cos_max= maxangle;
+  qh POSTmerging= True;
+  qh degen_mergeset= qh_settemp(qh TEMPsize);
+  qh facet_mergeset= qh_settemp(qh TEMPsize);
+  if (qh visible_list != qh facet_list) {  /* first call */
+    qh NEWfacets= True;
+    qh visible_list= qh newfacet_list= qh facet_list;
+    FORALLnew_facets {
+      newfacet->newfacet= True;
+       if (!newfacet->simplicial)
+        newfacet->newmerge= True;
+     zinc_(Zpostfacets);
+    }
+    qh newvertex_list= qh vertex_list;
+    FORALLvertices
+      vertex->newlist= True;
+    if (qh VERTEXneighbors) { /* a merge has occurred */
+      FORALLvertices
+        vertex->delridge= True; /* test for redundant, needed? */
+      if (qh MERGEexact) {
+        if (qh hull_dim <= qh_DIMreduceBuild)
+          qh_reducevertices(); /* was skipped during pre-merging */
+      }
+    }
+    if (!qh PREmerge && !qh MERGEexact)
+      qh_flippedmerges(qh newfacet_list, &othermerges);
+  }
+  qh_getmergeset_initial(qh newfacet_list);
+  qh_all_merges(False, vneighbors);
+  qh_settempfree(&qh facet_mergeset);
+  qh_settempfree(&qh degen_mergeset);
+} /* post_merge */
+
+/*-<a                             href="qh-merge.htm#TOC"
+  >-------------------------------</a><a name="all_merges">-</a>
+
+  qh_all_merges( othermerge, vneighbors )
+    merge all non-convex facets
+
+    set othermerge if already merged facets (for qh_reducevertices)
+    if vneighbors
+      tests vertex neighbors for convexity at end
+    qh.facet_mergeset lists the non-convex ridges in qh_newfacet_list
+    qh.degen_mergeset is defined
+    if qh.MERGEexact && !qh.POSTmerging,
+      does not merge coplanar facets
+
+  returns:
+    deleted facets added to qh.visible_list with facet->visible
+    deleted vertices added qh.delvertex_list with vertex->delvertex
+
+  notes:
+    unless !qh.MERGEindependent,
+      merges facets in independent sets
+    uses qh.newfacet_list as argument since merges call qh_removefacet()
+
+  design:
+    while merges occur
+      for each merge in qh.facet_mergeset
+        unless one of the facets was already merged in this pass
+          merge the facets
+        test merged facets for additional merges
+        add merges to qh.facet_mergeset
+      if vertices record neighboring facets
+        rename redundant vertices
+          update qh.facet_mergeset
+    if vneighbors ??
+      tests vertex neighbors for convexity at end
+*/
+void qh_all_merges(boolT othermerge, boolT vneighbors) {
+  facetT *facet1, *facet2;
+  mergeT *merge;
+  boolT wasmerge= True, isreduce;
+  void **freelistp;  /* used if !qh_NOmem by qh_memfree_() */
+  vertexT *vertex;
+  mergeType mergetype;
+  int numcoplanar=0, numconcave=0, numdegenredun= 0, numnewmerges= 0;
+
+  trace2((qh ferr, 2010, "qh_all_merges: starting to merge facets beginning from f%d\n",
+            getid_(qh newfacet_list)));
+  while (True) {
+    wasmerge= False;
+    while (qh_setsize(qh facet_mergeset)) {
+      while ((merge= (mergeT*)qh_setdellast(qh facet_mergeset))) {
+        facet1= merge->facet1;
+        facet2= merge->facet2;
+        mergetype= merge->type;
+        qh_memfree_(merge, (int)sizeof(mergeT), freelistp);
+        if (facet1->visible || facet2->visible) /*deleted facet*/
+          continue;
+        if ((facet1->newfacet && !facet1->tested)
+                || (facet2->newfacet && !facet2->tested)) {
+          if (qh MERGEindependent && mergetype <= MRGanglecoplanar)
+            continue;      /* perform independent sets of merges */
+        }
+        qh_merge_nonconvex(facet1, facet2, mergetype);
+        numdegenredun += qh_merge_degenredundant();
+        numnewmerges++;
+        wasmerge= True;
+        if (mergetype == MRGconcave)
+          numconcave++;
+        else /* MRGcoplanar or MRGanglecoplanar */
+          numcoplanar++;
+      } /* while setdellast */
+      if (qh POSTmerging && qh hull_dim <= qh_DIMreduceBuild
+      && numnewmerges > qh_MAXnewmerges) {
+        numnewmerges= 0;
+        qh_reducevertices();  /* otherwise large post merges too slow */
+      }
+      qh_getmergeset(qh newfacet_list); /* facet_mergeset */
+    } /* while mergeset */
+    if (qh VERTEXneighbors) {
+      isreduce= False;
+      if (qh hull_dim >=4 && qh POSTmerging) {
+        FORALLvertices
+          vertex->delridge= True;
+        isreduce= True;
+      }
+      if ((wasmerge || othermerge) && (!qh MERGEexact || qh POSTmerging)
+          && qh hull_dim <= qh_DIMreduceBuild) {
+        othermerge= False;
+        isreduce= True;
+      }
+      if (isreduce) {
+        if (qh_reducevertices()) {
+          qh_getmergeset(qh newfacet_list); /* facet_mergeset */
+          continue;
+        }
+      }
+    }
+    if (vneighbors && qh_test_vneighbors(/* qh.newfacet_list */))
+      continue;
+    break;
+  } /* while (True) */
+  if (qh CHECKfrequently && !qh MERGEexact) {
+    qh old_randomdist= qh RANDOMdist;
+    qh RANDOMdist= False;
+    qh_checkconvex(qh newfacet_list, qh_ALGORITHMfault);
+    /* qh_checkconnect(); [this is slow and it changes the facet order] */
+    qh RANDOMdist= qh old_randomdist;
+  }
+  trace1((qh ferr, 1009, "qh_all_merges: merged %d coplanar facets %d concave facets and %d degen or redundant facets.\n",
+    numcoplanar, numconcave, numdegenredun));
+  if (qh IStracing >= 4 && qh num_facets < 50)
+    qh_printlists();
+} /* all_merges */
+
+
+/*-<a                             href="qh-merge.htm#TOC"
+  >-------------------------------</a><a name="appendmergeset">-</a>
+
+  qh_appendmergeset( facet, neighbor, mergetype, angle )
+    appends an entry to qh.facet_mergeset or qh.degen_mergeset
+
+    angle ignored if NULL or !qh.ANGLEmerge
+
+  returns:
+    merge appended to facet_mergeset or degen_mergeset
+      sets ->degenerate or ->redundant if degen_mergeset
+
+  see:
+    qh_test_appendmerge()
+
+  design:
+    allocate merge entry
+    if regular merge
+      append to qh.facet_mergeset
+    else if degenerate merge and qh.facet_mergeset is all degenerate
+      append to qh.degen_mergeset
+    else if degenerate merge
+      prepend to qh.degen_mergeset
+    else if redundant merge
+      append to qh.degen_mergeset
+*/
+void qh_appendmergeset(facetT *facet, facetT *neighbor, mergeType mergetype, realT *angle) {
+  mergeT *merge, *lastmerge;
+  void **freelistp; /* used if !qh_NOmem by qh_memalloc_() */
+
+  if (facet->redundant)
+    return;
+  if (facet->degenerate && mergetype == MRGdegen)
+    return;
+  qh_memalloc_((int)sizeof(mergeT), freelistp, merge, mergeT);
+  merge->facet1= facet;
+  merge->facet2= neighbor;
+  merge->type= mergetype;
+  if (angle && qh ANGLEmerge)
+    merge->angle= *angle;
+  if (mergetype < MRGdegen)
+    qh_setappend(&(qh facet_mergeset), merge);
+  else if (mergetype == MRGdegen) {
+    facet->degenerate= True;
+    if (!(lastmerge= (mergeT*)qh_setlast(qh degen_mergeset))
+    || lastmerge->type == MRGdegen)
+      qh_setappend(&(qh degen_mergeset), merge);
+    else
+      qh_setaddnth(&(qh degen_mergeset), 0, merge);
+  }else if (mergetype == MRGredundant) {
+    facet->redundant= True;
+    qh_setappend(&(qh degen_mergeset), merge);
+  }else /* mergetype == MRGmirror */ {
+    if (facet->redundant || neighbor->redundant) {
+      qh_fprintf(qh ferr, 6092, "qhull error (qh_appendmergeset): facet f%d or f%d is already a mirrored facet\n",
+           facet->id, neighbor->id);
+      qh_errexit2(qh_ERRqhull, facet, neighbor);
+    }
+    if (!qh_setequal(facet->vertices, neighbor->vertices)) {
+      qh_fprintf(qh ferr, 6093, "qhull error (qh_appendmergeset): mirrored facets f%d and f%d do not have the same vertices\n",
+           facet->id, neighbor->id);
+      qh_errexit2(qh_ERRqhull, facet, neighbor);
+    }
+    facet->redundant= True;
+    neighbor->redundant= True;
+    qh_setappend(&(qh degen_mergeset), merge);
+  }
+} /* appendmergeset */
+
+
+/*-<a                             href="qh-merge.htm#TOC"
+  >-------------------------------</a><a name="basevertices">-</a>
+
+  qh_basevertices( samecycle )
+    return temporary set of base vertices for samecycle
+    samecycle is first facet in the cycle
+    assumes apex is SETfirst_( samecycle->vertices )
+
+  returns:
+    vertices(settemp)
+    all ->seen are cleared
+
+  notes:
+    uses qh_vertex_visit;
+
+  design:
+    for each facet in samecycle
+      for each unseen vertex in facet->vertices
+        append to result
+*/
+setT *qh_basevertices(facetT *samecycle) {
+  facetT *same;
+  vertexT *apex, *vertex, **vertexp;
+  setT *vertices= qh_settemp(qh TEMPsize);
+
+  apex= SETfirstt_(samecycle->vertices, vertexT);
+  apex->visitid= ++qh vertex_visit;
+  FORALLsame_cycle_(samecycle) {
+    if (same->mergeridge)
+      continue;
+    FOREACHvertex_(same->vertices) {
+      if (vertex->visitid != qh vertex_visit) {
+        qh_setappend(&vertices, vertex);
+        vertex->visitid= qh vertex_visit;
+        vertex->seen= False;
+      }
+    }
+  }
+  trace4((qh ferr, 4019, "qh_basevertices: found %d vertices\n",
+         qh_setsize(vertices)));
+  return vertices;
+} /* basevertices */
+
+/*-<a                             href="qh-merge.htm#TOC"
+  >-------------------------------</a><a name="checkconnect">-</a>
+
+  qh_checkconnect()
+    check that new facets are connected
+    new facets are on qh.newfacet_list
+
+  notes:
+    this is slow and it changes the order of the facets
+    uses qh.visit_id
+
+  design:
+    move first new facet to end of qh.facet_list
+    for all newly appended facets
+      append unvisited neighbors to end of qh.facet_list
+    for all new facets
+      report error if unvisited
+*/
+void qh_checkconnect(void /* qh.newfacet_list */) {
+  facetT *facet, *newfacet, *errfacet= NULL, *neighbor, **neighborp;
+
+  facet= qh newfacet_list;
+  qh_removefacet(facet);
+  qh_appendfacet(facet);
+  facet->visitid= ++qh visit_id;
+  FORALLfacet_(facet) {
+    FOREACHneighbor_(facet) {
+      if (neighbor->visitid != qh visit_id) {
+        qh_removefacet(neighbor);
+        qh_appendfacet(neighbor);
+        neighbor->visitid= qh visit_id;
+      }
+    }
+  }
+  FORALLnew_facets {
+    if (newfacet->visitid == qh visit_id)
+      break;
+    qh_fprintf(qh ferr, 6094, "qhull error: f%d is not attached to the new facets\n",
+         newfacet->id);
+    errfacet= newfacet;
+  }
+  if (errfacet)
+    qh_errexit(qh_ERRqhull, errfacet, NULL);
+} /* checkconnect */
+
+/*-<a                             href="qh-merge.htm#TOC"
+  >-------------------------------</a><a name="checkzero">-</a>
+
+  qh_checkzero( testall )
+    check that facets are clearly convex for qh.DISTround with qh.MERGEexact
+
+    if testall,
+      test all facets for qh.MERGEexact post-merging
+    else
+      test qh.newfacet_list
+
+    if qh.MERGEexact,
+      allows coplanar ridges
+      skips convexity test while qh.ZEROall_ok
+
+  returns:
+    True if all facets !flipped, !dupridge, normal
+         if all horizon facets are simplicial
+         if all vertices are clearly below neighbor
+         if all opposite vertices of horizon are below
+    clears qh.ZEROall_ok if any problems or coplanar facets
+
+  notes:
+    uses qh.vertex_visit
+    horizon facets may define multiple new facets
+
+  design:
+    for all facets in qh.newfacet_list or qh.facet_list
+      check for flagged faults (flipped, etc.)
+    for all facets in qh.newfacet_list or qh.facet_list
+      for each neighbor of facet
+        skip horizon facets for qh.newfacet_list
+        test the opposite vertex
+      if qh.newfacet_list
+        test the other vertices in the facet's horizon facet
+*/
+boolT qh_checkzero(boolT testall) {
+  facetT *facet, *neighbor, **neighborp;
+  facetT *horizon, *facetlist;
+  int neighbor_i;
+  vertexT *vertex, **vertexp;
+  realT dist;
+
+  if (testall)
+    facetlist= qh facet_list;
+  else {
+    facetlist= qh newfacet_list;
+    FORALLfacet_(facetlist) {
+      horizon= SETfirstt_(facet->neighbors, facetT);
+      if (!horizon->simplicial)
+        goto LABELproblem;
+      if (facet->flipped || facet->dupridge || !facet->normal)
+        goto LABELproblem;
+    }
+    if (qh MERGEexact && qh ZEROall_ok) {
+      trace2((qh ferr, 2011, "qh_checkzero: skip convexity check until first pre-merge\n"));
+      return True;
+    }
+  }
+  FORALLfacet_(facetlist) {
+    qh vertex_visit++;
+    neighbor_i= 0;
+    horizon= NULL;
+    FOREACHneighbor_(facet) {
+      if (!neighbor_i && !testall) {
+        horizon= neighbor;
+        neighbor_i++;
+        continue; /* horizon facet tested in qh_findhorizon */
+      }
+      vertex= SETelemt_(facet->vertices, neighbor_i++, vertexT);
+      vertex->visitid= qh vertex_visit;
+      zzinc_(Zdistzero);
+      qh_distplane(vertex->point, neighbor, &dist);
+      if (dist >= -qh DISTround) {
+        qh ZEROall_ok= False;
+        if (!qh MERGEexact || testall || dist > qh DISTround)
+          goto LABELnonconvex;
+      }
+    }
+    if (!testall && horizon) {
+      FOREACHvertex_(horizon->vertices) {
+        if (vertex->visitid != qh vertex_visit) {
+          zzinc_(Zdistzero);
+          qh_distplane(vertex->point, facet, &dist);
+          if (dist >= -qh DISTround) {
+            qh ZEROall_ok= False;
+            if (!qh MERGEexact || dist > qh DISTround)
+              goto LABELnonconvex;
+          }
+          break;
+        }
+      }
+    }
+  }
+  trace2((qh ferr, 2012, "qh_checkzero: testall %d, facets are %s\n", testall,
+        (qh MERGEexact && !testall) ?
+           "not concave, flipped, or duplicate ridged" : "clearly convex"));
+  return True;
+
+ LABELproblem:
+  qh ZEROall_ok= False;
+  trace2((qh ferr, 2013, "qh_checkzero: facet f%d needs pre-merging\n",
+       facet->id));
+  return False;
+
+ LABELnonconvex:
+  trace2((qh ferr, 2014, "qh_checkzero: facet f%d and f%d are not clearly convex.  v%d dist %.2g\n",
+         facet->id, neighbor->id, vertex->id, dist));
+  return False;
+} /* checkzero */
+
+/*-<a                             href="qh-merge.htm#TOC"
+  >-------------------------------</a><a name="compareangle">-</a>
+
+  qh_compareangle( angle1, angle2 )
+    used by qsort() to order merges by angle
+*/
+int qh_compareangle(const void *p1, const void *p2) {
+  const mergeT *a= *((mergeT *const*)p1), *b= *((mergeT *const*)p2);
+
+  return((a->angle > b->angle) ? 1 : -1);
+} /* compareangle */
+
+/*-<a                             href="qh-merge.htm#TOC"
+  >-------------------------------</a><a name="comparemerge">-</a>
+
+  qh_comparemerge( merge1, merge2 )
+    used by qsort() to order merges
+*/
+int qh_comparemerge(const void *p1, const void *p2) {
+  const mergeT *a= *((mergeT *const*)p1), *b= *((mergeT *const*)p2);
+
+  return(a->type - b->type);
+} /* comparemerge */
+
+/*-<a                             href="qh-merge.htm#TOC"
+  >-------------------------------</a><a name="comparevisit">-</a>
+
+  qh_comparevisit( vertex1, vertex2 )
+    used by qsort() to order vertices by their visitid
+*/
+int qh_comparevisit(const void *p1, const void *p2) {
+  const vertexT *a= *((vertexT *const*)p1), *b= *((vertexT *const*)p2);
+
+  return(a->visitid - b->visitid);
+} /* comparevisit */
+
+/*-<a                             href="qh-merge.htm#TOC"
+  >-------------------------------</a><a name="copynonconvex">-</a>
+
+  qh_copynonconvex( atridge )
+    set non-convex flag on other ridges (if any) between same neighbors
+
+  notes:
+    may be faster if use smaller ridge set
+
+  design:
+    for each ridge of atridge's top facet
+      if ridge shares the same neighbor
+        set nonconvex flag
+*/
+void qh_copynonconvex(ridgeT *atridge) {
+  facetT *facet, *otherfacet;
+  ridgeT *ridge, **ridgep;
+
+  facet= atridge->top;
+  otherfacet= atridge->bottom;
+  FOREACHridge_(facet->ridges) {
+    if (otherfacet == otherfacet_(ridge, facet) && ridge != atridge) {
+      ridge->nonconvex= True;
+      trace4((qh ferr, 4020, "qh_copynonconvex: moved nonconvex flag from r%d to r%d\n",
+              atridge->id, ridge->id));
+      break;
+    }
+  }
+} /* copynonconvex */
+
+/*-<a                             href="qh-merge.htm#TOC"
+  >-------------------------------</a><a name="degen_redundant_facet">-</a>
+
+  qh_degen_redundant_facet( facet )
+    check facet for degen. or redundancy
+
+  notes:
+    bumps vertex_visit
+    called if a facet was redundant but no longer is (qh_merge_degenredundant)
+    qh_appendmergeset() only appends first reference to facet (i.e., redundant)
+
+  see:
+    qh_degen_redundant_neighbors()
+
+  design:
+    test for redundant neighbor
+    test for degenerate facet
+*/
+void qh_degen_redundant_facet(facetT *facet) {
+  vertexT *vertex, **vertexp;
+  facetT *neighbor, **neighborp;
+
+  trace4((qh ferr, 4021, "qh_degen_redundant_facet: test facet f%d for degen/redundant\n",
+          facet->id));
+  FOREACHneighbor_(facet) {
+    qh vertex_visit++;
+    FOREACHvertex_(neighbor->vertices)
+      vertex->visitid= qh vertex_visit;
+    FOREACHvertex_(facet->vertices) {
+      if (vertex->visitid != qh vertex_visit)
+        break;
+    }
+    if (!vertex) {
+      qh_appendmergeset(facet, neighbor, MRGredundant, NULL);
+      trace2((qh ferr, 2015, "qh_degen_redundant_facet: f%d is contained in f%d.  merge\n", facet->id, neighbor->id));
+      return;
+    }
+  }
+  if (qh_setsize(facet->neighbors) < qh hull_dim) {
+    qh_appendmergeset(facet, facet, MRGdegen, NULL);
+    trace2((qh ferr, 2016, "qh_degen_redundant_neighbors: f%d is degenerate.\n", facet->id));
+  }
+} /* degen_redundant_facet */
+
+
+/*-<a                             href="qh-merge.htm#TOC"
+  >-------------------------------</a><a name="degen_redundant_neighbors">-</a>
+
+  qh_degen_redundant_neighbors( facet, delfacet,  )
+    append degenerate and redundant neighbors to facet_mergeset
+    if delfacet,
+      only checks neighbors of both delfacet and facet
+    also checks current facet for degeneracy
+
+  notes:
+    bumps vertex_visit
+    called for each qh_mergefacet() and qh_mergecycle()
+    merge and statistics occur in merge_nonconvex
+    qh_appendmergeset() only appends first reference to facet (i.e., redundant)
+      it appends redundant facets after degenerate ones
+
+    a degenerate facet has fewer than hull_dim neighbors
+    a redundant facet's vertices is a subset of its neighbor's vertices
+    tests for redundant merges first (appendmergeset is nop for others)
+    in a merge, only needs to test neighbors of merged facet
+
+  see:
+    qh_merge_degenredundant() and qh_degen_redundant_facet()
+
+  design:
+    test for degenerate facet
+    test for redundant neighbor
+    test for degenerate neighbor
+*/
+void qh_degen_redundant_neighbors(facetT *facet, facetT *delfacet) {
+  vertexT *vertex, **vertexp;
+  facetT *neighbor, **neighborp;
+  int size;
+
+  trace4((qh ferr, 4022, "qh_degen_redundant_neighbors: test neighbors of f%d with delfacet f%d\n",
+          facet->id, getid_(delfacet)));
+  if ((size= qh_setsize(facet->neighbors)) < qh hull_dim) {
+    qh_appendmergeset(facet, facet, MRGdegen, NULL);
+    trace2((qh ferr, 2017, "qh_degen_redundant_neighbors: f%d is degenerate with %d neighbors.\n", facet->id, size));
+  }
+  if (!delfacet)
+    delfacet= facet;
+  qh vertex_visit++;
+  FOREACHvertex_(facet->vertices)
+    vertex->visitid= qh vertex_visit;
+  FOREACHneighbor_(delfacet) {
+    /* uses early out instead of checking vertex count */
+    if (neighbor == facet)
+      continue;
+    FOREACHvertex_(neighbor->vertices) {
+      if (vertex->visitid != qh vertex_visit)
+        break;
+    }
+    if (!vertex) {
+      qh_appendmergeset(neighbor, facet, MRGredundant, NULL);
+      trace2((qh ferr, 2018, "qh_degen_redundant_neighbors: f%d is contained in f%d.  merge\n", neighbor->id, facet->id));
+    }
+  }
+  FOREACHneighbor_(delfacet) {   /* redundant merges occur first */
+    if (neighbor == facet)
+      continue;
+    if ((size= qh_setsize(neighbor->neighbors)) < qh hull_dim) {
+      qh_appendmergeset(neighbor, neighbor, MRGdegen, NULL);
+      trace2((qh ferr, 2019, "qh_degen_redundant_neighbors: f%d is degenerate with %d neighbors.  Neighbor of f%d.\n", neighbor->id, size, facet->id));
+    }
+  }
+} /* degen_redundant_neighbors */
+
+
+/*-<a                             href="qh-merge.htm#TOC"
+  >-------------------------------</a><a name="find_newvertex">-</a>
+
+  qh_find_newvertex( oldvertex, vertices, ridges )
+    locate new vertex for renaming old vertex
+    vertices is a set of possible new vertices
+      vertices sorted by number of deleted ridges
+
+  returns:
+    newvertex or NULL
+      each ridge includes both vertex and oldvertex
+    vertices sorted by number of deleted ridges
+
+  notes:
+    modifies vertex->visitid
+    new vertex is in one of the ridges
+    renaming will not cause a duplicate ridge
+    renaming will minimize the number of deleted ridges
+    newvertex may not be adjacent in the dual (though unlikely)
+
+  design:
+    for each vertex in vertices
+      set vertex->visitid to number of references in ridges
+    remove unvisited vertices
+    set qh.vertex_visit above all possible values
+    sort vertices by number of references in ridges
+    add each ridge to qh.hash_table
+    for each vertex in vertices
+      look for a vertex that would not cause a duplicate ridge after a rename
+*/
+vertexT *qh_find_newvertex(vertexT *oldvertex, setT *vertices, setT *ridges) {
+  vertexT *vertex, **vertexp;
+  setT *newridges;
+  ridgeT *ridge, **ridgep;
+  int size, hashsize;
+  int hash;
+
+#ifndef qh_NOtrace
+  if (qh IStracing >= 4) {
+    qh_fprintf(qh ferr, 8063, "qh_find_newvertex: find new vertex for v%d from ",
+             oldvertex->id);
+    FOREACHvertex_(vertices)
+      qh_fprintf(qh ferr, 8064, "v%d ", vertex->id);
+    FOREACHridge_(ridges)
+      qh_fprintf(qh ferr, 8065, "r%d ", ridge->id);
+    qh_fprintf(qh ferr, 8066, "\n");
+  }
+#endif
+  FOREACHvertex_(vertices)
+    vertex->visitid= 0;
+  FOREACHridge_(ridges) {
+    FOREACHvertex_(ridge->vertices)
+      vertex->visitid++;
+  }
+  FOREACHvertex_(vertices) {
+    if (!vertex->visitid) {
+      qh_setdelnth(vertices, SETindex_(vertices,vertex));
+      vertexp--; /* repeat since deleted this vertex */
+    }
+  }
+  qh vertex_visit += (unsigned int)qh_setsize(ridges);
+  if (!qh_setsize(vertices)) {
+    trace4((qh ferr, 4023, "qh_find_newvertex: vertices not in ridges for v%d\n",
+            oldvertex->id));
+    return NULL;
+  }
+  qsort(SETaddr_(vertices, vertexT), (size_t)qh_setsize(vertices),
+                sizeof(vertexT *), qh_comparevisit);
+  /* can now use qh vertex_visit */
+  if (qh PRINTstatistics) {
+    size= qh_setsize(vertices);
+    zinc_(Zintersect);
+    zadd_(Zintersecttot, size);
+    zmax_(Zintersectmax, size);
+  }
+  hashsize= qh_newhashtable(qh_setsize(ridges));
+  FOREACHridge_(ridges)
+    qh_hashridge(qh hash_table, hashsize, ridge, oldvertex);
+  FOREACHvertex_(vertices) {
+    newridges= qh_vertexridges(vertex);
+    FOREACHridge_(newridges) {
+      if (qh_hashridge_find(qh hash_table, hashsize, ridge, vertex, oldvertex, &hash)) {
+        zinc_(Zdupridge);
+        break;
+      }
+    }
+    qh_settempfree(&newridges);
+    if (!ridge)
+      break;  /* found a rename */
+  }
+  if (vertex) {
+    /* counted in qh_renamevertex */
+    trace2((qh ferr, 2020, "qh_find_newvertex: found v%d for old v%d from %d vertices and %d ridges.\n",
+      vertex->id, oldvertex->id, qh_setsize(vertices), qh_setsize(ridges)));
+  }else {
+    zinc_(Zfindfail);
+    trace0((qh ferr, 14, "qh_find_newvertex: no vertex for renaming v%d(all duplicated ridges) during p%d\n",
+      oldvertex->id, qh furthest_id));
+  }
+  qh_setfree(&qh hash_table);
+  return vertex;
+} /* find_newvertex */
+
+/*-<a                             href="qh-merge.htm#TOC"
+  >-------------------------------</a><a name="findbest_test">-</a>
+
+  qh_findbest_test( testcentrum, facet, neighbor, bestfacet, dist, mindist, maxdist )
+    test neighbor of facet for qh_findbestneighbor()
+    if testcentrum,
+      tests centrum (assumes it is defined)
+    else
+      tests vertices
+
+  returns:
+    if a better facet (i.e., vertices/centrum of facet closer to neighbor)
+      updates bestfacet, dist, mindist, and maxdist
+*/
+void qh_findbest_test(boolT testcentrum, facetT *facet, facetT *neighbor,
+      facetT **bestfacet, realT *distp, realT *mindistp, realT *maxdistp) {
+  realT dist, mindist, maxdist;
+
+  if (testcentrum) {
+    zzinc_(Zbestdist);
+    qh_distplane(facet->center, neighbor, &dist);
+    dist *= qh hull_dim; /* estimate furthest vertex */
+    if (dist < 0) {
+      maxdist= 0;
+      mindist= dist;
+      dist= -dist;
+    }else {
+      mindist= 0;
+      maxdist= dist;
+    }
+  }else
+    dist= qh_getdistance(facet, neighbor, &mindist, &maxdist);
+  if (dist < *distp) {
+    *bestfacet= neighbor;
+    *mindistp= mindist;
+    *maxdistp= maxdist;
+    *distp= dist;
+  }
+} /* findbest_test */
+
+/*-<a                             href="qh-merge.htm#TOC"
+  >-------------------------------</a><a name="findbestneighbor">-</a>
+
+  qh_findbestneighbor( facet, dist, mindist, maxdist )
+    finds best neighbor (least dist) of a facet for merging
+
+  returns:
+    returns min and max distances and their max absolute value
+
+  notes:
+    error if qh_ASvoronoi
+    avoids merging old into new
+    assumes ridge->nonconvex only set on one ridge between a pair of facets
+    could use an early out predicate but not worth it
+
+  design:
+    if a large facet
+      will test centrum
+    else
+      will test vertices
+    if a large facet
+      test nonconvex neighbors for best merge
+    else
+      test all neighbors for the best merge
+    if testing centrum
+      get distance information
+*/
+facetT *qh_findbestneighbor(facetT *facet, realT *distp, realT *mindistp, realT *maxdistp) {
+  facetT *neighbor, **neighborp, *bestfacet= NULL;
+  ridgeT *ridge, **ridgep;
+  boolT nonconvex= True, testcentrum= False;
+  int size= qh_setsize(facet->vertices);
+
+  if(qh CENTERtype==qh_ASvoronoi){
+    qh_fprintf(qh ferr, 6272, "qhull error: cannot call qh_findbestneighor for f%d while qh.CENTERtype is qh_ASvoronoi\n", facet->id);
+    qh_errexit(qh_ERRqhull, facet, NULL);
+  }
+  *distp= REALmax;
+  if (size > qh_BESTcentrum2 * qh hull_dim + qh_BESTcentrum) {
+    testcentrum= True;
+    zinc_(Zbestcentrum);
+    if (!facet->center)
+       facet->center= qh_getcentrum(facet);
+  }
+  if (size > qh hull_dim + qh_BESTnonconvex) {
+    FOREACHridge_(facet->ridges) {
+      if (ridge->nonconvex) {
+        neighbor= otherfacet_(ridge, facet);
+        qh_findbest_test(testcentrum, facet, neighbor,
+                          &bestfacet, distp, mindistp, maxdistp);
+      }
+    }
+  }
+  if (!bestfacet) {
+    nonconvex= False;
+    FOREACHneighbor_(facet)
+      qh_findbest_test(testcentrum, facet, neighbor,
+                        &bestfacet, distp, mindistp, maxdistp);
+  }
+  if (!bestfacet) {
+    qh_fprintf(qh ferr, 6095, "qhull internal error (qh_findbestneighbor): no neighbors for f%d\n", facet->id);
+
+    qh_errexit(qh_ERRqhull, facet, NULL);
+  }
+  if (testcentrum)
+    qh_getdistance(facet, bestfacet, mindistp, maxdistp);
+  trace3((qh ferr, 3002, "qh_findbestneighbor: f%d is best neighbor for f%d testcentrum? %d nonconvex? %d dist %2.2g min %2.2g max %2.2g\n",
+     bestfacet->id, facet->id, testcentrum, nonconvex, *distp, *mindistp, *maxdistp));
+  return(bestfacet);
+} /* findbestneighbor */
+
+
+/*-<a                             href="qh-merge.htm#TOC"
+  >-------------------------------</a><a name="flippedmerges">-</a>
+
+  qh_flippedmerges( facetlist, wasmerge )
+    merge flipped facets into best neighbor
+    assumes qh.facet_mergeset at top of temporary stack
+
+  returns:
+    no flipped facets on facetlist
+    sets wasmerge if merge occurred
+    degen/redundant merges passed through
+
+  notes:
+    othermerges not needed since qh.facet_mergeset is empty before & after
+      keep it in case of change
+
+  design:
+    append flipped facets to qh.facetmergeset
+    for each flipped merge
+      find best neighbor
+      merge facet into neighbor
+      merge degenerate and redundant facets
+    remove flipped merges from qh.facet_mergeset
+*/
+void qh_flippedmerges(facetT *facetlist, boolT *wasmerge) {
+  facetT *facet, *neighbor, *facet1;
+  realT dist, mindist, maxdist;
+  mergeT *merge, **mergep;
+  setT *othermerges;
+  int nummerge=0;
+
+  trace4((qh ferr, 4024, "qh_flippedmerges: begin\n"));
+  FORALLfacet_(facetlist) {
+    if (facet->flipped && !facet->visible)
+      qh_appendmergeset(facet, facet, MRGflip, NULL);
+  }
+  othermerges= qh_settemppop(); /* was facet_mergeset */
+  qh facet_mergeset= qh_settemp(qh TEMPsize);
+  qh_settemppush(othermerges);
+  FOREACHmerge_(othermerges) {
+    facet1= merge->facet1;
+    if (merge->type != MRGflip || facet1->visible)
+      continue;
+    if (qh TRACEmerge-1 == zzval_(Ztotmerge))
+      qhmem.IStracing= qh IStracing= qh TRACElevel;
+    neighbor= qh_findbestneighbor(facet1, &dist, &mindist, &maxdist);
+    trace0((qh ferr, 15, "qh_flippedmerges: merge flipped f%d into f%d dist %2.2g during p%d\n",
+      facet1->id, neighbor->id, dist, qh furthest_id));
+    qh_mergefacet(facet1, neighbor, &mindist, &maxdist, !qh_MERGEapex);
+    nummerge++;
+    if (qh PRINTstatistics) {
+      zinc_(Zflipped);
+      wadd_(Wflippedtot, dist);
+      wmax_(Wflippedmax, dist);
+    }
+    qh_merge_degenredundant();
+  }
+  FOREACHmerge_(othermerges) {
+    if (merge->facet1->visible || merge->facet2->visible)
+      qh_memfree(merge, (int)sizeof(mergeT));
+    else
+      qh_setappend(&qh facet_mergeset, merge);
+  }
+  qh_settempfree(&othermerges);
+  if (nummerge)
+    *wasmerge= True;
+  trace1((qh ferr, 1010, "qh_flippedmerges: merged %d flipped facets into a good neighbor\n", nummerge));
+} /* flippedmerges */
+
+
+/*-<a                             href="qh-merge.htm#TOC"
+  >-------------------------------</a><a name="forcedmerges">-</a>
+
+  qh_forcedmerges( wasmerge )
+    merge duplicated ridges
+
+  returns:
+    removes all duplicate ridges on facet_mergeset
+    wasmerge set if merge
+    qh.facet_mergeset may include non-forced merges(none for now)
+    qh.degen_mergeset includes degen/redun merges
+
+  notes:
+    duplicate ridges occur when the horizon is pinched,
+        i.e. a subridge occurs in more than two horizon ridges.
+     could rename vertices that pinch the horizon
+    assumes qh_merge_degenredundant() has not be called
+    othermerges isn't needed since facet_mergeset is empty afterwards
+      keep it in case of change
+
+  design:
+    for each duplicate ridge
+      find current facets by chasing f.replace links
+      check for wide merge due to duplicate ridge
+      determine best direction for facet
+      merge one facet into the other
+      remove duplicate ridges from qh.facet_mergeset
+*/
+void qh_forcedmerges(boolT *wasmerge) {
+  facetT *facet1, *facet2;
+  mergeT *merge, **mergep;
+  realT dist1, dist2, mindist1, mindist2, maxdist1, maxdist2;
+  setT *othermerges;
+  int nummerge=0, numflip=0;
+
+  if (qh TRACEmerge-1 == zzval_(Ztotmerge))
+    qhmem.IStracing= qh IStracing= qh TRACElevel;
+  trace4((qh ferr, 4025, "qh_forcedmerges: begin\n"));
+  othermerges= qh_settemppop(); /* was facet_mergeset */
+  qh facet_mergeset= qh_settemp(qh TEMPsize);
+  qh_settemppush(othermerges);
+  FOREACHmerge_(othermerges) {
+    if (merge->type != MRGridge)
+        continue;
+    if (qh TRACEmerge-1 == zzval_(Ztotmerge))
+        qhmem.IStracing= qh IStracing= qh TRACElevel;
+    facet1= merge->facet1;
+    facet2= merge->facet2;
+    while (facet1->visible)      /* must exist, no qh_merge_degenredunant */
+      facet1= facet1->f.replace; /* previously merged facet */
+    while (facet2->visible)
+      facet2= facet2->f.replace; /* previously merged facet */
+    if (facet1 == facet2)
+      continue;
+    if (!qh_setin(facet2->neighbors, facet1)) {
+      qh_fprintf(qh ferr, 6096, "qhull internal error (qh_forcedmerges): f%d and f%d had a duplicate ridge but as f%d and f%d they are no longer neighbors\n",
+               merge->facet1->id, merge->facet2->id, facet1->id, facet2->id);
+      qh_errexit2(qh_ERRqhull, facet1, facet2);
+    }
+    dist1= qh_getdistance(facet1, facet2, &mindist1, &maxdist1);
+    dist2= qh_getdistance(facet2, facet1, &mindist2, &maxdist2);
+    qh_check_dupridge(facet1, dist1, facet2, dist2);
+    if (dist1 < dist2)
+      qh_mergefacet(facet1, facet2, &mindist1, &maxdist1, !qh_MERGEapex);
+    else {
+      qh_mergefacet(facet2, facet1, &mindist2, &maxdist2, !qh_MERGEapex);
+      dist1= dist2;
+      facet1= facet2;
+    }
+    if (facet1->flipped) {
+      zinc_(Zmergeflipdup);
+      numflip++;
+    }else
+      nummerge++;
+    if (qh PRINTstatistics) {
+      zinc_(Zduplicate);
+      wadd_(Wduplicatetot, dist1);
+      wmax_(Wduplicatemax, dist1);
+    }
+  }
+  FOREACHmerge_(othermerges) {
+    if (merge->type == MRGridge)
+      qh_memfree(merge, (int)sizeof(mergeT));
+    else
+      qh_setappend(&qh facet_mergeset, merge);
+  }
+  qh_settempfree(&othermerges);
+  if (nummerge)
+    *wasmerge= True;
+  trace1((qh ferr, 1011, "qh_forcedmerges: merged %d facets and %d flipped facets across duplicated ridges\n",
+                nummerge, numflip));
+} /* forcedmerges */
+
+
+/*-<a                             href="qh-merge.htm#TOC"
+  >-------------------------------</a><a name="getmergeset">-</a>
+
+  qh_getmergeset( facetlist )
+    determines nonconvex facets on facetlist
+    tests !tested ridges and nonconvex ridges of !tested facets
+
+  returns:
+    returns sorted qh.facet_mergeset of facet-neighbor pairs to be merged
+    all ridges tested
+
+  notes:
+    assumes no nonconvex ridges with both facets tested
+    uses facet->tested/ridge->tested to prevent duplicate tests
+    can not limit tests to modified ridges since the centrum changed
+    uses qh.visit_id
+
+  see:
+    qh_getmergeset_initial()
+
+  design:
+    for each facet on facetlist
+      for each ridge of facet
+        if untested ridge
+          test ridge for convexity
+          if non-convex
+            append ridge to qh.facet_mergeset
+    sort qh.facet_mergeset by angle
+*/
+void qh_getmergeset(facetT *facetlist) {
+  facetT *facet, *neighbor, **neighborp;
+  ridgeT *ridge, **ridgep;
+  int nummerges;
+
+  nummerges= qh_setsize(qh facet_mergeset);
+  trace4((qh ferr, 4026, "qh_getmergeset: started.\n"));
+  qh visit_id++;
+  FORALLfacet_(facetlist) {
+    if (facet->tested)
+      continue;
+    facet->visitid= qh visit_id;
+    facet->tested= True;  /* must be non-simplicial due to merge */
+    FOREACHneighbor_(facet)
+      neighbor->seen= False;
+    FOREACHridge_(facet->ridges) {
+      if (ridge->tested && !ridge->nonconvex)
+        continue;
+      /* if tested & nonconvex, need to append merge */
+      neighbor= otherfacet_(ridge, facet);
+      if (neighbor->seen) {
+        ridge->tested= True;
+        ridge->nonconvex= False;
+      }else if (neighbor->visitid != qh visit_id) {
+        ridge->tested= True;
+        ridge->nonconvex= False;
+        neighbor->seen= True;      /* only one ridge is marked nonconvex */
+        if (qh_test_appendmerge(facet, neighbor))
+          ridge->nonconvex= True;
+      }
+    }
+  }
+  nummerges= qh_setsize(qh facet_mergeset);
+  if (qh ANGLEmerge)
+    qsort(SETaddr_(qh facet_mergeset, mergeT), (size_t)nummerges, sizeof(mergeT *), qh_compareangle);
+  else
+    qsort(SETaddr_(qh facet_mergeset, mergeT), (size_t)nummerges, sizeof(mergeT *), qh_comparemerge);
+  if (qh POSTmerging) {
+    zadd_(Zmergesettot2, nummerges);
+  }else {
+    zadd_(Zmergesettot, nummerges);
+    zmax_(Zmergesetmax, nummerges);
+  }
+  trace2((qh ferr, 2021, "qh_getmergeset: %d merges found\n", nummerges));
+} /* getmergeset */
+
+
+/*-<a                             href="qh-merge.htm#TOC"
+  >-------------------------------</a><a name="getmergeset_initial">-</a>
+
+  qh_getmergeset_initial( facetlist )
+    determine initial qh.facet_mergeset for facets
+    tests all facet/neighbor pairs on facetlist
+
+  returns:
+    sorted qh.facet_mergeset with nonconvex ridges
+    sets facet->tested, ridge->tested, and ridge->nonconvex
+
+  notes:
+    uses visit_id, assumes ridge->nonconvex is False
+
+  see:
+    qh_getmergeset()
+
+  design:
+    for each facet on facetlist
+      for each untested neighbor of facet
+        test facet and neighbor for convexity
+        if non-convex
+          append merge to qh.facet_mergeset
+          mark one of the ridges as nonconvex
+    sort qh.facet_mergeset by angle
+*/
+void qh_getmergeset_initial(facetT *facetlist) {
+  facetT *facet, *neighbor, **neighborp;
+  ridgeT *ridge, **ridgep;
+  int nummerges;
+
+  qh visit_id++;
+  FORALLfacet_(facetlist) {
+    facet->visitid= qh visit_id;
+    facet->tested= True;
+    FOREACHneighbor_(facet) {
+      if (neighbor->visitid != qh visit_id) {
+        if (qh_test_appendmerge(facet, neighbor)) {
+          FOREACHridge_(neighbor->ridges) {
+            if (facet == otherfacet_(ridge, neighbor)) {
+              ridge->nonconvex= True;
+              break;    /* only one ridge is marked nonconvex */
+            }
+          }
+        }
+      }
+    }
+    FOREACHridge_(facet->ridges)
+      ridge->tested= True;
+  }
+  nummerges= qh_setsize(qh facet_mergeset);
+  if (qh ANGLEmerge)
+    qsort(SETaddr_(qh facet_mergeset, mergeT), (size_t)nummerges, sizeof(mergeT *), qh_compareangle);
+  else
+    qsort(SETaddr_(qh facet_mergeset, mergeT), (size_t)nummerges, sizeof(mergeT *), qh_comparemerge);
+  if (qh POSTmerging) {
+    zadd_(Zmergeinittot2, nummerges);
+  }else {
+    zadd_(Zmergeinittot, nummerges);
+    zmax_(Zmergeinitmax, nummerges);
+  }
+  trace2((qh ferr, 2022, "qh_getmergeset_initial: %d merges found\n", nummerges));
+} /* getmergeset_initial */
+
+
+/*-<a                             href="qh-merge.htm#TOC"
+  >-------------------------------</a><a name="hashridge">-</a>
+
+  qh_hashridge( hashtable, hashsize, ridge, oldvertex )
+    add ridge to hashtable without oldvertex
+
+  notes:
+    assumes hashtable is large enough
+
+  design:
+    determine hash value for ridge without oldvertex
+    find next empty slot for ridge
+*/
+void qh_hashridge(setT *hashtable, int hashsize, ridgeT *ridge, vertexT *oldvertex) {
+  int hash;
+  ridgeT *ridgeA;
+
+  hash= qh_gethash(hashsize, ridge->vertices, qh hull_dim-1, 0, oldvertex);
+  while (True) {
+    if (!(ridgeA= SETelemt_(hashtable, hash, ridgeT))) {
+      SETelem_(hashtable, hash)= ridge;
+      break;
+    }else if (ridgeA == ridge)
+      break;
+    if (++hash == hashsize)
+      hash= 0;
+  }
+} /* hashridge */
+
+
+/*-<a                             href="qh-merge.htm#TOC"
+  >-------------------------------</a><a name="hashridge_find">-</a>
+
+  qh_hashridge_find( hashtable, hashsize, ridge, vertex, oldvertex, hashslot )
+    returns matching ridge without oldvertex in hashtable
+      for ridge without vertex
+    if oldvertex is NULL
+      matches with any one skip
+
+  returns:
+    matching ridge or NULL
+    if no match,
+      if ridge already in   table
+        hashslot= -1
+      else
+        hashslot= next NULL index
+
+  notes:
+    assumes hashtable is large enough
+    can't match ridge to itself
+
+  design:
+    get hash value for ridge without vertex
+    for each hashslot
+      return match if ridge matches ridgeA without oldvertex
+*/
+ridgeT *qh_hashridge_find(setT *hashtable, int hashsize, ridgeT *ridge,
+              vertexT *vertex, vertexT *oldvertex, int *hashslot) {
+  int hash;
+  ridgeT *ridgeA;
+
+  *hashslot= 0;
+  zinc_(Zhashridge);
+  hash= qh_gethash(hashsize, ridge->vertices, qh hull_dim-1, 0, vertex);
+  while ((ridgeA= SETelemt_(hashtable, hash, ridgeT))) {
+    if (ridgeA == ridge)
+      *hashslot= -1;
+    else {
+      zinc_(Zhashridgetest);
+      if (qh_setequal_except(ridge->vertices, vertex, ridgeA->vertices, oldvertex))
+        return ridgeA;
+    }
+    if (++hash == hashsize)
+      hash= 0;
+  }
+  if (!*hashslot)
+    *hashslot= hash;
+  return NULL;
+} /* hashridge_find */
+
+
+/*-<a                             href="qh-merge.htm#TOC"
+  >-------------------------------</a><a name="makeridges">-</a>
+
+  qh_makeridges( facet )
+    creates explicit ridges between simplicial facets
+
+  returns:
+    facet with ridges and without qh_MERGEridge
+    ->simplicial is False
+
+  notes:
+    allows qh_MERGEridge flag
+    uses existing ridges
+    duplicate neighbors ok if ridges already exist (qh_mergecycle_ridges)
+
+  see:
+    qh_mergecycle_ridges()
+
+  design:
+    look for qh_MERGEridge neighbors
+    mark neighbors that already have ridges
+    for each unprocessed neighbor of facet
+      create a ridge for neighbor and facet
+    if any qh_MERGEridge neighbors
+      delete qh_MERGEridge flags (already handled by qh_mark_dupridges)
+*/
+void qh_makeridges(facetT *facet) {
+  facetT *neighbor, **neighborp;
+  ridgeT *ridge, **ridgep;
+  int neighbor_i, neighbor_n;
+  boolT toporient, mergeridge= False;
+
+  if (!facet->simplicial)
+    return;
+  trace4((qh ferr, 4027, "qh_makeridges: make ridges for f%d\n", facet->id));
+  facet->simplicial= False;
+  FOREACHneighbor_(facet) {
+    if (neighbor == qh_MERGEridge)
+      mergeridge= True;
+    else
+      neighbor->seen= False;
+  }
+  FOREACHridge_(facet->ridges)
+    otherfacet_(ridge, facet)->seen= True;
+  FOREACHneighbor_i_(facet) {
+    if (neighbor == qh_MERGEridge)
+      continue;  /* fixed by qh_mark_dupridges */
+    else if (!neighbor->seen) {  /* no current ridges */
+      ridge= qh_newridge();
+      ridge->vertices= qh_setnew_delnthsorted(facet->vertices, qh hull_dim,
+                                                          neighbor_i, 0);
+      toporient= facet->toporient ^ (neighbor_i & 0x1);
+      if (toporient) {
+        ridge->top= facet;
+        ridge->bottom= neighbor;
+      }else {
+        ridge->top= neighbor;
+        ridge->bottom= facet;
+      }
+#if 0 /* this also works */
+      flip= (facet->toporient ^ neighbor->toporient)^(skip1 & 0x1) ^ (skip2 & 0x1);
+      if (facet->toporient ^ (skip1 & 0x1) ^ flip) {
+        ridge->top= neighbor;
+        ridge->bottom= facet;
+      }else {
+        ridge->top= facet;
+        ridge->bottom= neighbor;
+      }
+#endif
+      qh_setappend(&(facet->ridges), ridge);
+      qh_setappend(&(neighbor->ridges), ridge);
+    }
+  }
+  if (mergeridge) {
+    while (qh_setdel(facet->neighbors, qh_MERGEridge))
+      ; /* delete each one */
+  }
+} /* makeridges */
+
+
+/*-<a                             href="qh-merge.htm#TOC"
+  >-------------------------------</a><a name="mark_dupridges">-</a>
+
+  qh_mark_dupridges( facetlist )
+    add duplicated ridges to qh.facet_mergeset
+    facet->dupridge is true
+
+  returns:
+    duplicate ridges on qh.facet_mergeset
+    ->mergeridge/->mergeridge2 set
+    duplicate ridges marked by qh_MERGEridge and both sides facet->dupridge
+    no MERGEridges in neighbor sets
+
+  notes:
+    duplicate ridges occur when the horizon is pinched,
+        i.e. a subridge occurs in more than two horizon ridges.
+    could rename vertices that pinch the horizon (thus removing subridge)
+    uses qh.visit_id
+
+  design:
+    for all facets on facetlist
+      if facet contains a duplicate ridge
+        for each neighbor of facet
+          if neighbor marked qh_MERGEridge (one side of the merge)
+            set facet->mergeridge
+          else
+            if neighbor contains a duplicate ridge
+            and the back link is qh_MERGEridge
+              append duplicate ridge to qh.facet_mergeset
+   for each duplicate ridge
+     make ridge sets in preparation for merging
+     remove qh_MERGEridge from neighbor set
+   for each duplicate ridge
+     restore the missing neighbor from the neighbor set that was qh_MERGEridge
+     add the missing ridge for this neighbor
+*/
+void qh_mark_dupridges(facetT *facetlist) {
+  facetT *facet, *neighbor, **neighborp;
+  int nummerge=0;
+  mergeT *merge, **mergep;
+
+
+  trace4((qh ferr, 4028, "qh_mark_dupridges: identify duplicate ridges\n"));
+  FORALLfacet_(facetlist) {
+    if (facet->dupridge) {
+      FOREACHneighbor_(facet) {
+        if (neighbor == qh_MERGEridge) {
+          facet->mergeridge= True;
+          continue;
+        }
+        if (neighbor->dupridge
+        && !qh_setin(neighbor->neighbors, facet)) { /* qh_MERGEridge */
+          qh_appendmergeset(facet, neighbor, MRGridge, NULL);
+          facet->mergeridge2= True;
+          facet->mergeridge= True;
+          nummerge++;
+        }
+      }
+    }
+  }
+  if (!nummerge)
+    return;
+  FORALLfacet_(facetlist) {            /* gets rid of qh_MERGEridge */
+    if (facet->mergeridge && !facet->mergeridge2)
+      qh_makeridges(facet);
+  }
+  FOREACHmerge_(qh facet_mergeset) {   /* restore the missing neighbors */
+    if (merge->type == MRGridge) {
+      qh_setappend(&merge->facet2->neighbors, merge->facet1);
+      qh_makeridges(merge->facet1);   /* and the missing ridges */
+    }
+  }
+  trace1((qh ferr, 1012, "qh_mark_dupridges: found %d duplicated ridges\n",
+                nummerge));
+} /* mark_dupridges */
+
+/*-<a                             href="qh-merge.htm#TOC"
+  >-------------------------------</a><a name="maydropneighbor">-</a>
+
+  qh_maydropneighbor( facet )
+    drop neighbor relationship if no ridge between facet and neighbor
+
+  returns:
+    neighbor sets updated
+    appends degenerate facets to qh.facet_mergeset
+
+  notes:
+    won't cause redundant facets since vertex inclusion is the same
+    may drop vertex and neighbor if no ridge
+    uses qh.visit_id
+
+  design:
+    visit all neighbors with ridges
+    for each unvisited neighbor of facet
+      delete neighbor and facet from the neighbor sets
+      if neighbor becomes degenerate
+        append neighbor to qh.degen_mergeset
+    if facet is degenerate
+      append facet to qh.degen_mergeset
+*/
+void qh_maydropneighbor(facetT *facet) {
+  ridgeT *ridge, **ridgep;
+  realT angledegen= qh_ANGLEdegen;
+  facetT *neighbor, **neighborp;
+
+  qh visit_id++;
+  trace4((qh ferr, 4029, "qh_maydropneighbor: test f%d for no ridges to a neighbor\n",
+          facet->id));
+  FOREACHridge_(facet->ridges) {
+    ridge->top->visitid= qh visit_id;
+    ridge->bottom->visitid= qh visit_id;
+  }
+  FOREACHneighbor_(facet) {
+    if (neighbor->visitid != qh visit_id) {
+      trace0((qh ferr, 17, "qh_maydropneighbor: facets f%d and f%d are no longer neighbors during p%d\n",
+            facet->id, neighbor->id, qh furthest_id));
+      zinc_(Zdropneighbor);
+      qh_setdel(facet->neighbors, neighbor);
+      neighborp--;  /* repeat, deleted a neighbor */
+      qh_setdel(neighbor->neighbors, facet);
+      if (qh_setsize(neighbor->neighbors) < qh hull_dim) {
+        zinc_(Zdropdegen);
+        qh_appendmergeset(neighbor, neighbor, MRGdegen, &angledegen);
+        trace2((qh ferr, 2023, "qh_maydropneighbors: f%d is degenerate.\n", neighbor->id));
+      }
+    }
+  }
+  if (qh_setsize(facet->neighbors) < qh hull_dim) {
+    zinc_(Zdropdegen);
+    qh_appendmergeset(facet, facet, MRGdegen, &angledegen);
+    trace2((qh ferr, 2024, "qh_maydropneighbors: f%d is degenerate.\n", facet->id));
+  }
+} /* maydropneighbor */
+
+
+/*-<a                             href="qh-merge.htm#TOC"
+  >-------------------------------</a><a name="merge_degenredundant">-</a>
+
+  qh_merge_degenredundant()
+    merge all degenerate and redundant facets
+    qh.degen_mergeset contains merges from qh_degen_redundant_neighbors()
+
+  returns:
+    number of merges performed
+    resets facet->degenerate/redundant
+    if deleted (visible) facet has no neighbors
+      sets ->f.replace to NULL
+
+  notes:
+    redundant merges happen before degenerate ones
+    merging and renaming vertices can result in degen/redundant facets
+
+  design:
+    for each merge on qh.degen_mergeset
+      if redundant merge
+        if non-redundant facet merged into redundant facet
+          recheck facet for redundancy
+        else
+          merge redundant facet into other facet
+*/
+int qh_merge_degenredundant(void) {
+  int size;
+  mergeT *merge;
+  facetT *bestneighbor, *facet1, *facet2;
+  realT dist, mindist, maxdist;
+  vertexT *vertex, **vertexp;
+  int nummerges= 0;
+  mergeType mergetype;
+
+  while ((merge= (mergeT*)qh_setdellast(qh degen_mergeset))) {
+    facet1= merge->facet1;
+    facet2= merge->facet2;
+    mergetype= merge->type;
+    qh_memfree(merge, (int)sizeof(mergeT));
+    if (facet1->visible)
+      continue;
+    facet1->degenerate= False;
+    facet1->redundant= False;
+    if (qh TRACEmerge-1 == zzval_(Ztotmerge))
+      qhmem.IStracing= qh IStracing= qh TRACElevel;
+    if (mergetype == MRGredundant) {
+      zinc_(Zneighbor);
+      while (facet2->visible) {
+        if (!facet2->f.replace) {
+          qh_fprintf(qh ferr, 6097, "qhull internal error (qh_merge_degenredunant): f%d redundant but f%d has no replacement\n",
+               facet1->id, facet2->id);
+          qh_errexit2(qh_ERRqhull, facet1, facet2);
+        }
+        facet2= facet2->f.replace;
+      }
+      if (facet1 == facet2) {
+        qh_degen_redundant_facet(facet1); /* in case of others */
+        continue;
+      }
+      trace2((qh ferr, 2025, "qh_merge_degenredundant: facet f%d is contained in f%d, will merge\n",
+            facet1->id, facet2->id));
+      qh_mergefacet(facet1, facet2, NULL, NULL, !qh_MERGEapex);
+      /* merge distance is already accounted for */
+      nummerges++;
+    }else {  /* mergetype == MRGdegen, other merges may have fixed */
+      if (!(size= qh_setsize(facet1->neighbors))) {
+        zinc_(Zdelfacetdup);
+        trace2((qh ferr, 2026, "qh_merge_degenredundant: facet f%d has no neighbors.  Deleted\n", facet1->id));
+        qh_willdelete(facet1, NULL);
+        FOREACHvertex_(facet1->vertices) {
+          qh_setdel(vertex->neighbors, facet1);
+          if (!SETfirst_(vertex->neighbors)) {
+            zinc_(Zdegenvertex);
+            trace2((qh ferr, 2027, "qh_merge_degenredundant: deleted v%d because f%d has no neighbors\n",
+                 vertex->id, facet1->id));
+            vertex->deleted= True;
+            qh_setappend(&qh del_vertices, vertex);
+          }
+        }
+        nummerges++;
+      }else if (size < qh hull_dim) {
+        bestneighbor= qh_findbestneighbor(facet1, &dist, &mindist, &maxdist);
+        trace2((qh ferr, 2028, "qh_merge_degenredundant: facet f%d has %d neighbors, merge into f%d dist %2.2g\n",
+              facet1->id, size, bestneighbor->id, dist));
+        qh_mergefacet(facet1, bestneighbor, &mindist, &maxdist, !qh_MERGEapex);
+        nummerges++;
+        if (qh PRINTstatistics) {
+          zinc_(Zdegen);
+          wadd_(Wdegentot, dist);
+          wmax_(Wdegenmax, dist);
+        }
+      } /* else, another merge fixed the degeneracy and redundancy tested */
+    }
+  }
+  return nummerges;
+} /* merge_degenredundant */
+
+/*-<a                             href="qh-merge.htm#TOC"
+  >-------------------------------</a><a name="merge_nonconvex">-</a>
+
+  qh_merge_nonconvex( facet1, facet2, mergetype )
+    remove non-convex ridge between facet1 into facet2
+    mergetype gives why the facet's are non-convex
+
+  returns:
+    merges one of the facets into the best neighbor
+
+  design:
+    if one of the facets is a new facet
+      prefer merging new facet into old facet
+    find best neighbors for both facets
+    merge the nearest facet into its best neighbor
+    update the statistics
+*/
+void qh_merge_nonconvex(facetT *facet1, facetT *facet2, mergeType mergetype) {
+  facetT *bestfacet, *bestneighbor, *neighbor;
+  realT dist, dist2, mindist, mindist2, maxdist, maxdist2;
+
+  if (qh TRACEmerge-1 == zzval_(Ztotmerge))
+    qhmem.IStracing= qh IStracing= qh TRACElevel;
+  trace3((qh ferr, 3003, "qh_merge_nonconvex: merge #%d for f%d and f%d type %d\n",
+      zzval_(Ztotmerge) + 1, facet1->id, facet2->id, mergetype));
+  /* concave or coplanar */
+  if (!facet1->newfacet) {
+    bestfacet= facet2;   /* avoid merging old facet if new is ok */
+    facet2= facet1;
+    facet1= bestfacet;
+  }else
+    bestfacet= facet1;
+  bestneighbor= qh_findbestneighbor(bestfacet, &dist, &mindist, &maxdist);
+  neighbor= qh_findbestneighbor(facet2, &dist2, &mindist2, &maxdist2);
+  if (dist < dist2) {
+    qh_mergefacet(bestfacet, bestneighbor, &mindist, &maxdist, !qh_MERGEapex);
+  }else if (qh AVOIDold && !facet2->newfacet
+  && ((mindist >= -qh MAXcoplanar && maxdist <= qh max_outside)
+       || dist * 1.5 < dist2)) {
+    zinc_(Zavoidold);
+    wadd_(Wavoidoldtot, dist);
+    wmax_(Wavoidoldmax, dist);
+    trace2((qh ferr, 2029, "qh_merge_nonconvex: avoid merging old facet f%d dist %2.2g.  Use f%d dist %2.2g instead\n",
+           facet2->id, dist2, facet1->id, dist2));
+    qh_mergefacet(bestfacet, bestneighbor, &mindist, &maxdist, !qh_MERGEapex);
+  }else {
+    qh_mergefacet(facet2, neighbor, &mindist2, &maxdist2, !qh_MERGEapex);
+    dist= dist2;
+  }
+  if (qh PRINTstatistics) {
+    if (mergetype == MRGanglecoplanar) {
+      zinc_(Zacoplanar);
+      wadd_(Wacoplanartot, dist);
+      wmax_(Wacoplanarmax, dist);
+    }else if (mergetype == MRGconcave) {
+      zinc_(Zconcave);
+      wadd_(Wconcavetot, dist);
+      wmax_(Wconcavemax, dist);
+    }else { /* MRGcoplanar */
+      zinc_(Zcoplanar);
+      wadd_(Wcoplanartot, dist);
+      wmax_(Wcoplanarmax, dist);
+    }
+  }
+} /* merge_nonconvex */
+
+/*-<a                             href="qh-merge.htm#TOC"
+  >-------------------------------</a><a name="mergecycle">-</a>
+
+  qh_mergecycle( samecycle, newfacet )
+    merge a cycle of facets starting at samecycle into a newfacet
+    newfacet is a horizon facet with ->normal
+    samecycle facets are simplicial from an apex
+
+  returns:
+    initializes vertex neighbors on first merge
+    samecycle deleted (placed on qh.visible_list)
+    newfacet at end of qh.facet_list
+    deleted vertices on qh.del_vertices
+
+  see:
+    qh_mergefacet()
+    called by qh_mergecycle_all() for multiple, same cycle facets
+
+  design:
+    make vertex neighbors if necessary
+    make ridges for newfacet
+    merge neighbor sets of samecycle into newfacet
+    merge ridges of samecycle into newfacet
+    merge vertex neighbors of samecycle into newfacet
+    make apex of samecycle the apex of newfacet
+    if newfacet wasn't a new facet
+      add its vertices to qh.newvertex_list
+    delete samecycle facets a make newfacet a newfacet
+*/
+void qh_mergecycle(facetT *samecycle, facetT *newfacet) {
+  int traceonce= False, tracerestore= 0;
+  vertexT *apex;
+#ifndef qh_NOtrace
+  facetT *same;
+#endif
+
+  if (newfacet->tricoplanar) {
+    if (!qh TRInormals) {
+      qh_fprintf(qh ferr, 6224, "Qhull internal error (qh_mergecycle): does not work for tricoplanar facets.  Use option 'Q11'\n");
+      qh_errexit(qh_ERRqhull, newfacet, NULL);
+    }
+    newfacet->tricoplanar= False;
+    newfacet->keepcentrum= False;
+  }
+  if (!qh VERTEXneighbors)
+    qh_vertexneighbors();
+  zzinc_(Ztotmerge);
+  if (qh REPORTfreq2 && qh POSTmerging) {
+    if (zzval_(Ztotmerge) > qh mergereport + qh REPORTfreq2)
+      qh_tracemerging();
+  }
+#ifndef qh_NOtrace
+  if (qh TRACEmerge == zzval_(Ztotmerge))
+    qhmem.IStracing= qh IStracing= qh TRACElevel;
+  trace2((qh ferr, 2030, "qh_mergecycle: merge #%d for facets from cycle f%d into coplanar horizon f%d\n",
+        zzval_(Ztotmerge), samecycle->id, newfacet->id));
+  if (newfacet == qh tracefacet) {
+    tracerestore= qh IStracing;
+    qh IStracing= 4;
+    qh_fprintf(qh ferr, 8068, "qh_mergecycle: ========= trace merge %d of samecycle %d into trace f%d, furthest is p%d\n",
+               zzval_(Ztotmerge), samecycle->id, newfacet->id,  qh furthest_id);
+    traceonce= True;
+  }
+  if (qh IStracing >=4) {
+    qh_fprintf(qh ferr, 8069, "  same cycle:");
+    FORALLsame_cycle_(samecycle)
+      qh_fprintf(qh ferr, 8070, " f%d", same->id);
+    qh_fprintf(qh ferr, 8071, "\n");
+  }
+  if (qh IStracing >=4)
+    qh_errprint("MERGING CYCLE", samecycle, newfacet, NULL, NULL);
+#endif /* !qh_NOtrace */
+  apex= SETfirstt_(samecycle->vertices, vertexT);
+  qh_makeridges(newfacet);
+  qh_mergecycle_neighbors(samecycle, newfacet);
+  qh_mergecycle_ridges(samecycle, newfacet);
+  qh_mergecycle_vneighbors(samecycle, newfacet);
+  if (SETfirstt_(newfacet->vertices, vertexT) != apex)
+    qh_setaddnth(&newfacet->vertices, 0, apex);  /* apex has last id */
+  if (!newfacet->newfacet)
+    qh_newvertices(newfacet->vertices);
+  qh_mergecycle_facets(samecycle, newfacet);
+  qh_tracemerge(samecycle, newfacet);
+  /* check for degen_redundant_neighbors after qh_forcedmerges() */
+  if (traceonce) {
+    qh_fprintf(qh ferr, 8072, "qh_mergecycle: end of trace facet\n");
+    qh IStracing= tracerestore;
+  }
+} /* mergecycle */
+
+/*-<a                             href="qh-merge.htm#TOC"
+  >-------------------------------</a><a name="mergecycle_all">-</a>
+
+  qh_mergecycle_all( facetlist, wasmerge )
+    merge all samecycles of coplanar facets into horizon
+    don't merge facets with ->mergeridge (these already have ->normal)
+    all facets are simplicial from apex
+    all facet->cycledone == False
+
+  returns:
+    all newfacets merged into coplanar horizon facets
+    deleted vertices on  qh.del_vertices
+    sets wasmerge if any merge
+
+  see:
+    calls qh_mergecycle for multiple, same cycle facets
+
+  design:
+    for each facet on facetlist
+      skip facets with duplicate ridges and normals
+      check that facet is in a samecycle (->mergehorizon)
+      if facet only member of samecycle
+        sets vertex->delridge for all vertices except apex
+        merge facet into horizon
+      else
+        mark all facets in samecycle
+        remove facets with duplicate ridges from samecycle
+        merge samecycle into horizon (deletes facets from facetlist)
+*/
+void qh_mergecycle_all(facetT *facetlist, boolT *wasmerge) {
+  facetT *facet, *same, *prev, *horizon;
+  facetT *samecycle= NULL, *nextfacet, *nextsame;
+  vertexT *apex, *vertex, **vertexp;
+  int cycles=0, total=0, facets, nummerge;
+
+  trace2((qh ferr, 2031, "qh_mergecycle_all: begin\n"));
+  for (facet= facetlist; facet && (nextfacet= facet->next); facet= nextfacet) {
+    if (facet->normal)
+      continue;
+    if (!facet->mergehorizon) {
+      qh_fprintf(qh ferr, 6225, "Qhull internal error (qh_mergecycle_all): f%d without normal\n", facet->id);
+      qh_errexit(qh_ERRqhull, facet, NULL);
+    }
+    horizon= SETfirstt_(facet->neighbors, facetT);
+    if (facet->f.samecycle == facet) {
+      zinc_(Zonehorizon);
+      /* merge distance done in qh_findhorizon */
+      apex= SETfirstt_(facet->vertices, vertexT);
+      FOREACHvertex_(facet->vertices) {
+        if (vertex != apex)
+          vertex->delridge= True;
+      }
+      horizon->f.newcycle= NULL;
+      qh_mergefacet(facet, horizon, NULL, NULL, qh_MERGEapex);
+    }else {
+      samecycle= facet;
+      facets= 0;
+      prev= facet;
+      for (same= facet->f.samecycle; same;  /* FORALLsame_cycle_(facet) */
+           same= (same == facet ? NULL :nextsame)) { /* ends at facet */
+        nextsame= same->f.samecycle;
+        if (same->cycledone || same->visible)
+          qh_infiniteloop(same);
+        same->cycledone= True;
+        if (same->normal) {
+          prev->f.samecycle= same->f.samecycle; /* unlink ->mergeridge */
+          same->f.samecycle= NULL;
+        }else {
+          prev= same;
+          facets++;
+        }
+      }
+      while (nextfacet && nextfacet->cycledone)  /* will delete samecycle */
+        nextfacet= nextfacet->next;
+      horizon->f.newcycle= NULL;
+      qh_mergecycle(samecycle, horizon);
+      nummerge= horizon->nummerge + facets;
+      if (nummerge > qh_MAXnummerge)
+        horizon->nummerge= qh_MAXnummerge;
+      else
+        horizon->nummerge= (short unsigned int)nummerge;
+      zzinc_(Zcyclehorizon);
+      total += facets;
+      zzadd_(Zcyclefacettot, facets);
+      zmax_(Zcyclefacetmax, facets);
+    }
+    cycles++;
+  }
+  if (cycles)
+    *wasmerge= True;
+  trace1((qh ferr, 1013, "qh_mergecycle_all: merged %d same cycles or facets into coplanar horizons\n", cycles));
+} /* mergecycle_all */
+
+/*-<a                             href="qh-merge.htm#TOC"
+  >-------------------------------</a><a name="mergecycle_facets">-</a>
+
+  qh_mergecycle_facets( samecycle, newfacet )
+    finish merge of samecycle into newfacet
+
+  returns:
+    samecycle prepended to visible_list for later deletion and partitioning
+      each facet->f.replace == newfacet
+
+    newfacet moved to end of qh.facet_list
+      makes newfacet a newfacet (get's facet1->id if it was old)
+      sets newfacet->newmerge
+      clears newfacet->center (unless merging into a large facet)
+      clears newfacet->tested and ridge->tested for facet1
+
+    adds neighboring facets to facet_mergeset if redundant or degenerate
+
+  design:
+    make newfacet a new facet and set its flags
+    move samecycle facets to qh.visible_list for later deletion
+    unless newfacet is large
+      remove its centrum
+*/
+void qh_mergecycle_facets(facetT *samecycle, facetT *newfacet) {
+  facetT *same, *next;
+
+  trace4((qh ferr, 4030, "qh_mergecycle_facets: make newfacet new and samecycle deleted\n"));
+  qh_removefacet(newfacet);  /* append as a newfacet to end of qh facet_list */
+  qh_appendfacet(newfacet);
+  newfacet->newfacet= True;
+  newfacet->simplicial= False;
+  newfacet->newmerge= True;
+
+  for (same= samecycle->f.samecycle; same; same= (same == samecycle ?  NULL : next)) {
+    next= same->f.samecycle;  /* reused by willdelete */
+    qh_willdelete(same, newfacet);
+  }
+  if (newfacet->center
+      && qh_setsize(newfacet->vertices) <= qh hull_dim + qh_MAXnewcentrum) {
+    qh_memfree(newfacet->center, qh normal_size);
+    newfacet->center= NULL;
+  }
+  trace3((qh ferr, 3004, "qh_mergecycle_facets: merged facets from cycle f%d into f%d\n",
+             samecycle->id, newfacet->id));
+} /* mergecycle_facets */
+
+/*-<a                             href="qh-merge.htm#TOC"
+  >-------------------------------</a><a name="mergecycle_neighbors">-</a>
+
+  qh_mergecycle_neighbors( samecycle, newfacet )
+    add neighbors for samecycle facets to newfacet
+
+  returns:
+    newfacet with updated neighbors and vice-versa
+    newfacet has ridges
+    all neighbors of newfacet marked with qh.visit_id
+    samecycle facets marked with qh.visit_id-1
+    ridges updated for simplicial neighbors of samecycle with a ridge
+
+  notes:
+    assumes newfacet not in samecycle
+    usually, samecycle facets are new, simplicial facets without internal ridges
+      not so if horizon facet is coplanar to two different samecycles
+
+  see:
+    qh_mergeneighbors()
+
+  design:
+    check samecycle
+    delete neighbors from newfacet that are also in samecycle
+    for each neighbor of a facet in samecycle
+      if neighbor is simplicial
+        if first visit
+          move the neighbor relation to newfacet
+          update facet links for its ridges
+        else
+          make ridges for neighbor
+          remove samecycle reference
+      else
+        update neighbor sets
+*/
+void qh_mergecycle_neighbors(facetT *samecycle, facetT *newfacet) {
+  facetT *same, *neighbor, **neighborp;
+  int delneighbors= 0, newneighbors= 0;
+  unsigned int samevisitid;
+  ridgeT *ridge, **ridgep;
+
+  samevisitid= ++qh visit_id;
+  FORALLsame_cycle_(samecycle) {
+    if (same->visitid == samevisitid || same->visible)
+      qh_infiniteloop(samecycle);
+    same->visitid= samevisitid;
+  }
+  newfacet->visitid= ++qh visit_id;
+  trace4((qh ferr, 4031, "qh_mergecycle_neighbors: delete shared neighbors from newfacet\n"));
+  FOREACHneighbor_(newfacet) {
+    if (neighbor->visitid == samevisitid) {
+      SETref_(neighbor)= NULL;  /* samecycle neighbors deleted */
+      delneighbors++;
+    }else
+      neighbor->visitid= qh visit_id;
+  }
+  qh_setcompact(newfacet->neighbors);
+
+  trace4((qh ferr, 4032, "qh_mergecycle_neighbors: update neighbors\n"));
+  FORALLsame_cycle_(samecycle) {
+    FOREACHneighbor_(same) {
+      if (neighbor->visitid == samevisitid)
+        continue;
+      if (neighbor->simplicial) {
+        if (neighbor->visitid != qh visit_id) {
+          qh_setappend(&newfacet->neighbors, neighbor);
+          qh_setreplace(neighbor->neighbors, same, newfacet);
+          newneighbors++;
+          neighbor->visitid= qh visit_id;
+          FOREACHridge_(neighbor->ridges) { /* update ridge in case of qh_makeridges */
+            if (ridge->top == same) {
+              ridge->top= newfacet;
+              break;
+            }else if (ridge->bottom == same) {
+              ridge->bottom= newfacet;
+              break;
+            }
+          }
+        }else {
+          qh_makeridges(neighbor);
+          qh_setdel(neighbor->neighbors, same);
+          /* same can't be horizon facet for neighbor */
+        }
+      }else { /* non-simplicial neighbor */
+        qh_setdel(neighbor->neighbors, same);
+        if (neighbor->visitid != qh visit_id) {
+          qh_setappend(&neighbor->neighbors, newfacet);
+          qh_setappend(&newfacet->neighbors, neighbor);
+          neighbor->visitid= qh visit_id;
+          newneighbors++;
+        }
+      }
+    }
+  }
+  trace2((qh ferr, 2032, "qh_mergecycle_neighbors: deleted %d neighbors and added %d\n",
+             delneighbors, newneighbors));
+} /* mergecycle_neighbors */
+
+/*-<a                             href="qh-merge.htm#TOC"
+  >-------------------------------</a><a name="mergecycle_ridges">-</a>
+
+  qh_mergecycle_ridges( samecycle, newfacet )
+    add ridges/neighbors for facets in samecycle to newfacet
+    all new/old neighbors of newfacet marked with qh.visit_id
+    facets in samecycle marked with qh.visit_id-1
+    newfacet marked with qh.visit_id
+
+  returns:
+    newfacet has merged ridges
+
+  notes:
+    ridge already updated for simplicial neighbors of samecycle with a ridge
+
+  see:
+    qh_mergeridges()
+    qh_makeridges()
+
+  design:
+    remove ridges between newfacet and samecycle
+    for each facet in samecycle
+      for each ridge in facet
+        update facet pointers in ridge
+        skip ridges processed in qh_mergecycle_neighors
+        free ridges between newfacet and samecycle
+        free ridges between facets of samecycle (on 2nd visit)
+        append remaining ridges to newfacet
+      if simpilicial facet
+        for each neighbor of facet
+          if simplicial facet
+          and not samecycle facet or newfacet
+            make ridge between neighbor and newfacet
+*/
+void qh_mergecycle_ridges(facetT *samecycle, facetT *newfacet) {
+  facetT *same, *neighbor= NULL;
+  int numold=0, numnew=0;
+  int neighbor_i, neighbor_n;
+  unsigned int samevisitid;
+  ridgeT *ridge, **ridgep;
+  boolT toporient;
+  void **freelistp; /* used if !qh_NOmem by qh_memfree_() */
+
+  trace4((qh ferr, 4033, "qh_mergecycle_ridges: delete shared ridges from newfacet\n"));
+  samevisitid= qh visit_id -1;
+  FOREACHridge_(newfacet->ridges) {
+    neighbor= otherfacet_(ridge, newfacet);
+    if (neighbor->visitid == samevisitid)
+      SETref_(ridge)= NULL; /* ridge free'd below */
+  }
+  qh_setcompact(newfacet->ridges);
+
+  trace4((qh ferr, 4034, "qh_mergecycle_ridges: add ridges to newfacet\n"));
+  FORALLsame_cycle_(samecycle) {
+    FOREACHridge_(same->ridges) {
+      if (ridge->top == same) {
+        ridge->top= newfacet;
+        neighbor= ridge->bottom;
+      }else if (ridge->bottom == same) {
+        ridge->bottom= newfacet;
+        neighbor= ridge->top;
+      }else if (ridge->top == newfacet || ridge->bottom == newfacet) {
+        qh_setappend(&newfacet->ridges, ridge);
+        numold++;  /* already set by qh_mergecycle_neighbors */
+        continue;
+      }else {
+        qh_fprintf(qh ferr, 6098, "qhull internal error (qh_mergecycle_ridges): bad ridge r%d\n", ridge->id);
+        qh_errexit(qh_ERRqhull, NULL, ridge);
+      }
+      if (neighbor == newfacet) {
+        qh_setfree(&(ridge->vertices));
+        qh_memfree_(ridge, (int)sizeof(ridgeT), freelistp);
+        numold++;
+      }else if (neighbor->visitid == samevisitid) {
+        qh_setdel(neighbor->ridges, ridge);
+        qh_setfree(&(ridge->vertices));
+        qh_memfree_(ridge, (int)sizeof(ridgeT), freelistp);
+        numold++;
+      }else {
+        qh_setappend(&newfacet->ridges, ridge);
+        numold++;
+      }
+    }
+    if (same->ridges)
+      qh_settruncate(same->ridges, 0);
+    if (!same->simplicial)
+      continue;
+    FOREACHneighbor_i_(same) {       /* note: !newfact->simplicial */
+      if (neighbor->visitid != samevisitid && neighbor->simplicial) {
+        ridge= qh_newridge();
+        ridge->vertices= qh_setnew_delnthsorted(same->vertices, qh hull_dim,
+                                                          neighbor_i, 0);
+        toporient= same->toporient ^ (neighbor_i & 0x1);
+        if (toporient) {
+          ridge->top= newfacet;
+          ridge->bottom= neighbor;
+        }else {
+          ridge->top= neighbor;
+          ridge->bottom= newfacet;
+        }
+        qh_setappend(&(newfacet->ridges), ridge);
+        qh_setappend(&(neighbor->ridges), ridge);
+        numnew++;
+      }
+    }
+  }
+
+  trace2((qh ferr, 2033, "qh_mergecycle_ridges: found %d old ridges and %d new ones\n",
+             numold, numnew));
+} /* mergecycle_ridges */
+
+/*-<a                             href="qh-merge.htm#TOC"
+  >-------------------------------</a><a name="mergecycle_vneighbors">-</a>
+
+  qh_mergecycle_vneighbors( samecycle, newfacet )
+    create vertex neighbors for newfacet from vertices of facets in samecycle
+    samecycle marked with visitid == qh.visit_id - 1
+
+  returns:
+    newfacet vertices with updated neighbors
+    marks newfacet with qh.visit_id-1
+    deletes vertices that are merged away
+    sets delridge on all vertices (faster here than in mergecycle_ridges)
+
+  see:
+    qh_mergevertex_neighbors()
+
+  design:
+    for each vertex of samecycle facet
+      set vertex->delridge
+      delete samecycle facets from vertex neighbors
+      append newfacet to vertex neighbors
+      if vertex only in newfacet
+        delete it from newfacet
+        add it to qh.del_vertices for later deletion
+*/
+void qh_mergecycle_vneighbors(facetT *samecycle, facetT *newfacet) {
+  facetT *neighbor, **neighborp;
+  unsigned int mergeid;
+  vertexT *vertex, **vertexp, *apex;
+  setT *vertices;
+
+  trace4((qh ferr, 4035, "qh_mergecycle_vneighbors: update vertex neighbors for newfacet\n"));
+  mergeid= qh visit_id - 1;
+  newfacet->visitid= mergeid;
+  vertices= qh_basevertices(samecycle); /* temp */
+  apex= SETfirstt_(samecycle->vertices, vertexT);
+  qh_setappend(&vertices, apex);
+  FOREACHvertex_(vertices) {
+    vertex->delridge= True;
+    FOREACHneighbor_(vertex) {
+      if (neighbor->visitid == mergeid)
+        SETref_(neighbor)= NULL;
+    }
+    qh_setcompact(vertex->neighbors);
+    qh_setappend(&vertex->neighbors, newfacet);
+    if (!SETsecond_(vertex->neighbors)) {
+      zinc_(Zcyclevertex);
+      trace2((qh ferr, 2034, "qh_mergecycle_vneighbors: deleted v%d when merging cycle f%d into f%d\n",
+        vertex->id, samecycle->id, newfacet->id));
+      qh_setdelsorted(newfacet->vertices, vertex);
+      vertex->deleted= True;
+      qh_setappend(&qh del_vertices, vertex);
+    }
+  }
+  qh_settempfree(&vertices);
+  trace3((qh ferr, 3005, "qh_mergecycle_vneighbors: merged vertices from cycle f%d into f%d\n",
+             samecycle->id, newfacet->id));
+} /* mergecycle_vneighbors */
+
+/*-<a                             href="qh-merge.htm#TOC"
+  >-------------------------------</a><a name="mergefacet">-</a>
+
+  qh_mergefacet( facet1, facet2, mindist, maxdist, mergeapex )
+    merges facet1 into facet2
+    mergeapex==qh_MERGEapex if merging new facet into coplanar horizon
+
+  returns:
+    qh.max_outside and qh.min_vertex updated
+    initializes vertex neighbors on first merge
+
+  returns:
+    facet2 contains facet1's vertices, neighbors, and ridges
+      facet2 moved to end of qh.facet_list
+      makes facet2 a newfacet
+      sets facet2->newmerge set
+      clears facet2->center (unless merging into a large facet)
+      clears facet2->tested and ridge->tested for facet1
+
+    facet1 prepended to visible_list for later deletion and partitioning
+      facet1->f.replace == facet2
+
+    adds neighboring facets to facet_mergeset if redundant or degenerate
+
+  notes:
+    mindist/maxdist may be NULL (only if both NULL)
+    traces merge if fmax_(maxdist,-mindist) > TRACEdist
+
+  see:
+    qh_mergecycle()
+
+  design:
+    trace merge and check for degenerate simplex
+    make ridges for both facets
+    update qh.max_outside, qh.max_vertex, qh.min_vertex
+    update facet2->maxoutside and keepcentrum
+    update facet2->nummerge
+    update tested flags for facet2
+    if facet1 is simplicial
+      merge facet1 into facet2
+    else
+      merge facet1's neighbors into facet2
+      merge facet1's ridges into facet2
+      merge facet1's vertices into facet2
+      merge facet1's vertex neighbors into facet2
+      add facet2's vertices to qh.new_vertexlist
+      unless qh_MERGEapex
+        test facet2 for degenerate or redundant neighbors
+      move facet1 to qh.visible_list for later deletion
+      move facet2 to end of qh.newfacet_list
+*/
+void qh_mergefacet(facetT *facet1, facetT *facet2, realT *mindist, realT *maxdist, boolT mergeapex) {
+  boolT traceonce= False;
+  vertexT *vertex, **vertexp;
+  int tracerestore=0, nummerge;
+
+  if (facet1->tricoplanar || facet2->tricoplanar) {
+    if (!qh TRInormals) {
+      qh_fprintf(qh ferr, 6226, "Qhull internal error (qh_mergefacet): does not work for tricoplanar facets.  Use option 'Q11'\n");
+      qh_errexit2(qh_ERRqhull, facet1, facet2);
+    }
+    if (facet2->tricoplanar) {
+      facet2->tricoplanar= False;
+      facet2->keepcentrum= False;
+    }
+  }
+  zzinc_(Ztotmerge);
+  if (qh REPORTfreq2 && qh POSTmerging) {
+    if (zzval_(Ztotmerge) > qh mergereport + qh REPORTfreq2)
+      qh_tracemerging();
+  }
+#ifndef qh_NOtrace
+  if (qh build_cnt >= qh RERUN) {
+    if (mindist && (-*mindist > qh TRACEdist || *maxdist > qh TRACEdist)) {
+      tracerestore= 0;
+      qh IStracing= qh TRACElevel;
+      traceonce= True;
+      qh_fprintf(qh ferr, 8075, "qh_mergefacet: ========= trace wide merge #%d(%2.2g) for f%d into f%d, last point was p%d\n", zzval_(Ztotmerge),
+             fmax_(-*mindist, *maxdist), facet1->id, facet2->id, qh furthest_id);
+    }else if (facet1 == qh tracefacet || facet2 == qh tracefacet) {
+      tracerestore= qh IStracing;
+      qh IStracing= 4;
+      traceonce= True;
+      qh_fprintf(qh ferr, 8076, "qh_mergefacet: ========= trace merge #%d involving f%d, furthest is p%d\n",
+                 zzval_(Ztotmerge), qh tracefacet_id,  qh furthest_id);
+    }
+  }
+  if (qh IStracing >= 2) {
+    realT mergemin= -2;
+    realT mergemax= -2;
+
+    if (mindist) {
+      mergemin= *mindist;
+      mergemax= *maxdist;
+    }
+    qh_fprintf(qh ferr, 8077, "qh_mergefacet: #%d merge f%d into f%d, mindist= %2.2g, maxdist= %2.2g\n",
+    zzval_(Ztotmerge), facet1->id, facet2->id, mergemin, mergemax);
+  }
+#endif /* !qh_NOtrace */
+  if (facet1 == facet2 || facet1->visible || facet2->visible) {
+    qh_fprintf(qh ferr, 6099, "qhull internal error (qh_mergefacet): either f%d and f%d are the same or one is a visible facet\n",
+             facet1->id, facet2->id);
+    qh_errexit2(qh_ERRqhull, facet1, facet2);
+  }
+  if (qh num_facets - qh num_visible <= qh hull_dim + 1) {
+    qh_fprintf(qh ferr, 6227, "\n\
+qhull precision error: Only %d facets remain.  Can not merge another\n\
+pair.  The input is too degenerate or the convexity constraints are\n\
+too strong.\n", qh hull_dim+1);
+    if (qh hull_dim >= 5 && !qh MERGEexact)
+      qh_fprintf(qh ferr, 8079, "Option 'Qx' may avoid this problem.\n");
+    qh_errexit(qh_ERRprec, NULL, NULL);
+  }
+  if (!qh VERTEXneighbors)
+    qh_vertexneighbors();
+  qh_makeridges(facet1);
+  qh_makeridges(facet2);
+  if (qh IStracing >=4)
+    qh_errprint("MERGING", facet1, facet2, NULL, NULL);
+  if (mindist) {
+    maximize_(qh max_outside, *maxdist);
+    maximize_(qh max_vertex, *maxdist);
+#if qh_MAXoutside
+    maximize_(facet2->maxoutside, *maxdist);
+#endif
+    minimize_(qh min_vertex, *mindist);
+    if (!facet2->keepcentrum
+    && (*maxdist > qh WIDEfacet || *mindist < -qh WIDEfacet)) {
+      facet2->keepcentrum= True;
+      zinc_(Zwidefacet);
+    }
+  }
+  nummerge= facet1->nummerge + facet2->nummerge + 1;
+  if (nummerge >= qh_MAXnummerge)
+    facet2->nummerge= qh_MAXnummerge;
+  else
+    facet2->nummerge= (short unsigned int)nummerge;
+  facet2->newmerge= True;
+  facet2->dupridge= False;
+  qh_updatetested(facet1, facet2);
+  if (qh hull_dim > 2 && qh_setsize(facet1->vertices) == qh hull_dim)
+    qh_mergesimplex(facet1, facet2, mergeapex);
+  else {
+    qh vertex_visit++;
+    FOREACHvertex_(facet2->vertices)
+      vertex->visitid= qh vertex_visit;
+    if (qh hull_dim == 2)
+      qh_mergefacet2d(facet1, facet2);
+    else {
+      qh_mergeneighbors(facet1, facet2);
+      qh_mergevertices(facet1->vertices, &facet2->vertices);
+    }
+    qh_mergeridges(facet1, facet2);
+    qh_mergevertex_neighbors(facet1, facet2);
+    if (!facet2->newfacet)
+      qh_newvertices(facet2->vertices);
+  }
+  if (!mergeapex)
+    qh_degen_redundant_neighbors(facet2, facet1);
+  if (facet2->coplanar || !facet2->newfacet) {
+    zinc_(Zmergeintohorizon);
+  }else if (!facet1->newfacet && facet2->newfacet) {
+    zinc_(Zmergehorizon);
+  }else {
+    zinc_(Zmergenew);
+  }
+  qh_willdelete(facet1, facet2);
+  qh_removefacet(facet2);  /* append as a newfacet to end of qh facet_list */
+  qh_appendfacet(facet2);
+  facet2->newfacet= True;
+  facet2->tested= False;
+  qh_tracemerge(facet1, facet2);
+  if (traceonce) {
+    qh_fprintf(qh ferr, 8080, "qh_mergefacet: end of wide tracing\n");
+    qh IStracing= tracerestore;
+  }
+} /* mergefacet */
+
+
+/*-<a                             href="qh-merge.htm#TOC"
+  >-------------------------------</a><a name="mergefacet2d">-</a>
+
+  qh_mergefacet2d( facet1, facet2 )
+    in 2d, merges neighbors and vertices of facet1 into facet2
+
+  returns:
+    build ridges for neighbors if necessary
+    facet2 looks like a simplicial facet except for centrum, ridges
+      neighbors are opposite the corresponding vertex
+      maintains orientation of facet2
+
+  notes:
+    qh_mergefacet() retains non-simplicial structures
+      they are not needed in 2d, but later routines may use them
+    preserves qh.vertex_visit for qh_mergevertex_neighbors()
+
+  design:
+    get vertices and neighbors
+    determine new vertices and neighbors
+    set new vertices and neighbors and adjust orientation
+    make ridges for new neighbor if needed
+*/
+void qh_mergefacet2d(facetT *facet1, facetT *facet2) {
+  vertexT *vertex1A, *vertex1B, *vertex2A, *vertex2B, *vertexA, *vertexB;
+  facetT *neighbor1A, *neighbor1B, *neighbor2A, *neighbor2B, *neighborA, *neighborB;
+
+  vertex1A= SETfirstt_(facet1->vertices, vertexT);
+  vertex1B= SETsecondt_(facet1->vertices, vertexT);
+  vertex2A= SETfirstt_(facet2->vertices, vertexT);
+  vertex2B= SETsecondt_(facet2->vertices, vertexT);
+  neighbor1A= SETfirstt_(facet1->neighbors, facetT);
+  neighbor1B= SETsecondt_(facet1->neighbors, facetT);
+  neighbor2A= SETfirstt_(facet2->neighbors, facetT);
+  neighbor2B= SETsecondt_(facet2->neighbors, facetT);
+  if (vertex1A == vertex2A) {
+    vertexA= vertex1B;
+    vertexB= vertex2B;
+    neighborA= neighbor2A;
+    neighborB= neighbor1A;
+  }else if (vertex1A == vertex2B) {
+    vertexA= vertex1B;
+    vertexB= vertex2A;
+    neighborA= neighbor2B;
+    neighborB= neighbor1A;
+  }else if (vertex1B == vertex2A) {
+    vertexA= vertex1A;
+    vertexB= vertex2B;
+    neighborA= neighbor2A;
+    neighborB= neighbor1B;
+  }else { /* 1B == 2B */
+    vertexA= vertex1A;
+    vertexB= vertex2A;
+    neighborA= neighbor2B;
+    neighborB= neighbor1B;
+  }
+  /* vertexB always from facet2, neighborB always from facet1 */
+  if (vertexA->id > vertexB->id) {
+    SETfirst_(facet2->vertices)= vertexA;
+    SETsecond_(facet2->vertices)= vertexB;
+    if (vertexB == vertex2A)
+      facet2->toporient= !facet2->toporient;
+    SETfirst_(facet2->neighbors)= neighborA;
+    SETsecond_(facet2->neighbors)= neighborB;
+  }else {
+    SETfirst_(facet2->vertices)= vertexB;
+    SETsecond_(facet2->vertices)= vertexA;
+    if (vertexB == vertex2B)
+      facet2->toporient= !facet2->toporient;
+    SETfirst_(facet2->neighbors)= neighborB;
+    SETsecond_(facet2->neighbors)= neighborA;
+  }
+  qh_makeridges(neighborB);
+  qh_setreplace(neighborB->neighbors, facet1, facet2);
+  trace4((qh ferr, 4036, "qh_mergefacet2d: merged v%d and neighbor f%d of f%d into f%d\n",
+       vertexA->id, neighborB->id, facet1->id, facet2->id));
+} /* mergefacet2d */
+
+
+/*-<a                             href="qh-merge.htm#TOC"
+  >-------------------------------</a><a name="mergeneighbors">-</a>
+
+  qh_mergeneighbors( facet1, facet2 )
+    merges the neighbors of facet1 into facet2
+
+  see:
+    qh_mergecycle_neighbors()
+
+  design:
+    for each neighbor of facet1
+      if neighbor is also a neighbor of facet2
+        if neighbor is simpilicial
+          make ridges for later deletion as a degenerate facet
+        update its neighbor set
+      else
+        move the neighbor relation to facet2
+    remove the neighbor relation for facet1 and facet2
+*/
+void qh_mergeneighbors(facetT *facet1, facetT *facet2) {
+  facetT *neighbor, **neighborp;
+
+  trace4((qh ferr, 4037, "qh_mergeneighbors: merge neighbors of f%d and f%d\n",
+          facet1->id, facet2->id));
+  qh visit_id++;
+  FOREACHneighbor_(facet2) {
+    neighbor->visitid= qh visit_id;
+  }
+  FOREACHneighbor_(facet1) {
+    if (neighbor->visitid == qh visit_id) {
+      if (neighbor->simplicial)    /* is degen, needs ridges */
+        qh_makeridges(neighbor);
+      if (SETfirstt_(neighbor->neighbors, facetT) != facet1) /*keep newfacet->horizon*/
+        qh_setdel(neighbor->neighbors, facet1);
+      else {
+        qh_setdel(neighbor->neighbors, facet2);
+        qh_setreplace(neighbor->neighbors, facet1, facet2);
+      }
+    }else if (neighbor != facet2) {
+      qh_setappend(&(facet2->neighbors), neighbor);
+      qh_setreplace(neighbor->neighbors, facet1, facet2);
+    }
+  }
+  qh_setdel(facet1->neighbors, facet2);  /* here for makeridges */
+  qh_setdel(facet2->neighbors, facet1);
+} /* mergeneighbors */
+
+
+/*-<a                             href="qh-merge.htm#TOC"
+  >-------------------------------</a><a name="mergeridges">-</a>
+
+  qh_mergeridges( facet1, facet2 )
+    merges the ridge set of facet1 into facet2
+
+  returns:
+    may delete all ridges for a vertex
+    sets vertex->delridge on deleted ridges
+
+  see:
+    qh_mergecycle_ridges()
+
+  design:
+    delete ridges between facet1 and facet2
+      mark (delridge) vertices on these ridges for later testing
+    for each remaining ridge
+      rename facet1 to facet2
+*/
+void qh_mergeridges(facetT *facet1, facetT *facet2) {
+  ridgeT *ridge, **ridgep;
+  vertexT *vertex, **vertexp;
+
+  trace4((qh ferr, 4038, "qh_mergeridges: merge ridges of f%d and f%d\n",
+          facet1->id, facet2->id));
+  FOREACHridge_(facet2->ridges) {
+    if ((ridge->top == facet1) || (ridge->bottom == facet1)) {
+      FOREACHvertex_(ridge->vertices)
+        vertex->delridge= True;
+      qh_delridge(ridge);  /* expensive in high-d, could rebuild */
+      ridgep--; /*repeat*/
+    }
+  }
+  FOREACHridge_(facet1->ridges) {
+    if (ridge->top == facet1)
+      ridge->top= facet2;
+    else
+      ridge->bottom= facet2;
+    qh_setappend(&(facet2->ridges), ridge);
+  }
+} /* mergeridges */
+
+
+/*-<a                             href="qh-merge.htm#TOC"
+  >-------------------------------</a><a name="mergesimplex">-</a>
+
+  qh_mergesimplex( facet1, facet2, mergeapex )
+    merge simplicial facet1 into facet2
+    mergeapex==qh_MERGEapex if merging samecycle into horizon facet
+      vertex id is latest (most recently created)
+    facet1 may be contained in facet2
+    ridges exist for both facets
+
+  returns:
+    facet2 with updated vertices, ridges, neighbors
+    updated neighbors for facet1's vertices
+    facet1 not deleted
+    sets vertex->delridge on deleted ridges
+
+  notes:
+    special case code since this is the most common merge
+    called from qh_mergefacet()
+
+  design:
+    if qh_MERGEapex
+      add vertices of facet2 to qh.new_vertexlist if necessary
+      add apex to facet2
+    else
+      for each ridge between facet1 and facet2
+        set vertex->delridge
+      determine the apex for facet1 (i.e., vertex to be merged)
+      unless apex already in facet2
+        insert apex into vertices for facet2
+      add vertices of facet2 to qh.new_vertexlist if necessary
+      add apex to qh.new_vertexlist if necessary
+      for each vertex of facet1
+        if apex
+          rename facet1 to facet2 in its vertex neighbors
+        else
+          delete facet1 from vertex neighors
+          if only in facet2
+            add vertex to qh.del_vertices for later deletion
+      for each ridge of facet1
+        delete ridges between facet1 and facet2
+        append other ridges to facet2 after renaming facet to facet2
+*/
+void qh_mergesimplex(facetT *facet1, facetT *facet2, boolT mergeapex) {
+  vertexT *vertex, **vertexp, *apex;
+  ridgeT *ridge, **ridgep;
+  boolT issubset= False;
+  int vertex_i= -1, vertex_n;
+  facetT *neighbor, **neighborp, *otherfacet;
+
+  if (mergeapex) {
+    if (!facet2->newfacet)
+      qh_newvertices(facet2->vertices);  /* apex is new */
+    apex= SETfirstt_(facet1->vertices, vertexT);
+    if (SETfirstt_(facet2->vertices, vertexT) != apex)
+      qh_setaddnth(&facet2->vertices, 0, apex);  /* apex has last id */
+    else
+      issubset= True;
+  }else {
+    zinc_(Zmergesimplex);
+    FOREACHvertex_(facet1->vertices)
+      vertex->seen= False;
+    FOREACHridge_(facet1->ridges) {
+      if (otherfacet_(ridge, facet1) == facet2) {
+        FOREACHvertex_(ridge->vertices) {
+          vertex->seen= True;
+          vertex->delridge= True;
+        }
+        break;
+      }
+    }
+    FOREACHvertex_(facet1->vertices) {
+      if (!vertex->seen)
+        break;  /* must occur */
+    }
+    apex= vertex;
+    trace4((qh ferr, 4039, "qh_mergesimplex: merge apex v%d of f%d into facet f%d\n",
+          apex->id, facet1->id, facet2->id));
+    FOREACHvertex_i_(facet2->vertices) {
+      if (vertex->id < apex->id) {
+        break;
+      }else if (vertex->id == apex->id) {
+        issubset= True;
+        break;
+      }
+    }
+    if (!issubset)
+      qh_setaddnth(&facet2->vertices, vertex_i, apex);
+    if (!facet2->newfacet)
+      qh_newvertices(facet2->vertices);
+    else if (!apex->newlist) {
+      qh_removevertex(apex);
+      qh_appendvertex(apex);
+    }
+  }
+  trace4((qh ferr, 4040, "qh_mergesimplex: update vertex neighbors of f%d\n",
+          facet1->id));
+  FOREACHvertex_(facet1->vertices) {
+    if (vertex == apex && !issubset)
+      qh_setreplace(vertex->neighbors, facet1, facet2);
+    else {
+      qh_setdel(vertex->neighbors, facet1);
+      if (!SETsecond_(vertex->neighbors))
+        qh_mergevertex_del(vertex, facet1, facet2);
+    }
+  }
+  trace4((qh ferr, 4041, "qh_mergesimplex: merge ridges and neighbors of f%d into f%d\n",
+          facet1->id, facet2->id));
+  qh visit_id++;
+  FOREACHneighbor_(facet2)
+    neighbor->visitid= qh visit_id;
+  FOREACHridge_(facet1->ridges) {
+    otherfacet= otherfacet_(ridge, facet1);
+    if (otherfacet == facet2) {
+      qh_setdel(facet2->ridges, ridge);
+      qh_setfree(&(ridge->vertices));
+      qh_memfree(ridge, (int)sizeof(ridgeT));
+      qh_setdel(facet2->neighbors, facet1);
+    }else {
+      qh_setappend(&facet2->ridges, ridge);
+      if (otherfacet->visitid != qh visit_id) {
+        qh_setappend(&facet2->neighbors, otherfacet);
+        qh_setreplace(otherfacet->neighbors, facet1, facet2);
+        otherfacet->visitid= qh visit_id;
+      }else {
+        if (otherfacet->simplicial)    /* is degen, needs ridges */
+          qh_makeridges(otherfacet);
+        if (SETfirstt_(otherfacet->neighbors, facetT) != facet1)
+          qh_setdel(otherfacet->neighbors, facet1);
+        else {   /*keep newfacet->neighbors->horizon*/
+          qh_setdel(otherfacet->neighbors, facet2);
+          qh_setreplace(otherfacet->neighbors, facet1, facet2);
+        }
+      }
+      if (ridge->top == facet1) /* wait until after qh_makeridges */
+        ridge->top= facet2;
+      else
+        ridge->bottom= facet2;
+    }
+  }
+  SETfirst_(facet1->ridges)= NULL; /* it will be deleted */
+  trace3((qh ferr, 3006, "qh_mergesimplex: merged simplex f%d apex v%d into facet f%d\n",
+          facet1->id, getid_(apex), facet2->id));
+} /* mergesimplex */
+
+/*-<a                             href="qh-merge.htm#TOC"
+  >-------------------------------</a><a name="mergevertex_del">-</a>
+
+  qh_mergevertex_del( vertex, facet1, facet2 )
+    delete a vertex because of merging facet1 into facet2
+
+  returns:
+    deletes vertex from facet2
+    adds vertex to qh.del_vertices for later deletion
+*/
+void qh_mergevertex_del(vertexT *vertex, facetT *facet1, facetT *facet2) {
+
+  zinc_(Zmergevertex);
+  trace2((qh ferr, 2035, "qh_mergevertex_del: deleted v%d when merging f%d into f%d\n",
+          vertex->id, facet1->id, facet2->id));
+  qh_setdelsorted(facet2->vertices, vertex);
+  vertex->deleted= True;
+  qh_setappend(&qh del_vertices, vertex);
+} /* mergevertex_del */
+
+/*-<a                             href="qh-merge.htm#TOC"
+  >-------------------------------</a><a name="mergevertex_neighbors">-</a>
+
+  qh_mergevertex_neighbors( facet1, facet2 )
+    merge the vertex neighbors of facet1 to facet2
+
+  returns:
+    if vertex is current qh.vertex_visit
+      deletes facet1 from vertex->neighbors
+    else
+      renames facet1 to facet2 in vertex->neighbors
+    deletes vertices if only one neighbor
+
+  notes:
+    assumes vertex neighbor sets are good
+*/
+void qh_mergevertex_neighbors(facetT *facet1, facetT *facet2) {
+  vertexT *vertex, **vertexp;
+
+  trace4((qh ferr, 4042, "qh_mergevertex_neighbors: merge vertex neighbors of f%d and f%d\n",
+          facet1->id, facet2->id));
+  if (qh tracevertex) {
+    qh_fprintf(qh ferr, 8081, "qh_mergevertex_neighbors: of f%d and f%d at furthest p%d f0= %p\n",
+             facet1->id, facet2->id, qh furthest_id, qh tracevertex->neighbors->e[0].p);
+    qh_errprint("TRACE", NULL, NULL, NULL, qh tracevertex);
+  }
+  FOREACHvertex_(facet1->vertices) {
+    if (vertex->visitid != qh vertex_visit)
+      qh_setreplace(vertex->neighbors, facet1, facet2);
+    else {
+      qh_setdel(vertex->neighbors, facet1);
+      if (!SETsecond_(vertex->neighbors))
+        qh_mergevertex_del(vertex, facet1, facet2);
+    }
+  }
+  if (qh tracevertex)
+    qh_errprint("TRACE", NULL, NULL, NULL, qh tracevertex);
+} /* mergevertex_neighbors */
+
+
+/*-<a                             href="qh-merge.htm#TOC"
+  >-------------------------------</a><a name="mergevertices">-</a>
+
+  qh_mergevertices( vertices1, vertices2 )
+    merges the vertex set of facet1 into facet2
+
+  returns:
+    replaces vertices2 with merged set
+    preserves vertex_visit for qh_mergevertex_neighbors
+    updates qh.newvertex_list
+
+  design:
+    create a merged set of both vertices (in inverse id order)
+*/
+void qh_mergevertices(setT *vertices1, setT **vertices2) {
+  int newsize= qh_setsize(vertices1)+qh_setsize(*vertices2) - qh hull_dim + 1;
+  setT *mergedvertices;
+  vertexT *vertex, **vertexp, **vertex2= SETaddr_(*vertices2, vertexT);
+
+  mergedvertices= qh_settemp(newsize);
+  FOREACHvertex_(vertices1) {
+    if (!*vertex2 || vertex->id > (*vertex2)->id)
+      qh_setappend(&mergedvertices, vertex);
+    else {
+      while (*vertex2 && (*vertex2)->id > vertex->id)
+        qh_setappend(&mergedvertices, *vertex2++);
+      if (!*vertex2 || (*vertex2)->id < vertex->id)
+        qh_setappend(&mergedvertices, vertex);
+      else
+        qh_setappend(&mergedvertices, *vertex2++);
+    }
+  }
+  while (*vertex2)
+    qh_setappend(&mergedvertices, *vertex2++);
+  if (newsize < qh_setsize(mergedvertices)) {
+    qh_fprintf(qh ferr, 6100, "qhull internal error (qh_mergevertices): facets did not share a ridge\n");
+    qh_errexit(qh_ERRqhull, NULL, NULL);
+  }
+  qh_setfree(vertices2);
+  *vertices2= mergedvertices;
+  qh_settemppop();
+} /* mergevertices */
+
+
+/*-<a                             href="qh-merge.htm#TOC"
+  >-------------------------------</a><a name="neighbor_intersections">-</a>
+
+  qh_neighbor_intersections( vertex )
+    return intersection of all vertices in vertex->neighbors except for vertex
+
+  returns:
+    returns temporary set of vertices
+    does not include vertex
+    NULL if a neighbor is simplicial
+    NULL if empty set
+
+  notes:
+    used for renaming vertices
+
+  design:
+    initialize the intersection set with vertices of the first two neighbors
+    delete vertex from the intersection
+    for each remaining neighbor
+      intersect its vertex set with the intersection set
+      return NULL if empty
+    return the intersection set
+*/
+setT *qh_neighbor_intersections(vertexT *vertex) {
+  facetT *neighbor, **neighborp, *neighborA, *neighborB;
+  setT *intersect;
+  int neighbor_i, neighbor_n;
+
+  FOREACHneighbor_(vertex) {
+    if (neighbor->simplicial)
+      return NULL;
+  }
+  neighborA= SETfirstt_(vertex->neighbors, facetT);
+  neighborB= SETsecondt_(vertex->neighbors, facetT);
+  zinc_(Zintersectnum);
+  if (!neighborA)
+    return NULL;
+  if (!neighborB)
+    intersect= qh_setcopy(neighborA->vertices, 0);
+  else
+    intersect= qh_vertexintersect_new(neighborA->vertices, neighborB->vertices);
+  qh_settemppush(intersect);
+  qh_setdelsorted(intersect, vertex);
+  FOREACHneighbor_i_(vertex) {
+    if (neighbor_i >= 2) {
+      zinc_(Zintersectnum);
+      qh_vertexintersect(&intersect, neighbor->vertices);
+      if (!SETfirst_(intersect)) {
+        zinc_(Zintersectfail);
+        qh_settempfree(&intersect);
+        return NULL;
+      }
+    }
+  }
+  trace3((qh ferr, 3007, "qh_neighbor_intersections: %d vertices in neighbor intersection of v%d\n",
+          qh_setsize(intersect), vertex->id));
+  return intersect;
+} /* neighbor_intersections */
+
+/*-<a                             href="qh-merge.htm#TOC"
+  >-------------------------------</a><a name="newvertices">-</a>
+
+  qh_newvertices( vertices )
+    add vertices to end of qh.vertex_list (marks as new vertices)
+
+  returns:
+    vertices on qh.newvertex_list
+    vertex->newlist set
+*/
+void qh_newvertices(setT *vertices) {
+  vertexT *vertex, **vertexp;
+
+  FOREACHvertex_(vertices) {
+    if (!vertex->newlist) {
+      qh_removevertex(vertex);
+      qh_appendvertex(vertex);
+    }
+  }
+} /* newvertices */
+
+/*-<a                             href="qh-merge.htm#TOC"
+  >-------------------------------</a><a name="reducevertices">-</a>
+
+  qh_reducevertices()
+    reduce extra vertices, shared vertices, and redundant vertices
+    facet->newmerge is set if merged since last call
+    if !qh.MERGEvertices, only removes extra vertices
+
+  returns:
+    True if also merged degen_redundant facets
+    vertices are renamed if possible
+    clears facet->newmerge and vertex->delridge
+
+  notes:
+    ignored if 2-d
+
+  design:
+    merge any degenerate or redundant facets
+    for each newly merged facet
+      remove extra vertices
+    if qh.MERGEvertices
+      for each newly merged facet
+        for each vertex
+          if vertex was on a deleted ridge
+            rename vertex if it is shared
+      remove delridge flag from new vertices
+*/
+boolT qh_reducevertices(void) {
+  int numshare=0, numrename= 0;
+  boolT degenredun= False;
+  facetT *newfacet;
+  vertexT *vertex, **vertexp;
+
+  if (qh hull_dim == 2)
+    return False;
+  if (qh_merge_degenredundant())
+    degenredun= True;
+ LABELrestart:
+  FORALLnew_facets {
+    if (newfacet->newmerge) {
+      if (!qh MERGEvertices)
+        newfacet->newmerge= False;
+      qh_remove_extravertices(newfacet);
+    }
+  }
+  if (!qh MERGEvertices)
+    return False;
+  FORALLnew_facets {
+    if (newfacet->newmerge) {
+      newfacet->newmerge= False;
+      FOREACHvertex_(newfacet->vertices) {
+        if (vertex->delridge) {
+          if (qh_rename_sharedvertex(vertex, newfacet)) {
+            numshare++;
+            vertexp--; /* repeat since deleted vertex */
+          }
+        }
+      }
+    }
+  }
+  FORALLvertex_(qh newvertex_list) {
+    if (vertex->delridge && !vertex->deleted) {
+      vertex->delridge= False;
+      if (qh hull_dim >= 4 && qh_redundant_vertex(vertex)) {
+        numrename++;
+        if (qh_merge_degenredundant()) {
+          degenredun= True;
+          goto LABELrestart;
+        }
+      }
+    }
+  }
+  trace1((qh ferr, 1014, "qh_reducevertices: renamed %d shared vertices and %d redundant vertices. Degen? %d\n",
+          numshare, numrename, degenredun));
+  return degenredun;
+} /* reducevertices */
+
+/*-<a                             href="qh-merge.htm#TOC"
+  >-------------------------------</a><a name="redundant_vertex">-</a>
+
+  qh_redundant_vertex( vertex )
+    detect and rename a redundant vertex
+    vertices have full vertex->neighbors
+
+  returns:
+    returns true if find a redundant vertex
+      deletes vertex(vertex->deleted)
+
+  notes:
+    only needed if vertex->delridge and hull_dim >= 4
+    may add degenerate facets to qh.facet_mergeset
+    doesn't change vertex->neighbors or create redundant facets
+
+  design:
+    intersect vertices of all facet neighbors of vertex
+    determine ridges for these vertices
+    if find a new vertex for vertex amoung these ridges and vertices
+      rename vertex to the new vertex
+*/
+vertexT *qh_redundant_vertex(vertexT *vertex) {
+  vertexT *newvertex= NULL;
+  setT *vertices, *ridges;
+
+  trace3((qh ferr, 3008, "qh_redundant_vertex: check if v%d can be renamed\n", vertex->id));
+  if ((vertices= qh_neighbor_intersections(vertex))) {
+    ridges= qh_vertexridges(vertex);
+    if ((newvertex= qh_find_newvertex(vertex, vertices, ridges)))
+      qh_renamevertex(vertex, newvertex, ridges, NULL, NULL);
+    qh_settempfree(&ridges);
+    qh_settempfree(&vertices);
+  }
+  return newvertex;
+} /* redundant_vertex */
+
+/*-<a                             href="qh-merge.htm#TOC"
+  >-------------------------------</a><a name="remove_extravertices">-</a>
+
+  qh_remove_extravertices( facet )
+    remove extra vertices from non-simplicial facets
+
+  returns:
+    returns True if it finds them
+
+  design:
+    for each vertex in facet
+      if vertex not in a ridge (i.e., no longer used)
+        delete vertex from facet
+        delete facet from vertice's neighbors
+        unless vertex in another facet
+          add vertex to qh.del_vertices for later deletion
+*/
+boolT qh_remove_extravertices(facetT *facet) {
+  ridgeT *ridge, **ridgep;
+  vertexT *vertex, **vertexp;
+  boolT foundrem= False;
+
+  trace4((qh ferr, 4043, "qh_remove_extravertices: test f%d for extra vertices\n",
+          facet->id));
+  FOREACHvertex_(facet->vertices)
+    vertex->seen= False;
+  FOREACHridge_(facet->ridges) {
+    FOREACHvertex_(ridge->vertices)
+      vertex->seen= True;
+  }
+  FOREACHvertex_(facet->vertices) {
+    if (!vertex->seen) {
+      foundrem= True;
+      zinc_(Zremvertex);
+      qh_setdelsorted(facet->vertices, vertex);
+      qh_setdel(vertex->neighbors, facet);
+      if (!qh_setsize(vertex->neighbors)) {
+        vertex->deleted= True;
+        qh_setappend(&qh del_vertices, vertex);
+        zinc_(Zremvertexdel);
+        trace2((qh ferr, 2036, "qh_remove_extravertices: v%d deleted because it's lost all ridges\n", vertex->id));
+      }else
+        trace3((qh ferr, 3009, "qh_remove_extravertices: v%d removed from f%d because it's lost all ridges\n", vertex->id, facet->id));
+      vertexp--; /*repeat*/
+    }
+  }
+  return foundrem;
+} /* remove_extravertices */
+
+/*-<a                             href="qh-merge.htm#TOC"
+  >-------------------------------</a><a name="rename_sharedvertex">-</a>
+
+  qh_rename_sharedvertex( vertex, facet )
+    detect and rename if shared vertex in facet
+    vertices have full ->neighbors
+
+  returns:
+    newvertex or NULL
+    the vertex may still exist in other facets (i.e., a neighbor was pinched)
+    does not change facet->neighbors
+    updates vertex->neighbors
+
+  notes:
+    a shared vertex for a facet is only in ridges to one neighbor
+    this may undo a pinched facet
+
+    it does not catch pinches involving multiple facets.  These appear
+      to be difficult to detect, since an exhaustive search is too expensive.
+
+  design:
+    if vertex only has two neighbors
+      determine the ridges that contain the vertex
+      determine the vertices shared by both neighbors
+      if can find a new vertex in this set
+        rename the vertex to the new vertex
+*/
+vertexT *qh_rename_sharedvertex(vertexT *vertex, facetT *facet) {
+  facetT *neighbor, **neighborp, *neighborA= NULL;
+  setT *vertices, *ridges;
+  vertexT *newvertex;
+
+  if (qh_setsize(vertex->neighbors) == 2) {
+    neighborA= SETfirstt_(vertex->neighbors, facetT);
+    if (neighborA == facet)
+      neighborA= SETsecondt_(vertex->neighbors, facetT);
+  }else if (qh hull_dim == 3)
+    return NULL;
+  else {
+    qh visit_id++;
+    FOREACHneighbor_(facet)
+      neighbor->visitid= qh visit_id;
+    FOREACHneighbor_(vertex) {
+      if (neighbor->visitid == qh visit_id) {
+        if (neighborA)
+          return NULL;
+        neighborA= neighbor;
+      }
+    }
+    if (!neighborA) {
+      qh_fprintf(qh ferr, 6101, "qhull internal error (qh_rename_sharedvertex): v%d's neighbors not in f%d\n",
+        vertex->id, facet->id);
+      qh_errprint("ERRONEOUS", facet, NULL, NULL, vertex);
+      qh_errexit(qh_ERRqhull, NULL, NULL);
+    }
+  }
+  /* the vertex is shared by facet and neighborA */
+  ridges= qh_settemp(qh TEMPsize);
+  neighborA->visitid= ++qh visit_id;
+  qh_vertexridges_facet(vertex, facet, &ridges);
+  trace2((qh ferr, 2037, "qh_rename_sharedvertex: p%d(v%d) is shared by f%d(%d ridges) and f%d\n",
+    qh_pointid(vertex->point), vertex->id, facet->id, qh_setsize(ridges), neighborA->id));
+  zinc_(Zintersectnum);
+  vertices= qh_vertexintersect_new(facet->vertices, neighborA->vertices);
+  qh_setdel(vertices, vertex);
+  qh_settemppush(vertices);
+  if ((newvertex= qh_find_newvertex(vertex, vertices, ridges)))
+    qh_renamevertex(vertex, newvertex, ridges, facet, neighborA);
+  qh_settempfree(&vertices);
+  qh_settempfree(&ridges);
+  return newvertex;
+} /* rename_sharedvertex */
+
+/*-<a                             href="qh-merge.htm#TOC"
+  >-------------------------------</a><a name="renameridgevertex">-</a>
+
+  qh_renameridgevertex( ridge, oldvertex, newvertex )
+    renames oldvertex as newvertex in ridge
+
+  returns:
+
+  design:
+    delete oldvertex from ridge
+    if newvertex already in ridge
+      copy ridge->noconvex to another ridge if possible
+      delete the ridge
+    else
+      insert newvertex into the ridge
+      adjust the ridge's orientation
+*/
+void qh_renameridgevertex(ridgeT *ridge, vertexT *oldvertex, vertexT *newvertex) {
+  int nth= 0, oldnth;
+  facetT *temp;
+  vertexT *vertex, **vertexp;
+
+  oldnth= qh_setindex(ridge->vertices, oldvertex);
+  qh_setdelnthsorted(ridge->vertices, oldnth);
+  FOREACHvertex_(ridge->vertices) {
+    if (vertex == newvertex) {
+      zinc_(Zdelridge);
+      if (ridge->nonconvex) /* only one ridge has nonconvex set */
+        qh_copynonconvex(ridge);
+      trace2((qh ferr, 2038, "qh_renameridgevertex: ridge r%d deleted.  It contained both v%d and v%d\n",
+        ridge->id, oldvertex->id, newvertex->id));
+      qh_delridge(ridge);
+      return;
+    }
+    if (vertex->id < newvertex->id)
+      break;
+    nth++;
+  }
+  qh_setaddnth(&ridge->vertices, nth, newvertex);
+  if (abs(oldnth - nth)%2) {
+    trace3((qh ferr, 3010, "qh_renameridgevertex: swapped the top and bottom of ridge r%d\n",
+            ridge->id));
+    temp= ridge->top;
+    ridge->top= ridge->bottom;
+    ridge->bottom= temp;
+  }
+} /* renameridgevertex */
+
+
+/*-<a                             href="qh-merge.htm#TOC"
+  >-------------------------------</a><a name="renamevertex">-</a>
+
+  qh_renamevertex( oldvertex, newvertex, ridges, oldfacet, neighborA )
+    renames oldvertex as newvertex in ridges
+    gives oldfacet/neighborA if oldvertex is shared between two facets
+
+  returns:
+    oldvertex may still exist afterwards
+
+
+  notes:
+    can not change neighbors of newvertex (since it's a subset)
+
+  design:
+    for each ridge in ridges
+      rename oldvertex to newvertex and delete degenerate ridges
+    if oldfacet not defined
+      for each neighbor of oldvertex
+        delete oldvertex from neighbor's vertices
+        remove extra vertices from neighbor
+      add oldvertex to qh.del_vertices
+    else if oldvertex only between oldfacet and neighborA
+      delete oldvertex from oldfacet and neighborA
+      add oldvertex to qh.del_vertices
+    else oldvertex is in oldfacet and neighborA and other facets (i.e., pinched)
+      delete oldvertex from oldfacet
+      delete oldfacet from oldvertice's neighbors
+      remove extra vertices (e.g., oldvertex) from neighborA
+*/
+void qh_renamevertex(vertexT *oldvertex, vertexT *newvertex, setT *ridges, facetT *oldfacet, facetT *neighborA) {
+  facetT *neighbor, **neighborp;
+  ridgeT *ridge, **ridgep;
+  boolT istrace= False;
+
+  if (qh IStracing >= 2 || oldvertex->id == qh tracevertex_id ||
+        newvertex->id == qh tracevertex_id)
+    istrace= True;
+  FOREACHridge_(ridges)
+    qh_renameridgevertex(ridge, oldvertex, newvertex);
+  if (!oldfacet) {
+    zinc_(Zrenameall);
+    if (istrace)
+      qh_fprintf(qh ferr, 8082, "qh_renamevertex: renamed v%d to v%d in several facets\n",
+               oldvertex->id, newvertex->id);
+    FOREACHneighbor_(oldvertex) {
+      qh_maydropneighbor(neighbor);
+      qh_setdelsorted(neighbor->vertices, oldvertex);
+      if (qh_remove_extravertices(neighbor))
+        neighborp--; /* neighbor may be deleted */
+    }
+    if (!oldvertex->deleted) {
+      oldvertex->deleted= True;
+      qh_setappend(&qh del_vertices, oldvertex);
+    }
+  }else if (qh_setsize(oldvertex->neighbors) == 2) {
+    zinc_(Zrenameshare);
+    if (istrace)
+      qh_fprintf(qh ferr, 8083, "qh_renamevertex: renamed v%d to v%d in oldfacet f%d\n",
+               oldvertex->id, newvertex->id, oldfacet->id);
+    FOREACHneighbor_(oldvertex)
+      qh_setdelsorted(neighbor->vertices, oldvertex);
+    oldvertex->deleted= True;
+    qh_setappend(&qh del_vertices, oldvertex);
+  }else {
+    zinc_(Zrenamepinch);
+    if (istrace || qh IStracing)
+      qh_fprintf(qh ferr, 8084, "qh_renamevertex: renamed pinched v%d to v%d between f%d and f%d\n",
+               oldvertex->id, newvertex->id, oldfacet->id, neighborA->id);
+    qh_setdelsorted(oldfacet->vertices, oldvertex);
+    qh_setdel(oldvertex->neighbors, oldfacet);
+    qh_remove_extravertices(neighborA);
+  }
+} /* renamevertex */
+
+
+/*-<a                             href="qh-merge.htm#TOC"
+  >-------------------------------</a><a name="test_appendmerge">-</a>
+
+  qh_test_appendmerge( facet, neighbor )
+    tests facet/neighbor for convexity
+    appends to mergeset if non-convex
+    if pre-merging,
+      nop if qh.SKIPconvex, or qh.MERGEexact and coplanar
+
+  returns:
+    true if appends facet/neighbor to mergeset
+    sets facet->center as needed
+    does not change facet->seen
+
+  design:
+    if qh.cos_max is defined
+      if the angle between facet normals is too shallow
+        append an angle-coplanar merge to qh.mergeset
+        return True
+    make facet's centrum if needed
+    if facet's centrum is above the neighbor
+      set isconcave
+    else
+      if facet's centrum is not below the neighbor
+        set iscoplanar
+      make neighbor's centrum if needed
+      if neighbor's centrum is above the facet
+        set isconcave
+      else if neighbor's centrum is not below the facet
+        set iscoplanar
+   if isconcave or iscoplanar
+     get angle if needed
+     append concave or coplanar merge to qh.mergeset
+*/
+boolT qh_test_appendmerge(facetT *facet, facetT *neighbor) {
+  realT dist, dist2= -REALmax, angle= -REALmax;
+  boolT isconcave= False, iscoplanar= False, okangle= False;
+
+  if (qh SKIPconvex && !qh POSTmerging)
+    return False;
+  if ((!qh MERGEexact || qh POSTmerging) && qh cos_max < REALmax/2) {
+    angle= qh_getangle(facet->normal, neighbor->normal);
+    zinc_(Zangletests);
+    if (angle > qh cos_max) {
+      zinc_(Zcoplanarangle);
+      qh_appendmergeset(facet, neighbor, MRGanglecoplanar, &angle);
+      trace2((qh ferr, 2039, "qh_test_appendmerge: coplanar angle %4.4g between f%d and f%d\n",
+         angle, facet->id, neighbor->id));
+      return True;
+    }else
+      okangle= True;
+  }
+  if (!facet->center)
+    facet->center= qh_getcentrum(facet);
+  zzinc_(Zcentrumtests);
+  qh_distplane(facet->center, neighbor, &dist);
+  if (dist > qh centrum_radius)
+    isconcave= True;
+  else {
+    if (dist > -qh centrum_radius)
+      iscoplanar= True;
+    if (!neighbor->center)
+      neighbor->center= qh_getcentrum(neighbor);
+    zzinc_(Zcentrumtests);
+    qh_distplane(neighbor->center, facet, &dist2);
+    if (dist2 > qh centrum_radius)
+      isconcave= True;
+    else if (!iscoplanar && dist2 > -qh centrum_radius)
+      iscoplanar= True;
+  }
+  if (!isconcave && (!iscoplanar || (qh MERGEexact && !qh POSTmerging)))
+    return False;
+  if (!okangle && qh ANGLEmerge) {
+    angle= qh_getangle(facet->normal, neighbor->normal);
+    zinc_(Zangletests);
+  }
+  if (isconcave) {
+    zinc_(Zconcaveridge);
+    if (qh ANGLEmerge)
+      angle += qh_ANGLEconcave + 0.5;
+    qh_appendmergeset(facet, neighbor, MRGconcave, &angle);
+    trace0((qh ferr, 18, "qh_test_appendmerge: concave f%d to f%d dist %4.4g and reverse dist %4.4g angle %4.4g during p%d\n",
+           facet->id, neighbor->id, dist, dist2, angle, qh furthest_id));
+  }else /* iscoplanar */ {
+    zinc_(Zcoplanarcentrum);
+    qh_appendmergeset(facet, neighbor, MRGcoplanar, &angle);
+    trace2((qh ferr, 2040, "qh_test_appendmerge: coplanar f%d to f%d dist %4.4g, reverse dist %4.4g angle %4.4g\n",
+              facet->id, neighbor->id, dist, dist2, angle));
+  }
+  return True;
+} /* test_appendmerge */
+
+/*-<a                             href="qh-merge.htm#TOC"
+  >-------------------------------</a><a name="test_vneighbors">-</a>
+
+  qh_test_vneighbors()
+    test vertex neighbors for convexity
+    tests all facets on qh.newfacet_list
+
+  returns:
+    true if non-convex vneighbors appended to qh.facet_mergeset
+    initializes vertex neighbors if needed
+
+  notes:
+    assumes all facet neighbors have been tested
+    this can be expensive
+    this does not guarantee that a centrum is below all facets
+      but it is unlikely
+    uses qh.visit_id
+
+  design:
+    build vertex neighbors if necessary
+    for all new facets
+      for all vertices
+        for each unvisited facet neighbor of the vertex
+          test new facet and neighbor for convexity
+*/
+boolT qh_test_vneighbors(void /* qh.newfacet_list */) {
+  facetT *newfacet, *neighbor, **neighborp;
+  vertexT *vertex, **vertexp;
+  int nummerges= 0;
+
+  trace1((qh ferr, 1015, "qh_test_vneighbors: testing vertex neighbors for convexity\n"));
+  if (!qh VERTEXneighbors)
+    qh_vertexneighbors();
+  FORALLnew_facets
+    newfacet->seen= False;
+  FORALLnew_facets {
+    newfacet->seen= True;
+    newfacet->visitid= qh visit_id++;
+    FOREACHneighbor_(newfacet)
+      newfacet->visitid= qh visit_id;
+    FOREACHvertex_(newfacet->vertices) {
+      FOREACHneighbor_(vertex) {
+        if (neighbor->seen || neighbor->visitid == qh visit_id)
+          continue;
+        if (qh_test_appendmerge(newfacet, neighbor))
+          nummerges++;
+      }
+    }
+  }
+  zadd_(Ztestvneighbor, nummerges);
+  trace1((qh ferr, 1016, "qh_test_vneighbors: found %d non-convex, vertex neighbors\n",
+           nummerges));
+  return (nummerges > 0);
+} /* test_vneighbors */
+
+/*-<a                             href="qh-merge.htm#TOC"
+  >-------------------------------</a><a name="tracemerge">-</a>
+
+  qh_tracemerge( facet1, facet2 )
+    print trace message after merge
+*/
+void qh_tracemerge(facetT *facet1, facetT *facet2) {
+  boolT waserror= False;
+
+#ifndef qh_NOtrace
+  if (qh IStracing >= 4)
+    qh_errprint("MERGED", facet2, NULL, NULL, NULL);
+  if (facet2 == qh tracefacet || (qh tracevertex && qh tracevertex->newlist)) {
+    qh_fprintf(qh ferr, 8085, "qh_tracemerge: trace facet and vertex after merge of f%d and f%d, furthest p%d\n", facet1->id, facet2->id, qh furthest_id);
+    if (facet2 != qh tracefacet)
+      qh_errprint("TRACE", qh tracefacet,
+        (qh tracevertex && qh tracevertex->neighbors) ?
+           SETfirstt_(qh tracevertex->neighbors, facetT) : NULL,
+        NULL, qh tracevertex);
+  }
+  if (qh tracevertex) {
+    if (qh tracevertex->deleted)
+      qh_fprintf(qh ferr, 8086, "qh_tracemerge: trace vertex deleted at furthest p%d\n",
+            qh furthest_id);
+    else
+      qh_checkvertex(qh tracevertex);
+  }
+  if (qh tracefacet) {
+    qh_checkfacet(qh tracefacet, True, &waserror);
+    if (waserror)
+      qh_errexit(qh_ERRqhull, qh tracefacet, NULL);
+  }
+#endif /* !qh_NOtrace */
+  if (qh CHECKfrequently || qh IStracing >= 4) { /* can't check polygon here */
+    qh_checkfacet(facet2, True, &waserror);
+    if (waserror)
+      qh_errexit(qh_ERRqhull, NULL, NULL);
+  }
+} /* tracemerge */
+
+/*-<a                             href="qh-merge.htm#TOC"
+  >-------------------------------</a><a name="tracemerging">-</a>
+
+  qh_tracemerging()
+    print trace message during POSTmerging
+
+  returns:
+    updates qh.mergereport
+
+  notes:
+    called from qh_mergecycle() and qh_mergefacet()
+
+  see:
+    qh_buildtracing()
+*/
+void qh_tracemerging(void) {
+  realT cpu;
+  int total;
+  time_t timedata;
+  struct tm *tp;
+
+  qh mergereport= zzval_(Ztotmerge);
+  time(&timedata);
+  tp= localtime(&timedata);
+  cpu= qh_CPUclock;
+  cpu /= qh_SECticks;
+  total= zzval_(Ztotmerge) - zzval_(Zcyclehorizon) + zzval_(Zcyclefacettot);
+  qh_fprintf(qh ferr, 8087, "\n\
+At %d:%d:%d & %2.5g CPU secs, qhull has merged %d facets.  The hull\n\
+  contains %d facets and %d vertices.\n",
+      tp->tm_hour, tp->tm_min, tp->tm_sec, cpu,
+      total, qh num_facets - qh num_visible,
+      qh num_vertices-qh_setsize(qh del_vertices));
+} /* tracemerging */
+
+/*-<a                             href="qh-merge.htm#TOC"
+  >-------------------------------</a><a name="updatetested">-</a>
+
+  qh_updatetested( facet1, facet2 )
+    clear facet2->tested and facet1->ridge->tested for merge
+
+  returns:
+    deletes facet2->center unless it's already large
+      if so, clears facet2->ridge->tested
+
+  design:
+    clear facet2->tested
+    clear ridge->tested for facet1's ridges
+    if facet2 has a centrum
+      if facet2 is large
+        set facet2->keepcentrum
+      else if facet2 has 3 vertices due to many merges, or not large and post merging
+        clear facet2->keepcentrum
+      unless facet2->keepcentrum
+        clear facet2->center to recompute centrum later
+        clear ridge->tested for facet2's ridges
+*/
+void qh_updatetested(facetT *facet1, facetT *facet2) {
+  ridgeT *ridge, **ridgep;
+  int size;
+
+  facet2->tested= False;
+  FOREACHridge_(facet1->ridges)
+    ridge->tested= False;
+  if (!facet2->center)
+    return;
+  size= qh_setsize(facet2->vertices);
+  if (!facet2->keepcentrum) {
+    if (size > qh hull_dim + qh_MAXnewcentrum) {
+      facet2->keepcentrum= True;
+      zinc_(Zwidevertices);
+    }
+  }else if (size <= qh hull_dim + qh_MAXnewcentrum) {
+    /* center and keepcentrum was set */
+    if (size == qh hull_dim || qh POSTmerging)
+      facet2->keepcentrum= False; /* if many merges need to recompute centrum */
+  }
+  if (!facet2->keepcentrum) {
+    qh_memfree(facet2->center, qh normal_size);
+    facet2->center= NULL;
+    FOREACHridge_(facet2->ridges)
+      ridge->tested= False;
+  }
+} /* updatetested */
+
+/*-<a                             href="qh-merge.htm#TOC"
+  >-------------------------------</a><a name="vertexridges">-</a>
+
+  qh_vertexridges( vertex )
+    return temporary set of ridges adjacent to a vertex
+    vertex->neighbors defined
+
+  ntoes:
+    uses qh.visit_id
+    does not include implicit ridges for simplicial facets
+
+  design:
+    for each neighbor of vertex
+      add ridges that include the vertex to ridges
+*/
+setT *qh_vertexridges(vertexT *vertex) {
+  facetT *neighbor, **neighborp;
+  setT *ridges= qh_settemp(qh TEMPsize);
+  int size;
+
+  qh visit_id++;
+  FOREACHneighbor_(vertex)
+    neighbor->visitid= qh visit_id;
+  FOREACHneighbor_(vertex) {
+    if (*neighborp)   /* no new ridges in last neighbor */
+      qh_vertexridges_facet(vertex, neighbor, &ridges);
+  }
+  if (qh PRINTstatistics || qh IStracing) {
+    size= qh_setsize(ridges);
+    zinc_(Zvertexridge);
+    zadd_(Zvertexridgetot, size);
+    zmax_(Zvertexridgemax, size);
+    trace3((qh ferr, 3011, "qh_vertexridges: found %d ridges for v%d\n",
+             size, vertex->id));
+  }
+  return ridges;
+} /* vertexridges */
+
+/*-<a                             href="qh-merge.htm#TOC"
+  >-------------------------------</a><a name="vertexridges_facet">-</a>
+
+  qh_vertexridges_facet( vertex, facet, ridges )
+    add adjacent ridges for vertex in facet
+    neighbor->visitid==qh.visit_id if it hasn't been visited
+
+  returns:
+    ridges updated
+    sets facet->visitid to qh.visit_id-1
+
+  design:
+    for each ridge of facet
+      if ridge of visited neighbor (i.e., unprocessed)
+        if vertex in ridge
+          append ridge to vertex
+    mark facet processed
+*/
+void qh_vertexridges_facet(vertexT *vertex, facetT *facet, setT **ridges) {
+  ridgeT *ridge, **ridgep;
+  facetT *neighbor;
+
+  FOREACHridge_(facet->ridges) {
+    neighbor= otherfacet_(ridge, facet);
+    if (neighbor->visitid == qh visit_id
+    && qh_setin(ridge->vertices, vertex))
+      qh_setappend(ridges, ridge);
+  }
+  facet->visitid= qh visit_id-1;
+} /* vertexridges_facet */
+
+/*-<a                             href="qh-merge.htm#TOC"
+  >-------------------------------</a><a name="willdelete">-</a>
+
+  qh_willdelete( facet, replace )
+    moves facet to visible list
+    sets facet->f.replace to replace (may be NULL)
+
+  returns:
+    bumps qh.num_visible
+*/
+void qh_willdelete(facetT *facet, facetT *replace) {
+
+  qh_removefacet(facet);
+  qh_prependfacet(facet, &qh visible_list);
+  qh num_visible++;
+  facet->visible= True;
+  facet->f.replace= replace;
+} /* willdelete */
+
+#else /* qh_NOmerge */
+void qh_premerge(vertexT *apex, realT maxcentrum, realT maxangle) {
+}
+void qh_postmerge(const char *reason, realT maxcentrum, realT maxangle,
+                      boolT vneighbors) {
+}
+boolT qh_checkzero(boolT testall) {
+   }
+#endif /* qh_NOmerge */
+
diff --git a/xs/src/qhull/src/libqhull/merge.h b/xs/src/qhull/src/libqhull/merge.h
new file mode 100644
index 0000000000..7f5ec3fb61
--- /dev/null
+++ b/xs/src/qhull/src/libqhull/merge.h
@@ -0,0 +1,178 @@
+/*<html><pre>  -<a                             href="qh-merge.htm"
+  >-------------------------------</a><a name="TOP">-</a>
+
+   merge.h
+   header file for merge.c
+
+   see qh-merge.htm and merge.c
+
+   Copyright (c) 1993-2015 C.B. Barber.
+   $Id: //main/2015/qhull/src/libqhull/merge.h#1 $$Change: 1981 $
+   $DateTime: 2015/09/28 20:26:32 $$Author: bbarber $
+*/
+
+#ifndef qhDEFmerge
+#define qhDEFmerge 1
+
+#include "libqhull.h"
+
+
+/*============ -constants- ==============*/
+
+/*-<a                             href="qh-merge.htm#TOC"
+  >--------------------------------</a><a name="qh_ANGLEredundant">-</a>
+
+  qh_ANGLEredundant
+    indicates redundant merge in mergeT->angle
+*/
+#define qh_ANGLEredundant 6.0
+
+/*-<a                             href="qh-merge.htm#TOC"
+  >--------------------------------</a><a name="qh_ANGLEdegen">-</a>
+
+  qh_ANGLEdegen
+    indicates degenerate facet in mergeT->angle
+*/
+#define qh_ANGLEdegen     5.0
+
+/*-<a                             href="qh-merge.htm#TOC"
+  >--------------------------------</a><a name="qh_ANGLEconcave">-</a>
+
+  qh_ANGLEconcave
+    offset to indicate concave facets in mergeT->angle
+
+  notes:
+    concave facets are assigned the range of [2,4] in mergeT->angle
+    roundoff error may make the angle less than 2
+*/
+#define qh_ANGLEconcave  1.5
+
+/*-<a                             href="qh-merge.htm#TOC"
+  >--------------------------------</a><a name="MRG">-</a>
+
+  MRG... (mergeType)
+    indicates the type of a merge (mergeT->type)
+*/
+typedef enum {  /* in sort order for facet_mergeset */
+  MRGnone= 0,
+  MRGcoplanar,          /* centrum coplanar */
+  MRGanglecoplanar,     /* angle coplanar */
+                        /* could detect half concave ridges */
+  MRGconcave,           /* concave ridge */
+  MRGflip,              /* flipped facet. facet1 == facet2 */
+  MRGridge,             /* duplicate ridge (qh_MERGEridge) */
+                        /* degen and redundant go onto degen_mergeset */
+  MRGdegen,             /* degenerate facet (!enough neighbors) facet1 == facet2 */
+  MRGredundant,         /* redundant facet (vertex subset) */
+                        /* merge_degenredundant assumes degen < redundant */
+  MRGmirror,            /* mirror facet from qh_triangulate */
+  ENDmrg
+} mergeType;
+
+/*-<a                             href="qh-merge.htm#TOC"
+  >--------------------------------</a><a name="qh_MERGEapex">-</a>
+
+  qh_MERGEapex
+    flag for qh_mergefacet() to indicate an apex merge
+*/
+#define qh_MERGEapex     True
+
+/*============ -structures- ====================*/
+
+/*-<a                             href="qh-merge.htm#TOC"
+  >--------------------------------</a><a name="mergeT">-</a>
+
+  mergeT
+    structure used to merge facets
+*/
+
+typedef struct mergeT mergeT;
+struct mergeT {         /* initialize in qh_appendmergeset */
+  realT   angle;        /* angle between normals of facet1 and facet2 */
+  facetT *facet1;       /* will merge facet1 into facet2 */
+  facetT *facet2;
+  mergeType type;
+};
+
+
+/*=========== -macros- =========================*/
+
+/*-<a                             href="qh-merge.htm#TOC"
+  >--------------------------------</a><a name="FOREACHmerge_">-</a>
+
+  FOREACHmerge_( merges ) {...}
+    assign 'merge' to each merge in merges
+
+  notes:
+    uses 'mergeT *merge, **mergep;'
+    if qh_mergefacet(),
+      restart since qh.facet_mergeset may change
+    see <a href="qset.h#FOREACHsetelement_">FOREACHsetelement_</a>
+*/
+#define FOREACHmerge_( merges ) FOREACHsetelement_(mergeT, merges, merge)
+
+/*============ prototypes in alphabetical order after pre/postmerge =======*/
+
+void    qh_premerge(vertexT *apex, realT maxcentrum, realT maxangle);
+void    qh_postmerge(const char *reason, realT maxcentrum, realT maxangle,
+             boolT vneighbors);
+void    qh_all_merges(boolT othermerge, boolT vneighbors);
+void    qh_appendmergeset(facetT *facet, facetT *neighbor, mergeType mergetype, realT *angle);
+setT   *qh_basevertices( facetT *samecycle);
+void    qh_checkconnect(void /* qh.new_facets */);
+boolT   qh_checkzero(boolT testall);
+int     qh_compareangle(const void *p1, const void *p2);
+int     qh_comparemerge(const void *p1, const void *p2);
+int     qh_comparevisit(const void *p1, const void *p2);
+void    qh_copynonconvex(ridgeT *atridge);
+void    qh_degen_redundant_facet(facetT *facet);
+void    qh_degen_redundant_neighbors(facetT *facet, facetT *delfacet);
+vertexT *qh_find_newvertex(vertexT *oldvertex, setT *vertices, setT *ridges);
+void    qh_findbest_test(boolT testcentrum, facetT *facet, facetT *neighbor,
+           facetT **bestfacet, realT *distp, realT *mindistp, realT *maxdistp);
+facetT *qh_findbestneighbor(facetT *facet, realT *distp, realT *mindistp, realT *maxdistp);
+void    qh_flippedmerges(facetT *facetlist, boolT *wasmerge);
+void    qh_forcedmerges( boolT *wasmerge);
+void    qh_getmergeset(facetT *facetlist);
+void    qh_getmergeset_initial(facetT *facetlist);
+void    qh_hashridge(setT *hashtable, int hashsize, ridgeT *ridge, vertexT *oldvertex);
+ridgeT *qh_hashridge_find(setT *hashtable, int hashsize, ridgeT *ridge,
+              vertexT *vertex, vertexT *oldvertex, int *hashslot);
+void    qh_makeridges(facetT *facet);
+void    qh_mark_dupridges(facetT *facetlist);
+void    qh_maydropneighbor(facetT *facet);
+int     qh_merge_degenredundant(void);
+void    qh_merge_nonconvex( facetT *facet1, facetT *facet2, mergeType mergetype);
+void    qh_mergecycle(facetT *samecycle, facetT *newfacet);
+void    qh_mergecycle_all(facetT *facetlist, boolT *wasmerge);
+void    qh_mergecycle_facets( facetT *samecycle, facetT *newfacet);
+void    qh_mergecycle_neighbors(facetT *samecycle, facetT *newfacet);
+void    qh_mergecycle_ridges(facetT *samecycle, facetT *newfacet);
+void    qh_mergecycle_vneighbors( facetT *samecycle, facetT *newfacet);
+void    qh_mergefacet(facetT *facet1, facetT *facet2, realT *mindist, realT *maxdist, boolT mergeapex);
+void    qh_mergefacet2d(facetT *facet1, facetT *facet2);
+void    qh_mergeneighbors(facetT *facet1, facetT *facet2);
+void    qh_mergeridges(facetT *facet1, facetT *facet2);
+void    qh_mergesimplex(facetT *facet1, facetT *facet2, boolT mergeapex);
+void    qh_mergevertex_del(vertexT *vertex, facetT *facet1, facetT *facet2);
+void    qh_mergevertex_neighbors(facetT *facet1, facetT *facet2);
+void    qh_mergevertices(setT *vertices1, setT **vertices);
+setT   *qh_neighbor_intersections(vertexT *vertex);
+void    qh_newvertices(setT *vertices);
+boolT   qh_reducevertices(void);
+vertexT *qh_redundant_vertex(vertexT *vertex);
+boolT   qh_remove_extravertices(facetT *facet);
+vertexT *qh_rename_sharedvertex(vertexT *vertex, facetT *facet);
+void    qh_renameridgevertex(ridgeT *ridge, vertexT *oldvertex, vertexT *newvertex);
+void    qh_renamevertex(vertexT *oldvertex, vertexT *newvertex, setT *ridges,
+                        facetT *oldfacet, facetT *neighborA);
+boolT   qh_test_appendmerge(facetT *facet, facetT *neighbor);
+boolT   qh_test_vneighbors(void /* qh.newfacet_list */);
+void    qh_tracemerge(facetT *facet1, facetT *facet2);
+void    qh_tracemerging(void);
+void    qh_updatetested( facetT *facet1, facetT *facet2);
+setT   *qh_vertexridges(vertexT *vertex);
+void    qh_vertexridges_facet(vertexT *vertex, facetT *facet, setT **ridges);
+void    qh_willdelete(facetT *facet, facetT *replace);
+
+#endif /* qhDEFmerge */
diff --git a/xs/src/qhull/src/libqhull/poly.c b/xs/src/qhull/src/libqhull/poly.c
new file mode 100644
index 0000000000..b8db6a9ef7
--- /dev/null
+++ b/xs/src/qhull/src/libqhull/poly.c
@@ -0,0 +1,1205 @@
+/*<html><pre>  -<a                             href="qh-poly.htm"
+  >-------------------------------</a><a name="TOP">-</a>
+
+   poly.c
+   implements polygons and simplices
+
+   see qh-poly.htm, poly.h and libqhull.h
+
+   infrequent code is in poly2.c
+   (all but top 50 and their callers 12/3/95)
+
+   Copyright (c) 1993-2015 The Geometry Center.
+   $Id: //main/2015/qhull/src/libqhull/poly.c#3 $$Change: 2064 $
+   $DateTime: 2016/01/18 12:36:08 $$Author: bbarber $
+*/
+
+#include "qhull_a.h"
+
+/*======== functions in alphabetical order ==========*/
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="appendfacet">-</a>
+
+  qh_appendfacet( facet )
+    appends facet to end of qh.facet_list,
+
+  returns:
+    updates qh.newfacet_list, facet_next, facet_list
+    increments qh.numfacets
+
+  notes:
+    assumes qh.facet_list/facet_tail is defined (createsimplex)
+
+  see:
+    qh_removefacet()
+
+*/
+void qh_appendfacet(facetT *facet) {
+  facetT *tail= qh facet_tail;
+
+  if (tail == qh newfacet_list)
+    qh newfacet_list= facet;
+  if (tail == qh facet_next)
+    qh facet_next= facet;
+  facet->previous= tail->previous;
+  facet->next= tail;
+  if (tail->previous)
+    tail->previous->next= facet;
+  else
+    qh facet_list= facet;
+  tail->previous= facet;
+  qh num_facets++;
+  trace4((qh ferr, 4044, "qh_appendfacet: append f%d to facet_list\n", facet->id));
+} /* appendfacet */
+
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="appendvertex">-</a>
+
+  qh_appendvertex( vertex )
+    appends vertex to end of qh.vertex_list,
+
+  returns:
+    sets vertex->newlist
+    updates qh.vertex_list, newvertex_list
+    increments qh.num_vertices
+
+  notes:
+    assumes qh.vertex_list/vertex_tail is defined (createsimplex)
+
+*/
+void qh_appendvertex(vertexT *vertex) {
+  vertexT *tail= qh vertex_tail;
+
+  if (tail == qh newvertex_list)
+    qh newvertex_list= vertex;
+  vertex->newlist= True;
+  vertex->previous= tail->previous;
+  vertex->next= tail;
+  if (tail->previous)
+    tail->previous->next= vertex;
+  else
+    qh vertex_list= vertex;
+  tail->previous= vertex;
+  qh num_vertices++;
+  trace4((qh ferr, 4045, "qh_appendvertex: append v%d to vertex_list\n", vertex->id));
+} /* appendvertex */
+
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="attachnewfacets">-</a>
+
+  qh_attachnewfacets( )
+    attach horizon facets to new facets in qh.newfacet_list
+    newfacets have neighbor and ridge links to horizon but not vice versa
+    only needed for qh.ONLYgood
+
+  returns:
+    set qh.NEWfacets
+    horizon facets linked to new facets
+      ridges changed from visible facets to new facets
+      simplicial ridges deleted
+    qh.visible_list, no ridges valid
+    facet->f.replace is a newfacet (if any)
+
+  design:
+    delete interior ridges and neighbor sets by
+      for each visible, non-simplicial facet
+        for each ridge
+          if last visit or if neighbor is simplicial
+            if horizon neighbor
+              delete ridge for horizon's ridge set
+            delete ridge
+        erase neighbor set
+    attach horizon facets and new facets by
+      for all new facets
+        if corresponding horizon facet is simplicial
+          locate corresponding visible facet {may be more than one}
+          link visible facet to new facet
+          replace visible facet with new facet in horizon
+        else it's non-simplicial
+          for all visible neighbors of the horizon facet
+            link visible neighbor to new facet
+            delete visible neighbor from horizon facet
+          append new facet to horizon's neighbors
+          the first ridge of the new facet is the horizon ridge
+          link the new facet into the horizon ridge
+*/
+void qh_attachnewfacets(void /* qh.visible_list, newfacet_list */) {
+  facetT *newfacet= NULL, *neighbor, **neighborp, *horizon, *visible;
+  ridgeT *ridge, **ridgep;
+
+  qh NEWfacets= True;
+  trace3((qh ferr, 3012, "qh_attachnewfacets: delete interior ridges\n"));
+  qh visit_id++;
+  FORALLvisible_facets {
+    visible->visitid= qh visit_id;
+    if (visible->ridges) {
+      FOREACHridge_(visible->ridges) {
+        neighbor= otherfacet_(ridge, visible);
+        if (neighbor->visitid == qh visit_id
+            || (!neighbor->visible && neighbor->simplicial)) {
+          if (!neighbor->visible)  /* delete ridge for simplicial horizon */
+            qh_setdel(neighbor->ridges, ridge);
+          qh_setfree(&(ridge->vertices)); /* delete on 2nd visit */
+          qh_memfree(ridge, (int)sizeof(ridgeT));
+        }
+      }
+      SETfirst_(visible->ridges)= NULL;
+    }
+    SETfirst_(visible->neighbors)= NULL;
+  }
+  trace1((qh ferr, 1017, "qh_attachnewfacets: attach horizon facets to new facets\n"));
+  FORALLnew_facets {
+    horizon= SETfirstt_(newfacet->neighbors, facetT);
+    if (horizon->simplicial) {
+      visible= NULL;
+      FOREACHneighbor_(horizon) {   /* may have more than one horizon ridge */
+        if (neighbor->visible) {
+          if (visible) {
+            if (qh_setequal_skip(newfacet->vertices, 0, horizon->vertices,
+                                  SETindex_(horizon->neighbors, neighbor))) {
+              visible= neighbor;
+              break;
+            }
+          }else
+            visible= neighbor;
+        }
+      }
+      if (visible) {
+        visible->f.replace= newfacet;
+        qh_setreplace(horizon->neighbors, visible, newfacet);
+      }else {
+        qh_fprintf(qh ferr, 6102, "qhull internal error (qh_attachnewfacets): couldn't find visible facet for horizon f%d of newfacet f%d\n",
+                 horizon->id, newfacet->id);
+        qh_errexit2(qh_ERRqhull, horizon, newfacet);
+      }
+    }else { /* non-simplicial, with a ridge for newfacet */
+      FOREACHneighbor_(horizon) {    /* may hold for many new facets */
+        if (neighbor->visible) {
+          neighbor->f.replace= newfacet;
+          qh_setdelnth(horizon->neighbors,
+                        SETindex_(horizon->neighbors, neighbor));
+          neighborp--; /* repeat */
+        }
+      }
+      qh_setappend(&horizon->neighbors, newfacet);
+      ridge= SETfirstt_(newfacet->ridges, ridgeT);
+      if (ridge->top == horizon)
+        ridge->bottom= newfacet;
+      else
+        ridge->top= newfacet;
+      }
+  } /* newfacets */
+  if (qh PRINTstatistics) {
+    FORALLvisible_facets {
+      if (!visible->f.replace)
+        zinc_(Zinsidevisible);
+    }
+  }
+} /* attachnewfacets */
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="checkflipped">-</a>
+
+  qh_checkflipped( facet, dist, allerror )
+    checks facet orientation to interior point
+
+    if allerror set,
+      tests against qh.DISTround
+    else
+      tests against 0 since tested against DISTround before
+
+  returns:
+    False if it flipped orientation (sets facet->flipped)
+    distance if non-NULL
+*/
+boolT qh_checkflipped(facetT *facet, realT *distp, boolT allerror) {
+  realT dist;
+
+  if (facet->flipped && !distp)
+    return False;
+  zzinc_(Zdistcheck);
+  qh_distplane(qh interior_point, facet, &dist);
+  if (distp)
+    *distp= dist;
+  if ((allerror && dist > -qh DISTround)|| (!allerror && dist >= 0.0)) {
+    facet->flipped= True;
+    zzinc_(Zflippedfacets);
+    trace0((qh ferr, 19, "qh_checkflipped: facet f%d is flipped, distance= %6.12g during p%d\n",
+              facet->id, dist, qh furthest_id));
+    qh_precision("flipped facet");
+    return False;
+  }
+  return True;
+} /* checkflipped */
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="delfacet">-</a>
+
+  qh_delfacet( facet )
+    removes facet from facet_list and frees up its memory
+
+  notes:
+    assumes vertices and ridges already freed
+*/
+void qh_delfacet(facetT *facet) {
+  void **freelistp; /* used if !qh_NOmem by qh_memfree_() */
+
+  trace4((qh ferr, 4046, "qh_delfacet: delete f%d\n", facet->id));
+  if (facet == qh tracefacet)
+    qh tracefacet= NULL;
+  if (facet == qh GOODclosest)
+    qh GOODclosest= NULL;
+  qh_removefacet(facet);
+  if (!facet->tricoplanar || facet->keepcentrum) {
+    qh_memfree_(facet->normal, qh normal_size, freelistp);
+    if (qh CENTERtype == qh_ASvoronoi) {   /* braces for macro calls */
+      qh_memfree_(facet->center, qh center_size, freelistp);
+    }else /* AScentrum */ {
+      qh_memfree_(facet->center, qh normal_size, freelistp);
+    }
+  }
+  qh_setfree(&(facet->neighbors));
+  if (facet->ridges)
+    qh_setfree(&(facet->ridges));
+  qh_setfree(&(facet->vertices));
+  if (facet->outsideset)
+    qh_setfree(&(facet->outsideset));
+  if (facet->coplanarset)
+    qh_setfree(&(facet->coplanarset));
+  qh_memfree_(facet, (int)sizeof(facetT), freelistp);
+} /* delfacet */
+
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="deletevisible">-</a>
+
+  qh_deletevisible()
+    delete visible facets and vertices
+
+  returns:
+    deletes each facet and removes from facetlist
+    at exit, qh.visible_list empty (== qh.newfacet_list)
+
+  notes:
+    ridges already deleted
+    horizon facets do not reference facets on qh.visible_list
+    new facets in qh.newfacet_list
+    uses   qh.visit_id;
+*/
+void qh_deletevisible(void /*qh.visible_list*/) {
+  facetT *visible, *nextfacet;
+  vertexT *vertex, **vertexp;
+  int numvisible= 0, numdel= qh_setsize(qh del_vertices);
+
+  trace1((qh ferr, 1018, "qh_deletevisible: delete %d visible facets and %d vertices\n",
+         qh num_visible, numdel));
+  for (visible= qh visible_list; visible && visible->visible;
+                visible= nextfacet) { /* deleting current */
+    nextfacet= visible->next;
+    numvisible++;
+    qh_delfacet(visible);
+  }
+  if (numvisible != qh num_visible) {
+    qh_fprintf(qh ferr, 6103, "qhull internal error (qh_deletevisible): qh num_visible %d is not number of visible facets %d\n",
+             qh num_visible, numvisible);
+    qh_errexit(qh_ERRqhull, NULL, NULL);
+  }
+  qh num_visible= 0;
+  zadd_(Zvisfacettot, numvisible);
+  zmax_(Zvisfacetmax, numvisible);
+  zzadd_(Zdelvertextot, numdel);
+  zmax_(Zdelvertexmax, numdel);
+  FOREACHvertex_(qh del_vertices)
+    qh_delvertex(vertex);
+  qh_settruncate(qh del_vertices, 0);
+} /* deletevisible */
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="facetintersect">-</a>
+
+  qh_facetintersect( facetA, facetB, skipa, skipB, prepend )
+    return vertices for intersection of two simplicial facets
+    may include 1 prepended entry (if more, need to settemppush)
+
+  returns:
+    returns set of qh.hull_dim-1 + prepend vertices
+    returns skipped index for each test and checks for exactly one
+
+  notes:
+    does not need settemp since set in quick memory
+
+  see also:
+    qh_vertexintersect and qh_vertexintersect_new
+    use qh_setnew_delnthsorted to get nth ridge (no skip information)
+
+  design:
+    locate skipped vertex by scanning facet A's neighbors
+    locate skipped vertex by scanning facet B's neighbors
+    intersect the vertex sets
+*/
+setT *qh_facetintersect(facetT *facetA, facetT *facetB,
+                         int *skipA,int *skipB, int prepend) {
+  setT *intersect;
+  int dim= qh hull_dim, i, j;
+  facetT **neighborsA, **neighborsB;
+
+  neighborsA= SETaddr_(facetA->neighbors, facetT);
+  neighborsB= SETaddr_(facetB->neighbors, facetT);
+  i= j= 0;
+  if (facetB == *neighborsA++)
+    *skipA= 0;
+  else if (facetB == *neighborsA++)
+    *skipA= 1;
+  else if (facetB == *neighborsA++)
+    *skipA= 2;
+  else {
+    for (i=3; i < dim; i++) {
+      if (facetB == *neighborsA++) {
+        *skipA= i;
+        break;
+      }
+    }
+  }
+  if (facetA == *neighborsB++)
+    *skipB= 0;
+  else if (facetA == *neighborsB++)
+    *skipB= 1;
+  else if (facetA == *neighborsB++)
+    *skipB= 2;
+  else {
+    for (j=3; j < dim; j++) {
+      if (facetA == *neighborsB++) {
+        *skipB= j;
+        break;
+      }
+    }
+  }
+  if (i >= dim || j >= dim) {
+    qh_fprintf(qh ferr, 6104, "qhull internal error (qh_facetintersect): f%d or f%d not in others neighbors\n",
+            facetA->id, facetB->id);
+    qh_errexit2(qh_ERRqhull, facetA, facetB);
+  }
+  intersect= qh_setnew_delnthsorted(facetA->vertices, qh hull_dim, *skipA, prepend);
+  trace4((qh ferr, 4047, "qh_facetintersect: f%d skip %d matches f%d skip %d\n",
+          facetA->id, *skipA, facetB->id, *skipB));
+  return(intersect);
+} /* facetintersect */
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="gethash">-</a>
+
+  qh_gethash( hashsize, set, size, firstindex, skipelem )
+    return hashvalue for a set with firstindex and skipelem
+
+  notes:
+    returned hash is in [0,hashsize)
+    assumes at least firstindex+1 elements
+    assumes skipelem is NULL, in set, or part of hash
+
+    hashes memory addresses which may change over different runs of the same data
+    using sum for hash does badly in high d
+*/
+int qh_gethash(int hashsize, setT *set, int size, int firstindex, void *skipelem) {
+  void **elemp= SETelemaddr_(set, firstindex, void);
+  ptr_intT hash = 0, elem;
+  unsigned result;
+  int i;
+#ifdef _MSC_VER                   /* Microsoft Visual C++ -- warn about 64-bit issues */
+#pragma warning( push)            /* WARN64 -- ptr_intT holds a 64-bit pointer */
+#pragma warning( disable : 4311)  /* 'type cast': pointer truncation from 'void*' to 'ptr_intT' */
+#endif
+
+  switch (size-firstindex) {
+  case 1:
+    hash= (ptr_intT)(*elemp) - (ptr_intT) skipelem;
+    break;
+  case 2:
+    hash= (ptr_intT)(*elemp) + (ptr_intT)elemp[1] - (ptr_intT) skipelem;
+    break;
+  case 3:
+    hash= (ptr_intT)(*elemp) + (ptr_intT)elemp[1] + (ptr_intT)elemp[2]
+      - (ptr_intT) skipelem;
+    break;
+  case 4:
+    hash= (ptr_intT)(*elemp) + (ptr_intT)elemp[1] + (ptr_intT)elemp[2]
+      + (ptr_intT)elemp[3] - (ptr_intT) skipelem;
+    break;
+  case 5:
+    hash= (ptr_intT)(*elemp) + (ptr_intT)elemp[1] + (ptr_intT)elemp[2]
+      + (ptr_intT)elemp[3] + (ptr_intT)elemp[4] - (ptr_intT) skipelem;
+    break;
+  case 6:
+    hash= (ptr_intT)(*elemp) + (ptr_intT)elemp[1] + (ptr_intT)elemp[2]
+      + (ptr_intT)elemp[3] + (ptr_intT)elemp[4]+ (ptr_intT)elemp[5]
+      - (ptr_intT) skipelem;
+    break;
+  default:
+    hash= 0;
+    i= 3;
+    do {     /* this is about 10% in 10-d */
+      if ((elem= (ptr_intT)*elemp++) != (ptr_intT)skipelem) {
+        hash ^= (elem << i) + (elem >> (32-i));
+        i += 3;
+        if (i >= 32)
+          i -= 32;
+      }
+    }while (*elemp);
+    break;
+  }
+  if (hashsize<0) {
+    qh_fprintf(qh ferr, 6202, "qhull internal error: negative hashsize %d passed to qh_gethash [poly.c]\n", hashsize);
+    qh_errexit2(qh_ERRqhull, NULL, NULL);
+  }
+  result= (unsigned)hash;
+  result %= (unsigned)hashsize;
+  /* result= 0; for debugging */
+  return result;
+#ifdef _MSC_VER
+#pragma warning( pop)
+#endif
+} /* gethash */
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="makenewfacet">-</a>
+
+  qh_makenewfacet( vertices, toporient, horizon )
+    creates a toporient? facet from vertices
+
+  returns:
+    returns newfacet
+      adds newfacet to qh.facet_list
+      newfacet->vertices= vertices
+      if horizon
+        newfacet->neighbor= horizon, but not vice versa
+    newvertex_list updated with vertices
+*/
+facetT *qh_makenewfacet(setT *vertices, boolT toporient,facetT *horizon) {
+  facetT *newfacet;
+  vertexT *vertex, **vertexp;
+
+  FOREACHvertex_(vertices) {
+    if (!vertex->newlist) {
+      qh_removevertex(vertex);
+      qh_appendvertex(vertex);
+    }
+  }
+  newfacet= qh_newfacet();
+  newfacet->vertices= vertices;
+  newfacet->toporient= (unsigned char)toporient;
+  if (horizon)
+    qh_setappend(&(newfacet->neighbors), horizon);
+  qh_appendfacet(newfacet);
+  return(newfacet);
+} /* makenewfacet */
+
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="makenewplanes">-</a>
+
+  qh_makenewplanes()
+    make new hyperplanes for facets on qh.newfacet_list
+
+  returns:
+    all facets have hyperplanes or are marked for   merging
+    doesn't create hyperplane if horizon is coplanar (will merge)
+    updates qh.min_vertex if qh.JOGGLEmax
+
+  notes:
+    facet->f.samecycle is defined for facet->mergehorizon facets
+*/
+void qh_makenewplanes(void /* newfacet_list */) {
+  facetT *newfacet;
+
+  FORALLnew_facets {
+    if (!newfacet->mergehorizon)
+      qh_setfacetplane(newfacet);
+  }
+  if (qh JOGGLEmax < REALmax/2)
+    minimize_(qh min_vertex, -wwval_(Wnewvertexmax));
+} /* makenewplanes */
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="makenew_nonsimplicial">-</a>
+
+  qh_makenew_nonsimplicial( visible, apex, numnew )
+    make new facets for ridges of a visible facet
+
+  returns:
+    first newfacet, bumps numnew as needed
+    attaches new facets if !qh.ONLYgood
+    marks ridge neighbors for simplicial visible
+    if (qh.ONLYgood)
+      ridges on newfacet, horizon, and visible
+    else
+      ridge and neighbors between newfacet and   horizon
+      visible facet's ridges are deleted
+
+  notes:
+    qh.visit_id if visible has already been processed
+    sets neighbor->seen for building f.samecycle
+      assumes all 'seen' flags initially false
+
+  design:
+    for each ridge of visible facet
+      get neighbor of visible facet
+      if neighbor was already processed
+        delete the ridge (will delete all visible facets later)
+      if neighbor is a horizon facet
+        create a new facet
+        if neighbor coplanar
+          adds newfacet to f.samecycle for later merging
+        else
+          updates neighbor's neighbor set
+          (checks for non-simplicial facet with multiple ridges to visible facet)
+        updates neighbor's ridge set
+        (checks for simplicial neighbor to non-simplicial visible facet)
+        (deletes ridge if neighbor is simplicial)
+
+*/
+#ifndef qh_NOmerge
+facetT *qh_makenew_nonsimplicial(facetT *visible, vertexT *apex, int *numnew) {
+  void **freelistp; /* used if !qh_NOmem by qh_memfree_() */
+  ridgeT *ridge, **ridgep;
+  facetT *neighbor, *newfacet= NULL, *samecycle;
+  setT *vertices;
+  boolT toporient;
+  int ridgeid;
+
+  FOREACHridge_(visible->ridges) {
+    ridgeid= ridge->id;
+    neighbor= otherfacet_(ridge, visible);
+    if (neighbor->visible) {
+      if (!qh ONLYgood) {
+        if (neighbor->visitid == qh visit_id) {
+          qh_setfree(&(ridge->vertices));  /* delete on 2nd visit */
+          qh_memfree_(ridge, (int)sizeof(ridgeT), freelistp);
+        }
+      }
+    }else {  /* neighbor is an horizon facet */
+      toporient= (ridge->top == visible);
+      vertices= qh_setnew(qh hull_dim); /* makes sure this is quick */
+      qh_setappend(&vertices, apex);
+      qh_setappend_set(&vertices, ridge->vertices);
+      newfacet= qh_makenewfacet(vertices, toporient, neighbor);
+      (*numnew)++;
+      if (neighbor->coplanar) {
+        newfacet->mergehorizon= True;
+        if (!neighbor->seen) {
+          newfacet->f.samecycle= newfacet;
+          neighbor->f.newcycle= newfacet;
+        }else {
+          samecycle= neighbor->f.newcycle;
+          newfacet->f.samecycle= samecycle->f.samecycle;
+          samecycle->f.samecycle= newfacet;
+        }
+      }
+      if (qh ONLYgood) {
+        if (!neighbor->simplicial)
+          qh_setappend(&(newfacet->ridges), ridge);
+      }else {  /* qh_attachnewfacets */
+        if (neighbor->seen) {
+          if (neighbor->simplicial) {
+            qh_fprintf(qh ferr, 6105, "qhull internal error (qh_makenew_nonsimplicial): simplicial f%d sharing two ridges with f%d\n",
+                   neighbor->id, visible->id);
+            qh_errexit2(qh_ERRqhull, neighbor, visible);
+          }
+          qh_setappend(&(neighbor->neighbors), newfacet);
+        }else
+          qh_setreplace(neighbor->neighbors, visible, newfacet);
+        if (neighbor->simplicial) {
+          qh_setdel(neighbor->ridges, ridge);
+          qh_setfree(&(ridge->vertices));
+          qh_memfree(ridge, (int)sizeof(ridgeT));
+        }else {
+          qh_setappend(&(newfacet->ridges), ridge);
+          if (toporient)
+            ridge->top= newfacet;
+          else
+            ridge->bottom= newfacet;
+        }
+      trace4((qh ferr, 4048, "qh_makenew_nonsimplicial: created facet f%d from v%d and r%d of horizon f%d\n",
+            newfacet->id, apex->id, ridgeid, neighbor->id));
+      }
+    }
+    neighbor->seen= True;
+  } /* for each ridge */
+  if (!qh ONLYgood)
+    SETfirst_(visible->ridges)= NULL;
+  return newfacet;
+} /* makenew_nonsimplicial */
+#else /* qh_NOmerge */
+facetT *qh_makenew_nonsimplicial(facetT *visible, vertexT *apex, int *numnew) {
+  return NULL;
+}
+#endif /* qh_NOmerge */
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="makenew_simplicial">-</a>
+
+  qh_makenew_simplicial( visible, apex, numnew )
+    make new facets for simplicial visible facet and apex
+
+  returns:
+    attaches new facets if (!qh.ONLYgood)
+      neighbors between newfacet and horizon
+
+  notes:
+    nop if neighbor->seen or neighbor->visible(see qh_makenew_nonsimplicial)
+
+  design:
+    locate neighboring horizon facet for visible facet
+    determine vertices and orientation
+    create new facet
+    if coplanar,
+      add new facet to f.samecycle
+    update horizon facet's neighbor list
+*/
+facetT *qh_makenew_simplicial(facetT *visible, vertexT *apex, int *numnew) {
+  facetT *neighbor, **neighborp, *newfacet= NULL;
+  setT *vertices;
+  boolT flip, toporient;
+  int horizonskip= 0, visibleskip= 0;
+
+  FOREACHneighbor_(visible) {
+    if (!neighbor->seen && !neighbor->visible) {
+      vertices= qh_facetintersect(neighbor,visible, &horizonskip, &visibleskip, 1);
+      SETfirst_(vertices)= apex;
+      flip= ((horizonskip & 0x1) ^ (visibleskip & 0x1));
+      if (neighbor->toporient)
+        toporient= horizonskip & 0x1;
+      else
+        toporient= (horizonskip & 0x1) ^ 0x1;
+      newfacet= qh_makenewfacet(vertices, toporient, neighbor);
+      (*numnew)++;
+      if (neighbor->coplanar && (qh PREmerge || qh MERGEexact)) {
+#ifndef qh_NOmerge
+        newfacet->f.samecycle= newfacet;
+        newfacet->mergehorizon= True;
+#endif
+      }
+      if (!qh ONLYgood)
+        SETelem_(neighbor->neighbors, horizonskip)= newfacet;
+      trace4((qh ferr, 4049, "qh_makenew_simplicial: create facet f%d top %d from v%d and horizon f%d skip %d top %d and visible f%d skip %d, flip? %d\n",
+            newfacet->id, toporient, apex->id, neighbor->id, horizonskip,
+              neighbor->toporient, visible->id, visibleskip, flip));
+    }
+  }
+  return newfacet;
+} /* makenew_simplicial */
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="matchneighbor">-</a>
+
+  qh_matchneighbor( newfacet, newskip, hashsize, hashcount )
+    either match subridge of newfacet with neighbor or add to hash_table
+
+  returns:
+    duplicate ridges are unmatched and marked by qh_DUPLICATEridge
+
+  notes:
+    ridge is newfacet->vertices w/o newskip vertex
+    do not allocate memory (need to free hash_table cleanly)
+    uses linear hash chains
+
+  see also:
+    qh_matchduplicates
+
+  design:
+    for each possible matching facet in qh.hash_table
+      if vertices match
+        set ismatch, if facets have opposite orientation
+        if ismatch and matching facet doesn't have a match
+          match the facets by updating their neighbor sets
+        else
+          indicate a duplicate ridge
+          set facet hyperplane for later testing
+          add facet to hashtable
+          unless the other facet was already a duplicate ridge
+            mark both facets with a duplicate ridge
+            add other facet (if defined) to hash table
+*/
+void qh_matchneighbor(facetT *newfacet, int newskip, int hashsize, int *hashcount) {
+  boolT newfound= False;   /* True, if new facet is already in hash chain */
+  boolT same, ismatch;
+  int hash, scan;
+  facetT *facet, *matchfacet;
+  int skip, matchskip;
+
+  hash= qh_gethash(hashsize, newfacet->vertices, qh hull_dim, 1,
+                     SETelem_(newfacet->vertices, newskip));
+  trace4((qh ferr, 4050, "qh_matchneighbor: newfacet f%d skip %d hash %d hashcount %d\n",
+          newfacet->id, newskip, hash, *hashcount));
+  zinc_(Zhashlookup);
+  for (scan= hash; (facet= SETelemt_(qh hash_table, scan, facetT));
+       scan= (++scan >= hashsize ? 0 : scan)) {
+    if (facet == newfacet) {
+      newfound= True;
+      continue;
+    }
+    zinc_(Zhashtests);
+    if (qh_matchvertices(1, newfacet->vertices, newskip, facet->vertices, &skip, &same)) {
+      if (SETelem_(newfacet->vertices, newskip) ==
+          SETelem_(facet->vertices, skip)) {
+        qh_precision("two facets with the same vertices");
+        qh_fprintf(qh ferr, 6106, "qhull precision error: Vertex sets are the same for f%d and f%d.  Can not force output.\n",
+          facet->id, newfacet->id);
+        qh_errexit2(qh_ERRprec, facet, newfacet);
+      }
+      ismatch= (same == (boolT)((newfacet->toporient ^ facet->toporient)));
+      matchfacet= SETelemt_(facet->neighbors, skip, facetT);
+      if (ismatch && !matchfacet) {
+        SETelem_(facet->neighbors, skip)= newfacet;
+        SETelem_(newfacet->neighbors, newskip)= facet;
+        (*hashcount)--;
+        trace4((qh ferr, 4051, "qh_matchneighbor: f%d skip %d matched with new f%d skip %d\n",
+           facet->id, skip, newfacet->id, newskip));
+        return;
+      }
+      if (!qh PREmerge && !qh MERGEexact) {
+        qh_precision("a ridge with more than two neighbors");
+        qh_fprintf(qh ferr, 6107, "qhull precision error: facets f%d, f%d and f%d meet at a ridge with more than 2 neighbors.  Can not continue.\n",
+                 facet->id, newfacet->id, getid_(matchfacet));
+        qh_errexit2(qh_ERRprec, facet, newfacet);
+      }
+      SETelem_(newfacet->neighbors, newskip)= qh_DUPLICATEridge;
+      newfacet->dupridge= True;
+      if (!newfacet->normal)
+        qh_setfacetplane(newfacet);
+      qh_addhash(newfacet, qh hash_table, hashsize, hash);
+      (*hashcount)++;
+      if (!facet->normal)
+        qh_setfacetplane(facet);
+      if (matchfacet != qh_DUPLICATEridge) {
+        SETelem_(facet->neighbors, skip)= qh_DUPLICATEridge;
+        facet->dupridge= True;
+        if (!facet->normal)
+          qh_setfacetplane(facet);
+        if (matchfacet) {
+          matchskip= qh_setindex(matchfacet->neighbors, facet);
+          if (matchskip<0) {
+              qh_fprintf(qh ferr, 6260, "qhull internal error (qh_matchneighbor): matchfacet f%d is in f%d neighbors but not vice versa.  Can not continue.\n",
+                  matchfacet->id, facet->id);
+              qh_errexit2(qh_ERRqhull, matchfacet, facet);
+          }
+          SETelem_(matchfacet->neighbors, matchskip)= qh_DUPLICATEridge; /* matchskip>=0 by QH6260 */
+          matchfacet->dupridge= True;
+          if (!matchfacet->normal)
+            qh_setfacetplane(matchfacet);
+          qh_addhash(matchfacet, qh hash_table, hashsize, hash);
+          *hashcount += 2;
+        }
+      }
+      trace4((qh ferr, 4052, "qh_matchneighbor: new f%d skip %d duplicates ridge for f%d skip %d matching f%d ismatch %d at hash %d\n",
+           newfacet->id, newskip, facet->id, skip,
+           (matchfacet == qh_DUPLICATEridge ? -2 : getid_(matchfacet)),
+           ismatch, hash));
+      return; /* end of duplicate ridge */
+    }
+  }
+  if (!newfound)
+    SETelem_(qh hash_table, scan)= newfacet;  /* same as qh_addhash */
+  (*hashcount)++;
+  trace4((qh ferr, 4053, "qh_matchneighbor: no match for f%d skip %d at hash %d\n",
+           newfacet->id, newskip, hash));
+} /* matchneighbor */
+
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="matchnewfacets">-</a>
+
+  qh_matchnewfacets()
+    match newfacets in qh.newfacet_list to their newfacet neighbors
+
+  returns:
+    qh.newfacet_list with full neighbor sets
+      get vertices with nth neighbor by deleting nth vertex
+    if qh.PREmerge/MERGEexact or qh.FORCEoutput
+      sets facet->flippped if flipped normal (also prevents point partitioning)
+    if duplicate ridges and qh.PREmerge/MERGEexact
+      sets facet->dupridge
+      missing neighbor links identifies extra ridges to be merging (qh_MERGEridge)
+
+  notes:
+    newfacets already have neighbor[0] (horizon facet)
+    assumes qh.hash_table is NULL
+    vertex->neighbors has not been updated yet
+    do not allocate memory after qh.hash_table (need to free it cleanly)
+
+  design:
+    delete neighbor sets for all new facets
+    initialize a hash table
+    for all new facets
+      match facet with neighbors
+    if unmatched facets (due to duplicate ridges)
+      for each new facet with a duplicate ridge
+        match it with a facet
+    check for flipped facets
+*/
+void qh_matchnewfacets(void /* qh.newfacet_list */) {
+  int numnew=0, hashcount=0, newskip;
+  facetT *newfacet, *neighbor;
+  int dim= qh hull_dim, hashsize, neighbor_i, neighbor_n;
+  setT *neighbors;
+#ifndef qh_NOtrace
+  int facet_i, facet_n, numfree= 0;
+  facetT *facet;
+#endif
+
+  trace1((qh ferr, 1019, "qh_matchnewfacets: match neighbors for new facets.\n"));
+  FORALLnew_facets {
+    numnew++;
+    {  /* inline qh_setzero(newfacet->neighbors, 1, qh hull_dim); */
+      neighbors= newfacet->neighbors;
+      neighbors->e[neighbors->maxsize].i= dim+1; /*may be overwritten*/
+      memset((char *)SETelemaddr_(neighbors, 1, void), 0, dim * SETelemsize);
+    }
+  }
+
+  qh_newhashtable(numnew*(qh hull_dim-1)); /* twice what is normally needed,
+                                     but every ridge could be DUPLICATEridge */
+  hashsize= qh_setsize(qh hash_table);
+  FORALLnew_facets {
+    for (newskip=1; newskip<qh hull_dim; newskip++) /* furthest/horizon already matched */
+      /* hashsize>0 because hull_dim>1 and numnew>0 */
+      qh_matchneighbor(newfacet, newskip, hashsize, &hashcount);
+#if 0   /* use the following to trap hashcount errors */
+    {
+      int count= 0, k;
+      facetT *facet, *neighbor;
+
+      count= 0;
+      FORALLfacet_(qh newfacet_list) {  /* newfacet already in use */
+        for (k=1; k < qh hull_dim; k++) {
+          neighbor= SETelemt_(facet->neighbors, k, facetT);
+          if (!neighbor || neighbor == qh_DUPLICATEridge)
+            count++;
+        }
+        if (facet == newfacet)
+          break;
+      }
+      if (count != hashcount) {
+        qh_fprintf(qh ferr, 8088, "qh_matchnewfacets: after adding facet %d, hashcount %d != count %d\n",
+                 newfacet->id, hashcount, count);
+        qh_errexit(qh_ERRqhull, newfacet, NULL);
+      }
+    }
+#endif  /* end of trap code */
+  }
+  if (hashcount) {
+    FORALLnew_facets {
+      if (newfacet->dupridge) {
+        FOREACHneighbor_i_(newfacet) {
+          if (neighbor == qh_DUPLICATEridge) {
+            qh_matchduplicates(newfacet, neighbor_i, hashsize, &hashcount);
+                    /* this may report MERGEfacet */
+          }
+        }
+      }
+    }
+  }
+  if (hashcount) {
+    qh_fprintf(qh ferr, 6108, "qhull internal error (qh_matchnewfacets): %d neighbors did not match up\n",
+        hashcount);
+    qh_printhashtable(qh ferr);
+    qh_errexit(qh_ERRqhull, NULL, NULL);
+  }
+#ifndef qh_NOtrace
+  if (qh IStracing >= 2) {
+    FOREACHfacet_i_(qh hash_table) {
+      if (!facet)
+        numfree++;
+    }
+    qh_fprintf(qh ferr, 8089, "qh_matchnewfacets: %d new facets, %d unused hash entries .  hashsize %d\n",
+             numnew, numfree, qh_setsize(qh hash_table));
+  }
+#endif /* !qh_NOtrace */
+  qh_setfree(&qh hash_table);
+  if (qh PREmerge || qh MERGEexact) {
+    if (qh IStracing >= 4)
+      qh_printfacetlist(qh newfacet_list, NULL, qh_ALL);
+    FORALLnew_facets {
+      if (newfacet->normal)
+        qh_checkflipped(newfacet, NULL, qh_ALL);
+    }
+  }else if (qh FORCEoutput)
+    qh_checkflipped_all(qh newfacet_list);  /* prints warnings for flipped */
+} /* matchnewfacets */
+
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="matchvertices">-</a>
+
+  qh_matchvertices( firstindex, verticesA, skipA, verticesB, skipB, same )
+    tests whether vertices match with a single skip
+    starts match at firstindex since all new facets have a common vertex
+
+  returns:
+    true if matched vertices
+    skip index for each set
+    sets same iff vertices have the same orientation
+
+  notes:
+    assumes skipA is in A and both sets are the same size
+
+  design:
+    set up pointers
+    scan both sets checking for a match
+    test orientation
+*/
+boolT qh_matchvertices(int firstindex, setT *verticesA, int skipA,
+       setT *verticesB, int *skipB, boolT *same) {
+  vertexT **elemAp, **elemBp, **skipBp=NULL, **skipAp;
+
+  elemAp= SETelemaddr_(verticesA, firstindex, vertexT);
+  elemBp= SETelemaddr_(verticesB, firstindex, vertexT);
+  skipAp= SETelemaddr_(verticesA, skipA, vertexT);
+  do if (elemAp != skipAp) {
+    while (*elemAp != *elemBp++) {
+      if (skipBp)
+        return False;
+      skipBp= elemBp;  /* one extra like FOREACH */
+    }
+  }while (*(++elemAp));
+  if (!skipBp)
+    skipBp= ++elemBp;
+  *skipB= SETindex_(verticesB, skipB); /* i.e., skipBp - verticesB */
+  *same= !((skipA & 0x1) ^ (*skipB & 0x1)); /* result is 0 or 1 */
+  trace4((qh ferr, 4054, "qh_matchvertices: matched by skip %d(v%d) and skip %d(v%d) same? %d\n",
+          skipA, (*skipAp)->id, *skipB, (*(skipBp-1))->id, *same));
+  return(True);
+} /* matchvertices */
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="newfacet">-</a>
+
+  qh_newfacet()
+    return a new facet
+
+  returns:
+    all fields initialized or cleared   (NULL)
+    preallocates neighbors set
+*/
+facetT *qh_newfacet(void) {
+  facetT *facet;
+  void **freelistp; /* used if !qh_NOmem by qh_memalloc_() */
+
+  qh_memalloc_((int)sizeof(facetT), freelistp, facet, facetT);
+  memset((char *)facet, (size_t)0, sizeof(facetT));
+  if (qh facet_id == qh tracefacet_id)
+    qh tracefacet= facet;
+  facet->id= qh facet_id++;
+  facet->neighbors= qh_setnew(qh hull_dim);
+#if !qh_COMPUTEfurthest
+  facet->furthestdist= 0.0;
+#endif
+#if qh_MAXoutside
+  if (qh FORCEoutput && qh APPROXhull)
+    facet->maxoutside= qh MINoutside;
+  else
+    facet->maxoutside= qh DISTround;
+#endif
+  facet->simplicial= True;
+  facet->good= True;
+  facet->newfacet= True;
+  trace4((qh ferr, 4055, "qh_newfacet: created facet f%d\n", facet->id));
+  return(facet);
+} /* newfacet */
+
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="newridge">-</a>
+
+  qh_newridge()
+    return a new ridge
+*/
+ridgeT *qh_newridge(void) {
+  ridgeT *ridge;
+  void **freelistp;   /* used if !qh_NOmem by qh_memalloc_() */
+
+  qh_memalloc_((int)sizeof(ridgeT), freelistp, ridge, ridgeT);
+  memset((char *)ridge, (size_t)0, sizeof(ridgeT));
+  zinc_(Ztotridges);
+  if (qh ridge_id == UINT_MAX) {
+    qh_fprintf(qh ferr, 7074, "\
+qhull warning: more than 2^32 ridges.  Qhull results are OK.  Since the ridge ID wraps around to 0, two ridges may have the same identifier.\n");
+  }
+  ridge->id= qh ridge_id++;
+  trace4((qh ferr, 4056, "qh_newridge: created ridge r%d\n", ridge->id));
+  return(ridge);
+} /* newridge */
+
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="pointid">-</a>
+
+  qh_pointid(  point )
+    return id for a point,
+    returns qh_IDnone(-3) if null, qh_IDinterior(-2) if interior, or qh_IDunknown(-1) if not known
+
+  alternative code if point is in qh.first_point...
+    unsigned long id;
+    id= ((unsigned long)point - (unsigned long)qh.first_point)/qh.normal_size;
+
+  notes:
+    Valid points are non-negative
+    WARN64 -- id truncated to 32-bits, at most 2G points
+    NOerrors returned (QhullPoint::id)
+    if point not in point array
+      the code does a comparison of unrelated pointers.
+*/
+int qh_pointid(pointT *point) {
+  ptr_intT offset, id;
+
+  if (!point)
+    return qh_IDnone;
+  else if (point == qh interior_point)
+    return qh_IDinterior;
+  else if (point >= qh first_point
+  && point < qh first_point + qh num_points * qh hull_dim) {
+    offset= (ptr_intT)(point - qh first_point);
+    id= offset / qh hull_dim;
+  }else if ((id= qh_setindex(qh other_points, point)) != -1)
+    id += qh num_points;
+  else
+    return qh_IDunknown;
+  return (int)id;
+} /* pointid */
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="removefacet">-</a>
+
+  qh_removefacet( facet )
+    unlinks facet from qh.facet_list,
+
+  returns:
+    updates qh.facet_list .newfacet_list .facet_next visible_list
+    decrements qh.num_facets
+
+  see:
+    qh_appendfacet
+*/
+void qh_removefacet(facetT *facet) {
+  facetT *next= facet->next, *previous= facet->previous;
+
+  if (facet == qh newfacet_list)
+    qh newfacet_list= next;
+  if (facet == qh facet_next)
+    qh facet_next= next;
+  if (facet == qh visible_list)
+    qh visible_list= next;
+  if (previous) {
+    previous->next= next;
+    next->previous= previous;
+  }else {  /* 1st facet in qh facet_list */
+    qh facet_list= next;
+    qh facet_list->previous= NULL;
+  }
+  qh num_facets--;
+  trace4((qh ferr, 4057, "qh_removefacet: remove f%d from facet_list\n", facet->id));
+} /* removefacet */
+
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="removevertex">-</a>
+
+  qh_removevertex( vertex )
+    unlinks vertex from qh.vertex_list,
+
+  returns:
+    updates qh.vertex_list .newvertex_list
+    decrements qh.num_vertices
+*/
+void qh_removevertex(vertexT *vertex) {
+  vertexT *next= vertex->next, *previous= vertex->previous;
+
+  if (vertex == qh newvertex_list)
+    qh newvertex_list= next;
+  if (previous) {
+    previous->next= next;
+    next->previous= previous;
+  }else {  /* 1st vertex in qh vertex_list */
+    qh vertex_list= vertex->next;
+    qh vertex_list->previous= NULL;
+  }
+  qh num_vertices--;
+  trace4((qh ferr, 4058, "qh_removevertex: remove v%d from vertex_list\n", vertex->id));
+} /* removevertex */
+
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="updatevertices">-</a>
+
+  qh_updatevertices()
+    update vertex neighbors and delete interior vertices
+
+  returns:
+    if qh.VERTEXneighbors, updates neighbors for each vertex
+      if qh.newvertex_list,
+         removes visible neighbors  from vertex neighbors
+      if qh.newfacet_list
+         adds new facets to vertex neighbors
+    if qh.visible_list
+       interior vertices added to qh.del_vertices for later partitioning
+
+  design:
+    if qh.VERTEXneighbors
+      deletes references to visible facets from vertex neighbors
+      appends new facets to the neighbor list for each vertex
+      checks all vertices of visible facets
+        removes visible facets from neighbor lists
+        marks unused vertices for deletion
+*/
+void qh_updatevertices(void /*qh.newvertex_list, newfacet_list, visible_list*/) {
+  facetT *newfacet= NULL, *neighbor, **neighborp, *visible;
+  vertexT *vertex, **vertexp;
+
+  trace3((qh ferr, 3013, "qh_updatevertices: delete interior vertices and update vertex->neighbors\n"));
+  if (qh VERTEXneighbors) {
+    FORALLvertex_(qh newvertex_list) {
+      FOREACHneighbor_(vertex) {
+        if (neighbor->visible)
+          SETref_(neighbor)= NULL;
+      }
+      qh_setcompact(vertex->neighbors);
+    }
+    FORALLnew_facets {
+      FOREACHvertex_(newfacet->vertices)
+        qh_setappend(&vertex->neighbors, newfacet);
+    }
+    FORALLvisible_facets {
+      FOREACHvertex_(visible->vertices) {
+        if (!vertex->newlist && !vertex->deleted) {
+          FOREACHneighbor_(vertex) { /* this can happen under merging */
+            if (!neighbor->visible)
+              break;
+          }
+          if (neighbor)
+            qh_setdel(vertex->neighbors, visible);
+          else {
+            vertex->deleted= True;
+            qh_setappend(&qh del_vertices, vertex);
+            trace2((qh ferr, 2041, "qh_updatevertices: delete vertex p%d(v%d) in f%d\n",
+                  qh_pointid(vertex->point), vertex->id, visible->id));
+          }
+        }
+      }
+    }
+  }else {  /* !VERTEXneighbors */
+    FORALLvisible_facets {
+      FOREACHvertex_(visible->vertices) {
+        if (!vertex->newlist && !vertex->deleted) {
+          vertex->deleted= True;
+          qh_setappend(&qh del_vertices, vertex);
+          trace2((qh ferr, 2042, "qh_updatevertices: delete vertex p%d(v%d) in f%d\n",
+                  qh_pointid(vertex->point), vertex->id, visible->id));
+        }
+      }
+    }
+  }
+} /* updatevertices */
+
+
+
diff --git a/xs/src/qhull/src/libqhull/poly.h b/xs/src/qhull/src/libqhull/poly.h
new file mode 100644
index 0000000000..af8b42077f
--- /dev/null
+++ b/xs/src/qhull/src/libqhull/poly.h
@@ -0,0 +1,296 @@
+/*<html><pre>  -<a                             href="qh-poly.htm"
+  >-------------------------------</a><a name="TOP">-</a>
+
+   poly.h
+   header file for poly.c and poly2.c
+
+   see qh-poly.htm, libqhull.h and poly.c
+
+   Copyright (c) 1993-2015 The Geometry Center.
+   $Id: //main/2015/qhull/src/libqhull/poly.h#3 $$Change: 2047 $
+   $DateTime: 2016/01/04 22:03:18 $$Author: bbarber $
+*/
+
+#ifndef qhDEFpoly
+#define qhDEFpoly 1
+
+#include "libqhull.h"
+
+/*===============   constants ========================== */
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >--------------------------------</a><a name="ALGORITHMfault">-</a>
+
+  ALGORITHMfault
+    use as argument to checkconvex() to report errors during buildhull
+*/
+#define qh_ALGORITHMfault 0
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >--------------------------------</a><a name="DATAfault">-</a>
+
+  DATAfault
+    use as argument to checkconvex() to report errors during initialhull
+*/
+#define qh_DATAfault 1
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >--------------------------------</a><a name="DUPLICATEridge">-</a>
+
+  DUPLICATEridge
+    special value for facet->neighbor to indicate a duplicate ridge
+
+  notes:
+    set by matchneighbor, used by matchmatch and mark_dupridge
+*/
+#define qh_DUPLICATEridge (facetT *)1L
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >--------------------------------</a><a name="MERGEridge">-</a>
+
+  MERGEridge       flag in facet
+    special value for facet->neighbor to indicate a merged ridge
+
+  notes:
+    set by matchneighbor, used by matchmatch and mark_dupridge
+*/
+#define qh_MERGEridge (facetT *)2L
+
+
+/*============ -structures- ====================*/
+
+/*=========== -macros- =========================*/
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >--------------------------------</a><a name="FORALLfacet_">-</a>
+
+  FORALLfacet_( facetlist ) { ... }
+    assign 'facet' to each facet in facetlist
+
+  notes:
+    uses 'facetT *facet;'
+    assumes last facet is a sentinel
+
+  see:
+    FORALLfacets
+*/
+#define FORALLfacet_( facetlist ) if (facetlist ) for ( facet=( facetlist ); facet && facet->next; facet= facet->next )
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >--------------------------------</a><a name="FORALLnew_facets">-</a>
+
+  FORALLnew_facets { ... }
+    assign 'newfacet' to each facet in qh.newfacet_list
+
+  notes:
+    uses 'facetT *newfacet;'
+    at exit, newfacet==NULL
+*/
+#define FORALLnew_facets for ( newfacet=qh newfacet_list;newfacet && newfacet->next;newfacet=newfacet->next )
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >--------------------------------</a><a name="FORALLvertex_">-</a>
+
+  FORALLvertex_( vertexlist ) { ... }
+    assign 'vertex' to each vertex in vertexlist
+
+  notes:
+    uses 'vertexT *vertex;'
+    at exit, vertex==NULL
+*/
+#define FORALLvertex_( vertexlist ) for (vertex=( vertexlist );vertex && vertex->next;vertex= vertex->next )
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >--------------------------------</a><a name="FORALLvisible_facets">-</a>
+
+  FORALLvisible_facets { ... }
+    assign 'visible' to each visible facet in qh.visible_list
+
+  notes:
+    uses 'vacetT *visible;'
+    at exit, visible==NULL
+*/
+#define FORALLvisible_facets for (visible=qh visible_list; visible && visible->visible; visible= visible->next)
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >--------------------------------</a><a name="FORALLsame_">-</a>
+
+  FORALLsame_( newfacet ) { ... }
+    assign 'same' to each facet in newfacet->f.samecycle
+
+  notes:
+    uses 'facetT *same;'
+    stops when it returns to newfacet
+*/
+#define FORALLsame_(newfacet) for (same= newfacet->f.samecycle; same != newfacet; same= same->f.samecycle)
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >--------------------------------</a><a name="FORALLsame_cycle_">-</a>
+
+  FORALLsame_cycle_( newfacet ) { ... }
+    assign 'same' to each facet in newfacet->f.samecycle
+
+  notes:
+    uses 'facetT *same;'
+    at exit, same == NULL
+*/
+#define FORALLsame_cycle_(newfacet) \
+     for (same= newfacet->f.samecycle; \
+         same; same= (same == newfacet ?  NULL : same->f.samecycle))
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >--------------------------------</a><a name="FOREACHneighborA_">-</a>
+
+  FOREACHneighborA_( facet ) { ... }
+    assign 'neighborA' to each neighbor in facet->neighbors
+
+  FOREACHneighborA_( vertex ) { ... }
+    assign 'neighborA' to each neighbor in vertex->neighbors
+
+  declare:
+    facetT *neighborA, **neighborAp;
+
+  see:
+    <a href="qset.h#FOREACHsetelement_">FOREACHsetelement_</a>
+*/
+#define FOREACHneighborA_(facet)  FOREACHsetelement_(facetT, facet->neighbors, neighborA)
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >--------------------------------</a><a name="FOREACHvisible_">-</a>
+
+  FOREACHvisible_( facets ) { ... }
+    assign 'visible' to each facet in facets
+
+  notes:
+    uses 'facetT *facet, *facetp;'
+    see <a href="qset.h#FOREACHsetelement_">FOREACHsetelement_</a>
+*/
+#define FOREACHvisible_(facets) FOREACHsetelement_(facetT, facets, visible)
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >--------------------------------</a><a name="FOREACHnewfacet_">-</a>
+
+  FOREACHnewfacet_( facets ) { ... }
+    assign 'newfacet' to each facet in facets
+
+  notes:
+    uses 'facetT *newfacet, *newfacetp;'
+    see <a href="qset.h#FOREACHsetelement_">FOREACHsetelement_</a>
+*/
+#define FOREACHnewfacet_(facets) FOREACHsetelement_(facetT, facets, newfacet)
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >--------------------------------</a><a name="FOREACHvertexA_">-</a>
+
+  FOREACHvertexA_( vertices ) { ... }
+    assign 'vertexA' to each vertex in vertices
+
+  notes:
+    uses 'vertexT *vertexA, *vertexAp;'
+    see <a href="qset.h#FOREACHsetelement_">FOREACHsetelement_</a>
+*/
+#define FOREACHvertexA_(vertices) FOREACHsetelement_(vertexT, vertices, vertexA)
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >--------------------------------</a><a name="FOREACHvertexreverse12_">-</a>
+
+  FOREACHvertexreverse12_( vertices ) { ... }
+    assign 'vertex' to each vertex in vertices
+    reverse order of first two vertices
+
+  notes:
+    uses 'vertexT *vertex, *vertexp;'
+    see <a href="qset.h#FOREACHsetelement_">FOREACHsetelement_</a>
+*/
+#define FOREACHvertexreverse12_(vertices) FOREACHsetelementreverse12_(vertexT, vertices, vertex)
+
+
+/*=============== prototypes poly.c in alphabetical order ================*/
+
+void    qh_appendfacet(facetT *facet);
+void    qh_appendvertex(vertexT *vertex);
+void    qh_attachnewfacets(void /* qh.visible_list, qh.newfacet_list */);
+boolT   qh_checkflipped(facetT *facet, realT *dist, boolT allerror);
+void    qh_delfacet(facetT *facet);
+void    qh_deletevisible(void /*qh.visible_list, qh.horizon_list*/);
+setT   *qh_facetintersect(facetT *facetA, facetT *facetB, int *skipAp,int *skipBp, int extra);
+int     qh_gethash(int hashsize, setT *set, int size, int firstindex, void *skipelem);
+facetT *qh_makenewfacet(setT *vertices, boolT toporient, facetT *facet);
+void    qh_makenewplanes(void /* newfacet_list */);
+facetT *qh_makenew_nonsimplicial(facetT *visible, vertexT *apex, int *numnew);
+facetT *qh_makenew_simplicial(facetT *visible, vertexT *apex, int *numnew);
+void    qh_matchneighbor(facetT *newfacet, int newskip, int hashsize,
+                          int *hashcount);
+void    qh_matchnewfacets(void);
+boolT   qh_matchvertices(int firstindex, setT *verticesA, int skipA,
+                          setT *verticesB, int *skipB, boolT *same);
+facetT *qh_newfacet(void);
+ridgeT *qh_newridge(void);
+int     qh_pointid(pointT *point);
+void    qh_removefacet(facetT *facet);
+void    qh_removevertex(vertexT *vertex);
+void    qh_updatevertices(void);
+
+
+/*========== -prototypes poly2.c in alphabetical order ===========*/
+
+void    qh_addhash(void* newelem, setT *hashtable, int hashsize, int hash);
+void    qh_check_bestdist(void);
+void    qh_check_dupridge(facetT *facet1, realT dist1, facetT *facet2, realT dist2);
+void    qh_check_maxout(void);
+void    qh_check_output(void);
+void    qh_check_point(pointT *point, facetT *facet, realT *maxoutside, realT *maxdist, facetT **errfacet1, facetT **errfacet2);
+void    qh_check_points(void);
+void    qh_checkconvex(facetT *facetlist, int fault);
+void    qh_checkfacet(facetT *facet, boolT newmerge, boolT *waserrorp);
+void    qh_checkflipped_all(facetT *facetlist);
+void    qh_checkpolygon(facetT *facetlist);
+void    qh_checkvertex(vertexT *vertex);
+void    qh_clearcenters(qh_CENTER type);
+void    qh_createsimplex(setT *vertices);
+void    qh_delridge(ridgeT *ridge);
+void    qh_delvertex(vertexT *vertex);
+setT   *qh_facet3vertex(facetT *facet);
+facetT *qh_findbestfacet(pointT *point, boolT bestoutside,
+           realT *bestdist, boolT *isoutside);
+facetT *qh_findbestlower(facetT *upperfacet, pointT *point, realT *bestdistp, int *numpart);
+facetT *qh_findfacet_all(pointT *point, realT *bestdist, boolT *isoutside,
+                          int *numpart);
+int     qh_findgood(facetT *facetlist, int goodhorizon);
+void    qh_findgood_all(facetT *facetlist);
+void    qh_furthestnext(void /* qh.facet_list */);
+void    qh_furthestout(facetT *facet);
+void    qh_infiniteloop(facetT *facet);
+void    qh_initbuild(void);
+void    qh_initialhull(setT *vertices);
+setT   *qh_initialvertices(int dim, setT *maxpoints, pointT *points, int numpoints);
+vertexT *qh_isvertex(pointT *point, setT *vertices);
+vertexT *qh_makenewfacets(pointT *point /*horizon_list, visible_list*/);
+void    qh_matchduplicates(facetT *atfacet, int atskip, int hashsize, int *hashcount);
+void    qh_nearcoplanar(void /* qh.facet_list */);
+vertexT *qh_nearvertex(facetT *facet, pointT *point, realT *bestdistp);
+int     qh_newhashtable(int newsize);
+vertexT *qh_newvertex(pointT *point);
+ridgeT *qh_nextridge3d(ridgeT *atridge, facetT *facet, vertexT **vertexp);
+void    qh_outcoplanar(void /* facet_list */);
+pointT *qh_point(int id);
+void    qh_point_add(setT *set, pointT *point, void *elem);
+setT   *qh_pointfacet(void /*qh.facet_list*/);
+setT   *qh_pointvertex(void /*qh.facet_list*/);
+void    qh_prependfacet(facetT *facet, facetT **facetlist);
+void    qh_printhashtable(FILE *fp);
+void    qh_printlists(void);
+void    qh_resetlists(boolT stats, boolT resetVisible /*qh.newvertex_list qh.newfacet_list qh.visible_list*/);
+void    qh_setvoronoi_all(void);
+void    qh_triangulate(void /*qh.facet_list*/);
+void    qh_triangulate_facet(facetT *facetA, vertexT **first_vertex);
+void    qh_triangulate_link(facetT *oldfacetA, facetT *facetA, facetT *oldfacetB, facetT *facetB);
+void    qh_triangulate_mirror(facetT *facetA, facetT *facetB);
+void    qh_triangulate_null(facetT *facetA);
+void    qh_vertexintersect(setT **vertexsetA,setT *vertexsetB);
+setT   *qh_vertexintersect_new(setT *vertexsetA,setT *vertexsetB);
+void    qh_vertexneighbors(void /*qh.facet_list*/);
+boolT   qh_vertexsubset(setT *vertexsetA, setT *vertexsetB);
+
+
+#endif /* qhDEFpoly */
diff --git a/xs/src/qhull/src/libqhull/poly2.c b/xs/src/qhull/src/libqhull/poly2.c
new file mode 100644
index 0000000000..de3e6ad0bb
--- /dev/null
+++ b/xs/src/qhull/src/libqhull/poly2.c
@@ -0,0 +1,3222 @@
+/*<html><pre>  -<a                             href="qh-poly.htm"
+  >-------------------------------</a><a name="TOP">-</a>
+
+   poly2.c
+   implements polygons and simplices
+
+   see qh-poly.htm, poly.h and libqhull.h
+
+   frequently used code is in poly.c
+
+   Copyright (c) 1993-2015 The Geometry Center.
+   $Id: //main/2015/qhull/src/libqhull/poly2.c#11 $$Change: 2069 $
+   $DateTime: 2016/01/18 22:05:03 $$Author: bbarber $
+*/
+
+#include "qhull_a.h"
+
+/*======== functions in alphabetical order ==========*/
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="addhash">-</a>
+
+  qh_addhash( newelem, hashtable, hashsize, hash )
+    add newelem to linear hash table at hash if not already there
+*/
+void qh_addhash(void* newelem, setT *hashtable, int hashsize, int hash) {
+  int scan;
+  void *elem;
+
+  for (scan= (int)hash; (elem= SETelem_(hashtable, scan));
+       scan= (++scan >= hashsize ? 0 : scan)) {
+    if (elem == newelem)
+      break;
+  }
+  /* loop terminates because qh_HASHfactor >= 1.1 by qh_initbuffers */
+  if (!elem)
+    SETelem_(hashtable, scan)= newelem;
+} /* addhash */
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="check_bestdist">-</a>
+
+  qh_check_bestdist()
+    check that all points are within max_outside of the nearest facet
+    if qh.ONLYgood,
+      ignores !good facets
+
+  see:
+    qh_check_maxout(), qh_outerinner()
+
+  notes:
+    only called from qh_check_points()
+      seldom used since qh.MERGING is almost always set
+    if notverified>0 at end of routine
+      some points were well inside the hull.  If the hull contains
+      a lens-shaped component, these points were not verified.  Use
+      options 'Qi Tv' to verify all points.  (Exhaustive check also verifies)
+
+  design:
+    determine facet for each point (if any)
+    for each point
+      start with the assigned facet or with the first facet
+      find the best facet for the point and check all coplanar facets
+      error if point is outside of facet
+*/
+void qh_check_bestdist(void) {
+  boolT waserror= False, unassigned;
+  facetT *facet, *bestfacet, *errfacet1= NULL, *errfacet2= NULL;
+  facetT *facetlist;
+  realT dist, maxoutside, maxdist= -REALmax;
+  pointT *point;
+  int numpart= 0, facet_i, facet_n, notgood= 0, notverified= 0;
+  setT *facets;
+
+  trace1((qh ferr, 1020, "qh_check_bestdist: check points below nearest facet.  Facet_list f%d\n",
+      qh facet_list->id));
+  maxoutside= qh_maxouter();
+  maxoutside += qh DISTround;
+  /* one more qh.DISTround for check computation */
+  trace1((qh ferr, 1021, "qh_check_bestdist: check that all points are within %2.2g of best facet\n", maxoutside));
+  facets= qh_pointfacet(/*qh.facet_list*/);
+  if (!qh_QUICKhelp && qh PRINTprecision)
+    qh_fprintf(qh ferr, 8091, "\n\
+qhull output completed.  Verifying that %d points are\n\
+below %2.2g of the nearest %sfacet.\n",
+             qh_setsize(facets), maxoutside, (qh ONLYgood ?  "good " : ""));
+  FOREACHfacet_i_(facets) {  /* for each point with facet assignment */
+    if (facet)
+      unassigned= False;
+    else {
+      unassigned= True;
+      facet= qh facet_list;
+    }
+    point= qh_point(facet_i);
+    if (point == qh GOODpointp)
+      continue;
+    qh_distplane(point, facet, &dist);
+    numpart++;
+    bestfacet= qh_findbesthorizon(!qh_IScheckmax, point, facet, qh_NOupper, &dist, &numpart);
+    /* occurs after statistics reported */
+    maximize_(maxdist, dist);
+    if (dist > maxoutside) {
+      if (qh ONLYgood && !bestfacet->good
+          && !((bestfacet= qh_findgooddist(point, bestfacet, &dist, &facetlist))
+               && dist > maxoutside))
+        notgood++;
+      else {
+        waserror= True;
+        qh_fprintf(qh ferr, 6109, "qhull precision error: point p%d is outside facet f%d, distance= %6.8g maxoutside= %6.8g\n",
+                facet_i, bestfacet->id, dist, maxoutside);
+        if (errfacet1 != bestfacet) {
+          errfacet2= errfacet1;
+          errfacet1= bestfacet;
+        }
+      }
+    }else if (unassigned && dist < -qh MAXcoplanar)
+      notverified++;
+  }
+  qh_settempfree(&facets);
+  if (notverified && !qh DELAUNAY && !qh_QUICKhelp && qh PRINTprecision)
+    qh_fprintf(qh ferr, 8092, "\n%d points were well inside the hull.  If the hull contains\n\
+a lens-shaped component, these points were not verified.  Use\n\
+options 'Qci Tv' to verify all points.\n", notverified);
+  if (maxdist > qh outside_err) {
+    qh_fprintf(qh ferr, 6110, "qhull precision error (qh_check_bestdist): a coplanar point is %6.2g from convex hull.  The maximum value(qh.outside_err) is %6.2g\n",
+              maxdist, qh outside_err);
+    qh_errexit2(qh_ERRprec, errfacet1, errfacet2);
+  }else if (waserror && qh outside_err > REALmax/2)
+    qh_errexit2(qh_ERRprec, errfacet1, errfacet2);
+  /* else if waserror, the error was logged to qh.ferr but does not effect the output */
+  trace0((qh ferr, 20, "qh_check_bestdist: max distance outside %2.2g\n", maxdist));
+} /* check_bestdist */
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="check_dupridge">-</a>
+
+  qh_check_dupridge(facet1, dist1, facet2, dist2)
+    Check duplicate ridge between facet1 and facet2 for wide merge
+    dist1 is the maximum distance of facet1's vertices to facet2
+    dist2 is the maximum distance of facet2's vertices to facet1
+
+  Returns
+    Level 1 log of the duplicate ridge with the minimum distance between vertices
+    Throws error if the merge will increase the maximum facet width by qh_WIDEduplicate (100x)
+
+  called from:
+    qh_forcedmerges()
+*/
+#ifndef qh_NOmerge
+void qh_check_dupridge(facetT *facet1, realT dist1, facetT *facet2, realT dist2) {
+  vertexT *vertex, **vertexp, *vertexA, **vertexAp;
+  realT dist, innerplane, mergedist, outerplane, prevdist, ratio;
+  realT minvertex= REALmax;
+
+  mergedist= fmin_(dist1, dist2);
+  qh_outerinner(NULL, &outerplane, &innerplane);  /* ratio from qh_printsummary */
+  prevdist= fmax_(outerplane, innerplane);
+  maximize_(prevdist, qh ONEmerge + qh DISTround);
+  maximize_(prevdist, qh MINoutside + qh DISTround);
+  ratio= mergedist/prevdist;
+  FOREACHvertex_(facet1->vertices) {     /* The duplicate ridge is between facet1 and facet2, so either facet can be tested */
+    FOREACHvertexA_(facet1->vertices) {
+      if (vertex > vertexA){   /* Test each pair once */
+        dist= qh_pointdist(vertex->point, vertexA->point, qh hull_dim);
+        minimize_(minvertex, dist);
+      }
+    }
+  }
+  trace0((qh ferr, 16, "qh_check_dupridge: duplicate ridge between f%d and f%d due to nearly-coincident vertices (%2.2g), dist %2.2g, reverse dist %2.2g, ratio %2.2g while processing p%d\n",
+        facet1->id, facet2->id, minvertex, dist1, dist2, ratio, qh furthest_id));
+  if (ratio > qh_WIDEduplicate) {
+    qh_fprintf(qh ferr, 6271, "qhull precision error (qh_check_dupridge): wide merge (%.0f times wider) due to duplicate ridge with nearly coincident points (%2.2g) between f%d and f%d, merge dist %2.2g, while processing p%d\n- Ignore error with option 'Q12'\n- To be fixed in a later version of Qhull\n",
+          ratio, minvertex, facet1->id, facet2->id, mergedist, qh furthest_id);
+    if (qh DELAUNAY)
+      qh_fprintf(qh ferr, 8145, "- A bounding box for the input sites may alleviate this error.\n");
+    if(minvertex > qh_WIDEduplicate*prevdist)
+      qh_fprintf(qh ferr, 8146, "- Vertex distance %2.2g is greater than %d times maximum distance %2.2g\n  Please report to bradb@shore.net with steps to reproduce and all output\n",
+          minvertex, qh_WIDEduplicate, prevdist);
+    if (!qh NOwide)
+      qh_errexit2(qh_ERRqhull, facet1, facet2);
+  }
+} /* check_dupridge */
+#endif
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="check_maxout">-</a>
+
+  qh_check_maxout()
+    updates qh.max_outside by checking all points against bestfacet
+    if qh.ONLYgood, ignores !good facets
+
+  returns:
+    updates facet->maxoutside via qh_findbesthorizon()
+    sets qh.maxoutdone
+    if printing qh.min_vertex (qh_outerinner),
+      it is updated to the current vertices
+    removes inside/coplanar points from coplanarset as needed
+
+  notes:
+    defines coplanar as min_vertex instead of MAXcoplanar
+    may not need to check near-inside points because of qh.MAXcoplanar
+      and qh.KEEPnearinside (before it was -DISTround)
+
+  see also:
+    qh_check_bestdist()
+
+  design:
+    if qh.min_vertex is needed
+      for all neighbors of all vertices
+        test distance from vertex to neighbor
+    determine facet for each point (if any)
+    for each point with an assigned facet
+      find the best facet for the point and check all coplanar facets
+        (updates outer planes)
+    remove near-inside points from coplanar sets
+*/
+#ifndef qh_NOmerge
+void qh_check_maxout(void) {
+  facetT *facet, *bestfacet, *neighbor, **neighborp, *facetlist;
+  realT dist, maxoutside, minvertex, old_maxoutside;
+  pointT *point;
+  int numpart= 0, facet_i, facet_n, notgood= 0;
+  setT *facets, *vertices;
+  vertexT *vertex;
+
+  trace1((qh ferr, 1022, "qh_check_maxout: check and update maxoutside for each facet.\n"));
+  maxoutside= minvertex= 0;
+  if (qh VERTEXneighbors
+  && (qh PRINTsummary || qh KEEPinside || qh KEEPcoplanar
+        || qh TRACElevel || qh PRINTstatistics
+        || qh PRINTout[0] == qh_PRINTsummary || qh PRINTout[0] == qh_PRINTnone)) {
+    trace1((qh ferr, 1023, "qh_check_maxout: determine actual maxoutside and minvertex\n"));
+    vertices= qh_pointvertex(/*qh.facet_list*/);
+    FORALLvertices {
+      FOREACHneighbor_(vertex) {
+        zinc_(Zdistvertex);  /* distance also computed by main loop below */
+        qh_distplane(vertex->point, neighbor, &dist);
+        minimize_(minvertex, dist);
+        if (-dist > qh TRACEdist || dist > qh TRACEdist
+        || neighbor == qh tracefacet || vertex == qh tracevertex)
+          qh_fprintf(qh ferr, 8093, "qh_check_maxout: p%d(v%d) is %.2g from f%d\n",
+                    qh_pointid(vertex->point), vertex->id, dist, neighbor->id);
+      }
+    }
+    if (qh MERGING) {
+      wmin_(Wminvertex, qh min_vertex);
+    }
+    qh min_vertex= minvertex;
+    qh_settempfree(&vertices);
+  }
+  facets= qh_pointfacet(/*qh.facet_list*/);
+  do {
+    old_maxoutside= fmax_(qh max_outside, maxoutside);
+    FOREACHfacet_i_(facets) {     /* for each point with facet assignment */
+      if (facet) {
+        point= qh_point(facet_i);
+        if (point == qh GOODpointp)
+          continue;
+        zzinc_(Ztotcheck);
+        qh_distplane(point, facet, &dist);
+        numpart++;
+        bestfacet= qh_findbesthorizon(qh_IScheckmax, point, facet, !qh_NOupper, &dist, &numpart);
+        if (bestfacet && dist > maxoutside) {
+          if (qh ONLYgood && !bestfacet->good
+          && !((bestfacet= qh_findgooddist(point, bestfacet, &dist, &facetlist))
+               && dist > maxoutside))
+            notgood++;
+          else
+            maxoutside= dist;
+        }
+        if (dist > qh TRACEdist || (bestfacet && bestfacet == qh tracefacet))
+          qh_fprintf(qh ferr, 8094, "qh_check_maxout: p%d is %.2g above f%d\n",
+                     qh_pointid(point), dist, (bestfacet ? bestfacet->id : UINT_MAX));
+      }
+    }
+  }while
+    (maxoutside > 2*old_maxoutside);
+    /* if qh.maxoutside increases substantially, qh_SEARCHdist is not valid
+          e.g., RBOX 5000 s Z1 G1e-13 t1001200614 | qhull */
+  zzadd_(Zcheckpart, numpart);
+  qh_settempfree(&facets);
+  wval_(Wmaxout)= maxoutside - qh max_outside;
+  wmax_(Wmaxoutside, qh max_outside);
+  qh max_outside= maxoutside;
+  qh_nearcoplanar(/*qh.facet_list*/);
+  qh maxoutdone= True;
+  trace1((qh ferr, 1024, "qh_check_maxout: maxoutside %2.2g, min_vertex %2.2g, outside of not good %d\n",
+       maxoutside, qh min_vertex, notgood));
+} /* check_maxout */
+#else /* qh_NOmerge */
+void qh_check_maxout(void) {
+}
+#endif
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="check_output">-</a>
+
+  qh_check_output()
+    performs the checks at the end of qhull algorithm
+    Maybe called after voronoi output.  Will recompute otherwise centrums are Voronoi centers instead
+*/
+void qh_check_output(void) {
+  int i;
+
+  if (qh STOPcone)
+    return;
+  if (qh VERIFYoutput | qh IStracing | qh CHECKfrequently) {
+    qh_checkpolygon(qh facet_list);
+    qh_checkflipped_all(qh facet_list);
+    qh_checkconvex(qh facet_list, qh_ALGORITHMfault);
+  }else if (!qh MERGING && qh_newstats(qhstat precision, &i)) {
+    qh_checkflipped_all(qh facet_list);
+    qh_checkconvex(qh facet_list, qh_ALGORITHMfault);
+  }
+} /* check_output */
+
+
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="check_point">-</a>
+
+  qh_check_point( point, facet, maxoutside, maxdist, errfacet1, errfacet2 )
+    check that point is less than maxoutside from facet
+*/
+void qh_check_point(pointT *point, facetT *facet, realT *maxoutside, realT *maxdist, facetT **errfacet1, facetT **errfacet2) {
+  realT dist;
+
+  /* occurs after statistics reported */
+  qh_distplane(point, facet, &dist);
+  if (dist > *maxoutside) {
+    if (*errfacet1 != facet) {
+      *errfacet2= *errfacet1;
+      *errfacet1= facet;
+    }
+    qh_fprintf(qh ferr, 6111, "qhull precision error: point p%d is outside facet f%d, distance= %6.8g maxoutside= %6.8g\n",
+              qh_pointid(point), facet->id, dist, *maxoutside);
+  }
+  maximize_(*maxdist, dist);
+} /* qh_check_point */
+
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="check_points">-</a>
+
+  qh_check_points()
+    checks that all points are inside all facets
+
+  notes:
+    if many points and qh_check_maxout not called (i.e., !qh.MERGING),
+       calls qh_findbesthorizon (seldom done).
+    ignores flipped facets
+    maxoutside includes 2 qh.DISTrounds
+      one qh.DISTround for the computed distances in qh_check_points
+    qh_printafacet and qh_printsummary needs only one qh.DISTround
+    the computation for qh.VERIFYdirect does not account for qh.other_points
+
+  design:
+    if many points
+      use qh_check_bestdist()
+    else
+      for all facets
+        for all points
+          check that point is inside facet
+*/
+void qh_check_points(void) {
+  facetT *facet, *errfacet1= NULL, *errfacet2= NULL;
+  realT total, maxoutside, maxdist= -REALmax;
+  pointT *point, **pointp, *pointtemp;
+  boolT testouter;
+
+  maxoutside= qh_maxouter();
+  maxoutside += qh DISTround;
+  /* one more qh.DISTround for check computation */
+  trace1((qh ferr, 1025, "qh_check_points: check all points below %2.2g of all facet planes\n",
+          maxoutside));
+  if (qh num_good)   /* miss counts other_points and !good facets */
+     total= (float)qh num_good * (float)qh num_points;
+  else
+     total= (float)qh num_facets * (float)qh num_points;
+  if (total >= qh_VERIFYdirect && !qh maxoutdone) {
+    if (!qh_QUICKhelp && qh SKIPcheckmax && qh MERGING)
+      qh_fprintf(qh ferr, 7075, "qhull input warning: merging without checking outer planes('Q5' or 'Po').\n\
+Verify may report that a point is outside of a facet.\n");
+    qh_check_bestdist();
+  }else {
+    if (qh_MAXoutside && qh maxoutdone)
+      testouter= True;
+    else
+      testouter= False;
+    if (!qh_QUICKhelp) {
+      if (qh MERGEexact)
+        qh_fprintf(qh ferr, 7076, "qhull input warning: exact merge ('Qx').  Verify may report that a point\n\
+is outside of a facet.  See qh-optq.htm#Qx\n");
+      else if (qh SKIPcheckmax || qh NOnearinside)
+        qh_fprintf(qh ferr, 7077, "qhull input warning: no outer plane check ('Q5') or no processing of\n\
+near-inside points ('Q8').  Verify may report that a point is outside\n\
+of a facet.\n");
+    }
+    if (qh PRINTprecision) {
+      if (testouter)
+        qh_fprintf(qh ferr, 8098, "\n\
+Output completed.  Verifying that all points are below outer planes of\n\
+all %sfacets.  Will make %2.0f distance computations.\n",
+              (qh ONLYgood ?  "good " : ""), total);
+      else
+        qh_fprintf(qh ferr, 8099, "\n\
+Output completed.  Verifying that all points are below %2.2g of\n\
+all %sfacets.  Will make %2.0f distance computations.\n",
+              maxoutside, (qh ONLYgood ?  "good " : ""), total);
+    }
+    FORALLfacets {
+      if (!facet->good && qh ONLYgood)
+        continue;
+      if (facet->flipped)
+        continue;
+      if (!facet->normal) {
+        qh_fprintf(qh ferr, 7061, "qhull warning (qh_check_points): missing normal for facet f%d\n", facet->id);
+        continue;
+      }
+      if (testouter) {
+#if qh_MAXoutside
+        maxoutside= facet->maxoutside + 2* qh DISTround;
+        /* one DISTround to actual point and another to computed point */
+#endif
+      }
+      FORALLpoints {
+        if (point != qh GOODpointp)
+          qh_check_point(point, facet, &maxoutside, &maxdist, &errfacet1, &errfacet2);
+      }
+      FOREACHpoint_(qh other_points) {
+        if (point != qh GOODpointp)
+          qh_check_point(point, facet, &maxoutside, &maxdist, &errfacet1, &errfacet2);
+      }
+    }
+    if (maxdist > qh outside_err) {
+      qh_fprintf(qh ferr, 6112, "qhull precision error (qh_check_points): a coplanar point is %6.2g from convex hull.  The maximum value(qh.outside_err) is %6.2g\n",
+                maxdist, qh outside_err );
+      qh_errexit2( qh_ERRprec, errfacet1, errfacet2 );
+    }else if (errfacet1 && qh outside_err > REALmax/2)
+        qh_errexit2( qh_ERRprec, errfacet1, errfacet2 );
+    /* else if errfacet1, the error was logged to qh.ferr but does not effect the output */
+    trace0((qh ferr, 21, "qh_check_points: max distance outside %2.2g\n", maxdist));
+  }
+} /* check_points */
+
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="checkconvex">-</a>
+
+  qh_checkconvex( facetlist, fault )
+    check that each ridge in facetlist is convex
+    fault = qh_DATAfault if reporting errors
+          = qh_ALGORITHMfault otherwise
+
+  returns:
+    counts Zconcaveridges and Zcoplanarridges
+    errors if concaveridge or if merging an coplanar ridge
+
+  note:
+    if not merging,
+      tests vertices for neighboring simplicial facets
+    else if ZEROcentrum,
+      tests vertices for neighboring simplicial   facets
+    else
+      tests centrums of neighboring facets
+
+  design:
+    for all facets
+      report flipped facets
+      if ZEROcentrum and simplicial neighbors
+        test vertices for neighboring simplicial facets
+      else
+        test centrum against all neighbors
+*/
+void qh_checkconvex(facetT *facetlist, int fault) {
+  facetT *facet, *neighbor, **neighborp, *errfacet1=NULL, *errfacet2=NULL;
+  vertexT *vertex;
+  realT dist;
+  pointT *centrum;
+  boolT waserror= False, centrum_warning= False, tempcentrum= False, allsimplicial;
+  int neighbor_i;
+
+  trace1((qh ferr, 1026, "qh_checkconvex: check all ridges are convex\n"));
+  if (!qh RERUN) {
+    zzval_(Zconcaveridges)= 0;
+    zzval_(Zcoplanarridges)= 0;
+  }
+  FORALLfacet_(facetlist) {
+    if (facet->flipped) {
+      qh_precision("flipped facet");
+      qh_fprintf(qh ferr, 6113, "qhull precision error: f%d is flipped(interior point is outside)\n",
+               facet->id);
+      errfacet1= facet;
+      waserror= True;
+      continue;
+    }
+    if (qh MERGING && (!qh ZEROcentrum || !facet->simplicial || facet->tricoplanar))
+      allsimplicial= False;
+    else {
+      allsimplicial= True;
+      neighbor_i= 0;
+      FOREACHneighbor_(facet) {
+        vertex= SETelemt_(facet->vertices, neighbor_i++, vertexT);
+        if (!neighbor->simplicial || neighbor->tricoplanar) {
+          allsimplicial= False;
+          continue;
+        }
+        qh_distplane(vertex->point, neighbor, &dist);
+        if (dist > -qh DISTround) {
+          if (fault == qh_DATAfault) {
+            qh_precision("coplanar or concave ridge");
+            qh_fprintf(qh ferr, 6114, "qhull precision error: initial simplex is not convex. Distance=%.2g\n", dist);
+            qh_errexit(qh_ERRsingular, NULL, NULL);
+          }
+          if (dist > qh DISTround) {
+            zzinc_(Zconcaveridges);
+            qh_precision("concave ridge");
+            qh_fprintf(qh ferr, 6115, "qhull precision error: f%d is concave to f%d, since p%d(v%d) is %6.4g above\n",
+              facet->id, neighbor->id, qh_pointid(vertex->point), vertex->id, dist);
+            errfacet1= facet;
+            errfacet2= neighbor;
+            waserror= True;
+          }else if (qh ZEROcentrum) {
+            if (dist > 0) {     /* qh_checkzero checks that dist < - qh DISTround */
+              zzinc_(Zcoplanarridges);
+              qh_precision("coplanar ridge");
+              qh_fprintf(qh ferr, 6116, "qhull precision error: f%d is clearly not convex to f%d, since p%d(v%d) is %6.4g above\n",
+                facet->id, neighbor->id, qh_pointid(vertex->point), vertex->id, dist);
+              errfacet1= facet;
+              errfacet2= neighbor;
+              waserror= True;
+            }
+          }else {
+            zzinc_(Zcoplanarridges);
+            qh_precision("coplanar ridge");
+            trace0((qh ferr, 22, "qhull precision error: f%d may be coplanar to f%d, since p%d(v%d) is within %6.4g during p%d\n",
+              facet->id, neighbor->id, qh_pointid(vertex->point), vertex->id, dist, qh furthest_id));
+          }
+        }
+      }
+    }
+    if (!allsimplicial) {
+      if (qh CENTERtype == qh_AScentrum) {
+        if (!facet->center)
+          facet->center= qh_getcentrum(facet);
+        centrum= facet->center;
+      }else {
+        if (!centrum_warning && (!facet->simplicial || facet->tricoplanar)) {
+           centrum_warning= True;
+           qh_fprintf(qh ferr, 7062, "qhull warning: recomputing centrums for convexity test.  This may lead to false, precision errors.\n");
+        }
+        centrum= qh_getcentrum(facet);
+        tempcentrum= True;
+      }
+      FOREACHneighbor_(facet) {
+        if (qh ZEROcentrum && facet->simplicial && neighbor->simplicial)
+          continue;
+        if (facet->tricoplanar || neighbor->tricoplanar)
+          continue;
+        zzinc_(Zdistconvex);
+        qh_distplane(centrum, neighbor, &dist);
+        if (dist > qh DISTround) {
+          zzinc_(Zconcaveridges);
+          qh_precision("concave ridge");
+          qh_fprintf(qh ferr, 6117, "qhull precision error: f%d is concave to f%d.  Centrum of f%d is %6.4g above f%d\n",
+            facet->id, neighbor->id, facet->id, dist, neighbor->id);
+          errfacet1= facet;
+          errfacet2= neighbor;
+          waserror= True;
+        }else if (dist >= 0.0) {   /* if arithmetic always rounds the same,
+                                     can test against centrum radius instead */
+          zzinc_(Zcoplanarridges);
+          qh_precision("coplanar ridge");
+          qh_fprintf(qh ferr, 6118, "qhull precision error: f%d is coplanar or concave to f%d.  Centrum of f%d is %6.4g above f%d\n",
+            facet->id, neighbor->id, facet->id, dist, neighbor->id);
+          errfacet1= facet;
+          errfacet2= neighbor;
+          waserror= True;
+        }
+      }
+      if (tempcentrum)
+        qh_memfree(centrum, qh normal_size);
+    }
+  }
+  if (waserror && !qh FORCEoutput)
+    qh_errexit2(qh_ERRprec, errfacet1, errfacet2);
+} /* checkconvex */
+
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="checkfacet">-</a>
+
+  qh_checkfacet( facet, newmerge, waserror )
+    checks for consistency errors in facet
+    newmerge set if from merge.c
+
+  returns:
+    sets waserror if any error occurs
+
+  checks:
+    vertex ids are inverse sorted
+    unless newmerge, at least hull_dim neighbors and vertices (exactly if simplicial)
+    if non-simplicial, at least as many ridges as neighbors
+    neighbors are not duplicated
+    ridges are not duplicated
+    in 3-d, ridges=verticies
+    (qh.hull_dim-1) ridge vertices
+    neighbors are reciprocated
+    ridge neighbors are facet neighbors and a ridge for every neighbor
+    simplicial neighbors match facetintersect
+    vertex intersection matches vertices of common ridges
+    vertex neighbors and facet vertices agree
+    all ridges have distinct vertex sets
+
+  notes:
+    uses neighbor->seen
+
+  design:
+    check sets
+    check vertices
+    check sizes of neighbors and vertices
+    check for qh_MERGEridge and qh_DUPLICATEridge flags
+    check neighbor set
+    check ridge set
+    check ridges, neighbors, and vertices
+*/
+void qh_checkfacet(facetT *facet, boolT newmerge, boolT *waserrorp) {
+  facetT *neighbor, **neighborp, *errother=NULL;
+  ridgeT *ridge, **ridgep, *errridge= NULL, *ridge2;
+  vertexT *vertex, **vertexp;
+  unsigned previousid= INT_MAX;
+  int numneighbors, numvertices, numridges=0, numRvertices=0;
+  boolT waserror= False;
+  int skipA, skipB, ridge_i, ridge_n, i;
+  setT *intersection;
+
+  if (facet->visible) {
+    qh_fprintf(qh ferr, 6119, "qhull internal error (qh_checkfacet): facet f%d is on the visible_list\n",
+      facet->id);
+    qh_errexit(qh_ERRqhull, facet, NULL);
+  }
+  if (!facet->normal) {
+    qh_fprintf(qh ferr, 6120, "qhull internal error (qh_checkfacet): facet f%d does not have  a normal\n",
+      facet->id);
+    waserror= True;
+  }
+  qh_setcheck(facet->vertices, "vertices for f", facet->id);
+  qh_setcheck(facet->ridges, "ridges for f", facet->id);
+  qh_setcheck(facet->outsideset, "outsideset for f", facet->id);
+  qh_setcheck(facet->coplanarset, "coplanarset for f", facet->id);
+  qh_setcheck(facet->neighbors, "neighbors for f", facet->id);
+  FOREACHvertex_(facet->vertices) {
+    if (vertex->deleted) {
+      qh_fprintf(qh ferr, 6121, "qhull internal error (qh_checkfacet): deleted vertex v%d in f%d\n", vertex->id, facet->id);
+      qh_errprint("ERRONEOUS", NULL, NULL, NULL, vertex);
+      waserror= True;
+    }
+    if (vertex->id >= previousid) {
+      qh_fprintf(qh ferr, 6122, "qhull internal error (qh_checkfacet): vertices of f%d are not in descending id order at v%d\n", facet->id, vertex->id);
+      waserror= True;
+      break;
+    }
+    previousid= vertex->id;
+  }
+  numneighbors= qh_setsize(facet->neighbors);
+  numvertices= qh_setsize(facet->vertices);
+  numridges= qh_setsize(facet->ridges);
+  if (facet->simplicial) {
+    if (numvertices+numneighbors != 2*qh hull_dim
+    && !facet->degenerate && !facet->redundant) {
+      qh_fprintf(qh ferr, 6123, "qhull internal error (qh_checkfacet): for simplicial facet f%d, #vertices %d + #neighbors %d != 2*qh hull_dim\n",
+                facet->id, numvertices, numneighbors);
+      qh_setprint(qh ferr, "", facet->neighbors);
+      waserror= True;
+    }
+  }else { /* non-simplicial */
+    if (!newmerge
+    &&(numvertices < qh hull_dim || numneighbors < qh hull_dim)
+    && !facet->degenerate && !facet->redundant) {
+      qh_fprintf(qh ferr, 6124, "qhull internal error (qh_checkfacet): for facet f%d, #vertices %d or #neighbors %d < qh hull_dim\n",
+         facet->id, numvertices, numneighbors);
+       waserror= True;
+    }
+    /* in 3-d, can get a vertex twice in an edge list, e.g., RBOX 1000 s W1e-13 t995849315 D2 | QHULL d Tc Tv TP624 TW1e-13 T4 */
+    if (numridges < numneighbors
+    ||(qh hull_dim == 3 && numvertices > numridges && !qh NEWfacets)
+    ||(qh hull_dim == 2 && numridges + numvertices + numneighbors != 6)) {
+      if (!facet->degenerate && !facet->redundant) {
+        qh_fprintf(qh ferr, 6125, "qhull internal error (qh_checkfacet): for facet f%d, #ridges %d < #neighbors %d or(3-d) > #vertices %d or(2-d) not all 2\n",
+            facet->id, numridges, numneighbors, numvertices);
+        waserror= True;
+      }
+    }
+  }
+  FOREACHneighbor_(facet) {
+    if (neighbor == qh_MERGEridge || neighbor == qh_DUPLICATEridge) {
+      qh_fprintf(qh ferr, 6126, "qhull internal error (qh_checkfacet): facet f%d still has a MERGE or DUP neighbor\n", facet->id);
+      qh_errexit(qh_ERRqhull, facet, NULL);
+    }
+    neighbor->seen= True;
+  }
+  FOREACHneighbor_(facet) {
+    if (!qh_setin(neighbor->neighbors, facet)) {
+      qh_fprintf(qh ferr, 6127, "qhull internal error (qh_checkfacet): facet f%d has neighbor f%d, but f%d does not have neighbor f%d\n",
+              facet->id, neighbor->id, neighbor->id, facet->id);
+      errother= neighbor;
+      waserror= True;
+    }
+    if (!neighbor->seen) {
+      qh_fprintf(qh ferr, 6128, "qhull internal error (qh_checkfacet): facet f%d has a duplicate neighbor f%d\n",
+              facet->id, neighbor->id);
+      errother= neighbor;
+      waserror= True;
+    }
+    neighbor->seen= False;
+  }
+  FOREACHridge_(facet->ridges) {
+    qh_setcheck(ridge->vertices, "vertices for r", ridge->id);
+    ridge->seen= False;
+  }
+  FOREACHridge_(facet->ridges) {
+    if (ridge->seen) {
+      qh_fprintf(qh ferr, 6129, "qhull internal error (qh_checkfacet): facet f%d has a duplicate ridge r%d\n",
+              facet->id, ridge->id);
+      errridge= ridge;
+      waserror= True;
+    }
+    ridge->seen= True;
+    numRvertices= qh_setsize(ridge->vertices);
+    if (numRvertices != qh hull_dim - 1) {
+      qh_fprintf(qh ferr, 6130, "qhull internal error (qh_checkfacet): ridge between f%d and f%d has %d vertices\n",
+                ridge->top->id, ridge->bottom->id, numRvertices);
+      errridge= ridge;
+      waserror= True;
+    }
+    neighbor= otherfacet_(ridge, facet);
+    neighbor->seen= True;
+    if (!qh_setin(facet->neighbors, neighbor)) {
+      qh_fprintf(qh ferr, 6131, "qhull internal error (qh_checkfacet): for facet f%d, neighbor f%d of ridge r%d not in facet\n",
+           facet->id, neighbor->id, ridge->id);
+      errridge= ridge;
+      waserror= True;
+    }
+  }
+  if (!facet->simplicial) {
+    FOREACHneighbor_(facet) {
+      if (!neighbor->seen) {
+        qh_fprintf(qh ferr, 6132, "qhull internal error (qh_checkfacet): facet f%d does not have a ridge for neighbor f%d\n",
+              facet->id, neighbor->id);
+        errother= neighbor;
+        waserror= True;
+      }
+      intersection= qh_vertexintersect_new(facet->vertices, neighbor->vertices);
+      qh_settemppush(intersection);
+      FOREACHvertex_(facet->vertices) {
+        vertex->seen= False;
+        vertex->seen2= False;
+      }
+      FOREACHvertex_(intersection)
+        vertex->seen= True;
+      FOREACHridge_(facet->ridges) {
+        if (neighbor != otherfacet_(ridge, facet))
+            continue;
+        FOREACHvertex_(ridge->vertices) {
+          if (!vertex->seen) {
+            qh_fprintf(qh ferr, 6133, "qhull internal error (qh_checkfacet): vertex v%d in r%d not in f%d intersect f%d\n",
+                  vertex->id, ridge->id, facet->id, neighbor->id);
+            qh_errexit(qh_ERRqhull, facet, ridge);
+          }
+          vertex->seen2= True;
+        }
+      }
+      if (!newmerge) {
+        FOREACHvertex_(intersection) {
+          if (!vertex->seen2) {
+            if (qh IStracing >=3 || !qh MERGING) {
+              qh_fprintf(qh ferr, 6134, "qhull precision error (qh_checkfacet): vertex v%d in f%d intersect f%d but\n\
+ not in a ridge.  This is ok under merging.  Last point was p%d\n",
+                     vertex->id, facet->id, neighbor->id, qh furthest_id);
+              if (!qh FORCEoutput && !qh MERGING) {
+                qh_errprint("ERRONEOUS", facet, neighbor, NULL, vertex);
+                if (!qh MERGING)
+                  qh_errexit(qh_ERRqhull, NULL, NULL);
+              }
+            }
+          }
+        }
+      }
+      qh_settempfree(&intersection);
+    }
+  }else { /* simplicial */
+    FOREACHneighbor_(facet) {
+      if (neighbor->simplicial) {
+        skipA= SETindex_(facet->neighbors, neighbor);
+        skipB= qh_setindex(neighbor->neighbors, facet);
+        if (skipA<0 || skipB<0 || !qh_setequal_skip(facet->vertices, skipA, neighbor->vertices, skipB)) {
+          qh_fprintf(qh ferr, 6135, "qhull internal error (qh_checkfacet): facet f%d skip %d and neighbor f%d skip %d do not match \n",
+                   facet->id, skipA, neighbor->id, skipB);
+          errother= neighbor;
+          waserror= True;
+        }
+      }
+    }
+  }
+  if (qh hull_dim < 5 && (qh IStracing > 2 || qh CHECKfrequently)) {
+    FOREACHridge_i_(facet->ridges) {           /* expensive */
+      for (i=ridge_i+1; i < ridge_n; i++) {
+        ridge2= SETelemt_(facet->ridges, i, ridgeT);
+        if (qh_setequal(ridge->vertices, ridge2->vertices)) {
+          qh_fprintf(qh ferr, 6227, "Qhull internal error (qh_checkfacet): ridges r%d and r%d have the same vertices\n",
+                  ridge->id, ridge2->id);
+          errridge= ridge;
+          waserror= True;
+        }
+      }
+    }
+  }
+  if (waserror) {
+    qh_errprint("ERRONEOUS", facet, errother, errridge, NULL);
+    *waserrorp= True;
+  }
+} /* checkfacet */
+
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="checkflipped_all">-</a>
+
+  qh_checkflipped_all( facetlist )
+    checks orientation of facets in list against interior point
+*/
+void qh_checkflipped_all(facetT *facetlist) {
+  facetT *facet;
+  boolT waserror= False;
+  realT dist;
+
+  if (facetlist == qh facet_list)
+    zzval_(Zflippedfacets)= 0;
+  FORALLfacet_(facetlist) {
+    if (facet->normal && !qh_checkflipped(facet, &dist, !qh_ALL)) {
+      qh_fprintf(qh ferr, 6136, "qhull precision error: facet f%d is flipped, distance= %6.12g\n",
+              facet->id, dist);
+      if (!qh FORCEoutput) {
+        qh_errprint("ERRONEOUS", facet, NULL, NULL, NULL);
+        waserror= True;
+      }
+    }
+  }
+  if (waserror) {
+    qh_fprintf(qh ferr, 8101, "\n\
+A flipped facet occurs when its distance to the interior point is\n\
+greater than %2.2g, the maximum roundoff error.\n", -qh DISTround);
+    qh_errexit(qh_ERRprec, NULL, NULL);
+  }
+} /* checkflipped_all */
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="checkpolygon">-</a>
+
+  qh_checkpolygon( facetlist )
+    checks the correctness of the structure
+
+  notes:
+    call with either qh.facet_list or qh.newfacet_list
+    checks num_facets and num_vertices if qh.facet_list
+
+  design:
+    for each facet
+      checks facet and outside set
+    initializes vertexlist
+    for each facet
+      checks vertex set
+    if checking all facets(qh.facetlist)
+      check facet count
+      if qh.VERTEXneighbors
+        check vertex neighbors and count
+      check vertex count
+*/
+void qh_checkpolygon(facetT *facetlist) {
+  facetT *facet;
+  vertexT *vertex, **vertexp, *vertexlist;
+  int numfacets= 0, numvertices= 0, numridges= 0;
+  int totvneighbors= 0, totvertices= 0;
+  boolT waserror= False, nextseen= False, visibleseen= False;
+
+  trace1((qh ferr, 1027, "qh_checkpolygon: check all facets from f%d\n", facetlist->id));
+  if (facetlist != qh facet_list || qh ONLYgood)
+    nextseen= True;
+  FORALLfacet_(facetlist) {
+    if (facet == qh visible_list)
+      visibleseen= True;
+    if (!facet->visible) {
+      if (!nextseen) {
+        if (facet == qh facet_next)
+          nextseen= True;
+        else if (qh_setsize(facet->outsideset)) {
+          if (!qh NARROWhull
+#if !qh_COMPUTEfurthest
+               || facet->furthestdist >= qh MINoutside
+#endif
+                        ) {
+            qh_fprintf(qh ferr, 6137, "qhull internal error (qh_checkpolygon): f%d has outside points before qh facet_next\n",
+                     facet->id);
+            qh_errexit(qh_ERRqhull, facet, NULL);
+          }
+        }
+      }
+      numfacets++;
+      qh_checkfacet(facet, False, &waserror);
+    }
+  }
+  if (qh visible_list && !visibleseen && facetlist == qh facet_list) {
+    qh_fprintf(qh ferr, 6138, "qhull internal error (qh_checkpolygon): visible list f%d no longer on facet list\n", qh visible_list->id);
+    qh_printlists();
+    qh_errexit(qh_ERRqhull, qh visible_list, NULL);
+  }
+  if (facetlist == qh facet_list)
+    vertexlist= qh vertex_list;
+  else if (facetlist == qh newfacet_list)
+    vertexlist= qh newvertex_list;
+  else
+    vertexlist= NULL;
+  FORALLvertex_(vertexlist) {
+    vertex->seen= False;
+    vertex->visitid= 0;
+  }
+  FORALLfacet_(facetlist) {
+    if (facet->visible)
+      continue;
+    if (facet->simplicial)
+      numridges += qh hull_dim;
+    else
+      numridges += qh_setsize(facet->ridges);
+    FOREACHvertex_(facet->vertices) {
+      vertex->visitid++;
+      if (!vertex->seen) {
+        vertex->seen= True;
+        numvertices++;
+        if (qh_pointid(vertex->point) == qh_IDunknown) {
+          qh_fprintf(qh ferr, 6139, "qhull internal error (qh_checkpolygon): unknown point %p for vertex v%d first_point %p\n",
+                   vertex->point, vertex->id, qh first_point);
+          waserror= True;
+        }
+      }
+    }
+  }
+  qh vertex_visit += (unsigned int)numfacets;
+  if (facetlist == qh facet_list) {
+    if (numfacets != qh num_facets - qh num_visible) {
+      qh_fprintf(qh ferr, 6140, "qhull internal error (qh_checkpolygon): actual number of facets is %d, cumulative facet count is %d - %d visible facets\n",
+              numfacets, qh num_facets, qh num_visible);
+      waserror= True;
+    }
+    qh vertex_visit++;
+    if (qh VERTEXneighbors) {
+      FORALLvertices {
+        qh_setcheck(vertex->neighbors, "neighbors for v", vertex->id);
+        if (vertex->deleted)
+          continue;
+        totvneighbors += qh_setsize(vertex->neighbors);
+      }
+      FORALLfacet_(facetlist)
+        totvertices += qh_setsize(facet->vertices);
+      if (totvneighbors != totvertices) {
+        qh_fprintf(qh ferr, 6141, "qhull internal error (qh_checkpolygon): vertex neighbors inconsistent.  Totvneighbors %d, totvertices %d\n",
+                totvneighbors, totvertices);
+        waserror= True;
+      }
+    }
+    if (numvertices != qh num_vertices - qh_setsize(qh del_vertices)) {
+      qh_fprintf(qh ferr, 6142, "qhull internal error (qh_checkpolygon): actual number of vertices is %d, cumulative vertex count is %d\n",
+              numvertices, qh num_vertices - qh_setsize(qh del_vertices));
+      waserror= True;
+    }
+    if (qh hull_dim == 2 && numvertices != numfacets) {
+      qh_fprintf(qh ferr, 6143, "qhull internal error (qh_checkpolygon): #vertices %d != #facets %d\n",
+        numvertices, numfacets);
+      waserror= True;
+    }
+    if (qh hull_dim == 3 && numvertices + numfacets - numridges/2 != 2) {
+      qh_fprintf(qh ferr, 7063, "qhull warning: #vertices %d + #facets %d - #edges %d != 2\n\
+        A vertex appears twice in a edge list.  May occur during merging.",
+        numvertices, numfacets, numridges/2);
+      /* occurs if lots of merging and a vertex ends up twice in an edge list.  e.g., RBOX 1000 s W1e-13 t995849315 D2 | QHULL d Tc Tv */
+    }
+  }
+  if (waserror)
+    qh_errexit(qh_ERRqhull, NULL, NULL);
+} /* checkpolygon */
+
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="checkvertex">-</a>
+
+  qh_checkvertex( vertex )
+    check vertex for consistency
+    checks vertex->neighbors
+
+  notes:
+    neighbors checked efficiently in checkpolygon
+*/
+void qh_checkvertex(vertexT *vertex) {
+  boolT waserror= False;
+  facetT *neighbor, **neighborp, *errfacet=NULL;
+
+  if (qh_pointid(vertex->point) == qh_IDunknown) {
+    qh_fprintf(qh ferr, 6144, "qhull internal error (qh_checkvertex): unknown point id %p\n", vertex->point);
+    waserror= True;
+  }
+  if (vertex->id >= qh vertex_id) {
+    qh_fprintf(qh ferr, 6145, "qhull internal error (qh_checkvertex): unknown vertex id %d\n", vertex->id);
+    waserror= True;
+  }
+  if (!waserror && !vertex->deleted) {
+    if (qh_setsize(vertex->neighbors)) {
+      FOREACHneighbor_(vertex) {
+        if (!qh_setin(neighbor->vertices, vertex)) {
+          qh_fprintf(qh ferr, 6146, "qhull internal error (qh_checkvertex): neighbor f%d does not contain v%d\n", neighbor->id, vertex->id);
+          errfacet= neighbor;
+          waserror= True;
+        }
+      }
+    }
+  }
+  if (waserror) {
+    qh_errprint("ERRONEOUS", NULL, NULL, NULL, vertex);
+    qh_errexit(qh_ERRqhull, errfacet, NULL);
+  }
+} /* checkvertex */
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="clearcenters">-</a>
+
+  qh_clearcenters( type )
+    clear old data from facet->center
+
+  notes:
+    sets new centertype
+    nop if CENTERtype is the same
+*/
+void qh_clearcenters(qh_CENTER type) {
+  facetT *facet;
+
+  if (qh CENTERtype != type) {
+    FORALLfacets {
+      if (facet->tricoplanar && !facet->keepcentrum)
+          facet->center= NULL;  /* center is owned by the ->keepcentrum facet */
+      else if (qh CENTERtype == qh_ASvoronoi){
+        if (facet->center) {
+          qh_memfree(facet->center, qh center_size);
+          facet->center= NULL;
+        }
+      }else /* qh.CENTERtype == qh_AScentrum */ {
+        if (facet->center) {
+          qh_memfree(facet->center, qh normal_size);
+          facet->center= NULL;
+        }
+      }
+    }
+    qh CENTERtype= type;
+  }
+  trace2((qh ferr, 2043, "qh_clearcenters: switched to center type %d\n", type));
+} /* clearcenters */
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="createsimplex">-</a>
+
+  qh_createsimplex( vertices )
+    creates a simplex from a set of vertices
+
+  returns:
+    initializes qh.facet_list to the simplex
+    initializes qh.newfacet_list, .facet_tail
+    initializes qh.vertex_list, .newvertex_list, .vertex_tail
+
+  design:
+    initializes lists
+    for each vertex
+      create a new facet
+    for each new facet
+      create its neighbor set
+*/
+void qh_createsimplex(setT *vertices) {
+  facetT *facet= NULL, *newfacet;
+  boolT toporient= True;
+  int vertex_i, vertex_n, nth;
+  setT *newfacets= qh_settemp(qh hull_dim+1);
+  vertexT *vertex;
+
+  qh facet_list= qh newfacet_list= qh facet_tail= qh_newfacet();
+  qh num_facets= qh num_vertices= qh num_visible= 0;
+  qh vertex_list= qh newvertex_list= qh vertex_tail= qh_newvertex(NULL);
+  FOREACHvertex_i_(vertices) {
+    newfacet= qh_newfacet();
+    newfacet->vertices= qh_setnew_delnthsorted(vertices, vertex_n,
+                                                vertex_i, 0);
+    newfacet->toporient= (unsigned char)toporient;
+    qh_appendfacet(newfacet);
+    newfacet->newfacet= True;
+    qh_appendvertex(vertex);
+    qh_setappend(&newfacets, newfacet);
+    toporient ^= True;
+  }
+  FORALLnew_facets {
+    nth= 0;
+    FORALLfacet_(qh newfacet_list) {
+      if (facet != newfacet)
+        SETelem_(newfacet->neighbors, nth++)= facet;
+    }
+    qh_settruncate(newfacet->neighbors, qh hull_dim);
+  }
+  qh_settempfree(&newfacets);
+  trace1((qh ferr, 1028, "qh_createsimplex: created simplex\n"));
+} /* createsimplex */
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="delridge">-</a>
+
+  qh_delridge( ridge )
+    deletes ridge from data structures it belongs to
+    frees up its memory
+
+  notes:
+    in merge.c, caller sets vertex->delridge for each vertex
+    ridges also freed in qh_freeqhull
+*/
+void qh_delridge(ridgeT *ridge) {
+  void **freelistp; /* used if !qh_NOmem by qh_memfree_() */
+
+  qh_setdel(ridge->top->ridges, ridge);
+  qh_setdel(ridge->bottom->ridges, ridge);
+  qh_setfree(&(ridge->vertices));
+  qh_memfree_(ridge, (int)sizeof(ridgeT), freelistp);
+} /* delridge */
+
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="delvertex">-</a>
+
+  qh_delvertex( vertex )
+    deletes a vertex and frees its memory
+
+  notes:
+    assumes vertex->adjacencies have been updated if needed
+    unlinks from vertex_list
+*/
+void qh_delvertex(vertexT *vertex) {
+
+  if (vertex == qh tracevertex)
+    qh tracevertex= NULL;
+  qh_removevertex(vertex);
+  qh_setfree(&vertex->neighbors);
+  qh_memfree(vertex, (int)sizeof(vertexT));
+} /* delvertex */
+
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="facet3vertex">-</a>
+
+  qh_facet3vertex(  )
+    return temporary set of 3-d vertices in qh_ORIENTclock order
+
+  design:
+    if simplicial facet
+      build set from facet->vertices with facet->toporient
+    else
+      for each ridge in order
+        build set from ridge's vertices
+*/
+setT *qh_facet3vertex(facetT *facet) {
+  ridgeT *ridge, *firstridge;
+  vertexT *vertex;
+  int cntvertices, cntprojected=0;
+  setT *vertices;
+
+  cntvertices= qh_setsize(facet->vertices);
+  vertices= qh_settemp(cntvertices);
+  if (facet->simplicial) {
+    if (cntvertices != 3) {
+      qh_fprintf(qh ferr, 6147, "qhull internal error (qh_facet3vertex): only %d vertices for simplicial facet f%d\n",
+                  cntvertices, facet->id);
+      qh_errexit(qh_ERRqhull, facet, NULL);
+    }
+    qh_setappend(&vertices, SETfirst_(facet->vertices));
+    if (facet->toporient ^ qh_ORIENTclock)
+      qh_setappend(&vertices, SETsecond_(facet->vertices));
+    else
+      qh_setaddnth(&vertices, 0, SETsecond_(facet->vertices));
+    qh_setappend(&vertices, SETelem_(facet->vertices, 2));
+  }else {
+    ridge= firstridge= SETfirstt_(facet->ridges, ridgeT);   /* no infinite */
+    while ((ridge= qh_nextridge3d(ridge, facet, &vertex))) {
+      qh_setappend(&vertices, vertex);
+      if (++cntprojected > cntvertices || ridge == firstridge)
+        break;
+    }
+    if (!ridge || cntprojected != cntvertices) {
+      qh_fprintf(qh ferr, 6148, "qhull internal error (qh_facet3vertex): ridges for facet %d don't match up.  got at least %d\n",
+                  facet->id, cntprojected);
+      qh_errexit(qh_ERRqhull, facet, ridge);
+    }
+  }
+  return vertices;
+} /* facet3vertex */
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="findbestfacet">-</a>
+
+  qh_findbestfacet( point, bestoutside, bestdist, isoutside )
+    find facet that is furthest below a point
+
+    for Delaunay triangulations,
+      Use qh_setdelaunay() to lift point to paraboloid and scale by 'Qbb' if needed
+      Do not use options 'Qbk', 'QBk', or 'QbB' since they scale the coordinates.
+
+  returns:
+    if bestoutside is set (e.g., qh_ALL)
+      returns best facet that is not upperdelaunay
+      if Delaunay and inside, point is outside circumsphere of bestfacet
+    else
+      returns first facet below point
+      if point is inside, returns nearest, !upperdelaunay facet
+    distance to facet
+    isoutside set if outside of facet
+
+  notes:
+    For tricoplanar facets, this finds one of the tricoplanar facets closest
+    to the point.  For Delaunay triangulations, the point may be inside a
+    different tricoplanar facet. See <a href="../html/qh-code.htm#findfacet">locate a facet with qh_findbestfacet()</a>
+
+    If inside, qh_findbestfacet performs an exhaustive search
+       this may be too conservative.  Sometimes it is clearly required.
+
+    qh_findbestfacet is not used by qhull.
+    uses qh.visit_id and qh.coplanarset
+
+  see:
+    <a href="geom.c#findbest">qh_findbest</a>
+*/
+facetT *qh_findbestfacet(pointT *point, boolT bestoutside,
+           realT *bestdist, boolT *isoutside) {
+  facetT *bestfacet= NULL;
+  int numpart, totpart= 0;
+
+  bestfacet= qh_findbest(point, qh facet_list,
+                            bestoutside, !qh_ISnewfacets, bestoutside /* qh_NOupper */,
+                            bestdist, isoutside, &totpart);
+  if (*bestdist < -qh DISTround) {
+    bestfacet= qh_findfacet_all(point, bestdist, isoutside, &numpart);
+    totpart += numpart;
+    if ((isoutside && *isoutside && bestoutside)
+    || (isoutside && !*isoutside && bestfacet->upperdelaunay)) {
+      bestfacet= qh_findbest(point, bestfacet,
+                            bestoutside, False, bestoutside,
+                            bestdist, isoutside, &totpart);
+      totpart += numpart;
+    }
+  }
+  trace3((qh ferr, 3014, "qh_findbestfacet: f%d dist %2.2g isoutside %d totpart %d\n",
+      bestfacet->id, *bestdist, (isoutside ? *isoutside : UINT_MAX), totpart));
+  return bestfacet;
+} /* findbestfacet */
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="findbestlower">-</a>
+
+  qh_findbestlower( facet, point, bestdist, numpart )
+    returns best non-upper, non-flipped neighbor of facet for point
+    if needed, searches vertex neighbors
+
+  returns:
+    returns bestdist and updates numpart
+
+  notes:
+    if Delaunay and inside, point is outside of circumsphere of bestfacet
+    called by qh_findbest() for points above an upperdelaunay facet
+
+*/
+facetT *qh_findbestlower(facetT *upperfacet, pointT *point, realT *bestdistp, int *numpart) {
+  facetT *neighbor, **neighborp, *bestfacet= NULL;
+  realT bestdist= -REALmax/2 /* avoid underflow */;
+  realT dist;
+  vertexT *vertex;
+  boolT isoutside= False;  /* not used */
+
+  zinc_(Zbestlower);
+  FOREACHneighbor_(upperfacet) {
+    if (neighbor->upperdelaunay || neighbor->flipped)
+      continue;
+    (*numpart)++;
+    qh_distplane(point, neighbor, &dist);
+    if (dist > bestdist) {
+      bestfacet= neighbor;
+      bestdist= dist;
+    }
+  }
+  if (!bestfacet) {
+    zinc_(Zbestlowerv);
+    /* rarely called, numpart does not count nearvertex computations */
+    vertex= qh_nearvertex(upperfacet, point, &dist);
+    qh_vertexneighbors();
+    FOREACHneighbor_(vertex) {
+      if (neighbor->upperdelaunay || neighbor->flipped)
+        continue;
+      (*numpart)++;
+      qh_distplane(point, neighbor, &dist);
+      if (dist > bestdist) {
+        bestfacet= neighbor;
+        bestdist= dist;
+      }
+    }
+  }
+  if (!bestfacet) {
+    zinc_(Zbestlowerall);  /* invoked once per point in outsideset */
+    zmax_(Zbestloweralln, qh num_facets);
+    /* [dec'15] Previously reported as QH6228 */
+    trace3((qh ferr, 3025, "qh_findbestlower: all neighbors of facet %d are flipped or upper Delaunay.  Search all facets\n",
+        upperfacet->id));
+    /* rarely called */
+    bestfacet= qh_findfacet_all(point, &bestdist, &isoutside, numpart);
+  }
+  *bestdistp= bestdist;
+  trace3((qh ferr, 3015, "qh_findbestlower: f%d dist %2.2g for f%d p%d\n",
+          bestfacet->id, bestdist, upperfacet->id, qh_pointid(point)));
+  return bestfacet;
+} /* findbestlower */
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="findfacet_all">-</a>
+
+  qh_findfacet_all( point, bestdist, isoutside, numpart )
+    exhaustive search for facet below a point
+
+    for Delaunay triangulations,
+      Use qh_setdelaunay() to lift point to paraboloid and scale by 'Qbb' if needed
+      Do not use options 'Qbk', 'QBk', or 'QbB' since they scale the coordinates.
+
+  returns:
+    returns first facet below point
+    if point is inside,
+      returns nearest facet
+    distance to facet
+    isoutside if point is outside of the hull
+    number of distance tests
+
+  notes:
+    primarily for library users, rarely used by Qhull
+*/
+facetT *qh_findfacet_all(pointT *point, realT *bestdist, boolT *isoutside,
+                          int *numpart) {
+  facetT *bestfacet= NULL, *facet;
+  realT dist;
+  int totpart= 0;
+
+  *bestdist= -REALmax;
+  *isoutside= False;
+  FORALLfacets {
+    if (facet->flipped || !facet->normal)
+      continue;
+    totpart++;
+    qh_distplane(point, facet, &dist);
+    if (dist > *bestdist) {
+      *bestdist= dist;
+      bestfacet= facet;
+      if (dist > qh MINoutside) {
+        *isoutside= True;
+        break;
+      }
+    }
+  }
+  *numpart= totpart;
+  trace3((qh ferr, 3016, "qh_findfacet_all: f%d dist %2.2g isoutside %d totpart %d\n",
+          getid_(bestfacet), *bestdist, *isoutside, totpart));
+  return bestfacet;
+} /* findfacet_all */
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="findgood">-</a>
+
+  qh_findgood( facetlist, goodhorizon )
+    identify good facets for qh.PRINTgood
+    if qh.GOODvertex>0
+      facet includes point as vertex
+      if !match, returns goodhorizon
+      inactive if qh.MERGING
+    if qh.GOODpoint
+      facet is visible or coplanar (>0) or not visible (<0)
+    if qh.GOODthreshold
+      facet->normal matches threshold
+    if !goodhorizon and !match,
+      selects facet with closest angle
+      sets GOODclosest
+
+  returns:
+    number of new, good facets found
+    determines facet->good
+    may update qh.GOODclosest
+
+  notes:
+    qh_findgood_all further reduces the good region
+
+  design:
+    count good facets
+    mark good facets for qh.GOODpoint
+    mark good facets for qh.GOODthreshold
+    if necessary
+      update qh.GOODclosest
+*/
+int qh_findgood(facetT *facetlist, int goodhorizon) {
+  facetT *facet, *bestfacet= NULL;
+  realT angle, bestangle= REALmax, dist;
+  int  numgood=0;
+
+  FORALLfacet_(facetlist) {
+    if (facet->good)
+      numgood++;
+  }
+  if (qh GOODvertex>0 && !qh MERGING) {
+    FORALLfacet_(facetlist) {
+      if (!qh_isvertex(qh GOODvertexp, facet->vertices)) {
+        facet->good= False;
+        numgood--;
+      }
+    }
+  }
+  if (qh GOODpoint && numgood) {
+    FORALLfacet_(facetlist) {
+      if (facet->good && facet->normal) {
+        zinc_(Zdistgood);
+        qh_distplane(qh GOODpointp, facet, &dist);
+        if ((qh GOODpoint > 0) ^ (dist > 0.0)) {
+          facet->good= False;
+          numgood--;
+        }
+      }
+    }
+  }
+  if (qh GOODthreshold && (numgood || goodhorizon || qh GOODclosest)) {
+    FORALLfacet_(facetlist) {
+      if (facet->good && facet->normal) {
+        if (!qh_inthresholds(facet->normal, &angle)) {
+          facet->good= False;
+          numgood--;
+          if (angle < bestangle) {
+            bestangle= angle;
+            bestfacet= facet;
+          }
+        }
+      }
+    }
+    if (!numgood && (!goodhorizon || qh GOODclosest)) {
+      if (qh GOODclosest) {
+        if (qh GOODclosest->visible)
+          qh GOODclosest= NULL;
+        else {
+          qh_inthresholds(qh GOODclosest->normal, &angle);
+          if (angle < bestangle)
+            bestfacet= qh GOODclosest;
+        }
+      }
+      if (bestfacet && bestfacet != qh GOODclosest) {
+        if (qh GOODclosest)
+          qh GOODclosest->good= False;
+        qh GOODclosest= bestfacet;
+        bestfacet->good= True;
+        numgood++;
+        trace2((qh ferr, 2044, "qh_findgood: f%d is closest(%2.2g) to thresholds\n",
+           bestfacet->id, bestangle));
+        return numgood;
+      }
+    }else if (qh GOODclosest) { /* numgood > 0 */
+      qh GOODclosest->good= False;
+      qh GOODclosest= NULL;
+    }
+  }
+  zadd_(Zgoodfacet, numgood);
+  trace2((qh ferr, 2045, "qh_findgood: found %d good facets with %d good horizon\n",
+               numgood, goodhorizon));
+  if (!numgood && qh GOODvertex>0 && !qh MERGING)
+    return goodhorizon;
+  return numgood;
+} /* findgood */
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="findgood_all">-</a>
+
+  qh_findgood_all( facetlist )
+    apply other constraints for good facets (used by qh.PRINTgood)
+    if qh.GOODvertex
+      facet includes (>0) or doesn't include (<0) point as vertex
+      if last good facet and ONLYgood, prints warning and continues
+    if qh.SPLITthresholds
+      facet->normal matches threshold, or if none, the closest one
+    calls qh_findgood
+    nop if good not used
+
+  returns:
+    clears facet->good if not good
+    sets qh.num_good
+
+  notes:
+    this is like qh_findgood but more restrictive
+
+  design:
+    uses qh_findgood to mark good facets
+    marks facets for qh.GOODvertex
+    marks facets for qh.SPLITthreholds
+*/
+void qh_findgood_all(facetT *facetlist) {
+  facetT *facet, *bestfacet=NULL;
+  realT angle, bestangle= REALmax;
+  int  numgood=0, startgood;
+
+  if (!qh GOODvertex && !qh GOODthreshold && !qh GOODpoint
+  && !qh SPLITthresholds)
+    return;
+  if (!qh ONLYgood)
+    qh_findgood(qh facet_list, 0);
+  FORALLfacet_(facetlist) {
+    if (facet->good)
+      numgood++;
+  }
+  if (qh GOODvertex <0 || (qh GOODvertex > 0 && qh MERGING)) {
+    FORALLfacet_(facetlist) {
+      if (facet->good && ((qh GOODvertex > 0) ^ !!qh_isvertex(qh GOODvertexp, facet->vertices))) {
+        if (!--numgood) {
+          if (qh ONLYgood) {
+            qh_fprintf(qh ferr, 7064, "qhull warning: good vertex p%d does not match last good facet f%d.  Ignored.\n",
+               qh_pointid(qh GOODvertexp), facet->id);
+            return;
+          }else if (qh GOODvertex > 0)
+            qh_fprintf(qh ferr, 7065, "qhull warning: point p%d is not a vertex('QV%d').\n",
+                qh GOODvertex-1, qh GOODvertex-1);
+          else
+            qh_fprintf(qh ferr, 7066, "qhull warning: point p%d is a vertex for every facet('QV-%d').\n",
+                -qh GOODvertex - 1, -qh GOODvertex - 1);
+        }
+        facet->good= False;
+      }
+    }
+  }
+  startgood= numgood;
+  if (qh SPLITthresholds) {
+    FORALLfacet_(facetlist) {
+      if (facet->good) {
+        if (!qh_inthresholds(facet->normal, &angle)) {
+          facet->good= False;
+          numgood--;
+          if (angle < bestangle) {
+            bestangle= angle;
+            bestfacet= facet;
+          }
+        }
+      }
+    }
+    if (!numgood && bestfacet) {
+      bestfacet->good= True;
+      numgood++;
+      trace0((qh ferr, 23, "qh_findgood_all: f%d is closest(%2.2g) to thresholds\n",
+           bestfacet->id, bestangle));
+      return;
+    }
+  }
+  qh num_good= numgood;
+  trace0((qh ferr, 24, "qh_findgood_all: %d good facets remain out of %d facets\n",
+        numgood, startgood));
+} /* findgood_all */
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="furthestnext">-</a>
+
+  qh_furthestnext()
+    set qh.facet_next to facet with furthest of all furthest points
+    searches all facets on qh.facet_list
+
+  notes:
+    this may help avoid precision problems
+*/
+void qh_furthestnext(void /* qh.facet_list */) {
+  facetT *facet, *bestfacet= NULL;
+  realT dist, bestdist= -REALmax;
+
+  FORALLfacets {
+    if (facet->outsideset) {
+#if qh_COMPUTEfurthest
+      pointT *furthest;
+      furthest= (pointT*)qh_setlast(facet->outsideset);
+      zinc_(Zcomputefurthest);
+      qh_distplane(furthest, facet, &dist);
+#else
+      dist= facet->furthestdist;
+#endif
+      if (dist > bestdist) {
+        bestfacet= facet;
+        bestdist= dist;
+      }
+    }
+  }
+  if (bestfacet) {
+    qh_removefacet(bestfacet);
+    qh_prependfacet(bestfacet, &qh facet_next);
+    trace1((qh ferr, 1029, "qh_furthestnext: made f%d next facet(dist %.2g)\n",
+            bestfacet->id, bestdist));
+  }
+} /* furthestnext */
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="furthestout">-</a>
+
+  qh_furthestout( facet )
+    make furthest outside point the last point of outsideset
+
+  returns:
+    updates facet->outsideset
+    clears facet->notfurthest
+    sets facet->furthestdist
+
+  design:
+    determine best point of outsideset
+    make it the last point of outsideset
+*/
+void qh_furthestout(facetT *facet) {
+  pointT *point, **pointp, *bestpoint= NULL;
+  realT dist, bestdist= -REALmax;
+
+  FOREACHpoint_(facet->outsideset) {
+    qh_distplane(point, facet, &dist);
+    zinc_(Zcomputefurthest);
+    if (dist > bestdist) {
+      bestpoint= point;
+      bestdist= dist;
+    }
+  }
+  if (bestpoint) {
+    qh_setdel(facet->outsideset, point);
+    qh_setappend(&facet->outsideset, point);
+#if !qh_COMPUTEfurthest
+    facet->furthestdist= bestdist;
+#endif
+  }
+  facet->notfurthest= False;
+  trace3((qh ferr, 3017, "qh_furthestout: p%d is furthest outside point of f%d\n",
+          qh_pointid(point), facet->id));
+} /* furthestout */
+
+
+/*-<a                             href="qh-qhull.htm#TOC"
+  >-------------------------------</a><a name="infiniteloop">-</a>
+
+  qh_infiniteloop( facet )
+    report infinite loop error due to facet
+*/
+void qh_infiniteloop(facetT *facet) {
+
+  qh_fprintf(qh ferr, 6149, "qhull internal error (qh_infiniteloop): potential infinite loop detected\n");
+  qh_errexit(qh_ERRqhull, facet, NULL);
+} /* qh_infiniteloop */
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="initbuild">-</a>
+
+  qh_initbuild()
+    initialize hull and outside sets with point array
+    qh.FIRSTpoint/qh.NUMpoints is point array
+    if qh.GOODpoint
+      adds qh.GOODpoint to initial hull
+
+  returns:
+    qh_facetlist with initial hull
+    points partioned into outside sets, coplanar sets, or inside
+    initializes qh.GOODpointp, qh.GOODvertexp,
+
+  design:
+    initialize global variables used during qh_buildhull
+    determine precision constants and points with max/min coordinate values
+      if qh.SCALElast, scale last coordinate(for 'd')
+    build initial simplex
+    partition input points into facets of initial simplex
+    set up lists
+    if qh.ONLYgood
+      check consistency
+      add qh.GOODvertex if defined
+*/
+void qh_initbuild( void) {
+  setT *maxpoints, *vertices;
+  facetT *facet;
+  int i, numpart;
+  realT dist;
+  boolT isoutside;
+
+  qh furthest_id= qh_IDunknown;
+  qh lastreport= 0;
+  qh facet_id= qh vertex_id= qh ridge_id= 0;
+  qh visit_id= qh vertex_visit= 0;
+  qh maxoutdone= False;
+
+  if (qh GOODpoint > 0)
+    qh GOODpointp= qh_point(qh GOODpoint-1);
+  else if (qh GOODpoint < 0)
+    qh GOODpointp= qh_point(-qh GOODpoint-1);
+  if (qh GOODvertex > 0)
+    qh GOODvertexp= qh_point(qh GOODvertex-1);
+  else if (qh GOODvertex < 0)
+    qh GOODvertexp= qh_point(-qh GOODvertex-1);
+  if ((qh GOODpoint
+       && (qh GOODpointp < qh first_point  /* also catches !GOODpointp */
+           || qh GOODpointp > qh_point(qh num_points-1)))
+    || (qh GOODvertex
+        && (qh GOODvertexp < qh first_point  /* also catches !GOODvertexp */
+            || qh GOODvertexp > qh_point(qh num_points-1)))) {
+    qh_fprintf(qh ferr, 6150, "qhull input error: either QGn or QVn point is > p%d\n",
+             qh num_points-1);
+    qh_errexit(qh_ERRinput, NULL, NULL);
+  }
+  maxpoints= qh_maxmin(qh first_point, qh num_points, qh hull_dim);
+  if (qh SCALElast)
+    qh_scalelast(qh first_point, qh num_points, qh hull_dim,
+               qh MINlastcoord, qh MAXlastcoord, qh MAXwidth);
+  qh_detroundoff();
+  if (qh DELAUNAY && qh upper_threshold[qh hull_dim-1] > REALmax/2
+                  && qh lower_threshold[qh hull_dim-1] < -REALmax/2) {
+    for (i=qh_PRINTEND; i--; ) {
+      if (qh PRINTout[i] == qh_PRINTgeom && qh DROPdim < 0
+          && !qh GOODthreshold && !qh SPLITthresholds)
+        break;  /* in this case, don't set upper_threshold */
+    }
+    if (i < 0) {
+      if (qh UPPERdelaunay) { /* matches qh.upperdelaunay in qh_setfacetplane */
+        qh lower_threshold[qh hull_dim-1]= qh ANGLEround * qh_ZEROdelaunay;
+        qh GOODthreshold= True;
+      }else {
+        qh upper_threshold[qh hull_dim-1]= -qh ANGLEround * qh_ZEROdelaunay;
+        if (!qh GOODthreshold)
+          qh SPLITthresholds= True; /* build upper-convex hull even if Qg */
+          /* qh_initqhull_globals errors if Qg without Pdk/etc. */
+      }
+    }
+  }
+  vertices= qh_initialvertices(qh hull_dim, maxpoints, qh first_point, qh num_points);
+  qh_initialhull(vertices);  /* initial qh facet_list */
+  qh_partitionall(vertices, qh first_point, qh num_points);
+  if (qh PRINToptions1st || qh TRACElevel || qh IStracing) {
+    if (qh TRACElevel || qh IStracing)
+      qh_fprintf(qh ferr, 8103, "\nTrace level %d for %s | %s\n",
+         qh IStracing ? qh IStracing : qh TRACElevel, qh rbox_command, qh qhull_command);
+    qh_fprintf(qh ferr, 8104, "Options selected for Qhull %s:\n%s\n", qh_version, qh qhull_options);
+  }
+  qh_resetlists(False, qh_RESETvisible /*qh.visible_list newvertex_list newfacet_list */);
+  qh facet_next= qh facet_list;
+  qh_furthestnext(/* qh.facet_list */);
+  if (qh PREmerge) {
+    qh cos_max= qh premerge_cos;
+    qh centrum_radius= qh premerge_centrum;
+  }
+  if (qh ONLYgood) {
+    if (qh GOODvertex > 0 && qh MERGING) {
+      qh_fprintf(qh ferr, 6151, "qhull input error: 'Qg QVn' (only good vertex) does not work with merging.\nUse 'QJ' to joggle the input or 'Q0' to turn off merging.\n");
+      qh_errexit(qh_ERRinput, NULL, NULL);
+    }
+    if (!(qh GOODthreshold || qh GOODpoint
+         || (!qh MERGEexact && !qh PREmerge && qh GOODvertexp))) {
+      qh_fprintf(qh ferr, 6152, "qhull input error: 'Qg' (ONLYgood) needs a good threshold('Pd0D0'), a\n\
+good point(QGn or QG-n), or a good vertex with 'QJ' or 'Q0' (QVn).\n");
+      qh_errexit(qh_ERRinput, NULL, NULL);
+    }
+    if (qh GOODvertex > 0  && !qh MERGING  /* matches qh_partitionall */
+        && !qh_isvertex(qh GOODvertexp, vertices)) {
+      facet= qh_findbestnew(qh GOODvertexp, qh facet_list,
+                          &dist, !qh_ALL, &isoutside, &numpart);
+      zadd_(Zdistgood, numpart);
+      if (!isoutside) {
+        qh_fprintf(qh ferr, 6153, "qhull input error: point for QV%d is inside initial simplex.  It can not be made a vertex.\n",
+               qh_pointid(qh GOODvertexp));
+        qh_errexit(qh_ERRinput, NULL, NULL);
+      }
+      if (!qh_addpoint(qh GOODvertexp, facet, False)) {
+        qh_settempfree(&vertices);
+        qh_settempfree(&maxpoints);
+        return;
+      }
+    }
+    qh_findgood(qh facet_list, 0);
+  }
+  qh_settempfree(&vertices);
+  qh_settempfree(&maxpoints);
+  trace1((qh ferr, 1030, "qh_initbuild: initial hull created and points partitioned\n"));
+} /* initbuild */
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="initialhull">-</a>
+
+  qh_initialhull( vertices )
+    constructs the initial hull as a DIM3 simplex of vertices
+
+  design:
+    creates a simplex (initializes lists)
+    determines orientation of simplex
+    sets hyperplanes for facets
+    doubles checks orientation (in case of axis-parallel facets with Gaussian elimination)
+    checks for flipped facets and qh.NARROWhull
+    checks the result
+*/
+void qh_initialhull(setT *vertices) {
+  facetT *facet, *firstfacet, *neighbor, **neighborp;
+  realT dist, angle, minangle= REALmax;
+#ifndef qh_NOtrace
+  int k;
+#endif
+
+  qh_createsimplex(vertices);  /* qh.facet_list */
+  qh_resetlists(False, qh_RESETvisible);
+  qh facet_next= qh facet_list;      /* advance facet when processed */
+  qh interior_point= qh_getcenter(vertices);
+  firstfacet= qh facet_list;
+  qh_setfacetplane(firstfacet);
+  zinc_(Znumvisibility); /* needs to be in printsummary */
+  qh_distplane(qh interior_point, firstfacet, &dist);
+  if (dist > 0) {
+    FORALLfacets
+      facet->toporient ^= (unsigned char)True;
+  }
+  FORALLfacets
+    qh_setfacetplane(facet);
+  FORALLfacets {
+    if (!qh_checkflipped(facet, NULL, qh_ALL)) {/* due to axis-parallel facet */
+      trace1((qh ferr, 1031, "qh_initialhull: initial orientation incorrect.  Correct all facets\n"));
+      facet->flipped= False;
+      FORALLfacets {
+        facet->toporient ^= (unsigned char)True;
+        qh_orientoutside(facet);
+      }
+      break;
+    }
+  }
+  FORALLfacets {
+    if (!qh_checkflipped(facet, NULL, !qh_ALL)) {  /* can happen with 'R0.1' */
+      if (qh DELAUNAY && ! qh ATinfinity) {
+        if (qh UPPERdelaunay)
+          qh_fprintf(qh ferr, 6240, "Qhull precision error: Initial simplex is cocircular or cospherical.  Option 'Qs' searches all points.  Can not compute the upper Delaunay triangulation or upper Voronoi diagram of cocircular/cospherical points.\n");
+        else
+          qh_fprintf(qh ferr, 6239, "Qhull precision error: Initial simplex is cocircular or cospherical.  Use option 'Qz' for the Delaunay triangulation or Voronoi diagram of cocircular/cospherical points.  Option 'Qz' adds a point \"at infinity\".    Use option 'Qs' to search all points for the initial simplex.\n");
+        qh_errexit(qh_ERRinput, NULL, NULL);
+      }
+      qh_precision("initial simplex is flat");
+      qh_fprintf(qh ferr, 6154, "Qhull precision error: Initial simplex is flat (facet %d is coplanar with the interior point)\n",
+                 facet->id);
+      qh_errexit(qh_ERRsingular, NULL, NULL);  /* calls qh_printhelp_singular */
+    }
+    FOREACHneighbor_(facet) {
+      angle= qh_getangle(facet->normal, neighbor->normal);
+      minimize_( minangle, angle);
+    }
+  }
+  if (minangle < qh_MAXnarrow && !qh NOnarrow) {
+    realT diff= 1.0 + minangle;
+
+    qh NARROWhull= True;
+    qh_option("_narrow-hull", NULL, &diff);
+    if (minangle < qh_WARNnarrow && !qh RERUN && qh PRINTprecision)
+      qh_printhelp_narrowhull(qh ferr, minangle);
+  }
+  zzval_(Zprocessed)= qh hull_dim+1;
+  qh_checkpolygon(qh facet_list);
+  qh_checkconvex(qh facet_list,   qh_DATAfault);
+#ifndef qh_NOtrace
+  if (qh IStracing >= 1) {
+    qh_fprintf(qh ferr, 8105, "qh_initialhull: simplex constructed, interior point:");
+    for (k=0; k < qh hull_dim; k++)
+      qh_fprintf(qh ferr, 8106, " %6.4g", qh interior_point[k]);
+    qh_fprintf(qh ferr, 8107, "\n");
+  }
+#endif
+} /* initialhull */
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="initialvertices">-</a>
+
+  qh_initialvertices( dim, maxpoints, points, numpoints )
+    determines a non-singular set of initial vertices
+    maxpoints may include duplicate points
+
+  returns:
+    temporary set of dim+1 vertices in descending order by vertex id
+    if qh.RANDOMoutside && !qh.ALLpoints
+      picks random points
+    if dim >= qh_INITIALmax,
+      uses min/max x and max points with non-zero determinants
+
+  notes:
+    unless qh.ALLpoints,
+      uses maxpoints as long as determinate is non-zero
+*/
+setT *qh_initialvertices(int dim, setT *maxpoints, pointT *points, int numpoints) {
+  pointT *point, **pointp;
+  setT *vertices, *simplex, *tested;
+  realT randr;
+  int idx, point_i, point_n, k;
+  boolT nearzero= False;
+
+  vertices= qh_settemp(dim + 1);
+  simplex= qh_settemp(dim+1);
+  if (qh ALLpoints)
+    qh_maxsimplex(dim, NULL, points, numpoints, &simplex);
+  else if (qh RANDOMoutside) {
+    while (qh_setsize(simplex) != dim+1) {
+      randr= qh_RANDOMint;
+      randr= randr/(qh_RANDOMmax+1);
+      idx= (int)floor(qh num_points * randr);
+      while (qh_setin(simplex, qh_point(idx))) {
+        idx++; /* in case qh_RANDOMint always returns the same value */
+        idx= idx < qh num_points ? idx : 0;
+      }
+      qh_setappend(&simplex, qh_point(idx));
+    }
+  }else if (qh hull_dim >= qh_INITIALmax) {
+    tested= qh_settemp(dim+1);
+    qh_setappend(&simplex, SETfirst_(maxpoints));   /* max and min X coord */
+    qh_setappend(&simplex, SETsecond_(maxpoints));
+    qh_maxsimplex(fmin_(qh_INITIALsearch, dim), maxpoints, points, numpoints, &simplex);
+    k= qh_setsize(simplex);
+    FOREACHpoint_i_(maxpoints) {
+      if (point_i & 0x1) {     /* first pick up max. coord. points */
+        if (!qh_setin(simplex, point) && !qh_setin(tested, point)){
+          qh_detsimplex(point, simplex, k, &nearzero);
+          if (nearzero)
+            qh_setappend(&tested, point);
+          else {
+            qh_setappend(&simplex, point);
+            if (++k == dim)  /* use search for last point */
+              break;
+          }
+        }
+      }
+    }
+    while (k != dim && (point= (pointT*)qh_setdellast(maxpoints))) {
+      if (!qh_setin(simplex, point) && !qh_setin(tested, point)){
+        qh_detsimplex(point, simplex, k, &nearzero);
+        if (nearzero)
+          qh_setappend(&tested, point);
+        else {
+          qh_setappend(&simplex, point);
+          k++;
+        }
+      }
+    }
+    idx= 0;
+    while (k != dim && (point= qh_point(idx++))) {
+      if (!qh_setin(simplex, point) && !qh_setin(tested, point)){
+        qh_detsimplex(point, simplex, k, &nearzero);
+        if (!nearzero){
+          qh_setappend(&simplex, point);
+          k++;
+        }
+      }
+    }
+    qh_settempfree(&tested);
+    qh_maxsimplex(dim, maxpoints, points, numpoints, &simplex);
+  }else
+    qh_maxsimplex(dim, maxpoints, points, numpoints, &simplex);
+  FOREACHpoint_(simplex)
+    qh_setaddnth(&vertices, 0, qh_newvertex(point)); /* descending order */
+  qh_settempfree(&simplex);
+  return vertices;
+} /* initialvertices */
+
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="isvertex">-</a>
+
+  qh_isvertex( point, vertices )
+    returns vertex if point is in vertex set, else returns NULL
+
+  notes:
+    for qh.GOODvertex
+*/
+vertexT *qh_isvertex(pointT *point, setT *vertices) {
+  vertexT *vertex, **vertexp;
+
+  FOREACHvertex_(vertices) {
+    if (vertex->point == point)
+      return vertex;
+  }
+  return NULL;
+} /* isvertex */
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="makenewfacets">-</a>
+
+  qh_makenewfacets( point )
+    make new facets from point and qh.visible_list
+
+  returns:
+    qh.newfacet_list= list of new facets with hyperplanes and ->newfacet
+    qh.newvertex_list= list of vertices in new facets with ->newlist set
+
+    if (qh.ONLYgood)
+      newfacets reference horizon facets, but not vice versa
+      ridges reference non-simplicial horizon ridges, but not vice versa
+      does not change existing facets
+    else
+      sets qh.NEWfacets
+      new facets attached to horizon facets and ridges
+      for visible facets,
+        visible->r.replace is corresponding new facet
+
+  see also:
+    qh_makenewplanes() -- make hyperplanes for facets
+    qh_attachnewfacets() -- attachnewfacets if not done here(qh ONLYgood)
+    qh_matchnewfacets() -- match up neighbors
+    qh_updatevertices() -- update vertex neighbors and delvertices
+    qh_deletevisible() -- delete visible facets
+    qh_checkpolygon() --check the result
+    qh_triangulate() -- triangulate a non-simplicial facet
+
+  design:
+    for each visible facet
+      make new facets to its horizon facets
+      update its f.replace
+      clear its neighbor set
+*/
+vertexT *qh_makenewfacets(pointT *point /*visible_list*/) {
+  facetT *visible, *newfacet= NULL, *newfacet2= NULL, *neighbor, **neighborp;
+  vertexT *apex;
+  int numnew=0;
+
+  qh newfacet_list= qh facet_tail;
+  qh newvertex_list= qh vertex_tail;
+  apex= qh_newvertex(point);
+  qh_appendvertex(apex);
+  qh visit_id++;
+  if (!qh ONLYgood)
+    qh NEWfacets= True;
+  FORALLvisible_facets {
+    FOREACHneighbor_(visible)
+      neighbor->seen= False;
+    if (visible->ridges) {
+      visible->visitid= qh visit_id;
+      newfacet2= qh_makenew_nonsimplicial(visible, apex, &numnew);
+    }
+    if (visible->simplicial)
+      newfacet= qh_makenew_simplicial(visible, apex, &numnew);
+    if (!qh ONLYgood) {
+      if (newfacet2)  /* newfacet is null if all ridges defined */
+        newfacet= newfacet2;
+      if (newfacet)
+        visible->f.replace= newfacet;
+      else
+        zinc_(Zinsidevisible);
+      SETfirst_(visible->neighbors)= NULL;
+    }
+  }
+  trace1((qh ferr, 1032, "qh_makenewfacets: created %d new facets from point p%d to horizon\n",
+          numnew, qh_pointid(point)));
+  if (qh IStracing >= 4)
+    qh_printfacetlist(qh newfacet_list, NULL, qh_ALL);
+  return apex;
+} /* makenewfacets */
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="matchduplicates">-</a>
+
+  qh_matchduplicates( atfacet, atskip, hashsize, hashcount )
+    match duplicate ridges in qh.hash_table for atfacet/atskip
+    duplicates marked with ->dupridge and qh_DUPLICATEridge
+
+  returns:
+    picks match with worst merge (min distance apart)
+    updates hashcount
+
+  see also:
+    qh_matchneighbor
+
+  notes:
+
+  design:
+    compute hash value for atfacet and atskip
+    repeat twice -- once to make best matches, once to match the rest
+      for each possible facet in qh.hash_table
+        if it is a matching facet and pass 2
+          make match
+          unless tricoplanar, mark match for merging (qh_MERGEridge)
+          [e.g., tricoplanar RBOX s 1000 t993602376 | QHULL C-1e-3 d Qbb FA Qt]
+        if it is a matching facet and pass 1
+          test if this is a better match
+      if pass 1,
+        make best match (it will not be merged)
+*/
+#ifndef qh_NOmerge
+void qh_matchduplicates(facetT *atfacet, int atskip, int hashsize, int *hashcount) {
+  boolT same, ismatch;
+  int hash, scan;
+  facetT *facet, *newfacet, *maxmatch= NULL, *maxmatch2= NULL, *nextfacet;
+  int skip, newskip, nextskip= 0, maxskip= 0, maxskip2= 0, makematch;
+  realT maxdist= -REALmax, mindist, dist2, low, high;
+
+  hash= qh_gethash(hashsize, atfacet->vertices, qh hull_dim, 1,
+                     SETelem_(atfacet->vertices, atskip));
+  trace2((qh ferr, 2046, "qh_matchduplicates: find duplicate matches for f%d skip %d hash %d hashcount %d\n",
+          atfacet->id, atskip, hash, *hashcount));
+  for (makematch= 0; makematch < 2; makematch++) {
+    qh visit_id++;
+    for (newfacet= atfacet, newskip= atskip; newfacet; newfacet= nextfacet, newskip= nextskip) {
+      zinc_(Zhashlookup);
+      nextfacet= NULL;
+      newfacet->visitid= qh visit_id;
+      for (scan= hash; (facet= SETelemt_(qh hash_table, scan, facetT));
+           scan= (++scan >= hashsize ? 0 : scan)) {
+        if (!facet->dupridge || facet->visitid == qh visit_id)
+          continue;
+        zinc_(Zhashtests);
+        if (qh_matchvertices(1, newfacet->vertices, newskip, facet->vertices, &skip, &same)) {
+          ismatch= (same == (boolT)(newfacet->toporient ^ facet->toporient));
+          if (SETelemt_(facet->neighbors, skip, facetT) != qh_DUPLICATEridge) {
+            if (!makematch) {
+              qh_fprintf(qh ferr, 6155, "qhull internal error (qh_matchduplicates): missing dupridge at f%d skip %d for new f%d skip %d hash %d\n",
+                     facet->id, skip, newfacet->id, newskip, hash);
+              qh_errexit2(qh_ERRqhull, facet, newfacet);
+            }
+          }else if (ismatch && makematch) {
+            if (SETelemt_(newfacet->neighbors, newskip, facetT) == qh_DUPLICATEridge) {
+              SETelem_(facet->neighbors, skip)= newfacet;
+              if (newfacet->tricoplanar)
+                SETelem_(newfacet->neighbors, newskip)= facet;
+              else
+                SETelem_(newfacet->neighbors, newskip)= qh_MERGEridge;
+              *hashcount -= 2; /* removed two unmatched facets */
+              trace4((qh ferr, 4059, "qh_matchduplicates: duplicate f%d skip %d matched with new f%d skip %d merge\n",
+                    facet->id, skip, newfacet->id, newskip));
+            }
+          }else if (ismatch) {
+            mindist= qh_getdistance(facet, newfacet, &low, &high);
+            dist2= qh_getdistance(newfacet, facet, &low, &high);
+            minimize_(mindist, dist2);
+            if (mindist > maxdist) {
+              maxdist= mindist;
+              maxmatch= facet;
+              maxskip= skip;
+              maxmatch2= newfacet;
+              maxskip2= newskip;
+            }
+            trace3((qh ferr, 3018, "qh_matchduplicates: duplicate f%d skip %d new f%d skip %d at dist %2.2g, max is now f%d f%d\n",
+                    facet->id, skip, newfacet->id, newskip, mindist,
+                    maxmatch->id, maxmatch2->id));
+          }else { /* !ismatch */
+            nextfacet= facet;
+            nextskip= skip;
+          }
+        }
+        if (makematch && !facet
+        && SETelemt_(facet->neighbors, skip, facetT) == qh_DUPLICATEridge) {
+          qh_fprintf(qh ferr, 6156, "qhull internal error (qh_matchduplicates): no MERGEridge match for duplicate f%d skip %d at hash %d\n",
+                     newfacet->id, newskip, hash);
+          qh_errexit(qh_ERRqhull, newfacet, NULL);
+        }
+      }
+    } /* end of for each new facet at hash */
+    if (!makematch) {
+      if (!maxmatch) {
+        qh_fprintf(qh ferr, 6157, "qhull internal error (qh_matchduplicates): no maximum match at duplicate f%d skip %d at hash %d\n",
+                     atfacet->id, atskip, hash);
+        qh_errexit(qh_ERRqhull, atfacet, NULL);
+      }
+      SETelem_(maxmatch->neighbors, maxskip)= maxmatch2; /* maxmatch!=0 by QH6157 */
+      SETelem_(maxmatch2->neighbors, maxskip2)= maxmatch;
+      *hashcount -= 2; /* removed two unmatched facets */
+      zzinc_(Zmultiridge);
+      trace0((qh ferr, 25, "qh_matchduplicates: duplicate f%d skip %d matched with new f%d skip %d keep\n",
+              maxmatch->id, maxskip, maxmatch2->id, maxskip2));
+      qh_precision("ridge with multiple neighbors");
+      if (qh IStracing >= 4)
+        qh_errprint("DUPLICATED/MATCH", maxmatch, maxmatch2, NULL, NULL);
+    }
+  }
+} /* matchduplicates */
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="nearcoplanar">-</a>
+
+  qh_nearcoplanar()
+    for all facets, remove near-inside points from facet->coplanarset</li>
+    coplanar points defined by innerplane from qh_outerinner()
+
+  returns:
+    if qh KEEPcoplanar && !qh KEEPinside
+      facet->coplanarset only contains coplanar points
+    if qh.JOGGLEmax
+      drops inner plane by another qh.JOGGLEmax diagonal since a
+        vertex could shift out while a coplanar point shifts in
+
+  notes:
+    used for qh.PREmerge and qh.JOGGLEmax
+    must agree with computation of qh.NEARcoplanar in qh_detroundoff()
+  design:
+    if not keeping coplanar or inside points
+      free all coplanar sets
+    else if not keeping both coplanar and inside points
+      remove !coplanar or !inside points from coplanar sets
+*/
+void qh_nearcoplanar(void /* qh.facet_list */) {
+  facetT *facet;
+  pointT *point, **pointp;
+  int numpart;
+  realT dist, innerplane;
+
+  if (!qh KEEPcoplanar && !qh KEEPinside) {
+    FORALLfacets {
+      if (facet->coplanarset)
+        qh_setfree( &facet->coplanarset);
+    }
+  }else if (!qh KEEPcoplanar || !qh KEEPinside) {
+    qh_outerinner(NULL, NULL, &innerplane);
+    if (qh JOGGLEmax < REALmax/2)
+      innerplane -= qh JOGGLEmax * sqrt((realT)qh hull_dim);
+    numpart= 0;
+    FORALLfacets {
+      if (facet->coplanarset) {
+        FOREACHpoint_(facet->coplanarset) {
+          numpart++;
+          qh_distplane(point, facet, &dist);
+          if (dist < innerplane) {
+            if (!qh KEEPinside)
+              SETref_(point)= NULL;
+          }else if (!qh KEEPcoplanar)
+            SETref_(point)= NULL;
+        }
+        qh_setcompact(facet->coplanarset);
+      }
+    }
+    zzadd_(Zcheckpart, numpart);
+  }
+} /* nearcoplanar */
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="nearvertex">-</a>
+
+  qh_nearvertex( facet, point, bestdist )
+    return nearest vertex in facet to point
+
+  returns:
+    vertex and its distance
+
+  notes:
+    if qh.DELAUNAY
+      distance is measured in the input set
+    searches neighboring tricoplanar facets (requires vertexneighbors)
+      Slow implementation.  Recomputes vertex set for each point.
+    The vertex set could be stored in the qh.keepcentrum facet.
+*/
+vertexT *qh_nearvertex(facetT *facet, pointT *point, realT *bestdistp) {
+  realT bestdist= REALmax, dist;
+  vertexT *bestvertex= NULL, *vertex, **vertexp, *apex;
+  coordT *center;
+  facetT *neighbor, **neighborp;
+  setT *vertices;
+  int dim= qh hull_dim;
+
+  if (qh DELAUNAY)
+    dim--;
+  if (facet->tricoplanar) {
+    if (!qh VERTEXneighbors || !facet->center) {
+      qh_fprintf(qh ferr, 6158, "qhull internal error (qh_nearvertex): qh.VERTEXneighbors and facet->center required for tricoplanar facets\n");
+      qh_errexit(qh_ERRqhull, facet, NULL);
+    }
+    vertices= qh_settemp(qh TEMPsize);
+    apex= SETfirstt_(facet->vertices, vertexT);
+    center= facet->center;
+    FOREACHneighbor_(apex) {
+      if (neighbor->center == center) {
+        FOREACHvertex_(neighbor->vertices)
+          qh_setappend(&vertices, vertex);
+      }
+    }
+  }else
+    vertices= facet->vertices;
+  FOREACHvertex_(vertices) {
+    dist= qh_pointdist(vertex->point, point, -dim);
+    if (dist < bestdist) {
+      bestdist= dist;
+      bestvertex= vertex;
+    }
+  }
+  if (facet->tricoplanar)
+    qh_settempfree(&vertices);
+  *bestdistp= sqrt(bestdist);
+  if (!bestvertex) {
+      qh_fprintf(qh ferr, 6261, "qhull internal error (qh_nearvertex): did not find bestvertex for f%d p%d\n", facet->id, qh_pointid(point));
+      qh_errexit(qh_ERRqhull, facet, NULL);
+  }
+  trace3((qh ferr, 3019, "qh_nearvertex: v%d dist %2.2g for f%d p%d\n",
+        bestvertex->id, *bestdistp, facet->id, qh_pointid(point))); /* bestvertex!=0 by QH2161 */
+  return bestvertex;
+} /* nearvertex */
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="newhashtable">-</a>
+
+  qh_newhashtable( newsize )
+    returns size of qh.hash_table of at least newsize slots
+
+  notes:
+    assumes qh.hash_table is NULL
+    qh_HASHfactor determines the number of extra slots
+    size is not divisible by 2, 3, or 5
+*/
+int qh_newhashtable(int newsize) {
+  int size;
+
+  size= ((newsize+1)*qh_HASHfactor) | 0x1;  /* odd number */
+  while (True) {
+    if (newsize<0 || size<0) {
+        qh_fprintf(qhmem.ferr, 6236, "qhull error (qh_newhashtable): negative request (%d) or size (%d).  Did int overflow due to high-D?\n", newsize, size); /* WARN64 */
+        qh_errexit(qhmem_ERRmem, NULL, NULL);
+    }
+    if ((size%3) && (size%5))
+      break;
+    size += 2;
+    /* loop terminates because there is an infinite number of primes */
+  }
+  qh hash_table= qh_setnew(size);
+  qh_setzero(qh hash_table, 0, size);
+  return size;
+} /* newhashtable */
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="newvertex">-</a>
+
+  qh_newvertex( point )
+    returns a new vertex for point
+*/
+vertexT *qh_newvertex(pointT *point) {
+  vertexT *vertex;
+
+  zinc_(Ztotvertices);
+  vertex= (vertexT *)qh_memalloc((int)sizeof(vertexT));
+  memset((char *) vertex, (size_t)0, sizeof(vertexT));
+  if (qh vertex_id == UINT_MAX) {
+    qh_memfree(vertex, (int)sizeof(vertexT));
+    qh_fprintf(qh ferr, 6159, "qhull error: more than 2^32 vertices.  vertexT.id field overflows.  Vertices would not be sorted correctly.\n");
+    qh_errexit(qh_ERRqhull, NULL, NULL);
+  }
+  if (qh vertex_id == qh tracevertex_id)
+    qh tracevertex= vertex;
+  vertex->id= qh vertex_id++;
+  vertex->point= point;
+  trace4((qh ferr, 4060, "qh_newvertex: vertex p%d(v%d) created\n", qh_pointid(vertex->point),
+          vertex->id));
+  return(vertex);
+} /* newvertex */
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="nextridge3d">-</a>
+
+  qh_nextridge3d( atridge, facet, vertex )
+    return next ridge and vertex for a 3d facet
+    returns NULL on error
+    [for QhullFacet::nextRidge3d] Does not call qh_errexit nor access qh_qh.
+
+  notes:
+    in qh_ORIENTclock order
+    this is a O(n^2) implementation to trace all ridges
+    be sure to stop on any 2nd visit
+    same as QhullRidge::nextRidge3d
+    does not use qh_qh or qh_errexit [QhullFacet.cpp]
+
+  design:
+    for each ridge
+      exit if it is the ridge after atridge
+*/
+ridgeT *qh_nextridge3d(ridgeT *atridge, facetT *facet, vertexT **vertexp) {
+  vertexT *atvertex, *vertex, *othervertex;
+  ridgeT *ridge, **ridgep;
+
+  if ((atridge->top == facet) ^ qh_ORIENTclock)
+    atvertex= SETsecondt_(atridge->vertices, vertexT);
+  else
+    atvertex= SETfirstt_(atridge->vertices, vertexT);
+  FOREACHridge_(facet->ridges) {
+    if (ridge == atridge)
+      continue;
+    if ((ridge->top == facet) ^ qh_ORIENTclock) {
+      othervertex= SETsecondt_(ridge->vertices, vertexT);
+      vertex= SETfirstt_(ridge->vertices, vertexT);
+    }else {
+      vertex= SETsecondt_(ridge->vertices, vertexT);
+      othervertex= SETfirstt_(ridge->vertices, vertexT);
+    }
+    if (vertex == atvertex) {
+      if (vertexp)
+        *vertexp= othervertex;
+      return ridge;
+    }
+  }
+  return NULL;
+} /* nextridge3d */
+#else /* qh_NOmerge */
+void qh_matchduplicates(facetT *atfacet, int atskip, int hashsize, int *hashcount) {
+}
+ridgeT *qh_nextridge3d(ridgeT *atridge, facetT *facet, vertexT **vertexp) {
+
+  return NULL;
+}
+#endif /* qh_NOmerge */
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="outcoplanar">-</a>
+
+  qh_outcoplanar()
+    move points from all facets' outsidesets to their coplanarsets
+
+  notes:
+    for post-processing under qh.NARROWhull
+
+  design:
+    for each facet
+      for each outside point for facet
+        partition point into coplanar set
+*/
+void qh_outcoplanar(void /* facet_list */) {
+  pointT *point, **pointp;
+  facetT *facet;
+  realT dist;
+
+  trace1((qh ferr, 1033, "qh_outcoplanar: move outsideset to coplanarset for qh NARROWhull\n"));
+  FORALLfacets {
+    FOREACHpoint_(facet->outsideset) {
+      qh num_outside--;
+      if (qh KEEPcoplanar || qh KEEPnearinside) {
+        qh_distplane(point, facet, &dist);
+        zinc_(Zpartition);
+        qh_partitioncoplanar(point, facet, &dist);
+      }
+    }
+    qh_setfree(&facet->outsideset);
+  }
+} /* outcoplanar */
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="point">-</a>
+
+  qh_point( id )
+    return point for a point id, or NULL if unknown
+
+  alternative code:
+    return((pointT *)((unsigned   long)qh.first_point
+           + (unsigned long)((id)*qh.normal_size)));
+*/
+pointT *qh_point(int id) {
+
+  if (id < 0)
+    return NULL;
+  if (id < qh num_points)
+    return qh first_point + id * qh hull_dim;
+  id -= qh num_points;
+  if (id < qh_setsize(qh other_points))
+    return SETelemt_(qh other_points, id, pointT);
+  return NULL;
+} /* point */
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="point_add">-</a>
+
+  qh_point_add( set, point, elem )
+    stores elem at set[point.id]
+
+  returns:
+    access function for qh_pointfacet and qh_pointvertex
+
+  notes:
+    checks point.id
+*/
+void qh_point_add(setT *set, pointT *point, void *elem) {
+  int id, size;
+
+  SETreturnsize_(set, size);
+  if ((id= qh_pointid(point)) < 0)
+    qh_fprintf(qh ferr, 7067, "qhull internal warning (point_add): unknown point %p id %d\n",
+      point, id);
+  else if (id >= size) {
+    qh_fprintf(qh ferr, 6160, "qhull internal errror(point_add): point p%d is out of bounds(%d)\n",
+             id, size);
+    qh_errexit(qh_ERRqhull, NULL, NULL);
+  }else
+    SETelem_(set, id)= elem;
+} /* point_add */
+
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="pointfacet">-</a>
+
+  qh_pointfacet()
+    return temporary set of facet for each point
+    the set is indexed by point id
+
+  notes:
+    vertices assigned to one of the facets
+    coplanarset assigned to the facet
+    outside set assigned to the facet
+    NULL if no facet for point (inside)
+      includes qh.GOODpointp
+
+  access:
+    FOREACHfacet_i_(facets) { ... }
+    SETelem_(facets, i)
+
+  design:
+    for each facet
+      add each vertex
+      add each coplanar point
+      add each outside point
+*/
+setT *qh_pointfacet(void /*qh.facet_list*/) {
+  int numpoints= qh num_points + qh_setsize(qh other_points);
+  setT *facets;
+  facetT *facet;
+  vertexT *vertex, **vertexp;
+  pointT *point, **pointp;
+
+  facets= qh_settemp(numpoints);
+  qh_setzero(facets, 0, numpoints);
+  qh vertex_visit++;
+  FORALLfacets {
+    FOREACHvertex_(facet->vertices) {
+      if (vertex->visitid != qh vertex_visit) {
+        vertex->visitid= qh vertex_visit;
+        qh_point_add(facets, vertex->point, facet);
+      }
+    }
+    FOREACHpoint_(facet->coplanarset)
+      qh_point_add(facets, point, facet);
+    FOREACHpoint_(facet->outsideset)
+      qh_point_add(facets, point, facet);
+  }
+  return facets;
+} /* pointfacet */
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="pointvertex">-</a>
+
+  qh_pointvertex(  )
+    return temporary set of vertices indexed by point id
+    entry is NULL if no vertex for a point
+      this will include qh.GOODpointp
+
+  access:
+    FOREACHvertex_i_(vertices) { ... }
+    SETelem_(vertices, i)
+*/
+setT *qh_pointvertex(void /*qh.facet_list*/) {
+  int numpoints= qh num_points + qh_setsize(qh other_points);
+  setT *vertices;
+  vertexT *vertex;
+
+  vertices= qh_settemp(numpoints);
+  qh_setzero(vertices, 0, numpoints);
+  FORALLvertices
+    qh_point_add(vertices, vertex->point, vertex);
+  return vertices;
+} /* pointvertex */
+
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="prependfacet">-</a>
+
+  qh_prependfacet( facet, facetlist )
+    prepend facet to the start of a facetlist
+
+  returns:
+    increments qh.numfacets
+    updates facetlist, qh.facet_list, facet_next
+
+  notes:
+    be careful of prepending since it can lose a pointer.
+      e.g., can lose _next by deleting and then prepending before _next
+*/
+void qh_prependfacet(facetT *facet, facetT **facetlist) {
+  facetT *prevfacet, *list;
+
+
+  trace4((qh ferr, 4061, "qh_prependfacet: prepend f%d before f%d\n",
+          facet->id, getid_(*facetlist)));
+  if (!*facetlist)
+    (*facetlist)= qh facet_tail;
+  list= *facetlist;
+  prevfacet= list->previous;
+  facet->previous= prevfacet;
+  if (prevfacet)
+    prevfacet->next= facet;
+  list->previous= facet;
+  facet->next= *facetlist;
+  if (qh facet_list == list)  /* this may change *facetlist */
+    qh facet_list= facet;
+  if (qh facet_next == list)
+    qh facet_next= facet;
+  *facetlist= facet;
+  qh num_facets++;
+} /* prependfacet */
+
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="printhashtable">-</a>
+
+  qh_printhashtable( fp )
+    print hash table to fp
+
+  notes:
+    not in I/O to avoid bringing io.c in
+
+  design:
+    for each hash entry
+      if defined
+        if unmatched or will merge (NULL, qh_MERGEridge, qh_DUPLICATEridge)
+          print entry and neighbors
+*/
+void qh_printhashtable(FILE *fp) {
+  facetT *facet, *neighbor;
+  int id, facet_i, facet_n, neighbor_i= 0, neighbor_n= 0;
+  vertexT *vertex, **vertexp;
+
+  FOREACHfacet_i_(qh hash_table) {
+    if (facet) {
+      FOREACHneighbor_i_(facet) {
+        if (!neighbor || neighbor == qh_MERGEridge || neighbor == qh_DUPLICATEridge)
+          break;
+      }
+      if (neighbor_i == neighbor_n)
+        continue;
+      qh_fprintf(fp, 9283, "hash %d f%d ", facet_i, facet->id);
+      FOREACHvertex_(facet->vertices)
+        qh_fprintf(fp, 9284, "v%d ", vertex->id);
+      qh_fprintf(fp, 9285, "\n neighbors:");
+      FOREACHneighbor_i_(facet) {
+        if (neighbor == qh_MERGEridge)
+          id= -3;
+        else if (neighbor == qh_DUPLICATEridge)
+          id= -2;
+        else
+          id= getid_(neighbor);
+        qh_fprintf(fp, 9286, " %d", id);
+      }
+      qh_fprintf(fp, 9287, "\n");
+    }
+  }
+} /* printhashtable */
+
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="printlists">-</a>
+
+  qh_printlists( fp )
+    print out facet and vertex list for debugging (without 'f/v' tags)
+*/
+void qh_printlists(void) {
+  facetT *facet;
+  vertexT *vertex;
+  int count= 0;
+
+  qh_fprintf(qh ferr, 8108, "qh_printlists: facets:");
+  FORALLfacets {
+    if (++count % 100 == 0)
+      qh_fprintf(qh ferr, 8109, "\n     ");
+    qh_fprintf(qh ferr, 8110, " %d", facet->id);
+  }
+  qh_fprintf(qh ferr, 8111, "\n  new facets %d visible facets %d next facet for qh_addpoint %d\n  vertices(new %d):",
+     getid_(qh newfacet_list), getid_(qh visible_list), getid_(qh facet_next),
+     getid_(qh newvertex_list));
+  count = 0;
+  FORALLvertices {
+    if (++count % 100 == 0)
+      qh_fprintf(qh ferr, 8112, "\n     ");
+    qh_fprintf(qh ferr, 8113, " %d", vertex->id);
+  }
+  qh_fprintf(qh ferr, 8114, "\n");
+} /* printlists */
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="resetlists">-</a>
+
+  qh_resetlists( stats, qh_RESETvisible )
+    reset newvertex_list, newfacet_list, visible_list
+    if stats,
+      maintains statistics
+
+  returns:
+    visible_list is empty if qh_deletevisible was called
+*/
+void qh_resetlists(boolT stats, boolT resetVisible /*qh.newvertex_list newfacet_list visible_list*/) {
+  vertexT *vertex;
+  facetT *newfacet, *visible;
+  int totnew=0, totver=0;
+
+  if (stats) {
+    FORALLvertex_(qh newvertex_list)
+      totver++;
+    FORALLnew_facets
+      totnew++;
+    zadd_(Zvisvertextot, totver);
+    zmax_(Zvisvertexmax, totver);
+    zadd_(Znewfacettot, totnew);
+    zmax_(Znewfacetmax, totnew);
+  }
+  FORALLvertex_(qh newvertex_list)
+    vertex->newlist= False;
+  qh newvertex_list= NULL;
+  FORALLnew_facets
+    newfacet->newfacet= False;
+  qh newfacet_list= NULL;
+  if (resetVisible) {
+    FORALLvisible_facets {
+      visible->f.replace= NULL;
+      visible->visible= False;
+    }
+    qh num_visible= 0;
+  }
+  qh visible_list= NULL; /* may still have visible facets via qh_triangulate */
+  qh NEWfacets= False;
+} /* resetlists */
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="setvoronoi_all">-</a>
+
+  qh_setvoronoi_all()
+    compute Voronoi centers for all facets
+    includes upperDelaunay facets if qh.UPPERdelaunay ('Qu')
+
+  returns:
+    facet->center is the Voronoi center
+
+  notes:
+    this is unused/untested code
+      please email bradb@shore.net if this works ok for you
+
+  use:
+    FORALLvertices {...} to locate the vertex for a point.
+    FOREACHneighbor_(vertex) {...} to visit the Voronoi centers for a Voronoi cell.
+*/
+void qh_setvoronoi_all(void) {
+  facetT *facet;
+
+  qh_clearcenters(qh_ASvoronoi);
+  qh_vertexneighbors();
+
+  FORALLfacets {
+    if (!facet->normal || !facet->upperdelaunay || qh UPPERdelaunay) {
+      if (!facet->center)
+        facet->center= qh_facetcenter(facet->vertices);
+    }
+  }
+} /* setvoronoi_all */
+
+#ifndef qh_NOmerge
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="triangulate">-</a>
+
+  qh_triangulate()
+    triangulate non-simplicial facets on qh.facet_list,
+    if qh VORONOI, sets Voronoi centers of non-simplicial facets
+    nop if hasTriangulation
+
+  returns:
+    all facets simplicial
+    each tricoplanar facet has ->f.triowner == owner of ->center,normal,etc.
+
+  notes:
+    call after qh_check_output since may switch to Voronoi centers
+    Output may overwrite ->f.triowner with ->f.area
+*/
+void qh_triangulate(void /*qh.facet_list*/) {
+  facetT *facet, *nextfacet, *owner;
+  int onlygood= qh ONLYgood;
+  facetT *neighbor, *visible= NULL, *facet1, *facet2, *new_facet_list= NULL;
+  facetT *orig_neighbor= NULL, *otherfacet;
+  vertexT *new_vertex_list= NULL;
+  mergeT *merge;
+  mergeType mergetype;
+  int neighbor_i, neighbor_n;
+
+  if (qh hasTriangulation)
+      return;
+  trace1((qh ferr, 1034, "qh_triangulate: triangulate non-simplicial facets\n"));
+  if (qh hull_dim == 2)
+    return;
+  if (qh VORONOI) {  /* otherwise lose Voronoi centers [could rebuild vertex set from tricoplanar] */
+    qh_clearcenters(qh_ASvoronoi);
+    qh_vertexneighbors();
+  }
+  qh ONLYgood= False; /* for makenew_nonsimplicial */
+  qh visit_id++;
+  qh NEWfacets= True;
+  qh degen_mergeset= qh_settemp(qh TEMPsize);
+  qh newvertex_list= qh vertex_tail;
+  for (facet= qh facet_list; facet && facet->next; facet= nextfacet) { /* non-simplicial facets moved to end */
+    nextfacet= facet->next;
+    if (facet->visible || facet->simplicial)
+      continue;
+    /* triangulate all non-simplicial facets, otherwise merging does not work, e.g., RBOX c P-0.1 P+0.1 P+0.1 D3 | QHULL d Qt Tv */
+    if (!new_facet_list)
+      new_facet_list= facet;  /* will be moved to end */
+    qh_triangulate_facet(facet, &new_vertex_list);
+  }
+  trace2((qh ferr, 2047, "qh_triangulate: delete null facets from f%d -- apex same as second vertex\n", getid_(new_facet_list)));
+  for (facet= new_facet_list; facet && facet->next; facet= nextfacet) { /* null facets moved to end */
+    nextfacet= facet->next;
+    if (facet->visible)
+      continue;
+    if (facet->ridges) {
+      if (qh_setsize(facet->ridges) > 0) {
+        qh_fprintf(qh ferr, 6161, "qhull error (qh_triangulate): ridges still defined for f%d\n", facet->id);
+        qh_errexit(qh_ERRqhull, facet, NULL);
+      }
+      qh_setfree(&facet->ridges);
+    }
+    if (SETfirst_(facet->vertices) == SETsecond_(facet->vertices)) {
+      zinc_(Ztrinull);
+      qh_triangulate_null(facet);
+    }
+  }
+  trace2((qh ferr, 2048, "qh_triangulate: delete %d or more mirror facets -- same vertices and neighbors\n", qh_setsize(qh degen_mergeset)));
+  qh visible_list= qh facet_tail;
+  while ((merge= (mergeT*)qh_setdellast(qh degen_mergeset))) {
+    facet1= merge->facet1;
+    facet2= merge->facet2;
+    mergetype= merge->type;
+    qh_memfree(merge, (int)sizeof(mergeT));
+    if (mergetype == MRGmirror) {
+      zinc_(Ztrimirror);
+      qh_triangulate_mirror(facet1, facet2);
+    }
+  }
+  qh_settempfree(&qh degen_mergeset);
+  trace2((qh ferr, 2049, "qh_triangulate: update neighbor lists for vertices from v%d\n", getid_(new_vertex_list)));
+  qh newvertex_list= new_vertex_list;  /* all vertices of new facets */
+  qh visible_list= NULL;
+  qh_updatevertices(/*qh.newvertex_list, empty newfacet_list and visible_list*/);
+  qh_resetlists(False, !qh_RESETvisible /*qh.newvertex_list, empty newfacet_list and visible_list*/);
+
+  trace2((qh ferr, 2050, "qh_triangulate: identify degenerate tricoplanar facets from f%d\n", getid_(new_facet_list)));
+  trace2((qh ferr, 2051, "qh_triangulate: and replace facet->f.triowner with tricoplanar facets that own center, normal, etc.\n"));
+  FORALLfacet_(new_facet_list) {
+    if (facet->tricoplanar && !facet->visible) {
+      FOREACHneighbor_i_(facet) {
+        if (neighbor_i == 0) {  /* first iteration */
+          if (neighbor->tricoplanar)
+            orig_neighbor= neighbor->f.triowner;
+          else
+            orig_neighbor= neighbor;
+        }else {
+          if (neighbor->tricoplanar)
+            otherfacet= neighbor->f.triowner;
+          else
+            otherfacet= neighbor;
+          if (orig_neighbor == otherfacet) {
+            zinc_(Ztridegen);
+            facet->degenerate= True;
+            break;
+          }
+        }
+      }
+    }
+  }
+
+  trace2((qh ferr, 2052, "qh_triangulate: delete visible facets -- non-simplicial, null, and mirrored facets\n"));
+  owner= NULL;
+  visible= NULL;
+  for (facet= new_facet_list; facet && facet->next; facet= nextfacet) { /* may delete facet */
+    nextfacet= facet->next;
+    if (facet->visible) {
+      if (facet->tricoplanar) { /* a null or mirrored facet */
+        qh_delfacet(facet);
+        qh num_visible--;
+      }else {  /* a non-simplicial facet followed by its tricoplanars */
+        if (visible && !owner) {
+          /*  RBOX 200 s D5 t1001471447 | QHULL Qt C-0.01 Qx Qc Tv Qt -- f4483 had 6 vertices/neighbors and 8 ridges */
+          trace2((qh ferr, 2053, "qh_triangulate: all tricoplanar facets degenerate for non-simplicial facet f%d\n",
+                       visible->id));
+          qh_delfacet(visible);
+          qh num_visible--;
+        }
+        visible= facet;
+        owner= NULL;
+      }
+    }else if (facet->tricoplanar) {
+      if (facet->f.triowner != visible || visible==NULL) {
+        qh_fprintf(qh ferr, 6162, "qhull error (qh_triangulate): tricoplanar facet f%d not owned by its visible, non-simplicial facet f%d\n", facet->id, getid_(visible));
+        qh_errexit2(qh_ERRqhull, facet, visible);
+      }
+      if (owner)
+        facet->f.triowner= owner;
+      else if (!facet->degenerate) {
+        owner= facet;
+        nextfacet= visible->next; /* rescan tricoplanar facets with owner, visible!=0 by QH6162 */
+        facet->keepcentrum= True;  /* one facet owns ->normal, etc. */
+        facet->coplanarset= visible->coplanarset;
+        facet->outsideset= visible->outsideset;
+        visible->coplanarset= NULL;
+        visible->outsideset= NULL;
+        if (!qh TRInormals) { /* center and normal copied to tricoplanar facets */
+          visible->center= NULL;
+          visible->normal= NULL;
+        }
+        qh_delfacet(visible);
+        qh num_visible--;
+      }
+    }
+  }
+  if (visible && !owner) {
+    trace2((qh ferr, 2054, "qh_triangulate: all tricoplanar facets degenerate for last non-simplicial facet f%d\n",
+                 visible->id));
+    qh_delfacet(visible);
+    qh num_visible--;
+  }
+  qh NEWfacets= False;
+  qh ONLYgood= onlygood; /* restore value */
+  if (qh CHECKfrequently)
+    qh_checkpolygon(qh facet_list);
+  qh hasTriangulation= True;
+} /* triangulate */
+
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="triangulate_facet">-</a>
+
+  qh_triangulate_facet(qh, facetA, &firstVertex )
+    triangulate a non-simplicial facet
+      if qh.CENTERtype=qh_ASvoronoi, sets its Voronoi center
+  returns:
+    qh.newfacet_list == simplicial facets
+      facet->tricoplanar set and ->keepcentrum false
+      facet->degenerate set if duplicated apex
+      facet->f.trivisible set to facetA
+      facet->center copied from facetA (created if qh_ASvoronoi)
+        qh_eachvoronoi, qh_detvridge, qh_detvridge3 assume centers copied
+      facet->normal,offset,maxoutside copied from facetA
+
+  notes:
+      only called by qh_triangulate
+      qh_makenew_nonsimplicial uses neighbor->seen for the same
+      if qh.TRInormals, newfacet->normal will need qh_free
+        if qh.TRInormals and qh_AScentrum, newfacet->center will need qh_free
+        keepcentrum is also set on Zwidefacet in qh_mergefacet
+        freed by qh_clearcenters
+
+  see also:
+      qh_addpoint() -- add a point
+      qh_makenewfacets() -- construct a cone of facets for a new vertex
+
+  design:
+      if qh_ASvoronoi,
+         compute Voronoi center (facet->center)
+      select first vertex (highest ID to preserve ID ordering of ->vertices)
+      triangulate from vertex to ridges
+      copy facet->center, normal, offset
+      update vertex neighbors
+*/
+void qh_triangulate_facet(facetT *facetA, vertexT **first_vertex) {
+  facetT *newfacet;
+  facetT *neighbor, **neighborp;
+  vertexT *apex;
+  int numnew=0;
+
+  trace3((qh ferr, 3020, "qh_triangulate_facet: triangulate facet f%d\n", facetA->id));
+
+  if (qh IStracing >= 4)
+    qh_printfacet(qh ferr, facetA);
+  FOREACHneighbor_(facetA) {
+    neighbor->seen= False;
+    neighbor->coplanar= False;
+  }
+  if (qh CENTERtype == qh_ASvoronoi && !facetA->center  /* matches upperdelaunay in qh_setfacetplane() */
+        && fabs_(facetA->normal[qh hull_dim -1]) >= qh ANGLEround * qh_ZEROdelaunay) {
+    facetA->center= qh_facetcenter(facetA->vertices);
+  }
+  qh_willdelete(facetA, NULL);
+  qh newfacet_list= qh facet_tail;
+  facetA->visitid= qh visit_id;
+  apex= SETfirstt_(facetA->vertices, vertexT);
+  qh_makenew_nonsimplicial(facetA, apex, &numnew);
+  SETfirst_(facetA->neighbors)= NULL;
+  FORALLnew_facets {
+    newfacet->tricoplanar= True;
+    newfacet->f.trivisible= facetA;
+    newfacet->degenerate= False;
+    newfacet->upperdelaunay= facetA->upperdelaunay;
+    newfacet->good= facetA->good;
+    if (qh TRInormals) { /* 'Q11' triangulate duplicates ->normal and ->center */
+      newfacet->keepcentrum= True;
+      if(facetA->normal){
+        newfacet->normal= qh_memalloc(qh normal_size);
+        memcpy((char *)newfacet->normal, facetA->normal, qh normal_size);
+      }
+      if (qh CENTERtype == qh_AScentrum)
+        newfacet->center= qh_getcentrum(newfacet);
+      else if (qh CENTERtype == qh_ASvoronoi && facetA->center){
+        newfacet->center= qh_memalloc(qh center_size);
+        memcpy((char *)newfacet->center, facetA->center, qh center_size);
+      }
+    }else {
+      newfacet->keepcentrum= False;
+      /* one facet will have keepcentrum=True at end of qh_triangulate */
+      newfacet->normal= facetA->normal;
+      newfacet->center= facetA->center;
+    }
+    newfacet->offset= facetA->offset;
+#if qh_MAXoutside
+    newfacet->maxoutside= facetA->maxoutside;
+#endif
+  }
+  qh_matchnewfacets(/*qh.newfacet_list*/);
+  zinc_(Ztricoplanar);
+  zadd_(Ztricoplanartot, numnew);
+  zmax_(Ztricoplanarmax, numnew);
+  qh visible_list= NULL;
+  if (!(*first_vertex))
+    (*first_vertex)= qh newvertex_list;
+  qh newvertex_list= NULL;
+  qh_updatevertices(/*qh.newfacet_list, qh.empty visible_list and qh.newvertex_list*/);
+  qh_resetlists(False, !qh_RESETvisible /*qh.newfacet_list, qh.empty visible_list and qh.newvertex_list*/);
+} /* triangulate_facet */
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="triangulate_link">-</a>
+
+  qh_triangulate_link(oldfacetA, facetA, oldfacetB, facetB)
+    relink facetA to facetB via oldfacets
+  returns:
+    adds mirror facets to qh degen_mergeset (4-d and up only)
+  design:
+    if they are already neighbors, the opposing neighbors become MRGmirror facets
+*/
+void qh_triangulate_link(facetT *oldfacetA, facetT *facetA, facetT *oldfacetB, facetT *facetB) {
+  int errmirror= False;
+
+  trace3((qh ferr, 3021, "qh_triangulate_link: relink old facets f%d and f%d between neighbors f%d and f%d\n",
+         oldfacetA->id, oldfacetB->id, facetA->id, facetB->id));
+  if (qh_setin(facetA->neighbors, facetB)) {
+    if (!qh_setin(facetB->neighbors, facetA))
+      errmirror= True;
+    else
+      qh_appendmergeset(facetA, facetB, MRGmirror, NULL);
+  }else if (qh_setin(facetB->neighbors, facetA))
+    errmirror= True;
+  if (errmirror) {
+    qh_fprintf(qh ferr, 6163, "qhull error (qh_triangulate_link): mirror facets f%d and f%d do not match for old facets f%d and f%d\n",
+       facetA->id, facetB->id, oldfacetA->id, oldfacetB->id);
+    qh_errexit2(qh_ERRqhull, facetA, facetB);
+  }
+  qh_setreplace(facetB->neighbors, oldfacetB, facetA);
+  qh_setreplace(facetA->neighbors, oldfacetA, facetB);
+} /* triangulate_link */
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="triangulate_mirror">-</a>
+
+  qh_triangulate_mirror(facetA, facetB)
+    delete mirrored facets from qh_triangulate_null() and qh_triangulate_mirror
+      a mirrored facet shares the same vertices of a logical ridge
+  design:
+    since a null facet duplicates the first two vertices, the opposing neighbors absorb the null facet
+    if they are already neighbors, the opposing neighbors become MRGmirror facets
+*/
+void qh_triangulate_mirror(facetT *facetA, facetT *facetB) {
+  facetT *neighbor, *neighborB;
+  int neighbor_i, neighbor_n;
+
+  trace3((qh ferr, 3022, "qh_triangulate_mirror: delete mirrored facets f%d and f%d\n",
+         facetA->id, facetB->id));
+  FOREACHneighbor_i_(facetA) {
+    neighborB= SETelemt_(facetB->neighbors, neighbor_i, facetT);
+    if (neighbor == neighborB)
+      continue; /* occurs twice */
+    qh_triangulate_link(facetA, neighbor, facetB, neighborB);
+  }
+  qh_willdelete(facetA, NULL);
+  qh_willdelete(facetB, NULL);
+} /* triangulate_mirror */
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="triangulate_null">-</a>
+
+  qh_triangulate_null(facetA)
+    remove null facetA from qh_triangulate_facet()
+      a null facet has vertex #1 (apex) == vertex #2
+  returns:
+    adds facetA to ->visible for deletion after qh_updatevertices
+    qh degen_mergeset contains mirror facets (4-d and up only)
+  design:
+    since a null facet duplicates the first two vertices, the opposing neighbors absorb the null facet
+    if they are already neighbors, the opposing neighbors become MRGmirror facets
+*/
+void qh_triangulate_null(facetT *facetA) {
+  facetT *neighbor, *otherfacet;
+
+  trace3((qh ferr, 3023, "qh_triangulate_null: delete null facet f%d\n", facetA->id));
+  neighbor= SETfirstt_(facetA->neighbors, facetT);
+  otherfacet= SETsecondt_(facetA->neighbors, facetT);
+  qh_triangulate_link(facetA, neighbor, facetA, otherfacet);
+  qh_willdelete(facetA, NULL);
+} /* triangulate_null */
+
+#else /* qh_NOmerge */
+void qh_triangulate(void) {
+}
+#endif /* qh_NOmerge */
+
+   /*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="vertexintersect">-</a>
+
+  qh_vertexintersect( vertexsetA, vertexsetB )
+    intersects two vertex sets (inverse id ordered)
+    vertexsetA is a temporary set at the top of qhmem.tempstack
+
+  returns:
+    replaces vertexsetA with the intersection
+
+  notes:
+    could overwrite vertexsetA if currently too slow
+*/
+void qh_vertexintersect(setT **vertexsetA,setT *vertexsetB) {
+  setT *intersection;
+
+  intersection= qh_vertexintersect_new(*vertexsetA, vertexsetB);
+  qh_settempfree(vertexsetA);
+  *vertexsetA= intersection;
+  qh_settemppush(intersection);
+} /* vertexintersect */
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="vertexintersect_new">-</a>
+
+  qh_vertexintersect_new(  )
+    intersects two vertex sets (inverse id ordered)
+
+  returns:
+    a new set
+*/
+setT *qh_vertexintersect_new(setT *vertexsetA,setT *vertexsetB) {
+  setT *intersection= qh_setnew(qh hull_dim - 1);
+  vertexT **vertexA= SETaddr_(vertexsetA, vertexT);
+  vertexT **vertexB= SETaddr_(vertexsetB, vertexT);
+
+  while (*vertexA && *vertexB) {
+    if (*vertexA  == *vertexB) {
+      qh_setappend(&intersection, *vertexA);
+      vertexA++; vertexB++;
+    }else {
+      if ((*vertexA)->id > (*vertexB)->id)
+        vertexA++;
+      else
+        vertexB++;
+    }
+  }
+  return intersection;
+} /* vertexintersect_new */
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="vertexneighbors">-</a>
+
+  qh_vertexneighbors()
+    for each vertex in qh.facet_list,
+      determine its neighboring facets
+
+  returns:
+    sets qh.VERTEXneighbors
+      nop if qh.VERTEXneighbors already set
+      qh_addpoint() will maintain them
+
+  notes:
+    assumes all vertex->neighbors are NULL
+
+  design:
+    for each facet
+      for each vertex
+        append facet to vertex->neighbors
+*/
+void qh_vertexneighbors(void /*qh.facet_list*/) {
+  facetT *facet;
+  vertexT *vertex, **vertexp;
+
+  if (qh VERTEXneighbors)
+    return;
+  trace1((qh ferr, 1035, "qh_vertexneighbors: determining neighboring facets for each vertex\n"));
+  qh vertex_visit++;
+  FORALLfacets {
+    if (facet->visible)
+      continue;
+    FOREACHvertex_(facet->vertices) {
+      if (vertex->visitid != qh vertex_visit) {
+        vertex->visitid= qh vertex_visit;
+        vertex->neighbors= qh_setnew(qh hull_dim);
+      }
+      qh_setappend(&vertex->neighbors, facet);
+    }
+  }
+  qh VERTEXneighbors= True;
+} /* vertexneighbors */
+
+/*-<a                             href="qh-poly.htm#TOC"
+  >-------------------------------</a><a name="vertexsubset">-</a>
+
+  qh_vertexsubset( vertexsetA, vertexsetB )
+    returns True if vertexsetA is a subset of vertexsetB
+    assumes vertexsets are sorted
+
+  note:
+    empty set is a subset of any other set
+*/
+boolT qh_vertexsubset(setT *vertexsetA, setT *vertexsetB) {
+  vertexT **vertexA= (vertexT **) SETaddr_(vertexsetA, vertexT);
+  vertexT **vertexB= (vertexT **) SETaddr_(vertexsetB, vertexT);
+
+  while (True) {
+    if (!*vertexA)
+      return True;
+    if (!*vertexB)
+      return False;
+    if ((*vertexA)->id > (*vertexB)->id)
+      return False;
+    if (*vertexA  == *vertexB)
+      vertexA++;
+    vertexB++;
+  }
+  return False; /* avoid warnings */
+} /* vertexsubset */
diff --git a/xs/src/qhull/src/libqhull/qh-geom.htm b/xs/src/qhull/src/libqhull/qh-geom.htm
new file mode 100644
index 0000000000..6dc7465ebe
--- /dev/null
+++ b/xs/src/qhull/src/libqhull/qh-geom.htm
@@ -0,0 +1,295 @@
+<!-- Do not edit with Front Page, it adds too many spaces -->
+<html>
+<head>
+<meta http-equiv="Content-Type"
+content="text/html; charset=iso-8859-1">
+<title>geom.c, geom2.c -- geometric and floating point routines</title>
+</head>
+
+<body>
+<!-- Navigation links -->
+<p><a name="TOP"><b>Up:</b></a> <a
+href="http://www.qhull.org">Home page</a> for Qhull<br>
+<b>Up:</b> <a href="../../html/index.htm#TOC">Qhull manual</a>: Table of Contents <br>
+<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a>
+&#149; <a href="../../html/qh-quick.htm#options">Options</a>
+&#149; <a href="../../html/qh-opto.htm#output">Output</a>
+&#149; <a href="../../html/qh-optf.htm#format">Formats</a>
+&#149; <a href="../../html/qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="../../html/qh-optp.htm#print">Print</a>
+&#149; <a href="../../html/qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="../../html/qh-optc.htm#prec">Precision</a>
+&#149; <a href="../../html/qh-optt.htm#trace">Trace</a>
+&#149; <a href="index.htm">Functions</a><br>
+<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code: Table of Contents</a><br>
+<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
+<b>To:</b> <a href="qh-geom.htm#TOC">Geom</a> &#149; <a href="qh-globa.htm">Global</a>
+&#149; <a href="qh-io.htm">Io</a> &#149; <a href="qh-mem.htm">Mem</a>
+&#149; <a href="qh-merge.htm">Merge</a> &#149; <a href="qh-poly.htm">Poly</a>
+&#149; <a href="qh-qhull.htm">Qhull</a> &#149; <a href="qh-set.htm">Set</a>
+&#149; <a href="qh-stat.htm">Stat</a> &#149; <a href="qh-user.htm">User</a>
+</p>
+
+<hr>
+<!-- Main text of document. -->
+
+<h2>geom.c, geom2.c, random.c -- geometric and floating point routines</h2>
+<blockquote>
+<p>Geometrically, a vertex is a point with <em>d</em> coordinates
+and a facet is a halfspace. A <em>halfspace</em> is defined by an
+oriented hyperplane through the facet's vertices. A <em>hyperplane</em>
+is defined by <em>d</em> normalized coefficients and an offset. A
+point is <em>above</em> a facet if its distance to the facet is
+positive.</p>
+
+<p>Qhull uses floating point coordinates for input points,
+vertices, halfspace equations, centrums, and an interior point.</p>
+
+<p>Qhull may be configured for single precision or double
+precision floating point arithmetic (see <a href="user.h#realT">realT</a>
+). </p>
+
+<p>Each floating point operation may incur round-off error (see
+<a href="qh-merge.htm#TOC">Merge</a>). The maximum error for distance
+computations is determined at initialization. The roundoff error
+in halfspace computation is accounted for by computing the
+distance from vertices to the halfspace. </p>
+</blockquote>
+<p><b>Copyright &copy; 1995-2015 C.B. Barber</b></p>
+<hr>
+<p><a href="#TOP">&#187;</a> <b>Geom</b>
+<a name="TOC">&#149;</a> <a href="qh-globa.htm#TOC">Global</a> &#149;
+<a href="qh-io.htm#TOC">Io</a> &#149; <a href="qh-mem.htm#TOC">Mem</a> &#149;
+<a href="qh-merge.htm#TOC">Merge</a> &#149; <a href="qh-poly.htm#TOC">Poly</a> &#149;
+<a href="qh-qhull.htm#TOC">Qhull</a> &#149; <a href="qh-set.htm#TOC">Set</a> &#149;
+<a href="qh-stat.htm#TOC">Stat</a> &#149; <a href="qh-user.htm#TOC">User</a> </p>
+
+<h3>Index to <a href="geom.c">geom.c</a>,
+<a href="geom2.c">geom2.c</a>, <a href="geom.h">geom.h</a>,
+<a href="random.c">random.c</a>, <a href="random.h">random.h</a>
+</h3>
+
+<ul>
+<li><a href="#gtype">geometric data types and constants</a> </li>
+<li><a href="#gmacro">mathematical macros</a>
+</li>
+<li><a href="#gmath">mathematical functions</a> </li>
+<li><a href="#gcomp">computational geometry functions</a> </li>
+<li><a href="#gpoint">point array functions</a> </li>
+<li><a href="#gfacet">geometric facet functions</a> </li>
+<li><a href="#ground">geometric roundoff functions</a></li>
+</ul>
+
+<h3><a href="qh-geom.htm#TOC">&#187;</a><a name="gtype">geometric data types
+and constants</a></h3>
+
+<ul>
+<li><a href="libqhull.h#coordT">coordT</a> coordinates and
+coefficients are stored as realT</li>
+<li><a href="libqhull.h#pointT">pointT</a> a point is an array
+of <tt>DIM3</tt> coordinates </li>
+</ul>
+
+<h3><a href="qh-geom.htm#TOC">&#187;</a><a name="gmacro">mathematical macros</a></h3>
+
+<ul>
+<li><a href="geom.h#fabs_">fabs_</a> returns the absolute
+value of a </li>
+<li><a href="geom.h#fmax_">fmax_</a> returns the maximum
+value of a and b </li>
+<li><a href="geom.h#fmin_">fmin_</a> returns the minimum
+value of a and b </li>
+<li><a href="geom.h#maximize_">maximize_</a> maximize a value
+</li>
+<li><a href="geom.h#minimize_">minimize_</a> minimize a value
+</li>
+<li><a href="geom.h#det2_">det2_</a> compute a 2-d
+determinate </li>
+<li><a href="geom.h#det3_">det3_</a> compute a 3-d
+determinate </li>
+<li><a href="geom.h#dX">dX, dY, dZ</a> compute the difference
+between two coordinates </li>
+</ul>
+
+<h3><a href="qh-geom.htm#TOC">&#187;</a><a name="gmath">mathematical functions</a></h3>
+
+<ul>
+<li><a href="geom.c#backnormal">qh_backnormal</a> solve for
+normal using back substitution </li>
+<li><a href="geom2.c#crossproduct">qh_crossproduct</a>
+compute the cross product of two 3-d vectors </li>
+<li><a href="geom2.c#determinant">qh_determinant</a> compute
+the determinant of a square matrix </li>
+<li><a href="geom.c#gausselim">qh_gausselim</a> Gaussian
+elimination with partial pivoting </li>
+<li><a href="geom2.c#gram_schmidt">qh_gram_schmidt</a>
+implements Gram-Schmidt orthogonalization by rows </li>
+<li><a href="geom2.c#maxabsval">qh_maxabsval</a> return max
+absolute value of a vector </li>
+<li><a href="geom2.c#minabsval">qh_minabsval</a> return min
+absolute value of a dim vector </li>
+<li><a href="geom2.c#mindiff">qh_mindiff</a> return index of
+min absolute difference of two vectors </li>
+<li><a href="geom.c#normalize">qh_normalize</a> normalize a
+vector </li>
+<li><a href="geom.c#normalize2">qh_normalize2</a> normalize a
+vector and report if too small </li>
+<li><a href="geom2.c#printmatrix">qh_printmatrix</a> print
+matrix given by row vectors </li>
+<li><a href="random.c#rand">qh_rand/srand</a> generate random
+numbers </li>
+<li><a href="random.c#randomfactor">qh_randomfactor</a> return
+a random factor near 1.0 </li>
+<li><a href="random.c#randommatrix">qh_randommatrix</a>
+generate a random dimXdim matrix in range (-1,1) </li>
+</ul>
+
+<h3><a href="qh-geom.htm#TOC">&#187;</a><a name="gcomp">computational geometry functions</a></h3>
+
+<ul>
+<li><a href="geom2.c#detsimplex">qh_detsimplex</a> compute
+determinate of a simplex of points </li>
+<li><a href="io.c#detvnorm">qh_detvnorm</a> determine normal for Voronoi ridge </li>
+<li><a href="geom2.c#distnorm">qh_distnorm</a> compute
+distance from point to hyperplane as defined by normal and offset</li>
+<li><a href="geom2.c#facetarea_simplex">qh_facetarea_simplex</a>
+return area of a simplex</li>
+<li><a href="geom.c#getangle">qh_getangle</a> return cosine
+of angle (i.e., dot product) </li>
+<li><a href="geom.c#getcenter">qh_getcenter</a> return
+arithmetic center for a set of vertices </li>
+<li><a href="geom2.c#pointdist">qh_pointdist</a> return
+distance between two points </li>
+<li><a href="geom2.c#rotatepoints">qh_rotatepoints</a> rotate
+numpoints points by a row matrix </li>
+<li><a href="geom2.c#sethalfspace">qh_sethalfspace</a> set
+coords to dual of halfspace relative to an interior point </li>
+<li><a href="geom.c#sethyperplane_det">qh_sethyperplane_det</a>
+return hyperplane for oriented simplex using determinates
+</li>
+<li><a href="geom.c#sethyperplane_gauss">qh_sethyperplane_gauss</a>
+return hyperplane for oriented simplex using Gaussian
+elimination </li>
+<li><a href="geom2.c#voronoi_center">qh_voronoi_center</a>
+return Voronoi center for a set of points </li>
+</ul>
+
+<h3><a href="qh-geom.htm#TOC">&#187;</a><a name="gpoint">point array functions</a></h3>
+<ul>
+<li><a href="geom2.c#copypoints">qh_copypoints</a> return
+malloc'd copy of points</li>
+<li><a href="geom2.c#joggleinput">qh_joggleinput</a> joggle
+input points by qh.JOGGLEmax </li>
+<li><a href="geom2.c#maxmin">qh_maxmin</a> return max/min
+points for each dimension</li>
+<li><a href="geom2.c#maxsimplex">qh_maxsimplex</a> determines
+maximum simplex for a set of points </li>
+<li><a href="geom2.c#printpoints">qh_printpoints</a> print ids for a
+set of points </li>
+<li><a href="geom2.c#projectinput">qh_projectinput</a> project
+input using qh DELAUNAY and qh low_bound/high_bound </li>
+<li><a href="geom2.c#projectpoints">qh_projectpoints</a>
+project points along one or more dimensions </li>
+<li><a href="geom2.c#rotateinput">qh_rotateinput</a> rotate
+input points using row matrix </li>
+<li><a href="geom2.c#scaleinput">qh_scaleinput</a> scale
+input points using qh low_bound/high_bound </li>
+<li><a href="geom2.c#scalelast">qh_scalelast</a> scale last
+coordinate to [0,m] for Delaunay triangulations </li>
+<li><a href="geom2.c#scalepoints">qh_scalepoints</a> scale
+points to new lowbound and highbound </li>
+<li><a href="geom2.c#setdelaunay">qh_setdelaunay</a> project
+points to paraboloid for Delaunay triangulation </li>
+<li><a href="geom2.c#sethalfspace_all">qh_sethalfspace_all</a>
+generate dual for halfspace intersection with interior
+point </li>
+</ul>
+
+<h3><a href="qh-geom.htm#TOC">&#187;</a><a name="gfacet">geometric facet functions</a></h3>
+<ul>
+<li><a href="geom.c#distplane">qh_distplane</a> return
+distance from point to facet </li>
+<li><a href="geom2.c#facetarea">qh_facetarea</a> return area
+of a facet </li>
+<li><a href="geom2.c#facetcenter">qh_facetcenter</a> return
+Voronoi center for a facet's vertices </li>
+<li><a href="geom.c#findbest">qh_findbest</a> find visible
+facet or best facet for a point </li>
+<li><a href="geom.c#findbesthorizon">qh_findbesthorizon</a>
+update best new facet with horizon facets</li>
+<li><a href="geom.c#findbestnew">qh_findbestnew</a> find best
+new facet for point </li>
+<li><a href="geom2.c#getarea">qh_getarea</a> get area of all
+facets in facetlist, collect statistics </li>
+<li><a href="geom.c#getcentrum">qh_getcentrum</a> return
+centrum for a facet </li>
+<li><a href="geom.c#getdistance">qh_getdistance</a> returns
+the max and min distance of a facet's vertices to a
+neighboring facet</li>
+<li><a href="geom2.c#findgooddist">qh_findgooddist</a> find
+best good facet visible for point from facet </li>
+<li><a href="geom2.c#inthresholds">qh_inthresholds</a> return
+True if facet normal within 'Pdn' and 'PDn'</li>
+<li><a href="geom2.c#orientoutside">qh_orientoutside</a>
+orient facet so that <tt>qh.interior_point</tt> is inside</li>
+<li><a href="geom.c#projectpoint">qh_projectpoint</a> project
+point onto a facet </li>
+<li><a href="geom.c#setfacetplane">qh_setfacetplane</a> sets
+the hyperplane for a facet </li>
+<li><a href="geom2.c#sharpnewfacets">qh_sharpnewfacets</a> true
+if new facets contains a sharp corner</li>
+</ul>
+
+<h3><a href="qh-geom.htm#TOC">&#187;</a><a name="ground">geometric roundoff functions</a></h3>
+<ul>
+<li><a href="geom2.c#detjoggle">qh_detjoggle</a> determine
+default joggle for points and distance roundoff error</li>
+<li><a href="geom2.c#detroundoff">qh_detroundoff</a>
+determine maximum roundoff error and other precision constants</li>
+<li><a href="geom2.c#distround">qh_distround</a> compute
+maximum roundoff error due to a distance computation to a
+normalized hyperplane</li>
+<li><a href="geom2.c#divzero">qh_divzero</a> divide by a
+number that is nearly zero </li>
+<li><a href="geom2.c#maxouter">qh_maxouter</a> return maximum outer
+plane</li>
+<li><a href="geom2.c#outerinner">qh_outerinner</a> return actual
+outer and inner planes
+</ul>
+
+<p><!-- Navigation links --> </p>
+<hr>
+<p><b>Up:</b>
+<a href="http://www.qhull.org">Home page for
+Qhull</a> <br>
+<b>Up:</b> <a href="index.htm#TOC">Qhull manual: Table of Contents</a> <br>
+<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a>
+&#149; <a href="../../html/qh-quick.htm#options">Options</a>
+&#149; <a href="../../html/qh-opto.htm#output">Output</a>
+&#149; <a href="../../html/qh-optf.htm#format">Formats</a>
+&#149; <a href="../../html/qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="../../html/qh-optp.htm#print">Print</a>
+&#149; <a href="../../html/qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="../../html/qh-optc.htm#prec">Precision</a>
+&#149; <a href="../../html/qh-optt.htm#trace">Trace</a>
+&#149; <a href="index.htm">Functions</a><br>
+<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code: Table of Contents</a> <br>
+<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
+<b>To:</b> <a href="qh-geom.htm">Geom</a> &#149;
+<a href="qh-globa.htm">Global</a> &#149; <a href="qh-io.htm">Io</a>
+&#149; <a href="qh-mem.htm">Mem</a> &#149; <a href="qh-merge.htm">Merge</a>
+&#149; <a href="qh-poly.htm">Poly</a> &#149; <a href="qh-qhull.htm#TOC">Qhull</a>
+&#149; <a href="qh-set.htm">Set</a> &#149; <a href="qh-stat.htm">Stat</a>
+&#149; <a href="qh-user.htm">User</a><br>
+
+
+<p><!-- GC common information --> </p>
+<hr>
+<p><a href="http://www.geom.uiuc.edu/"><img
+src="../../html/qh--geom.gif" align="middle" width="40" height="40"></a><i>The
+Geometry Center Home Page </i></p>
+<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
+</a><br>
+Created: May 2, 1997 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
+</body>
+</html>
diff --git a/xs/src/qhull/src/libqhull/qh-globa.htm b/xs/src/qhull/src/libqhull/qh-globa.htm
new file mode 100644
index 0000000000..c87508b663
--- /dev/null
+++ b/xs/src/qhull/src/libqhull/qh-globa.htm
@@ -0,0 +1,165 @@
+<!-- Do not edit with Front Page, it adds too many spaces -->
+<html>
+<head>
+<meta http-equiv="Content-Type"
+content="text/html; charset=iso-8859-1">
+<title>global.c -- global variables and their functions</title>
+</head>
+
+<body>
+<!-- Navigation links -->
+<p><a name="TOP"><b>Up:</b></a> <a
+href="http://www.qhull.org">Home page</a> for Qhull<br>
+<b>Up:</b> <a href="../../html/index.htm#TOC">Qhull manual</a>: Table of Contents <br>
+<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a>
+&#149; <a href="../../html/qh-quick.htm#options">Options</a>
+&#149; <a href="../../html/qh-opto.htm#output">Output</a>
+&#149; <a href="../../html/qh-optf.htm#format">Formats</a>
+&#149; <a href="../../html/qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="../../html/qh-optp.htm#print">Print</a>
+&#149; <a href="../../html/qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="../../html/qh-optc.htm#prec">Precision</a>
+&#149; <a href="../../html/qh-optt.htm#trace">Trace</a>
+&#149; <a href="index.htm">Functions</a><br>
+<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code: Table of Contents</a><br>
+<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
+<b>To:</b> <a href="qh-geom.htm">Geom</a> &#149; <a href="qh-globa.htm#TOC">Global</a>
+&#149; <a href="qh-io.htm">Io</a> &#149; <a href="qh-mem.htm">Mem</a>
+&#149; <a href="qh-merge.htm">Merge</a> &#149; <a href="qh-poly.htm">Poly</a>
+&#149; <a href="qh-qhull.htm">Qhull</a> &#149; <a href="qh-set.htm">Set</a>
+&#149; <a href="qh-stat.htm">Stat</a> &#149; <a href="qh-user.htm">User</a>
+</p>
+
+<hr>
+<!-- Main text of document. -->
+
+<h2>global.c -- global variables and their functions</h2>
+<blockquote>
+<p>Qhull uses a global data structure, <tt>qh</tt>, to store
+globally defined constants, lists, sets, and variables. This
+allows multiple instances of Qhull to execute at the same time.
+The structure may be statically allocated or
+dynamically allocated with malloc().  See
+<a href="user.h#QHpointer">QHpointer</a>.
+</p>
+</blockquote>
+<p><b>Copyright &copy; 1995-2015 C.B. Barber</b></p>
+<hr>
+<p><a href="#TOP">&#187;</a> <a href="qh-geom.htm#TOC">Geom</a>
+<a name="TOC">&#149;</a> <b>Global</b> &#149;
+<a href="qh-io.htm#TOC">Io</a> &#149; <a href="qh-mem.htm#TOC">Mem</a> &#149;
+<a href="qh-merge.htm#TOC">Merge</a> &#149; <a href="qh-poly.htm#TOC">Poly</a> &#149;
+<a href="qh-qhull.htm#TOC">Qhull</a> &#149; <a href="qh-set.htm#TOC">Set</a> &#149;
+<a href="qh-stat.htm#TOC">Stat</a> &#149; <a href="qh-user.htm#TOC">User</a> </p>
+
+<h3>Index to <a href="global.c">global.c</a> and
+<a href="libqhull.h">libqhull.h</a></h3>
+
+<ul>
+<li><a href="#ovar">Qhull's global variables</a> </li>
+<li><a href="#ofunc">Global variable and initialization
+routines</a> </li>
+</ul>
+
+<h3><a href="qh-globa.htm#TOC">&#187;</a><a name="ovar">Qhull's global
+variables</a></h3>
+
+<ul>
+<li><a href=global.c#qh_version>qh_version</a> version string
+<li><a href="libqhull.h#qh">qh</a> all global variables for
+qhull are in <tt>qh,qhmem</tt>, and <tt>qhstat</tt></li>
+<li><a href="libqhull_r.h#qh">QHULL_LIB_CHECK</a> Check for compatible library</li>
+<li><a href="libqhull.h#qh-const">qh constants</a> configuration
+flags and constants for Qhull </li>
+<li><a href="libqhull.h#qh-prec">qh precision constants</a>
+precision constants for Qhull </li>
+<li><a href="libqhull.h#qh-codetern">qh internal constants</a>
+internal constants for Qhull </li>
+<li><a href="libqhull.h#qh-lists">qh facet and vertex lists</a>
+lists of facets and vertices </li>
+<li><a href="libqhull.h#qh-var">qh global variables</a> minimum
+and maximum distances, next visit ids, several flags, and
+other global variables. </li>
+<li><a href="libqhull.h#qh-set">qh global sets</a> global sets
+for merging, hashing, input, etc. </li>
+<li><a href="libqhull.h#qh-buf">qh global buffers</a> buffers
+for matrix operations and input </li>
+<li><a href="libqhull.h#qh-static">qh static variables</a>
+static variables for individual functions </li>
+</ul>
+
+<h3><a href="qh-globa.htm#TOC">&#187;</a><a name="ofunc">Global variable and
+initialization routines</a></h3>
+
+<ul>
+<li><a href="global.c#appendprint">qh_appendprint</a> append
+output format to <tt>qh.PRINTout</tt> </li>
+<li><a href="global.c#freebuffers">qh_freebuffers</a> free
+global memory buffers </li>
+<li><a href="global.c#freeqhull">qh_freeqhull</a> free memory
+used by qhull </li>
+<li><a href="global.c#init_A">qh_init_A</a> called before
+error handling initialized </li>
+<li><a href="global.c#init_B">qh_init_B</a> called after
+points are defined </li>
+<li><a href="global.c#init_qhull_command">qh_init_qhull_command</a>
+build <tt>qh.qhull_command</tt> from <tt>argc/argv</tt></li>
+<li><a href="global.c#initflags">qh_initflags</a> set flags
+and constants from command line </li>
+<li><a href="global.c#initqhull_buffers">qh_initqhull_buffers</a>
+initialize global memory buffers </li>
+<li><a href="global.c#initqhull_globals">qh_initqhull_globals</a>
+initialize global variables </li>
+<li><a href="global.c#initqhull_mem">qh_initqhull_mem</a>
+initialize Qhull memory management </li>
+<li><a href="global.c#initqhull_start">qh_initqhull_start</a>
+allocate qh_qh and call qh_initqhull_start2()
+<li><a href="global.c#initqhull_start2">qh_initqhull_start2</a>
+initialize default values at Qhull startup </li>
+<li><a href="global.c#initthresholds">qh_initthresholds</a>
+initialize 'Pdn' and 'PDn' thresholds </li>
+<li><a href="global.c#lib_check">qh_lib_check</a> check for compatible Qhull library.  Invoked by QHULL_LIB_CHECK at start of each program.</li>
+<li><a href="global.c#option">qh_option</a> append option
+description to <tt>qh.global_options</tt> </li>
+<li><a href="global.c#restore_qhull">qh_restore_qhull</a>
+restores a previously saved qhull </li>
+<li><a href="global.c#save_qhull">qh_save_qhull</a> saves
+qhull for a later qh_restore_qhull() </li>
+<li><a href="global.c#strtol">qh_strtol</a> duplicates
+strtod() and strtol() </li>
+</ul>
+
+<p><!-- Navigation links --> </p>
+<hr>
+<p><b>Up:</b>
+<a href="http://www.qhull.org">Home page for
+Qhull</a> <br>
+<b>Up:</b> <a href="../../html/index.htm#TOC">Qhull manual: Table of Contents</a> <br>
+<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a>
+&#149; <a href="../../html/qh-quick.htm#options">Options</a>
+&#149; <a href="../../html/qh-opto.htm#output">Output</a>
+&#149; <a href="../../html/qh-optf.htm#format">Formats</a>
+&#149; <a href="../../html/qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="../../html/qh-optp.htm#print">Print</a>
+&#149; <a href="../../html/qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="../../html/qh-optc.htm#prec">Precision</a>
+&#149; <a href="../../html/qh-optt.htm#trace">Trace</a>
+&#149; <a href="index.htm">Functions</a><br>
+<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code: Table of Contents</a> <br>
+<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
+<b>To:</b> <a href="qh-geom.htm">Geom</a> &#149;
+<a href="qh-globa.htm">Global</a> &#149; <a href="qh-io.htm">Io</a>
+&#149; <a href="qh-mem.htm">Mem</a> &#149; <a href="qh-merge.htm">Merge</a>
+&#149; <a href="qh-poly.htm">Poly</a> &#149; <a href="qh-qhull.htm#TOC">Qhull</a>
+&#149; <a href="qh-set.htm">Set</a> &#149; <a href="qh-stat.htm">Stat</a>
+&#149; <a href="qh-user.htm">User</a><br>
+<p><!-- GC common information --> </p>
+<hr>
+<p><a href="http://www.geom.uiuc.edu/"><img
+src="../../html/qh--geom.gif" align="middle" width="40" height="40"></a><i>The
+Geometry Center Home Page </i></p>
+<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
+</a><br>
+Created: May 2, 1997 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
+</body>
+</html>
diff --git a/xs/src/qhull/src/libqhull/qh-io.htm b/xs/src/qhull/src/libqhull/qh-io.htm
new file mode 100644
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+++ b/xs/src/qhull/src/libqhull/qh-io.htm
@@ -0,0 +1,305 @@
+<!-- Do not edit with Front Page, it adds too many spaces -->
+<html>
+<head>
+<meta http-equiv="Content-Type"
+content="text/html; charset=iso-8859-1">
+<title>io.c -- input and output operations</title>
+</head>
+
+<body>
+<!-- Navigation links -->
+<p><a name="TOP"><b>Up:</b></a> <a
+href="http://www.qhull.org">Home page</a> for Qhull<br>
+<b>Up:</b> <a href="../../html/index.htm#TOC">Qhull manual</a>: Table of Contents <br>
+<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a>
+&#149; <a href="../../html/qh-quick.htm#options">Options</a>
+&#149; <a href="../../html/qh-opto.htm#output">Output</a>
+&#149; <a href="../../html/qh-optf.htm#format">Formats</a>
+&#149; <a href="../../html/qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="../../html/qh-optp.htm#print">Print</a>
+&#149; <a href="../../html/qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="../../html/qh-optc.htm#prec">Precision</a>
+&#149; <a href="../../html/qh-optt.htm#trace">Trace</a>
+&#149; <a href="index.htm">Functions</a><br>
+<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code: Table of Contents</a><br>
+<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
+<b>To:</b> <a href="qh-geom.htm">Geom</a> &#149; <a href="qh-globa.htm">Global</a>
+&#149; <a href="qh-io.htm#TOC">Io</a> &#149; <a href="qh-mem.htm">Mem</a>
+&#149; <a href="qh-merge.htm">Merge</a> &#149; <a href="qh-poly.htm">Poly</a>
+&#149; <a href="qh-qhull.htm">Qhull</a> &#149; <a href="qh-set.htm">Set</a>
+&#149; <a href="qh-stat.htm">Stat</a> &#149; <a href="qh-user.htm">User</a>
+</p>
+<hr>
+
+<h2>io.c -- input and output operations</h2>
+<blockquote>
+
+<p>Qhull provides a wide range of input
+and output options. To organize the code, most output formats use
+the same driver: </p>
+
+<pre>
+    qh_printbegin( fp, format, facetlist, facets, printall );
+
+    FORALLfacet_( facetlist )
+      qh_printafacet( fp, format, facet, printall );
+
+    FOREACHfacet_( facets )
+      qh_printafacet( fp, format, facet, printall );
+
+    qh_printend( fp, format );
+</pre>
+
+<p>Note the 'printall' flag. It selects whether or not
+qh_skipfacet() is tested. </p>
+
+</blockquote>
+<p><b>Copyright &copy; 1995-2015 C.B. Barber</b></p>
+<hr>
+<p><a href="#TOP">&#187;</a> <a href="qh-geom.htm#TOC">Geom</a> <a name="TOC">&#149;</a>
+<a href="qh-globa.htm#TOC">Global</a> &#149; <b>Io</b> &#149;
+<a href="qh-mem.htm#TOC">Mem</a> &#149; <a href="qh-merge.htm#TOC">Merge</a> &#149;
+<a href="qh-poly.htm#TOC">Poly</a> &#149; <a href="qh-qhull.htm#TOC">Qhull</a> &#149;
+<a href="qh-set.htm#TOC">Set</a> &#149; <a href="qh-stat.htm#TOC">Stat</a> &#149;
+<a href="qh-user.htm#TOC">User</a> </p>
+
+<h3>Index to <a href="io.c">io.c</a> and <a href="io.h">io.h</a></h3>
+
+<ul>
+<li><a href="#iconst">io.h constants and types</a> </li>
+<li><a href="#ilevel">User level functions</a> </li>
+<li><a href="#iprint">Print functions for all output formats</a></li>
+<li><a href="#itext">Text output functions</a> </li>
+<li><a href="#iutil">Text utility functions</a></li>
+<li><a href="#igeom">Geomview output functions</a> </li>
+<li><a href="#iview">Geomview utility functions</a></li>
+</ul>
+
+<h3><a href="qh-io.htm#TOC">&#187;</a><a name="iconst">io.h constants and types</a></h3>
+
+<ul>
+<li><a href="io.h#qh_MAXfirst">qh_MAXfirst</a> maximum length
+of first two lines of stdin </li>
+<li><a href="io.h#qh_WHITESPACE">qh_WHITESPACE</a> possible
+values of white space </li>
+<li><a href="io.h#printvridgeT">printvridgeT</a> function to
+print results of qh_printvdiagram or qh_eachvoronoi</li>
+</ul>
+
+<h3><a href="qh-io.htm#TOC">&#187;</a><a name="ilevel">User level functions</a></h3>
+
+<ul>
+<li><a href="io.c#copyfilename">qh_copyfilename</a>
+copy filename identified by qh_skipfilename
+<li><a href="io.c#eachvoronoi_all">qh_eachvoronoi_all</a>
+visit each Voronoi ridge of the Voronoi diagram
+<li><a href="io.c#prepare_output">qh_prepare_output</a>
+prepare Qhull for output (called by qh_produce_output())
+<li><a href="io.c#printhelp_degenerate">qh_printhelp_degenerate</a>
+prints descriptive message for precision error </li>
+<li><a href="io.c#printhelp_singular">qh_printhelp_singular</a>
+print help message for singular data </li>
+<li><a href="libqhull.c#printsummary">qh_printsummary</a> print
+summary ('s')</li>
+<li><a href="io.c#produce_output">qh_produce_output</a>
+prints out the result of qhull()</li>
+<li><a href="io.c#produce_output">qh_produce_output2</a>
+prints out the result of qhull() without calling qh_prepare_output()</li>
+<li><a href="io.c#readfeasible">qh_readfeasible</a> read
+interior point from remainder and qh fin ('H')</li>
+<li><a href="io.c#readpoints">qh_readpoints</a> read input
+points </li>
+<li><a href="io.c#setfeasible">qh_setfeasible</a> set
+interior point from qh feasible_string ('Hn,n,n')</li>
+<li><a href="io.c#skipfilename">qh_skipfilename</a>
+skip filename in string
+</ul>
+
+<h3><a href="qh-io.htm#TOC">&#187;</a><a name="iprint">Print functions for all
+output formats</a></h3>
+
+<ul>
+<li><a href="io.c#countfacets">qh_countfacets</a> count good
+facets for printing and set visitid </li>
+<li><a href="io.c#markkeep">qh_markkeep</a> mark good facets
+that meet qh.KEEParea ('PAn'), qh.KEEPmerge ('PMn'), and qh.KEEPminArea ('PFn')</li>
+<li><a href="io.c#order_vertexneighbors">qh_order_vertexneighbors</a>
+order neighbors for a 3-d vertex by adjacency ('i', 'o')</li>
+<li><a href="io.c#printafacet">qh_printafacet</a> print facet
+in an output format </li>
+<li><a href="io.c#printbegin">qh_printbegin</a> print header
+for an output format </li>
+<li><a href="io.c#printend">qh_printend</a> print trailer for
+an output format </li>
+<li><a href="user.c#printfacetlist">qh_printfacetlist</a>
+print facets in a facetlist</li>
+<li><a href="io.c#printfacets">qh_printfacets</a> print
+facetlist and/or facet set in an output format </li>
+<li><a href="io.c#printneighborhood">qh_printneighborhood</a>
+print neighborhood of one or two facets ('Po')</li>
+<li><a href="io.c#produce_output">qh_produce_output</a>
+print the results of qh_qhull() </li>
+<li><a href="io.c#skipfacet">qh_skipfacet</a> True if not
+printing this facet ('Pdk:n', 'QVn', 'QGn')</li>
+<li><a href="io.c#facetvertices">qh_facetvertices</a> return
+vertices in a set of facets ('p')</li>
+</ul>
+
+<h3><a href="qh-io.htm#TOC">&#187;</a><a name="itext">Text output functions</a></h3>
+<ul>
+<li><a href="io.c#eachvoronoi">qh_eachvoronoi</a>
+print or visit each Voronoi ridge for an input site of the Voronoi diagram
+<li><a href="io.c#printextremes">qh_printextremes</a> print
+extreme points by point ID (vertices of convex hull) ('Fx')</li>
+<li><a href="io.c#printextremes_2d">qh_printextremes_2d</a> print
+2-d extreme points by point ID ('Fx')</li>
+<li><a href="io.c#printextremes_d">qh_printextremes_d</a> print
+extreme points of input sites for Delaunay triangulations ('Fx')</li>
+<li><a href="io.c#printfacet">qh_printfacet</a> print all
+fields of a facet ('f')</li>
+<li><a href="io.c#printfacet2math">qh_printfacet2math</a> print
+2-d Maple or Mathematica output for a facet ('FM' or 'm')</li>
+<li><a href="io.c#printfacet3math">qh_printfacet3math</a>
+print 3-d Maple or Mathematica facet ('FM' or 'm')</li>
+<li><a href="io.c#printfacet3vertex">qh_printfacet3vertex</a>
+print vertices for a 3-d facet ('i', 'o')</li>
+<li><a href="io.c#printfacetheader">qh_printfacetheader</a>
+prints header fields of a facet ('f')</li>
+<li><a href="io.c#printfacetNvertex_nonsimplicial">qh_printfacetNvertex_nonsimplicial</a>
+print vertices for an N-d non-simplicial facet ('i', 'Ft')</li>
+<li><a href="io.c#printfacetNvertex_simplicial">qh_printfacetNvertex_simplicial</a>
+print vertices for an N-d simplicial facet ('i', 'o', 'Ft')</li>
+<li><a href="io.c#printfacetridges">qh_printfacetridges</a>
+prints ridges of a facet ('f')</li>
+<li><a href="io.c#printpoints_out">qh_printpoints_out</a> prints
+vertices for facets by their point coordinates ('p')</li>
+<li><a href="io.c#printridge">qh_printridge</a> print all
+fields for a ridge ('f')</li>
+<li><a href="io.c#printvdiagram">qh_printvdiagram</a> print
+voronoi diagram as Voronoi vertices for each input pair</li>
+<li><a href="io.c#printvertex">qh_printvertex</a> print all
+fields for a vertex ('f')</li>
+<li><a href="io.c#printvertexlist">qh_printvertexlist</a>
+print vertices used by a list or set of facets ('f')</li>
+<li><a href="io.c#printvertices">qh_printvertices</a> print a
+set of vertices ('f')</li>
+<li><a href="io.c#printvneighbors">qh_printvneighbors</a>
+print vertex neighbors of vertices ('FN')</li>
+<li><a href="io.c#printvoronoi">qh_printvoronoi</a> print
+voronoi diagram in 'o' or 'G' format</li>
+</ul>
+
+<h3><a href="qh-io.htm#TOC">&#187;</a><a name="iutil">Text utility functions</a></h3>
+<ul>
+<li><a href="io.c#dfacet">dfacet</a> print facet by ID </li>
+<li><a href="io.c#dvertex">dvertex</a> print vertex by ID </li>
+<li><a href="io.c#compare_facetarea">qh_compare_facetarea</a>
+used by qsort() to order facets by area </li>
+<li><a href="io.c#compare_facetmerge">qh_compare_facetmerge</a>
+used by qsort() to order facets by number of merges </li>
+<li><a href="io.c#compare_facetvisit">qh_compare_facetvisit</a>
+used by qsort() to order facets by visit ID or ID </li>
+<li><a href="io.c#compare_vertexpoint">qh_compare_vertexpoint</a>
+used by qsort() to order vertices by point ID </li>
+<li><a href="io.c#detvnorm">qh_detvnorm</a> determine normal for Voronoi ridge </li>
+<li><a href="io.c#detvridge">qh_detvridge</a> determine Voronoi
+ridge for an input site
+<li><a href="io.c#detvridge3">qh_detvridge3</a> determine 3-d Voronoi
+ridge for an input site
+<li><a href="io.c#facet2point">qh_facet2point</a> return two
+projected temporary vertices for a 2-d facet ('m', 'G')</li>
+<li><a href="io.c#markvoronoi">qh_markvoronoi</a> mark Voronoi
+vertices for printing
+<li><a href="io.c#printcenter">qh_printcenter</a> print
+facet-&gt;center as centrum or Voronoi center ('Ft', 'v p', 'FC', 'f') </li>
+<li><a href="io.c#printpoint">qh_printpoint</a>, qh_printpointid, print
+coordinates of a point ('p', 'o', 'Fp', 'G', 'f')</li>
+<li><a href="io.c#printpoint3">qh_printpoint3</a> prints 2-d,
+3-d, or 4-d point as 3-d coordinates ('G')</li>
+<li><a href="io.c#printvdiagram2">qh_printvdiagram2</a> print
+voronoi diagram for each ridge of each vertex from qh_markvoronoi</li>
+<li><a href="io.c#printvnorm">qh_printvnorm</a> print
+separating plane of the Voronoi diagram for a pair of input sites</li>
+<li><a href="io.c#printvridge">qh_printvridge</a> print
+ridge of the Voronoi diagram for a pair of input sites</li>
+<li><a href="io.c#projectdim3">qh_projectdim3</a> project 2-d
+3-d or 4-d point to a 3-d point ('G')</li>
+</ul>
+
+<h3><a href="qh-io.htm#TOC">&#187;</a><a name="igeom">Geomview output functions</a></h3>
+<ul>
+<li><a href="io.c#printfacet2geom">qh_printfacet2geom</a>
+print facet as a 2-d VECT object </li>
+<li><a href="io.c#printfacet2geom_points">qh_printfacet2geom_points</a>
+print points as a 2-d VECT object with offset </li>
+<li><a href="io.c#printfacet3geom_nonsimplicial">qh_printfacet3geom_nonsimplicial</a>
+print Geomview OFF for a 3-d nonsimplicial facet. </li>
+<li><a href="io.c#printfacet3geom_points">qh_printfacet3geom_points</a>
+prints a 3-d facet as OFF Geomview object. </li>
+<li><a href="io.c#printfacet3geom_simplicial">qh_printfacet3geom_simplicial</a>
+print Geomview OFF for a 3-d simplicial facet. </li>
+<li><a href="io.c#printfacet4geom_nonsimplicial">qh_printfacet4geom_nonsimplicial</a>
+print Geomview 4OFF file for a 4d nonsimplicial facet </li>
+<li><a href="io.c#printfacet4geom_simplicial">qh_printfacet4geom_simplicial</a>
+print Geomview 4OFF file for a 4d simplicial facet </li>
+<li><a href="io.c#printhyperplaneintersection">qh_printhyperplaneintersection</a>
+print hyperplane intersection as OFF or 4OFF </li>
+<li><a href="io.c#printvoronoi">qh_printvoronoi</a> print
+voronoi diagram in 'o' or 'G' format</li>
+</ul>
+<h3><a href="qh-io.htm#TOC">&#187;</a><a name="iview">Geomview utility functions</a></h3>
+<ul>
+<li><a href="io.c#geomplanes">qh_geomplanes</a>
+    return outer and inner planes for Geomview</li>
+<li><a href="io.c#printcentrum">qh_printcentrum</a> print
+centrum for a facet in OOGL format </li>
+<li><a href="io.c#printend4geom">qh_printend4geom</a> helper
+function for qh_printbegin/printend </li>
+<li><a href="io.c#printhyperplaneintersection">qh_printhyperplaneintersection</a>
+print Geomview OFF or 4OFF for the intersection of two
+hyperplanes in 3-d or 4-d </li>
+<li><a href="io.c#printline3geom">qh_printline3geom</a> prints a
+line as a VECT </li>
+<li><a href="io.c#printpointvect">qh_printpointvect</a>
+prints a 2-d or 3-d point as 3-d VECT's </li>
+<li><a href="io.c#printpointvect2">qh_printpointvect2</a>
+prints a 2-d or 3-d point as 2 3-d VECT's </li>
+<li><a href="io.c#printspheres">qh_printspheres</a> prints 3-d
+vertices as OFF spheres </li>
+</ul>
+<p>
+<p><!-- Navigation links --> </p>
+<hr>
+<p><b>Up:</b>
+<a href="http://www.qhull.org">Home page for
+Qhull</a> <br>
+<b>Up:</b> <a href="../../html/index.htm#TOC">Qhull manual: Table of Contents</a> <br>
+<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a>
+&#149; <a href="../../html/qh-quick.htm#options">Options</a>
+&#149; <a href="../../html/qh-opto.htm#output">Output</a>
+&#149; <a href="../../html/qh-optf.htm#format">Formats</a>
+&#149; <a href="../../html/qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="../../html/qh-optp.htm#print">Print</a>
+&#149; <a href="../../html/qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="../../html/qh-optc.htm#prec">Precision</a>
+&#149; <a href="../../html/qh-optt.htm#trace">Trace</a>
+&#149; <a href="index.htm">Functions</a><br>
+<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code: Table of Contents</a> <br>
+<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
+<b>To:</b> <a href="qh-geom.htm">Geom</a> &#149;
+<a href="qh-globa.htm">Global</a> &#149; <a href="qh-io.htm">Io</a>
+&#149; <a href="qh-mem.htm">Mem</a> &#149; <a href="qh-merge.htm">Merge</a>
+&#149; <a href="qh-poly.htm">Poly</a> &#149; <a href="qh-qhull.htm#TOC">Qhull</a>
+&#149; <a href="qh-set.htm">Set</a> &#149; <a href="qh-stat.htm">Stat</a>
+&#149; <a href="qh-user.htm">User</a><br>
+</p>
+<p><!-- GC common information --> </p>
+<hr>
+<p><a href="http://www.geom.uiuc.edu/"><img
+src="../../html/qh--geom.gif" align="middle" width="40" height="40"></a><i>The
+Geometry Center Home Page </i></p>
+<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
+</a><br>
+Created: May 2, 1997 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
+</body>
+</html>
diff --git a/xs/src/qhull/src/libqhull/qh-mem.htm b/xs/src/qhull/src/libqhull/qh-mem.htm
new file mode 100644
index 0000000000..b993b22297
--- /dev/null
+++ b/xs/src/qhull/src/libqhull/qh-mem.htm
@@ -0,0 +1,145 @@
+<!-- Do not edit with Front Page, it adds too many spaces -->
+<html>
+<head>
+<meta http-equiv="Content-Type"
+content="text/html; charset=iso-8859-1">
+<title>mem.c -- memory operations</title>
+</head>
+
+<body>
+<!-- Navigation links -->
+<p><a name="TOP"><b>Up:</b></a> <a
+href="http://www.qhull.org">Home page</a> for Qhull<br>
+<b>Up:</b> <a href="../../html/index.htm#TOC">Qhull manual</a>: Table of Contents <br>
+<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a>
+&#149; <a href="../../html/qh-quick.htm#options">Options</a>
+&#149; <a href="../../html/qh-opto.htm#output">Output</a>
+&#149; <a href="../../html/qh-optf.htm#format">Formats</a>
+&#149; <a href="../../html/qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="../../html/qh-optp.htm#print">Print</a>
+&#149; <a href="../../html/qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="../../html/qh-optc.htm#prec">Precision</a>
+&#149; <a href="../../html/qh-optt.htm#trace">Trace</a>
+&#149; <a href="index.htm">Functions</a><br>
+<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code: Table of Contents</a><br>
+<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
+<b>To:</b> <a href="qh-geom.htm">Geom</a> &#149; <a href="qh-globa.htm">Global</a>
+&#149; <a href="qh-io.htm">Io</a> &#149; <a href="qh-mem.htm#TOC">Mem</a>
+&#149; <a href="qh-merge.htm">Merge</a> &#149; <a href="qh-poly.htm">Poly</a>
+&#149; <a href="qh-qhull.htm">Qhull</a> &#149; <a href="qh-set.htm">Set</a>
+&#149; <a href="qh-stat.htm">Stat</a> &#149; <a href="qh-user.htm">User</a>
+</p>
+<hr>
+
+<h2>mem.c -- memory operations</h2>
+<blockquote>
+<p>Qhull uses quick-fit memory allocation. It maintains a
+set of free lists for a variety of small allocations. A
+small request returns a block from the best fitting free
+list. If the free list is empty, Qhull allocates a block
+from a reserved buffer. </p>
+<p>Use 'T5' to trace memory allocations.</p>
+
+</blockquote>
+<p><b>Copyright &copy; 1995-2015 C.B. Barber</b></p>
+<hr>
+<p><a href="#TOP">&#187;</a> <a href="qh-geom.htm#TOC">Geom</a>
+<a name="TOC">&#149;</a> <a href="qh-globa.htm#TOC">Global</a> &#149;
+<a href="qh-io.htm#TOC">Io</a> &#149; <b>Mem</b>
+&#149; <a href="qh-merge.htm#TOC">Merge</a> &#149; <a href="qh-poly.htm#TOC">Poly</a>
+&#149; <a href="qh-qhull.htm#TOC">Qhull</a> &#149; <a href="qh-set.htm#TOC">Set</a>
+&#149; <a href="qh-stat.htm#TOC">Stat</a> &#149; <a href="qh-user.htm#TOC">User</a>
+</p>
+<h3>Index to <a href="mem.c">mem.c</a> and
+<a href="mem.h">mem.h</a></h3>
+<ul>
+<li><a href="#etype">mem.h data types</a> </li>
+<li><a href="#emacro">mem.h macros</a> </li>
+<li><a href="#efunc">User level functions</a> </li>
+</ul>
+<h3><a href="qh-mem.htm#TOC">&#187;</a><a name="etype">mem.h data types and constants</a></h3>
+<ul>
+<li><a href="mem.h#ptr_intT">ptr_intT</a> for casting
+a void* to an integer-type </li>
+<li><a href="mem.h#qhmemT">qhmemT</a> global memory
+structure for mem.c </li>
+<li><a href="mem.h#NOmem">qh_NOmem</a> disable memory allocation</li>
+</ul>
+<h3><a href="qh-mem.htm#TOC">&#187;</a><a name="emacro">mem.h macros</a></h3>
+<ul>
+<li><a href="mem.h#memalloc_">qh_memalloc_</a>
+allocate memory</li>
+<li><a href="mem.h#memfree_">qh_memfree_</a> free
+memory</li>
+</ul>
+<h3><a href="qh-mem.htm#TOC">&#187;</a><a name="efunc">User level
+functions</a></h3>
+<ul>
+<li><a href="mem.c#memalloc">qh_memalloc</a> allocate
+memory </li>
+<li><a href="mem.c#memcheck">qh_memcheck</a>
+quick check of memory for internal consistency</li>
+<li><a href="mem.c#memfree">qh_memfree</a> free
+memory </li>
+<li><a href="mem.c#meminit">qh_meminit</a> initialize
+memory </li>
+<li><a href="mem.c#memstatistics">qh_memstatistics</a>
+print memory statistics </li>
+<li><a href="mem.c#meminit">qh_memtotlong</a> return total, allocated long memory</li>
+<li><a href="mem.c#NOmem">qh_NOmem</a> allocation routines with malloc() and free()
+</ul>
+
+<h3><a href="qh-mem.htm#TOC">&#187;</a><a name="m">Initialization and
+termination functions</a></h3>
+<ul>
+<li><a href="mem.c#intcompare">qh_intcompare</a> used by
+qsort and bsearch to compare two integers </li>
+<li><a href="mem.c#memfreeshort">qh_memfreeshort</a>
+frees up all short and qhmem memory allocations </li>
+<li><a href="mem.c#meminit">qh_meminit</a> initialize
+memory </li>
+<li><a href="mem.c#meminitbuffers">qh_meminitbuffers</a>
+initialize qhmem </li>
+<li><a href="mem.c#memsetup">qh_memsetup</a> set up
+memory after running memsize() </li>
+<li><a href="mem.c#memsize">qh_memsize</a> define a free
+list for this size </li>
+<li><a href="mem.c#memstatistics">qh_memstatistics</a>
+print out memory statistics </li>
+</ul>
+
+<p><!-- Navigation links --> </p>
+<hr>
+<p><b>Up:</b>
+<a href="http://www.qhull.org">Home page for
+Qhull</a> <br>
+<b>Up:</b> <a href="../../html/index.htm#TOC">Qhull manual: Table of Contents</a> <br>
+<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a>
+&#149; <a href="../../html/qh-quick.htm#options">Options</a>
+&#149; <a href="../../html/qh-opto.htm#output">Output</a>
+&#149; <a href="../../html/qh-optf.htm#format">Formats</a>
+&#149; <a href="../../html/qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="../../html/qh-optp.htm#print">Print</a>
+&#149; <a href="../../html/qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="../../html/qh-optc.htm#prec">Precision</a>
+&#149; <a href="../../html/qh-optt.htm#trace">Trace</a>
+&#149; <a href="index.htm">Functions</a><br>
+<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code: Table of Contents</a> <br>
+<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
+<b>To:</b> <a href="qh-geom.htm">Geom</a> &#149;
+<a href="qh-globa.htm">Global</a> &#149; <a href="qh-io.htm">Io</a>
+&#149; <a href="qh-mem.htm">Mem</a> &#149; <a href="qh-merge.htm">Merge</a>
+&#149; <a href="qh-poly.htm">Poly</a> &#149; <a href="qh-qhull.htm#TOC">Qhull</a>
+&#149; <a href="qh-set.htm">Set</a> &#149; <a href="qh-stat.htm">Stat</a>
+&#149; <a href="qh-user.htm">User</a><br>
+</p>
+<p><!-- GC common information --> </p>
+<hr>
+<p><a href="http://www.geom.uiuc.edu/"><img
+src="../../html/qh--geom.gif" align="middle" width="40" height="40"></a><i>The
+Geometry Center Home Page </i></p>
+<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
+</a><br>
+Created: May 2, 1997 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
+</body>
+</html>
diff --git a/xs/src/qhull/src/libqhull/qh-merge.htm b/xs/src/qhull/src/libqhull/qh-merge.htm
new file mode 100644
index 0000000000..54b97c88ee
--- /dev/null
+++ b/xs/src/qhull/src/libqhull/qh-merge.htm
@@ -0,0 +1,366 @@
+<!-- Do not edit with Front Page, it adds too many spaces -->
+<html>
+<head>
+<meta http-equiv="Content-Type"
+content="text/html; charset=iso-8859-1">
+<title>merge.c -- facet merge operations</title>
+</head>
+
+<body>
+<!-- Navigation links -->
+<p><a name="TOP"><b>Up:</b></a> <a
+href="http://www.qhull.org">Home page</a> for Qhull<br>
+<b>Up:</b> <a href="../../html/index.htm#TOC">Qhull manual</a>: Table of Contents <br>
+<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a>
+&#149; <a href="../../html/qh-quick.htm#options">Options</a>
+&#149; <a href="../../html/qh-opto.htm#output">Output</a>
+&#149; <a href="../../html/qh-optf.htm#format">Formats</a>
+&#149; <a href="../../html/qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="../../html/qh-optp.htm#print">Print</a>
+&#149; <a href="../../html/qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="../../html/qh-optc.htm#prec">Precision</a>
+&#149; <a href="../../html/qh-optt.htm#trace">Trace</a>
+&#149; <a href="index.htm">Functions</a><br>
+<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code: Table of Contents</a><br>
+<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
+<b>To:</b> <a href="qh-geom.htm">Geom</a> &#149; <a href="qh-globa.htm">Global</a>
+&#149; <a href="qh-io.htm">Io</a> &#149; <a href="qh-mem.htm">Mem</a>
+&#149; <a href="qh-merge.htm#TOC">Merge</a> &#149; <a href="qh-poly.htm">Poly</a>
+&#149; <a href="qh-qhull.htm">Qhull</a> &#149; <a href="qh-set.htm">Set</a>
+&#149; <a href="qh-stat.htm">Stat</a> &#149; <a href="qh-user.htm">User</a>
+</p>
+<hr>
+
+<h2>merge.c -- facet merge operations</h2>
+<blockquote>
+<p>Qhull handles precision problems by merged facets or joggled input.
+Except for redundant vertices, it corrects a problem by
+merging two facets. When done, all facets are clearly
+convex. See <a href="../../html/qh-impre.htm">Imprecision in Qhull</a>
+for further information. </p>
+<p>Users may joggle the input ('<a href="../../html/qh-optq.htm#QJn">QJn</a>')
+instead of merging facets. </p>
+<p>Qhull detects and corrects the following problems: </p>
+<ul>
+<li><b>More than two facets meeting at a ridge. </b>When
+Qhull creates facets, it creates an even number
+of facets for each ridge. A convex hull always
+has two facets for each ridge. More than two
+facets may be created if non-adjacent facets
+share a vertex. This is called a <em>duplicate
+ridge</em>. In 2-d, a duplicate ridge would
+create a loop of facets. </li>
+</ul>
+<ul>
+<li><b>A facet contained in another facet. </b>Facet
+merging may leave all vertices of one facet as a
+subset of the vertices of another facet. This is
+called a <em>redundant facet</em>. </li>
+</ul>
+<ul>
+<li><b>A facet with fewer than three neighbors. </b>Facet
+merging may leave a facet with one or two
+neighbors. This is called a <em>degenerate facet</em>.
+</li>
+</ul>
+<ul>
+<li><b>A facet with flipped orientation. </b>A
+facet's hyperplane may define a halfspace that
+does not include the interior point.This is
+called a <em>flipped facet</em>. </li>
+</ul>
+<ul>
+<li><strong>A coplanar horizon facet.</strong> A
+newly processed point may be coplanar with an
+horizon facet. Qhull creates a new facet without
+a hyperplane. It links new facets for the same
+horizon facet together. This is called a <em>samecycle</em>.
+The new facet or samecycle is merged into the
+horizon facet. </li>
+</ul>
+<ul>
+<li><b>Concave facets. </b>A facet's centrum may be
+above a neighboring facet. If so, the facets meet
+at a concave angle. </li>
+</ul>
+<ul>
+<li><b>Coplanar facets. </b>A facet's centrum may be
+coplanar with a neighboring facet (i.e., it is
+neither clearly below nor clearly above the
+facet's hyperplane). Qhull removes coplanar
+facets in independent sets sorted by angle.</li>
+</ul>
+<ul>
+<li><b>Redundant vertex. </b>A vertex may have fewer
+than three neighboring facets. If so, it is
+redundant and may be renamed to an adjacent
+vertex without changing the topological
+structure.This is called a <em>redundant vertex</em>.
+</li>
+</ul>
+</blockquote>
+<p><b>Copyright &copy; 1995-2015 C.B. Barber</b></p>
+<hr>
+<p><a href="#TOP">&#187;</a> <a href="qh-geom.htm#TOC">Geom</a>
+<a name="TOC">&#149;</a> <a href="qh-globa.htm#TOC">Global</a>
+&#149; <a href="qh-io.htm#TOC">Io</a> &#149; <a href="qh-mem.htm#TOC">Mem</a>
+&#149; <b>Merge</b> &#149; <a href="qh-poly.htm#TOC">Poly</a>
+&#149; <a href="qh-qhull.htm#TOC">Qhull</a> &#149; <a href="qh-set.htm#TOC">Set</a>
+&#149; <a href="qh-stat.htm#TOC">Stat</a> &#149; <a href="qh-user.htm#TOC">User</a>
+</p>
+<h3>Index to <a href="merge.c">merge.c</a> and
+<a href="merge.h">merge.h</a></h3>
+<ul>
+<li><a href="#mtype">merge.h data types, macros, and
+global sets</a> </li>
+<li><a href="#mconst">merge.h constants</a> </li>
+</ul>
+<ul>
+<li><a href="#mtop">top-level merge functions</a> </li>
+<li><a href="#mset">functions for identifying merges</a></li>
+<li><a href="#mbest">functions for determining the
+best merge</a> </li>
+<li><a href="#mmerge">functions for merging facets</a>
+</li>
+<li><a href="#mcycle">functions for merging a cycle
+of facets</a> </li>
+<li><a href="#mrename">functions for renaming a
+vertex</a> </li>
+<li><a href="#mvertex">functions for identifying
+vertices for renaming</a> </li>
+<li><a href="#mcheck">functions for check and trace</a> </li>
+</ul>
+<h3><a href="qh-merge.htm#TOC">&#187;</a><a name="mtype">merge.h data
+types, macros, and global sets</a></h3>
+<ul>
+<li><a href="merge.h#mergeT">mergeT</a> structure to
+identify a merge of two facets</li>
+<li><a href="merge.h#FOREACHmerge_">FOREACHmerge_</a>
+assign 'merge' to each merge in merges </li>
+<li><a href="libqhull.h#qh-set">qh global sets</a>
+qh.facet_mergeset contains non-convex merges
+while qh.degen_mergeset contains degenerate and
+redundant facets</li>
+</ul>
+<h3><a href="qh-merge.htm#TOC">&#187;</a><a name="mconst">merge.h
+constants</a></h3>
+<ul>
+<li><a href="libqhull.h#qh-prec">qh precision constants</a>
+precision constants for Qhull </li>
+<li><a href="merge.h#MRG">MRG...</a> indicates the
+type of a merge (mergeT-&gt;type)</li>
+<li><a href="merge.h#qh_ANGLEredundant">qh_ANGLEredundant</a>
+indicates redundant merge in mergeT-&gt;angle </li>
+<li><a href="merge.h#qh_ANGLEdegen">qh_ANGLEdegen</a>
+indicates degenerate facet in mergeT-&gt;angle </li>
+<li><a href="merge.h#qh_ANGLEconcave">qh_ANGLEconcave</a>
+offset to indicate concave facets in
+mergeT-&gt;angle </li>
+<li><a href="merge.h#qh_MERGEapex">qh_MERGEapex</a>
+flag for qh_mergefacet() to indicate an apex
+merge </li>
+</ul>
+<h3><a href="qh-merge.htm#TOC">&#187;</a><a name="mtop">top-level merge
+functions</a></h3>
+<ul>
+<li><a href="merge.c#all_merges">qh_all_merges</a>
+merge all non-convex facets </li>
+<li><a href="merge.c#checkzero">qh_checkzero</a>
+check that facets are clearly convex </li>
+<li><a href="merge.c#flippedmerges">qh_flippedmerges</a>
+merge flipped facets into best neighbor </li>
+<li><a href="merge.c#forcedmerges">qh_forcedmerges</a>
+merge all duplicate ridges </li>
+<li><a href="merge.c#merge_degenredundant">qh_merge_degenredundant</a>
+merge degenerate and redundant facets </li>
+<li><a href="merge.c#merge_nonconvex">qh_merge_nonconvex</a>
+merge a non-convex ridge </li>
+<li><a href="merge.c#premerge">qh_premerge</a>
+pre-merge non-convex facets </li>
+<li><a href="merge.c#postmerge">qh_postmerge</a>
+post-merge nonconvex facets as defined by
+maxcentrum/maxangle </li>
+</ul>
+
+<h3><a href="qh-merge.htm#TOC">&#187;</a><a name="mset">functions for
+identifying merges</a></h3>
+<ul>
+<li><a href="merge.c#appendmergeset">qh_appendmergeset</a>
+appends an entry to qh.facet_mergeset</li>
+<li><a href="merge.c#compareangle">qh_compareangle</a>
+used by qsort() to order merges </li>
+<li><a href="merge.c#comparemerge">qh_comparemerge</a>
+used by qsort() to order merges </li>
+<li><a href="merge.c#degen_redundant_facet">qh_degen_redundant_facet</a>
+check for a degenerate and redundant facet</li>
+<li><a href="merge.c#degen_redundant_neighbors">qh_degen_redundant_neighbors</a>
+append degenerate and redundant neighbors to
+qh.degen_mergeset </li>
+<li><a href="merge.c#getmergeset_initial">qh_getmergeset_initial</a>
+build initial qh.facet_mergeset </li>
+<li><a href="merge.c#getmergeset">qh_getmergeset</a>
+update qh.facet_mergeset </li>
+<li><a href="merge.c#mark_dupridges">qh_mark_dupridges</a>
+add duplicated ridges to qh.facet_mergeset</li>
+<li><a href="merge.c#maydropneighbor">qh_maydropneighbor</a>
+drop neighbor relationship if no ridge between
+facet and neighbor </li>
+<li><a href="merge.c#test_appendmerge">qh_test_appendmerge</a>
+test a pair of facets for convexity and append to
+qh.facet_mergeset if non-convex </li>
+<li><a href="merge.c#test_vneighbors">qh_test_vneighbors</a>
+test vertex neighbors for convexity </li>
+</ul>
+
+<h3><a href="qh-merge.htm#TOC">&#187;</a><a name="mbest">functions for
+determining the best merge</a></h3>
+<ul>
+<li><a href="merge.c#findbest_test">qh_findbest_test</a>
+test neighbor for best merge </li>
+<li><a href="merge.c#findbestneighbor">qh_findbestneighbor</a>
+finds best neighbor of a facet for merging (i.e.,
+closest hyperplane) </li>
+</ul>
+
+<h3><a href="qh-merge.htm#TOC">&#187;</a><a name="mmerge">functions for
+merging facets</a></h3>
+<ul>
+<li><a href="merge.c#copynonconvex">qh_copynonconvex</a>
+copy non-convex flag to another ridge for the
+same neighbor </li>
+<li><a href="merge.c#makeridges">qh_makeridges</a>
+creates explicit ridges between simplicial facets
+</li>
+<li><a href="merge.c#mergefacet">qh_mergefacet</a>
+merges one facet into another facet</li>
+<li><a href="merge.c#mergeneighbors">qh_mergeneighbors</a>
+merges the neighbors of two facets </li>
+<li><a href="merge.c#mergeridges">qh_mergeridges</a>
+merges the ridge sets of two facets </li>
+<li><a href="merge.c#mergesimplex">qh_mergesimplex</a>
+merge a simplicial facet into another simplicial
+facet </li>
+<li><a href="merge.c#mergevertex_del">qh_mergevertex_del</a>
+delete a vertex due to merging one facet into
+another facet </li>
+<li><a href="merge.c#mergevertex_neighbors">qh_mergevertex_neighbors</a>
+merge the vertex neighbors of two facets </li>
+<li><a href="merge.c#mergevertices">qh_mergevertices</a>
+merge the vertex sets of two facets </li>
+<li><a href="merge.c#newvertices">qh_newvertices</a>
+register all vertices as new vertices </li>
+<li><a href="merge.c#updatetested">qh_updatetested</a>
+clear tested flags and centrums involved in a
+merge </li>
+<li><a href="merge.c#willdelete">qh_willdelete</a>
+moves facet to qh.visible_list; sets replacement
+or NULL </li>
+</ul>
+
+<h3><a href="qh-merge.htm#TOC">&#187;</a><a name="mcycle">functions for
+merging a cycle of facets</a></h3>
+<p>If a point is coplanar with an horizon facet, the
+corresponding new facets are linked together (a <em>samecycle</em>)
+for merging.</p>
+<ul>
+<li><a href="merge.c#basevertices">qh_basevertices</a>
+return temporary set of base vertices for a
+samecycle </li>
+<li><a href="merge.c#mergecycle">qh_mergecycle</a>
+merge a samecycle into a horizon facet </li>
+<li><a href="merge.c#mergecycle_all">qh_mergecycle_all</a>
+merge all samecycles into horizon facets</li>
+<li><a href="merge.c#mergecycle_facets">qh_mergecycle_facets</a>
+finish merge of samecycle </li>
+<li><a href="merge.c#mergecycle_neighbors">qh_mergecycle_neighbors</a>
+merge neighbor sets for samecycle </li>
+<li><a href="merge.c#mergecycle_ridges">qh_mergecycle_ridges</a>
+merge ridge sets for samecycle </li>
+<li><a href="merge.c#mergecycle_vneighbors">qh_mergecycle_vneighbors</a>
+merge vertex neighbor sets for samecycle </li>
+</ul>
+<h3><a href="qh-merge.htm#TOC">&#187;</a><a name="mrename">functions
+for renaming a vertex</a></h3>
+<ul>
+<li><a href="merge.c#comparevisit">qh_comparevisit</a>
+used by qsort() to order vertices by visitid</li>
+<li><a href="merge.c#reducevertices">qh_reducevertices</a>
+reduce vertex sets </li>
+<li><a href="merge.c#redundant_vertex">qh_redundant_vertex</a>
+returns true if detect and rename redundant
+vertex </li>
+<li><a href="merge.c#rename_sharedvertex">qh_rename_sharedvertex</a>
+detect and rename a shared vertex </li>
+<li><a href="merge.c#renameridgevertex">qh_renameridgevertex</a>
+rename oldvertex to newvertex in a ridge </li>
+<li><a href="merge.c#renamevertex">qh_renamevertex</a>
+rename oldvertex to newvertex in ridges </li>
+<li><a href="merge.c#remove_extravertices">qh_remove_extravertices</a>
+remove extra vertices in non-simplicial facets </li>
+</ul>
+
+<h3><a href="qh-merge.htm#TOC">&#187;</a><a name="mvertex">functions
+for identifying vertices for renaming</a></h3>
+<ul>
+<li><a href="merge.c#find_newvertex">qh_find_newvertex</a>
+locate new vertex for renaming old vertex </li>
+<li><a href="merge.c#hashridge">qh_hashridge</a> add
+ridge to hashtable </li>
+<li><a href="merge.c#hashridge_find">qh_hashridge_find</a>
+returns matching ridge in hashtable</li>
+<li><a href="merge.c#neighbor_intersections">qh_neighbor_intersections</a>
+return intersection of vertex sets for
+neighboring facets </li>
+<li><a href="merge.c#vertexridges">qh_vertexridges</a>
+return temporary set of ridges adjacent to a
+vertex </li>
+<li><a href="merge.c#vertexridges_facet">qh_vertexridges_facet</a>
+add adjacent ridges for a vertex in facet </li>
+</ul>
+
+<h3><a href="qh-merge.htm#TOC">&#187;</a><a name="mcheck">functions for check and
+trace</a></h3>
+<ul>
+<li><a href="merge.c#checkconnect">qh_checkconnect</a>
+check that new facets are connected </li>
+<li><a href="merge.c#tracemerge">qh_tracemerge</a>
+print trace message after merge </li>
+<li><a href="merge.c#tracemerging">qh_tracemerging</a>
+print trace message during post-merging </li>
+</ul>
+
+<p><!-- Navigation links --> </p>
+<hr>
+<p><b>Up:</b>
+<a href="http://www.qhull.org">Home page for
+Qhull</a> <br>
+<b>Up:</b> <a href="../../html/index.htm#TOC">Qhull manual: Table of Contents</a> <br>
+<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a>
+&#149; <a href="../../html/qh-quick.htm#options">Options</a>
+&#149; <a href="../../html/qh-opto.htm#output">Output</a>
+&#149; <a href="../../html/qh-optf.htm#format">Formats</a>
+&#149; <a href="../../html/qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="../../html/qh-optp.htm#print">Print</a>
+&#149; <a href="../../html/qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="../../html/qh-optc.htm#prec">Precision</a>
+&#149; <a href="../../html/qh-optt.htm#trace">Trace</a>
+&#149; <a href="index.htm">Functions</a><br>
+<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code: Table of Contents</a> <br>
+<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
+<b>To:</b> <a href="qh-geom.htm">Geom</a> &#149;
+<a href="qh-globa.htm">Global</a> &#149; <a href="qh-io.htm">Io</a>
+&#149; <a href="qh-mem.htm">Mem</a> &#149; <a href="qh-merge.htm">Merge</a>
+&#149; <a href="qh-poly.htm">Poly</a> &#149; <a href="qh-qhull.htm#TOC">Qhull</a>
+&#149; <a href="qh-set.htm">Set</a> &#149; <a href="qh-stat.htm">Stat</a>
+&#149; <a href="qh-user.htm">User</a><br>
+</p>
+<p><!-- GC common information --> </p>
+<hr>
+<p><a href="http://www.geom.uiuc.edu/"><img
+src="../../html/qh--geom.gif" align="middle" width="40" height="40"></a><i>The
+Geometry Center Home Page </i></p>
+<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
+</a><br>
+Created: May 2, 1997 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
+</body>
+</html>
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+<!-- Do not edit with Front Page, it adds too many spaces -->
+<html>
+<head>
+<meta http-equiv="Content-Type"
+content="text/html; charset=iso-8859-1">
+<title>poly.c, poly2.c -- polyhedron operations</title>
+</head>
+
+<body>
+<!-- Navigation links -->
+<p><a name="TOP"><b>Up:</b></a> <a
+href="http://www.qhull.org">Home page</a> for Qhull<br>
+<b>Up:</b> <a href="../../html/index.htm#TOC">Qhull manual</a>: Table of Contents <br>
+<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a>
+&#149; <a href="../../html/qh-quick.htm#options">Options</a>
+&#149; <a href="../../html/qh-opto.htm#output">Output</a>
+&#149; <a href="../../html/qh-optf.htm#format">Formats</a>
+&#149; <a href="../../html/qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="../../html/qh-optp.htm#print">Print</a>
+&#149; <a href="../../html/qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="../../html/qh-optc.htm#prec">Precision</a>
+&#149; <a href="../../html/qh-optt.htm#trace">Trace</a>
+&#149; <a href="index.htm">Functions</a><br>
+<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code: Table of Contents</a><br>
+<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
+<b>To:</b> <a href="qh-geom.htm">Geom</a> &#149; <a href="qh-globa.htm">Global</a>
+&#149; <a href="qh-io.htm">Io</a> &#149; <a href="qh-mem.htm">Mem</a>
+&#149; <a href="qh-merge.htm">Merge</a> &#149; <a href="qh-poly.htm#TOC">Poly</a>
+&#149; <a href="qh-qhull.htm">Qhull</a> &#149; <a href="qh-set.htm">Set</a>
+&#149; <a href="qh-stat.htm">Stat</a> &#149; <a href="qh-user.htm">User</a>
+</p>
+<hr>
+
+<h2>poly.c, poly2.c -- polyhedron operations</h2>
+<blockquote>
+
+<p>Qhull uses dimension-free terminology. Qhull builds a
+polyhedron in dimension <em>d. </em>A <em>polyhedron</em> is a
+simplicial complex of faces with geometric information for the
+top and bottom-level faces. A (<em>d-1</em>)-face is a <em>facet</em>,
+a (<em>d-2</em>)-face is a <em>ridge</em>, and a <em>0</em>-face
+is a <em>vertex</em>. For example in 3-d, a facet is a polygon
+and a ridge is an edge. A facet is built from a ridge (the <em>base</em>)
+and a vertex (the <em>apex</em>). See
+<a href="../../html/index.htm#structure">Qhull's data structures</a>.</p>
+
+<p>Qhull's primary data structure is a polyhedron. A
+polyhedron is a list of facets. Each facet has a set of
+neighboring facets and a set of vertices. Each facet has a
+hyperplane. For example, a tetrahedron has four facets.
+If its vertices are <em>a, b, c, d</em>, and its facets
+are <em>1, 2, 3, 4,</em> the tetrahedron is </p>
+<blockquote>
+<ul>
+<li>facet 1 <ul>
+    <li>vertices: b c d </li>
+    <li>neighbors: 2 3 4 </li>
+</ul>
+</li>
+<li>facet 2 <ul>
+    <li>vertices: a c d </li>
+    <li>neighbors: 1 3 4 </li>
+</ul>
+</li>
+<li>facet 3 <ul>
+    <li>vertices: a b d </li>
+    <li>neighbors: 1 2 4 </li>
+</ul>
+</li>
+<li>facet 4 <ul>
+    <li>vertices: a b c </li>
+    <li>neighbors: 1 2 3 </li>
+</ul>
+</li>
+</ul>
+</blockquote>
+<p>A facet may be simplicial or non-simplicial. In 3-d, a
+<i>simplicial facet</i> has three vertices and three
+neighbors. A <i>nonsimplicial facet</i> has more than
+three vertices and more than three neighbors. A
+nonsimplicial facet has a set of ridges and a centrum. </p>
+<p>
+A simplicial facet has an orientation. An <i>orientation</i>
+is either <i>top</i> or <i>bottom</i>.
+The flag, <tt>facet-&gt;toporient,</tt>
+defines the orientation of the facet's vertices.  For example in 3-d,
+'top' is left-handed orientation (i.e., the vertex order follows the direction
+of the left-hand fingers when the thumb is pointing away from the center).
+Except for axis-parallel facets in 5-d and higher, topological orientation
+determines the geometric orientation of the facet's hyperplane.
+
+<p>A nonsimplicial facet is due to merging two or more
+facets. The facet's ridge set determine a simplicial
+decomposition of the facet. Each ridge is a 1-face (i.e.,
+it has two vertices and two neighboring facets). The
+orientation of a ridge is determined by the order of the
+neighboring facets. The flag, <tt>facet-&gt;toporient,</tt>is
+ignored. </p>
+<p>A nonsimplicial facet has a centrum for testing
+convexity. A <i>centrum</i> is a point on the facet's
+hyperplane that is near the center of the facet. Except
+for large facets, it is the arithmetic average of the
+facet's vertices. </p>
+<p>A nonsimplicial facet is an approximation that is
+defined by offsets from the facet's hyperplane. When
+Qhull finishes, the <i>outer plane</i> is above all
+points while the <i>inner plane</i> is below the facet's
+vertices. This guarantees that any exact convex hull
+passes between the inner and outer planes. The outer
+plane is defined by <tt>facet-&gt;maxoutside</tt> while
+the inner plane is computed from the facet's vertices.</p>
+
+<p>Qhull 3.1 includes triangulation of non-simplicial facets
+('<a href="../../html/qh-optq.htm#Qt">Qt</a>').
+These facets,
+called <i>tricoplanar</i>, share the same normal. centrum, and Voronoi center.
+One facet (keepcentrum) owns these data structures.
+While tricoplanar facets are more accurate than the simplicial facets from
+joggled input, they
+may have zero area or flipped orientation.
+
+</blockquote>
+<p><b>Copyright &copy; 1995-2015 C.B. Barber</b></p>
+<hr>
+<p><a href="#TOP">&#187;</a> <a href="qh-geom.htm#TOC">Geom</a>
+<a name="TOC">&#149;</a> <a href="qh-globa.htm#TOC">Global</a>
+&#149; <a href="qh-io.htm#TOC">Io</a> &#149; <a href="qh-mem.htm#TOC">Mem</a>
+&#149; <a href="qh-merge.htm#TOC">Merge</a> &#149; <b>Poly</b>
+&#149; <a href="qh-qhull.htm#TOC">Qhull</a> &#149; <a href="qh-set.htm#TOC">Set</a>
+&#149; <a href="qh-stat.htm#TOC">Stat</a> &#149; <a href="qh-user.htm#TOC">User</a>
+</p>
+<h3>Index to <a href="poly.c">poly.c</a>,
+<a href="poly2.c">poly2.c</a>, <a href="poly.h">poly.h</a>,
+and <a href="libqhull.h">libqhull.h</a></h3>
+<ul>
+<li><a href="#ptype">Data types and global
+lists for polyhedrons</a> </li>
+<li><a href="#pconst">poly.h constants</a> </li>
+<li><a href="#pgall">Global FORALL macros</a> </li>
+<li><a href="#pall">FORALL macros</a> </li>
+<li><a href="#peach">FOREACH macros</a> </li>
+<li><a href="#pieach">Indexed FOREACH macros</a> </li>
+<li><a href="#pmacro">Other macros for polyhedrons</a><p>&nbsp;</li>
+<li><a href="#plist">Facetlist functions</a> </li>
+<li><a href="#pfacet">Facet functions</a> </li>
+<li><a href="#pvertex">Vertex, ridge, and point
+functions</a> </li>
+<li><a href="#phash">Hashtable functions</a> </li>
+<li><a href="#pnew">Allocation and deallocation
+functions</a> </li>
+<li><a href="#pcheck">Check functions</a> </li>
+</ul>
+<h3><a href="qh-poly.htm#TOC">&#187;</a><a name="ptype">Data
+types and global lists for polyhedrons</a></h3>
+<ul>
+<li><a href="libqhull.h#facetT">facetT</a> defines a
+facet </li>
+<li><a href="libqhull.h#ridgeT">ridgeT</a> defines a
+ridge </li>
+<li><a href="libqhull.h#vertexT">vertexT</a> defines a
+vertex </li>
+<li><a href="libqhull.h#qh-lists">qh facet and vertex
+lists</a> lists of facets and vertices </li>
+<li><a href="libqhull.h#qh-set">qh global sets</a>
+global sets for merging, hashing, input, etc. </li>
+</ul>
+<h3><a href="qh-poly.htm#TOC">&#187;</a><a name="pconst">poly.h constants</a></h3>
+<ul>
+<li><a href="poly.h#ALGORITHMfault">ALGORITHMfault</a>
+flag to not report errors in qh_checkconvex() </li>
+<li><a href="poly.h#DATAfault">DATAfault</a> flag to
+report errors in qh_checkconvex() </li>
+<li><a href="poly.h#DUPLICATEridge">DUPLICATEridge</a>
+special value for facet-&gt;neighbor to indicate
+a duplicate ridge </li>
+<li><a href="poly.h#MERGEridge">MERGEridge</a>
+special value for facet-&gt;neighbor to indicate
+a merged ridge </li>
+</ul>
+<h3><a href="qh-poly.htm#TOC">&#187;</a><a name="pgall">Global FORALL
+macros</a></h3>
+<ul>
+<li><a href="libqhull.h#FORALLfacets">FORALLfacets</a>
+assign 'facet' to each facet in qh.facet_list </li>
+<li><a href="poly.h#FORALLnew_facets">FORALLnew_facets</a>
+assign 'facet' to each facet in qh.newfacet_list </li>
+<li><a href="poly.h#FORALLvisible_facets">FORALLvisible_facets</a>
+assign 'visible' to each visible facet in
+qh.visible_list </li>
+<li><a href="libqhull.h#FORALLpoints">FORALLpoints</a>
+assign 'point' to each point in qh.first_point,
+qh.num_points </li>
+<li><a href="libqhull.h#FORALLvertices">FORALLvertices</a>
+assign 'vertex' to each vertex in qh.vertex_list </li>
+</ul>
+<h3><a href="qh-poly.htm#TOC">&#187;</a><a name="pall">FORALL macros</a></h3>
+<ul>
+<li><a href="poly.h#FORALLfacet_">FORALLfacet_</a>
+assign 'facet' to each facet in facetlist </li>
+<li><a href="libqhull.h#FORALLpoint_">FORALLpoint_</a>
+assign 'point' to each point in points array</li>
+<li><a href="poly.h#FORALLsame_">FORALLsame_</a>
+assign 'same' to each facet in samecycle</li>
+<li><a href="poly.h#FORALLsame_cycle_">FORALLsame_cycle_</a>
+assign 'same' to each facet in samecycle</li>
+<li><a href="poly.h#FORALLvertex_">FORALLvertex_</a>
+assign 'vertex' to each vertex in vertexlist </li>
+</ul>
+<h3><a href="qh-poly.htm#TOC">&#187;</a><a name="peach">FOREACH macros</a></h3>
+<ul>
+<li><a href="libqhull.h#FOREACHfacet_">FOREACHfacet_</a>
+assign 'facet' to each facet in facets </li>
+<li><a href="libqhull.h#FOREACHneighbor_">FOREACHneighbor_</a>
+assign 'neighbor' to each facet in
+facet-&gt;neighbors or vertex-&gt;neighbors</li>
+<li><a href="poly.h#FOREACHnewfacet_">FOREACHnewfacet_</a>
+assign 'newfacet' to each facet in facet set </li>
+<li><a href="libqhull.h#FOREACHpoint_">FOREACHpoint_</a>
+assign 'point' to each point in points set </li>
+<li><a href="libqhull.h#FOREACHridge_">FOREACHridge_</a>
+assign 'ridge' to each ridge in ridge set </li>
+<li><a href="libqhull.h#FOREACHvertex_">FOREACHvertex_</a>
+assign 'vertex' to each vertex in vertex set </li>
+<li><a href="poly.h#FOREACHvertexA_">FOREACHvertexA_</a>
+assign 'vertexA' to each vertex in vertex set</li>
+<li><a href="poly.h#FOREACHvisible_">FOREACHvisible_</a>
+assign 'visible' to each facet in facet set </li>
+</ul>
+<h3><a href="qh-poly.htm#TOC">&#187;</a><a name="pieach">Indexed
+FOREACH macros</a></h3>
+<ul>
+<li><a href="libqhull.h#FOREACHfacet_i_">FOREACHfacet_i_</a>
+assign 'facet' and 'facet_i' to each facet in
+facet set </li>
+<li><a href="libqhull.h#FOREACHneighbor_i_">FOREACHneighbor_i_</a>
+assign 'neighbor' and 'neighbor_i' to each facet
+in facet-&gt;neighbors or vertex-&gt;neighbors</li>
+<li><a href="libqhull.h#FOREACHpoint_i_">FOREACHpoint_i_</a>
+assign 'point' and 'point_i' to each point in
+points set </li>
+<li><a href="libqhull.h#FOREACHridge_i_">FOREACHridge_i_</a>
+assign 'ridge' and 'ridge_i' to each ridge in
+ridges set </li>
+<li><a href="libqhull.h#FOREACHvertex_i_">FOREACHvertex_i_</a>
+assign 'vertex' and 'vertex_i' to each vertex in
+vertices set </li>
+<li><a href="poly.h#FOREACHvertexreverse12_">FOREACHvertexreverse12_</a>
+assign 'vertex' to each vertex in vertex set;
+reverse the order of first two vertices </li>
+</ul>
+<h3><a href="qh-poly.htm#TOC">&#187;</a><a name="pmacro">Other macros for polyhedrons</a></h3>
+<ul>
+<li><a href="libqhull.h#getid_">getid_</a> return ID for
+a facet, ridge, or vertex </li>
+<li><a href="libqhull.h#otherfacet_">otherfacet_</a>
+return neighboring facet for a ridge in a facet </li>
+</ul>
+<h3><a href="qh-poly.htm#TOC">&#187;</a><a name="plist">Facetlist
+functions</a></h3>
+<ul>
+<li><a href="poly.c#appendfacet">qh_appendfacet</a>
+appends facet to end of qh.facet_list</li>
+<li><a href="poly.c#attachnewfacets">qh_attachnewfacets</a>
+attach new facets in qh.newfacet_list to the
+horizon </li>
+<li><a href="poly2.c#findgood">qh_findgood</a>
+identify good facets for qh.PRINTgood </li>
+<li><a href="poly2.c#findgood_all">qh_findgood_all</a>
+identify more good facets for qh.PRINTgood </li>
+<li><a href="poly2.c#furthestnext">qh_furthestnext</a>
+move facet with furthest of furthest points to
+facet_next </li>
+<li><a href="poly2.c#initialhull">qh_initialhull</a>
+construct the initial hull as a simplex of
+vertices </li>
+<li><a href="poly2.c#nearcoplanar">qh_nearcoplanar</a>
+  remove near-inside points from coplanar sets</li>
+<li><a href="poly2.c#prependfacet">qh_prependfacet</a>
+prepends facet to start of facetlist </li>
+<li><a href="user.c#printfacetlist">qh_printfacetlist</a>
+print facets in a facetlist</li>
+<li><a href="poly2.c#printlists">qh_printlists</a>
+print out facet list for debugging </li>
+<li><a href="poly.c#removefacet">qh_removefacet</a>
+unlinks facet from qh.facet_list</li>
+<li><a href="poly2.c#resetlists">qh_resetlists</a>
+reset qh.newvertex_list, qh.newfacet_list, and
+qh.visible_list </li>
+</ul>
+<h3><a href="qh-poly.htm#TOC">&#187;</a><a name="pfacet">Facet
+functions</a></h3>
+<ul>
+<li><a href="poly2.c#createsimplex">qh_createsimplex</a>
+create a simplex of facets from a set of vertices
+</li>
+<li><a href="poly2.c#findbestlower">qh_findbestlower</a> find best
+non-upper, non-flipped facet for point at upperfacet</li>
+<li><a href="poly2.c#furthestout">qh_furthestout</a>
+make furthest outside point the last point of a
+facet's outside set </li>
+<li><a href="poly.c#makenew_nonsimplicial">qh_makenew_nonsimplicial</a>
+make new facets from ridges of visible facets </li>
+<li><a href="poly.c#makenew_simplicial">qh_makenew_simplicial</a>
+make new facets for horizon neighbors </li>
+<li><a href="poly.c#makenewfacet">qh_makenewfacet</a>
+create a facet from vertices and apex </li>
+<li><a href="poly2.c#makenewfacets">qh_makenewfacets</a>
+make new facets from vertex, horizon facets, and
+visible facets </li>
+<li><a href="poly.c#makenewplanes">qh_makenewplanes</a>
+make new hyperplanes for facets </li>
+<li><a href="poly2.c#outcoplanar">qh_outcoplanar</a>
+move points from outside set to coplanar set </li>
+<li><a href="poly2.c#setvoronoi_all">qh_setvoronoi_all</a>
+compute Voronoi centers for all facets </li>
+<li><a href="poly2.c#triangulate">qh_triangulate</a>
+triangulate non-simplicial facets</li>
+<li><a href="poly2.c#triangulate_facet">qh_triangulate_facet</a>
+triangulate a non-simplicial facet</li>
+<li><a href="poly2.c#triangulate_link">qh_triangulate_link</a>
+link facets together from qh_triangulate</li>
+<li><a href="poly2.c#triangulate_mirror">qh_triangulate_mirror</a>
+delete mirrored facets from qh_triangulate</li>
+<li><a href="poly2.c#triangulate_null">qh_triangulate_null</a>
+delete null facet from qh_triangulate</li>
+</ul>
+<h3><a href="qh-poly.htm#TOC">&#187;</a><a name="pvertex">Vertex,
+ridge, and point functions</a></h3>
+<ul>
+<li><a href="poly.c#appendvertex">qh_appendvertex</a>
+append vertex to end of qh.vertex_list, </li>
+<li><a href="io.c#detvridge">qh_detvridge</a> determine Voronoi
+ridge for an input site
+<li><a href="io.c#detvridge3">qh_detvridge3</a> determine 3-d Voronoi
+ridge for an input site
+<li><a href="poly2.c#facet3vertex">qh_facet3vertex</a>
+return an oriented vertex set for a 3-d facet </li>
+<li><a href="poly.c#facetintersect">qh_facetintersect</a>
+return intersection of simplicial facets </li>
+<li><a href="poly2.c#initialvertices">qh_initialvertices</a>
+return non-singular set of initial vertices </li>
+<li><a href="poly2.c#isvertex">qh_isvertex</a> true
+if point is in a vertex set </li>
+<li><a href="poly2.c#nearvertex">qh_nearvertex</a>
+return nearest vertex to point </li>
+<li><a href="poly2.c#nextridge3d">qh_nextridge3d</a>
+iterate over each ridge and vertex for a 3-d
+facet </li>
+<li><a href="poly2.c#point">qh_point</a> return point
+for a point ID </li>
+<li><a href="poly2.c#pointfacet">qh_pointfacet</a>
+return temporary set of facets indexed by point
+ID </li>
+<li><a href="poly.c#pointid">qh_pointid</a> return ID
+for a point</li>
+<li><a href="poly2.c#pointvertex">qh_pointvertex</a>
+return temporary set of vertices indexed by point
+ID </li>
+<li><a href="poly.c#removevertex">qh_removevertex</a>
+unlink vertex from qh.vertex_list, </li>
+<li><a href="poly.c#updatevertices">qh_updatevertices</a>
+update vertex neighbors and delete interior
+vertices </li>
+<li><a href="poly2.c#vertexintersect">qh_vertexintersect</a>
+intersect two vertex sets </li>
+<li><a href="poly2.c#vertexintersect_new">qh_vertexintersect_new</a>
+return intersection of two vertex sets </li>
+<li><a href="poly2.c#vertexneighbors">qh_vertexneighbors</a>
+for each vertex in hull, determine facet
+neighbors </li>
+<li><a href="poly2.c#vertexsubset">qh_vertexsubset</a>
+returns True if vertexsetA is a subset of
+vertexsetB </li>
+</ul>
+<h3><a href="qh-poly.htm#TOC">&#187;</a><a name="phash">Hashtable functions</a></h3>
+<ul>
+<li><a href="poly2.c#addhash">qh_addhash</a> add hash
+element to linear hash table</li>
+<li><a href="poly.c#gethash">qh_gethash</a> return
+hash value for a set</li>
+<li><a href="poly2.c#matchduplicates">qh_matchduplicates</a>
+match duplicate ridges in hash table </li>
+<li><a href="poly.c#matchneighbor">qh_matchneighbor</a>
+try to match subridge of new facet with a
+neighbor </li>
+<li><a href="poly.c#matchnewfacets">qh_matchnewfacets</a>
+match new facets with their new facet neighbors </li>
+<li><a href="poly.c#matchvertices">qh_matchvertices</a>
+tests whether a facet and hash entry match at a
+ridge </li>
+<li><a href="poly2.c#newhashtable">qh_newhashtable</a>
+allocate a new qh.hash_table </li>
+<li><a href="poly2.c#printhashtable">qh_printhashtable</a>
+print hash table </li>
+</ul>
+<h3><a href="qh-poly.htm#TOC">&#187;</a><a name="pnew">Allocation and
+deallocation functions</a></h3>
+<ul>
+<li><a href="poly2.c#clearcenters">qh_clearcenters</a>
+clear old data from facet-&gt;center </li>
+<li><a href="poly.c#deletevisible">qh_deletevisible</a>
+delete visible facets and vertices </li>
+<li><a href="poly.c#delfacet">qh_delfacet</a> free up
+the memory occupied by a facet </li>
+<li><a href="poly2.c#delridge">qh_delridge</a> delete
+ridge</li>
+<li><a href="poly2.c#delvertex">qh_delvertex</a>
+delete vertex </li>
+<li><a href="poly.c#newfacet">qh_newfacet</a> create
+and allocate space for a facet </li>
+<li><a href="poly.c#newridge">qh_newridge</a> create
+and allocate space for a ridge </li>
+<li><a href="poly2.c#newvertex">qh_newvertex</a>
+create and allocate space for a vertex </li>
+</ul>
+<h3><a href="qh-poly.htm#TOC">&#187;</a><a name="pcheck">Check
+functions</a></h3>
+<ul>
+<li><a href="poly2.c#check_bestdist">qh_check_bestdist</a>
+check that points are not outside of facets </li>
+<li><a href="poly2.c#check_dupridge">qh_check_dupridge</a>
+check duplicate ridge between facet1 and facet2 for wide merge </li>
+<li><a href="poly2.c#check_maxout">qh_check_maxout</a>
+updates qh.max_outside and checks all points
+against bestfacet </li>
+<li><a href="poly2.c#check_output">qh_check_output</a>
+check topological and geometric output</li>
+<li><a href="poly2.c#check_point">qh_check_point</a>
+check that point is not outside of facet </li>
+<li><a href="poly2.c#check_points">qh_check_points</a>
+check that all points are inside all facets </li>
+<li><a href="poly2.c#checkconvex">qh_checkconvex</a>
+check that each ridge in facetlist is convex </li>
+<li><a href="poly2.c#checkfacet">qh_checkfacet</a>
+check for consistency errors in facet </li>
+<li><a href="poly.c#checkflipped">qh_checkflipped</a>
+check facet orientation to the interior point </li>
+<li><a href="poly2.c#checkflipped_all">qh_checkflipped_all</a>
+check facet orientation for a facet list </li>
+<li><a href="poly2.c#checkpolygon">qh_checkpolygon</a>
+check topological structure </li>
+<li><a href="poly2.c#checkvertex">qh_checkvertex</a>
+check vertex for consistency </li>
+<li><a href="poly2.c#infiniteloop">qh_infiniteloop</a>
+report error for a loop of facets </li>
+<li><a href="poly2.c#printlists">qh_printlists</a>
+print out facet list for debugging </li>
+</ul>
+
+
+<p><!-- Navigation links --> </p>
+<hr>
+<p><b>Up:</b>
+<a href="http://www.qhull.org">Home page for
+Qhull</a> <br>
+<b>Up:</b> <a href="../../html/index.htm#TOC">Qhull manual: Table of Contents</a> <br>
+<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a>
+&#149; <a href="../../html/qh-quick.htm#options">Options</a>
+&#149; <a href="../../html/qh-opto.htm#output">Output</a>
+&#149; <a href="../../html/qh-optf.htm#format">Formats</a>
+&#149; <a href="../../html/qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="../../html/qh-optp.htm#print">Print</a>
+&#149; <a href="../../html/qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="../../html/qh-optc.htm#prec">Precision</a>
+&#149; <a href="../../html/qh-optt.htm#trace">Trace</a>
+&#149; <a href="index.htm">Functions</a><br>
+<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code: Table of Contents</a> <br>
+<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
+<b>To:</b> <a href="qh-geom.htm">Geom</a> &#149;
+<a href="qh-globa.htm">Global</a> &#149; <a href="qh-io.htm">Io</a>
+&#149; <a href="qh-mem.htm">Mem</a> &#149; <a href="qh-merge.htm">Merge</a>
+&#149; <a href="qh-poly.htm">Poly</a> &#149; <a href="qh-qhull.htm#TOC">Qhull</a>
+&#149; <a href="qh-set.htm">Set</a> &#149; <a href="qh-stat.htm">Stat</a>
+&#149; <a href="qh-user.htm">User</a><br>
+</p>
+<p><!-- GC common information --> </p>
+<hr>
+<p><a href="http://www.geom.uiuc.edu/"><img
+src="../../html/qh--geom.gif" align="middle" width="40" height="40"></a><i>The
+Geometry Center Home Page </i></p>
+<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
+</a><br>
+Created: May 2, 1997 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
+</body>
+</html>
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+<!-- Do not edit with Front Page, it adds too many spaces -->
+<html>
+<head>
+<meta http-equiv="Content-Type"
+content="text/html; charset=iso-8859-1">
+<title>libqhull.c -- top-level functions and basic data types</title>
+</head>
+
+<body>
+<!-- Navigation links -->
+<p><a name="TOP"><b>Up:</b></a> <a
+href="http://www.qhull.org">Home page</a> for Qhull<br>
+<b>Up:</b> <a href="../../html/index.htm#TOC">Qhull manual</a>: Table of Contents <br>
+<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a>
+&#149; <a href="../../html/qh-quick.htm#options">Options</a>
+&#149; <a href="../../html/qh-opto.htm#output">Output</a>
+&#149; <a href="../../html/qh-optf.htm#format">Formats</a>
+&#149; <a href="../../html/qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="../../html/qh-optp.htm#print">Print</a>
+&#149; <a href="../../html/qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="../../html/qh-optc.htm#prec">Precision</a>
+&#149; <a href="../../html/qh-optt.htm#trace">Trace</a>
+&#149; <a href="index.htm">Functions</a><br>
+<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code: Table of Contents</a><br>
+<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
+<b>To:</b> <a href="qh-geom.htm">Geom</a> &#149; <a href="qh-globa.htm">Global</a>
+&#149; <a href="qh-io.htm">Io</a> &#149; <a href="qh-mem.htm">Mem</a>
+&#149; <a href="qh-merge.htm">Merge</a> &#149; <a href="qh-poly.htm">Poly</a>
+&#149; <a href="qh-qhull.htm#TOC">Qhull</a> &#149; <a href="qh-set.htm">Set</a>
+&#149; <a href="qh-stat.htm">Stat</a> &#149; <a href="qh-user.htm">User</a>
+</p>
+<hr>
+
+<h2>libqhull.c -- top-level functions and basic data types</h2>
+<blockquote>
+<p>Qhull implements the Quickhull algorithm for computing
+the convex hull. The Quickhull algorithm combines two
+well-known algorithms: the 2-d quickhull algorithm and
+the n-d beneath-beyond algorithm. See
+<a href="../../html/index.htm#description">Description of Qhull</a>. </p>
+<p>This section provides an index to the top-level
+functions and base data types.  The top-level header file, <tt>libqhull.h</tt>,
+contains prototypes for these functions.</p>
+</blockquote>
+<p><b>Copyright &copy; 1995-2015 C.B. Barber</b></p>
+<hr>
+<p><a href="#TOP">&#187;</a> <a href="qh-geom.htm#TOC">Geom</a>
+<a name="TOC">&#149;</a> <a href="qh-globa.htm#TOC">Global</a>
+&#149; <a href="qh-io.htm#TOC">Io</a> &#149; <a href="qh-mem.htm#TOC">Mem</a>
+&#149; <a href="qh-merge.htm#TOC">Merge</a> &#149; <a href="qh-poly.htm#TOC">Poly</a>
+&#149; <b>Qhull</b> &#149; <a href="qh-set.htm#TOC">Set</a>
+&#149; <a href="qh-stat.htm#TOC">Stat</a> &#149; <a href="qh-user.htm#TOC">User</a>
+</p>
+<h3>Index to <a href="libqhull.c">libqhull.c</a>,
+<a href="libqhull.h">libqhull.h</a>, and
+<a href="../qhull/unix.c">unix.c</a></h3>
+<ul>
+<li><a href="#qtype">libqhull.h and unix.c data types and
+constants</a> </li>
+<li><a href="#qmacro">libqhull.h other macros</a> </li>
+<li><a href="#qfunc">Quickhull routines in call order</a> </li>
+<li><a href="#qinit">Top-level routines for initializing and terminating Qhull</a></li>
+<li><a href="#qin">Top-level routines for reading and modifying the input</a></li>
+<li><a href="#qcall">Top-level routines for calling Qhull</a></li>
+<li><a href="#qout">Top-level routines for returning results</a></li>
+<li><a href="#qtest">Top-level routines for testing and debugging</a></li>
+</ul>
+
+<h3><a href="qh-qhull.htm#TOC">&#187;</a><a name="qtype">libqhull.h and unix.c
+data types and constants</a></h3>
+<ul>
+<li><a href="libqhull.h#flagT">flagT</a> Boolean flag as
+a bit </li>
+<li><a href="libqhull.h#boolT">boolT</a> boolean value,
+either True or False </li>
+<li><a href="libqhull.h#CENTERtype">CENTERtype</a> to
+distinguish facet-&gt;center </li>
+<li><a href="libqhull.h#qh_PRINT">qh_PRINT</a> output
+formats for printing (qh.PRINTout) </li>
+<li><a href="libqhull.h#qh_ALL">qh_ALL</a> argument flag
+for selecting everything </li>
+<li><a href="libqhull.h#qh_ERR">qh_ERR</a> Qhull exit
+codes for indicating errors </li>
+<li><a href="libqhull.h#qh_FILEstderr">qh_FILEstderr</a> Fake stderr
+to distinguish error output from normal output [C++ only]</li>
+<li><a href="../qhull/unix.c#prompt">qh_prompt</a> version and long prompt for Qhull</li>
+<li><a href="../qhull/unix.c#prompt2">qh_prompt2</a> synopsis for Qhull</li>
+<li><a href="../qhull/unix.c#prompt3">qh_prompt3</a> concise prompt for Qhull</li>
+<li><a href="global.c#qh_version">qh_version</a> version stamp</li>
+</ul>
+
+<h3><a href="qh-qhull.htm#TOC">&#187;</a><a name="qmacro">libqhull.h other
+macros</a></h3>
+<ul>
+<li><a href="qhull_a.h#traceN">traceN</a> print trace
+message if <em>qh.IStracing &gt;= N</em>. </li>
+<li><a href="qhull_a.h#QHULL_UNUSED">QHULL_UNUSED</a> declare an
+ unused variable to avoid warnings. </li>
+</ul>
+
+<h3><a href="qh-qhull.htm#TOC">&#187;</a><a name="qfunc">Quickhull
+routines in call order</a></h3>
+<ul>
+<li><a href="../qhull/unix.c#main">main</a> processes the
+command line, calls qhull() to do the work, and
+exits </li>
+<li><a href="libqhull.c#qhull">qh_qhull</a> construct
+the convex hull of a set of points </li>
+<li><a href="libqhull.c#build_withrestart">qh_build_withrestart</a>
+allow restarts while calling qh_buildhull</li>
+<li><a href="poly2.c#initbuild">qh_initbuild</a>
+initialize hull and outside sets with point array</li>
+<li><a href="libqhull.c#partitionall">qh_partitionall</a>
+partition all points into outside sets </li>
+<li><a href="libqhull.c#buildhull">qh_buildhull</a>
+construct a convex hull by adding points one at a
+time </li>
+<li><a href="libqhull.c#nextfurthest">qh_nextfurthest</a>
+return next furthest point for processing </li>
+<li><a href="libqhull.c#buildtracing">qh_buildtracing</a>
+trace an iteration of buildhull </li>
+<li><a href="libqhull.c#addpoint">qh_addpoint</a> add a
+point to the convex hull </li>
+<li><a href="libqhull.c#findhorizon">qh_findhorizon</a>
+find the horizon and visible facets for a point </li>
+<li><a href="libqhull.c#partitionvisible">qh_partitionvisible</a>
+partition points from facets in qh.visible_list
+to facets in qh.newfacet_list </li>
+<li><a href="libqhull.c#partitionpoint">qh_partitionpoint</a>
+partition a point as inside, coplanar with, or
+outside a facet </li>
+<li><a href="libqhull.c#partitioncoplanar">qh_partitioncoplanar</a>
+partition coplanar point into a facet </li>
+<li><a href="libqhull.c#precision">qh_precision</a> restart on precision errors if not merging and if 'QJn'</li>
+</ul>
+
+<h3><a href="qh-qhull.htm#TOC">&#187;</a><a name="qinit">Top-level routines for initializing and terminating Qhull (in other modules)</a></h3>
+<ul>
+<li><a href="global.c#freebuild">qh_freebuild</a>
+free memory used by qh_initbuild and qh_buildhull
+</li>
+<li><a href="global.c#checkflags">qh_checkflags</a>
+check flags for multiple frontends to qhull
+<li><a href="global.c#freeqhull">qh_freeqhull</a>
+free memory used by qhull </li>
+<li><a href="global.c#init_A">qh_init_A</a> called
+before error handling initialized </li>
+<li><a href="global.c#init_B">qh_init_B</a> called
+after points are defined </li>
+<li><a href="global.c#initflags">qh_initflags</a> set
+flags and constants from command line </li>
+<li><a href="rboxlib.c#rboxpoints">qh_rboxpoints</a>
+generate points for qhull </li>
+<li><a href="global.c#restore_qhull">qh_restore_qhull</a>
+restores a saved qhull </li>
+<li><a href="global.c#save_qhull">qh_save_qhull</a>
+saves qhull for later restoring </li>
+<li><a href="user.c#user_memsizes">qh_user_memsizes</a>
+define additional quick allocation sizes
+</li>
+</ul>
+
+<h3><a href="qh-qhull.htm#TOC">&#187;</a><a name="qin">Top-level routines for reading and modifying the input (in other modules)</a></h3>
+<ul>
+<li><a href="geom2.c#gram_schmidt">qh_gram_schmidt</a>
+implements Gram-Schmidt orthogonalization by rows </li>
+<li><a href="geom2.c#projectinput">qh_projectinput</a>
+project input along one or more dimensions +
+Delaunay projection </li>
+<li><a href="geom2.c#randommatrix">qh_randommatrix</a>
+generate a random dimXdim matrix in range (-1,1) </li>
+<li><a href="io.c#readpoints">qh_readpoints</a> read
+points from input </li>
+<li><a href="geom2.c#rotateinput">qh_rotateinput</a> rotate
+input points using row matrix </li>
+<li><a href="geom2.c#scaleinput">qh_scaleinput</a> scale
+input points using qh low_bound/high_bound </li>
+<li><a href="geom2.c#setdelaunay">qh_setdelaunay</a> project
+points to paraboloid for Delaunay triangulation </li>
+<li><a href="geom2.c#sethalfspace_all">qh_sethalfspace_all</a>
+generate dual for halfspace intersection with interior
+point </li>
+</ul>
+
+<h3><a href="qh-qhull.htm#TOC">&#187;</a><a name="qcall">Top-level routines for calling Qhull (in other modules)</a></h3>
+<ul>
+<li><a href="libqhull.c#addpoint">qh_addpoint</a> add
+point to convex hull </li>
+<li><a href="poly2.c#findbestfacet">qh_findbestfacet</a>
+find facet that is furthest below a point </li>
+<li><a href="poly2.c#findfacet_all">qh_findfacet_all</a>
+exhaustive search for facet below a point </li>
+<li><a href="libqhull.c#qhull">qh_qhull</a> construct
+the convex hull of a set of points </li>
+</ul>
+
+<h3><a href="qh-qhull.htm#TOC">&#187;</a><a name="qout">Top-level routines for returning results (in other modules)</a></h3>
+<ul>
+<li><a href="stat.c#collectstatistics">qh_collectstatistics</a>
+collect statistics for qh.facet_list </li>
+<li><a href="poly2.c#nearvertex">qh_nearvertex</a>
+return nearest vertex to point </li>
+<li><a href="poly2.c#point">qh_point</a> return point
+for a point ID </li>
+<li><a href="poly2.c#pointfacet">qh_pointfacet</a>
+return temporary set of facets indexed by point
+ID </li>
+<li><a href="poly.c#pointid">qh_pointid</a> return ID
+for a point</li>
+<li><a href="poly2.c#pointvertex">qh_pointvertex</a>
+return vertices (if any) for all points</li>
+<li><a href="stat.c#printallstatistics">qh_printallstatistics</a>
+print all statistics </li>
+<li><a href="io.c#printneighborhood">qh_printneighborhood</a>
+print neighborhood of one or two facets </li>
+<li><a href="libqhull.c#printsummary">qh_printsummary</a>
+print summary </li>
+<li><a href="io.c#produce_output">qh_produce_output</a>
+print the results of qh_qhull() </li>
+<li><a href="poly2.c#setvoronoi_all">qh_setvoronoi_all</a>
+compute Voronoi centers for all facets </li>
+</ul>
+
+<h3><a href="qh-qhull.htm#TOC">&#187;</a><a name="qtest">Top-level routines for testing and debugging (in other modules)</a></h3>
+<ul>
+<li><a href="io.c#dfacet">dfacet</a> print facet by
+ID from debugger </li>
+<li><a href="io.c#dvertex">dvertex</a> print vertex
+by ID from debugger </li>
+<li><a href="poly2.c#check_output">qh_check_output</a>
+check output </li>
+<li><a href="poly2.c#check_points">qh_check_points</a>
+verify that all points are inside the convex hull
+</li>
+<li><a href="user.c#errexit">qh_errexit</a> report
+error with a facet and a ridge</li>
+<li><a href="libqhull.c#errexit2">qh_errexit2</a> report
+error with two facets </li>
+<li><a href="user.c#errprint">qh_errprint</a> print
+erroneous facets, ridge, and vertex </li>
+<li><a href="user.c#printfacetlist">qh_printfacetlist</a>
+print all fields for a list of facets </li>
+</ul>
+
+<p><!-- Navigation links --> </p>
+<hr>
+<p><b>Up:</b>
+<a href="http://www.qhull.org">Home page for
+Qhull</a> <br>
+<b>Up:</b> <a href="../../html/index.htm#TOC">Qhull manual: Table of Contents</a> <br>
+<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a>
+&#149; <a href="../../html/qh-quick.htm#options">Options</a>
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+&#149; <a href="../../html/qh-optp.htm#print">Print</a>
+&#149; <a href="../../html/qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="../../html/qh-optc.htm#prec">Precision</a>
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+&#149; <a href="index.htm">Functions</a><br>
+<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code: Table of Contents</a> <br>
+<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
+<b>To:</b> <a href="qh-geom.htm">Geom</a> &#149;
+<a href="qh-globa.htm">Global</a> &#149; <a href="qh-io.htm">Io</a>
+&#149; <a href="qh-mem.htm">Mem</a> &#149; <a href="qh-merge.htm">Merge</a>
+&#149; <a href="qh-poly.htm">Poly</a> &#149; <a href="qh-qhull.htm#TOC">Qhull</a>
+&#149; <a href="qh-set.htm">Set</a> &#149; <a href="qh-stat.htm">Stat</a>
+&#149; <a href="qh-user.htm">User</a><br>
+</p>
+<p><!-- GC common information --> </p>
+<hr>
+<p><a href="http://www.geom.uiuc.edu/"><img
+src="../../html/qh--geom.gif" align="middle" width="40" height="40"></a><i>The
+Geometry Center Home Page </i></p>
+<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
+</a><br>
+Created: May 2, 1997 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
+</body>
+</html>
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+++ b/xs/src/qhull/src/libqhull/qh-set.htm
@@ -0,0 +1,308 @@
+<!-- Do not edit with Front Page, it adds too many spaces -->
+<html>
+<head>
+<meta http-equiv="Content-Type"
+content="text/html; charset=iso-8859-1">
+<title>qset.c -- set data type and operations</title>
+</head>
+
+<body>
+<!-- Navigation links -->
+<p><a name="TOP"><b>Up:</b></a> <a
+href="http://www.qhull.org">Home page</a> for Qhull<br>
+<b>Up:</b> <a href="../../html/index.htm#TOC">Qhull manual</a>: Table of Contents <br>
+<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a>
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+&#149; <a href="../../html/qh-optp.htm#print">Print</a>
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+&#149; <a href="index.htm">Functions</a><br>
+<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code: Table of Contents</a><br>
+<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
+<b>To:</b> <a href="qh-geom.htm">Geom</a> &#149; <a href="qh-globa.htm">Global</a>
+&#149; <a href="qh-io.htm">Io</a> &#149; <a href="qh-mem.htm">Mem</a>
+&#149; <a href="qh-merge.htm">Merge</a> &#149; <a href="qh-poly.htm">Poly</a>
+&#149; <a href="qh-qhull.htm">Qhull</a> &#149; <a href="qh-set.htm#TOC">Set</a>
+&#149; <a href="qh-stat.htm">Stat</a> &#149; <a href="qh-user.htm">User</a>
+</p>
+<hr>
+
+<h2>qset.c -- set data type and operations</h2>
+<blockquote>
+<p>Qhull's data structures are constructed from sets. The
+functions and macros in qset.c construct, iterate, and
+modify these sets. They are the most frequently called
+functions in Qhull. For this reason, efficiency is the
+primary concern. </p>
+<p>In Qhull, a <i>set</i> is represented by an unordered
+array of pointers with a maximum size and a NULL
+terminator (<a href="qset.h#setT">setT</a>).
+Most sets correspond to mathematical sets
+(i.e., the pointers are unique). Some sets are sorted to
+enforce uniqueness. Some sets are ordered. For example,
+the order of vertices in a ridge determine the ridge's
+orientation. If you reverse the order of adjacent
+vertices, the orientation reverses. Some sets are not
+mathematical sets. They may be indexed as an array and
+they may include NULL pointers. </p>
+<p>The most common operation on a set is to iterate its
+members. This is done with a 'FOREACH...' macro. Each set
+has a custom macro. For example, 'FOREACHvertex_'
+iterates over a set of vertices. Each vertex is assigned
+to the variable 'vertex' from the pointer 'vertexp'. </p>
+<p>Most sets are constructed by appending elements to the
+set. The last element of a set is either NULL or the
+index of the terminating NULL for a partially full set.
+If a set is full, appending an element copies the set to
+a larger array. </p>
+
+</blockquote>
+<p><b>Copyright &copy; 1995-2015 C.B. Barber</b></p>
+<hr>
+<p><a href="#TOP">&#187;</a> <a href="qh-geom.htm#TOC">Geom</a>
+<a name="TOC">&#149;</a> <a href="qh-globa.htm#TOC">Global</a> &#149;
+<a href="qh-io.htm#TOC">Io</a> &#149; <a href="qh-mem.htm#TOC">Mem</a> &#149;
+<a href="qh-merge.htm#TOC">Merge</a> &#149; <a href="qh-poly.htm#TOC">Poly</a>
+&#149; <a href="qh-qhull.htm#TOC">Qhull</a> &#149; <b>Set</b>
+&#149; <a href="qh-stat.htm#TOC">Stat</a> &#149; <a href="qh-user.htm#TOC">User</a>
+</p>
+<h3>Index to <a href="qset.c">qset.c</a> and
+<a href="qset.h">qset.h</a></h3>
+<ul>
+<li><a href="#stype">Data types and constants</a> </li>
+<li><a href="#seach">FOREACH macros</a> </li>
+<li><a href="#saccess">access and size macros</a> </li>
+<li><a href="#sint">internal macros</a> </li>
+<li><a href="#saddr">address macros</a><p>&nbsp;</li>
+
+<li><a href="#snew">Allocation and deallocation functions</a> </li>
+<li><a href="#spred">Access and predicate functions</a>
+</li>
+<li><a href="#sadd">Add functions</a> </li>
+<li><a href="#scheck">Check and print functions</a></li>
+<li><a href="#scopy">Copy, compact, and zero functions</a></li>
+<li><a href="#sdel">Delete functions</a> </li>
+<li><a href="#stemp">Temporary set functions</a> </li>
+</ul>
+<h3><a href="qh-set.htm#TOC">&#187;</a><a name="stype">Data types and
+constants</a></h3>
+<ul>
+<li><a href="qset.h#SETelemsize">SETelemsize</a> size
+of a set element in bytes </li>
+<li><a href="qset.h#setT">setT</a> a set with a
+maximum size and a current size</li>
+<li><a href="libqhull.h#qh-set">qh global sets</a>
+global sets for temporary sets, etc. </li>
+</ul>
+<h3><a href="qh-set.htm#TOC">&#187;</a><a name="seach">FOREACH macros</a></h3>
+<ul>
+<li><a href="qset.h#FOREACHelem_">FOREACHelem_</a>
+assign 'elem' to each element in a set </li>
+<li><a href="qset.h#FOREACHset_">FOREACHset_</a>
+assign 'set' to each set in a set of sets </li>
+<li><a href="qset.h#FOREACHsetelement_">FOREACHsetelement_</a>
+define a FOREACH iterator </li>
+<li><a href="qset.h#FOREACHsetelement_i_">FOREACHsetelement_i_</a>
+define an indexed FOREACH iterator </li>
+<li><a href="qset.h#FOREACHsetelementreverse_">FOREACHsetelementreverse_</a>
+define a reversed FOREACH iterator </li>
+<li><a href="qset.h#FOREACHsetelementreverse12_">FOREACHsetelementreverse12_</a>
+define a FOREACH iterator with e[1] and e[0]
+reversed </li>
+</ul>
+<h3><a href="qh-set.htm#TOC">&#187;</a><a name="saccess">Access and
+size macros</a></h3>
+<ul>
+<li><a href="qset.h#SETelem_">SETelem_</a> return the
+n'th element of set </li>
+<li><a href="qset.h#SETelemt_">SETelemt_</a> return
+the n'th element of set as a type</li>
+<li><a href="qset.h#SETempty_">SETempty_</a> return
+true (1) if set is empty </li>
+<li><a href="qset.h#SETfirst_">SETfirst_</a> return
+first element of set </li>
+<li><a href="qset.h#SETfirstt_">SETfirstt_</a> return
+first element of set as a type</li>
+<li><a href="qset.h#SETindex_">SETindex_</a> return
+index of elem in set </li>
+<li><a href="qset.h#SETreturnsize_">SETreturnsize_</a>
+return size of a set (normally use <a href="qset.c#setsize">qh_setsize</a>) </li>
+<li><a href="qset.h#SETsecond_">SETsecond_</a> return
+second element of set </li>
+<li><a href="qset.h#SETsecondt_">SETsecondt_</a>
+return second element of set as a type</li>
+<li><a href="qset.h#SETtruncate_">SETtruncate_</a>
+truncate set to size, i.e., qh_settruncate()</li>
+</ul>
+<h3><a href="qh-set.htm#TOC">&#187;</a><a name="sint">Internal macros</a></h3>
+<ul>
+<li><a href="qset.c#SETsizeaddr_">SETsizeaddr_</a>
+return pointer to end element of a set (indicates
+current size) </li>
+</ul>
+
+<h3><a href="qh-set.htm#TOC">&#187;</a><a name="saddr">address macros</a></h3>
+<ul>
+<li><a href="qset.h#SETaddr_">SETaddr_</a> return
+address of a set's elements </li>
+<li><a href="qset.h#SETelemaddr_">SETelemaddr_</a>
+return address of the n'th element of a set </li>
+<li><a href="qset.h#SETref_">SETref_</a> l.h.s. for
+modifying the current element in a FOREACH
+iteration </li>
+</ul>
+
+<h3><a href="qh-set.htm#TOC">&#187;</a><a name="snew">Allocation and
+deallocation functions</a></h3>
+<ul>
+<li><a href="qset.c#setfree">qh_setfree</a> free the
+space occupied by a set </li>
+<li><a href="qset.c#setfree2">qh_setfree2</a> free a
+set and its elements </li>
+<li><a href="qset.c#setfreelong">qh_setfreelong</a>
+free a set only if it is in long memory </li>
+<li><a href="qset.c#setnew">qh_setnew</a> create a new
+set </li>
+</ul>
+
+<h3><a href="qh-set.htm#TOC">&#187;</a><a name="spred">Access and
+predicate functions </a></h3>
+<ul>
+<li><a href="qset.c#setendpointer">qh_setendpointer</a> return
+pointer to NULL terminator of a set</li>
+<li><a href="qset.c#setequal">qh_setequal</a> return 1
+if two sorted sets are equal </li>
+<li><a href="qset.c#setequal_except">qh_setequal_except</a>
+return 1 if two sorted sets are equal except for
+an element </li>
+<li><a href="qset.c#setequal_skip">qh_setequal_skip</a>
+return 1 if two sorted sets are equal except for
+a pair of skipped elements </li>
+<li><a href="qset.c#setequal_skip">qh_setequal_skip</a>
+return 1 if two sorted sets are equal except for
+a pair of skipped elements </li>
+<li><a href="qset.c#setin">qh_setin</a> return 1 if an
+element is in a set </li>
+<li><a href="qset.c#setindex">qh_setindex</a> return
+the index of an element in a set </li>
+<li><a href="qset.c#setlast">qh_setlast</a> return
+last element of a set</li>
+<li><a href="qset.c#setsize">qh_setsize</a> returns
+the size of a set </li>
+</ul>
+
+<h3><a href="qh-set.htm#TOC">&#187;</a><a name="sadd">Add functions</a></h3>
+<ul>
+<li><a href="qset.c#setaddnth">qh_setaddnth</a> add a
+element as n'th element of sorted or unsorted set
+</li>
+<li><a href="qset.c#setaddsorted">qh_setaddsorted</a>
+add an element to a sorted set </li>
+<li><a href="qset.c#setappend">qh_setappend</a> append
+an element to a set </li>
+<li><a href="qset.c#setappend_set">qh_setappend_set</a>
+append a set of elements to a set </li>
+<li><a href="qset.c#setappend2ndlast">qh_setappend2ndlast</a>
+add an element as the next to the last element in
+a set </li>
+<li><a href="qset.c#setlarger">qh_setlarger</a> return
+a larger set with the same elements</li>
+<li><a href="qset.c#setreplace">qh_setreplace</a>
+replace one element with another in a set</li>
+<li><a href="qset.c#setunique">qh_setunique</a> add an
+element if it is not already in a set </li>
+</ul>
+
+<h3><a href="qh-set.htm#TOC">&#187;</a><a name="scheck">Check and print functions</a></h3>
+<ul>
+<li><a href="qset.c#setcheck">qh_setcheck</a> check a
+set for validity </li>
+<li><a href="qset.c#setprint">qh_setprint</a> print a
+set's elements to fp </li>
+</ul>
+
+<h3><a href="qh-set.htm#TOC">&#187;</a><a name="scopy">Copy, compact, and zero functions</a></h3>
+<ul>
+<li><a href="qset.c#setcompact">qh_setcompact</a>
+compact NULLs from an unsorted set </li>
+<li><a href="qset.c#setcopy">qh_setcopy</a> make a
+copy of a sorted or unsorted set </li>
+<li><a href="qset.c#setduplicate">qh_setduplicate</a>
+duplicate a set and its elements </li>
+<li><a href="qset.c#settruncate">qh_settruncate</a>
+truncate a set to size elements </li>
+<li><a href="qset.c#setzero">qh_setzero</a> zero the
+remainder of a set </li>
+</ul>
+
+<h3><a href="qh-set.htm#TOC">&#187;</a><a name="sdel">Delete functions</a></h3>
+<ul>
+<li><a href="qset.c#setdel">qh_setdel</a> delete an
+element from an unsorted set. </li>
+<li><a href="qset.c#setdellast">qh_setdellast</a>
+delete and return last element from a set</li>
+<li><a href="qset.c#setdelnth">qh_setdelnth</a> delete
+and return nth element from an unsorted set </li>
+<li><a href="qset.c#setdelnthsorted">qh_setdelnthsorted</a>
+delete and return nth element from a sorted set </li>
+<li><a href="qset.c#setdelsorted">qh_setdelsorted</a>
+delete an element from a sorted set </li>
+<li><a href="qset.c#setnew_delnthsorted">qh_setnew_delnthsorted</a>
+create a sorted set not containing the nth
+element </li>
+</ul>
+
+<h3><a href="qh-set.htm#TOC">&#187;</a><a name="stemp">Temporary set functions</a></h3>
+<ul>
+<li><a href="qset.c#settemp">qh_settemp</a> return a
+temporary set and append it qhmem.tempstack</li>
+<li><a href="qset.c#settempfree">qh_settempfree</a>
+free and pop a set from qhmem.tempstack</li>
+<li><a href="qset.c#settempfree_all">qh_settempfree_all</a>
+free all sets in qhmem.tempstack </li>
+<li><a href="qset.c#settemppop">qh_settemppop</a> pop
+a set from qhmem.tempstack (makes it permanent) </li>
+<li><a href="qset.c#settemppush">qh_settemppush</a>
+push a set unto qhmem.tempstack (makes it
+temporary) </li>
+</ul>
+
+<p><!-- Navigation links --> </p>
+<hr>
+<p><b>Up:</b>
+<a href="http://www.qhull.org">Home page for
+Qhull</a> <br>
+<b>Up:</b> <a href="../../html/index.htm#TOC">Qhull manual: Table of Contents</a> <br>
+<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a>
+&#149; <a href="../../html/qh-quick.htm#options">Options</a>
+&#149; <a href="../../html/qh-opto.htm#output">Output</a>
+&#149; <a href="../../html/qh-optf.htm#format">Formats</a>
+&#149; <a href="../../html/qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="../../html/qh-optp.htm#print">Print</a>
+&#149; <a href="../../html/qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="../../html/qh-optc.htm#prec">Precision</a>
+&#149; <a href="../../html/qh-optt.htm#trace">Trace</a>
+&#149; <a href="index.htm">Functions</a><br>
+<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code: Table of Contents</a> <br>
+<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
+<b>To:</b> <a href="qh-geom.htm">Geom</a> &#149;
+<a href="qh-globa.htm">Global</a> &#149; <a href="qh-io.htm">Io</a>
+&#149; <a href="qh-mem.htm">Mem</a> &#149; <a href="qh-merge.htm">Merge</a>
+&#149; <a href="qh-poly.htm">Poly</a> &#149; <a href="qh-qhull.htm#TOC">Qhull</a>
+&#149; <a href="qh-set.htm">Set</a> &#149; <a href="qh-stat.htm">Stat</a>
+&#149; <a href="qh-user.htm">User</a><br>
+</p>
+<p><!-- GC common information --> </p>
+<hr>
+<p><a href="http://www.geom.uiuc.edu/"><img
+src="../../html/qh--geom.gif" align="middle" width="40" height="40"></a><i>The
+Geometry Center Home Page </i></p>
+<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
+</a><br>
+Created: May 2, 1997 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
+</body>
+</html>
diff --git a/xs/src/qhull/src/libqhull/qh-stat.htm b/xs/src/qhull/src/libqhull/qh-stat.htm
new file mode 100644
index 0000000000..b968540312
--- /dev/null
+++ b/xs/src/qhull/src/libqhull/qh-stat.htm
@@ -0,0 +1,163 @@
+<!-- Do not edit with Front Page, it adds too many spaces -->
+<html>
+<head>
+<meta http-equiv="Content-Type"
+content="text/html; charset=iso-8859-1">
+<title>stat.c -- statistical operations</title>
+</head>
+
+<body>
+<!-- Navigation links -->
+<p><a name="TOP"><b>Up:</b></a> <a
+href="http://www.qhull.org">Home page</a> for Qhull<br>
+<b>Up:</b> <a href="../../html/index.htm#TOC">Qhull manual</a>: Table of Contents <br>
+<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a>
+&#149; <a href="../../html/qh-quick.htm#options">Options</a>
+&#149; <a href="../../html/qh-opto.htm#output">Output</a>
+&#149; <a href="../../html/qh-optf.htm#format">Formats</a>
+&#149; <a href="../../html/qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="../../html/qh-optp.htm#print">Print</a>
+&#149; <a href="../../html/qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="../../html/qh-optc.htm#prec">Precision</a>
+&#149; <a href="../../html/qh-optt.htm#trace">Trace</a>
+&#149; <a href="index.htm">Functions</a><br>
+<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code: Table of Contents</a><br>
+<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
+<b>To:</b> <a href="qh-geom.htm">Geom</a> &#149; <a href="qh-globa.htm">Global</a>
+&#149; <a href="qh-io.htm">Io</a> &#149; <a href="qh-mem.htm">Mem</a>
+&#149; <a href="qh-merge.htm">Merge</a> &#149; <a href="qh-poly.htm">Poly</a>
+&#149; <a href="qh-qhull.htm">Qhull</a> &#149; <a href="qh-set.htm">Set</a>
+&#149; <a href="qh-stat.htm#TOC">Stat</a> &#149; <a href="qh-user.htm">User</a>
+</p>
+<hr>
+
+<h2>stat.c -- statistical operations</h2>
+<blockquote>
+<p>Qhull records many statistics. These functions and
+macros make it inexpensive to add a statistic.
+<p>As with Qhull's global variables, the statistics data structure is
+accessed by a macro, 'qhstat'.  If qh_QHpointer is defined, the macro
+is 'qh_qhstat->', otherwise the macro is 'qh_qhstat.'.
+Statistics
+may be turned off in user.h. If so, all but the 'zz'
+statistics are ignored.</p>
+</blockquote>
+<p><b>Copyright &copy; 1995-2015 C.B. Barber</b></p>
+<hr>
+<p><a href="#TOP">&#187;</a> <a href="qh-geom.htm#TOC">Geom</a>
+<a name="TOC">&#149;</a> <a href="qh-globa.htm#TOC">Global</a>
+&#149; <a href="qh-io.htm#TOC">Io</a> &#149; <a href="qh-mem.htm#TOC">Mem</a>
+&#149; <a href="qh-merge.htm#TOC">Merge</a> &#149; <a href="qh-poly.htm#TOC">Poly</a>
+&#149; <a href="qh-qhull.htm#TOC">Qhull</a> &#149; <a href="qh-set.htm#TOC">Set</a>
+&#149; <b>Stat</b> &#149; <a href="qh-user.htm#TOC">User</a>
+</p>
+<h3>Index to <a href="stat.c">stat.c</a> and
+<a href="stat.h">stat.h</a></h3>
+<ul>
+<li><a href="#ttype">stat.h types</a> </li>
+<li><a href="#tconst">stat.h constants</a> </li>
+<li><a href="#tmacro">stat.h macros</a> </li>
+<li><a href="#tfunc">stat.c functions</a> </li>
+</ul>
+
+<h3><a href="qh-stat.htm#TOC">&#187;</a><a name="ttype">stat.h types</a></h3>
+<ul>
+<li><a href="stat.h#intrealT">intrealT</a> union of
+integer and real</li>
+<li><a href="stat.h#qhstat">qhstat</a> global data
+structure for statistics </li>
+</ul>
+<h3><a href="qh-stat.htm#TOC">&#187;</a><a name="tconst">stat.h
+constants</a></h3>
+<ul>
+<li><a href="stat.h#KEEPstatistics">qh_KEEPstatistics</a> 0 turns off most statistics</li>
+<li><a href="stat.h#statistics">Z..., W...</a> integer (Z) and real (W) statistics
+</li>
+<li><a href="stat.h#ZZstat">ZZstat</a> Z.../W... statistics that
+remain defined if qh_KEEPstatistics=0
+</li>
+<li><a href="stat.h#ztype">ztype</a> zdoc, zinc, etc.
+for definining statistics </li>
+</ul>
+<h3><a href="qh-stat.htm#TOC">&#187;</a><a name="tmacro">stat.h macros</a></h3>
+<ul>
+<li><a href="stat.h#MAYdebugx">MAYdebugx</a> called
+frequently for error trapping </li>
+<li><a href="stat.h#zadd_">zadd_/wadd_</a> add value
+to an integer or real statistic </li>
+<li><a href="stat.h#zdef_">zdef_</a> define a
+statistic </li>
+<li><a href="stat.h#zinc_">zinc_</a> increment an
+integer statistic </li>
+<li><a href="stat.h#zmax_">zmax_/wmax_</a> update
+integer or real maximum statistic </li>
+<li><a href="stat.h#zmin_">zmin_/wmin_</a> update
+integer or real minimum statistic </li>
+<li><a href="stat.h#zval_">zval_/wval_</a> set or
+return value of a statistic </li>
+</ul>
+
+<h3><a href="qh-stat.htm#TOC">&#187;</a><a name="tfunc">stat.c
+functions</a></h3>
+<ul>
+<li><a href="stat.c#allstatA">qh_allstatA</a> define
+statistics in groups of 20 </li>
+<li><a href="stat.c#allstatistics">qh_allstatistics</a>
+reset printed flag for all statistics </li>
+<li><a href="stat.c#collectstatistics">qh_collectstatistics</a>
+collect statistics for qh.facet_list </li>
+<li><a href="stat.c#freestatistics">qh_freestatistics</a>
+free memory used for statistics </li>
+<li><a href="stat.c#initstatistics">qh_initstatistics</a>
+allocate and initialize statistics </li>
+<li><a href="stat.c#newstats">qh_newstats</a> returns
+True if statistics for zdoc </li>
+<li><a href="stat.c#nostatistic">qh_nostatistic</a>
+true if no statistic to print </li>
+<li><a href="stat.c#printallstatistics">qh_printallstatistics</a>
+print all statistics </li>
+<li><a href="stat.c#printstatistics">qh_printstatistics</a>
+print statistics to a file </li>
+<li><a href="stat.c#printstatlevel">qh_printstatlevel</a>
+print level information for a statistic </li>
+<li><a href="stat.c#printstats">qh_printstats</a>
+print statistics for a zdoc group </li>
+<li><a href="stat.c#stddev">qh_stddev</a> compute the
+standard deviation and average from statistics </li>
+</ul>
+
+<p><!-- Navigation links --> </p>
+<hr>
+<p><b>Up:</b>
+<a href="http://www.qhull.org">Home page for
+Qhull</a> <br>
+<b>Up:</b> <a href="../../html/index.htm#TOC">Qhull manual: Table of Contents</a> <br>
+<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a>
+&#149; <a href="../../html/qh-quick.htm#options">Options</a>
+&#149; <a href="../../html/qh-opto.htm#output">Output</a>
+&#149; <a href="../../html/qh-optf.htm#format">Formats</a>
+&#149; <a href="../../html/qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="../../html/qh-optp.htm#print">Print</a>
+&#149; <a href="../../html/qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="../../html/qh-optc.htm#prec">Precision</a>
+&#149; <a href="../../html/qh-optt.htm#trace">Trace</a>
+&#149; <a href="index.htm">Functions</a><br>
+<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code: Table of Contents</a> <br>
+<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
+<b>To:</b> <a href="qh-geom.htm">Geom</a> &#149;
+<a href="qh-globa.htm">Global</a> &#149; <a href="qh-io.htm">Io</a>
+&#149; <a href="qh-mem.htm">Mem</a> &#149; <a href="qh-merge.htm">Merge</a>
+&#149; <a href="qh-poly.htm">Poly</a> &#149; <a href="qh-qhull.htm#TOC">Qhull</a>
+&#149; <a href="qh-set.htm">Set</a> &#149; <a href="qh-stat.htm">Stat</a>
+&#149; <a href="qh-user.htm">User</a><br>
+</p>
+<p><!-- GC common information --> </p>
+<hr>
+<p><a href="http://www.geom.uiuc.edu/"><img
+src="../../html/qh--geom.gif" align="middle" width="40" height="40"></a><i>The
+Geometry Center Home Page </i></p>
+<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
+</a><br>
+Created: May 2, 1997 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
+</body>
+</html>
diff --git a/xs/src/qhull/src/libqhull/qh-user.htm b/xs/src/qhull/src/libqhull/qh-user.htm
new file mode 100644
index 0000000000..6682f4b2fb
--- /dev/null
+++ b/xs/src/qhull/src/libqhull/qh-user.htm
@@ -0,0 +1,271 @@
+<!-- Do not edit with Front Page, it adds too many spaces -->
+<html>
+<head>
+<meta http-equiv="Content-Type"
+content="text/html; charset=iso-8859-1">
+<title>user.c -- user-definable operations</title>
+</head>
+
+<body>
+<!-- Navigation links -->
+<p><a name="TOP"><b>Up:</b></a> <a
+href="http://www.qhull.org">Home page</a> for Qhull<br>
+<b>Up:</b> <a href="../../html/index.htm#TOC">Qhull manual</a>: Table of Contents <br>
+<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a>
+&#149; <a href="../../html/qh-quick.htm#options">Options</a>
+&#149; <a href="../../html/qh-opto.htm#output">Output</a>
+&#149; <a href="../../html/qh-optf.htm#format">Formats</a>
+&#149; <a href="../../html/qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="../../html/qh-optp.htm#print">Print</a>
+&#149; <a href="../../html/qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="../../html/qh-optc.htm#prec">Precision</a>
+&#149; <a href="../../html/qh-optt.htm#trace">Trace</a>
+&#149; <a href="index.htm">Functions</a><br>
+<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code: Table of Contents</a><br>
+<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
+<b>To:</b> <a href="qh-geom.htm">Geom</a> &#149; <a href="qh-globa.htm">Global</a>
+&#149; <a href="qh-io.htm">Io</a> &#149; <a href="qh-mem.htm">Mem</a>
+&#149; <a href="qh-merge.htm">Merge</a> &#149; <a href="qh-poly.htm">Poly</a>
+&#149; <a href="qh-qhull.htm">Qhull</a> &#149; <a href="qh-set.htm">Set</a>
+&#149; <a href="qh-stat.htm">Stat</a> &#149; <a href="qh-user.htm#TOC">User</a>
+</p>
+<hr>
+<h2>user.c -- user-definable operations</h2>
+<blockquote>
+<p>This section contains functions and constants that the
+user may want to change. </p>
+
+</blockquote>
+<p><b>Copyright &copy; 1995-2015 C.B. Barber</b></p>
+<hr>
+<p><a href="#TOP">&#187;</a> <a href="qh-geom.htm#TOC">Geom</a>
+<a name="TOC">&#149;</a> <a href="qh-globa.htm#TOC">Global</a>
+&#149; <a href="qh-io.htm#TOC">Io</a> &#149; <a href="qh-mem.htm#TOC">Mem</a>
+&#149; <a href="qh-merge.htm#TOC">Merge</a> &#149; <a href="qh-poly.htm#TOC">Poly</a>
+&#149; <a href="qh-qhull.htm#TOC">Qhull</a> &#149; <a href="qh-set.htm#TOC">Set</a>
+&#149; <a href="qh-stat.htm#TOC">Stat</a> &#149; <b>User</b>
+</p>
+<h3>Index to <a href="user.c">user.c</a>, <a href="usermem.c">usermem.c</a>, <a href="userprintf.c">userprintf.c</a>, <a href="userprintf_rbox.c">userprintf_rbox.c</a> and
+<a href="user.h">user.h</a></h3>
+<ul>
+<li><a href="#qulllib">qhull library constants</a></li>
+<li><a href="#utype">user.h data types and
+configuration macros</a> </li>
+<li><a href="#ujoggle">joggle constants</a></li>
+<li><a href="#uperform">performance related constants</a></li>
+<li><a href="#umemory">memory constants</a></li>
+<li><a href="#ucond">conditional compilation</a></li>
+<li><a href="#umerge">merge constants</a> </li>
+<li><a href="#ufunc">user.c functions</a> </li>
+<li><a href="#u2func">usermem.c functions</a> </li>
+<li><a href="#u3func">userprintf.c functions</a> </li>
+</ul>
+
+<h3><a href="qh-user.htm#TOC">&#187;</a><a name="qulllib">Qhull library constants</a></h3>
+<ul>
+<li><a href="user.h#filenamelen">FILENAMElen</a> -- max length of TI or TO filename </li>
+<li><a href="user.h#msgcode">msgcode</a> -- unique message codes for qh_fprintf </li>
+<li><a href="user.h#qh_OPTIONline">qh_OPTIONline</a> -- max length of option line ('FO')</li>
+</ul>
+
+
+<h3><a href="qh-user.htm#TOC">&#187;</a><a name="utype">user.h data
+types and configuration macros</a></h3>
+<ul>
+<li><a href="user.h#realT">realT, qh_REAL...</a> size
+of floating point numbers </li>
+<li><a href="user.h#countT">countT, COUNTmax</a> size
+of counts and identifiers, typically 'int' or 'long long' </li>
+<li><a href="user.h#CPUclock">qh_CPUclock</a> clock()
+function for reporting the total time spent by
+Qhull </li>
+<li><a href="user.h#RANDOM">qh_RANDOM...</a> random
+number generator </li>
+</ul>
+
+<h3><a href="qh-user.htm#TOC">&#187;</a><a name="udef">definition constants</a></h3>
+<ul>
+<li><a href="user.h#DEFAULTbox">qh_DEFAULTbox</a>
+define default box size for rbox, 'Qbb', and 'QbB' (Geomview expects 0.5) </li>
+<li><a href="user.h#INFINITE">qh_INFINITE</a> on
+output, indicates Voronoi center at infinity </li>
+<li><a href="user.h#ORIENTclock">qh_ORIENTclock</a>
+define convention for orienting facets</li>
+<li><a href="user.h#ZEROdelaunay">qh_ZEROdelaunay</a>
+define facets that are ignored in Delaunay triangulations</li>
+</ul>
+
+<h3><a href="qh-user.htm#TOC">&#187;</a><a name="ujoggle">joggle constants</a></h3>
+<ul>
+<li><a href="user.h#JOGGLEagain">qh_JOGGLEagain</a>
+how often to retry before using qh_JOGGLEmaxincrease
+again </li>
+<li><a href="user.h#JOGGLEdefault">qh_JOGGLEdefault</a>
+default value for qh.JOGGLEmax for 'QP' </li>
+<li><a href="user.h#JOGGLEincrease">qh_JOGGLEincrease</a>
+factor to increase qh.JOGGLEmax on retrys for
+'QPn' </li>
+<li><a href="user.h#JOGGLEmaxincrease">qh_JOGGLEmaxincrease</a> max
+for increasing qh.JOGGLEmax relative to
+qh.MAXwidth </li>
+<li><a href="user.h#JOGGLEretry">qh_JOGGLEmaxretry</a>
+report error if this many retries </li>
+<li><a href="user.h#JOGGLEretry">qh_JOGGLEretry</a>
+how often to retry before using qh_JOGGLEmax </li>
+</ul>
+
+<h3><a href="qh-user.htm#TOC">&#187;</a><a name="uperform">performance
+related constants</a></h3>
+<ul>
+<li><a href="user.h#HASHfactor">qh_HASHfactor</a>
+total/used hash slots </li>
+<li><a href="user.h#INITIALmax">qh_INITIALmax</a> if
+dim &gt;= qh_INITIALmax, use min/max coordinate
+points for initial simplex </li>
+<li><a href="user.h#INITIALsearch">qh_INITIALsearch</a>
+if qh.INITIALmax, search points up to this
+dimension </li>
+<li><a href="user.h#NOtrace">qh_NOtrace</a> disallow
+tracing </li>
+<li><a href="user.h#VERIFYdirect">qh_VERIFYdirect</a>
+'Tv' verifies all <em>points X facets</em> if op
+count is smaller </li>
+</ul>
+
+<h3><a href="qh-user.htm#TOC">&#187;</a><a name="umemory">memory constants</a></h3>
+<ul>
+<li><a href="user.h#MEMalign">qh_MEMalign</a> memory
+alignment for qh_meminitbuffers() in global.c </li>
+<li><a href="user.h#MEMbufsize">qh_MEMbufsize</a>
+size of additional memory buffers </li>
+<li><a href="user.h#MEMinitbuf">qh_MEMinitbuf</a>
+size of initial memory buffer </li>
+</ul>
+
+<h3><a href="qh-user.htm#TOC">&#187;</a><a name="ucond">conditional compilation</a></h3>
+<ul>
+<li><a href="user.h#compiler">compiler</a> defined symbols,
+e.g., _STDC_ and _cplusplus
+
+<li><a href="user.h#COMPUTEfurthest">qh_COMPUTEfurthest</a>
+    compute furthest distance to an outside point instead of storing it with the facet
+<li><a href="user.h#KEEPstatistics">qh_KEEPstatistics</a>
+    enable statistic gathering and reporting with option 'Ts'
+<li><a href="user.h#MAXoutside">qh_MAXoutside</a>
+record outer plane for each facet
+<li><a href="user.h#NOmerge">qh_NOmerge</a>
+disable facet merging
+<li><a href="user.h#NOtrace">qh_NOtrace</a>
+disable tracing with option 'T4'
+<li><a href="user.h#QHpointer">qh_QHpointer</a>
+access global data with pointer or static structure
+<li><a href="user.h#QUICKhelp">qh_QUICKhelp</a>
+use abbreviated help messages, e.g., for degenerate inputs
+</ul>
+
+<h3><a href="qh-user.htm#TOC">&#187;</a><a name="umerge">merge
+constants</a></h3>
+<ul>
+<li><a href="user.h#BESTcentrum">qh_BESTcentrum</a>
+when does qh_findbestneighbor() test centrums? </li>
+<li><a href="user.h#BESTnonconvex">qh_BESTnonconvex</a>
+when does qh_findbestneighbor() test nonconvex
+ridges only? </li>
+<li><a href="user.h#COPLANARratio">qh_COPLANARratio</a>
+what is qh.MINvisible? </li>
+<li><a href="user.h#DIMreduceBuild">qh_DIMreduceBuild</a>
+max dimension for vertex reduction </li>
+<li><a href="user.h#DIMmergeVertex">qh_DIMmergeVertex</a>
+max dimension for vertex merging </li>
+<li><a href="user.h#DISToutside">qh_DISToutside</a>
+when is a point clearly outside of a facet for qh_findbestnew and qh_partitionall</li>
+<li><a href="user.h#MAXnarrow">qh_MAXnarrow</a> max.
+cosine for qh.NARROWhull </li>
+<li><a href="user.h#MAXnewcentrum">qh_MAXnewcentrum</a>
+when does qh_reducevertices_centrum() reset the
+centrum? </li>
+<li><a href="user.h#MAXnewmerges">qh_MAXnewmerges</a>
+when does qh_merge_nonconvex() call
+qh_reducevertices_centrums? </li>
+<li><a href="user.h#RATIOnearinside">qh_RATIOnearinside</a>
+ratio for retaining inside points for
+qh_check_maxout() </li>
+<li><a href="user.h#SEARCHdist">qh_SEARCHdist</a>
+when is facet coplanar with the best facet for qh_findbesthorizon</li>
+<li><a href="user.h#USEfindbestnew">qh_USEfindbestnew</a>
+when to use qh_findbestnew for qh_partitionpoint()</li>
+<li><a href="user.h#WARNnarrow">qh_WARNnarrow</a>
+max. cosine to warn about qh.NARROWhull </li>
+<li><a href="user.h#WIDEcoplanar">qh_WIDEcoplanar</a>
+what is a wide facet? </li>
+<li><a href="user.h#WIDEduplicate">qh_WIDEduplicate</a>
+what is a wide ratio on merging duplicate ridges? </li>
+</ul>
+
+<h3><a href="qh-user.htm#TOC">&#187;</a><a name="ufunc">user.c
+functions</a></h3>
+<ul>
+<li><a href="user.c#qhull_template">Qhull template</a> for calling qh_new_qhull from your program</li>
+<li><a href="user.c#errexit">qh_errexit</a> report
+error and exit qhull()</li>
+<li><a href="user.c#errprint">qh_errprint</a> print
+information about facets and ridges </li>
+<li><a href="user.c#new_qhull">qh_new_qhull</a> call qhull on an array
+of points</li>
+<li><a href="user.c#printfacetlist">qh_printfacetlist</a>
+print all fields of all facets </li>
+</ul>
+
+<h3><a href="qh-user.htm#TOC">&#187;</a><a name="u2func">usermem.c
+functions</a></h3>
+<ul>
+<li><a href="usermem.c#qh_exit">qh_exit</a> exit program, same as exit().  May be redefined as throw "QH10003.." by libqhullcpp/usermem_r-cpp.cpp</li>
+<li><a href="usermem.c#qh_fprintf_stderr">qh_fprintf_stderr</a> print to stderr when qh.ferr is not defined.</li>
+<li><a href="usermem.c#qh_free">qh_free</a> free memory, same as free().</li>
+<li><a href="usermem.c#qh_malloc">qh_malloc</a> allocate memory, same as malloc()</li>
+</ul>
+
+<h3><a href="qh-user.htm#TOC">&#187;</a><a name="u3func">userprintf.c
+ and userprintf_rbox,c functions</a></h3>
+<ul>
+<li><a href="userprintf.c#qh_fprintf">qh_fprintf</a> print
+information from Qhull, sames as fprintf(). </li>
+<li><a href="userprintf_rbox.c#qh_fprintf_rbox">qh_fprintf_rbox</a> print
+information from Rbox, sames as fprintf(). </li>
+</ul>
+
+<p><!-- Navigation links --> </p>
+<hr>
+<p><b>Up:</b>
+<a href="http://www.qhull.org">Home page for
+Qhull</a> <br>
+<b>Up:</b> <a href="../../html/index.htm#TOC">Qhull manual: Table of Contents</a> <br>
+<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a>
+&#149; <a href="../../html/qh-quick.htm#options">Options</a>
+&#149; <a href="../../html/qh-opto.htm#output">Output</a>
+&#149; <a href="../../html/qh-optf.htm#format">Formats</a>
+&#149; <a href="../../html/qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="../../html/qh-optp.htm#print">Print</a>
+&#149; <a href="../../html/qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="../../html/qh-optc.htm#prec">Precision</a>
+&#149; <a href="../../html/qh-optt.htm#trace">Trace</a>
+&#149; <a href="index.htm">Functions</a><br>
+<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code: Table of Contents</a> <br>
+<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
+<b>To:</b> <a href="qh-geom.htm">Geom</a> &#149;
+<a href="qh-globa.htm">Global</a> &#149; <a href="qh-io.htm">Io</a>
+&#149; <a href="qh-mem.htm">Mem</a> &#149; <a href="qh-merge.htm">Merge</a>
+&#149; <a href="qh-poly.htm">Poly</a> &#149; <a href="qh-qhull.htm#TOC">Qhull</a>
+&#149; <a href="qh-set.htm">Set</a> &#149; <a href="qh-stat.htm">Stat</a>
+&#149; <a href="qh-user.htm">User</a><br>
+</p>
+<p><!-- GC common information --> </p>
+<hr>
+<p><a href="http://www.geom.uiuc.edu/"><img
+src="../../html/qh--geom.gif" align="middle" width="40" height="40"></a><i>The
+Geometry Center Home Page </i></p>
+<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
+</a><br>
+Created: May 2, 1997 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
+</body>
+</html>
diff --git a/xs/src/qhull/src/libqhull/qhull-exports.def b/xs/src/qhull/src/libqhull/qhull-exports.def
new file mode 100644
index 0000000000..11a42b57ee
--- /dev/null
+++ b/xs/src/qhull/src/libqhull/qhull-exports.def
@@ -0,0 +1,417 @@
+; qhull-exports.def -- msvc module-definition file
+;
+;   Generated from depends.exe by cut-and-paste of exported symbols by mingw gcc
+;   [mar'11] 399 symbols 
+;   Annotate as DATA qh_last_random qh_qh qh_qhstat qhmem rbox rbox_inuse
+;   Annotate as __declspec for outside access in win32 -- qh_qh qh_qhstat
+;   Same as ../libqhullp/qhull_p-exports.def without qh_save_qhull and qh_restore_qhull
+;
+; $Id: //main/2015/qhull/src/libqhull/qhull-exports.def#3 $$Change: 2047 $
+; $DateTime: 2016/01/04 22:03:18 $$Author: bbarber $
+; 
+; Define qhull_VERSION in CMakeLists.txt, Makefile, qhull-exports.def, qhull_p-exports.def, qhull_r-exports.def, and qhull-warn.pri
+VERSION 7.0
+EXPORTS
+qh_addhash
+qh_addpoint
+qh_all_merges
+qh_allstatA
+qh_allstatB
+qh_allstatC
+qh_allstatD
+qh_allstatE
+qh_allstatE2
+qh_allstatF
+qh_allstatG
+qh_allstatH
+qh_allstatI
+qh_allstatistics
+qh_appendfacet
+qh_appendmergeset
+qh_appendprint
+qh_appendvertex
+qh_argv_to_command
+qh_argv_to_command_size
+qh_attachnewfacets
+qh_backnormal
+qh_basevertices
+qh_build_withrestart
+qh_buildhull
+qh_buildtracing
+qh_check_bestdist
+qh_check_dupridge
+qh_check_maxout
+qh_check_output
+qh_check_point
+qh_check_points
+qh_checkconnect
+qh_checkconvex
+qh_checkfacet
+qh_checkflags
+qh_checkflipped
+qh_checkflipped_all
+qh_checkpolygon
+qh_checkvertex
+qh_checkzero
+qh_clear_outputflags
+qh_clearcenters
+qh_clock
+qh_collectstatistics
+qh_compare_facetarea
+qh_compare_facetmerge
+qh_compare_facetvisit
+qh_compare_vertexpoint
+qh_compareangle
+qh_comparemerge
+qh_comparevisit
+qh_copyfilename
+qh_copynonconvex
+qh_copypoints
+qh_countfacets
+qh_createsimplex
+qh_crossproduct
+qh_degen_redundant_facet
+qh_degen_redundant_neighbors
+qh_deletevisible
+qh_delfacet
+qh_delridge
+qh_delvertex
+qh_determinant
+qh_detjoggle
+qh_detroundoff
+qh_detsimplex
+qh_detvnorm
+qh_detvridge
+qh_detvridge3
+qh_dfacet
+qh_distnorm
+qh_distplane
+qh_distround
+qh_divzero
+qh_dvertex
+qh_eachvoronoi
+qh_eachvoronoi_all
+qh_errexit
+qh_errexit2
+qh_errexit_rbox
+qh_errprint
+qh_exit
+qh_facet2point
+qh_facet3vertex
+qh_facetarea
+qh_facetarea_simplex
+qh_facetcenter
+qh_facetintersect
+qh_facetvertices
+qh_find_newvertex
+qh_findbest
+qh_findbest_test
+qh_findbestfacet
+qh_findbesthorizon
+qh_findbestlower
+qh_findbestneighbor
+qh_findbestnew
+qh_findfacet_all
+qh_findgood
+qh_findgood_all
+qh_findgooddist
+qh_findhorizon
+qh_flippedmerges
+qh_forcedmerges
+qh_fprintf
+qh_fprintf_rbox
+qh_fprintf_stderr
+qh_free
+qh_freebuffers
+qh_freebuild
+qh_freeqhull
+qh_freeqhull2
+qh_freestatistics
+qh_furthestnext
+qh_furthestout
+qh_gausselim
+qh_geomplanes
+qh_getangle
+qh_getarea
+qh_getcenter
+qh_getcentrum
+qh_getdistance
+qh_gethash
+qh_getmergeset
+qh_getmergeset_initial
+qh_gram_schmidt
+qh_hashridge
+qh_hashridge_find
+qh_infiniteloop
+qh_init_A
+qh_init_B
+qh_init_qhull_command
+qh_initbuild
+qh_initflags
+qh_initialhull
+qh_initialvertices
+qh_initqhull_buffers
+qh_initqhull_globals
+qh_initqhull_mem
+qh_initqhull_outputflags
+qh_initqhull_start
+qh_initqhull_start2
+qh_initstatistics
+qh_initthresholds
+qh_inthresholds
+qh_isvertex
+qh_joggleinput
+; Mark as DATA, otherwise links a separate qh_last_random.  No __declspec.
+qh_last_random      DATA
+qh_lib_check
+qh_makenew_nonsimplicial
+qh_makenew_simplicial
+qh_makenewfacet
+qh_makenewfacets
+qh_makenewplanes
+qh_makeridges
+qh_malloc
+qh_mark_dupridges
+qh_markkeep
+qh_markvoronoi
+qh_matchduplicates
+qh_matchneighbor
+qh_matchnewfacets
+qh_matchvertices
+qh_maxabsval
+qh_maxmin
+qh_maxouter
+qh_maxsimplex
+qh_maydropneighbor
+qh_memalloc
+qh_memfree
+qh_memfreeshort
+qh_meminit
+qh_meminitbuffers
+qh_memsetup
+qh_memsize
+qh_memstatistics
+qh_memtotal
+qh_merge_degenredundant
+qh_merge_nonconvex
+qh_mergecycle
+qh_mergecycle_all
+qh_mergecycle_facets
+qh_mergecycle_neighbors
+qh_mergecycle_ridges
+qh_mergecycle_vneighbors
+qh_mergefacet
+qh_mergefacet2d
+qh_mergeneighbors
+qh_mergeridges
+qh_mergesimplex
+qh_mergevertex_del
+qh_mergevertex_neighbors
+qh_mergevertices
+qh_minabsval
+qh_mindiff
+qh_nearcoplanar
+qh_nearvertex
+qh_neighbor_intersections
+qh_new_qhull
+qh_newfacet
+qh_newhashtable
+qh_newridge
+qh_newstats
+qh_newvertex
+qh_newvertices
+qh_nextfurthest
+qh_nextridge3d
+qh_normalize
+qh_normalize2
+qh_nostatistic
+qh_option
+qh_order_vertexneighbors
+qh_orientoutside
+qh_out1
+qh_out2n
+qh_out3n
+qh_outcoplanar
+qh_outerinner
+qh_partitionall
+qh_partitioncoplanar
+qh_partitionpoint
+qh_partitionvisible
+qh_point
+qh_point_add
+qh_pointdist
+qh_pointfacet
+qh_pointid
+qh_pointvertex
+qh_postmerge
+qh_precision
+qh_premerge
+qh_prepare_output
+qh_prependfacet
+qh_printafacet
+qh_printallstatistics
+qh_printbegin
+qh_printcenter
+qh_printcentrum
+qh_printend
+qh_printend4geom
+qh_printextremes
+qh_printextremes_2d
+qh_printextremes_d
+qh_printfacet
+qh_printfacet2geom
+qh_printfacet2geom_points
+qh_printfacet2math
+qh_printfacet3geom_nonsimplicial
+qh_printfacet3geom_points
+qh_printfacet3geom_simplicial
+qh_printfacet3math
+qh_printfacet3vertex
+qh_printfacet4geom_nonsimplicial
+qh_printfacet4geom_simplicial
+qh_printfacetNvertex_nonsimplicial
+qh_printfacetNvertex_simplicial
+qh_printfacetheader
+qh_printfacetlist
+qh_printfacetridges
+qh_printfacets
+qh_printhashtable
+qh_printhelp_degenerate
+qh_printhelp_narrowhull
+qh_printhelp_singular
+qh_printhyperplaneintersection
+qh_printline3geom
+qh_printlists
+qh_printmatrix
+qh_printneighborhood
+qh_printpoint
+qh_printpoint3
+qh_printpointid
+qh_printpoints
+qh_printpoints_out
+qh_printpointvect
+qh_printpointvect2
+qh_printridge
+qh_printspheres
+qh_printstatistics
+qh_printstatlevel
+qh_printstats
+qh_printsummary
+qh_printvdiagram
+qh_printvdiagram2
+qh_printvertex
+qh_printvertexlist
+qh_printvertices
+qh_printvneighbors
+qh_printvnorm
+qh_printvoronoi
+qh_printvridge
+qh_produce_output
+qh_produce_output2
+qh_projectdim3
+qh_projectinput
+qh_projectpoint
+qh_projectpoints
+; Mark as DATA, otherwise links a separate qh_qh.  qh_qh and qh_qhstat requires __declspec
+qh_qh               DATA
+qh_qhstat           DATA
+qh_qhull
+qh_rand
+qh_randomfactor
+qh_randommatrix
+qh_rboxpoints
+qh_readfeasible
+qh_readpoints
+qh_reducevertices
+qh_redundant_vertex
+qh_remove_extravertices
+qh_removefacet
+qh_removevertex
+qh_rename_sharedvertex
+qh_renameridgevertex
+qh_renamevertex
+qh_resetlists
+qh_rotateinput
+qh_rotatepoints
+qh_roundi
+qh_scaleinput
+qh_scalelast
+qh_scalepoints
+qh_setaddnth
+qh_setaddsorted
+qh_setappend
+qh_setappend2ndlast
+qh_setappend_set
+qh_setcheck
+qh_setcompact
+qh_setcopy
+qh_setdel
+qh_setdelaunay
+qh_setdellast
+qh_setdelnth
+qh_setdelnthsorted
+qh_setdelsorted
+qh_setduplicate
+qh_setequal
+qh_setequal_except
+qh_setequal_skip
+qh_setfacetplane
+qh_setfeasible
+qh_setfree
+qh_setfree2
+qh_setfreelong
+qh_sethalfspace
+qh_sethalfspace_all
+qh_sethyperplane_det
+qh_sethyperplane_gauss
+qh_setin
+qh_setindex
+qh_setlarger
+qh_setlast
+qh_setnew
+qh_setnew_delnthsorted
+qh_setprint
+qh_setreplace
+qh_setsize
+qh_settemp
+qh_settempfree
+qh_settempfree_all
+qh_settemppop
+qh_settemppush
+qh_settruncate
+qh_setunique
+qh_setvoronoi_all
+qh_setzero
+qh_sharpnewfacets
+qh_skipfacet
+qh_skipfilename
+qh_srand
+qh_stddev
+qh_strtod
+qh_strtol
+qh_test_appendmerge
+qh_test_vneighbors
+qh_tracemerge
+qh_tracemerging
+qh_triangulate
+qh_triangulate_facet
+qh_triangulate_link
+qh_triangulate_mirror
+qh_triangulate_null
+qh_updatetested
+qh_updatevertices
+qh_user_memsizes
+qh_version
+qh_version2
+qh_vertexintersect
+qh_vertexintersect_new
+qh_vertexneighbors
+qh_vertexridges
+qh_vertexridges_facet
+qh_vertexsubset
+qh_voronoi_center
+qh_willdelete
+; Mark as DATA, otherwise links a separate qhmem.  No __declspec
+qhmem                   DATA
+rbox			DATA
+rbox_inuse              DATA
diff --git a/xs/src/qhull/src/libqhull/qhull_a.h b/xs/src/qhull/src/libqhull/qhull_a.h
new file mode 100644
index 0000000000..729b723276
--- /dev/null
+++ b/xs/src/qhull/src/libqhull/qhull_a.h
@@ -0,0 +1,150 @@
+/*<html><pre>  -<a                             href="qh-qhull.htm"
+  >-------------------------------</a><a name="TOP">-</a>
+
+   qhull_a.h
+   all header files for compiling qhull with non-reentrant code
+   included before C++ headers for user_r.h:QHULL_CRTDBG
+
+   see qh-qhull.htm
+
+   see libqhull.h for user-level definitions
+
+   see user.h for user-definable constants
+
+   defines internal functions for libqhull.c global.c
+
+   Copyright (c) 1993-2015 The Geometry Center.
+   $Id: //main/2015/qhull/src/libqhull/qhull_a.h#4 $$Change: 2064 $
+   $DateTime: 2016/01/18 12:36:08 $$Author: bbarber $
+
+   Notes:  grep for ((" and (" to catch fprintf("lkasdjf");
+           full parens around (x?y:z)
+           use '#include "libqhull/qhull_a.h"' to avoid name clashes
+*/
+
+#ifndef qhDEFqhulla
+#define qhDEFqhulla 1
+
+#include "libqhull.h"  /* Includes user_r.h and data types */
+
+#include "stat.h"
+#include "random.h"
+#include "mem.h"
+#include "qset.h"
+#include "geom.h"
+#include "merge.h"
+#include "poly.h"
+#include "io.h"
+
+#include <setjmp.h>
+#include <string.h>
+#include <math.h>
+#include <float.h>    /* some compilers will not need float.h */
+#include <limits.h>
+#include <time.h>
+#include <ctype.h>
+#include <stdio.h>
+#include <stdlib.h>
+/*** uncomment here and qset.c
+     if string.h does not define memcpy()
+#include <memory.h>
+*/
+
+#if qh_CLOCKtype == 2  /* defined in user.h from libqhull.h */
+#include <sys/types.h>
+#include <sys/times.h>
+#include <unistd.h>
+#endif
+
+#ifdef _MSC_VER  /* Microsoft Visual C++ -- warning level 4 */
+#pragma warning( disable : 4100)  /* unreferenced formal parameter */
+#pragma warning( disable : 4127)  /* conditional expression is constant */
+#pragma warning( disable : 4706)  /* assignment within conditional function */
+#pragma warning( disable : 4996)  /* function was declared deprecated(strcpy, localtime, etc.) */
+#endif
+
+/* ======= -macros- =========== */
+
+/*-<a                             href="qh-qhull.htm#TOC"
+  >--------------------------------</a><a name="traceN">-</a>
+
+  traceN((qh ferr, 0Nnnn, "format\n", vars));
+    calls qh_fprintf if qh.IStracing >= N
+
+    Add debugging traps to the end of qh_fprintf
+
+  notes:
+    removing tracing reduces code size but doesn't change execution speed
+*/
+#ifndef qh_NOtrace
+#define trace0(args) {if (qh IStracing) qh_fprintf args;}
+#define trace1(args) {if (qh IStracing >= 1) qh_fprintf args;}
+#define trace2(args) {if (qh IStracing >= 2) qh_fprintf args;}
+#define trace3(args) {if (qh IStracing >= 3) qh_fprintf args;}
+#define trace4(args) {if (qh IStracing >= 4) qh_fprintf args;}
+#define trace5(args) {if (qh IStracing >= 5) qh_fprintf args;}
+#else /* qh_NOtrace */
+#define trace0(args) {}
+#define trace1(args) {}
+#define trace2(args) {}
+#define trace3(args) {}
+#define trace4(args) {}
+#define trace5(args) {}
+#endif /* qh_NOtrace */
+
+/*-<a                             href="qh-qhull.htm#TOC"
+  >--------------------------------</a><a name="QHULL_UNUSED">-</a>
+
+  Define an unused variable to avoid compiler warnings
+
+  Derived from Qt's corelib/global/qglobal.h
+
+*/
+
+#if defined(__cplusplus) && defined(__INTEL_COMPILER) && !defined(QHULL_OS_WIN)
+template <typename T>
+inline void qhullUnused(T &x) { (void)x; }
+#  define QHULL_UNUSED(x) qhullUnused(x);
+#else
+#  define QHULL_UNUSED(x) (void)x;
+#endif
+
+/***** -libqhull.c prototypes (alphabetical after qhull) ********************/
+
+void    qh_qhull(void);
+boolT   qh_addpoint(pointT *furthest, facetT *facet, boolT checkdist);
+void    qh_buildhull(void);
+void    qh_buildtracing(pointT *furthest, facetT *facet);
+void    qh_build_withrestart(void);
+void    qh_errexit2(int exitcode, facetT *facet, facetT *otherfacet);
+void    qh_findhorizon(pointT *point, facetT *facet, int *goodvisible,int *goodhorizon);
+pointT *qh_nextfurthest(facetT **visible);
+void    qh_partitionall(setT *vertices, pointT *points,int npoints);
+void    qh_partitioncoplanar(pointT *point, facetT *facet, realT *dist);
+void    qh_partitionpoint(pointT *point, facetT *facet);
+void    qh_partitionvisible(boolT allpoints, int *numpoints);
+void    qh_precision(const char *reason);
+void    qh_printsummary(FILE *fp);
+
+/***** -global.c internal prototypes (alphabetical) ***********************/
+
+void    qh_appendprint(qh_PRINT format);
+void    qh_freebuild(boolT allmem);
+void    qh_freebuffers(void);
+void    qh_initbuffers(coordT *points, int numpoints, int dim, boolT ismalloc);
+
+/***** -stat.c internal prototypes (alphabetical) ***********************/
+
+void    qh_allstatA(void);
+void    qh_allstatB(void);
+void    qh_allstatC(void);
+void    qh_allstatD(void);
+void    qh_allstatE(void);
+void    qh_allstatE2(void);
+void    qh_allstatF(void);
+void    qh_allstatG(void);
+void    qh_allstatH(void);
+void    qh_freebuffers(void);
+void    qh_initbuffers(coordT *points, int numpoints, int dim, boolT ismalloc);
+
+#endif /* qhDEFqhulla */
diff --git a/xs/src/qhull/src/libqhull/qhull_p-exports.def b/xs/src/qhull/src/libqhull/qhull_p-exports.def
new file mode 100644
index 0000000000..cadf8a4fa2
--- /dev/null
+++ b/xs/src/qhull/src/libqhull/qhull_p-exports.def
@@ -0,0 +1,418 @@
+; qhull_p-exports.def -- msvc module-definition file
+;
+;   Generated from depends.exe by cut-and-paste of exported symbols by mingw gcc
+;   [mar'11] 399 symbols [jan'15] added 3 symbols
+;   Annotate as DATA qh_last_random qh_qh qh_qhstat qhmem rbox rbox_inuse
+;   Annotate as __declspec for outside access in win32 -- qh_qh qh_qhstat
+;
+; $Id: //main/2011/qhull/src/libqhull/qhull-exports.def#2 $$Change: 1368 $
+; $DateTime: 2011/04/16 08:12:32 $$Author: bbarber $
+;
+; Define qhull_VERSION in CMakeLists.txt, Makefile, qhull-exports.def, qhull_p-exports.def, qhull_r-exports.def, and qhull-warn.pri
+VERSION 7.0
+EXPORTS
+qh_addhash
+qh_addpoint
+qh_all_merges
+qh_allstatA
+qh_allstatB
+qh_allstatC
+qh_allstatD
+qh_allstatE
+qh_allstatE2
+qh_allstatF
+qh_allstatG
+qh_allstatH
+qh_allstatI
+qh_allstatistics
+qh_appendfacet
+qh_appendmergeset
+qh_appendprint
+qh_appendvertex
+qh_argv_to_command
+qh_argv_to_command_size
+qh_attachnewfacets
+qh_backnormal
+qh_basevertices
+qh_build_withrestart
+qh_buildhull
+qh_buildtracing
+qh_check_bestdist
+qh_check_dupridge
+qh_check_maxout
+qh_check_output
+qh_check_point
+qh_check_points
+qh_checkconnect
+qh_checkconvex
+qh_checkfacet
+qh_checkflags
+qh_checkflipped
+qh_checkflipped_all
+qh_checkpolygon
+qh_checkvertex
+qh_checkzero
+qh_clear_outputflags
+qh_clearcenters
+qh_clock
+qh_collectstatistics
+qh_compare_facetarea
+qh_compare_facetmerge
+qh_compare_facetvisit
+qh_compare_vertexpoint
+qh_compareangle
+qh_comparemerge
+qh_comparevisit
+qh_copyfilename
+qh_copynonconvex
+qh_copypoints
+qh_countfacets
+qh_createsimplex
+qh_crossproduct
+qh_degen_redundant_facet
+qh_degen_redundant_neighbors
+qh_deletevisible
+qh_delfacet
+qh_delridge
+qh_delvertex
+qh_determinant
+qh_detjoggle
+qh_detroundoff
+qh_detsimplex
+qh_detvnorm
+qh_detvridge
+qh_detvridge3
+qh_dfacet
+qh_distnorm
+qh_distplane
+qh_distround
+qh_divzero
+qh_dvertex
+qh_eachvoronoi
+qh_eachvoronoi_all
+qh_errexit
+qh_errexit2
+qh_errexit_rbox
+qh_errprint
+qh_exit
+qh_facet2point
+qh_facet3vertex
+qh_facetarea
+qh_facetarea_simplex
+qh_facetcenter
+qh_facetintersect
+qh_facetvertices
+qh_find_newvertex
+qh_findbest
+qh_findbest_test
+qh_findbestfacet
+qh_findbesthorizon
+qh_findbestlower
+qh_findbestneighbor
+qh_findbestnew
+qh_findfacet_all
+qh_findgood
+qh_findgood_all
+qh_findgooddist
+qh_findhorizon
+qh_flippedmerges
+qh_forcedmerges
+qh_fprintf
+qh_fprintf_rbox
+qh_fprintf_stderr
+qh_free
+qh_freebuffers
+qh_freebuild
+qh_freeqhull
+qh_freeqhull2
+qh_freestatistics
+qh_furthestnext
+qh_furthestout
+qh_gausselim
+qh_geomplanes
+qh_getangle
+qh_getarea
+qh_getcenter
+qh_getcentrum
+qh_getdistance
+qh_gethash
+qh_getmergeset
+qh_getmergeset_initial
+qh_gram_schmidt
+qh_hashridge
+qh_hashridge_find
+qh_infiniteloop
+qh_init_A
+qh_init_B
+qh_init_qhull_command
+qh_initbuild
+qh_initflags
+qh_initialhull
+qh_initialvertices
+qh_initqhull_buffers
+qh_initqhull_globals
+qh_initqhull_mem
+qh_initqhull_outputflags
+qh_initqhull_start
+qh_initqhull_start2
+qh_initstatistics
+qh_initthresholds
+qh_inthresholds
+qh_isvertex
+qh_joggleinput
+; Mark as DATA, otherwise links a separate qh_last_random.  No __declspec.
+qh_last_random      DATA
+qh_lib_check
+qh_makenew_nonsimplicial
+qh_makenew_simplicial
+qh_makenewfacet
+qh_makenewfacets
+qh_makenewplanes
+qh_makeridges
+qh_malloc
+qh_mark_dupridges
+qh_markkeep
+qh_markvoronoi
+qh_matchduplicates
+qh_matchneighbor
+qh_matchnewfacets
+qh_matchvertices
+qh_maxabsval
+qh_maxmin
+qh_maxouter
+qh_maxsimplex
+qh_maydropneighbor
+qh_memalloc
+qh_memfree
+qh_memfreeshort
+qh_meminit
+qh_meminitbuffers
+qh_memsetup
+qh_memsize
+qh_memstatistics
+qh_memtotal
+qh_merge_degenredundant
+qh_merge_nonconvex
+qh_mergecycle
+qh_mergecycle_all
+qh_mergecycle_facets
+qh_mergecycle_neighbors
+qh_mergecycle_ridges
+qh_mergecycle_vneighbors
+qh_mergefacet
+qh_mergefacet2d
+qh_mergeneighbors
+qh_mergeridges
+qh_mergesimplex
+qh_mergevertex_del
+qh_mergevertex_neighbors
+qh_mergevertices
+qh_minabsval
+qh_mindiff
+qh_nearcoplanar
+qh_nearvertex
+qh_neighbor_intersections
+qh_new_qhull
+qh_newfacet
+qh_newhashtable
+qh_newridge
+qh_newstats
+qh_newvertex
+qh_newvertices
+qh_nextfurthest
+qh_nextridge3d
+qh_normalize
+qh_normalize2
+qh_nostatistic
+qh_option
+qh_order_vertexneighbors
+qh_orientoutside
+qh_out1
+qh_out2n
+qh_out3n
+qh_outcoplanar
+qh_outerinner
+qh_partitionall
+qh_partitioncoplanar
+qh_partitionpoint
+qh_partitionvisible
+qh_point
+qh_point_add
+qh_pointdist
+qh_pointfacet
+qh_pointid
+qh_pointvertex
+qh_postmerge
+qh_precision
+qh_premerge
+qh_prepare_output
+qh_prependfacet
+qh_printafacet
+qh_printallstatistics
+qh_printbegin
+qh_printcenter
+qh_printcentrum
+qh_printend
+qh_printend4geom
+qh_printextremes
+qh_printextremes_2d
+qh_printextremes_d
+qh_printfacet
+qh_printfacet2geom
+qh_printfacet2geom_points
+qh_printfacet2math
+qh_printfacet3geom_nonsimplicial
+qh_printfacet3geom_points
+qh_printfacet3geom_simplicial
+qh_printfacet3math
+qh_printfacet3vertex
+qh_printfacet4geom_nonsimplicial
+qh_printfacet4geom_simplicial
+qh_printfacetNvertex_nonsimplicial
+qh_printfacetNvertex_simplicial
+qh_printfacetheader
+qh_printfacetlist
+qh_printfacetridges
+qh_printfacets
+qh_printhashtable
+qh_printhelp_degenerate
+qh_printhelp_narrowhull
+qh_printhelp_singular
+qh_printhyperplaneintersection
+qh_printline3geom
+qh_printlists
+qh_printmatrix
+qh_printneighborhood
+qh_printpoint
+qh_printpoint3
+qh_printpointid
+qh_printpoints
+qh_printpoints_out
+qh_printpointvect
+qh_printpointvect2
+qh_printridge
+qh_printspheres
+qh_printstatistics
+qh_printstatlevel
+qh_printstats
+qh_printsummary
+qh_printvdiagram
+qh_printvdiagram2
+qh_printvertex
+qh_printvertexlist
+qh_printvertices
+qh_printvneighbors
+qh_printvnorm
+qh_printvoronoi
+qh_printvridge
+qh_produce_output
+qh_produce_output2
+qh_projectdim3
+qh_projectinput
+qh_projectpoint
+qh_projectpoints
+; Mark as DATA, otherwise links a separate qh_qh.  qh_qh and qh_qhstat requires __declspec
+qh_qh               DATA
+qh_qhstat           DATA
+qh_qhull
+qh_rand
+qh_randomfactor
+qh_randommatrix
+qh_rboxpoints
+qh_readfeasible
+qh_readpoints
+qh_reducevertices
+qh_redundant_vertex
+qh_remove_extravertices
+qh_removefacet
+qh_removevertex
+qh_rename_sharedvertex
+qh_renameridgevertex
+qh_renamevertex
+qh_resetlists
+qh_restore_qhull
+qh_rotateinput
+qh_rotatepoints
+qh_roundi
+qh_save_qhull
+qh_scaleinput
+qh_scalelast
+qh_scalepoints
+qh_setaddnth
+qh_setaddsorted
+qh_setappend
+qh_setappend2ndlast
+qh_setappend_set
+qh_setcheck
+qh_setcompact
+qh_setcopy
+qh_setdel
+qh_setdelaunay
+qh_setdellast
+qh_setdelnth
+qh_setdelnthsorted
+qh_setdelsorted
+qh_setduplicate
+qh_setequal
+qh_setequal_except
+qh_setequal_skip
+qh_setfacetplane
+qh_setfeasible
+qh_setfree
+qh_setfree2
+qh_setfreelong
+qh_sethalfspace
+qh_sethalfspace_all
+qh_sethyperplane_det
+qh_sethyperplane_gauss
+qh_setin
+qh_setindex
+qh_setlarger
+qh_setlast
+qh_setnew
+qh_setnew_delnthsorted
+qh_setprint
+qh_setreplace
+qh_setsize
+qh_settemp
+qh_settempfree
+qh_settempfree_all
+qh_settemppop
+qh_settemppush
+qh_settruncate
+qh_setunique
+qh_setvoronoi_all
+qh_setzero
+qh_sharpnewfacets
+qh_skipfacet
+qh_skipfilename
+qh_srand
+qh_stddev
+qh_strtod
+qh_strtol
+qh_test_appendmerge
+qh_test_vneighbors
+qh_tracemerge
+qh_tracemerging
+qh_triangulate
+qh_triangulate_facet
+qh_triangulate_link
+qh_triangulate_mirror
+qh_triangulate_null
+qh_updatetested
+qh_updatevertices
+qh_user_memsizes
+qh_version
+qh_version2
+qh_vertexintersect
+qh_vertexintersect_new
+qh_vertexneighbors
+qh_vertexridges
+qh_vertexridges_facet
+qh_vertexsubset
+qh_voronoi_center
+qh_willdelete
+; Mark as DATA, otherwise links a separate qhmem.  No __declspec
+qhmem                   DATA
+rbox			DATA
+rbox_inuse              DATA
diff --git a/xs/src/qhull/src/libqhull/qset.c b/xs/src/qhull/src/libqhull/qset.c
new file mode 100644
index 0000000000..a969252a75
--- /dev/null
+++ b/xs/src/qhull/src/libqhull/qset.c
@@ -0,0 +1,1340 @@
+/*<html><pre>  -<a                             href="qh-set.htm"
+  >-------------------------------</a><a name="TOP">-</a>
+
+   qset.c
+   implements set manipulations needed for quickhull
+
+   see qh-set.htm and qset.h
+
+   Be careful of strict aliasing (two pointers of different types
+   that reference the same location).  The last slot of a set is
+   either the actual size of the set plus 1, or the NULL terminator
+   of the set (i.e., setelemT).
+
+   Copyright (c) 1993-2015 The Geometry Center.
+   $Id: //main/2015/qhull/src/libqhull/qset.c#3 $$Change: 2062 $
+   $DateTime: 2016/01/17 13:13:18 $$Author: bbarber $
+*/
+
+#include "user.h" /* for QHULL_CRTDBG */
+#include "qset.h"
+#include "mem.h"
+#include <stdio.h>
+#include <string.h>
+/*** uncomment here and qhull_a.h
+     if string.h does not define memcpy()
+#include <memory.h>
+*/
+
+#ifndef qhDEFlibqhull
+typedef struct ridgeT ridgeT;
+typedef struct facetT facetT;
+void    qh_errexit(int exitcode, facetT *, ridgeT *);
+void    qh_fprintf(FILE *fp, int msgcode, const char *fmt, ... );
+#  ifdef _MSC_VER  /* Microsoft Visual C++ -- warning level 4 */
+#  pragma warning( disable : 4127)  /* conditional expression is constant */
+#  pragma warning( disable : 4706)  /* assignment within conditional function */
+#  endif
+#endif
+
+/*=============== internal macros ===========================*/
+
+/*============ functions in alphabetical order ===================*/
+
+/*-<a                             href="qh-set.htm#TOC"
+  >--------------------------------<a name="setaddnth">-</a>
+
+  qh_setaddnth( setp, nth, newelem)
+    adds newelem as n'th element of sorted or unsorted *setp
+
+  notes:
+    *setp and newelem must be defined
+    *setp may be a temp set
+    nth=0 is first element
+    errors if nth is out of bounds
+
+  design:
+    expand *setp if empty or full
+    move tail of *setp up one
+    insert newelem
+*/
+void qh_setaddnth(setT **setp, int nth, void *newelem) {
+  int oldsize, i;
+  setelemT *sizep;          /* avoid strict aliasing */
+  setelemT *oldp, *newp;
+
+  if (!*setp || (sizep= SETsizeaddr_(*setp))->i==0) {
+    qh_setlarger(setp);
+    sizep= SETsizeaddr_(*setp);
+  }
+  oldsize= sizep->i - 1;
+  if (nth < 0 || nth > oldsize) {
+    qh_fprintf(qhmem.ferr, 6171, "qhull internal error (qh_setaddnth): nth %d is out-of-bounds for set:\n", nth);
+    qh_setprint(qhmem.ferr, "", *setp);
+    qh_errexit(qhmem_ERRqhull, NULL, NULL);
+  }
+  sizep->i++;
+  oldp= (setelemT *)SETelemaddr_(*setp, oldsize, void);   /* NULL */
+  newp= oldp+1;
+  for (i=oldsize-nth+1; i--; )  /* move at least NULL  */
+    (newp--)->p= (oldp--)->p;       /* may overwrite *sizep */
+  newp->p= newelem;
+} /* setaddnth */
+
+
+/*-<a                              href="qh-set.htm#TOC"
+  >--------------------------------<a name="setaddsorted">-</a>
+
+  setaddsorted( setp, newelem )
+    adds an newelem into sorted *setp
+
+  notes:
+    *setp and newelem must be defined
+    *setp may be a temp set
+    nop if newelem already in set
+
+  design:
+    find newelem's position in *setp
+    insert newelem
+*/
+void qh_setaddsorted(setT **setp, void *newelem) {
+  int newindex=0;
+  void *elem, **elemp;
+
+  FOREACHelem_(*setp) {          /* could use binary search instead */
+    if (elem < newelem)
+      newindex++;
+    else if (elem == newelem)
+      return;
+    else
+      break;
+  }
+  qh_setaddnth(setp, newindex, newelem);
+} /* setaddsorted */
+
+
+/*-<a                             href="qh-set.htm#TOC"
+  >-------------------------------<a name="setappend">-</a>
+
+  qh_setappend( setp, newelem)
+    append newelem to *setp
+
+  notes:
+    *setp may be a temp set
+    *setp and newelem may be NULL
+
+  design:
+    expand *setp if empty or full
+    append newelem to *setp
+
+*/
+void qh_setappend(setT **setp, void *newelem) {
+  setelemT *sizep;  /* Avoid strict aliasing.  Writing to *endp may overwrite *sizep */
+  setelemT *endp;
+  int count;
+
+  if (!newelem)
+    return;
+  if (!*setp || (sizep= SETsizeaddr_(*setp))->i==0) {
+    qh_setlarger(setp);
+    sizep= SETsizeaddr_(*setp);
+  }
+  count= (sizep->i)++ - 1;
+  endp= (setelemT *)SETelemaddr_(*setp, count, void);
+  (endp++)->p= newelem;
+  endp->p= NULL;
+} /* setappend */
+
+/*-<a                             href="qh-set.htm#TOC"
+  >-------------------------------<a name="setappend_set">-</a>
+
+  qh_setappend_set( setp, setA)
+    appends setA to *setp
+
+  notes:
+    *setp can not be a temp set
+    *setp and setA may be NULL
+
+  design:
+    setup for copy
+    expand *setp if it is too small
+    append all elements of setA to *setp
+*/
+void qh_setappend_set(setT **setp, setT *setA) {
+  int sizeA, size;
+  setT *oldset;
+  setelemT *sizep;
+
+  if (!setA)
+    return;
+  SETreturnsize_(setA, sizeA);
+  if (!*setp)
+    *setp= qh_setnew(sizeA);
+  sizep= SETsizeaddr_(*setp);
+  if (!(size= sizep->i))
+    size= (*setp)->maxsize;
+  else
+    size--;
+  if (size + sizeA > (*setp)->maxsize) {
+    oldset= *setp;
+    *setp= qh_setcopy(oldset, sizeA);
+    qh_setfree(&oldset);
+    sizep= SETsizeaddr_(*setp);
+  }
+  if (sizeA > 0) {
+    sizep->i= size+sizeA+1;   /* memcpy may overwrite */
+    memcpy((char *)&((*setp)->e[size].p), (char *)&(setA->e[0].p), (size_t)(sizeA+1) * SETelemsize);
+  }
+} /* setappend_set */
+
+
+/*-<a                             href="qh-set.htm#TOC"
+  >-------------------------------<a name="setappend2ndlast">-</a>
+
+  qh_setappend2ndlast( setp, newelem )
+    makes newelem the next to the last element in *setp
+
+  notes:
+    *setp must have at least one element
+    newelem must be defined
+    *setp may be a temp set
+
+  design:
+    expand *setp if empty or full
+    move last element of *setp up one
+    insert newelem
+*/
+void qh_setappend2ndlast(setT **setp, void *newelem) {
+    setelemT *sizep;  /* Avoid strict aliasing.  Writing to *endp may overwrite *sizep */
+    setelemT *endp, *lastp;
+    int count;
+
+    if (!*setp || (sizep= SETsizeaddr_(*setp))->i==0) {
+        qh_setlarger(setp);
+        sizep= SETsizeaddr_(*setp);
+    }
+    count= (sizep->i)++ - 1;
+    endp= (setelemT *)SETelemaddr_(*setp, count, void); /* NULL */
+    lastp= endp-1;
+    *(endp++)= *lastp;
+    endp->p= NULL;    /* may overwrite *sizep */
+    lastp->p= newelem;
+} /* setappend2ndlast */
+
+/*-<a                             href="qh-set.htm#TOC"
+  >-------------------------------<a name="setcheck">-</a>
+
+  qh_setcheck( set, typename, id )
+    check set for validity
+    report errors with typename and id
+
+  design:
+    checks that maxsize, actual size, and NULL terminator agree
+*/
+void qh_setcheck(setT *set, const char *tname, unsigned id) {
+  int maxsize, size;
+  int waserr= 0;
+
+  if (!set)
+    return;
+  SETreturnsize_(set, size);
+  maxsize= set->maxsize;
+  if (size > maxsize || !maxsize) {
+    qh_fprintf(qhmem.ferr, 6172, "qhull internal error (qh_setcheck): actual size %d of %s%d is greater than max size %d\n",
+             size, tname, id, maxsize);
+    waserr= 1;
+  }else if (set->e[size].p) {
+    qh_fprintf(qhmem.ferr, 6173, "qhull internal error (qh_setcheck): %s%d(size %d max %d) is not null terminated.\n",
+             tname, id, size-1, maxsize);
+    waserr= 1;
+  }
+  if (waserr) {
+    qh_setprint(qhmem.ferr, "ERRONEOUS", set);
+    qh_errexit(qhmem_ERRqhull, NULL, NULL);
+  }
+} /* setcheck */
+
+
+/*-<a                             href="qh-set.htm#TOC"
+  >-------------------------------<a name="setcompact">-</a>
+
+  qh_setcompact( set )
+    remove internal NULLs from an unsorted set
+
+  returns:
+    updated set
+
+  notes:
+    set may be NULL
+    it would be faster to swap tail of set into holes, like qh_setdel
+
+  design:
+    setup pointers into set
+    skip NULLs while copying elements to start of set
+    update the actual size
+*/
+void qh_setcompact(setT *set) {
+  int size;
+  void **destp, **elemp, **endp, **firstp;
+
+  if (!set)
+    return;
+  SETreturnsize_(set, size);
+  destp= elemp= firstp= SETaddr_(set, void);
+  endp= destp + size;
+  while (1) {
+    if (!(*destp++ = *elemp++)) {
+      destp--;
+      if (elemp > endp)
+        break;
+    }
+  }
+  qh_settruncate(set, (int)(destp-firstp));   /* WARN64 */
+} /* setcompact */
+
+
+/*-<a                             href="qh-set.htm#TOC"
+  >-------------------------------<a name="setcopy">-</a>
+
+  qh_setcopy( set, extra )
+    make a copy of a sorted or unsorted set with extra slots
+
+  returns:
+    new set
+
+  design:
+    create a newset with extra slots
+    copy the elements to the newset
+
+*/
+setT *qh_setcopy(setT *set, int extra) {
+  setT *newset;
+  int size;
+
+  if (extra < 0)
+    extra= 0;
+  SETreturnsize_(set, size);
+  newset= qh_setnew(size+extra);
+  SETsizeaddr_(newset)->i= size+1;    /* memcpy may overwrite */
+  memcpy((char *)&(newset->e[0].p), (char *)&(set->e[0].p), (size_t)(size+1) * SETelemsize);
+  return(newset);
+} /* setcopy */
+
+
+/*-<a                             href="qh-set.htm#TOC"
+  >-------------------------------<a name="setdel">-</a>
+
+  qh_setdel( set, oldelem )
+    delete oldelem from an unsorted set
+
+  returns:
+    returns oldelem if found
+    returns NULL otherwise
+
+  notes:
+    set may be NULL
+    oldelem must not be NULL;
+    only deletes one copy of oldelem in set
+
+  design:
+    locate oldelem
+    update actual size if it was full
+    move the last element to the oldelem's location
+*/
+void *qh_setdel(setT *set, void *oldelem) {
+  setelemT *sizep;
+  setelemT *elemp;
+  setelemT *lastp;
+
+  if (!set)
+    return NULL;
+  elemp= (setelemT *)SETaddr_(set, void);
+  while (elemp->p != oldelem && elemp->p)
+    elemp++;
+  if (elemp->p) {
+    sizep= SETsizeaddr_(set);
+    if (!(sizep->i)--)         /*  if was a full set */
+      sizep->i= set->maxsize;  /*     *sizep= (maxsize-1)+ 1 */
+    lastp= (setelemT *)SETelemaddr_(set, sizep->i-1, void);
+    elemp->p= lastp->p;      /* may overwrite itself */
+    lastp->p= NULL;
+    return oldelem;
+  }
+  return NULL;
+} /* setdel */
+
+
+/*-<a                             href="qh-set.htm#TOC"
+  >-------------------------------<a name="setdellast">-</a>
+
+  qh_setdellast( set)
+    return last element of set or NULL
+
+  notes:
+    deletes element from set
+    set may be NULL
+
+  design:
+    return NULL if empty
+    if full set
+      delete last element and set actual size
+    else
+      delete last element and update actual size
+*/
+void *qh_setdellast(setT *set) {
+  int setsize;  /* actually, actual_size + 1 */
+  int maxsize;
+  setelemT *sizep;
+  void *returnvalue;
+
+  if (!set || !(set->e[0].p))
+    return NULL;
+  sizep= SETsizeaddr_(set);
+  if ((setsize= sizep->i)) {
+    returnvalue= set->e[setsize - 2].p;
+    set->e[setsize - 2].p= NULL;
+    sizep->i--;
+  }else {
+    maxsize= set->maxsize;
+    returnvalue= set->e[maxsize - 1].p;
+    set->e[maxsize - 1].p= NULL;
+    sizep->i= maxsize;
+  }
+  return returnvalue;
+} /* setdellast */
+
+
+/*-<a                             href="qh-set.htm#TOC"
+  >-------------------------------<a name="setdelnth">-</a>
+
+  qh_setdelnth( set, nth )
+    deletes nth element from unsorted set
+    0 is first element
+
+  returns:
+    returns the element (needs type conversion)
+
+  notes:
+    errors if nth invalid
+
+  design:
+    setup points and check nth
+    delete nth element and overwrite with last element
+*/
+void *qh_setdelnth(setT *set, int nth) {
+  void *elem;
+  setelemT *sizep;
+  setelemT *elemp, *lastp;
+
+  sizep= SETsizeaddr_(set);
+  if ((sizep->i--)==0)         /*  if was a full set */
+      sizep->i= set->maxsize;  /*     *sizep= (maxsize-1)+ 1 */
+  if (nth < 0 || nth >= sizep->i) {
+    qh_fprintf(qhmem.ferr, 6174, "qhull internal error (qh_setdelnth): nth %d is out-of-bounds for set:\n", nth);
+    qh_setprint(qhmem.ferr, "", set);
+    qh_errexit(qhmem_ERRqhull, NULL, NULL);
+  }
+  elemp= (setelemT *)SETelemaddr_(set, nth, void); /* nth valid by QH6174 */
+  lastp= (setelemT *)SETelemaddr_(set, sizep->i-1, void);
+  elem= elemp->p;
+  elemp->p= lastp->p;      /* may overwrite itself */
+  lastp->p= NULL;
+  return elem;
+} /* setdelnth */
+
+/*-<a                             href="qh-set.htm#TOC"
+  >-------------------------------<a name="setdelnthsorted">-</a>
+
+  qh_setdelnthsorted( set, nth )
+    deletes nth element from sorted set
+
+  returns:
+    returns the element (use type conversion)
+
+  notes:
+    errors if nth invalid
+
+  see also:
+    setnew_delnthsorted
+
+  design:
+    setup points and check nth
+    copy remaining elements down one
+    update actual size
+*/
+void *qh_setdelnthsorted(setT *set, int nth) {
+  void *elem;
+  setelemT *sizep;
+  setelemT *newp, *oldp;
+
+  sizep= SETsizeaddr_(set);
+  if (nth < 0 || (sizep->i && nth >= sizep->i-1) || nth >= set->maxsize) {
+    qh_fprintf(qhmem.ferr, 6175, "qhull internal error (qh_setdelnthsorted): nth %d is out-of-bounds for set:\n", nth);
+    qh_setprint(qhmem.ferr, "", set);
+    qh_errexit(qhmem_ERRqhull, NULL, NULL);
+  }
+  newp= (setelemT *)SETelemaddr_(set, nth, void);
+  elem= newp->p;
+  oldp= newp+1;
+  while (((newp++)->p= (oldp++)->p))
+    ; /* copy remaining elements and NULL */
+  if ((sizep->i--)==0)         /*  if was a full set */
+    sizep->i= set->maxsize;  /*     *sizep= (max size-1)+ 1 */
+  return elem;
+} /* setdelnthsorted */
+
+
+/*-<a                             href="qh-set.htm#TOC"
+  >-------------------------------<a name="setdelsorted">-</a>
+
+  qh_setdelsorted( set, oldelem )
+    deletes oldelem from sorted set
+
+  returns:
+    returns oldelem if it was deleted
+
+  notes:
+    set may be NULL
+
+  design:
+    locate oldelem in set
+    copy remaining elements down one
+    update actual size
+*/
+void *qh_setdelsorted(setT *set, void *oldelem) {
+  setelemT *sizep;
+  setelemT *newp, *oldp;
+
+  if (!set)
+    return NULL;
+  newp= (setelemT *)SETaddr_(set, void);
+  while(newp->p != oldelem && newp->p)
+    newp++;
+  if (newp->p) {
+    oldp= newp+1;
+    while (((newp++)->p= (oldp++)->p))
+      ; /* copy remaining elements */
+    sizep= SETsizeaddr_(set);
+    if ((sizep->i--)==0)    /*  if was a full set */
+      sizep->i= set->maxsize;  /*     *sizep= (max size-1)+ 1 */
+    return oldelem;
+  }
+  return NULL;
+} /* setdelsorted */
+
+
+/*-<a                             href="qh-set.htm#TOC"
+  >-------------------------------<a name="setduplicate">-</a>
+
+  qh_setduplicate( set, elemsize )
+    duplicate a set of elemsize elements
+
+  notes:
+    use setcopy if retaining old elements
+
+  design:
+    create a new set
+    for each elem of the old set
+      create a newelem
+      append newelem to newset
+*/
+setT *qh_setduplicate(setT *set, int elemsize) {
+  void          *elem, **elemp, *newElem;
+  setT          *newSet;
+  int           size;
+
+  if (!(size= qh_setsize(set)))
+    return NULL;
+  newSet= qh_setnew(size);
+  FOREACHelem_(set) {
+    newElem= qh_memalloc(elemsize);
+    memcpy(newElem, elem, (size_t)elemsize);
+    qh_setappend(&newSet, newElem);
+  }
+  return newSet;
+} /* setduplicate */
+
+
+/*-<a                             href="qh-set.htm#TOC"
+  >-------------------------------<a name="setendpointer">-</a>
+
+  qh_setendpointer( set )
+    Returns pointer to NULL terminator of a set's elements
+    set can not be NULL
+
+*/
+void **qh_setendpointer(setT *set) {
+
+  setelemT *sizep= SETsizeaddr_(set);
+  int n= sizep->i;
+  return (n ? &set->e[n-1].p : &sizep->p);
+} /* qh_setendpointer */
+
+/*-<a                             href="qh-set.htm#TOC"
+  >-------------------------------<a name="setequal">-</a>
+
+  qh_setequal( setA, setB )
+    returns 1 if two sorted sets are equal, otherwise returns 0
+
+  notes:
+    either set may be NULL
+
+  design:
+    check size of each set
+    setup pointers
+    compare elements of each set
+*/
+int qh_setequal(setT *setA, setT *setB) {
+  void **elemAp, **elemBp;
+  int sizeA= 0, sizeB= 0;
+
+  if (setA) {
+    SETreturnsize_(setA, sizeA);
+  }
+  if (setB) {
+    SETreturnsize_(setB, sizeB);
+  }
+  if (sizeA != sizeB)
+    return 0;
+  if (!sizeA)
+    return 1;
+  elemAp= SETaddr_(setA, void);
+  elemBp= SETaddr_(setB, void);
+  if (!memcmp((char *)elemAp, (char *)elemBp, sizeA*SETelemsize))
+    return 1;
+  return 0;
+} /* setequal */
+
+
+/*-<a                             href="qh-set.htm#TOC"
+  >-------------------------------<a name="setequal_except">-</a>
+
+  qh_setequal_except( setA, skipelemA, setB, skipelemB )
+    returns 1 if sorted setA and setB are equal except for skipelemA & B
+
+  returns:
+    false if either skipelemA or skipelemB are missing
+
+  notes:
+    neither set may be NULL
+
+    if skipelemB is NULL,
+      can skip any one element of setB
+
+  design:
+    setup pointers
+    search for skipelemA, skipelemB, and mismatches
+    check results
+*/
+int qh_setequal_except(setT *setA, void *skipelemA, setT *setB, void *skipelemB) {
+  void **elemA, **elemB;
+  int skip=0;
+
+  elemA= SETaddr_(setA, void);
+  elemB= SETaddr_(setB, void);
+  while (1) {
+    if (*elemA == skipelemA) {
+      skip++;
+      elemA++;
+    }
+    if (skipelemB) {
+      if (*elemB == skipelemB) {
+        skip++;
+        elemB++;
+      }
+    }else if (*elemA != *elemB) {
+      skip++;
+      if (!(skipelemB= *elemB++))
+        return 0;
+    }
+    if (!*elemA)
+      break;
+    if (*elemA++ != *elemB++)
+      return 0;
+  }
+  if (skip != 2 || *elemB)
+    return 0;
+  return 1;
+} /* setequal_except */
+
+
+/*-<a                             href="qh-set.htm#TOC"
+  >-------------------------------<a name="setequal_skip">-</a>
+
+  qh_setequal_skip( setA, skipA, setB, skipB )
+    returns 1 if sorted setA and setB are equal except for elements skipA & B
+
+  returns:
+    false if different size
+
+  notes:
+    neither set may be NULL
+
+  design:
+    setup pointers
+    search for mismatches while skipping skipA and skipB
+*/
+int qh_setequal_skip(setT *setA, int skipA, setT *setB, int skipB) {
+  void **elemA, **elemB, **skipAp, **skipBp;
+
+  elemA= SETaddr_(setA, void);
+  elemB= SETaddr_(setB, void);
+  skipAp= SETelemaddr_(setA, skipA, void);
+  skipBp= SETelemaddr_(setB, skipB, void);
+  while (1) {
+    if (elemA == skipAp)
+      elemA++;
+    if (elemB == skipBp)
+      elemB++;
+    if (!*elemA)
+      break;
+    if (*elemA++ != *elemB++)
+      return 0;
+  }
+  if (*elemB)
+    return 0;
+  return 1;
+} /* setequal_skip */
+
+
+/*-<a                             href="qh-set.htm#TOC"
+  >-------------------------------<a name="setfree">-</a>
+
+  qh_setfree( setp )
+    frees the space occupied by a sorted or unsorted set
+
+  returns:
+    sets setp to NULL
+
+  notes:
+    set may be NULL
+
+  design:
+    free array
+    free set
+*/
+void qh_setfree(setT **setp) {
+  int size;
+  void **freelistp;  /* used if !qh_NOmem by qh_memfree_() */
+
+  if (*setp) {
+    size= sizeof(setT) + ((*setp)->maxsize)*SETelemsize;
+    if (size <= qhmem.LASTsize) {
+      qh_memfree_(*setp, size, freelistp);
+    }else
+      qh_memfree(*setp, size);
+    *setp= NULL;
+  }
+} /* setfree */
+
+
+/*-<a                             href="qh-set.htm#TOC"
+  >-------------------------------<a name="setfree2">-</a>
+
+  qh_setfree2( setp, elemsize )
+    frees the space occupied by a set and its elements
+
+  notes:
+    set may be NULL
+
+  design:
+    free each element
+    free set
+*/
+void qh_setfree2(setT **setp, int elemsize) {
+  void          *elem, **elemp;
+
+  FOREACHelem_(*setp)
+    qh_memfree(elem, elemsize);
+  qh_setfree(setp);
+} /* setfree2 */
+
+
+
+/*-<a                             href="qh-set.htm#TOC"
+  >-------------------------------<a name="setfreelong">-</a>
+
+  qh_setfreelong( setp )
+    frees a set only if it's in long memory
+
+  returns:
+    sets setp to NULL if it is freed
+
+  notes:
+    set may be NULL
+
+  design:
+    if set is large
+      free it
+*/
+void qh_setfreelong(setT **setp) {
+  int size;
+
+  if (*setp) {
+    size= sizeof(setT) + ((*setp)->maxsize)*SETelemsize;
+    if (size > qhmem.LASTsize) {
+      qh_memfree(*setp, size);
+      *setp= NULL;
+    }
+  }
+} /* setfreelong */
+
+
+/*-<a                             href="qh-set.htm#TOC"
+  >-------------------------------<a name="setin">-</a>
+
+  qh_setin( set, setelem )
+    returns 1 if setelem is in a set, 0 otherwise
+
+  notes:
+    set may be NULL or unsorted
+
+  design:
+    scans set for setelem
+*/
+int qh_setin(setT *set, void *setelem) {
+  void *elem, **elemp;
+
+  FOREACHelem_(set) {
+    if (elem == setelem)
+      return 1;
+  }
+  return 0;
+} /* setin */
+
+
+/*-<a                             href="qh-set.htm#TOC"
+  >-------------------------------<a name="setindex">-</a>
+
+  qh_setindex( set, atelem )
+    returns the index of atelem in set.
+    returns -1, if not in set or maxsize wrong
+
+  notes:
+    set may be NULL and may contain nulls.
+    NOerrors returned (qh_pointid, QhullPoint::id)
+
+  design:
+    checks maxsize
+    scans set for atelem
+*/
+int qh_setindex(setT *set, void *atelem) {
+  void **elem;
+  int size, i;
+
+  if (!set)
+    return -1;
+  SETreturnsize_(set, size);
+  if (size > set->maxsize)
+    return -1;
+  elem= SETaddr_(set, void);
+  for (i=0; i < size; i++) {
+    if (*elem++ == atelem)
+      return i;
+  }
+  return -1;
+} /* setindex */
+
+
+/*-<a                             href="qh-set.htm#TOC"
+  >-------------------------------<a name="setlarger">-</a>
+
+  qh_setlarger( oldsetp )
+    returns a larger set that contains all elements of *oldsetp
+
+  notes:
+    the set is at least twice as large
+    if temp set, updates qhmem.tempstack
+
+  design:
+    creates a new set
+    copies the old set to the new set
+    updates pointers in tempstack
+    deletes the old set
+*/
+void qh_setlarger(setT **oldsetp) {
+  int size= 1;
+  setT *newset, *set, **setp, *oldset;
+  setelemT *sizep;
+  setelemT *newp, *oldp;
+
+  if (*oldsetp) {
+    oldset= *oldsetp;
+    SETreturnsize_(oldset, size);
+    qhmem.cntlarger++;
+    qhmem.totlarger += size+1;
+    newset= qh_setnew(2 * size);
+    oldp= (setelemT *)SETaddr_(oldset, void);
+    newp= (setelemT *)SETaddr_(newset, void);
+    memcpy((char *)newp, (char *)oldp, (size_t)(size+1) * SETelemsize);
+    sizep= SETsizeaddr_(newset);
+    sizep->i= size+1;
+    FOREACHset_((setT *)qhmem.tempstack) {
+      if (set == oldset)
+        *(setp-1)= newset;
+    }
+    qh_setfree(oldsetp);
+  }else
+    newset= qh_setnew(3);
+  *oldsetp= newset;
+} /* setlarger */
+
+
+/*-<a                             href="qh-set.htm#TOC"
+  >-------------------------------<a name="setlast">-</a>
+
+  qh_setlast( set )
+    return last element of set or NULL (use type conversion)
+
+  notes:
+    set may be NULL
+
+  design:
+    return last element
+*/
+void *qh_setlast(setT *set) {
+  int size;
+
+  if (set) {
+    size= SETsizeaddr_(set)->i;
+    if (!size)
+      return SETelem_(set, set->maxsize - 1);
+    else if (size > 1)
+      return SETelem_(set, size - 2);
+  }
+  return NULL;
+} /* setlast */
+
+
+/*-<a                             href="qh-set.htm#TOC"
+  >-------------------------------<a name="setnew">-</a>
+
+  qh_setnew( setsize )
+    creates and allocates space for a set
+
+  notes:
+    setsize means the number of elements (!including the NULL terminator)
+    use qh_settemp/qh_setfreetemp if set is temporary
+
+  design:
+    allocate memory for set
+    roundup memory if small set
+    initialize as empty set
+*/
+setT *qh_setnew(int setsize) {
+  setT *set;
+  int sizereceived; /* used if !qh_NOmem */
+  int size;
+  void **freelistp; /* used if !qh_NOmem by qh_memalloc_() */
+
+  if (!setsize)
+    setsize++;
+  size= sizeof(setT) + setsize * SETelemsize;
+  if (size>0 && size <= qhmem.LASTsize) {
+    qh_memalloc_(size, freelistp, set, setT);
+#ifndef qh_NOmem
+    sizereceived= qhmem.sizetable[ qhmem.indextable[size]];
+    if (sizereceived > size)
+      setsize += (sizereceived - size)/SETelemsize;
+#endif
+  }else
+    set= (setT*)qh_memalloc(size);
+  set->maxsize= setsize;
+  set->e[setsize].i= 1;
+  set->e[0].p= NULL;
+  return(set);
+} /* setnew */
+
+
+/*-<a                             href="qh-set.htm#TOC"
+  >-------------------------------<a name="setnew_delnthsorted">-</a>
+
+  qh_setnew_delnthsorted( set, size, nth, prepend )
+    creates a sorted set not containing nth element
+    if prepend, the first prepend elements are undefined
+
+  notes:
+    set must be defined
+    checks nth
+    see also: setdelnthsorted
+
+  design:
+    create new set
+    setup pointers and allocate room for prepend'ed entries
+    append head of old set to new set
+    append tail of old set to new set
+*/
+setT *qh_setnew_delnthsorted(setT *set, int size, int nth, int prepend) {
+  setT *newset;
+  void **oldp, **newp;
+  int tailsize= size - nth -1, newsize;
+
+  if (tailsize < 0) {
+    qh_fprintf(qhmem.ferr, 6176, "qhull internal error (qh_setnew_delnthsorted): nth %d is out-of-bounds for set:\n", nth);
+    qh_setprint(qhmem.ferr, "", set);
+    qh_errexit(qhmem_ERRqhull, NULL, NULL);
+  }
+  newsize= size-1 + prepend;
+  newset= qh_setnew(newsize);
+  newset->e[newset->maxsize].i= newsize+1;  /* may be overwritten */
+  oldp= SETaddr_(set, void);
+  newp= SETaddr_(newset, void) + prepend;
+  switch (nth) {
+  case 0:
+    break;
+  case 1:
+    *(newp++)= *oldp++;
+    break;
+  case 2:
+    *(newp++)= *oldp++;
+    *(newp++)= *oldp++;
+    break;
+  case 3:
+    *(newp++)= *oldp++;
+    *(newp++)= *oldp++;
+    *(newp++)= *oldp++;
+    break;
+  case 4:
+    *(newp++)= *oldp++;
+    *(newp++)= *oldp++;
+    *(newp++)= *oldp++;
+    *(newp++)= *oldp++;
+    break;
+  default:
+    memcpy((char *)newp, (char *)oldp, (size_t)nth * SETelemsize);
+    newp += nth;
+    oldp += nth;
+    break;
+  }
+  oldp++;
+  switch (tailsize) {
+  case 0:
+    break;
+  case 1:
+    *(newp++)= *oldp++;
+    break;
+  case 2:
+    *(newp++)= *oldp++;
+    *(newp++)= *oldp++;
+    break;
+  case 3:
+    *(newp++)= *oldp++;
+    *(newp++)= *oldp++;
+    *(newp++)= *oldp++;
+    break;
+  case 4:
+    *(newp++)= *oldp++;
+    *(newp++)= *oldp++;
+    *(newp++)= *oldp++;
+    *(newp++)= *oldp++;
+    break;
+  default:
+    memcpy((char *)newp, (char *)oldp, (size_t)tailsize * SETelemsize);
+    newp += tailsize;
+  }
+  *newp= NULL;
+  return(newset);
+} /* setnew_delnthsorted */
+
+
+/*-<a                             href="qh-set.htm#TOC"
+  >-------------------------------<a name="setprint">-</a>
+
+  qh_setprint( fp, string, set )
+    print set elements to fp with identifying string
+
+  notes:
+    never errors
+*/
+void qh_setprint(FILE *fp, const char* string, setT *set) {
+  int size, k;
+
+  if (!set)
+    qh_fprintf(fp, 9346, "%s set is null\n", string);
+  else {
+    SETreturnsize_(set, size);
+    qh_fprintf(fp, 9347, "%s set=%p maxsize=%d size=%d elems=",
+             string, set, set->maxsize, size);
+    if (size > set->maxsize)
+      size= set->maxsize+1;
+    for (k=0; k < size; k++)
+      qh_fprintf(fp, 9348, " %p", set->e[k].p);
+    qh_fprintf(fp, 9349, "\n");
+  }
+} /* setprint */
+
+/*-<a                             href="qh-set.htm#TOC"
+  >-------------------------------<a name="setreplace">-</a>
+
+  qh_setreplace( set, oldelem, newelem )
+    replaces oldelem in set with newelem
+
+  notes:
+    errors if oldelem not in the set
+    newelem may be NULL, but it turns the set into an indexed set (no FOREACH)
+
+  design:
+    find oldelem
+    replace with newelem
+*/
+void qh_setreplace(setT *set, void *oldelem, void *newelem) {
+  void **elemp;
+
+  elemp= SETaddr_(set, void);
+  while (*elemp != oldelem && *elemp)
+    elemp++;
+  if (*elemp)
+    *elemp= newelem;
+  else {
+    qh_fprintf(qhmem.ferr, 6177, "qhull internal error (qh_setreplace): elem %p not found in set\n",
+       oldelem);
+    qh_setprint(qhmem.ferr, "", set);
+    qh_errexit(qhmem_ERRqhull, NULL, NULL);
+  }
+} /* setreplace */
+
+
+/*-<a                             href="qh-set.htm#TOC"
+  >-------------------------------<a name="setsize">-</a>
+
+  qh_setsize( set )
+    returns the size of a set
+
+  notes:
+    errors if set's maxsize is incorrect
+    same as SETreturnsize_(set)
+    same code for qh_setsize [qset.c] and QhullSetBase::count
+
+  design:
+    determine actual size of set from maxsize
+*/
+int qh_setsize(setT *set) {
+  int size;
+  setelemT *sizep;
+
+  if (!set)
+    return(0);
+  sizep= SETsizeaddr_(set);
+  if ((size= sizep->i)) {
+    size--;
+    if (size > set->maxsize) {
+      qh_fprintf(qhmem.ferr, 6178, "qhull internal error (qh_setsize): current set size %d is greater than maximum size %d\n",
+               size, set->maxsize);
+      qh_setprint(qhmem.ferr, "set: ", set);
+      qh_errexit(qhmem_ERRqhull, NULL, NULL);
+    }
+  }else
+    size= set->maxsize;
+  return size;
+} /* setsize */
+
+/*-<a                             href="qh-set.htm#TOC"
+  >-------------------------------<a name="settemp">-</a>
+
+  qh_settemp( setsize )
+    return a stacked, temporary set of upto setsize elements
+
+  notes:
+    use settempfree or settempfree_all to release from qhmem.tempstack
+    see also qh_setnew
+
+  design:
+    allocate set
+    append to qhmem.tempstack
+
+*/
+setT *qh_settemp(int setsize) {
+  setT *newset;
+
+  newset= qh_setnew(setsize);
+  qh_setappend(&qhmem.tempstack, newset);
+  if (qhmem.IStracing >= 5)
+    qh_fprintf(qhmem.ferr, 8123, "qh_settemp: temp set %p of %d elements, depth %d\n",
+       newset, newset->maxsize, qh_setsize(qhmem.tempstack));
+  return newset;
+} /* settemp */
+
+/*-<a                             href="qh-set.htm#TOC"
+  >-------------------------------<a name="settempfree">-</a>
+
+  qh_settempfree( set )
+    free temporary set at top of qhmem.tempstack
+
+  notes:
+    nop if set is NULL
+    errors if set not from previous   qh_settemp
+
+  to locate errors:
+    use 'T2' to find source and then find mis-matching qh_settemp
+
+  design:
+    check top of qhmem.tempstack
+    free it
+*/
+void qh_settempfree(setT **set) {
+  setT *stackedset;
+
+  if (!*set)
+    return;
+  stackedset= qh_settemppop();
+  if (stackedset != *set) {
+    qh_settemppush(stackedset);
+    qh_fprintf(qhmem.ferr, 6179, "qhull internal error (qh_settempfree): set %p(size %d) was not last temporary allocated(depth %d, set %p, size %d)\n",
+             *set, qh_setsize(*set), qh_setsize(qhmem.tempstack)+1,
+             stackedset, qh_setsize(stackedset));
+    qh_errexit(qhmem_ERRqhull, NULL, NULL);
+  }
+  qh_setfree(set);
+} /* settempfree */
+
+/*-<a                             href="qh-set.htm#TOC"
+  >-------------------------------<a name="settempfree_all">-</a>
+
+  qh_settempfree_all(  )
+    free all temporary sets in qhmem.tempstack
+
+  design:
+    for each set in tempstack
+      free set
+    free qhmem.tempstack
+*/
+void qh_settempfree_all(void) {
+  setT *set, **setp;
+
+  FOREACHset_(qhmem.tempstack)
+    qh_setfree(&set);
+  qh_setfree(&qhmem.tempstack);
+} /* settempfree_all */
+
+/*-<a                             href="qh-set.htm#TOC"
+  >-------------------------------<a name="settemppop">-</a>
+
+  qh_settemppop(  )
+    pop and return temporary set from qhmem.tempstack
+
+  notes:
+    the returned set is permanent
+
+  design:
+    pop and check top of qhmem.tempstack
+*/
+setT *qh_settemppop(void) {
+  setT *stackedset;
+
+  stackedset= (setT*)qh_setdellast(qhmem.tempstack);
+  if (!stackedset) {
+    qh_fprintf(qhmem.ferr, 6180, "qhull internal error (qh_settemppop): pop from empty temporary stack\n");
+    qh_errexit(qhmem_ERRqhull, NULL, NULL);
+  }
+  if (qhmem.IStracing >= 5)
+    qh_fprintf(qhmem.ferr, 8124, "qh_settemppop: depth %d temp set %p of %d elements\n",
+       qh_setsize(qhmem.tempstack)+1, stackedset, qh_setsize(stackedset));
+  return stackedset;
+} /* settemppop */
+
+/*-<a                             href="qh-set.htm#TOC"
+  >-------------------------------<a name="settemppush">-</a>
+
+  qh_settemppush( set )
+    push temporary set unto qhmem.tempstack (makes it temporary)
+
+  notes:
+    duplicates settemp() for tracing
+
+  design:
+    append set to tempstack
+*/
+void qh_settemppush(setT *set) {
+  if (!set) {
+    qh_fprintf(qhmem.ferr, 6267, "qhull error (qh_settemppush): can not push a NULL temp\n");
+    qh_errexit(qhmem_ERRqhull, NULL, NULL);
+  }
+  qh_setappend(&qhmem.tempstack, set);
+  if (qhmem.IStracing >= 5)
+    qh_fprintf(qhmem.ferr, 8125, "qh_settemppush: depth %d temp set %p of %d elements\n",
+      qh_setsize(qhmem.tempstack), set, qh_setsize(set));
+} /* settemppush */
+
+
+/*-<a                             href="qh-set.htm#TOC"
+  >-------------------------------<a name="settruncate">-</a>
+
+  qh_settruncate( set, size )
+    truncate set to size elements
+
+  notes:
+    set must be defined
+
+  see:
+    SETtruncate_
+
+  design:
+    check size
+    update actual size of set
+*/
+void qh_settruncate(setT *set, int size) {
+
+  if (size < 0 || size > set->maxsize) {
+    qh_fprintf(qhmem.ferr, 6181, "qhull internal error (qh_settruncate): size %d out of bounds for set:\n", size);
+    qh_setprint(qhmem.ferr, "", set);
+    qh_errexit(qhmem_ERRqhull, NULL, NULL);
+  }
+  set->e[set->maxsize].i= size+1;   /* maybe overwritten */
+  set->e[size].p= NULL;
+} /* settruncate */
+
+/*-<a                             href="qh-set.htm#TOC"
+  >-------------------------------<a name="setunique">-</a>
+
+  qh_setunique( set, elem )
+    add elem to unsorted set unless it is already in set
+
+  notes:
+    returns 1 if it is appended
+
+  design:
+    if elem not in set
+      append elem to set
+*/
+int qh_setunique(setT **set, void *elem) {
+
+  if (!qh_setin(*set, elem)) {
+    qh_setappend(set, elem);
+    return 1;
+  }
+  return 0;
+} /* setunique */
+
+/*-<a                             href="qh-set.htm#TOC"
+  >-------------------------------<a name="setzero">-</a>
+
+  qh_setzero( set, index, size )
+    zero elements from index on
+    set actual size of set to size
+
+  notes:
+    set must be defined
+    the set becomes an indexed set (can not use FOREACH...)
+
+  see also:
+    qh_settruncate
+
+  design:
+    check index and size
+    update actual size
+    zero elements starting at e[index]
+*/
+void qh_setzero(setT *set, int idx, int size) {
+  int count;
+
+  if (idx < 0 || idx >= size || size > set->maxsize) {
+    qh_fprintf(qhmem.ferr, 6182, "qhull internal error (qh_setzero): index %d or size %d out of bounds for set:\n", idx, size);
+    qh_setprint(qhmem.ferr, "", set);
+    qh_errexit(qhmem_ERRqhull, NULL, NULL);
+  }
+  set->e[set->maxsize].i=  size+1;  /* may be overwritten */
+  count= size - idx + 1;   /* +1 for NULL terminator */
+  memset((char *)SETelemaddr_(set, idx, void), 0, (size_t)count * SETelemsize);
+} /* setzero */
+
+
diff --git a/xs/src/qhull/src/libqhull/qset.h b/xs/src/qhull/src/libqhull/qset.h
new file mode 100644
index 0000000000..7e4e7d14f6
--- /dev/null
+++ b/xs/src/qhull/src/libqhull/qset.h
@@ -0,0 +1,490 @@
+/*<html><pre>  -<a                             href="qh-set.htm"
+  >-------------------------------</a><a name="TOP">-</a>
+
+   qset.h
+     header file for qset.c that implements set
+
+   see qh-set.htm and qset.c
+
+   only uses mem.c, malloc/free
+
+   for error handling, writes message and calls
+      qh_errexit(qhmem_ERRqhull, NULL, NULL);
+
+   set operations satisfy the following properties:
+    - sets have a max size, the actual size (if different) is stored at the end
+    - every set is NULL terminated
+    - sets may be sorted or unsorted, the caller must distinguish this
+
+   Copyright (c) 1993-2015 The Geometry Center.
+   $Id: //main/2015/qhull/src/libqhull/qset.h#2 $$Change: 2062 $
+   $DateTime: 2016/01/17 13:13:18 $$Author: bbarber $
+*/
+
+#ifndef qhDEFset
+#define qhDEFset 1
+
+#include <stdio.h>
+
+/*================= -structures- ===============*/
+
+#ifndef DEFsetT
+#define DEFsetT 1
+typedef struct setT setT;   /* a set is a sorted or unsorted array of pointers */
+#endif
+
+/* [jan'15] Decided not to use countT.  Most sets are small.  The code uses signed tests */
+
+/*-<a                                      href="qh-set.htm#TOC"
+>----------------------------------------</a><a name="setT">-</a>
+
+setT
+  a set or list of pointers with maximum size and actual size.
+
+variations:
+  unsorted, unique   -- a list of unique pointers with NULL terminator
+                           user guarantees uniqueness
+  sorted             -- a sorted list of unique pointers with NULL terminator
+                           qset.c guarantees uniqueness
+  unsorted           -- a list of pointers terminated with NULL
+  indexed            -- an array of pointers with NULL elements
+
+structure for set of n elements:
+
+        --------------
+        |  maxsize
+        --------------
+        |  e[0] - a pointer, may be NULL for indexed sets
+        --------------
+        |  e[1]
+
+        --------------
+        |  ...
+        --------------
+        |  e[n-1]
+        --------------
+        |  e[n] = NULL
+        --------------
+        |  ...
+        --------------
+        |  e[maxsize] - n+1 or NULL (determines actual size of set)
+        --------------
+
+*/
+
+/*-- setelemT -- internal type to allow both pointers and indices
+*/
+typedef union setelemT setelemT;
+union setelemT {
+  void    *p;
+  int      i;         /* integer used for e[maxSize] */
+};
+
+struct setT {
+  int maxsize;          /* maximum number of elements (except NULL) */
+  setelemT e[1];        /* array of pointers, tail is NULL */
+                        /* last slot (unless NULL) is actual size+1
+                           e[maxsize]==NULL or e[e[maxsize]-1]==NULL */
+                        /* this may generate a warning since e[] contains
+                           maxsize elements */
+};
+
+/*=========== -constants- =========================*/
+
+/*-<a                                 href="qh-set.htm#TOC"
+  >-----------------------------------</a><a name="SETelemsize">-</a>
+
+  SETelemsize
+    size of a set element in bytes
+*/
+#define SETelemsize ((int)sizeof(setelemT))
+
+
+/*=========== -macros- =========================*/
+
+/*-<a                                 href="qh-set.htm#TOC"
+  >-----------------------------------</a><a name="FOREACHsetelement_">-</a>
+
+   FOREACHsetelement_(type, set, variable)
+     define FOREACH iterator
+
+   declare:
+     assumes *variable and **variablep are declared
+     no space in "variable)" [DEC Alpha cc compiler]
+
+   each iteration:
+     variable is set element
+     variablep is one beyond variable.
+
+   to repeat an element:
+     variablep--; / *repeat* /
+
+   at exit:
+     variable is NULL at end of loop
+
+   example:
+     #define FOREACHfacet_( facets ) FOREACHsetelement_( facetT, facets, facet )
+
+   notes:
+     use FOREACHsetelement_i_() if need index or include NULLs
+
+   WARNING:
+     nested loops can't use the same variable (define another FOREACH)
+
+     needs braces if nested inside another FOREACH
+     this includes intervening blocks, e.g. FOREACH...{ if () FOREACH...} )
+*/
+#define FOREACHsetelement_(type, set, variable) \
+        if (((variable= NULL), set)) for (\
+          variable##p= (type **)&((set)->e[0].p); \
+          (variable= *variable##p++);)
+
+/*-<a                                      href="qh-set.htm#TOC"
+  >----------------------------------------</a><a name="FOREACHsetelement_i_">-</a>
+
+   FOREACHsetelement_i_(type, set, variable)
+     define indexed FOREACH iterator
+
+   declare:
+     type *variable, variable_n, variable_i;
+
+   each iteration:
+     variable is set element, may be NULL
+     variable_i is index, variable_n is qh_setsize()
+
+   to repeat an element:
+     variable_i--; variable_n-- repeats for deleted element
+
+   at exit:
+     variable==NULL and variable_i==variable_n
+
+   example:
+     #define FOREACHfacet_i_( facets ) FOREACHsetelement_i_( facetT, facets, facet )
+
+   WARNING:
+     nested loops can't use the same variable (define another FOREACH)
+
+     needs braces if nested inside another FOREACH
+     this includes intervening blocks, e.g. FOREACH...{ if () FOREACH...} )
+*/
+#define FOREACHsetelement_i_(type, set, variable) \
+        if (((variable= NULL), set)) for (\
+          variable##_i= 0, variable= (type *)((set)->e[0].p), \
+                   variable##_n= qh_setsize(set);\
+          variable##_i < variable##_n;\
+          variable= (type *)((set)->e[++variable##_i].p) )
+
+/*-<a                                    href="qh-set.htm#TOC"
+  >--------------------------------------</a><a name="FOREACHsetelementreverse_">-</a>
+
+   FOREACHsetelementreverse_(type, set, variable)-
+     define FOREACH iterator in reverse order
+
+   declare:
+     assumes *variable and **variablep are declared
+     also declare 'int variabletemp'
+
+   each iteration:
+     variable is set element
+
+   to repeat an element:
+     variabletemp++; / *repeat* /
+
+   at exit:
+     variable is NULL
+
+   example:
+     #define FOREACHvertexreverse_( vertices ) FOREACHsetelementreverse_( vertexT, vertices, vertex )
+
+   notes:
+     use FOREACHsetelementreverse12_() to reverse first two elements
+     WARNING: needs braces if nested inside another FOREACH
+*/
+#define FOREACHsetelementreverse_(type, set, variable) \
+        if (((variable= NULL), set)) for (\
+           variable##temp= qh_setsize(set)-1, variable= qh_setlast(set);\
+           variable; variable= \
+           ((--variable##temp >= 0) ? SETelemt_(set, variable##temp, type) : NULL))
+
+/*-<a                                 href="qh-set.htm#TOC"
+  >-----------------------------------</a><a name="FOREACHsetelementreverse12_">-</a>
+
+   FOREACHsetelementreverse12_(type, set, variable)-
+     define FOREACH iterator with e[1] and e[0] reversed
+
+   declare:
+     assumes *variable and **variablep are declared
+
+   each iteration:
+     variable is set element
+     variablep is one after variable.
+
+   to repeat an element:
+     variablep--; / *repeat* /
+
+   at exit:
+     variable is NULL at end of loop
+
+   example
+     #define FOREACHvertexreverse12_( vertices ) FOREACHsetelementreverse12_( vertexT, vertices, vertex )
+
+   notes:
+     WARNING: needs braces if nested inside another FOREACH
+*/
+#define FOREACHsetelementreverse12_(type, set, variable) \
+        if (((variable= NULL), set)) for (\
+          variable##p= (type **)&((set)->e[1].p); \
+          (variable= *variable##p); \
+          variable##p == ((type **)&((set)->e[0].p))?variable##p += 2: \
+              (variable##p == ((type **)&((set)->e[1].p))?variable##p--:variable##p++))
+
+/*-<a                                 href="qh-set.htm#TOC"
+  >-----------------------------------</a><a name="FOREACHelem_">-</a>
+
+   FOREACHelem_( set )-
+     iterate elements in a set
+
+   declare:
+     void *elem, *elemp;
+
+   each iteration:
+     elem is set element
+     elemp is one beyond
+
+   to repeat an element:
+     elemp--; / *repeat* /
+
+   at exit:
+     elem == NULL at end of loop
+
+   example:
+     FOREACHelem_(set) {
+
+   notes:
+     WARNING: needs braces if nested inside another FOREACH
+*/
+#define FOREACHelem_(set) FOREACHsetelement_(void, set, elem)
+
+/*-<a                                 href="qh-set.htm#TOC"
+  >-----------------------------------</a><a name="FOREACHset_">-</a>
+
+   FOREACHset_( set )-
+     iterate a set of sets
+
+   declare:
+     setT *set, **setp;
+
+   each iteration:
+     set is set element
+     setp is one beyond
+
+   to repeat an element:
+     setp--; / *repeat* /
+
+   at exit:
+     set == NULL at end of loop
+
+   example
+     FOREACHset_(sets) {
+
+   notes:
+     WARNING: needs braces if nested inside another FOREACH
+*/
+#define FOREACHset_(sets) FOREACHsetelement_(setT, sets, set)
+
+/*-<a                                       href="qh-set.htm#TOC"
+  >-----------------------------------------</a><a name="SETindex_">-</a>
+
+   SETindex_( set, elem )
+     return index of elem in set
+
+   notes:
+     for use with FOREACH iteration
+     WARN64 -- Maximum set size is 2G
+
+   example:
+     i= SETindex_(ridges, ridge)
+*/
+#define SETindex_(set, elem) ((int)((void **)elem##p - (void **)&(set)->e[1].p))
+
+/*-<a                                     href="qh-set.htm#TOC"
+  >---------------------------------------</a><a name="SETref_">-</a>
+
+   SETref_( elem )
+     l.h.s. for modifying the current element in a FOREACH iteration
+
+   example:
+     SETref_(ridge)= anotherridge;
+*/
+#define SETref_(elem) (elem##p[-1])
+
+/*-<a                                     href="qh-set.htm#TOC"
+  >---------------------------------------</a><a name="SETelem_">-</a>
+
+   SETelem_(set, n)
+     return the n'th element of set
+
+   notes:
+      assumes that n is valid [0..size] and that set is defined
+      use SETelemt_() for type cast
+*/
+#define SETelem_(set, n)           ((set)->e[n].p)
+
+/*-<a                                     href="qh-set.htm#TOC"
+  >---------------------------------------</a><a name="SETelemt_">-</a>
+
+   SETelemt_(set, n, type)
+     return the n'th element of set as a type
+
+   notes:
+      assumes that n is valid [0..size] and that set is defined
+*/
+#define SETelemt_(set, n, type)    ((type*)((set)->e[n].p))
+
+/*-<a                                     href="qh-set.htm#TOC"
+  >---------------------------------------</a><a name="SETelemaddr_">-</a>
+
+   SETelemaddr_(set, n, type)
+     return address of the n'th element of a set
+
+   notes:
+      assumes that n is valid [0..size] and set is defined
+*/
+#define SETelemaddr_(set, n, type) ((type **)(&((set)->e[n].p)))
+
+/*-<a                                     href="qh-set.htm#TOC"
+  >---------------------------------------</a><a name="SETfirst_">-</a>
+
+   SETfirst_(set)
+     return first element of set
+
+*/
+#define SETfirst_(set)             ((set)->e[0].p)
+
+/*-<a                                     href="qh-set.htm#TOC"
+  >---------------------------------------</a><a name="SETfirstt_">-</a>
+
+   SETfirstt_(set, type)
+     return first element of set as a type
+
+*/
+#define SETfirstt_(set, type)      ((type*)((set)->e[0].p))
+
+/*-<a                                     href="qh-set.htm#TOC"
+  >---------------------------------------</a><a name="SETsecond_">-</a>
+
+   SETsecond_(set)
+     return second element of set
+
+*/
+#define SETsecond_(set)            ((set)->e[1].p)
+
+/*-<a                                     href="qh-set.htm#TOC"
+  >---------------------------------------</a><a name="SETsecondt_">-</a>
+
+   SETsecondt_(set, type)
+     return second element of set as a type
+*/
+#define SETsecondt_(set, type)     ((type*)((set)->e[1].p))
+
+/*-<a                                     href="qh-set.htm#TOC"
+  >---------------------------------------</a><a name="SETaddr_">-</a>
+
+   SETaddr_(set, type)
+       return address of set's elements
+*/
+#define SETaddr_(set,type)         ((type **)(&((set)->e[0].p)))
+
+/*-<a                                     href="qh-set.htm#TOC"
+  >---------------------------------------</a><a name="SETreturnsize_">-</a>
+
+   SETreturnsize_(set, size)
+     return size of a set
+
+   notes:
+      set must be defined
+      use qh_setsize(set) unless speed is critical
+*/
+#define SETreturnsize_(set, size) (((size)= ((set)->e[(set)->maxsize].i))?(--(size)):((size)= (set)->maxsize))
+
+/*-<a                                     href="qh-set.htm#TOC"
+  >---------------------------------------</a><a name="SETempty_">-</a>
+
+   SETempty_(set)
+     return true(1) if set is empty
+
+   notes:
+      set may be NULL
+*/
+#define SETempty_(set)            (!set || (SETfirst_(set) ? 0 : 1))
+
+/*-<a                             href="qh-set.htm#TOC"
+  >-------------------------------<a name="SETsizeaddr_">-</a>
+
+  SETsizeaddr_(set)
+    return pointer to 'actual size+1' of set (set CANNOT be NULL!!)
+    Its type is setelemT* for strict aliasing
+    All SETelemaddr_ must be cast to setelemT
+
+
+  notes:
+    *SETsizeaddr==NULL or e[*SETsizeaddr-1].p==NULL
+*/
+#define SETsizeaddr_(set) (&((set)->e[(set)->maxsize]))
+
+/*-<a                                     href="qh-set.htm#TOC"
+  >---------------------------------------</a><a name="SETtruncate_">-</a>
+
+   SETtruncate_(set, size)
+     truncate set to size
+
+   see:
+     qh_settruncate()
+
+*/
+#define SETtruncate_(set, size) {set->e[set->maxsize].i= size+1; /* maybe overwritten */ \
+      set->e[size].p= NULL;}
+
+/*======= prototypes in alphabetical order ============*/
+
+void  qh_setaddsorted(setT **setp, void *elem);
+void  qh_setaddnth(setT **setp, int nth, void *newelem);
+void  qh_setappend(setT **setp, void *elem);
+void  qh_setappend_set(setT **setp, setT *setA);
+void  qh_setappend2ndlast(setT **setp, void *elem);
+void  qh_setcheck(setT *set, const char *tname, unsigned id);
+void  qh_setcompact(setT *set);
+setT *qh_setcopy(setT *set, int extra);
+void *qh_setdel(setT *set, void *elem);
+void *qh_setdellast(setT *set);
+void *qh_setdelnth(setT *set, int nth);
+void *qh_setdelnthsorted(setT *set, int nth);
+void *qh_setdelsorted(setT *set, void *newelem);
+setT *qh_setduplicate( setT *set, int elemsize);
+void **qh_setendpointer(setT *set);
+int   qh_setequal(setT *setA, setT *setB);
+int   qh_setequal_except(setT *setA, void *skipelemA, setT *setB, void *skipelemB);
+int   qh_setequal_skip(setT *setA, int skipA, setT *setB, int skipB);
+void  qh_setfree(setT **set);
+void  qh_setfree2( setT **setp, int elemsize);
+void  qh_setfreelong(setT **set);
+int   qh_setin(setT *set, void *setelem);
+int   qh_setindex(setT *set, void *setelem);
+void  qh_setlarger(setT **setp);
+void *qh_setlast(setT *set);
+setT *qh_setnew(int size);
+setT *qh_setnew_delnthsorted(setT *set, int size, int nth, int prepend);
+void  qh_setprint(FILE *fp, const char* string, setT *set);
+void  qh_setreplace(setT *set, void *oldelem, void *newelem);
+int   qh_setsize(setT *set);
+setT *qh_settemp(int setsize);
+void  qh_settempfree(setT **set);
+void  qh_settempfree_all(void);
+setT *qh_settemppop(void);
+void  qh_settemppush(setT *set);
+void  qh_settruncate(setT *set, int size);
+int   qh_setunique(setT **set, void *elem);
+void  qh_setzero(setT *set, int idx, int size);
+
+
+#endif /* qhDEFset */
diff --git a/xs/src/qhull/src/libqhull/random.c b/xs/src/qhull/src/libqhull/random.c
new file mode 100644
index 0000000000..176d697aeb
--- /dev/null
+++ b/xs/src/qhull/src/libqhull/random.c
@@ -0,0 +1,245 @@
+/*<html><pre>  -<a                             href="index.htm#TOC"
+  >-------------------------------</a><a name="TOP">-</a>
+
+   random.c and utilities
+     Park & Miller's minimimal standard random number generator
+     argc/argv conversion
+
+     Used by rbox.  Do not use 'qh' 
+*/
+
+#include "libqhull.h"
+#include "random.h"
+
+#include <string.h>
+#include <stdio.h>
+#include <stdlib.h>
+
+#ifdef _MSC_VER  /* Microsoft Visual C++ -- warning level 4 */
+#pragma warning( disable : 4706)  /* assignment within conditional function */
+#pragma warning( disable : 4996)  /* function was declared deprecated(strcpy, localtime, etc.) */
+#endif
+
+/*-<a                             href="qh-globa.htm#TOC"
+ >-------------------------------</a><a name="argv_to_command">-</a>
+
+ qh_argv_to_command( argc, argv, command, max_size )
+
+    build command from argc/argv
+    max_size is at least
+
+ returns:
+    a space-delimited string of options (just as typed)
+    returns false if max_size is too short
+
+ notes:
+    silently removes
+    makes option string easy to input and output
+    matches qh_argv_to_command_size()
+
+    argc may be 0
+*/
+int qh_argv_to_command(int argc, char *argv[], char* command, int max_size) {
+  int i, remaining;
+  char *s;
+  *command= '\0';  /* max_size > 0 */
+
+  if (argc) {
+    if ((s= strrchr( argv[0], '\\')) /* get filename w/o .exe extension */
+    || (s= strrchr( argv[0], '/')))
+        s++;
+    else
+        s= argv[0];
+    if ((int)strlen(s) < max_size)   /* WARN64 */
+        strcpy(command, s);
+    else
+        goto error_argv;
+    if ((s= strstr(command, ".EXE"))
+    ||  (s= strstr(command, ".exe")))
+        *s= '\0';
+  }
+  for (i=1; i < argc; i++) {
+    s= argv[i];
+    remaining= max_size - (int)strlen(command) - (int)strlen(s) - 2;   /* WARN64 */
+    if (!*s || strchr(s, ' ')) {
+      char *t= command + strlen(command);
+      remaining -= 2;
+      if (remaining < 0) {
+        goto error_argv;
+      }
+      *t++= ' ';
+      *t++= '"';
+      while (*s) {
+        if (*s == '"') {
+          if (--remaining < 0)
+            goto error_argv;
+          *t++= '\\';
+        }
+        *t++= *s++;
+      }
+      *t++= '"';
+      *t= '\0';
+    }else if (remaining < 0) {
+      goto error_argv;
+    }else
+      strcat(command, " ");
+      strcat(command, s);
+  }
+  return 1;
+
+error_argv:
+  return 0;
+} /* argv_to_command */
+
+/*-<a                             href="qh-globa.htm#TOC"
+>-------------------------------</a><a name="argv_to_command_size">-</a>
+
+qh_argv_to_command_size( argc, argv )
+
+    return size to allocate for qh_argv_to_command()
+
+notes:
+    argc may be 0
+    actual size is usually shorter
+*/
+int qh_argv_to_command_size(int argc, char *argv[]) {
+    unsigned int count= 1; /* null-terminator if argc==0 */
+    int i;
+    char *s;
+
+    for (i=0; i<argc; i++){
+      count += (int)strlen(argv[i]) + 1;   /* WARN64 */
+      if (i>0 && strchr(argv[i], ' ')) {
+        count += 2;  /* quote delimiters */
+        for (s=argv[i]; *s; s++) {
+          if (*s == '"') {
+            count++;
+          }
+        }
+      }
+    }
+    return count;
+} /* argv_to_command_size */
+
+/*-<a                             href="qh-geom.htm#TOC"
+  >-------------------------------</a><a name="rand">-</a>
+
+  qh_rand()
+  qh_srand( seed )
+    generate pseudo-random number between 1 and 2^31 -2
+
+  notes:
+    For qhull and rbox, called from qh_RANDOMint(),etc. [user.h]
+
+    From Park & Miller's minimal standard random number generator
+      Communications of the ACM, 31:1192-1201, 1988.
+    Does not use 0 or 2^31 -1
+      this is silently enforced by qh_srand()
+    Can make 'Rn' much faster by moving qh_rand to qh_distplane
+*/
+
+/* Global variables and constants */
+
+int qh_last_random= 1;  /* define as global variable instead of using qh */
+
+#define qh_rand_a 16807
+#define qh_rand_m 2147483647
+#define qh_rand_q 127773  /* m div a */
+#define qh_rand_r 2836    /* m mod a */
+
+int qh_rand( void) {
+    int lo, hi, test;
+    int seed = qh_last_random;
+
+    hi = seed / qh_rand_q;  /* seed div q */
+    lo = seed % qh_rand_q;  /* seed mod q */
+    test = qh_rand_a * lo - qh_rand_r * hi;
+    if (test > 0)
+        seed= test;
+    else
+        seed= test + qh_rand_m;
+    qh_last_random= seed;
+    /* seed = seed < qh_RANDOMmax/2 ? 0 : qh_RANDOMmax;  for testing */
+    /* seed = qh_RANDOMmax;  for testing */
+    return seed;
+} /* rand */
+
+void qh_srand( int seed) {
+    if (seed < 1)
+        qh_last_random= 1;
+    else if (seed >= qh_rand_m)
+        qh_last_random= qh_rand_m - 1;
+    else
+        qh_last_random= seed;
+} /* qh_srand */
+
+/*-<a                             href="qh-geom.htm#TOC"
+>-------------------------------</a><a name="randomfactor">-</a>
+
+qh_randomfactor( scale, offset )
+  return a random factor r * scale + offset
+
+notes:
+  qh.RANDOMa/b are defined in global.c
+*/
+realT qh_randomfactor(realT scale, realT offset) {
+    realT randr;
+
+    randr= qh_RANDOMint;
+    return randr * scale + offset;
+} /* randomfactor */
+
+/*-<a                             href="qh-geom.htm#TOC"
+>-------------------------------</a><a name="randommatrix">-</a>
+
+qh_randommatrix( buffer, dim, rows )
+  generate a random dim X dim matrix in range [-1,1]
+  assumes buffer is [dim+1, dim]
+
+returns:
+  sets buffer to random numbers
+  sets rows to rows of buffer
+  sets row[dim] as scratch row
+*/
+void qh_randommatrix(realT *buffer, int dim, realT **rows) {
+    int i, k;
+    realT **rowi, *coord, realr;
+
+    coord= buffer;
+    rowi= rows;
+    for (i=0; i < dim; i++) {
+        *(rowi++)= coord;
+        for (k=0; k < dim; k++) {
+            realr= qh_RANDOMint;
+            *(coord++)= 2.0 * realr/(qh_RANDOMmax+1) - 1.0;
+        }
+    }
+    *rowi= coord;
+} /* randommatrix */
+
+/*-<a                             href="qh-globa.htm#TOC"
+  >-------------------------------</a><a name="strtol">-</a>
+
+  qh_strtol( s, endp) qh_strtod( s, endp)
+    internal versions of strtol() and strtod()
+    does not skip trailing spaces
+  notes:
+    some implementations of strtol()/strtod() skip trailing spaces
+*/
+double qh_strtod(const char *s, char **endp) {
+  double result;
+
+  result= strtod(s, endp);
+  if (s < (*endp) && (*endp)[-1] == ' ')
+    (*endp)--;
+  return result;
+} /* strtod */
+
+int qh_strtol(const char *s, char **endp) {
+  int result;
+
+  result= (int) strtol(s, endp, 10);     /* WARN64 */
+  if (s< (*endp) && (*endp)[-1] == ' ')
+    (*endp)--;
+  return result;
+} /* strtol */
diff --git a/xs/src/qhull/src/libqhull/random.h b/xs/src/qhull/src/libqhull/random.h
new file mode 100644
index 0000000000..0c6896b765
--- /dev/null
+++ b/xs/src/qhull/src/libqhull/random.h
@@ -0,0 +1,34 @@
+/*<html><pre>  -<a                             href="qh-geom.htm"
+  >-------------------------------</a><a name="TOP">-</a>
+
+  random.h
+    header file for random and utility routines
+
+   see qh-geom.htm and random.c
+
+   Copyright (c) 1993-2015 The Geometry Center.
+   $Id: //main/2015/qhull/src/libqhull/random.h#2 $$Change: 2026 $
+   $DateTime: 2015/11/07 22:44:39 $$Author: bbarber $
+*/
+
+#ifndef qhDEFrandom
+#define qhDEFrandom 1
+
+#include "libqhull.h"
+
+/*============= prototypes in alphabetical order ======= */
+
+
+int     qh_argv_to_command(int argc, char *argv[], char* command, int max_size);
+int     qh_argv_to_command_size(int argc, char *argv[]);
+int     qh_rand( void);
+void    qh_srand( int seed);
+realT   qh_randomfactor(realT scale, realT offset);
+void    qh_randommatrix(realT *buffer, int dim, realT **row);
+int     qh_strtol(const char *s, char **endp);
+double  qh_strtod(const char *s, char **endp);
+
+#endif /* qhDEFrandom */
+
+
+
diff --git a/xs/src/qhull/src/libqhull/rboxlib.c b/xs/src/qhull/src/libqhull/rboxlib.c
new file mode 100644
index 0000000000..f945133fa0
--- /dev/null
+++ b/xs/src/qhull/src/libqhull/rboxlib.c
@@ -0,0 +1,870 @@
+/*<html><pre>  -<a                             href="index.htm#TOC"
+  >-------------------------------</a><a name="TOP">-</a>
+
+   rboxlib.c
+     Generate input points
+
+   notes:
+     For documentation, see prompt[] of rbox.c
+     50 points generated for 'rbox D4'
+
+   WARNING:
+     incorrect range if qh_RANDOMmax is defined wrong (user.h)
+*/
+
+#include "libqhull.h"  /* First for user.h */
+#include "random.h"
+
+#include <ctype.h>
+#include <limits.h>
+#include <math.h>
+#include <setjmp.h>
+#include <string.h>
+#include <time.h>
+#include <stdio.h>
+#include <stdlib.h>
+
+#ifdef _MSC_VER  /* Microsoft Visual C++ */
+#pragma warning( disable : 4706)  /* assignment within conditional expression. */
+#pragma warning( disable : 4996)  /* this function (strncat,sprintf,strcpy) or variable may be unsafe. */
+#endif
+
+#define MAXdim 200
+#define PI 3.1415926535897932384
+
+/* ------------------------------ prototypes ----------------*/
+int qh_roundi( double a);
+void qh_out1( double a);
+void qh_out2n( double a, double b);
+void qh_out3n( double a, double b, double c);
+void qh_outcoord(int iscdd, double *coord, int dim);
+void qh_outcoincident(int coincidentpoints, double radius, int iscdd, double *coord, int dim);
+
+void    qh_fprintf_rbox(FILE *fp, int msgcode, const char *fmt, ... );
+void    qh_free(void *mem);
+void   *qh_malloc(size_t size);
+int     qh_rand( void);
+void    qh_srand( int seed);
+
+
+/* ------------------------------ globals -------------------*/
+
+/* No state is carried between rbox requests */
+typedef struct rboxT rboxT;
+struct rboxT {
+  FILE *fout;
+  FILE *ferr;
+  int isinteger;
+  double out_offset;
+  jmp_buf errexit;        /* exit label for rboxpoints, defined by setjmp(), called by qh_errexit_rbox() */
+  char  jmpXtra[40];      /* extra bytes in case jmp_buf is defined wrong by compiler */
+};
+
+
+int rbox_inuse= 0;
+rboxT rbox;
+
+/*-<a                             href="qh-qhull.htm#TOC"
+  >-------------------------------</a><a name="rboxpoints">-</a>
+
+  qh_rboxpoints( fout, ferr, rbox_command )
+    Generate points to fout according to rbox options
+    Report errors on ferr
+
+  returns:
+    0 (qh_ERRnone) on success
+    1 (qh_ERRinput) on input error
+    4 (qh_ERRmem) on memory error
+    5 (qh_ERRqhull) on internal error
+
+  notes:
+    To avoid using stdio, redefine qh_malloc, qh_free, and qh_fprintf_rbox (user.c)
+
+  design:
+    Straight line code (consider defining a struct and functions):
+
+    Parse arguments into variables
+    Determine the number of points
+    Generate the points
+*/
+int qh_rboxpoints(FILE* fout, FILE* ferr, char* rbox_command) {
+  int i,j,k;
+  int gendim;
+  int coincidentcount=0, coincidenttotal=0, coincidentpoints=0;
+  int cubesize, diamondsize, seed=0, count, apex;
+  int dim=3, numpoints=0, totpoints, addpoints=0;
+  int issphere=0, isaxis=0,  iscdd=0, islens=0, isregular=0, iswidth=0, addcube=0;
+  int isgap=0, isspiral=0, NOcommand=0, adddiamond=0;
+  int israndom=0, istime=0;
+  int isbox=0, issimplex=0, issimplex2=0, ismesh=0;
+  double width=0.0, gap=0.0, radius=0.0, coincidentradius=0.0;
+  double coord[MAXdim], offset, meshm=3.0, meshn=4.0, meshr=5.0;
+  double *coordp, *simplex= NULL, *simplexp;
+  int nthroot, mult[MAXdim];
+  double norm, factor, randr, rangap, lensangle=0, lensbase=1;
+  double anglediff, angle, x, y, cube=0.0, diamond=0.0;
+  double box= qh_DEFAULTbox; /* scale all numbers before output */
+  double randmax= qh_RANDOMmax;
+  char command[200], seedbuf[200];
+  char *s= command, *t, *first_point= NULL;
+  time_t timedata;
+  int exitcode;
+
+  if (rbox_inuse) {
+    qh_fprintf_rbox(rbox.ferr, 6188, "rbox error: rbox in use by another process.  Please lock calls to rbox.\n");
+    return qh_ERRqhull;
+  }
+  rbox_inuse= True;
+  rbox.ferr= ferr;
+  rbox.fout= fout;
+
+  exitcode= setjmp(rbox.errexit);
+  if (exitcode) {
+    /* same code for error exit and normal return.  qh.NOerrexit is set */
+    if (simplex)
+        qh_free(simplex);
+    rbox_inuse= False;
+    return exitcode;
+  }
+
+  *command= '\0';
+  strncat(command, rbox_command, sizeof(command)-strlen(command)-1);
+
+  while (*s && !isspace(*s))  /* skip program name */
+    s++;
+  while (*s) {
+    while (*s && isspace(*s))
+      s++;
+    if (*s == '-')
+      s++;
+    if (!*s)
+      break;
+    if (isdigit(*s)) {
+      numpoints= qh_strtol(s, &s);
+      continue;
+    }
+    /* ============= read flags =============== */
+    switch (*s++) {
+    case 'c':
+      addcube= 1;
+      t= s;
+      while (isspace(*t))
+        t++;
+      if (*t == 'G')
+        cube= qh_strtod(++t, &s);
+      break;
+    case 'd':
+      adddiamond= 1;
+      t= s;
+      while (isspace(*t))
+        t++;
+      if (*t == 'G')
+        diamond= qh_strtod(++t, &s);
+      break;
+    case 'h':
+      iscdd= 1;
+      break;
+    case 'l':
+      isspiral= 1;
+      break;
+    case 'n':
+      NOcommand= 1;
+      break;
+    case 'r':
+      isregular= 1;
+      break;
+    case 's':
+      issphere= 1;
+      break;
+    case 't':
+      istime= 1;
+      if (isdigit(*s)) {
+        seed= qh_strtol(s, &s);
+        israndom= 0;
+      }else
+        israndom= 1;
+      break;
+    case 'x':
+      issimplex= 1;
+      break;
+    case 'y':
+      issimplex2= 1;
+      break;
+    case 'z':
+      rbox.isinteger= 1;
+      break;
+    case 'B':
+      box= qh_strtod(s, &s);
+      isbox= 1;
+      break;
+    case 'C':
+      if (*s)
+        coincidentpoints=  qh_strtol(s, &s);
+      if (*s == ',') {
+        ++s;
+        coincidentradius=  qh_strtod(s, &s);
+      }
+      if (*s == ',') {
+        ++s;
+        coincidenttotal=  qh_strtol(s, &s);
+      }
+      if (*s && !isspace(*s)) {
+        qh_fprintf_rbox(rbox.ferr, 7080, "rbox error: arguments for 'Cn,r,m' are not 'int', 'float', and 'int'.  Remaining string is '%s'\n", s);
+        qh_errexit_rbox(qh_ERRinput);
+      }
+      if (coincidentpoints==0){
+        qh_fprintf_rbox(rbox.ferr, 6268, "rbox error: missing arguments for 'Cn,r,m' where n is the number of coincident points, r is the radius (default 0.0), and m is the number of points\n");
+        qh_errexit_rbox(qh_ERRinput);
+      }
+      if (coincidentpoints<0 || coincidenttotal<0 || coincidentradius<0.0){
+        qh_fprintf_rbox(rbox.ferr, 6269, "rbox error: negative arguments for 'Cn,m,r' where n (%d) is the number of coincident points, m (%d) is the number of points, and r (%.2g) is the radius (default 0.0)\n", coincidentpoints, coincidenttotal, coincidentradius);
+        qh_errexit_rbox(qh_ERRinput);
+      }
+      break;
+    case 'D':
+      dim= qh_strtol(s, &s);
+      if (dim < 1
+      || dim > MAXdim) {
+        qh_fprintf_rbox(rbox.ferr, 6189, "rbox error: dimension, D%d, out of bounds (>=%d or <=0)", dim, MAXdim);
+        qh_errexit_rbox(qh_ERRinput);
+      }
+      break;
+    case 'G':
+      if (isdigit(*s))
+        gap= qh_strtod(s, &s);
+      else
+        gap= 0.5;
+      isgap= 1;
+      break;
+    case 'L':
+      if (isdigit(*s))
+        radius= qh_strtod(s, &s);
+      else
+        radius= 10;
+      islens= 1;
+      break;
+    case 'M':
+      ismesh= 1;
+      if (*s)
+        meshn= qh_strtod(s, &s);
+      if (*s == ',') {
+        ++s;
+        meshm= qh_strtod(s, &s);
+      }else
+        meshm= 0.0;
+      if (*s == ',') {
+        ++s;
+        meshr= qh_strtod(s, &s);
+      }else
+        meshr= sqrt(meshn*meshn + meshm*meshm);
+      if (*s && !isspace(*s)) {
+        qh_fprintf_rbox(rbox.ferr, 7069, "rbox warning: assuming 'M3,4,5' since mesh args are not integers or reals\n");
+        meshn= 3.0, meshm=4.0, meshr=5.0;
+      }
+      break;
+    case 'O':
+      rbox.out_offset= qh_strtod(s, &s);
+      break;
+    case 'P':
+      if (!first_point)
+        first_point= s-1;
+      addpoints++;
+      while (*s && !isspace(*s))   /* read points later */
+        s++;
+      break;
+    case 'W':
+      width= qh_strtod(s, &s);
+      iswidth= 1;
+      break;
+    case 'Z':
+      if (isdigit(*s))
+        radius= qh_strtod(s, &s);
+      else
+        radius= 1.0;
+      isaxis= 1;
+      break;
+    default:
+      qh_fprintf_rbox(rbox.ferr, 7070, "rbox error: unknown flag at %s.\nExecute 'rbox' without arguments for documentation.\n", s);
+      qh_errexit_rbox(qh_ERRinput);
+    }
+    if (*s && !isspace(*s)) {
+      qh_fprintf_rbox(rbox.ferr, 7071, "rbox error: missing space between flags at %s.\n", s);
+      qh_errexit_rbox(qh_ERRinput);
+    }
+  }
+
+  /* ============= defaults, constants, and sizes =============== */
+  if (rbox.isinteger && !isbox)
+    box= qh_DEFAULTzbox;
+  if (addcube) {
+    cubesize= (int)floor(ldexp(1.0,dim)+0.5);
+    if (cube == 0.0)
+      cube= box;
+  }else
+    cubesize= 0;
+  if (adddiamond) {
+    diamondsize= 2*dim;
+    if (diamond == 0.0)
+      diamond= box;
+  }else
+    diamondsize= 0;
+  if (islens) {
+    if (isaxis) {
+        qh_fprintf_rbox(rbox.ferr, 6190, "rbox error: can not combine 'Ln' with 'Zn'\n");
+        qh_errexit_rbox(qh_ERRinput);
+    }
+    if (radius <= 1.0) {
+        qh_fprintf_rbox(rbox.ferr, 6191, "rbox error: lens radius %.2g should be greater than 1.0\n",
+               radius);
+        qh_errexit_rbox(qh_ERRinput);
+    }
+    lensangle= asin(1.0/radius);
+    lensbase= radius * cos(lensangle);
+  }
+
+  if (!numpoints) {
+    if (issimplex2)
+        ; /* ok */
+    else if (isregular + issimplex + islens + issphere + isaxis + isspiral + iswidth + ismesh) {
+        qh_fprintf_rbox(rbox.ferr, 6192, "rbox error: missing count\n");
+        qh_errexit_rbox(qh_ERRinput);
+    }else if (adddiamond + addcube + addpoints)
+        ; /* ok */
+    else {
+        numpoints= 50;  /* ./rbox D4 is the test case */
+        issphere= 1;
+    }
+  }
+  if ((issimplex + islens + isspiral + ismesh > 1)
+  || (issimplex + issphere + isspiral + ismesh > 1)) {
+    qh_fprintf_rbox(rbox.ferr, 6193, "rbox error: can only specify one of 'l', 's', 'x', 'Ln', or 'Mn,m,r' ('Ln s' is ok).\n");
+    qh_errexit_rbox(qh_ERRinput);
+  }
+  if (coincidentpoints>0 && (numpoints == 0 || coincidenttotal > numpoints)) {
+    qh_fprintf_rbox(rbox.ferr, 6270, "rbox error: 'Cn,r,m' requested n coincident points for each of m points.  Either there is no points or m (%d) is greater than the number of points (%d).\n", coincidenttotal, numpoints);
+    qh_errexit_rbox(qh_ERRinput);
+  }
+  if (coincidenttotal == 0)
+    coincidenttotal= numpoints;
+
+  /* ============= print header with total points =============== */
+  if (issimplex || ismesh)
+    totpoints= numpoints;
+  else if (issimplex2)
+    totpoints= numpoints+dim+1;
+  else if (isregular) {
+    totpoints= numpoints;
+    if (dim == 2) {
+        if (islens)
+          totpoints += numpoints - 2;
+    }else if (dim == 3) {
+        if (islens)
+          totpoints += 2 * numpoints;
+      else if (isgap)
+        totpoints += 1 + numpoints;
+      else
+        totpoints += 2;
+    }
+  }else
+    totpoints= numpoints + isaxis;
+  totpoints += cubesize + diamondsize + addpoints;
+  totpoints += coincidentpoints*coincidenttotal;
+
+  /* ============= seed randoms =============== */
+  if (istime == 0) {
+    for (s=command; *s; s++) {
+      if (issimplex2 && *s == 'y') /* make 'y' same seed as 'x' */
+        i= 'x';
+      else
+        i= *s;
+      seed= 11*seed + i;
+    }
+  }else if (israndom) {
+    seed= (int)time(&timedata);
+    sprintf(seedbuf, " t%d", seed);  /* appends an extra t, not worth removing */
+    strncat(command, seedbuf, sizeof(command)-strlen(command)-1);
+    t= strstr(command, " t ");
+    if (t)
+      strcpy(t+1, t+3); /* remove " t " */
+  } /* else, seed explicitly set to n */
+  qh_RANDOMseed_(seed);
+
+  /* ============= print header =============== */
+
+  if (iscdd)
+      qh_fprintf_rbox(rbox.fout, 9391, "%s\nbegin\n        %d %d %s\n",
+      NOcommand ? "" : command,
+      totpoints, dim+1,
+      rbox.isinteger ? "integer" : "real");
+  else if (NOcommand)
+      qh_fprintf_rbox(rbox.fout, 9392, "%d\n%d\n", dim, totpoints);
+  else
+      /* qh_fprintf_rbox special cases 9393 to append 'command' to the RboxPoints.comment() */
+      qh_fprintf_rbox(rbox.fout, 9393, "%d %s\n%d\n", dim, command, totpoints);
+
+  /* ============= explicit points =============== */
+  if ((s= first_point)) {
+    while (s && *s) { /* 'P' */
+      count= 0;
+      if (iscdd)
+        qh_out1( 1.0);
+      while (*++s) {
+        qh_out1( qh_strtod(s, &s));
+        count++;
+        if (isspace(*s) || !*s)
+          break;
+        if (*s != ',') {
+          qh_fprintf_rbox(rbox.ferr, 6194, "rbox error: missing comma after coordinate in %s\n\n", s);
+          qh_errexit_rbox(qh_ERRinput);
+        }
+      }
+      if (count < dim) {
+        for (k=dim-count; k--; )
+          qh_out1( 0.0);
+      }else if (count > dim) {
+        qh_fprintf_rbox(rbox.ferr, 6195, "rbox error: %d coordinates instead of %d coordinates in %s\n\n",
+                  count, dim, s);
+        qh_errexit_rbox(qh_ERRinput);
+      }
+      qh_fprintf_rbox(rbox.fout, 9394, "\n");
+      while ((s= strchr(s, 'P'))) {
+        if (isspace(s[-1]))
+          break;
+      }
+    }
+  }
+
+  /* ============= simplex distribution =============== */
+  if (issimplex+issimplex2) {
+    if (!(simplex= (double*)qh_malloc( dim * (dim+1) * sizeof(double)))) {
+      qh_fprintf_rbox(rbox.ferr, 6196, "rbox error: insufficient memory for simplex\n");
+      qh_errexit_rbox(qh_ERRmem); /* qh_ERRmem */
+    }
+    simplexp= simplex;
+    if (isregular) {
+      for (i=0; i<dim; i++) {
+        for (k=0; k<dim; k++)
+          *(simplexp++)= i==k ? 1.0 : 0.0;
+      }
+      for (k=0; k<dim; k++)
+        *(simplexp++)= -1.0;
+    }else {
+      for (i=0; i<dim+1; i++) {
+        for (k=0; k<dim; k++) {
+          randr= qh_RANDOMint;
+          *(simplexp++)= 2.0 * randr/randmax - 1.0;
+        }
+      }
+    }
+    if (issimplex2) {
+        simplexp= simplex;
+      for (i=0; i<dim+1; i++) {
+        if (iscdd)
+          qh_out1( 1.0);
+        for (k=0; k<dim; k++)
+          qh_out1( *(simplexp++) * box);
+        qh_fprintf_rbox(rbox.fout, 9395, "\n");
+      }
+    }
+    for (j=0; j<numpoints; j++) {
+      if (iswidth)
+        apex= qh_RANDOMint % (dim+1);
+      else
+        apex= -1;
+      for (k=0; k<dim; k++)
+        coord[k]= 0.0;
+      norm= 0.0;
+      for (i=0; i<dim+1; i++) {
+        randr= qh_RANDOMint;
+        factor= randr/randmax;
+        if (i == apex)
+          factor *= width;
+        norm += factor;
+        for (k=0; k<dim; k++) {
+          simplexp= simplex + i*dim + k;
+          coord[k] += factor * (*simplexp);
+        }
+      }
+      for (k=0; k<dim; k++)
+        coord[k] *= box/norm;
+      qh_outcoord(iscdd, coord, dim);
+      if(coincidentcount++ < coincidenttotal)
+        qh_outcoincident(coincidentpoints, coincidentradius, iscdd, coord, dim);
+    }
+    isregular= 0; /* continue with isbox */
+    numpoints= 0;
+  }
+
+  /* ============= mesh distribution =============== */
+  if (ismesh) {
+    nthroot= (int)(pow((double)numpoints, 1.0/dim) + 0.99999);
+    for (k=dim; k--; )
+      mult[k]= 0;
+    for (i=0; i < numpoints; i++) {
+      coordp= coord;
+      for (k=0; k < dim; k++) {
+        if (k == 0)
+          *(coordp++)= mult[0] * meshn + mult[1] * (-meshm);
+        else if (k == 1)
+          *(coordp++)= mult[0] * meshm + mult[1] * meshn;
+        else
+          *(coordp++)= mult[k] * meshr;
+      }
+      qh_outcoord(iscdd, coord, dim);
+      if(coincidentcount++ < coincidenttotal)
+          qh_outcoincident(coincidentpoints, coincidentradius, iscdd, coord, dim);
+      for (k=0; k < dim; k++) {
+        if (++mult[k] < nthroot)
+          break;
+        mult[k]= 0;
+      }
+    }
+  }
+  /* ============= regular points for 's' =============== */
+  else if (isregular && !islens) {
+    if (dim != 2 && dim != 3) {
+      qh_free(simplex);
+      qh_fprintf_rbox(rbox.ferr, 6197, "rbox error: regular points can be used only in 2-d and 3-d\n\n");
+      qh_errexit_rbox(qh_ERRinput);
+    }
+    if (!isaxis || radius == 0.0) {
+      isaxis= 1;
+      radius= 1.0;
+    }
+    if (dim == 3) {
+      if (iscdd)
+        qh_out1( 1.0);
+      qh_out3n( 0.0, 0.0, -box);
+      if (!isgap) {
+        if (iscdd)
+          qh_out1( 1.0);
+        qh_out3n( 0.0, 0.0, box);
+      }
+    }
+    angle= 0.0;
+    anglediff= 2.0 * PI/numpoints;
+    for (i=0; i < numpoints; i++) {
+      angle += anglediff;
+      x= radius * cos(angle);
+      y= radius * sin(angle);
+      if (dim == 2) {
+        if (iscdd)
+          qh_out1( 1.0);
+        qh_out2n( x*box, y*box);
+      }else {
+        norm= sqrt(1.0 + x*x + y*y);
+        if (iscdd)
+          qh_out1( 1.0);
+        qh_out3n( box*x/norm, box*y/norm, box/norm);
+        if (isgap) {
+          x *= 1-gap;
+          y *= 1-gap;
+          norm= sqrt(1.0 + x*x + y*y);
+          if (iscdd)
+            qh_out1( 1.0);
+          qh_out3n( box*x/norm, box*y/norm, box/norm);
+        }
+      }
+    }
+  }
+  /* ============= regular points for 'r Ln D2' =============== */
+  else if (isregular && islens && dim == 2) {
+    double cos_0;
+
+    angle= lensangle;
+    anglediff= 2 * lensangle/(numpoints - 1);
+    cos_0= cos(lensangle);
+    for (i=0; i < numpoints; i++, angle -= anglediff) {
+      x= radius * sin(angle);
+      y= radius * (cos(angle) - cos_0);
+      if (iscdd)
+        qh_out1( 1.0);
+      qh_out2n( x*box, y*box);
+      if (i != 0 && i != numpoints - 1) {
+        if (iscdd)
+          qh_out1( 1.0);
+        qh_out2n( x*box, -y*box);
+      }
+    }
+  }
+  /* ============= regular points for 'r Ln D3' =============== */
+  else if (isregular && islens && dim != 2) {
+    if (dim != 3) {
+      qh_free(simplex);
+      qh_fprintf_rbox(rbox.ferr, 6198, "rbox error: regular points can be used only in 2-d and 3-d\n\n");
+      qh_errexit_rbox(qh_ERRinput);
+    }
+    angle= 0.0;
+    anglediff= 2* PI/numpoints;
+    if (!isgap) {
+      isgap= 1;
+      gap= 0.5;
+    }
+    offset= sqrt(radius * radius - (1-gap)*(1-gap)) - lensbase;
+    for (i=0; i < numpoints; i++, angle += anglediff) {
+      x= cos(angle);
+      y= sin(angle);
+      if (iscdd)
+        qh_out1( 1.0);
+      qh_out3n( box*x, box*y, 0.0);
+      x *= 1-gap;
+      y *= 1-gap;
+      if (iscdd)
+        qh_out1( 1.0);
+      qh_out3n( box*x, box*y, box * offset);
+      if (iscdd)
+        qh_out1( 1.0);
+      qh_out3n( box*x, box*y, -box * offset);
+    }
+  }
+  /* ============= apex of 'Zn' distribution + gendim =============== */
+  else {
+    if (isaxis) {
+      gendim= dim-1;
+      if (iscdd)
+        qh_out1( 1.0);
+      for (j=0; j < gendim; j++)
+        qh_out1( 0.0);
+      qh_out1( -box);
+      qh_fprintf_rbox(rbox.fout, 9398, "\n");
+    }else if (islens)
+      gendim= dim-1;
+    else
+      gendim= dim;
+    /* ============= generate random point in unit cube =============== */
+    for (i=0; i < numpoints; i++) {
+      norm= 0.0;
+      for (j=0; j < gendim; j++) {
+        randr= qh_RANDOMint;
+        coord[j]= 2.0 * randr/randmax - 1.0;
+        norm += coord[j] * coord[j];
+      }
+      norm= sqrt(norm);
+      /* ============= dim-1 point of 'Zn' distribution ========== */
+      if (isaxis) {
+        if (!isgap) {
+          isgap= 1;
+          gap= 1.0;
+        }
+        randr= qh_RANDOMint;
+        rangap= 1.0 - gap * randr/randmax;
+        factor= radius * rangap / norm;
+        for (j=0; j<gendim; j++)
+          coord[j]= factor * coord[j];
+      /* ============= dim-1 point of 'Ln s' distribution =========== */
+      }else if (islens && issphere) {
+        if (!isgap) {
+          isgap= 1;
+          gap= 1.0;
+        }
+        randr= qh_RANDOMint;
+        rangap= 1.0 - gap * randr/randmax;
+        factor= rangap / norm;
+        for (j=0; j<gendim; j++)
+          coord[j]= factor * coord[j];
+      /* ============= dim-1 point of 'Ln' distribution ========== */
+      }else if (islens && !issphere) {
+        if (!isgap) {
+          isgap= 1;
+          gap= 1.0;
+        }
+        j= qh_RANDOMint % gendim;
+        if (coord[j] < 0)
+          coord[j]= -1.0 - coord[j] * gap;
+        else
+          coord[j]= 1.0 - coord[j] * gap;
+      /* ============= point of 'l' distribution =============== */
+      }else if (isspiral) {
+        if (dim != 3) {
+          qh_free(simplex);
+          qh_fprintf_rbox(rbox.ferr, 6199, "rbox error: spiral distribution is available only in 3d\n\n");
+          qh_errexit_rbox(qh_ERRinput);
+        }
+        coord[0]= cos(2*PI*i/(numpoints - 1));
+        coord[1]= sin(2*PI*i/(numpoints - 1));
+        coord[2]= 2.0*(double)i/(double)(numpoints-1) - 1.0;
+      /* ============= point of 's' distribution =============== */
+      }else if (issphere) {
+        factor= 1.0/norm;
+        if (iswidth) {
+          randr= qh_RANDOMint;
+          factor *= 1.0 - width * randr/randmax;
+        }
+        for (j=0; j<dim; j++)
+          coord[j]= factor * coord[j];
+      }
+      /* ============= project 'Zn s' point in to sphere =============== */
+      if (isaxis && issphere) {
+        coord[dim-1]= 1.0;
+        norm= 1.0;
+        for (j=0; j<gendim; j++)
+          norm += coord[j] * coord[j];
+        norm= sqrt(norm);
+        for (j=0; j<dim; j++)
+          coord[j]= coord[j] / norm;
+        if (iswidth) {
+          randr= qh_RANDOMint;
+          coord[dim-1] *= 1 - width * randr/randmax;
+        }
+      /* ============= project 'Zn' point onto cube =============== */
+      }else if (isaxis && !issphere) {  /* not very interesting */
+        randr= qh_RANDOMint;
+        coord[dim-1]= 2.0 * randr/randmax - 1.0;
+      /* ============= project 'Ln' point out to sphere =============== */
+      }else if (islens) {
+        coord[dim-1]= lensbase;
+        for (j=0, norm= 0; j<dim; j++)
+          norm += coord[j] * coord[j];
+        norm= sqrt(norm);
+        for (j=0; j<dim; j++)
+          coord[j]= coord[j] * radius/ norm;
+        coord[dim-1] -= lensbase;
+        if (iswidth) {
+          randr= qh_RANDOMint;
+          coord[dim-1] *= 1 - width * randr/randmax;
+        }
+        if (qh_RANDOMint > randmax/2)
+          coord[dim-1]= -coord[dim-1];
+      /* ============= project 'Wn' point toward boundary =============== */
+      }else if (iswidth && !issphere) {
+        j= qh_RANDOMint % gendim;
+        if (coord[j] < 0)
+          coord[j]= -1.0 - coord[j] * width;
+        else
+          coord[j]= 1.0 - coord[j] * width;
+      }
+      /* ============= scale point to box =============== */
+      for (k=0; k<dim; k++)
+          coord[k]= coord[k] * box;
+
+      /* ============= write output =============== */
+      qh_outcoord(iscdd, coord, dim);
+      if(coincidentcount++ < coincidenttotal)
+        qh_outcoincident(coincidentpoints, coincidentradius, iscdd, coord, dim);
+    }
+  }
+
+  /* ============= write cube vertices =============== */
+  if (addcube) {
+    for (j=0; j<cubesize; j++) {
+      if (iscdd)
+        qh_out1( 1.0);
+      for (k=dim-1; k>=0; k--) {
+        if (j & ( 1 << k))
+          qh_out1( cube);
+        else
+          qh_out1( -cube);
+      }
+      qh_fprintf_rbox(rbox.fout, 9400, "\n");
+    }
+  }
+
+  /* ============= write diamond vertices =============== */
+  if (adddiamond) {
+    for (j=0; j<diamondsize; j++) {
+      if (iscdd)
+        qh_out1( 1.0);
+      for (k=dim-1; k>=0; k--) {
+        if (j/2 != k)
+          qh_out1( 0.0);
+        else if (j & 0x1)
+          qh_out1( diamond);
+        else
+          qh_out1( -diamond);
+      }
+      qh_fprintf_rbox(rbox.fout, 9401, "\n");
+    }
+  }
+
+  if (iscdd)
+    qh_fprintf_rbox(rbox.fout, 9402, "end\nhull\n");
+
+  /* same code for error exit and normal return */
+  qh_free(simplex);
+  rbox_inuse= False;
+  return qh_ERRnone;
+} /* rboxpoints */
+
+/*------------------------------------------------
+outxxx - output functions for qh_rboxpoints
+*/
+int qh_roundi( double a) {
+  if (a < 0.0) {
+    if (a - 0.5 < INT_MIN) {
+      qh_fprintf_rbox(rbox.ferr, 6200, "rbox input error: negative coordinate %2.2g is too large.  Reduce 'Bn'\n", a);
+      qh_errexit_rbox(qh_ERRinput);
+    }
+    return (int)(a - 0.5);
+  }else {
+    if (a + 0.5 > INT_MAX) {
+      qh_fprintf_rbox(rbox.ferr, 6201, "rbox input error: coordinate %2.2g is too large.  Reduce 'Bn'\n", a);
+      qh_errexit_rbox(qh_ERRinput);
+    }
+    return (int)(a + 0.5);
+  }
+} /* qh_roundi */
+
+void qh_out1(double a) {
+
+  if (rbox.isinteger)
+    qh_fprintf_rbox(rbox.fout, 9403, "%d ", qh_roundi( a+rbox.out_offset));
+  else
+    qh_fprintf_rbox(rbox.fout, 9404, qh_REAL_1, a+rbox.out_offset);
+} /* qh_out1 */
+
+void qh_out2n( double a, double b) {
+
+  if (rbox.isinteger)
+    qh_fprintf_rbox(rbox.fout, 9405, "%d %d\n", qh_roundi(a+rbox.out_offset), qh_roundi(b+rbox.out_offset));
+  else
+    qh_fprintf_rbox(rbox.fout, 9406, qh_REAL_2n, a+rbox.out_offset, b+rbox.out_offset);
+} /* qh_out2n */
+
+void qh_out3n( double a, double b, double c) {
+
+  if (rbox.isinteger)
+    qh_fprintf_rbox(rbox.fout, 9407, "%d %d %d\n", qh_roundi(a+rbox.out_offset), qh_roundi(b+rbox.out_offset), qh_roundi(c+rbox.out_offset));
+  else
+    qh_fprintf_rbox(rbox.fout, 9408, qh_REAL_3n, a+rbox.out_offset, b+rbox.out_offset, c+rbox.out_offset);
+} /* qh_out3n */
+
+void qh_outcoord(int iscdd, double *coord, int dim) {
+    double *p= coord;
+    int k;
+
+    if (iscdd)
+      qh_out1( 1.0);
+    for (k=0; k < dim; k++)
+      qh_out1(*(p++));
+    qh_fprintf_rbox(rbox.fout, 9396, "\n");
+} /* qh_outcoord */
+
+void qh_outcoincident(int coincidentpoints, double radius, int iscdd, double *coord, int dim) {
+  double *p;
+  double randr, delta;
+  int i,k;
+  double randmax= qh_RANDOMmax;
+
+  for (i= 0; i<coincidentpoints; i++) {
+    p= coord;
+    if (iscdd)
+      qh_out1( 1.0);
+    for (k=0; k < dim; k++) {
+      randr= qh_RANDOMint;
+      delta= 2.0 * randr/randmax - 1.0; /* -1..+1 */
+      delta *= radius;
+      qh_out1(*(p++) + delta);
+    }
+    qh_fprintf_rbox(rbox.fout, 9410, "\n");
+  }
+} /* qh_outcoincident */
+
+/*------------------------------------------------
+   Only called from qh_rboxpoints or qh_fprintf_rbox
+   qh_fprintf_rbox is only called from qh_rboxpoints
+*/
+void qh_errexit_rbox(int exitcode)
+{
+    longjmp(rbox.errexit, exitcode);
+} /* qh_errexit_rbox */
+
diff --git a/xs/src/qhull/src/libqhull/stat.c b/xs/src/qhull/src/libqhull/stat.c
new file mode 100644
index 0000000000..70196bbb0d
--- /dev/null
+++ b/xs/src/qhull/src/libqhull/stat.c
@@ -0,0 +1,717 @@
+/*<html><pre>  -<a                             href="qh-stat.htm"
+  >-------------------------------</a><a name="TOP">-</a>
+
+   stat.c
+   contains all statistics that are collected for qhull
+
+   see qh-stat.htm and stat.h
+
+   Copyright (c) 1993-2015 The Geometry Center.
+   $Id: //main/2015/qhull/src/libqhull/stat.c#5 $$Change: 2062 $
+   $DateTime: 2016/01/17 13:13:18 $$Author: bbarber $
+*/
+
+#include "qhull_a.h"
+
+/*============ global data structure ==========*/
+
+#if qh_QHpointer
+qhstatT *qh_qhstat=NULL;  /* global data structure */
+#else
+qhstatT qh_qhstat;   /* add "={0}" if this causes a compiler error */
+#endif
+
+/*========== functions in alphabetic order ================*/
+
+/*-<a                             href="qh-stat.htm#TOC"
+  >-------------------------------</a><a name="allstatA">-</a>
+
+  qh_allstatA()
+    define statistics in groups of 20
+
+  notes:
+    (otherwise, 'gcc -O2' uses too much memory)
+    uses qhstat.next
+*/
+void qh_allstatA(void) {
+
+   /* zdef_(type,name,doc,average) */
+  zzdef_(zdoc, Zdoc2, "precision statistics", -1);
+  zdef_(zinc, Znewvertex, NULL, -1);
+  zdef_(wadd, Wnewvertex, "ave. distance of a new vertex to a facet(!0s)", Znewvertex);
+  zzdef_(wmax, Wnewvertexmax, "max. distance of a new vertex to a facet", -1);
+  zdef_(wmax, Wvertexmax, "max. distance of an output vertex to a facet", -1);
+  zdef_(wmin, Wvertexmin, "min. distance of an output vertex to a facet", -1);
+  zdef_(wmin, Wmindenom, "min. denominator in hyperplane computation", -1);
+
+  qhstat precision= qhstat next;  /* call qh_precision for each of these */
+  zzdef_(zdoc, Zdoc3, "precision problems (corrected unless 'Q0' or an error)", -1);
+  zzdef_(zinc, Zcoplanarridges, "coplanar half ridges in output", -1);
+  zzdef_(zinc, Zconcaveridges, "concave half ridges in output", -1);
+  zzdef_(zinc, Zflippedfacets, "flipped facets", -1);
+  zzdef_(zinc, Zcoplanarhorizon, "coplanar horizon facets for new vertices", -1);
+  zzdef_(zinc, Zcoplanarpart, "coplanar points during partitioning", -1);
+  zzdef_(zinc, Zminnorm, "degenerate hyperplanes recomputed with gaussian elimination", -1);
+  zzdef_(zinc, Znearlysingular, "nearly singular or axis-parallel hyperplanes", -1);
+  zzdef_(zinc, Zback0, "zero divisors during back substitute", -1);
+  zzdef_(zinc, Zgauss0, "zero divisors during gaussian elimination", -1);
+  zzdef_(zinc, Zmultiridge, "ridges with multiple neighbors", -1);
+}
+void qh_allstatB(void) {
+  zzdef_(zdoc, Zdoc1, "summary information", -1);
+  zdef_(zinc, Zvertices, "number of vertices in output", -1);
+  zdef_(zinc, Znumfacets, "number of facets in output", -1);
+  zdef_(zinc, Znonsimplicial, "number of non-simplicial facets in output", -1);
+  zdef_(zinc, Znowsimplicial, "number of simplicial facets that were merged", -1);
+  zdef_(zinc, Znumridges, "number of ridges in output", -1);
+  zdef_(zadd, Znumridges, "average number of ridges per facet", Znumfacets);
+  zdef_(zmax, Zmaxridges, "maximum number of ridges", -1);
+  zdef_(zadd, Znumneighbors, "average number of neighbors per facet", Znumfacets);
+  zdef_(zmax, Zmaxneighbors, "maximum number of neighbors", -1);
+  zdef_(zadd, Znumvertices, "average number of vertices per facet", Znumfacets);
+  zdef_(zmax, Zmaxvertices, "maximum number of vertices", -1);
+  zdef_(zadd, Znumvneighbors, "average number of neighbors per vertex", Zvertices);
+  zdef_(zmax, Zmaxvneighbors, "maximum number of neighbors", -1);
+  zdef_(wadd, Wcpu, "cpu seconds for qhull after input", -1);
+  zdef_(zinc, Ztotvertices, "vertices created altogether", -1);
+  zzdef_(zinc, Zsetplane, "facets created altogether", -1);
+  zdef_(zinc, Ztotridges, "ridges created altogether", -1);
+  zdef_(zinc, Zpostfacets, "facets before post merge", -1);
+  zdef_(zadd, Znummergetot, "average merges per facet(at most 511)", Znumfacets);
+  zdef_(zmax, Znummergemax, "  maximum merges for a facet(at most 511)", -1);
+  zdef_(zinc, Zangle, NULL, -1);
+  zdef_(wadd, Wangle, "average angle(cosine) of facet normals for all ridges", Zangle);
+  zdef_(wmax, Wanglemax, "  maximum angle(cosine) of facet normals across a ridge", -1);
+  zdef_(wmin, Wanglemin, "  minimum angle(cosine) of facet normals across a ridge", -1);
+  zdef_(wadd, Wareatot, "total area of facets", -1);
+  zdef_(wmax, Wareamax, "  maximum facet area", -1);
+  zdef_(wmin, Wareamin, "  minimum facet area", -1);
+}
+void qh_allstatC(void) {
+  zdef_(zdoc, Zdoc9, "build hull statistics", -1);
+  zzdef_(zinc, Zprocessed, "points processed", -1);
+  zzdef_(zinc, Zretry, "retries due to precision problems", -1);
+  zdef_(wmax, Wretrymax, "  max. random joggle", -1);
+  zdef_(zmax, Zmaxvertex, "max. vertices at any one time", -1);
+  zdef_(zinc, Ztotvisible, "ave. visible facets per iteration", Zprocessed);
+  zdef_(zinc, Zinsidevisible, "  ave. visible facets without an horizon neighbor", Zprocessed);
+  zdef_(zadd, Zvisfacettot,  "  ave. facets deleted per iteration", Zprocessed);
+  zdef_(zmax, Zvisfacetmax,  "    maximum", -1);
+  zdef_(zadd, Zvisvertextot, "ave. visible vertices per iteration", Zprocessed);
+  zdef_(zmax, Zvisvertexmax, "    maximum", -1);
+  zdef_(zinc, Ztothorizon, "ave. horizon facets per iteration", Zprocessed);
+  zdef_(zadd, Znewfacettot,  "ave. new or merged facets per iteration", Zprocessed);
+  zdef_(zmax, Znewfacetmax,  "    maximum(includes initial simplex)", -1);
+  zdef_(wadd, Wnewbalance, "average new facet balance", Zprocessed);
+  zdef_(wadd, Wnewbalance2, "  standard deviation", -1);
+  zdef_(wadd, Wpbalance, "average partition balance", Zpbalance);
+  zdef_(wadd, Wpbalance2, "  standard deviation", -1);
+  zdef_(zinc, Zpbalance, "  number of trials", -1);
+  zdef_(zinc, Zsearchpoints, "searches of all points for initial simplex", -1);
+  zdef_(zinc, Zdetsimplex, "determinants computed(area & initial hull)", -1);
+  zdef_(zinc, Znoarea, "determinants not computed because vertex too low", -1);
+  zdef_(zinc, Znotmax, "points ignored(!above max_outside)", -1);
+  zdef_(zinc, Znotgood, "points ignored(!above a good facet)", -1);
+  zdef_(zinc, Znotgoodnew, "points ignored(didn't create a good new facet)", -1);
+  zdef_(zinc, Zgoodfacet, "good facets found", -1);
+  zzdef_(zinc, Znumvisibility, "distance tests for facet visibility", -1);
+  zdef_(zinc, Zdistvertex, "distance tests to report minimum vertex", -1);
+  zzdef_(zinc, Ztotcheck, "points checked for facets' outer planes", -1);
+  zzdef_(zinc, Zcheckpart, "  ave. distance tests per check", Ztotcheck);
+}
+void qh_allstatD(void) {
+  zdef_(zinc, Zvisit, "resets of visit_id", -1);
+  zdef_(zinc, Zvvisit, "  resets of vertex_visit", -1);
+  zdef_(zmax, Zvisit2max, "  max visit_id/2", -1);
+  zdef_(zmax, Zvvisit2max, "  max vertex_visit/2", -1);
+
+  zdef_(zdoc, Zdoc4, "partitioning statistics(see previous for outer planes)", -1);
+  zzdef_(zadd, Zdelvertextot, "total vertices deleted", -1);
+  zdef_(zmax, Zdelvertexmax, "    maximum vertices deleted per iteration", -1);
+  zdef_(zinc, Zfindbest, "calls to findbest", -1);
+  zdef_(zadd, Zfindbesttot, " ave. facets tested", Zfindbest);
+  zdef_(zmax, Zfindbestmax, " max. facets tested", -1);
+  zdef_(zadd, Zfindcoplanar, " ave. coplanar search", Zfindbest);
+  zdef_(zinc, Zfindnew, "calls to findbestnew", -1);
+  zdef_(zadd, Zfindnewtot, " ave. facets tested", Zfindnew);
+  zdef_(zmax, Zfindnewmax, " max. facets tested", -1);
+  zdef_(zinc, Zfindnewjump, " ave. clearly better", Zfindnew);
+  zdef_(zinc, Zfindnewsharp, " calls due to qh_sharpnewfacets", -1);
+  zdef_(zinc, Zfindhorizon, "calls to findhorizon", -1);
+  zdef_(zadd, Zfindhorizontot, " ave. facets tested", Zfindhorizon);
+  zdef_(zmax, Zfindhorizonmax, " max. facets tested", -1);
+  zdef_(zinc, Zfindjump,       " ave. clearly better", Zfindhorizon);
+  zdef_(zinc, Zparthorizon, " horizon facets better than bestfacet", -1);
+  zdef_(zinc, Zpartangle, "angle tests for repartitioned coplanar points", -1);
+  zdef_(zinc, Zpartflip, "  repartitioned coplanar points for flipped orientation", -1);
+}
+void qh_allstatE(void) {
+  zdef_(zinc, Zpartinside, "inside points", -1);
+  zdef_(zinc, Zpartnear, "  inside points kept with a facet", -1);
+  zdef_(zinc, Zcoplanarinside, "  inside points that were coplanar with a facet", -1);
+  zdef_(zinc, Zbestlower, "calls to findbestlower", -1);
+  zdef_(zinc, Zbestlowerv, "  with search of vertex neighbors", -1);
+  zdef_(zinc, Zbestlowerall, "  with rare search of all facets", -1);
+  zdef_(zmax, Zbestloweralln, "  facets per search of all facets", -1);
+  zdef_(wadd, Wmaxout, "difference in max_outside at final check", -1);
+  zzdef_(zinc, Zpartitionall, "distance tests for initial partition", -1);
+  zdef_(zinc, Ztotpartition, "partitions of a point", -1);
+  zzdef_(zinc, Zpartition, "distance tests for partitioning", -1);
+  zzdef_(zinc, Zdistcheck, "distance tests for checking flipped facets", -1);
+  zzdef_(zinc, Zdistconvex, "distance tests for checking convexity", -1);
+  zdef_(zinc, Zdistgood, "distance tests for checking good point", -1);
+  zdef_(zinc, Zdistio, "distance tests for output", -1);
+  zdef_(zinc, Zdiststat, "distance tests for statistics", -1);
+  zdef_(zinc, Zdistplane, "total number of distance tests", -1);
+  zdef_(zinc, Ztotpartcoplanar, "partitions of coplanar points or deleted vertices", -1);
+  zzdef_(zinc, Zpartcoplanar, "   distance tests for these partitions", -1);
+  zdef_(zinc, Zcomputefurthest, "distance tests for computing furthest", -1);
+}
+void qh_allstatE2(void) {
+  zdef_(zdoc, Zdoc5, "statistics for matching ridges", -1);
+  zdef_(zinc, Zhashlookup, "total lookups for matching ridges of new facets", -1);
+  zdef_(zinc, Zhashtests, "average number of tests to match a ridge", Zhashlookup);
+  zdef_(zinc, Zhashridge, "total lookups of subridges(duplicates and boundary)", -1);
+  zdef_(zinc, Zhashridgetest, "average number of tests per subridge", Zhashridge);
+  zdef_(zinc, Zdupsame, "duplicated ridges in same merge cycle", -1);
+  zdef_(zinc, Zdupflip, "duplicated ridges with flipped facets", -1);
+
+  zdef_(zdoc, Zdoc6, "statistics for determining merges", -1);
+  zdef_(zinc, Zangletests, "angles computed for ridge convexity", -1);
+  zdef_(zinc, Zbestcentrum, "best merges used centrum instead of vertices",-1);
+  zzdef_(zinc, Zbestdist, "distance tests for best merge", -1);
+  zzdef_(zinc, Zcentrumtests, "distance tests for centrum convexity", -1);
+  zzdef_(zinc, Zdistzero, "distance tests for checking simplicial convexity", -1);
+  zdef_(zinc, Zcoplanarangle, "coplanar angles in getmergeset", -1);
+  zdef_(zinc, Zcoplanarcentrum, "coplanar centrums in getmergeset", -1);
+  zdef_(zinc, Zconcaveridge, "concave ridges in getmergeset", -1);
+}
+void qh_allstatF(void) {
+  zdef_(zdoc, Zdoc7, "statistics for merging", -1);
+  zdef_(zinc, Zpremergetot, "merge iterations", -1);
+  zdef_(zadd, Zmergeinittot, "ave. initial non-convex ridges per iteration", Zpremergetot);
+  zdef_(zadd, Zmergeinitmax, "  maximum", -1);
+  zdef_(zadd, Zmergesettot, "  ave. additional non-convex ridges per iteration", Zpremergetot);
+  zdef_(zadd, Zmergesetmax, "  maximum additional in one pass", -1);
+  zdef_(zadd, Zmergeinittot2, "initial non-convex ridges for post merging", -1);
+  zdef_(zadd, Zmergesettot2, "  additional non-convex ridges", -1);
+  zdef_(wmax, Wmaxoutside, "max distance of vertex or coplanar point above facet(w/roundoff)", -1);
+  zdef_(wmin, Wminvertex, "max distance of merged vertex below facet(or roundoff)", -1);
+  zdef_(zinc, Zwidefacet, "centrums frozen due to a wide merge", -1);
+  zdef_(zinc, Zwidevertices, "centrums frozen due to extra vertices", -1);
+  zzdef_(zinc, Ztotmerge, "total number of facets or cycles of facets merged", -1);
+  zdef_(zinc, Zmergesimplex, "merged a simplex", -1);
+  zdef_(zinc, Zonehorizon, "simplices merged into coplanar horizon", -1);
+  zzdef_(zinc, Zcyclehorizon, "cycles of facets merged into coplanar horizon", -1);
+  zzdef_(zadd, Zcyclefacettot, "  ave. facets per cycle", Zcyclehorizon);
+  zdef_(zmax, Zcyclefacetmax, "  max. facets", -1);
+  zdef_(zinc, Zmergeintohorizon, "new facets merged into horizon", -1);
+  zdef_(zinc, Zmergenew, "new facets merged", -1);
+  zdef_(zinc, Zmergehorizon, "horizon facets merged into new facets", -1);
+  zdef_(zinc, Zmergevertex, "vertices deleted by merging", -1);
+  zdef_(zinc, Zcyclevertex, "vertices deleted by merging into coplanar horizon", -1);
+  zdef_(zinc, Zdegenvertex, "vertices deleted by degenerate facet", -1);
+  zdef_(zinc, Zmergeflipdup, "merges due to flipped facets in duplicated ridge", -1);
+  zdef_(zinc, Zneighbor, "merges due to redundant neighbors", -1);
+  zdef_(zadd, Ztestvneighbor, "non-convex vertex neighbors", -1);
+}
+void qh_allstatG(void) {
+  zdef_(zinc, Zacoplanar, "merges due to angle coplanar facets", -1);
+  zdef_(wadd, Wacoplanartot, "  average merge distance", Zacoplanar);
+  zdef_(wmax, Wacoplanarmax, "  maximum merge distance", -1);
+  zdef_(zinc, Zcoplanar, "merges due to coplanar facets", -1);
+  zdef_(wadd, Wcoplanartot, "  average merge distance", Zcoplanar);
+  zdef_(wmax, Wcoplanarmax, "  maximum merge distance", -1);
+  zdef_(zinc, Zconcave, "merges due to concave facets", -1);
+  zdef_(wadd, Wconcavetot, "  average merge distance", Zconcave);
+  zdef_(wmax, Wconcavemax, "  maximum merge distance", -1);
+  zdef_(zinc, Zavoidold, "coplanar/concave merges due to avoiding old merge", -1);
+  zdef_(wadd, Wavoidoldtot, "  average merge distance", Zavoidold);
+  zdef_(wmax, Wavoidoldmax, "  maximum merge distance", -1);
+  zdef_(zinc, Zdegen, "merges due to degenerate facets", -1);
+  zdef_(wadd, Wdegentot, "  average merge distance", Zdegen);
+  zdef_(wmax, Wdegenmax, "  maximum merge distance", -1);
+  zdef_(zinc, Zflipped, "merges due to removing flipped facets", -1);
+  zdef_(wadd, Wflippedtot, "  average merge distance", Zflipped);
+  zdef_(wmax, Wflippedmax, "  maximum merge distance", -1);
+  zdef_(zinc, Zduplicate, "merges due to duplicated ridges", -1);
+  zdef_(wadd, Wduplicatetot, "  average merge distance", Zduplicate);
+  zdef_(wmax, Wduplicatemax, "  maximum merge distance", -1);
+}
+void qh_allstatH(void) {
+  zdef_(zdoc, Zdoc8, "renamed vertex statistics", -1);
+  zdef_(zinc, Zrenameshare, "renamed vertices shared by two facets", -1);
+  zdef_(zinc, Zrenamepinch, "renamed vertices in a pinched facet", -1);
+  zdef_(zinc, Zrenameall, "renamed vertices shared by multiple facets", -1);
+  zdef_(zinc, Zfindfail, "rename failures due to duplicated ridges", -1);
+  zdef_(zinc, Zdupridge, "  duplicate ridges detected", -1);
+  zdef_(zinc, Zdelridge, "deleted ridges due to renamed vertices", -1);
+  zdef_(zinc, Zdropneighbor, "dropped neighbors due to renamed vertices", -1);
+  zdef_(zinc, Zdropdegen, "degenerate facets due to dropped neighbors", -1);
+  zdef_(zinc, Zdelfacetdup, "  facets deleted because of no neighbors", -1);
+  zdef_(zinc, Zremvertex, "vertices removed from facets due to no ridges", -1);
+  zdef_(zinc, Zremvertexdel, "  deleted", -1);
+  zdef_(zinc, Zintersectnum, "vertex intersections for locating redundant vertices", -1);
+  zdef_(zinc, Zintersectfail, "intersections failed to find a redundant vertex", -1);
+  zdef_(zinc, Zintersect, "intersections found redundant vertices", -1);
+  zdef_(zadd, Zintersecttot, "   ave. number found per vertex", Zintersect);
+  zdef_(zmax, Zintersectmax, "   max. found for a vertex", -1);
+  zdef_(zinc, Zvertexridge, NULL, -1);
+  zdef_(zadd, Zvertexridgetot, "  ave. number of ridges per tested vertex", Zvertexridge);
+  zdef_(zmax, Zvertexridgemax, "  max. number of ridges per tested vertex", -1);
+
+  zdef_(zdoc, Zdoc10, "memory usage statistics(in bytes)", -1);
+  zdef_(zadd, Zmemfacets, "for facets and their normals, neighbor and vertex sets", -1);
+  zdef_(zadd, Zmemvertices, "for vertices and their neighbor sets", -1);
+  zdef_(zadd, Zmempoints, "for input points and outside and coplanar sets",-1);
+  zdef_(zadd, Zmemridges, "for ridges and their vertex sets", -1);
+} /* allstat */
+
+void qh_allstatI(void) {
+  qhstat vridges= qhstat next;
+  zzdef_(zdoc, Zdoc11, "Voronoi ridge statistics", -1);
+  zzdef_(zinc, Zridge, "non-simplicial Voronoi vertices for all ridges", -1);
+  zzdef_(wadd, Wridge, "  ave. distance to ridge", Zridge);
+  zzdef_(wmax, Wridgemax, "  max. distance to ridge", -1);
+  zzdef_(zinc, Zridgemid, "bounded ridges", -1);
+  zzdef_(wadd, Wridgemid, "  ave. distance of midpoint to ridge", Zridgemid);
+  zzdef_(wmax, Wridgemidmax, "  max. distance of midpoint to ridge", -1);
+  zzdef_(zinc, Zridgeok, "bounded ridges with ok normal", -1);
+  zzdef_(wadd, Wridgeok, "  ave. angle to ridge", Zridgeok);
+  zzdef_(wmax, Wridgeokmax, "  max. angle to ridge", -1);
+  zzdef_(zinc, Zridge0, "bounded ridges with near-zero normal", -1);
+  zzdef_(wadd, Wridge0, "  ave. angle to ridge", Zridge0);
+  zzdef_(wmax, Wridge0max, "  max. angle to ridge", -1);
+
+  zdef_(zdoc, Zdoc12, "Triangulation statistics(Qt)", -1);
+  zdef_(zinc, Ztricoplanar, "non-simplicial facets triangulated", -1);
+  zdef_(zadd, Ztricoplanartot, "  ave. new facets created(may be deleted)", Ztricoplanar);
+  zdef_(zmax, Ztricoplanarmax, "  max. new facets created", -1);
+  zdef_(zinc, Ztrinull, "null new facets deleted(duplicated vertex)", -1);
+  zdef_(zinc, Ztrimirror, "mirrored pairs of new facets deleted(same vertices)", -1);
+  zdef_(zinc, Ztridegen, "degenerate new facets in output(same ridge)", -1);
+} /* allstat */
+
+/*-<a                             href="qh-stat.htm#TOC"
+  >-------------------------------</a><a name="allstatistics">-</a>
+
+  qh_allstatistics()
+    reset printed flag for all statistics
+*/
+void qh_allstatistics(void) {
+  int i;
+
+  for(i=ZEND; i--; )
+    qhstat printed[i]= False;
+} /* allstatistics */
+
+#if qh_KEEPstatistics
+/*-<a                             href="qh-stat.htm#TOC"
+  >-------------------------------</a><a name="collectstatistics">-</a>
+
+  qh_collectstatistics()
+    collect statistics for qh.facet_list
+
+*/
+void qh_collectstatistics(void) {
+  facetT *facet, *neighbor, **neighborp;
+  vertexT *vertex, **vertexp;
+  realT dotproduct, dist;
+  int sizneighbors, sizridges, sizvertices, i;
+
+  qh old_randomdist= qh RANDOMdist;
+  qh RANDOMdist= False;
+  zval_(Zmempoints)= qh num_points * qh normal_size +
+                             sizeof(qhT) + sizeof(qhstatT);
+  zval_(Zmemfacets)= 0;
+  zval_(Zmemridges)= 0;
+  zval_(Zmemvertices)= 0;
+  zval_(Zangle)= 0;
+  wval_(Wangle)= 0.0;
+  zval_(Znumridges)= 0;
+  zval_(Znumfacets)= 0;
+  zval_(Znumneighbors)= 0;
+  zval_(Znumvertices)= 0;
+  zval_(Znumvneighbors)= 0;
+  zval_(Znummergetot)= 0;
+  zval_(Znummergemax)= 0;
+  zval_(Zvertices)= qh num_vertices - qh_setsize(qh del_vertices);
+  if (qh MERGING || qh APPROXhull || qh JOGGLEmax < REALmax/2)
+    wmax_(Wmaxoutside, qh max_outside);
+  if (qh MERGING)
+    wmin_(Wminvertex, qh min_vertex);
+  FORALLfacets
+    facet->seen= False;
+  if (qh DELAUNAY) {
+    FORALLfacets {
+      if (facet->upperdelaunay != qh UPPERdelaunay)
+        facet->seen= True; /* remove from angle statistics */
+    }
+  }
+  FORALLfacets {
+    if (facet->visible && qh NEWfacets)
+      continue;
+    sizvertices= qh_setsize(facet->vertices);
+    sizneighbors= qh_setsize(facet->neighbors);
+    sizridges= qh_setsize(facet->ridges);
+    zinc_(Znumfacets);
+    zadd_(Znumvertices, sizvertices);
+    zmax_(Zmaxvertices, sizvertices);
+    zadd_(Znumneighbors, sizneighbors);
+    zmax_(Zmaxneighbors, sizneighbors);
+    zadd_(Znummergetot, facet->nummerge);
+    i= facet->nummerge; /* avoid warnings */
+    zmax_(Znummergemax, i);
+    if (!facet->simplicial) {
+      if (sizvertices == qh hull_dim) {
+        zinc_(Znowsimplicial);
+      }else {
+        zinc_(Znonsimplicial);
+      }
+    }
+    if (sizridges) {
+      zadd_(Znumridges, sizridges);
+      zmax_(Zmaxridges, sizridges);
+    }
+    zadd_(Zmemfacets, sizeof(facetT) + qh normal_size + 2*sizeof(setT)
+       + SETelemsize * (sizneighbors + sizvertices));
+    if (facet->ridges) {
+      zadd_(Zmemridges,
+         sizeof(setT) + SETelemsize * sizridges + sizridges *
+         (sizeof(ridgeT) + sizeof(setT) + SETelemsize * (qh hull_dim-1))/2);
+    }
+    if (facet->outsideset)
+      zadd_(Zmempoints, sizeof(setT) + SETelemsize * qh_setsize(facet->outsideset));
+    if (facet->coplanarset)
+      zadd_(Zmempoints, sizeof(setT) + SETelemsize * qh_setsize(facet->coplanarset));
+    if (facet->seen) /* Delaunay upper envelope */
+      continue;
+    facet->seen= True;
+    FOREACHneighbor_(facet) {
+      if (neighbor == qh_DUPLICATEridge || neighbor == qh_MERGEridge
+          || neighbor->seen || !facet->normal || !neighbor->normal)
+        continue;
+      dotproduct= qh_getangle(facet->normal, neighbor->normal);
+      zinc_(Zangle);
+      wadd_(Wangle, dotproduct);
+      wmax_(Wanglemax, dotproduct)
+      wmin_(Wanglemin, dotproduct)
+    }
+    if (facet->normal) {
+      FOREACHvertex_(facet->vertices) {
+        zinc_(Zdiststat);
+        qh_distplane(vertex->point, facet, &dist);
+        wmax_(Wvertexmax, dist);
+        wmin_(Wvertexmin, dist);
+      }
+    }
+  }
+  FORALLvertices {
+    if (vertex->deleted)
+      continue;
+    zadd_(Zmemvertices, sizeof(vertexT));
+    if (vertex->neighbors) {
+      sizneighbors= qh_setsize(vertex->neighbors);
+      zadd_(Znumvneighbors, sizneighbors);
+      zmax_(Zmaxvneighbors, sizneighbors);
+      zadd_(Zmemvertices, sizeof(vertexT) + SETelemsize * sizneighbors);
+    }
+  }
+  qh RANDOMdist= qh old_randomdist;
+} /* collectstatistics */
+#endif /* qh_KEEPstatistics */
+
+/*-<a                             href="qh-stat.htm#TOC"
+  >-------------------------------</a><a name="freestatistics">-</a>
+
+  qh_freestatistics(  )
+    free memory used for statistics
+*/
+void qh_freestatistics(void) {
+
+#if qh_QHpointer
+  qh_free(qh_qhstat);
+  qh_qhstat= NULL;
+#endif
+} /* freestatistics */
+
+/*-<a                             href="qh-stat.htm#TOC"
+  >-------------------------------</a><a name="initstatistics">-</a>
+
+  qh_initstatistics(  )
+    allocate and initialize statistics
+
+  notes:
+    uses qh_malloc() instead of qh_memalloc() since mem.c not set up yet
+    NOerrors -- qh_initstatistics can not use qh_errexit(), qh_fprintf, or qh.ferr
+    On first call, only qhmem.ferr is defined.  qh_memalloc is not setup.
+    Also invoked by QhullQh().
+*/
+void qh_initstatistics(void) {
+  int i;
+  realT realx;
+  int intx;
+
+#if qh_QHpointer
+  if(qh_qhstat){  /* qh_initstatistics may be called from Qhull::resetStatistics() */
+      qh_free(qh_qhstat);
+      qh_qhstat= 0;
+  }
+  if (!(qh_qhstat= (qhstatT *)qh_malloc(sizeof(qhstatT)))) {
+    qh_fprintf_stderr(6183, "qhull error (qh_initstatistics): insufficient memory\n");
+    qh_exit(qh_ERRmem);  /* can not use qh_errexit() */
+  }
+#endif
+
+  qhstat next= 0;
+  qh_allstatA();
+  qh_allstatB();
+  qh_allstatC();
+  qh_allstatD();
+  qh_allstatE();
+  qh_allstatE2();
+  qh_allstatF();
+  qh_allstatG();
+  qh_allstatH();
+  qh_allstatI();
+  if (qhstat next > (int)sizeof(qhstat id)) {
+    qh_fprintf(qhmem.ferr, 6184, "qhull error (qh_initstatistics): increase size of qhstat.id[].\n\
+      qhstat.next %d should be <= sizeof(qhstat id) %d\n", qhstat next, (int)sizeof(qhstat id));
+#if 0 /* for locating error, Znumridges should be duplicated */
+    for(i=0; i < ZEND; i++) {
+      int j;
+      for(j=i+1; j < ZEND; j++) {
+        if (qhstat id[i] == qhstat id[j]) {
+          qh_fprintf(qhmem.ferr, 6185, "qhull error (qh_initstatistics): duplicated statistic %d at indices %d and %d\n",
+              qhstat id[i], i, j);
+        }
+      }
+    }
+#endif
+    qh_exit(qh_ERRqhull);  /* can not use qh_errexit() */
+  }
+  qhstat init[zinc].i= 0;
+  qhstat init[zadd].i= 0;
+  qhstat init[zmin].i= INT_MAX;
+  qhstat init[zmax].i= INT_MIN;
+  qhstat init[wadd].r= 0;
+  qhstat init[wmin].r= REALmax;
+  qhstat init[wmax].r= -REALmax;
+  for(i=0; i < ZEND; i++) {
+    if (qhstat type[i] > ZTYPEreal) {
+      realx= qhstat init[(unsigned char)(qhstat type[i])].r;
+      qhstat stats[i].r= realx;
+    }else if (qhstat type[i] != zdoc) {
+      intx= qhstat init[(unsigned char)(qhstat type[i])].i;
+      qhstat stats[i].i= intx;
+    }
+  }
+} /* initstatistics */
+
+/*-<a                             href="qh-stat.htm#TOC"
+  >-------------------------------</a><a name="newstats">-</a>
+
+  qh_newstats(  )
+    returns True if statistics for zdoc
+
+  returns:
+    next zdoc
+*/
+boolT qh_newstats(int idx, int *nextindex) {
+  boolT isnew= False;
+  int start, i;
+
+  if (qhstat type[qhstat id[idx]] == zdoc)
+    start= idx+1;
+  else
+    start= idx;
+  for(i= start; i < qhstat next && qhstat type[qhstat id[i]] != zdoc; i++) {
+    if (!qh_nostatistic(qhstat id[i]) && !qhstat printed[qhstat id[i]])
+        isnew= True;
+  }
+  *nextindex= i;
+  return isnew;
+} /* newstats */
+
+/*-<a                             href="qh-stat.htm#TOC"
+  >-------------------------------</a><a name="nostatistic">-</a>
+
+  qh_nostatistic( index )
+    true if no statistic to print
+*/
+boolT qh_nostatistic(int i) {
+
+  if ((qhstat type[i] > ZTYPEreal
+       &&qhstat stats[i].r == qhstat init[(unsigned char)(qhstat type[i])].r)
+      || (qhstat type[i] < ZTYPEreal
+          &&qhstat stats[i].i == qhstat init[(unsigned char)(qhstat type[i])].i))
+    return True;
+  return False;
+} /* nostatistic */
+
+#if qh_KEEPstatistics
+/*-<a                             href="qh-stat.htm#TOC"
+  >-------------------------------</a><a name="printallstatistics">-</a>
+
+  qh_printallstatistics( fp, string )
+    print all statistics with header 'string'
+*/
+void qh_printallstatistics(FILE *fp, const char *string) {
+
+  qh_allstatistics();
+  qh_collectstatistics();
+  qh_printstatistics(fp, string);
+  qh_memstatistics(fp);
+}
+
+
+/*-<a                             href="qh-stat.htm#TOC"
+  >-------------------------------</a><a name="printstatistics">-</a>
+
+  qh_printstatistics( fp, string )
+    print statistics to a file with header 'string'
+    skips statistics with qhstat.printed[] (reset with qh_allstatistics)
+
+  see:
+    qh_printallstatistics()
+*/
+void qh_printstatistics(FILE *fp, const char *string) {
+  int i, k;
+  realT ave;
+
+  if (qh num_points != qh num_vertices) {
+    wval_(Wpbalance)= 0;
+    wval_(Wpbalance2)= 0;
+  }else
+    wval_(Wpbalance2)= qh_stddev(zval_(Zpbalance), wval_(Wpbalance),
+                                 wval_(Wpbalance2), &ave);
+  wval_(Wnewbalance2)= qh_stddev(zval_(Zprocessed), wval_(Wnewbalance),
+                                 wval_(Wnewbalance2), &ave);
+  qh_fprintf(fp, 9350, "\n\
+%s\n\
+ qhull invoked by: %s | %s\n%s with options:\n%s\n", string, qh rbox_command,
+     qh qhull_command, qh_version, qh qhull_options);
+  qh_fprintf(fp, 9351, "\nprecision constants:\n\
+ %6.2g max. abs. coordinate in the (transformed) input('Qbd:n')\n\
+ %6.2g max. roundoff error for distance computation('En')\n\
+ %6.2g max. roundoff error for angle computations\n\
+ %6.2g min. distance for outside points ('Wn')\n\
+ %6.2g min. distance for visible facets ('Vn')\n\
+ %6.2g max. distance for coplanar facets ('Un')\n\
+ %6.2g max. facet width for recomputing centrum and area\n\
+",
+  qh MAXabs_coord, qh DISTround, qh ANGLEround, qh MINoutside,
+        qh MINvisible, qh MAXcoplanar, qh WIDEfacet);
+  if (qh KEEPnearinside)
+    qh_fprintf(fp, 9352, "\
+ %6.2g max. distance for near-inside points\n", qh NEARinside);
+  if (qh premerge_cos < REALmax/2) qh_fprintf(fp, 9353, "\
+ %6.2g max. cosine for pre-merge angle\n", qh premerge_cos);
+  if (qh PREmerge) qh_fprintf(fp, 9354, "\
+ %6.2g radius of pre-merge centrum\n", qh premerge_centrum);
+  if (qh postmerge_cos < REALmax/2) qh_fprintf(fp, 9355, "\
+ %6.2g max. cosine for post-merge angle\n", qh postmerge_cos);
+  if (qh POSTmerge) qh_fprintf(fp, 9356, "\
+ %6.2g radius of post-merge centrum\n", qh postmerge_centrum);
+  qh_fprintf(fp, 9357, "\
+ %6.2g max. distance for merging two simplicial facets\n\
+ %6.2g max. roundoff error for arithmetic operations\n\
+ %6.2g min. denominator for divisions\n\
+  zero diagonal for Gauss: ", qh ONEmerge, REALepsilon, qh MINdenom);
+  for(k=0; k < qh hull_dim; k++)
+    qh_fprintf(fp, 9358, "%6.2e ", qh NEARzero[k]);
+  qh_fprintf(fp, 9359, "\n\n");
+  for(i=0 ; i < qhstat next; )
+    qh_printstats(fp, i, &i);
+} /* printstatistics */
+#endif /* qh_KEEPstatistics */
+
+/*-<a                             href="qh-stat.htm#TOC"
+  >-------------------------------</a><a name="printstatlevel">-</a>
+
+  qh_printstatlevel( fp, id )
+    print level information for a statistic
+
+  notes:
+    nop if id >= ZEND, printed, or same as initial value
+*/
+void qh_printstatlevel(FILE *fp, int id) {
+#define NULLfield "       "
+
+  if (id >= ZEND || qhstat printed[id])
+    return;
+  if (qhstat type[id] == zdoc) {
+    qh_fprintf(fp, 9360, "%s\n", qhstat doc[id]);
+    return;
+  }
+  if (qh_nostatistic(id) || !qhstat doc[id])
+    return;
+  qhstat printed[id]= True;
+  if (qhstat count[id] != -1
+      && qhstat stats[(unsigned char)(qhstat count[id])].i == 0)
+    qh_fprintf(fp, 9361, " *0 cnt*");
+  else if (qhstat type[id] >= ZTYPEreal && qhstat count[id] == -1)
+    qh_fprintf(fp, 9362, "%7.2g", qhstat stats[id].r);
+  else if (qhstat type[id] >= ZTYPEreal && qhstat count[id] != -1)
+    qh_fprintf(fp, 9363, "%7.2g", qhstat stats[id].r/ qhstat stats[(unsigned char)(qhstat count[id])].i);
+  else if (qhstat type[id] < ZTYPEreal && qhstat count[id] == -1)
+    qh_fprintf(fp, 9364, "%7d", qhstat stats[id].i);
+  else if (qhstat type[id] < ZTYPEreal && qhstat count[id] != -1)
+    qh_fprintf(fp, 9365, "%7.3g", (realT) qhstat stats[id].i / qhstat stats[(unsigned char)(qhstat count[id])].i);
+  qh_fprintf(fp, 9366, " %s\n", qhstat doc[id]);
+} /* printstatlevel */
+
+
+/*-<a                             href="qh-stat.htm#TOC"
+  >-------------------------------</a><a name="printstats">-</a>
+
+  qh_printstats( fp, index, nextindex )
+    print statistics for a zdoc group
+
+  returns:
+    next zdoc if non-null
+*/
+void qh_printstats(FILE *fp, int idx, int *nextindex) {
+  int j, nexti;
+
+  if (qh_newstats(idx, &nexti)) {
+    qh_fprintf(fp, 9367, "\n");
+    for (j=idx; j<nexti; j++)
+      qh_printstatlevel(fp, qhstat id[j]);
+  }
+  if (nextindex)
+    *nextindex= nexti;
+} /* printstats */
+
+#if qh_KEEPstatistics
+
+/*-<a                             href="qh-stat.htm#TOC"
+  >-------------------------------</a><a name="stddev">-</a>
+
+  qh_stddev( num, tot, tot2, ave )
+    compute the standard deviation and average from statistics
+
+    tot2 is the sum of the squares
+  notes:
+    computes r.m.s.:
+      (x-ave)^2
+      == x^2 - 2x tot/num +   (tot/num)^2
+      == tot2 - 2 tot tot/num + tot tot/num
+      == tot2 - tot ave
+*/
+realT qh_stddev(int num, realT tot, realT tot2, realT *ave) {
+  realT stddev;
+
+  *ave= tot/num;
+  stddev= sqrt(tot2/num - *ave * *ave);
+  return stddev;
+} /* stddev */
+
+#endif /* qh_KEEPstatistics */
+
+#if !qh_KEEPstatistics
+void    qh_collectstatistics(void) {}
+void    qh_printallstatistics(FILE *fp, char *string) {};
+void    qh_printstatistics(FILE *fp, char *string) {}
+#endif
+
diff --git a/xs/src/qhull/src/libqhull/stat.h b/xs/src/qhull/src/libqhull/stat.h
new file mode 100644
index 0000000000..d86fc0a87a
--- /dev/null
+++ b/xs/src/qhull/src/libqhull/stat.h
@@ -0,0 +1,543 @@
+/*<html><pre>  -<a                             href="qh-stat.htm"
+  >-------------------------------</a><a name="TOP">-</a>
+
+   stat.h
+     contains all statistics that are collected for qhull
+
+   see qh-stat.htm and stat.c
+
+   Copyright (c) 1993-2015 The Geometry Center.
+   $Id: //main/2015/qhull/src/libqhull/stat.h#4 $$Change: 2062 $
+   $DateTime: 2016/01/17 13:13:18 $$Author: bbarber $
+
+   recompile qhull if you change this file
+
+   Integer statistics are Z* while real statistics are W*.
+
+   define maydebugx to call a routine at every statistic event
+
+*/
+
+#ifndef qhDEFstat
+#define qhDEFstat 1
+
+#include "libqhull.h"
+
+/*-<a                             href="qh-stat.htm#TOC"
+  >-------------------------------</a><a name="KEEPstatistics">-</a>
+
+  qh_KEEPstatistics
+    0 turns off statistic gathering (except zzdef/zzinc/zzadd/zzval/wwval)
+*/
+#ifndef qh_KEEPstatistics
+#define qh_KEEPstatistics 1
+#endif
+
+/*-<a                             href="qh-stat.htm#TOC"
+  >-------------------------------</a><a name="statistics">-</a>
+
+  Zxxx for integers, Wxxx for reals
+
+  notes:
+    be sure that all statistics are defined in stat.c
+      otherwise initialization may core dump
+    can pick up all statistics by:
+      grep '[zw].*_[(][ZW]' *.c >z.x
+    remove trailers with query">-</a>
+    remove leaders with  query-replace-regexp [ ^I]+  (
+*/
+#if qh_KEEPstatistics
+enum qh_statistics {     /* alphabetical after Z/W */
+    Zacoplanar,
+    Wacoplanarmax,
+    Wacoplanartot,
+    Zangle,
+    Wangle,
+    Wanglemax,
+    Wanglemin,
+    Zangletests,
+    Wareatot,
+    Wareamax,
+    Wareamin,
+    Zavoidold,
+    Wavoidoldmax,
+    Wavoidoldtot,
+    Zback0,
+    Zbestcentrum,
+    Zbestdist,
+    Zbestlower,
+    Zbestlowerall,
+    Zbestloweralln,
+    Zbestlowerv,
+    Zcentrumtests,
+    Zcheckpart,
+    Zcomputefurthest,
+    Zconcave,
+    Wconcavemax,
+    Wconcavetot,
+    Zconcaveridges,
+    Zconcaveridge,
+    Zcoplanar,
+    Wcoplanarmax,
+    Wcoplanartot,
+    Zcoplanarangle,
+    Zcoplanarcentrum,
+    Zcoplanarhorizon,
+    Zcoplanarinside,
+    Zcoplanarpart,
+    Zcoplanarridges,
+    Wcpu,
+    Zcyclefacetmax,
+    Zcyclefacettot,
+    Zcyclehorizon,
+    Zcyclevertex,
+    Zdegen,
+    Wdegenmax,
+    Wdegentot,
+    Zdegenvertex,
+    Zdelfacetdup,
+    Zdelridge,
+    Zdelvertextot,
+    Zdelvertexmax,
+    Zdetsimplex,
+    Zdistcheck,
+    Zdistconvex,
+    Zdistgood,
+    Zdistio,
+    Zdistplane,
+    Zdiststat,
+    Zdistvertex,
+    Zdistzero,
+    Zdoc1,
+    Zdoc2,
+    Zdoc3,
+    Zdoc4,
+    Zdoc5,
+    Zdoc6,
+    Zdoc7,
+    Zdoc8,
+    Zdoc9,
+    Zdoc10,
+    Zdoc11,
+    Zdoc12,
+    Zdropdegen,
+    Zdropneighbor,
+    Zdupflip,
+    Zduplicate,
+    Wduplicatemax,
+    Wduplicatetot,
+    Zdupridge,
+    Zdupsame,
+    Zflipped,
+    Wflippedmax,
+    Wflippedtot,
+    Zflippedfacets,
+    Zfindbest,
+    Zfindbestmax,
+    Zfindbesttot,
+    Zfindcoplanar,
+    Zfindfail,
+    Zfindhorizon,
+    Zfindhorizonmax,
+    Zfindhorizontot,
+    Zfindjump,
+    Zfindnew,
+    Zfindnewmax,
+    Zfindnewtot,
+    Zfindnewjump,
+    Zfindnewsharp,
+    Zgauss0,
+    Zgoodfacet,
+    Zhashlookup,
+    Zhashridge,
+    Zhashridgetest,
+    Zhashtests,
+    Zinsidevisible,
+    Zintersect,
+    Zintersectfail,
+    Zintersectmax,
+    Zintersectnum,
+    Zintersecttot,
+    Zmaxneighbors,
+    Wmaxout,
+    Wmaxoutside,
+    Zmaxridges,
+    Zmaxvertex,
+    Zmaxvertices,
+    Zmaxvneighbors,
+    Zmemfacets,
+    Zmempoints,
+    Zmemridges,
+    Zmemvertices,
+    Zmergeflipdup,
+    Zmergehorizon,
+    Zmergeinittot,
+    Zmergeinitmax,
+    Zmergeinittot2,
+    Zmergeintohorizon,
+    Zmergenew,
+    Zmergesettot,
+    Zmergesetmax,
+    Zmergesettot2,
+    Zmergesimplex,
+    Zmergevertex,
+    Wmindenom,
+    Wminvertex,
+    Zminnorm,
+    Zmultiridge,
+    Znearlysingular,
+    Zneighbor,
+    Wnewbalance,
+    Wnewbalance2,
+    Znewfacettot,
+    Znewfacetmax,
+    Znewvertex,
+    Wnewvertex,
+    Wnewvertexmax,
+    Znoarea,
+    Znonsimplicial,
+    Znowsimplicial,
+    Znotgood,
+    Znotgoodnew,
+    Znotmax,
+    Znumfacets,
+    Znummergemax,
+    Znummergetot,
+    Znumneighbors,
+    Znumridges,
+    Znumvertices,
+    Znumvisibility,
+    Znumvneighbors,
+    Zonehorizon,
+    Zpartangle,
+    Zpartcoplanar,
+    Zpartflip,
+    Zparthorizon,
+    Zpartinside,
+    Zpartition,
+    Zpartitionall,
+    Zpartnear,
+    Zpbalance,
+    Wpbalance,
+    Wpbalance2,
+    Zpostfacets,
+    Zpremergetot,
+    Zprocessed,
+    Zremvertex,
+    Zremvertexdel,
+    Zrenameall,
+    Zrenamepinch,
+    Zrenameshare,
+    Zretry,
+    Wretrymax,
+    Zridge,
+    Wridge,
+    Wridgemax,
+    Zridge0,
+    Wridge0,
+    Wridge0max,
+    Zridgemid,
+    Wridgemid,
+    Wridgemidmax,
+    Zridgeok,
+    Wridgeok,
+    Wridgeokmax,
+    Zsearchpoints,
+    Zsetplane,
+    Ztestvneighbor,
+    Ztotcheck,
+    Ztothorizon,
+    Ztotmerge,
+    Ztotpartcoplanar,
+    Ztotpartition,
+    Ztotridges,
+    Ztotvertices,
+    Ztotvisible,
+    Ztricoplanar,
+    Ztricoplanarmax,
+    Ztricoplanartot,
+    Ztridegen,
+    Ztrimirror,
+    Ztrinull,
+    Wvertexmax,
+    Wvertexmin,
+    Zvertexridge,
+    Zvertexridgetot,
+    Zvertexridgemax,
+    Zvertices,
+    Zvisfacettot,
+    Zvisfacetmax,
+    Zvisit,
+    Zvisit2max,
+    Zvisvertextot,
+    Zvisvertexmax,
+    Zvvisit,
+    Zvvisit2max,
+    Zwidefacet,
+    Zwidevertices,
+    ZEND};
+
+/*-<a                             href="qh-stat.htm#TOC"
+  >-------------------------------</a><a name="ZZstat">-</a>
+
+  Zxxx/Wxxx statistics that remain defined if qh_KEEPstatistics=0
+
+  notes:
+    be sure to use zzdef, zzinc, etc. with these statistics (no double checking!)
+*/
+#else
+enum qh_statistics {     /* for zzdef etc. macros */
+  Zback0,
+  Zbestdist,
+  Zcentrumtests,
+  Zcheckpart,
+  Zconcaveridges,
+  Zcoplanarhorizon,
+  Zcoplanarpart,
+  Zcoplanarridges,
+  Zcyclefacettot,
+  Zcyclehorizon,
+  Zdelvertextot,
+  Zdistcheck,
+  Zdistconvex,
+  Zdistzero,
+  Zdoc1,
+  Zdoc2,
+  Zdoc3,
+  Zdoc11,
+  Zflippedfacets,
+  Zgauss0,
+  Zminnorm,
+  Zmultiridge,
+  Znearlysingular,
+  Wnewvertexmax,
+  Znumvisibility,
+  Zpartcoplanar,
+  Zpartition,
+  Zpartitionall,
+  Zprocessed,
+  Zretry,
+  Zridge,
+  Wridge,
+  Wridgemax,
+  Zridge0,
+  Wridge0,
+  Wridge0max,
+  Zridgemid,
+  Wridgemid,
+  Wridgemidmax,
+  Zridgeok,
+  Wridgeok,
+  Wridgeokmax,
+  Zsetplane,
+  Ztotcheck,
+  Ztotmerge,
+    ZEND};
+#endif
+
+/*-<a                             href="qh-stat.htm#TOC"
+  >-------------------------------</a><a name="ztype">-</a>
+
+  ztype
+    the type of a statistic sets its initial value.
+
+  notes:
+    The type should be the same as the macro for collecting the statistic
+*/
+enum ztypes {zdoc,zinc,zadd,zmax,zmin,ZTYPEreal,wadd,wmax,wmin,ZTYPEend};
+
+/*========== macros and constants =============*/
+
+/*-<a                             href="qh-stat.htm#TOC"
+  >--------------------------------</a><a name="MAYdebugx">-</a>
+
+  MAYdebugx
+    define as maydebug() to be called frequently for error trapping
+*/
+#define MAYdebugx
+
+/*-<a                             href="qh-stat.htm#TOC"
+  >--------------------------------</a><a name="zdef_">-</a>
+
+  zzdef_, zdef_( type, name, doc, -1)
+    define a statistic (assumes 'qhstat.next= 0;')
+
+  zdef_( type, name, doc, count)
+    define an averaged statistic
+    printed as name/count
+*/
+#define zzdef_(stype,name,string,cnt) qhstat id[qhstat next++]=name; \
+   qhstat doc[name]= string; qhstat count[name]= cnt; qhstat type[name]= stype
+#if qh_KEEPstatistics
+#define zdef_(stype,name,string,cnt) qhstat id[qhstat next++]=name; \
+   qhstat doc[name]= string; qhstat count[name]= cnt; qhstat type[name]= stype
+#else
+#define zdef_(type,name,doc,count)
+#endif
+
+/*-<a                             href="qh-stat.htm#TOC"
+  >--------------------------------</a><a name="zinc_">-</a>
+
+  zzinc_( name ), zinc_( name)
+    increment an integer statistic
+*/
+#define zzinc_(id) {MAYdebugx; qhstat stats[id].i++;}
+#if qh_KEEPstatistics
+#define zinc_(id) {MAYdebugx; qhstat stats[id].i++;}
+#else
+#define zinc_(id) {}
+#endif
+
+/*-<a                             href="qh-stat.htm#TOC"
+  >--------------------------------</a><a name="zadd_">-</a>
+
+  zzadd_( name, value ), zadd_( name, value ), wadd_( name, value )
+    add value to an integer or real statistic
+*/
+#define zzadd_(id, val) {MAYdebugx; qhstat stats[id].i += (val);}
+#define wwadd_(id, val) {MAYdebugx; qhstat stats[id].r += (val);}
+#if qh_KEEPstatistics
+#define zadd_(id, val) {MAYdebugx; qhstat stats[id].i += (val);}
+#define wadd_(id, val) {MAYdebugx; qhstat stats[id].r += (val);}
+#else
+#define zadd_(id, val) {}
+#define wadd_(id, val) {}
+#endif
+
+/*-<a                             href="qh-stat.htm#TOC"
+  >--------------------------------</a><a name="zval_">-</a>
+
+  zzval_( name ), zval_( name ), wwval_( name )
+    set or return value of a statistic
+*/
+#define zzval_(id) ((qhstat stats[id]).i)
+#define wwval_(id) ((qhstat stats[id]).r)
+#if qh_KEEPstatistics
+#define zval_(id) ((qhstat stats[id]).i)
+#define wval_(id) ((qhstat stats[id]).r)
+#else
+#define zval_(id) qhstat tempi
+#define wval_(id) qhstat tempr
+#endif
+
+/*-<a                             href="qh-stat.htm#TOC"
+  >--------------------------------</a><a name="zmax_">-</a>
+
+  zmax_( id, val ), wmax_( id, value )
+    maximize id with val
+*/
+#define wwmax_(id, val) {MAYdebugx; maximize_(qhstat stats[id].r,(val));}
+#if qh_KEEPstatistics
+#define zmax_(id, val) {MAYdebugx; maximize_(qhstat stats[id].i,(val));}
+#define wmax_(id, val) {MAYdebugx; maximize_(qhstat stats[id].r,(val));}
+#else
+#define zmax_(id, val) {}
+#define wmax_(id, val) {}
+#endif
+
+/*-<a                             href="qh-stat.htm#TOC"
+  >--------------------------------</a><a name="zmin_">-</a>
+
+  zmin_( id, val ), wmin_( id, value )
+    minimize id with val
+*/
+#if qh_KEEPstatistics
+#define zmin_(id, val) {MAYdebugx; minimize_(qhstat stats[id].i,(val));}
+#define wmin_(id, val) {MAYdebugx; minimize_(qhstat stats[id].r,(val));}
+#else
+#define zmin_(id, val) {}
+#define wmin_(id, val) {}
+#endif
+
+/*================== stat.h types ==============*/
+
+
+/*-<a                             href="qh-stat.htm#TOC"
+  >--------------------------------</a><a name="intrealT">-</a>
+
+  intrealT
+    union of integer and real, used for statistics
+*/
+typedef union intrealT intrealT;    /* union of int and realT */
+union intrealT {
+    int i;
+    realT r;
+};
+
+/*-<a                             href="qh-stat.htm#TOC"
+  >--------------------------------</a><a name="qhstat">-</a>
+
+  qhstat
+    global data structure for statistics, similar to qh and qhrbox
+
+  notes:
+   access to qh_qhstat is via the "qhstat" macro.  There are two choices
+   qh_QHpointer = 1     access globals via a pointer
+                        enables qh_saveqhull() and qh_restoreqhull()
+                = 0     qh_qhstat is a static data structure
+                        only one instance of qhull() can be active at a time
+                        default value
+   qh_QHpointer is defined in libqhull.h
+   qh_QHpointer_dllimport and qh_dllimport define qh_qh as __declspec(dllimport) [libqhull.h]
+
+   allocated in stat.c using qh_malloc()
+*/
+#ifndef DEFqhstatT
+#define DEFqhstatT 1
+typedef struct qhstatT qhstatT;
+#endif
+
+#if qh_QHpointer_dllimport
+#define qhstat qh_qhstat->
+__declspec(dllimport) extern qhstatT *qh_qhstat;
+#elif qh_QHpointer
+#define qhstat qh_qhstat->
+extern qhstatT *qh_qhstat;
+#elif qh_dllimport
+#define qhstat qh_qhstat.
+__declspec(dllimport) extern qhstatT qh_qhstat;
+#else
+#define qhstat qh_qhstat.
+extern qhstatT qh_qhstat;
+#endif
+struct qhstatT {
+  intrealT   stats[ZEND];     /* integer and real statistics */
+  unsigned   char id[ZEND+10]; /* id's in print order */
+  const char *doc[ZEND];       /* array of documentation strings */
+  short int  count[ZEND];     /* -1 if none, else index of count to use */
+  char       type[ZEND];      /* type, see ztypes above */
+  char       printed[ZEND];   /* true, if statistic has been printed */
+  intrealT   init[ZTYPEend];  /* initial values by types, set initstatistics */
+
+  int        next;            /* next index for zdef_ */
+  int        precision;       /* index for precision problems */
+  int        vridges;         /* index for Voronoi ridges */
+  int        tempi;
+  realT      tempr;
+};
+
+/*========== function prototypes ===========*/
+
+void    qh_allstatA(void);
+void    qh_allstatB(void);
+void    qh_allstatC(void);
+void    qh_allstatD(void);
+void    qh_allstatE(void);
+void    qh_allstatE2(void);
+void    qh_allstatF(void);
+void    qh_allstatG(void);
+void    qh_allstatH(void);
+void    qh_allstatI(void);
+void    qh_allstatistics(void);
+void    qh_collectstatistics(void);
+void    qh_freestatistics(void);
+void    qh_initstatistics(void);
+boolT   qh_newstats(int idx, int *nextindex);
+boolT   qh_nostatistic(int i);
+void    qh_printallstatistics(FILE *fp, const char *string);
+void    qh_printstatistics(FILE *fp, const char *string);
+void    qh_printstatlevel(FILE *fp, int id);
+void    qh_printstats(FILE *fp, int idx, int *nextindex);
+realT   qh_stddev(int num, realT tot, realT tot2, realT *ave);
+
+#endif   /* qhDEFstat */
diff --git a/xs/src/qhull/src/libqhull/user.c b/xs/src/qhull/src/libqhull/user.c
new file mode 100644
index 0000000000..d4726eaa31
--- /dev/null
+++ b/xs/src/qhull/src/libqhull/user.c
@@ -0,0 +1,538 @@
+/*<html><pre>  -<a                             href="qh-user.htm"
+  >-------------------------------</a><a name="TOP">-</a>
+
+   user.c
+   user redefinable functions
+
+   see user2.c for qh_fprintf, qh_malloc, qh_free
+
+   see README.txt  see COPYING.txt for copyright information.
+
+   see libqhull.h for data structures, macros, and user-callable functions.
+
+   see user_eg.c, user_eg2.c, and unix.c for examples.
+
+   see user.h for user-definable constants
+
+      use qh_NOmem in mem.h to turn off memory management
+      use qh_NOmerge in user.h to turn off facet merging
+      set qh_KEEPstatistics in user.h to 0 to turn off statistics
+
+   This is unsupported software.  You're welcome to make changes,
+   but you're on your own if something goes wrong.  Use 'Tc' to
+   check frequently.  Usually qhull will report an error if
+   a data structure becomes inconsistent.  If so, it also reports
+   the last point added to the hull, e.g., 102.  You can then trace
+   the execution of qhull with "T4P102".
+
+   Please report any errors that you fix to qhull@qhull.org
+
+   Qhull-template is a template for calling qhull from within your application
+
+   if you recompile and load this module, then user.o will not be loaded
+   from qhull.a
+
+   you can add additional quick allocation sizes in qh_user_memsizes
+
+   if the other functions here are redefined to not use qh_print...,
+   then io.o will not be loaded from qhull.a.  See user_eg.c for an
+   example.  We recommend keeping io.o for the extra debugging
+   information it supplies.
+*/
+
+#include "qhull_a.h"
+
+#include <stdarg.h>
+
+/*-<a                             href="qh-user.htm#TOC"
+  >-------------------------------</a><a name="qhull_template">-</a>
+
+  Qhull-template
+    Template for calling qhull from inside your program
+
+  returns:
+    exit code(see qh_ERR... in libqhull.h)
+    all memory freed
+
+  notes:
+    This can be called any number of times.
+*/
+#if 0
+{
+  int dim;                  /* dimension of points */
+  int numpoints;            /* number of points */
+  coordT *points;           /* array of coordinates for each point */
+  boolT ismalloc;           /* True if qhull should free points in qh_freeqhull() or reallocation */
+  char flags[]= "qhull Tv"; /* option flags for qhull, see qh_opt.htm */
+  FILE *outfile= stdout;    /* output from qh_produce_output()
+                               use NULL to skip qh_produce_output() */
+  FILE *errfile= stderr;    /* error messages from qhull code */
+  int exitcode;             /* 0 if no error from qhull */
+  facetT *facet;            /* set by FORALLfacets */
+  int curlong, totlong;     /* memory remaining after qh_memfreeshort */
+
+  QHULL_LIB_CHECK /* Check for compatible library */
+
+#if qh_QHpointer  /* see user.h */
+  if (qh_qh){ /* should be NULL */
+      qh_printf_stderr(6238, "Qhull link error.  The global variable qh_qh was not initialized\n\
+              to NULL by global.c.  Please compile this program with -Dqh_QHpointer_dllimport\n\
+              as well as -Dqh_QHpointer, or use libqhullstatic, or use a different tool chain.\n\n");
+      exit(1);
+  }
+#endif
+
+  /* initialize dim, numpoints, points[], ismalloc here */
+  exitcode= qh_new_qhull(dim, numpoints, points, ismalloc,
+                      flags, outfile, errfile);
+  if (!exitcode) {                  /* if no error */
+    /* 'qh facet_list' contains the convex hull */
+    FORALLfacets {
+       /* ... your code ... */
+    }
+  }
+  qh_freeqhull(!qh_ALL);
+  qh_memfreeshort(&curlong, &totlong);
+  if (curlong || totlong)
+    qh_fprintf(errfile, 7068, "qhull internal warning (main): did not free %d bytes of long memory(%d pieces)\n", totlong, curlong);
+}
+#endif
+
+/*-<a                             href="qh-user.htm#TOC"
+  >-------------------------------</a><a name="new_qhull">-</a>
+
+  qh_new_qhull( dim, numpoints, points, ismalloc, qhull_cmd, outfile, errfile )
+    build new qhull data structure and return exitcode (0 if no errors)
+    if numpoints=0 and points=NULL, initializes qhull
+
+  notes:
+    do not modify points until finished with results.
+      The qhull data structure contains pointers into the points array.
+    do not call qhull functions before qh_new_qhull().
+      The qhull data structure is not initialized until qh_new_qhull().
+
+    Default errfile is stderr, outfile may be null
+    qhull_cmd must start with "qhull "
+    projects points to a new point array for Delaunay triangulations ('d' and 'v')
+    transforms points into a new point array for halfspace intersection ('H')
+
+
+  To allow multiple, concurrent calls to qhull()
+    - set qh_QHpointer in user.h
+    - use qh_save_qhull and qh_restore_qhull to swap the global data structure between calls.
+    - use qh_freeqhull(qh_ALL) to free intermediate convex hulls
+
+  see:
+      Qhull-template at the beginning of this file.
+      An example of using qh_new_qhull is user_eg.c
+*/
+int qh_new_qhull(int dim, int numpoints, coordT *points, boolT ismalloc,
+                char *qhull_cmd, FILE *outfile, FILE *errfile) {
+  /* gcc may issue a "might be clobbered" warning for dim, points, and ismalloc [-Wclobbered].
+     These parameters are not referenced after a longjmp() and hence not clobbered.
+     See http://stackoverflow.com/questions/7721854/what-sense-do-these-clobbered-variable-warnings-make */
+  int exitcode, hulldim;
+  boolT new_ismalloc;
+  static boolT firstcall = True;
+  coordT *new_points;
+  if(!errfile){
+      errfile= stderr;
+  }
+  if (firstcall) {
+    qh_meminit(errfile);
+    firstcall= False;
+  } else {
+    qh_memcheck();
+  }
+  if (strncmp(qhull_cmd, "qhull ", (size_t)6)) {
+    qh_fprintf(errfile, 6186, "qhull error (qh_new_qhull): start qhull_cmd argument with \"qhull \"\n");
+    return qh_ERRinput;
+  }
+  qh_initqhull_start(NULL, outfile, errfile);
+  if(numpoints==0 && points==NULL){
+      trace1((qh ferr, 1047, "qh_new_qhull: initialize Qhull\n"));
+      return 0;
+  }
+  trace1((qh ferr, 1044, "qh_new_qhull: build new Qhull for %d %d-d points with %s\n", numpoints, dim, qhull_cmd));
+  exitcode = setjmp(qh errexit);
+  if (!exitcode)
+  {
+    qh NOerrexit = False;
+    qh_initflags(qhull_cmd);
+    if (qh DELAUNAY)
+      qh PROJECTdelaunay= True;
+    if (qh HALFspace) {
+      /* points is an array of halfspaces,
+         the last coordinate of each halfspace is its offset */
+      hulldim= dim-1;
+      qh_setfeasible(hulldim);
+      new_points= qh_sethalfspace_all(dim, numpoints, points, qh feasible_point);
+      new_ismalloc= True;
+      if (ismalloc)
+        qh_free(points);
+    }else {
+      hulldim= dim;
+      new_points= points;
+      new_ismalloc= ismalloc;
+    }
+    qh_init_B(new_points, numpoints, hulldim, new_ismalloc);
+    qh_qhull();
+    qh_check_output();
+    if (outfile) {
+      qh_produce_output();
+    }else {
+      qh_prepare_output();
+    }
+    if (qh VERIFYoutput && !qh STOPpoint && !qh STOPcone)
+      qh_check_points();
+  }
+  qh NOerrexit = True;
+  return exitcode;
+} /* new_qhull */
+
+/*-<a                             href="qh-user.htm#TOC"
+  >-------------------------------</a><a name="errexit">-</a>
+
+  qh_errexit( exitcode, facet, ridge )
+    report and exit from an error
+    report facet and ridge if non-NULL
+    reports useful information such as last point processed
+    set qh.FORCEoutput to print neighborhood of facet
+
+  see:
+    qh_errexit2() in libqhull.c for printing 2 facets
+
+  design:
+    check for error within error processing
+    compute qh.hulltime
+    print facet and ridge (if any)
+    report commandString, options, qh.furthest_id
+    print summary and statistics (including precision statistics)
+    if qh_ERRsingular
+      print help text for singular data set
+    exit program via long jump (if defined) or exit()
+*/
+void qh_errexit(int exitcode, facetT *facet, ridgeT *ridge) {
+
+  if (qh ERREXITcalled) {
+    qh_fprintf(qh ferr, 8126, "\nqhull error while processing previous error.  Exit program\n");
+    qh_exit(qh_ERRqhull);
+  }
+  qh ERREXITcalled= True;
+  if (!qh QHULLfinished)
+    qh hulltime= qh_CPUclock - qh hulltime;
+  qh_errprint("ERRONEOUS", facet, NULL, ridge, NULL);
+  qh_fprintf(qh ferr, 8127, "\nWhile executing: %s | %s\n", qh rbox_command, qh qhull_command);
+  qh_fprintf(qh ferr, 8128, "Options selected for Qhull %s:\n%s\n", qh_version, qh qhull_options);
+  if (qh furthest_id >= 0) {
+    qh_fprintf(qh ferr, 8129, "Last point added to hull was p%d.", qh furthest_id);
+    if (zzval_(Ztotmerge))
+      qh_fprintf(qh ferr, 8130, "  Last merge was #%d.", zzval_(Ztotmerge));
+    if (qh QHULLfinished)
+      qh_fprintf(qh ferr, 8131, "\nQhull has finished constructing the hull.");
+    else if (qh POSTmerging)
+      qh_fprintf(qh ferr, 8132, "\nQhull has started post-merging.");
+    qh_fprintf(qh ferr, 8133, "\n");
+  }
+  if (qh FORCEoutput && (qh QHULLfinished || (!facet && !ridge)))
+    qh_produce_output();
+  else if (exitcode != qh_ERRinput) {
+    if (exitcode != qh_ERRsingular && zzval_(Zsetplane) > qh hull_dim+1) {
+      qh_fprintf(qh ferr, 8134, "\nAt error exit:\n");
+      qh_printsummary(qh ferr);
+      if (qh PRINTstatistics) {
+        qh_collectstatistics();
+        qh_printstatistics(qh ferr, "at error exit");
+        qh_memstatistics(qh ferr);
+      }
+    }
+    if (qh PRINTprecision)
+      qh_printstats(qh ferr, qhstat precision, NULL);
+  }
+  if (!exitcode)
+    exitcode= qh_ERRqhull;
+  else if (exitcode == qh_ERRsingular)
+    qh_printhelp_singular(qh ferr);
+  else if (exitcode == qh_ERRprec && !qh PREmerge)
+    qh_printhelp_degenerate(qh ferr);
+  if (qh NOerrexit) {
+    qh_fprintf(qh ferr, 6187, "qhull error while ending program, or qh->NOerrexit not cleared after setjmp(). Exit program with error.\n");
+    qh_exit(qh_ERRqhull);
+  }
+  qh ERREXITcalled= False;
+  qh NOerrexit= True;
+  qh ALLOWrestart= False;  /* longjmp will undo qh_build_withrestart */
+  longjmp(qh errexit, exitcode);
+} /* errexit */
+
+
+/*-<a                             href="qh-user.htm#TOC"
+  >-------------------------------</a><a name="errprint">-</a>
+
+  qh_errprint( fp, string, atfacet, otherfacet, atridge, atvertex )
+    prints out the information of facets and ridges to fp
+    also prints neighbors and geomview output
+
+  notes:
+    except for string, any parameter may be NULL
+*/
+void qh_errprint(const char *string, facetT *atfacet, facetT *otherfacet, ridgeT *atridge, vertexT *atvertex) {
+  int i;
+
+  if (atfacet) {
+    qh_fprintf(qh ferr, 8135, "%s FACET:\n", string);
+    qh_printfacet(qh ferr, atfacet);
+  }
+  if (otherfacet) {
+    qh_fprintf(qh ferr, 8136, "%s OTHER FACET:\n", string);
+    qh_printfacet(qh ferr, otherfacet);
+  }
+  if (atridge) {
+    qh_fprintf(qh ferr, 8137, "%s RIDGE:\n", string);
+    qh_printridge(qh ferr, atridge);
+    if (atridge->top && atridge->top != atfacet && atridge->top != otherfacet)
+      qh_printfacet(qh ferr, atridge->top);
+    if (atridge->bottom
+        && atridge->bottom != atfacet && atridge->bottom != otherfacet)
+      qh_printfacet(qh ferr, atridge->bottom);
+    if (!atfacet)
+      atfacet= atridge->top;
+    if (!otherfacet)
+      otherfacet= otherfacet_(atridge, atfacet);
+  }
+  if (atvertex) {
+    qh_fprintf(qh ferr, 8138, "%s VERTEX:\n", string);
+    qh_printvertex(qh ferr, atvertex);
+  }
+  if (qh fout && qh FORCEoutput && atfacet && !qh QHULLfinished && !qh IStracing) {
+    qh_fprintf(qh ferr, 8139, "ERRONEOUS and NEIGHBORING FACETS to output\n");
+    for (i=0; i < qh_PRINTEND; i++)  /* use fout for geomview output */
+      qh_printneighborhood(qh fout, qh PRINTout[i], atfacet, otherfacet,
+                            !qh_ALL);
+  }
+} /* errprint */
+
+
+/*-<a                             href="qh-user.htm#TOC"
+  >-------------------------------</a><a name="printfacetlist">-</a>
+
+  qh_printfacetlist( fp, facetlist, facets, printall )
+    print all fields for a facet list and/or set of facets to fp
+    if !printall,
+      only prints good facets
+
+  notes:
+    also prints all vertices
+*/
+void qh_printfacetlist(facetT *facetlist, setT *facets, boolT printall) {
+  facetT *facet, **facetp;
+
+  qh_printbegin(qh ferr, qh_PRINTfacets, facetlist, facets, printall);
+  FORALLfacet_(facetlist)
+    qh_printafacet(qh ferr, qh_PRINTfacets, facet, printall);
+  FOREACHfacet_(facets)
+    qh_printafacet(qh ferr, qh_PRINTfacets, facet, printall);
+  qh_printend(qh ferr, qh_PRINTfacets, facetlist, facets, printall);
+} /* printfacetlist */
+
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="printhelp_degenerate">-</a>
+
+  qh_printhelp_degenerate( fp )
+    prints descriptive message for precision error
+
+  notes:
+    no message if qh_QUICKhelp
+*/
+void qh_printhelp_degenerate(FILE *fp) {
+
+  if (qh MERGEexact || qh PREmerge || qh JOGGLEmax < REALmax/2)
+    qh_fprintf(fp, 9368, "\n\
+A Qhull error has occurred.  Qhull should have corrected the above\n\
+precision error.  Please send the input and all of the output to\n\
+qhull_bug@qhull.org\n");
+  else if (!qh_QUICKhelp) {
+    qh_fprintf(fp, 9369, "\n\
+Precision problems were detected during construction of the convex hull.\n\
+This occurs because convex hull algorithms assume that calculations are\n\
+exact, but floating-point arithmetic has roundoff errors.\n\
+\n\
+To correct for precision problems, do not use 'Q0'.  By default, Qhull\n\
+selects 'C-0' or 'Qx' and merges non-convex facets.  With option 'QJ',\n\
+Qhull joggles the input to prevent precision problems.  See \"Imprecision\n\
+in Qhull\" (qh-impre.htm).\n\
+\n\
+If you use 'Q0', the output may include\n\
+coplanar ridges, concave ridges, and flipped facets.  In 4-d and higher,\n\
+Qhull may produce a ridge with four neighbors or two facets with the same \n\
+vertices.  Qhull reports these events when they occur.  It stops when a\n\
+concave ridge, flipped facet, or duplicate facet occurs.\n");
+#if REALfloat
+    qh_fprintf(fp, 9370, "\
+\n\
+Qhull is currently using single precision arithmetic.  The following\n\
+will probably remove the precision problems:\n\
+  - recompile qhull for realT precision(#define REALfloat 0 in user.h).\n");
+#endif
+    if (qh DELAUNAY && !qh SCALElast && qh MAXabs_coord > 1e4)
+      qh_fprintf(fp, 9371, "\
+\n\
+When computing the Delaunay triangulation of coordinates > 1.0,\n\
+  - use 'Qbb' to scale the last coordinate to [0,m] (max previous coordinate)\n");
+    if (qh DELAUNAY && !qh ATinfinity)
+      qh_fprintf(fp, 9372, "\
+When computing the Delaunay triangulation:\n\
+  - use 'Qz' to add a point at-infinity.  This reduces precision problems.\n");
+
+    qh_fprintf(fp, 9373, "\
+\n\
+If you need triangular output:\n\
+  - use option 'Qt' to triangulate the output\n\
+  - use option 'QJ' to joggle the input points and remove precision errors\n\
+  - use option 'Ft'.  It triangulates non-simplicial facets with added points.\n\
+\n\
+If you must use 'Q0',\n\
+try one or more of the following options.  They can not guarantee an output.\n\
+  - use 'QbB' to scale the input to a cube.\n\
+  - use 'Po' to produce output and prevent partitioning for flipped facets\n\
+  - use 'V0' to set min. distance to visible facet as 0 instead of roundoff\n\
+  - use 'En' to specify a maximum roundoff error less than %2.2g.\n\
+  - options 'Qf', 'Qbb', and 'QR0' may also help\n",
+               qh DISTround);
+    qh_fprintf(fp, 9374, "\
+\n\
+To guarantee simplicial output:\n\
+  - use option 'Qt' to triangulate the output\n\
+  - use option 'QJ' to joggle the input points and remove precision errors\n\
+  - use option 'Ft' to triangulate the output by adding points\n\
+  - use exact arithmetic (see \"Imprecision in Qhull\", qh-impre.htm)\n\
+");
+  }
+} /* printhelp_degenerate */
+
+
+/*-<a                             href="qh-globa.htm#TOC"
+  >-------------------------------</a><a name="printhelp_narrowhull">-</a>
+
+  qh_printhelp_narrowhull( minangle )
+    Warn about a narrow hull
+
+  notes:
+    Alternatively, reduce qh_WARNnarrow in user.h
+
+*/
+void qh_printhelp_narrowhull(FILE *fp, realT minangle) {
+
+    qh_fprintf(fp, 9375, "qhull precision warning: \n\
+The initial hull is narrow (cosine of min. angle is %.16f).\n\
+Is the input lower dimensional (e.g., on a plane in 3-d)?  Qhull may\n\
+produce a wide facet.  Options 'QbB' (scale to unit box) or 'Qbb' (scale\n\
+last coordinate) may remove this warning.  Use 'Pp' to skip this warning.\n\
+See 'Limitations' in qh-impre.htm.\n",
+          -minangle);   /* convert from angle between normals to angle between facets */
+} /* printhelp_narrowhull */
+
+/*-<a                             href="qh-io.htm#TOC"
+  >-------------------------------</a><a name="printhelp_singular">-</a>
+
+  qh_printhelp_singular( fp )
+    prints descriptive message for singular input
+*/
+void qh_printhelp_singular(FILE *fp) {
+  facetT *facet;
+  vertexT *vertex, **vertexp;
+  realT min, max, *coord, dist;
+  int i,k;
+
+  qh_fprintf(fp, 9376, "\n\
+The input to qhull appears to be less than %d dimensional, or a\n\
+computation has overflowed.\n\n\
+Qhull could not construct a clearly convex simplex from points:\n",
+           qh hull_dim);
+  qh_printvertexlist(fp, "", qh facet_list, NULL, qh_ALL);
+  if (!qh_QUICKhelp)
+    qh_fprintf(fp, 9377, "\n\
+The center point is coplanar with a facet, or a vertex is coplanar\n\
+with a neighboring facet.  The maximum round off error for\n\
+computing distances is %2.2g.  The center point, facets and distances\n\
+to the center point are as follows:\n\n", qh DISTround);
+  qh_printpointid(fp, "center point", qh hull_dim, qh interior_point, qh_IDunknown);
+  qh_fprintf(fp, 9378, "\n");
+  FORALLfacets {
+    qh_fprintf(fp, 9379, "facet");
+    FOREACHvertex_(facet->vertices)
+      qh_fprintf(fp, 9380, " p%d", qh_pointid(vertex->point));
+    zinc_(Zdistio);
+    qh_distplane(qh interior_point, facet, &dist);
+    qh_fprintf(fp, 9381, " distance= %4.2g\n", dist);
+  }
+  if (!qh_QUICKhelp) {
+    if (qh HALFspace)
+      qh_fprintf(fp, 9382, "\n\
+These points are the dual of the given halfspaces.  They indicate that\n\
+the intersection is degenerate.\n");
+    qh_fprintf(fp, 9383,"\n\
+These points either have a maximum or minimum x-coordinate, or\n\
+they maximize the determinant for k coordinates.  Trial points\n\
+are first selected from points that maximize a coordinate.\n");
+    if (qh hull_dim >= qh_INITIALmax)
+      qh_fprintf(fp, 9384, "\n\
+Because of the high dimension, the min x-coordinate and max-coordinate\n\
+points are used if the determinant is non-zero.  Option 'Qs' will\n\
+do a better, though much slower, job.  Instead of 'Qs', you can change\n\
+the points by randomly rotating the input with 'QR0'.\n");
+  }
+  qh_fprintf(fp, 9385, "\nThe min and max coordinates for each dimension are:\n");
+  for (k=0; k < qh hull_dim; k++) {
+    min= REALmax;
+    max= -REALmin;
+    for (i=qh num_points, coord= qh first_point+k; i--; coord += qh hull_dim) {
+      maximize_(max, *coord);
+      minimize_(min, *coord);
+    }
+    qh_fprintf(fp, 9386, "  %d:  %8.4g  %8.4g  difference= %4.4g\n", k, min, max, max-min);
+  }
+  if (!qh_QUICKhelp) {
+    qh_fprintf(fp, 9387, "\n\
+If the input should be full dimensional, you have several options that\n\
+may determine an initial simplex:\n\
+  - use 'QJ'  to joggle the input and make it full dimensional\n\
+  - use 'QbB' to scale the points to the unit cube\n\
+  - use 'QR0' to randomly rotate the input for different maximum points\n\
+  - use 'Qs'  to search all points for the initial simplex\n\
+  - use 'En'  to specify a maximum roundoff error less than %2.2g.\n\
+  - trace execution with 'T3' to see the determinant for each point.\n",
+                     qh DISTround);
+#if REALfloat
+    qh_fprintf(fp, 9388, "\
+  - recompile qhull for realT precision(#define REALfloat 0 in libqhull.h).\n");
+#endif
+    qh_fprintf(fp, 9389, "\n\
+If the input is lower dimensional:\n\
+  - use 'QJ' to joggle the input and make it full dimensional\n\
+  - use 'Qbk:0Bk:0' to delete coordinate k from the input.  You should\n\
+    pick the coordinate with the least range.  The hull will have the\n\
+    correct topology.\n\
+  - determine the flat containing the points, rotate the points\n\
+    into a coordinate plane, and delete the other coordinates.\n\
+  - add one or more points to make the input full dimensional.\n\
+");
+  }
+} /* printhelp_singular */
+
+/*-<a                             href="qh-globa.htm#TOC"
+  >-------------------------------</a><a name="user_memsizes">-</a>
+
+  qh_user_memsizes()
+    allocate up to 10 additional, quick allocation sizes
+
+  notes:
+    increase maximum number of allocations in qh_initqhull_mem()
+*/
+void qh_user_memsizes(void) {
+
+  /* qh_memsize(size); */
+} /* user_memsizes */
+
+
diff --git a/xs/src/qhull/src/libqhull/user.h b/xs/src/qhull/src/libqhull/user.h
new file mode 100644
index 0000000000..523aa7b4e8
--- /dev/null
+++ b/xs/src/qhull/src/libqhull/user.h
@@ -0,0 +1,909 @@
+/*<html><pre>  -<a                             href="qh-user.htm"
+  >-------------------------------</a><a name="TOP">-</a>
+
+   user.h
+   user redefinable constants
+
+   for each source file, user.h is included first
+   see qh-user.htm.  see COPYING for copyright information.
+
+   See user.c for sample code.
+
+   before reading any code, review libqhull.h for data structure definitions and
+   the "qh" macro.
+
+Sections:
+   ============= qhull library constants ======================
+   ============= data types and configuration macros ==========
+   ============= performance related constants ================
+   ============= memory constants =============================
+   ============= joggle constants =============================
+   ============= conditional compilation ======================
+   ============= -merge constants- ============================
+
+Code flags --
+  NOerrors -- the code does not call qh_errexit()
+  WARN64 -- the code may be incompatible with 64-bit pointers
+
+*/
+
+#include <time.h>
+
+#ifndef qhDEFuser
+#define qhDEFuser 1
+
+/* Derived from Qt's corelib/global/qglobal.h */
+#if !defined(SAG_COM) && !defined(__CYGWIN__) && (defined(WIN64) || defined(_WIN64) || defined(__WIN64__) || defined(WIN32) || defined(_WIN32) || defined(__WIN32__) || defined(__NT__))
+#   define QHULL_OS_WIN
+#elif defined(__MWERKS__) && defined(__INTEL__) /* Metrowerks discontinued before the release of Intel Macs */
+#   define QHULL_OS_WIN
+#endif
+/*============================================================*/
+/*============= qhull library constants ======================*/
+/*============================================================*/
+
+/*-<a                             href="qh-user.htm#TOC"
+  >--------------------------------</a><a name="filenamelen">-</a>
+
+  FILENAMElen -- max length for TI and TO filenames
+
+*/
+
+#define qh_FILENAMElen 500
+
+/*-<a                             href="qh-user.htm#TOC"
+  >--------------------------------</a><a name="msgcode">-</a>
+
+  msgcode -- Unique message codes for qh_fprintf
+
+  If add new messages, assign these values and increment in user.h and user_r.h
+  See QhullError.h for 10000 errors.
+
+  def counters =  [27, 1048, 2059, 3026, 4068, 5003,
+     6273, 7081, 8147, 9411, 10000, 11029]
+
+  See: qh_ERR* [libqhull.h]
+*/
+
+#define MSG_TRACE0 0
+#define MSG_TRACE1 1000
+#define MSG_TRACE2 2000
+#define MSG_TRACE3 3000
+#define MSG_TRACE4 4000
+#define MSG_TRACE5 5000
+#define MSG_ERROR  6000   /* errors written to qh.ferr */
+#define MSG_WARNING 7000
+#define MSG_STDERR  8000  /* log messages Written to qh.ferr */
+#define MSG_OUTPUT  9000
+#define MSG_QHULL_ERROR 10000 /* errors thrown by QhullError.cpp (QHULLlastError is in QhullError.h) */
+#define MSG_FIXUP  11000  /* FIXUP QH11... */
+#define MSG_MAXLEN  3000 /* qh_printhelp_degenerate() in user.c */
+
+
+/*-<a                             href="qh-user.htm#TOC"
+  >--------------------------------</a><a name="qh_OPTIONline">-</a>
+
+  qh_OPTIONline -- max length of an option line 'FO'
+*/
+#define qh_OPTIONline 80
+
+/*============================================================*/
+/*============= data types and configuration macros ==========*/
+/*============================================================*/
+
+/*-<a                             href="qh-user.htm#TOC"
+  >--------------------------------</a><a name="realT">-</a>
+
+  realT
+    set the size of floating point numbers
+
+  qh_REALdigits
+    maximimum number of significant digits
+
+  qh_REAL_1, qh_REAL_2n, qh_REAL_3n
+    format strings for printf
+
+  qh_REALmax, qh_REALmin
+    maximum and minimum (near zero) values
+
+  qh_REALepsilon
+    machine roundoff.  Maximum roundoff error for addition and multiplication.
+
+  notes:
+   Select whether to store floating point numbers in single precision (float)
+   or double precision (double).
+
+   Use 'float' to save about 8% in time and 25% in space.  This is particularly
+   helpful if high-d where convex hulls are space limited.  Using 'float' also
+   reduces the printed size of Qhull's output since numbers have 8 digits of
+   precision.
+
+   Use 'double' when greater arithmetic precision is needed.  This is needed
+   for Delaunay triangulations and Voronoi diagrams when you are not merging
+   facets.
+
+   If 'double' gives insufficient precision, your data probably includes
+   degeneracies.  If so you should use facet merging (done by default)
+   or exact arithmetic (see imprecision section of manual, qh-impre.htm).
+   You may also use option 'Po' to force output despite precision errors.
+
+   You may use 'long double', but many format statements need to be changed
+   and you may need a 'long double' square root routine.  S. Grundmann
+   (sg@eeiwzb.et.tu-dresden.de) has done this.  He reports that the code runs
+   much slower with little gain in precision.
+
+   WARNING: on some machines,    int f(){realT a= REALmax;return (a == REALmax);}
+      returns False.  Use (a > REALmax/2) instead of (a == REALmax).
+
+   REALfloat =   1      all numbers are 'float' type
+             =   0      all numbers are 'double' type
+*/
+#define REALfloat 0
+
+#if (REALfloat == 1)
+#define realT float
+#define REALmax FLT_MAX
+#define REALmin FLT_MIN
+#define REALepsilon FLT_EPSILON
+#define qh_REALdigits 8   /* maximum number of significant digits */
+#define qh_REAL_1 "%6.8g "
+#define qh_REAL_2n "%6.8g %6.8g\n"
+#define qh_REAL_3n "%6.8g %6.8g %6.8g\n"
+
+#elif (REALfloat == 0)
+#define realT double
+#define REALmax DBL_MAX
+#define REALmin DBL_MIN
+#define REALepsilon DBL_EPSILON
+#define qh_REALdigits 16    /* maximum number of significant digits */
+#define qh_REAL_1 "%6.16g "
+#define qh_REAL_2n "%6.16g %6.16g\n"
+#define qh_REAL_3n "%6.16g %6.16g %6.16g\n"
+
+#else
+#error unknown float option
+#endif
+
+/*-<a                             href="qh-user.htm#TOC"
+  >--------------------------------</a><a name="CPUclock">-</a>
+
+  qh_CPUclock
+    define the clock() function for reporting the total time spent by Qhull
+    returns CPU ticks as a 'long int'
+    qh_CPUclock is only used for reporting the total time spent by Qhull
+
+  qh_SECticks
+    the number of clock ticks per second
+
+  notes:
+    looks for CLOCKS_PER_SEC, CLOCKS_PER_SECOND, or assumes microseconds
+    to define a custom clock, set qh_CLOCKtype to 0
+
+    if your system does not use clock() to return CPU ticks, replace
+    qh_CPUclock with the corresponding function.  It is converted
+    to 'unsigned long' to prevent wrap-around during long runs.  By default,
+    <time.h> defines clock_t as 'long'
+
+   Set qh_CLOCKtype to
+
+     1          for CLOCKS_PER_SEC, CLOCKS_PER_SECOND, or microsecond
+                Note:  may fail if more than 1 hour elapsed time
+
+     2          use qh_clock() with POSIX times() (see global.c)
+*/
+#define qh_CLOCKtype 1  /* change to the desired number */
+
+#if (qh_CLOCKtype == 1)
+
+#if defined(CLOCKS_PER_SECOND)
+#define qh_CPUclock    ((unsigned long)clock())  /* return CPU clock */
+#define qh_SECticks CLOCKS_PER_SECOND
+
+#elif defined(CLOCKS_PER_SEC)
+#define qh_CPUclock    ((unsigned long)clock())  /* return CPU clock */
+#define qh_SECticks CLOCKS_PER_SEC
+
+#elif defined(CLK_TCK)
+#define qh_CPUclock    ((unsigned long)clock())  /* return CPU clock */
+#define qh_SECticks CLK_TCK
+
+#else
+#define qh_CPUclock    ((unsigned long)clock())  /* return CPU clock */
+#define qh_SECticks 1E6
+#endif
+
+#elif (qh_CLOCKtype == 2)
+#define qh_CPUclock    qh_clock()  /* return CPU clock */
+#define qh_SECticks 100
+
+#else /* qh_CLOCKtype == ? */
+#error unknown clock option
+#endif
+
+/*-<a                             href="qh-user.htm#TOC"
+  >--------------------------------</a><a name="RANDOM">-</a>
+
+  qh_RANDOMtype, qh_RANDOMmax, qh_RANDOMseed
+    define random number generator
+
+    qh_RANDOMint generates a random integer between 0 and qh_RANDOMmax.
+    qh_RANDOMseed sets the random number seed for qh_RANDOMint
+
+  Set qh_RANDOMtype (default 5) to:
+    1       for random() with 31 bits (UCB)
+    2       for rand() with RAND_MAX or 15 bits (system 5)
+    3       for rand() with 31 bits (Sun)
+    4       for lrand48() with 31 bits (Solaris)
+    5       for qh_rand() with 31 bits (included with Qhull)
+
+  notes:
+    Random numbers are used by rbox to generate point sets.  Random
+    numbers are used by Qhull to rotate the input ('QRn' option),
+    simulate a randomized algorithm ('Qr' option), and to simulate
+    roundoff errors ('Rn' option).
+
+    Random number generators differ between systems.  Most systems provide
+    rand() but the period varies.  The period of rand() is not critical
+    since qhull does not normally use random numbers.
+
+    The default generator is Park & Miller's minimal standard random
+    number generator [CACM 31:1195 '88].  It is included with Qhull.
+
+    If qh_RANDOMmax is wrong, qhull will report a warning and Geomview
+    output will likely be invisible.
+*/
+#define qh_RANDOMtype 5   /* *** change to the desired number *** */
+
+#if (qh_RANDOMtype == 1)
+#define qh_RANDOMmax ((realT)0x7fffffffUL)  /* 31 bits, random()/MAX */
+#define qh_RANDOMint random()
+#define qh_RANDOMseed_(seed) srandom(seed);
+
+#elif (qh_RANDOMtype == 2)
+#ifdef RAND_MAX
+#define qh_RANDOMmax ((realT)RAND_MAX)
+#else
+#define qh_RANDOMmax ((realT)32767)   /* 15 bits (System 5) */
+#endif
+#define qh_RANDOMint  rand()
+#define qh_RANDOMseed_(seed) srand((unsigned)seed);
+
+#elif (qh_RANDOMtype == 3)
+#define qh_RANDOMmax ((realT)0x7fffffffUL)  /* 31 bits, Sun */
+#define qh_RANDOMint  rand()
+#define qh_RANDOMseed_(seed) srand((unsigned)seed);
+
+#elif (qh_RANDOMtype == 4)
+#define qh_RANDOMmax ((realT)0x7fffffffUL)  /* 31 bits, lrand38()/MAX */
+#define qh_RANDOMint lrand48()
+#define qh_RANDOMseed_(seed) srand48(seed);
+
+#elif (qh_RANDOMtype == 5)
+#define qh_RANDOMmax ((realT)2147483646UL)  /* 31 bits, qh_rand/MAX */
+#define qh_RANDOMint qh_rand()
+#define qh_RANDOMseed_(seed) qh_srand(seed);
+/* unlike rand(), never returns 0 */
+
+#else
+#error: unknown random option
+#endif
+
+/*-<a                             href="qh-user.htm#TOC"
+  >--------------------------------</a><a name="ORIENTclock">-</a>
+
+  qh_ORIENTclock
+    0 for inward pointing normals by Geomview convention
+*/
+#define qh_ORIENTclock 0
+
+
+/*============================================================*/
+/*============= joggle constants =============================*/
+/*============================================================*/
+
+/*-<a                             href="qh-user.htm#TOC"
+>--------------------------------</a><a name="JOGGLEdefault">-</a>
+
+qh_JOGGLEdefault
+default qh.JOGGLEmax is qh.DISTround * qh_JOGGLEdefault
+
+notes:
+rbox s r 100 | qhull QJ1e-15 QR0 generates 90% faults at distround 7e-16
+rbox s r 100 | qhull QJ1e-14 QR0 generates 70% faults
+rbox s r 100 | qhull QJ1e-13 QR0 generates 35% faults
+rbox s r 100 | qhull QJ1e-12 QR0 generates 8% faults
+rbox s r 100 | qhull QJ1e-11 QR0 generates 1% faults
+rbox s r 100 | qhull QJ1e-10 QR0 generates 0% faults
+rbox 1000 W0 | qhull QJ1e-12 QR0 generates 86% faults
+rbox 1000 W0 | qhull QJ1e-11 QR0 generates 20% faults
+rbox 1000 W0 | qhull QJ1e-10 QR0 generates 2% faults
+the later have about 20 points per facet, each of which may interfere
+
+pick a value large enough to avoid retries on most inputs
+*/
+#define qh_JOGGLEdefault 30000.0
+
+/*-<a                             href="qh-user.htm#TOC"
+>--------------------------------</a><a name="JOGGLEincrease">-</a>
+
+qh_JOGGLEincrease
+factor to increase qh.JOGGLEmax on qh_JOGGLEretry or qh_JOGGLEagain
+*/
+#define qh_JOGGLEincrease 10.0
+
+/*-<a                             href="qh-user.htm#TOC"
+>--------------------------------</a><a name="JOGGLEretry">-</a>
+
+qh_JOGGLEretry
+if ZZretry = qh_JOGGLEretry, increase qh.JOGGLEmax
+
+notes:
+try twice at the original value in case of bad luck the first time
+*/
+#define qh_JOGGLEretry 2
+
+/*-<a                             href="qh-user.htm#TOC"
+>--------------------------------</a><a name="JOGGLEagain">-</a>
+
+qh_JOGGLEagain
+every following qh_JOGGLEagain, increase qh.JOGGLEmax
+
+notes:
+1 is OK since it's already failed qh_JOGGLEretry times
+*/
+#define qh_JOGGLEagain 1
+
+/*-<a                             href="qh-user.htm#TOC"
+>--------------------------------</a><a name="JOGGLEmaxincrease">-</a>
+
+qh_JOGGLEmaxincrease
+maximum qh.JOGGLEmax due to qh_JOGGLEincrease
+relative to qh.MAXwidth
+
+notes:
+qh.joggleinput will retry at this value until qh_JOGGLEmaxretry
+*/
+#define qh_JOGGLEmaxincrease 1e-2
+
+/*-<a                             href="qh-user.htm#TOC"
+>--------------------------------</a><a name="JOGGLEmaxretry">-</a>
+
+qh_JOGGLEmaxretry
+stop after qh_JOGGLEmaxretry attempts
+*/
+#define qh_JOGGLEmaxretry 100
+
+/*============================================================*/
+/*============= performance related constants ================*/
+/*============================================================*/
+
+/*-<a                             href="qh-user.htm#TOC"
+  >--------------------------------</a><a name="HASHfactor">-</a>
+
+  qh_HASHfactor
+    total hash slots / used hash slots.  Must be at least 1.1.
+
+  notes:
+    =2 for at worst 50% occupancy for qh.hash_table and normally 25% occupancy
+*/
+#define qh_HASHfactor 2
+
+/*-<a                             href="qh-user.htm#TOC"
+  >--------------------------------</a><a name="VERIFYdirect">-</a>
+
+  qh_VERIFYdirect
+    with 'Tv' verify all points against all facets if op count is smaller
+
+  notes:
+    if greater, calls qh_check_bestdist() instead
+*/
+#define qh_VERIFYdirect 1000000
+
+/*-<a                             href="qh-user.htm#TOC"
+  >--------------------------------</a><a name="INITIALsearch">-</a>
+
+  qh_INITIALsearch
+     if qh_INITIALmax, search points up to this dimension
+*/
+#define qh_INITIALsearch 6
+
+/*-<a                             href="qh-user.htm#TOC"
+  >--------------------------------</a><a name="INITIALmax">-</a>
+
+  qh_INITIALmax
+    if dim >= qh_INITIALmax, use min/max coordinate points for initial simplex
+
+  notes:
+    from points with non-zero determinants
+    use option 'Qs' to override (much slower)
+*/
+#define qh_INITIALmax 8
+
+/*============================================================*/
+/*============= memory constants =============================*/
+/*============================================================*/
+
+/*-<a                             href="qh-user.htm#TOC"
+  >--------------------------------</a><a name="MEMalign">-</a>
+
+  qh_MEMalign
+    memory alignment for qh_meminitbuffers() in global.c
+
+  notes:
+    to avoid bus errors, memory allocation must consider alignment requirements.
+    malloc() automatically takes care of alignment.   Since mem.c manages
+    its own memory, we need to explicitly specify alignment in
+    qh_meminitbuffers().
+
+    A safe choice is sizeof(double).  sizeof(float) may be used if doubles
+    do not occur in data structures and pointers are the same size.  Be careful
+    of machines (e.g., DEC Alpha) with large pointers.
+
+    If using gcc, best alignment is  [fmax_() is defined in geom_r.h]
+              #define qh_MEMalign fmax_(__alignof__(realT),__alignof__(void *))
+*/
+#define qh_MEMalign ((int)(fmax_(sizeof(realT), sizeof(void *))))
+
+/*-<a                             href="qh-user.htm#TOC"
+  >--------------------------------</a><a name="MEMbufsize">-</a>
+
+  qh_MEMbufsize
+    size of additional memory buffers
+
+  notes:
+    used for qh_meminitbuffers() in global.c
+*/
+#define qh_MEMbufsize 0x10000       /* allocate 64K memory buffers */
+
+/*-<a                             href="qh-user.htm#TOC"
+  >--------------------------------</a><a name="MEMinitbuf">-</a>
+
+  qh_MEMinitbuf
+    size of initial memory buffer
+
+  notes:
+    use for qh_meminitbuffers() in global.c
+*/
+#define qh_MEMinitbuf 0x20000      /* initially allocate 128K buffer */
+
+/*-<a                             href="qh-user.htm#TOC"
+  >--------------------------------</a><a name="INFINITE">-</a>
+
+  qh_INFINITE
+    on output, indicates Voronoi center at infinity
+*/
+#define qh_INFINITE  -10.101
+
+/*-<a                             href="qh-user.htm#TOC"
+  >--------------------------------</a><a name="DEFAULTbox">-</a>
+
+  qh_DEFAULTbox
+    default box size (Geomview expects 0.5)
+
+  qh_DEFAULTbox
+    default box size for integer coorindate (rbox only)
+*/
+#define qh_DEFAULTbox 0.5
+#define qh_DEFAULTzbox 1e6
+
+/*============================================================*/
+/*============= conditional compilation ======================*/
+/*============================================================*/
+
+/*-<a                             href="qh-user.htm#TOC"
+  >--------------------------------</a><a name="compiler">-</a>
+
+  __cplusplus
+    defined by C++ compilers
+
+  __MSC_VER
+    defined by Microsoft Visual C++
+
+  __MWERKS__ && __INTEL__
+    defined by Metrowerks when compiling for Windows (not Intel-based Macintosh)
+
+  __MWERKS__ && __POWERPC__
+    defined by Metrowerks when compiling for PowerPC-based Macintosh
+  __STDC__
+    defined for strict ANSI C
+*/
+
+/*-<a                             href="qh-user.htm#TOC"
+  >--------------------------------</a><a name="COMPUTEfurthest">-</a>
+
+  qh_COMPUTEfurthest
+    compute furthest distance to an outside point instead of storing it with the facet
+    =1 to compute furthest
+
+  notes:
+    computing furthest saves memory but costs time
+      about 40% more distance tests for partitioning
+      removes facet->furthestdist
+*/
+#define qh_COMPUTEfurthest 0
+
+/*-<a                             href="qh-user.htm#TOC"
+  >--------------------------------</a><a name="KEEPstatistics">-</a>
+
+  qh_KEEPstatistics
+    =0 removes most of statistic gathering and reporting
+
+  notes:
+    if 0, code size is reduced by about 4%.
+*/
+#define qh_KEEPstatistics 1
+
+/*-<a                             href="qh-user.htm#TOC"
+  >--------------------------------</a><a name="MAXoutside">-</a>
+
+  qh_MAXoutside
+    record outer plane for each facet
+    =1 to record facet->maxoutside
+
+  notes:
+    this takes a realT per facet and slightly slows down qhull
+    it produces better outer planes for geomview output
+*/
+#define qh_MAXoutside 1
+
+/*-<a                             href="qh-user.htm#TOC"
+  >--------------------------------</a><a name="NOmerge">-</a>
+
+  qh_NOmerge
+    disables facet merging if defined
+
+  notes:
+    This saves about 10% space.
+
+    Unless 'Q0'
+      qh_NOmerge sets 'QJ' to avoid precision errors
+
+    #define qh_NOmerge
+
+  see:
+    <a href="mem.h#NOmem">qh_NOmem</a> in mem.c
+
+    see user.c/user_eg.c for removing io.o
+*/
+
+/*-<a                             href="qh-user.htm#TOC"
+  >--------------------------------</a><a name="NOtrace">-</a>
+
+  qh_NOtrace
+    no tracing if defined
+
+  notes:
+    This saves about 5% space.
+
+    #define qh_NOtrace
+*/
+
+/*-<a                             href="qh-user.htm#TOC"
+  >--------------------------------</a><a name="QHpointer">-</a>
+
+  qh_QHpointer
+    access global data with pointer or static structure
+
+  qh_QHpointer  = 1     access globals via a pointer to allocated memory
+                        enables qh_saveqhull() and qh_restoreqhull()
+                        [2010, gcc] costs about 4% in time and 4% in space
+                        [2003, msvc] costs about 8% in time and 2% in space
+
+                = 0     qh_qh and qh_qhstat are static data structures
+                        only one instance of qhull() can be active at a time
+                        default value
+
+  qh_QHpointer_dllimport and qh_dllimport define qh_qh as __declspec(dllimport) [libqhull.h]
+  It is required for msvc-2005.  It is not needed for gcc.
+
+  notes:
+    [jan'16] qh_QHpointer is deprecated for Qhull.  Use libqhull_r instead.
+    all global variables for qhull are in qh, qhmem, and qhstat
+    qh is defined in libqhull.h
+    qhmem is defined in mem.h
+    qhstat is defined in stat.h
+
+*/
+#ifdef qh_QHpointer
+#if qh_dllimport
+#error QH6207 Qhull error: Use qh_QHpointer_dllimport instead of qh_dllimport with qh_QHpointer
+#endif
+#else
+#define qh_QHpointer 0
+#if qh_QHpointer_dllimport
+#error QH6234 Qhull error: Use qh_dllimport instead of qh_QHpointer_dllimport when qh_QHpointer is not defined
+#endif
+#endif
+#if 0  /* sample code */
+    qhT *oldqhA, *oldqhB;
+
+    exitcode= qh_new_qhull(dim, numpoints, points, ismalloc,
+                      flags, outfile, errfile);
+    /* use results from first call to qh_new_qhull */
+    oldqhA= qh_save_qhull();
+    exitcode= qh_new_qhull(dimB, numpointsB, pointsB, ismalloc,
+                      flags, outfile, errfile);
+    /* use results from second call to qh_new_qhull */
+    oldqhB= qh_save_qhull();
+    qh_restore_qhull(&oldqhA);
+    /* use results from first call to qh_new_qhull */
+    qh_freeqhull(qh_ALL);  /* frees all memory used by first call */
+    qh_restore_qhull(&oldqhB);
+    /* use results from second call to qh_new_qhull */
+    qh_freeqhull(!qh_ALL); /* frees long memory used by second call */
+    qh_memfreeshort(&curlong, &totlong);  /* frees short memory and memory allocator */
+#endif
+
+/*-<a                             href="qh-user.htm#TOC"
+  >--------------------------------</a><a name="QUICKhelp">-</a>
+
+  qh_QUICKhelp
+    =1 to use abbreviated help messages, e.g., for degenerate inputs
+*/
+#define qh_QUICKhelp    0
+
+/*============================================================*/
+/*============= -merge constants- ============================*/
+/*============================================================*/
+/*
+   These constants effect facet merging.  You probably will not need
+   to modify them.  They effect the performance of facet merging.
+*/
+
+/*-<a                             href="qh-user.htm#TOC"
+  >--------------------------------</a><a name="DIMmergeVertex">-</a>
+
+  qh_DIMmergeVertex
+    max dimension for vertex merging (it is not effective in high-d)
+*/
+#define qh_DIMmergeVertex 6
+
+/*-<a                             href="qh-user.htm#TOC"
+  >--------------------------------</a><a name="DIMreduceBuild">-</a>
+
+  qh_DIMreduceBuild
+     max dimension for vertex reduction during build (slow in high-d)
+*/
+#define qh_DIMreduceBuild 5
+
+/*-<a                             href="qh-user.htm#TOC"
+  >--------------------------------</a><a name="BESTcentrum">-</a>
+
+  qh_BESTcentrum
+     if > 2*dim+n vertices, qh_findbestneighbor() tests centrums (faster)
+     else, qh_findbestneighbor() tests all vertices (much better merges)
+
+  qh_BESTcentrum2
+     if qh_BESTcentrum2 * DIM3 + BESTcentrum < #vertices tests centrums
+*/
+#define qh_BESTcentrum 20
+#define qh_BESTcentrum2 2
+
+/*-<a                             href="qh-user.htm#TOC"
+  >--------------------------------</a><a name="BESTnonconvex">-</a>
+
+  qh_BESTnonconvex
+    if > dim+n neighbors, qh_findbestneighbor() tests nonconvex ridges.
+
+  notes:
+    It is needed because qh_findbestneighbor is slow for large facets
+*/
+#define qh_BESTnonconvex 15
+
+/*-<a                             href="qh-user.htm#TOC"
+  >--------------------------------</a><a name="MAXnewmerges">-</a>
+
+  qh_MAXnewmerges
+    if >n newmerges, qh_merge_nonconvex() calls qh_reducevertices_centrums.
+
+  notes:
+    It is needed because postmerge can merge many facets at once
+*/
+#define qh_MAXnewmerges 2
+
+/*-<a                             href="qh-user.htm#TOC"
+  >--------------------------------</a><a name="MAXnewcentrum">-</a>
+
+  qh_MAXnewcentrum
+    if <= dim+n vertices (n approximates the number of merges),
+      reset the centrum in qh_updatetested() and qh_mergecycle_facets()
+
+  notes:
+    needed to reduce cost and because centrums may move too much if
+    many vertices in high-d
+*/
+#define qh_MAXnewcentrum 5
+
+/*-<a                             href="qh-user.htm#TOC"
+  >--------------------------------</a><a name="COPLANARratio">-</a>
+
+  qh_COPLANARratio
+    for 3-d+ merging, qh.MINvisible is n*premerge_centrum
+
+  notes:
+    for non-merging, it's DISTround
+*/
+#define qh_COPLANARratio 3
+
+/*-<a                             href="qh-user.htm#TOC"
+  >--------------------------------</a><a name="DISToutside">-</a>
+
+  qh_DISToutside
+    When is a point clearly outside of a facet?
+    Stops search in qh_findbestnew or qh_partitionall
+    qh_findbest uses qh.MINoutside since since it is only called if no merges.
+
+  notes:
+    'Qf' always searches for best facet
+    if !qh.MERGING, same as qh.MINoutside.
+    if qh_USEfindbestnew, increase value since neighboring facets may be ill-behaved
+      [Note: Zdelvertextot occurs normally with interior points]
+            RBOX 1000 s Z1 G1e-13 t1001188774 | QHULL Tv
+    When there is a sharp edge, need to move points to a
+    clearly good facet; otherwise may be lost in another partitioning.
+    if too big then O(n^2) behavior for partitioning in cone
+    if very small then important points not processed
+    Needed in qh_partitionall for
+      RBOX 1000 s Z1 G1e-13 t1001032651 | QHULL Tv
+    Needed in qh_findbestnew for many instances of
+      RBOX 1000 s Z1 G1e-13 t | QHULL Tv
+
+  See:
+    qh_DISToutside -- when is a point clearly outside of a facet
+    qh_SEARCHdist -- when is facet coplanar with the best facet?
+    qh_USEfindbestnew -- when to use qh_findbestnew for qh_partitionpoint()
+*/
+#define qh_DISToutside ((qh_USEfindbestnew ? 2 : 1) * \
+     fmax_((qh MERGING ? 2 : 1)*qh MINoutside, qh max_outside))
+
+/*-<a                             href="qh-user.htm#TOC"
+  >--------------------------------</a><a name="RATIOnearinside">-</a>
+
+  qh_RATIOnearinside
+    ratio of qh.NEARinside to qh.ONEmerge for retaining inside points for
+    qh_check_maxout().
+
+  notes:
+    This is overkill since do not know the correct value.
+    It effects whether 'Qc' reports all coplanar points
+    Not used for 'd' since non-extreme points are coplanar
+*/
+#define qh_RATIOnearinside 5
+
+/*-<a                             href="qh-user.htm#TOC"
+  >--------------------------------</a><a name="SEARCHdist">-</a>
+
+  qh_SEARCHdist
+    When is a facet coplanar with the best facet?
+    qh_findbesthorizon: all coplanar facets of the best facet need to be searched.
+
+  See:
+    qh_DISToutside -- when is a point clearly outside of a facet
+    qh_SEARCHdist -- when is facet coplanar with the best facet?
+    qh_USEfindbestnew -- when to use qh_findbestnew for qh_partitionpoint()
+*/
+#define qh_SEARCHdist ((qh_USEfindbestnew ? 2 : 1) * \
+      (qh max_outside + 2 * qh DISTround + fmax_( qh MINvisible, qh MAXcoplanar)));
+
+/*-<a                             href="qh-user.htm#TOC"
+  >--------------------------------</a><a name="USEfindbestnew">-</a>
+
+  qh_USEfindbestnew
+     Always use qh_findbestnew for qh_partitionpoint, otherwise use
+     qh_findbestnew if merged new facet or sharpnewfacets.
+
+  See:
+    qh_DISToutside -- when is a point clearly outside of a facet
+    qh_SEARCHdist -- when is facet coplanar with the best facet?
+    qh_USEfindbestnew -- when to use qh_findbestnew for qh_partitionpoint()
+*/
+#define qh_USEfindbestnew (zzval_(Ztotmerge) > 50)
+
+/*-<a                             href="qh-user.htm#TOC"
+  >--------------------------------</a><a name="WIDEcoplanar">-</a>
+
+  qh_WIDEcoplanar
+    n*MAXcoplanar or n*MINvisible for a WIDEfacet
+
+    if vertex is further than qh.WIDEfacet from the hyperplane
+    then its ridges are not counted in computing the area, and
+    the facet's centrum is frozen.
+
+  notes:
+   qh.WIDEfacet= max(qh.MAXoutside,qh_WIDEcoplanar*qh.MAXcoplanar,
+      qh_WIDEcoplanar * qh.MINvisible);
+*/
+#define qh_WIDEcoplanar 6
+
+/*-<a                             href="qh-user.htm#TOC"
+  >--------------------------------</a><a name="WIDEduplicate">-</a>
+
+  qh_WIDEduplicate
+    Merge ratio for errexit from qh_forcedmerges due to duplicate ridge
+    Override with option Q12 no-wide-duplicate
+
+    Notes:
+      Merging a duplicate ridge can lead to very wide facets.
+      A future release of qhull will avoid duplicate ridges by removing duplicate sub-ridges from the horizon
+*/
+#define qh_WIDEduplicate 100
+
+/*-<a                             href="qh-user.htm#TOC"
+  >--------------------------------</a><a name="MAXnarrow">-</a>
+
+  qh_MAXnarrow
+    max. cosine in initial hull that sets qh.NARROWhull
+
+  notes:
+    If qh.NARROWhull, the initial partition does not make
+    coplanar points.  If narrow, a coplanar point can be
+    coplanar to two facets of opposite orientations and
+    distant from the exact convex hull.
+
+    Conservative estimate.  Don't actually see problems until it is -1.0
+*/
+#define qh_MAXnarrow -0.99999999
+
+/*-<a                             href="qh-user.htm#TOC"
+  >--------------------------------</a><a name="WARNnarrow">-</a>
+
+  qh_WARNnarrow
+    max. cosine in initial hull to warn about qh.NARROWhull
+
+  notes:
+    this is a conservative estimate.
+    Don't actually see problems until it is -1.0.  See qh-impre.htm
+*/
+#define qh_WARNnarrow -0.999999999999999
+
+/*-<a                             href="qh-user.htm#TOC"
+  >--------------------------------</a><a name="ZEROdelaunay">-</a>
+
+  qh_ZEROdelaunay
+    a zero Delaunay facet occurs for input sites coplanar with their convex hull
+    the last normal coefficient of a zero Delaunay facet is within
+        qh_ZEROdelaunay * qh.ANGLEround of 0
+
+  notes:
+    qh_ZEROdelaunay does not allow for joggled input ('QJ').
+
+    You can avoid zero Delaunay facets by surrounding the input with a box.
+
+    Use option 'PDk:-n' to explicitly define zero Delaunay facets
+      k= dimension of input sites (e.g., 3 for 3-d Delaunay triangulation)
+      n= the cutoff for zero Delaunay facets (e.g., 'PD3:-1e-12')
+*/
+#define qh_ZEROdelaunay 2
+
+/*============================================================*/
+/*============= Microsoft DevStudio ==========================*/
+/*============================================================*/
+
+/*
+   Finding Memory Leaks Using the CRT Library
+   https://msdn.microsoft.com/en-us/library/x98tx3cf(v=vs.100).aspx
+
+   Reports enabled in qh_lib_check for Debug window and stderr
+
+   From 2005=>msvcr80d, 2010=>msvcr100d, 2012=>msvcr110d
+
+   Watch: {,,msvcr80d.dll}_crtBreakAlloc  Value from {n} in the leak report
+   _CrtSetBreakAlloc(689); // qh_lib_check() [global_r.c]
+
+   Examples
+     http://free-cad.sourceforge.net/SrcDocu/d2/d7f/MemDebug_8cpp_source.html
+     https://github.com/illlust/Game/blob/master/library/MemoryLeak.cpp
+*/
+#if 0   /* off (0) by default for QHULL_CRTDBG */
+#define QHULL_CRTDBG
+#endif
+
+#if defined(_MSC_VER) && defined(_DEBUG) && defined(QHULL_CRTDBG)
+#define _CRTDBG_MAP_ALLOC
+#include <stdlib.h>
+#include <crtdbg.h>
+#endif
+#endif /* qh_DEFuser */
+
+
+
diff --git a/xs/src/qhull/src/libqhull/usermem.c b/xs/src/qhull/src/libqhull/usermem.c
new file mode 100644
index 0000000000..0e99e8f66c
--- /dev/null
+++ b/xs/src/qhull/src/libqhull/usermem.c
@@ -0,0 +1,94 @@
+/*<html><pre>  -<a                             href="qh-user.htm"
+  >-------------------------------</a><a name="TOP">-</a>
+
+   usermem.c
+   qh_exit(), qh_free(), and qh_malloc()
+
+   See README.txt.
+
+   If you redefine one of these functions you must redefine all of them.
+   If you recompile and load this file, then usermem.o will not be loaded
+   from qhull.a or qhull.lib
+
+   See libqhull.h for data structures, macros, and user-callable functions.
+   See user.c for qhull-related, redefinable functions
+   see user.h for user-definable constants
+   See userprintf.c for qh_fprintf and userprintf_rbox.c for qh_fprintf_rbox
+
+   Please report any errors that you fix to qhull@qhull.org
+*/
+
+#include "libqhull.h"
+
+#include <stdarg.h>
+#include <stdlib.h>
+
+/*-<a                             href="qh-user.htm#TOC"
+  >-------------------------------</a><a name="qh_exit">-</a>
+
+  qh_exit( exitcode )
+    exit program
+
+  notes:
+    qh_exit() is called when qh_errexit() and longjmp() are not available.
+
+    This is the only use of exit() in Qhull
+    To replace qh_exit with 'throw', see libqhullcpp/usermem_r-cpp.cpp
+*/
+void qh_exit(int exitcode) {
+    exit(exitcode);
+} /* exit */
+
+/*-<a                             href="qh-user.htm#TOC"
+  >-------------------------------</a><a name="qh_fprintf_stderr">-</a>
+
+  qh_fprintf_stderr( msgcode, format, list of args )
+    fprintf to stderr with msgcode (non-zero)
+
+  notes:
+    qh_fprintf_stderr() is called when qh.ferr is not defined, usually due to an initialization error
+    
+    It is typically followed by qh_errexit().
+
+    Redefine this function to avoid using stderr
+
+    Use qh_fprintf [userprintf.c] for normal printing
+*/
+void qh_fprintf_stderr(int msgcode, const char *fmt, ... ) {
+    va_list args;
+
+    va_start(args, fmt);
+    if(msgcode)
+      fprintf(stderr, "QH%.4d ", msgcode);
+    vfprintf(stderr, fmt, args);
+    va_end(args);
+} /* fprintf_stderr */
+
+/*-<a                             href="qh-user.htm#TOC"
+>-------------------------------</a><a name="qh_free">-</a>
+
+  qh_free( mem )
+    free memory
+
+  notes:
+    same as free()
+    No calls to qh_errexit() 
+*/
+void qh_free(void *mem) {
+    free(mem);
+} /* free */
+
+/*-<a                             href="qh-user.htm#TOC"
+    >-------------------------------</a><a name="qh_malloc">-</a>
+
+    qh_malloc( mem )
+      allocate memory
+
+    notes:
+      same as malloc()
+*/
+void *qh_malloc(size_t size) {
+    return malloc(size);
+} /* malloc */
+
+
diff --git a/xs/src/qhull/src/libqhull/userprintf.c b/xs/src/qhull/src/libqhull/userprintf.c
new file mode 100644
index 0000000000..190d7cd79b
--- /dev/null
+++ b/xs/src/qhull/src/libqhull/userprintf.c
@@ -0,0 +1,66 @@
+/*<html><pre>  -<a                             href="qh-user.htm"
+  >-------------------------------</a><a name="TOP">-</a>
+
+   userprintf.c
+   qh_fprintf()
+
+   see README.txt  see COPYING.txt for copyright information.
+
+   If you recompile and load this file, then userprintf.o will not be loaded
+   from qhull.a or qhull.lib
+
+   See libqhull.h for data structures, macros, and user-callable functions.
+   See user.c for qhull-related, redefinable functions
+   see user.h for user-definable constants
+   See usermem.c for qh_exit(), qh_free(), and qh_malloc()
+   see Qhull.cpp and RboxPoints.cpp for examples.
+
+   Please report any errors that you fix to qhull@qhull.org
+*/
+
+#include "libqhull.h"
+#include "mem.h"
+
+#include <stdarg.h>
+#include <stdio.h>
+#include <stdlib.h>
+
+/*-<a                             href="qh-user.htm#TOC"
+   >-------------------------------</a><a name="qh_fprintf">-</a>
+
+   qh_fprintf(fp, msgcode, format, list of args )
+     print arguments to *fp according to format
+     Use qh_fprintf_rbox() for rboxlib.c
+
+   notes:
+     same as fprintf()
+     fgets() is not trapped like fprintf()
+     exit qh_fprintf via qh_errexit()
+     may be called for errors in qh_initstatistics and qh_meminit
+*/
+
+void qh_fprintf(FILE *fp, int msgcode, const char *fmt, ... ) {
+    va_list args;
+
+    if (!fp) {
+        /* could use qhmem.ferr, but probably better to be cautious */
+        qh_fprintf_stderr(6232, "Qhull internal error (userprintf.c): fp is 0.  Wrong qh_fprintf called.\n");
+        qh_errexit(6232, NULL, NULL);
+    }
+    va_start(args, fmt);
+#if qh_QHpointer
+    if (qh_qh && qh ANNOTATEoutput) {
+#else
+    if (qh ANNOTATEoutput) {
+#endif
+      fprintf(fp, "[QH%.4d]", msgcode);
+    }else if (msgcode >= MSG_ERROR && msgcode < MSG_STDERR ) {
+      fprintf(fp, "QH%.4d ", msgcode);
+    }
+    vfprintf(fp, fmt, args);
+    va_end(args);
+
+    /* Place debugging traps here. Use with option 'Tn' */
+
+} /* qh_fprintf */
+
diff --git a/xs/src/qhull/src/libqhull/userprintf_rbox.c b/xs/src/qhull/src/libqhull/userprintf_rbox.c
new file mode 100644
index 0000000000..8edd2001aa
--- /dev/null
+++ b/xs/src/qhull/src/libqhull/userprintf_rbox.c
@@ -0,0 +1,53 @@
+/*<html><pre>  -<a                             href="qh-user.htm"
+  >-------------------------------</a><a name="TOP">-</a>
+
+   userprintf_rbox.c
+   qh_fprintf_rbox()
+
+   see README.txt  see COPYING.txt for copyright information.
+
+   If you recompile and load this file, then userprintf_rbox.o will not be loaded
+   from qhull.a or qhull.lib
+
+   See libqhull.h for data structures, macros, and user-callable functions.
+   See user.c for qhull-related, redefinable functions
+   see user.h for user-definable constants
+   See usermem.c for qh_exit(), qh_free(), and qh_malloc()
+   see Qhull.cpp and RboxPoints.cpp for examples.
+
+   Please report any errors that you fix to qhull@qhull.org
+*/
+
+#include "libqhull.h"
+
+#include <stdarg.h>
+#include <stdio.h>
+#include <stdlib.h>
+
+/*-<a                             href="qh-user.htm#TOC"
+   >-------------------------------</a><a name="qh_fprintf_rbox">-</a>
+
+   qh_fprintf_rbox(fp, msgcode, format, list of args )
+     print arguments to *fp according to format
+     Use qh_fprintf_rbox() for rboxlib.c
+
+   notes:
+     same as fprintf()
+     fgets() is not trapped like fprintf()
+     exit qh_fprintf_rbox via qh_errexit_rbox()
+*/
+
+void qh_fprintf_rbox(FILE *fp, int msgcode, const char *fmt, ... ) {
+    va_list args;
+
+    if (!fp) {
+        qh_fprintf_stderr(6231, "Qhull internal error (userprintf_rbox.c): fp is 0.  Wrong qh_fprintf_rbox called.\n");
+        qh_errexit_rbox(6231);
+    }
+    if (msgcode >= MSG_ERROR && msgcode < MSG_STDERR)
+      fprintf(fp, "QH%.4d ", msgcode);
+    va_start(args, fmt);
+    vfprintf(fp, fmt, args);
+    va_end(args);
+} /* qh_fprintf_rbox */
+
diff --git a/xs/src/qhull/src/libqhull_r/Makefile b/xs/src/qhull/src/libqhull_r/Makefile
new file mode 100644
index 0000000000..5c40969e01
--- /dev/null
+++ b/xs/src/qhull/src/libqhull_r/Makefile
@@ -0,0 +1,240 @@
+# Simple gcc Makefile for reentrant qhull and rbox (default gcc/g++)
+#
+#   make help
+#   See README.txt and ../../Makefile
+#       
+# Variables
+#   BINDIR         directory where to copy executables
+#   DESTDIR        destination directory for 'make install'
+#   DOCDIR         directory where to copy html documentation
+#   INCDIR         directory where to copy headers
+#   LIBDIR         directory where to copy libraries
+#   MANDIR         directory where to copy manual pages
+#   PRINTMAN       command for printing manual pages
+#   PRINTC         command for printing C files
+#   CC             ANSI C or C++ compiler
+#   CC_OPTS1       options used to compile .c files
+#   CC_OPTS2       options used to link .o files
+#   CC_OPTS3       options to build shared libraries
+#
+#   LIBQHULL_OBJS  .o files for linking
+#   LIBQHULL_HDRS  .h files for printing
+#   CFILES         .c files for printing
+#   DOCFILES       documentation files
+#   FILES          miscellaneous files for printing
+#   TFILES         .txt versions of html files
+#   FILES          all other files
+#   LIBQHULL_OBJS  specifies the object files of libqhullstatic_r.a
+#
+# Results
+#   rbox           Generates points sets for qhull, qconvex, etc.
+#   qhull          Computes convex hulls and related structures
+#   qconvex, qdelaunay, qhalf, qvoronoi
+#                  Specializations of qhull for each geometric structure
+#   libqhullstatic_r.a Static library for reentrant qhull
+#   testqset_r     Standalone test of reentrant qset_r.c with mem_r.c
+#   user_eg        An example of using qhull (reentrant)
+#   user_eg2       An example of using qhull (reentrant)
+#
+# Make targets
+#   make           Build results using gcc or another compiler
+#   make clean     Remove object files
+#   make cleanall  Remove generated files
+#   make doc       Print documentation
+#   make help
+#   make install   Copy qhull, rbox, qhull.1, rbox.1 to BINDIR, MANDIR
+#   make new       Rebuild qhull and rbox from source
+#   make printall  Print all files
+#   make qtest     Quick test of qset, rbox, and qhull
+#   make test      Quck test of qhull, qconvex, etc.
+#
+# Do not replace tabs with spaces.  Needed for build rules
+# Unix line endings (\n)
+# $Id: //main/2015/qhull/src/libqhull_r/Makefile#6 $
+
+DESTDIR = /usr/local
+BINDIR	= $(DESTDIR)/bin
+INCDIR	= $(DESTDIR)/include
+LIBDIR	= $(DESTDIR)/lib
+DOCDIR	= $(DESTDIR)/share/doc/qhull
+MANDIR	= $(DESTDIR)/share/man/man1
+
+# if you do not have enscript, try a2ps or just use lpr.  The files are text.
+PRINTMAN = enscript -2rl
+PRINTC = enscript -2r
+# PRINTMAN = lpr
+# PRINTC = lpr
+
+#for Gnu's gcc compiler, -O3 for optimization, -g for debugging, -pg for profiling
+# -fpic  needed for gcc x86_64-linux-gnu.  Not needed for mingw
+CC        = gcc
+CC_OPTS1  = -O3 -ansi -I../../src -fpic $(CC_WARNINGS)
+
+# for Sun's cc compiler, -fast or O2 for optimization, -g for debugging, -Xc for ANSI
+#CC       = cc
+#CC_OPTS1 = -Xc -v -fast -I../../src 
+
+# for Silicon Graphics cc compiler, -O2 for optimization, -g for debugging
+#CC       = cc
+#CC_OPTS1 = -ansi -O2 -I../../src 
+
+# for Next cc compiler with fat executable
+#CC       = cc
+#CC_OPTS1 = -ansi -O2 -I../../src -arch m68k -arch i386 -arch hppa
+
+# For loader, ld, 
+CC_OPTS2 = $(CC_OPTS1)
+
+# Default targets for make
+
+all: qhull_links qhull_all qtest
+
+help:
+	head -n 50 Makefile
+
+clean:
+	rm -f *.o 
+	# Delete linked files from other directories [qhull_links]
+	rm -f qconvex_r.c unix_r.c qdelaun_r.c qhalf_r.c qvoronoi_r.c rbox_r.c
+	rm -f user_eg_r.c user_eg2_r.c testqset_r.c
+	
+cleanall: clean
+	rm -f qconvex qdelaunay qhalf qvoronoi qhull *.exe
+	rm -f core user_eg_r user_eg2_r testqset_r libqhullstatic_r.a
+
+doc: 
+	$(PRINTMAN) $(TXTFILES) $(DOCFILES)
+
+install:
+	mkdir -p $(BINDIR)
+	mkdir -p $(DOCDIR)
+	mkdir -p $(INCDIR)/libqhull
+	mkdir -p $(MANDIR)
+	cp -p qconvex qdelaunay qhalf qhull qvoronoi rbox $(BINDIR)
+	cp -p libqhullstatic_r.a $(LIBDIR)
+	cp -p ../../html/qhull.man $(MANDIR)/qhull.1
+	cp -p ../../html/rbox.man $(MANDIR)/rbox.1
+	cp -p ../../html/* $(DOCDIR)
+	cp *.h $(INCDIR)/libqhull_r
+
+new:	cleanall all
+
+printall: doc printh printc printf
+
+printh:
+	$(PRINTC) $(LIBQHULL_HDRS)
+
+printc:
+	$(PRINTC) $(CFILES)
+
+# LIBQHULL_OBJS_1 ordered by frequency of execution with small files at end.  Better locality.
+# Same definitions as ../../Makefile
+
+LIBQHULLS_OBJS_1= global_r.o stat_r.o geom2_r.o poly2_r.o merge_r.o \
+        libqhull_r.o geom_r.o poly_r.o qset_r.o mem_r.o random_r.o 
+
+LIBQHULLS_OBJS_2= $(LIBQHULLS_OBJS_1) usermem_r.o userprintf_r.o io_r.o user_r.o
+
+LIBQHULLS_OBJS= $(LIBQHULLS_OBJS_2)  rboxlib_r.o userprintf_rbox_r.o
+
+LIBQHULL_HDRS= user_r.h libqhull_r.h qhull_ra.h geom_r.h \
+        io_r.h mem_r.h merge_r.h poly_r.h random_r.h \
+        qset_r.h stat_r.h
+
+# CFILES ordered alphabetically after libqhull.c 
+CFILES= ../qhull/unix_r.c libqhull_r.c geom_r.c geom2_r.c global_r.c io_r.c \
+	mem_r.c merge_r.c poly_r.c poly2_r.c random_r.c rboxlib_r.c \
+	qset_r.c stat_r.c user_r.c usermem_r.c userprintf_r.c \
+	../qconvex/qconvex.c ../qdelaunay/qdelaun.c ../qhalf/qhalf.c ../qvoronoi/qvoronoi.c
+
+TXTFILES= ../../Announce.txt ../../REGISTER.txt ../../COPYING.txt ../../README.txt ../Changes.txt
+DOCFILES= ../../html/rbox.txt ../../html/qhull.txt
+
+.c.o:
+	$(CC) -c $(CC_OPTS1) -o $@ $<
+
+# Work around problems with ../ in Red Hat Linux
+qhull_links:
+	# On MINSYS, 'ln -s' may create a copy instead of a symbolic link
+	[ -f qconvex_r.c ]  || ln -s ../qconvex/qconvex_r.c
+	[ -f qdelaun_r.c ]  || ln -s ../qdelaunay/qdelaun_r.c
+	[ -f qhalf_r.c ]    || ln -s ../qhalf/qhalf_r.c
+	[ -f qvoronoi_r.c ] || ln -s ../qvoronoi/qvoronoi_r.c
+	[ -f rbox_r.c ]     || ln -s ../rbox/rbox_r.c
+	[ -f testqset_r.c ] || ln -s ../testqset_r/testqset_r.c
+	[ -f unix_r.c ]     || ln -s ../qhull/unix_r.c
+	[ -f user_eg_r.c ]  || ln -s ../user_eg/user_eg_r.c
+	[ -f user_eg2_r.c ] || ln -s ../user_eg2/user_eg2_r.c
+
+# compile qhull without using bin/libqhullstatic_r.a
+qhull_all: qconvex_r.o qdelaun_r.o qhalf_r.o qvoronoi_r.o unix_r.o user_eg_r.o user_eg2_r.o rbox_r.o testqset_r.o $(LIBQHULLS_OBJS)
+	$(CC) -o qconvex $(CC_OPTS2) -lm $(LIBQHULLS_OBJS_2) qconvex_r.o
+	$(CC) -o qdelaunay $(CC_OPTS2) -lm $(LIBQHULLS_OBJS_2) qdelaun_r.o
+	$(CC) -o qhalf $(CC_OPTS2) -lm $(LIBQHULLS_OBJS_2) qhalf_r.o
+	$(CC) -o qvoronoi $(CC_OPTS2) -lm $(LIBQHULLS_OBJS_2) qvoronoi_r.o
+	$(CC) -o qhull $(CC_OPTS2) -lm $(LIBQHULLS_OBJS_2) unix_r.o 
+	$(CC) -o rbox $(CC_OPTS2) -lm $(LIBQHULLS_OBJS) rbox_r.o
+	$(CC) -o user_eg $(CC_OPTS2) -lm $(LIBQHULLS_OBJS_2) user_eg_r.o 
+	$(CC) -o user_eg2 $(CC_OPTS2) -lm $(LIBQHULLS_OBJS_1) user_eg2_r.o  usermem_r.o userprintf_r.o io_r.o
+	$(CC) -o testqset_r $(CC_OPTS2) -lm mem_r.o qset_r.o usermem_r.o testqset_r.o
+	-ar -rs libqhullstatic_r.a $(LIBQHULLS_OBJS)
+	#libqhullstatic_r.a is not needed for qhull
+	#If 'ar -rs' fails try using 'ar -s' with 'ranlib'
+	#ranlib libqhullstatic_r.a
+
+qtest:
+	@echo ============================================
+	@echo == make qtest ==============================
+	@echo ============================================
+	@echo -n "== "
+	@date
+	@echo
+	@echo Testing qset.c and mem.c with testqset
+	./testqset_r 10000
+	@echo Run the qhull smoketest
+	./rbox D4 | ./qhull
+	@echo ============================================
+	@echo == To smoketest qhull programs
+	@echo '==     make test'
+	@echo ============================================
+	@echo
+	@echo ============================================
+	@echo == For all make targets
+	@echo '==     make help'
+	@echo ============================================
+	@echo
+
+test: qtest
+	@echo ==============================
+	@echo ========= qconvex ============
+	@echo ==============================
+	-./rbox 10 | ./qconvex Tv 
+	@echo
+	@echo ==============================
+	@echo ========= qdelaunay ==========
+	@echo ==============================
+	-./rbox 10 | ./qdelaunay Tv 
+	@echo
+	@echo ==============================
+	@echo ========= qhalf ==============
+	@echo ==============================
+	-./rbox 10 | ./qconvex FQ FV n Tv | ./qhalf Tv
+	@echo
+	@echo ==============================
+	@echo ========= qvoronoi ===========
+	@echo ==============================
+	-./rbox 10 | ./qvoronoi Tv
+	@echo
+	@echo ==============================
+	@echo ========= user_eg ============
+	@echo == w/o shared library ========
+	@echo ==============================
+	-./user_eg
+	@echo
+	@echo ==============================
+	@echo ========= user_eg2 ===========
+	@echo ==============================
+	-./user_eg2
+	@echo
+
+# end of Makefile
diff --git a/xs/src/qhull/src/libqhull_r/geom2_r.c b/xs/src/qhull/src/libqhull_r/geom2_r.c
new file mode 100644
index 0000000000..48addba1cf
--- /dev/null
+++ b/xs/src/qhull/src/libqhull_r/geom2_r.c
@@ -0,0 +1,2096 @@
+/*<html><pre>  -<a                             href="qh-geom_r.htm"
+  >-------------------------------</a><a name="TOP">-</a>
+
+
+   geom2_r.c
+   infrequently used geometric routines of qhull
+
+   see qh-geom_r.htm and geom_r.h
+
+   Copyright (c) 1993-2015 The Geometry Center.
+   $Id: //main/2015/qhull/src/libqhull_r/geom2_r.c#6 $$Change: 2065 $
+   $DateTime: 2016/01/18 13:51:04 $$Author: bbarber $
+
+   frequently used code goes into geom_r.c
+*/
+
+#include "qhull_ra.h"
+
+/*================== functions in alphabetic order ============*/
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >-------------------------------</a><a name="copypoints">-</a>
+
+  qh_copypoints(qh, points, numpoints, dimension)
+    return qh_malloc'd copy of points
+  
+  notes:
+    qh_free the returned points to avoid a memory leak
+*/
+coordT *qh_copypoints(qhT *qh, coordT *points, int numpoints, int dimension) {
+  int size;
+  coordT *newpoints;
+
+  size= numpoints * dimension * (int)sizeof(coordT);
+  if (!(newpoints= (coordT*)qh_malloc((size_t)size))) {
+    qh_fprintf(qh, qh->ferr, 6004, "qhull error: insufficient memory to copy %d points\n",
+        numpoints);
+    qh_errexit(qh, qh_ERRmem, NULL, NULL);
+  }
+  memcpy((char *)newpoints, (char *)points, (size_t)size); /* newpoints!=0 by QH6004 */
+  return newpoints;
+} /* copypoints */
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >-------------------------------</a><a name="crossproduct">-</a>
+
+  qh_crossproduct( dim, vecA, vecB, vecC )
+    crossproduct of 2 dim vectors
+    C= A x B
+
+  notes:
+    from Glasner, Graphics Gems I, p. 639
+    only defined for dim==3
+*/
+void qh_crossproduct(int dim, realT vecA[3], realT vecB[3], realT vecC[3]){
+
+  if (dim == 3) {
+    vecC[0]=   det2_(vecA[1], vecA[2],
+                     vecB[1], vecB[2]);
+    vecC[1]= - det2_(vecA[0], vecA[2],
+                     vecB[0], vecB[2]);
+    vecC[2]=   det2_(vecA[0], vecA[1],
+                     vecB[0], vecB[1]);
+  }
+} /* vcross */
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >-------------------------------</a><a name="determinant">-</a>
+
+  qh_determinant(qh, rows, dim, nearzero )
+    compute signed determinant of a square matrix
+    uses qh.NEARzero to test for degenerate matrices
+
+  returns:
+    determinant
+    overwrites rows and the matrix
+    if dim == 2 or 3
+      nearzero iff determinant < qh->NEARzero[dim-1]
+      (!quite correct, not critical)
+    if dim >= 4
+      nearzero iff diagonal[k] < qh->NEARzero[k]
+*/
+realT qh_determinant(qhT *qh, realT **rows, int dim, boolT *nearzero) {
+  realT det=0;
+  int i;
+  boolT sign= False;
+
+  *nearzero= False;
+  if (dim < 2) {
+    qh_fprintf(qh, qh->ferr, 6005, "qhull internal error (qh_determinate): only implemented for dimension >= 2\n");
+    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+  }else if (dim == 2) {
+    det= det2_(rows[0][0], rows[0][1],
+                 rows[1][0], rows[1][1]);
+    if (fabs_(det) < 10*qh->NEARzero[1])  /* not really correct, what should this be? */
+      *nearzero= True;
+  }else if (dim == 3) {
+    det= det3_(rows[0][0], rows[0][1], rows[0][2],
+                 rows[1][0], rows[1][1], rows[1][2],
+                 rows[2][0], rows[2][1], rows[2][2]);
+    if (fabs_(det) < 10*qh->NEARzero[2])  /* what should this be?  det 5.5e-12 was flat for qh_maxsimplex of qdelaunay 0,0 27,27 -36,36 -9,63 */
+      *nearzero= True;
+  }else {
+    qh_gausselim(qh, rows, dim, dim, &sign, nearzero);  /* if nearzero, diagonal still ok*/
+    det= 1.0;
+    for (i=dim; i--; )
+      det *= (rows[i])[i];
+    if (sign)
+      det= -det;
+  }
+  return det;
+} /* determinant */
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >-------------------------------</a><a name="detjoggle">-</a>
+
+  qh_detjoggle(qh, points, numpoints, dimension )
+    determine default max joggle for point array
+      as qh_distround * qh_JOGGLEdefault
+
+  returns:
+    initial value for JOGGLEmax from points and REALepsilon
+
+  notes:
+    computes DISTround since qh_maxmin not called yet
+    if qh->SCALElast, last dimension will be scaled later to MAXwidth
+
+    loop duplicated from qh_maxmin
+*/
+realT qh_detjoggle(qhT *qh, pointT *points, int numpoints, int dimension) {
+  realT abscoord, distround, joggle, maxcoord, mincoord;
+  pointT *point, *pointtemp;
+  realT maxabs= -REALmax;
+  realT sumabs= 0;
+  realT maxwidth= 0;
+  int k;
+
+  for (k=0; k < dimension; k++) {
+    if (qh->SCALElast && k == dimension-1)
+      abscoord= maxwidth;
+    else if (qh->DELAUNAY && k == dimension-1) /* will qh_setdelaunay() */
+      abscoord= 2 * maxabs * maxabs;  /* may be low by qh->hull_dim/2 */
+    else {
+      maxcoord= -REALmax;
+      mincoord= REALmax;
+      FORALLpoint_(qh, points, numpoints) {
+        maximize_(maxcoord, point[k]);
+        minimize_(mincoord, point[k]);
+      }
+      maximize_(maxwidth, maxcoord-mincoord);
+      abscoord= fmax_(maxcoord, -mincoord);
+    }
+    sumabs += abscoord;
+    maximize_(maxabs, abscoord);
+  } /* for k */
+  distround= qh_distround(qh, qh->hull_dim, maxabs, sumabs);
+  joggle= distround * qh_JOGGLEdefault;
+  maximize_(joggle, REALepsilon * qh_JOGGLEdefault);
+  trace2((qh, qh->ferr, 2001, "qh_detjoggle: joggle=%2.2g maxwidth=%2.2g\n", joggle, maxwidth));
+  return joggle;
+} /* detjoggle */
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >-------------------------------</a><a name="detroundoff">-</a>
+
+  qh_detroundoff(qh)
+    determine maximum roundoff errors from
+      REALepsilon, REALmax, REALmin, qh.hull_dim, qh.MAXabs_coord,
+      qh.MAXsumcoord, qh.MAXwidth, qh.MINdenom_1
+
+    accounts for qh.SETroundoff, qh.RANDOMdist, qh->MERGEexact
+      qh.premerge_cos, qh.postmerge_cos, qh.premerge_centrum,
+      qh.postmerge_centrum, qh.MINoutside,
+      qh_RATIOnearinside, qh_COPLANARratio, qh_WIDEcoplanar
+
+  returns:
+    sets qh.DISTround, etc. (see below)
+    appends precision constants to qh.qhull_options
+
+  see:
+    qh_maxmin() for qh.NEARzero
+
+  design:
+    determine qh.DISTround for distance computations
+    determine minimum denominators for qh_divzero
+    determine qh.ANGLEround for angle computations
+    adjust qh.premerge_cos,... for roundoff error
+    determine qh.ONEmerge for maximum error due to a single merge
+    determine qh.NEARinside, qh.MAXcoplanar, qh.MINvisible,
+      qh.MINoutside, qh.WIDEfacet
+    initialize qh.max_vertex and qh.minvertex
+*/
+void qh_detroundoff(qhT *qh) {
+
+  qh_option(qh, "_max-width", NULL, &qh->MAXwidth);
+  if (!qh->SETroundoff) {
+    qh->DISTround= qh_distround(qh, qh->hull_dim, qh->MAXabs_coord, qh->MAXsumcoord);
+    if (qh->RANDOMdist)
+      qh->DISTround += qh->RANDOMfactor * qh->MAXabs_coord;
+    qh_option(qh, "Error-roundoff", NULL, &qh->DISTround);
+  }
+  qh->MINdenom= qh->MINdenom_1 * qh->MAXabs_coord;
+  qh->MINdenom_1_2= sqrt(qh->MINdenom_1 * qh->hull_dim) ;  /* if will be normalized */
+  qh->MINdenom_2= qh->MINdenom_1_2 * qh->MAXabs_coord;
+                                              /* for inner product */
+  qh->ANGLEround= 1.01 * qh->hull_dim * REALepsilon;
+  if (qh->RANDOMdist)
+    qh->ANGLEround += qh->RANDOMfactor;
+  if (qh->premerge_cos < REALmax/2) {
+    qh->premerge_cos -= qh->ANGLEround;
+    if (qh->RANDOMdist)
+      qh_option(qh, "Angle-premerge-with-random", NULL, &qh->premerge_cos);
+  }
+  if (qh->postmerge_cos < REALmax/2) {
+    qh->postmerge_cos -= qh->ANGLEround;
+    if (qh->RANDOMdist)
+      qh_option(qh, "Angle-postmerge-with-random", NULL, &qh->postmerge_cos);
+  }
+  qh->premerge_centrum += 2 * qh->DISTround;    /*2 for centrum and distplane()*/
+  qh->postmerge_centrum += 2 * qh->DISTround;
+  if (qh->RANDOMdist && (qh->MERGEexact || qh->PREmerge))
+    qh_option(qh, "Centrum-premerge-with-random", NULL, &qh->premerge_centrum);
+  if (qh->RANDOMdist && qh->POSTmerge)
+    qh_option(qh, "Centrum-postmerge-with-random", NULL, &qh->postmerge_centrum);
+  { /* compute ONEmerge, max vertex offset for merging simplicial facets */
+    realT maxangle= 1.0, maxrho;
+
+    minimize_(maxangle, qh->premerge_cos);
+    minimize_(maxangle, qh->postmerge_cos);
+    /* max diameter * sin theta + DISTround for vertex to its hyperplane */
+    qh->ONEmerge= sqrt((realT)qh->hull_dim) * qh->MAXwidth *
+      sqrt(1.0 - maxangle * maxangle) + qh->DISTround;
+    maxrho= qh->hull_dim * qh->premerge_centrum + qh->DISTround;
+    maximize_(qh->ONEmerge, maxrho);
+    maxrho= qh->hull_dim * qh->postmerge_centrum + qh->DISTround;
+    maximize_(qh->ONEmerge, maxrho);
+    if (qh->MERGING)
+      qh_option(qh, "_one-merge", NULL, &qh->ONEmerge);
+  }
+  qh->NEARinside= qh->ONEmerge * qh_RATIOnearinside; /* only used if qh->KEEPnearinside */
+  if (qh->JOGGLEmax < REALmax/2 && (qh->KEEPcoplanar || qh->KEEPinside)) {
+    realT maxdist;             /* adjust qh.NEARinside for joggle */
+    qh->KEEPnearinside= True;
+    maxdist= sqrt((realT)qh->hull_dim) * qh->JOGGLEmax + qh->DISTround;
+    maxdist= 2*maxdist;        /* vertex and coplanar point can joggle in opposite directions */
+    maximize_(qh->NEARinside, maxdist);  /* must agree with qh_nearcoplanar() */
+  }
+  if (qh->KEEPnearinside)
+    qh_option(qh, "_near-inside", NULL, &qh->NEARinside);
+  if (qh->JOGGLEmax < qh->DISTround) {
+    qh_fprintf(qh, qh->ferr, 6006, "qhull error: the joggle for 'QJn', %.2g, is below roundoff for distance computations, %.2g\n",
+         qh->JOGGLEmax, qh->DISTround);
+    qh_errexit(qh, qh_ERRinput, NULL, NULL);
+  }
+  if (qh->MINvisible > REALmax/2) {
+    if (!qh->MERGING)
+      qh->MINvisible= qh->DISTround;
+    else if (qh->hull_dim <= 3)
+      qh->MINvisible= qh->premerge_centrum;
+    else
+      qh->MINvisible= qh_COPLANARratio * qh->premerge_centrum;
+    if (qh->APPROXhull && qh->MINvisible > qh->MINoutside)
+      qh->MINvisible= qh->MINoutside;
+    qh_option(qh, "Visible-distance", NULL, &qh->MINvisible);
+  }
+  if (qh->MAXcoplanar > REALmax/2) {
+    qh->MAXcoplanar= qh->MINvisible;
+    qh_option(qh, "U-coplanar-distance", NULL, &qh->MAXcoplanar);
+  }
+  if (!qh->APPROXhull) {             /* user may specify qh->MINoutside */
+    qh->MINoutside= 2 * qh->MINvisible;
+    if (qh->premerge_cos < REALmax/2)
+      maximize_(qh->MINoutside, (1- qh->premerge_cos) * qh->MAXabs_coord);
+    qh_option(qh, "Width-outside", NULL, &qh->MINoutside);
+  }
+  qh->WIDEfacet= qh->MINoutside;
+  maximize_(qh->WIDEfacet, qh_WIDEcoplanar * qh->MAXcoplanar);
+  maximize_(qh->WIDEfacet, qh_WIDEcoplanar * qh->MINvisible);
+  qh_option(qh, "_wide-facet", NULL, &qh->WIDEfacet);
+  if (qh->MINvisible > qh->MINoutside + 3 * REALepsilon
+  && !qh->BESToutside && !qh->FORCEoutput)
+    qh_fprintf(qh, qh->ferr, 7001, "qhull input warning: minimum visibility V%.2g is greater than \nminimum outside W%.2g.  Flipped facets are likely.\n",
+             qh->MINvisible, qh->MINoutside);
+  qh->max_vertex= qh->DISTround;
+  qh->min_vertex= -qh->DISTround;
+  /* numeric constants reported in printsummary */
+} /* detroundoff */
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >-------------------------------</a><a name="detsimplex">-</a>
+
+  qh_detsimplex(qh, apex, points, dim, nearzero )
+    compute determinant of a simplex with point apex and base points
+
+  returns:
+     signed determinant and nearzero from qh_determinant
+
+  notes:
+     uses qh.gm_matrix/qh.gm_row (assumes they're big enough)
+
+  design:
+    construct qm_matrix by subtracting apex from points
+    compute determinate
+*/
+realT qh_detsimplex(qhT *qh, pointT *apex, setT *points, int dim, boolT *nearzero) {
+  pointT *coorda, *coordp, *gmcoord, *point, **pointp;
+  coordT **rows;
+  int k,  i=0;
+  realT det;
+
+  zinc_(Zdetsimplex);
+  gmcoord= qh->gm_matrix;
+  rows= qh->gm_row;
+  FOREACHpoint_(points) {
+    if (i == dim)
+      break;
+    rows[i++]= gmcoord;
+    coordp= point;
+    coorda= apex;
+    for (k=dim; k--; )
+      *(gmcoord++)= *coordp++ - *coorda++;
+  }
+  if (i < dim) {
+    qh_fprintf(qh, qh->ferr, 6007, "qhull internal error (qh_detsimplex): #points %d < dimension %d\n",
+               i, dim);
+    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+  }
+  det= qh_determinant(qh, rows, dim, nearzero);
+  trace2((qh, qh->ferr, 2002, "qh_detsimplex: det=%2.2g for point p%d, dim %d, nearzero? %d\n",
+          det, qh_pointid(qh, apex), dim, *nearzero));
+  return det;
+} /* detsimplex */
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >-------------------------------</a><a name="distnorm">-</a>
+
+  qh_distnorm( dim, point, normal, offset )
+    return distance from point to hyperplane at normal/offset
+
+  returns:
+    dist
+
+  notes:
+    dist > 0 if point is outside of hyperplane
+
+  see:
+    qh_distplane in geom_r.c
+*/
+realT qh_distnorm(int dim, pointT *point, pointT *normal, realT *offsetp) {
+  coordT *normalp= normal, *coordp= point;
+  realT dist;
+  int k;
+
+  dist= *offsetp;
+  for (k=dim; k--; )
+    dist += *(coordp++) * *(normalp++);
+  return dist;
+} /* distnorm */
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >-------------------------------</a><a name="distround">-</a>
+
+  qh_distround(qh, dimension, maxabs, maxsumabs )
+    compute maximum round-off error for a distance computation
+      to a normalized hyperplane
+    maxabs is the maximum absolute value of a coordinate
+    maxsumabs is the maximum possible sum of absolute coordinate values
+
+  returns:
+    max dist round for REALepsilon
+
+  notes:
+    calculate roundoff error according to Golub & van Loan, 1983, Lemma 3.2-1, "Rounding Errors"
+    use sqrt(dim) since one vector is normalized
+      or use maxsumabs since one vector is < 1
+*/
+realT qh_distround(qhT *qh, int dimension, realT maxabs, realT maxsumabs) {
+  realT maxdistsum, maxround;
+
+  maxdistsum= sqrt((realT)dimension) * maxabs;
+  minimize_( maxdistsum, maxsumabs);
+  maxround= REALepsilon * (dimension * maxdistsum * 1.01 + maxabs);
+              /* adds maxabs for offset */
+  trace4((qh, qh->ferr, 4008, "qh_distround: %2.2g maxabs %2.2g maxsumabs %2.2g maxdistsum %2.2g\n",
+                 maxround, maxabs, maxsumabs, maxdistsum));
+  return maxround;
+} /* distround */
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >-------------------------------</a><a name="divzero">-</a>
+
+  qh_divzero( numer, denom, mindenom1, zerodiv )
+    divide by a number that's nearly zero
+    mindenom1= minimum denominator for dividing into 1.0
+
+  returns:
+    quotient
+    sets zerodiv and returns 0.0 if it would overflow
+
+  design:
+    if numer is nearly zero and abs(numer) < abs(denom)
+      return numer/denom
+    else if numer is nearly zero
+      return 0 and zerodiv
+    else if denom/numer non-zero
+      return numer/denom
+    else
+      return 0 and zerodiv
+*/
+realT qh_divzero(realT numer, realT denom, realT mindenom1, boolT *zerodiv) {
+  realT temp, numerx, denomx;
+
+
+  if (numer < mindenom1 && numer > -mindenom1) {
+    numerx= fabs_(numer);
+    denomx= fabs_(denom);
+    if (numerx < denomx) {
+      *zerodiv= False;
+      return numer/denom;
+    }else {
+      *zerodiv= True;
+      return 0.0;
+    }
+  }
+  temp= denom/numer;
+  if (temp > mindenom1 || temp < -mindenom1) {
+    *zerodiv= False;
+    return numer/denom;
+  }else {
+    *zerodiv= True;
+    return 0.0;
+  }
+} /* divzero */
+
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >-------------------------------</a><a name="facetarea">-</a>
+
+  qh_facetarea(qh, facet )
+    return area for a facet
+
+  notes:
+    if non-simplicial,
+      uses centrum to triangulate facet and sums the projected areas.
+    if (qh->DELAUNAY),
+      computes projected area instead for last coordinate
+    assumes facet->normal exists
+    projecting tricoplanar facets to the hyperplane does not appear to make a difference
+
+  design:
+    if simplicial
+      compute area
+    else
+      for each ridge
+        compute area from centrum to ridge
+    negate area if upper Delaunay facet
+*/
+realT qh_facetarea(qhT *qh, facetT *facet) {
+  vertexT *apex;
+  pointT *centrum;
+  realT area= 0.0;
+  ridgeT *ridge, **ridgep;
+
+  if (facet->simplicial) {
+    apex= SETfirstt_(facet->vertices, vertexT);
+    area= qh_facetarea_simplex(qh, qh->hull_dim, apex->point, facet->vertices,
+                    apex, facet->toporient, facet->normal, &facet->offset);
+  }else {
+    if (qh->CENTERtype == qh_AScentrum)
+      centrum= facet->center;
+    else
+      centrum= qh_getcentrum(qh, facet);
+    FOREACHridge_(facet->ridges)
+      area += qh_facetarea_simplex(qh, qh->hull_dim, centrum, ridge->vertices,
+                 NULL, (boolT)(ridge->top == facet),  facet->normal, &facet->offset);
+    if (qh->CENTERtype != qh_AScentrum)
+      qh_memfree(qh, centrum, qh->normal_size);
+  }
+  if (facet->upperdelaunay && qh->DELAUNAY)
+    area= -area;  /* the normal should be [0,...,1] */
+  trace4((qh, qh->ferr, 4009, "qh_facetarea: f%d area %2.2g\n", facet->id, area));
+  return area;
+} /* facetarea */
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >-------------------------------</a><a name="facetarea_simplex">-</a>
+
+  qh_facetarea_simplex(qh, dim, apex, vertices, notvertex, toporient, normal, offset )
+    return area for a simplex defined by
+      an apex, a base of vertices, an orientation, and a unit normal
+    if simplicial or tricoplanar facet,
+      notvertex is defined and it is skipped in vertices
+
+  returns:
+    computes area of simplex projected to plane [normal,offset]
+    returns 0 if vertex too far below plane (qh->WIDEfacet)
+      vertex can't be apex of tricoplanar facet
+
+  notes:
+    if (qh->DELAUNAY),
+      computes projected area instead for last coordinate
+    uses qh->gm_matrix/gm_row and qh->hull_dim
+    helper function for qh_facetarea
+
+  design:
+    if Notvertex
+      translate simplex to apex
+    else
+      project simplex to normal/offset
+      translate simplex to apex
+    if Delaunay
+      set last row/column to 0 with -1 on diagonal
+    else
+      set last row to Normal
+    compute determinate
+    scale and flip sign for area
+*/
+realT qh_facetarea_simplex(qhT *qh, int dim, coordT *apex, setT *vertices,
+        vertexT *notvertex,  boolT toporient, coordT *normal, realT *offset) {
+  pointT *coorda, *coordp, *gmcoord;
+  coordT **rows, *normalp;
+  int k,  i=0;
+  realT area, dist;
+  vertexT *vertex, **vertexp;
+  boolT nearzero;
+
+  gmcoord= qh->gm_matrix;
+  rows= qh->gm_row;
+  FOREACHvertex_(vertices) {
+    if (vertex == notvertex)
+      continue;
+    rows[i++]= gmcoord;
+    coorda= apex;
+    coordp= vertex->point;
+    normalp= normal;
+    if (notvertex) {
+      for (k=dim; k--; )
+        *(gmcoord++)= *coordp++ - *coorda++;
+    }else {
+      dist= *offset;
+      for (k=dim; k--; )
+        dist += *coordp++ * *normalp++;
+      if (dist < -qh->WIDEfacet) {
+        zinc_(Znoarea);
+        return 0.0;
+      }
+      coordp= vertex->point;
+      normalp= normal;
+      for (k=dim; k--; )
+        *(gmcoord++)= (*coordp++ - dist * *normalp++) - *coorda++;
+    }
+  }
+  if (i != dim-1) {
+    qh_fprintf(qh, qh->ferr, 6008, "qhull internal error (qh_facetarea_simplex): #points %d != dim %d -1\n",
+               i, dim);
+    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+  }
+  rows[i]= gmcoord;
+  if (qh->DELAUNAY) {
+    for (i=0; i < dim-1; i++)
+      rows[i][dim-1]= 0.0;
+    for (k=dim; k--; )
+      *(gmcoord++)= 0.0;
+    rows[dim-1][dim-1]= -1.0;
+  }else {
+    normalp= normal;
+    for (k=dim; k--; )
+      *(gmcoord++)= *normalp++;
+  }
+  zinc_(Zdetsimplex);
+  area= qh_determinant(qh, rows, dim, &nearzero);
+  if (toporient)
+    area= -area;
+  area *= qh->AREAfactor;
+  trace4((qh, qh->ferr, 4010, "qh_facetarea_simplex: area=%2.2g for point p%d, toporient %d, nearzero? %d\n",
+          area, qh_pointid(qh, apex), toporient, nearzero));
+  return area;
+} /* facetarea_simplex */
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >-------------------------------</a><a name="facetcenter">-</a>
+
+  qh_facetcenter(qh, vertices )
+    return Voronoi center (Voronoi vertex) for a facet's vertices
+
+  returns:
+    return temporary point equal to the center
+
+  see:
+    qh_voronoi_center()
+*/
+pointT *qh_facetcenter(qhT *qh, setT *vertices) {
+  setT *points= qh_settemp(qh, qh_setsize(qh, vertices));
+  vertexT *vertex, **vertexp;
+  pointT *center;
+
+  FOREACHvertex_(vertices)
+    qh_setappend(qh, &points, vertex->point);
+  center= qh_voronoi_center(qh, qh->hull_dim-1, points);
+  qh_settempfree(qh, &points);
+  return center;
+} /* facetcenter */
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >-------------------------------</a><a name="findgooddist">-</a>
+
+  qh_findgooddist(qh, point, facetA, dist, facetlist )
+    find best good facet visible for point from facetA
+    assumes facetA is visible from point
+
+  returns:
+    best facet, i.e., good facet that is furthest from point
+      distance to best facet
+      NULL if none
+
+    moves good, visible facets (and some other visible facets)
+      to end of qh->facet_list
+
+  notes:
+    uses qh->visit_id
+
+  design:
+    initialize bestfacet if facetA is good
+    move facetA to end of facetlist
+    for each facet on facetlist
+      for each unvisited neighbor of facet
+        move visible neighbors to end of facetlist
+        update best good neighbor
+        if no good neighbors, update best facet
+*/
+facetT *qh_findgooddist(qhT *qh, pointT *point, facetT *facetA, realT *distp,
+               facetT **facetlist) {
+  realT bestdist= -REALmax, dist;
+  facetT *neighbor, **neighborp, *bestfacet=NULL, *facet;
+  boolT goodseen= False;
+
+  if (facetA->good) {
+    zzinc_(Zcheckpart);  /* calls from check_bestdist occur after print stats */
+    qh_distplane(qh, point, facetA, &bestdist);
+    bestfacet= facetA;
+    goodseen= True;
+  }
+  qh_removefacet(qh, facetA);
+  qh_appendfacet(qh, facetA);
+  *facetlist= facetA;
+  facetA->visitid= ++qh->visit_id;
+  FORALLfacet_(*facetlist) {
+    FOREACHneighbor_(facet) {
+      if (neighbor->visitid == qh->visit_id)
+        continue;
+      neighbor->visitid= qh->visit_id;
+      if (goodseen && !neighbor->good)
+        continue;
+      zzinc_(Zcheckpart);
+      qh_distplane(qh, point, neighbor, &dist);
+      if (dist > 0) {
+        qh_removefacet(qh, neighbor);
+        qh_appendfacet(qh, neighbor);
+        if (neighbor->good) {
+          goodseen= True;
+          if (dist > bestdist) {
+            bestdist= dist;
+            bestfacet= neighbor;
+          }
+        }
+      }
+    }
+  }
+  if (bestfacet) {
+    *distp= bestdist;
+    trace2((qh, qh->ferr, 2003, "qh_findgooddist: p%d is %2.2g above good facet f%d\n",
+      qh_pointid(qh, point), bestdist, bestfacet->id));
+    return bestfacet;
+  }
+  trace4((qh, qh->ferr, 4011, "qh_findgooddist: no good facet for p%d above f%d\n",
+      qh_pointid(qh, point), facetA->id));
+  return NULL;
+}  /* findgooddist */
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >-------------------------------</a><a name="getarea">-</a>
+
+  qh_getarea(qh, facetlist )
+    set area of all facets in facetlist
+    collect statistics
+    nop if hasAreaVolume
+
+  returns:
+    sets qh->totarea/totvol to total area and volume of convex hull
+    for Delaunay triangulation, computes projected area of the lower or upper hull
+      ignores upper hull if qh->ATinfinity
+
+  notes:
+    could compute outer volume by expanding facet area by rays from interior
+    the following attempt at perpendicular projection underestimated badly:
+      qh.totoutvol += (-dist + facet->maxoutside + qh->DISTround)
+                            * area/ qh->hull_dim;
+  design:
+    for each facet on facetlist
+      compute facet->area
+      update qh.totarea and qh.totvol
+*/
+void qh_getarea(qhT *qh, facetT *facetlist) {
+  realT area;
+  realT dist;
+  facetT *facet;
+
+  if (qh->hasAreaVolume)
+    return;
+  if (qh->REPORTfreq)
+    qh_fprintf(qh, qh->ferr, 8020, "computing area of each facet and volume of the convex hull\n");
+  else
+    trace1((qh, qh->ferr, 1001, "qh_getarea: computing volume and area for each facet\n"));
+  qh->totarea= qh->totvol= 0.0;
+  FORALLfacet_(facetlist) {
+    if (!facet->normal)
+      continue;
+    if (facet->upperdelaunay && qh->ATinfinity)
+      continue;
+    if (!facet->isarea) {
+      facet->f.area= qh_facetarea(qh, facet);
+      facet->isarea= True;
+    }
+    area= facet->f.area;
+    if (qh->DELAUNAY) {
+      if (facet->upperdelaunay == qh->UPPERdelaunay)
+        qh->totarea += area;
+    }else {
+      qh->totarea += area;
+      qh_distplane(qh, qh->interior_point, facet, &dist);
+      qh->totvol += -dist * area/ qh->hull_dim;
+    }
+    if (qh->PRINTstatistics) {
+      wadd_(Wareatot, area);
+      wmax_(Wareamax, area);
+      wmin_(Wareamin, area);
+    }
+  }
+  qh->hasAreaVolume= True;
+} /* getarea */
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >-------------------------------</a><a name="gram_schmidt">-</a>
+
+  qh_gram_schmidt(qh, dim, row )
+    implements Gram-Schmidt orthogonalization by rows
+
+  returns:
+    false if zero norm
+    overwrites rows[dim][dim]
+
+  notes:
+    see Golub & van Loan, 1983, Algorithm 6.2-2, "Modified Gram-Schmidt"
+    overflow due to small divisors not handled
+
+  design:
+    for each row
+      compute norm for row
+      if non-zero, normalize row
+      for each remaining rowA
+        compute inner product of row and rowA
+        reduce rowA by row * inner product
+*/
+boolT qh_gram_schmidt(qhT *qh, int dim, realT **row) {
+  realT *rowi, *rowj, norm;
+  int i, j, k;
+
+  for (i=0; i < dim; i++) {
+    rowi= row[i];
+    for (norm= 0.0, k= dim; k--; rowi++)
+      norm += *rowi * *rowi;
+    norm= sqrt(norm);
+    wmin_(Wmindenom, norm);
+    if (norm == 0.0)  /* either 0 or overflow due to sqrt */
+      return False;
+    for (k=dim; k--; )
+      *(--rowi) /= norm;
+    for (j=i+1; j < dim; j++) {
+      rowj= row[j];
+      for (norm= 0.0, k=dim; k--; )
+        norm += *rowi++ * *rowj++;
+      for (k=dim; k--; )
+        *(--rowj) -= *(--rowi) * norm;
+    }
+  }
+  return True;
+} /* gram_schmidt */
+
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >-------------------------------</a><a name="inthresholds">-</a>
+
+  qh_inthresholds(qh, normal, angle )
+    return True if normal within qh.lower_/upper_threshold
+
+  returns:
+    estimate of angle by summing of threshold diffs
+      angle may be NULL
+      smaller "angle" is better
+
+  notes:
+    invalid if qh.SPLITthresholds
+
+  see:
+    qh.lower_threshold in qh_initbuild()
+    qh_initthresholds()
+
+  design:
+    for each dimension
+      test threshold
+*/
+boolT qh_inthresholds(qhT *qh, coordT *normal, realT *angle) {
+  boolT within= True;
+  int k;
+  realT threshold;
+
+  if (angle)
+    *angle= 0.0;
+  for (k=0; k < qh->hull_dim; k++) {
+    threshold= qh->lower_threshold[k];
+    if (threshold > -REALmax/2) {
+      if (normal[k] < threshold)
+        within= False;
+      if (angle) {
+        threshold -= normal[k];
+        *angle += fabs_(threshold);
+      }
+    }
+    if (qh->upper_threshold[k] < REALmax/2) {
+      threshold= qh->upper_threshold[k];
+      if (normal[k] > threshold)
+        within= False;
+      if (angle) {
+        threshold -= normal[k];
+        *angle += fabs_(threshold);
+      }
+    }
+  }
+  return within;
+} /* inthresholds */
+
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >-------------------------------</a><a name="joggleinput">-</a>
+
+  qh_joggleinput(qh)
+    randomly joggle input to Qhull by qh.JOGGLEmax
+    initial input is qh.first_point/qh.num_points of qh.hull_dim
+      repeated calls use qh.input_points/qh.num_points
+
+  returns:
+    joggles points at qh.first_point/qh.num_points
+    copies data to qh.input_points/qh.input_malloc if first time
+    determines qh.JOGGLEmax if it was zero
+    if qh.DELAUNAY
+      computes the Delaunay projection of the joggled points
+
+  notes:
+    if qh.DELAUNAY, unnecessarily joggles the last coordinate
+    the initial 'QJn' may be set larger than qh_JOGGLEmaxincrease
+
+  design:
+    if qh.DELAUNAY
+      set qh.SCALElast for reduced precision errors
+    if first call
+      initialize qh.input_points to the original input points
+      if qh.JOGGLEmax == 0
+        determine default qh.JOGGLEmax
+    else
+      increase qh.JOGGLEmax according to qh.build_cnt
+    joggle the input by adding a random number in [-qh.JOGGLEmax,qh.JOGGLEmax]
+    if qh.DELAUNAY
+      sets the Delaunay projection
+*/
+void qh_joggleinput(qhT *qh) {
+  int i, seed, size;
+  coordT *coordp, *inputp;
+  realT randr, randa, randb;
+
+  if (!qh->input_points) { /* first call */
+    qh->input_points= qh->first_point;
+    qh->input_malloc= qh->POINTSmalloc;
+    size= qh->num_points * qh->hull_dim * sizeof(coordT);
+    if (!(qh->first_point=(coordT*)qh_malloc((size_t)size))) {
+      qh_fprintf(qh, qh->ferr, 6009, "qhull error: insufficient memory to joggle %d points\n",
+          qh->num_points);
+      qh_errexit(qh, qh_ERRmem, NULL, NULL);
+    }
+    qh->POINTSmalloc= True;
+    if (qh->JOGGLEmax == 0.0) {
+      qh->JOGGLEmax= qh_detjoggle(qh, qh->input_points, qh->num_points, qh->hull_dim);
+      qh_option(qh, "QJoggle", NULL, &qh->JOGGLEmax);
+    }
+  }else {                 /* repeated call */
+    if (!qh->RERUN && qh->build_cnt > qh_JOGGLEretry) {
+      if (((qh->build_cnt-qh_JOGGLEretry-1) % qh_JOGGLEagain) == 0) {
+        realT maxjoggle= qh->MAXwidth * qh_JOGGLEmaxincrease;
+        if (qh->JOGGLEmax < maxjoggle) {
+          qh->JOGGLEmax *= qh_JOGGLEincrease;
+          minimize_(qh->JOGGLEmax, maxjoggle);
+        }
+      }
+    }
+    qh_option(qh, "QJoggle", NULL, &qh->JOGGLEmax);
+  }
+  if (qh->build_cnt > 1 && qh->JOGGLEmax > fmax_(qh->MAXwidth/4, 0.1)) {
+      qh_fprintf(qh, qh->ferr, 6010, "qhull error: the current joggle for 'QJn', %.2g, is too large for the width\nof the input.  If possible, recompile Qhull with higher-precision reals.\n",
+                qh->JOGGLEmax);
+      qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+  }
+  /* for some reason, using qh->ROTATErandom and qh_RANDOMseed does not repeat the run. Use 'TRn' instead */
+  seed= qh_RANDOMint;
+  qh_option(qh, "_joggle-seed", &seed, NULL);
+  trace0((qh, qh->ferr, 6, "qh_joggleinput: joggle input by %2.2g with seed %d\n",
+    qh->JOGGLEmax, seed));
+  inputp= qh->input_points;
+  coordp= qh->first_point;
+  randa= 2.0 * qh->JOGGLEmax/qh_RANDOMmax;
+  randb= -qh->JOGGLEmax;
+  size= qh->num_points * qh->hull_dim;
+  for (i=size; i--; ) {
+    randr= qh_RANDOMint;
+    *(coordp++)= *(inputp++) + (randr * randa + randb);
+  }
+  if (qh->DELAUNAY) {
+    qh->last_low= qh->last_high= qh->last_newhigh= REALmax;
+    qh_setdelaunay(qh, qh->hull_dim, qh->num_points, qh->first_point);
+  }
+} /* joggleinput */
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >-------------------------------</a><a name="maxabsval">-</a>
+
+  qh_maxabsval( normal, dim )
+    return pointer to maximum absolute value of a dim vector
+    returns NULL if dim=0
+*/
+realT *qh_maxabsval(realT *normal, int dim) {
+  realT maxval= -REALmax;
+  realT *maxp= NULL, *colp, absval;
+  int k;
+
+  for (k=dim, colp= normal; k--; colp++) {
+    absval= fabs_(*colp);
+    if (absval > maxval) {
+      maxval= absval;
+      maxp= colp;
+    }
+  }
+  return maxp;
+} /* maxabsval */
+
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >-------------------------------</a><a name="maxmin">-</a>
+
+  qh_maxmin(qh, points, numpoints, dimension )
+    return max/min points for each dimension
+    determine max and min coordinates
+
+  returns:
+    returns a temporary set of max and min points
+      may include duplicate points. Does not include qh.GOODpoint
+    sets qh.NEARzero, qh.MAXabs_coord, qh.MAXsumcoord, qh.MAXwidth
+         qh.MAXlastcoord, qh.MINlastcoord
+    initializes qh.max_outside, qh.min_vertex, qh.WAScoplanar, qh.ZEROall_ok
+
+  notes:
+    loop duplicated in qh_detjoggle()
+
+  design:
+    initialize global precision variables
+    checks definition of REAL...
+    for each dimension
+      for each point
+        collect maximum and minimum point
+      collect maximum of maximums and minimum of minimums
+      determine qh.NEARzero for Gaussian Elimination
+*/
+setT *qh_maxmin(qhT *qh, pointT *points, int numpoints, int dimension) {
+  int k;
+  realT maxcoord, temp;
+  pointT *minimum, *maximum, *point, *pointtemp;
+  setT *set;
+
+  qh->max_outside= 0.0;
+  qh->MAXabs_coord= 0.0;
+  qh->MAXwidth= -REALmax;
+  qh->MAXsumcoord= 0.0;
+  qh->min_vertex= 0.0;
+  qh->WAScoplanar= False;
+  if (qh->ZEROcentrum)
+    qh->ZEROall_ok= True;
+  if (REALmin < REALepsilon && REALmin < REALmax && REALmin > -REALmax
+  && REALmax > 0.0 && -REALmax < 0.0)
+    ; /* all ok */
+  else {
+    qh_fprintf(qh, qh->ferr, 6011, "qhull error: floating point constants in user.h are wrong\n\
+REALepsilon %g REALmin %g REALmax %g -REALmax %g\n",
+             REALepsilon, REALmin, REALmax, -REALmax);
+    qh_errexit(qh, qh_ERRinput, NULL, NULL);
+  }
+  set= qh_settemp(qh, 2*dimension);
+  for (k=0; k < dimension; k++) {
+    if (points == qh->GOODpointp)
+      minimum= maximum= points + dimension;
+    else
+      minimum= maximum= points;
+    FORALLpoint_(qh, points, numpoints) {
+      if (point == qh->GOODpointp)
+        continue;
+      if (maximum[k] < point[k])
+        maximum= point;
+      else if (minimum[k] > point[k])
+        minimum= point;
+    }
+    if (k == dimension-1) {
+      qh->MINlastcoord= minimum[k];
+      qh->MAXlastcoord= maximum[k];
+    }
+    if (qh->SCALElast && k == dimension-1)
+      maxcoord= qh->MAXwidth;
+    else {
+      maxcoord= fmax_(maximum[k], -minimum[k]);
+      if (qh->GOODpointp) {
+        temp= fmax_(qh->GOODpointp[k], -qh->GOODpointp[k]);
+        maximize_(maxcoord, temp);
+      }
+      temp= maximum[k] - minimum[k];
+      maximize_(qh->MAXwidth, temp);
+    }
+    maximize_(qh->MAXabs_coord, maxcoord);
+    qh->MAXsumcoord += maxcoord;
+    qh_setappend(qh, &set, maximum);
+    qh_setappend(qh, &set, minimum);
+    /* calculation of qh NEARzero is based on Golub & van Loan, 1983,
+       Eq. 4.4-13 for "Gaussian elimination with complete pivoting".
+       Golub & van Loan say that n^3 can be ignored and 10 be used in
+       place of rho */
+    qh->NEARzero[k]= 80 * qh->MAXsumcoord * REALepsilon;
+  }
+  if (qh->IStracing >=1)
+    qh_printpoints(qh, qh->ferr, "qh_maxmin: found the max and min points(by dim):", set);
+  return(set);
+} /* maxmin */
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >-------------------------------</a><a name="maxouter">-</a>
+
+  qh_maxouter(qh)
+    return maximum distance from facet to outer plane
+    normally this is qh.max_outside+qh.DISTround
+    does not include qh.JOGGLEmax
+
+  see:
+    qh_outerinner()
+
+  notes:
+    need to add another qh.DISTround if testing actual point with computation
+
+  for joggle:
+    qh_setfacetplane() updated qh.max_outer for Wnewvertexmax (max distance to vertex)
+    need to use Wnewvertexmax since could have a coplanar point for a high
+      facet that is replaced by a low facet
+    need to add qh.JOGGLEmax if testing input points
+*/
+realT qh_maxouter(qhT *qh) {
+  realT dist;
+
+  dist= fmax_(qh->max_outside, qh->DISTround);
+  dist += qh->DISTround;
+  trace4((qh, qh->ferr, 4012, "qh_maxouter: max distance from facet to outer plane is %2.2g max_outside is %2.2g\n", dist, qh->max_outside));
+  return dist;
+} /* maxouter */
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >-------------------------------</a><a name="maxsimplex">-</a>
+
+  qh_maxsimplex(qh, dim, maxpoints, points, numpoints, simplex )
+    determines maximum simplex for a set of points
+    starts from points already in simplex
+    skips qh.GOODpointp (assumes that it isn't in maxpoints)
+
+  returns:
+    simplex with dim+1 points
+
+  notes:
+    assumes at least pointsneeded points in points
+    maximizes determinate for x,y,z,w, etc.
+    uses maxpoints as long as determinate is clearly non-zero
+
+  design:
+    initialize simplex with at least two points
+      (find points with max or min x coordinate)
+    for each remaining dimension
+      add point that maximizes the determinate
+        (use points from maxpoints first)
+*/
+void qh_maxsimplex(qhT *qh, int dim, setT *maxpoints, pointT *points, int numpoints, setT **simplex) {
+  pointT *point, **pointp, *pointtemp, *maxpoint, *minx=NULL, *maxx=NULL;
+  boolT nearzero, maxnearzero= False;
+  int k, sizinit;
+  realT maxdet= -REALmax, det, mincoord= REALmax, maxcoord= -REALmax;
+
+  sizinit= qh_setsize(qh, *simplex);
+  if (sizinit < 2) {
+    if (qh_setsize(qh, maxpoints) >= 2) {
+      FOREACHpoint_(maxpoints) {
+        if (maxcoord < point[0]) {
+          maxcoord= point[0];
+          maxx= point;
+        }
+        if (mincoord > point[0]) {
+          mincoord= point[0];
+          minx= point;
+        }
+      }
+    }else {
+      FORALLpoint_(qh, points, numpoints) {
+        if (point == qh->GOODpointp)
+          continue;
+        if (maxcoord < point[0]) {
+          maxcoord= point[0];
+          maxx= point;
+        }
+        if (mincoord > point[0]) {
+          mincoord= point[0];
+          minx= point;
+        }
+      }
+    }
+    qh_setunique(qh, simplex, minx);
+    if (qh_setsize(qh, *simplex) < 2)
+      qh_setunique(qh, simplex, maxx);
+    sizinit= qh_setsize(qh, *simplex);
+    if (sizinit < 2) {
+      qh_precision(qh, "input has same x coordinate");
+      if (zzval_(Zsetplane) > qh->hull_dim+1) {
+        qh_fprintf(qh, qh->ferr, 6012, "qhull precision error (qh_maxsimplex for voronoi_center):\n%d points with the same x coordinate.\n",
+                 qh_setsize(qh, maxpoints)+numpoints);
+        qh_errexit(qh, qh_ERRprec, NULL, NULL);
+      }else {
+        qh_fprintf(qh, qh->ferr, 6013, "qhull input error: input is less than %d-dimensional since it has the same x coordinate\n", qh->hull_dim);
+        qh_errexit(qh, qh_ERRinput, NULL, NULL);
+      }
+    }
+  }
+  for (k=sizinit; k < dim+1; k++) {
+    maxpoint= NULL;
+    maxdet= -REALmax;
+    FOREACHpoint_(maxpoints) {
+      if (!qh_setin(*simplex, point)) {
+        det= qh_detsimplex(qh, point, *simplex, k, &nearzero);
+        if ((det= fabs_(det)) > maxdet) {
+          maxdet= det;
+          maxpoint= point;
+          maxnearzero= nearzero;
+        }
+      }
+    }
+    if (!maxpoint || maxnearzero) {
+      zinc_(Zsearchpoints);
+      if (!maxpoint) {
+        trace0((qh, qh->ferr, 7, "qh_maxsimplex: searching all points for %d-th initial vertex.\n", k+1));
+      }else {
+        trace0((qh, qh->ferr, 8, "qh_maxsimplex: searching all points for %d-th initial vertex, better than p%d det %2.2g\n",
+                k+1, qh_pointid(qh, maxpoint), maxdet));
+      }
+      FORALLpoint_(qh, points, numpoints) {
+        if (point == qh->GOODpointp)
+          continue;
+        if (!qh_setin(*simplex, point)) {
+          det= qh_detsimplex(qh, point, *simplex, k, &nearzero);
+          if ((det= fabs_(det)) > maxdet) {
+            maxdet= det;
+            maxpoint= point;
+            maxnearzero= nearzero;
+          }
+        }
+      }
+    } /* !maxpoint */
+    if (!maxpoint) {
+      qh_fprintf(qh, qh->ferr, 6014, "qhull internal error (qh_maxsimplex): not enough points available\n");
+      qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+    }
+    qh_setappend(qh, simplex, maxpoint);
+    trace1((qh, qh->ferr, 1002, "qh_maxsimplex: selected point p%d for %d`th initial vertex, det=%2.2g\n",
+            qh_pointid(qh, maxpoint), k+1, maxdet));
+  } /* k */
+} /* maxsimplex */
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >-------------------------------</a><a name="minabsval">-</a>
+
+  qh_minabsval( normal, dim )
+    return minimum absolute value of a dim vector
+*/
+realT qh_minabsval(realT *normal, int dim) {
+  realT minval= 0;
+  realT maxval= 0;
+  realT *colp;
+  int k;
+
+  for (k=dim, colp=normal; k--; colp++) {
+    maximize_(maxval, *colp);
+    minimize_(minval, *colp);
+  }
+  return fmax_(maxval, -minval);
+} /* minabsval */
+
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >-------------------------------</a><a name="mindiff">-</a>
+
+  qh_mindif(qh, vecA, vecB, dim )
+    return index of min abs. difference of two vectors
+*/
+int qh_mindiff(realT *vecA, realT *vecB, int dim) {
+  realT mindiff= REALmax, diff;
+  realT *vecAp= vecA, *vecBp= vecB;
+  int k, mink= 0;
+
+  for (k=0; k < dim; k++) {
+    diff= *vecAp++ - *vecBp++;
+    diff= fabs_(diff);
+    if (diff < mindiff) {
+      mindiff= diff;
+      mink= k;
+    }
+  }
+  return mink;
+} /* mindiff */
+
+
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >-------------------------------</a><a name="orientoutside">-</a>
+
+  qh_orientoutside(qh, facet  )
+    make facet outside oriented via qh.interior_point
+
+  returns:
+    True if facet reversed orientation.
+*/
+boolT qh_orientoutside(qhT *qh, facetT *facet) {
+  int k;
+  realT dist;
+
+  qh_distplane(qh, qh->interior_point, facet, &dist);
+  if (dist > 0) {
+    for (k=qh->hull_dim; k--; )
+      facet->normal[k]= -facet->normal[k];
+    facet->offset= -facet->offset;
+    return True;
+  }
+  return False;
+} /* orientoutside */
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >-------------------------------</a><a name="outerinner">-</a>
+
+  qh_outerinner(qh, facet, outerplane, innerplane  )
+    if facet and qh.maxoutdone (i.e., qh_check_maxout)
+      returns outer and inner plane for facet
+    else
+      returns maximum outer and inner plane
+    accounts for qh.JOGGLEmax
+
+  see:
+    qh_maxouter(qh), qh_check_bestdist(), qh_check_points()
+
+  notes:
+    outerplaner or innerplane may be NULL
+    facet is const
+    Does not error (QhullFacet)
+
+    includes qh.DISTround for actual points
+    adds another qh.DISTround if testing with floating point arithmetic
+*/
+void qh_outerinner(qhT *qh, facetT *facet, realT *outerplane, realT *innerplane) {
+  realT dist, mindist;
+  vertexT *vertex, **vertexp;
+
+  if (outerplane) {
+    if (!qh_MAXoutside || !facet || !qh->maxoutdone) {
+      *outerplane= qh_maxouter(qh);       /* includes qh.DISTround */
+    }else { /* qh_MAXoutside ... */
+#if qh_MAXoutside
+      *outerplane= facet->maxoutside + qh->DISTround;
+#endif
+
+    }
+    if (qh->JOGGLEmax < REALmax/2)
+      *outerplane += qh->JOGGLEmax * sqrt((realT)qh->hull_dim);
+  }
+  if (innerplane) {
+    if (facet) {
+      mindist= REALmax;
+      FOREACHvertex_(facet->vertices) {
+        zinc_(Zdistio);
+        qh_distplane(qh, vertex->point, facet, &dist);
+        minimize_(mindist, dist);
+      }
+      *innerplane= mindist - qh->DISTround;
+    }else
+      *innerplane= qh->min_vertex - qh->DISTround;
+    if (qh->JOGGLEmax < REALmax/2)
+      *innerplane -= qh->JOGGLEmax * sqrt((realT)qh->hull_dim);
+  }
+} /* outerinner */
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >-------------------------------</a><a name="pointdist">-</a>
+
+  qh_pointdist( point1, point2, dim )
+    return distance between two points
+
+  notes:
+    returns distance squared if 'dim' is negative
+*/
+coordT qh_pointdist(pointT *point1, pointT *point2, int dim) {
+  coordT dist, diff;
+  int k;
+
+  dist= 0.0;
+  for (k= (dim > 0 ? dim : -dim); k--; ) {
+    diff= *point1++ - *point2++;
+    dist += diff * diff;
+  }
+  if (dim > 0)
+    return(sqrt(dist));
+  return dist;
+} /* pointdist */
+
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >-------------------------------</a><a name="printmatrix">-</a>
+
+  qh_printmatrix(qh, fp, string, rows, numrow, numcol )
+    print matrix to fp given by row vectors
+    print string as header
+    qh may be NULL if fp is defined
+
+  notes:
+    print a vector by qh_printmatrix(qh, fp, "", &vect, 1, len)
+*/
+void qh_printmatrix(qhT *qh, FILE *fp, const char *string, realT **rows, int numrow, int numcol) {
+  realT *rowp;
+  realT r; /*bug fix*/
+  int i,k;
+
+  qh_fprintf(qh, fp, 9001, "%s\n", string);
+  for (i=0; i < numrow; i++) {
+    rowp= rows[i];
+    for (k=0; k < numcol; k++) {
+      r= *rowp++;
+      qh_fprintf(qh, fp, 9002, "%6.3g ", r);
+    }
+    qh_fprintf(qh, fp, 9003, "\n");
+  }
+} /* printmatrix */
+
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >-------------------------------</a><a name="printpoints">-</a>
+
+  qh_printpoints(qh, fp, string, points )
+    print pointids to fp for a set of points
+    if string, prints string and 'p' point ids
+*/
+void qh_printpoints(qhT *qh, FILE *fp, const char *string, setT *points) {
+  pointT *point, **pointp;
+
+  if (string) {
+    qh_fprintf(qh, fp, 9004, "%s", string);
+    FOREACHpoint_(points)
+      qh_fprintf(qh, fp, 9005, " p%d", qh_pointid(qh, point));
+    qh_fprintf(qh, fp, 9006, "\n");
+  }else {
+    FOREACHpoint_(points)
+      qh_fprintf(qh, fp, 9007, " %d", qh_pointid(qh, point));
+    qh_fprintf(qh, fp, 9008, "\n");
+  }
+} /* printpoints */
+
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >-------------------------------</a><a name="projectinput">-</a>
+
+  qh_projectinput(qh)
+    project input points using qh.lower_bound/upper_bound and qh->DELAUNAY
+    if qh.lower_bound[k]=qh.upper_bound[k]= 0,
+      removes dimension k
+    if halfspace intersection
+      removes dimension k from qh.feasible_point
+    input points in qh->first_point, num_points, input_dim
+
+  returns:
+    new point array in qh->first_point of qh->hull_dim coordinates
+    sets qh->POINTSmalloc
+    if qh->DELAUNAY
+      projects points to paraboloid
+      lowbound/highbound is also projected
+    if qh->ATinfinity
+      adds point "at-infinity"
+    if qh->POINTSmalloc
+      frees old point array
+
+  notes:
+    checks that qh.hull_dim agrees with qh.input_dim, PROJECTinput, and DELAUNAY
+
+
+  design:
+    sets project[k] to -1 (delete), 0 (keep), 1 (add for Delaunay)
+    determines newdim and newnum for qh->hull_dim and qh->num_points
+    projects points to newpoints
+    projects qh.lower_bound to itself
+    projects qh.upper_bound to itself
+    if qh->DELAUNAY
+      if qh->ATINFINITY
+        projects points to paraboloid
+        computes "infinity" point as vertex average and 10% above all points
+      else
+        uses qh_setdelaunay to project points to paraboloid
+*/
+void qh_projectinput(qhT *qh) {
+  int k,i;
+  int newdim= qh->input_dim, newnum= qh->num_points;
+  signed char *project;
+  int projectsize= (qh->input_dim+1)*sizeof(*project);
+  pointT *newpoints, *coord, *infinity;
+  realT paraboloid, maxboloid= 0;
+
+  project= (signed char*)qh_memalloc(qh, projectsize);
+  memset((char*)project, 0, (size_t)projectsize);
+  for (k=0; k < qh->input_dim; k++) {   /* skip Delaunay bound */
+    if (qh->lower_bound[k] == 0 && qh->upper_bound[k] == 0) {
+      project[k]= -1;
+      newdim--;
+    }
+  }
+  if (qh->DELAUNAY) {
+    project[k]= 1;
+    newdim++;
+    if (qh->ATinfinity)
+      newnum++;
+  }
+  if (newdim != qh->hull_dim) {
+    qh_memfree(qh, project, projectsize);
+    qh_fprintf(qh, qh->ferr, 6015, "qhull internal error (qh_projectinput): dimension after projection %d != hull_dim %d\n", newdim, qh->hull_dim);
+    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+  }
+  if (!(newpoints= qh->temp_malloc= (coordT*)qh_malloc(newnum*newdim*sizeof(coordT)))){
+    qh_memfree(qh, project, projectsize);
+    qh_fprintf(qh, qh->ferr, 6016, "qhull error: insufficient memory to project %d points\n",
+           qh->num_points);
+    qh_errexit(qh, qh_ERRmem, NULL, NULL);
+  }
+  /* qh_projectpoints throws error if mismatched dimensions */
+  qh_projectpoints(qh, project, qh->input_dim+1, qh->first_point,
+                    qh->num_points, qh->input_dim, newpoints, newdim);
+  trace1((qh, qh->ferr, 1003, "qh_projectinput: updating lower and upper_bound\n"));
+  qh_projectpoints(qh, project, qh->input_dim+1, qh->lower_bound,
+                    1, qh->input_dim+1, qh->lower_bound, newdim+1);
+  qh_projectpoints(qh, project, qh->input_dim+1, qh->upper_bound,
+                    1, qh->input_dim+1, qh->upper_bound, newdim+1);
+  if (qh->HALFspace) {
+    if (!qh->feasible_point) {
+      qh_memfree(qh, project, projectsize);
+      qh_fprintf(qh, qh->ferr, 6017, "qhull internal error (qh_projectinput): HALFspace defined without qh.feasible_point\n");
+      qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+    }
+    qh_projectpoints(qh, project, qh->input_dim, qh->feasible_point,
+                      1, qh->input_dim, qh->feasible_point, newdim);
+  }
+  qh_memfree(qh, project, projectsize);
+  if (qh->POINTSmalloc)
+    qh_free(qh->first_point);
+  qh->first_point= newpoints;
+  qh->POINTSmalloc= True;
+  qh->temp_malloc= NULL;
+  if (qh->DELAUNAY && qh->ATinfinity) {
+    coord= qh->first_point;
+    infinity= qh->first_point + qh->hull_dim * qh->num_points;
+    for (k=qh->hull_dim-1; k--; )
+      infinity[k]= 0.0;
+    for (i=qh->num_points; i--; ) {
+      paraboloid= 0.0;
+      for (k=0; k < qh->hull_dim-1; k++) {
+        paraboloid += *coord * *coord;
+        infinity[k] += *coord;
+        coord++;
+      }
+      *(coord++)= paraboloid;
+      maximize_(maxboloid, paraboloid);
+    }
+    /* coord == infinity */
+    for (k=qh->hull_dim-1; k--; )
+      *(coord++) /= qh->num_points;
+    *(coord++)= maxboloid * 1.1;
+    qh->num_points++;
+    trace0((qh, qh->ferr, 9, "qh_projectinput: projected points to paraboloid for Delaunay\n"));
+  }else if (qh->DELAUNAY)  /* !qh->ATinfinity */
+    qh_setdelaunay(qh, qh->hull_dim, qh->num_points, qh->first_point);
+} /* projectinput */
+
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >-------------------------------</a><a name="projectpoints">-</a>
+
+  qh_projectpoints(qh, project, n, points, numpoints, dim, newpoints, newdim )
+    project points/numpoints/dim to newpoints/newdim
+    if project[k] == -1
+      delete dimension k
+    if project[k] == 1
+      add dimension k by duplicating previous column
+    n is size of project
+
+  notes:
+    newpoints may be points if only adding dimension at end
+
+  design:
+    check that 'project' and 'newdim' agree
+    for each dimension
+      if project == -1
+        skip dimension
+      else
+        determine start of column in newpoints
+        determine start of column in points
+          if project == +1, duplicate previous column
+        copy dimension (column) from points to newpoints
+*/
+void qh_projectpoints(qhT *qh, signed char *project, int n, realT *points,
+        int numpoints, int dim, realT *newpoints, int newdim) {
+  int testdim= dim, oldk=0, newk=0, i,j=0,k;
+  realT *newp, *oldp;
+
+  for (k=0; k < n; k++)
+    testdim += project[k];
+  if (testdim != newdim) {
+    qh_fprintf(qh, qh->ferr, 6018, "qhull internal error (qh_projectpoints): newdim %d should be %d after projection\n",
+      newdim, testdim);
+    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+  }
+  for (j=0; j<n; j++) {
+    if (project[j] == -1)
+      oldk++;
+    else {
+      newp= newpoints+newk++;
+      if (project[j] == +1) {
+        if (oldk >= dim)
+          continue;
+        oldp= points+oldk;
+      }else
+        oldp= points+oldk++;
+      for (i=numpoints; i--; ) {
+        *newp= *oldp;
+        newp += newdim;
+        oldp += dim;
+      }
+    }
+    if (oldk >= dim)
+      break;
+  }
+  trace1((qh, qh->ferr, 1004, "qh_projectpoints: projected %d points from dim %d to dim %d\n",
+    numpoints, dim, newdim));
+} /* projectpoints */
+
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >-------------------------------</a><a name="rotateinput">-</a>
+
+  qh_rotateinput(qh, rows )
+    rotate input using row matrix
+    input points given by qh->first_point, num_points, hull_dim
+    assumes rows[dim] is a scratch buffer
+    if qh->POINTSmalloc, overwrites input points, else mallocs a new array
+
+  returns:
+    rotated input
+    sets qh->POINTSmalloc
+
+  design:
+    see qh_rotatepoints
+*/
+void qh_rotateinput(qhT *qh, realT **rows) {
+
+  if (!qh->POINTSmalloc) {
+    qh->first_point= qh_copypoints(qh, qh->first_point, qh->num_points, qh->hull_dim);
+    qh->POINTSmalloc= True;
+  }
+  qh_rotatepoints(qh, qh->first_point, qh->num_points, qh->hull_dim, rows);
+}  /* rotateinput */
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >-------------------------------</a><a name="rotatepoints">-</a>
+
+  qh_rotatepoints(qh, points, numpoints, dim, row )
+    rotate numpoints points by a d-dim row matrix
+    assumes rows[dim] is a scratch buffer
+
+  returns:
+    rotated points in place
+
+  design:
+    for each point
+      for each coordinate
+        use row[dim] to compute partial inner product
+      for each coordinate
+        rotate by partial inner product
+*/
+void qh_rotatepoints(qhT *qh, realT *points, int numpoints, int dim, realT **row) {
+  realT *point, *rowi, *coord= NULL, sum, *newval;
+  int i,j,k;
+
+  if (qh->IStracing >= 1)
+    qh_printmatrix(qh, qh->ferr, "qh_rotatepoints: rotate points by", row, dim, dim);
+  for (point= points, j= numpoints; j--; point += dim) {
+    newval= row[dim];
+    for (i=0; i < dim; i++) {
+      rowi= row[i];
+      coord= point;
+      for (sum= 0.0, k= dim; k--; )
+        sum += *rowi++ * *coord++;
+      *(newval++)= sum;
+    }
+    for (k=dim; k--; )
+      *(--coord)= *(--newval);
+  }
+} /* rotatepoints */
+
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >-------------------------------</a><a name="scaleinput">-</a>
+
+  qh_scaleinput(qh)
+    scale input points using qh->low_bound/high_bound
+    input points given by qh->first_point, num_points, hull_dim
+    if qh->POINTSmalloc, overwrites input points, else mallocs a new array
+
+  returns:
+    scales coordinates of points to low_bound[k], high_bound[k]
+    sets qh->POINTSmalloc
+
+  design:
+    see qh_scalepoints
+*/
+void qh_scaleinput(qhT *qh) {
+
+  if (!qh->POINTSmalloc) {
+    qh->first_point= qh_copypoints(qh, qh->first_point, qh->num_points, qh->hull_dim);
+    qh->POINTSmalloc= True;
+  }
+  qh_scalepoints(qh, qh->first_point, qh->num_points, qh->hull_dim,
+       qh->lower_bound, qh->upper_bound);
+}  /* scaleinput */
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >-------------------------------</a><a name="scalelast">-</a>
+
+  qh_scalelast(qh, points, numpoints, dim, low, high, newhigh )
+    scale last coordinate to [0,m] for Delaunay triangulations
+    input points given by points, numpoints, dim
+
+  returns:
+    changes scale of last coordinate from [low, high] to [0, newhigh]
+    overwrites last coordinate of each point
+    saves low/high/newhigh in qh.last_low, etc. for qh_setdelaunay()
+
+  notes:
+    when called by qh_setdelaunay, low/high may not match actual data
+
+  design:
+    compute scale and shift factors
+    apply to last coordinate of each point
+*/
+void qh_scalelast(qhT *qh, coordT *points, int numpoints, int dim, coordT low,
+                   coordT high, coordT newhigh) {
+  realT scale, shift;
+  coordT *coord;
+  int i;
+  boolT nearzero= False;
+
+  trace4((qh, qh->ferr, 4013, "qh_scalelast: scale last coordinate from [%2.2g, %2.2g] to [0,%2.2g]\n",
+    low, high, newhigh));
+  qh->last_low= low;
+  qh->last_high= high;
+  qh->last_newhigh= newhigh;
+  scale= qh_divzero(newhigh, high - low,
+                  qh->MINdenom_1, &nearzero);
+  if (nearzero) {
+    if (qh->DELAUNAY)
+      qh_fprintf(qh, qh->ferr, 6019, "qhull input error: can not scale last coordinate.  Input is cocircular\n   or cospherical.   Use option 'Qz' to add a point at infinity.\n");
+    else
+      qh_fprintf(qh, qh->ferr, 6020, "qhull input error: can not scale last coordinate.  New bounds [0, %2.2g] are too wide for\nexisting bounds [%2.2g, %2.2g] (width %2.2g)\n",
+                newhigh, low, high, high-low);
+    qh_errexit(qh, qh_ERRinput, NULL, NULL);
+  }
+  shift= - low * newhigh / (high-low);
+  coord= points + dim - 1;
+  for (i=numpoints; i--; coord += dim)
+    *coord= *coord * scale + shift;
+} /* scalelast */
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >-------------------------------</a><a name="scalepoints">-</a>
+
+  qh_scalepoints(qh, points, numpoints, dim, newlows, newhighs )
+    scale points to new lowbound and highbound
+    retains old bound when newlow= -REALmax or newhigh= +REALmax
+
+  returns:
+    scaled points
+    overwrites old points
+
+  design:
+    for each coordinate
+      compute current low and high bound
+      compute scale and shift factors
+      scale all points
+      enforce new low and high bound for all points
+*/
+void qh_scalepoints(qhT *qh, pointT *points, int numpoints, int dim,
+        realT *newlows, realT *newhighs) {
+  int i,k;
+  realT shift, scale, *coord, low, high, newlow, newhigh, mincoord, maxcoord;
+  boolT nearzero= False;
+
+  for (k=0; k < dim; k++) {
+    newhigh= newhighs[k];
+    newlow= newlows[k];
+    if (newhigh > REALmax/2 && newlow < -REALmax/2)
+      continue;
+    low= REALmax;
+    high= -REALmax;
+    for (i=numpoints, coord=points+k; i--; coord += dim) {
+      minimize_(low, *coord);
+      maximize_(high, *coord);
+    }
+    if (newhigh > REALmax/2)
+      newhigh= high;
+    if (newlow < -REALmax/2)
+      newlow= low;
+    if (qh->DELAUNAY && k == dim-1 && newhigh < newlow) {
+      qh_fprintf(qh, qh->ferr, 6021, "qhull input error: 'Qb%d' or 'QB%d' inverts paraboloid since high bound %.2g < low bound %.2g\n",
+               k, k, newhigh, newlow);
+      qh_errexit(qh, qh_ERRinput, NULL, NULL);
+    }
+    scale= qh_divzero(newhigh - newlow, high - low,
+                  qh->MINdenom_1, &nearzero);
+    if (nearzero) {
+      qh_fprintf(qh, qh->ferr, 6022, "qhull input error: %d'th dimension's new bounds [%2.2g, %2.2g] too wide for\nexisting bounds [%2.2g, %2.2g]\n",
+              k, newlow, newhigh, low, high);
+      qh_errexit(qh, qh_ERRinput, NULL, NULL);
+    }
+    shift= (newlow * high - low * newhigh)/(high-low);
+    coord= points+k;
+    for (i=numpoints; i--; coord += dim)
+      *coord= *coord * scale + shift;
+    coord= points+k;
+    if (newlow < newhigh) {
+      mincoord= newlow;
+      maxcoord= newhigh;
+    }else {
+      mincoord= newhigh;
+      maxcoord= newlow;
+    }
+    for (i=numpoints; i--; coord += dim) {
+      minimize_(*coord, maxcoord);  /* because of roundoff error */
+      maximize_(*coord, mincoord);
+    }
+    trace0((qh, qh->ferr, 10, "qh_scalepoints: scaled %d'th coordinate [%2.2g, %2.2g] to [%.2g, %.2g] for %d points by %2.2g and shifted %2.2g\n",
+      k, low, high, newlow, newhigh, numpoints, scale, shift));
+  }
+} /* scalepoints */
+
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >-------------------------------</a><a name="setdelaunay">-</a>
+
+  qh_setdelaunay(qh, dim, count, points )
+    project count points to dim-d paraboloid for Delaunay triangulation
+
+    dim is one more than the dimension of the input set
+    assumes dim is at least 3 (i.e., at least a 2-d Delaunay triangulation)
+
+    points is a dim*count realT array.  The first dim-1 coordinates
+    are the coordinates of the first input point.  array[dim] is
+    the first coordinate of the second input point.  array[2*dim] is
+    the first coordinate of the third input point.
+
+    if qh.last_low defined (i.e., 'Qbb' called qh_scalelast)
+      calls qh_scalelast to scale the last coordinate the same as the other points
+
+  returns:
+    for each point
+      sets point[dim-1] to sum of squares of coordinates
+    scale points to 'Qbb' if needed
+
+  notes:
+    to project one point, use
+      qh_setdelaunay(qh, qh->hull_dim, 1, point)
+
+    Do not use options 'Qbk', 'QBk', or 'QbB' since they scale
+    the coordinates after the original projection.
+
+*/
+void qh_setdelaunay(qhT *qh, int dim, int count, pointT *points) {
+  int i, k;
+  coordT *coordp, coord;
+  realT paraboloid;
+
+  trace0((qh, qh->ferr, 11, "qh_setdelaunay: project %d points to paraboloid for Delaunay triangulation\n", count));
+  coordp= points;
+  for (i=0; i < count; i++) {
+    coord= *coordp++;
+    paraboloid= coord*coord;
+    for (k=dim-2; k--; ) {
+      coord= *coordp++;
+      paraboloid += coord*coord;
+    }
+    *coordp++ = paraboloid;
+  }
+  if (qh->last_low < REALmax/2)
+    qh_scalelast(qh, points, count, dim, qh->last_low, qh->last_high, qh->last_newhigh);
+} /* setdelaunay */
+
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >-------------------------------</a><a name="sethalfspace">-</a>
+
+  qh_sethalfspace(qh, dim, coords, nextp, normal, offset, feasible )
+    set point to dual of halfspace relative to feasible point
+    halfspace is normal coefficients and offset.
+
+  returns:
+    false and prints error if feasible point is outside of hull
+    overwrites coordinates for point at dim coords
+    nextp= next point (coords)
+    does not call qh_errexit
+
+  design:
+    compute distance from feasible point to halfspace
+    divide each normal coefficient by -dist
+*/
+boolT qh_sethalfspace(qhT *qh, int dim, coordT *coords, coordT **nextp,
+         coordT *normal, coordT *offset, coordT *feasible) {
+  coordT *normp= normal, *feasiblep= feasible, *coordp= coords;
+  realT dist;
+  realT r; /*bug fix*/
+  int k;
+  boolT zerodiv;
+
+  dist= *offset;
+  for (k=dim; k--; )
+    dist += *(normp++) * *(feasiblep++);
+  if (dist > 0)
+    goto LABELerroroutside;
+  normp= normal;
+  if (dist < -qh->MINdenom) {
+    for (k=dim; k--; )
+      *(coordp++)= *(normp++) / -dist;
+  }else {
+    for (k=dim; k--; ) {
+      *(coordp++)= qh_divzero(*(normp++), -dist, qh->MINdenom_1, &zerodiv);
+      if (zerodiv)
+        goto LABELerroroutside;
+    }
+  }
+  *nextp= coordp;
+  if (qh->IStracing >= 4) {
+    qh_fprintf(qh, qh->ferr, 8021, "qh_sethalfspace: halfspace at offset %6.2g to point: ", *offset);
+    for (k=dim, coordp=coords; k--; ) {
+      r= *coordp++;
+      qh_fprintf(qh, qh->ferr, 8022, " %6.2g", r);
+    }
+    qh_fprintf(qh, qh->ferr, 8023, "\n");
+  }
+  return True;
+LABELerroroutside:
+  feasiblep= feasible;
+  normp= normal;
+  qh_fprintf(qh, qh->ferr, 6023, "qhull input error: feasible point is not clearly inside halfspace\nfeasible point: ");
+  for (k=dim; k--; )
+    qh_fprintf(qh, qh->ferr, 8024, qh_REAL_1, r=*(feasiblep++));
+  qh_fprintf(qh, qh->ferr, 8025, "\n     halfspace: ");
+  for (k=dim; k--; )
+    qh_fprintf(qh, qh->ferr, 8026, qh_REAL_1, r=*(normp++));
+  qh_fprintf(qh, qh->ferr, 8027, "\n     at offset: ");
+  qh_fprintf(qh, qh->ferr, 8028, qh_REAL_1, *offset);
+  qh_fprintf(qh, qh->ferr, 8029, " and distance: ");
+  qh_fprintf(qh, qh->ferr, 8030, qh_REAL_1, dist);
+  qh_fprintf(qh, qh->ferr, 8031, "\n");
+  return False;
+} /* sethalfspace */
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >-------------------------------</a><a name="sethalfspace_all">-</a>
+
+  qh_sethalfspace_all(qh, dim, count, halfspaces, feasible )
+    generate dual for halfspace intersection with feasible point
+    array of count halfspaces
+      each halfspace is normal coefficients followed by offset
+      the origin is inside the halfspace if the offset is negative
+    feasible is a point inside all halfspaces (http://www.qhull.org/html/qhalf.htm#notes)
+
+  returns:
+    malloc'd array of count X dim-1 points
+
+  notes:
+    call before qh_init_B or qh_initqhull_globals
+    free memory when done
+    unused/untested code: please email bradb@shore.net if this works ok for you
+    if using option 'Fp', qh->feasible_point must be set (e.g., to 'feasible')
+    qh->feasible_point is a malloc'd array that is freed by qh_freebuffers.
+
+  design:
+    see qh_sethalfspace
+*/
+coordT *qh_sethalfspace_all(qhT *qh, int dim, int count, coordT *halfspaces, pointT *feasible) {
+  int i, newdim;
+  pointT *newpoints;
+  coordT *coordp, *normalp, *offsetp;
+
+  trace0((qh, qh->ferr, 12, "qh_sethalfspace_all: compute dual for halfspace intersection\n"));
+  newdim= dim - 1;
+  if (!(newpoints=(coordT*)qh_malloc(count*newdim*sizeof(coordT)))){
+    qh_fprintf(qh, qh->ferr, 6024, "qhull error: insufficient memory to compute dual of %d halfspaces\n",
+          count);
+    qh_errexit(qh, qh_ERRmem, NULL, NULL);
+  }
+  coordp= newpoints;
+  normalp= halfspaces;
+  for (i=0; i < count; i++) {
+    offsetp= normalp + newdim;
+    if (!qh_sethalfspace(qh, newdim, coordp, &coordp, normalp, offsetp, feasible)) {
+      qh_free(newpoints);  /* feasible is not inside halfspace as reported by qh_sethalfspace */
+      qh_fprintf(qh, qh->ferr, 8032, "The halfspace was at index %d\n", i);
+      qh_errexit(qh, qh_ERRinput, NULL, NULL);
+    }
+    normalp= offsetp + 1;
+  }
+  return newpoints;
+} /* sethalfspace_all */
+
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >-------------------------------</a><a name="sharpnewfacets">-</a>
+
+  qh_sharpnewfacets(qh)
+
+  returns:
+    true if could be an acute angle (facets in different quadrants)
+
+  notes:
+    for qh_findbest
+
+  design:
+    for all facets on qh.newfacet_list
+      if two facets are in different quadrants
+        set issharp
+*/
+boolT qh_sharpnewfacets(qhT *qh) {
+  facetT *facet;
+  boolT issharp = False;
+  int *quadrant, k;
+
+  quadrant= (int*)qh_memalloc(qh, qh->hull_dim * sizeof(int));
+  FORALLfacet_(qh->newfacet_list) {
+    if (facet == qh->newfacet_list) {
+      for (k=qh->hull_dim; k--; )
+        quadrant[ k]= (facet->normal[ k] > 0);
+    }else {
+      for (k=qh->hull_dim; k--; ) {
+        if (quadrant[ k] != (facet->normal[ k] > 0)) {
+          issharp= True;
+          break;
+        }
+      }
+    }
+    if (issharp)
+      break;
+  }
+  qh_memfree(qh, quadrant, qh->hull_dim * sizeof(int));
+  trace3((qh, qh->ferr, 3001, "qh_sharpnewfacets: %d\n", issharp));
+  return issharp;
+} /* sharpnewfacets */
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >-------------------------------</a><a name="voronoi_center">-</a>
+
+  qh_voronoi_center(qh, dim, points )
+    return Voronoi center for a set of points
+    dim is the orginal dimension of the points
+    gh.gm_matrix/qh.gm_row are scratch buffers
+
+  returns:
+    center as a temporary point (qh_memalloc)
+    if non-simplicial,
+      returns center for max simplex of points
+
+  notes:
+    only called by qh_facetcenter
+    from Bowyer & Woodwark, A Programmer's Geometry, 1983, p. 65
+
+  design:
+    if non-simplicial
+      determine max simplex for points
+    translate point0 of simplex to origin
+    compute sum of squares of diagonal
+    compute determinate
+    compute Voronoi center (see Bowyer & Woodwark)
+*/
+pointT *qh_voronoi_center(qhT *qh, int dim, setT *points) {
+  pointT *point, **pointp, *point0;
+  pointT *center= (pointT*)qh_memalloc(qh, qh->center_size);
+  setT *simplex;
+  int i, j, k, size= qh_setsize(qh, points);
+  coordT *gmcoord;
+  realT *diffp, sum2, *sum2row, *sum2p, det, factor;
+  boolT nearzero, infinite;
+
+  if (size == dim+1)
+    simplex= points;
+  else if (size < dim+1) {
+    qh_memfree(qh, center, qh->center_size);
+    qh_fprintf(qh, qh->ferr, 6025, "qhull internal error (qh_voronoi_center):\n  need at least %d points to construct a Voronoi center\n",
+             dim+1);
+    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+    simplex= points;  /* never executed -- avoids warning */
+  }else {
+    simplex= qh_settemp(qh, dim+1);
+    qh_maxsimplex(qh, dim, points, NULL, 0, &simplex);
+  }
+  point0= SETfirstt_(simplex, pointT);
+  gmcoord= qh->gm_matrix;
+  for (k=0; k < dim; k++) {
+    qh->gm_row[k]= gmcoord;
+    FOREACHpoint_(simplex) {
+      if (point != point0)
+        *(gmcoord++)= point[k] - point0[k];
+    }
+  }
+  sum2row= gmcoord;
+  for (i=0; i < dim; i++) {
+    sum2= 0.0;
+    for (k=0; k < dim; k++) {
+      diffp= qh->gm_row[k] + i;
+      sum2 += *diffp * *diffp;
+    }
+    *(gmcoord++)= sum2;
+  }
+  det= qh_determinant(qh, qh->gm_row, dim, &nearzero);
+  factor= qh_divzero(0.5, det, qh->MINdenom, &infinite);
+  if (infinite) {
+    for (k=dim; k--; )
+      center[k]= qh_INFINITE;
+    if (qh->IStracing)
+      qh_printpoints(qh, qh->ferr, "qh_voronoi_center: at infinity for ", simplex);
+  }else {
+    for (i=0; i < dim; i++) {
+      gmcoord= qh->gm_matrix;
+      sum2p= sum2row;
+      for (k=0; k < dim; k++) {
+        qh->gm_row[k]= gmcoord;
+        if (k == i) {
+          for (j=dim; j--; )
+            *(gmcoord++)= *sum2p++;
+        }else {
+          FOREACHpoint_(simplex) {
+            if (point != point0)
+              *(gmcoord++)= point[k] - point0[k];
+          }
+        }
+      }
+      center[i]= qh_determinant(qh, qh->gm_row, dim, &nearzero)*factor + point0[i];
+    }
+#ifndef qh_NOtrace
+    if (qh->IStracing >= 3) {
+      qh_fprintf(qh, qh->ferr, 8033, "qh_voronoi_center: det %2.2g factor %2.2g ", det, factor);
+      qh_printmatrix(qh, qh->ferr, "center:", &center, 1, dim);
+      if (qh->IStracing >= 5) {
+        qh_printpoints(qh, qh->ferr, "points", simplex);
+        FOREACHpoint_(simplex)
+          qh_fprintf(qh, qh->ferr, 8034, "p%d dist %.2g, ", qh_pointid(qh, point),
+                   qh_pointdist(point, center, dim));
+        qh_fprintf(qh, qh->ferr, 8035, "\n");
+      }
+    }
+#endif
+  }
+  if (simplex != points)
+    qh_settempfree(qh, &simplex);
+  return center;
+} /* voronoi_center */
+
diff --git a/xs/src/qhull/src/libqhull_r/geom_r.c b/xs/src/qhull/src/libqhull_r/geom_r.c
new file mode 100644
index 0000000000..8104813cad
--- /dev/null
+++ b/xs/src/qhull/src/libqhull_r/geom_r.c
@@ -0,0 +1,1234 @@
+/*<html><pre>  -<a                             href="qh-geom_r.htm"
+  >-------------------------------</a><a name="TOP">-</a>
+
+   geom_r.c
+   geometric routines of qhull
+
+   see qh-geom_r.htm and geom_r.h
+
+   Copyright (c) 1993-2015 The Geometry Center.
+   $Id: //main/2015/qhull/src/libqhull_r/geom_r.c#2 $$Change: 1995 $
+   $DateTime: 2015/10/13 21:59:42 $$Author: bbarber $
+
+   infrequent code goes into geom2_r.c
+*/
+
+#include "qhull_ra.h"
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >-------------------------------</a><a name="distplane">-</a>
+
+  qh_distplane(qh, point, facet, dist )
+    return distance from point to facet
+
+  returns:
+    dist
+    if qh.RANDOMdist, joggles result
+
+  notes:
+    dist > 0 if point is above facet (i.e., outside)
+    does not error (for qh_sortfacets, qh_outerinner)
+
+  see:
+    qh_distnorm in geom2_r.c
+    qh_distplane [geom_r.c], QhullFacet::distance, and QhullHyperplane::distance are copies
+*/
+void qh_distplane(qhT *qh, pointT *point, facetT *facet, realT *dist) {
+  coordT *normal= facet->normal, *coordp, randr;
+  int k;
+
+  switch (qh->hull_dim){
+  case 2:
+    *dist= facet->offset + point[0] * normal[0] + point[1] * normal[1];
+    break;
+  case 3:
+    *dist= facet->offset + point[0] * normal[0] + point[1] * normal[1] + point[2] * normal[2];
+    break;
+  case 4:
+    *dist= facet->offset+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3];
+    break;
+  case 5:
+    *dist= facet->offset+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3]+point[4]*normal[4];
+    break;
+  case 6:
+    *dist= facet->offset+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3]+point[4]*normal[4]+point[5]*normal[5];
+    break;
+  case 7:
+    *dist= facet->offset+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3]+point[4]*normal[4]+point[5]*normal[5]+point[6]*normal[6];
+    break;
+  case 8:
+    *dist= facet->offset+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3]+point[4]*normal[4]+point[5]*normal[5]+point[6]*normal[6]+point[7]*normal[7];
+    break;
+  default:
+    *dist= facet->offset;
+    coordp= point;
+    for (k=qh->hull_dim; k--; )
+      *dist += *coordp++ * *normal++;
+    break;
+  }
+  zinc_(Zdistplane);
+  if (!qh->RANDOMdist && qh->IStracing < 4)
+    return;
+  if (qh->RANDOMdist) {
+    randr= qh_RANDOMint;
+    *dist += (2.0 * randr / qh_RANDOMmax - 1.0) *
+      qh->RANDOMfactor * qh->MAXabs_coord;
+  }
+  if (qh->IStracing >= 4) {
+    qh_fprintf(qh, qh->ferr, 8001, "qh_distplane: ");
+    qh_fprintf(qh, qh->ferr, 8002, qh_REAL_1, *dist);
+    qh_fprintf(qh, qh->ferr, 8003, "from p%d to f%d\n", qh_pointid(qh, point), facet->id);
+  }
+  return;
+} /* distplane */
+
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >-------------------------------</a><a name="findbest">-</a>
+
+  qh_findbest(qh, point, startfacet, bestoutside, qh_ISnewfacets, qh_NOupper, dist, isoutside, numpart )
+    find facet that is furthest below a point
+    for upperDelaunay facets
+      returns facet only if !qh_NOupper and clearly above
+
+  input:
+    starts search at 'startfacet' (can not be flipped)
+    if !bestoutside(qh_ALL), stops at qh.MINoutside
+
+  returns:
+    best facet (reports error if NULL)
+    early out if isoutside defined and bestdist > qh.MINoutside
+    dist is distance to facet
+    isoutside is true if point is outside of facet
+    numpart counts the number of distance tests
+
+  see also:
+    qh_findbestnew()
+
+  notes:
+    If merging (testhorizon), searches horizon facets of coplanar best facets because
+    after qh_distplane, this and qh_partitionpoint are the most expensive in 3-d
+      avoid calls to distplane, function calls, and real number operations.
+    caller traces result
+    Optimized for outside points.   Tried recording a search set for qh_findhorizon.
+    Made code more complicated.
+
+  when called by qh_partitionvisible():
+    indicated by qh_ISnewfacets
+    qh.newfacet_list is list of simplicial, new facets
+    qh_findbestnew set if qh_sharpnewfacets returns True (to use qh_findbestnew)
+    qh.bestfacet_notsharp set if qh_sharpnewfacets returns False
+
+  when called by qh_findfacet(), qh_partitionpoint(), qh_partitioncoplanar(),
+                 qh_check_bestdist(), qh_addpoint()
+    indicated by !qh_ISnewfacets
+    returns best facet in neighborhood of given facet
+      this is best facet overall if dist > -   qh.MAXcoplanar
+        or hull has at least a "spherical" curvature
+
+  design:
+    initialize and test for early exit
+    repeat while there are better facets
+      for each neighbor of facet
+        exit if outside facet found
+        test for better facet
+    if point is inside and partitioning
+      test for new facets with a "sharp" intersection
+      if so, future calls go to qh_findbestnew()
+    test horizon facets
+*/
+facetT *qh_findbest(qhT *qh, pointT *point, facetT *startfacet,
+                     boolT bestoutside, boolT isnewfacets, boolT noupper,
+                     realT *dist, boolT *isoutside, int *numpart) {
+  realT bestdist= -REALmax/2 /* avoid underflow */;
+  facetT *facet, *neighbor, **neighborp;
+  facetT *bestfacet= NULL, *lastfacet= NULL;
+  int oldtrace= qh->IStracing;
+  unsigned int visitid= ++qh->visit_id;
+  int numpartnew=0;
+  boolT testhorizon = True; /* needed if precise, e.g., rbox c D6 | qhull Q0 Tv */
+
+  zinc_(Zfindbest);
+  if (qh->IStracing >= 3 || (qh->TRACElevel && qh->TRACEpoint >= 0 && qh->TRACEpoint == qh_pointid(qh, point))) {
+    if (qh->TRACElevel > qh->IStracing)
+      qh->IStracing= qh->TRACElevel;
+    qh_fprintf(qh, qh->ferr, 8004, "qh_findbest: point p%d starting at f%d isnewfacets? %d, unless %d exit if > %2.2g\n",
+             qh_pointid(qh, point), startfacet->id, isnewfacets, bestoutside, qh->MINoutside);
+    qh_fprintf(qh, qh->ferr, 8005, "  testhorizon? %d noupper? %d", testhorizon, noupper);
+    qh_fprintf(qh, qh->ferr, 8006, "  Last point added was p%d.", qh->furthest_id);
+    qh_fprintf(qh, qh->ferr, 8007, "  Last merge was #%d.  max_outside %2.2g\n", zzval_(Ztotmerge), qh->max_outside);
+  }
+  if (isoutside)
+    *isoutside= True;
+  if (!startfacet->flipped) {  /* test startfacet */
+    *numpart= 1;
+    qh_distplane(qh, point, startfacet, dist);  /* this code is duplicated below */
+    if (!bestoutside && *dist >= qh->MINoutside
+    && (!startfacet->upperdelaunay || !noupper)) {
+      bestfacet= startfacet;
+      goto LABELreturn_best;
+    }
+    bestdist= *dist;
+    if (!startfacet->upperdelaunay) {
+      bestfacet= startfacet;
+    }
+  }else
+    *numpart= 0;
+  startfacet->visitid= visitid;
+  facet= startfacet;
+  while (facet) {
+    trace4((qh, qh->ferr, 4001, "qh_findbest: neighbors of f%d, bestdist %2.2g f%d\n",
+                facet->id, bestdist, getid_(bestfacet)));
+    lastfacet= facet;
+    FOREACHneighbor_(facet) {
+      if (!neighbor->newfacet && isnewfacets)
+        continue;
+      if (neighbor->visitid == visitid)
+        continue;
+      neighbor->visitid= visitid;
+      if (!neighbor->flipped) {  /* code duplicated above */
+        (*numpart)++;
+        qh_distplane(qh, point, neighbor, dist);
+        if (*dist > bestdist) {
+          if (!bestoutside && *dist >= qh->MINoutside
+          && (!neighbor->upperdelaunay || !noupper)) {
+            bestfacet= neighbor;
+            goto LABELreturn_best;
+          }
+          if (!neighbor->upperdelaunay) {
+            bestfacet= neighbor;
+            bestdist= *dist;
+            break; /* switch to neighbor */
+          }else if (!bestfacet) {
+            bestdist= *dist;
+            break; /* switch to neighbor */
+          }
+        } /* end of *dist>bestdist */
+      } /* end of !flipped */
+    } /* end of FOREACHneighbor */
+    facet= neighbor;  /* non-NULL only if *dist>bestdist */
+  } /* end of while facet (directed search) */
+  if (isnewfacets) {
+    if (!bestfacet) {
+      bestdist= -REALmax/2;
+      bestfacet= qh_findbestnew(qh, point, startfacet->next, &bestdist, bestoutside, isoutside, &numpartnew);
+      testhorizon= False; /* qh_findbestnew calls qh_findbesthorizon */
+    }else if (!qh->findbest_notsharp && bestdist < - qh->DISTround) {
+      if (qh_sharpnewfacets(qh)) {
+        /* seldom used, qh_findbestnew will retest all facets */
+        zinc_(Zfindnewsharp);
+        bestfacet= qh_findbestnew(qh, point, bestfacet, &bestdist, bestoutside, isoutside, &numpartnew);
+        testhorizon= False; /* qh_findbestnew calls qh_findbesthorizon */
+        qh->findbestnew= True;
+      }else
+        qh->findbest_notsharp= True;
+    }
+  }
+  if (!bestfacet)
+    bestfacet= qh_findbestlower(qh, lastfacet, point, &bestdist, numpart);
+  if (testhorizon)
+    bestfacet= qh_findbesthorizon(qh, !qh_IScheckmax, point, bestfacet, noupper, &bestdist, &numpartnew);
+  *dist= bestdist;
+  if (isoutside && bestdist < qh->MINoutside)
+    *isoutside= False;
+LABELreturn_best:
+  zadd_(Zfindbesttot, *numpart);
+  zmax_(Zfindbestmax, *numpart);
+  (*numpart) += numpartnew;
+  qh->IStracing= oldtrace;
+  return bestfacet;
+}  /* findbest */
+
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >-------------------------------</a><a name="findbesthorizon">-</a>
+
+  qh_findbesthorizon(qh, qh_IScheckmax, point, startfacet, qh_NOupper, &bestdist, &numpart )
+    search coplanar and better horizon facets from startfacet/bestdist
+    ischeckmax turns off statistics and minsearch update
+    all arguments must be initialized
+  returns(ischeckmax):
+    best facet
+  returns(!ischeckmax):
+    best facet that is not upperdelaunay
+    allows upperdelaunay that is clearly outside
+  returns:
+    bestdist is distance to bestfacet
+    numpart -- updates number of distance tests
+
+  notes:
+    no early out -- use qh_findbest() or qh_findbestnew()
+    Searches coplanar or better horizon facets
+
+  when called by qh_check_maxout() (qh_IScheckmax)
+    startfacet must be closest to the point
+      Otherwise, if point is beyond and below startfacet, startfacet may be a local minimum
+      even though other facets are below the point.
+    updates facet->maxoutside for good, visited facets
+    may return NULL
+
+    searchdist is qh.max_outside + 2 * DISTround
+      + max( MINvisible('Vn'), MAXcoplanar('Un'));
+    This setting is a guess.  It must be at least max_outside + 2*DISTround
+    because a facet may have a geometric neighbor across a vertex
+
+  design:
+    for each horizon facet of coplanar best facets
+      continue if clearly inside
+      unless upperdelaunay or clearly outside
+         update best facet
+*/
+facetT *qh_findbesthorizon(qhT *qh, boolT ischeckmax, pointT* point, facetT *startfacet, boolT noupper, realT *bestdist, int *numpart) {
+  facetT *bestfacet= startfacet;
+  realT dist;
+  facetT *neighbor, **neighborp, *facet;
+  facetT *nextfacet= NULL; /* optimize last facet of coplanarfacetset */
+  int numpartinit= *numpart, coplanarfacetset_size;
+  unsigned int visitid= ++qh->visit_id;
+  boolT newbest= False; /* for tracing */
+  realT minsearch, searchdist;  /* skip facets that are too far from point */
+
+  if (!ischeckmax) {
+    zinc_(Zfindhorizon);
+  }else {
+#if qh_MAXoutside
+    if ((!qh->ONLYgood || startfacet->good) && *bestdist > startfacet->maxoutside)
+      startfacet->maxoutside= *bestdist;
+#endif
+  }
+  searchdist= qh_SEARCHdist; /* multiple of qh.max_outside and precision constants */
+  minsearch= *bestdist - searchdist;
+  if (ischeckmax) {
+    /* Always check coplanar facets.  Needed for RBOX 1000 s Z1 G1e-13 t996564279 | QHULL Tv */
+    minimize_(minsearch, -searchdist);
+  }
+  coplanarfacetset_size= 0;
+  facet= startfacet;
+  while (True) {
+    trace4((qh, qh->ferr, 4002, "qh_findbesthorizon: neighbors of f%d bestdist %2.2g f%d ischeckmax? %d noupper? %d minsearch %2.2g searchdist %2.2g\n",
+                facet->id, *bestdist, getid_(bestfacet), ischeckmax, noupper,
+                minsearch, searchdist));
+    FOREACHneighbor_(facet) {
+      if (neighbor->visitid == visitid)
+        continue;
+      neighbor->visitid= visitid;
+      if (!neighbor->flipped) {
+        qh_distplane(qh, point, neighbor, &dist);
+        (*numpart)++;
+        if (dist > *bestdist) {
+          if (!neighbor->upperdelaunay || ischeckmax || (!noupper && dist >= qh->MINoutside)) {
+            bestfacet= neighbor;
+            *bestdist= dist;
+            newbest= True;
+            if (!ischeckmax) {
+              minsearch= dist - searchdist;
+              if (dist > *bestdist + searchdist) {
+                zinc_(Zfindjump);  /* everything in qh.coplanarfacetset at least searchdist below */
+                coplanarfacetset_size= 0;
+              }
+            }
+          }
+        }else if (dist < minsearch)
+          continue;  /* if ischeckmax, dist can't be positive */
+#if qh_MAXoutside
+        if (ischeckmax && dist > neighbor->maxoutside)
+          neighbor->maxoutside= dist;
+#endif
+      } /* end of !flipped */
+      if (nextfacet) {
+        if (!coplanarfacetset_size++) {
+          SETfirst_(qh->coplanarfacetset)= nextfacet;
+          SETtruncate_(qh->coplanarfacetset, 1);
+        }else
+          qh_setappend(qh, &qh->coplanarfacetset, nextfacet); /* Was needed for RBOX 1000 s W1e-13 P0 t996547055 | QHULL d Qbb Qc Tv
+                                                 and RBOX 1000 s Z1 G1e-13 t996564279 | qhull Tv  */
+      }
+      nextfacet= neighbor;
+    } /* end of EACHneighbor */
+    facet= nextfacet;
+    if (facet)
+      nextfacet= NULL;
+    else if (!coplanarfacetset_size)
+      break;
+    else if (!--coplanarfacetset_size) {
+      facet= SETfirstt_(qh->coplanarfacetset, facetT);
+      SETtruncate_(qh->coplanarfacetset, 0);
+    }else
+      facet= (facetT*)qh_setdellast(qh->coplanarfacetset);
+  } /* while True, for each facet in qh.coplanarfacetset */
+  if (!ischeckmax) {
+    zadd_(Zfindhorizontot, *numpart - numpartinit);
+    zmax_(Zfindhorizonmax, *numpart - numpartinit);
+    if (newbest)
+      zinc_(Zparthorizon);
+  }
+  trace4((qh, qh->ferr, 4003, "qh_findbesthorizon: newbest? %d bestfacet f%d bestdist %2.2g\n", newbest, getid_(bestfacet), *bestdist));
+  return bestfacet;
+}  /* findbesthorizon */
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >-------------------------------</a><a name="findbestnew">-</a>
+
+  qh_findbestnew(qh, point, startfacet, dist, isoutside, numpart )
+    find best newfacet for point
+    searches all of qh.newfacet_list starting at startfacet
+    searches horizon facets of coplanar best newfacets
+    searches all facets if startfacet == qh.facet_list
+  returns:
+    best new or horizon facet that is not upperdelaunay
+    early out if isoutside and not 'Qf'
+    dist is distance to facet
+    isoutside is true if point is outside of facet
+    numpart is number of distance tests
+
+  notes:
+    Always used for merged new facets (see qh_USEfindbestnew)
+    Avoids upperdelaunay facet unless (isoutside and outside)
+
+    Uses qh.visit_id, qh.coplanarfacetset.
+    If share visit_id with qh_findbest, coplanarfacetset is incorrect.
+
+    If merging (testhorizon), searches horizon facets of coplanar best facets because
+    a point maybe coplanar to the bestfacet, below its horizon facet,
+    and above a horizon facet of a coplanar newfacet.  For example,
+      rbox 1000 s Z1 G1e-13 | qhull
+      rbox 1000 s W1e-13 P0 t992110337 | QHULL d Qbb Qc
+
+    qh_findbestnew() used if
+       qh_sharpnewfacets -- newfacets contains a sharp angle
+       if many merges, qh_premerge found a merge, or 'Qf' (qh.findbestnew)
+
+  see also:
+    qh_partitionall() and qh_findbest()
+
+  design:
+    for each new facet starting from startfacet
+      test distance from point to facet
+      return facet if clearly outside
+      unless upperdelaunay and a lowerdelaunay exists
+         update best facet
+    test horizon facets
+*/
+facetT *qh_findbestnew(qhT *qh, pointT *point, facetT *startfacet,
+           realT *dist, boolT bestoutside, boolT *isoutside, int *numpart) {
+  realT bestdist= -REALmax/2;
+  facetT *bestfacet= NULL, *facet;
+  int oldtrace= qh->IStracing, i;
+  unsigned int visitid= ++qh->visit_id;
+  realT distoutside= 0.0;
+  boolT isdistoutside; /* True if distoutside is defined */
+  boolT testhorizon = True; /* needed if precise, e.g., rbox c D6 | qhull Q0 Tv */
+
+  if (!startfacet) {
+    if (qh->MERGING)
+      qh_fprintf(qh, qh->ferr, 6001, "qhull precision error (qh_findbestnew): merging has formed and deleted a cone of new facets.  Can not continue.\n");
+    else
+      qh_fprintf(qh, qh->ferr, 6002, "qhull internal error (qh_findbestnew): no new facets for point p%d\n",
+              qh->furthest_id);
+    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+  }
+  zinc_(Zfindnew);
+  if (qh->BESToutside || bestoutside)
+    isdistoutside= False;
+  else {
+    isdistoutside= True;
+    distoutside= qh_DISToutside; /* multiple of qh.MINoutside & qh.max_outside, see user.h */
+  }
+  if (isoutside)
+    *isoutside= True;
+  *numpart= 0;
+  if (qh->IStracing >= 3 || (qh->TRACElevel && qh->TRACEpoint >= 0 && qh->TRACEpoint == qh_pointid(qh, point))) {
+    if (qh->TRACElevel > qh->IStracing)
+      qh->IStracing= qh->TRACElevel;
+    qh_fprintf(qh, qh->ferr, 8008, "qh_findbestnew: point p%d facet f%d. Stop? %d if dist > %2.2g\n",
+             qh_pointid(qh, point), startfacet->id, isdistoutside, distoutside);
+    qh_fprintf(qh, qh->ferr, 8009, "  Last point added p%d visitid %d.",  qh->furthest_id, visitid);
+    qh_fprintf(qh, qh->ferr, 8010, "  Last merge was #%d.\n", zzval_(Ztotmerge));
+  }
+  /* visit all new facets starting with startfacet, maybe qh->facet_list */
+  for (i=0, facet=startfacet; i < 2; i++, facet= qh->newfacet_list) {
+    FORALLfacet_(facet) {
+      if (facet == startfacet && i)
+        break;
+      facet->visitid= visitid;
+      if (!facet->flipped) {
+        qh_distplane(qh, point, facet, dist);
+        (*numpart)++;
+        if (*dist > bestdist) {
+          if (!facet->upperdelaunay || *dist >= qh->MINoutside) {
+            bestfacet= facet;
+            if (isdistoutside && *dist >= distoutside)
+              goto LABELreturn_bestnew;
+            bestdist= *dist;
+          }
+        }
+      } /* end of !flipped */
+    } /* FORALLfacet from startfacet or qh->newfacet_list */
+  }
+  if (testhorizon || !bestfacet) /* testhorizon is always True.  Keep the same code as qh_findbest */
+    bestfacet= qh_findbesthorizon(qh, !qh_IScheckmax, point, bestfacet ? bestfacet : startfacet,
+                                        !qh_NOupper, &bestdist, numpart);
+  *dist= bestdist;
+  if (isoutside && *dist < qh->MINoutside)
+    *isoutside= False;
+LABELreturn_bestnew:
+  zadd_(Zfindnewtot, *numpart);
+  zmax_(Zfindnewmax, *numpart);
+  trace4((qh, qh->ferr, 4004, "qh_findbestnew: bestfacet f%d bestdist %2.2g\n", getid_(bestfacet), *dist));
+  qh->IStracing= oldtrace;
+  return bestfacet;
+}  /* findbestnew */
+
+/* ============ hyperplane functions -- keep code together [?] ============ */
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >-------------------------------</a><a name="backnormal">-</a>
+
+  qh_backnormal(qh, rows, numrow, numcol, sign, normal, nearzero )
+    given an upper-triangular rows array and a sign,
+    solve for normal equation x using back substitution over rows U
+
+  returns:
+     normal= x
+
+     if will not be able to divzero() when normalized(qh.MINdenom_2 and qh.MINdenom_1_2),
+       if fails on last row
+         this means that the hyperplane intersects [0,..,1]
+         sets last coordinate of normal to sign
+       otherwise
+         sets tail of normal to [...,sign,0,...], i.e., solves for b= [0...0]
+         sets nearzero
+
+  notes:
+     assumes numrow == numcol-1
+
+     see Golub & van Loan, 1983, Eq. 4.4-9 for "Gaussian elimination with complete pivoting"
+
+     solves Ux=b where Ax=b and PA=LU
+     b= [0,...,0,sign or 0]  (sign is either -1 or +1)
+     last row of A= [0,...,0,1]
+
+     1) Ly=Pb == y=b since P only permutes the 0's of   b
+
+  design:
+    for each row from end
+      perform back substitution
+      if near zero
+        use qh_divzero for division
+        if zero divide and not last row
+          set tail of normal to 0
+*/
+void qh_backnormal(qhT *qh, realT **rows, int numrow, int numcol, boolT sign,
+        coordT *normal, boolT *nearzero) {
+  int i, j;
+  coordT *normalp, *normal_tail, *ai, *ak;
+  realT diagonal;
+  boolT waszero;
+  int zerocol= -1;
+
+  normalp= normal + numcol - 1;
+  *normalp--= (sign ? -1.0 : 1.0);
+  for (i=numrow; i--; ) {
+    *normalp= 0.0;
+    ai= rows[i] + i + 1;
+    ak= normalp+1;
+    for (j=i+1; j < numcol; j++)
+      *normalp -= *ai++ * *ak++;
+    diagonal= (rows[i])[i];
+    if (fabs_(diagonal) > qh->MINdenom_2)
+      *(normalp--) /= diagonal;
+    else {
+      waszero= False;
+      *normalp= qh_divzero(*normalp, diagonal, qh->MINdenom_1_2, &waszero);
+      if (waszero) {
+        zerocol= i;
+        *(normalp--)= (sign ? -1.0 : 1.0);
+        for (normal_tail= normalp+2; normal_tail < normal + numcol; normal_tail++)
+          *normal_tail= 0.0;
+      }else
+        normalp--;
+    }
+  }
+  if (zerocol != -1) {
+    zzinc_(Zback0);
+    *nearzero= True;
+    trace4((qh, qh->ferr, 4005, "qh_backnormal: zero diagonal at column %d.\n", i));
+    qh_precision(qh, "zero diagonal on back substitution");
+  }
+} /* backnormal */
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >-------------------------------</a><a name="gausselim">-</a>
+
+  qh_gausselim(qh, rows, numrow, numcol, sign )
+    Gaussian elimination with partial pivoting
+
+  returns:
+    rows is upper triangular (includes row exchanges)
+    flips sign for each row exchange
+    sets nearzero if pivot[k] < qh.NEARzero[k], else clears it
+
+  notes:
+    if nearzero, the determinant's sign may be incorrect.
+    assumes numrow <= numcol
+
+  design:
+    for each row
+      determine pivot and exchange rows if necessary
+      test for near zero
+      perform gaussian elimination step
+*/
+void qh_gausselim(qhT *qh, realT **rows, int numrow, int numcol, boolT *sign, boolT *nearzero) {
+  realT *ai, *ak, *rowp, *pivotrow;
+  realT n, pivot, pivot_abs= 0.0, temp;
+  int i, j, k, pivoti, flip=0;
+
+  *nearzero= False;
+  for (k=0; k < numrow; k++) {
+    pivot_abs= fabs_((rows[k])[k]);
+    pivoti= k;
+    for (i=k+1; i < numrow; i++) {
+      if ((temp= fabs_((rows[i])[k])) > pivot_abs) {
+        pivot_abs= temp;
+        pivoti= i;
+      }
+    }
+    if (pivoti != k) {
+      rowp= rows[pivoti];
+      rows[pivoti]= rows[k];
+      rows[k]= rowp;
+      *sign ^= 1;
+      flip ^= 1;
+    }
+    if (pivot_abs <= qh->NEARzero[k]) {
+      *nearzero= True;
+      if (pivot_abs == 0.0) {   /* remainder of column == 0 */
+        if (qh->IStracing >= 4) {
+          qh_fprintf(qh, qh->ferr, 8011, "qh_gausselim: 0 pivot at column %d. (%2.2g < %2.2g)\n", k, pivot_abs, qh->DISTround);
+          qh_printmatrix(qh, qh->ferr, "Matrix:", rows, numrow, numcol);
+        }
+        zzinc_(Zgauss0);
+        qh_precision(qh, "zero pivot for Gaussian elimination");
+        goto LABELnextcol;
+      }
+    }
+    pivotrow= rows[k] + k;
+    pivot= *pivotrow++;  /* signed value of pivot, and remainder of row */
+    for (i=k+1; i < numrow; i++) {
+      ai= rows[i] + k;
+      ak= pivotrow;
+      n= (*ai++)/pivot;   /* divzero() not needed since |pivot| >= |*ai| */
+      for (j= numcol - (k+1); j--; )
+        *ai++ -= n * *ak++;
+    }
+  LABELnextcol:
+    ;
+  }
+  wmin_(Wmindenom, pivot_abs);  /* last pivot element */
+  if (qh->IStracing >= 5)
+    qh_printmatrix(qh, qh->ferr, "qh_gausselem: result", rows, numrow, numcol);
+} /* gausselim */
+
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >-------------------------------</a><a name="getangle">-</a>
+
+  qh_getangle(qh, vect1, vect2 )
+    returns the dot product of two vectors
+    if qh.RANDOMdist, joggles result
+
+  notes:
+    the angle may be > 1.0 or < -1.0 because of roundoff errors
+
+*/
+realT qh_getangle(qhT *qh, pointT *vect1, pointT *vect2) {
+  realT angle= 0, randr;
+  int k;
+
+  for (k=qh->hull_dim; k--; )
+    angle += *vect1++ * *vect2++;
+  if (qh->RANDOMdist) {
+    randr= qh_RANDOMint;
+    angle += (2.0 * randr / qh_RANDOMmax - 1.0) *
+      qh->RANDOMfactor;
+  }
+  trace4((qh, qh->ferr, 4006, "qh_getangle: %2.2g\n", angle));
+  return(angle);
+} /* getangle */
+
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >-------------------------------</a><a name="getcenter">-</a>
+
+  qh_getcenter(qh, vertices )
+    returns arithmetic center of a set of vertices as a new point
+
+  notes:
+    allocates point array for center
+*/
+pointT *qh_getcenter(qhT *qh, setT *vertices) {
+  int k;
+  pointT *center, *coord;
+  vertexT *vertex, **vertexp;
+  int count= qh_setsize(qh, vertices);
+
+  if (count < 2) {
+    qh_fprintf(qh, qh->ferr, 6003, "qhull internal error (qh_getcenter): not defined for %d points\n", count);
+    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+  }
+  center= (pointT *)qh_memalloc(qh, qh->normal_size);
+  for (k=0; k < qh->hull_dim; k++) {
+    coord= center+k;
+    *coord= 0.0;
+    FOREACHvertex_(vertices)
+      *coord += vertex->point[k];
+    *coord /= count;  /* count>=2 by QH6003 */
+  }
+  return(center);
+} /* getcenter */
+
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >-------------------------------</a><a name="getcentrum">-</a>
+
+  qh_getcentrum(qh, facet )
+    returns the centrum for a facet as a new point
+
+  notes:
+    allocates the centrum
+*/
+pointT *qh_getcentrum(qhT *qh, facetT *facet) {
+  realT dist;
+  pointT *centrum, *point;
+
+  point= qh_getcenter(qh, facet->vertices);
+  zzinc_(Zcentrumtests);
+  qh_distplane(qh, point, facet, &dist);
+  centrum= qh_projectpoint(qh, point, facet, dist);
+  qh_memfree(qh, point, qh->normal_size);
+  trace4((qh, qh->ferr, 4007, "qh_getcentrum: for f%d, %d vertices dist= %2.2g\n",
+          facet->id, qh_setsize(qh, facet->vertices), dist));
+  return centrum;
+} /* getcentrum */
+
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >-------------------------------</a><a name="getdistance">-</a>
+
+  qh_getdistance(qh, facet, neighbor, mindist, maxdist )
+    returns the maxdist and mindist distance of any vertex from neighbor
+
+  returns:
+    the max absolute value
+
+  design:
+    for each vertex of facet that is not in neighbor
+      test the distance from vertex to neighbor
+*/
+realT qh_getdistance(qhT *qh, facetT *facet, facetT *neighbor, realT *mindist, realT *maxdist) {
+  vertexT *vertex, **vertexp;
+  realT dist, maxd, mind;
+
+  FOREACHvertex_(facet->vertices)
+    vertex->seen= False;
+  FOREACHvertex_(neighbor->vertices)
+    vertex->seen= True;
+  mind= 0.0;
+  maxd= 0.0;
+  FOREACHvertex_(facet->vertices) {
+    if (!vertex->seen) {
+      zzinc_(Zbestdist);
+      qh_distplane(qh, vertex->point, neighbor, &dist);
+      if (dist < mind)
+        mind= dist;
+      else if (dist > maxd)
+        maxd= dist;
+    }
+  }
+  *mindist= mind;
+  *maxdist= maxd;
+  mind= -mind;
+  if (maxd > mind)
+    return maxd;
+  else
+    return mind;
+} /* getdistance */
+
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >-------------------------------</a><a name="normalize">-</a>
+
+  qh_normalize(qh, normal, dim, toporient )
+    normalize a vector and report if too small
+    does not use min norm
+
+  see:
+    qh_normalize2
+*/
+void qh_normalize(qhT *qh, coordT *normal, int dim, boolT toporient) {
+  qh_normalize2(qh, normal, dim, toporient, NULL, NULL);
+} /* normalize */
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >-------------------------------</a><a name="normalize2">-</a>
+
+  qh_normalize2(qh, normal, dim, toporient, minnorm, ismin )
+    normalize a vector and report if too small
+    qh.MINdenom/MINdenom1 are the upper limits for divide overflow
+
+  returns:
+    normalized vector
+    flips sign if !toporient
+    if minnorm non-NULL,
+      sets ismin if normal < minnorm
+
+  notes:
+    if zero norm
+       sets all elements to sqrt(1.0/dim)
+    if divide by zero (divzero())
+       sets largest element to   +/-1
+       bumps Znearlysingular
+
+  design:
+    computes norm
+    test for minnorm
+    if not near zero
+      normalizes normal
+    else if zero norm
+      sets normal to standard value
+    else
+      uses qh_divzero to normalize
+      if nearzero
+        sets norm to direction of maximum value
+*/
+void qh_normalize2(qhT *qh, coordT *normal, int dim, boolT toporient,
+            realT *minnorm, boolT *ismin) {
+  int k;
+  realT *colp, *maxp, norm= 0, temp, *norm1, *norm2, *norm3;
+  boolT zerodiv;
+
+  norm1= normal+1;
+  norm2= normal+2;
+  norm3= normal+3;
+  if (dim == 2)
+    norm= sqrt((*normal)*(*normal) + (*norm1)*(*norm1));
+  else if (dim == 3)
+    norm= sqrt((*normal)*(*normal) + (*norm1)*(*norm1) + (*norm2)*(*norm2));
+  else if (dim == 4) {
+    norm= sqrt((*normal)*(*normal) + (*norm1)*(*norm1) + (*norm2)*(*norm2)
+               + (*norm3)*(*norm3));
+  }else if (dim > 4) {
+    norm= (*normal)*(*normal) + (*norm1)*(*norm1) + (*norm2)*(*norm2)
+               + (*norm3)*(*norm3);
+    for (k=dim-4, colp=normal+4; k--; colp++)
+      norm += (*colp) * (*colp);
+    norm= sqrt(norm);
+  }
+  if (minnorm) {
+    if (norm < *minnorm)
+      *ismin= True;
+    else
+      *ismin= False;
+  }
+  wmin_(Wmindenom, norm);
+  if (norm > qh->MINdenom) {
+    if (!toporient)
+      norm= -norm;
+    *normal /= norm;
+    *norm1 /= norm;
+    if (dim == 2)
+      ; /* all done */
+    else if (dim == 3)
+      *norm2 /= norm;
+    else if (dim == 4) {
+      *norm2 /= norm;
+      *norm3 /= norm;
+    }else if (dim >4) {
+      *norm2 /= norm;
+      *norm3 /= norm;
+      for (k=dim-4, colp=normal+4; k--; )
+        *colp++ /= norm;
+    }
+  }else if (norm == 0.0) {
+    temp= sqrt(1.0/dim);
+    for (k=dim, colp=normal; k--; )
+      *colp++ = temp;
+  }else {
+    if (!toporient)
+      norm= -norm;
+    for (k=dim, colp=normal; k--; colp++) { /* k used below */
+      temp= qh_divzero(*colp, norm, qh->MINdenom_1, &zerodiv);
+      if (!zerodiv)
+        *colp= temp;
+      else {
+        maxp= qh_maxabsval(normal, dim);
+        temp= ((*maxp * norm >= 0.0) ? 1.0 : -1.0);
+        for (k=dim, colp=normal; k--; colp++)
+          *colp= 0.0;
+        *maxp= temp;
+        zzinc_(Znearlysingular);
+        trace0((qh, qh->ferr, 1, "qh_normalize: norm=%2.2g too small during p%d\n",
+               norm, qh->furthest_id));
+        return;
+      }
+    }
+  }
+} /* normalize */
+
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >-------------------------------</a><a name="projectpoint">-</a>
+
+  qh_projectpoint(qh, point, facet, dist )
+    project point onto a facet by dist
+
+  returns:
+    returns a new point
+
+  notes:
+    if dist= distplane(point,facet)
+      this projects point to hyperplane
+    assumes qh_memfree_() is valid for normal_size
+*/
+pointT *qh_projectpoint(qhT *qh, pointT *point, facetT *facet, realT dist) {
+  pointT *newpoint, *np, *normal;
+  int normsize= qh->normal_size;
+  int k;
+  void **freelistp; /* used if !qh_NOmem by qh_memalloc_() */
+
+  qh_memalloc_(qh, normsize, freelistp, newpoint, pointT);
+  np= newpoint;
+  normal= facet->normal;
+  for (k=qh->hull_dim; k--; )
+    *(np++)= *point++ - dist * *normal++;
+  return(newpoint);
+} /* projectpoint */
+
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >-------------------------------</a><a name="setfacetplane">-</a>
+
+  qh_setfacetplane(qh, facet )
+    sets the hyperplane for a facet
+    if qh.RANDOMdist, joggles hyperplane
+
+  notes:
+    uses global buffers qh.gm_matrix and qh.gm_row
+    overwrites facet->normal if already defined
+    updates Wnewvertex if PRINTstatistics
+    sets facet->upperdelaunay if upper envelope of Delaunay triangulation
+
+  design:
+    copy vertex coordinates to qh.gm_matrix/gm_row
+    compute determinate
+    if nearzero
+      recompute determinate with gaussian elimination
+      if nearzero
+        force outside orientation by testing interior point
+*/
+void qh_setfacetplane(qhT *qh, facetT *facet) {
+  pointT *point;
+  vertexT *vertex, **vertexp;
+  int normsize= qh->normal_size;
+  int k,i, oldtrace= 0;
+  realT dist;
+  void **freelistp; /* used if !qh_NOmem by qh_memalloc_() */
+  coordT *coord, *gmcoord;
+  pointT *point0= SETfirstt_(facet->vertices, vertexT)->point;
+  boolT nearzero= False;
+
+  zzinc_(Zsetplane);
+  if (!facet->normal)
+    qh_memalloc_(qh, normsize, freelistp, facet->normal, coordT);
+  if (facet == qh->tracefacet) {
+    oldtrace= qh->IStracing;
+    qh->IStracing= 5;
+    qh_fprintf(qh, qh->ferr, 8012, "qh_setfacetplane: facet f%d created.\n", facet->id);
+    qh_fprintf(qh, qh->ferr, 8013, "  Last point added to hull was p%d.", qh->furthest_id);
+    if (zzval_(Ztotmerge))
+      qh_fprintf(qh, qh->ferr, 8014, "  Last merge was #%d.", zzval_(Ztotmerge));
+    qh_fprintf(qh, qh->ferr, 8015, "\n\nCurrent summary is:\n");
+      qh_printsummary(qh, qh->ferr);
+  }
+  if (qh->hull_dim <= 4) {
+    i= 0;
+    if (qh->RANDOMdist) {
+      gmcoord= qh->gm_matrix;
+      FOREACHvertex_(facet->vertices) {
+        qh->gm_row[i++]= gmcoord;
+        coord= vertex->point;
+        for (k=qh->hull_dim; k--; )
+          *(gmcoord++)= *coord++ * qh_randomfactor(qh, qh->RANDOMa, qh->RANDOMb);
+      }
+    }else {
+      FOREACHvertex_(facet->vertices)
+       qh->gm_row[i++]= vertex->point;
+    }
+    qh_sethyperplane_det(qh, qh->hull_dim, qh->gm_row, point0, facet->toporient,
+                facet->normal, &facet->offset, &nearzero);
+  }
+  if (qh->hull_dim > 4 || nearzero) {
+    i= 0;
+    gmcoord= qh->gm_matrix;
+    FOREACHvertex_(facet->vertices) {
+      if (vertex->point != point0) {
+        qh->gm_row[i++]= gmcoord;
+        coord= vertex->point;
+        point= point0;
+        for (k=qh->hull_dim; k--; )
+          *(gmcoord++)= *coord++ - *point++;
+      }
+    }
+    qh->gm_row[i]= gmcoord;  /* for areasimplex */
+    if (qh->RANDOMdist) {
+      gmcoord= qh->gm_matrix;
+      for (i=qh->hull_dim-1; i--; ) {
+        for (k=qh->hull_dim; k--; )
+          *(gmcoord++) *= qh_randomfactor(qh, qh->RANDOMa, qh->RANDOMb);
+      }
+    }
+    qh_sethyperplane_gauss(qh, qh->hull_dim, qh->gm_row, point0, facet->toporient,
+                facet->normal, &facet->offset, &nearzero);
+    if (nearzero) {
+      if (qh_orientoutside(qh, facet)) {
+        trace0((qh, qh->ferr, 2, "qh_setfacetplane: flipped orientation after testing interior_point during p%d\n", qh->furthest_id));
+      /* this is part of using Gaussian Elimination.  For example in 5-d
+           1 1 1 1 0
+           1 1 1 1 1
+           0 0 0 1 0
+           0 1 0 0 0
+           1 0 0 0 0
+           norm= 0.38 0.38 -0.76 0.38 0
+         has a determinate of 1, but g.e. after subtracting pt. 0 has
+         0's in the diagonal, even with full pivoting.  It does work
+         if you subtract pt. 4 instead. */
+      }
+    }
+  }
+  facet->upperdelaunay= False;
+  if (qh->DELAUNAY) {
+    if (qh->UPPERdelaunay) {     /* matches qh_triangulate_facet and qh.lower_threshold in qh_initbuild */
+      if (facet->normal[qh->hull_dim -1] >= qh->ANGLEround * qh_ZEROdelaunay)
+        facet->upperdelaunay= True;
+    }else {
+      if (facet->normal[qh->hull_dim -1] > -qh->ANGLEround * qh_ZEROdelaunay)
+        facet->upperdelaunay= True;
+    }
+  }
+  if (qh->PRINTstatistics || qh->IStracing || qh->TRACElevel || qh->JOGGLEmax < REALmax) {
+    qh->old_randomdist= qh->RANDOMdist;
+    qh->RANDOMdist= False;
+    FOREACHvertex_(facet->vertices) {
+      if (vertex->point != point0) {
+        boolT istrace= False;
+        zinc_(Zdiststat);
+        qh_distplane(qh, vertex->point, facet, &dist);
+        dist= fabs_(dist);
+        zinc_(Znewvertex);
+        wadd_(Wnewvertex, dist);
+        if (dist > wwval_(Wnewvertexmax)) {
+          wwval_(Wnewvertexmax)= dist;
+          if (dist > qh->max_outside) {
+            qh->max_outside= dist;  /* used by qh_maxouter(qh) */
+            if (dist > qh->TRACEdist)
+              istrace= True;
+          }
+        }else if (-dist > qh->TRACEdist)
+          istrace= True;
+        if (istrace) {
+          qh_fprintf(qh, qh->ferr, 8016, "qh_setfacetplane: ====== vertex p%d(v%d) increases max_outside to %2.2g for new facet f%d last p%d\n",
+                qh_pointid(qh, vertex->point), vertex->id, dist, facet->id, qh->furthest_id);
+          qh_errprint(qh, "DISTANT", facet, NULL, NULL, NULL);
+        }
+      }
+    }
+    qh->RANDOMdist= qh->old_randomdist;
+  }
+  if (qh->IStracing >= 3) {
+    qh_fprintf(qh, qh->ferr, 8017, "qh_setfacetplane: f%d offset %2.2g normal: ",
+             facet->id, facet->offset);
+    for (k=0; k < qh->hull_dim; k++)
+      qh_fprintf(qh, qh->ferr, 8018, "%2.2g ", facet->normal[k]);
+    qh_fprintf(qh, qh->ferr, 8019, "\n");
+  }
+  if (facet == qh->tracefacet)
+    qh->IStracing= oldtrace;
+} /* setfacetplane */
+
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >-------------------------------</a><a name="sethyperplane_det">-</a>
+
+  qh_sethyperplane_det(qh, dim, rows, point0, toporient, normal, offset, nearzero )
+    given dim X dim array indexed by rows[], one row per point,
+        toporient(flips all signs),
+        and point0 (any row)
+    set normalized hyperplane equation from oriented simplex
+
+  returns:
+    normal (normalized)
+    offset (places point0 on the hyperplane)
+    sets nearzero if hyperplane not through points
+
+  notes:
+    only defined for dim == 2..4
+    rows[] is not modified
+    solves det(P-V_0, V_n-V_0, ..., V_1-V_0)=0, i.e. every point is on hyperplane
+    see Bower & Woodworth, A programmer's geometry, Butterworths 1983.
+
+  derivation of 3-d minnorm
+    Goal: all vertices V_i within qh.one_merge of hyperplane
+    Plan: exactly translate the facet so that V_0 is the origin
+          exactly rotate the facet so that V_1 is on the x-axis and y_2=0.
+          exactly rotate the effective perturbation to only effect n_0
+             this introduces a factor of sqrt(3)
+    n_0 = ((y_2-y_0)*(z_1-z_0) - (z_2-z_0)*(y_1-y_0)) / norm
+    Let M_d be the max coordinate difference
+    Let M_a be the greater of M_d and the max abs. coordinate
+    Let u be machine roundoff and distround be max error for distance computation
+    The max error for n_0 is sqrt(3) u M_a M_d / norm.  n_1 is approx. 1 and n_2 is approx. 0
+    The max error for distance of V_1 is sqrt(3) u M_a M_d M_d / norm.  Offset=0 at origin
+    Then minnorm = 1.8 u M_a M_d M_d / qh.ONEmerge
+    Note that qh.one_merge is approx. 45.5 u M_a and norm is usually about M_d M_d
+
+  derivation of 4-d minnorm
+    same as above except rotate the facet so that V_1 on x-axis and w_2, y_3, w_3=0
+     [if two vertices fixed on x-axis, can rotate the other two in yzw.]
+    n_0 = det3_(...) = y_2 det2_(z_1, w_1, z_3, w_3) = - y_2 w_1 z_3
+     [all other terms contain at least two factors nearly zero.]
+    The max error for n_0 is sqrt(4) u M_a M_d M_d / norm
+    Then minnorm = 2 u M_a M_d M_d M_d / qh.ONEmerge
+    Note that qh.one_merge is approx. 82 u M_a and norm is usually about M_d M_d M_d
+*/
+void qh_sethyperplane_det(qhT *qh, int dim, coordT **rows, coordT *point0,
+          boolT toporient, coordT *normal, realT *offset, boolT *nearzero) {
+  realT maxround, dist;
+  int i;
+  pointT *point;
+
+
+  if (dim == 2) {
+    normal[0]= dY(1,0);
+    normal[1]= dX(0,1);
+    qh_normalize2(qh, normal, dim, toporient, NULL, NULL);
+    *offset= -(point0[0]*normal[0]+point0[1]*normal[1]);
+    *nearzero= False;  /* since nearzero norm => incident points */
+  }else if (dim == 3) {
+    normal[0]= det2_(dY(2,0), dZ(2,0),
+                     dY(1,0), dZ(1,0));
+    normal[1]= det2_(dX(1,0), dZ(1,0),
+                     dX(2,0), dZ(2,0));
+    normal[2]= det2_(dX(2,0), dY(2,0),
+                     dX(1,0), dY(1,0));
+    qh_normalize2(qh, normal, dim, toporient, NULL, NULL);
+    *offset= -(point0[0]*normal[0] + point0[1]*normal[1]
+               + point0[2]*normal[2]);
+    maxround= qh->DISTround;
+    for (i=dim; i--; ) {
+      point= rows[i];
+      if (point != point0) {
+        dist= *offset + (point[0]*normal[0] + point[1]*normal[1]
+               + point[2]*normal[2]);
+        if (dist > maxround || dist < -maxround) {
+          *nearzero= True;
+          break;
+        }
+      }
+    }
+  }else if (dim == 4) {
+    normal[0]= - det3_(dY(2,0), dZ(2,0), dW(2,0),
+                        dY(1,0), dZ(1,0), dW(1,0),
+                        dY(3,0), dZ(3,0), dW(3,0));
+    normal[1]=   det3_(dX(2,0), dZ(2,0), dW(2,0),
+                        dX(1,0), dZ(1,0), dW(1,0),
+                        dX(3,0), dZ(3,0), dW(3,0));
+    normal[2]= - det3_(dX(2,0), dY(2,0), dW(2,0),
+                        dX(1,0), dY(1,0), dW(1,0),
+                        dX(3,0), dY(3,0), dW(3,0));
+    normal[3]=   det3_(dX(2,0), dY(2,0), dZ(2,0),
+                        dX(1,0), dY(1,0), dZ(1,0),
+                        dX(3,0), dY(3,0), dZ(3,0));
+    qh_normalize2(qh, normal, dim, toporient, NULL, NULL);
+    *offset= -(point0[0]*normal[0] + point0[1]*normal[1]
+               + point0[2]*normal[2] + point0[3]*normal[3]);
+    maxround= qh->DISTround;
+    for (i=dim; i--; ) {
+      point= rows[i];
+      if (point != point0) {
+        dist= *offset + (point[0]*normal[0] + point[1]*normal[1]
+               + point[2]*normal[2] + point[3]*normal[3]);
+        if (dist > maxround || dist < -maxround) {
+          *nearzero= True;
+          break;
+        }
+      }
+    }
+  }
+  if (*nearzero) {
+    zzinc_(Zminnorm);
+    trace0((qh, qh->ferr, 3, "qh_sethyperplane_det: degenerate norm during p%d.\n", qh->furthest_id));
+    zzinc_(Znearlysingular);
+  }
+} /* sethyperplane_det */
+
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >-------------------------------</a><a name="sethyperplane_gauss">-</a>
+
+  qh_sethyperplane_gauss(qh, dim, rows, point0, toporient, normal, offset, nearzero )
+    given(dim-1) X dim array of rows[i]= V_{i+1} - V_0 (point0)
+    set normalized hyperplane equation from oriented simplex
+
+  returns:
+    normal (normalized)
+    offset (places point0 on the hyperplane)
+
+  notes:
+    if nearzero
+      orientation may be incorrect because of incorrect sign flips in gausselim
+    solves [V_n-V_0,...,V_1-V_0, 0 .. 0 1] * N == [0 .. 0 1]
+        or [V_n-V_0,...,V_1-V_0, 0 .. 0 1] * N == [0]
+    i.e., N is normal to the hyperplane, and the unnormalized
+        distance to [0 .. 1] is either 1 or   0
+
+  design:
+    perform gaussian elimination
+    flip sign for negative values
+    perform back substitution
+    normalize result
+    compute offset
+*/
+void qh_sethyperplane_gauss(qhT *qh, int dim, coordT **rows, pointT *point0,
+                boolT toporient, coordT *normal, coordT *offset, boolT *nearzero) {
+  coordT *pointcoord, *normalcoef;
+  int k;
+  boolT sign= toporient, nearzero2= False;
+
+  qh_gausselim(qh, rows, dim-1, dim, &sign, nearzero);
+  for (k=dim-1; k--; ) {
+    if ((rows[k])[k] < 0)
+      sign ^= 1;
+  }
+  if (*nearzero) {
+    zzinc_(Znearlysingular);
+    trace0((qh, qh->ferr, 4, "qh_sethyperplane_gauss: nearly singular or axis parallel hyperplane during p%d.\n", qh->furthest_id));
+    qh_backnormal(qh, rows, dim-1, dim, sign, normal, &nearzero2);
+  }else {
+    qh_backnormal(qh, rows, dim-1, dim, sign, normal, &nearzero2);
+    if (nearzero2) {
+      zzinc_(Znearlysingular);
+      trace0((qh, qh->ferr, 5, "qh_sethyperplane_gauss: singular or axis parallel hyperplane at normalization during p%d.\n", qh->furthest_id));
+    }
+  }
+  if (nearzero2)
+    *nearzero= True;
+  qh_normalize2(qh, normal, dim, True, NULL, NULL);
+  pointcoord= point0;
+  normalcoef= normal;
+  *offset= -(*pointcoord++ * *normalcoef++);
+  for (k=dim-1; k--; )
+    *offset -= *pointcoord++ * *normalcoef++;
+} /* sethyperplane_gauss */
+
+
+
diff --git a/xs/src/qhull/src/libqhull_r/geom_r.h b/xs/src/qhull/src/libqhull_r/geom_r.h
new file mode 100644
index 0000000000..d73e953453
--- /dev/null
+++ b/xs/src/qhull/src/libqhull_r/geom_r.h
@@ -0,0 +1,184 @@
+/*<html><pre>  -<a                             href="qh-geom_r.htm"
+  >-------------------------------</a><a name="TOP">-</a>
+
+  geom_r.h
+    header file for geometric routines
+
+   see qh-geom_r.htm and geom_r.c
+
+   Copyright (c) 1993-2015 The Geometry Center.
+   $Id: //main/2015/qhull/src/libqhull_r/geom_r.h#3 $$Change: 2079 $
+   $DateTime: 2016/02/07 17:43:34 $$Author: bbarber $
+*/
+
+#ifndef qhDEFgeom
+#define qhDEFgeom 1
+
+#include "libqhull_r.h"
+
+/* ============ -macros- ======================== */
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >--------------------------------</a><a name="fabs_">-</a>
+
+  fabs_(a)
+    returns the absolute value of a
+*/
+#define fabs_( a ) ((( a ) < 0 ) ? -( a ):( a ))
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >--------------------------------</a><a name="fmax_">-</a>
+
+  fmax_(a,b)
+    returns the maximum value of a and b
+*/
+#define fmax_( a,b )  ( ( a ) < ( b ) ? ( b ) : ( a ) )
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >--------------------------------</a><a name="fmin_">-</a>
+
+  fmin_(a,b)
+    returns the minimum value of a and b
+*/
+#define fmin_( a,b )  ( ( a ) > ( b ) ? ( b ) : ( a ) )
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >--------------------------------</a><a name="maximize_">-</a>
+
+  maximize_(maxval, val)
+    set maxval to val if val is greater than maxval
+*/
+#define maximize_( maxval, val ) { if (( maxval ) < ( val )) ( maxval )= ( val ); }
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >--------------------------------</a><a name="minimize_">-</a>
+
+  minimize_(minval, val)
+    set minval to val if val is less than minval
+*/
+#define minimize_( minval, val ) { if (( minval ) > ( val )) ( minval )= ( val ); }
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >--------------------------------</a><a name="det2_">-</a>
+
+  det2_(a1, a2,
+        b1, b2)
+
+    compute a 2-d determinate
+*/
+#define det2_( a1,a2,b1,b2 ) (( a1 )*( b2 ) - ( a2 )*( b1 ))
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >--------------------------------</a><a name="det3_">-</a>
+
+  det3_(a1, a2, a3,
+       b1, b2, b3,
+       c1, c2, c3)
+
+    compute a 3-d determinate
+*/
+#define det3_( a1,a2,a3,b1,b2,b3,c1,c2,c3 ) ( ( a1 )*det2_( b2,b3,c2,c3 ) \
+                - ( b1 )*det2_( a2,a3,c2,c3 ) + ( c1 )*det2_( a2,a3,b2,b3 ) )
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >--------------------------------</a><a name="dX">-</a>
+
+  dX( p1, p2 )
+  dY( p1, p2 )
+  dZ( p1, p2 )
+
+    given two indices into rows[],
+
+    compute the difference between X, Y, or Z coordinates
+*/
+#define dX( p1,p2 )  ( *( rows[p1] ) - *( rows[p2] ))
+#define dY( p1,p2 )  ( *( rows[p1]+1 ) - *( rows[p2]+1 ))
+#define dZ( p1,p2 )  ( *( rows[p1]+2 ) - *( rows[p2]+2 ))
+#define dW( p1,p2 )  ( *( rows[p1]+3 ) - *( rows[p2]+3 ))
+
+/*============= prototypes in alphabetical order, infrequent at end ======= */
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+void    qh_backnormal(qhT *qh, realT **rows, int numrow, int numcol, boolT sign, coordT *normal, boolT *nearzero);
+void    qh_distplane(qhT *qh, pointT *point, facetT *facet, realT *dist);
+facetT *qh_findbest(qhT *qh, pointT *point, facetT *startfacet,
+                     boolT bestoutside, boolT isnewfacets, boolT noupper,
+                     realT *dist, boolT *isoutside, int *numpart);
+facetT *qh_findbesthorizon(qhT *qh, boolT ischeckmax, pointT *point,
+                     facetT *startfacet, boolT noupper, realT *bestdist, int *numpart);
+facetT *qh_findbestnew(qhT *qh, pointT *point, facetT *startfacet, realT *dist,
+                     boolT bestoutside, boolT *isoutside, int *numpart);
+void    qh_gausselim(qhT *qh, realT **rows, int numrow, int numcol, boolT *sign, boolT *nearzero);
+realT   qh_getangle(qhT *qh, pointT *vect1, pointT *vect2);
+pointT *qh_getcenter(qhT *qh, setT *vertices);
+pointT *qh_getcentrum(qhT *qh, facetT *facet);
+realT   qh_getdistance(qhT *qh, facetT *facet, facetT *neighbor, realT *mindist, realT *maxdist);
+void    qh_normalize(qhT *qh, coordT *normal, int dim, boolT toporient);
+void    qh_normalize2(qhT *qh, coordT *normal, int dim, boolT toporient,
+            realT *minnorm, boolT *ismin);
+pointT *qh_projectpoint(qhT *qh, pointT *point, facetT *facet, realT dist);
+
+void    qh_setfacetplane(qhT *qh, facetT *newfacets);
+void    qh_sethyperplane_det(qhT *qh, int dim, coordT **rows, coordT *point0,
+              boolT toporient, coordT *normal, realT *offset, boolT *nearzero);
+void    qh_sethyperplane_gauss(qhT *qh, int dim, coordT **rows, pointT *point0,
+             boolT toporient, coordT *normal, coordT *offset, boolT *nearzero);
+boolT   qh_sharpnewfacets(qhT *qh);
+
+/*========= infrequently used code in geom2_r.c =============*/
+
+coordT *qh_copypoints(qhT *qh, coordT *points, int numpoints, int dimension);
+void    qh_crossproduct(int dim, realT vecA[3], realT vecB[3], realT vecC[3]);
+realT   qh_determinant(qhT *qh, realT **rows, int dim, boolT *nearzero);
+realT   qh_detjoggle(qhT *qh, pointT *points, int numpoints, int dimension);
+void    qh_detroundoff(qhT *qh);
+realT   qh_detsimplex(qhT *qh, pointT *apex, setT *points, int dim, boolT *nearzero);
+realT   qh_distnorm(int dim, pointT *point, pointT *normal, realT *offsetp);
+realT   qh_distround(qhT *qh, int dimension, realT maxabs, realT maxsumabs);
+realT   qh_divzero(realT numer, realT denom, realT mindenom1, boolT *zerodiv);
+realT   qh_facetarea(qhT *qh, facetT *facet);
+realT   qh_facetarea_simplex(qhT *qh, int dim, coordT *apex, setT *vertices,
+          vertexT *notvertex,  boolT toporient, coordT *normal, realT *offset);
+pointT *qh_facetcenter(qhT *qh, setT *vertices);
+facetT *qh_findgooddist(qhT *qh, pointT *point, facetT *facetA, realT *distp, facetT **facetlist);
+void    qh_getarea(qhT *qh, facetT *facetlist);
+boolT   qh_gram_schmidt(qhT *qh, int dim, realT **rows);
+boolT   qh_inthresholds(qhT *qh, coordT *normal, realT *angle);
+void    qh_joggleinput(qhT *qh);
+realT  *qh_maxabsval(realT *normal, int dim);
+setT   *qh_maxmin(qhT *qh, pointT *points, int numpoints, int dimension);
+realT   qh_maxouter(qhT *qh);
+void    qh_maxsimplex(qhT *qh, int dim, setT *maxpoints, pointT *points, int numpoints, setT **simplex);
+realT   qh_minabsval(realT *normal, int dim);
+int     qh_mindiff(realT *vecA, realT *vecB, int dim);
+boolT   qh_orientoutside(qhT *qh, facetT *facet);
+void    qh_outerinner(qhT *qh, facetT *facet, realT *outerplane, realT *innerplane);
+coordT  qh_pointdist(pointT *point1, pointT *point2, int dim);
+void    qh_printmatrix(qhT *qh, FILE *fp, const char *string, realT **rows, int numrow, int numcol);
+void    qh_printpoints(qhT *qh, FILE *fp, const char *string, setT *points);
+void    qh_projectinput(qhT *qh);
+void    qh_projectpoints(qhT *qh, signed char *project, int n, realT *points,
+             int numpoints, int dim, realT *newpoints, int newdim);
+void    qh_rotateinput(qhT *qh, realT **rows);
+void    qh_rotatepoints(qhT *qh, realT *points, int numpoints, int dim, realT **rows);
+void    qh_scaleinput(qhT *qh);
+void    qh_scalelast(qhT *qh, coordT *points, int numpoints, int dim, coordT low,
+                   coordT high, coordT newhigh);
+void    qh_scalepoints(qhT *qh, pointT *points, int numpoints, int dim,
+                realT *newlows, realT *newhighs);
+boolT   qh_sethalfspace(qhT *qh, int dim, coordT *coords, coordT **nextp,
+              coordT *normal, coordT *offset, coordT *feasible);
+coordT *qh_sethalfspace_all(qhT *qh, int dim, int count, coordT *halfspaces, pointT *feasible);
+pointT *qh_voronoi_center(qhT *qh, int dim, setT *points);
+
+#ifdef __cplusplus
+} /* extern "C"*/
+#endif
+
+#endif /* qhDEFgeom */
+
+
+
diff --git a/xs/src/qhull/src/libqhull_r/global_r.c b/xs/src/qhull/src/libqhull_r/global_r.c
new file mode 100644
index 0000000000..eef465ca14
--- /dev/null
+++ b/xs/src/qhull/src/libqhull_r/global_r.c
@@ -0,0 +1,2100 @@
+
+/*<html><pre>  -<a                             href="qh-globa_r.htm"
+  >-------------------------------</a><a name="TOP">-</a>
+
+   global_r.c
+   initializes all the globals of the qhull application
+
+   see README
+
+   see libqhull_r.h for qh.globals and function prototypes
+
+   see qhull_ra.h for internal functions
+
+   Copyright (c) 1993-2015 The Geometry Center.
+   $Id: //main/2015/qhull/src/libqhull_r/global_r.c#16 $$Change: 2066 $
+   $DateTime: 2016/01/18 19:29:17 $$Author: bbarber $
+ */
+
+#include "qhull_ra.h"
+
+/*========= qh->definition -- globals defined in libqhull_r.h =======================*/
+
+/*-<a                             href  ="qh-globa_r.htm#TOC"
+  >--------------------------------</a><a name="qh_version">-</a>
+
+  qh_version
+    version string by year and date
+    qh_version2 for Unix users and -V
+
+    the revision increases on code changes only
+
+  notes:
+    change date:    Changes.txt, Announce.txt, index.htm, README.txt,
+                    qhull-news.html, Eudora signatures, CMakeLists.txt
+    change version: README.txt, qh-get.htm, File_id.diz, Makefile.txt, CMakeLists.txt
+    check that CmakeLists @version is the same as qh_version2
+    change year:    Copying.txt
+    check download size
+    recompile user_eg_r.c, rbox_r.c, libqhull_r.c, qconvex_r.c, qdelaun_r.c qvoronoi_r.c, qhalf_r.c, testqset_r.c
+*/
+
+const char qh_version[]= "2015.2.r 2016/01/18";
+const char qh_version2[]= "qhull_r 7.2.0 (2015.2.r 2016/01/18)";
+
+/*-<a                             href="qh-globa_r.htm#TOC"
+  >-------------------------------</a><a name="appendprint">-</a>
+
+  qh_appendprint(qh, printFormat )
+    append printFormat to qh.PRINTout unless already defined
+*/
+void qh_appendprint(qhT *qh, qh_PRINT format) {
+  int i;
+
+  for (i=0; i < qh_PRINTEND; i++) {
+    if (qh->PRINTout[i] == format && format != qh_PRINTqhull)
+      break;
+    if (!qh->PRINTout[i]) {
+      qh->PRINTout[i]= format;
+      break;
+    }
+  }
+} /* appendprint */
+
+/*-<a                             href="qh-globa_r.htm#TOC"
+  >-------------------------------</a><a name="checkflags">-</a>
+
+  qh_checkflags(qh, commandStr, hiddenFlags )
+    errors if commandStr contains hiddenFlags
+    hiddenFlags starts and ends with a space and is space delimited (checked)
+
+  notes:
+    ignores first word (e.g., "qconvex i")
+    use qh_strtol/strtod since strtol/strtod may or may not skip trailing spaces
+
+  see:
+    qh_initflags() initializes Qhull according to commandStr
+*/
+void qh_checkflags(qhT *qh, char *command, char *hiddenflags) {
+  char *s= command, *t, *chkerr; /* qh_skipfilename is non-const */
+  char key, opt, prevopt;
+  char chkkey[]= "   ";
+  char chkopt[]=  "    ";
+  char chkopt2[]= "     ";
+  boolT waserr= False;
+
+  if (*hiddenflags != ' ' || hiddenflags[strlen(hiddenflags)-1] != ' ') {
+    qh_fprintf(qh, qh->ferr, 6026, "qhull error (qh_checkflags): hiddenflags must start and end with a space: \"%s\"", hiddenflags);
+    qh_errexit(qh, qh_ERRinput, NULL, NULL);
+  }
+  if (strpbrk(hiddenflags, ",\n\r\t")) {
+    qh_fprintf(qh, qh->ferr, 6027, "qhull error (qh_checkflags): hiddenflags contains commas, newlines, or tabs: \"%s\"", hiddenflags);
+    qh_errexit(qh, qh_ERRinput, NULL, NULL);
+  }
+  while (*s && !isspace(*s))  /* skip program name */
+    s++;
+  while (*s) {
+    while (*s && isspace(*s))
+      s++;
+    if (*s == '-')
+      s++;
+    if (!*s)
+      break;
+    key = *s++;
+    chkerr = NULL;
+    if (key == 'T' && (*s == 'I' || *s == 'O')) {  /* TI or TO 'file name' */
+      s= qh_skipfilename(qh, ++s);
+      continue;
+    }
+    chkkey[1]= key;
+    if (strstr(hiddenflags, chkkey)) {
+      chkerr= chkkey;
+    }else if (isupper(key)) {
+      opt= ' ';
+      prevopt= ' ';
+      chkopt[1]= key;
+      chkopt2[1]= key;
+      while (!chkerr && *s && !isspace(*s)) {
+        opt= *s++;
+        if (isalpha(opt)) {
+          chkopt[2]= opt;
+          if (strstr(hiddenflags, chkopt))
+            chkerr= chkopt;
+          if (prevopt != ' ') {
+            chkopt2[2]= prevopt;
+            chkopt2[3]= opt;
+            if (strstr(hiddenflags, chkopt2))
+              chkerr= chkopt2;
+          }
+        }else if (key == 'Q' && isdigit(opt) && prevopt != 'b'
+              && (prevopt == ' ' || islower(prevopt))) {
+            chkopt[2]= opt;
+            if (strstr(hiddenflags, chkopt))
+              chkerr= chkopt;
+        }else {
+          qh_strtod(s-1, &t);
+          if (s < t)
+            s= t;
+        }
+        prevopt= opt;
+      }
+    }
+    if (chkerr) {
+      *chkerr= '\'';
+      chkerr[strlen(chkerr)-1]=  '\'';
+      qh_fprintf(qh, qh->ferr, 6029, "qhull error: option %s is not used with this program.\n             It may be used with qhull.\n", chkerr);
+      waserr= True;
+    }
+  }
+  if (waserr)
+    qh_errexit(qh, qh_ERRinput, NULL, NULL);
+} /* checkflags */
+
+/*-<a                             href="qh-globa_r.htm#TOC"
+  >-------------------------------</a><a name="qh_clear_outputflags">-</a>
+
+  qh_clear_outputflags(qh)
+    Clear output flags for QhullPoints
+*/
+void qh_clear_outputflags(qhT *qh) {
+  int i,k;
+
+  qh->ANNOTATEoutput= False;
+  qh->DOintersections= False;
+  qh->DROPdim= -1;
+  qh->FORCEoutput= False;
+  qh->GETarea= False;
+  qh->GOODpoint= 0;
+  qh->GOODpointp= NULL;
+  qh->GOODthreshold= False;
+  qh->GOODvertex= 0;
+  qh->GOODvertexp= NULL;
+  qh->IStracing= 0;
+  qh->KEEParea= False;
+  qh->KEEPmerge= False;
+  qh->KEEPminArea= REALmax;
+  qh->PRINTcentrums= False;
+  qh->PRINTcoplanar= False;
+  qh->PRINTdots= False;
+  qh->PRINTgood= False;
+  qh->PRINTinner= False;
+  qh->PRINTneighbors= False;
+  qh->PRINTnoplanes= False;
+  qh->PRINToptions1st= False;
+  qh->PRINTouter= False;
+  qh->PRINTprecision= True;
+  qh->PRINTridges= False;
+  qh->PRINTspheres= False;
+  qh->PRINTstatistics= False;
+  qh->PRINTsummary= False;
+  qh->PRINTtransparent= False;
+  qh->SPLITthresholds= False;
+  qh->TRACElevel= 0;
+  qh->TRInormals= False;
+  qh->USEstdout= False;
+  qh->VERIFYoutput= False;
+  for (k=qh->input_dim+1; k--; ) {  /* duplicated in qh_initqhull_buffers and qh_clear_outputflags */
+    qh->lower_threshold[k]= -REALmax;
+    qh->upper_threshold[k]= REALmax;
+    qh->lower_bound[k]= -REALmax;
+    qh->upper_bound[k]= REALmax;
+  }
+
+  for (i=0; i < qh_PRINTEND; i++) {
+    qh->PRINTout[i]= qh_PRINTnone;
+  }
+
+  if (!qh->qhull_commandsiz2)
+      qh->qhull_commandsiz2= (int)strlen(qh->qhull_command); /* WARN64 */
+  else {
+      qh->qhull_command[qh->qhull_commandsiz2]= '\0';
+  }
+  if (!qh->qhull_optionsiz2)
+    qh->qhull_optionsiz2= (int)strlen(qh->qhull_options);  /* WARN64 */
+  else {
+    qh->qhull_options[qh->qhull_optionsiz2]= '\0';
+    qh->qhull_optionlen= qh_OPTIONline;  /* start a new line */
+  }
+} /* clear_outputflags */
+
+/*-<a                             href="qh-globa_r.htm#TOC"
+  >-------------------------------</a><a name="clock">-</a>
+
+  qh_clock()
+    return user CPU time in 100ths (qh_SECtick)
+    only defined for qh_CLOCKtype == 2
+
+  notes:
+    use first value to determine time 0
+    from Stevens '92 8.15
+*/
+unsigned long qh_clock(qhT *qh) {
+
+#if (qh_CLOCKtype == 2)
+  struct tms time;
+  static long clktck;  /* initialized first call and never updated */
+  double ratio, cpu;
+  unsigned long ticks;
+
+  if (!clktck) {
+    if ((clktck= sysconf(_SC_CLK_TCK)) < 0) {
+      qh_fprintf(qh, qh->ferr, 6030, "qhull internal error (qh_clock): sysconf() failed.  Use qh_CLOCKtype 1 in user.h\n");
+      qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+    }
+  }
+  if (times(&time) == -1) {
+    qh_fprintf(qh, qh->ferr, 6031, "qhull internal error (qh_clock): times() failed.  Use qh_CLOCKtype 1 in user.h\n");
+    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+  }
+  ratio= qh_SECticks / (double)clktck;
+  ticks= time.tms_utime * ratio;
+  return ticks;
+#else
+  qh_fprintf(qh, qh->ferr, 6032, "qhull internal error (qh_clock): use qh_CLOCKtype 2 in user.h\n");
+  qh_errexit(qh, qh_ERRqhull, NULL, NULL); /* never returns */
+  return 0;
+#endif
+} /* clock */
+
+/*-<a                             href="qh-globa_r.htm#TOC"
+  >-------------------------------</a><a name="freebuffers">-</a>
+
+  qh_freebuffers()
+    free up global memory buffers
+
+  notes:
+    must match qh_initbuffers()
+*/
+void qh_freebuffers(qhT *qh) {
+
+  trace5((qh, qh->ferr, 5001, "qh_freebuffers: freeing up global memory buffers\n"));
+  /* allocated by qh_initqhull_buffers */
+  qh_memfree(qh, qh->NEARzero, qh->hull_dim * sizeof(realT));
+  qh_memfree(qh, qh->lower_threshold, (qh->input_dim+1) * sizeof(realT));
+  qh_memfree(qh, qh->upper_threshold, (qh->input_dim+1) * sizeof(realT));
+  qh_memfree(qh, qh->lower_bound, (qh->input_dim+1) * sizeof(realT));
+  qh_memfree(qh, qh->upper_bound, (qh->input_dim+1) * sizeof(realT));
+  qh_memfree(qh, qh->gm_matrix, (qh->hull_dim+1) * qh->hull_dim * sizeof(coordT));
+  qh_memfree(qh, qh->gm_row, (qh->hull_dim+1) * sizeof(coordT *));
+  qh->NEARzero= qh->lower_threshold= qh->upper_threshold= NULL;
+  qh->lower_bound= qh->upper_bound= NULL;
+  qh->gm_matrix= NULL;
+  qh->gm_row= NULL;
+  qh_setfree(qh, &qh->other_points);
+  qh_setfree(qh, &qh->del_vertices);
+  qh_setfree(qh, &qh->coplanarfacetset);
+  if (qh->line)                /* allocated by qh_readinput, freed if no error */
+    qh_free(qh->line);
+  if (qh->half_space)
+    qh_free(qh->half_space);
+  if (qh->temp_malloc)
+    qh_free(qh->temp_malloc);
+  if (qh->feasible_point)      /* allocated by qh_readfeasible */
+    qh_free(qh->feasible_point);
+  if (qh->feasible_string)     /* allocated by qh_initflags */
+    qh_free(qh->feasible_string);
+  qh->line= qh->feasible_string= NULL;
+  qh->half_space= qh->feasible_point= qh->temp_malloc= NULL;
+  /* usually allocated by qh_readinput */
+  if (qh->first_point && qh->POINTSmalloc) {
+    qh_free(qh->first_point);
+    qh->first_point= NULL;
+  }
+  if (qh->input_points && qh->input_malloc) { /* set by qh_joggleinput */
+    qh_free(qh->input_points);
+    qh->input_points= NULL;
+  }
+  trace5((qh, qh->ferr, 5002, "qh_freebuffers: finished\n"));
+} /* freebuffers */
+
+
+/*-<a                             href="qh-globa_r.htm#TOC"
+  >-------------------------------</a><a name="freebuild">-</a>
+
+  qh_freebuild(qh, allmem )
+    free global memory used by qh_initbuild and qh_buildhull
+    if !allmem,
+      does not free short memory (e.g., facetT, freed by qh_memfreeshort)
+
+  design:
+    free centrums
+    free each vertex
+    mark unattached ridges
+    for each facet
+      free ridges
+      free outside set, coplanar set, neighbor set, ridge set, vertex set
+      free facet
+    free hash table
+    free interior point
+    free merge set
+    free temporary sets
+*/
+void qh_freebuild(qhT *qh, boolT allmem) {
+  facetT *facet;
+  vertexT *vertex;
+  ridgeT *ridge, **ridgep;
+  mergeT *merge, **mergep;
+
+  trace1((qh, qh->ferr, 1005, "qh_freebuild: free memory from qh_inithull and qh_buildhull\n"));
+  if (qh->del_vertices)
+    qh_settruncate(qh, qh->del_vertices, 0);
+  if (allmem) {
+    while ((vertex= qh->vertex_list)) {
+      if (vertex->next)
+        qh_delvertex(qh, vertex);
+      else {
+        qh_memfree(qh, vertex, (int)sizeof(vertexT));
+        qh->newvertex_list= qh->vertex_list= NULL;
+      }
+    }
+  }else if (qh->VERTEXneighbors) {
+    FORALLvertices
+      qh_setfreelong(qh, &(vertex->neighbors));
+  }
+  qh->VERTEXneighbors= False;
+  qh->GOODclosest= NULL;
+  if (allmem) {
+    FORALLfacets {
+      FOREACHridge_(facet->ridges)
+        ridge->seen= False;
+    }
+    FORALLfacets {
+      if (facet->visible) {
+        FOREACHridge_(facet->ridges) {
+          if (!otherfacet_(ridge, facet)->visible)
+            ridge->seen= True;  /* an unattached ridge */
+        }
+      }
+    }
+    while ((facet= qh->facet_list)) {
+      FOREACHridge_(facet->ridges) {
+        if (ridge->seen) {
+          qh_setfree(qh, &(ridge->vertices));
+          qh_memfree(qh, ridge, (int)sizeof(ridgeT));
+        }else
+          ridge->seen= True;
+      }
+      qh_setfree(qh, &(facet->outsideset));
+      qh_setfree(qh, &(facet->coplanarset));
+      qh_setfree(qh, &(facet->neighbors));
+      qh_setfree(qh, &(facet->ridges));
+      qh_setfree(qh, &(facet->vertices));
+      if (facet->next)
+        qh_delfacet(qh, facet);
+      else {
+        qh_memfree(qh, facet, (int)sizeof(facetT));
+        qh->visible_list= qh->newfacet_list= qh->facet_list= NULL;
+      }
+    }
+  }else {
+    FORALLfacets {
+      qh_setfreelong(qh, &(facet->outsideset));
+      qh_setfreelong(qh, &(facet->coplanarset));
+      if (!facet->simplicial) {
+        qh_setfreelong(qh, &(facet->neighbors));
+        qh_setfreelong(qh, &(facet->ridges));
+        qh_setfreelong(qh, &(facet->vertices));
+      }
+    }
+  }
+  qh_setfree(qh, &(qh->hash_table));
+  qh_memfree(qh, qh->interior_point, qh->normal_size);
+  qh->interior_point= NULL;
+  FOREACHmerge_(qh->facet_mergeset)  /* usually empty */
+    qh_memfree(qh, merge, (int)sizeof(mergeT));
+  qh->facet_mergeset= NULL;  /* temp set */
+  qh->degen_mergeset= NULL;  /* temp set */
+  qh_settempfree_all(qh);
+} /* freebuild */
+
+/*-<a                             href="qh-globa_r.htm#TOC"
+  >-------------------------------</a><a name="freeqhull">-</a>
+
+  qh_freeqhull(qh, allmem )
+
+  free global memory and set qhT to 0
+  if !allmem,
+    does not free short memory (freed by qh_memfreeshort unless qh_NOmem)
+
+notes:
+  sets qh.NOerrexit in case caller forgets to
+  Does not throw errors
+
+see:
+  see qh_initqhull_start2()
+  For libqhull_r, qhstatT is part of qhT
+
+design:
+  free global and temporary memory from qh_initbuild and qh_buildhull
+  free buffers
+*/
+void qh_freeqhull(qhT *qh, boolT allmem) {
+
+  qh->NOerrexit= True;  /* no more setjmp since called at exit and ~QhullQh */
+  trace1((qh, qh->ferr, 1006, "qh_freeqhull: free global memory\n"));
+  qh_freebuild(qh, allmem);
+  qh_freebuffers(qh);
+  /* memset is the same in qh_freeqhull() and qh_initqhull_start2() */
+  memset((char *)qh, 0, sizeof(qhT)-sizeof(qhmemT)-sizeof(qhstatT));
+  qh->NOerrexit= True;
+} /* freeqhull2 */
+
+/*-<a                             href="qh-globa_r.htm#TOC"
+  >-------------------------------</a><a name="init_A">-</a>
+
+  qh_init_A(qh, infile, outfile, errfile, argc, argv )
+    initialize memory and stdio files
+    convert input options to option string (qh.qhull_command)
+
+  notes:
+    infile may be NULL if qh_readpoints() is not called
+
+    errfile should always be defined.  It is used for reporting
+    errors.  outfile is used for output and format options.
+
+    argc/argv may be 0/NULL
+
+    called before error handling initialized
+    qh_errexit() may not be used
+*/
+void qh_init_A(qhT *qh, FILE *infile, FILE *outfile, FILE *errfile, int argc, char *argv[]) {
+  qh_meminit(qh, errfile);
+  qh_initqhull_start(qh, infile, outfile, errfile);
+  qh_init_qhull_command(qh, argc, argv);
+} /* init_A */
+
+/*-<a                             href="qh-globa_r.htm#TOC"
+  >-------------------------------</a><a name="init_B">-</a>
+
+  qh_init_B(qh, points, numpoints, dim, ismalloc )
+    initialize globals for points array
+
+    points has numpoints dim-dimensional points
+      points[0] is the first coordinate of the first point
+      points[1] is the second coordinate of the first point
+      points[dim] is the first coordinate of the second point
+
+    ismalloc=True
+      Qhull will call qh_free(points) on exit or input transformation
+    ismalloc=False
+      Qhull will allocate a new point array if needed for input transformation
+
+    qh.qhull_command
+      is the option string.
+      It is defined by qh_init_B(), qh_qhull_command(), or qh_initflags
+
+  returns:
+    if qh.PROJECTinput or (qh.DELAUNAY and qh.PROJECTdelaunay)
+      projects the input to a new point array
+
+        if qh.DELAUNAY,
+          qh.hull_dim is increased by one
+        if qh.ATinfinity,
+          qh_projectinput adds point-at-infinity for Delaunay tri.
+
+    if qh.SCALEinput
+      changes the upper and lower bounds of the input, see qh_scaleinput(qh)
+
+    if qh.ROTATEinput
+      rotates the input by a random rotation, see qh_rotateinput()
+      if qh.DELAUNAY
+        rotates about the last coordinate
+
+  notes:
+    called after points are defined
+    qh_errexit() may be used
+*/
+void qh_init_B(qhT *qh, coordT *points, int numpoints, int dim, boolT ismalloc) {
+  qh_initqhull_globals(qh, points, numpoints, dim, ismalloc);
+  if (qh->qhmem.LASTsize == 0)
+    qh_initqhull_mem(qh);
+  /* mem_r.c and qset_r.c are initialized */
+  qh_initqhull_buffers(qh);
+  qh_initthresholds(qh, qh->qhull_command);
+  if (qh->PROJECTinput || (qh->DELAUNAY && qh->PROJECTdelaunay))
+    qh_projectinput(qh);
+  if (qh->SCALEinput)
+    qh_scaleinput(qh);
+  if (qh->ROTATErandom >= 0) {
+    qh_randommatrix(qh, qh->gm_matrix, qh->hull_dim, qh->gm_row);
+    if (qh->DELAUNAY) {
+      int k, lastk= qh->hull_dim-1;
+      for (k=0; k < lastk; k++) {
+        qh->gm_row[k][lastk]= 0.0;
+        qh->gm_row[lastk][k]= 0.0;
+      }
+      qh->gm_row[lastk][lastk]= 1.0;
+    }
+    qh_gram_schmidt(qh, qh->hull_dim, qh->gm_row);
+    qh_rotateinput(qh, qh->gm_row);
+  }
+} /* init_B */
+
+/*-<a                             href="qh-globa_r.htm#TOC"
+  >-------------------------------</a><a name="init_qhull_command">-</a>
+
+  qh_init_qhull_command(qh, argc, argv )
+    build qh.qhull_command from argc/argv
+    Calls qh_exit if qhull_command is too short
+
+  returns:
+    a space-delimited string of options (just as typed)
+
+  notes:
+    makes option string easy to input and output
+
+    argc/argv may be 0/NULL
+*/
+void qh_init_qhull_command(qhT *qh, int argc, char *argv[]) {
+
+  if (!qh_argv_to_command(argc, argv, qh->qhull_command, (int)sizeof(qh->qhull_command))){
+    /* Assumes qh.ferr is defined. */
+    qh_fprintf(qh, qh->ferr, 6033, "qhull input error: more than %d characters in command line.\n",
+          (int)sizeof(qh->qhull_command));
+    qh_exit(qh_ERRinput);  /* error reported, can not use qh_errexit */
+  }
+} /* init_qhull_command */
+
+/*-<a                             href="qh-globa_r.htm#TOC"
+  >-------------------------------</a><a name="initflags">-</a>
+
+  qh_initflags(qh, commandStr )
+    set flags and initialized constants from commandStr
+    calls qh_exit() if qh->NOerrexit
+
+  returns:
+    sets qh.qhull_command to command if needed
+
+  notes:
+    ignores first word (e.g., "qhull d")
+    use qh_strtol/strtod since strtol/strtod may or may not skip trailing spaces
+
+  see:
+    qh_initthresholds() continues processing of 'Pdn' and 'PDn'
+    'prompt' in unix_r.c for documentation
+
+  design:
+    for each space-delimited option group
+      if top-level option
+        check syntax
+        append appropriate option to option string
+        set appropriate global variable or append printFormat to print options
+      else
+        for each sub-option
+          check syntax
+          append appropriate option to option string
+          set appropriate global variable or append printFormat to print options
+*/
+void qh_initflags(qhT *qh, char *command) {
+  int k, i, lastproject;
+  char *s= command, *t, *prev_s, *start, key;
+  boolT isgeom= False, wasproject;
+  realT r;
+
+  if(qh->NOerrexit){
+    qh_fprintf(qh, qh->ferr, 6245, "qhull initflags error: qh.NOerrexit was not cleared before calling qh_initflags().  It should be cleared after setjmp().  Exit qhull.");
+    qh_exit(6245);
+  }
+  if (command <= &qh->qhull_command[0] || command > &qh->qhull_command[0] + sizeof(qh->qhull_command)) {
+    if (command != &qh->qhull_command[0]) {
+      *qh->qhull_command= '\0';
+      strncat(qh->qhull_command, command, sizeof(qh->qhull_command)-strlen(qh->qhull_command)-1);
+    }
+    while (*s && !isspace(*s))  /* skip program name */
+      s++;
+  }
+  while (*s) {
+    while (*s && isspace(*s))
+      s++;
+    if (*s == '-')
+      s++;
+    if (!*s)
+      break;
+    prev_s= s;
+    switch (*s++) {
+    case 'd':
+      qh_option(qh, "delaunay", NULL, NULL);
+      qh->DELAUNAY= True;
+      break;
+    case 'f':
+      qh_option(qh, "facets", NULL, NULL);
+      qh_appendprint(qh, qh_PRINTfacets);
+      break;
+    case 'i':
+      qh_option(qh, "incidence", NULL, NULL);
+      qh_appendprint(qh, qh_PRINTincidences);
+      break;
+    case 'm':
+      qh_option(qh, "mathematica", NULL, NULL);
+      qh_appendprint(qh, qh_PRINTmathematica);
+      break;
+    case 'n':
+      qh_option(qh, "normals", NULL, NULL);
+      qh_appendprint(qh, qh_PRINTnormals);
+      break;
+    case 'o':
+      qh_option(qh, "offFile", NULL, NULL);
+      qh_appendprint(qh, qh_PRINToff);
+      break;
+    case 'p':
+      qh_option(qh, "points", NULL, NULL);
+      qh_appendprint(qh, qh_PRINTpoints);
+      break;
+    case 's':
+      qh_option(qh, "summary", NULL, NULL);
+      qh->PRINTsummary= True;
+      break;
+    case 'v':
+      qh_option(qh, "voronoi", NULL, NULL);
+      qh->VORONOI= True;
+      qh->DELAUNAY= True;
+      break;
+    case 'A':
+      if (!isdigit(*s) && *s != '.' && *s != '-')
+        qh_fprintf(qh, qh->ferr, 7002, "qhull warning: no maximum cosine angle given for option 'An'.  Ignored.\n");
+      else {
+        if (*s == '-') {
+          qh->premerge_cos= -qh_strtod(s, &s);
+          qh_option(qh, "Angle-premerge-", NULL, &qh->premerge_cos);
+          qh->PREmerge= True;
+        }else {
+          qh->postmerge_cos= qh_strtod(s, &s);
+          qh_option(qh, "Angle-postmerge", NULL, &qh->postmerge_cos);
+          qh->POSTmerge= True;
+        }
+        qh->MERGING= True;
+      }
+      break;
+    case 'C':
+      if (!isdigit(*s) && *s != '.' && *s != '-')
+        qh_fprintf(qh, qh->ferr, 7003, "qhull warning: no centrum radius given for option 'Cn'.  Ignored.\n");
+      else {
+        if (*s == '-') {
+          qh->premerge_centrum= -qh_strtod(s, &s);
+          qh_option(qh, "Centrum-premerge-", NULL, &qh->premerge_centrum);
+          qh->PREmerge= True;
+        }else {
+          qh->postmerge_centrum= qh_strtod(s, &s);
+          qh_option(qh, "Centrum-postmerge", NULL, &qh->postmerge_centrum);
+          qh->POSTmerge= True;
+        }
+        qh->MERGING= True;
+      }
+      break;
+    case 'E':
+      if (*s == '-')
+        qh_fprintf(qh, qh->ferr, 7004, "qhull warning: negative maximum roundoff given for option 'An'.  Ignored.\n");
+      else if (!isdigit(*s))
+        qh_fprintf(qh, qh->ferr, 7005, "qhull warning: no maximum roundoff given for option 'En'.  Ignored.\n");
+      else {
+        qh->DISTround= qh_strtod(s, &s);
+        qh_option(qh, "Distance-roundoff", NULL, &qh->DISTround);
+        qh->SETroundoff= True;
+      }
+      break;
+    case 'H':
+      start= s;
+      qh->HALFspace= True;
+      qh_strtod(s, &t);
+      while (t > s)  {
+        if (*t && !isspace(*t)) {
+          if (*t == ',')
+            t++;
+          else
+            qh_fprintf(qh, qh->ferr, 7006, "qhull warning: origin for Halfspace intersection should be 'Hn,n,n,...'\n");
+        }
+        s= t;
+        qh_strtod(s, &t);
+      }
+      if (start < t) {
+        if (!(qh->feasible_string= (char*)calloc((size_t)(t-start+1), (size_t)1))) {
+          qh_fprintf(qh, qh->ferr, 6034, "qhull error: insufficient memory for 'Hn,n,n'\n");
+          qh_errexit(qh, qh_ERRmem, NULL, NULL);
+        }
+        strncpy(qh->feasible_string, start, (size_t)(t-start));
+        qh_option(qh, "Halfspace-about", NULL, NULL);
+        qh_option(qh, qh->feasible_string, NULL, NULL);
+      }else
+        qh_option(qh, "Halfspace", NULL, NULL);
+      break;
+    case 'R':
+      if (!isdigit(*s))
+        qh_fprintf(qh, qh->ferr, 7007, "qhull warning: missing random perturbation for option 'Rn'.  Ignored\n");
+      else {
+        qh->RANDOMfactor= qh_strtod(s, &s);
+        qh_option(qh, "Random_perturb", NULL, &qh->RANDOMfactor);
+        qh->RANDOMdist= True;
+      }
+      break;
+    case 'V':
+      if (!isdigit(*s) && *s != '-')
+        qh_fprintf(qh, qh->ferr, 7008, "qhull warning: missing visible distance for option 'Vn'.  Ignored\n");
+      else {
+        qh->MINvisible= qh_strtod(s, &s);
+        qh_option(qh, "Visible", NULL, &qh->MINvisible);
+      }
+      break;
+    case 'U':
+      if (!isdigit(*s) && *s != '-')
+        qh_fprintf(qh, qh->ferr, 7009, "qhull warning: missing coplanar distance for option 'Un'.  Ignored\n");
+      else {
+        qh->MAXcoplanar= qh_strtod(s, &s);
+        qh_option(qh, "U-coplanar", NULL, &qh->MAXcoplanar);
+      }
+      break;
+    case 'W':
+      if (*s == '-')
+        qh_fprintf(qh, qh->ferr, 7010, "qhull warning: negative outside width for option 'Wn'.  Ignored.\n");
+      else if (!isdigit(*s))
+        qh_fprintf(qh, qh->ferr, 7011, "qhull warning: missing outside width for option 'Wn'.  Ignored\n");
+      else {
+        qh->MINoutside= qh_strtod(s, &s);
+        qh_option(qh, "W-outside", NULL, &qh->MINoutside);
+        qh->APPROXhull= True;
+      }
+      break;
+    /************  sub menus ***************/
+    case 'F':
+      while (*s && !isspace(*s)) {
+        switch (*s++) {
+        case 'a':
+          qh_option(qh, "Farea", NULL, NULL);
+          qh_appendprint(qh, qh_PRINTarea);
+          qh->GETarea= True;
+          break;
+        case 'A':
+          qh_option(qh, "FArea-total", NULL, NULL);
+          qh->GETarea= True;
+          break;
+        case 'c':
+          qh_option(qh, "Fcoplanars", NULL, NULL);
+          qh_appendprint(qh, qh_PRINTcoplanars);
+          break;
+        case 'C':
+          qh_option(qh, "FCentrums", NULL, NULL);
+          qh_appendprint(qh, qh_PRINTcentrums);
+          break;
+        case 'd':
+          qh_option(qh, "Fd-cdd-in", NULL, NULL);
+          qh->CDDinput= True;
+          break;
+        case 'D':
+          qh_option(qh, "FD-cdd-out", NULL, NULL);
+          qh->CDDoutput= True;
+          break;
+        case 'F':
+          qh_option(qh, "FFacets-xridge", NULL, NULL);
+          qh_appendprint(qh, qh_PRINTfacets_xridge);
+          break;
+        case 'i':
+          qh_option(qh, "Finner", NULL, NULL);
+          qh_appendprint(qh, qh_PRINTinner);
+          break;
+        case 'I':
+          qh_option(qh, "FIDs", NULL, NULL);
+          qh_appendprint(qh, qh_PRINTids);
+          break;
+        case 'm':
+          qh_option(qh, "Fmerges", NULL, NULL);
+          qh_appendprint(qh, qh_PRINTmerges);
+          break;
+        case 'M':
+          qh_option(qh, "FMaple", NULL, NULL);
+          qh_appendprint(qh, qh_PRINTmaple);
+          break;
+        case 'n':
+          qh_option(qh, "Fneighbors", NULL, NULL);
+          qh_appendprint(qh, qh_PRINTneighbors);
+          break;
+        case 'N':
+          qh_option(qh, "FNeighbors-vertex", NULL, NULL);
+          qh_appendprint(qh, qh_PRINTvneighbors);
+          break;
+        case 'o':
+          qh_option(qh, "Fouter", NULL, NULL);
+          qh_appendprint(qh, qh_PRINTouter);
+          break;
+        case 'O':
+          if (qh->PRINToptions1st) {
+            qh_option(qh, "FOptions", NULL, NULL);
+            qh_appendprint(qh, qh_PRINToptions);
+          }else
+            qh->PRINToptions1st= True;
+          break;
+        case 'p':
+          qh_option(qh, "Fpoint-intersect", NULL, NULL);
+          qh_appendprint(qh, qh_PRINTpointintersect);
+          break;
+        case 'P':
+          qh_option(qh, "FPoint-nearest", NULL, NULL);
+          qh_appendprint(qh, qh_PRINTpointnearest);
+          break;
+        case 'Q':
+          qh_option(qh, "FQhull", NULL, NULL);
+          qh_appendprint(qh, qh_PRINTqhull);
+          break;
+        case 's':
+          qh_option(qh, "Fsummary", NULL, NULL);
+          qh_appendprint(qh, qh_PRINTsummary);
+          break;
+        case 'S':
+          qh_option(qh, "FSize", NULL, NULL);
+          qh_appendprint(qh, qh_PRINTsize);
+          qh->GETarea= True;
+          break;
+        case 't':
+          qh_option(qh, "Ftriangles", NULL, NULL);
+          qh_appendprint(qh, qh_PRINTtriangles);
+          break;
+        case 'v':
+          /* option set in qh_initqhull_globals */
+          qh_appendprint(qh, qh_PRINTvertices);
+          break;
+        case 'V':
+          qh_option(qh, "FVertex-average", NULL, NULL);
+          qh_appendprint(qh, qh_PRINTaverage);
+          break;
+        case 'x':
+          qh_option(qh, "Fxtremes", NULL, NULL);
+          qh_appendprint(qh, qh_PRINTextremes);
+          break;
+        default:
+          s--;
+          qh_fprintf(qh, qh->ferr, 7012, "qhull warning: unknown 'F' output option %c, rest ignored\n", (int)s[0]);
+          while (*++s && !isspace(*s));
+          break;
+        }
+      }
+      break;
+    case 'G':
+      isgeom= True;
+      qh_appendprint(qh, qh_PRINTgeom);
+      while (*s && !isspace(*s)) {
+        switch (*s++) {
+        case 'a':
+          qh_option(qh, "Gall-points", NULL, NULL);
+          qh->PRINTdots= True;
+          break;
+        case 'c':
+          qh_option(qh, "Gcentrums", NULL, NULL);
+          qh->PRINTcentrums= True;
+          break;
+        case 'h':
+          qh_option(qh, "Gintersections", NULL, NULL);
+          qh->DOintersections= True;
+          break;
+        case 'i':
+          qh_option(qh, "Ginner", NULL, NULL);
+          qh->PRINTinner= True;
+          break;
+        case 'n':
+          qh_option(qh, "Gno-planes", NULL, NULL);
+          qh->PRINTnoplanes= True;
+          break;
+        case 'o':
+          qh_option(qh, "Gouter", NULL, NULL);
+          qh->PRINTouter= True;
+          break;
+        case 'p':
+          qh_option(qh, "Gpoints", NULL, NULL);
+          qh->PRINTcoplanar= True;
+          break;
+        case 'r':
+          qh_option(qh, "Gridges", NULL, NULL);
+          qh->PRINTridges= True;
+          break;
+        case 't':
+          qh_option(qh, "Gtransparent", NULL, NULL);
+          qh->PRINTtransparent= True;
+          break;
+        case 'v':
+          qh_option(qh, "Gvertices", NULL, NULL);
+          qh->PRINTspheres= True;
+          break;
+        case 'D':
+          if (!isdigit(*s))
+            qh_fprintf(qh, qh->ferr, 6035, "qhull input error: missing dimension for option 'GDn'\n");
+          else {
+            if (qh->DROPdim >= 0)
+              qh_fprintf(qh, qh->ferr, 7013, "qhull warning: can only drop one dimension.  Previous 'GD%d' ignored\n",
+                   qh->DROPdim);
+            qh->DROPdim= qh_strtol(s, &s);
+            qh_option(qh, "GDrop-dim", &qh->DROPdim, NULL);
+          }
+          break;
+        default:
+          s--;
+          qh_fprintf(qh, qh->ferr, 7014, "qhull warning: unknown 'G' print option %c, rest ignored\n", (int)s[0]);
+          while (*++s && !isspace(*s));
+          break;
+        }
+      }
+      break;
+    case 'P':
+      while (*s && !isspace(*s)) {
+        switch (*s++) {
+        case 'd': case 'D':  /* see qh_initthresholds() */
+          key= s[-1];
+          i= qh_strtol(s, &s);
+          r= 0;
+          if (*s == ':') {
+            s++;
+            r= qh_strtod(s, &s);
+          }
+          if (key == 'd')
+            qh_option(qh, "Pdrop-facets-dim-less", &i, &r);
+          else
+            qh_option(qh, "PDrop-facets-dim-more", &i, &r);
+          break;
+        case 'g':
+          qh_option(qh, "Pgood-facets", NULL, NULL);
+          qh->PRINTgood= True;
+          break;
+        case 'G':
+          qh_option(qh, "PGood-facet-neighbors", NULL, NULL);
+          qh->PRINTneighbors= True;
+          break;
+        case 'o':
+          qh_option(qh, "Poutput-forced", NULL, NULL);
+          qh->FORCEoutput= True;
+          break;
+        case 'p':
+          qh_option(qh, "Pprecision-ignore", NULL, NULL);
+          qh->PRINTprecision= False;
+          break;
+        case 'A':
+          if (!isdigit(*s))
+            qh_fprintf(qh, qh->ferr, 6036, "qhull input error: missing facet count for keep area option 'PAn'\n");
+          else {
+            qh->KEEParea= qh_strtol(s, &s);
+            qh_option(qh, "PArea-keep", &qh->KEEParea, NULL);
+            qh->GETarea= True;
+          }
+          break;
+        case 'F':
+          if (!isdigit(*s))
+            qh_fprintf(qh, qh->ferr, 6037, "qhull input error: missing facet area for option 'PFn'\n");
+          else {
+            qh->KEEPminArea= qh_strtod(s, &s);
+            qh_option(qh, "PFacet-area-keep", NULL, &qh->KEEPminArea);
+            qh->GETarea= True;
+          }
+          break;
+        case 'M':
+          if (!isdigit(*s))
+            qh_fprintf(qh, qh->ferr, 6038, "qhull input error: missing merge count for option 'PMn'\n");
+          else {
+            qh->KEEPmerge= qh_strtol(s, &s);
+            qh_option(qh, "PMerge-keep", &qh->KEEPmerge, NULL);
+          }
+          break;
+        default:
+          s--;
+          qh_fprintf(qh, qh->ferr, 7015, "qhull warning: unknown 'P' print option %c, rest ignored\n", (int)s[0]);
+          while (*++s && !isspace(*s));
+          break;
+        }
+      }
+      break;
+    case 'Q':
+      lastproject= -1;
+      while (*s && !isspace(*s)) {
+        switch (*s++) {
+        case 'b': case 'B':  /* handled by qh_initthresholds */
+          key= s[-1];
+          if (key == 'b' && *s == 'B') {
+            s++;
+            r= qh_DEFAULTbox;
+            qh->SCALEinput= True;
+            qh_option(qh, "QbBound-unit-box", NULL, &r);
+            break;
+          }
+          if (key == 'b' && *s == 'b') {
+            s++;
+            qh->SCALElast= True;
+            qh_option(qh, "Qbbound-last", NULL, NULL);
+            break;
+          }
+          k= qh_strtol(s, &s);
+          r= 0.0;
+          wasproject= False;
+          if (*s == ':') {
+            s++;
+            if ((r= qh_strtod(s, &s)) == 0.0) {
+              t= s;            /* need true dimension for memory allocation */
+              while (*t && !isspace(*t)) {
+                if (toupper(*t++) == 'B'
+                 && k == qh_strtol(t, &t)
+                 && *t++ == ':'
+                 && qh_strtod(t, &t) == 0.0) {
+                  qh->PROJECTinput++;
+                  trace2((qh, qh->ferr, 2004, "qh_initflags: project dimension %d\n", k));
+                  qh_option(qh, "Qb-project-dim", &k, NULL);
+                  wasproject= True;
+                  lastproject= k;
+                  break;
+                }
+              }
+            }
+          }
+          if (!wasproject) {
+            if (lastproject == k && r == 0.0)
+              lastproject= -1;  /* doesn't catch all possible sequences */
+            else if (key == 'b') {
+              qh->SCALEinput= True;
+              if (r == 0.0)
+                r= -qh_DEFAULTbox;
+              qh_option(qh, "Qbound-dim-low", &k, &r);
+            }else {
+              qh->SCALEinput= True;
+              if (r == 0.0)
+                r= qh_DEFAULTbox;
+              qh_option(qh, "QBound-dim-high", &k, &r);
+            }
+          }
+          break;
+        case 'c':
+          qh_option(qh, "Qcoplanar-keep", NULL, NULL);
+          qh->KEEPcoplanar= True;
+          break;
+        case 'f':
+          qh_option(qh, "Qfurthest-outside", NULL, NULL);
+          qh->BESToutside= True;
+          break;
+        case 'g':
+          qh_option(qh, "Qgood-facets-only", NULL, NULL);
+          qh->ONLYgood= True;
+          break;
+        case 'i':
+          qh_option(qh, "Qinterior-keep", NULL, NULL);
+          qh->KEEPinside= True;
+          break;
+        case 'm':
+          qh_option(qh, "Qmax-outside-only", NULL, NULL);
+          qh->ONLYmax= True;
+          break;
+        case 'r':
+          qh_option(qh, "Qrandom-outside", NULL, NULL);
+          qh->RANDOMoutside= True;
+          break;
+        case 's':
+          qh_option(qh, "Qsearch-initial-simplex", NULL, NULL);
+          qh->ALLpoints= True;
+          break;
+        case 't':
+          qh_option(qh, "Qtriangulate", NULL, NULL);
+          qh->TRIangulate= True;
+          break;
+        case 'T':
+          qh_option(qh, "QTestPoints", NULL, NULL);
+          if (!isdigit(*s))
+            qh_fprintf(qh, qh->ferr, 6039, "qhull input error: missing number of test points for option 'QTn'\n");
+          else {
+            qh->TESTpoints= qh_strtol(s, &s);
+            qh_option(qh, "QTestPoints", &qh->TESTpoints, NULL);
+          }
+          break;
+        case 'u':
+          qh_option(qh, "QupperDelaunay", NULL, NULL);
+          qh->UPPERdelaunay= True;
+          break;
+        case 'v':
+          qh_option(qh, "Qvertex-neighbors-convex", NULL, NULL);
+          qh->TESTvneighbors= True;
+          break;
+        case 'x':
+          qh_option(qh, "Qxact-merge", NULL, NULL);
+          qh->MERGEexact= True;
+          break;
+        case 'z':
+          qh_option(qh, "Qz-infinity-point", NULL, NULL);
+          qh->ATinfinity= True;
+          break;
+        case '0':
+          qh_option(qh, "Q0-no-premerge", NULL, NULL);
+          qh->NOpremerge= True;
+          break;
+        case '1':
+          if (!isdigit(*s)) {
+            qh_option(qh, "Q1-no-angle-sort", NULL, NULL);
+            qh->ANGLEmerge= False;
+            break;
+          }
+          switch (*s++) {
+          case '0':
+            qh_option(qh, "Q10-no-narrow", NULL, NULL);
+            qh->NOnarrow= True;
+            break;
+          case '1':
+            qh_option(qh, "Q11-trinormals Qtriangulate", NULL, NULL);
+            qh->TRInormals= True;
+            qh->TRIangulate= True;
+            break;
+          case '2':
+              qh_option(qh, "Q12-no-wide-dup", NULL, NULL);
+              qh->NOwide= True;
+            break;
+          default:
+            s--;
+            qh_fprintf(qh, qh->ferr, 7016, "qhull warning: unknown 'Q' qhull option 1%c, rest ignored\n", (int)s[0]);
+            while (*++s && !isspace(*s));
+            break;
+          }
+          break;
+        case '2':
+          qh_option(qh, "Q2-no-merge-independent", NULL, NULL);
+          qh->MERGEindependent= False;
+          goto LABELcheckdigit;
+          break; /* no warnings */
+        case '3':
+          qh_option(qh, "Q3-no-merge-vertices", NULL, NULL);
+          qh->MERGEvertices= False;
+        LABELcheckdigit:
+          if (isdigit(*s))
+            qh_fprintf(qh, qh->ferr, 7017, "qhull warning: can not follow '1', '2', or '3' with a digit.  '%c' skipped.\n",
+                     *s++);
+          break;
+        case '4':
+          qh_option(qh, "Q4-avoid-old-into-new", NULL, NULL);
+          qh->AVOIDold= True;
+          break;
+        case '5':
+          qh_option(qh, "Q5-no-check-outer", NULL, NULL);
+          qh->SKIPcheckmax= True;
+          break;
+        case '6':
+          qh_option(qh, "Q6-no-concave-merge", NULL, NULL);
+          qh->SKIPconvex= True;
+          break;
+        case '7':
+          qh_option(qh, "Q7-no-breadth-first", NULL, NULL);
+          qh->VIRTUALmemory= True;
+          break;
+        case '8':
+          qh_option(qh, "Q8-no-near-inside", NULL, NULL);
+          qh->NOnearinside= True;
+          break;
+        case '9':
+          qh_option(qh, "Q9-pick-furthest", NULL, NULL);
+          qh->PICKfurthest= True;
+          break;
+        case 'G':
+          i= qh_strtol(s, &t);
+          if (qh->GOODpoint)
+            qh_fprintf(qh, qh->ferr, 7018, "qhull warning: good point already defined for option 'QGn'.  Ignored\n");
+          else if (s == t)
+            qh_fprintf(qh, qh->ferr, 7019, "qhull warning: missing good point id for option 'QGn'.  Ignored\n");
+          else if (i < 0 || *s == '-') {
+            qh->GOODpoint= i-1;
+            qh_option(qh, "QGood-if-dont-see-point", &i, NULL);
+          }else {
+            qh->GOODpoint= i+1;
+            qh_option(qh, "QGood-if-see-point", &i, NULL);
+          }
+          s= t;
+          break;
+        case 'J':
+          if (!isdigit(*s) && *s != '-')
+            qh->JOGGLEmax= 0.0;
+          else {
+            qh->JOGGLEmax= (realT) qh_strtod(s, &s);
+            qh_option(qh, "QJoggle", NULL, &qh->JOGGLEmax);
+          }
+          break;
+        case 'R':
+          if (!isdigit(*s) && *s != '-')
+            qh_fprintf(qh, qh->ferr, 7020, "qhull warning: missing random seed for option 'QRn'.  Ignored\n");
+          else {
+            qh->ROTATErandom= i= qh_strtol(s, &s);
+            if (i > 0)
+              qh_option(qh, "QRotate-id", &i, NULL );
+            else if (i < -1)
+              qh_option(qh, "QRandom-seed", &i, NULL );
+          }
+          break;
+        case 'V':
+          i= qh_strtol(s, &t);
+          if (qh->GOODvertex)
+            qh_fprintf(qh, qh->ferr, 7021, "qhull warning: good vertex already defined for option 'QVn'.  Ignored\n");
+          else if (s == t)
+            qh_fprintf(qh, qh->ferr, 7022, "qhull warning: no good point id given for option 'QVn'.  Ignored\n");
+          else if (i < 0) {
+            qh->GOODvertex= i - 1;
+            qh_option(qh, "QV-good-facets-not-point", &i, NULL);
+          }else {
+            qh_option(qh, "QV-good-facets-point", &i, NULL);
+            qh->GOODvertex= i + 1;
+          }
+          s= t;
+          break;
+        default:
+          s--;
+          qh_fprintf(qh, qh->ferr, 7023, "qhull warning: unknown 'Q' qhull option %c, rest ignored\n", (int)s[0]);
+          while (*++s && !isspace(*s));
+          break;
+        }
+      }
+      break;
+    case 'T':
+      while (*s && !isspace(*s)) {
+        if (isdigit(*s) || *s == '-')
+          qh->IStracing= qh_strtol(s, &s);
+        else switch (*s++) {
+        case 'a':
+          qh_option(qh, "Tannotate-output", NULL, NULL);
+          qh->ANNOTATEoutput= True;
+          break;
+        case 'c':
+          qh_option(qh, "Tcheck-frequently", NULL, NULL);
+          qh->CHECKfrequently= True;
+          break;
+        case 's':
+          qh_option(qh, "Tstatistics", NULL, NULL);
+          qh->PRINTstatistics= True;
+          break;
+        case 'v':
+          qh_option(qh, "Tverify", NULL, NULL);
+          qh->VERIFYoutput= True;
+          break;
+        case 'z':
+          if (qh->ferr == qh_FILEstderr) {
+            /* The C++ interface captures the output in qh_fprint_qhull() */
+            qh_option(qh, "Tz-stdout", NULL, NULL);
+            qh->USEstdout= True;
+          }else if (!qh->fout)
+            qh_fprintf(qh, qh->ferr, 7024, "qhull warning: output file undefined(stdout).  Option 'Tz' ignored.\n");
+          else {
+            qh_option(qh, "Tz-stdout", NULL, NULL);
+            qh->USEstdout= True;
+            qh->ferr= qh->fout;
+            qh->qhmem.ferr= qh->fout;
+          }
+          break;
+        case 'C':
+          if (!isdigit(*s))
+            qh_fprintf(qh, qh->ferr, 7025, "qhull warning: missing point id for cone for trace option 'TCn'.  Ignored\n");
+          else {
+            i= qh_strtol(s, &s);
+            qh_option(qh, "TCone-stop", &i, NULL);
+            qh->STOPcone= i + 1;
+          }
+          break;
+        case 'F':
+          if (!isdigit(*s))
+            qh_fprintf(qh, qh->ferr, 7026, "qhull warning: missing frequency count for trace option 'TFn'.  Ignored\n");
+          else {
+            qh->REPORTfreq= qh_strtol(s, &s);
+            qh_option(qh, "TFacet-log", &qh->REPORTfreq, NULL);
+            qh->REPORTfreq2= qh->REPORTfreq/2;  /* for tracemerging() */
+          }
+          break;
+        case 'I':
+          if (!isspace(*s))
+            qh_fprintf(qh, qh->ferr, 7027, "qhull warning: missing space between 'TI' and filename, %s\n", s);
+          while (isspace(*s))
+            s++;
+          t= qh_skipfilename(qh, s);
+          {
+            char filename[qh_FILENAMElen];
+
+            qh_copyfilename(qh, filename, (int)sizeof(filename), s, (int)(t-s));   /* WARN64 */
+            s= t;
+            if (!freopen(filename, "r", stdin)) {
+              qh_fprintf(qh, qh->ferr, 6041, "qhull error: could not open file \"%s\".", filename);
+              qh_errexit(qh, qh_ERRinput, NULL, NULL);
+            }else {
+              qh_option(qh, "TInput-file", NULL, NULL);
+              qh_option(qh, filename, NULL, NULL);
+            }
+          }
+          break;
+        case 'O':
+            if (!isspace(*s))
+                qh_fprintf(qh, qh->ferr, 7028, "qhull warning: missing space between 'TO' and filename, %s\n", s);
+            while (isspace(*s))
+                s++;
+            t= qh_skipfilename(qh, s);
+            {
+              char filename[qh_FILENAMElen];
+
+              qh_copyfilename(qh, filename, (int)sizeof(filename), s, (int)(t-s));  /* WARN64 */
+              s= t;
+              if (!qh->fout) {
+                qh_fprintf(qh, qh->ferr, 6266, "qhull input warning: qh.fout was not set by caller.  Cannot use option 'TO' to redirect output.  Ignoring option 'TO'\n");
+              }else if (!freopen(filename, "w", qh->fout)) {
+                qh_fprintf(qh, qh->ferr, 6044, "qhull error: could not open file \"%s\".", filename);
+                qh_errexit(qh, qh_ERRinput, NULL, NULL);
+              }else {
+                qh_option(qh, "TOutput-file", NULL, NULL);
+              qh_option(qh, filename, NULL, NULL);
+            }
+          }
+          break;
+        case 'P':
+          if (!isdigit(*s))
+            qh_fprintf(qh, qh->ferr, 7029, "qhull warning: missing point id for trace option 'TPn'.  Ignored\n");
+          else {
+            qh->TRACEpoint= qh_strtol(s, &s);
+            qh_option(qh, "Trace-point", &qh->TRACEpoint, NULL);
+          }
+          break;
+        case 'M':
+          if (!isdigit(*s))
+            qh_fprintf(qh, qh->ferr, 7030, "qhull warning: missing merge id for trace option 'TMn'.  Ignored\n");
+          else {
+            qh->TRACEmerge= qh_strtol(s, &s);
+            qh_option(qh, "Trace-merge", &qh->TRACEmerge, NULL);
+          }
+          break;
+        case 'R':
+          if (!isdigit(*s))
+            qh_fprintf(qh, qh->ferr, 7031, "qhull warning: missing rerun count for trace option 'TRn'.  Ignored\n");
+          else {
+            qh->RERUN= qh_strtol(s, &s);
+            qh_option(qh, "TRerun", &qh->RERUN, NULL);
+          }
+          break;
+        case 'V':
+          i= qh_strtol(s, &t);
+          if (s == t)
+            qh_fprintf(qh, qh->ferr, 7032, "qhull warning: missing furthest point id for trace option 'TVn'.  Ignored\n");
+          else if (i < 0) {
+            qh->STOPpoint= i - 1;
+            qh_option(qh, "TV-stop-before-point", &i, NULL);
+          }else {
+            qh->STOPpoint= i + 1;
+            qh_option(qh, "TV-stop-after-point", &i, NULL);
+          }
+          s= t;
+          break;
+        case 'W':
+          if (!isdigit(*s))
+            qh_fprintf(qh, qh->ferr, 7033, "qhull warning: missing max width for trace option 'TWn'.  Ignored\n");
+          else {
+            qh->TRACEdist= (realT) qh_strtod(s, &s);
+            qh_option(qh, "TWide-trace", NULL, &qh->TRACEdist);
+          }
+          break;
+        default:
+          s--;
+          qh_fprintf(qh, qh->ferr, 7034, "qhull warning: unknown 'T' trace option %c, rest ignored\n", (int)s[0]);
+          while (*++s && !isspace(*s));
+          break;
+        }
+      }
+      break;
+    default:
+      qh_fprintf(qh, qh->ferr, 7035, "qhull warning: unknown flag %c(%x)\n", (int)s[-1],
+               (int)s[-1]);
+      break;
+    }
+    if (s-1 == prev_s && *s && !isspace(*s)) {
+      qh_fprintf(qh, qh->ferr, 7036, "qhull warning: missing space after flag %c(%x); reserved for menu. Skipped.\n",
+               (int)*prev_s, (int)*prev_s);
+      while (*s && !isspace(*s))
+        s++;
+    }
+  }
+  if (qh->STOPcone && qh->JOGGLEmax < REALmax/2)
+    qh_fprintf(qh, qh->ferr, 7078, "qhull warning: 'TCn' (stopCone) ignored when used with 'QJn' (joggle)\n");
+  if (isgeom && !qh->FORCEoutput && qh->PRINTout[1])
+    qh_fprintf(qh, qh->ferr, 7037, "qhull warning: additional output formats are not compatible with Geomview\n");
+  /* set derived values in qh_initqhull_globals */
+} /* initflags */
+
+
+/*-<a                             href="qh-globa_r.htm#TOC"
+  >-------------------------------</a><a name="initqhull_buffers">-</a>
+
+  qh_initqhull_buffers(qh)
+    initialize global memory buffers
+
+  notes:
+    must match qh_freebuffers()
+*/
+void qh_initqhull_buffers(qhT *qh) {
+  int k;
+
+  qh->TEMPsize= (qh->qhmem.LASTsize - sizeof(setT))/SETelemsize;
+  if (qh->TEMPsize <= 0 || qh->TEMPsize > qh->qhmem.LASTsize)
+    qh->TEMPsize= 8;  /* e.g., if qh_NOmem */
+  qh->other_points= qh_setnew(qh, qh->TEMPsize);
+  qh->del_vertices= qh_setnew(qh, qh->TEMPsize);
+  qh->coplanarfacetset= qh_setnew(qh, qh->TEMPsize);
+  qh->NEARzero= (realT *)qh_memalloc(qh, qh->hull_dim * sizeof(realT));
+  qh->lower_threshold= (realT *)qh_memalloc(qh, (qh->input_dim+1) * sizeof(realT));
+  qh->upper_threshold= (realT *)qh_memalloc(qh, (qh->input_dim+1) * sizeof(realT));
+  qh->lower_bound= (realT *)qh_memalloc(qh, (qh->input_dim+1) * sizeof(realT));
+  qh->upper_bound= (realT *)qh_memalloc(qh, (qh->input_dim+1) * sizeof(realT));
+  for (k=qh->input_dim+1; k--; ) {  /* duplicated in qh_initqhull_buffers and qh_clear_outputflags */
+    qh->lower_threshold[k]= -REALmax;
+    qh->upper_threshold[k]= REALmax;
+    qh->lower_bound[k]= -REALmax;
+    qh->upper_bound[k]= REALmax;
+  }
+  qh->gm_matrix= (coordT *)qh_memalloc(qh, (qh->hull_dim+1) * qh->hull_dim * sizeof(coordT));
+  qh->gm_row= (coordT **)qh_memalloc(qh, (qh->hull_dim+1) * sizeof(coordT *));
+} /* initqhull_buffers */
+
+/*-<a                             href="qh-globa_r.htm#TOC"
+  >-------------------------------</a><a name="initqhull_globals">-</a>
+
+  qh_initqhull_globals(qh, points, numpoints, dim, ismalloc )
+    initialize globals
+    if ismalloc
+      points were malloc'd and qhull should free at end
+
+  returns:
+    sets qh.first_point, num_points, input_dim, hull_dim and others
+    seeds random number generator (seed=1 if tracing)
+    modifies qh.hull_dim if ((qh.DELAUNAY and qh.PROJECTdelaunay) or qh.PROJECTinput)
+    adjust user flags as needed
+    also checks DIM3 dependencies and constants
+
+  notes:
+    do not use qh_point() since an input transformation may move them elsewhere
+
+  see:
+    qh_initqhull_start() sets default values for non-zero globals
+
+  design:
+    initialize points array from input arguments
+    test for qh.ZEROcentrum
+      (i.e., use opposite vertex instead of cetrum for convexity testing)
+    initialize qh.CENTERtype, qh.normal_size,
+      qh.center_size, qh.TRACEpoint/level,
+    initialize and test random numbers
+    qh_initqhull_outputflags() -- adjust and test output flags
+*/
+void qh_initqhull_globals(qhT *qh, coordT *points, int numpoints, int dim, boolT ismalloc) {
+  int seed, pointsneeded, extra= 0, i, randi, k;
+  realT randr;
+  realT factorial;
+
+  time_t timedata;
+
+  trace0((qh, qh->ferr, 13, "qh_initqhull_globals: for %s | %s\n", qh->rbox_command,
+      qh->qhull_command));
+  qh->POINTSmalloc= ismalloc;
+  qh->first_point= points;
+  qh->num_points= numpoints;
+  qh->hull_dim= qh->input_dim= dim;
+  if (!qh->NOpremerge && !qh->MERGEexact && !qh->PREmerge && qh->JOGGLEmax > REALmax/2) {
+    qh->MERGING= True;
+    if (qh->hull_dim <= 4) {
+      qh->PREmerge= True;
+      qh_option(qh, "_pre-merge", NULL, NULL);
+    }else {
+      qh->MERGEexact= True;
+      qh_option(qh, "Qxact_merge", NULL, NULL);
+    }
+  }else if (qh->MERGEexact)
+    qh->MERGING= True;
+  if (!qh->NOpremerge && qh->JOGGLEmax > REALmax/2) {
+#ifdef qh_NOmerge
+    qh->JOGGLEmax= 0.0;
+#endif
+  }
+  if (qh->TRIangulate && qh->JOGGLEmax < REALmax/2 && qh->PRINTprecision)
+    qh_fprintf(qh, qh->ferr, 7038, "qhull warning: joggle('QJ') always produces simplicial output.  Triangulated output('Qt') does nothing.\n");
+  if (qh->JOGGLEmax < REALmax/2 && qh->DELAUNAY && !qh->SCALEinput && !qh->SCALElast) {
+    qh->SCALElast= True;
+    qh_option(qh, "Qbbound-last-qj", NULL, NULL);
+  }
+  if (qh->MERGING && !qh->POSTmerge && qh->premerge_cos > REALmax/2
+  && qh->premerge_centrum == 0) {
+    qh->ZEROcentrum= True;
+    qh->ZEROall_ok= True;
+    qh_option(qh, "_zero-centrum", NULL, NULL);
+  }
+  if (qh->JOGGLEmax < REALmax/2 && REALepsilon > 2e-8 && qh->PRINTprecision)
+    qh_fprintf(qh, qh->ferr, 7039, "qhull warning: real epsilon, %2.2g, is probably too large for joggle('QJn')\nRecompile with double precision reals(see user.h).\n",
+          REALepsilon);
+#ifdef qh_NOmerge
+  if (qh->MERGING) {
+    qh_fprintf(qh, qh->ferr, 6045, "qhull input error: merging not installed(qh_NOmerge + 'Qx', 'Cn' or 'An')\n");
+    qh_errexit(qh, qh_ERRinput, NULL, NULL);
+  }
+#endif
+  if (qh->DELAUNAY && qh->KEEPcoplanar && !qh->KEEPinside) {
+    qh->KEEPinside= True;
+    qh_option(qh, "Qinterior-keep", NULL, NULL);
+  }
+  if (qh->DELAUNAY && qh->HALFspace) {
+    qh_fprintf(qh, qh->ferr, 6046, "qhull input error: can not use Delaunay('d') or Voronoi('v') with halfspace intersection('H')\n");
+    qh_errexit(qh, qh_ERRinput, NULL, NULL);
+  }
+  if (!qh->DELAUNAY && (qh->UPPERdelaunay || qh->ATinfinity)) {
+    qh_fprintf(qh, qh->ferr, 6047, "qhull input error: use upper-Delaunay('Qu') or infinity-point('Qz') with Delaunay('d') or Voronoi('v')\n");
+    qh_errexit(qh, qh_ERRinput, NULL, NULL);
+  }
+  if (qh->UPPERdelaunay && qh->ATinfinity) {
+    qh_fprintf(qh, qh->ferr, 6048, "qhull input error: can not use infinity-point('Qz') with upper-Delaunay('Qu')\n");
+    qh_errexit(qh, qh_ERRinput, NULL, NULL);
+  }
+  if (qh->SCALElast && !qh->DELAUNAY && qh->PRINTprecision)
+    qh_fprintf(qh, qh->ferr, 7040, "qhull input warning: option 'Qbb' (scale-last-coordinate) is normally used with 'd' or 'v'\n");
+  qh->DOcheckmax= (!qh->SKIPcheckmax && qh->MERGING );
+  qh->KEEPnearinside= (qh->DOcheckmax && !(qh->KEEPinside && qh->KEEPcoplanar)
+                          && !qh->NOnearinside);
+  if (qh->MERGING)
+    qh->CENTERtype= qh_AScentrum;
+  else if (qh->VORONOI)
+    qh->CENTERtype= qh_ASvoronoi;
+  if (qh->TESTvneighbors && !qh->MERGING) {
+    qh_fprintf(qh, qh->ferr, 6049, "qhull input error: test vertex neighbors('Qv') needs a merge option\n");
+    qh_errexit(qh, qh_ERRinput, NULL ,NULL);
+  }
+  if (qh->PROJECTinput || (qh->DELAUNAY && qh->PROJECTdelaunay)) {
+    qh->hull_dim -= qh->PROJECTinput;
+    if (qh->DELAUNAY) {
+      qh->hull_dim++;
+      if (qh->ATinfinity)
+        extra= 1;
+    }
+  }
+  if (qh->hull_dim <= 1) {
+    qh_fprintf(qh, qh->ferr, 6050, "qhull error: dimension %d must be > 1\n", qh->hull_dim);
+    qh_errexit(qh, qh_ERRinput, NULL, NULL);
+  }
+  for (k=2, factorial=1.0; k < qh->hull_dim; k++)
+    factorial *= k;
+  qh->AREAfactor= 1.0 / factorial;
+  trace2((qh, qh->ferr, 2005, "qh_initqhull_globals: initialize globals.  dim %d numpoints %d malloc? %d projected %d to hull_dim %d\n",
+        dim, numpoints, ismalloc, qh->PROJECTinput, qh->hull_dim));
+  qh->normal_size= qh->hull_dim * sizeof(coordT);
+  qh->center_size= qh->normal_size - sizeof(coordT);
+  pointsneeded= qh->hull_dim+1;
+  if (qh->hull_dim > qh_DIMmergeVertex) {
+    qh->MERGEvertices= False;
+    qh_option(qh, "Q3-no-merge-vertices-dim-high", NULL, NULL);
+  }
+  if (qh->GOODpoint)
+    pointsneeded++;
+#ifdef qh_NOtrace
+  if (qh->IStracing) {
+    qh_fprintf(qh, qh->ferr, 6051, "qhull input error: tracing is not installed(qh_NOtrace in user.h)");
+    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+  }
+#endif
+  if (qh->RERUN > 1) {
+    qh->TRACElastrun= qh->IStracing; /* qh_build_withrestart duplicates next conditional */
+    if (qh->IStracing != -1)
+      qh->IStracing= 0;
+  }else if (qh->TRACEpoint != qh_IDunknown || qh->TRACEdist < REALmax/2 || qh->TRACEmerge) {
+    qh->TRACElevel= (qh->IStracing? qh->IStracing : 3);
+    qh->IStracing= 0;
+  }
+  if (qh->ROTATErandom == 0 || qh->ROTATErandom == -1) {
+    seed= (int)time(&timedata);
+    if (qh->ROTATErandom  == -1) {
+      seed= -seed;
+      qh_option(qh, "QRandom-seed", &seed, NULL );
+    }else
+      qh_option(qh, "QRotate-random", &seed, NULL);
+    qh->ROTATErandom= seed;
+  }
+  seed= qh->ROTATErandom;
+  if (seed == INT_MIN)    /* default value */
+    seed= 1;
+  else if (seed < 0)
+    seed= -seed;
+  qh_RANDOMseed_(qh, seed);
+  randr= 0.0;
+  for (i=1000; i--; ) {
+    randi= qh_RANDOMint;
+    randr += randi;
+    if (randi > qh_RANDOMmax) {
+      qh_fprintf(qh, qh->ferr, 8036, "\
+qhull configuration error (qh_RANDOMmax in user.h):\n\
+   random integer %d > qh_RANDOMmax(qh, %.8g)\n",
+               randi, qh_RANDOMmax);
+      qh_errexit(qh, qh_ERRinput, NULL, NULL);
+    }
+  }
+  qh_RANDOMseed_(qh, seed);
+  randr = randr/1000;
+  if (randr < qh_RANDOMmax * 0.1
+  || randr > qh_RANDOMmax * 0.9)
+    qh_fprintf(qh, qh->ferr, 8037, "\
+qhull configuration warning (qh_RANDOMmax in user.h):\n\
+   average of 1000 random integers (%.2g) is much different than expected (%.2g).\n\
+   Is qh_RANDOMmax (%.2g) wrong?\n",
+             randr, qh_RANDOMmax * 0.5, qh_RANDOMmax);
+  qh->RANDOMa= 2.0 * qh->RANDOMfactor/qh_RANDOMmax;
+  qh->RANDOMb= 1.0 - qh->RANDOMfactor;
+  if (qh_HASHfactor < 1.1) {
+    qh_fprintf(qh, qh->ferr, 6052, "qhull internal error (qh_initqhull_globals): qh_HASHfactor %d must be at least 1.1.  Qhull uses linear hash probing\n",
+      qh_HASHfactor);
+    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+  }
+  if (numpoints+extra < pointsneeded) {
+    qh_fprintf(qh, qh->ferr, 6214, "qhull input error: not enough points(%d) to construct initial simplex (need %d)\n",
+            numpoints, pointsneeded);
+    qh_errexit(qh, qh_ERRinput, NULL, NULL);
+  }
+  qh_initqhull_outputflags(qh);
+} /* initqhull_globals */
+
+/*-<a                             href="qh-globa_r.htm#TOC"
+  >-------------------------------</a><a name="initqhull_mem">-</a>
+
+  qh_initqhull_mem(qh, )
+    initialize mem_r.c for qhull
+    qh.hull_dim and qh.normal_size determine some of the allocation sizes
+    if qh.MERGING,
+      includes ridgeT
+    calls qh_user_memsizes(qh) to add up to 10 additional sizes for quick allocation
+      (see numsizes below)
+
+  returns:
+    mem_r.c already for qh_memalloc/qh_memfree (errors if called beforehand)
+
+  notes:
+    qh_produceoutput() prints memsizes
+
+*/
+void qh_initqhull_mem(qhT *qh) {
+  int numsizes;
+  int i;
+
+  numsizes= 8+10;
+  qh_meminitbuffers(qh, qh->IStracing, qh_MEMalign, numsizes,
+                     qh_MEMbufsize, qh_MEMinitbuf);
+  qh_memsize(qh, (int)sizeof(vertexT));
+  if (qh->MERGING) {
+    qh_memsize(qh, (int)sizeof(ridgeT));
+    qh_memsize(qh, (int)sizeof(mergeT));
+  }
+  qh_memsize(qh, (int)sizeof(facetT));
+  i= sizeof(setT) + (qh->hull_dim - 1) * SETelemsize;  /* ridge.vertices */
+  qh_memsize(qh, i);
+  qh_memsize(qh, qh->normal_size);        /* normal */
+  i += SETelemsize;                 /* facet.vertices, .ridges, .neighbors */
+  qh_memsize(qh, i);
+  qh_user_memsizes(qh);
+  qh_memsetup(qh);
+} /* initqhull_mem */
+
+/*-<a                             href="qh-globa_r.htm#TOC"
+  >-------------------------------</a><a name="initqhull_outputflags">-</a>
+
+  qh_initqhull_outputflags
+    initialize flags concerned with output
+
+  returns:
+    adjust user flags as needed
+
+  see:
+    qh_clear_outputflags() resets the flags
+
+  design:
+    test for qh.PRINTgood (i.e., only print 'good' facets)
+    check for conflicting print output options
+*/
+void qh_initqhull_outputflags(qhT *qh) {
+  boolT printgeom= False, printmath= False, printcoplanar= False;
+  int i;
+
+  trace3((qh, qh->ferr, 3024, "qh_initqhull_outputflags: %s\n", qh->qhull_command));
+  if (!(qh->PRINTgood || qh->PRINTneighbors)) {
+    if (qh->KEEParea || qh->KEEPminArea < REALmax/2 || qh->KEEPmerge || qh->DELAUNAY
+        || (!qh->ONLYgood && (qh->GOODvertex || qh->GOODpoint))) {
+      qh->PRINTgood= True;
+      qh_option(qh, "Pgood", NULL, NULL);
+    }
+  }
+  if (qh->PRINTtransparent) {
+    if (qh->hull_dim != 4 || !qh->DELAUNAY || qh->VORONOI || qh->DROPdim >= 0) {
+      qh_fprintf(qh, qh->ferr, 6215, "qhull input error: transparent Delaunay('Gt') needs 3-d Delaunay('d') w/o 'GDn'\n");
+      qh_errexit(qh, qh_ERRinput, NULL, NULL);
+    }
+    qh->DROPdim = 3;
+    qh->PRINTridges = True;
+  }
+  for (i=qh_PRINTEND; i--; ) {
+    if (qh->PRINTout[i] == qh_PRINTgeom)
+      printgeom= True;
+    else if (qh->PRINTout[i] == qh_PRINTmathematica || qh->PRINTout[i] == qh_PRINTmaple)
+      printmath= True;
+    else if (qh->PRINTout[i] == qh_PRINTcoplanars)
+      printcoplanar= True;
+    else if (qh->PRINTout[i] == qh_PRINTpointnearest)
+      printcoplanar= True;
+    else if (qh->PRINTout[i] == qh_PRINTpointintersect && !qh->HALFspace) {
+      qh_fprintf(qh, qh->ferr, 6053, "qhull input error: option 'Fp' is only used for \nhalfspace intersection('Hn,n,n').\n");
+      qh_errexit(qh, qh_ERRinput, NULL, NULL);
+    }else if (qh->PRINTout[i] == qh_PRINTtriangles && (qh->HALFspace || qh->VORONOI)) {
+      qh_fprintf(qh, qh->ferr, 6054, "qhull input error: option 'Ft' is not available for Voronoi vertices or halfspace intersection\n");
+      qh_errexit(qh, qh_ERRinput, NULL, NULL);
+    }else if (qh->PRINTout[i] == qh_PRINTcentrums && qh->VORONOI) {
+      qh_fprintf(qh, qh->ferr, 6055, "qhull input error: option 'FC' is not available for Voronoi vertices('v')\n");
+      qh_errexit(qh, qh_ERRinput, NULL, NULL);
+    }else if (qh->PRINTout[i] == qh_PRINTvertices) {
+      if (qh->VORONOI)
+        qh_option(qh, "Fvoronoi", NULL, NULL);
+      else
+        qh_option(qh, "Fvertices", NULL, NULL);
+    }
+  }
+  if (printcoplanar && qh->DELAUNAY && qh->JOGGLEmax < REALmax/2) {
+    if (qh->PRINTprecision)
+      qh_fprintf(qh, qh->ferr, 7041, "qhull input warning: 'QJ' (joggle) will usually prevent coincident input sites for options 'Fc' and 'FP'\n");
+  }
+  if (printmath && (qh->hull_dim > 3 || qh->VORONOI)) {
+    qh_fprintf(qh, qh->ferr, 6056, "qhull input error: Mathematica and Maple output is only available for 2-d and 3-d convex hulls and 2-d Delaunay triangulations\n");
+    qh_errexit(qh, qh_ERRinput, NULL, NULL);
+  }
+  if (printgeom) {
+    if (qh->hull_dim > 4) {
+      qh_fprintf(qh, qh->ferr, 6057, "qhull input error: Geomview output is only available for 2-d, 3-d and 4-d\n");
+      qh_errexit(qh, qh_ERRinput, NULL, NULL);
+    }
+    if (qh->PRINTnoplanes && !(qh->PRINTcoplanar + qh->PRINTcentrums
+     + qh->PRINTdots + qh->PRINTspheres + qh->DOintersections + qh->PRINTridges)) {
+      qh_fprintf(qh, qh->ferr, 6058, "qhull input error: no output specified for Geomview\n");
+      qh_errexit(qh, qh_ERRinput, NULL, NULL);
+    }
+    if (qh->VORONOI && (qh->hull_dim > 3 || qh->DROPdim >= 0)) {
+      qh_fprintf(qh, qh->ferr, 6059, "qhull input error: Geomview output for Voronoi diagrams only for 2-d\n");
+      qh_errexit(qh, qh_ERRinput, NULL, NULL);
+    }
+    /* can not warn about furthest-site Geomview output: no lower_threshold */
+    if (qh->hull_dim == 4 && qh->DROPdim == -1 &&
+        (qh->PRINTcoplanar || qh->PRINTspheres || qh->PRINTcentrums)) {
+      qh_fprintf(qh, qh->ferr, 7042, "qhull input warning: coplanars, vertices, and centrums output not\n\
+available for 4-d output(ignored).  Could use 'GDn' instead.\n");
+      qh->PRINTcoplanar= qh->PRINTspheres= qh->PRINTcentrums= False;
+    }
+  }
+  if (!qh->KEEPcoplanar && !qh->KEEPinside && !qh->ONLYgood) {
+    if ((qh->PRINTcoplanar && qh->PRINTspheres) || printcoplanar) {
+      if (qh->QHULLfinished) {
+        qh_fprintf(qh, qh->ferr, 7072, "qhull output warning: ignoring coplanar points, option 'Qc' was not set for the first run of qhull.\n");
+      }else {
+        qh->KEEPcoplanar = True;
+        qh_option(qh, "Qcoplanar", NULL, NULL);
+      }
+    }
+  }
+  qh->PRINTdim= qh->hull_dim;
+  if (qh->DROPdim >=0) {    /* after Geomview checks */
+    if (qh->DROPdim < qh->hull_dim) {
+      qh->PRINTdim--;
+      if (!printgeom || qh->hull_dim < 3)
+        qh_fprintf(qh, qh->ferr, 7043, "qhull input warning: drop dimension 'GD%d' is only available for 3-d/4-d Geomview\n", qh->DROPdim);
+    }else
+      qh->DROPdim= -1;
+  }else if (qh->VORONOI) {
+    qh->DROPdim= qh->hull_dim-1;
+    qh->PRINTdim= qh->hull_dim-1;
+  }
+} /* qh_initqhull_outputflags */
+
+/*-<a                             href="qh-globa_r.htm#TOC"
+  >-------------------------------</a><a name="initqhull_start">-</a>
+
+  qh_initqhull_start(qh, infile, outfile, errfile )
+    allocate memory if needed and call qh_initqhull_start2()
+*/
+void qh_initqhull_start(qhT *qh, FILE *infile, FILE *outfile, FILE *errfile) {
+
+  qh_initstatistics(qh);
+  qh_initqhull_start2(qh, infile, outfile, errfile);
+} /* initqhull_start */
+
+/*-<a                             href="qh-globa_r.htm#TOC"
+  >-------------------------------</a><a name="initqhull_start2">-</a>
+
+  qh_initqhull_start2(qh, infile, outfile, errfile )
+    start initialization of qhull
+    initialize statistics, stdio, default values for global variables
+    assumes qh is allocated
+  notes:
+    report errors elsewhere, error handling and g_qhull_output [Qhull.cpp, QhullQh()] not in initialized
+  see:
+    qh_maxmin() determines the precision constants
+    qh_freeqhull()
+*/
+void qh_initqhull_start2(qhT *qh, FILE *infile, FILE *outfile, FILE *errfile) {
+  time_t timedata;
+  int seed;
+
+  qh_CPUclock; /* start the clock(for qh_clock).  One-shot. */
+  /* memset is the same in qh_freeqhull() and qh_initqhull_start2() */
+  memset((char *)qh, 0, sizeof(qhT)-sizeof(qhmemT)-sizeof(qhstatT));   /* every field is 0, FALSE, NULL */
+  qh->NOerrexit= True;
+  qh->ANGLEmerge= True;
+  qh->DROPdim= -1;
+  qh->ferr= errfile;
+  qh->fin= infile;
+  qh->fout= outfile;
+  qh->furthest_id= qh_IDunknown;
+  qh->JOGGLEmax= REALmax;
+  qh->KEEPminArea = REALmax;
+  qh->last_low= REALmax;
+  qh->last_high= REALmax;
+  qh->last_newhigh= REALmax;
+  qh->last_random= 1;
+  qh->max_outside= 0.0;
+  qh->max_vertex= 0.0;
+  qh->MAXabs_coord= 0.0;
+  qh->MAXsumcoord= 0.0;
+  qh->MAXwidth= -REALmax;
+  qh->MERGEindependent= True;
+  qh->MINdenom_1= fmax_(1.0/REALmax, REALmin); /* used by qh_scalepoints */
+  qh->MINoutside= 0.0;
+  qh->MINvisible= REALmax;
+  qh->MAXcoplanar= REALmax;
+  qh->outside_err= REALmax;
+  qh->premerge_centrum= 0.0;
+  qh->premerge_cos= REALmax;
+  qh->PRINTprecision= True;
+  qh->PRINTradius= 0.0;
+  qh->postmerge_cos= REALmax;
+  qh->postmerge_centrum= 0.0;
+  qh->ROTATErandom= INT_MIN;
+  qh->MERGEvertices= True;
+  qh->totarea= 0.0;
+  qh->totvol= 0.0;
+  qh->TRACEdist= REALmax;
+  qh->TRACEpoint= qh_IDunknown; /* recompile or use 'TPn' */
+  qh->tracefacet_id= UINT_MAX;  /* recompile to trace a facet */
+  qh->tracevertex_id= UINT_MAX; /* recompile to trace a vertex */
+  seed= (int)time(&timedata);
+  qh_RANDOMseed_(qh, seed);
+  qh->run_id= qh_RANDOMint;
+  if(!qh->run_id)
+      qh->run_id++;  /* guarantee non-zero */
+  qh_option(qh, "run-id", &qh->run_id, NULL);
+  strcat(qh->qhull, "qhull");
+} /* initqhull_start2 */
+
+/*-<a                             href="qh-globa_r.htm#TOC"
+  >-------------------------------</a><a name="initthresholds">-</a>
+
+  qh_initthresholds(qh, commandString )
+    set thresholds for printing and scaling from commandString
+
+  returns:
+    sets qh.GOODthreshold or qh.SPLITthreshold if 'Pd0D1' used
+
+  see:
+    qh_initflags(), 'Qbk' 'QBk' 'Pdk' and 'PDk'
+    qh_inthresholds()
+
+  design:
+    for each 'Pdn' or 'PDn' option
+      check syntax
+      set qh.lower_threshold or qh.upper_threshold
+    set qh.GOODthreshold if an unbounded threshold is used
+    set qh.SPLITthreshold if a bounded threshold is used
+*/
+void qh_initthresholds(qhT *qh, char *command) {
+  realT value;
+  int idx, maxdim, k;
+  char *s= command; /* non-const due to strtol */
+  char key;
+
+  maxdim= qh->input_dim;
+  if (qh->DELAUNAY && (qh->PROJECTdelaunay || qh->PROJECTinput))
+    maxdim++;
+  while (*s) {
+    if (*s == '-')
+      s++;
+    if (*s == 'P') {
+      s++;
+      while (*s && !isspace(key= *s++)) {
+        if (key == 'd' || key == 'D') {
+          if (!isdigit(*s)) {
+            qh_fprintf(qh, qh->ferr, 7044, "qhull warning: no dimension given for Print option '%c' at: %s.  Ignored\n",
+                    key, s-1);
+            continue;
+          }
+          idx= qh_strtol(s, &s);
+          if (idx >= qh->hull_dim) {
+            qh_fprintf(qh, qh->ferr, 7045, "qhull warning: dimension %d for Print option '%c' is >= %d.  Ignored\n",
+                idx, key, qh->hull_dim);
+            continue;
+          }
+          if (*s == ':') {
+            s++;
+            value= qh_strtod(s, &s);
+            if (fabs((double)value) > 1.0) {
+              qh_fprintf(qh, qh->ferr, 7046, "qhull warning: value %2.4g for Print option %c is > +1 or < -1.  Ignored\n",
+                      value, key);
+              continue;
+            }
+          }else
+            value= 0.0;
+          if (key == 'd')
+            qh->lower_threshold[idx]= value;
+          else
+            qh->upper_threshold[idx]= value;
+        }
+      }
+    }else if (*s == 'Q') {
+      s++;
+      while (*s && !isspace(key= *s++)) {
+        if (key == 'b' && *s == 'B') {
+          s++;
+          for (k=maxdim; k--; ) {
+            qh->lower_bound[k]= -qh_DEFAULTbox;
+            qh->upper_bound[k]= qh_DEFAULTbox;
+          }
+        }else if (key == 'b' && *s == 'b')
+          s++;
+        else if (key == 'b' || key == 'B') {
+          if (!isdigit(*s)) {
+            qh_fprintf(qh, qh->ferr, 7047, "qhull warning: no dimension given for Qhull option %c.  Ignored\n",
+                    key);
+            continue;
+          }
+          idx= qh_strtol(s, &s);
+          if (idx >= maxdim) {
+            qh_fprintf(qh, qh->ferr, 7048, "qhull warning: dimension %d for Qhull option %c is >= %d.  Ignored\n",
+                idx, key, maxdim);
+            continue;
+          }
+          if (*s == ':') {
+            s++;
+            value= qh_strtod(s, &s);
+          }else if (key == 'b')
+            value= -qh_DEFAULTbox;
+          else
+            value= qh_DEFAULTbox;
+          if (key == 'b')
+            qh->lower_bound[idx]= value;
+          else
+            qh->upper_bound[idx]= value;
+        }
+      }
+    }else {
+      while (*s && !isspace(*s))
+        s++;
+    }
+    while (isspace(*s))
+      s++;
+  }
+  for (k=qh->hull_dim; k--; ) {
+    if (qh->lower_threshold[k] > -REALmax/2) {
+      qh->GOODthreshold= True;
+      if (qh->upper_threshold[k] < REALmax/2) {
+        qh->SPLITthresholds= True;
+        qh->GOODthreshold= False;
+        break;
+      }
+    }else if (qh->upper_threshold[k] < REALmax/2)
+      qh->GOODthreshold= True;
+  }
+} /* initthresholds */
+
+/*-<a                             href="qh-globa_r.htm#TOC"
+  >-------------------------------</a><a name="lib_check">-</a>
+
+  qh_lib_check( qhullLibraryType, qhTsize, vertexTsize, ridgeTsize, facetTsize, setTsize, qhmemTsize )
+    Report error if library does not agree with caller
+
+  notes:
+    NOerrors -- qh_lib_check can not call qh_errexit()
+*/
+void qh_lib_check(int qhullLibraryType, int qhTsize, int vertexTsize, int ridgeTsize, int facetTsize, int setTsize, int qhmemTsize) {
+    boolT iserror= False;
+
+#if defined(_MSC_VER) && defined(_DEBUG) && defined(QHULL_CRTDBG)  /* user_r.h */
+    // _CrtSetBreakAlloc(744);  /* Break at memalloc {744}, or 'watch' _crtBreakAlloc */
+    _CrtSetDbgFlag( _CRTDBG_ALLOC_MEM_DF | _CRTDBG_DELAY_FREE_MEM_DF | _CRTDBG_LEAK_CHECK_DF | _CrtSetDbgFlag(_CRTDBG_REPORT_FLAG) );
+    _CrtSetReportMode( _CRT_ERROR, _CRTDBG_MODE_FILE | _CRTDBG_MODE_DEBUG );
+    _CrtSetReportFile( _CRT_ERROR, _CRTDBG_FILE_STDERR );
+    _CrtSetReportMode( _CRT_WARN, _CRTDBG_MODE_FILE | _CRTDBG_MODE_DEBUG );
+    _CrtSetReportFile( _CRT_WARN, _CRTDBG_FILE_STDERR );
+    _CrtSetReportMode( _CRT_ASSERT, _CRTDBG_MODE_FILE | _CRTDBG_MODE_DEBUG );
+    _CrtSetReportFile( _CRT_ASSERT, _CRTDBG_FILE_STDERR );
+#endif
+
+    if (qhullLibraryType==QHULL_NON_REENTRANT) { /* 0 */
+        qh_fprintf_stderr(6257, "qh_lib_check: Incorrect qhull library called.  Caller uses non-reentrant Qhull with a static qhT.  Library is reentrant.\n");
+        iserror= True;
+    }else if (qhullLibraryType==QHULL_QH_POINTER) { /* 1 */
+        qh_fprintf_stderr(6258, "qh_lib_check: Incorrect qhull library called.  Caller uses non-reentrant Qhull with a dynamic qhT via qh_QHpointer.  Library is reentrant.\n");
+        iserror= True;
+    }else if (qhullLibraryType!=QHULL_REENTRANT) { /* 2 */
+        qh_fprintf_stderr(6262, "qh_lib_check: Expecting qhullLibraryType QHULL_NON_REENTRANT(0), QHULL_QH_POINTER(1), or QHULL_REENTRANT(2).  Got %d\n", qhullLibraryType);
+        iserror= True;
+    }
+    if (qhTsize != sizeof(qhT)) {
+        qh_fprintf_stderr(6249, "qh_lib_check: Incorrect qhull library called.  Size of qhT for caller is %d, but for library is %d.\n", qhTsize, sizeof(qhT));
+        iserror= True;
+    }
+    if (vertexTsize != sizeof(vertexT)) {
+        qh_fprintf_stderr(6250, "qh_lib_check: Incorrect qhull library called.  Size of vertexT for caller is %d, but for library is %d.\n", vertexTsize, sizeof(vertexT));
+        iserror= True;
+    }
+    if (ridgeTsize != sizeof(ridgeT)) {
+        qh_fprintf_stderr(6251, "qh_lib_check: Incorrect qhull library called.  Size of ridgeT for caller is %d, but for library is %d.\n", ridgeTsize, sizeof(ridgeT));
+        iserror= True;
+    }
+    if (facetTsize != sizeof(facetT)) {
+        qh_fprintf_stderr(6252, "qh_lib_check: Incorrect qhull library called.  Size of facetT for caller is %d, but for library is %d.\n", facetTsize, sizeof(facetT));
+        iserror= True;
+    }
+    if (setTsize && setTsize != sizeof(setT)) {
+        qh_fprintf_stderr(6253, "qh_lib_check: Incorrect qhull library called.  Size of setT for caller is %d, but for library is %d.\n", setTsize, sizeof(setT));
+        iserror= True;
+    }
+    if (qhmemTsize && qhmemTsize != sizeof(qhmemT)) {
+        qh_fprintf_stderr(6254, "qh_lib_check: Incorrect qhull library called.  Size of qhmemT for caller is %d, but for library is %d.\n", qhmemTsize, sizeof(qhmemT));
+        iserror= True;
+    }
+    if (iserror) {
+        qh_fprintf_stderr(6259, "qh_lib_check: Cannot continue.  Library '%s' is reentrant (e.g., qhull_r.so)\n", qh_version2);
+        qh_exit(qh_ERRqhull);  /* can not use qh_errexit() */
+    }
+} /* lib_check */
+
+/*-<a                             href="qh-globa_r.htm#TOC"
+  >-------------------------------</a><a name="option">-</a>
+
+  qh_option(qh, option, intVal, realVal )
+    add an option description to qh.qhull_options
+
+  notes:
+    NOerrors -- qh_option can not call qh_errexit() [qh_initqhull_start2]
+    will be printed with statistics ('Ts') and errors
+    strlen(option) < 40
+*/
+void qh_option(qhT *qh, const char *option, int *i, realT *r) {
+  char buf[200];
+  int len, maxlen;
+
+  sprintf(buf, "  %s", option);
+  if (i)
+    sprintf(buf+strlen(buf), " %d", *i);
+  if (r)
+    sprintf(buf+strlen(buf), " %2.2g", *r);
+  len= (int)strlen(buf);  /* WARN64 */
+  qh->qhull_optionlen += len;
+  maxlen= sizeof(qh->qhull_options) - len -1;
+  maximize_(maxlen, 0);
+  if (qh->qhull_optionlen >= qh_OPTIONline && maxlen > 0) {
+    qh->qhull_optionlen= len;
+    strncat(qh->qhull_options, "\n", (size_t)(maxlen--));
+  }
+  strncat(qh->qhull_options, buf, (size_t)maxlen);
+} /* option */
+
+/*-<a                             href="qh-globa_r.htm#TOC"
+  >-------------------------------</a><a name="zero">-</a>
+
+  qh_zero( qh, errfile )
+    Initialize and zero Qhull's memory for qh_new_qhull()
+
+  notes:
+    Not needed in global.c because static variables are initialized to zero
+*/
+void qh_zero(qhT *qh, FILE *errfile) {
+    memset((char *)qh, 0, sizeof(qhT));   /* every field is 0, FALSE, NULL */
+    qh->NOerrexit= True;
+    qh_meminit(qh, errfile);
+} /* zero */
+
diff --git a/xs/src/qhull/src/libqhull_r/index.htm b/xs/src/qhull/src/libqhull_r/index.htm
new file mode 100644
index 0000000000..c62030e06b
--- /dev/null
+++ b/xs/src/qhull/src/libqhull_r/index.htm
@@ -0,0 +1,266 @@
+<!-- Do not edit with Front Page, it adds too many spaces -->
+<html>
+<head>
+<meta http-equiv="Content-Type"
+content="text/html; charset=iso-8859-1">
+<title>Reentrant Qhull functions, macros, and data structures</title>
+</head>
+
+<body>
+<!-- Navigation links -->
+<p><a name="TOP"><b>Up:</b></a> <a
+href="http://www.qhull.org">Home page</a> for Qhull<br>
+<b>Up:</b> <a href="../../html/index.htm#TOC">Qhull manual</a>: Table of Contents <br>
+<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a>
+&#149; <a href="../../html/qh-quick.htm#options">Options</a>
+&#149; <a href="../../html/qh-opto.htm#output">Output</a>
+&#149; <a href="../../html/qh-optf.htm#format">Formats</a>
+&#149; <a href="../../html/qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="../../html/qh-optp.htm#print">Print</a>
+&#149; <a href="../../html/qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="../../html/qh-optc.htm#prec">Precision</a>
+&#149; <a href="../../html/qh-optt.htm#trace">Trace</a>
+&#149; <a href="index.htm">Functions</a><br>
+<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code</a><br>
+<b>To:</b> <a href="#TOC">Qhull files</a><br>
+<b>To:</b> <a href="qh-geom_r.htm">Geom</a> &#149; <a href="qh-globa_r.htm">Global</a>
+&#149; <a href="qh-io_r.htm">Io</a> &#149; <a href="qh-mem_r.htm">Mem</a>
+&#149; <a href="qh-merge_r.htm">Merge</a> &#149; <a href="qh-poly_r.htm">Poly</a>
+&#149; <a href="qh-qhull_r.htm">Qhull</a> &#149; <a href="qh-set_r.htm">Set</a>
+&#149; <a href="qh-stat_r.htm">Stat</a> &#149; <a href="qh-user_r.htm">User</a>
+
+<hr>
+<!-- Main text of document. -->
+
+<h1>Reentrant Qhull functions, macros, and data structures</h1>
+<blockquote>
+<p>The following sections provide an overview and index to
+reentrant Qhull's functions, macros, and data structures.
+Each section starts with an introduction.
+See also <a href=../../html/qh-code.htm#library>Calling
+Qhull from C programs</a> and <a href="../../html/qh-code.htm#cpp">Calling Qhull from C++ programs</a>.</p>
+
+<p>Qhull uses the following conventions:</p>
+<blockquote>
+
+<ul>
+<li>in code, global variables start with &quot;qh &quot;
+<li>in documentation, global variables start with 'qh.'
+<li>constants start with an upper case word
+<li>important globals include an '_'
+<li>functions, macros, and constants start with &quot;qh_&quot;</li>
+<li>data types end in &quot;T&quot;</li>
+<li>macros with arguments end in &quot;_&quot;</li>
+<li>iterators are macros that use local variables</li>
+<li>iterators for sets start with &quot;FOREACH&quot;</li>
+<li>iterators for lists start with &quot;FORALL&quot;</li>
+<li>qhull options are in single quotes (e.g., 'Pdn')</li>
+<li>lists are sorted alphabetically</li>
+<li>preprocessor directives on left margin for older compilers</li>
+</ul>
+</blockquote>
+<p>
+Reentrant Qhull is nearly the same as non-reentrant Qhull.  In reentrant
+Qhull, the qhT data structure is the first parameter to most functions. Qhull accesses
+this data structure with 'qh->...'.
+In non-reentrant Qhull, the global data structure is either a struct (qh_QHpointer==0)
+or a pointer (qh_QHpointer==1).  The non-reentrant code looks different because this data
+structure is accessed via the 'qh' macro.   This macro expands to 'qh_qh.' or 'qh_qh->' (resp.).
+<p>
+When reading code with an editor, a search for
+'<i>&quot;function</i>'
+will locate the header of <i>qh_function</i>.  A search for '<i>* function</i>'
+will locate the tail of <i>qh_function</i>.
+
+<p>A useful starting point is <a href="libqhull_r.h">libqhull_r.h</a>.  It defines most
+of Qhull data structures and top-level functions.  Search for <i>'PFn'</i> to
+determine the corresponding constant in Qhull.  Search for <i>'Fp'</i> to
+determine the corresponding <a href="libqhull_r.h#qh_PRINT">qh_PRINT...</a> constant.
+Search <a href="io_r.c">io_r.c</a> to learn how the print function is implemented.</p>
+
+<p>If your web browser is configured for .c and .h files, the function, macro, and data type links
+go to the corresponding source location.  To configure your web browser for .c and .h files.
+<ul>
+<li>In the Download Preferences or Options panel, add file extensions 'c' and 'h' to mime type 'text/html'.
+<li>Opera 12.10
+<ol>
+<li>In Tools > Preferences > Advanced > Downloads
+<li>Uncheck 'Hide file types opened with Opera'
+<li>Quick find 'html'
+<li>Select 'text/html' > Edit
+<li>Add File extensions 'c,h,'
+<li>Click 'OK'
+</ol>
+<li>Internet Explorer -- Mime types are not available from 'Internet Options'.    Is there a registry key for these settings?
+<li>Firefox -- Mime types are not available from 'Preferences'.  Is there an add-on to change the file extensions for a mime type?
+<li>Chrome -- Can Chrome be configured?
+</ul>
+
+<p>
+Please report documentation and link errors
+to <a href="mailto:qhull-bug@qhull.org">qhull-bug@qhull.org</a>.
+</blockquote>
+
+<p><b>Copyright &copy; 1997-2015 C.B. Barber</b></p>
+
+<hr>
+
+<h2><a href="#TOP">&#187;</a><a name="TOC">Qhull files</a> </h2>
+<blockquote>
+
+<p>This sections lists the .c and .h files for Qhull. Please
+refer to these files for detailed information.</p>
+<blockquote>
+
+<dl>
+<dt><a href="../../Makefile"><b>Makefile</b></a><b>, </b><a href="../../CMakeLists.txt"><b>CMakeLists.txt</b></a></dt>
+<dd><tt>Makefile</tt> is preconfigured for gcc.  <tt>CMakeLists.txt</tt> supports multiple
+platforms with <a href=http://www.cmake.org/>CMake</a>.
+Qhull includes project files for Visual Studio and Qt.
+</dd>
+
+<dt>&nbsp;</dt>
+<dt><a href="libqhull_r.h"><b>libqhull_r.h</b></a> </dt>
+<dd>Include file for the Qhull library (<tt>libqhull.so</tt>, <tt>qhull.dll</tt>, <tt>libqhullstatic.a</tt>).
+Data structures are documented under <a href="qh-poly_r.htm">Poly</a>.
+Global variables are documented under <a href="qh-globa_r.htm">Global</a>.
+Other data structures and variables are documented under
+<a href="qh-qhull_r.htm#TOC">Qhull</a> or <a href="qh-geom_r.htm"><b>Geom</b></a><b>.</b></dd>
+
+<dt>&nbsp;</dt>
+<dt><a href="qh-geom_r.htm"><b>Geom</b></a><b>, </b>
+<a href="geom_r.h"><b>geom_r.h</b></a><b>, </b>
+<a href="geom_r.c"><b>geom_r.c</b></a><b>, </b>
+<a href="geom2_r.c"><b>geom2_r.c</b></a><b>, </b>
+<a href="random_r.c"><b>random_r.c</b></a><b>, </b>
+<a href="random_r.h"><b>random_r.h</b></a></dt>
+<dd>Geometric routines. These routines implement mathematical
+functions such as Gaussian elimination and geometric
+routines needed for Qhull. Frequently used routines are
+in <tt>geom_r.c</tt> while infrequent ones are in <tt>geom2_r.c</tt>.
+</dd>
+
+<dt>&nbsp;</dt>
+<dt><a href="qh-globa_r.htm"><b>Global</b></a><b>, </b>
+<a href="global_r.c"><b>global_r.c</b></a><b>, </b>
+<a href="libqhull_r.h"><b>libqhull_r.h</b></a> </dt>
+<dd>Global routines. Qhull uses a global data structure, <tt>qh</tt>,
+to store globally defined constants, lists, sets, and
+variables.
+<tt>global_r.c</tt> initializes and frees these
+structures. </dd>
+
+<dt>&nbsp;</dt>
+<dt><a href="qh-io_r.htm"><b>Io</b></a><b>, </b><a href="io_r.h"><b>io_r.h</b></a><b>,
+</b><a href="io_r.c"><b>io_r.c</b></a> </dt>
+<dd>Input and output routines. Qhull provides a wide range of
+input and output options.</dd>
+
+<dt>&nbsp;</dt>
+<dt><a href="qh-mem_r.htm"><b>Mem</b></a><b>, </b>
+<a href="mem_r.h"><b>mem_r.h</b></a><b>, </b>
+<a href="mem_r.c"><b>mem_r.c</b></a> </dt>
+<dd>Memory routines. Qhull provides memory allocation and
+deallocation. It uses quick-fit allocation.</dd>
+
+<dt>&nbsp;</dt>
+<dt><a href="qh-merge_r.htm"><b>Merge</b></a><b>, </b>
+<a href="merge_r.h"><b>merge_r.h</b></a><b>, </b>
+<a href="merge_r.c"><b>merge_r.c</b></a> </dt>
+<dd>Merge routines. Qhull handles precision problems by
+merged facets or joggled input. These routines merge simplicial facets,
+merge non-simplicial facets, merge cycles of facets, and
+rename redundant vertices.</dd>
+
+<dt>&nbsp;</dt>
+<dt><a href="qh-poly_r.htm"><b>Poly</b></a><b>, </b>
+<a href="poly_r.h"><b>poly_r.h</b></a><b>, </b>
+<a href="poly_r.c"><b>poly_r.c</b></a><b>, </b>
+<a href="poly2_r.c"><b>poly2_r.c</b></a><b>, </b>
+<a href="libqhull_r.h"><b>libqhull_r.h</b></a> </dt>
+<dd>Polyhedral routines. Qhull produces a polyhedron as a
+list of facets with vertices, neighbors, ridges, and
+geometric information. <tt>libqhull_r.h</tt> defines the main
+data structures. Frequently used routines are in <tt>poly_r.c</tt>
+while infrequent ones are in <tt>poly2_r.c</tt>.</dd>
+
+<dt>&nbsp;</dt>
+<dt><a href="qh-qhull_r.htm#TOC"><b>Qhull</b></a><b>, </b>
+<a href="libqhull_r.c"><b>libqhull_r.c</b></a><b>, </b>
+<a href="libqhull_r.h"><b>libqhull_r.h</b></a><b>, </b>
+<a href="qhull_ra.h"><b>qhull_ra.h</b></a><b>, </b>
+<a href="../qhull/unix_r.c"><b>unix_r.c</b></a> <b>, </b>
+<a href="../qconvex/qconvex_r.c"><b>qconvex_r.c</b></a> <b>, </b>
+<a href="../qdelaunay/qdelaun_r.c"><b>qdelaun_r.c</b></a> <b>, </b>
+<a href="../qhalf/qhalf_r.c"><b>qhalf_r.c</b></a> <b>, </b>
+<a href="../qvoronoi/qvoronoi_r.c"><b>qvoronoi_r.c</b></a> </dt>
+<dd>Top-level routines. The Quickhull algorithm is
+implemented by <tt>libqhull_r.c</tt>. <tt>qhull_ra.h</tt>
+includes all header files. </dd>
+
+<dt>&nbsp;</dt>
+<dt><a href="qh-set_r.htm"><b>Set</b></a><b>, </b>
+<a href="qset_r.h"><b>qset_r.h</b></a><b>, </b>
+<a href="qset_r.c"><b>qset_r.c</b></a> </dt>
+<dd>Set routines. Qhull implements its data structures as
+sets. A set is an array of pointers that is expanded as
+needed. This is a separate package that may be used in
+other applications. </dd>
+
+<dt>&nbsp;</dt>
+<dt><a href="qh-stat_r.htm"><b>Stat</b></a><b>, </b>
+<a href="stat_r.h"><b>stat_r.h</b></a><b>, </b>
+<a href="stat_r.c"><b>stat_r.c</b></a> </dt>
+<dd>Statistical routines. Qhull maintains statistics about
+its implementation. </dd>
+
+<dt>&nbsp;</dt>
+<dt><a href="qh-user_r.htm"><b>User</b></a><b>, </b>
+<a href="user_r.h"><b>user_r.h</b></a><b>, </b>
+<a href="user_r.c"><b>user_r.c</b></a><b>, </b>
+<a href="../user_eg/user_eg_r.c"><b>user_eg_r.c</b></a><b>, </b>
+<a href="../user_eg2/user_eg2_r.c"><b>user_eg2_r.c</b></a><b>, </b>
+<a href="../user_eg3/user_eg3_r.cpp"><b>user_eg3_r.cpp</b></a><b>, </b>
+</dt>
+<dd>User-defined routines. Qhull allows the user to configure
+the code with defined constants and specialized routines.
+</dd>
+</dl>
+</blockquote>
+
+</blockquote>
+<p><!-- Navigation links --> </p>
+<hr>
+<p><b>Up:</b>
+<a href="http://www.qhull.org">Home page for
+Qhull</a> <br>
+<b>Up:</b> <a href="../../html/index.htm#TOC">Qhull manual: Table of Contents</a> <br>
+<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a>
+&#149; <a href="../../html/qh-quick.htm#options">Options</a>
+&#149; <a href="../../html/qh-opto.htm#output">Output</a>
+&#149; <a href="../../html/qh-optf.htm#format">Formats</a>
+&#149; <a href="../../html/qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="../../html/qh-optp.htm#print">Print</a>
+&#149; <a href="../../html/qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="../../html/qh-optc.htm#prec">Precision</a>
+&#149; <a href="../../html/qh-optt.htm#trace">Trace</a>
+&#149; <a href="index.htm">Functions</a><br>
+<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code: Table of Contents</a> <br>
+<b>To:</b> <a href="#TOC">Qhull files</a><br>
+<b>To:</b> <a href="qh-geom_r.htm">Geom</a> &#149;
+<a href="qh-globa_r.htm">Global</a> &#149; <a href="qh-io_r.htm">Io</a>
+&#149; <a href="qh-mem_r.htm">Mem</a> &#149; <a href="qh-merge_r.htm">Merge</a>
+&#149; <a href="qh-poly_r.htm">Poly</a> &#149; <a href="qh-qhull_r.htm#TOC">Qhull</a>
+&#149; <a href="qh-set_r.htm">Set</a> &#149; <a href="qh-stat_r.htm">Stat</a>
+&#149; <a href="qh-user_r.htm">User</a><br>
+
+<p><!-- GC common information --> </p>
+<hr>
+<p><a href="http://www.geom.uiuc.edu/"><img
+src="../../html/qh--geom.gif" align="middle" width="40" height="40"></a><i>The
+Geometry Center Home Page </i></p>
+<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
+</a><br>
+Created: May 2, 1997 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
+</body>
+</html>
diff --git a/xs/src/qhull/src/libqhull_r/io_r.c b/xs/src/qhull/src/libqhull_r/io_r.c
new file mode 100644
index 0000000000..9721a000dd
--- /dev/null
+++ b/xs/src/qhull/src/libqhull_r/io_r.c
@@ -0,0 +1,4062 @@
+/*<html><pre>  -<a                             href="qh-io_r.htm"
+  >-------------------------------</a><a name="TOP">-</a>
+
+   io_r.c
+   Input/Output routines of qhull application
+
+   see qh-io_r.htm and io_r.h
+
+   see user_r.c for qh_errprint and qh_printfacetlist
+
+   unix_r.c calls qh_readpoints and qh_produce_output
+
+   unix_r.c and user_r.c are the only callers of io_r.c functions
+   This allows the user to avoid loading io_r.o from qhull.a
+
+   Copyright (c) 1993-2015 The Geometry Center.
+   $Id: //main/2015/qhull/src/libqhull_r/io_r.c#4 $$Change: 2064 $
+   $DateTime: 2016/01/18 12:36:08 $$Author: bbarber $
+*/
+
+#include "qhull_ra.h"
+
+/*========= -functions in alphabetical order after qh_produce_output(qh)  =====*/
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="produce_output">-</a>
+
+  qh_produce_output(qh)
+  qh_produce_output2(qh)
+    prints out the result of qhull in desired format
+    qh_produce_output2(qh) does not call qh_prepare_output(qh)
+    if qh.GETarea
+      computes and prints area and volume
+    qh.PRINTout[] is an array of output formats
+
+  notes:
+    prints output in qh.PRINTout order
+*/
+void qh_produce_output(qhT *qh) {
+    int tempsize= qh_setsize(qh, qh->qhmem.tempstack);
+
+    qh_prepare_output(qh);
+    qh_produce_output2(qh);
+    if (qh_setsize(qh, qh->qhmem.tempstack) != tempsize) {
+        qh_fprintf(qh, qh->ferr, 6206, "qhull internal error (qh_produce_output): temporary sets not empty(%d)\n",
+            qh_setsize(qh, qh->qhmem.tempstack));
+        qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+    }
+} /* produce_output */
+
+
+void qh_produce_output2(qhT *qh) {
+  int i, tempsize= qh_setsize(qh, qh->qhmem.tempstack), d_1;
+
+  if (qh->PRINTsummary)
+    qh_printsummary(qh, qh->ferr);
+  else if (qh->PRINTout[0] == qh_PRINTnone)
+    qh_printsummary(qh, qh->fout);
+  for (i=0; i < qh_PRINTEND; i++)
+    qh_printfacets(qh, qh->fout, qh->PRINTout[i], qh->facet_list, NULL, !qh_ALL);
+  qh_allstatistics(qh);
+  if (qh->PRINTprecision && !qh->MERGING && (qh->JOGGLEmax > REALmax/2 || qh->RERUN))
+    qh_printstats(qh, qh->ferr, qh->qhstat.precision, NULL);
+  if (qh->VERIFYoutput && (zzval_(Zridge) > 0 || zzval_(Zridgemid) > 0))
+    qh_printstats(qh, qh->ferr, qh->qhstat.vridges, NULL);
+  if (qh->PRINTstatistics) {
+    qh_printstatistics(qh, qh->ferr, "");
+    qh_memstatistics(qh, qh->ferr);
+    d_1= sizeof(setT) + (qh->hull_dim - 1) * SETelemsize;
+    qh_fprintf(qh, qh->ferr, 8040, "\
+    size in bytes: merge %d ridge %d vertex %d facet %d\n\
+         normal %d ridge vertices %d facet vertices or neighbors %d\n",
+            (int)sizeof(mergeT), (int)sizeof(ridgeT),
+            (int)sizeof(vertexT), (int)sizeof(facetT),
+            qh->normal_size, d_1, d_1 + SETelemsize);
+  }
+  if (qh_setsize(qh, qh->qhmem.tempstack) != tempsize) {
+    qh_fprintf(qh, qh->ferr, 6065, "qhull internal error (qh_produce_output2): temporary sets not empty(%d)\n",
+             qh_setsize(qh, qh->qhmem.tempstack));
+    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+  }
+} /* produce_output2 */
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="dfacet">-</a>
+
+  qh_dfacet(qh, id )
+    print facet by id, for debugging
+
+*/
+void qh_dfacet(qhT *qh, unsigned id) {
+  facetT *facet;
+
+  FORALLfacets {
+    if (facet->id == id) {
+      qh_printfacet(qh, qh->fout, facet);
+      break;
+    }
+  }
+} /* dfacet */
+
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="dvertex">-</a>
+
+  qh_dvertex(qh, id )
+    print vertex by id, for debugging
+*/
+void qh_dvertex(qhT *qh, unsigned id) {
+  vertexT *vertex;
+
+  FORALLvertices {
+    if (vertex->id == id) {
+      qh_printvertex(qh, qh->fout, vertex);
+      break;
+    }
+  }
+} /* dvertex */
+
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="compare_facetarea">-</a>
+
+  qh_compare_facetarea(p1, p2 )
+    used by qsort() to order facets by area
+*/
+int qh_compare_facetarea(const void *p1, const void *p2) {
+  const facetT *a= *((facetT *const*)p1), *b= *((facetT *const*)p2);
+
+  if (!a->isarea)
+    return -1;
+  if (!b->isarea)
+    return 1;
+  if (a->f.area > b->f.area)
+    return 1;
+  else if (a->f.area == b->f.area)
+    return 0;
+  return -1;
+} /* compare_facetarea */
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="compare_facetmerge">-</a>
+
+  qh_compare_facetmerge(p1, p2 )
+    used by qsort() to order facets by number of merges
+*/
+int qh_compare_facetmerge(const void *p1, const void *p2) {
+  const facetT *a= *((facetT *const*)p1), *b= *((facetT *const*)p2);
+
+  return(a->nummerge - b->nummerge);
+} /* compare_facetvisit */
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="compare_facetvisit">-</a>
+
+  qh_compare_facetvisit(p1, p2 )
+    used by qsort() to order facets by visit id or id
+*/
+int qh_compare_facetvisit(const void *p1, const void *p2) {
+  const facetT *a= *((facetT *const*)p1), *b= *((facetT *const*)p2);
+  int i,j;
+
+  if (!(i= a->visitid))
+    i= 0 - a->id; /* do not convert to int, sign distinguishes id from visitid */
+  if (!(j= b->visitid))
+    j= 0 - b->id;
+  return(i - j);
+} /* compare_facetvisit */
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="compare_vertexpoint">-</a>
+
+  qh_compare_vertexpoint( p1, p2 )
+    used by qsort() to order vertices by point id
+
+  Not usable in qhulllib_r since qh_pointid depends on qh
+
+  int qh_compare_vertexpoint(const void *p1, const void *p2) {
+  const vertexT *a= *((vertexT *const*)p1), *b= *((vertexT *const*)p2);
+
+  return((qh_pointid(qh, a->point) > qh_pointid(qh, b->point)?1:-1));
+}*/
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="copyfilename">-</a>
+
+  qh_copyfilename(qh, dest, size, source, length )
+    copy filename identified by qh_skipfilename()
+
+  notes:
+    see qh_skipfilename() for syntax
+*/
+void qh_copyfilename(qhT *qh, char *filename, int size, const char* source, int length) {
+  char c= *source;
+
+  if (length > size + 1) {
+      qh_fprintf(qh, qh->ferr, 6040, "qhull error: filename is more than %d characters, %s\n",  size-1, source);
+      qh_errexit(qh, qh_ERRinput, NULL, NULL);
+  }
+  strncpy(filename, source, length);
+  filename[length]= '\0';
+  if (c == '\'' || c == '"') {
+    char *s= filename + 1;
+    char *t= filename;
+    while (*s) {
+      if (*s == c) {
+          if (s[-1] == '\\')
+              t[-1]= c;
+      }else
+          *t++= *s;
+      s++;
+    }
+    *t= '\0';
+  }
+} /* copyfilename */
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="countfacets">-</a>
+
+  qh_countfacets(qh, facetlist, facets, printall,
+          numfacets, numsimplicial, totneighbors, numridges, numcoplanar, numtricoplanars  )
+    count good facets for printing and set visitid
+    if allfacets, ignores qh_skipfacet()
+
+  notes:
+    qh_printsummary and qh_countfacets must match counts
+
+  returns:
+    numfacets, numsimplicial, total neighbors, numridges, coplanars
+    each facet with ->visitid indicating 1-relative position
+      ->visitid==0 indicates not good
+
+  notes
+    numfacets >= numsimplicial
+    if qh.NEWfacets,
+      does not count visible facets (matches qh_printafacet)
+
+  design:
+    for all facets on facetlist and in facets set
+      unless facet is skipped or visible (i.e., will be deleted)
+        mark facet->visitid
+        update counts
+*/
+void qh_countfacets(qhT *qh, facetT *facetlist, setT *facets, boolT printall,
+    int *numfacetsp, int *numsimplicialp, int *totneighborsp, int *numridgesp, int *numcoplanarsp, int *numtricoplanarsp) {
+  facetT *facet, **facetp;
+  int numfacets= 0, numsimplicial= 0, numridges= 0, totneighbors= 0, numcoplanars= 0, numtricoplanars= 0;
+
+  FORALLfacet_(facetlist) {
+    if ((facet->visible && qh->NEWfacets)
+    || (!printall && qh_skipfacet(qh, facet)))
+      facet->visitid= 0;
+    else {
+      facet->visitid= ++numfacets;
+      totneighbors += qh_setsize(qh, facet->neighbors);
+      if (facet->simplicial) {
+        numsimplicial++;
+        if (facet->keepcentrum && facet->tricoplanar)
+          numtricoplanars++;
+      }else
+        numridges += qh_setsize(qh, facet->ridges);
+      if (facet->coplanarset)
+        numcoplanars += qh_setsize(qh, facet->coplanarset);
+    }
+  }
+
+  FOREACHfacet_(facets) {
+    if ((facet->visible && qh->NEWfacets)
+    || (!printall && qh_skipfacet(qh, facet)))
+      facet->visitid= 0;
+    else {
+      facet->visitid= ++numfacets;
+      totneighbors += qh_setsize(qh, facet->neighbors);
+      if (facet->simplicial){
+        numsimplicial++;
+        if (facet->keepcentrum && facet->tricoplanar)
+          numtricoplanars++;
+      }else
+        numridges += qh_setsize(qh, facet->ridges);
+      if (facet->coplanarset)
+        numcoplanars += qh_setsize(qh, facet->coplanarset);
+    }
+  }
+  qh->visit_id += numfacets+1;
+  *numfacetsp= numfacets;
+  *numsimplicialp= numsimplicial;
+  *totneighborsp= totneighbors;
+  *numridgesp= numridges;
+  *numcoplanarsp= numcoplanars;
+  *numtricoplanarsp= numtricoplanars;
+} /* countfacets */
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="detvnorm">-</a>
+
+  qh_detvnorm(qh, vertex, vertexA, centers, offset )
+    compute separating plane of the Voronoi diagram for a pair of input sites
+    centers= set of facets (i.e., Voronoi vertices)
+      facet->visitid= 0 iff vertex-at-infinity (i.e., unbounded)
+
+  assumes:
+    qh_ASvoronoi and qh_vertexneighbors() already set
+
+  returns:
+    norm
+      a pointer into qh.gm_matrix to qh.hull_dim-1 reals
+      copy the data before reusing qh.gm_matrix
+    offset
+      if 'QVn'
+        sign adjusted so that qh.GOODvertexp is inside
+      else
+        sign adjusted so that vertex is inside
+
+    qh.gm_matrix= simplex of points from centers relative to first center
+
+  notes:
+    in io_r.c so that code for 'v Tv' can be removed by removing io_r.c
+    returns pointer into qh.gm_matrix to avoid tracking of temporary memory
+
+  design:
+    determine midpoint of input sites
+    build points as the set of Voronoi vertices
+    select a simplex from points (if necessary)
+      include midpoint if the Voronoi region is unbounded
+    relocate the first vertex of the simplex to the origin
+    compute the normalized hyperplane through the simplex
+    orient the hyperplane toward 'QVn' or 'vertex'
+    if 'Tv' or 'Ts'
+      if bounded
+        test that hyperplane is the perpendicular bisector of the input sites
+      test that Voronoi vertices not in the simplex are still on the hyperplane
+    free up temporary memory
+*/
+pointT *qh_detvnorm(qhT *qh, vertexT *vertex, vertexT *vertexA, setT *centers, realT *offsetp) {
+  facetT *facet, **facetp;
+  int  i, k, pointid, pointidA, point_i, point_n;
+  setT *simplex= NULL;
+  pointT *point, **pointp, *point0, *midpoint, *normal, *inpoint;
+  coordT *coord, *gmcoord, *normalp;
+  setT *points= qh_settemp(qh, qh->TEMPsize);
+  boolT nearzero= False;
+  boolT unbounded= False;
+  int numcenters= 0;
+  int dim= qh->hull_dim - 1;
+  realT dist, offset, angle, zero= 0.0;
+
+  midpoint= qh->gm_matrix + qh->hull_dim * qh->hull_dim;  /* last row */
+  for (k=0; k < dim; k++)
+    midpoint[k]= (vertex->point[k] + vertexA->point[k])/2;
+  FOREACHfacet_(centers) {
+    numcenters++;
+    if (!facet->visitid)
+      unbounded= True;
+    else {
+      if (!facet->center)
+        facet->center= qh_facetcenter(qh, facet->vertices);
+      qh_setappend(qh, &points, facet->center);
+    }
+  }
+  if (numcenters > dim) {
+    simplex= qh_settemp(qh, qh->TEMPsize);
+    qh_setappend(qh, &simplex, vertex->point);
+    if (unbounded)
+      qh_setappend(qh, &simplex, midpoint);
+    qh_maxsimplex(qh, dim, points, NULL, 0, &simplex);
+    qh_setdelnth(qh, simplex, 0);
+  }else if (numcenters == dim) {
+    if (unbounded)
+      qh_setappend(qh, &points, midpoint);
+    simplex= points;
+  }else {
+    qh_fprintf(qh, qh->ferr, 6216, "qhull internal error (qh_detvnorm): too few points(%d) to compute separating plane\n", numcenters);
+    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+  }
+  i= 0;
+  gmcoord= qh->gm_matrix;
+  point0= SETfirstt_(simplex, pointT);
+  FOREACHpoint_(simplex) {
+    if (qh->IStracing >= 4)
+      qh_printmatrix(qh, qh->ferr, "qh_detvnorm: Voronoi vertex or midpoint",
+                              &point, 1, dim);
+    if (point != point0) {
+      qh->gm_row[i++]= gmcoord;
+      coord= point0;
+      for (k=dim; k--; )
+        *(gmcoord++)= *point++ - *coord++;
+    }
+  }
+  qh->gm_row[i]= gmcoord;  /* does not overlap midpoint, may be used later for qh_areasimplex */
+  normal= gmcoord;
+  qh_sethyperplane_gauss(qh, dim, qh->gm_row, point0, True,
+                normal, &offset, &nearzero);
+  if (qh->GOODvertexp == vertexA->point)
+    inpoint= vertexA->point;
+  else
+    inpoint= vertex->point;
+  zinc_(Zdistio);
+  dist= qh_distnorm(dim, inpoint, normal, &offset);
+  if (dist > 0) {
+    offset= -offset;
+    normalp= normal;
+    for (k=dim; k--; ) {
+      *normalp= -(*normalp);
+      normalp++;
+    }
+  }
+  if (qh->VERIFYoutput || qh->PRINTstatistics) {
+    pointid= qh_pointid(qh, vertex->point);
+    pointidA= qh_pointid(qh, vertexA->point);
+    if (!unbounded) {
+      zinc_(Zdiststat);
+      dist= qh_distnorm(dim, midpoint, normal, &offset);
+      if (dist < 0)
+        dist= -dist;
+      zzinc_(Zridgemid);
+      wwmax_(Wridgemidmax, dist);
+      wwadd_(Wridgemid, dist);
+      trace4((qh, qh->ferr, 4014, "qh_detvnorm: points %d %d midpoint dist %2.2g\n",
+                 pointid, pointidA, dist));
+      for (k=0; k < dim; k++)
+        midpoint[k]= vertexA->point[k] - vertex->point[k];  /* overwrites midpoint! */
+      qh_normalize(qh, midpoint, dim, False);
+      angle= qh_distnorm(dim, midpoint, normal, &zero); /* qh_detangle uses dim+1 */
+      if (angle < 0.0)
+        angle= angle + 1.0;
+      else
+        angle= angle - 1.0;
+      if (angle < 0.0)
+        angle -= angle;
+      trace4((qh, qh->ferr, 4015, "qh_detvnorm: points %d %d angle %2.2g nearzero %d\n",
+                 pointid, pointidA, angle, nearzero));
+      if (nearzero) {
+        zzinc_(Zridge0);
+        wwmax_(Wridge0max, angle);
+        wwadd_(Wridge0, angle);
+      }else {
+        zzinc_(Zridgeok)
+        wwmax_(Wridgeokmax, angle);
+        wwadd_(Wridgeok, angle);
+      }
+    }
+    if (simplex != points) {
+      FOREACHpoint_i_(qh, points) {
+        if (!qh_setin(simplex, point)) {
+          facet= SETelemt_(centers, point_i, facetT);
+          zinc_(Zdiststat);
+          dist= qh_distnorm(dim, point, normal, &offset);
+          if (dist < 0)
+            dist= -dist;
+          zzinc_(Zridge);
+          wwmax_(Wridgemax, dist);
+          wwadd_(Wridge, dist);
+          trace4((qh, qh->ferr, 4016, "qh_detvnorm: points %d %d Voronoi vertex %d dist %2.2g\n",
+                             pointid, pointidA, facet->visitid, dist));
+        }
+      }
+    }
+  }
+  *offsetp= offset;
+  if (simplex != points)
+    qh_settempfree(qh, &simplex);
+  qh_settempfree(qh, &points);
+  return normal;
+} /* detvnorm */
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="detvridge">-</a>
+
+  qh_detvridge(qh, vertexA )
+    determine Voronoi ridge from 'seen' neighbors of vertexA
+    include one vertex-at-infinite if an !neighbor->visitid
+
+  returns:
+    temporary set of centers (facets, i.e., Voronoi vertices)
+    sorted by center id
+*/
+setT *qh_detvridge(qhT *qh, vertexT *vertex) {
+  setT *centers= qh_settemp(qh, qh->TEMPsize);
+  setT *tricenters= qh_settemp(qh, qh->TEMPsize);
+  facetT *neighbor, **neighborp;
+  boolT firstinf= True;
+
+  FOREACHneighbor_(vertex) {
+    if (neighbor->seen) {
+      if (neighbor->visitid) {
+        if (!neighbor->tricoplanar || qh_setunique(qh, &tricenters, neighbor->center))
+          qh_setappend(qh, &centers, neighbor);
+      }else if (firstinf) {
+        firstinf= False;
+        qh_setappend(qh, &centers, neighbor);
+      }
+    }
+  }
+  qsort(SETaddr_(centers, facetT), (size_t)qh_setsize(qh, centers),
+             sizeof(facetT *), qh_compare_facetvisit);
+  qh_settempfree(qh, &tricenters);
+  return centers;
+} /* detvridge */
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="detvridge3">-</a>
+
+  qh_detvridge3(qh, atvertex, vertex )
+    determine 3-d Voronoi ridge from 'seen' neighbors of atvertex and vertex
+    include one vertex-at-infinite for !neighbor->visitid
+    assumes all facet->seen2= True
+
+  returns:
+    temporary set of centers (facets, i.e., Voronoi vertices)
+    listed in adjacency order (!oriented)
+    all facet->seen2= True
+
+  design:
+    mark all neighbors of atvertex
+    for each adjacent neighbor of both atvertex and vertex
+      if neighbor selected
+        add neighbor to set of Voronoi vertices
+*/
+setT *qh_detvridge3(qhT *qh, vertexT *atvertex, vertexT *vertex) {
+  setT *centers= qh_settemp(qh, qh->TEMPsize);
+  setT *tricenters= qh_settemp(qh, qh->TEMPsize);
+  facetT *neighbor, **neighborp, *facet= NULL;
+  boolT firstinf= True;
+
+  FOREACHneighbor_(atvertex)
+    neighbor->seen2= False;
+  FOREACHneighbor_(vertex) {
+    if (!neighbor->seen2) {
+      facet= neighbor;
+      break;
+    }
+  }
+  while (facet) {
+    facet->seen2= True;
+    if (neighbor->seen) {
+      if (facet->visitid) {
+        if (!facet->tricoplanar || qh_setunique(qh, &tricenters, facet->center))
+          qh_setappend(qh, &centers, facet);
+      }else if (firstinf) {
+        firstinf= False;
+        qh_setappend(qh, &centers, facet);
+      }
+    }
+    FOREACHneighbor_(facet) {
+      if (!neighbor->seen2) {
+        if (qh_setin(vertex->neighbors, neighbor))
+          break;
+        else
+          neighbor->seen2= True;
+      }
+    }
+    facet= neighbor;
+  }
+  if (qh->CHECKfrequently) {
+    FOREACHneighbor_(vertex) {
+      if (!neighbor->seen2) {
+          qh_fprintf(qh, qh->ferr, 6217, "qhull internal error (qh_detvridge3): neighbors of vertex p%d are not connected at facet %d\n",
+                 qh_pointid(qh, vertex->point), neighbor->id);
+        qh_errexit(qh, qh_ERRqhull, neighbor, NULL);
+      }
+    }
+  }
+  FOREACHneighbor_(atvertex)
+    neighbor->seen2= True;
+  qh_settempfree(qh, &tricenters);
+  return centers;
+} /* detvridge3 */
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="eachvoronoi">-</a>
+
+  qh_eachvoronoi(qh, fp, printvridge, vertex, visitall, innerouter, inorder )
+    if visitall,
+      visit all Voronoi ridges for vertex (i.e., an input site)
+    else
+      visit all unvisited Voronoi ridges for vertex
+      all vertex->seen= False if unvisited
+    assumes
+      all facet->seen= False
+      all facet->seen2= True (for qh_detvridge3)
+      all facet->visitid == 0 if vertex_at_infinity
+                         == index of Voronoi vertex
+                         >= qh.num_facets if ignored
+    innerouter:
+      qh_RIDGEall--  both inner (bounded) and outer(unbounded) ridges
+      qh_RIDGEinner- only inner
+      qh_RIDGEouter- only outer
+
+    if inorder
+      orders vertices for 3-d Voronoi diagrams
+
+  returns:
+    number of visited ridges (does not include previously visited ridges)
+
+    if printvridge,
+      calls printvridge( fp, vertex, vertexA, centers)
+        fp== any pointer (assumes FILE*)
+        vertex,vertexA= pair of input sites that define a Voronoi ridge
+        centers= set of facets (i.e., Voronoi vertices)
+                 ->visitid == index or 0 if vertex_at_infinity
+                 ordered for 3-d Voronoi diagram
+  notes:
+    uses qh.vertex_visit
+
+  see:
+    qh_eachvoronoi_all()
+
+  design:
+    mark selected neighbors of atvertex
+    for each selected neighbor (either Voronoi vertex or vertex-at-infinity)
+      for each unvisited vertex
+        if atvertex and vertex share more than d-1 neighbors
+          bump totalcount
+          if printvridge defined
+            build the set of shared neighbors (i.e., Voronoi vertices)
+            call printvridge
+*/
+int qh_eachvoronoi(qhT *qh, FILE *fp, printvridgeT printvridge, vertexT *atvertex, boolT visitall, qh_RIDGE innerouter, boolT inorder) {
+  boolT unbounded;
+  int count;
+  facetT *neighbor, **neighborp, *neighborA, **neighborAp;
+  setT *centers;
+  setT *tricenters= qh_settemp(qh, qh->TEMPsize);
+
+  vertexT *vertex, **vertexp;
+  boolT firstinf;
+  unsigned int numfacets= (unsigned int)qh->num_facets;
+  int totridges= 0;
+
+  qh->vertex_visit++;
+  atvertex->seen= True;
+  if (visitall) {
+    FORALLvertices
+      vertex->seen= False;
+  }
+  FOREACHneighbor_(atvertex) {
+    if (neighbor->visitid < numfacets)
+      neighbor->seen= True;
+  }
+  FOREACHneighbor_(atvertex) {
+    if (neighbor->seen) {
+      FOREACHvertex_(neighbor->vertices) {
+        if (vertex->visitid != qh->vertex_visit && !vertex->seen) {
+          vertex->visitid= qh->vertex_visit;
+          count= 0;
+          firstinf= True;
+          qh_settruncate(qh, tricenters, 0);
+          FOREACHneighborA_(vertex) {
+            if (neighborA->seen) {
+              if (neighborA->visitid) {
+                if (!neighborA->tricoplanar || qh_setunique(qh, &tricenters, neighborA->center))
+                  count++;
+              }else if (firstinf) {
+                count++;
+                firstinf= False;
+              }
+            }
+          }
+          if (count >= qh->hull_dim - 1) {  /* e.g., 3 for 3-d Voronoi */
+            if (firstinf) {
+              if (innerouter == qh_RIDGEouter)
+                continue;
+              unbounded= False;
+            }else {
+              if (innerouter == qh_RIDGEinner)
+                continue;
+              unbounded= True;
+            }
+            totridges++;
+            trace4((qh, qh->ferr, 4017, "qh_eachvoronoi: Voronoi ridge of %d vertices between sites %d and %d\n",
+                  count, qh_pointid(qh, atvertex->point), qh_pointid(qh, vertex->point)));
+            if (printvridge && fp) {
+              if (inorder && qh->hull_dim == 3+1) /* 3-d Voronoi diagram */
+                centers= qh_detvridge3(qh, atvertex, vertex);
+              else
+                centers= qh_detvridge(qh, vertex);
+              (*printvridge)(qh, fp, atvertex, vertex, centers, unbounded);
+              qh_settempfree(qh, &centers);
+            }
+          }
+        }
+      }
+    }
+  }
+  FOREACHneighbor_(atvertex)
+    neighbor->seen= False;
+  qh_settempfree(qh, &tricenters);
+  return totridges;
+} /* eachvoronoi */
+
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="eachvoronoi_all">-</a>
+
+  qh_eachvoronoi_all(qh, fp, printvridge, isUpper, innerouter, inorder )
+    visit all Voronoi ridges
+
+    innerouter:
+      see qh_eachvoronoi()
+
+    if inorder
+      orders vertices for 3-d Voronoi diagrams
+
+  returns
+    total number of ridges
+
+    if isUpper == facet->upperdelaunay  (i.e., a Vornoi vertex)
+      facet->visitid= Voronoi vertex index(same as 'o' format)
+    else
+      facet->visitid= 0
+
+    if printvridge,
+      calls printvridge( fp, vertex, vertexA, centers)
+      [see qh_eachvoronoi]
+
+  notes:
+    Not used for qhull.exe
+    same effect as qh_printvdiagram but ridges not sorted by point id
+*/
+int qh_eachvoronoi_all(qhT *qh, FILE *fp, printvridgeT printvridge, boolT isUpper, qh_RIDGE innerouter, boolT inorder) {
+  facetT *facet;
+  vertexT *vertex;
+  int numcenters= 1;  /* vertex 0 is vertex-at-infinity */
+  int totridges= 0;
+
+  qh_clearcenters(qh, qh_ASvoronoi);
+  qh_vertexneighbors(qh);
+  maximize_(qh->visit_id, (unsigned) qh->num_facets);
+  FORALLfacets {
+    facet->visitid= 0;
+    facet->seen= False;
+    facet->seen2= True;
+  }
+  FORALLfacets {
+    if (facet->upperdelaunay == isUpper)
+      facet->visitid= numcenters++;
+  }
+  FORALLvertices
+    vertex->seen= False;
+  FORALLvertices {
+    if (qh->GOODvertex > 0 && qh_pointid(qh, vertex->point)+1 != qh->GOODvertex)
+      continue;
+    totridges += qh_eachvoronoi(qh, fp, printvridge, vertex,
+                   !qh_ALL, innerouter, inorder);
+  }
+  return totridges;
+} /* eachvoronoi_all */
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="facet2point">-</a>
+
+  qh_facet2point(qh, facet, point0, point1, mindist )
+    return two projected temporary vertices for a 2-d facet
+    may be non-simplicial
+
+  returns:
+    point0 and point1 oriented and projected to the facet
+    returns mindist (maximum distance below plane)
+*/
+void qh_facet2point(qhT *qh, facetT *facet, pointT **point0, pointT **point1, realT *mindist) {
+  vertexT *vertex0, *vertex1;
+  realT dist;
+
+  if (facet->toporient ^ qh_ORIENTclock) {
+    vertex0= SETfirstt_(facet->vertices, vertexT);
+    vertex1= SETsecondt_(facet->vertices, vertexT);
+  }else {
+    vertex1= SETfirstt_(facet->vertices, vertexT);
+    vertex0= SETsecondt_(facet->vertices, vertexT);
+  }
+  zadd_(Zdistio, 2);
+  qh_distplane(qh, vertex0->point, facet, &dist);
+  *mindist= dist;
+  *point0= qh_projectpoint(qh, vertex0->point, facet, dist);
+  qh_distplane(qh, vertex1->point, facet, &dist);
+  minimize_(*mindist, dist);
+  *point1= qh_projectpoint(qh, vertex1->point, facet, dist);
+} /* facet2point */
+
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="facetvertices">-</a>
+
+  qh_facetvertices(qh, facetlist, facets, allfacets )
+    returns temporary set of vertices in a set and/or list of facets
+    if allfacets, ignores qh_skipfacet()
+
+  returns:
+    vertices with qh.vertex_visit
+
+  notes:
+    optimized for allfacets of facet_list
+
+  design:
+    if allfacets of facet_list
+      create vertex set from vertex_list
+    else
+      for each selected facet in facets or facetlist
+        append unvisited vertices to vertex set
+*/
+setT *qh_facetvertices(qhT *qh, facetT *facetlist, setT *facets, boolT allfacets) {
+  setT *vertices;
+  facetT *facet, **facetp;
+  vertexT *vertex, **vertexp;
+
+  qh->vertex_visit++;
+  if (facetlist == qh->facet_list && allfacets && !facets) {
+    vertices= qh_settemp(qh, qh->num_vertices);
+    FORALLvertices {
+      vertex->visitid= qh->vertex_visit;
+      qh_setappend(qh, &vertices, vertex);
+    }
+  }else {
+    vertices= qh_settemp(qh, qh->TEMPsize);
+    FORALLfacet_(facetlist) {
+      if (!allfacets && qh_skipfacet(qh, facet))
+        continue;
+      FOREACHvertex_(facet->vertices) {
+        if (vertex->visitid != qh->vertex_visit) {
+          vertex->visitid= qh->vertex_visit;
+          qh_setappend(qh, &vertices, vertex);
+        }
+      }
+    }
+  }
+  FOREACHfacet_(facets) {
+    if (!allfacets && qh_skipfacet(qh, facet))
+      continue;
+    FOREACHvertex_(facet->vertices) {
+      if (vertex->visitid != qh->vertex_visit) {
+        vertex->visitid= qh->vertex_visit;
+        qh_setappend(qh, &vertices, vertex);
+      }
+    }
+  }
+  return vertices;
+} /* facetvertices */
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >-------------------------------</a><a name="geomplanes">-</a>
+
+  qh_geomplanes(qh, facet, outerplane, innerplane )
+    return outer and inner planes for Geomview
+    qh.PRINTradius is size of vertices and points (includes qh.JOGGLEmax)
+
+  notes:
+    assume precise calculations in io.c with roundoff covered by qh_GEOMepsilon
+*/
+void qh_geomplanes(qhT *qh, facetT *facet, realT *outerplane, realT *innerplane) {
+  realT radius;
+
+  if (qh->MERGING || qh->JOGGLEmax < REALmax/2) {
+    qh_outerinner(qh, facet, outerplane, innerplane);
+    radius= qh->PRINTradius;
+    if (qh->JOGGLEmax < REALmax/2)
+      radius -= qh->JOGGLEmax * sqrt((realT)qh->hull_dim);  /* already accounted for in qh_outerinner() */
+    *outerplane += radius;
+    *innerplane -= radius;
+    if (qh->PRINTcoplanar || qh->PRINTspheres) {
+      *outerplane += qh->MAXabs_coord * qh_GEOMepsilon;
+      *innerplane -= qh->MAXabs_coord * qh_GEOMepsilon;
+    }
+  }else
+    *innerplane= *outerplane= 0;
+} /* geomplanes */
+
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="markkeep">-</a>
+
+  qh_markkeep(qh, facetlist )
+    mark good facets that meet qh.KEEParea, qh.KEEPmerge, and qh.KEEPminArea
+    ignores visible facets (!part of convex hull)
+
+  returns:
+    may clear facet->good
+    recomputes qh.num_good
+
+  design:
+    get set of good facets
+    if qh.KEEParea
+      sort facets by area
+      clear facet->good for all but n largest facets
+    if qh.KEEPmerge
+      sort facets by merge count
+      clear facet->good for all but n most merged facets
+    if qh.KEEPminarea
+      clear facet->good if area too small
+    update qh.num_good
+*/
+void qh_markkeep(qhT *qh, facetT *facetlist) {
+  facetT *facet, **facetp;
+  setT *facets= qh_settemp(qh, qh->num_facets);
+  int size, count;
+
+  trace2((qh, qh->ferr, 2006, "qh_markkeep: only keep %d largest and/or %d most merged facets and/or min area %.2g\n",
+          qh->KEEParea, qh->KEEPmerge, qh->KEEPminArea));
+  FORALLfacet_(facetlist) {
+    if (!facet->visible && facet->good)
+      qh_setappend(qh, &facets, facet);
+  }
+  size= qh_setsize(qh, facets);
+  if (qh->KEEParea) {
+    qsort(SETaddr_(facets, facetT), (size_t)size,
+             sizeof(facetT *), qh_compare_facetarea);
+    if ((count= size - qh->KEEParea) > 0) {
+      FOREACHfacet_(facets) {
+        facet->good= False;
+        if (--count == 0)
+          break;
+      }
+    }
+  }
+  if (qh->KEEPmerge) {
+    qsort(SETaddr_(facets, facetT), (size_t)size,
+             sizeof(facetT *), qh_compare_facetmerge);
+    if ((count= size - qh->KEEPmerge) > 0) {
+      FOREACHfacet_(facets) {
+        facet->good= False;
+        if (--count == 0)
+          break;
+      }
+    }
+  }
+  if (qh->KEEPminArea < REALmax/2) {
+    FOREACHfacet_(facets) {
+      if (!facet->isarea || facet->f.area < qh->KEEPminArea)
+        facet->good= False;
+    }
+  }
+  qh_settempfree(qh, &facets);
+  count= 0;
+  FORALLfacet_(facetlist) {
+    if (facet->good)
+      count++;
+  }
+  qh->num_good= count;
+} /* markkeep */
+
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="markvoronoi">-</a>
+
+  qh_markvoronoi(qh, facetlist, facets, printall, isLower, numcenters )
+    mark voronoi vertices for printing by site pairs
+
+  returns:
+    temporary set of vertices indexed by pointid
+    isLower set if printing lower hull (i.e., at least one facet is lower hull)
+    numcenters= total number of Voronoi vertices
+    bumps qh.printoutnum for vertex-at-infinity
+    clears all facet->seen and sets facet->seen2
+
+    if selected
+      facet->visitid= Voronoi vertex id
+    else if upper hull (or 'Qu' and lower hull)
+      facet->visitid= 0
+    else
+      facet->visitid >= qh->num_facets
+
+  notes:
+    ignores qh.ATinfinity, if defined
+*/
+setT *qh_markvoronoi(qhT *qh, facetT *facetlist, setT *facets, boolT printall, boolT *isLowerp, int *numcentersp) {
+  int numcenters=0;
+  facetT *facet, **facetp;
+  setT *vertices;
+  boolT isLower= False;
+
+  qh->printoutnum++;
+  qh_clearcenters(qh, qh_ASvoronoi);  /* in case, qh_printvdiagram2 called by user */
+  qh_vertexneighbors(qh);
+  vertices= qh_pointvertex(qh);
+  if (qh->ATinfinity)
+    SETelem_(vertices, qh->num_points-1)= NULL;
+  qh->visit_id++;
+  maximize_(qh->visit_id, (unsigned) qh->num_facets);
+  FORALLfacet_(facetlist) {
+    if (printall || !qh_skipfacet(qh, facet)) {
+      if (!facet->upperdelaunay) {
+        isLower= True;
+        break;
+      }
+    }
+  }
+  FOREACHfacet_(facets) {
+    if (printall || !qh_skipfacet(qh, facet)) {
+      if (!facet->upperdelaunay) {
+        isLower= True;
+        break;
+      }
+    }
+  }
+  FORALLfacets {
+    if (facet->normal && (facet->upperdelaunay == isLower))
+      facet->visitid= 0;  /* facetlist or facets may overwrite */
+    else
+      facet->visitid= qh->visit_id;
+    facet->seen= False;
+    facet->seen2= True;
+  }
+  numcenters++;  /* qh_INFINITE */
+  FORALLfacet_(facetlist) {
+    if (printall || !qh_skipfacet(qh, facet))
+      facet->visitid= numcenters++;
+  }
+  FOREACHfacet_(facets) {
+    if (printall || !qh_skipfacet(qh, facet))
+      facet->visitid= numcenters++;
+  }
+  *isLowerp= isLower;
+  *numcentersp= numcenters;
+  trace2((qh, qh->ferr, 2007, "qh_markvoronoi: isLower %d numcenters %d\n", isLower, numcenters));
+  return vertices;
+} /* markvoronoi */
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="order_vertexneighbors">-</a>
+
+  qh_order_vertexneighbors(qh, vertex )
+    order facet neighbors of a 2-d or 3-d vertex by adjacency
+
+  notes:
+    does not orient the neighbors
+
+  design:
+    initialize a new neighbor set with the first facet in vertex->neighbors
+    while vertex->neighbors non-empty
+      select next neighbor in the previous facet's neighbor set
+    set vertex->neighbors to the new neighbor set
+*/
+void qh_order_vertexneighbors(qhT *qh, vertexT *vertex) {
+  setT *newset;
+  facetT *facet, *neighbor, **neighborp;
+
+  trace4((qh, qh->ferr, 4018, "qh_order_vertexneighbors: order neighbors of v%d for 3-d\n", vertex->id));
+  newset= qh_settemp(qh, qh_setsize(qh, vertex->neighbors));
+  facet= (facetT*)qh_setdellast(vertex->neighbors);
+  qh_setappend(qh, &newset, facet);
+  while (qh_setsize(qh, vertex->neighbors)) {
+    FOREACHneighbor_(vertex) {
+      if (qh_setin(facet->neighbors, neighbor)) {
+        qh_setdel(vertex->neighbors, neighbor);
+        qh_setappend(qh, &newset, neighbor);
+        facet= neighbor;
+        break;
+      }
+    }
+    if (!neighbor) {
+      qh_fprintf(qh, qh->ferr, 6066, "qhull internal error (qh_order_vertexneighbors): no neighbor of v%d for f%d\n",
+        vertex->id, facet->id);
+      qh_errexit(qh, qh_ERRqhull, facet, NULL);
+    }
+  }
+  qh_setfree(qh, &vertex->neighbors);
+  qh_settemppop(qh);
+  vertex->neighbors= newset;
+} /* order_vertexneighbors */
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="prepare_output">-</a>
+
+  qh_prepare_output(qh, )
+    prepare for qh_produce_output2(qh) according to
+      qh.KEEPminArea, KEEParea, KEEPmerge, GOODvertex, GOODthreshold, GOODpoint, ONLYgood, SPLITthresholds
+    does not reset facet->good
+
+  notes
+    except for PRINTstatistics, no-op if previously called with same options
+*/
+void qh_prepare_output(qhT *qh) {
+  if (qh->VORONOI) {
+    qh_clearcenters(qh, qh_ASvoronoi);  /* must be before qh_triangulate */
+    qh_vertexneighbors(qh);
+  }
+  if (qh->TRIangulate && !qh->hasTriangulation) {
+    qh_triangulate(qh);
+    if (qh->VERIFYoutput && !qh->CHECKfrequently)
+      qh_checkpolygon(qh, qh->facet_list);
+  }
+  qh_findgood_all(qh, qh->facet_list);
+  if (qh->GETarea)
+    qh_getarea(qh, qh->facet_list);
+  if (qh->KEEParea || qh->KEEPmerge || qh->KEEPminArea < REALmax/2)
+    qh_markkeep(qh, qh->facet_list);
+  if (qh->PRINTstatistics)
+    qh_collectstatistics(qh);
+}
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="printafacet">-</a>
+
+  qh_printafacet(qh, fp, format, facet, printall )
+    print facet to fp in given output format (see qh.PRINTout)
+
+  returns:
+    nop if !printall and qh_skipfacet()
+    nop if visible facet and NEWfacets and format != PRINTfacets
+    must match qh_countfacets
+
+  notes
+    preserves qh.visit_id
+    facet->normal may be null if PREmerge/MERGEexact and STOPcone before merge
+
+  see
+    qh_printbegin() and qh_printend()
+
+  design:
+    test for printing facet
+    call appropriate routine for format
+    or output results directly
+*/
+void qh_printafacet(qhT *qh, FILE *fp, qh_PRINT format, facetT *facet, boolT printall) {
+  realT color[4], offset, dist, outerplane, innerplane;
+  boolT zerodiv;
+  coordT *point, *normp, *coordp, **pointp, *feasiblep;
+  int k;
+  vertexT *vertex, **vertexp;
+  facetT *neighbor, **neighborp;
+
+  if (!printall && qh_skipfacet(qh, facet))
+    return;
+  if (facet->visible && qh->NEWfacets && format != qh_PRINTfacets)
+    return;
+  qh->printoutnum++;
+  switch (format) {
+  case qh_PRINTarea:
+    if (facet->isarea) {
+      qh_fprintf(qh, fp, 9009, qh_REAL_1, facet->f.area);
+      qh_fprintf(qh, fp, 9010, "\n");
+    }else
+      qh_fprintf(qh, fp, 9011, "0\n");
+    break;
+  case qh_PRINTcoplanars:
+    qh_fprintf(qh, fp, 9012, "%d", qh_setsize(qh, facet->coplanarset));
+    FOREACHpoint_(facet->coplanarset)
+      qh_fprintf(qh, fp, 9013, " %d", qh_pointid(qh, point));
+    qh_fprintf(qh, fp, 9014, "\n");
+    break;
+  case qh_PRINTcentrums:
+    qh_printcenter(qh, fp, format, NULL, facet);
+    break;
+  case qh_PRINTfacets:
+    qh_printfacet(qh, fp, facet);
+    break;
+  case qh_PRINTfacets_xridge:
+    qh_printfacetheader(qh, fp, facet);
+    break;
+  case qh_PRINTgeom:  /* either 2 , 3, or 4-d by qh_printbegin */
+    if (!facet->normal)
+      break;
+    for (k=qh->hull_dim; k--; ) {
+      color[k]= (facet->normal[k]+1.0)/2.0;
+      maximize_(color[k], -1.0);
+      minimize_(color[k], +1.0);
+    }
+    qh_projectdim3(qh, color, color);
+    if (qh->PRINTdim != qh->hull_dim)
+      qh_normalize2(qh, color, 3, True, NULL, NULL);
+    if (qh->hull_dim <= 2)
+      qh_printfacet2geom(qh, fp, facet, color);
+    else if (qh->hull_dim == 3) {
+      if (facet->simplicial)
+        qh_printfacet3geom_simplicial(qh, fp, facet, color);
+      else
+        qh_printfacet3geom_nonsimplicial(qh, fp, facet, color);
+    }else {
+      if (facet->simplicial)
+        qh_printfacet4geom_simplicial(qh, fp, facet, color);
+      else
+        qh_printfacet4geom_nonsimplicial(qh, fp, facet, color);
+    }
+    break;
+  case qh_PRINTids:
+    qh_fprintf(qh, fp, 9015, "%d\n", facet->id);
+    break;
+  case qh_PRINTincidences:
+  case qh_PRINToff:
+  case qh_PRINTtriangles:
+    if (qh->hull_dim == 3 && format != qh_PRINTtriangles)
+      qh_printfacet3vertex(qh, fp, facet, format);
+    else if (facet->simplicial || qh->hull_dim == 2 || format == qh_PRINToff)
+      qh_printfacetNvertex_simplicial(qh, fp, facet, format);
+    else
+      qh_printfacetNvertex_nonsimplicial(qh, fp, facet, qh->printoutvar++, format);
+    break;
+  case qh_PRINTinner:
+    qh_outerinner(qh, facet, NULL, &innerplane);
+    offset= facet->offset - innerplane;
+    goto LABELprintnorm;
+    break; /* prevent warning */
+  case qh_PRINTmerges:
+    qh_fprintf(qh, fp, 9016, "%d\n", facet->nummerge);
+    break;
+  case qh_PRINTnormals:
+    offset= facet->offset;
+    goto LABELprintnorm;
+    break; /* prevent warning */
+  case qh_PRINTouter:
+    qh_outerinner(qh, facet, &outerplane, NULL);
+    offset= facet->offset - outerplane;
+  LABELprintnorm:
+    if (!facet->normal) {
+      qh_fprintf(qh, fp, 9017, "no normal for facet f%d\n", facet->id);
+      break;
+    }
+    if (qh->CDDoutput) {
+      qh_fprintf(qh, fp, 9018, qh_REAL_1, -offset);
+      for (k=0; k < qh->hull_dim; k++)
+        qh_fprintf(qh, fp, 9019, qh_REAL_1, -facet->normal[k]);
+    }else {
+      for (k=0; k < qh->hull_dim; k++)
+        qh_fprintf(qh, fp, 9020, qh_REAL_1, facet->normal[k]);
+      qh_fprintf(qh, fp, 9021, qh_REAL_1, offset);
+    }
+    qh_fprintf(qh, fp, 9022, "\n");
+    break;
+  case qh_PRINTmathematica:  /* either 2 or 3-d by qh_printbegin */
+  case qh_PRINTmaple:
+    if (qh->hull_dim == 2)
+      qh_printfacet2math(qh, fp, facet, format, qh->printoutvar++);
+    else
+      qh_printfacet3math(qh, fp, facet, format, qh->printoutvar++);
+    break;
+  case qh_PRINTneighbors:
+    qh_fprintf(qh, fp, 9023, "%d", qh_setsize(qh, facet->neighbors));
+    FOREACHneighbor_(facet)
+      qh_fprintf(qh, fp, 9024, " %d",
+               neighbor->visitid ? neighbor->visitid - 1: 0 - neighbor->id);
+    qh_fprintf(qh, fp, 9025, "\n");
+    break;
+  case qh_PRINTpointintersect:
+    if (!qh->feasible_point) {
+      qh_fprintf(qh, qh->ferr, 6067, "qhull input error (qh_printafacet): option 'Fp' needs qh->feasible_point\n");
+      qh_errexit(qh, qh_ERRinput, NULL, NULL);
+    }
+    if (facet->offset > 0)
+      goto LABELprintinfinite;
+    point= coordp= (coordT*)qh_memalloc(qh, qh->normal_size);
+    normp= facet->normal;
+    feasiblep= qh->feasible_point;
+    if (facet->offset < -qh->MINdenom) {
+      for (k=qh->hull_dim; k--; )
+        *(coordp++)= (*(normp++) / - facet->offset) + *(feasiblep++);
+    }else {
+      for (k=qh->hull_dim; k--; ) {
+        *(coordp++)= qh_divzero(*(normp++), facet->offset, qh->MINdenom_1,
+                                 &zerodiv) + *(feasiblep++);
+        if (zerodiv) {
+          qh_memfree(qh, point, qh->normal_size);
+          goto LABELprintinfinite;
+        }
+      }
+    }
+    qh_printpoint(qh, fp, NULL, point);
+    qh_memfree(qh, point, qh->normal_size);
+    break;
+  LABELprintinfinite:
+    for (k=qh->hull_dim; k--; )
+      qh_fprintf(qh, fp, 9026, qh_REAL_1, qh_INFINITE);
+    qh_fprintf(qh, fp, 9027, "\n");
+    break;
+  case qh_PRINTpointnearest:
+    FOREACHpoint_(facet->coplanarset) {
+      int id, id2;
+      vertex= qh_nearvertex(qh, facet, point, &dist);
+      id= qh_pointid(qh, vertex->point);
+      id2= qh_pointid(qh, point);
+      qh_fprintf(qh, fp, 9028, "%d %d %d " qh_REAL_1 "\n", id, id2, facet->id, dist);
+    }
+    break;
+  case qh_PRINTpoints:  /* VORONOI only by qh_printbegin */
+    if (qh->CDDoutput)
+      qh_fprintf(qh, fp, 9029, "1 ");
+    qh_printcenter(qh, fp, format, NULL, facet);
+    break;
+  case qh_PRINTvertices:
+    qh_fprintf(qh, fp, 9030, "%d", qh_setsize(qh, facet->vertices));
+    FOREACHvertex_(facet->vertices)
+      qh_fprintf(qh, fp, 9031, " %d", qh_pointid(qh, vertex->point));
+    qh_fprintf(qh, fp, 9032, "\n");
+    break;
+  default:
+    break;
+  }
+} /* printafacet */
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="printbegin">-</a>
+
+  qh_printbegin(qh, )
+    prints header for all output formats
+
+  returns:
+    checks for valid format
+
+  notes:
+    uses qh.visit_id for 3/4off
+    changes qh.interior_point if printing centrums
+    qh_countfacets clears facet->visitid for non-good facets
+
+  see
+    qh_printend() and qh_printafacet()
+
+  design:
+    count facets and related statistics
+    print header for format
+*/
+void qh_printbegin(qhT *qh, FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall) {
+  int numfacets, numsimplicial, numridges, totneighbors, numcoplanars, numtricoplanars;
+  int i, num;
+  facetT *facet, **facetp;
+  vertexT *vertex, **vertexp;
+  setT *vertices;
+  pointT *point, **pointp, *pointtemp;
+
+  qh->printoutnum= 0;
+  qh_countfacets(qh, facetlist, facets, printall, &numfacets, &numsimplicial,
+      &totneighbors, &numridges, &numcoplanars, &numtricoplanars);
+  switch (format) {
+  case qh_PRINTnone:
+    break;
+  case qh_PRINTarea:
+    qh_fprintf(qh, fp, 9033, "%d\n", numfacets);
+    break;
+  case qh_PRINTcoplanars:
+    qh_fprintf(qh, fp, 9034, "%d\n", numfacets);
+    break;
+  case qh_PRINTcentrums:
+    if (qh->CENTERtype == qh_ASnone)
+      qh_clearcenters(qh, qh_AScentrum);
+    qh_fprintf(qh, fp, 9035, "%d\n%d\n", qh->hull_dim, numfacets);
+    break;
+  case qh_PRINTfacets:
+  case qh_PRINTfacets_xridge:
+    if (facetlist)
+      qh_printvertexlist(qh, fp, "Vertices and facets:\n", facetlist, facets, printall);
+    break;
+  case qh_PRINTgeom:
+    if (qh->hull_dim > 4)  /* qh_initqhull_globals also checks */
+      goto LABELnoformat;
+    if (qh->VORONOI && qh->hull_dim > 3)  /* PRINTdim == DROPdim == hull_dim-1 */
+      goto LABELnoformat;
+    if (qh->hull_dim == 2 && (qh->PRINTridges || qh->DOintersections))
+      qh_fprintf(qh, qh->ferr, 7049, "qhull warning: output for ridges and intersections not implemented in 2-d\n");
+    if (qh->hull_dim == 4 && (qh->PRINTinner || qh->PRINTouter ||
+                             (qh->PRINTdim == 4 && qh->PRINTcentrums)))
+      qh_fprintf(qh, qh->ferr, 7050, "qhull warning: output for outer/inner planes and centrums not implemented in 4-d\n");
+    if (qh->PRINTdim == 4 && (qh->PRINTspheres))
+      qh_fprintf(qh, qh->ferr, 7051, "qhull warning: output for vertices not implemented in 4-d\n");
+    if (qh->PRINTdim == 4 && qh->DOintersections && qh->PRINTnoplanes)
+      qh_fprintf(qh, qh->ferr, 7052, "qhull warning: 'Gnh' generates no output in 4-d\n");
+    if (qh->PRINTdim == 2) {
+      qh_fprintf(qh, fp, 9036, "{appearance {linewidth 3} LIST # %s | %s\n",
+              qh->rbox_command, qh->qhull_command);
+    }else if (qh->PRINTdim == 3) {
+      qh_fprintf(qh, fp, 9037, "{appearance {+edge -evert linewidth 2} LIST # %s | %s\n",
+              qh->rbox_command, qh->qhull_command);
+    }else if (qh->PRINTdim == 4) {
+      qh->visit_id++;
+      num= 0;
+      FORALLfacet_(facetlist)    /* get number of ridges to be printed */
+        qh_printend4geom(qh, NULL, facet, &num, printall);
+      FOREACHfacet_(facets)
+        qh_printend4geom(qh, NULL, facet, &num, printall);
+      qh->ridgeoutnum= num;
+      qh->printoutvar= 0;  /* counts number of ridges in output */
+      qh_fprintf(qh, fp, 9038, "LIST # %s | %s\n", qh->rbox_command, qh->qhull_command);
+    }
+
+    if (qh->PRINTdots) {
+      qh->printoutnum++;
+      num= qh->num_points + qh_setsize(qh, qh->other_points);
+      if (qh->DELAUNAY && qh->ATinfinity)
+        num--;
+      if (qh->PRINTdim == 4)
+        qh_fprintf(qh, fp, 9039, "4VECT %d %d 1\n", num, num);
+      else
+        qh_fprintf(qh, fp, 9040, "VECT %d %d 1\n", num, num);
+
+      for (i=num; i--; ) {
+        if (i % 20 == 0)
+          qh_fprintf(qh, fp, 9041, "\n");
+        qh_fprintf(qh, fp, 9042, "1 ");
+      }
+      qh_fprintf(qh, fp, 9043, "# 1 point per line\n1 ");
+      for (i=num-1; i--; ) { /* num at least 3 for D2 */
+        if (i % 20 == 0)
+          qh_fprintf(qh, fp, 9044, "\n");
+        qh_fprintf(qh, fp, 9045, "0 ");
+      }
+      qh_fprintf(qh, fp, 9046, "# 1 color for all\n");
+      FORALLpoints {
+        if (!qh->DELAUNAY || !qh->ATinfinity || qh_pointid(qh, point) != qh->num_points-1) {
+          if (qh->PRINTdim == 4)
+            qh_printpoint(qh, fp, NULL, point);
+            else
+              qh_printpoint3(qh, fp, point);
+        }
+      }
+      FOREACHpoint_(qh->other_points) {
+        if (qh->PRINTdim == 4)
+          qh_printpoint(qh, fp, NULL, point);
+        else
+          qh_printpoint3(qh, fp, point);
+      }
+      qh_fprintf(qh, fp, 9047, "0 1 1 1  # color of points\n");
+    }
+
+    if (qh->PRINTdim == 4  && !qh->PRINTnoplanes)
+      /* 4dview loads up multiple 4OFF objects slowly */
+      qh_fprintf(qh, fp, 9048, "4OFF %d %d 1\n", 3*qh->ridgeoutnum, qh->ridgeoutnum);
+    qh->PRINTcradius= 2 * qh->DISTround;  /* include test DISTround */
+    if (qh->PREmerge) {
+      maximize_(qh->PRINTcradius, qh->premerge_centrum + qh->DISTround);
+    }else if (qh->POSTmerge)
+      maximize_(qh->PRINTcradius, qh->postmerge_centrum + qh->DISTround);
+    qh->PRINTradius= qh->PRINTcradius;
+    if (qh->PRINTspheres + qh->PRINTcoplanar)
+      maximize_(qh->PRINTradius, qh->MAXabs_coord * qh_MINradius);
+    if (qh->premerge_cos < REALmax/2) {
+      maximize_(qh->PRINTradius, (1- qh->premerge_cos) * qh->MAXabs_coord);
+    }else if (!qh->PREmerge && qh->POSTmerge && qh->postmerge_cos < REALmax/2) {
+      maximize_(qh->PRINTradius, (1- qh->postmerge_cos) * qh->MAXabs_coord);
+    }
+    maximize_(qh->PRINTradius, qh->MINvisible);
+    if (qh->JOGGLEmax < REALmax/2)
+      qh->PRINTradius += qh->JOGGLEmax * sqrt((realT)qh->hull_dim);
+    if (qh->PRINTdim != 4 &&
+        (qh->PRINTcoplanar || qh->PRINTspheres || qh->PRINTcentrums)) {
+      vertices= qh_facetvertices(qh, facetlist, facets, printall);
+      if (qh->PRINTspheres && qh->PRINTdim <= 3)
+        qh_printspheres(qh, fp, vertices, qh->PRINTradius);
+      if (qh->PRINTcoplanar || qh->PRINTcentrums) {
+        qh->firstcentrum= True;
+        if (qh->PRINTcoplanar&& !qh->PRINTspheres) {
+          FOREACHvertex_(vertices)
+            qh_printpointvect2(qh, fp, vertex->point, NULL, qh->interior_point, qh->PRINTradius);
+        }
+        FORALLfacet_(facetlist) {
+          if (!printall && qh_skipfacet(qh, facet))
+            continue;
+          if (!facet->normal)
+            continue;
+          if (qh->PRINTcentrums && qh->PRINTdim <= 3)
+            qh_printcentrum(qh, fp, facet, qh->PRINTcradius);
+          if (!qh->PRINTcoplanar)
+            continue;
+          FOREACHpoint_(facet->coplanarset)
+            qh_printpointvect2(qh, fp, point, facet->normal, NULL, qh->PRINTradius);
+          FOREACHpoint_(facet->outsideset)
+            qh_printpointvect2(qh, fp, point, facet->normal, NULL, qh->PRINTradius);
+        }
+        FOREACHfacet_(facets) {
+          if (!printall && qh_skipfacet(qh, facet))
+            continue;
+          if (!facet->normal)
+            continue;
+          if (qh->PRINTcentrums && qh->PRINTdim <= 3)
+            qh_printcentrum(qh, fp, facet, qh->PRINTcradius);
+          if (!qh->PRINTcoplanar)
+            continue;
+          FOREACHpoint_(facet->coplanarset)
+            qh_printpointvect2(qh, fp, point, facet->normal, NULL, qh->PRINTradius);
+          FOREACHpoint_(facet->outsideset)
+            qh_printpointvect2(qh, fp, point, facet->normal, NULL, qh->PRINTradius);
+        }
+      }
+      qh_settempfree(qh, &vertices);
+    }
+    qh->visit_id++; /* for printing hyperplane intersections */
+    break;
+  case qh_PRINTids:
+    qh_fprintf(qh, fp, 9049, "%d\n", numfacets);
+    break;
+  case qh_PRINTincidences:
+    if (qh->VORONOI && qh->PRINTprecision)
+      qh_fprintf(qh, qh->ferr, 7053, "qhull warning: writing Delaunay.  Use 'p' or 'o' for Voronoi centers\n");
+    qh->printoutvar= qh->vertex_id;  /* centrum id for non-simplicial facets */
+    if (qh->hull_dim <= 3)
+      qh_fprintf(qh, fp, 9050, "%d\n", numfacets);
+    else
+      qh_fprintf(qh, fp, 9051, "%d\n", numsimplicial+numridges);
+    break;
+  case qh_PRINTinner:
+  case qh_PRINTnormals:
+  case qh_PRINTouter:
+    if (qh->CDDoutput)
+      qh_fprintf(qh, fp, 9052, "%s | %s\nbegin\n    %d %d real\n", qh->rbox_command,
+            qh->qhull_command, numfacets, qh->hull_dim+1);
+    else
+      qh_fprintf(qh, fp, 9053, "%d\n%d\n", qh->hull_dim+1, numfacets);
+    break;
+  case qh_PRINTmathematica:
+  case qh_PRINTmaple:
+    if (qh->hull_dim > 3)  /* qh_initbuffers also checks */
+      goto LABELnoformat;
+    if (qh->VORONOI)
+      qh_fprintf(qh, qh->ferr, 7054, "qhull warning: output is the Delaunay triangulation\n");
+    if (format == qh_PRINTmaple) {
+      if (qh->hull_dim == 2)
+        qh_fprintf(qh, fp, 9054, "PLOT(CURVES(\n");
+      else
+        qh_fprintf(qh, fp, 9055, "PLOT3D(POLYGONS(\n");
+    }else
+      qh_fprintf(qh, fp, 9056, "{\n");
+    qh->printoutvar= 0;   /* counts number of facets for notfirst */
+    break;
+  case qh_PRINTmerges:
+    qh_fprintf(qh, fp, 9057, "%d\n", numfacets);
+    break;
+  case qh_PRINTpointintersect:
+    qh_fprintf(qh, fp, 9058, "%d\n%d\n", qh->hull_dim, numfacets);
+    break;
+  case qh_PRINTneighbors:
+    qh_fprintf(qh, fp, 9059, "%d\n", numfacets);
+    break;
+  case qh_PRINToff:
+  case qh_PRINTtriangles:
+    if (qh->VORONOI)
+      goto LABELnoformat;
+    num = qh->hull_dim;
+    if (format == qh_PRINToff || qh->hull_dim == 2)
+      qh_fprintf(qh, fp, 9060, "%d\n%d %d %d\n", num,
+        qh->num_points+qh_setsize(qh, qh->other_points), numfacets, totneighbors/2);
+    else { /* qh_PRINTtriangles */
+      qh->printoutvar= qh->num_points+qh_setsize(qh, qh->other_points); /* first centrum */
+      if (qh->DELAUNAY)
+        num--;  /* drop last dimension */
+      qh_fprintf(qh, fp, 9061, "%d\n%d %d %d\n", num, qh->printoutvar
+        + numfacets - numsimplicial, numsimplicial + numridges, totneighbors/2);
+    }
+    FORALLpoints
+      qh_printpointid(qh, qh->fout, NULL, num, point, qh_IDunknown);
+    FOREACHpoint_(qh->other_points)
+      qh_printpointid(qh, qh->fout, NULL, num, point, qh_IDunknown);
+    if (format == qh_PRINTtriangles && qh->hull_dim > 2) {
+      FORALLfacets {
+        if (!facet->simplicial && facet->visitid)
+          qh_printcenter(qh, qh->fout, format, NULL, facet);
+      }
+    }
+    break;
+  case qh_PRINTpointnearest:
+    qh_fprintf(qh, fp, 9062, "%d\n", numcoplanars);
+    break;
+  case qh_PRINTpoints:
+    if (!qh->VORONOI)
+      goto LABELnoformat;
+    if (qh->CDDoutput)
+      qh_fprintf(qh, fp, 9063, "%s | %s\nbegin\n%d %d real\n", qh->rbox_command,
+           qh->qhull_command, numfacets, qh->hull_dim);
+    else
+      qh_fprintf(qh, fp, 9064, "%d\n%d\n", qh->hull_dim-1, numfacets);
+    break;
+  case qh_PRINTvertices:
+    qh_fprintf(qh, fp, 9065, "%d\n", numfacets);
+    break;
+  case qh_PRINTsummary:
+  default:
+  LABELnoformat:
+    qh_fprintf(qh, qh->ferr, 6068, "qhull internal error (qh_printbegin): can not use this format for dimension %d\n",
+         qh->hull_dim);
+    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+  }
+} /* printbegin */
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="printcenter">-</a>
+
+  qh_printcenter(qh, fp, string, facet )
+    print facet->center as centrum or Voronoi center
+    string may be NULL.  Don't include '%' codes.
+    nop if qh->CENTERtype neither CENTERvoronoi nor CENTERcentrum
+    if upper envelope of Delaunay triangulation and point at-infinity
+      prints qh_INFINITE instead;
+
+  notes:
+    defines facet->center if needed
+    if format=PRINTgeom, adds a 0 if would otherwise be 2-d
+    Same as QhullFacet::printCenter
+*/
+void qh_printcenter(qhT *qh, FILE *fp, qh_PRINT format, const char *string, facetT *facet) {
+  int k, num;
+
+  if (qh->CENTERtype != qh_ASvoronoi && qh->CENTERtype != qh_AScentrum)
+    return;
+  if (string)
+    qh_fprintf(qh, fp, 9066, string);
+  if (qh->CENTERtype == qh_ASvoronoi) {
+    num= qh->hull_dim-1;
+    if (!facet->normal || !facet->upperdelaunay || !qh->ATinfinity) {
+      if (!facet->center)
+        facet->center= qh_facetcenter(qh, facet->vertices);
+      for (k=0; k < num; k++)
+        qh_fprintf(qh, fp, 9067, qh_REAL_1, facet->center[k]);
+    }else {
+      for (k=0; k < num; k++)
+        qh_fprintf(qh, fp, 9068, qh_REAL_1, qh_INFINITE);
+    }
+  }else /* qh->CENTERtype == qh_AScentrum */ {
+    num= qh->hull_dim;
+    if (format == qh_PRINTtriangles && qh->DELAUNAY)
+      num--;
+    if (!facet->center)
+      facet->center= qh_getcentrum(qh, facet);
+    for (k=0; k < num; k++)
+      qh_fprintf(qh, fp, 9069, qh_REAL_1, facet->center[k]);
+  }
+  if (format == qh_PRINTgeom && num == 2)
+    qh_fprintf(qh, fp, 9070, " 0\n");
+  else
+    qh_fprintf(qh, fp, 9071, "\n");
+} /* printcenter */
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="printcentrum">-</a>
+
+  qh_printcentrum(qh, fp, facet, radius )
+    print centrum for a facet in OOGL format
+    radius defines size of centrum
+    2-d or 3-d only
+
+  returns:
+    defines facet->center if needed
+*/
+void qh_printcentrum(qhT *qh, FILE *fp, facetT *facet, realT radius) {
+  pointT *centrum, *projpt;
+  boolT tempcentrum= False;
+  realT xaxis[4], yaxis[4], normal[4], dist;
+  realT green[3]={0, 1, 0};
+  vertexT *apex;
+  int k;
+
+  if (qh->CENTERtype == qh_AScentrum) {
+    if (!facet->center)
+      facet->center= qh_getcentrum(qh, facet);
+    centrum= facet->center;
+  }else {
+    centrum= qh_getcentrum(qh, facet);
+    tempcentrum= True;
+  }
+  qh_fprintf(qh, fp, 9072, "{appearance {-normal -edge normscale 0} ");
+  if (qh->firstcentrum) {
+    qh->firstcentrum= False;
+    qh_fprintf(qh, fp, 9073, "{INST geom { define centrum CQUAD  # f%d\n\
+-0.3 -0.3 0.0001     0 0 1 1\n\
+ 0.3 -0.3 0.0001     0 0 1 1\n\
+ 0.3  0.3 0.0001     0 0 1 1\n\
+-0.3  0.3 0.0001     0 0 1 1 } transform { \n", facet->id);
+  }else
+    qh_fprintf(qh, fp, 9074, "{INST geom { : centrum } transform { # f%d\n", facet->id);
+  apex= SETfirstt_(facet->vertices, vertexT);
+  qh_distplane(qh, apex->point, facet, &dist);
+  projpt= qh_projectpoint(qh, apex->point, facet, dist);
+  for (k=qh->hull_dim; k--; ) {
+    xaxis[k]= projpt[k] - centrum[k];
+    normal[k]= facet->normal[k];
+  }
+  if (qh->hull_dim == 2) {
+    xaxis[2]= 0;
+    normal[2]= 0;
+  }else if (qh->hull_dim == 4) {
+    qh_projectdim3(qh, xaxis, xaxis);
+    qh_projectdim3(qh, normal, normal);
+    qh_normalize2(qh, normal, qh->PRINTdim, True, NULL, NULL);
+  }
+  qh_crossproduct(3, xaxis, normal, yaxis);
+  qh_fprintf(qh, fp, 9075, "%8.4g %8.4g %8.4g 0\n", xaxis[0], xaxis[1], xaxis[2]);
+  qh_fprintf(qh, fp, 9076, "%8.4g %8.4g %8.4g 0\n", yaxis[0], yaxis[1], yaxis[2]);
+  qh_fprintf(qh, fp, 9077, "%8.4g %8.4g %8.4g 0\n", normal[0], normal[1], normal[2]);
+  qh_printpoint3(qh, fp, centrum);
+  qh_fprintf(qh, fp, 9078, "1 }}}\n");
+  qh_memfree(qh, projpt, qh->normal_size);
+  qh_printpointvect(qh, fp, centrum, facet->normal, NULL, radius, green);
+  if (tempcentrum)
+    qh_memfree(qh, centrum, qh->normal_size);
+} /* printcentrum */
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="printend">-</a>
+
+  qh_printend(qh, fp, format )
+    prints trailer for all output formats
+
+  see:
+    qh_printbegin() and qh_printafacet()
+
+*/
+void qh_printend(qhT *qh, FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall) {
+  int num;
+  facetT *facet, **facetp;
+
+  if (!qh->printoutnum)
+    qh_fprintf(qh, qh->ferr, 7055, "qhull warning: no facets printed\n");
+  switch (format) {
+  case qh_PRINTgeom:
+    if (qh->hull_dim == 4 && qh->DROPdim < 0  && !qh->PRINTnoplanes) {
+      qh->visit_id++;
+      num= 0;
+      FORALLfacet_(facetlist)
+        qh_printend4geom(qh, fp, facet,&num, printall);
+      FOREACHfacet_(facets)
+        qh_printend4geom(qh, fp, facet, &num, printall);
+      if (num != qh->ridgeoutnum || qh->printoutvar != qh->ridgeoutnum) {
+        qh_fprintf(qh, qh->ferr, 6069, "qhull internal error (qh_printend): number of ridges %d != number printed %d and at end %d\n", qh->ridgeoutnum, qh->printoutvar, num);
+        qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+      }
+    }else
+      qh_fprintf(qh, fp, 9079, "}\n");
+    break;
+  case qh_PRINTinner:
+  case qh_PRINTnormals:
+  case qh_PRINTouter:
+    if (qh->CDDoutput)
+      qh_fprintf(qh, fp, 9080, "end\n");
+    break;
+  case qh_PRINTmaple:
+    qh_fprintf(qh, fp, 9081, "));\n");
+    break;
+  case qh_PRINTmathematica:
+    qh_fprintf(qh, fp, 9082, "}\n");
+    break;
+  case qh_PRINTpoints:
+    if (qh->CDDoutput)
+      qh_fprintf(qh, fp, 9083, "end\n");
+    break;
+  default:
+    break;
+  }
+} /* printend */
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="printend4geom">-</a>
+
+  qh_printend4geom(qh, fp, facet, numridges, printall )
+    helper function for qh_printbegin/printend
+
+  returns:
+    number of printed ridges
+
+  notes:
+    just counts printed ridges if fp=NULL
+    uses facet->visitid
+    must agree with qh_printfacet4geom...
+
+  design:
+    computes color for facet from its normal
+    prints each ridge of facet
+*/
+void qh_printend4geom(qhT *qh, FILE *fp, facetT *facet, int *nump, boolT printall) {
+  realT color[3];
+  int i, num= *nump;
+  facetT *neighbor, **neighborp;
+  ridgeT *ridge, **ridgep;
+
+  if (!printall && qh_skipfacet(qh, facet))
+    return;
+  if (qh->PRINTnoplanes || (facet->visible && qh->NEWfacets))
+    return;
+  if (!facet->normal)
+    return;
+  if (fp) {
+    for (i=0; i < 3; i++) {
+      color[i]= (facet->normal[i]+1.0)/2.0;
+      maximize_(color[i], -1.0);
+      minimize_(color[i], +1.0);
+    }
+  }
+  facet->visitid= qh->visit_id;
+  if (facet->simplicial) {
+    FOREACHneighbor_(facet) {
+      if (neighbor->visitid != qh->visit_id) {
+        if (fp)
+          qh_fprintf(qh, fp, 9084, "3 %d %d %d %8.4g %8.4g %8.4g 1 # f%d f%d\n",
+                 3*num, 3*num+1, 3*num+2, color[0], color[1], color[2],
+                 facet->id, neighbor->id);
+        num++;
+      }
+    }
+  }else {
+    FOREACHridge_(facet->ridges) {
+      neighbor= otherfacet_(ridge, facet);
+      if (neighbor->visitid != qh->visit_id) {
+        if (fp)
+          qh_fprintf(qh, fp, 9085, "3 %d %d %d %8.4g %8.4g %8.4g 1 #r%d f%d f%d\n",
+                 3*num, 3*num+1, 3*num+2, color[0], color[1], color[2],
+                 ridge->id, facet->id, neighbor->id);
+        num++;
+      }
+    }
+  }
+  *nump= num;
+} /* printend4geom */
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="printextremes">-</a>
+
+  qh_printextremes(qh, fp, facetlist, facets, printall )
+    print extreme points for convex hulls or halfspace intersections
+
+  notes:
+    #points, followed by ids, one per line
+
+    sorted by id
+    same order as qh_printpoints_out if no coplanar/interior points
+*/
+void qh_printextremes(qhT *qh, FILE *fp, facetT *facetlist, setT *facets, boolT printall) {
+  setT *vertices, *points;
+  pointT *point;
+  vertexT *vertex, **vertexp;
+  int id;
+  int numpoints=0, point_i, point_n;
+  int allpoints= qh->num_points + qh_setsize(qh, qh->other_points);
+
+  points= qh_settemp(qh, allpoints);
+  qh_setzero(qh, points, 0, allpoints);
+  vertices= qh_facetvertices(qh, facetlist, facets, printall);
+  FOREACHvertex_(vertices) {
+    id= qh_pointid(qh, vertex->point);
+    if (id >= 0) {
+      SETelem_(points, id)= vertex->point;
+      numpoints++;
+    }
+  }
+  qh_settempfree(qh, &vertices);
+  qh_fprintf(qh, fp, 9086, "%d\n", numpoints);
+  FOREACHpoint_i_(qh, points) {
+    if (point)
+      qh_fprintf(qh, fp, 9087, "%d\n", point_i);
+  }
+  qh_settempfree(qh, &points);
+} /* printextremes */
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="printextremes_2d">-</a>
+
+  qh_printextremes_2d(qh, fp, facetlist, facets, printall )
+    prints point ids for facets in qh_ORIENTclock order
+
+  notes:
+    #points, followed by ids, one per line
+    if facetlist/facets are disjoint than the output includes skips
+    errors if facets form a loop
+    does not print coplanar points
+*/
+void qh_printextremes_2d(qhT *qh, FILE *fp, facetT *facetlist, setT *facets, boolT printall) {
+  int numfacets, numridges, totneighbors, numcoplanars, numsimplicial, numtricoplanars;
+  setT *vertices;
+  facetT *facet, *startfacet, *nextfacet;
+  vertexT *vertexA, *vertexB;
+
+  qh_countfacets(qh, facetlist, facets, printall, &numfacets, &numsimplicial,
+      &totneighbors, &numridges, &numcoplanars, &numtricoplanars); /* marks qh->visit_id */
+  vertices= qh_facetvertices(qh, facetlist, facets, printall);
+  qh_fprintf(qh, fp, 9088, "%d\n", qh_setsize(qh, vertices));
+  qh_settempfree(qh, &vertices);
+  if (!numfacets)
+    return;
+  facet= startfacet= facetlist ? facetlist : SETfirstt_(facets, facetT);
+  qh->vertex_visit++;
+  qh->visit_id++;
+  do {
+    if (facet->toporient ^ qh_ORIENTclock) {
+      vertexA= SETfirstt_(facet->vertices, vertexT);
+      vertexB= SETsecondt_(facet->vertices, vertexT);
+      nextfacet= SETfirstt_(facet->neighbors, facetT);
+    }else {
+      vertexA= SETsecondt_(facet->vertices, vertexT);
+      vertexB= SETfirstt_(facet->vertices, vertexT);
+      nextfacet= SETsecondt_(facet->neighbors, facetT);
+    }
+    if (facet->visitid == qh->visit_id) {
+      qh_fprintf(qh, qh->ferr, 6218, "Qhull internal error (qh_printextremes_2d): loop in facet list.  facet %d nextfacet %d\n",
+                 facet->id, nextfacet->id);
+      qh_errexit2(qh, qh_ERRqhull, facet, nextfacet);
+    }
+    if (facet->visitid) {
+      if (vertexA->visitid != qh->vertex_visit) {
+        vertexA->visitid= qh->vertex_visit;
+        qh_fprintf(qh, fp, 9089, "%d\n", qh_pointid(qh, vertexA->point));
+      }
+      if (vertexB->visitid != qh->vertex_visit) {
+        vertexB->visitid= qh->vertex_visit;
+        qh_fprintf(qh, fp, 9090, "%d\n", qh_pointid(qh, vertexB->point));
+      }
+    }
+    facet->visitid= qh->visit_id;
+    facet= nextfacet;
+  }while (facet && facet != startfacet);
+} /* printextremes_2d */
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="printextremes_d">-</a>
+
+  qh_printextremes_d(qh, fp, facetlist, facets, printall )
+    print extreme points of input sites for Delaunay triangulations
+
+  notes:
+    #points, followed by ids, one per line
+
+    unordered
+*/
+void qh_printextremes_d(qhT *qh, FILE *fp, facetT *facetlist, setT *facets, boolT printall) {
+  setT *vertices;
+  vertexT *vertex, **vertexp;
+  boolT upperseen, lowerseen;
+  facetT *neighbor, **neighborp;
+  int numpoints=0;
+
+  vertices= qh_facetvertices(qh, facetlist, facets, printall);
+  qh_vertexneighbors(qh);
+  FOREACHvertex_(vertices) {
+    upperseen= lowerseen= False;
+    FOREACHneighbor_(vertex) {
+      if (neighbor->upperdelaunay)
+        upperseen= True;
+      else
+        lowerseen= True;
+    }
+    if (upperseen && lowerseen) {
+      vertex->seen= True;
+      numpoints++;
+    }else
+      vertex->seen= False;
+  }
+  qh_fprintf(qh, fp, 9091, "%d\n", numpoints);
+  FOREACHvertex_(vertices) {
+    if (vertex->seen)
+      qh_fprintf(qh, fp, 9092, "%d\n", qh_pointid(qh, vertex->point));
+  }
+  qh_settempfree(qh, &vertices);
+} /* printextremes_d */
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="printfacet">-</a>
+
+  qh_printfacet(qh, fp, facet )
+    prints all fields of a facet to fp
+
+  notes:
+    ridges printed in neighbor order
+*/
+void qh_printfacet(qhT *qh, FILE *fp, facetT *facet) {
+
+  qh_printfacetheader(qh, fp, facet);
+  if (facet->ridges)
+    qh_printfacetridges(qh, fp, facet);
+} /* printfacet */
+
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="printfacet2geom">-</a>
+
+  qh_printfacet2geom(qh, fp, facet, color )
+    print facet as part of a 2-d VECT for Geomview
+
+    notes:
+      assume precise calculations in io_r.c with roundoff covered by qh_GEOMepsilon
+      mindist is calculated within io_r.c.  maxoutside is calculated elsewhere
+      so a DISTround error may have occurred.
+*/
+void qh_printfacet2geom(qhT *qh, FILE *fp, facetT *facet, realT color[3]) {
+  pointT *point0, *point1;
+  realT mindist, innerplane, outerplane;
+  int k;
+
+  qh_facet2point(qh, facet, &point0, &point1, &mindist);
+  qh_geomplanes(qh, facet, &outerplane, &innerplane);
+  if (qh->PRINTouter || (!qh->PRINTnoplanes && !qh->PRINTinner))
+    qh_printfacet2geom_points(qh, fp, point0, point1, facet, outerplane, color);
+  if (qh->PRINTinner || (!qh->PRINTnoplanes && !qh->PRINTouter &&
+                outerplane - innerplane > 2 * qh->MAXabs_coord * qh_GEOMepsilon)) {
+    for (k=3; k--; )
+      color[k]= 1.0 - color[k];
+    qh_printfacet2geom_points(qh, fp, point0, point1, facet, innerplane, color);
+  }
+  qh_memfree(qh, point1, qh->normal_size);
+  qh_memfree(qh, point0, qh->normal_size);
+} /* printfacet2geom */
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="printfacet2geom_points">-</a>
+
+  qh_printfacet2geom_points(qh, fp, point1, point2, facet, offset, color )
+    prints a 2-d facet as a VECT with 2 points at some offset.
+    The points are on the facet's plane.
+*/
+void qh_printfacet2geom_points(qhT *qh, FILE *fp, pointT *point1, pointT *point2,
+                               facetT *facet, realT offset, realT color[3]) {
+  pointT *p1= point1, *p2= point2;
+
+  qh_fprintf(qh, fp, 9093, "VECT 1 2 1 2 1 # f%d\n", facet->id);
+  if (offset != 0.0) {
+    p1= qh_projectpoint(qh, p1, facet, -offset);
+    p2= qh_projectpoint(qh, p2, facet, -offset);
+  }
+  qh_fprintf(qh, fp, 9094, "%8.4g %8.4g %8.4g\n%8.4g %8.4g %8.4g\n",
+           p1[0], p1[1], 0.0, p2[0], p2[1], 0.0);
+  if (offset != 0.0) {
+    qh_memfree(qh, p1, qh->normal_size);
+    qh_memfree(qh, p2, qh->normal_size);
+  }
+  qh_fprintf(qh, fp, 9095, "%8.4g %8.4g %8.4g 1.0\n", color[0], color[1], color[2]);
+} /* printfacet2geom_points */
+
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="printfacet2math">-</a>
+
+  qh_printfacet2math(qh, fp, facet, format, notfirst )
+    print 2-d Maple or Mathematica output for a facet
+    may be non-simplicial
+
+  notes:
+    use %16.8f since Mathematica 2.2 does not handle exponential format
+    see qh_printfacet3math
+*/
+void qh_printfacet2math(qhT *qh, FILE *fp, facetT *facet, qh_PRINT format, int notfirst) {
+  pointT *point0, *point1;
+  realT mindist;
+  const char *pointfmt;
+
+  qh_facet2point(qh, facet, &point0, &point1, &mindist);
+  if (notfirst)
+    qh_fprintf(qh, fp, 9096, ",");
+  if (format == qh_PRINTmaple)
+    pointfmt= "[[%16.8f, %16.8f], [%16.8f, %16.8f]]\n";
+  else
+    pointfmt= "Line[{{%16.8f, %16.8f}, {%16.8f, %16.8f}}]\n";
+  qh_fprintf(qh, fp, 9097, pointfmt, point0[0], point0[1], point1[0], point1[1]);
+  qh_memfree(qh, point1, qh->normal_size);
+  qh_memfree(qh, point0, qh->normal_size);
+} /* printfacet2math */
+
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="printfacet3geom_nonsimplicial">-</a>
+
+  qh_printfacet3geom_nonsimplicial(qh, fp, facet, color )
+    print Geomview OFF for a 3-d nonsimplicial facet.
+    if DOintersections, prints ridges to unvisited neighbors(qh->visit_id)
+
+  notes
+    uses facet->visitid for intersections and ridges
+*/
+void qh_printfacet3geom_nonsimplicial(qhT *qh, FILE *fp, facetT *facet, realT color[3]) {
+  ridgeT *ridge, **ridgep;
+  setT *projectedpoints, *vertices;
+  vertexT *vertex, **vertexp, *vertexA, *vertexB;
+  pointT *projpt, *point, **pointp;
+  facetT *neighbor;
+  realT dist, outerplane, innerplane;
+  int cntvertices, k;
+  realT black[3]={0, 0, 0}, green[3]={0, 1, 0};
+
+  qh_geomplanes(qh, facet, &outerplane, &innerplane);
+  vertices= qh_facet3vertex(qh, facet); /* oriented */
+  cntvertices= qh_setsize(qh, vertices);
+  projectedpoints= qh_settemp(qh, cntvertices);
+  FOREACHvertex_(vertices) {
+    zinc_(Zdistio);
+    qh_distplane(qh, vertex->point, facet, &dist);
+    projpt= qh_projectpoint(qh, vertex->point, facet, dist);
+    qh_setappend(qh, &projectedpoints, projpt);
+  }
+  if (qh->PRINTouter || (!qh->PRINTnoplanes && !qh->PRINTinner))
+    qh_printfacet3geom_points(qh, fp, projectedpoints, facet, outerplane, color);
+  if (qh->PRINTinner || (!qh->PRINTnoplanes && !qh->PRINTouter &&
+                outerplane - innerplane > 2 * qh->MAXabs_coord * qh_GEOMepsilon)) {
+    for (k=3; k--; )
+      color[k]= 1.0 - color[k];
+    qh_printfacet3geom_points(qh, fp, projectedpoints, facet, innerplane, color);
+  }
+  FOREACHpoint_(projectedpoints)
+    qh_memfree(qh, point, qh->normal_size);
+  qh_settempfree(qh, &projectedpoints);
+  qh_settempfree(qh, &vertices);
+  if ((qh->DOintersections || qh->PRINTridges)
+  && (!facet->visible || !qh->NEWfacets)) {
+    facet->visitid= qh->visit_id;
+    FOREACHridge_(facet->ridges) {
+      neighbor= otherfacet_(ridge, facet);
+      if (neighbor->visitid != qh->visit_id) {
+        if (qh->DOintersections)
+          qh_printhyperplaneintersection(qh, fp, facet, neighbor, ridge->vertices, black);
+        if (qh->PRINTridges) {
+          vertexA= SETfirstt_(ridge->vertices, vertexT);
+          vertexB= SETsecondt_(ridge->vertices, vertexT);
+          qh_printline3geom(qh, fp, vertexA->point, vertexB->point, green);
+        }
+      }
+    }
+  }
+} /* printfacet3geom_nonsimplicial */
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="printfacet3geom_points">-</a>
+
+  qh_printfacet3geom_points(qh, fp, points, facet, offset )
+    prints a 3-d facet as OFF Geomview object.
+    offset is relative to the facet's hyperplane
+    Facet is determined as a list of points
+*/
+void qh_printfacet3geom_points(qhT *qh, FILE *fp, setT *points, facetT *facet, realT offset, realT color[3]) {
+  int k, n= qh_setsize(qh, points), i;
+  pointT *point, **pointp;
+  setT *printpoints;
+
+  qh_fprintf(qh, fp, 9098, "{ OFF %d 1 1 # f%d\n", n, facet->id);
+  if (offset != 0.0) {
+    printpoints= qh_settemp(qh, n);
+    FOREACHpoint_(points)
+      qh_setappend(qh, &printpoints, qh_projectpoint(qh, point, facet, -offset));
+  }else
+    printpoints= points;
+  FOREACHpoint_(printpoints) {
+    for (k=0; k < qh->hull_dim; k++) {
+      if (k == qh->DROPdim)
+        qh_fprintf(qh, fp, 9099, "0 ");
+      else
+        qh_fprintf(qh, fp, 9100, "%8.4g ", point[k]);
+    }
+    if (printpoints != points)
+      qh_memfree(qh, point, qh->normal_size);
+    qh_fprintf(qh, fp, 9101, "\n");
+  }
+  if (printpoints != points)
+    qh_settempfree(qh, &printpoints);
+  qh_fprintf(qh, fp, 9102, "%d ", n);
+  for (i=0; i < n; i++)
+    qh_fprintf(qh, fp, 9103, "%d ", i);
+  qh_fprintf(qh, fp, 9104, "%8.4g %8.4g %8.4g 1.0 }\n", color[0], color[1], color[2]);
+} /* printfacet3geom_points */
+
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="printfacet3geom_simplicial">-</a>
+
+  qh_printfacet3geom_simplicial(qh, )
+    print Geomview OFF for a 3-d simplicial facet.
+
+  notes:
+    may flip color
+    uses facet->visitid for intersections and ridges
+
+    assume precise calculations in io_r.c with roundoff covered by qh_GEOMepsilon
+    innerplane may be off by qh->DISTround.  Maxoutside is calculated elsewhere
+    so a DISTround error may have occurred.
+*/
+void qh_printfacet3geom_simplicial(qhT *qh, FILE *fp, facetT *facet, realT color[3]) {
+  setT *points, *vertices;
+  vertexT *vertex, **vertexp, *vertexA, *vertexB;
+  facetT *neighbor, **neighborp;
+  realT outerplane, innerplane;
+  realT black[3]={0, 0, 0}, green[3]={0, 1, 0};
+  int k;
+
+  qh_geomplanes(qh, facet, &outerplane, &innerplane);
+  vertices= qh_facet3vertex(qh, facet);
+  points= qh_settemp(qh, qh->TEMPsize);
+  FOREACHvertex_(vertices)
+    qh_setappend(qh, &points, vertex->point);
+  if (qh->PRINTouter || (!qh->PRINTnoplanes && !qh->PRINTinner))
+    qh_printfacet3geom_points(qh, fp, points, facet, outerplane, color);
+  if (qh->PRINTinner || (!qh->PRINTnoplanes && !qh->PRINTouter &&
+              outerplane - innerplane > 2 * qh->MAXabs_coord * qh_GEOMepsilon)) {
+    for (k=3; k--; )
+      color[k]= 1.0 - color[k];
+    qh_printfacet3geom_points(qh, fp, points, facet, innerplane, color);
+  }
+  qh_settempfree(qh, &points);
+  qh_settempfree(qh, &vertices);
+  if ((qh->DOintersections || qh->PRINTridges)
+  && (!facet->visible || !qh->NEWfacets)) {
+    facet->visitid= qh->visit_id;
+    FOREACHneighbor_(facet) {
+      if (neighbor->visitid != qh->visit_id) {
+        vertices= qh_setnew_delnthsorted(qh, facet->vertices, qh->hull_dim,
+                          SETindex_(facet->neighbors, neighbor), 0);
+        if (qh->DOintersections)
+           qh_printhyperplaneintersection(qh, fp, facet, neighbor, vertices, black);
+        if (qh->PRINTridges) {
+          vertexA= SETfirstt_(vertices, vertexT);
+          vertexB= SETsecondt_(vertices, vertexT);
+          qh_printline3geom(qh, fp, vertexA->point, vertexB->point, green);
+        }
+        qh_setfree(qh, &vertices);
+      }
+    }
+  }
+} /* printfacet3geom_simplicial */
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="printfacet3math">-</a>
+
+  qh_printfacet3math(qh, fp, facet, notfirst )
+    print 3-d Maple or Mathematica output for a facet
+
+  notes:
+    may be non-simplicial
+    use %16.8f since Mathematica 2.2 does not handle exponential format
+    see qh_printfacet2math
+*/
+void qh_printfacet3math(qhT *qh, FILE *fp, facetT *facet, qh_PRINT format, int notfirst) {
+  vertexT *vertex, **vertexp;
+  setT *points, *vertices;
+  pointT *point, **pointp;
+  boolT firstpoint= True;
+  realT dist;
+  const char *pointfmt, *endfmt;
+
+  if (notfirst)
+    qh_fprintf(qh, fp, 9105, ",\n");
+  vertices= qh_facet3vertex(qh, facet);
+  points= qh_settemp(qh, qh_setsize(qh, vertices));
+  FOREACHvertex_(vertices) {
+    zinc_(Zdistio);
+    qh_distplane(qh, vertex->point, facet, &dist);
+    point= qh_projectpoint(qh, vertex->point, facet, dist);
+    qh_setappend(qh, &points, point);
+  }
+  if (format == qh_PRINTmaple) {
+    qh_fprintf(qh, fp, 9106, "[");
+    pointfmt= "[%16.8f, %16.8f, %16.8f]";
+    endfmt= "]";
+  }else {
+    qh_fprintf(qh, fp, 9107, "Polygon[{");
+    pointfmt= "{%16.8f, %16.8f, %16.8f}";
+    endfmt= "}]";
+  }
+  FOREACHpoint_(points) {
+    if (firstpoint)
+      firstpoint= False;
+    else
+      qh_fprintf(qh, fp, 9108, ",\n");
+    qh_fprintf(qh, fp, 9109, pointfmt, point[0], point[1], point[2]);
+  }
+  FOREACHpoint_(points)
+    qh_memfree(qh, point, qh->normal_size);
+  qh_settempfree(qh, &points);
+  qh_settempfree(qh, &vertices);
+  qh_fprintf(qh, fp, 9110, "%s", endfmt);
+} /* printfacet3math */
+
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="printfacet3vertex">-</a>
+
+  qh_printfacet3vertex(qh, fp, facet, format )
+    print vertices in a 3-d facet as point ids
+
+  notes:
+    prints number of vertices first if format == qh_PRINToff
+    the facet may be non-simplicial
+*/
+void qh_printfacet3vertex(qhT *qh, FILE *fp, facetT *facet, qh_PRINT format) {
+  vertexT *vertex, **vertexp;
+  setT *vertices;
+
+  vertices= qh_facet3vertex(qh, facet);
+  if (format == qh_PRINToff)
+    qh_fprintf(qh, fp, 9111, "%d ", qh_setsize(qh, vertices));
+  FOREACHvertex_(vertices)
+    qh_fprintf(qh, fp, 9112, "%d ", qh_pointid(qh, vertex->point));
+  qh_fprintf(qh, fp, 9113, "\n");
+  qh_settempfree(qh, &vertices);
+} /* printfacet3vertex */
+
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="printfacet4geom_nonsimplicial">-</a>
+
+  qh_printfacet4geom_nonsimplicial(qh, )
+    print Geomview 4OFF file for a 4d nonsimplicial facet
+    prints all ridges to unvisited neighbors (qh.visit_id)
+    if qh.DROPdim
+      prints in OFF format
+
+  notes:
+    must agree with printend4geom()
+*/
+void qh_printfacet4geom_nonsimplicial(qhT *qh, FILE *fp, facetT *facet, realT color[3]) {
+  facetT *neighbor;
+  ridgeT *ridge, **ridgep;
+  vertexT *vertex, **vertexp;
+  pointT *point;
+  int k;
+  realT dist;
+
+  facet->visitid= qh->visit_id;
+  if (qh->PRINTnoplanes || (facet->visible && qh->NEWfacets))
+    return;
+  FOREACHridge_(facet->ridges) {
+    neighbor= otherfacet_(ridge, facet);
+    if (neighbor->visitid == qh->visit_id)
+      continue;
+    if (qh->PRINTtransparent && !neighbor->good)
+      continue;
+    if (qh->DOintersections)
+      qh_printhyperplaneintersection(qh, fp, facet, neighbor, ridge->vertices, color);
+    else {
+      if (qh->DROPdim >= 0)
+        qh_fprintf(qh, fp, 9114, "OFF 3 1 1 # f%d\n", facet->id);
+      else {
+        qh->printoutvar++;
+        qh_fprintf(qh, fp, 9115, "# r%d between f%d f%d\n", ridge->id, facet->id, neighbor->id);
+      }
+      FOREACHvertex_(ridge->vertices) {
+        zinc_(Zdistio);
+        qh_distplane(qh, vertex->point,facet, &dist);
+        point=qh_projectpoint(qh, vertex->point,facet, dist);
+        for (k=0; k < qh->hull_dim; k++) {
+          if (k != qh->DROPdim)
+            qh_fprintf(qh, fp, 9116, "%8.4g ", point[k]);
+        }
+        qh_fprintf(qh, fp, 9117, "\n");
+        qh_memfree(qh, point, qh->normal_size);
+      }
+      if (qh->DROPdim >= 0)
+        qh_fprintf(qh, fp, 9118, "3 0 1 2 %8.4g %8.4g %8.4g\n", color[0], color[1], color[2]);
+    }
+  }
+} /* printfacet4geom_nonsimplicial */
+
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="printfacet4geom_simplicial">-</a>
+
+  qh_printfacet4geom_simplicial(qh, fp, facet, color )
+    print Geomview 4OFF file for a 4d simplicial facet
+    prints triangles for unvisited neighbors (qh.visit_id)
+
+  notes:
+    must agree with printend4geom()
+*/
+void qh_printfacet4geom_simplicial(qhT *qh, FILE *fp, facetT *facet, realT color[3]) {
+  setT *vertices;
+  facetT *neighbor, **neighborp;
+  vertexT *vertex, **vertexp;
+  int k;
+
+  facet->visitid= qh->visit_id;
+  if (qh->PRINTnoplanes || (facet->visible && qh->NEWfacets))
+    return;
+  FOREACHneighbor_(facet) {
+    if (neighbor->visitid == qh->visit_id)
+      continue;
+    if (qh->PRINTtransparent && !neighbor->good)
+      continue;
+    vertices= qh_setnew_delnthsorted(qh, facet->vertices, qh->hull_dim,
+                          SETindex_(facet->neighbors, neighbor), 0);
+    if (qh->DOintersections)
+      qh_printhyperplaneintersection(qh, fp, facet, neighbor, vertices, color);
+    else {
+      if (qh->DROPdim >= 0)
+        qh_fprintf(qh, fp, 9119, "OFF 3 1 1 # ridge between f%d f%d\n",
+                facet->id, neighbor->id);
+      else {
+        qh->printoutvar++;
+        qh_fprintf(qh, fp, 9120, "# ridge between f%d f%d\n", facet->id, neighbor->id);
+      }
+      FOREACHvertex_(vertices) {
+        for (k=0; k < qh->hull_dim; k++) {
+          if (k != qh->DROPdim)
+            qh_fprintf(qh, fp, 9121, "%8.4g ", vertex->point[k]);
+        }
+        qh_fprintf(qh, fp, 9122, "\n");
+      }
+      if (qh->DROPdim >= 0)
+        qh_fprintf(qh, fp, 9123, "3 0 1 2 %8.4g %8.4g %8.4g\n", color[0], color[1], color[2]);
+    }
+    qh_setfree(qh, &vertices);
+  }
+} /* printfacet4geom_simplicial */
+
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="printfacetNvertex_nonsimplicial">-</a>
+
+  qh_printfacetNvertex_nonsimplicial(qh, fp, facet, id, format )
+    print vertices for an N-d non-simplicial facet
+    triangulates each ridge to the id
+*/
+void qh_printfacetNvertex_nonsimplicial(qhT *qh, FILE *fp, facetT *facet, int id, qh_PRINT format) {
+  vertexT *vertex, **vertexp;
+  ridgeT *ridge, **ridgep;
+
+  if (facet->visible && qh->NEWfacets)
+    return;
+  FOREACHridge_(facet->ridges) {
+    if (format == qh_PRINTtriangles)
+      qh_fprintf(qh, fp, 9124, "%d ", qh->hull_dim);
+    qh_fprintf(qh, fp, 9125, "%d ", id);
+    if ((ridge->top == facet) ^ qh_ORIENTclock) {
+      FOREACHvertex_(ridge->vertices)
+        qh_fprintf(qh, fp, 9126, "%d ", qh_pointid(qh, vertex->point));
+    }else {
+      FOREACHvertexreverse12_(ridge->vertices)
+        qh_fprintf(qh, fp, 9127, "%d ", qh_pointid(qh, vertex->point));
+    }
+    qh_fprintf(qh, fp, 9128, "\n");
+  }
+} /* printfacetNvertex_nonsimplicial */
+
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="printfacetNvertex_simplicial">-</a>
+
+  qh_printfacetNvertex_simplicial(qh, fp, facet, format )
+    print vertices for an N-d simplicial facet
+    prints vertices for non-simplicial facets
+      2-d facets (orientation preserved by qh_mergefacet2d)
+      PRINToff ('o') for 4-d and higher
+*/
+void qh_printfacetNvertex_simplicial(qhT *qh, FILE *fp, facetT *facet, qh_PRINT format) {
+  vertexT *vertex, **vertexp;
+
+  if (format == qh_PRINToff || format == qh_PRINTtriangles)
+    qh_fprintf(qh, fp, 9129, "%d ", qh_setsize(qh, facet->vertices));
+  if ((facet->toporient ^ qh_ORIENTclock)
+  || (qh->hull_dim > 2 && !facet->simplicial)) {
+    FOREACHvertex_(facet->vertices)
+      qh_fprintf(qh, fp, 9130, "%d ", qh_pointid(qh, vertex->point));
+  }else {
+    FOREACHvertexreverse12_(facet->vertices)
+      qh_fprintf(qh, fp, 9131, "%d ", qh_pointid(qh, vertex->point));
+  }
+  qh_fprintf(qh, fp, 9132, "\n");
+} /* printfacetNvertex_simplicial */
+
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="printfacetheader">-</a>
+
+  qh_printfacetheader(qh, fp, facet )
+    prints header fields of a facet to fp
+
+  notes:
+    for 'f' output and debugging
+    Same as QhullFacet::printHeader()
+*/
+void qh_printfacetheader(qhT *qh, FILE *fp, facetT *facet) {
+  pointT *point, **pointp, *furthest;
+  facetT *neighbor, **neighborp;
+  realT dist;
+
+  if (facet == qh_MERGEridge) {
+    qh_fprintf(qh, fp, 9133, " MERGEridge\n");
+    return;
+  }else if (facet == qh_DUPLICATEridge) {
+    qh_fprintf(qh, fp, 9134, " DUPLICATEridge\n");
+    return;
+  }else if (!facet) {
+    qh_fprintf(qh, fp, 9135, " NULLfacet\n");
+    return;
+  }
+  qh->old_randomdist= qh->RANDOMdist;
+  qh->RANDOMdist= False;
+  qh_fprintf(qh, fp, 9136, "- f%d\n", facet->id);
+  qh_fprintf(qh, fp, 9137, "    - flags:");
+  if (facet->toporient)
+    qh_fprintf(qh, fp, 9138, " top");
+  else
+    qh_fprintf(qh, fp, 9139, " bottom");
+  if (facet->simplicial)
+    qh_fprintf(qh, fp, 9140, " simplicial");
+  if (facet->tricoplanar)
+    qh_fprintf(qh, fp, 9141, " tricoplanar");
+  if (facet->upperdelaunay)
+    qh_fprintf(qh, fp, 9142, " upperDelaunay");
+  if (facet->visible)
+    qh_fprintf(qh, fp, 9143, " visible");
+  if (facet->newfacet)
+    qh_fprintf(qh, fp, 9144, " new");
+  if (facet->tested)
+    qh_fprintf(qh, fp, 9145, " tested");
+  if (!facet->good)
+    qh_fprintf(qh, fp, 9146, " notG");
+  if (facet->seen)
+    qh_fprintf(qh, fp, 9147, " seen");
+  if (facet->coplanar)
+    qh_fprintf(qh, fp, 9148, " coplanar");
+  if (facet->mergehorizon)
+    qh_fprintf(qh, fp, 9149, " mergehorizon");
+  if (facet->keepcentrum)
+    qh_fprintf(qh, fp, 9150, " keepcentrum");
+  if (facet->dupridge)
+    qh_fprintf(qh, fp, 9151, " dupridge");
+  if (facet->mergeridge && !facet->mergeridge2)
+    qh_fprintf(qh, fp, 9152, " mergeridge1");
+  if (facet->mergeridge2)
+    qh_fprintf(qh, fp, 9153, " mergeridge2");
+  if (facet->newmerge)
+    qh_fprintf(qh, fp, 9154, " newmerge");
+  if (facet->flipped)
+    qh_fprintf(qh, fp, 9155, " flipped");
+  if (facet->notfurthest)
+    qh_fprintf(qh, fp, 9156, " notfurthest");
+  if (facet->degenerate)
+    qh_fprintf(qh, fp, 9157, " degenerate");
+  if (facet->redundant)
+    qh_fprintf(qh, fp, 9158, " redundant");
+  qh_fprintf(qh, fp, 9159, "\n");
+  if (facet->isarea)
+    qh_fprintf(qh, fp, 9160, "    - area: %2.2g\n", facet->f.area);
+  else if (qh->NEWfacets && facet->visible && facet->f.replace)
+    qh_fprintf(qh, fp, 9161, "    - replacement: f%d\n", facet->f.replace->id);
+  else if (facet->newfacet) {
+    if (facet->f.samecycle && facet->f.samecycle != facet)
+      qh_fprintf(qh, fp, 9162, "    - shares same visible/horizon as f%d\n", facet->f.samecycle->id);
+  }else if (facet->tricoplanar /* !isarea */) {
+    if (facet->f.triowner)
+      qh_fprintf(qh, fp, 9163, "    - owner of normal & centrum is facet f%d\n", facet->f.triowner->id);
+  }else if (facet->f.newcycle)
+    qh_fprintf(qh, fp, 9164, "    - was horizon to f%d\n", facet->f.newcycle->id);
+  if (facet->nummerge)
+    qh_fprintf(qh, fp, 9165, "    - merges: %d\n", facet->nummerge);
+  qh_printpointid(qh, fp, "    - normal: ", qh->hull_dim, facet->normal, qh_IDunknown);
+  qh_fprintf(qh, fp, 9166, "    - offset: %10.7g\n", facet->offset);
+  if (qh->CENTERtype == qh_ASvoronoi || facet->center)
+    qh_printcenter(qh, fp, qh_PRINTfacets, "    - center: ", facet);
+#if qh_MAXoutside
+  if (facet->maxoutside > qh->DISTround)
+    qh_fprintf(qh, fp, 9167, "    - maxoutside: %10.7g\n", facet->maxoutside);
+#endif
+  if (!SETempty_(facet->outsideset)) {
+    furthest= (pointT*)qh_setlast(facet->outsideset);
+    if (qh_setsize(qh, facet->outsideset) < 6) {
+      qh_fprintf(qh, fp, 9168, "    - outside set(furthest p%d):\n", qh_pointid(qh, furthest));
+      FOREACHpoint_(facet->outsideset)
+        qh_printpoint(qh, fp, "     ", point);
+    }else if (qh_setsize(qh, facet->outsideset) < 21) {
+      qh_printpoints(qh, fp, "    - outside set:", facet->outsideset);
+    }else {
+      qh_fprintf(qh, fp, 9169, "    - outside set:  %d points.", qh_setsize(qh, facet->outsideset));
+      qh_printpoint(qh, fp, "  Furthest", furthest);
+    }
+#if !qh_COMPUTEfurthest
+    qh_fprintf(qh, fp, 9170, "    - furthest distance= %2.2g\n", facet->furthestdist);
+#endif
+  }
+  if (!SETempty_(facet->coplanarset)) {
+    furthest= (pointT*)qh_setlast(facet->coplanarset);
+    if (qh_setsize(qh, facet->coplanarset) < 6) {
+      qh_fprintf(qh, fp, 9171, "    - coplanar set(furthest p%d):\n", qh_pointid(qh, furthest));
+      FOREACHpoint_(facet->coplanarset)
+        qh_printpoint(qh, fp, "     ", point);
+    }else if (qh_setsize(qh, facet->coplanarset) < 21) {
+      qh_printpoints(qh, fp, "    - coplanar set:", facet->coplanarset);
+    }else {
+      qh_fprintf(qh, fp, 9172, "    - coplanar set:  %d points.", qh_setsize(qh, facet->coplanarset));
+      qh_printpoint(qh, fp, "  Furthest", furthest);
+    }
+    zinc_(Zdistio);
+    qh_distplane(qh, furthest, facet, &dist);
+    qh_fprintf(qh, fp, 9173, "      furthest distance= %2.2g\n", dist);
+  }
+  qh_printvertices(qh, fp, "    - vertices:", facet->vertices);
+  qh_fprintf(qh, fp, 9174, "    - neighboring facets:");
+  FOREACHneighbor_(facet) {
+    if (neighbor == qh_MERGEridge)
+      qh_fprintf(qh, fp, 9175, " MERGE");
+    else if (neighbor == qh_DUPLICATEridge)
+      qh_fprintf(qh, fp, 9176, " DUP");
+    else
+      qh_fprintf(qh, fp, 9177, " f%d", neighbor->id);
+  }
+  qh_fprintf(qh, fp, 9178, "\n");
+  qh->RANDOMdist= qh->old_randomdist;
+} /* printfacetheader */
+
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="printfacetridges">-</a>
+
+  qh_printfacetridges(qh, fp, facet )
+    prints ridges of a facet to fp
+
+  notes:
+    ridges printed in neighbor order
+    assumes the ridges exist
+    for 'f' output
+    same as QhullFacet::printRidges
+*/
+void qh_printfacetridges(qhT *qh, FILE *fp, facetT *facet) {
+  facetT *neighbor, **neighborp;
+  ridgeT *ridge, **ridgep;
+  int numridges= 0;
+
+
+  if (facet->visible && qh->NEWfacets) {
+    qh_fprintf(qh, fp, 9179, "    - ridges(ids may be garbage):");
+    FOREACHridge_(facet->ridges)
+      qh_fprintf(qh, fp, 9180, " r%d", ridge->id);
+    qh_fprintf(qh, fp, 9181, "\n");
+  }else {
+    qh_fprintf(qh, fp, 9182, "    - ridges:\n");
+    FOREACHridge_(facet->ridges)
+      ridge->seen= False;
+    if (qh->hull_dim == 3) {
+      ridge= SETfirstt_(facet->ridges, ridgeT);
+      while (ridge && !ridge->seen) {
+        ridge->seen= True;
+        qh_printridge(qh, fp, ridge);
+        numridges++;
+        ridge= qh_nextridge3d(ridge, facet, NULL);
+        }
+    }else {
+      FOREACHneighbor_(facet) {
+        FOREACHridge_(facet->ridges) {
+          if (otherfacet_(ridge,facet) == neighbor) {
+            ridge->seen= True;
+            qh_printridge(qh, fp, ridge);
+            numridges++;
+          }
+        }
+      }
+    }
+    if (numridges != qh_setsize(qh, facet->ridges)) {
+      qh_fprintf(qh, fp, 9183, "     - all ridges:");
+      FOREACHridge_(facet->ridges)
+        qh_fprintf(qh, fp, 9184, " r%d", ridge->id);
+        qh_fprintf(qh, fp, 9185, "\n");
+    }
+    FOREACHridge_(facet->ridges) {
+      if (!ridge->seen)
+        qh_printridge(qh, fp, ridge);
+    }
+  }
+} /* printfacetridges */
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="printfacets">-</a>
+
+  qh_printfacets(qh, fp, format, facetlist, facets, printall )
+    prints facetlist and/or facet set in output format
+
+  notes:
+    also used for specialized formats ('FO' and summary)
+    turns off 'Rn' option since want actual numbers
+*/
+void qh_printfacets(qhT *qh, FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall) {
+  int numfacets, numsimplicial, numridges, totneighbors, numcoplanars, numtricoplanars;
+  facetT *facet, **facetp;
+  setT *vertices;
+  coordT *center;
+  realT outerplane, innerplane;
+
+  qh->old_randomdist= qh->RANDOMdist;
+  qh->RANDOMdist= False;
+  if (qh->CDDoutput && (format == qh_PRINTcentrums || format == qh_PRINTpointintersect || format == qh_PRINToff))
+    qh_fprintf(qh, qh->ferr, 7056, "qhull warning: CDD format is not available for centrums, halfspace\nintersections, and OFF file format.\n");
+  if (format == qh_PRINTnone)
+    ; /* print nothing */
+  else if (format == qh_PRINTaverage) {
+    vertices= qh_facetvertices(qh, facetlist, facets, printall);
+    center= qh_getcenter(qh, vertices);
+    qh_fprintf(qh, fp, 9186, "%d 1\n", qh->hull_dim);
+    qh_printpointid(qh, fp, NULL, qh->hull_dim, center, qh_IDunknown);
+    qh_memfree(qh, center, qh->normal_size);
+    qh_settempfree(qh, &vertices);
+  }else if (format == qh_PRINTextremes) {
+    if (qh->DELAUNAY)
+      qh_printextremes_d(qh, fp, facetlist, facets, printall);
+    else if (qh->hull_dim == 2)
+      qh_printextremes_2d(qh, fp, facetlist, facets, printall);
+    else
+      qh_printextremes(qh, fp, facetlist, facets, printall);
+  }else if (format == qh_PRINToptions)
+    qh_fprintf(qh, fp, 9187, "Options selected for Qhull %s:\n%s\n", qh_version, qh->qhull_options);
+  else if (format == qh_PRINTpoints && !qh->VORONOI)
+    qh_printpoints_out(qh, fp, facetlist, facets, printall);
+  else if (format == qh_PRINTqhull)
+    qh_fprintf(qh, fp, 9188, "%s | %s\n", qh->rbox_command, qh->qhull_command);
+  else if (format == qh_PRINTsize) {
+    qh_fprintf(qh, fp, 9189, "0\n2 ");
+    qh_fprintf(qh, fp, 9190, qh_REAL_1, qh->totarea);
+    qh_fprintf(qh, fp, 9191, qh_REAL_1, qh->totvol);
+    qh_fprintf(qh, fp, 9192, "\n");
+  }else if (format == qh_PRINTsummary) {
+    qh_countfacets(qh, facetlist, facets, printall, &numfacets, &numsimplicial,
+      &totneighbors, &numridges, &numcoplanars, &numtricoplanars);
+    vertices= qh_facetvertices(qh, facetlist, facets, printall);
+    qh_fprintf(qh, fp, 9193, "10 %d %d %d %d %d %d %d %d %d %d\n2 ", qh->hull_dim,
+                qh->num_points + qh_setsize(qh, qh->other_points),
+                qh->num_vertices, qh->num_facets - qh->num_visible,
+                qh_setsize(qh, vertices), numfacets, numcoplanars,
+                numfacets - numsimplicial, zzval_(Zdelvertextot),
+                numtricoplanars);
+    qh_settempfree(qh, &vertices);
+    qh_outerinner(qh, NULL, &outerplane, &innerplane);
+    qh_fprintf(qh, fp, 9194, qh_REAL_2n, outerplane, innerplane);
+  }else if (format == qh_PRINTvneighbors)
+    qh_printvneighbors(qh, fp, facetlist, facets, printall);
+  else if (qh->VORONOI && format == qh_PRINToff)
+    qh_printvoronoi(qh, fp, format, facetlist, facets, printall);
+  else if (qh->VORONOI && format == qh_PRINTgeom) {
+    qh_printbegin(qh, fp, format, facetlist, facets, printall);
+    qh_printvoronoi(qh, fp, format, facetlist, facets, printall);
+    qh_printend(qh, fp, format, facetlist, facets, printall);
+  }else if (qh->VORONOI
+  && (format == qh_PRINTvertices || format == qh_PRINTinner || format == qh_PRINTouter))
+    qh_printvdiagram(qh, fp, format, facetlist, facets, printall);
+  else {
+    qh_printbegin(qh, fp, format, facetlist, facets, printall);
+    FORALLfacet_(facetlist)
+      qh_printafacet(qh, fp, format, facet, printall);
+    FOREACHfacet_(facets)
+      qh_printafacet(qh, fp, format, facet, printall);
+    qh_printend(qh, fp, format, facetlist, facets, printall);
+  }
+  qh->RANDOMdist= qh->old_randomdist;
+} /* printfacets */
+
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="printhyperplaneintersection">-</a>
+
+  qh_printhyperplaneintersection(qh, fp, facet1, facet2, vertices, color )
+    print Geomview OFF or 4OFF for the intersection of two hyperplanes in 3-d or 4-d
+*/
+void qh_printhyperplaneintersection(qhT *qh, FILE *fp, facetT *facet1, facetT *facet2,
+                   setT *vertices, realT color[3]) {
+  realT costheta, denominator, dist1, dist2, s, t, mindenom, p[4];
+  vertexT *vertex, **vertexp;
+  int i, k;
+  boolT nearzero1, nearzero2;
+
+  costheta= qh_getangle(qh, facet1->normal, facet2->normal);
+  denominator= 1 - costheta * costheta;
+  i= qh_setsize(qh, vertices);
+  if (qh->hull_dim == 3)
+    qh_fprintf(qh, fp, 9195, "VECT 1 %d 1 %d 1 ", i, i);
+  else if (qh->hull_dim == 4 && qh->DROPdim >= 0)
+    qh_fprintf(qh, fp, 9196, "OFF 3 1 1 ");
+  else
+    qh->printoutvar++;
+  qh_fprintf(qh, fp, 9197, "# intersect f%d f%d\n", facet1->id, facet2->id);
+  mindenom= 1 / (10.0 * qh->MAXabs_coord);
+  FOREACHvertex_(vertices) {
+    zadd_(Zdistio, 2);
+    qh_distplane(qh, vertex->point, facet1, &dist1);
+    qh_distplane(qh, vertex->point, facet2, &dist2);
+    s= qh_divzero(-dist1 + costheta * dist2, denominator,mindenom,&nearzero1);
+    t= qh_divzero(-dist2 + costheta * dist1, denominator,mindenom,&nearzero2);
+    if (nearzero1 || nearzero2)
+      s= t= 0.0;
+    for (k=qh->hull_dim; k--; )
+      p[k]= vertex->point[k] + facet1->normal[k] * s + facet2->normal[k] * t;
+    if (qh->PRINTdim <= 3) {
+      qh_projectdim3(qh, p, p);
+      qh_fprintf(qh, fp, 9198, "%8.4g %8.4g %8.4g # ", p[0], p[1], p[2]);
+    }else
+      qh_fprintf(qh, fp, 9199, "%8.4g %8.4g %8.4g %8.4g # ", p[0], p[1], p[2], p[3]);
+    if (nearzero1+nearzero2)
+      qh_fprintf(qh, fp, 9200, "p%d(coplanar facets)\n", qh_pointid(qh, vertex->point));
+    else
+      qh_fprintf(qh, fp, 9201, "projected p%d\n", qh_pointid(qh, vertex->point));
+  }
+  if (qh->hull_dim == 3)
+    qh_fprintf(qh, fp, 9202, "%8.4g %8.4g %8.4g 1.0\n", color[0], color[1], color[2]);
+  else if (qh->hull_dim == 4 && qh->DROPdim >= 0)
+    qh_fprintf(qh, fp, 9203, "3 0 1 2 %8.4g %8.4g %8.4g 1.0\n", color[0], color[1], color[2]);
+} /* printhyperplaneintersection */
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="printline3geom">-</a>
+
+  qh_printline3geom(qh, fp, pointA, pointB, color )
+    prints a line as a VECT
+    prints 0's for qh.DROPdim
+
+  notes:
+    if pointA == pointB,
+      it's a 1 point VECT
+*/
+void qh_printline3geom(qhT *qh, FILE *fp, pointT *pointA, pointT *pointB, realT color[3]) {
+  int k;
+  realT pA[4], pB[4];
+
+  qh_projectdim3(qh, pointA, pA);
+  qh_projectdim3(qh, pointB, pB);
+  if ((fabs(pA[0] - pB[0]) > 1e-3) ||
+      (fabs(pA[1] - pB[1]) > 1e-3) ||
+      (fabs(pA[2] - pB[2]) > 1e-3)) {
+    qh_fprintf(qh, fp, 9204, "VECT 1 2 1 2 1\n");
+    for (k=0; k < 3; k++)
+       qh_fprintf(qh, fp, 9205, "%8.4g ", pB[k]);
+    qh_fprintf(qh, fp, 9206, " # p%d\n", qh_pointid(qh, pointB));
+  }else
+    qh_fprintf(qh, fp, 9207, "VECT 1 1 1 1 1\n");
+  for (k=0; k < 3; k++)
+    qh_fprintf(qh, fp, 9208, "%8.4g ", pA[k]);
+  qh_fprintf(qh, fp, 9209, " # p%d\n", qh_pointid(qh, pointA));
+  qh_fprintf(qh, fp, 9210, "%8.4g %8.4g %8.4g 1\n", color[0], color[1], color[2]);
+}
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="printneighborhood">-</a>
+
+  qh_printneighborhood(qh, fp, format, facetA, facetB, printall )
+    print neighborhood of one or two facets
+
+  notes:
+    calls qh_findgood_all()
+    bumps qh.visit_id
+*/
+void qh_printneighborhood(qhT *qh, FILE *fp, qh_PRINT format, facetT *facetA, facetT *facetB, boolT printall) {
+  facetT *neighbor, **neighborp, *facet;
+  setT *facets;
+
+  if (format == qh_PRINTnone)
+    return;
+  qh_findgood_all(qh, qh->facet_list);
+  if (facetA == facetB)
+    facetB= NULL;
+  facets= qh_settemp(qh, 2*(qh_setsize(qh, facetA->neighbors)+1));
+  qh->visit_id++;
+  for (facet= facetA; facet; facet= ((facet == facetA) ? facetB : NULL)) {
+    if (facet->visitid != qh->visit_id) {
+      facet->visitid= qh->visit_id;
+      qh_setappend(qh, &facets, facet);
+    }
+    FOREACHneighbor_(facet) {
+      if (neighbor->visitid == qh->visit_id)
+        continue;
+      neighbor->visitid= qh->visit_id;
+      if (printall || !qh_skipfacet(qh, neighbor))
+        qh_setappend(qh, &facets, neighbor);
+    }
+  }
+  qh_printfacets(qh, fp, format, NULL, facets, printall);
+  qh_settempfree(qh, &facets);
+} /* printneighborhood */
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="printpoint">-</a>
+
+  qh_printpoint(qh, fp, string, point )
+  qh_printpointid(qh, fp, string, dim, point, id )
+    prints the coordinates of a point
+
+  returns:
+    if string is defined
+      prints 'string p%d'.  Skips p%d if id=qh_IDunknown(-1) or qh_IDnone(-3)
+
+  notes:
+    nop if point is NULL
+    Same as QhullPoint's printPoint
+*/
+void qh_printpoint(qhT *qh, FILE *fp, const char *string, pointT *point) {
+  int id= qh_pointid(qh, point);
+
+  qh_printpointid(qh, fp, string, qh->hull_dim, point, id);
+} /* printpoint */
+
+void qh_printpointid(qhT *qh, FILE *fp, const char *string, int dim, pointT *point, int id) {
+  int k;
+  realT r; /*bug fix*/
+
+  if (!point)
+    return;
+  if (string) {
+    qh_fprintf(qh, fp, 9211, "%s", string);
+    if (id != qh_IDunknown && id != qh_IDnone)
+      qh_fprintf(qh, fp, 9212, " p%d: ", id);
+  }
+  for (k=dim; k--; ) {
+    r= *point++;
+    if (string)
+      qh_fprintf(qh, fp, 9213, " %8.4g", r);
+    else
+      qh_fprintf(qh, fp, 9214, qh_REAL_1, r);
+  }
+  qh_fprintf(qh, fp, 9215, "\n");
+} /* printpointid */
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="printpoint3">-</a>
+
+  qh_printpoint3(qh, fp, point )
+    prints 2-d, 3-d, or 4-d point as Geomview 3-d coordinates
+*/
+void qh_printpoint3(qhT *qh, FILE *fp, pointT *point) {
+  int k;
+  realT p[4];
+
+  qh_projectdim3(qh, point, p);
+  for (k=0; k < 3; k++)
+    qh_fprintf(qh, fp, 9216, "%8.4g ", p[k]);
+  qh_fprintf(qh, fp, 9217, " # p%d\n", qh_pointid(qh, point));
+} /* printpoint3 */
+
+/*----------------------------------------
+-printpoints- print pointids for a set of points starting at index
+   see geom_r.c
+*/
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="printpoints_out">-</a>
+
+  qh_printpoints_out(qh, fp, facetlist, facets, printall )
+    prints vertices, coplanar/inside points, for facets by their point coordinates
+    allows qh.CDDoutput
+
+  notes:
+    same format as qhull input
+    if no coplanar/interior points,
+      same order as qh_printextremes
+*/
+void qh_printpoints_out(qhT *qh, FILE *fp, facetT *facetlist, setT *facets, boolT printall) {
+  int allpoints= qh->num_points + qh_setsize(qh, qh->other_points);
+  int numpoints=0, point_i, point_n;
+  setT *vertices, *points;
+  facetT *facet, **facetp;
+  pointT *point, **pointp;
+  vertexT *vertex, **vertexp;
+  int id;
+
+  points= qh_settemp(qh, allpoints);
+  qh_setzero(qh, points, 0, allpoints);
+  vertices= qh_facetvertices(qh, facetlist, facets, printall);
+  FOREACHvertex_(vertices) {
+    id= qh_pointid(qh, vertex->point);
+    if (id >= 0)
+      SETelem_(points, id)= vertex->point;
+  }
+  if (qh->KEEPinside || qh->KEEPcoplanar || qh->KEEPnearinside) {
+    FORALLfacet_(facetlist) {
+      if (!printall && qh_skipfacet(qh, facet))
+        continue;
+      FOREACHpoint_(facet->coplanarset) {
+        id= qh_pointid(qh, point);
+        if (id >= 0)
+          SETelem_(points, id)= point;
+      }
+    }
+    FOREACHfacet_(facets) {
+      if (!printall && qh_skipfacet(qh, facet))
+        continue;
+      FOREACHpoint_(facet->coplanarset) {
+        id= qh_pointid(qh, point);
+        if (id >= 0)
+          SETelem_(points, id)= point;
+      }
+    }
+  }
+  qh_settempfree(qh, &vertices);
+  FOREACHpoint_i_(qh, points) {
+    if (point)
+      numpoints++;
+  }
+  if (qh->CDDoutput)
+    qh_fprintf(qh, fp, 9218, "%s | %s\nbegin\n%d %d real\n", qh->rbox_command,
+             qh->qhull_command, numpoints, qh->hull_dim + 1);
+  else
+    qh_fprintf(qh, fp, 9219, "%d\n%d\n", qh->hull_dim, numpoints);
+  FOREACHpoint_i_(qh, points) {
+    if (point) {
+      if (qh->CDDoutput)
+        qh_fprintf(qh, fp, 9220, "1 ");
+      qh_printpoint(qh, fp, NULL, point);
+    }
+  }
+  if (qh->CDDoutput)
+    qh_fprintf(qh, fp, 9221, "end\n");
+  qh_settempfree(qh, &points);
+} /* printpoints_out */
+
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="printpointvect">-</a>
+
+  qh_printpointvect(qh, fp, point, normal, center, radius, color )
+    prints a 2-d, 3-d, or 4-d point as 3-d VECT's relative to normal or to center point
+*/
+void qh_printpointvect(qhT *qh, FILE *fp, pointT *point, coordT *normal, pointT *center, realT radius, realT color[3]) {
+  realT diff[4], pointA[4];
+  int k;
+
+  for (k=qh->hull_dim; k--; ) {
+    if (center)
+      diff[k]= point[k]-center[k];
+    else if (normal)
+      diff[k]= normal[k];
+    else
+      diff[k]= 0;
+  }
+  if (center)
+    qh_normalize2(qh, diff, qh->hull_dim, True, NULL, NULL);
+  for (k=qh->hull_dim; k--; )
+    pointA[k]= point[k]+diff[k] * radius;
+  qh_printline3geom(qh, fp, point, pointA, color);
+} /* printpointvect */
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="printpointvect2">-</a>
+
+  qh_printpointvect2(qh, fp, point, normal, center, radius )
+    prints a 2-d, 3-d, or 4-d point as 2 3-d VECT's for an imprecise point
+*/
+void qh_printpointvect2(qhT *qh, FILE *fp, pointT *point, coordT *normal, pointT *center, realT radius) {
+  realT red[3]={1, 0, 0}, yellow[3]={1, 1, 0};
+
+  qh_printpointvect(qh, fp, point, normal, center, radius, red);
+  qh_printpointvect(qh, fp, point, normal, center, -radius, yellow);
+} /* printpointvect2 */
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="printridge">-</a>
+
+  qh_printridge(qh, fp, ridge )
+    prints the information in a ridge
+
+  notes:
+    for qh_printfacetridges()
+    same as operator<< [QhullRidge.cpp]
+*/
+void qh_printridge(qhT *qh, FILE *fp, ridgeT *ridge) {
+
+  qh_fprintf(qh, fp, 9222, "     - r%d", ridge->id);
+  if (ridge->tested)
+    qh_fprintf(qh, fp, 9223, " tested");
+  if (ridge->nonconvex)
+    qh_fprintf(qh, fp, 9224, " nonconvex");
+  qh_fprintf(qh, fp, 9225, "\n");
+  qh_printvertices(qh, fp, "           vertices:", ridge->vertices);
+  if (ridge->top && ridge->bottom)
+    qh_fprintf(qh, fp, 9226, "           between f%d and f%d\n",
+            ridge->top->id, ridge->bottom->id);
+} /* printridge */
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="printspheres">-</a>
+
+  qh_printspheres(qh, fp, vertices, radius )
+    prints 3-d vertices as OFF spheres
+
+  notes:
+    inflated octahedron from Stuart Levy earth/mksphere2
+*/
+void qh_printspheres(qhT *qh, FILE *fp, setT *vertices, realT radius) {
+  vertexT *vertex, **vertexp;
+
+  qh->printoutnum++;
+  qh_fprintf(qh, fp, 9227, "{appearance {-edge -normal normscale 0} {\n\
+INST geom {define vsphere OFF\n\
+18 32 48\n\
+\n\
+0 0 1\n\
+1 0 0\n\
+0 1 0\n\
+-1 0 0\n\
+0 -1 0\n\
+0 0 -1\n\
+0.707107 0 0.707107\n\
+0 -0.707107 0.707107\n\
+0.707107 -0.707107 0\n\
+-0.707107 0 0.707107\n\
+-0.707107 -0.707107 0\n\
+0 0.707107 0.707107\n\
+-0.707107 0.707107 0\n\
+0.707107 0.707107 0\n\
+0.707107 0 -0.707107\n\
+0 0.707107 -0.707107\n\
+-0.707107 0 -0.707107\n\
+0 -0.707107 -0.707107\n\
+\n\
+3 0 6 11\n\
+3 0 7 6 \n\
+3 0 9 7 \n\
+3 0 11 9\n\
+3 1 6 8 \n\
+3 1 8 14\n\
+3 1 13 6\n\
+3 1 14 13\n\
+3 2 11 13\n\
+3 2 12 11\n\
+3 2 13 15\n\
+3 2 15 12\n\
+3 3 9 12\n\
+3 3 10 9\n\
+3 3 12 16\n\
+3 3 16 10\n\
+3 4 7 10\n\
+3 4 8 7\n\
+3 4 10 17\n\
+3 4 17 8\n\
+3 5 14 17\n\
+3 5 15 14\n\
+3 5 16 15\n\
+3 5 17 16\n\
+3 6 13 11\n\
+3 7 8 6\n\
+3 9 10 7\n\
+3 11 12 9\n\
+3 14 8 17\n\
+3 15 13 14\n\
+3 16 12 15\n\
+3 17 10 16\n} transforms { TLIST\n");
+  FOREACHvertex_(vertices) {
+    qh_fprintf(qh, fp, 9228, "%8.4g 0 0 0 # v%d\n 0 %8.4g 0 0\n0 0 %8.4g 0\n",
+      radius, vertex->id, radius, radius);
+    qh_printpoint3(qh, fp, vertex->point);
+    qh_fprintf(qh, fp, 9229, "1\n");
+  }
+  qh_fprintf(qh, fp, 9230, "}}}\n");
+} /* printspheres */
+
+
+/*----------------------------------------------
+-printsummary-
+                see libqhull_r.c
+*/
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="printvdiagram">-</a>
+
+  qh_printvdiagram(qh, fp, format, facetlist, facets, printall )
+    print voronoi diagram
+      # of pairs of input sites
+      #indices site1 site2 vertex1 ...
+
+    sites indexed by input point id
+      point 0 is the first input point
+    vertices indexed by 'o' and 'p' order
+      vertex 0 is the 'vertex-at-infinity'
+      vertex 1 is the first Voronoi vertex
+
+  see:
+    qh_printvoronoi()
+    qh_eachvoronoi_all()
+
+  notes:
+    if all facets are upperdelaunay,
+      prints upper hull (furthest-site Voronoi diagram)
+*/
+void qh_printvdiagram(qhT *qh, FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall) {
+  setT *vertices;
+  int totcount, numcenters;
+  boolT isLower;
+  qh_RIDGE innerouter= qh_RIDGEall;
+  printvridgeT printvridge= NULL;
+
+  if (format == qh_PRINTvertices) {
+    innerouter= qh_RIDGEall;
+    printvridge= qh_printvridge;
+  }else if (format == qh_PRINTinner) {
+    innerouter= qh_RIDGEinner;
+    printvridge= qh_printvnorm;
+  }else if (format == qh_PRINTouter) {
+    innerouter= qh_RIDGEouter;
+    printvridge= qh_printvnorm;
+  }else {
+    qh_fprintf(qh, qh->ferr, 6219, "Qhull internal error (qh_printvdiagram): unknown print format %d.\n", format);
+    qh_errexit(qh, qh_ERRinput, NULL, NULL);
+  }
+  vertices= qh_markvoronoi(qh, facetlist, facets, printall, &isLower, &numcenters);
+  totcount= qh_printvdiagram2(qh, NULL, NULL, vertices, innerouter, False);
+  qh_fprintf(qh, fp, 9231, "%d\n", totcount);
+  totcount= qh_printvdiagram2(qh, fp, printvridge, vertices, innerouter, True /* inorder*/);
+  qh_settempfree(qh, &vertices);
+#if 0  /* for testing qh_eachvoronoi_all */
+  qh_fprintf(qh, fp, 9232, "\n");
+  totcount= qh_eachvoronoi_all(qh, fp, printvridge, qh->UPPERdelaunay, innerouter, True /* inorder*/);
+  qh_fprintf(qh, fp, 9233, "%d\n", totcount);
+#endif
+} /* printvdiagram */
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="printvdiagram2">-</a>
+
+  qh_printvdiagram2(qh, fp, printvridge, vertices, innerouter, inorder )
+    visit all pairs of input sites (vertices) for selected Voronoi vertices
+    vertices may include NULLs
+
+  innerouter:
+    qh_RIDGEall   print inner ridges(bounded) and outer ridges(unbounded)
+    qh_RIDGEinner print only inner ridges
+    qh_RIDGEouter print only outer ridges
+
+  inorder:
+    print 3-d Voronoi vertices in order
+
+  assumes:
+    qh_markvoronoi marked facet->visitid for Voronoi vertices
+    all facet->seen= False
+    all facet->seen2= True
+
+  returns:
+    total number of Voronoi ridges
+    if printvridge,
+      calls printvridge( fp, vertex, vertexA, centers) for each ridge
+      [see qh_eachvoronoi()]
+
+  see:
+    qh_eachvoronoi_all()
+*/
+int qh_printvdiagram2(qhT *qh, FILE *fp, printvridgeT printvridge, setT *vertices, qh_RIDGE innerouter, boolT inorder) {
+  int totcount= 0;
+  int vertex_i, vertex_n;
+  vertexT *vertex;
+
+  FORALLvertices
+    vertex->seen= False;
+  FOREACHvertex_i_(qh, vertices) {
+    if (vertex) {
+      if (qh->GOODvertex > 0 && qh_pointid(qh, vertex->point)+1 != qh->GOODvertex)
+        continue;
+      totcount += qh_eachvoronoi(qh, fp, printvridge, vertex, !qh_ALL, innerouter, inorder);
+    }
+  }
+  return totcount;
+} /* printvdiagram2 */
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="printvertex">-</a>
+
+  qh_printvertex(qh, fp, vertex )
+    prints the information in a vertex
+    Duplicated as operator<< [QhullVertex.cpp]
+*/
+void qh_printvertex(qhT *qh, FILE *fp, vertexT *vertex) {
+  pointT *point;
+  int k, count= 0;
+  facetT *neighbor, **neighborp;
+  realT r; /*bug fix*/
+
+  if (!vertex) {
+    qh_fprintf(qh, fp, 9234, "  NULLvertex\n");
+    return;
+  }
+  qh_fprintf(qh, fp, 9235, "- p%d(v%d):", qh_pointid(qh, vertex->point), vertex->id);
+  point= vertex->point;
+  if (point) {
+    for (k=qh->hull_dim; k--; ) {
+      r= *point++;
+      qh_fprintf(qh, fp, 9236, " %5.2g", r);
+    }
+  }
+  if (vertex->deleted)
+    qh_fprintf(qh, fp, 9237, " deleted");
+  if (vertex->delridge)
+    qh_fprintf(qh, fp, 9238, " ridgedeleted");
+  qh_fprintf(qh, fp, 9239, "\n");
+  if (vertex->neighbors) {
+    qh_fprintf(qh, fp, 9240, "  neighbors:");
+    FOREACHneighbor_(vertex) {
+      if (++count % 100 == 0)
+        qh_fprintf(qh, fp, 9241, "\n     ");
+      qh_fprintf(qh, fp, 9242, " f%d", neighbor->id);
+    }
+    qh_fprintf(qh, fp, 9243, "\n");
+  }
+} /* printvertex */
+
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="printvertexlist">-</a>
+
+  qh_printvertexlist(qh, fp, string, facetlist, facets, printall )
+    prints vertices used by a facetlist or facet set
+    tests qh_skipfacet() if !printall
+*/
+void qh_printvertexlist(qhT *qh, FILE *fp, const char* string, facetT *facetlist,
+                         setT *facets, boolT printall) {
+  vertexT *vertex, **vertexp;
+  setT *vertices;
+
+  vertices= qh_facetvertices(qh, facetlist, facets, printall);
+  qh_fprintf(qh, fp, 9244, "%s", string);
+  FOREACHvertex_(vertices)
+    qh_printvertex(qh, fp, vertex);
+  qh_settempfree(qh, &vertices);
+} /* printvertexlist */
+
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="printvertices">-</a>
+
+  qh_printvertices(qh, fp, string, vertices )
+    prints vertices in a set
+    duplicated as printVertexSet [QhullVertex.cpp]
+*/
+void qh_printvertices(qhT *qh, FILE *fp, const char* string, setT *vertices) {
+  vertexT *vertex, **vertexp;
+
+  qh_fprintf(qh, fp, 9245, "%s", string);
+  FOREACHvertex_(vertices)
+    qh_fprintf(qh, fp, 9246, " p%d(v%d)", qh_pointid(qh, vertex->point), vertex->id);
+  qh_fprintf(qh, fp, 9247, "\n");
+} /* printvertices */
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="printvneighbors">-</a>
+
+  qh_printvneighbors(qh, fp, facetlist, facets, printall )
+    print vertex neighbors of vertices in facetlist and facets ('FN')
+
+  notes:
+    qh_countfacets clears facet->visitid for non-printed facets
+
+  design:
+    collect facet count and related statistics
+    if necessary, build neighbor sets for each vertex
+    collect vertices in facetlist and facets
+    build a point array for point->vertex and point->coplanar facet
+    for each point
+      list vertex neighbors or coplanar facet
+*/
+void qh_printvneighbors(qhT *qh, FILE *fp, facetT* facetlist, setT *facets, boolT printall) {
+  int numfacets, numsimplicial, numridges, totneighbors, numneighbors, numcoplanars, numtricoplanars;
+  setT *vertices, *vertex_points, *coplanar_points;
+  int numpoints= qh->num_points + qh_setsize(qh, qh->other_points);
+  vertexT *vertex, **vertexp;
+  int vertex_i, vertex_n;
+  facetT *facet, **facetp, *neighbor, **neighborp;
+  pointT *point, **pointp;
+
+  qh_countfacets(qh, facetlist, facets, printall, &numfacets, &numsimplicial,
+      &totneighbors, &numridges, &numcoplanars, &numtricoplanars);  /* sets facet->visitid */
+  qh_fprintf(qh, fp, 9248, "%d\n", numpoints);
+  qh_vertexneighbors(qh);
+  vertices= qh_facetvertices(qh, facetlist, facets, printall);
+  vertex_points= qh_settemp(qh, numpoints);
+  coplanar_points= qh_settemp(qh, numpoints);
+  qh_setzero(qh, vertex_points, 0, numpoints);
+  qh_setzero(qh, coplanar_points, 0, numpoints);
+  FOREACHvertex_(vertices)
+    qh_point_add(qh, vertex_points, vertex->point, vertex);
+  FORALLfacet_(facetlist) {
+    FOREACHpoint_(facet->coplanarset)
+      qh_point_add(qh, coplanar_points, point, facet);
+  }
+  FOREACHfacet_(facets) {
+    FOREACHpoint_(facet->coplanarset)
+      qh_point_add(qh, coplanar_points, point, facet);
+  }
+  FOREACHvertex_i_(qh, vertex_points) {
+    if (vertex) {
+      numneighbors= qh_setsize(qh, vertex->neighbors);
+      qh_fprintf(qh, fp, 9249, "%d", numneighbors);
+      if (qh->hull_dim == 3)
+        qh_order_vertexneighbors(qh, vertex);
+      else if (qh->hull_dim >= 4)
+        qsort(SETaddr_(vertex->neighbors, facetT), (size_t)numneighbors,
+             sizeof(facetT *), qh_compare_facetvisit);
+      FOREACHneighbor_(vertex)
+        qh_fprintf(qh, fp, 9250, " %d",
+                 neighbor->visitid ? neighbor->visitid - 1 : 0 - neighbor->id);
+      qh_fprintf(qh, fp, 9251, "\n");
+    }else if ((facet= SETelemt_(coplanar_points, vertex_i, facetT)))
+      qh_fprintf(qh, fp, 9252, "1 %d\n",
+                  facet->visitid ? facet->visitid - 1 : 0 - facet->id);
+    else
+      qh_fprintf(qh, fp, 9253, "0\n");
+  }
+  qh_settempfree(qh, &coplanar_points);
+  qh_settempfree(qh, &vertex_points);
+  qh_settempfree(qh, &vertices);
+} /* printvneighbors */
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="printvoronoi">-</a>
+
+  qh_printvoronoi(qh, fp, format, facetlist, facets, printall )
+    print voronoi diagram in 'o' or 'G' format
+    for 'o' format
+      prints voronoi centers for each facet and for infinity
+      for each vertex, lists ids of printed facets or infinity
+      assumes facetlist and facets are disjoint
+    for 'G' format
+      prints an OFF object
+      adds a 0 coordinate to center
+      prints infinity but does not list in vertices
+
+  see:
+    qh_printvdiagram()
+
+  notes:
+    if 'o',
+      prints a line for each point except "at-infinity"
+    if all facets are upperdelaunay,
+      reverses lower and upper hull
+*/
+void qh_printvoronoi(qhT *qh, FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall) {
+  int k, numcenters, numvertices= 0, numneighbors, numinf, vid=1, vertex_i, vertex_n;
+  facetT *facet, **facetp, *neighbor, **neighborp;
+  setT *vertices;
+  vertexT *vertex;
+  boolT isLower;
+  unsigned int numfacets= (unsigned int) qh->num_facets;
+
+  vertices= qh_markvoronoi(qh, facetlist, facets, printall, &isLower, &numcenters);
+  FOREACHvertex_i_(qh, vertices) {
+    if (vertex) {
+      numvertices++;
+      numneighbors = numinf = 0;
+      FOREACHneighbor_(vertex) {
+        if (neighbor->visitid == 0)
+          numinf= 1;
+        else if (neighbor->visitid < numfacets)
+          numneighbors++;
+      }
+      if (numinf && !numneighbors) {
+        SETelem_(vertices, vertex_i)= NULL;
+        numvertices--;
+      }
+    }
+  }
+  if (format == qh_PRINTgeom)
+    qh_fprintf(qh, fp, 9254, "{appearance {+edge -face} OFF %d %d 1 # Voronoi centers and cells\n",
+                numcenters, numvertices);
+  else
+    qh_fprintf(qh, fp, 9255, "%d\n%d %d 1\n", qh->hull_dim-1, numcenters, qh_setsize(qh, vertices));
+  if (format == qh_PRINTgeom) {
+    for (k=qh->hull_dim-1; k--; )
+      qh_fprintf(qh, fp, 9256, qh_REAL_1, 0.0);
+    qh_fprintf(qh, fp, 9257, " 0 # infinity not used\n");
+  }else {
+    for (k=qh->hull_dim-1; k--; )
+      qh_fprintf(qh, fp, 9258, qh_REAL_1, qh_INFINITE);
+    qh_fprintf(qh, fp, 9259, "\n");
+  }
+  FORALLfacet_(facetlist) {
+    if (facet->visitid && facet->visitid < numfacets) {
+      if (format == qh_PRINTgeom)
+        qh_fprintf(qh, fp, 9260, "# %d f%d\n", vid++, facet->id);
+      qh_printcenter(qh, fp, format, NULL, facet);
+    }
+  }
+  FOREACHfacet_(facets) {
+    if (facet->visitid && facet->visitid < numfacets) {
+      if (format == qh_PRINTgeom)
+        qh_fprintf(qh, fp, 9261, "# %d f%d\n", vid++, facet->id);
+      qh_printcenter(qh, fp, format, NULL, facet);
+    }
+  }
+  FOREACHvertex_i_(qh, vertices) {
+    numneighbors= 0;
+    numinf=0;
+    if (vertex) {
+      if (qh->hull_dim == 3)
+        qh_order_vertexneighbors(qh, vertex);
+      else if (qh->hull_dim >= 4)
+        qsort(SETaddr_(vertex->neighbors, facetT),
+             (size_t)qh_setsize(qh, vertex->neighbors),
+             sizeof(facetT *), qh_compare_facetvisit);
+      FOREACHneighbor_(vertex) {
+        if (neighbor->visitid == 0)
+          numinf= 1;
+        else if (neighbor->visitid < numfacets)
+          numneighbors++;
+      }
+    }
+    if (format == qh_PRINTgeom) {
+      if (vertex) {
+        qh_fprintf(qh, fp, 9262, "%d", numneighbors);
+        FOREACHneighbor_(vertex) {
+          if (neighbor->visitid && neighbor->visitid < numfacets)
+            qh_fprintf(qh, fp, 9263, " %d", neighbor->visitid);
+        }
+        qh_fprintf(qh, fp, 9264, " # p%d(v%d)\n", vertex_i, vertex->id);
+      }else
+        qh_fprintf(qh, fp, 9265, " # p%d is coplanar or isolated\n", vertex_i);
+    }else {
+      if (numinf)
+        numneighbors++;
+      qh_fprintf(qh, fp, 9266, "%d", numneighbors);
+      if (vertex) {
+        FOREACHneighbor_(vertex) {
+          if (neighbor->visitid == 0) {
+            if (numinf) {
+              numinf= 0;
+              qh_fprintf(qh, fp, 9267, " %d", neighbor->visitid);
+            }
+          }else if (neighbor->visitid < numfacets)
+            qh_fprintf(qh, fp, 9268, " %d", neighbor->visitid);
+        }
+      }
+      qh_fprintf(qh, fp, 9269, "\n");
+    }
+  }
+  if (format == qh_PRINTgeom)
+    qh_fprintf(qh, fp, 9270, "}\n");
+  qh_settempfree(qh, &vertices);
+} /* printvoronoi */
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="printvnorm">-</a>
+
+  qh_printvnorm(qh, fp, vertex, vertexA, centers, unbounded )
+    print one separating plane of the Voronoi diagram for a pair of input sites
+    unbounded==True if centers includes vertex-at-infinity
+
+  assumes:
+    qh_ASvoronoi and qh_vertexneighbors() already set
+
+  note:
+    parameter unbounded is UNUSED by this callback
+
+  see:
+    qh_printvdiagram()
+    qh_eachvoronoi()
+*/
+void qh_printvnorm(qhT *qh, FILE *fp, vertexT *vertex, vertexT *vertexA, setT *centers, boolT unbounded) {
+  pointT *normal;
+  realT offset;
+  int k;
+  QHULL_UNUSED(unbounded);
+
+  normal= qh_detvnorm(qh, vertex, vertexA, centers, &offset);
+  qh_fprintf(qh, fp, 9271, "%d %d %d ",
+      2+qh->hull_dim, qh_pointid(qh, vertex->point), qh_pointid(qh, vertexA->point));
+  for (k=0; k< qh->hull_dim-1; k++)
+    qh_fprintf(qh, fp, 9272, qh_REAL_1, normal[k]);
+  qh_fprintf(qh, fp, 9273, qh_REAL_1, offset);
+  qh_fprintf(qh, fp, 9274, "\n");
+} /* printvnorm */
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="printvridge">-</a>
+
+  qh_printvridge(qh, fp, vertex, vertexA, centers, unbounded )
+    print one ridge of the Voronoi diagram for a pair of input sites
+    unbounded==True if centers includes vertex-at-infinity
+
+  see:
+    qh_printvdiagram()
+
+  notes:
+    the user may use a different function
+    parameter unbounded is UNUSED
+*/
+void qh_printvridge(qhT *qh, FILE *fp, vertexT *vertex, vertexT *vertexA, setT *centers, boolT unbounded) {
+  facetT *facet, **facetp;
+  QHULL_UNUSED(unbounded);
+
+  qh_fprintf(qh, fp, 9275, "%d %d %d", qh_setsize(qh, centers)+2,
+       qh_pointid(qh, vertex->point), qh_pointid(qh, vertexA->point));
+  FOREACHfacet_(centers)
+    qh_fprintf(qh, fp, 9276, " %d", facet->visitid);
+  qh_fprintf(qh, fp, 9277, "\n");
+} /* printvridge */
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="projectdim3">-</a>
+
+  qh_projectdim3(qh, source, destination )
+    project 2-d 3-d or 4-d point to a 3-d point
+    uses qh.DROPdim and qh.hull_dim
+    source and destination may be the same
+
+  notes:
+    allocate 4 elements to destination just in case
+*/
+void qh_projectdim3(qhT *qh, pointT *source, pointT *destination) {
+  int i,k;
+
+  for (k=0, i=0; k < qh->hull_dim; k++) {
+    if (qh->hull_dim == 4) {
+      if (k != qh->DROPdim)
+        destination[i++]= source[k];
+    }else if (k == qh->DROPdim)
+      destination[i++]= 0;
+    else
+      destination[i++]= source[k];
+  }
+  while (i < 3)
+    destination[i++]= 0.0;
+} /* projectdim3 */
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="readfeasible">-</a>
+
+  qh_readfeasible(qh, dim, curline )
+    read feasible point from current line and qh.fin
+
+  returns:
+    number of lines read from qh.fin
+    sets qh.feasible_point with malloc'd coordinates
+
+  notes:
+    checks for qh.HALFspace
+    assumes dim > 1
+
+  see:
+    qh_setfeasible
+*/
+int qh_readfeasible(qhT *qh, int dim, const char *curline) {
+  boolT isfirst= True;
+  int linecount= 0, tokcount= 0;
+  const char *s;
+  char *t, firstline[qh_MAXfirst+1];
+  coordT *coords, value;
+
+  if (!qh->HALFspace) {
+    qh_fprintf(qh, qh->ferr, 6070, "qhull input error: feasible point(dim 1 coords) is only valid for halfspace intersection\n");
+    qh_errexit(qh, qh_ERRinput, NULL, NULL);
+  }
+  if (qh->feasible_string)
+    qh_fprintf(qh, qh->ferr, 7057, "qhull input warning: feasible point(dim 1 coords) overrides 'Hn,n,n' feasible point for halfspace intersection\n");
+  if (!(qh->feasible_point= (coordT*)qh_malloc(dim* sizeof(coordT)))) {
+    qh_fprintf(qh, qh->ferr, 6071, "qhull error: insufficient memory for feasible point\n");
+    qh_errexit(qh, qh_ERRmem, NULL, NULL);
+  }
+  coords= qh->feasible_point;
+  while ((s= (isfirst ?  curline : fgets(firstline, qh_MAXfirst, qh->fin)))) {
+    if (isfirst)
+      isfirst= False;
+    else
+      linecount++;
+    while (*s) {
+      while (isspace(*s))
+        s++;
+      value= qh_strtod(s, &t);
+      if (s == t)
+        break;
+      s= t;
+      *(coords++)= value;
+      if (++tokcount == dim) {
+        while (isspace(*s))
+          s++;
+        qh_strtod(s, &t);
+        if (s != t) {
+          qh_fprintf(qh, qh->ferr, 6072, "qhull input error: coordinates for feasible point do not finish out the line: %s\n",
+               s);
+          qh_errexit(qh, qh_ERRinput, NULL, NULL);
+        }
+        return linecount;
+      }
+    }
+  }
+  qh_fprintf(qh, qh->ferr, 6073, "qhull input error: only %d coordinates.  Could not read %d-d feasible point.\n",
+           tokcount, dim);
+  qh_errexit(qh, qh_ERRinput, NULL, NULL);
+  return 0;
+} /* readfeasible */
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="readpoints">-</a>
+
+  qh_readpoints(qh, numpoints, dimension, ismalloc )
+    read points from qh.fin into qh.first_point, qh.num_points
+    qh.fin is lines of coordinates, one per vertex, first line number of points
+    if 'rbox D4',
+      gives message
+    if qh.ATinfinity,
+      adds point-at-infinity for Delaunay triangulations
+
+  returns:
+    number of points, array of point coordinates, dimension, ismalloc True
+    if qh.DELAUNAY & !qh.PROJECTinput, projects points to paraboloid
+        and clears qh.PROJECTdelaunay
+    if qh.HALFspace, reads optional feasible point, reads halfspaces,
+        converts to dual.
+
+  for feasible point in "cdd format" in 3-d:
+    3 1
+    coordinates
+    comments
+    begin
+    n 4 real/integer
+    ...
+    end
+
+  notes:
+    dimension will change in qh_initqhull_globals if qh.PROJECTinput
+    uses malloc() since qh_mem not initialized
+    FIXUP QH11012: qh_readpoints needs rewriting, too long
+*/
+coordT *qh_readpoints(qhT *qh, int *numpoints, int *dimension, boolT *ismalloc) {
+  coordT *points, *coords, *infinity= NULL;
+  realT paraboloid, maxboloid= -REALmax, value;
+  realT *coordp= NULL, *offsetp= NULL, *normalp= NULL;
+  char *s= 0, *t, firstline[qh_MAXfirst+1];
+  int diminput=0, numinput=0, dimfeasible= 0, newnum, k, tempi;
+  int firsttext=0, firstshort=0, firstlong=0, firstpoint=0;
+  int tokcount= 0, linecount=0, maxcount, coordcount=0;
+  boolT islong, isfirst= True, wasbegin= False;
+  boolT isdelaunay= qh->DELAUNAY && !qh->PROJECTinput;
+
+  if (qh->CDDinput) {
+    while ((s= fgets(firstline, qh_MAXfirst, qh->fin))) {
+      linecount++;
+      if (qh->HALFspace && linecount == 1 && isdigit(*s)) {
+        dimfeasible= qh_strtol(s, &s);
+        while (isspace(*s))
+          s++;
+        if (qh_strtol(s, &s) == 1)
+          linecount += qh_readfeasible(qh, dimfeasible, s);
+        else
+          dimfeasible= 0;
+      }else if (!memcmp(firstline, "begin", (size_t)5) || !memcmp(firstline, "BEGIN", (size_t)5))
+        break;
+      else if (!*qh->rbox_command)
+        strncat(qh->rbox_command, s, sizeof(qh->rbox_command)-1);
+    }
+    if (!s) {
+      qh_fprintf(qh, qh->ferr, 6074, "qhull input error: missing \"begin\" for cdd-formated input\n");
+      qh_errexit(qh, qh_ERRinput, NULL, NULL);
+    }
+  }
+  while (!numinput && (s= fgets(firstline, qh_MAXfirst, qh->fin))) {
+    linecount++;
+    if (!memcmp(s, "begin", (size_t)5) || !memcmp(s, "BEGIN", (size_t)5))
+      wasbegin= True;
+    while (*s) {
+      while (isspace(*s))
+        s++;
+      if (!*s)
+        break;
+      if (!isdigit(*s)) {
+        if (!*qh->rbox_command) {
+          strncat(qh->rbox_command, s, sizeof(qh->rbox_command)-1);
+          firsttext= linecount;
+        }
+        break;
+      }
+      if (!diminput)
+        diminput= qh_strtol(s, &s);
+      else {
+        numinput= qh_strtol(s, &s);
+        if (numinput == 1 && diminput >= 2 && qh->HALFspace && !qh->CDDinput) {
+          linecount += qh_readfeasible(qh, diminput, s); /* checks if ok */
+          dimfeasible= diminput;
+          diminput= numinput= 0;
+        }else
+          break;
+      }
+    }
+  }
+  if (!s) {
+    qh_fprintf(qh, qh->ferr, 6075, "qhull input error: short input file.  Did not find dimension and number of points\n");
+    qh_errexit(qh, qh_ERRinput, NULL, NULL);
+  }
+  if (diminput > numinput) {
+    tempi= diminput;    /* exchange dim and n, e.g., for cdd input format */
+    diminput= numinput;
+    numinput= tempi;
+  }
+  if (diminput < 2) {
+    qh_fprintf(qh, qh->ferr, 6220,"qhull input error: dimension %d(first number) should be at least 2\n",
+            diminput);
+    qh_errexit(qh, qh_ERRinput, NULL, NULL);
+  }
+  if (isdelaunay) {
+    qh->PROJECTdelaunay= False;
+    if (qh->CDDinput)
+      *dimension= diminput;
+    else
+      *dimension= diminput+1;
+    *numpoints= numinput;
+    if (qh->ATinfinity)
+      (*numpoints)++;
+  }else if (qh->HALFspace) {
+    *dimension= diminput - 1;
+    *numpoints= numinput;
+    if (diminput < 3) {
+      qh_fprintf(qh, qh->ferr, 6221,"qhull input error: dimension %d(first number, includes offset) should be at least 3 for halfspaces\n",
+            diminput);
+      qh_errexit(qh, qh_ERRinput, NULL, NULL);
+    }
+    if (dimfeasible) {
+      if (dimfeasible != *dimension) {
+        qh_fprintf(qh, qh->ferr, 6222,"qhull input error: dimension %d of feasible point is not one less than dimension %d for halfspaces\n",
+          dimfeasible, diminput);
+        qh_errexit(qh, qh_ERRinput, NULL, NULL);
+      }
+    }else
+      qh_setfeasible(qh, *dimension);
+  }else {
+    if (qh->CDDinput)
+      *dimension= diminput-1;
+    else
+      *dimension= diminput;
+    *numpoints= numinput;
+  }
+  qh->normal_size= *dimension * sizeof(coordT); /* for tracing with qh_printpoint */
+  if (qh->HALFspace) {
+    qh->half_space= coordp= (coordT*)qh_malloc(qh->normal_size + sizeof(coordT));
+    if (qh->CDDinput) {
+      offsetp= qh->half_space;
+      normalp= offsetp + 1;
+    }else {
+      normalp= qh->half_space;
+      offsetp= normalp + *dimension;
+    }
+  }
+  qh->maxline= diminput * (qh_REALdigits + 5);
+  maximize_(qh->maxline, 500);
+  qh->line= (char*)qh_malloc((qh->maxline+1) * sizeof(char));
+  *ismalloc= True;  /* use malloc since memory not setup */
+  coords= points= qh->temp_malloc=  /* numinput and diminput >=2 by QH6220 */
+        (coordT*)qh_malloc((*numpoints)*(*dimension)*sizeof(coordT));
+  if (!coords || !qh->line || (qh->HALFspace && !qh->half_space)) {
+    qh_fprintf(qh, qh->ferr, 6076, "qhull error: insufficient memory to read %d points\n",
+            numinput);
+    qh_errexit(qh, qh_ERRmem, NULL, NULL);
+  }
+  if (isdelaunay && qh->ATinfinity) {
+    infinity= points + numinput * (*dimension);
+    for (k= (*dimension) - 1; k--; )
+      infinity[k]= 0.0;
+  }
+  maxcount= numinput * diminput;
+  paraboloid= 0.0;
+  while ((s= (isfirst ?  s : fgets(qh->line, qh->maxline, qh->fin)))) {
+    if (!isfirst) {
+      linecount++;
+      if (*s == 'e' || *s == 'E') {
+        if (!memcmp(s, "end", (size_t)3) || !memcmp(s, "END", (size_t)3)) {
+          if (qh->CDDinput )
+            break;
+          else if (wasbegin)
+            qh_fprintf(qh, qh->ferr, 7058, "qhull input warning: the input appears to be in cdd format.  If so, use 'Fd'\n");
+        }
+      }
+    }
+    islong= False;
+    while (*s) {
+      while (isspace(*s))
+        s++;
+      value= qh_strtod(s, &t);
+      if (s == t) {
+        if (!*qh->rbox_command)
+         strncat(qh->rbox_command, s, sizeof(qh->rbox_command)-1);
+        if (*s && !firsttext)
+          firsttext= linecount;
+        if (!islong && !firstshort && coordcount)
+          firstshort= linecount;
+        break;
+      }
+      if (!firstpoint)
+        firstpoint= linecount;
+      s= t;
+      if (++tokcount > maxcount)
+        continue;
+      if (qh->HALFspace) {
+        if (qh->CDDinput)
+          *(coordp++)= -value; /* both coefficients and offset */
+        else
+          *(coordp++)= value;
+      }else {
+        *(coords++)= value;
+        if (qh->CDDinput && !coordcount) {
+          if (value != 1.0) {
+            qh_fprintf(qh, qh->ferr, 6077, "qhull input error: for cdd format, point at line %d does not start with '1'\n",
+                   linecount);
+            qh_errexit(qh, qh_ERRinput, NULL, NULL);
+          }
+          coords--;
+        }else if (isdelaunay) {
+          paraboloid += value * value;
+          if (qh->ATinfinity) {
+            if (qh->CDDinput)
+              infinity[coordcount-1] += value;
+            else
+              infinity[coordcount] += value;
+          }
+        }
+      }
+      if (++coordcount == diminput) {
+        coordcount= 0;
+        if (isdelaunay) {
+          *(coords++)= paraboloid;
+          maximize_(maxboloid, paraboloid);
+          paraboloid= 0.0;
+        }else if (qh->HALFspace) {
+          if (!qh_sethalfspace(qh, *dimension, coords, &coords, normalp, offsetp, qh->feasible_point)) {
+            qh_fprintf(qh, qh->ferr, 8048, "The halfspace was on line %d\n", linecount);
+            if (wasbegin)
+              qh_fprintf(qh, qh->ferr, 8049, "The input appears to be in cdd format.  If so, you should use option 'Fd'\n");
+            qh_errexit(qh, qh_ERRinput, NULL, NULL);
+          }
+          coordp= qh->half_space;
+        }
+        while (isspace(*s))
+          s++;
+        if (*s) {
+          islong= True;
+          if (!firstlong)
+            firstlong= linecount;
+        }
+      }
+    }
+    if (!islong && !firstshort && coordcount)
+      firstshort= linecount;
+    if (!isfirst && s - qh->line >= qh->maxline) {
+      qh_fprintf(qh, qh->ferr, 6078, "qhull input error: line %d contained more than %d characters\n",
+              linecount, (int) (s - qh->line));   /* WARN64 */
+      qh_errexit(qh, qh_ERRinput, NULL, NULL);
+    }
+    isfirst= False;
+  }
+  if (tokcount != maxcount) {
+    newnum= fmin_(numinput, tokcount/diminput);
+    qh_fprintf(qh, qh->ferr, 7073,"\
+qhull warning: instead of %d %d-dimensional points, input contains\n\
+%d points and %d extra coordinates.  Line %d is the first\npoint",
+       numinput, diminput, tokcount/diminput, tokcount % diminput, firstpoint);
+    if (firsttext)
+      qh_fprintf(qh, qh->ferr, 8051, ", line %d is the first comment", firsttext);
+    if (firstshort)
+      qh_fprintf(qh, qh->ferr, 8052, ", line %d is the first short\nline", firstshort);
+    if (firstlong)
+      qh_fprintf(qh, qh->ferr, 8053, ", line %d is the first long line", firstlong);
+    qh_fprintf(qh, qh->ferr, 8054, ".  Continue with %d points.\n", newnum);
+    numinput= newnum;
+    if (isdelaunay && qh->ATinfinity) {
+      for (k= tokcount % diminput; k--; )
+        infinity[k] -= *(--coords);
+      *numpoints= newnum+1;
+    }else {
+      coords -= tokcount % diminput;
+      *numpoints= newnum;
+    }
+  }
+  if (isdelaunay && qh->ATinfinity) {
+    for (k= (*dimension) -1; k--; )
+      infinity[k] /= numinput;
+    if (coords == infinity)
+      coords += (*dimension) -1;
+    else {
+      for (k=0; k < (*dimension) -1; k++)
+        *(coords++)= infinity[k];
+    }
+    *(coords++)= maxboloid * 1.1;
+  }
+  if (qh->rbox_command[0]) {
+    qh->rbox_command[strlen(qh->rbox_command)-1]= '\0';
+    if (!strcmp(qh->rbox_command, "./rbox D4"))
+      qh_fprintf(qh, qh->ferr, 8055, "\n\
+This is the qhull test case.  If any errors or core dumps occur,\n\
+recompile qhull with 'make new'.  If errors still occur, there is\n\
+an incompatibility.  You should try a different compiler.  You can also\n\
+change the choices in user.h.  If you discover the source of the problem,\n\
+please send mail to qhull_bug@qhull.org.\n\
+\n\
+Type 'qhull' for a short list of options.\n");
+  }
+  qh_free(qh->line);
+  qh->line= NULL;
+  if (qh->half_space) {
+    qh_free(qh->half_space);
+    qh->half_space= NULL;
+  }
+  qh->temp_malloc= NULL;
+  trace1((qh, qh->ferr, 1008,"qh_readpoints: read in %d %d-dimensional points\n",
+          numinput, diminput));
+  return(points);
+} /* readpoints */
+
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="setfeasible">-</a>
+
+  qh_setfeasible(qh, dim )
+    set qh.feasible_point from qh.feasible_string in "n,n,n" or "n n n" format
+
+  notes:
+    "n,n,n" already checked by qh_initflags()
+    see qh_readfeasible()
+    called only once from qh_new_qhull, otherwise leaks memory
+*/
+void qh_setfeasible(qhT *qh, int dim) {
+  int tokcount= 0;
+  char *s;
+  coordT *coords, value;
+
+  if (!(s= qh->feasible_string)) {
+    qh_fprintf(qh, qh->ferr, 6223, "\
+qhull input error: halfspace intersection needs a feasible point.\n\
+Either prepend the input with 1 point or use 'Hn,n,n'.  See manual.\n");
+    qh_errexit(qh, qh_ERRinput, NULL, NULL);
+  }
+  if (!(qh->feasible_point= (pointT*)qh_malloc(dim * sizeof(coordT)))) {
+    qh_fprintf(qh, qh->ferr, 6079, "qhull error: insufficient memory for 'Hn,n,n'\n");
+    qh_errexit(qh, qh_ERRmem, NULL, NULL);
+  }
+  coords= qh->feasible_point;
+  while (*s) {
+    value= qh_strtod(s, &s);
+    if (++tokcount > dim) {
+      qh_fprintf(qh, qh->ferr, 7059, "qhull input warning: more coordinates for 'H%s' than dimension %d\n",
+          qh->feasible_string, dim);
+      break;
+    }
+    *(coords++)= value;
+    if (*s)
+      s++;
+  }
+  while (++tokcount <= dim)
+    *(coords++)= 0.0;
+} /* setfeasible */
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="skipfacet">-</a>
+
+  qh_skipfacet(qh, facet )
+    returns 'True' if this facet is not to be printed
+
+  notes:
+    based on the user provided slice thresholds and 'good' specifications
+*/
+boolT qh_skipfacet(qhT *qh, facetT *facet) {
+  facetT *neighbor, **neighborp;
+
+  if (qh->PRINTneighbors) {
+    if (facet->good)
+      return !qh->PRINTgood;
+    FOREACHneighbor_(facet) {
+      if (neighbor->good)
+        return False;
+    }
+    return True;
+  }else if (qh->PRINTgood)
+    return !facet->good;
+  else if (!facet->normal)
+    return True;
+  return(!qh_inthresholds(qh, facet->normal, NULL));
+} /* skipfacet */
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="skipfilename">-</a>
+
+  qh_skipfilename(qh, string )
+    returns pointer to character after filename
+
+  notes:
+    skips leading spaces
+    ends with spacing or eol
+    if starts with ' or " ends with the same, skipping \' or \"
+    For qhull, qh_argv_to_command() only uses double quotes
+*/
+char *qh_skipfilename(qhT *qh, char *filename) {
+  char *s= filename;  /* non-const due to return */
+  char c;
+
+  while (*s && isspace(*s))
+    s++;
+  c= *s++;
+  if (c == '\0') {
+    qh_fprintf(qh, qh->ferr, 6204, "qhull input error: filename expected, none found.\n");
+    qh_errexit(qh, qh_ERRinput, NULL, NULL);
+  }
+  if (c == '\'' || c == '"') {
+    while (*s !=c || s[-1] == '\\') {
+      if (!*s) {
+        qh_fprintf(qh, qh->ferr, 6203, "qhull input error: missing quote after filename -- %s\n", filename);
+        qh_errexit(qh, qh_ERRinput, NULL, NULL);
+      }
+      s++;
+    }
+    s++;
+  }
+  else while (*s && !isspace(*s))
+      s++;
+  return s;
+} /* skipfilename */
+
diff --git a/xs/src/qhull/src/libqhull_r/io_r.h b/xs/src/qhull/src/libqhull_r/io_r.h
new file mode 100644
index 0000000000..12e05ae7ac
--- /dev/null
+++ b/xs/src/qhull/src/libqhull_r/io_r.h
@@ -0,0 +1,167 @@
+/*<html><pre>  -<a                             href="qh-io_r.htm"
+  >-------------------------------</a><a name="TOP">-</a>
+
+   io_r.h
+   declarations of Input/Output functions
+
+   see README, libqhull_r.h and io_r.c
+
+   Copyright (c) 1993-2015 The Geometry Center.
+   $Id: //main/2015/qhull/src/libqhull_r/io_r.h#3 $$Change: 2079 $
+   $DateTime: 2016/02/07 17:43:34 $$Author: bbarber $
+*/
+
+#ifndef qhDEFio
+#define qhDEFio 1
+
+#include "libqhull_r.h"
+
+/*============ constants and flags ==================*/
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >--------------------------------</a><a name="qh_MAXfirst">-</a>
+
+  qh_MAXfirst
+    maximum length of first two lines of stdin
+*/
+#define qh_MAXfirst  200
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >--------------------------------</a><a name="qh_MINradius">-</a>
+
+  qh_MINradius
+    min radius for Gp and Gv, fraction of maxcoord
+*/
+#define qh_MINradius 0.02
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >--------------------------------</a><a name="qh_GEOMepsilon">-</a>
+
+  qh_GEOMepsilon
+    adjust outer planes for 'lines closer' and geomview roundoff.
+    This prevents bleed through.
+*/
+#define qh_GEOMepsilon 2e-3
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >--------------------------------</a><a name="qh_WHITESPACE">-</a>
+
+  qh_WHITESPACE
+    possible values of white space
+*/
+#define qh_WHITESPACE " \n\t\v\r\f"
+
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >--------------------------------</a><a name="RIDGE">-</a>
+
+  qh_RIDGE
+    to select which ridges to print in qh_eachvoronoi
+*/
+typedef enum
+{
+    qh_RIDGEall = 0, qh_RIDGEinner, qh_RIDGEouter
+}
+qh_RIDGE;
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >--------------------------------</a><a name="printvridgeT">-</a>
+
+  printvridgeT
+    prints results of qh_printvdiagram
+
+  see:
+    <a href="io_r.c#printvridge">qh_printvridge</a> for an example
+*/
+typedef void (*printvridgeT)(qhT *qh, FILE *fp, vertexT *vertex, vertexT *vertexA, setT *centers, boolT unbounded);
+
+/*============== -prototypes in alphabetical order =========*/
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+void    qh_dfacet(qhT *qh, unsigned id);
+void    qh_dvertex(qhT *qh, unsigned id);
+int     qh_compare_facetarea(const void *p1, const void *p2);
+int     qh_compare_facetmerge(const void *p1, const void *p2);
+int     qh_compare_facetvisit(const void *p1, const void *p2);
+/* int  qh_compare_vertexpoint(const void *p1, const void *p2); Not useable since it depends on qh */
+void    qh_copyfilename(qhT *qh, char *filename, int size, const char* source, int length);
+void    qh_countfacets(qhT *qh, facetT *facetlist, setT *facets, boolT printall,
+              int *numfacetsp, int *numsimplicialp, int *totneighborsp,
+              int *numridgesp, int *numcoplanarsp, int *numnumtricoplanarsp);
+pointT *qh_detvnorm(qhT *qh, vertexT *vertex, vertexT *vertexA, setT *centers, realT *offsetp);
+setT   *qh_detvridge(qhT *qh, vertexT *vertex);
+setT   *qh_detvridge3(qhT *qh, vertexT *atvertex, vertexT *vertex);
+int     qh_eachvoronoi(qhT *qh, FILE *fp, printvridgeT printvridge, vertexT *atvertex, boolT visitall, qh_RIDGE innerouter, boolT inorder);
+int     qh_eachvoronoi_all(qhT *qh, FILE *fp, printvridgeT printvridge, boolT isUpper, qh_RIDGE innerouter, boolT inorder);
+void    qh_facet2point(qhT *qh, facetT *facet, pointT **point0, pointT **point1, realT *mindist);
+setT   *qh_facetvertices(qhT *qh, facetT *facetlist, setT *facets, boolT allfacets);
+void    qh_geomplanes(qhT *qh, facetT *facet, realT *outerplane, realT *innerplane);
+void    qh_markkeep(qhT *qh, facetT *facetlist);
+setT   *qh_markvoronoi(qhT *qh, facetT *facetlist, setT *facets, boolT printall, boolT *isLowerp, int *numcentersp);
+void    qh_order_vertexneighbors(qhT *qh, vertexT *vertex);
+void    qh_prepare_output(qhT *qh);
+void    qh_printafacet(qhT *qh, FILE *fp, qh_PRINT format, facetT *facet, boolT printall);
+void    qh_printbegin(qhT *qh, FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall);
+void    qh_printcenter(qhT *qh, FILE *fp, qh_PRINT format, const char *string, facetT *facet);
+void    qh_printcentrum(qhT *qh, FILE *fp, facetT *facet, realT radius);
+void    qh_printend(qhT *qh, FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall);
+void    qh_printend4geom(qhT *qh, FILE *fp, facetT *facet, int *num, boolT printall);
+void    qh_printextremes(qhT *qh, FILE *fp, facetT *facetlist, setT *facets, boolT printall);
+void    qh_printextremes_2d(qhT *qh, FILE *fp, facetT *facetlist, setT *facets, boolT printall);
+void    qh_printextremes_d(qhT *qh, FILE *fp, facetT *facetlist, setT *facets, boolT printall);
+void    qh_printfacet(qhT *qh, FILE *fp, facetT *facet);
+void    qh_printfacet2math(qhT *qh, FILE *fp, facetT *facet, qh_PRINT format, int notfirst);
+void    qh_printfacet2geom(qhT *qh, FILE *fp, facetT *facet, realT color[3]);
+void    qh_printfacet2geom_points(qhT *qh, FILE *fp, pointT *point1, pointT *point2,
+                               facetT *facet, realT offset, realT color[3]);
+void    qh_printfacet3math(qhT *qh, FILE *fp, facetT *facet, qh_PRINT format, int notfirst);
+void    qh_printfacet3geom_nonsimplicial(qhT *qh, FILE *fp, facetT *facet, realT color[3]);
+void    qh_printfacet3geom_points(qhT *qh, FILE *fp, setT *points, facetT *facet, realT offset, realT color[3]);
+void    qh_printfacet3geom_simplicial(qhT *qh, FILE *fp, facetT *facet, realT color[3]);
+void    qh_printfacet3vertex(qhT *qh, FILE *fp, facetT *facet, qh_PRINT format);
+void    qh_printfacet4geom_nonsimplicial(qhT *qh, FILE *fp, facetT *facet, realT color[3]);
+void    qh_printfacet4geom_simplicial(qhT *qh, FILE *fp, facetT *facet, realT color[3]);
+void    qh_printfacetNvertex_nonsimplicial(qhT *qh, FILE *fp, facetT *facet, int id, qh_PRINT format);
+void    qh_printfacetNvertex_simplicial(qhT *qh, FILE *fp, facetT *facet, qh_PRINT format);
+void    qh_printfacetheader(qhT *qh, FILE *fp, facetT *facet);
+void    qh_printfacetridges(qhT *qh, FILE *fp, facetT *facet);
+void    qh_printfacets(qhT *qh, FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall);
+void    qh_printhyperplaneintersection(qhT *qh, FILE *fp, facetT *facet1, facetT *facet2,
+                   setT *vertices, realT color[3]);
+void    qh_printneighborhood(qhT *qh, FILE *fp, qh_PRINT format, facetT *facetA, facetT *facetB, boolT printall);
+void    qh_printline3geom(qhT *qh, FILE *fp, pointT *pointA, pointT *pointB, realT color[3]);
+void    qh_printpoint(qhT *qh, FILE *fp, const char *string, pointT *point);
+void    qh_printpointid(qhT *qh, FILE *fp, const char *string, int dim, pointT *point, int id);
+void    qh_printpoint3(qhT *qh, FILE *fp, pointT *point);
+void    qh_printpoints_out(qhT *qh, FILE *fp, facetT *facetlist, setT *facets, boolT printall);
+void    qh_printpointvect(qhT *qh, FILE *fp, pointT *point, coordT *normal, pointT *center, realT radius, realT color[3]);
+void    qh_printpointvect2(qhT *qh, FILE *fp, pointT *point, coordT *normal, pointT *center, realT radius);
+void    qh_printridge(qhT *qh, FILE *fp, ridgeT *ridge);
+void    qh_printspheres(qhT *qh, FILE *fp, setT *vertices, realT radius);
+void    qh_printvdiagram(qhT *qh, FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall);
+int     qh_printvdiagram2(qhT *qh, FILE *fp, printvridgeT printvridge, setT *vertices, qh_RIDGE innerouter, boolT inorder);
+void    qh_printvertex(qhT *qh, FILE *fp, vertexT *vertex);
+void    qh_printvertexlist(qhT *qh, FILE *fp, const char* string, facetT *facetlist,
+                         setT *facets, boolT printall);
+void    qh_printvertices(qhT *qh, FILE *fp, const char* string, setT *vertices);
+void    qh_printvneighbors(qhT *qh, FILE *fp, facetT* facetlist, setT *facets, boolT printall);
+void    qh_printvoronoi(qhT *qh, FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall);
+void    qh_printvnorm(qhT *qh, FILE *fp, vertexT *vertex, vertexT *vertexA, setT *centers, boolT unbounded);
+void    qh_printvridge(qhT *qh, FILE *fp, vertexT *vertex, vertexT *vertexA, setT *centers, boolT unbounded);
+void    qh_produce_output(qhT *qh);
+void    qh_produce_output2(qhT *qh);
+void    qh_projectdim3(qhT *qh, pointT *source, pointT *destination);
+int     qh_readfeasible(qhT *qh, int dim, const char *curline);
+coordT *qh_readpoints(qhT *qh, int *numpoints, int *dimension, boolT *ismalloc);
+void    qh_setfeasible(qhT *qh, int dim);
+boolT   qh_skipfacet(qhT *qh, facetT *facet);
+char   *qh_skipfilename(qhT *qh, char *filename);
+
+#ifdef __cplusplus
+} /* extern "C" */
+#endif
+
+#endif /* qhDEFio */
diff --git a/xs/src/qhull/src/libqhull_r/libqhull_r.c b/xs/src/qhull/src/libqhull_r/libqhull_r.c
new file mode 100644
index 0000000000..0fe0c980dc
--- /dev/null
+++ b/xs/src/qhull/src/libqhull_r/libqhull_r.c
@@ -0,0 +1,1403 @@
+/*<html><pre>  -<a                             href="qh-qhull_r.htm"
+  >-------------------------------</a><a name="TOP">-</a>
+
+   libqhull_r.c
+   Quickhull algorithm for convex hulls
+
+   qhull() and top-level routines
+
+   see qh-qhull_r.htm, libqhull.h, unix_r.c
+
+   see qhull_ra.h for internal functions
+
+   Copyright (c) 1993-2015 The Geometry Center.
+   $Id: //main/2015/qhull/src/libqhull_r/libqhull_r.c#2 $$Change: 2047 $
+   $DateTime: 2016/01/04 22:03:18 $$Author: bbarber $
+*/
+
+#include "qhull_ra.h"
+
+/*============= functions in alphabetic order after qhull() =======*/
+
+/*-<a                             href="qh-qhull_r.htm#TOC"
+  >-------------------------------</a><a name="qhull">-</a>
+
+  qh_qhull(qh)
+    compute DIM3 convex hull of qh.num_points starting at qh.first_point
+    qh->contains all global options and variables
+
+  returns:
+    returns polyhedron
+      qh.facet_list, qh.num_facets, qh.vertex_list, qh.num_vertices,
+
+    returns global variables
+      qh.hulltime, qh.max_outside, qh.interior_point, qh.max_vertex, qh.min_vertex
+
+    returns precision constants
+      qh.ANGLEround, centrum_radius, cos_max, DISTround, MAXabs_coord, ONEmerge
+
+  notes:
+    unless needed for output
+      qh.max_vertex and qh.min_vertex are max/min due to merges
+
+  see:
+    to add individual points to either qh.num_points
+      use qh_addpoint()
+
+    if qh.GETarea
+      qh_produceoutput() returns qh.totarea and qh.totvol via qh_getarea()
+
+  design:
+    record starting time
+    initialize hull and partition points
+    build convex hull
+    unless early termination
+      update facet->maxoutside for vertices, coplanar, and near-inside points
+    error if temporary sets exist
+    record end time
+*/
+
+void qh_qhull(qhT *qh) {
+  int numoutside;
+
+  qh->hulltime= qh_CPUclock;
+  if (qh->RERUN || qh->JOGGLEmax < REALmax/2)
+    qh_build_withrestart(qh);
+  else {
+    qh_initbuild(qh);
+    qh_buildhull(qh);
+  }
+  if (!qh->STOPpoint && !qh->STOPcone) {
+    if (qh->ZEROall_ok && !qh->TESTvneighbors && qh->MERGEexact)
+      qh_checkzero(qh, qh_ALL);
+    if (qh->ZEROall_ok && !qh->TESTvneighbors && !qh->WAScoplanar) {
+      trace2((qh, qh->ferr, 2055, "qh_qhull: all facets are clearly convex and no coplanar points.  Post-merging and check of maxout not needed.\n"));
+      qh->DOcheckmax= False;
+    }else {
+      if (qh->MERGEexact || (qh->hull_dim > qh_DIMreduceBuild && qh->PREmerge))
+        qh_postmerge(qh, "First post-merge", qh->premerge_centrum, qh->premerge_cos,
+             (qh->POSTmerge ? False : qh->TESTvneighbors));
+      else if (!qh->POSTmerge && qh->TESTvneighbors)
+        qh_postmerge(qh, "For testing vertex neighbors", qh->premerge_centrum,
+             qh->premerge_cos, True);
+      if (qh->POSTmerge)
+        qh_postmerge(qh, "For post-merging", qh->postmerge_centrum,
+             qh->postmerge_cos, qh->TESTvneighbors);
+      if (qh->visible_list == qh->facet_list) { /* i.e., merging done */
+        qh->findbestnew= True;
+        qh_partitionvisible(qh /*qh.visible_list*/, !qh_ALL, &numoutside);
+        qh->findbestnew= False;
+        qh_deletevisible(qh /*qh.visible_list*/);
+        qh_resetlists(qh, False, qh_RESETvisible /*qh.visible_list newvertex_list newfacet_list */);
+      }
+    }
+    if (qh->DOcheckmax){
+      if (qh->REPORTfreq) {
+        qh_buildtracing(qh, NULL, NULL);
+        qh_fprintf(qh, qh->ferr, 8115, "\nTesting all coplanar points.\n");
+      }
+      qh_check_maxout(qh);
+    }
+    if (qh->KEEPnearinside && !qh->maxoutdone)
+      qh_nearcoplanar(qh);
+  }
+  if (qh_setsize(qh, qh->qhmem.tempstack) != 0) {
+    qh_fprintf(qh, qh->ferr, 6164, "qhull internal error (qh_qhull): temporary sets not empty(%d)\n",
+             qh_setsize(qh, qh->qhmem.tempstack));
+    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+  }
+  qh->hulltime= qh_CPUclock - qh->hulltime;
+  qh->QHULLfinished= True;
+  trace1((qh, qh->ferr, 1036, "Qhull: algorithm completed\n"));
+} /* qhull */
+
+/*-<a                             href="qh-qhull_r.htm#TOC"
+  >-------------------------------</a><a name="addpoint">-</a>
+
+  qh_addpoint(qh, furthest, facet, checkdist )
+    add point (usually furthest point) above facet to hull
+    if checkdist,
+      check that point is above facet.
+      if point is not outside of the hull, uses qh_partitioncoplanar()
+      assumes that facet is defined by qh_findbestfacet()
+    else if facet specified,
+      assumes that point is above facet (major damage if below)
+    for Delaunay triangulations,
+      Use qh_setdelaunay() to lift point to paraboloid and scale by 'Qbb' if needed
+      Do not use options 'Qbk', 'QBk', or 'QbB' since they scale the coordinates.
+
+  returns:
+    returns False if user requested an early termination
+     qh.visible_list, newfacet_list, delvertex_list, NEWfacets may be defined
+    updates qh.facet_list, qh.num_facets, qh.vertex_list, qh.num_vertices
+    clear qh.maxoutdone (will need to call qh_check_maxout() for facet->maxoutside)
+    if unknown point, adds a pointer to qh.other_points
+      do not deallocate the point's coordinates
+
+  notes:
+    assumes point is near its best facet and not at a local minimum of a lens
+      distributions.  Use qh_findbestfacet to avoid this case.
+    uses qh.visible_list, qh.newfacet_list, qh.delvertex_list, qh.NEWfacets
+
+  see also:
+    qh_triangulate() -- triangulate non-simplicial facets
+
+  design:
+    add point to other_points if needed
+    if checkdist
+      if point not above facet
+        partition coplanar point
+        exit
+    exit if pre STOPpoint requested
+    find horizon and visible facets for point
+    make new facets for point to horizon
+    make hyperplanes for point
+    compute balance statistics
+    match neighboring new facets
+    update vertex neighbors and delete interior vertices
+    exit if STOPcone requested
+    merge non-convex new facets
+    if merge found, many merges, or 'Qf'
+       use qh_findbestnew() instead of qh_findbest()
+    partition outside points from visible facets
+    delete visible facets
+    check polyhedron if requested
+    exit if post STOPpoint requested
+    reset working lists of facets and vertices
+*/
+boolT qh_addpoint(qhT *qh, pointT *furthest, facetT *facet, boolT checkdist) {
+  int goodvisible, goodhorizon;
+  vertexT *vertex;
+  facetT *newfacet;
+  realT dist, newbalance, pbalance;
+  boolT isoutside= False;
+  int numpart, numpoints, numnew, firstnew;
+
+  qh->maxoutdone= False;
+  if (qh_pointid(qh, furthest) == qh_IDunknown)
+    qh_setappend(qh, &qh->other_points, furthest);
+  if (!facet) {
+    qh_fprintf(qh, qh->ferr, 6213, "qhull internal error (qh_addpoint): NULL facet.  Need to call qh_findbestfacet first\n");
+    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+  }
+  if (checkdist) {
+    facet= qh_findbest(qh, furthest, facet, !qh_ALL, !qh_ISnewfacets, !qh_NOupper,
+                        &dist, &isoutside, &numpart);
+    zzadd_(Zpartition, numpart);
+    if (!isoutside) {
+      zinc_(Znotmax);  /* last point of outsideset is no longer furthest. */
+      facet->notfurthest= True;
+      qh_partitioncoplanar(qh, furthest, facet, &dist);
+      return True;
+    }
+  }
+  qh_buildtracing(qh, furthest, facet);
+  if (qh->STOPpoint < 0 && qh->furthest_id == -qh->STOPpoint-1) {
+    facet->notfurthest= True;
+    return False;
+  }
+  qh_findhorizon(qh, furthest, facet, &goodvisible, &goodhorizon);
+  if (qh->ONLYgood && !(goodvisible+goodhorizon) && !qh->GOODclosest) {
+    zinc_(Znotgood);
+    facet->notfurthest= True;
+    /* last point of outsideset is no longer furthest.  This is ok
+       since all points of the outside are likely to be bad */
+    qh_resetlists(qh, False, qh_RESETvisible /*qh.visible_list newvertex_list newfacet_list */);
+    return True;
+  }
+  zzinc_(Zprocessed);
+  firstnew= qh->facet_id;
+  vertex= qh_makenewfacets(qh, furthest /*visible_list, attaches if !ONLYgood */);
+  qh_makenewplanes(qh /* newfacet_list */);
+  numnew= qh->facet_id - firstnew;
+  newbalance= numnew - (realT) (qh->num_facets-qh->num_visible)
+                         * qh->hull_dim/qh->num_vertices;
+  wadd_(Wnewbalance, newbalance);
+  wadd_(Wnewbalance2, newbalance * newbalance);
+  if (qh->ONLYgood
+  && !qh_findgood(qh, qh->newfacet_list, goodhorizon) && !qh->GOODclosest) {
+    FORALLnew_facets
+      qh_delfacet(qh, newfacet);
+    qh_delvertex(qh, vertex);
+    qh_resetlists(qh, True, qh_RESETvisible /*qh.visible_list newvertex_list newfacet_list */);
+    zinc_(Znotgoodnew);
+    facet->notfurthest= True;
+    return True;
+  }
+  if (qh->ONLYgood)
+    qh_attachnewfacets(qh /*visible_list*/);
+  qh_matchnewfacets(qh);
+  qh_updatevertices(qh);
+  if (qh->STOPcone && qh->furthest_id == qh->STOPcone-1) {
+    facet->notfurthest= True;
+    return False;  /* visible_list etc. still defined */
+  }
+  qh->findbestnew= False;
+  if (qh->PREmerge || qh->MERGEexact) {
+    qh_premerge(qh, vertex, qh->premerge_centrum, qh->premerge_cos);
+    if (qh_USEfindbestnew)
+      qh->findbestnew= True;
+    else {
+      FORALLnew_facets {
+        if (!newfacet->simplicial) {
+          qh->findbestnew= True;  /* use qh_findbestnew instead of qh_findbest*/
+          break;
+        }
+      }
+    }
+  }else if (qh->BESToutside)
+    qh->findbestnew= True;
+  qh_partitionvisible(qh /*qh.visible_list*/, !qh_ALL, &numpoints);
+  qh->findbestnew= False;
+  qh->findbest_notsharp= False;
+  zinc_(Zpbalance);
+  pbalance= numpoints - (realT) qh->hull_dim /* assumes all points extreme */
+                * (qh->num_points - qh->num_vertices)/qh->num_vertices;
+  wadd_(Wpbalance, pbalance);
+  wadd_(Wpbalance2, pbalance * pbalance);
+  qh_deletevisible(qh /*qh.visible_list*/);
+  zmax_(Zmaxvertex, qh->num_vertices);
+  qh->NEWfacets= False;
+  if (qh->IStracing >= 4) {
+    if (qh->num_facets < 2000)
+      qh_printlists(qh);
+    qh_printfacetlist(qh, qh->newfacet_list, NULL, True);
+    qh_checkpolygon(qh, qh->facet_list);
+  }else if (qh->CHECKfrequently) {
+    if (qh->num_facets < 50)
+      qh_checkpolygon(qh, qh->facet_list);
+    else
+      qh_checkpolygon(qh, qh->newfacet_list);
+  }
+  if (qh->STOPpoint > 0 && qh->furthest_id == qh->STOPpoint-1)
+    return False;
+  qh_resetlists(qh, True, qh_RESETvisible /*qh.visible_list newvertex_list newfacet_list */);
+  /* qh_triangulate(qh); to test qh.TRInormals */
+  trace2((qh, qh->ferr, 2056, "qh_addpoint: added p%d new facets %d new balance %2.2g point balance %2.2g\n",
+    qh_pointid(qh, furthest), numnew, newbalance, pbalance));
+  return True;
+} /* addpoint */
+
+/*-<a                             href="qh-qhull_r.htm#TOC"
+  >-------------------------------</a><a name="build_withrestart">-</a>
+
+  qh_build_withrestart(qh)
+    allow restarts due to qh.JOGGLEmax while calling qh_buildhull()
+       qh_errexit always undoes qh_build_withrestart()
+    qh.FIRSTpoint/qh.NUMpoints is point array
+       it may be moved by qh_joggleinput(qh)
+*/
+void qh_build_withrestart(qhT *qh) {
+  int restart;
+
+  qh->ALLOWrestart= True;
+  while (True) {
+    restart= setjmp(qh->restartexit); /* simple statement for CRAY J916 */
+    if (restart) {       /* only from qh_precision() */
+      zzinc_(Zretry);
+      wmax_(Wretrymax, qh->JOGGLEmax);
+      /* QH7078 warns about using 'TCn' with 'QJn' */
+      qh->STOPcone= qh_IDunknown; /* if break from joggle, prevents normal output */
+    }
+    if (!qh->RERUN && qh->JOGGLEmax < REALmax/2) {
+      if (qh->build_cnt > qh_JOGGLEmaxretry) {
+        qh_fprintf(qh, qh->ferr, 6229, "qhull precision error: %d attempts to construct a convex hull\n\
+        with joggled input.  Increase joggle above 'QJ%2.2g'\n\
+        or modify qh_JOGGLE... parameters in user.h\n",
+           qh->build_cnt, qh->JOGGLEmax);
+        qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+      }
+      if (qh->build_cnt && !restart)
+        break;
+    }else if (qh->build_cnt && qh->build_cnt >= qh->RERUN)
+      break;
+    qh->STOPcone= 0;
+    qh_freebuild(qh, True);  /* first call is a nop */
+    qh->build_cnt++;
+    if (!qh->qhull_optionsiz)
+      qh->qhull_optionsiz= (int)strlen(qh->qhull_options);   /* WARN64 */
+    else {
+      qh->qhull_options [qh->qhull_optionsiz]= '\0';
+      qh->qhull_optionlen= qh_OPTIONline;  /* starts a new line */
+    }
+    qh_option(qh, "_run", &qh->build_cnt, NULL);
+    if (qh->build_cnt == qh->RERUN) {
+      qh->IStracing= qh->TRACElastrun;  /* duplicated from qh_initqhull_globals */
+      if (qh->TRACEpoint != qh_IDunknown || qh->TRACEdist < REALmax/2 || qh->TRACEmerge) {
+        qh->TRACElevel= (qh->IStracing? qh->IStracing : 3);
+        qh->IStracing= 0;
+      }
+      qh->qhmem.IStracing= qh->IStracing;
+    }
+    if (qh->JOGGLEmax < REALmax/2)
+      qh_joggleinput(qh);
+    qh_initbuild(qh);
+    qh_buildhull(qh);
+    if (qh->JOGGLEmax < REALmax/2 && !qh->MERGING)
+      qh_checkconvex(qh, qh->facet_list, qh_ALGORITHMfault);
+  }
+  qh->ALLOWrestart= False;
+} /* qh_build_withrestart */
+
+/*-<a                             href="qh-qhull_r.htm#TOC"
+  >-------------------------------</a><a name="buildhull">-</a>
+
+  qh_buildhull(qh)
+    construct a convex hull by adding outside points one at a time
+
+  returns:
+
+  notes:
+    may be called multiple times
+    checks facet and vertex lists for incorrect flags
+    to recover from STOPcone, call qh_deletevisible and qh_resetlists
+
+  design:
+    check visible facet and newfacet flags
+    check newlist vertex flags and qh.STOPcone/STOPpoint
+    for each facet with a furthest outside point
+      add point to facet
+      exit if qh.STOPcone or qh.STOPpoint requested
+    if qh.NARROWhull for initial simplex
+      partition remaining outside points to coplanar sets
+*/
+void qh_buildhull(qhT *qh) {
+  facetT *facet;
+  pointT *furthest;
+  vertexT *vertex;
+  int id;
+
+  trace1((qh, qh->ferr, 1037, "qh_buildhull: start build hull\n"));
+  FORALLfacets {
+    if (facet->visible || facet->newfacet) {
+      qh_fprintf(qh, qh->ferr, 6165, "qhull internal error (qh_buildhull): visible or new facet f%d in facet list\n",
+                   facet->id);
+      qh_errexit(qh, qh_ERRqhull, facet, NULL);
+    }
+  }
+  FORALLvertices {
+    if (vertex->newlist) {
+      qh_fprintf(qh, qh->ferr, 6166, "qhull internal error (qh_buildhull): new vertex f%d in vertex list\n",
+                   vertex->id);
+      qh_errprint(qh, "ERRONEOUS", NULL, NULL, NULL, vertex);
+      qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+    }
+    id= qh_pointid(qh, vertex->point);
+    if ((qh->STOPpoint>0 && id == qh->STOPpoint-1) ||
+        (qh->STOPpoint<0 && id == -qh->STOPpoint-1) ||
+        (qh->STOPcone>0 && id == qh->STOPcone-1)) {
+      trace1((qh, qh->ferr, 1038,"qh_buildhull: stop point or cone P%d in initial hull\n", id));
+      return;
+    }
+  }
+  qh->facet_next= qh->facet_list;      /* advance facet when processed */
+  while ((furthest= qh_nextfurthest(qh, &facet))) {
+    qh->num_outside--;  /* if ONLYmax, furthest may not be outside */
+    if (!qh_addpoint(qh, furthest, facet, qh->ONLYmax))
+      break;
+  }
+  if (qh->NARROWhull) /* move points from outsideset to coplanarset */
+    qh_outcoplanar(qh /* facet_list */ );
+  if (qh->num_outside && !furthest) {
+    qh_fprintf(qh, qh->ferr, 6167, "qhull internal error (qh_buildhull): %d outside points were never processed.\n", qh->num_outside);
+    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+  }
+  trace1((qh, qh->ferr, 1039, "qh_buildhull: completed the hull construction\n"));
+} /* buildhull */
+
+
+/*-<a                             href="qh-qhull_r.htm#TOC"
+  >-------------------------------</a><a name="buildtracing">-</a>
+
+  qh_buildtracing(qh, furthest, facet )
+    trace an iteration of qh_buildhull() for furthest point and facet
+    if !furthest, prints progress message
+
+  returns:
+    tracks progress with qh.lastreport
+    updates qh.furthest_id (-3 if furthest is NULL)
+    also resets visit_id, vertext_visit on wrap around
+
+  see:
+    qh_tracemerging()
+
+  design:
+    if !furthest
+      print progress message
+      exit
+    if 'TFn' iteration
+      print progress message
+    else if tracing
+      trace furthest point and facet
+    reset qh.visit_id and qh.vertex_visit if overflow may occur
+    set qh.furthest_id for tracing
+*/
+void qh_buildtracing(qhT *qh, pointT *furthest, facetT *facet) {
+  realT dist= 0;
+  float cpu;
+  int total, furthestid;
+  time_t timedata;
+  struct tm *tp;
+  vertexT *vertex;
+
+  qh->old_randomdist= qh->RANDOMdist;
+  qh->RANDOMdist= False;
+  if (!furthest) {
+    time(&timedata);
+    tp= localtime(&timedata);
+    cpu= (float)qh_CPUclock - (float)qh->hulltime;
+    cpu /= (float)qh_SECticks;
+    total= zzval_(Ztotmerge) - zzval_(Zcyclehorizon) + zzval_(Zcyclefacettot);
+    qh_fprintf(qh, qh->ferr, 8118, "\n\
+At %02d:%02d:%02d & %2.5g CPU secs, qhull has created %d facets and merged %d.\n\
+ The current hull contains %d facets and %d vertices.  Last point was p%d\n",
+      tp->tm_hour, tp->tm_min, tp->tm_sec, cpu, qh->facet_id -1,
+      total, qh->num_facets, qh->num_vertices, qh->furthest_id);
+    return;
+  }
+  furthestid= qh_pointid(qh, furthest);
+  if (qh->TRACEpoint == furthestid) {
+    qh->IStracing= qh->TRACElevel;
+    qh->qhmem.IStracing= qh->TRACElevel;
+  }else if (qh->TRACEpoint != qh_IDunknown && qh->TRACEdist < REALmax/2) {
+    qh->IStracing= 0;
+    qh->qhmem.IStracing= 0;
+  }
+  if (qh->REPORTfreq && (qh->facet_id-1 > qh->lastreport+qh->REPORTfreq)) {
+    qh->lastreport= qh->facet_id-1;
+    time(&timedata);
+    tp= localtime(&timedata);
+    cpu= (float)qh_CPUclock - (float)qh->hulltime;
+    cpu /= (float)qh_SECticks;
+    total= zzval_(Ztotmerge) - zzval_(Zcyclehorizon) + zzval_(Zcyclefacettot);
+    zinc_(Zdistio);
+    qh_distplane(qh, furthest, facet, &dist);
+    qh_fprintf(qh, qh->ferr, 8119, "\n\
+At %02d:%02d:%02d & %2.5g CPU secs, qhull has created %d facets and merged %d.\n\
+ The current hull contains %d facets and %d vertices.  There are %d\n\
+ outside points.  Next is point p%d(v%d), %2.2g above f%d.\n",
+      tp->tm_hour, tp->tm_min, tp->tm_sec, cpu, qh->facet_id -1,
+      total, qh->num_facets, qh->num_vertices, qh->num_outside+1,
+      furthestid, qh->vertex_id, dist, getid_(facet));
+  }else if (qh->IStracing >=1) {
+    cpu= (float)qh_CPUclock - (float)qh->hulltime;
+    cpu /= (float)qh_SECticks;
+    qh_distplane(qh, furthest, facet, &dist);
+    qh_fprintf(qh, qh->ferr, 8120, "qh_addpoint: add p%d(v%d) to hull of %d facets(%2.2g above f%d) and %d outside at %4.4g CPU secs.  Previous was p%d.\n",
+      furthestid, qh->vertex_id, qh->num_facets, dist,
+      getid_(facet), qh->num_outside+1, cpu, qh->furthest_id);
+  }
+  zmax_(Zvisit2max, (int)qh->visit_id/2);
+  if (qh->visit_id > (unsigned) INT_MAX) { /* 31 bits */
+    zinc_(Zvisit);
+    qh->visit_id= 0;
+    FORALLfacets
+      facet->visitid= 0;
+  }
+  zmax_(Zvvisit2max, (int)qh->vertex_visit/2);
+  if (qh->vertex_visit > (unsigned) INT_MAX) { /* 31 bits */ 
+    zinc_(Zvvisit);
+    qh->vertex_visit= 0;
+    FORALLvertices
+      vertex->visitid= 0;
+  }
+  qh->furthest_id= furthestid;
+  qh->RANDOMdist= qh->old_randomdist;
+} /* buildtracing */
+
+/*-<a                             href="qh-qhull_r.htm#TOC"
+  >-------------------------------</a><a name="errexit2">-</a>
+
+  qh_errexit2(qh, exitcode, facet, otherfacet )
+    return exitcode to system after an error
+    report two facets
+
+  returns:
+    assumes exitcode non-zero
+
+  see:
+    normally use qh_errexit() in user.c(reports a facet and a ridge)
+*/
+void qh_errexit2(qhT *qh, int exitcode, facetT *facet, facetT *otherfacet) {
+
+  qh_errprint(qh, "ERRONEOUS", facet, otherfacet, NULL, NULL);
+  qh_errexit(qh, exitcode, NULL, NULL);
+} /* errexit2 */
+
+
+/*-<a                             href="qh-qhull_r.htm#TOC"
+  >-------------------------------</a><a name="findhorizon">-</a>
+
+  qh_findhorizon(qh, point, facet, goodvisible, goodhorizon )
+    given a visible facet, find the point's horizon and visible facets
+    for all facets, !facet-visible
+
+  returns:
+    returns qh.visible_list/num_visible with all visible facets
+      marks visible facets with ->visible
+    updates count of good visible and good horizon facets
+    updates qh.max_outside, qh.max_vertex, facet->maxoutside
+
+  see:
+    similar to qh_delpoint()
+
+  design:
+    move facet to qh.visible_list at end of qh.facet_list
+    for all visible facets
+     for each unvisited neighbor of a visible facet
+       compute distance of point to neighbor
+       if point above neighbor
+         move neighbor to end of qh.visible_list
+       else if point is coplanar with neighbor
+         update qh.max_outside, qh.max_vertex, neighbor->maxoutside
+         mark neighbor coplanar (will create a samecycle later)
+         update horizon statistics
+*/
+void qh_findhorizon(qhT *qh, pointT *point, facetT *facet, int *goodvisible, int *goodhorizon) {
+  facetT *neighbor, **neighborp, *visible;
+  int numhorizon= 0, coplanar= 0;
+  realT dist;
+
+  trace1((qh, qh->ferr, 1040,"qh_findhorizon: find horizon for point p%d facet f%d\n",qh_pointid(qh, point),facet->id));
+  *goodvisible= *goodhorizon= 0;
+  zinc_(Ztotvisible);
+  qh_removefacet(qh, facet);  /* visible_list at end of qh->facet_list */
+  qh_appendfacet(qh, facet);
+  qh->num_visible= 1;
+  if (facet->good)
+    (*goodvisible)++;
+  qh->visible_list= facet;
+  facet->visible= True;
+  facet->f.replace= NULL;
+  if (qh->IStracing >=4)
+    qh_errprint(qh, "visible", facet, NULL, NULL, NULL);
+  qh->visit_id++;
+  FORALLvisible_facets {
+    if (visible->tricoplanar && !qh->TRInormals) {
+      qh_fprintf(qh, qh->ferr, 6230, "Qhull internal error (qh_findhorizon): does not work for tricoplanar facets.  Use option 'Q11'\n");
+      qh_errexit(qh, qh_ERRqhull, visible, NULL);
+    }
+    visible->visitid= qh->visit_id;
+    FOREACHneighbor_(visible) {
+      if (neighbor->visitid == qh->visit_id)
+        continue;
+      neighbor->visitid= qh->visit_id;
+      zzinc_(Znumvisibility);
+      qh_distplane(qh, point, neighbor, &dist);
+      if (dist > qh->MINvisible) {
+        zinc_(Ztotvisible);
+        qh_removefacet(qh, neighbor);  /* append to end of qh->visible_list */
+        qh_appendfacet(qh, neighbor);
+        neighbor->visible= True;
+        neighbor->f.replace= NULL;
+        qh->num_visible++;
+        if (neighbor->good)
+          (*goodvisible)++;
+        if (qh->IStracing >=4)
+          qh_errprint(qh, "visible", neighbor, NULL, NULL, NULL);
+      }else {
+        if (dist > - qh->MAXcoplanar) {
+          neighbor->coplanar= True;
+          zzinc_(Zcoplanarhorizon);
+          qh_precision(qh, "coplanar horizon");
+          coplanar++;
+          if (qh->MERGING) {
+            if (dist > 0) {
+              maximize_(qh->max_outside, dist);
+              maximize_(qh->max_vertex, dist);
+#if qh_MAXoutside
+              maximize_(neighbor->maxoutside, dist);
+#endif
+            }else
+              minimize_(qh->min_vertex, dist);  /* due to merge later */
+          }
+          trace2((qh, qh->ferr, 2057, "qh_findhorizon: point p%d is coplanar to horizon f%d, dist=%2.7g < qh->MINvisible(%2.7g)\n",
+              qh_pointid(qh, point), neighbor->id, dist, qh->MINvisible));
+        }else
+          neighbor->coplanar= False;
+        zinc_(Ztothorizon);
+        numhorizon++;
+        if (neighbor->good)
+          (*goodhorizon)++;
+        if (qh->IStracing >=4)
+          qh_errprint(qh, "horizon", neighbor, NULL, NULL, NULL);
+      }
+    }
+  }
+  if (!numhorizon) {
+    qh_precision(qh, "empty horizon");
+    qh_fprintf(qh, qh->ferr, 6168, "qhull precision error (qh_findhorizon): empty horizon\n\
+QhullPoint p%d was above all facets.\n", qh_pointid(qh, point));
+    qh_printfacetlist(qh, qh->facet_list, NULL, True);
+    qh_errexit(qh, qh_ERRprec, NULL, NULL);
+  }
+  trace1((qh, qh->ferr, 1041, "qh_findhorizon: %d horizon facets(good %d), %d visible(good %d), %d coplanar\n",
+       numhorizon, *goodhorizon, qh->num_visible, *goodvisible, coplanar));
+  if (qh->IStracing >= 4 && qh->num_facets < 50)
+    qh_printlists(qh);
+} /* findhorizon */
+
+/*-<a                             href="qh-qhull_r.htm#TOC"
+  >-------------------------------</a><a name="nextfurthest">-</a>
+
+  qh_nextfurthest(qh, visible )
+    returns next furthest point and visible facet for qh_addpoint()
+    starts search at qh.facet_next
+
+  returns:
+    removes furthest point from outside set
+    NULL if none available
+    advances qh.facet_next over facets with empty outside sets
+
+  design:
+    for each facet from qh.facet_next
+      if empty outside set
+        advance qh.facet_next
+      else if qh.NARROWhull
+        determine furthest outside point
+        if furthest point is not outside
+          advance qh.facet_next(point will be coplanar)
+    remove furthest point from outside set
+*/
+pointT *qh_nextfurthest(qhT *qh, facetT **visible) {
+  facetT *facet;
+  int size, idx;
+  realT randr, dist;
+  pointT *furthest;
+
+  while ((facet= qh->facet_next) != qh->facet_tail) {
+    if (!facet->outsideset) {
+      qh->facet_next= facet->next;
+      continue;
+    }
+    SETreturnsize_(facet->outsideset, size);
+    if (!size) {
+      qh_setfree(qh, &facet->outsideset);
+      qh->facet_next= facet->next;
+      continue;
+    }
+    if (qh->NARROWhull) {
+      if (facet->notfurthest)
+        qh_furthestout(qh, facet);
+      furthest= (pointT*)qh_setlast(facet->outsideset);
+#if qh_COMPUTEfurthest
+      qh_distplane(qh, furthest, facet, &dist);
+      zinc_(Zcomputefurthest);
+#else
+      dist= facet->furthestdist;
+#endif
+      if (dist < qh->MINoutside) { /* remainder of outside set is coplanar for qh_outcoplanar */
+        qh->facet_next= facet->next;
+        continue;
+      }
+    }
+    if (!qh->RANDOMoutside && !qh->VIRTUALmemory) {
+      if (qh->PICKfurthest) {
+        qh_furthestnext(qh /* qh->facet_list */);
+        facet= qh->facet_next;
+      }
+      *visible= facet;
+      return((pointT*)qh_setdellast(facet->outsideset));
+    }
+    if (qh->RANDOMoutside) {
+      int outcoplanar = 0;
+      if (qh->NARROWhull) {
+        FORALLfacets {
+          if (facet == qh->facet_next)
+            break;
+          if (facet->outsideset)
+            outcoplanar += qh_setsize(qh, facet->outsideset);
+        }
+      }
+      randr= qh_RANDOMint;
+      randr= randr/(qh_RANDOMmax+1);
+      idx= (int)floor((qh->num_outside - outcoplanar) * randr);
+      FORALLfacet_(qh->facet_next) {
+        if (facet->outsideset) {
+          SETreturnsize_(facet->outsideset, size);
+          if (!size)
+            qh_setfree(qh, &facet->outsideset);
+          else if (size > idx) {
+            *visible= facet;
+            return((pointT*)qh_setdelnth(qh, facet->outsideset, idx));
+          }else
+            idx -= size;
+        }
+      }
+      qh_fprintf(qh, qh->ferr, 6169, "qhull internal error (qh_nextfurthest): num_outside %d is too low\nby at least %d, or a random real %g >= 1.0\n",
+              qh->num_outside, idx+1, randr);
+      qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+    }else { /* VIRTUALmemory */
+      facet= qh->facet_tail->previous;
+      if (!(furthest= (pointT*)qh_setdellast(facet->outsideset))) {
+        if (facet->outsideset)
+          qh_setfree(qh, &facet->outsideset);
+        qh_removefacet(qh, facet);
+        qh_prependfacet(qh, facet, &qh->facet_list);
+        continue;
+      }
+      *visible= facet;
+      return furthest;
+    }
+  }
+  return NULL;
+} /* nextfurthest */
+
+/*-<a                             href="qh-qhull_r.htm#TOC"
+  >-------------------------------</a><a name="partitionall">-</a>
+
+  qh_partitionall(qh, vertices, points, numpoints )
+    partitions all points in points/numpoints to the outsidesets of facets
+    vertices= vertices in qh.facet_list(!partitioned)
+
+  returns:
+    builds facet->outsideset
+    does not partition qh.GOODpoint
+    if qh.ONLYgood && !qh.MERGING,
+      does not partition qh.GOODvertex
+
+  notes:
+    faster if qh.facet_list sorted by anticipated size of outside set
+
+  design:
+    initialize pointset with all points
+    remove vertices from pointset
+    remove qh.GOODpointp from pointset (unless it's qh.STOPcone or qh.STOPpoint)
+    for all facets
+      for all remaining points in pointset
+        compute distance from point to facet
+        if point is outside facet
+          remove point from pointset (by not reappending)
+          update bestpoint
+          append point or old bestpoint to facet's outside set
+      append bestpoint to facet's outside set (furthest)
+    for all points remaining in pointset
+      partition point into facets' outside sets and coplanar sets
+*/
+void qh_partitionall(qhT *qh, setT *vertices, pointT *points, int numpoints){
+  setT *pointset;
+  vertexT *vertex, **vertexp;
+  pointT *point, **pointp, *bestpoint;
+  int size, point_i, point_n, point_end, remaining, i, id;
+  facetT *facet;
+  realT bestdist= -REALmax, dist, distoutside;
+
+  trace1((qh, qh->ferr, 1042, "qh_partitionall: partition all points into outside sets\n"));
+  pointset= qh_settemp(qh, numpoints);
+  qh->num_outside= 0;
+  pointp= SETaddr_(pointset, pointT);
+  for (i=numpoints, point= points; i--; point += qh->hull_dim)
+    *(pointp++)= point;
+  qh_settruncate(qh, pointset, numpoints);
+  FOREACHvertex_(vertices) {
+    if ((id= qh_pointid(qh, vertex->point)) >= 0)
+      SETelem_(pointset, id)= NULL;
+  }
+  id= qh_pointid(qh, qh->GOODpointp);
+  if (id >=0 && qh->STOPcone-1 != id && -qh->STOPpoint-1 != id)
+    SETelem_(pointset, id)= NULL;
+  if (qh->GOODvertexp && qh->ONLYgood && !qh->MERGING) { /* matches qhull()*/
+    if ((id= qh_pointid(qh, qh->GOODvertexp)) >= 0)
+      SETelem_(pointset, id)= NULL;
+  }
+  if (!qh->BESToutside) {  /* matches conditional for qh_partitionpoint below */
+    distoutside= qh_DISToutside; /* multiple of qh.MINoutside & qh.max_outside, see user.h */
+    zval_(Ztotpartition)= qh->num_points - qh->hull_dim - 1; /*misses GOOD... */
+    remaining= qh->num_facets;
+    point_end= numpoints;
+    FORALLfacets {
+      size= point_end/(remaining--) + 100;
+      facet->outsideset= qh_setnew(qh, size);
+      bestpoint= NULL;
+      point_end= 0;
+      FOREACHpoint_i_(qh, pointset) {
+        if (point) {
+          zzinc_(Zpartitionall);
+          qh_distplane(qh, point, facet, &dist);
+          if (dist < distoutside)
+            SETelem_(pointset, point_end++)= point;
+          else {
+            qh->num_outside++;
+            if (!bestpoint) {
+              bestpoint= point;
+              bestdist= dist;
+            }else if (dist > bestdist) {
+              qh_setappend(qh, &facet->outsideset, bestpoint);
+              bestpoint= point;
+              bestdist= dist;
+            }else
+              qh_setappend(qh, &facet->outsideset, point);
+          }
+        }
+      }
+      if (bestpoint) {
+        qh_setappend(qh, &facet->outsideset, bestpoint);
+#if !qh_COMPUTEfurthest
+        facet->furthestdist= bestdist;
+#endif
+      }else
+        qh_setfree(qh, &facet->outsideset);
+      qh_settruncate(qh, pointset, point_end);
+    }
+  }
+  /* if !qh->BESToutside, pointset contains points not assigned to outsideset */
+  if (qh->BESToutside || qh->MERGING || qh->KEEPcoplanar || qh->KEEPinside) {
+    qh->findbestnew= True;
+    FOREACHpoint_i_(qh, pointset) {
+      if (point)
+        qh_partitionpoint(qh, point, qh->facet_list);
+    }
+    qh->findbestnew= False;
+  }
+  zzadd_(Zpartitionall, zzval_(Zpartition));
+  zzval_(Zpartition)= 0;
+  qh_settempfree(qh, &pointset);
+  if (qh->IStracing >= 4)
+    qh_printfacetlist(qh, qh->facet_list, NULL, True);
+} /* partitionall */
+
+
+/*-<a                             href="qh-qhull_r.htm#TOC"
+  >-------------------------------</a><a name="partitioncoplanar">-</a>
+
+  qh_partitioncoplanar(qh, point, facet, dist )
+    partition coplanar point to a facet
+    dist is distance from point to facet
+    if dist NULL,
+      searches for bestfacet and does nothing if inside
+    if qh.findbestnew set,
+      searches new facets instead of using qh_findbest()
+
+  returns:
+    qh.max_ouside updated
+    if qh.KEEPcoplanar or qh.KEEPinside
+      point assigned to best coplanarset
+
+  notes:
+    facet->maxoutside is updated at end by qh_check_maxout
+
+  design:
+    if dist undefined
+      find best facet for point
+      if point sufficiently below facet (depends on qh.NEARinside and qh.KEEPinside)
+        exit
+    if keeping coplanar/nearinside/inside points
+      if point is above furthest coplanar point
+        append point to coplanar set (it is the new furthest)
+        update qh.max_outside
+      else
+        append point one before end of coplanar set
+    else if point is clearly outside of qh.max_outside and bestfacet->coplanarset
+    and bestfacet is more than perpendicular to facet
+      repartition the point using qh_findbest() -- it may be put on an outsideset
+    else
+      update qh.max_outside
+*/
+void qh_partitioncoplanar(qhT *qh, pointT *point, facetT *facet, realT *dist) {
+  facetT *bestfacet;
+  pointT *oldfurthest;
+  realT bestdist, dist2= 0, angle;
+  int numpart= 0, oldfindbest;
+  boolT isoutside;
+
+  qh->WAScoplanar= True;
+  if (!dist) {
+    if (qh->findbestnew)
+      bestfacet= qh_findbestnew(qh, point, facet, &bestdist, qh_ALL, &isoutside, &numpart);
+    else
+      bestfacet= qh_findbest(qh, point, facet, qh_ALL, !qh_ISnewfacets, qh->DELAUNAY,
+                          &bestdist, &isoutside, &numpart);
+    zinc_(Ztotpartcoplanar);
+    zzadd_(Zpartcoplanar, numpart);
+    if (!qh->DELAUNAY && !qh->KEEPinside) { /*  for 'd', bestdist skips upperDelaunay facets */
+      if (qh->KEEPnearinside) {
+        if (bestdist < -qh->NEARinside) {
+          zinc_(Zcoplanarinside);
+          trace4((qh, qh->ferr, 4062, "qh_partitioncoplanar: point p%d is more than near-inside facet f%d dist %2.2g findbestnew %d\n",
+                  qh_pointid(qh, point), bestfacet->id, bestdist, qh->findbestnew));
+          return;
+        }
+      }else if (bestdist < -qh->MAXcoplanar) {
+          trace4((qh, qh->ferr, 4063, "qh_partitioncoplanar: point p%d is inside facet f%d dist %2.2g findbestnew %d\n",
+                  qh_pointid(qh, point), bestfacet->id, bestdist, qh->findbestnew));
+        zinc_(Zcoplanarinside);
+        return;
+      }
+    }
+  }else {
+    bestfacet= facet;
+    bestdist= *dist;
+  }
+  if (bestdist > qh->max_outside) {
+    if (!dist && facet != bestfacet) {
+      zinc_(Zpartangle);
+      angle= qh_getangle(qh, facet->normal, bestfacet->normal);
+      if (angle < 0) {
+        /* typically due to deleted vertex and coplanar facets, e.g.,
+             RBOX 1000 s Z1 G1e-13 t1001185205 | QHULL Tv */
+        zinc_(Zpartflip);
+        trace2((qh, qh->ferr, 2058, "qh_partitioncoplanar: repartition point p%d from f%d.  It is above flipped facet f%d dist %2.2g\n",
+                qh_pointid(qh, point), facet->id, bestfacet->id, bestdist));
+        oldfindbest= qh->findbestnew;
+        qh->findbestnew= False;
+        qh_partitionpoint(qh, point, bestfacet);
+        qh->findbestnew= oldfindbest;
+        return;
+      }
+    }
+    qh->max_outside= bestdist;
+    if (bestdist > qh->TRACEdist) {
+      qh_fprintf(qh, qh->ferr, 8122, "qh_partitioncoplanar: ====== p%d from f%d increases max_outside to %2.2g of f%d last p%d\n",
+                     qh_pointid(qh, point), facet->id, bestdist, bestfacet->id, qh->furthest_id);
+      qh_errprint(qh, "DISTANT", facet, bestfacet, NULL, NULL);
+    }
+  }
+  if (qh->KEEPcoplanar + qh->KEEPinside + qh->KEEPnearinside) {
+    oldfurthest= (pointT*)qh_setlast(bestfacet->coplanarset);
+    if (oldfurthest) {
+      zinc_(Zcomputefurthest);
+      qh_distplane(qh, oldfurthest, bestfacet, &dist2);
+    }
+    if (!oldfurthest || dist2 < bestdist)
+      qh_setappend(qh, &bestfacet->coplanarset, point);
+    else
+      qh_setappend2ndlast(qh, &bestfacet->coplanarset, point);
+  }
+  trace4((qh, qh->ferr, 4064, "qh_partitioncoplanar: point p%d is coplanar with facet f%d(or inside) dist %2.2g\n",
+          qh_pointid(qh, point), bestfacet->id, bestdist));
+} /* partitioncoplanar */
+
+/*-<a                             href="qh-qhull_r.htm#TOC"
+  >-------------------------------</a><a name="partitionpoint">-</a>
+
+  qh_partitionpoint(qh, point, facet )
+    assigns point to an outside set, coplanar set, or inside set (i.e., dropt)
+    if qh.findbestnew
+      uses qh_findbestnew() to search all new facets
+    else
+      uses qh_findbest()
+
+  notes:
+    after qh_distplane(), this and qh_findbest() are most expensive in 3-d
+
+  design:
+    find best facet for point
+      (either exhaustive search of new facets or directed search from facet)
+    if qh.NARROWhull
+      retain coplanar and nearinside points as outside points
+    if point is outside bestfacet
+      if point above furthest point for bestfacet
+        append point to outside set (it becomes the new furthest)
+        if outside set was empty
+          move bestfacet to end of qh.facet_list (i.e., after qh.facet_next)
+        update bestfacet->furthestdist
+      else
+        append point one before end of outside set
+    else if point is coplanar to bestfacet
+      if keeping coplanar points or need to update qh.max_outside
+        partition coplanar point into bestfacet
+    else if near-inside point
+      partition as coplanar point into bestfacet
+    else is an inside point
+      if keeping inside points
+        partition as coplanar point into bestfacet
+*/
+void qh_partitionpoint(qhT *qh, pointT *point, facetT *facet) {
+  realT bestdist;
+  boolT isoutside;
+  facetT *bestfacet;
+  int numpart;
+#if qh_COMPUTEfurthest
+  realT dist;
+#endif
+
+  if (qh->findbestnew)
+    bestfacet= qh_findbestnew(qh, point, facet, &bestdist, qh->BESToutside, &isoutside, &numpart);
+  else
+    bestfacet= qh_findbest(qh, point, facet, qh->BESToutside, qh_ISnewfacets, !qh_NOupper,
+                          &bestdist, &isoutside, &numpart);
+  zinc_(Ztotpartition);
+  zzadd_(Zpartition, numpart);
+  if (qh->NARROWhull) {
+    if (qh->DELAUNAY && !isoutside && bestdist >= -qh->MAXcoplanar)
+      qh_precision(qh, "nearly incident point(narrow hull)");
+    if (qh->KEEPnearinside) {
+      if (bestdist >= -qh->NEARinside)
+        isoutside= True;
+    }else if (bestdist >= -qh->MAXcoplanar)
+      isoutside= True;
+  }
+
+  if (isoutside) {
+    if (!bestfacet->outsideset
+    || !qh_setlast(bestfacet->outsideset)) {
+      qh_setappend(qh, &(bestfacet->outsideset), point);
+      if (!bestfacet->newfacet) {
+        qh_removefacet(qh, bestfacet);  /* make sure it's after qh->facet_next */
+        qh_appendfacet(qh, bestfacet);
+      }
+#if !qh_COMPUTEfurthest
+      bestfacet->furthestdist= bestdist;
+#endif
+    }else {
+#if qh_COMPUTEfurthest
+      zinc_(Zcomputefurthest);
+      qh_distplane(qh, oldfurthest, bestfacet, &dist);
+      if (dist < bestdist)
+        qh_setappend(qh, &(bestfacet->outsideset), point);
+      else
+        qh_setappend2ndlast(qh, &(bestfacet->outsideset), point);
+#else
+      if (bestfacet->furthestdist < bestdist) {
+        qh_setappend(qh, &(bestfacet->outsideset), point);
+        bestfacet->furthestdist= bestdist;
+      }else
+        qh_setappend2ndlast(qh, &(bestfacet->outsideset), point);
+#endif
+    }
+    qh->num_outside++;
+    trace4((qh, qh->ferr, 4065, "qh_partitionpoint: point p%d is outside facet f%d new? %d (or narrowhull)\n",
+          qh_pointid(qh, point), bestfacet->id, bestfacet->newfacet));
+  }else if (qh->DELAUNAY || bestdist >= -qh->MAXcoplanar) { /* for 'd', bestdist skips upperDelaunay facets */
+    zzinc_(Zcoplanarpart);
+    if (qh->DELAUNAY)
+      qh_precision(qh, "nearly incident point");
+    if ((qh->KEEPcoplanar + qh->KEEPnearinside) || bestdist > qh->max_outside)
+      qh_partitioncoplanar(qh, point, bestfacet, &bestdist);
+    else {
+      trace4((qh, qh->ferr, 4066, "qh_partitionpoint: point p%d is coplanar to facet f%d (dropped)\n",
+          qh_pointid(qh, point), bestfacet->id));
+    }
+  }else if (qh->KEEPnearinside && bestdist > -qh->NEARinside) {
+    zinc_(Zpartnear);
+    qh_partitioncoplanar(qh, point, bestfacet, &bestdist);
+  }else {
+    zinc_(Zpartinside);
+    trace4((qh, qh->ferr, 4067, "qh_partitionpoint: point p%d is inside all facets, closest to f%d dist %2.2g\n",
+          qh_pointid(qh, point), bestfacet->id, bestdist));
+    if (qh->KEEPinside)
+      qh_partitioncoplanar(qh, point, bestfacet, &bestdist);
+  }
+} /* partitionpoint */
+
+/*-<a                             href="qh-qhull_r.htm#TOC"
+  >-------------------------------</a><a name="partitionvisible">-</a>
+
+  qh_partitionvisible(qh, allpoints, numoutside )
+    partitions points in visible facets to qh.newfacet_list
+    qh.visible_list= visible facets
+    for visible facets
+      1st neighbor (if any) points to a horizon facet or a new facet
+    if allpoints(!used),
+      repartitions coplanar points
+
+  returns:
+    updates outside sets and coplanar sets of qh.newfacet_list
+    updates qh.num_outside (count of outside points)
+
+  notes:
+    qh.findbest_notsharp should be clear (extra work if set)
+
+  design:
+    for all visible facets with outside set or coplanar set
+      select a newfacet for visible facet
+      if outside set
+        partition outside set into new facets
+      if coplanar set and keeping coplanar/near-inside/inside points
+        if allpoints
+          partition coplanar set into new facets, may be assigned outside
+        else
+          partition coplanar set into coplanar sets of new facets
+    for each deleted vertex
+      if allpoints
+        partition vertex into new facets, may be assigned outside
+      else
+        partition vertex into coplanar sets of new facets
+*/
+void qh_partitionvisible(qhT *qh /*qh.visible_list*/, boolT allpoints, int *numoutside) {
+  facetT *visible, *newfacet;
+  pointT *point, **pointp;
+  int coplanar=0, size;
+  unsigned count;
+  vertexT *vertex, **vertexp;
+
+  if (qh->ONLYmax)
+    maximize_(qh->MINoutside, qh->max_vertex);
+  *numoutside= 0;
+  FORALLvisible_facets {
+    if (!visible->outsideset && !visible->coplanarset)
+      continue;
+    newfacet= visible->f.replace;
+    count= 0;
+    while (newfacet && newfacet->visible) {
+      newfacet= newfacet->f.replace;
+      if (count++ > qh->facet_id)
+        qh_infiniteloop(qh, visible);
+    }
+    if (!newfacet)
+      newfacet= qh->newfacet_list;
+    if (newfacet == qh->facet_tail) {
+      qh_fprintf(qh, qh->ferr, 6170, "qhull precision error (qh_partitionvisible): all new facets deleted as\n        degenerate facets. Can not continue.\n");
+      qh_errexit(qh, qh_ERRprec, NULL, NULL);
+    }
+    if (visible->outsideset) {
+      size= qh_setsize(qh, visible->outsideset);
+      *numoutside += size;
+      qh->num_outside -= size;
+      FOREACHpoint_(visible->outsideset)
+        qh_partitionpoint(qh, point, newfacet);
+    }
+    if (visible->coplanarset && (qh->KEEPcoplanar + qh->KEEPinside + qh->KEEPnearinside)) {
+      size= qh_setsize(qh, visible->coplanarset);
+      coplanar += size;
+      FOREACHpoint_(visible->coplanarset) {
+        if (allpoints) /* not used */
+          qh_partitionpoint(qh, point, newfacet);
+        else
+          qh_partitioncoplanar(qh, point, newfacet, NULL);
+      }
+    }
+  }
+  FOREACHvertex_(qh->del_vertices) {
+    if (vertex->point) {
+      if (allpoints) /* not used */
+        qh_partitionpoint(qh, vertex->point, qh->newfacet_list);
+      else
+        qh_partitioncoplanar(qh, vertex->point, qh->newfacet_list, NULL);
+    }
+  }
+  trace1((qh, qh->ferr, 1043,"qh_partitionvisible: partitioned %d points from outsidesets and %d points from coplanarsets\n", *numoutside, coplanar));
+} /* partitionvisible */
+
+
+
+/*-<a                             href="qh-qhull_r.htm#TOC"
+  >-------------------------------</a><a name="precision">-</a>
+
+  qh_precision(qh, reason )
+    restart on precision errors if not merging and if 'QJn'
+*/
+void qh_precision(qhT *qh, const char *reason) {
+
+  if (qh->ALLOWrestart && !qh->PREmerge && !qh->MERGEexact) {
+    if (qh->JOGGLEmax < REALmax/2) {
+      trace0((qh, qh->ferr, 26, "qh_precision: qhull restart because of %s\n", reason));
+      /* May be called repeatedly if qh->ALLOWrestart */
+      longjmp(qh->restartexit, qh_ERRprec);
+    }
+  }
+} /* qh_precision */
+
+/*-<a                             href="qh-qhull_r.htm#TOC"
+  >-------------------------------</a><a name="printsummary">-</a>
+
+  qh_printsummary(qh, fp )
+    prints summary to fp
+
+  notes:
+    not in io_r.c so that user_eg.c can prevent io_r.c from loading
+    qh_printsummary and qh_countfacets must match counts
+
+  design:
+    determine number of points, vertices, and coplanar points
+    print summary
+*/
+void qh_printsummary(qhT *qh, FILE *fp) {
+  realT ratio, outerplane, innerplane;
+  float cpu;
+  int size, id, nummerged, numvertices, numcoplanars= 0, nonsimplicial=0;
+  int goodused;
+  facetT *facet;
+  const char *s;
+  int numdel= zzval_(Zdelvertextot);
+  int numtricoplanars= 0;
+
+  size= qh->num_points + qh_setsize(qh, qh->other_points);
+  numvertices= qh->num_vertices - qh_setsize(qh, qh->del_vertices);
+  id= qh_pointid(qh, qh->GOODpointp);
+  FORALLfacets {
+    if (facet->coplanarset)
+      numcoplanars += qh_setsize(qh, facet->coplanarset);
+    if (facet->good) {
+      if (facet->simplicial) {
+        if (facet->keepcentrum && facet->tricoplanar)
+          numtricoplanars++;
+      }else if (qh_setsize(qh, facet->vertices) != qh->hull_dim)
+        nonsimplicial++;
+    }
+  }
+  if (id >=0 && qh->STOPcone-1 != id && -qh->STOPpoint-1 != id)
+    size--;
+  if (qh->STOPcone || qh->STOPpoint)
+      qh_fprintf(qh, fp, 9288, "\nAt a premature exit due to 'TVn', 'TCn', 'TRn', or precision error with 'QJn'.");
+  if (qh->UPPERdelaunay)
+    goodused= qh->GOODvertex + qh->GOODpoint + qh->SPLITthresholds;
+  else if (qh->DELAUNAY)
+    goodused= qh->GOODvertex + qh->GOODpoint + qh->GOODthreshold;
+  else
+    goodused= qh->num_good;
+  nummerged= zzval_(Ztotmerge) - zzval_(Zcyclehorizon) + zzval_(Zcyclefacettot);
+  if (qh->VORONOI) {
+    if (qh->UPPERdelaunay)
+      qh_fprintf(qh, fp, 9289, "\n\
+Furthest-site Voronoi vertices by the convex hull of %d points in %d-d:\n\n", size, qh->hull_dim);
+    else
+      qh_fprintf(qh, fp, 9290, "\n\
+Voronoi diagram by the convex hull of %d points in %d-d:\n\n", size, qh->hull_dim);
+    qh_fprintf(qh, fp, 9291, "  Number of Voronoi regions%s: %d\n",
+              qh->ATinfinity ? " and at-infinity" : "", numvertices);
+    if (numdel)
+      qh_fprintf(qh, fp, 9292, "  Total number of deleted points due to merging: %d\n", numdel);
+    if (numcoplanars - numdel > 0)
+      qh_fprintf(qh, fp, 9293, "  Number of nearly incident points: %d\n", numcoplanars - numdel);
+    else if (size - numvertices - numdel > 0)
+      qh_fprintf(qh, fp, 9294, "  Total number of nearly incident points: %d\n", size - numvertices - numdel);
+    qh_fprintf(qh, fp, 9295, "  Number of%s Voronoi vertices: %d\n",
+              goodused ? " 'good'" : "", qh->num_good);
+    if (nonsimplicial)
+      qh_fprintf(qh, fp, 9296, "  Number of%s non-simplicial Voronoi vertices: %d\n",
+              goodused ? " 'good'" : "", nonsimplicial);
+  }else if (qh->DELAUNAY) {
+    if (qh->UPPERdelaunay)
+      qh_fprintf(qh, fp, 9297, "\n\
+Furthest-site Delaunay triangulation by the convex hull of %d points in %d-d:\n\n", size, qh->hull_dim);
+    else
+      qh_fprintf(qh, fp, 9298, "\n\
+Delaunay triangulation by the convex hull of %d points in %d-d:\n\n", size, qh->hull_dim);
+    qh_fprintf(qh, fp, 9299, "  Number of input sites%s: %d\n",
+              qh->ATinfinity ? " and at-infinity" : "", numvertices);
+    if (numdel)
+      qh_fprintf(qh, fp, 9300, "  Total number of deleted points due to merging: %d\n", numdel);
+    if (numcoplanars - numdel > 0)
+      qh_fprintf(qh, fp, 9301, "  Number of nearly incident points: %d\n", numcoplanars - numdel);
+    else if (size - numvertices - numdel > 0)
+      qh_fprintf(qh, fp, 9302, "  Total number of nearly incident points: %d\n", size - numvertices - numdel);
+    qh_fprintf(qh, fp, 9303, "  Number of%s Delaunay regions: %d\n",
+              goodused ? " 'good'" : "", qh->num_good);
+    if (nonsimplicial)
+      qh_fprintf(qh, fp, 9304, "  Number of%s non-simplicial Delaunay regions: %d\n",
+              goodused ? " 'good'" : "", nonsimplicial);
+  }else if (qh->HALFspace) {
+    qh_fprintf(qh, fp, 9305, "\n\
+Halfspace intersection by the convex hull of %d points in %d-d:\n\n", size, qh->hull_dim);
+    qh_fprintf(qh, fp, 9306, "  Number of halfspaces: %d\n", size);
+    qh_fprintf(qh, fp, 9307, "  Number of non-redundant halfspaces: %d\n", numvertices);
+    if (numcoplanars) {
+      if (qh->KEEPinside && qh->KEEPcoplanar)
+        s= "similar and redundant";
+      else if (qh->KEEPinside)
+        s= "redundant";
+      else
+        s= "similar";
+      qh_fprintf(qh, fp, 9308, "  Number of %s halfspaces: %d\n", s, numcoplanars);
+    }
+    qh_fprintf(qh, fp, 9309, "  Number of intersection points: %d\n", qh->num_facets - qh->num_visible);
+    if (goodused)
+      qh_fprintf(qh, fp, 9310, "  Number of 'good' intersection points: %d\n", qh->num_good);
+    if (nonsimplicial)
+      qh_fprintf(qh, fp, 9311, "  Number of%s non-simplicial intersection points: %d\n",
+              goodused ? " 'good'" : "", nonsimplicial);
+  }else {
+    qh_fprintf(qh, fp, 9312, "\n\
+Convex hull of %d points in %d-d:\n\n", size, qh->hull_dim);
+    qh_fprintf(qh, fp, 9313, "  Number of vertices: %d\n", numvertices);
+    if (numcoplanars) {
+      if (qh->KEEPinside && qh->KEEPcoplanar)
+        s= "coplanar and interior";
+      else if (qh->KEEPinside)
+        s= "interior";
+      else
+        s= "coplanar";
+      qh_fprintf(qh, fp, 9314, "  Number of %s points: %d\n", s, numcoplanars);
+    }
+    qh_fprintf(qh, fp, 9315, "  Number of facets: %d\n", qh->num_facets - qh->num_visible);
+    if (goodused)
+      qh_fprintf(qh, fp, 9316, "  Number of 'good' facets: %d\n", qh->num_good);
+    if (nonsimplicial)
+      qh_fprintf(qh, fp, 9317, "  Number of%s non-simplicial facets: %d\n",
+              goodused ? " 'good'" : "", nonsimplicial);
+  }
+  if (numtricoplanars)
+      qh_fprintf(qh, fp, 9318, "  Number of triangulated facets: %d\n", numtricoplanars);
+  qh_fprintf(qh, fp, 9319, "\nStatistics for: %s | %s",
+                      qh->rbox_command, qh->qhull_command);
+  if (qh->ROTATErandom != INT_MIN)
+    qh_fprintf(qh, fp, 9320, " QR%d\n\n", qh->ROTATErandom);
+  else
+    qh_fprintf(qh, fp, 9321, "\n\n");
+  qh_fprintf(qh, fp, 9322, "  Number of points processed: %d\n", zzval_(Zprocessed));
+  qh_fprintf(qh, fp, 9323, "  Number of hyperplanes created: %d\n", zzval_(Zsetplane));
+  if (qh->DELAUNAY)
+    qh_fprintf(qh, fp, 9324, "  Number of facets in hull: %d\n", qh->num_facets - qh->num_visible);
+  qh_fprintf(qh, fp, 9325, "  Number of distance tests for qhull: %d\n", zzval_(Zpartition)+
+      zzval_(Zpartitionall)+zzval_(Znumvisibility)+zzval_(Zpartcoplanar));
+#if 0  /* NOTE: must print before printstatistics() */
+  {realT stddev, ave;
+  qh_fprintf(qh, fp, 9326, "  average new facet balance: %2.2g\n",
+          wval_(Wnewbalance)/zval_(Zprocessed));
+  stddev= qh_stddev(zval_(Zprocessed), wval_(Wnewbalance),
+                                 wval_(Wnewbalance2), &ave);
+  qh_fprintf(qh, fp, 9327, "  new facet standard deviation: %2.2g\n", stddev);
+  qh_fprintf(qh, fp, 9328, "  average partition balance: %2.2g\n",
+          wval_(Wpbalance)/zval_(Zpbalance));
+  stddev= qh_stddev(zval_(Zpbalance), wval_(Wpbalance),
+                                 wval_(Wpbalance2), &ave);
+  qh_fprintf(qh, fp, 9329, "  partition standard deviation: %2.2g\n", stddev);
+  }
+#endif
+  if (nummerged) {
+    qh_fprintf(qh, fp, 9330,"  Number of distance tests for merging: %d\n",zzval_(Zbestdist)+
+          zzval_(Zcentrumtests)+zzval_(Zdistconvex)+zzval_(Zdistcheck)+
+          zzval_(Zdistzero));
+    qh_fprintf(qh, fp, 9331,"  Number of distance tests for checking: %d\n",zzval_(Zcheckpart));
+    qh_fprintf(qh, fp, 9332,"  Number of merged facets: %d\n", nummerged);
+  }
+  if (!qh->RANDOMoutside && qh->QHULLfinished) {
+    cpu= (float)qh->hulltime;
+    cpu /= (float)qh_SECticks;
+    wval_(Wcpu)= cpu;
+    qh_fprintf(qh, fp, 9333, "  CPU seconds to compute hull (after input): %2.4g\n", cpu);
+  }
+  if (qh->RERUN) {
+    if (!qh->PREmerge && !qh->MERGEexact)
+      qh_fprintf(qh, fp, 9334, "  Percentage of runs with precision errors: %4.1f\n",
+           zzval_(Zretry)*100.0/qh->build_cnt);  /* careful of order */
+  }else if (qh->JOGGLEmax < REALmax/2) {
+    if (zzval_(Zretry))
+      qh_fprintf(qh, fp, 9335, "  After %d retries, input joggled by: %2.2g\n",
+         zzval_(Zretry), qh->JOGGLEmax);
+    else
+      qh_fprintf(qh, fp, 9336, "  Input joggled by: %2.2g\n", qh->JOGGLEmax);
+  }
+  if (qh->totarea != 0.0)
+    qh_fprintf(qh, fp, 9337, "  %s facet area:   %2.8g\n",
+            zzval_(Ztotmerge) ? "Approximate" : "Total", qh->totarea);
+  if (qh->totvol != 0.0)
+    qh_fprintf(qh, fp, 9338, "  %s volume:       %2.8g\n",
+            zzval_(Ztotmerge) ? "Approximate" : "Total", qh->totvol);
+  if (qh->MERGING) {
+    qh_outerinner(qh, NULL, &outerplane, &innerplane);
+    if (outerplane > 2 * qh->DISTround) {
+      qh_fprintf(qh, fp, 9339, "  Maximum distance of %spoint above facet: %2.2g",
+            (qh->QHULLfinished ? "" : "merged "), outerplane);
+      ratio= outerplane/(qh->ONEmerge + qh->DISTround);
+      /* don't report ratio if MINoutside is large */
+      if (ratio > 0.05 && 2* qh->ONEmerge > qh->MINoutside && qh->JOGGLEmax > REALmax/2)
+        qh_fprintf(qh, fp, 9340, " (%.1fx)\n", ratio);
+      else
+        qh_fprintf(qh, fp, 9341, "\n");
+    }
+    if (innerplane < -2 * qh->DISTround) {
+      qh_fprintf(qh, fp, 9342, "  Maximum distance of %svertex below facet: %2.2g",
+            (qh->QHULLfinished ? "" : "merged "), innerplane);
+      ratio= -innerplane/(qh->ONEmerge+qh->DISTround);
+      if (ratio > 0.05 && qh->JOGGLEmax > REALmax/2)
+        qh_fprintf(qh, fp, 9343, " (%.1fx)\n", ratio);
+      else
+        qh_fprintf(qh, fp, 9344, "\n");
+    }
+  }
+  qh_fprintf(qh, fp, 9345, "\n");
+} /* printsummary */
+
+
diff --git a/xs/src/qhull/src/libqhull_r/libqhull_r.h b/xs/src/qhull/src/libqhull_r/libqhull_r.h
new file mode 100644
index 0000000000..363e6da6a7
--- /dev/null
+++ b/xs/src/qhull/src/libqhull_r/libqhull_r.h
@@ -0,0 +1,1134 @@
+/*<html><pre>  -<a                             href="qh-qhull_r.htm"
+  >-------------------------------</a><a name="TOP">-</a>
+
+   libqhull_r.h
+   user-level header file for using qhull.a library
+
+   see qh-qhull_r.htm, qhull_ra.h
+
+   Copyright (c) 1993-2015 The Geometry Center.
+   $Id: //main/2015/qhull/src/libqhull_r/libqhull_r.h#8 $$Change: 2079 $
+   $DateTime: 2016/02/07 17:43:34 $$Author: bbarber $
+
+   includes function prototypes for libqhull_r.c, geom_r.c, global_r.c, io_r.c, user.c
+
+   use mem_r.h for mem_r.c
+   use qset_r.h for qset_r.c
+
+   see unix_r.c for an example of using libqhull_r.h
+
+   recompile qhull if you change this file
+*/
+
+#ifndef qhDEFlibqhull
+#define qhDEFlibqhull 1
+
+/*=========================== -included files ==============*/
+
+/* user_r.h first for QHULL_CRTDBG */
+#include "user_r.h"      /* user definable constants (e.g., realT). */
+
+#include "mem_r.h"   /* Needed for qhT in libqhull_r.h */
+#include "qset_r.h"   /* Needed for QHULL_LIB_CHECK */
+/* include stat_r.h after defining boolT.  statT needed for qhT in libqhull_r.h */
+
+#include <setjmp.h>
+#include <float.h>
+#include <time.h>
+#include <stdio.h>
+
+#ifndef __STDC__
+#ifndef __cplusplus
+#if     !_MSC_VER
+#error  Neither __STDC__ nor __cplusplus is defined.  Please use strict ANSI C or C++ to compile
+#error  Qhull.  You may need to turn off compiler extensions in your project configuration.  If
+#error  your compiler is a standard C compiler, you can delete this warning from libqhull_r.h
+#endif
+#endif
+#endif
+
+/*============ constants and basic types ====================*/
+
+extern const char qh_version[]; /* defined in global_r.c */
+extern const char qh_version2[]; /* defined in global_r.c */
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >--------------------------------</a><a name="coordT">-</a>
+
+  coordT
+    coordinates and coefficients are stored as realT (i.e., double)
+
+  notes:
+    Qhull works well if realT is 'float'.  If so joggle (QJ) is not effective.
+
+    Could use 'float' for data and 'double' for calculations (realT vs. coordT)
+      This requires many type casts, and adjusted error bounds.
+      Also C compilers may do expressions in double anyway.
+*/
+#define coordT realT
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >--------------------------------</a><a name="pointT">-</a>
+
+  pointT
+    a point is an array of coordinates, usually qh.hull_dim
+    qh_pointid returns
+      qh_IDnone if point==0 or qh is undefined
+      qh_IDinterior for qh.interior_point
+      qh_IDunknown if point is neither in qh.first_point... nor qh.other_points
+
+  notes:
+    qh.STOPcone and qh.STOPpoint assume that qh_IDunknown==-1 (other negative numbers indicate points)
+    qh_IDunknown is also returned by getid_() for unknown facet, ridge, or vertex
+*/
+#define pointT coordT
+typedef enum
+{
+    qh_IDnone = -3, qh_IDinterior = -2, qh_IDunknown = -1
+}
+qh_pointT;
+
+/*-<a                             href="qh-qhull_r.htm#TOC"
+  >--------------------------------</a><a name="flagT">-</a>
+
+  flagT
+    Boolean flag as a bit
+*/
+#define flagT unsigned int
+
+/*-<a                             href="qh-qhull_r.htm#TOC"
+  >--------------------------------</a><a name="boolT">-</a>
+
+  boolT
+    boolean value, either True or False
+
+  notes:
+    needed for portability
+    Use qh_False/qh_True as synonyms
+*/
+#define boolT unsigned int
+#ifdef False
+#undef False
+#endif
+#ifdef True
+#undef True
+#endif
+#define False 0
+#define True 1
+#define qh_False 0
+#define qh_True 1
+
+#include "stat_r.h"  /* needs boolT */
+
+/*-<a                             href="qh-qhull_r.htm#TOC"
+  >--------------------------------</a><a name="CENTERtype">-</a>
+
+  qh_CENTER
+    to distinguish facet->center
+*/
+typedef enum
+{
+    qh_ASnone = 0,   /* If not MERGING and not VORONOI */
+    qh_ASvoronoi,    /* Set by qh_clearcenters on qh_prepare_output, or if not MERGING and VORONOI */
+    qh_AScentrum     /* If MERGING (assumed during merging) */
+}
+qh_CENTER;
+
+/*-<a                             href="qh-qhull_r.htm#TOC"
+  >--------------------------------</a><a name="qh_PRINT">-</a>
+
+  qh_PRINT
+    output formats for printing (qh.PRINTout).
+    'Fa' 'FV' 'Fc' 'FC'
+
+
+   notes:
+   some of these names are similar to qhT names.  The similar names are only
+   used in switch statements in qh_printbegin() etc.
+*/
+typedef enum {qh_PRINTnone= 0,
+  qh_PRINTarea, qh_PRINTaverage,           /* 'Fa' 'FV' 'Fc' 'FC' */
+  qh_PRINTcoplanars, qh_PRINTcentrums,
+  qh_PRINTfacets, qh_PRINTfacets_xridge,   /* 'f' 'FF' 'G' 'FI' 'Fi' 'Fn' */
+  qh_PRINTgeom, qh_PRINTids, qh_PRINTinner, qh_PRINTneighbors,
+  qh_PRINTnormals, qh_PRINTouter, qh_PRINTmaple, /* 'n' 'Fo' 'i' 'm' 'Fm' 'FM', 'o' */
+  qh_PRINTincidences, qh_PRINTmathematica, qh_PRINTmerges, qh_PRINToff,
+  qh_PRINToptions, qh_PRINTpointintersect, /* 'FO' 'Fp' 'FP' 'p' 'FQ' 'FS' */
+  qh_PRINTpointnearest, qh_PRINTpoints, qh_PRINTqhull, qh_PRINTsize,
+  qh_PRINTsummary, qh_PRINTtriangles,      /* 'Fs' 'Ft' 'Fv' 'FN' 'Fx' */
+  qh_PRINTvertices, qh_PRINTvneighbors, qh_PRINTextremes,
+  qh_PRINTEND} qh_PRINT;
+
+/*-<a                             href="qh-qhull_r.htm#TOC"
+  >--------------------------------</a><a name="qh_ALL">-</a>
+
+  qh_ALL
+    argument flag for selecting everything
+*/
+#define qh_ALL      True
+#define qh_NOupper  True     /* argument for qh_findbest */
+#define qh_IScheckmax  True     /* argument for qh_findbesthorizon */
+#define qh_ISnewfacets  True     /* argument for qh_findbest */
+#define qh_RESETvisible  True     /* argument for qh_resetlists */
+
+/*-<a                             href="qh-qhull_r.htm#TOC"
+  >--------------------------------</a><a name="qh_ERR">-</a>
+
+  qh_ERR
+    Qhull exit codes, for indicating errors
+    See: MSG_ERROR and MSG_WARNING [user.h]
+*/
+#define qh_ERRnone  0    /* no error occurred during qhull */
+#define qh_ERRinput 1    /* input inconsistency */
+#define qh_ERRsingular 2 /* singular input data */
+#define qh_ERRprec  3    /* precision error */
+#define qh_ERRmem   4    /* insufficient memory, matches mem_r.h */
+#define qh_ERRqhull 5    /* internal error detected, matches mem_r.h */
+
+/*-<a                             href="qh-qhull_r.htm#TOC"
+>--------------------------------</a><a name="qh_FILEstderr">-</a>
+
+qh_FILEstderr
+Fake stderr to distinguish error output from normal output
+For C++ interface.  Must redefine qh_fprintf_qhull
+*/
+#define qh_FILEstderr ((FILE*)1)
+
+/* ============ -structures- ====================
+   each of the following structures is defined by a typedef
+   all realT and coordT fields occur at the beginning of a structure
+        (otherwise space may be wasted due to alignment)
+   define all flags together and pack into 32-bit number
+
+   DEFqhT and DEFsetT are likewise defined in
+   mem_r.h, qset_r.h, and stat_r.h.
+
+*/
+
+typedef struct vertexT vertexT;
+typedef struct ridgeT ridgeT;
+typedef struct facetT facetT;
+
+#ifndef DEFqhT
+#define DEFqhT 1
+typedef struct qhT qhT;          /* defined below */
+#endif
+
+#ifndef DEFsetT
+#define DEFsetT 1
+typedef struct setT setT;          /* defined in qset_r.h */
+#endif
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >--------------------------------</a><a name="facetT">-</a>
+
+  facetT
+    defines a facet
+
+  notes:
+   qhull() generates the hull as a list of facets.
+
+  topological information:
+    f.previous,next     doubly-linked list of facets
+    f.vertices          set of vertices
+    f.ridges            set of ridges
+    f.neighbors         set of neighbors
+    f.toporient         True if facet has top-orientation (else bottom)
+
+  geometric information:
+    f.offset,normal     hyperplane equation
+    f.maxoutside        offset to outer plane -- all points inside
+    f.center            centrum for testing convexity or Voronoi center for output
+    f.simplicial        True if facet is simplicial
+    f.flipped           True if facet does not include qh.interior_point
+
+  for constructing hull:
+    f.visible           True if facet on list of visible facets (will be deleted)
+    f.newfacet          True if facet on list of newly created facets
+    f.coplanarset       set of points coplanar with this facet
+                        (includes near-inside points for later testing)
+    f.outsideset        set of points outside of this facet
+    f.furthestdist      distance to furthest point of outside set
+    f.visitid           marks visited facets during a loop
+    f.replace           replacement facet for to-be-deleted, visible facets
+    f.samecycle,newcycle cycle of facets for merging into horizon facet
+
+  see below for other flags and fields
+*/
+struct facetT {
+#if !qh_COMPUTEfurthest
+  coordT   furthestdist;/* distance to furthest point of outsideset */
+#endif
+#if qh_MAXoutside
+  coordT   maxoutside;  /* max computed distance of point to facet
+                        Before QHULLfinished this is an approximation
+                        since maxdist not always set for mergefacet
+                        Actual outer plane is +DISTround and
+                        computed outer plane is +2*DISTround */
+#endif
+  coordT   offset;      /* exact offset of hyperplane from origin */
+  coordT  *normal;      /* normal of hyperplane, hull_dim coefficients */
+                        /*   if ->tricoplanar, shared with a neighbor */
+  union {               /* in order of testing */
+   realT   area;        /* area of facet, only in io_r.c if  ->isarea */
+   facetT *replace;     /*  replacement facet if ->visible and NEWfacets
+                             is NULL only if qh_mergedegen_redundant or interior */
+   facetT *samecycle;   /*  cycle of facets from the same visible/horizon intersection,
+                             if ->newfacet */
+   facetT *newcycle;    /*  in horizon facet, current samecycle of new facets */
+   facetT *trivisible;  /* visible facet for ->tricoplanar facets during qh_triangulate() */
+   facetT *triowner;    /* owner facet for ->tricoplanar, !isarea facets w/ ->keepcentrum */
+  }f;
+  coordT  *center;      /* set according to qh.CENTERtype */
+                        /*   qh_ASnone:    no center (not MERGING) */
+                        /*   qh_AScentrum: centrum for testing convexity (qh_getcentrum) */
+                        /*                 assumed qh_AScentrum while merging */
+                        /*   qh_ASvoronoi: Voronoi center (qh_facetcenter) */
+                        /* after constructing the hull, it may be changed (qh_clearcenter) */
+                        /* if tricoplanar and !keepcentrum, shared with a neighbor */
+  facetT  *previous;    /* previous facet in the facet_list */
+  facetT  *next;        /* next facet in the facet_list */
+  setT    *vertices;    /* vertices for this facet, inverse sorted by ID
+                           if simplicial, 1st vertex was apex/furthest */
+  setT    *ridges;      /* explicit ridges for nonsimplicial facets.
+                           for simplicial facets, neighbors define the ridges */
+  setT    *neighbors;   /* neighbors of the facet.  If simplicial, the kth
+                           neighbor is opposite the kth vertex, and the first
+                           neighbor is the horizon facet for the first vertex*/
+  setT    *outsideset;  /* set of points outside this facet
+                           if non-empty, last point is furthest
+                           if NARROWhull, includes coplanars for partitioning*/
+  setT    *coplanarset; /* set of points coplanar with this facet
+                           > qh.min_vertex and <= facet->max_outside
+                           a point is assigned to the furthest facet
+                           if non-empty, last point is furthest away */
+  unsigned visitid;     /* visit_id, for visiting all neighbors,
+                           all uses are independent */
+  unsigned id;          /* unique identifier from qh.facet_id */
+  unsigned nummerge:9;  /* number of merges */
+#define qh_MAXnummerge 511 /*     2^9-1, 32 flags total, see "flags:" in io_r.c */
+  flagT    tricoplanar:1; /* True if TRIangulate and simplicial and coplanar with a neighbor */
+                          /*   all tricoplanars share the same apex */
+                          /*   all tricoplanars share the same ->center, ->normal, ->offset, ->maxoutside */
+                          /*     ->keepcentrum is true for the owner.  It has the ->coplanareset */
+                          /*   if ->degenerate, does not span facet (one logical ridge) */
+                          /*   during qh_triangulate, f.trivisible points to original facet */
+  flagT    newfacet:1;  /* True if facet on qh.newfacet_list (new or merged) */
+  flagT    visible:1;   /* True if visible facet (will be deleted) */
+  flagT    toporient:1; /* True if created with top orientation
+                           after merging, use ridge orientation */
+  flagT    simplicial:1;/* True if simplicial facet, ->ridges may be implicit */
+  flagT    seen:1;      /* used to perform operations only once, like visitid */
+  flagT    seen2:1;     /* used to perform operations only once, like visitid */
+  flagT    flipped:1;   /* True if facet is flipped */
+  flagT    upperdelaunay:1; /* True if facet is upper envelope of Delaunay triangulation */
+  flagT    notfurthest:1; /* True if last point of outsideset is not furthest*/
+
+/*-------- flags primarily for output ---------*/
+  flagT    good:1;      /* True if a facet marked good for output */
+  flagT    isarea:1;    /* True if facet->f.area is defined */
+
+/*-------- flags for merging ------------------*/
+  flagT    dupridge:1;  /* True if duplicate ridge in facet */
+  flagT    mergeridge:1; /* True if facet or neighbor contains a qh_MERGEridge
+                            ->normal defined (also defined for mergeridge2) */
+  flagT    mergeridge2:1; /* True if neighbor contains a qh_MERGEridge (qhT *qh, mark_dupridges */
+  flagT    coplanar:1;  /* True if horizon facet is coplanar at last use */
+  flagT     mergehorizon:1; /* True if will merge into horizon (->coplanar) */
+  flagT     cycledone:1;/* True if mergecycle_all already done */
+  flagT    tested:1;    /* True if facet convexity has been tested (false after merge */
+  flagT    keepcentrum:1; /* True if keep old centrum after a merge, or marks owner for ->tricoplanar */
+  flagT    newmerge:1;  /* True if facet is newly merged for reducevertices */
+  flagT    degenerate:1; /* True if facet is degenerate (degen_mergeset or ->tricoplanar) */
+  flagT    redundant:1;  /* True if facet is redundant (degen_mergeset) */
+};
+
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >--------------------------------</a><a name="ridgeT">-</a>
+
+  ridgeT
+    defines a ridge
+
+  notes:
+  a ridge is hull_dim-1 simplex between two neighboring facets.  If the
+  facets are non-simplicial, there may be more than one ridge between
+  two facets.  E.G. a 4-d hypercube has two triangles between each pair
+  of neighboring facets.
+
+  topological information:
+    vertices            a set of vertices
+    top,bottom          neighboring facets with orientation
+
+  geometric information:
+    tested              True if ridge is clearly convex
+    nonconvex           True if ridge is non-convex
+*/
+struct ridgeT {
+  setT    *vertices;    /* vertices belonging to this ridge, inverse sorted by ID
+                           NULL if a degen ridge (matchsame) */
+  facetT  *top;         /* top facet this ridge is part of */
+  facetT  *bottom;      /* bottom facet this ridge is part of */
+  unsigned id;          /* unique identifier.  Same size as vertex_id and ridge_id */
+  flagT    seen:1;      /* used to perform operations only once */
+  flagT    tested:1;    /* True when ridge is tested for convexity */
+  flagT    nonconvex:1; /* True if getmergeset detected a non-convex neighbor
+                           only one ridge between neighbors may have nonconvex */
+};
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >--------------------------------</a><a name="vertexT">-</a>
+
+  vertexT
+     defines a vertex
+
+  topological information:
+    next,previous       doubly-linked list of all vertices
+    neighbors           set of adjacent facets (only if qh.VERTEXneighbors)
+
+  geometric information:
+    point               array of DIM3 coordinates
+*/
+struct vertexT {
+  vertexT *next;        /* next vertex in vertex_list */
+  vertexT *previous;    /* previous vertex in vertex_list */
+  pointT  *point;       /* hull_dim coordinates (coordT) */
+  setT    *neighbors;   /* neighboring facets of vertex, qh_vertexneighbors()
+                           inits in io_r.c or after first merge */
+  unsigned id;          /* unique identifier.  Same size as qh.vertex_id and qh.ridge_id */
+  unsigned visitid;    /* for use with qh.vertex_visit, size must match */
+  flagT    seen:1;      /* used to perform operations only once */
+  flagT    seen2:1;     /* another seen flag */
+  flagT    delridge:1;  /* vertex was part of a deleted ridge */
+  flagT    deleted:1;   /* true if vertex on qh.del_vertices */
+  flagT    newlist:1;   /* true if vertex on qh.newvertex_list */
+};
+
+/*======= -global variables -qh ============================*/
+
+/*-<a                             href="qh-globa_r.htm#TOC"
+  >--------------------------------</a><a name="qh">-</a>
+
+  qhT
+   All global variables for qhull are in qhT.  It includes qhmemT, qhstatT, and rbox globals
+
+   This version of Qhull is reentrant, but it is not thread-safe.
+
+   Do not run separate threads on the same instance of qhT.
+
+   QHULL_LIB_CHECK checks that a program and the corresponding
+   qhull library were built with the same type of header files.
+*/
+
+#define QHULL_NON_REENTRANT 0
+#define QHULL_QH_POINTER 1
+#define QHULL_REENTRANT 2
+
+#define QHULL_LIB_TYPE QHULL_REENTRANT
+
+#define QHULL_LIB_CHECK qh_lib_check(QHULL_LIB_TYPE, sizeof(qhT), sizeof(vertexT), sizeof(ridgeT), sizeof(facetT), sizeof(setT), sizeof(qhmemT));
+#define QHULL_LIB_CHECK_RBOX qh_lib_check(QHULL_LIB_TYPE, sizeof(qhT), sizeof(vertexT), sizeof(ridgeT), sizeof(facetT), 0, 0);
+
+struct qhT {
+
+/*-<a                             href="qh-globa_r.htm#TOC"
+  >--------------------------------</a><a name="qh-const">-</a>
+
+  qh constants
+    configuration flags and constants for Qhull
+
+  notes:
+    The user configures Qhull by defining flags.  They are
+    copied into qh by qh_setflags().  qh-quick_r.htm#options defines the flags.
+*/
+  boolT ALLpoints;        /* true 'Qs' if search all points for initial simplex */
+  boolT ANGLEmerge;       /* true 'Qa' if sort potential merges by angle */
+  boolT APPROXhull;       /* true 'Wn' if MINoutside set */
+  realT   MINoutside;     /*   'Wn' min. distance for an outside point */
+  boolT ANNOTATEoutput;   /* true 'Ta' if annotate output with message codes */
+  boolT ATinfinity;       /* true 'Qz' if point num_points-1 is "at-infinity"
+                             for improving precision in Delaunay triangulations */
+  boolT AVOIDold;         /* true 'Q4' if avoid old->new merges */
+  boolT BESToutside;      /* true 'Qf' if partition points into best outsideset */
+  boolT CDDinput;         /* true 'Pc' if input uses CDD format (1.0/offset first) */
+  boolT CDDoutput;        /* true 'PC' if print normals in CDD format (offset first) */
+  boolT CHECKfrequently;  /* true 'Tc' if checking frequently */
+  realT premerge_cos;     /*   'A-n'   cos_max when pre merging */
+  realT postmerge_cos;    /*   'An'    cos_max when post merging */
+  boolT DELAUNAY;         /* true 'd' if computing DELAUNAY triangulation */
+  boolT DOintersections;  /* true 'Gh' if print hyperplane intersections */
+  int   DROPdim;          /* drops dim 'GDn' for 4-d -> 3-d output */
+  boolT FORCEoutput;      /* true 'Po' if forcing output despite degeneracies */
+  int   GOODpoint;        /* 1+n for 'QGn', good facet if visible/not(-) from point n*/
+  pointT *GOODpointp;     /*   the actual point */
+  boolT GOODthreshold;    /* true if qh.lower_threshold/upper_threshold defined
+                             false if qh.SPLITthreshold */
+  int   GOODvertex;       /* 1+n, good facet if vertex for point n */
+  pointT *GOODvertexp;     /*   the actual point */
+  boolT HALFspace;        /* true 'Hn,n,n' if halfspace intersection */
+  boolT ISqhullQh;        /* Set by Qhull.cpp on initialization */
+  int   IStracing;        /* trace execution, 0=none, 1=least, 4=most, -1=events */
+  int   KEEParea;         /* 'PAn' number of largest facets to keep */
+  boolT KEEPcoplanar;     /* true 'Qc' if keeping nearest facet for coplanar points */
+  boolT KEEPinside;       /* true 'Qi' if keeping nearest facet for inside points
+                              set automatically if 'd Qc' */
+  int   KEEPmerge;        /* 'PMn' number of facets to keep with most merges */
+  realT KEEPminArea;      /* 'PFn' minimum facet area to keep */
+  realT MAXcoplanar;      /* 'Un' max distance below a facet to be coplanar*/
+  boolT MERGEexact;       /* true 'Qx' if exact merges (coplanar, degen, dupridge, flipped) */
+  boolT MERGEindependent; /* true 'Q2' if merging independent sets */
+  boolT MERGING;          /* true if exact-, pre- or post-merging, with angle and centrum tests */
+  realT   premerge_centrum;  /*   'C-n' centrum_radius when pre merging.  Default is round-off */
+  realT   postmerge_centrum; /*   'Cn' centrum_radius when post merging.  Default is round-off */
+  boolT MERGEvertices;    /* true 'Q3' if merging redundant vertices */
+  realT MINvisible;       /* 'Vn' min. distance for a facet to be visible */
+  boolT NOnarrow;         /* true 'Q10' if no special processing for narrow distributions */
+  boolT NOnearinside;     /* true 'Q8' if ignore near-inside points when partitioning */
+  boolT NOpremerge;       /* true 'Q0' if no defaults for C-0 or Qx */
+  boolT NOwide;           /* true 'Q12' if no error on wide merge due to duplicate ridge */
+  boolT ONLYgood;         /* true 'Qg' if process points with good visible or horizon facets */
+  boolT ONLYmax;          /* true 'Qm' if only process points that increase max_outside */
+  boolT PICKfurthest;     /* true 'Q9' if process furthest of furthest points*/
+  boolT POSTmerge;        /* true if merging after buildhull (Cn or An) */
+  boolT PREmerge;         /* true if merging during buildhull (C-n or A-n) */
+                        /* NOTE: some of these names are similar to qh_PRINT names */
+  boolT PRINTcentrums;    /* true 'Gc' if printing centrums */
+  boolT PRINTcoplanar;    /* true 'Gp' if printing coplanar points */
+  int   PRINTdim;         /* print dimension for Geomview output */
+  boolT PRINTdots;        /* true 'Ga' if printing all points as dots */
+  boolT PRINTgood;        /* true 'Pg' if printing good facets */
+  boolT PRINTinner;       /* true 'Gi' if printing inner planes */
+  boolT PRINTneighbors;   /* true 'PG' if printing neighbors of good facets */
+  boolT PRINTnoplanes;    /* true 'Gn' if printing no planes */
+  boolT PRINToptions1st;  /* true 'FO' if printing options to stderr */
+  boolT PRINTouter;       /* true 'Go' if printing outer planes */
+  boolT PRINTprecision;   /* false 'Pp' if not reporting precision problems */
+  qh_PRINT PRINTout[qh_PRINTEND]; /* list of output formats to print */
+  boolT PRINTridges;      /* true 'Gr' if print ridges */
+  boolT PRINTspheres;     /* true 'Gv' if print vertices as spheres */
+  boolT PRINTstatistics;  /* true 'Ts' if printing statistics to stderr */
+  boolT PRINTsummary;     /* true 's' if printing summary to stderr */
+  boolT PRINTtransparent; /* true 'Gt' if print transparent outer ridges */
+  boolT PROJECTdelaunay;  /* true if DELAUNAY, no readpoints() and
+                             need projectinput() for Delaunay in qh_init_B */
+  int   PROJECTinput;     /* number of projected dimensions 'bn:0Bn:0' */
+  boolT QUICKhelp;        /* true if quick help message for degen input */
+  boolT RANDOMdist;       /* true if randomly change distplane and setfacetplane */
+  realT RANDOMfactor;     /*    maximum random perturbation */
+  realT RANDOMa;          /*    qh_randomfactor is randr * RANDOMa + RANDOMb */
+  realT RANDOMb;
+  boolT RANDOMoutside;    /* true if select a random outside point */
+  int   REPORTfreq;       /* buildtracing reports every n facets */
+  int   REPORTfreq2;      /* tracemerging reports every REPORTfreq/2 facets */
+  int   RERUN;            /* 'TRn' rerun qhull n times (qh.build_cnt) */
+  int   ROTATErandom;     /* 'QRn' seed, 0 time, >= rotate input */
+  boolT SCALEinput;       /* true 'Qbk' if scaling input */
+  boolT SCALElast;        /* true 'Qbb' if scale last coord to max prev coord */
+  boolT SETroundoff;      /* true 'E' if qh.DISTround is predefined */
+  boolT SKIPcheckmax;     /* true 'Q5' if skip qh_check_maxout */
+  boolT SKIPconvex;       /* true 'Q6' if skip convexity testing during pre-merge */
+  boolT SPLITthresholds;  /* true if upper_/lower_threshold defines a region
+                               used only for printing (!for qh.ONLYgood) */
+  int   STOPcone;         /* 'TCn' 1+n for stopping after cone for point n */
+                          /*       also used by qh_build_withresart for err exit*/
+  int   STOPpoint;        /* 'TVn' 'TV-n' 1+n for stopping after/before(-)
+                                        adding point n */
+  int   TESTpoints;       /* 'QTn' num of test points after qh.num_points.  Test points always coplanar. */
+  boolT TESTvneighbors;   /*  true 'Qv' if test vertex neighbors at end */
+  int   TRACElevel;       /* 'Tn' conditional IStracing level */
+  int   TRACElastrun;     /*  qh.TRACElevel applies to last qh.RERUN */
+  int   TRACEpoint;       /* 'TPn' start tracing when point n is a vertex */
+  realT TRACEdist;        /* 'TWn' start tracing when merge distance too big */
+  int   TRACEmerge;       /* 'TMn' start tracing before this merge */
+  boolT TRIangulate;      /* true 'Qt' if triangulate non-simplicial facets */
+  boolT TRInormals;       /* true 'Q11' if triangulate duplicates ->normal and ->center (sets Qt) */
+  boolT UPPERdelaunay;    /* true 'Qu' if computing furthest-site Delaunay */
+  boolT USEstdout;        /* true 'Tz' if using stdout instead of stderr */
+  boolT VERIFYoutput;     /* true 'Tv' if verify output at end of qhull */
+  boolT VIRTUALmemory;    /* true 'Q7' if depth-first processing in buildhull */
+  boolT VORONOI;          /* true 'v' if computing Voronoi diagram */
+
+  /*--------input constants ---------*/
+  realT AREAfactor;       /* 1/(hull_dim-1)! for converting det's to area */
+  boolT DOcheckmax;       /* true if calling qh_check_maxout (qhT *qh, qh_initqhull_globals) */
+  char  *feasible_string;  /* feasible point 'Hn,n,n' for halfspace intersection */
+  coordT *feasible_point;  /*    as coordinates, both malloc'd */
+  boolT GETarea;          /* true 'Fa', 'FA', 'FS', 'PAn', 'PFn' if compute facet area/Voronoi volume in io_r.c */
+  boolT KEEPnearinside;   /* true if near-inside points in coplanarset */
+  int   hull_dim;         /* dimension of hull, set by initbuffers */
+  int   input_dim;        /* dimension of input, set by initbuffers */
+  int   num_points;       /* number of input points */
+  pointT *first_point;    /* array of input points, see POINTSmalloc */
+  boolT POINTSmalloc;     /*   true if qh.first_point/num_points allocated */
+  pointT *input_points;   /* copy of original qh.first_point for input points for qh_joggleinput */
+  boolT input_malloc;     /* true if qh.input_points malloc'd */
+  char  qhull_command[256];/* command line that invoked this program */
+  int   qhull_commandsiz2; /*    size of qhull_command at qh_clear_outputflags */
+  char  rbox_command[256]; /* command line that produced the input points */
+  char  qhull_options[512];/* descriptive list of options */
+  int   qhull_optionlen;  /*    length of last line */
+  int   qhull_optionsiz;  /*    size of qhull_options at qh_build_withrestart */
+  int   qhull_optionsiz2; /*    size of qhull_options at qh_clear_outputflags */
+  int   run_id;           /* non-zero, random identifier for this instance of qhull */
+  boolT VERTEXneighbors;  /* true if maintaining vertex neighbors */
+  boolT ZEROcentrum;      /* true if 'C-0' or 'C-0 Qx'.  sets ZEROall_ok */
+  realT *upper_threshold; /* don't print if facet->normal[k]>=upper_threshold[k]
+                             must set either GOODthreshold or SPLITthreshold
+                             if Delaunay, default is 0.0 for upper envelope */
+  realT *lower_threshold; /* don't print if facet->normal[k] <=lower_threshold[k] */
+  realT *upper_bound;     /* scale point[k] to new upper bound */
+  realT *lower_bound;     /* scale point[k] to new lower bound
+                             project if both upper_ and lower_bound == 0 */
+
+/*-<a                             href="qh-globa_r.htm#TOC"
+  >--------------------------------</a><a name="qh-prec">-</a>
+
+  qh precision constants
+    precision constants for Qhull
+
+  notes:
+    qh_detroundoff(qh) computes the maximum roundoff error for distance
+    and other computations.  It also sets default values for the
+    qh constants above.
+*/
+  realT ANGLEround;       /* max round off error for angles */
+  realT centrum_radius;   /* max centrum radius for convexity (roundoff added) */
+  realT cos_max;          /* max cosine for convexity (roundoff added) */
+  realT DISTround;        /* max round off error for distances, 'E' overrides qh_distround() */
+  realT MAXabs_coord;     /* max absolute coordinate */
+  realT MAXlastcoord;     /* max last coordinate for qh_scalelast */
+  realT MAXsumcoord;      /* max sum of coordinates */
+  realT MAXwidth;         /* max rectilinear width of point coordinates */
+  realT MINdenom_1;       /* min. abs. value for 1/x */
+  realT MINdenom;         /*    use divzero if denominator < MINdenom */
+  realT MINdenom_1_2;     /* min. abs. val for 1/x that allows normalization */
+  realT MINdenom_2;       /*    use divzero if denominator < MINdenom_2 */
+  realT MINlastcoord;     /* min. last coordinate for qh_scalelast */
+  boolT NARROWhull;       /* set in qh_initialhull if angle < qh_MAXnarrow */
+  realT *NEARzero;        /* hull_dim array for near zero in gausselim */
+  realT NEARinside;       /* keep points for qh_check_maxout if close to facet */
+  realT ONEmerge;         /* max distance for merging simplicial facets */
+  realT outside_err;      /* application's epsilon for coplanar points
+                             qh_check_bestdist() qh_check_points() reports error if point outside */
+  realT WIDEfacet;        /* size of wide facet for skipping ridge in
+                             area computation and locking centrum */
+
+/*-<a                             href="qh-globa_r.htm#TOC"
+  >--------------------------------</a><a name="qh-codetern">-</a>
+
+  qh internal constants
+    internal constants for Qhull
+*/
+  char qhull[sizeof("qhull")]; /* "qhull" for checking ownership while debugging */
+  jmp_buf errexit;        /* exit label for qh_errexit, defined by setjmp() and NOerrexit */
+  char jmpXtra[40];       /* extra bytes in case jmp_buf is defined wrong by compiler */
+  jmp_buf restartexit;    /* restart label for qh_errexit, defined by setjmp() and ALLOWrestart */
+  char jmpXtra2[40];      /* extra bytes in case jmp_buf is defined wrong by compiler*/
+  FILE *fin;              /* pointer to input file, init by qh_initqhull_start */
+  FILE *fout;             /* pointer to output file */
+  FILE *ferr;             /* pointer to error file */
+  pointT *interior_point; /* center point of the initial simplex*/
+  int normal_size;     /* size in bytes for facet normals and point coords*/
+  int center_size;     /* size in bytes for Voronoi centers */
+  int   TEMPsize;         /* size for small, temporary sets (in quick mem) */
+
+/*-<a                             href="qh-globa_r.htm#TOC"
+  >--------------------------------</a><a name="qh-lists">-</a>
+
+  qh facet and vertex lists
+    defines lists of facets, new facets, visible facets, vertices, and
+    new vertices.  Includes counts, next ids, and trace ids.
+  see:
+    qh_resetlists()
+*/
+  facetT *facet_list;     /* first facet */
+  facetT  *facet_tail;     /* end of facet_list (dummy facet) */
+  facetT *facet_next;     /* next facet for buildhull()
+                             previous facets do not have outside sets
+                             NARROWhull: previous facets may have coplanar outside sets for qh_outcoplanar */
+  facetT *newfacet_list;  /* list of new facets to end of facet_list */
+  facetT *visible_list;   /* list of visible facets preceding newfacet_list,
+                             facet->visible set */
+  int       num_visible;  /* current number of visible facets */
+  unsigned tracefacet_id;  /* set at init, then can print whenever */
+  facetT *tracefacet;     /*   set in newfacet/mergefacet, undone in delfacet*/
+  unsigned tracevertex_id;  /* set at buildtracing, can print whenever */
+  vertexT *tracevertex;     /*   set in newvertex, undone in delvertex*/
+  vertexT *vertex_list;     /* list of all vertices, to vertex_tail */
+  vertexT  *vertex_tail;    /*      end of vertex_list (dummy vertex) */
+  vertexT *newvertex_list; /* list of vertices in newfacet_list, to vertex_tail
+                             all vertices have 'newlist' set */
+  int   num_facets;       /* number of facets in facet_list
+                             includes visible faces (num_visible) */
+  int   num_vertices;     /* number of vertices in facet_list */
+  int   num_outside;      /* number of points in outsidesets (for tracing and RANDOMoutside)
+                               includes coplanar outsideset points for NARROWhull/qh_outcoplanar() */
+  int   num_good;         /* number of good facets (after findgood_all) */
+  unsigned facet_id;      /* ID of next, new facet from newfacet() */
+  unsigned ridge_id;      /* ID of next, new ridge from newridge() */
+  unsigned vertex_id;     /* ID of next, new vertex from newvertex() */
+
+/*-<a                             href="qh-globa_r.htm#TOC"
+  >--------------------------------</a><a name="qh-var">-</a>
+
+  qh global variables
+    defines minimum and maximum distances, next visit ids, several flags,
+    and other global variables.
+    initialize in qh_initbuild or qh_maxmin if used in qh_buildhull
+*/
+  unsigned long hulltime; /* ignore time to set up input and randomize */
+                          /*   use unsigned to avoid wrap-around errors */
+  boolT ALLOWrestart;     /* true if qh_precision can use qh.restartexit */
+  int   build_cnt;        /* number of calls to qh_initbuild */
+  qh_CENTER CENTERtype;   /* current type of facet->center, qh_CENTER */
+  int   furthest_id;      /* pointid of furthest point, for tracing */
+  facetT *GOODclosest;    /* closest facet to GOODthreshold in qh_findgood */
+  boolT hasAreaVolume;    /* true if totarea, totvol was defined by qh_getarea */
+  boolT hasTriangulation; /* true if triangulation created by qh_triangulate */
+  realT JOGGLEmax;        /* set 'QJn' if randomly joggle input */
+  boolT maxoutdone;       /* set qh_check_maxout(), cleared by qh_addpoint() */
+  realT max_outside;      /* maximum distance from a point to a facet,
+                               before roundoff, not simplicial vertices
+                               actual outer plane is +DISTround and
+                               computed outer plane is +2*DISTround */
+  realT max_vertex;       /* maximum distance (>0) from vertex to a facet,
+                               before roundoff, due to a merge */
+  realT min_vertex;       /* minimum distance (<0) from vertex to a facet,
+                               before roundoff, due to a merge
+                               if qh.JOGGLEmax, qh_makenewplanes sets it
+                               recomputed if qh.DOcheckmax, default -qh.DISTround */
+  boolT NEWfacets;        /* true while visible facets invalid due to new or merge
+                              from makecone/attachnewfacets to deletevisible */
+  boolT findbestnew;      /* true if partitioning calls qh_findbestnew */
+  boolT findbest_notsharp; /* true if new facets are at least 90 degrees */
+  boolT NOerrexit;        /* true if qh.errexit is not available, cleared after setjmp */
+  realT PRINTcradius;     /* radius for printing centrums */
+  realT PRINTradius;      /* radius for printing vertex spheres and points */
+  boolT POSTmerging;      /* true when post merging */
+  int   printoutvar;      /* temporary variable for qh_printbegin, etc. */
+  int   printoutnum;      /* number of facets printed */
+  boolT QHULLfinished;    /* True after qhull() is finished */
+  realT totarea;          /* 'FA': total facet area computed by qh_getarea, hasAreaVolume */
+  realT totvol;           /* 'FA': total volume computed by qh_getarea, hasAreaVolume */
+  unsigned int visit_id;  /* unique ID for searching neighborhoods, */
+  unsigned int vertex_visit; /* unique ID for searching vertices, reset with qh_buildtracing */
+  boolT ZEROall_ok;       /* True if qh_checkzero always succeeds */
+  boolT WAScoplanar;      /* True if qh_partitioncoplanar (qhT *qh, qh_check_maxout) */
+
+/*-<a                             href="qh-globa_r.htm#TOC"
+  >--------------------------------</a><a name="qh-set">-</a>
+
+  qh global sets
+    defines sets for merging, initial simplex, hashing, extra input points,
+    and deleted vertices
+*/
+  setT *facet_mergeset;   /* temporary set of merges to be done */
+  setT *degen_mergeset;   /* temporary set of degenerate and redundant merges */
+  setT *hash_table;       /* hash table for matching ridges in qh_matchfacets
+                             size is setsize() */
+  setT *other_points;     /* additional points */
+  setT *del_vertices;     /* vertices to partition and delete with visible
+                             facets.  Have deleted set for checkfacet */
+
+/*-<a                             href="qh-globa_r.htm#TOC"
+  >--------------------------------</a><a name="qh-buf">-</a>
+
+  qh global buffers
+    defines buffers for maxtrix operations, input, and error messages
+*/
+  coordT *gm_matrix;      /* (dim+1)Xdim matrix for geom_r.c */
+  coordT **gm_row;        /* array of gm_matrix rows */
+  char* line;             /* malloc'd input line of maxline+1 chars */
+  int maxline;
+  coordT *half_space;     /* malloc'd input array for halfspace (qh.normal_size+coordT) */
+  coordT *temp_malloc;    /* malloc'd input array for points */
+
+/*-<a                             href="qh-globa_r.htm#TOC"
+  >--------------------------------</a><a name="qh-static">-</a>
+
+  qh static variables
+    defines static variables for individual functions
+
+  notes:
+    do not use 'static' within a function.  Multiple instances of qhull
+    may exist.
+
+    do not assume zero initialization, 'QPn' may cause a restart
+*/
+  boolT ERREXITcalled;    /* true during qh_errexit (qhT *qh, prevents duplicate calls */
+  boolT firstcentrum;     /* for qh_printcentrum */
+  boolT old_randomdist;   /* save RANDOMdist flag during io, tracing, or statistics */
+  setT *coplanarfacetset;  /* set of coplanar facets for searching qh_findbesthorizon() */
+  realT last_low;         /* qh_scalelast parameters for qh_setdelaunay */
+  realT last_high;
+  realT last_newhigh;
+  unsigned lastreport;    /* for qh_buildtracing */
+  int mergereport;        /* for qh_tracemerging */
+  setT *old_tempstack;    /* for saving qh->qhmem.tempstack in save_qhull */
+  int   ridgeoutnum;      /* number of ridges for 4OFF output (qh_printbegin,etc) */
+
+/*-<a                             href="qh-globa_r.htm#TOC"
+  >--------------------------------</a><a name="qh-const">-</a>
+
+  qh memory management, rbox globals, and statistics
+
+  Replaces global data structures defined for libqhull
+*/
+  int     last_random;    /* Last random number from qh_rand (random_r.c) */
+  jmp_buf rbox_errexit;   /* errexit from rboxlib_r.c, defined by qh_rboxpoints() only */
+  char    jmpXtra3[40];   /* extra bytes in case jmp_buf is defined wrong by compiler */
+  int     rbox_isinteger;
+  double  rbox_out_offset;
+  void *  cpp_object;     /* C++ pointer.  Currently used by RboxPoints.qh_fprintf_rbox */
+
+  /* Last, otherwise zero'd by qh_initqhull_start2 (global_r.c */
+  qhmemT  qhmem;          /* Qhull managed memory (mem_r.h) */
+  /* After qhmem because its size depends on the number of statistics */
+  qhstatT qhstat;         /* Qhull statistics (stat_r.h) */
+};
+
+/*=========== -macros- =========================*/
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >--------------------------------</a><a name="otherfacet_">-</a>
+
+  otherfacet_(ridge, facet)
+    return neighboring facet for a ridge in facet
+*/
+#define otherfacet_(ridge, facet) \
+                        (((ridge)->top == (facet)) ? (ridge)->bottom : (ridge)->top)
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >--------------------------------</a><a name="getid_">-</a>
+
+  getid_(p)
+    return int ID for facet, ridge, or vertex
+    return qh_IDunknown(-1) if NULL
+*/
+#define getid_(p)       ((p) ? (int)((p)->id) : qh_IDunknown)
+
+/*============== FORALL macros ===================*/
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >--------------------------------</a><a name="FORALLfacets">-</a>
+
+  FORALLfacets { ... }
+    assign 'facet' to each facet in qh.facet_list
+
+  notes:
+    uses 'facetT *facet;'
+    assumes last facet is a sentinel
+    assumes qh defined
+
+  see:
+    FORALLfacet_( facetlist )
+*/
+#define FORALLfacets for (facet=qh->facet_list;facet && facet->next;facet=facet->next)
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >--------------------------------</a><a name="FORALLpoints">-</a>
+
+  FORALLpoints { ... }
+    assign 'point' to each point in qh.first_point, qh.num_points
+
+  notes:
+    assumes qh defined
+
+  declare:
+    coordT *point, *pointtemp;
+*/
+#define FORALLpoints FORALLpoint_(qh, qh->first_point, qh->num_points)
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >--------------------------------</a><a name="FORALLpoint_">-</a>
+
+  FORALLpoint_( qh, points, num) { ... }
+    assign 'point' to each point in points array of num points
+
+  declare:
+    coordT *point, *pointtemp;
+*/
+#define FORALLpoint_(qh, points, num) for (point= (points), \
+      pointtemp= (points)+qh->hull_dim*(num); point < pointtemp; point += qh->hull_dim)
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >--------------------------------</a><a name="FORALLvertices">-</a>
+
+  FORALLvertices { ... }
+    assign 'vertex' to each vertex in qh.vertex_list
+
+  declare:
+    vertexT *vertex;
+
+  notes:
+    assumes qh.vertex_list terminated with a sentinel
+    assumes qh defined
+*/
+#define FORALLvertices for (vertex=qh->vertex_list;vertex && vertex->next;vertex= vertex->next)
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >--------------------------------</a><a name="FOREACHfacet_">-</a>
+
+  FOREACHfacet_( facets ) { ... }
+    assign 'facet' to each facet in facets
+
+  declare:
+    facetT *facet, **facetp;
+
+  see:
+    <a href="qset_r.h#FOREACHsetelement_">FOREACHsetelement_</a>
+*/
+#define FOREACHfacet_(facets)    FOREACHsetelement_(facetT, facets, facet)
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >--------------------------------</a><a name="FOREACHneighbor_">-</a>
+
+  FOREACHneighbor_( facet ) { ... }
+    assign 'neighbor' to each neighbor in facet->neighbors
+
+  FOREACHneighbor_( vertex ) { ... }
+    assign 'neighbor' to each neighbor in vertex->neighbors
+
+  declare:
+    facetT *neighbor, **neighborp;
+
+  see:
+    <a href="qset_r.h#FOREACHsetelement_">FOREACHsetelement_</a>
+*/
+#define FOREACHneighbor_(facet)  FOREACHsetelement_(facetT, facet->neighbors, neighbor)
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >--------------------------------</a><a name="FOREACHpoint_">-</a>
+
+  FOREACHpoint_( points ) { ... }
+    assign 'point' to each point in points set
+
+  declare:
+    pointT *point, **pointp;
+
+  see:
+    <a href="qset_r.h#FOREACHsetelement_">FOREACHsetelement_</a>
+*/
+#define FOREACHpoint_(points)    FOREACHsetelement_(pointT, points, point)
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >--------------------------------</a><a name="FOREACHridge_">-</a>
+
+  FOREACHridge_( ridges ) { ... }
+    assign 'ridge' to each ridge in ridges set
+
+  declare:
+    ridgeT *ridge, **ridgep;
+
+  see:
+    <a href="qset_r.h#FOREACHsetelement_">FOREACHsetelement_</a>
+*/
+#define FOREACHridge_(ridges)    FOREACHsetelement_(ridgeT, ridges, ridge)
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >--------------------------------</a><a name="FOREACHvertex_">-</a>
+
+  FOREACHvertex_( vertices ) { ... }
+    assign 'vertex' to each vertex in vertices set
+
+  declare:
+    vertexT *vertex, **vertexp;
+
+  see:
+    <a href="qset_r.h#FOREACHsetelement_">FOREACHsetelement_</a>
+*/
+#define FOREACHvertex_(vertices) FOREACHsetelement_(vertexT, vertices,vertex)
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >--------------------------------</a><a name="FOREACHfacet_i_">-</a>
+
+  FOREACHfacet_i_( qh, facets ) { ... }
+    assign 'facet' and 'facet_i' for each facet in facets set
+
+  declare:
+    facetT *facet;
+    int     facet_n, facet_i;
+
+  see:
+    <a href="qset_r.h#FOREACHsetelement_i_">FOREACHsetelement_i_</a>
+*/
+#define FOREACHfacet_i_(qh, facets)    FOREACHsetelement_i_(qh, facetT, facets, facet)
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >--------------------------------</a><a name="FOREACHneighbor_i_">-</a>
+
+  FOREACHneighbor_i_( qh, facet ) { ... }
+    assign 'neighbor' and 'neighbor_i' for each neighbor in facet->neighbors
+
+  FOREACHneighbor_i_( qh, vertex ) { ... }
+    assign 'neighbor' and 'neighbor_i' for each neighbor in vertex->neighbors
+
+  declare:
+    facetT *neighbor;
+    int     neighbor_n, neighbor_i;
+
+  see:
+    <a href="qset_r.h#FOREACHsetelement_i_">FOREACHsetelement_i_</a>
+*/
+#define FOREACHneighbor_i_(qh, facet)  FOREACHsetelement_i_(qh, facetT, facet->neighbors, neighbor)
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >--------------------------------</a><a name="FOREACHpoint_i_">-</a>
+
+  FOREACHpoint_i_( qh, points ) { ... }
+    assign 'point' and 'point_i' for each point in points set
+
+  declare:
+    pointT *point;
+    int     point_n, point_i;
+
+  see:
+    <a href="qset_r.h#FOREACHsetelement_i_">FOREACHsetelement_i_</a>
+*/
+#define FOREACHpoint_i_(qh, points)    FOREACHsetelement_i_(qh, pointT, points, point)
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >--------------------------------</a><a name="FOREACHridge_i_">-</a>
+
+  FOREACHridge_i_( qh, ridges ) { ... }
+    assign 'ridge' and 'ridge_i' for each ridge in ridges set
+
+  declare:
+    ridgeT *ridge;
+    int     ridge_n, ridge_i;
+
+  see:
+    <a href="qset_r.h#FOREACHsetelement_i_">FOREACHsetelement_i_</a>
+*/
+#define FOREACHridge_i_(qh, ridges)    FOREACHsetelement_i_(qh, ridgeT, ridges, ridge)
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >--------------------------------</a><a name="FOREACHvertex_i_">-</a>
+
+  FOREACHvertex_i_( qh, vertices ) { ... }
+    assign 'vertex' and 'vertex_i' for each vertex in vertices set
+
+  declare:
+    vertexT *vertex;
+    int     vertex_n, vertex_i;
+
+  see:
+    <a href="qset_r.h#FOREACHsetelement_i_">FOREACHsetelement_i_</a>
+*/
+#define FOREACHvertex_i_(qh, vertices) FOREACHsetelement_i_(qh, vertexT, vertices,vertex)
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+/********* -libqhull_r.c prototypes (duplicated from qhull_ra.h) **********************/
+
+void    qh_qhull(qhT *qh);
+boolT   qh_addpoint(qhT *qh, pointT *furthest, facetT *facet, boolT checkdist);
+void    qh_printsummary(qhT *qh, FILE *fp);
+
+/********* -user.c prototypes (alphabetical) **********************/
+
+void    qh_errexit(qhT *qh, int exitcode, facetT *facet, ridgeT *ridge);
+void    qh_errprint(qhT *qh, const char* string, facetT *atfacet, facetT *otherfacet, ridgeT *atridge, vertexT *atvertex);
+int     qh_new_qhull(qhT *qh, int dim, int numpoints, coordT *points, boolT ismalloc,
+                char *qhull_cmd, FILE *outfile, FILE *errfile);
+void    qh_printfacetlist(qhT *qh, facetT *facetlist, setT *facets, boolT printall);
+void    qh_printhelp_degenerate(qhT *qh, FILE *fp);
+void    qh_printhelp_narrowhull(qhT *qh, FILE *fp, realT minangle);
+void    qh_printhelp_singular(qhT *qh, FILE *fp);
+void    qh_user_memsizes(qhT *qh);
+
+/********* -usermem_r.c prototypes (alphabetical) **********************/
+void    qh_exit(int exitcode);
+void    qh_fprintf_stderr(int msgcode, const char *fmt, ... );
+void    qh_free(void *mem);
+void   *qh_malloc(size_t size);
+
+/********* -userprintf_r.c and userprintf_rbox_r.c prototypes **********************/
+void    qh_fprintf(qhT *qh, FILE *fp, int msgcode, const char *fmt, ... );
+void    qh_fprintf_rbox(qhT *qh, FILE *fp, int msgcode, const char *fmt, ... );
+
+/***** -geom_r.c/geom2_r.c/random_r.c prototypes (duplicated from geom_r.h, random_r.h) ****************/
+
+facetT *qh_findbest(qhT *qh, pointT *point, facetT *startfacet,
+                     boolT bestoutside, boolT newfacets, boolT noupper,
+                     realT *dist, boolT *isoutside, int *numpart);
+facetT *qh_findbestnew(qhT *qh, pointT *point, facetT *startfacet,
+                     realT *dist, boolT bestoutside, boolT *isoutside, int *numpart);
+boolT   qh_gram_schmidt(qhT *qh, int dim, realT **rows);
+void    qh_outerinner(qhT *qh, facetT *facet, realT *outerplane, realT *innerplane);
+void    qh_printsummary(qhT *qh, FILE *fp);
+void    qh_projectinput(qhT *qh);
+void    qh_randommatrix(qhT *qh, realT *buffer, int dim, realT **row);
+void    qh_rotateinput(qhT *qh, realT **rows);
+void    qh_scaleinput(qhT *qh);
+void    qh_setdelaunay(qhT *qh, int dim, int count, pointT *points);
+coordT  *qh_sethalfspace_all(qhT *qh, int dim, int count, coordT *halfspaces, pointT *feasible);
+
+/***** -global_r.c prototypes (alphabetical) ***********************/
+
+unsigned long qh_clock(qhT *qh);
+void    qh_checkflags(qhT *qh, char *command, char *hiddenflags);
+void    qh_clear_outputflags(qhT *qh);
+void    qh_freebuffers(qhT *qh);
+void    qh_freeqhull(qhT *qh, boolT allmem);
+void    qh_init_A(qhT *qh, FILE *infile, FILE *outfile, FILE *errfile, int argc, char *argv[]);
+void    qh_init_B(qhT *qh, coordT *points, int numpoints, int dim, boolT ismalloc);
+void    qh_init_qhull_command(qhT *qh, int argc, char *argv[]);
+void    qh_initbuffers(qhT *qh, coordT *points, int numpoints, int dim, boolT ismalloc);
+void    qh_initflags(qhT *qh, char *command);
+void    qh_initqhull_buffers(qhT *qh);
+void    qh_initqhull_globals(qhT *qh, coordT *points, int numpoints, int dim, boolT ismalloc);
+void    qh_initqhull_mem(qhT *qh);
+void    qh_initqhull_outputflags(qhT *qh);
+void    qh_initqhull_start(qhT *qh, FILE *infile, FILE *outfile, FILE *errfile);
+void    qh_initqhull_start2(qhT *qh, FILE *infile, FILE *outfile, FILE *errfile);
+void    qh_initthresholds(qhT *qh, char *command);
+void    qh_lib_check(int qhullLibraryType, int qhTsize, int vertexTsize, int ridgeTsize, int facetTsize, int setTsize, int qhmemTsize);
+void    qh_option(qhT *qh, const char *option, int *i, realT *r);
+void    qh_zero(qhT *qh, FILE *errfile);
+
+/***** -io_r.c prototypes (duplicated from io_r.h) ***********************/
+
+void    qh_dfacet(qhT *qh, unsigned id);
+void    qh_dvertex(qhT *qh, unsigned id);
+void    qh_printneighborhood(qhT *qh, FILE *fp, qh_PRINT format, facetT *facetA, facetT *facetB, boolT printall);
+void    qh_produce_output(qhT *qh);
+coordT *qh_readpoints(qhT *qh, int *numpoints, int *dimension, boolT *ismalloc);
+
+
+/********* -mem_r.c prototypes (duplicated from mem_r.h) **********************/
+
+void qh_meminit(qhT *qh, FILE *ferr);
+void qh_memfreeshort(qhT *qh, int *curlong, int *totlong);
+
+/********* -poly_r.c/poly2_r.c prototypes (duplicated from poly_r.h) **********************/
+
+void    qh_check_output(qhT *qh);
+void    qh_check_points(qhT *qh);
+setT   *qh_facetvertices(qhT *qh, facetT *facetlist, setT *facets, boolT allfacets);
+facetT *qh_findbestfacet(qhT *qh, pointT *point, boolT bestoutside,
+           realT *bestdist, boolT *isoutside);
+vertexT *qh_nearvertex(qhT *qh, facetT *facet, pointT *point, realT *bestdistp);
+pointT *qh_point(qhT *qh, int id);
+setT   *qh_pointfacet(qhT *qh /*qh.facet_list*/);
+int     qh_pointid(qhT *qh, pointT *point);
+setT   *qh_pointvertex(qhT *qh /*qh.facet_list*/);
+void    qh_setvoronoi_all(qhT *qh);
+void    qh_triangulate(qhT *qh /*qh.facet_list*/);
+
+/********* -rboxpoints_r.c prototypes **********************/
+int     qh_rboxpoints(qhT *qh, char* rbox_command);
+void    qh_errexit_rbox(qhT *qh, int exitcode);
+
+/********* -stat_r.c prototypes (duplicated from stat_r.h) **********************/
+
+void    qh_collectstatistics(qhT *qh);
+void    qh_printallstatistics(qhT *qh, FILE *fp, const char *string);
+
+#ifdef __cplusplus
+} /* extern "C" */
+#endif
+
+#endif /* qhDEFlibqhull */
diff --git a/xs/src/qhull/src/libqhull_r/libqhull_r.pro b/xs/src/qhull/src/libqhull_r/libqhull_r.pro
new file mode 100644
index 0000000000..6b8db44b75
--- /dev/null
+++ b/xs/src/qhull/src/libqhull_r/libqhull_r.pro
@@ -0,0 +1,67 @@
+# -------------------------------------------------
+# libqhull_r.pro -- Qt project for Qhull shared library
+#
+# It uses reentrant Qhull
+# -------------------------------------------------
+
+include(../qhull-warn.pri)
+
+DESTDIR = ../../lib
+DLLDESTDIR = ../../bin
+TEMPLATE = lib
+CONFIG += shared warn_on
+CONFIG -= qt
+
+build_pass:CONFIG(debug, debug|release):{
+    TARGET = qhull_rd
+    OBJECTS_DIR = Debug
+}else:build_pass:CONFIG(release, debug|release):{
+    TARGET = qhull_r
+    OBJECTS_DIR = Release
+}
+win32-msvc* : QMAKE_LFLAGS += /INCREMENTAL:NO
+
+win32-msvc* : DEF_FILE += ../../src/libqhull_r/qhull_r-exports.def
+
+# libqhull_r/libqhull_r.pro and ../qhull-libqhull-src_r.pri have the same SOURCES and HEADERS
+
+SOURCES += ../libqhull_r/global_r.c
+SOURCES += ../libqhull_r/stat_r.c
+SOURCES += ../libqhull_r/geom2_r.c
+SOURCES += ../libqhull_r/poly2_r.c
+SOURCES += ../libqhull_r/merge_r.c
+SOURCES += ../libqhull_r/libqhull_r.c
+SOURCES += ../libqhull_r/geom_r.c
+SOURCES += ../libqhull_r/poly_r.c
+SOURCES += ../libqhull_r/qset_r.c
+SOURCES += ../libqhull_r/mem_r.c
+SOURCES += ../libqhull_r/random_r.c
+SOURCES += ../libqhull_r/usermem_r.c
+SOURCES += ../libqhull_r/userprintf_r.c
+SOURCES += ../libqhull_r/io_r.c
+SOURCES += ../libqhull_r/user_r.c
+SOURCES += ../libqhull_r/rboxlib_r.c
+SOURCES += ../libqhull_r/userprintf_rbox_r.c
+
+HEADERS += ../libqhull_r/geom_r.h
+HEADERS += ../libqhull_r/io_r.h
+HEADERS += ../libqhull_r/libqhull_r.h
+HEADERS += ../libqhull_r/mem_r.h
+HEADERS += ../libqhull_r/merge_r.h
+HEADERS += ../libqhull_r/poly_r.h
+HEADERS += ../libqhull_r/random_r.h
+HEADERS += ../libqhull_r/qhull_ra.h
+HEADERS += ../libqhull_r/qset_r.h
+HEADERS += ../libqhull_r/stat_r.h
+HEADERS += ../libqhull_r/user_r.h
+
+OTHER_FILES += qh-geom_r.htm
+OTHER_FILES += qh-globa_r.htm
+OTHER_FILES += qh-io_r.htm
+OTHER_FILES += qh-mem_r.htm
+OTHER_FILES += qh-merge_r.htm
+OTHER_FILES += qh-poly_r.htm
+OTHER_FILES += qh-qhull_r.htm
+OTHER_FILES += qh-set_r.htm
+OTHER_FILES += qh-stat_r.htm
+OTHER_FILES += qh-user_r.htm
diff --git a/xs/src/qhull/src/libqhull_r/mem_r.c b/xs/src/qhull/src/libqhull_r/mem_r.c
new file mode 100644
index 0000000000..801a8c76a1
--- /dev/null
+++ b/xs/src/qhull/src/libqhull_r/mem_r.c
@@ -0,0 +1,562 @@
+/*<html><pre>  -<a                             href="qh-mem_r.htm"
+  >-------------------------------</a><a name="TOP">-</a>
+
+  mem_r.c
+    memory management routines for qhull
+
+  See libqhull/mem_r.c for a standalone program.
+
+  To initialize memory:
+
+    qh_meminit(qh, stderr);
+    qh_meminitbuffers(qh, qh->IStracing, qh_MEMalign, 7, qh_MEMbufsize,qh_MEMinitbuf);
+    qh_memsize(qh, (int)sizeof(facetT));
+    qh_memsize(qh, (int)sizeof(facetT));
+    ...
+    qh_memsetup(qh);
+
+  To free up all memory buffers:
+    qh_memfreeshort(qh, &curlong, &totlong);
+
+  if qh_NOmem,
+    malloc/free is used instead of mem.c
+
+  notes:
+    uses Quickfit algorithm (freelists for commonly allocated sizes)
+    assumes small sizes for freelists (it discards the tail of memory buffers)
+
+  see:
+    qh-mem_r.htm and mem_r.h
+    global_r.c (qh_initbuffers) for an example of using mem_r.c
+
+  Copyright (c) 1993-2015 The Geometry Center.
+  $Id: //main/2015/qhull/src/libqhull_r/mem_r.c#5 $$Change: 2065 $
+  $DateTime: 2016/01/18 13:51:04 $$Author: bbarber $
+*/
+
+#include "libqhull_r.h"  /* includes user_r.h and mem_r.h */
+
+#include <string.h>
+#include <stdio.h>
+#include <stdlib.h>
+
+#ifndef qh_NOmem
+
+/*============= internal functions ==============*/
+
+static int qh_intcompare(const void *i, const void *j);
+
+/*========== functions in alphabetical order ======== */
+
+/*-<a                             href="qh-mem_r.htm#TOC"
+  >-------------------------------</a><a name="intcompare">-</a>
+
+  qh_intcompare( i, j )
+    used by qsort and bsearch to compare two integers
+*/
+static int qh_intcompare(const void *i, const void *j) {
+  return(*((const int *)i) - *((const int *)j));
+} /* intcompare */
+
+
+/*-<a                             href="qh-mem_r.htm#TOC"
+  >--------------------------------</a><a name="memalloc">-</a>
+
+  qh_memalloc( qh, insize )
+    returns object of insize bytes
+    qhmem is the global memory structure
+
+  returns:
+    pointer to allocated memory
+    errors if insufficient memory
+
+  notes:
+    use explicit type conversion to avoid type warnings on some compilers
+    actual object may be larger than insize
+    use qh_memalloc_() for inline code for quick allocations
+    logs allocations if 'T5'
+    caller is responsible for freeing the memory.
+    short memory is freed on shutdown by qh_memfreeshort unless qh_NOmem
+
+  design:
+    if size < qh->qhmem.LASTsize
+      if qh->qhmem.freelists[size] non-empty
+        return first object on freelist
+      else
+        round up request to size of qh->qhmem.freelists[size]
+        allocate new allocation buffer if necessary
+        allocate object from allocation buffer
+    else
+      allocate object with qh_malloc() in user.c
+*/
+void *qh_memalloc(qhT *qh, int insize) {
+  void **freelistp, *newbuffer;
+  int idx, size, n;
+  int outsize, bufsize;
+  void *object;
+
+  if (insize<0) {
+      qh_fprintf(qh, qh->qhmem.ferr, 6235, "qhull error (qh_memalloc): negative request size (%d).  Did int overflow due to high-D?\n", insize); /* WARN64 */
+      qh_errexit(qh, qhmem_ERRmem, NULL, NULL);
+  }
+  if (insize>=0 && insize <= qh->qhmem.LASTsize) {
+    idx= qh->qhmem.indextable[insize];
+    outsize= qh->qhmem.sizetable[idx];
+    qh->qhmem.totshort += outsize;
+    freelistp= qh->qhmem.freelists+idx;
+    if ((object= *freelistp)) {
+      qh->qhmem.cntquick++;
+      qh->qhmem.totfree -= outsize;
+      *freelistp= *((void **)*freelistp);  /* replace freelist with next object */
+#ifdef qh_TRACEshort
+      n= qh->qhmem.cntshort+qh->qhmem.cntquick+qh->qhmem.freeshort;
+      if (qh->qhmem.IStracing >= 5)
+          qh_fprintf(qh, qh->qhmem.ferr, 8141, "qh_mem %p n %8d alloc quick: %d bytes (tot %d cnt %d)\n", object, n, outsize, qh->qhmem.totshort, qh->qhmem.cntshort+qh->qhmem.cntquick-qh->qhmem.freeshort);
+#endif
+      return(object);
+    }else {
+      qh->qhmem.cntshort++;
+      if (outsize > qh->qhmem.freesize) {
+        qh->qhmem.totdropped += qh->qhmem.freesize;
+        if (!qh->qhmem.curbuffer)
+          bufsize= qh->qhmem.BUFinit;
+        else
+          bufsize= qh->qhmem.BUFsize;
+        if (!(newbuffer= qh_malloc((size_t)bufsize))) {
+          qh_fprintf(qh, qh->qhmem.ferr, 6080, "qhull error (qh_memalloc): insufficient memory to allocate short memory buffer (%d bytes)\n", bufsize);
+          qh_errexit(qh, qhmem_ERRmem, NULL, NULL);
+        }
+        *((void **)newbuffer)= qh->qhmem.curbuffer;  /* prepend newbuffer to curbuffer
+                                                    list.  newbuffer!=0 by QH6080 */
+        qh->qhmem.curbuffer= newbuffer;
+        size= (sizeof(void **) + qh->qhmem.ALIGNmask) & ~qh->qhmem.ALIGNmask;
+        qh->qhmem.freemem= (void *)((char *)newbuffer+size);
+        qh->qhmem.freesize= bufsize - size;
+        qh->qhmem.totbuffer += bufsize - size; /* easier to check */
+        /* Periodically test totbuffer.  It matches at beginning and exit of every call */
+        n = qh->qhmem.totshort + qh->qhmem.totfree + qh->qhmem.totdropped + qh->qhmem.freesize - outsize;
+        if (qh->qhmem.totbuffer != n) {
+            qh_fprintf(qh, qh->qhmem.ferr, 6212, "qh_memalloc internal error: short totbuffer %d != totshort+totfree... %d\n", qh->qhmem.totbuffer, n);
+            qh_errexit(qh, qhmem_ERRmem, NULL, NULL);
+        }
+      }
+      object= qh->qhmem.freemem;
+      qh->qhmem.freemem= (void *)((char *)qh->qhmem.freemem + outsize);
+      qh->qhmem.freesize -= outsize;
+      qh->qhmem.totunused += outsize - insize;
+#ifdef qh_TRACEshort
+      n= qh->qhmem.cntshort+qh->qhmem.cntquick+qh->qhmem.freeshort;
+      if (qh->qhmem.IStracing >= 5)
+          qh_fprintf(qh, qh->qhmem.ferr, 8140, "qh_mem %p n %8d alloc short: %d bytes (tot %d cnt %d)\n", object, n, outsize, qh->qhmem.totshort, qh->qhmem.cntshort+qh->qhmem.cntquick-qh->qhmem.freeshort);
+#endif
+      return object;
+    }
+  }else {                     /* long allocation */
+    if (!qh->qhmem.indextable) {
+      qh_fprintf(qh, qh->qhmem.ferr, 6081, "qhull internal error (qh_memalloc): qhmem has not been initialized.\n");
+      qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
+    }
+    outsize= insize;
+    qh->qhmem.cntlong++;
+    qh->qhmem.totlong += outsize;
+    if (qh->qhmem.maxlong < qh->qhmem.totlong)
+      qh->qhmem.maxlong= qh->qhmem.totlong;
+    if (!(object= qh_malloc((size_t)outsize))) {
+      qh_fprintf(qh, qh->qhmem.ferr, 6082, "qhull error (qh_memalloc): insufficient memory to allocate %d bytes\n", outsize);
+      qh_errexit(qh, qhmem_ERRmem, NULL, NULL);
+    }
+    if (qh->qhmem.IStracing >= 5)
+      qh_fprintf(qh, qh->qhmem.ferr, 8057, "qh_mem %p n %8d alloc long: %d bytes (tot %d cnt %d)\n", object, qh->qhmem.cntlong+qh->qhmem.freelong, outsize, qh->qhmem.totlong, qh->qhmem.cntlong-qh->qhmem.freelong);
+  }
+  return(object);
+} /* memalloc */
+
+
+/*-<a                             href="qh-mem_r.htm#TOC"
+  >--------------------------------</a><a name="memcheck">-</a>
+
+  qh_memcheck(qh)
+*/
+void qh_memcheck(qhT *qh) {
+  int i, count, totfree= 0;
+  void *object;
+
+  if (!qh) {
+    qh_fprintf_stderr(6243, "qh_memcheck(qh) error: qh is 0.  It does not point to a qhT");
+    qh_exit(qhmem_ERRqhull);  /* can not use qh_errexit() */
+  }
+  if (qh->qhmem.ferr == 0 || qh->qhmem.IStracing < 0 || qh->qhmem.IStracing > 10 || (((qh->qhmem.ALIGNmask+1) & qh->qhmem.ALIGNmask) != 0)) {
+    qh_fprintf_stderr(6244, "qh_memcheck error: either qh->qhmem is overwritten or qh->qhmem is not initialized.  Call qh_mem_new() or qh_new_qhull() before calling qh_mem routines.  ferr 0x%x IsTracing %d ALIGNmask 0x%x", qh->qhmem.ferr, qh->qhmem.IStracing, qh->qhmem.ALIGNmask);
+    qh_exit(qhmem_ERRqhull);  /* can not use qh_errexit() */
+  }
+  if (qh->qhmem.IStracing != 0)
+    qh_fprintf(qh, qh->qhmem.ferr, 8143, "qh_memcheck: check size of freelists on qh->qhmem\nqh_memcheck: A segmentation fault indicates an overwrite of qh->qhmem\n");
+  for (i=0; i < qh->qhmem.TABLEsize; i++) {
+    count=0;
+    for (object= qh->qhmem.freelists[i]; object; object= *((void **)object))
+      count++;
+    totfree += qh->qhmem.sizetable[i] * count;
+  }
+  if (totfree != qh->qhmem.totfree) {
+    qh_fprintf(qh, qh->qhmem.ferr, 6211, "Qhull internal error (qh_memcheck): totfree %d not equal to freelist total %d\n", qh->qhmem.totfree, totfree);
+    qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
+  }
+  if (qh->qhmem.IStracing != 0)
+    qh_fprintf(qh, qh->qhmem.ferr, 8144, "qh_memcheck: total size of freelists totfree is the same as qh->qhmem.totfree\n", totfree);
+} /* memcheck */
+
+/*-<a                             href="qh-mem_r.htm#TOC"
+  >--------------------------------</a><a name="memfree">-</a>
+
+  qh_memfree(qh, object, insize )
+    free up an object of size bytes
+    size is insize from qh_memalloc
+
+  notes:
+    object may be NULL
+    type checking warns if using (void **)object
+    use qh_memfree_() for quick free's of small objects
+
+  design:
+    if size <= qh->qhmem.LASTsize
+      append object to corresponding freelist
+    else
+      call qh_free(object)
+*/
+void qh_memfree(qhT *qh, void *object, int insize) {
+  void **freelistp;
+  int idx, outsize;
+
+  if (!object)
+    return;
+  if (insize <= qh->qhmem.LASTsize) {
+    qh->qhmem.freeshort++;
+    idx= qh->qhmem.indextable[insize];
+    outsize= qh->qhmem.sizetable[idx];
+    qh->qhmem.totfree += outsize;
+    qh->qhmem.totshort -= outsize;
+    freelistp= qh->qhmem.freelists + idx;
+    *((void **)object)= *freelistp;
+    *freelistp= object;
+#ifdef qh_TRACEshort
+    idx= qh->qhmem.cntshort+qh->qhmem.cntquick+qh->qhmem.freeshort;
+    if (qh->qhmem.IStracing >= 5)
+        qh_fprintf(qh, qh->qhmem.ferr, 8142, "qh_mem %p n %8d free short: %d bytes (tot %d cnt %d)\n", object, idx, outsize, qh->qhmem.totshort, qh->qhmem.cntshort+qh->qhmem.cntquick-qh->qhmem.freeshort);
+#endif
+  }else {
+    qh->qhmem.freelong++;
+    qh->qhmem.totlong -= insize;
+    if (qh->qhmem.IStracing >= 5)
+      qh_fprintf(qh, qh->qhmem.ferr, 8058, "qh_mem %p n %8d free long: %d bytes (tot %d cnt %d)\n", object, qh->qhmem.cntlong+qh->qhmem.freelong, insize, qh->qhmem.totlong, qh->qhmem.cntlong-qh->qhmem.freelong);
+    qh_free(object);
+  }
+} /* memfree */
+
+
+/*-<a                             href="qh-mem_r.htm#TOC"
+  >-------------------------------</a><a name="memfreeshort">-</a>
+
+  qh_memfreeshort(qh, curlong, totlong )
+    frees up all short and qhmem memory allocations
+
+  returns:
+    number and size of current long allocations
+  
+  notes:
+    if qh_NOmem (qh_malloc() for all allocations), 
+       short objects (e.g., facetT) are not recovered.
+       use qh_freeqhull(qh, qh_ALL) instead.
+ 
+  see:
+    qh_freeqhull(qh, allMem)
+    qh_memtotal(qh, curlong, totlong, curshort, totshort, maxlong, totbuffer);
+*/
+void qh_memfreeshort(qhT *qh, int *curlong, int *totlong) {
+  void *buffer, *nextbuffer;
+  FILE *ferr;
+
+  *curlong= qh->qhmem.cntlong - qh->qhmem.freelong;
+  *totlong= qh->qhmem.totlong;
+  for (buffer= qh->qhmem.curbuffer; buffer; buffer= nextbuffer) {
+    nextbuffer= *((void **) buffer);
+    qh_free(buffer);
+  }
+  qh->qhmem.curbuffer= NULL;
+  if (qh->qhmem.LASTsize) {
+    qh_free(qh->qhmem.indextable);
+    qh_free(qh->qhmem.freelists);
+    qh_free(qh->qhmem.sizetable);
+  }
+  ferr= qh->qhmem.ferr;
+  memset((char *)&qh->qhmem, 0, sizeof(qh->qhmem));  /* every field is 0, FALSE, NULL */
+  qh->qhmem.ferr= ferr;
+} /* memfreeshort */
+
+
+/*-<a                             href="qh-mem_r.htm#TOC"
+  >--------------------------------</a><a name="meminit">-</a>
+
+  qh_meminit(qh, ferr )
+    initialize qhmem and test sizeof( void*)
+    Does not throw errors.  qh_exit on failure
+*/
+void qh_meminit(qhT *qh, FILE *ferr) {
+
+  memset((char *)&qh->qhmem, 0, sizeof(qh->qhmem));  /* every field is 0, FALSE, NULL */
+  if (ferr)
+      qh->qhmem.ferr= ferr;
+  else
+      qh->qhmem.ferr= stderr;
+  if (sizeof(void*) < sizeof(int)) {
+    qh_fprintf(qh, qh->qhmem.ferr, 6083, "qhull internal error (qh_meminit): sizeof(void*) %d < sizeof(int) %d.  qset.c will not work\n", (int)sizeof(void*), (int)sizeof(int));
+    qh_exit(qhmem_ERRqhull);  /* can not use qh_errexit() */
+  }
+  if (sizeof(void*) > sizeof(ptr_intT)) {
+      qh_fprintf(qh, qh->qhmem.ferr, 6084, "qhull internal error (qh_meminit): sizeof(void*) %d > sizeof(ptr_intT) %d. Change ptr_intT in mem.h to 'long long'\n", (int)sizeof(void*), (int)sizeof(ptr_intT));
+      qh_exit(qhmem_ERRqhull);  /* can not use qh_errexit() */
+  }
+  qh_memcheck(qh);
+} /* meminit */
+
+/*-<a                             href="qh-mem_r.htm#TOC"
+  >-------------------------------</a><a name="meminitbuffers">-</a>
+
+  qh_meminitbuffers(qh, tracelevel, alignment, numsizes, bufsize, bufinit )
+    initialize qhmem
+    if tracelevel >= 5, trace memory allocations
+    alignment= desired address alignment for memory allocations
+    numsizes= number of freelists
+    bufsize=  size of additional memory buffers for short allocations
+    bufinit=  size of initial memory buffer for short allocations
+*/
+void qh_meminitbuffers(qhT *qh, int tracelevel, int alignment, int numsizes, int bufsize, int bufinit) {
+
+  qh->qhmem.IStracing= tracelevel;
+  qh->qhmem.NUMsizes= numsizes;
+  qh->qhmem.BUFsize= bufsize;
+  qh->qhmem.BUFinit= bufinit;
+  qh->qhmem.ALIGNmask= alignment-1;
+  if (qh->qhmem.ALIGNmask & ~qh->qhmem.ALIGNmask) {
+    qh_fprintf(qh, qh->qhmem.ferr, 6085, "qhull internal error (qh_meminit): memory alignment %d is not a power of 2\n", alignment);
+    qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
+  }
+  qh->qhmem.sizetable= (int *) calloc((size_t)numsizes, sizeof(int));
+  qh->qhmem.freelists= (void **) calloc((size_t)numsizes, sizeof(void *));
+  if (!qh->qhmem.sizetable || !qh->qhmem.freelists) {
+    qh_fprintf(qh, qh->qhmem.ferr, 6086, "qhull error (qh_meminit): insufficient memory\n");
+    qh_errexit(qh, qhmem_ERRmem, NULL, NULL);
+  }
+  if (qh->qhmem.IStracing >= 1)
+    qh_fprintf(qh, qh->qhmem.ferr, 8059, "qh_meminitbuffers: memory initialized with alignment %d\n", alignment);
+} /* meminitbuffers */
+
+/*-<a                             href="qh-mem_r.htm#TOC"
+  >-------------------------------</a><a name="memsetup">-</a>
+
+  qh_memsetup(qh)
+    set up memory after running memsize()
+*/
+void qh_memsetup(qhT *qh) {
+  int k,i;
+
+  qsort(qh->qhmem.sizetable, (size_t)qh->qhmem.TABLEsize, sizeof(int), qh_intcompare);
+  qh->qhmem.LASTsize= qh->qhmem.sizetable[qh->qhmem.TABLEsize-1];
+  if(qh->qhmem.LASTsize >= qh->qhmem.BUFsize || qh->qhmem.LASTsize >= qh->qhmem.BUFinit) {
+    qh_fprintf(qh, qh->qhmem.ferr, 6087, "qhull error (qh_memsetup): largest mem size %d is >= buffer size %d or initial buffer size %d\n",
+            qh->qhmem.LASTsize, qh->qhmem.BUFsize, qh->qhmem.BUFinit);
+    qh_errexit(qh, qhmem_ERRmem, NULL, NULL);
+  }
+  if (!(qh->qhmem.indextable= (int *)qh_malloc((qh->qhmem.LASTsize+1) * sizeof(int)))) {
+    qh_fprintf(qh, qh->qhmem.ferr, 6088, "qhull error (qh_memsetup): insufficient memory\n");
+    qh_errexit(qh, qhmem_ERRmem, NULL, NULL);
+  }
+  for (k=qh->qhmem.LASTsize+1; k--; )
+    qh->qhmem.indextable[k]= k;
+  i= 0;
+  for (k=0; k <= qh->qhmem.LASTsize; k++) {
+    if (qh->qhmem.indextable[k] <= qh->qhmem.sizetable[i])
+      qh->qhmem.indextable[k]= i;
+    else
+      qh->qhmem.indextable[k]= ++i;
+  }
+} /* memsetup */
+
+/*-<a                             href="qh-mem_r.htm#TOC"
+  >-------------------------------</a><a name="memsize">-</a>
+
+  qh_memsize(qh, size )
+    define a free list for this size
+*/
+void qh_memsize(qhT *qh, int size) {
+  int k;
+
+  if(qh->qhmem.LASTsize) {
+    qh_fprintf(qh, qh->qhmem.ferr, 6089, "qhull error (qh_memsize): called after qhmem_setup\n");
+    qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
+  }
+  size= (size + qh->qhmem.ALIGNmask) & ~qh->qhmem.ALIGNmask;
+  for (k=qh->qhmem.TABLEsize; k--; ) {
+    if (qh->qhmem.sizetable[k] == size)
+      return;
+  }
+  if (qh->qhmem.TABLEsize < qh->qhmem.NUMsizes)
+    qh->qhmem.sizetable[qh->qhmem.TABLEsize++]= size;
+  else
+    qh_fprintf(qh, qh->qhmem.ferr, 7060, "qhull warning (memsize): free list table has room for only %d sizes\n", qh->qhmem.NUMsizes);
+} /* memsize */
+
+
+/*-<a                             href="qh-mem_r.htm#TOC"
+  >-------------------------------</a><a name="memstatistics">-</a>
+
+  qh_memstatistics(qh, fp )
+    print out memory statistics
+
+    Verifies that qh->qhmem.totfree == sum of freelists
+*/
+void qh_memstatistics(qhT *qh, FILE *fp) {
+  int i;
+  int count;
+  void *object;
+
+  qh_memcheck(qh);
+  qh_fprintf(qh, fp, 9278, "\nmemory statistics:\n\
+%7d quick allocations\n\
+%7d short allocations\n\
+%7d long allocations\n\
+%7d short frees\n\
+%7d long frees\n\
+%7d bytes of short memory in use\n\
+%7d bytes of short memory in freelists\n\
+%7d bytes of dropped short memory\n\
+%7d bytes of unused short memory (estimated)\n\
+%7d bytes of long memory allocated (max, except for input)\n\
+%7d bytes of long memory in use (in %d pieces)\n\
+%7d bytes of short memory buffers (minus links)\n\
+%7d bytes per short memory buffer (initially %d bytes)\n",
+           qh->qhmem.cntquick, qh->qhmem.cntshort, qh->qhmem.cntlong,
+           qh->qhmem.freeshort, qh->qhmem.freelong,
+           qh->qhmem.totshort, qh->qhmem.totfree,
+           qh->qhmem.totdropped + qh->qhmem.freesize, qh->qhmem.totunused,
+           qh->qhmem.maxlong, qh->qhmem.totlong, qh->qhmem.cntlong - qh->qhmem.freelong,
+           qh->qhmem.totbuffer, qh->qhmem.BUFsize, qh->qhmem.BUFinit);
+  if (qh->qhmem.cntlarger) {
+    qh_fprintf(qh, fp, 9279, "%7d calls to qh_setlarger\n%7.2g     average copy size\n",
+           qh->qhmem.cntlarger, ((float)qh->qhmem.totlarger)/(float)qh->qhmem.cntlarger);
+    qh_fprintf(qh, fp, 9280, "  freelists(bytes->count):");
+  }
+  for (i=0; i < qh->qhmem.TABLEsize; i++) {
+    count=0;
+    for (object= qh->qhmem.freelists[i]; object; object= *((void **)object))
+      count++;
+    qh_fprintf(qh, fp, 9281, " %d->%d", qh->qhmem.sizetable[i], count);
+  }
+  qh_fprintf(qh, fp, 9282, "\n\n");
+} /* memstatistics */
+
+
+/*-<a                             href="qh-mem_r.htm#TOC"
+  >-------------------------------</a><a name="NOmem">-</a>
+
+  qh_NOmem
+    turn off quick-fit memory allocation
+
+  notes:
+    uses qh_malloc() and qh_free() instead
+*/
+#else /* qh_NOmem */
+
+void *qh_memalloc(qhT *qh, int insize) {
+  void *object;
+
+  if (!(object= qh_malloc((size_t)insize))) {
+    qh_fprintf(qh, qh->qhmem.ferr, 6090, "qhull error (qh_memalloc): insufficient memory\n");
+    qh_errexit(qh, qhmem_ERRmem, NULL, NULL);
+  }
+  qh->qhmem.cntlong++;
+  qh->qhmem.totlong += insize;
+  if (qh->qhmem.maxlong < qh->qhmem.totlong)
+      qh->qhmem.maxlong= qh->qhmem.totlong;
+  if (qh->qhmem.IStracing >= 5)
+    qh_fprintf(qh, qh->qhmem.ferr, 8060, "qh_mem %p n %8d alloc long: %d bytes (tot %d cnt %d)\n", object, qh->qhmem.cntlong+qh->qhmem.freelong, insize, qh->qhmem.totlong, qh->qhmem.cntlong-qh->qhmem.freelong);
+  return object;
+}
+
+void qh_memfree(qhT *qh, void *object, int insize) {
+
+  if (!object)
+    return;
+  qh_free(object);
+  qh->qhmem.freelong++;
+  qh->qhmem.totlong -= insize;
+  if (qh->qhmem.IStracing >= 5)
+    qh_fprintf(qh, qh->qhmem.ferr, 8061, "qh_mem %p n %8d free long: %d bytes (tot %d cnt %d)\n", object, qh->qhmem.cntlong+qh->qhmem.freelong, insize, qh->qhmem.totlong, qh->qhmem.cntlong-qh->qhmem.freelong);
+}
+
+void qh_memfreeshort(qhT *qh, int *curlong, int *totlong) {
+  *totlong= qh->qhmem.totlong;
+  *curlong= qh->qhmem.cntlong - qh->qhmem.freelong;
+  memset((char *)&qh->qhmem, 0, sizeof(qh->qhmem));  /* every field is 0, FALSE, NULL */
+}
+
+void qh_meminit(qhT *qh, FILE *ferr) {
+
+  memset((char *)&qh->qhmem, 0, sizeof(qh->qhmem));  /* every field is 0, FALSE, NULL */
+  if (ferr)
+      qh->qhmem.ferr= ferr;
+  else
+      qh->qhmem.ferr= stderr;
+  if (sizeof(void*) < sizeof(int)) {
+    qh_fprintf(qh, qh->qhmem.ferr, 6091, "qhull internal error (qh_meminit): sizeof(void*) %d < sizeof(int) %d.  qset.c will not work\n", (int)sizeof(void*), (int)sizeof(int));
+    qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
+  }
+}
+
+void qh_meminitbuffers(qhT *qh, int tracelevel, int alignment, int numsizes, int bufsize, int bufinit) {
+
+  qh->qhmem.IStracing= tracelevel;
+}
+
+void qh_memsetup(qhT *qh) {
+
+}
+
+void qh_memsize(qhT *qh, int size) {
+
+}
+
+void qh_memstatistics(qhT *qh, FILE *fp) {
+
+  qh_fprintf(qh, fp, 9409, "\nmemory statistics:\n\
+%7d long allocations\n\
+%7d long frees\n\
+%7d bytes of long memory allocated (max, except for input)\n\
+%7d bytes of long memory in use (in %d pieces)\n",
+           qh->qhmem.cntlong,
+           qh->qhmem.freelong,
+           qh->qhmem.maxlong, qh->qhmem.totlong, qh->qhmem.cntlong - qh->qhmem.freelong);
+}
+
+#endif /* qh_NOmem */
+
+/*-<a                             href="qh-mem_r.htm#TOC"
+>-------------------------------</a><a name="memtotlong">-</a>
+
+  qh_memtotal(qh, totlong, curlong, totshort, curshort, maxlong, totbuffer )
+    Return the total, allocated long and short memory
+
+  returns:
+    Returns the total current bytes of long and short allocations
+    Returns the current count of long and short allocations
+    Returns the maximum long memory and total short buffer (minus one link per buffer)
+    Does not error (for deprecated UsingLibQhull.cpp (libqhullpcpp))
+*/
+void qh_memtotal(qhT *qh, int *totlong, int *curlong, int *totshort, int *curshort, int *maxlong, int *totbuffer) {
+    *totlong= qh->qhmem.totlong;
+    *curlong= qh->qhmem.cntlong - qh->qhmem.freelong;
+    *totshort= qh->qhmem.totshort;
+    *curshort= qh->qhmem.cntshort + qh->qhmem.cntquick - qh->qhmem.freeshort;
+    *maxlong= qh->qhmem.maxlong;
+    *totbuffer= qh->qhmem.totbuffer;
+} /* memtotlong */
+
diff --git a/xs/src/qhull/src/libqhull_r/mem_r.h b/xs/src/qhull/src/libqhull_r/mem_r.h
new file mode 100644
index 0000000000..25b5513330
--- /dev/null
+++ b/xs/src/qhull/src/libqhull_r/mem_r.h
@@ -0,0 +1,234 @@
+/*<html><pre>  -<a                             href="qh-mem_r.htm"
+  >-------------------------------</a><a name="TOP">-</a>
+
+   mem_r.h
+     prototypes for memory management functions
+
+   see qh-mem_r.htm, mem_r.c and qset_r.h
+
+   for error handling, writes message and calls
+     qh_errexit(qhT *qh, qhmem_ERRmem, NULL, NULL) if insufficient memory
+       and
+     qh_errexit(qhT *qh, qhmem_ERRqhull, NULL, NULL) otherwise
+
+   Copyright (c) 1993-2015 The Geometry Center.
+   $Id: //main/2015/qhull/src/libqhull_r/mem_r.h#4 $$Change: 2079 $
+   $DateTime: 2016/02/07 17:43:34 $$Author: bbarber $
+*/
+
+#ifndef qhDEFmem
+#define qhDEFmem 1
+
+#include <stdio.h>
+
+#ifndef DEFsetT
+#define DEFsetT 1
+typedef struct setT setT;          /* defined in qset_r.h */
+#endif
+
+#ifndef DEFqhT
+#define DEFqhT 1
+typedef struct qhT qhT;          /* defined in libqhull_r.h */
+#endif
+
+/*-<a                             href="qh-mem_r.htm#TOC"
+  >-------------------------------</a><a name="NOmem">-</a>
+
+  qh_NOmem
+    turn off quick-fit memory allocation
+
+  notes:
+    mem_r.c implements Quickfit memory allocation for about 20% time
+    savings.  If it fails on your machine, try to locate the
+    problem, and send the answer to qhull@qhull.org.  If this can
+    not be done, define qh_NOmem to use malloc/free instead.
+
+   #define qh_NOmem
+*/
+
+/*-<a                             href="qh-mem_r.htm#TOC"
+>-------------------------------</a><a name="TRACEshort">-</a>
+
+qh_TRACEshort
+Trace short and quick memory allocations at T5
+
+*/
+#define qh_TRACEshort
+
+/*-------------------------------------------
+    to avoid bus errors, memory allocation must consider alignment requirements.
+    malloc() automatically takes care of alignment.   Since mem_r.c manages
+    its own memory, we need to explicitly specify alignment in
+    qh_meminitbuffers().
+
+    A safe choice is sizeof(double).  sizeof(float) may be used if doubles
+    do not occur in data structures and pointers are the same size.  Be careful
+    of machines (e.g., DEC Alpha) with large pointers.  If gcc is available,
+    use __alignof__(double) or fmax_(__alignof__(float), __alignof__(void *)).
+
+   see <a href="user.h#MEMalign">qh_MEMalign</a> in user.h for qhull's alignment
+*/
+
+#define qhmem_ERRmem 4    /* matches qh_ERRmem in libqhull_r.h */
+#define qhmem_ERRqhull 5  /* matches qh_ERRqhull in libqhull_r.h */
+
+/*-<a                             href="qh-mem_r.htm#TOC"
+  >--------------------------------</a><a name="ptr_intT">-</a>
+
+  ptr_intT
+    for casting a void * to an integer-type that holds a pointer
+    Used for integer expressions (e.g., computing qh_gethash() in poly_r.c)
+
+  notes:
+    WARN64 -- these notes indicate 64-bit issues
+    On 64-bit machines, a pointer may be larger than an 'int'.
+    qh_meminit()/mem_r.c checks that 'ptr_intT' holds a 'void*'
+    ptr_intT is typically a signed value, but not necessarily so
+    size_t is typically unsigned, but should match the parameter type
+    Qhull uses int instead of size_t except for system calls such as malloc, qsort, qh_malloc, etc.
+    This matches Qt convention and is easier to work with.
+*/
+#if (defined(__MINGW64__)) && defined(_WIN64)
+typedef long long ptr_intT;
+#elif (_MSC_VER) && defined(_WIN64)
+typedef long long ptr_intT;
+#else
+typedef long ptr_intT;
+#endif
+
+/*-<a                             href="qh-mem_r.htm#TOC"
+  >--------------------------------</a><a name="qhmemT">-</a>
+
+  qhmemT
+    global memory structure for mem_r.c
+
+ notes:
+   users should ignore qhmem except for writing extensions
+   qhmem is allocated in mem_r.c
+
+   qhmem could be swapable like qh and qhstat, but then
+   multiple qh's and qhmem's would need to keep in synch.
+   A swapable qhmem would also waste memory buffers.  As long
+   as memory operations are atomic, there is no problem with
+   multiple qh structures being active at the same time.
+   If you need separate address spaces, you can swap the
+   contents of qh->qhmem.
+*/
+typedef struct qhmemT qhmemT;
+
+/* Update qhmem in mem_r.c if add or remove fields */
+struct qhmemT {               /* global memory management variables */
+  int      BUFsize;           /* size of memory allocation buffer */
+  int      BUFinit;           /* initial size of memory allocation buffer */
+  int      TABLEsize;         /* actual number of sizes in free list table */
+  int      NUMsizes;          /* maximum number of sizes in free list table */
+  int      LASTsize;          /* last size in free list table */
+  int      ALIGNmask;         /* worst-case alignment, must be 2^n-1 */
+  void   **freelists;          /* free list table, linked by offset 0 */
+  int     *sizetable;         /* size of each freelist */
+  int     *indextable;        /* size->index table */
+  void    *curbuffer;         /* current buffer, linked by offset 0 */
+  void    *freemem;           /*   free memory in curbuffer */
+  int      freesize;          /*   size of freemem in bytes */
+  setT    *tempstack;         /* stack of temporary memory, managed by users */
+  FILE    *ferr;              /* file for reporting errors when 'qh' may be undefined */
+  int      IStracing;         /* =5 if tracing memory allocations */
+  int      cntquick;          /* count of quick allocations */
+                              /* Note: removing statistics doesn't effect speed */
+  int      cntshort;          /* count of short allocations */
+  int      cntlong;           /* count of long allocations */
+  int      freeshort;         /* count of short memfrees */
+  int      freelong;          /* count of long memfrees */
+  int      totbuffer;         /* total short memory buffers minus buffer links */
+  int      totdropped;        /* total dropped memory at end of short memory buffers (e.g., freesize) */
+  int      totfree;           /* total size of free, short memory on freelists */
+  int      totlong;           /* total size of long memory in use */
+  int      maxlong;           /*   maximum totlong */
+  int      totshort;          /* total size of short memory in use */
+  int      totunused;         /* total unused short memory (estimated, short size - request size of first allocations) */
+  int      cntlarger;         /* count of setlarger's */
+  int      totlarger;         /* total copied by setlarger */
+};
+
+
+/*==================== -macros ====================*/
+
+/*-<a                             href="qh-mem_r.htm#TOC"
+  >--------------------------------</a><a name="memalloc_">-</a>
+
+  qh_memalloc_(qh, insize, freelistp, object, type)
+    returns object of size bytes
+        assumes size<=qh->qhmem.LASTsize and void **freelistp is a temp
+*/
+
+#if defined qh_NOmem
+#define qh_memalloc_(qh, insize, freelistp, object, type) {\
+  object= (type*)qh_memalloc(qh, insize); }
+#elif defined qh_TRACEshort
+#define qh_memalloc_(qh, insize, freelistp, object, type) {\
+    freelistp= NULL; /* Avoid warnings */ \
+    object= (type*)qh_memalloc(qh, insize); }
+#else /* !qh_NOmem */
+
+#define qh_memalloc_(qh, insize, freelistp, object, type) {\
+  freelistp= qh->qhmem.freelists + qh->qhmem.indextable[insize];\
+  if ((object= (type*)*freelistp)) {\
+    qh->qhmem.totshort += qh->qhmem.sizetable[qh->qhmem.indextable[insize]]; \
+    qh->qhmem.totfree -= qh->qhmem.sizetable[qh->qhmem.indextable[insize]]; \
+    qh->qhmem.cntquick++;  \
+    *freelistp= *((void **)*freelistp);\
+  }else object= (type*)qh_memalloc(qh, insize);}
+#endif
+
+/*-<a                             href="qh-mem_r.htm#TOC"
+  >--------------------------------</a><a name="memfree_">-</a>
+
+  qh_memfree_(qh, object, insize, freelistp)
+    free up an object
+
+  notes:
+    object may be NULL
+    assumes size<=qh->qhmem.LASTsize and void **freelistp is a temp
+*/
+#if defined qh_NOmem
+#define qh_memfree_(qh, object, insize, freelistp) {\
+  qh_memfree(qh, object, insize); }
+#elif defined qh_TRACEshort
+#define qh_memfree_(qh, object, insize, freelistp) {\
+    freelistp= NULL; /* Avoid warnings */ \
+    qh_memfree(qh, object, insize); }
+#else /* !qh_NOmem */
+
+#define qh_memfree_(qh, object, insize, freelistp) {\
+  if (object) { \
+    qh->qhmem.freeshort++;\
+    freelistp= qh->qhmem.freelists + qh->qhmem.indextable[insize];\
+    qh->qhmem.totshort -= qh->qhmem.sizetable[qh->qhmem.indextable[insize]]; \
+    qh->qhmem.totfree += qh->qhmem.sizetable[qh->qhmem.indextable[insize]]; \
+    *((void **)object)= *freelistp;\
+    *freelistp= object;}}
+#endif
+
+/*=============== prototypes in alphabetical order ============*/
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+void *qh_memalloc(qhT *qh, int insize);
+void qh_memcheck(qhT *qh);
+void qh_memfree(qhT *qh, void *object, int insize);
+void qh_memfreeshort(qhT *qh, int *curlong, int *totlong);
+void qh_meminit(qhT *qh, FILE *ferr);
+void qh_meminitbuffers(qhT *qh, int tracelevel, int alignment, int numsizes,
+                        int bufsize, int bufinit);
+void qh_memsetup(qhT *qh);
+void qh_memsize(qhT *qh, int size);
+void qh_memstatistics(qhT *qh, FILE *fp);
+void qh_memtotal(qhT *qh, int *totlong, int *curlong, int *totshort, int *curshort, int *maxlong, int *totbuffer);
+
+#ifdef __cplusplus
+} /* extern "C" */
+#endif
+
+#endif /* qhDEFmem */
diff --git a/xs/src/qhull/src/libqhull_r/merge_r.c b/xs/src/qhull/src/libqhull_r/merge_r.c
new file mode 100644
index 0000000000..e5823de8d1
--- /dev/null
+++ b/xs/src/qhull/src/libqhull_r/merge_r.c
@@ -0,0 +1,3627 @@
+/*<html><pre>  -<a                             href="qh-merge_r.htm#TOC"
+  >-------------------------------</a><a name="TOP">-</a>
+
+   merge_r.c
+   merges non-convex facets
+
+   see qh-merge_r.htm and merge_r.h
+
+   other modules call qh_premerge() and qh_postmerge()
+
+   the user may call qh_postmerge() to perform additional merges.
+
+   To remove deleted facets and vertices (qhull() in libqhull_r.c):
+     qh_partitionvisible(qh, !qh_ALL, &numoutside);  // visible_list, newfacet_list
+     qh_deletevisible();         // qh.visible_list
+     qh_resetlists(qh, False, qh_RESETvisible);       // qh.visible_list newvertex_list newfacet_list
+
+   assumes qh.CENTERtype= centrum
+
+   merges occur in qh_mergefacet and in qh_mergecycle
+   vertex->neighbors not set until the first merge occurs
+
+   Copyright (c) 1993-2015 C.B. Barber.
+   $Id: //main/2015/qhull/src/libqhull_r/merge_r.c#5 $$Change: 2064 $
+   $DateTime: 2016/01/18 12:36:08 $$Author: bbarber $
+*/
+
+#include "qhull_ra.h"
+
+#ifndef qh_NOmerge
+
+/*===== functions(alphabetical after premerge and postmerge) ======*/
+
+/*-<a                             href="qh-merge_r.htm#TOC"
+  >-------------------------------</a><a name="premerge">-</a>
+
+  qh_premerge(qh, apex, maxcentrum )
+    pre-merge nonconvex facets in qh.newfacet_list for apex
+    maxcentrum defines coplanar and concave (qh_test_appendmerge)
+
+  returns:
+    deleted facets added to qh.visible_list with facet->visible set
+
+  notes:
+    uses globals, qh.MERGEexact, qh.PREmerge
+
+  design:
+    mark duplicate ridges in qh.newfacet_list
+    merge facet cycles in qh.newfacet_list
+    merge duplicate ridges and concave facets in qh.newfacet_list
+    check merged facet cycles for degenerate and redundant facets
+    merge degenerate and redundant facets
+    collect coplanar and concave facets
+    merge concave, coplanar, degenerate, and redundant facets
+*/
+void qh_premerge(qhT *qh, vertexT *apex, realT maxcentrum, realT maxangle) {
+  boolT othermerge= False;
+  facetT *newfacet;
+
+  if (qh->ZEROcentrum && qh_checkzero(qh, !qh_ALL))
+    return;
+  trace2((qh, qh->ferr, 2008, "qh_premerge: premerge centrum %2.2g angle %2.2g for apex v%d facetlist f%d\n",
+            maxcentrum, maxangle, apex->id, getid_(qh->newfacet_list)));
+  if (qh->IStracing >= 4 && qh->num_facets < 50)
+    qh_printlists(qh);
+  qh->centrum_radius= maxcentrum;
+  qh->cos_max= maxangle;
+  qh->degen_mergeset= qh_settemp(qh, qh->TEMPsize);
+  qh->facet_mergeset= qh_settemp(qh, qh->TEMPsize);
+  if (qh->hull_dim >=3) {
+    qh_mark_dupridges(qh, qh->newfacet_list); /* facet_mergeset */
+    qh_mergecycle_all(qh, qh->newfacet_list, &othermerge);
+    qh_forcedmerges(qh, &othermerge /* qh->facet_mergeset */);
+    FORALLnew_facets {  /* test samecycle merges */
+      if (!newfacet->simplicial && !newfacet->mergeridge)
+        qh_degen_redundant_neighbors(qh, newfacet, NULL);
+    }
+    if (qh_merge_degenredundant(qh))
+      othermerge= True;
+  }else /* qh->hull_dim == 2 */
+    qh_mergecycle_all(qh, qh->newfacet_list, &othermerge);
+  qh_flippedmerges(qh, qh->newfacet_list, &othermerge);
+  if (!qh->MERGEexact || zzval_(Ztotmerge)) {
+    zinc_(Zpremergetot);
+    qh->POSTmerging= False;
+    qh_getmergeset_initial(qh, qh->newfacet_list);
+    qh_all_merges(qh, othermerge, False);
+  }
+  qh_settempfree(qh, &qh->facet_mergeset);
+  qh_settempfree(qh, &qh->degen_mergeset);
+} /* premerge */
+
+/*-<a                             href="qh-merge_r.htm#TOC"
+  >-------------------------------</a><a name="postmerge">-</a>
+
+  qh_postmerge(qh, reason, maxcentrum, maxangle, vneighbors )
+    post-merge nonconvex facets as defined by maxcentrum and maxangle
+    'reason' is for reporting progress
+    if vneighbors,
+      calls qh_test_vneighbors at end of qh_all_merge
+    if firstmerge,
+      calls qh_reducevertices before qh_getmergeset
+
+  returns:
+    if first call (qh.visible_list != qh.facet_list),
+      builds qh.facet_newlist, qh.newvertex_list
+    deleted facets added to qh.visible_list with facet->visible
+    qh.visible_list == qh.facet_list
+
+  notes:
+
+
+  design:
+    if first call
+      set qh.visible_list and qh.newfacet_list to qh.facet_list
+      add all facets to qh.newfacet_list
+      mark non-simplicial facets, facet->newmerge
+      set qh.newvertext_list to qh.vertex_list
+      add all vertices to qh.newvertex_list
+      if a pre-merge occured
+        set vertex->delridge {will retest the ridge}
+        if qh.MERGEexact
+          call qh_reducevertices()
+      if no pre-merging
+        merge flipped facets
+    determine non-convex facets
+    merge all non-convex facets
+*/
+void qh_postmerge(qhT *qh, const char *reason, realT maxcentrum, realT maxangle,
+                      boolT vneighbors) {
+  facetT *newfacet;
+  boolT othermerges= False;
+  vertexT *vertex;
+
+  if (qh->REPORTfreq || qh->IStracing) {
+    qh_buildtracing(qh, NULL, NULL);
+    qh_printsummary(qh, qh->ferr);
+    if (qh->PRINTstatistics)
+      qh_printallstatistics(qh, qh->ferr, "reason");
+    qh_fprintf(qh, qh->ferr, 8062, "\n%s with 'C%.2g' and 'A%.2g'\n",
+        reason, maxcentrum, maxangle);
+  }
+  trace2((qh, qh->ferr, 2009, "qh_postmerge: postmerge.  test vneighbors? %d\n",
+            vneighbors));
+  qh->centrum_radius= maxcentrum;
+  qh->cos_max= maxangle;
+  qh->POSTmerging= True;
+  qh->degen_mergeset= qh_settemp(qh, qh->TEMPsize);
+  qh->facet_mergeset= qh_settemp(qh, qh->TEMPsize);
+  if (qh->visible_list != qh->facet_list) {  /* first call */
+    qh->NEWfacets= True;
+    qh->visible_list= qh->newfacet_list= qh->facet_list;
+    FORALLnew_facets {
+      newfacet->newfacet= True;
+       if (!newfacet->simplicial)
+        newfacet->newmerge= True;
+     zinc_(Zpostfacets);
+    }
+    qh->newvertex_list= qh->vertex_list;
+    FORALLvertices
+      vertex->newlist= True;
+    if (qh->VERTEXneighbors) { /* a merge has occurred */
+      FORALLvertices
+        vertex->delridge= True; /* test for redundant, needed? */
+      if (qh->MERGEexact) {
+        if (qh->hull_dim <= qh_DIMreduceBuild)
+          qh_reducevertices(qh); /* was skipped during pre-merging */
+      }
+    }
+    if (!qh->PREmerge && !qh->MERGEexact)
+      qh_flippedmerges(qh, qh->newfacet_list, &othermerges);
+  }
+  qh_getmergeset_initial(qh, qh->newfacet_list);
+  qh_all_merges(qh, False, vneighbors);
+  qh_settempfree(qh, &qh->facet_mergeset);
+  qh_settempfree(qh, &qh->degen_mergeset);
+} /* post_merge */
+
+/*-<a                             href="qh-merge_r.htm#TOC"
+  >-------------------------------</a><a name="all_merges">-</a>
+
+  qh_all_merges(qh, othermerge, vneighbors )
+    merge all non-convex facets
+
+    set othermerge if already merged facets (for qh_reducevertices)
+    if vneighbors
+      tests vertex neighbors for convexity at end
+    qh.facet_mergeset lists the non-convex ridges in qh_newfacet_list
+    qh.degen_mergeset is defined
+    if qh.MERGEexact && !qh.POSTmerging,
+      does not merge coplanar facets
+
+  returns:
+    deleted facets added to qh.visible_list with facet->visible
+    deleted vertices added qh.delvertex_list with vertex->delvertex
+
+  notes:
+    unless !qh.MERGEindependent,
+      merges facets in independent sets
+    uses qh.newfacet_list as argument since merges call qh_removefacet()
+
+  design:
+    while merges occur
+      for each merge in qh.facet_mergeset
+        unless one of the facets was already merged in this pass
+          merge the facets
+        test merged facets for additional merges
+        add merges to qh.facet_mergeset
+      if vertices record neighboring facets
+        rename redundant vertices
+          update qh.facet_mergeset
+    if vneighbors ??
+      tests vertex neighbors for convexity at end
+*/
+void qh_all_merges(qhT *qh, boolT othermerge, boolT vneighbors) {
+  facetT *facet1, *facet2;
+  mergeT *merge;
+  boolT wasmerge= True, isreduce;
+  void **freelistp;  /* used if !qh_NOmem by qh_memfree_() */
+  vertexT *vertex;
+  mergeType mergetype;
+  int numcoplanar=0, numconcave=0, numdegenredun= 0, numnewmerges= 0;
+
+  trace2((qh, qh->ferr, 2010, "qh_all_merges: starting to merge facets beginning from f%d\n",
+            getid_(qh->newfacet_list)));
+  while (True) {
+    wasmerge= False;
+    while (qh_setsize(qh, qh->facet_mergeset)) {
+      while ((merge= (mergeT*)qh_setdellast(qh->facet_mergeset))) {
+        facet1= merge->facet1;
+        facet2= merge->facet2;
+        mergetype= merge->type;
+        qh_memfree_(qh, merge, (int)sizeof(mergeT), freelistp);
+        if (facet1->visible || facet2->visible) /*deleted facet*/
+          continue;
+        if ((facet1->newfacet && !facet1->tested)
+                || (facet2->newfacet && !facet2->tested)) {
+          if (qh->MERGEindependent && mergetype <= MRGanglecoplanar)
+            continue;      /* perform independent sets of merges */
+        }
+        qh_merge_nonconvex(qh, facet1, facet2, mergetype);
+        numdegenredun += qh_merge_degenredundant(qh);
+        numnewmerges++;
+        wasmerge= True;
+        if (mergetype == MRGconcave)
+          numconcave++;
+        else /* MRGcoplanar or MRGanglecoplanar */
+          numcoplanar++;
+      } /* while setdellast */
+      if (qh->POSTmerging && qh->hull_dim <= qh_DIMreduceBuild
+      && numnewmerges > qh_MAXnewmerges) {
+        numnewmerges= 0;
+        qh_reducevertices(qh);  /* otherwise large post merges too slow */
+      }
+      qh_getmergeset(qh, qh->newfacet_list); /* facet_mergeset */
+    } /* while mergeset */
+    if (qh->VERTEXneighbors) {
+      isreduce= False;
+      if (qh->hull_dim >=4 && qh->POSTmerging) {
+        FORALLvertices
+          vertex->delridge= True;
+        isreduce= True;
+      }
+      if ((wasmerge || othermerge) && (!qh->MERGEexact || qh->POSTmerging)
+          && qh->hull_dim <= qh_DIMreduceBuild) {
+        othermerge= False;
+        isreduce= True;
+      }
+      if (isreduce) {
+        if (qh_reducevertices(qh)) {
+          qh_getmergeset(qh, qh->newfacet_list); /* facet_mergeset */
+          continue;
+        }
+      }
+    }
+    if (vneighbors && qh_test_vneighbors(qh /* qh->newfacet_list */))
+      continue;
+    break;
+  } /* while (True) */
+  if (qh->CHECKfrequently && !qh->MERGEexact) {
+    qh->old_randomdist= qh->RANDOMdist;
+    qh->RANDOMdist= False;
+    qh_checkconvex(qh, qh->newfacet_list, qh_ALGORITHMfault);
+    /* qh_checkconnect(qh); [this is slow and it changes the facet order] */
+    qh->RANDOMdist= qh->old_randomdist;
+  }
+  trace1((qh, qh->ferr, 1009, "qh_all_merges: merged %d coplanar facets %d concave facets and %d degen or redundant facets.\n",
+    numcoplanar, numconcave, numdegenredun));
+  if (qh->IStracing >= 4 && qh->num_facets < 50)
+    qh_printlists(qh);
+} /* all_merges */
+
+
+/*-<a                             href="qh-merge_r.htm#TOC"
+  >-------------------------------</a><a name="appendmergeset">-</a>
+
+  qh_appendmergeset(qh, facet, neighbor, mergetype, angle )
+    appends an entry to qh.facet_mergeset or qh.degen_mergeset
+
+    angle ignored if NULL or !qh.ANGLEmerge
+
+  returns:
+    merge appended to facet_mergeset or degen_mergeset
+      sets ->degenerate or ->redundant if degen_mergeset
+
+  see:
+    qh_test_appendmerge()
+
+  design:
+    allocate merge entry
+    if regular merge
+      append to qh.facet_mergeset
+    else if degenerate merge and qh.facet_mergeset is all degenerate
+      append to qh.degen_mergeset
+    else if degenerate merge
+      prepend to qh.degen_mergeset
+    else if redundant merge
+      append to qh.degen_mergeset
+*/
+void qh_appendmergeset(qhT *qh, facetT *facet, facetT *neighbor, mergeType mergetype, realT *angle) {
+  mergeT *merge, *lastmerge;
+  void **freelistp; /* used if !qh_NOmem by qh_memalloc_() */
+
+  if (facet->redundant)
+    return;
+  if (facet->degenerate && mergetype == MRGdegen)
+    return;
+  qh_memalloc_(qh, (int)sizeof(mergeT), freelistp, merge, mergeT);
+  merge->facet1= facet;
+  merge->facet2= neighbor;
+  merge->type= mergetype;
+  if (angle && qh->ANGLEmerge)
+    merge->angle= *angle;
+  if (mergetype < MRGdegen)
+    qh_setappend(qh, &(qh->facet_mergeset), merge);
+  else if (mergetype == MRGdegen) {
+    facet->degenerate= True;
+    if (!(lastmerge= (mergeT*)qh_setlast(qh->degen_mergeset))
+    || lastmerge->type == MRGdegen)
+      qh_setappend(qh, &(qh->degen_mergeset), merge);
+    else
+      qh_setaddnth(qh, &(qh->degen_mergeset), 0, merge);
+  }else if (mergetype == MRGredundant) {
+    facet->redundant= True;
+    qh_setappend(qh, &(qh->degen_mergeset), merge);
+  }else /* mergetype == MRGmirror */ {
+    if (facet->redundant || neighbor->redundant) {
+      qh_fprintf(qh, qh->ferr, 6092, "qhull error (qh_appendmergeset): facet f%d or f%d is already a mirrored facet\n",
+           facet->id, neighbor->id);
+      qh_errexit2(qh, qh_ERRqhull, facet, neighbor);
+    }
+    if (!qh_setequal(facet->vertices, neighbor->vertices)) {
+      qh_fprintf(qh, qh->ferr, 6093, "qhull error (qh_appendmergeset): mirrored facets f%d and f%d do not have the same vertices\n",
+           facet->id, neighbor->id);
+      qh_errexit2(qh, qh_ERRqhull, facet, neighbor);
+    }
+    facet->redundant= True;
+    neighbor->redundant= True;
+    qh_setappend(qh, &(qh->degen_mergeset), merge);
+  }
+} /* appendmergeset */
+
+
+/*-<a                             href="qh-merge_r.htm#TOC"
+  >-------------------------------</a><a name="basevertices">-</a>
+
+  qh_basevertices(qh, samecycle )
+    return temporary set of base vertices for samecycle
+    samecycle is first facet in the cycle
+    assumes apex is SETfirst_( samecycle->vertices )
+
+  returns:
+    vertices(settemp)
+    all ->seen are cleared
+
+  notes:
+    uses qh_vertex_visit;
+
+  design:
+    for each facet in samecycle
+      for each unseen vertex in facet->vertices
+        append to result
+*/
+setT *qh_basevertices(qhT *qh, facetT *samecycle) {
+  facetT *same;
+  vertexT *apex, *vertex, **vertexp;
+  setT *vertices= qh_settemp(qh, qh->TEMPsize);
+
+  apex= SETfirstt_(samecycle->vertices, vertexT);
+  apex->visitid= ++qh->vertex_visit;
+  FORALLsame_cycle_(samecycle) {
+    if (same->mergeridge)
+      continue;
+    FOREACHvertex_(same->vertices) {
+      if (vertex->visitid != qh->vertex_visit) {
+        qh_setappend(qh, &vertices, vertex);
+        vertex->visitid= qh->vertex_visit;
+        vertex->seen= False;
+      }
+    }
+  }
+  trace4((qh, qh->ferr, 4019, "qh_basevertices: found %d vertices\n",
+         qh_setsize(qh, vertices)));
+  return vertices;
+} /* basevertices */
+
+/*-<a                             href="qh-merge_r.htm#TOC"
+  >-------------------------------</a><a name="checkconnect">-</a>
+
+  qh_checkconnect(qh)
+    check that new facets are connected
+    new facets are on qh.newfacet_list
+
+  notes:
+    this is slow and it changes the order of the facets
+    uses qh.visit_id
+
+  design:
+    move first new facet to end of qh.facet_list
+    for all newly appended facets
+      append unvisited neighbors to end of qh.facet_list
+    for all new facets
+      report error if unvisited
+*/
+void qh_checkconnect(qhT *qh /* qh->newfacet_list */) {
+  facetT *facet, *newfacet, *errfacet= NULL, *neighbor, **neighborp;
+
+  facet= qh->newfacet_list;
+  qh_removefacet(qh, facet);
+  qh_appendfacet(qh, facet);
+  facet->visitid= ++qh->visit_id;
+  FORALLfacet_(facet) {
+    FOREACHneighbor_(facet) {
+      if (neighbor->visitid != qh->visit_id) {
+        qh_removefacet(qh, neighbor);
+        qh_appendfacet(qh, neighbor);
+        neighbor->visitid= qh->visit_id;
+      }
+    }
+  }
+  FORALLnew_facets {
+    if (newfacet->visitid == qh->visit_id)
+      break;
+    qh_fprintf(qh, qh->ferr, 6094, "qhull error: f%d is not attached to the new facets\n",
+         newfacet->id);
+    errfacet= newfacet;
+  }
+  if (errfacet)
+    qh_errexit(qh, qh_ERRqhull, errfacet, NULL);
+} /* checkconnect */
+
+/*-<a                             href="qh-merge_r.htm#TOC"
+  >-------------------------------</a><a name="checkzero">-</a>
+
+  qh_checkzero(qh, testall )
+    check that facets are clearly convex for qh.DISTround with qh.MERGEexact
+
+    if testall,
+      test all facets for qh.MERGEexact post-merging
+    else
+      test qh.newfacet_list
+
+    if qh.MERGEexact,
+      allows coplanar ridges
+      skips convexity test while qh.ZEROall_ok
+
+  returns:
+    True if all facets !flipped, !dupridge, normal
+         if all horizon facets are simplicial
+         if all vertices are clearly below neighbor
+         if all opposite vertices of horizon are below
+    clears qh.ZEROall_ok if any problems or coplanar facets
+
+  notes:
+    uses qh.vertex_visit
+    horizon facets may define multiple new facets
+
+  design:
+    for all facets in qh.newfacet_list or qh.facet_list
+      check for flagged faults (flipped, etc.)
+    for all facets in qh.newfacet_list or qh.facet_list
+      for each neighbor of facet
+        skip horizon facets for qh.newfacet_list
+        test the opposite vertex
+      if qh.newfacet_list
+        test the other vertices in the facet's horizon facet
+*/
+boolT qh_checkzero(qhT *qh, boolT testall) {
+  facetT *facet, *neighbor, **neighborp;
+  facetT *horizon, *facetlist;
+  int neighbor_i;
+  vertexT *vertex, **vertexp;
+  realT dist;
+
+  if (testall)
+    facetlist= qh->facet_list;
+  else {
+    facetlist= qh->newfacet_list;
+    FORALLfacet_(facetlist) {
+      horizon= SETfirstt_(facet->neighbors, facetT);
+      if (!horizon->simplicial)
+        goto LABELproblem;
+      if (facet->flipped || facet->dupridge || !facet->normal)
+        goto LABELproblem;
+    }
+    if (qh->MERGEexact && qh->ZEROall_ok) {
+      trace2((qh, qh->ferr, 2011, "qh_checkzero: skip convexity check until first pre-merge\n"));
+      return True;
+    }
+  }
+  FORALLfacet_(facetlist) {
+    qh->vertex_visit++;
+    neighbor_i= 0;
+    horizon= NULL;
+    FOREACHneighbor_(facet) {
+      if (!neighbor_i && !testall) {
+        horizon= neighbor;
+        neighbor_i++;
+        continue; /* horizon facet tested in qh_findhorizon */
+      }
+      vertex= SETelemt_(facet->vertices, neighbor_i++, vertexT);
+      vertex->visitid= qh->vertex_visit;
+      zzinc_(Zdistzero);
+      qh_distplane(qh, vertex->point, neighbor, &dist);
+      if (dist >= -qh->DISTround) {
+        qh->ZEROall_ok= False;
+        if (!qh->MERGEexact || testall || dist > qh->DISTround)
+          goto LABELnonconvex;
+      }
+    }
+    if (!testall && horizon) {
+      FOREACHvertex_(horizon->vertices) {
+        if (vertex->visitid != qh->vertex_visit) {
+          zzinc_(Zdistzero);
+          qh_distplane(qh, vertex->point, facet, &dist);
+          if (dist >= -qh->DISTround) {
+            qh->ZEROall_ok= False;
+            if (!qh->MERGEexact || dist > qh->DISTround)
+              goto LABELnonconvex;
+          }
+          break;
+        }
+      }
+    }
+  }
+  trace2((qh, qh->ferr, 2012, "qh_checkzero: testall %d, facets are %s\n", testall,
+        (qh->MERGEexact && !testall) ?
+           "not concave, flipped, or duplicate ridged" : "clearly convex"));
+  return True;
+
+ LABELproblem:
+  qh->ZEROall_ok= False;
+  trace2((qh, qh->ferr, 2013, "qh_checkzero: facet f%d needs pre-merging\n",
+       facet->id));
+  return False;
+
+ LABELnonconvex:
+  trace2((qh, qh->ferr, 2014, "qh_checkzero: facet f%d and f%d are not clearly convex.  v%d dist %.2g\n",
+         facet->id, neighbor->id, vertex->id, dist));
+  return False;
+} /* checkzero */
+
+/*-<a                             href="qh-merge_r.htm#TOC"
+  >-------------------------------</a><a name="compareangle">-</a>
+
+  qh_compareangle(angle1, angle2 )
+    used by qsort() to order merges by angle
+*/
+int qh_compareangle(const void *p1, const void *p2) {
+  const mergeT *a= *((mergeT *const*)p1), *b= *((mergeT *const*)p2);
+
+  return((a->angle > b->angle) ? 1 : -1);
+} /* compareangle */
+
+/*-<a                             href="qh-merge_r.htm#TOC"
+  >-------------------------------</a><a name="comparemerge">-</a>
+
+  qh_comparemerge(merge1, merge2 )
+    used by qsort() to order merges
+*/
+int qh_comparemerge(const void *p1, const void *p2) {
+  const mergeT *a= *((mergeT *const*)p1), *b= *((mergeT *const*)p2);
+
+  return(a->type - b->type);
+} /* comparemerge */
+
+/*-<a                             href="qh-merge_r.htm#TOC"
+  >-------------------------------</a><a name="comparevisit">-</a>
+
+  qh_comparevisit(vertex1, vertex2 )
+    used by qsort() to order vertices by their visitid
+*/
+int qh_comparevisit(const void *p1, const void *p2) {
+  const vertexT *a= *((vertexT *const*)p1), *b= *((vertexT *const*)p2);
+
+  return(a->visitid - b->visitid);
+} /* comparevisit */
+
+/*-<a                             href="qh-merge_r.htm#TOC"
+  >-------------------------------</a><a name="copynonconvex">-</a>
+
+  qh_copynonconvex(qh, atridge )
+    set non-convex flag on other ridges (if any) between same neighbors
+
+  notes:
+    may be faster if use smaller ridge set
+
+  design:
+    for each ridge of atridge's top facet
+      if ridge shares the same neighbor
+        set nonconvex flag
+*/
+void qh_copynonconvex(qhT *qh, ridgeT *atridge) {
+  facetT *facet, *otherfacet;
+  ridgeT *ridge, **ridgep;
+
+  facet= atridge->top;
+  otherfacet= atridge->bottom;
+  FOREACHridge_(facet->ridges) {
+    if (otherfacet == otherfacet_(ridge, facet) && ridge != atridge) {
+      ridge->nonconvex= True;
+      trace4((qh, qh->ferr, 4020, "qh_copynonconvex: moved nonconvex flag from r%d to r%d\n",
+              atridge->id, ridge->id));
+      break;
+    }
+  }
+} /* copynonconvex */
+
+/*-<a                             href="qh-merge_r.htm#TOC"
+  >-------------------------------</a><a name="degen_redundant_facet">-</a>
+
+  qh_degen_redundant_facet(qh, facet )
+    check facet for degen. or redundancy
+
+  notes:
+    bumps vertex_visit
+    called if a facet was redundant but no longer is (qh_merge_degenredundant)
+    qh_appendmergeset() only appends first reference to facet (i.e., redundant)
+
+  see:
+    qh_degen_redundant_neighbors()
+
+  design:
+    test for redundant neighbor
+    test for degenerate facet
+*/
+void qh_degen_redundant_facet(qhT *qh, facetT *facet) {
+  vertexT *vertex, **vertexp;
+  facetT *neighbor, **neighborp;
+
+  trace4((qh, qh->ferr, 4021, "qh_degen_redundant_facet: test facet f%d for degen/redundant\n",
+          facet->id));
+  FOREACHneighbor_(facet) {
+    qh->vertex_visit++;
+    FOREACHvertex_(neighbor->vertices)
+      vertex->visitid= qh->vertex_visit;
+    FOREACHvertex_(facet->vertices) {
+      if (vertex->visitid != qh->vertex_visit)
+        break;
+    }
+    if (!vertex) {
+      qh_appendmergeset(qh, facet, neighbor, MRGredundant, NULL);
+      trace2((qh, qh->ferr, 2015, "qh_degen_redundant_facet: f%d is contained in f%d.  merge\n", facet->id, neighbor->id));
+      return;
+    }
+  }
+  if (qh_setsize(qh, facet->neighbors) < qh->hull_dim) {
+    qh_appendmergeset(qh, facet, facet, MRGdegen, NULL);
+    trace2((qh, qh->ferr, 2016, "qh_degen_redundant_neighbors: f%d is degenerate.\n", facet->id));
+  }
+} /* degen_redundant_facet */
+
+
+/*-<a                             href="qh-merge_r.htm#TOC"
+  >-------------------------------</a><a name="degen_redundant_neighbors">-</a>
+
+  qh_degen_redundant_neighbors(qh, facet, delfacet,  )
+    append degenerate and redundant neighbors to facet_mergeset
+    if delfacet,
+      only checks neighbors of both delfacet and facet
+    also checks current facet for degeneracy
+
+  notes:
+    bumps vertex_visit
+    called for each qh_mergefacet() and qh_mergecycle()
+    merge and statistics occur in merge_nonconvex
+    qh_appendmergeset() only appends first reference to facet (i.e., redundant)
+      it appends redundant facets after degenerate ones
+
+    a degenerate facet has fewer than hull_dim neighbors
+    a redundant facet's vertices is a subset of its neighbor's vertices
+    tests for redundant merges first (appendmergeset is nop for others)
+    in a merge, only needs to test neighbors of merged facet
+
+  see:
+    qh_merge_degenredundant() and qh_degen_redundant_facet()
+
+  design:
+    test for degenerate facet
+    test for redundant neighbor
+    test for degenerate neighbor
+*/
+void qh_degen_redundant_neighbors(qhT *qh, facetT *facet, facetT *delfacet) {
+  vertexT *vertex, **vertexp;
+  facetT *neighbor, **neighborp;
+  int size;
+
+  trace4((qh, qh->ferr, 4022, "qh_degen_redundant_neighbors: test neighbors of f%d with delfacet f%d\n",
+          facet->id, getid_(delfacet)));
+  if ((size= qh_setsize(qh, facet->neighbors)) < qh->hull_dim) {
+    qh_appendmergeset(qh, facet, facet, MRGdegen, NULL);
+    trace2((qh, qh->ferr, 2017, "qh_degen_redundant_neighbors: f%d is degenerate with %d neighbors.\n", facet->id, size));
+  }
+  if (!delfacet)
+    delfacet= facet;
+  qh->vertex_visit++;
+  FOREACHvertex_(facet->vertices)
+    vertex->visitid= qh->vertex_visit;
+  FOREACHneighbor_(delfacet) {
+    /* uses early out instead of checking vertex count */
+    if (neighbor == facet)
+      continue;
+    FOREACHvertex_(neighbor->vertices) {
+      if (vertex->visitid != qh->vertex_visit)
+        break;
+    }
+    if (!vertex) {
+      qh_appendmergeset(qh, neighbor, facet, MRGredundant, NULL);
+      trace2((qh, qh->ferr, 2018, "qh_degen_redundant_neighbors: f%d is contained in f%d.  merge\n", neighbor->id, facet->id));
+    }
+  }
+  FOREACHneighbor_(delfacet) {   /* redundant merges occur first */
+    if (neighbor == facet)
+      continue;
+    if ((size= qh_setsize(qh, neighbor->neighbors)) < qh->hull_dim) {
+      qh_appendmergeset(qh, neighbor, neighbor, MRGdegen, NULL);
+      trace2((qh, qh->ferr, 2019, "qh_degen_redundant_neighbors: f%d is degenerate with %d neighbors.  Neighbor of f%d.\n", neighbor->id, size, facet->id));
+    }
+  }
+} /* degen_redundant_neighbors */
+
+
+/*-<a                             href="qh-merge_r.htm#TOC"
+  >-------------------------------</a><a name="find_newvertex">-</a>
+
+  qh_find_newvertex(qh, oldvertex, vertices, ridges )
+    locate new vertex for renaming old vertex
+    vertices is a set of possible new vertices
+      vertices sorted by number of deleted ridges
+
+  returns:
+    newvertex or NULL
+      each ridge includes both vertex and oldvertex
+    vertices sorted by number of deleted ridges
+
+  notes:
+    modifies vertex->visitid
+    new vertex is in one of the ridges
+    renaming will not cause a duplicate ridge
+    renaming will minimize the number of deleted ridges
+    newvertex may not be adjacent in the dual (though unlikely)
+
+  design:
+    for each vertex in vertices
+      set vertex->visitid to number of references in ridges
+    remove unvisited vertices
+    set qh.vertex_visit above all possible values
+    sort vertices by number of references in ridges
+    add each ridge to qh.hash_table
+    for each vertex in vertices
+      look for a vertex that would not cause a duplicate ridge after a rename
+*/
+vertexT *qh_find_newvertex(qhT *qh, vertexT *oldvertex, setT *vertices, setT *ridges) {
+  vertexT *vertex, **vertexp;
+  setT *newridges;
+  ridgeT *ridge, **ridgep;
+  int size, hashsize;
+  int hash;
+
+#ifndef qh_NOtrace
+  if (qh->IStracing >= 4) {
+    qh_fprintf(qh, qh->ferr, 8063, "qh_find_newvertex: find new vertex for v%d from ",
+             oldvertex->id);
+    FOREACHvertex_(vertices)
+      qh_fprintf(qh, qh->ferr, 8064, "v%d ", vertex->id);
+    FOREACHridge_(ridges)
+      qh_fprintf(qh, qh->ferr, 8065, "r%d ", ridge->id);
+    qh_fprintf(qh, qh->ferr, 8066, "\n");
+  }
+#endif
+  FOREACHvertex_(vertices)
+    vertex->visitid= 0;
+  FOREACHridge_(ridges) {
+    FOREACHvertex_(ridge->vertices)
+      vertex->visitid++;
+  }
+  FOREACHvertex_(vertices) {
+    if (!vertex->visitid) {
+      qh_setdelnth(qh, vertices, SETindex_(vertices,vertex));
+      vertexp--; /* repeat since deleted this vertex */
+    }
+  }
+  qh->vertex_visit += (unsigned int)qh_setsize(qh, ridges);
+  if (!qh_setsize(qh, vertices)) {
+    trace4((qh, qh->ferr, 4023, "qh_find_newvertex: vertices not in ridges for v%d\n",
+            oldvertex->id));
+    return NULL;
+  }
+  qsort(SETaddr_(vertices, vertexT), (size_t)qh_setsize(qh, vertices),
+                sizeof(vertexT *), qh_comparevisit);
+  /* can now use qh->vertex_visit */
+  if (qh->PRINTstatistics) {
+    size= qh_setsize(qh, vertices);
+    zinc_(Zintersect);
+    zadd_(Zintersecttot, size);
+    zmax_(Zintersectmax, size);
+  }
+  hashsize= qh_newhashtable(qh, qh_setsize(qh, ridges));
+  FOREACHridge_(ridges)
+    qh_hashridge(qh, qh->hash_table, hashsize, ridge, oldvertex);
+  FOREACHvertex_(vertices) {
+    newridges= qh_vertexridges(qh, vertex);
+    FOREACHridge_(newridges) {
+      if (qh_hashridge_find(qh, qh->hash_table, hashsize, ridge, vertex, oldvertex, &hash)) {
+        zinc_(Zdupridge);
+        break;
+      }
+    }
+    qh_settempfree(qh, &newridges);
+    if (!ridge)
+      break;  /* found a rename */
+  }
+  if (vertex) {
+    /* counted in qh_renamevertex */
+    trace2((qh, qh->ferr, 2020, "qh_find_newvertex: found v%d for old v%d from %d vertices and %d ridges.\n",
+      vertex->id, oldvertex->id, qh_setsize(qh, vertices), qh_setsize(qh, ridges)));
+  }else {
+    zinc_(Zfindfail);
+    trace0((qh, qh->ferr, 14, "qh_find_newvertex: no vertex for renaming v%d(all duplicated ridges) during p%d\n",
+      oldvertex->id, qh->furthest_id));
+  }
+  qh_setfree(qh, &qh->hash_table);
+  return vertex;
+} /* find_newvertex */
+
+/*-<a                             href="qh-merge_r.htm#TOC"
+  >-------------------------------</a><a name="findbest_test">-</a>
+
+  qh_findbest_test(qh, testcentrum, facet, neighbor, bestfacet, dist, mindist, maxdist )
+    test neighbor of facet for qh_findbestneighbor()
+    if testcentrum,
+      tests centrum (assumes it is defined)
+    else
+      tests vertices
+
+  returns:
+    if a better facet (i.e., vertices/centrum of facet closer to neighbor)
+      updates bestfacet, dist, mindist, and maxdist
+*/
+void qh_findbest_test(qhT *qh, boolT testcentrum, facetT *facet, facetT *neighbor,
+      facetT **bestfacet, realT *distp, realT *mindistp, realT *maxdistp) {
+  realT dist, mindist, maxdist;
+
+  if (testcentrum) {
+    zzinc_(Zbestdist);
+    qh_distplane(qh, facet->center, neighbor, &dist);
+    dist *= qh->hull_dim; /* estimate furthest vertex */
+    if (dist < 0) {
+      maxdist= 0;
+      mindist= dist;
+      dist= -dist;
+    }else {
+      mindist= 0;
+      maxdist= dist;
+    }
+  }else
+    dist= qh_getdistance(qh, facet, neighbor, &mindist, &maxdist);
+  if (dist < *distp) {
+    *bestfacet= neighbor;
+    *mindistp= mindist;
+    *maxdistp= maxdist;
+    *distp= dist;
+  }
+} /* findbest_test */
+
+/*-<a                             href="qh-merge_r.htm#TOC"
+  >-------------------------------</a><a name="findbestneighbor">-</a>
+
+  qh_findbestneighbor(qh, facet, dist, mindist, maxdist )
+    finds best neighbor (least dist) of a facet for merging
+
+  returns:
+    returns min and max distances and their max absolute value
+
+  notes:
+    error if qh_ASvoronoi
+    avoids merging old into new
+    assumes ridge->nonconvex only set on one ridge between a pair of facets
+    could use an early out predicate but not worth it
+
+  design:
+    if a large facet
+      will test centrum
+    else
+      will test vertices
+    if a large facet
+      test nonconvex neighbors for best merge
+    else
+      test all neighbors for the best merge
+    if testing centrum
+      get distance information
+*/
+facetT *qh_findbestneighbor(qhT *qh, facetT *facet, realT *distp, realT *mindistp, realT *maxdistp) {
+  facetT *neighbor, **neighborp, *bestfacet= NULL;
+  ridgeT *ridge, **ridgep;
+  boolT nonconvex= True, testcentrum= False;
+  int size= qh_setsize(qh, facet->vertices);
+
+  if(qh->CENTERtype==qh_ASvoronoi){
+    qh_fprintf(qh, qh->ferr, 6272, "qhull error: cannot call qh_findbestneighor for f%d while qh.CENTERtype is qh_ASvoronoi\n", facet->id);
+    qh_errexit(qh, qh_ERRqhull, facet, NULL);
+  }
+  *distp= REALmax;
+  if (size > qh_BESTcentrum2 * qh->hull_dim + qh_BESTcentrum) {
+    testcentrum= True;
+    zinc_(Zbestcentrum);
+    if (!facet->center)
+       facet->center= qh_getcentrum(qh, facet);
+  }
+  if (size > qh->hull_dim + qh_BESTnonconvex) {
+    FOREACHridge_(facet->ridges) {
+      if (ridge->nonconvex) {
+        neighbor= otherfacet_(ridge, facet);
+        qh_findbest_test(qh, testcentrum, facet, neighbor,
+                          &bestfacet, distp, mindistp, maxdistp);
+      }
+    }
+  }
+  if (!bestfacet) {
+    nonconvex= False;
+    FOREACHneighbor_(facet)
+      qh_findbest_test(qh, testcentrum, facet, neighbor,
+                        &bestfacet, distp, mindistp, maxdistp);
+  }
+  if (!bestfacet) {
+    qh_fprintf(qh, qh->ferr, 6095, "qhull internal error (qh_findbestneighbor): no neighbors for f%d\n", facet->id);
+    qh_errexit(qh, qh_ERRqhull, facet, NULL);
+  }
+  if (testcentrum)
+    qh_getdistance(qh, facet, bestfacet, mindistp, maxdistp);
+  trace3((qh, qh->ferr, 3002, "qh_findbestneighbor: f%d is best neighbor for f%d testcentrum? %d nonconvex? %d dist %2.2g min %2.2g max %2.2g\n",
+     bestfacet->id, facet->id, testcentrum, nonconvex, *distp, *mindistp, *maxdistp));
+  return(bestfacet);
+} /* findbestneighbor */
+
+
+/*-<a                             href="qh-merge_r.htm#TOC"
+  >-------------------------------</a><a name="flippedmerges">-</a>
+
+  qh_flippedmerges(qh, facetlist, wasmerge )
+    merge flipped facets into best neighbor
+    assumes qh.facet_mergeset at top of temporary stack
+
+  returns:
+    no flipped facets on facetlist
+    sets wasmerge if merge occurred
+    degen/redundant merges passed through
+
+  notes:
+    othermerges not needed since qh.facet_mergeset is empty before & after
+      keep it in case of change
+
+  design:
+    append flipped facets to qh.facetmergeset
+    for each flipped merge
+      find best neighbor
+      merge facet into neighbor
+      merge degenerate and redundant facets
+    remove flipped merges from qh.facet_mergeset
+*/
+void qh_flippedmerges(qhT *qh, facetT *facetlist, boolT *wasmerge) {
+  facetT *facet, *neighbor, *facet1;
+  realT dist, mindist, maxdist;
+  mergeT *merge, **mergep;
+  setT *othermerges;
+  int nummerge=0;
+
+  trace4((qh, qh->ferr, 4024, "qh_flippedmerges: begin\n"));
+  FORALLfacet_(facetlist) {
+    if (facet->flipped && !facet->visible)
+      qh_appendmergeset(qh, facet, facet, MRGflip, NULL);
+  }
+  othermerges= qh_settemppop(qh); /* was facet_mergeset */
+  qh->facet_mergeset= qh_settemp(qh, qh->TEMPsize);
+  qh_settemppush(qh, othermerges);
+  FOREACHmerge_(othermerges) {
+    facet1= merge->facet1;
+    if (merge->type != MRGflip || facet1->visible)
+      continue;
+    if (qh->TRACEmerge-1 == zzval_(Ztotmerge))
+      qh->qhmem.IStracing= qh->IStracing= qh->TRACElevel;
+    neighbor= qh_findbestneighbor(qh, facet1, &dist, &mindist, &maxdist);
+    trace0((qh, qh->ferr, 15, "qh_flippedmerges: merge flipped f%d into f%d dist %2.2g during p%d\n",
+      facet1->id, neighbor->id, dist, qh->furthest_id));
+    qh_mergefacet(qh, facet1, neighbor, &mindist, &maxdist, !qh_MERGEapex);
+    nummerge++;
+    if (qh->PRINTstatistics) {
+      zinc_(Zflipped);
+      wadd_(Wflippedtot, dist);
+      wmax_(Wflippedmax, dist);
+    }
+    qh_merge_degenredundant(qh);
+  }
+  FOREACHmerge_(othermerges) {
+    if (merge->facet1->visible || merge->facet2->visible)
+      qh_memfree(qh, merge, (int)sizeof(mergeT));
+    else
+      qh_setappend(qh, &qh->facet_mergeset, merge);
+  }
+  qh_settempfree(qh, &othermerges);
+  if (nummerge)
+    *wasmerge= True;
+  trace1((qh, qh->ferr, 1010, "qh_flippedmerges: merged %d flipped facets into a good neighbor\n", nummerge));
+} /* flippedmerges */
+
+
+/*-<a                             href="qh-merge_r.htm#TOC"
+  >-------------------------------</a><a name="forcedmerges">-</a>
+
+  qh_forcedmerges(qh, wasmerge )
+    merge duplicated ridges
+
+  returns:
+    removes all duplicate ridges on facet_mergeset
+    wasmerge set if merge
+    qh.facet_mergeset may include non-forced merges(none for now)
+    qh.degen_mergeset includes degen/redun merges
+
+  notes:
+    duplicate ridges occur when the horizon is pinched,
+        i.e. a subridge occurs in more than two horizon ridges.
+     could rename vertices that pinch the horizon
+    assumes qh_merge_degenredundant() has not be called
+    othermerges isn't needed since facet_mergeset is empty afterwards
+      keep it in case of change
+
+  design:
+    for each duplicate ridge
+      find current facets by chasing f.replace links
+      check for wide merge due to duplicate ridge
+      determine best direction for facet
+      merge one facet into the other
+      remove duplicate ridges from qh.facet_mergeset
+*/
+void qh_forcedmerges(qhT *qh, boolT *wasmerge) {
+  facetT *facet1, *facet2;
+  mergeT *merge, **mergep;
+  realT dist1, dist2, mindist1, mindist2, maxdist1, maxdist2;
+  setT *othermerges;
+  int nummerge=0, numflip=0;
+
+  if (qh->TRACEmerge-1 == zzval_(Ztotmerge))
+    qh->qhmem.IStracing= qh->IStracing= qh->TRACElevel;
+  trace4((qh, qh->ferr, 4025, "qh_forcedmerges: begin\n"));
+  othermerges= qh_settemppop(qh); /* was facet_mergeset */
+  qh->facet_mergeset= qh_settemp(qh, qh->TEMPsize);
+  qh_settemppush(qh, othermerges);
+  FOREACHmerge_(othermerges) {
+    if (merge->type != MRGridge)
+        continue;
+    if (qh->TRACEmerge-1 == zzval_(Ztotmerge))
+        qh->qhmem.IStracing= qh->IStracing= qh->TRACElevel;
+    facet1= merge->facet1;
+    facet2= merge->facet2;
+    while (facet1->visible)      /* must exist, no qh_merge_degenredunant */
+      facet1= facet1->f.replace; /* previously merged facet */
+    while (facet2->visible)
+      facet2= facet2->f.replace; /* previously merged facet */
+    if (facet1 == facet2)
+      continue;
+    if (!qh_setin(facet2->neighbors, facet1)) {
+      qh_fprintf(qh, qh->ferr, 6096, "qhull internal error (qh_forcedmerges): f%d and f%d had a duplicate ridge but as f%d and f%d they are no longer neighbors\n",
+               merge->facet1->id, merge->facet2->id, facet1->id, facet2->id);
+      qh_errexit2(qh, qh_ERRqhull, facet1, facet2);
+    }
+    dist1= qh_getdistance(qh, facet1, facet2, &mindist1, &maxdist1);
+    dist2= qh_getdistance(qh, facet2, facet1, &mindist2, &maxdist2);
+    qh_check_dupridge(qh, facet1, dist1, facet2, dist2);
+    if (dist1 < dist2)
+      qh_mergefacet(qh, facet1, facet2, &mindist1, &maxdist1, !qh_MERGEapex);
+    else {
+      qh_mergefacet(qh, facet2, facet1, &mindist2, &maxdist2, !qh_MERGEapex);
+      dist1= dist2;
+      facet1= facet2;
+    }
+    if (facet1->flipped) {
+      zinc_(Zmergeflipdup);
+      numflip++;
+    }else
+      nummerge++;
+    if (qh->PRINTstatistics) {
+      zinc_(Zduplicate);
+      wadd_(Wduplicatetot, dist1);
+      wmax_(Wduplicatemax, dist1);
+    }
+  }
+  FOREACHmerge_(othermerges) {
+    if (merge->type == MRGridge)
+      qh_memfree(qh, merge, (int)sizeof(mergeT));
+    else
+      qh_setappend(qh, &qh->facet_mergeset, merge);
+  }
+  qh_settempfree(qh, &othermerges);
+  if (nummerge)
+    *wasmerge= True;
+  trace1((qh, qh->ferr, 1011, "qh_forcedmerges: merged %d facets and %d flipped facets across duplicated ridges\n",
+                nummerge, numflip));
+} /* forcedmerges */
+
+
+/*-<a                             href="qh-merge_r.htm#TOC"
+  >-------------------------------</a><a name="getmergeset">-</a>
+
+  qh_getmergeset(qh, facetlist )
+    determines nonconvex facets on facetlist
+    tests !tested ridges and nonconvex ridges of !tested facets
+
+  returns:
+    returns sorted qh.facet_mergeset of facet-neighbor pairs to be merged
+    all ridges tested
+
+  notes:
+    assumes no nonconvex ridges with both facets tested
+    uses facet->tested/ridge->tested to prevent duplicate tests
+    can not limit tests to modified ridges since the centrum changed
+    uses qh.visit_id
+
+  see:
+    qh_getmergeset_initial()
+
+  design:
+    for each facet on facetlist
+      for each ridge of facet
+        if untested ridge
+          test ridge for convexity
+          if non-convex
+            append ridge to qh.facet_mergeset
+    sort qh.facet_mergeset by angle
+*/
+void qh_getmergeset(qhT *qh, facetT *facetlist) {
+  facetT *facet, *neighbor, **neighborp;
+  ridgeT *ridge, **ridgep;
+  int nummerges;
+
+  nummerges= qh_setsize(qh, qh->facet_mergeset);
+  trace4((qh, qh->ferr, 4026, "qh_getmergeset: started.\n"));
+  qh->visit_id++;
+  FORALLfacet_(facetlist) {
+    if (facet->tested)
+      continue;
+    facet->visitid= qh->visit_id;
+    facet->tested= True;  /* must be non-simplicial due to merge */
+    FOREACHneighbor_(facet)
+      neighbor->seen= False;
+    FOREACHridge_(facet->ridges) {
+      if (ridge->tested && !ridge->nonconvex)
+        continue;
+      /* if tested & nonconvex, need to append merge */
+      neighbor= otherfacet_(ridge, facet);
+      if (neighbor->seen) {
+        ridge->tested= True;
+        ridge->nonconvex= False;
+      }else if (neighbor->visitid != qh->visit_id) {
+        ridge->tested= True;
+        ridge->nonconvex= False;
+        neighbor->seen= True;      /* only one ridge is marked nonconvex */
+        if (qh_test_appendmerge(qh, facet, neighbor))
+          ridge->nonconvex= True;
+      }
+    }
+  }
+  nummerges= qh_setsize(qh, qh->facet_mergeset);
+  if (qh->ANGLEmerge)
+    qsort(SETaddr_(qh->facet_mergeset, mergeT), (size_t)nummerges, sizeof(mergeT *), qh_compareangle);
+  else
+    qsort(SETaddr_(qh->facet_mergeset, mergeT), (size_t)nummerges, sizeof(mergeT *), qh_comparemerge);
+  if (qh->POSTmerging) {
+    zadd_(Zmergesettot2, nummerges);
+  }else {
+    zadd_(Zmergesettot, nummerges);
+    zmax_(Zmergesetmax, nummerges);
+  }
+  trace2((qh, qh->ferr, 2021, "qh_getmergeset: %d merges found\n", nummerges));
+} /* getmergeset */
+
+
+/*-<a                             href="qh-merge_r.htm#TOC"
+  >-------------------------------</a><a name="getmergeset_initial">-</a>
+
+  qh_getmergeset_initial(qh, facetlist )
+    determine initial qh.facet_mergeset for facets
+    tests all facet/neighbor pairs on facetlist
+
+  returns:
+    sorted qh.facet_mergeset with nonconvex ridges
+    sets facet->tested, ridge->tested, and ridge->nonconvex
+
+  notes:
+    uses visit_id, assumes ridge->nonconvex is False
+
+  see:
+    qh_getmergeset()
+
+  design:
+    for each facet on facetlist
+      for each untested neighbor of facet
+        test facet and neighbor for convexity
+        if non-convex
+          append merge to qh.facet_mergeset
+          mark one of the ridges as nonconvex
+    sort qh.facet_mergeset by angle
+*/
+void qh_getmergeset_initial(qhT *qh, facetT *facetlist) {
+  facetT *facet, *neighbor, **neighborp;
+  ridgeT *ridge, **ridgep;
+  int nummerges;
+
+  qh->visit_id++;
+  FORALLfacet_(facetlist) {
+    facet->visitid= qh->visit_id;
+    facet->tested= True;
+    FOREACHneighbor_(facet) {
+      if (neighbor->visitid != qh->visit_id) {
+        if (qh_test_appendmerge(qh, facet, neighbor)) {
+          FOREACHridge_(neighbor->ridges) {
+            if (facet == otherfacet_(ridge, neighbor)) {
+              ridge->nonconvex= True;
+              break;    /* only one ridge is marked nonconvex */
+            }
+          }
+        }
+      }
+    }
+    FOREACHridge_(facet->ridges)
+      ridge->tested= True;
+  }
+  nummerges= qh_setsize(qh, qh->facet_mergeset);
+  if (qh->ANGLEmerge)
+    qsort(SETaddr_(qh->facet_mergeset, mergeT), (size_t)nummerges, sizeof(mergeT *), qh_compareangle);
+  else
+    qsort(SETaddr_(qh->facet_mergeset, mergeT), (size_t)nummerges, sizeof(mergeT *), qh_comparemerge);
+  if (qh->POSTmerging) {
+    zadd_(Zmergeinittot2, nummerges);
+  }else {
+    zadd_(Zmergeinittot, nummerges);
+    zmax_(Zmergeinitmax, nummerges);
+  }
+  trace2((qh, qh->ferr, 2022, "qh_getmergeset_initial: %d merges found\n", nummerges));
+} /* getmergeset_initial */
+
+
+/*-<a                             href="qh-merge_r.htm#TOC"
+  >-------------------------------</a><a name="hashridge">-</a>
+
+  qh_hashridge(qh, hashtable, hashsize, ridge, oldvertex )
+    add ridge to hashtable without oldvertex
+
+  notes:
+    assumes hashtable is large enough
+
+  design:
+    determine hash value for ridge without oldvertex
+    find next empty slot for ridge
+*/
+void qh_hashridge(qhT *qh, setT *hashtable, int hashsize, ridgeT *ridge, vertexT *oldvertex) {
+  int hash;
+  ridgeT *ridgeA;
+
+  hash= qh_gethash(qh, hashsize, ridge->vertices, qh->hull_dim-1, 0, oldvertex);
+  while (True) {
+    if (!(ridgeA= SETelemt_(hashtable, hash, ridgeT))) {
+      SETelem_(hashtable, hash)= ridge;
+      break;
+    }else if (ridgeA == ridge)
+      break;
+    if (++hash == hashsize)
+      hash= 0;
+  }
+} /* hashridge */
+
+
+/*-<a                             href="qh-merge_r.htm#TOC"
+  >-------------------------------</a><a name="hashridge_find">-</a>
+
+  qh_hashridge_find(qh, hashtable, hashsize, ridge, vertex, oldvertex, hashslot )
+    returns matching ridge without oldvertex in hashtable
+      for ridge without vertex
+    if oldvertex is NULL
+      matches with any one skip
+
+  returns:
+    matching ridge or NULL
+    if no match,
+      if ridge already in   table
+        hashslot= -1
+      else
+        hashslot= next NULL index
+
+  notes:
+    assumes hashtable is large enough
+    can't match ridge to itself
+
+  design:
+    get hash value for ridge without vertex
+    for each hashslot
+      return match if ridge matches ridgeA without oldvertex
+*/
+ridgeT *qh_hashridge_find(qhT *qh, setT *hashtable, int hashsize, ridgeT *ridge,
+              vertexT *vertex, vertexT *oldvertex, int *hashslot) {
+  int hash;
+  ridgeT *ridgeA;
+
+  *hashslot= 0;
+  zinc_(Zhashridge);
+  hash= qh_gethash(qh, hashsize, ridge->vertices, qh->hull_dim-1, 0, vertex);
+  while ((ridgeA= SETelemt_(hashtable, hash, ridgeT))) {
+    if (ridgeA == ridge)
+      *hashslot= -1;
+    else {
+      zinc_(Zhashridgetest);
+      if (qh_setequal_except(ridge->vertices, vertex, ridgeA->vertices, oldvertex))
+        return ridgeA;
+    }
+    if (++hash == hashsize)
+      hash= 0;
+  }
+  if (!*hashslot)
+    *hashslot= hash;
+  return NULL;
+} /* hashridge_find */
+
+
+/*-<a                             href="qh-merge_r.htm#TOC"
+  >-------------------------------</a><a name="makeridges">-</a>
+
+  qh_makeridges(qh, facet )
+    creates explicit ridges between simplicial facets
+
+  returns:
+    facet with ridges and without qh_MERGEridge
+    ->simplicial is False
+
+  notes:
+    allows qh_MERGEridge flag
+    uses existing ridges
+    duplicate neighbors ok if ridges already exist (qh_mergecycle_ridges)
+
+  see:
+    qh_mergecycle_ridges()
+
+  design:
+    look for qh_MERGEridge neighbors
+    mark neighbors that already have ridges
+    for each unprocessed neighbor of facet
+      create a ridge for neighbor and facet
+    if any qh_MERGEridge neighbors
+      delete qh_MERGEridge flags (already handled by qh_mark_dupridges)
+*/
+void qh_makeridges(qhT *qh, facetT *facet) {
+  facetT *neighbor, **neighborp;
+  ridgeT *ridge, **ridgep;
+  int neighbor_i, neighbor_n;
+  boolT toporient, mergeridge= False;
+
+  if (!facet->simplicial)
+    return;
+  trace4((qh, qh->ferr, 4027, "qh_makeridges: make ridges for f%d\n", facet->id));
+  facet->simplicial= False;
+  FOREACHneighbor_(facet) {
+    if (neighbor == qh_MERGEridge)
+      mergeridge= True;
+    else
+      neighbor->seen= False;
+  }
+  FOREACHridge_(facet->ridges)
+    otherfacet_(ridge, facet)->seen= True;
+  FOREACHneighbor_i_(qh, facet) {
+    if (neighbor == qh_MERGEridge)
+      continue;  /* fixed by qh_mark_dupridges */
+    else if (!neighbor->seen) {  /* no current ridges */
+      ridge= qh_newridge(qh);
+      ridge->vertices= qh_setnew_delnthsorted(qh, facet->vertices, qh->hull_dim,
+                                                          neighbor_i, 0);
+      toporient= facet->toporient ^ (neighbor_i & 0x1);
+      if (toporient) {
+        ridge->top= facet;
+        ridge->bottom= neighbor;
+      }else {
+        ridge->top= neighbor;
+        ridge->bottom= facet;
+      }
+#if 0 /* this also works */
+      flip= (facet->toporient ^ neighbor->toporient)^(skip1 & 0x1) ^ (skip2 & 0x1);
+      if (facet->toporient ^ (skip1 & 0x1) ^ flip) {
+        ridge->top= neighbor;
+        ridge->bottom= facet;
+      }else {
+        ridge->top= facet;
+        ridge->bottom= neighbor;
+      }
+#endif
+      qh_setappend(qh, &(facet->ridges), ridge);
+      qh_setappend(qh, &(neighbor->ridges), ridge);
+    }
+  }
+  if (mergeridge) {
+    while (qh_setdel(facet->neighbors, qh_MERGEridge))
+      ; /* delete each one */
+  }
+} /* makeridges */
+
+
+/*-<a                             href="qh-merge_r.htm#TOC"
+  >-------------------------------</a><a name="mark_dupridges">-</a>
+
+  qh_mark_dupridges(qh, facetlist )
+    add duplicated ridges to qh.facet_mergeset
+    facet->dupridge is true
+
+  returns:
+    duplicate ridges on qh.facet_mergeset
+    ->mergeridge/->mergeridge2 set
+    duplicate ridges marked by qh_MERGEridge and both sides facet->dupridge
+    no MERGEridges in neighbor sets
+
+  notes:
+    duplicate ridges occur when the horizon is pinched,
+        i.e. a subridge occurs in more than two horizon ridges.
+    could rename vertices that pinch the horizon (thus removing subridge)
+    uses qh.visit_id
+
+  design:
+    for all facets on facetlist
+      if facet contains a duplicate ridge
+        for each neighbor of facet
+          if neighbor marked qh_MERGEridge (one side of the merge)
+            set facet->mergeridge
+          else
+            if neighbor contains a duplicate ridge
+            and the back link is qh_MERGEridge
+              append duplicate ridge to qh.facet_mergeset
+   for each duplicate ridge
+     make ridge sets in preparation for merging
+     remove qh_MERGEridge from neighbor set
+   for each duplicate ridge
+     restore the missing neighbor from the neighbor set that was qh_MERGEridge
+     add the missing ridge for this neighbor
+*/
+void qh_mark_dupridges(qhT *qh, facetT *facetlist) {
+  facetT *facet, *neighbor, **neighborp;
+  int nummerge=0;
+  mergeT *merge, **mergep;
+
+
+  trace4((qh, qh->ferr, 4028, "qh_mark_dupridges: identify duplicate ridges\n"));
+  FORALLfacet_(facetlist) {
+    if (facet->dupridge) {
+      FOREACHneighbor_(facet) {
+        if (neighbor == qh_MERGEridge) {
+          facet->mergeridge= True;
+          continue;
+        }
+        if (neighbor->dupridge
+        && !qh_setin(neighbor->neighbors, facet)) { /* qh_MERGEridge */
+          qh_appendmergeset(qh, facet, neighbor, MRGridge, NULL);
+          facet->mergeridge2= True;
+          facet->mergeridge= True;
+          nummerge++;
+        }
+      }
+    }
+  }
+  if (!nummerge)
+    return;
+  FORALLfacet_(facetlist) {            /* gets rid of qh_MERGEridge */
+    if (facet->mergeridge && !facet->mergeridge2)
+      qh_makeridges(qh, facet);
+  }
+  FOREACHmerge_(qh->facet_mergeset) {   /* restore the missing neighbors */
+    if (merge->type == MRGridge) {
+      qh_setappend(qh, &merge->facet2->neighbors, merge->facet1);
+      qh_makeridges(qh, merge->facet1);   /* and the missing ridges */
+    }
+  }
+  trace1((qh, qh->ferr, 1012, "qh_mark_dupridges: found %d duplicated ridges\n",
+                nummerge));
+} /* mark_dupridges */
+
+/*-<a                             href="qh-merge_r.htm#TOC"
+  >-------------------------------</a><a name="maydropneighbor">-</a>
+
+  qh_maydropneighbor(qh, facet )
+    drop neighbor relationship if no ridge between facet and neighbor
+
+  returns:
+    neighbor sets updated
+    appends degenerate facets to qh.facet_mergeset
+
+  notes:
+    won't cause redundant facets since vertex inclusion is the same
+    may drop vertex and neighbor if no ridge
+    uses qh.visit_id
+
+  design:
+    visit all neighbors with ridges
+    for each unvisited neighbor of facet
+      delete neighbor and facet from the neighbor sets
+      if neighbor becomes degenerate
+        append neighbor to qh.degen_mergeset
+    if facet is degenerate
+      append facet to qh.degen_mergeset
+*/
+void qh_maydropneighbor(qhT *qh, facetT *facet) {
+  ridgeT *ridge, **ridgep;
+  realT angledegen= qh_ANGLEdegen;
+  facetT *neighbor, **neighborp;
+
+  qh->visit_id++;
+  trace4((qh, qh->ferr, 4029, "qh_maydropneighbor: test f%d for no ridges to a neighbor\n",
+          facet->id));
+  FOREACHridge_(facet->ridges) {
+    ridge->top->visitid= qh->visit_id;
+    ridge->bottom->visitid= qh->visit_id;
+  }
+  FOREACHneighbor_(facet) {
+    if (neighbor->visitid != qh->visit_id) {
+      trace0((qh, qh->ferr, 17, "qh_maydropneighbor: facets f%d and f%d are no longer neighbors during p%d\n",
+            facet->id, neighbor->id, qh->furthest_id));
+      zinc_(Zdropneighbor);
+      qh_setdel(facet->neighbors, neighbor);
+      neighborp--;  /* repeat, deleted a neighbor */
+      qh_setdel(neighbor->neighbors, facet);
+      if (qh_setsize(qh, neighbor->neighbors) < qh->hull_dim) {
+        zinc_(Zdropdegen);
+        qh_appendmergeset(qh, neighbor, neighbor, MRGdegen, &angledegen);
+        trace2((qh, qh->ferr, 2023, "qh_maydropneighbors: f%d is degenerate.\n", neighbor->id));
+      }
+    }
+  }
+  if (qh_setsize(qh, facet->neighbors) < qh->hull_dim) {
+    zinc_(Zdropdegen);
+    qh_appendmergeset(qh, facet, facet, MRGdegen, &angledegen);
+    trace2((qh, qh->ferr, 2024, "qh_maydropneighbors: f%d is degenerate.\n", facet->id));
+  }
+} /* maydropneighbor */
+
+
+/*-<a                             href="qh-merge_r.htm#TOC"
+  >-------------------------------</a><a name="merge_degenredundant">-</a>
+
+  qh_merge_degenredundant(qh)
+    merge all degenerate and redundant facets
+    qh.degen_mergeset contains merges from qh_degen_redundant_neighbors()
+
+  returns:
+    number of merges performed
+    resets facet->degenerate/redundant
+    if deleted (visible) facet has no neighbors
+      sets ->f.replace to NULL
+
+  notes:
+    redundant merges happen before degenerate ones
+    merging and renaming vertices can result in degen/redundant facets
+
+  design:
+    for each merge on qh.degen_mergeset
+      if redundant merge
+        if non-redundant facet merged into redundant facet
+          recheck facet for redundancy
+        else
+          merge redundant facet into other facet
+*/
+int qh_merge_degenredundant(qhT *qh) {
+  int size;
+  mergeT *merge;
+  facetT *bestneighbor, *facet1, *facet2;
+  realT dist, mindist, maxdist;
+  vertexT *vertex, **vertexp;
+  int nummerges= 0;
+  mergeType mergetype;
+
+  while ((merge= (mergeT*)qh_setdellast(qh->degen_mergeset))) {
+    facet1= merge->facet1;
+    facet2= merge->facet2;
+    mergetype= merge->type;
+    qh_memfree(qh, merge, (int)sizeof(mergeT));
+    if (facet1->visible)
+      continue;
+    facet1->degenerate= False;
+    facet1->redundant= False;
+    if (qh->TRACEmerge-1 == zzval_(Ztotmerge))
+      qh->qhmem.IStracing= qh->IStracing= qh->TRACElevel;
+    if (mergetype == MRGredundant) {
+      zinc_(Zneighbor);
+      while (facet2->visible) {
+        if (!facet2->f.replace) {
+          qh_fprintf(qh, qh->ferr, 6097, "qhull internal error (qh_merge_degenredunant): f%d redundant but f%d has no replacement\n",
+               facet1->id, facet2->id);
+          qh_errexit2(qh, qh_ERRqhull, facet1, facet2);
+        }
+        facet2= facet2->f.replace;
+      }
+      if (facet1 == facet2) {
+        qh_degen_redundant_facet(qh, facet1); /* in case of others */
+        continue;
+      }
+      trace2((qh, qh->ferr, 2025, "qh_merge_degenredundant: facet f%d is contained in f%d, will merge\n",
+            facet1->id, facet2->id));
+      qh_mergefacet(qh, facet1, facet2, NULL, NULL, !qh_MERGEapex);
+      /* merge distance is already accounted for */
+      nummerges++;
+    }else {  /* mergetype == MRGdegen, other merges may have fixed */
+      if (!(size= qh_setsize(qh, facet1->neighbors))) {
+        zinc_(Zdelfacetdup);
+        trace2((qh, qh->ferr, 2026, "qh_merge_degenredundant: facet f%d has no neighbors.  Deleted\n", facet1->id));
+        qh_willdelete(qh, facet1, NULL);
+        FOREACHvertex_(facet1->vertices) {
+          qh_setdel(vertex->neighbors, facet1);
+          if (!SETfirst_(vertex->neighbors)) {
+            zinc_(Zdegenvertex);
+            trace2((qh, qh->ferr, 2027, "qh_merge_degenredundant: deleted v%d because f%d has no neighbors\n",
+                 vertex->id, facet1->id));
+            vertex->deleted= True;
+            qh_setappend(qh, &qh->del_vertices, vertex);
+          }
+        }
+        nummerges++;
+      }else if (size < qh->hull_dim) {
+        bestneighbor= qh_findbestneighbor(qh, facet1, &dist, &mindist, &maxdist);
+        trace2((qh, qh->ferr, 2028, "qh_merge_degenredundant: facet f%d has %d neighbors, merge into f%d dist %2.2g\n",
+              facet1->id, size, bestneighbor->id, dist));
+        qh_mergefacet(qh, facet1, bestneighbor, &mindist, &maxdist, !qh_MERGEapex);
+        nummerges++;
+        if (qh->PRINTstatistics) {
+          zinc_(Zdegen);
+          wadd_(Wdegentot, dist);
+          wmax_(Wdegenmax, dist);
+        }
+      } /* else, another merge fixed the degeneracy and redundancy tested */
+    }
+  }
+  return nummerges;
+} /* merge_degenredundant */
+
+/*-<a                             href="qh-merge_r.htm#TOC"
+  >-------------------------------</a><a name="merge_nonconvex">-</a>
+
+  qh_merge_nonconvex(qh, facet1, facet2, mergetype )
+    remove non-convex ridge between facet1 into facet2
+    mergetype gives why the facet's are non-convex
+
+  returns:
+    merges one of the facets into the best neighbor
+
+  design:
+    if one of the facets is a new facet
+      prefer merging new facet into old facet
+    find best neighbors for both facets
+    merge the nearest facet into its best neighbor
+    update the statistics
+*/
+void qh_merge_nonconvex(qhT *qh, facetT *facet1, facetT *facet2, mergeType mergetype) {
+  facetT *bestfacet, *bestneighbor, *neighbor;
+  realT dist, dist2, mindist, mindist2, maxdist, maxdist2;
+
+  if (qh->TRACEmerge-1 == zzval_(Ztotmerge))
+    qh->qhmem.IStracing= qh->IStracing= qh->TRACElevel;
+  trace3((qh, qh->ferr, 3003, "qh_merge_nonconvex: merge #%d for f%d and f%d type %d\n",
+      zzval_(Ztotmerge) + 1, facet1->id, facet2->id, mergetype));
+  /* concave or coplanar */
+  if (!facet1->newfacet) {
+    bestfacet= facet2;   /* avoid merging old facet if new is ok */
+    facet2= facet1;
+    facet1= bestfacet;
+  }else
+    bestfacet= facet1;
+  bestneighbor= qh_findbestneighbor(qh, bestfacet, &dist, &mindist, &maxdist);
+  neighbor= qh_findbestneighbor(qh, facet2, &dist2, &mindist2, &maxdist2);
+  if (dist < dist2) {
+    qh_mergefacet(qh, bestfacet, bestneighbor, &mindist, &maxdist, !qh_MERGEapex);
+  }else if (qh->AVOIDold && !facet2->newfacet
+  && ((mindist >= -qh->MAXcoplanar && maxdist <= qh->max_outside)
+       || dist * 1.5 < dist2)) {
+    zinc_(Zavoidold);
+    wadd_(Wavoidoldtot, dist);
+    wmax_(Wavoidoldmax, dist);
+    trace2((qh, qh->ferr, 2029, "qh_merge_nonconvex: avoid merging old facet f%d dist %2.2g.  Use f%d dist %2.2g instead\n",
+           facet2->id, dist2, facet1->id, dist2));
+    qh_mergefacet(qh, bestfacet, bestneighbor, &mindist, &maxdist, !qh_MERGEapex);
+  }else {
+    qh_mergefacet(qh, facet2, neighbor, &mindist2, &maxdist2, !qh_MERGEapex);
+    dist= dist2;
+  }
+  if (qh->PRINTstatistics) {
+    if (mergetype == MRGanglecoplanar) {
+      zinc_(Zacoplanar);
+      wadd_(Wacoplanartot, dist);
+      wmax_(Wacoplanarmax, dist);
+    }else if (mergetype == MRGconcave) {
+      zinc_(Zconcave);
+      wadd_(Wconcavetot, dist);
+      wmax_(Wconcavemax, dist);
+    }else { /* MRGcoplanar */
+      zinc_(Zcoplanar);
+      wadd_(Wcoplanartot, dist);
+      wmax_(Wcoplanarmax, dist);
+    }
+  }
+} /* merge_nonconvex */
+
+/*-<a                             href="qh-merge_r.htm#TOC"
+  >-------------------------------</a><a name="mergecycle">-</a>
+
+  qh_mergecycle(qh, samecycle, newfacet )
+    merge a cycle of facets starting at samecycle into a newfacet
+    newfacet is a horizon facet with ->normal
+    samecycle facets are simplicial from an apex
+
+  returns:
+    initializes vertex neighbors on first merge
+    samecycle deleted (placed on qh.visible_list)
+    newfacet at end of qh.facet_list
+    deleted vertices on qh.del_vertices
+
+  see:
+    qh_mergefacet()
+    called by qh_mergecycle_all() for multiple, same cycle facets
+
+  design:
+    make vertex neighbors if necessary
+    make ridges for newfacet
+    merge neighbor sets of samecycle into newfacet
+    merge ridges of samecycle into newfacet
+    merge vertex neighbors of samecycle into newfacet
+    make apex of samecycle the apex of newfacet
+    if newfacet wasn't a new facet
+      add its vertices to qh.newvertex_list
+    delete samecycle facets a make newfacet a newfacet
+*/
+void qh_mergecycle(qhT *qh, facetT *samecycle, facetT *newfacet) {
+  int traceonce= False, tracerestore= 0;
+  vertexT *apex;
+#ifndef qh_NOtrace
+  facetT *same;
+#endif
+
+  if (newfacet->tricoplanar) {
+    if (!qh->TRInormals) {
+      qh_fprintf(qh, qh->ferr, 6224, "Qhull internal error (qh_mergecycle): does not work for tricoplanar facets.  Use option 'Q11'\n");
+      qh_errexit(qh, qh_ERRqhull, newfacet, NULL);
+    }
+    newfacet->tricoplanar= False;
+    newfacet->keepcentrum= False;
+  }
+  if (!qh->VERTEXneighbors)
+    qh_vertexneighbors(qh);
+  zzinc_(Ztotmerge);
+  if (qh->REPORTfreq2 && qh->POSTmerging) {
+    if (zzval_(Ztotmerge) > qh->mergereport + qh->REPORTfreq2)
+      qh_tracemerging(qh);
+  }
+#ifndef qh_NOtrace
+  if (qh->TRACEmerge == zzval_(Ztotmerge))
+    qh->qhmem.IStracing= qh->IStracing= qh->TRACElevel;
+  trace2((qh, qh->ferr, 2030, "qh_mergecycle: merge #%d for facets from cycle f%d into coplanar horizon f%d\n",
+        zzval_(Ztotmerge), samecycle->id, newfacet->id));
+  if (newfacet == qh->tracefacet) {
+    tracerestore= qh->IStracing;
+    qh->IStracing= 4;
+    qh_fprintf(qh, qh->ferr, 8068, "qh_mergecycle: ========= trace merge %d of samecycle %d into trace f%d, furthest is p%d\n",
+               zzval_(Ztotmerge), samecycle->id, newfacet->id,  qh->furthest_id);
+    traceonce= True;
+  }
+  if (qh->IStracing >=4) {
+    qh_fprintf(qh, qh->ferr, 8069, "  same cycle:");
+    FORALLsame_cycle_(samecycle)
+      qh_fprintf(qh, qh->ferr, 8070, " f%d", same->id);
+    qh_fprintf(qh, qh->ferr, 8071, "\n");
+  }
+  if (qh->IStracing >=4)
+    qh_errprint(qh, "MERGING CYCLE", samecycle, newfacet, NULL, NULL);
+#endif /* !qh_NOtrace */
+  apex= SETfirstt_(samecycle->vertices, vertexT);
+  qh_makeridges(qh, newfacet);
+  qh_mergecycle_neighbors(qh, samecycle, newfacet);
+  qh_mergecycle_ridges(qh, samecycle, newfacet);
+  qh_mergecycle_vneighbors(qh, samecycle, newfacet);
+  if (SETfirstt_(newfacet->vertices, vertexT) != apex)
+    qh_setaddnth(qh, &newfacet->vertices, 0, apex);  /* apex has last id */
+  if (!newfacet->newfacet)
+    qh_newvertices(qh, newfacet->vertices);
+  qh_mergecycle_facets(qh, samecycle, newfacet);
+  qh_tracemerge(qh, samecycle, newfacet);
+  /* check for degen_redundant_neighbors after qh_forcedmerges() */
+  if (traceonce) {
+    qh_fprintf(qh, qh->ferr, 8072, "qh_mergecycle: end of trace facet\n");
+    qh->IStracing= tracerestore;
+  }
+} /* mergecycle */
+
+/*-<a                             href="qh-merge_r.htm#TOC"
+  >-------------------------------</a><a name="mergecycle_all">-</a>
+
+  qh_mergecycle_all(qh, facetlist, wasmerge )
+    merge all samecycles of coplanar facets into horizon
+    don't merge facets with ->mergeridge (these already have ->normal)
+    all facets are simplicial from apex
+    all facet->cycledone == False
+
+  returns:
+    all newfacets merged into coplanar horizon facets
+    deleted vertices on  qh.del_vertices
+    sets wasmerge if any merge
+
+  see:
+    calls qh_mergecycle for multiple, same cycle facets
+
+  design:
+    for each facet on facetlist
+      skip facets with duplicate ridges and normals
+      check that facet is in a samecycle (->mergehorizon)
+      if facet only member of samecycle
+        sets vertex->delridge for all vertices except apex
+        merge facet into horizon
+      else
+        mark all facets in samecycle
+        remove facets with duplicate ridges from samecycle
+        merge samecycle into horizon (deletes facets from facetlist)
+*/
+void qh_mergecycle_all(qhT *qh, facetT *facetlist, boolT *wasmerge) {
+  facetT *facet, *same, *prev, *horizon;
+  facetT *samecycle= NULL, *nextfacet, *nextsame;
+  vertexT *apex, *vertex, **vertexp;
+  int cycles=0, total=0, facets, nummerge;
+
+  trace2((qh, qh->ferr, 2031, "qh_mergecycle_all: begin\n"));
+  for (facet= facetlist; facet && (nextfacet= facet->next); facet= nextfacet) {
+    if (facet->normal)
+      continue;
+    if (!facet->mergehorizon) {
+      qh_fprintf(qh, qh->ferr, 6225, "Qhull internal error (qh_mergecycle_all): f%d without normal\n", facet->id);
+      qh_errexit(qh, qh_ERRqhull, facet, NULL);
+    }
+    horizon= SETfirstt_(facet->neighbors, facetT);
+    if (facet->f.samecycle == facet) {
+      zinc_(Zonehorizon);
+      /* merge distance done in qh_findhorizon */
+      apex= SETfirstt_(facet->vertices, vertexT);
+      FOREACHvertex_(facet->vertices) {
+        if (vertex != apex)
+          vertex->delridge= True;
+      }
+      horizon->f.newcycle= NULL;
+      qh_mergefacet(qh, facet, horizon, NULL, NULL, qh_MERGEapex);
+    }else {
+      samecycle= facet;
+      facets= 0;
+      prev= facet;
+      for (same= facet->f.samecycle; same;  /* FORALLsame_cycle_(facet) */
+           same= (same == facet ? NULL :nextsame)) { /* ends at facet */
+        nextsame= same->f.samecycle;
+        if (same->cycledone || same->visible)
+          qh_infiniteloop(qh, same);
+        same->cycledone= True;
+        if (same->normal) {
+          prev->f.samecycle= same->f.samecycle; /* unlink ->mergeridge */
+          same->f.samecycle= NULL;
+        }else {
+          prev= same;
+          facets++;
+        }
+      }
+      while (nextfacet && nextfacet->cycledone)  /* will delete samecycle */
+        nextfacet= nextfacet->next;
+      horizon->f.newcycle= NULL;
+      qh_mergecycle(qh, samecycle, horizon);
+      nummerge= horizon->nummerge + facets;
+      if (nummerge > qh_MAXnummerge)
+        horizon->nummerge= qh_MAXnummerge;
+      else
+        horizon->nummerge= (short unsigned int)nummerge;
+      zzinc_(Zcyclehorizon);
+      total += facets;
+      zzadd_(Zcyclefacettot, facets);
+      zmax_(Zcyclefacetmax, facets);
+    }
+    cycles++;
+  }
+  if (cycles)
+    *wasmerge= True;
+  trace1((qh, qh->ferr, 1013, "qh_mergecycle_all: merged %d same cycles or facets into coplanar horizons\n", cycles));
+} /* mergecycle_all */
+
+/*-<a                             href="qh-merge_r.htm#TOC"
+  >-------------------------------</a><a name="mergecycle_facets">-</a>
+
+  qh_mergecycle_facets(qh, samecycle, newfacet )
+    finish merge of samecycle into newfacet
+
+  returns:
+    samecycle prepended to visible_list for later deletion and partitioning
+      each facet->f.replace == newfacet
+
+    newfacet moved to end of qh.facet_list
+      makes newfacet a newfacet (get's facet1->id if it was old)
+      sets newfacet->newmerge
+      clears newfacet->center (unless merging into a large facet)
+      clears newfacet->tested and ridge->tested for facet1
+
+    adds neighboring facets to facet_mergeset if redundant or degenerate
+
+  design:
+    make newfacet a new facet and set its flags
+    move samecycle facets to qh.visible_list for later deletion
+    unless newfacet is large
+      remove its centrum
+*/
+void qh_mergecycle_facets(qhT *qh, facetT *samecycle, facetT *newfacet) {
+  facetT *same, *next;
+
+  trace4((qh, qh->ferr, 4030, "qh_mergecycle_facets: make newfacet new and samecycle deleted\n"));
+  qh_removefacet(qh, newfacet);  /* append as a newfacet to end of qh->facet_list */
+  qh_appendfacet(qh, newfacet);
+  newfacet->newfacet= True;
+  newfacet->simplicial= False;
+  newfacet->newmerge= True;
+
+  for (same= samecycle->f.samecycle; same; same= (same == samecycle ?  NULL : next)) {
+    next= same->f.samecycle;  /* reused by willdelete */
+    qh_willdelete(qh, same, newfacet);
+  }
+  if (newfacet->center
+      && qh_setsize(qh, newfacet->vertices) <= qh->hull_dim + qh_MAXnewcentrum) {
+    qh_memfree(qh, newfacet->center, qh->normal_size);
+    newfacet->center= NULL;
+  }
+  trace3((qh, qh->ferr, 3004, "qh_mergecycle_facets: merged facets from cycle f%d into f%d\n",
+             samecycle->id, newfacet->id));
+} /* mergecycle_facets */
+
+/*-<a                             href="qh-merge_r.htm#TOC"
+  >-------------------------------</a><a name="mergecycle_neighbors">-</a>
+
+  qh_mergecycle_neighbors(qh, samecycle, newfacet )
+    add neighbors for samecycle facets to newfacet
+
+  returns:
+    newfacet with updated neighbors and vice-versa
+    newfacet has ridges
+    all neighbors of newfacet marked with qh.visit_id
+    samecycle facets marked with qh.visit_id-1
+    ridges updated for simplicial neighbors of samecycle with a ridge
+
+  notes:
+    assumes newfacet not in samecycle
+    usually, samecycle facets are new, simplicial facets without internal ridges
+      not so if horizon facet is coplanar to two different samecycles
+
+  see:
+    qh_mergeneighbors()
+
+  design:
+    check samecycle
+    delete neighbors from newfacet that are also in samecycle
+    for each neighbor of a facet in samecycle
+      if neighbor is simplicial
+        if first visit
+          move the neighbor relation to newfacet
+          update facet links for its ridges
+        else
+          make ridges for neighbor
+          remove samecycle reference
+      else
+        update neighbor sets
+*/
+void qh_mergecycle_neighbors(qhT *qh, facetT *samecycle, facetT *newfacet) {
+  facetT *same, *neighbor, **neighborp;
+  int delneighbors= 0, newneighbors= 0;
+  unsigned int samevisitid;
+  ridgeT *ridge, **ridgep;
+
+  samevisitid= ++qh->visit_id;
+  FORALLsame_cycle_(samecycle) {
+    if (same->visitid == samevisitid || same->visible)
+      qh_infiniteloop(qh, samecycle);
+    same->visitid= samevisitid;
+  }
+  newfacet->visitid= ++qh->visit_id;
+  trace4((qh, qh->ferr, 4031, "qh_mergecycle_neighbors: delete shared neighbors from newfacet\n"));
+  FOREACHneighbor_(newfacet) {
+    if (neighbor->visitid == samevisitid) {
+      SETref_(neighbor)= NULL;  /* samecycle neighbors deleted */
+      delneighbors++;
+    }else
+      neighbor->visitid= qh->visit_id;
+  }
+  qh_setcompact(qh, newfacet->neighbors);
+
+  trace4((qh, qh->ferr, 4032, "qh_mergecycle_neighbors: update neighbors\n"));
+  FORALLsame_cycle_(samecycle) {
+    FOREACHneighbor_(same) {
+      if (neighbor->visitid == samevisitid)
+        continue;
+      if (neighbor->simplicial) {
+        if (neighbor->visitid != qh->visit_id) {
+          qh_setappend(qh, &newfacet->neighbors, neighbor);
+          qh_setreplace(qh, neighbor->neighbors, same, newfacet);
+          newneighbors++;
+          neighbor->visitid= qh->visit_id;
+          FOREACHridge_(neighbor->ridges) { /* update ridge in case of qh_makeridges */
+            if (ridge->top == same) {
+              ridge->top= newfacet;
+              break;
+            }else if (ridge->bottom == same) {
+              ridge->bottom= newfacet;
+              break;
+            }
+          }
+        }else {
+          qh_makeridges(qh, neighbor);
+          qh_setdel(neighbor->neighbors, same);
+          /* same can't be horizon facet for neighbor */
+        }
+      }else { /* non-simplicial neighbor */
+        qh_setdel(neighbor->neighbors, same);
+        if (neighbor->visitid != qh->visit_id) {
+          qh_setappend(qh, &neighbor->neighbors, newfacet);
+          qh_setappend(qh, &newfacet->neighbors, neighbor);
+          neighbor->visitid= qh->visit_id;
+          newneighbors++;
+        }
+      }
+    }
+  }
+  trace2((qh, qh->ferr, 2032, "qh_mergecycle_neighbors: deleted %d neighbors and added %d\n",
+             delneighbors, newneighbors));
+} /* mergecycle_neighbors */
+
+/*-<a                             href="qh-merge_r.htm#TOC"
+  >-------------------------------</a><a name="mergecycle_ridges">-</a>
+
+  qh_mergecycle_ridges(qh, samecycle, newfacet )
+    add ridges/neighbors for facets in samecycle to newfacet
+    all new/old neighbors of newfacet marked with qh.visit_id
+    facets in samecycle marked with qh.visit_id-1
+    newfacet marked with qh.visit_id
+
+  returns:
+    newfacet has merged ridges
+
+  notes:
+    ridge already updated for simplicial neighbors of samecycle with a ridge
+
+  see:
+    qh_mergeridges()
+    qh_makeridges()
+
+  design:
+    remove ridges between newfacet and samecycle
+    for each facet in samecycle
+      for each ridge in facet
+        update facet pointers in ridge
+        skip ridges processed in qh_mergecycle_neighors
+        free ridges between newfacet and samecycle
+        free ridges between facets of samecycle (on 2nd visit)
+        append remaining ridges to newfacet
+      if simpilicial facet
+        for each neighbor of facet
+          if simplicial facet
+          and not samecycle facet or newfacet
+            make ridge between neighbor and newfacet
+*/
+void qh_mergecycle_ridges(qhT *qh, facetT *samecycle, facetT *newfacet) {
+  facetT *same, *neighbor= NULL;
+  int numold=0, numnew=0;
+  int neighbor_i, neighbor_n;
+  unsigned int samevisitid;
+  ridgeT *ridge, **ridgep;
+  boolT toporient;
+  void **freelistp; /* used if !qh_NOmem by qh_memfree_() */
+
+  trace4((qh, qh->ferr, 4033, "qh_mergecycle_ridges: delete shared ridges from newfacet\n"));
+  samevisitid= qh->visit_id -1;
+  FOREACHridge_(newfacet->ridges) {
+    neighbor= otherfacet_(ridge, newfacet);
+    if (neighbor->visitid == samevisitid)
+      SETref_(ridge)= NULL; /* ridge free'd below */
+  }
+  qh_setcompact(qh, newfacet->ridges);
+
+  trace4((qh, qh->ferr, 4034, "qh_mergecycle_ridges: add ridges to newfacet\n"));
+  FORALLsame_cycle_(samecycle) {
+    FOREACHridge_(same->ridges) {
+      if (ridge->top == same) {
+        ridge->top= newfacet;
+        neighbor= ridge->bottom;
+      }else if (ridge->bottom == same) {
+        ridge->bottom= newfacet;
+        neighbor= ridge->top;
+      }else if (ridge->top == newfacet || ridge->bottom == newfacet) {
+        qh_setappend(qh, &newfacet->ridges, ridge);
+        numold++;  /* already set by qh_mergecycle_neighbors */
+        continue;
+      }else {
+        qh_fprintf(qh, qh->ferr, 6098, "qhull internal error (qh_mergecycle_ridges): bad ridge r%d\n", ridge->id);
+        qh_errexit(qh, qh_ERRqhull, NULL, ridge);
+      }
+      if (neighbor == newfacet) {
+        qh_setfree(qh, &(ridge->vertices));
+        qh_memfree_(qh, ridge, (int)sizeof(ridgeT), freelistp);
+        numold++;
+      }else if (neighbor->visitid == samevisitid) {
+        qh_setdel(neighbor->ridges, ridge);
+        qh_setfree(qh, &(ridge->vertices));
+        qh_memfree_(qh, ridge, (int)sizeof(ridgeT), freelistp);
+        numold++;
+      }else {
+        qh_setappend(qh, &newfacet->ridges, ridge);
+        numold++;
+      }
+    }
+    if (same->ridges)
+      qh_settruncate(qh, same->ridges, 0);
+    if (!same->simplicial)
+      continue;
+    FOREACHneighbor_i_(qh, same) {       /* note: !newfact->simplicial */
+      if (neighbor->visitid != samevisitid && neighbor->simplicial) {
+        ridge= qh_newridge(qh);
+        ridge->vertices= qh_setnew_delnthsorted(qh, same->vertices, qh->hull_dim,
+                                                          neighbor_i, 0);
+        toporient= same->toporient ^ (neighbor_i & 0x1);
+        if (toporient) {
+          ridge->top= newfacet;
+          ridge->bottom= neighbor;
+        }else {
+          ridge->top= neighbor;
+          ridge->bottom= newfacet;
+        }
+        qh_setappend(qh, &(newfacet->ridges), ridge);
+        qh_setappend(qh, &(neighbor->ridges), ridge);
+        numnew++;
+      }
+    }
+  }
+
+  trace2((qh, qh->ferr, 2033, "qh_mergecycle_ridges: found %d old ridges and %d new ones\n",
+             numold, numnew));
+} /* mergecycle_ridges */
+
+/*-<a                             href="qh-merge_r.htm#TOC"
+  >-------------------------------</a><a name="mergecycle_vneighbors">-</a>
+
+  qh_mergecycle_vneighbors(qh, samecycle, newfacet )
+    create vertex neighbors for newfacet from vertices of facets in samecycle
+    samecycle marked with visitid == qh.visit_id - 1
+
+  returns:
+    newfacet vertices with updated neighbors
+    marks newfacet with qh.visit_id-1
+    deletes vertices that are merged away
+    sets delridge on all vertices (faster here than in mergecycle_ridges)
+
+  see:
+    qh_mergevertex_neighbors()
+
+  design:
+    for each vertex of samecycle facet
+      set vertex->delridge
+      delete samecycle facets from vertex neighbors
+      append newfacet to vertex neighbors
+      if vertex only in newfacet
+        delete it from newfacet
+        add it to qh.del_vertices for later deletion
+*/
+void qh_mergecycle_vneighbors(qhT *qh, facetT *samecycle, facetT *newfacet) {
+  facetT *neighbor, **neighborp;
+  unsigned int mergeid;
+  vertexT *vertex, **vertexp, *apex;
+  setT *vertices;
+
+  trace4((qh, qh->ferr, 4035, "qh_mergecycle_vneighbors: update vertex neighbors for newfacet\n"));
+  mergeid= qh->visit_id - 1;
+  newfacet->visitid= mergeid;
+  vertices= qh_basevertices(qh, samecycle); /* temp */
+  apex= SETfirstt_(samecycle->vertices, vertexT);
+  qh_setappend(qh, &vertices, apex);
+  FOREACHvertex_(vertices) {
+    vertex->delridge= True;
+    FOREACHneighbor_(vertex) {
+      if (neighbor->visitid == mergeid)
+        SETref_(neighbor)= NULL;
+    }
+    qh_setcompact(qh, vertex->neighbors);
+    qh_setappend(qh, &vertex->neighbors, newfacet);
+    if (!SETsecond_(vertex->neighbors)) {
+      zinc_(Zcyclevertex);
+      trace2((qh, qh->ferr, 2034, "qh_mergecycle_vneighbors: deleted v%d when merging cycle f%d into f%d\n",
+        vertex->id, samecycle->id, newfacet->id));
+      qh_setdelsorted(newfacet->vertices, vertex);
+      vertex->deleted= True;
+      qh_setappend(qh, &qh->del_vertices, vertex);
+    }
+  }
+  qh_settempfree(qh, &vertices);
+  trace3((qh, qh->ferr, 3005, "qh_mergecycle_vneighbors: merged vertices from cycle f%d into f%d\n",
+             samecycle->id, newfacet->id));
+} /* mergecycle_vneighbors */
+
+/*-<a                             href="qh-merge_r.htm#TOC"
+  >-------------------------------</a><a name="mergefacet">-</a>
+
+  qh_mergefacet(qh, facet1, facet2, mindist, maxdist, mergeapex )
+    merges facet1 into facet2
+    mergeapex==qh_MERGEapex if merging new facet into coplanar horizon
+
+  returns:
+    qh.max_outside and qh.min_vertex updated
+    initializes vertex neighbors on first merge
+
+  returns:
+    facet2 contains facet1's vertices, neighbors, and ridges
+      facet2 moved to end of qh.facet_list
+      makes facet2 a newfacet
+      sets facet2->newmerge set
+      clears facet2->center (unless merging into a large facet)
+      clears facet2->tested and ridge->tested for facet1
+
+    facet1 prepended to visible_list for later deletion and partitioning
+      facet1->f.replace == facet2
+
+    adds neighboring facets to facet_mergeset if redundant or degenerate
+
+  notes:
+    mindist/maxdist may be NULL (only if both NULL)
+    traces merge if fmax_(maxdist,-mindist) > TRACEdist
+
+  see:
+    qh_mergecycle()
+
+  design:
+    trace merge and check for degenerate simplex
+    make ridges for both facets
+    update qh.max_outside, qh.max_vertex, qh.min_vertex
+    update facet2->maxoutside and keepcentrum
+    update facet2->nummerge
+    update tested flags for facet2
+    if facet1 is simplicial
+      merge facet1 into facet2
+    else
+      merge facet1's neighbors into facet2
+      merge facet1's ridges into facet2
+      merge facet1's vertices into facet2
+      merge facet1's vertex neighbors into facet2
+      add facet2's vertices to qh.new_vertexlist
+      unless qh_MERGEapex
+        test facet2 for degenerate or redundant neighbors
+      move facet1 to qh.visible_list for later deletion
+      move facet2 to end of qh.newfacet_list
+*/
+void qh_mergefacet(qhT *qh, facetT *facet1, facetT *facet2, realT *mindist, realT *maxdist, boolT mergeapex) {
+  boolT traceonce= False;
+  vertexT *vertex, **vertexp;
+  int tracerestore=0, nummerge;
+
+  if (facet1->tricoplanar || facet2->tricoplanar) {
+    if (!qh->TRInormals) {
+      qh_fprintf(qh, qh->ferr, 6226, "Qhull internal error (qh_mergefacet): does not work for tricoplanar facets.  Use option 'Q11'\n");
+      qh_errexit2(qh, qh_ERRqhull, facet1, facet2);
+    }
+    if (facet2->tricoplanar) {
+      facet2->tricoplanar= False;
+      facet2->keepcentrum= False;
+    }
+  }
+  zzinc_(Ztotmerge);
+  if (qh->REPORTfreq2 && qh->POSTmerging) {
+    if (zzval_(Ztotmerge) > qh->mergereport + qh->REPORTfreq2)
+      qh_tracemerging(qh);
+  }
+#ifndef qh_NOtrace
+  if (qh->build_cnt >= qh->RERUN) {
+    if (mindist && (-*mindist > qh->TRACEdist || *maxdist > qh->TRACEdist)) {
+      tracerestore= 0;
+      qh->IStracing= qh->TRACElevel;
+      traceonce= True;
+      qh_fprintf(qh, qh->ferr, 8075, "qh_mergefacet: ========= trace wide merge #%d(%2.2g) for f%d into f%d, last point was p%d\n", zzval_(Ztotmerge),
+             fmax_(-*mindist, *maxdist), facet1->id, facet2->id, qh->furthest_id);
+    }else if (facet1 == qh->tracefacet || facet2 == qh->tracefacet) {
+      tracerestore= qh->IStracing;
+      qh->IStracing= 4;
+      traceonce= True;
+      qh_fprintf(qh, qh->ferr, 8076, "qh_mergefacet: ========= trace merge #%d involving f%d, furthest is p%d\n",
+                 zzval_(Ztotmerge), qh->tracefacet_id,  qh->furthest_id);
+    }
+  }
+  if (qh->IStracing >= 2) {
+    realT mergemin= -2;
+    realT mergemax= -2;
+
+    if (mindist) {
+      mergemin= *mindist;
+      mergemax= *maxdist;
+    }
+    qh_fprintf(qh, qh->ferr, 8077, "qh_mergefacet: #%d merge f%d into f%d, mindist= %2.2g, maxdist= %2.2g\n",
+    zzval_(Ztotmerge), facet1->id, facet2->id, mergemin, mergemax);
+  }
+#endif /* !qh_NOtrace */
+  if (facet1 == facet2 || facet1->visible || facet2->visible) {
+    qh_fprintf(qh, qh->ferr, 6099, "qhull internal error (qh_mergefacet): either f%d and f%d are the same or one is a visible facet\n",
+             facet1->id, facet2->id);
+    qh_errexit2(qh, qh_ERRqhull, facet1, facet2);
+  }
+  if (qh->num_facets - qh->num_visible <= qh->hull_dim + 1) {
+    qh_fprintf(qh, qh->ferr, 6227, "\n\
+qhull precision error: Only %d facets remain.  Can not merge another\n\
+pair.  The input is too degenerate or the convexity constraints are\n\
+too strong.\n", qh->hull_dim+1);
+    if (qh->hull_dim >= 5 && !qh->MERGEexact)
+      qh_fprintf(qh, qh->ferr, 8079, "Option 'Qx' may avoid this problem.\n");
+    qh_errexit(qh, qh_ERRprec, NULL, NULL);
+  }
+  if (!qh->VERTEXneighbors)
+    qh_vertexneighbors(qh);
+  qh_makeridges(qh, facet1);
+  qh_makeridges(qh, facet2);
+  if (qh->IStracing >=4)
+    qh_errprint(qh, "MERGING", facet1, facet2, NULL, NULL);
+  if (mindist) {
+    maximize_(qh->max_outside, *maxdist);
+    maximize_(qh->max_vertex, *maxdist);
+#if qh_MAXoutside
+    maximize_(facet2->maxoutside, *maxdist);
+#endif
+    minimize_(qh->min_vertex, *mindist);
+    if (!facet2->keepcentrum
+    && (*maxdist > qh->WIDEfacet || *mindist < -qh->WIDEfacet)) {
+      facet2->keepcentrum= True;
+      zinc_(Zwidefacet);
+    }
+  }
+  nummerge= facet1->nummerge + facet2->nummerge + 1;
+  if (nummerge >= qh_MAXnummerge)
+    facet2->nummerge= qh_MAXnummerge;
+  else
+    facet2->nummerge= (short unsigned int)nummerge;
+  facet2->newmerge= True;
+  facet2->dupridge= False;
+  qh_updatetested(qh, facet1, facet2);
+  if (qh->hull_dim > 2 && qh_setsize(qh, facet1->vertices) == qh->hull_dim)
+    qh_mergesimplex(qh, facet1, facet2, mergeapex);
+  else {
+    qh->vertex_visit++;
+    FOREACHvertex_(facet2->vertices)
+      vertex->visitid= qh->vertex_visit;
+    if (qh->hull_dim == 2)
+      qh_mergefacet2d(qh, facet1, facet2);
+    else {
+      qh_mergeneighbors(qh, facet1, facet2);
+      qh_mergevertices(qh, facet1->vertices, &facet2->vertices);
+    }
+    qh_mergeridges(qh, facet1, facet2);
+    qh_mergevertex_neighbors(qh, facet1, facet2);
+    if (!facet2->newfacet)
+      qh_newvertices(qh, facet2->vertices);
+  }
+  if (!mergeapex)
+    qh_degen_redundant_neighbors(qh, facet2, facet1);
+  if (facet2->coplanar || !facet2->newfacet) {
+    zinc_(Zmergeintohorizon);
+  }else if (!facet1->newfacet && facet2->newfacet) {
+    zinc_(Zmergehorizon);
+  }else {
+    zinc_(Zmergenew);
+  }
+  qh_willdelete(qh, facet1, facet2);
+  qh_removefacet(qh, facet2);  /* append as a newfacet to end of qh->facet_list */
+  qh_appendfacet(qh, facet2);
+  facet2->newfacet= True;
+  facet2->tested= False;
+  qh_tracemerge(qh, facet1, facet2);
+  if (traceonce) {
+    qh_fprintf(qh, qh->ferr, 8080, "qh_mergefacet: end of wide tracing\n");
+    qh->IStracing= tracerestore;
+  }
+} /* mergefacet */
+
+
+/*-<a                             href="qh-merge_r.htm#TOC"
+  >-------------------------------</a><a name="mergefacet2d">-</a>
+
+  qh_mergefacet2d(qh, facet1, facet2 )
+    in 2d, merges neighbors and vertices of facet1 into facet2
+
+  returns:
+    build ridges for neighbors if necessary
+    facet2 looks like a simplicial facet except for centrum, ridges
+      neighbors are opposite the corresponding vertex
+      maintains orientation of facet2
+
+  notes:
+    qh_mergefacet() retains non-simplicial structures
+      they are not needed in 2d, but later routines may use them
+    preserves qh.vertex_visit for qh_mergevertex_neighbors()
+
+  design:
+    get vertices and neighbors
+    determine new vertices and neighbors
+    set new vertices and neighbors and adjust orientation
+    make ridges for new neighbor if needed
+*/
+void qh_mergefacet2d(qhT *qh, facetT *facet1, facetT *facet2) {
+  vertexT *vertex1A, *vertex1B, *vertex2A, *vertex2B, *vertexA, *vertexB;
+  facetT *neighbor1A, *neighbor1B, *neighbor2A, *neighbor2B, *neighborA, *neighborB;
+
+  vertex1A= SETfirstt_(facet1->vertices, vertexT);
+  vertex1B= SETsecondt_(facet1->vertices, vertexT);
+  vertex2A= SETfirstt_(facet2->vertices, vertexT);
+  vertex2B= SETsecondt_(facet2->vertices, vertexT);
+  neighbor1A= SETfirstt_(facet1->neighbors, facetT);
+  neighbor1B= SETsecondt_(facet1->neighbors, facetT);
+  neighbor2A= SETfirstt_(facet2->neighbors, facetT);
+  neighbor2B= SETsecondt_(facet2->neighbors, facetT);
+  if (vertex1A == vertex2A) {
+    vertexA= vertex1B;
+    vertexB= vertex2B;
+    neighborA= neighbor2A;
+    neighborB= neighbor1A;
+  }else if (vertex1A == vertex2B) {
+    vertexA= vertex1B;
+    vertexB= vertex2A;
+    neighborA= neighbor2B;
+    neighborB= neighbor1A;
+  }else if (vertex1B == vertex2A) {
+    vertexA= vertex1A;
+    vertexB= vertex2B;
+    neighborA= neighbor2A;
+    neighborB= neighbor1B;
+  }else { /* 1B == 2B */
+    vertexA= vertex1A;
+    vertexB= vertex2A;
+    neighborA= neighbor2B;
+    neighborB= neighbor1B;
+  }
+  /* vertexB always from facet2, neighborB always from facet1 */
+  if (vertexA->id > vertexB->id) {
+    SETfirst_(facet2->vertices)= vertexA;
+    SETsecond_(facet2->vertices)= vertexB;
+    if (vertexB == vertex2A)
+      facet2->toporient= !facet2->toporient;
+    SETfirst_(facet2->neighbors)= neighborA;
+    SETsecond_(facet2->neighbors)= neighborB;
+  }else {
+    SETfirst_(facet2->vertices)= vertexB;
+    SETsecond_(facet2->vertices)= vertexA;
+    if (vertexB == vertex2B)
+      facet2->toporient= !facet2->toporient;
+    SETfirst_(facet2->neighbors)= neighborB;
+    SETsecond_(facet2->neighbors)= neighborA;
+  }
+  qh_makeridges(qh, neighborB);
+  qh_setreplace(qh, neighborB->neighbors, facet1, facet2);
+  trace4((qh, qh->ferr, 4036, "qh_mergefacet2d: merged v%d and neighbor f%d of f%d into f%d\n",
+       vertexA->id, neighborB->id, facet1->id, facet2->id));
+} /* mergefacet2d */
+
+
+/*-<a                             href="qh-merge_r.htm#TOC"
+  >-------------------------------</a><a name="mergeneighbors">-</a>
+
+  qh_mergeneighbors(qh, facet1, facet2 )
+    merges the neighbors of facet1 into facet2
+
+  see:
+    qh_mergecycle_neighbors()
+
+  design:
+    for each neighbor of facet1
+      if neighbor is also a neighbor of facet2
+        if neighbor is simpilicial
+          make ridges for later deletion as a degenerate facet
+        update its neighbor set
+      else
+        move the neighbor relation to facet2
+    remove the neighbor relation for facet1 and facet2
+*/
+void qh_mergeneighbors(qhT *qh, facetT *facet1, facetT *facet2) {
+  facetT *neighbor, **neighborp;
+
+  trace4((qh, qh->ferr, 4037, "qh_mergeneighbors: merge neighbors of f%d and f%d\n",
+          facet1->id, facet2->id));
+  qh->visit_id++;
+  FOREACHneighbor_(facet2) {
+    neighbor->visitid= qh->visit_id;
+  }
+  FOREACHneighbor_(facet1) {
+    if (neighbor->visitid == qh->visit_id) {
+      if (neighbor->simplicial)    /* is degen, needs ridges */
+        qh_makeridges(qh, neighbor);
+      if (SETfirstt_(neighbor->neighbors, facetT) != facet1) /*keep newfacet->horizon*/
+        qh_setdel(neighbor->neighbors, facet1);
+      else {
+        qh_setdel(neighbor->neighbors, facet2);
+        qh_setreplace(qh, neighbor->neighbors, facet1, facet2);
+      }
+    }else if (neighbor != facet2) {
+      qh_setappend(qh, &(facet2->neighbors), neighbor);
+      qh_setreplace(qh, neighbor->neighbors, facet1, facet2);
+    }
+  }
+  qh_setdel(facet1->neighbors, facet2);  /* here for makeridges */
+  qh_setdel(facet2->neighbors, facet1);
+} /* mergeneighbors */
+
+
+/*-<a                             href="qh-merge_r.htm#TOC"
+  >-------------------------------</a><a name="mergeridges">-</a>
+
+  qh_mergeridges(qh, facet1, facet2 )
+    merges the ridge set of facet1 into facet2
+
+  returns:
+    may delete all ridges for a vertex
+    sets vertex->delridge on deleted ridges
+
+  see:
+    qh_mergecycle_ridges()
+
+  design:
+    delete ridges between facet1 and facet2
+      mark (delridge) vertices on these ridges for later testing
+    for each remaining ridge
+      rename facet1 to facet2
+*/
+void qh_mergeridges(qhT *qh, facetT *facet1, facetT *facet2) {
+  ridgeT *ridge, **ridgep;
+  vertexT *vertex, **vertexp;
+
+  trace4((qh, qh->ferr, 4038, "qh_mergeridges: merge ridges of f%d and f%d\n",
+          facet1->id, facet2->id));
+  FOREACHridge_(facet2->ridges) {
+    if ((ridge->top == facet1) || (ridge->bottom == facet1)) {
+      FOREACHvertex_(ridge->vertices)
+        vertex->delridge= True;
+      qh_delridge(qh, ridge);  /* expensive in high-d, could rebuild */
+      ridgep--; /*repeat*/
+    }
+  }
+  FOREACHridge_(facet1->ridges) {
+    if (ridge->top == facet1)
+      ridge->top= facet2;
+    else
+      ridge->bottom= facet2;
+    qh_setappend(qh, &(facet2->ridges), ridge);
+  }
+} /* mergeridges */
+
+
+/*-<a                             href="qh-merge_r.htm#TOC"
+  >-------------------------------</a><a name="mergesimplex">-</a>
+
+  qh_mergesimplex(qh, facet1, facet2, mergeapex )
+    merge simplicial facet1 into facet2
+    mergeapex==qh_MERGEapex if merging samecycle into horizon facet
+      vertex id is latest (most recently created)
+    facet1 may be contained in facet2
+    ridges exist for both facets
+
+  returns:
+    facet2 with updated vertices, ridges, neighbors
+    updated neighbors for facet1's vertices
+    facet1 not deleted
+    sets vertex->delridge on deleted ridges
+
+  notes:
+    special case code since this is the most common merge
+    called from qh_mergefacet()
+
+  design:
+    if qh_MERGEapex
+      add vertices of facet2 to qh.new_vertexlist if necessary
+      add apex to facet2
+    else
+      for each ridge between facet1 and facet2
+        set vertex->delridge
+      determine the apex for facet1 (i.e., vertex to be merged)
+      unless apex already in facet2
+        insert apex into vertices for facet2
+      add vertices of facet2 to qh.new_vertexlist if necessary
+      add apex to qh.new_vertexlist if necessary
+      for each vertex of facet1
+        if apex
+          rename facet1 to facet2 in its vertex neighbors
+        else
+          delete facet1 from vertex neighors
+          if only in facet2
+            add vertex to qh.del_vertices for later deletion
+      for each ridge of facet1
+        delete ridges between facet1 and facet2
+        append other ridges to facet2 after renaming facet to facet2
+*/
+void qh_mergesimplex(qhT *qh, facetT *facet1, facetT *facet2, boolT mergeapex) {
+  vertexT *vertex, **vertexp, *apex;
+  ridgeT *ridge, **ridgep;
+  boolT issubset= False;
+  int vertex_i= -1, vertex_n;
+  facetT *neighbor, **neighborp, *otherfacet;
+
+  if (mergeapex) {
+    if (!facet2->newfacet)
+      qh_newvertices(qh, facet2->vertices);  /* apex is new */
+    apex= SETfirstt_(facet1->vertices, vertexT);
+    if (SETfirstt_(facet2->vertices, vertexT) != apex)
+      qh_setaddnth(qh, &facet2->vertices, 0, apex);  /* apex has last id */
+    else
+      issubset= True;
+  }else {
+    zinc_(Zmergesimplex);
+    FOREACHvertex_(facet1->vertices)
+      vertex->seen= False;
+    FOREACHridge_(facet1->ridges) {
+      if (otherfacet_(ridge, facet1) == facet2) {
+        FOREACHvertex_(ridge->vertices) {
+          vertex->seen= True;
+          vertex->delridge= True;
+        }
+        break;
+      }
+    }
+    FOREACHvertex_(facet1->vertices) {
+      if (!vertex->seen)
+        break;  /* must occur */
+    }
+    apex= vertex;
+    trace4((qh, qh->ferr, 4039, "qh_mergesimplex: merge apex v%d of f%d into facet f%d\n",
+          apex->id, facet1->id, facet2->id));
+    FOREACHvertex_i_(qh, facet2->vertices) {
+      if (vertex->id < apex->id) {
+        break;
+      }else if (vertex->id == apex->id) {
+        issubset= True;
+        break;
+      }
+    }
+    if (!issubset)
+      qh_setaddnth(qh, &facet2->vertices, vertex_i, apex);
+    if (!facet2->newfacet)
+      qh_newvertices(qh, facet2->vertices);
+    else if (!apex->newlist) {
+      qh_removevertex(qh, apex);
+      qh_appendvertex(qh, apex);
+    }
+  }
+  trace4((qh, qh->ferr, 4040, "qh_mergesimplex: update vertex neighbors of f%d\n",
+          facet1->id));
+  FOREACHvertex_(facet1->vertices) {
+    if (vertex == apex && !issubset)
+      qh_setreplace(qh, vertex->neighbors, facet1, facet2);
+    else {
+      qh_setdel(vertex->neighbors, facet1);
+      if (!SETsecond_(vertex->neighbors))
+        qh_mergevertex_del(qh, vertex, facet1, facet2);
+    }
+  }
+  trace4((qh, qh->ferr, 4041, "qh_mergesimplex: merge ridges and neighbors of f%d into f%d\n",
+          facet1->id, facet2->id));
+  qh->visit_id++;
+  FOREACHneighbor_(facet2)
+    neighbor->visitid= qh->visit_id;
+  FOREACHridge_(facet1->ridges) {
+    otherfacet= otherfacet_(ridge, facet1);
+    if (otherfacet == facet2) {
+      qh_setdel(facet2->ridges, ridge);
+      qh_setfree(qh, &(ridge->vertices));
+      qh_memfree(qh, ridge, (int)sizeof(ridgeT));
+      qh_setdel(facet2->neighbors, facet1);
+    }else {
+      qh_setappend(qh, &facet2->ridges, ridge);
+      if (otherfacet->visitid != qh->visit_id) {
+        qh_setappend(qh, &facet2->neighbors, otherfacet);
+        qh_setreplace(qh, otherfacet->neighbors, facet1, facet2);
+        otherfacet->visitid= qh->visit_id;
+      }else {
+        if (otherfacet->simplicial)    /* is degen, needs ridges */
+          qh_makeridges(qh, otherfacet);
+        if (SETfirstt_(otherfacet->neighbors, facetT) != facet1)
+          qh_setdel(otherfacet->neighbors, facet1);
+        else {   /*keep newfacet->neighbors->horizon*/
+          qh_setdel(otherfacet->neighbors, facet2);
+          qh_setreplace(qh, otherfacet->neighbors, facet1, facet2);
+        }
+      }
+      if (ridge->top == facet1) /* wait until after qh_makeridges */
+        ridge->top= facet2;
+      else
+        ridge->bottom= facet2;
+    }
+  }
+  SETfirst_(facet1->ridges)= NULL; /* it will be deleted */
+  trace3((qh, qh->ferr, 3006, "qh_mergesimplex: merged simplex f%d apex v%d into facet f%d\n",
+          facet1->id, getid_(apex), facet2->id));
+} /* mergesimplex */
+
+/*-<a                             href="qh-merge_r.htm#TOC"
+  >-------------------------------</a><a name="mergevertex_del">-</a>
+
+  qh_mergevertex_del(qh, vertex, facet1, facet2 )
+    delete a vertex because of merging facet1 into facet2
+
+  returns:
+    deletes vertex from facet2
+    adds vertex to qh.del_vertices for later deletion
+*/
+void qh_mergevertex_del(qhT *qh, vertexT *vertex, facetT *facet1, facetT *facet2) {
+
+  zinc_(Zmergevertex);
+  trace2((qh, qh->ferr, 2035, "qh_mergevertex_del: deleted v%d when merging f%d into f%d\n",
+          vertex->id, facet1->id, facet2->id));
+  qh_setdelsorted(facet2->vertices, vertex);
+  vertex->deleted= True;
+  qh_setappend(qh, &qh->del_vertices, vertex);
+} /* mergevertex_del */
+
+/*-<a                             href="qh-merge_r.htm#TOC"
+  >-------------------------------</a><a name="mergevertex_neighbors">-</a>
+
+  qh_mergevertex_neighbors(qh, facet1, facet2 )
+    merge the vertex neighbors of facet1 to facet2
+
+  returns:
+    if vertex is current qh.vertex_visit
+      deletes facet1 from vertex->neighbors
+    else
+      renames facet1 to facet2 in vertex->neighbors
+    deletes vertices if only one neighbor
+
+  notes:
+    assumes vertex neighbor sets are good
+*/
+void qh_mergevertex_neighbors(qhT *qh, facetT *facet1, facetT *facet2) {
+  vertexT *vertex, **vertexp;
+
+  trace4((qh, qh->ferr, 4042, "qh_mergevertex_neighbors: merge vertex neighbors of f%d and f%d\n",
+          facet1->id, facet2->id));
+  if (qh->tracevertex) {
+    qh_fprintf(qh, qh->ferr, 8081, "qh_mergevertex_neighbors: of f%d and f%d at furthest p%d f0= %p\n",
+             facet1->id, facet2->id, qh->furthest_id, qh->tracevertex->neighbors->e[0].p);
+    qh_errprint(qh, "TRACE", NULL, NULL, NULL, qh->tracevertex);
+  }
+  FOREACHvertex_(facet1->vertices) {
+    if (vertex->visitid != qh->vertex_visit)
+      qh_setreplace(qh, vertex->neighbors, facet1, facet2);
+    else {
+      qh_setdel(vertex->neighbors, facet1);
+      if (!SETsecond_(vertex->neighbors))
+        qh_mergevertex_del(qh, vertex, facet1, facet2);
+    }
+  }
+  if (qh->tracevertex)
+    qh_errprint(qh, "TRACE", NULL, NULL, NULL, qh->tracevertex);
+} /* mergevertex_neighbors */
+
+
+/*-<a                             href="qh-merge_r.htm#TOC"
+  >-------------------------------</a><a name="mergevertices">-</a>
+
+  qh_mergevertices(qh, vertices1, vertices2 )
+    merges the vertex set of facet1 into facet2
+
+  returns:
+    replaces vertices2 with merged set
+    preserves vertex_visit for qh_mergevertex_neighbors
+    updates qh.newvertex_list
+
+  design:
+    create a merged set of both vertices (in inverse id order)
+*/
+void qh_mergevertices(qhT *qh, setT *vertices1, setT **vertices2) {
+  int newsize= qh_setsize(qh, vertices1)+qh_setsize(qh, *vertices2) - qh->hull_dim + 1;
+  setT *mergedvertices;
+  vertexT *vertex, **vertexp, **vertex2= SETaddr_(*vertices2, vertexT);
+
+  mergedvertices= qh_settemp(qh, newsize);
+  FOREACHvertex_(vertices1) {
+    if (!*vertex2 || vertex->id > (*vertex2)->id)
+      qh_setappend(qh, &mergedvertices, vertex);
+    else {
+      while (*vertex2 && (*vertex2)->id > vertex->id)
+        qh_setappend(qh, &mergedvertices, *vertex2++);
+      if (!*vertex2 || (*vertex2)->id < vertex->id)
+        qh_setappend(qh, &mergedvertices, vertex);
+      else
+        qh_setappend(qh, &mergedvertices, *vertex2++);
+    }
+  }
+  while (*vertex2)
+    qh_setappend(qh, &mergedvertices, *vertex2++);
+  if (newsize < qh_setsize(qh, mergedvertices)) {
+    qh_fprintf(qh, qh->ferr, 6100, "qhull internal error (qh_mergevertices): facets did not share a ridge\n");
+    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+  }
+  qh_setfree(qh, vertices2);
+  *vertices2= mergedvertices;
+  qh_settemppop(qh);
+} /* mergevertices */
+
+
+/*-<a                             href="qh-merge_r.htm#TOC"
+  >-------------------------------</a><a name="neighbor_intersections">-</a>
+
+  qh_neighbor_intersections(qh, vertex )
+    return intersection of all vertices in vertex->neighbors except for vertex
+
+  returns:
+    returns temporary set of vertices
+    does not include vertex
+    NULL if a neighbor is simplicial
+    NULL if empty set
+
+  notes:
+    used for renaming vertices
+
+  design:
+    initialize the intersection set with vertices of the first two neighbors
+    delete vertex from the intersection
+    for each remaining neighbor
+      intersect its vertex set with the intersection set
+      return NULL if empty
+    return the intersection set
+*/
+setT *qh_neighbor_intersections(qhT *qh, vertexT *vertex) {
+  facetT *neighbor, **neighborp, *neighborA, *neighborB;
+  setT *intersect;
+  int neighbor_i, neighbor_n;
+
+  FOREACHneighbor_(vertex) {
+    if (neighbor->simplicial)
+      return NULL;
+  }
+  neighborA= SETfirstt_(vertex->neighbors, facetT);
+  neighborB= SETsecondt_(vertex->neighbors, facetT);
+  zinc_(Zintersectnum);
+  if (!neighborA)
+    return NULL;
+  if (!neighborB)
+    intersect= qh_setcopy(qh, neighborA->vertices, 0);
+  else
+    intersect= qh_vertexintersect_new(qh, neighborA->vertices, neighborB->vertices);
+  qh_settemppush(qh, intersect);
+  qh_setdelsorted(intersect, vertex);
+  FOREACHneighbor_i_(qh, vertex) {
+    if (neighbor_i >= 2) {
+      zinc_(Zintersectnum);
+      qh_vertexintersect(qh, &intersect, neighbor->vertices);
+      if (!SETfirst_(intersect)) {
+        zinc_(Zintersectfail);
+        qh_settempfree(qh, &intersect);
+        return NULL;
+      }
+    }
+  }
+  trace3((qh, qh->ferr, 3007, "qh_neighbor_intersections: %d vertices in neighbor intersection of v%d\n",
+          qh_setsize(qh, intersect), vertex->id));
+  return intersect;
+} /* neighbor_intersections */
+
+/*-<a                             href="qh-merge_r.htm#TOC"
+  >-------------------------------</a><a name="newvertices">-</a>
+
+  qh_newvertices(qh, vertices )
+    add vertices to end of qh.vertex_list (marks as new vertices)
+
+  returns:
+    vertices on qh.newvertex_list
+    vertex->newlist set
+*/
+void qh_newvertices(qhT *qh, setT *vertices) {
+  vertexT *vertex, **vertexp;
+
+  FOREACHvertex_(vertices) {
+    if (!vertex->newlist) {
+      qh_removevertex(qh, vertex);
+      qh_appendvertex(qh, vertex);
+    }
+  }
+} /* newvertices */
+
+/*-<a                             href="qh-merge_r.htm#TOC"
+  >-------------------------------</a><a name="reducevertices">-</a>
+
+  qh_reducevertices(qh)
+    reduce extra vertices, shared vertices, and redundant vertices
+    facet->newmerge is set if merged since last call
+    if !qh.MERGEvertices, only removes extra vertices
+
+  returns:
+    True if also merged degen_redundant facets
+    vertices are renamed if possible
+    clears facet->newmerge and vertex->delridge
+
+  notes:
+    ignored if 2-d
+
+  design:
+    merge any degenerate or redundant facets
+    for each newly merged facet
+      remove extra vertices
+    if qh.MERGEvertices
+      for each newly merged facet
+        for each vertex
+          if vertex was on a deleted ridge
+            rename vertex if it is shared
+      remove delridge flag from new vertices
+*/
+boolT qh_reducevertices(qhT *qh) {
+  int numshare=0, numrename= 0;
+  boolT degenredun= False;
+  facetT *newfacet;
+  vertexT *vertex, **vertexp;
+
+  if (qh->hull_dim == 2)
+    return False;
+  if (qh_merge_degenredundant(qh))
+    degenredun= True;
+ LABELrestart:
+  FORALLnew_facets {
+    if (newfacet->newmerge) {
+      if (!qh->MERGEvertices)
+        newfacet->newmerge= False;
+      qh_remove_extravertices(qh, newfacet);
+    }
+  }
+  if (!qh->MERGEvertices)
+    return False;
+  FORALLnew_facets {
+    if (newfacet->newmerge) {
+      newfacet->newmerge= False;
+      FOREACHvertex_(newfacet->vertices) {
+        if (vertex->delridge) {
+          if (qh_rename_sharedvertex(qh, vertex, newfacet)) {
+            numshare++;
+            vertexp--; /* repeat since deleted vertex */
+          }
+        }
+      }
+    }
+  }
+  FORALLvertex_(qh->newvertex_list) {
+    if (vertex->delridge && !vertex->deleted) {
+      vertex->delridge= False;
+      if (qh->hull_dim >= 4 && qh_redundant_vertex(qh, vertex)) {
+        numrename++;
+        if (qh_merge_degenredundant(qh)) {
+          degenredun= True;
+          goto LABELrestart;
+        }
+      }
+    }
+  }
+  trace1((qh, qh->ferr, 1014, "qh_reducevertices: renamed %d shared vertices and %d redundant vertices. Degen? %d\n",
+          numshare, numrename, degenredun));
+  return degenredun;
+} /* reducevertices */
+
+/*-<a                             href="qh-merge_r.htm#TOC"
+  >-------------------------------</a><a name="redundant_vertex">-</a>
+
+  qh_redundant_vertex(qh, vertex )
+    detect and rename a redundant vertex
+    vertices have full vertex->neighbors
+
+  returns:
+    returns true if find a redundant vertex
+      deletes vertex(vertex->deleted)
+
+  notes:
+    only needed if vertex->delridge and hull_dim >= 4
+    may add degenerate facets to qh.facet_mergeset
+    doesn't change vertex->neighbors or create redundant facets
+
+  design:
+    intersect vertices of all facet neighbors of vertex
+    determine ridges for these vertices
+    if find a new vertex for vertex amoung these ridges and vertices
+      rename vertex to the new vertex
+*/
+vertexT *qh_redundant_vertex(qhT *qh, vertexT *vertex) {
+  vertexT *newvertex= NULL;
+  setT *vertices, *ridges;
+
+  trace3((qh, qh->ferr, 3008, "qh_redundant_vertex: check if v%d can be renamed\n", vertex->id));
+  if ((vertices= qh_neighbor_intersections(qh, vertex))) {
+    ridges= qh_vertexridges(qh, vertex);
+    if ((newvertex= qh_find_newvertex(qh, vertex, vertices, ridges)))
+      qh_renamevertex(qh, vertex, newvertex, ridges, NULL, NULL);
+    qh_settempfree(qh, &ridges);
+    qh_settempfree(qh, &vertices);
+  }
+  return newvertex;
+} /* redundant_vertex */
+
+/*-<a                             href="qh-merge_r.htm#TOC"
+  >-------------------------------</a><a name="remove_extravertices">-</a>
+
+  qh_remove_extravertices(qh, facet )
+    remove extra vertices from non-simplicial facets
+
+  returns:
+    returns True if it finds them
+
+  design:
+    for each vertex in facet
+      if vertex not in a ridge (i.e., no longer used)
+        delete vertex from facet
+        delete facet from vertice's neighbors
+        unless vertex in another facet
+          add vertex to qh.del_vertices for later deletion
+*/
+boolT qh_remove_extravertices(qhT *qh, facetT *facet) {
+  ridgeT *ridge, **ridgep;
+  vertexT *vertex, **vertexp;
+  boolT foundrem= False;
+
+  trace4((qh, qh->ferr, 4043, "qh_remove_extravertices: test f%d for extra vertices\n",
+          facet->id));
+  FOREACHvertex_(facet->vertices)
+    vertex->seen= False;
+  FOREACHridge_(facet->ridges) {
+    FOREACHvertex_(ridge->vertices)
+      vertex->seen= True;
+  }
+  FOREACHvertex_(facet->vertices) {
+    if (!vertex->seen) {
+      foundrem= True;
+      zinc_(Zremvertex);
+      qh_setdelsorted(facet->vertices, vertex);
+      qh_setdel(vertex->neighbors, facet);
+      if (!qh_setsize(qh, vertex->neighbors)) {
+        vertex->deleted= True;
+        qh_setappend(qh, &qh->del_vertices, vertex);
+        zinc_(Zremvertexdel);
+        trace2((qh, qh->ferr, 2036, "qh_remove_extravertices: v%d deleted because it's lost all ridges\n", vertex->id));
+      }else
+        trace3((qh, qh->ferr, 3009, "qh_remove_extravertices: v%d removed from f%d because it's lost all ridges\n", vertex->id, facet->id));
+      vertexp--; /*repeat*/
+    }
+  }
+  return foundrem;
+} /* remove_extravertices */
+
+/*-<a                             href="qh-merge_r.htm#TOC"
+  >-------------------------------</a><a name="rename_sharedvertex">-</a>
+
+  qh_rename_sharedvertex(qh, vertex, facet )
+    detect and rename if shared vertex in facet
+    vertices have full ->neighbors
+
+  returns:
+    newvertex or NULL
+    the vertex may still exist in other facets (i.e., a neighbor was pinched)
+    does not change facet->neighbors
+    updates vertex->neighbors
+
+  notes:
+    a shared vertex for a facet is only in ridges to one neighbor
+    this may undo a pinched facet
+
+    it does not catch pinches involving multiple facets.  These appear
+      to be difficult to detect, since an exhaustive search is too expensive.
+
+  design:
+    if vertex only has two neighbors
+      determine the ridges that contain the vertex
+      determine the vertices shared by both neighbors
+      if can find a new vertex in this set
+        rename the vertex to the new vertex
+*/
+vertexT *qh_rename_sharedvertex(qhT *qh, vertexT *vertex, facetT *facet) {
+  facetT *neighbor, **neighborp, *neighborA= NULL;
+  setT *vertices, *ridges;
+  vertexT *newvertex;
+
+  if (qh_setsize(qh, vertex->neighbors) == 2) {
+    neighborA= SETfirstt_(vertex->neighbors, facetT);
+    if (neighborA == facet)
+      neighborA= SETsecondt_(vertex->neighbors, facetT);
+  }else if (qh->hull_dim == 3)
+    return NULL;
+  else {
+    qh->visit_id++;
+    FOREACHneighbor_(facet)
+      neighbor->visitid= qh->visit_id;
+    FOREACHneighbor_(vertex) {
+      if (neighbor->visitid == qh->visit_id) {
+        if (neighborA)
+          return NULL;
+        neighborA= neighbor;
+      }
+    }
+    if (!neighborA) {
+      qh_fprintf(qh, qh->ferr, 6101, "qhull internal error (qh_rename_sharedvertex): v%d's neighbors not in f%d\n",
+        vertex->id, facet->id);
+      qh_errprint(qh, "ERRONEOUS", facet, NULL, NULL, vertex);
+      qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+    }
+  }
+  /* the vertex is shared by facet and neighborA */
+  ridges= qh_settemp(qh, qh->TEMPsize);
+  neighborA->visitid= ++qh->visit_id;
+  qh_vertexridges_facet(qh, vertex, facet, &ridges);
+  trace2((qh, qh->ferr, 2037, "qh_rename_sharedvertex: p%d(v%d) is shared by f%d(%d ridges) and f%d\n",
+    qh_pointid(qh, vertex->point), vertex->id, facet->id, qh_setsize(qh, ridges), neighborA->id));
+  zinc_(Zintersectnum);
+  vertices= qh_vertexintersect_new(qh, facet->vertices, neighborA->vertices);
+  qh_setdel(vertices, vertex);
+  qh_settemppush(qh, vertices);
+  if ((newvertex= qh_find_newvertex(qh, vertex, vertices, ridges)))
+    qh_renamevertex(qh, vertex, newvertex, ridges, facet, neighborA);
+  qh_settempfree(qh, &vertices);
+  qh_settempfree(qh, &ridges);
+  return newvertex;
+} /* rename_sharedvertex */
+
+/*-<a                             href="qh-merge_r.htm#TOC"
+  >-------------------------------</a><a name="renameridgevertex">-</a>
+
+  qh_renameridgevertex(qh, ridge, oldvertex, newvertex )
+    renames oldvertex as newvertex in ridge
+
+  returns:
+
+  design:
+    delete oldvertex from ridge
+    if newvertex already in ridge
+      copy ridge->noconvex to another ridge if possible
+      delete the ridge
+    else
+      insert newvertex into the ridge
+      adjust the ridge's orientation
+*/
+void qh_renameridgevertex(qhT *qh, ridgeT *ridge, vertexT *oldvertex, vertexT *newvertex) {
+  int nth= 0, oldnth;
+  facetT *temp;
+  vertexT *vertex, **vertexp;
+
+  oldnth= qh_setindex(ridge->vertices, oldvertex);
+  qh_setdelnthsorted(qh, ridge->vertices, oldnth);
+  FOREACHvertex_(ridge->vertices) {
+    if (vertex == newvertex) {
+      zinc_(Zdelridge);
+      if (ridge->nonconvex) /* only one ridge has nonconvex set */
+        qh_copynonconvex(qh, ridge);
+      trace2((qh, qh->ferr, 2038, "qh_renameridgevertex: ridge r%d deleted.  It contained both v%d and v%d\n",
+        ridge->id, oldvertex->id, newvertex->id));
+      qh_delridge(qh, ridge);
+      return;
+    }
+    if (vertex->id < newvertex->id)
+      break;
+    nth++;
+  }
+  qh_setaddnth(qh, &ridge->vertices, nth, newvertex);
+  if (abs(oldnth - nth)%2) {
+    trace3((qh, qh->ferr, 3010, "qh_renameridgevertex: swapped the top and bottom of ridge r%d\n",
+            ridge->id));
+    temp= ridge->top;
+    ridge->top= ridge->bottom;
+    ridge->bottom= temp;
+  }
+} /* renameridgevertex */
+
+
+/*-<a                             href="qh-merge_r.htm#TOC"
+  >-------------------------------</a><a name="renamevertex">-</a>
+
+  qh_renamevertex(qh, oldvertex, newvertex, ridges, oldfacet, neighborA )
+    renames oldvertex as newvertex in ridges
+    gives oldfacet/neighborA if oldvertex is shared between two facets
+
+  returns:
+    oldvertex may still exist afterwards
+
+
+  notes:
+    can not change neighbors of newvertex (since it's a subset)
+
+  design:
+    for each ridge in ridges
+      rename oldvertex to newvertex and delete degenerate ridges
+    if oldfacet not defined
+      for each neighbor of oldvertex
+        delete oldvertex from neighbor's vertices
+        remove extra vertices from neighbor
+      add oldvertex to qh.del_vertices
+    else if oldvertex only between oldfacet and neighborA
+      delete oldvertex from oldfacet and neighborA
+      add oldvertex to qh.del_vertices
+    else oldvertex is in oldfacet and neighborA and other facets (i.e., pinched)
+      delete oldvertex from oldfacet
+      delete oldfacet from oldvertice's neighbors
+      remove extra vertices (e.g., oldvertex) from neighborA
+*/
+void qh_renamevertex(qhT *qh, vertexT *oldvertex, vertexT *newvertex, setT *ridges, facetT *oldfacet, facetT *neighborA) {
+  facetT *neighbor, **neighborp;
+  ridgeT *ridge, **ridgep;
+  boolT istrace= False;
+
+  if (qh->IStracing >= 2 || oldvertex->id == qh->tracevertex_id ||
+        newvertex->id == qh->tracevertex_id)
+    istrace= True;
+  FOREACHridge_(ridges)
+    qh_renameridgevertex(qh, ridge, oldvertex, newvertex);
+  if (!oldfacet) {
+    zinc_(Zrenameall);
+    if (istrace)
+      qh_fprintf(qh, qh->ferr, 8082, "qh_renamevertex: renamed v%d to v%d in several facets\n",
+               oldvertex->id, newvertex->id);
+    FOREACHneighbor_(oldvertex) {
+      qh_maydropneighbor(qh, neighbor);
+      qh_setdelsorted(neighbor->vertices, oldvertex);
+      if (qh_remove_extravertices(qh, neighbor))
+        neighborp--; /* neighbor may be deleted */
+    }
+    if (!oldvertex->deleted) {
+      oldvertex->deleted= True;
+      qh_setappend(qh, &qh->del_vertices, oldvertex);
+    }
+  }else if (qh_setsize(qh, oldvertex->neighbors) == 2) {
+    zinc_(Zrenameshare);
+    if (istrace)
+      qh_fprintf(qh, qh->ferr, 8083, "qh_renamevertex: renamed v%d to v%d in oldfacet f%d\n",
+               oldvertex->id, newvertex->id, oldfacet->id);
+    FOREACHneighbor_(oldvertex)
+      qh_setdelsorted(neighbor->vertices, oldvertex);
+    oldvertex->deleted= True;
+    qh_setappend(qh, &qh->del_vertices, oldvertex);
+  }else {
+    zinc_(Zrenamepinch);
+    if (istrace || qh->IStracing)
+      qh_fprintf(qh, qh->ferr, 8084, "qh_renamevertex: renamed pinched v%d to v%d between f%d and f%d\n",
+               oldvertex->id, newvertex->id, oldfacet->id, neighborA->id);
+    qh_setdelsorted(oldfacet->vertices, oldvertex);
+    qh_setdel(oldvertex->neighbors, oldfacet);
+    qh_remove_extravertices(qh, neighborA);
+  }
+} /* renamevertex */
+
+
+/*-<a                             href="qh-merge_r.htm#TOC"
+  >-------------------------------</a><a name="test_appendmerge">-</a>
+
+  qh_test_appendmerge(qh, facet, neighbor )
+    tests facet/neighbor for convexity
+    appends to mergeset if non-convex
+    if pre-merging,
+      nop if qh.SKIPconvex, or qh.MERGEexact and coplanar
+
+  returns:
+    true if appends facet/neighbor to mergeset
+    sets facet->center as needed
+    does not change facet->seen
+
+  design:
+    if qh.cos_max is defined
+      if the angle between facet normals is too shallow
+        append an angle-coplanar merge to qh.mergeset
+        return True
+    make facet's centrum if needed
+    if facet's centrum is above the neighbor
+      set isconcave
+    else
+      if facet's centrum is not below the neighbor
+        set iscoplanar
+      make neighbor's centrum if needed
+      if neighbor's centrum is above the facet
+        set isconcave
+      else if neighbor's centrum is not below the facet
+        set iscoplanar
+   if isconcave or iscoplanar
+     get angle if needed
+     append concave or coplanar merge to qh.mergeset
+*/
+boolT qh_test_appendmerge(qhT *qh, facetT *facet, facetT *neighbor) {
+  realT dist, dist2= -REALmax, angle= -REALmax;
+  boolT isconcave= False, iscoplanar= False, okangle= False;
+
+  if (qh->SKIPconvex && !qh->POSTmerging)
+    return False;
+  if ((!qh->MERGEexact || qh->POSTmerging) && qh->cos_max < REALmax/2) {
+    angle= qh_getangle(qh, facet->normal, neighbor->normal);
+    zinc_(Zangletests);
+    if (angle > qh->cos_max) {
+      zinc_(Zcoplanarangle);
+      qh_appendmergeset(qh, facet, neighbor, MRGanglecoplanar, &angle);
+      trace2((qh, qh->ferr, 2039, "qh_test_appendmerge: coplanar angle %4.4g between f%d and f%d\n",
+         angle, facet->id, neighbor->id));
+      return True;
+    }else
+      okangle= True;
+  }
+  if (!facet->center)
+    facet->center= qh_getcentrum(qh, facet);
+  zzinc_(Zcentrumtests);
+  qh_distplane(qh, facet->center, neighbor, &dist);
+  if (dist > qh->centrum_radius)
+    isconcave= True;
+  else {
+    if (dist > -qh->centrum_radius)
+      iscoplanar= True;
+    if (!neighbor->center)
+      neighbor->center= qh_getcentrum(qh, neighbor);
+    zzinc_(Zcentrumtests);
+    qh_distplane(qh, neighbor->center, facet, &dist2);
+    if (dist2 > qh->centrum_radius)
+      isconcave= True;
+    else if (!iscoplanar && dist2 > -qh->centrum_radius)
+      iscoplanar= True;
+  }
+  if (!isconcave && (!iscoplanar || (qh->MERGEexact && !qh->POSTmerging)))
+    return False;
+  if (!okangle && qh->ANGLEmerge) {
+    angle= qh_getangle(qh, facet->normal, neighbor->normal);
+    zinc_(Zangletests);
+  }
+  if (isconcave) {
+    zinc_(Zconcaveridge);
+    if (qh->ANGLEmerge)
+      angle += qh_ANGLEconcave + 0.5;
+    qh_appendmergeset(qh, facet, neighbor, MRGconcave, &angle);
+    trace0((qh, qh->ferr, 18, "qh_test_appendmerge: concave f%d to f%d dist %4.4g and reverse dist %4.4g angle %4.4g during p%d\n",
+           facet->id, neighbor->id, dist, dist2, angle, qh->furthest_id));
+  }else /* iscoplanar */ {
+    zinc_(Zcoplanarcentrum);
+    qh_appendmergeset(qh, facet, neighbor, MRGcoplanar, &angle);
+    trace2((qh, qh->ferr, 2040, "qh_test_appendmerge: coplanar f%d to f%d dist %4.4g, reverse dist %4.4g angle %4.4g\n",
+              facet->id, neighbor->id, dist, dist2, angle));
+  }
+  return True;
+} /* test_appendmerge */
+
+/*-<a                             href="qh-merge_r.htm#TOC"
+  >-------------------------------</a><a name="test_vneighbors">-</a>
+
+  qh_test_vneighbors(qh)
+    test vertex neighbors for convexity
+    tests all facets on qh.newfacet_list
+
+  returns:
+    true if non-convex vneighbors appended to qh.facet_mergeset
+    initializes vertex neighbors if needed
+
+  notes:
+    assumes all facet neighbors have been tested
+    this can be expensive
+    this does not guarantee that a centrum is below all facets
+      but it is unlikely
+    uses qh.visit_id
+
+  design:
+    build vertex neighbors if necessary
+    for all new facets
+      for all vertices
+        for each unvisited facet neighbor of the vertex
+          test new facet and neighbor for convexity
+*/
+boolT qh_test_vneighbors(qhT *qh /* qh->newfacet_list */) {
+  facetT *newfacet, *neighbor, **neighborp;
+  vertexT *vertex, **vertexp;
+  int nummerges= 0;
+
+  trace1((qh, qh->ferr, 1015, "qh_test_vneighbors: testing vertex neighbors for convexity\n"));
+  if (!qh->VERTEXneighbors)
+    qh_vertexneighbors(qh);
+  FORALLnew_facets
+    newfacet->seen= False;
+  FORALLnew_facets {
+    newfacet->seen= True;
+    newfacet->visitid= qh->visit_id++;
+    FOREACHneighbor_(newfacet)
+      newfacet->visitid= qh->visit_id;
+    FOREACHvertex_(newfacet->vertices) {
+      FOREACHneighbor_(vertex) {
+        if (neighbor->seen || neighbor->visitid == qh->visit_id)
+          continue;
+        if (qh_test_appendmerge(qh, newfacet, neighbor))
+          nummerges++;
+      }
+    }
+  }
+  zadd_(Ztestvneighbor, nummerges);
+  trace1((qh, qh->ferr, 1016, "qh_test_vneighbors: found %d non-convex, vertex neighbors\n",
+           nummerges));
+  return (nummerges > 0);
+} /* test_vneighbors */
+
+/*-<a                             href="qh-merge_r.htm#TOC"
+  >-------------------------------</a><a name="tracemerge">-</a>
+
+  qh_tracemerge(qh, facet1, facet2 )
+    print trace message after merge
+*/
+void qh_tracemerge(qhT *qh, facetT *facet1, facetT *facet2) {
+  boolT waserror= False;
+
+#ifndef qh_NOtrace
+  if (qh->IStracing >= 4)
+    qh_errprint(qh, "MERGED", facet2, NULL, NULL, NULL);
+  if (facet2 == qh->tracefacet || (qh->tracevertex && qh->tracevertex->newlist)) {
+    qh_fprintf(qh, qh->ferr, 8085, "qh_tracemerge: trace facet and vertex after merge of f%d and f%d, furthest p%d\n", facet1->id, facet2->id, qh->furthest_id);
+    if (facet2 != qh->tracefacet)
+      qh_errprint(qh, "TRACE", qh->tracefacet,
+        (qh->tracevertex && qh->tracevertex->neighbors) ?
+           SETfirstt_(qh->tracevertex->neighbors, facetT) : NULL,
+        NULL, qh->tracevertex);
+  }
+  if (qh->tracevertex) {
+    if (qh->tracevertex->deleted)
+      qh_fprintf(qh, qh->ferr, 8086, "qh_tracemerge: trace vertex deleted at furthest p%d\n",
+            qh->furthest_id);
+    else
+      qh_checkvertex(qh, qh->tracevertex);
+  }
+  if (qh->tracefacet) {
+    qh_checkfacet(qh, qh->tracefacet, True, &waserror);
+    if (waserror)
+      qh_errexit(qh, qh_ERRqhull, qh->tracefacet, NULL);
+  }
+#endif /* !qh_NOtrace */
+  if (qh->CHECKfrequently || qh->IStracing >= 4) { /* can't check polygon here */
+    qh_checkfacet(qh, facet2, True, &waserror);
+    if (waserror)
+      qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+  }
+} /* tracemerge */
+
+/*-<a                             href="qh-merge_r.htm#TOC"
+  >-------------------------------</a><a name="tracemerging">-</a>
+
+  qh_tracemerging(qh)
+    print trace message during POSTmerging
+
+  returns:
+    updates qh.mergereport
+
+  notes:
+    called from qh_mergecycle() and qh_mergefacet()
+
+  see:
+    qh_buildtracing()
+*/
+void qh_tracemerging(qhT *qh) {
+  realT cpu;
+  int total;
+  time_t timedata;
+  struct tm *tp;
+
+  qh->mergereport= zzval_(Ztotmerge);
+  time(&timedata);
+  tp= localtime(&timedata);
+  cpu= qh_CPUclock;
+  cpu /= qh_SECticks;
+  total= zzval_(Ztotmerge) - zzval_(Zcyclehorizon) + zzval_(Zcyclefacettot);
+  qh_fprintf(qh, qh->ferr, 8087, "\n\
+At %d:%d:%d & %2.5g CPU secs, qhull has merged %d facets.  The hull\n\
+  contains %d facets and %d vertices.\n",
+      tp->tm_hour, tp->tm_min, tp->tm_sec, cpu,
+      total, qh->num_facets - qh->num_visible,
+      qh->num_vertices-qh_setsize(qh, qh->del_vertices));
+} /* tracemerging */
+
+/*-<a                             href="qh-merge_r.htm#TOC"
+  >-------------------------------</a><a name="updatetested">-</a>
+
+  qh_updatetested(qh, facet1, facet2 )
+    clear facet2->tested and facet1->ridge->tested for merge
+
+  returns:
+    deletes facet2->center unless it's already large
+      if so, clears facet2->ridge->tested
+
+  design:
+    clear facet2->tested
+    clear ridge->tested for facet1's ridges
+    if facet2 has a centrum
+      if facet2 is large
+        set facet2->keepcentrum
+      else if facet2 has 3 vertices due to many merges, or not large and post merging
+        clear facet2->keepcentrum
+      unless facet2->keepcentrum
+        clear facet2->center to recompute centrum later
+        clear ridge->tested for facet2's ridges
+*/
+void qh_updatetested(qhT *qh, facetT *facet1, facetT *facet2) {
+  ridgeT *ridge, **ridgep;
+  int size;
+
+  facet2->tested= False;
+  FOREACHridge_(facet1->ridges)
+    ridge->tested= False;
+  if (!facet2->center)
+    return;
+  size= qh_setsize(qh, facet2->vertices);
+  if (!facet2->keepcentrum) {
+    if (size > qh->hull_dim + qh_MAXnewcentrum) {
+      facet2->keepcentrum= True;
+      zinc_(Zwidevertices);
+    }
+  }else if (size <= qh->hull_dim + qh_MAXnewcentrum) {
+    /* center and keepcentrum was set */
+    if (size == qh->hull_dim || qh->POSTmerging)
+      facet2->keepcentrum= False; /* if many merges need to recompute centrum */
+  }
+  if (!facet2->keepcentrum) {
+    qh_memfree(qh, facet2->center, qh->normal_size);
+    facet2->center= NULL;
+    FOREACHridge_(facet2->ridges)
+      ridge->tested= False;
+  }
+} /* updatetested */
+
+/*-<a                             href="qh-merge_r.htm#TOC"
+  >-------------------------------</a><a name="vertexridges">-</a>
+
+  qh_vertexridges(qh, vertex )
+    return temporary set of ridges adjacent to a vertex
+    vertex->neighbors defined
+
+  ntoes:
+    uses qh.visit_id
+    does not include implicit ridges for simplicial facets
+
+  design:
+    for each neighbor of vertex
+      add ridges that include the vertex to ridges
+*/
+setT *qh_vertexridges(qhT *qh, vertexT *vertex) {
+  facetT *neighbor, **neighborp;
+  setT *ridges= qh_settemp(qh, qh->TEMPsize);
+  int size;
+
+  qh->visit_id++;
+  FOREACHneighbor_(vertex)
+    neighbor->visitid= qh->visit_id;
+  FOREACHneighbor_(vertex) {
+    if (*neighborp)   /* no new ridges in last neighbor */
+      qh_vertexridges_facet(qh, vertex, neighbor, &ridges);
+  }
+  if (qh->PRINTstatistics || qh->IStracing) {
+    size= qh_setsize(qh, ridges);
+    zinc_(Zvertexridge);
+    zadd_(Zvertexridgetot, size);
+    zmax_(Zvertexridgemax, size);
+    trace3((qh, qh->ferr, 3011, "qh_vertexridges: found %d ridges for v%d\n",
+             size, vertex->id));
+  }
+  return ridges;
+} /* vertexridges */
+
+/*-<a                             href="qh-merge_r.htm#TOC"
+  >-------------------------------</a><a name="vertexridges_facet">-</a>
+
+  qh_vertexridges_facet(qh, vertex, facet, ridges )
+    add adjacent ridges for vertex in facet
+    neighbor->visitid==qh.visit_id if it hasn't been visited
+
+  returns:
+    ridges updated
+    sets facet->visitid to qh.visit_id-1
+
+  design:
+    for each ridge of facet
+      if ridge of visited neighbor (i.e., unprocessed)
+        if vertex in ridge
+          append ridge to vertex
+    mark facet processed
+*/
+void qh_vertexridges_facet(qhT *qh, vertexT *vertex, facetT *facet, setT **ridges) {
+  ridgeT *ridge, **ridgep;
+  facetT *neighbor;
+
+  FOREACHridge_(facet->ridges) {
+    neighbor= otherfacet_(ridge, facet);
+    if (neighbor->visitid == qh->visit_id
+    && qh_setin(ridge->vertices, vertex))
+      qh_setappend(qh, ridges, ridge);
+  }
+  facet->visitid= qh->visit_id-1;
+} /* vertexridges_facet */
+
+/*-<a                             href="qh-merge_r.htm#TOC"
+  >-------------------------------</a><a name="willdelete">-</a>
+
+  qh_willdelete(qh, facet, replace )
+    moves facet to visible list
+    sets facet->f.replace to replace (may be NULL)
+
+  returns:
+    bumps qh.num_visible
+*/
+void qh_willdelete(qhT *qh, facetT *facet, facetT *replace) {
+
+  qh_removefacet(qh, facet);
+  qh_prependfacet(qh, facet, &qh->visible_list);
+  qh->num_visible++;
+  facet->visible= True;
+  facet->f.replace= replace;
+} /* willdelete */
+
+#else /* qh_NOmerge */
+void qh_premerge(qhT *qh, vertexT *apex, realT maxcentrum, realT maxangle) {
+}
+void qh_postmerge(qhT *qh, const char *reason, realT maxcentrum, realT maxangle,
+                      boolT vneighbors) {
+}
+boolT qh_checkzero(qhT *qh, boolT testall) {
+   }
+#endif /* qh_NOmerge */
+
diff --git a/xs/src/qhull/src/libqhull_r/merge_r.h b/xs/src/qhull/src/libqhull_r/merge_r.h
new file mode 100644
index 0000000000..30a51815da
--- /dev/null
+++ b/xs/src/qhull/src/libqhull_r/merge_r.h
@@ -0,0 +1,186 @@
+/*<html><pre>  -<a                             href="qh-merge_r.htm"
+  >-------------------------------</a><a name="TOP">-</a>
+
+   merge_r.h
+   header file for merge_r.c
+
+   see qh-merge_r.htm and merge_r.c
+
+   Copyright (c) 1993-2015 C.B. Barber.
+   $Id: //main/2015/qhull/src/libqhull_r/merge_r.h#3 $$Change: 2079 $
+   $DateTime: 2016/02/07 17:43:34 $$Author: bbarber $
+*/
+
+#ifndef qhDEFmerge
+#define qhDEFmerge 1
+
+#include "libqhull_r.h"
+
+
+/*============ -constants- ==============*/
+
+/*-<a                             href="qh-merge_r.htm#TOC"
+  >--------------------------------</a><a name="qh_ANGLEredundant">-</a>
+
+  qh_ANGLEredundant
+    indicates redundant merge in mergeT->angle
+*/
+#define qh_ANGLEredundant 6.0
+
+/*-<a                             href="qh-merge_r.htm#TOC"
+  >--------------------------------</a><a name="qh_ANGLEdegen">-</a>
+
+  qh_ANGLEdegen
+    indicates degenerate facet in mergeT->angle
+*/
+#define qh_ANGLEdegen     5.0
+
+/*-<a                             href="qh-merge_r.htm#TOC"
+  >--------------------------------</a><a name="qh_ANGLEconcave">-</a>
+
+  qh_ANGLEconcave
+    offset to indicate concave facets in mergeT->angle
+
+  notes:
+    concave facets are assigned the range of [2,4] in mergeT->angle
+    roundoff error may make the angle less than 2
+*/
+#define qh_ANGLEconcave  1.5
+
+/*-<a                             href="qh-merge_r.htm#TOC"
+  >--------------------------------</a><a name="MRG">-</a>
+
+  MRG... (mergeType)
+    indicates the type of a merge (mergeT->type)
+*/
+typedef enum {  /* in sort order for facet_mergeset */
+  MRGnone= 0,
+  MRGcoplanar,          /* centrum coplanar */
+  MRGanglecoplanar,     /* angle coplanar */
+                        /* could detect half concave ridges */
+  MRGconcave,           /* concave ridge */
+  MRGflip,              /* flipped facet. facet1 == facet2 */
+  MRGridge,             /* duplicate ridge (qh_MERGEridge) */
+                        /* degen and redundant go onto degen_mergeset */
+  MRGdegen,             /* degenerate facet (!enough neighbors) facet1 == facet2 */
+  MRGredundant,         /* redundant facet (vertex subset) */
+                        /* merge_degenredundant assumes degen < redundant */
+  MRGmirror,            /* mirror facet from qh_triangulate */
+  ENDmrg
+} mergeType;
+
+/*-<a                             href="qh-merge_r.htm#TOC"
+  >--------------------------------</a><a name="qh_MERGEapex">-</a>
+
+  qh_MERGEapex
+    flag for qh_mergefacet() to indicate an apex merge
+*/
+#define qh_MERGEapex     True
+
+/*============ -structures- ====================*/
+
+/*-<a                             href="qh-merge_r.htm#TOC"
+  >--------------------------------</a><a name="mergeT">-</a>
+
+  mergeT
+    structure used to merge facets
+*/
+
+typedef struct mergeT mergeT;
+struct mergeT {         /* initialize in qh_appendmergeset */
+  realT   angle;        /* angle between normals of facet1 and facet2 */
+  facetT *facet1;       /* will merge facet1 into facet2 */
+  facetT *facet2;
+  mergeType type;
+};
+
+
+/*=========== -macros- =========================*/
+
+/*-<a                             href="qh-merge_r.htm#TOC"
+  >--------------------------------</a><a name="FOREACHmerge_">-</a>
+
+  FOREACHmerge_( merges ) {...}
+    assign 'merge' to each merge in merges
+
+  notes:
+    uses 'mergeT *merge, **mergep;'
+    if qh_mergefacet(),
+      restart since qh.facet_mergeset may change
+    see <a href="qset_r.h#FOREACHsetelement_">FOREACHsetelement_</a>
+*/
+#define FOREACHmerge_( merges ) FOREACHsetelement_(mergeT, merges, merge)
+
+/*============ prototypes in alphabetical order after pre/postmerge =======*/
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+void    qh_premerge(qhT *qh, vertexT *apex, realT maxcentrum, realT maxangle);
+void    qh_postmerge(qhT *qh, const char *reason, realT maxcentrum, realT maxangle,
+             boolT vneighbors);
+void    qh_all_merges(qhT *qh, boolT othermerge, boolT vneighbors);
+void    qh_appendmergeset(qhT *qh, facetT *facet, facetT *neighbor, mergeType mergetype, realT *angle);
+setT   *qh_basevertices(qhT *qh, facetT *samecycle);
+void    qh_checkconnect(qhT *qh /* qh.new_facets */);
+boolT   qh_checkzero(qhT *qh, boolT testall);
+int     qh_compareangle(const void *p1, const void *p2);
+int     qh_comparemerge(const void *p1, const void *p2);
+int     qh_comparevisit(const void *p1, const void *p2);
+void    qh_copynonconvex(qhT *qh, ridgeT *atridge);
+void    qh_degen_redundant_facet(qhT *qh, facetT *facet);
+void    qh_degen_redundant_neighbors(qhT *qh, facetT *facet, facetT *delfacet);
+vertexT *qh_find_newvertex(qhT *qh, vertexT *oldvertex, setT *vertices, setT *ridges);
+void    qh_findbest_test(qhT *qh, boolT testcentrum, facetT *facet, facetT *neighbor,
+           facetT **bestfacet, realT *distp, realT *mindistp, realT *maxdistp);
+facetT *qh_findbestneighbor(qhT *qh, facetT *facet, realT *distp, realT *mindistp, realT *maxdistp);
+void    qh_flippedmerges(qhT *qh, facetT *facetlist, boolT *wasmerge);
+void    qh_forcedmerges(qhT *qh, boolT *wasmerge);
+void    qh_getmergeset(qhT *qh, facetT *facetlist);
+void    qh_getmergeset_initial(qhT *qh, facetT *facetlist);
+void    qh_hashridge(qhT *qh, setT *hashtable, int hashsize, ridgeT *ridge, vertexT *oldvertex);
+ridgeT *qh_hashridge_find(qhT *qh, setT *hashtable, int hashsize, ridgeT *ridge,
+              vertexT *vertex, vertexT *oldvertex, int *hashslot);
+void    qh_makeridges(qhT *qh, facetT *facet);
+void    qh_mark_dupridges(qhT *qh, facetT *facetlist);
+void    qh_maydropneighbor(qhT *qh, facetT *facet);
+int     qh_merge_degenredundant(qhT *qh);
+void    qh_merge_nonconvex(qhT *qh, facetT *facet1, facetT *facet2, mergeType mergetype);
+void    qh_mergecycle(qhT *qh, facetT *samecycle, facetT *newfacet);
+void    qh_mergecycle_all(qhT *qh, facetT *facetlist, boolT *wasmerge);
+void    qh_mergecycle_facets(qhT *qh, facetT *samecycle, facetT *newfacet);
+void    qh_mergecycle_neighbors(qhT *qh, facetT *samecycle, facetT *newfacet);
+void    qh_mergecycle_ridges(qhT *qh, facetT *samecycle, facetT *newfacet);
+void    qh_mergecycle_vneighbors(qhT *qh, facetT *samecycle, facetT *newfacet);
+void    qh_mergefacet(qhT *qh, facetT *facet1, facetT *facet2, realT *mindist, realT *maxdist, boolT mergeapex);
+void    qh_mergefacet2d(qhT *qh, facetT *facet1, facetT *facet2);
+void    qh_mergeneighbors(qhT *qh, facetT *facet1, facetT *facet2);
+void    qh_mergeridges(qhT *qh, facetT *facet1, facetT *facet2);
+void    qh_mergesimplex(qhT *qh, facetT *facet1, facetT *facet2, boolT mergeapex);
+void    qh_mergevertex_del(qhT *qh, vertexT *vertex, facetT *facet1, facetT *facet2);
+void    qh_mergevertex_neighbors(qhT *qh, facetT *facet1, facetT *facet2);
+void    qh_mergevertices(qhT *qh, setT *vertices1, setT **vertices);
+setT   *qh_neighbor_intersections(qhT *qh, vertexT *vertex);
+void    qh_newvertices(qhT *qh, setT *vertices);
+boolT   qh_reducevertices(qhT *qh);
+vertexT *qh_redundant_vertex(qhT *qh, vertexT *vertex);
+boolT   qh_remove_extravertices(qhT *qh, facetT *facet);
+vertexT *qh_rename_sharedvertex(qhT *qh, vertexT *vertex, facetT *facet);
+void    qh_renameridgevertex(qhT *qh, ridgeT *ridge, vertexT *oldvertex, vertexT *newvertex);
+void    qh_renamevertex(qhT *qh, vertexT *oldvertex, vertexT *newvertex, setT *ridges,
+                        facetT *oldfacet, facetT *neighborA);
+boolT   qh_test_appendmerge(qhT *qh, facetT *facet, facetT *neighbor);
+boolT   qh_test_vneighbors(qhT *qh /* qh.newfacet_list */);
+void    qh_tracemerge(qhT *qh, facetT *facet1, facetT *facet2);
+void    qh_tracemerging(qhT *qh);
+void    qh_updatetested(qhT *qh, facetT *facet1, facetT *facet2);
+setT   *qh_vertexridges(qhT *qh, vertexT *vertex);
+void    qh_vertexridges_facet(qhT *qh, vertexT *vertex, facetT *facet, setT **ridges);
+void    qh_willdelete(qhT *qh, facetT *facet, facetT *replace);
+
+#ifdef __cplusplus
+} /* extern "C" */
+#endif
+
+#endif /* qhDEFmerge */
diff --git a/xs/src/qhull/src/libqhull_r/poly2_r.c b/xs/src/qhull/src/libqhull_r/poly2_r.c
new file mode 100644
index 0000000000..b8ae9af9f4
--- /dev/null
+++ b/xs/src/qhull/src/libqhull_r/poly2_r.c
@@ -0,0 +1,3222 @@
+/*<html><pre>  -<a                             href="qh-poly_r.htm"
+  >-------------------------------</a><a name="TOP">-</a>
+
+   poly2_r.c
+   implements polygons and simplicies
+
+   see qh-poly_r.htm, poly_r.h and libqhull_r.h
+
+   frequently used code is in poly_r.c
+
+   Copyright (c) 1993-2015 The Geometry Center.
+   $Id: //main/2015/qhull/src/libqhull_r/poly2_r.c#10 $$Change: 2069 $
+   $DateTime: 2016/01/18 22:05:03 $$Author: bbarber $
+*/
+
+#include "qhull_ra.h"
+
+/*======== functions in alphabetical order ==========*/
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="addhash">-</a>
+
+  qh_addhash( newelem, hashtable, hashsize, hash )
+    add newelem to linear hash table at hash if not already there
+*/
+void qh_addhash(void *newelem, setT *hashtable, int hashsize, int hash) {
+  int scan;
+  void *elem;
+
+  for (scan= (int)hash; (elem= SETelem_(hashtable, scan));
+       scan= (++scan >= hashsize ? 0 : scan)) {
+    if (elem == newelem)
+      break;
+  }
+  /* loop terminates because qh_HASHfactor >= 1.1 by qh_initbuffers */
+  if (!elem)
+    SETelem_(hashtable, scan)= newelem;
+} /* addhash */
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="check_bestdist">-</a>
+
+  qh_check_bestdist(qh)
+    check that all points are within max_outside of the nearest facet
+    if qh.ONLYgood,
+      ignores !good facets
+
+  see:
+    qh_check_maxout(), qh_outerinner()
+
+  notes:
+    only called from qh_check_points()
+      seldom used since qh.MERGING is almost always set
+    if notverified>0 at end of routine
+      some points were well inside the hull.  If the hull contains
+      a lens-shaped component, these points were not verified.  Use
+      options 'Qi Tv' to verify all points.  (Exhaustive check also verifies)
+
+  design:
+    determine facet for each point (if any)
+    for each point
+      start with the assigned facet or with the first facet
+      find the best facet for the point and check all coplanar facets
+      error if point is outside of facet
+*/
+void qh_check_bestdist(qhT *qh) {
+  boolT waserror= False, unassigned;
+  facetT *facet, *bestfacet, *errfacet1= NULL, *errfacet2= NULL;
+  facetT *facetlist;
+  realT dist, maxoutside, maxdist= -REALmax;
+  pointT *point;
+  int numpart= 0, facet_i, facet_n, notgood= 0, notverified= 0;
+  setT *facets;
+
+  trace1((qh, qh->ferr, 1020, "qh_check_bestdist: check points below nearest facet.  Facet_list f%d\n",
+      qh->facet_list->id));
+  maxoutside= qh_maxouter(qh);
+  maxoutside += qh->DISTround;
+  /* one more qh.DISTround for check computation */
+  trace1((qh, qh->ferr, 1021, "qh_check_bestdist: check that all points are within %2.2g of best facet\n", maxoutside));
+  facets= qh_pointfacet(qh /*qh.facet_list*/);
+  if (!qh_QUICKhelp && qh->PRINTprecision)
+    qh_fprintf(qh, qh->ferr, 8091, "\n\
+qhull output completed.  Verifying that %d points are\n\
+below %2.2g of the nearest %sfacet.\n",
+             qh_setsize(qh, facets), maxoutside, (qh->ONLYgood ?  "good " : ""));
+  FOREACHfacet_i_(qh, facets) {  /* for each point with facet assignment */
+    if (facet)
+      unassigned= False;
+    else {
+      unassigned= True;
+      facet= qh->facet_list;
+    }
+    point= qh_point(qh, facet_i);
+    if (point == qh->GOODpointp)
+      continue;
+    qh_distplane(qh, point, facet, &dist);
+    numpart++;
+    bestfacet= qh_findbesthorizon(qh, !qh_IScheckmax, point, facet, qh_NOupper, &dist, &numpart);
+    /* occurs after statistics reported */
+    maximize_(maxdist, dist);
+    if (dist > maxoutside) {
+      if (qh->ONLYgood && !bestfacet->good
+          && !((bestfacet= qh_findgooddist(qh, point, bestfacet, &dist, &facetlist))
+               && dist > maxoutside))
+        notgood++;
+      else {
+        waserror= True;
+        qh_fprintf(qh, qh->ferr, 6109, "qhull precision error: point p%d is outside facet f%d, distance= %6.8g maxoutside= %6.8g\n",
+                facet_i, bestfacet->id, dist, maxoutside);
+        if (errfacet1 != bestfacet) {
+          errfacet2= errfacet1;
+          errfacet1= bestfacet;
+        }
+      }
+    }else if (unassigned && dist < -qh->MAXcoplanar)
+      notverified++;
+  }
+  qh_settempfree(qh, &facets);
+  if (notverified && !qh->DELAUNAY && !qh_QUICKhelp && qh->PRINTprecision)
+    qh_fprintf(qh, qh->ferr, 8092, "\n%d points were well inside the hull.  If the hull contains\n\
+a lens-shaped component, these points were not verified.  Use\n\
+options 'Qci Tv' to verify all points.\n", notverified);
+  if (maxdist > qh->outside_err) {
+    qh_fprintf(qh, qh->ferr, 6110, "qhull precision error (qh_check_bestdist): a coplanar point is %6.2g from convex hull.  The maximum value(qh.outside_err) is %6.2g\n",
+              maxdist, qh->outside_err);
+    qh_errexit2(qh, qh_ERRprec, errfacet1, errfacet2);
+  }else if (waserror && qh->outside_err > REALmax/2)
+    qh_errexit2(qh, qh_ERRprec, errfacet1, errfacet2);
+  /* else if waserror, the error was logged to qh.ferr but does not effect the output */
+  trace0((qh, qh->ferr, 20, "qh_check_bestdist: max distance outside %2.2g\n", maxdist));
+} /* check_bestdist */
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="check_dupridge">-</a>
+
+  qh_check_dupridge(qh, facet1, dist1, facet2, dist2)
+    Check duplicate ridge between facet1 and facet2 for wide merge
+    dist1 is the maximum distance of facet1's vertices to facet2
+    dist2 is the maximum distance of facet2's vertices to facet1
+
+  Returns
+    Level 1 log of the duplicate ridge with the minimum distance between vertices
+    Throws error if the merge will increase the maximum facet width by qh_WIDEduplicate (100x)
+
+  called from:
+    qh_forcedmerges()
+*/
+#ifndef qh_NOmerge
+void qh_check_dupridge(qhT *qh, facetT *facet1, realT dist1, facetT *facet2, realT dist2) {
+  vertexT *vertex, **vertexp, *vertexA, **vertexAp;
+  realT dist, innerplane, mergedist, outerplane, prevdist, ratio;
+  realT minvertex= REALmax;
+
+  mergedist= fmin_(dist1, dist2);
+  qh_outerinner(qh, NULL, &outerplane, &innerplane);  /* ratio from qh_printsummary */
+  prevdist= fmax_(outerplane, innerplane);
+  maximize_(prevdist, qh->ONEmerge + qh->DISTround);
+  maximize_(prevdist, qh->MINoutside + qh->DISTround);
+  ratio= mergedist/prevdist;
+  FOREACHvertex_(facet1->vertices) {     /* The duplicate ridge is between facet1 and facet2, so either facet can be tested */
+    FOREACHvertexA_(facet1->vertices) {
+      if (vertex > vertexA){   /* Test each pair once */
+        dist= qh_pointdist(vertex->point, vertexA->point, qh->hull_dim);
+        minimize_(minvertex, dist);
+      }
+    }
+  }
+  trace0((qh, qh->ferr, 16, "qh_check_dupridge: duplicate ridge between f%d and f%d due to nearly-coincident vertices (%2.2g), dist %2.2g, reverse dist %2.2g, ratio %2.2g while processing p%d\n",
+        facet1->id, facet2->id, minvertex, dist1, dist2, ratio, qh->furthest_id));
+  if (ratio > qh_WIDEduplicate) {
+    qh_fprintf(qh, qh->ferr, 6271, "qhull precision error (qh_check_dupridge): wide merge (%.0f times wider) due to duplicate ridge with nearly coincident points (%2.2g) between f%d and f%d, merge dist %2.2g, while processing p%d\n- Ignore error with option 'Q12'\n- To be fixed in a later version of Qhull\n",
+          ratio, minvertex, facet1->id, facet2->id, mergedist, qh->furthest_id);
+    if (qh->DELAUNAY)
+      qh_fprintf(qh, qh->ferr, 8145, "- A bounding box for the input sites may alleviate this error.\n");
+    if(minvertex > qh_WIDEduplicate*prevdist)
+      qh_fprintf(qh, qh->ferr, 8146, "- Vertex distance %2.2g is greater than %d times maximum distance %2.2g\n  Please report to bradb@shore.net with steps to reproduce and all output\n",
+          minvertex, qh_WIDEduplicate, prevdist);
+    if (!qh->NOwide)
+      qh_errexit2(qh, qh_ERRqhull, facet1, facet2);
+  }
+} /* check_dupridge */
+#endif
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="check_maxout">-</a>
+
+  qh_check_maxout(qh)
+    updates qh.max_outside by checking all points against bestfacet
+    if qh.ONLYgood, ignores !good facets
+
+  returns:
+    updates facet->maxoutside via qh_findbesthorizon()
+    sets qh.maxoutdone
+    if printing qh.min_vertex (qh_outerinner),
+      it is updated to the current vertices
+    removes inside/coplanar points from coplanarset as needed
+
+  notes:
+    defines coplanar as min_vertex instead of MAXcoplanar
+    may not need to check near-inside points because of qh.MAXcoplanar
+      and qh.KEEPnearinside (before it was -DISTround)
+
+  see also:
+    qh_check_bestdist()
+
+  design:
+    if qh.min_vertex is needed
+      for all neighbors of all vertices
+        test distance from vertex to neighbor
+    determine facet for each point (if any)
+    for each point with an assigned facet
+      find the best facet for the point and check all coplanar facets
+        (updates outer planes)
+    remove near-inside points from coplanar sets
+*/
+#ifndef qh_NOmerge
+void qh_check_maxout(qhT *qh) {
+  facetT *facet, *bestfacet, *neighbor, **neighborp, *facetlist;
+  realT dist, maxoutside, minvertex, old_maxoutside;
+  pointT *point;
+  int numpart= 0, facet_i, facet_n, notgood= 0;
+  setT *facets, *vertices;
+  vertexT *vertex;
+
+  trace1((qh, qh->ferr, 1022, "qh_check_maxout: check and update maxoutside for each facet.\n"));
+  maxoutside= minvertex= 0;
+  if (qh->VERTEXneighbors
+  && (qh->PRINTsummary || qh->KEEPinside || qh->KEEPcoplanar
+        || qh->TRACElevel || qh->PRINTstatistics
+        || qh->PRINTout[0] == qh_PRINTsummary || qh->PRINTout[0] == qh_PRINTnone)) {
+    trace1((qh, qh->ferr, 1023, "qh_check_maxout: determine actual maxoutside and minvertex\n"));
+    vertices= qh_pointvertex(qh /*qh.facet_list*/);
+    FORALLvertices {
+      FOREACHneighbor_(vertex) {
+        zinc_(Zdistvertex);  /* distance also computed by main loop below */
+        qh_distplane(qh, vertex->point, neighbor, &dist);
+        minimize_(minvertex, dist);
+        if (-dist > qh->TRACEdist || dist > qh->TRACEdist
+        || neighbor == qh->tracefacet || vertex == qh->tracevertex)
+          qh_fprintf(qh, qh->ferr, 8093, "qh_check_maxout: p%d(v%d) is %.2g from f%d\n",
+                    qh_pointid(qh, vertex->point), vertex->id, dist, neighbor->id);
+      }
+    }
+    if (qh->MERGING) {
+      wmin_(Wminvertex, qh->min_vertex);
+    }
+    qh->min_vertex= minvertex;
+    qh_settempfree(qh, &vertices);
+  }
+  facets= qh_pointfacet(qh /*qh.facet_list*/);
+  do {
+    old_maxoutside= fmax_(qh->max_outside, maxoutside);
+    FOREACHfacet_i_(qh, facets) {     /* for each point with facet assignment */
+      if (facet) {
+        point= qh_point(qh, facet_i);
+        if (point == qh->GOODpointp)
+          continue;
+        zzinc_(Ztotcheck);
+        qh_distplane(qh, point, facet, &dist);
+        numpart++;
+        bestfacet= qh_findbesthorizon(qh, qh_IScheckmax, point, facet, !qh_NOupper, &dist, &numpart);
+        if (bestfacet && dist > maxoutside) {
+          if (qh->ONLYgood && !bestfacet->good
+          && !((bestfacet= qh_findgooddist(qh, point, bestfacet, &dist, &facetlist))
+               && dist > maxoutside))
+            notgood++;
+          else
+            maxoutside= dist;
+        }
+        if (dist > qh->TRACEdist || (bestfacet && bestfacet == qh->tracefacet))
+          qh_fprintf(qh, qh->ferr, 8094, "qh_check_maxout: p%d is %.2g above f%d\n",
+          qh_pointid(qh, point), dist, (bestfacet ? bestfacet->id : UINT_MAX));
+      }
+    }
+  }while
+    (maxoutside > 2*old_maxoutside);
+    /* if qh.maxoutside increases substantially, qh_SEARCHdist is not valid
+          e.g., RBOX 5000 s Z1 G1e-13 t1001200614 | qhull */
+  zzadd_(Zcheckpart, numpart);
+  qh_settempfree(qh, &facets);
+  wval_(Wmaxout)= maxoutside - qh->max_outside;
+  wmax_(Wmaxoutside, qh->max_outside);
+  qh->max_outside= maxoutside;
+  qh_nearcoplanar(qh /*qh.facet_list*/);
+  qh->maxoutdone= True;
+  trace1((qh, qh->ferr, 1024, "qh_check_maxout: maxoutside %2.2g, min_vertex %2.2g, outside of not good %d\n",
+       maxoutside, qh->min_vertex, notgood));
+} /* check_maxout */
+#else /* qh_NOmerge */
+void qh_check_maxout(qhT *qh) {
+}
+#endif
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="check_output">-</a>
+
+  qh_check_output(qh)
+    performs the checks at the end of qhull algorithm
+    Maybe called after voronoi output.  Will recompute otherwise centrums are Voronoi centers instead
+*/
+void qh_check_output(qhT *qh) {
+  int i;
+
+  if (qh->STOPcone)
+    return;
+  if (qh->VERIFYoutput | qh->IStracing | qh->CHECKfrequently) {
+    qh_checkpolygon(qh, qh->facet_list);
+    qh_checkflipped_all(qh, qh->facet_list);
+    qh_checkconvex(qh, qh->facet_list, qh_ALGORITHMfault);
+  }else if (!qh->MERGING && qh_newstats(qh, qh->qhstat.precision, &i)) {
+    qh_checkflipped_all(qh, qh->facet_list);
+    qh_checkconvex(qh, qh->facet_list, qh_ALGORITHMfault);
+  }
+} /* check_output */
+
+
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="check_point">-</a>
+
+  qh_check_point(qh, point, facet, maxoutside, maxdist, errfacet1, errfacet2 )
+    check that point is less than maxoutside from facet
+*/
+void qh_check_point(qhT *qh, pointT *point, facetT *facet, realT *maxoutside, realT *maxdist, facetT **errfacet1, facetT **errfacet2) {
+  realT dist;
+
+  /* occurs after statistics reported */
+  qh_distplane(qh, point, facet, &dist);
+  if (dist > *maxoutside) {
+    if (*errfacet1 != facet) {
+      *errfacet2= *errfacet1;
+      *errfacet1= facet;
+    }
+    qh_fprintf(qh, qh->ferr, 6111, "qhull precision error: point p%d is outside facet f%d, distance= %6.8g maxoutside= %6.8g\n",
+              qh_pointid(qh, point), facet->id, dist, *maxoutside);
+  }
+  maximize_(*maxdist, dist);
+} /* qh_check_point */
+
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="check_points">-</a>
+
+  qh_check_points(qh)
+    checks that all points are inside all facets
+
+  notes:
+    if many points and qh_check_maxout not called (i.e., !qh.MERGING),
+       calls qh_findbesthorizon (seldom done).
+    ignores flipped facets
+    maxoutside includes 2 qh.DISTrounds
+      one qh.DISTround for the computed distances in qh_check_points
+    qh_printafacet and qh_printsummary needs only one qh.DISTround
+    the computation for qh.VERIFYdirect does not account for qh.other_points
+
+  design:
+    if many points
+      use qh_check_bestdist()
+    else
+      for all facets
+        for all points
+          check that point is inside facet
+*/
+void qh_check_points(qhT *qh) {
+  facetT *facet, *errfacet1= NULL, *errfacet2= NULL;
+  realT total, maxoutside, maxdist= -REALmax;
+  pointT *point, **pointp, *pointtemp;
+  boolT testouter;
+
+  maxoutside= qh_maxouter(qh);
+  maxoutside += qh->DISTround;
+  /* one more qh.DISTround for check computation */
+  trace1((qh, qh->ferr, 1025, "qh_check_points: check all points below %2.2g of all facet planes\n",
+          maxoutside));
+  if (qh->num_good)   /* miss counts other_points and !good facets */
+     total= (float)qh->num_good * (float)qh->num_points;
+  else
+     total= (float)qh->num_facets * (float)qh->num_points;
+  if (total >= qh_VERIFYdirect && !qh->maxoutdone) {
+    if (!qh_QUICKhelp && qh->SKIPcheckmax && qh->MERGING)
+      qh_fprintf(qh, qh->ferr, 7075, "qhull input warning: merging without checking outer planes('Q5' or 'Po').\n\
+Verify may report that a point is outside of a facet.\n");
+    qh_check_bestdist(qh);
+  }else {
+    if (qh_MAXoutside && qh->maxoutdone)
+      testouter= True;
+    else
+      testouter= False;
+    if (!qh_QUICKhelp) {
+      if (qh->MERGEexact)
+        qh_fprintf(qh, qh->ferr, 7076, "qhull input warning: exact merge ('Qx').  Verify may report that a point\n\
+is outside of a facet.  See qh-optq.htm#Qx\n");
+      else if (qh->SKIPcheckmax || qh->NOnearinside)
+        qh_fprintf(qh, qh->ferr, 7077, "qhull input warning: no outer plane check ('Q5') or no processing of\n\
+near-inside points ('Q8').  Verify may report that a point is outside\n\
+of a facet.\n");
+    }
+    if (qh->PRINTprecision) {
+      if (testouter)
+        qh_fprintf(qh, qh->ferr, 8098, "\n\
+Output completed.  Verifying that all points are below outer planes of\n\
+all %sfacets.  Will make %2.0f distance computations.\n",
+              (qh->ONLYgood ?  "good " : ""), total);
+      else
+        qh_fprintf(qh, qh->ferr, 8099, "\n\
+Output completed.  Verifying that all points are below %2.2g of\n\
+all %sfacets.  Will make %2.0f distance computations.\n",
+              maxoutside, (qh->ONLYgood ?  "good " : ""), total);
+    }
+    FORALLfacets {
+      if (!facet->good && qh->ONLYgood)
+        continue;
+      if (facet->flipped)
+        continue;
+      if (!facet->normal) {
+        qh_fprintf(qh, qh->ferr, 7061, "qhull warning (qh_check_points): missing normal for facet f%d\n", facet->id);
+        continue;
+      }
+      if (testouter) {
+#if qh_MAXoutside
+        maxoutside= facet->maxoutside + 2* qh->DISTround;
+        /* one DISTround to actual point and another to computed point */
+#endif
+      }
+      FORALLpoints {
+        if (point != qh->GOODpointp)
+          qh_check_point(qh, point, facet, &maxoutside, &maxdist, &errfacet1, &errfacet2);
+      }
+      FOREACHpoint_(qh->other_points) {
+        if (point != qh->GOODpointp)
+          qh_check_point(qh, point, facet, &maxoutside, &maxdist, &errfacet1, &errfacet2);
+      }
+    }
+    if (maxdist > qh->outside_err) {
+      qh_fprintf(qh, qh->ferr, 6112, "qhull precision error (qh_check_points): a coplanar point is %6.2g from convex hull.  The maximum value(qh.outside_err) is %6.2g\n",
+                maxdist, qh->outside_err );
+      qh_errexit2(qh, qh_ERRprec, errfacet1, errfacet2 );
+    }else if (errfacet1 && qh->outside_err > REALmax/2)
+        qh_errexit2(qh, qh_ERRprec, errfacet1, errfacet2 );
+    /* else if errfacet1, the error was logged to qh.ferr but does not effect the output */
+    trace0((qh, qh->ferr, 21, "qh_check_points: max distance outside %2.2g\n", maxdist));
+  }
+} /* check_points */
+
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="checkconvex">-</a>
+
+  qh_checkconvex(qh, facetlist, fault )
+    check that each ridge in facetlist is convex
+    fault = qh_DATAfault if reporting errors
+          = qh_ALGORITHMfault otherwise
+
+  returns:
+    counts Zconcaveridges and Zcoplanarridges
+    errors if concaveridge or if merging an coplanar ridge
+
+  note:
+    if not merging,
+      tests vertices for neighboring simplicial facets
+    else if ZEROcentrum,
+      tests vertices for neighboring simplicial   facets
+    else
+      tests centrums of neighboring facets
+
+  design:
+    for all facets
+      report flipped facets
+      if ZEROcentrum and simplicial neighbors
+        test vertices for neighboring simplicial facets
+      else
+        test centrum against all neighbors
+*/
+void qh_checkconvex(qhT *qh, facetT *facetlist, int fault) {
+  facetT *facet, *neighbor, **neighborp, *errfacet1=NULL, *errfacet2=NULL;
+  vertexT *vertex;
+  realT dist;
+  pointT *centrum;
+  boolT waserror= False, centrum_warning= False, tempcentrum= False, allsimplicial;
+  int neighbor_i;
+
+  trace1((qh, qh->ferr, 1026, "qh_checkconvex: check all ridges are convex\n"));
+  if (!qh->RERUN) {
+    zzval_(Zconcaveridges)= 0;
+    zzval_(Zcoplanarridges)= 0;
+  }
+  FORALLfacet_(facetlist) {
+    if (facet->flipped) {
+      qh_precision(qh, "flipped facet");
+      qh_fprintf(qh, qh->ferr, 6113, "qhull precision error: f%d is flipped(interior point is outside)\n",
+               facet->id);
+      errfacet1= facet;
+      waserror= True;
+      continue;
+    }
+    if (qh->MERGING && (!qh->ZEROcentrum || !facet->simplicial || facet->tricoplanar))
+      allsimplicial= False;
+    else {
+      allsimplicial= True;
+      neighbor_i= 0;
+      FOREACHneighbor_(facet) {
+        vertex= SETelemt_(facet->vertices, neighbor_i++, vertexT);
+        if (!neighbor->simplicial || neighbor->tricoplanar) {
+          allsimplicial= False;
+          continue;
+        }
+        qh_distplane(qh, vertex->point, neighbor, &dist);
+        if (dist > -qh->DISTround) {
+          if (fault == qh_DATAfault) {
+            qh_precision(qh, "coplanar or concave ridge");
+            qh_fprintf(qh, qh->ferr, 6114, "qhull precision error: initial simplex is not convex. Distance=%.2g\n", dist);
+            qh_errexit(qh, qh_ERRsingular, NULL, NULL);
+          }
+          if (dist > qh->DISTround) {
+            zzinc_(Zconcaveridges);
+            qh_precision(qh, "concave ridge");
+            qh_fprintf(qh, qh->ferr, 6115, "qhull precision error: f%d is concave to f%d, since p%d(v%d) is %6.4g above\n",
+              facet->id, neighbor->id, qh_pointid(qh, vertex->point), vertex->id, dist);
+            errfacet1= facet;
+            errfacet2= neighbor;
+            waserror= True;
+          }else if (qh->ZEROcentrum) {
+            if (dist > 0) {     /* qh_checkzero checks that dist < - qh->DISTround */
+              zzinc_(Zcoplanarridges);
+              qh_precision(qh, "coplanar ridge");
+              qh_fprintf(qh, qh->ferr, 6116, "qhull precision error: f%d is clearly not convex to f%d, since p%d(v%d) is %6.4g above\n",
+                facet->id, neighbor->id, qh_pointid(qh, vertex->point), vertex->id, dist);
+              errfacet1= facet;
+              errfacet2= neighbor;
+              waserror= True;
+            }
+          }else {
+            zzinc_(Zcoplanarridges);
+            qh_precision(qh, "coplanar ridge");
+            trace0((qh, qh->ferr, 22, "qhull precision error: f%d may be coplanar to f%d, since p%d(v%d) is within %6.4g during p%d\n",
+              facet->id, neighbor->id, qh_pointid(qh, vertex->point), vertex->id, dist, qh->furthest_id));
+          }
+        }
+      }
+    }
+    if (!allsimplicial) {
+      if (qh->CENTERtype == qh_AScentrum) {
+        if (!facet->center)
+          facet->center= qh_getcentrum(qh, facet);
+        centrum= facet->center;
+      }else {
+        if (!centrum_warning && (!facet->simplicial || facet->tricoplanar)) {
+           centrum_warning= True;
+           qh_fprintf(qh, qh->ferr, 7062, "qhull warning: recomputing centrums for convexity test.  This may lead to false, precision errors.\n");
+        }
+        centrum= qh_getcentrum(qh, facet);
+        tempcentrum= True;
+      }
+      FOREACHneighbor_(facet) {
+        if (qh->ZEROcentrum && facet->simplicial && neighbor->simplicial)
+          continue;
+        if (facet->tricoplanar || neighbor->tricoplanar)
+          continue;
+        zzinc_(Zdistconvex);
+        qh_distplane(qh, centrum, neighbor, &dist);
+        if (dist > qh->DISTround) {
+          zzinc_(Zconcaveridges);
+          qh_precision(qh, "concave ridge");
+          qh_fprintf(qh, qh->ferr, 6117, "qhull precision error: f%d is concave to f%d.  Centrum of f%d is %6.4g above f%d\n",
+            facet->id, neighbor->id, facet->id, dist, neighbor->id);
+          errfacet1= facet;
+          errfacet2= neighbor;
+          waserror= True;
+        }else if (dist >= 0.0) {   /* if arithmetic always rounds the same,
+                                     can test against centrum radius instead */
+          zzinc_(Zcoplanarridges);
+          qh_precision(qh, "coplanar ridge");
+          qh_fprintf(qh, qh->ferr, 6118, "qhull precision error: f%d is coplanar or concave to f%d.  Centrum of f%d is %6.4g above f%d\n",
+            facet->id, neighbor->id, facet->id, dist, neighbor->id);
+          errfacet1= facet;
+          errfacet2= neighbor;
+          waserror= True;
+        }
+      }
+      if (tempcentrum)
+        qh_memfree(qh, centrum, qh->normal_size);
+    }
+  }
+  if (waserror && !qh->FORCEoutput)
+    qh_errexit2(qh, qh_ERRprec, errfacet1, errfacet2);
+} /* checkconvex */
+
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="checkfacet">-</a>
+
+  qh_checkfacet(qh, facet, newmerge, waserror )
+    checks for consistency errors in facet
+    newmerge set if from merge_r.c
+
+  returns:
+    sets waserror if any error occurs
+
+  checks:
+    vertex ids are inverse sorted
+    unless newmerge, at least hull_dim neighbors and vertices (exactly if simplicial)
+    if non-simplicial, at least as many ridges as neighbors
+    neighbors are not duplicated
+    ridges are not duplicated
+    in 3-d, ridges=verticies
+    (qh.hull_dim-1) ridge vertices
+    neighbors are reciprocated
+    ridge neighbors are facet neighbors and a ridge for every neighbor
+    simplicial neighbors match facetintersect
+    vertex intersection matches vertices of common ridges
+    vertex neighbors and facet vertices agree
+    all ridges have distinct vertex sets
+
+  notes:
+    uses neighbor->seen
+
+  design:
+    check sets
+    check vertices
+    check sizes of neighbors and vertices
+    check for qh_MERGEridge and qh_DUPLICATEridge flags
+    check neighbor set
+    check ridge set
+    check ridges, neighbors, and vertices
+*/
+void qh_checkfacet(qhT *qh, facetT *facet, boolT newmerge, boolT *waserrorp) {
+  facetT *neighbor, **neighborp, *errother=NULL;
+  ridgeT *ridge, **ridgep, *errridge= NULL, *ridge2;
+  vertexT *vertex, **vertexp;
+  unsigned previousid= INT_MAX;
+  int numneighbors, numvertices, numridges=0, numRvertices=0;
+  boolT waserror= False;
+  int skipA, skipB, ridge_i, ridge_n, i;
+  setT *intersection;
+
+  if (facet->visible) {
+    qh_fprintf(qh, qh->ferr, 6119, "qhull internal error (qh_checkfacet): facet f%d is on the visible_list\n",
+      facet->id);
+    qh_errexit(qh, qh_ERRqhull, facet, NULL);
+  }
+  if (!facet->normal) {
+    qh_fprintf(qh, qh->ferr, 6120, "qhull internal error (qh_checkfacet): facet f%d does not have  a normal\n",
+      facet->id);
+    waserror= True;
+  }
+  qh_setcheck(qh, facet->vertices, "vertices for f", facet->id);
+  qh_setcheck(qh, facet->ridges, "ridges for f", facet->id);
+  qh_setcheck(qh, facet->outsideset, "outsideset for f", facet->id);
+  qh_setcheck(qh, facet->coplanarset, "coplanarset for f", facet->id);
+  qh_setcheck(qh, facet->neighbors, "neighbors for f", facet->id);
+  FOREACHvertex_(facet->vertices) {
+    if (vertex->deleted) {
+      qh_fprintf(qh, qh->ferr, 6121, "qhull internal error (qh_checkfacet): deleted vertex v%d in f%d\n", vertex->id, facet->id);
+      qh_errprint(qh, "ERRONEOUS", NULL, NULL, NULL, vertex);
+      waserror= True;
+    }
+    if (vertex->id >= previousid) {
+      qh_fprintf(qh, qh->ferr, 6122, "qhull internal error (qh_checkfacet): vertices of f%d are not in descending id order at v%d\n", facet->id, vertex->id);
+      waserror= True;
+      break;
+    }
+    previousid= vertex->id;
+  }
+  numneighbors= qh_setsize(qh, facet->neighbors);
+  numvertices= qh_setsize(qh, facet->vertices);
+  numridges= qh_setsize(qh, facet->ridges);
+  if (facet->simplicial) {
+    if (numvertices+numneighbors != 2*qh->hull_dim
+    && !facet->degenerate && !facet->redundant) {
+      qh_fprintf(qh, qh->ferr, 6123, "qhull internal error (qh_checkfacet): for simplicial facet f%d, #vertices %d + #neighbors %d != 2*qh->hull_dim\n",
+                facet->id, numvertices, numneighbors);
+      qh_setprint(qh, qh->ferr, "", facet->neighbors);
+      waserror= True;
+    }
+  }else { /* non-simplicial */
+    if (!newmerge
+    &&(numvertices < qh->hull_dim || numneighbors < qh->hull_dim)
+    && !facet->degenerate && !facet->redundant) {
+      qh_fprintf(qh, qh->ferr, 6124, "qhull internal error (qh_checkfacet): for facet f%d, #vertices %d or #neighbors %d < qh->hull_dim\n",
+         facet->id, numvertices, numneighbors);
+       waserror= True;
+    }
+    /* in 3-d, can get a vertex twice in an edge list, e.g., RBOX 1000 s W1e-13 t995849315 D2 | QHULL d Tc Tv TP624 TW1e-13 T4 */
+    if (numridges < numneighbors
+    ||(qh->hull_dim == 3 && numvertices > numridges && !qh->NEWfacets)
+    ||(qh->hull_dim == 2 && numridges + numvertices + numneighbors != 6)) {
+      if (!facet->degenerate && !facet->redundant) {
+        qh_fprintf(qh, qh->ferr, 6125, "qhull internal error (qh_checkfacet): for facet f%d, #ridges %d < #neighbors %d or(3-d) > #vertices %d or(2-d) not all 2\n",
+            facet->id, numridges, numneighbors, numvertices);
+        waserror= True;
+      }
+    }
+  }
+  FOREACHneighbor_(facet) {
+    if (neighbor == qh_MERGEridge || neighbor == qh_DUPLICATEridge) {
+      qh_fprintf(qh, qh->ferr, 6126, "qhull internal error (qh_checkfacet): facet f%d still has a MERGE or DUP neighbor\n", facet->id);
+      qh_errexit(qh, qh_ERRqhull, facet, NULL);
+    }
+    neighbor->seen= True;
+  }
+  FOREACHneighbor_(facet) {
+    if (!qh_setin(neighbor->neighbors, facet)) {
+      qh_fprintf(qh, qh->ferr, 6127, "qhull internal error (qh_checkfacet): facet f%d has neighbor f%d, but f%d does not have neighbor f%d\n",
+              facet->id, neighbor->id, neighbor->id, facet->id);
+      errother= neighbor;
+      waserror= True;
+    }
+    if (!neighbor->seen) {
+      qh_fprintf(qh, qh->ferr, 6128, "qhull internal error (qh_checkfacet): facet f%d has a duplicate neighbor f%d\n",
+              facet->id, neighbor->id);
+      errother= neighbor;
+      waserror= True;
+    }
+    neighbor->seen= False;
+  }
+  FOREACHridge_(facet->ridges) {
+    qh_setcheck(qh, ridge->vertices, "vertices for r", ridge->id);
+    ridge->seen= False;
+  }
+  FOREACHridge_(facet->ridges) {
+    if (ridge->seen) {
+      qh_fprintf(qh, qh->ferr, 6129, "qhull internal error (qh_checkfacet): facet f%d has a duplicate ridge r%d\n",
+              facet->id, ridge->id);
+      errridge= ridge;
+      waserror= True;
+    }
+    ridge->seen= True;
+    numRvertices= qh_setsize(qh, ridge->vertices);
+    if (numRvertices != qh->hull_dim - 1) {
+      qh_fprintf(qh, qh->ferr, 6130, "qhull internal error (qh_checkfacet): ridge between f%d and f%d has %d vertices\n",
+                ridge->top->id, ridge->bottom->id, numRvertices);
+      errridge= ridge;
+      waserror= True;
+    }
+    neighbor= otherfacet_(ridge, facet);
+    neighbor->seen= True;
+    if (!qh_setin(facet->neighbors, neighbor)) {
+      qh_fprintf(qh, qh->ferr, 6131, "qhull internal error (qh_checkfacet): for facet f%d, neighbor f%d of ridge r%d not in facet\n",
+           facet->id, neighbor->id, ridge->id);
+      errridge= ridge;
+      waserror= True;
+    }
+  }
+  if (!facet->simplicial) {
+    FOREACHneighbor_(facet) {
+      if (!neighbor->seen) {
+        qh_fprintf(qh, qh->ferr, 6132, "qhull internal error (qh_checkfacet): facet f%d does not have a ridge for neighbor f%d\n",
+              facet->id, neighbor->id);
+        errother= neighbor;
+        waserror= True;
+      }
+      intersection= qh_vertexintersect_new(qh, facet->vertices, neighbor->vertices);
+      qh_settemppush(qh, intersection);
+      FOREACHvertex_(facet->vertices) {
+        vertex->seen= False;
+        vertex->seen2= False;
+      }
+      FOREACHvertex_(intersection)
+        vertex->seen= True;
+      FOREACHridge_(facet->ridges) {
+        if (neighbor != otherfacet_(ridge, facet))
+            continue;
+        FOREACHvertex_(ridge->vertices) {
+          if (!vertex->seen) {
+            qh_fprintf(qh, qh->ferr, 6133, "qhull internal error (qh_checkfacet): vertex v%d in r%d not in f%d intersect f%d\n",
+                  vertex->id, ridge->id, facet->id, neighbor->id);
+            qh_errexit(qh, qh_ERRqhull, facet, ridge);
+          }
+          vertex->seen2= True;
+        }
+      }
+      if (!newmerge) {
+        FOREACHvertex_(intersection) {
+          if (!vertex->seen2) {
+            if (qh->IStracing >=3 || !qh->MERGING) {
+              qh_fprintf(qh, qh->ferr, 6134, "qhull precision error (qh_checkfacet): vertex v%d in f%d intersect f%d but\n\
+ not in a ridge.  This is ok under merging.  Last point was p%d\n",
+                     vertex->id, facet->id, neighbor->id, qh->furthest_id);
+              if (!qh->FORCEoutput && !qh->MERGING) {
+                qh_errprint(qh, "ERRONEOUS", facet, neighbor, NULL, vertex);
+                if (!qh->MERGING)
+                  qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+              }
+            }
+          }
+        }
+      }
+      qh_settempfree(qh, &intersection);
+    }
+  }else { /* simplicial */
+    FOREACHneighbor_(facet) {
+      if (neighbor->simplicial) {
+        skipA= SETindex_(facet->neighbors, neighbor);
+        skipB= qh_setindex(neighbor->neighbors, facet);
+        if (skipA<0 || skipB<0 || !qh_setequal_skip(facet->vertices, skipA, neighbor->vertices, skipB)) {
+          qh_fprintf(qh, qh->ferr, 6135, "qhull internal error (qh_checkfacet): facet f%d skip %d and neighbor f%d skip %d do not match \n",
+                   facet->id, skipA, neighbor->id, skipB);
+          errother= neighbor;
+          waserror= True;
+        }
+      }
+    }
+  }
+  if (qh->hull_dim < 5 && (qh->IStracing > 2 || qh->CHECKfrequently)) {
+    FOREACHridge_i_(qh, facet->ridges) {           /* expensive */
+      for (i=ridge_i+1; i < ridge_n; i++) {
+        ridge2= SETelemt_(facet->ridges, i, ridgeT);
+        if (qh_setequal(ridge->vertices, ridge2->vertices)) {
+          qh_fprintf(qh, qh->ferr, 6227, "Qhull internal error (qh_checkfacet): ridges r%d and r%d have the same vertices\n",
+                  ridge->id, ridge2->id);
+          errridge= ridge;
+          waserror= True;
+        }
+      }
+    }
+  }
+  if (waserror) {
+    qh_errprint(qh, "ERRONEOUS", facet, errother, errridge, NULL);
+    *waserrorp= True;
+  }
+} /* checkfacet */
+
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="checkflipped_all">-</a>
+
+  qh_checkflipped_all(qh, facetlist )
+    checks orientation of facets in list against interior point
+*/
+void qh_checkflipped_all(qhT *qh, facetT *facetlist) {
+  facetT *facet;
+  boolT waserror= False;
+  realT dist;
+
+  if (facetlist == qh->facet_list)
+    zzval_(Zflippedfacets)= 0;
+  FORALLfacet_(facetlist) {
+    if (facet->normal && !qh_checkflipped(qh, facet, &dist, !qh_ALL)) {
+      qh_fprintf(qh, qh->ferr, 6136, "qhull precision error: facet f%d is flipped, distance= %6.12g\n",
+              facet->id, dist);
+      if (!qh->FORCEoutput) {
+        qh_errprint(qh, "ERRONEOUS", facet, NULL, NULL, NULL);
+        waserror= True;
+      }
+    }
+  }
+  if (waserror) {
+    qh_fprintf(qh, qh->ferr, 8101, "\n\
+A flipped facet occurs when its distance to the interior point is\n\
+greater than %2.2g, the maximum roundoff error.\n", -qh->DISTround);
+    qh_errexit(qh, qh_ERRprec, NULL, NULL);
+  }
+} /* checkflipped_all */
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="checkpolygon">-</a>
+
+  qh_checkpolygon(qh, facetlist )
+    checks the correctness of the structure
+
+  notes:
+    call with either qh.facet_list or qh.newfacet_list
+    checks num_facets and num_vertices if qh.facet_list
+
+  design:
+    for each facet
+      checks facet and outside set
+    initializes vertexlist
+    for each facet
+      checks vertex set
+    if checking all facets(qh.facetlist)
+      check facet count
+      if qh.VERTEXneighbors
+        check vertex neighbors and count
+      check vertex count
+*/
+void qh_checkpolygon(qhT *qh, facetT *facetlist) {
+  facetT *facet;
+  vertexT *vertex, **vertexp, *vertexlist;
+  int numfacets= 0, numvertices= 0, numridges= 0;
+  int totvneighbors= 0, totvertices= 0;
+  boolT waserror= False, nextseen= False, visibleseen= False;
+
+  trace1((qh, qh->ferr, 1027, "qh_checkpolygon: check all facets from f%d\n", facetlist->id));
+  if (facetlist != qh->facet_list || qh->ONLYgood)
+    nextseen= True;
+  FORALLfacet_(facetlist) {
+    if (facet == qh->visible_list)
+      visibleseen= True;
+    if (!facet->visible) {
+      if (!nextseen) {
+        if (facet == qh->facet_next)
+          nextseen= True;
+        else if (qh_setsize(qh, facet->outsideset)) {
+          if (!qh->NARROWhull
+#if !qh_COMPUTEfurthest
+               || facet->furthestdist >= qh->MINoutside
+#endif
+                        ) {
+            qh_fprintf(qh, qh->ferr, 6137, "qhull internal error (qh_checkpolygon): f%d has outside points before qh->facet_next\n",
+                     facet->id);
+            qh_errexit(qh, qh_ERRqhull, facet, NULL);
+          }
+        }
+      }
+      numfacets++;
+      qh_checkfacet(qh, facet, False, &waserror);
+    }
+  }
+  if (qh->visible_list && !visibleseen && facetlist == qh->facet_list) {
+    qh_fprintf(qh, qh->ferr, 6138, "qhull internal error (qh_checkpolygon): visible list f%d no longer on facet list\n", qh->visible_list->id);
+    qh_printlists(qh);
+    qh_errexit(qh, qh_ERRqhull, qh->visible_list, NULL);
+  }
+  if (facetlist == qh->facet_list)
+    vertexlist= qh->vertex_list;
+  else if (facetlist == qh->newfacet_list)
+    vertexlist= qh->newvertex_list;
+  else
+    vertexlist= NULL;
+  FORALLvertex_(vertexlist) {
+    vertex->seen= False;
+    vertex->visitid= 0;
+  }
+  FORALLfacet_(facetlist) {
+    if (facet->visible)
+      continue;
+    if (facet->simplicial)
+      numridges += qh->hull_dim;
+    else
+      numridges += qh_setsize(qh, facet->ridges);
+    FOREACHvertex_(facet->vertices) {
+      vertex->visitid++;
+      if (!vertex->seen) {
+        vertex->seen= True;
+        numvertices++;
+        if (qh_pointid(qh, vertex->point) == qh_IDunknown) {
+          qh_fprintf(qh, qh->ferr, 6139, "qhull internal error (qh_checkpolygon): unknown point %p for vertex v%d first_point %p\n",
+                   vertex->point, vertex->id, qh->first_point);
+          waserror= True;
+        }
+      }
+    }
+  }
+  qh->vertex_visit += (unsigned int)numfacets;
+  if (facetlist == qh->facet_list) {
+    if (numfacets != qh->num_facets - qh->num_visible) {
+      qh_fprintf(qh, qh->ferr, 6140, "qhull internal error (qh_checkpolygon): actual number of facets is %d, cumulative facet count is %d - %d visible facets\n",
+              numfacets, qh->num_facets, qh->num_visible);
+      waserror= True;
+    }
+    qh->vertex_visit++;
+    if (qh->VERTEXneighbors) {
+      FORALLvertices {
+        qh_setcheck(qh, vertex->neighbors, "neighbors for v", vertex->id);
+        if (vertex->deleted)
+          continue;
+        totvneighbors += qh_setsize(qh, vertex->neighbors);
+      }
+      FORALLfacet_(facetlist)
+        totvertices += qh_setsize(qh, facet->vertices);
+      if (totvneighbors != totvertices) {
+        qh_fprintf(qh, qh->ferr, 6141, "qhull internal error (qh_checkpolygon): vertex neighbors inconsistent.  Totvneighbors %d, totvertices %d\n",
+                totvneighbors, totvertices);
+        waserror= True;
+      }
+    }
+    if (numvertices != qh->num_vertices - qh_setsize(qh, qh->del_vertices)) {
+      qh_fprintf(qh, qh->ferr, 6142, "qhull internal error (qh_checkpolygon): actual number of vertices is %d, cumulative vertex count is %d\n",
+              numvertices, qh->num_vertices - qh_setsize(qh, qh->del_vertices));
+      waserror= True;
+    }
+    if (qh->hull_dim == 2 && numvertices != numfacets) {
+      qh_fprintf(qh, qh->ferr, 6143, "qhull internal error (qh_checkpolygon): #vertices %d != #facets %d\n",
+        numvertices, numfacets);
+      waserror= True;
+    }
+    if (qh->hull_dim == 3 && numvertices + numfacets - numridges/2 != 2) {
+      qh_fprintf(qh, qh->ferr, 7063, "qhull warning: #vertices %d + #facets %d - #edges %d != 2\n\
+        A vertex appears twice in a edge list.  May occur during merging.",
+        numvertices, numfacets, numridges/2);
+      /* occurs if lots of merging and a vertex ends up twice in an edge list.  e.g., RBOX 1000 s W1e-13 t995849315 D2 | QHULL d Tc Tv */
+    }
+  }
+  if (waserror)
+    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+} /* checkpolygon */
+
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="checkvertex">-</a>
+
+  qh_checkvertex(qh, vertex )
+    check vertex for consistency
+    checks vertex->neighbors
+
+  notes:
+    neighbors checked efficiently in checkpolygon
+*/
+void qh_checkvertex(qhT *qh, vertexT *vertex) {
+  boolT waserror= False;
+  facetT *neighbor, **neighborp, *errfacet=NULL;
+
+  if (qh_pointid(qh, vertex->point) == qh_IDunknown) {
+    qh_fprintf(qh, qh->ferr, 6144, "qhull internal error (qh_checkvertex): unknown point id %p\n", vertex->point);
+    waserror= True;
+  }
+  if (vertex->id >= qh->vertex_id) {
+    qh_fprintf(qh, qh->ferr, 6145, "qhull internal error (qh_checkvertex): unknown vertex id %d\n", vertex->id);
+    waserror= True;
+  }
+  if (!waserror && !vertex->deleted) {
+    if (qh_setsize(qh, vertex->neighbors)) {
+      FOREACHneighbor_(vertex) {
+        if (!qh_setin(neighbor->vertices, vertex)) {
+          qh_fprintf(qh, qh->ferr, 6146, "qhull internal error (qh_checkvertex): neighbor f%d does not contain v%d\n", neighbor->id, vertex->id);
+          errfacet= neighbor;
+          waserror= True;
+        }
+      }
+    }
+  }
+  if (waserror) {
+    qh_errprint(qh, "ERRONEOUS", NULL, NULL, NULL, vertex);
+    qh_errexit(qh, qh_ERRqhull, errfacet, NULL);
+  }
+} /* checkvertex */
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="clearcenters">-</a>
+
+  qh_clearcenters(qh, type )
+    clear old data from facet->center
+
+  notes:
+    sets new centertype
+    nop if CENTERtype is the same
+*/
+void qh_clearcenters(qhT *qh, qh_CENTER type) {
+  facetT *facet;
+
+  if (qh->CENTERtype != type) {
+    FORALLfacets {
+      if (facet->tricoplanar && !facet->keepcentrum)
+          facet->center= NULL;  /* center is owned by the ->keepcentrum facet */
+      else if (qh->CENTERtype == qh_ASvoronoi){
+        if (facet->center) {
+          qh_memfree(qh, facet->center, qh->center_size);
+          facet->center= NULL;
+        }
+      }else /* qh->CENTERtype == qh_AScentrum */ {
+        if (facet->center) {
+          qh_memfree(qh, facet->center, qh->normal_size);
+          facet->center= NULL;
+        }
+      }
+    }
+    qh->CENTERtype= type;
+  }
+  trace2((qh, qh->ferr, 2043, "qh_clearcenters: switched to center type %d\n", type));
+} /* clearcenters */
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="createsimplex">-</a>
+
+  qh_createsimplex(qh, vertices )
+    creates a simplex from a set of vertices
+
+  returns:
+    initializes qh.facet_list to the simplex
+    initializes qh.newfacet_list, .facet_tail
+    initializes qh.vertex_list, .newvertex_list, .vertex_tail
+
+  design:
+    initializes lists
+    for each vertex
+      create a new facet
+    for each new facet
+      create its neighbor set
+*/
+void qh_createsimplex(qhT *qh, setT *vertices) {
+  facetT *facet= NULL, *newfacet;
+  boolT toporient= True;
+  int vertex_i, vertex_n, nth;
+  setT *newfacets= qh_settemp(qh, qh->hull_dim+1);
+  vertexT *vertex;
+
+  qh->facet_list= qh->newfacet_list= qh->facet_tail= qh_newfacet(qh);
+  qh->num_facets= qh->num_vertices= qh->num_visible= 0;
+  qh->vertex_list= qh->newvertex_list= qh->vertex_tail= qh_newvertex(qh, NULL);
+  FOREACHvertex_i_(qh, vertices) {
+    newfacet= qh_newfacet(qh);
+    newfacet->vertices= qh_setnew_delnthsorted(qh, vertices, vertex_n,
+                                                vertex_i, 0);
+    newfacet->toporient= (unsigned char)toporient;
+    qh_appendfacet(qh, newfacet);
+    newfacet->newfacet= True;
+    qh_appendvertex(qh, vertex);
+    qh_setappend(qh, &newfacets, newfacet);
+    toporient ^= True;
+  }
+  FORALLnew_facets {
+    nth= 0;
+    FORALLfacet_(qh->newfacet_list) {
+      if (facet != newfacet)
+        SETelem_(newfacet->neighbors, nth++)= facet;
+    }
+    qh_settruncate(qh, newfacet->neighbors, qh->hull_dim);
+  }
+  qh_settempfree(qh, &newfacets);
+  trace1((qh, qh->ferr, 1028, "qh_createsimplex: created simplex\n"));
+} /* createsimplex */
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="delridge">-</a>
+
+  qh_delridge(qh, ridge )
+    deletes ridge from data structures it belongs to
+    frees up its memory
+
+  notes:
+    in merge_r.c, caller sets vertex->delridge for each vertex
+    ridges also freed in qh_freeqhull
+*/
+void qh_delridge(qhT *qh, ridgeT *ridge) {
+  void **freelistp; /* used if !qh_NOmem by qh_memfree_() */
+
+  qh_setdel(ridge->top->ridges, ridge);
+  qh_setdel(ridge->bottom->ridges, ridge);
+  qh_setfree(qh, &(ridge->vertices));
+  qh_memfree_(qh, ridge, (int)sizeof(ridgeT), freelistp);
+} /* delridge */
+
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="delvertex">-</a>
+
+  qh_delvertex(qh, vertex )
+    deletes a vertex and frees its memory
+
+  notes:
+    assumes vertex->adjacencies have been updated if needed
+    unlinks from vertex_list
+*/
+void qh_delvertex(qhT *qh, vertexT *vertex) {
+
+  if (vertex == qh->tracevertex)
+    qh->tracevertex= NULL;
+  qh_removevertex(qh, vertex);
+  qh_setfree(qh, &vertex->neighbors);
+  qh_memfree(qh, vertex, (int)sizeof(vertexT));
+} /* delvertex */
+
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="facet3vertex">-</a>
+
+  qh_facet3vertex(qh, )
+    return temporary set of 3-d vertices in qh_ORIENTclock order
+
+  design:
+    if simplicial facet
+      build set from facet->vertices with facet->toporient
+    else
+      for each ridge in order
+        build set from ridge's vertices
+*/
+setT *qh_facet3vertex(qhT *qh, facetT *facet) {
+  ridgeT *ridge, *firstridge;
+  vertexT *vertex;
+  int cntvertices, cntprojected=0;
+  setT *vertices;
+
+  cntvertices= qh_setsize(qh, facet->vertices);
+  vertices= qh_settemp(qh, cntvertices);
+  if (facet->simplicial) {
+    if (cntvertices != 3) {
+      qh_fprintf(qh, qh->ferr, 6147, "qhull internal error (qh_facet3vertex): only %d vertices for simplicial facet f%d\n",
+                  cntvertices, facet->id);
+      qh_errexit(qh, qh_ERRqhull, facet, NULL);
+    }
+    qh_setappend(qh, &vertices, SETfirst_(facet->vertices));
+    if (facet->toporient ^ qh_ORIENTclock)
+      qh_setappend(qh, &vertices, SETsecond_(facet->vertices));
+    else
+      qh_setaddnth(qh, &vertices, 0, SETsecond_(facet->vertices));
+    qh_setappend(qh, &vertices, SETelem_(facet->vertices, 2));
+  }else {
+    ridge= firstridge= SETfirstt_(facet->ridges, ridgeT);   /* no infinite */
+    while ((ridge= qh_nextridge3d(ridge, facet, &vertex))) {
+      qh_setappend(qh, &vertices, vertex);
+      if (++cntprojected > cntvertices || ridge == firstridge)
+        break;
+    }
+    if (!ridge || cntprojected != cntvertices) {
+      qh_fprintf(qh, qh->ferr, 6148, "qhull internal error (qh_facet3vertex): ridges for facet %d don't match up.  got at least %d\n",
+                  facet->id, cntprojected);
+      qh_errexit(qh, qh_ERRqhull, facet, ridge);
+    }
+  }
+  return vertices;
+} /* facet3vertex */
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="findbestfacet">-</a>
+
+  qh_findbestfacet(qh, point, bestoutside, bestdist, isoutside )
+    find facet that is furthest below a point
+
+    for Delaunay triangulations,
+      Use qh_setdelaunay() to lift point to paraboloid and scale by 'Qbb' if needed
+      Do not use options 'Qbk', 'QBk', or 'QbB' since they scale the coordinates.
+
+  returns:
+    if bestoutside is set (e.g., qh_ALL)
+      returns best facet that is not upperdelaunay
+      if Delaunay and inside, point is outside circumsphere of bestfacet
+    else
+      returns first facet below point
+      if point is inside, returns nearest, !upperdelaunay facet
+    distance to facet
+    isoutside set if outside of facet
+
+  notes:
+    For tricoplanar facets, this finds one of the tricoplanar facets closest
+    to the point.  For Delaunay triangulations, the point may be inside a
+    different tricoplanar facet. See <a href="../html/qh-code.htm#findfacet">locate a facet with qh_findbestfacet()</a>
+
+    If inside, qh_findbestfacet performs an exhaustive search
+       this may be too conservative.  Sometimes it is clearly required.
+
+    qh_findbestfacet is not used by qhull.
+    uses qh.visit_id and qh.coplanarset
+
+  see:
+    <a href="geom_r.c#findbest">qh_findbest</a>
+*/
+facetT *qh_findbestfacet(qhT *qh, pointT *point, boolT bestoutside,
+           realT *bestdist, boolT *isoutside) {
+  facetT *bestfacet= NULL;
+  int numpart, totpart= 0;
+
+  bestfacet= qh_findbest(qh, point, qh->facet_list,
+                            bestoutside, !qh_ISnewfacets, bestoutside /* qh_NOupper */,
+                            bestdist, isoutside, &totpart);
+  if (*bestdist < -qh->DISTround) {
+    bestfacet= qh_findfacet_all(qh, point, bestdist, isoutside, &numpart);
+    totpart += numpart;
+    if ((isoutside && *isoutside && bestoutside)
+    || (isoutside && !*isoutside && bestfacet->upperdelaunay)) {
+      bestfacet= qh_findbest(qh, point, bestfacet,
+                            bestoutside, False, bestoutside,
+                            bestdist, isoutside, &totpart);
+      totpart += numpart;
+    }
+  }
+  trace3((qh, qh->ferr, 3014, "qh_findbestfacet: f%d dist %2.2g isoutside %d totpart %d\n",
+          bestfacet->id, *bestdist, (isoutside ? *isoutside : UINT_MAX), totpart));
+  return bestfacet;
+} /* findbestfacet */
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="findbestlower">-</a>
+
+  qh_findbestlower(qh, facet, point, bestdist, numpart )
+    returns best non-upper, non-flipped neighbor of facet for point
+    if needed, searches vertex neighbors
+
+  returns:
+    returns bestdist and updates numpart
+
+  notes:
+    if Delaunay and inside, point is outside of circumsphere of bestfacet
+    called by qh_findbest() for points above an upperdelaunay facet
+
+*/
+facetT *qh_findbestlower(qhT *qh, facetT *upperfacet, pointT *point, realT *bestdistp, int *numpart) {
+  facetT *neighbor, **neighborp, *bestfacet= NULL;
+  realT bestdist= -REALmax/2 /* avoid underflow */;
+  realT dist;
+  vertexT *vertex;
+  boolT isoutside= False;  /* not used */
+
+  zinc_(Zbestlower);
+  FOREACHneighbor_(upperfacet) {
+    if (neighbor->upperdelaunay || neighbor->flipped)
+      continue;
+    (*numpart)++;
+    qh_distplane(qh, point, neighbor, &dist);
+    if (dist > bestdist) {
+      bestfacet= neighbor;
+      bestdist= dist;
+    }
+  }
+  if (!bestfacet) {
+    zinc_(Zbestlowerv);
+    /* rarely called, numpart does not count nearvertex computations */
+    vertex= qh_nearvertex(qh, upperfacet, point, &dist);
+    qh_vertexneighbors(qh);
+    FOREACHneighbor_(vertex) {
+      if (neighbor->upperdelaunay || neighbor->flipped)
+        continue;
+      (*numpart)++;
+      qh_distplane(qh, point, neighbor, &dist);
+      if (dist > bestdist) {
+        bestfacet= neighbor;
+        bestdist= dist;
+      }
+    }
+  }
+  if (!bestfacet) {
+    zinc_(Zbestlowerall);  /* invoked once per point in outsideset */
+    zmax_(Zbestloweralln, qh->num_facets);
+    /* [dec'15] Previously reported as QH6228 */
+    trace3((qh, qh->ferr, 3025, "qh_findbestlower: all neighbors of facet %d are flipped or upper Delaunay.  Search all facets\n",
+       upperfacet->id));
+    /* rarely called */
+    bestfacet= qh_findfacet_all(qh, point, &bestdist, &isoutside, numpart);
+  }
+  *bestdistp= bestdist;
+  trace3((qh, qh->ferr, 3015, "qh_findbestlower: f%d dist %2.2g for f%d p%d\n",
+          bestfacet->id, bestdist, upperfacet->id, qh_pointid(qh, point)));
+  return bestfacet;
+} /* findbestlower */
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="findfacet_all">-</a>
+
+  qh_findfacet_all(qh, point, bestdist, isoutside, numpart )
+    exhaustive search for facet below a point
+
+    for Delaunay triangulations,
+      Use qh_setdelaunay() to lift point to paraboloid and scale by 'Qbb' if needed
+      Do not use options 'Qbk', 'QBk', or 'QbB' since they scale the coordinates.
+
+  returns:
+    returns first facet below point
+    if point is inside,
+      returns nearest facet
+    distance to facet
+    isoutside if point is outside of the hull
+    number of distance tests
+
+  notes:
+    primarily for library users, rarely used by Qhull
+*/
+facetT *qh_findfacet_all(qhT *qh, pointT *point, realT *bestdist, boolT *isoutside,
+                          int *numpart) {
+  facetT *bestfacet= NULL, *facet;
+  realT dist;
+  int totpart= 0;
+
+  *bestdist= -REALmax;
+  *isoutside= False;
+  FORALLfacets {
+    if (facet->flipped || !facet->normal)
+      continue;
+    totpart++;
+    qh_distplane(qh, point, facet, &dist);
+    if (dist > *bestdist) {
+      *bestdist= dist;
+      bestfacet= facet;
+      if (dist > qh->MINoutside) {
+        *isoutside= True;
+        break;
+      }
+    }
+  }
+  *numpart= totpart;
+  trace3((qh, qh->ferr, 3016, "qh_findfacet_all: f%d dist %2.2g isoutside %d totpart %d\n",
+          getid_(bestfacet), *bestdist, *isoutside, totpart));
+  return bestfacet;
+} /* findfacet_all */
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="findgood">-</a>
+
+  qh_findgood(qh, facetlist, goodhorizon )
+    identify good facets for qh.PRINTgood
+    if qh.GOODvertex>0
+      facet includes point as vertex
+      if !match, returns goodhorizon
+      inactive if qh.MERGING
+    if qh.GOODpoint
+      facet is visible or coplanar (>0) or not visible (<0)
+    if qh.GOODthreshold
+      facet->normal matches threshold
+    if !goodhorizon and !match,
+      selects facet with closest angle
+      sets GOODclosest
+
+  returns:
+    number of new, good facets found
+    determines facet->good
+    may update qh.GOODclosest
+
+  notes:
+    qh_findgood_all further reduces the good region
+
+  design:
+    count good facets
+    mark good facets for qh.GOODpoint
+    mark good facets for qh.GOODthreshold
+    if necessary
+      update qh.GOODclosest
+*/
+int qh_findgood(qhT *qh, facetT *facetlist, int goodhorizon) {
+  facetT *facet, *bestfacet= NULL;
+  realT angle, bestangle= REALmax, dist;
+  int  numgood=0;
+
+  FORALLfacet_(facetlist) {
+    if (facet->good)
+      numgood++;
+  }
+  if (qh->GOODvertex>0 && !qh->MERGING) {
+    FORALLfacet_(facetlist) {
+      if (!qh_isvertex(qh->GOODvertexp, facet->vertices)) {
+        facet->good= False;
+        numgood--;
+      }
+    }
+  }
+  if (qh->GOODpoint && numgood) {
+    FORALLfacet_(facetlist) {
+      if (facet->good && facet->normal) {
+        zinc_(Zdistgood);
+        qh_distplane(qh, qh->GOODpointp, facet, &dist);
+        if ((qh->GOODpoint > 0) ^ (dist > 0.0)) {
+          facet->good= False;
+          numgood--;
+        }
+      }
+    }
+  }
+  if (qh->GOODthreshold && (numgood || goodhorizon || qh->GOODclosest)) {
+    FORALLfacet_(facetlist) {
+      if (facet->good && facet->normal) {
+        if (!qh_inthresholds(qh, facet->normal, &angle)) {
+          facet->good= False;
+          numgood--;
+          if (angle < bestangle) {
+            bestangle= angle;
+            bestfacet= facet;
+          }
+        }
+      }
+    }
+    if (!numgood && (!goodhorizon || qh->GOODclosest)) {
+      if (qh->GOODclosest) {
+        if (qh->GOODclosest->visible)
+          qh->GOODclosest= NULL;
+        else {
+          qh_inthresholds(qh, qh->GOODclosest->normal, &angle);
+          if (angle < bestangle)
+            bestfacet= qh->GOODclosest;
+        }
+      }
+      if (bestfacet && bestfacet != qh->GOODclosest) {
+        if (qh->GOODclosest)
+          qh->GOODclosest->good= False;
+        qh->GOODclosest= bestfacet;
+        bestfacet->good= True;
+        numgood++;
+        trace2((qh, qh->ferr, 2044, "qh_findgood: f%d is closest(%2.2g) to thresholds\n",
+           bestfacet->id, bestangle));
+        return numgood;
+      }
+    }else if (qh->GOODclosest) { /* numgood > 0 */
+      qh->GOODclosest->good= False;
+      qh->GOODclosest= NULL;
+    }
+  }
+  zadd_(Zgoodfacet, numgood);
+  trace2((qh, qh->ferr, 2045, "qh_findgood: found %d good facets with %d good horizon\n",
+               numgood, goodhorizon));
+  if (!numgood && qh->GOODvertex>0 && !qh->MERGING)
+    return goodhorizon;
+  return numgood;
+} /* findgood */
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="findgood_all">-</a>
+
+  qh_findgood_all(qh, facetlist )
+    apply other constraints for good facets (used by qh.PRINTgood)
+    if qh.GOODvertex
+      facet includes (>0) or doesn't include (<0) point as vertex
+      if last good facet and ONLYgood, prints warning and continues
+    if qh.SPLITthresholds
+      facet->normal matches threshold, or if none, the closest one
+    calls qh_findgood
+    nop if good not used
+
+  returns:
+    clears facet->good if not good
+    sets qh.num_good
+
+  notes:
+    this is like qh_findgood but more restrictive
+
+  design:
+    uses qh_findgood to mark good facets
+    marks facets for qh.GOODvertex
+    marks facets for qh.SPLITthreholds
+*/
+void qh_findgood_all(qhT *qh, facetT *facetlist) {
+  facetT *facet, *bestfacet=NULL;
+  realT angle, bestangle= REALmax;
+  int  numgood=0, startgood;
+
+  if (!qh->GOODvertex && !qh->GOODthreshold && !qh->GOODpoint
+  && !qh->SPLITthresholds)
+    return;
+  if (!qh->ONLYgood)
+    qh_findgood(qh, qh->facet_list, 0);
+  FORALLfacet_(facetlist) {
+    if (facet->good)
+      numgood++;
+  }
+  if (qh->GOODvertex <0 || (qh->GOODvertex > 0 && qh->MERGING)) {
+    FORALLfacet_(facetlist) {
+      if (facet->good && ((qh->GOODvertex > 0) ^ !!qh_isvertex(qh->GOODvertexp, facet->vertices))) {
+        if (!--numgood) {
+          if (qh->ONLYgood) {
+            qh_fprintf(qh, qh->ferr, 7064, "qhull warning: good vertex p%d does not match last good facet f%d.  Ignored.\n",
+               qh_pointid(qh, qh->GOODvertexp), facet->id);
+            return;
+          }else if (qh->GOODvertex > 0)
+            qh_fprintf(qh, qh->ferr, 7065, "qhull warning: point p%d is not a vertex('QV%d').\n",
+                qh->GOODvertex-1, qh->GOODvertex-1);
+          else
+            qh_fprintf(qh, qh->ferr, 7066, "qhull warning: point p%d is a vertex for every facet('QV-%d').\n",
+                -qh->GOODvertex - 1, -qh->GOODvertex - 1);
+        }
+        facet->good= False;
+      }
+    }
+  }
+  startgood= numgood;
+  if (qh->SPLITthresholds) {
+    FORALLfacet_(facetlist) {
+      if (facet->good) {
+        if (!qh_inthresholds(qh, facet->normal, &angle)) {
+          facet->good= False;
+          numgood--;
+          if (angle < bestangle) {
+            bestangle= angle;
+            bestfacet= facet;
+          }
+        }
+      }
+    }
+    if (!numgood && bestfacet) {
+      bestfacet->good= True;
+      numgood++;
+      trace0((qh, qh->ferr, 23, "qh_findgood_all: f%d is closest(%2.2g) to thresholds\n",
+           bestfacet->id, bestangle));
+      return;
+    }
+  }
+  qh->num_good= numgood;
+  trace0((qh, qh->ferr, 24, "qh_findgood_all: %d good facets remain out of %d facets\n",
+        numgood, startgood));
+} /* findgood_all */
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="furthestnext">-</a>
+
+  qh_furthestnext()
+    set qh.facet_next to facet with furthest of all furthest points
+    searches all facets on qh.facet_list
+
+  notes:
+    this may help avoid precision problems
+*/
+void qh_furthestnext(qhT *qh /* qh->facet_list */) {
+  facetT *facet, *bestfacet= NULL;
+  realT dist, bestdist= -REALmax;
+
+  FORALLfacets {
+    if (facet->outsideset) {
+#if qh_COMPUTEfurthest
+      pointT *furthest;
+      furthest= (pointT*)qh_setlast(facet->outsideset);
+      zinc_(Zcomputefurthest);
+      qh_distplane(qh, furthest, facet, &dist);
+#else
+      dist= facet->furthestdist;
+#endif
+      if (dist > bestdist) {
+        bestfacet= facet;
+        bestdist= dist;
+      }
+    }
+  }
+  if (bestfacet) {
+    qh_removefacet(qh, bestfacet);
+    qh_prependfacet(qh, bestfacet, &qh->facet_next);
+    trace1((qh, qh->ferr, 1029, "qh_furthestnext: made f%d next facet(dist %.2g)\n",
+            bestfacet->id, bestdist));
+  }
+} /* furthestnext */
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="furthestout">-</a>
+
+  qh_furthestout(qh, facet )
+    make furthest outside point the last point of outsideset
+
+  returns:
+    updates facet->outsideset
+    clears facet->notfurthest
+    sets facet->furthestdist
+
+  design:
+    determine best point of outsideset
+    make it the last point of outsideset
+*/
+void qh_furthestout(qhT *qh, facetT *facet) {
+  pointT *point, **pointp, *bestpoint= NULL;
+  realT dist, bestdist= -REALmax;
+
+  FOREACHpoint_(facet->outsideset) {
+    qh_distplane(qh, point, facet, &dist);
+    zinc_(Zcomputefurthest);
+    if (dist > bestdist) {
+      bestpoint= point;
+      bestdist= dist;
+    }
+  }
+  if (bestpoint) {
+    qh_setdel(facet->outsideset, point);
+    qh_setappend(qh, &facet->outsideset, point);
+#if !qh_COMPUTEfurthest
+    facet->furthestdist= bestdist;
+#endif
+  }
+  facet->notfurthest= False;
+  trace3((qh, qh->ferr, 3017, "qh_furthestout: p%d is furthest outside point of f%d\n",
+          qh_pointid(qh, point), facet->id));
+} /* furthestout */
+
+
+/*-<a                             href="qh-qhull_r.htm#TOC"
+  >-------------------------------</a><a name="infiniteloop">-</a>
+
+  qh_infiniteloop(qh, facet )
+    report infinite loop error due to facet
+*/
+void qh_infiniteloop(qhT *qh, facetT *facet) {
+
+  qh_fprintf(qh, qh->ferr, 6149, "qhull internal error (qh_infiniteloop): potential infinite loop detected\n");
+  qh_errexit(qh, qh_ERRqhull, facet, NULL);
+} /* qh_infiniteloop */
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="initbuild">-</a>
+
+  qh_initbuild()
+    initialize hull and outside sets with point array
+    qh.FIRSTpoint/qh.NUMpoints is point array
+    if qh.GOODpoint
+      adds qh.GOODpoint to initial hull
+
+  returns:
+    qh_facetlist with initial hull
+    points partioned into outside sets, coplanar sets, or inside
+    initializes qh.GOODpointp, qh.GOODvertexp,
+
+  design:
+    initialize global variables used during qh_buildhull
+    determine precision constants and points with max/min coordinate values
+      if qh.SCALElast, scale last coordinate(for 'd')
+    build initial simplex
+    partition input points into facets of initial simplex
+    set up lists
+    if qh.ONLYgood
+      check consistency
+      add qh.GOODvertex if defined
+*/
+void qh_initbuild(qhT *qh) {
+  setT *maxpoints, *vertices;
+  facetT *facet;
+  int i, numpart;
+  realT dist;
+  boolT isoutside;
+
+  qh->furthest_id= qh_IDunknown;
+  qh->lastreport= 0;
+  qh->facet_id= qh->vertex_id= qh->ridge_id= 0;
+  qh->visit_id= qh->vertex_visit= 0;
+  qh->maxoutdone= False;
+
+  if (qh->GOODpoint > 0)
+    qh->GOODpointp= qh_point(qh, qh->GOODpoint-1);
+  else if (qh->GOODpoint < 0)
+    qh->GOODpointp= qh_point(qh, -qh->GOODpoint-1);
+  if (qh->GOODvertex > 0)
+    qh->GOODvertexp= qh_point(qh, qh->GOODvertex-1);
+  else if (qh->GOODvertex < 0)
+    qh->GOODvertexp= qh_point(qh, -qh->GOODvertex-1);
+  if ((qh->GOODpoint
+       && (qh->GOODpointp < qh->first_point  /* also catches !GOODpointp */
+           || qh->GOODpointp > qh_point(qh, qh->num_points-1)))
+    || (qh->GOODvertex
+        && (qh->GOODvertexp < qh->first_point  /* also catches !GOODvertexp */
+            || qh->GOODvertexp > qh_point(qh, qh->num_points-1)))) {
+    qh_fprintf(qh, qh->ferr, 6150, "qhull input error: either QGn or QVn point is > p%d\n",
+             qh->num_points-1);
+    qh_errexit(qh, qh_ERRinput, NULL, NULL);
+  }
+  maxpoints= qh_maxmin(qh, qh->first_point, qh->num_points, qh->hull_dim);
+  if (qh->SCALElast)
+    qh_scalelast(qh, qh->first_point, qh->num_points, qh->hull_dim,
+               qh->MINlastcoord, qh->MAXlastcoord, qh->MAXwidth);
+  qh_detroundoff(qh);
+  if (qh->DELAUNAY && qh->upper_threshold[qh->hull_dim-1] > REALmax/2
+                  && qh->lower_threshold[qh->hull_dim-1] < -REALmax/2) {
+    for (i=qh_PRINTEND; i--; ) {
+      if (qh->PRINTout[i] == qh_PRINTgeom && qh->DROPdim < 0
+          && !qh->GOODthreshold && !qh->SPLITthresholds)
+        break;  /* in this case, don't set upper_threshold */
+    }
+    if (i < 0) {
+      if (qh->UPPERdelaunay) { /* matches qh.upperdelaunay in qh_setfacetplane */
+        qh->lower_threshold[qh->hull_dim-1]= qh->ANGLEround * qh_ZEROdelaunay;
+        qh->GOODthreshold= True;
+      }else {
+        qh->upper_threshold[qh->hull_dim-1]= -qh->ANGLEround * qh_ZEROdelaunay;
+        if (!qh->GOODthreshold)
+          qh->SPLITthresholds= True; /* build upper-convex hull even if Qg */
+          /* qh_initqhull_globals errors if Qg without Pdk/etc. */
+      }
+    }
+  }
+  vertices= qh_initialvertices(qh, qh->hull_dim, maxpoints, qh->first_point, qh->num_points);
+  qh_initialhull(qh, vertices);  /* initial qh->facet_list */
+  qh_partitionall(qh, vertices, qh->first_point, qh->num_points);
+  if (qh->PRINToptions1st || qh->TRACElevel || qh->IStracing) {
+    if (qh->TRACElevel || qh->IStracing)
+      qh_fprintf(qh, qh->ferr, 8103, "\nTrace level %d for %s | %s\n",
+         qh->IStracing ? qh->IStracing : qh->TRACElevel, qh->rbox_command, qh->qhull_command);
+    qh_fprintf(qh, qh->ferr, 8104, "Options selected for Qhull %s:\n%s\n", qh_version, qh->qhull_options);
+  }
+  qh_resetlists(qh, False, qh_RESETvisible /*qh.visible_list newvertex_list newfacet_list */);
+  qh->facet_next= qh->facet_list;
+  qh_furthestnext(qh /* qh->facet_list */);
+  if (qh->PREmerge) {
+    qh->cos_max= qh->premerge_cos;
+    qh->centrum_radius= qh->premerge_centrum;
+  }
+  if (qh->ONLYgood) {
+    if (qh->GOODvertex > 0 && qh->MERGING) {
+      qh_fprintf(qh, qh->ferr, 6151, "qhull input error: 'Qg QVn' (only good vertex) does not work with merging.\nUse 'QJ' to joggle the input or 'Q0' to turn off merging.\n");
+      qh_errexit(qh, qh_ERRinput, NULL, NULL);
+    }
+    if (!(qh->GOODthreshold || qh->GOODpoint
+         || (!qh->MERGEexact && !qh->PREmerge && qh->GOODvertexp))) {
+      qh_fprintf(qh, qh->ferr, 6152, "qhull input error: 'Qg' (ONLYgood) needs a good threshold('Pd0D0'), a\n\
+good point(QGn or QG-n), or a good vertex with 'QJ' or 'Q0' (QVn).\n");
+      qh_errexit(qh, qh_ERRinput, NULL, NULL);
+    }
+    if (qh->GOODvertex > 0  && !qh->MERGING  /* matches qh_partitionall */
+        && !qh_isvertex(qh->GOODvertexp, vertices)) {
+      facet= qh_findbestnew(qh, qh->GOODvertexp, qh->facet_list,
+                          &dist, !qh_ALL, &isoutside, &numpart);
+      zadd_(Zdistgood, numpart);
+      if (!isoutside) {
+        qh_fprintf(qh, qh->ferr, 6153, "qhull input error: point for QV%d is inside initial simplex.  It can not be made a vertex.\n",
+               qh_pointid(qh, qh->GOODvertexp));
+        qh_errexit(qh, qh_ERRinput, NULL, NULL);
+      }
+      if (!qh_addpoint(qh, qh->GOODvertexp, facet, False)) {
+        qh_settempfree(qh, &vertices);
+        qh_settempfree(qh, &maxpoints);
+        return;
+      }
+    }
+    qh_findgood(qh, qh->facet_list, 0);
+  }
+  qh_settempfree(qh, &vertices);
+  qh_settempfree(qh, &maxpoints);
+  trace1((qh, qh->ferr, 1030, "qh_initbuild: initial hull created and points partitioned\n"));
+} /* initbuild */
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="initialhull">-</a>
+
+  qh_initialhull(qh, vertices )
+    constructs the initial hull as a DIM3 simplex of vertices
+
+  design:
+    creates a simplex (initializes lists)
+    determines orientation of simplex
+    sets hyperplanes for facets
+    doubles checks orientation (in case of axis-parallel facets with Gaussian elimination)
+    checks for flipped facets and qh.NARROWhull
+    checks the result
+*/
+void qh_initialhull(qhT *qh, setT *vertices) {
+  facetT *facet, *firstfacet, *neighbor, **neighborp;
+  realT dist, angle, minangle= REALmax;
+#ifndef qh_NOtrace
+  int k;
+#endif
+
+  qh_createsimplex(qh, vertices);  /* qh->facet_list */
+  qh_resetlists(qh, False, qh_RESETvisible);
+  qh->facet_next= qh->facet_list;      /* advance facet when processed */
+  qh->interior_point= qh_getcenter(qh, vertices);
+  firstfacet= qh->facet_list;
+  qh_setfacetplane(qh, firstfacet);
+  zinc_(Znumvisibility); /* needs to be in printsummary */
+  qh_distplane(qh, qh->interior_point, firstfacet, &dist);
+  if (dist > 0) {
+    FORALLfacets
+      facet->toporient ^= (unsigned char)True;
+  }
+  FORALLfacets
+    qh_setfacetplane(qh, facet);
+  FORALLfacets {
+    if (!qh_checkflipped(qh, facet, NULL, qh_ALL)) {/* due to axis-parallel facet */
+      trace1((qh, qh->ferr, 1031, "qh_initialhull: initial orientation incorrect.  Correct all facets\n"));
+      facet->flipped= False;
+      FORALLfacets {
+        facet->toporient ^= (unsigned char)True;
+        qh_orientoutside(qh, facet);
+      }
+      break;
+    }
+  }
+  FORALLfacets {
+    if (!qh_checkflipped(qh, facet, NULL, !qh_ALL)) {  /* can happen with 'R0.1' */
+      if (qh->DELAUNAY && ! qh->ATinfinity) {
+        if (qh->UPPERdelaunay)
+          qh_fprintf(qh, qh->ferr, 6240, "Qhull precision error: Initial simplex is cocircular or cospherical.  Option 'Qs' searches all points.  Can not compute the upper Delaunay triangulation or upper Voronoi diagram of cocircular/cospherical points.\n");
+        else
+          qh_fprintf(qh, qh->ferr, 6239, "Qhull precision error: Initial simplex is cocircular or cospherical.  Use option 'Qz' for the Delaunay triangulation or Voronoi diagram of cocircular/cospherical points.  Option 'Qz' adds a point \"at infinity\".  Use option 'Qs' to search all points for the initial simplex.\n");
+        qh_errexit(qh, qh_ERRinput, NULL, NULL);
+      }
+      qh_precision(qh, "initial simplex is flat");
+      qh_fprintf(qh, qh->ferr, 6154, "Qhull precision error: Initial simplex is flat (facet %d is coplanar with the interior point)\n",
+                   facet->id);
+      qh_errexit(qh, qh_ERRsingular, NULL, NULL);  /* calls qh_printhelp_singular */
+    }
+    FOREACHneighbor_(facet) {
+      angle= qh_getangle(qh, facet->normal, neighbor->normal);
+      minimize_( minangle, angle);
+    }
+  }
+  if (minangle < qh_MAXnarrow && !qh->NOnarrow) {
+    realT diff= 1.0 + minangle;
+
+    qh->NARROWhull= True;
+    qh_option(qh, "_narrow-hull", NULL, &diff);
+    if (minangle < qh_WARNnarrow && !qh->RERUN && qh->PRINTprecision)
+      qh_printhelp_narrowhull(qh, qh->ferr, minangle);
+  }
+  zzval_(Zprocessed)= qh->hull_dim+1;
+  qh_checkpolygon(qh, qh->facet_list);
+  qh_checkconvex(qh, qh->facet_list,   qh_DATAfault);
+#ifndef qh_NOtrace
+  if (qh->IStracing >= 1) {
+    qh_fprintf(qh, qh->ferr, 8105, "qh_initialhull: simplex constructed, interior point:");
+    for (k=0; k < qh->hull_dim; k++)
+      qh_fprintf(qh, qh->ferr, 8106, " %6.4g", qh->interior_point[k]);
+    qh_fprintf(qh, qh->ferr, 8107, "\n");
+  }
+#endif
+} /* initialhull */
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="initialvertices">-</a>
+
+  qh_initialvertices(qh, dim, maxpoints, points, numpoints )
+    determines a non-singular set of initial vertices
+    maxpoints may include duplicate points
+
+  returns:
+    temporary set of dim+1 vertices in descending order by vertex id
+    if qh.RANDOMoutside && !qh.ALLpoints
+      picks random points
+    if dim >= qh_INITIALmax,
+      uses min/max x and max points with non-zero determinants
+
+  notes:
+    unless qh.ALLpoints,
+      uses maxpoints as long as determinate is non-zero
+*/
+setT *qh_initialvertices(qhT *qh, int dim, setT *maxpoints, pointT *points, int numpoints) {
+  pointT *point, **pointp;
+  setT *vertices, *simplex, *tested;
+  realT randr;
+  int idx, point_i, point_n, k;
+  boolT nearzero= False;
+
+  vertices= qh_settemp(qh, dim + 1);
+  simplex= qh_settemp(qh, dim+1);
+  if (qh->ALLpoints)
+    qh_maxsimplex(qh, dim, NULL, points, numpoints, &simplex);
+  else if (qh->RANDOMoutside) {
+    while (qh_setsize(qh, simplex) != dim+1) {
+      randr= qh_RANDOMint;
+      randr= randr/(qh_RANDOMmax+1);
+      idx= (int)floor(qh->num_points * randr);
+      while (qh_setin(simplex, qh_point(qh, idx))) {
+            idx++; /* in case qh_RANDOMint always returns the same value */
+        idx= idx < qh->num_points ? idx : 0;
+      }
+      qh_setappend(qh, &simplex, qh_point(qh, idx));
+    }
+  }else if (qh->hull_dim >= qh_INITIALmax) {
+    tested= qh_settemp(qh, dim+1);
+    qh_setappend(qh, &simplex, SETfirst_(maxpoints));   /* max and min X coord */
+    qh_setappend(qh, &simplex, SETsecond_(maxpoints));
+    qh_maxsimplex(qh, fmin_(qh_INITIALsearch, dim), maxpoints, points, numpoints, &simplex);
+    k= qh_setsize(qh, simplex);
+    FOREACHpoint_i_(qh, maxpoints) {
+      if (point_i & 0x1) {     /* first pick up max. coord. points */
+        if (!qh_setin(simplex, point) && !qh_setin(tested, point)){
+          qh_detsimplex(qh, point, simplex, k, &nearzero);
+          if (nearzero)
+            qh_setappend(qh, &tested, point);
+          else {
+            qh_setappend(qh, &simplex, point);
+            if (++k == dim)  /* use search for last point */
+              break;
+          }
+        }
+      }
+    }
+    while (k != dim && (point= (pointT*)qh_setdellast(maxpoints))) {
+      if (!qh_setin(simplex, point) && !qh_setin(tested, point)){
+        qh_detsimplex(qh, point, simplex, k, &nearzero);
+        if (nearzero)
+          qh_setappend(qh, &tested, point);
+        else {
+          qh_setappend(qh, &simplex, point);
+          k++;
+        }
+      }
+    }
+    idx= 0;
+    while (k != dim && (point= qh_point(qh, idx++))) {
+      if (!qh_setin(simplex, point) && !qh_setin(tested, point)){
+        qh_detsimplex(qh, point, simplex, k, &nearzero);
+        if (!nearzero){
+          qh_setappend(qh, &simplex, point);
+          k++;
+        }
+      }
+    }
+    qh_settempfree(qh, &tested);
+    qh_maxsimplex(qh, dim, maxpoints, points, numpoints, &simplex);
+  }else
+    qh_maxsimplex(qh, dim, maxpoints, points, numpoints, &simplex);
+  FOREACHpoint_(simplex)
+    qh_setaddnth(qh, &vertices, 0, qh_newvertex(qh, point)); /* descending order */
+  qh_settempfree(qh, &simplex);
+  return vertices;
+} /* initialvertices */
+
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="isvertex">-</a>
+
+  qh_isvertex( point, vertices )
+    returns vertex if point is in vertex set, else returns NULL
+
+  notes:
+    for qh.GOODvertex
+*/
+vertexT *qh_isvertex(pointT *point, setT *vertices) {
+  vertexT *vertex, **vertexp;
+
+  FOREACHvertex_(vertices) {
+    if (vertex->point == point)
+      return vertex;
+  }
+  return NULL;
+} /* isvertex */
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="makenewfacets">-</a>
+
+  qh_makenewfacets(qh, point )
+    make new facets from point and qh.visible_list
+
+  returns:
+    qh.newfacet_list= list of new facets with hyperplanes and ->newfacet
+    qh.newvertex_list= list of vertices in new facets with ->newlist set
+
+    if (qh.ONLYgood)
+      newfacets reference horizon facets, but not vice versa
+      ridges reference non-simplicial horizon ridges, but not vice versa
+      does not change existing facets
+    else
+      sets qh.NEWfacets
+      new facets attached to horizon facets and ridges
+      for visible facets,
+        visible->r.replace is corresponding new facet
+
+  see also:
+    qh_makenewplanes() -- make hyperplanes for facets
+    qh_attachnewfacets() -- attachnewfacets if not done here(qh->ONLYgood)
+    qh_matchnewfacets() -- match up neighbors
+    qh_updatevertices() -- update vertex neighbors and delvertices
+    qh_deletevisible() -- delete visible facets
+    qh_checkpolygon() --check the result
+    qh_triangulate() -- triangulate a non-simplicial facet
+
+  design:
+    for each visible facet
+      make new facets to its horizon facets
+      update its f.replace
+      clear its neighbor set
+*/
+vertexT *qh_makenewfacets(qhT *qh, pointT *point /*visible_list*/) {
+  facetT *visible, *newfacet= NULL, *newfacet2= NULL, *neighbor, **neighborp;
+  vertexT *apex;
+  int numnew=0;
+
+  qh->newfacet_list= qh->facet_tail;
+  qh->newvertex_list= qh->vertex_tail;
+  apex= qh_newvertex(qh, point);
+  qh_appendvertex(qh, apex);
+  qh->visit_id++;
+  if (!qh->ONLYgood)
+    qh->NEWfacets= True;
+  FORALLvisible_facets {
+    FOREACHneighbor_(visible)
+      neighbor->seen= False;
+    if (visible->ridges) {
+      visible->visitid= qh->visit_id;
+      newfacet2= qh_makenew_nonsimplicial(qh, visible, apex, &numnew);
+    }
+    if (visible->simplicial)
+      newfacet= qh_makenew_simplicial(qh, visible, apex, &numnew);
+    if (!qh->ONLYgood) {
+      if (newfacet2)  /* newfacet is null if all ridges defined */
+        newfacet= newfacet2;
+      if (newfacet)
+        visible->f.replace= newfacet;
+      else
+        zinc_(Zinsidevisible);
+      SETfirst_(visible->neighbors)= NULL;
+    }
+  }
+  trace1((qh, qh->ferr, 1032, "qh_makenewfacets: created %d new facets from point p%d to horizon\n",
+          numnew, qh_pointid(qh, point)));
+  if (qh->IStracing >= 4)
+    qh_printfacetlist(qh, qh->newfacet_list, NULL, qh_ALL);
+  return apex;
+} /* makenewfacets */
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="matchduplicates">-</a>
+
+  qh_matchduplicates(qh, atfacet, atskip, hashsize, hashcount )
+    match duplicate ridges in qh.hash_table for atfacet/atskip
+    duplicates marked with ->dupridge and qh_DUPLICATEridge
+
+  returns:
+    picks match with worst merge (min distance apart)
+    updates hashcount
+
+  see also:
+    qh_matchneighbor
+
+  notes:
+
+  design:
+    compute hash value for atfacet and atskip
+    repeat twice -- once to make best matches, once to match the rest
+      for each possible facet in qh.hash_table
+        if it is a matching facet and pass 2
+          make match
+          unless tricoplanar, mark match for merging (qh_MERGEridge)
+          [e.g., tricoplanar RBOX s 1000 t993602376 | QHULL C-1e-3 d Qbb FA Qt]
+        if it is a matching facet and pass 1
+          test if this is a better match
+      if pass 1,
+        make best match (it will not be merged)
+*/
+#ifndef qh_NOmerge
+void qh_matchduplicates(qhT *qh, facetT *atfacet, int atskip, int hashsize, int *hashcount) {
+  boolT same, ismatch;
+  int hash, scan;
+  facetT *facet, *newfacet, *maxmatch= NULL, *maxmatch2= NULL, *nextfacet;
+  int skip, newskip, nextskip= 0, maxskip= 0, maxskip2= 0, makematch;
+  realT maxdist= -REALmax, mindist, dist2, low, high;
+
+  hash= qh_gethash(qh, hashsize, atfacet->vertices, qh->hull_dim, 1,
+                     SETelem_(atfacet->vertices, atskip));
+  trace2((qh, qh->ferr, 2046, "qh_matchduplicates: find duplicate matches for f%d skip %d hash %d hashcount %d\n",
+          atfacet->id, atskip, hash, *hashcount));
+  for (makematch= 0; makematch < 2; makematch++) {
+    qh->visit_id++;
+    for (newfacet= atfacet, newskip= atskip; newfacet; newfacet= nextfacet, newskip= nextskip) {
+      zinc_(Zhashlookup);
+      nextfacet= NULL;
+      newfacet->visitid= qh->visit_id;
+      for (scan= hash; (facet= SETelemt_(qh->hash_table, scan, facetT));
+           scan= (++scan >= hashsize ? 0 : scan)) {
+        if (!facet->dupridge || facet->visitid == qh->visit_id)
+          continue;
+        zinc_(Zhashtests);
+        if (qh_matchvertices(qh, 1, newfacet->vertices, newskip, facet->vertices, &skip, &same)) {
+          ismatch= (same == (boolT)(newfacet->toporient ^ facet->toporient));
+          if (SETelemt_(facet->neighbors, skip, facetT) != qh_DUPLICATEridge) {
+            if (!makematch) {
+              qh_fprintf(qh, qh->ferr, 6155, "qhull internal error (qh_matchduplicates): missing dupridge at f%d skip %d for new f%d skip %d hash %d\n",
+                     facet->id, skip, newfacet->id, newskip, hash);
+              qh_errexit2(qh, qh_ERRqhull, facet, newfacet);
+            }
+          }else if (ismatch && makematch) {
+            if (SETelemt_(newfacet->neighbors, newskip, facetT) == qh_DUPLICATEridge) {
+              SETelem_(facet->neighbors, skip)= newfacet;
+              if (newfacet->tricoplanar)
+                SETelem_(newfacet->neighbors, newskip)= facet;
+              else
+                SETelem_(newfacet->neighbors, newskip)= qh_MERGEridge;
+              *hashcount -= 2; /* removed two unmatched facets */
+              trace4((qh, qh->ferr, 4059, "qh_matchduplicates: duplicate f%d skip %d matched with new f%d skip %d merge\n",
+                    facet->id, skip, newfacet->id, newskip));
+            }
+          }else if (ismatch) {
+            mindist= qh_getdistance(qh, facet, newfacet, &low, &high);
+            dist2= qh_getdistance(qh, newfacet, facet, &low, &high);
+            minimize_(mindist, dist2);
+            if (mindist > maxdist) {
+              maxdist= mindist;
+              maxmatch= facet;
+              maxskip= skip;
+              maxmatch2= newfacet;
+              maxskip2= newskip;
+            }
+            trace3((qh, qh->ferr, 3018, "qh_matchduplicates: duplicate f%d skip %d new f%d skip %d at dist %2.2g, max is now f%d f%d\n",
+                    facet->id, skip, newfacet->id, newskip, mindist,
+                    maxmatch->id, maxmatch2->id));
+          }else { /* !ismatch */
+            nextfacet= facet;
+            nextskip= skip;
+          }
+        }
+        if (makematch && !facet
+        && SETelemt_(facet->neighbors, skip, facetT) == qh_DUPLICATEridge) {
+          qh_fprintf(qh, qh->ferr, 6156, "qhull internal error (qh_matchduplicates): no MERGEridge match for duplicate f%d skip %d at hash %d\n",
+                     newfacet->id, newskip, hash);
+          qh_errexit(qh, qh_ERRqhull, newfacet, NULL);
+        }
+      }
+    } /* end of for each new facet at hash */
+    if (!makematch) {
+      if (!maxmatch) {
+        qh_fprintf(qh, qh->ferr, 6157, "qhull internal error (qh_matchduplicates): no maximum match at duplicate f%d skip %d at hash %d\n",
+                     atfacet->id, atskip, hash);
+        qh_errexit(qh, qh_ERRqhull, atfacet, NULL);
+      }
+      SETelem_(maxmatch->neighbors, maxskip)= maxmatch2; /* maxmatch!=0 by QH6157 */
+      SETelem_(maxmatch2->neighbors, maxskip2)= maxmatch;
+      *hashcount -= 2; /* removed two unmatched facets */
+      zzinc_(Zmultiridge);
+      trace0((qh, qh->ferr, 25, "qh_matchduplicates: duplicate f%d skip %d matched with new f%d skip %d keep\n",
+              maxmatch->id, maxskip, maxmatch2->id, maxskip2));
+      qh_precision(qh, "ridge with multiple neighbors");
+      if (qh->IStracing >= 4)
+        qh_errprint(qh, "DUPLICATED/MATCH", maxmatch, maxmatch2, NULL, NULL);
+    }
+  }
+} /* matchduplicates */
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="nearcoplanar">-</a>
+
+  qh_nearcoplanar()
+    for all facets, remove near-inside points from facet->coplanarset</li>
+    coplanar points defined by innerplane from qh_outerinner()
+
+  returns:
+    if qh->KEEPcoplanar && !qh->KEEPinside
+      facet->coplanarset only contains coplanar points
+    if qh.JOGGLEmax
+      drops inner plane by another qh.JOGGLEmax diagonal since a
+        vertex could shift out while a coplanar point shifts in
+
+  notes:
+    used for qh.PREmerge and qh.JOGGLEmax
+    must agree with computation of qh.NEARcoplanar in qh_detroundoff(qh)
+  design:
+    if not keeping coplanar or inside points
+      free all coplanar sets
+    else if not keeping both coplanar and inside points
+      remove !coplanar or !inside points from coplanar sets
+*/
+void qh_nearcoplanar(qhT *qh /* qh.facet_list */) {
+  facetT *facet;
+  pointT *point, **pointp;
+  int numpart;
+  realT dist, innerplane;
+
+  if (!qh->KEEPcoplanar && !qh->KEEPinside) {
+    FORALLfacets {
+      if (facet->coplanarset)
+        qh_setfree(qh, &facet->coplanarset);
+    }
+  }else if (!qh->KEEPcoplanar || !qh->KEEPinside) {
+    qh_outerinner(qh, NULL, NULL, &innerplane);
+    if (qh->JOGGLEmax < REALmax/2)
+      innerplane -= qh->JOGGLEmax * sqrt((realT)qh->hull_dim);
+    numpart= 0;
+    FORALLfacets {
+      if (facet->coplanarset) {
+        FOREACHpoint_(facet->coplanarset) {
+          numpart++;
+          qh_distplane(qh, point, facet, &dist);
+          if (dist < innerplane) {
+            if (!qh->KEEPinside)
+              SETref_(point)= NULL;
+          }else if (!qh->KEEPcoplanar)
+            SETref_(point)= NULL;
+        }
+        qh_setcompact(qh, facet->coplanarset);
+      }
+    }
+    zzadd_(Zcheckpart, numpart);
+  }
+} /* nearcoplanar */
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="nearvertex">-</a>
+
+  qh_nearvertex(qh, facet, point, bestdist )
+    return nearest vertex in facet to point
+
+  returns:
+    vertex and its distance
+
+  notes:
+    if qh.DELAUNAY
+      distance is measured in the input set
+    searches neighboring tricoplanar facets (requires vertexneighbors)
+      Slow implementation.  Recomputes vertex set for each point.
+    The vertex set could be stored in the qh.keepcentrum facet.
+*/
+vertexT *qh_nearvertex(qhT *qh, facetT *facet, pointT *point, realT *bestdistp) {
+  realT bestdist= REALmax, dist;
+  vertexT *bestvertex= NULL, *vertex, **vertexp, *apex;
+  coordT *center;
+  facetT *neighbor, **neighborp;
+  setT *vertices;
+  int dim= qh->hull_dim;
+
+  if (qh->DELAUNAY)
+    dim--;
+  if (facet->tricoplanar) {
+    if (!qh->VERTEXneighbors || !facet->center) {
+      qh_fprintf(qh, qh->ferr, 6158, "qhull internal error (qh_nearvertex): qh.VERTEXneighbors and facet->center required for tricoplanar facets\n");
+      qh_errexit(qh, qh_ERRqhull, facet, NULL);
+    }
+    vertices= qh_settemp(qh, qh->TEMPsize);
+    apex= SETfirstt_(facet->vertices, vertexT);
+    center= facet->center;
+    FOREACHneighbor_(apex) {
+      if (neighbor->center == center) {
+        FOREACHvertex_(neighbor->vertices)
+          qh_setappend(qh, &vertices, vertex);
+      }
+    }
+  }else
+    vertices= facet->vertices;
+  FOREACHvertex_(vertices) {
+    dist= qh_pointdist(vertex->point, point, -dim);
+    if (dist < bestdist) {
+      bestdist= dist;
+      bestvertex= vertex;
+    }
+  }
+  if (facet->tricoplanar)
+    qh_settempfree(qh, &vertices);
+  *bestdistp= sqrt(bestdist);
+  if (!bestvertex) {
+      qh_fprintf(qh, qh->ferr, 6261, "qhull internal error (qh_nearvertex): did not find bestvertex for f%d p%d\n", facet->id, qh_pointid(qh, point));
+      qh_errexit(qh, qh_ERRqhull, facet, NULL);
+  }
+  trace3((qh, qh->ferr, 3019, "qh_nearvertex: v%d dist %2.2g for f%d p%d\n",
+        bestvertex->id, *bestdistp, facet->id, qh_pointid(qh, point))); /* bestvertex!=0 by QH2161 */
+  return bestvertex;
+} /* nearvertex */
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="newhashtable">-</a>
+
+  qh_newhashtable(qh, newsize )
+    returns size of qh.hash_table of at least newsize slots
+
+  notes:
+    assumes qh.hash_table is NULL
+    qh_HASHfactor determines the number of extra slots
+    size is not divisible by 2, 3, or 5
+*/
+int qh_newhashtable(qhT *qh, int newsize) {
+  int size;
+
+  size= ((newsize+1)*qh_HASHfactor) | 0x1;  /* odd number */
+  while (True) {
+    if (newsize<0 || size<0) {
+        qh_fprintf(qh, qh->qhmem.ferr, 6236, "qhull error (qh_newhashtable): negative request (%d) or size (%d).  Did int overflow due to high-D?\n", newsize, size); /* WARN64 */
+        qh_errexit(qh, qhmem_ERRmem, NULL, NULL);
+    }
+    if ((size%3) && (size%5))
+      break;
+    size += 2;
+    /* loop terminates because there is an infinite number of primes */
+  }
+  qh->hash_table= qh_setnew(qh, size);
+  qh_setzero(qh, qh->hash_table, 0, size);
+  return size;
+} /* newhashtable */
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="newvertex">-</a>
+
+  qh_newvertex(qh, point )
+    returns a new vertex for point
+*/
+vertexT *qh_newvertex(qhT *qh, pointT *point) {
+  vertexT *vertex;
+
+  zinc_(Ztotvertices);
+  vertex= (vertexT *)qh_memalloc(qh, (int)sizeof(vertexT));
+  memset((char *) vertex, (size_t)0, sizeof(vertexT));
+  if (qh->vertex_id == UINT_MAX) {
+    qh_memfree(qh, vertex, (int)sizeof(vertexT));
+    qh_fprintf(qh, qh->ferr, 6159, "qhull error: more than 2^32 vertices.  vertexT.id field overflows.  Vertices would not be sorted correctly.\n");
+    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+  }
+  if (qh->vertex_id == qh->tracevertex_id)
+    qh->tracevertex= vertex;
+  vertex->id= qh->vertex_id++;
+  vertex->point= point;
+  trace4((qh, qh->ferr, 4060, "qh_newvertex: vertex p%d(v%d) created\n", qh_pointid(qh, vertex->point),
+          vertex->id));
+  return(vertex);
+} /* newvertex */
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="nextridge3d">-</a>
+
+  qh_nextridge3d( atridge, facet, vertex )
+    return next ridge and vertex for a 3d facet
+    returns NULL on error
+    [for QhullFacet::nextRidge3d] Does not call qh_errexit nor access qhT.
+
+  notes:
+    in qh_ORIENTclock order
+    this is a O(n^2) implementation to trace all ridges
+    be sure to stop on any 2nd visit
+    same as QhullRidge::nextRidge3d
+    does not use qhT or qh_errexit [QhullFacet.cpp]
+
+  design:
+    for each ridge
+      exit if it is the ridge after atridge
+*/
+ridgeT *qh_nextridge3d(ridgeT *atridge, facetT *facet, vertexT **vertexp) {
+  vertexT *atvertex, *vertex, *othervertex;
+  ridgeT *ridge, **ridgep;
+
+  if ((atridge->top == facet) ^ qh_ORIENTclock)
+    atvertex= SETsecondt_(atridge->vertices, vertexT);
+  else
+    atvertex= SETfirstt_(atridge->vertices, vertexT);
+  FOREACHridge_(facet->ridges) {
+    if (ridge == atridge)
+      continue;
+    if ((ridge->top == facet) ^ qh_ORIENTclock) {
+      othervertex= SETsecondt_(ridge->vertices, vertexT);
+      vertex= SETfirstt_(ridge->vertices, vertexT);
+    }else {
+      vertex= SETsecondt_(ridge->vertices, vertexT);
+      othervertex= SETfirstt_(ridge->vertices, vertexT);
+    }
+    if (vertex == atvertex) {
+      if (vertexp)
+        *vertexp= othervertex;
+      return ridge;
+    }
+  }
+  return NULL;
+} /* nextridge3d */
+#else /* qh_NOmerge */
+void qh_matchduplicates(qhT *qh, facetT *atfacet, int atskip, int hashsize, int *hashcount) {
+}
+ridgeT *qh_nextridge3d(ridgeT *atridge, facetT *facet, vertexT **vertexp) {
+
+  return NULL;
+}
+#endif /* qh_NOmerge */
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="outcoplanar">-</a>
+
+  qh_outcoplanar()
+    move points from all facets' outsidesets to their coplanarsets
+
+  notes:
+    for post-processing under qh.NARROWhull
+
+  design:
+    for each facet
+      for each outside point for facet
+        partition point into coplanar set
+*/
+void qh_outcoplanar(qhT *qh /* facet_list */) {
+  pointT *point, **pointp;
+  facetT *facet;
+  realT dist;
+
+  trace1((qh, qh->ferr, 1033, "qh_outcoplanar: move outsideset to coplanarset for qh->NARROWhull\n"));
+  FORALLfacets {
+    FOREACHpoint_(facet->outsideset) {
+      qh->num_outside--;
+      if (qh->KEEPcoplanar || qh->KEEPnearinside) {
+        qh_distplane(qh, point, facet, &dist);
+        zinc_(Zpartition);
+        qh_partitioncoplanar(qh, point, facet, &dist);
+      }
+    }
+    qh_setfree(qh, &facet->outsideset);
+  }
+} /* outcoplanar */
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="point">-</a>
+
+  qh_point(qh, id )
+    return point for a point id, or NULL if unknown
+
+  alternative code:
+    return((pointT *)((unsigned   long)qh.first_point
+           + (unsigned long)((id)*qh.normal_size)));
+*/
+pointT *qh_point(qhT *qh, int id) {
+
+  if (id < 0)
+    return NULL;
+  if (id < qh->num_points)
+    return qh->first_point + id * qh->hull_dim;
+  id -= qh->num_points;
+  if (id < qh_setsize(qh, qh->other_points))
+    return SETelemt_(qh->other_points, id, pointT);
+  return NULL;
+} /* point */
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="point_add">-</a>
+
+  qh_point_add(qh, set, point, elem )
+    stores elem at set[point.id]
+
+  returns:
+    access function for qh_pointfacet and qh_pointvertex
+
+  notes:
+    checks point.id
+*/
+void qh_point_add(qhT *qh, setT *set, pointT *point, void *elem) {
+  int id, size;
+
+  SETreturnsize_(set, size);
+  if ((id= qh_pointid(qh, point)) < 0)
+    qh_fprintf(qh, qh->ferr, 7067, "qhull internal warning (point_add): unknown point %p id %d\n",
+      point, id);
+  else if (id >= size) {
+    qh_fprintf(qh, qh->ferr, 6160, "qhull internal errror(point_add): point p%d is out of bounds(%d)\n",
+             id, size);
+    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+  }else
+    SETelem_(set, id)= elem;
+} /* point_add */
+
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="pointfacet">-</a>
+
+  qh_pointfacet()
+    return temporary set of facet for each point
+    the set is indexed by point id
+
+  notes:
+    vertices assigned to one of the facets
+    coplanarset assigned to the facet
+    outside set assigned to the facet
+    NULL if no facet for point (inside)
+      includes qh.GOODpointp
+
+  access:
+    FOREACHfacet_i_(qh, facets) { ... }
+    SETelem_(facets, i)
+
+  design:
+    for each facet
+      add each vertex
+      add each coplanar point
+      add each outside point
+*/
+setT *qh_pointfacet(qhT *qh /*qh.facet_list*/) {
+  int numpoints= qh->num_points + qh_setsize(qh, qh->other_points);
+  setT *facets;
+  facetT *facet;
+  vertexT *vertex, **vertexp;
+  pointT *point, **pointp;
+
+  facets= qh_settemp(qh, numpoints);
+  qh_setzero(qh, facets, 0, numpoints);
+  qh->vertex_visit++;
+  FORALLfacets {
+    FOREACHvertex_(facet->vertices) {
+      if (vertex->visitid != qh->vertex_visit) {
+        vertex->visitid= qh->vertex_visit;
+        qh_point_add(qh, facets, vertex->point, facet);
+      }
+    }
+    FOREACHpoint_(facet->coplanarset)
+      qh_point_add(qh, facets, point, facet);
+    FOREACHpoint_(facet->outsideset)
+      qh_point_add(qh, facets, point, facet);
+  }
+  return facets;
+} /* pointfacet */
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="pointvertex">-</a>
+
+  qh_pointvertex(qh, )
+    return temporary set of vertices indexed by point id
+    entry is NULL if no vertex for a point
+      this will include qh.GOODpointp
+
+  access:
+    FOREACHvertex_i_(qh, vertices) { ... }
+    SETelem_(vertices, i)
+*/
+setT *qh_pointvertex(qhT *qh /*qh.facet_list*/) {
+  int numpoints= qh->num_points + qh_setsize(qh, qh->other_points);
+  setT *vertices;
+  vertexT *vertex;
+
+  vertices= qh_settemp(qh, numpoints);
+  qh_setzero(qh, vertices, 0, numpoints);
+  FORALLvertices
+    qh_point_add(qh, vertices, vertex->point, vertex);
+  return vertices;
+} /* pointvertex */
+
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="prependfacet">-</a>
+
+  qh_prependfacet(qh, facet, facetlist )
+    prepend facet to the start of a facetlist
+
+  returns:
+    increments qh.numfacets
+    updates facetlist, qh.facet_list, facet_next
+
+  notes:
+    be careful of prepending since it can lose a pointer.
+      e.g., can lose _next by deleting and then prepending before _next
+*/
+void qh_prependfacet(qhT *qh, facetT *facet, facetT **facetlist) {
+  facetT *prevfacet, *list;
+
+
+  trace4((qh, qh->ferr, 4061, "qh_prependfacet: prepend f%d before f%d\n",
+          facet->id, getid_(*facetlist)));
+  if (!*facetlist)
+    (*facetlist)= qh->facet_tail;
+  list= *facetlist;
+  prevfacet= list->previous;
+  facet->previous= prevfacet;
+  if (prevfacet)
+    prevfacet->next= facet;
+  list->previous= facet;
+  facet->next= *facetlist;
+  if (qh->facet_list == list)  /* this may change *facetlist */
+    qh->facet_list= facet;
+  if (qh->facet_next == list)
+    qh->facet_next= facet;
+  *facetlist= facet;
+  qh->num_facets++;
+} /* prependfacet */
+
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="printhashtable">-</a>
+
+  qh_printhashtable(qh, fp )
+    print hash table to fp
+
+  notes:
+    not in I/O to avoid bringing io_r.c in
+
+  design:
+    for each hash entry
+      if defined
+        if unmatched or will merge (NULL, qh_MERGEridge, qh_DUPLICATEridge)
+          print entry and neighbors
+*/
+void qh_printhashtable(qhT *qh, FILE *fp) {
+  facetT *facet, *neighbor;
+  int id, facet_i, facet_n, neighbor_i= 0, neighbor_n= 0;
+  vertexT *vertex, **vertexp;
+
+  FOREACHfacet_i_(qh, qh->hash_table) {
+    if (facet) {
+      FOREACHneighbor_i_(qh, facet) {
+        if (!neighbor || neighbor == qh_MERGEridge || neighbor == qh_DUPLICATEridge)
+          break;
+      }
+      if (neighbor_i == neighbor_n)
+        continue;
+      qh_fprintf(qh, fp, 9283, "hash %d f%d ", facet_i, facet->id);
+      FOREACHvertex_(facet->vertices)
+        qh_fprintf(qh, fp, 9284, "v%d ", vertex->id);
+      qh_fprintf(qh, fp, 9285, "\n neighbors:");
+      FOREACHneighbor_i_(qh, facet) {
+        if (neighbor == qh_MERGEridge)
+          id= -3;
+        else if (neighbor == qh_DUPLICATEridge)
+          id= -2;
+        else
+          id= getid_(neighbor);
+        qh_fprintf(qh, fp, 9286, " %d", id);
+      }
+      qh_fprintf(qh, fp, 9287, "\n");
+    }
+  }
+} /* printhashtable */
+
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="printlists">-</a>
+
+  qh_printlists(qh, fp )
+    print out facet and vertex list for debugging (without 'f/v' tags)
+*/
+void qh_printlists(qhT *qh) {
+  facetT *facet;
+  vertexT *vertex;
+  int count= 0;
+
+  qh_fprintf(qh, qh->ferr, 8108, "qh_printlists: facets:");
+  FORALLfacets {
+    if (++count % 100 == 0)
+      qh_fprintf(qh, qh->ferr, 8109, "\n     ");
+    qh_fprintf(qh, qh->ferr, 8110, " %d", facet->id);
+  }
+  qh_fprintf(qh, qh->ferr, 8111, "\n  new facets %d visible facets %d next facet for qh_addpoint %d\n  vertices(new %d):",
+     getid_(qh->newfacet_list), getid_(qh->visible_list), getid_(qh->facet_next),
+     getid_(qh->newvertex_list));
+  count = 0;
+  FORALLvertices {
+    if (++count % 100 == 0)
+      qh_fprintf(qh, qh->ferr, 8112, "\n     ");
+    qh_fprintf(qh, qh->ferr, 8113, " %d", vertex->id);
+  }
+  qh_fprintf(qh, qh->ferr, 8114, "\n");
+} /* printlists */
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="resetlists">-</a>
+
+  qh_resetlists(qh, stats, qh_RESETvisible )
+    reset newvertex_list, newfacet_list, visible_list
+    if stats,
+      maintains statistics
+
+  returns:
+    visible_list is empty if qh_deletevisible was called
+*/
+void qh_resetlists(qhT *qh, boolT stats, boolT resetVisible /*qh.newvertex_list newfacet_list visible_list*/) {
+  vertexT *vertex;
+  facetT *newfacet, *visible;
+  int totnew=0, totver=0;
+
+  if (stats) {
+    FORALLvertex_(qh->newvertex_list)
+      totver++;
+    FORALLnew_facets
+      totnew++;
+    zadd_(Zvisvertextot, totver);
+    zmax_(Zvisvertexmax, totver);
+    zadd_(Znewfacettot, totnew);
+    zmax_(Znewfacetmax, totnew);
+  }
+  FORALLvertex_(qh->newvertex_list)
+    vertex->newlist= False;
+  qh->newvertex_list= NULL;
+  FORALLnew_facets
+    newfacet->newfacet= False;
+  qh->newfacet_list= NULL;
+  if (resetVisible) {
+    FORALLvisible_facets {
+      visible->f.replace= NULL;
+      visible->visible= False;
+    }
+    qh->num_visible= 0;
+  }
+  qh->visible_list= NULL; /* may still have visible facets via qh_triangulate */
+  qh->NEWfacets= False;
+} /* resetlists */
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="setvoronoi_all">-</a>
+
+  qh_setvoronoi_all(qh)
+    compute Voronoi centers for all facets
+    includes upperDelaunay facets if qh.UPPERdelaunay ('Qu')
+
+  returns:
+    facet->center is the Voronoi center
+
+  notes:
+    this is unused/untested code
+      please email bradb@shore.net if this works ok for you
+
+  use:
+    FORALLvertices {...} to locate the vertex for a point.
+    FOREACHneighbor_(vertex) {...} to visit the Voronoi centers for a Voronoi cell.
+*/
+void qh_setvoronoi_all(qhT *qh) {
+  facetT *facet;
+
+  qh_clearcenters(qh, qh_ASvoronoi);
+  qh_vertexneighbors(qh);
+
+  FORALLfacets {
+    if (!facet->normal || !facet->upperdelaunay || qh->UPPERdelaunay) {
+      if (!facet->center)
+        facet->center= qh_facetcenter(qh, facet->vertices);
+    }
+  }
+} /* setvoronoi_all */
+
+#ifndef qh_NOmerge
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="triangulate">-</a>
+
+  qh_triangulate()
+    triangulate non-simplicial facets on qh.facet_list,
+    if qh->VORONOI, sets Voronoi centers of non-simplicial facets
+    nop if hasTriangulation
+
+  returns:
+    all facets simplicial
+    each tricoplanar facet has ->f.triowner == owner of ->center,normal,etc.
+
+  notes:
+    call after qh_check_output since may switch to Voronoi centers
+    Output may overwrite ->f.triowner with ->f.area
+*/
+void qh_triangulate(qhT *qh /*qh.facet_list*/) {
+  facetT *facet, *nextfacet, *owner;
+  int onlygood= qh->ONLYgood;
+  facetT *neighbor, *visible= NULL, *facet1, *facet2, *new_facet_list= NULL;
+  facetT *orig_neighbor= NULL, *otherfacet;
+  vertexT *new_vertex_list= NULL;
+  mergeT *merge;
+  mergeType mergetype;
+  int neighbor_i, neighbor_n;
+
+  if (qh->hasTriangulation)
+      return;
+  trace1((qh, qh->ferr, 1034, "qh_triangulate: triangulate non-simplicial facets\n"));
+  if (qh->hull_dim == 2)
+    return;
+  if (qh->VORONOI) {  /* otherwise lose Voronoi centers [could rebuild vertex set from tricoplanar] */
+    qh_clearcenters(qh, qh_ASvoronoi);
+    qh_vertexneighbors(qh);
+  }
+  qh->ONLYgood= False; /* for makenew_nonsimplicial */
+  qh->visit_id++;
+  qh->NEWfacets= True;
+  qh->degen_mergeset= qh_settemp(qh, qh->TEMPsize);
+  qh->newvertex_list= qh->vertex_tail;
+  for (facet= qh->facet_list; facet && facet->next; facet= nextfacet) { /* non-simplicial facets moved to end */
+    nextfacet= facet->next;
+    if (facet->visible || facet->simplicial)
+      continue;
+    /* triangulate all non-simplicial facets, otherwise merging does not work, e.g., RBOX c P-0.1 P+0.1 P+0.1 D3 | QHULL d Qt Tv */
+    if (!new_facet_list)
+      new_facet_list= facet;  /* will be moved to end */
+    qh_triangulate_facet(qh, facet, &new_vertex_list);
+  }
+  trace2((qh, qh->ferr, 2047, "qh_triangulate: delete null facets from f%d -- apex same as second vertex\n", getid_(new_facet_list)));
+  for (facet= new_facet_list; facet && facet->next; facet= nextfacet) { /* null facets moved to end */
+    nextfacet= facet->next;
+    if (facet->visible)
+      continue;
+    if (facet->ridges) {
+      if (qh_setsize(qh, facet->ridges) > 0) {
+        qh_fprintf(qh, qh->ferr, 6161, "qhull error (qh_triangulate): ridges still defined for f%d\n", facet->id);
+        qh_errexit(qh, qh_ERRqhull, facet, NULL);
+      }
+      qh_setfree(qh, &facet->ridges);
+    }
+    if (SETfirst_(facet->vertices) == SETsecond_(facet->vertices)) {
+      zinc_(Ztrinull);
+      qh_triangulate_null(qh, facet);
+    }
+  }
+  trace2((qh, qh->ferr, 2048, "qh_triangulate: delete %d or more mirror facets -- same vertices and neighbors\n", qh_setsize(qh, qh->degen_mergeset)));
+  qh->visible_list= qh->facet_tail;
+  while ((merge= (mergeT*)qh_setdellast(qh->degen_mergeset))) {
+    facet1= merge->facet1;
+    facet2= merge->facet2;
+    mergetype= merge->type;
+    qh_memfree(qh, merge, (int)sizeof(mergeT));
+    if (mergetype == MRGmirror) {
+      zinc_(Ztrimirror);
+      qh_triangulate_mirror(qh, facet1, facet2);
+    }
+  }
+  qh_settempfree(qh, &qh->degen_mergeset);
+  trace2((qh, qh->ferr, 2049, "qh_triangulate: update neighbor lists for vertices from v%d\n", getid_(new_vertex_list)));
+  qh->newvertex_list= new_vertex_list;  /* all vertices of new facets */
+  qh->visible_list= NULL;
+  qh_updatevertices(qh /*qh.newvertex_list, empty newfacet_list and visible_list*/);
+  qh_resetlists(qh, False, !qh_RESETvisible /*qh.newvertex_list, empty newfacet_list and visible_list*/);
+
+  trace2((qh, qh->ferr, 2050, "qh_triangulate: identify degenerate tricoplanar facets from f%d\n", getid_(new_facet_list)));
+  trace2((qh, qh->ferr, 2051, "qh_triangulate: and replace facet->f.triowner with tricoplanar facets that own center, normal, etc.\n"));
+  FORALLfacet_(new_facet_list) {
+    if (facet->tricoplanar && !facet->visible) {
+      FOREACHneighbor_i_(qh, facet) {
+        if (neighbor_i == 0) {  /* first iteration */
+          if (neighbor->tricoplanar)
+            orig_neighbor= neighbor->f.triowner;
+          else
+            orig_neighbor= neighbor;
+        }else {
+          if (neighbor->tricoplanar)
+            otherfacet= neighbor->f.triowner;
+          else
+            otherfacet= neighbor;
+          if (orig_neighbor == otherfacet) {
+            zinc_(Ztridegen);
+            facet->degenerate= True;
+            break;
+          }
+        }
+      }
+    }
+  }
+
+  trace2((qh, qh->ferr, 2052, "qh_triangulate: delete visible facets -- non-simplicial, null, and mirrored facets\n"));
+  owner= NULL;
+  visible= NULL;
+  for (facet= new_facet_list; facet && facet->next; facet= nextfacet) { /* may delete facet */
+    nextfacet= facet->next;
+    if (facet->visible) {
+      if (facet->tricoplanar) { /* a null or mirrored facet */
+        qh_delfacet(qh, facet);
+        qh->num_visible--;
+      }else {  /* a non-simplicial facet followed by its tricoplanars */
+        if (visible && !owner) {
+          /*  RBOX 200 s D5 t1001471447 | QHULL Qt C-0.01 Qx Qc Tv Qt -- f4483 had 6 vertices/neighbors and 8 ridges */
+          trace2((qh, qh->ferr, 2053, "qh_triangulate: all tricoplanar facets degenerate for non-simplicial facet f%d\n",
+                       visible->id));
+          qh_delfacet(qh, visible);
+          qh->num_visible--;
+        }
+        visible= facet;
+        owner= NULL;
+      }
+    }else if (facet->tricoplanar) {
+      if (facet->f.triowner != visible || visible==NULL) {
+        qh_fprintf(qh, qh->ferr, 6162, "qhull error (qh_triangulate): tricoplanar facet f%d not owned by its visible, non-simplicial facet f%d\n", facet->id, getid_(visible));
+        qh_errexit2(qh, qh_ERRqhull, facet, visible);
+      }
+      if (owner)
+        facet->f.triowner= owner;
+      else if (!facet->degenerate) {
+        owner= facet;
+        nextfacet= visible->next; /* rescan tricoplanar facets with owner, visible!=0 by QH6162 */
+        facet->keepcentrum= True;  /* one facet owns ->normal, etc. */
+        facet->coplanarset= visible->coplanarset;
+        facet->outsideset= visible->outsideset;
+        visible->coplanarset= NULL;
+        visible->outsideset= NULL;
+        if (!qh->TRInormals) { /* center and normal copied to tricoplanar facets */
+          visible->center= NULL;
+          visible->normal= NULL;
+        }
+        qh_delfacet(qh, visible);
+        qh->num_visible--;
+      }
+    }
+  }
+  if (visible && !owner) {
+    trace2((qh, qh->ferr, 2054, "qh_triangulate: all tricoplanar facets degenerate for last non-simplicial facet f%d\n",
+                 visible->id));
+    qh_delfacet(qh, visible);
+    qh->num_visible--;
+  }
+  qh->NEWfacets= False;
+  qh->ONLYgood= onlygood; /* restore value */
+  if (qh->CHECKfrequently)
+    qh_checkpolygon(qh, qh->facet_list);
+  qh->hasTriangulation= True;
+} /* triangulate */
+
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="triangulate_facet">-</a>
+
+  qh_triangulate_facet(qh, facetA, &firstVertex )
+    triangulate a non-simplicial facet
+      if qh.CENTERtype=qh_ASvoronoi, sets its Voronoi center
+  returns:
+    qh.newfacet_list == simplicial facets
+      facet->tricoplanar set and ->keepcentrum false
+      facet->degenerate set if duplicated apex
+      facet->f.trivisible set to facetA
+      facet->center copied from facetA (created if qh_ASvoronoi)
+        qh_eachvoronoi, qh_detvridge, qh_detvridge3 assume centers copied
+      facet->normal,offset,maxoutside copied from facetA
+
+  notes:
+      only called by qh_triangulate
+      qh_makenew_nonsimplicial uses neighbor->seen for the same
+      if qh.TRInormals, newfacet->normal will need qh_free
+        if qh.TRInormals and qh_AScentrum, newfacet->center will need qh_free
+        keepcentrum is also set on Zwidefacet in qh_mergefacet
+        freed by qh_clearcenters
+
+  see also:
+      qh_addpoint() -- add a point
+      qh_makenewfacets() -- construct a cone of facets for a new vertex
+
+  design:
+      if qh_ASvoronoi,
+         compute Voronoi center (facet->center)
+      select first vertex (highest ID to preserve ID ordering of ->vertices)
+      triangulate from vertex to ridges
+      copy facet->center, normal, offset
+      update vertex neighbors
+*/
+void qh_triangulate_facet(qhT *qh, facetT *facetA, vertexT **first_vertex) {
+  facetT *newfacet;
+  facetT *neighbor, **neighborp;
+  vertexT *apex;
+  int numnew=0;
+
+  trace3((qh, qh->ferr, 3020, "qh_triangulate_facet: triangulate facet f%d\n", facetA->id));
+
+  if (qh->IStracing >= 4)
+    qh_printfacet(qh, qh->ferr, facetA);
+  FOREACHneighbor_(facetA) {
+    neighbor->seen= False;
+    neighbor->coplanar= False;
+  }
+  if (qh->CENTERtype == qh_ASvoronoi && !facetA->center  /* matches upperdelaunay in qh_setfacetplane() */
+        && fabs_(facetA->normal[qh->hull_dim -1]) >= qh->ANGLEround * qh_ZEROdelaunay) {
+    facetA->center= qh_facetcenter(qh, facetA->vertices);
+  }
+  qh_willdelete(qh, facetA, NULL);
+  qh->newfacet_list= qh->facet_tail;
+  facetA->visitid= qh->visit_id;
+  apex= SETfirstt_(facetA->vertices, vertexT);
+  qh_makenew_nonsimplicial(qh, facetA, apex, &numnew);
+  SETfirst_(facetA->neighbors)= NULL;
+  FORALLnew_facets {
+    newfacet->tricoplanar= True;
+    newfacet->f.trivisible= facetA;
+    newfacet->degenerate= False;
+    newfacet->upperdelaunay= facetA->upperdelaunay;
+    newfacet->good= facetA->good;
+    if (qh->TRInormals) { /* 'Q11' triangulate duplicates ->normal and ->center */
+      newfacet->keepcentrum= True;
+      if(facetA->normal){
+        newfacet->normal= qh_memalloc(qh, qh->normal_size);
+        memcpy((char *)newfacet->normal, facetA->normal, qh->normal_size);
+      }
+      if (qh->CENTERtype == qh_AScentrum)
+        newfacet->center= qh_getcentrum(qh, newfacet);
+      else if (qh->CENTERtype == qh_ASvoronoi && facetA->center){
+        newfacet->center= qh_memalloc(qh, qh->center_size);
+        memcpy((char *)newfacet->center, facetA->center, qh->center_size);
+      }
+    }else {
+      newfacet->keepcentrum= False;
+      /* one facet will have keepcentrum=True at end of qh_triangulate */
+      newfacet->normal= facetA->normal;
+      newfacet->center= facetA->center;
+    }
+    newfacet->offset= facetA->offset;
+#if qh_MAXoutside
+    newfacet->maxoutside= facetA->maxoutside;
+#endif
+  }
+  qh_matchnewfacets(qh /*qh.newfacet_list*/);
+  zinc_(Ztricoplanar);
+  zadd_(Ztricoplanartot, numnew);
+  zmax_(Ztricoplanarmax, numnew);
+  qh->visible_list= NULL;
+  if (!(*first_vertex))
+    (*first_vertex)= qh->newvertex_list;
+  qh->newvertex_list= NULL;
+  qh_updatevertices(qh /*qh.newfacet_list, qh.empty visible_list and qh.newvertex_list*/);
+  qh_resetlists(qh, False, !qh_RESETvisible /*qh.newfacet_list, qh.empty visible_list and qh.newvertex_list*/);
+} /* triangulate_facet */
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="triangulate_link">-</a>
+
+  qh_triangulate_link(qh, oldfacetA, facetA, oldfacetB, facetB)
+    relink facetA to facetB via oldfacets
+  returns:
+    adds mirror facets to qh->degen_mergeset (4-d and up only)
+  design:
+    if they are already neighbors, the opposing neighbors become MRGmirror facets
+*/
+void qh_triangulate_link(qhT *qh, facetT *oldfacetA, facetT *facetA, facetT *oldfacetB, facetT *facetB) {
+  int errmirror= False;
+
+  trace3((qh, qh->ferr, 3021, "qh_triangulate_link: relink old facets f%d and f%d between neighbors f%d and f%d\n",
+         oldfacetA->id, oldfacetB->id, facetA->id, facetB->id));
+  if (qh_setin(facetA->neighbors, facetB)) {
+    if (!qh_setin(facetB->neighbors, facetA))
+      errmirror= True;
+    else
+      qh_appendmergeset(qh, facetA, facetB, MRGmirror, NULL);
+  }else if (qh_setin(facetB->neighbors, facetA))
+    errmirror= True;
+  if (errmirror) {
+    qh_fprintf(qh, qh->ferr, 6163, "qhull error (qh_triangulate_link): mirror facets f%d and f%d do not match for old facets f%d and f%d\n",
+       facetA->id, facetB->id, oldfacetA->id, oldfacetB->id);
+    qh_errexit2(qh, qh_ERRqhull, facetA, facetB);
+  }
+  qh_setreplace(qh, facetB->neighbors, oldfacetB, facetA);
+  qh_setreplace(qh, facetA->neighbors, oldfacetA, facetB);
+} /* triangulate_link */
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="triangulate_mirror">-</a>
+
+  qh_triangulate_mirror(qh, facetA, facetB)
+    delete mirrored facets from qh_triangulate_null() and qh_triangulate_mirror
+      a mirrored facet shares the same vertices of a logical ridge
+  design:
+    since a null facet duplicates the first two vertices, the opposing neighbors absorb the null facet
+    if they are already neighbors, the opposing neighbors become MRGmirror facets
+*/
+void qh_triangulate_mirror(qhT *qh, facetT *facetA, facetT *facetB) {
+  facetT *neighbor, *neighborB;
+  int neighbor_i, neighbor_n;
+
+  trace3((qh, qh->ferr, 3022, "qh_triangulate_mirror: delete mirrored facets f%d and f%d\n",
+         facetA->id, facetB->id));
+  FOREACHneighbor_i_(qh, facetA) {
+    neighborB= SETelemt_(facetB->neighbors, neighbor_i, facetT);
+    if (neighbor == neighborB)
+      continue; /* occurs twice */
+    qh_triangulate_link(qh, facetA, neighbor, facetB, neighborB);
+  }
+  qh_willdelete(qh, facetA, NULL);
+  qh_willdelete(qh, facetB, NULL);
+} /* triangulate_mirror */
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="triangulate_null">-</a>
+
+  qh_triangulate_null(qh, facetA)
+    remove null facetA from qh_triangulate_facet()
+      a null facet has vertex #1 (apex) == vertex #2
+  returns:
+    adds facetA to ->visible for deletion after qh_updatevertices
+    qh->degen_mergeset contains mirror facets (4-d and up only)
+  design:
+    since a null facet duplicates the first two vertices, the opposing neighbors absorb the null facet
+    if they are already neighbors, the opposing neighbors become MRGmirror facets
+*/
+void qh_triangulate_null(qhT *qh, facetT *facetA) {
+  facetT *neighbor, *otherfacet;
+
+  trace3((qh, qh->ferr, 3023, "qh_triangulate_null: delete null facet f%d\n", facetA->id));
+  neighbor= SETfirstt_(facetA->neighbors, facetT);
+  otherfacet= SETsecondt_(facetA->neighbors, facetT);
+  qh_triangulate_link(qh, facetA, neighbor, facetA, otherfacet);
+  qh_willdelete(qh, facetA, NULL);
+} /* triangulate_null */
+
+#else /* qh_NOmerge */
+void qh_triangulate(qhT *qh) {
+}
+#endif /* qh_NOmerge */
+
+   /*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="vertexintersect">-</a>
+
+  qh_vertexintersect(qh, vertexsetA, vertexsetB )
+    intersects two vertex sets (inverse id ordered)
+    vertexsetA is a temporary set at the top of qh->qhmem.tempstack
+
+  returns:
+    replaces vertexsetA with the intersection
+
+  notes:
+    could overwrite vertexsetA if currently too slow
+*/
+void qh_vertexintersect(qhT *qh, setT **vertexsetA,setT *vertexsetB) {
+  setT *intersection;
+
+  intersection= qh_vertexintersect_new(qh, *vertexsetA, vertexsetB);
+  qh_settempfree(qh, vertexsetA);
+  *vertexsetA= intersection;
+  qh_settemppush(qh, intersection);
+} /* vertexintersect */
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="vertexintersect_new">-</a>
+
+  qh_vertexintersect_new(qh, )
+    intersects two vertex sets (inverse id ordered)
+
+  returns:
+    a new set
+*/
+setT *qh_vertexintersect_new(qhT *qh, setT *vertexsetA,setT *vertexsetB) {
+  setT *intersection= qh_setnew(qh, qh->hull_dim - 1);
+  vertexT **vertexA= SETaddr_(vertexsetA, vertexT);
+  vertexT **vertexB= SETaddr_(vertexsetB, vertexT);
+
+  while (*vertexA && *vertexB) {
+    if (*vertexA  == *vertexB) {
+      qh_setappend(qh, &intersection, *vertexA);
+      vertexA++; vertexB++;
+    }else {
+      if ((*vertexA)->id > (*vertexB)->id)
+        vertexA++;
+      else
+        vertexB++;
+    }
+  }
+  return intersection;
+} /* vertexintersect_new */
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="vertexneighbors">-</a>
+
+  qh_vertexneighbors(qh)
+    for each vertex in qh.facet_list,
+      determine its neighboring facets
+
+  returns:
+    sets qh.VERTEXneighbors
+      nop if qh.VERTEXneighbors already set
+      qh_addpoint() will maintain them
+
+  notes:
+    assumes all vertex->neighbors are NULL
+
+  design:
+    for each facet
+      for each vertex
+        append facet to vertex->neighbors
+*/
+void qh_vertexneighbors(qhT *qh /*qh.facet_list*/) {
+  facetT *facet;
+  vertexT *vertex, **vertexp;
+
+  if (qh->VERTEXneighbors)
+    return;
+  trace1((qh, qh->ferr, 1035, "qh_vertexneighbors: determining neighboring facets for each vertex\n"));
+  qh->vertex_visit++;
+  FORALLfacets {
+    if (facet->visible)
+      continue;
+    FOREACHvertex_(facet->vertices) {
+      if (vertex->visitid != qh->vertex_visit) {
+        vertex->visitid= qh->vertex_visit;
+        vertex->neighbors= qh_setnew(qh, qh->hull_dim);
+      }
+      qh_setappend(qh, &vertex->neighbors, facet);
+    }
+  }
+  qh->VERTEXneighbors= True;
+} /* vertexneighbors */
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="vertexsubset">-</a>
+
+  qh_vertexsubset( vertexsetA, vertexsetB )
+    returns True if vertexsetA is a subset of vertexsetB
+    assumes vertexsets are sorted
+
+  note:
+    empty set is a subset of any other set
+*/
+boolT qh_vertexsubset(setT *vertexsetA, setT *vertexsetB) {
+  vertexT **vertexA= (vertexT **) SETaddr_(vertexsetA, vertexT);
+  vertexT **vertexB= (vertexT **) SETaddr_(vertexsetB, vertexT);
+
+  while (True) {
+    if (!*vertexA)
+      return True;
+    if (!*vertexB)
+      return False;
+    if ((*vertexA)->id > (*vertexB)->id)
+      return False;
+    if (*vertexA  == *vertexB)
+      vertexA++;
+    vertexB++;
+  }
+  return False; /* avoid warnings */
+} /* vertexsubset */
diff --git a/xs/src/qhull/src/libqhull_r/poly_r.c b/xs/src/qhull/src/libqhull_r/poly_r.c
new file mode 100644
index 0000000000..e5b4797437
--- /dev/null
+++ b/xs/src/qhull/src/libqhull_r/poly_r.c
@@ -0,0 +1,1205 @@
+/*<html><pre>  -<a                             href="qh-poly_r.htm"
+  >-------------------------------</a><a name="TOP">-</a>
+
+   poly_r.c
+   implements polygons and simplices
+
+   see qh-poly_r.htm, poly_r.h and libqhull_r.h
+
+   infrequent code is in poly2_r.c
+   (all but top 50 and their callers 12/3/95)
+
+   Copyright (c) 1993-2015 The Geometry Center.
+   $Id: //main/2015/qhull/src/libqhull_r/poly_r.c#3 $$Change: 2064 $
+   $DateTime: 2016/01/18 12:36:08 $$Author: bbarber $
+*/
+
+#include "qhull_ra.h"
+
+/*======== functions in alphabetical order ==========*/
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="appendfacet">-</a>
+
+  qh_appendfacet(qh, facet )
+    appends facet to end of qh.facet_list,
+
+  returns:
+    updates qh.newfacet_list, facet_next, facet_list
+    increments qh.numfacets
+
+  notes:
+    assumes qh.facet_list/facet_tail is defined (createsimplex)
+
+  see:
+    qh_removefacet()
+
+*/
+void qh_appendfacet(qhT *qh, facetT *facet) {
+  facetT *tail= qh->facet_tail;
+
+  if (tail == qh->newfacet_list)
+    qh->newfacet_list= facet;
+  if (tail == qh->facet_next)
+    qh->facet_next= facet;
+  facet->previous= tail->previous;
+  facet->next= tail;
+  if (tail->previous)
+    tail->previous->next= facet;
+  else
+    qh->facet_list= facet;
+  tail->previous= facet;
+  qh->num_facets++;
+  trace4((qh, qh->ferr, 4044, "qh_appendfacet: append f%d to facet_list\n", facet->id));
+} /* appendfacet */
+
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="appendvertex">-</a>
+
+  qh_appendvertex(qh, vertex )
+    appends vertex to end of qh.vertex_list,
+
+  returns:
+    sets vertex->newlist
+    updates qh.vertex_list, newvertex_list
+    increments qh.num_vertices
+
+  notes:
+    assumes qh.vertex_list/vertex_tail is defined (createsimplex)
+
+*/
+void qh_appendvertex(qhT *qh, vertexT *vertex) {
+  vertexT *tail= qh->vertex_tail;
+
+  if (tail == qh->newvertex_list)
+    qh->newvertex_list= vertex;
+  vertex->newlist= True;
+  vertex->previous= tail->previous;
+  vertex->next= tail;
+  if (tail->previous)
+    tail->previous->next= vertex;
+  else
+    qh->vertex_list= vertex;
+  tail->previous= vertex;
+  qh->num_vertices++;
+  trace4((qh, qh->ferr, 4045, "qh_appendvertex: append v%d to vertex_list\n", vertex->id));
+} /* appendvertex */
+
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="attachnewfacets">-</a>
+
+  qh_attachnewfacets(qh, )
+    attach horizon facets to new facets in qh.newfacet_list
+    newfacets have neighbor and ridge links to horizon but not vice versa
+    only needed for qh.ONLYgood
+
+  returns:
+    set qh.NEWfacets
+    horizon facets linked to new facets
+      ridges changed from visible facets to new facets
+      simplicial ridges deleted
+    qh.visible_list, no ridges valid
+    facet->f.replace is a newfacet (if any)
+
+  design:
+    delete interior ridges and neighbor sets by
+      for each visible, non-simplicial facet
+        for each ridge
+          if last visit or if neighbor is simplicial
+            if horizon neighbor
+              delete ridge for horizon's ridge set
+            delete ridge
+        erase neighbor set
+    attach horizon facets and new facets by
+      for all new facets
+        if corresponding horizon facet is simplicial
+          locate corresponding visible facet {may be more than one}
+          link visible facet to new facet
+          replace visible facet with new facet in horizon
+        else it's non-simplicial
+          for all visible neighbors of the horizon facet
+            link visible neighbor to new facet
+            delete visible neighbor from horizon facet
+          append new facet to horizon's neighbors
+          the first ridge of the new facet is the horizon ridge
+          link the new facet into the horizon ridge
+*/
+void qh_attachnewfacets(qhT *qh /* qh.visible_list, newfacet_list */) {
+  facetT *newfacet= NULL, *neighbor, **neighborp, *horizon, *visible;
+  ridgeT *ridge, **ridgep;
+
+  qh->NEWfacets= True;
+  trace3((qh, qh->ferr, 3012, "qh_attachnewfacets: delete interior ridges\n"));
+  qh->visit_id++;
+  FORALLvisible_facets {
+    visible->visitid= qh->visit_id;
+    if (visible->ridges) {
+      FOREACHridge_(visible->ridges) {
+        neighbor= otherfacet_(ridge, visible);
+        if (neighbor->visitid == qh->visit_id
+            || (!neighbor->visible && neighbor->simplicial)) {
+          if (!neighbor->visible)  /* delete ridge for simplicial horizon */
+            qh_setdel(neighbor->ridges, ridge);
+          qh_setfree(qh, &(ridge->vertices)); /* delete on 2nd visit */
+          qh_memfree(qh, ridge, (int)sizeof(ridgeT));
+        }
+      }
+      SETfirst_(visible->ridges)= NULL;
+    }
+    SETfirst_(visible->neighbors)= NULL;
+  }
+  trace1((qh, qh->ferr, 1017, "qh_attachnewfacets: attach horizon facets to new facets\n"));
+  FORALLnew_facets {
+    horizon= SETfirstt_(newfacet->neighbors, facetT);
+    if (horizon->simplicial) {
+      visible= NULL;
+      FOREACHneighbor_(horizon) {   /* may have more than one horizon ridge */
+        if (neighbor->visible) {
+          if (visible) {
+            if (qh_setequal_skip(newfacet->vertices, 0, horizon->vertices,
+                                  SETindex_(horizon->neighbors, neighbor))) {
+              visible= neighbor;
+              break;
+            }
+          }else
+            visible= neighbor;
+        }
+      }
+      if (visible) {
+        visible->f.replace= newfacet;
+        qh_setreplace(qh, horizon->neighbors, visible, newfacet);
+      }else {
+        qh_fprintf(qh, qh->ferr, 6102, "qhull internal error (qh_attachnewfacets): couldn't find visible facet for horizon f%d of newfacet f%d\n",
+                 horizon->id, newfacet->id);
+        qh_errexit2(qh, qh_ERRqhull, horizon, newfacet);
+      }
+    }else { /* non-simplicial, with a ridge for newfacet */
+      FOREACHneighbor_(horizon) {    /* may hold for many new facets */
+        if (neighbor->visible) {
+          neighbor->f.replace= newfacet;
+          qh_setdelnth(qh, horizon->neighbors,
+                        SETindex_(horizon->neighbors, neighbor));
+          neighborp--; /* repeat */
+        }
+      }
+      qh_setappend(qh, &horizon->neighbors, newfacet);
+      ridge= SETfirstt_(newfacet->ridges, ridgeT);
+      if (ridge->top == horizon)
+        ridge->bottom= newfacet;
+      else
+        ridge->top= newfacet;
+      }
+  } /* newfacets */
+  if (qh->PRINTstatistics) {
+    FORALLvisible_facets {
+      if (!visible->f.replace)
+        zinc_(Zinsidevisible);
+    }
+  }
+} /* attachnewfacets */
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="checkflipped">-</a>
+
+  qh_checkflipped(qh, facet, dist, allerror )
+    checks facet orientation to interior point
+
+    if allerror set,
+      tests against qh.DISTround
+    else
+      tests against 0 since tested against DISTround before
+
+  returns:
+    False if it flipped orientation (sets facet->flipped)
+    distance if non-NULL
+*/
+boolT qh_checkflipped(qhT *qh, facetT *facet, realT *distp, boolT allerror) {
+  realT dist;
+
+  if (facet->flipped && !distp)
+    return False;
+  zzinc_(Zdistcheck);
+  qh_distplane(qh, qh->interior_point, facet, &dist);
+  if (distp)
+    *distp= dist;
+  if ((allerror && dist > -qh->DISTround)|| (!allerror && dist >= 0.0)) {
+    facet->flipped= True;
+    zzinc_(Zflippedfacets);
+    trace0((qh, qh->ferr, 19, "qh_checkflipped: facet f%d is flipped, distance= %6.12g during p%d\n",
+              facet->id, dist, qh->furthest_id));
+    qh_precision(qh, "flipped facet");
+    return False;
+  }
+  return True;
+} /* checkflipped */
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="delfacet">-</a>
+
+  qh_delfacet(qh, facet )
+    removes facet from facet_list and frees up its memory
+
+  notes:
+    assumes vertices and ridges already freed
+*/
+void qh_delfacet(qhT *qh, facetT *facet) {
+  void **freelistp; /* used if !qh_NOmem by qh_memfree_() */
+
+  trace4((qh, qh->ferr, 4046, "qh_delfacet: delete f%d\n", facet->id));
+  if (facet == qh->tracefacet)
+    qh->tracefacet= NULL;
+  if (facet == qh->GOODclosest)
+    qh->GOODclosest= NULL;
+  qh_removefacet(qh, facet);
+  if (!facet->tricoplanar || facet->keepcentrum) {
+    qh_memfree_(qh, facet->normal, qh->normal_size, freelistp);
+    if (qh->CENTERtype == qh_ASvoronoi) {   /* braces for macro calls */
+      qh_memfree_(qh, facet->center, qh->center_size, freelistp);
+    }else /* AScentrum */ {
+      qh_memfree_(qh, facet->center, qh->normal_size, freelistp);
+    }
+  }
+  qh_setfree(qh, &(facet->neighbors));
+  if (facet->ridges)
+    qh_setfree(qh, &(facet->ridges));
+  qh_setfree(qh, &(facet->vertices));
+  if (facet->outsideset)
+    qh_setfree(qh, &(facet->outsideset));
+  if (facet->coplanarset)
+    qh_setfree(qh, &(facet->coplanarset));
+  qh_memfree_(qh, facet, (int)sizeof(facetT), freelistp);
+} /* delfacet */
+
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="deletevisible">-</a>
+
+  qh_deletevisible()
+    delete visible facets and vertices
+
+  returns:
+    deletes each facet and removes from facetlist
+    at exit, qh.visible_list empty (== qh.newfacet_list)
+
+  notes:
+    ridges already deleted
+    horizon facets do not reference facets on qh.visible_list
+    new facets in qh.newfacet_list
+    uses   qh.visit_id;
+*/
+void qh_deletevisible(qhT *qh /*qh.visible_list*/) {
+  facetT *visible, *nextfacet;
+  vertexT *vertex, **vertexp;
+  int numvisible= 0, numdel= qh_setsize(qh, qh->del_vertices);
+
+  trace1((qh, qh->ferr, 1018, "qh_deletevisible: delete %d visible facets and %d vertices\n",
+         qh->num_visible, numdel));
+  for (visible= qh->visible_list; visible && visible->visible;
+                visible= nextfacet) { /* deleting current */
+    nextfacet= visible->next;
+    numvisible++;
+    qh_delfacet(qh, visible);
+  }
+  if (numvisible != qh->num_visible) {
+    qh_fprintf(qh, qh->ferr, 6103, "qhull internal error (qh_deletevisible): qh->num_visible %d is not number of visible facets %d\n",
+             qh->num_visible, numvisible);
+    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+  }
+  qh->num_visible= 0;
+  zadd_(Zvisfacettot, numvisible);
+  zmax_(Zvisfacetmax, numvisible);
+  zzadd_(Zdelvertextot, numdel);
+  zmax_(Zdelvertexmax, numdel);
+  FOREACHvertex_(qh->del_vertices)
+    qh_delvertex(qh, vertex);
+  qh_settruncate(qh, qh->del_vertices, 0);
+} /* deletevisible */
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="facetintersect">-</a>
+
+  qh_facetintersect(qh, facetA, facetB, skipa, skipB, prepend )
+    return vertices for intersection of two simplicial facets
+    may include 1 prepended entry (if more, need to settemppush)
+
+  returns:
+    returns set of qh.hull_dim-1 + prepend vertices
+    returns skipped index for each test and checks for exactly one
+
+  notes:
+    does not need settemp since set in quick memory
+
+  see also:
+    qh_vertexintersect and qh_vertexintersect_new
+    use qh_setnew_delnthsorted to get nth ridge (no skip information)
+
+  design:
+    locate skipped vertex by scanning facet A's neighbors
+    locate skipped vertex by scanning facet B's neighbors
+    intersect the vertex sets
+*/
+setT *qh_facetintersect(qhT *qh, facetT *facetA, facetT *facetB,
+                         int *skipA,int *skipB, int prepend) {
+  setT *intersect;
+  int dim= qh->hull_dim, i, j;
+  facetT **neighborsA, **neighborsB;
+
+  neighborsA= SETaddr_(facetA->neighbors, facetT);
+  neighborsB= SETaddr_(facetB->neighbors, facetT);
+  i= j= 0;
+  if (facetB == *neighborsA++)
+    *skipA= 0;
+  else if (facetB == *neighborsA++)
+    *skipA= 1;
+  else if (facetB == *neighborsA++)
+    *skipA= 2;
+  else {
+    for (i=3; i < dim; i++) {
+      if (facetB == *neighborsA++) {
+        *skipA= i;
+        break;
+      }
+    }
+  }
+  if (facetA == *neighborsB++)
+    *skipB= 0;
+  else if (facetA == *neighborsB++)
+    *skipB= 1;
+  else if (facetA == *neighborsB++)
+    *skipB= 2;
+  else {
+    for (j=3; j < dim; j++) {
+      if (facetA == *neighborsB++) {
+        *skipB= j;
+        break;
+      }
+    }
+  }
+  if (i >= dim || j >= dim) {
+    qh_fprintf(qh, qh->ferr, 6104, "qhull internal error (qh_facetintersect): f%d or f%d not in others neighbors\n",
+            facetA->id, facetB->id);
+    qh_errexit2(qh, qh_ERRqhull, facetA, facetB);
+  }
+  intersect= qh_setnew_delnthsorted(qh, facetA->vertices, qh->hull_dim, *skipA, prepend);
+  trace4((qh, qh->ferr, 4047, "qh_facetintersect: f%d skip %d matches f%d skip %d\n",
+          facetA->id, *skipA, facetB->id, *skipB));
+  return(intersect);
+} /* facetintersect */
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="gethash">-</a>
+
+  qh_gethash(qh, hashsize, set, size, firstindex, skipelem )
+    return hashvalue for a set with firstindex and skipelem
+
+  notes:
+    returned hash is in [0,hashsize)
+    assumes at least firstindex+1 elements
+    assumes skipelem is NULL, in set, or part of hash
+
+    hashes memory addresses which may change over different runs of the same data
+    using sum for hash does badly in high d
+*/
+int qh_gethash(qhT *qh, int hashsize, setT *set, int size, int firstindex, void *skipelem) {
+  void **elemp= SETelemaddr_(set, firstindex, void);
+  ptr_intT hash = 0, elem;
+  unsigned result;
+  int i;
+#ifdef _MSC_VER                   /* Microsoft Visual C++ -- warn about 64-bit issues */
+#pragma warning( push)            /* WARN64 -- ptr_intT holds a 64-bit pointer */
+#pragma warning( disable : 4311)  /* 'type cast': pointer truncation from 'void*' to 'ptr_intT' */
+#endif
+
+  switch (size-firstindex) {
+  case 1:
+    hash= (ptr_intT)(*elemp) - (ptr_intT) skipelem;
+    break;
+  case 2:
+    hash= (ptr_intT)(*elemp) + (ptr_intT)elemp[1] - (ptr_intT) skipelem;
+    break;
+  case 3:
+    hash= (ptr_intT)(*elemp) + (ptr_intT)elemp[1] + (ptr_intT)elemp[2]
+      - (ptr_intT) skipelem;
+    break;
+  case 4:
+    hash= (ptr_intT)(*elemp) + (ptr_intT)elemp[1] + (ptr_intT)elemp[2]
+      + (ptr_intT)elemp[3] - (ptr_intT) skipelem;
+    break;
+  case 5:
+    hash= (ptr_intT)(*elemp) + (ptr_intT)elemp[1] + (ptr_intT)elemp[2]
+      + (ptr_intT)elemp[3] + (ptr_intT)elemp[4] - (ptr_intT) skipelem;
+    break;
+  case 6:
+    hash= (ptr_intT)(*elemp) + (ptr_intT)elemp[1] + (ptr_intT)elemp[2]
+      + (ptr_intT)elemp[3] + (ptr_intT)elemp[4]+ (ptr_intT)elemp[5]
+      - (ptr_intT) skipelem;
+    break;
+  default:
+    hash= 0;
+    i= 3;
+    do {     /* this is about 10% in 10-d */
+      if ((elem= (ptr_intT)*elemp++) != (ptr_intT)skipelem) {
+        hash ^= (elem << i) + (elem >> (32-i));
+        i += 3;
+        if (i >= 32)
+          i -= 32;
+      }
+    }while (*elemp);
+    break;
+  }
+  if (hashsize<0) {
+    qh_fprintf(qh, qh->ferr, 6202, "qhull internal error: negative hashsize %d passed to qh_gethash [poly.c]\n", hashsize);
+    qh_errexit2(qh, qh_ERRqhull, NULL, NULL);
+  }
+  result= (unsigned)hash;
+  result %= (unsigned)hashsize;
+  /* result= 0; for debugging */
+  return result;
+#ifdef _MSC_VER
+#pragma warning( pop)
+#endif
+} /* gethash */
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="makenewfacet">-</a>
+
+  qh_makenewfacet(qh, vertices, toporient, horizon )
+    creates a toporient? facet from vertices
+
+  returns:
+    returns newfacet
+      adds newfacet to qh.facet_list
+      newfacet->vertices= vertices
+      if horizon
+        newfacet->neighbor= horizon, but not vice versa
+    newvertex_list updated with vertices
+*/
+facetT *qh_makenewfacet(qhT *qh, setT *vertices, boolT toporient,facetT *horizon) {
+  facetT *newfacet;
+  vertexT *vertex, **vertexp;
+
+  FOREACHvertex_(vertices) {
+    if (!vertex->newlist) {
+      qh_removevertex(qh, vertex);
+      qh_appendvertex(qh, vertex);
+    }
+  }
+  newfacet= qh_newfacet(qh);
+  newfacet->vertices= vertices;
+  newfacet->toporient= (unsigned char)toporient;
+  if (horizon)
+    qh_setappend(qh, &(newfacet->neighbors), horizon);
+  qh_appendfacet(qh, newfacet);
+  return(newfacet);
+} /* makenewfacet */
+
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="makenewplanes">-</a>
+
+  qh_makenewplanes()
+    make new hyperplanes for facets on qh.newfacet_list
+
+  returns:
+    all facets have hyperplanes or are marked for   merging
+    doesn't create hyperplane if horizon is coplanar (will merge)
+    updates qh.min_vertex if qh.JOGGLEmax
+
+  notes:
+    facet->f.samecycle is defined for facet->mergehorizon facets
+*/
+void qh_makenewplanes(qhT *qh /* qh.newfacet_list */) {
+  facetT *newfacet;
+
+  FORALLnew_facets {
+    if (!newfacet->mergehorizon)
+      qh_setfacetplane(qh, newfacet);
+  }
+  if (qh->JOGGLEmax < REALmax/2)
+    minimize_(qh->min_vertex, -wwval_(Wnewvertexmax));
+} /* makenewplanes */
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="makenew_nonsimplicial">-</a>
+
+  qh_makenew_nonsimplicial(qh, visible, apex, numnew )
+    make new facets for ridges of a visible facet
+
+  returns:
+    first newfacet, bumps numnew as needed
+    attaches new facets if !qh.ONLYgood
+    marks ridge neighbors for simplicial visible
+    if (qh.ONLYgood)
+      ridges on newfacet, horizon, and visible
+    else
+      ridge and neighbors between newfacet and   horizon
+      visible facet's ridges are deleted
+
+  notes:
+    qh.visit_id if visible has already been processed
+    sets neighbor->seen for building f.samecycle
+      assumes all 'seen' flags initially false
+
+  design:
+    for each ridge of visible facet
+      get neighbor of visible facet
+      if neighbor was already processed
+        delete the ridge (will delete all visible facets later)
+      if neighbor is a horizon facet
+        create a new facet
+        if neighbor coplanar
+          adds newfacet to f.samecycle for later merging
+        else
+          updates neighbor's neighbor set
+          (checks for non-simplicial facet with multiple ridges to visible facet)
+        updates neighbor's ridge set
+        (checks for simplicial neighbor to non-simplicial visible facet)
+        (deletes ridge if neighbor is simplicial)
+
+*/
+#ifndef qh_NOmerge
+facetT *qh_makenew_nonsimplicial(qhT *qh, facetT *visible, vertexT *apex, int *numnew) {
+  void **freelistp; /* used if !qh_NOmem by qh_memfree_() */
+  ridgeT *ridge, **ridgep;
+  facetT *neighbor, *newfacet= NULL, *samecycle;
+  setT *vertices;
+  boolT toporient;
+  int ridgeid;
+
+  FOREACHridge_(visible->ridges) {
+    ridgeid= ridge->id;
+    neighbor= otherfacet_(ridge, visible);
+    if (neighbor->visible) {
+      if (!qh->ONLYgood) {
+        if (neighbor->visitid == qh->visit_id) {
+          qh_setfree(qh, &(ridge->vertices));  /* delete on 2nd visit */
+          qh_memfree_(qh, ridge, (int)sizeof(ridgeT), freelistp);
+        }
+      }
+    }else {  /* neighbor is an horizon facet */
+      toporient= (ridge->top == visible);
+      vertices= qh_setnew(qh, qh->hull_dim); /* makes sure this is quick */
+      qh_setappend(qh, &vertices, apex);
+      qh_setappend_set(qh, &vertices, ridge->vertices);
+      newfacet= qh_makenewfacet(qh, vertices, toporient, neighbor);
+      (*numnew)++;
+      if (neighbor->coplanar) {
+        newfacet->mergehorizon= True;
+        if (!neighbor->seen) {
+          newfacet->f.samecycle= newfacet;
+          neighbor->f.newcycle= newfacet;
+        }else {
+          samecycle= neighbor->f.newcycle;
+          newfacet->f.samecycle= samecycle->f.samecycle;
+          samecycle->f.samecycle= newfacet;
+        }
+      }
+      if (qh->ONLYgood) {
+        if (!neighbor->simplicial)
+          qh_setappend(qh, &(newfacet->ridges), ridge);
+      }else {  /* qh_attachnewfacets */
+        if (neighbor->seen) {
+          if (neighbor->simplicial) {
+            qh_fprintf(qh, qh->ferr, 6105, "qhull internal error (qh_makenew_nonsimplicial): simplicial f%d sharing two ridges with f%d\n",
+                   neighbor->id, visible->id);
+            qh_errexit2(qh, qh_ERRqhull, neighbor, visible);
+          }
+          qh_setappend(qh, &(neighbor->neighbors), newfacet);
+        }else
+          qh_setreplace(qh, neighbor->neighbors, visible, newfacet);
+        if (neighbor->simplicial) {
+          qh_setdel(neighbor->ridges, ridge);
+          qh_setfree(qh, &(ridge->vertices));
+          qh_memfree(qh, ridge, (int)sizeof(ridgeT));
+        }else {
+          qh_setappend(qh, &(newfacet->ridges), ridge);
+          if (toporient)
+            ridge->top= newfacet;
+          else
+            ridge->bottom= newfacet;
+        }
+      trace4((qh, qh->ferr, 4048, "qh_makenew_nonsimplicial: created facet f%d from v%d and r%d of horizon f%d\n",
+            newfacet->id, apex->id, ridgeid, neighbor->id));
+      }
+    }
+    neighbor->seen= True;
+  } /* for each ridge */
+  if (!qh->ONLYgood)
+    SETfirst_(visible->ridges)= NULL;
+  return newfacet;
+} /* makenew_nonsimplicial */
+#else /* qh_NOmerge */
+facetT *qh_makenew_nonsimplicial(qhT *qh, facetT *visible, vertexT *apex, int *numnew) {
+  return NULL;
+}
+#endif /* qh_NOmerge */
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="makenew_simplicial">-</a>
+
+  qh_makenew_simplicial(qh, visible, apex, numnew )
+    make new facets for simplicial visible facet and apex
+
+  returns:
+    attaches new facets if (!qh.ONLYgood)
+      neighbors between newfacet and horizon
+
+  notes:
+    nop if neighbor->seen or neighbor->visible(see qh_makenew_nonsimplicial)
+
+  design:
+    locate neighboring horizon facet for visible facet
+    determine vertices and orientation
+    create new facet
+    if coplanar,
+      add new facet to f.samecycle
+    update horizon facet's neighbor list
+*/
+facetT *qh_makenew_simplicial(qhT *qh, facetT *visible, vertexT *apex, int *numnew) {
+  facetT *neighbor, **neighborp, *newfacet= NULL;
+  setT *vertices;
+  boolT flip, toporient;
+  int horizonskip= 0, visibleskip= 0;
+
+  FOREACHneighbor_(visible) {
+    if (!neighbor->seen && !neighbor->visible) {
+      vertices= qh_facetintersect(qh, neighbor,visible, &horizonskip, &visibleskip, 1);
+      SETfirst_(vertices)= apex;
+      flip= ((horizonskip & 0x1) ^ (visibleskip & 0x1));
+      if (neighbor->toporient)
+        toporient= horizonskip & 0x1;
+      else
+        toporient= (horizonskip & 0x1) ^ 0x1;
+      newfacet= qh_makenewfacet(qh, vertices, toporient, neighbor);
+      (*numnew)++;
+      if (neighbor->coplanar && (qh->PREmerge || qh->MERGEexact)) {
+#ifndef qh_NOmerge
+        newfacet->f.samecycle= newfacet;
+        newfacet->mergehorizon= True;
+#endif
+      }
+      if (!qh->ONLYgood)
+        SETelem_(neighbor->neighbors, horizonskip)= newfacet;
+      trace4((qh, qh->ferr, 4049, "qh_makenew_simplicial: create facet f%d top %d from v%d and horizon f%d skip %d top %d and visible f%d skip %d, flip? %d\n",
+            newfacet->id, toporient, apex->id, neighbor->id, horizonskip,
+              neighbor->toporient, visible->id, visibleskip, flip));
+    }
+  }
+  return newfacet;
+} /* makenew_simplicial */
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="matchneighbor">-</a>
+
+  qh_matchneighbor(qh, newfacet, newskip, hashsize, hashcount )
+    either match subridge of newfacet with neighbor or add to hash_table
+
+  returns:
+    duplicate ridges are unmatched and marked by qh_DUPLICATEridge
+
+  notes:
+    ridge is newfacet->vertices w/o newskip vertex
+    do not allocate memory (need to free hash_table cleanly)
+    uses linear hash chains
+
+  see also:
+    qh_matchduplicates
+
+  design:
+    for each possible matching facet in qh.hash_table
+      if vertices match
+        set ismatch, if facets have opposite orientation
+        if ismatch and matching facet doesn't have a match
+          match the facets by updating their neighbor sets
+        else
+          indicate a duplicate ridge
+          set facet hyperplane for later testing
+          add facet to hashtable
+          unless the other facet was already a duplicate ridge
+            mark both facets with a duplicate ridge
+            add other facet (if defined) to hash table
+*/
+void qh_matchneighbor(qhT *qh, facetT *newfacet, int newskip, int hashsize, int *hashcount) {
+  boolT newfound= False;   /* True, if new facet is already in hash chain */
+  boolT same, ismatch;
+  int hash, scan;
+  facetT *facet, *matchfacet;
+  int skip, matchskip;
+
+  hash= qh_gethash(qh, hashsize, newfacet->vertices, qh->hull_dim, 1,
+                     SETelem_(newfacet->vertices, newskip));
+  trace4((qh, qh->ferr, 4050, "qh_matchneighbor: newfacet f%d skip %d hash %d hashcount %d\n",
+          newfacet->id, newskip, hash, *hashcount));
+  zinc_(Zhashlookup);
+  for (scan= hash; (facet= SETelemt_(qh->hash_table, scan, facetT));
+       scan= (++scan >= hashsize ? 0 : scan)) {
+    if (facet == newfacet) {
+      newfound= True;
+      continue;
+    }
+    zinc_(Zhashtests);
+    if (qh_matchvertices(qh, 1, newfacet->vertices, newskip, facet->vertices, &skip, &same)) {
+      if (SETelem_(newfacet->vertices, newskip) ==
+          SETelem_(facet->vertices, skip)) {
+        qh_precision(qh, "two facets with the same vertices");
+        qh_fprintf(qh, qh->ferr, 6106, "qhull precision error: Vertex sets are the same for f%d and f%d.  Can not force output.\n",
+          facet->id, newfacet->id);
+        qh_errexit2(qh, qh_ERRprec, facet, newfacet);
+      }
+      ismatch= (same == (boolT)((newfacet->toporient ^ facet->toporient)));
+      matchfacet= SETelemt_(facet->neighbors, skip, facetT);
+      if (ismatch && !matchfacet) {
+        SETelem_(facet->neighbors, skip)= newfacet;
+        SETelem_(newfacet->neighbors, newskip)= facet;
+        (*hashcount)--;
+        trace4((qh, qh->ferr, 4051, "qh_matchneighbor: f%d skip %d matched with new f%d skip %d\n",
+           facet->id, skip, newfacet->id, newskip));
+        return;
+      }
+      if (!qh->PREmerge && !qh->MERGEexact) {
+        qh_precision(qh, "a ridge with more than two neighbors");
+        qh_fprintf(qh, qh->ferr, 6107, "qhull precision error: facets f%d, f%d and f%d meet at a ridge with more than 2 neighbors.  Can not continue.\n",
+                 facet->id, newfacet->id, getid_(matchfacet));
+        qh_errexit2(qh, qh_ERRprec, facet, newfacet);
+      }
+      SETelem_(newfacet->neighbors, newskip)= qh_DUPLICATEridge;
+      newfacet->dupridge= True;
+      if (!newfacet->normal)
+        qh_setfacetplane(qh, newfacet);
+      qh_addhash(newfacet, qh->hash_table, hashsize, hash);
+      (*hashcount)++;
+      if (!facet->normal)
+        qh_setfacetplane(qh, facet);
+      if (matchfacet != qh_DUPLICATEridge) {
+        SETelem_(facet->neighbors, skip)= qh_DUPLICATEridge;
+        facet->dupridge= True;
+        if (!facet->normal)
+          qh_setfacetplane(qh, facet);
+        if (matchfacet) {
+          matchskip= qh_setindex(matchfacet->neighbors, facet);
+          if (matchskip<0) {
+              qh_fprintf(qh, qh->ferr, 6260, "qhull internal error (qh_matchneighbor): matchfacet f%d is in f%d neighbors but not vice versa.  Can not continue.\n",
+                  matchfacet->id, facet->id);
+              qh_errexit2(qh, qh_ERRqhull, matchfacet, facet);
+          }
+          SETelem_(matchfacet->neighbors, matchskip)= qh_DUPLICATEridge; /* matchskip>=0 by QH6260 */
+          matchfacet->dupridge= True;
+          if (!matchfacet->normal)
+            qh_setfacetplane(qh, matchfacet);
+          qh_addhash(matchfacet, qh->hash_table, hashsize, hash);
+          *hashcount += 2;
+        }
+      }
+      trace4((qh, qh->ferr, 4052, "qh_matchneighbor: new f%d skip %d duplicates ridge for f%d skip %d matching f%d ismatch %d at hash %d\n",
+           newfacet->id, newskip, facet->id, skip,
+           (matchfacet == qh_DUPLICATEridge ? -2 : getid_(matchfacet)),
+           ismatch, hash));
+      return; /* end of duplicate ridge */
+    }
+  }
+  if (!newfound)
+    SETelem_(qh->hash_table, scan)= newfacet;  /* same as qh_addhash */
+  (*hashcount)++;
+  trace4((qh, qh->ferr, 4053, "qh_matchneighbor: no match for f%d skip %d at hash %d\n",
+           newfacet->id, newskip, hash));
+} /* matchneighbor */
+
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="matchnewfacets">-</a>
+
+  qh_matchnewfacets()
+    match newfacets in qh.newfacet_list to their newfacet neighbors
+
+  returns:
+    qh.newfacet_list with full neighbor sets
+      get vertices with nth neighbor by deleting nth vertex
+    if qh.PREmerge/MERGEexact or qh.FORCEoutput
+      sets facet->flippped if flipped normal (also prevents point partitioning)
+    if duplicate ridges and qh.PREmerge/MERGEexact
+      sets facet->dupridge
+      missing neighbor links identifies extra ridges to be merging (qh_MERGEridge)
+
+  notes:
+    newfacets already have neighbor[0] (horizon facet)
+    assumes qh.hash_table is NULL
+    vertex->neighbors has not been updated yet
+    do not allocate memory after qh.hash_table (need to free it cleanly)
+
+  design:
+    delete neighbor sets for all new facets
+    initialize a hash table
+    for all new facets
+      match facet with neighbors
+    if unmatched facets (due to duplicate ridges)
+      for each new facet with a duplicate ridge
+        match it with a facet
+    check for flipped facets
+*/
+void qh_matchnewfacets(qhT *qh /* qh.newfacet_list */) {
+  int numnew=0, hashcount=0, newskip;
+  facetT *newfacet, *neighbor;
+  int dim= qh->hull_dim, hashsize, neighbor_i, neighbor_n;
+  setT *neighbors;
+#ifndef qh_NOtrace
+  int facet_i, facet_n, numfree= 0;
+  facetT *facet;
+#endif
+
+  trace1((qh, qh->ferr, 1019, "qh_matchnewfacets: match neighbors for new facets.\n"));
+  FORALLnew_facets {
+    numnew++;
+    {  /* inline qh_setzero(qh, newfacet->neighbors, 1, qh->hull_dim); */
+      neighbors= newfacet->neighbors;
+      neighbors->e[neighbors->maxsize].i= dim+1; /*may be overwritten*/
+      memset((char *)SETelemaddr_(neighbors, 1, void), 0, dim * SETelemsize);
+    }
+  }
+
+  qh_newhashtable(qh, numnew*(qh->hull_dim-1)); /* twice what is normally needed,
+                                     but every ridge could be DUPLICATEridge */
+  hashsize= qh_setsize(qh, qh->hash_table);
+  FORALLnew_facets {
+    for (newskip=1; newskip<qh->hull_dim; newskip++) /* furthest/horizon already matched */
+      /* hashsize>0 because hull_dim>1 and numnew>0 */
+      qh_matchneighbor(qh, newfacet, newskip, hashsize, &hashcount);
+#if 0   /* use the following to trap hashcount errors */
+    {
+      int count= 0, k;
+      facetT *facet, *neighbor;
+
+      count= 0;
+      FORALLfacet_(qh->newfacet_list) {  /* newfacet already in use */
+        for (k=1; k < qh->hull_dim; k++) {
+          neighbor= SETelemt_(facet->neighbors, k, facetT);
+          if (!neighbor || neighbor == qh_DUPLICATEridge)
+            count++;
+        }
+        if (facet == newfacet)
+          break;
+      }
+      if (count != hashcount) {
+        qh_fprintf(qh, qh->ferr, 8088, "qh_matchnewfacets: after adding facet %d, hashcount %d != count %d\n",
+                 newfacet->id, hashcount, count);
+        qh_errexit(qh, qh_ERRqhull, newfacet, NULL);
+      }
+    }
+#endif  /* end of trap code */
+  }
+  if (hashcount) {
+    FORALLnew_facets {
+      if (newfacet->dupridge) {
+        FOREACHneighbor_i_(qh, newfacet) {
+          if (neighbor == qh_DUPLICATEridge) {
+            qh_matchduplicates(qh, newfacet, neighbor_i, hashsize, &hashcount);
+                    /* this may report MERGEfacet */
+          }
+        }
+      }
+    }
+  }
+  if (hashcount) {
+    qh_fprintf(qh, qh->ferr, 6108, "qhull internal error (qh_matchnewfacets): %d neighbors did not match up\n",
+        hashcount);
+    qh_printhashtable(qh, qh->ferr);
+    qh_errexit(qh, qh_ERRqhull, NULL, NULL);
+  }
+#ifndef qh_NOtrace
+  if (qh->IStracing >= 2) {
+    FOREACHfacet_i_(qh, qh->hash_table) {
+      if (!facet)
+        numfree++;
+    }
+    qh_fprintf(qh, qh->ferr, 8089, "qh_matchnewfacets: %d new facets, %d unused hash entries .  hashsize %d\n",
+             numnew, numfree, qh_setsize(qh, qh->hash_table));
+  }
+#endif /* !qh_NOtrace */
+  qh_setfree(qh, &qh->hash_table);
+  if (qh->PREmerge || qh->MERGEexact) {
+    if (qh->IStracing >= 4)
+      qh_printfacetlist(qh, qh->newfacet_list, NULL, qh_ALL);
+    FORALLnew_facets {
+      if (newfacet->normal)
+        qh_checkflipped(qh, newfacet, NULL, qh_ALL);
+    }
+  }else if (qh->FORCEoutput)
+    qh_checkflipped_all(qh, qh->newfacet_list);  /* prints warnings for flipped */
+} /* matchnewfacets */
+
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="matchvertices">-</a>
+
+  qh_matchvertices(qh, firstindex, verticesA, skipA, verticesB, skipB, same )
+    tests whether vertices match with a single skip
+    starts match at firstindex since all new facets have a common vertex
+
+  returns:
+    true if matched vertices
+    skip index for each set
+    sets same iff vertices have the same orientation
+
+  notes:
+    assumes skipA is in A and both sets are the same size
+
+  design:
+    set up pointers
+    scan both sets checking for a match
+    test orientation
+*/
+boolT qh_matchvertices(qhT *qh, int firstindex, setT *verticesA, int skipA,
+       setT *verticesB, int *skipB, boolT *same) {
+  vertexT **elemAp, **elemBp, **skipBp=NULL, **skipAp;
+
+  elemAp= SETelemaddr_(verticesA, firstindex, vertexT);
+  elemBp= SETelemaddr_(verticesB, firstindex, vertexT);
+  skipAp= SETelemaddr_(verticesA, skipA, vertexT);
+  do if (elemAp != skipAp) {
+    while (*elemAp != *elemBp++) {
+      if (skipBp)
+        return False;
+      skipBp= elemBp;  /* one extra like FOREACH */
+    }
+  }while (*(++elemAp));
+  if (!skipBp)
+    skipBp= ++elemBp;
+  *skipB= SETindex_(verticesB, skipB); /* i.e., skipBp - verticesB */
+  *same= !((skipA & 0x1) ^ (*skipB & 0x1)); /* result is 0 or 1 */
+  trace4((qh, qh->ferr, 4054, "qh_matchvertices: matched by skip %d(v%d) and skip %d(v%d) same? %d\n",
+          skipA, (*skipAp)->id, *skipB, (*(skipBp-1))->id, *same));
+  return(True);
+} /* matchvertices */
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="newfacet">-</a>
+
+  qh_newfacet(qh)
+    return a new facet
+
+  returns:
+    all fields initialized or cleared   (NULL)
+    preallocates neighbors set
+*/
+facetT *qh_newfacet(qhT *qh) {
+  facetT *facet;
+  void **freelistp; /* used if !qh_NOmem by qh_memalloc_() */
+
+  qh_memalloc_(qh, (int)sizeof(facetT), freelistp, facet, facetT);
+  memset((char *)facet, (size_t)0, sizeof(facetT));
+  if (qh->facet_id == qh->tracefacet_id)
+    qh->tracefacet= facet;
+  facet->id= qh->facet_id++;
+  facet->neighbors= qh_setnew(qh, qh->hull_dim);
+#if !qh_COMPUTEfurthest
+  facet->furthestdist= 0.0;
+#endif
+#if qh_MAXoutside
+  if (qh->FORCEoutput && qh->APPROXhull)
+    facet->maxoutside= qh->MINoutside;
+  else
+    facet->maxoutside= qh->DISTround;
+#endif
+  facet->simplicial= True;
+  facet->good= True;
+  facet->newfacet= True;
+  trace4((qh, qh->ferr, 4055, "qh_newfacet: created facet f%d\n", facet->id));
+  return(facet);
+} /* newfacet */
+
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="newridge">-</a>
+
+  qh_newridge()
+    return a new ridge
+*/
+ridgeT *qh_newridge(qhT *qh) {
+  ridgeT *ridge;
+  void **freelistp;   /* used if !qh_NOmem by qh_memalloc_() */
+
+  qh_memalloc_(qh, (int)sizeof(ridgeT), freelistp, ridge, ridgeT);
+  memset((char *)ridge, (size_t)0, sizeof(ridgeT));
+  zinc_(Ztotridges);
+  if (qh->ridge_id == UINT_MAX) {
+    qh_fprintf(qh, qh->ferr, 7074, "\
+qhull warning: more than 2^32 ridges.  Qhull results are OK.  Since the ridge ID wraps around to 0, two ridges may have the same identifier.\n");
+  }
+  ridge->id= qh->ridge_id++;
+  trace4((qh, qh->ferr, 4056, "qh_newridge: created ridge r%d\n", ridge->id));
+  return(ridge);
+} /* newridge */
+
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="pointid">-</a>
+
+  qh_pointid(qh, point )
+    return id for a point,
+    returns qh_IDnone(-3) if null, qh_IDinterior(-2) if interior, or qh_IDunknown(-1) if not known
+
+  alternative code if point is in qh.first_point...
+    unsigned long id;
+    id= ((unsigned long)point - (unsigned long)qh.first_point)/qh.normal_size;
+
+  notes:
+    Valid points are non-negative
+    WARN64 -- id truncated to 32-bits, at most 2G points
+    NOerrors returned (QhullPoint::id)
+    if point not in point array
+      the code does a comparison of unrelated pointers.
+*/
+int qh_pointid(qhT *qh, pointT *point) {
+  ptr_intT offset, id;
+
+  if (!point || !qh)
+    return qh_IDnone;
+  else if (point == qh->interior_point)
+    return qh_IDinterior;
+  else if (point >= qh->first_point
+  && point < qh->first_point + qh->num_points * qh->hull_dim) {
+    offset= (ptr_intT)(point - qh->first_point);
+    id= offset / qh->hull_dim;
+  }else if ((id= qh_setindex(qh->other_points, point)) != -1)
+    id += qh->num_points;
+  else
+    return qh_IDunknown;
+  return (int)id;
+} /* pointid */
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="removefacet">-</a>
+
+  qh_removefacet(qh, facet )
+    unlinks facet from qh.facet_list,
+
+  returns:
+    updates qh.facet_list .newfacet_list .facet_next visible_list
+    decrements qh.num_facets
+
+  see:
+    qh_appendfacet
+*/
+void qh_removefacet(qhT *qh, facetT *facet) {
+  facetT *next= facet->next, *previous= facet->previous;
+
+  if (facet == qh->newfacet_list)
+    qh->newfacet_list= next;
+  if (facet == qh->facet_next)
+    qh->facet_next= next;
+  if (facet == qh->visible_list)
+    qh->visible_list= next;
+  if (previous) {
+    previous->next= next;
+    next->previous= previous;
+  }else {  /* 1st facet in qh->facet_list */
+    qh->facet_list= next;
+    qh->facet_list->previous= NULL;
+  }
+  qh->num_facets--;
+  trace4((qh, qh->ferr, 4057, "qh_removefacet: remove f%d from facet_list\n", facet->id));
+} /* removefacet */
+
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="removevertex">-</a>
+
+  qh_removevertex(qh, vertex )
+    unlinks vertex from qh.vertex_list,
+
+  returns:
+    updates qh.vertex_list .newvertex_list
+    decrements qh.num_vertices
+*/
+void qh_removevertex(qhT *qh, vertexT *vertex) {
+  vertexT *next= vertex->next, *previous= vertex->previous;
+
+  if (vertex == qh->newvertex_list)
+    qh->newvertex_list= next;
+  if (previous) {
+    previous->next= next;
+    next->previous= previous;
+  }else {  /* 1st vertex in qh->vertex_list */
+    qh->vertex_list= vertex->next;
+    qh->vertex_list->previous= NULL;
+  }
+  qh->num_vertices--;
+  trace4((qh, qh->ferr, 4058, "qh_removevertex: remove v%d from vertex_list\n", vertex->id));
+} /* removevertex */
+
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >-------------------------------</a><a name="updatevertices">-</a>
+
+  qh_updatevertices()
+    update vertex neighbors and delete interior vertices
+
+  returns:
+    if qh.VERTEXneighbors, updates neighbors for each vertex
+      if qh.newvertex_list,
+         removes visible neighbors  from vertex neighbors
+      if qh.newfacet_list
+         adds new facets to vertex neighbors
+    if qh.visible_list
+       interior vertices added to qh.del_vertices for later partitioning
+
+  design:
+    if qh.VERTEXneighbors
+      deletes references to visible facets from vertex neighbors
+      appends new facets to the neighbor list for each vertex
+      checks all vertices of visible facets
+        removes visible facets from neighbor lists
+        marks unused vertices for deletion
+*/
+void qh_updatevertices(qhT *qh /*qh.newvertex_list, newfacet_list, visible_list*/) {
+  facetT *newfacet= NULL, *neighbor, **neighborp, *visible;
+  vertexT *vertex, **vertexp;
+
+  trace3((qh, qh->ferr, 3013, "qh_updatevertices: delete interior vertices and update vertex->neighbors\n"));
+  if (qh->VERTEXneighbors) {
+    FORALLvertex_(qh->newvertex_list) {
+      FOREACHneighbor_(vertex) {
+        if (neighbor->visible)
+          SETref_(neighbor)= NULL;
+      }
+      qh_setcompact(qh, vertex->neighbors);
+    }
+    FORALLnew_facets {
+      FOREACHvertex_(newfacet->vertices)
+        qh_setappend(qh, &vertex->neighbors, newfacet);
+    }
+    FORALLvisible_facets {
+      FOREACHvertex_(visible->vertices) {
+        if (!vertex->newlist && !vertex->deleted) {
+          FOREACHneighbor_(vertex) { /* this can happen under merging */
+            if (!neighbor->visible)
+              break;
+          }
+          if (neighbor)
+            qh_setdel(vertex->neighbors, visible);
+          else {
+            vertex->deleted= True;
+            qh_setappend(qh, &qh->del_vertices, vertex);
+            trace2((qh, qh->ferr, 2041, "qh_updatevertices: delete vertex p%d(v%d) in f%d\n",
+                  qh_pointid(qh, vertex->point), vertex->id, visible->id));
+          }
+        }
+      }
+    }
+  }else {  /* !VERTEXneighbors */
+    FORALLvisible_facets {
+      FOREACHvertex_(visible->vertices) {
+        if (!vertex->newlist && !vertex->deleted) {
+          vertex->deleted= True;
+          qh_setappend(qh, &qh->del_vertices, vertex);
+          trace2((qh, qh->ferr, 2042, "qh_updatevertices: delete vertex p%d(v%d) in f%d\n",
+                  qh_pointid(qh, vertex->point), vertex->id, visible->id));
+        }
+      }
+    }
+  }
+} /* updatevertices */
+
+
+
diff --git a/xs/src/qhull/src/libqhull_r/poly_r.h b/xs/src/qhull/src/libqhull_r/poly_r.h
new file mode 100644
index 0000000000..c71511bd69
--- /dev/null
+++ b/xs/src/qhull/src/libqhull_r/poly_r.h
@@ -0,0 +1,303 @@
+/*<html><pre>  -<a                             href="qh-poly_r.htm"
+  >-------------------------------</a><a name="TOP">-</a>
+
+   poly_r.h
+   header file for poly_r.c and poly2_r.c
+
+   see qh-poly_r.htm, libqhull_r.h and poly_r.c
+
+   Copyright (c) 1993-2015 The Geometry Center.
+   $Id: //main/2015/qhull/src/libqhull_r/poly_r.h#5 $$Change: 2079 $
+   $DateTime: 2016/02/07 17:43:34 $$Author: bbarber $
+*/
+
+#ifndef qhDEFpoly
+#define qhDEFpoly 1
+
+#include "libqhull_r.h"
+
+/*===============   constants ========================== */
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >--------------------------------</a><a name="ALGORITHMfault">-</a>
+
+  ALGORITHMfault
+    use as argument to checkconvex() to report errors during buildhull
+*/
+#define qh_ALGORITHMfault 0
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >--------------------------------</a><a name="DATAfault">-</a>
+
+  DATAfault
+    use as argument to checkconvex() to report errors during initialhull
+*/
+#define qh_DATAfault 1
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >--------------------------------</a><a name="DUPLICATEridge">-</a>
+
+  DUPLICATEridge
+    special value for facet->neighbor to indicate a duplicate ridge
+
+  notes:
+    set by matchneighbor, used by matchmatch and mark_dupridge
+*/
+#define qh_DUPLICATEridge (facetT *)1L
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >--------------------------------</a><a name="MERGEridge">-</a>
+
+  MERGEridge       flag in facet
+    special value for facet->neighbor to indicate a merged ridge
+
+  notes:
+    set by matchneighbor, used by matchmatch and mark_dupridge
+*/
+#define qh_MERGEridge (facetT *)2L
+
+
+/*============ -structures- ====================*/
+
+/*=========== -macros- =========================*/
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >--------------------------------</a><a name="FORALLfacet_">-</a>
+
+  FORALLfacet_( facetlist ) { ... }
+    assign 'facet' to each facet in facetlist
+
+  notes:
+    uses 'facetT *facet;'
+    assumes last facet is a sentinel
+
+  see:
+    FORALLfacets
+*/
+#define FORALLfacet_( facetlist ) if (facetlist ) for ( facet=( facetlist ); facet && facet->next; facet= facet->next )
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >--------------------------------</a><a name="FORALLnew_facets">-</a>
+
+  FORALLnew_facets { ... }
+    assign 'newfacet' to each facet in qh.newfacet_list
+
+  notes:
+    uses 'facetT *newfacet;'
+    at exit, newfacet==NULL
+*/
+#define FORALLnew_facets for ( newfacet=qh->newfacet_list;newfacet && newfacet->next;newfacet=newfacet->next )
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >--------------------------------</a><a name="FORALLvertex_">-</a>
+
+  FORALLvertex_( vertexlist ) { ... }
+    assign 'vertex' to each vertex in vertexlist
+
+  notes:
+    uses 'vertexT *vertex;'
+    at exit, vertex==NULL
+*/
+#define FORALLvertex_( vertexlist ) for (vertex=( vertexlist );vertex && vertex->next;vertex= vertex->next )
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >--------------------------------</a><a name="FORALLvisible_facets">-</a>
+
+  FORALLvisible_facets { ... }
+    assign 'visible' to each visible facet in qh.visible_list
+
+  notes:
+    uses 'vacetT *visible;'
+    at exit, visible==NULL
+*/
+#define FORALLvisible_facets for (visible=qh->visible_list; visible && visible->visible; visible= visible->next)
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >--------------------------------</a><a name="FORALLsame_">-</a>
+
+  FORALLsame_( newfacet ) { ... }
+    assign 'same' to each facet in newfacet->f.samecycle
+
+  notes:
+    uses 'facetT *same;'
+    stops when it returns to newfacet
+*/
+#define FORALLsame_(newfacet) for (same= newfacet->f.samecycle; same != newfacet; same= same->f.samecycle)
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >--------------------------------</a><a name="FORALLsame_cycle_">-</a>
+
+  FORALLsame_cycle_( newfacet ) { ... }
+    assign 'same' to each facet in newfacet->f.samecycle
+
+  notes:
+    uses 'facetT *same;'
+    at exit, same == NULL
+*/
+#define FORALLsame_cycle_(newfacet) \
+     for (same= newfacet->f.samecycle; \
+         same; same= (same == newfacet ?  NULL : same->f.samecycle))
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >--------------------------------</a><a name="FOREACHneighborA_">-</a>
+
+  FOREACHneighborA_( facet ) { ... }
+    assign 'neighborA' to each neighbor in facet->neighbors
+
+  FOREACHneighborA_( vertex ) { ... }
+    assign 'neighborA' to each neighbor in vertex->neighbors
+
+  declare:
+    facetT *neighborA, **neighborAp;
+
+  see:
+    <a href="qset_r.h#FOREACHsetelement_">FOREACHsetelement_</a>
+*/
+#define FOREACHneighborA_(facet)  FOREACHsetelement_(facetT, facet->neighbors, neighborA)
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >--------------------------------</a><a name="FOREACHvisible_">-</a>
+
+  FOREACHvisible_( facets ) { ... }
+    assign 'visible' to each facet in facets
+
+  notes:
+    uses 'facetT *facet, *facetp;'
+    see <a href="qset_r.h#FOREACHsetelement_">FOREACHsetelement_</a>
+*/
+#define FOREACHvisible_(facets) FOREACHsetelement_(facetT, facets, visible)
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >--------------------------------</a><a name="FOREACHnewfacet_">-</a>
+
+  FOREACHnewfacet_( facets ) { ... }
+    assign 'newfacet' to each facet in facets
+
+  notes:
+    uses 'facetT *newfacet, *newfacetp;'
+    see <a href="qset_r.h#FOREACHsetelement_">FOREACHsetelement_</a>
+*/
+#define FOREACHnewfacet_(facets) FOREACHsetelement_(facetT, facets, newfacet)
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >--------------------------------</a><a name="FOREACHvertexA_">-</a>
+
+  FOREACHvertexA_( vertices ) { ... }
+    assign 'vertexA' to each vertex in vertices
+
+  notes:
+    uses 'vertexT *vertexA, *vertexAp;'
+    see <a href="qset_r.h#FOREACHsetelement_">FOREACHsetelement_</a>
+*/
+#define FOREACHvertexA_(vertices) FOREACHsetelement_(vertexT, vertices, vertexA)
+
+/*-<a                             href="qh-poly_r.htm#TOC"
+  >--------------------------------</a><a name="FOREACHvertexreverse12_">-</a>
+
+  FOREACHvertexreverse12_( vertices ) { ... }
+    assign 'vertex' to each vertex in vertices
+    reverse order of first two vertices
+
+  notes:
+    uses 'vertexT *vertex, *vertexp;'
+    see <a href="qset_r.h#FOREACHsetelement_">FOREACHsetelement_</a>
+*/
+#define FOREACHvertexreverse12_(vertices) FOREACHsetelementreverse12_(vertexT, vertices, vertex)
+
+
+/*=============== prototypes poly_r.c in alphabetical order ================*/
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+void    qh_appendfacet(qhT *qh, facetT *facet);
+void    qh_appendvertex(qhT *qh, vertexT *vertex);
+void    qh_attachnewfacets(qhT *qh /* qh.visible_list, qh.newfacet_list */);
+boolT   qh_checkflipped(qhT *qh, facetT *facet, realT *dist, boolT allerror);
+void    qh_delfacet(qhT *qh, facetT *facet);
+void    qh_deletevisible(qhT *qh /* qh.visible_list, qh.horizon_list */);
+setT   *qh_facetintersect(qhT *qh, facetT *facetA, facetT *facetB, int *skipAp,int *skipBp, int extra);
+int     qh_gethash(qhT *qh, int hashsize, setT *set, int size, int firstindex, void *skipelem);
+facetT *qh_makenewfacet(qhT *qh, setT *vertices, boolT toporient, facetT *facet);
+void    qh_makenewplanes(qhT *qh /* qh.newfacet_list */);
+facetT *qh_makenew_nonsimplicial(qhT *qh, facetT *visible, vertexT *apex, int *numnew);
+facetT *qh_makenew_simplicial(qhT *qh, facetT *visible, vertexT *apex, int *numnew);
+void    qh_matchneighbor(qhT *qh, facetT *newfacet, int newskip, int hashsize,
+                          int *hashcount);
+void    qh_matchnewfacets(qhT *qh);
+boolT   qh_matchvertices(qhT *qh, int firstindex, setT *verticesA, int skipA,
+                          setT *verticesB, int *skipB, boolT *same);
+facetT *qh_newfacet(qhT *qh);
+ridgeT *qh_newridge(qhT *qh);
+int     qh_pointid(qhT *qh, pointT *point);
+void    qh_removefacet(qhT *qh, facetT *facet);
+void    qh_removevertex(qhT *qh, vertexT *vertex);
+void    qh_updatevertices(qhT *qh);
+
+
+/*========== -prototypes poly2_r.c in alphabetical order ===========*/
+
+void    qh_addhash(void *newelem, setT *hashtable, int hashsize, int hash);
+void    qh_check_bestdist(qhT *qh);
+void    qh_check_dupridge(qhT *qh, facetT *facet1, realT dist1, facetT *facet2, realT dist2);
+void    qh_check_maxout(qhT *qh);
+void    qh_check_output(qhT *qh);
+void    qh_check_point(qhT *qh, pointT *point, facetT *facet, realT *maxoutside, realT *maxdist, facetT **errfacet1, facetT **errfacet2);
+void    qh_check_points(qhT *qh);
+void    qh_checkconvex(qhT *qh, facetT *facetlist, int fault);
+void    qh_checkfacet(qhT *qh, facetT *facet, boolT newmerge, boolT *waserrorp);
+void    qh_checkflipped_all(qhT *qh, facetT *facetlist);
+void    qh_checkpolygon(qhT *qh, facetT *facetlist);
+void    qh_checkvertex(qhT *qh, vertexT *vertex);
+void    qh_clearcenters(qhT *qh, qh_CENTER type);
+void    qh_createsimplex(qhT *qh, setT *vertices);
+void    qh_delridge(qhT *qh, ridgeT *ridge);
+void    qh_delvertex(qhT *qh, vertexT *vertex);
+setT   *qh_facet3vertex(qhT *qh, facetT *facet);
+facetT *qh_findbestfacet(qhT *qh, pointT *point, boolT bestoutside,
+           realT *bestdist, boolT *isoutside);
+facetT *qh_findbestlower(qhT *qh, facetT *upperfacet, pointT *point, realT *bestdistp, int *numpart);
+facetT *qh_findfacet_all(qhT *qh, pointT *point, realT *bestdist, boolT *isoutside,
+                          int *numpart);
+int     qh_findgood(qhT *qh, facetT *facetlist, int goodhorizon);
+void    qh_findgood_all(qhT *qh, facetT *facetlist);
+void    qh_furthestnext(qhT *qh /* qh.facet_list */);
+void    qh_furthestout(qhT *qh, facetT *facet);
+void    qh_infiniteloop(qhT *qh, facetT *facet);
+void    qh_initbuild(qhT *qh);
+void    qh_initialhull(qhT *qh, setT *vertices);
+setT   *qh_initialvertices(qhT *qh, int dim, setT *maxpoints, pointT *points, int numpoints);
+vertexT *qh_isvertex(pointT *point, setT *vertices);
+vertexT *qh_makenewfacets(qhT *qh, pointT *point /*horizon_list, visible_list*/);
+void    qh_matchduplicates(qhT *qh, facetT *atfacet, int atskip, int hashsize, int *hashcount);
+void    qh_nearcoplanar(qhT *qh /* qh.facet_list */);
+vertexT *qh_nearvertex(qhT *qh, facetT *facet, pointT *point, realT *bestdistp);
+int     qh_newhashtable(qhT *qh, int newsize);
+vertexT *qh_newvertex(qhT *qh, pointT *point);
+ridgeT *qh_nextridge3d(ridgeT *atridge, facetT *facet, vertexT **vertexp);
+void    qh_outcoplanar(qhT *qh /* qh.facet_list */);
+pointT *qh_point(qhT *qh, int id);
+void    qh_point_add(qhT *qh, setT *set, pointT *point, void *elem);
+setT   *qh_pointfacet(qhT *qh /*qh.facet_list*/);
+setT   *qh_pointvertex(qhT *qh /*qh.facet_list*/);
+void    qh_prependfacet(qhT *qh, facetT *facet, facetT **facetlist);
+void    qh_printhashtable(qhT *qh, FILE *fp);
+void    qh_printlists(qhT *qh);
+void    qh_resetlists(qhT *qh, boolT stats, boolT resetVisible /*qh.newvertex_list qh.newfacet_list qh.visible_list*/);
+void    qh_setvoronoi_all(qhT *qh);
+void    qh_triangulate(qhT *qh /*qh.facet_list*/);
+void    qh_triangulate_facet(qhT *qh, facetT *facetA, vertexT **first_vertex);
+void    qh_triangulate_link(qhT *qh, facetT *oldfacetA, facetT *facetA, facetT *oldfacetB, facetT *facetB);
+void    qh_triangulate_mirror(qhT *qh, facetT *facetA, facetT *facetB);
+void    qh_triangulate_null(qhT *qh, facetT *facetA);
+void    qh_vertexintersect(qhT *qh, setT **vertexsetA,setT *vertexsetB);
+setT   *qh_vertexintersect_new(qhT *qh, setT *vertexsetA,setT *vertexsetB);
+void    qh_vertexneighbors(qhT *qh /*qh.facet_list*/);
+boolT   qh_vertexsubset(setT *vertexsetA, setT *vertexsetB);
+
+#ifdef __cplusplus
+} /* extern "C" */
+#endif
+
+#endif /* qhDEFpoly */
diff --git a/xs/src/qhull/src/libqhull_r/qh-geom_r.htm b/xs/src/qhull/src/libqhull_r/qh-geom_r.htm
new file mode 100644
index 0000000000..eeefc0c758
--- /dev/null
+++ b/xs/src/qhull/src/libqhull_r/qh-geom_r.htm
@@ -0,0 +1,295 @@
+<!-- Do not edit with Front Page, it adds too many spaces -->
+<html>
+<head>
+<meta http-equiv="Content-Type"
+content="text/html; charset=iso-8859-1">
+<title>geom_r.c, geom2_r.c -- geometric and floating point routines</title>
+</head>
+
+<body>
+<!-- Navigation links -->
+<p><a name="TOP"><b>Up:</b></a> <a
+href="http://www.qhull.org">Home page</a> for Qhull<br>
+<b>Up:</b> <a href="../../html/index.htm#TOC">Qhull manual</a>: Table of Contents <br>
+<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a>
+&#149; <a href="../../html/qh-quick.htm#options">Options</a>
+&#149; <a href="../../html/qh-opto.htm#output">Output</a>
+&#149; <a href="../../html/qh-optf.htm#format">Formats</a>
+&#149; <a href="../../html/qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="../../html/qh-optp.htm#print">Print</a>
+&#149; <a href="../../html/qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="../../html/qh-optc.htm#prec">Precision</a>
+&#149; <a href="../../html/qh-optt.htm#trace">Trace</a>
+&#149; <a href="index.htm">Functions</a><br>
+<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code: Table of Contents</a><br>
+<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
+<b>To:</b> <a href="qh-geom_r.htm#TOC">Geom</a> &#149; <a href="qh-globa_r.htm">Global</a>
+&#149; <a href="qh-io_r.htm">Io</a> &#149; <a href="qh-mem_r.htm">Mem</a>
+&#149; <a href="qh-merge_r.htm">Merge</a> &#149; <a href="qh-poly_r.htm">Poly</a>
+&#149; <a href="qh-qhull_r.htm">Qhull</a> &#149; <a href="qh-set_r.htm">Set</a>
+&#149; <a href="qh-stat_r.htm">Stat</a> &#149; <a href="qh-user_r.htm">User</a>
+</p>
+
+<hr>
+<!-- Main text of document. -->
+
+<h2>geom_r.c, geom2_r.c, random_r.c -- geometric and floating point routines</h2>
+<blockquote>
+<p>Geometrically, a vertex is a point with <em>d</em> coordinates
+and a facet is a halfspace. A <em>halfspace</em> is defined by an
+oriented hyperplane through the facet's vertices. A <em>hyperplane</em>
+is defined by <em>d</em> normalized coefficients and an offset. A
+point is <em>above</em> a facet if its distance to the facet is
+positive.</p>
+
+<p>Qhull uses floating point coordinates for input points,
+vertices, halfspace equations, centrums, and an interior point.</p>
+
+<p>Qhull may be configured for single precision or double
+precision floating point arithmetic (see <a href="user_r.h#realT">realT</a>
+). </p>
+
+<p>Each floating point operation may incur round-off error (see
+<a href="qh-merge_r.htm#TOC">Merge</a>). The maximum error for distance
+computations is determined at initialization. The roundoff error
+in halfspace computation is accounted for by computing the
+distance from vertices to the halfspace. </p>
+</blockquote>
+<p><b>Copyright &copy; 1995-2015 C.B. Barber</b></p>
+<hr>
+<p><a href="#TOP">&#187;</a> <b>Geom</b>
+<a name="TOC">&#149;</a> <a href="qh-globa_r.htm#TOC">Global</a> &#149;
+<a href="qh-io_r.htm#TOC">Io</a> &#149; <a href="qh-mem_r.htm#TOC">Mem</a> &#149;
+<a href="qh-merge_r.htm#TOC">Merge</a> &#149; <a href="qh-poly_r.htm#TOC">Poly</a> &#149;
+<a href="qh-qhull_r.htm#TOC">Qhull</a> &#149; <a href="qh-set_r.htm#TOC">Set</a> &#149;
+<a href="qh-stat_r.htm#TOC">Stat</a> &#149; <a href="qh-user_r.htm#TOC">User</a> </p>
+
+<h3>Index to <a href="geom_r.c">geom_r.c</a>,
+<a href="geom2_r.c">geom2_r.c</a>, <a href="geom_r.h">geom_r.h</a>,
+<a href="random_r.c">random_r.c</a>, <a href="random_r.h">random_r.h</a>
+</h3>
+
+<ul>
+<li><a href="#gtype">geometric data types and constants</a> </li>
+<li><a href="#gmacro">mathematical macros</a>
+</li>
+<li><a href="#gmath">mathematical functions</a> </li>
+<li><a href="#gcomp">computational geometry functions</a> </li>
+<li><a href="#gpoint">point array functions</a> </li>
+<li><a href="#gfacet">geometric facet functions</a> </li>
+<li><a href="#ground">geometric roundoff functions</a></li>
+</ul>
+
+<h3><a href="qh-geom_r.htm#TOC">&#187;</a><a name="gtype">geometric data types
+and constants</a></h3>
+
+<ul>
+<li><a href="libqhull_r.h#coordT">coordT</a> coordinates and
+coefficients are stored as realT</li>
+<li><a href="libqhull_r.h#pointT">pointT</a> a point is an array
+of <tt>DIM3</tt> coordinates </li>
+</ul>
+
+<h3><a href="qh-geom_r.htm#TOC">&#187;</a><a name="gmacro">mathematical macros</a></h3>
+
+<ul>
+<li><a href="geom_r.h#fabs_">fabs_</a> returns the absolute
+value of a </li>
+<li><a href="geom_r.h#fmax_">fmax_</a> returns the maximum
+value of a and b </li>
+<li><a href="geom_r.h#fmin_">fmin_</a> returns the minimum
+value of a and b </li>
+<li><a href="geom_r.h#maximize_">maximize_</a> maximize a value
+</li>
+<li><a href="geom_r.h#minimize_">minimize_</a> minimize a value
+</li>
+<li><a href="geom_r.h#det2_">det2_</a> compute a 2-d
+determinate </li>
+<li><a href="geom_r.h#det3_">det3_</a> compute a 3-d
+determinate </li>
+<li><a href="geom_r.h#dX">dX, dY, dZ</a> compute the difference
+between two coordinates </li>
+</ul>
+
+<h3><a href="qh-geom_r.htm#TOC">&#187;</a><a name="gmath">mathematical functions</a></h3>
+
+<ul>
+<li><a href="geom_r.c#backnormal">qh_backnormal</a> solve for
+normal using back substitution </li>
+<li><a href="geom2_r.c#crossproduct">qh_crossproduct</a>
+compute the cross product of two 3-d vectors </li>
+<li><a href="geom2_r.c#determinant">qh_determinant</a> compute
+the determinant of a square matrix </li>
+<li><a href="geom_r.c#gausselim">qh_gausselim</a> Gaussian
+elimination with partial pivoting </li>
+<li><a href="geom2_r.c#gram_schmidt">qh_gram_schmidt</a>
+implements Gram-Schmidt orthogonalization by rows </li>
+<li><a href="geom2_r.c#maxabsval">qh_maxabsval</a> return max
+absolute value of a vector </li>
+<li><a href="geom2_r.c#minabsval">qh_minabsval</a> return min
+absolute value of a dim vector </li>
+<li><a href="geom2_r.c#mindiff">qh_mindiff</a> return index of
+min absolute difference of two vectors </li>
+<li><a href="geom_r.c#normalize">qh_normalize</a> normalize a
+vector </li>
+<li><a href="geom_r.c#normalize2">qh_normalize2</a> normalize a
+vector and report if too small </li>
+<li><a href="geom2_r.c#printmatrix">qh_printmatrix</a> print
+matrix given by row vectors </li>
+<li><a href="random_r.c#rand">qh_rand/srand</a> generate random
+numbers </li>
+<li><a href="random_r.c#randomfactor">qh_randomfactor</a> return
+a random factor near 1.0 </li>
+<li><a href="random_r.c#randommatrix">qh_randommatrix</a>
+generate a random dimXdim matrix in range (-1,1) </li>
+</ul>
+
+<h3><a href="qh-geom_r.htm#TOC">&#187;</a><a name="gcomp">computational geometry functions</a></h3>
+
+<ul>
+<li><a href="geom2_r.c#detsimplex">qh_detsimplex</a> compute
+determinate of a simplex of points </li>
+<li><a href="io_r.c#detvnorm">qh_detvnorm</a> determine normal for Voronoi ridge </li>
+<li><a href="geom2_r.c#distnorm">qh_distnorm</a> compute
+distance from point to hyperplane as defined by normal and offset</li>
+<li><a href="geom2_r.c#facetarea_simplex">qh_facetarea_simplex</a>
+return area of a simplex</li>
+<li><a href="geom_r.c#getangle">qh_getangle</a> return cosine
+of angle (i.e., dot product) </li>
+<li><a href="geom_r.c#getcenter">qh_getcenter</a> return
+arithmetic center for a set of vertices </li>
+<li><a href="geom2_r.c#pointdist">qh_pointdist</a> return
+distance between two points </li>
+<li><a href="geom2_r.c#rotatepoints">qh_rotatepoints</a> rotate
+numpoints points by a row matrix </li>
+<li><a href="geom2_r.c#sethalfspace">qh_sethalfspace</a> set
+coords to dual of halfspace relative to an interior point </li>
+<li><a href="geom_r.c#sethyperplane_det">qh_sethyperplane_det</a>
+return hyperplane for oriented simplex using determinates
+</li>
+<li><a href="geom_r.c#sethyperplane_gauss">qh_sethyperplane_gauss</a>
+return hyperplane for oriented simplex using Gaussian
+elimination </li>
+<li><a href="geom2_r.c#voronoi_center">qh_voronoi_center</a>
+return Voronoi center for a set of points </li>
+</ul>
+
+<h3><a href="qh-geom_r.htm#TOC">&#187;</a><a name="gpoint">point array functions</a></h3>
+<ul>
+<li><a href="geom2_r.c#copypoints">qh_copypoints</a> return
+malloc'd copy of points</li>
+<li><a href="geom2_r.c#joggleinput">qh_joggleinput</a> joggle
+input points by qh.JOGGLEmax </li>
+<li><a href="geom2_r.c#maxmin">qh_maxmin</a> return max/min
+points for each dimension</li>
+<li><a href="geom2_r.c#maxsimplex">qh_maxsimplex</a> determines
+maximum simplex for a set of points </li>
+<li><a href="geom2_r.c#printpoints">qh_printpoints</a> print ids for a
+set of points </li>
+<li><a href="geom2_r.c#projectinput">qh_projectinput</a> project
+input using qh DELAUNAY and qh low_bound/high_bound </li>
+<li><a href="geom2_r.c#projectpoints">qh_projectpoints</a>
+project points along one or more dimensions </li>
+<li><a href="geom2_r.c#rotateinput">qh_rotateinput</a> rotate
+input points using row matrix </li>
+<li><a href="geom2_r.c#scaleinput">qh_scaleinput</a> scale
+input points using qh low_bound/high_bound </li>
+<li><a href="geom2_r.c#scalelast">qh_scalelast</a> scale last
+coordinate to [0,m] for Delaunay triangulations </li>
+<li><a href="geom2_r.c#scalepoints">qh_scalepoints</a> scale
+points to new lowbound and highbound </li>
+<li><a href="geom2_r.c#setdelaunay">qh_setdelaunay</a> project
+points to paraboloid for Delaunay triangulation </li>
+<li><a href="geom2_r.c#sethalfspace_all">qh_sethalfspace_all</a>
+generate dual for halfspace intersection with interior
+point </li>
+</ul>
+
+<h3><a href="qh-geom_r.htm#TOC">&#187;</a><a name="gfacet">geometric facet functions</a></h3>
+<ul>
+<li><a href="geom_r.c#distplane">qh_distplane</a> return
+distance from point to facet </li>
+<li><a href="geom2_r.c#facetarea">qh_facetarea</a> return area
+of a facet </li>
+<li><a href="geom2_r.c#facetcenter">qh_facetcenter</a> return
+Voronoi center for a facet's vertices </li>
+<li><a href="geom_r.c#findbest">qh_findbest</a> find visible
+facet or best facet for a point </li>
+<li><a href="geom_r.c#findbesthorizon">qh_findbesthorizon</a>
+update best new facet with horizon facets</li>
+<li><a href="geom_r.c#findbestnew">qh_findbestnew</a> find best
+new facet for point </li>
+<li><a href="geom2_r.c#getarea">qh_getarea</a> get area of all
+facets in facetlist, collect statistics </li>
+<li><a href="geom_r.c#getcentrum">qh_getcentrum</a> return
+centrum for a facet </li>
+<li><a href="geom_r.c#getdistance">qh_getdistance</a> returns
+the max and min distance of a facet's vertices to a
+neighboring facet</li>
+<li><a href="geom2_r.c#findgooddist">qh_findgooddist</a> find
+best good facet visible for point from facet </li>
+<li><a href="geom2_r.c#inthresholds">qh_inthresholds</a> return
+True if facet normal within 'Pdn' and 'PDn'</li>
+<li><a href="geom2_r.c#orientoutside">qh_orientoutside</a>
+orient facet so that <tt>qh.interior_point</tt> is inside</li>
+<li><a href="geom_r.c#projectpoint">qh_projectpoint</a> project
+point onto a facet </li>
+<li><a href="geom_r.c#setfacetplane">qh_setfacetplane</a> sets
+the hyperplane for a facet </li>
+<li><a href="geom2_r.c#sharpnewfacets">qh_sharpnewfacets</a> true
+if new facets contains a sharp corner</li>
+</ul>
+
+<h3><a href="qh-geom_r.htm#TOC">&#187;</a><a name="ground">geometric roundoff functions</a></h3>
+<ul>
+<li><a href="geom2_r.c#detjoggle">qh_detjoggle</a> determine
+default joggle for points and distance roundoff error</li>
+<li><a href="geom2_r.c#detroundoff">qh_detroundoff</a>
+determine maximum roundoff error and other precision constants</li>
+<li><a href="geom2_r.c#distround">qh_distround</a> compute
+maximum roundoff error due to a distance computation to a
+normalized hyperplane</li>
+<li><a href="geom2_r.c#divzero">qh_divzero</a> divide by a
+number that is nearly zero </li>
+<li><a href="geom2_r.c#maxouter">qh_maxouter</a> return maximum outer
+plane</li>
+<li><a href="geom2_r.c#outerinner">qh_outerinner</a> return actual
+outer and inner planes
+</ul>
+
+<p><!-- Navigation links --> </p>
+<hr>
+<p><b>Up:</b>
+<a href="http://www.qhull.org">Home page for
+Qhull</a> <br>
+<b>Up:</b> <a href="index.htm#TOC">Qhull manual: Table of Contents</a> <br>
+<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a>
+&#149; <a href="../../html/qh-quick.htm#options">Options</a>
+&#149; <a href="../../html/qh-opto.htm#output">Output</a>
+&#149; <a href="../../html/qh-optf.htm#format">Formats</a>
+&#149; <a href="../../html/qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="../../html/qh-optp.htm#print">Print</a>
+&#149; <a href="../../html/qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="../../html/qh-optc.htm#prec">Precision</a>
+&#149; <a href="../../html/qh-optt.htm#trace">Trace</a>
+&#149; <a href="index.htm">Functions</a><br>
+<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code: Table of Contents</a> <br>
+<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
+<b>To:</b> <a href="qh-geom_r.htm">Geom</a> &#149;
+<a href="qh-globa_r.htm">Global</a> &#149; <a href="qh-io_r.htm">Io</a>
+&#149; <a href="qh-mem_r.htm">Mem</a> &#149; <a href="qh-merge_r.htm">Merge</a>
+&#149; <a href="qh-poly_r.htm">Poly</a> &#149; <a href="qh-qhull_r.htm#TOC">Qhull</a>
+&#149; <a href="qh-set_r.htm">Set</a> &#149; <a href="qh-stat_r.htm">Stat</a>
+&#149; <a href="qh-user_r.htm">User</a><br>
+
+
+<p><!-- GC common information --> </p>
+<hr>
+<p><a href="http://www.geom.uiuc.edu/"><img
+src="../../html/qh--geom.gif" align="middle" width="40" height="40"></a><i>The
+Geometry Center Home Page </i></p>
+<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
+</a><br>
+Created: May 2, 1997 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
+</body>
+</html>
diff --git a/xs/src/qhull/src/libqhull_r/qh-globa_r.htm b/xs/src/qhull/src/libqhull_r/qh-globa_r.htm
new file mode 100644
index 0000000000..45437a0597
--- /dev/null
+++ b/xs/src/qhull/src/libqhull_r/qh-globa_r.htm
@@ -0,0 +1,163 @@
+<!-- Do not edit with Front Page, it adds too many spaces -->
+<html>
+<head>
+<meta http-equiv="Content-Type"
+content="text/html; charset=iso-8859-1">
+<title>global_r.c -- global variables and their functions</title>
+</head>
+
+<body>
+<!-- Navigation links -->
+<p><a name="TOP"><b>Up:</b></a> <a
+href="http://www.qhull.org">Home page</a> for Qhull<br>
+<b>Up:</b> <a href="../../html/index.htm#TOC">Qhull manual</a>: Table of Contents <br>
+<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a>
+&#149; <a href="../../html/qh-quick.htm#options">Options</a>
+&#149; <a href="../../html/qh-opto.htm#output">Output</a>
+&#149; <a href="../../html/qh-optf.htm#format">Formats</a>
+&#149; <a href="../../html/qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="../../html/qh-optp.htm#print">Print</a>
+&#149; <a href="../../html/qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="../../html/qh-optc.htm#prec">Precision</a>
+&#149; <a href="../../html/qh-optt.htm#trace">Trace</a>
+&#149; <a href="index.htm">Functions</a><br>
+<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code: Table of Contents</a><br>
+<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
+<b>To:</b> <a href="qh-geom_r.htm">Geom</a> &#149; <a href="qh-globa_r.htm#TOC">Global</a>
+&#149; <a href="qh-io_r.htm">Io</a> &#149; <a href="qh-mem_r.htm">Mem</a>
+&#149; <a href="qh-merge_r.htm">Merge</a> &#149; <a href="qh-poly_r.htm">Poly</a>
+&#149; <a href="qh-qhull_r.htm">Qhull</a> &#149; <a href="qh-set_r.htm">Set</a>
+&#149; <a href="qh-stat_r.htm">Stat</a> &#149; <a href="qh-user_r.htm">User</a>
+</p>
+
+<hr>
+<!-- Main text of document. -->
+
+<h2>global_r.c -- global variables and their functions</h2>
+<blockquote>
+<p>Qhull uses a data structure, <tt>qhT</tt>, to store
+globally defined constants, lists, sets, and variables. It is passed as the
+first argument to most functions.
+</p>
+</blockquote>
+<p><b>Copyright &copy; 1995-2015 C.B. Barber</b></p>
+<hr>
+<p><a href="#TOP">&#187;</a> <a href="qh-geom_r.htm#TOC">Geom</a>
+<a name="TOC">&#149;</a> <b>Global</b> &#149;
+<a href="qh-io_r.htm#TOC">Io</a> &#149; <a href="qh-mem_r.htm#TOC">Mem</a> &#149;
+<a href="qh-merge_r.htm#TOC">Merge</a> &#149; <a href="qh-poly_r.htm#TOC">Poly</a> &#149;
+<a href="qh-qhull_r.htm#TOC">Qhull</a> &#149; <a href="qh-set_r.htm#TOC">Set</a> &#149;
+<a href="qh-stat_r.htm#TOC">Stat</a> &#149; <a href="qh-user_r.htm#TOC">User</a> </p>
+
+<h3>Index to <a href="global_r.c">global_r.c</a> and
+<a href="libqhull_r.h">libqhull_r.h</a></h3>
+
+<ul>
+<li><a href="#ovar">Qhull's global variables</a> </li>
+<li><a href="#ofunc">Global variable and initialization
+routines</a> </li>
+</ul>
+
+<h3><a href="qh-globa_r.htm#TOC">&#187;</a><a name="ovar">Qhull's global
+variables</a></h3>
+
+<ul>
+<li><a href=global_r.c#qh_version>qh_version</a> version string
+<li><a href="libqhull_r.h#qh">qh</a> all global variables for
+qhull are in <tt>qh,qhmem</tt>, and <tt>qhstat</tt></li>
+<li><a href="libqhull_r.h#qh">QHULL_LIB_CHECK</a> Check for compatible library</li>
+<li><a href="libqhull_r.h#qh-const">qh constants</a> configuration
+flags and constants for Qhull </li>
+<li><a href="libqhull_r.h#qh-prec">qh precision constants</a>
+precision constants for Qhull </li>
+<li><a href="libqhull_r.h#qh-codetern">qh internal constants</a>
+internal constants for Qhull </li>
+<li><a href="libqhull_r.h#qh-lists">qh facet and vertex lists</a>
+lists of facets and vertices </li>
+<li><a href="libqhull_r.h#qh-var">qh global variables</a> minimum
+and maximum distances, next visit ids, several flags, and
+other global variables. </li>
+<li><a href="libqhull_r.h#qh-set">qh global sets</a> global sets
+for merging, hashing, input, etc. </li>
+<li><a href="libqhull_r.h#qh-buf">qh global buffers</a> buffers
+for matrix operations and input </li>
+<li><a href="libqhull_r.h#qh-static">qh static variables</a>
+static variables for individual functions </li>
+</ul>
+
+<h3><a href="qh-globa_r.htm#TOC">&#187;</a><a name="ofunc">Global variable and
+initialization routines</a></h3>
+
+<ul>
+<li><a href="global_r.c#appendprint">qh_appendprint</a> append
+output format to <tt>qh.PRINTout</tt> </li>
+<li><a href="global_r.c#freebuffers">qh_freebuffers</a> free
+global memory buffers </li>
+<li><a href="global_r.c#freeqhull">qh_freeqhull</a> free memory
+used by qhull </li>
+<li><a href="global_r.c#init_A">qh_init_A</a> called before
+error handling initialized </li>
+<li><a href="global_r.c#init_B">qh_init_B</a> called after
+points are defined </li>
+<li><a href="global_r.c#init_qhull_command">qh_init_qhull_command</a>
+build <tt>qh.qhull_command</tt> from <tt>argc/argv</tt></li>
+<li><a href="global_r.c#initflags">qh_initflags</a> set flags
+and constants from command line </li>
+<li><a href="global_r.c#initqhull_buffers">qh_initqhull_buffers</a>
+initialize global memory buffers </li>
+<li><a href="global_r.c#initqhull_globals">qh_initqhull_globals</a>
+initialize global variables </li>
+<li><a href="global_r.c#initqhull_mem">qh_initqhull_mem</a>
+initialize Qhull memory management </li>
+<li><a href="global_r.c#initqhull_start">qh_initqhull_start</a>
+allocate qh_qh and call qh_initqhull_start2()
+<li><a href="global_r.c#initqhull_start2">qh_initqhull_start2</a>
+initialize default values at Qhull startup </li>
+<li><a href="global_r.c#initthresholds">qh_initthresholds</a>
+initialize 'Pdn' and 'PDn' thresholds </li>
+<li><a href="global_r.c#lib_check">qh_lib_check</a> check for compatible Qhull library.  Invoked by QHULL_LIB_CHECK at start of each program.</li>
+<li><a href="global_r.c#option">qh_option</a> append option
+description to <tt>qh.global_options</tt> </li>
+<li><a href="global_r.c#restore_qhull">qh_restore_qhull</a>
+restores a previously saved qhull </li>
+<li><a href="global_r.c#save_qhull">qh_save_qhull</a> saves
+qhull for a later qh_restore_qhull() </li>
+<li><a href="global_r.c#strtol">qh_strtol</a> duplicates
+strtod() and strtol() </li>
+<li><a href="global_r.c#zero">qh_zero</a> zeroes qhT before first use</li>
+</ul>
+
+<p><!-- Navigation links --> </p>
+<hr>
+<p><b>Up:</b>
+<a href="http://www.qhull.org">Home page for
+Qhull</a> <br>
+<b>Up:</b> <a href="../../html/index.htm#TOC">Qhull manual: Table of Contents</a> <br>
+<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a>
+&#149; <a href="../../html/qh-quick.htm#options">Options</a>
+&#149; <a href="../../html/qh-opto.htm#output">Output</a>
+&#149; <a href="../../html/qh-optf.htm#format">Formats</a>
+&#149; <a href="../../html/qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="../../html/qh-optp.htm#print">Print</a>
+&#149; <a href="../../html/qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="../../html/qh-optc.htm#prec">Precision</a>
+&#149; <a href="../../html/qh-optt.htm#trace">Trace</a>
+&#149; <a href="index.htm">Functions</a><br>
+<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code: Table of Contents</a> <br>
+<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
+<b>To:</b> <a href="qh-geom_r.htm">Geom</a> &#149;
+<a href="qh-globa_r.htm">Global</a> &#149; <a href="qh-io_r.htm">Io</a>
+&#149; <a href="qh-mem_r.htm">Mem</a> &#149; <a href="qh-merge_r.htm">Merge</a>
+&#149; <a href="qh-poly_r.htm">Poly</a> &#149; <a href="qh-qhull_r.htm#TOC">Qhull</a>
+&#149; <a href="qh-set_r.htm">Set</a> &#149; <a href="qh-stat_r.htm">Stat</a>
+&#149; <a href="qh-user_r.htm">User</a><br>
+<p><!-- GC common information --> </p>
+<hr>
+<p><a href="http://www.geom.uiuc.edu/"><img
+src="../../html/qh--geom.gif" align="middle" width="40" height="40"></a><i>The
+Geometry Center Home Page </i></p>
+<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
+</a><br>
+Created: May 2, 1997 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
+</body>
+</html>
diff --git a/xs/src/qhull/src/libqhull_r/qh-io_r.htm b/xs/src/qhull/src/libqhull_r/qh-io_r.htm
new file mode 100644
index 0000000000..8a8a96300f
--- /dev/null
+++ b/xs/src/qhull/src/libqhull_r/qh-io_r.htm
@@ -0,0 +1,305 @@
+<!-- Do not edit with Front Page, it adds too many spaces -->
+<html>
+<head>
+<meta http-equiv="Content-Type"
+content="text/html; charset=iso-8859-1">
+<title>io_r.c -- input and output operations</title>
+</head>
+
+<body>
+<!-- Navigation links -->
+<p><a name="TOP"><b>Up:</b></a> <a
+href="http://www.qhull.org">Home page</a> for Qhull<br>
+<b>Up:</b> <a href="../../html/index.htm#TOC">Qhull manual</a>: Table of Contents <br>
+<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a>
+&#149; <a href="../../html/qh-quick.htm#options">Options</a>
+&#149; <a href="../../html/qh-opto.htm#output">Output</a>
+&#149; <a href="../../html/qh-optf.htm#format">Formats</a>
+&#149; <a href="../../html/qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="../../html/qh-optp.htm#print">Print</a>
+&#149; <a href="../../html/qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="../../html/qh-optc.htm#prec">Precision</a>
+&#149; <a href="../../html/qh-optt.htm#trace">Trace</a>
+&#149; <a href="index.htm">Functions</a><br>
+<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code: Table of Contents</a><br>
+<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
+<b>To:</b> <a href="qh-geom_r.htm">Geom</a> &#149; <a href="qh-globa_r.htm">Global</a>
+&#149; <a href="qh-io_r.htm#TOC">Io</a> &#149; <a href="qh-mem_r.htm">Mem</a>
+&#149; <a href="qh-merge_r.htm">Merge</a> &#149; <a href="qh-poly_r.htm">Poly</a>
+&#149; <a href="qh-qhull_r.htm">Qhull</a> &#149; <a href="qh-set_r.htm">Set</a>
+&#149; <a href="qh-stat_r.htm">Stat</a> &#149; <a href="qh-user_r.htm">User</a>
+</p>
+<hr>
+
+<h2>io_r.c -- input and output operations</h2>
+<blockquote>
+
+<p>Qhull provides a wide range of input
+and output options. To organize the code, most output formats use
+the same driver: </p>
+
+<pre>
+    qh_printbegin( fp, format, facetlist, facets, printall );
+
+    FORALLfacet_( facetlist )
+      qh_printafacet( fp, format, facet, printall );
+
+    FOREACHfacet_( facets )
+      qh_printafacet( fp, format, facet, printall );
+
+    qh_printend( fp, format );
+</pre>
+
+<p>Note the 'printall' flag. It selects whether or not
+qh_skipfacet() is tested. </p>
+
+</blockquote>
+<p><b>Copyright &copy; 1995-2015 C.B. Barber</b></p>
+<hr>
+<p><a href="#TOP">&#187;</a> <a href="qh-geom_r.htm#TOC">Geom</a> <a name="TOC">&#149;</a>
+<a href="qh-globa_r.htm#TOC">Global</a> &#149; <b>Io</b> &#149;
+<a href="qh-mem_r.htm#TOC">Mem</a> &#149; <a href="qh-merge_r.htm#TOC">Merge</a> &#149;
+<a href="qh-poly_r.htm#TOC">Poly</a> &#149; <a href="qh-qhull_r.htm#TOC">Qhull</a> &#149;
+<a href="qh-set_r.htm#TOC">Set</a> &#149; <a href="qh-stat_r.htm#TOC">Stat</a> &#149;
+<a href="qh-user_r.htm#TOC">User</a> </p>
+
+<h3>Index to <a href="io_r.c">io_r.c</a> and <a href="io_r.h">io_r.h</a></h3>
+
+<ul>
+<li><a href="#iconst">io_r.h constants and types</a> </li>
+<li><a href="#ilevel">User level functions</a> </li>
+<li><a href="#iprint">Print functions for all output formats</a></li>
+<li><a href="#itext">Text output functions</a> </li>
+<li><a href="#iutil">Text utility functions</a></li>
+<li><a href="#igeom">Geomview output functions</a> </li>
+<li><a href="#iview">Geomview utility functions</a></li>
+</ul>
+
+<h3><a href="qh-io_r.htm#TOC">&#187;</a><a name="iconst">io_r.h constants and types</a></h3>
+
+<ul>
+<li><a href="io_r.h#qh_MAXfirst">qh_MAXfirst</a> maximum length
+of first two lines of stdin </li>
+<li><a href="io_r.h#qh_WHITESPACE">qh_WHITESPACE</a> possible
+values of white space </li>
+<li><a href="io_r.h#printvridgeT">printvridgeT</a> function to
+print results of qh_printvdiagram or qh_eachvoronoi</li>
+</ul>
+
+<h3><a href="qh-io_r.htm#TOC">&#187;</a><a name="ilevel">User level functions</a></h3>
+
+<ul>
+<li><a href="io_r.c#copyfilename">qh_copyfilename</a>
+copy filename identified by qh_skipfilename
+<li><a href="io_r.c#eachvoronoi_all">qh_eachvoronoi_all</a>
+visit each Voronoi ridge of the Voronoi diagram
+<li><a href="io_r.c#prepare_output">qh_prepare_output</a>
+prepare Qhull for output (called by qh_produce_output())
+<li><a href="io_r.c#printhelp_degenerate">qh_printhelp_degenerate</a>
+prints descriptive message for precision error </li>
+<li><a href="io_r.c#printhelp_singular">qh_printhelp_singular</a>
+print help message for singular data </li>
+<li><a href="libqhull_r.c#printsummary">qh_printsummary</a> print
+summary ('s')</li>
+<li><a href="io_r.c#produce_output">qh_produce_output</a>
+prints out the result of qhull()</li>
+<li><a href="io_r.c#produce_output">qh_produce_output2</a>
+prints out the result of qhull() without calling qh_prepare_output()</li>
+<li><a href="io_r.c#readfeasible">qh_readfeasible</a> read
+interior point from remainder and qh fin ('H')</li>
+<li><a href="io_r.c#readpoints">qh_readpoints</a> read input
+points </li>
+<li><a href="io_r.c#setfeasible">qh_setfeasible</a> set
+interior point from qh feasible_string ('Hn,n,n')</li>
+<li><a href="io_r.c#skipfilename">qh_skipfilename</a>
+skip filename in string
+</ul>
+
+<h3><a href="qh-io_r.htm#TOC">&#187;</a><a name="iprint">Print functions for all
+output formats</a></h3>
+
+<ul>
+<li><a href="io_r.c#countfacets">qh_countfacets</a> count good
+facets for printing and set visitid </li>
+<li><a href="io_r.c#markkeep">qh_markkeep</a> mark good facets
+that meet qh.KEEParea ('PAn'), qh.KEEPmerge ('PMn'), and qh.KEEPminArea ('PFn')</li>
+<li><a href="io_r.c#order_vertexneighbors">qh_order_vertexneighbors</a>
+order neighbors for a 3-d vertex by adjacency ('i', 'o')</li>
+<li><a href="io_r.c#printafacet">qh_printafacet</a> print facet
+in an output format </li>
+<li><a href="io_r.c#printbegin">qh_printbegin</a> print header
+for an output format </li>
+<li><a href="io_r.c#printend">qh_printend</a> print trailer for
+an output format </li>
+<li><a href="user_r.c#printfacetlist">qh_printfacetlist</a>
+print facets in a facetlist</li>
+<li><a href="io_r.c#printfacets">qh_printfacets</a> print
+facetlist and/or facet set in an output format </li>
+<li><a href="io_r.c#printneighborhood">qh_printneighborhood</a>
+print neighborhood of one or two facets ('Po')</li>
+<li><a href="io_r.c#produce_output">qh_produce_output</a>
+print the results of qh_qhull() </li>
+<li><a href="io_r.c#skipfacet">qh_skipfacet</a> True if not
+printing this facet ('Pdk:n', 'QVn', 'QGn')</li>
+<li><a href="io_r.c#facetvertices">qh_facetvertices</a> return
+vertices in a set of facets ('p')</li>
+</ul>
+
+<h3><a href="qh-io_r.htm#TOC">&#187;</a><a name="itext">Text output functions</a></h3>
+<ul>
+<li><a href="io_r.c#eachvoronoi">qh_eachvoronoi</a>
+print or visit each Voronoi ridge for an input site of the Voronoi diagram
+<li><a href="io_r.c#printextremes">qh_printextremes</a> print
+extreme points by point ID (vertices of convex hull) ('Fx')</li>
+<li><a href="io_r.c#printextremes_2d">qh_printextremes_2d</a> print
+2-d extreme points by point ID ('Fx')</li>
+<li><a href="io_r.c#printextremes_d">qh_printextremes_d</a> print
+extreme points of input sites for Delaunay triangulations ('Fx')</li>
+<li><a href="io_r.c#printfacet">qh_printfacet</a> print all
+fields of a facet ('f')</li>
+<li><a href="io_r.c#printfacet2math">qh_printfacet2math</a> print
+2-d Maple or Mathematica output for a facet ('FM' or 'm')</li>
+<li><a href="io_r.c#printfacet3math">qh_printfacet3math</a>
+print 3-d Maple or Mathematica facet ('FM' or 'm')</li>
+<li><a href="io_r.c#printfacet3vertex">qh_printfacet3vertex</a>
+print vertices for a 3-d facet ('i', 'o')</li>
+<li><a href="io_r.c#printfacetheader">qh_printfacetheader</a>
+prints header fields of a facet ('f')</li>
+<li><a href="io_r.c#printfacetNvertex_nonsimplicial">qh_printfacetNvertex_nonsimplicial</a>
+print vertices for an N-d non-simplicial facet ('i', 'Ft')</li>
+<li><a href="io_r.c#printfacetNvertex_simplicial">qh_printfacetNvertex_simplicial</a>
+print vertices for an N-d simplicial facet ('i', 'o', 'Ft')</li>
+<li><a href="io_r.c#printfacetridges">qh_printfacetridges</a>
+prints ridges of a facet ('f')</li>
+<li><a href="io_r.c#printpoints_out">qh_printpoints_out</a> prints
+vertices for facets by their point coordinates ('p')</li>
+<li><a href="io_r.c#printridge">qh_printridge</a> print all
+fields for a ridge ('f')</li>
+<li><a href="io_r.c#printvdiagram">qh_printvdiagram</a> print
+voronoi diagram as Voronoi vertices for each input pair</li>
+<li><a href="io_r.c#printvertex">qh_printvertex</a> print all
+fields for a vertex ('f')</li>
+<li><a href="io_r.c#printvertexlist">qh_printvertexlist</a>
+print vertices used by a list or set of facets ('f')</li>
+<li><a href="io_r.c#printvertices">qh_printvertices</a> print a
+set of vertices ('f')</li>
+<li><a href="io_r.c#printvneighbors">qh_printvneighbors</a>
+print vertex neighbors of vertices ('FN')</li>
+<li><a href="io_r.c#printvoronoi">qh_printvoronoi</a> print
+voronoi diagram in 'o' or 'G' format</li>
+</ul>
+
+<h3><a href="qh-io_r.htm#TOC">&#187;</a><a name="iutil">Text utility functions</a></h3>
+<ul>
+<li><a href="io_r.c#dfacet">dfacet</a> print facet by ID </li>
+<li><a href="io_r.c#dvertex">dvertex</a> print vertex by ID </li>
+<li><a href="io_r.c#compare_facetarea">qh_compare_facetarea</a>
+used by qsort() to order facets by area </li>
+<li><a href="io_r.c#compare_facetmerge">qh_compare_facetmerge</a>
+used by qsort() to order facets by number of merges </li>
+<li><a href="io_r.c#compare_facetvisit">qh_compare_facetvisit</a>
+used by qsort() to order facets by visit ID or ID </li>
+<li><a href="io_r.c#compare_vertexpoint">qh_compare_vertexpoint</a>
+used by qsort() to order vertices by point ID </li>
+<li><a href="io_r.c#detvnorm">qh_detvnorm</a> determine normal for Voronoi ridge </li>
+<li><a href="io_r.c#detvridge">qh_detvridge</a> determine Voronoi
+ridge for an input site
+<li><a href="io_r.c#detvridge3">qh_detvridge3</a> determine 3-d Voronoi
+ridge for an input site
+<li><a href="io_r.c#facet2point">qh_facet2point</a> return two
+projected temporary vertices for a 2-d facet ('m', 'G')</li>
+<li><a href="io_r.c#markvoronoi">qh_markvoronoi</a> mark Voronoi
+vertices for printing
+<li><a href="io_r.c#printcenter">qh_printcenter</a> print
+facet-&gt;center as centrum or Voronoi center ('Ft', 'v p', 'FC', 'f') </li>
+<li><a href="io_r.c#printpoint">qh_printpoint</a>, qh_printpointid, print
+coordinates of a point ('p', 'o', 'Fp', 'G', 'f')</li>
+<li><a href="io_r.c#printpoint3">qh_printpoint3</a> prints 2-d,
+3-d, or 4-d point as 3-d coordinates ('G')</li>
+<li><a href="io_r.c#printvdiagram2">qh_printvdiagram2</a> print
+voronoi diagram for each ridge of each vertex from qh_markvoronoi</li>
+<li><a href="io_r.c#printvnorm">qh_printvnorm</a> print
+separating plane of the Voronoi diagram for a pair of input sites</li>
+<li><a href="io_r.c#printvridge">qh_printvridge</a> print
+ridge of the Voronoi diagram for a pair of input sites</li>
+<li><a href="io_r.c#projectdim3">qh_projectdim3</a> project 2-d
+3-d or 4-d point to a 3-d point ('G')</li>
+</ul>
+
+<h3><a href="qh-io_r.htm#TOC">&#187;</a><a name="igeom">Geomview output functions</a></h3>
+<ul>
+<li><a href="io_r.c#printfacet2geom">qh_printfacet2geom</a>
+print facet as a 2-d VECT object </li>
+<li><a href="io_r.c#printfacet2geom_points">qh_printfacet2geom_points</a>
+print points as a 2-d VECT object with offset </li>
+<li><a href="io_r.c#printfacet3geom_nonsimplicial">qh_printfacet3geom_nonsimplicial</a>
+print Geomview OFF for a 3-d nonsimplicial facet. </li>
+<li><a href="io_r.c#printfacet3geom_points">qh_printfacet3geom_points</a>
+prints a 3-d facet as OFF Geomview object. </li>
+<li><a href="io_r.c#printfacet3geom_simplicial">qh_printfacet3geom_simplicial</a>
+print Geomview OFF for a 3-d simplicial facet. </li>
+<li><a href="io_r.c#printfacet4geom_nonsimplicial">qh_printfacet4geom_nonsimplicial</a>
+print Geomview 4OFF file for a 4d nonsimplicial facet </li>
+<li><a href="io_r.c#printfacet4geom_simplicial">qh_printfacet4geom_simplicial</a>
+print Geomview 4OFF file for a 4d simplicial facet </li>
+<li><a href="io_r.c#printhyperplaneintersection">qh_printhyperplaneintersection</a>
+print hyperplane intersection as OFF or 4OFF </li>
+<li><a href="io_r.c#printvoronoi">qh_printvoronoi</a> print
+voronoi diagram in 'o' or 'G' format</li>
+</ul>
+<h3><a href="qh-io_r.htm#TOC">&#187;</a><a name="iview">Geomview utility functions</a></h3>
+<ul>
+<li><a href="io_r.c#geomplanes">qh_geomplanes</a>
+    return outer and inner planes for Geomview</li>
+<li><a href="io_r.c#printcentrum">qh_printcentrum</a> print
+centrum for a facet in OOGL format </li>
+<li><a href="io_r.c#printend4geom">qh_printend4geom</a> helper
+function for qh_printbegin/printend </li>
+<li><a href="io_r.c#printhyperplaneintersection">qh_printhyperplaneintersection</a>
+print Geomview OFF or 4OFF for the intersection of two
+hyperplanes in 3-d or 4-d </li>
+<li><a href="io_r.c#printline3geom">qh_printline3geom</a> prints a
+line as a VECT </li>
+<li><a href="io_r.c#printpointvect">qh_printpointvect</a>
+prints a 2-d or 3-d point as 3-d VECT's </li>
+<li><a href="io_r.c#printpointvect2">qh_printpointvect2</a>
+prints a 2-d or 3-d point as 2 3-d VECT's </li>
+<li><a href="io_r.c#printspheres">qh_printspheres</a> prints 3-d
+vertices as OFF spheres </li>
+</ul>
+<p>
+<p><!-- Navigation links --> </p>
+<hr>
+<p><b>Up:</b>
+<a href="http://www.qhull.org">Home page for
+Qhull</a> <br>
+<b>Up:</b> <a href="../../html/index.htm#TOC">Qhull manual: Table of Contents</a> <br>
+<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a>
+&#149; <a href="../../html/qh-quick.htm#options">Options</a>
+&#149; <a href="../../html/qh-opto.htm#output">Output</a>
+&#149; <a href="../../html/qh-optf.htm#format">Formats</a>
+&#149; <a href="../../html/qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="../../html/qh-optp.htm#print">Print</a>
+&#149; <a href="../../html/qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="../../html/qh-optc.htm#prec">Precision</a>
+&#149; <a href="../../html/qh-optt.htm#trace">Trace</a>
+&#149; <a href="index.htm">Functions</a><br>
+<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code: Table of Contents</a> <br>
+<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
+<b>To:</b> <a href="qh-geom_r.htm">Geom</a> &#149;
+<a href="qh-globa_r.htm">Global</a> &#149; <a href="qh-io_r.htm">Io</a>
+&#149; <a href="qh-mem_r.htm">Mem</a> &#149; <a href="qh-merge_r.htm">Merge</a>
+&#149; <a href="qh-poly_r.htm">Poly</a> &#149; <a href="qh-qhull_r.htm#TOC">Qhull</a>
+&#149; <a href="qh-set_r.htm">Set</a> &#149; <a href="qh-stat_r.htm">Stat</a>
+&#149; <a href="qh-user_r.htm">User</a><br>
+</p>
+<p><!-- GC common information --> </p>
+<hr>
+<p><a href="http://www.geom.uiuc.edu/"><img
+src="../../html/qh--geom.gif" align="middle" width="40" height="40"></a><i>The
+Geometry Center Home Page </i></p>
+<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
+</a><br>
+Created: May 2, 1997 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
+</body>
+</html>
diff --git a/xs/src/qhull/src/libqhull_r/qh-mem_r.htm b/xs/src/qhull/src/libqhull_r/qh-mem_r.htm
new file mode 100644
index 0000000000..db59119cb9
--- /dev/null
+++ b/xs/src/qhull/src/libqhull_r/qh-mem_r.htm
@@ -0,0 +1,145 @@
+<!-- Do not edit with Front Page, it adds too many spaces -->
+<html>
+<head>
+<meta http-equiv="Content-Type"
+content="text/html; charset=iso-8859-1">
+<title>mem_r.c -- memory operations</title>
+</head>
+
+<body>
+<!-- Navigation links -->
+<p><a name="TOP"><b>Up:</b></a> <a
+href="http://www.qhull.org">Home page</a> for Qhull<br>
+<b>Up:</b> <a href="../../html/index.htm#TOC">Qhull manual</a>: Table of Contents <br>
+<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a>
+&#149; <a href="../../html/qh-quick.htm#options">Options</a>
+&#149; <a href="../../html/qh-opto.htm#output">Output</a>
+&#149; <a href="../../html/qh-optf.htm#format">Formats</a>
+&#149; <a href="../../html/qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="../../html/qh-optp.htm#print">Print</a>
+&#149; <a href="../../html/qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="../../html/qh-optc.htm#prec">Precision</a>
+&#149; <a href="../../html/qh-optt.htm#trace">Trace</a>
+&#149; <a href="index.htm">Functions</a><br>
+<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code: Table of Contents</a><br>
+<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
+<b>To:</b> <a href="qh-geom_r.htm">Geom</a> &#149; <a href="qh-globa_r.htm">Global</a>
+&#149; <a href="qh-io_r.htm">Io</a> &#149; <a href="qh-mem_r.htm#TOC">Mem</a>
+&#149; <a href="qh-merge_r.htm">Merge</a> &#149; <a href="qh-poly_r.htm">Poly</a>
+&#149; <a href="qh-qhull_r.htm">Qhull</a> &#149; <a href="qh-set_r.htm">Set</a>
+&#149; <a href="qh-stat_r.htm">Stat</a> &#149; <a href="qh-user_r.htm">User</a>
+</p>
+<hr>
+
+<h2>mem_r.c -- memory operations</h2>
+<blockquote>
+<p>Qhull uses quick-fit memory allocation. It maintains a
+set of free lists for a variety of small allocations. A
+small request returns a block from the best fitting free
+list. If the free list is empty, Qhull allocates a block
+from a reserved buffer. </p>
+<p>Use 'T5' to trace memory allocations.</p>
+
+</blockquote>
+<p><b>Copyright &copy; 1995-2015 C.B. Barber</b></p>
+<hr>
+<p><a href="#TOP">&#187;</a> <a href="qh-geom_r.htm#TOC">Geom</a>
+<a name="TOC">&#149;</a> <a href="qh-globa_r.htm#TOC">Global</a> &#149;
+<a href="qh-io_r.htm#TOC">Io</a> &#149; <b>Mem</b>
+&#149; <a href="qh-merge_r.htm#TOC">Merge</a> &#149; <a href="qh-poly_r.htm#TOC">Poly</a>
+&#149; <a href="qh-qhull_r.htm#TOC">Qhull</a> &#149; <a href="qh-set_r.htm#TOC">Set</a>
+&#149; <a href="qh-stat_r.htm#TOC">Stat</a> &#149; <a href="qh-user_r.htm#TOC">User</a>
+</p>
+<h3>Index to <a href="mem_r.c">mem_r.c</a> and
+<a href="mem_r.h">mem_r.h</a></h3>
+<ul>
+<li><a href="#etype">mem_r.h data types</a> </li>
+<li><a href="#emacro">mem_r.h macros</a> </li>
+<li><a href="#efunc">User level functions</a> </li>
+</ul>
+<h3><a href="qh-mem_r.htm#TOC">&#187;</a><a name="etype">mem_r.h data types and constants</a></h3>
+<ul>
+<li><a href="mem_r.h#ptr_intT">ptr_intT</a> for casting
+a void* to an integer-type </li>
+<li><a href="mem_r.h#qhmemT">qhmemT</a> global memory
+structure for mem_r.c </li>
+<li><a href="mem_r.h#NOmem">qh_NOmem</a> disable memory allocation</li>
+</ul>
+<h3><a href="qh-mem_r.htm#TOC">&#187;</a><a name="emacro">mem_r.h macros</a></h3>
+<ul>
+<li><a href="mem_r.h#memalloc_">qh_memalloc_</a>
+allocate memory</li>
+<li><a href="mem_r.h#memfree_">qh_memfree_</a> free
+memory</li>
+</ul>
+<h3><a href="qh-mem_r.htm#TOC">&#187;</a><a name="efunc">User level
+functions</a></h3>
+<ul>
+<li><a href="mem_r.c#memalloc">qh_memalloc</a> allocate
+memory </li>
+<li><a href="mem_r.c#memcheck">qh_memcheck</a>
+quick check of memory for internal consistency</li>
+<li><a href="mem_r.c#memfree">qh_memfree</a> free
+memory </li>
+<li><a href="mem_r.c#meminit">qh_meminit</a> initialize
+memory </li>
+<li><a href="mem_r.c#memstatistics">qh_memstatistics</a>
+print memory statistics </li>
+<li><a href="mem_r.c#meminit">qh_memtotlong</a> return total, allocated long memory</li>
+<li><a href="mem_r.c#NOmem">qh_NOmem</a> allocation routines with malloc() and free()
+</ul>
+
+<h3><a href="qh-mem_r.htm#TOC">&#187;</a><a name="m">Initialization and
+termination functions</a></h3>
+<ul>
+<li><a href="mem_r.c#intcompare">qh_intcompare</a> used by
+qsort and bsearch to compare two integers </li>
+<li><a href="mem_r.c#memfreeshort">qh_memfreeshort</a>
+frees up all short and qhmem memory allocations </li>
+<li><a href="mem_r.c#meminit">qh_meminit</a> initialize
+memory </li>
+<li><a href="mem_r.c#meminitbuffers">qh_meminitbuffers</a>
+initialize qhmem </li>
+<li><a href="mem_r.c#memsetup">qh_memsetup</a> set up
+memory after running memsize() </li>
+<li><a href="mem_r.c#memsize">qh_memsize</a> define a free
+list for this size </li>
+<li><a href="mem_r.c#memstatistics">qh_memstatistics</a>
+print out memory statistics </li>
+</ul>
+
+<p><!-- Navigation links --> </p>
+<hr>
+<p><b>Up:</b>
+<a href="http://www.qhull.org">Home page for
+Qhull</a> <br>
+<b>Up:</b> <a href="../../html/index.htm#TOC">Qhull manual: Table of Contents</a> <br>
+<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a>
+&#149; <a href="../../html/qh-quick.htm#options">Options</a>
+&#149; <a href="../../html/qh-opto.htm#output">Output</a>
+&#149; <a href="../../html/qh-optf.htm#format">Formats</a>
+&#149; <a href="../../html/qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="../../html/qh-optp.htm#print">Print</a>
+&#149; <a href="../../html/qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="../../html/qh-optc.htm#prec">Precision</a>
+&#149; <a href="../../html/qh-optt.htm#trace">Trace</a>
+&#149; <a href="index.htm">Functions</a><br>
+<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code: Table of Contents</a> <br>
+<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
+<b>To:</b> <a href="qh-geom_r.htm">Geom</a> &#149;
+<a href="qh-globa_r.htm">Global</a> &#149; <a href="qh-io_r.htm">Io</a>
+&#149; <a href="qh-mem_r.htm">Mem</a> &#149; <a href="qh-merge_r.htm">Merge</a>
+&#149; <a href="qh-poly_r.htm">Poly</a> &#149; <a href="qh-qhull_r.htm#TOC">Qhull</a>
+&#149; <a href="qh-set_r.htm">Set</a> &#149; <a href="qh-stat_r.htm">Stat</a>
+&#149; <a href="qh-user_r.htm">User</a><br>
+</p>
+<p><!-- GC common information --> </p>
+<hr>
+<p><a href="http://www.geom.uiuc.edu/"><img
+src="../../html/qh--geom.gif" align="middle" width="40" height="40"></a><i>The
+Geometry Center Home Page </i></p>
+<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
+</a><br>
+Created: May 2, 1997 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
+</body>
+</html>
diff --git a/xs/src/qhull/src/libqhull_r/qh-merge_r.htm b/xs/src/qhull/src/libqhull_r/qh-merge_r.htm
new file mode 100644
index 0000000000..63e5135be1
--- /dev/null
+++ b/xs/src/qhull/src/libqhull_r/qh-merge_r.htm
@@ -0,0 +1,366 @@
+<!-- Do not edit with Front Page, it adds too many spaces -->
+<html>
+<head>
+<meta http-equiv="Content-Type"
+content="text/html; charset=iso-8859-1">
+<title>merge_r.c -- facet merge operations</title>
+</head>
+
+<body>
+<!-- Navigation links -->
+<p><a name="TOP"><b>Up:</b></a> <a
+href="http://www.qhull.org">Home page</a> for Qhull<br>
+<b>Up:</b> <a href="../../html/index.htm#TOC">Qhull manual</a>: Table of Contents <br>
+<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a>
+&#149; <a href="../../html/qh-quick.htm#options">Options</a>
+&#149; <a href="../../html/qh-opto.htm#output">Output</a>
+&#149; <a href="../../html/qh-optf.htm#format">Formats</a>
+&#149; <a href="../../html/qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="../../html/qh-optp.htm#print">Print</a>
+&#149; <a href="../../html/qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="../../html/qh-optc.htm#prec">Precision</a>
+&#149; <a href="../../html/qh-optt.htm#trace">Trace</a>
+&#149; <a href="index.htm">Functions</a><br>
+<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code: Table of Contents</a><br>
+<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
+<b>To:</b> <a href="qh-geom_r.htm">Geom</a> &#149; <a href="qh-globa_r.htm">Global</a>
+&#149; <a href="qh-io_r.htm">Io</a> &#149; <a href="qh-mem_r.htm">Mem</a>
+&#149; <a href="qh-merge_r.htm#TOC">Merge</a> &#149; <a href="qh-poly_r.htm">Poly</a>
+&#149; <a href="qh-qhull_r.htm">Qhull</a> &#149; <a href="qh-set_r.htm">Set</a>
+&#149; <a href="qh-stat_r.htm">Stat</a> &#149; <a href="qh-user_r.htm">User</a>
+</p>
+<hr>
+
+<h2>merge_r.c -- facet merge operations</h2>
+<blockquote>
+<p>Qhull handles precision problems by merged facets or joggled input.
+Except for redundant vertices, it corrects a problem by
+merging two facets. When done, all facets are clearly
+convex. See <a href="../../html/qh-impre.htm">Imprecision in Qhull</a>
+for further information. </p>
+<p>Users may joggle the input ('<a href="../../html/qh-optq.htm#QJn">QJn</a>')
+instead of merging facets. </p>
+<p>Qhull detects and corrects the following problems: </p>
+<ul>
+<li><b>More than two facets meeting at a ridge. </b>When
+Qhull creates facets, it creates an even number
+of facets for each ridge. A convex hull always
+has two facets for each ridge. More than two
+facets may be created if non-adjacent facets
+share a vertex. This is called a <em>duplicate
+ridge</em>. In 2-d, a duplicate ridge would
+create a loop of facets. </li>
+</ul>
+<ul>
+<li><b>A facet contained in another facet. </b>Facet
+merging may leave all vertices of one facet as a
+subset of the vertices of another facet. This is
+called a <em>redundant facet</em>. </li>
+</ul>
+<ul>
+<li><b>A facet with fewer than three neighbors. </b>Facet
+merging may leave a facet with one or two
+neighbors. This is called a <em>degenerate facet</em>.
+</li>
+</ul>
+<ul>
+<li><b>A facet with flipped orientation. </b>A
+facet's hyperplane may define a halfspace that
+does not include the interior point.This is
+called a <em>flipped facet</em>. </li>
+</ul>
+<ul>
+<li><strong>A coplanar horizon facet.</strong> A
+newly processed point may be coplanar with an
+horizon facet. Qhull creates a new facet without
+a hyperplane. It links new facets for the same
+horizon facet together. This is called a <em>samecycle</em>.
+The new facet or samecycle is merged into the
+horizon facet. </li>
+</ul>
+<ul>
+<li><b>Concave facets. </b>A facet's centrum may be
+above a neighboring facet. If so, the facets meet
+at a concave angle. </li>
+</ul>
+<ul>
+<li><b>Coplanar facets. </b>A facet's centrum may be
+coplanar with a neighboring facet (i.e., it is
+neither clearly below nor clearly above the
+facet's hyperplane). Qhull removes coplanar
+facets in independent sets sorted by angle.</li>
+</ul>
+<ul>
+<li><b>Redundant vertex. </b>A vertex may have fewer
+than three neighboring facets. If so, it is
+redundant and may be renamed to an adjacent
+vertex without changing the topological
+structure.This is called a <em>redundant vertex</em>.
+</li>
+</ul>
+</blockquote>
+<p><b>Copyright &copy; 1995-2015 C.B. Barber</b></p>
+<hr>
+<p><a href="#TOP">&#187;</a> <a href="qh-geom_r.htm#TOC">Geom</a>
+<a name="TOC">&#149;</a> <a href="qh-globa_r.htm#TOC">Global</a>
+&#149; <a href="qh-io_r.htm#TOC">Io</a> &#149; <a href="qh-mem_r.htm#TOC">Mem</a>
+&#149; <b>Merge</b> &#149; <a href="qh-poly_r.htm#TOC">Poly</a>
+&#149; <a href="qh-qhull_r.htm#TOC">Qhull</a> &#149; <a href="qh-set_r.htm#TOC">Set</a>
+&#149; <a href="qh-stat_r.htm#TOC">Stat</a> &#149; <a href="qh-user_r.htm#TOC">User</a>
+</p>
+<h3>Index to <a href="merge_r.c">merge_r.c</a> and
+<a href="merge_r.h">merge_r.h</a></h3>
+<ul>
+<li><a href="#mtype">merge_r.h data types, macros, and
+global sets</a> </li>
+<li><a href="#mconst">merge_r.h constants</a> </li>
+</ul>
+<ul>
+<li><a href="#mtop">top-level merge functions</a> </li>
+<li><a href="#mset">functions for identifying merges</a></li>
+<li><a href="#mbest">functions for determining the
+best merge</a> </li>
+<li><a href="#mmerge">functions for merging facets</a>
+</li>
+<li><a href="#mcycle">functions for merging a cycle
+of facets</a> </li>
+<li><a href="#mrename">functions for renaming a
+vertex</a> </li>
+<li><a href="#mvertex">functions for identifying
+vertices for renaming</a> </li>
+<li><a href="#mcheck">functions for check and trace</a> </li>
+</ul>
+<h3><a href="qh-merge_r.htm#TOC">&#187;</a><a name="mtype">merge_r.h data
+types, macros, and global sets</a></h3>
+<ul>
+<li><a href="merge_r.h#mergeT">mergeT</a> structure to
+identify a merge of two facets</li>
+<li><a href="merge_r.h#FOREACHmerge_">FOREACHmerge_</a>
+assign 'merge' to each merge in merges </li>
+<li><a href="libqhull_r.h#qh-set">qh global sets</a>
+qh.facet_mergeset contains non-convex merges
+while qh.degen_mergeset contains degenerate and
+redundant facets</li>
+</ul>
+<h3><a href="qh-merge_r.htm#TOC">&#187;</a><a name="mconst">merge_r.h
+constants</a></h3>
+<ul>
+<li><a href="libqhull_r.h#qh-prec">qh precision constants</a>
+precision constants for Qhull </li>
+<li><a href="merge_r.h#MRG">MRG...</a> indicates the
+type of a merge (mergeT-&gt;type)</li>
+<li><a href="merge_r.h#qh_ANGLEredundant">qh_ANGLEredundant</a>
+indicates redundant merge in mergeT-&gt;angle </li>
+<li><a href="merge_r.h#qh_ANGLEdegen">qh_ANGLEdegen</a>
+indicates degenerate facet in mergeT-&gt;angle </li>
+<li><a href="merge_r.h#qh_ANGLEconcave">qh_ANGLEconcave</a>
+offset to indicate concave facets in
+mergeT-&gt;angle </li>
+<li><a href="merge_r.h#qh_MERGEapex">qh_MERGEapex</a>
+flag for qh_mergefacet() to indicate an apex
+merge </li>
+</ul>
+<h3><a href="qh-merge_r.htm#TOC">&#187;</a><a name="mtop">top-level merge
+functions</a></h3>
+<ul>
+<li><a href="merge_r.c#all_merges">qh_all_merges</a>
+merge all non-convex facets </li>
+<li><a href="merge_r.c#checkzero">qh_checkzero</a>
+check that facets are clearly convex </li>
+<li><a href="merge_r.c#flippedmerges">qh_flippedmerges</a>
+merge flipped facets into best neighbor </li>
+<li><a href="merge_r.c#forcedmerges">qh_forcedmerges</a>
+merge all duplicate ridges </li>
+<li><a href="merge_r.c#merge_degenredundant">qh_merge_degenredundant</a>
+merge degenerate and redundant facets </li>
+<li><a href="merge_r.c#merge_nonconvex">qh_merge_nonconvex</a>
+merge a non-convex ridge </li>
+<li><a href="merge_r.c#premerge">qh_premerge</a>
+pre-merge non-convex facets </li>
+<li><a href="merge_r.c#postmerge">qh_postmerge</a>
+post-merge nonconvex facets as defined by
+maxcentrum/maxangle </li>
+</ul>
+
+<h3><a href="qh-merge_r.htm#TOC">&#187;</a><a name="mset">functions for
+identifying merges</a></h3>
+<ul>
+<li><a href="merge_r.c#appendmergeset">qh_appendmergeset</a>
+appends an entry to qh.facet_mergeset</li>
+<li><a href="merge_r.c#compareangle">qh_compareangle</a>
+used by qsort() to order merges </li>
+<li><a href="merge_r.c#comparemerge">qh_comparemerge</a>
+used by qsort() to order merges </li>
+<li><a href="merge_r.c#degen_redundant_facet">qh_degen_redundant_facet</a>
+check for a degenerate and redundant facet</li>
+<li><a href="merge_r.c#degen_redundant_neighbors">qh_degen_redundant_neighbors</a>
+append degenerate and redundant neighbors to
+qh.degen_mergeset </li>
+<li><a href="merge_r.c#getmergeset_initial">qh_getmergeset_initial</a>
+build initial qh.facet_mergeset </li>
+<li><a href="merge_r.c#getmergeset">qh_getmergeset</a>
+update qh.facet_mergeset </li>
+<li><a href="merge_r.c#mark_dupridges">qh_mark_dupridges</a>
+add duplicated ridges to qh.facet_mergeset</li>
+<li><a href="merge_r.c#maydropneighbor">qh_maydropneighbor</a>
+drop neighbor relationship if no ridge between
+facet and neighbor </li>
+<li><a href="merge_r.c#test_appendmerge">qh_test_appendmerge</a>
+test a pair of facets for convexity and append to
+qh.facet_mergeset if non-convex </li>
+<li><a href="merge_r.c#test_vneighbors">qh_test_vneighbors</a>
+test vertex neighbors for convexity </li>
+</ul>
+
+<h3><a href="qh-merge_r.htm#TOC">&#187;</a><a name="mbest">functions for
+determining the best merge</a></h3>
+<ul>
+<li><a href="merge_r.c#findbest_test">qh_findbest_test</a>
+test neighbor for best merge </li>
+<li><a href="merge_r.c#findbestneighbor">qh_findbestneighbor</a>
+finds best neighbor of a facet for merging (i.e.,
+closest hyperplane) </li>
+</ul>
+
+<h3><a href="qh-merge_r.htm#TOC">&#187;</a><a name="mmerge">functions for
+merging facets</a></h3>
+<ul>
+<li><a href="merge_r.c#copynonconvex">qh_copynonconvex</a>
+copy non-convex flag to another ridge for the
+same neighbor </li>
+<li><a href="merge_r.c#makeridges">qh_makeridges</a>
+creates explicit ridges between simplicial facets
+</li>
+<li><a href="merge_r.c#mergefacet">qh_mergefacet</a>
+merges one facet into another facet</li>
+<li><a href="merge_r.c#mergeneighbors">qh_mergeneighbors</a>
+merges the neighbors of two facets </li>
+<li><a href="merge_r.c#mergeridges">qh_mergeridges</a>
+merges the ridge sets of two facets </li>
+<li><a href="merge_r.c#mergesimplex">qh_mergesimplex</a>
+merge a simplicial facet into another simplicial
+facet </li>
+<li><a href="merge_r.c#mergevertex_del">qh_mergevertex_del</a>
+delete a vertex due to merging one facet into
+another facet </li>
+<li><a href="merge_r.c#mergevertex_neighbors">qh_mergevertex_neighbors</a>
+merge the vertex neighbors of two facets </li>
+<li><a href="merge_r.c#mergevertices">qh_mergevertices</a>
+merge the vertex sets of two facets </li>
+<li><a href="merge_r.c#newvertices">qh_newvertices</a>
+register all vertices as new vertices </li>
+<li><a href="merge_r.c#updatetested">qh_updatetested</a>
+clear tested flags and centrums involved in a
+merge </li>
+<li><a href="merge_r.c#willdelete">qh_willdelete</a>
+moves facet to qh.visible_list; sets replacement
+or NULL </li>
+</ul>
+
+<h3><a href="qh-merge_r.htm#TOC">&#187;</a><a name="mcycle">functions for
+merging a cycle of facets</a></h3>
+<p>If a point is coplanar with an horizon facet, the
+corresponding new facets are linked together (a <em>samecycle</em>)
+for merging.</p>
+<ul>
+<li><a href="merge_r.c#basevertices">qh_basevertices</a>
+return temporary set of base vertices for a
+samecycle </li>
+<li><a href="merge_r.c#mergecycle">qh_mergecycle</a>
+merge a samecycle into a horizon facet </li>
+<li><a href="merge_r.c#mergecycle_all">qh_mergecycle_all</a>
+merge all samecycles into horizon facets</li>
+<li><a href="merge_r.c#mergecycle_facets">qh_mergecycle_facets</a>
+finish merge of samecycle </li>
+<li><a href="merge_r.c#mergecycle_neighbors">qh_mergecycle_neighbors</a>
+merge neighbor sets for samecycle </li>
+<li><a href="merge_r.c#mergecycle_ridges">qh_mergecycle_ridges</a>
+merge ridge sets for samecycle </li>
+<li><a href="merge_r.c#mergecycle_vneighbors">qh_mergecycle_vneighbors</a>
+merge vertex neighbor sets for samecycle </li>
+</ul>
+<h3><a href="qh-merge_r.htm#TOC">&#187;</a><a name="mrename">functions
+for renaming a vertex</a></h3>
+<ul>
+<li><a href="merge_r.c#comparevisit">qh_comparevisit</a>
+used by qsort() to order vertices by visitid</li>
+<li><a href="merge_r.c#reducevertices">qh_reducevertices</a>
+reduce vertex sets </li>
+<li><a href="merge_r.c#redundant_vertex">qh_redundant_vertex</a>
+returns true if detect and rename redundant
+vertex </li>
+<li><a href="merge_r.c#rename_sharedvertex">qh_rename_sharedvertex</a>
+detect and rename a shared vertex </li>
+<li><a href="merge_r.c#renameridgevertex">qh_renameridgevertex</a>
+rename oldvertex to newvertex in a ridge </li>
+<li><a href="merge_r.c#renamevertex">qh_renamevertex</a>
+rename oldvertex to newvertex in ridges </li>
+<li><a href="merge_r.c#remove_extravertices">qh_remove_extravertices</a>
+remove extra vertices in non-simplicial facets </li>
+</ul>
+
+<h3><a href="qh-merge_r.htm#TOC">&#187;</a><a name="mvertex">functions
+for identifying vertices for renaming</a></h3>
+<ul>
+<li><a href="merge_r.c#find_newvertex">qh_find_newvertex</a>
+locate new vertex for renaming old vertex </li>
+<li><a href="merge_r.c#hashridge">qh_hashridge</a> add
+ridge to hashtable </li>
+<li><a href="merge_r.c#hashridge_find">qh_hashridge_find</a>
+returns matching ridge in hashtable</li>
+<li><a href="merge_r.c#neighbor_intersections">qh_neighbor_intersections</a>
+return intersection of vertex sets for
+neighboring facets </li>
+<li><a href="merge_r.c#vertexridges">qh_vertexridges</a>
+return temporary set of ridges adjacent to a
+vertex </li>
+<li><a href="merge_r.c#vertexridges_facet">qh_vertexridges_facet</a>
+add adjacent ridges for a vertex in facet </li>
+</ul>
+
+<h3><a href="qh-merge_r.htm#TOC">&#187;</a><a name="mcheck">functions for check and
+trace</a></h3>
+<ul>
+<li><a href="merge_r.c#checkconnect">qh_checkconnect</a>
+check that new facets are connected </li>
+<li><a href="merge_r.c#tracemerge">qh_tracemerge</a>
+print trace message after merge </li>
+<li><a href="merge_r.c#tracemerging">qh_tracemerging</a>
+print trace message during post-merging </li>
+</ul>
+
+<p><!-- Navigation links --> </p>
+<hr>
+<p><b>Up:</b>
+<a href="http://www.qhull.org">Home page for
+Qhull</a> <br>
+<b>Up:</b> <a href="../../html/index.htm#TOC">Qhull manual: Table of Contents</a> <br>
+<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a>
+&#149; <a href="../../html/qh-quick.htm#options">Options</a>
+&#149; <a href="../../html/qh-opto.htm#output">Output</a>
+&#149; <a href="../../html/qh-optf.htm#format">Formats</a>
+&#149; <a href="../../html/qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="../../html/qh-optp.htm#print">Print</a>
+&#149; <a href="../../html/qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="../../html/qh-optc.htm#prec">Precision</a>
+&#149; <a href="../../html/qh-optt.htm#trace">Trace</a>
+&#149; <a href="index.htm">Functions</a><br>
+<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code: Table of Contents</a> <br>
+<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
+<b>To:</b> <a href="qh-geom_r.htm">Geom</a> &#149;
+<a href="qh-globa_r.htm">Global</a> &#149; <a href="qh-io_r.htm">Io</a>
+&#149; <a href="qh-mem_r.htm">Mem</a> &#149; <a href="qh-merge_r.htm">Merge</a>
+&#149; <a href="qh-poly_r.htm">Poly</a> &#149; <a href="qh-qhull_r.htm#TOC">Qhull</a>
+&#149; <a href="qh-set_r.htm">Set</a> &#149; <a href="qh-stat_r.htm">Stat</a>
+&#149; <a href="qh-user_r.htm">User</a><br>
+</p>
+<p><!-- GC common information --> </p>
+<hr>
+<p><a href="http://www.geom.uiuc.edu/"><img
+src="../../html/qh--geom.gif" align="middle" width="40" height="40"></a><i>The
+Geometry Center Home Page </i></p>
+<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
+</a><br>
+Created: May 2, 1997 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
+</body>
+</html>
diff --git a/xs/src/qhull/src/libqhull_r/qh-poly_r.htm b/xs/src/qhull/src/libqhull_r/qh-poly_r.htm
new file mode 100644
index 0000000000..c5b6f2f836
--- /dev/null
+++ b/xs/src/qhull/src/libqhull_r/qh-poly_r.htm
@@ -0,0 +1,485 @@
+<!-- Do not edit with Front Page, it adds too many spaces -->
+<html>
+<head>
+<meta http-equiv="Content-Type"
+content="text/html; charset=iso-8859-1">
+<title>poly_r.c, poly2_r.c -- polyhedron operations</title>
+</head>
+
+<body>
+<!-- Navigation links -->
+<p><a name="TOP"><b>Up:</b></a> <a
+href="http://www.qhull.org">Home page</a> for Qhull<br>
+<b>Up:</b> <a href="../../html/index.htm#TOC">Qhull manual</a>: Table of Contents <br>
+<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a>
+&#149; <a href="../../html/qh-quick.htm#options">Options</a>
+&#149; <a href="../../html/qh-opto.htm#output">Output</a>
+&#149; <a href="../../html/qh-optf.htm#format">Formats</a>
+&#149; <a href="../../html/qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="../../html/qh-optp.htm#print">Print</a>
+&#149; <a href="../../html/qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="../../html/qh-optc.htm#prec">Precision</a>
+&#149; <a href="../../html/qh-optt.htm#trace">Trace</a>
+&#149; <a href="index.htm">Functions</a><br>
+<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code: Table of Contents</a><br>
+<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
+<b>To:</b> <a href="qh-geom_r.htm">Geom</a> &#149; <a href="qh-globa_r.htm">Global</a>
+&#149; <a href="qh-io_r.htm">Io</a> &#149; <a href="qh-mem_r.htm">Mem</a>
+&#149; <a href="qh-merge_r.htm">Merge</a> &#149; <a href="qh-poly_r.htm#TOC">Poly</a>
+&#149; <a href="qh-qhull_r.htm">Qhull</a> &#149; <a href="qh-set_r.htm">Set</a>
+&#149; <a href="qh-stat_r.htm">Stat</a> &#149; <a href="qh-user_r.htm">User</a>
+</p>
+<hr>
+
+<h2>poly_r.c, poly2_r.c -- polyhedron operations</h2>
+<blockquote>
+
+<p>Qhull uses dimension-free terminology. Qhull builds a
+polyhedron in dimension <em>d. </em>A <em>polyhedron</em> is a
+simplicial complex of faces with geometric information for the
+top and bottom-level faces. A (<em>d-1</em>)-face is a <em>facet</em>,
+a (<em>d-2</em>)-face is a <em>ridge</em>, and a <em>0</em>-face
+is a <em>vertex</em>. For example in 3-d, a facet is a polygon
+and a ridge is an edge. A facet is built from a ridge (the <em>base</em>)
+and a vertex (the <em>apex</em>). See
+<a href="../../html/index.htm#structure">Qhull's data structures</a>.</p>
+
+<p>Qhull's primary data structure is a polyhedron. A
+polyhedron is a list of facets. Each facet has a set of
+neighboring facets and a set of vertices. Each facet has a
+hyperplane. For example, a tetrahedron has four facets.
+If its vertices are <em>a, b, c, d</em>, and its facets
+are <em>1, 2, 3, 4,</em> the tetrahedron is </p>
+<blockquote>
+<ul>
+<li>facet 1 <ul>
+    <li>vertices: b c d </li>
+    <li>neighbors: 2 3 4 </li>
+</ul>
+</li>
+<li>facet 2 <ul>
+    <li>vertices: a c d </li>
+    <li>neighbors: 1 3 4 </li>
+</ul>
+</li>
+<li>facet 3 <ul>
+    <li>vertices: a b d </li>
+    <li>neighbors: 1 2 4 </li>
+</ul>
+</li>
+<li>facet 4 <ul>
+    <li>vertices: a b c </li>
+    <li>neighbors: 1 2 3 </li>
+</ul>
+</li>
+</ul>
+</blockquote>
+<p>A facet may be simplicial or non-simplicial. In 3-d, a
+<i>simplicial facet</i> has three vertices and three
+neighbors. A <i>nonsimplicial facet</i> has more than
+three vertices and more than three neighbors. A
+nonsimplicial facet has a set of ridges and a centrum. </p>
+<p>
+A simplicial facet has an orientation. An <i>orientation</i>
+is either <i>top</i> or <i>bottom</i>.
+The flag, <tt>facet-&gt;toporient,</tt>
+defines the orientation of the facet's vertices.  For example in 3-d,
+'top' is left-handed orientation (i.e., the vertex order follows the direction
+of the left-hand fingers when the thumb is pointing away from the center).
+Except for axis-parallel facets in 5-d and higher, topological orientation
+determines the geometric orientation of the facet's hyperplane.
+
+<p>A nonsimplicial facet is due to merging two or more
+facets. The facet's ridge set determine a simplicial
+decomposition of the facet. Each ridge is a 1-face (i.e.,
+it has two vertices and two neighboring facets). The
+orientation of a ridge is determined by the order of the
+neighboring facets. The flag, <tt>facet-&gt;toporient,</tt>is
+ignored. </p>
+<p>A nonsimplicial facet has a centrum for testing
+convexity. A <i>centrum</i> is a point on the facet's
+hyperplane that is near the center of the facet. Except
+for large facets, it is the arithmetic average of the
+facet's vertices. </p>
+<p>A nonsimplicial facet is an approximation that is
+defined by offsets from the facet's hyperplane. When
+Qhull finishes, the <i>outer plane</i> is above all
+points while the <i>inner plane</i> is below the facet's
+vertices. This guarantees that any exact convex hull
+passes between the inner and outer planes. The outer
+plane is defined by <tt>facet-&gt;maxoutside</tt> while
+the inner plane is computed from the facet's vertices.</p>
+
+<p>Qhull 3.1 includes triangulation of non-simplicial facets
+('<a href="../../html/qh-optq.htm#Qt">Qt</a>').
+These facets,
+called <i>tricoplanar</i>, share the same normal. centrum, and Voronoi center.
+One facet (keepcentrum) owns these data structures.
+While tricoplanar facets are more accurate than the simplicial facets from
+joggled input, they
+may have zero area or flipped orientation.
+
+</blockquote>
+<p><b>Copyright &copy; 1995-2015 C.B. Barber</b></p>
+<hr>
+<p><a href="#TOP">&#187;</a> <a href="qh-geom_r.htm#TOC">Geom</a>
+<a name="TOC">&#149;</a> <a href="qh-globa_r.htm#TOC">Global</a>
+&#149; <a href="qh-io_r.htm#TOC">Io</a> &#149; <a href="qh-mem_r.htm#TOC">Mem</a>
+&#149; <a href="qh-merge_r.htm#TOC">Merge</a> &#149; <b>Poly</b>
+&#149; <a href="qh-qhull_r.htm#TOC">Qhull</a> &#149; <a href="qh-set_r.htm#TOC">Set</a>
+&#149; <a href="qh-stat_r.htm#TOC">Stat</a> &#149; <a href="qh-user_r.htm#TOC">User</a>
+</p>
+<h3>Index to <a href="poly_r.c">poly_r.c</a>,
+<a href="poly2_r.c">poly2_r.c</a>, <a href="poly_r.h">poly_r.h</a>,
+and <a href="libqhull_r.h">libqhull_r.h</a></h3>
+<ul>
+<li><a href="#ptype">Data types and global
+lists for polyhedrons</a> </li>
+<li><a href="#pconst">poly_r.h constants</a> </li>
+<li><a href="#pgall">Global FORALL macros</a> </li>
+<li><a href="#pall">FORALL macros</a> </li>
+<li><a href="#peach">FOREACH macros</a> </li>
+<li><a href="#pieach">Indexed FOREACH macros</a> </li>
+<li><a href="#pmacro">Other macros for polyhedrons</a><p>&nbsp;</li>
+<li><a href="#plist">Facetlist functions</a> </li>
+<li><a href="#pfacet">Facet functions</a> </li>
+<li><a href="#pvertex">Vertex, ridge, and point
+functions</a> </li>
+<li><a href="#phash">Hashtable functions</a> </li>
+<li><a href="#pnew">Allocation and deallocation
+functions</a> </li>
+<li><a href="#pcheck">Check functions</a> </li>
+</ul>
+<h3><a href="qh-poly_r.htm#TOC">&#187;</a><a name="ptype">Data
+types and global lists for polyhedrons</a></h3>
+<ul>
+<li><a href="libqhull_r.h#facetT">facetT</a> defines a
+facet </li>
+<li><a href="libqhull_r.h#ridgeT">ridgeT</a> defines a
+ridge </li>
+<li><a href="libqhull_r.h#vertexT">vertexT</a> defines a
+vertex </li>
+<li><a href="libqhull_r.h#qh-lists">qh facet and vertex
+lists</a> lists of facets and vertices </li>
+<li><a href="libqhull_r.h#qh-set">qh global sets</a>
+global sets for merging, hashing, input, etc. </li>
+</ul>
+<h3><a href="qh-poly_r.htm#TOC">&#187;</a><a name="pconst">poly_r.h constants</a></h3>
+<ul>
+<li><a href="poly_r.h#ALGORITHMfault">ALGORITHMfault</a>
+flag to not report errors in qh_checkconvex() </li>
+<li><a href="poly_r.h#DATAfault">DATAfault</a> flag to
+report errors in qh_checkconvex() </li>
+<li><a href="poly_r.h#DUPLICATEridge">DUPLICATEridge</a>
+special value for facet-&gt;neighbor to indicate
+a duplicate ridge </li>
+<li><a href="poly_r.h#MERGEridge">MERGEridge</a>
+special value for facet-&gt;neighbor to indicate
+a merged ridge </li>
+</ul>
+<h3><a href="qh-poly_r.htm#TOC">&#187;</a><a name="pgall">Global FORALL
+macros</a></h3>
+<ul>
+<li><a href="libqhull_r.h#FORALLfacets">FORALLfacets</a>
+assign 'facet' to each facet in qh.facet_list </li>
+<li><a href="poly_r.h#FORALLnew_facets">FORALLnew_facets</a>
+assign 'facet' to each facet in qh.newfacet_list </li>
+<li><a href="poly_r.h#FORALLvisible_facets">FORALLvisible_facets</a>
+assign 'visible' to each visible facet in
+qh.visible_list </li>
+<li><a href="libqhull_r.h#FORALLpoints">FORALLpoints</a>
+assign 'point' to each point in qh.first_point,
+qh.num_points </li>
+<li><a href="libqhull_r.h#FORALLvertices">FORALLvertices</a>
+assign 'vertex' to each vertex in qh.vertex_list </li>
+</ul>
+<h3><a href="qh-poly_r.htm#TOC">&#187;</a><a name="pall">FORALL macros</a></h3>
+<ul>
+<li><a href="poly_r.h#FORALLfacet_">FORALLfacet_</a>
+assign 'facet' to each facet in facetlist </li>
+<li><a href="libqhull_r.h#FORALLpoint_">FORALLpoint_</a>
+assign 'point' to each point in points array</li>
+<li><a href="poly_r.h#FORALLsame_">FORALLsame_</a>
+assign 'same' to each facet in samecycle</li>
+<li><a href="poly_r.h#FORALLsame_cycle_">FORALLsame_cycle_</a>
+assign 'same' to each facet in samecycle</li>
+<li><a href="poly_r.h#FORALLvertex_">FORALLvertex_</a>
+assign 'vertex' to each vertex in vertexlist </li>
+</ul>
+<h3><a href="qh-poly_r.htm#TOC">&#187;</a><a name="peach">FOREACH macros</a></h3>
+<ul>
+<li><a href="libqhull_r.h#FOREACHfacet_">FOREACHfacet_</a>
+assign 'facet' to each facet in facets </li>
+<li><a href="libqhull_r.h#FOREACHneighbor_">FOREACHneighbor_</a>
+assign 'neighbor' to each facet in
+facet-&gt;neighbors or vertex-&gt;neighbors</li>
+<li><a href="poly_r.h#FOREACHnewfacet_">FOREACHnewfacet_</a>
+assign 'newfacet' to each facet in facet set </li>
+<li><a href="libqhull_r.h#FOREACHpoint_">FOREACHpoint_</a>
+assign 'point' to each point in points set </li>
+<li><a href="libqhull_r.h#FOREACHridge_">FOREACHridge_</a>
+assign 'ridge' to each ridge in ridge set </li>
+<li><a href="libqhull_r.h#FOREACHvertex_">FOREACHvertex_</a>
+assign 'vertex' to each vertex in vertex set </li>
+<li><a href="poly_r.h#FOREACHvertexA_">FOREACHvertexA_</a>
+assign 'vertexA' to each vertex in vertex set</li>
+<li><a href="poly_r.h#FOREACHvisible_">FOREACHvisible_</a>
+assign 'visible' to each facet in facet set </li>
+</ul>
+<h3><a href="qh-poly_r.htm#TOC">&#187;</a><a name="pieach">Indexed
+FOREACH macros</a></h3>
+<ul>
+<li><a href="libqhull_r.h#FOREACHfacet_i_">FOREACHfacet_i_</a>
+assign 'facet' and 'facet_i' to each facet in
+facet set </li>
+<li><a href="libqhull_r.h#FOREACHneighbor_i_">FOREACHneighbor_i_</a>
+assign 'neighbor' and 'neighbor_i' to each facet
+in facet-&gt;neighbors or vertex-&gt;neighbors</li>
+<li><a href="libqhull_r.h#FOREACHpoint_i_">FOREACHpoint_i_</a>
+assign 'point' and 'point_i' to each point in
+points set </li>
+<li><a href="libqhull_r.h#FOREACHridge_i_">FOREACHridge_i_</a>
+assign 'ridge' and 'ridge_i' to each ridge in
+ridges set </li>
+<li><a href="libqhull_r.h#FOREACHvertex_i_">FOREACHvertex_i_</a>
+assign 'vertex' and 'vertex_i' to each vertex in
+vertices set </li>
+<li><a href="poly_r.h#FOREACHvertexreverse12_">FOREACHvertexreverse12_</a>
+assign 'vertex' to each vertex in vertex set;
+reverse the order of first two vertices </li>
+</ul>
+<h3><a href="qh-poly_r.htm#TOC">&#187;</a><a name="pmacro">Other macros for polyhedrons</a></h3>
+<ul>
+<li><a href="libqhull_r.h#getid_">getid_</a> return ID for
+a facet, ridge, or vertex </li>
+<li><a href="libqhull_r.h#otherfacet_">otherfacet_</a>
+return neighboring facet for a ridge in a facet </li>
+</ul>
+<h3><a href="qh-poly_r.htm#TOC">&#187;</a><a name="plist">Facetlist
+functions</a></h3>
+<ul>
+<li><a href="poly_r.c#appendfacet">qh_appendfacet</a>
+appends facet to end of qh.facet_list</li>
+<li><a href="poly_r.c#attachnewfacets">qh_attachnewfacets</a>
+attach new facets in qh.newfacet_list to the
+horizon </li>
+<li><a href="poly2_r.c#findgood">qh_findgood</a>
+identify good facets for qh.PRINTgood </li>
+<li><a href="poly2_r.c#findgood_all">qh_findgood_all</a>
+identify more good facets for qh.PRINTgood </li>
+<li><a href="poly2_r.c#furthestnext">qh_furthestnext</a>
+move facet with furthest of furthest points to
+facet_next </li>
+<li><a href="poly2_r.c#initialhull">qh_initialhull</a>
+construct the initial hull as a simplex of
+vertices </li>
+<li><a href="poly2_r.c#nearcoplanar">qh_nearcoplanar</a>
+  remove near-inside points from coplanar sets</li>
+<li><a href="poly2_r.c#prependfacet">qh_prependfacet</a>
+prepends facet to start of facetlist </li>
+<li><a href="user_r.c#printfacetlist">qh_printfacetlist</a>
+print facets in a facetlist</li>
+<li><a href="poly2_r.c#printlists">qh_printlists</a>
+print out facet list for debugging </li>
+<li><a href="poly_r.c#removefacet">qh_removefacet</a>
+unlinks facet from qh.facet_list</li>
+<li><a href="poly2_r.c#resetlists">qh_resetlists</a>
+reset qh.newvertex_list, qh.newfacet_list, and
+qh.visible_list </li>
+</ul>
+<h3><a href="qh-poly_r.htm#TOC">&#187;</a><a name="pfacet">Facet
+functions</a></h3>
+<ul>
+<li><a href="poly2_r.c#createsimplex">qh_createsimplex</a>
+create a simplex of facets from a set of vertices
+</li>
+<li><a href="poly2_r.c#findbestlower">qh_findbestlower</a> find best
+non-upper, non-flipped facet for point at upperfacet</li>
+<li><a href="poly2_r.c#furthestout">qh_furthestout</a>
+make furthest outside point the last point of a
+facet's outside set </li>
+<li><a href="poly_r.c#makenew_nonsimplicial">qh_makenew_nonsimplicial</a>
+make new facets from ridges of visible facets </li>
+<li><a href="poly_r.c#makenew_simplicial">qh_makenew_simplicial</a>
+make new facets for horizon neighbors </li>
+<li><a href="poly_r.c#makenewfacet">qh_makenewfacet</a>
+create a facet from vertices and apex </li>
+<li><a href="poly2_r.c#makenewfacets">qh_makenewfacets</a>
+make new facets from vertex, horizon facets, and
+visible facets </li>
+<li><a href="poly_r.c#makenewplanes">qh_makenewplanes</a>
+make new hyperplanes for facets </li>
+<li><a href="poly2_r.c#outcoplanar">qh_outcoplanar</a>
+move points from outside set to coplanar set </li>
+<li><a href="poly2_r.c#setvoronoi_all">qh_setvoronoi_all</a>
+compute Voronoi centers for all facets </li>
+<li><a href="poly2_r.c#triangulate">qh_triangulate</a>
+triangulate non-simplicial facets</li>
+<li><a href="poly2_r.c#triangulate_facet">qh_triangulate_facet</a>
+triangulate a non-simplicial facet</li>
+<li><a href="poly2_r.c#triangulate_link">qh_triangulate_link</a>
+link facets together from qh_triangulate</li>
+<li><a href="poly2_r.c#triangulate_mirror">qh_triangulate_mirror</a>
+delete mirrored facets from qh_triangulate</li>
+<li><a href="poly2_r.c#triangulate_null">qh_triangulate_null</a>
+delete null facet from qh_triangulate</li>
+</ul>
+<h3><a href="qh-poly_r.htm#TOC">&#187;</a><a name="pvertex">Vertex,
+ridge, and point functions</a></h3>
+<ul>
+<li><a href="poly_r.c#appendvertex">qh_appendvertex</a>
+append vertex to end of qh.vertex_list, </li>
+<li><a href="io_r.c#detvridge">qh_detvridge</a> determine Voronoi
+ridge for an input site
+<li><a href="io_r.c#detvridge3">qh_detvridge3</a> determine 3-d Voronoi
+ridge for an input site
+<li><a href="poly2_r.c#facet3vertex">qh_facet3vertex</a>
+return an oriented vertex set for a 3-d facet </li>
+<li><a href="poly_r.c#facetintersect">qh_facetintersect</a>
+return intersection of simplicial facets </li>
+<li><a href="poly2_r.c#initialvertices">qh_initialvertices</a>
+return non-singular set of initial vertices </li>
+<li><a href="poly2_r.c#isvertex">qh_isvertex</a> true
+if point is in a vertex set </li>
+<li><a href="poly2_r.c#nearvertex">qh_nearvertex</a>
+return nearest vertex to point </li>
+<li><a href="poly2_r.c#nextridge3d">qh_nextridge3d</a>
+iterate over each ridge and vertex for a 3-d
+facet </li>
+<li><a href="poly2_r.c#point">qh_point</a> return point
+for a point ID </li>
+<li><a href="poly2_r.c#pointfacet">qh_pointfacet</a>
+return temporary set of facets indexed by point
+ID </li>
+<li><a href="poly_r.c#pointid">qh_pointid</a> return ID
+for a point</li>
+<li><a href="poly2_r.c#pointvertex">qh_pointvertex</a>
+return temporary set of vertices indexed by point
+ID </li>
+<li><a href="poly_r.c#removevertex">qh_removevertex</a>
+unlink vertex from qh.vertex_list, </li>
+<li><a href="poly_r.c#updatevertices">qh_updatevertices</a>
+update vertex neighbors and delete interior
+vertices </li>
+<li><a href="poly2_r.c#vertexintersect">qh_vertexintersect</a>
+intersect two vertex sets </li>
+<li><a href="poly2_r.c#vertexintersect_new">qh_vertexintersect_new</a>
+return intersection of two vertex sets </li>
+<li><a href="poly2_r.c#vertexneighbors">qh_vertexneighbors</a>
+for each vertex in hull, determine facet
+neighbors </li>
+<li><a href="poly2_r.c#vertexsubset">qh_vertexsubset</a>
+returns True if vertexsetA is a subset of
+vertexsetB </li>
+</ul>
+<h3><a href="qh-poly_r.htm#TOC">&#187;</a><a name="phash">Hashtable functions</a></h3>
+<ul>
+<li><a href="poly2_r.c#addhash">qh_addhash</a> add hash
+element to linear hash table</li>
+<li><a href="poly_r.c#gethash">qh_gethash</a> return
+hash value for a set</li>
+<li><a href="poly2_r.c#matchduplicates">qh_matchduplicates</a>
+match duplicate ridges in hash table </li>
+<li><a href="poly_r.c#matchneighbor">qh_matchneighbor</a>
+try to match subridge of new facet with a
+neighbor </li>
+<li><a href="poly_r.c#matchnewfacets">qh_matchnewfacets</a>
+match new facets with their new facet neighbors </li>
+<li><a href="poly_r.c#matchvertices">qh_matchvertices</a>
+tests whether a facet and hash entry match at a
+ridge </li>
+<li><a href="poly2_r.c#newhashtable">qh_newhashtable</a>
+allocate a new qh_r.hash_table </li>
+<li><a href="poly2_r.c#printhashtable">qh_printhashtable</a>
+print hash table </li>
+</ul>
+<h3><a href="qh-poly_r.htm#TOC">&#187;</a><a name="pnew">Allocation and
+deallocation functions</a></h3>
+<ul>
+<li><a href="poly2_r.c#clearcenters">qh_clearcenters</a>
+clear old data from facet-&gt;center </li>
+<li><a href="poly_r.c#deletevisible">qh_deletevisible</a>
+delete visible facets and vertices </li>
+<li><a href="poly_r.c#delfacet">qh_delfacet</a> free up
+the memory occupied by a facet </li>
+<li><a href="poly2_r.c#delridge">qh_delridge</a> delete
+ridge</li>
+<li><a href="poly2_r.c#delvertex">qh_delvertex</a>
+delete vertex </li>
+<li><a href="poly_r.c#newfacet">qh_newfacet</a> create
+and allocate space for a facet </li>
+<li><a href="poly_r.c#newridge">qh_newridge</a> create
+and allocate space for a ridge </li>
+<li><a href="poly2_r.c#newvertex">qh_newvertex</a>
+create and allocate space for a vertex </li>
+</ul>
+<h3><a href="qh-poly_r.htm#TOC">&#187;</a><a name="pcheck">Check
+functions</a></h3>
+<ul>
+<li><a href="poly2_r.c#check_bestdist">qh_check_bestdist</a>
+check that points are not outside of facets </li>
+<li><a href="poly2_r.c#check_dupridge">qh_check_dupridge</a>
+check duplicate ridge between facet1 and facet2 for wide merge </li>
+<li><a href="poly2_r.c#check_maxout">qh_check_maxout</a>
+updates qh.max_outside and checks all points
+against bestfacet </li>
+<li><a href="poly2_r.c#check_output">qh_check_output</a>
+check topological and geometric output</li>
+<li><a href="poly2_r.c#check_point">qh_check_point</a>
+check that point is not outside of facet </li>
+<li><a href="poly2_r.c#check_points">qh_check_points</a>
+check that all points are inside all facets </li>
+<li><a href="poly2_r.c#checkconvex">qh_checkconvex</a>
+check that each ridge in facetlist is convex </li>
+<li><a href="poly2_r.c#checkfacet">qh_checkfacet</a>
+check for consistency errors in facet </li>
+<li><a href="poly_r.c#checkflipped">qh_checkflipped</a>
+check facet orientation to the interior point </li>
+<li><a href="poly2_r.c#checkflipped_all">qh_checkflipped_all</a>
+check facet orientation for a facet list </li>
+<li><a href="poly2_r.c#checkpolygon">qh_checkpolygon</a>
+check topological structure </li>
+<li><a href="poly2_r.c#checkvertex">qh_checkvertex</a>
+check vertex for consistency </li>
+<li><a href="poly2_r.c#infiniteloop">qh_infiniteloop</a>
+report error for a loop of facets </li>
+<li><a href="poly2_r.c#printlists">qh_printlists</a>
+print out facet list for debugging </li>
+</ul>
+
+
+<p><!-- Navigation links --> </p>
+<hr>
+<p><b>Up:</b>
+<a href="http://www.qhull.org">Home page for
+Qhull</a> <br>
+<b>Up:</b> <a href="../../html/index.htm#TOC">Qhull manual: Table of Contents</a> <br>
+<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a>
+&#149; <a href="../../html/qh-quick.htm#options">Options</a>
+&#149; <a href="../../html/qh-opto.htm#output">Output</a>
+&#149; <a href="../../html/qh-optf.htm#format">Formats</a>
+&#149; <a href="../../html/qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="../../html/qh-optp.htm#print">Print</a>
+&#149; <a href="../../html/qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="../../html/qh-optc.htm#prec">Precision</a>
+&#149; <a href="../../html/qh-optt.htm#trace">Trace</a>
+&#149; <a href="index.htm">Functions</a><br>
+<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code: Table of Contents</a> <br>
+<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
+<b>To:</b> <a href="qh-geom_r.htm">Geom</a> &#149;
+<a href="qh-globa_r.htm">Global</a> &#149; <a href="qh-io_r.htm">Io</a>
+&#149; <a href="qh-mem_r.htm">Mem</a> &#149; <a href="qh-merge_r.htm">Merge</a>
+&#149; <a href="qh-poly_r.htm">Poly</a> &#149; <a href="qh-qhull_r.htm#TOC">Qhull</a>
+&#149; <a href="qh-set_r.htm">Set</a> &#149; <a href="qh-stat_r.htm">Stat</a>
+&#149; <a href="qh-user_r.htm">User</a><br>
+</p>
+<p><!-- GC common information --> </p>
+<hr>
+<p><a href="http://www.geom.uiuc.edu/"><img
+src="../../html/qh--geom.gif" align="middle" width="40" height="40"></a><i>The
+Geometry Center Home Page </i></p>
+<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
+</a><br>
+Created: May 2, 1997 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
+</body>
+</html>
diff --git a/xs/src/qhull/src/libqhull_r/qh-qhull_r.htm b/xs/src/qhull/src/libqhull_r/qh-qhull_r.htm
new file mode 100644
index 0000000000..25d5e49722
--- /dev/null
+++ b/xs/src/qhull/src/libqhull_r/qh-qhull_r.htm
@@ -0,0 +1,279 @@
+<!-- Do not edit with Front Page, it adds too many spaces -->
+<html>
+<head>
+<meta http-equiv="Content-Type"
+content="text/html; charset=iso-8859-1">
+<title>libqhull_r.c -- top-level functions and basic data types</title>
+</head>
+
+<body>
+<!-- Navigation links -->
+<p><a name="TOP"><b>Up:</b></a> <a
+href="http://www.qhull.org">Home page</a> for Qhull<br>
+<b>Up:</b> <a href="../../html/index.htm#TOC">Qhull manual</a>: Table of Contents <br>
+<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a>
+&#149; <a href="../../html/qh-quick.htm#options">Options</a>
+&#149; <a href="../../html/qh-opto.htm#output">Output</a>
+&#149; <a href="../../html/qh-optf.htm#format">Formats</a>
+&#149; <a href="../../html/qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="../../html/qh-optp.htm#print">Print</a>
+&#149; <a href="../../html/qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="../../html/qh-optc.htm#prec">Precision</a>
+&#149; <a href="../../html/qh-optt.htm#trace">Trace</a>
+&#149; <a href="index.htm">Functions</a><br>
+<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code: Table of Contents</a><br>
+<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
+<b>To:</b> <a href="qh-geom_r.htm">Geom</a> &#149; <a href="qh-globa_r.htm">Global</a>
+&#149; <a href="qh-io_r.htm">Io</a> &#149; <a href="qh-mem_r.htm">Mem</a>
+&#149; <a href="qh-merge_r.htm">Merge</a> &#149; <a href="qh-poly_r.htm">Poly</a>
+&#149; <a href="qh-qhull_r.htm#TOC">Qhull</a> &#149; <a href="qh-set_r.htm">Set</a>
+&#149; <a href="qh-stat_r.htm">Stat</a> &#149; <a href="qh-user_r.htm">User</a>
+</p>
+<hr>
+
+<h2>libqhull_r.c -- top-level functions and basic data types</h2>
+<blockquote>
+<p>Qhull implements the Quickhull algorithm for computing
+the convex hull. The Quickhull algorithm combines two
+well-known algorithms: the 2-d quickhull algorithm and
+the n-d beneath-beyond algorithm. See
+<a href="../../html/index.htm#description">Description of Qhull</a>. </p>
+<p>This section provides an index to the top-level
+functions and base data types.  The top-level header file, <tt>libqhull_r.h</tt>,
+contains prototypes for these functions.</p>
+</blockquote>
+<p><b>Copyright &copy; 1995-2015 C.B. Barber</b></p>
+<hr>
+<p><a href="#TOP">&#187;</a> <a href="qh-geom_r.htm#TOC">Geom</a>
+<a name="TOC">&#149;</a> <a href="qh-globa_r.htm#TOC">Global</a>
+&#149; <a href="qh-io_r.htm#TOC">Io</a> &#149; <a href="qh-mem_r.htm#TOC">Mem</a>
+&#149; <a href="qh-merge_r.htm#TOC">Merge</a> &#149; <a href="qh-poly_r.htm#TOC">Poly</a>
+&#149; <b>Qhull</b> &#149; <a href="qh-set_r.htm#TOC">Set</a>
+&#149; <a href="qh-stat_r.htm#TOC">Stat</a> &#149; <a href="qh-user_r.htm#TOC">User</a>
+</p>
+<h3>Index to <a href="libqhull_r.c">libqhull_r.c</a>,
+<a href="libqhull_r.h">libqhull_r.h</a>, and
+<a href="../qhull/unix_r.c">unix_r.c</a></h3>
+<ul>
+<li><a href="#qtype">libqhull_r.h and unix_r.c data types and
+constants</a> </li>
+<li><a href="#qmacro">libqhull_r.h other macros</a> </li>
+<li><a href="#qfunc">Quickhull routines in call order</a> </li>
+<li><a href="#qinit">Top-level routines for initializing and terminating Qhull</a></li>
+<li><a href="#qin">Top-level routines for reading and modifying the input</a></li>
+<li><a href="#qcall">Top-level routines for calling Qhull</a></li>
+<li><a href="#qout">Top-level routines for returning results</a></li>
+<li><a href="#qtest">Top-level routines for testing and debugging</a></li>
+</ul>
+
+<h3><a href="qh-qhull_r.htm#TOC">&#187;</a><a name="qtype">libqhull_r.h and unix_r.c
+data types and constants</a></h3>
+<ul>
+<li><a href="libqhull_r.h#flagT">flagT</a> Boolean flag as
+a bit </li>
+<li><a href="libqhull_r.h#boolT">boolT</a> boolean value,
+either True or False </li>
+<li><a href="libqhull_r.h#CENTERtype">CENTERtype</a> to
+distinguish facet-&gt;center </li>
+<li><a href="libqhull_r.h#qh_PRINT">qh_PRINT</a> output
+formats for printing (qh.PRINTout) </li>
+<li><a href="libqhull_r.h#qh_ALL">qh_ALL</a> argument flag
+for selecting everything </li>
+<li><a href="libqhull_r.h#qh_ERR">qh_ERR</a> Qhull exit
+codes for indicating errors </li>
+<li><a href="libqhull_r.h#qh_FILEstderr">qh_FILEstderr</a> Fake stderr
+to distinguish error output from normal output [C++ only]</li>
+<li><a href="../qhull/unix_r.c#prompt">qh_prompt</a> version and long prompt for Qhull</li>
+<li><a href="../qhull/unix_r.c#prompt2">qh_prompt2</a> synopsis for Qhull</li>
+<li><a href="../qhull/unix_r.c#prompt3">qh_prompt3</a> concise prompt for Qhull</li>
+<li><a href="global_r.c#qh_version">qh_version</a> version stamp</li>
+</ul>
+
+<h3><a href="qh-qhull_r.htm#TOC">&#187;</a><a name="qmacro">libqhull_r.h other
+macros</a></h3>
+<ul>
+<li><a href="qhull_ra.h#traceN">traceN</a> print trace
+message if <em>qh.IStracing &gt;= N</em>. </li>
+<li><a href="qhull_ra.h#QHULL_UNUSED">QHULL_UNUSED</a> declare an
+ unused variable to avoid warnings. </li>
+</ul>
+
+<h3><a href="qh-qhull_r.htm#TOC">&#187;</a><a name="qfunc">Quickhull
+routines in call order</a></h3>
+<ul>
+<li><a href="../qhull/unix_r.c#main">main</a> processes the
+command line, calls qhull() to do the work, and
+exits </li>
+<li><a href="libqhull_r.c#qhull">qh_qhull</a> construct
+the convex hull of a set of points </li>
+<li><a href="libqhull_r.c#build_withrestart">qh_build_withrestart</a>
+allow restarts while calling qh_buildhull</li>
+<li><a href="poly2_r.c#initbuild">qh_initbuild</a>
+initialize hull and outside sets with point array</li>
+<li><a href="libqhull_r.c#partitionall">qh_partitionall</a>
+partition all points into outside sets </li>
+<li><a href="libqhull_r.c#buildhull">qh_buildhull</a>
+construct a convex hull by adding points one at a
+time </li>
+<li><a href="libqhull_r.c#nextfurthest">qh_nextfurthest</a>
+return next furthest point for processing </li>
+<li><a href="libqhull_r.c#buildtracing">qh_buildtracing</a>
+trace an iteration of buildhull </li>
+<li><a href="libqhull_r.c#addpoint">qh_addpoint</a> add a
+point to the convex hull </li>
+<li><a href="libqhull_r.c#findhorizon">qh_findhorizon</a>
+find the horizon and visible facets for a point </li>
+<li><a href="libqhull_r.c#partitionvisible">qh_partitionvisible</a>
+partition points from facets in qh.visible_list
+to facets in qh.newfacet_list </li>
+<li><a href="libqhull_r.c#partitionpoint">qh_partitionpoint</a>
+partition a point as inside, coplanar with, or
+outside a facet </li>
+<li><a href="libqhull_r.c#partitioncoplanar">qh_partitioncoplanar</a>
+partition coplanar point into a facet </li>
+<li><a href="libqhull_r.c#precision">qh_precision</a> restart on precision errors if not merging and if 'QJn'</li>
+</ul>
+
+<h3><a href="qh-qhull_r.htm#TOC">&#187;</a><a name="qinit">Top-level routines for initializing and terminating Qhull (in other modules)</a></h3>
+<ul>
+<li><a href="global_r.c#freebuild">qh_freebuild</a>
+free memory used by qh_initbuild and qh_buildhull
+</li>
+<li><a href="global_r.c#checkflags">qh_checkflags</a>
+check flags for multiple frontends to qhull
+<li><a href="global_r.c#freeqhull">qh_freeqhull</a>
+free memory used by qhull </li>
+<li><a href="global_r.c#init_A">qh_init_A</a> called
+before error handling initialized </li>
+<li><a href="global_r.c#init_B">qh_init_B</a> called
+after points are defined </li>
+<li><a href="global_r.c#initflags">qh_initflags</a> set
+flags and constants from command line </li>
+<li><a href="rboxlib_r.c#rboxpoints">qh_rboxpoints</a>
+generate points for qhull </li>
+<li><a href="global_r.c#restore_qhull">qh_restore_qhull</a>
+restores a saved qhull </li>
+<li><a href="global_r.c#save_qhull">qh_save_qhull</a>
+saves qhull for later restoring </li>
+<li><a href="user_r.c#user_memsizes">qh_user_memsizes</a>
+define additional quick allocation sizes
+</li>
+</ul>
+
+<h3><a href="qh-qhull_r.htm#TOC">&#187;</a><a name="qin">Top-level routines for reading and modifying the input (in other modules)</a></h3>
+<ul>
+<li><a href="geom2_r.c#gram_schmidt">qh_gram_schmidt</a>
+implements Gram-Schmidt orthogonalization by rows </li>
+<li><a href="geom2_r.c#projectinput">qh_projectinput</a>
+project input along one or more dimensions +
+Delaunay projection </li>
+<li><a href="geom2_r.c#randommatrix">qh_randommatrix</a>
+generate a random dimXdim matrix in range (-1,1) </li>
+<li><a href="io_r.c#readpoints">qh_readpoints</a> read
+points from input </li>
+<li><a href="geom2_r.c#rotateinput">qh_rotateinput</a> rotate
+input points using row matrix </li>
+<li><a href="geom2_r.c#scaleinput">qh_scaleinput</a> scale
+input points using qh low_bound/high_bound </li>
+<li><a href="geom2_r.c#setdelaunay">qh_setdelaunay</a> project
+points to paraboloid for Delaunay triangulation </li>
+<li><a href="geom2_r.c#sethalfspace_all">qh_sethalfspace_all</a>
+generate dual for halfspace intersection with interior
+point </li>
+</ul>
+
+<h3><a href="qh-qhull_r.htm#TOC">&#187;</a><a name="qcall">Top-level routines for calling Qhull (in other modules)</a></h3>
+<ul>
+<li><a href="libqhull_r.c#addpoint">qh_addpoint</a> add
+point to convex hull </li>
+<li><a href="poly2_r.c#findbestfacet">qh_findbestfacet</a>
+find facet that is furthest below a point </li>
+<li><a href="poly2_r.c#findfacet_all">qh_findfacet_all</a>
+exhaustive search for facet below a point </li>
+<li><a href="libqhull_r.c#qhull">qh_qhull</a> construct
+the convex hull of a set of points </li>
+</ul>
+
+<h3><a href="qh-qhull_r.htm#TOC">&#187;</a><a name="qout">Top-level routines for returning results (in other modules)</a></h3>
+<ul>
+<li><a href="stat_r.c#collectstatistics">qh_collectstatistics</a>
+collect statistics for qh.facet_list </li>
+<li><a href="poly2_r.c#nearvertex">qh_nearvertex</a>
+return nearest vertex to point </li>
+<li><a href="poly2_r.c#point">qh_point</a> return point
+for a point ID </li>
+<li><a href="poly2_r.c#pointfacet">qh_pointfacet</a>
+return temporary set of facets indexed by point
+ID </li>
+<li><a href="poly_r.c#pointid">qh_pointid</a> return ID
+for a point</li>
+<li><a href="poly2_r.c#pointvertex">qh_pointvertex</a>
+return vertices (if any) for all points</li>
+<li><a href="stat_r.c#printallstatistics">qh_printallstatistics</a>
+print all statistics </li>
+<li><a href="io_r.c#printneighborhood">qh_printneighborhood</a>
+print neighborhood of one or two facets </li>
+<li><a href="libqhull_r.c#printsummary">qh_printsummary</a>
+print summary </li>
+<li><a href="io_r.c#produce_output">qh_produce_output</a>
+print the results of qh_qhull() </li>
+<li><a href="poly2_r.c#setvoronoi_all">qh_setvoronoi_all</a>
+compute Voronoi centers for all facets </li>
+</ul>
+
+<h3><a href="qh-qhull_r.htm#TOC">&#187;</a><a name="qtest">Top-level routines for testing and debugging (in other modules)</a></h3>
+<ul>
+<li><a href="io_r.c#dfacet">dfacet</a> print facet by
+ID from debugger </li>
+<li><a href="io_r.c#dvertex">dvertex</a> print vertex
+by ID from debugger </li>
+<li><a href="poly2_r.c#check_output">qh_check_output</a>
+check output </li>
+<li><a href="poly2_r.c#check_points">qh_check_points</a>
+verify that all points are inside the convex hull
+</li>
+<li><a href="user_r.c#errexit">qh_errexit</a> report
+error with a facet and a ridge</li>
+<li><a href="libqhull_r.c#errexit2">qh_errexit2</a> report
+error with two facets </li>
+<li><a href="user_r.c#errprint">qh_errprint</a> print
+erroneous facets, ridge, and vertex </li>
+<li><a href="user_r.c#printfacetlist">qh_printfacetlist</a>
+print all fields for a list of facets </li>
+</ul>
+
+<p><!-- Navigation links --> </p>
+<hr>
+<p><b>Up:</b>
+<a href="http://www.qhull.org">Home page for
+Qhull</a> <br>
+<b>Up:</b> <a href="../../html/index.htm#TOC">Qhull manual: Table of Contents</a> <br>
+<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a>
+&#149; <a href="../../html/qh-quick.htm#options">Options</a>
+&#149; <a href="../../html/qh-opto.htm#output">Output</a>
+&#149; <a href="../../html/qh-optf.htm#format">Formats</a>
+&#149; <a href="../../html/qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="../../html/qh-optp.htm#print">Print</a>
+&#149; <a href="../../html/qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="../../html/qh-optc.htm#prec">Precision</a>
+&#149; <a href="../../html/qh-optt.htm#trace">Trace</a>
+&#149; <a href="index.htm">Functions</a><br>
+<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code: Table of Contents</a> <br>
+<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
+<b>To:</b> <a href="qh-geom_r.htm">Geom</a> &#149;
+<a href="qh-globa_r.htm">Global</a> &#149; <a href="qh-io_r.htm">Io</a>
+&#149; <a href="qh-mem_r.htm">Mem</a> &#149; <a href="qh-merge_r.htm">Merge</a>
+&#149; <a href="qh-poly_r.htm">Poly</a> &#149; <a href="qh-qhull_r.htm#TOC">Qhull</a>
+&#149; <a href="qh-set_r.htm">Set</a> &#149; <a href="qh-stat_r.htm">Stat</a>
+&#149; <a href="qh-user_r.htm">User</a><br>
+</p>
+<p><!-- GC common information --> </p>
+<hr>
+<p><a href="http://www.geom.uiuc.edu/"><img
+src="../../html/qh--geom.gif" align="middle" width="40" height="40"></a><i>The
+Geometry Center Home Page </i></p>
+<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
+</a><br>
+Created: May 2, 1997 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
+</body>
+</html>
diff --git a/xs/src/qhull/src/libqhull_r/qh-set_r.htm b/xs/src/qhull/src/libqhull_r/qh-set_r.htm
new file mode 100644
index 0000000000..cf8ab63af9
--- /dev/null
+++ b/xs/src/qhull/src/libqhull_r/qh-set_r.htm
@@ -0,0 +1,308 @@
+<!-- Do not edit with Front Page, it adds too many spaces -->
+<html>
+<head>
+<meta http-equiv="Content-Type"
+content="text/html; charset=iso-8859-1">
+<title>qset_r.c -- set data type and operations</title>
+</head>
+
+<body>
+<!-- Navigation links -->
+<p><a name="TOP"><b>Up:</b></a> <a
+href="http://www.qhull.org">Home page</a> for Qhull<br>
+<b>Up:</b> <a href="../../html/index.htm#TOC">Qhull manual</a>: Table of Contents <br>
+<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a>
+&#149; <a href="../../html/qh-quick.htm#options">Options</a>
+&#149; <a href="../../html/qh-opto.htm#output">Output</a>
+&#149; <a href="../../html/qh-optf.htm#format">Formats</a>
+&#149; <a href="../../html/qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="../../html/qh-optp.htm#print">Print</a>
+&#149; <a href="../../html/qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="../../html/qh-optc.htm#prec">Precision</a>
+&#149; <a href="../../html/qh-optt.htm#trace">Trace</a>
+&#149; <a href="index.htm">Functions</a><br>
+<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code: Table of Contents</a><br>
+<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
+<b>To:</b> <a href="qh-geom_r.htm">Geom</a> &#149; <a href="qh-globa_r.htm">Global</a>
+&#149; <a href="qh-io_r.htm">Io</a> &#149; <a href="qh-mem_r.htm">Mem</a>
+&#149; <a href="qh-merge_r.htm">Merge</a> &#149; <a href="qh-poly_r.htm">Poly</a>
+&#149; <a href="qh-qhull_r.htm">Qhull</a> &#149; <a href="qh-set_r.htm#TOC">Set</a>
+&#149; <a href="qh-stat_r.htm">Stat</a> &#149; <a href="qh-user_r.htm">User</a>
+</p>
+<hr>
+
+<h2>qset_r.c -- set data type and operations</h2>
+<blockquote>
+<p>Qhull's data structures are constructed from sets. The
+functions and macros in qset_r.c construct, iterate, and
+modify these sets. They are the most frequently called
+functions in Qhull. For this reason, efficiency is the
+primary concern. </p>
+<p>In Qhull, a <i>set</i> is represented by an unordered
+array of pointers with a maximum size and a NULL
+terminator (<a href="qset_r.h#setT">setT</a>).
+Most sets correspond to mathematical sets
+(i.e., the pointers are unique). Some sets are sorted to
+enforce uniqueness. Some sets are ordered. For example,
+the order of vertices in a ridge determine the ridge's
+orientation. If you reverse the order of adjacent
+vertices, the orientation reverses. Some sets are not
+mathematical sets. They may be indexed as an array and
+they may include NULL pointers. </p>
+<p>The most common operation on a set is to iterate its
+members. This is done with a 'FOREACH...' macro. Each set
+has a custom macro. For example, 'FOREACHvertex_'
+iterates over a set of vertices. Each vertex is assigned
+to the variable 'vertex' from the pointer 'vertexp'. </p>
+<p>Most sets are constructed by appending elements to the
+set. The last element of a set is either NULL or the
+index of the terminating NULL for a partially full set.
+If a set is full, appending an element copies the set to
+a larger array. </p>
+
+</blockquote>
+<p><b>Copyright &copy; 1995-2015 C.B. Barber</b></p>
+<hr>
+<p><a href="#TOP">&#187;</a> <a href="qh-geom_r.htm#TOC">Geom</a>
+<a name="TOC">&#149;</a> <a href="qh-globa_r.htm#TOC">Global</a> &#149;
+<a href="qh-io_r.htm#TOC">Io</a> &#149; <a href="qh-mem_r.htm#TOC">Mem</a> &#149;
+<a href="qh-merge_r.htm#TOC">Merge</a> &#149; <a href="qh-poly_r.htm#TOC">Poly</a>
+&#149; <a href="qh-qhull_r.htm#TOC">Qhull</a> &#149; <b>Set</b>
+&#149; <a href="qh-stat_r.htm#TOC">Stat</a> &#149; <a href="qh-user_r.htm#TOC">User</a>
+</p>
+<h3>Index to <a href="qset_r.c">qset_r.c</a> and
+<a href="qset_r.h">qset_r.h</a></h3>
+<ul>
+<li><a href="#stype">Data types and constants</a> </li>
+<li><a href="#seach">FOREACH macros</a> </li>
+<li><a href="#saccess">access and size macros</a> </li>
+<li><a href="#sint">internal macros</a> </li>
+<li><a href="#saddr">address macros</a><p>&nbsp;</li>
+
+<li><a href="#snew">Allocation and deallocation functions</a> </li>
+<li><a href="#spred">Access and predicate functions</a>
+</li>
+<li><a href="#sadd">Add functions</a> </li>
+<li><a href="#scheck">Check and print functions</a></li>
+<li><a href="#scopy">Copy, compact, and zero functions</a></li>
+<li><a href="#sdel">Delete functions</a> </li>
+<li><a href="#stemp">Temporary set functions</a> </li>
+</ul>
+<h3><a href="qh-set_r.htm#TOC">&#187;</a><a name="stype">Data types and
+constants</a></h3>
+<ul>
+<li><a href="qset_r.h#SETelemsize">SETelemsize</a> size
+of a set element in bytes </li>
+<li><a href="qset_r.h#setT">setT</a> a set with a
+maximum size and a current size</li>
+<li><a href="libqhull_r.h#qh-set">qh global sets</a>
+global sets for temporary sets, etc. </li>
+</ul>
+<h3><a href="qh-set_r.htm#TOC">&#187;</a><a name="seach">FOREACH macros</a></h3>
+<ul>
+<li><a href="qset_r.h#FOREACHelem_">FOREACHelem_</a>
+assign 'elem' to each element in a set </li>
+<li><a href="qset_r.h#FOREACHset_">FOREACHset_</a>
+assign 'set' to each set in a set of sets </li>
+<li><a href="qset_r.h#FOREACHsetelement_">FOREACHsetelement_</a>
+define a FOREACH iterator </li>
+<li><a href="qset_r.h#FOREACHsetelement_i_">FOREACHsetelement_i_</a>
+define an indexed FOREACH iterator </li>
+<li><a href="qset_r.h#FOREACHsetelementreverse_">FOREACHsetelementreverse_</a>
+define a reversed FOREACH iterator </li>
+<li><a href="qset_r.h#FOREACHsetelementreverse12_">FOREACHsetelementreverse12_</a>
+define a FOREACH iterator with e[1] and e[0]
+reversed </li>
+</ul>
+<h3><a href="qh-set_r.htm#TOC">&#187;</a><a name="saccess">Access and
+size macros</a></h3>
+<ul>
+<li><a href="qset_r.h#SETelem_">SETelem_</a> return the
+n'th element of set </li>
+<li><a href="qset_r.h#SETelemt_">SETelemt_</a> return
+the n'th element of set as a type</li>
+<li><a href="qset_r.h#SETempty_">SETempty_</a> return
+true (1) if set is empty </li>
+<li><a href="qset_r.h#SETfirst_">SETfirst_</a> return
+first element of set </li>
+<li><a href="qset_r.h#SETfirstt_">SETfirstt_</a> return
+first element of set as a type</li>
+<li><a href="qset_r.h#SETindex_">SETindex_</a> return
+index of elem in set </li>
+<li><a href="qset_r.h#SETreturnsize_">SETreturnsize_</a>
+return size of a set (normally use <a href="qset_r.c#setsize">qh_setsize</a>) </li>
+<li><a href="qset_r.h#SETsecond_">SETsecond_</a> return
+second element of set </li>
+<li><a href="qset_r.h#SETsecondt_">SETsecondt_</a>
+return second element of set as a type</li>
+<li><a href="qset_r.h#SETtruncate_">SETtruncate_</a>
+truncate set to size, i.e., qh_settruncate()</li>
+</ul>
+<h3><a href="qh-set_r.htm#TOC">&#187;</a><a name="sint">Internal macros</a></h3>
+<ul>
+<li><a href="qset_r.c#SETsizeaddr_">SETsizeaddr_</a>
+return pointer to end element of a set (indicates
+current size) </li>
+</ul>
+
+<h3><a href="qh-set_r.htm#TOC">&#187;</a><a name="saddr">address macros</a></h3>
+<ul>
+<li><a href="qset_r.h#SETaddr_">SETaddr_</a> return
+address of a set's elements </li>
+<li><a href="qset_r.h#SETelemaddr_">SETelemaddr_</a>
+return address of the n'th element of a set </li>
+<li><a href="qset_r.h#SETref_">SETref_</a> l_r.h.s. for
+modifying the current element in a FOREACH
+iteration </li>
+</ul>
+
+<h3><a href="qh-set_r.htm#TOC">&#187;</a><a name="snew">Allocation and
+deallocation functions</a></h3>
+<ul>
+<li><a href="qset_r.c#setfree">qh_setfree</a> free the
+space occupied by a set </li>
+<li><a href="qset_r.c#setfree2">qh_setfree2</a> free a
+set and its elements </li>
+<li><a href="qset_r.c#setfreelong">qh_setfreelong</a>
+free a set only if it is in long memory </li>
+<li><a href="qset_r.c#setnew">qh_setnew</a> create a new
+set </li>
+</ul>
+
+<h3><a href="qh-set_r.htm#TOC">&#187;</a><a name="spred">Access and
+predicate functions </a></h3>
+<ul>
+<li><a href="qset_r.c#setendpointer">qh_setendpointer</a> return
+pointer to NULL terminator of a set</li>
+<li><a href="qset_r.c#setequal">qh_setequal</a> return 1
+if two sorted sets are equal </li>
+<li><a href="qset_r.c#setequal_except">qh_setequal_except</a>
+return 1 if two sorted sets are equal except for
+an element </li>
+<li><a href="qset_r.c#setequal_skip">qh_setequal_skip</a>
+return 1 if two sorted sets are equal except for
+a pair of skipped elements </li>
+<li><a href="qset_r.c#setequal_skip">qh_setequal_skip</a>
+return 1 if two sorted sets are equal except for
+a pair of skipped elements </li>
+<li><a href="qset_r.c#setin">qh_setin</a> return 1 if an
+element is in a set </li>
+<li><a href="qset_r.c#setindex">qh_setindex</a> return
+the index of an element in a set </li>
+<li><a href="qset_r.c#setlast">qh_setlast</a> return
+last element of a set</li>
+<li><a href="qset_r.c#setsize">qh_setsize</a> returns
+the size of a set </li>
+</ul>
+
+<h3><a href="qh-set_r.htm#TOC">&#187;</a><a name="sadd">Add functions</a></h3>
+<ul>
+<li><a href="qset_r.c#setaddnth">qh_setaddnth</a> add a
+element as n'th element of sorted or unsorted set
+</li>
+<li><a href="qset_r.c#setaddsorted">qh_setaddsorted</a>
+add an element to a sorted set </li>
+<li><a href="qset_r.c#setappend">qh_setappend</a> append
+an element to a set </li>
+<li><a href="qset_r.c#setappend_set">qh_setappend_set</a>
+append a set of elements to a set </li>
+<li><a href="qset_r.c#setappend2ndlast">qh_setappend2ndlast</a>
+add an element as the next to the last element in
+a set </li>
+<li><a href="qset_r.c#setlarger">qh_setlarger</a> return
+a larger set with the same elements</li>
+<li><a href="qset_r.c#setreplace">qh_setreplace</a>
+replace one element with another in a set</li>
+<li><a href="qset_r.c#setunique">qh_setunique</a> add an
+element if it is not already in a set </li>
+</ul>
+
+<h3><a href="qh-set_r.htm#TOC">&#187;</a><a name="scheck">Check and print functions</a></h3>
+<ul>
+<li><a href="qset_r.c#setcheck">qh_setcheck</a> check a
+set for validity </li>
+<li><a href="qset_r.c#setprint">qh_setprint</a> print a
+set's elements to fp </li>
+</ul>
+
+<h3><a href="qh-set_r.htm#TOC">&#187;</a><a name="scopy">Copy, compact, and zero functions</a></h3>
+<ul>
+<li><a href="qset_r.c#setcompact">qh_setcompact</a>
+compact NULLs from an unsorted set </li>
+<li><a href="qset_r.c#setcopy">qh_setcopy</a> make a
+copy of a sorted or unsorted set </li>
+<li><a href="qset_r.c#setduplicate">qh_setduplicate</a>
+duplicate a set and its elements </li>
+<li><a href="qset_r.c#settruncate">qh_settruncate</a>
+truncate a set to size elements </li>
+<li><a href="qset_r.c#setzero">qh_setzero</a> zero the
+remainder of a set </li>
+</ul>
+
+<h3><a href="qh-set_r.htm#TOC">&#187;</a><a name="sdel">Delete functions</a></h3>
+<ul>
+<li><a href="qset_r.c#setdel">qh_setdel</a> delete an
+element from an unsorted set. </li>
+<li><a href="qset_r.c#setdellast">qh_setdellast</a>
+delete and return last element from a set</li>
+<li><a href="qset_r.c#setdelnth">qh_setdelnth</a> delete
+and return nth element from an unsorted set </li>
+<li><a href="qset_r.c#setdelnthsorted">qh_setdelnthsorted</a>
+delete and return nth element from a sorted set </li>
+<li><a href="qset_r.c#setdelsorted">qh_setdelsorted</a>
+delete an element from a sorted set </li>
+<li><a href="qset_r.c#setnew_delnthsorted">qh_setnew_delnthsorted</a>
+create a sorted set not containing the nth
+element </li>
+</ul>
+
+<h3><a href="qh-set_r.htm#TOC">&#187;</a><a name="stemp">Temporary set functions</a></h3>
+<ul>
+<li><a href="qset_r.c#settemp">qh_settemp</a> return a
+temporary set and append it qhmem.tempstack</li>
+<li><a href="qset_r.c#settempfree">qh_settempfree</a>
+free and pop a set from qhmem.tempstack</li>
+<li><a href="qset_r.c#settempfree_all">qh_settempfree_all</a>
+free all sets in qhmem.tempstack </li>
+<li><a href="qset_r.c#settemppop">qh_settemppop</a> pop
+a set from qhmem.tempstack (makes it permanent) </li>
+<li><a href="qset_r.c#settemppush">qh_settemppush</a>
+push a set unto qhmem.tempstack (makes it
+temporary) </li>
+</ul>
+
+<p><!-- Navigation links --> </p>
+<hr>
+<p><b>Up:</b>
+<a href="http://www.qhull.org">Home page for
+Qhull</a> <br>
+<b>Up:</b> <a href="../../html/index.htm#TOC">Qhull manual: Table of Contents</a> <br>
+<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a>
+&#149; <a href="../../html/qh-quick.htm#options">Options</a>
+&#149; <a href="../../html/qh-opto.htm#output">Output</a>
+&#149; <a href="../../html/qh-optf.htm#format">Formats</a>
+&#149; <a href="../../html/qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="../../html/qh-optp.htm#print">Print</a>
+&#149; <a href="../../html/qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="../../html/qh-optc.htm#prec">Precision</a>
+&#149; <a href="../../html/qh-optt.htm#trace">Trace</a>
+&#149; <a href="index.htm">Functions</a><br>
+<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code: Table of Contents</a> <br>
+<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
+<b>To:</b> <a href="qh-geom_r.htm">Geom</a> &#149;
+<a href="qh-globa_r.htm">Global</a> &#149; <a href="qh-io_r.htm">Io</a>
+&#149; <a href="qh-mem_r.htm">Mem</a> &#149; <a href="qh-merge_r.htm">Merge</a>
+&#149; <a href="qh-poly_r.htm">Poly</a> &#149; <a href="qh-qhull_r.htm#TOC">Qhull</a>
+&#149; <a href="qh-set_r.htm">Set</a> &#149; <a href="qh-stat_r.htm">Stat</a>
+&#149; <a href="qh-user_r.htm">User</a><br>
+</p>
+<p><!-- GC common information --> </p>
+<hr>
+<p><a href="http://www.geom.uiuc.edu/"><img
+src="../../html/qh--geom.gif" align="middle" width="40" height="40"></a><i>The
+Geometry Center Home Page </i></p>
+<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
+</a><br>
+Created: May 2, 1997 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
+</body>
+</html>
diff --git a/xs/src/qhull/src/libqhull_r/qh-stat_r.htm b/xs/src/qhull/src/libqhull_r/qh-stat_r.htm
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--- /dev/null
+++ b/xs/src/qhull/src/libqhull_r/qh-stat_r.htm
@@ -0,0 +1,161 @@
+<!-- Do not edit with Front Page, it adds too many spaces -->
+<html>
+<head>
+<meta http-equiv="Content-Type"
+content="text/html; charset=iso-8859-1">
+<title>stat_r.c -- statistical operations</title>
+</head>
+
+<body>
+<!-- Navigation links -->
+<p><a name="TOP"><b>Up:</b></a> <a
+href="http://www.qhull.org">Home page</a> for Qhull<br>
+<b>Up:</b> <a href="../../html/index.htm#TOC">Qhull manual</a>: Table of Contents <br>
+<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a>
+&#149; <a href="../../html/qh-quick.htm#options">Options</a>
+&#149; <a href="../../html/qh-opto.htm#output">Output</a>
+&#149; <a href="../../html/qh-optf.htm#format">Formats</a>
+&#149; <a href="../../html/qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="../../html/qh-optp.htm#print">Print</a>
+&#149; <a href="../../html/qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="../../html/qh-optc.htm#prec">Precision</a>
+&#149; <a href="../../html/qh-optt.htm#trace">Trace</a>
+&#149; <a href="index.htm">Functions</a><br>
+<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code: Table of Contents</a><br>
+<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
+<b>To:</b> <a href="qh-geom_r.htm">Geom</a> &#149; <a href="qh-globa_r.htm">Global</a>
+&#149; <a href="qh-io_r.htm">Io</a> &#149; <a href="qh-mem_r.htm">Mem</a>
+&#149; <a href="qh-merge_r.htm">Merge</a> &#149; <a href="qh-poly_r.htm">Poly</a>
+&#149; <a href="qh-qhull_r.htm">Qhull</a> &#149; <a href="qh-set_r.htm">Set</a>
+&#149; <a href="qh-stat_r.htm#TOC">Stat</a> &#149; <a href="qh-user_r.htm">User</a>
+</p>
+<hr>
+
+<h2>stat_r.c -- statistical operations</h2>
+<blockquote>
+<p>Qhull records many statistics. These functions and
+macros make it inexpensive to add a statistic.
+<p>As with Qhull's global variables, the statistics data structure is
+accessed by a macro, 'qhstat'.  If qh_QHpointer is defined, the macro
+is 'qh_qhstat->', otherwise the macro is 'qh_qhstat.'.
+Statistics
+may be turned off in user_r.h. If so, all but the 'zz'
+statistics are ignored.</p>
+</blockquote>
+<p><b>Copyright &copy; 1995-2015 C.B. Barber</b></p>
+<hr>
+<p><a href="#TOP">&#187;</a> <a href="qh-geom_r.htm#TOC">Geom</a>
+<a name="TOC">&#149;</a> <a href="qh-globa_r.htm#TOC">Global</a>
+&#149; <a href="qh-io_r.htm#TOC">Io</a> &#149; <a href="qh-mem_r.htm#TOC">Mem</a>
+&#149; <a href="qh-merge_r.htm#TOC">Merge</a> &#149; <a href="qh-poly_r.htm#TOC">Poly</a>
+&#149; <a href="qh-qhull_r.htm#TOC">Qhull</a> &#149; <a href="qh-set_r.htm#TOC">Set</a>
+&#149; <b>Stat</b> &#149; <a href="qh-user_r.htm#TOC">User</a>
+</p>
+<h3>Index to <a href="stat_r.c">stat_r.c</a> and
+<a href="stat_r.h">stat_r.h</a></h3>
+<ul>
+<li><a href="#ttype">stat_r.h types</a> </li>
+<li><a href="#tconst">stat_r.h constants</a> </li>
+<li><a href="#tmacro">stat_r.h macros</a> </li>
+<li><a href="#tfunc">stat_r.c functions</a> </li>
+</ul>
+
+<h3><a href="qh-stat_r.htm#TOC">&#187;</a><a name="ttype">stat_r.h types</a></h3>
+<ul>
+<li><a href="stat_r.h#intrealT">intrealT</a> union of
+integer and real</li>
+<li><a href="stat_r.h#qhstat">qhstat</a> global data
+structure for statistics </li>
+</ul>
+<h3><a href="qh-stat_r.htm#TOC">&#187;</a><a name="tconst">stat_r.h
+constants</a></h3>
+<ul>
+<li><a href="stat_r.h#KEEPstatistics">qh_KEEPstatistics</a> 0 turns off most statistics</li>
+<li><a href="stat_r.h#statistics">Z..., W...</a> integer (Z) and real (W) statistics
+</li>
+<li><a href="stat_r.h#ZZstat">ZZstat</a> Z.../W... statistics that
+remain defined if qh_KEEPstatistics=0
+</li>
+<li><a href="stat_r.h#ztype">ztype</a> zdoc, zinc, etc.
+for definining statistics </li>
+</ul>
+<h3><a href="qh-stat_r.htm#TOC">&#187;</a><a name="tmacro">stat_r.h macros</a></h3>
+<ul>
+<li><a href="stat_r.h#MAYdebugx">MAYdebugx</a> called
+frequently for error trapping </li>
+<li><a href="stat_r.h#zadd_">zadd_/wadd_</a> add value
+to an integer or real statistic </li>
+<li><a href="stat_r.h#zdef_">zdef_</a> define a
+statistic </li>
+<li><a href="stat_r.h#zinc_">zinc_</a> increment an
+integer statistic </li>
+<li><a href="stat_r.h#zmax_">zmax_/wmax_</a> update
+integer or real maximum statistic </li>
+<li><a href="stat_r.h#zmin_">zmin_/wmin_</a> update
+integer or real minimum statistic </li>
+<li><a href="stat_r.h#zval_">zval_/wval_</a> set or
+return value of a statistic </li>
+</ul>
+
+<h3><a href="qh-stat_r.htm#TOC">&#187;</a><a name="tfunc">stat_r.c
+functions</a></h3>
+<ul>
+<li><a href="stat_r.c#allstatA">qh_allstatA</a> define
+statistics in groups of 20 </li>
+<li><a href="stat_r.c#allstatistics">qh_allstatistics</a>
+reset printed flag for all statistics </li>
+<li><a href="stat_r.c#collectstatistics">qh_collectstatistics</a>
+collect statistics for qh.facet_list </li>
+<li><a href="stat_r.c#initstatistics">qh_initstatistics</a>
+allocate and initialize statistics </li>
+<li><a href="stat_r.c#newstats">qh_newstats</a> returns
+True if statistics for zdoc </li>
+<li><a href="stat_r.c#nostatistic">qh_nostatistic</a>
+true if no statistic to print </li>
+<li><a href="stat_r.c#printallstatistics">qh_printallstatistics</a>
+print all statistics </li>
+<li><a href="stat_r.c#printstatistics">qh_printstatistics</a>
+print statistics to a file </li>
+<li><a href="stat_r.c#printstatlevel">qh_printstatlevel</a>
+print level information for a statistic </li>
+<li><a href="stat_r.c#printstats">qh_printstats</a>
+print statistics for a zdoc group </li>
+<li><a href="stat_r.c#stddev">qh_stddev</a> compute the
+standard deviation and average from statistics </li>
+</ul>
+
+<p><!-- Navigation links --> </p>
+<hr>
+<p><b>Up:</b>
+<a href="http://www.qhull.org">Home page for
+Qhull</a> <br>
+<b>Up:</b> <a href="../../html/index.htm#TOC">Qhull manual: Table of Contents</a> <br>
+<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a>
+&#149; <a href="../../html/qh-quick.htm#options">Options</a>
+&#149; <a href="../../html/qh-opto.htm#output">Output</a>
+&#149; <a href="../../html/qh-optf.htm#format">Formats</a>
+&#149; <a href="../../html/qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="../../html/qh-optp.htm#print">Print</a>
+&#149; <a href="../../html/qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="../../html/qh-optc.htm#prec">Precision</a>
+&#149; <a href="../../html/qh-optt.htm#trace">Trace</a>
+&#149; <a href="index.htm">Functions</a><br>
+<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code: Table of Contents</a> <br>
+<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
+<b>To:</b> <a href="qh-geom_r.htm">Geom</a> &#149;
+<a href="qh-globa_r.htm">Global</a> &#149; <a href="qh-io_r.htm">Io</a>
+&#149; <a href="qh-mem_r.htm">Mem</a> &#149; <a href="qh-merge_r.htm">Merge</a>
+&#149; <a href="qh-poly_r.htm">Poly</a> &#149; <a href="qh-qhull_r.htm#TOC">Qhull</a>
+&#149; <a href="qh-set_r.htm">Set</a> &#149; <a href="qh-stat_r.htm">Stat</a>
+&#149; <a href="qh-user_r.htm">User</a><br>
+</p>
+<p><!-- GC common information --> </p>
+<hr>
+<p><a href="http://www.geom.uiuc.edu/"><img
+src="../../html/qh--geom.gif" align="middle" width="40" height="40"></a><i>The
+Geometry Center Home Page </i></p>
+<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
+</a><br>
+Created: May 2, 1997 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
+</body>
+</html>
diff --git a/xs/src/qhull/src/libqhull_r/qh-user_r.htm b/xs/src/qhull/src/libqhull_r/qh-user_r.htm
new file mode 100644
index 0000000000..909fec6564
--- /dev/null
+++ b/xs/src/qhull/src/libqhull_r/qh-user_r.htm
@@ -0,0 +1,271 @@
+<!-- Do not edit with Front Page, it adds too many spaces -->
+<html>
+<head>
+<meta http-equiv="Content-Type"
+content="text/html; charset=iso-8859-1">
+<title>user_r.c -- user-definable operations</title>
+</head>
+
+<body>
+<!-- Navigation links -->
+<p><a name="TOP"><b>Up:</b></a> <a
+href="http://www.qhull.org">Home page</a> for Qhull<br>
+<b>Up:</b> <a href="../../html/index.htm#TOC">Qhull manual</a>: Table of Contents <br>
+<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a>
+&#149; <a href="../../html/qh-quick.htm#options">Options</a>
+&#149; <a href="../../html/qh-opto.htm#output">Output</a>
+&#149; <a href="../../html/qh-optf.htm#format">Formats</a>
+&#149; <a href="../../html/qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="../../html/qh-optp.htm#print">Print</a>
+&#149; <a href="../../html/qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="../../html/qh-optc.htm#prec">Precision</a>
+&#149; <a href="../../html/qh-optt.htm#trace">Trace</a>
+&#149; <a href="index.htm">Functions</a><br>
+<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code: Table of Contents</a><br>
+<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
+<b>To:</b> <a href="qh-geom_r.htm">Geom</a> &#149; <a href="qh-globa_r.htm">Global</a>
+&#149; <a href="qh-io_r.htm">Io</a> &#149; <a href="qh-mem_r.htm">Mem</a>
+&#149; <a href="qh-merge_r.htm">Merge</a> &#149; <a href="qh-poly_r.htm">Poly</a>
+&#149; <a href="qh-qhull_r.htm">Qhull</a> &#149; <a href="qh-set_r.htm">Set</a>
+&#149; <a href="qh-stat_r.htm">Stat</a> &#149; <a href="qh-user_r.htm#TOC">User</a>
+</p>
+<hr>
+<h2>user_r.c -- user-definable operations</h2>
+<blockquote>
+<p>This section contains functions and constants that the
+user may want to change. </p>
+
+</blockquote>
+<p><b>Copyright &copy; 1995-2015 C.B. Barber</b></p>
+<hr>
+<p><a href="#TOP">&#187;</a> <a href="qh-geom_r.htm#TOC">Geom</a>
+<a name="TOC">&#149;</a> <a href="qh-globa_r.htm#TOC">Global</a>
+&#149; <a href="qh-io_r.htm#TOC">Io</a> &#149; <a href="qh-mem_r.htm#TOC">Mem</a>
+&#149; <a href="qh-merge_r.htm#TOC">Merge</a> &#149; <a href="qh-poly_r.htm#TOC">Poly</a>
+&#149; <a href="qh-qhull_r.htm#TOC">Qhull</a> &#149; <a href="qh-set_r.htm#TOC">Set</a>
+&#149; <a href="qh-stat_r.htm#TOC">Stat</a> &#149; <b>User</b>
+</p>
+<h3>Index to <a href="user_r.c">user_r.c</a>, <a href="usermem_r.c">usermem_r.c</a>, <a href="userprintf_r.c">userprintf_r.c</a>, <a href="userprintf_rbox_r.c">userprintf_rbox_r.c</a> and
+<a href="user_r.h">user_r.h</a></h3>
+<ul>
+<li><a href="#qulllib">qhull library constants</a></li>
+<li><a href="#utype">user_r.h data types and
+configuration macros</a> </li>
+<li><a href="#ujoggle">joggle constants</a></li>
+<li><a href="#uperform">performance related constants</a></li>
+<li><a href="#umemory">memory constants</a></li>
+<li><a href="#ucond">conditional compilation</a></li>
+<li><a href="#umerge">merge constants</a> </li>
+<li><a href="#ufunc">user_r.c functions</a> </li>
+<li><a href="#u2func">usermem_r.c functions</a> </li>
+<li><a href="#u3func">userprintf_r.c functions</a> </li>
+</ul>
+
+<h3><a href="qh-user_r.htm#TOC">&#187;</a><a name="qulllib">Qhull library constants</a></h3>
+<ul>
+<li><a href="user_r.h#filenamelen">FILENAMElen</a> -- max length of TI or TO filename </li>
+<li><a href="user_r.h#msgcode">msgcode</a> -- unique message codes for qh_fprintf </li>
+<li><a href="user_r.h#qh_OPTIONline">qh_OPTIONline</a> -- max length of option line ('FO')</li>
+</ul>
+
+
+<h3><a href="qh-user_r.htm#TOC">&#187;</a><a name="utype">user_r.h data
+types and configuration macros</a></h3>
+<ul>
+<li><a href="user_r.h#realT">realT, qh_REAL...</a> size
+of floating point numbers </li>
+<li><a href="user_r.h#countT">countT, COUNTmax</a> size
+of counts and identifiers, typically 'int' or 'long long' </li>
+<li><a href="user_r.h#CPUclock">qh_CPUclock</a> clock()
+function for reporting the total time spent by
+Qhull </li>
+<li><a href="user_r.h#RANDOM">qh_RANDOM...</a> random
+number generator </li>
+</ul>
+
+<h3><a href="qh-user_r.htm#TOC">&#187;</a><a name="udef">definition constants</a></h3>
+<ul>
+<li><a href="user_r.h#DEFAULTbox">qh_DEFAULTbox</a>
+define default box size for rbox, 'Qbb', and 'QbB' (Geomview expects 0.5) </li>
+<li><a href="user_r.h#INFINITE">qh_INFINITE</a> on
+output, indicates Voronoi center at infinity </li>
+<li><a href="user_r.h#ORIENTclock">qh_ORIENTclock</a>
+define convention for orienting facets</li>
+<li><a href="user_r.h#ZEROdelaunay">qh_ZEROdelaunay</a>
+define facets that are ignored in Delaunay triangulations</li>
+</ul>
+
+<h3><a href="qh-user_r.htm#TOC">&#187;</a><a name="ujoggle">joggle constants</a></h3>
+<ul>
+<li><a href="user_r.h#JOGGLEagain">qh_JOGGLEagain</a>
+how often to retry before using qh_JOGGLEmaxincrease
+again </li>
+<li><a href="user_r.h#JOGGLEdefault">qh_JOGGLEdefault</a>
+default value for qh.JOGGLEmax for 'QP' </li>
+<li><a href="user_r.h#JOGGLEincrease">qh_JOGGLEincrease</a>
+factor to increase qh.JOGGLEmax on retrys for
+'QPn' </li>
+<li><a href="user_r.h#JOGGLEmaxincrease">qh_JOGGLEmaxincrease</a> max
+for increasing qh.JOGGLEmax relative to
+qh.MAXwidth </li>
+<li><a href="user_r.h#JOGGLEretry">qh_JOGGLEmaxretry</a>
+report error if this many retries </li>
+<li><a href="user_r.h#JOGGLEretry">qh_JOGGLEretry</a>
+how often to retry before using qh_JOGGLEmax </li>
+</ul>
+
+<h3><a href="qh-user_r.htm#TOC">&#187;</a><a name="uperform">performance
+related constants</a></h3>
+<ul>
+<li><a href="user_r.h#HASHfactor">qh_HASHfactor</a>
+total/used hash slots </li>
+<li><a href="user_r.h#INITIALmax">qh_INITIALmax</a> if
+dim &gt;= qh_INITIALmax, use min/max coordinate
+points for initial simplex </li>
+<li><a href="user_r.h#INITIALsearch">qh_INITIALsearch</a>
+if qh.INITIALmax, search points up to this
+dimension </li>
+<li><a href="user_r.h#NOtrace">qh_NOtrace</a> disallow
+tracing </li>
+<li><a href="user_r.h#VERIFYdirect">qh_VERIFYdirect</a>
+'Tv' verifies all <em>points X facets</em> if op
+count is smaller </li>
+</ul>
+
+<h3><a href="qh-user_r.htm#TOC">&#187;</a><a name="umemory">memory constants</a></h3>
+<ul>
+<li><a href="user_r.h#MEMalign">qh_MEMalign</a> memory
+alignment for qh_meminitbuffers() in global_r.c </li>
+<li><a href="user_r.h#MEMbufsize">qh_MEMbufsize</a>
+size of additional memory buffers </li>
+<li><a href="user_r.h#MEMinitbuf">qh_MEMinitbuf</a>
+size of initial memory buffer </li>
+</ul>
+
+<h3><a href="qh-user_r.htm#TOC">&#187;</a><a name="ucond">conditional compilation</a></h3>
+<ul>
+<li><a href="user_r.h#compiler">compiler</a> defined symbols,
+e.g., _STDC_ and _cplusplus
+
+<li><a href="user_r.h#COMPUTEfurthest">qh_COMPUTEfurthest</a>
+    compute furthest distance to an outside point instead of storing it with the facet
+<li><a href="user_r.h#KEEPstatistics">qh_KEEPstatistics</a>
+    enable statistic gathering and reporting with option 'Ts'
+<li><a href="user_r.h#MAXoutside">qh_MAXoutside</a>
+record outer plane for each facet
+<li><a href="user_r.h#NOmerge">qh_NOmerge</a>
+disable facet merging
+<li><a href="user_r.h#NOtrace">qh_NOtrace</a>
+disable tracing with option 'T4'
+<li><a href="user_r.h#QHpointer">qh_QHpointer</a>
+access global data with pointer or static structure
+<li><a href="user_r.h#QUICKhelp">qh_QUICKhelp</a>
+use abbreviated help messages, e.g., for degenerate inputs
+</ul>
+
+<h3><a href="qh-user_r.htm#TOC">&#187;</a><a name="umerge">merge
+constants</a></h3>
+<ul>
+<li><a href="user_r.h#BESTcentrum">qh_BESTcentrum</a>
+when does qh_findbestneighbor() test centrums? </li>
+<li><a href="user_r.h#BESTnonconvex">qh_BESTnonconvex</a>
+when does qh_findbestneighbor() test nonconvex
+ridges only? </li>
+<li><a href="user_r.h#COPLANARratio">qh_COPLANARratio</a>
+what is qh.MINvisible? </li>
+<li><a href="user_r.h#DIMreduceBuild">qh_DIMreduceBuild</a>
+max dimension for vertex reduction </li>
+<li><a href="user_r.h#DIMmergeVertex">qh_DIMmergeVertex</a>
+max dimension for vertex merging </li>
+<li><a href="user_r.h#DISToutside">qh_DISToutside</a>
+when is a point clearly outside of a facet for qh_findbestnew and qh_partitionall</li>
+<li><a href="user_r.h#MAXnarrow">qh_MAXnarrow</a> max.
+cosine for qh.NARROWhull </li>
+<li><a href="user_r.h#MAXnewcentrum">qh_MAXnewcentrum</a>
+when does qh_reducevertices_centrum() reset the
+centrum? </li>
+<li><a href="user_r.h#MAXnewmerges">qh_MAXnewmerges</a>
+when does qh_merge_nonconvex() call
+qh_reducevertices_centrums? </li>
+<li><a href="user_r.h#RATIOnearinside">qh_RATIOnearinside</a>
+ratio for retaining inside points for
+qh_check_maxout() </li>
+<li><a href="user_r.h#SEARCHdist">qh_SEARCHdist</a>
+when is facet coplanar with the best facet for qh_findbesthorizon</li>
+<li><a href="user_r.h#USEfindbestnew">qh_USEfindbestnew</a>
+when to use qh_findbestnew for qh_partitionpoint()</li>
+<li><a href="user_r.h#WARNnarrow">qh_WARNnarrow</a>
+max. cosine to warn about qh.NARROWhull </li>
+<li><a href="user_r.h#WIDEcoplanar">qh_WIDEcoplanar</a>
+what is a wide facet? </li>
+<li><a href="user_r.h#WIDEduplicate">qh_WIDEduplicate</a>
+what is a wide ratio on merging duplicate ridges? </li>
+</ul>
+
+<h3><a href="qh-user_r.htm#TOC">&#187;</a><a name="ufunc">user_r.c
+functions</a></h3>
+<ul>
+<li><a href="user_r.c#qhull_template">Qhull template</a> for calling qh_new_qhull from your program</li>
+<li><a href="user_r.c#errexit">qh_errexit</a> report
+error and exit qhull()</li>
+<li><a href="user_r.c#errprint">qh_errprint</a> print
+information about facets and ridges </li>
+<li><a href="user_r.c#new_qhull">qh_new_qhull</a> call qhull on an array
+of points</li>
+<li><a href="user_r.c#printfacetlist">qh_printfacetlist</a>
+print all fields of all facets </li>
+</ul>
+
+<h3><a href="qh-user_r.htm#TOC">&#187;</a><a name="u2func">usermem_r.c
+functions</a></h3>
+<ul>
+<li><a href="usermem_r.c#qh_exit">qh_exit</a> exit program, same as exit().  May be redefined as throw "QH10003.." by libqhullcpp/usermem_r-cpp.cpp</li>
+<li><a href="usermem_r.c#qh_fprintf_stderr">qh_fprintf_stderr</a> print to stderr when qh->ferr is not defined.</li>
+<li><a href="usermem_r.c#qh_free">qh_free</a> free memory, same as free().</li>
+<li><a href="usermem_r.c#qh_malloc">qh_malloc</a> allocate memory, same as malloc()</li>
+</ul>
+
+<h3><a href="qh-user_r.htm#TOC">&#187;</a><a name="u3func">userprintf_r.c
+ and userprintf_rbox,c functions</a></h3>
+<ul>
+<li><a href="userprintf_r.c#qh_fprintf">qh_fprintf</a> print
+information from Qhull, sames as fprintf(). </li>
+<li><a href="userprintf_rbox_r.c#qh_fprintf_rbox">qh_fprintf_rbox</a> print
+information from Rbox, sames as fprintf(). </li>
+</ul>
+
+<p><!-- Navigation links --> </p>
+<hr>
+<p><b>Up:</b>
+<a href="http://www.qhull.org">Home page for
+Qhull</a> <br>
+<b>Up:</b> <a href="../../html/index.htm#TOC">Qhull manual: Table of Contents</a> <br>
+<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a>
+&#149; <a href="../../html/qh-quick.htm#options">Options</a>
+&#149; <a href="../../html/qh-opto.htm#output">Output</a>
+&#149; <a href="../../html/qh-optf.htm#format">Formats</a>
+&#149; <a href="../../html/qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="../../html/qh-optp.htm#print">Print</a>
+&#149; <a href="../../html/qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="../../html/qh-optc.htm#prec">Precision</a>
+&#149; <a href="../../html/qh-optt.htm#trace">Trace</a>
+&#149; <a href="index.htm">Functions</a><br>
+<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code: Table of Contents</a> <br>
+<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
+<b>To:</b> <a href="qh-geom_r.htm">Geom</a> &#149;
+<a href="qh-globa_r.htm">Global</a> &#149; <a href="qh-io_r.htm">Io</a>
+&#149; <a href="qh-mem_r.htm">Mem</a> &#149; <a href="qh-merge_r.htm">Merge</a>
+&#149; <a href="qh-poly_r.htm">Poly</a> &#149; <a href="qh-qhull_r.htm#TOC">Qhull</a>
+&#149; <a href="qh-set_r.htm">Set</a> &#149; <a href="qh-stat_r.htm">Stat</a>
+&#149; <a href="qh-user_r.htm">User</a><br>
+</p>
+<p><!-- GC common information --> </p>
+<hr>
+<p><a href="http://www.geom.uiuc.edu/"><img
+src="../../html/qh--geom.gif" align="middle" width="40" height="40"></a><i>The
+Geometry Center Home Page </i></p>
+<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
+</a><br>
+Created: May 2, 1997 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
+</body>
+</html>
diff --git a/xs/src/qhull/src/libqhull_r/qhull_r-exports.def b/xs/src/qhull/src/libqhull_r/qhull_r-exports.def
new file mode 100644
index 0000000000..325d57c3b8
--- /dev/null
+++ b/xs/src/qhull/src/libqhull_r/qhull_r-exports.def
@@ -0,0 +1,404 @@
+; qhull_r-exports.def -- msvc module-definition file
+;
+;   Generated from depends.exe by cut-and-paste of exported symbols by mingw gcc
+;   [jan'14] 391 symbols 
+;   Same as ../libqhullp/qhull-exports.def without DATA items (reentrant)
+;
+; $Id: //main/2015/qhull/src/libqhull_r/qhull_r-exports.def#3 $$Change: 2047 $
+; $DateTime: 2016/01/04 22:03:18 $$Author: bbarber $
+; 
+; Define qhull_VERSION in CMakeLists.txt, Makefile, qhull-exports.def, qhull_p-exports.def, qhull_r-exports.def, and qhull-warn.pri
+VERSION 7.0
+EXPORTS
+qh_addhash
+qh_addpoint
+qh_all_merges
+qh_allstatA
+qh_allstatB
+qh_allstatC
+qh_allstatD
+qh_allstatE
+qh_allstatE2
+qh_allstatF
+qh_allstatG
+qh_allstatH
+qh_allstatI
+qh_allstatistics
+qh_appendfacet
+qh_appendmergeset
+qh_appendprint
+qh_appendvertex
+qh_argv_to_command
+qh_argv_to_command_size
+qh_attachnewfacets
+qh_backnormal
+qh_basevertices
+qh_build_withrestart
+qh_buildhull
+qh_buildtracing
+qh_check_bestdist
+qh_check_dupridge
+qh_check_maxout
+qh_check_output
+qh_check_point
+qh_check_points
+qh_checkconnect
+qh_checkconvex
+qh_checkfacet
+qh_checkflags
+qh_checkflipped
+qh_checkflipped_all
+qh_checkpolygon
+qh_checkvertex
+qh_checkzero
+qh_clear_outputflags
+qh_clearcenters
+qh_clock
+qh_collectstatistics
+qh_compare_facetarea
+qh_compare_facetmerge
+qh_compare_facetvisit
+qh_compareangle
+qh_comparemerge
+qh_comparevisit
+qh_copyfilename
+qh_copynonconvex
+qh_copypoints
+qh_countfacets
+qh_createsimplex
+qh_crossproduct
+qh_degen_redundant_facet
+qh_degen_redundant_neighbors
+qh_deletevisible
+qh_delfacet
+qh_delridge
+qh_delvertex
+qh_determinant
+qh_detjoggle
+qh_detroundoff
+qh_detsimplex
+qh_detvnorm
+qh_detvridge
+qh_detvridge3
+qh_dfacet
+qh_distnorm
+qh_distplane
+qh_distround
+qh_divzero
+qh_dvertex
+qh_eachvoronoi
+qh_eachvoronoi_all
+qh_errexit
+qh_errexit2
+qh_errexit_rbox
+qh_errprint
+qh_exit
+qh_facet2point
+qh_facet3vertex
+qh_facetarea
+qh_facetarea_simplex
+qh_facetcenter
+qh_facetintersect
+qh_facetvertices
+qh_find_newvertex
+qh_findbest
+qh_findbest_test
+qh_findbestfacet
+qh_findbesthorizon
+qh_findbestlower
+qh_findbestneighbor
+qh_findbestnew
+qh_findfacet_all
+qh_findgood
+qh_findgood_all
+qh_findgooddist
+qh_findhorizon
+qh_flippedmerges
+qh_forcedmerges
+qh_fprintf
+qh_fprintf_rbox
+qh_fprintf_stderr
+qh_free
+qh_freebuffers
+qh_freebuild
+qh_freeqhull
+qh_furthestnext
+qh_furthestout
+qh_gausselim
+qh_geomplanes
+qh_getangle
+qh_getarea
+qh_getcenter
+qh_getcentrum
+qh_getdistance
+qh_gethash
+qh_getmergeset
+qh_getmergeset_initial
+qh_gram_schmidt
+qh_hashridge
+qh_hashridge_find
+qh_infiniteloop
+qh_init_A
+qh_init_B
+qh_init_qhull_command
+qh_initbuild
+qh_initflags
+qh_initialhull
+qh_initialvertices
+qh_initqhull_buffers
+qh_initqhull_globals
+qh_initqhull_mem
+qh_initqhull_outputflags
+qh_initqhull_start
+qh_initqhull_start2
+qh_initstatistics
+qh_initthresholds
+qh_inthresholds
+qh_isvertex
+qh_joggleinput
+qh_lib_check
+qh_makenew_nonsimplicial
+qh_makenew_simplicial
+qh_makenewfacet
+qh_makenewfacets
+qh_makenewplanes
+qh_makeridges
+qh_malloc
+qh_mark_dupridges
+qh_markkeep
+qh_markvoronoi
+qh_matchduplicates
+qh_matchneighbor
+qh_matchnewfacets
+qh_matchvertices
+qh_maxabsval
+qh_maxmin
+qh_maxouter
+qh_maxsimplex
+qh_maydropneighbor
+qh_memalloc
+qh_memfree
+qh_memfreeshort
+qh_meminit
+qh_meminitbuffers
+qh_memsetup
+qh_memsize
+qh_memstatistics
+qh_memtotal
+qh_merge_degenredundant
+qh_merge_nonconvex
+qh_mergecycle
+qh_mergecycle_all
+qh_mergecycle_facets
+qh_mergecycle_neighbors
+qh_mergecycle_ridges
+qh_mergecycle_vneighbors
+qh_mergefacet
+qh_mergefacet2d
+qh_mergeneighbors
+qh_mergeridges
+qh_mergesimplex
+qh_mergevertex_del
+qh_mergevertex_neighbors
+qh_mergevertices
+qh_minabsval
+qh_mindiff
+qh_nearcoplanar
+qh_nearvertex
+qh_neighbor_intersections
+qh_new_qhull
+qh_newfacet
+qh_newhashtable
+qh_newridge
+qh_newstats
+qh_newvertex
+qh_newvertices
+qh_nextfurthest
+qh_nextridge3d
+qh_normalize
+qh_normalize2
+qh_nostatistic
+qh_option
+qh_order_vertexneighbors
+qh_orientoutside
+qh_out1
+qh_out2n
+qh_out3n
+qh_outcoplanar
+qh_outerinner
+qh_partitionall
+qh_partitioncoplanar
+qh_partitionpoint
+qh_partitionvisible
+qh_point
+qh_point_add
+qh_pointdist
+qh_pointfacet
+qh_pointid
+qh_pointvertex
+qh_postmerge
+qh_precision
+qh_premerge
+qh_prepare_output
+qh_prependfacet
+qh_printafacet
+qh_printallstatistics
+qh_printbegin
+qh_printcenter
+qh_printcentrum
+qh_printend
+qh_printend4geom
+qh_printextremes
+qh_printextremes_2d
+qh_printextremes_d
+qh_printfacet
+qh_printfacet2geom
+qh_printfacet2geom_points
+qh_printfacet2math
+qh_printfacet3geom_nonsimplicial
+qh_printfacet3geom_points
+qh_printfacet3geom_simplicial
+qh_printfacet3math
+qh_printfacet3vertex
+qh_printfacet4geom_nonsimplicial
+qh_printfacet4geom_simplicial
+qh_printfacetNvertex_nonsimplicial
+qh_printfacetNvertex_simplicial
+qh_printfacetheader
+qh_printfacetlist
+qh_printfacetridges
+qh_printfacets
+qh_printhashtable
+qh_printhelp_degenerate
+qh_printhelp_narrowhull
+qh_printhelp_singular
+qh_printhyperplaneintersection
+qh_printline3geom
+qh_printlists
+qh_printmatrix
+qh_printneighborhood
+qh_printpoint
+qh_printpoint3
+qh_printpointid
+qh_printpoints
+qh_printpoints_out
+qh_printpointvect
+qh_printpointvect2
+qh_printridge
+qh_printspheres
+qh_printstatistics
+qh_printstatlevel
+qh_printstats
+qh_printsummary
+qh_printvdiagram
+qh_printvdiagram2
+qh_printvertex
+qh_printvertexlist
+qh_printvertices
+qh_printvneighbors
+qh_printvnorm
+qh_printvoronoi
+qh_printvridge
+qh_produce_output
+qh_produce_output2
+qh_projectdim3
+qh_projectinput
+qh_projectpoint
+qh_projectpoints
+qh_qhull
+qh_rand
+qh_randomfactor
+qh_randommatrix
+qh_rboxpoints
+qh_readfeasible
+qh_readpoints
+qh_reducevertices
+qh_redundant_vertex
+qh_remove_extravertices
+qh_removefacet
+qh_removevertex
+qh_rename_sharedvertex
+qh_renameridgevertex
+qh_renamevertex
+qh_resetlists
+qh_rotateinput
+qh_rotatepoints
+qh_roundi
+qh_scaleinput
+qh_scalelast
+qh_scalepoints
+qh_setaddnth
+qh_setaddsorted
+qh_setappend
+qh_setappend2ndlast
+qh_setappend_set
+qh_setcheck
+qh_setcompact
+qh_setcopy
+qh_setdel
+qh_setdelaunay
+qh_setdellast
+qh_setdelnth
+qh_setdelnthsorted
+qh_setdelsorted
+qh_setduplicate
+qh_setequal
+qh_setequal_except
+qh_setequal_skip
+qh_setfacetplane
+qh_setfeasible
+qh_setfree
+qh_setfree2
+qh_setfreelong
+qh_sethalfspace
+qh_sethalfspace_all
+qh_sethyperplane_det
+qh_sethyperplane_gauss
+qh_setin
+qh_setindex
+qh_setlarger
+qh_setlast
+qh_setnew
+qh_setnew_delnthsorted
+qh_setprint
+qh_setreplace
+qh_setsize
+qh_settemp
+qh_settempfree
+qh_settempfree_all
+qh_settemppop
+qh_settemppush
+qh_settruncate
+qh_setunique
+qh_setvoronoi_all
+qh_setzero
+qh_sharpnewfacets
+qh_skipfacet
+qh_skipfilename
+qh_srand
+qh_stddev
+qh_strtod
+qh_strtol
+qh_test_appendmerge
+qh_test_vneighbors
+qh_tracemerge
+qh_tracemerging
+qh_triangulate
+qh_triangulate_facet
+qh_triangulate_link
+qh_triangulate_mirror
+qh_triangulate_null
+qh_updatetested
+qh_updatevertices
+qh_user_memsizes
+qh_version
+qh_version2
+qh_vertexintersect
+qh_vertexintersect_new
+qh_vertexneighbors
+qh_vertexridges
+qh_vertexridges_facet
+qh_vertexsubset
+qh_voronoi_center
+qh_willdelete
+qh_zero
diff --git a/xs/src/qhull/src/libqhull_r/qhull_ra.h b/xs/src/qhull/src/libqhull_r/qhull_ra.h
new file mode 100644
index 0000000000..5c5bd8779c
--- /dev/null
+++ b/xs/src/qhull/src/libqhull_r/qhull_ra.h
@@ -0,0 +1,158 @@
+/*<html><pre>  -<a                             href="qh-qhull_r.htm"
+  >-------------------------------</a><a name="TOP">-</a>
+
+   qhull_ra.h
+   all header files for compiling qhull with reentrant code
+   included before C++ headers for user_r.h:QHULL_CRTDBG
+
+   see qh-qhull.htm
+
+   see libqhull_r.h for user-level definitions
+
+   see user_r.h for user-definable constants
+
+   defines internal functions for libqhull_r.c global_r.c
+
+   Copyright (c) 1993-2015 The Geometry Center.
+   $Id: //main/2015/qhull/src/libqhull_r/qhull_ra.h#6 $$Change: 2079 $
+   $DateTime: 2016/02/07 17:43:34 $$Author: bbarber $
+
+   Notes:  grep for ((" and (" to catch fprintf("lkasdjf");
+           full parens around (x?y:z)
+           use '#include "libqhull_r/qhull_ra.h"' to avoid name clashes
+*/
+
+#ifndef qhDEFqhulla
+#define qhDEFqhulla 1
+
+#include "libqhull_r.h"  /* Includes user_r.h and data types */
+
+#include "stat_r.h"
+#include "random_r.h"
+#include "mem_r.h"
+#include "qset_r.h"
+#include "geom_r.h"
+#include "merge_r.h"
+#include "poly_r.h"
+#include "io_r.h"
+
+#include <setjmp.h>
+#include <string.h>
+#include <math.h>
+#include <float.h>    /* some compilers will not need float.h */
+#include <limits.h>
+#include <time.h>
+#include <ctype.h>
+#include <stdio.h>
+#include <stdlib.h>
+/*** uncomment here and qset_r.c
+     if string.h does not define memcpy()
+#include <memory.h>
+*/
+
+#if qh_CLOCKtype == 2  /* defined in user_r.h from libqhull_r.h */
+#include <sys/types.h>
+#include <sys/times.h>
+#include <unistd.h>
+#endif
+
+#ifdef _MSC_VER  /* Microsoft Visual C++ -- warning level 4 */
+#pragma warning( disable : 4100)  /* unreferenced formal parameter */
+#pragma warning( disable : 4127)  /* conditional expression is constant */
+#pragma warning( disable : 4706)  /* assignment within conditional function */
+#pragma warning( disable : 4996)  /* function was declared deprecated(strcpy, localtime, etc.) */
+#endif
+
+/* ======= -macros- =========== */
+
+/*-<a                             href="qh-qhull_r.htm#TOC"
+  >--------------------------------</a><a name="traceN">-</a>
+
+  traceN((qh, qh->ferr, 0Nnnn, "format\n", vars));
+    calls qh_fprintf if qh.IStracing >= N
+
+    Add debugging traps to the end of qh_fprintf
+
+  notes:
+    removing tracing reduces code size but doesn't change execution speed
+*/
+#ifndef qh_NOtrace
+#define trace0(args) {if (qh->IStracing) qh_fprintf args;}
+#define trace1(args) {if (qh->IStracing >= 1) qh_fprintf args;}
+#define trace2(args) {if (qh->IStracing >= 2) qh_fprintf args;}
+#define trace3(args) {if (qh->IStracing >= 3) qh_fprintf args;}
+#define trace4(args) {if (qh->IStracing >= 4) qh_fprintf args;}
+#define trace5(args) {if (qh->IStracing >= 5) qh_fprintf args;}
+#else /* qh_NOtrace */
+#define trace0(args) {}
+#define trace1(args) {}
+#define trace2(args) {}
+#define trace3(args) {}
+#define trace4(args) {}
+#define trace5(args) {}
+#endif /* qh_NOtrace */
+
+/*-<a                             href="qh-qhull_r.htm#TOC"
+  >--------------------------------</a><a name="QHULL_UNUSED">-</a>
+
+  Define an unused variable to avoid compiler warnings
+
+  Derived from Qt's corelib/global/qglobal.h
+
+*/
+
+#if defined(__cplusplus) && defined(__INTEL_COMPILER) && !defined(QHULL_OS_WIN)
+template <typename T>
+inline void qhullUnused(T &x) { (void)x; }
+#  define QHULL_UNUSED(x) qhullUnused(x);
+#else
+#  define QHULL_UNUSED(x) (void)x;
+#endif
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+/***** -libqhull_r.c prototypes (alphabetical after qhull) ********************/
+
+void    qh_qhull(qhT *qh);
+boolT   qh_addpoint(qhT *qh, pointT *furthest, facetT *facet, boolT checkdist);
+void    qh_buildhull(qhT *qh);
+void    qh_buildtracing(qhT *qh, pointT *furthest, facetT *facet);
+void    qh_build_withrestart(qhT *qh);
+void    qh_errexit2(qhT *qh, int exitcode, facetT *facet, facetT *otherfacet);
+void    qh_findhorizon(qhT *qh, pointT *point, facetT *facet, int *goodvisible,int *goodhorizon);
+pointT *qh_nextfurthest(qhT *qh, facetT **visible);
+void    qh_partitionall(qhT *qh, setT *vertices, pointT *points,int npoints);
+void    qh_partitioncoplanar(qhT *qh, pointT *point, facetT *facet, realT *dist);
+void    qh_partitionpoint(qhT *qh, pointT *point, facetT *facet);
+void    qh_partitionvisible(qhT *qh, boolT allpoints, int *numpoints);
+void    qh_precision(qhT *qh, const char *reason);
+void    qh_printsummary(qhT *qh, FILE *fp);
+
+/***** -global_r.c internal prototypes (alphabetical) ***********************/
+
+void    qh_appendprint(qhT *qh, qh_PRINT format);
+void    qh_freebuild(qhT *qh, boolT allmem);
+void    qh_freebuffers(qhT *qh);
+void    qh_initbuffers(qhT *qh, coordT *points, int numpoints, int dim, boolT ismalloc);
+
+/***** -stat_r.c internal prototypes (alphabetical) ***********************/
+
+void    qh_allstatA(qhT *qh);
+void    qh_allstatB(qhT *qh);
+void    qh_allstatC(qhT *qh);
+void    qh_allstatD(qhT *qh);
+void    qh_allstatE(qhT *qh);
+void    qh_allstatE2(qhT *qh);
+void    qh_allstatF(qhT *qh);
+void    qh_allstatG(qhT *qh);
+void    qh_allstatH(qhT *qh);
+void    qh_freebuffers(qhT *qh);
+void    qh_initbuffers(qhT *qh, coordT *points, int numpoints, int dim, boolT ismalloc);
+
+#ifdef __cplusplus
+} /* extern "C" */
+#endif
+
+#endif /* qhDEFqhulla */
diff --git a/xs/src/qhull/src/libqhull_r/qset_r.c b/xs/src/qhull/src/libqhull_r/qset_r.c
new file mode 100644
index 0000000000..15cd3c0e29
--- /dev/null
+++ b/xs/src/qhull/src/libqhull_r/qset_r.c
@@ -0,0 +1,1340 @@
+/*<html><pre>  -<a                             href="qh-set_r.htm"
+  >-------------------------------</a><a name="TOP">-</a>
+
+   qset_r.c
+   implements set manipulations needed for quickhull
+
+   see qh-set_r.htm and qset_r.h
+
+   Be careful of strict aliasing (two pointers of different types
+   that reference the same location).  The last slot of a set is
+   either the actual size of the set plus 1, or the NULL terminator
+   of the set (i.e., setelemT).
+
+   Copyright (c) 1993-2015 The Geometry Center.
+   $Id: //main/2015/qhull/src/libqhull_r/qset_r.c#3 $$Change: 2062 $
+   $DateTime: 2016/01/17 13:13:18 $$Author: bbarber $
+*/
+
+#include "libqhull_r.h" /* for qhT and QHULL_CRTDBG */
+#include "qset_r.h"
+#include "mem_r.h"
+#include <stdio.h>
+#include <string.h>
+/*** uncomment here and qhull_ra.h
+     if string.h does not define memcpy()
+#include <memory.h>
+*/
+
+#ifndef qhDEFlibqhull
+typedef struct ridgeT ridgeT;
+typedef struct facetT facetT;
+void    qh_errexit(qhT *qh, int exitcode, facetT *, ridgeT *);
+void    qh_fprintf(qhT *qh, FILE *fp, int msgcode, const char *fmt, ... );
+#  ifdef _MSC_VER  /* Microsoft Visual C++ -- warning level 4 */
+#  pragma warning( disable : 4127)  /* conditional expression is constant */
+#  pragma warning( disable : 4706)  /* assignment within conditional function */
+#  endif
+#endif
+
+/*=============== internal macros ===========================*/
+
+/*============ functions in alphabetical order ===================*/
+
+/*-<a                             href="qh-set_r.htm#TOC"
+  >--------------------------------<a name="setaddnth">-</a>
+
+  qh_setaddnth(qh, setp, nth, newelem)
+    adds newelem as n'th element of sorted or unsorted *setp
+
+  notes:
+    *setp and newelem must be defined
+    *setp may be a temp set
+    nth=0 is first element
+    errors if nth is out of bounds
+
+  design:
+    expand *setp if empty or full
+    move tail of *setp up one
+    insert newelem
+*/
+void qh_setaddnth(qhT *qh, setT **setp, int nth, void *newelem) {
+  int oldsize, i;
+  setelemT *sizep;          /* avoid strict aliasing */
+  setelemT *oldp, *newp;
+
+  if (!*setp || (sizep= SETsizeaddr_(*setp))->i==0) {
+    qh_setlarger(qh, setp);
+    sizep= SETsizeaddr_(*setp);
+  }
+  oldsize= sizep->i - 1;
+  if (nth < 0 || nth > oldsize) {
+    qh_fprintf(qh, qh->qhmem.ferr, 6171, "qhull internal error (qh_setaddnth): nth %d is out-of-bounds for set:\n", nth);
+    qh_setprint(qh, qh->qhmem.ferr, "", *setp);
+    qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
+  }
+  sizep->i++;
+  oldp= (setelemT *)SETelemaddr_(*setp, oldsize, void);   /* NULL */
+  newp= oldp+1;
+  for (i=oldsize-nth+1; i--; )  /* move at least NULL  */
+    (newp--)->p= (oldp--)->p;       /* may overwrite *sizep */
+  newp->p= newelem;
+} /* setaddnth */
+
+
+/*-<a                              href="qh-set_r.htm#TOC"
+  >--------------------------------<a name="setaddsorted">-</a>
+
+  setaddsorted( setp, newelem )
+    adds an newelem into sorted *setp
+
+  notes:
+    *setp and newelem must be defined
+    *setp may be a temp set
+    nop if newelem already in set
+
+  design:
+    find newelem's position in *setp
+    insert newelem
+*/
+void qh_setaddsorted(qhT *qh, setT **setp, void *newelem) {
+  int newindex=0;
+  void *elem, **elemp;
+
+  FOREACHelem_(*setp) {          /* could use binary search instead */
+    if (elem < newelem)
+      newindex++;
+    else if (elem == newelem)
+      return;
+    else
+      break;
+  }
+  qh_setaddnth(qh, setp, newindex, newelem);
+} /* setaddsorted */
+
+
+/*-<a                             href="qh-set_r.htm#TOC"
+  >-------------------------------<a name="setappend">-</a>
+
+  qh_setappend(qh, setp, newelem)
+    append newelem to *setp
+
+  notes:
+    *setp may be a temp set
+    *setp and newelem may be NULL
+
+  design:
+    expand *setp if empty or full
+    append newelem to *setp
+
+*/
+void qh_setappend(qhT *qh, setT **setp, void *newelem) {
+  setelemT *sizep;  /* Avoid strict aliasing.  Writing to *endp may overwrite *sizep */
+  setelemT *endp;
+  int count;
+
+  if (!newelem)
+    return;
+  if (!*setp || (sizep= SETsizeaddr_(*setp))->i==0) {
+    qh_setlarger(qh, setp);
+    sizep= SETsizeaddr_(*setp);
+  }
+  count= (sizep->i)++ - 1;
+  endp= (setelemT *)SETelemaddr_(*setp, count, void);
+  (endp++)->p= newelem;
+  endp->p= NULL;
+} /* setappend */
+
+/*-<a                             href="qh-set_r.htm#TOC"
+  >-------------------------------<a name="setappend_set">-</a>
+
+  qh_setappend_set(qh, setp, setA)
+    appends setA to *setp
+
+  notes:
+    *setp can not be a temp set
+    *setp and setA may be NULL
+
+  design:
+    setup for copy
+    expand *setp if it is too small
+    append all elements of setA to *setp
+*/
+void qh_setappend_set(qhT *qh, setT **setp, setT *setA) {
+  int sizeA, size;
+  setT *oldset;
+  setelemT *sizep;
+
+  if (!setA)
+    return;
+  SETreturnsize_(setA, sizeA);
+  if (!*setp)
+    *setp= qh_setnew(qh, sizeA);
+  sizep= SETsizeaddr_(*setp);
+  if (!(size= sizep->i))
+    size= (*setp)->maxsize;
+  else
+    size--;
+  if (size + sizeA > (*setp)->maxsize) {
+    oldset= *setp;
+    *setp= qh_setcopy(qh, oldset, sizeA);
+    qh_setfree(qh, &oldset);
+    sizep= SETsizeaddr_(*setp);
+  }
+  if (sizeA > 0) {
+    sizep->i= size+sizeA+1;   /* memcpy may overwrite */
+    memcpy((char *)&((*setp)->e[size].p), (char *)&(setA->e[0].p), (size_t)(sizeA+1) * SETelemsize);
+  }
+} /* setappend_set */
+
+
+/*-<a                             href="qh-set_r.htm#TOC"
+  >-------------------------------<a name="setappend2ndlast">-</a>
+
+  qh_setappend2ndlast(qh, setp, newelem )
+    makes newelem the next to the last element in *setp
+
+  notes:
+    *setp must have at least one element
+    newelem must be defined
+    *setp may be a temp set
+
+  design:
+    expand *setp if empty or full
+    move last element of *setp up one
+    insert newelem
+*/
+void qh_setappend2ndlast(qhT *qh, setT **setp, void *newelem) {
+    setelemT *sizep;  /* Avoid strict aliasing.  Writing to *endp may overwrite *sizep */
+    setelemT *endp, *lastp;
+    int count;
+
+    if (!*setp || (sizep= SETsizeaddr_(*setp))->i==0) {
+        qh_setlarger(qh, setp);
+        sizep= SETsizeaddr_(*setp);
+    }
+    count= (sizep->i)++ - 1;
+    endp= (setelemT *)SETelemaddr_(*setp, count, void); /* NULL */
+    lastp= endp-1;
+    *(endp++)= *lastp;
+    endp->p= NULL;    /* may overwrite *sizep */
+    lastp->p= newelem;
+} /* setappend2ndlast */
+
+/*-<a                             href="qh-set_r.htm#TOC"
+  >-------------------------------<a name="setcheck">-</a>
+
+  qh_setcheck(qh, set, typename, id )
+    check set for validity
+    report errors with typename and id
+
+  design:
+    checks that maxsize, actual size, and NULL terminator agree
+*/
+void qh_setcheck(qhT *qh, setT *set, const char *tname, unsigned id) {
+  int maxsize, size;
+  int waserr= 0;
+
+  if (!set)
+    return;
+  SETreturnsize_(set, size);
+  maxsize= set->maxsize;
+  if (size > maxsize || !maxsize) {
+    qh_fprintf(qh, qh->qhmem.ferr, 6172, "qhull internal error (qh_setcheck): actual size %d of %s%d is greater than max size %d\n",
+             size, tname, id, maxsize);
+    waserr= 1;
+  }else if (set->e[size].p) {
+    qh_fprintf(qh, qh->qhmem.ferr, 6173, "qhull internal error (qh_setcheck): %s%d(size %d max %d) is not null terminated.\n",
+             tname, id, size-1, maxsize);
+    waserr= 1;
+  }
+  if (waserr) {
+    qh_setprint(qh, qh->qhmem.ferr, "ERRONEOUS", set);
+    qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
+  }
+} /* setcheck */
+
+
+/*-<a                             href="qh-set_r.htm#TOC"
+  >-------------------------------<a name="setcompact">-</a>
+
+  qh_setcompact(qh, set )
+    remove internal NULLs from an unsorted set
+
+  returns:
+    updated set
+
+  notes:
+    set may be NULL
+    it would be faster to swap tail of set into holes, like qh_setdel
+
+  design:
+    setup pointers into set
+    skip NULLs while copying elements to start of set
+    update the actual size
+*/
+void qh_setcompact(qhT *qh, setT *set) {
+  int size;
+  void **destp, **elemp, **endp, **firstp;
+
+  if (!set)
+    return;
+  SETreturnsize_(set, size);
+  destp= elemp= firstp= SETaddr_(set, void);
+  endp= destp + size;
+  while (1) {
+    if (!(*destp++ = *elemp++)) {
+      destp--;
+      if (elemp > endp)
+        break;
+    }
+  }
+  qh_settruncate(qh, set, (int)(destp-firstp));   /* WARN64 */
+} /* setcompact */
+
+
+/*-<a                             href="qh-set_r.htm#TOC"
+  >-------------------------------<a name="setcopy">-</a>
+
+  qh_setcopy(qh, set, extra )
+    make a copy of a sorted or unsorted set with extra slots
+
+  returns:
+    new set
+
+  design:
+    create a newset with extra slots
+    copy the elements to the newset
+
+*/
+setT *qh_setcopy(qhT *qh, setT *set, int extra) {
+  setT *newset;
+  int size;
+
+  if (extra < 0)
+    extra= 0;
+  SETreturnsize_(set, size);
+  newset= qh_setnew(qh, size+extra);
+  SETsizeaddr_(newset)->i= size+1;    /* memcpy may overwrite */
+  memcpy((char *)&(newset->e[0].p), (char *)&(set->e[0].p), (size_t)(size+1) * SETelemsize);
+  return(newset);
+} /* setcopy */
+
+
+/*-<a                             href="qh-set_r.htm#TOC"
+  >-------------------------------<a name="setdel">-</a>
+
+  qh_setdel(set, oldelem )
+    delete oldelem from an unsorted set
+
+  returns:
+    returns oldelem if found
+    returns NULL otherwise
+
+  notes:
+    set may be NULL
+    oldelem must not be NULL;
+    only deletes one copy of oldelem in set
+
+  design:
+    locate oldelem
+    update actual size if it was full
+    move the last element to the oldelem's location
+*/
+void *qh_setdel(setT *set, void *oldelem) {
+  setelemT *sizep;
+  setelemT *elemp;
+  setelemT *lastp;
+
+  if (!set)
+    return NULL;
+  elemp= (setelemT *)SETaddr_(set, void);
+  while (elemp->p != oldelem && elemp->p)
+    elemp++;
+  if (elemp->p) {
+    sizep= SETsizeaddr_(set);
+    if (!(sizep->i)--)         /*  if was a full set */
+      sizep->i= set->maxsize;  /*     *sizep= (maxsize-1)+ 1 */
+    lastp= (setelemT *)SETelemaddr_(set, sizep->i-1, void);
+    elemp->p= lastp->p;      /* may overwrite itself */
+    lastp->p= NULL;
+    return oldelem;
+  }
+  return NULL;
+} /* setdel */
+
+
+/*-<a                             href="qh-set_r.htm#TOC"
+  >-------------------------------<a name="setdellast">-</a>
+
+  qh_setdellast(set)
+    return last element of set or NULL
+
+  notes:
+    deletes element from set
+    set may be NULL
+
+  design:
+    return NULL if empty
+    if full set
+      delete last element and set actual size
+    else
+      delete last element and update actual size
+*/
+void *qh_setdellast(setT *set) {
+  int setsize;  /* actually, actual_size + 1 */
+  int maxsize;
+  setelemT *sizep;
+  void *returnvalue;
+
+  if (!set || !(set->e[0].p))
+    return NULL;
+  sizep= SETsizeaddr_(set);
+  if ((setsize= sizep->i)) {
+    returnvalue= set->e[setsize - 2].p;
+    set->e[setsize - 2].p= NULL;
+    sizep->i--;
+  }else {
+    maxsize= set->maxsize;
+    returnvalue= set->e[maxsize - 1].p;
+    set->e[maxsize - 1].p= NULL;
+    sizep->i= maxsize;
+  }
+  return returnvalue;
+} /* setdellast */
+
+
+/*-<a                             href="qh-set_r.htm#TOC"
+  >-------------------------------<a name="setdelnth">-</a>
+
+  qh_setdelnth(qh, set, nth )
+    deletes nth element from unsorted set
+    0 is first element
+
+  returns:
+    returns the element (needs type conversion)
+
+  notes:
+    errors if nth invalid
+
+  design:
+    setup points and check nth
+    delete nth element and overwrite with last element
+*/
+void *qh_setdelnth(qhT *qh, setT *set, int nth) {
+  void *elem;
+  setelemT *sizep;
+  setelemT *elemp, *lastp;
+
+  sizep= SETsizeaddr_(set);
+  if ((sizep->i--)==0)         /*  if was a full set */
+    sizep->i= set->maxsize;  /*     *sizep= (maxsize-1)+ 1 */
+  if (nth < 0 || nth >= sizep->i) {
+    qh_fprintf(qh, qh->qhmem.ferr, 6174, "qhull internal error (qh_setdelnth): nth %d is out-of-bounds for set:\n", nth);
+    qh_setprint(qh, qh->qhmem.ferr, "", set);
+    qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
+  }
+  elemp= (setelemT *)SETelemaddr_(set, nth, void); /* nth valid by QH6174 */
+  lastp= (setelemT *)SETelemaddr_(set, sizep->i-1, void);
+  elem= elemp->p;
+  elemp->p= lastp->p;      /* may overwrite itself */
+  lastp->p= NULL;
+  return elem;
+} /* setdelnth */
+
+/*-<a                             href="qh-set_r.htm#TOC"
+  >-------------------------------<a name="setdelnthsorted">-</a>
+
+  qh_setdelnthsorted(qh, set, nth )
+    deletes nth element from sorted set
+
+  returns:
+    returns the element (use type conversion)
+
+  notes:
+    errors if nth invalid
+
+  see also:
+    setnew_delnthsorted
+
+  design:
+    setup points and check nth
+    copy remaining elements down one
+    update actual size
+*/
+void *qh_setdelnthsorted(qhT *qh, setT *set, int nth) {
+  void *elem;
+  setelemT *sizep;
+  setelemT *newp, *oldp;
+
+  sizep= SETsizeaddr_(set);
+  if (nth < 0 || (sizep->i && nth >= sizep->i-1) || nth >= set->maxsize) {
+    qh_fprintf(qh, qh->qhmem.ferr, 6175, "qhull internal error (qh_setdelnthsorted): nth %d is out-of-bounds for set:\n", nth);
+    qh_setprint(qh, qh->qhmem.ferr, "", set);
+    qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
+  }
+  newp= (setelemT *)SETelemaddr_(set, nth, void);
+  elem= newp->p;
+  oldp= newp+1;
+  while (((newp++)->p= (oldp++)->p))
+    ; /* copy remaining elements and NULL */
+  if ((sizep->i--)==0)         /*  if was a full set */
+    sizep->i= set->maxsize;  /*     *sizep= (max size-1)+ 1 */
+  return elem;
+} /* setdelnthsorted */
+
+
+/*-<a                             href="qh-set_r.htm#TOC"
+  >-------------------------------<a name="setdelsorted">-</a>
+
+  qh_setdelsorted(set, oldelem )
+    deletes oldelem from sorted set
+
+  returns:
+    returns oldelem if it was deleted
+
+  notes:
+    set may be NULL
+
+  design:
+    locate oldelem in set
+    copy remaining elements down one
+    update actual size
+*/
+void *qh_setdelsorted(setT *set, void *oldelem) {
+  setelemT *sizep;
+  setelemT *newp, *oldp;
+
+  if (!set)
+    return NULL;
+  newp= (setelemT *)SETaddr_(set, void);
+  while(newp->p != oldelem && newp->p)
+    newp++;
+  if (newp->p) {
+    oldp= newp+1;
+    while (((newp++)->p= (oldp++)->p))
+      ; /* copy remaining elements */
+    sizep= SETsizeaddr_(set);
+    if ((sizep->i--)==0)    /*  if was a full set */
+      sizep->i= set->maxsize;  /*     *sizep= (max size-1)+ 1 */
+    return oldelem;
+  }
+  return NULL;
+} /* setdelsorted */
+
+
+/*-<a                             href="qh-set_r.htm#TOC"
+  >-------------------------------<a name="setduplicate">-</a>
+
+  qh_setduplicate(qh, set, elemsize )
+    duplicate a set of elemsize elements
+
+  notes:
+    use setcopy if retaining old elements
+
+  design:
+    create a new set
+    for each elem of the old set
+      create a newelem
+      append newelem to newset
+*/
+setT *qh_setduplicate(qhT *qh, setT *set, int elemsize) {
+  void          *elem, **elemp, *newElem;
+  setT          *newSet;
+  int           size;
+
+  if (!(size= qh_setsize(qh, set)))
+    return NULL;
+  newSet= qh_setnew(qh, size);
+  FOREACHelem_(set) {
+    newElem= qh_memalloc(qh, elemsize);
+    memcpy(newElem, elem, (size_t)elemsize);
+    qh_setappend(qh, &newSet, newElem);
+  }
+  return newSet;
+} /* setduplicate */
+
+
+/*-<a                             href="qh-set_r.htm#TOC"
+  >-------------------------------<a name="setendpointer">-</a>
+
+  qh_setendpointer( set )
+    Returns pointer to NULL terminator of a set's elements
+    set can not be NULL
+
+*/
+void **qh_setendpointer(setT *set) {
+
+  setelemT *sizep= SETsizeaddr_(set);
+  int n= sizep->i;
+  return (n ? &set->e[n-1].p : &sizep->p);
+} /* qh_setendpointer */
+
+/*-<a                             href="qh-set_r.htm#TOC"
+  >-------------------------------<a name="setequal">-</a>
+
+  qh_setequal( setA, setB )
+    returns 1 if two sorted sets are equal, otherwise returns 0
+
+  notes:
+    either set may be NULL
+
+  design:
+    check size of each set
+    setup pointers
+    compare elements of each set
+*/
+int qh_setequal(setT *setA, setT *setB) {
+  void **elemAp, **elemBp;
+  int sizeA= 0, sizeB= 0;
+
+  if (setA) {
+    SETreturnsize_(setA, sizeA);
+  }
+  if (setB) {
+    SETreturnsize_(setB, sizeB);
+  }
+  if (sizeA != sizeB)
+    return 0;
+  if (!sizeA)
+    return 1;
+  elemAp= SETaddr_(setA, void);
+  elemBp= SETaddr_(setB, void);
+  if (!memcmp((char *)elemAp, (char *)elemBp, sizeA*SETelemsize))
+    return 1;
+  return 0;
+} /* setequal */
+
+
+/*-<a                             href="qh-set_r.htm#TOC"
+  >-------------------------------<a name="setequal_except">-</a>
+
+  qh_setequal_except( setA, skipelemA, setB, skipelemB )
+    returns 1 if sorted setA and setB are equal except for skipelemA & B
+
+  returns:
+    false if either skipelemA or skipelemB are missing
+
+  notes:
+    neither set may be NULL
+
+    if skipelemB is NULL,
+      can skip any one element of setB
+
+  design:
+    setup pointers
+    search for skipelemA, skipelemB, and mismatches
+    check results
+*/
+int qh_setequal_except(setT *setA, void *skipelemA, setT *setB, void *skipelemB) {
+  void **elemA, **elemB;
+  int skip=0;
+
+  elemA= SETaddr_(setA, void);
+  elemB= SETaddr_(setB, void);
+  while (1) {
+    if (*elemA == skipelemA) {
+      skip++;
+      elemA++;
+    }
+    if (skipelemB) {
+      if (*elemB == skipelemB) {
+        skip++;
+        elemB++;
+      }
+    }else if (*elemA != *elemB) {
+      skip++;
+      if (!(skipelemB= *elemB++))
+        return 0;
+    }
+    if (!*elemA)
+      break;
+    if (*elemA++ != *elemB++)
+      return 0;
+  }
+  if (skip != 2 || *elemB)
+    return 0;
+  return 1;
+} /* setequal_except */
+
+
+/*-<a                             href="qh-set_r.htm#TOC"
+  >-------------------------------<a name="setequal_skip">-</a>
+
+  qh_setequal_skip( setA, skipA, setB, skipB )
+    returns 1 if sorted setA and setB are equal except for elements skipA & B
+
+  returns:
+    false if different size
+
+  notes:
+    neither set may be NULL
+
+  design:
+    setup pointers
+    search for mismatches while skipping skipA and skipB
+*/
+int qh_setequal_skip(setT *setA, int skipA, setT *setB, int skipB) {
+  void **elemA, **elemB, **skipAp, **skipBp;
+
+  elemA= SETaddr_(setA, void);
+  elemB= SETaddr_(setB, void);
+  skipAp= SETelemaddr_(setA, skipA, void);
+  skipBp= SETelemaddr_(setB, skipB, void);
+  while (1) {
+    if (elemA == skipAp)
+      elemA++;
+    if (elemB == skipBp)
+      elemB++;
+    if (!*elemA)
+      break;
+    if (*elemA++ != *elemB++)
+      return 0;
+  }
+  if (*elemB)
+    return 0;
+  return 1;
+} /* setequal_skip */
+
+
+/*-<a                             href="qh-set_r.htm#TOC"
+  >-------------------------------<a name="setfree">-</a>
+
+  qh_setfree(qh, setp )
+    frees the space occupied by a sorted or unsorted set
+
+  returns:
+    sets setp to NULL
+
+  notes:
+    set may be NULL
+
+  design:
+    free array
+    free set
+*/
+void qh_setfree(qhT *qh, setT **setp) {
+  int size;
+  void **freelistp;  /* used if !qh_NOmem by qh_memfree_() */
+
+  if (*setp) {
+    size= sizeof(setT) + ((*setp)->maxsize)*SETelemsize;
+    if (size <= qh->qhmem.LASTsize) {
+      qh_memfree_(qh, *setp, size, freelistp);
+    }else
+      qh_memfree(qh, *setp, size);
+    *setp= NULL;
+  }
+} /* setfree */
+
+
+/*-<a                             href="qh-set_r.htm#TOC"
+  >-------------------------------<a name="setfree2">-</a>
+
+  qh_setfree2(qh, setp, elemsize )
+    frees the space occupied by a set and its elements
+
+  notes:
+    set may be NULL
+
+  design:
+    free each element
+    free set
+*/
+void qh_setfree2(qhT *qh, setT **setp, int elemsize) {
+  void          *elem, **elemp;
+
+  FOREACHelem_(*setp)
+    qh_memfree(qh, elem, elemsize);
+  qh_setfree(qh, setp);
+} /* setfree2 */
+
+
+
+/*-<a                             href="qh-set_r.htm#TOC"
+  >-------------------------------<a name="setfreelong">-</a>
+
+  qh_setfreelong(qh, setp )
+    frees a set only if it's in long memory
+
+  returns:
+    sets setp to NULL if it is freed
+
+  notes:
+    set may be NULL
+
+  design:
+    if set is large
+      free it
+*/
+void qh_setfreelong(qhT *qh, setT **setp) {
+  int size;
+
+  if (*setp) {
+    size= sizeof(setT) + ((*setp)->maxsize)*SETelemsize;
+    if (size > qh->qhmem.LASTsize) {
+      qh_memfree(qh, *setp, size);
+      *setp= NULL;
+    }
+  }
+} /* setfreelong */
+
+
+/*-<a                             href="qh-set_r.htm#TOC"
+  >-------------------------------<a name="setin">-</a>
+
+  qh_setin(set, setelem )
+    returns 1 if setelem is in a set, 0 otherwise
+
+  notes:
+    set may be NULL or unsorted
+
+  design:
+    scans set for setelem
+*/
+int qh_setin(setT *set, void *setelem) {
+  void *elem, **elemp;
+
+  FOREACHelem_(set) {
+    if (elem == setelem)
+      return 1;
+  }
+  return 0;
+} /* setin */
+
+
+/*-<a                             href="qh-set_r.htm#TOC"
+  >-------------------------------<a name="setindex">-</a>
+
+  qh_setindex(set, atelem )
+    returns the index of atelem in set.
+    returns -1, if not in set or maxsize wrong
+
+  notes:
+    set may be NULL and may contain nulls.
+    NOerrors returned (qh_pointid, QhullPoint::id)
+
+  design:
+    checks maxsize
+    scans set for atelem
+*/
+int qh_setindex(setT *set, void *atelem) {
+  void **elem;
+  int size, i;
+
+  if (!set)
+    return -1;
+  SETreturnsize_(set, size);
+  if (size > set->maxsize)
+    return -1;
+  elem= SETaddr_(set, void);
+  for (i=0; i < size; i++) {
+    if (*elem++ == atelem)
+      return i;
+  }
+  return -1;
+} /* setindex */
+
+
+/*-<a                             href="qh-set_r.htm#TOC"
+  >-------------------------------<a name="setlarger">-</a>
+
+  qh_setlarger(qh, oldsetp )
+    returns a larger set that contains all elements of *oldsetp
+
+  notes:
+    the set is at least twice as large
+    if temp set, updates qh->qhmem.tempstack
+
+  design:
+    creates a new set
+    copies the old set to the new set
+    updates pointers in tempstack
+    deletes the old set
+*/
+void qh_setlarger(qhT *qh, setT **oldsetp) {
+  int size= 1;
+  setT *newset, *set, **setp, *oldset;
+  setelemT *sizep;
+  setelemT *newp, *oldp;
+
+  if (*oldsetp) {
+    oldset= *oldsetp;
+    SETreturnsize_(oldset, size);
+    qh->qhmem.cntlarger++;
+    qh->qhmem.totlarger += size+1;
+    newset= qh_setnew(qh, 2 * size);
+    oldp= (setelemT *)SETaddr_(oldset, void);
+    newp= (setelemT *)SETaddr_(newset, void);
+    memcpy((char *)newp, (char *)oldp, (size_t)(size+1) * SETelemsize);
+    sizep= SETsizeaddr_(newset);
+    sizep->i= size+1;
+    FOREACHset_((setT *)qh->qhmem.tempstack) {
+      if (set == oldset)
+        *(setp-1)= newset;
+    }
+    qh_setfree(qh, oldsetp);
+  }else
+    newset= qh_setnew(qh, 3);
+  *oldsetp= newset;
+} /* setlarger */
+
+
+/*-<a                             href="qh-set_r.htm#TOC"
+  >-------------------------------<a name="setlast">-</a>
+
+  qh_setlast( set )
+    return last element of set or NULL (use type conversion)
+
+  notes:
+    set may be NULL
+
+  design:
+    return last element
+*/
+void *qh_setlast(setT *set) {
+  int size;
+
+  if (set) {
+    size= SETsizeaddr_(set)->i;
+    if (!size)
+      return SETelem_(set, set->maxsize - 1);
+    else if (size > 1)
+      return SETelem_(set, size - 2);
+  }
+  return NULL;
+} /* setlast */
+
+
+/*-<a                             href="qh-set_r.htm#TOC"
+  >-------------------------------<a name="setnew">-</a>
+
+  qh_setnew(qh, setsize )
+    creates and allocates space for a set
+
+  notes:
+    setsize means the number of elements (!including the NULL terminator)
+    use qh_settemp/qh_setfreetemp if set is temporary
+
+  design:
+    allocate memory for set
+    roundup memory if small set
+    initialize as empty set
+*/
+setT *qh_setnew(qhT *qh, int setsize) {
+  setT *set;
+  int sizereceived; /* used if !qh_NOmem */
+  int size;
+  void **freelistp; /* used if !qh_NOmem by qh_memalloc_() */
+
+  if (!setsize)
+    setsize++;
+  size= sizeof(setT) + setsize * SETelemsize;
+  if (size>0 && size <= qh->qhmem.LASTsize) {
+    qh_memalloc_(qh, size, freelistp, set, setT);
+#ifndef qh_NOmem
+    sizereceived= qh->qhmem.sizetable[ qh->qhmem.indextable[size]];
+    if (sizereceived > size)
+      setsize += (sizereceived - size)/SETelemsize;
+#endif
+  }else
+    set= (setT*)qh_memalloc(qh, size);
+  set->maxsize= setsize;
+  set->e[setsize].i= 1;
+  set->e[0].p= NULL;
+  return(set);
+} /* setnew */
+
+
+/*-<a                             href="qh-set_r.htm#TOC"
+  >-------------------------------<a name="setnew_delnthsorted">-</a>
+
+  qh_setnew_delnthsorted(qh, set, size, nth, prepend )
+    creates a sorted set not containing nth element
+    if prepend, the first prepend elements are undefined
+
+  notes:
+    set must be defined
+    checks nth
+    see also: setdelnthsorted
+
+  design:
+    create new set
+    setup pointers and allocate room for prepend'ed entries
+    append head of old set to new set
+    append tail of old set to new set
+*/
+setT *qh_setnew_delnthsorted(qhT *qh, setT *set, int size, int nth, int prepend) {
+  setT *newset;
+  void **oldp, **newp;
+  int tailsize= size - nth -1, newsize;
+
+  if (tailsize < 0) {
+    qh_fprintf(qh, qh->qhmem.ferr, 6176, "qhull internal error (qh_setnew_delnthsorted): nth %d is out-of-bounds for set:\n", nth);
+    qh_setprint(qh, qh->qhmem.ferr, "", set);
+    qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
+  }
+  newsize= size-1 + prepend;
+  newset= qh_setnew(qh, newsize);
+  newset->e[newset->maxsize].i= newsize+1;  /* may be overwritten */
+  oldp= SETaddr_(set, void);
+  newp= SETaddr_(newset, void) + prepend;
+  switch (nth) {
+  case 0:
+    break;
+  case 1:
+    *(newp++)= *oldp++;
+    break;
+  case 2:
+    *(newp++)= *oldp++;
+    *(newp++)= *oldp++;
+    break;
+  case 3:
+    *(newp++)= *oldp++;
+    *(newp++)= *oldp++;
+    *(newp++)= *oldp++;
+    break;
+  case 4:
+    *(newp++)= *oldp++;
+    *(newp++)= *oldp++;
+    *(newp++)= *oldp++;
+    *(newp++)= *oldp++;
+    break;
+  default:
+    memcpy((char *)newp, (char *)oldp, (size_t)nth * SETelemsize);
+    newp += nth;
+    oldp += nth;
+    break;
+  }
+  oldp++;
+  switch (tailsize) {
+  case 0:
+    break;
+  case 1:
+    *(newp++)= *oldp++;
+    break;
+  case 2:
+    *(newp++)= *oldp++;
+    *(newp++)= *oldp++;
+    break;
+  case 3:
+    *(newp++)= *oldp++;
+    *(newp++)= *oldp++;
+    *(newp++)= *oldp++;
+    break;
+  case 4:
+    *(newp++)= *oldp++;
+    *(newp++)= *oldp++;
+    *(newp++)= *oldp++;
+    *(newp++)= *oldp++;
+    break;
+  default:
+    memcpy((char *)newp, (char *)oldp, (size_t)tailsize * SETelemsize);
+    newp += tailsize;
+  }
+  *newp= NULL;
+  return(newset);
+} /* setnew_delnthsorted */
+
+
+/*-<a                             href="qh-set_r.htm#TOC"
+  >-------------------------------<a name="setprint">-</a>
+
+  qh_setprint(qh, fp, string, set )
+    print set elements to fp with identifying string
+
+  notes:
+    never errors
+*/
+void qh_setprint(qhT *qh, FILE *fp, const char* string, setT *set) {
+  int size, k;
+
+  if (!set)
+    qh_fprintf(qh, fp, 9346, "%s set is null\n", string);
+  else {
+    SETreturnsize_(set, size);
+    qh_fprintf(qh, fp, 9347, "%s set=%p maxsize=%d size=%d elems=",
+             string, set, set->maxsize, size);
+    if (size > set->maxsize)
+      size= set->maxsize+1;
+    for (k=0; k < size; k++)
+      qh_fprintf(qh, fp, 9348, " %p", set->e[k].p);
+    qh_fprintf(qh, fp, 9349, "\n");
+  }
+} /* setprint */
+
+/*-<a                             href="qh-set_r.htm#TOC"
+  >-------------------------------<a name="setreplace">-</a>
+
+  qh_setreplace(qh, set, oldelem, newelem )
+    replaces oldelem in set with newelem
+
+  notes:
+    errors if oldelem not in the set
+    newelem may be NULL, but it turns the set into an indexed set (no FOREACH)
+
+  design:
+    find oldelem
+    replace with newelem
+*/
+void qh_setreplace(qhT *qh, setT *set, void *oldelem, void *newelem) {
+  void **elemp;
+
+  elemp= SETaddr_(set, void);
+  while (*elemp != oldelem && *elemp)
+    elemp++;
+  if (*elemp)
+    *elemp= newelem;
+  else {
+    qh_fprintf(qh, qh->qhmem.ferr, 6177, "qhull internal error (qh_setreplace): elem %p not found in set\n",
+       oldelem);
+    qh_setprint(qh, qh->qhmem.ferr, "", set);
+    qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
+  }
+} /* setreplace */
+
+
+/*-<a                             href="qh-set_r.htm#TOC"
+  >-------------------------------<a name="setsize">-</a>
+
+  qh_setsize(qh, set )
+    returns the size of a set
+
+  notes:
+    errors if set's maxsize is incorrect
+    same as SETreturnsize_(set)
+    same code for qh_setsize [qset_r.c] and QhullSetBase::count
+
+  design:
+    determine actual size of set from maxsize
+*/
+int qh_setsize(qhT *qh, setT *set) {
+  int size;
+  setelemT *sizep;
+
+  if (!set)
+    return(0);
+  sizep= SETsizeaddr_(set);
+  if ((size= sizep->i)) {
+    size--;
+    if (size > set->maxsize) {
+      qh_fprintf(qh, qh->qhmem.ferr, 6178, "qhull internal error (qh_setsize): current set size %d is greater than maximum size %d\n",
+               size, set->maxsize);
+      qh_setprint(qh, qh->qhmem.ferr, "set: ", set);
+      qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
+    }
+  }else
+    size= set->maxsize;
+  return size;
+} /* setsize */
+
+/*-<a                             href="qh-set_r.htm#TOC"
+  >-------------------------------<a name="settemp">-</a>
+
+  qh_settemp(qh, setsize )
+    return a stacked, temporary set of upto setsize elements
+
+  notes:
+    use settempfree or settempfree_all to release from qh->qhmem.tempstack
+    see also qh_setnew
+
+  design:
+    allocate set
+    append to qh->qhmem.tempstack
+
+*/
+setT *qh_settemp(qhT *qh, int setsize) {
+  setT *newset;
+
+  newset= qh_setnew(qh, setsize);
+  qh_setappend(qh, &qh->qhmem.tempstack, newset);
+  if (qh->qhmem.IStracing >= 5)
+    qh_fprintf(qh, qh->qhmem.ferr, 8123, "qh_settemp: temp set %p of %d elements, depth %d\n",
+       newset, newset->maxsize, qh_setsize(qh, qh->qhmem.tempstack));
+  return newset;
+} /* settemp */
+
+/*-<a                             href="qh-set_r.htm#TOC"
+  >-------------------------------<a name="settempfree">-</a>
+
+  qh_settempfree(qh, set )
+    free temporary set at top of qh->qhmem.tempstack
+
+  notes:
+    nop if set is NULL
+    errors if set not from previous   qh_settemp
+
+  to locate errors:
+    use 'T2' to find source and then find mis-matching qh_settemp
+
+  design:
+    check top of qh->qhmem.tempstack
+    free it
+*/
+void qh_settempfree(qhT *qh, setT **set) {
+  setT *stackedset;
+
+  if (!*set)
+    return;
+  stackedset= qh_settemppop(qh);
+  if (stackedset != *set) {
+    qh_settemppush(qh, stackedset);
+    qh_fprintf(qh, qh->qhmem.ferr, 6179, "qhull internal error (qh_settempfree): set %p(size %d) was not last temporary allocated(depth %d, set %p, size %d)\n",
+             *set, qh_setsize(qh, *set), qh_setsize(qh, qh->qhmem.tempstack)+1,
+             stackedset, qh_setsize(qh, stackedset));
+    qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
+  }
+  qh_setfree(qh, set);
+} /* settempfree */
+
+/*-<a                             href="qh-set_r.htm#TOC"
+  >-------------------------------<a name="settempfree_all">-</a>
+
+  qh_settempfree_all(qh)
+    free all temporary sets in qh->qhmem.tempstack
+
+  design:
+    for each set in tempstack
+      free set
+    free qh->qhmem.tempstack
+*/
+void qh_settempfree_all(qhT *qh) {
+  setT *set, **setp;
+
+  FOREACHset_(qh->qhmem.tempstack)
+    qh_setfree(qh, &set);
+  qh_setfree(qh, &qh->qhmem.tempstack);
+} /* settempfree_all */
+
+/*-<a                             href="qh-set_r.htm#TOC"
+  >-------------------------------<a name="settemppop">-</a>
+
+  qh_settemppop(qh)
+    pop and return temporary set from qh->qhmem.tempstack
+
+  notes:
+    the returned set is permanent
+
+  design:
+    pop and check top of qh->qhmem.tempstack
+*/
+setT *qh_settemppop(qhT *qh) {
+  setT *stackedset;
+
+  stackedset= (setT*)qh_setdellast(qh->qhmem.tempstack);
+  if (!stackedset) {
+    qh_fprintf(qh, qh->qhmem.ferr, 6180, "qhull internal error (qh_settemppop): pop from empty temporary stack\n");
+    qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
+  }
+  if (qh->qhmem.IStracing >= 5)
+    qh_fprintf(qh, qh->qhmem.ferr, 8124, "qh_settemppop: depth %d temp set %p of %d elements\n",
+       qh_setsize(qh, qh->qhmem.tempstack)+1, stackedset, qh_setsize(qh, stackedset));
+  return stackedset;
+} /* settemppop */
+
+/*-<a                             href="qh-set_r.htm#TOC"
+  >-------------------------------<a name="settemppush">-</a>
+
+  qh_settemppush(qh, set )
+    push temporary set unto qh->qhmem.tempstack (makes it temporary)
+
+  notes:
+    duplicates settemp() for tracing
+
+  design:
+    append set to tempstack
+*/
+void qh_settemppush(qhT *qh, setT *set) {
+  if (!set) {
+    qh_fprintf(qh, qh->qhmem.ferr, 6267, "qhull error (qh_settemppush): can not push a NULL temp\n");
+    qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
+  }
+  qh_setappend(qh, &qh->qhmem.tempstack, set);
+  if (qh->qhmem.IStracing >= 5)
+    qh_fprintf(qh, qh->qhmem.ferr, 8125, "qh_settemppush: depth %d temp set %p of %d elements\n",
+      qh_setsize(qh, qh->qhmem.tempstack), set, qh_setsize(qh, set));
+} /* settemppush */
+
+
+/*-<a                             href="qh-set_r.htm#TOC"
+  >-------------------------------<a name="settruncate">-</a>
+
+  qh_settruncate(qh, set, size )
+    truncate set to size elements
+
+  notes:
+    set must be defined
+
+  see:
+    SETtruncate_
+
+  design:
+    check size
+    update actual size of set
+*/
+void qh_settruncate(qhT *qh, setT *set, int size) {
+
+  if (size < 0 || size > set->maxsize) {
+    qh_fprintf(qh, qh->qhmem.ferr, 6181, "qhull internal error (qh_settruncate): size %d out of bounds for set:\n", size);
+    qh_setprint(qh, qh->qhmem.ferr, "", set);
+    qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
+  }
+  set->e[set->maxsize].i= size+1;   /* maybe overwritten */
+  set->e[size].p= NULL;
+} /* settruncate */
+
+/*-<a                             href="qh-set_r.htm#TOC"
+  >-------------------------------<a name="setunique">-</a>
+
+  qh_setunique(qh, set, elem )
+    add elem to unsorted set unless it is already in set
+
+  notes:
+    returns 1 if it is appended
+
+  design:
+    if elem not in set
+      append elem to set
+*/
+int qh_setunique(qhT *qh, setT **set, void *elem) {
+
+  if (!qh_setin(*set, elem)) {
+    qh_setappend(qh, set, elem);
+    return 1;
+  }
+  return 0;
+} /* setunique */
+
+/*-<a                             href="qh-set_r.htm#TOC"
+  >-------------------------------<a name="setzero">-</a>
+
+  qh_setzero(qh, set, index, size )
+    zero elements from index on
+    set actual size of set to size
+
+  notes:
+    set must be defined
+    the set becomes an indexed set (can not use FOREACH...)
+
+  see also:
+    qh_settruncate
+
+  design:
+    check index and size
+    update actual size
+    zero elements starting at e[index]
+*/
+void qh_setzero(qhT *qh, setT *set, int idx, int size) {
+  int count;
+
+  if (idx < 0 || idx >= size || size > set->maxsize) {
+    qh_fprintf(qh, qh->qhmem.ferr, 6182, "qhull internal error (qh_setzero): index %d or size %d out of bounds for set:\n", idx, size);
+    qh_setprint(qh, qh->qhmem.ferr, "", set);
+    qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
+  }
+  set->e[set->maxsize].i=  size+1;  /* may be overwritten */
+  count= size - idx + 1;   /* +1 for NULL terminator */
+  memset((char *)SETelemaddr_(set, idx, void), 0, (size_t)count * SETelemsize);
+} /* setzero */
+
+
diff --git a/xs/src/qhull/src/libqhull_r/qset_r.h b/xs/src/qhull/src/libqhull_r/qset_r.h
new file mode 100644
index 0000000000..7ba199d6f4
--- /dev/null
+++ b/xs/src/qhull/src/libqhull_r/qset_r.h
@@ -0,0 +1,502 @@
+/*<html><pre>  -<a                             href="qh-set_r.htm"
+  >-------------------------------</a><a name="TOP">-</a>
+
+   qset_r.h
+     header file for qset_r.c that implements set
+
+   see qh-set_r.htm and qset_r.c
+
+   only uses mem_r.c, malloc/free
+
+   for error handling, writes message and calls
+      qh_errexit(qhT *qh, qhmem_ERRqhull, NULL, NULL);
+
+   set operations satisfy the following properties:
+    - sets have a max size, the actual size (if different) is stored at the end
+    - every set is NULL terminated
+    - sets may be sorted or unsorted, the caller must distinguish this
+
+   Copyright (c) 1993-2015 The Geometry Center.
+   $Id: //main/2015/qhull/src/libqhull_r/qset_r.h#4 $$Change: 2079 $
+   $DateTime: 2016/02/07 17:43:34 $$Author: bbarber $
+*/
+
+#ifndef qhDEFset
+#define qhDEFset 1
+
+#include <stdio.h>
+
+/*================= -structures- ===============*/
+
+#ifndef DEFsetT
+#define DEFsetT 1
+typedef struct setT setT;   /* a set is a sorted or unsorted array of pointers */
+#endif
+
+#ifndef DEFqhT
+#define DEFqhT 1
+typedef struct qhT qhT;          /* defined in libqhull_r.h */
+#endif
+
+/* [jan'15] Decided not to use countT.  Most sets are small.  The code uses signed tests */
+
+/*-<a                                      href="qh-set_r.htm#TOC"
+>----------------------------------------</a><a name="setT">-</a>
+
+setT
+  a set or list of pointers with maximum size and actual size.
+
+variations:
+  unsorted, unique   -- a list of unique pointers with NULL terminator
+                           user guarantees uniqueness
+  sorted             -- a sorted list of unique pointers with NULL terminator
+                           qset_r.c guarantees uniqueness
+  unsorted           -- a list of pointers terminated with NULL
+  indexed            -- an array of pointers with NULL elements
+
+structure for set of n elements:
+
+        --------------
+        |  maxsize
+        --------------
+        |  e[0] - a pointer, may be NULL for indexed sets
+        --------------
+        |  e[1]
+
+        --------------
+        |  ...
+        --------------
+        |  e[n-1]
+        --------------
+        |  e[n] = NULL
+        --------------
+        |  ...
+        --------------
+        |  e[maxsize] - n+1 or NULL (determines actual size of set)
+        --------------
+
+*/
+
+/*-- setelemT -- internal type to allow both pointers and indices
+*/
+typedef union setelemT setelemT;
+union setelemT {
+  void    *p;
+  int   i;         /* integer used for e[maxSize] */
+};
+
+struct setT {
+  int maxsize;          /* maximum number of elements (except NULL) */
+  setelemT e[1];        /* array of pointers, tail is NULL */
+                        /* last slot (unless NULL) is actual size+1
+                           e[maxsize]==NULL or e[e[maxsize]-1]==NULL */
+                        /* this may generate a warning since e[] contains
+                           maxsize elements */
+};
+
+/*=========== -constants- =========================*/
+
+/*-<a                                 href="qh-set_r.htm#TOC"
+  >-----------------------------------</a><a name="SETelemsize">-</a>
+
+  SETelemsize
+    size of a set element in bytes
+*/
+#define SETelemsize ((int)sizeof(setelemT))
+
+
+/*=========== -macros- =========================*/
+
+/*-<a                                 href="qh-set_r.htm#TOC"
+  >-----------------------------------</a><a name="FOREACHsetelement_">-</a>
+
+   FOREACHsetelement_(type, set, variable)
+     define FOREACH iterator
+
+   declare:
+     assumes *variable and **variablep are declared
+     no space in "variable)" [DEC Alpha cc compiler]
+
+   each iteration:
+     variable is set element
+     variablep is one beyond variable.
+
+   to repeat an element:
+     variablep--; / *repeat* /
+
+   at exit:
+     variable is NULL at end of loop
+
+   example:
+     #define FOREACHfacet_( facets ) FOREACHsetelement_( facetT, facets, facet )
+
+   notes:
+     use FOREACHsetelement_i_() if need index or include NULLs
+
+   WARNING:
+     nested loops can't use the same variable (define another FOREACH)
+
+     needs braces if nested inside another FOREACH
+     this includes intervening blocks, e.g. FOREACH...{ if () FOREACH...} )
+*/
+#define FOREACHsetelement_(type, set, variable) \
+        if (((variable= NULL), set)) for (\
+          variable##p= (type **)&((set)->e[0].p); \
+          (variable= *variable##p++);)
+
+/*-<a                                      href="qh-set_r.htm#TOC"
+  >----------------------------------------</a><a name="FOREACHsetelement_i_">-</a>
+
+   FOREACHsetelement_i_(qh, type, set, variable)
+     define indexed FOREACH iterator
+
+   declare:
+     type *variable, variable_n, variable_i;
+
+   each iteration:
+     variable is set element, may be NULL
+     variable_i is index, variable_n is qh_setsize()
+
+   to repeat an element:
+     variable_i--; variable_n-- repeats for deleted element
+
+   at exit:
+     variable==NULL and variable_i==variable_n
+
+   example:
+     #define FOREACHfacet_i_( qh, facets ) FOREACHsetelement_i_( qh, facetT, facets, facet )
+
+   WARNING:
+     nested loops can't use the same variable (define another FOREACH)
+
+     needs braces if nested inside another FOREACH
+     this includes intervening blocks, e.g. FOREACH...{ if () FOREACH...} )
+*/
+#define FOREACHsetelement_i_(qh, type, set, variable) \
+        if (((variable= NULL), set)) for (\
+          variable##_i= 0, variable= (type *)((set)->e[0].p), \
+                   variable##_n= qh_setsize(qh, set);\
+          variable##_i < variable##_n;\
+          variable= (type *)((set)->e[++variable##_i].p) )
+
+/*-<a                                    href="qh-set_r.htm#TOC"
+  >--------------------------------------</a><a name="FOREACHsetelementreverse_">-</a>
+
+   FOREACHsetelementreverse_(qh, type, set, variable)-
+     define FOREACH iterator in reverse order
+
+   declare:
+     assumes *variable and **variablep are declared
+     also declare 'int variabletemp'
+
+   each iteration:
+     variable is set element
+
+   to repeat an element:
+     variabletemp++; / *repeat* /
+
+   at exit:
+     variable is NULL
+
+   example:
+     #define FOREACHvertexreverse_( vertices ) FOREACHsetelementreverse_( vertexT, vertices, vertex )
+
+   notes:
+     use FOREACHsetelementreverse12_() to reverse first two elements
+     WARNING: needs braces if nested inside another FOREACH
+*/
+#define FOREACHsetelementreverse_(qh, type, set, variable) \
+        if (((variable= NULL), set)) for (\
+           variable##temp= qh_setsize(qh, set)-1, variable= qh_setlast(qh, set);\
+           variable; variable= \
+           ((--variable##temp >= 0) ? SETelemt_(set, variable##temp, type) : NULL))
+
+/*-<a                                 href="qh-set_r.htm#TOC"
+  >-----------------------------------</a><a name="FOREACHsetelementreverse12_">-</a>
+
+   FOREACHsetelementreverse12_(type, set, variable)-
+     define FOREACH iterator with e[1] and e[0] reversed
+
+   declare:
+     assumes *variable and **variablep are declared
+
+   each iteration:
+     variable is set element
+     variablep is one after variable.
+
+   to repeat an element:
+     variablep--; / *repeat* /
+
+   at exit:
+     variable is NULL at end of loop
+
+   example
+     #define FOREACHvertexreverse12_( vertices ) FOREACHsetelementreverse12_( vertexT, vertices, vertex )
+
+   notes:
+     WARNING: needs braces if nested inside another FOREACH
+*/
+#define FOREACHsetelementreverse12_(type, set, variable) \
+        if (((variable= NULL), set)) for (\
+          variable##p= (type **)&((set)->e[1].p); \
+          (variable= *variable##p); \
+          variable##p == ((type **)&((set)->e[0].p))?variable##p += 2: \
+              (variable##p == ((type **)&((set)->e[1].p))?variable##p--:variable##p++))
+
+/*-<a                                 href="qh-set_r.htm#TOC"
+  >-----------------------------------</a><a name="FOREACHelem_">-</a>
+
+   FOREACHelem_( set )-
+     iterate elements in a set
+
+   declare:
+     void *elem, *elemp;
+
+   each iteration:
+     elem is set element
+     elemp is one beyond
+
+   to repeat an element:
+     elemp--; / *repeat* /
+
+   at exit:
+     elem == NULL at end of loop
+
+   example:
+     FOREACHelem_(set) {
+
+   notes:
+     WARNING: needs braces if nested inside another FOREACH
+*/
+#define FOREACHelem_(set) FOREACHsetelement_(void, set, elem)
+
+/*-<a                                 href="qh-set_r.htm#TOC"
+  >-----------------------------------</a><a name="FOREACHset_">-</a>
+
+   FOREACHset_( set )-
+     iterate a set of sets
+
+   declare:
+     setT *set, **setp;
+
+   each iteration:
+     set is set element
+     setp is one beyond
+
+   to repeat an element:
+     setp--; / *repeat* /
+
+   at exit:
+     set == NULL at end of loop
+
+   example
+     FOREACHset_(sets) {
+
+   notes:
+     WARNING: needs braces if nested inside another FOREACH
+*/
+#define FOREACHset_(sets) FOREACHsetelement_(setT, sets, set)
+
+/*-<a                                       href="qh-set_r.htm#TOC"
+  >-----------------------------------------</a><a name="SETindex_">-</a>
+
+   SETindex_( set, elem )
+     return index of elem in set
+
+   notes:
+     for use with FOREACH iteration
+     WARN64 -- Maximum set size is 2G
+
+   example:
+     i= SETindex_(ridges, ridge)
+*/
+#define SETindex_(set, elem) ((int)((void **)elem##p - (void **)&(set)->e[1].p))
+
+/*-<a                                     href="qh-set_r.htm#TOC"
+  >---------------------------------------</a><a name="SETref_">-</a>
+
+   SETref_( elem )
+     l.h.s. for modifying the current element in a FOREACH iteration
+
+   example:
+     SETref_(ridge)= anotherridge;
+*/
+#define SETref_(elem) (elem##p[-1])
+
+/*-<a                                     href="qh-set_r.htm#TOC"
+  >---------------------------------------</a><a name="SETelem_">-</a>
+
+   SETelem_(set, n)
+     return the n'th element of set
+
+   notes:
+      assumes that n is valid [0..size] and that set is defined
+      use SETelemt_() for type cast
+*/
+#define SETelem_(set, n)           ((set)->e[n].p)
+
+/*-<a                                     href="qh-set_r.htm#TOC"
+  >---------------------------------------</a><a name="SETelemt_">-</a>
+
+   SETelemt_(set, n, type)
+     return the n'th element of set as a type
+
+   notes:
+      assumes that n is valid [0..size] and that set is defined
+*/
+#define SETelemt_(set, n, type)    ((type*)((set)->e[n].p))
+
+/*-<a                                     href="qh-set_r.htm#TOC"
+  >---------------------------------------</a><a name="SETelemaddr_">-</a>
+
+   SETelemaddr_(set, n, type)
+     return address of the n'th element of a set
+
+   notes:
+      assumes that n is valid [0..size] and set is defined
+*/
+#define SETelemaddr_(set, n, type) ((type **)(&((set)->e[n].p)))
+
+/*-<a                                     href="qh-set_r.htm#TOC"
+  >---------------------------------------</a><a name="SETfirst_">-</a>
+
+   SETfirst_(set)
+     return first element of set
+
+*/
+#define SETfirst_(set)             ((set)->e[0].p)
+
+/*-<a                                     href="qh-set_r.htm#TOC"
+  >---------------------------------------</a><a name="SETfirstt_">-</a>
+
+   SETfirstt_(set, type)
+     return first element of set as a type
+
+*/
+#define SETfirstt_(set, type)      ((type*)((set)->e[0].p))
+
+/*-<a                                     href="qh-set_r.htm#TOC"
+  >---------------------------------------</a><a name="SETsecond_">-</a>
+
+   SETsecond_(set)
+     return second element of set
+
+*/
+#define SETsecond_(set)            ((set)->e[1].p)
+
+/*-<a                                     href="qh-set_r.htm#TOC"
+  >---------------------------------------</a><a name="SETsecondt_">-</a>
+
+   SETsecondt_(set, type)
+     return second element of set as a type
+*/
+#define SETsecondt_(set, type)     ((type*)((set)->e[1].p))
+
+/*-<a                                     href="qh-set_r.htm#TOC"
+  >---------------------------------------</a><a name="SETaddr_">-</a>
+
+   SETaddr_(set, type)
+       return address of set's elements
+*/
+#define SETaddr_(set,type)         ((type **)(&((set)->e[0].p)))
+
+/*-<a                                     href="qh-set_r.htm#TOC"
+  >---------------------------------------</a><a name="SETreturnsize_">-</a>
+
+   SETreturnsize_(set, size)
+     return size of a set
+
+   notes:
+      set must be defined
+      use qh_setsize(qhT *qh, set) unless speed is critical
+*/
+#define SETreturnsize_(set, size) (((size)= ((set)->e[(set)->maxsize].i))?(--(size)):((size)= (set)->maxsize))
+
+/*-<a                                     href="qh-set_r.htm#TOC"
+  >---------------------------------------</a><a name="SETempty_">-</a>
+
+   SETempty_(set)
+     return true(1) if set is empty
+
+   notes:
+      set may be NULL
+*/
+#define SETempty_(set)            (!set || (SETfirst_(set) ? 0 : 1))
+
+/*-<a                             href="qh-set_r.htm#TOC"
+  >-------------------------------<a name="SETsizeaddr_">-</a>
+
+  SETsizeaddr_(set)
+    return pointer to 'actual size+1' of set (set CANNOT be NULL!!)
+    Its type is setelemT* for strict aliasing
+    All SETelemaddr_ must be cast to setelemT
+
+
+  notes:
+    *SETsizeaddr==NULL or e[*SETsizeaddr-1].p==NULL
+*/
+#define SETsizeaddr_(set) (&((set)->e[(set)->maxsize]))
+
+/*-<a                                     href="qh-set_r.htm#TOC"
+  >---------------------------------------</a><a name="SETtruncate_">-</a>
+
+   SETtruncate_(set, size)
+     truncate set to size
+
+   see:
+     qh_settruncate()
+
+*/
+#define SETtruncate_(set, size) {set->e[set->maxsize].i= size+1; /* maybe overwritten */ \
+      set->e[size].p= NULL;}
+
+/*======= prototypes in alphabetical order ============*/
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+void  qh_setaddsorted(qhT *qh, setT **setp, void *elem);
+void  qh_setaddnth(qhT *qh, setT **setp, int nth, void *newelem);
+void  qh_setappend(qhT *qh, setT **setp, void *elem);
+void  qh_setappend_set(qhT *qh, setT **setp, setT *setA);
+void  qh_setappend2ndlast(qhT *qh, setT **setp, void *elem);
+void  qh_setcheck(qhT *qh, setT *set, const char *tname, unsigned id);
+void  qh_setcompact(qhT *qh, setT *set);
+setT *qh_setcopy(qhT *qh, setT *set, int extra);
+void *qh_setdel(setT *set, void *elem);
+void *qh_setdellast(setT *set);
+void *qh_setdelnth(qhT *qh, setT *set, int nth);
+void *qh_setdelnthsorted(qhT *qh, setT *set, int nth);
+void *qh_setdelsorted(setT *set, void *newelem);
+setT *qh_setduplicate(qhT *qh, setT *set, int elemsize);
+void **qh_setendpointer(setT *set);
+int   qh_setequal(setT *setA, setT *setB);
+int   qh_setequal_except(setT *setA, void *skipelemA, setT *setB, void *skipelemB);
+int   qh_setequal_skip(setT *setA, int skipA, setT *setB, int skipB);
+void  qh_setfree(qhT *qh, setT **set);
+void  qh_setfree2(qhT *qh, setT **setp, int elemsize);
+void  qh_setfreelong(qhT *qh, setT **set);
+int   qh_setin(setT *set, void *setelem);
+int qh_setindex(setT *set, void *setelem);
+void  qh_setlarger(qhT *qh, setT **setp);
+void *qh_setlast(setT *set);
+setT *qh_setnew(qhT *qh, int size);
+setT *qh_setnew_delnthsorted(qhT *qh, setT *set, int size, int nth, int prepend);
+void  qh_setprint(qhT *qh, FILE *fp, const char* string, setT *set);
+void  qh_setreplace(qhT *qh, setT *set, void *oldelem, void *newelem);
+int qh_setsize(qhT *qh, setT *set);
+setT *qh_settemp(qhT *qh, int setsize);
+void  qh_settempfree(qhT *qh, setT **set);
+void  qh_settempfree_all(qhT *qh);
+setT *qh_settemppop(qhT *qh);
+void  qh_settemppush(qhT *qh, setT *set);
+void  qh_settruncate(qhT *qh, setT *set, int size);
+int   qh_setunique(qhT *qh, setT **set, void *elem);
+void  qh_setzero(qhT *qh, setT *set, int idx, int size);
+
+#ifdef __cplusplus
+} /* extern "C" */
+#endif
+
+#endif /* qhDEFset */
diff --git a/xs/src/qhull/src/libqhull_r/random_r.c b/xs/src/qhull/src/libqhull_r/random_r.c
new file mode 100644
index 0000000000..1fefb51c36
--- /dev/null
+++ b/xs/src/qhull/src/libqhull_r/random_r.c
@@ -0,0 +1,247 @@
+/*<html><pre>  -<a                             href="index_r.htm#TOC"
+  >-------------------------------</a><a name="TOP">-</a>
+
+   random_r.c and utilities
+     Park & Miller's minimimal standard random number generator
+     argc/argv conversion
+
+     Used by rbox.  Do not use 'qh' 
+*/
+
+#include "libqhull_r.h"
+#include "random_r.h"
+
+#include <string.h>
+#include <stdio.h>
+#include <stdlib.h>
+
+#ifdef _MSC_VER  /* Microsoft Visual C++ -- warning level 4 */
+#pragma warning( disable : 4706)  /* assignment within conditional function */
+#pragma warning( disable : 4996)  /* function was declared deprecated(strcpy, localtime, etc.) */
+#endif
+
+/*-<a                             href="qh-globa_r.htm#TOC"
+ >-------------------------------</a><a name="argv_to_command">-</a>
+
+ qh_argv_to_command(argc, argv, command, max_size )
+
+    build command from argc/argv
+    max_size is at least
+
+ returns:
+    a space-delimited string of options (just as typed)
+    returns false if max_size is too short
+
+ notes:
+    silently removes
+    makes option string easy to input and output
+    matches qh_argv_to_command_size()
+
+    argc may be 0
+*/
+int qh_argv_to_command(int argc, char *argv[], char* command, int max_size) {
+  int i, remaining;
+  char *s;
+  *command= '\0';  /* max_size > 0 */
+
+  if (argc) {
+    if ((s= strrchr( argv[0], '\\')) /* get filename w/o .exe extension */
+    || (s= strrchr( argv[0], '/')))
+        s++;
+    else
+        s= argv[0];
+    if ((int)strlen(s) < max_size)   /* WARN64 */
+        strcpy(command, s);
+    else
+        goto error_argv;
+    if ((s= strstr(command, ".EXE"))
+    ||  (s= strstr(command, ".exe")))
+        *s= '\0';
+  }
+  for (i=1; i < argc; i++) {
+    s= argv[i];
+    remaining= max_size - (int)strlen(command) - (int)strlen(s) - 2;   /* WARN64 */
+    if (!*s || strchr(s, ' ')) {
+      char *t= command + strlen(command);
+      remaining -= 2;
+      if (remaining < 0) {
+        goto error_argv;
+      }
+      *t++= ' ';
+      *t++= '"';
+      while (*s) {
+        if (*s == '"') {
+          if (--remaining < 0)
+            goto error_argv;
+          *t++= '\\';
+        }
+        *t++= *s++;
+      }
+      *t++= '"';
+      *t= '\0';
+    }else if (remaining < 0) {
+      goto error_argv;
+    }else
+      strcat(command, " ");
+      strcat(command, s);
+  }
+  return 1;
+
+error_argv:
+  return 0;
+} /* argv_to_command */
+
+/*-<a                             href="qh-globa_r.htm#TOC"
+>-------------------------------</a><a name="argv_to_command_size">-</a>
+
+qh_argv_to_command_size(argc, argv )
+
+    return size to allocate for qh_argv_to_command()
+
+notes:
+    argc may be 0
+    actual size is usually shorter
+*/
+int qh_argv_to_command_size(int argc, char *argv[]) {
+    unsigned int count= 1; /* null-terminator if argc==0 */
+    int i;
+    char *s;
+
+    for (i=0; i<argc; i++){
+      count += (int)strlen(argv[i]) + 1;   /* WARN64 */
+      if (i>0 && strchr(argv[i], ' ')) {
+        count += 2;  /* quote delimiters */
+        for (s=argv[i]; *s; s++) {
+          if (*s == '"') {
+            count++;
+          }
+        }
+      }
+    }
+    return count;
+} /* argv_to_command_size */
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+  >-------------------------------</a><a name="rand">-</a>
+
+  qh_rand()
+  qh_srand(qh, seed )
+    generate pseudo-random number between 1 and 2^31 -2
+
+  notes:
+    For qhull and rbox, called from qh_RANDOMint(),etc. [user.h]
+
+    From Park & Miller's minimal standard random number generator
+      Communications of the ACM, 31:1192-1201, 1988.
+    Does not use 0 or 2^31 -1
+      this is silently enforced by qh_srand()
+    Can make 'Rn' much faster by moving qh_rand to qh_distplane
+*/
+
+/* Global variables and constants */
+
+#define qh_rand_a 16807
+#define qh_rand_m 2147483647
+#define qh_rand_q 127773  /* m div a */
+#define qh_rand_r 2836    /* m mod a */
+
+int qh_rand(qhT *qh) {
+    int lo, hi, test;
+    int seed = qh->last_random;
+
+    hi = seed / qh_rand_q;  /* seed div q */
+    lo = seed % qh_rand_q;  /* seed mod q */
+    test = qh_rand_a * lo - qh_rand_r * hi;
+    if (test > 0)
+        seed= test;
+    else
+        seed= test + qh_rand_m;
+    qh->last_random= seed;
+    /* seed = seed < qh_RANDOMmax/2 ? 0 : qh_RANDOMmax;  for testing */
+    /* seed = qh_RANDOMmax;  for testing */
+    return seed;
+} /* rand */
+
+void qh_srand(qhT *qh, int seed) {
+    if (seed < 1)
+        qh->last_random= 1;
+    else if (seed >= qh_rand_m)
+        qh->last_random= qh_rand_m - 1;
+    else
+        qh->last_random= seed;
+} /* qh_srand */
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+>-------------------------------</a><a name="randomfactor">-</a>
+
+qh_randomfactor(qh, scale, offset )
+  return a random factor r * scale + offset
+
+notes:
+  qh.RANDOMa/b are defined in global_r.c
+  qh_RANDOMint requires 'qh'
+*/
+realT qh_randomfactor(qhT *qh, realT scale, realT offset) {
+    realT randr;
+
+    randr= qh_RANDOMint;
+    return randr * scale + offset;
+} /* randomfactor */
+
+/*-<a                             href="qh-geom_r.htm#TOC"
+>-------------------------------</a><a name="randommatrix">-</a>
+
+qh_randommatrix(qh, buffer, dim, rows )
+  generate a random dim X dim matrix in range [-1,1]
+  assumes buffer is [dim+1, dim]
+
+  returns:
+    sets buffer to random numbers
+    sets rows to rows of buffer
+    sets row[dim] as scratch row
+
+  notes:
+    qh_RANDOMint requires 'qh'
+*/
+void qh_randommatrix(qhT *qh, realT *buffer, int dim, realT **rows) {
+    int i, k;
+    realT **rowi, *coord, realr;
+
+    coord= buffer;
+    rowi= rows;
+    for (i=0; i < dim; i++) {
+        *(rowi++)= coord;
+        for (k=0; k < dim; k++) {
+            realr= qh_RANDOMint;
+            *(coord++)= 2.0 * realr/(qh_RANDOMmax+1) - 1.0;
+        }
+    }
+    *rowi= coord;
+} /* randommatrix */
+
+/*-<a                             href="qh-globa_r.htm#TOC"
+  >-------------------------------</a><a name="strtol">-</a>
+
+  qh_strtol( s, endp) qh_strtod( s, endp)
+    internal versions of strtol() and strtod()
+    does not skip trailing spaces
+  notes:
+    some implementations of strtol()/strtod() skip trailing spaces
+*/
+double qh_strtod(const char *s, char **endp) {
+  double result;
+
+  result= strtod(s, endp);
+  if (s < (*endp) && (*endp)[-1] == ' ')
+    (*endp)--;
+  return result;
+} /* strtod */
+
+int qh_strtol(const char *s, char **endp) {
+  int result;
+
+  result= (int) strtol(s, endp, 10);     /* WARN64 */
+  if (s< (*endp) && (*endp)[-1] == ' ')
+    (*endp)--;
+  return result;
+} /* strtol */
diff --git a/xs/src/qhull/src/libqhull_r/random_r.h b/xs/src/qhull/src/libqhull_r/random_r.h
new file mode 100644
index 0000000000..dc884b33cb
--- /dev/null
+++ b/xs/src/qhull/src/libqhull_r/random_r.h
@@ -0,0 +1,41 @@
+/*<html><pre>  -<a                             href="qh-geom_r.htm"
+  >-------------------------------</a><a name="TOP">-</a>
+
+  random.h
+    header file for random and utility routines
+
+   see qh-geom_r.htm and random_r.c
+
+   Copyright (c) 1993-2015 The Geometry Center.
+   $Id: //main/2015/qhull/src/libqhull_r/random_r.h#4 $$Change: 2079 $
+   $DateTime: 2016/02/07 17:43:34 $$Author: bbarber $
+*/
+
+#ifndef qhDEFrandom
+#define qhDEFrandom 1
+
+#include "libqhull_r.h"
+
+/*============= prototypes in alphabetical order ======= */
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+int     qh_argv_to_command(int argc, char *argv[], char* command, int max_size);
+int     qh_argv_to_command_size(int argc, char *argv[]);
+int     qh_rand(qhT *qh);
+void    qh_srand(qhT *qh, int seed);
+realT   qh_randomfactor(qhT *qh, realT scale, realT offset);
+void    qh_randommatrix(qhT *qh, realT *buffer, int dim, realT **row);
+int     qh_strtol(const char *s, char **endp);
+double  qh_strtod(const char *s, char **endp);
+
+#ifdef __cplusplus
+} /* extern "C" */
+#endif
+
+#endif /* qhDEFrandom */
+
+
+
diff --git a/xs/src/qhull/src/libqhull_r/rboxlib_r.c b/xs/src/qhull/src/libqhull_r/rboxlib_r.c
new file mode 100644
index 0000000000..6c0c7e35ef
--- /dev/null
+++ b/xs/src/qhull/src/libqhull_r/rboxlib_r.c
@@ -0,0 +1,842 @@
+/*<html><pre>  -<a                             href="index_r.htm#TOC"
+  >-------------------------------</a><a name="TOP">-</a>
+
+   rboxlib_r.c
+     Generate input points
+
+   notes:
+     For documentation, see prompt[] of rbox_r.c
+     50 points generated for 'rbox D4'
+
+   WARNING:
+     incorrect range if qh_RANDOMmax is defined wrong (user_r.h)
+*/
+
+#include "libqhull_r.h"  /* First for user_r.h */
+#include "random_r.h"
+
+#include <ctype.h>
+#include <limits.h>
+#include <math.h>
+#include <setjmp.h>
+#include <string.h>
+#include <time.h>
+#include <stdio.h>
+#include <stdlib.h>
+
+#ifdef _MSC_VER  /* Microsoft Visual C++ */
+#pragma warning( disable : 4706)  /* assignment within conditional expression. */
+#pragma warning( disable : 4996)  /* this function (strncat,sprintf,strcpy) or variable may be unsafe. */
+#endif
+
+#define MAXdim 200
+#define PI 3.1415926535897932384
+
+/* ------------------------------ prototypes ----------------*/
+int qh_roundi(qhT *qh, double a);
+void qh_out1(qhT *qh, double a);
+void qh_out2n(qhT *qh, double a, double b);
+void qh_out3n(qhT *qh, double a, double b, double c);
+void qh_outcoord(qhT *qh, int iscdd, double *coord, int dim);
+void qh_outcoincident(qhT *qh, int coincidentpoints, double radius, int iscdd, double *coord, int dim);
+
+void    qh_fprintf_rbox(qhT *qh, FILE *fp, int msgcode, const char *fmt, ... );
+void    qh_free(void *mem);
+void   *qh_malloc(size_t size);
+int     qh_rand(qhT *qh);
+void    qh_srand(qhT *qh, int seed);
+
+/*-<a                             href="qh-qhull_r.htm#TOC"
+  >-------------------------------</a><a name="rboxpoints">-</a>
+
+  qh_rboxpoints(qh, rbox_command )
+    Generate points to qh->fout according to rbox options
+    Report errors on qh->ferr
+
+  returns:
+    0 (qh_ERRnone) on success
+    1 (qh_ERRinput) on input error
+    4 (qh_ERRmem) on memory error
+    5 (qh_ERRqhull) on internal error
+
+  notes:
+    To avoid using stdio, redefine qh_malloc, qh_free, and qh_fprintf_rbox (user_r.c)
+
+  design:
+    Straight line code (consider defining a struct and functions):
+
+    Parse arguments into variables
+    Determine the number of points
+    Generate the points
+*/
+int qh_rboxpoints(qhT *qh, char* rbox_command) {
+  int i,j,k;
+  int gendim;
+  int coincidentcount=0, coincidenttotal=0, coincidentpoints=0;
+  int cubesize, diamondsize, seed=0, count, apex;
+  int dim=3 , numpoints= 0, totpoints, addpoints=0;
+  int issphere=0, isaxis=0,  iscdd= 0, islens= 0, isregular=0, iswidth=0, addcube=0;
+  int isgap=0, isspiral=0, NOcommand= 0, adddiamond=0;
+  int israndom=0, istime=0;
+  int isbox=0, issimplex=0, issimplex2=0, ismesh=0;
+  double width=0.0, gap=0.0, radius=0.0, coincidentradius=0.0;
+  double coord[MAXdim], offset, meshm=3.0, meshn=4.0, meshr=5.0;
+  double *coordp, *simplex= NULL, *simplexp;
+  int nthroot, mult[MAXdim];
+  double norm, factor, randr, rangap, lensangle= 0, lensbase= 1;
+  double anglediff, angle, x, y, cube= 0.0, diamond= 0.0;
+  double box= qh_DEFAULTbox; /* scale all numbers before output */
+  double randmax= qh_RANDOMmax;
+  char command[200], seedbuf[200];
+  char *s= command, *t, *first_point= NULL;
+  time_t timedata;
+  int exitcode;
+
+  exitcode= setjmp(qh->rbox_errexit);
+  if (exitcode) {
+    /* same code for error exit and normal return, qh->NOerrexit is set */
+    if (simplex)
+        qh_free(simplex);
+    return exitcode;
+  }
+
+  *command= '\0';
+  strncat(command, rbox_command, sizeof(command)-strlen(command)-1);
+
+  while (*s && !isspace(*s))  /* skip program name */
+    s++;
+  while (*s) {
+    while (*s && isspace(*s))
+      s++;
+    if (*s == '-')
+      s++;
+    if (!*s)
+      break;
+    if (isdigit(*s)) {
+      numpoints= qh_strtol(s, &s);
+      continue;
+    }
+    /* ============= read flags =============== */
+    switch (*s++) {
+    case 'c':
+      addcube= 1;
+      t= s;
+      while (isspace(*t))
+        t++;
+      if (*t == 'G')
+        cube= qh_strtod(++t, &s);
+      break;
+    case 'd':
+      adddiamond= 1;
+      t= s;
+      while (isspace(*t))
+        t++;
+      if (*t == 'G')
+        diamond= qh_strtod(++t, &s);
+      break;
+    case 'h':
+      iscdd= 1;
+      break;
+    case 'l':
+      isspiral= 1;
+      break;
+    case 'n':
+      NOcommand= 1;
+      break;
+    case 'r':
+      isregular= 1;
+      break;
+    case 's':
+      issphere= 1;
+      break;
+    case 't':
+      istime= 1;
+      if (isdigit(*s)) {
+        seed= qh_strtol(s, &s);
+        israndom= 0;
+      }else
+        israndom= 1;
+      break;
+    case 'x':
+      issimplex= 1;
+      break;
+    case 'y':
+      issimplex2= 1;
+      break;
+    case 'z':
+      qh->rbox_isinteger= 1;
+      break;
+    case 'B':
+      box= qh_strtod(s, &s);
+      isbox= 1;
+      break;
+    case 'C':
+      if (*s)
+        coincidentpoints=  qh_strtol(s, &s);
+      if (*s == ',') {
+        ++s;
+        coincidentradius=  qh_strtod(s, &s);
+      }
+      if (*s == ',') {
+        ++s;
+        coincidenttotal=  qh_strtol(s, &s);
+      }
+      if (*s && !isspace(*s)) {
+        qh_fprintf_rbox(qh, qh->ferr, 7080, "rbox error: arguments for 'Cn,r,m' are not 'int', 'float', and 'int'.  Remaining string is '%s'\n", s);
+        qh_errexit_rbox(qh, qh_ERRinput);
+      }
+      if (coincidentpoints==0){
+        qh_fprintf_rbox(qh, qh->ferr, 6268, "rbox error: missing arguments for 'Cn,r,m' where n is the number of coincident points, r is the radius (default 0.0), and m is the number of points\n");
+        qh_errexit_rbox(qh, qh_ERRinput);
+      }
+      if (coincidentpoints<0 || coincidenttotal<0 || coincidentradius<0.0){
+        qh_fprintf_rbox(qh, qh->ferr, 6269, "rbox error: negative arguments for 'Cn,m,r' where n (%d) is the number of coincident points, m (%d) is the number of points, and r (%.2g) is the radius (default 0.0)\n", coincidentpoints, coincidenttotal, coincidentradius);
+        qh_errexit_rbox(qh, qh_ERRinput);
+      }
+      break;
+    case 'D':
+      dim= qh_strtol(s, &s);
+      if (dim < 1
+      || dim > MAXdim) {
+        qh_fprintf_rbox(qh, qh->ferr, 6189, "rbox error: dimension, D%d, out of bounds (>=%d or <=0)", dim, MAXdim);
+        qh_errexit_rbox(qh, qh_ERRinput);
+      }
+      break;
+    case 'G':
+      if (isdigit(*s))
+        gap= qh_strtod(s, &s);
+      else
+        gap= 0.5;
+      isgap= 1;
+      break;
+    case 'L':
+      if (isdigit(*s))
+        radius= qh_strtod(s, &s);
+      else
+        radius= 10;
+      islens= 1;
+      break;
+    case 'M':
+      ismesh= 1;
+      if (*s)
+        meshn= qh_strtod(s, &s);
+      if (*s == ',') {
+        ++s;
+        meshm= qh_strtod(s, &s);
+      }else
+        meshm= 0.0;
+      if (*s == ',') {
+        ++s;
+        meshr= qh_strtod(s, &s);
+      }else
+        meshr= sqrt(meshn*meshn + meshm*meshm);
+      if (*s && !isspace(*s)) {
+        qh_fprintf_rbox(qh, qh->ferr, 7069, "rbox warning: assuming 'M3,4,5' since mesh args are not integers or reals\n");
+        meshn= 3.0, meshm=4.0, meshr=5.0;
+      }
+      break;
+    case 'O':
+      qh->rbox_out_offset= qh_strtod(s, &s);
+      break;
+    case 'P':
+      if (!first_point)
+        first_point= s-1;
+      addpoints++;
+      while (*s && !isspace(*s))   /* read points later */
+        s++;
+      break;
+    case 'W':
+      width= qh_strtod(s, &s);
+      iswidth= 1;
+      break;
+    case 'Z':
+      if (isdigit(*s))
+        radius= qh_strtod(s, &s);
+      else
+        radius= 1.0;
+      isaxis= 1;
+      break;
+    default:
+      qh_fprintf_rbox(qh, qh->ferr, 7070, "rbox error: unknown flag at %s.\nExecute 'rbox' without arguments for documentation.\n", s);
+      qh_errexit_rbox(qh, qh_ERRinput);
+    }
+    if (*s && !isspace(*s)) {
+      qh_fprintf_rbox(qh, qh->ferr, 7071, "rbox error: missing space between flags at %s.\n", s);
+      qh_errexit_rbox(qh, qh_ERRinput);
+    }
+  }
+
+  /* ============= defaults, constants, and sizes =============== */
+  if (qh->rbox_isinteger && !isbox)
+    box= qh_DEFAULTzbox;
+  if (addcube) {
+    cubesize= (int)floor(ldexp(1.0,dim)+0.5);
+    if (cube == 0.0)
+      cube= box;
+  }else
+    cubesize= 0;
+  if (adddiamond) {
+    diamondsize= 2*dim;
+    if (diamond == 0.0)
+      diamond= box;
+  }else
+    diamondsize= 0;
+  if (islens) {
+    if (isaxis) {
+        qh_fprintf_rbox(qh, qh->ferr, 6190, "rbox error: can not combine 'Ln' with 'Zn'\n");
+        qh_errexit_rbox(qh, qh_ERRinput);
+    }
+    if (radius <= 1.0) {
+        qh_fprintf_rbox(qh, qh->ferr, 6191, "rbox error: lens radius %.2g should be greater than 1.0\n",
+               radius);
+        qh_errexit_rbox(qh, qh_ERRinput);
+    }
+    lensangle= asin(1.0/radius);
+    lensbase= radius * cos(lensangle);
+  }
+
+  if (!numpoints) {
+    if (issimplex2)
+        ; /* ok */
+    else if (isregular + issimplex + islens + issphere + isaxis + isspiral + iswidth + ismesh) {
+        qh_fprintf_rbox(qh, qh->ferr, 6192, "rbox error: missing count\n");
+        qh_errexit_rbox(qh, qh_ERRinput);
+    }else if (adddiamond + addcube + addpoints)
+        ; /* ok */
+    else {
+        numpoints= 50;  /* ./rbox D4 is the test case */
+        issphere= 1;
+    }
+  }
+  if ((issimplex + islens + isspiral + ismesh > 1)
+  || (issimplex + issphere + isspiral + ismesh > 1)) {
+    qh_fprintf_rbox(qh, qh->ferr, 6193, "rbox error: can only specify one of 'l', 's', 'x', 'Ln', or 'Mn,m,r' ('Ln s' is ok).\n");
+    qh_errexit_rbox(qh, qh_ERRinput);
+  }
+  if (coincidentpoints>0 && (numpoints == 0 || coincidenttotal > numpoints)) {
+    qh_fprintf_rbox(qh, qh->ferr, 6270, "rbox error: 'Cn,r,m' requested n coincident points for each of m points.  Either there is no points or m (%d) is greater than the number of points (%d).\n", coincidenttotal, numpoints);
+    qh_errexit_rbox(qh, qh_ERRinput);
+  }
+  if (coincidenttotal == 0)
+    coincidenttotal= numpoints;
+
+  /* ============= print header with total points =============== */
+  if (issimplex || ismesh)
+    totpoints= numpoints;
+  else if (issimplex2)
+    totpoints= numpoints+dim+1;
+  else if (isregular) {
+    totpoints= numpoints;
+    if (dim == 2) {
+        if (islens)
+          totpoints += numpoints - 2;
+    }else if (dim == 3) {
+        if (islens)
+          totpoints += 2 * numpoints;
+      else if (isgap)
+        totpoints += 1 + numpoints;
+      else
+        totpoints += 2;
+    }
+  }else
+    totpoints= numpoints + isaxis;
+  totpoints += cubesize + diamondsize + addpoints;
+  totpoints += coincidentpoints*coincidenttotal;
+
+  /* ============= seed randoms =============== */
+  if (istime == 0) {
+    for (s=command; *s; s++) {
+      if (issimplex2 && *s == 'y') /* make 'y' same seed as 'x' */
+        i= 'x';
+      else
+        i= *s;
+      seed= 11*seed + i;
+    }
+  }else if (israndom) {
+    seed= (int)time(&timedata);
+    sprintf(seedbuf, " t%d", seed);  /* appends an extra t, not worth removing */
+    strncat(command, seedbuf, sizeof(command)-strlen(command)-1);
+    t= strstr(command, " t ");
+    if (t)
+      strcpy(t+1, t+3); /* remove " t " */
+  } /* else, seed explicitly set to n */
+  qh_RANDOMseed_(qh, seed);
+
+  /* ============= print header =============== */
+
+  if (iscdd)
+      qh_fprintf_rbox(qh, qh->fout, 9391, "%s\nbegin\n        %d %d %s\n",
+      NOcommand ? "" : command,
+      totpoints, dim+1,
+      qh->rbox_isinteger ? "integer" : "real");
+  else if (NOcommand)
+      qh_fprintf_rbox(qh, qh->fout, 9392, "%d\n%d\n", dim, totpoints);
+  else
+      /* qh_fprintf_rbox special cases 9393 to append 'command' to the RboxPoints.comment() */
+      qh_fprintf_rbox(qh, qh->fout, 9393, "%d %s\n%d\n", dim, command, totpoints);
+
+  /* ============= explicit points =============== */
+  if ((s= first_point)) {
+    while (s && *s) { /* 'P' */
+      count= 0;
+      if (iscdd)
+        qh_out1(qh, 1.0);
+      while (*++s) {
+        qh_out1(qh, qh_strtod(s, &s));
+        count++;
+        if (isspace(*s) || !*s)
+          break;
+        if (*s != ',') {
+          qh_fprintf_rbox(qh, qh->ferr, 6194, "rbox error: missing comma after coordinate in %s\n\n", s);
+          qh_errexit_rbox(qh, qh_ERRinput);
+        }
+      }
+      if (count < dim) {
+        for (k=dim-count; k--; )
+          qh_out1(qh, 0.0);
+      }else if (count > dim) {
+        qh_fprintf_rbox(qh, qh->ferr, 6195, "rbox error: %d coordinates instead of %d coordinates in %s\n\n",
+                  count, dim, s);
+        qh_errexit_rbox(qh, qh_ERRinput);
+      }
+      qh_fprintf_rbox(qh, qh->fout, 9394, "\n");
+      while ((s= strchr(s, 'P'))) {
+        if (isspace(s[-1]))
+          break;
+      }
+    }
+  }
+
+  /* ============= simplex distribution =============== */
+  if (issimplex+issimplex2) {
+    if (!(simplex= (double*)qh_malloc( dim * (dim+1) * sizeof(double)))) {
+      qh_fprintf_rbox(qh, qh->ferr, 6196, "rbox error: insufficient memory for simplex\n");
+      qh_errexit_rbox(qh, qh_ERRmem); /* qh_ERRmem */
+    }
+    simplexp= simplex;
+    if (isregular) {
+      for (i=0; i<dim; i++) {
+        for (k=0; k<dim; k++)
+          *(simplexp++)= i==k ? 1.0 : 0.0;
+      }
+      for (k=0; k<dim; k++)
+        *(simplexp++)= -1.0;
+    }else {
+      for (i=0; i<dim+1; i++) {
+        for (k=0; k<dim; k++) {
+          randr= qh_RANDOMint;
+          *(simplexp++)= 2.0 * randr/randmax - 1.0;
+        }
+      }
+    }
+    if (issimplex2) {
+        simplexp= simplex;
+      for (i=0; i<dim+1; i++) {
+        if (iscdd)
+          qh_out1(qh, 1.0);
+        for (k=0; k<dim; k++)
+          qh_out1(qh, *(simplexp++) * box);
+        qh_fprintf_rbox(qh, qh->fout, 9395, "\n");
+      }
+    }
+    for (j=0; j<numpoints; j++) {
+      if (iswidth)
+        apex= qh_RANDOMint % (dim+1);
+      else
+        apex= -1;
+      for (k=0; k<dim; k++)
+        coord[k]= 0.0;
+      norm= 0.0;
+      for (i=0; i<dim+1; i++) {
+        randr= qh_RANDOMint;
+        factor= randr/randmax;
+        if (i == apex)
+          factor *= width;
+        norm += factor;
+        for (k=0; k<dim; k++) {
+          simplexp= simplex + i*dim + k;
+          coord[k] += factor * (*simplexp);
+        }
+      }
+      for (k=0; k<dim; k++)
+        coord[k] *= box/norm;
+      qh_outcoord(qh, iscdd, coord, dim);
+      if(coincidentcount++ < coincidenttotal)
+        qh_outcoincident(qh, coincidentpoints, coincidentradius, iscdd, coord, dim);
+    }
+    isregular= 0; /* continue with isbox */
+    numpoints= 0;
+  }
+
+  /* ============= mesh distribution =============== */
+  if (ismesh) {
+    nthroot= (int)(pow((double)numpoints, 1.0/dim) + 0.99999);
+    for (k=dim; k--; )
+      mult[k]= 0;
+    for (i=0; i < numpoints; i++) {
+      coordp= coord;
+      for (k=0; k < dim; k++) {
+        if (k == 0)
+          *(coordp++)= mult[0] * meshn + mult[1] * (-meshm);
+        else if (k == 1)
+          *(coordp++)= mult[0] * meshm + mult[1] * meshn;
+        else
+          *(coordp++)= mult[k] * meshr;
+      }
+      qh_outcoord(qh, iscdd, coord, dim);
+      if(coincidentcount++ < coincidenttotal)
+        qh_outcoincident(qh, coincidentpoints, coincidentradius, iscdd, coord, dim);
+      for (k=0; k < dim; k++) {
+        if (++mult[k] < nthroot)
+          break;
+        mult[k]= 0;
+      }
+    }
+  }
+  /* ============= regular points for 's' =============== */
+  else if (isregular && !islens) {
+    if (dim != 2 && dim != 3) {
+      qh_free(simplex);
+      qh_fprintf_rbox(qh, qh->ferr, 6197, "rbox error: regular points can be used only in 2-d and 3-d\n\n");
+      qh_errexit_rbox(qh, qh_ERRinput);
+    }
+    if (!isaxis || radius == 0.0) {
+      isaxis= 1;
+      radius= 1.0;
+    }
+    if (dim == 3) {
+      if (iscdd)
+        qh_out1(qh, 1.0);
+      qh_out3n(qh, 0.0, 0.0, -box);
+      if (!isgap) {
+        if (iscdd)
+          qh_out1(qh, 1.0);
+        qh_out3n(qh, 0.0, 0.0, box);
+      }
+    }
+    angle= 0.0;
+    anglediff= 2.0 * PI/numpoints;
+    for (i=0; i < numpoints; i++) {
+      angle += anglediff;
+      x= radius * cos(angle);
+      y= radius * sin(angle);
+      if (dim == 2) {
+        if (iscdd)
+          qh_out1(qh, 1.0);
+        qh_out2n(qh, x*box, y*box);
+      }else {
+        norm= sqrt(1.0 + x*x + y*y);
+        if (iscdd)
+          qh_out1(qh, 1.0);
+        qh_out3n(qh, box*x/norm, box*y/norm, box/norm);
+        if (isgap) {
+          x *= 1-gap;
+          y *= 1-gap;
+          norm= sqrt(1.0 + x*x + y*y);
+          if (iscdd)
+            qh_out1(qh, 1.0);
+          qh_out3n(qh, box*x/norm, box*y/norm, box/norm);
+        }
+      }
+    }
+  }
+  /* ============= regular points for 'r Ln D2' =============== */
+  else if (isregular && islens && dim == 2) {
+    double cos_0;
+
+    angle= lensangle;
+    anglediff= 2 * lensangle/(numpoints - 1);
+    cos_0= cos(lensangle);
+    for (i=0; i < numpoints; i++, angle -= anglediff) {
+      x= radius * sin(angle);
+      y= radius * (cos(angle) - cos_0);
+      if (iscdd)
+        qh_out1(qh, 1.0);
+      qh_out2n(qh, x*box, y*box);
+      if (i != 0 && i != numpoints - 1) {
+        if (iscdd)
+          qh_out1(qh, 1.0);
+        qh_out2n(qh, x*box, -y*box);
+      }
+    }
+  }
+  /* ============= regular points for 'r Ln D3' =============== */
+  else if (isregular && islens && dim != 2) {
+    if (dim != 3) {
+      qh_free(simplex);
+      qh_fprintf_rbox(qh, qh->ferr, 6198, "rbox error: regular points can be used only in 2-d and 3-d\n\n");
+      qh_errexit_rbox(qh, qh_ERRinput);
+    }
+    angle= 0.0;
+    anglediff= 2* PI/numpoints;
+    if (!isgap) {
+      isgap= 1;
+      gap= 0.5;
+    }
+    offset= sqrt(radius * radius - (1-gap)*(1-gap)) - lensbase;
+    for (i=0; i < numpoints; i++, angle += anglediff) {
+      x= cos(angle);
+      y= sin(angle);
+      if (iscdd)
+        qh_out1(qh, 1.0);
+      qh_out3n(qh, box*x, box*y, 0.0);
+      x *= 1-gap;
+      y *= 1-gap;
+      if (iscdd)
+        qh_out1(qh, 1.0);
+      qh_out3n(qh, box*x, box*y, box * offset);
+      if (iscdd)
+        qh_out1(qh, 1.0);
+      qh_out3n(qh, box*x, box*y, -box * offset);
+    }
+  }
+  /* ============= apex of 'Zn' distribution + gendim =============== */
+  else {
+    if (isaxis) {
+      gendim= dim-1;
+      if (iscdd)
+        qh_out1(qh, 1.0);
+      for (j=0; j < gendim; j++)
+        qh_out1(qh, 0.0);
+      qh_out1(qh, -box);
+      qh_fprintf_rbox(qh, qh->fout, 9398, "\n");
+    }else if (islens)
+      gendim= dim-1;
+    else
+      gendim= dim;
+    /* ============= generate random point in unit cube =============== */
+    for (i=0; i < numpoints; i++) {
+      norm= 0.0;
+      for (j=0; j < gendim; j++) {
+        randr= qh_RANDOMint;
+        coord[j]= 2.0 * randr/randmax - 1.0;
+        norm += coord[j] * coord[j];
+      }
+      norm= sqrt(norm);
+      /* ============= dim-1 point of 'Zn' distribution ========== */
+      if (isaxis) {
+        if (!isgap) {
+          isgap= 1;
+          gap= 1.0;
+        }
+        randr= qh_RANDOMint;
+        rangap= 1.0 - gap * randr/randmax;
+        factor= radius * rangap / norm;
+        for (j=0; j<gendim; j++)
+          coord[j]= factor * coord[j];
+      /* ============= dim-1 point of 'Ln s' distribution =========== */
+      }else if (islens && issphere) {
+        if (!isgap) {
+          isgap= 1;
+          gap= 1.0;
+        }
+        randr= qh_RANDOMint;
+        rangap= 1.0 - gap * randr/randmax;
+        factor= rangap / norm;
+        for (j=0; j<gendim; j++)
+          coord[j]= factor * coord[j];
+      /* ============= dim-1 point of 'Ln' distribution ========== */
+      }else if (islens && !issphere) {
+        if (!isgap) {
+          isgap= 1;
+          gap= 1.0;
+        }
+        j= qh_RANDOMint % gendim;
+        if (coord[j] < 0)
+          coord[j]= -1.0 - coord[j] * gap;
+        else
+          coord[j]= 1.0 - coord[j] * gap;
+      /* ============= point of 'l' distribution =============== */
+      }else if (isspiral) {
+        if (dim != 3) {
+          qh_free(simplex);
+          qh_fprintf_rbox(qh, qh->ferr, 6199, "rbox error: spiral distribution is available only in 3d\n\n");
+          qh_errexit_rbox(qh, qh_ERRinput);
+        }
+        coord[0]= cos(2*PI*i/(numpoints - 1));
+        coord[1]= sin(2*PI*i/(numpoints - 1));
+        coord[2]= 2.0*(double)i/(double)(numpoints-1) - 1.0;
+      /* ============= point of 's' distribution =============== */
+      }else if (issphere) {
+        factor= 1.0/norm;
+        if (iswidth) {
+          randr= qh_RANDOMint;
+          factor *= 1.0 - width * randr/randmax;
+        }
+        for (j=0; j<dim; j++)
+          coord[j]= factor * coord[j];
+      }
+      /* ============= project 'Zn s' point in to sphere =============== */
+      if (isaxis && issphere) {
+        coord[dim-1]= 1.0;
+        norm= 1.0;
+        for (j=0; j<gendim; j++)
+          norm += coord[j] * coord[j];
+        norm= sqrt(norm);
+        for (j=0; j<dim; j++)
+          coord[j]= coord[j] / norm;
+        if (iswidth) {
+          randr= qh_RANDOMint;
+          coord[dim-1] *= 1 - width * randr/randmax;
+        }
+      /* ============= project 'Zn' point onto cube =============== */
+      }else if (isaxis && !issphere) {  /* not very interesting */
+        randr= qh_RANDOMint;
+        coord[dim-1]= 2.0 * randr/randmax - 1.0;
+      /* ============= project 'Ln' point out to sphere =============== */
+      }else if (islens) {
+        coord[dim-1]= lensbase;
+        for (j=0, norm= 0; j<dim; j++)
+          norm += coord[j] * coord[j];
+        norm= sqrt(norm);
+        for (j=0; j<dim; j++)
+          coord[j]= coord[j] * radius/ norm;
+        coord[dim-1] -= lensbase;
+        if (iswidth) {
+          randr= qh_RANDOMint;
+          coord[dim-1] *= 1 - width * randr/randmax;
+        }
+        if (qh_RANDOMint > randmax/2)
+          coord[dim-1]= -coord[dim-1];
+      /* ============= project 'Wn' point toward boundary =============== */
+      }else if (iswidth && !issphere) {
+        j= qh_RANDOMint % gendim;
+        if (coord[j] < 0)
+          coord[j]= -1.0 - coord[j] * width;
+        else
+          coord[j]= 1.0 - coord[j] * width;
+      }
+      /* ============= scale point to box =============== */
+      for (k=0; k<dim; k++)
+          coord[k]= coord[k] * box;
+
+      /* ============= write output =============== */
+      qh_outcoord(qh, iscdd, coord, dim);
+      if(coincidentcount++ < coincidenttotal)
+        qh_outcoincident(qh, coincidentpoints, coincidentradius, iscdd, coord, dim);
+    }
+  }
+
+  /* ============= write cube vertices =============== */
+  if (addcube) {
+    for (j=0; j<cubesize; j++) {
+      if (iscdd)
+        qh_out1(qh, 1.0);
+      for (k=dim-1; k>=0; k--) {
+        if (j & ( 1 << k))
+          qh_out1(qh, cube);
+        else
+          qh_out1(qh, -cube);
+      }
+      qh_fprintf_rbox(qh, qh->fout, 9400, "\n");
+    }
+  }
+
+  /* ============= write diamond vertices =============== */
+  if (adddiamond) {
+    for (j=0; j<diamondsize; j++) {
+      if (iscdd)
+        qh_out1(qh, 1.0);
+      for (k=dim-1; k>=0; k--) {
+        if (j/2 != k)
+          qh_out1(qh, 0.0);
+        else if (j & 0x1)
+          qh_out1(qh, diamond);
+        else
+          qh_out1(qh, -diamond);
+      }
+      qh_fprintf_rbox(qh, qh->fout, 9401, "\n");
+    }
+  }
+
+  if (iscdd)
+    qh_fprintf_rbox(qh, qh->fout, 9402, "end\nhull\n");
+
+  /* same code for error exit and normal return */
+  qh_free(simplex);
+  return qh_ERRnone;
+} /* rboxpoints */
+
+/*------------------------------------------------
+outxxx - output functions for qh_rboxpoints
+*/
+int qh_roundi(qhT *qh, double a) {
+  if (a < 0.0) {
+    if (a - 0.5 < INT_MIN) {
+      qh_fprintf_rbox(qh, qh->ferr, 6200, "rbox input error: negative coordinate %2.2g is too large.  Reduce 'Bn'\n", a);
+      qh_errexit_rbox(qh, qh_ERRinput);
+    }
+    return (int)(a - 0.5);
+  }else {
+    if (a + 0.5 > INT_MAX) {
+      qh_fprintf_rbox(qh, qh->ferr, 6201, "rbox input error: coordinate %2.2g is too large.  Reduce 'Bn'\n", a);
+      qh_errexit_rbox(qh, qh_ERRinput);
+    }
+    return (int)(a + 0.5);
+  }
+} /* qh_roundi */
+
+void qh_out1(qhT *qh, double a) {
+
+  if (qh->rbox_isinteger)
+    qh_fprintf_rbox(qh, qh->fout, 9403, "%d ", qh_roundi(qh, a+qh->rbox_out_offset));
+  else
+    qh_fprintf_rbox(qh, qh->fout, 9404, qh_REAL_1, a+qh->rbox_out_offset);
+} /* qh_out1 */
+
+void qh_out2n(qhT *qh, double a, double b) {
+
+  if (qh->rbox_isinteger)
+    qh_fprintf_rbox(qh, qh->fout, 9405, "%d %d\n", qh_roundi(qh, a+qh->rbox_out_offset), qh_roundi(qh, b+qh->rbox_out_offset));
+  else
+    qh_fprintf_rbox(qh, qh->fout, 9406, qh_REAL_2n, a+qh->rbox_out_offset, b+qh->rbox_out_offset);
+} /* qh_out2n */
+
+void qh_out3n(qhT *qh, double a, double b, double c) {
+
+  if (qh->rbox_isinteger)
+    qh_fprintf_rbox(qh, qh->fout, 9407, "%d %d %d\n", qh_roundi(qh, a+qh->rbox_out_offset), qh_roundi(qh, b+qh->rbox_out_offset), qh_roundi(qh, c+qh->rbox_out_offset));
+  else
+    qh_fprintf_rbox(qh, qh->fout, 9408, qh_REAL_3n, a+qh->rbox_out_offset, b+qh->rbox_out_offset, c+qh->rbox_out_offset);
+} /* qh_out3n */
+
+void qh_outcoord(qhT *qh, int iscdd, double *coord, int dim) {
+    double *p= coord;
+    int k;
+
+    if (iscdd)
+      qh_out1(qh, 1.0);
+    for (k=0; k < dim; k++)
+      qh_out1(qh, *(p++));
+    qh_fprintf_rbox(qh, qh->fout, 9396, "\n");
+} /* qh_outcoord */
+
+void qh_outcoincident(qhT *qh, int coincidentpoints, double radius, int iscdd, double *coord, int dim) {
+  double *p;
+  double randr, delta;
+  int i,k;
+  double randmax= qh_RANDOMmax;
+
+  for (i= 0; i<coincidentpoints; i++) {
+    p= coord;
+    if (iscdd)
+      qh_out1(qh, 1.0);
+    for (k=0; k < dim; k++) {
+      randr= qh_RANDOMint;
+      delta= 2.0 * randr/randmax - 1.0; /* -1..+1 */
+      delta *= radius;
+      qh_out1(qh, *(p++) + delta);
+    }
+    qh_fprintf_rbox(qh, qh->fout, 9410, "\n");
+  }
+} /* qh_outcoincident */
+
+/*------------------------------------------------
+   Only called from qh_rboxpoints or qh_fprintf_rbox
+   qh_fprintf_rbox is only called from qh_rboxpoints
+*/
+void qh_errexit_rbox(qhT *qh, int exitcode)
+{
+    longjmp(qh->rbox_errexit, exitcode);
+} /* qh_errexit_rbox */
+
diff --git a/xs/src/qhull/src/libqhull_r/stat_r.c b/xs/src/qhull/src/libqhull_r/stat_r.c
new file mode 100644
index 0000000000..0f3ff0d3d4
--- /dev/null
+++ b/xs/src/qhull/src/libqhull_r/stat_r.c
@@ -0,0 +1,682 @@
+/*<html><pre>  -<a                             href="qh-stat_r.htm"
+  >-------------------------------</a><a name="TOP">-</a>
+
+   stat_r.c
+   contains all statistics that are collected for qhull
+
+   see qh-stat_r.htm and stat_r.h
+
+   Copyright (c) 1993-2015 The Geometry Center.
+   $Id: //main/2015/qhull/src/libqhull_r/stat_r.c#5 $$Change: 2062 $
+   $DateTime: 2016/01/17 13:13:18 $$Author: bbarber $
+*/
+
+#include "qhull_ra.h"
+
+/*========== functions in alphabetic order ================*/
+
+/*-<a                             href="qh-stat_r.htm#TOC"
+  >-------------------------------</a><a name="allstatA">-</a>
+
+  qh_allstatA()
+    define statistics in groups of 20
+
+  notes:
+    (otherwise, 'gcc -O2' uses too much memory)
+    uses qhstat.next
+*/
+void qh_allstatA(qhT *qh) {
+
+   /* zdef_(type,name,doc,average) */
+  zzdef_(zdoc, Zdoc2, "precision statistics", -1);
+  zdef_(zinc, Znewvertex, NULL, -1);
+  zdef_(wadd, Wnewvertex, "ave. distance of a new vertex to a facet(!0s)", Znewvertex);
+  zzdef_(wmax, Wnewvertexmax, "max. distance of a new vertex to a facet", -1);
+  zdef_(wmax, Wvertexmax, "max. distance of an output vertex to a facet", -1);
+  zdef_(wmin, Wvertexmin, "min. distance of an output vertex to a facet", -1);
+  zdef_(wmin, Wmindenom, "min. denominator in hyperplane computation", -1);
+
+  qh->qhstat.precision= qh->qhstat.next;  /* call qh_precision for each of these */
+  zzdef_(zdoc, Zdoc3, "precision problems (corrected unless 'Q0' or an error)", -1);
+  zzdef_(zinc, Zcoplanarridges, "coplanar half ridges in output", -1);
+  zzdef_(zinc, Zconcaveridges, "concave half ridges in output", -1);
+  zzdef_(zinc, Zflippedfacets, "flipped facets", -1);
+  zzdef_(zinc, Zcoplanarhorizon, "coplanar horizon facets for new vertices", -1);
+  zzdef_(zinc, Zcoplanarpart, "coplanar points during partitioning", -1);
+  zzdef_(zinc, Zminnorm, "degenerate hyperplanes recomputed with gaussian elimination", -1);
+  zzdef_(zinc, Znearlysingular, "nearly singular or axis-parallel hyperplanes", -1);
+  zzdef_(zinc, Zback0, "zero divisors during back substitute", -1);
+  zzdef_(zinc, Zgauss0, "zero divisors during gaussian elimination", -1);
+  zzdef_(zinc, Zmultiridge, "ridges with multiple neighbors", -1);
+}
+void qh_allstatB(qhT *qh) {
+  zzdef_(zdoc, Zdoc1, "summary information", -1);
+  zdef_(zinc, Zvertices, "number of vertices in output", -1);
+  zdef_(zinc, Znumfacets, "number of facets in output", -1);
+  zdef_(zinc, Znonsimplicial, "number of non-simplicial facets in output", -1);
+  zdef_(zinc, Znowsimplicial, "number of simplicial facets that were merged", -1);
+  zdef_(zinc, Znumridges, "number of ridges in output", -1);
+  zdef_(zadd, Znumridges, "average number of ridges per facet", Znumfacets);
+  zdef_(zmax, Zmaxridges, "maximum number of ridges", -1);
+  zdef_(zadd, Znumneighbors, "average number of neighbors per facet", Znumfacets);
+  zdef_(zmax, Zmaxneighbors, "maximum number of neighbors", -1);
+  zdef_(zadd, Znumvertices, "average number of vertices per facet", Znumfacets);
+  zdef_(zmax, Zmaxvertices, "maximum number of vertices", -1);
+  zdef_(zadd, Znumvneighbors, "average number of neighbors per vertex", Zvertices);
+  zdef_(zmax, Zmaxvneighbors, "maximum number of neighbors", -1);
+  zdef_(wadd, Wcpu, "cpu seconds for qhull after input", -1);
+  zdef_(zinc, Ztotvertices, "vertices created altogether", -1);
+  zzdef_(zinc, Zsetplane, "facets created altogether", -1);
+  zdef_(zinc, Ztotridges, "ridges created altogether", -1);
+  zdef_(zinc, Zpostfacets, "facets before post merge", -1);
+  zdef_(zadd, Znummergetot, "average merges per facet(at most 511)", Znumfacets);
+  zdef_(zmax, Znummergemax, "  maximum merges for a facet(at most 511)", -1);
+  zdef_(zinc, Zangle, NULL, -1);
+  zdef_(wadd, Wangle, "average angle(cosine) of facet normals for all ridges", Zangle);
+  zdef_(wmax, Wanglemax, "  maximum angle(cosine) of facet normals across a ridge", -1);
+  zdef_(wmin, Wanglemin, "  minimum angle(cosine) of facet normals across a ridge", -1);
+  zdef_(wadd, Wareatot, "total area of facets", -1);
+  zdef_(wmax, Wareamax, "  maximum facet area", -1);
+  zdef_(wmin, Wareamin, "  minimum facet area", -1);
+}
+void qh_allstatC(qhT *qh) {
+  zdef_(zdoc, Zdoc9, "build hull statistics", -1);
+  zzdef_(zinc, Zprocessed, "points processed", -1);
+  zzdef_(zinc, Zretry, "retries due to precision problems", -1);
+  zdef_(wmax, Wretrymax, "  max. random joggle", -1);
+  zdef_(zmax, Zmaxvertex, "max. vertices at any one time", -1);
+  zdef_(zinc, Ztotvisible, "ave. visible facets per iteration", Zprocessed);
+  zdef_(zinc, Zinsidevisible, "  ave. visible facets without an horizon neighbor", Zprocessed);
+  zdef_(zadd, Zvisfacettot,  "  ave. facets deleted per iteration", Zprocessed);
+  zdef_(zmax, Zvisfacetmax,  "    maximum", -1);
+  zdef_(zadd, Zvisvertextot, "ave. visible vertices per iteration", Zprocessed);
+  zdef_(zmax, Zvisvertexmax, "    maximum", -1);
+  zdef_(zinc, Ztothorizon, "ave. horizon facets per iteration", Zprocessed);
+  zdef_(zadd, Znewfacettot,  "ave. new or merged facets per iteration", Zprocessed);
+  zdef_(zmax, Znewfacetmax,  "    maximum(includes initial simplex)", -1);
+  zdef_(wadd, Wnewbalance, "average new facet balance", Zprocessed);
+  zdef_(wadd, Wnewbalance2, "  standard deviation", -1);
+  zdef_(wadd, Wpbalance, "average partition balance", Zpbalance);
+  zdef_(wadd, Wpbalance2, "  standard deviation", -1);
+  zdef_(zinc, Zpbalance, "  number of trials", -1);
+  zdef_(zinc, Zsearchpoints, "searches of all points for initial simplex", -1);
+  zdef_(zinc, Zdetsimplex, "determinants computed(area & initial hull)", -1);
+  zdef_(zinc, Znoarea, "determinants not computed because vertex too low", -1);
+  zdef_(zinc, Znotmax, "points ignored(!above max_outside)", -1);
+  zdef_(zinc, Znotgood, "points ignored(!above a good facet)", -1);
+  zdef_(zinc, Znotgoodnew, "points ignored(didn't create a good new facet)", -1);
+  zdef_(zinc, Zgoodfacet, "good facets found", -1);
+  zzdef_(zinc, Znumvisibility, "distance tests for facet visibility", -1);
+  zdef_(zinc, Zdistvertex, "distance tests to report minimum vertex", -1);
+  zzdef_(zinc, Ztotcheck, "points checked for facets' outer planes", -1);
+  zzdef_(zinc, Zcheckpart, "  ave. distance tests per check", Ztotcheck);
+}
+void qh_allstatD(qhT *qh) {
+  zdef_(zinc, Zvisit, "resets of visit_id", -1);
+  zdef_(zinc, Zvvisit, "  resets of vertex_visit", -1);
+  zdef_(zmax, Zvisit2max, "  max visit_id/2", -1);
+  zdef_(zmax, Zvvisit2max, "  max vertex_visit/2", -1);
+
+  zdef_(zdoc, Zdoc4, "partitioning statistics(see previous for outer planes)", -1);
+  zzdef_(zadd, Zdelvertextot, "total vertices deleted", -1);
+  zdef_(zmax, Zdelvertexmax, "    maximum vertices deleted per iteration", -1);
+  zdef_(zinc, Zfindbest, "calls to findbest", -1);
+  zdef_(zadd, Zfindbesttot, " ave. facets tested", Zfindbest);
+  zdef_(zmax, Zfindbestmax, " max. facets tested", -1);
+  zdef_(zadd, Zfindcoplanar, " ave. coplanar search", Zfindbest);
+  zdef_(zinc, Zfindnew, "calls to findbestnew", -1);
+  zdef_(zadd, Zfindnewtot, " ave. facets tested", Zfindnew);
+  zdef_(zmax, Zfindnewmax, " max. facets tested", -1);
+  zdef_(zinc, Zfindnewjump, " ave. clearly better", Zfindnew);
+  zdef_(zinc, Zfindnewsharp, " calls due to qh_sharpnewfacets", -1);
+  zdef_(zinc, Zfindhorizon, "calls to findhorizon", -1);
+  zdef_(zadd, Zfindhorizontot, " ave. facets tested", Zfindhorizon);
+  zdef_(zmax, Zfindhorizonmax, " max. facets tested", -1);
+  zdef_(zinc, Zfindjump,       " ave. clearly better", Zfindhorizon);
+  zdef_(zinc, Zparthorizon, " horizon facets better than bestfacet", -1);
+  zdef_(zinc, Zpartangle, "angle tests for repartitioned coplanar points", -1);
+  zdef_(zinc, Zpartflip, "  repartitioned coplanar points for flipped orientation", -1);
+}
+void qh_allstatE(qhT *qh) {
+  zdef_(zinc, Zpartinside, "inside points", -1);
+  zdef_(zinc, Zpartnear, "  inside points kept with a facet", -1);
+  zdef_(zinc, Zcoplanarinside, "  inside points that were coplanar with a facet", -1);
+  zdef_(zinc, Zbestlower, "calls to findbestlower", -1);
+  zdef_(zinc, Zbestlowerv, "  with search of vertex neighbors", -1);
+  zdef_(zinc, Zbestlowerall, "  with rare search of all facets", -1);
+  zdef_(zmax, Zbestloweralln, "  facets per search of all facets", -1);
+  zdef_(wadd, Wmaxout, "difference in max_outside at final check", -1);
+  zzdef_(zinc, Zpartitionall, "distance tests for initial partition", -1);
+  zdef_(zinc, Ztotpartition, "partitions of a point", -1);
+  zzdef_(zinc, Zpartition, "distance tests for partitioning", -1);
+  zzdef_(zinc, Zdistcheck, "distance tests for checking flipped facets", -1);
+  zzdef_(zinc, Zdistconvex, "distance tests for checking convexity", -1);
+  zdef_(zinc, Zdistgood, "distance tests for checking good point", -1);
+  zdef_(zinc, Zdistio, "distance tests for output", -1);
+  zdef_(zinc, Zdiststat, "distance tests for statistics", -1);
+  zdef_(zinc, Zdistplane, "total number of distance tests", -1);
+  zdef_(zinc, Ztotpartcoplanar, "partitions of coplanar points or deleted vertices", -1);
+  zzdef_(zinc, Zpartcoplanar, "   distance tests for these partitions", -1);
+  zdef_(zinc, Zcomputefurthest, "distance tests for computing furthest", -1);
+}
+void qh_allstatE2(qhT *qh) {
+  zdef_(zdoc, Zdoc5, "statistics for matching ridges", -1);
+  zdef_(zinc, Zhashlookup, "total lookups for matching ridges of new facets", -1);
+  zdef_(zinc, Zhashtests, "average number of tests to match a ridge", Zhashlookup);
+  zdef_(zinc, Zhashridge, "total lookups of subridges(duplicates and boundary)", -1);
+  zdef_(zinc, Zhashridgetest, "average number of tests per subridge", Zhashridge);
+  zdef_(zinc, Zdupsame, "duplicated ridges in same merge cycle", -1);
+  zdef_(zinc, Zdupflip, "duplicated ridges with flipped facets", -1);
+
+  zdef_(zdoc, Zdoc6, "statistics for determining merges", -1);
+  zdef_(zinc, Zangletests, "angles computed for ridge convexity", -1);
+  zdef_(zinc, Zbestcentrum, "best merges used centrum instead of vertices",-1);
+  zzdef_(zinc, Zbestdist, "distance tests for best merge", -1);
+  zzdef_(zinc, Zcentrumtests, "distance tests for centrum convexity", -1);
+  zzdef_(zinc, Zdistzero, "distance tests for checking simplicial convexity", -1);
+  zdef_(zinc, Zcoplanarangle, "coplanar angles in getmergeset", -1);
+  zdef_(zinc, Zcoplanarcentrum, "coplanar centrums in getmergeset", -1);
+  zdef_(zinc, Zconcaveridge, "concave ridges in getmergeset", -1);
+}
+void qh_allstatF(qhT *qh) {
+  zdef_(zdoc, Zdoc7, "statistics for merging", -1);
+  zdef_(zinc, Zpremergetot, "merge iterations", -1);
+  zdef_(zadd, Zmergeinittot, "ave. initial non-convex ridges per iteration", Zpremergetot);
+  zdef_(zadd, Zmergeinitmax, "  maximum", -1);
+  zdef_(zadd, Zmergesettot, "  ave. additional non-convex ridges per iteration", Zpremergetot);
+  zdef_(zadd, Zmergesetmax, "  maximum additional in one pass", -1);
+  zdef_(zadd, Zmergeinittot2, "initial non-convex ridges for post merging", -1);
+  zdef_(zadd, Zmergesettot2, "  additional non-convex ridges", -1);
+  zdef_(wmax, Wmaxoutside, "max distance of vertex or coplanar point above facet(w/roundoff)", -1);
+  zdef_(wmin, Wminvertex, "max distance of merged vertex below facet(or roundoff)", -1);
+  zdef_(zinc, Zwidefacet, "centrums frozen due to a wide merge", -1);
+  zdef_(zinc, Zwidevertices, "centrums frozen due to extra vertices", -1);
+  zzdef_(zinc, Ztotmerge, "total number of facets or cycles of facets merged", -1);
+  zdef_(zinc, Zmergesimplex, "merged a simplex", -1);
+  zdef_(zinc, Zonehorizon, "simplices merged into coplanar horizon", -1);
+  zzdef_(zinc, Zcyclehorizon, "cycles of facets merged into coplanar horizon", -1);
+  zzdef_(zadd, Zcyclefacettot, "  ave. facets per cycle", Zcyclehorizon);
+  zdef_(zmax, Zcyclefacetmax, "  max. facets", -1);
+  zdef_(zinc, Zmergeintohorizon, "new facets merged into horizon", -1);
+  zdef_(zinc, Zmergenew, "new facets merged", -1);
+  zdef_(zinc, Zmergehorizon, "horizon facets merged into new facets", -1);
+  zdef_(zinc, Zmergevertex, "vertices deleted by merging", -1);
+  zdef_(zinc, Zcyclevertex, "vertices deleted by merging into coplanar horizon", -1);
+  zdef_(zinc, Zdegenvertex, "vertices deleted by degenerate facet", -1);
+  zdef_(zinc, Zmergeflipdup, "merges due to flipped facets in duplicated ridge", -1);
+  zdef_(zinc, Zneighbor, "merges due to redundant neighbors", -1);
+  zdef_(zadd, Ztestvneighbor, "non-convex vertex neighbors", -1);
+}
+void qh_allstatG(qhT *qh) {
+  zdef_(zinc, Zacoplanar, "merges due to angle coplanar facets", -1);
+  zdef_(wadd, Wacoplanartot, "  average merge distance", Zacoplanar);
+  zdef_(wmax, Wacoplanarmax, "  maximum merge distance", -1);
+  zdef_(zinc, Zcoplanar, "merges due to coplanar facets", -1);
+  zdef_(wadd, Wcoplanartot, "  average merge distance", Zcoplanar);
+  zdef_(wmax, Wcoplanarmax, "  maximum merge distance", -1);
+  zdef_(zinc, Zconcave, "merges due to concave facets", -1);
+  zdef_(wadd, Wconcavetot, "  average merge distance", Zconcave);
+  zdef_(wmax, Wconcavemax, "  maximum merge distance", -1);
+  zdef_(zinc, Zavoidold, "coplanar/concave merges due to avoiding old merge", -1);
+  zdef_(wadd, Wavoidoldtot, "  average merge distance", Zavoidold);
+  zdef_(wmax, Wavoidoldmax, "  maximum merge distance", -1);
+  zdef_(zinc, Zdegen, "merges due to degenerate facets", -1);
+  zdef_(wadd, Wdegentot, "  average merge distance", Zdegen);
+  zdef_(wmax, Wdegenmax, "  maximum merge distance", -1);
+  zdef_(zinc, Zflipped, "merges due to removing flipped facets", -1);
+  zdef_(wadd, Wflippedtot, "  average merge distance", Zflipped);
+  zdef_(wmax, Wflippedmax, "  maximum merge distance", -1);
+  zdef_(zinc, Zduplicate, "merges due to duplicated ridges", -1);
+  zdef_(wadd, Wduplicatetot, "  average merge distance", Zduplicate);
+  zdef_(wmax, Wduplicatemax, "  maximum merge distance", -1);
+}
+void qh_allstatH(qhT *qh) {
+  zdef_(zdoc, Zdoc8, "renamed vertex statistics", -1);
+  zdef_(zinc, Zrenameshare, "renamed vertices shared by two facets", -1);
+  zdef_(zinc, Zrenamepinch, "renamed vertices in a pinched facet", -1);
+  zdef_(zinc, Zrenameall, "renamed vertices shared by multiple facets", -1);
+  zdef_(zinc, Zfindfail, "rename failures due to duplicated ridges", -1);
+  zdef_(zinc, Zdupridge, "  duplicate ridges detected", -1);
+  zdef_(zinc, Zdelridge, "deleted ridges due to renamed vertices", -1);
+  zdef_(zinc, Zdropneighbor, "dropped neighbors due to renamed vertices", -1);
+  zdef_(zinc, Zdropdegen, "degenerate facets due to dropped neighbors", -1);
+  zdef_(zinc, Zdelfacetdup, "  facets deleted because of no neighbors", -1);
+  zdef_(zinc, Zremvertex, "vertices removed from facets due to no ridges", -1);
+  zdef_(zinc, Zremvertexdel, "  deleted", -1);
+  zdef_(zinc, Zintersectnum, "vertex intersections for locating redundant vertices", -1);
+  zdef_(zinc, Zintersectfail, "intersections failed to find a redundant vertex", -1);
+  zdef_(zinc, Zintersect, "intersections found redundant vertices", -1);
+  zdef_(zadd, Zintersecttot, "   ave. number found per vertex", Zintersect);
+  zdef_(zmax, Zintersectmax, "   max. found for a vertex", -1);
+  zdef_(zinc, Zvertexridge, NULL, -1);
+  zdef_(zadd, Zvertexridgetot, "  ave. number of ridges per tested vertex", Zvertexridge);
+  zdef_(zmax, Zvertexridgemax, "  max. number of ridges per tested vertex", -1);
+
+  zdef_(zdoc, Zdoc10, "memory usage statistics(in bytes)", -1);
+  zdef_(zadd, Zmemfacets, "for facets and their normals, neighbor and vertex sets", -1);
+  zdef_(zadd, Zmemvertices, "for vertices and their neighbor sets", -1);
+  zdef_(zadd, Zmempoints, "for input points, outside and coplanar sets, and qhT",-1);
+  zdef_(zadd, Zmemridges, "for ridges and their vertex sets", -1);
+} /* allstat */
+
+void qh_allstatI(qhT *qh) {
+  qh->qhstat.vridges= qh->qhstat.next;
+  zzdef_(zdoc, Zdoc11, "Voronoi ridge statistics", -1);
+  zzdef_(zinc, Zridge, "non-simplicial Voronoi vertices for all ridges", -1);
+  zzdef_(wadd, Wridge, "  ave. distance to ridge", Zridge);
+  zzdef_(wmax, Wridgemax, "  max. distance to ridge", -1);
+  zzdef_(zinc, Zridgemid, "bounded ridges", -1);
+  zzdef_(wadd, Wridgemid, "  ave. distance of midpoint to ridge", Zridgemid);
+  zzdef_(wmax, Wridgemidmax, "  max. distance of midpoint to ridge", -1);
+  zzdef_(zinc, Zridgeok, "bounded ridges with ok normal", -1);
+  zzdef_(wadd, Wridgeok, "  ave. angle to ridge", Zridgeok);
+  zzdef_(wmax, Wridgeokmax, "  max. angle to ridge", -1);
+  zzdef_(zinc, Zridge0, "bounded ridges with near-zero normal", -1);
+  zzdef_(wadd, Wridge0, "  ave. angle to ridge", Zridge0);
+  zzdef_(wmax, Wridge0max, "  max. angle to ridge", -1);
+
+  zdef_(zdoc, Zdoc12, "Triangulation statistics(Qt)", -1);
+  zdef_(zinc, Ztricoplanar, "non-simplicial facets triangulated", -1);
+  zdef_(zadd, Ztricoplanartot, "  ave. new facets created(may be deleted)", Ztricoplanar);
+  zdef_(zmax, Ztricoplanarmax, "  max. new facets created", -1);
+  zdef_(zinc, Ztrinull, "null new facets deleted(duplicated vertex)", -1);
+  zdef_(zinc, Ztrimirror, "mirrored pairs of new facets deleted(same vertices)", -1);
+  zdef_(zinc, Ztridegen, "degenerate new facets in output(same ridge)", -1);
+} /* allstat */
+
+/*-<a                             href="qh-stat_r.htm#TOC"
+  >-------------------------------</a><a name="allstatistics">-</a>
+
+  qh_allstatistics()
+    reset printed flag for all statistics
+*/
+void qh_allstatistics(qhT *qh) {
+  int i;
+
+  for(i=ZEND; i--; )
+    qh->qhstat.printed[i]= False;
+} /* allstatistics */
+
+#if qh_KEEPstatistics
+/*-<a                             href="qh-stat_r.htm#TOC"
+  >-------------------------------</a><a name="collectstatistics">-</a>
+
+  qh_collectstatistics()
+    collect statistics for qh.facet_list
+
+*/
+void qh_collectstatistics(qhT *qh) {
+  facetT *facet, *neighbor, **neighborp;
+  vertexT *vertex, **vertexp;
+  realT dotproduct, dist;
+  int sizneighbors, sizridges, sizvertices, i;
+
+  qh->old_randomdist= qh->RANDOMdist;
+  qh->RANDOMdist= False;
+  zval_(Zmempoints)= qh->num_points * qh->normal_size + sizeof(qhT);
+  zval_(Zmemfacets)= 0;
+  zval_(Zmemridges)= 0;
+  zval_(Zmemvertices)= 0;
+  zval_(Zangle)= 0;
+  wval_(Wangle)= 0.0;
+  zval_(Znumridges)= 0;
+  zval_(Znumfacets)= 0;
+  zval_(Znumneighbors)= 0;
+  zval_(Znumvertices)= 0;
+  zval_(Znumvneighbors)= 0;
+  zval_(Znummergetot)= 0;
+  zval_(Znummergemax)= 0;
+  zval_(Zvertices)= qh->num_vertices - qh_setsize(qh, qh->del_vertices);
+  if (qh->MERGING || qh->APPROXhull || qh->JOGGLEmax < REALmax/2)
+    wmax_(Wmaxoutside, qh->max_outside);
+  if (qh->MERGING)
+    wmin_(Wminvertex, qh->min_vertex);
+  FORALLfacets
+    facet->seen= False;
+  if (qh->DELAUNAY) {
+    FORALLfacets {
+      if (facet->upperdelaunay != qh->UPPERdelaunay)
+        facet->seen= True; /* remove from angle statistics */
+    }
+  }
+  FORALLfacets {
+    if (facet->visible && qh->NEWfacets)
+      continue;
+    sizvertices= qh_setsize(qh, facet->vertices);
+    sizneighbors= qh_setsize(qh, facet->neighbors);
+    sizridges= qh_setsize(qh, facet->ridges);
+    zinc_(Znumfacets);
+    zadd_(Znumvertices, sizvertices);
+    zmax_(Zmaxvertices, sizvertices);
+    zadd_(Znumneighbors, sizneighbors);
+    zmax_(Zmaxneighbors, sizneighbors);
+    zadd_(Znummergetot, facet->nummerge);
+    i= facet->nummerge; /* avoid warnings */
+    zmax_(Znummergemax, i);
+    if (!facet->simplicial) {
+      if (sizvertices == qh->hull_dim) {
+        zinc_(Znowsimplicial);
+      }else {
+        zinc_(Znonsimplicial);
+      }
+    }
+    if (sizridges) {
+      zadd_(Znumridges, sizridges);
+      zmax_(Zmaxridges, sizridges);
+    }
+    zadd_(Zmemfacets, sizeof(facetT) + qh->normal_size + 2*sizeof(setT)
+       + SETelemsize * (sizneighbors + sizvertices));
+    if (facet->ridges) {
+      zadd_(Zmemridges,
+         sizeof(setT) + SETelemsize * sizridges + sizridges *
+         (sizeof(ridgeT) + sizeof(setT) + SETelemsize * (qh->hull_dim-1))/2);
+    }
+    if (facet->outsideset)
+      zadd_(Zmempoints, sizeof(setT) + SETelemsize * qh_setsize(qh, facet->outsideset));
+    if (facet->coplanarset)
+      zadd_(Zmempoints, sizeof(setT) + SETelemsize * qh_setsize(qh, facet->coplanarset));
+    if (facet->seen) /* Delaunay upper envelope */
+      continue;
+    facet->seen= True;
+    FOREACHneighbor_(facet) {
+      if (neighbor == qh_DUPLICATEridge || neighbor == qh_MERGEridge
+          || neighbor->seen || !facet->normal || !neighbor->normal)
+        continue;
+      dotproduct= qh_getangle(qh, facet->normal, neighbor->normal);
+      zinc_(Zangle);
+      wadd_(Wangle, dotproduct);
+      wmax_(Wanglemax, dotproduct)
+      wmin_(Wanglemin, dotproduct)
+    }
+    if (facet->normal) {
+      FOREACHvertex_(facet->vertices) {
+        zinc_(Zdiststat);
+        qh_distplane(qh, vertex->point, facet, &dist);
+        wmax_(Wvertexmax, dist);
+        wmin_(Wvertexmin, dist);
+      }
+    }
+  }
+  FORALLvertices {
+    if (vertex->deleted)
+      continue;
+    zadd_(Zmemvertices, sizeof(vertexT));
+    if (vertex->neighbors) {
+      sizneighbors= qh_setsize(qh, vertex->neighbors);
+      zadd_(Znumvneighbors, sizneighbors);
+      zmax_(Zmaxvneighbors, sizneighbors);
+      zadd_(Zmemvertices, sizeof(vertexT) + SETelemsize * sizneighbors);
+    }
+  }
+  qh->RANDOMdist= qh->old_randomdist;
+} /* collectstatistics */
+#endif /* qh_KEEPstatistics */
+
+/*-<a                             href="qh-stat_r.htm#TOC"
+  >-------------------------------</a><a name="initstatistics">-</a>
+
+  qh_initstatistics(qh)
+    initialize statistics
+
+  notes:
+  NOerrors -- qh_initstatistics can not use qh_errexit(), qh_fprintf, or qh.ferr
+  On first call, only qhmem.ferr is defined.  qh_memalloc is not setup.
+  Also invoked by QhullQh().
+*/
+void qh_initstatistics(qhT *qh) {
+  int i;
+  realT realx;
+  int intx;
+
+  qh->qhstat.next= 0;
+  qh_allstatA(qh);
+  qh_allstatB(qh);
+  qh_allstatC(qh);
+  qh_allstatD(qh);
+  qh_allstatE(qh);
+  qh_allstatE2(qh);
+  qh_allstatF(qh);
+  qh_allstatG(qh);
+  qh_allstatH(qh);
+  qh_allstatI(qh);
+  if (qh->qhstat.next > (int)sizeof(qh->qhstat.id)) {
+    qh_fprintf(qh, qh->qhmem.ferr, 6184, "qhull error (qh_initstatistics): increase size of qhstat.id[].\n\
+      qhstat.next %d should be <= sizeof(qh->qhstat.id) %d\n", qh->qhstat.next, (int)sizeof(qh->qhstat.id));
+#if 0 /* for locating error, Znumridges should be duplicated */
+    for(i=0; i < ZEND; i++) {
+      int j;
+      for(j=i+1; j < ZEND; j++) {
+        if (qh->qhstat.id[i] == qh->qhstat.id[j]) {
+          qh_fprintf(qh, qh->qhmem.ferr, 6185, "qhull error (qh_initstatistics): duplicated statistic %d at indices %d and %d\n",
+              qh->qhstat.id[i], i, j);
+        }
+      }
+    }
+#endif
+    qh_exit(qh_ERRqhull);  /* can not use qh_errexit() */
+  }
+  qh->qhstat.init[zinc].i= 0;
+  qh->qhstat.init[zadd].i= 0;
+  qh->qhstat.init[zmin].i= INT_MAX;
+  qh->qhstat.init[zmax].i= INT_MIN;
+  qh->qhstat.init[wadd].r= 0;
+  qh->qhstat.init[wmin].r= REALmax;
+  qh->qhstat.init[wmax].r= -REALmax;
+  for(i=0; i < ZEND; i++) {
+    if (qh->qhstat.type[i] > ZTYPEreal) {
+      realx= qh->qhstat.init[(unsigned char)(qh->qhstat.type[i])].r;
+      qh->qhstat.stats[i].r= realx;
+    }else if (qh->qhstat.type[i] != zdoc) {
+      intx= qh->qhstat.init[(unsigned char)(qh->qhstat.type[i])].i;
+      qh->qhstat.stats[i].i= intx;
+    }
+  }
+} /* initstatistics */
+
+/*-<a                             href="qh-stat_r.htm#TOC"
+  >-------------------------------</a><a name="newstats">-</a>
+
+  qh_newstats(qh, )
+    returns True if statistics for zdoc
+
+  returns:
+    next zdoc
+*/
+boolT qh_newstats(qhT *qh, int idx, int *nextindex) {
+  boolT isnew= False;
+  int start, i;
+
+  if (qh->qhstat.type[qh->qhstat.id[idx]] == zdoc)
+    start= idx+1;
+  else
+    start= idx;
+  for(i= start; i < qh->qhstat.next && qh->qhstat.type[qh->qhstat.id[i]] != zdoc; i++) {
+    if (!qh_nostatistic(qh, qh->qhstat.id[i]) && !qh->qhstat.printed[qh->qhstat.id[i]])
+        isnew= True;
+  }
+  *nextindex= i;
+  return isnew;
+} /* newstats */
+
+/*-<a                             href="qh-stat_r.htm#TOC"
+  >-------------------------------</a><a name="nostatistic">-</a>
+
+  qh_nostatistic(qh, index )
+    true if no statistic to print
+*/
+boolT qh_nostatistic(qhT *qh, int i) {
+
+  if ((qh->qhstat.type[i] > ZTYPEreal
+       &&qh->qhstat.stats[i].r == qh->qhstat.init[(unsigned char)(qh->qhstat.type[i])].r)
+      || (qh->qhstat.type[i] < ZTYPEreal
+          &&qh->qhstat.stats[i].i == qh->qhstat.init[(unsigned char)(qh->qhstat.type[i])].i))
+    return True;
+  return False;
+} /* nostatistic */
+
+#if qh_KEEPstatistics
+/*-<a                             href="qh-stat_r.htm#TOC"
+  >-------------------------------</a><a name="printallstatistics">-</a>
+
+  qh_printallstatistics(qh, fp, string )
+    print all statistics with header 'string'
+*/
+void qh_printallstatistics(qhT *qh, FILE *fp, const char *string) {
+
+  qh_allstatistics(qh);
+  qh_collectstatistics(qh);
+  qh_printstatistics(qh, fp, string);
+  qh_memstatistics(qh, fp);
+}
+
+
+/*-<a                             href="qh-stat_r.htm#TOC"
+  >-------------------------------</a><a name="printstatistics">-</a>
+
+  qh_printstatistics(qh, fp, string )
+    print statistics to a file with header 'string'
+    skips statistics with qhstat.printed[] (reset with qh_allstatistics)
+
+  see:
+    qh_printallstatistics()
+*/
+void qh_printstatistics(qhT *qh, FILE *fp, const char *string) {
+  int i, k;
+  realT ave;
+
+  if (qh->num_points != qh->num_vertices) {
+    wval_(Wpbalance)= 0;
+    wval_(Wpbalance2)= 0;
+  }else
+    wval_(Wpbalance2)= qh_stddev(zval_(Zpbalance), wval_(Wpbalance),
+                                 wval_(Wpbalance2), &ave);
+  wval_(Wnewbalance2)= qh_stddev(zval_(Zprocessed), wval_(Wnewbalance),
+                                 wval_(Wnewbalance2), &ave);
+  qh_fprintf(qh, fp, 9350, "\n\
+%s\n\
+ qhull invoked by: %s | %s\n%s with options:\n%s\n", string, qh->rbox_command,
+     qh->qhull_command, qh_version, qh->qhull_options);
+  qh_fprintf(qh, fp, 9351, "\nprecision constants:\n\
+ %6.2g max. abs. coordinate in the (transformed) input('Qbd:n')\n\
+ %6.2g max. roundoff error for distance computation('En')\n\
+ %6.2g max. roundoff error for angle computations\n\
+ %6.2g min. distance for outside points ('Wn')\n\
+ %6.2g min. distance for visible facets ('Vn')\n\
+ %6.2g max. distance for coplanar facets ('Un')\n\
+ %6.2g max. facet width for recomputing centrum and area\n\
+",
+  qh->MAXabs_coord, qh->DISTround, qh->ANGLEround, qh->MINoutside,
+        qh->MINvisible, qh->MAXcoplanar, qh->WIDEfacet);
+  if (qh->KEEPnearinside)
+    qh_fprintf(qh, fp, 9352, "\
+ %6.2g max. distance for near-inside points\n", qh->NEARinside);
+  if (qh->premerge_cos < REALmax/2) qh_fprintf(qh, fp, 9353, "\
+ %6.2g max. cosine for pre-merge angle\n", qh->premerge_cos);
+  if (qh->PREmerge) qh_fprintf(qh, fp, 9354, "\
+ %6.2g radius of pre-merge centrum\n", qh->premerge_centrum);
+  if (qh->postmerge_cos < REALmax/2) qh_fprintf(qh, fp, 9355, "\
+ %6.2g max. cosine for post-merge angle\n", qh->postmerge_cos);
+  if (qh->POSTmerge) qh_fprintf(qh, fp, 9356, "\
+ %6.2g radius of post-merge centrum\n", qh->postmerge_centrum);
+  qh_fprintf(qh, fp, 9357, "\
+ %6.2g max. distance for merging two simplicial facets\n\
+ %6.2g max. roundoff error for arithmetic operations\n\
+ %6.2g min. denominator for divisions\n\
+  zero diagonal for Gauss: ", qh->ONEmerge, REALepsilon, qh->MINdenom);
+  for(k=0; k < qh->hull_dim; k++)
+    qh_fprintf(qh, fp, 9358, "%6.2e ", qh->NEARzero[k]);
+  qh_fprintf(qh, fp, 9359, "\n\n");
+  for(i=0 ; i < qh->qhstat.next; )
+    qh_printstats(qh, fp, i, &i);
+} /* printstatistics */
+#endif /* qh_KEEPstatistics */
+
+/*-<a                             href="qh-stat_r.htm#TOC"
+  >-------------------------------</a><a name="printstatlevel">-</a>
+
+  qh_printstatlevel(qh, fp, id )
+    print level information for a statistic
+
+  notes:
+    nop if id >= ZEND, printed, or same as initial value
+*/
+void qh_printstatlevel(qhT *qh, FILE *fp, int id) {
+#define NULLfield "       "
+
+  if (id >= ZEND || qh->qhstat.printed[id])
+    return;
+  if (qh->qhstat.type[id] == zdoc) {
+    qh_fprintf(qh, fp, 9360, "%s\n", qh->qhstat.doc[id]);
+    return;
+  }
+  if (qh_nostatistic(qh, id) || !qh->qhstat.doc[id])
+    return;
+  qh->qhstat.printed[id]= True;
+  if (qh->qhstat.count[id] != -1
+      && qh->qhstat.stats[(unsigned char)(qh->qhstat.count[id])].i == 0)
+    qh_fprintf(qh, fp, 9361, " *0 cnt*");
+  else if (qh->qhstat.type[id] >= ZTYPEreal && qh->qhstat.count[id] == -1)
+    qh_fprintf(qh, fp, 9362, "%7.2g", qh->qhstat.stats[id].r);
+  else if (qh->qhstat.type[id] >= ZTYPEreal && qh->qhstat.count[id] != -1)
+    qh_fprintf(qh, fp, 9363, "%7.2g", qh->qhstat.stats[id].r/ qh->qhstat.stats[(unsigned char)(qh->qhstat.count[id])].i);
+  else if (qh->qhstat.type[id] < ZTYPEreal && qh->qhstat.count[id] == -1)
+    qh_fprintf(qh, fp, 9364, "%7d", qh->qhstat.stats[id].i);
+  else if (qh->qhstat.type[id] < ZTYPEreal && qh->qhstat.count[id] != -1)
+    qh_fprintf(qh, fp, 9365, "%7.3g", (realT) qh->qhstat.stats[id].i / qh->qhstat.stats[(unsigned char)(qh->qhstat.count[id])].i);
+  qh_fprintf(qh, fp, 9366, " %s\n", qh->qhstat.doc[id]);
+} /* printstatlevel */
+
+
+/*-<a                             href="qh-stat_r.htm#TOC"
+  >-------------------------------</a><a name="printstats">-</a>
+
+  qh_printstats(qh, fp, index, nextindex )
+    print statistics for a zdoc group
+
+  returns:
+    next zdoc if non-null
+*/
+void qh_printstats(qhT *qh, FILE *fp, int idx, int *nextindex) {
+  int j, nexti;
+
+  if (qh_newstats(qh, idx, &nexti)) {
+    qh_fprintf(qh, fp, 9367, "\n");
+    for (j=idx; j<nexti; j++)
+      qh_printstatlevel(qh, fp, qh->qhstat.id[j]);
+  }
+  if (nextindex)
+    *nextindex= nexti;
+} /* printstats */
+
+#if qh_KEEPstatistics
+
+/*-<a                             href="qh-stat_r.htm#TOC"
+  >-------------------------------</a><a name="stddev">-</a>
+
+  qh_stddev(num, tot, tot2, ave )
+    compute the standard deviation and average from statistics
+
+    tot2 is the sum of the squares
+  notes:
+    computes r.m.s.:
+      (x-ave)^2
+      == x^2 - 2x tot/num +   (tot/num)^2
+      == tot2 - 2 tot tot/num + tot tot/num
+      == tot2 - tot ave
+*/
+realT qh_stddev(int num, realT tot, realT tot2, realT *ave) {
+  realT stddev;
+
+  *ave= tot/num;
+  stddev= sqrt(tot2/num - *ave * *ave);
+  return stddev;
+} /* stddev */
+
+#endif /* qh_KEEPstatistics */
+
+#if !qh_KEEPstatistics
+void    qh_collectstatistics(qhT *qh) {}
+void    qh_printallstatistics(qhT *qh, FILE *fp, char *string) {};
+void    qh_printstatistics(qhT *qh, FILE *fp, char *string) {}
+#endif
+
diff --git a/xs/src/qhull/src/libqhull_r/stat_r.h b/xs/src/qhull/src/libqhull_r/stat_r.h
new file mode 100644
index 0000000000..75e7d10578
--- /dev/null
+++ b/xs/src/qhull/src/libqhull_r/stat_r.h
@@ -0,0 +1,533 @@
+/*<html><pre>  -<a                             href="qh-stat_r.htm"
+  >-------------------------------</a><a name="TOP">-</a>
+
+   stat_r.h
+     contains all statistics that are collected for qhull
+
+   see qh-stat_r.htm and stat_r.c
+
+   Copyright (c) 1993-2015 The Geometry Center.
+   $Id: //main/2015/qhull/src/libqhull_r/stat_r.h#5 $$Change: 2079 $
+   $DateTime: 2016/02/07 17:43:34 $$Author: bbarber $
+
+   recompile qhull if you change this file
+
+   Integer statistics are Z* while real statistics are W*.
+
+   define MAYdebugx to call a routine at every statistic event
+
+*/
+
+#ifndef qhDEFstat
+#define qhDEFstat 1
+
+/* Depends on realT.  Do not include libqhull_r to avoid circular dependency */
+
+#ifndef DEFqhT
+#define DEFqhT 1
+typedef struct qhT qhT;         /* Defined by libqhull_r.h */
+#endif
+
+#ifndef DEFqhstatT
+#define DEFqhstatT 1
+typedef struct qhstatT qhstatT; /* Defined here */
+#endif
+
+/*-<a                             href="qh-stat_r.htm#TOC"
+  >-------------------------------</a><a name="KEEPstatistics">-</a>
+
+  qh_KEEPstatistics
+    0 turns off statistic gathering (except zzdef/zzinc/zzadd/zzval/wwval)
+*/
+#ifndef qh_KEEPstatistics
+#define qh_KEEPstatistics 1
+#endif
+
+/*-<a                             href="qh-stat_r.htm#TOC"
+  >-------------------------------</a><a name="statistics">-</a>
+
+  Zxxx for integers, Wxxx for reals
+
+  notes:
+    be sure that all statistics are defined in stat_r.c
+      otherwise initialization may core dump
+    can pick up all statistics by:
+      grep '[zw].*_[(][ZW]' *.c >z.x
+    remove trailers with query">-</a>
+    remove leaders with  query-replace-regexp [ ^I]+  (
+*/
+#if qh_KEEPstatistics
+enum qh_statistics {     /* alphabetical after Z/W */
+    Zacoplanar,
+    Wacoplanarmax,
+    Wacoplanartot,
+    Zangle,
+    Wangle,
+    Wanglemax,
+    Wanglemin,
+    Zangletests,
+    Wareatot,
+    Wareamax,
+    Wareamin,
+    Zavoidold,
+    Wavoidoldmax,
+    Wavoidoldtot,
+    Zback0,
+    Zbestcentrum,
+    Zbestdist,
+    Zbestlower,
+    Zbestlowerall,
+    Zbestloweralln,
+    Zbestlowerv,
+    Zcentrumtests,
+    Zcheckpart,
+    Zcomputefurthest,
+    Zconcave,
+    Wconcavemax,
+    Wconcavetot,
+    Zconcaveridges,
+    Zconcaveridge,
+    Zcoplanar,
+    Wcoplanarmax,
+    Wcoplanartot,
+    Zcoplanarangle,
+    Zcoplanarcentrum,
+    Zcoplanarhorizon,
+    Zcoplanarinside,
+    Zcoplanarpart,
+    Zcoplanarridges,
+    Wcpu,
+    Zcyclefacetmax,
+    Zcyclefacettot,
+    Zcyclehorizon,
+    Zcyclevertex,
+    Zdegen,
+    Wdegenmax,
+    Wdegentot,
+    Zdegenvertex,
+    Zdelfacetdup,
+    Zdelridge,
+    Zdelvertextot,
+    Zdelvertexmax,
+    Zdetsimplex,
+    Zdistcheck,
+    Zdistconvex,
+    Zdistgood,
+    Zdistio,
+    Zdistplane,
+    Zdiststat,
+    Zdistvertex,
+    Zdistzero,
+    Zdoc1,
+    Zdoc2,
+    Zdoc3,
+    Zdoc4,
+    Zdoc5,
+    Zdoc6,
+    Zdoc7,
+    Zdoc8,
+    Zdoc9,
+    Zdoc10,
+    Zdoc11,
+    Zdoc12,
+    Zdropdegen,
+    Zdropneighbor,
+    Zdupflip,
+    Zduplicate,
+    Wduplicatemax,
+    Wduplicatetot,
+    Zdupridge,
+    Zdupsame,
+    Zflipped,
+    Wflippedmax,
+    Wflippedtot,
+    Zflippedfacets,
+    Zfindbest,
+    Zfindbestmax,
+    Zfindbesttot,
+    Zfindcoplanar,
+    Zfindfail,
+    Zfindhorizon,
+    Zfindhorizonmax,
+    Zfindhorizontot,
+    Zfindjump,
+    Zfindnew,
+    Zfindnewmax,
+    Zfindnewtot,
+    Zfindnewjump,
+    Zfindnewsharp,
+    Zgauss0,
+    Zgoodfacet,
+    Zhashlookup,
+    Zhashridge,
+    Zhashridgetest,
+    Zhashtests,
+    Zinsidevisible,
+    Zintersect,
+    Zintersectfail,
+    Zintersectmax,
+    Zintersectnum,
+    Zintersecttot,
+    Zmaxneighbors,
+    Wmaxout,
+    Wmaxoutside,
+    Zmaxridges,
+    Zmaxvertex,
+    Zmaxvertices,
+    Zmaxvneighbors,
+    Zmemfacets,
+    Zmempoints,
+    Zmemridges,
+    Zmemvertices,
+    Zmergeflipdup,
+    Zmergehorizon,
+    Zmergeinittot,
+    Zmergeinitmax,
+    Zmergeinittot2,
+    Zmergeintohorizon,
+    Zmergenew,
+    Zmergesettot,
+    Zmergesetmax,
+    Zmergesettot2,
+    Zmergesimplex,
+    Zmergevertex,
+    Wmindenom,
+    Wminvertex,
+    Zminnorm,
+    Zmultiridge,
+    Znearlysingular,
+    Zneighbor,
+    Wnewbalance,
+    Wnewbalance2,
+    Znewfacettot,
+    Znewfacetmax,
+    Znewvertex,
+    Wnewvertex,
+    Wnewvertexmax,
+    Znoarea,
+    Znonsimplicial,
+    Znowsimplicial,
+    Znotgood,
+    Znotgoodnew,
+    Znotmax,
+    Znumfacets,
+    Znummergemax,
+    Znummergetot,
+    Znumneighbors,
+    Znumridges,
+    Znumvertices,
+    Znumvisibility,
+    Znumvneighbors,
+    Zonehorizon,
+    Zpartangle,
+    Zpartcoplanar,
+    Zpartflip,
+    Zparthorizon,
+    Zpartinside,
+    Zpartition,
+    Zpartitionall,
+    Zpartnear,
+    Zpbalance,
+    Wpbalance,
+    Wpbalance2,
+    Zpostfacets,
+    Zpremergetot,
+    Zprocessed,
+    Zremvertex,
+    Zremvertexdel,
+    Zrenameall,
+    Zrenamepinch,
+    Zrenameshare,
+    Zretry,
+    Wretrymax,
+    Zridge,
+    Wridge,
+    Wridgemax,
+    Zridge0,
+    Wridge0,
+    Wridge0max,
+    Zridgemid,
+    Wridgemid,
+    Wridgemidmax,
+    Zridgeok,
+    Wridgeok,
+    Wridgeokmax,
+    Zsearchpoints,
+    Zsetplane,
+    Ztestvneighbor,
+    Ztotcheck,
+    Ztothorizon,
+    Ztotmerge,
+    Ztotpartcoplanar,
+    Ztotpartition,
+    Ztotridges,
+    Ztotvertices,
+    Ztotvisible,
+    Ztricoplanar,
+    Ztricoplanarmax,
+    Ztricoplanartot,
+    Ztridegen,
+    Ztrimirror,
+    Ztrinull,
+    Wvertexmax,
+    Wvertexmin,
+    Zvertexridge,
+    Zvertexridgetot,
+    Zvertexridgemax,
+    Zvertices,
+    Zvisfacettot,
+    Zvisfacetmax,
+    Zvisit,
+    Zvisit2max,
+    Zvisvertextot,
+    Zvisvertexmax,
+    Zvvisit,
+    Zvvisit2max,
+    Zwidefacet,
+    Zwidevertices,
+    ZEND};
+
+/*-<a                             href="qh-stat_r.htm#TOC"
+  >-------------------------------</a><a name="ZZstat">-</a>
+
+  Zxxx/Wxxx statistics that remain defined if qh_KEEPstatistics=0
+
+  notes:
+    be sure to use zzdef, zzinc, etc. with these statistics (no double checking!)
+*/
+#else
+enum qh_statistics {     /* for zzdef etc. macros */
+  Zback0,
+  Zbestdist,
+  Zcentrumtests,
+  Zcheckpart,
+  Zconcaveridges,
+  Zcoplanarhorizon,
+  Zcoplanarpart,
+  Zcoplanarridges,
+  Zcyclefacettot,
+  Zcyclehorizon,
+  Zdelvertextot,
+  Zdistcheck,
+  Zdistconvex,
+  Zdistzero,
+  Zdoc1,
+  Zdoc2,
+  Zdoc3,
+  Zdoc11,
+  Zflippedfacets,
+  Zgauss0,
+  Zminnorm,
+  Zmultiridge,
+  Znearlysingular,
+  Wnewvertexmax,
+  Znumvisibility,
+  Zpartcoplanar,
+  Zpartition,
+  Zpartitionall,
+  Zprocessed,
+  Zretry,
+  Zridge,
+  Wridge,
+  Wridgemax,
+  Zridge0,
+  Wridge0,
+  Wridge0max,
+  Zridgemid,
+  Wridgemid,
+  Wridgemidmax,
+  Zridgeok,
+  Wridgeok,
+  Wridgeokmax,
+  Zsetplane,
+  Ztotcheck,
+  Ztotmerge,
+    ZEND};
+#endif
+
+/*-<a                             href="qh-stat_r.htm#TOC"
+  >-------------------------------</a><a name="ztype">-</a>
+
+  ztype
+    the type of a statistic sets its initial value.
+
+  notes:
+    The type should be the same as the macro for collecting the statistic
+*/
+enum ztypes {zdoc,zinc,zadd,zmax,zmin,ZTYPEreal,wadd,wmax,wmin,ZTYPEend};
+
+/*========== macros and constants =============*/
+
+/*-<a                             href="qh-stat_r.htm#TOC"
+  >--------------------------------</a><a name="MAYdebugx">-</a>
+
+  MAYdebugx
+    define as maydebug() to be called frequently for error trapping
+*/
+#define MAYdebugx
+
+/*-<a                             href="qh-stat_r.htm#TOC"
+  >--------------------------------</a><a name="zdef_">-</a>
+
+  zzdef_, zdef_( type, name, doc, -1)
+    define a statistic (assumes 'qhstat.next= 0;')
+
+  zdef_( type, name, doc, count)
+    define an averaged statistic
+    printed as name/count
+*/
+#define zzdef_(stype,name,string,cnt) qh->qhstat.id[qh->qhstat.next++]=name; \
+   qh->qhstat.doc[name]= string; qh->qhstat.count[name]= cnt; qh->qhstat.type[name]= stype
+#if qh_KEEPstatistics
+#define zdef_(stype,name,string,cnt) qh->qhstat.id[qh->qhstat.next++]=name; \
+   qh->qhstat.doc[name]= string; qh->qhstat.count[name]= cnt; qh->qhstat.type[name]= stype
+#else
+#define zdef_(type,name,doc,count)
+#endif
+
+/*-<a                             href="qh-stat_r.htm#TOC"
+  >--------------------------------</a><a name="zinc_">-</a>
+
+  zzinc_( name ), zinc_( name)
+    increment an integer statistic
+*/
+#define zzinc_(id) {MAYdebugx; qh->qhstat.stats[id].i++;}
+#if qh_KEEPstatistics
+#define zinc_(id) {MAYdebugx; qh->qhstat.stats[id].i++;}
+#else
+#define zinc_(id) {}
+#endif
+
+/*-<a                             href="qh-stat_r.htm#TOC"
+  >--------------------------------</a><a name="zadd_">-</a>
+
+  zzadd_( name, value ), zadd_( name, value ), wadd_( name, value )
+    add value to an integer or real statistic
+*/
+#define zzadd_(id, val) {MAYdebugx; qh->qhstat.stats[id].i += (val);}
+#define wwadd_(id, val) {MAYdebugx; qh->qhstat.stats[id].r += (val);}
+#if qh_KEEPstatistics
+#define zadd_(id, val) {MAYdebugx; qh->qhstat.stats[id].i += (val);}
+#define wadd_(id, val) {MAYdebugx; qh->qhstat.stats[id].r += (val);}
+#else
+#define zadd_(id, val) {}
+#define wadd_(id, val) {}
+#endif
+
+/*-<a                             href="qh-stat_r.htm#TOC"
+  >--------------------------------</a><a name="zval_">-</a>
+
+  zzval_( name ), zval_( name ), wwval_( name )
+    set or return value of a statistic
+*/
+#define zzval_(id) ((qh->qhstat.stats[id]).i)
+#define wwval_(id) ((qh->qhstat.stats[id]).r)
+#if qh_KEEPstatistics
+#define zval_(id) ((qh->qhstat.stats[id]).i)
+#define wval_(id) ((qh->qhstat.stats[id]).r)
+#else
+#define zval_(id) qh->qhstat.tempi
+#define wval_(id) qh->qhstat.tempr
+#endif
+
+/*-<a                             href="qh-stat_r.htm#TOC"
+  >--------------------------------</a><a name="zmax_">-</a>
+
+  zmax_( id, val ), wmax_( id, value )
+    maximize id with val
+*/
+#define wwmax_(id, val) {MAYdebugx; maximize_(qh->qhstat.stats[id].r,(val));}
+#if qh_KEEPstatistics
+#define zmax_(id, val) {MAYdebugx; maximize_(qh->qhstat.stats[id].i,(val));}
+#define wmax_(id, val) {MAYdebugx; maximize_(qh->qhstat.stats[id].r,(val));}
+#else
+#define zmax_(id, val) {}
+#define wmax_(id, val) {}
+#endif
+
+/*-<a                             href="qh-stat_r.htm#TOC"
+  >--------------------------------</a><a name="zmin_">-</a>
+
+  zmin_( id, val ), wmin_( id, value )
+    minimize id with val
+*/
+#if qh_KEEPstatistics
+#define zmin_(id, val) {MAYdebugx; minimize_(qh->qhstat.stats[id].i,(val));}
+#define wmin_(id, val) {MAYdebugx; minimize_(qh->qhstat.stats[id].r,(val));}
+#else
+#define zmin_(id, val) {}
+#define wmin_(id, val) {}
+#endif
+
+/*================== stat_r.h types ==============*/
+
+
+/*-<a                             href="qh-stat_r.htm#TOC"
+  >--------------------------------</a><a name="intrealT">-</a>
+
+  intrealT
+    union of integer and real, used for statistics
+*/
+typedef union intrealT intrealT;    /* union of int and realT */
+union intrealT {
+    int i;
+    realT r;
+};
+
+/*-<a                             href="qh-stat_r.htm#TOC"
+  >--------------------------------</a><a name="qhstat">-</a>
+
+  qhstat
+    Data structure for statistics, similar to qh and qhrbox
+
+    Allocated as part of qhT (libqhull_r.h)
+*/
+
+struct qhstatT {
+  intrealT   stats[ZEND];     /* integer and real statistics */
+  unsigned   char id[ZEND+10]; /* id's in print order */
+  const char *doc[ZEND];       /* array of documentation strings */
+  short int  count[ZEND];     /* -1 if none, else index of count to use */
+  char       type[ZEND];      /* type, see ztypes above */
+  char       printed[ZEND];   /* true, if statistic has been printed */
+  intrealT   init[ZTYPEend];  /* initial values by types, set initstatistics */
+
+  int        next;            /* next index for zdef_ */
+  int        precision;       /* index for precision problems */
+  int        vridges;         /* index for Voronoi ridges */
+  int        tempi;
+  realT      tempr;
+};
+
+/*========== function prototypes ===========*/
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+void    qh_allstatA(qhT *qh);
+void    qh_allstatB(qhT *qh);
+void    qh_allstatC(qhT *qh);
+void    qh_allstatD(qhT *qh);
+void    qh_allstatE(qhT *qh);
+void    qh_allstatE2(qhT *qh);
+void    qh_allstatF(qhT *qh);
+void    qh_allstatG(qhT *qh);
+void    qh_allstatH(qhT *qh);
+void    qh_allstatI(qhT *qh);
+void    qh_allstatistics(qhT *qh);
+void    qh_collectstatistics(qhT *qh);
+void    qh_initstatistics(qhT *qh);
+boolT   qh_newstats(qhT *qh, int idx, int *nextindex);
+boolT   qh_nostatistic(qhT *qh, int i);
+void    qh_printallstatistics(qhT *qh, FILE *fp, const char *string);
+void    qh_printstatistics(qhT *qh, FILE *fp, const char *string);
+void    qh_printstatlevel(qhT *qh, FILE *fp, int id);
+void    qh_printstats(qhT *qh, FILE *fp, int idx, int *nextindex);
+realT   qh_stddev(int num, realT tot, realT tot2, realT *ave);
+
+#ifdef __cplusplus
+} /* extern "C" */
+#endif
+
+#endif   /* qhDEFstat */
diff --git a/xs/src/qhull/src/libqhull_r/user_r.c b/xs/src/qhull/src/libqhull_r/user_r.c
new file mode 100644
index 0000000000..bf7ed1d8d6
--- /dev/null
+++ b/xs/src/qhull/src/libqhull_r/user_r.c
@@ -0,0 +1,527 @@
+/*<html><pre>  -<a                             href="qh-user_r.htm"
+  >-------------------------------</a><a name="TOP">-</a>
+
+   user.c
+   user redefinable functions
+
+   see user2_r.c for qh_fprintf, qh_malloc, qh_free
+
+   see README.txt  see COPYING.txt for copyright information.
+
+   see libqhull_r.h for data structures, macros, and user-callable functions.
+
+   see user_eg.c, user_eg2.c, and unix.c for examples.
+
+   see user.h for user-definable constants
+
+      use qh_NOmem in mem_r.h to turn off memory management
+      use qh_NOmerge in user.h to turn off facet merging
+      set qh_KEEPstatistics in user.h to 0 to turn off statistics
+
+   This is unsupported software.  You're welcome to make changes,
+   but you're on your own if something goes wrong.  Use 'Tc' to
+   check frequently.  Usually qhull will report an error if
+   a data structure becomes inconsistent.  If so, it also reports
+   the last point added to the hull, e.g., 102.  You can then trace
+   the execution of qhull with "T4P102".
+
+   Please report any errors that you fix to qhull@qhull.org
+
+   Qhull-template is a template for calling qhull from within your application
+
+   if you recompile and load this module, then user.o will not be loaded
+   from qhull.a
+
+   you can add additional quick allocation sizes in qh_user_memsizes
+
+   if the other functions here are redefined to not use qh_print...,
+   then io.o will not be loaded from qhull.a.  See user_eg_r.c for an
+   example.  We recommend keeping io.o for the extra debugging
+   information it supplies.
+*/
+
+#include "qhull_ra.h"
+
+#include <stdarg.h>
+
+/*-<a                             href="qh-user_r.htm#TOC"
+  >-------------------------------</a><a name="qhull_template">-</a>
+
+  Qhull-template
+    Template for calling qhull from inside your program
+
+  returns:
+    exit code(see qh_ERR... in libqhull_r.h)
+    all memory freed
+
+  notes:
+    This can be called any number of times.
+
+*/
+#if 0
+{
+  int dim;                  /* dimension of points */
+  int numpoints;            /* number of points */
+  coordT *points;           /* array of coordinates for each point */
+  boolT ismalloc;           /* True if qhull should free points in qh_freeqhull() or reallocation */
+  char flags[]= "qhull Tv"; /* option flags for qhull, see qh_opt.htm */
+  FILE *outfile= stdout;    /* output from qh_produce_output(qh)
+                               use NULL to skip qh_produce_output(qh) */
+  FILE *errfile= stderr;    /* error messages from qhull code */
+  int exitcode;             /* 0 if no error from qhull */
+  facetT *facet;            /* set by FORALLfacets */
+  int curlong, totlong;     /* memory remaining after qh_memfreeshort */
+
+  qhT qh_qh;                /* Qhull's data structure.  First argument of most calls */
+  qhT *qh= &qh_qh;          /* Alternatively -- qhT *qh= (qhT*)malloc(sizeof(qhT)) */
+
+  QHULL_LIB_CHECK /* Check for compatible library */
+
+  qh_zero(qh, errfile);
+
+  /* initialize dim, numpoints, points[], ismalloc here */
+  exitcode= qh_new_qhull(qh, dim, numpoints, points, ismalloc,
+                      flags, outfile, errfile);
+  if (!exitcode) {                  /* if no error */
+    /* 'qh->facet_list' contains the convex hull */
+    FORALLfacets {
+       /* ... your code ... */
+    }
+  }
+  qh_freeqhull(qh, !qh_ALL);
+  qh_memfreeshort(qh, &curlong, &totlong);
+  if (curlong || totlong)
+    qh_fprintf(qh, errfile, 7068, "qhull internal warning (main): did not free %d bytes of long memory(%d pieces)\n", totlong, curlong);
+}
+#endif
+
+/*-<a                             href="qh-user_r.htm#TOC"
+  >-------------------------------</a><a name="new_qhull">-</a>
+
+  qh_new_qhull(qh, dim, numpoints, points, ismalloc, qhull_cmd, outfile, errfile )
+    Run qhull and return results in qh.
+    Returns exitcode (0 if no errors).
+    Before first call, either call qh_zero(qh, errfile), or set qh to all zero.
+
+  notes:
+    do not modify points until finished with results.
+      The qhull data structure contains pointers into the points array.
+    do not call qhull functions before qh_new_qhull().
+      The qhull data structure is not initialized until qh_new_qhull().
+    do not call qh_init_A (global_r.c)
+
+    Default errfile is stderr, outfile may be null
+    qhull_cmd must start with "qhull "
+    projects points to a new point array for Delaunay triangulations ('d' and 'v')
+    transforms points into a new point array for halfspace intersection ('H')
+
+  see:
+    Qhull-template at the beginning of this file.
+    An example of using qh_new_qhull is user_eg_r.c
+*/
+int qh_new_qhull(qhT *qh, int dim, int numpoints, coordT *points, boolT ismalloc,
+                char *qhull_cmd, FILE *outfile, FILE *errfile) {
+  /* gcc may issue a "might be clobbered" warning for dim, points, and ismalloc [-Wclobbered].
+     These parameters are not referenced after a longjmp() and hence not clobbered.
+     See http://stackoverflow.com/questions/7721854/what-sense-do-these-clobbered-variable-warnings-make */
+  int exitcode, hulldim;
+  boolT new_ismalloc;
+  coordT *new_points;
+
+  if(!errfile){
+    errfile= stderr;
+  }
+  if (!qh->qhmem.ferr) {
+    qh_meminit(qh, errfile);
+  } else {
+    qh_memcheck(qh);
+  }
+  if (strncmp(qhull_cmd, "qhull ", (size_t)6)) {
+    qh_fprintf(qh, errfile, 6186, "qhull error (qh_new_qhull): start qhull_cmd argument with \"qhull \"\n");
+    return qh_ERRinput;
+  }
+  qh_initqhull_start(qh, NULL, outfile, errfile);
+  trace1((qh, qh->ferr, 1044, "qh_new_qhull: build new Qhull for %d %d-d points with %s\n", numpoints, dim, qhull_cmd));
+  exitcode = setjmp(qh->errexit);
+  if (!exitcode)
+  {
+    qh->NOerrexit = False;
+    qh_initflags(qh, qhull_cmd);
+    if (qh->DELAUNAY)
+      qh->PROJECTdelaunay= True;
+    if (qh->HALFspace) {
+      /* points is an array of halfspaces,
+         the last coordinate of each halfspace is its offset */
+      hulldim= dim-1;
+      qh_setfeasible(qh, hulldim);
+      new_points= qh_sethalfspace_all(qh, dim, numpoints, points, qh->feasible_point);
+      new_ismalloc= True;
+      if (ismalloc)
+        qh_free(points);
+    }else {
+      hulldim= dim;
+      new_points= points;
+      new_ismalloc= ismalloc;
+    }
+    qh_init_B(qh, new_points, numpoints, hulldim, new_ismalloc);
+    qh_qhull(qh);
+    qh_check_output(qh);
+    if (outfile) {
+      qh_produce_output(qh);
+    }else {
+      qh_prepare_output(qh);
+    }
+    if (qh->VERIFYoutput && !qh->STOPpoint && !qh->STOPcone)
+      qh_check_points(qh);
+  }
+  qh->NOerrexit = True;
+  return exitcode;
+} /* new_qhull */
+
+/*-<a                             href="qh-user_r.htm#TOC"
+  >-------------------------------</a><a name="errexit">-</a>
+
+  qh_errexit(qh, exitcode, facet, ridge )
+    report and exit from an error
+    report facet and ridge if non-NULL
+    reports useful information such as last point processed
+    set qh.FORCEoutput to print neighborhood of facet
+
+  see:
+    qh_errexit2() in libqhull_r.c for printing 2 facets
+
+  design:
+    check for error within error processing
+    compute qh.hulltime
+    print facet and ridge (if any)
+    report commandString, options, qh.furthest_id
+    print summary and statistics (including precision statistics)
+    if qh_ERRsingular
+      print help text for singular data set
+    exit program via long jump (if defined) or exit()
+*/
+void qh_errexit(qhT *qh, int exitcode, facetT *facet, ridgeT *ridge) {
+
+  if (qh->ERREXITcalled) {
+    qh_fprintf(qh, qh->ferr, 8126, "\nqhull error while processing previous error.  Exit program\n");
+    qh_exit(qh_ERRqhull);
+  }
+  qh->ERREXITcalled= True;
+  if (!qh->QHULLfinished)
+    qh->hulltime= qh_CPUclock - qh->hulltime;
+  qh_errprint(qh, "ERRONEOUS", facet, NULL, ridge, NULL);
+  qh_fprintf(qh, qh->ferr, 8127, "\nWhile executing: %s | %s\n", qh->rbox_command, qh->qhull_command);
+  qh_fprintf(qh, qh->ferr, 8128, "Options selected for Qhull %s:\n%s\n", qh_version, qh->qhull_options);
+  if (qh->furthest_id >= 0) {
+    qh_fprintf(qh, qh->ferr, 8129, "Last point added to hull was p%d.", qh->furthest_id);
+    if (zzval_(Ztotmerge))
+      qh_fprintf(qh, qh->ferr, 8130, "  Last merge was #%d.", zzval_(Ztotmerge));
+    if (qh->QHULLfinished)
+      qh_fprintf(qh, qh->ferr, 8131, "\nQhull has finished constructing the hull.");
+    else if (qh->POSTmerging)
+      qh_fprintf(qh, qh->ferr, 8132, "\nQhull has started post-merging.");
+    qh_fprintf(qh, qh->ferr, 8133, "\n");
+  }
+  if (qh->FORCEoutput && (qh->QHULLfinished || (!facet && !ridge)))
+    qh_produce_output(qh);
+  else if (exitcode != qh_ERRinput) {
+    if (exitcode != qh_ERRsingular && zzval_(Zsetplane) > qh->hull_dim+1) {
+      qh_fprintf(qh, qh->ferr, 8134, "\nAt error exit:\n");
+      qh_printsummary(qh, qh->ferr);
+      if (qh->PRINTstatistics) {
+        qh_collectstatistics(qh);
+        qh_printstatistics(qh, qh->ferr, "at error exit");
+        qh_memstatistics(qh, qh->ferr);
+      }
+    }
+    if (qh->PRINTprecision)
+      qh_printstats(qh, qh->ferr, qh->qhstat.precision, NULL);
+  }
+  if (!exitcode)
+    exitcode= qh_ERRqhull;
+  else if (exitcode == qh_ERRsingular)
+    qh_printhelp_singular(qh, qh->ferr);
+  else if (exitcode == qh_ERRprec && !qh->PREmerge)
+    qh_printhelp_degenerate(qh, qh->ferr);
+  if (qh->NOerrexit) {
+    qh_fprintf(qh, qh->ferr, 6187, "qhull error while ending program, or qh->NOerrexit not cleared after setjmp(). Exit program with error.\n");
+    qh_exit(qh_ERRqhull);
+  }
+  qh->ERREXITcalled= False;
+  qh->NOerrexit= True;
+  qh->ALLOWrestart= False;  /* longjmp will undo qh_build_withrestart */
+  longjmp(qh->errexit, exitcode);
+} /* errexit */
+
+
+/*-<a                             href="qh-user_r.htm#TOC"
+  >-------------------------------</a><a name="errprint">-</a>
+
+  qh_errprint(qh, fp, string, atfacet, otherfacet, atridge, atvertex )
+    prints out the information of facets and ridges to fp
+    also prints neighbors and geomview output
+
+  notes:
+    except for string, any parameter may be NULL
+*/
+void qh_errprint(qhT *qh, const char *string, facetT *atfacet, facetT *otherfacet, ridgeT *atridge, vertexT *atvertex) {
+  int i;
+
+  if (atfacet) {
+    qh_fprintf(qh, qh->ferr, 8135, "%s FACET:\n", string);
+    qh_printfacet(qh, qh->ferr, atfacet);
+  }
+  if (otherfacet) {
+    qh_fprintf(qh, qh->ferr, 8136, "%s OTHER FACET:\n", string);
+    qh_printfacet(qh, qh->ferr, otherfacet);
+  }
+  if (atridge) {
+    qh_fprintf(qh, qh->ferr, 8137, "%s RIDGE:\n", string);
+    qh_printridge(qh, qh->ferr, atridge);
+    if (atridge->top && atridge->top != atfacet && atridge->top != otherfacet)
+      qh_printfacet(qh, qh->ferr, atridge->top);
+    if (atridge->bottom
+        && atridge->bottom != atfacet && atridge->bottom != otherfacet)
+      qh_printfacet(qh, qh->ferr, atridge->bottom);
+    if (!atfacet)
+      atfacet= atridge->top;
+    if (!otherfacet)
+      otherfacet= otherfacet_(atridge, atfacet);
+  }
+  if (atvertex) {
+    qh_fprintf(qh, qh->ferr, 8138, "%s VERTEX:\n", string);
+    qh_printvertex(qh, qh->ferr, atvertex);
+  }
+  if (qh->fout && qh->FORCEoutput && atfacet && !qh->QHULLfinished && !qh->IStracing) {
+    qh_fprintf(qh, qh->ferr, 8139, "ERRONEOUS and NEIGHBORING FACETS to output\n");
+    for (i=0; i < qh_PRINTEND; i++)  /* use fout for geomview output */
+      qh_printneighborhood(qh, qh->fout, qh->PRINTout[i], atfacet, otherfacet,
+                            !qh_ALL);
+  }
+} /* errprint */
+
+
+/*-<a                             href="qh-user_r.htm#TOC"
+  >-------------------------------</a><a name="printfacetlist">-</a>
+
+  qh_printfacetlist(qh, fp, facetlist, facets, printall )
+    print all fields for a facet list and/or set of facets to fp
+    if !printall,
+      only prints good facets
+
+  notes:
+    also prints all vertices
+*/
+void qh_printfacetlist(qhT *qh, facetT *facetlist, setT *facets, boolT printall) {
+  facetT *facet, **facetp;
+
+  qh_printbegin(qh, qh->ferr, qh_PRINTfacets, facetlist, facets, printall);
+  FORALLfacet_(facetlist)
+    qh_printafacet(qh, qh->ferr, qh_PRINTfacets, facet, printall);
+  FOREACHfacet_(facets)
+    qh_printafacet(qh, qh->ferr, qh_PRINTfacets, facet, printall);
+  qh_printend(qh, qh->ferr, qh_PRINTfacets, facetlist, facets, printall);
+} /* printfacetlist */
+
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="printhelp_degenerate">-</a>
+
+  qh_printhelp_degenerate(qh, fp )
+    prints descriptive message for precision error
+
+  notes:
+    no message if qh_QUICKhelp
+*/
+void qh_printhelp_degenerate(qhT *qh, FILE *fp) {
+
+  if (qh->MERGEexact || qh->PREmerge || qh->JOGGLEmax < REALmax/2)
+    qh_fprintf(qh, fp, 9368, "\n\
+A Qhull error has occurred.  Qhull should have corrected the above\n\
+precision error.  Please send the input and all of the output to\n\
+qhull_bug@qhull.org\n");
+  else if (!qh_QUICKhelp) {
+    qh_fprintf(qh, fp, 9369, "\n\
+Precision problems were detected during construction of the convex hull.\n\
+This occurs because convex hull algorithms assume that calculations are\n\
+exact, but floating-point arithmetic has roundoff errors.\n\
+\n\
+To correct for precision problems, do not use 'Q0'.  By default, Qhull\n\
+selects 'C-0' or 'Qx' and merges non-convex facets.  With option 'QJ',\n\
+Qhull joggles the input to prevent precision problems.  See \"Imprecision\n\
+in Qhull\" (qh-impre.htm).\n\
+\n\
+If you use 'Q0', the output may include\n\
+coplanar ridges, concave ridges, and flipped facets.  In 4-d and higher,\n\
+Qhull may produce a ridge with four neighbors or two facets with the same \n\
+vertices.  Qhull reports these events when they occur.  It stops when a\n\
+concave ridge, flipped facet, or duplicate facet occurs.\n");
+#if REALfloat
+    qh_fprintf(qh, fp, 9370, "\
+\n\
+Qhull is currently using single precision arithmetic.  The following\n\
+will probably remove the precision problems:\n\
+  - recompile qhull for realT precision(#define REALfloat 0 in user.h).\n");
+#endif
+    if (qh->DELAUNAY && !qh->SCALElast && qh->MAXabs_coord > 1e4)
+      qh_fprintf(qh, fp, 9371, "\
+\n\
+When computing the Delaunay triangulation of coordinates > 1.0,\n\
+  - use 'Qbb' to scale the last coordinate to [0,m] (max previous coordinate)\n");
+    if (qh->DELAUNAY && !qh->ATinfinity)
+      qh_fprintf(qh, fp, 9372, "\
+When computing the Delaunay triangulation:\n\
+  - use 'Qz' to add a point at-infinity.  This reduces precision problems.\n");
+
+    qh_fprintf(qh, fp, 9373, "\
+\n\
+If you need triangular output:\n\
+  - use option 'Qt' to triangulate the output\n\
+  - use option 'QJ' to joggle the input points and remove precision errors\n\
+  - use option 'Ft'.  It triangulates non-simplicial facets with added points.\n\
+\n\
+If you must use 'Q0',\n\
+try one or more of the following options.  They can not guarantee an output.\n\
+  - use 'QbB' to scale the input to a cube.\n\
+  - use 'Po' to produce output and prevent partitioning for flipped facets\n\
+  - use 'V0' to set min. distance to visible facet as 0 instead of roundoff\n\
+  - use 'En' to specify a maximum roundoff error less than %2.2g.\n\
+  - options 'Qf', 'Qbb', and 'QR0' may also help\n",
+               qh->DISTround);
+    qh_fprintf(qh, fp, 9374, "\
+\n\
+To guarantee simplicial output:\n\
+  - use option 'Qt' to triangulate the output\n\
+  - use option 'QJ' to joggle the input points and remove precision errors\n\
+  - use option 'Ft' to triangulate the output by adding points\n\
+  - use exact arithmetic (see \"Imprecision in Qhull\", qh-impre.htm)\n\
+");
+  }
+} /* printhelp_degenerate */
+
+
+/*-<a                             href="qh-globa_r.htm#TOC"
+  >-------------------------------</a><a name="printhelp_narrowhull">-</a>
+
+  qh_printhelp_narrowhull(qh, minangle )
+    Warn about a narrow hull
+
+  notes:
+    Alternatively, reduce qh_WARNnarrow in user.h
+
+*/
+void qh_printhelp_narrowhull(qhT *qh, FILE *fp, realT minangle) {
+
+    qh_fprintf(qh, fp, 9375, "qhull precision warning: \n\
+The initial hull is narrow (cosine of min. angle is %.16f).\n\
+Is the input lower dimensional (e.g., on a plane in 3-d)?  Qhull may\n\
+produce a wide facet.  Options 'QbB' (scale to unit box) or 'Qbb' (scale\n\
+last coordinate) may remove this warning.  Use 'Pp' to skip this warning.\n\
+See 'Limitations' in qh-impre.htm.\n",
+          -minangle);   /* convert from angle between normals to angle between facets */
+} /* printhelp_narrowhull */
+
+/*-<a                             href="qh-io_r.htm#TOC"
+  >-------------------------------</a><a name="printhelp_singular">-</a>
+
+  qh_printhelp_singular(qh, fp )
+    prints descriptive message for singular input
+*/
+void qh_printhelp_singular(qhT *qh, FILE *fp) {
+  facetT *facet;
+  vertexT *vertex, **vertexp;
+  realT min, max, *coord, dist;
+  int i,k;
+
+  qh_fprintf(qh, fp, 9376, "\n\
+The input to qhull appears to be less than %d dimensional, or a\n\
+computation has overflowed.\n\n\
+Qhull could not construct a clearly convex simplex from points:\n",
+           qh->hull_dim);
+  qh_printvertexlist(qh, fp, "", qh->facet_list, NULL, qh_ALL);
+  if (!qh_QUICKhelp)
+    qh_fprintf(qh, fp, 9377, "\n\
+The center point is coplanar with a facet, or a vertex is coplanar\n\
+with a neighboring facet.  The maximum round off error for\n\
+computing distances is %2.2g.  The center point, facets and distances\n\
+to the center point are as follows:\n\n", qh->DISTround);
+  qh_printpointid(qh, fp, "center point", qh->hull_dim, qh->interior_point, qh_IDunknown);
+  qh_fprintf(qh, fp, 9378, "\n");
+  FORALLfacets {
+    qh_fprintf(qh, fp, 9379, "facet");
+    FOREACHvertex_(facet->vertices)
+      qh_fprintf(qh, fp, 9380, " p%d", qh_pointid(qh, vertex->point));
+    zinc_(Zdistio);
+    qh_distplane(qh, qh->interior_point, facet, &dist);
+    qh_fprintf(qh, fp, 9381, " distance= %4.2g\n", dist);
+  }
+  if (!qh_QUICKhelp) {
+    if (qh->HALFspace)
+      qh_fprintf(qh, fp, 9382, "\n\
+These points are the dual of the given halfspaces.  They indicate that\n\
+the intersection is degenerate.\n");
+    qh_fprintf(qh, fp, 9383,"\n\
+These points either have a maximum or minimum x-coordinate, or\n\
+they maximize the determinant for k coordinates.  Trial points\n\
+are first selected from points that maximize a coordinate.\n");
+    if (qh->hull_dim >= qh_INITIALmax)
+      qh_fprintf(qh, fp, 9384, "\n\
+Because of the high dimension, the min x-coordinate and max-coordinate\n\
+points are used if the determinant is non-zero.  Option 'Qs' will\n\
+do a better, though much slower, job.  Instead of 'Qs', you can change\n\
+the points by randomly rotating the input with 'QR0'.\n");
+  }
+  qh_fprintf(qh, fp, 9385, "\nThe min and max coordinates for each dimension are:\n");
+  for (k=0; k < qh->hull_dim; k++) {
+    min= REALmax;
+    max= -REALmin;
+    for (i=qh->num_points, coord= qh->first_point+k; i--; coord += qh->hull_dim) {
+      maximize_(max, *coord);
+      minimize_(min, *coord);
+    }
+    qh_fprintf(qh, fp, 9386, "  %d:  %8.4g  %8.4g  difference= %4.4g\n", k, min, max, max-min);
+  }
+  if (!qh_QUICKhelp) {
+    qh_fprintf(qh, fp, 9387, "\n\
+If the input should be full dimensional, you have several options that\n\
+may determine an initial simplex:\n\
+  - use 'QJ'  to joggle the input and make it full dimensional\n\
+  - use 'QbB' to scale the points to the unit cube\n\
+  - use 'QR0' to randomly rotate the input for different maximum points\n\
+  - use 'Qs'  to search all points for the initial simplex\n\
+  - use 'En'  to specify a maximum roundoff error less than %2.2g.\n\
+  - trace execution with 'T3' to see the determinant for each point.\n",
+                     qh->DISTround);
+#if REALfloat
+    qh_fprintf(qh, fp, 9388, "\
+  - recompile qhull for realT precision(#define REALfloat 0 in libqhull_r.h).\n");
+#endif
+    qh_fprintf(qh, fp, 9389, "\n\
+If the input is lower dimensional:\n\
+  - use 'QJ' to joggle the input and make it full dimensional\n\
+  - use 'Qbk:0Bk:0' to delete coordinate k from the input.  You should\n\
+    pick the coordinate with the least range.  The hull will have the\n\
+    correct topology.\n\
+  - determine the flat containing the points, rotate the points\n\
+    into a coordinate plane, and delete the other coordinates.\n\
+  - add one or more points to make the input full dimensional.\n\
+");
+  }
+} /* printhelp_singular */
+
+/*-<a                             href="qh-globa_r.htm#TOC"
+  >-------------------------------</a><a name="user_memsizes">-</a>
+
+  qh_user_memsizes(qh)
+    allocate up to 10 additional, quick allocation sizes
+
+  notes:
+    increase maximum number of allocations in qh_initqhull_mem()
+*/
+void qh_user_memsizes(qhT *qh) {
+
+  QHULL_UNUSED(qh)
+  /* qh_memsize(qh, size); */
+} /* user_memsizes */
+
+
diff --git a/xs/src/qhull/src/libqhull_r/user_r.h b/xs/src/qhull/src/libqhull_r/user_r.h
new file mode 100644
index 0000000000..7cca65a804
--- /dev/null
+++ b/xs/src/qhull/src/libqhull_r/user_r.h
@@ -0,0 +1,882 @@
+/*<html><pre>  -<a                             href="qh-user_r.htm"
+  >-------------------------------</a><a name="TOP">-</a>
+
+   user.h
+   user redefinable constants
+
+   for each source file, user_r.h is included first
+
+   see qh-user_r.htm.  see COPYING for copyright information.
+
+   See user_r.c for sample code.
+
+   before reading any code, review libqhull_r.h for data structure definitions
+
+Sections:
+   ============= qhull library constants ======================
+   ============= data types and configuration macros ==========
+   ============= performance related constants ================
+   ============= memory constants =============================
+   ============= joggle constants =============================
+   ============= conditional compilation ======================
+   ============= -merge constants- ============================
+
+Code flags --
+  NOerrors -- the code does not call qh_errexit()
+  WARN64 -- the code may be incompatible with 64-bit pointers
+
+*/
+
+#include <time.h>
+
+#ifndef qhDEFuser
+#define qhDEFuser 1
+
+/* Derived from Qt's corelib/global/qglobal.h */
+#if !defined(SAG_COM) && !defined(__CYGWIN__) && (defined(WIN64) || defined(_WIN64) || defined(__WIN64__) || defined(WIN32) || defined(_WIN32) || defined(__WIN32__) || defined(__NT__))
+#   define QHULL_OS_WIN
+#elif defined(__MWERKS__) && defined(__INTEL__) /* Metrowerks discontinued before the release of Intel Macs */
+#   define QHULL_OS_WIN
+#endif
+
+/*============================================================*/
+/*============= qhull library constants ======================*/
+/*============================================================*/
+
+/*-<a                             href="qh-user_r.htm#TOC"
+  >--------------------------------</a><a name="filenamelen">-</a>
+
+  FILENAMElen -- max length for TI and TO filenames
+
+*/
+
+#define qh_FILENAMElen 500
+
+/*-<a                             href="qh-user_r.htm#TOC"
+  >--------------------------------</a><a name="msgcode">-</a>
+
+  msgcode -- Unique message codes for qh_fprintf
+
+  If add new messages, assign these values and increment in user.h and user_r.h
+  See QhullError.h for 10000 errors.
+
+  def counters =  [27, 1048, 2059, 3026, 4068, 5003,
+     6273, 7081, 8147, 9411, 10000, 11029]
+
+  See: qh_ERR* [libqhull_r.h]
+*/
+
+#define MSG_TRACE0 0
+#define MSG_TRACE1 1000
+#define MSG_TRACE2 2000
+#define MSG_TRACE3 3000
+#define MSG_TRACE4 4000
+#define MSG_TRACE5 5000
+#define MSG_ERROR  6000   /* errors written to qh.ferr */
+#define MSG_WARNING 7000
+#define MSG_STDERR  8000  /* log messages Written to qh.ferr */
+#define MSG_OUTPUT  9000
+#define MSG_QHULL_ERROR 10000 /* errors thrown by QhullError.cpp (QHULLlastError is in QhullError.h) */
+#define MSG_FIXUP  11000  /* FIXUP QH11... */
+#define MSG_MAXLEN  3000 /* qh_printhelp_degenerate() in user.c */
+
+
+/*-<a                             href="qh-user_r.htm#TOC"
+  >--------------------------------</a><a name="qh_OPTIONline">-</a>
+
+  qh_OPTIONline -- max length of an option line 'FO'
+*/
+#define qh_OPTIONline 80
+
+/*============================================================*/
+/*============= data types and configuration macros ==========*/
+/*============================================================*/
+
+/*-<a                             href="qh-user_r.htm#TOC"
+  >--------------------------------</a><a name="realT">-</a>
+
+  realT
+    set the size of floating point numbers
+
+  qh_REALdigits
+    maximimum number of significant digits
+
+  qh_REAL_1, qh_REAL_2n, qh_REAL_3n
+    format strings for printf
+
+  qh_REALmax, qh_REALmin
+    maximum and minimum (near zero) values
+
+  qh_REALepsilon
+    machine roundoff.  Maximum roundoff error for addition and multiplication.
+
+  notes:
+   Select whether to store floating point numbers in single precision (float)
+   or double precision (double).
+
+   Use 'float' to save about 8% in time and 25% in space.  This is particularly
+   helpful if high-d where convex hulls are space limited.  Using 'float' also
+   reduces the printed size of Qhull's output since numbers have 8 digits of
+   precision.
+
+   Use 'double' when greater arithmetic precision is needed.  This is needed
+   for Delaunay triangulations and Voronoi diagrams when you are not merging
+   facets.
+
+   If 'double' gives insufficient precision, your data probably includes
+   degeneracies.  If so you should use facet merging (done by default)
+   or exact arithmetic (see imprecision section of manual, qh-impre.htm).
+   You may also use option 'Po' to force output despite precision errors.
+
+   You may use 'long double', but many format statements need to be changed
+   and you may need a 'long double' square root routine.  S. Grundmann
+   (sg@eeiwzb.et.tu-dresden.de) has done this.  He reports that the code runs
+   much slower with little gain in precision.
+
+   WARNING: on some machines,    int f(){realT a= REALmax;return (a == REALmax);}
+      returns False.  Use (a > REALmax/2) instead of (a == REALmax).
+
+   REALfloat =   1      all numbers are 'float' type
+             =   0      all numbers are 'double' type
+*/
+#define REALfloat 1
+
+#if (REALfloat == 1)
+#define realT float
+#define REALmax FLT_MAX
+#define REALmin FLT_MIN
+#define REALepsilon FLT_EPSILON
+#define qh_REALdigits 8   /* maximum number of significant digits */
+#define qh_REAL_1 "%6.8g "
+#define qh_REAL_2n "%6.8g %6.8g\n"
+#define qh_REAL_3n "%6.8g %6.8g %6.8g\n"
+
+#elif (REALfloat == 0)
+#define realT double
+#define REALmax DBL_MAX
+#define REALmin DBL_MIN
+#define REALepsilon DBL_EPSILON
+#define qh_REALdigits 16    /* maximum number of significant digits */
+#define qh_REAL_1 "%6.16g "
+#define qh_REAL_2n "%6.16g %6.16g\n"
+#define qh_REAL_3n "%6.16g %6.16g %6.16g\n"
+
+#else
+#error unknown float option
+#endif
+
+/*-<a                             href="qh-user_r.htm#TOC"
+  >--------------------------------</a><a name="countT">-</a>
+
+  countT
+    The type for counts and identifiers (e.g., the number of points, vertex identifiers)
+    Currently used by C++ code-only.  Decided against using it for setT because most sets are small.
+
+    Defined as 'int' for C-code compatibility and QH11026
+
+    FIXUP QH11026 countT may be defined as a unsigned value, but several code issues need to be solved first.  See countT in Changes.txt
+*/
+
+#ifndef DEFcountT
+#define DEFcountT 1
+typedef int countT;
+#endif
+#define COUNTmax 0x7fffffff
+
+
+/*-<a                             href="qh-user_r.htm#TOC"
+  >--------------------------------</a><a name="CPUclock">-</a>
+
+  qh_CPUclock
+    define the clock() function for reporting the total time spent by Qhull
+    returns CPU ticks as a 'long int'
+    qh_CPUclock is only used for reporting the total time spent by Qhull
+
+  qh_SECticks
+    the number of clock ticks per second
+
+  notes:
+    looks for CLOCKS_PER_SEC, CLOCKS_PER_SECOND, or assumes microseconds
+    to define a custom clock, set qh_CLOCKtype to 0
+
+    if your system does not use clock() to return CPU ticks, replace
+    qh_CPUclock with the corresponding function.  It is converted
+    to 'unsigned long' to prevent wrap-around during long runs.  By default,
+    <time.h> defines clock_t as 'long'
+
+   Set qh_CLOCKtype to
+
+     1          for CLOCKS_PER_SEC, CLOCKS_PER_SECOND, or microsecond
+                Note:  may fail if more than 1 hour elapsed time
+
+     2          use qh_clock() with POSIX times() (see global_r.c)
+*/
+#define qh_CLOCKtype 1  /* change to the desired number */
+
+#if (qh_CLOCKtype == 1)
+
+#if defined(CLOCKS_PER_SECOND)
+#define qh_CPUclock    ((unsigned long)clock())  /* return CPU clock */
+#define qh_SECticks CLOCKS_PER_SECOND
+
+#elif defined(CLOCKS_PER_SEC)
+#define qh_CPUclock    ((unsigned long)clock())  /* return CPU clock */
+#define qh_SECticks CLOCKS_PER_SEC
+
+#elif defined(CLK_TCK)
+#define qh_CPUclock    ((unsigned long)clock())  /* return CPU clock */
+#define qh_SECticks CLK_TCK
+
+#else
+#define qh_CPUclock    ((unsigned long)clock())  /* return CPU clock */
+#define qh_SECticks 1E6
+#endif
+
+#elif (qh_CLOCKtype == 2)
+#define qh_CPUclock    qh_clock()  /* return CPU clock */
+#define qh_SECticks 100
+
+#else /* qh_CLOCKtype == ? */
+#error unknown clock option
+#endif
+
+/*-<a                             href="qh-user_r.htm#TOC"
+  >--------------------------------</a><a name="RANDOM">-</a>
+
+  qh_RANDOMtype, qh_RANDOMmax, qh_RANDOMseed
+    define random number generator
+
+    qh_RANDOMint generates a random integer between 0 and qh_RANDOMmax.
+    qh_RANDOMseed sets the random number seed for qh_RANDOMint
+
+  Set qh_RANDOMtype (default 5) to:
+    1       for random() with 31 bits (UCB)
+    2       for rand() with RAND_MAX or 15 bits (system 5)
+    3       for rand() with 31 bits (Sun)
+    4       for lrand48() with 31 bits (Solaris)
+    5       for qh_rand(qh) with 31 bits (included with Qhull, requires 'qh')
+
+  notes:
+    Random numbers are used by rbox to generate point sets.  Random
+    numbers are used by Qhull to rotate the input ('QRn' option),
+    simulate a randomized algorithm ('Qr' option), and to simulate
+    roundoff errors ('Rn' option).
+
+    Random number generators differ between systems.  Most systems provide
+    rand() but the period varies.  The period of rand() is not critical
+    since qhull does not normally use random numbers.
+
+    The default generator is Park & Miller's minimal standard random
+    number generator [CACM 31:1195 '88].  It is included with Qhull.
+
+    If qh_RANDOMmax is wrong, qhull will report a warning and Geomview
+    output will likely be invisible.
+*/
+#define qh_RANDOMtype 5   /* *** change to the desired number *** */
+
+#if (qh_RANDOMtype == 1)
+#define qh_RANDOMmax ((realT)0x7fffffffUL)  /* 31 bits, random()/MAX */
+#define qh_RANDOMint random()
+#define qh_RANDOMseed_(qh, seed) srandom(seed);
+
+#elif (qh_RANDOMtype == 2)
+#ifdef RAND_MAX
+#define qh_RANDOMmax ((realT)RAND_MAX)
+#else
+#define qh_RANDOMmax ((realT)32767)   /* 15 bits (System 5) */
+#endif
+#define qh_RANDOMint  rand()
+#define qh_RANDOMseed_(qh, seed) srand((unsigned)seed);
+
+#elif (qh_RANDOMtype == 3)
+#define qh_RANDOMmax ((realT)0x7fffffffUL)  /* 31 bits, Sun */
+#define qh_RANDOMint  rand()
+#define qh_RANDOMseed_(qh, seed) srand((unsigned)seed);
+
+#elif (qh_RANDOMtype == 4)
+#define qh_RANDOMmax ((realT)0x7fffffffUL)  /* 31 bits, lrand38()/MAX */
+#define qh_RANDOMint lrand48()
+#define qh_RANDOMseed_(qh, seed) srand48(seed);
+
+#elif (qh_RANDOMtype == 5)  /* 'qh' is an implicit parameter */
+#define qh_RANDOMmax ((realT)2147483646UL)  /* 31 bits, qh_rand/MAX */
+#define qh_RANDOMint qh_rand(qh)
+#define qh_RANDOMseed_(qh, seed) qh_srand(qh, seed);
+/* unlike rand(), never returns 0 */
+
+#else
+#error: unknown random option
+#endif
+
+/*-<a                             href="qh-user_r.htm#TOC"
+  >--------------------------------</a><a name="ORIENTclock">-</a>
+
+  qh_ORIENTclock
+    0 for inward pointing normals by Geomview convention
+*/
+#define qh_ORIENTclock 0
+
+
+/*============================================================*/
+/*============= joggle constants =============================*/
+/*============================================================*/
+
+/*-<a                             href="qh-user_r.htm#TOC"
+>--------------------------------</a><a name="JOGGLEdefault">-</a>
+
+qh_JOGGLEdefault
+default qh.JOGGLEmax is qh.DISTround * qh_JOGGLEdefault
+
+notes:
+rbox s r 100 | qhull QJ1e-15 QR0 generates 90% faults at distround 7e-16
+rbox s r 100 | qhull QJ1e-14 QR0 generates 70% faults
+rbox s r 100 | qhull QJ1e-13 QR0 generates 35% faults
+rbox s r 100 | qhull QJ1e-12 QR0 generates 8% faults
+rbox s r 100 | qhull QJ1e-11 QR0 generates 1% faults
+rbox s r 100 | qhull QJ1e-10 QR0 generates 0% faults
+rbox 1000 W0 | qhull QJ1e-12 QR0 generates 86% faults
+rbox 1000 W0 | qhull QJ1e-11 QR0 generates 20% faults
+rbox 1000 W0 | qhull QJ1e-10 QR0 generates 2% faults
+the later have about 20 points per facet, each of which may interfere
+
+pick a value large enough to avoid retries on most inputs
+*/
+#define qh_JOGGLEdefault 30000.0
+
+/*-<a                             href="qh-user_r.htm#TOC"
+>--------------------------------</a><a name="JOGGLEincrease">-</a>
+
+qh_JOGGLEincrease
+factor to increase qh.JOGGLEmax on qh_JOGGLEretry or qh_JOGGLEagain
+*/
+#define qh_JOGGLEincrease 10.0
+
+/*-<a                             href="qh-user_r.htm#TOC"
+>--------------------------------</a><a name="JOGGLEretry">-</a>
+
+qh_JOGGLEretry
+if ZZretry = qh_JOGGLEretry, increase qh.JOGGLEmax
+
+notes:
+try twice at the original value in case of bad luck the first time
+*/
+#define qh_JOGGLEretry 2
+
+/*-<a                             href="qh-user_r.htm#TOC"
+>--------------------------------</a><a name="JOGGLEagain">-</a>
+
+qh_JOGGLEagain
+every following qh_JOGGLEagain, increase qh.JOGGLEmax
+
+notes:
+1 is OK since it's already failed qh_JOGGLEretry times
+*/
+#define qh_JOGGLEagain 1
+
+/*-<a                             href="qh-user_r.htm#TOC"
+>--------------------------------</a><a name="JOGGLEmaxincrease">-</a>
+
+qh_JOGGLEmaxincrease
+maximum qh.JOGGLEmax due to qh_JOGGLEincrease
+relative to qh.MAXwidth
+
+notes:
+qh.joggleinput will retry at this value until qh_JOGGLEmaxretry
+*/
+#define qh_JOGGLEmaxincrease 1e-2
+
+/*-<a                             href="qh-user_r.htm#TOC"
+>--------------------------------</a><a name="JOGGLEmaxretry">-</a>
+
+qh_JOGGLEmaxretry
+stop after qh_JOGGLEmaxretry attempts
+*/
+#define qh_JOGGLEmaxretry 100
+
+/*============================================================*/
+/*============= performance related constants ================*/
+/*============================================================*/
+
+/*-<a                             href="qh-user_r.htm#TOC"
+  >--------------------------------</a><a name="HASHfactor">-</a>
+
+  qh_HASHfactor
+    total hash slots / used hash slots.  Must be at least 1.1.
+
+  notes:
+    =2 for at worst 50% occupancy for qh.hash_table and normally 25% occupancy
+*/
+#define qh_HASHfactor 2
+
+/*-<a                             href="qh-user_r.htm#TOC"
+  >--------------------------------</a><a name="VERIFYdirect">-</a>
+
+  qh_VERIFYdirect
+    with 'Tv' verify all points against all facets if op count is smaller
+
+  notes:
+    if greater, calls qh_check_bestdist() instead
+*/
+#define qh_VERIFYdirect 1000000
+
+/*-<a                             href="qh-user_r.htm#TOC"
+  >--------------------------------</a><a name="INITIALsearch">-</a>
+
+  qh_INITIALsearch
+     if qh_INITIALmax, search points up to this dimension
+*/
+#define qh_INITIALsearch 6
+
+/*-<a                             href="qh-user_r.htm#TOC"
+  >--------------------------------</a><a name="INITIALmax">-</a>
+
+  qh_INITIALmax
+    if dim >= qh_INITIALmax, use min/max coordinate points for initial simplex
+
+  notes:
+    from points with non-zero determinants
+    use option 'Qs' to override (much slower)
+*/
+#define qh_INITIALmax 8
+
+/*============================================================*/
+/*============= memory constants =============================*/
+/*============================================================*/
+
+/*-<a                             href="qh-user_r.htm#TOC"
+  >--------------------------------</a><a name="MEMalign">-</a>
+
+  qh_MEMalign
+    memory alignment for qh_meminitbuffers() in global_r.c
+
+  notes:
+    to avoid bus errors, memory allocation must consider alignment requirements.
+    malloc() automatically takes care of alignment.   Since mem_r.c manages
+    its own memory, we need to explicitly specify alignment in
+    qh_meminitbuffers().
+
+    A safe choice is sizeof(double).  sizeof(float) may be used if doubles
+    do not occur in data structures and pointers are the same size.  Be careful
+    of machines (e.g., DEC Alpha) with large pointers.
+
+    If using gcc, best alignment is [fmax_() is defined in geom_r.h]
+              #define qh_MEMalign fmax_(__alignof__(realT),__alignof__(void *))
+*/
+#define qh_MEMalign ((int)(fmax_(sizeof(realT), sizeof(void *))))
+
+/*-<a                             href="qh-user_r.htm#TOC"
+  >--------------------------------</a><a name="MEMbufsize">-</a>
+
+  qh_MEMbufsize
+    size of additional memory buffers
+
+  notes:
+    used for qh_meminitbuffers() in global_r.c
+*/
+#define qh_MEMbufsize 0x10000       /* allocate 64K memory buffers */
+
+/*-<a                             href="qh-user_r.htm#TOC"
+  >--------------------------------</a><a name="MEMinitbuf">-</a>
+
+  qh_MEMinitbuf
+    size of initial memory buffer
+
+  notes:
+    use for qh_meminitbuffers() in global_r.c
+*/
+#define qh_MEMinitbuf 0x20000      /* initially allocate 128K buffer */
+
+/*-<a                             href="qh-user_r.htm#TOC"
+  >--------------------------------</a><a name="INFINITE">-</a>
+
+  qh_INFINITE
+    on output, indicates Voronoi center at infinity
+*/
+#define qh_INFINITE  -10.101
+
+/*-<a                             href="qh-user_r.htm#TOC"
+  >--------------------------------</a><a name="DEFAULTbox">-</a>
+
+  qh_DEFAULTbox
+    default box size (Geomview expects 0.5)
+
+  qh_DEFAULTbox
+    default box size for integer coorindate (rbox only)
+*/
+#define qh_DEFAULTbox 0.5
+#define qh_DEFAULTzbox 1e6
+
+/*============================================================*/
+/*============= conditional compilation ======================*/
+/*============================================================*/
+
+/*-<a                             href="qh-user_r.htm#TOC"
+  >--------------------------------</a><a name="compiler">-</a>
+
+  __cplusplus
+    defined by C++ compilers
+
+  __MSC_VER
+    defined by Microsoft Visual C++
+
+  __MWERKS__ && __INTEL__
+    defined by Metrowerks when compiling for Windows (not Intel-based Macintosh)
+
+  __MWERKS__ && __POWERPC__
+    defined by Metrowerks when compiling for PowerPC-based Macintosh
+
+  __STDC__
+    defined for strict ANSI C
+*/
+
+/*-<a                             href="qh-user_r.htm#TOC"
+  >--------------------------------</a><a name="COMPUTEfurthest">-</a>
+
+  qh_COMPUTEfurthest
+    compute furthest distance to an outside point instead of storing it with the facet
+    =1 to compute furthest
+
+  notes:
+    computing furthest saves memory but costs time
+      about 40% more distance tests for partitioning
+      removes facet->furthestdist
+*/
+#define qh_COMPUTEfurthest 0
+
+/*-<a                             href="qh-user_r.htm#TOC"
+  >--------------------------------</a><a name="KEEPstatistics">-</a>
+
+  qh_KEEPstatistics
+    =0 removes most of statistic gathering and reporting
+
+  notes:
+    if 0, code size is reduced by about 4%.
+*/
+#define qh_KEEPstatistics 1
+
+/*-<a                             href="qh-user_r.htm#TOC"
+  >--------------------------------</a><a name="MAXoutside">-</a>
+
+  qh_MAXoutside
+    record outer plane for each facet
+    =1 to record facet->maxoutside
+
+  notes:
+    this takes a realT per facet and slightly slows down qhull
+    it produces better outer planes for geomview output
+*/
+#define qh_MAXoutside 1
+
+/*-<a                             href="qh-user_r.htm#TOC"
+  >--------------------------------</a><a name="NOmerge">-</a>
+
+  qh_NOmerge
+    disables facet merging if defined
+
+  notes:
+    This saves about 10% space.
+
+    Unless 'Q0'
+      qh_NOmerge sets 'QJ' to avoid precision errors
+
+    #define qh_NOmerge
+
+  see:
+    <a href="mem_r.h#NOmem">qh_NOmem</a> in mem_r.c
+
+    see user_r.c/user_eg.c for removing io_r.o
+*/
+
+/*-<a                             href="qh-user_r.htm#TOC"
+  >--------------------------------</a><a name="NOtrace">-</a>
+
+  qh_NOtrace
+    no tracing if defined
+
+  notes:
+    This saves about 5% space.
+
+    #define qh_NOtrace
+*/
+
+#if 0  /* sample code */
+    exitcode= qh_new_qhull(qhT *qh, dim, numpoints, points, ismalloc,
+                      flags, outfile, errfile);
+    qh_freeqhull(qhT *qh, !qh_ALL); /* frees long memory used by second call */
+    qh_memfreeshort(qhT *qh, &curlong, &totlong);  /* frees short memory and memory allocator */
+#endif
+
+/*-<a                             href="qh-user_r.htm#TOC"
+  >--------------------------------</a><a name="QUICKhelp">-</a>
+
+  qh_QUICKhelp
+    =1 to use abbreviated help messages, e.g., for degenerate inputs
+*/
+#define qh_QUICKhelp    0
+
+/*============================================================*/
+/*============= -merge constants- ============================*/
+/*============================================================*/
+/*
+   These constants effect facet merging.  You probably will not need
+   to modify them.  They effect the performance of facet merging.
+*/
+
+/*-<a                             href="qh-user_r.htm#TOC"
+  >--------------------------------</a><a name="DIMmergeVertex">-</a>
+
+  qh_DIMmergeVertex
+    max dimension for vertex merging (it is not effective in high-d)
+*/
+#define qh_DIMmergeVertex 6
+
+/*-<a                             href="qh-user_r.htm#TOC"
+  >--------------------------------</a><a name="DIMreduceBuild">-</a>
+
+  qh_DIMreduceBuild
+     max dimension for vertex reduction during build (slow in high-d)
+*/
+#define qh_DIMreduceBuild 5
+
+/*-<a                             href="qh-user_r.htm#TOC"
+  >--------------------------------</a><a name="BESTcentrum">-</a>
+
+  qh_BESTcentrum
+     if > 2*dim+n vertices, qh_findbestneighbor() tests centrums (faster)
+     else, qh_findbestneighbor() tests all vertices (much better merges)
+
+  qh_BESTcentrum2
+     if qh_BESTcentrum2 * DIM3 + BESTcentrum < #vertices tests centrums
+*/
+#define qh_BESTcentrum 20
+#define qh_BESTcentrum2 2
+
+/*-<a                             href="qh-user_r.htm#TOC"
+  >--------------------------------</a><a name="BESTnonconvex">-</a>
+
+  qh_BESTnonconvex
+    if > dim+n neighbors, qh_findbestneighbor() tests nonconvex ridges.
+
+  notes:
+    It is needed because qh_findbestneighbor is slow for large facets
+*/
+#define qh_BESTnonconvex 15
+
+/*-<a                             href="qh-user_r.htm#TOC"
+  >--------------------------------</a><a name="MAXnewmerges">-</a>
+
+  qh_MAXnewmerges
+    if >n newmerges, qh_merge_nonconvex() calls qh_reducevertices_centrums.
+
+  notes:
+    It is needed because postmerge can merge many facets at once
+*/
+#define qh_MAXnewmerges 2
+
+/*-<a                             href="qh-user_r.htm#TOC"
+  >--------------------------------</a><a name="MAXnewcentrum">-</a>
+
+  qh_MAXnewcentrum
+    if <= dim+n vertices (n approximates the number of merges),
+      reset the centrum in qh_updatetested() and qh_mergecycle_facets()
+
+  notes:
+    needed to reduce cost and because centrums may move too much if
+    many vertices in high-d
+*/
+#define qh_MAXnewcentrum 5
+
+/*-<a                             href="qh-user_r.htm#TOC"
+  >--------------------------------</a><a name="COPLANARratio">-</a>
+
+  qh_COPLANARratio
+    for 3-d+ merging, qh.MINvisible is n*premerge_centrum
+
+  notes:
+    for non-merging, it's DISTround
+*/
+#define qh_COPLANARratio 3
+
+/*-<a                             href="qh-user_r.htm#TOC"
+  >--------------------------------</a><a name="DISToutside">-</a>
+
+  qh_DISToutside
+    When is a point clearly outside of a facet?
+    Stops search in qh_findbestnew or qh_partitionall
+    qh_findbest uses qh.MINoutside since since it is only called if no merges.
+
+  notes:
+    'Qf' always searches for best facet
+    if !qh.MERGING, same as qh.MINoutside.
+    if qh_USEfindbestnew, increase value since neighboring facets may be ill-behaved
+      [Note: Zdelvertextot occurs normally with interior points]
+            RBOX 1000 s Z1 G1e-13 t1001188774 | QHULL Tv
+    When there is a sharp edge, need to move points to a
+    clearly good facet; otherwise may be lost in another partitioning.
+    if too big then O(n^2) behavior for partitioning in cone
+    if very small then important points not processed
+    Needed in qh_partitionall for
+      RBOX 1000 s Z1 G1e-13 t1001032651 | QHULL Tv
+    Needed in qh_findbestnew for many instances of
+      RBOX 1000 s Z1 G1e-13 t | QHULL Tv
+
+  See:
+    qh_DISToutside -- when is a point clearly outside of a facet
+    qh_SEARCHdist -- when is facet coplanar with the best facet?
+    qh_USEfindbestnew -- when to use qh_findbestnew for qh_partitionpoint()
+*/
+#define qh_DISToutside ((qh_USEfindbestnew ? 2 : 1) * \
+     fmax_((qh->MERGING ? 2 : 1)*qh->MINoutside, qh->max_outside))
+
+/*-<a                             href="qh-user_r.htm#TOC"
+  >--------------------------------</a><a name="RATIOnearinside">-</a>
+
+  qh_RATIOnearinside
+    ratio of qh.NEARinside to qh.ONEmerge for retaining inside points for
+    qh_check_maxout().
+
+  notes:
+    This is overkill since do not know the correct value.
+    It effects whether 'Qc' reports all coplanar points
+    Not used for 'd' since non-extreme points are coplanar
+*/
+#define qh_RATIOnearinside 5
+
+/*-<a                             href="qh-user_r.htm#TOC"
+  >--------------------------------</a><a name="SEARCHdist">-</a>
+
+  qh_SEARCHdist
+    When is a facet coplanar with the best facet?
+    qh_findbesthorizon: all coplanar facets of the best facet need to be searched.
+
+  See:
+    qh_DISToutside -- when is a point clearly outside of a facet
+    qh_SEARCHdist -- when is facet coplanar with the best facet?
+    qh_USEfindbestnew -- when to use qh_findbestnew for qh_partitionpoint()
+*/
+#define qh_SEARCHdist ((qh_USEfindbestnew ? 2 : 1) * \
+      (qh->max_outside + 2 * qh->DISTround + fmax_( qh->MINvisible, qh->MAXcoplanar)));
+
+/*-<a                             href="qh-user_r.htm#TOC"
+  >--------------------------------</a><a name="USEfindbestnew">-</a>
+
+  qh_USEfindbestnew
+     Always use qh_findbestnew for qh_partitionpoint, otherwise use
+     qh_findbestnew if merged new facet or sharpnewfacets.
+
+  See:
+    qh_DISToutside -- when is a point clearly outside of a facet
+    qh_SEARCHdist -- when is facet coplanar with the best facet?
+    qh_USEfindbestnew -- when to use qh_findbestnew for qh_partitionpoint()
+*/
+#define qh_USEfindbestnew (zzval_(Ztotmerge) > 50)
+
+/*-<a                             href="qh-user_r.htm#TOC"
+  >--------------------------------</a><a name="WIDEcoplanar">-</a>
+
+  qh_WIDEcoplanar
+    n*MAXcoplanar or n*MINvisible for a WIDEfacet
+
+    if vertex is further than qh.WIDEfacet from the hyperplane
+    then its ridges are not counted in computing the area, and
+    the facet's centrum is frozen.
+
+  notes:
+   qh.WIDEfacet= max(qh.MAXoutside,qh_WIDEcoplanar*qh.MAXcoplanar,
+      qh_WIDEcoplanar * qh.MINvisible);
+*/
+#define qh_WIDEcoplanar 6
+
+/*-<a                             href="qh-user_r.htm#TOC"
+  >--------------------------------</a><a name="WIDEduplicate">-</a>
+
+  qh_WIDEduplicate
+    Merge ratio for errexit from qh_forcedmerges due to duplicate ridge
+    Override with option Q12 no-wide-duplicate
+
+    Notes:
+      Merging a duplicate ridge can lead to very wide facets.
+      A future release of qhull will avoid duplicate ridges by removing duplicate sub-ridges from the horizon
+*/
+#define qh_WIDEduplicate 100
+
+/*-<a                             href="qh-user_r.htm#TOC"
+  >--------------------------------</a><a name="MAXnarrow">-</a>
+
+  qh_MAXnarrow
+    max. cosine in initial hull that sets qh.NARROWhull
+
+  notes:
+    If qh.NARROWhull, the initial partition does not make
+    coplanar points.  If narrow, a coplanar point can be
+    coplanar to two facets of opposite orientations and
+    distant from the exact convex hull.
+
+    Conservative estimate.  Don't actually see problems until it is -1.0
+*/
+#define qh_MAXnarrow -0.99999999
+
+/*-<a                             href="qh-user_r.htm#TOC"
+  >--------------------------------</a><a name="WARNnarrow">-</a>
+
+  qh_WARNnarrow
+    max. cosine in initial hull to warn about qh.NARROWhull
+
+  notes:
+    this is a conservative estimate.
+    Don't actually see problems until it is -1.0.  See qh-impre.htm
+*/
+#define qh_WARNnarrow -0.999999999999999
+
+/*-<a                             href="qh-user_r.htm#TOC"
+  >--------------------------------</a><a name="ZEROdelaunay">-</a>
+
+  qh_ZEROdelaunay
+    a zero Delaunay facet occurs for input sites coplanar with their convex hull
+    the last normal coefficient of a zero Delaunay facet is within
+        qh_ZEROdelaunay * qh.ANGLEround of 0
+
+  notes:
+    qh_ZEROdelaunay does not allow for joggled input ('QJ').
+
+    You can avoid zero Delaunay facets by surrounding the input with a box.
+
+    Use option 'PDk:-n' to explicitly define zero Delaunay facets
+      k= dimension of input sites (e.g., 3 for 3-d Delaunay triangulation)
+      n= the cutoff for zero Delaunay facets (e.g., 'PD3:-1e-12')
+*/
+#define qh_ZEROdelaunay 2
+
+/*============================================================*/
+/*============= Microsoft DevStudio ==========================*/
+/*============================================================*/
+
+/*
+   Finding Memory Leaks Using the CRT Library
+   https://msdn.microsoft.com/en-us/library/x98tx3cf(v=vs.100).aspx
+
+   Reports enabled in qh_lib_check for Debug window and stderr
+
+   From 2005=>msvcr80d, 2010=>msvcr100d, 2012=>msvcr110d
+
+   Watch: {,,msvcr80d.dll}_crtBreakAlloc  Value from {n} in the leak report
+   _CrtSetBreakAlloc(689); // qh_lib_check() [global_r.c]
+
+   Examples
+     http://free-cad.sourceforge.net/SrcDocu/d2/d7f/MemDebug_8cpp_source.html
+     https://github.com/illlust/Game/blob/master/library/MemoryLeak.cpp
+*/
+#if 0   /* off (0) by default for QHULL_CRTDBG */
+#define QHULL_CRTDBG
+#endif
+
+#if defined(_MSC_VER) && defined(_DEBUG) && defined(QHULL_CRTDBG)
+#define _CRTDBG_MAP_ALLOC
+#include <stdlib.h>
+#include <crtdbg.h>
+#endif
+
+#endif /* qh_DEFuser */
+
+
+
diff --git a/xs/src/qhull/src/libqhull_r/usermem_r.c b/xs/src/qhull/src/libqhull_r/usermem_r.c
new file mode 100644
index 0000000000..3297b03185
--- /dev/null
+++ b/xs/src/qhull/src/libqhull_r/usermem_r.c
@@ -0,0 +1,94 @@
+/*<html><pre>  -<a                             href="qh-user_r.htm"
+  >-------------------------------</a><a name="TOP">-</a>
+
+   usermem_r.c
+   qh_exit(), qh_free(), and qh_malloc()
+
+   See README.txt.
+
+   If you redefine one of these functions you must redefine all of them.
+   If you recompile and load this file, then usermem.o will not be loaded
+   from qhull.a or qhull.lib
+
+   See libqhull_r.h for data structures, macros, and user-callable functions.
+   See user_r.c for qhull-related, redefinable functions
+   see user_r.h for user-definable constants
+   See userprintf_r.c for qh_fprintf and userprintf_rbox_r.c for qh_fprintf_rbox
+
+   Please report any errors that you fix to qhull@qhull.org
+*/
+
+#include "libqhull_r.h"
+
+#include <stdarg.h>
+#include <stdlib.h>
+
+/*-<a                             href="qh-user_r.htm#TOC"
+  >-------------------------------</a><a name="qh_exit">-</a>
+
+  qh_exit( exitcode )
+    exit program
+
+  notes:
+    qh_exit() is called when qh_errexit() and longjmp() are not available.
+
+    This is the only use of exit() in Qhull
+    To replace qh_exit with 'throw', see libqhullcpp/usermem_r-cpp.cpp
+*/
+void qh_exit(int exitcode) {
+    exit(exitcode);
+} /* exit */
+
+/*-<a                             href="qh-user_r.htm#TOC"
+  >-------------------------------</a><a name="qh_fprintf_stderr">-</a>
+
+  qh_fprintf_stderr( msgcode, format, list of args )
+    fprintf to stderr with msgcode (non-zero)
+
+  notes:
+    qh_fprintf_stderr() is called when qh->ferr is not defined, usually due to an initialization error
+    
+    It is typically followed by qh_errexit().
+
+    Redefine this function to avoid using stderr
+
+    Use qh_fprintf [userprintf_r.c] for normal printing
+*/
+void qh_fprintf_stderr(int msgcode, const char *fmt, ... ) {
+    va_list args;
+
+    va_start(args, fmt);
+    if(msgcode)
+      fprintf(stderr, "QH%.4d ", msgcode);
+    vfprintf(stderr, fmt, args);
+    va_end(args);
+} /* fprintf_stderr */
+
+/*-<a                             href="qh-user_r.htm#TOC"
+>-------------------------------</a><a name="qh_free">-</a>
+
+  qh_free(qhT *qh, mem )
+    free memory
+
+  notes:
+    same as free()
+    No calls to qh_errexit() 
+*/
+void qh_free(void *mem) {
+    free(mem);
+} /* free */
+
+/*-<a                             href="qh-user_r.htm#TOC"
+    >-------------------------------</a><a name="qh_malloc">-</a>
+
+    qh_malloc( mem )
+      allocate memory
+
+    notes:
+      same as malloc()
+*/
+void *qh_malloc(size_t size) {
+    return malloc(size);
+} /* malloc */
+
+
diff --git a/xs/src/qhull/src/libqhull_r/userprintf_r.c b/xs/src/qhull/src/libqhull_r/userprintf_r.c
new file mode 100644
index 0000000000..6004491a1c
--- /dev/null
+++ b/xs/src/qhull/src/libqhull_r/userprintf_r.c
@@ -0,0 +1,65 @@
+/*<html><pre>  -<a                             href="qh-user_r.htm"
+  >-------------------------------</a><a name="TOP">-</a>
+
+   userprintf_r.c
+   qh_fprintf()
+
+   see README.txt  see COPYING.txt for copyright information.
+
+   If you recompile and load this file, then userprintf_r.o will not be loaded
+   from qhull.a or qhull.lib
+
+   See libqhull_r.h for data structures, macros, and user-callable functions.
+   See user_r.c for qhull-related, redefinable functions
+   see user_r.h for user-definable constants
+   See usermem_r.c for qh_exit(), qh_free(), and qh_malloc()
+   see Qhull.cpp and RboxPoints.cpp for examples.
+
+   Please report any errors that you fix to qhull@qhull.org
+*/
+
+#include "libqhull_r.h"
+
+#include <stdarg.h>
+#include <stdio.h>
+#include <stdlib.h>
+
+/*-<a                             href="qh-user_r.htm#TOC"
+   >-------------------------------</a><a name="qh_fprintf">-</a>
+
+   qh_fprintf(qh, fp, msgcode, format, list of args )
+     print arguments to *fp according to format
+     Use qh_fprintf_rbox() for rboxlib_r.c
+
+   notes:
+     same as fprintf()
+     fgets() is not trapped like fprintf()
+     exit qh_fprintf via qh_errexit()
+     may be called for errors in qh_initstatistics and qh_meminit
+*/
+
+void qh_fprintf(qhT *qh, FILE *fp, int msgcode, const char *fmt, ... ) {
+    va_list args;
+
+    if (!fp) {
+        if(!qh){
+            qh_fprintf_stderr(6241, "userprintf_r.c: fp and qh not defined for qh_fprintf '%s'", fmt);
+            qh_exit(qhmem_ERRqhull);  /* can not use qh_errexit() */
+        }
+        /* could use qh->qhmem.ferr, but probably better to be cautious */
+        qh_fprintf_stderr(6232, "Qhull internal error (userprintf_r.c): fp is 0.  Wrong qh_fprintf called.\n");
+        qh_errexit(qh, 6232, NULL, NULL);
+    }
+    va_start(args, fmt);
+    if (qh && qh->ANNOTATEoutput) {
+      fprintf(fp, "[QH%.4d]", msgcode);
+    }else if (msgcode >= MSG_ERROR && msgcode < MSG_STDERR ) {
+      fprintf(fp, "QH%.4d ", msgcode);
+    }
+    vfprintf(fp, fmt, args);
+    va_end(args);
+
+    /* Place debugging traps here. Use with option 'Tn' */
+
+} /* qh_fprintf */
+
diff --git a/xs/src/qhull/src/libqhull_r/userprintf_rbox_r.c b/xs/src/qhull/src/libqhull_r/userprintf_rbox_r.c
new file mode 100644
index 0000000000..1e721a22ae
--- /dev/null
+++ b/xs/src/qhull/src/libqhull_r/userprintf_rbox_r.c
@@ -0,0 +1,53 @@
+/*<html><pre>  -<a                             href="qh-user_r.htm"
+  >-------------------------------</a><a name="TOP">-</a>
+
+   userprintf_rbox_r.c
+   qh_fprintf_rbox()
+
+   see README.txt  see COPYING.txt for copyright information.
+
+   If you recompile and load this file, then userprintf_rbox_r.o will not be loaded
+   from qhull.a or qhull.lib
+
+   See libqhull_r.h for data structures, macros, and user-callable functions.
+   See user_r.c for qhull-related, redefinable functions
+   see user_r.h for user-definable constants
+   See usermem_r.c for qh_exit(), qh_free(), and qh_malloc()
+   see Qhull.cpp and RboxPoints.cpp for examples.
+
+   Please report any errors that you fix to qhull@qhull.org
+*/
+
+#include "libqhull_r.h"
+
+#include <stdarg.h>
+#include <stdio.h>
+#include <stdlib.h>
+
+/*-<a                             href="qh-user_r.htm#TOC"
+   >-------------------------------</a><a name="qh_fprintf_rbox">-</a>
+
+   qh_fprintf_rbox(qh, fp, msgcode, format, list of args )
+     print arguments to *fp according to format
+     Use qh_fprintf_rbox() for rboxlib_r.c
+
+   notes:
+     same as fprintf()
+     fgets() is not trapped like fprintf()
+     exit qh_fprintf_rbox via qh_errexit_rbox()
+*/
+
+void qh_fprintf_rbox(qhT *qh, FILE *fp, int msgcode, const char *fmt, ... ) {
+    va_list args;
+
+    if (!fp) {
+        qh_fprintf_stderr(6231, "Qhull internal error (userprintf_rbox_r.c): fp is 0.  Wrong qh_fprintf_rbox called.\n");
+        qh_errexit_rbox(qh, 6231);
+    }
+    if (msgcode >= MSG_ERROR && msgcode < MSG_STDERR)
+      fprintf(fp, "QH%.4d ", msgcode);
+    va_start(args, fmt);
+    vfprintf(fp, fmt, args);
+    va_end(args);
+} /* qh_fprintf_rbox */
+
diff --git a/xs/src/qhull/src/libqhullcpp/Coordinates.cpp b/xs/src/qhull/src/libqhullcpp/Coordinates.cpp
new file mode 100644
index 0000000000..806b438aba
--- /dev/null
+++ b/xs/src/qhull/src/libqhullcpp/Coordinates.cpp
@@ -0,0 +1,198 @@
+/****************************************************************************
+**
+** Copyright (c) 2009-2015 C.B. Barber. All rights reserved.
+** $Id: //main/2015/qhull/src/libqhullcpp/Coordinates.cpp#4 $$Change: 2066 $
+** $DateTime: 2016/01/18 19:29:17 $$Author: bbarber $
+**
+****************************************************************************/
+
+#include "libqhullcpp/Coordinates.h"
+
+#include "libqhullcpp/functionObjects.h"
+#include "libqhullcpp/QhullError.h"
+
+#include <iostream>
+#include <iterator>
+#include <algorithm>
+
+#ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
+#endif
+
+namespace orgQhull {
+
+#//! Coordinates -- vector of coordT (normally double)
+
+#//!\name Constructor
+
+#//!\name Element access
+
+// Inefficient without result-value-optimization or implicitly shared object
+Coordinates Coordinates::
+mid(countT idx, countT length) const
+{
+    countT newLength= length;
+    if(length<0 || idx+length > count()){
+        newLength= count()-idx;
+    }
+    Coordinates result;
+    if(newLength>0){
+        std::copy(begin()+idx, begin()+(idx+newLength), std::back_inserter(result));
+    }
+    return result;
+}//mid
+
+coordT Coordinates::
+value(countT idx, const coordT &defaultValue) const
+{
+    return ((idx < 0 || idx >= count()) ? defaultValue : (*this)[idx]);
+}//value
+
+#//!\name GetSet
+
+Coordinates Coordinates::
+operator+(const Coordinates &other) const
+{
+    Coordinates result(*this);
+    std::copy(other.begin(), other.end(), std::back_inserter(result));
+    return result;
+}//operator+
+
+Coordinates & Coordinates::
+operator+=(const Coordinates &other)
+{
+    if(&other==this){
+        Coordinates clone(other);
+        std::copy(clone.begin(), clone.end(), std::back_inserter(*this));
+    }else{
+        std::copy(other.begin(), other.end(), std::back_inserter(*this));
+    }
+    return *this;
+}//operator+=
+
+#//!\name Read-write
+
+void Coordinates::
+append(int pointDimension, coordT *c)
+{
+    if(c){
+        coordT *p= c;
+        for(int i= 0; i<pointDimension; ++i){
+            coordinate_array.push_back(*p++);
+        }
+    }
+}//append dim coordT
+
+coordT Coordinates::
+takeAt(countT idx)
+{
+    coordT c= at(idx);
+    erase(begin()+idx);
+    return c;
+}//takeAt
+
+coordT Coordinates::
+takeLast()
+{
+    coordT c= last();
+    removeLast();
+    return c;
+}//takeLast
+
+void Coordinates::
+swap(countT idx, countT other)
+{
+    coordT c= at(idx);
+    at(idx)= at(other);
+    at(other)= c;
+}//swap
+
+#//!\name Search
+
+bool Coordinates::
+contains(const coordT &t) const
+{
+    CoordinatesIterator i(*this);
+    return i.findNext(t);
+}//contains
+
+countT Coordinates::
+count(const coordT &t) const
+{
+    CoordinatesIterator i(*this);
+    countT result= 0;
+    while(i.findNext(t)){
+        ++result;
+    }
+    return result;
+}//count
+
+countT Coordinates::
+indexOf(const coordT &t, countT from) const
+{
+    if(from<0){
+        from += count();
+        if(from<0){
+            from= 0;
+        }
+    }
+    if(from<count()){
+        const_iterator i= begin()+from;
+        while(i!=constEnd()){
+            if(*i==t){
+                return (static_cast<countT>(i-begin())); // WARN64 coordinate index
+            }
+            ++i;
+        }
+    }
+    return -1;
+}//indexOf
+
+countT Coordinates::
+lastIndexOf(const coordT &t, countT from) const
+{
+    if(from<0){
+        from += count();
+    }else if(from>=count()){
+        from= count()-1;
+    }
+    if(from>=0){
+        const_iterator i= begin()+from+1;
+        while(i-- != constBegin()){
+            if(*i==t){
+                return (static_cast<countT>(i-begin())); // WARN64 coordinate index
+            }
+        }
+    }
+    return -1;
+}//lastIndexOf
+
+void Coordinates::
+removeAll(const coordT &t)
+{
+    MutableCoordinatesIterator i(*this);
+    while(i.findNext(t)){
+        i.remove();
+    }
+}//removeAll
+
+}//namespace orgQhull
+
+#//!\name Global functions
+
+using std::endl;
+using std::istream;
+using std::ostream;
+using std::string;
+using std::ws;
+using orgQhull::Coordinates;
+
+ostream &
+operator<<(ostream &os, const Coordinates &cs)
+{
+    Coordinates::const_iterator c= cs.begin();
+    for(countT i=cs.count(); i--; ){
+        os << *c++ << " ";
+    }
+    return os;
+}//operator<<
+
diff --git a/xs/src/qhull/src/libqhullcpp/Coordinates.h b/xs/src/qhull/src/libqhullcpp/Coordinates.h
new file mode 100644
index 0000000000..df8bd11386
--- /dev/null
+++ b/xs/src/qhull/src/libqhullcpp/Coordinates.h
@@ -0,0 +1,303 @@
+/****************************************************************************
+**
+** Copyright (c) 2009-2015 C.B. Barber. All rights reserved.
+** $Id: //main/2015/qhull/src/libqhullcpp/Coordinates.h#6 $$Change: 2079 $
+** $DateTime: 2016/02/07 17:43:34 $$Author: bbarber $
+**
+****************************************************************************/
+
+#ifndef QHCOORDINATES_H
+#define QHCOORDINATES_H
+
+#include "libqhull_r/qhull_ra.h"
+#include "libqhullcpp/QhullError.h"
+#include "libqhullcpp/QhullIterator.h"
+
+#include <cstddef> // ptrdiff_t, size_t
+#include <ostream>
+// Requires STL vector class.  Can use with another vector class such as QList.
+#include <vector>
+
+namespace orgQhull {
+
+#//!\name Defined here
+    //! An std::vector of point coordinates independent of dimension
+    //! Used by PointCoordinates for RboxPoints and by Qhull for feasiblePoint
+    //! A QhullPoint refers to previously allocated coordinates
+    class Coordinates;
+    class MutableCoordinatesIterator;
+
+class Coordinates {
+
+private:
+#//!\name Fields
+    std::vector<coordT> coordinate_array;
+
+public:
+#//!\name Subtypes
+
+    class const_iterator;
+    class iterator;
+    typedef iterator Iterator;
+    typedef const_iterator ConstIterator;
+
+    typedef coordT              value_type;
+    typedef const value_type   *const_pointer;
+    typedef const value_type &  const_reference;
+    typedef value_type *        pointer;
+    typedef value_type &        reference;
+    typedef ptrdiff_t           difference_type;
+    typedef countT              size_type;
+
+#//!\name Construct
+                        Coordinates() {};
+    explicit            Coordinates(const std::vector<coordT> &other) : coordinate_array(other) {}
+                        Coordinates(const Coordinates &other) : coordinate_array(other.coordinate_array) {}
+    Coordinates &       operator=(const Coordinates &other) { coordinate_array= other.coordinate_array; return *this; }
+    Coordinates &       operator=(const std::vector<coordT> &other) { coordinate_array= other; return *this; }
+                        ~Coordinates() {}
+
+#//!\name Conversion
+
+#ifndef QHULL_NO_STL
+    std::vector<coordT> toStdVector() const { return coordinate_array; }
+#endif //QHULL_NO_STL
+#ifdef QHULL_USES_QT
+    QList<coordT>       toQList() const;
+#endif //QHULL_USES_QT
+
+#//!\name GetSet
+    countT              count() const { return static_cast<countT>(size()); }
+    coordT *            data() { return isEmpty() ? 0 : &at(0); }
+    const coordT *      data() const { return const_cast<const pointT*>(isEmpty() ? 0 : &at(0)); }
+    bool                isEmpty() const { return coordinate_array.empty(); }
+    bool                operator==(const Coordinates &other) const  { return coordinate_array==other.coordinate_array; }
+    bool                operator!=(const Coordinates &other) const  { return coordinate_array!=other.coordinate_array; }
+    size_t              size() const { return coordinate_array.size(); }
+
+#//!\name Element access
+    coordT &            at(countT idx) { return coordinate_array.at(idx); }
+    const coordT &      at(countT idx) const { return coordinate_array.at(idx); }
+    coordT &            back() { return coordinate_array.back(); }
+    const coordT &      back() const { return coordinate_array.back(); }
+    coordT &            first() { return front(); }
+    const coordT &      first() const { return front(); }
+    coordT &            front() { return coordinate_array.front(); }
+    const coordT &      front() const { return coordinate_array.front(); }
+    coordT &            last() { return back(); }
+    const coordT &      last() const { return back(); }
+    Coordinates         mid(countT idx, countT length= -1) const; //!<\todo countT -1 indicates
+    coordT &            operator[](countT idx) { return coordinate_array.operator[](idx); }
+    const coordT &      operator[](countT idx) const { return coordinate_array.operator[](idx); }
+    coordT              value(countT idx, const coordT &defaultValue) const;
+
+#//!\name Iterator
+    iterator            begin() { return iterator(coordinate_array.begin()); }
+    const_iterator      begin() const { return const_iterator(coordinate_array.begin()); }
+    const_iterator      constBegin() const { return begin(); }
+    const_iterator      constEnd() const { return end(); }
+    iterator            end() { return iterator(coordinate_array.end()); }
+    const_iterator      end() const { return const_iterator(coordinate_array.end()); }
+
+#//!\name GetSet
+    Coordinates         operator+(const Coordinates &other) const;
+
+#//!\name Modify
+    void                append(int pointDimension, coordT *c);
+    void                append(const coordT &c) { push_back(c); }
+    void                clear() { coordinate_array.clear(); }
+    iterator            erase(iterator idx) { return iterator(coordinate_array.erase(idx.base())); }
+    iterator            erase(iterator beginIterator, iterator endIterator) { return iterator(coordinate_array.erase(beginIterator.base(), endIterator.base())); }
+    void                insert(countT before, const coordT &c) { insert(begin()+before, c); }
+    iterator            insert(iterator before, const coordT &c) { return iterator(coordinate_array.insert(before.base(), c)); }
+    void                move(countT from, countT to) { insert(to, takeAt(from)); }
+    Coordinates &       operator+=(const Coordinates &other);
+    Coordinates &       operator+=(const coordT &c) { append(c); return *this; }
+    Coordinates &       operator<<(const Coordinates &other) { return *this += other; }
+    Coordinates &       operator<<(const coordT &c) { return *this += c; }
+    void                pop_back() { coordinate_array.pop_back(); }
+    void                pop_front() { removeFirst(); }
+    void                prepend(const coordT &c) { insert(begin(), c); }
+    void                push_back(const coordT &c) { coordinate_array.push_back(c); }
+    void                push_front(const coordT &c) { insert(begin(), c); }
+                        //removeAll below
+    void                removeAt(countT idx) { erase(begin()+idx); }
+    void                removeFirst() { erase(begin()); }
+    void                removeLast() { erase(--end()); }
+    void                replace(countT idx, const coordT &c) { (*this)[idx]= c; }
+    void                reserve(countT i) { coordinate_array.reserve(i); }
+    void                swap(countT idx, countT other);
+    coordT              takeAt(countT idx);
+    coordT              takeFirst() { return takeAt(0); }
+    coordT              takeLast();
+
+#//!\name Search
+    bool                contains(const coordT &t) const;
+    countT              count(const coordT &t) const;
+    countT              indexOf(const coordT &t, countT from = 0) const;
+    countT              lastIndexOf(const coordT &t, countT from = -1) const;
+    void                removeAll(const coordT &t);
+
+#//!\name Coordinates::iterator -- from QhullPoints, forwarding to coordinate_array
+    // before const_iterator for conversion with comparison operators
+    // Reviewed corelib/tools/qlist.h and corelib/tools/qvector.h w/o QT_STRICT_ITERATORS
+    class iterator {
+
+    private:
+        std::vector<coordT>::iterator i;
+        friend class const_iterator;
+
+    public:
+        typedef std::random_access_iterator_tag  iterator_category;
+        typedef coordT      value_type;
+        typedef value_type *pointer;
+        typedef value_type &reference;
+        typedef ptrdiff_t   difference_type;
+
+                        iterator() {}
+                        iterator(const iterator &other) { i= other.i; }
+        explicit        iterator(const std::vector<coordT>::iterator &vi) { i= vi; }
+        iterator &      operator=(const iterator &other) { i= other.i; return *this; }
+        std::vector<coordT>::iterator &base() { return i; }
+        coordT &        operator*() const { return *i; }
+        // No operator->() when the base type is double
+        coordT &        operator[](countT idx) const { return i[idx]; }
+
+        bool            operator==(const iterator &other) const { return i==other.i; }
+        bool            operator!=(const iterator &other) const { return i!=other.i; }
+        bool            operator<(const iterator &other) const { return i<other.i; }
+        bool            operator<=(const iterator &other) const { return i<=other.i; }
+        bool            operator>(const iterator &other) const { return i>other.i; }
+        bool            operator>=(const iterator &other) const { return i>=other.i; }
+              // reinterpret_cast to break circular dependency
+        bool            operator==(const Coordinates::const_iterator &other) const { return *this==reinterpret_cast<const iterator &>(other); }
+        bool            operator!=(const Coordinates::const_iterator &other) const { return *this!=reinterpret_cast<const iterator &>(other); }
+        bool            operator<(const Coordinates::const_iterator &other) const { return *this<reinterpret_cast<const iterator &>(other); }
+        bool            operator<=(const Coordinates::const_iterator &other) const { return *this<=reinterpret_cast<const iterator &>(other); }
+        bool            operator>(const Coordinates::const_iterator &other) const { return *this>reinterpret_cast<const iterator &>(other); }
+        bool            operator>=(const Coordinates::const_iterator &other) const { return *this>=reinterpret_cast<const iterator &>(other); }
+
+        iterator &      operator++() { ++i; return *this; }
+        iterator        operator++(int) { return iterator(i++); }
+        iterator &      operator--() { --i; return *this; }
+        iterator        operator--(int) { return iterator(i--); }
+        iterator &      operator+=(countT idx) { i += idx; return *this; }
+        iterator &      operator-=(countT idx) { i -= idx; return *this; }
+        iterator        operator+(countT idx) const { return iterator(i+idx); }
+        iterator        operator-(countT idx) const { return iterator(i-idx); }
+        difference_type operator-(iterator other) const { return i-other.i; }
+    };//Coordinates::iterator
+
+#//!\name Coordinates::const_iterator
+    class const_iterator {
+
+    private:
+        std::vector<coordT>::const_iterator i;
+
+    public:
+        typedef std::random_access_iterator_tag  iterator_category;
+        typedef coordT            value_type;
+        typedef const value_type *pointer;
+        typedef const value_type &reference;
+        typedef ptrdiff_t         difference_type;
+
+                        const_iterator() {}
+                        const_iterator(const const_iterator &other) { i= other.i; }
+                        const_iterator(const iterator &o) : i(o.i) {}
+        explicit        const_iterator(const std::vector<coordT>::const_iterator &vi) { i= vi; }
+        const_iterator &operator=(const const_iterator &other) { i= other.i; return *this; }
+        const coordT &  operator*() const { return *i; }
+        // No operator->() when the base type is double
+        const coordT &  operator[](countT idx) const { return i[idx]; }
+
+        bool            operator==(const const_iterator &other) const { return i==other.i; }
+        bool            operator!=(const const_iterator &other) const { return i!=other.i; }
+        bool            operator<(const const_iterator &other) const { return i<other.i; }
+        bool            operator<=(const const_iterator &other) const { return i<=other.i; }
+        bool            operator>(const const_iterator &other) const { return i>other.i; }
+        bool            operator>=(const const_iterator &other) const { return i>=other.i; }
+
+        const_iterator & operator++() { ++i; return *this; } 
+        const_iterator  operator++(int) { return const_iterator(i++); }
+        const_iterator & operator--() { --i; return *this; }
+        const_iterator  operator--(int) { return const_iterator(i--); }
+        const_iterator & operator+=(countT idx) { i += idx; return *this; }
+        const_iterator & operator-=(countT idx) { i -= idx; return *this; }
+        const_iterator  operator+(countT idx) const { return const_iterator(i+idx); }
+        const_iterator  operator-(countT idx) const { return const_iterator(i-idx); }
+        difference_type operator-(const_iterator other) const { return i-other.i; }
+    };//Coordinates::const_iterator
+
+};//Coordinates
+
+//class CoordinatesIterator
+//QHULL_DECLARE_SEQUENTIAL_ITERATOR(Coordinates, coordT)
+
+class CoordinatesIterator
+{
+    typedef Coordinates::const_iterator const_iterator;
+
+private:
+    const Coordinates * c;
+    const_iterator      i;
+
+public:
+                        CoordinatesIterator(const Coordinates &container): c(&container), i(c->constBegin()) {}
+    CoordinatesIterator &operator=(const Coordinates &container) { c= &container; i= c->constBegin(); return *this; }
+                        ~CoordinatesIterator() {}
+
+    bool                findNext(const coordT &t) { while (i != c->constEnd()) if(*i++ == t){ return true;} return false; }
+    bool                findPrevious(const coordT &t) { while (i != c->constBegin())if (*(--i) == t){ return true;} return false;  }
+    bool                hasNext() const { return i != c->constEnd(); }
+    bool                hasPrevious() const { return i != c->constBegin(); }
+    const coordT &      next() { return *i++; }
+    const coordT &      previous() { return *--i; }
+    const coordT &      peekNext() const { return *i; }
+    const coordT &      peekPrevious() const { const_iterator p= i; return *--p; }
+    void                toFront() { i= c->constBegin(); }
+    void                toBack() { i= c->constEnd(); }
+};//CoordinatesIterator
+
+//class MutableCoordinatesIterator
+//QHULL_DECLARE_MUTABLE_SEQUENTIAL_ITERATOR(Coordinates, coordT)
+class MutableCoordinatesIterator
+{
+    typedef Coordinates::iterator iterator;
+    typedef Coordinates::const_iterator const_iterator;
+
+private:
+    Coordinates *       c;
+    iterator            i;
+    iterator            n;
+    bool                item_exists() const { return const_iterator(n) != c->constEnd(); }
+
+public:
+                        MutableCoordinatesIterator(Coordinates &container) : c(&container) { i= c->begin(); n= c->end(); }
+    MutableCoordinatesIterator &operator=(Coordinates &container) { c= &container; i= c->begin(); n= c->end(); return *this; }
+                        ~MutableCoordinatesIterator() {}
+
+    bool                findNext(const coordT &t) { while(c->constEnd()!=const_iterator(n= i)){ if(*i++==t){ return true;}} return false; }
+    bool                findPrevious(const coordT &t) { while(c->constBegin()!=const_iterator(i)){ if(*(n= --i)== t){ return true;}} n= c->end(); return false;  }
+    bool                hasNext() const { return (c->constEnd()!=const_iterator(i)); }
+    bool                hasPrevious() const { return (c->constBegin()!=const_iterator(i)); }
+    void                insert(const coordT &t) { n= i= c->insert(i, t); ++i; }
+    coordT &            next() { n= i++; return *n; }
+    coordT &            peekNext() const { return *i; }
+    coordT &            peekPrevious() const { iterator p= i; return *--p; }
+    coordT &            previous() { n= --i; return *n; }
+    void                remove() { if(c->constEnd()!=const_iterator(n)){ i= c->erase(n); n= c->end();} }
+    void                setValue(const coordT &t) const { if(c->constEnd()!=const_iterator(n)){ *n= t;} }
+    void                toFront() { i= c->begin(); n= c->end(); }
+    void                toBack() { i= c->end(); n= i; }
+    coordT &            value() { QHULL_ASSERT(item_exists()); return *n; }
+    const coordT &      value() const { QHULL_ASSERT(item_exists()); return *n; }
+};//MutableCoordinatesIterator
+
+
+}//namespace orgQhull
+
+#//!\name Global
+
+std::ostream &operator<<(std::ostream &os, const orgQhull::Coordinates &c);
+
+#endif // QHCOORDINATES_H
diff --git a/xs/src/qhull/src/libqhullcpp/PointCoordinates.cpp b/xs/src/qhull/src/libqhullcpp/PointCoordinates.cpp
new file mode 100644
index 0000000000..a5b71e901d
--- /dev/null
+++ b/xs/src/qhull/src/libqhullcpp/PointCoordinates.cpp
@@ -0,0 +1,348 @@
+/****************************************************************************
+**
+** Copyright (c) 2009-2015 C.B. Barber. All rights reserved.
+** $Id: //main/2015/qhull/src/libqhullcpp/PointCoordinates.cpp#3 $$Change: 2066 $
+** $DateTime: 2016/01/18 19:29:17 $$Author: bbarber $
+**
+****************************************************************************/
+
+#include "libqhullcpp/PointCoordinates.h"
+
+#include "libqhullcpp/QhullError.h"
+#include "libqhullcpp/QhullPoint.h"
+
+#include <iterator>
+#include <iostream>
+
+using std::istream;
+using std::string;
+using std::ws;
+
+#ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
+#pragma warning( disable : 4996)  // function was declared deprecated(strcpy, localtime, etc.)
+#endif
+
+namespace orgQhull {
+
+#//! PointCoordinates -- vector of PointCoordinates
+
+#//!\name Constructors
+
+PointCoordinates::
+PointCoordinates()
+: QhullPoints()
+, point_coordinates()
+, describe_points()
+{
+}
+
+PointCoordinates::
+PointCoordinates(const std::string &aComment)
+: QhullPoints()
+, point_coordinates()
+, describe_points(aComment)
+{
+}
+
+PointCoordinates::
+PointCoordinates(int pointDimension, const std::string &aComment)
+: QhullPoints()
+, point_coordinates()
+, describe_points(aComment)
+{
+    setDimension(pointDimension);
+}
+
+//! Qhull and QhullQh constructors are the same
+PointCoordinates::
+PointCoordinates(const Qhull &q)
+: QhullPoints(q)
+, point_coordinates()
+, describe_points()
+{
+}
+
+PointCoordinates::
+PointCoordinates(const Qhull &q, const std::string &aComment)
+: QhullPoints(q)
+, point_coordinates()
+, describe_points(aComment)
+{
+}
+
+PointCoordinates::
+PointCoordinates(const Qhull &q, int pointDimension, const std::string &aComment)
+: QhullPoints(q)
+, point_coordinates()
+, describe_points(aComment)
+{
+    setDimension(pointDimension);
+}
+
+PointCoordinates::
+PointCoordinates(const Qhull &q, int pointDimension, const std::string &aComment, countT coordinatesCount, const coordT *c)
+: QhullPoints(q)
+, point_coordinates()
+, describe_points(aComment)
+{
+    setDimension(pointDimension);
+    append(coordinatesCount, c);
+}
+
+PointCoordinates::
+PointCoordinates(QhullQh *qqh)
+: QhullPoints(qqh)
+, point_coordinates()
+, describe_points()
+{
+}
+
+PointCoordinates::
+PointCoordinates(QhullQh *qqh, const std::string &aComment)
+: QhullPoints(qqh)
+, point_coordinates()
+, describe_points(aComment)
+{
+}
+
+PointCoordinates::
+PointCoordinates(QhullQh *qqh, int pointDimension, const std::string &aComment)
+: QhullPoints(qqh)
+, point_coordinates()
+, describe_points(aComment)
+{
+    setDimension(pointDimension);
+}
+
+PointCoordinates::
+PointCoordinates(QhullQh *qqh, int pointDimension, const std::string &aComment, countT coordinatesCount, const coordT *c)
+: QhullPoints(qqh)
+, point_coordinates()
+, describe_points(aComment)
+{
+    setDimension(pointDimension);
+    append(coordinatesCount, c);
+}
+
+PointCoordinates::
+PointCoordinates(const PointCoordinates &other)
+: QhullPoints(other)
+, point_coordinates(other.point_coordinates)
+, describe_points(other.describe_points)
+{
+    makeValid();  // Update point_first and point_end
+}
+
+PointCoordinates & PointCoordinates::
+operator=(const PointCoordinates &other)
+{
+    QhullPoints::operator=(other);
+    point_coordinates= other.point_coordinates;
+    describe_points= other.describe_points;
+    makeValid(); // Update point_first and point_end
+    return *this;
+}//operator=
+
+PointCoordinates::
+~PointCoordinates()
+{ }
+
+#//!\name GetSet
+
+void PointCoordinates::
+checkValid() const
+{
+    if(getCoordinates().data()!=data()
+    || getCoordinates().count()!=coordinateCount()){
+        throw QhullError(10060, "Qhull error: first point (%x) is not PointCoordinates.data() or count (%d) is not PointCoordinates.count (%d)", coordinateCount(), getCoordinates().count(), 0.0, data());
+    }
+}//checkValid
+
+void PointCoordinates::
+setDimension(int i)
+{
+    if(i<0){
+        throw QhullError(10062, "Qhull error: can not set PointCoordinates dimension to %d", i);
+    }
+    int currentDimension=QhullPoints::dimension();
+    if(currentDimension!=0 && i!=currentDimension){
+        throw QhullError(10063, "Qhull error: can not change PointCoordinates dimension (from %d to %d)", currentDimension, i);
+    }
+    QhullPoints::setDimension(i);
+}//setDimension
+
+#//!\name Foreach
+
+Coordinates::ConstIterator PointCoordinates::
+beginCoordinates(countT pointIndex) const
+{
+    return point_coordinates.begin()+indexOffset(pointIndex);
+}
+
+Coordinates::Iterator PointCoordinates::
+beginCoordinates(countT pointIndex)
+{
+    return point_coordinates.begin()+indexOffset(pointIndex);
+}
+
+#//!\name Methods
+
+void PointCoordinates::
+append(countT coordinatesCount, const coordT *c)
+{
+    if(coordinatesCount<=0){
+        return;
+    }
+    if(includesCoordinates(c)){
+        throw QhullError(10065, "Qhull error: can not append a subset of PointCoordinates to itself.  The coordinates for point %d may move.", indexOf(c, QhullError::NOthrow));
+    }
+    reserveCoordinates(coordinatesCount);
+    std::copy(c, c+coordinatesCount, std::back_inserter(point_coordinates));
+    makeValid();
+}//append coordT
+
+void PointCoordinates::
+append(const PointCoordinates &other)
+{
+    setDimension(other.dimension());
+    append(other.coordinateCount(), other.data());
+}//append PointCoordinates
+
+void PointCoordinates::
+append(const QhullPoint &p)
+{
+    setDimension(p.dimension());
+    append(p.dimension(), p.coordinates());
+}//append QhullPoint
+
+void PointCoordinates::
+appendComment(const std::string &s){
+    if(char c= s[0] && describe_points.empty()){
+        if(c=='-' || isdigit(c)){
+            throw QhullError(10028, "Qhull argument error: comments can not start with a number or minus, %s", 0, 0, 0.0, s.c_str());
+        }
+    }
+    describe_points += s;
+}//appendComment
+
+//! Read PointCoordinates from istream.  First two numbers are dimension and count.  A non-digit starts a rboxCommand.
+//! Overwrites describe_points.  See qh_readpoints [io.c]
+void PointCoordinates::
+appendPoints(istream &in)
+{
+    int inDimension;
+    countT inCount;
+    in >> ws >> inDimension >> ws;
+    if(!in.good()){
+        in.clear();
+        string remainder;
+        getline(in, remainder);
+        throw QhullError(10005, "Qhull error: input did not start with dimension or count -- %s", 0, 0, 0, remainder.c_str());
+    }
+    char c= (char)in.peek();
+    if(c!='-' && !isdigit(c)){         // Comments start with a non-digit
+        getline(in, describe_points);
+        in >> ws;
+    }
+    in >> inCount >> ws;
+    if(!in.good()){
+        in.clear();
+        string remainder;
+        getline(in, remainder);
+        throw QhullError(10009, "Qhull error: input did not start with dimension and count -- %d %s", inDimension, 0, 0, remainder.c_str());
+    }
+    c= (char)in.peek();
+    if(c!='-' && !isdigit(c)){         // Comments start with a non-digit
+        getline(in, describe_points);
+        in >> ws;
+    }
+    if(inCount<inDimension){           // Count may precede dimension
+        std::swap(inCount, inDimension);
+    }
+    setDimension(inDimension);
+    reserveCoordinates(inCount*inDimension);
+    countT coordinatesCount= 0;
+    while(!in.eof()){
+        realT p;
+        in >> p >> ws;
+        if(in.fail()){
+            in.clear();
+            string remainder;
+            getline(in, remainder);
+            throw QhullError(10008, "Qhull error: failed to read coordinate %d  of point %d\n   %s", coordinatesCount % inDimension, coordinatesCount/inDimension, 0, remainder.c_str());
+        }else{
+            point_coordinates.push_back(p);
+            coordinatesCount++;
+        }
+    }
+    if(coordinatesCount != inCount*inDimension){
+        if(coordinatesCount%inDimension==0){
+            throw QhullError(10006, "Qhull error: expected %d %d-d PointCoordinates but read %i PointCoordinates", int(inCount), inDimension, 0.0, int(coordinatesCount/inDimension));
+        }else{
+            throw QhullError(10012, "Qhull error: expected %d %d-d PointCoordinates but read %i PointCoordinates plus %f extra coordinates", inCount, inDimension, float(coordinatesCount%inDimension), coordinatesCount/inDimension);
+        }
+    }
+    makeValid();
+}//appendPoints istream
+
+PointCoordinates PointCoordinates::
+operator+(const PointCoordinates &other) const
+{
+    PointCoordinates pc= *this;
+    pc << other;
+    return pc;
+}//operator+
+
+void PointCoordinates::
+reserveCoordinates(countT newCoordinates)
+{
+    // vector::reserve is not const
+    point_coordinates.reserve((countT)point_coordinates.size()+newCoordinates); // WARN64
+    makeValid();
+}//reserveCoordinates
+
+#//!\name Helpers
+
+countT PointCoordinates::
+indexOffset(countT i) const {
+    countT n= i*dimension();
+    countT coordinatesCount= point_coordinates.count();
+    if(i<0 || n>coordinatesCount){
+        throw QhullError(10061, "Qhull error: point_coordinates is too short (%d) for point %d", coordinatesCount, i);
+    }
+    return n;
+}
+
+}//namespace orgQhull
+
+#//!\name Global functions
+
+using std::endl;
+using std::ostream;
+
+using orgQhull::Coordinates;
+using orgQhull::PointCoordinates;
+
+ostream&
+operator<<(ostream &os, const PointCoordinates &p)
+{
+    p.checkValid();
+    countT count= p.count();
+    int dimension= p.dimension();
+    string comment= p.comment();
+    if(comment.empty()){
+        os << dimension << endl;
+    }else{
+        os << dimension << " " << comment << endl;
+    }
+    os << count << endl;
+    Coordinates::ConstIterator c= p.beginCoordinates();
+    for(countT i=0; i<count; i++){
+        for(int j=0; j<dimension; j++){
+            os << *c++ << " ";
+        }
+        os << endl;
+    }
+    return os;
+}//operator<<
+
diff --git a/xs/src/qhull/src/libqhullcpp/PointCoordinates.h b/xs/src/qhull/src/libqhullcpp/PointCoordinates.h
new file mode 100644
index 0000000000..4c63cdfca3
--- /dev/null
+++ b/xs/src/qhull/src/libqhullcpp/PointCoordinates.h
@@ -0,0 +1,161 @@
+/****************************************************************************
+**
+** Copyright (c) 2009-2015 C.B. Barber. All rights reserved.
+** $Id: //main/2015/qhull/src/libqhullcpp/PointCoordinates.h#4 $$Change: 2079 $
+** $DateTime: 2016/02/07 17:43:34 $$Author: bbarber $
+**
+****************************************************************************/
+
+#ifndef QHPOINTCOORDINATES_H
+#define QHPOINTCOORDINATES_H
+
+#include "libqhull_r/qhull_ra.h"
+#include "libqhullcpp/QhullPoints.h"
+#include "libqhullcpp/Coordinates.h"
+
+#include <ostream>
+#include <string>
+
+#ifndef QHULL_NO_STL
+#include <vector>
+#endif
+
+namespace orgQhull {
+
+#//!\name Defined here
+    //! QhullPoints with Coordinates and description
+    //! Inherited by RboxPoints
+    class PointCoordinates;
+
+class PointCoordinates : public QhullPoints {
+
+private:
+#//!\name Fields
+    Coordinates         point_coordinates;      //! std::vector of point coordinates
+                                                //! may have extraCoordinates()
+    std::string         describe_points;          //! Comment describing PointCoordinates
+
+public:
+#//!\name Construct
+    //! QhullPoint, PointCoordinates, and QhullPoints have similar constructors
+    //! If Qhull/QhullQh is not initialized, then dimension()==0                        PointCoordinates();
+                        PointCoordinates();
+    explicit            PointCoordinates(const std::string &aComment);
+                        PointCoordinates(int pointDimension, const std::string &aComment);
+                        //! Qhull/QhullQh used for dimension() and QhullPoint equality
+    explicit            PointCoordinates(const Qhull &q);
+                        PointCoordinates(const Qhull &q, const std::string &aComment);
+                        PointCoordinates(const Qhull &q, int pointDimension, const std::string &aComment);
+                        PointCoordinates(const Qhull &q, int pointDimension, const std::string &aComment, countT coordinatesCount, const coordT *c); // may be invalid
+                        //! Use append() and appendPoints() for Coordinates and vector<coordT>
+    explicit            PointCoordinates(QhullQh *qqh);
+                        PointCoordinates(QhullQh *qqh, const std::string &aComment);
+                        PointCoordinates(QhullQh *qqh, int pointDimension, const std::string &aComment);
+                        PointCoordinates(QhullQh *qqh, int pointDimension, const std::string &aComment, countT coordinatesCount, const coordT *c); // may be invalid
+                        //! Use append() and appendPoints() for Coordinates and vector<coordT>
+                        PointCoordinates(const PointCoordinates &other);
+    PointCoordinates &  operator=(const PointCoordinates &other);
+                        ~PointCoordinates();
+
+#//!\name Convert
+    //! QhullPoints coordinates, constData, data, count, size
+#ifndef QHULL_NO_STL
+    void                append(const std::vector<coordT> &otherCoordinates) { if(!otherCoordinates.empty()){ append((int)otherCoordinates.size(), &otherCoordinates[0]); } }
+    std::vector<coordT> toStdVector() const { return point_coordinates.toStdVector(); }
+#endif //QHULL_NO_STL
+#ifdef QHULL_USES_QT
+    void                append(const QList<coordT> &pointCoordinates) { if(!pointCoordinates.isEmpty()){ append(pointCoordinates.count(), &pointCoordinates[0]); } }
+    QList<coordT>       toQList() const { return point_coordinates.toQList(); }
+#endif //QHULL_USES_QT
+
+#//!\name GetSet
+    //! See QhullPoints for coordinates, coordinateCount, dimension, empty, isEmpty, ==, !=
+    void                checkValid() const;
+    std::string         comment() const { return describe_points; }
+    void                makeValid() { defineAs(point_coordinates.count(), point_coordinates.data()); }
+    const Coordinates & getCoordinates() const { return point_coordinates; }
+    void                setComment(const std::string &s) { describe_points= s; }
+    void                setDimension(int i);
+
+private:
+    //! disable QhullPoints.defineAs()
+    void                defineAs(countT coordinatesCount, coordT *c) { QhullPoints::defineAs(coordinatesCount, c); }
+public:
+
+#//!\name ElementAccess
+    //! See QhullPoints for at, back, first, front, last, mid, [], value
+
+#//!\name Foreach
+    //! See QhullPoints for begin, constBegin, end
+    Coordinates::ConstIterator  beginCoordinates() const { return point_coordinates.begin(); }
+    Coordinates::Iterator       beginCoordinates() { return point_coordinates.begin(); }
+    Coordinates::ConstIterator  beginCoordinates(countT pointIndex) const;
+    Coordinates::Iterator       beginCoordinates(countT pointIndex);
+    Coordinates::ConstIterator  endCoordinates() const { return point_coordinates.end(); }
+    Coordinates::Iterator       endCoordinates() { return point_coordinates.end(); }
+
+#//!\name Search
+    //! See QhullPoints for contains, count, indexOf, lastIndexOf
+
+#//!\name GetSet
+    PointCoordinates    operator+(const PointCoordinates &other) const;
+
+#//!\name Modify
+    //FIXUP QH11001: Add clear() and other modify operators from Coordinates.h.  Include QhullPoint::operator=()
+    void                append(countT coordinatesCount, const coordT *c);  //! Dimension previously defined
+    void                append(const coordT &c) { append(1, &c); } //! Dimension previously defined
+    void                append(const QhullPoint &p);
+    //! See convert for std::vector and QList
+    void                append(const Coordinates &c) { append(c.count(), c.data()); }
+    void                append(const PointCoordinates &other);
+    void                appendComment(const std::string &s);
+    void                appendPoints(std::istream &in);
+    PointCoordinates &  operator+=(const PointCoordinates &other) { append(other); return *this; }
+    PointCoordinates &  operator+=(const coordT &c) { append(c); return *this; }
+    PointCoordinates &  operator+=(const QhullPoint &p) { append(p); return *this; }
+    PointCoordinates &  operator<<(const PointCoordinates &other) { return *this += other; }
+    PointCoordinates &  operator<<(const coordT &c) { return *this += c; }
+    PointCoordinates &  operator<<(const QhullPoint &p) { return *this += p; }
+    // reserve() is non-const
+    void                reserveCoordinates(countT newCoordinates);
+
+#//!\name Helpers
+private:
+    int                 indexOffset(int i) const;
+
+};//PointCoordinates
+
+// No references to QhullPoint.  Prevents use of QHULL_DECLARE_SEQUENTIAL_ITERATOR(PointCoordinates, QhullPoint)
+class PointCoordinatesIterator
+{
+    typedef PointCoordinates::const_iterator const_iterator;
+
+private:
+    const PointCoordinates *c;
+    const_iterator      i;
+
+public:
+                        PointCoordinatesIterator(const PointCoordinates &container) : c(&container), i(c->constBegin()) {}
+                        PointCoordinatesIterator &operator=(const PointCoordinates &container) { c = &container; i = c->constBegin(); return *this; }
+
+    void                toFront() { i = c->constBegin(); }
+    void                toBack() { i = c->constEnd(); }
+    bool                hasNext() const { return i != c->constEnd(); }
+    const QhullPoint    next() { return *i++; }
+    const QhullPoint    peekNext() const { return *i; }
+    bool                hasPrevious() const { return i != c->constBegin(); }
+    const QhullPoint    previous() { return *--i; }
+    const QhullPoint    peekPrevious() const { const_iterator p = i; return *--p; }
+    bool                findNext(const QhullPoint &t) { while(i != c->constEnd()){ if (*i++ == t) return true;} return false; }
+    bool                findPrevious(const QhullPoint &t) { while(i != c->constBegin()){ if (*(--i) == t) return true;} return false;  }
+};//CoordinatesIterator
+
+// FIXUP QH11002:  Add MutablePointCoordinatesIterator after adding modify operators
+\
+}//namespace orgQhull
+
+#//!\name Global
+
+std::ostream &          operator<<(std::ostream &os, const orgQhull::PointCoordinates &p);
+
+#endif // QHPOINTCOORDINATES_H
diff --git a/xs/src/qhull/src/libqhullcpp/Qhull.cpp b/xs/src/qhull/src/libqhullcpp/Qhull.cpp
new file mode 100644
index 0000000000..7124a15cdc
--- /dev/null
+++ b/xs/src/qhull/src/libqhullcpp/Qhull.cpp
@@ -0,0 +1,352 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
+** $Id: //main/2015/qhull/src/libqhullcpp/Qhull.cpp#4 $$Change: 2078 $
+** $DateTime: 2016/02/07 16:53:56 $$Author: bbarber $
+**
+****************************************************************************/
+
+#//! Qhull -- invoke qhull from C++
+#//! Compile libqhull_r and Qhull together due to use of setjmp/longjmp()
+
+#include "libqhullcpp/Qhull.h"
+
+#include "libqhullcpp/QhullError.h"
+#include "libqhullcpp/RboxPoints.h"
+#include "libqhullcpp/QhullQh.h"
+#include "libqhullcpp/QhullFacet.h"
+#include "libqhullcpp/QhullFacetList.h"
+
+#include <iostream>
+
+using std::cerr;
+using std::string;
+using std::vector;
+using std::ostream;
+
+#ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
+#pragma warning( disable : 4611)  // interaction between '_setjmp' and C++ object destruction is non-portable
+#pragma warning( disable : 4996)  // function was declared deprecated(strcpy, localtime, etc.)
+#endif
+
+namespace orgQhull {
+
+#//!\name Global variables
+
+const char s_unsupported_options[]=" Fd TI ";
+const char s_not_output_options[]= " Fd TI A C d E H P Qb QbB Qbb Qc Qf Qg Qi Qm QJ Qr QR Qs Qt Qv Qx Qz Q0 Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 R Tc TC TM TP TR Tv TV TW U v V W ";
+
+#//!\name Constructor, destructor, etc.
+Qhull::
+Qhull()
+: qh_qh(0)
+, origin_point()
+, run_called(false)
+, feasible_point()
+{
+    allocateQhullQh();
+}//Qhull
+
+//! Invokes Qhull on rboxPoints
+//! Same as runQhull()
+//! For rbox commands, see http://www.qhull.org/html/rbox.htm or html/rbox.htm
+//! For qhull commands, see http://www.qhull.org/html/qhull.htm or html/qhull.htm
+Qhull::
+Qhull(const RboxPoints &rboxPoints, const char *qhullCommand2)
+: qh_qh(0)
+, origin_point()
+, run_called(false)
+, feasible_point()
+{
+    allocateQhullQh();
+    runQhull(rboxPoints, qhullCommand2);
+}//Qhull rbox
+
+//! Invokes Qhull on a set of input points
+//! Same as runQhull()
+//! For qhull commands, see http://www.qhull.org/html/qhull.htm or html/qhull.htm
+Qhull::
+Qhull(const char *inputComment2, int pointDimension, int pointCount, const realT *pointCoordinates, const char *qhullCommand2)
+: qh_qh(0)
+, origin_point()
+, run_called(false)
+, feasible_point()
+{
+    allocateQhullQh();
+    runQhull(inputComment2, pointDimension, pointCount, pointCoordinates, qhullCommand2);
+}//Qhull points
+
+void Qhull::
+allocateQhullQh()
+{
+  QHULL_LIB_CHECK /* Check for compatible library */
+
+    qh_qh= new QhullQh;
+    void *p= qh_qh;
+    void *p2= static_cast<qhT *>(qh_qh);
+    char *s= static_cast<char *>(p);
+    char *s2= static_cast<char *>(p2);
+    if(s!=s2){
+        throw QhullError(10074, "Qhull error: QhullQh at a different address than base type QhT (%d bytes).  Please report compiler to qhull.org", int(s2-s));
+    }
+}//allocateQhullQh
+
+Qhull::
+~Qhull() throw()
+{
+    // Except for cerr, does not throw errors
+    if(qh_qh->hasQhullMessage()){
+        cerr<< "\nQhull output at end\n"; //FIXUP QH11005: where should error and log messages go on ~Qhull?
+        cerr<< qh_qh->qhullMessage();
+        qh_qh->clearQhullMessage();
+    }
+    delete qh_qh;
+    qh_qh= 0;
+}//~Qhull
+
+#//!\name GetSet
+
+void Qhull::
+checkIfQhullInitialized()
+{
+    if(!initialized()){ // qh_initqhull_buffers() not called
+        throw QhullError(10023, "Qhull error: checkIfQhullInitialized failed.  Call runQhull() first.");
+    }
+}//checkIfQhullInitialized
+
+//! Return feasiblePoint for halfspace intersection
+//! If called before runQhull(), then it returns the value from setFeasiblePoint.  qh.feasible_string overrides this value if it is defined.
+Coordinates Qhull::
+feasiblePoint() const
+{
+    Coordinates result;
+    if(qh_qh->feasible_point){
+        result.append(qh_qh->hull_dim, qh_qh->feasible_point);
+    }else{
+        result= feasible_point;
+    }
+    return result;
+}//feasiblePoint
+
+//! Return origin point for qh.input_dim
+QhullPoint Qhull::
+inputOrigin()
+{
+    QhullPoint result= origin();
+    result.setDimension(qh_qh->input_dim);
+    return result;
+}//inputOrigin
+
+#//!\name GetValue
+
+double Qhull::
+area(){
+    checkIfQhullInitialized();
+    if(!qh_qh->hasAreaVolume){
+        QH_TRY_(qh_qh){ // no object creation -- destructors skipped on longjmp()
+            qh_getarea(qh_qh, qh_qh->facet_list);
+        }
+        qh_qh->NOerrexit= true;
+        qh_qh->maybeThrowQhullMessage(QH_TRY_status);
+    }
+    return qh_qh->totarea;
+}//area
+
+double Qhull::
+volume(){
+    checkIfQhullInitialized();
+    if(!qh_qh->hasAreaVolume){
+        QH_TRY_(qh_qh){ // no object creation -- destructors skipped on longjmp()
+            qh_getarea(qh_qh, qh_qh->facet_list);
+        }
+        qh_qh->NOerrexit= true;
+        qh_qh->maybeThrowQhullMessage(QH_TRY_status);
+    }
+    return qh_qh->totvol;
+}//volume
+
+#//!\name Foreach
+
+//! Define QhullVertex::neighborFacets().
+//! Automatically called if merging facets or computing the Voronoi diagram.
+//! Noop if called multiple times.
+void Qhull::
+defineVertexNeighborFacets(){
+    checkIfQhullInitialized();
+    if(!qh_qh->hasAreaVolume){
+        QH_TRY_(qh_qh){ // no object creation -- destructors skipped on longjmp()
+            qh_vertexneighbors(qh_qh);
+        }
+        qh_qh->NOerrexit= true;
+        qh_qh->maybeThrowQhullMessage(QH_TRY_status);
+    }
+}//defineVertexNeighborFacets
+
+QhullFacetList Qhull::
+facetList() const{
+    return QhullFacetList(beginFacet(), endFacet());
+}//facetList
+
+QhullPoints Qhull::
+points() const
+{
+    return QhullPoints(qh_qh, qh_qh->hull_dim, qh_qh->num_points*qh_qh->hull_dim, qh_qh->first_point);
+}//points
+
+QhullPointSet Qhull::
+otherPoints() const
+{
+    return QhullPointSet(qh_qh, qh_qh->other_points);
+}//otherPoints
+
+//! Return vertices of the convex hull.
+QhullVertexList Qhull::
+vertexList() const{
+    return QhullVertexList(beginVertex(), endVertex());
+}//vertexList
+
+#//!\name Methods
+
+void Qhull::
+outputQhull()
+{
+    checkIfQhullInitialized();
+    QH_TRY_(qh_qh){ // no object creation -- destructors skipped on longjmp()
+        qh_produce_output2(qh_qh);
+    }
+    qh_qh->NOerrexit= true;
+    qh_qh->maybeThrowQhullMessage(QH_TRY_status);
+}//outputQhull
+
+void Qhull::
+outputQhull(const char *outputflags)
+{
+    checkIfQhullInitialized();
+    string cmd(" "); // qh_checkflags skips first word
+    cmd += outputflags;
+    char *command= const_cast<char*>(cmd.c_str());
+    QH_TRY_(qh_qh){ // no object creation -- destructors skipped on longjmp()
+        qh_clear_outputflags(qh_qh);
+        char *s = qh_qh->qhull_command + strlen(qh_qh->qhull_command) + 1; //space
+        strncat(qh_qh->qhull_command, command, sizeof(qh_qh->qhull_command)-strlen(qh_qh->qhull_command)-1);
+        qh_checkflags(qh_qh, command, const_cast<char *>(s_not_output_options));
+        qh_initflags(qh_qh, s);
+        qh_initqhull_outputflags(qh_qh);
+        if(qh_qh->KEEPminArea < REALmax/2
+           || (0 != qh_qh->KEEParea + qh_qh->KEEPmerge + qh_qh->GOODvertex
+                    + qh_qh->GOODthreshold + qh_qh->GOODpoint + qh_qh->SPLITthresholds)){
+            facetT *facet;
+            qh_qh->ONLYgood= False;
+            FORALLfacet_(qh_qh->facet_list) {
+                facet->good= True;
+            }
+            qh_prepare_output(qh_qh);
+        }
+        qh_produce_output2(qh_qh);
+        if(qh_qh->VERIFYoutput && !qh_qh->STOPpoint && !qh_qh->STOPcone){
+            qh_check_points(qh_qh);
+        }
+    }
+    qh_qh->NOerrexit= true;
+    qh_qh->maybeThrowQhullMessage(QH_TRY_status);
+}//outputQhull
+
+//! For qhull commands, see http://www.qhull.org/html/qhull.htm or html/qhull.htm
+void Qhull::
+runQhull(const RboxPoints &rboxPoints, const char *qhullCommand2)
+{
+    runQhull(rboxPoints.comment().c_str(), rboxPoints.dimension(), rboxPoints.count(), &*rboxPoints.coordinates(), qhullCommand2);
+}//runQhull, RboxPoints
+
+//! pointCoordinates is a array of points, input sites ('d' or 'v'), or halfspaces with offset last ('H')
+//! Derived from qh_new_qhull [user.c]
+//! For rbox commands, see http://www.qhull.org/html/rbox.htm or html/rbox.htm
+//! For qhull commands, see http://www.qhull.org/html/qhull.htm or html/qhull.htm
+void Qhull::
+runQhull(const char *inputComment, int pointDimension, int pointCount, const realT *pointCoordinates, const char *qhullCommand)
+{
+  /* gcc may issue a "might be clobbered" warning for pointDimension and pointCoordinates [-Wclobbered].
+     These parameters are not referenced after a longjmp() and hence not clobbered.
+     See http://stackoverflow.com/questions/7721854/what-sense-do-these-clobbered-variable-warnings-make */
+    if(run_called){
+        throw QhullError(10027, "Qhull error: runQhull called twice.  Only one call allowed.");
+    }
+    run_called= true;
+    string s("qhull ");
+    s += qhullCommand;
+    char *command= const_cast<char*>(s.c_str());
+    /************* Expansion of QH_TRY_ for debugging
+    int QH_TRY_status;
+    if(qh_qh->NOerrexit){
+        qh_qh->NOerrexit= False;
+        QH_TRY_status= setjmp(qh_qh->errexit);
+    }else{
+        QH_TRY_status= QH_TRY_ERROR;
+    }
+    if(!QH_TRY_status){
+    *************/
+    QH_TRY_(qh_qh){ // no object creation -- destructors are skipped on longjmp()
+        qh_checkflags(qh_qh, command, const_cast<char *>(s_unsupported_options));
+        qh_initflags(qh_qh, command);
+        *qh_qh->rbox_command= '\0';
+        strncat( qh_qh->rbox_command, inputComment, sizeof(qh_qh->rbox_command)-1);
+        if(qh_qh->DELAUNAY){
+            qh_qh->PROJECTdelaunay= True;   // qh_init_B() calls qh_projectinput()
+        }
+        pointT *newPoints= const_cast<pointT*>(pointCoordinates);
+        int newDimension= pointDimension;
+        int newIsMalloc= False;
+        if(qh_qh->HALFspace){
+            --newDimension;
+            initializeFeasiblePoint(newDimension);
+            newPoints= qh_sethalfspace_all(qh_qh, pointDimension, pointCount, newPoints, qh_qh->feasible_point);
+            newIsMalloc= True;
+        }
+        qh_init_B(qh_qh, newPoints, pointCount, newDimension, newIsMalloc);
+        qh_qhull(qh_qh);
+        qh_check_output(qh_qh);
+        qh_prepare_output(qh_qh);
+        if(qh_qh->VERIFYoutput && !qh_qh->STOPpoint && !qh_qh->STOPcone){
+            qh_check_points(qh_qh);
+        }
+    }
+    qh_qh->NOerrexit= true;
+    for(int k= qh_qh->hull_dim; k--; ){  // Do not move into QH_TRY block.  It may throw an error
+        origin_point << 0.0;
+    }
+    qh_qh->maybeThrowQhullMessage(QH_TRY_status);
+}//runQhull
+
+#//!\name Helpers -- be careful of allocating C++ objects due to setjmp/longjmp() error handling by qh_... routines
+
+//! initialize qh.feasible_point for half-space intersection
+//! Sets from qh.feasible_string if available, otherwise from Qhull::feasible_point
+//! called only once from runQhull(), otherwise it leaks memory (the same as qh_setFeasible)
+void Qhull::
+initializeFeasiblePoint(int hulldim)
+{
+    if(qh_qh->feasible_string){
+        qh_setfeasible(qh_qh, hulldim);
+    }else{
+        if(feasible_point.isEmpty()){
+            qh_fprintf(qh_qh, qh_qh->ferr, 6209, "qhull error: missing feasible point for halfspace intersection.  Use option 'Hn,n' or Qhull::setFeasiblePoint before runQhull()\n");
+            qh_errexit(qh_qh, qh_ERRmem, NULL, NULL);
+        }
+        if(feasible_point.size()!=(size_t)hulldim){
+            qh_fprintf(qh_qh, qh_qh->ferr, 6210, "qhull error: dimension of feasiblePoint should be %d.  It is %u", hulldim, feasible_point.size());
+            qh_errexit(qh_qh, qh_ERRmem, NULL, NULL);
+        }
+        if (!(qh_qh->feasible_point= (coordT*)qh_malloc(hulldim * sizeof(coordT)))) {
+            qh_fprintf(qh_qh, qh_qh->ferr, 6202, "qhull error: insufficient memory for feasible point\n");
+            qh_errexit(qh_qh, qh_ERRmem, NULL, NULL);
+        }
+        coordT *t= qh_qh->feasible_point;
+        // No qh_... routines after here -- longjmp() ignores destructor
+        for(Coordinates::ConstIterator p=feasible_point.begin(); p<feasible_point.end(); p++){
+            *t++= *p;
+        }
+    }
+}//initializeFeasiblePoint
+
+}//namespace orgQhull
+
diff --git a/xs/src/qhull/src/libqhullcpp/Qhull.h b/xs/src/qhull/src/libqhullcpp/Qhull.h
new file mode 100644
index 0000000000..e3ad9d8e16
--- /dev/null
+++ b/xs/src/qhull/src/libqhullcpp/Qhull.h
@@ -0,0 +1,132 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
+** $Id: //main/2015/qhull/src/libqhullcpp/Qhull.h#3 $$Change: 2066 $
+** $DateTime: 2016/01/18 19:29:17 $$Author: bbarber $
+**
+****************************************************************************/
+
+#ifndef QHULLCPP_H
+#define QHULLCPP_H
+
+#include "libqhullcpp/QhullPoint.h"
+#include "libqhullcpp/QhullVertex.h"
+#include "libqhullcpp/QhullFacet.h"
+
+namespace orgQhull {
+
+/***
+   Compile qhullcpp and libqhull with the same compiler.  setjmp() and longjmp() must be the same.
+
+   #define QHULL_NO_STL
+      Do not supply conversions to STL
+      Coordinates.h requires <vector>.  It could be rewritten for another vector class such as QList
+   #define QHULL_USES_QT
+      Supply conversions to QT
+      qhulltest requires QT.  It is defined in RoadTest.h
+
+  #define QHULL_ASSERT
+      Defined by QhullError.h
+      It invokes assert()
+*/
+
+#//!\name Used here
+    class QhullFacetList;
+    class QhullPoints;
+    class QhullQh;
+    class RboxPoints;
+
+#//!\name Defined here
+    class Qhull;
+
+//! Interface to Qhull from C++
+class Qhull {
+
+private:
+#//!\name Members and friends
+    QhullQh *           qh_qh;          //! qhT for this instance
+    Coordinates         origin_point;   //! origin for qh_qh->hull_dim.  Set by runQhull()
+    bool                run_called;     //! True at start of runQhull.  Errors if call again.
+    Coordinates         feasible_point;  //! feasible point for half-space intersection (alternative to qh.feasible_string for qh.feasible_point)
+
+public:
+#//!\name Constructors
+                        Qhull();      //!< call runQhull() next
+                        Qhull(const RboxPoints &rboxPoints, const char *qhullCommand2);
+                        Qhull(const char *inputComment2, int pointDimension, int pointCount, const realT *pointCoordinates, const char *qhullCommand2);
+                        ~Qhull() throw();
+private:                //! Disable copy constructor and assignment.  Qhull owns QhullQh.
+                        Qhull(const Qhull &);
+    Qhull &             operator=(const Qhull &);
+
+private:
+    void                allocateQhullQh();
+
+public:
+
+#//!\name GetSet
+    void                checkIfQhullInitialized();
+    int                 dimension() const { return qh_qh->input_dim; } //!< Dimension of input and result
+    void                disableOutputStream() { qh_qh->disableOutputStream(); }
+    void                enableOutputStream() { qh_qh->enableOutputStream(); }
+    countT              facetCount() const { return qh_qh->num_facets; }
+    Coordinates         feasiblePoint() const; 
+    int                 hullDimension() const { return qh_qh->hull_dim; } //!< Dimension of the computed hull
+    bool                hasOutputStream() const { return qh_qh->hasOutputStream(); }
+    bool                initialized() const { return (qh_qh->hull_dim>0); }
+    const char *        inputComment() const { return qh_qh->rbox_command; }
+    QhullPoint          inputOrigin();
+                        //! non-const due to QhullPoint
+    QhullPoint          origin() { QHULL_ASSERT(initialized()); return QhullPoint(qh_qh, origin_point.data()); }
+    QhullQh *           qh() const { return qh_qh; };
+    const char *        qhullCommand() const { return qh_qh->qhull_command; }
+    const char *        rboxCommand() const { return qh_qh->rbox_command; }
+    int                 rotateRandom() const { return qh_qh->ROTATErandom; } //!< Return QRn for repeating QR0 runs
+    void                setFeasiblePoint(const Coordinates &c) { feasible_point= c; } //!< Sets qh.feasible_point via initializeFeasiblePoint
+    countT              vertexCount() const { return qh_qh->num_vertices; }
+
+#//!\name Delegated to QhullQh
+    double              angleEpsilon() const { return qh_qh->angleEpsilon(); } //!< Epsilon for hyperplane angle equality
+    void                appendQhullMessage(const std::string &s) { qh_qh->appendQhullMessage(s); }
+    void                clearQhullMessage() { qh_qh->clearQhullMessage(); }
+    double              distanceEpsilon() const { return qh_qh->distanceEpsilon(); } //!< Epsilon for distance to hyperplane
+    double              factorEpsilon() const { return qh_qh->factorEpsilon(); }  //!< Factor for angleEpsilon and distanceEpsilon
+    std::string         qhullMessage() const { return qh_qh->qhullMessage(); }
+    bool                hasQhullMessage() const { return qh_qh->hasQhullMessage(); }
+    int                 qhullStatus() const { return qh_qh->qhullStatus(); }
+    void                setErrorStream(std::ostream *os) { qh_qh->setErrorStream(os); }
+    void                setFactorEpsilon(double a) { qh_qh->setFactorEpsilon(a); }
+    void                setOutputStream(std::ostream *os) { qh_qh->setOutputStream(os); }
+
+#//!\name ForEach
+    QhullFacet          beginFacet() const { return QhullFacet(qh_qh, qh_qh->facet_list); }
+    QhullVertex         beginVertex() const { return QhullVertex(qh_qh, qh_qh->vertex_list); }
+    void                defineVertexNeighborFacets(); //!< Automatically called if merging facets or Voronoi diagram
+    QhullFacet          endFacet() const { return QhullFacet(qh_qh, qh_qh->facet_tail); }
+    QhullVertex         endVertex() const { return QhullVertex(qh_qh, qh_qh->vertex_tail); }
+    QhullFacetList      facetList() const;
+    QhullFacet          firstFacet() const { return beginFacet(); }
+    QhullVertex         firstVertex() const { return beginVertex(); }
+    QhullPoints         points() const;
+    QhullPointSet       otherPoints() const;
+                        //! Same as points().coordinates()
+    coordT *            pointCoordinateBegin() const { return qh_qh->first_point; }
+    coordT *            pointCoordinateEnd() const { return qh_qh->first_point + qh_qh->num_points*qh_qh->hull_dim; }
+    QhullVertexList     vertexList() const;
+
+#//!\name Methods
+    double              area();
+    void                outputQhull();
+    void                outputQhull(const char * outputflags);
+    void                runQhull(const RboxPoints &rboxPoints, const char *qhullCommand2);
+    void                runQhull(const char *inputComment2, int pointDimension, int pointCount, const realT *pointCoordinates, const char *qhullCommand2);
+    double              volume();
+
+#//!\name Helpers
+private:
+    void                initializeFeasiblePoint(int hulldim);
+};//Qhull
+
+}//namespace orgQhull
+
+#endif // QHULLCPP_H
diff --git a/xs/src/qhull/src/libqhullcpp/QhullError.h b/xs/src/qhull/src/libqhullcpp/QhullError.h
new file mode 100644
index 0000000000..08d50aa0ff
--- /dev/null
+++ b/xs/src/qhull/src/libqhullcpp/QhullError.h
@@ -0,0 +1,62 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
+** $Id: //main/2015/qhull/src/libqhullcpp/QhullError.h#2 $$Change: 2066 $
+** $DateTime: 2016/01/18 19:29:17 $$Author: bbarber $
+**
+****************************************************************************/
+
+#ifndef QHULLERROR_H
+#define QHULLERROR_H
+
+#include "libqhullcpp/RoadError.h"
+// No dependencies on libqhull
+
+#ifndef QHULL_ASSERT
+#define QHULL_ASSERT assert
+#include <assert.h>
+#endif
+
+namespace orgQhull {
+
+#//!\name Defined here
+    //! QhullError -- std::exception class for Qhull
+    class QhullError;
+
+class QhullError : public RoadError {
+
+public:
+#//!\name Constants
+    enum {
+        QHULLfirstError= 10000, //MSG_QHULL_ERROR in Qhull's user.h
+        QHULLlastError= 10078,
+        NOthrow= 1 //! For flag to indexOf()
+    };
+
+#//!\name Constructors
+    // default constructors
+    QhullError() : RoadError() {};
+    QhullError(const QhullError &other) : RoadError(other) {}
+    QhullError(int code, const std::string &message) : RoadError(code, message) {};
+    QhullError(int code, const char *fmt) : RoadError(code, fmt) {};
+    QhullError(int code, const char *fmt, int d) : RoadError(code, fmt, d) {};
+    QhullError(int code, const char *fmt, int d, int d2) : RoadError(code, fmt, d, d2) {};
+    QhullError(int code, const char *fmt, int d, int d2, float f) : RoadError(code, fmt, d, d2, f) {};
+    QhullError(int code, const char *fmt, int d, int d2, float f, const char *s) : RoadError(code, fmt, d, d2, f, s) {};
+    QhullError(int code, const char *fmt, int d, int d2, float f, const void *x) : RoadError(code, fmt, d, d2, f, x) {};
+    QhullError(int code, const char *fmt, int d, int d2, float f, int i) : RoadError(code, fmt, d, d2, f, i) {};
+    QhullError(int code, const char *fmt, int d, int d2, float f, long long i) : RoadError(code, fmt, d, d2, f, i) {};
+    QhullError(int code, const char *fmt, int d, int d2, float f, double e) : RoadError(code, fmt, d, d2, f, e) {};
+    QhullError &operator=(const QhullError &other) { this->RoadError::operator=(other); return *this; }
+    ~QhullError() throw() {}
+
+};//class QhullError
+
+
+}//namespace orgQhull
+
+#//!\name Global
+
+inline std::ostream &operator<<(std::ostream &os, const orgQhull::QhullError &e) { return os << e.what(); }
+
+#endif // QHULLERROR_H
diff --git a/xs/src/qhull/src/libqhullcpp/QhullFacet.cpp b/xs/src/qhull/src/libqhullcpp/QhullFacet.cpp
new file mode 100644
index 0000000000..40d3828a4c
--- /dev/null
+++ b/xs/src/qhull/src/libqhullcpp/QhullFacet.cpp
@@ -0,0 +1,519 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
+** $Id: //main/2015/qhull/src/libqhullcpp/QhullFacet.cpp#3 $$Change: 2066 $
+** $DateTime: 2016/01/18 19:29:17 $$Author: bbarber $
+**
+****************************************************************************/
+
+#//! QhullFacet -- Qhull's facet structure, facetT, as a C++ class
+
+#include "libqhullcpp/QhullFacet.h"
+
+#include "libqhullcpp/QhullError.h"
+#include "libqhullcpp/Qhull.h"
+#include "libqhullcpp/QhullSet.h"
+#include "libqhullcpp/QhullPoint.h"
+#include "libqhullcpp/QhullPointSet.h"
+#include "libqhullcpp/QhullRidge.h"
+#include "libqhullcpp/QhullFacetSet.h"
+#include "libqhullcpp/QhullVertex.h"
+
+#include <ostream>
+
+using std::endl;
+using std::ostream;
+
+#ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
+#pragma warning( disable : 4611)  // interaction between '_setjmp' and C++ object destruction is non-portable
+#pragma warning( disable : 4996)  // function was declared deprecated(strcpy, localtime, etc.)
+#endif
+
+namespace orgQhull {
+
+#//!\name Class objects
+facetT QhullFacet::
+s_empty_facet= {0,0,0,0,{0},
+        0,0,0,0,0,
+        0,0,0,0,0,
+        0,0,0,0,0,
+        0,0,0,0,0,
+        0,0,0,0,0,
+        0,0,0,0,0,
+        0,0,0,0};
+
+#//!\name Constructors
+
+QhullFacet::
+QhullFacet(const Qhull &q) 
+: qh_facet(&s_empty_facet)
+, qh_qh(q.qh())
+{
+}
+
+QhullFacet::
+QhullFacet(const Qhull &q, facetT *f) 
+: qh_facet(f ? f : &s_empty_facet)
+, qh_qh(q.qh())
+{
+}
+
+#//!\name GetSet
+
+//! Return voronoi center or facet centrum.  Derived from qh_printcenter [io_r.c]
+//! if printFormat=qh_PRINTtriangles and qh.DELAUNAY, returns centrum of a Delaunay facet
+//! Sets center if needed
+//! Code duplicated for PrintCenter and getCenter
+//! Returns QhullPoint() if none or qh_INFINITE
+QhullPoint QhullFacet::
+getCenter(qh_PRINT printFormat)
+{
+    if(!qh_qh){
+        // returns QhullPoint()
+    }else if(qh_qh->CENTERtype==qh_ASvoronoi){
+        if(!qh_facet->normal || !qh_facet->upperdelaunay || !qh_qh->ATinfinity){
+            if(!qh_facet->center){
+                QH_TRY_(qh_qh){ // no object creation -- destructors skipped on longjmp()
+                    qh_facet->center= qh_facetcenter(qh_qh, qh_facet->vertices);
+                }
+                qh_qh->NOerrexit= true;
+                qh_qh->maybeThrowQhullMessage(QH_TRY_status);
+            }
+            return QhullPoint(qh_qh, qh_qh->hull_dim-1, qh_facet->center);
+        }
+    }else if(qh_qh->CENTERtype==qh_AScentrum){
+        volatile int numCoords= qh_qh->hull_dim;
+        if(printFormat==qh_PRINTtriangles && qh_qh->DELAUNAY){
+            numCoords--;
+        }
+        if(!qh_facet->center){
+            QH_TRY_(qh_qh){ // no object creation -- destructors skipped on longjmp()
+                qh_facet->center= qh_getcentrum(qh_qh, getFacetT());
+            }
+            qh_qh->NOerrexit= true;
+            qh_qh->maybeThrowQhullMessage(QH_TRY_status);
+        }
+        return QhullPoint(qh_qh, numCoords, qh_facet->center);
+    }
+    return QhullPoint();
+ }//getCenter
+
+//! Return innerplane clearly below the vertices
+//! from io_r.c[qh_PRINTinner]
+QhullHyperplane QhullFacet::
+innerplane() const{
+    QhullHyperplane h;
+    if(qh_qh){
+        realT inner;
+        // Does not error, TRY_QHULL_ not needed
+        qh_outerinner(qh_qh, const_cast<facetT *>(getFacetT()), NULL, &inner);
+        h= hyperplane();
+        h.setOffset(h.offset()-inner); //inner is negative
+    }
+    return h;
+}//innerplane
+
+//! Return outerplane clearly above all points
+//! from io_r.c[qh_PRINTouter]
+QhullHyperplane QhullFacet::
+outerplane() const{
+    QhullHyperplane h;
+    if(qh_qh){
+        realT outer;
+        // Does not error, TRY_QHULL_ not needed
+        qh_outerinner(qh_qh, const_cast<facetT *>(getFacetT()), &outer, NULL);
+        h= hyperplane();
+        h.setOffset(h.offset()-outer); //outer is positive
+    }
+    return h;
+}//outerplane
+
+//! Set by qh_triangulate for option 'Qt'.
+//! Errors if tricoplanar and facetArea() or qh_getarea() called first.
+QhullFacet QhullFacet::
+tricoplanarOwner() const
+{
+    if(qh_facet->tricoplanar){
+        if(qh_facet->isarea){
+            throw QhullError(10018, "Qhull error: facetArea() or qh_getarea() previously called.  triCoplanarOwner() is not available.");
+        }
+        return QhullFacet(qh_qh, qh_facet->f.triowner);
+    }
+    return QhullFacet(qh_qh); 
+}//tricoplanarOwner
+
+QhullPoint QhullFacet::
+voronoiVertex()
+{
+    if(qh_qh && qh_qh->CENTERtype!=qh_ASvoronoi){
+          throw QhullError(10052, "Error: QhullFacet.voronoiVertex() requires option 'v' (qh_ASvoronoi)");
+    }
+    return getCenter();
+}//voronoiVertex
+
+#//!\name Value
+
+//! Disables tricoplanarOwner()
+double QhullFacet::
+facetArea()
+{
+    if(qh_qh && !qh_facet->isarea){
+        QH_TRY_(qh_qh){ // no object creation -- destructors skipped on longjmp()
+            qh_facet->f.area= qh_facetarea(qh_qh, qh_facet);
+            qh_facet->isarea= True;
+        }
+        qh_qh->NOerrexit= true;
+        qh_qh->maybeThrowQhullMessage(QH_TRY_status);
+    }
+    return qh_facet->f.area;
+}//facetArea
+
+#//!\name Foreach
+
+QhullPointSet QhullFacet::
+coplanarPoints() const
+{
+    return QhullPointSet(qh_qh, qh_facet->coplanarset);
+}//coplanarPoints
+
+QhullFacetSet QhullFacet::
+neighborFacets() const
+{
+    return QhullFacetSet(qh_qh, qh_facet->neighbors);
+}//neighborFacets
+
+QhullPointSet QhullFacet::
+outsidePoints() const
+{
+    return QhullPointSet(qh_qh, qh_facet->outsideset);
+}//outsidePoints
+
+QhullRidgeSet QhullFacet::
+ridges() const
+{
+    return QhullRidgeSet(qh_qh, qh_facet->ridges);
+}//ridges
+
+QhullVertexSet QhullFacet::
+vertices() const
+{
+    return QhullVertexSet(qh_qh, qh_facet->vertices);
+}//vertices
+
+}//namespace orgQhull
+
+#//!\name operator<<
+
+using std::ostream;
+
+using orgQhull::QhullFacet;
+using orgQhull::QhullFacetSet;
+using orgQhull::QhullPoint;
+using orgQhull::QhullPointSet;
+using orgQhull::QhullRidge;
+using orgQhull::QhullRidgeSet;
+using orgQhull::QhullSetBase;
+using orgQhull::QhullVertexSet;
+
+ostream &
+operator<<(ostream &os, const QhullFacet::PrintFacet &pr)
+{
+    os << pr.message;
+    QhullFacet f= *pr.facet;
+    if(f.getFacetT()==0){ // Special values from set iterator
+        os << " NULLfacet" << endl;
+        return os;
+    }
+    if(f.getFacetT()==qh_MERGEridge){
+        os << " MERGEridge" << endl;
+        return os;
+    }
+    if(f.getFacetT()==qh_DUPLICATEridge){
+        os << " DUPLICATEridge" << endl;
+        return os;
+    }
+    os << f.printHeader();
+    if(!f.ridges().isEmpty()){
+        os << f.printRidges();
+    }
+    return os;
+}//operator<< PrintFacet
+
+//! Print Voronoi center or facet centrum to stream.  Same as qh_printcenter [_r.]
+//! Code duplicated for PrintCenter and getCenter
+//! Sets center if needed
+ostream &
+operator<<(ostream &os, const QhullFacet::PrintCenter &pr)
+{
+    facetT *f= pr.facet->getFacetT();
+    if(pr.facet->qh()->CENTERtype!=qh_ASvoronoi && pr.facet->qh()->CENTERtype!=qh_AScentrum){
+        return os;
+    }
+    if (pr.message){
+        os << pr.message;
+    }
+    int numCoords;
+    if(pr.facet->qh()->CENTERtype==qh_ASvoronoi){
+        numCoords= pr.facet->qh()->hull_dim-1;
+        if(!f->normal || !f->upperdelaunay || !pr.facet->qh()->ATinfinity){
+            if(!f->center){
+                f->center= qh_facetcenter(pr.facet->qh(), f->vertices);
+            }
+            for(int k=0; k<numCoords; k++){
+                os << f->center[k] << " "; // FIXUP QH11010 qh_REAL_1
+            }
+        }else{
+            for(int k=0; k<numCoords; k++){
+                os << qh_INFINITE << " "; // FIXUP QH11010 qh_REAL_1
+            }
+        }
+    }else{ // qh CENTERtype==qh_AScentrum
+        numCoords= pr.facet->qh()->hull_dim;
+        if(pr.print_format==qh_PRINTtriangles && pr.facet->qh()->DELAUNAY){
+            numCoords--;
+        }
+        if(!f->center){
+            f->center= qh_getcentrum(pr.facet->qh(), f);
+        }
+        for(int k=0; k<numCoords; k++){
+            os << f->center[k] << " "; // FIXUP QH11010 qh_REAL_1
+        }
+    }
+    if(pr.print_format==qh_PRINTgeom && numCoords==2){
+        os << " 0";
+    }
+    os << endl;
+    return os;
+}//operator<< PrintCenter
+
+//! Print flags for facet to stream.  Space prefix.  From qh_printfacetheader [io_r.c]
+ostream &
+operator<<(ostream &os, const QhullFacet::PrintFlags &p)
+{
+    const facetT *f= p.facet->getFacetT();
+    if(p.message){
+        os << p.message;
+    }
+
+    os << (p.facet->isTopOrient() ? " top" : " bottom");
+    if(p.facet->isSimplicial()){
+        os << " simplicial";
+    }
+    if(p.facet->isTriCoplanar()){
+        os << " tricoplanar";
+    }
+    if(p.facet->isUpperDelaunay()){
+        os << " upperDelaunay";
+    }
+    if(f->visible){
+        os << " visible";
+    }
+    if(f->newfacet){
+        os << " new";
+    }
+    if(f->tested){
+        os << " tested";
+    }
+    if(!f->good){
+        os << " notG";
+    }
+    if(f->seen){
+        os << " seen";
+    }
+    if(f->coplanar){
+        os << " coplanar";
+    }
+    if(f->mergehorizon){
+        os << " mergehorizon";
+    }
+    if(f->keepcentrum){
+        os << " keepcentrum";
+    }
+    if(f->dupridge){
+        os << " dupridge";
+    }
+    if(f->mergeridge && !f->mergeridge2){
+        os << " mergeridge1";
+    }
+    if(f->mergeridge2){
+        os << " mergeridge2";
+    }
+    if(f->newmerge){
+        os << " newmerge";
+    }
+    if(f->flipped){
+        os << " flipped";
+    }
+    if(f->notfurthest){
+        os << " notfurthest";
+    }
+    if(f->degenerate){
+        os << " degenerate";
+    }
+    if(f->redundant){
+        os << " redundant";
+    }
+    os << endl;
+    return os;
+}//operator<< PrintFlags
+
+//! Print header for facet to stream. Space prefix.  From qh_printfacetheader [io_r.c]
+ostream &
+operator<<(ostream &os, const QhullFacet::PrintHeader &pr)
+{
+    QhullFacet facet= *pr.facet;
+    facetT *f= facet.getFacetT();
+    os << "- f" << facet.id() << endl;
+    os << facet.printFlags("    - flags:");
+    if(f->isarea){
+        os << "    - area: " << f->f.area << endl; //FIXUP QH11010 2.2g
+    }else if(pr.facet->qh()->NEWfacets && f->visible && f->f.replace){
+        os << "    - replacement: f" << f->f.replace->id << endl;
+    }else if(f->newfacet){
+        if(f->f.samecycle && f->f.samecycle != f){
+            os << "    - shares same visible/horizon as f" << f->f.samecycle->id << endl;
+        }
+    }else if(f->tricoplanar /* !isarea */){
+        if(f->f.triowner){
+            os << "    - owner of normal & centrum is facet f" << f->f.triowner->id << endl;
+        }
+    }else if(f->f.newcycle){
+        os << "    - was horizon to f" << f->f.newcycle->id << endl;
+    }
+    if(f->nummerge){
+        os << "    - merges: " << f->nummerge << endl;
+    }
+    os << facet.hyperplane().print("    - normal: ", "\n    - offset: "); // FIXUP QH11010 %10.7g
+    if(pr.facet->qh()->CENTERtype==qh_ASvoronoi || f->center){
+        os << facet.printCenter(qh_PRINTfacets, "    - center: ");
+    }
+#if qh_MAXoutside
+    if(f->maxoutside > pr.facet->qh()->DISTround){
+        os << "    - maxoutside: " << f->maxoutside << endl; //FIXUP QH11010 %10.7g
+    }
+#endif
+    QhullPointSet ps= facet.outsidePoints();
+    if(!ps.isEmpty()){
+        QhullPoint furthest= ps.last();
+        if (ps.size() < 6) {
+            os << "    - outside set(furthest p" << furthest.id() << "):" << endl;
+            for(QhullPointSet::iterator i=ps.begin(); i!=ps.end(); ++i){
+                QhullPoint p= *i;
+                os << p.print("     ");
+            }
+        }else if(ps.size()<21){
+            os << ps.print("    - outside set:");
+        }else{
+            os << "    - outside set:  " << ps.size() << " points.";
+            os << furthest.print("  Furthest");
+        }
+#if !qh_COMPUTEfurthest
+        os << "    - furthest distance= " << f->furthestdist << endl; //FIXUP QH11010 %2.2g
+#endif
+    }
+    QhullPointSet cs= facet.coplanarPoints();
+    if(!cs.isEmpty()){
+        QhullPoint furthest= cs.last();
+        if (cs.size() < 6) {
+            os << "    - coplanar set(furthest p" << furthest.id() << "):" << endl;
+            for(QhullPointSet::iterator i=cs.begin(); i!=cs.end(); ++i){
+                QhullPoint p= *i;
+                os << p.print("     ");
+            }
+        }else if(cs.size()<21){
+            os << cs.print("    - coplanar set:");
+        }else{
+            os << "    - coplanar set:  " << cs.size() << " points.";
+            os << furthest.print("  Furthest");
+        }
+        // FIXUP QH11027 Can/should zinc_(Zdistio) be called from C++ interface
+        double d= facet.distance(furthest);
+        os << "      furthest distance= " << d << endl; //FIXUP QH11010 %2.2g
+    }
+    QhullVertexSet vs= facet.vertices();
+    if(!vs.isEmpty()){
+        os << vs.print("    - vertices:");
+    }
+    QhullFacetSet fs= facet.neighborFacets();
+    fs.selectAll();
+    if(!fs.isEmpty()){
+        os << fs.printIdentifiers("    - neighboring facets:");
+    }
+    return os;
+}//operator<< PrintHeader
+
+
+//! Print ridges of facet to stream.  Same as qh_printfacetridges [io_r.c]
+ostream &
+operator<<(ostream &os, const QhullFacet::PrintRidges &pr)
+{
+    const QhullFacet facet= *pr.facet;
+    facetT *f= facet.getFacetT();
+    QhullRidgeSet rs= facet.ridges();
+    if(!rs.isEmpty()){
+        if(f->visible && pr.facet->qh()->NEWfacets){
+            os << "    - ridges(ids may be garbage):";
+            for(QhullRidgeSet::iterator i=rs.begin(); i!=rs.end(); ++i){
+                QhullRidge r= *i;
+                os << " r" << r.id();
+            }
+            os << endl;
+        }else{
+            os << "    - ridges:" << endl;
+        }
+
+        // Keep track of printed ridges
+        for(QhullRidgeSet::iterator i=rs.begin(); i!=rs.end(); ++i){
+            QhullRidge r= *i;
+            r.getRidgeT()->seen= false;
+        }
+        int ridgeCount= 0;
+        if(facet.dimension()==3){
+            for(QhullRidge r= rs.first(); !r.getRidgeT()->seen; r= r.nextRidge3d(facet)){
+                r.getRidgeT()->seen= true;
+                os << r.print("");
+                ++ridgeCount;
+                if(!r.hasNextRidge3d(facet)){
+                    break;
+                }
+            }
+        }else {
+            QhullFacetSet ns(facet.neighborFacets());
+            for(QhullFacetSet::iterator i=ns.begin(); i!=ns.end(); ++i){
+                QhullFacet neighbor= *i;
+                QhullRidgeSet nrs(neighbor.ridges());
+                for(QhullRidgeSet::iterator j=nrs.begin(); j!=nrs.end(); ++j){
+                    QhullRidge r= *j;
+                    if(r.otherFacet(neighbor)==facet){
+                        r.getRidgeT()->seen= true;
+                        os << r.print("");
+                        ridgeCount++;
+                    }
+                }
+            }
+        }
+        if(ridgeCount!=rs.count()){
+            os << "     - all ridges:";
+            for(QhullRidgeSet::iterator i=rs.begin(); i!=rs.end(); ++i){
+                QhullRidge r= *i;
+                os << " r" << r.id();
+            }
+            os << endl;
+        }
+        for(QhullRidgeSet::iterator i=rs.begin(); i!=rs.end(); ++i){
+            QhullRidge r= *i;
+            if(!r.getRidgeT()->seen){
+                os << r.print("");
+            }
+        }
+    }
+    return os;
+}//operator<< PrintRidges
+
+// "No conversion" error if defined inline
+ostream &
+operator<<(ostream &os, QhullFacet &f)
+{
+    os << f.print("");
+    return os;
+}//<< QhullFacet
diff --git a/xs/src/qhull/src/libqhullcpp/QhullFacet.h b/xs/src/qhull/src/libqhullcpp/QhullFacet.h
new file mode 100644
index 0000000000..ae4f008fd2
--- /dev/null
+++ b/xs/src/qhull/src/libqhullcpp/QhullFacet.h
@@ -0,0 +1,151 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
+** $Id: //main/2015/qhull/src/libqhullcpp/QhullFacet.h#4 $$Change: 2079 $
+** $DateTime: 2016/02/07 17:43:34 $$Author: bbarber $
+**
+****************************************************************************/
+
+#ifndef QHULLFACET_H
+#define QHULLFACET_H
+
+#include "libqhull_r/qhull_ra.h"
+#include "libqhullcpp/QhullHyperplane.h"
+#include "libqhullcpp/QhullPoint.h"
+#include "libqhullcpp/QhullSet.h"
+#include "libqhullcpp/QhullPointSet.h"
+
+#include <ostream>
+
+namespace orgQhull {
+
+#//!\name Used here
+    class Coordinates;
+    class Qhull;
+    class QhullFacetSet;
+    class QhullRidge;
+    class QhullVertex;
+    class QhullVertexSet;
+
+#//!\name Defined here
+    class QhullFacet;
+    typedef QhullSet<QhullRidge>  QhullRidgeSet;
+
+//! A QhullFacet is the C++ equivalent to Qhull's facetT*
+class QhullFacet {
+
+#//!\name Defined here
+public:
+    typedef facetT *   base_type;  // for QhullVertexSet
+
+private:
+#//!\name Fields -- no additions (QhullFacetSet of facetT*)
+    facetT *            qh_facet;  //!< Corresponding facetT, may be 0 for corner cases (e.g., *facetSet.end()==0) and tricoplanarOwner()
+    QhullQh *           qh_qh;     //!< QhullQh/qhT for facetT, may be 0
+
+#//!\name Class objects
+    static facetT       s_empty_facet; // needed for shallow copy
+
+public:
+#//!\name Constructors
+                        QhullFacet() : qh_facet(&s_empty_facet), qh_qh(0) {}
+    explicit            QhullFacet(const Qhull &q);
+                        QhullFacet(const Qhull &q, facetT *f);
+    explicit            QhullFacet(QhullQh *qqh) : qh_facet(&s_empty_facet), qh_qh(qqh) {}
+                        QhullFacet(QhullQh *qqh, facetT *f) : qh_facet(f ? f : &s_empty_facet), qh_qh(qqh) {}
+                        // Creates an alias.  Does not copy QhullFacet.  Needed for return by value and parameter passing
+                        QhullFacet(const QhullFacet &other) : qh_facet(other.qh_facet ? other.qh_facet : &s_empty_facet), qh_qh(other.qh_qh) {}
+                        // Creates an alias.  Does not copy QhullFacet.  Needed for vector<QhullFacet>
+    QhullFacet &        operator=(const QhullFacet &other) { qh_facet= other.qh_facet ? other.qh_facet : &s_empty_facet; qh_qh= other.qh_qh; return *this; }
+                        ~QhullFacet() {}
+
+
+#//!\name GetSet
+    int                 dimension() const { return (qh_qh ? qh_qh->hull_dim : 0); }
+    QhullPoint          getCenter() { return getCenter(qh_PRINTpoints); }
+    QhullPoint          getCenter(qh_PRINT printFormat);
+    facetT *            getBaseT() const { return getFacetT(); } //!< For QhullSet<QhullFacet>
+                        // Do not define facetT().  It conflicts with return type facetT*
+    facetT *            getFacetT() const { return qh_facet; }
+    QhullHyperplane     hyperplane() const { return QhullHyperplane(qh_qh, dimension(), qh_facet->normal, qh_facet->offset); }
+    countT              id() const { return (qh_facet ? qh_facet->id : (int)qh_IDunknown); }
+    QhullHyperplane     innerplane() const;
+    bool                isValid() const { return qh_qh && qh_facet && qh_facet != &s_empty_facet; }
+    bool                isGood() const { return qh_facet && qh_facet->good; }
+    bool                isSimplicial() const { return qh_facet && qh_facet->simplicial; }
+    bool                isTopOrient() const { return qh_facet && qh_facet->toporient; }
+    bool                isTriCoplanar() const { return qh_facet && qh_facet->tricoplanar; }
+    bool                isUpperDelaunay() const { return qh_facet && qh_facet->upperdelaunay; }
+    QhullFacet          next() const { return QhullFacet(qh_qh, qh_facet->next); }
+    bool                operator==(const QhullFacet &other) const { return qh_facet==other.qh_facet; }
+    bool                operator!=(const QhullFacet &other) const { return !operator==(other); }
+    QhullHyperplane     outerplane() const;
+    QhullFacet          previous() const { return QhullFacet(qh_qh, qh_facet->previous); }
+    QhullQh *           qh() const { return qh_qh; }
+    QhullFacet          tricoplanarOwner() const;
+    QhullPoint          voronoiVertex();
+
+#//!\name value
+    //! Undefined if c.size() != dimension()
+    double              distance(const Coordinates &c) const { return distance(c.data()); }
+    double              distance(const pointT *p) const { return distance(QhullPoint(qh_qh, const_cast<coordT *>(p))); }
+    double              distance(const QhullPoint &p) const { return hyperplane().distance(p); }
+    double              facetArea();
+
+#//!\name foreach
+    // Can not inline.  Otherwise circular reference
+    QhullPointSet       coplanarPoints() const;
+    QhullFacetSet       neighborFacets() const;
+    QhullPointSet       outsidePoints() const;
+    QhullRidgeSet       ridges() const;
+    QhullVertexSet      vertices() const;
+
+#//!\name IO
+    struct PrintCenter{
+        QhullFacet *    facet;  // non-const due to facet.center()
+        const char *    message;
+        qh_PRINT        print_format;
+                        PrintCenter(QhullFacet &f, qh_PRINT printFormat, const char * s) : facet(&f), message(s), print_format(printFormat){}
+    };//PrintCenter
+    PrintCenter         printCenter(qh_PRINT printFormat, const char *message) { return PrintCenter(*this, printFormat, message); }
+
+    struct PrintFacet{
+        QhullFacet *    facet;  // non-const due to f->center()
+        const char *    message;
+        explicit        PrintFacet(QhullFacet &f, const char * s) : facet(&f), message(s) {}
+    };//PrintFacet
+    PrintFacet          print(const char *message) { return PrintFacet(*this, message); }
+
+    struct PrintFlags{
+        const QhullFacet *facet;
+        const char *    message;
+                        PrintFlags(const QhullFacet &f, const char *s) : facet(&f), message(s) {}
+    };//PrintFlags
+    PrintFlags          printFlags(const char *message) const { return PrintFlags(*this, message); }
+
+    struct PrintHeader{
+        QhullFacet *    facet;  // non-const due to f->center()
+                        PrintHeader(QhullFacet &f) : facet(&f) {}
+    };//PrintHeader
+    PrintHeader         printHeader() { return PrintHeader(*this); }
+
+    struct PrintRidges{
+        const QhullFacet *facet;
+                        PrintRidges(QhullFacet &f) : facet(&f) {}
+    };//PrintRidges
+    PrintRidges         printRidges() { return PrintRidges(*this); }
+
+};//class QhullFacet
+
+}//namespace orgQhull
+
+#//!\name Global
+
+std::ostream &operator<<(std::ostream &os, const orgQhull::QhullFacet::PrintFacet &pr);
+std::ostream &operator<<(std::ostream &os, const orgQhull::QhullFacet::PrintCenter &pr);
+std::ostream &operator<<(std::ostream &os, const orgQhull::QhullFacet::PrintFlags &pr);
+std::ostream &operator<<(std::ostream &os, const orgQhull::QhullFacet::PrintHeader &pr);
+std::ostream &operator<<(std::ostream &os, const orgQhull::QhullFacet::PrintRidges &pr);
+std::ostream &operator<<(std::ostream &os, orgQhull::QhullFacet &f); // non-const due to qh_getcenter()
+
+#endif // QHULLFACET_H
diff --git a/xs/src/qhull/src/libqhullcpp/QhullFacetList.cpp b/xs/src/qhull/src/libqhullcpp/QhullFacetList.cpp
new file mode 100644
index 0000000000..9e6ddfe9ec
--- /dev/null
+++ b/xs/src/qhull/src/libqhullcpp/QhullFacetList.cpp
@@ -0,0 +1,174 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
+** $Id: //main/2015/qhull/src/libqhullcpp/QhullFacetList.cpp#3 $$Change: 2066 $
+** $DateTime: 2016/01/18 19:29:17 $$Author: bbarber $
+**
+****************************************************************************/
+
+#//! QhullFacetList -- Qhull's linked facets, as a C++ class
+
+#include "libqhullcpp/QhullFacetList.h"
+
+#include "libqhullcpp/QhullFacet.h"
+#include "libqhullcpp/QhullPoint.h"
+#include "libqhullcpp/QhullRidge.h"
+#include "libqhullcpp/QhullVertex.h"
+
+using std::string;
+using std::vector;
+
+#ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
+#pragma warning( disable : 4611)  // interaction between '_setjmp' and C++ object destruction is non-portable
+#pragma warning( disable : 4996)  // function was declared deprecated(strcpy, localtime, etc.)
+#endif
+
+namespace orgQhull {
+
+#//!\name Constructors
+
+QhullFacetList::
+QhullFacetList(const Qhull &q, facetT *b, facetT *e ) 
+: QhullLinkedList<QhullFacet>(QhullFacet(q, b), QhullFacet(q, e))
+, select_all(false)
+{
+}
+
+#//!\name Conversions
+
+// See qt_qhull.cpp for QList conversions
+
+#ifndef QHULL_NO_STL
+std::vector<QhullFacet> QhullFacetList::
+toStdVector() const
+{
+    QhullLinkedListIterator<QhullFacet> i(*this);
+    std::vector<QhullFacet> vs;
+    while(i.hasNext()){
+        QhullFacet f= i.next();
+        if(isSelectAll() || f.isGood()){
+            vs.push_back(f);
+        }
+    }
+    return vs;
+}//toStdVector
+#endif //QHULL_NO_STL
+
+#ifndef QHULL_NO_STL
+//! Same as PrintVertices
+std::vector<QhullVertex> QhullFacetList::
+vertices_toStdVector() const
+{
+    std::vector<QhullVertex> vs;
+    QhullVertexSet qvs(qh(), first().getFacetT(), 0, isSelectAll());
+
+    for(QhullVertexSet::iterator i=qvs.begin(); i!=qvs.end(); ++i){
+        vs.push_back(*i);
+    }
+    return vs;
+}//vertices_toStdVector
+#endif //QHULL_NO_STL
+
+#//!\name GetSet
+
+bool QhullFacetList::
+contains(const QhullFacet &facet) const
+{
+    if(isSelectAll()){
+        return QhullLinkedList<QhullFacet>::contains(facet);
+    }
+    for(QhullFacetList::const_iterator i=begin(); i != end(); ++i){
+        QhullFacet f= *i;
+        if(f==facet && f.isGood()){
+            return true;
+        }
+    }
+    return false;
+}//contains
+
+int QhullFacetList::
+count() const
+{
+    if(isSelectAll()){
+        return QhullLinkedList<QhullFacet>::count();
+    }
+    int counter= 0;
+    for(QhullFacetList::const_iterator i=begin(); i != end(); ++i){
+        if((*i).isGood()){
+            counter++;
+        }
+    }
+    return counter;
+}//count
+
+int QhullFacetList::
+count(const QhullFacet &facet) const
+{
+    if(isSelectAll()){
+        return QhullLinkedList<QhullFacet>::count(facet);
+    }
+    int counter= 0;
+    for(QhullFacetList::const_iterator i=begin(); i != end(); ++i){
+        QhullFacet f= *i;
+        if(f==facet && f.isGood()){
+            counter++;
+        }
+    }
+    return counter;
+}//count
+
+}//namespace orgQhull
+
+#//!\name Global functions
+
+using std::endl;
+using std::ostream;
+using orgQhull::QhullFacet;
+using orgQhull::QhullFacetList;
+using orgQhull::QhullVertex;
+using orgQhull::QhullVertexSet;
+
+ostream &
+operator<<(ostream &os, const QhullFacetList::PrintFacetList &pr)
+{
+    os << pr.print_message;
+    QhullFacetList fs= *pr.facet_list;
+    os << "Vertices for " << fs.count() << " facets" << endl;
+    os << fs.printVertices();
+    os << fs.printFacets();
+    return os;
+}//operator<<
+
+//! Print facet list to stream.  From qh_printafacet [io_r.c]
+ostream &
+operator<<(ostream &os, const QhullFacetList::PrintFacets &pr)
+{
+    for(QhullFacetList::const_iterator i= pr.facet_list->begin(); i != pr.facet_list->end(); ++i){
+        QhullFacet f= *i;
+        if(pr.facet_list->isSelectAll() || f.isGood()){
+            os << f.print("");
+        }
+    }
+    return os;
+}//printFacets
+
+//! Print vertices of good faces in facet list to stream.  From qh_printvertexlist [io_r.c]
+//! Same as vertices_toStdVector
+ostream &
+operator<<(ostream &os, const QhullFacetList::PrintVertices &pr)
+{
+    QhullVertexSet vs(pr.facet_list->qh(), pr.facet_list->first().getFacetT(), NULL, pr.facet_list->isSelectAll());
+    for(QhullVertexSet::iterator i=vs.begin(); i!=vs.end(); ++i){
+        QhullVertex v= *i;
+        os << v.print("");
+    }
+    return os;
+}//printVertices
+
+std::ostream &
+operator<<(ostream &os, const QhullFacetList &fs)
+{
+    os << fs.printFacets();
+    return os;
+}//QhullFacetList
+
diff --git a/xs/src/qhull/src/libqhullcpp/QhullFacetList.h b/xs/src/qhull/src/libqhullcpp/QhullFacetList.h
new file mode 100644
index 0000000000..e61e568403
--- /dev/null
+++ b/xs/src/qhull/src/libqhullcpp/QhullFacetList.h
@@ -0,0 +1,106 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
+** $Id: //main/2015/qhull/src/libqhullcpp/QhullFacetList.h#2 $$Change: 2066 $
+** $DateTime: 2016/01/18 19:29:17 $$Author: bbarber $
+**
+****************************************************************************/
+
+#ifndef QHULLFACETLIST_H
+#define QHULLFACETLIST_H
+
+#include "libqhullcpp/QhullLinkedList.h"
+#include "libqhullcpp/QhullFacet.h"
+
+#include <ostream>
+
+#ifndef QHULL_NO_STL
+#include <vector>
+#endif
+
+namespace orgQhull {
+
+#//!\name Used here
+    class Qhull;
+    class QhullFacet;
+    class QhullQh;
+
+#//!\name Defined here
+    //! QhullFacetList -- List of QhullFacet/facetT, as a C++ class.  
+    //!\see QhullFacetSet.h
+    class QhullFacetList;
+    //! QhullFacetListIterator -- if(f.isGood()){ ... }
+    typedef QhullLinkedListIterator<QhullFacet> QhullFacetListIterator;
+
+class QhullFacetList : public QhullLinkedList<QhullFacet> {
+
+#//!\name  Fields
+private:
+    bool                select_all;   //! True if include bad facets.  Default is false.
+
+#//!\name Constructors
+public:
+                        QhullFacetList(const Qhull &q, facetT *b, facetT *e);
+                        QhullFacetList(QhullQh *qqh, facetT *b, facetT *e);
+                        QhullFacetList(QhullFacet b, QhullFacet e) : QhullLinkedList<QhullFacet>(b, e), select_all(false) {}
+                        //Copy constructor copies pointer but not contents.  Needed for return by value and parameter passing.
+                        QhullFacetList(const QhullFacetList &other) : QhullLinkedList<QhullFacet>(*other.begin(), *other.end()), select_all(other.select_all) {}
+    QhullFacetList &    operator=(const QhullFacetList &other) { QhullLinkedList<QhullFacet>::operator =(other); select_all= other.select_all; return *this; }
+                        ~QhullFacetList() {}
+
+private:                //!Disable default constructor.  See QhullLinkedList
+                    QhullFacetList();
+public:
+
+#//!\name Conversion
+#ifndef QHULL_NO_STL
+    std::vector<QhullFacet> toStdVector() const;
+    std::vector<QhullVertex> vertices_toStdVector() const;
+#endif //QHULL_NO_STL
+#ifdef QHULL_USES_QT
+    QList<QhullFacet>   toQList() const;
+    QList<QhullVertex>  vertices_toQList() const;
+#endif //QHULL_USES_QT
+
+#//!\name GetSet
+                        //! Filtered by facet.isGood().  May be 0 when !isEmpty().
+    countT              count() const;
+    bool                contains(const QhullFacet &f) const;
+    countT              count(const QhullFacet &f) const;
+    bool                isSelectAll() const { return select_all; }
+    QhullQh *           qh() const { return first().qh(); }
+    void                selectAll() { select_all= true; }
+    void                selectGood() { select_all= false; }
+                        //!< operator==() does not depend on isGood()
+
+#//!\name IO
+    struct PrintFacetList{
+        const QhullFacetList *facet_list;
+        const char *    print_message;   //!< non-null message
+                        PrintFacetList(const QhullFacetList &fl, const char *message) : facet_list(&fl), print_message(message) {}
+    };//PrintFacetList
+    PrintFacetList      print(const char *message) const  { return PrintFacetList(*this, message); }
+
+    struct PrintFacets{
+        const QhullFacetList *facet_list;
+                        PrintFacets(const QhullFacetList &fl) : facet_list(&fl) {}
+    };//PrintFacets
+    PrintFacets         printFacets() const { return PrintFacets(*this); }
+
+    struct PrintVertices{
+        const QhullFacetList *facet_list;
+                        PrintVertices(const QhullFacetList &fl) : facet_list(&fl) {}
+    };//PrintVertices
+    PrintVertices       printVertices() const { return PrintVertices(*this); }
+};//class QhullFacetList
+
+}//namespace orgQhull
+
+#//!\name == Global namespace =========================================
+
+std::ostream &operator<<(std::ostream &os, const orgQhull::QhullFacetList::PrintFacetList &p);
+std::ostream &operator<<(std::ostream &os, const orgQhull::QhullFacetList::PrintFacets &p);
+std::ostream &operator<<(std::ostream &os, const orgQhull::QhullFacetList::PrintVertices &p);
+std::ostream &operator<<(std::ostream &os, const orgQhull::QhullFacetList &fs);
+
+#endif // QHULLFACETLIST_H
diff --git a/xs/src/qhull/src/libqhullcpp/QhullFacetSet.cpp b/xs/src/qhull/src/libqhullcpp/QhullFacetSet.cpp
new file mode 100644
index 0000000000..d30c21e26a
--- /dev/null
+++ b/xs/src/qhull/src/libqhullcpp/QhullFacetSet.cpp
@@ -0,0 +1,147 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
+** $Id: //main/2015/qhull/src/libqhullcpp/QhullFacetSet.cpp#2 $$Change: 2066 $
+** $DateTime: 2016/01/18 19:29:17 $$Author: bbarber $
+**
+****************************************************************************/
+
+#//! QhullFacetSet -- Qhull's linked facets, as a C++ class
+
+#include "libqhullcpp/QhullFacetSet.h"
+
+#include "libqhullcpp/QhullFacet.h"
+#include "libqhullcpp/QhullPoint.h"
+#include "libqhullcpp/QhullRidge.h"
+#include "libqhullcpp/QhullVertex.h"
+
+#ifndef QHULL_NO_STL
+using std::vector;
+#endif
+
+#ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
+#pragma warning( disable : 4611)  // interaction between '_setjmp' and C++ object destruction is non-portable
+#pragma warning( disable : 4996)  // function was declared deprecated(strcpy, localtime, etc.)
+#endif
+
+namespace orgQhull {
+
+#//!\name Conversions
+
+// See qt-qhull.cpp for QList conversions
+
+#ifndef QHULL_NO_STL
+std::vector<QhullFacet> QhullFacetSet::
+toStdVector() const
+{
+    QhullSetIterator<QhullFacet> i(*this);
+    std::vector<QhullFacet> vs;
+    while(i.hasNext()){
+        QhullFacet f= i.next();
+        if(isSelectAll() || f.isGood()){
+            vs.push_back(f);
+        }
+    }
+    return vs;
+}//toStdVector
+#endif //QHULL_NO_STL
+
+#//!\name GetSet
+
+bool QhullFacetSet::
+contains(const QhullFacet &facet) const
+{
+    if(isSelectAll()){
+        return QhullSet<QhullFacet>::contains(facet);
+    }
+    for(QhullFacetSet::const_iterator i=begin(); i != end(); ++i){
+        QhullFacet f= *i;
+        if(f==facet && f.isGood()){
+            return true;
+        }
+    }
+    return false;
+}//contains
+
+int QhullFacetSet::
+count() const
+{
+    if(isSelectAll()){
+        return QhullSet<QhullFacet>::count();
+    }
+    int counter= 0;
+    for(QhullFacetSet::const_iterator i=begin(); i != end(); ++i){
+        QhullFacet f= *i;
+        if(f.isGood()){
+            counter++;
+        }
+    }
+    return counter;
+}//count
+
+int QhullFacetSet::
+count(const QhullFacet &facet) const
+{
+    if(isSelectAll()){
+        return QhullSet<QhullFacet>::count(facet);
+    }
+    int counter= 0;
+    for(QhullFacetSet::const_iterator i=begin(); i != end(); ++i){
+        QhullFacet f= *i;
+        if(f==facet && f.isGood()){
+            counter++;
+        }
+    }
+    return counter;
+}//count
+
+}//namespace orgQhull
+
+#//!\name Global functions
+
+using std::endl;
+using std::ostream;
+using orgQhull::QhullFacet;
+using orgQhull::QhullFacetSet;
+
+ostream &
+operator<<(ostream &os, const QhullFacetSet &fs)
+{
+    os << fs.print("");
+    return os;
+}//<<QhullFacetSet
+
+ostream &
+
+operator<<(ostream &os, const QhullFacetSet::PrintFacetSet &pr)
+{
+    os << pr.print_message;
+    QhullFacetSet fs= *pr.facet_set;
+    for(QhullFacetSet::iterator i=fs.begin(); i != fs.end(); ++i){
+        QhullFacet f= *i;
+        if(fs.isSelectAll() || f.isGood()){
+            os << f;
+        }
+    }
+    return os;
+}//<< QhullFacetSet::PrintFacetSet
+
+//! Print facet identifiers to stream.  Space prefix.  From qh_printfacetheader [io_r.c]
+ostream &
+operator<<(ostream &os, const QhullFacetSet::PrintIdentifiers &p)
+{
+    os << p.print_message;
+    for(QhullFacetSet::const_iterator i=p.facet_set->begin(); i!=p.facet_set->end(); ++i){
+        const QhullFacet f= *i;
+        if(f.getFacetT()==qh_MERGEridge){
+            os << " MERGE";
+        }else if(f.getFacetT()==qh_DUPLICATEridge){
+            os << " DUP";
+        }else if(p.facet_set->isSelectAll() || f.isGood()){
+            os << " f" << f.id();
+        }
+    }
+    os << endl;
+    return os;
+}//<<QhullFacetSet::PrintIdentifiers
+
diff --git a/xs/src/qhull/src/libqhullcpp/QhullFacetSet.h b/xs/src/qhull/src/libqhullcpp/QhullFacetSet.h
new file mode 100644
index 0000000000..ee3208559c
--- /dev/null
+++ b/xs/src/qhull/src/libqhullcpp/QhullFacetSet.h
@@ -0,0 +1,97 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
+** $Id: //main/2015/qhull/src/libqhullcpp/QhullFacetSet.h#2 $$Change: 2066 $
+** $DateTime: 2016/01/18 19:29:17 $$Author: bbarber $
+**
+****************************************************************************/
+
+#ifndef QHULLFACETSET_H
+#define QHULLFACETSET_H
+
+#include "libqhullcpp/QhullSet.h"
+#include "libqhullcpp/QhullFacet.h"
+
+#include <ostream>
+
+namespace orgQhull {
+
+#//!\name Used here
+    class Qhull;
+
+#//!\name Defined here
+    //! QhullFacetSet -- a set of Qhull facets, as a C++ class.  See QhullFacetList.h
+    class QhullFacetSet;
+    typedef QhullSetIterator<QhullFacet> QhullFacetSetIterator;
+
+class QhullFacetSet : public QhullSet<QhullFacet> {
+
+#//!\name Defined here
+public:
+    typedef facetT *   base_type;  // for QhullVertexSet
+
+private:
+#//!\name Fields
+    bool                select_all;   //! True if include bad facets.  Default is false.
+
+public:
+#//!\name Constructor
+                        //Conversion from setT* is not type-safe.  Implicit conversion for void* to T
+                        QhullFacetSet(const Qhull &q, setT *s) : QhullSet<QhullFacet>(q, s), select_all(false) {}
+                        QhullFacetSet(QhullQh *qqh, setT *s) : QhullSet<QhullFacet>(qqh, s), select_all(false) {}
+                        //!Copy constructor copies pointers but not contents.  Needed for return by value and parameter passing.
+                        QhullFacetSet(const QhullFacetSet &other) : QhullSet<QhullFacet>(other), select_all(other.select_all) {}
+                        //!Assignment copies pointers but not contents.
+    QhullFacetSet &     operator=(const QhullFacetSet &other) { QhullSet<QhullFacet>::operator=(other); select_all= other.select_all; return *this; }
+
+private:
+                        //!Disable default constructor.  See QhullSetBase
+                        QhullFacetSet();
+public:
+
+#//!\name Conversion
+#ifndef QHULL_NO_STL
+    std::vector<QhullFacet> toStdVector() const;
+#endif //QHULL_NO_STL
+#ifdef QHULL_USES_QT
+    QList<QhullFacet>   toQList() const;
+#endif //QHULL_USES_QT
+
+#//!\name GetSet
+                        //! Filtered by facet.isGood().  May be 0 when !isEmpty().
+    countT              count() const;
+    bool                contains(const QhullFacet &f) const;
+    countT              count(const QhullFacet &f) const;
+    bool                isSelectAll() const { return select_all; }
+                        //! operator==() does not depend on isGood()
+    void                selectAll() { select_all= true; }
+    void                selectGood() { select_all= false; }
+
+#//!\name IO
+    // Not same as QhullFacetList#IO.  A QhullFacetSet is a component of a QhullFacetList.
+
+    struct PrintFacetSet{
+        const QhullFacetSet *facet_set;
+        const char *    print_message;  //!< non-null message
+                        PrintFacetSet(const char *message, const QhullFacetSet *s) : facet_set(s), print_message(message) {}
+    };//PrintFacetSet
+    const PrintFacetSet print(const char *message) const { return PrintFacetSet(message, this); }
+
+    struct PrintIdentifiers{
+        const QhullFacetSet *facet_set;
+        const char *    print_message;  //!< non-null message
+                        PrintIdentifiers(const char *message, const QhullFacetSet *s) : facet_set(s), print_message(message) {}
+    };//PrintIdentifiers
+    PrintIdentifiers    printIdentifiers(const char *message) const { return PrintIdentifiers(message, this); }
+
+};//class QhullFacetSet
+
+}//namespace orgQhull
+
+#//!\name == Global namespace =========================================
+
+std::ostream &operator<<(std::ostream &os, const orgQhull::QhullFacetSet &fs);
+std::ostream &operator<<(std::ostream &os, const orgQhull::QhullFacetSet::PrintFacetSet &pr);
+std::ostream &operator<<(std::ostream &os, const orgQhull::QhullFacetSet::PrintIdentifiers &p);
+
+#endif // QHULLFACETSET_H
diff --git a/xs/src/qhull/src/libqhullcpp/QhullHyperplane.cpp b/xs/src/qhull/src/libqhullcpp/QhullHyperplane.cpp
new file mode 100644
index 0000000000..ed5cc4bae1
--- /dev/null
+++ b/xs/src/qhull/src/libqhullcpp/QhullHyperplane.cpp
@@ -0,0 +1,187 @@
+/****************************************************************************
+**
+** Copyright (c) 2009-2015 C.B. Barber. All rights reserved.
+** $Id: //main/2015/qhull/src/libqhullcpp/QhullHyperplane.cpp#3 $$Change: 2066 $
+** $DateTime: 2016/01/18 19:29:17 $$Author: bbarber $
+**
+****************************************************************************/
+
+#include "libqhullcpp/QhullHyperplane.h"
+
+#include "libqhullcpp/Qhull.h"
+#include "libqhullcpp/QhullPoint.h"
+
+#include <iostream>
+
+
+#ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
+#endif
+
+namespace orgQhull {
+
+#//!\name Constructors
+
+QhullHyperplane::
+QhullHyperplane(const Qhull &q) 
+: hyperplane_coordinates(0)
+, qh_qh(q.qh())
+, hyperplane_offset(0.0)
+, hyperplane_dimension(0)
+{
+}
+
+QhullHyperplane::
+QhullHyperplane(const Qhull &q, int hyperplaneDimension, coordT *c, coordT hyperplaneOffset) 
+: hyperplane_coordinates(c)
+, qh_qh(q.qh())
+, hyperplane_offset(hyperplaneOffset)
+, hyperplane_dimension(hyperplaneDimension)
+{
+}
+
+#//!\name Conversions
+
+// See qt-qhull.cpp for QList conversions
+
+#ifndef QHULL_NO_STL
+std::vector<coordT> QhullHyperplane::
+toStdVector() const
+{
+    QhullHyperplaneIterator i(*this);
+    std::vector<coordT> fs;
+    while(i.hasNext()){
+        fs.push_back(i.next());
+    }
+    fs.push_back(hyperplane_offset);
+    return fs;
+}//toStdVector
+#endif //QHULL_NO_STL
+
+#//!\name GetSet
+
+//! Return true if equal
+//! If qh_qh defined, tests qh.distanceEpsilon and qh.angleEpsilon
+//! otherwise, tests equal coordinates and offset
+bool QhullHyperplane::
+operator==(const QhullHyperplane &other) const
+{
+    if(hyperplane_dimension!=other.hyperplane_dimension || !hyperplane_coordinates || !other.hyperplane_coordinates){
+        return false;
+    }
+    double d= fabs(hyperplane_offset-other.hyperplane_offset);
+    if(d > (qh_qh ? qh_qh->distanceEpsilon() : 0.0)){
+        return false;
+    }
+    double angle= hyperplaneAngle(other);
+
+    double a= fabs(angle-1.0);
+    if(a > (qh_qh ? qh_qh->angleEpsilon() : 0.0)){
+        return false;
+    }
+    return true;
+}//operator==
+
+#//!\name Methods
+
+//! Return distance from point to hyperplane.
+//!   If greater than zero, the point is above the facet (i.e., outside).
+// qh_distplane [geom_r.c], QhullFacet::distance, and QhullHyperplane::distance are copies
+//    Does not support RANDOMdist or logging
+double QhullHyperplane::
+distance(const QhullPoint &p) const
+{
+    const coordT *point= p.coordinates();
+    int dim= p.dimension();
+    QHULL_ASSERT(dim==dimension());
+    const coordT *normal= coordinates();
+    double dist;
+
+    switch (dim){
+  case 2:
+      dist= offset() + point[0] * normal[0] + point[1] * normal[1];
+      break;
+  case 3:
+      dist= offset() + point[0] * normal[0] + point[1] * normal[1] + point[2] * normal[2];
+      break;
+  case 4:
+      dist= offset()+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3];
+      break;
+  case 5:
+      dist= offset()+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3]+point[4]*normal[4];
+      break;
+  case 6:
+      dist= offset()+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3]+point[4]*normal[4]+point[5]*normal[5];
+      break;
+  case 7:
+      dist= offset()+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3]+point[4]*normal[4]+point[5]*normal[5]+point[6]*normal[6];
+      break;
+  case 8:
+      dist= offset()+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3]+point[4]*normal[4]+point[5]*normal[5]+point[6]*normal[6]+point[7]*normal[7];
+      break;
+  default:
+      dist= offset();
+      for (int k=dim; k--; )
+          dist += *point++ * *normal++;
+      break;
+    }
+    return dist;
+}//distance
+
+double QhullHyperplane::
+hyperplaneAngle(const QhullHyperplane &other) const
+{
+    volatile realT result= 0.0;
+    QH_TRY_(qh_qh){ // no object creation -- destructors skipped on longjmp()
+        result= qh_getangle(qh_qh, hyperplane_coordinates, other.hyperplane_coordinates);
+    }
+    qh_qh->NOerrexit= true;
+    qh_qh->maybeThrowQhullMessage(QH_TRY_status);
+    return result;
+}//hyperplaneAngle
+
+double QhullHyperplane::
+norm() const {
+    double d= 0.0;
+    const coordT *c= coordinates();
+    for (int k=dimension(); k--; ){
+        d += *c * *c;
+        ++c;
+    }
+    return sqrt(d);
+}//norm
+
+}//namespace orgQhull
+
+#//!\name Global functions
+
+using std::ostream;
+using orgQhull::QhullHyperplane;
+
+#//!\name GetSet<<
+
+ostream &
+operator<<(ostream &os, const QhullHyperplane &p)
+{
+    os << p.print("");
+    return os;
+}
+
+ostream &
+operator<<(ostream &os, const QhullHyperplane::PrintHyperplane &pr)
+{
+    os << pr.print_message;
+    QhullHyperplane p= *pr.hyperplane;
+    const realT *c= p.coordinates();
+    for(int k=p.dimension(); k--; ){
+        realT r= *c++;
+        if(pr.print_message){
+            os << " " << r; // FIXUP QH11010 %8.4g
+        }else{
+            os << " " << r; // FIXUP QH11010 qh_REAL_1
+        }
+    }
+    os << pr.hyperplane_offset_message << " " << p.offset();
+    os << std::endl;
+    return os;
+}//PrintHyperplane
+
diff --git a/xs/src/qhull/src/libqhullcpp/QhullHyperplane.h b/xs/src/qhull/src/libqhullcpp/QhullHyperplane.h
new file mode 100644
index 0000000000..2868ce5c99
--- /dev/null
+++ b/xs/src/qhull/src/libqhullcpp/QhullHyperplane.h
@@ -0,0 +1,123 @@
+/****************************************************************************
+**
+** Copyright (c) 2009-2015 C.B. Barber. All rights reserved.
+** $Id: //main/2015/qhull/src/libqhullcpp/QhullHyperplane.h#4 $$Change: 2079 $
+** $DateTime: 2016/02/07 17:43:34 $$Author: bbarber $
+**
+****************************************************************************/
+
+#ifndef QHHYPERPLANE_H
+#define QHHYPERPLANE_H
+
+#include "libqhull_r/qhull_ra.h"
+#include "libqhullcpp/QhullError.h"
+#include "libqhullcpp/QhullIterator.h"
+#include "libqhullcpp/QhullQh.h"
+
+#include <ostream>
+
+namespace orgQhull {
+
+#//!\name Used here
+    class Qhull;
+    class QhullPoint;
+
+#//!\name Defined here
+    //! QhullHyperplane as an offset, dimension, and pointer to coordinates
+    class QhullHyperplane;
+    //! Java-style iterator for QhullHyperplane coordinates
+    class QhullHyperplaneIterator;
+
+class QhullHyperplane { // Similar to QhullPoint
+public:
+#//!\name Subtypes
+    typedef const coordT *                  iterator;
+    typedef const coordT *                  const_iterator;
+    typedef QhullHyperplane::iterator       Iterator;
+    typedef QhullHyperplane::const_iterator ConstIterator;
+
+private:
+#//!\name Fields
+    coordT *            hyperplane_coordinates;  //!< Normal to hyperplane.   facetT.normal is normalized to 1.0
+    QhullQh *           qh_qh;                  //!< qhT for distanceEpsilon() in operator==
+    coordT              hyperplane_offset;      //!< Distance from hyperplane to origin
+    int                 hyperplane_dimension;   //!< Dimension of hyperplane
+
+#//!\name Construct
+public:
+                        QhullHyperplane() : hyperplane_coordinates(0), qh_qh(0), hyperplane_offset(0.0), hyperplane_dimension(0) {}
+    explicit            QhullHyperplane(const Qhull &q);
+                        QhullHyperplane(const Qhull &q, int hyperplaneDimension, coordT *c, coordT hyperplaneOffset);
+    explicit            QhullHyperplane(QhullQh *qqh) : hyperplane_coordinates(0), qh_qh(qqh), hyperplane_offset(0.0), hyperplane_dimension(0) {}
+                        QhullHyperplane(QhullQh *qqh, int hyperplaneDimension, coordT *c, coordT hyperplaneOffset) : hyperplane_coordinates(c), qh_qh(qqh), hyperplane_offset(hyperplaneOffset), hyperplane_dimension(hyperplaneDimension) {}
+                        // Creates an alias.  Does not copy the hyperplane's coordinates.  Needed for return by value and parameter passing.
+                        QhullHyperplane(const QhullHyperplane &other)  : hyperplane_coordinates(other.hyperplane_coordinates), qh_qh(other.qh_qh), hyperplane_offset(other.hyperplane_offset), hyperplane_dimension(other.hyperplane_dimension) {}
+                        // Creates an alias.  Does not copy the hyperplane's coordinates.  Needed for vector<QhullHyperplane>
+    QhullHyperplane &   operator=(const QhullHyperplane &other) { hyperplane_coordinates= other.hyperplane_coordinates; qh_qh= other.qh_qh; hyperplane_offset= other.hyperplane_offset; hyperplane_dimension= other.hyperplane_dimension; return *this; }
+                        ~QhullHyperplane() {}
+
+#//!\name Conversions --
+//! Includes offset at end
+#ifndef QHULL_NO_STL
+    std::vector<coordT> toStdVector() const;
+#endif //QHULL_NO_STL
+#ifdef QHULL_USES_QT
+    QList<coordT>       toQList() const;
+#endif //QHULL_USES_QT
+
+#//!\name GetSet
+public:
+    const coordT *      coordinates() const { return hyperplane_coordinates; }
+    coordT *            coordinates() { return hyperplane_coordinates; }
+    void                defineAs(int hyperplaneDimension, coordT *c, coordT hyperplaneOffset) { QHULL_ASSERT(hyperplaneDimension>=0); hyperplane_coordinates= c; hyperplane_dimension= hyperplaneDimension; hyperplane_offset= hyperplaneOffset; }
+    //! Creates an alias to other using the same qh_qh
+    void                defineAs(QhullHyperplane &other) { hyperplane_coordinates= other.coordinates(); hyperplane_dimension= other.dimension();  hyperplane_offset= other.offset(); }
+    int                 dimension() const { return hyperplane_dimension; }
+    bool                isValid() const { return hyperplane_coordinates!=0 && hyperplane_dimension>0; }
+    coordT              offset() const { return hyperplane_offset; }
+    bool                operator==(const QhullHyperplane &other) const;
+    bool                operator!=(const QhullHyperplane &other) const { return !operator==(other); }
+    const coordT &      operator[](int idx) const { QHULL_ASSERT(idx>=0 && idx<hyperplane_dimension); return *(hyperplane_coordinates+idx); }
+    coordT &            operator[](int idx) { QHULL_ASSERT(idx>=0 && idx<hyperplane_dimension); return *(hyperplane_coordinates+idx); }
+    void                setCoordinates(coordT *c) { hyperplane_coordinates= c; }
+    void                setDimension(int hyperplaneDimension) { hyperplane_dimension= hyperplaneDimension; }
+    void                setOffset(coordT hyperplaneOffset) { hyperplane_offset= hyperplaneOffset; }
+
+#//!\name iterator
+    iterator            begin() { return hyperplane_coordinates; }
+    const_iterator      begin() const { return hyperplane_coordinates; }
+    const_iterator      constBegin() const { return hyperplane_coordinates; }
+    const_iterator      constEnd() const { return hyperplane_coordinates+hyperplane_dimension; }
+    int                 count() { return hyperplane_dimension; }
+    iterator            end() { return hyperplane_coordinates+hyperplane_dimension; }
+    const_iterator      end() const { return hyperplane_coordinates+hyperplane_dimension; }
+    size_t              size() { return (size_t)hyperplane_dimension; }
+
+#//!\name Methods
+    double              distance(const QhullPoint &p) const;
+    double              hyperplaneAngle(const QhullHyperplane &other) const;
+    double              norm() const;
+
+#//!\name IO
+    struct PrintHyperplane{
+        const QhullHyperplane  *hyperplane;
+        const char *    print_message;      //!< non-null message
+        const char *    hyperplane_offset_message;  //!< non-null message
+                        PrintHyperplane(const char *message, const char *offsetMessage, const QhullHyperplane &p) : hyperplane(&p), print_message(message), hyperplane_offset_message(offsetMessage) {}
+    };//PrintHyperplane
+    PrintHyperplane          print(const char *message) const { return PrintHyperplane(message, "", *this); }
+    PrintHyperplane          print(const char *message, const char *offsetMessage) const { return PrintHyperplane(message, offsetMessage, *this); }
+
+};//QhullHyperplane
+
+QHULL_DECLARE_SEQUENTIAL_ITERATOR(QhullHyperplane, coordT)
+
+}//namespace orgQhull
+
+#//!\name Global
+
+std::ostream &operator<<(std::ostream &os, const orgQhull::QhullHyperplane::PrintHyperplane &pr);
+std::ostream &operator<<(std::ostream &os, const orgQhull::QhullHyperplane &p);
+
+#endif // QHHYPERPLANE_H
+
diff --git a/xs/src/qhull/src/libqhullcpp/QhullIterator.h b/xs/src/qhull/src/libqhullcpp/QhullIterator.h
new file mode 100644
index 0000000000..ec60496bf7
--- /dev/null
+++ b/xs/src/qhull/src/libqhullcpp/QhullIterator.h
@@ -0,0 +1,173 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
+** $Id: //main/2015/qhull/src/libqhullcpp/QhullIterator.h#4 $$Change: 2079 $
+** $DateTime: 2016/02/07 17:43:34 $$Author: bbarber $
+**
+****************************************************************************/
+
+#ifndef QHULLITERATOR_H
+#define QHULLITERATOR_H
+
+#include "libqhull_r/qhull_ra.h"
+
+#include <assert.h>
+#include <iterator>
+#include <string>
+#include <vector>
+
+namespace orgQhull {
+
+#//!\name Defined here
+    //! Only QHULL_DECLARE_SEQUENTIAL_ITERATOR is used in libqhullcpp.  The others need further development
+    //! QHULL_DECLARE_SEQUENTIAL_ITERATOR(C) -- Declare a Java-style iterator
+    //! QHULL_DECLARE_MUTABLE_SEQUENTIAL_ITERATOR(C) -- Declare a mutable Java-style iterator
+    //! QHULL_DECLARE_SET_ITERATOR(C) -- Declare a set iterator
+    //! QHULL_DECLARE_MUTABLE_SET_ITERATOR(C) -- Declare a mutable set iterator
+    //! Derived from Qt/core/tools/qiterator.h and qset_r.h/FOREACHsetelement_()
+
+// Stores C* as done in Mutable...  Assumes the container is not deleted.
+// C::const_iterator is an STL-style iterator that returns T&
+#define QHULL_DECLARE_SEQUENTIAL_ITERATOR(C, T) \
+    \
+    class C##Iterator \
+    { \
+        typedef C::const_iterator const_iterator; \
+        const C *c; \
+        const_iterator i; \
+        public: \
+        inline C##Iterator(const C &container) \
+        : c(&container), i(c->constBegin()) {} \
+        inline C##Iterator &operator=(const C &container) \
+        { c = &container; i = c->constBegin(); return *this; } \
+        inline void toFront() { i = c->constBegin(); } \
+        inline void toBack() { i = c->constEnd(); } \
+        inline bool hasNext() const { return i != c->constEnd(); } \
+        inline const T &next() { return *i++; } \
+        inline const T &peekNext() const { return *i; } \
+        inline bool hasPrevious() const { return i != c->constBegin(); } \
+        inline const T &previous() { return *--i; } \
+        inline const T &peekPrevious() const { const_iterator p = i; return *--p; } \
+        inline bool findNext(const T &t) \
+        { while (i != c->constEnd()) if (*i++ == t) return true; return false; } \
+        inline bool findPrevious(const T &t) \
+        { while (i != c->constBegin()) if (*(--i) == t) return true; \
+        return false;  } \
+    };//C##Iterator
+
+// Remove setShareable() from Q_DECLARE_MUTABLE_SEQUENTIAL_ITERATOR
+// Uses QHULL_ASSERT (assert.h)
+// Duplicated in MutablePointIterator without insert or remove
+// Not used in libqhullcpp.  See Coordinates.h
+#define QHULL_DECLARE_MUTABLE_SEQUENTIAL_ITERATOR(C, T) \
+    class Mutable##C##Iterator \
+    { \
+        typedef C::iterator iterator; \
+        typedef C::const_iterator const_iterator; \
+        C *c; \
+        iterator i, n; \
+        inline bool item_exists() const { return const_iterator(n) != c->constEnd(); } \
+        public: \
+        inline Mutable##C##Iterator(C &container) \
+        : c(&container) \
+        { i = c->begin(); n = c->end(); } \
+        inline ~Mutable##C##Iterator() \
+        {} \
+        inline Mutable##C##Iterator &operator=(C &container) \
+        { c = &container; \
+        i = c->begin(); n = c->end(); return *this; } \
+        inline void toFront() { i = c->begin(); n = c->end(); } \
+        inline void toBack() { i = c->end(); n = i; } \
+        inline bool hasNext() const { return c->constEnd() != const_iterator(i); } \
+        inline T &next() { n = i++; return *n; } \
+        inline T &peekNext() const { return *i; } \
+        inline bool hasPrevious() const { return c->constBegin() != const_iterator(i); } \
+        inline T &previous() { n = --i; return *n; } \
+        inline T &peekPrevious() const { iterator p = i; return *--p; } \
+        inline void remove() \
+        { if (c->constEnd() != const_iterator(n)) { i = c->erase(n); n = c->end(); } } \
+        inline void setValue(const T &t) const { if (c->constEnd() != const_iterator(n)) *n = t; } \
+        inline T &value() { QHULL_ASSERT(item_exists()); return *n; } \
+        inline const T &value() const { QHULL_ASSERT(item_exists()); return *n; } \
+        inline void insert(const T &t) { n = i = c->insert(i, t); ++i; } \
+        inline bool findNext(const T &t) \
+        { while (c->constEnd() != const_iterator(n = i)) if (*i++ == t) return true; return false; } \
+        inline bool findPrevious(const T &t) \
+        { while (c->constBegin() != const_iterator(i)) if (*(n = --i) == t) return true; \
+        n = c->end(); return false;  } \
+    };//Mutable##C##Iterator
+
+// Not used in libqhullcpp.
+#define QHULL_DECLARE_SET_ITERATOR(C) \
+\
+    template <class T> \
+    class Qhull##C##Iterator \
+    { \
+        typedef typename Qhull##C<T>::const_iterator const_iterator; \
+        Qhull##C<T> c; \
+        const_iterator i; \
+    public: \
+        inline Qhull##C##Iterator(const Qhull##C<T> &container) \
+        : c(container), i(c.constBegin()) {} \
+        inline Qhull##C##Iterator &operator=(const Qhull##C<T> &container) \
+        { c = container; i = c.constBegin(); return *this; } \
+        inline void toFront() { i = c.constBegin(); } \
+        inline void toBack() { i = c.constEnd(); } \
+        inline bool hasNext() const { return i != c.constEnd(); } \
+        inline const T &next() { return *i++; } \
+        inline const T &peekNext() const { return *i; } \
+        inline bool hasPrevious() const { return i != c.constBegin(); } \
+        inline const T &previous() { return *--i; } \
+        inline const T &peekPrevious() const { const_iterator p = i; return *--p; } \
+        inline bool findNext(const T &t) \
+        { while (i != c.constEnd()) if (*i++ == t) return true; return false; } \
+        inline bool findPrevious(const T &t) \
+        { while (i != c.constBegin()) if (*(--i) == t) return true; \
+        return false;  } \
+    };//Qhull##C##Iterator
+
+// Not used in libqhullcpp.
+#define QHULL_DECLARE_MUTABLE_SET_ITERATOR(C) \
+\
+template <class T> \
+class QhullMutable##C##Iterator \
+{ \
+    typedef typename Qhull##C::iterator iterator; \
+    typedef typename Qhull##C::const_iterator const_iterator; \
+    Qhull##C *c; \
+    iterator i, n; \
+    inline bool item_exists() const { return const_iterator(n) != c->constEnd(); } \
+public: \
+    inline Mutable##C##Iterator(Qhull##C &container) \
+        : c(&container) \
+    { c->setSharable(false); i = c->begin(); n = c->end(); } \
+    inline ~Mutable##C##Iterator() \
+    { c->setSharable(true); } \
+    inline Mutable##C##Iterator &operator=(Qhull##C &container) \
+    { c->setSharable(true); c = &container; c->setSharable(false); \
+      i = c->begin(); n = c->end(); return *this; } \
+    inline void toFront() { i = c->begin(); n = c->end(); } \
+    inline void toBack() { i = c->end(); n = i; } \
+    inline bool hasNext() const { return c->constEnd() != const_iterator(i); } \
+    inline T &next() { n = i++; return *n; } \
+    inline T &peekNext() const { return *i; } \
+    inline bool hasPrevious() const { return c->constBegin() != const_iterator(i); } \
+    inline T &previous() { n = --i; return *n; } \
+    inline T &peekPrevious() const { iterator p = i; return *--p; } \
+    inline void remove() \
+    { if (c->constEnd() != const_iterator(n)) { i = c->erase(n); n = c->end(); } } \
+    inline void setValue(const T &t) const { if (c->constEnd() != const_iterator(n)) *n = t; } \
+    inline T &value() { Q_ASSERT(item_exists()); return *n; } \
+    inline const T &value() const { Q_ASSERT(item_exists()); return *n; } \
+    inline void insert(const T &t) { n = i = c->insert(i, t); ++i; } \
+    inline bool findNext(const T &t) \
+    { while (c->constEnd() != const_iterator(n = i)) if (*i++ == t) return true; return false; } \
+    inline bool findPrevious(const T &t) \
+    { while (c->constBegin() != const_iterator(i)) if (*(n = --i) == t) return true; \
+      n = c->end(); return false;  } \
+};//QhullMutable##C##Iterator
+
+}//namespace orgQhull
+
+#endif // QHULLITERATOR_H
+
diff --git a/xs/src/qhull/src/libqhullcpp/QhullLinkedList.h b/xs/src/qhull/src/libqhullcpp/QhullLinkedList.h
new file mode 100644
index 0000000000..d4caf52c18
--- /dev/null
+++ b/xs/src/qhull/src/libqhullcpp/QhullLinkedList.h
@@ -0,0 +1,388 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
+** $Id: //main/2015/qhull/src/libqhullcpp/QhullLinkedList.h#7 $$Change: 2079 $
+** $DateTime: 2016/02/07 17:43:34 $$Author: bbarber $
+**
+****************************************************************************/
+
+#ifndef QHULLLINKEDLIST_H
+#define QHULLLINKEDLIST_H
+
+#include "libqhull_r/qhull_ra.h"
+#include "libqhullcpp/QhullError.h"
+
+#include <cstddef>  // ptrdiff_t, size_t
+
+#ifdef QHULL_USES_QT
+#include <QtCore/QList>
+#endif
+
+#ifndef QHULL_NO_STL
+#include <algorithm>
+#include <iterator>
+#include <vector>
+#endif
+
+namespace orgQhull {
+
+#//!\name Defined here
+    //! QhullLinkedList<T> -- A linked list modeled on QLinkedList.
+    //!   T is an opaque type with T(B *b), b=t.getBaseT(), t=t.next(), and t=t.prev().  The end node is a sentinel.
+    //!   QhullQh/qhT owns the contents.
+    //!   QhullLinkedList does not define erase(), clear(), removeFirst(), removeLast(), pop_back(), pop_front(), fromStdList()
+    //!   Derived from Qt/core/tools/qlinkedlist.h and libqhull_r.h/FORALLfacets_()
+    //! QhullLinkedList<T>::const_iterator -- STL-style iterator
+    //! QhullLinkedList<T>::iterator -- STL-style iterator
+    //! QhullLinkedListIterator<T> -- Java-style iterator
+    //!   Derived from Qt/core/tools/qiterator.h
+    //!   Works with Qt's foreach keyword [Qt/src/corelib/global/qglobal.h]
+
+template <typename T>
+class QhullLinkedList
+{
+#//!\name Defined here
+public:
+    class const_iterator;
+    class iterator;
+    typedef const_iterator  ConstIterator;
+    typedef iterator    Iterator;
+    typedef ptrdiff_t   difference_type;
+    typedef countT      size_type;
+    typedef T           value_type;
+    typedef const value_type *const_pointer;
+    typedef const value_type &const_reference;
+    typedef value_type *pointer;
+    typedef value_type &reference;
+
+#//!\name Fields
+private:
+    T                   begin_node;
+    T                   end_node;     //! Sentinel node at end of list
+
+#//!\name Constructors
+public:
+                        QhullLinkedList<T>(T b, T e) : begin_node(b), end_node(e) {}
+                        //! Copy constructor copies begin_node and end_node, but not the list elements.  Needed for return by value and parameter passing.
+                        QhullLinkedList<T>(const QhullLinkedList<T> &other) : begin_node(other.begin_node), end_node(other.end_node) {}
+                        //! Copy assignment copies begin_node and end_node, but not the list elements.
+                        QhullLinkedList<T> & operator=(const QhullLinkedList<T> &other) { begin_node= other.begin_node; end_node= other.end_node; return *this; }
+                        ~QhullLinkedList<T>() {}
+
+private:
+                        //!disabled since a sentinel must be allocated as the private type
+                        QhullLinkedList<T>() {}
+
+public:
+
+#//!\name Conversions
+#ifndef QHULL_NO_STL
+    std::vector<T>      toStdVector() const;
+#endif
+#ifdef QHULL_USES_QT
+    QList<T>            toQList() const;
+#endif
+
+#//!\name GetSet
+    countT              count() const;
+                        //count(t) under #//!\name Search
+    bool                isEmpty() const { return (begin_node==end_node); }
+    bool                operator==(const QhullLinkedList<T> &o) const;
+    bool                operator!=(const QhullLinkedList<T> &o) const { return !operator==(o); }
+    size_t              size() const { return count(); }
+
+#//!\name Element access
+    //! For back() and last(), return T instead of T& (T is computed)
+    const T             back() const { return last(); }
+    T                   back() { return last(); }
+    const T &           first() const { QHULL_ASSERT(!isEmpty()); return begin_node; }
+    T &                 first() { QHULL_ASSERT(!isEmpty()); return begin_node; }
+    const T &           front() const { return first(); }
+    T &                 front() { return first(); }
+    const T             last() const { QHULL_ASSERT(!isEmpty()); return *--end(); }
+    T                   last() { QHULL_ASSERT(!isEmpty()); return *--end(); }
+
+#//!\name Modify -- Allocation of opaque types not implemented.
+
+#//!\name Search
+    bool                contains(const T &t) const;
+    countT              count(const T &t) const;
+
+#//!\name Iterator
+    iterator            begin() { return begin_node; }
+    const_iterator      begin() const { return begin_node; }
+    const_iterator      constBegin() const { return begin_node; }
+    const_iterator      constEnd() const { return end_node; }
+    iterator            end() { return end_node; }
+    const_iterator      end() const { return end_node; }
+
+    class iterator {
+
+    private:
+        T               i;
+        friend class const_iterator;
+
+    public:
+        typedef std::bidirectional_iterator_tag  iterator_category;
+        typedef T           value_type;
+        typedef value_type *pointer;
+        typedef value_type &reference;
+        typedef ptrdiff_t   difference_type;
+
+                        iterator() : i() {}
+                        iterator(const T &t) : i(t) {}  //!< Automatic conversion to iterator
+                        iterator(const iterator &o) : i(o.i) {}
+        iterator &      operator=(const iterator &o) { i= o.i; return *this; }
+
+        const T &       operator*() const { return i; }
+        T &             operator*() { return i; }
+        // Do not define operator[]
+        const T *       operator->() const { return &i; }
+        T *             operator->() { return &i; }
+        bool            operator==(const iterator &o) const { return i == o.i; }
+        bool            operator!=(const iterator &o) const { return !operator==(o); }
+        bool            operator==(const const_iterator &o) const { return i==reinterpret_cast<const iterator &>(o).i; }
+        bool            operator!=(const const_iterator &o) const { return !operator==(o); }
+        iterator &      operator++() { i= i.next(); return *this; }
+        iterator        operator++(int) { iterator o= i; i= i.next(); return o; }
+        iterator &      operator--() { i= i.previous(); return *this; }
+        iterator        operator--(int) { iterator o= i; i= i.previous(); return o; }
+        iterator        operator+(int j) const;
+        iterator        operator-(int j) const { return operator+(-j); }
+        iterator &      operator+=(int j) { return (*this= *this + j); }
+        iterator &      operator-=(int j) { return (*this= *this - j); }
+    };//QhullLinkedList::iterator
+
+    class const_iterator {
+
+    private:
+        T               i;
+
+    public:
+        typedef std::bidirectional_iterator_tag  iterator_category;
+        typedef T                 value_type;
+        typedef const value_type *pointer;
+        typedef const value_type &reference;
+        typedef ptrdiff_t         difference_type;
+
+                        const_iterator() : i() {}
+                        const_iterator(const T &t) : i(t) {}  //!< Automatic conversion to const_iterator
+                        const_iterator(const iterator &o) : i(o.i) {}
+                        const_iterator(const const_iterator &o) : i(o.i) {}
+        const_iterator &operator=(const const_iterator &o) { i= o.i; return *this; }
+
+        const T &       operator*() const { return i; }
+        const T *       operator->() const { return i; }
+        bool            operator==(const const_iterator &o) const { return i == o.i; }
+        bool            operator!=(const const_iterator &o) const { return !operator==(o); }
+                        // No comparisons or iterator diff
+        const_iterator &operator++() { i= i.next(); return *this; }
+        const_iterator  operator++(int) { const_iterator o= i; i= i.next(); return o; }
+        const_iterator &operator--() { i= i.previous(); return *this; }
+        const_iterator  operator--(int) { const_iterator o= i; i= i.previous(); return o; }
+        const_iterator  operator+(int j) const;
+        const_iterator  operator-(int j) const { return operator+(-j); }
+        const_iterator &operator+=(int j) { return (*this= *this + j); }
+        const_iterator &operator-=(int j) { return (*this= *this - j); }
+    };//QhullLinkedList::const_iterator
+
+};//QhullLinkedList
+
+template <typename T>
+class QhullLinkedListIterator // FIXUP QH11016 define QhullMutableLinkedListIterator
+{
+    typedef typename QhullLinkedList<T>::const_iterator const_iterator;
+    const QhullLinkedList<T> *c;
+    const_iterator      i;
+
+public:
+                        QhullLinkedListIterator(const QhullLinkedList<T> &container) : c(&container), i(c->constBegin()) {}
+    QhullLinkedListIterator & operator=(const QhullLinkedList<T> &container) { c= &container; i= c->constBegin(); return *this; }
+    bool                findNext(const T &t);
+    bool                findPrevious(const T &t);
+    bool                hasNext() const { return i != c->constEnd(); }
+    bool                hasPrevious() const { return i != c->constBegin(); }
+    T                   next() { return *i++; }
+    T                   peekNext() const { return *i; }
+    T                   peekPrevious() const { const_iterator p= i; return *--p; }
+    T                   previous() { return *--i; }
+    void                toFront() { i= c->constBegin(); }
+    void                toBack() { i= c->constEnd(); }
+};//QhullLinkedListIterator
+
+#//!\name == Definitions =========================================
+
+#//!\name Conversion
+
+#ifndef QHULL_NO_STL
+template <typename T>
+std::vector<T> QhullLinkedList<T>::
+toStdVector() const
+{
+    std::vector<T> tmp;
+    std::copy(constBegin(), constEnd(), std::back_inserter(tmp));
+    return tmp;
+}//toStdVector
+#endif
+
+#ifdef QHULL_USES_QT
+template <typename T>
+QList<T>  QhullLinkedList<T>::
+toQList() const
+{
+    QhullLinkedListIterator<T> i(*this);
+    QList<T> ls;
+    while(i.hasNext()){
+        ls.append(i.next());
+    }
+    return ls;
+}//toQList
+#endif
+
+#//!\name GetSet
+
+template <typename T>
+countT QhullLinkedList<T>::
+count() const
+{
+    const_iterator i= begin_node;
+    countT c= 0;
+    while(i != end_node){
+        c++;
+        i++;
+    }
+    return c;
+}//count
+
+#//!\name Search
+
+template <typename T>
+bool QhullLinkedList<T>::
+contains(const T &t) const
+{
+    const_iterator i= begin_node;
+    while(i != end_node){
+        if(i==t){
+            return true;
+        }
+        i++;
+    }
+    return false;
+}//contains
+
+template <typename T>
+countT QhullLinkedList<T>::
+count(const T &t) const
+{
+    const_iterator i= begin_node;
+    countT c= 0;
+    while(i != end_node){
+        if(i==t){
+            c++;
+        }
+        i++;
+    }
+    return c;
+}//count
+
+template <typename T>
+bool QhullLinkedList<T>::
+operator==(const QhullLinkedList<T> &l) const
+{
+    if(begin_node==l.begin_node){
+        return (end_node==l.end_node);
+    }
+    T i= begin_node;
+    T il= l.begin_node;
+    while(i != end_node){
+        if(i != il){
+            return false;
+        }
+        i= static_cast<T>(i.next());
+        il= static_cast<T>(il.next());
+    }
+    if(il != l.end_node){
+        return false;
+    }
+    return true;
+}//operator==
+
+#//!\name Iterator
+
+template <typename T>
+typename QhullLinkedList<T>::iterator  QhullLinkedList<T>::iterator::
+operator+(int j) const
+{
+    T n= i;
+    if(j>0){
+        while(j--){
+            n= n.next();
+        }
+    }else{
+        while(j++){
+            n= n.previous();
+        }
+    }
+    return iterator(n);
+}//operator+
+
+template <typename T>
+typename QhullLinkedList<T>::const_iterator  QhullLinkedList<T>::const_iterator::
+operator+(int j) const
+{
+    T n= i;
+    if(j>0){
+        while(j--){
+            n= n.next();
+        }
+    }else{
+        while(j++){
+            n= n.previous();
+        }
+    }
+    return const_iterator(n);
+}//operator+
+
+#//!\name QhullLinkedListIterator
+
+template <typename T>
+bool QhullLinkedListIterator<T>::
+findNext(const T &t)
+{
+    while(i != c->constEnd()){
+        if (*i++ == t){
+            return true;
+        }
+    }
+    return false;
+}//findNext
+
+template <typename T>
+bool QhullLinkedListIterator<T>::
+findPrevious(const T &t)
+{
+    while(i!=c->constBegin()){
+        if(*(--i)==t){
+            return true;
+        }
+    }
+    return false;
+}//findNext
+
+}//namespace orgQhull
+
+#//!\name Global
+
+template <typename T>
+std::ostream &
+operator<<(std::ostream &os, const orgQhull::QhullLinkedList<T> &qs)
+{
+    typename orgQhull::QhullLinkedList<T>::const_iterator i;
+    for(i= qs.begin(); i != qs.end(); ++i){
+        os << *i;
+    }
+    return os;
+}//operator<<
+
+#endif // QHULLLINKEDLIST_H
+
diff --git a/xs/src/qhull/src/libqhullcpp/QhullPoint.cpp b/xs/src/qhull/src/libqhullcpp/QhullPoint.cpp
new file mode 100644
index 0000000000..f5e9124609
--- /dev/null
+++ b/xs/src/qhull/src/libqhullcpp/QhullPoint.cpp
@@ -0,0 +1,203 @@
+/****************************************************************************
+**
+** Copyright (c) 2009-2015 C.B. Barber. All rights reserved.
+** $Id: //main/2015/qhull/src/libqhullcpp/QhullPoint.cpp#3 $$Change: 2066 $
+** $DateTime: 2016/01/18 19:29:17 $$Author: bbarber $
+**
+****************************************************************************/
+
+#include "libqhullcpp/QhullPoint.h"
+
+#include "libqhullcpp/QhullError.h"
+#include "libqhullcpp/Qhull.h"
+
+#include <iostream>
+#include <algorithm>
+
+#ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
+#endif
+
+namespace orgQhull {
+
+#//!\name Constructors
+
+
+QhullPoint::
+QhullPoint(const Qhull &q) 
+: point_coordinates(0)
+, qh_qh(q.qh())
+, point_dimension(q.hullDimension())
+{
+}//QhullPoint
+
+QhullPoint::
+QhullPoint(const Qhull &q, coordT *c) 
+: point_coordinates(c)
+, qh_qh(q.qh())
+, point_dimension(q.hullDimension())
+{
+    QHULL_ASSERT(q.hullDimension()>0);
+}//QhullPoint dim, coordT
+
+QhullPoint::
+QhullPoint(const Qhull &q, int pointDimension, coordT *c) 
+: point_coordinates(c)
+, qh_qh(q.qh())
+, point_dimension(pointDimension)
+{
+}//QhullPoint dim, coordT
+
+//! QhullPoint of Coordinates with point_dimension==c.count()
+QhullPoint::
+QhullPoint(const Qhull &q, Coordinates &c) 
+: point_coordinates(c.data())
+, qh_qh(q.qh())
+, point_dimension(c.count())
+{
+}//QhullPoint Coordinates
+
+#//!\name Conversions
+
+// See qt-qhull.cpp for QList conversion
+
+#ifndef QHULL_NO_STL
+std::vector<coordT> QhullPoint::
+toStdVector() const
+{
+    QhullPointIterator i(*this);
+    std::vector<coordT> vs;
+    while(i.hasNext()){
+        vs.push_back(i.next());
+    }
+    return vs;
+}//toStdVector
+#endif //QHULL_NO_STL
+
+#//!\name GetSet
+
+//! QhullPoint is equal if it has the same address and dimension
+//! If !qh_qh, returns true if dimension and coordinates are equal
+//! If qh_qh, returns true if the distance between points is less than qh_qh->distanceEpsilon()
+//!\todo Compares distance with distance-to-hyperplane (distanceEpsilon).   Is that correct?
+bool QhullPoint::
+operator==(const QhullPoint &other) const
+{
+    if(point_dimension!=other.point_dimension){
+        return false;
+    }
+    const coordT *c= point_coordinates;
+    const coordT *c2= other.point_coordinates;
+    if(c==c2){
+        return true;
+    }
+    if(!c || !c2){
+        return false;
+    }
+    if(!qh_qh || qh_qh->hull_dim==0){
+        for(int k= point_dimension; k--; ){
+            if(*c++ != *c2++){
+                return false;
+            }
+        }
+        return true;
+    }
+    double dist2= 0.0;
+    for(int k= point_dimension; k--; ){
+        double diff= *c++ - *c2++;
+        dist2 += diff*diff;
+    }
+    dist2= sqrt(dist2);
+    return (dist2 < qh_qh->distanceEpsilon());
+}//operator==
+
+#//!\name Methods
+
+//! Return distance between two points.
+double QhullPoint::
+distance(const QhullPoint &p) const
+{
+    const coordT *c= point_coordinates;
+    const coordT *c2= p.point_coordinates;
+    int dim= point_dimension;
+    if(dim!=p.point_dimension){
+        throw QhullError(10075, "QhullPoint error: Expecting dimension %d for distance().  Got %d", dim, p.point_dimension);
+    }
+    if(!c || !c2){
+        throw QhullError(10076, "QhullPoint error: Cannot compute distance() for undefined point");
+    }
+    double dist;
+
+    switch(dim){
+  case 2:
+      dist= (c[0]-c2[0])*(c[0]-c2[0]) + (c[1]-c2[1])*(c[1]-c2[1]);
+      break;
+  case 3:
+      dist= (c[0]-c2[0])*(c[0]-c2[0]) + (c[1]-c2[1])*(c[1]-c2[1]) + (c[2]-c2[2])*(c[2]-c2[2]);
+      break;
+  case 4:
+      dist= (c[0]-c2[0])*(c[0]-c2[0]) + (c[1]-c2[1])*(c[1]-c2[1]) + (c[2]-c2[2])*(c[2]-c2[2]) + (c[3]-c2[3])*(c[3]-c2[3]);
+      break;
+  case 5:
+      dist= (c[0]-c2[0])*(c[0]-c2[0]) + (c[1]-c2[1])*(c[1]-c2[1]) + (c[2]-c2[2])*(c[2]-c2[2]) + (c[3]-c2[3])*(c[3]-c2[3]) + (c[4]-c2[4])*(c[4]-c2[4]);
+      break;
+  case 6:
+      dist= (c[0]-c2[0])*(c[0]-c2[0]) + (c[1]-c2[1])*(c[1]-c2[1]) + (c[2]-c2[2])*(c[2]-c2[2]) + (c[3]-c2[3])*(c[3]-c2[3]) + (c[4]-c2[4])*(c[4]-c2[4]) + (c[5]-c2[5])*(c[5]-c2[5]);
+      break;
+  case 7:
+      dist= (c[0]-c2[0])*(c[0]-c2[0]) + (c[1]-c2[1])*(c[1]-c2[1]) + (c[2]-c2[2])*(c[2]-c2[2]) + (c[3]-c2[3])*(c[3]-c2[3]) + (c[4]-c2[4])*(c[4]-c2[4]) + (c[5]-c2[5])*(c[5]-c2[5]) + (c[6]-c2[6])*(c[6]-c2[6]);
+      break;
+  case 8:
+      dist= (c[0]-c2[0])*(c[0]-c2[0]) + (c[1]-c2[1])*(c[1]-c2[1]) + (c[2]-c2[2])*(c[2]-c2[2]) + (c[3]-c2[3])*(c[3]-c2[3]) + (c[4]-c2[4])*(c[4]-c2[4]) + (c[5]-c2[5])*(c[5]-c2[5]) + (c[6]-c2[6])*(c[6]-c2[6]) + (c[7]-c2[7])*(c[7]-c2[7]);
+      break;
+  default:
+      dist= 0.0;
+      for(int k=dim; k--; ){
+          dist += (*c - *c2) * (*c - *c2);
+          ++c;
+          ++c2;
+      }
+      break;
+    }
+    return sqrt(dist);
+}//distance
+
+}//namespace orgQhull
+
+#//!\name Global functions
+
+using std::ostream;
+using orgQhull::QhullPoint;
+
+//! Same as qh_printpointid [io.c]
+ostream &
+operator<<(ostream &os, const QhullPoint::PrintPoint &pr)
+{
+    QhullPoint p= *pr.point; 
+    countT i= p.id();
+    if(pr.point_message){
+        if(*pr.point_message){
+            os << pr.point_message << " ";
+        }
+        if(pr.with_identifier && (i!=qh_IDunknown) && (i!=qh_IDnone)){
+            os << "p" << i << ": ";
+        }
+    }
+    const realT *c= p.coordinates();
+    for(int k=p.dimension(); k--; ){
+        realT r= *c++;
+        if(pr.point_message){
+            os << " " << r; // FIXUP QH11010 %8.4g
+        }else{
+            os << " " << r; // FIXUP QH11010 qh_REAL_1
+        }
+    }
+    os << std::endl;
+    return os;
+}//printPoint
+
+ostream & 
+operator<<(ostream &os, const QhullPoint &p)
+{
+    os << p.print(""); 
+    return os;
+}//operator<<
diff --git a/xs/src/qhull/src/libqhullcpp/QhullPoint.h b/xs/src/qhull/src/libqhullcpp/QhullPoint.h
new file mode 100644
index 0000000000..17f94ab364
--- /dev/null
+++ b/xs/src/qhull/src/libqhullcpp/QhullPoint.h
@@ -0,0 +1,136 @@
+/****************************************************************************
+**
+** Copyright (c) 2009-2015 C.B. Barber. All rights reserved.
+** $Id: //main/2015/qhull/src/libqhullcpp/QhullPoint.h#4 $$Change: 2079 $
+** $DateTime: 2016/02/07 17:43:34 $$Author: bbarber $
+**
+****************************************************************************/
+
+#ifndef QHPOINT_H
+#define QHPOINT_H
+
+#include "libqhull_r/qhull_ra.h"
+#include "libqhullcpp/QhullError.h"
+#include "libqhullcpp/QhullIterator.h"
+#include "libqhullcpp/QhullQh.h"
+#include "libqhullcpp/Coordinates.h"
+
+#include <ostream>
+
+namespace orgQhull {
+
+#//!\name Defined here
+    class QhullPoint;  //!<  QhullPoint as a pointer and dimension to shared memory
+    class QhullPointIterator; //!< Java-style iterator for QhullPoint coordinates
+
+#//!\name Used here
+    class Qhull;
+
+//! A QhullPoint is a dimension and an array of coordinates.
+//! With Qhull/QhullQh, a QhullPoint has an identifier.  Point equality is relative to qh.distanceEpsilon
+class QhullPoint {
+
+#//!\name Iterators
+public:
+    typedef coordT *                    base_type;  // for QhullPointSet
+    typedef const coordT *              iterator;
+    typedef const coordT *              const_iterator;
+    typedef QhullPoint::iterator        Iterator;
+    typedef QhullPoint::const_iterator  ConstIterator;
+
+#//!\name Fields
+protected: // For QhullPoints::iterator, QhullPoints::const_iterator
+    coordT *            point_coordinates;  //!< Pointer to first coordinate,   0 if undefined
+    QhullQh *           qh_qh;              //!< qhT for this instance of Qhull.  0 if undefined.
+                                            //!< operator==() returns true if points within sqrt(qh_qh->distanceEpsilon())
+                                            //!< If !qh_qh, id() is -3, and operator==() requires equal coordinates
+    int                 point_dimension;    //!< Default dimension is qh_qh->hull_dim
+public:
+
+#//!\name Constructors
+    //! QhullPoint, PointCoordinates, and QhullPoints have similar constructors
+    //! If Qhull/QhullQh is not initialized, then QhullPoint.dimension() is zero unless explicitly set
+    //! Cannot define QhullPoints(int pointDimension) since it is ambiguous with QhullPoints(QhullQh *qqh)
+                        QhullPoint() : point_coordinates(0), qh_qh(0), point_dimension(0) {}
+                        QhullPoint(int pointDimension, coordT *c) : point_coordinates(c), qh_qh(0), point_dimension(pointDimension) { QHULL_ASSERT(pointDimension>0); }
+    explicit            QhullPoint(const Qhull &q);
+                        QhullPoint(const Qhull &q, coordT *c);
+                        QhullPoint(const Qhull &q, Coordinates &c);
+                        QhullPoint(const Qhull &q, int pointDimension, coordT *c);
+    explicit            QhullPoint(QhullQh *qqh) : point_coordinates(0), qh_qh(qqh), point_dimension(qqh->hull_dim) {}
+                        QhullPoint(QhullQh *qqh, coordT *c) : point_coordinates(c), qh_qh(qqh), point_dimension(qqh->hull_dim) { QHULL_ASSERT(qqh->hull_dim>0); }
+                        QhullPoint(QhullQh *qqh, Coordinates &c) : point_coordinates(c.data()), qh_qh(qqh), point_dimension(c.count()) {}
+                        QhullPoint(QhullQh *qqh, int pointDimension, coordT *c) : point_coordinates(c), qh_qh(qqh), point_dimension(pointDimension) {}
+                        //! Creates an alias.  Does not make a deep copy of the point.  Needed for return by value and parameter passing.
+                        QhullPoint(const QhullPoint &other) : point_coordinates(other.point_coordinates), qh_qh(other.qh_qh), point_dimension(other.point_dimension) {}
+                        //! Creates an alias.  Does not make a deep copy of the point.  Needed for vector<QhullPoint>
+    QhullPoint &        operator=(const QhullPoint &other) { point_coordinates= other.point_coordinates; qh_qh= other.qh_qh; point_dimension= other.point_dimension; return *this; }
+                        ~QhullPoint() {}
+
+
+#//!\name Conversions
+
+#ifndef QHULL_NO_STL
+    std::vector<coordT> toStdVector() const;
+#endif //QHULL_NO_STL
+#ifdef QHULL_USES_QT
+    QList<coordT>       toQList() const;
+#endif //QHULL_USES_QT
+
+#//!\name GetSet
+public:
+    const coordT *      coordinates() const { return point_coordinates; }  //!< 0 if undefined
+    coordT *            coordinates() { return point_coordinates; }        //!< 0 if undefined
+    void                defineAs(coordT *c) { QHULL_ASSERT(point_dimension>0); point_coordinates= c; }
+    void                defineAs(int pointDimension, coordT *c) { QHULL_ASSERT(pointDimension>=0); point_coordinates= c; point_dimension= pointDimension; }
+    void                defineAs(QhullPoint &other) { point_coordinates= other.point_coordinates; qh_qh= other.qh_qh; point_dimension= other.point_dimension; }
+    int                 dimension() const { return point_dimension; }
+    coordT *            getBaseT() const { return point_coordinates; } // for QhullPointSet
+    countT              id() const { return qh_pointid(qh_qh, point_coordinates); } // NOerrors
+    bool                isValid() const { return (point_coordinates!=0 && point_dimension>0); };
+    bool                operator==(const QhullPoint &other) const;
+    bool                operator!=(const QhullPoint &other) const { return ! operator==(other); }
+    const coordT &      operator[](int idx) const { QHULL_ASSERT(point_coordinates!=0 && idx>=0 && idx<point_dimension); return *(point_coordinates+idx); } //!< 0 to hull_dim-1
+    coordT &            operator[](int idx) { QHULL_ASSERT(point_coordinates!=0 && idx>=0 && idx<point_dimension); return *(point_coordinates+idx); } //!< 0 to hull_dim-1
+    QhullQh *           qh() { return qh_qh; }
+    void                setCoordinates(coordT *c) { point_coordinates= c; }
+    void                setDimension(int pointDimension) { point_dimension= pointDimension; }
+
+#//!\name foreach
+    iterator            begin() { return point_coordinates; }
+    const_iterator      begin() const { return point_coordinates; }
+    const_iterator      constBegin() const { return point_coordinates; }
+    const_iterator      constEnd() const { return (point_coordinates ? point_coordinates+point_dimension : 0); }
+    int                 count() { return (point_coordinates ? point_dimension : 0); }
+    iterator            end() { return (point_coordinates ? point_coordinates+point_dimension : 0); }
+    const_iterator      end() const { return (point_coordinates ? point_coordinates+point_dimension : 0); }
+    size_t              size() { return (size_t)(point_coordinates ? point_dimension : 0); }
+
+#//!\name Methods
+    void                advancePoint(countT idx) { if(point_coordinates) { point_coordinates += idx*point_dimension; } }
+    double              distance(const QhullPoint &p) const;
+
+#//!\name IO
+
+    struct PrintPoint{
+        const QhullPoint *point;
+        const char *    point_message;
+        bool            with_identifier;
+                        PrintPoint(const char *message, bool withIdentifier, const QhullPoint &p) : point(&p), point_message(message), with_identifier(withIdentifier) {}
+    };//PrintPoint
+    PrintPoint          print(const char *message) const { return PrintPoint(message, false, *this); }
+    PrintPoint          printWithIdentifier(const char *message) const { return PrintPoint(message, true, *this); }
+
+};//QhullPoint
+
+QHULL_DECLARE_SEQUENTIAL_ITERATOR(QhullPoint, coordT)
+
+}//namespace orgQhull
+
+#//!\name Global
+
+std::ostream &operator<<(std::ostream &os, const orgQhull::QhullPoint::PrintPoint &pr);
+std::ostream &operator<<(std::ostream &os, const orgQhull::QhullPoint &p);
+
+#endif // QHPOINT_H
+
diff --git a/xs/src/qhull/src/libqhullcpp/QhullPointSet.cpp b/xs/src/qhull/src/libqhullcpp/QhullPointSet.cpp
new file mode 100644
index 0000000000..561fd6c76a
--- /dev/null
+++ b/xs/src/qhull/src/libqhullcpp/QhullPointSet.cpp
@@ -0,0 +1,62 @@
+/****************************************************************************
+**
+** Copyright (c) 2009-2015 C.B. Barber. All rights reserved.
+** $Id: //main/2015/qhull/src/libqhullcpp/QhullPointSet.cpp#2 $$Change: 2066 $
+** $DateTime: 2016/01/18 19:29:17 $$Author: bbarber $
+**
+****************************************************************************/
+
+#include "libqhullcpp/QhullPointSet.h"
+
+#include <iostream>
+#include <algorithm>
+
+#ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
+#endif
+
+namespace orgQhull {
+
+// Implemented via QhullSet.h
+
+}//namespace orgQhull
+
+#//!\name Global functions
+
+using std::endl;
+using std::ostream;
+using orgQhull::QhullPoint;
+using orgQhull::QhullPointSet;
+using orgQhull::QhullPointSetIterator;
+
+ostream &
+operator<<(ostream &os, const QhullPointSet::PrintIdentifiers &pr)
+{
+    os << pr.print_message;
+    const QhullPointSet s= *pr.point_set;
+    QhullPointSetIterator i(s);
+    while(i.hasNext()){
+        if(i.hasPrevious()){
+            os << " ";
+        }
+        const QhullPoint point= i.next();
+        countT id= point.id();
+        os << "p" << id;
+
+    }
+    os << endl;
+    return os;
+}//PrintIdentifiers
+
+ostream &
+operator<<(ostream &os, const QhullPointSet::PrintPointSet &pr)
+{
+    os << pr.print_message;
+    const QhullPointSet s= *pr.point_set;
+    for(QhullPointSet::const_iterator i=s.begin(); i != s.end(); ++i){
+        const QhullPoint point= *i;
+        os << point;
+    }
+    return os;
+}//printPointSet
+
+
diff --git a/xs/src/qhull/src/libqhullcpp/QhullPointSet.h b/xs/src/qhull/src/libqhullcpp/QhullPointSet.h
new file mode 100644
index 0000000000..8562e170ea
--- /dev/null
+++ b/xs/src/qhull/src/libqhullcpp/QhullPointSet.h
@@ -0,0 +1,77 @@
+/****************************************************************************
+**
+** Copyright (c) 2009-2015 C.B. Barber. All rights reserved.
+** $Id: //main/2015/qhull/src/libqhullcpp/QhullPointSet.h#4 $$Change: 2079 $
+** $DateTime: 2016/02/07 17:43:34 $$Author: bbarber $
+**
+****************************************************************************/
+
+#ifndef QHULLPOINTSET_H
+#define QHULLPOINTSET_H
+
+#include "libqhull_r/qhull_ra.h"
+#include "libqhullcpp/QhullSet.h"
+#include "libqhullcpp/QhullPoint.h"
+
+#include <ostream>
+
+namespace orgQhull {
+
+#//!\name Used here
+    class Qhull;
+    class QhullPoint;
+
+#//!\name Defined here
+    //! QhullPointSet -- a set of coordinate pointers with input dimension
+    // with const_iterator and iterator
+    class QhullPointSet;
+
+class QhullPointSet : public QhullSet<QhullPoint> {
+
+private:
+#//!\name Fields
+    // no fields
+public:
+
+#//!\name Construct
+                        QhullPointSet(const Qhull &q, setT *s) : QhullSet<QhullPoint>(q, s) {}
+                        //Conversion from setT* is not type-safe.  Implicit conversion for void* to T
+                        QhullPointSet(QhullQh *qqh, setT *s) : QhullSet<QhullPoint>(qqh, s) {}
+                        //Copy constructor copies pointer but not contents.  Needed for return by value and parameter passing.
+                        QhullPointSet(const QhullPointSet &other) : QhullSet<QhullPoint>(other) {}
+                        //!Assignment copies pointers but not contents.
+    QhullPointSet &     operator=(const QhullPointSet &other) { QhullSet<QhullPoint>::operator=(other); return *this; }
+                        ~QhullPointSet() {}
+
+                        //!Default constructor disabled.
+private:
+                        QhullPointSet();
+public:
+
+#//!\name IO
+    struct PrintIdentifiers{
+        const QhullPointSet *point_set;
+        const char *    print_message; //!< non-null message
+        PrintIdentifiers(const char *message, const QhullPointSet *s) : point_set(s), print_message(message) {}
+    };//PrintIdentifiers
+    PrintIdentifiers printIdentifiers(const char *message) const { return PrintIdentifiers(message, this); }
+
+    struct PrintPointSet{
+        const QhullPointSet *point_set;
+        const char *    print_message;  //!< non-null message
+        PrintPointSet(const char *message, const QhullPointSet &s) : point_set(&s), print_message(message) {}
+    };//PrintPointSet
+    PrintPointSet       print(const char *message) const { return PrintPointSet(message, *this); }
+
+};//QhullPointSet
+
+typedef QhullSetIterator<QhullPoint>  QhullPointSetIterator;
+
+}//namespace orgQhull
+
+#//!\name Global
+
+std::ostream &operator<<(std::ostream &os, const orgQhull::QhullPointSet::PrintIdentifiers &pr);
+std::ostream &operator<<(std::ostream &os, const orgQhull::QhullPointSet::PrintPointSet &pr);
+
+#endif // QHULLPOINTSET_H
diff --git a/xs/src/qhull/src/libqhullcpp/QhullPoints.cpp b/xs/src/qhull/src/libqhullcpp/QhullPoints.cpp
new file mode 100644
index 0000000000..2320b5007a
--- /dev/null
+++ b/xs/src/qhull/src/libqhullcpp/QhullPoints.cpp
@@ -0,0 +1,320 @@
+/****************************************************************************
+**
+** Copyright (c) 2009-2015 C.B. Barber. All rights reserved.
+** $Id: //main/2015/qhull/src/libqhullcpp/QhullPoints.cpp#3 $$Change: 2066 $
+** $DateTime: 2016/01/18 19:29:17 $$Author: bbarber $
+**
+****************************************************************************/
+
+#include "libqhullcpp/QhullPoints.h"
+
+#include "libqhullcpp/Qhull.h"
+
+#include <iostream>
+
+#ifndef QHULL_NO_STL
+#include <vector>
+#endif
+
+#ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
+#endif
+
+namespace orgQhull {
+
+#//!\name Constructors
+
+QhullPoints::
+QhullPoints(const Qhull &q)
+: point_first(0)
+, point_end(0)
+, qh_qh(q.qh())
+, point_dimension(q.hullDimension())
+{
+}//QhullPoints Qhull
+
+QhullPoints::
+QhullPoints(const Qhull &q, countT coordinateCount2, coordT *c)
+: point_first(c)
+, point_end(c+coordinateCount2)
+, qh_qh(q.qh())
+, point_dimension(q.hullDimension())
+{
+    QHULL_ASSERT(q.hullDimension());
+    QHULL_ASSERT(coordinateCount2>=0);
+}//QhullPoints Qhull dim
+
+QhullPoints::
+QhullPoints(const Qhull &q, int pointDimension, countT coordinateCount2, coordT *c)
+: point_first(c)
+, point_end(c+coordinateCount2)
+, qh_qh(q.qh())
+, point_dimension(pointDimension)
+{
+    QHULL_ASSERT(pointDimension>=0);
+    QHULL_ASSERT(coordinateCount2>=0);
+}//QhullPoints Qhull dim coordT
+
+QhullPoints::
+QhullPoints(QhullQh *qqh, int pointDimension, countT coordinateCount2, coordT *c)
+: point_first(c)
+, point_end(c+coordinateCount2)
+, qh_qh(qqh)
+, point_dimension(pointDimension)
+{
+    QHULL_ASSERT(pointDimension>=0);
+    QHULL_ASSERT(coordinateCount2>=0);
+}//QhullPoints QhullQh dim coordT
+
+#//!\name Conversions
+// See qt-qhull.cpp for QList conversion
+
+#ifndef QHULL_NO_STL
+std::vector<QhullPoint> QhullPoints::
+toStdVector() const
+{
+    QhullPointsIterator i(*this);
+    std::vector<QhullPoint> vs;
+    while(i.hasNext()){
+        vs.push_back(i.next());
+    }
+    return vs;
+}//toStdVector
+#endif //QHULL_NO_STL
+
+#//!\name GetSet
+
+countT QhullPoints::
+extraCoordinatesCount() const
+{
+    if(point_dimension>0){
+        return (countT)((point_end-point_first)%(size_t)point_dimension);
+    }
+    return 0;
+}//extraCoordinatesCount
+
+//! QhullPoints is equal if the same address, or if the coordinates are identical
+//! Use QhullPoint.operator==() for DISTround equality
+bool QhullPoints::
+operator==(const QhullPoints &other) const
+{
+    if((point_end-point_first) != (other.point_end-other.point_first)){
+        return false;
+    }
+    if(point_dimension!=other.point_dimension){
+        return false;
+    }
+    if(point_first==other.point_first){
+        return true;
+    }
+    if(!qh_qh || qh_qh->hull_dim==0){
+        const coordT *c= point_first;
+        const coordT *c2= other.point_first;
+        while(c<point_end){
+            if(*c++!=*c2++){
+                return false;
+            }
+        }
+    }else{
+        const_iterator i= begin();
+        const_iterator i2= other.begin();
+        while(i<end()){
+            if(*i++!=*i2++){
+                return false;
+            }
+        }
+    }
+    return true;
+}//operator==
+
+//! Reset QhullPoints to QhullQh and its hullDimension()
+//! Does not free up old qh_qh
+void QhullPoints::
+resetQhullQh(QhullQh *qqh)
+{
+    qh_qh= qqh;
+    point_dimension= (qqh ? qqh->hull_dim : 0);
+    point_first= 0;
+    point_end= 0;
+}//resetQhullQh
+
+QhullPoint QhullPoints::
+value(countT idx) const
+{
+    QhullPoint p(qh_qh);
+    if(idx>=0 && idx<count()){
+        p.defineAs(point_dimension, point_first+idx*point_dimension);
+    }
+    return p;
+}//value
+
+QhullPoint QhullPoints::
+value(countT idx, QhullPoint &defaultValue) const
+{
+    QhullPoint p(qh_qh);
+    if(idx>=0 && idx<count()){
+        p.defineAs(point_dimension, point_first+idx*point_dimension);
+    }else{
+        p.defineAs(defaultValue);
+    }
+    return p;
+}//value
+
+#//!\name Methods
+
+bool QhullPoints::
+contains(const QhullPoint &t) const
+{
+    const_iterator i= begin();
+    while(i != end()){
+        if(*i==t){
+            return true;
+        }
+        i++;
+    }
+    return false;
+}//contains
+
+countT QhullPoints::
+count(const QhullPoint &t) const
+{
+    countT n= 0;
+    const_iterator i= begin();
+    while(i != end()){
+        if(*i==t){
+            ++n;
+        }
+        i++;
+    }
+    return n;
+}//count
+
+countT QhullPoints::
+indexOf(const coordT *pointCoordinates) const
+{
+    if(!includesCoordinates(pointCoordinates) || point_dimension==0){
+        return -1;
+    }
+    size_t offset= pointCoordinates-point_first;
+    countT idx= (countT)(offset/(size_t)point_dimension);
+    countT extra= (countT)(offset%(size_t)point_dimension);
+    if(extra!=0){
+        throw QhullError(10066, "Qhull error: coordinates %x are not at point boundary (extra %d at index %d)", extra, idx, 0.0, pointCoordinates);
+    }
+    return idx;
+}//indexOf coordT
+
+countT QhullPoints::
+indexOf(const coordT *pointCoordinates, int noThrow) const
+{
+    size_t extra= 0;
+    if(noThrow){
+        if(!includesCoordinates(pointCoordinates) || point_dimension==0){
+            return -1;
+        }
+        extra= (pointCoordinates-point_first)%(size_t)point_dimension;
+    }
+    return indexOf(pointCoordinates-extra);
+}//indexOf coordT noThrow
+
+countT QhullPoints::
+indexOf(const QhullPoint &t) const
+{
+    countT j=0;
+    const_iterator i= begin();
+    while(i!=end()){
+        if(*i==t){
+            return j;
+        }
+        ++i;
+        ++j;
+    }
+    return -1;
+}//indexOf
+
+countT QhullPoints::
+lastIndexOf(const QhullPoint &t) const
+{
+    countT j= count();
+    const_iterator i= end();
+    while(i != begin()){
+        --i;
+        --j;
+        if(*i==t){
+            return j;
+        }
+    }
+    return -1;
+}//lastIndexOf
+
+QhullPoints QhullPoints::
+mid(countT idx, countT length) const
+{
+    countT n= count();
+    if(idx<0 || idx>=n){
+        n= 0;
+    }else if(length<0 || idx+length>=n){
+        n -= idx;
+    }else{
+        n -= idx+length;
+    }
+    return QhullPoints(qh_qh, point_dimension, n*point_dimension, point_first+idx*point_dimension);
+}//mid
+
+#//!\name QhullPointsIterator
+
+bool QhullPointsIterator::
+findNext(const QhullPoint &p)
+{
+    while(i!=ps->constEnd()){
+        if(*i++ == p){
+            return true;
+        }
+    }
+    return false;
+}//findNext
+
+bool QhullPointsIterator::
+findPrevious(const QhullPoint &p)
+{
+    while(i!=ps->constBegin()){
+        if(*--i == p){
+            return true;
+        }
+    }
+    return false;
+}//findPrevious
+
+}//namespace orgQhull
+
+#//!\name Global functions
+
+using std::ostream;
+using orgQhull::QhullPoint;
+using orgQhull::QhullPoints;
+using orgQhull::QhullPointsIterator;
+
+ostream &
+operator<<(ostream &os, const QhullPoints &p)
+{
+    QhullPointsIterator i(p);
+    while(i.hasNext()){
+        os << i.next();
+    }
+    return os;
+}//operator<<QhullPoints
+
+ostream &
+operator<<(ostream &os, const QhullPoints::PrintPoints &pr)
+{
+    os << pr.point_message;
+    QhullPoints ps= *pr.points;
+    for(QhullPoints::iterator i=ps.begin(); i!=ps.end(); ++i){
+        QhullPoint p= *i;
+        if(pr.with_identifier){
+            os << p.printWithIdentifier("");
+        }else{
+            os << p.print("");
+        }
+    }
+    return os;
+}//<<PrintPoints
diff --git a/xs/src/qhull/src/libqhullcpp/QhullPoints.h b/xs/src/qhull/src/libqhullcpp/QhullPoints.h
new file mode 100644
index 0000000000..ce169a159e
--- /dev/null
+++ b/xs/src/qhull/src/libqhullcpp/QhullPoints.h
@@ -0,0 +1,266 @@
+/****************************************************************************
+**
+** Copyright (c) 2009-2015 C.B. Barber. All rights reserved.
+** $Id: //main/2015/qhull/src/libqhullcpp/QhullPoints.h#5 $$Change: 2079 $
+** $DateTime: 2016/02/07 17:43:34 $$Author: bbarber $
+**
+****************************************************************************/
+
+#ifndef QHULLPOINTS_H
+#define QHULLPOINTS_H
+
+#include "libqhull_r/qhull_ra.h"
+#include "libqhullcpp/QhullPoint.h"
+
+#include <cstddef>  // ptrdiff_t, size_t
+#include <ostream>
+
+namespace orgQhull {
+
+#//!\name Defined here
+    class QhullPoints;          //!< One or more points Coordinate pointers with dimension and iterators
+    class QhullPointsIterator;  //!< Java-style iterator
+
+//! QhullPoints are an array of QhullPoint as pointers into an array of coordinates.
+//! For Qhull/QhullQh, QhullPoints must use hull_dim.  Can change QhullPoint to input_dim if needed for Delaunay input site
+class QhullPoints {
+
+private:
+#//!\name Fields
+    coordT *            point_first; //!< First coordinate of an array of points of point_dimension
+    coordT *            point_end;   //!< End of point coordinates (end>=first).  Trailing coordinates ignored
+    QhullQh *           qh_qh;       //!< Maybe initialized NULL to allow ownership by RboxPoints
+                                     //!< qh_qh used for QhullPoint() and qh_qh->hull_dim in constructor
+    int                 point_dimension;  //!< Dimension, >=0
+
+public:
+#//!\name Subtypes
+    class const_iterator;
+    class iterator;
+    typedef QhullPoints::const_iterator ConstIterator;
+    typedef QhullPoints::iterator       Iterator;
+
+#//!\name Construct
+    //! QhullPoint, PointCoordinates, and QhullPoints have similar constructors
+    //! If Qhull/QhullQh is not initialized, then QhullPoints.dimension() is zero unless explicitly set
+    //! Cannot define QhullPoints(int pointDimension) since it is ambiguous with QhullPoints(QhullQh *qqh)
+                        QhullPoints() : point_first(0), point_end(0), qh_qh(0), point_dimension(0) { }
+                        QhullPoints(int pointDimension, countT coordinateCount2, coordT *c) : point_first(c), point_end(c+coordinateCount2), qh_qh(0), point_dimension(pointDimension) { QHULL_ASSERT(pointDimension>=0); }
+    explicit            QhullPoints(const Qhull &q);
+                        QhullPoints(const Qhull &q, countT coordinateCount2, coordT *c);
+                        QhullPoints(const Qhull &q, int pointDimension, countT coordinateCount2, coordT *c);
+    explicit            QhullPoints(QhullQh *qqh) : point_first(0), point_end(0), qh_qh(qqh), point_dimension(qqh ? qqh->hull_dim : 0) { }
+                        QhullPoints(QhullQh *qqh, countT coordinateCount2, coordT *c) : point_first(c), point_end(c+coordinateCount2), qh_qh(qqh), point_dimension(qqh ? qqh->hull_dim : 0) { QHULL_ASSERT(qqh && qqh->hull_dim>0); }
+                        QhullPoints(QhullQh *qqh, int pointDimension, countT coordinateCount2, coordT *c);
+                        //! Copy constructor copies pointers but not contents.  Needed for return by value and parameter passing.
+                        QhullPoints(const QhullPoints &other)  : point_first(other.point_first), point_end(other.point_end), qh_qh(other.qh_qh), point_dimension(other.point_dimension) {}
+    QhullPoints &       operator=(const QhullPoints &other) { point_first= other.point_first; point_end= other.point_end; qh_qh= other.qh_qh; point_dimension= other.point_dimension; return *this; }
+                        ~QhullPoints() {}
+
+public:
+
+#//!\name Conversion
+
+#ifndef QHULL_NO_STL
+    std::vector<QhullPoint> toStdVector() const;
+#endif //QHULL_NO_STL
+#ifdef QHULL_USES_QT
+    QList<QhullPoint>   toQList() const;
+#endif //QHULL_USES_QT
+
+#//!\name GetSet
+    // Constructs QhullPoint.  Cannot return reference.
+    const QhullPoint    at(countT idx) const { /* point_first==0 caught by point_end assert */ coordT *p= point_first+idx*point_dimension; QHULL_ASSERT(p<point_end); return QhullPoint(qh_qh, point_dimension, p); }
+    // Constructs QhullPoint.  Cannot return reference.
+    const QhullPoint    back() const { return last(); }
+    QhullPoint          back() { return last(); }
+    ConstIterator       begin() const { return ConstIterator(*this); }
+    Iterator            begin() { return Iterator(*this); }
+    ConstIterator       constBegin() const { return ConstIterator(*this); }
+    const coordT *      constData() const { return point_first; }
+    ConstIterator       constEnd() const { return ConstIterator(qh_qh, point_dimension, point_end); }
+    coordT *            coordinates() const { return point_first; }
+    countT              coordinateCount() const { return (countT)(point_end-point_first); } // WARN64
+    countT              count() const { return (countT)size(); } // WARN64
+    const coordT *      data() const { return point_first; }
+    coordT *            data() { return point_first; }
+    void                defineAs(int pointDimension, countT coordinatesCount, coordT *c) { QHULL_ASSERT(pointDimension>=0 && coordinatesCount>=0 && c!=0); point_first= c; point_end= c+coordinatesCount; point_dimension= pointDimension; }
+    void                defineAs(countT coordinatesCount, coordT *c) { QHULL_ASSERT((point_dimension>0 && coordinatesCount>=0 && c!=0) || (c==0 && coordinatesCount==0)); point_first= c; point_end= c+coordinatesCount; }
+    void                defineAs(const QhullPoints &other) { point_first= other.point_first; point_end= other.point_end; qh_qh= other.qh_qh; point_dimension= other.point_dimension; }
+    int                 dimension() const { return point_dimension; }
+    ConstIterator       end() const { return ConstIterator(qh_qh, point_dimension, point_end); }
+    Iterator            end() { return Iterator(qh_qh, point_dimension, point_end); }
+    coordT *            extraCoordinates() const { return extraCoordinatesCount() ? (point_end-extraCoordinatesCount()) : 0; }
+    countT              extraCoordinatesCount() const;  // WARN64
+    // Constructs QhullPoint.  Cannot return reference.
+    const QhullPoint    first() const { return QhullPoint(qh_qh, point_dimension, point_first); }
+    QhullPoint          first() { return QhullPoint(qh_qh, point_dimension, point_first); }
+    // Constructs QhullPoint.  Cannot return reference.
+    const QhullPoint    front() const { return first(); }
+    QhullPoint          front() { return first(); }
+    bool                includesCoordinates(const coordT *c) const { return c>=point_first && c<point_end; }
+    bool                isEmpty() const { return (point_end==point_first || point_dimension==0); }
+    // Constructs QhullPoint.  Cannot return reference.
+    const QhullPoint    last() const { QHULL_ASSERT(point_first!=0); return QhullPoint(qh_qh, point_dimension, point_end - point_dimension); }
+    QhullPoint          last() { QHULL_ASSERT(point_first!=0); return QhullPoint(qh_qh, point_dimension, point_end - point_dimension); }
+    bool                operator==(const QhullPoints &other) const;
+    bool                operator!=(const QhullPoints &other) const { return ! operator==(other); }
+    QhullPoint          operator[](countT idx) const { return at(idx); }
+    QhullQh *           qh() const { return qh_qh; }
+    void                resetQhullQh(QhullQh *qqh);
+    void                setDimension(int d) { point_dimension= d; }
+    size_t              size() const { return point_dimension ? (point_end-point_first)/point_dimension : 0; }
+    QhullPoint          value(countT idx) const;
+    QhullPoint          value(countT idx, QhullPoint &defaultValue) const;
+
+#//!\name Methods
+    bool                contains(const QhullPoint &t) const;
+    countT              count(const QhullPoint &t) const;
+    countT              indexOf(const coordT *pointCoordinates) const;
+    countT              indexOf(const coordT *pointCoordinates, int noThrow) const;
+    countT              indexOf(const QhullPoint &t) const;
+    countT              lastIndexOf(const QhullPoint &t) const;
+    //! Returns a subset of the points, not a copy
+    QhullPoints         mid(countT idx, countT length= -1) const;
+
+#//!\name QhullPoints::iterator
+    // Modeled on qlist.h w/o QT_STRICT_ITERATORS
+    // before const_iterator for conversion with comparison operators
+    // See: QhullSet.h
+    class iterator : public QhullPoint {
+
+    public:
+        typedef std::random_access_iterator_tag  iterator_category;
+        typedef QhullPoint      value_type;
+        typedef value_type *    pointer;
+        typedef value_type &    reference;
+        typedef ptrdiff_t       difference_type;
+
+        explicit        iterator(const QhullPoints &ps) : QhullPoint(ps.qh(), ps.dimension(), ps.coordinates()) {}
+                        iterator(const int pointDimension, coordT *c): QhullPoint(pointDimension, c) {}
+                        iterator(const Qhull &q, coordT *c): QhullPoint(q, c) {}
+                        iterator(const Qhull &q, int pointDimension, coordT *c): QhullPoint(q, pointDimension, c) {}
+                        iterator(QhullQh *qqh, coordT *c): QhullPoint(qqh, c) {}
+                        iterator(QhullQh *qqh, int pointDimension, coordT *c): QhullPoint(qqh, pointDimension, c) {}
+                        iterator(const iterator &other): QhullPoint(*other) {}
+        iterator &      operator=(const iterator &other) { defineAs( const_cast<iterator &>(other)); return *this; }
+
+        // Need 'const QhullPoint' to maintain const
+        const QhullPoint & operator*() const { return *this; }
+        QhullPoint &    operator*() { return *this; }
+        const QhullPoint * operator->() const { return this; }
+        QhullPoint *    operator->() { return this; }
+        // value instead of reference since advancePoint() modifies self
+        QhullPoint      operator[](countT idx) const { QhullPoint result= *this; result.advancePoint(idx); return result; }
+        bool            operator==(const iterator &o) const { QHULL_ASSERT(qh_qh==o.qh_qh); return (point_coordinates==o.point_coordinates && point_dimension==o.point_dimension); }
+        bool            operator!=(const iterator &o) const { return !operator==(o); }
+        bool            operator<(const iterator &o) const  { QHULL_ASSERT(qh_qh==o.qh_qh); return point_coordinates < o.point_coordinates; }
+        bool            operator<=(const iterator &o) const { QHULL_ASSERT(qh_qh==o.qh_qh); return point_coordinates <= o.point_coordinates; }
+        bool            operator>(const iterator &o) const  { QHULL_ASSERT(qh_qh==o.qh_qh); return point_coordinates > o.point_coordinates; }
+        bool            operator>=(const iterator &o) const { QHULL_ASSERT(qh_qh==o.qh_qh); return point_coordinates >= o.point_coordinates; }
+        // reinterpret_cast to break circular dependency
+        bool            operator==(const QhullPoints::const_iterator &o) const { QHULL_ASSERT(qh_qh==reinterpret_cast<const iterator &>(o).qh_qh); return (point_coordinates==reinterpret_cast<const iterator &>(o).point_coordinates && point_dimension==reinterpret_cast<const iterator &>(o).point_dimension); }
+        bool            operator!=(const QhullPoints::const_iterator &o) const { return !operator==(reinterpret_cast<const iterator &>(o)); }
+        bool            operator<(const QhullPoints::const_iterator &o) const  { QHULL_ASSERT(qh_qh==reinterpret_cast<const iterator &>(o).qh_qh); return point_coordinates < reinterpret_cast<const iterator &>(o).point_coordinates; }
+        bool            operator<=(const QhullPoints::const_iterator &o) const { QHULL_ASSERT(qh_qh==reinterpret_cast<const iterator &>(o).qh_qh); return point_coordinates <= reinterpret_cast<const iterator &>(o).point_coordinates; }
+        bool            operator>(const QhullPoints::const_iterator &o) const  { QHULL_ASSERT(qh_qh==reinterpret_cast<const iterator &>(o).qh_qh); return point_coordinates > reinterpret_cast<const iterator &>(o).point_coordinates; }
+        bool            operator>=(const QhullPoints::const_iterator &o) const { QHULL_ASSERT(qh_qh==reinterpret_cast<const iterator &>(o).qh_qh); return point_coordinates >= reinterpret_cast<const iterator &>(o).point_coordinates; }
+        iterator &      operator++() { advancePoint(1); return *this; }
+        iterator        operator++(int) { iterator n= *this; operator++(); return iterator(n); }
+        iterator &      operator--() { advancePoint(-1); return *this; }
+        iterator        operator--(int) { iterator n= *this; operator--(); return iterator(n); }
+        iterator &      operator+=(countT idx) { advancePoint(idx); return *this; }
+        iterator &      operator-=(countT idx) { advancePoint(-idx); return *this; }
+        iterator        operator+(countT idx) const { iterator n= *this; n.advancePoint(idx); return n; }
+        iterator        operator-(countT idx) const { iterator n= *this; n.advancePoint(-idx); return n; }
+        difference_type operator-(iterator o) const { QHULL_ASSERT(qh_qh==o.qh_qh && point_dimension==o.point_dimension); return (point_dimension ? (point_coordinates-o.point_coordinates)/point_dimension : 0); }
+    };//QhullPoints::iterator
+
+#//!\name QhullPoints::const_iterator
+    //!\todo FIXUP QH11018 const_iterator same as iterator.  SHould have a common definition
+    class const_iterator : public QhullPoint {
+
+    public:
+        typedef std::random_access_iterator_tag  iterator_category;
+        typedef QhullPoint          value_type;
+        typedef const value_type *  pointer;
+        typedef const value_type &  reference;
+        typedef ptrdiff_t           difference_type;
+
+                        const_iterator(const QhullPoints::iterator &o) : QhullPoint(*o) {}
+        explicit        const_iterator(const QhullPoints &ps) : QhullPoint(ps.qh(), ps.dimension(), ps.coordinates()) {}
+                        const_iterator(const int pointDimension, coordT *c): QhullPoint(pointDimension, c) {}
+                        const_iterator(const Qhull &q, coordT *c): QhullPoint(q, c) {}
+                        const_iterator(const Qhull &q, int pointDimension, coordT *c): QhullPoint(q, pointDimension, c) {}
+                        const_iterator(QhullQh *qqh, coordT *c): QhullPoint(qqh, c) {}
+                        const_iterator(QhullQh *qqh, int pointDimension, coordT *c): QhullPoint(qqh, pointDimension, c) {}
+                        const_iterator(const const_iterator &o) : QhullPoint(*o) {}
+        const_iterator &operator=(const const_iterator &o) { defineAs(const_cast<const_iterator &>(o)); return *this; }
+
+        // value/non-const since advancePoint(1), etc. modifies self
+        const QhullPoint & operator*() const { return *this; }
+        const QhullPoint * operator->() const { return this; }
+        // value instead of reference since advancePoint() modifies self
+        const QhullPoint operator[](countT idx) const { QhullPoint n= *this; n.advancePoint(idx); return n; }
+        bool            operator==(const const_iterator &o) const { QHULL_ASSERT(qh_qh==o.qh_qh); return (point_coordinates==o.point_coordinates && point_dimension==o.point_dimension); }
+        bool            operator!=(const const_iterator &o) const { return ! operator==(o); }
+        bool            operator<(const const_iterator &o) const  { QHULL_ASSERT(qh_qh==o.qh_qh); return point_coordinates < o.point_coordinates; }
+        bool            operator<=(const const_iterator &o) const { QHULL_ASSERT(qh_qh==o.qh_qh); return point_coordinates <= o.point_coordinates; }
+        bool            operator>(const const_iterator &o) const  { QHULL_ASSERT(qh_qh==o.qh_qh); return point_coordinates > o.point_coordinates; }
+        bool            operator>=(const const_iterator &o) const { QHULL_ASSERT(qh_qh==o.qh_qh); return point_coordinates >= o.point_coordinates; }
+        const_iterator &operator++() { advancePoint(1); return *this; }
+        const_iterator  operator++(int) { const_iterator n= *this; operator++(); return const_iterator(n); }
+        const_iterator &operator--() { advancePoint(-1); return *this; }
+        const_iterator  operator--(int) { const_iterator n= *this; operator--(); return const_iterator(n); }
+        const_iterator &operator+=(countT idx) { advancePoint(idx); return *this; }
+        const_iterator &operator-=(countT idx) { advancePoint(-idx); return *this; }
+        const_iterator  operator+(countT idx) const { const_iterator n= *this; n.advancePoint(idx); return n; }
+        const_iterator  operator-(countT idx) const { const_iterator n= *this; n.advancePoint(-idx); return n; }
+        difference_type operator-(const_iterator o) const { QHULL_ASSERT(qh_qh==o.qh_qh && point_dimension==o.point_dimension); return (point_dimension ? (point_coordinates-o.point_coordinates)/point_dimension : 0); }
+    };//QhullPoints::const_iterator
+
+#//!\name IO
+    struct PrintPoints{
+        const QhullPoints  *points;
+        const char *    point_message;
+        bool            with_identifier;
+        PrintPoints(const char *message, bool withIdentifier, const QhullPoints &ps) : points(&ps), point_message(message), with_identifier(withIdentifier) {}
+    };//PrintPoints
+    PrintPoints          print(const char *message) const { return PrintPoints(message, false, *this); }
+    PrintPoints          printWithIdentifier(const char *message) const { return PrintPoints(message, true, *this); }
+};//QhullPoints
+
+// Instead of QHULL_DECLARE_SEQUENTIAL_ITERATOR because next(),etc would return a reference to a temporary
+class QhullPointsIterator
+{
+    typedef QhullPoints::const_iterator const_iterator;
+
+#//!\name Fields
+private:
+    const QhullPoints  *ps;
+    const_iterator      i;
+
+public:
+                        QhullPointsIterator(const QhullPoints &other) : ps(&other), i(ps->constBegin()) {}
+    QhullPointsIterator &operator=(const QhullPoints &other) { ps = &other; i = ps->constBegin(); return *this; }
+
+    bool                findNext(const QhullPoint &t);
+    bool                findPrevious(const QhullPoint &t);
+    bool                hasNext() const { return i != ps->constEnd(); }
+    bool                hasPrevious() const { return i != ps->constBegin(); }
+    QhullPoint          next() { return *i++; }
+    QhullPoint          peekNext() const { return *i; }
+    QhullPoint          peekPrevious() const { const_iterator p = i; return *--p; }
+    QhullPoint          previous() { return *--i; }
+    void                toBack() { i = ps->constEnd(); }
+    void                toFront() { i = ps->constBegin(); }
+};//QhullPointsIterator
+
+}//namespace orgQhull
+
+#//!\name Global
+
+std::ostream &          operator<<(std::ostream &os, const orgQhull::QhullPoints &p);
+std::ostream &          operator<<(std::ostream &os, const orgQhull::QhullPoints::PrintPoints &pr);
+
+#endif // QHULLPOINTS_H
diff --git a/xs/src/qhull/src/libqhullcpp/QhullQh.cpp b/xs/src/qhull/src/libqhullcpp/QhullQh.cpp
new file mode 100644
index 0000000000..3635337001
--- /dev/null
+++ b/xs/src/qhull/src/libqhullcpp/QhullQh.cpp
@@ -0,0 +1,237 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
+** $Id: //main/2015/qhull/src/libqhullcpp/QhullQh.cpp#5 $$Change: 2066 $
+** $DateTime: 2016/01/18 19:29:17 $$Author: bbarber $
+**
+****************************************************************************/
+
+#//! QhullQh -- Qhull's global data structure, qhT, as a C++ class
+
+
+#include "libqhullcpp/QhullQh.h"
+
+#include "libqhullcpp/QhullError.h"
+#include "libqhullcpp/QhullStat.h"
+
+#include <sstream>
+#include <iostream>
+
+#include <stdarg.h>
+
+using std::cerr;
+using std::string;
+using std::vector;
+using std::ostream;
+
+#ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
+#pragma warning( disable : 4611)  // interaction between '_setjmp' and C++ object destruction is non-portable
+#pragma warning( disable : 4996)  // function was declared deprecated(strcpy, localtime, etc.)
+#endif
+
+namespace orgQhull {
+
+#//!\name Global variables
+const double QhullQh::
+default_factor_epsilon= 1.0;
+
+#//!\name Constructor, destructor, etc.
+
+//! Derived from qh_new_qhull[user.c]
+QhullQh::
+QhullQh()
+: qhull_status(qh_ERRnone)
+, qhull_message()
+, error_stream(0)
+, output_stream(0)
+, factor_epsilon(QhullQh::default_factor_epsilon)
+, use_output_stream(false)
+{
+    // NOerrors: TRY_QHULL_ not needed since these routines do not call qh_errexit()
+    qh_meminit(this, NULL);
+    qh_initstatistics(this);
+    qh_initqhull_start2(this, NULL, NULL, qh_FILEstderr);  // Initialize qhT
+    this->ISqhullQh= True;
+}//QhullQh
+
+QhullQh::
+~QhullQh()
+{
+    checkAndFreeQhullMemory();
+}//~QhullQh
+
+#//!\name Methods
+
+//! Check memory for internal consistency
+//! Free global memory used by qh_initbuild and qh_buildhull
+//! Zero the qhT data structure, except for memory (qhmemT) and statistics (qhstatT)
+//! Check and free short memory (e.g., facetT)
+//! Zero the qhmemT data structure
+void QhullQh::
+checkAndFreeQhullMemory()
+{
+#ifdef qh_NOmem
+    qh_freeqhull(this, qh_ALL);
+#else
+    qh_memcheck(this);
+    qh_freeqhull(this, !qh_ALL);
+    countT curlong;
+    countT totlong;
+    qh_memfreeshort(this, &curlong, &totlong);
+    if (curlong || totlong)
+        throw QhullError(10026, "Qhull error: qhull did not free %d bytes of long memory (%d pieces).", totlong, curlong);
+#endif
+}//checkAndFreeQhullMemory
+
+#//!\name Messaging
+
+void QhullQh::
+appendQhullMessage(const string &s)
+{
+    if(output_stream && use_output_stream && this->USEstdout){ 
+        *output_stream << s;
+    }else if(error_stream){
+        *error_stream << s;
+    }else{
+        qhull_message += s;
+    }
+}//appendQhullMessage
+
+//! clearQhullMessage does not throw errors (~Qhull)
+void QhullQh::
+clearQhullMessage()
+{
+    qhull_status= qh_ERRnone;
+    qhull_message.clear();
+    RoadError::clearGlobalLog();
+}//clearQhullMessage
+
+//! hasQhullMessage does not throw errors (~Qhull)
+bool QhullQh::
+hasQhullMessage() const
+{
+    return (!qhull_message.empty() || qhull_status!=qh_ERRnone);
+    //FIXUP QH11006 -- inconsistent usage with Rbox.  hasRboxMessage just tests rbox_status.  No appendRboxMessage()
+}
+
+void QhullQh::
+maybeThrowQhullMessage(int exitCode)
+{
+    if(!NOerrexit){
+        if(qhull_message.size()>0){
+            qhull_message.append("\n");
+        }
+        if(exitCode || qhull_status==qh_ERRnone){
+            qhull_status= 10073;
+        }else{
+            qhull_message.append("QH10073: ");
+        }
+        qhull_message.append("Cannot call maybeThrowQhullMessage() from QH_TRY_().  Or missing 'qh->NOerrexit=true;' after QH_TRY_(){...}.");
+    }
+    if(qhull_status==qh_ERRnone){
+        qhull_status= exitCode;
+    }
+    if(qhull_status!=qh_ERRnone){
+        QhullError e(qhull_status, qhull_message);
+        clearQhullMessage();
+        throw e; // FIXUP QH11007: copy constructor is expensive if logging
+    }
+}//maybeThrowQhullMessage
+
+void QhullQh::
+maybeThrowQhullMessage(int exitCode, int noThrow)  throw()
+{
+    QHULL_UNUSED(noThrow);
+
+    if(qhull_status==qh_ERRnone){
+        qhull_status= exitCode;
+    }
+    if(qhull_status!=qh_ERRnone){
+        QhullError e(qhull_status, qhull_message);
+        e.logErrorLastResort();
+    }
+}//maybeThrowQhullMessage
+
+//! qhullMessage does not throw errors (~Qhull)
+std::string QhullQh::
+qhullMessage() const
+{
+    if(qhull_message.empty() && qhull_status!=qh_ERRnone){
+        return "qhull: no message for error.  Check cerr or error stream\n";
+    }else{
+        return qhull_message;
+    }
+}//qhullMessage
+
+int QhullQh::
+qhullStatus() const
+{
+    return qhull_status;
+}//qhullStatus
+
+void QhullQh::
+setErrorStream(ostream *os)
+{
+    error_stream= os;
+}//setErrorStream
+
+//! Updates use_output_stream
+void QhullQh::
+setOutputStream(ostream *os)
+{
+    output_stream= os;
+    use_output_stream= (os!=0);
+}//setOutputStream
+
+}//namespace orgQhull
+
+/*-<a                             href="qh_qh-user.htm#TOC"
+ >-------------------------------</a><a name="qh_fprintf">-</a>
+
+  qh_fprintf(qhT *qh, fp, msgcode, format, list of args )
+    replaces qh_fprintf() in userprintf_r.c
+
+notes:
+    only called from libqhull
+    same as fprintf() and RboxPoints.qh_fprintf_rbox()
+    fgets() is not trapped like fprintf()
+    Do not throw errors from here.  Use qh_errexit;
+*/
+extern "C"
+void qh_fprintf(qhT *qh, FILE *fp, int msgcode, const char *fmt, ... ) {
+    va_list args;
+
+    using namespace orgQhull;
+
+    if(!qh->ISqhullQh){
+        qh_fprintf_stderr(10025, "Qhull error: qh_fprintf called from a Qhull instance without QhullQh defined\n");
+        qh_exit(10025);
+    }
+    QhullQh *qhullQh= static_cast<QhullQh *>(qh);
+    va_start(args, fmt);
+    if(msgcode<MSG_OUTPUT || fp == qh_FILEstderr){
+        if(msgcode>=MSG_ERROR && msgcode<MSG_WARNING){
+            if(qhullQh->qhull_status<MSG_ERROR || qhullQh->qhull_status>=MSG_WARNING){
+                qhullQh->qhull_status= msgcode;
+            }
+        }
+        char newMessage[MSG_MAXLEN];
+        // RoadError will add the message tag
+        vsnprintf(newMessage, sizeof(newMessage), fmt, args);
+        qhullQh->appendQhullMessage(newMessage);
+        va_end(args);
+        return;
+    }
+    if(qhullQh->output_stream && qhullQh->use_output_stream){
+        char newMessage[MSG_MAXLEN];
+        vsnprintf(newMessage, sizeof(newMessage), fmt, args);
+        *qhullQh->output_stream << newMessage;
+        va_end(args);
+        return;
+    }
+    // FIXUP QH11008: how do users trap messages and handle input?  A callback?
+    char newMessage[MSG_MAXLEN];
+    vsnprintf(newMessage, sizeof(newMessage), fmt, args);
+    qhullQh->appendQhullMessage(newMessage);
+    va_end(args);
+} /* qh_fprintf */
diff --git a/xs/src/qhull/src/libqhullcpp/QhullQh.h b/xs/src/qhull/src/libqhullcpp/QhullQh.h
new file mode 100644
index 0000000000..c3b277ff0f
--- /dev/null
+++ b/xs/src/qhull/src/libqhullcpp/QhullQh.h
@@ -0,0 +1,110 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
+** $Id: //main/2015/qhull/src/libqhullcpp/QhullQh.h#2 $$Change: 2079 $
+** $DateTime: 2016/02/07 17:43:34 $$Author: bbarber $
+**
+****************************************************************************/
+
+#ifndef QHULLQH_H
+#define QHULLQH_H
+
+#include "libqhull_r/qhull_ra.h"
+
+#include <string>
+
+#ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
+#pragma warning( disable : 4611)  /* interaction between '_setjmp' and C++ object destruction is non-portable */
+/* setjmp should not be implemented with 'catch' */
+#endif
+
+//! Use QH_TRY_ or QH_TRY_NOTHROW_ to call a libqhull_r routine that may invoke qh_errexit()
+//! QH_TRY_(qh){...} qh->NOerrexit=true;
+//! No object creation -- longjmp() skips object destructors
+//! To test for error when done -- qh->maybeThrowQhullMessage(QH_TRY_status);
+//! Use the same compiler for QH_TRY_, libqhullcpp, and libqhull_r.  setjmp() is not portable between compilers.
+
+#define QH_TRY_ERROR 10071
+
+#define QH_TRY_(qh) \
+    int QH_TRY_status; \
+    if(qh->NOerrexit){ \
+        qh->NOerrexit= False; \
+        QH_TRY_status= setjmp(qh->errexit); \
+    }else{ \
+        throw QhullError(QH_TRY_ERROR, "Cannot invoke QH_TRY_() from inside a QH_TRY_.  Or missing 'qh->NOerrexit=true' after previously called QH_TRY_(qh){...}"); \
+    } \
+    if(!QH_TRY_status)
+
+#define QH_TRY_NO_THROW_(qh) \
+    int QH_TRY_status; \
+    if(qh->NOerrexit){ \
+        qh->NOerrexit= False; \
+        QH_TRY_status= setjmp(qh->errexit); \
+    }else{ \
+        QH_TRY_status= QH_TRY_ERROR; \
+    } \
+    if(!QH_TRY_status)
+
+namespace orgQhull {
+
+#//!\name Defined here
+    //! QhullQh -- Qhull's global data structure, qhT, as a C++ class
+    class QhullQh;
+
+//! POD type equivalent to qhT.  No virtual members
+class QhullQh : public qhT {
+
+#//!\name Constants
+
+#//!\name Fields
+private:
+    int                 qhull_status;   //!< qh_ERRnone if valid
+    std::string         qhull_message;  //!< Returned messages from libqhull_r
+    std::ostream *      error_stream;   //!< overrides errorMessage, use appendQhullMessage()
+    std::ostream *      output_stream;  //!< send output to stream
+    double              factor_epsilon; //!< Factor to increase ANGLEround and DISTround for hyperplane equality
+    bool                use_output_stream; //!< True if using output_stream
+
+    friend void         ::qh_fprintf(qhT *qh, FILE *fp, int msgcode, const char *fmt, ... );
+
+    static const double default_factor_epsilon;  //!< Default factor_epsilon is 1.0, never updated
+
+#//!\name Constructors
+public:
+                        QhullQh();
+                        ~QhullQh();
+private:
+                        //!disable copy constructor and assignment
+                        QhullQh(const QhullQh &);
+    QhullQh &           operator=(const QhullQh &);
+public:
+
+#//!\name GetSet
+    double              factorEpsilon() const { return factor_epsilon; }
+    void                setFactorEpsilon(double a) { factor_epsilon= a; }
+    void                disableOutputStream() { use_output_stream= false; }
+    void                enableOutputStream() { use_output_stream= true; }
+
+#//!\name Messaging
+    void                appendQhullMessage(const std::string &s);
+    void                clearQhullMessage();
+    std::string         qhullMessage() const;
+    bool                hasOutputStream() const { return use_output_stream; }
+    bool                hasQhullMessage() const;
+    void                maybeThrowQhullMessage(int exitCode);
+    void                maybeThrowQhullMessage(int exitCode, int noThrow) throw();
+    int                 qhullStatus() const;
+    void                setErrorStream(std::ostream *os);
+    void                setOutputStream(std::ostream *os);
+
+#//!\name Methods
+    double              angleEpsilon() const { return this->ANGLEround*factor_epsilon; } //!< Epsilon for hyperplane angle equality
+    void                checkAndFreeQhullMemory();
+    double              distanceEpsilon() const { return this->DISTround*factor_epsilon; } //!< Epsilon for distance to hyperplane
+
+};//class QhullQh
+
+}//namespace orgQhull
+
+#endif // QHULLQH_H
diff --git a/xs/src/qhull/src/libqhullcpp/QhullRidge.cpp b/xs/src/qhull/src/libqhullcpp/QhullRidge.cpp
new file mode 100644
index 0000000000..7a01812805
--- /dev/null
+++ b/xs/src/qhull/src/libqhullcpp/QhullRidge.cpp
@@ -0,0 +1,124 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
+** $Id: //main/2015/qhull/src/libqhullcpp/QhullRidge.cpp#3 $$Change: 2066 $
+** $DateTime: 2016/01/18 19:29:17 $$Author: bbarber $
+**
+****************************************************************************/
+
+#//! QhullRidge -- Qhull's ridge structure, ridgeT, as a C++ class
+
+#include "libqhullcpp/QhullRidge.h"
+
+#include "libqhullcpp/QhullSets.h"
+#include "libqhullcpp/QhullVertex.h"
+#include "libqhullcpp/Qhull.h"
+
+#ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
+#pragma warning( disable : 4611)  // interaction between '_setjmp' and C++ object destruction is non-portable
+#pragma warning( disable : 4996)  // function was declared deprecated(strcpy, localtime, etc.)
+#endif
+
+namespace orgQhull {
+
+#//!\name Class objects
+ridgeT QhullRidge::
+s_empty_ridge= {0,0,0,0,0,
+                0,0};
+
+#//!\name Constructors
+
+QhullRidge::QhullRidge(const Qhull &q)
+: qh_ridge(&s_empty_ridge)
+, qh_qh(q.qh())
+{
+}//Default
+
+QhullRidge::QhullRidge(const Qhull &q, ridgeT *r)
+: qh_ridge(r ? r : &s_empty_ridge)
+, qh_qh(q.qh())
+{
+}//ridgeT
+
+#//!\name foreach
+
+//! Return True if nextRidge3d
+//! Simplicial facets may have incomplete ridgeSets
+//! Does not use qh_errexit()
+bool QhullRidge::
+hasNextRidge3d(const QhullFacet &f) const
+{
+    if(!qh_qh){
+        return false;
+    }
+    vertexT *v= 0;
+    // Does not call qh_errexit(), TRY_QHULL_ not needed
+    ridgeT *ridge= qh_nextridge3d(getRidgeT(), f.getFacetT(), &v);
+    return (ridge!=0);
+}//hasNextRidge3d
+
+//! Return next ridge and optional vertex for a 3d facet and ridge
+//! Does not use qh_errexit()
+QhullRidge QhullRidge::
+nextRidge3d(const QhullFacet &f, QhullVertex *nextVertex) const
+{
+    vertexT *v= 0;
+    ridgeT *ridge= 0;
+    if(qh_qh){
+        // Does not call qh_errexit(), TRY_QHULL_ not needed
+        ridge= qh_nextridge3d(getRidgeT(), f.getFacetT(), &v);
+        if(!ridge){
+            throw QhullError(10030, "Qhull error nextRidge3d:  missing next ridge for facet %d ridge %d.  Does facet contain ridge?", f.id(), id());
+        }
+    }
+    if(nextVertex!=0){
+        *nextVertex= QhullVertex(qh_qh, v);
+    }
+    return QhullRidge(qh_qh, ridge);
+}//nextRidge3d
+
+}//namespace orgQhull
+
+#//!\name Global functions
+
+using std::endl;
+using std::ostream;
+using orgQhull::QhullRidge;
+using orgQhull::QhullVertex;
+
+ostream &
+operator<<(ostream &os, const QhullRidge &r)
+{
+    os << r.print("");
+    return os;
+}//<< QhullRidge
+
+//! Duplicate of qh_printridge [io_r.c]
+ostream &
+operator<<(ostream &os, const QhullRidge::PrintRidge &pr)
+{
+    if(*pr.print_message){
+        os << pr.print_message << " ";
+    }else{
+        os << "     - ";
+    }
+    QhullRidge r= *pr.ridge;
+    os << "r" << r.id();
+    if(r.getRidgeT()->tested){
+        os << " tested";
+    }
+    if(r.getRidgeT()->nonconvex){
+        os << " nonconvex";
+    }
+    os << endl;
+    os << r.vertices().print("           vertices:");
+    if(r.getRidgeT()->top && r.getRidgeT()->bottom){
+        os << "           between f" << r.topFacet().id() << " and f" << r.bottomFacet().id() << endl;
+    }else if(r.getRidgeT()->top){
+        os << "           top f" << r.topFacet().id() << endl;
+    }else if(r.getRidgeT()->bottom){
+        os << "           bottom f" << r.bottomFacet().id() << endl;
+    }
+
+    return os;
+}//<< PrintRidge
diff --git a/xs/src/qhull/src/libqhullcpp/QhullRidge.h b/xs/src/qhull/src/libqhullcpp/QhullRidge.h
new file mode 100644
index 0000000000..924340fb09
--- /dev/null
+++ b/xs/src/qhull/src/libqhullcpp/QhullRidge.h
@@ -0,0 +1,112 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
+** $Id: //main/2015/qhull/src/libqhullcpp/QhullRidge.h#4 $$Change: 2079 $
+** $DateTime: 2016/02/07 17:43:34 $$Author: bbarber $
+**
+****************************************************************************/
+
+#ifndef QHULLRIDGE_H
+#define QHULLRIDGE_H
+
+#include "libqhull_r/qhull_ra.h"
+#include "libqhullcpp/QhullSet.h"
+#include "libqhullcpp/QhullVertex.h"
+#include "libqhullcpp/QhullVertexSet.h"
+#include "libqhullcpp/QhullFacet.h"
+
+#include <ostream>
+
+namespace orgQhull {
+
+#//!\name Used here
+    class Qhull;
+    class QhullVertex;
+    class QhullVertexSet;
+    class QhullFacet;
+
+#//!\name Defined here
+    //! QhullRidge -- Qhull's ridge structure, ridgeT [libqhull.h], as a C++ class
+    class QhullRidge;
+    typedef QhullSet<QhullRidge>  QhullRidgeSet;
+    typedef QhullSetIterator<QhullRidge>  QhullRidgeSetIterator;
+    // see QhullSets.h for QhullRidgeSet and QhullRidgeSetIterator -- avoids circular references
+
+/************************
+a ridge is hull_dim-1 simplex between two neighboring facets.  If the
+facets are non-simplicial, there may be more than one ridge between
+two facets.  E.G. a 4-d hypercube has two triangles between each pair
+of neighboring facets.
+
+topological information:
+    vertices            a set of vertices
+    top,bottom          neighboring facets with orientation
+
+geometric information:
+    tested              True if ridge is clearly convex
+    nonconvex           True if ridge is non-convex
+*/
+
+class QhullRidge {
+
+#//!\name Defined here
+public:
+    typedef ridgeT *   base_type;  // for QhullRidgeSet
+
+#//!\name Fields
+private:
+    ridgeT *            qh_ridge;  //!< Corresponding ridgeT, never 0
+    QhullQh *           qh_qh;     //!< QhullQh/qhT for ridgeT, may be 0
+
+#//!\name Class objects
+    static ridgeT       s_empty_ridge;
+
+public:
+#//!\name Constants
+
+#//!\name Constructors
+                        QhullRidge() : qh_ridge(&s_empty_ridge), qh_qh(0) {}
+    explicit            QhullRidge(const Qhull &q);
+                        QhullRidge(const Qhull &q, ridgeT *r);
+    explicit            QhullRidge(QhullQh *qqh) : qh_ridge(&s_empty_ridge), qh_qh(qqh) {}
+                        QhullRidge(QhullQh *qqh, ridgeT *r) : qh_ridge(r ? r : &s_empty_ridge), qh_qh(qqh) {}
+                        // Creates an alias.  Does not copy QhullRidge.  Needed for return by value and parameter passing
+                        QhullRidge(const QhullRidge &other) : qh_ridge(other.qh_ridge), qh_qh(other.qh_qh) {}
+                        // Creates an alias.  Does not copy QhullRidge.  Needed for vector<QhullRidge>
+    QhullRidge &        operator=(const QhullRidge &other) { qh_ridge= other.qh_ridge; qh_qh= other.qh_qh; return *this; }
+                        ~QhullRidge() {}
+
+#//!\name GetSet
+    QhullFacet          bottomFacet() const { return QhullFacet(qh_qh, qh_ridge->bottom); }
+    int                 dimension() const { return ((qh_qh && qh_qh->hull_dim) ? qh_qh->hull_dim-1 : 0); }
+    ridgeT *            getBaseT() const { return getRidgeT(); } //!< For QhullSet<QhullRidge>
+    ridgeT *            getRidgeT() const { return qh_ridge; }
+    countT              id() const { return qh_ridge->id; }
+    bool                isValid() const { return (qh_qh && qh_ridge != &s_empty_ridge); }
+    bool                operator==(const QhullRidge &other) const { return qh_ridge==other.qh_ridge; }
+    bool                operator!=(const QhullRidge &other) const { return !operator==(other); }
+    QhullFacet          otherFacet(const QhullFacet &f) const { return QhullFacet(qh_qh, (qh_ridge->top==f.getFacetT() ? qh_ridge->bottom : qh_ridge->top)); }
+    QhullFacet          topFacet() const { return QhullFacet(qh_qh, qh_ridge->top); }
+
+#//!\name foreach
+    bool                hasNextRidge3d(const QhullFacet &f) const;
+    QhullRidge          nextRidge3d(const QhullFacet &f) const { return nextRidge3d(f, 0); }
+    QhullRidge          nextRidge3d(const QhullFacet &f, QhullVertex *nextVertex) const;
+    QhullVertexSet      vertices() const { return QhullVertexSet(qh_qh, qh_ridge->vertices); }
+
+#//!\name IO
+
+    struct PrintRidge{
+        const QhullRidge *ridge;
+        const char *    print_message;    //!< non-null message
+                        PrintRidge(const char *message, const QhullRidge &r) : ridge(&r), print_message(message) {}
+    };//PrintRidge
+    PrintRidge          print(const char* message) const { return PrintRidge(message, *this); }
+};//class QhullRidge
+
+}//namespace orgQhull
+
+std::ostream &operator<<(std::ostream &os, const orgQhull::QhullRidge &r);
+std::ostream &operator<<(std::ostream &os, const orgQhull::QhullRidge::PrintRidge &pr);
+
+#endif // QHULLRIDGE_H
diff --git a/xs/src/qhull/src/libqhullcpp/QhullSet.cpp b/xs/src/qhull/src/libqhullcpp/QhullSet.cpp
new file mode 100644
index 0000000000..dfdc3c51f3
--- /dev/null
+++ b/xs/src/qhull/src/libqhullcpp/QhullSet.cpp
@@ -0,0 +1,62 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
+** $Id: //main/2015/qhull/src/libqhullcpp/QhullSet.cpp#3 $$Change: 2066 $
+** $DateTime: 2016/01/18 19:29:17 $$Author: bbarber $
+**
+****************************************************************************/
+
+#//! QhullSet -- Qhull's set structure, setT, as a C++ class
+
+#include "libqhullcpp/QhullSet.h"
+
+#include "libqhullcpp/Qhull.h"
+#include "libqhullcpp/QhullError.h"
+
+#ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
+#endif
+
+namespace orgQhull {
+
+#//!\name Class objects
+
+setT QhullSetBase::
+s_empty_set;
+
+#//!\name Constructors
+
+QhullSetBase::
+QhullSetBase(const Qhull &q, setT *s) 
+: qh_set(s ? s : &s_empty_set)
+, qh_qh(q.qh())
+{
+}
+
+#//!\name Class methods
+
+// Same code for qh_setsize [qset_r.c] and QhullSetBase::count [static]
+countT QhullSetBase::
+count(const setT *set)
+{
+    countT size;
+    const setelemT *sizep;
+
+    if (!set){
+        return(0);
+    }
+    sizep= SETsizeaddr_(set);
+    if ((size= sizep->i)) {
+        size--;
+        if (size > set->maxsize) {
+            // FIXUP QH11022 How to add additional output to a error? -- qh_setprint(qhmem.ferr, "set: ", set);
+            throw QhullError(10032, "QhullSet internal error: current set size %d is greater than maximum size %d\n",
+                size, set->maxsize);
+        }
+    }else{
+        size= set->maxsize;
+    }
+    return size;
+}//count
+
+}//namespace orgQhull
+
diff --git a/xs/src/qhull/src/libqhullcpp/QhullSet.h b/xs/src/qhull/src/libqhullcpp/QhullSet.h
new file mode 100644
index 0000000000..afb6b51d9f
--- /dev/null
+++ b/xs/src/qhull/src/libqhullcpp/QhullSet.h
@@ -0,0 +1,462 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
+** $Id: //main/2015/qhull/src/libqhullcpp/QhullSet.h#6 $$Change: 2079 $
+** $DateTime: 2016/02/07 17:43:34 $$Author: bbarber $
+**
+****************************************************************************/
+
+#ifndef QhullSet_H
+#define QhullSet_H
+
+#include "libqhull_r/qhull_ra.h"
+#include "libqhullcpp/QhullError.h"
+#include "libqhullcpp/QhullQh.h"
+
+#include <cstddef>  // ptrdiff_t, size_t
+
+#ifndef QHULL_NO_STL
+#include <vector>
+#endif
+
+#ifdef QHULL_USES_QT
+ #include <QtCore/QList>
+#endif
+
+namespace orgQhull {
+
+#//!\name Used here
+    class Qhull;
+
+#//!\name Defined here
+    class QhullSetBase;  //! Base class for QhullSet<T>
+    //! QhullSet<T> defined below
+    //! QhullSetIterator<T> defined below
+    //! \see QhullPointSet, QhullLinkedList<T>
+
+//! QhullSetBase is a wrapper for Qhull's setT of void* pointers
+//! \see libqhull_r/qset.h
+class QhullSetBase {
+
+private:
+#//!\name Fields --
+    setT *              qh_set;
+    QhullQh *           qh_qh;             //! Provides access to setT memory allocator
+
+#//!\name Class objects
+    static setT         s_empty_set;  //! Used if setT* is NULL
+
+public:
+#//!\name Constructors
+                        QhullSetBase(const Qhull &q, setT *s);
+                        QhullSetBase(QhullQh *qqh, setT *s) : qh_set(s ? s : &s_empty_set), qh_qh(qqh) {}
+                        //! Copy constructor copies the pointer but not the set.  Needed for return by value and parameter passing.
+                        QhullSetBase(const QhullSetBase &other) : qh_set(other.qh_set), qh_qh(other.qh_qh) {}
+    QhullSetBase &      operator=(const QhullSetBase &other) { qh_set= other.qh_set; qh_qh= other.qh_qh; return *this; }
+                        ~QhullSetBase() {}
+
+private:
+                        //!disabled since memory allocation for QhullSet not defined
+                        QhullSetBase() {}
+public:
+
+#//!\name GetSet
+    countT              count() const { return QhullSetBase::count(qh_set); }
+    void                defineAs(setT *s) { qh_set= s ? s : &s_empty_set; } //!< Not type-safe since setT may contain any type
+    void                forceEmpty() { qh_set= &s_empty_set; }
+    setT *              getSetT() const { return qh_set; }
+    bool                isEmpty() const { return SETempty_(qh_set); }
+    QhullQh *           qh() const { return qh_qh; }
+    setT **             referenceSetT() { return &qh_set; }
+    size_t              size() const { return QhullSetBase::count(qh_set); }
+
+#//!\name Element
+protected:
+    void **             beginPointer() const { return &qh_set->e[0].p; }
+    void **             elementPointer(countT idx) const { QHULL_ASSERT(idx>=0 && idx<qh_set->maxsize); return &SETelem_(qh_set, idx); }
+                        //! Always points to 0
+    void **             endPointer() const { return qh_setendpointer(qh_set); }
+
+#//!\name Class methods
+public:
+    static countT       count(const setT *set);
+    //s may be null
+    static bool         isEmpty(const setT *s) { return SETempty_(s); }
+};//QhullSetBase
+
+
+//! QhullSet<T> -- A read-only wrapper to Qhull's collection class, setT.
+//!  QhullSet is similar to STL's <vector> and Qt's QVector
+//!  QhullSet is unrelated to STL and Qt's set and map types (e.g., QSet and QMap)
+//!  T is a Qhull type that defines 'base_type' and getBaseT() (e.g., QhullFacet with base_type 'facetT *'
+//!  A QhullSet does not own its contents -- erase(), clear(), removeFirst(), removeLast(), pop_back(), pop_front(), fromStdList() not defined
+//!  QhullSetIterator is faster than STL-style iterator/const_iterator
+//!  Qhull's FOREACHelement_() [qset_r.h] maybe more efficient than QhullSet.  It uses a NULL terminator instead of an end pointer.  STL requires an end pointer.
+//!  Derived from QhullLinkedList.h and Qt/core/tools/qlist.h w/o QT_STRICT_ITERATORS
+template <typename T>
+class QhullSet : public QhullSetBase {
+
+private:
+#//!\name Fields -- see QhullSetBase
+
+#//!\name Class objects
+    static setT         s_empty_set;  //! Workaround for no setT allocator.  Used if setT* is NULL
+
+public:
+#//!\name Defined here
+    class iterator;
+    class const_iterator;
+    typedef typename QhullSet<T>::iterator Iterator;
+    typedef typename QhullSet<T>::const_iterator ConstIterator;
+
+#//!\name Constructors
+                        QhullSet<T>(const Qhull &q, setT *s) : QhullSetBase(q, s) { }
+                        QhullSet<T>(QhullQh *qqh, setT *s) : QhullSetBase(qqh, s) { }
+                        //Conversion from setT* is not type-safe.  Implicit conversion for void* to T
+                        //Copy constructor copies pointer but not contents.  Needed for return by value.
+                        QhullSet<T>(const QhullSet<T> &other) : QhullSetBase(other) {}
+    QhullSet<T> &       operator=(const QhullSet<T> &other) { QhullSetBase::operator=(other); return *this; }
+                        ~QhullSet<T>() {}
+
+private:
+                        //!Disable default constructor.  See QhullSetBase
+                        QhullSet<T>();
+public:
+
+#//!\name Conversion
+
+#ifndef QHULL_NO_STL
+    std::vector<T> toStdVector() const;
+#endif
+#ifdef QHULL_USES_QT
+    QList<typename T> toQList() const;
+#endif
+
+#//!\name GetSet -- see QhullSetBase for count(), empty(), isEmpty(), size()
+    using QhullSetBase::count;
+    using QhullSetBase::isEmpty;
+    // operator== defined for QhullSets of the same type
+    bool                operator==(const QhullSet<T> &other) const { return qh_setequal(getSetT(), other.getSetT()); }
+    bool                operator!=(const QhullSet<T> &other) const { return !operator==(other); }
+
+#//!\name Element access
+    // Constructs T.  Cannot return reference.
+    const T             at(countT idx) const { return operator[](idx); }
+    // Constructs T.  Cannot return reference.
+    const T             back() const { return last(); }
+    T                   back() { return last(); }
+    //! end element is NULL
+    const typename T::base_type * constData() const { return reinterpret_cast<const typename T::base_type *>(beginPointer()); }
+    typename T::base_type *     data() { return reinterpret_cast<typename T::base_type *>(beginPointer()); }
+    const typename T::base_type *data() const { return reinterpret_cast<const typename T::base_type *>(beginPointer()); }
+    typename T::base_type *     endData() { return reinterpret_cast<typename T::base_type *>(endPointer()); }
+    const typename T::base_type * endData() const { return reinterpret_cast<const typename T::base_type *>(endPointer()); }
+    // Constructs T.  Cannot return reference.
+    const T             first() const { QHULL_ASSERT(!isEmpty()); return T(qh(), *data()); }
+    T                   first() { QHULL_ASSERT(!isEmpty()); return T(qh(), *data()); }
+    // Constructs T.  Cannot return reference.
+    const T             front() const { return first(); }
+    T                   front() { return first(); }
+    // Constructs T.  Cannot return reference.
+    const T             last() const { QHULL_ASSERT(!isEmpty()); return T(qh(), *(endData()-1)); }
+    T                   last() { QHULL_ASSERT(!isEmpty()); return T(qh(), *(endData()-1)); }
+    // mid() not available.  No setT constructor
+    // Constructs T.  Cannot return reference.
+    const T             operator[](countT idx) const { const typename T::base_type *p= reinterpret_cast<typename T::base_type *>(elementPointer(idx)); QHULL_ASSERT(idx>=0 && p < endData()); return T(qh(), *p); }
+    T                   operator[](countT idx) { typename T::base_type *p= reinterpret_cast<typename T::base_type *>(elementPointer(idx)); QHULL_ASSERT(idx>=0 && p < endData()); return T(qh(), *p); }
+    const T             second() const { return operator[](1); }
+    T                   second() { return operator[](1); }
+    T                   value(countT idx) const;
+    T                   value(countT idx, const T &defaultValue) const;
+
+#//!\name Read-write -- Not available, no setT constructor
+
+#//!\name iterator
+    iterator            begin() { return iterator(qh(), reinterpret_cast<typename T::base_type *>(beginPointer())); }
+    const_iterator      begin() const { return const_iterator(qh(), data()); }
+    const_iterator      constBegin() const { return const_iterator(qh(), data()); }
+    const_iterator      constEnd() const { return const_iterator(qh(), endData()); }
+    iterator            end() { return iterator(qh(), endData()); }
+    const_iterator      end() const { return const_iterator(qh(), endData()); }
+
+#//!\name Search
+    bool                contains(const T &t) const;
+    countT              count(const T &t) const;
+    countT              indexOf(const T &t) const { /* no qh_qh */ return qh_setindex(getSetT(), t.getBaseT()); }
+    countT              lastIndexOf(const T &t) const;
+
+    // before const_iterator for conversion with comparison operators
+    class iterator {
+        friend class const_iterator;
+    private:
+        typename T::base_type *  i;  // e.g., facetT**, first for debugger
+        QhullQh *       qh_qh;
+
+    public:
+        typedef ptrdiff_t       difference_type;
+        typedef std::bidirectional_iterator_tag  iterator_category;
+        typedef T               value_type;
+
+                        iterator(QhullQh *qqh, typename T::base_type *p) : i(p), qh_qh(qqh) {}
+                        iterator(const iterator &o) : i(o.i), qh_qh(o.qh_qh) {}
+        iterator &      operator=(const iterator &o) { i= o.i; qh_qh= o.qh_qh; return *this; }
+
+        // Constructs T.  Cannot return reference.  
+        T               operator*() const { return T(qh_qh, *i); }
+        //operator->() n/a, value-type
+        // Constructs T.  Cannot return reference.  
+        T               operator[](countT idx) const { return T(qh_qh, *(i+idx)); } //!< No error checking
+        bool            operator==(const iterator &o) const { return i == o.i; }
+        bool            operator!=(const iterator &o) const { return !operator==(o); }
+        bool            operator==(const const_iterator &o) const { return (i==reinterpret_cast<const iterator &>(o).i); }
+        bool            operator!=(const const_iterator &o) const { return !operator==(o); }
+
+        //! Assumes same point set
+        countT          operator-(const iterator &o) const { return (countT)(i-o.i); } //WARN64
+        bool            operator>(const iterator &o) const { return i>o.i; }
+        bool            operator<=(const iterator &o) const { return !operator>(o); }
+        bool            operator<(const iterator &o) const { return i<o.i; }
+        bool            operator>=(const iterator &o) const { return !operator<(o); }
+        bool            operator>(const const_iterator &o) const { return (i > reinterpret_cast<const iterator &>(o).i); }
+        bool            operator<=(const const_iterator &o) const { return !operator>(o); }
+        bool            operator<(const const_iterator &o) const { return (i < reinterpret_cast<const iterator &>(o).i); }
+        bool            operator>=(const const_iterator &o) const { return !operator<(o); }
+
+        //! No error checking
+        iterator &      operator++() { ++i; return *this; }
+        iterator        operator++(int) { iterator o= *this; ++i; return o; }
+        iterator &      operator--() { --i; return *this; }
+        iterator        operator--(int) { iterator o= *this; --i; return o; }
+        iterator        operator+(countT j) const { return iterator(qh_qh, i+j); }
+        iterator        operator-(countT j) const { return operator+(-j); }
+        iterator &      operator+=(countT j) { i += j; return *this; }
+        iterator &      operator-=(countT j) { i -= j; return *this; }
+    };//QhullPointSet::iterator
+
+    class const_iterator {
+    private:
+        const typename T::base_type *  i;  // e.g., const facetT**, first for debugger
+        QhullQh *       qh_qh;
+
+    public:
+        typedef ptrdiff_t       difference_type;
+        typedef std::random_access_iterator_tag  iterator_category;
+        typedef T               value_type;
+
+                        const_iterator(QhullQh *qqh, const typename T::base_type * p) : i(p), qh_qh(qqh) {}
+                        const_iterator(const const_iterator &o) : i(o.i), qh_qh(o.qh_qh) {}
+                        const_iterator(const iterator &o) : i(o.i), qh_qh(o.qh_qh) {}
+        const_iterator &operator=(const const_iterator &o) { i= o.i; qh_qh= o.qh_qh; return *this; }
+
+        // Constructs T.  Cannot return reference.  Retaining 'const T' return type for consistency with QList/QVector
+        const T         operator*() const { return T(qh_qh, *i); }
+        const T         operator[](countT idx) const { return T(qh_qh, *(i+idx)); }  //!< No error checking
+        //operator->() n/a, value-type
+        bool            operator==(const const_iterator &o) const { return i == o.i; }
+        bool            operator!=(const const_iterator &o) const { return !operator==(o); }
+
+        //! Assumes same point set
+        countT          operator-(const const_iterator &o) { return (countT)(i-o.i); } //WARN64
+        bool            operator>(const const_iterator &o) const { return i>o.i; }
+        bool            operator<=(const const_iterator &o) const { return !operator>(o); }
+        bool            operator<(const const_iterator &o) const { return i<o.i; }
+        bool            operator>=(const const_iterator &o) const { return !operator<(o); }
+
+        //!< No error checking
+        const_iterator &operator++() { ++i; return *this; }
+        const_iterator  operator++(int) { const_iterator o= *this; ++i; return o; }
+        const_iterator &operator--() { --i; return *this; }
+        const_iterator  operator--(int) { const_iterator o= *this; --i; return o; }
+        const_iterator  operator+(int j) const { return const_iterator(qh_qh, i+j); }
+        const_iterator  operator-(int j) const { return operator+(-j); }
+        const_iterator &operator+=(int j) { i += j; return *this; }
+        const_iterator &operator-=(int j) { i -= j; return *this; }
+    };//QhullPointSet::const_iterator
+
+};//class QhullSet
+
+
+//! Faster then interator/const_iterator due to T::base_type
+template <typename T>
+class QhullSetIterator {
+
+#//!\name Subtypes
+    typedef typename QhullSet<T>::const_iterator const_iterator;
+
+private:
+#//!\name Fields
+    const typename T::base_type *  i;  // e.g., facetT**, first for debugger
+    const typename T::base_type *  begin_i;  // must be initialized after i
+    const typename T::base_type *  end_i;
+    QhullQh *                qh_qh;
+
+public:
+#//!\name Constructors
+                        QhullSetIterator<T>(const QhullSet<T> &s) : i(s.data()), begin_i(i), end_i(s.endData()), qh_qh(s.qh()) {}
+                        QhullSetIterator<T>(const QhullSetIterator<T> &o) : i(o.i), begin_i(o.begin_i), end_i(o.end_i), qh_qh(o.qh_qh) {}
+    QhullSetIterator<T> &operator=(const QhullSetIterator<T> &o) { i= o.i; begin_i= o.begin_i; end_i= o.end_i; qh_qh= o.qh_qh; return *this; }
+
+#//!\name ReadOnly
+    countT              countRemaining() { return (countT)(end_i-i); } // WARN64
+
+#//!\name Search
+    bool                findNext(const T &t);
+    bool                findPrevious(const T &t);
+
+#//!\name Foreach
+    bool                hasNext() const { return i != end_i; }
+    bool                hasPrevious() const { return i != begin_i; }
+    T                   next() { return T(qh_qh, *i++); }
+    T                   peekNext() const { return T(qh_qh, *i); }
+    T                   peekPrevious() const { const typename T::base_type *p = i; return T(qh_qh, *--p); }
+    T                   previous() { return T(qh_qh, *--i); }
+    void                toBack() { i = end_i; }
+    void                toFront() { i = begin_i; }
+};//class QhullSetIterator
+
+#//!\name == Definitions =========================================
+
+#//!\name Conversions
+
+// See qt-qhull.cpp for QList conversion
+
+#ifndef QHULL_NO_STL
+template <typename T>
+std::vector<T> QhullSet<T>::
+toStdVector() const
+{
+	typename QhullSet<T>::const_iterator i = begin();
+	typename QhullSet<T>::const_iterator e = end();
+    std::vector<T> vs;
+    while(i!=e){
+        vs.push_back(*i++);
+    }
+    return vs;
+}//toStdVector
+#endif //QHULL_NO_STL
+
+#ifdef QHULL_USES_QT
+template <typename T>
+QList<T> QhullSet<T>::
+toQList() const
+{
+    QhullSet<T>::const_iterator i= begin();
+    QhullSet<T>::const_iterator e= end();
+    QList<T> vs;
+    while(i!=e){
+        vs.append(*i++);
+    }
+    return vs;
+}//toQList
+#endif
+
+#//!\name Element
+
+template <typename T>
+T QhullSet<T>::
+value(countT idx) const
+{
+    // Avoid call to qh_setsize() and assert in elementPointer()
+    const typename T::base_type *p= reinterpret_cast<const typename T::base_type *>(&SETelem_(getSetT(), idx));
+    return (idx>=0 && p<endData()) ? T(qh(), *p) : T(qh());
+}//value
+
+template <typename T>
+T QhullSet<T>::
+value(countT idx, const T &defaultValue) const
+{
+    // Avoid call to qh_setsize() and assert in elementPointer()
+    const typename T::base_type *p= reinterpret_cast<const typename T::base_type *>(&SETelem_(getSetT(), idx));
+    return (idx>=0 && p<endData() ? T(qh(), *p) : defaultValue);
+}//value
+
+#//!\name Search
+
+template <typename T>
+bool QhullSet<T>::
+contains(const T &t) const
+{
+    setT *s= getSetT();
+    void *p= t.getBaseT();  // contains() is not inline for better error reporting
+    int result= qh_setin(s, p);
+    return result!=0;
+}//contains
+
+template <typename T>
+countT QhullSet<T>::
+count(const T &t) const
+{
+    countT n= 0;
+    const typename T::base_type *i= data();
+    const typename T::base_type *e= endData();
+    typename T::base_type p= t.getBaseT();
+    while(i<e){
+        if(*i==p){
+            n++;
+        }
+        i++;
+    }
+    return n;
+}//count
+
+template <typename T>
+countT QhullSet<T>::
+lastIndexOf(const T &t) const
+{
+    const typename T::base_type *b= data();
+    const typename T::base_type *i= endData();
+    typename T::base_type p= t.getBaseT();
+    while(--i>=b){
+        if(*i==p){
+            break;
+        }
+    }
+    return (countT)(i-b); // WARN64
+}//lastIndexOf
+
+#//!\name QhullSetIterator
+
+template <typename T>
+bool QhullSetIterator<T>::
+findNext(const T &t)
+{
+    typename T::base_type p= t.getBaseT();
+    while(i!=end_i){
+        if(*(++i)==p){
+            return true;
+        }
+    }
+    return false;
+}//findNext
+
+template <typename T>
+bool QhullSetIterator<T>::
+findPrevious(const T &t)
+{
+    typename T::base_type p= t.getBaseT();
+    while(i!=begin_i){
+        if(*(--i)==p){
+            return true;
+        }
+    }
+    return false;
+}//findPrevious
+
+}//namespace orgQhull
+
+
+#//!\name == Global namespace =========================================
+
+template <typename T>
+std::ostream &
+operator<<(std::ostream &os, const orgQhull::QhullSet<T> &qs)
+{
+    const typename T::base_type *i= qs.data();
+    const typename T::base_type *e= qs.endData();
+    while(i!=e){
+        os << T(qs.qh(), *i++);
+    }
+    return os;
+}//operator<<
+
+#endif // QhullSet_H
diff --git a/xs/src/qhull/src/libqhullcpp/QhullSets.h b/xs/src/qhull/src/libqhullcpp/QhullSets.h
new file mode 100644
index 0000000000..d0f200cbcf
--- /dev/null
+++ b/xs/src/qhull/src/libqhullcpp/QhullSets.h
@@ -0,0 +1,27 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
+** $Id: //main/2015/qhull/src/libqhullcpp/QhullSets.h#2 $$Change: 2066 $
+** $DateTime: 2016/01/18 19:29:17 $$Author: bbarber $
+**
+****************************************************************************/
+
+#ifndef QHULLSETS_H
+#define QHULLSETS_H
+
+#include "libqhullcpp/QhullSet.h"
+
+namespace orgQhull {
+
+    //See: QhullFacetSet.h
+    //See: QhullPointSet.h
+    //See: QhullVertexSet.h
+
+    // Avoid circular references between QhullFacet, QhullRidge, and QhullVertex
+    class QhullRidge;
+    typedef QhullSet<QhullRidge>  QhullRidgeSet;
+    typedef QhullSetIterator<QhullRidge>  QhullRidgeSetIterator;
+
+}//namespace orgQhull
+
+#endif // QHULLSETS_H
diff --git a/xs/src/qhull/src/libqhullcpp/QhullStat.cpp b/xs/src/qhull/src/libqhullcpp/QhullStat.cpp
new file mode 100644
index 0000000000..c4fe6c4918
--- /dev/null
+++ b/xs/src/qhull/src/libqhullcpp/QhullStat.cpp
@@ -0,0 +1,42 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
+** $Id: //main/2015/qhull/src/libqhullcpp/QhullStat.cpp#3 $$Change: 2066 $
+** $DateTime: 2016/01/18 19:29:17 $$Author: bbarber $
+**
+****************************************************************************/
+
+#//! QhullStat -- Qhull's global data structure, statT, as a C++ class
+
+#include "libqhullcpp/QhullStat.h"
+
+#include "libqhullcpp/QhullError.h"
+
+#include <sstream>
+#include <iostream>
+
+using std::cerr;
+using std::string;
+using std::vector;
+using std::ostream;
+
+#ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
+#endif
+
+namespace orgQhull {
+
+#//!\name Constructor, destructor, etc.
+
+//! If qh_QHpointer==0, invoke with placement new on qh_stat;
+QhullStat::
+QhullStat()
+{
+}//QhullStat
+
+QhullStat::
+~QhullStat()
+{
+}//~QhullStat
+
+}//namespace orgQhull
+
diff --git a/xs/src/qhull/src/libqhullcpp/QhullStat.h b/xs/src/qhull/src/libqhullcpp/QhullStat.h
new file mode 100644
index 0000000000..54bde8fc79
--- /dev/null
+++ b/xs/src/qhull/src/libqhullcpp/QhullStat.h
@@ -0,0 +1,49 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
+** $Id: //main/2015/qhull/src/libqhullcpp/QhullStat.h#2 $$Change: 2079 $
+** $DateTime: 2016/02/07 17:43:34 $$Author: bbarber $
+**
+****************************************************************************/
+
+#ifndef QHULLSTAT_H
+#define QHULLSTAT_H
+
+#include "libqhull_r/qhull_ra.h"
+
+#include <string>
+#include <vector>
+
+namespace orgQhull {
+
+#//!\name defined here
+    //! QhullStat -- Qhull's statistics, qhstatT, as a C++ class
+    //! Statistics defined with zzdef_() control Qhull's behavior, summarize its result, and report precision problems.
+    class QhullStat;
+
+class QhullStat : public qhstatT {
+
+private:
+#//!\name Fields (empty) -- POD type equivalent to qhstatT.  No data or virtual members
+
+public:
+#//!\name Constants
+
+#//!\name class methods
+
+#//!\name constructor, assignment, destructor, invariant
+                        QhullStat();
+                        ~QhullStat();
+
+private:
+    //!disable copy constructor and assignment
+                        QhullStat(const QhullStat &);
+    QhullStat &         operator=(const QhullStat &);
+public:
+
+#//!\name Access
+};//class QhullStat
+
+}//namespace orgQhull
+
+#endif // QHULLSTAT_H
diff --git a/xs/src/qhull/src/libqhullcpp/QhullVertex.cpp b/xs/src/qhull/src/libqhullcpp/QhullVertex.cpp
new file mode 100644
index 0000000000..fd7aef0893
--- /dev/null
+++ b/xs/src/qhull/src/libqhullcpp/QhullVertex.cpp
@@ -0,0 +1,112 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
+** $Id: //main/2015/qhull/src/libqhullcpp/QhullVertex.cpp#3 $$Change: 2066 $
+** $DateTime: 2016/01/18 19:29:17 $$Author: bbarber $
+**
+****************************************************************************/
+
+#//! QhullVertex -- Qhull's vertex structure, vertexT, as a C++ class
+
+#include "libqhullcpp/QhullVertex.h"
+
+#include "libqhullcpp/Qhull.h"
+#include "libqhullcpp/QhullPoint.h"
+#include "libqhullcpp/QhullFacetSet.h"
+#include "libqhullcpp/QhullFacet.h"
+
+#ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
+#pragma warning( disable : 4611)  // interaction between '_setjmp' and C++ object destruction is non-portable
+#pragma warning( disable : 4996)  // function was declared deprecated(strcpy, localtime, etc.)
+#endif
+
+namespace orgQhull {
+
+#//!\name Class objects
+vertexT QhullVertex::
+s_empty_vertex= {0,0,0,0,0,
+                 0,0,0,0,0,
+                 0};
+
+#//!\name Constructors
+
+QhullVertex::QhullVertex(const Qhull &q)
+: qh_vertex(&s_empty_vertex)
+, qh_qh(q.qh())
+{
+}//Default
+
+QhullVertex::QhullVertex(const Qhull &q, vertexT *v)
+: qh_vertex(v ? v : &s_empty_vertex)
+, qh_qh(q.qh())
+{
+}//vertexT
+
+#//!\name foreach
+
+//! Return neighboring facets for a vertex
+//! If neither merging nor Voronoi diagram, requires Qhull::defineVertexNeighborFacets() beforehand.
+QhullFacetSet QhullVertex::
+neighborFacets() const
+{
+    if(!neighborFacetsDefined()){
+        throw QhullError(10034, "Qhull error: neighboring facets of vertex %d not defined.  Please call Qhull::defineVertexNeighborFacets() beforehand.", id());
+    }
+    return QhullFacetSet(qh_qh, qh_vertex->neighbors);
+}//neighborFacets
+
+}//namespace orgQhull
+
+#//!\name Global functions
+
+using std::endl;
+using std::ostream;
+using std::string;
+using std::vector;
+using orgQhull::QhullPoint;
+using orgQhull::QhullFacet;
+using orgQhull::QhullFacetSet;
+using orgQhull::QhullFacetSetIterator;
+using orgQhull::QhullVertex;
+
+//! Duplicate of qh_printvertex [io_r.c]
+ostream &
+operator<<(ostream &os, const QhullVertex::PrintVertex &pr)
+{
+    QhullVertex v= *pr.vertex;
+    QhullPoint p= v.point();
+    if(*pr.print_message){
+        os << pr.print_message << " ";
+    }else{
+        os << "- ";
+    }
+    os << "p" << p.id() << " (v" << v.id() << "): ";
+    const realT *c= p.coordinates();
+    for(int k= p.dimension(); k--; ){
+        os << " " << *c++; // FIXUP QH11010 %5.2g
+    }
+    if(v.getVertexT()->deleted){
+        os << " deleted";
+    }
+    if(v.getVertexT()->delridge){
+        os << " ridgedeleted";
+    }
+    os << endl;
+    if(v.neighborFacetsDefined()){
+        QhullFacetSetIterator i= v.neighborFacets();
+        if(i.hasNext()){
+            os << " neighborFacets:";
+            countT count= 0;
+            while(i.hasNext()){
+                if(++count % 100 == 0){
+                    os << endl << "     ";
+                }
+                QhullFacet f= i.next();
+                os << " f" << f.id();
+            }
+            os << endl;
+        }
+    }
+    return os;
+}//<< PrintVertex
+
diff --git a/xs/src/qhull/src/libqhullcpp/QhullVertex.h b/xs/src/qhull/src/libqhullcpp/QhullVertex.h
new file mode 100644
index 0000000000..0137766db5
--- /dev/null
+++ b/xs/src/qhull/src/libqhullcpp/QhullVertex.h
@@ -0,0 +1,104 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
+** $Id: //main/2015/qhull/src/libqhullcpp/QhullVertex.h#4 $$Change: 2079 $
+** $DateTime: 2016/02/07 17:43:34 $$Author: bbarber $
+**
+****************************************************************************/
+
+#ifndef QHULLVERTEX_H
+#define QHULLVERTEX_H
+
+#include "libqhull_r/qhull_ra.h"
+#include "libqhullcpp/QhullPoint.h"
+#include "libqhullcpp/QhullLinkedList.h"
+#include "libqhullcpp/QhullSet.h"
+
+#include <ostream>
+
+namespace orgQhull {
+
+#//!\name Used here
+    class QhullFacetSet;
+
+#//!\name Defined here
+    //! QhullVertex -- Qhull's vertex structure, vertexT [libqhull_r.h], as a C++ class
+    class QhullVertex;
+    typedef QhullLinkedList<QhullVertex> QhullVertexList;
+    typedef QhullLinkedListIterator<QhullVertex> QhullVertexListIterator;
+
+
+/*********************
+  topological information:
+    next,previous       doubly-linked list of all vertices
+    neighborFacets           set of adjacent facets (only if qh.VERTEXneighbors)
+
+  geometric information:
+    point               array of DIM coordinates
+*/
+
+class QhullVertex {
+
+#//!\name Defined here
+public:
+    typedef vertexT *   base_type;  // for QhullVertexSet
+
+private:
+#//!\name Fields
+    vertexT *           qh_vertex;  //!< Corresponding vertexT, never 0
+    QhullQh *           qh_qh;      //!< QhullQh/qhT for vertexT, may be 0
+
+#//!\name Class objects
+    static vertexT      s_empty_vertex;  // needed for shallow copy
+
+public:
+#//!\name Constants
+
+#//!\name Constructors
+                        QhullVertex() : qh_vertex(&s_empty_vertex), qh_qh(0) {}
+    explicit            QhullVertex(const Qhull &q);
+                        QhullVertex(const Qhull &q, vertexT *v);
+    explicit            QhullVertex(QhullQh *qqh) : qh_vertex(&s_empty_vertex), qh_qh(qqh) {}
+                        QhullVertex(QhullQh *qqh, vertexT *v) : qh_vertex(v ? v : &s_empty_vertex), qh_qh(qqh) {}
+                        // Creates an alias.  Does not copy QhullVertex.  Needed for return by value and parameter passing
+                        QhullVertex(const QhullVertex &other) : qh_vertex(other.qh_vertex), qh_qh(other.qh_qh) {}
+                        // Creates an alias.  Does not copy QhullVertex.  Needed for vector<QhullVertex>
+    QhullVertex &       operator=(const QhullVertex &other) { qh_vertex= other.qh_vertex; qh_qh= other.qh_qh; return *this; }
+                        ~QhullVertex() {}
+
+#//!\name GetSet
+    int                 dimension() const { return (qh_qh ? qh_qh->hull_dim : 0); }
+    vertexT *           getBaseT() const { return getVertexT(); } //!< For QhullSet<QhullVertex>
+    vertexT *           getVertexT() const { return qh_vertex; }
+    countT              id() const { return qh_vertex->id; }
+    bool                isValid() const { return (qh_qh && qh_vertex != &s_empty_vertex); }
+                        //! True if defineVertexNeighborFacets() already called.  Auotomatically set for facet merging, Voronoi diagrams
+    bool                neighborFacetsDefined() const { return qh_vertex->neighbors != 0; }
+    QhullVertex         next() const { return QhullVertex(qh_qh, qh_vertex->next); }
+    bool                operator==(const QhullVertex &other) const { return qh_vertex==other.qh_vertex; }
+    bool                operator!=(const QhullVertex &other) const { return !operator==(other); }
+    QhullPoint          point() const { return QhullPoint(qh_qh, qh_vertex->point); }
+    QhullVertex         previous() const { return QhullVertex(qh_qh, qh_vertex->previous); }
+    QhullQh *           qh() const { return qh_qh; }
+
+#//!\name foreach
+    //See also QhullVertexList
+    QhullFacetSet       neighborFacets() const;
+
+#//!\name IO
+    struct PrintVertex{
+        const QhullVertex *vertex;
+        const char *    print_message;    //!< non-null message
+                        PrintVertex(const char *message, const QhullVertex &v) : vertex(&v), print_message(message) {}
+    };//PrintVertex
+    PrintVertex         print(const char *message) const { return PrintVertex(message, *this); }
+};//class QhullVertex
+
+}//namespace orgQhull
+
+#//!\name GLobal
+
+std::ostream &operator<<(std::ostream &os, const orgQhull::QhullVertex::PrintVertex &pr);
+inline std::ostream &operator<<(std::ostream &os, const orgQhull::QhullVertex &v) { os << v.print(""); return os; }
+
+#endif // QHULLVERTEX_H
diff --git a/xs/src/qhull/src/libqhullcpp/QhullVertexSet.cpp b/xs/src/qhull/src/libqhullcpp/QhullVertexSet.cpp
new file mode 100644
index 0000000000..00ba62d196
--- /dev/null
+++ b/xs/src/qhull/src/libqhullcpp/QhullVertexSet.cpp
@@ -0,0 +1,161 @@
+/****************************************************************************
+**
+** Copyright (c) 2009-2015 C.B. Barber. All rights reserved.
+** $Id: //main/2015/qhull/src/libqhullcpp/QhullVertexSet.cpp#3 $$Change: 2066 $
+** $DateTime: 2016/01/18 19:29:17 $$Author: bbarber $
+**
+****************************************************************************/
+
+#//! QhullVertexSet -- Qhull's linked Vertexs, as a C++ class
+
+#include "libqhullcpp/QhullVertexSet.h"
+
+#include "libqhullcpp/QhullVertex.h"
+#include "libqhullcpp/QhullPoint.h"
+#include "libqhullcpp/QhullRidge.h"
+#include "libqhullcpp/QhullVertex.h"
+#include "libqhullcpp/Qhull.h"
+
+using std::string;
+using std::vector;
+
+#ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
+#pragma warning( disable : 4611)  /* interaction between '_setjmp' and C++ object destruction is non-portable */
+                                    /* setjmp should not be implemented with 'catch' */
+#endif
+
+namespace orgQhull {
+
+QhullVertexSet::
+QhullVertexSet(const Qhull &q, facetT *facetlist, setT *facetset, bool allfacets)
+: QhullSet<QhullVertex>(q.qh(), 0)
+, qhsettemp_defined(false)
+{
+    QH_TRY_(q.qh()){ // no object creation -- destructors skipped on longjmp()
+        setT *vertices= qh_facetvertices(q.qh(), facetlist, facetset, allfacets);
+        defineAs(vertices);
+        qhsettemp_defined= true;
+    }
+    q.qh()->NOerrexit= true;
+    q.qh()->maybeThrowQhullMessage(QH_TRY_status);
+}//QhullVertexSet facetlist facetset
+
+//! Return tempory QhullVertexSet of vertices for a list and/or a set of facets
+//! Sets qhsettemp_defined (disallows copy constructor and assignment to prevent double-free)
+QhullVertexSet::
+QhullVertexSet(QhullQh *qqh, facetT *facetlist, setT *facetset, bool allfacets)
+: QhullSet<QhullVertex>(qqh, 0)
+, qhsettemp_defined(false)
+{
+    QH_TRY_(qh()){ // no object creation -- destructors skipped on longjmp()
+        setT *vertices= qh_facetvertices(qh(), facetlist, facetset, allfacets);
+        defineAs(vertices);
+        qhsettemp_defined= true;
+    }
+    qh()->NOerrexit= true;
+    qh()->maybeThrowQhullMessage(QH_TRY_status);
+}//QhullVertexSet facetlist facetset
+
+//! Copy constructor for argument passing and returning a result
+//! Only copies a pointer to the set.
+//! Throws an error if qhsettemp_defined, otherwise have a double-free
+//!\todo Convert QhullVertexSet to a shared pointer with reference counting
+QhullVertexSet::
+QhullVertexSet(const QhullVertexSet &other)
+: QhullSet<QhullVertex>(other)
+, qhsettemp_defined(false)
+{
+    if(other.qhsettemp_defined){
+        throw QhullError(10077, "QhullVertexSet: Cannot use copy constructor since qhsettemp_defined (e.g., QhullVertexSet for a set and/or list of QhFacet).  Contains %d vertices", other.count());
+    }
+}//copy constructor
+
+//! Copy assignment only copies a pointer to the set.
+//! Throws an error if qhsettemp_defined, otherwise have a double-free
+QhullVertexSet & QhullVertexSet::
+operator=(const QhullVertexSet &other)
+{
+    QhullSet<QhullVertex>::operator=(other);
+    qhsettemp_defined= false;
+    if(other.qhsettemp_defined){
+        throw QhullError(10078, "QhullVertexSet: Cannot use copy constructor since qhsettemp_defined (e.g., QhullVertexSet for a set and/or list of QhFacet).  Contains %d vertices", other.count());
+    }
+    return *this;
+}//assignment
+
+void QhullVertexSet::
+freeQhSetTemp()
+{
+    if(qhsettemp_defined){
+        qhsettemp_defined= false;
+        QH_TRY_(qh()){ // no object creation -- destructors skipped on longjmp()
+            qh_settempfree(qh(), referenceSetT()); // errors if not top of tempstack or if qhmem corrupted
+        }
+        qh()->NOerrexit= true;
+        qh()->maybeThrowQhullMessage(QH_TRY_status, QhullError::NOthrow);
+    }
+}//freeQhSetTemp
+
+QhullVertexSet::
+~QhullVertexSet()
+{
+    freeQhSetTemp();
+}//~QhullVertexSet
+
+//FIXUP -- Move conditional, QhullVertexSet code to QhullVertexSet.cpp
+#ifndef QHULL_NO_STL
+std::vector<QhullVertex> QhullVertexSet::
+toStdVector() const
+{
+    QhullSetIterator<QhullVertex> i(*this);
+    std::vector<QhullVertex> vs;
+    while(i.hasNext()){
+        QhullVertex v= i.next();
+        vs.push_back(v);
+    }
+    return vs;
+}//toStdVector
+#endif //QHULL_NO_STL
+
+}//namespace orgQhull
+
+#//!\name Global functions
+
+using std::endl;
+using std::ostream;
+using orgQhull::QhullPoint;
+using orgQhull::QhullVertex;
+using orgQhull::QhullVertexSet;
+using orgQhull::QhullVertexSetIterator;
+
+//! Print Vertex identifiers to stream.  Space prefix.  From qh_printVertexheader [io_r.c]
+ostream &
+operator<<(ostream &os, const QhullVertexSet::PrintIdentifiers &pr)
+{
+    os << pr.print_message;
+    for(QhullVertexSet::const_iterator i= pr.vertex_set->begin(); i!=pr.vertex_set->end(); ++i){
+        const QhullVertex v= *i;
+        os << " v" << v.id();
+    }
+    os << endl;
+    return os;
+}//<<QhullVertexSet::PrintIdentifiers
+
+//! Duplicate of printvertices [io_r.c]
+ostream &
+operator<<(ostream &os, const QhullVertexSet::PrintVertexSet &pr){
+
+    os << pr.print_message;
+    const QhullVertexSet *vs= pr.vertex_set;
+    QhullVertexSetIterator i= *vs;
+    while(i.hasNext()){
+        const QhullVertex v= i.next();
+        const QhullPoint p= v.point();
+        os << " p" << p.id() << "(v" << v.id() << ")";
+    }
+    os << endl;
+
+    return os;
+}//<< PrintVertexSet
+
+
diff --git a/xs/src/qhull/src/libqhullcpp/QhullVertexSet.h b/xs/src/qhull/src/libqhullcpp/QhullVertexSet.h
new file mode 100644
index 0000000000..a3a11c1241
--- /dev/null
+++ b/xs/src/qhull/src/libqhullcpp/QhullVertexSet.h
@@ -0,0 +1,86 @@
+/****************************************************************************
+**
+** Copyright (c) 2009-2015 C.B. Barber. All rights reserved.
+** $Id: //main/2015/qhull/src/libqhullcpp/QhullVertexSet.h#2 $$Change: 2066 $
+** $DateTime: 2016/01/18 19:29:17 $$Author: bbarber $
+**
+****************************************************************************/
+
+#ifndef QHULLVERTEXSET_H
+#define QHULLVERTEXSET_H
+
+#include "libqhullcpp/QhullSet.h"
+#include "libqhullcpp/QhullVertex.h"
+
+#include <ostream>
+
+namespace orgQhull {
+
+#//!\name Used here
+
+#//!\name Defined here
+    //! QhullVertexSet -- a set of Qhull Vertices, as a C++ class.
+    //! See Qhull
+    class QhullVertexSet;
+    typedef QhullSetIterator<QhullVertex> QhullVertexSetIterator;
+
+class QhullVertexSet : public QhullSet<QhullVertex> {
+
+private:
+#//!\name Fields
+    bool                qhsettemp_defined;  //! Set was allocated with qh_settemp()
+
+public:
+#//!\name Constructor
+                        QhullVertexSet(const Qhull &q, setT *s) : QhullSet<QhullVertex>(q, s), qhsettemp_defined(false) {}
+                        QhullVertexSet(const Qhull &q, facetT *facetlist, setT *facetset, bool allfacets);
+                        //Conversion from setT* is not type-safe.  Implicit conversion for void* to T
+                        QhullVertexSet(QhullQh *qqh, setT *s) : QhullSet<QhullVertex>(qqh, s), qhsettemp_defined(false) {}
+                        QhullVertexSet(QhullQh *qqh, facetT *facetlist, setT *facetset, bool allfacets);
+                        //Copy constructor and assignment copies pointer but not contents.  Throws error if qhsettemp_defined.  Needed for return by value.
+                        QhullVertexSet(const QhullVertexSet &other);
+    QhullVertexSet &    operator=(const QhullVertexSet &other);
+                        ~QhullVertexSet();
+
+private:                //!Default constructor disabled.  Will implement allocation later
+                        QhullVertexSet();
+public:
+
+#//!\name Destructor
+    void                freeQhSetTemp();
+
+#//!\name Conversion
+#ifndef QHULL_NO_STL
+    std::vector<QhullVertex> toStdVector() const;
+#endif //QHULL_NO_STL
+#ifdef QHULL_USES_QT
+    QList<QhullVertex>   toQList() const;
+#endif //QHULL_USES_QT
+
+#//!\name IO
+    struct PrintVertexSet{
+        const QhullVertexSet *vertex_set;
+        const char *    print_message;     //!< non-null message
+                        
+                        PrintVertexSet(const char *message, const QhullVertexSet *s) : vertex_set(s), print_message(message) {}
+    };//PrintVertexSet
+    const PrintVertexSet print(const char *message) const { return PrintVertexSet(message, this); }
+
+    struct PrintIdentifiers{
+        const QhullVertexSet *vertex_set;
+        const char *    print_message;    //!< non-null message
+                        PrintIdentifiers(const char *message, const QhullVertexSet *s) : vertex_set(s), print_message(message) {}
+    };//PrintIdentifiers
+    PrintIdentifiers    printIdentifiers(const char *message) const { return PrintIdentifiers(message, this); }
+
+};//class QhullVertexSet
+
+}//namespace orgQhull
+
+#//!\name Global
+
+std::ostream &operator<<(std::ostream &os, const orgQhull::QhullVertexSet::PrintVertexSet &pr);
+std::ostream &operator<<(std::ostream &os, const orgQhull::QhullVertexSet::PrintIdentifiers &p);
+inline std::ostream &operator<<(std::ostream &os, const orgQhull::QhullVertexSet &vs) { os << vs.print(""); return os; }
+
+#endif // QHULLVERTEXSET_H
diff --git a/xs/src/qhull/src/libqhullcpp/RboxPoints.cpp b/xs/src/qhull/src/libqhullcpp/RboxPoints.cpp
new file mode 100644
index 0000000000..d7acd9fce0
--- /dev/null
+++ b/xs/src/qhull/src/libqhullcpp/RboxPoints.cpp
@@ -0,0 +1,224 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
+** $Id: //main/2015/qhull/src/libqhullcpp/RboxPoints.cpp#3 $$Change: 2066 $
+** $DateTime: 2016/01/18 19:29:17 $$Author: bbarber $
+**
+****************************************************************************/
+
+#include "libqhullcpp/RboxPoints.h"
+
+#include "libqhullcpp/QhullError.h"
+
+#include <iostream>
+
+using std::cerr;
+using std::endl;
+using std::istream;
+using std::ostream;
+using std::ostringstream;
+using std::string;
+using std::vector;
+using std::ws;
+
+#ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
+#pragma warning( disable : 4996)  // function was declared deprecated(strcpy, localtime, etc.)
+#endif
+
+namespace orgQhull {
+
+#//! RboxPoints -- generate random PointCoordinates for qhull (rbox)
+
+
+#//!\name Constructors
+RboxPoints::
+RboxPoints()
+: PointCoordinates("rbox")
+, rbox_new_count(0)
+, rbox_status(qh_ERRnone)
+, rbox_message()
+{
+    allocateQhullQh();
+}
+
+//! Allocate and generate points according to rboxCommand
+//! For rbox commands, see http://www.qhull.org/html/rbox.htm or html/rbox.htm
+//! Same as appendPoints()
+RboxPoints::
+RboxPoints(const char *rboxCommand)
+: PointCoordinates("rbox")
+, rbox_new_count(0)
+, rbox_status(qh_ERRnone)
+, rbox_message()
+{
+    allocateQhullQh();
+    // rbox arguments added to comment() via qh_rboxpoints > qh_fprintf_rbox
+    appendPoints(rboxCommand);
+}
+
+RboxPoints::
+~RboxPoints()
+{
+    delete qh();
+    resetQhullQh(0);
+}
+
+// RboxPoints and qh_rboxpoints has several fields in qhT (rbox_errexit..cpp_object)
+// It shares last_random with qh_rand and qh_srand
+// The other fields are unused
+void RboxPoints::
+allocateQhullQh()
+{
+    QHULL_LIB_CHECK /* Check for compatible library */
+    resetQhullQh(new QhullQh);
+}//allocateQhullQh
+
+#//!\name Messaging
+
+void RboxPoints::
+clearRboxMessage()
+{
+    rbox_status= qh_ERRnone;
+    rbox_message.clear();
+}//clearRboxMessage
+
+std::string RboxPoints::
+rboxMessage() const
+{
+    if(rbox_status!=qh_ERRnone){
+        return rbox_message;
+    }
+    if(isEmpty()){
+        return "rbox warning: no points generated\n";
+    }
+    return "rbox: OK\n";
+}//rboxMessage
+
+int RboxPoints::
+rboxStatus() const
+{
+    return rbox_status;
+}
+
+bool RboxPoints::
+hasRboxMessage() const
+{
+    return (rbox_status!=qh_ERRnone);
+}
+
+#//!\name Methods
+
+//! Appends points as defined by rboxCommand
+//! Appends rboxCommand to comment
+//! For rbox commands, see http://www.qhull.org/html/rbox.htm or html/rbox.htm
+void RboxPoints::
+appendPoints(const char *rboxCommand)
+{
+    string s("rbox ");
+    s += rboxCommand;
+    char *command= const_cast<char*>(s.c_str());
+    if(qh()->cpp_object){
+        throw QhullError(10001, "Qhull error: conflicting user of cpp_object for RboxPoints::appendPoints() or corrupted qh_qh");
+    }
+    if(extraCoordinatesCount()!=0){
+        throw QhullError(10067, "Qhull error: Extra coordinates (%d) prior to calling RboxPoints::appendPoints.  Was %s", extraCoordinatesCount(), 0, 0.0, comment().c_str());
+    }
+    countT previousCount= count();
+    qh()->cpp_object= this;           // for qh_fprintf_rbox()
+    int status= qh_rboxpoints(qh(), command);
+    qh()->cpp_object= 0;
+    if(rbox_status==qh_ERRnone){
+        rbox_status= status;
+    }
+    if(rbox_status!=qh_ERRnone){
+        throw QhullError(rbox_status, rbox_message);
+    }
+    if(extraCoordinatesCount()!=0){
+        throw QhullError(10002, "Qhull error: extra coordinates (%d) for PointCoordinates (%x)", extraCoordinatesCount(), 0, 0.0, coordinates());
+    }
+    if(previousCount+newCount()!=count()){
+        throw QhullError(10068, "Qhull error: rbox specified %d points but got %d points for command '%s'", newCount(), count()-previousCount, 0.0, comment().c_str());
+    }
+}//appendPoints
+
+}//namespace orgQhull
+
+#//!\name Global functions
+
+/*-<a                             href="qh-user.htm#TOC"
+>-------------------------------</a><a name="qh_fprintf_rbox">-</a>
+
+  qh_fprintf_rbox(qh, fp, msgcode, format, list of args )
+    fp is ignored (replaces qh_fprintf_rbox() in userprintf_rbox.c)
+    cpp_object == RboxPoints
+
+notes:
+    only called from qh_rboxpoints()
+    same as fprintf() and Qhull.qh_fprintf()
+    fgets() is not trapped like fprintf()
+    Do not throw errors from here.  Use qh_errexit_rbox;
+    A similar technique can be used for qh_fprintf to capture all of its output
+*/
+extern "C"
+void qh_fprintf_rbox(qhT *qh, FILE*, int msgcode, const char *fmt, ... ) {
+    va_list args;
+
+    using namespace orgQhull;
+
+    if(!qh->cpp_object){
+        qh_errexit_rbox(qh, 10072);
+    }
+    RboxPoints *out= reinterpret_cast<RboxPoints *>(qh->cpp_object);
+    va_start(args, fmt);
+    if(msgcode<MSG_OUTPUT){
+        char newMessage[MSG_MAXLEN];
+        // RoadError provides the message tag
+        vsnprintf(newMessage, sizeof(newMessage), fmt, args);
+        out->rbox_message += newMessage;
+        if(out->rbox_status<MSG_ERROR || out->rbox_status>=MSG_STDERR){
+            out->rbox_status= msgcode;
+        }
+        va_end(args);
+        return;
+    }
+    switch(msgcode){
+    case 9391:
+    case 9392:
+        out->rbox_message += "RboxPoints error: options 'h', 'n' not supported.\n";
+        qh_errexit_rbox(qh, 10010);
+        /* never returns */
+    case 9393:  // FIXUP QH11026 countT vs. int
+        {
+            int dimension= va_arg(args, int);
+            string command(va_arg(args, char*));
+            countT count= va_arg(args, countT);
+            out->setDimension(dimension);
+            out->appendComment(" \"");
+            out->appendComment(command.substr(command.find(' ')+1));
+            out->appendComment("\"");
+            out->setNewCount(count);
+            out->reservePoints();
+        }
+        break;
+    case 9407:
+        *out << va_arg(args, int);
+        // fall through
+    case 9405:
+        *out << va_arg(args, int);
+        // fall through
+    case 9403:
+        *out << va_arg(args, int);
+        break;
+    case 9408:
+        *out << va_arg(args, double);
+        // fall through
+    case 9406:
+        *out << va_arg(args, double);
+        // fall through
+    case 9404:
+        *out << va_arg(args, double);
+        break;
+    }
+    va_end(args);
+} /* qh_fprintf_rbox */
+
diff --git a/xs/src/qhull/src/libqhullcpp/RboxPoints.h b/xs/src/qhull/src/libqhullcpp/RboxPoints.h
new file mode 100644
index 0000000000..e8ec72b14a
--- /dev/null
+++ b/xs/src/qhull/src/libqhullcpp/RboxPoints.h
@@ -0,0 +1,69 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
+** $Id: //main/2015/qhull/src/libqhullcpp/RboxPoints.h#4 $$Change: 2079 $
+** $DateTime: 2016/02/07 17:43:34 $$Author: bbarber $
+**
+****************************************************************************/
+
+#ifndef RBOXPOINTS_H
+#define RBOXPOINTS_H
+
+#include "libqhull_r/qhull_ra.h"
+#include "libqhullcpp/QhullPoint.h"
+#include "libqhullcpp/PointCoordinates.h"
+
+#include <stdarg.h>
+#include <string>
+#include <vector>
+#include <istream>
+#include <ostream>
+#include <sstream>
+
+namespace orgQhull {
+
+#//!\name Defined here
+    //! RboxPoints -- generate random PointCoordinates for Qhull
+    class RboxPoints;
+
+class RboxPoints : public PointCoordinates {
+
+private:
+#//!\name Fields and friends
+                        //! PointCoordinates.qh() is owned by RboxPoints
+    countT              rbox_new_count;     //! Number of points for PointCoordinates
+    int                 rbox_status;    //! error status from rboxpoints.  qh_ERRnone if none.
+    std::string         rbox_message;   //! stderr from rboxpoints
+
+    // '::' is required for friend references
+    friend void ::qh_fprintf_rbox(qhT *qh, FILE *fp, int msgcode, const char *fmt, ... );
+
+public:
+#//!\name Construct
+                        RboxPoints();
+    explicit            RboxPoints(const char *rboxCommand);
+                        ~RboxPoints();
+private:                // Disable copy constructor and assignment.  RboxPoints owns QhullQh.
+                        RboxPoints(const RboxPoints &);
+                        RboxPoints &operator=(const RboxPoints &);
+private:
+    void                allocateQhullQh();
+
+public:
+#//!\name GetSet
+    void                clearRboxMessage();
+    countT              newCount() const { return rbox_new_count; }
+    std::string         rboxMessage() const;
+    int                 rboxStatus() const;
+    bool                hasRboxMessage() const;
+    void                setNewCount(countT pointCount) { QHULL_ASSERT(pointCount>=0); rbox_new_count= pointCount; }
+
+#//!\name Modify
+    void                appendPoints(const char* rboxCommand);
+    using               PointCoordinates::appendPoints;
+    void                reservePoints() { reserveCoordinates((count()+newCount())*dimension()); }
+};//class RboxPoints
+
+}//namespace orgQhull
+
+#endif // RBOXPOINTS_H
diff --git a/xs/src/qhull/src/libqhullcpp/RoadError.cpp b/xs/src/qhull/src/libqhullcpp/RoadError.cpp
new file mode 100644
index 0000000000..1d41ec1bc1
--- /dev/null
+++ b/xs/src/qhull/src/libqhullcpp/RoadError.cpp
@@ -0,0 +1,158 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
+** $Id: //main/2015/qhull/src/libqhullcpp/RoadError.cpp#2 $$Change: 2066 $
+** $DateTime: 2016/01/18 19:29:17 $$Author: bbarber $
+**
+****************************************************************************/
+
+#//! RoadError -- All exceptions thrown by Qhull are RoadErrors
+#//! Do not throw RoadError's from destructors.  Use e.logError() instead.
+
+#include "libqhullcpp/RoadError.h"
+
+#include <string>
+#include <sstream>
+#include <iostream>
+
+using std::cerr;
+using std::cout;
+using std::string;
+
+#ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
+#endif
+
+namespace orgQhull {
+
+#//!\name Class fields
+
+//! Identifies error messages from Qhull and Road for web searches.
+//! See QhullError.h#QHULLlastError and user.h#MSG_ERROR
+const char * RoadError::
+ROADtag= "QH";
+
+std::ostringstream RoadError::
+global_log;
+
+#//!\name Constructor
+
+RoadError::
+RoadError()
+: error_code(0)
+, log_event()
+, error_message()
+{ }
+
+RoadError::
+RoadError(const RoadError &other)
+: error_code(other.error_code)
+, log_event(other.log_event)
+, error_message(other.error_message)
+{
+}//copy construct
+
+RoadError::
+RoadError(int code, const std::string &message)
+: error_code(code)
+, log_event(message.c_str())
+, error_message(log_event.toString(ROADtag, error_code))
+{
+    log_event.cstr_1= error_message.c_str(); // overwrites initial value
+}
+
+RoadError::
+RoadError(int code, const char *fmt)
+: error_code(code)
+, log_event(fmt)
+, error_message()
+{ }
+
+RoadError::
+RoadError(int code, const char *fmt, int d)
+: error_code(code)
+, log_event(fmt, d)
+, error_message()
+{ }
+
+RoadError::
+RoadError(int code, const char *fmt, int d, int d2)
+: error_code(code)
+, log_event(fmt, d, d2)
+, error_message()
+{ }
+
+RoadError::
+RoadError(int code, const char *fmt, int d, int d2, float f)
+: error_code(code)
+, log_event(fmt, d, d2, f)
+, error_message()
+{ }
+
+RoadError::
+RoadError(int code, const char *fmt, int d, int d2, float f, const char *s)
+: error_code(code)
+, log_event(fmt, d, d2, f, s)
+, error_message(log_event.toString(ROADtag, code)) // char * may go out of scope
+{ }
+
+RoadError::
+RoadError(int code, const char *fmt, int d, int d2, float f, const void *x)
+: error_code(code)
+, log_event(fmt, d, d2, f, x)
+, error_message()
+{ }
+
+RoadError::
+RoadError(int code, const char *fmt, int d, int d2, float f, int i)
+: error_code(code)
+, log_event(fmt, d, d2, f, i)
+, error_message()
+{ }
+
+RoadError::
+RoadError(int code, const char *fmt, int d, int d2, float f, long long i)
+: error_code(code)
+, log_event(fmt, d, d2, f, i)
+, error_message()
+{ }
+
+RoadError::
+RoadError(int code, const char *fmt, int d, int d2, float f, double e)
+: error_code(code)
+, log_event(fmt, d, d2, f, e)
+, error_message()
+{ }
+
+RoadError & RoadError::
+operator=(const RoadError &other)
+{
+    error_code= other.error_code;
+    error_message= other.error_message;
+    log_event= other.log_event;
+    return *this;
+}//operator=
+
+#//!\name Virtual
+const char * RoadError::
+what() const throw()
+{
+    if(error_message.empty()){
+        error_message= log_event.toString(ROADtag, error_code);
+    }
+    return error_message.c_str();
+}//what
+
+#//!\name Updates
+
+//! Log error instead of throwing it.
+//! Not reentrant, so avoid using it if possible
+//!\todo Redesign with a thread-local stream or a reentrant ostringstream
+void RoadError::
+logErrorLastResort() const
+{
+    global_log << what() << endl;
+}//logError
+
+
+}//namespace orgQhull
+
diff --git a/xs/src/qhull/src/libqhullcpp/RoadError.h b/xs/src/qhull/src/libqhullcpp/RoadError.h
new file mode 100644
index 0000000000..1c9f6cdd5a
--- /dev/null
+++ b/xs/src/qhull/src/libqhullcpp/RoadError.h
@@ -0,0 +1,88 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
+** $Id: //main/2015/qhull/src/libqhullcpp/RoadError.h#4 $$Change: 2079 $
+** $DateTime: 2016/02/07 17:43:34 $$Author: bbarber $
+**
+****************************************************************************/
+
+#ifndef ROADERROR_H
+#define ROADERROR_H
+
+#include "libqhull_r/user_r.h"  /* for QHULL_CRTDBG */
+#include "libqhullcpp/RoadLogEvent.h"
+
+#include <iostream>
+#include <sstream>
+#include <stdexcept>
+#include <string>
+
+using std::endl;
+
+namespace orgQhull {
+
+#//!\name Defined here
+    //! RoadError -- Report and log errors
+    //!  See discussion in Saylan, G., "Practical C++ error handling in hybrid environments," Dr. Dobb's Journal, p. 50-55, March 2007.
+    //!   He uses an auto_ptr to track a stringstream.  It constructs a string on the fly.  RoadError uses the copy constructor to transform RoadLogEvent into a string
+    class RoadError;
+
+class RoadError : public std::exception {
+
+private:
+#//!\name Fields
+    int                 error_code;  //! Non-zero code (not logged), maybe returned as program status
+    RoadLogEvent        log_event;   //! Format string w/ arguments
+    mutable std::string error_message;  //! Formated error message.  Must be after log_event.
+
+#//!\name Class fields
+    static const char  *  ROADtag;
+    static std::ostringstream  global_log; //!< May be replaced with any ostream object
+                                    //!< Not reentrant -- only used by RoadError::logErrorLastResort()
+
+public:
+#//!\name Constants
+
+#//!\name Constructors
+    RoadError();
+    RoadError(const RoadError &other);  //! Called on throw, generates error_message
+    RoadError(int code, const std::string &message);
+    RoadError(int code, const char *fmt);
+    RoadError(int code, const char *fmt, int d);
+    RoadError(int code, const char *fmt, int d, int d2);
+    RoadError(int code, const char *fmt, int d, int d2, float f);
+    RoadError(int code, const char *fmt, int d, int d2, float f, const char *s);
+    RoadError(int code, const char *fmt, int d, int d2, float f, const void *x);
+    RoadError(int code, const char *fmt, int d, int d2, float f, int i);
+    RoadError(int code, const char *fmt, int d, int d2, float f, long long i);
+    RoadError(int code, const char *fmt, int d, int d2, float f, double e);
+
+    RoadError &         operator=(const RoadError &other);
+                        ~RoadError() throw() {};
+
+#//!\name Class methods
+
+    static void         clearGlobalLog() { global_log.seekp(0); }
+    static bool         emptyGlobalLog() { return global_log.tellp()<=0; }
+    static const char  *stringGlobalLog() { return global_log.str().c_str(); }
+
+#//!\name Virtual
+    virtual const char *what() const throw();
+
+#//!\name GetSet
+    bool                isValid() const { return log_event.isValid(); }
+    int                 errorCode() const { return error_code; };
+   // FIXUP QH11021 should RoadError provide errorMessage().  Currently what()
+    RoadLogEvent        roadLogEvent() const { return log_event; };
+
+#//!\name Update
+    void                logErrorLastResort() const;
+};//class RoadError
+
+}//namespace orgQhull
+
+#//!\name Global
+
+inline std::ostream &   operator<<(std::ostream &os, const orgQhull::RoadError &e) { return os << e.what(); }
+
+#endif // ROADERROR_H
diff --git a/xs/src/qhull/src/libqhullcpp/RoadLogEvent.cpp b/xs/src/qhull/src/libqhullcpp/RoadLogEvent.cpp
new file mode 100644
index 0000000000..9a9cf5960a
--- /dev/null
+++ b/xs/src/qhull/src/libqhullcpp/RoadLogEvent.cpp
@@ -0,0 +1,122 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
+** $Id: //main/2015/qhull/src/libqhullcpp/RoadLogEvent.cpp#3 $$Change: 2066 $
+** $Date: 2016/01/18 $$Author: bbarber $
+**
+****************************************************************************/
+
+#//! RoadLogEvent -- All exceptions thrown by Qhull are RoadErrors
+
+#include "libqhullcpp/RoadLogEvent.h"
+
+#include <string>
+#include <sstream>
+#include <iostream>
+
+using std::cout;
+using std::endl;
+using std::ostringstream;
+using std::string;
+
+#ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
+#endif
+
+namespace orgQhull {
+
+#//!\name Conversion
+string RoadLogEvent::
+toString(const char *tag, int code) const
+{
+    ostringstream os;
+    if(tag && code){
+        os << tag << code;
+        if(format_string){
+            os << " ";
+        }
+    }
+    if(!format_string){
+        return os.str();
+    }
+    const char *s= format_string;
+    int dCount= 0;  // Count of %d
+    int fCount= 0;  // Count of %f
+    char extraCode= '\0';
+    while(*s){
+        if(*s!='%'){
+            os << *s++;
+        }else{
+            char c= *++s;
+            s++;
+            switch(c){
+            case 'd':
+                if(++dCount>2){
+                    os << " ERROR_three_%d_in_format ";
+                }else if(dCount==2){
+                    os << int_2;
+                }else{
+                    os << int_1;
+                }
+                break;
+            case 'e':
+                if(firstExtraCode(os, c, &extraCode)){
+                    os << double_1;
+                }
+                break;
+            case 'f':
+                if(++fCount>1){
+                    os << " ERROR_two_%f_in_format ";
+                }else{
+                    os << float_1;
+                }
+                break;
+            case 'i':
+                if(firstExtraCode(os, c, &extraCode)){
+                    os << int64_1;
+                }
+                break;
+            case 's':
+                if(firstExtraCode(os, c, &extraCode)){
+                    os << cstr_1;
+                }
+                break;
+            case 'u':
+                if(firstExtraCode(os, c, &extraCode)){
+                    os << "0x" << std::hex << int64_1 << std::dec;
+                }
+                break;
+            case 'x':
+                if(firstExtraCode(os, c, &extraCode)){
+                    os << void_1;
+                }
+                break;
+            case '%':
+                os << c;
+                break;
+            default:
+                os << " ERROR_%" << c << "_not_defined_in_format";
+                break;
+            }
+        }
+    }
+    if(s[-1]!='\n'){
+        os << endl;
+    }
+    return os.str();
+}//toString
+
+#//!\name Class helpers (static)
+
+//! True if this char is the first extra code
+bool RoadLogEvent::
+firstExtraCode(std::ostream &os, char c, char *extraCode){
+    if(*extraCode){
+        os << " ERROR_%" << *extraCode << "_and_%" << c << "_in_format ";
+        return false;
+    }
+    *extraCode= c;
+    return true;
+}//firstExtraCode
+
+}//namespace orgQhull
+
diff --git a/xs/src/qhull/src/libqhullcpp/RoadLogEvent.h b/xs/src/qhull/src/libqhullcpp/RoadLogEvent.h
new file mode 100644
index 0000000000..7c4cfba0de
--- /dev/null
+++ b/xs/src/qhull/src/libqhullcpp/RoadLogEvent.h
@@ -0,0 +1,77 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
+** $Id: //main/2015/qhull/src/libqhullcpp/RoadLogEvent.h#1 $$Change: 1981 $
+** $DateTime: 2015/09/28 20:26:32 $$Author: bbarber $
+**
+****************************************************************************/
+
+#ifndef ROADLOGEVENT_H
+#define ROADLOGEVENT_H
+
+#include <ostream>
+#include <stdexcept>
+#include <string>
+
+namespace orgQhull {
+
+#//!\name Defined here
+    //! RoadLogEvent -- Record an event for the RoadLog
+    struct RoadLogEvent;
+
+struct RoadLogEvent {
+
+public:
+#//!\name Fields
+    const char *    format_string; //! Format string (a literal with format codes, for logging)
+    int             int_1;       //! Integer argument (%d, for logging)
+    int             int_2;       //! Integer argument (%d, for logging)
+    float           float_1;     //! Float argument (%f, for logging)
+    union {                      //! One additional argument (for logging)
+        const char *cstr_1;      //!   Cstr argument (%s) -- type checked at construct-time
+        const void *void_1;      //!   Void* argument (%x) -- Use upper-case codes for object types
+        long long   int64_1;     //!   signed int64 (%i).  Ambiguous if unsigned is also defined.
+        double      double_1;    //!   Double argument (%e)
+    };
+
+#//!\name Constants
+
+#//!\name Constructors
+    RoadLogEvent() : format_string(0), int_1(0), int_2(0), float_1(0), int64_1(0) {};
+    explicit RoadLogEvent(const char *fmt) : format_string(fmt), int_1(0), int_2(0), float_1(0), int64_1(0) {};
+    RoadLogEvent(const char *fmt, int d) : format_string(fmt), int_1(d), int_2(0), float_1(0), int64_1(0) {};
+    RoadLogEvent(const char *fmt, int d, int d2) : format_string(fmt), int_1(d), int_2(d2), float_1(0), int64_1(0) {};
+    RoadLogEvent(const char *fmt, int d, int d2, float f) : format_string(fmt), int_1(d), int_2(d2), float_1(f), int64_1(0) {};
+    RoadLogEvent(const char *fmt, int d, int d2, float f, const char *s) : format_string(fmt), int_1(d), int_2(d2), float_1(f), cstr_1(s) {};
+    RoadLogEvent(const char *fmt, int d, int d2, float f, const void *x) : format_string(fmt), int_1(d), int_2(d2), float_1(f), void_1(x) {};
+    RoadLogEvent(const char *fmt, int d, int d2, float f, int i) : format_string(fmt), int_1(d), int_2(d2), float_1(f), int64_1(i) {};
+    RoadLogEvent(const char *fmt, int d, int d2, float f, long long i) : format_string(fmt), int_1(d), int_2(d2), float_1(f), int64_1(i) {};
+    RoadLogEvent(const char *fmt, int d, int d2, float f, double g) : format_string(fmt), int_1(d), int_2(d2), float_1(f), double_1(g) {};
+    ~RoadLogEvent() {};
+    //! Default copy constructor and assignment
+
+#//!\name GetSet
+    bool                isValid() const { return format_string!=0; }
+    int                 int1() const { return int_1; };
+    int                 int2() const { return int_2; };
+    float               float1() const { return float_1; };
+    const char *        format() const { return format_string; };
+    const char *        cstr1() const { return cstr_1; };
+    const void *        void1() const { return void_1; };
+    long long           int64() const { return int64_1; };
+    double              double1() const { return double_1; };
+
+#//!\name Conversion
+
+    std::string        toString(const char* tag, int code) const;
+
+private:
+#//!\name Class helpers
+    static bool         firstExtraCode(std::ostream &os, char c, char *extraCode);
+
+
+};//class RoadLogEvent
+
+}//namespace orgQhull
+
+#endif // ROADLOGEVENT_H
diff --git a/xs/src/qhull/src/libqhullcpp/functionObjects.h b/xs/src/qhull/src/libqhullcpp/functionObjects.h
new file mode 100644
index 0000000000..3645c0713a
--- /dev/null
+++ b/xs/src/qhull/src/libqhullcpp/functionObjects.h
@@ -0,0 +1,67 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
+** $Id: //main/2015/qhull/src/libqhullcpp/functionObjects.h#1 $$Change: 1981 $
+** $DateTime: 2015/09/28 20:26:32 $$Author: bbarber $
+**
+****************************************************************************/
+
+#ifndef QHFUNCTIONOBJECTS_H
+#define QHFUNCTIONOBJECTS_H
+
+#include <stdlib.h>
+#include <math.h>
+
+namespace orgQhull {
+
+#//!\name Defined here
+
+    //! Sum of absolute values of the elements in a container
+    class AbsoluteSumOf;
+    //! Sum of the elements in a container
+    class SumOf;
+    //! Sum of squares of the elements in a container
+    class SumSquaresOf;
+
+#//!\name Class
+
+//! Absolute sum of the elements in a container
+class AbsoluteSumOf
+{
+private:
+    double sum;
+public:
+    inline AbsoluteSumOf() : sum(0.0) {}
+    inline void operator()(double v) { sum += fabs(v); }
+    inline operator double() { return sum; }
+};//AbsoluteSumOf
+
+//! Sum of the elements in a container
+class SumOf
+{
+private:
+    double sum;
+public:
+    inline SumOf() : sum(0.0) {}
+    inline void operator()(double v) { sum += v; }
+    inline operator double() { return sum; }
+};//SumOf
+
+
+//! Sum of squares of the elements in a container
+class SumSquaresOf
+{
+private:
+    double sum;
+public:
+    inline SumSquaresOf() : sum(0.0) {}
+    inline void operator()(double v) { sum += v*v; }
+    inline operator double() { return sum; }
+};//SumSquaresOf
+
+
+}//orgQhull
+
+
+#endif //QHFUNCTIONOBJECTS_H
+
diff --git a/xs/src/qhull/src/libqhullcpp/libqhullcpp.pro b/xs/src/qhull/src/libqhullcpp/libqhullcpp.pro
new file mode 100644
index 0000000000..89b967bef2
--- /dev/null
+++ b/xs/src/qhull/src/libqhullcpp/libqhullcpp.pro
@@ -0,0 +1,71 @@
+# -------------------------------------------------
+# libqhullcpp.pro -- Qt project for Qhull cpp shared library
+#
+# It uses reentrant Qhull
+# -------------------------------------------------
+
+include(../qhull-warn.pri)
+
+DESTDIR = ../../lib
+TEMPLATE = lib
+# Do not create libqhullcpp as a shared library.  Qhull C++ classes may change layout and size. 
+CONFIG += staticlib warn_on
+CONFIG -= qt rtti
+build_pass:CONFIG(debug, debug|release):{
+   TARGET = qhullcpp_d
+   OBJECTS_DIR = Debug
+}else:build_pass:CONFIG(release, debug|release):{
+   TARGET = qhullcpp
+   OBJECTS_DIR = Release
+}
+MOC_DIR = moc
+
+INCLUDEPATH += ../../src
+INCLUDEPATH += $$PWD # for MOC_DIR
+
+CONFIG += qhull_warn_shadow qhull_warn_conversion
+
+SOURCES += ../libqhullcpp/Coordinates.cpp
+SOURCES += ../libqhullcpp/PointCoordinates.cpp
+SOURCES += ../libqhullcpp/Qhull.cpp
+SOURCES += ../libqhullcpp/QhullFacet.cpp
+SOURCES += ../libqhullcpp/QhullFacetList.cpp
+SOURCES += ../libqhullcpp/QhullFacetSet.cpp
+SOURCES += ../libqhullcpp/QhullHyperplane.cpp
+SOURCES += ../libqhullcpp/QhullPoint.cpp
+SOURCES += ../libqhullcpp/QhullPoints.cpp
+SOURCES += ../libqhullcpp/QhullPointSet.cpp
+SOURCES += ../libqhullcpp/QhullQh.cpp
+SOURCES += ../libqhullcpp/QhullRidge.cpp
+SOURCES += ../libqhullcpp/QhullSet.cpp
+SOURCES += ../libqhullcpp/QhullStat.cpp
+SOURCES += ../libqhullcpp/QhullVertex.cpp
+SOURCES += ../libqhullcpp/QhullVertexSet.cpp
+SOURCES += ../libqhullcpp/RboxPoints.cpp
+SOURCES += ../libqhullcpp/RoadError.cpp
+SOURCES += ../libqhullcpp/RoadLogEvent.cpp
+
+HEADERS += ../libqhullcpp/Coordinates.h
+HEADERS += ../libqhullcpp/functionObjects.h
+HEADERS += ../libqhullcpp/PointCoordinates.h
+HEADERS += ../libqhullcpp/Qhull.h
+HEADERS += ../libqhullcpp/QhullError.h
+HEADERS += ../libqhullcpp/QhullFacet.h
+HEADERS += ../libqhullcpp/QhullFacetList.h
+HEADERS += ../libqhullcpp/QhullFacetSet.h
+HEADERS += ../libqhullcpp/QhullHyperplane.h
+HEADERS += ../libqhullcpp/QhullIterator.h
+HEADERS += ../libqhullcpp/QhullLinkedList.h
+HEADERS += ../libqhullcpp/QhullPoint.h
+HEADERS += ../libqhullcpp/QhullPoints.h
+HEADERS += ../libqhullcpp/QhullPointSet.h
+HEADERS += ../libqhullcpp/QhullQh.h
+HEADERS += ../libqhullcpp/QhullRidge.h
+HEADERS += ../libqhullcpp/QhullSet.h
+HEADERS += ../libqhullcpp/QhullSets.h
+HEADERS += ../libqhullcpp/QhullStat.h
+HEADERS += ../libqhullcpp/QhullVertex.h
+HEADERS += ../libqhullcpp/QhullVertexSet.h
+HEADERS += ../libqhullcpp/RboxPoints.h
+HEADERS += ../libqhullcpp/RoadError.h
+HEADERS += ../libqhullcpp/RoadLogEvent.h
diff --git a/xs/src/qhull/src/libqhullcpp/qt-qhull.cpp b/xs/src/qhull/src/libqhullcpp/qt-qhull.cpp
new file mode 100644
index 0000000000..895f591a85
--- /dev/null
+++ b/xs/src/qhull/src/libqhullcpp/qt-qhull.cpp
@@ -0,0 +1,130 @@
+/****************************************************************************
+**
+** Copyright (c) 2009-2015 C.B. Barber. All rights reserved.
+** $Id: //main/2015/qhull/src/libqhullcpp/qt-qhull.cpp#1 $$Change: 1981 $
+** $DateTime: 2015/09/28 20:26:32 $$Author: bbarber $
+**
+****************************************************************************/
+
+#include <QList>
+#include "qhulltest/RoadTest.h"
+
+#ifndef QHULL_USES_QT
+#define QHULL_USES_QT 1
+#endif
+
+#include "Coordinates.h"
+#include "QhullFacetList.h"
+#include "QhullFacetSet.h"
+#include "QhullHyperplane.h"
+#include "QhullPoint.h"
+#include "QhullPoints.h"
+#include "QhullPointSet.h"
+#include "QhullVertex.h"
+#include "QhullVertexSet.h"
+
+namespace orgQhull {
+
+#//!\name Conversions
+
+QList<coordT> Coordinates::
+toQList() const
+{
+    CoordinatesIterator i(*this);
+    QList<coordT> cs;
+    while(i.hasNext()){
+        cs.append(i.next());
+    }
+    return cs;
+}//toQList
+
+QList<QhullFacet> QhullFacetList::
+toQList() const
+{
+    QhullLinkedListIterator<QhullFacet> i(*this);
+    QList<QhullFacet> vs;
+    while(i.hasNext()){
+        QhullFacet f= i.next();
+        if(isSelectAll() || f.isGood()){
+            vs.append(f);
+        }
+    }
+    return vs;
+}//toQList
+
+//! Same as PrintVertices
+QList<QhullVertex> QhullFacetList::
+vertices_toQList() const
+{
+    QList<QhullVertex> vs;
+    QhullVertexSet qvs(qh(), first().getFacetT(), NULL, isSelectAll());
+    for(QhullVertexSet::iterator i=qvs.begin(); i!=qvs.end(); ++i){
+        vs.push_back(*i);
+    }
+    return vs;
+}//vertices_toQList
+
+QList<QhullFacet> QhullFacetSet::
+toQList() const
+{
+    QhullSetIterator<QhullFacet> i(*this);
+    QList<QhullFacet> vs;
+    while(i.hasNext()){
+        QhullFacet f= i.next();
+        if(isSelectAll() || f.isGood()){
+            vs.append(f);
+        }
+    }
+    return vs;
+}//toQList
+
+#ifdef QHULL_USES_QT
+QList<coordT> QhullHyperplane::
+toQList() const
+{
+    QhullHyperplaneIterator i(*this);
+    QList<coordT> fs;
+    while(i.hasNext()){
+        fs.append(i.next());
+    }
+    fs.append(hyperplane_offset);
+    return fs;
+}//toQList
+#endif //QHULL_USES_QT
+
+QList<coordT> QhullPoint::
+toQList() const
+{
+    QhullPointIterator i(*this);
+    QList<coordT> vs;
+    while(i.hasNext()){
+        vs.append(i.next());
+    }
+    return vs;
+}//toQList
+
+QList<QhullPoint> QhullPoints::
+toQList() const
+{
+    QhullPointsIterator i(*this);
+    QList<QhullPoint> vs;
+    while(i.hasNext()){
+        vs.append(i.next());
+    }
+    return vs;
+}//toQList
+
+/******
+QList<QhullPoint> QhullPointSet::
+toQList() const
+{
+    QhullPointSetIterator i(*this);
+    QList<QhullPoint> vs;
+    while(i.hasNext()){
+        vs.append(i.next());
+    }
+    return vs;
+}//toQList
+*/
+}//orgQhull
+
diff --git a/xs/src/qhull/src/libqhullcpp/usermem_r-cpp.cpp b/xs/src/qhull/src/libqhullcpp/usermem_r-cpp.cpp
new file mode 100644
index 0000000000..bb9534d098
--- /dev/null
+++ b/xs/src/qhull/src/libqhullcpp/usermem_r-cpp.cpp
@@ -0,0 +1,93 @@
+/*<html><pre>  -<a                             href="qh-user_r.htm"
+  >-------------------------------</a><a name="TOP">-</a>
+
+   usermem_r-cpp.cpp
+
+   Redefine qh_exit() as 'throw std::runtime_error("QH10003 ...")'
+
+   This file is not included in the Qhull builds.
+
+   qhull_r calls qh_exit() when qh_errexit() is not available.  For example,
+   it calls qh_exit() if you linked the wrong qhull library.
+
+   The C++ interface avoids most of the calls to qh_exit().
+
+   If needed, include usermem_r-cpp.o before libqhullstatic_r.a.  You may need to
+   override duplicate symbol errors (e.g. /FORCE:MULTIPLE for DevStudio).  It
+   may produce a warning about throwing an error from C code.
+*/
+
+extern "C" {
+    void    qh_exit(int exitcode);
+}
+
+#include <stdexcept>
+#include <stdlib.h>
+
+/*-<a                             href="qh-user_r.htm#TOC"
+  >-------------------------------</a><a name="qh_exit">-</a>
+
+  qh_exit( exitcode )
+    exit program
+
+  notes:
+    same as exit()
+*/
+void qh_exit(int exitcode) {
+    exitcode= exitcode;
+    throw std::runtime_error("QH10003 Qhull error.  See stderr or errfile.");
+} /* exit */
+
+/*-<a                             href="qh-user_r.htm#TOC"
+  >-------------------------------</a><a name="qh_fprintf_stderr">-</a>
+
+  qh_fprintf_stderr( msgcode, format, list of args )
+    fprintf to stderr with msgcode (non-zero)
+
+  notes:
+    qh_fprintf_stderr() is called when qh->ferr is not defined, usually due to an initialization error
+
+    It is typically followed by qh_errexit().
+
+    Redefine this function to avoid using stderr
+
+    Use qh_fprintf [userprintf_r.c] for normal printing
+*/
+void qh_fprintf_stderr(int msgcode, const char *fmt, ... ) {
+    va_list args;
+
+    va_start(args, fmt);
+    if(msgcode)
+      fprintf(stderr, "QH%.4d ", msgcode);
+    vfprintf(stderr, fmt, args);
+    va_end(args);
+} /* fprintf_stderr */
+
+/*-<a                             href="qh-user_r.htm#TOC"
+>-------------------------------</a><a name="qh_free">-</a>
+
+  qh_free(qhT *qh, mem )
+    free memory
+
+  notes:
+    same as free()
+    No calls to qh_errexit()
+*/
+void qh_free(void *mem) {
+    free(mem);
+} /* free */
+
+/*-<a                             href="qh-user_r.htm#TOC"
+    >-------------------------------</a><a name="qh_malloc">-</a>
+
+    qh_malloc( mem )
+      allocate memory
+
+    notes:
+      same as malloc()
+*/
+void *qh_malloc(size_t size) {
+    return malloc(size);
+} /* malloc */
+
+
diff --git a/xs/src/qhull/src/libqhullstatic/libqhullstatic.pro b/xs/src/qhull/src/libqhullstatic/libqhullstatic.pro
new file mode 100644
index 0000000000..1a516db73c
--- /dev/null
+++ b/xs/src/qhull/src/libqhullstatic/libqhullstatic.pro
@@ -0,0 +1,19 @@
+# -------------------------------------------------
+# libqhullstatic.pro -- Qt project for Qhull static library
+#   Built with qh_QHpointer=0.  See libqhullp.pro
+# -------------------------------------------------
+
+include(../qhull-warn.pri)
+include(../qhull-libqhull-src.pri)
+
+DESTDIR = ../../lib
+TEMPLATE = lib
+CONFIG += staticlib warn_on
+CONFIG -= qt
+build_pass:CONFIG(debug, debug|release):{
+    TARGET = qhullstatic_d
+    OBJECTS_DIR = Debug
+}else:build_pass:CONFIG(release, debug|release):{
+    TARGET = qhullstatic
+    OBJECTS_DIR = Release
+}
diff --git a/xs/src/qhull/src/libqhullstatic_r/libqhullstatic_r.pro b/xs/src/qhull/src/libqhullstatic_r/libqhullstatic_r.pro
new file mode 100644
index 0000000000..2f5bf4d076
--- /dev/null
+++ b/xs/src/qhull/src/libqhullstatic_r/libqhullstatic_r.pro
@@ -0,0 +1,21 @@
+# -------------------------------------------------
+# libqhullstatic_r.pro -- Qt project for Qhull static library
+#
+# It uses reeentrant Qhull
+# -------------------------------------------------
+
+include(../qhull-warn.pri)
+
+DESTDIR = ../../lib
+TEMPLATE = lib
+CONFIG += staticlib warn_on
+CONFIG -= qt
+build_pass:CONFIG(debug, debug|release):{
+    TARGET = qhullstatic_rd
+    OBJECTS_DIR = Debug
+}else:build_pass:CONFIG(release, debug|release):{
+    TARGET = qhullstatic_r
+    OBJECTS_DIR = Release
+}
+
+include(../qhull-libqhull-src_r.pri)
diff --git a/xs/src/qhull/src/qconvex/qconvex.c b/xs/src/qhull/src/qconvex/qconvex.c
new file mode 100644
index 0000000000..41bd666da1
--- /dev/null
+++ b/xs/src/qhull/src/qconvex/qconvex.c
@@ -0,0 +1,326 @@
+/*<html><pre>  -<a                             href="../libqhull/qh-qhull.htm"
+  >-------------------------------</a><a name="TOP">-</a>
+
+   qconvex.c
+      compute convex hulls using qhull
+
+   see unix.c for full interface
+
+   Copyright (c) 1993-2015, The Geometry Center
+*/
+
+#include "libqhull/libqhull.h"
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include <ctype.h>
+#include <math.h>
+
+#if __cplusplus
+extern "C" {
+  int isatty(int);
+}
+
+#elif _MSC_VER
+#include <io.h>
+#define isatty _isatty
+/* int _isatty(int); */
+
+#else
+int isatty(int);  /* returns 1 if stdin is a tty
+                   if "Undefined symbol" this can be deleted along with call in main() */
+#endif
+
+/*-<a                             href="../libqhull/qh-qhull.htm#TOC"
+  >-------------------------------</a><a name="prompt">-</a>
+
+  qh_prompt
+    long prompt for qconvex
+
+  notes:
+    restricted version of libqhull.c
+
+  see:
+    concise prompt below
+*/
+
+/* duplicated in qconvex.htm */
+char hidden_options[]=" d v H Qbb Qf Qg Qm Qr Qu Qv Qx Qz TR E V Fp Gt Q0 Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 ";
+
+char qh_prompta[]= "\n\
+qconvex- compute the convex hull\n\
+    http://www.qhull.org  %s\n\
+\n\
+input (stdin):\n\
+    first lines: dimension and number of points (or vice-versa).\n\
+    other lines: point coordinates, best if one point per line\n\
+    comments:    start with a non-numeric character\n\
+\n\
+options:\n\
+    Qt   - triangulated output\n\
+    QJ   - joggled input instead of merged facets\n\
+    Qc   - keep coplanar points with nearest facet\n\
+    Qi   - keep interior points with nearest facet\n\
+\n\
+Qhull control options:\n\
+    Qbk:n   - scale coord k so that low bound is n\n\
+      QBk:n - scale coord k so that upper bound is n (QBk is %2.2g)\n\
+    QbB  - scale input to unit cube centered at the origin\n\
+    Qbk:0Bk:0 - remove k-th coordinate from input\n\
+    QJn  - randomly joggle input in range [-n,n]\n\
+    QRn  - random rotation (n=seed, n=0 time, n=-1 time/no rotate)\n\
+%s%s%s%s";  /* split up qh_prompt for Visual C++ */
+char qh_promptb[]= "\
+    Qs   - search all points for the initial simplex\n\
+    QGn  - good facet if visible from point n, -n for not visible\n\
+    QVn  - good facet if it includes point n, -n if not\n\
+\n\
+";
+char qh_promptc[]= "\
+Trace options:\n\
+    T4   - trace at level n, 4=all, 5=mem/gauss, -1= events\n\
+    Tc   - check frequently during execution\n\
+    Ts   - print statistics\n\
+    Tv   - verify result: structure, convexity, and point inclusion\n\
+    Tz   - send all output to stdout\n\
+    TFn  - report summary when n or more facets created\n\
+    TI file - input data from file, no spaces or single quotes\n\
+    TO file - output results to file, may be enclosed in single quotes\n\
+    TPn  - turn on tracing when point n added to hull\n\
+     TMn - turn on tracing at merge n\n\
+     TWn - trace merge facets when width > n\n\
+    TVn  - stop qhull after adding point n, -n for before (see TCn)\n\
+     TCn - stop qhull after building cone for point n (see TVn)\n\
+\n\
+Precision options:\n\
+    Cn   - radius of centrum (roundoff added).  Merge facets if non-convex\n\
+     An  - cosine of maximum angle.  Merge facets if cosine > n or non-convex\n\
+           C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge\n\
+    Rn   - randomly perturb computations by a factor of [1-n,1+n]\n\
+    Un   - max distance below plane for a new, coplanar point\n\
+    Wn   - min facet width for outside point (before roundoff)\n\
+\n\
+Output formats (may be combined; if none, produces a summary to stdout):\n\
+    f    - facet dump\n\
+    G    - Geomview output (see below)\n\
+    i    - vertices incident to each facet\n\
+    m    - Mathematica output (2-d and 3-d)\n\
+    n    - normals with offsets\n\
+    o    - OFF file format (dim, points and facets; Voronoi regions)\n\
+    p    - point coordinates \n\
+    s    - summary (stderr)\n\
+\n\
+";
+char qh_promptd[]= "\
+More formats:\n\
+    Fa   - area for each facet\n\
+    FA   - compute total area and volume for option 's'\n\
+    Fc   - count plus coplanar points for each facet\n\
+           use 'Qc' (default) for coplanar and 'Qi' for interior\n\
+    FC   - centrum for each facet\n\
+    Fd   - use cdd format for input (homogeneous with offset first)\n\
+    FD   - use cdd format for numeric output (offset first)\n\
+    FF   - facet dump without ridges\n\
+    Fi   - inner plane for each facet\n\
+    FI   - ID for each facet\n\
+    Fm   - merge count for each facet (511 max)\n\
+    Fn   - count plus neighboring facets for each facet\n\
+    FN   - count plus neighboring facets for each point\n\
+    Fo   - outer plane (or max_outside) for each facet\n\
+    FO   - options and precision constants\n\
+    FP   - nearest vertex for each coplanar point\n\
+    FQ   - command used for qconvex\n\
+    Fs   - summary: #int (8), dimension, #points, tot vertices, tot facets,\n\
+                      for output: #vertices, #facets,\n\
+                                  #coplanar points, #non-simplicial facets\n\
+                    #real (2), max outer plane, min vertex\n\
+    FS   - sizes:   #int (0) \n\
+                    #real (2) tot area, tot volume\n\
+    Ft   - triangulation with centrums for non-simplicial facets (OFF format)\n\
+    Fv   - count plus vertices for each facet\n\
+    FV   - average of vertices (a feasible point for 'H')\n\
+    Fx   - extreme points (in order for 2-d)\n\
+\n\
+";
+char qh_prompte[]= "\
+Geomview output (2-d, 3-d, and 4-d)\n\
+    Ga   - all points as dots\n\
+     Gp  -  coplanar points and vertices as radii\n\
+     Gv  -  vertices as spheres\n\
+    Gi   - inner planes only\n\
+     Gn  -  no planes\n\
+     Go  -  outer planes only\n\
+    Gc   - centrums\n\
+    Gh   - hyperplane intersections\n\
+    Gr   - ridges\n\
+    GDn  - drop dimension n in 3-d and 4-d output\n\
+\n\
+Print options:\n\
+    PAn  - keep n largest facets by area\n\
+    Pdk:n - drop facet if normal[k] <= n (default 0.0)\n\
+    PDk:n - drop facet if normal[k] >= n\n\
+    Pg   - print good facets (needs 'QGn' or 'QVn')\n\
+    PFn  - keep facets whose area is at least n\n\
+    PG   - print neighbors of good facets\n\
+    PMn  - keep n facets with most merges\n\
+    Po   - force output.  If error, output neighborhood of facet\n\
+    Pp   - do not report precision problems\n\
+\n\
+    .    - list of all options\n\
+    -    - one line descriptions of all options\n\
+    -V   - version\n\
+";
+/* for opts, don't assign 'e' or 'E' to a flag (already used for exponent) */
+
+/*-<a                             href="../libqhull/qh-qhull.htm#TOC"
+  >-------------------------------</a><a name="prompt2">-</a>
+
+  qh_prompt2
+    synopsis for qhull
+*/
+char qh_prompt2[]= "\n\
+qconvex- compute the convex hull.  Qhull %s\n\
+    input (stdin): dimension, number of points, point coordinates\n\
+    comments start with a non-numeric character\n\
+\n\
+options (qconvex.htm):\n\
+    Qt   - triangulated output\n\
+    QJ   - joggled input instead of merged facets\n\
+    Tv   - verify result: structure, convexity, and point inclusion\n\
+    .    - concise list of all options\n\
+    -    - one-line description of all options\n\
+    -V   - version\n\
+\n\
+output options (subset):\n\
+    s    - summary of results (default)\n\
+    i    - vertices incident to each facet\n\
+    n    - normals with offsets\n\
+    p    - vertex coordinates (includes coplanar points if 'Qc')\n\
+    Fx   - extreme points (convex hull vertices)\n\
+    FA   - report total area and volume\n\
+    FS   - compute total area and volume\n\
+    o    - OFF format (dim, n, points, facets)\n\
+    G    - Geomview output (2-d, 3-d, and 4-d)\n\
+    m    - Mathematica output (2-d and 3-d)\n\
+    QVn  - print facets that include point n, -n if not\n\
+    TO file- output results to file, may be enclosed in single quotes\n\
+\n\
+examples:\n\
+    rbox c D2 | qconvex s n                    rbox c D2 | qconvex i\n\
+    rbox c D2 | qconvex o                      rbox 1000 s | qconvex s Tv FA\n\
+    rbox c d D2 | qconvex s Qc Fx              rbox y 1000 W0 | qconvex s n\n\
+    rbox y 1000 W0 | qconvex s QJ              rbox d G1 D12 | qconvex QR0 FA Pp\n\
+    rbox c D7 | qconvex FA TF1000\n\
+\n\
+";
+/* for opts, don't assign 'e' or 'E' to a flag (already used for exponent) */
+
+/*-<a                             href="../libqhull/qh-qhull.htm#TOC"
+  >-------------------------------</a><a name="prompt3">-</a>
+
+  qh_prompt3
+    concise prompt for qhull
+*/
+char qh_prompt3[]= "\n\
+Qhull %s.\n\
+Except for 'F.' and 'PG', upper-case options take an argument.\n\
+\n\
+ incidences     mathematica    normals        OFF_format     points\n\
+ summary        facet_dump\n\
+\n\
+ Farea          FArea_total    Fcoplanars     FCentrums      Fd_cdd_in\n\
+ FD_cdd_out     FFacet_xridge  Finner         FIDs           Fmerges\n\
+ Fneighbors     FNeigh_vertex  Fouter         FOptions       FPoint_near\n\
+ FQhull         Fsummary       FSize          Fvertices      FVertex_ave\n\
+ Fxtremes       FMaple\n\
+\n\
+ Gvertices      Gpoints        Gall_points    Gno_planes     Ginner\n\
+ Gcentrums      Ghyperplanes   Gridges        Gouter         GDrop_dim\n\
+\n\
+ PArea_keep     Pdrop d0:0D0   PFacet_area_keep Pgood        PGood_neighbors\n\
+ PMerge_keep    Poutput_forced Pprecision_not\n\
+\n\
+ QbBound 0:0.5  QbB_scale_box  Qcoplanar      QGood_point    Qinterior\n\
+ QJoggle        Qrandom        QRotate        Qsearch_1st    Qtriangulate\n\
+ QVertex_good\n\
+\n\
+ T4_trace       Tcheck_often   Tstatistics    Tverify        Tz_stdout\n\
+ TFacet_log     TInput_file    TPoint_trace   TMerge_trace   TOutput_file\n\
+ TWide_trace    TVertex_stop   TCone_stop\n\
+\n\
+ Angle_max      Centrum_size   Random_dist    Ucoplanar_max  Wide_outside\n\
+";
+
+/*-<a                             href="../libqhull/qh-qhull.htm"
+  >-------------------------------</a><a name="main">-</a>
+
+  main( argc, argv )
+    processes the command line, calls qhull() to do the work, and exits
+
+  design:
+    initializes data structures
+    reads points
+    finishes initialization
+    computes convex hull and other structures
+    checks the result
+    writes the output
+    frees memory
+*/
+int main(int argc, char *argv[]) {
+  int curlong, totlong; /* used !qh_NOmem */
+  int exitcode, numpoints, dim;
+  coordT *points;
+  boolT ismalloc;
+
+  QHULL_LIB_CHECK /* Check for compatible library */
+
+  if ((argc == 1) && isatty( 0 /*stdin*/)) {
+    fprintf(stdout, qh_prompt2, qh_version);
+    exit(qh_ERRnone);
+  }
+  if (argc > 1 && *argv[1] == '-' && !*(argv[1]+1)) {
+    fprintf(stdout, qh_prompta, qh_version, qh_DEFAULTbox,
+                qh_promptb, qh_promptc, qh_promptd, qh_prompte);
+    exit(qh_ERRnone);
+  }
+  if (argc > 1 && *argv[1] == '.' && !*(argv[1]+1)) {
+    fprintf(stdout, qh_prompt3, qh_version);
+    exit(qh_ERRnone);
+  }
+  if (argc > 1 && *argv[1] == '-' && *(argv[1]+1)=='V') {
+      fprintf(stdout, "%s\n", qh_version2);
+      exit(qh_ERRnone);
+  }
+  qh_init_A(stdin, stdout, stderr, argc, argv);  /* sets qh qhull_command */
+  exitcode= setjmp(qh errexit); /* simple statement for CRAY J916 */
+  if (!exitcode) {
+    qh NOerrexit = False;
+    qh_checkflags(qh qhull_command, hidden_options);
+    qh_initflags(qh qhull_command);
+    points= qh_readpoints(&numpoints, &dim, &ismalloc);
+    if (dim >= 5) {
+      qh_option("Qxact_merge", NULL, NULL);
+      qh MERGEexact= True; /* 'Qx' always */
+    }
+    qh_init_B(points, numpoints, dim, ismalloc);
+    qh_qhull();
+    qh_check_output();
+    qh_produce_output();
+    if (qh VERIFYoutput && !qh FORCEoutput && !qh STOPpoint && !qh STOPcone)
+      qh_check_points();
+    exitcode= qh_ERRnone;
+  }
+  qh NOerrexit= True;  /* no more setjmp */
+#ifdef qh_NOmem
+  qh_freeqhull(qh_ALL);
+#else
+  qh_freeqhull(!qh_ALL);
+  qh_memfreeshort(&curlong, &totlong);
+  if (curlong || totlong)
+    qh_fprintf_stderr(6263, "qhull internal warning (main): did not free %d bytes of long memory(%d pieces)\n",
+       totlong, curlong);
+#endif
+  return exitcode;
+} /* main */
+
diff --git a/xs/src/qhull/src/qconvex/qconvex.pro b/xs/src/qhull/src/qconvex/qconvex.pro
new file mode 100644
index 0000000000..1bf631bff6
--- /dev/null
+++ b/xs/src/qhull/src/qconvex/qconvex.pro
@@ -0,0 +1,9 @@
+# -------------------------------------------------
+# qconvex.pro -- Qt project file for qconvex.exe
+# -------------------------------------------------
+
+include(../qhull-app-c.pri)
+
+TARGET = qconvex
+
+SOURCES += qconvex.c
diff --git a/xs/src/qhull/src/qconvex/qconvex_r.c b/xs/src/qhull/src/qconvex/qconvex_r.c
new file mode 100644
index 0000000000..abf68ce37e
--- /dev/null
+++ b/xs/src/qhull/src/qconvex/qconvex_r.c
@@ -0,0 +1,328 @@
+/*<html><pre>  -<a                             href="../libqhull/qh-qhull.htm"
+  >-------------------------------</a><a name="TOP">-</a>
+
+   qconvex.c
+      compute convex hulls using qhull
+
+   see unix.c for full interface
+
+   Copyright (c) 1993-2015, The Geometry Center
+*/
+
+#include "libqhull_r/libqhull_r.h"
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include <ctype.h>
+#include <math.h>
+
+#if __cplusplus
+extern "C" {
+  int isatty(int);
+}
+
+#elif _MSC_VER
+#include <io.h>
+#define isatty _isatty
+/* int _isatty(int); */
+
+#else
+int isatty(int);  /* returns 1 if stdin is a tty
+                   if "Undefined symbol" this can be deleted along with call in main() */
+#endif
+
+/*-<a                             href="../libqhull/qh-qhull.htm#TOC"
+  >-------------------------------</a><a name="prompt">-</a>
+
+  qh_prompt
+    long prompt for qconvex
+
+  notes:
+    restricted version of libqhull.c
+
+  see:
+    concise prompt below
+*/
+
+/* duplicated in qconvex.htm */
+char hidden_options[]=" d v H Qbb Qf Qg Qm Qr Qu Qv Qx Qz TR E V Fp Gt Q0 Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 ";
+
+char qh_prompta[]= "\n\
+qconvex- compute the convex hull\n\
+    http://www.qhull.org  %s\n\
+\n\
+input (stdin):\n\
+    first lines: dimension and number of points (or vice-versa).\n\
+    other lines: point coordinates, best if one point per line\n\
+    comments:    start with a non-numeric character\n\
+\n\
+options:\n\
+    Qt   - triangulated output\n\
+    QJ   - joggled input instead of merged facets\n\
+    Qc   - keep coplanar points with nearest facet\n\
+    Qi   - keep interior points with nearest facet\n\
+\n\
+Qhull control options:\n\
+    Qbk:n   - scale coord k so that low bound is n\n\
+      QBk:n - scale coord k so that upper bound is n (QBk is %2.2g)\n\
+    QbB  - scale input to unit cube centered at the origin\n\
+    Qbk:0Bk:0 - remove k-th coordinate from input\n\
+    QJn  - randomly joggle input in range [-n,n]\n\
+    QRn  - random rotation (n=seed, n=0 time, n=-1 time/no rotate)\n\
+%s%s%s%s";  /* split up qh_prompt for Visual C++ */
+char qh_promptb[]= "\
+    Qs   - search all points for the initial simplex\n\
+    QGn  - good facet if visible from point n, -n for not visible\n\
+    QVn  - good facet if it includes point n, -n if not\n\
+\n\
+";
+char qh_promptc[]= "\
+Trace options:\n\
+    T4   - trace at level n, 4=all, 5=mem/gauss, -1= events\n\
+    Tc   - check frequently during execution\n\
+    Ts   - print statistics\n\
+    Tv   - verify result: structure, convexity, and point inclusion\n\
+    Tz   - send all output to stdout\n\
+    TFn  - report summary when n or more facets created\n\
+    TI file - input data from file, no spaces or single quotes\n\
+    TO file - output results to file, may be enclosed in single quotes\n\
+    TPn  - turn on tracing when point n added to hull\n\
+     TMn - turn on tracing at merge n\n\
+     TWn - trace merge facets when width > n\n\
+    TVn  - stop qhull after adding point n, -n for before (see TCn)\n\
+     TCn - stop qhull after building cone for point n (see TVn)\n\
+\n\
+Precision options:\n\
+    Cn   - radius of centrum (roundoff added).  Merge facets if non-convex\n\
+     An  - cosine of maximum angle.  Merge facets if cosine > n or non-convex\n\
+           C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge\n\
+    Rn   - randomly perturb computations by a factor of [1-n,1+n]\n\
+    Un   - max distance below plane for a new, coplanar point\n\
+    Wn   - min facet width for outside point (before roundoff)\n\
+\n\
+Output formats (may be combined; if none, produces a summary to stdout):\n\
+    f    - facet dump\n\
+    G    - Geomview output (see below)\n\
+    i    - vertices incident to each facet\n\
+    m    - Mathematica output (2-d and 3-d)\n\
+    n    - normals with offsets\n\
+    o    - OFF file format (dim, points and facets; Voronoi regions)\n\
+    p    - point coordinates \n\
+    s    - summary (stderr)\n\
+\n\
+";
+char qh_promptd[]= "\
+More formats:\n\
+    Fa   - area for each facet\n\
+    FA   - compute total area and volume for option 's'\n\
+    Fc   - count plus coplanar points for each facet\n\
+           use 'Qc' (default) for coplanar and 'Qi' for interior\n\
+    FC   - centrum for each facet\n\
+    Fd   - use cdd format for input (homogeneous with offset first)\n\
+    FD   - use cdd format for numeric output (offset first)\n\
+    FF   - facet dump without ridges\n\
+    Fi   - inner plane for each facet\n\
+    FI   - ID for each facet\n\
+    Fm   - merge count for each facet (511 max)\n\
+    Fn   - count plus neighboring facets for each facet\n\
+    FN   - count plus neighboring facets for each point\n\
+    Fo   - outer plane (or max_outside) for each facet\n\
+    FO   - options and precision constants\n\
+    FP   - nearest vertex for each coplanar point\n\
+    FQ   - command used for qconvex\n\
+    Fs   - summary: #int (8), dimension, #points, tot vertices, tot facets,\n\
+                      for output: #vertices, #facets,\n\
+                                  #coplanar points, #non-simplicial facets\n\
+                    #real (2), max outer plane, min vertex\n\
+    FS   - sizes:   #int (0) \n\
+                    #real (2) tot area, tot volume\n\
+    Ft   - triangulation with centrums for non-simplicial facets (OFF format)\n\
+    Fv   - count plus vertices for each facet\n\
+    FV   - average of vertices (a feasible point for 'H')\n\
+    Fx   - extreme points (in order for 2-d)\n\
+\n\
+";
+char qh_prompte[]= "\
+Geomview output (2-d, 3-d, and 4-d)\n\
+    Ga   - all points as dots\n\
+     Gp  -  coplanar points and vertices as radii\n\
+     Gv  -  vertices as spheres\n\
+    Gi   - inner planes only\n\
+     Gn  -  no planes\n\
+     Go  -  outer planes only\n\
+    Gc   - centrums\n\
+    Gh   - hyperplane intersections\n\
+    Gr   - ridges\n\
+    GDn  - drop dimension n in 3-d and 4-d output\n\
+\n\
+Print options:\n\
+    PAn  - keep n largest facets by area\n\
+    Pdk:n - drop facet if normal[k] <= n (default 0.0)\n\
+    PDk:n - drop facet if normal[k] >= n\n\
+    Pg   - print good facets (needs 'QGn' or 'QVn')\n\
+    PFn  - keep facets whose area is at least n\n\
+    PG   - print neighbors of good facets\n\
+    PMn  - keep n facets with most merges\n\
+    Po   - force output.  If error, output neighborhood of facet\n\
+    Pp   - do not report precision problems\n\
+\n\
+    .    - list of all options\n\
+    -    - one line descriptions of all options\n\
+    -V   - version\n\
+";
+/* for opts, don't assign 'e' or 'E' to a flag (already used for exponent) */
+
+/*-<a                             href="../libqhull/qh-qhull.htm#TOC"
+  >-------------------------------</a><a name="prompt2">-</a>
+
+  qh_prompt2
+    synopsis for qhull
+*/
+char qh_prompt2[]= "\n\
+qconvex- compute the convex hull.  Qhull %s\n\
+    input (stdin): dimension, number of points, point coordinates\n\
+    comments start with a non-numeric character\n\
+\n\
+options (qconvex.htm):\n\
+    Qt   - triangulated output\n\
+    QJ   - joggled input instead of merged facets\n\
+    Tv   - verify result: structure, convexity, and point inclusion\n\
+    .    - concise list of all options\n\
+    -    - one-line description of all options\n\
+    -V   - version\n\
+\n\
+output options (subset):\n\
+    s    - summary of results (default)\n\
+    i    - vertices incident to each facet\n\
+    n    - normals with offsets\n\
+    p    - vertex coordinates (includes coplanar points if 'Qc')\n\
+    Fx   - extreme points (convex hull vertices)\n\
+    FA   - report total area and volume\n\
+    FS   - compute total area and volume\n\
+    o    - OFF format (dim, n, points, facets)\n\
+    G    - Geomview output (2-d, 3-d, and 4-d)\n\
+    m    - Mathematica output (2-d and 3-d)\n\
+    QVn  - print facets that include point n, -n if not\n\
+    TO file- output results to file, may be enclosed in single quotes\n\
+\n\
+examples:\n\
+    rbox c D2 | qconvex s n                    rbox c D2 | qconvex i\n\
+    rbox c D2 | qconvex o                      rbox 1000 s | qconvex s Tv FA\n\
+    rbox c d D2 | qconvex s Qc Fx              rbox y 1000 W0 | qconvex s n\n\
+    rbox y 1000 W0 | qconvex s QJ              rbox d G1 D12 | qconvex QR0 FA Pp\n\
+    rbox c D7 | qconvex FA TF1000\n\
+\n\
+";
+/* for opts, don't assign 'e' or 'E' to a flag (already used for exponent) */
+
+/*-<a                             href="../libqhull/qh-qhull.htm#TOC"
+  >-------------------------------</a><a name="prompt3">-</a>
+
+  qh_prompt3
+    concise prompt for qhull
+*/
+char qh_prompt3[]= "\n\
+Qhull %s.\n\
+Except for 'F.' and 'PG', upper-case options take an argument.\n\
+\n\
+ incidences     mathematica    normals        OFF_format     points\n\
+ summary        facet_dump\n\
+\n\
+ Farea          FArea_total    Fcoplanars     FCentrums      Fd_cdd_in\n\
+ FD_cdd_out     FFacet_xridge  Finner         FIDs           Fmerges\n\
+ Fneighbors     FNeigh_vertex  Fouter         FOptions       FPoint_near\n\
+ FQhull         Fsummary       FSize          Fvertices      FVertex_ave\n\
+ Fxtremes       FMaple\n\
+\n\
+ Gvertices      Gpoints        Gall_points    Gno_planes     Ginner\n\
+ Gcentrums      Ghyperplanes   Gridges        Gouter         GDrop_dim\n\
+\n\
+ PArea_keep     Pdrop d0:0D0   PFacet_area_keep Pgood        PGood_neighbors\n\
+ PMerge_keep    Poutput_forced Pprecision_not\n\
+\n\
+ QbBound 0:0.5  QbB_scale_box  Qcoplanar      QGood_point    Qinterior\n\
+ QJoggle        Qrandom        QRotate        Qsearch_1st    Qtriangulate\n\
+ QVertex_good\n\
+\n\
+ T4_trace       Tcheck_often   Tstatistics    Tverify        Tz_stdout\n\
+ TFacet_log     TInput_file    TPoint_trace   TMerge_trace   TOutput_file\n\
+ TWide_trace    TVertex_stop   TCone_stop\n\
+\n\
+ Angle_max      Centrum_size   Random_dist    Ucoplanar_max  Wide_outside\n\
+";
+
+/*-<a                             href="../libqhull/qh-qhull.htm"
+  >-------------------------------</a><a name="main">-</a>
+
+  main( argc, argv )
+    processes the command line, calls qhull() to do the work, and exits
+
+  design:
+    initializes data structures
+    reads points
+    finishes initialization
+    computes convex hull and other structures
+    checks the result
+    writes the output
+    frees memory
+*/
+int main(int argc, char *argv[]) {
+  int curlong, totlong; /* used !qh_NOmem */
+  int exitcode, numpoints, dim;
+  coordT *points;
+  boolT ismalloc;
+  qhT qh_qh;
+  qhT *qh= &qh_qh;
+
+  QHULL_LIB_CHECK /* Check for compatible library */
+
+  if ((argc == 1) && isatty( 0 /*stdin*/)) {
+    fprintf(stdout, qh_prompt2, qh_version);
+    exit(qh_ERRnone);
+  }
+  if (argc > 1 && *argv[1] == '-' && !*(argv[1]+1)) {
+    fprintf(stdout, qh_prompta, qh_version, qh_DEFAULTbox,
+                qh_promptb, qh_promptc, qh_promptd, qh_prompte);
+    exit(qh_ERRnone);
+  }
+  if (argc > 1 && *argv[1] == '.' && !*(argv[1]+1)) {
+    fprintf(stdout, qh_prompt3, qh_version);
+    exit(qh_ERRnone);
+  }
+  if (argc > 1 && *argv[1] == '-' && *(argv[1]+1)=='V') {
+      fprintf(stdout, "%s\n", qh_version2);
+      exit(qh_ERRnone);
+  }
+  qh_init_A(qh, stdin, stdout, stderr, argc, argv);  /* sets qh->qhull_command */
+  exitcode= setjmp(qh->errexit); /* simple statement for CRAY J916 */
+  if (!exitcode) {
+    qh->NOerrexit = False;
+    qh_checkflags(qh, qh->qhull_command, hidden_options);
+    qh_initflags(qh, qh->qhull_command);
+    points= qh_readpoints(qh, &numpoints, &dim, &ismalloc);
+    if (dim >= 5) {
+      qh_option(qh, "Qxact_merge", NULL, NULL);
+      qh->MERGEexact= True; /* 'Qx' always */
+    }
+    qh_init_B(qh, points, numpoints, dim, ismalloc);
+    qh_qhull(qh);
+    qh_check_output(qh);
+    qh_produce_output(qh);
+    if (qh->VERIFYoutput && !qh->FORCEoutput && !qh->STOPpoint && !qh->STOPcone)
+      qh_check_points(qh);
+    exitcode= qh_ERRnone;
+  }
+  qh->NOerrexit= True;  /* no more setjmp */
+#ifdef qh_NOmem
+  qh_freeqhull(qh, qh_ALL);
+#else
+  qh_freeqhull(qh, !qh_ALL);
+  qh_memfreeshort(qh, &curlong, &totlong);
+  if (curlong || totlong)
+    qh_fprintf_stderr(6263, "qhull internal warning (main): did not free %d bytes of long memory(%d pieces)\n",
+       totlong, curlong);
+#endif
+  return exitcode;
+} /* main */
+
diff --git a/xs/src/qhull/src/qdelaunay/qdelaun.c b/xs/src/qhull/src/qdelaunay/qdelaun.c
new file mode 100644
index 0000000000..9011d9fcc0
--- /dev/null
+++ b/xs/src/qhull/src/qdelaunay/qdelaun.c
@@ -0,0 +1,315 @@
+/*<html><pre>  -<a                             href="../libqhull/qh-qhull.htm"
+  >-------------------------------</a><a name="TOP">-</a>
+
+   qdelaun.c
+     compute Delaunay triangulations and furthest-point Delaunay
+     triangulations using qhull
+
+   see unix.c for full interface
+
+   Copyright (c) 1993-2015, The Geometry Center
+*/
+
+#include "libqhull/libqhull.h"
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include <ctype.h>
+#include <math.h>
+
+#if __cplusplus
+extern "C" {
+  int isatty(int);
+}
+
+#elif _MSC_VER
+#include <io.h>
+#define isatty _isatty
+/* int _isatty(int); */
+
+#else
+int isatty(int);  /* returns 1 if stdin is a tty
+                   if "Undefined symbol" this can be deleted along with call in main() */
+#endif
+
+/*-<a                             href="../libqhull/qh-qhull.htm#TOC"
+  >-------------------------------</a><a name="prompt">-</a>
+
+  qh_prompt
+    long prompt for qhull
+
+  notes:
+    restricted version of libqhull.c
+
+  see:
+    concise prompt below
+*/
+
+/* duplicated in qdelau_f.htm and qdelaun.htm */
+char hidden_options[]=" d n v H U Qb QB Qc Qf Qg Qi Qm Qr QR Qv Qx TR E V FC Fi Fo Ft Fp FV Q0 Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 ";
+
+char qh_prompta[]= "\n\
+qdelaunay- compute the Delaunay triangulation\n\
+    http://www.qhull.org  %s\n\
+\n\
+input (stdin):\n\
+    first lines: dimension and number of points (or vice-versa).\n\
+    other lines: point coordinates, best if one point per line\n\
+    comments:    start with a non-numeric character\n\
+\n\
+options:\n\
+    Qu   - compute furthest-site Delaunay triangulation\n\
+    Qt   - triangulated output\n\
+    QJ   - joggled input instead of merged facets\n\
+\n\
+Qhull control options:\n\
+    QJn  - randomly joggle input in range [-n,n]\n\
+%s%s%s%s";  /* split up qh_prompt for Visual C++ */
+char qh_promptb[]= "\
+    Qs   - search all points for the initial simplex\n\
+    Qz   - add point-at-infinity to Delaunay triangulation\n\
+    QGn  - print Delaunay region if visible from point n, -n if not\n\
+    QVn  - print Delaunay regions that include point n, -n if not\n\
+\n\
+";
+char qh_promptc[]= "\
+Trace options:\n\
+    T4   - trace at level n, 4=all, 5=mem/gauss, -1= events\n\
+    Tc   - check frequently during execution\n\
+    Ts   - print statistics\n\
+    Tv   - verify result: structure, convexity, and in-circle test\n\
+    Tz   - send all output to stdout\n\
+    TFn  - report summary when n or more facets created\n\
+    TI file - input data from file, no spaces or single quotes\n\
+    TO file - output results to file, may be enclosed in single quotes\n\
+    TPn  - turn on tracing when point n added to hull\n\
+     TMn - turn on tracing at merge n\n\
+     TWn - trace merge facets when width > n\n\
+    TVn  - stop qhull after adding point n, -n for before (see TCn)\n\
+     TCn - stop qhull after building cone for point n (see TVn)\n\
+\n\
+Precision options:\n\
+    Cn   - radius of centrum (roundoff added).  Merge facets if non-convex\n\
+     An  - cosine of maximum angle.  Merge facets if cosine > n or non-convex\n\
+           C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge\n\
+    Rn   - randomly perturb computations by a factor of [1-n,1+n]\n\
+    Wn   - min facet width for outside point (before roundoff)\n\
+\n\
+Output formats (may be combined; if none, produces a summary to stdout):\n\
+    f    - facet dump\n\
+    G    - Geomview output (see below)\n\
+    i    - vertices incident to each Delaunay region\n\
+    m    - Mathematica output (2-d only, lifted to a paraboloid)\n\
+    o    - OFF format (dim, points, and facets as a paraboloid)\n\
+    p    - point coordinates (lifted to a paraboloid)\n\
+    s    - summary (stderr)\n\
+\n\
+";
+char qh_promptd[]= "\
+More formats:\n\
+    Fa   - area for each Delaunay region\n\
+    FA   - compute total area for option 's'\n\
+    Fc   - count plus coincident points for each Delaunay region\n\
+    Fd   - use cdd format for input (homogeneous with offset first)\n\
+    FD   - use cdd format for numeric output (offset first)\n\
+    FF   - facet dump without ridges\n\
+    FI   - ID of each Delaunay region\n\
+    Fm   - merge count for each Delaunay region (511 max)\n\
+    FM   - Maple output (2-d only, lifted to a paraboloid)\n\
+    Fn   - count plus neighboring region for each Delaunay region\n\
+    FN   - count plus neighboring region for each point\n\
+    FO   - options and precision constants\n\
+    FP   - nearest point and distance for each coincident point\n\
+    FQ   - command used for qdelaunay\n\
+    Fs   - summary: #int (8), dimension, #points, tot vertices, tot facets,\n\
+                    for output: #vertices, #Delaunay regions,\n\
+                                #coincident points, #non-simplicial regions\n\
+                    #real (2), max outer plane, min vertex\n\
+    FS   - sizes:   #int (0)\n\
+                    #real (2), tot area, 0\n\
+    Fv   - count plus vertices for each Delaunay region\n\
+    Fx   - extreme points of Delaunay triangulation (on convex hull)\n\
+\n\
+";
+char qh_prompte[]= "\
+Geomview options (2-d and 3-d)\n\
+    Ga   - all points as dots\n\
+     Gp  -  coplanar points and vertices as radii\n\
+     Gv  -  vertices as spheres\n\
+    Gi   - inner planes only\n\
+     Gn  -  no planes\n\
+     Go  -  outer planes only\n\
+    Gc     - centrums\n\
+    Gh   - hyperplane intersections\n\
+    Gr   - ridges\n\
+    GDn  - drop dimension n in 3-d and 4-d output\n\
+    Gt   - transparent outer ridges to view 3-d Delaunay\n\
+\n\
+Print options:\n\
+    PAn  - keep n largest Delaunay regions by area\n\
+    Pdk:n - drop facet if normal[k] <= n (default 0.0)\n\
+    PDk:n - drop facet if normal[k] >= n\n\
+    Pg   - print good Delaunay regions (needs 'QGn' or 'QVn')\n\
+    PFn  - keep Delaunay regions whose area is at least n\n\
+    PG   - print neighbors of good regions (needs 'QGn' or 'QVn')\n\
+    PMn  - keep n Delaunay regions with most merges\n\
+    Po   - force output.  If error, output neighborhood of facet\n\
+    Pp   - do not report precision problems\n\
+\n\
+    .    - list of all options\n\
+    -    - one line descriptions of all options\n\
+    -V   - version\n\
+";
+/* for opts, don't assign 'e' or 'E' to a flag (already used for exponent) */
+
+/*-<a                             href="../libqhull/qh-qhull.htm#TOC"
+  >-------------------------------</a><a name="prompt2">-</a>
+
+  qh_prompt2
+    synopsis for qhull
+*/
+char qh_prompt2[]= "\n\
+qdelaunay- compute the Delaunay triangulation.  Qhull %s\n\
+    input (stdin): dimension, number of points, point coordinates\n\
+    comments start with a non-numeric character\n\
+\n\
+options (qdelaun.htm):\n\
+    Qu   - furthest-site Delaunay triangulation\n\
+    Qt   - triangulated output\n\
+    QJ   - joggled input instead of merged facets\n\
+    Tv   - verify result: structure, convexity, and in-circle test\n\
+    .    - concise list of all options\n\
+    -    - one-line description of all options\n\
+    -V   - version\n\
+\n\
+output options (subset):\n\
+    s    - summary of results (default)\n\
+    i    - vertices incident to each Delaunay region\n\
+    Fx   - extreme points (vertices of the convex hull)\n\
+    o    - OFF format (shows the points lifted to a paraboloid)\n\
+    G    - Geomview output (2-d and 3-d points lifted to a paraboloid)\n\
+    m    - Mathematica output (2-d inputs lifted to a paraboloid)\n\
+    QVn  - print Delaunay regions that include point n, -n if not\n\
+    TO file- output results to file, may be enclosed in single quotes\n\
+\n\
+examples:\n\
+    rbox c P0 D2 | qdelaunay s o          rbox c P0 D2 | qdelaunay i\n\
+    rbox c P0 D2 | qdelaunay Fv           rbox c P0 D2 | qdelaunay s Qu Fv\n\
+    rbox c G1 d D2 | qdelaunay s i        rbox c G1 d D2 | qdelaunay Qt\n\
+    rbox M3,4 z 100 D2 | qdelaunay s      rbox M3,4 z 100 D2 | qdelaunay s Qt\n\
+\n\
+";
+/* for opts, don't assign 'e' or 'E' to a flag (already used for exponent) */
+
+/*-<a                             href="../libqhull/qh-qhull.htm#TOC"
+  >-------------------------------</a><a name="prompt3">-</a>
+
+  qh_prompt3
+    concise prompt for qhull
+*/
+char qh_prompt3[]= "\n\
+Qhull %s.\n\
+Except for 'F.' and 'PG', upper-case options take an argument.\n\
+\n\
+ incidences     mathematica    OFF_format     points_lifted  summary\n\
+ facet_dump\n\
+\n\
+ Farea          FArea_total    Fcoincident    Fd_cdd_in      FD_cdd_out\n\
+ FF_dump_xridge FIDs           Fmerges        Fneighbors     FNeigh_vertex\n\
+ FOptions       FPoint_near    FQdelaun       Fsummary       FSize\n\
+ Fvertices      Fxtremes       FMaple\n\
+\n\
+ Gvertices      Gpoints        Gall_points    Gno_planes     Ginner\n\
+ Gcentrums      Ghyperplanes   Gridges        Gouter         GDrop_dim\n\
+ Gtransparent\n\
+\n\
+ PArea_keep     Pdrop d0:0D0   Pgood          PFacet_area_keep\n\
+ PGood_neighbors PMerge_keep   Poutput_forced Pprecision_not\n\
+\n\
+ QGood_point    QJoggle        Qsearch_1st    Qtriangulate   QupperDelaunay\n\
+ QVertex_good   Qzinfinite\n\
+\n\
+ T4_trace       Tcheck_often   Tstatistics    Tverify        Tz_stdout\n\
+ TFacet_log     TInput_file    TPoint_trace   TMerge_trace   TOutput_file\n\
+ TWide_trace    TVertex_stop   TCone_stop\n\
+\n\
+ Angle_max      Centrum_size   Random_dist    Wide_outside\n\
+";
+
+/*-<a                             href="../libqhull/qh-qhull.htm#TOC"
+  >-------------------------------</a><a name="main">-</a>
+
+  main( argc, argv )
+    processes the command line, calls qhull() to do the work, and exits
+
+  design:
+    initializes data structures
+    reads points
+    finishes initialization
+    computes convex hull and other structures
+    checks the result
+    writes the output
+    frees memory
+*/
+int main(int argc, char *argv[]) {
+  int curlong, totlong; /* used !qh_NOmem */
+  int exitcode, numpoints, dim;
+  coordT *points;
+  boolT ismalloc;
+
+  QHULL_LIB_CHECK /* Check for compatible library */
+
+  if ((argc == 1) && isatty( 0 /*stdin*/)) {
+    fprintf(stdout, qh_prompt2, qh_version);
+    exit(qh_ERRnone);
+  }
+  if (argc > 1 && *argv[1] == '-' && !*(argv[1]+1)) {
+    fprintf(stdout, qh_prompta, qh_version,
+                qh_promptb, qh_promptc, qh_promptd, qh_prompte);
+    exit(qh_ERRnone);
+  }
+  if (argc > 1 && *argv[1] == '.' && !*(argv[1]+1)) {
+    fprintf(stdout, qh_prompt3, qh_version);
+    exit(qh_ERRnone);
+  }
+  if (argc > 1 && *argv[1] == '-' && *(argv[1]+1)=='V') {
+      fprintf(stdout, "%s\n", qh_version2);
+      exit(qh_ERRnone);
+  }
+  qh_init_A(stdin, stdout, stderr, argc, argv);  /* sets qh qhull_command */
+  exitcode= setjmp(qh errexit); /* simple statement for CRAY J916 */
+  if (!exitcode) {
+    qh NOerrexit = False;
+    qh_option("delaunay  Qbbound-last", NULL, NULL);
+    qh DELAUNAY= True;     /* 'd'   */
+    qh SCALElast= True;    /* 'Qbb' */
+    qh KEEPcoplanar= True; /* 'Qc', to keep coplanars in 'p' */
+    qh_checkflags(qh qhull_command, hidden_options);
+    qh_initflags(qh qhull_command);
+    points= qh_readpoints(&numpoints, &dim, &ismalloc);
+    if (dim >= 5) {
+      qh_option("Qxact_merge", NULL, NULL);
+      qh MERGEexact= True; /* 'Qx' always */
+    }
+    qh_init_B(points, numpoints, dim, ismalloc);
+    qh_qhull();
+    qh_check_output();
+    qh_produce_output();
+    if (qh VERIFYoutput && !qh FORCEoutput && !qh STOPpoint && !qh STOPcone)
+      qh_check_points();
+    exitcode= qh_ERRnone;
+  }
+  qh NOerrexit= True;  /* no more setjmp */
+#ifdef qh_NOmem
+  qh_freeqhull(qh_ALL);
+#else
+  qh_freeqhull(!qh_ALL);
+  qh_memfreeshort(&curlong, &totlong);
+  if (curlong || totlong)
+    qh_fprintf_stderr(6263, "qhull internal warning (main): did not free %d bytes of long memory(%d pieces)\n",
+       totlong, curlong);
+#endif
+  return exitcode;
+} /* main */
+
diff --git a/xs/src/qhull/src/qdelaunay/qdelaun_r.c b/xs/src/qhull/src/qdelaunay/qdelaun_r.c
new file mode 100644
index 0000000000..0854b8bb97
--- /dev/null
+++ b/xs/src/qhull/src/qdelaunay/qdelaun_r.c
@@ -0,0 +1,317 @@
+/*<html><pre>  -<a                             href="../libqhull/qh-qhull.htm"
+  >-------------------------------</a><a name="TOP">-</a>
+
+   qdelaun.c
+     compute Delaunay triangulations and furthest-point Delaunay
+     triangulations using qhull
+
+   see unix.c for full interface
+
+   Copyright (c) 1993-2015, The Geometry Center
+*/
+
+#include "libqhull_r/libqhull_r.h"
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include <ctype.h>
+#include <math.h>
+
+#if __cplusplus
+extern "C" {
+  int isatty(int);
+}
+
+#elif _MSC_VER
+#include <io.h>
+#define isatty _isatty
+/* int _isatty(int); */
+
+#else
+int isatty(int);  /* returns 1 if stdin is a tty
+                   if "Undefined symbol" this can be deleted along with call in main() */
+#endif
+
+/*-<a                             href="../libqhull/qh-qhull.htm#TOC"
+  >-------------------------------</a><a name="prompt">-</a>
+
+  qh_prompt
+    long prompt for qhull
+
+  notes:
+    restricted version of libqhull.c
+
+  see:
+    concise prompt below
+*/
+
+/* duplicated in qdelau_f.htm and qdelaun.htm */
+char hidden_options[]=" d n v H U Qb QB Qc Qf Qg Qi Qm Qr QR Qv Qx TR E V FC Fi Fo Ft Fp FV Q0 Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 ";
+
+char qh_prompta[]= "\n\
+qdelaunay- compute the Delaunay triangulation\n\
+    http://www.qhull.org  %s\n\
+\n\
+input (stdin):\n\
+    first lines: dimension and number of points (or vice-versa).\n\
+    other lines: point coordinates, best if one point per line\n\
+    comments:    start with a non-numeric character\n\
+\n\
+options:\n\
+    Qu   - compute furthest-site Delaunay triangulation\n\
+    Qt   - triangulated output\n\
+    QJ   - joggled input instead of merged facets\n\
+\n\
+Qhull control options:\n\
+    QJn  - randomly joggle input in range [-n,n]\n\
+%s%s%s%s";  /* split up qh_prompt for Visual C++ */
+char qh_promptb[]= "\
+    Qs   - search all points for the initial simplex\n\
+    Qz   - add point-at-infinity to Delaunay triangulation\n\
+    QGn  - print Delaunay region if visible from point n, -n if not\n\
+    QVn  - print Delaunay regions that include point n, -n if not\n\
+\n\
+";
+char qh_promptc[]= "\
+Trace options:\n\
+    T4   - trace at level n, 4=all, 5=mem/gauss, -1= events\n\
+    Tc   - check frequently during execution\n\
+    Ts   - print statistics\n\
+    Tv   - verify result: structure, convexity, and in-circle test\n\
+    Tz   - send all output to stdout\n\
+    TFn  - report summary when n or more facets created\n\
+    TI file - input data from file, no spaces or single quotes\n\
+    TO file - output results to file, may be enclosed in single quotes\n\
+    TPn  - turn on tracing when point n added to hull\n\
+     TMn - turn on tracing at merge n\n\
+     TWn - trace merge facets when width > n\n\
+    TVn  - stop qhull after adding point n, -n for before (see TCn)\n\
+     TCn - stop qhull after building cone for point n (see TVn)\n\
+\n\
+Precision options:\n\
+    Cn   - radius of centrum (roundoff added).  Merge facets if non-convex\n\
+     An  - cosine of maximum angle.  Merge facets if cosine > n or non-convex\n\
+           C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge\n\
+    Rn   - randomly perturb computations by a factor of [1-n,1+n]\n\
+    Wn   - min facet width for outside point (before roundoff)\n\
+\n\
+Output formats (may be combined; if none, produces a summary to stdout):\n\
+    f    - facet dump\n\
+    G    - Geomview output (see below)\n\
+    i    - vertices incident to each Delaunay region\n\
+    m    - Mathematica output (2-d only, lifted to a paraboloid)\n\
+    o    - OFF format (dim, points, and facets as a paraboloid)\n\
+    p    - point coordinates (lifted to a paraboloid)\n\
+    s    - summary (stderr)\n\
+\n\
+";
+char qh_promptd[]= "\
+More formats:\n\
+    Fa   - area for each Delaunay region\n\
+    FA   - compute total area for option 's'\n\
+    Fc   - count plus coincident points for each Delaunay region\n\
+    Fd   - use cdd format for input (homogeneous with offset first)\n\
+    FD   - use cdd format for numeric output (offset first)\n\
+    FF   - facet dump without ridges\n\
+    FI   - ID of each Delaunay region\n\
+    Fm   - merge count for each Delaunay region (511 max)\n\
+    FM   - Maple output (2-d only, lifted to a paraboloid)\n\
+    Fn   - count plus neighboring region for each Delaunay region\n\
+    FN   - count plus neighboring region for each point\n\
+    FO   - options and precision constants\n\
+    FP   - nearest point and distance for each coincident point\n\
+    FQ   - command used for qdelaunay\n\
+    Fs   - summary: #int (8), dimension, #points, tot vertices, tot facets,\n\
+                    for output: #vertices, #Delaunay regions,\n\
+                                #coincident points, #non-simplicial regions\n\
+                    #real (2), max outer plane, min vertex\n\
+    FS   - sizes:   #int (0)\n\
+                    #real (2), tot area, 0\n\
+    Fv   - count plus vertices for each Delaunay region\n\
+    Fx   - extreme points of Delaunay triangulation (on convex hull)\n\
+\n\
+";
+char qh_prompte[]= "\
+Geomview options (2-d and 3-d)\n\
+    Ga   - all points as dots\n\
+     Gp  -  coplanar points and vertices as radii\n\
+     Gv  -  vertices as spheres\n\
+    Gi   - inner planes only\n\
+     Gn  -  no planes\n\
+     Go  -  outer planes only\n\
+    Gc     - centrums\n\
+    Gh   - hyperplane intersections\n\
+    Gr   - ridges\n\
+    GDn  - drop dimension n in 3-d and 4-d output\n\
+    Gt   - transparent outer ridges to view 3-d Delaunay\n\
+\n\
+Print options:\n\
+    PAn  - keep n largest Delaunay regions by area\n\
+    Pdk:n - drop facet if normal[k] <= n (default 0.0)\n\
+    PDk:n - drop facet if normal[k] >= n\n\
+    Pg   - print good Delaunay regions (needs 'QGn' or 'QVn')\n\
+    PFn  - keep Delaunay regions whose area is at least n\n\
+    PG   - print neighbors of good regions (needs 'QGn' or 'QVn')\n\
+    PMn  - keep n Delaunay regions with most merges\n\
+    Po   - force output.  If error, output neighborhood of facet\n\
+    Pp   - do not report precision problems\n\
+\n\
+    .    - list of all options\n\
+    -    - one line descriptions of all options\n\
+    -V   - version\n\
+";
+/* for opts, don't assign 'e' or 'E' to a flag (already used for exponent) */
+
+/*-<a                             href="../libqhull/qh-qhull.htm#TOC"
+  >-------------------------------</a><a name="prompt2">-</a>
+
+  qh_prompt2
+    synopsis for qhull
+*/
+char qh_prompt2[]= "\n\
+qdelaunay- compute the Delaunay triangulation.  Qhull %s\n\
+    input (stdin): dimension, number of points, point coordinates\n\
+    comments start with a non-numeric character\n\
+\n\
+options (qdelaun.htm):\n\
+    Qu   - furthest-site Delaunay triangulation\n\
+    Qt   - triangulated output\n\
+    QJ   - joggled input instead of merged facets\n\
+    Tv   - verify result: structure, convexity, and in-circle test\n\
+    .    - concise list of all options\n\
+    -    - one-line description of all options\n\
+    -V   - version\n\
+\n\
+output options (subset):\n\
+    s    - summary of results (default)\n\
+    i    - vertices incident to each Delaunay region\n\
+    Fx   - extreme points (vertices of the convex hull)\n\
+    o    - OFF format (shows the points lifted to a paraboloid)\n\
+    G    - Geomview output (2-d and 3-d points lifted to a paraboloid)\n\
+    m    - Mathematica output (2-d inputs lifted to a paraboloid)\n\
+    QVn  - print Delaunay regions that include point n, -n if not\n\
+    TO file- output results to file, may be enclosed in single quotes\n\
+\n\
+examples:\n\
+    rbox c P0 D2 | qdelaunay s o          rbox c P0 D2 | qdelaunay i\n\
+    rbox c P0 D2 | qdelaunay Fv           rbox c P0 D2 | qdelaunay s Qu Fv\n\
+    rbox c G1 d D2 | qdelaunay s i        rbox c G1 d D2 | qdelaunay Qt\n\
+    rbox M3,4 z 100 D2 | qdelaunay s      rbox M3,4 z 100 D2 | qdelaunay s Qt\n\
+\n\
+";
+/* for opts, don't assign 'e' or 'E' to a flag (already used for exponent) */
+
+/*-<a                             href="../libqhull/qh-qhull.htm#TOC"
+  >-------------------------------</a><a name="prompt3">-</a>
+
+  qh_prompt3
+    concise prompt for qhull
+*/
+char qh_prompt3[]= "\n\
+Qhull %s.\n\
+Except for 'F.' and 'PG', upper-case options take an argument.\n\
+\n\
+ incidences     mathematica    OFF_format     points_lifted  summary\n\
+ facet_dump\n\
+\n\
+ Farea          FArea_total    Fcoincident    Fd_cdd_in      FD_cdd_out\n\
+ FF_dump_xridge FIDs           Fmerges        Fneighbors     FNeigh_vertex\n\
+ FOptions       FPoint_near    FQdelaun       Fsummary       FSize\n\
+ Fvertices      Fxtremes       FMaple\n\
+\n\
+ Gvertices      Gpoints        Gall_points    Gno_planes     Ginner\n\
+ Gcentrums      Ghyperplanes   Gridges        Gouter         GDrop_dim\n\
+ Gtransparent\n\
+\n\
+ PArea_keep     Pdrop d0:0D0   Pgood          PFacet_area_keep\n\
+ PGood_neighbors PMerge_keep   Poutput_forced Pprecision_not\n\
+\n\
+ QGood_point    QJoggle        Qsearch_1st    Qtriangulate   QupperDelaunay\n\
+ QVertex_good   Qzinfinite\n\
+\n\
+ T4_trace       Tcheck_often   Tstatistics    Tverify        Tz_stdout\n\
+ TFacet_log     TInput_file    TPoint_trace   TMerge_trace   TOutput_file\n\
+ TWide_trace    TVertex_stop   TCone_stop\n\
+\n\
+ Angle_max      Centrum_size   Random_dist    Wide_outside\n\
+";
+
+/*-<a                             href="../libqhull/qh-qhull.htm#TOC"
+  >-------------------------------</a><a name="main">-</a>
+
+  main( argc, argv )
+    processes the command line, calls qhull() to do the work, and exits
+
+  design:
+    initializes data structures
+    reads points
+    finishes initialization
+    computes convex hull and other structures
+    checks the result
+    writes the output
+    frees memory
+*/
+int main(int argc, char *argv[]) {
+  int curlong, totlong; /* used !qh_NOmem */
+  int exitcode, numpoints, dim;
+  coordT *points;
+  boolT ismalloc;
+  qhT qh_qh;
+  qhT *qh= &qh_qh;
+
+  QHULL_LIB_CHECK /* Check for compatible library */
+
+  if ((argc == 1) && isatty( 0 /*stdin*/)) {
+    fprintf(stdout, qh_prompt2, qh_version);
+    exit(qh_ERRnone);
+  }
+  if (argc > 1 && *argv[1] == '-' && !*(argv[1]+1)) {
+    fprintf(stdout, qh_prompta, qh_version,
+                qh_promptb, qh_promptc, qh_promptd, qh_prompte);
+    exit(qh_ERRnone);
+  }
+  if (argc > 1 && *argv[1] == '.' && !*(argv[1]+1)) {
+    fprintf(stdout, qh_prompt3, qh_version);
+    exit(qh_ERRnone);
+  }
+  if (argc > 1 && *argv[1] == '-' && *(argv[1]+1)=='V') {
+      fprintf(stdout, "%s\n", qh_version2);
+      exit(qh_ERRnone);
+  }
+  qh_init_A(qh, stdin, stdout, stderr, argc, argv);  /* sets qh->qhull_command */
+  exitcode= setjmp(qh->errexit); /* simple statement for CRAY J916 */
+  if (!exitcode) {
+    qh->NOerrexit = False;
+    qh_option(qh, "delaunay  Qbbound-last", NULL, NULL);
+    qh->DELAUNAY= True;     /* 'd'   */
+    qh->SCALElast= True;    /* 'Qbb' */
+    qh->KEEPcoplanar= True; /* 'Qc', to keep coplanars in 'p' */
+    qh_checkflags(qh, qh->qhull_command, hidden_options);
+    qh_initflags(qh, qh->qhull_command);
+    points= qh_readpoints(qh, &numpoints, &dim, &ismalloc);
+    if (dim >= 5) {
+      qh_option(qh, "Qxact_merge", NULL, NULL);
+      qh->MERGEexact= True; /* 'Qx' always */
+    }
+    qh_init_B(qh, points, numpoints, dim, ismalloc);
+    qh_qhull(qh);
+    qh_check_output(qh);
+    qh_produce_output(qh);
+    if (qh->VERIFYoutput && !qh->FORCEoutput && !qh->STOPpoint && !qh->STOPcone)
+      qh_check_points(qh);
+    exitcode= qh_ERRnone;
+  }
+  qh->NOerrexit= True;  /* no more setjmp */
+#ifdef qh_NOmem
+  qh_freeqhull(qh, qh_ALL);
+#else
+  qh_freeqhull(qh, !qh_ALL);
+  qh_memfreeshort(qh, &curlong, &totlong);
+  if (curlong || totlong)
+    qh_fprintf_stderr(6263, "qhull internal warning (main): did not free %d bytes of long memory(%d pieces)\n",
+       totlong, curlong);
+#endif
+  return exitcode;
+} /* main */
+
diff --git a/xs/src/qhull/src/qdelaunay/qdelaunay.pro b/xs/src/qhull/src/qdelaunay/qdelaunay.pro
new file mode 100644
index 0000000000..138ac0589d
--- /dev/null
+++ b/xs/src/qhull/src/qdelaunay/qdelaunay.pro
@@ -0,0 +1,9 @@
+# -------------------------------------------------
+# qdelaunay.pro -- Qt project file for qvoronoi.exe
+# -------------------------------------------------
+
+include(../qhull-app-c.pri)
+
+TARGET = qdelaunay
+
+SOURCES += qdelaun.c
diff --git a/xs/src/qhull/src/qhalf/qhalf.c b/xs/src/qhull/src/qhalf/qhalf.c
new file mode 100644
index 0000000000..4a5889ed78
--- /dev/null
+++ b/xs/src/qhull/src/qhalf/qhalf.c
@@ -0,0 +1,316 @@
+/*<html><pre>  -<a                             href="../libqhull/qh-qhull.htm"
+  >-------------------------------</a><a name="TOP">-</a>
+
+   qhalf.c
+     compute the intersection of halfspaces about a point
+
+   see unix.c for full interface
+
+   Copyright (c) 1993-2015, The Geometry Center
+*/
+
+#include "libqhull/libqhull.h"
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include <ctype.h>
+#include <math.h>
+
+#if __cplusplus
+extern "C" {
+  int isatty(int);
+}
+
+#elif _MSC_VER
+#include <io.h>
+#define isatty _isatty
+/* int _isatty(int); */
+
+#else
+int isatty(int);  /* returns 1 if stdin is a tty
+                   if "Undefined symbol" this can be deleted along with call in main() */
+#endif
+
+/*-<a                             href="../libqhull/qh-qhull.htm#TOC"
+  >-------------------------------</a><a name="prompt">-</a>
+
+  qh_prompt
+    long prompt for qhull
+
+  notes:
+    restricted version of libqhull.c
+
+  see:
+    concise prompt below
+*/
+
+/* duplicated in qhalf.htm */
+char hidden_options[]=" d n v Qbb QbB Qf Qg Qm Qr QR Qv Qx Qz TR E V Fa FA FC FD FS Ft FV Gt Q0 Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 ";
+
+char qh_prompta[]= "\n\
+qhalf- compute the intersection of halfspaces about a point\n\
+    http://www.qhull.org  %s\n\
+\n\
+input (stdin):\n\
+    optional interior point: dimension, 1, coordinates\n\
+    first lines: dimension+1 and number of halfspaces\n\
+    other lines: halfspace coefficients followed by offset\n\
+    comments:    start with a non-numeric character\n\
+\n\
+options:\n\
+    Hn,n - specify coordinates of interior point\n\
+    Qt   - triangulated output\n\
+    QJ   - joggled input instead of merged facets\n\
+    Qc   - keep coplanar halfspaces\n\
+    Qi   - keep other redundant halfspaces\n\
+\n\
+Qhull control options:\n\
+    QJn  - randomly joggle input in range [-n,n]\n\
+%s%s%s%s";  /* split up qh_prompt for Visual C++ */
+char qh_promptb[]= "\
+    Qbk:0Bk:0 - remove k-th coordinate from input\n\
+    Qs   - search all halfspaces for the initial simplex\n\
+    QGn  - print intersection if visible to halfspace n, -n for not\n\
+    QVn  - print intersections for halfspace n, -n if not\n\
+\n\
+";
+char qh_promptc[]= "\
+Trace options:\n\
+    T4   - trace at level n, 4=all, 5=mem/gauss, -1= events\n\
+    Tc   - check frequently during execution\n\
+    Ts   - print statistics\n\
+    Tv   - verify result: structure, convexity, and redundancy\n\
+    Tz   - send all output to stdout\n\
+    TFn  - report summary when n or more facets created\n\
+    TI file - input data from file, no spaces or single quotes\n\
+    TO file - output results to file, may be enclosed in single quotes\n\
+    TPn  - turn on tracing when halfspace n added to intersection\n\
+    TMn  - turn on tracing at merge n\n\
+    TWn  - trace merge facets when width > n\n\
+    TVn  - stop qhull after adding halfspace n, -n for before (see TCn)\n\
+    TCn  - stop qhull after building cone for halfspace n (see TVn)\n\
+\n\
+Precision options:\n\
+    Cn   - radius of centrum (roundoff added).  Merge facets if non-convex\n\
+     An  - cosine of maximum angle.  Merge facets if cosine > n or non-convex\n\
+           C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge\n\
+    Rn   - randomly perturb computations by a factor of [1-n,1+n]\n\
+    Un   - max distance below plane for a new, coplanar halfspace\n\
+    Wn   - min facet width for outside halfspace (before roundoff)\n\
+\n\
+Output formats (may be combined; if none, produces a summary to stdout):\n\
+    f    - facet dump\n\
+    G    - Geomview output (dual convex hull)\n\
+    i    - non-redundant halfspaces incident to each intersection\n\
+    m    - Mathematica output (dual convex hull)\n\
+    o    - OFF format (dual convex hull: dimension, points, and facets)\n\
+    p    - vertex coordinates of dual convex hull (coplanars if 'Qc' or 'Qi')\n\
+    s    - summary (stderr)\n\
+\n\
+";
+char qh_promptd[]= "\
+More formats:\n\
+    Fc   - count plus redundant halfspaces for each intersection\n\
+         -   Qc (default) for coplanar and Qi for other redundant\n\
+    Fd   - use cdd format for input (homogeneous with offset first)\n\
+    FF   - facet dump without ridges\n\
+    FI   - ID of each intersection\n\
+    Fm   - merge count for each intersection (511 max)\n\
+    FM   - Maple output (dual convex hull)\n\
+    Fn   - count plus neighboring intersections for each intersection\n\
+    FN   - count plus intersections for each non-redundant halfspace\n\
+    FO   - options and precision constants\n\
+    Fp   - dim, count, and intersection coordinates\n\
+    FP   - nearest halfspace and distance for each redundant halfspace\n\
+    FQ   - command used for qhalf\n\
+    Fs   - summary: #int (8), dim, #halfspaces, #non-redundant, #intersections\n\
+                      for output: #non-redundant, #intersections, #coplanar\n\
+                                  halfspaces, #non-simplicial intersections\n\
+                    #real (2), max outer plane, min vertex\n\
+    Fv   - count plus non-redundant halfspaces for each intersection\n\
+    Fx   - non-redundant halfspaces\n\
+\n\
+";
+char qh_prompte[]= "\
+Geomview output (2-d, 3-d and 4-d; dual convex hull)\n\
+    Ga   - all points (i.e., transformed halfspaces) as dots\n\
+     Gp  -  coplanar points and vertices as radii\n\
+     Gv  -  vertices (i.e., non-redundant halfspaces) as spheres\n\
+    Gi   - inner planes (i.e., halfspace intersections) only\n\
+     Gn  -  no planes\n\
+     Go  -  outer planes only\n\
+    Gc   - centrums\n\
+    Gh   - hyperplane intersections\n\
+    Gr   - ridges\n\
+    GDn  - drop dimension n in 3-d and 4-d output\n\
+\n\
+Print options:\n\
+    PAn  - keep n largest facets (i.e., intersections) by area\n\
+    Pdk:n- drop facet if normal[k] <= n (default 0.0)\n\
+    PDk:n- drop facet if normal[k] >= n\n\
+    Pg   - print good facets (needs 'QGn' or 'QVn')\n\
+    PFn  - keep facets whose area is at least n\n\
+    PG   - print neighbors of good facets\n\
+    PMn  - keep n facets with most merges\n\
+    Po   - force output.  If error, output neighborhood of facet\n\
+    Pp   - do not report precision problems\n\
+\n\
+    .    - list of all options\n\
+    -    - one line descriptions of all options\n\
+    -V   - version\n\
+";
+/* for opts, don't assign 'e' or 'E' to a flag (already used for exponent) */
+
+/*-<a                             href="../libqhull/qh-qhull.htm#TOC"
+  >-------------------------------</a><a name="prompt2">-</a>
+
+  qh_prompt2
+    synopsis for qhull
+*/
+char qh_prompt2[]= "\n\
+qhalf- halfspace intersection about a point.  Qhull %s\n\
+    input (stdin): [dim, 1, interior point], dim+1, n, coefficients+offset\n\
+    comments start with a non-numeric character\n\
+\n\
+options (qhalf.htm):\n\
+    Hn,n - specify coordinates of interior point\n\
+    Qt   - triangulated output\n\
+    QJ   - joggled input instead of merged facets\n\
+    Tv   - verify result: structure, convexity, and redundancy\n\
+    .    - concise list of all options\n\
+    -    - one-line description of all options\n\
+    -V   - version\n\
+\n\
+output options (subset):\n\
+    s    - summary of results (default)\n\
+    Fp   - intersection coordinates\n\
+    Fv   - non-redundant halfspaces incident to each intersection\n\
+    Fx   - non-redundant halfspaces\n\
+    o    - OFF file format (dual convex hull)\n\
+    G    - Geomview output (dual convex hull)\n\
+    m    - Mathematica output (dual convex hull)\n\
+    QVn  - print intersections for halfspace n, -n if not\n\
+    TO file - output results to file, may be enclosed in single quotes\n\
+\n\
+examples:\n\
+    rbox d | qconvex FQ n | qhalf s H0,0,0 Fp\n\
+    rbox c | qconvex FQ FV n | qhalf s i\n\
+    rbox c | qconvex FQ FV n | qhalf s o\n\
+\n\
+";
+/* for opts, don't assign 'e' or 'E' to a flag (already used for exponent) */
+
+/*-<a                             href="../libqhull/qh-qhull.htm#TOC"
+  >-------------------------------</a><a name="prompt3">-</a>
+
+  qh_prompt3
+    concise prompt for qhull
+*/
+char qh_prompt3[]= "\n\
+Qhull %s.\n\
+Except for 'F.' and 'PG', upper_case options take an argument.\n\
+\n\
+ incidences     Geomview       mathematica    OFF_format     point_dual\n\
+ summary        facet_dump\n\
+\n\
+ Fc_redundant   Fd_cdd_in      FF_dump_xridge FIDs           Fmerges\n\
+ Fneighbors     FN_intersect   FOptions       Fp_coordinates FP_nearest\n\
+ FQhalf         Fsummary       Fv_halfspace   FMaple         Fx_non_redundant\n\
+\n\
+ Gvertices      Gpoints        Gall_points    Gno_planes     Ginner\n\
+ Gcentrums      Ghyperplanes   Gridges        Gouter         GDrop_dim\n\
+\n\
+ PArea_keep     Pdrop d0:0D0   Pgood          PFacet_area_keep\n\
+ PGood_neighbors PMerge_keep   Poutput_forced Pprecision_not\n\
+\n\
+ Qbk:0Bk:0_drop Qcoplanar      QG_half_good   Qi_redundant   QJoggle\n\
+ Qsearch_1st    Qtriangulate   QVertex_good\n\
+\n\
+ T4_trace       Tcheck_often   Tstatistics    Tverify        Tz_stdout\n\
+ TFacet_log     TInput_file    TPoint_trace   TMerge_trace   TOutput_file\n\
+ TWide_trace    TVertex_stop   TCone_stop\n\
+\n\
+ Angle_max      Centrum_size   Random_dist    Ucoplanar_max  Wide_outside\n\
+";
+
+/*-<a                             href="../libqhull/qh-qhull.htm#TOC"
+  >-------------------------------</a><a name="main">-</a>
+
+  main( argc, argv )
+    processes the command line, calls qhull() to do the work, and exits
+
+  design:
+    initializes data structures
+    reads points
+    finishes initialization
+    computes convex hull and other structures
+    checks the result
+    writes the output
+    frees memory
+*/
+int main(int argc, char *argv[]) {
+  int curlong, totlong; /* used !qh_NOmem */
+  int exitcode, numpoints, dim;
+  coordT *points;
+  boolT ismalloc;
+
+  QHULL_LIB_CHECK /* Check for compatible library */
+
+  if ((argc == 1) && isatty( 0 /*stdin*/)) {
+    fprintf(stdout, qh_prompt2, qh_version);
+    exit(qh_ERRnone);
+  }
+  if (argc > 1 && *argv[1] == '-' && !*(argv[1]+1)) {
+    fprintf(stdout, qh_prompta, qh_version,
+        qh_promptb, qh_promptc, qh_promptd, qh_prompte);
+    exit(qh_ERRnone);
+  }
+  if (argc > 1 && *argv[1] == '.' && !*(argv[1]+1)) {
+    fprintf(stdout, qh_prompt3, qh_version);
+    exit(qh_ERRnone);
+  }
+  if (argc > 1 && *argv[1] == '-' && *(argv[1]+1)=='V') {
+      fprintf(stdout, "%s\n", qh_version2);
+      exit(qh_ERRnone);
+  }
+  qh_init_A(stdin, stdout, stderr, argc, argv);  /* sets qh qhull_command */
+  exitcode= setjmp(qh errexit); /* simple statement for CRAY J916 */
+  if (!exitcode) {
+    qh NOerrexit = False;
+    qh_option("Halfspace", NULL, NULL);
+    qh HALFspace= True;    /* 'H'   */
+    qh_checkflags(qh qhull_command, hidden_options);
+    qh_initflags(qh qhull_command);
+    if (qh SCALEinput) {
+      fprintf(qh ferr, "\
+qhull error: options 'Qbk:n' and 'QBk:n' are not used with qhalf.\n\
+             Use 'Qbk:0Bk:0 to drop dimension k.\n");
+      qh_errexit(qh_ERRinput, NULL, NULL);
+    }
+    points= qh_readpoints(&numpoints, &dim, &ismalloc);
+    if (dim >= 5) {
+      qh_option("Qxact_merge", NULL, NULL);
+      qh MERGEexact= True; /* 'Qx' always */
+    }
+    qh_init_B(points, numpoints, dim, ismalloc);
+    qh_qhull();
+    qh_check_output();
+    qh_produce_output();
+    if (qh VERIFYoutput && !qh FORCEoutput && !qh STOPpoint && !qh STOPcone)
+      qh_check_points();
+    exitcode= qh_ERRnone;
+  }
+  qh NOerrexit= True;  /* no more setjmp */
+#ifdef qh_NOmem
+  qh_freeqhull(qh_ALL);
+#else
+  qh_freeqhull(!qh_ALL);
+  qh_memfreeshort(&curlong, &totlong);
+  if (curlong || totlong)
+    qh_fprintf_stderr(6263, "qhull internal warning (main): did not free %d bytes of long memory(%d pieces)\n",
+       totlong, curlong);
+#endif
+  return exitcode;
+} /* main */
+
diff --git a/xs/src/qhull/src/qhalf/qhalf.pro b/xs/src/qhull/src/qhalf/qhalf.pro
new file mode 100644
index 0000000000..ebad387893
--- /dev/null
+++ b/xs/src/qhull/src/qhalf/qhalf.pro
@@ -0,0 +1,9 @@
+# -------------------------------------------------
+# qhalf.pro -- Qt project file for qconvex.exe
+# -------------------------------------------------
+
+include(../qhull-app-c.pri)
+
+TARGET = qhalf
+
+SOURCES += qhalf.c
diff --git a/xs/src/qhull/src/qhalf/qhalf_r.c b/xs/src/qhull/src/qhalf/qhalf_r.c
new file mode 100644
index 0000000000..c49d777f95
--- /dev/null
+++ b/xs/src/qhull/src/qhalf/qhalf_r.c
@@ -0,0 +1,318 @@
+/*<html><pre>  -<a                             href="../libqhull/qh-qhull.htm"
+  >-------------------------------</a><a name="TOP">-</a>
+
+   qhalf.c
+     compute the intersection of halfspaces about a point
+
+   see unix.c for full interface
+
+   Copyright (c) 1993-2015, The Geometry Center
+*/
+
+#include "libqhull_r/libqhull_r.h"
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include <ctype.h>
+#include <math.h>
+
+#if __cplusplus
+extern "C" {
+  int isatty(int);
+}
+
+#elif _MSC_VER
+#include <io.h>
+#define isatty _isatty
+/* int _isatty(int); */
+
+#else
+int isatty(int);  /* returns 1 if stdin is a tty
+                   if "Undefined symbol" this can be deleted along with call in main() */
+#endif
+
+/*-<a                             href="../libqhull/qh-qhull.htm#TOC"
+  >-------------------------------</a><a name="prompt">-</a>
+
+  qh_prompt
+    long prompt for qhull
+
+  notes:
+    restricted version of libqhull.c
+
+  see:
+    concise prompt below
+*/
+
+/* duplicated in qhalf.htm */
+char hidden_options[]=" d n v Qbb QbB Qf Qg Qm Qr QR Qv Qx Qz TR E V Fa FA FC FD FS Ft FV Gt Q0 Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 ";
+
+char qh_prompta[]= "\n\
+qhalf- compute the intersection of halfspaces about a point\n\
+    http://www.qhull.org  %s\n\
+\n\
+input (stdin):\n\
+    optional interior point: dimension, 1, coordinates\n\
+    first lines: dimension+1 and number of halfspaces\n\
+    other lines: halfspace coefficients followed by offset\n\
+    comments:    start with a non-numeric character\n\
+\n\
+options:\n\
+    Hn,n - specify coordinates of interior point\n\
+    Qt   - triangulated output\n\
+    QJ   - joggled input instead of merged facets\n\
+    Qc   - keep coplanar halfspaces\n\
+    Qi   - keep other redundant halfspaces\n\
+\n\
+Qhull control options:\n\
+    QJn  - randomly joggle input in range [-n,n]\n\
+%s%s%s%s";  /* split up qh_prompt for Visual C++ */
+char qh_promptb[]= "\
+    Qbk:0Bk:0 - remove k-th coordinate from input\n\
+    Qs   - search all halfspaces for the initial simplex\n\
+    QGn  - print intersection if visible to halfspace n, -n for not\n\
+    QVn  - print intersections for halfspace n, -n if not\n\
+\n\
+";
+char qh_promptc[]= "\
+Trace options:\n\
+    T4   - trace at level n, 4=all, 5=mem/gauss, -1= events\n\
+    Tc   - check frequently during execution\n\
+    Ts   - print statistics\n\
+    Tv   - verify result: structure, convexity, and redundancy\n\
+    Tz   - send all output to stdout\n\
+    TFn  - report summary when n or more facets created\n\
+    TI file - input data from file, no spaces or single quotes\n\
+    TO file - output results to file, may be enclosed in single quotes\n\
+    TPn  - turn on tracing when halfspace n added to intersection\n\
+    TMn  - turn on tracing at merge n\n\
+    TWn  - trace merge facets when width > n\n\
+    TVn  - stop qhull after adding halfspace n, -n for before (see TCn)\n\
+    TCn  - stop qhull after building cone for halfspace n (see TVn)\n\
+\n\
+Precision options:\n\
+    Cn   - radius of centrum (roundoff added).  Merge facets if non-convex\n\
+     An  - cosine of maximum angle.  Merge facets if cosine > n or non-convex\n\
+           C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge\n\
+    Rn   - randomly perturb computations by a factor of [1-n,1+n]\n\
+    Un   - max distance below plane for a new, coplanar halfspace\n\
+    Wn   - min facet width for outside halfspace (before roundoff)\n\
+\n\
+Output formats (may be combined; if none, produces a summary to stdout):\n\
+    f    - facet dump\n\
+    G    - Geomview output (dual convex hull)\n\
+    i    - non-redundant halfspaces incident to each intersection\n\
+    m    - Mathematica output (dual convex hull)\n\
+    o    - OFF format (dual convex hull: dimension, points, and facets)\n\
+    p    - vertex coordinates of dual convex hull (coplanars if 'Qc' or 'Qi')\n\
+    s    - summary (stderr)\n\
+\n\
+";
+char qh_promptd[]= "\
+More formats:\n\
+    Fc   - count plus redundant halfspaces for each intersection\n\
+         -   Qc (default) for coplanar and Qi for other redundant\n\
+    Fd   - use cdd format for input (homogeneous with offset first)\n\
+    FF   - facet dump without ridges\n\
+    FI   - ID of each intersection\n\
+    Fm   - merge count for each intersection (511 max)\n\
+    FM   - Maple output (dual convex hull)\n\
+    Fn   - count plus neighboring intersections for each intersection\n\
+    FN   - count plus intersections for each non-redundant halfspace\n\
+    FO   - options and precision constants\n\
+    Fp   - dim, count, and intersection coordinates\n\
+    FP   - nearest halfspace and distance for each redundant halfspace\n\
+    FQ   - command used for qhalf\n\
+    Fs   - summary: #int (8), dim, #halfspaces, #non-redundant, #intersections\n\
+                      for output: #non-redundant, #intersections, #coplanar\n\
+                                  halfspaces, #non-simplicial intersections\n\
+                    #real (2), max outer plane, min vertex\n\
+    Fv   - count plus non-redundant halfspaces for each intersection\n\
+    Fx   - non-redundant halfspaces\n\
+\n\
+";
+char qh_prompte[]= "\
+Geomview output (2-d, 3-d and 4-d; dual convex hull)\n\
+    Ga   - all points (i.e., transformed halfspaces) as dots\n\
+     Gp  -  coplanar points and vertices as radii\n\
+     Gv  -  vertices (i.e., non-redundant halfspaces) as spheres\n\
+    Gi   - inner planes (i.e., halfspace intersections) only\n\
+     Gn  -  no planes\n\
+     Go  -  outer planes only\n\
+    Gc   - centrums\n\
+    Gh   - hyperplane intersections\n\
+    Gr   - ridges\n\
+    GDn  - drop dimension n in 3-d and 4-d output\n\
+\n\
+Print options:\n\
+    PAn  - keep n largest facets (i.e., intersections) by area\n\
+    Pdk:n- drop facet if normal[k] <= n (default 0.0)\n\
+    PDk:n- drop facet if normal[k] >= n\n\
+    Pg   - print good facets (needs 'QGn' or 'QVn')\n\
+    PFn  - keep facets whose area is at least n\n\
+    PG   - print neighbors of good facets\n\
+    PMn  - keep n facets with most merges\n\
+    Po   - force output.  If error, output neighborhood of facet\n\
+    Pp   - do not report precision problems\n\
+\n\
+    .    - list of all options\n\
+    -    - one line descriptions of all options\n\
+    -V   - version\n\
+";
+/* for opts, don't assign 'e' or 'E' to a flag (already used for exponent) */
+
+/*-<a                             href="../libqhull/qh-qhull.htm#TOC"
+  >-------------------------------</a><a name="prompt2">-</a>
+
+  qh_prompt2
+    synopsis for qhull
+*/
+char qh_prompt2[]= "\n\
+qhalf- halfspace intersection about a point.  Qhull %s\n\
+    input (stdin): [dim, 1, interior point], dim+1, n, coefficients+offset\n\
+    comments start with a non-numeric character\n\
+\n\
+options (qhalf.htm):\n\
+    Hn,n - specify coordinates of interior point\n\
+    Qt   - triangulated output\n\
+    QJ   - joggled input instead of merged facets\n\
+    Tv   - verify result: structure, convexity, and redundancy\n\
+    .    - concise list of all options\n\
+    -    - one-line description of all options\n\
+    -V   - version\n\
+\n\
+output options (subset):\n\
+    s    - summary of results (default)\n\
+    Fp   - intersection coordinates\n\
+    Fv   - non-redundant halfspaces incident to each intersection\n\
+    Fx   - non-redundant halfspaces\n\
+    o    - OFF file format (dual convex hull)\n\
+    G    - Geomview output (dual convex hull)\n\
+    m    - Mathematica output (dual convex hull)\n\
+    QVn  - print intersections for halfspace n, -n if not\n\
+    TO file - output results to file, may be enclosed in single quotes\n\
+\n\
+examples:\n\
+    rbox d | qconvex FQ n | qhalf s H0,0,0 Fp\n\
+    rbox c | qconvex FQ FV n | qhalf s i\n\
+    rbox c | qconvex FQ FV n | qhalf s o\n\
+\n\
+";
+/* for opts, don't assign 'e' or 'E' to a flag (already used for exponent) */
+
+/*-<a                             href="../libqhull/qh-qhull.htm#TOC"
+  >-------------------------------</a><a name="prompt3">-</a>
+
+  qh_prompt3
+    concise prompt for qhull
+*/
+char qh_prompt3[]= "\n\
+Qhull %s.\n\
+Except for 'F.' and 'PG', upper_case options take an argument.\n\
+\n\
+ incidences     Geomview       mathematica    OFF_format     point_dual\n\
+ summary        facet_dump\n\
+\n\
+ Fc_redundant   Fd_cdd_in      FF_dump_xridge FIDs           Fmerges\n\
+ Fneighbors     FN_intersect   FOptions       Fp_coordinates FP_nearest\n\
+ FQhalf         Fsummary       Fv_halfspace   FMaple         Fx_non_redundant\n\
+\n\
+ Gvertices      Gpoints        Gall_points    Gno_planes     Ginner\n\
+ Gcentrums      Ghyperplanes   Gridges        Gouter         GDrop_dim\n\
+\n\
+ PArea_keep     Pdrop d0:0D0   Pgood          PFacet_area_keep\n\
+ PGood_neighbors PMerge_keep   Poutput_forced Pprecision_not\n\
+\n\
+ Qbk:0Bk:0_drop Qcoplanar      QG_half_good   Qi_redundant   QJoggle\n\
+ Qsearch_1st    Qtriangulate   QVertex_good\n\
+\n\
+ T4_trace       Tcheck_often   Tstatistics    Tverify        Tz_stdout\n\
+ TFacet_log     TInput_file    TPoint_trace   TMerge_trace   TOutput_file\n\
+ TWide_trace    TVertex_stop   TCone_stop\n\
+\n\
+ Angle_max      Centrum_size   Random_dist    Ucoplanar_max  Wide_outside\n\
+";
+
+/*-<a                             href="../libqhull/qh-qhull.htm#TOC"
+  >-------------------------------</a><a name="main">-</a>
+
+  main( argc, argv )
+    processes the command line, calls qhull() to do the work, and exits
+
+  design:
+    initializes data structures
+    reads points
+    finishes initialization
+    computes convex hull and other structures
+    checks the result
+    writes the output
+    frees memory
+*/
+int main(int argc, char *argv[]) {
+  int curlong, totlong; /* used !qh_NOmem */
+  int exitcode, numpoints, dim;
+  coordT *points;
+  boolT ismalloc;
+  qhT qh_qh;
+  qhT *qh= &qh_qh;
+
+  QHULL_LIB_CHECK /* Check for compatible library */
+
+  if ((argc == 1) && isatty( 0 /*stdin*/)) {
+    fprintf(stdout, qh_prompt2, qh_version);
+    exit(qh_ERRnone);
+  }
+  if (argc > 1 && *argv[1] == '-' && !*(argv[1]+1)) {
+    fprintf(stdout, qh_prompta, qh_version,
+        qh_promptb, qh_promptc, qh_promptd, qh_prompte);
+    exit(qh_ERRnone);
+  }
+  if (argc > 1 && *argv[1] == '.' && !*(argv[1]+1)) {
+    fprintf(stdout, qh_prompt3, qh_version);
+    exit(qh_ERRnone);
+  }
+  if (argc > 1 && *argv[1] == '-' && *(argv[1]+1)=='V') {
+      fprintf(stdout, "%s\n", qh_version2);
+      exit(qh_ERRnone);
+  }
+  qh_init_A(qh, stdin, stdout, stderr, argc, argv);  /* sets qh->qhull_command */
+  exitcode= setjmp(qh->errexit); /* simple statement for CRAY J916 */
+  if (!exitcode) {
+    qh->NOerrexit = False;
+    qh_option(qh, "Halfspace", NULL, NULL);
+    qh->HALFspace= True;    /* 'H'   */
+    qh_checkflags(qh, qh->qhull_command, hidden_options);
+    qh_initflags(qh, qh->qhull_command);
+    if (qh->SCALEinput) {
+      fprintf(qh->ferr, "\
+qhull error: options 'Qbk:n' and 'QBk:n' are not used with qhalf.\n\
+             Use 'Qbk:0Bk:0 to drop dimension k.\n");
+      qh_errexit(qh, qh_ERRinput, NULL, NULL);
+    }
+    points= qh_readpoints(qh, &numpoints, &dim, &ismalloc);
+    if (dim >= 5) {
+      qh_option(qh, "Qxact_merge", NULL, NULL);
+      qh->MERGEexact= True; /* 'Qx' always */
+    }
+    qh_init_B(qh, points, numpoints, dim, ismalloc);
+    qh_qhull(qh);
+    qh_check_output(qh);
+    qh_produce_output(qh);
+    if (qh->VERIFYoutput && !qh->FORCEoutput && !qh->STOPpoint && !qh->STOPcone)
+      qh_check_points(qh);
+    exitcode= qh_ERRnone;
+  }
+  qh->NOerrexit= True;  /* no more setjmp */
+#ifdef qh_NOmem
+  qh_freeqhull(qh, qh_ALL);
+#else
+  qh_freeqhull(qh, !qh_ALL);
+  qh_memfreeshort(qh, &curlong, &totlong);
+  if (curlong || totlong)
+    qh_fprintf_stderr(6263, "qhull internal warning (main): did not free %d bytes of long memory(%d pieces)\n",
+       totlong, curlong);
+#endif
+  return exitcode;
+} /* main */
+
diff --git a/xs/src/qhull/src/qhull-all.pro b/xs/src/qhull/src/qhull-all.pro
new file mode 100644
index 0000000000..1d3a0ac6f3
--- /dev/null
+++ b/xs/src/qhull/src/qhull-all.pro
@@ -0,0 +1,94 @@
+# -------------------------------------------------
+# qhull-all.pro -- Qt project to build executables and static libraries
+#
+# To build with Qt on mingw
+#   Download Qt SDK, install Perl
+#   /c/qt/2010.05/qt> ./configure -static -platform win32-g++ -fast -no-qt3support
+#
+# To build DevStudio sln and proj files (Qhull ships with cmake derived files)
+# qmake is in Qt's bin directory
+# mkdir -p build && cd build && qmake -tp vc -r ../src/qhull-all.pro
+# Additional Library Directories -- C:\qt\Qt5.2.0\5.2.0\msvc2012_64\lib
+# libqhullcpp and libqhullstatic refered to $(QTDIR) but apparently didn't retrieve (should be %QTDIR%?)
+# libqhull_r also needs ..\..\lib
+# Need to change build/x64/Debug/*.lib to lib/ (or copy libs by hand, each time)
+# Additional Build Dependencies
+# See README.txt -- Need to add Build Dependencies, disable rtti, rename targets to qhull.dll, qhull6_p.dll and qhull6_pd.dll
+# -------------------------------------------------
+
+TEMPLATE = subdirs
+CONFIG += ordered
+
+SUBDIRS += libqhull_r      #shared library with reentrant code
+SUBDIRS += libqhullstatic  #static library
+SUBDIRS += libqhullstatic_r #static library with reentrant code
+SUBDIRS += libqhullcpp     #static library for C++ interface with libqhullstatic_r
+
+SUBDIRS += qhull           #qhull program linked to libqhullstatic_r
+SUBDIRS += rbox         
+SUBDIRS += qconvex         #qhull programs linked to libqhullstatic
+SUBDIRS += qdelaunay
+SUBDIRS += qhalf
+SUBDIRS += qvoronoi
+
+SUBDIRS += user_eg         #user programs linked to libqhull_r
+SUBDIRS += user_eg2  
+SUBDIRS += user_eg3        #user program with libqhullcpp and libqhullstatic_r
+
+SUBDIRS += qhulltest       #C++ test program with Qt, libqhullcpp, and libqhullstatic_r
+SUBDIRS += testqset        #test program for qset.c with mem.c
+SUBDIRS += testqset_r      #test program for qset_r.c with mem_r.c
+                           #See eg/q_test for qhull tests
+
+OTHER_FILES += Changes.txt
+OTHER_FILES += CMakeLists.txt
+OTHER_FILES += Make-config.sh
+OTHER_FILES += ../Announce.txt
+OTHER_FILES += ../CMakeLists.txt
+OTHER_FILES += ../COPYING.txt
+OTHER_FILES += ../File_id.diz
+OTHER_FILES += ../index.htm
+OTHER_FILES += ../Makefile
+OTHER_FILES += ../README.txt
+OTHER_FILES += ../REGISTER.txt
+OTHER_FILES += ../eg/q_eg
+OTHER_FILES += ../eg/q_egtest
+OTHER_FILES += ../eg/q_test
+OTHER_FILES += ../html/index.htm
+OTHER_FILES += ../html/qconvex.htm
+OTHER_FILES += ../html/qdelau_f.htm
+OTHER_FILES += ../html/qdelaun.htm
+OTHER_FILES += ../html/qhalf.htm
+OTHER_FILES += ../html/qh-code.htm
+OTHER_FILES += ../html/qh-eg.htm
+OTHER_FILES += ../html/qh-faq.htm
+OTHER_FILES += ../html/qh-get.htm
+OTHER_FILES += ../html/qh-impre.htm
+OTHER_FILES += ../html/qh-optc.htm
+OTHER_FILES += ../html/qh-optf.htm
+OTHER_FILES += ../html/qh-optg.htm
+OTHER_FILES += ../html/qh-opto.htm
+OTHER_FILES += ../html/qh-optp.htm
+OTHER_FILES += ../html/qh-optq.htm
+OTHER_FILES += ../html/qh-optt.htm
+OTHER_FILES += ../html/qh-quick.htm
+OTHER_FILES += ../html/qhull.htm
+OTHER_FILES += ../html/qhull.man
+OTHER_FILES += ../html/qhull.txt
+OTHER_FILES += ../html/qhull-cpp.xml
+OTHER_FILES += ../html/qvoron_f.htm
+OTHER_FILES += ../html/qvoronoi.htm
+OTHER_FILES += ../html/rbox.htm
+OTHER_FILES += ../html/rbox.man
+OTHER_FILES += ../html/rbox.txt
+OTHER_FILES += ../src/libqhull/Makefile
+OTHER_FILES += ../src/libqhull_r/Makefile
+OTHER_FILES += ../src/libqhull_r/qhull_r-exports.def
+OTHER_FILES += ../src/qconvex/qconvex_r.c
+OTHER_FILES += ../src/qdelaunay/qdelaun_r.c
+OTHER_FILES += ../src/qhalf/qhalf_r.c
+OTHER_FILES += ../src/qhull/rbox_r.c
+OTHER_FILES += ../src/qvoronoi/qvoronoi_r.c
+OTHER_FILES += ../src/qhull/unix.c
+OTHER_FILES += ../src/user_eg/user_eg.c
+OTHER_FILES += ../src/user_eg2/user_eg2.c
diff --git a/xs/src/qhull/src/qhull-app-c.pri b/xs/src/qhull/src/qhull-app-c.pri
new file mode 100644
index 0000000000..05e5a00f28
--- /dev/null
+++ b/xs/src/qhull/src/qhull-app-c.pri
@@ -0,0 +1,24 @@
+# -------------------------------------------------
+# qhull-app-c.pri -- Qt include project for C qhull applications linked to libqhull
+# -------------------------------------------------
+
+include(qhull-warn.pri)
+
+DESTDIR = ../../bin
+TEMPLATE = app
+CONFIG += console warn_on
+CONFIG -= qt
+
+LIBS += -L../../lib
+build_pass:CONFIG(debug, debug|release){
+   LIBS += -lqhullstatic_d
+   OBJECTS_DIR = Debug
+}else:build_pass:CONFIG(release, debug|release){
+   LIBS += -lqhullstatic
+   OBJECTS_DIR = Release
+}
+win32-msvc* : QMAKE_LFLAGS += /INCREMENTAL:NO
+
+INCLUDEPATH += ..
+CONFIG += qhull_warn_conversion
+
diff --git a/xs/src/qhull/src/qhull-app-c_r.pri b/xs/src/qhull/src/qhull-app-c_r.pri
new file mode 100644
index 0000000000..9c2ef5600b
--- /dev/null
+++ b/xs/src/qhull/src/qhull-app-c_r.pri
@@ -0,0 +1,26 @@
+# -------------------------------------------------
+# qhull-app-c_r.pri -- Qt include project for C qhull applications linked to qhullstatic_r
+#
+# It uses reentrant Qhull
+# -------------------------------------------------
+
+include(qhull-warn.pri)
+
+DESTDIR = ../../bin
+TEMPLATE = app
+CONFIG += console warn_on
+CONFIG -= qt
+
+LIBS += -L../../lib
+build_pass:CONFIG(debug, debug|release){
+   LIBS += -lqhullstatic_rd
+   OBJECTS_DIR = Debug
+}else:build_pass:CONFIG(release, debug|release){
+   LIBS += -lqhullstatic_r
+   OBJECTS_DIR = Release
+}
+win32-msvc* : QMAKE_LFLAGS += /INCREMENTAL:NO
+
+INCLUDEPATH += ..
+CONFIG += qhull_warn_conversion
+
diff --git a/xs/src/qhull/src/qhull-app-cpp.pri b/xs/src/qhull/src/qhull-app-cpp.pri
new file mode 100644
index 0000000000..a6f17d8ec4
--- /dev/null
+++ b/xs/src/qhull/src/qhull-app-cpp.pri
@@ -0,0 +1,23 @@
+# -------------------------------------------------
+# qhull-app-cpp.pri -- Qt include project for qhull as C++ classes
+# -------------------------------------------------
+
+include(qhull-warn.pri)
+
+DESTDIR = ../../bin
+TEMPLATE = app
+CONFIG += console warn_on
+CONFIG -= rtti
+LIBS += -L../../lib
+build_pass:CONFIG(debug, debug|release){
+   LIBS += -lqhullcpp_d
+   LIBS += -lqhullstatic_rd  # Must be last, otherwise qh_fprintf,etc. are loaded from here instead of qhullcpp-d.lib
+   OBJECTS_DIR = Debug
+}else:build_pass:CONFIG(release, debug|release){
+   LIBS += -lqhullcpp
+   LIBS += -lqhullstatic_r  # Must be last, otherwise qh_fprintf,etc. are loaded from here instead of qhullcpp.lib
+   OBJECTS_DIR = Release
+}
+win32-msvc* : QMAKE_LFLAGS += /INCREMENTAL:NO
+
+INCLUDEPATH += ../../src # "libqhull_r/qhull_a.h"
diff --git a/xs/src/qhull/src/qhull-app-shared.pri b/xs/src/qhull/src/qhull-app-shared.pri
new file mode 100644
index 0000000000..1f4026a6aa
--- /dev/null
+++ b/xs/src/qhull/src/qhull-app-shared.pri
@@ -0,0 +1,27 @@
+# -------------------------------------------------
+# qhull-app-shared.pri -- Deprecated Qt include project for C qhull applications linked with libqhull (shared library)
+# -------------------------------------------------
+
+include(qhull-warn.pri)
+
+DESTDIR = ../../bin
+TEMPLATE = app
+CONFIG += console warn_on
+CONFIG -= qt
+
+LIBS += -L../../lib
+build_pass:CONFIG(debug, debug|release){
+   LIBS += -lqhull_d
+   OBJECTS_DIR = Debug
+}else:build_pass:CONFIG(release, debug|release){
+   LIBS += -lqhull
+   OBJECTS_DIR = Release
+}
+win32-msvc* : QMAKE_LFLAGS += /INCREMENTAL:NO
+
+win32-msvc* : DEFINES += qh_dllimport # libqhull/user.h
+
+INCLUDEPATH += ../libqhull
+CONFIG += qhull_warn_conversion
+
+
diff --git a/xs/src/qhull/src/qhull-app-shared_r.pri b/xs/src/qhull/src/qhull-app-shared_r.pri
new file mode 100644
index 0000000000..e55c1a65f8
--- /dev/null
+++ b/xs/src/qhull/src/qhull-app-shared_r.pri
@@ -0,0 +1,29 @@
+# -------------------------------------------------
+# qhull-app-shared_r.pri -- Qt include project for C qhull applications linked with libqhull_r (shared library)
+#
+# It uses reentrant Qhull
+# -------------------------------------------------
+
+include(qhull-warn.pri)
+
+DESTDIR = ../../bin
+TEMPLATE = app
+CONFIG += console warn_on
+CONFIG -= qt
+
+LIBS += -L../../lib
+build_pass:CONFIG(debug, debug|release){
+   LIBS += -lqhull_rd
+   OBJECTS_DIR = Debug
+}else:build_pass:CONFIG(release, debug|release){
+   LIBS += -lqhull_r
+   OBJECTS_DIR = Release
+}
+win32-msvc* : QMAKE_LFLAGS += /INCREMENTAL:NO
+
+win32-msvc* : DEFINES += qh_dllimport # libqhull_r/user.h
+
+INCLUDEPATH += ..
+CONFIG += qhull_warn_conversion
+
+
diff --git a/xs/src/qhull/src/qhull-libqhull-src.pri b/xs/src/qhull/src/qhull-libqhull-src.pri
new file mode 100644
index 0000000000..e7aff3f781
--- /dev/null
+++ b/xs/src/qhull/src/qhull-libqhull-src.pri
@@ -0,0 +1,39 @@
+# -------------------------------------------------
+# qhull-libqhull-src.pri -- Qt include project for libqhull sources and headers
+#   libqhull.pro, libqhullp.pro, and libqhulldll.pro are the same for SOURCES and HEADERS
+# -------------------------------------------------
+
+# Order object files by frequency of execution.  Small files at end.
+# Current directory is caller
+
+# libqhull/libqhull.pro and ../qhull-libqhull-src.pri have the same SOURCES and HEADERS
+SOURCES += ../libqhull/global.c
+SOURCES += ../libqhull/stat.c
+SOURCES += ../libqhull/geom2.c
+SOURCES += ../libqhull/poly2.c
+SOURCES += ../libqhull/merge.c
+SOURCES += ../libqhull/libqhull.c
+SOURCES += ../libqhull/geom.c
+SOURCES += ../libqhull/poly.c
+SOURCES += ../libqhull/qset.c
+SOURCES += ../libqhull/mem.c
+SOURCES += ../libqhull/random.c
+SOURCES += ../libqhull/usermem.c
+SOURCES += ../libqhull/userprintf.c
+SOURCES += ../libqhull/io.c
+SOURCES += ../libqhull/user.c
+SOURCES += ../libqhull/rboxlib.c
+SOURCES += ../libqhull/userprintf_rbox.c
+
+# [2014] qmake locates the headers in the shadow build directory not the src directory
+HEADERS += ../libqhull/geom.h
+HEADERS += ../libqhull/io.h
+HEADERS += ../libqhull/libqhull.h
+HEADERS += ../libqhull/mem.h
+HEADERS += ../libqhull/merge.h
+HEADERS += ../libqhull/poly.h
+HEADERS += ../libqhull/random.h
+HEADERS += ../libqhull/qhull_a.h
+HEADERS += ../libqhull/qset.h
+HEADERS += ../libqhull/stat.h
+HEADERS += ../libqhull/user.h
diff --git a/xs/src/qhull/src/qhull-libqhull-src_r.pri b/xs/src/qhull/src/qhull-libqhull-src_r.pri
new file mode 100644
index 0000000000..3b53291b1b
--- /dev/null
+++ b/xs/src/qhull/src/qhull-libqhull-src_r.pri
@@ -0,0 +1,39 @@
+# -------------------------------------------------
+# qhull-libqhull-src_r.pri -- Qt include project for libqhull_r sources and headers
+#
+# It uses reentrant Qhull
+# -------------------------------------------------
+
+# Order object files by frequency of execution.  Small files at end.
+# Current directory is caller
+
+# libqhull_r/libqhull_r.pro and ../qhull-libqhull-src_r.pri have the same SOURCES and HEADERS
+SOURCES += ../libqhull_r/global_r.c
+SOURCES += ../libqhull_r/stat_r.c
+SOURCES += ../libqhull_r/geom2_r.c
+SOURCES += ../libqhull_r/poly2_r.c
+SOURCES += ../libqhull_r/merge_r.c
+SOURCES += ../libqhull_r/libqhull_r.c
+SOURCES += ../libqhull_r/geom_r.c
+SOURCES += ../libqhull_r/poly_r.c
+SOURCES += ../libqhull_r/qset_r.c
+SOURCES += ../libqhull_r/mem_r.c
+SOURCES += ../libqhull_r/random_r.c
+SOURCES += ../libqhull_r/usermem_r.c
+SOURCES += ../libqhull_r/userprintf_r.c
+SOURCES += ../libqhull_r/io_r.c
+SOURCES += ../libqhull_r/user_r.c
+SOURCES += ../libqhull_r/rboxlib_r.c
+SOURCES += ../libqhull_r/userprintf_rbox_r.c
+
+HEADERS += ../libqhull_r/geom_r.h
+HEADERS += ../libqhull_r/io_r.h
+HEADERS += ../libqhull_r/libqhull_r.h
+HEADERS += ../libqhull_r/mem_r.h
+HEADERS += ../libqhull_r/merge_r.h
+HEADERS += ../libqhull_r/poly_r.h
+HEADERS += ../libqhull_r/random_r.h
+HEADERS += ../libqhull_r/qhull_ra.h
+HEADERS += ../libqhull_r/qset_r.h
+HEADERS += ../libqhull_r/stat_r.h
+HEADERS += ../libqhull_r/user_r.h
diff --git a/xs/src/qhull/src/qhull-warn.pri b/xs/src/qhull/src/qhull-warn.pri
new file mode 100644
index 0000000000..7d0e7fa2f4
--- /dev/null
+++ b/xs/src/qhull/src/qhull-warn.pri
@@ -0,0 +1,57 @@
+# -------------------------------------------------
+# qhull-warn.pri -- Qt project warnings for warn_on
+#   CONFIG += qhull_warn_all        # Qhull compiles with all warnings except for qhull_warn_shadow and qhull_warn_conversion
+#   CONFIG += qhull_warn_conversion # Warn in Qt and Qhull about conversion errors
+#   CONFIG += qhull_warn_error      # Turn warnings into errors
+#   CONFIG += qhull_warn_shadow     # Warn in Qt about shadowing of functions and fields
+# -------------------------------------------------
+
+# [apr'11] VERSION works erratically for msvc builds
+# VERSION = 7.2.0
+qhull_SOVERSION = 7
+
+# Uncomment to report warnings as errors
+#CONFIG += qhull_warn_error
+
+*g++{
+    qhull_warn_error{
+        QMAKE_CFLAGS_WARN_ON += -Werror
+        QMAKE_CXXFLAGS_WARN_ON += -Werror
+    }
+
+    QMAKE_CFLAGS_WARN_ON += -Wcast-qual -Wextra -Wshadow -Wwrite-strings
+
+    QMAKE_CXXFLAGS_WARN_ON += -Wcast-qual -Wextra -Wwrite-strings
+    QMAKE_CXXFLAGS_WARN_ON += -Wno-sign-conversion
+
+    qhull_warn_shadow{
+        QMAKE_CXXFLAGS_WARN_ON += -Wshadow     # Shadowing occurs in Qt, e.g., nested foreach
+    }
+
+    qhull_warn_conversion{
+        QMAKE_CFLAGS_WARN_ON += -Wno-sign-conversion   # libqhullstatic has many size_t vs. int warnings
+        QMAKE_CFLAGS_WARN_ON += -Wconversion           # libqhullstatic has no workaround for bit-field conversions
+        QMAKE_CXXFLAGS_WARN_ON += -Wconversion         # Qt has conversion errors for qbitarray and qpalette
+    }
+
+    qhull_warn_all{
+        QMAKE_CFLAGS_WARN_ON += -Waddress -Warray-bounds -Wchar-subscripts -Wclobbered -Wcomment -Wempty-body
+        QMAKE_CFLAGS_WARN_ON += -Wformat -Wignored-qualifiers -Wimplicit-function-declaration -Wimplicit-int
+        QMAKE_CFLAGS_WARN_ON += -Wmain -Wmissing-braces -Wmissing-field-initializers -Wmissing-parameter-type
+        QMAKE_CFLAGS_WARN_ON += -Wnonnull -Wold-style-declaration -Woverride-init -Wparentheses
+        QMAKE_CFLAGS_WARN_ON += -Wpointer-sign -Wreturn-type -Wsequence-point -Wsign-compare
+        QMAKE_CFLAGS_WARN_ON += -Wsign-compare -Wstrict-aliasing -Wstrict-overflow=1 -Wswitch
+        QMAKE_CFLAGS_WARN_ON += -Wtrigraphs -Wtype-limits -Wuninitialized -Wuninitialized
+        QMAKE_CFLAGS_WARN_ON += -Wunknown-pragmas -Wunused-function -Wunused-label -Wunused-parameter
+        QMAKE_CFLAGS_WARN_ON += -Wunused-value -Wunused-variable -Wvolatile-register-var
+
+        QMAKE_CXXFLAGS_WARN_ON += -Waddress -Warray-bounds -Wc++0x-compat -Wchar-subscripts
+        QMAKE_CXXFLAGS_WARN_ON += -Wclobbered -Wcomment -Wempty-body -Wenum-compare
+        QMAKE_CXXFLAGS_WARN_ON += -Wformat -Wignored-qualifiers -Wmain -Wmissing-braces
+        QMAKE_CXXFLAGS_WARN_ON += -Wmissing-field-initializers -Wparentheses -Wreorder -Wreturn-type
+        QMAKE_CXXFLAGS_WARN_ON += -Wsequence-point -Wsign-compare -Wsign-compare -Wstrict-aliasing
+        QMAKE_CXXFLAGS_WARN_ON += -Wstrict-overflow=1 -Wswitch -Wtrigraphs -Wtype-limits
+        QMAKE_CXXFLAGS_WARN_ON += -Wuninitialized -Wunknown-pragmas -Wunused-function -Wunused-label
+        QMAKE_CXXFLAGS_WARN_ON += -Wunused-parameter -Wunused-value -Wunused-variable -Wvolatile-register-var
+    }
+}
diff --git a/xs/src/qhull/src/qhull/qhull.pro b/xs/src/qhull/src/qhull/qhull.pro
new file mode 100644
index 0000000000..8393728567
--- /dev/null
+++ b/xs/src/qhull/src/qhull/qhull.pro
@@ -0,0 +1,9 @@
+# -------------------------------------------------
+# qhull.pro -- Qt project file for qhull.exe with libqhullstatic_r
+# -------------------------------------------------
+
+include(../qhull-app-c_r.pri)
+
+TARGET = qhull
+
+SOURCES += unix_r.c
diff --git a/xs/src/qhull/src/qhull/unix.c b/xs/src/qhull/src/qhull/unix.c
new file mode 100644
index 0000000000..892a819c31
--- /dev/null
+++ b/xs/src/qhull/src/qhull/unix.c
@@ -0,0 +1,372 @@
+/*<html><pre>  -<a                             href="../libqhull/qh-qhull.htm"
+  >-------------------------------</a><a name="TOP">-</a>
+
+   unix.c
+     command line interface to qhull
+         includes SIOUX interface for Macintoshes
+
+   see qh-qhull.htm
+
+   Copyright (c) 1993-2015 The Geometry Center.
+   $Id: //main/2015/qhull/src/qhull/unix.c#4 $$Change: 2066 $
+   $DateTime: 2016/01/18 19:29:17 $$Author: bbarber $
+*/
+
+#include "libqhull/libqhull.h"
+#include "libqhull/qset.h"
+
+#include <ctype.h>
+#include <math.h>
+#include <string.h>
+#include <stdio.h>
+#include <stdlib.h>
+
+#if __cplusplus
+extern "C" {
+  int isatty(int);
+}
+
+#elif _MSC_VER
+#include <io.h>
+#define isatty _isatty
+/* int _isatty(int); */
+
+#else
+int isatty(int);  /* returns 1 if stdin is a tty
+                   if "Undefined symbol" this can be deleted along with call in main() */
+#endif
+
+/*-<a                             href="../libqhull/qh-qhull.htm#TOC"
+  >-------------------------------</a><a name="prompt">-</a>
+
+  qh_prompt
+    long prompt for qhull
+
+  see:
+    concise prompt below
+*/
+char qh_prompta[]= "\n\
+qhull- compute convex hulls and related structures.\n\
+    http://www.qhull.org  %s\n\
+\n\
+input (stdin):\n\
+    first lines: dimension and number of points (or vice-versa).\n\
+    other lines: point coordinates, best if one point per line\n\
+    comments:    start with a non-numeric character\n\
+    halfspaces:  use dim plus one and put offset after coefficients.\n\
+                 May be preceded by a single interior point ('H').\n\
+\n\
+options:\n\
+    d    - Delaunay triangulation by lifting points to a paraboloid\n\
+    d Qu - furthest-site Delaunay triangulation (upper convex hull)\n\
+    v    - Voronoi diagram (dual of the Delaunay triangulation)\n\
+    v Qu - furthest-site Voronoi diagram\n\
+    Hn,n,... - halfspace intersection about point [n,n,0,...]\n\
+    Qt   - triangulated output\n\
+    QJ   - joggled input instead of merged facets\n\
+    Qc   - keep coplanar points with nearest facet\n\
+    Qi   - keep interior points with nearest facet\n\
+\n\
+Qhull control options:\n\
+    Qbk:n   - scale coord k so that low bound is n\n\
+      QBk:n - scale coord k so that upper bound is n (QBk is %2.2g)\n\
+    QbB  - scale input to unit cube centered at the origin\n\
+    Qbb  - scale last coordinate to [0,m] for Delaunay triangulations\n\
+    Qbk:0Bk:0 - remove k-th coordinate from input\n\
+    QJn  - randomly joggle input in range [-n,n]\n\
+    QRn  - random rotation (n=seed, n=0 time, n=-1 time/no rotate)\n\
+%s%s%s%s";  /* split up qh_prompt for Visual C++ */
+char qh_promptb[]= "\
+    Qf   - partition point to furthest outside facet\n\
+    Qg   - only build good facets (needs 'QGn', 'QVn', or 'PdD')\n\
+    Qm   - only process points that would increase max_outside\n\
+    Qr   - process random outside points instead of furthest ones\n\
+    Qs   - search all points for the initial simplex\n\
+    Qu   - for 'd' or 'v', compute upper hull without point at-infinity\n\
+              returns furthest-site Delaunay triangulation\n\
+    Qv   - test vertex neighbors for convexity\n\
+    Qx   - exact pre-merges (skips coplanar and angle-coplanar facets)\n\
+    Qz   - add point-at-infinity to Delaunay triangulation\n\
+    QGn  - good facet if visible from point n, -n for not visible\n\
+    QVn  - good facet if it includes point n, -n if not\n\
+    Q0   - turn off default premerge with 'C-0'/'Qx'\n\
+    Q1     - sort merges by type instead of angle\n\
+    Q2   - merge all non-convex at once instead of independent sets\n\
+    Q3   - do not merge redundant vertices\n\
+    Q4   - avoid old->new merges\n\
+    Q5   - do not correct outer planes at end of qhull\n\
+    Q6   - do not pre-merge concave or coplanar facets\n\
+    Q7   - depth-first processing instead of breadth-first\n\
+    Q8   - do not process near-inside points\n\
+    Q9   - process furthest of furthest points\n\
+    Q10  - no special processing for narrow distributions\n\
+    Q11  - copy normals and recompute centrums for tricoplanar facets\n\
+    Q12  - no error on wide merge due to duplicate ridge\n\
+\n\
+";
+char qh_promptc[]= "\
+Topts- Trace options:\n\
+    T4   - trace at level n, 4=all, 5=mem/gauss, -1= events\n\
+    Ta   - annotate output with message codes\n\
+    Tc   - check frequently during execution\n\
+    Ts   - print statistics\n\
+    Tv   - verify result: structure, convexity, and point inclusion\n\
+    Tz   - send all output to stdout\n\
+    TFn  - report summary when n or more facets created\n\
+    TI file - input data from file, no spaces or single quotes\n\
+    TO file - output results to file, may be enclosed in single quotes\n\
+    TPn  - turn on tracing when point n added to hull\n\
+     TMn - turn on tracing at merge n\n\
+     TWn - trace merge facets when width > n\n\
+    TRn  - rerun qhull n times.  Use with 'QJn'\n\
+    TVn  - stop qhull after adding point n, -n for before (see TCn)\n\
+     TCn - stop qhull after building cone for point n (see TVn)\n\
+\n\
+Precision options:\n\
+    Cn   - radius of centrum (roundoff added).  Merge facets if non-convex\n\
+     An  - cosine of maximum angle.  Merge facets if cosine > n or non-convex\n\
+           C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge\n\
+    En   - max roundoff error for distance computation\n\
+    Rn   - randomly perturb computations by a factor of [1-n,1+n]\n\
+    Vn   - min distance above plane for a visible facet (default 3C-n or En)\n\
+    Un   - max distance below plane for a new, coplanar point (default Vn)\n\
+    Wn   - min facet width for outside point (before roundoff, default 2Vn)\n\
+\n\
+Output formats (may be combined; if none, produces a summary to stdout):\n\
+    f    - facet dump\n\
+    G    - Geomview output (see below)\n\
+    i    - vertices incident to each facet\n\
+    m    - Mathematica output (2-d and 3-d)\n\
+    o    - OFF format (dim, points and facets; Voronoi regions)\n\
+    n    - normals with offsets\n\
+    p    - vertex coordinates or Voronoi vertices (coplanar points if 'Qc')\n\
+    s    - summary (stderr)\n\
+\n\
+";
+char qh_promptd[]= "\
+More formats:\n\
+    Fa   - area for each facet\n\
+    FA   - compute total area and volume for option 's'\n\
+    Fc   - count plus coplanar points for each facet\n\
+           use 'Qc' (default) for coplanar and 'Qi' for interior\n\
+    FC   - centrum or Voronoi center for each facet\n\
+    Fd   - use cdd format for input (homogeneous with offset first)\n\
+    FD   - use cdd format for numeric output (offset first)\n\
+    FF   - facet dump without ridges\n\
+    Fi   - inner plane for each facet\n\
+           for 'v', separating hyperplanes for bounded Voronoi regions\n\
+    FI   - ID of each facet\n\
+    Fm   - merge count for each facet (511 max)\n\
+    FM   - Maple output (2-d and 3-d)\n\
+    Fn   - count plus neighboring facets for each facet\n\
+    FN   - count plus neighboring facets for each point\n\
+    Fo   - outer plane (or max_outside) for each facet\n\
+           for 'v', separating hyperplanes for unbounded Voronoi regions\n\
+    FO   - options and precision constants\n\
+    Fp   - dim, count, and intersection coordinates (halfspace only)\n\
+    FP   - nearest vertex and distance for each coplanar point\n\
+    FQ   - command used for qhull\n\
+    Fs   - summary: #int (8), dimension, #points, tot vertices, tot facets,\n\
+                      output: #vertices, #facets, #coplanars, #nonsimplicial\n\
+                    #real (2), max outer plane, min vertex\n\
+    FS   - sizes:   #int (0)\n\
+                    #real (2) tot area, tot volume\n\
+    Ft   - triangulation with centrums for non-simplicial facets (OFF format)\n\
+    Fv   - count plus vertices for each facet\n\
+           for 'v', Voronoi diagram as Voronoi vertices for pairs of sites\n\
+    FV   - average of vertices (a feasible point for 'H')\n\
+    Fx   - extreme points (in order for 2-d)\n\
+\n\
+";
+char qh_prompte[]= "\
+Geomview options (2-d, 3-d, and 4-d; 2-d Voronoi)\n\
+    Ga   - all points as dots\n\
+     Gp  -  coplanar points and vertices as radii\n\
+     Gv  -  vertices as spheres\n\
+    Gi   - inner planes only\n\
+     Gn  -  no planes\n\
+     Go  -  outer planes only\n\
+    Gc   - centrums\n\
+    Gh   - hyperplane intersections\n\
+    Gr   - ridges\n\
+    GDn  - drop dimension n in 3-d and 4-d output\n\
+    Gt   - for 3-d 'd', transparent outer ridges\n\
+\n\
+Print options:\n\
+    PAn  - keep n largest facets by area\n\
+    Pdk:n - drop facet if normal[k] <= n (default 0.0)\n\
+    PDk:n - drop facet if normal[k] >= n\n\
+    Pg   - print good facets (needs 'QGn' or 'QVn')\n\
+    PFn  - keep facets whose area is at least n\n\
+    PG   - print neighbors of good facets\n\
+    PMn  - keep n facets with most merges\n\
+    Po   - force output.  If error, output neighborhood of facet\n\
+    Pp   - do not report precision problems\n\
+\n\
+    .    - list of all options\n\
+    -    - one line descriptions of all options\n\
+    -V   - version\n\
+";
+/* for opts, don't assign 'e' or 'E' to a flag (already used for exponent) */
+
+/*-<a                             href="../libqhull/qh-qhull.htm#TOC"
+  >-------------------------------</a><a name="prompt2">-</a>
+
+  qh_prompt2
+    synopsis for qhull
+*/
+char qh_prompt2[]= "\n\
+qhull- compute convex hulls and related structures.  Qhull %s\n\
+    input (stdin): dimension, n, point coordinates\n\
+    comments start with a non-numeric character\n\
+    halfspace: use dim+1 and put offsets after coefficients\n\
+\n\
+options (qh-quick.htm):\n\
+    d    - Delaunay triangulation by lifting points to a paraboloid\n\
+    d Qu - furthest-site Delaunay triangulation (upper convex hull)\n\
+    v    - Voronoi diagram as the dual of the Delaunay triangulation\n\
+    v Qu - furthest-site Voronoi diagram\n\
+    H1,1 - Halfspace intersection about [1,1,0,...] via polar duality\n\
+    Qt   - triangulated output\n\
+    QJ   - joggled input instead of merged facets\n\
+    Tv   - verify result: structure, convexity, and point inclusion\n\
+    .    - concise list of all options\n\
+    -    - one-line description of each option\n\
+    -V   - version\n\
+\n\
+Output options (subset):\n\
+    s    - summary of results (default)\n\
+    i    - vertices incident to each facet\n\
+    n    - normals with offsets\n\
+    p    - vertex coordinates (if 'Qc', includes coplanar points)\n\
+           if 'v', Voronoi vertices\n\
+    Fp   - halfspace intersections\n\
+    Fx   - extreme points (convex hull vertices)\n\
+    FA   - compute total area and volume\n\
+    o    - OFF format (if 'v', outputs Voronoi regions)\n\
+    G    - Geomview output (2-d, 3-d and 4-d)\n\
+    m    - Mathematica output (2-d and 3-d)\n\
+    QVn  - print facets that include point n, -n if not\n\
+    TO file- output results to file, may be enclosed in single quotes\n\
+\n\
+examples:\n\
+    rbox D4 | qhull Tv                        rbox 1000 s | qhull Tv s FA\n\
+    rbox 10 D2 | qhull d QJ s i TO result     rbox 10 D2 | qhull v Qbb Qt p\n\
+    rbox 10 D2 | qhull d Qu QJ m              rbox 10 D2 | qhull v Qu QJ o\n\
+    rbox c d D2 | qhull Qc s f Fx | more      rbox c | qhull FV n | qhull H Fp\n\
+    rbox d D12 | qhull QR0 FA                 rbox c D7 | qhull FA TF1000\n\
+    rbox y 1000 W0 | qhull                    rbox c | qhull n\n\
+\n\
+";
+/* for opts, don't assign 'e' or 'E' to a flag (already used for exponent) */
+
+/*-<a                             href="../libqhull/qh-qhull.htm#TOC"
+  >-------------------------------</a><a name="prompt3">-</a>
+
+  qh_prompt3
+    concise prompt for qhull
+*/
+char qh_prompt3[]= "\n\
+Qhull %s.\n\
+Except for 'F.' and 'PG', upper-case options take an argument.\n\
+\n\
+ delaunay       voronoi        Geomview       Halfspace      facet_dump\n\
+ incidences     mathematica    normals        OFF_format     points\n\
+ summary\n\
+\n\
+ Farea          FArea-total    Fcoplanars     FCentrums      Fd-cdd-in\n\
+ FD-cdd-out     FF-dump-xridge Finner         FIDs           Fmerges\n\
+ Fneighbors     FNeigh-vertex  Fouter         FOptions       Fpoint-intersect\n\
+ FPoint_near    FQhull         Fsummary       FSize          Ftriangles\n\
+ Fvertices      Fvoronoi       FVertex-ave    Fxtremes       FMaple\n\
+\n\
+ Gvertices      Gpoints        Gall_points    Gno_planes     Ginner\n\
+ Gcentrums      Ghyperplanes   Gridges        Gouter         GDrop_dim\n\
+ Gtransparent\n\
+\n\
+ PArea-keep     Pdrop d0:0D0   Pgood          PFacet_area_keep\n\
+ PGood_neighbors PMerge-keep   Poutput_forced Pprecision_not\n\
+\n\
+ QbBound 0:0.5  Qbk:0Bk:0_drop QbB-scale-box  Qbb-scale-last Qcoplanar\n\
+ Qfurthest      Qgood_only     QGood_point    Qinterior      Qmax_out\n\
+ QJoggle        Qrandom        QRotate        Qsearch_1st    Qtriangulate\n\
+ QupperDelaunay QVertex_good   Qvneighbors    Qxact_merge    Qzinfinite\n\
+\n\
+ Q0_no_premerge Q1_no_angle    Q2_no_independ Q3_no_redundant Q4_no_old\n\
+ Q5_no_check_out Q6_no_concave Q7_depth_first Q8_no_near_in  Q9_pick_furthest\n\
+ Q10_no_narrow  Q11_trinormals Q12_no_wide_dup\n\
+\n\
+ T4_trace       Tannotate      Tcheck_often   Tstatistics    Tverify\n\
+ Tz_stdout      TFacet_log     TInput_file    TPoint_trace   TMerge_trace\n\
+ TOutput_file   TRerun         TWide_trace    TVertex_stop   TCone_stop\n\
+\n\
+ Angle_max      Centrum_size   Error_round    Random_dist    Visible_min\n\
+ Ucoplanar_max  Wide_outside\n\
+";
+
+/*-<a                             href="../libqhull/qh-qhull.htm#TOC"
+  >-------------------------------</a><a name="main">-</a>
+
+  main( argc, argv )
+    processes the command line, calls qhull() to do the work, and exits
+
+  design:
+    initializes data structures
+    reads points
+    finishes initialization
+    computes convex hull and other structures
+    checks the result
+    writes the output
+    frees memory
+*/
+int main(int argc, char *argv[]) {
+  int curlong, totlong; /* used !qh_NOmem */
+  int exitcode, numpoints, dim;
+  coordT *points;
+  boolT ismalloc;
+
+  QHULL_LIB_CHECK /* Check for compatible library */
+
+  if ((argc == 1) && isatty( 0 /*stdin*/)) {
+    fprintf(stdout, qh_prompt2, qh_version);
+    exit(qh_ERRnone);
+  }
+  if (argc > 1 && *argv[1] == '-' && !*(argv[1]+1)) {
+    fprintf(stdout, qh_prompta, qh_version, qh_DEFAULTbox,
+                qh_promptb, qh_promptc, qh_promptd, qh_prompte);
+    exit(qh_ERRnone);
+  }
+  if (argc > 1 && *argv[1] == '.' && !*(argv[1]+1)) {
+    fprintf(stdout, qh_prompt3, qh_version);
+    exit(qh_ERRnone);
+  }
+  if (argc > 1 && *argv[1] == '-' && *(argv[1]+1)=='V') {
+      fprintf(stdout, "%s\n", qh_version2);
+      exit(qh_ERRnone);
+  }
+  qh_init_A(stdin, stdout, stderr, argc, argv);  /* sets qh qhull_command */
+  exitcode= setjmp(qh errexit); /* simple statement for CRAY J916 */
+  if (!exitcode) {
+    qh_initflags(qh qhull_command);
+    points= qh_readpoints(&numpoints, &dim, &ismalloc);
+    qh_init_B(points, numpoints, dim, ismalloc);
+    qh_qhull();
+    qh_check_output();
+    qh_produce_output();
+    if (qh VERIFYoutput && !qh FORCEoutput && !qh STOPpoint && !qh STOPcone)
+      qh_check_points();
+    exitcode= qh_ERRnone;
+  }
+  qh NOerrexit= True;  /* no more setjmp */
+#ifdef qh_NOmem
+  qh_freeqhull( qh_ALL);
+#else
+  qh_freeqhull( !qh_ALL);
+  qh_memfreeshort(&curlong, &totlong);
+  if (curlong || totlong)
+    qh_fprintf_stderr(6263, "qhull internal warning (main): did not free %d bytes of long memory(%d pieces)\n",
+       totlong, curlong);
+#endif
+  return exitcode;
+} /* main */
+
diff --git a/xs/src/qhull/src/qhull/unix_r.c b/xs/src/qhull/src/qhull/unix_r.c
new file mode 100644
index 0000000000..3f999f7fa9
--- /dev/null
+++ b/xs/src/qhull/src/qhull/unix_r.c
@@ -0,0 +1,374 @@
+/*<html><pre>  -<a                             href="../libqhull/qh-qhull.htm"
+  >-------------------------------</a><a name="TOP">-</a>
+
+   unix.c
+     command line interface to qhull
+         includes SIOUX interface for Macintoshes
+
+   see qh-qhull.htm
+
+   Copyright (c) 1993-2015 The Geometry Center.
+   $Id: //main/2015/qhull/src/qhull/unix_r.c#6 $$Change: 2066 $
+   $DateTime: 2016/01/18 19:29:17 $$Author: bbarber $
+*/
+
+#include "libqhull_r/libqhull_r.h"
+
+#include <ctype.h>
+#include <math.h>
+#include <string.h>
+#include <stdio.h>
+#include <stdlib.h>
+
+#if __cplusplus
+extern "C" {
+  int isatty(int);
+}
+
+#elif _MSC_VER
+#include <io.h>
+#define isatty _isatty
+/* int _isatty(int); */
+
+#else
+int isatty(int);  /* returns 1 if stdin is a tty
+                   if "Undefined symbol" this can be deleted along with call in main() */
+#endif
+
+/*-<a                             href="../libqhull/qh-qhull.htm#TOC"
+  >-------------------------------</a><a name="prompt">-</a>
+
+  qh_prompt
+    long prompt for qhull
+
+  see:
+    concise prompt below
+*/
+char qh_prompta[]= "\n\
+qhull- compute convex hulls and related structures.\n\
+    http://www.qhull.org  %s\n\
+\n\
+input (stdin):\n\
+    first lines: dimension and number of points (or vice-versa).\n\
+    other lines: point coordinates, best if one point per line\n\
+    comments:    start with a non-numeric character\n\
+    halfspaces:  use dim plus one and put offset after coefficients.\n\
+                 May be preceded by a single interior point ('H').\n\
+\n\
+options:\n\
+    d    - Delaunay triangulation by lifting points to a paraboloid\n\
+    d Qu - furthest-site Delaunay triangulation (upper convex hull)\n\
+    v    - Voronoi diagram (dual of the Delaunay triangulation)\n\
+    v Qu - furthest-site Voronoi diagram\n\
+    Hn,n,... - halfspace intersection about point [n,n,0,...]\n\
+    Qt   - triangulated output\n\
+    QJ   - joggled input instead of merged facets\n\
+    Qc   - keep coplanar points with nearest facet\n\
+    Qi   - keep interior points with nearest facet\n\
+\n\
+Qhull control options:\n\
+    Qbk:n   - scale coord k so that low bound is n\n\
+      QBk:n - scale coord k so that upper bound is n (QBk is %2.2g)\n\
+    QbB  - scale input to unit cube centered at the origin\n\
+    Qbb  - scale last coordinate to [0,m] for Delaunay triangulations\n\
+    Qbk:0Bk:0 - remove k-th coordinate from input\n\
+    QJn  - randomly joggle input in range [-n,n]\n\
+    QRn  - random rotation (n=seed, n=0 time, n=-1 time/no rotate)\n\
+%s%s%s%s";  /* split up qh_prompt for Visual C++ */
+char qh_promptb[]= "\
+    Qf   - partition point to furthest outside facet\n\
+    Qg   - only build good facets (needs 'QGn', 'QVn', or 'PdD')\n\
+    Qm   - only process points that would increase max_outside\n\
+    Qr   - process random outside points instead of furthest ones\n\
+    Qs   - search all points for the initial simplex\n\
+    Qu   - for 'd' or 'v', compute upper hull without point at-infinity\n\
+              returns furthest-site Delaunay triangulation\n\
+    Qv   - test vertex neighbors for convexity\n\
+    Qx   - exact pre-merges (skips coplanar and angle-coplanar facets)\n\
+    Qz   - add point-at-infinity to Delaunay triangulation\n\
+    QGn  - good facet if visible from point n, -n for not visible\n\
+    QVn  - good facet if it includes point n, -n if not\n\
+    Q0   - turn off default premerge with 'C-0'/'Qx'\n\
+    Q1     - sort merges by type instead of angle\n\
+    Q2   - merge all non-convex at once instead of independent sets\n\
+    Q3   - do not merge redundant vertices\n\
+    Q4   - avoid old->new merges\n\
+    Q5   - do not correct outer planes at end of qhull\n\
+    Q6   - do not pre-merge concave or coplanar facets\n\
+    Q7   - depth-first processing instead of breadth-first\n\
+    Q8   - do not process near-inside points\n\
+    Q9   - process furthest of furthest points\n\
+    Q10  - no special processing for narrow distributions\n\
+    Q11  - copy normals and recompute centrums for tricoplanar facets\n\
+    Q12  - no error on wide merge due to duplicate ridge\n\
+\n\
+";
+char qh_promptc[]= "\
+Topts- Trace options:\n\
+    T4   - trace at level n, 4=all, 5=mem/gauss, -1= events\n\
+    Ta   - annotate output with message codes\n\
+    Tc   - check frequently during execution\n\
+    Ts   - print statistics\n\
+    Tv   - verify result: structure, convexity, and point inclusion\n\
+    Tz   - send all output to stdout\n\
+    TFn  - report summary when n or more facets created\n\
+    TI file - input data from file, no spaces or single quotes\n\
+    TO file - output results to file, may be enclosed in single quotes\n\
+    TPn  - turn on tracing when point n added to hull\n\
+     TMn - turn on tracing at merge n\n\
+     TWn - trace merge facets when width > n\n\
+    TRn  - rerun qhull n times.  Use with 'QJn'\n\
+    TVn  - stop qhull after adding point n, -n for before (see TCn)\n\
+     TCn - stop qhull after building cone for point n (see TVn)\n\
+\n\
+Precision options:\n\
+    Cn   - radius of centrum (roundoff added).  Merge facets if non-convex\n\
+     An  - cosine of maximum angle.  Merge facets if cosine > n or non-convex\n\
+           C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge\n\
+    En   - max roundoff error for distance computation\n\
+    Rn   - randomly perturb computations by a factor of [1-n,1+n]\n\
+    Vn   - min distance above plane for a visible facet (default 3C-n or En)\n\
+    Un   - max distance below plane for a new, coplanar point (default Vn)\n\
+    Wn   - min facet width for outside point (before roundoff, default 2Vn)\n\
+\n\
+Output formats (may be combined; if none, produces a summary to stdout):\n\
+    f    - facet dump\n\
+    G    - Geomview output (see below)\n\
+    i    - vertices incident to each facet\n\
+    m    - Mathematica output (2-d and 3-d)\n\
+    o    - OFF format (dim, points and facets; Voronoi regions)\n\
+    n    - normals with offsets\n\
+    p    - vertex coordinates or Voronoi vertices (coplanar points if 'Qc')\n\
+    s    - summary (stderr)\n\
+\n\
+";
+char qh_promptd[]= "\
+More formats:\n\
+    Fa   - area for each facet\n\
+    FA   - compute total area and volume for option 's'\n\
+    Fc   - count plus coplanar points for each facet\n\
+           use 'Qc' (default) for coplanar and 'Qi' for interior\n\
+    FC   - centrum or Voronoi center for each facet\n\
+    Fd   - use cdd format for input (homogeneous with offset first)\n\
+    FD   - use cdd format for numeric output (offset first)\n\
+    FF   - facet dump without ridges\n\
+    Fi   - inner plane for each facet\n\
+           for 'v', separating hyperplanes for bounded Voronoi regions\n\
+    FI   - ID of each facet\n\
+    Fm   - merge count for each facet (511 max)\n\
+    FM   - Maple output (2-d and 3-d)\n\
+    Fn   - count plus neighboring facets for each facet\n\
+    FN   - count plus neighboring facets for each point\n\
+    Fo   - outer plane (or max_outside) for each facet\n\
+           for 'v', separating hyperplanes for unbounded Voronoi regions\n\
+    FO   - options and precision constants\n\
+    Fp   - dim, count, and intersection coordinates (halfspace only)\n\
+    FP   - nearest vertex and distance for each coplanar point\n\
+    FQ   - command used for qhull\n\
+    Fs   - summary: #int (8), dimension, #points, tot vertices, tot facets,\n\
+                      output: #vertices, #facets, #coplanars, #nonsimplicial\n\
+                    #real (2), max outer plane, min vertex\n\
+    FS   - sizes:   #int (0)\n\
+                    #real (2) tot area, tot volume\n\
+    Ft   - triangulation with centrums for non-simplicial facets (OFF format)\n\
+    Fv   - count plus vertices for each facet\n\
+           for 'v', Voronoi diagram as Voronoi vertices for pairs of sites\n\
+    FV   - average of vertices (a feasible point for 'H')\n\
+    Fx   - extreme points (in order for 2-d)\n\
+\n\
+";
+char qh_prompte[]= "\
+Geomview options (2-d, 3-d, and 4-d; 2-d Voronoi)\n\
+    Ga   - all points as dots\n\
+     Gp  -  coplanar points and vertices as radii\n\
+     Gv  -  vertices as spheres\n\
+    Gi   - inner planes only\n\
+     Gn  -  no planes\n\
+     Go  -  outer planes only\n\
+    Gc   - centrums\n\
+    Gh   - hyperplane intersections\n\
+    Gr   - ridges\n\
+    GDn  - drop dimension n in 3-d and 4-d output\n\
+    Gt   - for 3-d 'd', transparent outer ridges\n\
+\n\
+Print options:\n\
+    PAn  - keep n largest facets by area\n\
+    Pdk:n - drop facet if normal[k] <= n (default 0.0)\n\
+    PDk:n - drop facet if normal[k] >= n\n\
+    Pg   - print good facets (needs 'QGn' or 'QVn')\n\
+    PFn  - keep facets whose area is at least n\n\
+    PG   - print neighbors of good facets\n\
+    PMn  - keep n facets with most merges\n\
+    Po   - force output.  If error, output neighborhood of facet\n\
+    Pp   - do not report precision problems\n\
+\n\
+    .    - list of all options\n\
+    -    - one line descriptions of all options\n\
+    -V   - version\n\
+";
+/* for opts, don't assign 'e' or 'E' to a flag (already used for exponent) */
+
+/*-<a                             href="../libqhull/qh-qhull.htm#TOC"
+  >-------------------------------</a><a name="prompt2">-</a>
+
+  qh_prompt2
+    synopsis for qhull
+*/
+char qh_prompt2[]= "\n\
+qhull- compute convex hulls and related structures.  Qhull %s\n\
+    input (stdin): dimension, n, point coordinates\n\
+    comments start with a non-numeric character\n\
+    halfspace: use dim+1 and put offsets after coefficients\n\
+\n\
+options (qh-quick.htm):\n\
+    d    - Delaunay triangulation by lifting points to a paraboloid\n\
+    d Qu - furthest-site Delaunay triangulation (upper convex hull)\n\
+    v    - Voronoi diagram as the dual of the Delaunay triangulation\n\
+    v Qu - furthest-site Voronoi diagram\n\
+    H1,1 - Halfspace intersection about [1,1,0,...] via polar duality\n\
+    Qt   - triangulated output\n\
+    QJ   - joggled input instead of merged facets\n\
+    Tv   - verify result: structure, convexity, and point inclusion\n\
+    .    - concise list of all options\n\
+    -    - one-line description of each option\n\
+    -V   - version\n\
+\n\
+Output options (subset):\n\
+    s    - summary of results (default)\n\
+    i    - vertices incident to each facet\n\
+    n    - normals with offsets\n\
+    p    - vertex coordinates (if 'Qc', includes coplanar points)\n\
+           if 'v', Voronoi vertices\n\
+    Fp   - halfspace intersections\n\
+    Fx   - extreme points (convex hull vertices)\n\
+    FA   - compute total area and volume\n\
+    o    - OFF format (if 'v', outputs Voronoi regions)\n\
+    G    - Geomview output (2-d, 3-d and 4-d)\n\
+    m    - Mathematica output (2-d and 3-d)\n\
+    QVn  - print facets that include point n, -n if not\n\
+    TO file- output results to file, may be enclosed in single quotes\n\
+\n\
+examples:\n\
+    rbox D4 | qhull Tv                        rbox 1000 s | qhull Tv s FA\n\
+    rbox 10 D2 | qhull d QJ s i TO result     rbox 10 D2 | qhull v Qbb Qt p\n\
+    rbox 10 D2 | qhull d Qu QJ m              rbox 10 D2 | qhull v Qu QJ o\n\
+    rbox c d D2 | qhull Qc s f Fx | more      rbox c | qhull FV n | qhull H Fp\n\
+    rbox d D12 | qhull QR0 FA                 rbox c D7 | qhull FA TF1000\n\
+    rbox y 1000 W0 | qhull                    rbox c | qhull n\n\
+\n\
+";
+/* for opts, don't assign 'e' or 'E' to a flag (already used for exponent) */
+
+/*-<a                             href="../libqhull/qh-qhull.htm#TOC"
+  >-------------------------------</a><a name="prompt3">-</a>
+
+  qh_prompt3
+    concise prompt for qhull
+*/
+char qh_prompt3[]= "\n\
+Qhull %s.\n\
+Except for 'F.' and 'PG', upper-case options take an argument.\n\
+\n\
+ delaunay       voronoi        Geomview       Halfspace      facet_dump\n\
+ incidences     mathematica    normals        OFF_format     points\n\
+ summary\n\
+\n\
+ Farea          FArea-total    Fcoplanars     FCentrums      Fd-cdd-in\n\
+ FD-cdd-out     FF-dump-xridge Finner         FIDs           Fmerges\n\
+ Fneighbors     FNeigh-vertex  Fouter         FOptions       Fpoint-intersect\n\
+ FPoint_near    FQhull         Fsummary       FSize          Ftriangles\n\
+ Fvertices      Fvoronoi       FVertex-ave    Fxtremes       FMaple\n\
+\n\
+ Gvertices      Gpoints        Gall_points    Gno_planes     Ginner\n\
+ Gcentrums      Ghyperplanes   Gridges        Gouter         GDrop_dim\n\
+ Gtransparent\n\
+\n\
+ PArea-keep     Pdrop d0:0D0   Pgood          PFacet_area_keep\n\
+ PGood_neighbors PMerge-keep   Poutput_forced Pprecision_not\n\
+\n\
+ QbBound 0:0.5  Qbk:0Bk:0_drop QbB-scale-box  Qbb-scale-last Qcoplanar\n\
+ Qfurthest      Qgood_only     QGood_point    Qinterior      Qmax_out\n\
+ QJoggle        Qrandom        QRotate        Qsearch_1st    Qtriangulate\n\
+ QupperDelaunay QVertex_good   Qvneighbors    Qxact_merge    Qzinfinite\n\
+\n\
+ Q0_no_premerge Q1_no_angle    Q2_no_independ Q3_no_redundant Q4_no_old\n\
+ Q5_no_check_out Q6_no_concave Q7_depth_first Q8_no_near_in  Q9_pick_furthest\n\
+ Q10_no_narrow  Q11_trinormals Q12_no_wide_dup\n\
+\n\
+ T4_trace       Tannotate      Tcheck_often   Tstatistics    Tverify\n\
+ Tz_stdout      TFacet_log     TInput_file    TPoint_trace   TMerge_trace\n\
+ TOutput_file   TRerun         TWide_trace    TVertex_stop   TCone_stop\n\
+\n\
+ Angle_max      Centrum_size   Error_round    Random_dist    Visible_min\n\
+ Ucoplanar_max  Wide_outside\n\
+";
+
+/*-<a                             href="../libqhull/qh-qhull.htm#TOC"
+  >-------------------------------</a><a name="main">-</a>
+
+  main( argc, argv )
+    processes the command line, calls qhull() to do the work, and exits
+
+  design:
+    initializes data structures
+    reads points
+    finishes initialization
+    computes convex hull and other structures
+    checks the result
+    writes the output
+    frees memory
+*/
+int main(int argc, char *argv[]) {
+  int curlong, totlong; /* used !qh_NOmem */
+  int exitcode, numpoints, dim;
+  coordT *points;
+  boolT ismalloc;
+  qhT qh_qh;
+  qhT *qh= &qh_qh;
+
+  QHULL_LIB_CHECK /* Check for compatible library */
+
+  if ((argc == 1) && isatty( 0 /*stdin*/)) {
+    fprintf(stdout, qh_prompt2, qh_version);
+    exit(qh_ERRnone);
+  }
+  if (argc > 1 && *argv[1] == '-' && !*(argv[1]+1)) {
+    fprintf(stdout, qh_prompta, qh_version, qh_DEFAULTbox,
+                qh_promptb, qh_promptc, qh_promptd, qh_prompte);
+    exit(qh_ERRnone);
+  }
+  if (argc > 1 && *argv[1] == '.' && !*(argv[1]+1)) {
+    fprintf(stdout, qh_prompt3, qh_version);
+    exit(qh_ERRnone);
+  }
+  if (argc > 1 && *argv[1] == '-' && *(argv[1]+1)=='V') {
+      fprintf(stdout, "%s\n", qh_version2);
+      exit(qh_ERRnone);
+  }
+  qh_init_A(qh, stdin, stdout, stderr, argc, argv);  /* sets qh->qhull_command */
+  exitcode= setjmp(qh->errexit); /* simple statement for CRAY J916 */
+  if (!exitcode) {
+    qh->NOerrexit = False;
+    qh_initflags(qh, qh->qhull_command);
+    points= qh_readpoints(qh, &numpoints, &dim, &ismalloc);
+    qh_init_B(qh, points, numpoints, dim, ismalloc);
+    qh_qhull(qh);
+    qh_check_output(qh);
+    qh_produce_output(qh);
+    if (qh->VERIFYoutput && !qh->FORCEoutput && !qh->STOPpoint && !qh->STOPcone)
+      qh_check_points(qh);
+    exitcode= qh_ERRnone;
+  }
+  qh->NOerrexit= True;  /* no more setjmp */
+#ifdef qh_NOmem
+  qh_freeqhull(qh, qh_ALL);
+#else
+  qh_freeqhull(qh, !qh_ALL);
+  qh_memfreeshort(qh, &curlong, &totlong);
+  if (curlong || totlong)
+    qh_fprintf_stderr(6263, "qhull internal warning (main): did not free %d bytes of long memory(%d pieces)\n",
+       totlong, curlong);
+#endif
+  return exitcode;
+} /* main */
+
diff --git a/xs/src/qhull/src/qhulltest/Coordinates_test.cpp b/xs/src/qhull/src/qhulltest/Coordinates_test.cpp
new file mode 100644
index 0000000000..3e8658a5bd
--- /dev/null
+++ b/xs/src/qhull/src/qhulltest/Coordinates_test.cpp
@@ -0,0 +1,539 @@
+/****************************************************************************
+**
+** Copyright (c) 2009-2015 C.B. Barber. All rights reserved.
+** $Id: //main/2015/qhull/src/qhulltest/Coordinates_test.cpp#2 $$Change: 2062 $
+** $DateTime: 2016/01/17 13:13:18 $$Author: bbarber $
+**
+****************************************************************************/
+
+//pre-compiled headers
+#include <iostream>
+#include "qhulltest/RoadTest.h" // QT_VERSION
+
+#include "libqhullcpp/Coordinates.h"
+#include "libqhullcpp/QhullError.h"
+#include "libqhullcpp/RboxPoints.h"
+#include "libqhullcpp/Qhull.h"
+
+using std::cout;
+using std::endl;
+using std::ostringstream;
+using std::ostream;
+using std::string;
+
+namespace orgQhull {
+
+class Coordinates_test : public RoadTest
+{
+    Q_OBJECT
+
+#//!\name Test slots
+private slots:
+    void t_construct();
+    void t_convert();
+    void t_element();
+    void t_readonly();
+    void t_operator();
+    void t_const_iterator();
+    void t_iterator();
+    void t_coord_iterator();
+    void t_mutable_coord_iterator();
+    void t_readwrite();
+    void t_search();
+    void t_io();
+};//Coordinates_test
+
+void
+add_Coordinates_test()
+{
+    new Coordinates_test();  // RoadTest::s_testcases
+}
+
+void Coordinates_test::
+t_construct()
+{
+    Coordinates c;
+    QCOMPARE(c.size(), 0U);
+    QVERIFY(c.isEmpty());
+    c << 1.0;
+    QCOMPARE(c.count(), 1);
+    Coordinates c2(c);
+    c2 << 2.0;
+    QCOMPARE(c2.count(), 2);
+    Coordinates c3;
+    c3 = c2;
+    QCOMPARE(c3.count(), 2);
+    QCOMPARE(c3[0]+c3[1], 3.0);
+    QVERIFY(c2==c3);
+    std::vector<coordT> vc;
+    vc.push_back(3.0);
+    vc.push_back(4.0);
+    Coordinates c4(vc);
+    QCOMPARE(c4[0]+c4[1], 7.0);
+    Coordinates c5(c3);
+    QVERIFY(c5==c3);
+    c5= vc;
+    QVERIFY(c5!=c3);
+    QVERIFY(c5==c4);
+}//t_construct
+
+void Coordinates_test::
+t_convert()
+{
+    Coordinates c;
+    c << 1.0 << 3.0;
+    QCOMPARE(c.data()[1], 3.0);
+    coordT *c2= c.data();
+    const coordT *c3= c.data();
+    QCOMPARE(c2, c3);
+    std::vector<coordT> vc= c.toStdVector();
+    QCOMPARE((size_t)vc.size(), c.size());
+    for(int k= (int)vc.size(); k--; ){
+        QCOMPARE(vc[k], c[k]);
+    }
+    QList<coordT> qc= c.toQList();
+    QCOMPARE(qc.count(), c.count());
+    for(int k= qc.count(); k--; ){
+        QCOMPARE(qc[k], c[k]);
+    }
+    Coordinates c4;
+    c4= std::vector<double>(2, 0.0);
+    QCOMPARE(c4.back(), 0.0);
+    Coordinates c5(std::vector<double>(2, 0.0));
+    QCOMPARE(c4.size(), c5.size());
+    QVERIFY(c4==c5);
+}//t_convert
+
+void Coordinates_test::
+t_element()
+{
+    Coordinates c;
+    c << 1.0 << -2.0;
+    c.at(1)= -3;
+    QCOMPARE(c.at(1), -3.0);
+    QCOMPARE(c.back(), -3.0);
+    QCOMPARE(c.front(), 1.0);
+    c[1]= -2.0;
+    QCOMPARE(c[1],-2.0);
+    QCOMPARE(c.first(), 1.0);
+    c.first()= 2.0;
+    QCOMPARE(c.first(), 2.0);
+    QCOMPARE(c.last(), -2.0);
+    c.last()= 0.0;
+    QCOMPARE(c.first()+c.last(), 2.0);
+    coordT *c4= &c.first();
+    const coordT *c5= &c.first();
+    QCOMPARE(c4, c5);
+    coordT *c6= &c.last();
+    const coordT *c7= &c.last();
+    QCOMPARE(c6, c7);
+    Coordinates c2= c.mid(1);
+    QCOMPARE(c2.count(), 1);
+    c << 3.0;
+    Coordinates c3= c.mid(1,1);
+    QCOMPARE(c2, c3);
+    QCOMPARE(c3.value(-1, -1.0), -1.0);
+    QCOMPARE(c3.value(3, 4.0), 4.0);
+    QCOMPARE(c.value(2, 4.0), 3.0);
+}//t_element
+
+void Coordinates_test::
+t_readonly()
+{
+    Coordinates c;
+    QCOMPARE(c.size(), 0u);
+    QCOMPARE(c.count(), 0);
+    QVERIFY(c.isEmpty());
+    c << 1.0 << -2.0;
+    QCOMPARE(c.size(), 2u);
+    QCOMPARE(c.count(), 2);
+    QVERIFY(!c.isEmpty());
+}//t_readonly
+
+void Coordinates_test::
+t_operator()
+{
+    Coordinates c;
+    Coordinates c2(c);
+    QVERIFY(c==c2);
+    QVERIFY(!(c!=c2));
+    c << 1.0;
+    QVERIFY(!(c==c2));
+    QVERIFY(c!=c2);
+    c2 << 1.0;
+    QVERIFY(c==c2);
+    QVERIFY(!(c!=c2));
+    c[0]= 0.0;
+    QVERIFY(c!=c2);
+    Coordinates c3= c+c2;
+    QCOMPARE(c3.count(), 2);
+    QCOMPARE(c3[0], 0.0);
+    QCOMPARE(c3[1], 1.0);
+    c3 += c3;
+    QCOMPARE(c3.count(), 4);
+    QCOMPARE(c3[2], 0.0);
+    QCOMPARE(c3[3], 1.0);
+    c3 += c2;
+    QCOMPARE(c3[4], 1.0);
+    c3 += 5.0;
+    QCOMPARE(c3.count(), 6);
+    QCOMPARE(c3[5], 5.0);
+    // << checked above
+}//t_operator
+
+void Coordinates_test::
+t_const_iterator()
+{
+    Coordinates c;
+    QCOMPARE(c.begin(), c.end());
+    // begin and end checked elsewhere
+    c << 1.0 << 3.0;
+    Coordinates::const_iterator i= c.begin();
+    QCOMPARE(*i, 1.0);
+    QCOMPARE(i[1], 3.0);
+    // i[1]= -3.0; // compiler error
+    // operator-> is not applicable to double
+    QCOMPARE(*i++, 1.0);
+    QCOMPARE(*i, 3.0);
+    QCOMPARE(*i--, 3.0);
+    QCOMPARE(*i, 1.0);
+    QCOMPARE(*(i+1), 3.0);
+    QCOMPARE(*++i, 3.0);
+    QCOMPARE(*(i-1), 1.0);
+    QCOMPARE(*--i, 1.0);
+    QVERIFY(i==c.begin());
+    QVERIFY(i==c.constBegin());
+    QVERIFY(i!=c.end());
+    QVERIFY(i!=c.constEnd());
+    QVERIFY(i<c.end());
+    QVERIFY(i>=c.begin());
+    QVERIFY(i+1<=c.end());
+    QVERIFY(i+1>c.begin());
+    Coordinates::iterator i2= c.begin();
+    Coordinates::const_iterator i3(i2);
+    QCOMPARE(*i3, 1.0);
+    QCOMPARE(i3[1], 3.0);
+}//t_const_iterator
+
+void Coordinates_test::
+t_iterator()
+{
+    Coordinates c;
+    QCOMPARE(c.begin(), c.end());
+    // begin and end checked elsewhere
+    c << 1.0 << 3.0;
+    Coordinates::iterator i= c.begin();
+    QCOMPARE(*i, 1.0);
+    QCOMPARE(i[1], 3.0);
+    *i= -1.0;
+    QCOMPARE(*i, -1.0);
+    i[1]= -3.0;
+    QCOMPARE(i[1], -3.0);
+    *i= 1.0;
+    // operator-> is not applicable to double
+    QCOMPARE(*i++, 1.0);
+    QCOMPARE(*i, -3.0);
+    *i= 3.0;
+    QCOMPARE(*i--, 3.0);
+    QCOMPARE(*i, 1.0);
+    QCOMPARE(*(i+1), 3.0);
+    QCOMPARE(*++i, 3.0);
+    QCOMPARE(*(i-1), 1.0);
+    QCOMPARE(*--i, 1.0);
+    QVERIFY(i==c.begin());
+    QVERIFY(i==c.constBegin());
+    QVERIFY(i!=c.end());
+    QVERIFY(i!=c.constEnd());
+    QVERIFY(i<c.end());
+    QVERIFY(i>=c.begin());
+    QVERIFY(i+1<=c.end());
+    QVERIFY(i+1>c.begin());
+}//t_iterator
+
+void Coordinates_test::
+t_coord_iterator()
+{
+    Coordinates c;
+    c << 1.0 << 3.0;
+    CoordinatesIterator i(c);
+    CoordinatesIterator i2= c;
+    QVERIFY(i.findNext(1.0));
+    QVERIFY(!i.findNext(2.0));
+    QVERIFY(!i.findNext(3.0));
+    QVERIFY(i.findPrevious(3.0));
+    QVERIFY(!i.findPrevious(2.0));
+    QVERIFY(!i.findPrevious(1.0));
+    QVERIFY(i2.findNext(3.0));
+    QVERIFY(i2.findPrevious(3.0));
+    QVERIFY(i2.findNext(3.0));
+    QVERIFY(i2.findPrevious(1.0));
+    QVERIFY(i2.hasNext());
+    QVERIFY(!i2.hasPrevious());
+    QVERIFY(i.hasNext());
+    QVERIFY(!i.hasPrevious());
+    i.toBack();
+    i2.toFront();
+    QVERIFY(!i.hasNext());
+    QVERIFY(i.hasPrevious());
+    QVERIFY(i2.hasNext());
+    QVERIFY(!i2.hasPrevious());
+    Coordinates c2;
+    i2= c2;
+    QVERIFY(!i2.hasNext());
+    QVERIFY(!i2.hasPrevious());
+    i2.toBack();
+    QVERIFY(!i2.hasNext());
+    QVERIFY(!i2.hasPrevious());
+    QCOMPARE(i.peekPrevious(), 3.0);
+    QCOMPARE(i.previous(), 3.0);
+    QCOMPARE(i.previous(), 1.0);
+    QVERIFY(!i.hasPrevious());
+    QCOMPARE(i.peekNext(), 1.0);
+    // i.peekNext()= 1.0; // compiler error
+    QCOMPARE(i.next(), 1.0);
+    QCOMPARE(i.peekNext(), 3.0);
+    QCOMPARE(i.next(), 3.0);
+    QVERIFY(!i.hasNext());
+    i.toFront();
+    QCOMPARE(i.next(), 1.0);
+}//t_coord_iterator
+
+void Coordinates_test::
+t_mutable_coord_iterator()
+{
+    // Same tests as CoordinatesIterator
+    Coordinates c;
+    c << 1.0 << 3.0;
+    MutableCoordinatesIterator i(c);
+    MutableCoordinatesIterator i2= c;
+    QVERIFY(i.findNext(1.0));
+    QVERIFY(!i.findNext(2.0));
+    QVERIFY(!i.findNext(3.0));
+    QVERIFY(i.findPrevious(3.0));
+    QVERIFY(!i.findPrevious(2.0));
+    QVERIFY(!i.findPrevious(1.0));
+    QVERIFY(i2.findNext(3.0));
+    QVERIFY(i2.findPrevious(3.0));
+    QVERIFY(i2.findNext(3.0));
+    QVERIFY(i2.findPrevious(1.0));
+    QVERIFY(i2.hasNext());
+    QVERIFY(!i2.hasPrevious());
+    QVERIFY(i.hasNext());
+    QVERIFY(!i.hasPrevious());
+    i.toBack();
+    i2.toFront();
+    QVERIFY(!i.hasNext());
+    QVERIFY(i.hasPrevious());
+    QVERIFY(i2.hasNext());
+    QVERIFY(!i2.hasPrevious());
+    Coordinates c2;
+    i2= c2;
+    QVERIFY(!i2.hasNext());
+    QVERIFY(!i2.hasPrevious());
+    i2.toBack();
+    QVERIFY(!i2.hasNext());
+    QVERIFY(!i2.hasPrevious());
+    QCOMPARE(i.peekPrevious(), 3.0);
+    QCOMPARE(i.peekPrevious(), 3.0);
+    QCOMPARE(i.previous(), 3.0);
+    QCOMPARE(i.previous(), 1.0);
+    QVERIFY(!i.hasPrevious());
+    QCOMPARE(i.peekNext(), 1.0);
+    QCOMPARE(i.next(), 1.0);
+    QCOMPARE(i.peekNext(), 3.0);
+    QCOMPARE(i.next(), 3.0);
+    QVERIFY(!i.hasNext());
+    i.toFront();
+    QCOMPARE(i.next(), 1.0);
+
+    // Mutable tests
+    i.toFront();
+    i.peekNext()= -1.0;
+    QCOMPARE(i.peekNext(), -1.0);
+    QCOMPARE((i.next()= 1.0), 1.0);
+    QCOMPARE(i.peekPrevious(), 1.0);
+    i.remove();
+    QCOMPARE(c.count(), 1);
+    i.remove();
+    QCOMPARE(c.count(), 1);
+    QCOMPARE(i.peekNext(), 3.0);
+    i.insert(1.0);
+    i.insert(2.0);
+    QCOMPARE(c.count(), 3);
+    QCOMPARE(i.peekNext(), 3.0);
+    QCOMPARE(i.peekPrevious(), 2.0);
+    i.peekPrevious()= -2.0;
+    QCOMPARE(i.peekPrevious(), -2.0);
+    QCOMPARE((i.previous()= 2.0), 2.0);
+    QCOMPARE(i.peekNext(), 2.0);
+    i.toBack();
+    i.remove();
+    QCOMPARE(c.count(), 3); // unchanged
+    i.toFront();
+    i.remove();
+    QCOMPARE(c.count(), 3); // unchanged
+    QCOMPARE(i.peekNext(), 1.0);
+    i.remove();
+    QCOMPARE(c.count(), 3); // unchanged
+    i.insert(0.0);
+    QCOMPARE(c.count(), 4);
+    QCOMPARE(i.value(), 0.0);
+    QCOMPARE(i.peekPrevious(), 0.0);
+    i.setValue(-10.0);
+    QCOMPARE(c.count(), 4); // unchanged
+    QCOMPARE(i.peekNext(), 1.0);
+    QCOMPARE(i.peekPrevious(), -10.0);
+    i.findNext(1.0);
+    i.setValue(-1.0);
+    QCOMPARE(i.peekPrevious(), -1.0);
+    i.setValue(1.0);
+    QCOMPARE(i.peekPrevious(), 1.0);
+    QCOMPARE(i.value(), 1.0);
+    i.findPrevious(1.0);
+    i.setValue(-1.0);
+    QCOMPARE(i.peekNext(), -1.0);
+    i.toBack();
+    QCOMPARE(i.previous(), 3.0);
+    i.setValue(-3.0);
+    QCOMPARE(i.peekNext(), -3.0);
+    double d= i.value();
+    QCOMPARE(d, -3.0);
+    QCOMPARE(i.previous(), 2.0);
+}//t_mutable_coord_iterator
+
+void Coordinates_test::
+t_readwrite()
+{
+    Coordinates c;
+    c.clear();
+    QCOMPARE(c.count(), 0);
+    c << 1.0 << 3.0;
+    c.clear();
+    QCOMPARE(c.count(), 0);
+    coordT c2[4]= { 0.0, 1.0, 2.0, 3.0};
+    c.append(4, c2);
+    QCOMPARE(c.count(), 4);
+    QCOMPARE(c[0], 0.0);
+    QCOMPARE(c[1], 1.0);
+    QCOMPARE(c[3], 3.0);
+    c.clear();
+    c << 1.0 << 3.0;
+    c.erase(c.begin(), c.end());
+    QCOMPARE(c.count(), 0);
+    c << 1.0 << 0.0;
+    Coordinates::iterator i= c.erase(c.begin());
+    QCOMPARE(*i, 0.0);
+    i= c.insert(c.end(), 1.0);
+    QCOMPARE(*i, 1.0);
+    QCOMPARE(c.count(), 2);
+    c.pop_back();
+    QCOMPARE(c.count(), 1);   // 0
+    QCOMPARE(c[0], 0.0);
+    c.push_back(2.0);
+    QCOMPARE(c.count(), 2);
+    c.append(3.0);
+    QCOMPARE(c.count(), 3);   // 0, 2, 3
+    QCOMPARE(c[2], 3.0);
+    c.insert(0, 4.0);
+    QCOMPARE(c[0], 4.0);
+    QCOMPARE(c[3], 3.0);
+    c.insert(c.count(), 5.0);
+    QCOMPARE(c.count(), 5);   // 4, 0, 2, 3, 5
+    QCOMPARE(c[4], 5.0);
+    c.move(4, 0);
+    QCOMPARE(c.count(), 5);   // 5, 4, 0, 2, 3
+    QCOMPARE(c[0], 5.0);
+    c.pop_front();
+    QCOMPARE(c.count(), 4);
+    QCOMPARE(c[0], 4.0);
+    c.prepend(6.0);
+    QCOMPARE(c.count(), 5);   // 6, 4, 0, 2, 3
+    QCOMPARE(c[0], 6.0);
+    c.push_front(7.0);
+    QCOMPARE(c.count(), 6);
+    QCOMPARE(c[0], 7.0);
+    c.removeAt(1);
+    QCOMPARE(c.count(), 5);   // 7, 4, 0, 2, 3
+    QCOMPARE(c[1], 4.0);
+    c.removeFirst();
+    QCOMPARE(c.count(), 4);   // 4, 0, 2, 3
+    QCOMPARE(c[0], 4.0);
+    c.removeLast();
+    QCOMPARE(c.count(), 3);
+    QCOMPARE(c.last(), 2.0);
+    c.replace(2, 8.0);
+    QCOMPARE(c.count(), 3);   // 4, 0, 8
+    QCOMPARE(c[2], 8.0);
+    c.swap(0, 2);
+    QCOMPARE(c[2], 4.0);
+    double d= c.takeAt(2);
+    QCOMPARE(c.count(), 2);   // 8, 0
+    QCOMPARE(d, 4.0);
+    double d2= c.takeFirst();
+    QCOMPARE(c.count(), 1);   // 0
+    QCOMPARE(d2, 8.0);
+    double d3= c.takeLast();
+    QVERIFY(c.isEmpty()); \
+    QCOMPARE(d3, 0.0);
+}//t_readwrite
+
+void Coordinates_test::
+t_search()
+{
+    Coordinates c;
+    c << 1.0 << 3.0 << 1.0;
+    QVERIFY(c.contains(1.0));
+    QVERIFY(c.contains(3.0));
+    QVERIFY(!c.contains(0.0));
+    QCOMPARE(c.count(1.0), 2);
+    QCOMPARE(c.count(3.0), 1);
+    QCOMPARE(c.count(0.0), 0);
+    QCOMPARE(c.indexOf(1.0), 0);
+    QCOMPARE(c.indexOf(3.0), 1);
+    QCOMPARE(c.indexOf(1.0, -1), 2);
+    QCOMPARE(c.indexOf(3.0, -1), -1);
+    QCOMPARE(c.indexOf(3.0, -2), 1);
+    QCOMPARE(c.indexOf(1.0, -3), 0);
+    QCOMPARE(c.indexOf(1.0, -4), 0);
+    QCOMPARE(c.indexOf(1.0, 1), 2);
+    QCOMPARE(c.indexOf(3.0, 2), -1);
+    QCOMPARE(c.indexOf(1.0, 2), 2);
+    QCOMPARE(c.indexOf(1.0, 3), -1);
+    QCOMPARE(c.indexOf(1.0, 4), -1);
+    QCOMPARE(c.lastIndexOf(1.0), 2);
+    QCOMPARE(c.lastIndexOf(3.0), 1);
+    QCOMPARE(c.lastIndexOf(1.0, -1), 2);
+    QCOMPARE(c.lastIndexOf(3.0, -1), 1);
+    QCOMPARE(c.lastIndexOf(3.0, -2), 1);
+    QCOMPARE(c.lastIndexOf(1.0, -3), 0);
+    QCOMPARE(c.lastIndexOf(1.0, -4), -1);
+    QCOMPARE(c.lastIndexOf(1.0, 1), 0);
+    QCOMPARE(c.lastIndexOf(3.0, 2), 1);
+    QCOMPARE(c.lastIndexOf(1.0, 2), 2);
+    QCOMPARE(c.lastIndexOf(1.0, 3), 2);
+    QCOMPARE(c.lastIndexOf(1.0, 4), 2);
+    c.removeAll(3.0);
+    QCOMPARE(c.count(), 2);
+    c.removeAll(4.0);
+    QCOMPARE(c.count(), 2);
+    c.removeAll(1.0);
+    QCOMPARE(c.count(), 0);
+    c.removeAll(4.0);
+    QCOMPARE(c.count(), 0);
+}//t_search
+
+void Coordinates_test::
+t_io()
+{
+    Coordinates c;
+    c << 1.0 << 2.0 << 3.0;
+    ostringstream os;
+    os << "Coordinates 1-2-3\n" << c;
+    cout << os.str();
+    QString s= QString::fromStdString(os.str());
+    QCOMPARE(s.count("2"), 2);
+}//t_io
+
+}//orgQhull
+
+#include "moc/Coordinates_test.moc"
diff --git a/xs/src/qhull/src/qhulltest/PointCoordinates_test.cpp b/xs/src/qhull/src/qhulltest/PointCoordinates_test.cpp
new file mode 100644
index 0000000000..09285954df
--- /dev/null
+++ b/xs/src/qhull/src/qhulltest/PointCoordinates_test.cpp
@@ -0,0 +1,478 @@
+/****************************************************************************
+**
+** Copyright (c) 2009-2015 C.B. Barber. All rights reserved.
+** $Id: //main/2015/qhull/src/qhulltest/PointCoordinates_test.cpp#2 $$Change: 2062 $
+** $DateTime: 2016/01/17 13:13:18 $$Author: bbarber $
+**
+****************************************************************************/
+
+//pre-compiled headers
+#include <iostream>
+#include "qhulltest/RoadTest.h" // QT_VERSION
+
+#include "libqhullcpp/PointCoordinates.h"
+#include "libqhullcpp/QhullError.h"
+#include "libqhullcpp/RboxPoints.h"
+#include "libqhullcpp/Qhull.h"
+
+using std::cout;
+using std::endl;
+using std::ostringstream;
+using std::ostream;
+using std::string;
+using std::stringstream;
+
+namespace orgQhull {
+
+class PointCoordinates_test : public RoadTest
+{
+    Q_OBJECT
+
+#//!\name Test slots
+private slots:
+    void t_construct_q();
+    void t_construct_qh();
+    void t_convert();
+    void t_getset();
+    void t_element();
+    void t_foreach();
+    void t_search();
+    void t_modify();
+    void t_append_points();
+    void t_coord_iterator();
+    void t_io();
+};//PointCoordinates_test
+
+void
+add_PointCoordinates_test()
+{
+    new PointCoordinates_test();  // RoadTest::s_testcases
+}
+
+void PointCoordinates_test::
+t_construct_q()
+{
+    Qhull q;
+    PointCoordinates pc(q);
+    QCOMPARE(pc.size(), 0U);
+    QCOMPARE(pc.coordinateCount(), 0);
+    QCOMPARE(pc.dimension(), 0);
+    QCOMPARE(pc.coordinates(), (coordT *)0);
+    QVERIFY(pc.isEmpty());
+    pc.checkValid();
+    PointCoordinates pc7(q, 2, "test explicit dimension");
+    QCOMPARE(pc7.dimension(), 2);
+    QCOMPARE(pc7.count(), 0);
+    QVERIFY(pc7.isEmpty());
+    QCOMPARE(pc7.comment(), std::string("test explicit dimension"));
+    pc7.checkValid();
+    PointCoordinates pc2(q, "Test pc2");
+    QCOMPARE(pc2.count(), 0);
+    QVERIFY(pc2.isEmpty());
+    QCOMPARE(pc2.comment(), std::string("Test pc2"));
+    pc2.checkValid();
+    PointCoordinates pc3(q, 3, "Test 3-d pc3");
+    QCOMPARE(pc3.dimension(), 3);
+    QVERIFY(pc3.isEmpty());
+    pc3.checkValid();
+    coordT c[]= { 0.0, 1.0, 2.0, 3.0, 4.0, 5.0 };
+    PointCoordinates pc4(q, 2, "Test 2-d pc4", 6, c);
+    QCOMPARE(pc4.dimension(), 2);
+    QCOMPARE(pc4.count(), 3);
+    QCOMPARE(pc4.size(), 3u);
+    QVERIFY(!pc4.isEmpty());
+    pc4.checkValid();
+    QhullPoint p= pc4[2];
+    QCOMPARE(p[1], 5.0);
+    // QhullPoint refers to PointCoordinates
+    p[1] += 1.0;
+    QCOMPARE(pc4[2][1], 6.0);
+    PointCoordinates pc5(q, 4, "Test 4-d pc5 with insufficient coordinates", 6, c);
+    QCOMPARE(pc5.dimension(), 4);
+    QCOMPARE(pc5.count(), 1);
+    QCOMPARE(pc5.extraCoordinatesCount(), 2);
+    QCOMPARE(pc5.extraCoordinates()[1], 5.0);
+    QVERIFY(!pc5.isEmpty());;
+    std::vector<coordT> vc;
+    vc.push_back(3.0);
+    vc.push_back(4.0);
+    vc.push_back(5.0);
+    vc.push_back(6.0);
+    vc.push_back(7.0);
+    vc.push_back(9.0);
+    pc5.append(2, &vc[3]); // Copy of vc[]
+    pc5.checkValid();
+    QhullPoint p5(q, 4, &vc[1]);
+    QCOMPARE(pc5[1], p5);
+    PointCoordinates pc6(pc5); // Makes copy of point_coordinates
+    QCOMPARE(pc6[1], p5);
+    QVERIFY(pc6==pc5);
+    QhullPoint p6= pc5[1];  // Refers to pc5.coordinates
+    pc5[1][0] += 1.0;
+    QCOMPARE(pc5[1], p6);
+    QVERIFY(pc5[1]!=p5);
+    QVERIFY(pc6!=pc5);
+    pc6= pc5;
+    QVERIFY(pc6==pc5);
+    PointCoordinates pc8(q);
+    pc6= pc8;
+    QVERIFY(pc6!=pc5);
+    QVERIFY(pc6.isEmpty());
+}//t_construct_q
+
+void PointCoordinates_test::
+t_construct_qh()
+{
+    QhullQh qh;
+    PointCoordinates pc(&qh);
+    QCOMPARE(pc.size(), 0U);
+    QCOMPARE(pc.coordinateCount(), 0);
+    QCOMPARE(pc.dimension(), 0);
+    QCOMPARE(pc.coordinates(), (coordT *)0);
+    QVERIFY(pc.isEmpty());
+    pc.checkValid();
+    PointCoordinates pc7(&qh, 2, "test explicit dimension");
+    QCOMPARE(pc7.dimension(), 2);
+    QCOMPARE(pc7.count(), 0);
+    QVERIFY(pc7.isEmpty());
+    QCOMPARE(pc7.comment(), std::string("test explicit dimension"));
+    pc7.checkValid();
+    PointCoordinates pc2(&qh, "Test pc2");
+    QCOMPARE(pc2.count(), 0);
+    QVERIFY(pc2.isEmpty());
+    QCOMPARE(pc2.comment(), std::string("Test pc2"));
+    pc2.checkValid();
+    PointCoordinates pc3(&qh, 3, "Test 3-d pc3");
+    QCOMPARE(pc3.dimension(), 3);
+    QVERIFY(pc3.isEmpty());
+    pc3.checkValid();
+    coordT c[]= { 0.0, 1.0, 2.0, 3.0, 4.0, 5.0 };
+    PointCoordinates pc4(&qh, 2, "Test 2-d pc4", 6, c);
+    QCOMPARE(pc4.dimension(), 2);
+    QCOMPARE(pc4.count(), 3);
+    QCOMPARE(pc4.size(), 3u);
+    QVERIFY(!pc4.isEmpty());
+    pc4.checkValid();
+    QhullPoint p= pc4[2];
+    QCOMPARE(p[1], 5.0);
+    // QhullPoint refers to PointCoordinates
+    p[1] += 1.0;
+    QCOMPARE(pc4[2][1], 6.0);
+    PointCoordinates pc5(&qh, 4, "Test 4-d pc5 with insufficient coordinates", 6, c);
+    QCOMPARE(pc5.dimension(), 4);
+    QCOMPARE(pc5.count(), 1);
+    QCOMPARE(pc5.extraCoordinatesCount(), 2);
+    QCOMPARE(pc5.extraCoordinates()[1], 5.0);
+    QVERIFY(!pc5.isEmpty());;
+    std::vector<coordT> vc;
+    vc.push_back(3.0);
+    vc.push_back(4.0);
+    vc.push_back(5.0);
+    vc.push_back(6.0);
+    vc.push_back(7.0);
+    vc.push_back(9.0);
+    pc5.append(2, &vc[3]); // Copy of vc[]
+    pc5.checkValid();
+    QhullPoint p5(&qh, 4, &vc[1]);
+    QCOMPARE(pc5[1], p5);
+    PointCoordinates pc6(pc5); // Makes copy of point_coordinates
+    QCOMPARE(pc6[1], p5);
+    QVERIFY(pc6==pc5);
+    QhullPoint p6= pc5[1];  // Refers to pc5.coordinates
+    pc5[1][0] += 1.0;
+    QCOMPARE(pc5[1], p6);
+    QVERIFY(pc5[1]!=p5);
+    QVERIFY(pc6!=pc5);
+    pc6= pc5;
+    QVERIFY(pc6==pc5);
+    PointCoordinates pc8(&qh);
+    pc6= pc8;
+    QVERIFY(pc6!=pc5);
+    QVERIFY(pc6.isEmpty());
+}//t_construct_qh
+
+void PointCoordinates_test::
+t_convert()
+{
+    Qhull q;
+    //defineAs tested above
+    coordT c[]= {0.0, 1.0, 2.0, 3.0, 4.0, 5.0};
+    PointCoordinates ps(q, 3, "two 3-d points", 6, c);
+    QCOMPARE(ps.dimension(), 3);
+    QCOMPARE(ps.size(), 2u);
+    const coordT *c2= ps.constData();
+    QVERIFY(c!=c2);
+    QCOMPARE(c[0], c2[0]);
+    const coordT *c3= ps.data();
+    QCOMPARE(c3, c2);
+    coordT *c4= ps.data();
+    QCOMPARE(c4, c2);
+    std::vector<coordT> vs= ps.toStdVector();
+    QCOMPARE(vs.size(), 6u);
+    QCOMPARE(vs[5], 5.0);
+    QList<coordT> qs= ps.toQList();
+    QCOMPARE(qs.size(), 6);
+    QCOMPARE(qs[5], 5.0);
+}//t_convert
+
+void PointCoordinates_test::
+t_getset()
+{
+    // See t_construct() for test of coordinates, coordinateCount, dimension, empty, isEmpty, ==, !=
+    // See t_construct() for test of checkValid, comment, setDimension
+    Qhull q;
+    PointCoordinates pc(q, "Coordinates c");
+    pc.setComment("New comment");
+    QCOMPARE(pc.comment(), std::string("New comment"));
+    pc.checkValid();
+    pc.makeValid();  // A no-op
+    pc.checkValid();
+    Coordinates cs= pc.getCoordinates();
+    QVERIFY(cs.isEmpty());
+    PointCoordinates pc2(pc);
+    pc.setDimension(3);
+    QVERIFY(pc2!=pc);
+    coordT c[]= {0.0, 1.0, 2.0, 3.0, 4.0, 5.0};
+    pc.append(6, c);
+    pc.checkValid();
+    pc.makeValid();  // A no-op
+    QhullPoint p= pc[0];
+    QCOMPARE(p[2], 2.0);
+    try{
+        pc.setDimension(2);
+        QFAIL("setDimension(2) did not fail for 3-d.");
+    }catch (const std::exception &e) {
+        const char *s= e.what();
+        cout << "INFO   : Caught " << s;
+    }
+}//t_getset
+
+void PointCoordinates_test::
+t_element()
+{
+    Qhull q;
+    coordT c[]= {0.0, 1.0, 2.0, 3.0, 4.0, 5.0};
+    PointCoordinates pc(q, 2, "2-d points", 6, c);
+    QhullPoint p= pc.at(0);
+    QCOMPARE(p, pc[0]);
+    QCOMPARE(p, pc.first());
+    QCOMPARE(p, pc.value(0));
+    p= pc.back();
+    QCOMPARE(p, pc[2]);
+    QCOMPARE(p, pc.last());
+    QCOMPARE(p, pc.value(2));
+    QhullPoints ps= pc.mid(1, 2);
+    QCOMPARE(ps[1], p);
+}//t_element
+
+void PointCoordinates_test::
+t_foreach()
+{
+    Qhull q;
+    coordT c[]= {0.0, 1.0, 2.0, 3.0, 4.0, 5.0};
+    PointCoordinates pc(q, 2, "2-d points", 6, c);
+    QhullPoints::Iterator i= pc.begin();
+    QhullPoint p= pc[0];
+    QCOMPARE(*i, p);
+    QCOMPARE((*i)[0], 0.0);
+    QhullPoint p3= pc[2];
+    i= pc.end();
+    QCOMPARE(i[-1], p3);
+    const PointCoordinates pc2(q, 2, "2-d points", 6, c);
+    QhullPoints::ConstIterator i2= pc.begin();
+    const QhullPoint p0= pc2[0];
+    QCOMPARE(*i2, p0);
+    QCOMPARE((*i2)[0], 0.0);
+    QhullPoints::ConstIterator i3= i2;
+    QCOMPARE(i3, i2);
+    QCOMPARE((*i3)[0], 0.0);
+    i3= pc.constEnd();
+    --i3;
+    QhullPoint p2= pc2[2];
+    QCOMPARE(*i3, p2);
+    i= pc.end();
+    QVERIFY(i-1==i3);
+    i2= pc2.end();
+    QVERIFY(i2-1!=i3);
+    QCOMPARE(*(i2-1), *i3);
+    foreach(QhullPoint p3, pc){ //Qt only
+        QVERIFY(p3[0]>=0.0);
+        QVERIFY(p3[0]<=5.0);
+    }
+    Coordinates::ConstIterator i4= pc.beginCoordinates();
+    QCOMPARE(*i4, 0.0);
+    Coordinates::Iterator i5= pc.beginCoordinates();
+    QCOMPARE(*i5, 0.0);
+    i4= pc.beginCoordinates(1);
+    QCOMPARE(*i4, 2.0);
+    i5= pc.beginCoordinates(1);
+    QCOMPARE(*i5, 2.0);
+    i4= pc.endCoordinates();
+    QCOMPARE(*--i4, 5.0);
+    i5= pc.endCoordinates();
+    QCOMPARE(*--i5, 5.0);
+}//t_foreach
+
+void PointCoordinates_test::
+t_search()
+{
+    Qhull q;
+    coordT c[]= {0.0, 1.0, 2.0, 3.0, 4.0, 5.0};
+    PointCoordinates pc(q, 2, "2-d points", 6, c);
+    QhullPoint p0= pc[0];
+    QhullPoint p2= pc[2];
+    QVERIFY(pc.contains(p0));
+    QVERIFY(pc.contains(p2));
+    QCOMPARE(pc.count(p0), 1);
+    QCOMPARE(pc.indexOf(p2), 2);
+    QCOMPARE(pc.lastIndexOf(p0), 0);
+}//t_search
+
+void PointCoordinates_test::
+t_modify()
+{
+    Qhull q;
+    coordT c[]= {0.0, 1.0, 2.0, 3.0, 4.0, 5.0};
+    PointCoordinates pc(q, 2, "2-d points", 6, c);
+    coordT c3[]= {0.0, 1.0, 2.0, 3.0, 4.0, 5.0};
+    PointCoordinates pc5(q, 2, "test explicit dimension");
+    pc5.append(6, c3); // 0-5
+    QVERIFY(pc5==pc);
+    PointCoordinates pc2(q, 2, "2-d");
+    coordT c2[]= {6.0, 7.0, 8.0, 9.0, 10.0, 11.0};
+    pc2.append(6, c2);
+    QCOMPARE(pc2.count(), 3);
+    pc2.append(14.0);
+    QCOMPARE(pc2.count(), 3);
+    QCOMPARE(pc2.extraCoordinatesCount(), 1);
+    pc2.append(15.0); // 6-11, 14,15
+    QCOMPARE(pc2.count(), 4);
+    QCOMPARE(pc2.extraCoordinatesCount(), 0);
+    QhullPoint p(pc[0]);
+    pc2.append(p); // 6-11, 14,15, 0,1
+    QCOMPARE(pc2.count(), 5);
+    QCOMPARE(pc2.extraCoordinatesCount(), 0);
+    QCOMPARE(pc2.lastIndexOf(p), 4);
+    pc.append(pc2); // Invalidates p
+    QCOMPARE(pc.count(), 8); // 0-11, 14,15, 0,1
+    QCOMPARE(pc.extraCoordinatesCount(), 0);
+    QCOMPARE(pc.lastIndexOf(pc[0]), 7);
+    pc.appendComment(" operators");
+    QCOMPARE(pc.comment(), std::string("2-d points operators"));
+    pc.checkValid();
+    // see t_append_points for appendPoints
+    PointCoordinates pc3= pc+pc2;
+    pc3.checkValid();
+    QCOMPARE(pc3.count(), 13);
+    QCOMPARE(pc3[6][0], 14.0);
+    QCOMPARE(pc3[8][0], 6.0);
+    pc3 += pc;
+    QCOMPARE(pc3.count(), 21);
+    QCOMPARE(pc3[14][0], 2.0);
+    pc3 += 12.0;
+    pc3 += 14.0;
+    QCOMPARE(pc3.count(), 22);
+    QCOMPARE(pc3.last()[0], 12.0);
+    // QhullPoint p3= pc3.first(); // += throws error because append may move the data
+    QhullPoint p3= pc2.first();
+    pc3 += p3;
+    QCOMPARE(pc3.count(), 23);
+    QCOMPARE(pc3.last()[0], 6.0);
+    pc3 << pc;
+    QCOMPARE(pc3.count(), 31);
+    QCOMPARE(pc3.last()[0], 0.0);
+    pc3 << 12.0 << 14.0;
+    QCOMPARE(pc3.count(), 32);
+    QCOMPARE(pc3.last()[0], 12.0);
+    PointCoordinates pc4(pc3);
+    pc4.reserveCoordinates(100);
+    QVERIFY(pc3==pc4);
+}//t_modify
+
+void PointCoordinates_test::
+t_append_points()
+{
+    Qhull q;
+    PointCoordinates pc(q, 2, "stringstream");
+    stringstream s("2 3 1 2 3 4 5 6");
+    pc.appendPoints(s);
+    QCOMPARE(pc.count(), 3);
+}//t_append_points
+
+void PointCoordinates_test::
+t_coord_iterator()
+{
+    Qhull q;
+    PointCoordinates c(q, 2, "2-d");
+    c << 0.0 << 1.0 << 2.0 << 3.0 << 4.0 << 5.0;
+    PointCoordinatesIterator i(c);
+    QhullPoint p0(c[0]);
+    QhullPoint p1(c[1]);
+    QhullPoint p2(c[2]);
+    coordT c2[] = {-1.0, -2.0};
+    QhullPoint p3(q, 2, c2);
+    PointCoordinatesIterator i2= c;
+    QVERIFY(i.findNext(p1));
+    QVERIFY(!i.findNext(p1));
+    QVERIFY(!i.findNext(p2));
+    QVERIFY(!i.findNext(p3));
+    QVERIFY(i.findPrevious(p2));
+    QVERIFY(!i.findPrevious(p2));
+    QVERIFY(!i.findPrevious(p0));
+    QVERIFY(!i.findPrevious(p3));
+    QVERIFY(i2.findNext(p2));
+    QVERIFY(i2.findPrevious(p0));
+    QVERIFY(i2.findNext(p1));
+    QVERIFY(i2.findPrevious(p0));
+    QVERIFY(i2.hasNext());
+    QVERIFY(!i2.hasPrevious());
+    QVERIFY(i.hasNext());
+    QVERIFY(!i.hasPrevious());
+    i.toBack();
+    i2.toFront();
+    QVERIFY(!i.hasNext());
+    QVERIFY(i.hasPrevious());
+    QVERIFY(i2.hasNext());
+    QVERIFY(!i2.hasPrevious());
+    PointCoordinates c3(q);
+    PointCoordinatesIterator i3= c3;
+    QVERIFY(!i3.hasNext());
+    QVERIFY(!i3.hasPrevious());
+    i3.toBack();
+    QVERIFY(!i3.hasNext());
+    QVERIFY(!i3.hasPrevious());
+    QCOMPARE(i.peekPrevious(), p2);
+    QCOMPARE(i.previous(), p2);
+    QCOMPARE(i.previous(), p1);
+    QCOMPARE(i.previous(), p0);
+    QVERIFY(!i.hasPrevious());
+    QCOMPARE(i.peekNext(), p0);
+    // i.peekNext()= 1.0; // compiler error
+    QCOMPARE(i.next(), p0);
+    QCOMPARE(i.peekNext(), p1);
+    QCOMPARE(i.next(), p1);
+    QCOMPARE(i.next(), p2);
+    QVERIFY(!i.hasNext());
+    i.toFront();
+    QCOMPARE(i.next(), p0);
+}//t_coord_iterator
+
+void PointCoordinates_test::
+t_io()
+{
+    Qhull q;
+    PointCoordinates c(q);
+    ostringstream os;
+    os << "PointCoordinates 0-d\n" << c;
+    c.setDimension(2);
+    c << 1.0 << 2.0 << 3.0 << 1.0 << 2.0 << 3.0;
+    os << "PointCoordinates 1,2 3,1 2,3\n" << c;
+    cout << os.str();
+    QString s= QString::fromStdString(os.str());
+    QCOMPARE(s.count("0"), 3);
+    QCOMPARE(s.count("2"), 5);
+}//t_io
+
+}//orgQhull
+
+#include "moc/PointCoordinates_test.moc"
diff --git a/xs/src/qhull/src/qhulltest/QhullFacetList_test.cpp b/xs/src/qhull/src/qhulltest/QhullFacetList_test.cpp
new file mode 100644
index 0000000000..5a09d01da9
--- /dev/null
+++ b/xs/src/qhull/src/qhulltest/QhullFacetList_test.cpp
@@ -0,0 +1,196 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
+** $Id: //main/2015/qhull/src/qhulltest/QhullFacetList_test.cpp#3 $$Change: 2062 $
+** $DateTime: 2016/01/17 13:13:18 $$Author: bbarber $
+**
+****************************************************************************/
+
+//pre-compiled headers
+#include <iostream>
+#include "qhulltest/RoadTest.h" // QT_VERSION
+
+#include "libqhullcpp/QhullFacetList.h"
+#include "libqhullcpp/QhullError.h"
+#include "libqhullcpp/QhullFacet.h"
+#include "libqhullcpp/QhullVertex.h"
+#include "libqhullcpp/QhullVertexSet.h"
+#include "libqhullcpp/Qhull.h"
+#include "libqhullcpp/RboxPoints.h"
+
+using std::cout;
+using std::endl;
+using std::ostringstream;
+using std::ostream;
+using std::string;
+
+namespace orgQhull {
+
+class QhullFacetList_test : public RoadTest
+{
+    Q_OBJECT
+
+#//!\name Test slots
+private slots:
+    void cleanup();
+    void t_construct_qh();
+    void t_construct_q();
+    void t_convert();
+    void t_readonly();
+    void t_foreach();
+    void t_io();
+};//QhullFacetList_test
+
+void
+add_QhullFacetList_test()
+{
+    new QhullFacetList_test();  // RoadTest::s_testcases
+}
+
+//Executed after each testcase
+void QhullFacetList_test::
+cleanup()
+{
+    RoadTest::cleanup();
+}
+
+void QhullFacetList_test::
+t_construct_qh()
+{
+    RboxPoints rcube("c");
+    Qhull q(rcube,"QR0");  // rotated unit cube
+    QhullFacetList fs2= q.facetList();
+    QVERIFY(!fs2.isEmpty());
+    QCOMPARE(fs2.count(),6);
+    QhullFacetList fs3(q.endFacet(), q.endFacet());
+    QVERIFY(fs3.isEmpty());
+    QhullFacetList fs4(q.endFacet().previous(), q.endFacet());
+    QCOMPARE(fs4.count(), 1);
+    QhullFacetList fs5(q.beginFacet(), q.endFacet());
+    QCOMPARE(fs2.count(), fs5.count());
+    QVERIFY(fs2==fs5);
+    QhullFacetList fs6= fs2; // copy constructor
+    QVERIFY(fs6==fs2);
+    std::vector<QhullFacet> fv= fs2.toStdVector();
+    QCOMPARE(fv.size(), 6u);
+}//t_construct_qh
+
+void QhullFacetList_test::
+t_construct_q()
+{
+    RboxPoints rcube("c");
+    Qhull q(rcube,"QR0");  // rotated unit cube
+    QhullFacetList fs2= q.facetList();
+    QVERIFY(!fs2.isEmpty());
+    QCOMPARE(fs2.count(),6);
+    QhullFacetList fs3(q.endFacet(), q.endFacet());
+    QVERIFY(fs3.isEmpty());
+    QhullFacetList fs4(q.endFacet().previous(), q.endFacet());
+    QCOMPARE(fs4.count(), 1);
+    QhullFacetList fs5(q.beginFacet(), q.endFacet());
+    QCOMPARE(fs2.count(), fs5.count());
+    QVERIFY(fs2==fs5);
+    QhullFacetList fs6= fs2; // copy constructor
+    QVERIFY(fs6==fs2);
+    std::vector<QhullFacet> fv= fs2.toStdVector();
+    QCOMPARE(fv.size(), 6u);
+}//t_construct_q
+
+void QhullFacetList_test::
+t_convert()
+{
+    RboxPoints rcube("c");
+    Qhull q(rcube,"QR0 QV2");  // rotated unit cube
+    QhullFacetList fs2= q.facetList();
+    QVERIFY(!fs2.isSelectAll());
+    QVERIFY(!fs2.isEmpty());
+    QCOMPARE(fs2.count(),3);
+    std::vector<QhullFacet> fv= fs2.toStdVector();
+    QCOMPARE(fv.size(), 3u);
+    QList<QhullFacet> fv2= fs2.toQList();
+    QCOMPARE(fv2.size(), 3);
+    std::vector<QhullVertex> fv5= fs2.vertices_toStdVector();
+    QCOMPARE(fv5.size(), 7u);
+    QList<QhullVertex> fv6= fs2.vertices_toQList();
+    QCOMPARE(fv6.size(), 7);
+    fs2.selectAll();
+    QVERIFY(fs2.isSelectAll());
+    std::vector<QhullFacet> fv3= fs2.toStdVector();
+    QCOMPARE(fv3.size(), 6u);
+    QList<QhullFacet> fv4= fs2.toQList();
+    QCOMPARE(fv4.size(), 6);
+    std::vector<QhullVertex> fv7= fs2.vertices_toStdVector();
+    QCOMPARE(fv7.size(), 8u);
+    QList<QhullVertex> fv8= fs2.vertices_toQList();
+    QCOMPARE(fv8.size(), 8);
+}//t_convert
+
+//! Spot check properties and read-only.  See QhullLinkedList_test
+void QhullFacetList_test::
+t_readonly()
+{
+    RboxPoints rcube("c");
+    Qhull q(rcube,"QV0");  // good facets are adjacent to point 0
+    QhullFacetList fs= q.facetList();
+    QVERIFY(!fs.isSelectAll());
+    QCOMPARE(fs.count(), 3);
+    QCOMPARE(fs.first(), q.firstFacet());
+    fs.selectAll();
+    QVERIFY(fs.isSelectAll());
+    QCOMPARE(fs.count(), 6);
+    fs.selectGood();
+    QVERIFY(!fs.isSelectAll());
+    QCOMPARE(fs.count(), 3);
+    fs.selectAll();
+    QVERIFY(fs.isSelectAll());
+    QCOMPARE(fs.count(), 6);
+    QhullFacet f= fs.first();
+    QhullFacet f2= fs.last();
+    fs.selectAll();
+    QVERIFY(fs.contains(f));
+    QVERIFY(fs.contains(f2));
+    QVERIFY(f.isGood());
+    QVERIFY(!f2.isGood());
+    fs.selectGood();
+    QVERIFY(fs.contains(f));
+    QVERIFY(!fs.contains(f2));
+}//t_readonly
+
+void QhullFacetList_test::
+t_foreach()
+{
+    RboxPoints rcube("c");
+    // Spot check predicates and accessors.  See QhullLinkedList_test
+    Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
+    QhullFacetList fs= q.facetList();
+    QVERIFY(fs.contains(q.firstFacet()));
+    QhullFacet f= q.firstFacet().next();
+    QVERIFY(fs.contains(f));
+    QCOMPARE(fs.first(), *fs.begin());
+    QCOMPARE(*(fs.end()-1), fs.last());
+    QCOMPARE(fs.first(), q.firstFacet());
+    QCOMPARE(*fs.begin(), q.beginFacet());
+    QCOMPARE(*fs.end(), q.endFacet());
+}//t_foreach
+
+void QhullFacetList_test::
+t_io()
+{
+    RboxPoints rcube("c");
+    {
+        Qhull q(rcube,"QR0 QV0");   // good facets are adjacent to point 0
+        QhullFacetList fs= q.facetList();
+        ostringstream os;
+        os << fs.print("Show all of FacetList\n");
+        os << "\nFacets only\n" << fs;
+        os << "\nVertices only\n" << fs.printVertices();
+        cout << os.str();
+        QString facets= QString::fromStdString(os.str());
+        QCOMPARE(facets.count("(v"), 2*7+12*3*2);
+        QCOMPARE(facets.count(QRegExp("f\\d")), 2*3*7 + 13*3*2);
+    }
+}//t_io
+
+}//orgQhull
+
+#include "moc/QhullFacetList_test.moc"
diff --git a/xs/src/qhull/src/qhulltest/QhullFacetSet_test.cpp b/xs/src/qhull/src/qhulltest/QhullFacetSet_test.cpp
new file mode 100644
index 0000000000..a7fe123a28
--- /dev/null
+++ b/xs/src/qhull/src/qhulltest/QhullFacetSet_test.cpp
@@ -0,0 +1,153 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
+** $Id: //main/2015/qhull/src/qhulltest/QhullFacetSet_test.cpp#3 $$Change: 2062 $
+** $DateTime: 2016/01/17 13:13:18 $$Author: bbarber $
+**
+****************************************************************************/
+
+//pre-compiled headers
+#include <iostream>
+#include "qhulltest/RoadTest.h" // QT_VERSION
+
+#include "libqhullcpp/QhullFacetSet.h"
+#include "libqhullcpp/QhullError.h"
+#include "libqhullcpp/QhullFacet.h"
+#include "libqhullcpp/Qhull.h"
+#include "libqhullcpp/RboxPoints.h"
+
+using std::cout;
+using std::endl;
+using std::ostringstream;
+using std::ostream;
+using std::string;
+
+namespace orgQhull {
+
+class QhullFacetSet_test : public RoadTest
+{
+    Q_OBJECT
+
+#//!\name Test slots
+private slots:
+    void cleanup();
+    void t_construct();
+    void t_convert();
+    void t_readonly();
+    void t_foreach();
+    void t_io();
+};//QhullFacetSet_test
+
+void
+add_QhullFacetSet_test()
+{
+    new QhullFacetSet_test();  // RoadTest::s_testcases
+}
+
+//Executed after each testcase
+void QhullFacetSet_test::
+cleanup()
+{
+    RoadTest::cleanup();
+}
+
+void QhullFacetSet_test::
+t_construct()
+{
+    RboxPoints rcube("c");
+    Qhull q(rcube,"QR0");  // rotated unit cube
+    QhullFacet f= q.firstFacet();
+    QhullFacetSet fs2= f.neighborFacets();
+    QVERIFY(!fs2.isEmpty());
+    QCOMPARE(fs2.count(),4);
+    QhullFacetSet fs4= fs2; // copy constructor
+    QVERIFY(fs4==fs2);
+    QhullFacetSet fs3(q, q.qh()->facet_mergeset);
+    QVERIFY(fs3.isEmpty());
+}//t_construct
+
+void QhullFacetSet_test::
+t_convert()
+{
+    RboxPoints rcube("c");
+    Qhull q2(rcube,"QR0 QV2");  // rotated unit cube
+    QhullFacet f2= q2.firstFacet();
+    QhullFacetSet fs2= f2.neighborFacets();
+    QVERIFY(!fs2.isSelectAll());
+    QCOMPARE(fs2.count(),2);
+    std::vector<QhullFacet> fv= fs2.toStdVector();
+    QCOMPARE(fv.size(), 2u);
+    QList<QhullFacet> fv2= fs2.toQList();
+    QCOMPARE(fv2.size(), 2);
+    fs2.selectAll();
+    QVERIFY(fs2.isSelectAll());
+    std::vector<QhullFacet> fv3= fs2.toStdVector();
+    QCOMPARE(fv3.size(), 4u);
+    QList<QhullFacet> fv4= fs2.toQList();
+    QCOMPARE(fv4.size(), 4);
+}//t_convert
+
+//! Spot check properties and read-only.  See QhullSet_test
+void QhullFacetSet_test::
+t_readonly()
+{
+    RboxPoints rcube("c");
+    Qhull q(rcube,"QV0");  // good facets are adjacent to point 0
+    QhullFacetSet fs= q.firstFacet().neighborFacets();
+    QVERIFY(!fs.isSelectAll());
+    QCOMPARE(fs.count(), 2);
+    fs.selectAll();
+    QVERIFY(fs.isSelectAll());
+    QCOMPARE(fs.count(), 4);
+    fs.selectGood();
+    QVERIFY(!fs.isSelectAll());
+    QCOMPARE(fs.count(), 2);
+    QhullFacet f= fs.first();
+    QhullFacet f2= fs.last();
+    fs.selectAll();
+    QVERIFY(fs.contains(f));
+    QVERIFY(fs.contains(f2));
+    QVERIFY(f.isGood());
+    QVERIFY(!f2.isGood());
+    fs.selectGood();
+    QVERIFY(fs.contains(f));
+    QVERIFY(!fs.contains(f2));
+}//t_readonly
+
+void QhullFacetSet_test::
+t_foreach()
+{
+    RboxPoints rcube("c");
+    // Spot check predicates and accessors.  See QhullLinkedList_test
+    Qhull q(rcube,"QR0");  // rotated unit cube
+    QhullFacetSet fs= q.firstFacet().neighborFacets();
+    QVERIFY(!fs.contains(q.firstFacet()));
+    QVERIFY(fs.contains(fs.first()));
+    QhullFacet f= q.firstFacet().next();
+    if(!fs.contains(f)){  // check if 'f' is the facet opposite firstFacet()
+        f= f.next();
+    }
+    QVERIFY(fs.contains(f));
+    QCOMPARE(fs.first(), *fs.begin());
+    QCOMPARE(*(fs.end()-1), fs.last());
+}//t_foreach
+
+void QhullFacetSet_test::
+t_io()
+{
+    RboxPoints rcube("c");
+    {
+        Qhull q(rcube,"QR0 QV0");   // good facets are adjacent to point 0
+        QhullFacetSet fs= q.firstFacet().neighborFacets();
+        ostringstream os;
+        os << fs.print("Neighbors of first facet with point 0");
+        os << fs.printIdentifiers("\nFacet identifiers: ");
+        cout << os.str();
+        QString facets= QString::fromStdString(os.str());
+        QCOMPARE(facets.count(QRegExp(" f[0-9]")), 2+13*2);
+    }
+}//t_io
+
+}//orgQhull
+
+#include "moc/QhullFacetSet_test.moc"
diff --git a/xs/src/qhull/src/qhulltest/QhullFacet_test.cpp b/xs/src/qhull/src/qhulltest/QhullFacet_test.cpp
new file mode 100644
index 0000000000..271f63753c
--- /dev/null
+++ b/xs/src/qhull/src/qhulltest/QhullFacet_test.cpp
@@ -0,0 +1,283 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
+** $Id: //main/2015/qhull/src/qhulltest/QhullFacet_test.cpp#4 $$Change: 2062 $
+** $DateTime: 2016/01/17 13:13:18 $$Author: bbarber $
+**
+****************************************************************************/
+
+//pre-compiled headers
+#include <iostream>
+#include "qhulltest/RoadTest.h" // QT_VERSION
+
+#include "libqhullcpp/QhullFacet.h"
+#include "libqhullcpp/QhullError.h"
+#include "libqhullcpp/Coordinates.h"
+#include "libqhullcpp/RboxPoints.h"
+#include "libqhullcpp/QhullFacetList.h"
+#include "libqhullcpp/QhullFacetSet.h"
+#include "libqhullcpp/QhullPointSet.h"
+#include "libqhullcpp/QhullRidge.h"
+#include "libqhullcpp/Qhull.h"
+
+using std::cout;
+using std::endl;
+using std::ostringstream;
+using std::ostream;
+using std::string;
+
+namespace orgQhull {
+
+class QhullFacet_test : public RoadTest
+{
+    Q_OBJECT
+
+#//!\name Test slots
+private slots:
+    void cleanup();
+    void t_construct_qh();
+    void t_constructConvert();
+    void t_getSet();
+    void t_value();
+    void t_foreach();
+    void t_io();
+};//QhullFacet_test
+
+void
+add_QhullFacet_test()
+{
+    new QhullFacet_test();  // RoadTest::s_testcases
+}
+
+//Executed after each testcase
+void QhullFacet_test::
+cleanup()
+{
+    RoadTest::cleanup();
+}
+
+void QhullFacet_test::
+t_construct_qh()
+{
+    // Qhull.runQhull() constructs QhullFacets as facetT
+    QhullQh qh;
+    QhullFacet f(&qh);
+    QVERIFY(!f.isValid());
+    QCOMPARE(f.dimension(),0);
+}//t_construct_qh
+
+void QhullFacet_test::
+t_constructConvert()
+{
+    // Qhull.runQhull() constructs QhullFacets as facetT
+    Qhull q2;
+    QhullFacet f(q2);
+    QVERIFY(!f.isValid());
+    QCOMPARE(f.dimension(),0);
+    RboxPoints rcube("c");
+    Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
+    QhullFacet f2(q.beginFacet());
+    QCOMPARE(f2.dimension(),3);
+    f= f2; // copy assignment
+    QVERIFY(f.isValid());
+    QCOMPARE(f.dimension(),3);
+    QhullFacet f5= f2;
+    QVERIFY(f5==f2);
+    QVERIFY(f5==f);
+    QhullFacet f3(q, f2.getFacetT());
+    QCOMPARE(f,f3);
+    QhullFacet f4(q, f2.getBaseT());
+    QCOMPARE(f,f4);
+}//t_constructConvert
+
+void QhullFacet_test::
+t_getSet()
+{
+    RboxPoints rcube("c");
+    {
+        Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
+        cout << " rbox c | qhull Qt QR0 QR" << q.rotateRandom() << "   distanceEpsilon " << q.distanceEpsilon() << endl;
+        QCOMPARE(q.facetCount(), 12);
+        QCOMPARE(q.vertexCount(), 8);
+        QhullFacetListIterator i(q.facetList());
+        while(i.hasNext()){
+            const QhullFacet f= i.next();
+            cout << f.id() << endl;
+            QCOMPARE(f.dimension(),3);
+            QVERIFY(f.id()>0 && f.id()<=39);
+            QVERIFY(f.isValid());
+            if(i.hasNext()){
+                QCOMPARE(f.next(), i.peekNext());
+                QVERIFY(f.next()!=f);
+            }
+            QVERIFY(i.hasPrevious());
+            QCOMPARE(f, i.peekPrevious());
+        }
+
+        // test tricoplanarOwner
+        QhullFacet facet = q.beginFacet();
+        QhullFacet tricoplanarOwner = facet.tricoplanarOwner();
+        int tricoplanarCount= 0;
+        i.toFront();
+        while(i.hasNext()){
+            const QhullFacet f= i.next();
+            if(f.tricoplanarOwner()==tricoplanarOwner){
+                tricoplanarCount++;
+            }
+        }
+        QCOMPARE(tricoplanarCount, 2);
+        int tricoplanarCount2= 0;
+        foreach (QhullFacet f, q.facetList()){  // Qt only
+            QhullHyperplane h= f.hyperplane();
+            cout << "Hyperplane: " << h;
+            QCOMPARE(h.count(), 3);
+            QCOMPARE(h.offset(), -0.5);
+            double n= h.norm();
+            QCOMPARE(n, 1.0);
+            QhullHyperplane hi= f.innerplane();
+            QCOMPARE(hi.count(), 3);
+            double innerOffset= hi.offset()+0.5;
+            cout << "InnerPlane: " << hi << "   innerOffset+0.5 " << innerOffset << endl;
+            QVERIFY(innerOffset >= 0.0-(2*q.distanceEpsilon())); // A guessed epsilon.  It needs to account for roundoff due to rotation of the vertices
+            QhullHyperplane ho= f.outerplane();
+            QCOMPARE(ho.count(), 3);
+            double outerOffset= ho.offset()+0.5;
+            cout << "OuterPlane: " << ho << "   outerOffset+0.5 " << outerOffset << endl;
+            QVERIFY(outerOffset <= 0.0+(2*q.distanceEpsilon())); // A guessed epsilon.  It needs to account for roundoff due to rotation of the vertices
+            QVERIFY(outerOffset-innerOffset < 1e-7);
+            for(int k= 0; k<3; k++){
+                QVERIFY(ho[k]==hi[k]);
+                QVERIFY(ho[k]==h[k]);
+            }
+            QhullPoint center= f.getCenter();
+            cout << "Center: " << center;
+            double d= f.distance(center);
+            QVERIFY(d < innerOffset-outerOffset);
+            QhullPoint center2= f.getCenter(qh_PRINTcentrums);
+            QCOMPARE(center, center2);
+            if(f.tricoplanarOwner()==tricoplanarOwner){
+                tricoplanarCount2++;
+            }
+            cout << endl;
+        }
+        QCOMPARE(tricoplanarCount2, 2);
+        Qhull q2(rcube,"d Qz Qt QR0");  // 3-d triangulation of Delaunay triangulation (the cube)
+        cout << " rbox c | qhull d Qz Qt QR0 QR" << q2.rotateRandom() << "   distanceEpsilon " << q2.distanceEpsilon() << endl;
+        QhullFacet f2= q2.firstFacet();
+        QhullPoint center3= f2.getCenter(qh_PRINTtriangles);
+        QCOMPARE(center3.dimension(), 3);
+        QhullPoint center4= f2.getCenter();
+        QCOMPARE(center4.dimension(), 4);
+        for(int k= 0; k<3; k++){
+            QVERIFY(center4[k]==center3[k]);
+        }
+        Qhull q3(rcube,"v Qz QR0");  // Voronoi diagram of a cube (one vertex)
+        cout << " rbox c | qhull v Qz QR0 QR" << q3.rotateRandom() << "   distanceEpsilon " << q3.distanceEpsilon() << endl;
+
+        q3.setFactorEpsilon(400); // Voronoi vertices are not necessarily within distance episilon
+        QhullPoint origin= q3.inputOrigin();
+        int voronoiCount= 0;
+        foreach(QhullFacet f, q3.facetList()){ //Qt only
+            if(f.isGood()){
+                ++voronoiCount;
+                QhullPoint p= f.voronoiVertex();
+                cout << p.print("Voronoi vertex: ")
+                    << " Is it within " << q3.factorEpsilon() << " * distanceEpsilon (" << q3.distanceEpsilon() << ") of the origin?" << endl;
+                QCOMPARE(p, origin);
+            }
+        }
+        QCOMPARE(voronoiCount, 1);
+    }
+}//t_getSet
+
+void QhullFacet_test::
+t_value()
+{
+    RboxPoints rcube("c");
+    {
+        Qhull q(rcube, "");
+        coordT c[]= {0.0, 0.0, 0.0};
+        foreach (QhullFacet f, q.facetList()){  // Qt only
+            double d= f.distance(q.origin());
+            QCOMPARE(d, -0.5);
+            double d0= f.distance(c);
+            QCOMPARE(d0, -0.5);
+            double facetArea= f.facetArea();
+            QCOMPARE(facetArea, 1.0);
+            #if qh_MAXoutside
+                double maxoutside= f.getFacetT()->maxoutside;
+                QVERIFY(maxoutside<1e-7);
+            #endif
+        }
+    }
+}//t_value
+
+void QhullFacet_test::
+t_foreach()
+{
+    RboxPoints rcube("c W0 300");  // cube plus 300 points on its surface
+    {
+        Qhull q(rcube, "QR0 Qc"); // keep coplanars, thick facet, and rotate the cube
+        int coplanarCount= 0;
+        foreach(const QhullFacet f, q.facetList()){
+            QhullPointSet coplanars= f.coplanarPoints();
+            coplanarCount += coplanars.count();
+            QhullFacetSet neighbors= f.neighborFacets();
+            QCOMPARE(neighbors.count(), 4);
+            QhullPointSet outsides= f.outsidePoints();
+            QCOMPARE(outsides.count(), 0);
+            QhullRidgeSet ridges= f.ridges();
+            QCOMPARE(ridges.count(), 4);
+            QhullVertexSet vertices= f.vertices();
+            QCOMPARE(vertices.count(), 4);
+            int ridgeCount= 0;
+            QhullRidge r= ridges.first();
+            for(int r0= r.id(); ridgeCount==0 || r.id()!=r0; r= r.nextRidge3d(f)){
+                ++ridgeCount;
+                if(!r.hasNextRidge3d(f)){
+                    QFAIL("Unexpected simplicial facet.  They only have ridges to non-simplicial neighbors.");
+                }
+            }
+            QCOMPARE(ridgeCount, 4);
+        }
+        QCOMPARE(coplanarCount, 300);
+    }
+}//t_foreach
+
+void QhullFacet_test::
+t_io()
+{
+    RboxPoints rcube("c");
+    {
+        Qhull q(rcube, "");
+        QhullFacet f= q.beginFacet();
+        cout << f;
+        ostringstream os;
+        os << f.print("\nWith a message\n");
+        os << "\nPrint header for the same facet\n";
+        os << f.printHeader();
+        os << "\nPrint each component\n";
+        os << f.printFlags("    - flags:");
+        os << f.printCenter(qh_PRINTfacets, "    - center: ");
+        os << f.printRidges();
+        cout << os.str();
+        ostringstream os2;
+        os2 << f;
+        QString facetString2= QString::fromStdString(os2.str());
+        facetString2.replace(QRegExp("\\s\\s+"), " ");
+        ostringstream os3;
+        q.qh()->setOutputStream(&os3);
+        q.outputQhull("f");
+        QString facetsString= QString::fromStdString(os3.str());
+        QString facetString3= facetsString.mid(facetsString.indexOf("- f1\n"));
+        facetString3= facetString3.left(facetString3.indexOf("\n- f")+1);
+        facetString3.replace(QRegExp("\\s\\s+"), " ");
+        QCOMPARE(facetString2, facetString3);
+    }
+}//t_io
+
+// toQhullFacet is static_cast only
+
+}//orgQhull
+
+#include "moc/QhullFacet_test.moc"
diff --git a/xs/src/qhull/src/qhulltest/QhullHyperplane_test.cpp b/xs/src/qhull/src/qhulltest/QhullHyperplane_test.cpp
new file mode 100644
index 0000000000..d016989a97
--- /dev/null
+++ b/xs/src/qhull/src/qhulltest/QhullHyperplane_test.cpp
@@ -0,0 +1,429 @@
+/****************************************************************************
+**
+** Copyright (c) 2009-2015 C.B. Barber. All rights reserved.
+** $Id: //main/2015/qhull/src/qhulltest/QhullHyperplane_test.cpp#4 $$Change: 2064 $
+** $DateTime: 2016/01/18 12:36:08 $$Author: bbarber $
+**
+****************************************************************************/
+
+//pre-compiled headers
+#include <iostream>
+#include "qhulltest/RoadTest.h" // QT_VERSION
+
+#include "libqhullcpp/QhullHyperplane.h"
+#include "libqhullcpp/QhullError.h"
+#include "libqhullcpp/RboxPoints.h"
+#include "libqhullcpp/QhullFacet.h"
+#include "libqhullcpp/QhullFacetList.h"
+#include "libqhullcpp/QhullFacetSet.h"
+#include "libqhullcpp/Qhull.h"
+
+#include <numeric>
+#include <vector>
+
+using std::cout;
+using std::endl;
+using std::ostringstream;
+using std::ostream;
+using std::string;
+
+namespace orgQhull {
+
+class QhullHyperplane_test : public RoadTest
+{
+    Q_OBJECT
+
+#//!\name Test slots
+private slots:
+    void cleanup();
+    void t_construct();
+    void t_construct_qh();
+    void t_convert();
+    void t_readonly();
+    void t_define();
+    void t_value();
+    void t_operator();
+    void t_iterator();
+    void t_const_iterator();
+    void t_qhullHyperplane_iterator();
+    void t_io();
+};//QhullHyperplane_test
+
+void
+add_QhullHyperplane_test()
+{
+    new QhullHyperplane_test();  // RoadTest::s_testcases
+}
+
+//Executed after each testcase
+void QhullHyperplane_test::
+cleanup()
+{
+    RoadTest::cleanup();
+}
+
+void QhullHyperplane_test::
+t_construct()
+{
+    QhullHyperplane h4;
+    QVERIFY(!h4.isValid());
+    QCOMPARE(h4.dimension(), 0);
+    // Qhull.runQhull() constructs QhullFacets as facetT
+    RboxPoints rcube("c");
+    Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
+    QhullHyperplane h(q);
+    QVERIFY(!h.isValid());
+    QCOMPARE(h.dimension(), 0);
+    QCOMPARE(h.coordinates(),static_cast<double *>(0));
+    QhullFacet f= q.firstFacet();
+    QhullHyperplane h2(f.hyperplane());
+    QVERIFY(h2.isValid());
+    QCOMPARE(h2.dimension(), 3);
+    h= h2;
+    QCOMPARE(h, h2);
+    QhullHyperplane h3(q, h2.dimension(), h2.coordinates(), h2.offset());
+    QCOMPARE(h2, h3);
+    QhullHyperplane h5= h2; // copy constructor
+    QVERIFY(h5==h2);
+}//t_construct
+
+void QhullHyperplane_test::
+t_construct_qh()
+{
+    // Qhull.runQhull() constructs QhullFacets as facetT
+    RboxPoints rcube("c");
+    Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
+    QhullFacet f= q.firstFacet();
+    QhullHyperplane h2(f.hyperplane());
+    QVERIFY(h2.isValid());
+    QCOMPARE(h2.dimension(), 3);
+    // h= h2;  // copy assignment disabled, ambiguous
+    QhullHyperplane h3(q.qh(), h2.dimension(), h2.coordinates(), h2.offset());
+    QCOMPARE(h2, h3);
+    QhullHyperplane h5= h2; // copy constructor
+    QVERIFY(h5==h2);
+}//t_construct_qh
+
+void QhullHyperplane_test::
+t_convert()
+{
+    RboxPoints rcube("c");
+    Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
+    QhullHyperplane h= q.firstFacet().hyperplane();
+    std::vector<double> fs= h.toStdVector();
+    QCOMPARE(fs.size(), 4u);
+    double offset= fs.back();
+    fs.pop_back();
+    QCOMPARE(offset, -0.5);
+
+    double squareNorm= inner_product(fs.begin(), fs.end(), fs.begin(), 0.0);
+    QCOMPARE(squareNorm, 1.0);
+    QList<double> qs= h.toQList();
+    QCOMPARE(qs.size(), 4);
+    double offset2= qs.takeLast();
+    QCOMPARE(offset2, -0.5);
+    double squareNorm2= std::inner_product(qs.begin(), qs.end(), qs.begin(), 0.0);
+    QCOMPARE(squareNorm2, 1.0);
+}//t_convert
+
+void QhullHyperplane_test::
+t_readonly()
+{
+    RboxPoints rcube("c");
+    {
+        Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
+        QhullFacetList fs= q.facetList();
+        QhullFacetListIterator i(fs);
+        while(i.hasNext()){
+            QhullFacet f= i.next();
+            QhullHyperplane h= f.hyperplane();
+            int id= f.id();
+            cout << "h" << id << endl;
+            QVERIFY(h.isValid());
+            QCOMPARE(h.dimension(),3);
+            const coordT *c= h.coordinates();
+            coordT *c2= h.coordinates();
+            QCOMPARE(c, c2);
+            const coordT *c3= h.begin();
+            QCOMPARE(c, c3);
+            QCOMPARE(h.offset(), -0.5);
+            int j= h.end()-h.begin();
+            QCOMPARE(j, 3);
+            double squareNorm= std::inner_product(h.begin(), h.end(), h.begin(), 0.0);
+            QCOMPARE(squareNorm, 1.0);
+        }
+        QhullHyperplane h2= fs.first().hyperplane();
+        QhullHyperplane h3= fs.last().hyperplane();
+        QVERIFY(h2!=h3);
+        QVERIFY(h3.coordinates()!=h2.coordinates());
+    }
+}//t_readonly
+
+void QhullHyperplane_test::
+t_define()
+{
+    RboxPoints rcube("c");
+    {
+        Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
+        QhullFacetList fs= q.facetList();
+        QhullHyperplane h= fs.first().hyperplane();
+        QhullHyperplane h2= h;
+        QVERIFY(h==h2);
+        QhullHyperplane h3= fs.last().hyperplane();
+        QVERIFY(h2!=h3);
+
+        QhullHyperplane h4= h3;
+        h4.defineAs(h2);
+        QVERIFY(h2==h4);
+        QhullHyperplane p5= h3;
+        p5.defineAs(h2.dimension(), h2.coordinates(), h2.offset());
+        QVERIFY(h2==p5);
+        QhullHyperplane h6= h3;
+        h6.setCoordinates(h2.coordinates());
+        QCOMPARE(h2.coordinates(), h6.coordinates());
+        h6.setOffset(h2.offset());
+        QCOMPARE(h2.offset(), h6.offset());
+        QVERIFY(h2==h6);
+        h6.setDimension(2);
+        QCOMPARE(h6.dimension(), 2);
+        QVERIFY(h2!=h6);
+    }
+}//t_define
+
+void QhullHyperplane_test::
+t_value()
+{
+    RboxPoints rcube("c G1");
+    Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
+    QhullFacet f= q.firstFacet();
+    QhullFacet f2= f.neighborFacets().at(0);
+    const QhullHyperplane h= f.hyperplane();
+    const QhullHyperplane h2= f2.hyperplane();   // At right angles
+    double dist= h.distance(q.origin());
+    QCOMPARE(dist, -1.0);
+    double norm= h.norm();
+    QCOMPARE(norm, 1.0);
+    double angle= h.hyperplaneAngle(h2);
+    cout << "angle " << angle << endl;
+    QCOMPARE(angle+1.0, 1.0); // qFuzzyCompare does not work for 0.0
+    QVERIFY(h==h);
+    QVERIFY(h!=h2);
+}//t_value
+
+void QhullHyperplane_test::
+t_operator()
+{
+    RboxPoints rcube("c");
+    Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
+    const QhullHyperplane h= q.firstFacet().hyperplane();
+    //operator== and operator!= tested elsewhere
+    const coordT *c= h.coordinates();
+    for(int k=h.dimension(); k--; ){
+        QCOMPARE(c[k], h[k]);
+    }
+    //h[0]= 10.0; // compiler error, const
+    QhullHyperplane h2= q.firstFacet().hyperplane();
+    h2[0]= 10.0;  // Overwrites Hyperplane coordinate!
+    QCOMPARE(h2[0], 10.0);
+}//t_operator
+
+void QhullHyperplane_test::
+t_iterator()
+{
+    RboxPoints rcube("c");
+    {
+        Qhull q(rcube,"QR0");  // rotated unit cube
+        QhullHyperplane h= q.firstFacet().hyperplane();
+        QCOMPARE(h.count(), 3);
+        QCOMPARE(h.size(), 3u);
+        QhullHyperplane::Iterator i= h.begin();
+        QhullHyperplane::iterator i2= h.begin();
+        QVERIFY(i==i2);
+        QVERIFY(i>=i2);
+        QVERIFY(i<=i2);
+        i= h.begin();
+        QVERIFY(i==i2);
+        i2= h.end();
+        QVERIFY(i!=i2);
+        double d3= *i;
+        i2--;
+        double d2= *i2;
+        QCOMPARE(d3, h[0]);
+        QCOMPARE(d2, h[2]);
+        QhullHyperplane::Iterator i3(i2);
+        QCOMPARE(*i2, *i3);
+
+        (i3= i)++;
+        QCOMPARE((*i3), h[1]);
+        QVERIFY(i==i);
+        QVERIFY(i!=i2);
+        QVERIFY(i<i2);
+        QVERIFY(i<=i2);
+        QVERIFY(i2>i);
+        QVERIFY(i2>=i);
+
+        QhullHyperplane::ConstIterator i4= h.begin();
+        QVERIFY(i==i4); // iterator COMP const_iterator
+        QVERIFY(i<=i4);
+        QVERIFY(i>=i4);
+        QVERIFY(i4==i); // const_iterator COMP iterator
+        QVERIFY(i4<=i);
+        QVERIFY(i4>=i);
+        QVERIFY(i>=i4);
+        QVERIFY(i4<=i);
+        QVERIFY(i2!=i4);
+        QVERIFY(i2>i4);
+        QVERIFY(i2>=i4);
+        QVERIFY(i4!=i2);
+        QVERIFY(i4<i2);
+        QVERIFY(i4<=i2);
+        ++i4;
+        QVERIFY(i<i4);
+        QVERIFY(i<=i4);
+        QVERIFY(i4>i);
+        QVERIFY(i4>=i);
+
+        i= h.begin();
+        i2= h.begin();
+        QCOMPARE(i, i2++);
+        QCOMPARE(*i2, h[1]);
+        QCOMPARE(++i, i2);
+        QCOMPARE(i, i2--);
+        QCOMPARE(i2, h.begin());
+        QCOMPARE(--i, i2);
+        QCOMPARE(i2 += 3, h.end());
+        QCOMPARE(i2 -= 3, h.begin());
+        QCOMPARE(i2+0, h.begin());
+        QCOMPARE(i2+3, h.end());
+        i2 += 3;
+        i= i2-0;
+        QCOMPARE(i, i2);
+        i= i2-3;
+        QCOMPARE(i, h.begin());
+        QCOMPARE(i2-i, 3);
+
+        //h.begin end tested above
+
+        // QhullHyperplane is const-only
+    }
+}//t_iterator
+
+void QhullHyperplane_test::
+t_const_iterator()
+{
+    RboxPoints rcube("c");
+    {
+        Qhull q(rcube,"QR0");  // rotated unit cube
+        QhullHyperplane h= q.firstFacet().hyperplane();
+        QhullHyperplane::ConstIterator i= h.begin();
+        QhullHyperplane::const_iterator i2= h.begin();
+        QVERIFY(i==i2);
+        QVERIFY(i>=i2);
+        QVERIFY(i<=i2);
+        i= h.begin();
+        QVERIFY(i==i2);
+        i2= h.end();
+        QVERIFY(i!=i2);
+        double d3= *i;
+        i2--;
+        double d2= *i2;
+        QCOMPARE(d3, h[0]);
+        QCOMPARE(d2, h[2]);
+        QhullHyperplane::ConstIterator i3(i2);
+        QCOMPARE(*i2, *i3);
+
+        (i3= i)++;
+        QCOMPARE((*i3), h[1]);
+        QVERIFY(i==i);
+        QVERIFY(i!=i2);
+        QVERIFY(i<i2);
+        QVERIFY(i<=i2);
+        QVERIFY(i2>i);
+        QVERIFY(i2>=i);
+
+        // See t_iterator for const_iterator COMP iterator
+
+        i= h.begin();
+        i2= h.constBegin();
+        QCOMPARE(i, i2++);
+        QCOMPARE(*i2, h[1]);
+        QCOMPARE(++i, i2);
+        QCOMPARE(i, i2--);
+        QCOMPARE(i2, h.constBegin());
+        QCOMPARE(--i, i2);
+        QCOMPARE(i2+=3, h.constEnd());
+        QCOMPARE(i2-=3, h.constBegin());
+        QCOMPARE(i2+0, h.constBegin());
+        QCOMPARE(i2+3, h.constEnd());
+        i2 += 3;
+        i= i2-0;
+        QCOMPARE(i, i2);
+        i= i2-3;
+        QCOMPARE(i, h.constBegin());
+        QCOMPARE(i2-i, 3);
+
+        // QhullHyperplane is const-only
+    }
+}//t_const_iterator
+
+void QhullHyperplane_test::
+t_qhullHyperplane_iterator()
+{
+    RboxPoints rcube("c");
+    Qhull q(rcube,"QR0");  // rotated unit cube
+    QhullHyperplane h = q.firstFacet().hyperplane();
+    QhullHyperplaneIterator i2(h);
+    QCOMPARE(h.dimension(), 3);
+    QhullHyperplaneIterator i= h;
+    QVERIFY(i2.hasNext());
+    QVERIFY(!i2.hasPrevious());
+    QVERIFY(i.hasNext());
+    QVERIFY(!i.hasPrevious());
+    i2.toBack();
+    i.toFront();
+    QVERIFY(!i2.hasNext());
+    QVERIFY(i2.hasPrevious());
+    QVERIFY(i.hasNext());
+    QVERIFY(!i.hasPrevious());
+
+    // i at front, i2 at end/back, 3 coordinates
+    QCOMPARE(i.peekNext(), h[0]);
+    QCOMPARE(i2.peekPrevious(), h[2]);
+    QCOMPARE(i2.previous(), h[2]);
+    QCOMPARE(i2.previous(), h[1]);
+    QCOMPARE(i2.previous(), h[0]);
+    QVERIFY(!i2.hasPrevious());
+    QCOMPARE(i.peekNext(), h[0]);
+    // i.peekNext()= 1.0; // compiler error, i is const
+    QCOMPARE(i.next(), h[0]);
+    QCOMPARE(i.peekNext(), h[1]);
+    QCOMPARE(i.next(), h[1]);
+    QCOMPARE(i.next(), h[2]);
+    QVERIFY(!i.hasNext());
+    i.toFront();
+    QCOMPARE(i.next(), h[0]);
+}//t_qhullHyperplane_iterator
+
+void QhullHyperplane_test::
+t_io()
+{
+    RboxPoints rcube("c");
+    {
+        Qhull q(rcube, "");
+        QhullHyperplane h= q.firstFacet().hyperplane();
+        ostringstream os;
+        os << "Hyperplane:\n";
+        os << h;
+        os << h.print("message");
+        os << h.print(" and a message ", " offset ");
+        cout << os.str();
+        QString s= QString::fromStdString(os.str());
+        QCOMPARE(s.count("1"), 3);
+        // QCOMPARE(s.count(QRegExp("f\\d")), 3*7 + 13*3*2);
+    }
+}//t_io
+
+
+}//orgQhull
+
+#include "moc/QhullHyperplane_test.moc"
diff --git a/xs/src/qhull/src/qhulltest/QhullLinkedList_test.cpp b/xs/src/qhull/src/qhulltest/QhullLinkedList_test.cpp
new file mode 100644
index 0000000000..e0cde4050f
--- /dev/null
+++ b/xs/src/qhull/src/qhulltest/QhullLinkedList_test.cpp
@@ -0,0 +1,330 @@
+/****************************************************************************
+**
+** Copyright (c) 2009-2015 C.B. Barber. All rights reserved.
+** $Id: //main/2015/qhull/src/qhulltest/QhullLinkedList_test.cpp#3 $$Change: 2062 $
+** $DateTime: 2016/01/17 13:13:18 $$Author: bbarber $
+**
+****************************************************************************/
+
+//pre-compiled headers
+#include <QtCore/QList>
+#include "qhulltest/RoadTest.h"
+
+#include "libqhullcpp/QhullLinkedList.h"
+#include "libqhullcpp/Qhull.h"
+#include "libqhullcpp/QhullVertex.h"
+#include "libqhullcpp/RboxPoints.h"
+
+namespace orgQhull {
+
+class QhullLinkedList_test : public RoadTest
+{
+    Q_OBJECT
+
+#//!\name Test slots
+private slots:
+    void cleanup();
+    void t_construct();
+    void t_convert();
+    void t_element();
+    void t_search();
+    void t_iterator();
+    void t_const_iterator();
+    void t_QhullLinkedList_iterator();
+    void t_io();
+};//QhullLinkedList_test
+
+void
+add_QhullLinkedList_test()
+{
+    new QhullLinkedList_test();  // RoadTest::s_testcases
+}
+
+//Executed after each testcase
+void QhullLinkedList_test::
+cleanup()
+{
+    RoadTest::cleanup();
+}
+
+void QhullLinkedList_test::
+t_construct()
+{
+    // QhullLinkedList vs; //private (compiler error).  No memory allocation
+    RboxPoints rcube("c");
+    {
+        Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
+        QCOMPARE(q.facetCount(), 12);
+        QhullVertexList vs = QhullVertexList(q.beginVertex(), q.endVertex());
+        QCOMPARE(vs.count(), 8);
+        QCOMPARE(vs.size(), 8u);
+        QVERIFY(!vs.isEmpty());
+        QhullVertexList vs2 = q.vertexList();
+        QCOMPARE(vs2.count(), 8);
+        QCOMPARE(vs2.size(),8u);
+        QVERIFY(!vs2.isEmpty());
+        QVERIFY(vs==vs2);
+        // vs= vs2; // disabled.  Would not copy the vertices
+        QhullVertexList vs3= vs2; // copy constructor
+        QVERIFY(vs3==vs2);
+    }
+}//t_construct
+
+void QhullLinkedList_test::
+t_convert()
+{
+    RboxPoints rcube("c");
+    {
+        Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
+        QCOMPARE(q.facetCount(), 12);
+        QhullVertexList vs = q.vertexList();
+        QCOMPARE(vs.size(), 8u);
+        QVERIFY(!vs.isEmpty());
+        std::vector<QhullVertex> vs2= vs.toStdVector();
+        QCOMPARE(vs2.size(), vs.size());
+        QhullVertexList::Iterator i= vs.begin();
+        for(int k= 0; k<(int)vs2.size(); k++){
+            QCOMPARE(vs2[k], *i++);
+        }
+        QList<QhullVertex> vs3= vs.toQList();
+        QCOMPARE(vs3.count(), vs.count());
+        i= vs.begin();
+        for(int k= 0; k<vs3.count(); k++){
+            QCOMPARE(vs3[k], *i++);
+        }
+        QhullVertexList vs4(q.endVertex(), q.endVertex());
+        QVERIFY(vs4.isEmpty());
+        QVERIFY(vs==vs);
+        QVERIFY(vs4==vs4);
+        QVERIFY(vs!=vs4);
+    }
+}//t_convert
+
+//ReadOnly tested by t_convert
+
+void QhullLinkedList_test::
+t_element()
+{
+    RboxPoints rcube("c");
+    Qhull q(rcube,"QR0");  // rotated unit cube
+    QhullVertexList vs = q.vertexList();
+    QhullVertex v= vs.first();
+    QCOMPARE(v.previous(), QhullVertex(NULL));
+    QCOMPARE(vs.front(), vs.first());
+    QhullVertex v2= vs.last();
+    QCOMPARE(v2.next().next(), QhullVertex(NULL)); // sentinel has NULL next
+    QCOMPARE(vs.back(), v2);
+    QCOMPARE(vs.back(), vs.last());
+}//t_element
+
+void QhullLinkedList_test::
+t_search()
+{
+    RboxPoints rcube("c");
+    Qhull q(rcube,"QR0");  // rotated unit cube
+    QhullVertexList vs = q.vertexList();
+    QhullVertex v(q);
+    QVERIFY(!vs.contains(v));
+    QCOMPARE(vs.count(v), 0);
+    QhullVertex v2= *vs.begin();
+    QhullVertex v3= vs.last();
+    QVERIFY(vs.contains(v2));
+    QCOMPARE(vs.count(v2), 1);
+    QVERIFY(vs.contains(v3));
+    QCOMPARE(vs.count(v3), 1);
+}//t_search
+
+void QhullLinkedList_test::
+t_iterator()
+{
+    RboxPoints rcube("c");
+    {
+        Qhull q(rcube,"QR0");  // rotated unit cube
+        QhullVertexList vs = q.vertexList();
+        QhullVertexList::Iterator i= vs.begin();
+        QhullVertexList::iterator i2= vs.begin();
+        QVERIFY(i==i2);
+        // No comparisons
+        i= vs.begin();
+        QVERIFY(i==i2);
+        i2= vs.end();
+        QVERIFY(i!=i2);
+        QhullVertex v3(*i);
+        i2--;
+        QhullVertex v8= *i2;
+        QhullVertex v= vs.first();
+        QhullVertex v2= v.next();
+        QCOMPARE(v3.id(), v.id());
+        QCOMPARE(v8.id(), vs.last().id());
+        QhullVertexList::Iterator i3(i2);
+        QCOMPARE(*i2, *i3);
+
+        (i3= i)++;
+        QCOMPARE((*i3).id(), v2.id());
+        QVERIFY(i==i);
+        QVERIFY(i!=i2);
+
+        QhullVertexList::ConstIterator i4= vs.begin();
+        QVERIFY(i==i4); // iterator COMP const_iterator
+        QVERIFY(i4==i); // const_iterator COMP iterator
+        QVERIFY(i2!=i4);
+        QVERIFY(i4!=i2);
+        ++i4;
+
+        i= vs.begin();
+        i2= vs.begin();
+        QCOMPARE(i, i2++);
+        QCOMPARE(*i2, v2);
+        QCOMPARE(++i, i2);
+        QCOMPARE(i, i2--);
+        QCOMPARE(i2, vs.begin());
+        QCOMPARE(--i, i2);
+        QCOMPARE(i2 += 8, vs.end());
+        QCOMPARE(i2 -= 8, vs.begin());
+        QCOMPARE(i2+0, vs.begin());
+        QCOMPARE(i2+8, vs.end());
+        i2 += 8;
+        i= i2-0;
+        QCOMPARE(i, i2);
+        i= i2-8;
+        QCOMPARE(i, vs.begin());
+
+        //vs.begin end tested above
+
+        // QhullVertexList is const-only
+    }
+}//t_iterator
+
+void QhullLinkedList_test::
+t_const_iterator()
+{
+    RboxPoints rcube("c");
+    {
+        Qhull q(rcube,"QR0");  // rotated unit cube
+        QhullVertexList vs = q.vertexList();
+        QhullVertexList::ConstIterator i= vs.begin();
+        QhullVertexList::const_iterator i2= vs.begin();
+        QVERIFY(i==i2);
+        i= vs.begin();
+        QVERIFY(i==i2);
+        i2= vs.end();
+        QVERIFY(i!=i2);
+        QhullVertex v3(*i);
+        i2--;
+        QhullVertex v8= *i2;
+        QhullVertex v= vs.first();
+        QhullVertex v2= v.next();
+        QCOMPARE(v3.id(), v.id());
+        QCOMPARE(v8.id(), vs.last().id());
+        QhullVertexList::ConstIterator i3(i2);
+        QCOMPARE(*i2, *i3);
+
+        (i3= i)++;
+        QCOMPARE((*i3).id(), v2.id());
+        QVERIFY(i==i);
+        QVERIFY(i!=i2);
+
+        // See t_iterator for const_iterator COMP iterator
+
+        i= vs.begin();
+        i2= vs.constBegin();
+        QCOMPARE(i, i2++);
+        QCOMPARE(*i2, v2);
+        QCOMPARE(++i, i2);
+        QCOMPARE(i, i2--);
+        QCOMPARE(i2, vs.constBegin());
+        QCOMPARE(--i, i2);
+        QCOMPARE(i2 += 8, vs.constEnd());
+        QCOMPARE(i2 -= 8, vs.constBegin());
+        QCOMPARE(i2+0, vs.constBegin());
+        QCOMPARE(i2+8, vs.constEnd());
+        i2 += 8;
+        i= i2-0;
+        QCOMPARE(i, i2);
+        i= i2-8;
+        QCOMPARE(i, vs.constBegin());
+
+        // QhullVertexList is const-only
+    }
+}//t_const_iterator
+
+void QhullLinkedList_test::
+t_QhullLinkedList_iterator()
+{
+    RboxPoints rcube("c");
+    Qhull q(rcube,"QR0");  // rotated unit cube
+    QhullVertexList vs(q.endVertex(), q.endVertex());
+    QhullVertexListIterator i= vs;
+    QCOMPARE(vs.count(), 0);
+    QVERIFY(!i.hasNext());
+    QVERIFY(!i.hasPrevious());
+    i.toBack();
+    QVERIFY(!i.hasNext());
+    QVERIFY(!i.hasPrevious());
+
+    QhullVertexList vs2 = q.vertexList();
+    QhullVertexListIterator i2(vs2);
+    QCOMPARE(vs2.count(), 8);
+    i= vs2;
+    QVERIFY(i2.hasNext());
+    QVERIFY(!i2.hasPrevious());
+    QVERIFY(i.hasNext());
+    QVERIFY(!i.hasPrevious());
+    i2.toBack();
+    i.toFront();
+    QVERIFY(!i2.hasNext());
+    QVERIFY(i2.hasPrevious());
+    QVERIFY(i.hasNext());
+    QVERIFY(!i.hasPrevious());
+
+    // i at front, i2 at end/back, 4 neighbors
+    QhullVertexList vs3 = q.vertexList(); // same as vs2
+    QhullVertex v3(vs3.first());
+    QhullVertex v4= vs3.first();
+    QCOMPARE(v3, v4);
+    QVERIFY(v3==v4);
+    QhullVertex v5(v4.next());
+    QVERIFY(v4!=v5);
+    QhullVertex v6(v5.next());
+    QhullVertex v7(v6.next());
+    QhullVertex v8(vs3.last());
+    QCOMPARE(i2.peekPrevious(), v8);
+    i2.previous();
+    i2.previous();
+    i2.previous();
+    i2.previous();
+    QCOMPARE(i2.previous(), v7);
+    QCOMPARE(i2.previous(), v6);
+    QCOMPARE(i2.previous(), v5);
+    QCOMPARE(i2.previous(), v4);
+    QVERIFY(!i2.hasPrevious());
+    QCOMPARE(i.peekNext(), v4);
+    // i.peekNext()= 1.0; // compiler error
+    QCOMPARE(i.next(), v4);
+    QCOMPARE(i.peekNext(), v5);
+    QCOMPARE(i.next(), v5);
+    QCOMPARE(i.next(), v6);
+    QCOMPARE(i.next(), v7);
+    i.next();
+    i.next();
+    i.next();
+    QCOMPARE(i.next(), v8);
+    QVERIFY(!i.hasNext());
+    i.toFront();
+    QCOMPARE(i.next(), v4);
+}//t_QhullLinkedList_iterator
+
+void QhullLinkedList_test::
+t_io()
+{
+    RboxPoints rcube("c");
+    Qhull q(rcube,"QR0");  // rotated unit cube
+    QhullVertexList vs(q.endVertex(), q.endVertex());
+    std::cout << "INFO:     empty QhullVertextList" << vs << std::endl;
+    QhullVertexList vs2= q.vertexList();
+    std::cout << "INFO:   " << vs2 << std::endl;
+}//t_io
+
+}//namespace orgQhull
+
+#include "moc/QhullLinkedList_test.moc"
diff --git a/xs/src/qhull/src/qhulltest/QhullPointSet_test.cpp b/xs/src/qhull/src/qhulltest/QhullPointSet_test.cpp
new file mode 100644
index 0000000000..ff633a5189
--- /dev/null
+++ b/xs/src/qhull/src/qhulltest/QhullPointSet_test.cpp
@@ -0,0 +1,378 @@
+/****************************************************************************
+**
+** Copyright (p) 2009-2015 C.B. Barber. All rights reserved.
+** $Id: //main/2015/qhull/src/qhulltest/QhullPointSet_test.cpp#3 $$Change: 2062 $
+** $DateTime: 2016/01/17 13:13:18 $$Author: bbarber $
+**
+****************************************************************************/
+
+//pre-compiled header
+#include <iostream>
+#include "RoadTest.h" // QT_VERSION
+
+#include "libqhullcpp/QhullPointSet.h"
+#include "libqhullcpp/RboxPoints.h"
+#include "libqhullcpp/QhullPoint.h"
+#include "libqhullcpp/QhullFacet.h"
+#include "libqhullcpp/QhullFacetList.h"
+#include "libqhullcpp/Qhull.h"
+
+using std::cout;
+using std::endl;
+using std::ostringstream;
+
+namespace orgQhull {
+
+class QhullPointSet_test : public RoadTest
+{
+    Q_OBJECT
+
+#//!\name Test slots
+private slots:
+    void cleanup();
+    void t_construct();
+    void t_convert();
+    void t_element();
+    void t_iterator();
+    void t_const_iterator();
+    void t_search();
+    void t_pointset_iterator();
+    void t_io();
+};//QhullPointSet_test
+
+void
+add_QhullPointSet_test()
+{
+    new QhullPointSet_test();  // RoadTest::s_testcases
+}
+
+//Executed after each testcase
+void QhullPointSet_test::
+cleanup()
+{
+    RoadTest::cleanup();
+}
+
+void QhullPointSet_test::
+t_construct()
+{
+    // Default constructor is disallowed (i.e., private)
+    RboxPoints rcube("c W0 1000");
+    Qhull q(rcube,"Qc");  // cube with 1000 coplanar points
+    int coplanarCount= 0;
+    foreach(QhullFacet f, q.facetList()){
+        QhullPointSet ps(q, f.getFacetT()->outsideset);
+        QVERIFY(ps.isEmpty());
+        QCOMPARE(ps.count(), 0);
+        QCOMPARE(ps.size(), 0u);
+        QhullPointSet ps2(q.qh(), f.getFacetT()->coplanarset);
+        QVERIFY(!ps2.isEmpty());
+        coplanarCount += ps2.count();
+        QCOMPARE(ps2.count(), (int)ps2.size());
+        QhullPointSet ps3(ps2);
+        QVERIFY(!ps3.isEmpty());
+        QCOMPARE(ps3.count(), ps2.count());
+        QVERIFY(ps3==ps2);
+        QVERIFY(ps3!=ps);
+        QhullPointSet ps4= ps3;
+        QVERIFY(ps4==ps2);
+    }
+    QCOMPARE(coplanarCount, 1000);
+}//t_construct
+
+void QhullPointSet_test::
+t_convert()
+{
+    RboxPoints rcube("c W0 1000");
+    Qhull q(rcube,"Qc");  // cube with 1000 coplanar points
+    QhullFacet f= q.firstFacet();
+    QhullPointSet ps= f.coplanarPoints();
+    QVERIFY(ps.count()>=1);   // Sometimes no coplanar points
+    std::vector<QhullPoint> vs= ps.toStdVector();
+    QCOMPARE(vs.size(), ps.size());
+    QhullPoint p= ps[0];
+    QhullPoint p2= vs[0];
+    QCOMPARE(p, p2);
+    QList<QhullPoint> qs= ps.toQList();
+    QCOMPARE(qs.size(), static_cast<int>(ps.size()));
+    QhullPoint p3= qs[0];
+    QCOMPARE(p3, p);
+}//t_convert
+
+// readonly tested in t_construct
+//   empty, isEmpty, ==, !=, size
+
+void QhullPointSet_test::
+t_element()
+{
+    RboxPoints rcube("c W0 1000");
+    Qhull q(rcube,"Qc");  // cube with 1000 coplanar points
+    QhullFacet f= q.firstFacet();
+    QhullPointSet ps= f.coplanarPoints();
+    QVERIFY(ps.count()>=3);  // Sometimes no coplanar points
+    QhullPoint p= ps[0];
+    QCOMPARE(p, ps[0]);
+    QhullPoint p2= ps[ps.count()-1];
+    QCOMPARE(ps.at(1), ps[1]);
+    QCOMPARE(ps.second(), ps[1]);
+    QCOMPARE(ps.first(), p);
+    QCOMPARE(ps.front(), ps.first());
+    QCOMPARE(ps.last(), p2);
+    QCOMPARE(ps.back(), ps.last());
+    QhullPoint p8(q);
+    QCOMPARE(ps.value(2), ps[2]);
+    QCOMPARE(ps.value(-1), p8);
+    QCOMPARE(ps.value(ps.count()), p8);
+    QCOMPARE(ps.value(ps.count(), p), p);
+    QVERIFY(ps.value(1, p)!=p);
+    QhullPointSet ps8= f.coplanarPoints();
+    QhullPointSet::Iterator i= ps8.begin();
+    foreach(QhullPoint p9, ps){  // Qt only
+        QCOMPARE(p9.dimension(), 3);
+        QCOMPARE(p9, *i++);
+    }
+}//t_element
+
+void QhullPointSet_test::
+t_iterator()
+{
+    RboxPoints rcube("c W0 1000");
+    Qhull q(rcube,"Qc");  // cube with 1000 coplanar points
+    QhullFacet f= q.firstFacet();
+    QhullPointSet ps= f.coplanarPoints();
+    QVERIFY(ps.count()>=3);  // Sometimes no coplanar points
+    QhullPointSet::Iterator i= ps.begin();
+    QhullPointSet::iterator i2= ps.begin();
+    QVERIFY(i==i2);
+    QVERIFY(i>=i2);
+    QVERIFY(i<=i2);
+    i= ps.begin();
+    QVERIFY(i==i2);
+    i2= ps.end();
+    QVERIFY(i!=i2);
+    QhullPoint p= *i;
+    QCOMPARE(p.dimension(), q.dimension());
+    QCOMPARE(p, ps[0]);
+    i2--;
+    QhullPoint p2= *i2;
+    QCOMPARE(p2.dimension(), q.dimension());
+    QCOMPARE(p2, ps.last());
+    QhullPointSet::Iterator i5(i2);
+    QCOMPARE(*i2, *i5);
+    QhullPointSet::Iterator i3= i+1;
+    QVERIFY(i!=i3);
+    QCOMPARE(i[1], *i3);
+    (i3= i)++;
+    QCOMPARE((*i3)[0], ps[1][0]);
+    QCOMPARE((*i3).dimension(), 3);
+
+    QVERIFY(i==i);
+    QVERIFY(i!=i3);
+    QVERIFY(i<i3);
+    QVERIFY(i<=i3);
+    QVERIFY(i3>i);
+    QVERIFY(i3>=i);
+
+    QhullPointSet::ConstIterator i4= ps.begin();
+    QVERIFY(i==i4); // iterator COMP const_iterator
+    QVERIFY(i<=i4);
+    QVERIFY(i>=i4);
+    QVERIFY(i4==i); // const_iterator COMP iterator
+    QVERIFY(i4<=i);
+    QVERIFY(i4>=i);
+    QVERIFY(i>=i4);
+    QVERIFY(i4<=i);
+    QVERIFY(i2!=i4);
+    QVERIFY(i2>i4);
+    QVERIFY(i2>=i4);
+    QVERIFY(i4!=i2);
+    QVERIFY(i4<i2);
+    QVERIFY(i4<=i2);
+    ++i4;
+    QVERIFY(i!=i4); // iterator COMP const_iterator
+    QVERIFY(i<i4);
+    QVERIFY(i<=i4);
+    QVERIFY(i4>i);
+    QVERIFY(i4>=i);
+    i4= ps.constBegin();
+    QVERIFY(i==i4); // iterator COMP const_iterator
+    QCOMPARE(i4+ps.count(), ps.constEnd());
+
+    i= ps.begin();
+    i2= ps.begin();
+    QCOMPARE(i, i2++);
+    QCOMPARE(*i2, ps[1]);
+    QCOMPARE(++i, i2);
+    QCOMPARE(i, i2--);
+    QCOMPARE(i2, ps.begin());
+    QCOMPARE(--i, i2);
+    QCOMPARE(i2+=ps.count(), ps.end());
+    QCOMPARE(i2-=ps.count(), ps.begin());
+    QCOMPARE(i2+0, ps.begin());
+    QCOMPARE(i2+ps.count(), ps.end());
+    i2 += ps.count();
+    i= i2-0;
+    QCOMPARE(i, i2);
+    i= i2-ps.count();
+    QCOMPARE(i, ps.begin());
+    QCOMPARE(i2-i, ps.count());
+
+    //ps.begin end tested above
+
+    // QhullPointSet is const-only
+}//t_iterator
+
+void QhullPointSet_test::
+t_const_iterator()
+{
+    RboxPoints rcube("c W0 1000");
+    Qhull q(rcube,"Qc");  // cube with 1000 coplanar points
+    QhullFacet f= q.firstFacet();
+    QhullPointSet ps= f.coplanarPoints();
+    QVERIFY(ps.count()>=3);  // Sometimes no coplanar points
+    QhullPointSet::ConstIterator i= ps.begin();
+    QhullPointSet::const_iterator i2= ps.begin();
+    QVERIFY(i==i2);
+    QVERIFY(i>=i2);
+    QVERIFY(i<=i2);
+
+    // See t_iterator for const_iterator COMP iterator
+
+    i= ps.begin();
+    QVERIFY(i==i2);
+    i2= ps.end();
+    QVERIFY(i!=i2);
+    QhullPoint p= *i; // QhullPoint is the base class for QhullPointSet::iterator
+    QCOMPARE(p.dimension(), q.dimension());
+    QCOMPARE(p, ps[0]);
+    i2--;
+    QhullPoint p2= *i2;
+    QCOMPARE(p2.dimension(), q.dimension());
+    QCOMPARE(p2, ps.last());
+    QhullPointSet::ConstIterator i5(i2);
+    QCOMPARE(*i2, *i5);
+
+
+    QhullPointSet::ConstIterator i3= i+1;
+    QVERIFY(i!=i3);
+    QCOMPARE(i[1], *i3);
+
+    QVERIFY(i==i);
+    QVERIFY(i!=i3);
+    QVERIFY(i<i3);
+    QVERIFY(i<=i3);
+    QVERIFY(i3>i);
+    QVERIFY(i3>=i);
+
+    // QhullPointSet is const-only
+}//t_const_iterator
+
+
+void QhullPointSet_test::
+t_search()
+{
+    RboxPoints rcube("c W0 1000");
+    Qhull q(rcube,"Qc");  // cube with 1000 coplanar points
+    QhullFacet f= q.firstFacet();
+    QhullPointSet ps= f.coplanarPoints();
+    QVERIFY(ps.count()>=3);  // Sometimes no coplanar points
+    QhullPoint p= ps.first();
+    QhullPoint p2= ps.last();
+    QVERIFY(ps.contains(p));
+    QVERIFY(ps.contains(p2));
+    QVERIFY(p!=p2);
+    QhullPoint p3= ps[2];
+    QVERIFY(ps.contains(p3));
+    QVERIFY(p!=p3);
+    QCOMPARE(ps.indexOf(p), 0);
+    QCOMPARE(ps.indexOf(p2), ps.count()-1);
+    QCOMPARE(ps.indexOf(p3), 2);
+    QhullPoint p4(q);
+    QCOMPARE(ps.indexOf(p4), -1);
+    QCOMPARE(ps.lastIndexOf(p), 0);
+    QCOMPARE(ps.lastIndexOf(p2), ps.count()-1);
+    QCOMPARE(ps.lastIndexOf(p3), 2);
+    QCOMPARE(ps.lastIndexOf(p4), -1);
+}//t_search
+
+void QhullPointSet_test::
+t_pointset_iterator()
+{
+    RboxPoints rcube("c W0 1000");
+    Qhull q(rcube,"Qc");  // cube with 1000 coplanar points
+    QhullFacet f= q.firstFacet();
+    QhullPointSet ps2= f.outsidePoints();
+    QVERIFY(ps2.count()==0); // No outside points after constructing the convex hull
+    QhullPointSetIterator i2= ps2;
+    QCOMPARE(i2.countRemaining(), 0);
+    QVERIFY(!i2.hasNext());
+    QVERIFY(!i2.hasPrevious());
+    i2.toBack();
+    QVERIFY(!i2.hasNext());
+    QVERIFY(!i2.hasPrevious());
+
+    QhullPointSet ps= f.coplanarPoints();
+    QVERIFY(ps.count()>=3);  // Sometimes no coplanar points
+    QhullPointSetIterator i(ps);
+    i2= ps;
+    QCOMPARE(i2.countRemaining(), ps.count());
+    QVERIFY(i2.hasNext());
+    QVERIFY(!i2.hasPrevious());
+    QVERIFY(i.hasNext());
+    QVERIFY(!i.hasPrevious());
+    i2.toBack();
+    QCOMPARE(i2.countRemaining(), 0);
+    i.toFront();
+    QCOMPARE(i.countRemaining(), ps.count());
+    QCOMPARE(i2.countRemaining(), 0);
+    QVERIFY(!i2.hasNext());
+    QVERIFY(i2.hasPrevious());
+    QVERIFY(i.hasNext());
+    QVERIFY(!i.hasPrevious());
+
+    QhullPoint p= ps[0];
+    QhullPoint p2(ps[0]);
+    QCOMPARE(p, p2);
+    QVERIFY(p==p2);
+    QhullPoint p3(ps.last());
+ // p2[0]= 0.0;
+    QVERIFY(p==p2);
+    QCOMPARE(i2.peekPrevious(), p3);
+    QCOMPARE(i2.previous(), p3);
+    QCOMPARE(i2.previous(), ps[ps.count()-2]);
+    QVERIFY(i2.hasPrevious());
+    QCOMPARE(i.peekNext(), p);
+    // i.peekNext()= 1.0; // compiler error
+    QCOMPARE(i.next(), p);
+    QCOMPARE(i.countRemaining(), ps.count()-1);
+    QhullPoint p4= i.peekNext();
+    QVERIFY(p4!=p3);
+    QCOMPARE(i.next(), p4);
+    QVERIFY(i.hasNext());
+    i.toFront();
+    QCOMPARE(i.next(), p);
+}//t_pointset_iterator
+
+void QhullPointSet_test::
+t_io()
+{
+    ostringstream os;
+    RboxPoints rcube("c W0 120");
+    Qhull q(rcube,"Qc");  // cube with 100 coplanar points
+    QhullFacet f= q.firstFacet();
+    QhullPointSet ps= f.coplanarPoints();
+    QVERIFY(ps.count()>=3);  // Sometimes no coplanar points
+    os << "QhullPointSet from coplanarPoints\n" << ps << endl;
+    os << ps.print("\nWith message\n");
+    os << ps.printIdentifiers("\nCoplanar points: ");
+    os << "\nAs a point set:\n";
+    os << ps;
+    cout << os.str();
+    QString s= QString::fromStdString(os.str());
+    QCOMPARE(s.count(" 0.5\n"), 3*ps.count());
+    QCOMPARE(s.count("p"), ps.count()+4);
+}//t_io
+
+}//orgQhull
+
+#include "moc/QhullPointSet_test.moc"
diff --git a/xs/src/qhull/src/qhulltest/QhullPoint_test.cpp b/xs/src/qhull/src/qhulltest/QhullPoint_test.cpp
new file mode 100644
index 0000000000..1528086a15
--- /dev/null
+++ b/xs/src/qhull/src/qhulltest/QhullPoint_test.cpp
@@ -0,0 +1,437 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
+** $Id: //main/2015/qhull/src/qhulltest/QhullPoint_test.cpp#3 $$Change: 2062 $
+** $DateTime: 2016/01/17 13:13:18 $$Author: bbarber $
+**
+****************************************************************************/
+
+//pre-compiled headers
+#include <iostream>
+#include "RoadTest.h" // QT_VERSION
+
+#include "libqhullcpp/QhullPoint.h"
+#include "libqhullcpp/Coordinates.h"
+#include "libqhullcpp/RboxPoints.h"
+#include "libqhullcpp/QhullError.h"
+#include "libqhullcpp/QhullFacet.h"
+#include "libqhullcpp/QhullPoint.h"
+#include "libqhullcpp/Qhull.h"
+
+#include <numeric>
+
+using std::cout;
+using std::endl;
+using std::ostringstream;
+using std::ostream;
+using std::string;
+
+namespace orgQhull {
+
+class QhullPoint_test : public RoadTest
+{
+    Q_OBJECT
+
+#//!\name Test slots
+private slots:
+    void cleanup();
+    void t_construct();
+    void t_convert();
+    void t_readonly();
+    void t_define();
+    void t_operator();
+    void t_iterator();
+    void t_const_iterator();
+    void t_qhullpoint_iterator();
+    void t_method();
+    void t_io();
+};//QhullPoint_test
+
+void
+add_QhullPoint_test()
+{
+    new QhullPoint_test();  // RoadTest::s_testcases
+}
+
+//Executed after each test
+void QhullPoint_test::
+cleanup()
+{
+    RoadTest::cleanup();
+}
+
+void QhullPoint_test::
+t_construct()
+{
+    QhullPoint p12;
+    QVERIFY(!p12.isValid());
+    QCOMPARE(p12.coordinates(), (coordT *)0);
+    QCOMPARE(p12.dimension(), 0);
+    QCOMPARE(p12.qh(), (QhullQh *)0);
+    QCOMPARE(p12.id(), -3);
+    QCOMPARE(p12.begin(), p12.end());
+    QCOMPARE(p12.constBegin(), p12.constEnd());
+
+    RboxPoints rcube("c");
+    Qhull q(rcube, "Qt QR0");  // triangulation of rotated unit cube
+    QhullPoint p(q);
+    QVERIFY(!p.isValid());
+    QCOMPARE(p.dimension(),3);
+    QCOMPARE(p.coordinates(),static_cast<double *>(0));
+    QhullPoint p7(q.qh());
+    QCOMPARE(p, p7);
+
+    // copy constructor and copy assignment
+    QhullVertex v2(q.beginVertex());
+    QhullPoint p2(v2.point());
+    QVERIFY(p2.isValid());
+    QCOMPARE(p2.dimension(),3);
+    QVERIFY(p2!=p12);
+    p= p2;
+    QCOMPARE(p, p2);
+
+    QhullPoint p3(q, p2.dimension(), p2.coordinates());
+    QCOMPARE(p3, p2);
+    QhullPoint p8(q, p2.coordinates()); // Qhull defines dimension
+    QCOMPARE(p8, p2);
+    QhullPoint p9(q.qh(), p2.dimension(), p2.coordinates());
+    QCOMPARE(p9, p2);
+    QhullPoint p10(q.qh(), p2.coordinates()); // Qhull defines dimension
+    QCOMPARE(p10, p2);
+
+    Coordinates c;
+    c << 0.0 << 0.0 << 0.0;
+    QhullPoint p6(q, c);
+    QCOMPARE(p6, q.origin());
+    QhullPoint p11(q.qh(), c);
+    QCOMPARE(p11, q.origin());
+
+    QhullPoint p5= p2; // copy constructor
+    QVERIFY(p5==p2);
+}//t_construct
+
+void QhullPoint_test::
+t_convert()
+{
+    RboxPoints rcube("c");
+    Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
+    QhullVertex v= q.firstVertex();
+    QhullPoint p= v.point();
+    std::vector<double> vs= p.toStdVector();
+    QCOMPARE(vs.size(), 3u);
+    for(int k=3; k--; ){
+        QCOMPARE(vs[k], p[k]);
+    }
+    QList<double> qs= p.toQList();
+    QCOMPARE(qs.size(), 3);
+    for(int k=3; k--; ){
+        QCOMPARE(qs[k], p[k]);
+    }
+}//t_convert
+
+void QhullPoint_test::
+t_readonly()
+{
+    RboxPoints rcube("c");
+    {
+        Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
+        QhullVertexList vs= q.vertexList();
+        cout << "Point ids in 'rbox c'\n";
+        QhullVertexListIterator i(vs);
+        while(i.hasNext()){
+            QhullPoint p= i.next().point();
+            int id= p.id();
+            cout << "p" << id << endl;
+            QVERIFY(p.isValid());
+            QCOMPARE(p.dimension(),3);
+            QCOMPARE(id, p.id());
+            QVERIFY(p.id()>=0 && p.id()<9);
+            const coordT *c= p.coordinates();
+            coordT *c2= p.coordinates();
+            QCOMPARE(c, c2);
+            QCOMPARE(p.dimension(), 3);
+            QCOMPARE(q.qh(), p.qh());
+        }
+        QhullPoint p2= vs.first().point();
+        QhullPoint p3= vs.last().point();
+        QVERIFY(p2!=p3);
+        QVERIFY(p3.coordinates()!=p2.coordinates());
+    }
+}//t_readonly
+
+void QhullPoint_test::
+t_define()
+{
+    RboxPoints rcube("c");
+    {
+        Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
+        QhullVertexList vs= q.vertexList();
+        QhullPoint p= vs.first().point();
+        QhullPoint p2= p;
+        QVERIFY(p==p2);
+        QhullPoint p3= vs.last().point();
+        QVERIFY(p2!=p3);
+        int idx= (p3.coordinates()-p2.coordinates())/p2.dimension();
+        QVERIFY(idx>-8 && idx<8);
+        p2.advancePoint(idx);
+        QVERIFY(p2==p3);
+        p2.advancePoint(-idx);
+        QVERIFY(p2==p);
+        p2.advancePoint(0);
+        QVERIFY(p2==p);
+
+        QhullPoint p4= p3;
+        QVERIFY(p4==p3);
+        p4.defineAs(p2);
+        QVERIFY(p2==p4);
+        QhullPoint p5= p3;
+        p5.defineAs(p2.dimension(), p2.coordinates());
+        QVERIFY(p2==p5);
+        QhullPoint p6= p3;
+        p6.setCoordinates(p2.coordinates());
+        QCOMPARE(p2.coordinates(), p6.coordinates());
+        QVERIFY(p2==p6);
+        p6.setDimension(2);
+        QCOMPARE(p6.dimension(), 2);
+        QVERIFY(p2!=p6);
+    }
+}//t_define
+
+void QhullPoint_test::
+t_operator()
+{
+    RboxPoints rcube("c");
+    Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
+    const QhullPoint p= q.firstVertex().point();
+    //operator== and operator!= tested elsewhere
+    const coordT *c= p.coordinates();
+    for(int k=p.dimension(); k--; ){
+        QCOMPARE(c[k], p[k]);
+    }
+    //p[0]= 10.0; // compiler error, const
+    QhullPoint p2= q.firstVertex().point();
+    p2[0]= 10.0;  // Overwrites point coordinate
+    QCOMPARE(p2[0], 10.0);
+}//t_operator
+
+void QhullPoint_test::
+t_iterator()
+{
+    RboxPoints rcube("c");
+    {
+        Qhull q(rcube,"QR0");  // rotated unit cube
+        QhullPoint p2(q);
+        QCOMPARE(p2.begin(), p2.end());
+
+        QhullPoint p= q.firstVertex().point();
+        QhullPoint::Iterator i= p.begin();
+        QhullPoint::iterator i2= p.begin();
+        QVERIFY(i==i2);
+        QVERIFY(i>=i2);
+        QVERIFY(i<=i2);
+        i= p.begin();
+        QVERIFY(i==i2);
+        i2= p.end();
+        QVERIFY(i!=i2);
+        double d3= *i;
+        i2--;
+        double d2= *i2;
+        QCOMPARE(d3, p[0]);
+        QCOMPARE(d2, p[2]);
+        QhullPoint::Iterator i3(i2);
+        QCOMPARE(*i2, *i3);
+
+        (i3= i)++;
+        QCOMPARE((*i3), p[1]);
+        QVERIFY(i==i);
+        QVERIFY(i!=i2);
+        QVERIFY(i<i2);
+        QVERIFY(i<=i2);
+        QVERIFY(i2>i);
+        QVERIFY(i2>=i);
+
+        QhullPoint::ConstIterator i4= p.begin();
+        QVERIFY(i==i4); // iterator COMP const_iterator
+        QVERIFY(i<=i4);
+        QVERIFY(i>=i4);
+        QVERIFY(i4==i); // const_iterator COMP iterator
+        QVERIFY(i4<=i);
+        QVERIFY(i4>=i);
+        QVERIFY(i>=i4);
+        QVERIFY(i4<=i);
+        QVERIFY(i2!=i4);
+        QVERIFY(i2>i4);
+        QVERIFY(i2>=i4);
+        QVERIFY(i4!=i2);
+        QVERIFY(i4<i2);
+        QVERIFY(i4<=i2);
+        ++i4;
+        QVERIFY(i<i4);
+        QVERIFY(i<=i4);
+        QVERIFY(i4>i);
+        QVERIFY(i4>=i);
+
+        i= p.begin();
+        i2= p.begin();
+        QCOMPARE(i, i2++);
+        QCOMPARE(*i2, p[1]);
+        QCOMPARE(++i, i2);
+        QCOMPARE(i, i2--);
+        QCOMPARE(i2, p.begin());
+        QCOMPARE(--i, i2);
+        QCOMPARE(i2 += 3, p.end());
+        QCOMPARE(i2 -= 3, p.begin());
+        QCOMPARE(i2+0, p.begin());
+        QCOMPARE(i2+3, p.end());
+        i2 += 3;
+        i= i2-0;
+        QCOMPARE(i, i2);
+        i= i2-3;
+        QCOMPARE(i, p.begin());
+        QCOMPARE(i2-i, 3);
+
+        //p.begin end tested above
+
+        // QhullPoint is const-only
+    }
+}//t_iterator
+
+void QhullPoint_test::
+t_const_iterator()
+{
+    RboxPoints rcube("c");
+    {
+        Qhull q(rcube,"QR0");  // rotated unit cube
+        QhullPoint p= q.firstVertex().point();
+        QhullPoint::ConstIterator i= p.begin();
+        QhullPoint::const_iterator i2= p.begin();
+        QVERIFY(i==i2);
+        QVERIFY(i>=i2);
+        QVERIFY(i<=i2);
+        i= p.begin();
+        QVERIFY(i==i2);
+        i2= p.end();
+        QVERIFY(i!=i2);
+        double d3= *i;
+        i2--;
+        double d2= *i2;
+        QCOMPARE(d3, p[0]);
+        QCOMPARE(d2, p[2]);
+        QhullPoint::ConstIterator i3(i2);
+        QCOMPARE(*i2, *i3);
+
+        (i3= i)++;
+        QCOMPARE((*i3), p[1]);
+        QVERIFY(i==i);
+        QVERIFY(i!=i2);
+        QVERIFY(i<i2);
+        QVERIFY(i<=i2);
+        QVERIFY(i2>i);
+        QVERIFY(i2>=i);
+
+        // See t_iterator for const_iterator COMP iterator
+
+        i= p.begin();
+        i2= p.constBegin();
+        QCOMPARE(i, i2++);
+        QCOMPARE(*i2, p[1]);
+        QCOMPARE(++i, i2);
+        QCOMPARE(i, i2--);
+        QCOMPARE(i2, p.constBegin());
+        QCOMPARE(--i, i2);
+        QCOMPARE(i2+=3, p.constEnd());
+        QCOMPARE(i2-=3, p.constBegin());
+        QCOMPARE(i2+0, p.constBegin());
+        QCOMPARE(i2+3, p.constEnd());
+        i2 += 3;
+        i= i2-0;
+        QCOMPARE(i, i2);
+        i= i2-3;
+        QCOMPARE(i, p.constBegin());
+        QCOMPARE(i2-i, 3);
+
+        // QhullPoint is const-only
+    }
+}//t_const_iterator
+
+void QhullPoint_test::
+t_qhullpoint_iterator()
+{
+    RboxPoints rcube("c");
+    Qhull q(rcube,"QR0");  // rotated unit cube
+
+    QhullPoint p2(q);
+    QhullPointIterator i= p2;
+    QCOMPARE(p2.dimension(), 3);
+    QVERIFY(!i.hasNext());
+    QVERIFY(!i.hasPrevious());
+    i.toBack();
+    QVERIFY(!i.hasNext());
+    QVERIFY(!i.hasPrevious());
+
+    QhullPoint p = q.firstVertex().point();
+    QhullPointIterator i2(p);
+    QCOMPARE(p.dimension(), 3);
+    i= p;
+    QVERIFY(i2.hasNext());
+    QVERIFY(!i2.hasPrevious());
+    QVERIFY(i.hasNext());
+    QVERIFY(!i.hasPrevious());
+    i2.toBack();
+    i.toFront();
+    QVERIFY(!i2.hasNext());
+    QVERIFY(i2.hasPrevious());
+    QVERIFY(i.hasNext());
+    QVERIFY(!i.hasPrevious());
+
+    // i at front, i2 at end/back, 3 coordinates
+    QCOMPARE(i.peekNext(), p[0]);
+    QCOMPARE(i2.peekPrevious(), p[2]);
+    QCOMPARE(i2.previous(), p[2]);
+    QCOMPARE(i2.previous(), p[1]);
+    QCOMPARE(i2.previous(), p[0]);
+    QVERIFY(!i2.hasPrevious());
+    QCOMPARE(i.peekNext(), p[0]);
+    // i.peekNext()= 1.0; // compiler error, i is const
+    QCOMPARE(i.next(), p[0]);
+    QCOMPARE(i.peekNext(), p[1]);
+    QCOMPARE(i.next(), p[1]);
+    QCOMPARE(i.next(), p[2]);
+    QVERIFY(!i.hasNext());
+    i.toFront();
+    QCOMPARE(i.next(), p[0]);
+}//t_qhullpoint_iterator
+
+void QhullPoint_test::
+t_method()
+{
+    // advancePoint tested above
+    RboxPoints rcube("c");
+    Qhull q(rcube, "");
+    QhullPoint p = q.firstVertex().point();
+    double dist= p.distance(q.origin());
+    QCOMPARE(dist, sqrt(double(2.0+1.0))/2); // half diagonal of unit cube
+}//t_qhullpoint_iterator
+
+void QhullPoint_test::
+t_io()
+{
+    RboxPoints rcube("c");
+    {
+        Qhull q(rcube, "");
+        QhullPoint p= q.beginVertex().point();
+        ostringstream os;
+        os << "Point:\n";
+        os << p;
+        os << "Point w/ print:\n";
+        os << p.print(" message ");
+        os << p.printWithIdentifier(" Point with id and a message ");
+        cout << os.str();
+        QString s= QString::fromStdString(os.str());
+        QCOMPARE(s.count("p"), 2);
+    }
+}//t_io
+
+}//orgQhull
+
+#include "moc/QhullPoint_test.moc"
diff --git a/xs/src/qhull/src/qhulltest/QhullPoints_test.cpp b/xs/src/qhull/src/qhulltest/QhullPoints_test.cpp
new file mode 100644
index 0000000000..c2d8347e28
--- /dev/null
+++ b/xs/src/qhull/src/qhulltest/QhullPoints_test.cpp
@@ -0,0 +1,561 @@
+/****************************************************************************
+**
+** Copyright (p) 2009-2015 C.B. Barber. All rights reserved.
+** $Id: //main/2015/qhull/src/qhulltest/QhullPoints_test.cpp#3 $$Change: 2062 $
+** $DateTime: 2016/01/17 13:13:18 $$Author: bbarber $
+**
+****************************************************************************/
+
+//pre-compiled header
+#include <iostream>
+#include "qhulltest/RoadTest.h" // QT_VERSION
+
+#include "libqhullcpp/QhullPoints.h"
+#include "libqhullcpp/RboxPoints.h"
+#include "libqhullcpp/Qhull.h"
+
+using std::cout;
+using std::endl;
+using std::ostringstream;
+
+namespace orgQhull {
+
+class QhullPoints_test : public RoadTest
+{
+    Q_OBJECT
+
+#//!\name Test slots
+private slots:
+    void cleanup();
+    void t_construct_q();
+    void t_construct_qh();
+    void t_convert();
+    void t_getset();
+    void t_element();
+    void t_iterator();
+    void t_const_iterator();
+    void t_search();
+    void t_points_iterator();
+    void t_io();
+};//QhullPoints_test
+
+void
+add_QhullPoints_test()
+{
+    new QhullPoints_test();  // RoadTest::s_testcases
+}
+
+//Executed after each testcase
+void QhullPoints_test::
+cleanup()
+{
+    RoadTest::cleanup();
+}
+
+void QhullPoints_test::
+t_construct_q()
+{
+    Qhull q;
+    QhullPoints ps(q);
+    QCOMPARE(ps.dimension(), 0);
+    QVERIFY(ps.isEmpty());
+    QCOMPARE(ps.count(), 0);
+    QCOMPARE(ps.size(), 0u);
+    QCOMPARE(ps.coordinateCount(), 0);
+    coordT c[]= {0.0, 1.0, 2.0, 3.0, 4.0, 5.0};
+    QhullPoints ps2(q);
+    ps2.defineAs(2, 6, c);
+    QCOMPARE(ps2.dimension(), 2);
+    QVERIFY(!ps2.isEmpty());
+    QCOMPARE(ps2.count(), 3);
+    QCOMPARE(ps2.size(), 3u);
+    QCOMPARE(ps2.coordinates(), c);
+    QhullPoints ps3(q, 2, 6, c);
+    QCOMPARE(ps3.dimension(), 2);
+    QVERIFY(!ps3.isEmpty());
+    QCOMPARE(ps3.coordinates(), ps2.coordinates());
+    QVERIFY(ps3==ps2);
+    QVERIFY(ps3!=ps);
+    QhullPoints ps4= ps3;
+    QVERIFY(ps4==ps3);
+    // ps4= ps3; //compiler error
+    QhullPoints ps5(ps4);
+    QVERIFY(ps5==ps4);
+    QVERIFY(!(ps5!=ps4));
+    coordT c2[]= {0.0, 1.0, 2.0, 3.0, 4.0, 5.0};
+    QhullPoints ps6(q, 2, 6, c2);
+    QVERIFY(ps6==ps2);
+
+    RboxPoints rbox("c D2");
+    Qhull q2(rbox, "");
+    QhullPoints ps8(q2);
+    QCOMPARE(ps8.dimension(), 2);
+    QCOMPARE(ps8.count(), 0);
+    QCOMPARE(ps8.size(), 0u);
+    QCOMPARE(ps8.coordinateCount(), 0);
+    coordT c3[]= {0.0, 1.0, 2.0, 3.0, 4.0, 5.0};
+    QhullPoints ps9(q2, 6, c3);
+    QCOMPARE(ps9.dimension(), 2);
+    QCOMPARE(ps9.coordinateCount(), 6);
+    QCOMPARE(ps9.count(), 3);
+    QCOMPARE(ps9.coordinates(), c3);
+    QCOMPARE(ps9, ps2);  // DISTround
+    c3[1]= 1.0+1e-17;
+    QCOMPARE(ps9, ps2);  // DISTround
+    c3[1]= 1.0+1e-15;
+    QVERIFY(ps9!=ps2);  // DISTround
+
+    ps9.defineAs(6, c2);
+    QCOMPARE(ps9.dimension(), 2);
+    QCOMPARE(ps9.coordinateCount(), 6);
+    QCOMPARE(ps9.count(), 3);
+    QCOMPARE(ps9.coordinates(), c2);
+}//t_construct_q
+
+void QhullPoints_test::
+t_construct_qh()
+{
+    Qhull q;
+    QhullQh *qh= q.qh();
+    QhullPoints ps(qh);
+    QCOMPARE(ps.dimension(), 0);
+    QVERIFY(ps.isEmpty());
+    QCOMPARE(ps.count(), 0);
+    QCOMPARE(ps.size(), 0u);
+    QCOMPARE(ps.coordinateCount(), 0);
+    coordT c[]= {0.0, 1.0, 2.0, 3.0, 4.0, 5.0};
+    QhullPoints ps2(qh);
+    ps2.defineAs(2, 6, c);
+    QCOMPARE(ps2.dimension(), 2);
+    QVERIFY(!ps2.isEmpty());
+    QCOMPARE(ps2.count(), 3);
+    QCOMPARE(ps2.size(), 3u);
+    QCOMPARE(ps2.coordinates(), c);
+    QhullPoints ps3(qh, 2, 6, c);
+    QCOMPARE(ps3.dimension(), 2);
+    QVERIFY(!ps3.isEmpty());
+    QCOMPARE(ps3.coordinates(), ps2.coordinates());
+    QVERIFY(ps3==ps2);
+    QVERIFY(ps3!=ps);
+    QhullPoints ps4= ps3;
+    QVERIFY(ps4==ps3);
+    // ps4= ps3; //compiler error
+    QhullPoints ps5(ps4);
+    QVERIFY(ps5==ps4);
+    QVERIFY(!(ps5!=ps4));
+    coordT c2[]= {0.0, 1.0, 2.0, 3.0, 4.0, 5.0};
+    QhullPoints ps6(qh, 2, 6, c2);
+    QVERIFY(ps6==ps2);
+
+    RboxPoints rbox("c D2");
+    Qhull q2(rbox, "");
+    QhullPoints ps8(q2.qh());
+    QCOMPARE(ps8.dimension(), 2);
+    QCOMPARE(ps8.count(), 0);
+    QCOMPARE(ps8.size(), 0u);
+    QCOMPARE(ps8.coordinateCount(), 0);
+    coordT c3[]= {10.0, 11.0, 12.0, 13.0, 14.0, 15.0};
+    QhullPoints ps9(q2.qh(), 6, c3);
+    QCOMPARE(ps9.dimension(), 2);
+    QCOMPARE(ps9.coordinateCount(), 6);
+    QCOMPARE(ps9.count(), 3);
+    QCOMPARE(ps9.coordinates(), c3);
+    ps9.defineAs(6, c2);
+    QCOMPARE(ps9.dimension(), 2);
+    QCOMPARE(ps9.coordinateCount(), 6);
+    QCOMPARE(ps9.count(), 3);
+    QCOMPARE(ps9.coordinates(), c2);
+}//t_construct_qh
+
+void QhullPoints_test::
+t_convert()
+{
+    Qhull q;
+    //defineAs tested above
+    coordT c[]= {0.0, 1.0, 2.0, 3.0, 4.0, 5.0};
+    QhullPoints ps(q, 3, 6, c);
+    QCOMPARE(ps.dimension(), 3);
+    QCOMPARE(ps.size(), 2u);
+    const coordT *c2= ps.constData();
+    QCOMPARE(c, c2);
+    const coordT *c3= ps.data();
+    QCOMPARE(c, c3);
+    coordT *c4= ps.data();
+    QCOMPARE(c, c4);
+    std::vector<QhullPoint> vs= ps.toStdVector();
+    QCOMPARE(vs.size(), 2u);
+    QhullPoint p= vs[1];
+    QCOMPARE(p[2], 5.0);
+    QList<QhullPoint> qs= ps.toQList();
+    QCOMPARE(qs.size(), 2);
+    QhullPoint p2= qs[1];
+    QCOMPARE(p2[2], 5.0);
+}//t_convert
+
+void QhullPoints_test::
+t_getset()
+{
+    Qhull q;
+    //See t_construct for coordinates, count, defineAs, dimension, isempty, ==, !=, size
+    coordT c[]= {0.0, 1.0, 2.0, 3.0, 4.0, 5.0};
+    QhullPoints ps(q, 3, 6, c);
+    QhullPoints ps2(q, 3, 6, c);
+    QCOMPARE(ps2.dimension(), 3);
+    QCOMPARE(ps2.coordinates(), c);
+    QCOMPARE(ps2.count(), 2);
+    QCOMPARE(ps2.coordinateCount(), 6);
+    coordT c2[]= {-1.0, -2.0, -3.0, -4.0, -5.0, -6.0};
+    ps2.defineAs(6, c2);
+    QCOMPARE(ps2.coordinates(), c2);
+    QCOMPARE(ps2.count(), 2);
+    QCOMPARE(ps2.size(), 2u);
+    QCOMPARE(ps2.dimension(), 3);
+    QVERIFY(!ps2.isEmpty());
+    QVERIFY(ps!=ps2);
+    // ps2= ps; // assignment not available, compiler error
+    ps2.defineAs(ps);
+    QVERIFY(ps==ps2);
+    ps2.setDimension(2);
+    QCOMPARE(ps2.dimension(), 2);
+    QCOMPARE(ps2.coordinates(), c);
+    QVERIFY(!ps2.isEmpty());
+    QCOMPARE(ps2.count(), 3);
+    QCOMPARE(ps2.size(), 3u);
+    QVERIFY(ps!=ps2);
+    QhullPoints ps3(ps2);
+    ps3.setDimension(3);
+    ps3.defineAs(5, c2);
+    QCOMPARE(ps3.count(), 1);
+    QCOMPARE(ps3.extraCoordinatesCount(), 2);
+    QCOMPARE(ps3.extraCoordinates()[0], -4.0);
+    QVERIFY(ps3.includesCoordinates(ps3.data()));
+    QVERIFY(ps3.includesCoordinates(ps3.data()+ps3.count()-1));
+    QVERIFY(!ps3.includesCoordinates(ps3.data()-1));
+    QVERIFY(!ps3.includesCoordinates(ps3.data()+ps3.coordinateCount()));
+}//t_getset
+
+
+void QhullPoints_test::
+t_element()
+{
+    Qhull q;
+    coordT c[]= {0.0, 1.0, 2.0, 3.0, 4.0, 5.0};
+    QhullPoints ps(q, 2, 6, c);
+    QCOMPARE(ps.count(), 3);
+    QhullPoint p(q, 2, c);
+    QCOMPARE(ps[0], p);
+    QCOMPARE(ps.at(1), ps[1]);
+    QCOMPARE(ps.first(), p);
+    QCOMPARE(ps.front(), ps.first());
+    QCOMPARE(ps.last(), ps.at(2));
+    QCOMPARE(ps.back(), ps.last());
+    QhullPoints ps2= ps.mid(2);
+    QCOMPARE(ps2.count(), 1);
+    QhullPoints ps3= ps.mid(3);
+    QVERIFY(ps3.isEmpty());
+    QhullPoints ps4= ps.mid(10);
+    QVERIFY(ps4.isEmpty());
+    QhullPoints ps5= ps.mid(-1);
+    QVERIFY(ps5.isEmpty());
+    QhullPoints ps6= ps.mid(1, 1);
+    QCOMPARE(ps6.count(), 1);
+    QCOMPARE(ps6[0], ps[1]);
+    QhullPoints ps7= ps.mid(1, 10);
+    QCOMPARE(ps7.count(), 2);
+    QCOMPARE(ps7[1], ps[2]);
+    QhullPoint p8(q);
+    QCOMPARE(ps.value(2), ps[2]);
+    QCOMPARE(ps.value(-1), p8);
+    QCOMPARE(ps.value(3), p8);
+    QCOMPARE(ps.value(3, p), p);
+    QVERIFY(ps.value(1, p)!=p);
+    foreach(QhullPoint p9, ps){  // Qt only
+        QCOMPARE(p9.dimension(), 2);
+        QVERIFY(p9[0]==0.0 || p9[0]==2.0 || p9[0]==4.0);
+    }
+}//t_element
+
+void QhullPoints_test::
+t_iterator()
+{
+    Qhull q;
+    coordT c[]= {0.0, 1.0, 2.0};
+    QhullPoints ps(q, 1, 3, c);
+    QCOMPARE(ps.dimension(), 1);
+    QhullPoints::Iterator i(ps);
+    QhullPoints::iterator i2= ps.begin();
+    QVERIFY(i==i2);
+    QVERIFY(i>=i2);
+    QVERIFY(i<=i2);
+    i= ps.begin();
+    QVERIFY(i==i2);
+    i2= ps.end();
+    QVERIFY(i!=i2);
+    QhullPoint p(i); // QhullPoint is the base class for QhullPoints::iterator
+    QCOMPARE(p.dimension(), ps.dimension());
+    QCOMPARE(p.coordinates(), ps.coordinates());
+    i2--;
+    QhullPoint p2= *i2;
+    QCOMPARE(p[0], 0.0);
+    QCOMPARE(p2[0], 2.0);
+    QhullPoints::Iterator i5(i2);
+    QCOMPARE(*i2, *i5);
+    coordT c3[]= {0.0, -1.0, -2.0};
+    QhullPoints::Iterator i3(q, 1, c3);
+    QVERIFY(i!=i3);
+    QCOMPARE(*i, *i3);
+
+    (i3= i)++;
+    QCOMPARE((*i3)[0], 1.0);
+    QCOMPARE(i3->dimension(), 1);
+    QCOMPARE(i3[0][0], 1.0);
+    QCOMPARE(i3[0], ps[1]);
+
+    QVERIFY(i==i);
+    QVERIFY(i!=i2);
+    QVERIFY(i<i2);
+    QVERIFY(i<=i2);
+    QVERIFY(i2>i);
+    QVERIFY(i2>=i);
+
+    QhullPoints::ConstIterator i4(q, 1, c);
+    QVERIFY(i==i4); // iterator COMP const_iterator
+    QVERIFY(i<=i4);
+    QVERIFY(i>=i4);
+    QVERIFY(i4==i); // const_iterator COMP iterator
+    QVERIFY(i4<=i);
+    QVERIFY(i4>=i);
+    QVERIFY(i>=i4);
+    QVERIFY(i4<=i);
+    QVERIFY(i2!=i4);
+    QVERIFY(i2>i4);
+    QVERIFY(i2>=i4);
+    QVERIFY(i4!=i2);
+    QVERIFY(i4<i2);
+    QVERIFY(i4<=i2);
+    ++i4;
+    QVERIFY(i<i4);
+    QVERIFY(i<=i4);
+    QVERIFY(i4>i);
+    QVERIFY(i4>=i);
+
+    i= ps.begin();
+    i2= ps.begin();
+    QCOMPARE(i, i2++);
+    QCOMPARE(*i2, ps[1]);
+    QCOMPARE(++i, i2);
+    QCOMPARE(i, i2--);
+    QCOMPARE(i2, ps.begin());
+    QCOMPARE(--i, i2);
+    QCOMPARE(i2+=3, ps.end());
+    QCOMPARE(i2-=3, ps.begin());
+    QCOMPARE(i2+0, ps.begin());
+    QCOMPARE(i2+3, ps.end());
+    i2 += 3;
+    i= i2-0;
+    QCOMPARE(i, i2);
+    i= i2-3;
+    QCOMPARE(i, ps.begin());
+    QCOMPARE(i2-i, 3);
+
+    //ps.begin end tested above
+
+    // QhullPoints is const-only
+}//t_iterator
+
+void QhullPoints_test::
+t_const_iterator()
+{
+    Qhull q;
+    coordT c[]= {0.0, 1.0, 2.0};
+    const QhullPoints ps(q, 1, 3, c);
+    QhullPoints::ConstIterator i(ps);
+    QhullPoints::const_iterator i2= ps.begin();
+    QVERIFY(i==i2);
+    QVERIFY(i>=i2);
+    QVERIFY(i<=i2);
+    i= ps.begin();
+    QVERIFY(i==i2);
+    i2= ps.end();
+    QVERIFY(i!=i2);
+    QhullPoint p(i);
+    QCOMPARE(p.dimension(), ps.dimension());
+    QCOMPARE(p.coordinates(), ps.coordinates());
+    i2--;
+    QhullPoint p2= *i2;
+    QCOMPARE(p[0], 0.0);
+    QCOMPARE(p2[0], 2.0);
+    QhullPoints::ConstIterator i5(i2);
+    QCOMPARE(*i2, *i5);
+    coordT c3[]= {0.0, -1.0, -2.0};
+    QhullPoints::ConstIterator i3(q, 1, c3);
+    QVERIFY(i!=i3);
+    QCOMPARE(*i, *i3);
+
+    (i3= i)++;
+    QCOMPARE((*i3)[0], 1.0);
+    QCOMPARE(i3->dimension(), 1);
+    QCOMPARE(i3[0][0], 1.0);
+    QCOMPARE(i3[0][0], 1.0);
+    QCOMPARE(i3[0], ps[1]);
+
+    QVERIFY(i==i);
+    QVERIFY(i!=i2);
+    QVERIFY(i<i2);
+    QVERIFY(i<=i2);
+    QVERIFY(i2>i);
+    QVERIFY(i2>=i);
+
+    // See t_iterator for const_iterator COMP iterator
+
+    i= ps.begin();
+    i2= ps.constBegin();
+    QCOMPARE(i, i2++);
+    QCOMPARE(*i2, ps[1]);
+    QCOMPARE(++i, i2);
+    QCOMPARE(i, i2--);
+    QCOMPARE(i2, ps.constBegin());
+    QCOMPARE(--i, i2);
+    QCOMPARE(i2+=3, ps.constEnd());
+    QCOMPARE(i2-=3, ps.constBegin());
+    QCOMPARE(i2+0, ps.constBegin());
+    QCOMPARE(i2+3, ps.constEnd());
+    i2 += 3;
+    i= i2-0;
+    QCOMPARE(i, i2);
+    i= i2-3;
+    QCOMPARE(i, ps.constBegin());
+    QCOMPARE(i2-i, 3);
+
+    // QhullPoints is const-only
+}//t_const_iterator
+
+
+void QhullPoints_test::
+t_search()
+{
+    Qhull q;
+    coordT c[]= {0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 0, 1};
+    QhullPoints ps(q, 2, 8, c); //2-d array of 4 points
+    QhullPoint p= ps.first();
+    QhullPoint p2= ps.last();
+    QVERIFY(ps.contains(p));
+    QVERIFY(ps.contains(p2));
+    QVERIFY(p==p2);
+    QhullPoint p5= ps[2];
+    QVERIFY(p!=p5);
+    QVERIFY(ps.contains(p5));
+    coordT c2[]= {0.0, 1.0, 2.0, 3.0};
+    QhullPoint p3(q, 2, c2); //2-d point
+    QVERIFY(ps.contains(p3));
+    QhullPoint p4(q, 3, c2); //3-d point
+    QVERIFY(!ps.contains(p4));
+    p4.defineAs(2, c); //2-d point
+    QVERIFY(ps.contains(p4));
+    p4.defineAs(2, c+1); //2-d point
+    QVERIFY(!ps.contains(p4));
+    QhullPoint p6(q, 2, c2+2); //2-d point
+    QCOMPARE(ps.count(p), 2);
+    QCOMPARE(ps.count(p2), 2);
+    QCOMPARE(ps.count(p3), 2);
+    QCOMPARE(ps.count(p4), 0);
+    QCOMPARE(ps.count(p6), 1);
+    QCOMPARE(ps.indexOf(&ps[0][0]), 0);
+    //QCOMPARE(ps.indexOf(ps.end()), -1); //ps.end() is a QhullPoint which may match
+    QCOMPARE(ps.indexOf(0), -1);
+    QCOMPARE(ps.indexOf(&ps[3][0]), 3);
+    QCOMPARE(ps.indexOf(&ps[3][1], QhullError::NOthrow), 3);
+    QCOMPARE(ps.indexOf(ps.data()+ps.coordinateCount(), QhullError::NOthrow), -1);
+    QCOMPARE(ps.indexOf(p), 0);
+    QCOMPARE(ps.indexOf(p2), 0);
+    QCOMPARE(ps.indexOf(p3), 0);
+    QCOMPARE(ps.indexOf(p4), -1);
+    QCOMPARE(ps.indexOf(p5), 2);
+    QCOMPARE(ps.indexOf(p6), 1);
+    QCOMPARE(ps.lastIndexOf(p), 3);
+    QCOMPARE(ps.lastIndexOf(p4), -1);
+    QCOMPARE(ps.lastIndexOf(p6), 1);
+    QhullPoints ps3(q);
+    QCOMPARE(ps3.indexOf(ps3.data()), -1);
+    QCOMPARE(ps3.indexOf(ps3.data()+1, QhullError::NOthrow), -1);
+    QCOMPARE(ps3.indexOf(p), -1);
+    QCOMPARE(ps3.lastIndexOf(p), -1);
+    QhullPoints ps4(q, 2, 0, c);
+    QCOMPARE(ps4.indexOf(p), -1);
+    QCOMPARE(ps4.lastIndexOf(p), -1);
+}//t_search
+
+void QhullPoints_test::
+t_points_iterator()
+{
+    Qhull q;
+    coordT c2[]= {0.0};
+    QhullPoints ps2(q, 0, 0, c2); // 0-dimensional
+    QhullPointsIterator i2= ps2;
+    QVERIFY(!i2.hasNext());
+    QVERIFY(!i2.hasPrevious());
+    i2.toBack();
+    QVERIFY(!i2.hasNext());
+    QVERIFY(!i2.hasPrevious());
+
+    coordT c[]= {0.0, 1.0, 2.0, 3.0, 4.0, 5.0};
+    QhullPoints ps(q, 3, 6, c); // 3-dimensional
+    QhullPointsIterator i(ps);
+    i2= ps;
+    QVERIFY(i2.hasNext());
+    QVERIFY(!i2.hasPrevious());
+    QVERIFY(i.hasNext());
+    QVERIFY(!i.hasPrevious());
+    i2.toBack();
+    i.toFront();
+    QVERIFY(!i2.hasNext());
+    QVERIFY(i2.hasPrevious());
+    QVERIFY(i.hasNext());
+    QVERIFY(!i.hasPrevious());
+
+    QhullPoint p= ps[0];
+    QhullPoint p2(ps[0]);
+    QCOMPARE(p, p2);
+    QVERIFY(p==p2);
+    QhullPoint p3(ps[1]);
+ // p2[0]= 0.0;
+    QVERIFY(p==p2);
+    QCOMPARE(i2.peekPrevious(), p3);
+    QCOMPARE(i2.previous(), p3);
+    QCOMPARE(i2.previous(), p);
+    QVERIFY(!i2.hasPrevious());
+    QCOMPARE(i.peekNext(), p);
+    // i.peekNext()= 1.0; // compiler error
+    QCOMPARE(i.next(), p);
+    QCOMPARE(i.peekNext(), p3);
+    QCOMPARE(i.next(), p3);
+    QVERIFY(!i.hasNext());
+    i.toFront();
+    QCOMPARE(i.next(), p);
+}//t_points_iterator
+
+void QhullPoints_test::
+t_io()
+{
+    Qhull q;
+    QhullPoints ps(q);
+    ostringstream os;
+    os << "Empty QhullPoints\n" << ps << endl;
+    coordT c[]= {0.0, 1.0, 2.0, 3.0, 4.0, 5.0};
+    QhullPoints ps2(q, 3, 6, c); // 3-dimensional explicit
+    os << "QhullPoints from c[]\n" << ps2 << endl;
+
+    RboxPoints rcube("c");
+    Qhull q2(rcube,"Qt QR0");  // triangulation of rotated unit cube
+    QhullPoints ps3= q2.points();
+    os << "QhullPoints\n" << ps3;
+    os << ps3.print("message\n");
+    os << ps3.printWithIdentifier("w/ identifiers\n");
+    cout << os.str();
+    QString s= QString::fromStdString(os.str());
+    QCOMPARE(s.count("p"), 8+1);
+}//t_io
+
+}//orgQhull
+
+#include "moc/QhullPoints_test.moc"
diff --git a/xs/src/qhull/src/qhulltest/QhullRidge_test.cpp b/xs/src/qhull/src/qhulltest/QhullRidge_test.cpp
new file mode 100644
index 0000000000..420a7f06d3
--- /dev/null
+++ b/xs/src/qhull/src/qhulltest/QhullRidge_test.cpp
@@ -0,0 +1,159 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
+** $Id: //main/2015/qhull/src/qhulltest/QhullRidge_test.cpp#3 $$Change: 2062 $
+** $DateTime: 2016/01/17 13:13:18 $$Author: bbarber $
+**
+****************************************************************************/
+
+//pre-compiled headers
+#include <iostream>
+#include "RoadTest.h" // QT_VERSION
+
+#include "libqhullcpp/QhullRidge.h"
+#include "libqhullcpp/QhullError.h"
+#include "libqhullcpp/RboxPoints.h"
+#include "libqhullcpp/QhullFacet.h"
+#include "libqhullcpp/Qhull.h"
+
+using std::cout;
+using std::endl;
+using std::ostringstream;
+using std::ostream;
+using std::string;
+
+namespace orgQhull {
+
+class QhullRidge_test : public RoadTest
+{
+    Q_OBJECT
+
+#//!\name Test slots
+private slots:
+    void cleanup();
+    void t_construct();
+    void t_getSet();
+    void t_foreach();
+    void t_io();
+};//QhullRidge_test
+
+void
+add_QhullRidge_test()
+{
+    new QhullRidge_test();  // RoadTest::s_testcases
+}
+
+//Executed after each testcase
+void QhullRidge_test::
+cleanup()
+{
+    RoadTest::cleanup();
+}
+
+void QhullRidge_test::
+t_construct()
+{
+    // Qhull.runQhull() constructs QhullFacets as facetT
+    RboxPoints rcube("c");
+    Qhull q(rcube,"QR0");  // triangulation of rotated unit cube
+    QhullRidge r(q);
+    QVERIFY(!r.isValid());
+    QCOMPARE(r.dimension(),2);
+    QhullFacet f(q.firstFacet());
+    QhullRidgeSet rs(f.ridges());
+    QVERIFY(!rs.isEmpty()); // Simplicial facets do not have ridges()
+    QhullRidge r2(rs.first());
+    QCOMPARE(r2.dimension(), 2); // One dimension lower than the facet
+    r= r2;
+    QVERIFY(r.isValid());
+    QCOMPARE(r.dimension(), 2);
+    QhullRidge r3(q, r2.getRidgeT());
+    QCOMPARE(r,r3);
+    QhullRidge r4(q, r2.getBaseT());
+    QCOMPARE(r,r4);
+    QhullRidge r5= r2; // copy constructor
+    QVERIFY(r5==r2);
+    QVERIFY(r5==r);
+}//t_construct
+
+void QhullRidge_test::
+t_getSet()
+{
+    RboxPoints rcube("c");
+    {
+        Qhull q(rcube,"QR0");  // triangulation of rotated unit cube
+        QCOMPARE(q.facetCount(), 6);
+        QCOMPARE(q.vertexCount(), 8);
+        QhullFacet f(q.firstFacet());
+        QhullRidgeSet rs= f.ridges();
+        QhullRidgeSetIterator i(rs);
+        while(i.hasNext()){
+            const QhullRidge r= i.next();
+            cout << r.id() << endl;
+            QVERIFY(r.bottomFacet()!=r.topFacet());
+            QCOMPARE(r.dimension(), 2); // Ridge one-dimension less than facet
+            QVERIFY(r.id()>=0 && r.id()<9*27);
+            QVERIFY(r.isValid());
+            QVERIFY(r==r);
+            QVERIFY(r==i.peekPrevious());
+            QCOMPARE(r.otherFacet(r.bottomFacet()),r.topFacet());
+            QCOMPARE(r.otherFacet(r.topFacet()),r.bottomFacet());
+        }
+    }
+}//t_getSet
+
+void QhullRidge_test::
+t_foreach()
+{
+    RboxPoints rcube("c");  // cube
+    {
+        Qhull q(rcube, "QR0"); // rotated cube
+        QhullFacet f(q.firstFacet());
+        foreach (const QhullRidge &r, f.ridges()){  // Qt only
+            QhullVertexSet vs= r.vertices();
+            QCOMPARE(vs.count(), 2);
+            foreach (const QhullVertex &v, vs){  // Qt only
+                QVERIFY(f.vertices().contains(v));
+            }
+        }
+        QhullRidgeSet rs= f.ridges();
+        QhullRidge r= rs.first();
+        QhullRidge r2= r;
+        QList<QhullVertex> vs;
+        int count= 0;
+        while(!count || r2!=r){
+            ++count;
+            QhullVertex v(q);
+            QVERIFY2(r2.hasNextRidge3d(f),"A cube should only have non-simplicial facets.");
+            QhullRidge r3= r2.nextRidge3d(f, &v);
+            QVERIFY(!vs.contains(v));
+            vs << v;
+            r2= r2.nextRidge3d(f);
+            QCOMPARE(r3, r2);
+        }
+        QCOMPARE(vs.count(), rs.count());
+        QCOMPARE(count, rs.count());
+    }
+}//t_foreach
+
+void QhullRidge_test::
+t_io()
+{
+    RboxPoints rcube("c");
+    {
+        Qhull q(rcube, "");
+        QhullFacet f(q.firstFacet());
+        QhullRidgeSet rs= f.ridges();
+        QhullRidge r= rs.first();
+        ostringstream os;
+        os << "Ridges\n" << rs << "Ridge\n" << r;
+        os << r.print("\nRidge with message");
+        cout << os.str();
+        QString s= QString::fromStdString(os.str());
+        QCOMPARE(s.count(" r"), 6);
+    }
+}//t_io
+
+}//orgQhull
+
+#include "moc/QhullRidge_test.moc"
diff --git a/xs/src/qhull/src/qhulltest/QhullSet_test.cpp b/xs/src/qhull/src/qhulltest/QhullSet_test.cpp
new file mode 100644
index 0000000000..87fcf4acf2
--- /dev/null
+++ b/xs/src/qhull/src/qhulltest/QhullSet_test.cpp
@@ -0,0 +1,434 @@
+/****************************************************************************
+**
+** Copyright (c) 2009-2015 C.B. Barber. All rights reserved.
+** $Id: //main/2015/qhull/src/qhulltest/QhullSet_test.cpp#3 $$Change: 2062 $
+** $DateTime: 2016/01/17 13:13:18 $$Author: bbarber $
+**
+****************************************************************************/
+
+//pre-compiled headers
+#include <iostream>
+#include "RoadTest.h" // QT_VERSION
+
+#include "libqhullcpp/QhullRidge.h"
+#include "libqhullcpp/QhullFacetSet.h"
+#include "libqhullcpp/Qhull.h"
+#include "libqhullcpp/RboxPoints.h"
+
+#include <QtCore/QList>
+
+using std::cout;
+using std::endl;
+
+namespace orgQhull {
+
+class QhullSet_test : public RoadTest
+{
+    Q_OBJECT
+
+#//!\name Test slots
+private slots:
+    void cleanup();
+    void t_qhullsetbase();
+    void t_convert();
+    void t_element();
+    void t_search();
+    void t_iterator();
+    void t_const_iterator();
+    void t_qhullset_iterator();
+    void t_io();
+};//QhullSet_test
+
+void
+add_QhullSet_test()
+{
+    new QhullSet_test();  // RoadTest::s_testcases
+}
+
+//Executed after each testcase
+void QhullSet_test::
+cleanup()
+{
+    RoadTest::cleanup();
+}
+
+// Test QhullFacetSet and QhullSet.
+// Use QhullRidgeSet to test methods overloaded by QhullFacetSet
+
+void QhullSet_test::
+t_qhullsetbase()
+{
+    RboxPoints rcube("c");
+    {
+        Qhull q(rcube,"QR0");  // triangulation of rotated unit cube
+        // Fake an empty set.  Default constructor not defined.  No memory allocation.
+        QhullFacet f4 = q.beginFacet();
+        QhullFacetSet fs = f4.neighborFacets();
+        fs.defineAs(q.qh()->other_points); // Force an empty set
+        QVERIFY(fs.isEmpty());
+        QCOMPARE(fs.count(), 0);
+        QCOMPARE(fs.size(), 0u);
+        QCOMPARE(fs.begin(), fs.end()); // beginPointer(), endPointer()
+        QVERIFY(QhullSetBase::isEmpty(fs.getSetT()));
+
+        QhullRidgeSet rs = f4.ridges();
+        QVERIFY(!rs.isEmpty());
+        QCOMPARE(rs.count(), 4);
+        QCOMPARE(rs.size(), 4u);
+        QVERIFY(rs.begin()!=rs.end());
+        QVERIFY(!QhullSetBase::isEmpty(rs.getSetT()));
+        QhullRidgeSet rs2= rs; // copy constructor
+        // rs= rs2; // disabled.  Would not copy ridges
+        QCOMPARE(rs2, rs);
+
+        QCOMPARE(q.facetCount(), 6);
+        QhullFacet f = q.beginFacet();
+        QhullFacetSet fs2 = f.neighborFacets();
+        QCOMPARE(fs2.count(), 4);
+        QCOMPARE(fs2.size(), 4u);
+        QVERIFY(!fs2.isEmpty());
+        QVERIFY(!QhullSetBase::isEmpty(fs2.getSetT()));
+        QVERIFY(fs!=fs2);
+        setT *s= fs2.getSetT();
+        fs.defineAs(s);
+        QVERIFY(fs==fs2);
+        QCOMPARE(fs[1], fs2[1]); // elementPointer
+        QhullFacetSet fs3(fs2);
+        QVERIFY(fs3==fs);
+        // fs= fs2; // disabled.  Would not copy facets
+        QhullFacetSet fs4= fs2; // copy constructor
+        QVERIFY(fs4==fs2);
+    }
+}//t_qhullsetbase
+
+// constructors tested by t_qhullsetbase
+
+void QhullSet_test::
+t_convert()
+{
+    RboxPoints rcube("c");
+    {
+        Qhull q(rcube,"QR0");  // rotated unit cube
+        QhullFacet f= q.firstFacet();
+        f= f.next();
+        QhullRidgeSet rs= f.ridges();
+        QCOMPARE(rs.count(),4);
+        std::vector<QhullRidge> rv= rs.toStdVector();
+        QCOMPARE(rv.size(), 4u);
+        QList<QhullRidge> rv2= rs.toQList();
+        QCOMPARE(rv2.size(), 4);
+        std::vector<QhullRidge>::iterator i= rv.begin();
+        foreach(QhullRidge r, rv2){  // Qt only
+            QhullRidge r2= *i++;
+            QCOMPARE(r, r2);
+        }
+
+        Qhull q2(rcube,"Qt QR0");  // triangulation of rotated unit cube
+        QCOMPARE(q2.facetCount(), 12);
+        QhullFacet f2 = q2.beginFacet();
+        QhullFacetSet fs = f2.neighborFacets();
+        QCOMPARE(fs.size(), 3U);
+        std::vector<QhullFacet> vs= fs.toStdVector();
+        QCOMPARE(vs.size(), fs.size());
+        for(int k= fs.count(); k--; ){
+            QCOMPARE(vs[k], fs[k]);
+        }
+        QList<QhullFacet> qv= fs.toQList();
+        QCOMPARE(qv.count(), fs.count());
+        for(int k= fs.count(); k--; ){
+            QCOMPARE(qv[k], fs[k]);
+        }
+    }
+}//t_convert
+
+//ReadOnly (count, isEmpty) tested by t_convert
+//  operator== tested by t_search
+
+void QhullSet_test::
+t_element()
+{
+    RboxPoints rcube("c");
+    Qhull q(rcube,"QR0");  // rotated unit cube
+    QhullFacet f = q.beginFacet();
+    QhullFacetSet fs = f.neighborFacets();
+
+    QCOMPARE(fs.at(1), fs[1]);
+    QCOMPARE(fs.first(), fs[0]);
+    QCOMPARE(fs.front(), fs.first());
+    QCOMPARE(fs.last(), fs.at(3));
+    QCOMPARE(fs.back(), fs.last());
+    facetT **d = fs.data();
+    facetT * const *d2= fs.data();
+    facetT * const *d3= fs.constData();
+    QVERIFY(d==d2);
+    QVERIFY(d2==d3);
+    QCOMPARE(QhullFacet(q, *d), fs.first());
+    QhullFacetSet::iterator i(q.qh(), d+4);
+    QCOMPARE(i, fs.end());
+    QCOMPARE(d[4], static_cast<facetT *>(0));
+    QhullFacet f4(q, d[4]);
+    QVERIFY(!f4.isValid());
+    QCOMPARE(fs.second(), fs[1]);
+    const QhullFacet f2= fs.second();
+    QVERIFY(f2==fs[1]);
+    const QhullFacet f3= fs[1];
+    QCOMPARE(f2, f3);
+
+    QCOMPARE(fs.value(2), fs[2]);
+    QCOMPARE(fs.value(-1), QhullFacet());
+    QCOMPARE(fs.value(10), QhullFacet());
+    QCOMPARE(fs.value(2, f), fs[2]);
+    QCOMPARE(fs.value(4, f), f);
+    // mid() not available (read-only)
+}//t_element
+
+void QhullSet_test::
+t_search()
+{
+    RboxPoints rcube("c");
+    Qhull q(rcube,"QR0");  // rotated unit cube
+    QhullFacet f = q.beginFacet();
+    QhullFacetSet fs = f.neighborFacets();
+    QhullFacet f2= *fs.begin();
+    QhullFacet f3= fs.last();
+    QVERIFY(fs.contains(f2));
+    QVERIFY(fs.contains(f3));
+    QVERIFY(!fs.contains(f));
+
+    QhullFacetSet fs2= f2.neighborFacets();
+    QVERIFY(fs==fs);
+    QVERIFY(fs!=fs2);
+    QCOMPARE(fs.count(f2), 1);
+    QCOMPARE(fs.count(f3), 1);
+    QCOMPARE(fs.count(f), 0);
+    QCOMPARE(fs.indexOf(f2), 0);
+    QCOMPARE(fs.indexOf(f3), 3);
+    QCOMPARE(fs.indexOf(f), -1);
+    QCOMPARE(fs.lastIndexOf(f2), 0);
+    QCOMPARE(fs.lastIndexOf(f3), 3);
+    QCOMPARE(fs.lastIndexOf(f), -1);
+}//t_search
+
+void QhullSet_test::
+t_iterator()
+{
+    RboxPoints rcube("c");
+    {
+        Qhull q(rcube,"QR0");  // rotated unit cube
+        QhullFacet f = q.beginFacet();
+        QhullFacetSet fs = f.neighborFacets();
+        QhullFacetSet::Iterator i= fs.begin();
+        QhullFacetSet::iterator i2= fs.begin();
+        QVERIFY(i==i2);
+        QVERIFY(i>=i2);
+        QVERIFY(i<=i2);
+        i= fs.begin();
+        QVERIFY(i==i2);
+        i2= fs.end();
+        QVERIFY(i!=i2);
+        QhullFacet f3(*i);
+        i2--;
+        QhullFacet f2= *i2;
+        QCOMPARE(f3.id(), fs[0].id());
+        QCOMPARE(f2.id(), fs[3].id());
+        QhullFacetSet::Iterator i3(i2);
+        QCOMPARE(*i2, *i3);
+
+        (i3= i)++;
+        QCOMPARE((*i3).id(), fs[1].id());
+        QVERIFY(i==i);
+        QVERIFY(i!=i2);
+        QVERIFY(i<i2);
+        QVERIFY(i<=i2);
+        QVERIFY(i2>i);
+        QVERIFY(i2>=i);
+
+        QhullFacetSet::ConstIterator i4= fs.begin();
+        QVERIFY(i==i4); // iterator COMP const_iterator
+        QVERIFY(i<=i4);
+        QVERIFY(i>=i4);
+        QVERIFY(i4==i); // const_iterator COMP iterator
+        QVERIFY(i4<=i);
+        QVERIFY(i4>=i);
+        QVERIFY(i>=i4);
+        QVERIFY(i4<=i);
+        QVERIFY(i2!=i4);
+        QVERIFY(i2>i4);
+        QVERIFY(i2>=i4);
+        QVERIFY(i4!=i2);
+        QVERIFY(i4<i2);
+        QVERIFY(i4<=i2);
+        ++i4;
+        QVERIFY(i<i4);
+        QVERIFY(i<=i4);
+        QVERIFY(i4>i);
+        QVERIFY(i4>=i);
+
+        i= fs.begin();
+        i2= fs.begin();
+        QCOMPARE(i, i2++);
+        QCOMPARE(*i2, fs[1]);
+        QCOMPARE(++i, i2);
+        QCOMPARE(i, i2--);
+        QCOMPARE(i2, fs.begin());
+        QCOMPARE(--i, i2);
+        QCOMPARE(i2 += 4, fs.end());
+        QCOMPARE(i2 -= 4, fs.begin());
+        QCOMPARE(i2+0, fs.begin());
+        QCOMPARE(i2+4, fs.end());
+        i2 += 4;
+        i= i2-0;
+        QCOMPARE(i, i2);
+        i= i2-4;
+        QCOMPARE(i, fs.begin());
+        QCOMPARE(i2-i, 4);
+
+        //fs.begin end tested above
+
+        // QhullFacetSet is const-only
+    }
+}//t_iterator
+
+void QhullSet_test::
+t_const_iterator()
+{
+    RboxPoints rcube("c");
+    {
+        Qhull q(rcube,"QR0");  // rotated unit cube
+        QhullFacet f = q.beginFacet();
+        QhullFacetSet fs = f.neighborFacets();
+        QhullFacetSet::ConstIterator i= fs.begin();
+        QhullFacetSet::const_iterator i2= fs.begin();
+        QVERIFY(i==i2);
+        QVERIFY(i>=i2);
+        QVERIFY(i<=i2);
+        i= fs.begin();
+        QVERIFY(i==i2);
+        i2= fs.end();
+        QVERIFY(i!=i2);
+        QhullFacet f3(*i);
+        i2--;
+        QhullFacet f2= *i2;
+        QCOMPARE(f3.id(), fs[0].id());
+        QCOMPARE(f2.id(), fs[3].id());
+        QhullFacetSet::ConstIterator i3(i2);
+        QCOMPARE(*i2, *i3);
+
+        (i3= i)++;
+        QCOMPARE((*i3).id(), fs[1].id());
+        QVERIFY(i==i);
+        QVERIFY(i!=i2);
+        QVERIFY(i<i2);
+        QVERIFY(i<=i2);
+        QVERIFY(i2>i);
+        QVERIFY(i2>=i);
+
+        // See t_iterator for const_iterator COMP iterator
+
+        i= fs.begin();
+        i2= fs.constBegin();
+        QCOMPARE(i, i2++);
+        QCOMPARE(*i2, fs[1]);
+        QCOMPARE(++i, i2);
+        QCOMPARE(i, i2--);
+        QCOMPARE(i2, fs.constBegin());
+        QCOMPARE(--i, i2);
+        QCOMPARE(i2+=4, fs.constEnd());
+        QCOMPARE(i2-=4, fs.constBegin());
+        QCOMPARE(i2+0, fs.constBegin());
+        QCOMPARE(i2+4, fs.constEnd());
+        i2 += 4;
+        i= i2-0;
+        QCOMPARE(i, i2);
+        i= i2-4;
+        QCOMPARE(i, fs.constBegin());
+        QCOMPARE(i2-i, 4);
+
+        // QhullFacetSet is const-only
+    }
+}//t_const_iterator
+
+void QhullSet_test::
+t_qhullset_iterator()
+{
+    RboxPoints rcube("c");
+    Qhull q(rcube,"QR0");  // rotated unit cube
+    // Fake an empty set.  Default constructor not defined.  No memory allocation.
+    QhullFacet f = q.beginFacet();
+    QhullFacetSet fs = f.neighborFacets();
+    fs.defineAs(q.qh()->other_points);
+    QhullFacetSetIterator i(fs);
+    QCOMPARE(fs.count(), 0);
+    QVERIFY(!i.hasNext());
+    QVERIFY(!i.hasPrevious());
+    i.toBack();
+    QVERIFY(!i.hasNext());
+    QVERIFY(!i.hasPrevious());
+
+    QhullFacet f2 = q.beginFacet();
+    QhullFacetSet fs2 = f2.neighborFacets();
+    QhullFacetSetIterator i2(fs2);
+    QCOMPARE(fs2.count(), 4);
+    i= fs2;
+    QVERIFY(i2.hasNext());
+    QVERIFY(!i2.hasPrevious());
+    QVERIFY(i.hasNext());
+    QVERIFY(!i.hasPrevious());
+    i2.toBack();
+    i.toFront();
+    QVERIFY(!i2.hasNext());
+    QVERIFY(i2.hasPrevious());
+    QVERIFY(i.hasNext());
+    QVERIFY(!i.hasPrevious());
+
+    // i at front, i2 at end/back, 4 neighbors
+    QhullFacetSet fs3 = f2.neighborFacets(); // same as fs2
+    QhullFacet f3(fs2[0]);
+    QhullFacet f4= fs3[0];
+    QCOMPARE(f3, f4);
+    QVERIFY(f3==f4);
+    QhullFacet f5(fs3[1]);
+    QVERIFY(f4!=f5);
+    QhullFacet f6(fs3[2]);
+    QhullFacet f7(fs3[3]);
+    QCOMPARE(i2.peekPrevious(), f7);
+    QCOMPARE(i2.previous(), f7);
+    QCOMPARE(i2.previous(), f6);
+    QCOMPARE(i2.previous(), f5);
+    QCOMPARE(i2.previous(), f4);
+    QVERIFY(!i2.hasPrevious());
+    QCOMPARE(i.peekNext(), f4);
+    // i.peekNext()= 1.0; // compiler error
+    QCOMPARE(i.next(), f4);
+    QCOMPARE(i.peekNext(), f5);
+    QCOMPARE(i.next(), f5);
+    QCOMPARE(i.next(), f6);
+    QCOMPARE(i.next(), f7);
+    QVERIFY(!i.hasNext());
+    i.toFront();
+    QCOMPARE(i.next(), f4);
+}//t_qhullset_iterator
+
+void QhullSet_test::
+t_io()
+{
+    RboxPoints rcube("c");
+    Qhull q(rcube,"QR0");  // rotated unit cube
+    // Fake an empty set.  Default constructor not defined.  No memory allocation.
+    QhullFacet f= q.beginFacet();
+    QhullFacetSet fs= f.neighborFacets();
+    fs.defineAs(q.qh()->other_points);
+    cout << "INFO:     empty set" << fs << std::endl;
+    QhullFacet f2= q.beginFacet();
+    QhullFacetSet fs2= f2.neighborFacets();
+    cout << "INFO:   Neighboring facets\n";
+    cout << fs2 << std::endl;
+
+    QhullRidgeSet rs= f.ridges();
+    cout << "INFO:   Ridges for a facet\n";
+    cout << rs << std::endl;
+}//t_io
+
+}//namespace orgQhull
+
+#include "moc/QhullSet_test.moc"
diff --git a/xs/src/qhull/src/qhulltest/QhullVertexSet_test.cpp b/xs/src/qhull/src/qhulltest/QhullVertexSet_test.cpp
new file mode 100644
index 0000000000..41caacd290
--- /dev/null
+++ b/xs/src/qhull/src/qhulltest/QhullVertexSet_test.cpp
@@ -0,0 +1,152 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
+** $Id: //main/2015/qhull/src/qhulltest/QhullVertexSet_test.cpp#3 $$Change: 2062 $
+** $DateTime: 2016/01/17 13:13:18 $$Author: bbarber $
+**
+****************************************************************************/
+
+//pre-compiled headers
+#include <iostream>
+#include "qhulltest/RoadTest.h" // QT_VERSION
+
+#include "libqhullcpp/QhullVertexSet.h"
+#include "libqhullcpp/QhullVertex.h"
+#include "libqhullcpp/Qhull.h"
+#include "libqhullcpp/QhullError.h"
+#include "libqhullcpp/QhullFacet.h"
+#include "libqhullcpp/RboxPoints.h"
+
+using std::cout;
+using std::endl;
+using std::ostringstream;
+using std::ostream;
+using std::string;
+
+namespace orgQhull {
+
+class QhullVertexSet_test : public RoadTest
+{
+    Q_OBJECT
+
+#//!\name Test slots
+private slots:
+    void cleanup();
+    void t_construct();
+    void t_convert();
+    void t_readonly();
+    void t_foreach();
+    void t_io();
+};//QhullVertexSet_test
+
+void
+add_QhullVertexSet_test()
+{
+    new QhullVertexSet_test();  // RoadTest::s_testcases
+}
+
+//Executed after each testcase
+void QhullVertexSet_test::
+cleanup()
+{
+    RoadTest::cleanup();
+}
+
+void QhullVertexSet_test::
+t_construct()
+{
+    RboxPoints rcube("c");
+    Qhull q(rcube,"QR0");  // rotated unit cube
+    cout << "INFO   : Cube rotated by QR" << q.rotateRandom() << std::endl;
+    QhullFacet f= q.firstFacet();
+    QhullVertexSet vs= f.vertices();
+    QVERIFY(!vs.isEmpty());
+    QCOMPARE(vs.count(),4);
+    QhullVertexSet vs4= vs; // copy constructor
+    QVERIFY(vs4==vs);
+    QhullVertexSet vs3(q, q.qh()->del_vertices);
+    QVERIFY(vs3.isEmpty());
+}//t_construct
+
+void QhullVertexSet_test::
+t_convert()
+{
+    RboxPoints rcube("c");
+    Qhull q(rcube,"QR0 QV2");  // rotated unit cube with "good" facets adjacent to point 0
+    cout << "INFO   : Cube rotated by QR" << q.rotateRandom() << std::endl;
+    QhullFacet f= q.firstFacet();
+    QhullVertexSet vs2= f.vertices();
+    QCOMPARE(vs2.count(),4);
+    std::vector<QhullVertex> fv= vs2.toStdVector();
+    QCOMPARE(fv.size(), 4u);
+    QList<QhullVertex> fv2= vs2.toQList();
+    QCOMPARE(fv2.size(), 4);
+    std::vector<QhullVertex> fv3= vs2.toStdVector();
+    QCOMPARE(fv3.size(), 4u);
+    QList<QhullVertex> fv4= vs2.toQList();
+    QCOMPARE(fv4.size(), 4);
+}//t_convert
+
+//! Spot check properties and read-only.  See QhullSet_test
+void QhullVertexSet_test::
+t_readonly()
+{
+    RboxPoints rcube("c");
+    Qhull q(rcube,"QV0");  // good facets are adjacent to point 0
+    QhullVertexSet vs= q.firstFacet().vertices();
+    QCOMPARE(vs.count(), 4);
+    QCOMPARE(vs.count(), 4);
+    QhullVertex v= vs.first();
+    QhullVertex v2= vs.last();
+    QVERIFY(vs.contains(v));
+    QVERIFY(vs.contains(v2));
+}//t_readonly
+
+void QhullVertexSet_test::
+t_foreach()
+{
+    RboxPoints rcube("c");
+    // Spot check predicates and accessors.  See QhullLinkedList_test
+    Qhull q(rcube,"QR0");  // rotated unit cube
+    cout << "INFO   : Cube rotated by QR" << q.rotateRandom() << std::endl;
+    QhullVertexSet vs= q.firstFacet().vertices();
+    QVERIFY(vs.contains(vs.first()));
+    QVERIFY(vs.contains(vs.last()));
+    QCOMPARE(vs.first(), *vs.begin());
+    QCOMPARE(*(vs.end()-1), vs.last());
+}//t_foreach
+
+void QhullVertexSet_test::
+t_io()
+{
+    RboxPoints rcube("c");
+    {
+        Qhull q(rcube,"QR0 QV0");   // good facets are adjacent to point 0
+        cout << "INFO   : Cube rotated by QR" << q.rotateRandom() << std::endl;
+        QhullVertexSet vs= q.firstFacet().vertices();
+        ostringstream os;
+        os << vs.print("Vertices of first facet with point 0");
+        os << vs.printIdentifiers("\nVertex identifiers: ");
+        cout<< os.str();
+        QString vertices= QString::fromStdString(os.str());
+        QCOMPARE(vertices.count(QRegExp(" v[0-9]")), 4);
+    }
+}//t_io
+
+#ifdef QHULL_USES_QT
+QList<QhullVertex> QhullVertexSet::
+toQList() const
+{
+    QhullSetIterator<QhullVertex> i(*this);
+    QList<QhullVertex> vs;
+    while(i.hasNext()){
+        QhullVertex v= i.next();
+        vs.append(v);
+    }
+    return vs;
+}//toQList
+#endif //QHULL_USES_QT
+
+}//orgQhull
+
+#include "moc/QhullVertexSet_test.moc"
diff --git a/xs/src/qhull/src/qhulltest/QhullVertex_test.cpp b/xs/src/qhull/src/qhulltest/QhullVertex_test.cpp
new file mode 100644
index 0000000000..fb6ec9640a
--- /dev/null
+++ b/xs/src/qhull/src/qhulltest/QhullVertex_test.cpp
@@ -0,0 +1,184 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
+** $Id: //main/2015/qhull/src/qhulltest/QhullVertex_test.cpp#3 $$Change: 2062 $
+** $DateTime: 2016/01/17 13:13:18 $$Author: bbarber $
+**
+****************************************************************************/
+
+//pre-compiled headers
+#include <iostream>
+#include "RoadTest.h" // QT_VERSION
+
+#include "libqhullcpp/QhullVertex.h"
+#include "libqhullcpp/Coordinates.h"
+#include "libqhullcpp/QhullError.h"
+#include "libqhullcpp/RboxPoints.h"
+#include "libqhullcpp/QhullFacet.h"
+#include "libqhullcpp/QhullFacetSet.h"
+#include "libqhullcpp/QhullVertexSet.h"
+#include "libqhullcpp/Qhull.h"
+
+using std::cout;
+using std::endl;
+using std::ostringstream;
+using std::ostream;
+using std::string;
+
+namespace orgQhull {
+
+class QhullVertex_test : public RoadTest
+{
+    Q_OBJECT
+
+#//!\name Test slots
+private slots:
+    void cleanup();
+    void t_constructConvert();
+    void t_getSet();
+    void t_foreach();
+    void t_io();
+};//QhullVertex_test
+
+void
+add_QhullVertex_test()
+{
+    new QhullVertex_test();  // RoadTest::s_testcases
+}
+
+//Executed after each testcase
+void QhullVertex_test::
+cleanup()
+{
+    RoadTest::cleanup();
+}
+
+void QhullVertex_test::
+t_constructConvert()
+{
+    QhullVertex v6;
+    QVERIFY(!v6.isValid());
+    QCOMPARE(v6.dimension(),0);
+    // Qhull.runQhull() constructs QhullFacets as facetT
+    RboxPoints rcube("c");
+    Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
+    QhullVertex v(q);
+    QVERIFY(!v.isValid());
+    QCOMPARE(v.dimension(),3);
+    QhullVertex v2(q.beginVertex());
+    QCOMPARE(v2.dimension(),3);
+    v= v2;  // copy assignment
+    QVERIFY(v.isValid());
+    QCOMPARE(v.dimension(),3);
+    QhullVertex v5= v2; // copy constructor
+    QVERIFY(v5==v2);
+    QVERIFY(v5==v);
+    QhullVertex v3(q, v2.getVertexT());
+    QCOMPARE(v,v3);
+    QhullVertex v4(q, v2.getBaseT());
+    QCOMPARE(v,v4);
+}//t_constructConvert
+
+void QhullVertex_test::
+t_getSet()
+{
+    RboxPoints rcube("c");
+    {
+        Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
+        QCOMPARE(q.facetCount(), 12);
+        QCOMPARE(q.vertexCount(), 8);
+
+        // Also spot-test QhullVertexList.  See QhullLinkedList_test.cpp
+        QhullVertexList vs= q.vertexList();
+        QhullVertexListIterator i(vs);
+        while(i.hasNext()){
+            const QhullVertex v= i.next();
+            cout << v.id() << endl;
+            QCOMPARE(v.dimension(),3);
+            QVERIFY(v.id()>=0 && v.id()<9);
+            QVERIFY(v.isValid());
+            if(i.hasNext()){
+                QCOMPARE(v.next(), i.peekNext());
+                QVERIFY(v.next()!=v);
+                QVERIFY(v.next().previous()==v);
+            }
+            QVERIFY(i.hasPrevious());
+            QCOMPARE(v, i.peekPrevious());
+        }
+
+        // test point()
+        foreach (QhullVertex v, q.vertexList()){  // Qt only
+            QhullPoint p= v.point();
+            int j= p.id();
+            cout << "Point " << j << ":\n" << p << endl;
+            QVERIFY(j>=0 && j<8);
+        }
+    }
+}//t_getSet
+
+void QhullVertex_test::
+t_foreach()
+{
+    RboxPoints rcube("c W0 300");  // 300 points on surface of cube
+    {
+        Qhull q(rcube, "QR0 Qc"); // keep coplanars, thick facet, and rotate the cube
+        foreach (QhullVertex v, q.vertexList()){  // Qt only
+            QhullFacetSet fs= v.neighborFacets();
+            QCOMPARE(fs.count(), 3);
+            foreach (QhullFacet f, fs){  // Qt only
+                QVERIFY(f.vertices().contains(v));
+            }
+        }
+    }
+}//t_foreach
+
+void QhullVertex_test::
+t_io()
+{
+    RboxPoints rcube("c");
+    {
+        Qhull q(rcube, "");
+        QhullVertex v= q.beginVertex();
+        ostringstream os;
+        os << "Vertex and vertices:\n";
+        os << v;
+        QhullVertexSet vs= q.firstFacet().vertices();
+        os << vs;
+        os << "\nVertex and vertices with message:\n";
+        os << v.print("Vertex");
+        os << vs.print("\nVertices:");
+        cout << os.str();
+        QString s= QString::fromStdString(os.str());
+        QCOMPARE(s.count("(v"), 10);
+        QCOMPARE(s.count(": f"), 2);
+    }
+    RboxPoints r10("10 D3");  // Without QhullVertex::facetNeighbors
+    {
+        Qhull q(r10, "");
+        QhullVertex v= q.beginVertex();
+        ostringstream os;
+        os << "\nTry again with simplicial facets.  No neighboring facets listed for vertices.\n";
+        os << "Vertex and vertices:\n";
+        os << v;
+        q.defineVertexNeighborFacets();
+        os << "This time with neighborFacets() defined for all vertices:\n";
+        os << v;
+        cout << os.str();
+        QString s= QString::fromStdString(os.str());
+        QCOMPARE(s.count(": f"), 1);
+
+        Qhull q2(r10, "v"); // Voronoi diagram
+        QhullVertex v2= q2.beginVertex();
+        ostringstream os2;
+        os2 << "\nTry again with Voronoi diagram of simplicial facets.  Neighboring facets automatically defined for vertices.\n";
+        os2 << "Vertex and vertices:\n";
+        os2 << v2;
+        cout << os2.str();
+        QString s2= QString::fromStdString(os2.str());
+        QCOMPARE(s2.count(": f"), 1);
+    }
+}//t_io
+
+}//orgQhull
+
+#include "moc/QhullVertex_test.moc"
diff --git a/xs/src/qhull/src/qhulltest/Qhull_test.cpp b/xs/src/qhull/src/qhulltest/Qhull_test.cpp
new file mode 100644
index 0000000000..cc3918a050
--- /dev/null
+++ b/xs/src/qhull/src/qhulltest/Qhull_test.cpp
@@ -0,0 +1,360 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
+** $Id: //main/2015/qhull/src/qhulltest/Qhull_test.cpp#4 $$Change: 2062 $
+** $DateTime: 2016/01/17 13:13:18 $$Author: bbarber $
+**
+****************************************************************************/
+
+//pre-compiled headers
+#include <iostream>
+#include "qhulltest/RoadTest.h" // QT_VERSION
+
+#include "libqhullcpp/Qhull.h"
+#include "libqhullcpp/QhullError.h"
+#include "libqhullcpp/RboxPoints.h"
+#include "libqhullcpp/QhullFacetList.h"
+
+using std::cout;
+using std::endl;
+using std::string;
+
+namespace orgQhull {
+
+//! Test C++ interface to Qhull
+//! See eg/q_test for tests of Qhull commands
+class Qhull_test : public RoadTest
+{
+    Q_OBJECT
+
+#//!\name Test slots
+private slots:
+    void cleanup();
+    void t_construct();
+    void t_attribute();
+    void t_message();
+    void t_getSet();
+    void t_getQh();
+    void t_getValue();
+    void t_foreach();
+    void t_modify();
+};//Qhull_test
+
+void
+add_Qhull_test()
+{
+    new Qhull_test();  // RoadTest::s_testcases
+}
+
+//Executed after each testcase
+void Qhull_test::
+cleanup()
+{
+    RoadTest::cleanup();
+}
+
+void Qhull_test::
+t_construct()
+{
+    {
+        Qhull q;
+        QCOMPARE(q.dimension(),0);
+        QVERIFY(q.qh()!=0);
+        QCOMPARE(QString(q.qhullCommand()),QString(""));
+        QCOMPARE(QString(q.rboxCommand()),QString(""));
+        try{
+            QCOMPARE(q.area(),0.0);
+            QFAIL("area() did not fail.");
+        }catch (const std::exception &e) {
+            cout << "INFO   : Caught " << e.what();
+        }
+    }
+    {
+        RboxPoints rbox("10000");
+        Qhull q(rbox, "QR0"); // Random points in a randomly rotated cube.
+        QCOMPARE(q.dimension(),3);
+        QVERIFY(q.volume() < 1.0);
+        QVERIFY(q.volume() > 0.99);
+    }
+    {
+        double points[] = {
+            0, 0,
+            1, 0,
+            1, 1
+        };
+        Qhull q("triangle", 2, 3, points, "");
+        QCOMPARE(q.dimension(),2);
+        QCOMPARE(q.facetCount(),3);
+        QCOMPARE(q.vertexCount(),3);
+        QCOMPARE(q.dimension(),2);
+        QCOMPARE(q.area(), 2.0+sqrt(2.0)); // length of boundary
+        QCOMPARE(q.volume(), 0.5);        // the 2-d area
+    }
+}//t_construct
+
+void Qhull_test::
+t_attribute()
+{
+    RboxPoints rcube("c");
+    {
+        double normals[] = {
+            0,  -1, -0.5,
+           -1,   0, -0.5,
+            1,   0, -0.5,
+            0,   1, -0.5
+        };
+        Qhull q;
+        Coordinates feasible;
+        feasible << 0.0 << 0.0;
+        q.setFeasiblePoint(feasible);
+        Coordinates c(std::vector<double>(2, 0.0));
+        QVERIFY(q.feasiblePoint()==c);
+        q.setOutputStream(&cout);
+        q.runQhull("normals of square", 3, 4, normals, "H"); // halfspace intersect
+        QVERIFY(q.feasiblePoint()==c); // from qh.feasible_point after runQhull()
+        QCOMPARE(q.facetList().count(), 4); // Vertices of square
+        cout << "Expecting summary of halfspace intersection\n";
+        q.outputQhull();
+        q.qh()->disableOutputStream();  // Same as q.disableOutputStream()
+        cout << "Expecting no output from qh_fprintf() in Qhull.cpp\n";
+        q.outputQhull();
+    }
+}//t_attribute
+
+//! No QhullMessage for errors outside of qhull
+void Qhull_test::
+t_message()
+{
+    RboxPoints rcube("c");
+    {
+        Qhull q;
+        QCOMPARE(q.qhullMessage(), string(""));
+        QCOMPARE(q.qhullStatus(), qh_ERRnone);
+        QVERIFY(!q.hasQhullMessage());
+        try{
+            q.runQhull(rcube, "Fd");
+            QFAIL("runQhull Fd did not fail.");
+        }catch (const std::exception &e) {
+            const char *s= e.what();
+            cout << "INFO   : Caught " << s;
+            QCOMPARE(QString::fromStdString(s).left(6), QString("QH6029"));
+            // FIXUP QH11025 -- review decision to clearQhullMessage at QhullError()            // Cleared when copied to QhullError
+            QVERIFY(!q.hasQhullMessage());
+            // QCOMPARE(q.qhullMessage(), QString::fromStdString(s).remove(0, 7));
+            // QCOMPARE(q.qhullStatus(), 6029);
+            q.clearQhullMessage();
+            QVERIFY(!q.hasQhullMessage());
+        }
+        q.appendQhullMessage("Append 1");
+        QVERIFY(q.hasQhullMessage());
+        QCOMPARE(QString::fromStdString(q.qhullMessage()), QString("Append 1"));
+        q.appendQhullMessage("\nAppend 2\n");
+        QCOMPARE(QString::fromStdString(q.qhullMessage()), QString("Append 1\nAppend 2\n"));
+        q.clearQhullMessage();
+        QVERIFY(!q.hasQhullMessage());
+        QCOMPARE(QString::fromStdString(q.qhullMessage()), QString(""));
+    }
+    {
+        cout << "INFO   : Error stream without output stream\n";
+        Qhull q;
+        q.setErrorStream(&cout);
+        q.setOutputStream(0);
+        try{
+            q.runQhull(rcube, "Fd");
+            QFAIL("runQhull Fd did not fail.");
+        }catch (const QhullError &e) {
+            cout << "INFO   : Caught " << e;
+            QCOMPARE(e.errorCode(), 6029);
+        }
+        //FIXUP QH11025 Qhullmessage cleared when QhullError thrown.  Switched to e
+        //QVERIFY(q.hasQhullMessage());
+        //QCOMPARE(QString::fromStdString(q.qhullMessage()).left(6), QString("QH6029"));
+        q.clearQhullMessage();
+        QVERIFY(!q.hasQhullMessage());
+    }
+    {
+        cout << "INFO   : Error output sent to output stream without error stream\n";
+        Qhull q;
+        q.setErrorStream(0);
+        q.setOutputStream(&cout);
+        try{
+            q.runQhull(rcube, "Tz H0");
+            QFAIL("runQhull TZ did not fail.");
+        }catch (const std::exception &e) {
+            const char *s= e.what();
+            cout << "INFO   : Caught " << s;
+            QCOMPARE(QString::fromLatin1(s).left(6), QString("QH6023"));
+        }
+        //FIXUP QH11025 Qhullmessage cleared when QhullError thrown.  Switched to e
+        //QVERIFY(q.hasQhullMessage());
+        //QCOMPARE(QString::fromStdString(q.qhullMessage()).left(17), QString("qhull: no message"));
+        //QCOMPARE(q.qhullStatus(), 6023);
+        q.clearQhullMessage();
+        QVERIFY(!q.hasQhullMessage());
+    }
+    {
+        cout << "INFO   : No error stream or output stream\n";
+        Qhull q;
+        q.setErrorStream(0);
+        q.setOutputStream(0);
+        try{
+            q.runQhull(rcube, "Fd");
+            QFAIL("outputQhull did not fail.");
+        }catch (const std::exception &e) {
+            const char *s= e.what();
+            cout << "INFO   : Caught " << s;
+            QCOMPARE(QString::fromLatin1(s).left(6), QString("QH6029"));
+        }
+        //FIXUP QH11025 Qhullmessage cleared when QhullError thrown.  Switched to e
+        //QVERIFY(q.hasQhullMessage());
+        //QCOMPARE(QString::fromStdString(q.qhullMessage()).left(9), QString("qhull err"));
+        //QCOMPARE(q.qhullStatus(), 6029);
+        q.clearQhullMessage();
+        QVERIFY(!q.hasQhullMessage());
+    }
+}//t_message
+
+void Qhull_test::
+t_getSet()
+{
+    RboxPoints rcube("c");
+    {
+        Qhull q;
+        QVERIFY(!q.initialized());
+        q.runQhull(rcube, "s");
+        QVERIFY(q.initialized());
+        QCOMPARE(q.dimension(), 3);
+        QhullPoint p= q.origin();
+        QCOMPARE(p.dimension(), 3);
+        QCOMPARE(p[0]+p[1]+p[2], 0.0);
+        q.setErrorStream(&cout);
+        q.outputQhull();
+    }
+    {
+        Qhull q;
+        q.runQhull(rcube, "");
+        q.setOutputStream(&cout);
+        q.outputQhull();
+    }
+}//t_getSet
+
+void Qhull_test::
+t_getQh()
+{
+    RboxPoints rcube("c");
+    {
+        Qhull q;
+        q.runQhull(rcube, "s");
+        QCOMPARE(QString(q.qhullCommand()), QString("qhull s"));
+        QCOMPARE(QString(q.rboxCommand()), QString("rbox \"c\""));
+        QCOMPARE(q.facetCount(), 6);
+        QCOMPARE(q.vertexCount(), 8);
+        // Sample fields from Qhull's qhT [libqhull.h]
+        QCOMPARE(q.qh()->ALLpoints, 0u);
+        QCOMPARE(q.qh()->GOODpoint, 0);
+        QCOMPARE(q.qh()->IStracing, 0);
+        QCOMPARE(q.qh()->MAXcoplanar+1.0, 1.0); // fuzzy compare
+        QCOMPARE(q.qh()->MERGING, 1u);
+        QCOMPARE(q.qh()->input_dim, 3);
+        QCOMPARE(QString(q.qh()->qhull_options).left(8), QString("  run-id"));
+        QCOMPARE(q.qh()->num_facets, 6);
+        QCOMPARE(q.qh()->hasTriangulation, 0u);
+        QCOMPARE(q.qh()->max_outside - q.qh()->min_vertex + 1.0, 1.0); // fuzzy compare
+        QCOMPARE(*q.qh()->gm_matrix+1.0, 1.0); // fuzzy compare
+    }
+}//t_getQh
+
+void Qhull_test::
+t_getValue()
+{
+    RboxPoints rcube("c");
+    {
+        Qhull q;
+        q.runQhull(rcube, "");
+        QCOMPARE(q.area(), 6.0);
+        QCOMPARE(q.volume(), 1.0);
+    }
+}//t_getValue
+
+void Qhull_test::
+t_foreach()
+{
+    RboxPoints rcube("c");
+    {
+        Qhull q;
+        QCOMPARE(q.beginFacet(),q.endFacet());
+        QCOMPARE(q.beginVertex(),q.endVertex());
+        q.runQhull(rcube, "");
+        QCOMPARE(q.facetList().count(), 6);
+
+        // defineVertexNeighborFacets() tested in QhullVertex_test::t_io()
+
+        QhullFacetList facets(q.beginFacet(), q.endFacet());
+        QCOMPARE(facets.count(), 6);
+        QCOMPARE(q.firstFacet(), q.beginFacet());
+        QhullVertexList vertices(q.beginVertex(), q.endVertex());
+        QCOMPARE(vertices.count(), 8);
+        QCOMPARE(q.firstVertex(), q.beginVertex());
+        QhullPoints ps= q.points();
+        QCOMPARE(ps.count(), 8);
+        QhullPointSet ps2= q.otherPoints();
+        QCOMPARE(ps2.count(), 0);
+        // ps2= q.otherPoints(); //disabled, would not copy the points
+        QCOMPARE(q.facetCount(), 6);
+        QCOMPARE(q.vertexCount(), 8);
+        coordT *c= q.pointCoordinateBegin(); // of q.points()
+        QVERIFY(*c==0.5 || *c==-0.5);
+        coordT *c3= q.pointCoordinateEnd();
+        QVERIFY(c3[-1]==0.5 || c3[-1]==-0.5);
+        QCOMPARE(c3-c, 8*3);
+        QCOMPARE(q.vertexList().count(), 8);
+    }
+}//t_foreach
+
+void Qhull_test::
+t_modify()
+{
+    //addPoint() tested in t_foreach
+    RboxPoints diamond("d");
+    Qhull q(diamond, "o");
+    q.setOutputStream(&cout);
+    cout << "Expecting vertexList and facetList of a 3-d diamond.\n";
+    q.outputQhull();
+    cout << "Expecting normals of a 3-d diamond.\n";
+    q.outputQhull("n");
+    // runQhull tested in t_attribute(), t_message(), etc.
+}//t_modify
+
+}//orgQhull
+
+// Redefine Qhull's usermem_r.c in order to report erroneous calls to qh_exit
+void qh_exit(int exitcode) {
+    cout << "FAIL!  : Qhull called qh_exit().  Qhull's error handling not available.\n.. See the corresponding Qhull:qhull_message or setErrorStream().\n";
+    exit(exitcode);
+}
+void qh_fprintf_stderr(int msgcode, const char *fmt, ... ) {
+    va_list args;
+
+    va_start(args, fmt);
+    if(msgcode)
+        fprintf(stderr, "QH%.4d ", msgcode);
+    vfprintf(stderr, fmt, args);
+    va_end(args);
+} /* fprintf_stderr */
+void qh_free(void *mem) {
+    free(mem);
+}
+void *qh_malloc(size_t size) {
+    return malloc(size);
+}
+
+#if 0
+template<> char * QTest::
+toString(const std::string &s)
+{
+    QByteArray ba = s.c_str();
+    return qstrdup(ba.data());
+}
+#endif
+
+#include "moc/Qhull_test.moc"
diff --git a/xs/src/qhull/src/qhulltest/RboxPoints_test.cpp b/xs/src/qhull/src/qhulltest/RboxPoints_test.cpp
new file mode 100644
index 0000000000..4f4ea984f8
--- /dev/null
+++ b/xs/src/qhull/src/qhulltest/RboxPoints_test.cpp
@@ -0,0 +1,215 @@
+/****************************************************************************
+**
+** Copyright (c) 2006-2015 C.B. Barber. All rights reserved.
+** $Id: //main/2015/qhull/src/qhulltest/RboxPoints_test.cpp#2 $$Change: 2062 $
+** $DateTime: 2016/01/17 13:13:18 $$Author: bbarber $
+**
+****************************************************************************/
+
+//pre-compiled headers
+#include <iostream>
+#include "RoadTest.h" // QT_VERSION
+
+#include "libqhullcpp/RboxPoints.h"
+#include "libqhullcpp/QhullError.h"
+
+using std::cout;
+using std::endl;
+using std::ostringstream;
+using std::string;
+using std::stringstream;
+
+namespace orgQhull {
+
+//! Test C++ interface to Rbox
+//! See eg/q_test for tests of rbox commands
+class RboxPoints_test : public RoadTest
+{
+    Q_OBJECT
+
+#//!\name Test slots
+private slots:
+    void t_construct();
+    void t_error();
+    void t_test();
+    void t_getSet();
+    void t_foreach();
+    void t_change();
+    void t_ostream();
+};
+
+void
+add_RboxPoints_test()
+{
+    new RboxPoints_test();  // RoadTest::s_testcases
+}
+
+void RboxPoints_test::
+t_construct()
+{
+    RboxPoints rp;
+    QCOMPARE(rp.dimension(), 0);
+    QCOMPARE(rp.count(), 0);
+    QVERIFY(QString::fromStdString(rp.comment()) != QString(""));
+    QVERIFY(rp.isEmpty());
+    QVERIFY(!rp.hasRboxMessage());
+    QCOMPARE(rp.rboxStatus(), qh_ERRnone);
+    QCOMPARE(QString::fromStdString(rp.rboxMessage()), QString("rbox warning: no points generated\n"));
+
+    RboxPoints rp2("c"); // 3-d cube
+    QCOMPARE(rp2.dimension(), 3);
+    QCOMPARE(rp2.count(), 8);
+    QCOMPARE(QString::fromStdString(rp2.comment()), QString("rbox \"c\""));
+    QVERIFY(!rp2.isEmpty());
+    QVERIFY(!rp2.hasRboxMessage());
+    QCOMPARE(rp2.rboxStatus(), qh_ERRnone);
+    QCOMPARE(QString::fromStdString(rp2.rboxMessage()), QString("rbox: OK\n"));
+}//t_construct
+
+void RboxPoints_test::
+t_error()
+{
+    RboxPoints rp;
+    try{
+        rp.appendPoints("D0 c");
+        QFAIL("'D0 c' did not fail.");
+    }catch (const std::exception &e) {
+        const char *s= e.what();
+        cout << "INFO   : Caught " << s;
+        QCOMPARE(QString(s).left(6), QString("QH6189"));
+        QVERIFY(rp.hasRboxMessage());
+        QCOMPARE(QString::fromStdString(rp.rboxMessage()).left(8), QString("rbox err"));
+        QCOMPARE(rp.rboxStatus(), 6189);
+        rp.clearRboxMessage();
+        QVERIFY(!rp.hasRboxMessage());
+    }
+    try{
+        RboxPoints rp2;
+        rp2.setDimension(-1);
+        QFAIL("setDimension(-1) did not fail.");
+    }catch (const RoadError &e) {
+        const char *s= e.what();
+        cout << "INFO   : Caught " << s;
+        QCOMPARE(QString(s).left(7), QString("QH10062"));
+        QCOMPARE(e.errorCode(), 10062);
+        QCOMPARE(QString::fromStdString(e.what()), QString(s));
+        RoadLogEvent logEvent= e.roadLogEvent();
+        QCOMPARE(logEvent.int1(), -1);
+    }
+}//t_error
+
+void RboxPoints_test::
+t_test()
+{
+    // isEmpty -- t_construct
+}//t_test
+
+void RboxPoints_test::
+t_getSet()
+{
+    // comment -- t_construct
+    // count -- t_construct
+    // dimension -- t_construct
+
+    RboxPoints rp;
+    QCOMPARE(rp.dimension(), 0);
+    rp.setDimension(2);
+    QCOMPARE(rp.dimension(), 2);
+    try{
+        rp.setDimension(102);
+        QFAIL("setDimension(102) did not fail.");
+    }catch (const std::exception &e) {
+        cout << "INFO   : Caught " << e.what();
+    }
+    QCOMPARE(rp.newCount(), 0);
+    rp.appendPoints("D2 P1 P2");
+    QCOMPARE(rp.count(), 2);
+    QCOMPARE(rp.newCount(), 2); // From previous appendPoints();
+    PointCoordinates pc(rp.qh(), 2, "Test qh() and <<");
+    pc << 1.0 << 0.0 << 2.0 << 0.0;
+    QCOMPARE(pc.dimension(), 2);
+    QCOMPARE(pc.count(), 2);
+    QVERIFY(rp==pc);
+    rp.setNewCount(10);  // Normally only used by appendPoints for rbox processing
+    QCOMPARE(rp.newCount(), 10);
+    rp.reservePoints();
+    QVERIFY(rp==pc);
+}//t_getSet
+
+void RboxPoints_test::
+t_foreach()
+{
+    RboxPoints rp("c");
+    Coordinates::ConstIterator cci= rp.beginCoordinates();
+    orgQhull::Coordinates::Iterator ci= rp.beginCoordinates();
+    QCOMPARE(*cci, -0.5);
+    QCOMPARE(*ci, *cci);
+    int i=1;
+    while(++cci<rp.endCoordinates()){
+        QVERIFY(++ci<rp.endCoordinates());
+        QCOMPARE(*cci, *ci);
+        i++;
+    }
+    QVERIFY(++ci==rp.endCoordinates());
+    QCOMPARE(i, 8*3);
+    orgQhull::Coordinates::Iterator ci4= rp.beginCoordinates(4);
+    QCOMPARE(rp.endCoordinates()-ci4, 4*3);
+    orgQhull::Coordinates::ConstIterator cci4= rp.beginCoordinates(4);
+    orgQhull::Coordinates::ConstIterator cci5= rp.endCoordinates();
+    QCOMPARE(cci5-cci4, 4*3);
+}//t_foreach
+
+void RboxPoints_test::
+t_change()
+{
+    RboxPoints rp("c D2");
+    stringstream s;
+    s << "4 count" << endl;
+    s << "2 dimension" << endl;
+    s << "1 2 3 4 5 6 7 8" << endl;
+    rp.appendPoints(s);
+    QCOMPARE(rp.count(), 8);
+    orgQhull::Coordinates::Iterator ci= rp.beginCoordinates(7);
+    QCOMPARE(*ci, 7.0);
+    try{
+        stringstream s2;
+        s2 << "4 count" << endl;
+        s2 << "2 dimension" << endl;
+        s2 << "1 2 3 4 5 6 7 " << endl;
+        rp.appendPoints(s2);
+        QFAIL("incomplete appendPoints() did not fail.");
+    }catch (const std::exception &e) {
+        cout << "INFO   : Caught " << e.what();
+    }
+    RboxPoints rp2;
+    rp2.append(rp);
+    QCOMPARE(rp2.count(), 8);
+    orgQhull::Coordinates::ConstIterator cci2= rp2.beginCoordinates(6);
+    QCOMPARE(*(cci2+1), 6.0);
+    rp2.appendPoints("D2 10 P0");
+    QCOMPARE(rp2.count(), 19);
+    orgQhull::Coordinates::ConstIterator cie= rp2.beginCoordinates(8);
+    QCOMPARE(*cie, 0.0);
+    RboxPoints rp3;
+    coordT points[] = { 0, 1,1,0,1,1,0,0};
+    rp3.setDimension(2);
+    rp3.append(8,points);
+    QCOMPARE(rp3.count(), 4);
+    orgQhull::Coordinates::Iterator ci3= rp3.beginCoordinates(3);
+    QCOMPARE(*ci3, 0.0);
+}//t_change
+
+void RboxPoints_test::
+t_ostream()
+{
+    RboxPoints rp("c D2");
+    ostringstream oss;
+    oss << rp;
+    string s= oss.str();
+    QString qs= QString::fromStdString(s);
+    QCOMPARE(qs.count("-0.5"), 4);
+}//t_ostream
+
+}//orgQhull
+
+#include "moc/RboxPoints_test.moc"
diff --git a/xs/src/qhull/src/qhulltest/RoadTest.cpp b/xs/src/qhull/src/qhulltest/RoadTest.cpp
new file mode 100644
index 0000000000..05c87f3ded
--- /dev/null
+++ b/xs/src/qhull/src/qhulltest/RoadTest.cpp
@@ -0,0 +1,94 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
+** $Id: //main/2015/qhull/src/qhulltest/RoadTest.cpp#2 $$Change: 2062 $
+** $Date: 2016/01/17 $$Author: bbarber $
+**
+****************************************************************************/
+
+//pre-compiled headers
+#include <iostream>
+#include "RoadTest.h" // QT_VERSION
+
+#include <stdexcept>
+
+using std::cout;
+using std::endl;
+
+namespace orgQhull {
+
+#//!\name class variable
+
+QList<RoadTest*> RoadTest::
+s_testcases;
+
+int RoadTest::
+s_test_count= 0;
+
+int RoadTest::
+s_test_fail= 0;
+
+QStringList RoadTest::
+s_failed_tests;
+
+#//!\name Slot
+
+//! Executed after each test
+void RoadTest::
+cleanup()
+{
+    s_test_count++;
+    if(QTest::currentTestFailed()){
+        recordFailedTest();
+    }
+}//cleanup
+
+#//!\name Helper
+
+void RoadTest::
+recordFailedTest()
+{
+    s_test_fail++;
+    QString className= metaObject()->className();
+    s_failed_tests << className + "::" + QTest::currentTestFunction();
+}
+
+#//!\name class function
+
+void RoadTest::
+deleteTests()
+{
+    foreach(RoadTest *testcase, s_testcases){
+        delete testcase;
+    }
+    s_failed_tests.clear();
+}
+
+int RoadTest::
+runTests(QStringList arguments)
+{
+    int result= 0; // assume success
+
+    foreach(RoadTest *testcase, s_testcases){
+        try{
+            result += QTest::qExec(testcase, arguments);
+        }catch(const std::exception &e){
+            cout << "FAIL!  : Threw error ";
+            cout << e.what() << endl;
+    s_test_count++;
+            testcase->recordFailedTest();
+            // Qt 4.5.2 OK.  In Qt 4.3.3, qtestcase did not clear currentTestObject
+        }
+    }
+    if(s_test_fail){
+        cout << "Failed " << s_test_fail << " of " << s_test_count << " tests.\n";
+        cout << s_failed_tests.join("\n").toLocal8Bit().constData() << std::endl;
+    }else{
+        cout << "Passed " << s_test_count << " tests.\n";
+    }
+    return result;
+}//runTests
+
+}//orgQhull
+
+#include "moc/moc_RoadTest.cpp"
diff --git a/xs/src/qhull/src/qhulltest/RoadTest.h b/xs/src/qhull/src/qhulltest/RoadTest.h
new file mode 100644
index 0000000000..adfe0bf8c1
--- /dev/null
+++ b/xs/src/qhull/src/qhulltest/RoadTest.h
@@ -0,0 +1,102 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
+** $Id: //main/2015/qhull/src/qhulltest/RoadTest.h#2 $$Change: 2062 $
+** $Date: 2016/01/17 $$Author: bbarber $
+**
+****************************************************************************/
+
+#ifndef ROADTEST_H
+#define ROADTEST_H
+
+//pre-compiled with RoadTest.h
+#include <QObject>    // Qt C++ Framework
+#include <QtTest/QtTest>
+
+#define QHULL_USES_QT 1
+
+namespace orgQhull {
+
+#//!\name Defined here
+
+    //! RoadTest -- Generic test for Qt's QTest
+    class RoadTest;
+    //! TESTadd_(t) -- Add a RoadTest
+
+/** Test Name objects using Qt's QTestLib
+
+Template:
+
+class Name_test : public RoadTest
+{
+    Q_OBJECT
+#//!\name Test slot
+private slots:
+    void t_name();
+    //Executed before any test
+    void initTestCase();
+    void init();          // Each test
+    //Executed after each test
+    void cleanup(); //RoadTest::cleanup();
+    // Executed after last test
+    void cleanupTestCase();
+};
+
+void
+add_Name_test()
+{
+    new Name_test();  // RoadTest::s_testcases
+}
+
+Send additional output to cout
+*/
+
+class RoadTest : public QObject
+{
+    Q_OBJECT
+
+#//!\name Class globals
+protected:
+    static QList<RoadTest *>
+                        s_testcases; ///! List of testcases to execute.  Initialized via add_...()
+    static int          s_test_count; ///! Total number of tests executed
+    static int          s_test_fail; ///! Number of failed tests
+    static QStringList  s_failed_tests; ///! List of failed tests
+
+#//!\name Test slots
+public slots:
+    void cleanup();
+
+public:
+#//!\name Constructors, etc.
+                        RoadTest()  { s_testcases.append(this); }
+    virtual             ~RoadTest() {} // Derived from QObject
+
+#//!\name Helper
+    void                recordFailedTest();
+
+
+#//!\name Class functions
+    static void         deleteTests();
+    static int          runTests(QStringList arguments);
+
+};//RoadTest
+
+#define TESTadd_(t) extern void t(); t();
+
+
+}//orgQhull
+
+namespace QTest{
+
+template<>
+inline char *
+toString(const std::string &s)
+{
+    return qstrdup(s.c_str());
+}
+
+}//namespace QTest
+
+#endif //ROADTEST_H
+
diff --git a/xs/src/qhull/src/qhulltest/qhulltest.cpp b/xs/src/qhull/src/qhulltest/qhulltest.cpp
new file mode 100644
index 0000000000..5bfe16e9cf
--- /dev/null
+++ b/xs/src/qhull/src/qhulltest/qhulltest.cpp
@@ -0,0 +1,94 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2015 C.B. Barber. All rights reserved.
+** $Id: //main/2015/qhull/src/qhulltest/qhulltest.cpp#5 $$Change: 2079 $
+** $DateTime: 2016/02/07 17:43:34 $$Author: bbarber $
+**
+****************************************************************************/
+
+//pre-compiled headers
+#include "libqhull_r/user_r.h"
+
+#include <iostream>
+#include "RoadTest.h" // QT_VERSION
+
+#include "libqhullcpp/RoadError.h"
+#include "libqhull_r/qhull_ra.h"
+
+#include <sstream>
+#include <stdexcept>
+#include <string>
+
+using std::cout;
+using std::endl;
+
+namespace orgQhull {
+
+void addQhullTests(QStringList &args)
+{
+    TESTadd_(add_Qhull_test);
+
+    if(args.contains("--all")){
+        args.removeAll("--all");
+        // up-to-date
+        TESTadd_(add_Coordinates_test);
+        TESTadd_(add_PointCoordinates_test);
+        TESTadd_(add_QhullFacet_test);
+        TESTadd_(add_QhullFacetList_test);
+        TESTadd_(add_QhullFacetSet_test);
+        TESTadd_(add_QhullHyperplane_test);
+        TESTadd_(add_QhullLinkedList_test);
+        TESTadd_(add_QhullPoint_test);
+        TESTadd_(add_QhullPoints_test);
+        TESTadd_(add_QhullPointSet_test);
+        TESTadd_(add_QhullRidge_test);
+        TESTadd_(add_QhullSet_test);
+        TESTadd_(add_QhullVertex_test);
+        TESTadd_(add_QhullVertexSet_test);
+        TESTadd_(add_RboxPoints_test);
+        // qhullStat
+        TESTadd_(add_Qhull_test);
+    }//--all
+}//addQhullTests
+
+int main(int argc, char *argv[])
+{
+
+    QCoreApplication app(argc, argv);
+    QStringList args= app.arguments();
+    bool isAll= args.contains("--all");
+
+    QHULL_LIB_CHECK /* Check for compatible library */
+
+    addQhullTests(args);
+    int status=1010;
+    try{
+        status= RoadTest::runTests(args);
+    }catch(const std::exception &e){
+        cout << "FAIL!  : runTests() did not catch error\n";
+        cout << e.what() << endl;
+        if(!RoadError::emptyGlobalLog()){
+            cout << RoadError::stringGlobalLog() << endl;
+            RoadError::clearGlobalLog();
+        }
+    }
+    if(!RoadError::emptyGlobalLog()){
+        cout << RoadError::stringGlobalLog() << endl;
+        RoadError::clearGlobalLog();
+    }
+    if(isAll){
+        cout << "Finished test of libqhullcpp.  Test libqhull_r with eg/q_test after building libqhull_r/Makefile" << endl;
+    }else{
+        cout << "Finished test of one class.  Test all classes with 'qhulltest --all'" << endl;
+    }
+    RoadTest::deleteTests();
+    return status;
+}
+
+}//orgQhull
+
+int main(int argc, char *argv[])
+{
+    return orgQhull::main(argc, argv); // Needs RoadTest:: for TESTadd_() linkage
+}
+
diff --git a/xs/src/qhull/src/qhulltest/qhulltest.pro b/xs/src/qhull/src/qhulltest/qhulltest.pro
new file mode 100644
index 0000000000..0da34d3755
--- /dev/null
+++ b/xs/src/qhull/src/qhulltest/qhulltest.pro
@@ -0,0 +1,36 @@
+# -------------------------------------------------
+# qhulltest.pro -- Qt project for qhulltest.exe (QTestLib)
+# cd $qh/build/qhulltest && qmake -tp vc -r ../../src/qhulltest/qhulltest.pro
+# -------------------------------------------------
+
+include(../qhull-app-cpp.pri)
+
+TARGET = qhulltest
+QT += testlib
+MOC_DIR = moc
+INCLUDEPATH += ..  # for MOC_DIR
+
+PRECOMPILED_HEADER = RoadTest.h
+
+HEADERS += RoadTest.h
+
+SOURCES += ../libqhullcpp/qt-qhull.cpp
+SOURCES += Coordinates_test.cpp
+SOURCES += PointCoordinates_test.cpp
+SOURCES += Qhull_test.cpp
+SOURCES += QhullFacet_test.cpp
+SOURCES += QhullFacetList_test.cpp
+SOURCES += QhullFacetSet_test.cpp
+SOURCES += QhullHyperplane_test.cpp
+SOURCES += QhullLinkedList_test.cpp
+SOURCES += QhullPoint_test.cpp
+SOURCES += QhullPoints_test.cpp
+SOURCES += QhullPointSet_test.cpp
+SOURCES += QhullRidge_test.cpp
+SOURCES += QhullSet_test.cpp
+SOURCES += qhulltest.cpp
+SOURCES += QhullVertex_test.cpp
+SOURCES += QhullVertexSet_test.cpp
+SOURCES += RboxPoints_test.cpp
+SOURCES += RoadTest.cpp
+
diff --git a/xs/src/qhull/src/qvoronoi/qvoronoi.c b/xs/src/qhull/src/qvoronoi/qvoronoi.c
new file mode 100644
index 0000000000..b93d237114
--- /dev/null
+++ b/xs/src/qhull/src/qvoronoi/qvoronoi.c
@@ -0,0 +1,303 @@
+/*<html><pre>  -<a                             href="../libqhull/qh-qhull.htm"
+  >-------------------------------</a><a name="TOP">-</a>
+
+   qvoronoi.c
+     compute Voronoi diagrams and furthest-point Voronoi
+     diagrams using qhull
+
+   see unix.c for full interface
+
+   Copyright (c) 1993-2015, The Geometry Center
+*/
+
+#include "libqhull/libqhull.h"
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include <ctype.h>
+#include <math.h>
+
+#if __cplusplus
+extern "C" {
+  int isatty(int);
+}
+
+#elif _MSC_VER
+#include <io.h>
+#define isatty _isatty
+/* int _isatty(int); */
+
+#else
+int isatty(int);  /* returns 1 if stdin is a tty
+                   if "Undefined symbol" this can be deleted along with call in main() */
+#endif
+
+/*-<a                             href="../libqhull/qh-qhull.htm#TOC"
+  >-------------------------------</a><a name="prompt">-</a>
+
+  qh_prompt
+    long prompt for qhull
+
+  notes:
+    restricted version of libqhull.c
+
+  see:
+    concise prompt below
+*/
+
+/* duplicated in qvoron_f.htm and qvoronoi.htm
+   QJ and Qt are deprecated, but allowed for backwards compatibility
+*/
+char hidden_options[]=" d n m v H U Qb QB Qc Qf Qg Qi Qm Qr QR Qv Qx TR E V Fa FA FC Fp FS Ft FV Pv Gt Q0 Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 ";
+
+char qh_prompta[]= "\n\
+qvoronoi- compute the Voronoi diagram\n\
+    http://www.qhull.org  %s\n\
+\n\
+input (stdin):\n\
+    first lines: dimension and number of points (or vice-versa).\n\
+    other lines: point coordinates, best if one point per line\n\
+    comments:    start with a non-numeric character\n\
+\n\
+options:\n\
+    Qu   - compute furthest-site Voronoi diagram\n\
+\n\
+Qhull control options:\n\
+    Qz   - add point-at-infinity to Voronoi diagram\n\
+%s%s%s%s";  /* split up qh_prompt for Visual C++ */
+char qh_promptb[]= "\
+    Qs   - search all points for the initial simplex\n\
+    QGn  - Voronoi vertices if visible from point n, -n if not\n\
+    QVn  - Voronoi vertices for input point n, -n if not\n\
+\n\
+";
+char qh_promptc[]= "\
+Trace options:\n\
+    T4   - trace at level n, 4=all, 5=mem/gauss, -1= events\n\
+    Tc   - check frequently during execution\n\
+    Ts   - statistics\n\
+    Tv   - verify result: structure, convexity, and in-circle test\n\
+    Tz   - send all output to stdout\n\
+    TFn  - report summary when n or more facets created\n\
+    TI file - input data from file, no spaces or single quotes\n\
+    TO file - output results to file, may be enclosed in single quotes\n\
+    TPn  - turn on tracing when point n added to hull\n\
+     TMn - turn on tracing at merge n\n\
+     TWn - trace merge facets when width > n\n\
+    TVn  - stop qhull after adding point n, -n for before (see TCn)\n\
+     TCn - stop qhull after building cone for point n (see TVn)\n\
+\n\
+Precision options:\n\
+    Cn   - radius of centrum (roundoff added).  Merge facets if non-convex\n\
+     An  - cosine of maximum angle.  Merge facets if cosine > n or non-convex\n\
+           C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge\n\
+    Rn   - randomly perturb computations by a factor of [1-n,1+n]\n\
+    Wn   - min facet width for non-coincident point (before roundoff)\n\
+\n\
+Output formats (may be combined; if none, produces a summary to stdout):\n\
+    s    - summary to stderr\n\
+    p    - Voronoi vertices\n\
+    o    - OFF format (dim, Voronoi vertices, and Voronoi regions)\n\
+    i    - Delaunay regions (use 'Pp' to avoid warning)\n\
+    f    - facet dump\n\
+\n\
+";
+char qh_promptd[]= "\
+More formats:\n\
+    Fc   - count plus coincident points (by Voronoi vertex)\n\
+    Fd   - use cdd format for input (homogeneous with offset first)\n\
+    FD   - use cdd format for output (offset first)\n\
+    FF   - facet dump without ridges\n\
+    Fi   - separating hyperplanes for bounded Voronoi regions\n\
+    FI   - ID for each Voronoi vertex\n\
+    Fm   - merge count for each Voronoi vertex (511 max)\n\
+    Fn   - count plus neighboring Voronoi vertices for each Voronoi vertex\n\
+    FN   - count and Voronoi vertices for each Voronoi region\n\
+    Fo   - separating hyperplanes for unbounded Voronoi regions\n\
+    FO   - options and precision constants\n\
+    FP   - nearest point and distance for each coincident point\n\
+    FQ   - command used for qvoronoi\n\
+    Fs   - summary: #int (8), dimension, #points, tot vertices, tot facets,\n\
+                    for output: #Voronoi regions, #Voronoi vertices,\n\
+                                #coincident points, #non-simplicial regions\n\
+                    #real (2), max outer plane and min vertex\n\
+    Fv   - Voronoi diagram as Voronoi vertices between adjacent input sites\n\
+    Fx   - extreme points of Delaunay triangulation (on convex hull)\n\
+\n\
+";
+char qh_prompte[]= "\
+Geomview options (2-d only)\n\
+    Ga   - all points as dots\n\
+     Gp  -  coplanar points and vertices as radii\n\
+     Gv  -  vertices as spheres\n\
+    Gi   - inner planes only\n\
+     Gn  -  no planes\n\
+     Go  -  outer planes only\n\
+    Gc   - centrums\n\
+    Gh   - hyperplane intersections\n\
+    Gr   - ridges\n\
+    GDn  - drop dimension n in 3-d and 4-d output\n\
+\n\
+Print options:\n\
+    PAn  - keep n largest Voronoi vertices by 'area'\n\
+    Pdk:n - drop facet if normal[k] <= n (default 0.0)\n\
+    PDk:n - drop facet if normal[k] >= n\n\
+    Pg   - print good Voronoi vertices (needs 'QGn' or 'QVn')\n\
+    PFn  - keep Voronoi vertices whose 'area' is at least n\n\
+    PG   - print neighbors of good Voronoi vertices\n\
+    PMn  - keep n Voronoi vertices with most merges\n\
+    Po   - force output.  If error, output neighborhood of facet\n\
+    Pp   - do not report precision problems\n\
+\n\
+    .    - list of all options\n\
+    -    - one line descriptions of all options\n\
+    -V   - version\n\
+";
+/* for opts, don't assign 'e' or 'E' to a flag (already used for exponent) */
+
+/*-<a                             href="../libqhull/qh-qhull.htm#TOC"
+  >-------------------------------</a><a name="prompt2">-</a>
+
+  qh_prompt2
+    synopsis for qhull
+*/
+char qh_prompt2[]= "\n\
+qvoronoi- compute the Voronoi diagram.  Qhull %s\n\
+    input (stdin): dimension, number of points, point coordinates\n\
+    comments start with a non-numeric character\n\
+\n\
+options (qvoronoi.htm):\n\
+    Qu   - compute furthest-site Voronoi diagram\n\
+    Tv   - verify result: structure, convexity, and in-circle test\n\
+    .    - concise list of all options\n\
+    -    - one-line description of all options\n\
+    -V   - version\n\
+\n\
+output options (subset):\n\
+    s    - summary of results (default)\n\
+    p    - Voronoi vertices\n\
+    o    - OFF file format (dim, Voronoi vertices, and Voronoi regions)\n\
+    FN   - count and Voronoi vertices for each Voronoi region\n\
+    Fv   - Voronoi diagram as Voronoi vertices between adjacent input sites\n\
+    Fi   - separating hyperplanes for bounded regions, 'Fo' for unbounded\n\
+    G    - Geomview output (2-d only)\n\
+    QVn  - Voronoi vertices for input point n, -n if not\n\
+    TO file- output results to file, may be enclosed in single quotes\n\
+\n\
+examples:\n\
+rbox c P0 D2 | qvoronoi s o         rbox c P0 D2 | qvoronoi Fi\n\
+rbox c P0 D2 | qvoronoi Fo          rbox c P0 D2 | qvoronoi Fv\n\
+rbox c P0 D2 | qvoronoi s Qu Fv     rbox c P0 D2 | qvoronoi Qu Fo\n\
+rbox c G1 d D2 | qvoronoi s p       rbox c P0 D2 | qvoronoi s Fv QV0\n\
+\n\
+";
+/* for opts, don't assign 'e' or 'E' to a flag (already used for exponent) */
+
+/*-<a                             href="../libqhull/qh-qhull.htm#TOC"
+  >-------------------------------</a><a name="prompt3">-</a>
+
+  qh_prompt3
+    concise prompt for qhull
+*/
+char qh_prompt3[]= "\n\
+Qhull %s.\n\
+Except for 'F.' and 'PG', upper-case options take an argument.\n\
+\n\
+ OFF_format     p_vertices     i_delaunay     summary        facet_dump\n\
+\n\
+ Fcoincident    Fd_cdd_in      FD_cdd_out     FF-dump-xridge Fi_bounded\n\
+ Fxtremes       Fmerges        Fneighbors     FNeigh_region  FOptions\n\
+ Fo_unbounded   FPoint_near    FQvoronoi      Fsummary       Fvoronoi\n\
+ FIDs\n\
+\n\
+ Gvertices      Gpoints        Gall_points    Gno_planes     Ginner\n\
+ Gcentrums      Ghyperplanes   Gridges        Gouter         GDrop_dim\n\
+\n\
+ PArea_keep     Pdrop d0:0D0   Pgood          PFacet_area_keep\n\
+ PGood_neighbors PMerge_keep   Poutput_forced Pprecision_not\n\
+\n\
+ QG_vertex_good Qsearch_1st    Qupper_voronoi QV_point_good  Qzinfinite\n\
+ T4_trace       Tcheck_often   Tstatistics    Tverify        Tz_stdout\n\
+ TFacet_log     TInput_file    TPoint_trace   TMerge_trace   TOutput_file\n\
+ TWide_trace    TVertex_stop   TCone_stop\n\
+\n\
+ Angle_max      Centrum_size   Random_dist    Wide_outside\n\
+";
+
+/*-<a                             href="../libqhull/qh-qhull.htm#TOC"
+  >-------------------------------</a><a name="main">-</a>
+
+  main( argc, argv )
+    processes the command line, calls qhull() to do the work, and exits
+
+  design:
+    initializes data structures
+    reads points
+    finishes initialization
+    computes convex hull and other structures
+    checks the result
+    writes the output
+    frees memory
+*/
+int main(int argc, char *argv[]) {
+  int curlong, totlong; /* used !qh_NOmem */
+  int exitcode, numpoints, dim;
+  coordT *points;
+  boolT ismalloc;
+
+  QHULL_LIB_CHECK /* Check for compatible library */
+
+  if ((argc == 1) && isatty( 0 /*stdin*/)) {
+    fprintf(stdout, qh_prompt2, qh_version);
+    exit(qh_ERRnone);
+  }
+  if (argc > 1 && *argv[1] == '-' && !*(argv[1]+1)) {
+    fprintf(stdout, qh_prompta, qh_version,
+                qh_promptb, qh_promptc, qh_promptd, qh_prompte);
+    exit(qh_ERRnone);
+  }
+  if (argc > 1 && *argv[1] == '.' && !*(argv[1]+1)) {
+    fprintf(stdout, qh_prompt3, qh_version);
+    exit(qh_ERRnone);
+  }
+  if (argc > 1 && *argv[1] == '-' && *(argv[1]+1)=='V') {
+      fprintf(stdout, "%s\n", qh_version2);
+      exit(qh_ERRnone);
+  }
+  qh_init_A(stdin, stdout, stderr, argc, argv);  /* sets qh qhull_command */
+  exitcode= setjmp(qh errexit); /* simple statement for CRAY J916 */
+  if (!exitcode) {
+    qh NOerrexit= False;
+    qh_option("voronoi  _bbound-last  _coplanar-keep", NULL, NULL);
+    qh DELAUNAY= True;     /* 'v'   */
+    qh VORONOI= True;
+    qh SCALElast= True;    /* 'Qbb' */
+    qh_checkflags(qh qhull_command, hidden_options);
+    qh_initflags(qh qhull_command);
+    points= qh_readpoints(&numpoints, &dim, &ismalloc);
+    if (dim >= 5) {
+      qh_option("_merge-exact", NULL, NULL);
+      qh MERGEexact= True; /* 'Qx' always */
+    }
+    qh_init_B(points, numpoints, dim, ismalloc);
+    qh_qhull();
+    qh_check_output();
+    qh_produce_output();
+    if (qh VERIFYoutput && !qh FORCEoutput && !qh STOPpoint && !qh STOPcone)
+      qh_check_points();
+    exitcode= qh_ERRnone;
+  }
+  qh NOerrexit= True;  /* no more setjmp */
+#ifdef qh_NOmem
+  qh_freeqhull(qh_ALL);
+#else
+  qh_freeqhull(!qh_ALL);
+  qh_memfreeshort(&curlong, &totlong);
+  if (curlong || totlong)
+    qh_fprintf_stderr(6263, "qhull internal warning (main): did not free %d bytes of long memory(%d pieces)\n",
+       totlong, curlong);
+#endif
+  return exitcode;
+} /* main */
+
diff --git a/xs/src/qhull/src/qvoronoi/qvoronoi.pro b/xs/src/qhull/src/qvoronoi/qvoronoi.pro
new file mode 100644
index 0000000000..4646c84472
--- /dev/null
+++ b/xs/src/qhull/src/qvoronoi/qvoronoi.pro
@@ -0,0 +1,9 @@
+# -------------------------------------------------
+# qvoronoi.pro -- Qt project file for qvoronoi.exe
+# -------------------------------------------------
+
+include(../qhull-app-c.pri)
+
+TARGET = qvoronoi
+
+SOURCES += qvoronoi.c
diff --git a/xs/src/qhull/src/qvoronoi/qvoronoi_r.c b/xs/src/qhull/src/qvoronoi/qvoronoi_r.c
new file mode 100644
index 0000000000..6323c8b496
--- /dev/null
+++ b/xs/src/qhull/src/qvoronoi/qvoronoi_r.c
@@ -0,0 +1,305 @@
+/*<html><pre>  -<a                             href="../libqhull/qh-qhull.htm"
+  >-------------------------------</a><a name="TOP">-</a>
+
+   qvoronoi.c
+     compute Voronoi diagrams and furthest-point Voronoi
+     diagrams using qhull
+
+   see unix.c for full interface
+
+   Copyright (c) 1993-2015, The Geometry Center
+*/
+
+#include "libqhull_r/libqhull_r.h"
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include <ctype.h>
+#include <math.h>
+
+#if __cplusplus
+extern "C" {
+  int isatty(int);
+}
+
+#elif _MSC_VER
+#include <io.h>
+#define isatty _isatty
+/* int _isatty(int); */
+
+#else
+int isatty(int);  /* returns 1 if stdin is a tty
+                   if "Undefined symbol" this can be deleted along with call in main() */
+#endif
+
+/*-<a                             href="../libqhull/qh-qhull.htm#TOC"
+  >-------------------------------</a><a name="prompt">-</a>
+
+  qh_prompt
+    long prompt for qhull
+
+  notes:
+    restricted version of libqhull.c
+
+  see:
+    concise prompt below
+*/
+
+/* duplicated in qvoron_f.htm and qvoronoi.htm
+   QJ and Qt are deprecated, but allowed for backwards compatibility
+*/
+char hidden_options[]=" d n m v H U Qb QB Qc Qf Qg Qi Qm Qr QR Qv Qx TR E V Fa FA FC Fp FS Ft FV Pv Gt Q0 Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 ";
+
+char qh_prompta[]= "\n\
+qvoronoi- compute the Voronoi diagram\n\
+    http://www.qhull.org  %s\n\
+\n\
+input (stdin):\n\
+    first lines: dimension and number of points (or vice-versa).\n\
+    other lines: point coordinates, best if one point per line\n\
+    comments:    start with a non-numeric character\n\
+\n\
+options:\n\
+    Qu   - compute furthest-site Voronoi diagram\n\
+\n\
+Qhull control options:\n\
+    Qz   - add point-at-infinity to Voronoi diagram\n\
+%s%s%s%s";  /* split up qh_prompt for Visual C++ */
+char qh_promptb[]= "\
+    Qs   - search all points for the initial simplex\n\
+    QGn  - Voronoi vertices if visible from point n, -n if not\n\
+    QVn  - Voronoi vertices for input point n, -n if not\n\
+\n\
+";
+char qh_promptc[]= "\
+Trace options:\n\
+    T4   - trace at level n, 4=all, 5=mem/gauss, -1= events\n\
+    Tc   - check frequently during execution\n\
+    Ts   - statistics\n\
+    Tv   - verify result: structure, convexity, and in-circle test\n\
+    Tz   - send all output to stdout\n\
+    TFn  - report summary when n or more facets created\n\
+    TI file - input data from file, no spaces or single quotes\n\
+    TO file - output results to file, may be enclosed in single quotes\n\
+    TPn  - turn on tracing when point n added to hull\n\
+     TMn - turn on tracing at merge n\n\
+     TWn - trace merge facets when width > n\n\
+    TVn  - stop qhull after adding point n, -n for before (see TCn)\n\
+     TCn - stop qhull after building cone for point n (see TVn)\n\
+\n\
+Precision options:\n\
+    Cn   - radius of centrum (roundoff added).  Merge facets if non-convex\n\
+     An  - cosine of maximum angle.  Merge facets if cosine > n or non-convex\n\
+           C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge\n\
+    Rn   - randomly perturb computations by a factor of [1-n,1+n]\n\
+    Wn   - min facet width for non-coincident point (before roundoff)\n\
+\n\
+Output formats (may be combined; if none, produces a summary to stdout):\n\
+    s    - summary to stderr\n\
+    p    - Voronoi vertices\n\
+    o    - OFF format (dim, Voronoi vertices, and Voronoi regions)\n\
+    i    - Delaunay regions (use 'Pp' to avoid warning)\n\
+    f    - facet dump\n\
+\n\
+";
+char qh_promptd[]= "\
+More formats:\n\
+    Fc   - count plus coincident points (by Voronoi vertex)\n\
+    Fd   - use cdd format for input (homogeneous with offset first)\n\
+    FD   - use cdd format for output (offset first)\n\
+    FF   - facet dump without ridges\n\
+    Fi   - separating hyperplanes for bounded Voronoi regions\n\
+    FI   - ID for each Voronoi vertex\n\
+    Fm   - merge count for each Voronoi vertex (511 max)\n\
+    Fn   - count plus neighboring Voronoi vertices for each Voronoi vertex\n\
+    FN   - count and Voronoi vertices for each Voronoi region\n\
+    Fo   - separating hyperplanes for unbounded Voronoi regions\n\
+    FO   - options and precision constants\n\
+    FP   - nearest point and distance for each coincident point\n\
+    FQ   - command used for qvoronoi\n\
+    Fs   - summary: #int (8), dimension, #points, tot vertices, tot facets,\n\
+                    for output: #Voronoi regions, #Voronoi vertices,\n\
+                                #coincident points, #non-simplicial regions\n\
+                    #real (2), max outer plane and min vertex\n\
+    Fv   - Voronoi diagram as Voronoi vertices between adjacent input sites\n\
+    Fx   - extreme points of Delaunay triangulation (on convex hull)\n\
+\n\
+";
+char qh_prompte[]= "\
+Geomview options (2-d only)\n\
+    Ga   - all points as dots\n\
+     Gp  -  coplanar points and vertices as radii\n\
+     Gv  -  vertices as spheres\n\
+    Gi   - inner planes only\n\
+     Gn  -  no planes\n\
+     Go  -  outer planes only\n\
+    Gc   - centrums\n\
+    Gh   - hyperplane intersections\n\
+    Gr   - ridges\n\
+    GDn  - drop dimension n in 3-d and 4-d output\n\
+\n\
+Print options:\n\
+    PAn  - keep n largest Voronoi vertices by 'area'\n\
+    Pdk:n - drop facet if normal[k] <= n (default 0.0)\n\
+    PDk:n - drop facet if normal[k] >= n\n\
+    Pg   - print good Voronoi vertices (needs 'QGn' or 'QVn')\n\
+    PFn  - keep Voronoi vertices whose 'area' is at least n\n\
+    PG   - print neighbors of good Voronoi vertices\n\
+    PMn  - keep n Voronoi vertices with most merges\n\
+    Po   - force output.  If error, output neighborhood of facet\n\
+    Pp   - do not report precision problems\n\
+\n\
+    .    - list of all options\n\
+    -    - one line descriptions of all options\n\
+    -V   - version\n\
+";
+/* for opts, don't assign 'e' or 'E' to a flag (already used for exponent) */
+
+/*-<a                             href="../libqhull/qh-qhull.htm#TOC"
+  >-------------------------------</a><a name="prompt2">-</a>
+
+  qh_prompt2
+    synopsis for qhull
+*/
+char qh_prompt2[]= "\n\
+qvoronoi- compute the Voronoi diagram.  Qhull %s\n\
+    input (stdin): dimension, number of points, point coordinates\n\
+    comments start with a non-numeric character\n\
+\n\
+options (qvoronoi.htm):\n\
+    Qu   - compute furthest-site Voronoi diagram\n\
+    Tv   - verify result: structure, convexity, and in-circle test\n\
+    .    - concise list of all options\n\
+    -    - one-line description of all options\n\
+    -V   - version\n\
+\n\
+output options (subset):\n\
+    s    - summary of results (default)\n\
+    p    - Voronoi vertices\n\
+    o    - OFF file format (dim, Voronoi vertices, and Voronoi regions)\n\
+    FN   - count and Voronoi vertices for each Voronoi region\n\
+    Fv   - Voronoi diagram as Voronoi vertices between adjacent input sites\n\
+    Fi   - separating hyperplanes for bounded regions, 'Fo' for unbounded\n\
+    G    - Geomview output (2-d only)\n\
+    QVn  - Voronoi vertices for input point n, -n if not\n\
+    TO file- output results to file, may be enclosed in single quotes\n\
+\n\
+examples:\n\
+rbox c P0 D2 | qvoronoi s o         rbox c P0 D2 | qvoronoi Fi\n\
+rbox c P0 D2 | qvoronoi Fo          rbox c P0 D2 | qvoronoi Fv\n\
+rbox c P0 D2 | qvoronoi s Qu Fv     rbox c P0 D2 | qvoronoi Qu Fo\n\
+rbox c G1 d D2 | qvoronoi s p       rbox c P0 D2 | qvoronoi s Fv QV0\n\
+\n\
+";
+/* for opts, don't assign 'e' or 'E' to a flag (already used for exponent) */
+
+/*-<a                             href="../libqhull/qh-qhull.htm#TOC"
+  >-------------------------------</a><a name="prompt3">-</a>
+
+  qh_prompt3
+    concise prompt for qhull
+*/
+char qh_prompt3[]= "\n\
+Qhull %s.\n\
+Except for 'F.' and 'PG', upper-case options take an argument.\n\
+\n\
+ OFF_format     p_vertices     i_delaunay     summary        facet_dump\n\
+\n\
+ Fcoincident    Fd_cdd_in      FD_cdd_out     FF-dump-xridge Fi_bounded\n\
+ Fxtremes       Fmerges        Fneighbors     FNeigh_region  FOptions\n\
+ Fo_unbounded   FPoint_near    FQvoronoi      Fsummary       Fvoronoi\n\
+ FIDs\n\
+\n\
+ Gvertices      Gpoints        Gall_points    Gno_planes     Ginner\n\
+ Gcentrums      Ghyperplanes   Gridges        Gouter         GDrop_dim\n\
+\n\
+ PArea_keep     Pdrop d0:0D0   Pgood          PFacet_area_keep\n\
+ PGood_neighbors PMerge_keep   Poutput_forced Pprecision_not\n\
+\n\
+ QG_vertex_good Qsearch_1st    Qupper_voronoi QV_point_good  Qzinfinite\n\
+ T4_trace       Tcheck_often   Tstatistics    Tverify        Tz_stdout\n\
+ TFacet_log     TInput_file    TPoint_trace   TMerge_trace   TOutput_file\n\
+ TWide_trace    TVertex_stop   TCone_stop\n\
+\n\
+ Angle_max      Centrum_size   Random_dist    Wide_outside\n\
+";
+
+/*-<a                             href="../libqhull/qh-qhull.htm#TOC"
+  >-------------------------------</a><a name="main">-</a>
+
+  main( argc, argv )
+    processes the command line, calls qhull() to do the work, and exits
+
+  design:
+    initializes data structures
+    reads points
+    finishes initialization
+    computes convex hull and other structures
+    checks the result
+    writes the output
+    frees memory
+*/
+int main(int argc, char *argv[]) {
+  int curlong, totlong; /* used !qh_NOmem */
+  int exitcode, numpoints, dim;
+  coordT *points;
+  boolT ismalloc;
+  qhT qh_qh;
+  qhT *qh= &qh_qh;
+
+  QHULL_LIB_CHECK /* Check for compatible library */
+
+  if ((argc == 1) && isatty( 0 /*stdin*/)) {
+    fprintf(stdout, qh_prompt2, qh_version);
+    exit(qh_ERRnone);
+  }
+  if (argc > 1 && *argv[1] == '-' && !*(argv[1]+1)) {
+    fprintf(stdout, qh_prompta, qh_version,
+                qh_promptb, qh_promptc, qh_promptd, qh_prompte);
+    exit(qh_ERRnone);
+  }
+  if (argc > 1 && *argv[1] == '.' && !*(argv[1]+1)) {
+    fprintf(stdout, qh_prompt3, qh_version);
+    exit(qh_ERRnone);
+  }
+  if (argc > 1 && *argv[1] == '-' && *(argv[1]+1)=='V') {
+      fprintf(stdout, "%s\n", qh_version2);
+      exit(qh_ERRnone);
+  }
+  qh_init_A(qh, stdin, stdout, stderr, argc, argv);  /* sets qh->qhull_command */
+  exitcode= setjmp(qh->errexit); /* simple statement for CRAY J916 */
+  if (!exitcode) {
+    qh->NOerrexit = False;
+    qh_option(qh, "voronoi  _bbound-last  _coplanar-keep", NULL, NULL);
+    qh->DELAUNAY= True;     /* 'v'   */
+    qh->VORONOI= True;
+    qh->SCALElast= True;    /* 'Qbb' */
+    qh_checkflags(qh, qh->qhull_command, hidden_options);
+    qh_initflags(qh, qh->qhull_command);
+    points= qh_readpoints(qh, &numpoints, &dim, &ismalloc);
+    if (dim >= 5) {
+      qh_option(qh, "_merge-exact", NULL, NULL);
+      qh->MERGEexact= True; /* 'Qx' always */
+    }
+    qh_init_B(qh, points, numpoints, dim, ismalloc);
+    qh_qhull(qh);
+    qh_check_output(qh);
+    qh_produce_output(qh);
+    if (qh->VERIFYoutput && !qh->FORCEoutput && !qh->STOPpoint && !qh->STOPcone)
+      qh_check_points(qh);
+    exitcode= qh_ERRnone;
+  }
+  qh->NOerrexit= True;  /* no more setjmp */
+#ifdef qh_NOmem
+  qh_freeqhull(qh, qh_ALL);
+#else
+  qh_freeqhull(qh, !qh_ALL);
+  qh_memfreeshort(qh, &curlong, &totlong);
+  if (curlong || totlong)
+    qh_fprintf_stderr(6263, "qhull internal warning (main): did not free %d bytes of long memory(%d pieces)\n",
+       totlong, curlong);
+#endif
+  return exitcode;
+} /* main */
+
diff --git a/xs/src/qhull/src/rbox/rbox.c b/xs/src/qhull/src/rbox/rbox.c
new file mode 100644
index 0000000000..d7c51b1aaf
--- /dev/null
+++ b/xs/src/qhull/src/rbox/rbox.c
@@ -0,0 +1,88 @@
+/*<html><pre>  -<a                             href="../libqhull/index.htm#TOC"
+  >-------------------------------</a><a name="TOP">-</a>
+
+   rbox.c
+     rbox program for generating input points for qhull.
+
+   notes:
+     50 points generated for 'rbox D4'
+
+*/
+
+#include "libqhull/libqhull.h"
+#include "libqhull/random.h"
+
+#include <stdarg.h>
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+
+#ifdef _MSC_VER  /* Microsoft Visual C++ -- warning level 4 */
+#pragma warning( disable : 4706)  /* assignment within conditional function */
+#endif
+
+char prompt[]= "\n\
+-rbox- generate various point distributions.  Default is random in cube.\n\
+\n\
+args (any order, space separated):                    Version: 2016/01/18\n\
+  3000    number of random points in cube, lens, spiral, sphere or grid\n\
+  D3      dimension 3-d\n\
+  c       add a unit cube to the output ('c G2.0' sets size)\n\
+  d       add a unit diamond to the output ('d G2.0' sets size)\n\
+  l       generate a regular 3-d spiral\n\
+  r       generate a regular polygon, ('r s Z1 G0.1' makes a cone)\n\
+  s       generate cospherical points\n\
+  x       generate random points in simplex, may use 'r' or 'Wn'\n\
+  y       same as 'x', plus simplex\n\
+  Cn,r,m  add n nearly coincident points within radius r of m points\n\
+  Pn,m,r  add point [n,m,r] first, pads with 0, maybe repeated\n\
+\n\
+  Ln      lens distribution of radius n.  Also 's', 'r', 'G', 'W'.\n\
+  Mn,m,r  lattice(Mesh) rotated by [n,-m,0], [m,n,0], [0,0,r], ...\n\
+          '27 M1,0,1' is {0,1,2} x {0,1,2} x {0,1,2}.  Try 'M3,4 z'.\n\
+  W0.1    random distribution within 0.1 of the cube's or sphere's surface\n\
+  Z0.5 s  random points in a 0.5 disk projected to a sphere\n\
+  Z0.5 s G0.6 same as Z0.5 within a 0.6 gap\n\
+\n\
+  Bn      bounding box coordinates, default %2.2g\n\
+  h       output as homogeneous coordinates for cdd\n\
+  n       remove command line from the first line of output\n\
+  On      offset coordinates by n\n\
+  t       use time as the random number seed(default is command line)\n\
+  tn      use n as the random number seed\n\
+  z       print integer coordinates, default 'Bn' is %2.2g\n\
+";
+
+/*--------------------------------------------
+-rbox-  main procedure of rbox application
+*/
+int main(int argc, char **argv) {
+  char *command;
+  int command_size;
+  int return_status;
+
+  QHULL_LIB_CHECK_RBOX
+
+  if (argc == 1) {
+    printf(prompt, qh_DEFAULTbox, qh_DEFAULTzbox);
+    return 1;
+  }
+  if (argc == 2 && strcmp(argv[1], "D4")==0)
+    qh_fprintf_stderr(0, "\nStarting the rbox smoketest for qhull.  An immediate failure indicates\nthat non-reentrant rbox was linked to reentrant routines.  An immediate\nfailure of qhull may indicate that qhull was linked to the wrong\nqhull library.  Also try 'rbox D4 | qhull T1'\n");
+
+  command_size= qh_argv_to_command_size(argc, argv);
+  if ((command= (char *)qh_malloc((size_t)command_size))) {
+    if (!qh_argv_to_command(argc, argv, command, command_size)) {
+      qh_fprintf_stderr(6264, "rbox internal error: allocated insufficient memory (%d) for arguments\n", command_size);
+      return_status= qh_ERRinput;
+    }else{
+      return_status= qh_rboxpoints(stdout, stderr, command);
+    }
+    qh_free(command);
+  }else {
+    qh_fprintf_stderr(6265, "rbox error: insufficient memory for %d bytes\n", command_size);
+    return_status= qh_ERRmem;
+  }
+  return return_status;
+}/*main*/
+
diff --git a/xs/src/qhull/src/rbox/rbox.pro b/xs/src/qhull/src/rbox/rbox.pro
new file mode 100644
index 0000000000..6c21bdb6df
--- /dev/null
+++ b/xs/src/qhull/src/rbox/rbox.pro
@@ -0,0 +1,9 @@
+# -------------------------------------------------
+# rbox.pro -- Qt project for rbox.exe with libqhullstatic
+# -------------------------------------------------
+
+include(../qhull-app-c.pri)
+
+TARGET = rbox
+
+SOURCES += rbox.c
diff --git a/xs/src/qhull/src/rbox/rbox_r.c b/xs/src/qhull/src/rbox/rbox_r.c
new file mode 100644
index 0000000000..6ec74d914b
--- /dev/null
+++ b/xs/src/qhull/src/rbox/rbox_r.c
@@ -0,0 +1,78 @@
+
+/*<html><pre>  -<a                             href="../libqhull/index.htm#TOC"
+  >-------------------------------</a><a name="TOP">-</a>
+
+   rbox.c
+     rbox program for generating input points for qhull.
+
+   notes:
+     50 points generated for 'rbox D4'
+
+*/
+
+#include "libqhull_r/libqhull_r.h"
+#include "libqhull/random_r.h"
+
+#include <stdarg.h>
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+
+#ifdef _MSC_VER  /* Microsoft Visual C++ -- warning level 4 */
+#pragma warning( disable : 4706)  /* assignment within conditional function */
+#endif
+
+char prompt[]= "\n\
+-rbox- generate various point distributions.  Default is random in cube.\n\
+\n\
+args (any order, space separated):                    Version: 2016/01/18 r\n\
+  3000    number of random points in cube, lens, spiral, sphere or grid\n\
+  D3      dimension 3-d\n\
+  c       add a unit cube to the output ('c G2.0' sets size)\n\
+  d       add a unit diamond to the output ('d G2.0' sets size)\n\
+  l       generate a regular 3-d spiral\n\
+  r       generate a regular polygon, ('r s Z1 G0.1' makes a cone)\n\
+  s       generate cospherical points\n\
+  x       generate random points in simplex, may use 'r' or 'Wn'\n\
+  y       same as 'x', plus simplex\n\
+  Cn,r,m  add n nearly coincident points within radius r of m points\n\
+  Pn,m,r  add point [n,m,r] first, pads with 0, maybe repeated\n\
+\n\
+  Ln      lens distribution of radius n.  Also 's', 'r', 'G', 'W'.\n\
+  Mn,m,r  lattice(Mesh) rotated by [n,-m,0], [m,n,0], [0,0,r], ...\n\
+          '27 M1,0,1' is {0,1,2} x {0,1,2} x {0,1,2}.  Try 'M3,4 z'.\n\
+  W0.1    random distribution within 0.1 of the cube's or sphere's surface\n\
+  Z0.5 s  random points in a 0.5 disk projected to a sphere\n\
+  Z0.5 s G0.6 same as Z0.5 within a 0.6 gap\n\
+\n\
+  Bn      bounding box coordinates, default %2.2g\n\
+  h       output as homogeneous coordinates for cdd\n\
+  n       remove command line from the first line of output\n\
+  On      offset coordinates by n\n\
+  t       use time as the random number seed(default is command line)\n\
+  tn      use n as the random number seed\n\
+  z       print integer coordinates, default 'Bn' is %2.2g\n\
+";
+
+/*--------------------------------------------
+-rbox-  main procedure of rbox application
+*/
+int main(int argc, char **argv) {
+  int return_status;
+  qhT qh_qh;
+  qhT *qh= &qh_qh;
+
+  QHULL_LIB_CHECK_RBOX
+
+  if (argc == 1) {
+    printf(prompt, qh_DEFAULTbox, qh_DEFAULTzbox);
+    return 1;
+  }
+  if (argc == 2 && strcmp(argv[1], "D4")==0)
+    qh_fprintf_stderr(0, "\nStarting the rbox smoketest for qhull.  An immediate failure indicates\nthat reentrant rbox was linked to non-reentrant routines.  An immediate\nfailure of qhull may indicate that qhull was linked to the wrong\nqhull library.  Also try 'rbox D4 | qhull T1'\n");
+
+  qh_init_A(qh, stdin, stdout, stderr, argc, argv);  /*no qh_errexit, sets qh->qhull_command */
+  return_status= qh_rboxpoints(qh, qh->qhull_command); /* Traps its own errors, qh_errexit_rbox() */
+  return return_status;
+}/*main*/
+
diff --git a/xs/src/qhull/src/testqset/testqset.c b/xs/src/qhull/src/testqset/testqset.c
new file mode 100644
index 0000000000..61057eef9c
--- /dev/null
+++ b/xs/src/qhull/src/testqset/testqset.c
@@ -0,0 +1,891 @@
+/*<html><pre>  -<a                             href="../libqhull/index.htm#TOC"
+  >-------------------------------</a><a name="TOP">-</a>
+
+   testset.c -- test qset.c and its use of mem.c
+
+   The test sets are pointers to int.  Normally a set is a pointer to a type (e.g., facetT, ridgeT, etc.).
+   For consistency in notation, an "int" is typedef'd to i2T
+
+Functions and macros from qset.h.  Counts occurrences in this test.  Does not correspond to thoroughness.
+    qh_setaddsorted -- 4 tests
+    qh_setaddnth -- 1 test
+    qh_setappend -- 7 tests
+    qh_setappend_set -- 1 test
+    qh_setappend2ndlast -- 1 test
+    qh_setcheck -- lots of tests
+    qh_setcompact -- 7 tests
+    qh_setcopy -- 3 tests
+    qh_setdel -- 1 tests
+    qh_setdellast -- 1 tests
+    qh_setdelnth -- 2 tests
+    qh_setdelnthsorted -- 2 tests
+    qh_setdelsorted -- 1 test
+    qh_setduplicate -- not testable here
+    qh_setequal -- 4 tests
+    qh_setequal_except -- 2 tests
+    qh_setequal_skip -- 2 tests
+    qh_setfree -- 11+ tests
+    qh_setfree2 -- not testable here
+    qh_setfreelong -- 2 tests
+    qh_setin -- 3 tests
+    qh_setindex -- 4 tests
+    qh_setlarger -- 1 test
+    qh_setlast -- 2 tests
+    qh_setnew -- 6 tests
+    qh_setnew_delnthsorted
+    qh_setprint -- tested elsewhere
+    qh_setreplace -- 1 test
+    qh_setsize -- 9+ tests
+    qh_settemp -- 2 tests
+    qh_settempfree -- 1 test
+    qh_settempfree_all -- 1 test
+    qh_settemppop -- 1 test
+    qh_settemppush -- 1 test
+    qh_settruncate -- 3 tests
+    qh_setunique -- 3 tests
+    qh_setzero -- 1 test
+    FOREACHint_ -- 2 test
+    FOREACHint4_
+    FOREACHint_i_ -- 1 test
+    FOREACHintreverse_
+    FOREACHintreverse12_
+    FOREACHsetelement_ -- 1 test
+    FOREACHsetelement_i_ -- 1 test
+    FOREACHsetelementreverse_ -- 1 test
+    FOREACHsetelementreverse12_ -- 1 test
+    SETelem_ -- 3 tests
+    SETelemaddr_ -- 2 tests
+    SETelemt_ -- not tested (generic)
+    SETempty_ -- 1 test
+    SETfirst_ -- 4 tests
+    SETfirstt_ -- 2 tests
+    SETindex_ -- 2 tests
+    SETref_ -- 2 tests
+    SETreturnsize_ -- 2 tests
+    SETsecond_ -- 1 test
+    SETsecondt_ -- 2 tests
+    SETtruncate_ -- 2 tests
+
+    Copyright (c) 2012-2015 C.B. Barber. All rights reserved.
+    $Id: //main/2015/qhull/src/testqset/testqset.c#4 $$Change: 2062 $
+    $DateTime: 2016/01/17 13:13:18 $$Author: bbarber $
+*/
+
+#include "libqhull/user.h"  /* QHULL_CRTDBG */
+#include "libqhull/qset.h"
+#include "libqhull/mem.h"
+
+#include <stdarg.h>
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+
+typedef int i2T;
+#define MAXerrorCount 100 /* quit after n errors */
+
+#define FOREACHint_( ints ) FOREACHsetelement_( i2T, ints, i2)
+#define FOREACHint4_( ints ) FOREACHsetelement_( i2T, ints, i4)
+#define FOREACHint_i_( ints ) FOREACHsetelement_i_( i2T, ints, i2)
+#define FOREACHintreverse_( ints ) FOREACHsetelementreverse_( i2T, ints, i2)
+#define FOREACHintreverse12_( ints ) FOREACHsetelementreverse12_( i2T, ints, i2)
+
+enum {
+    MAXint= 0x7fffffff,
+};
+
+char prompt[]= "testqset N [M] [T5] -- Test qset.c and mem.c\n\
+  \n\
+  If this test fails then qhull will not work.\n\
+  \n\
+  Test qsets of 0..N integers with a check every M iterations (default ~log10)\n\
+  Additional checking and logging if M is 1\n\
+  \n\
+  T5 turns on memory logging (qset does not log)\n\
+  \n\
+  For example:\n\
+    testqset 10000\n\
+";
+
+int error_count= 0;  /* Global error_count.  checkSetContents() keeps its own error count.  It exits on too many errors */
+
+/* Macros normally defined in geom.h */
+#define fmax_( a,b )  ( ( a ) < ( b ) ? ( b ) : ( a ) )
+
+/* Macros normally defined in user.h */
+
+#define realT double
+#define qh_MEMalign ((int)(fmax_(sizeof(realT), sizeof(void *))))
+#define qh_MEMbufsize 0x10000       /* allocate 64K memory buffers */
+#define qh_MEMinitbuf 0x20000      /* initially allocate 128K buffer */
+
+/* Macros normally defined in QhullSet.h */
+
+
+/* Functions normally defined in user.h for usermem.c */
+
+void    qh_exit(int exitcode);
+void    qh_fprintf_stderr(int msgcode, const char *fmt, ... );
+void    qh_free(void *mem);
+void   *qh_malloc(size_t size);
+
+/* Normally defined in user.c */
+
+void    qh_errexit(int exitcode, void *f, void *r)
+{
+    (void)f; /* unused */
+    (void)r; /* unused */
+    qh_exit(exitcode);
+}
+
+/* Normally defined in userprintf.c */
+
+void    qh_fprintf(FILE *fp, int msgcode, const char *fmt, ... )
+{
+    static int needs_cr= 0;  /* True if qh_fprintf needs a CR */
+
+    size_t fmtlen= strlen(fmt);
+    va_list args;
+
+    if (!fp) {
+        /* Do not use qh_fprintf_stderr.  This is a standalone program */
+        fprintf(stderr, "QH6232 qh_fprintf: fp not defined for '%s'", fmt);
+        qh_errexit(6232, NULL, NULL);
+    }
+    if(fmtlen>0){
+        if(fmt[fmtlen-1]=='\n'){
+            if(needs_cr && fmtlen>1){
+                fprintf(fp, "\n");
+            }
+            needs_cr= 0;
+        }else{
+            needs_cr= 1;
+        }
+    }
+    if(msgcode>=6000 && msgcode<7000){
+        fprintf(fp, "Error TQ%d ", msgcode);
+    }
+    va_start(args, fmt);
+    vfprintf(fp, fmt, args);
+    va_end(args);
+}
+
+/* Defined below in order of use */
+int main(int argc, char **argv);
+void readOptions(int argc, char **argv, const char *promptstr, int *numInts, int *checkEvery, int *traceLevel);
+void setupMemory(int tracelevel, int numInts, int **intarray);
+
+void testSetappendSettruncate(int numInts, int *intarray, int checkEvery);
+void testSetdelSetadd(int numInts, int *intarray, int checkEvery);
+void testSetappendSet(int numInts, int *intarray, int checkEvery);
+void testSetcompactCopy(int numInts, int *intarray, int checkEvery);
+void testSetequalInEtc(int numInts, int *intarray, int checkEvery);
+void testSettemp(int numInts, int *intarray, int checkEvery);
+void testSetlastEtc(int numInts, int *intarray, int checkEvery);
+void testSetdelsortedEtc(int numInts, int *intarray, int checkEvery);
+
+int log_i(setT *set, const char *s, int i, int numInts, int checkEvery);
+void checkSetContents(const char *name, setT *set, int count, int rangeA, int rangeB, int rangeC);
+
+int main(int argc, char **argv) {
+    int *intarray= NULL;
+    int numInts;
+    int checkEvery= MAXint;
+    int curlong, totlong;
+    int traceLevel= 4; /* 4 normally, no tracing since qset does not log.  5 for memory tracing */
+
+#if defined(_MSC_VER) && defined(_DEBUG) && defined(QHULL_CRTDBG)  /* user.h */
+    _CrtSetDbgFlag( _CRTDBG_ALLOC_MEM_DF | _CRTDBG_DELAY_FREE_MEM_DF | _CRTDBG_LEAK_CHECK_DF | _CrtSetDbgFlag(_CRTDBG_REPORT_FLAG) );
+    _CrtSetReportMode( _CRT_ERROR, _CRTDBG_MODE_FILE | _CRTDBG_MODE_DEBUG );
+    _CrtSetReportFile( _CRT_ERROR, _CRTDBG_FILE_STDERR );
+#endif
+
+    readOptions(argc, argv, prompt, &numInts, &checkEvery, &traceLevel);
+    setupMemory(traceLevel, numInts, &intarray);
+
+    testSetappendSettruncate(numInts, intarray, checkEvery);
+    testSetdelSetadd(numInts, intarray, checkEvery);
+    testSetappendSet(numInts, intarray, checkEvery);
+    testSetcompactCopy(numInts, intarray, checkEvery);
+    testSetequalInEtc(numInts, intarray, checkEvery);
+    testSettemp(numInts, intarray, checkEvery);
+    testSetlastEtc(numInts, intarray, checkEvery);
+    testSetdelsortedEtc(numInts, intarray, checkEvery);
+    printf("\n\nNot testing qh_setduplicate and qh_setfree2.\n  These routines use heap-allocated set contents.  See qhull tests.\n");
+
+    qh_memstatistics(stdout);
+    qh_memfreeshort(&curlong, &totlong);
+    if (curlong || totlong){
+        qh_fprintf(stderr, 8043, "qh_memfreeshort: did not free %d bytes of long memory(%d pieces)\n", totlong, curlong);
+        error_count++;
+    }
+    if(error_count){
+        qh_fprintf(stderr, 8012, "testqset: %d errors\n\n", error_count);
+        exit(1);
+    }else{
+        printf("testqset: OK\n\n");
+    }
+    return 0;
+}/*main*/
+
+void readOptions(int argc, char **argv, const char *promptstr, int *numInts, int *checkEvery, int *traceLevel)
+{
+    long numIntsArg;
+    long checkEveryArg;
+    char *endp;
+    int isTracing= 0;
+
+    if (argc < 2 || argc > 4) {
+        printf("%s", promptstr);
+        exit(0);
+    }
+    numIntsArg= strtol(argv[1], &endp, 10);
+    if(numIntsArg<1){
+        qh_fprintf(stderr, 6301, "First argument should be 1 or greater.  Got '%s'\n", argv[1]);
+        exit(1);
+    }
+    if(numIntsArg>MAXint){
+        qh_fprintf(stderr, 6302, "qset does not currently support 64-bit ints.  Maximum count is %d\n", MAXint);
+        exit(1);
+    }
+    *numInts= (int)numIntsArg;
+
+    if(argc==3 && argv[2][0]=='T' && argv[2][1]=='5' ){
+        isTracing= 1;
+        *traceLevel= 5;
+    }
+    if(argc==4 || (argc==3 && !isTracing)){
+        checkEveryArg= strtol(argv[2], &endp, 10);
+        if(checkEveryArg<1){
+            qh_fprintf(stderr, 6321, "checkEvery argument should be 1 or greater.  Got '%s'\n", argv[2]);
+            exit(1);
+        }
+        if(checkEveryArg>MAXint){
+            qh_fprintf(stderr, 6322, "qset does not currently support 64-bit ints.  Maximum checkEvery is %d\n", MAXint);
+            exit(1);
+        }
+        if(argc==4){
+            if(argv[3][0]=='T' && argv[3][1]=='5' ){
+                isTracing= 1;
+                *traceLevel= 5;
+            }else{
+                qh_fprintf(stderr, 6242, "Optional third argument must be 'T5'.  Got '%s'\n", argv[3]);
+                exit(1);
+            }
+        }
+        *checkEvery= (int)checkEveryArg;
+    }
+}/*readOptions*/
+
+void setupMemory(int tracelevel, int numInts, int **intarray)
+{
+    int i;
+    if(numInts<0 || numInts*(int)sizeof(int)<0){
+        qh_fprintf(stderr, 6303, "qset does not currently support 64-bit ints.  Integer overflow\n");
+        exit(1);
+    }
+    *intarray= qh_malloc(numInts * sizeof(int));
+    if(!*intarray){
+        qh_fprintf(stderr, 6304, "Failed to allocate %d bytes of memory\n", numInts * sizeof(int));
+        exit(1);
+    }
+    for(i= 0; i<numInts; i++){
+        (*intarray)[i] =i;
+    }
+
+    qh_meminit(stderr);
+    qh_meminitbuffers(tracelevel, qh_MEMalign, 4 /*sizes*/, qh_MEMbufsize,qh_MEMinitbuf);
+    qh_memsize(10);
+    qh_memsize(20);
+    qh_memsize(30);
+    qh_memsize(40);
+    qh_memsetup();
+
+    qh_fprintf(stderr, 8001, "SETelemsize is %d bytes for pointer-to-int\n", SETelemsize);
+}/*setupMemmory*/
+
+void testSetappendSettruncate(int numInts, int *intarray, int checkEvery)
+{
+    setT *ints= qh_setnew(4);
+    int i, isCheck;
+
+    qh_fprintf(stderr, 8002, "\n\nTesting qh_setappend 0..%d.  Test", numInts-1);
+    for(i= 0; i<numInts; i++){
+        isCheck= log_i(ints, "i", i, numInts, checkEvery);
+        qh_setappend(&ints, intarray+i);
+        if(isCheck){
+            checkSetContents("qh_setappend", ints, i+1, 0, -1, -1);
+        }
+    }
+
+    qh_fprintf(stderr, 8014, "\n\nTesting qh_settruncate %d and 0.  Test", numInts/2);
+    if(numInts>=2){
+        isCheck= log_i(ints, "n", numInts/2, numInts, checkEvery);
+        qh_settruncate(ints, numInts/2);
+        checkSetContents("qh_settruncate by half", ints, numInts/2, 0, -1, -1);
+    }
+    isCheck= log_i(ints, "n", 0, numInts, checkEvery);
+    qh_settruncate(ints, 0);
+    checkSetContents("qh_settruncate", ints, 0, -1, -1, -1);
+
+    qh_fprintf(stderr, 8003, "\n\nTesting qh_setappend2ndlast 0,0..%d.  Test 0", numInts-1);
+    qh_setfree(&ints);
+    ints= qh_setnew(4);
+    qh_setappend(&ints, intarray+0);
+    for(i= 0; i<numInts; i++){
+        isCheck= log_i(ints, "i", i, numInts, checkEvery);
+        qh_setappend2ndlast(&ints, intarray+i);
+        if(isCheck){
+            checkSetContents("qh_setappend2ndlast", ints, i+2, 0, 0, -1);
+        }
+    }
+    qh_fprintf(stderr, 8015, "\n\nTesting SETtruncate_ %d and 0.  Test", numInts/2);
+    if(numInts>=2){
+        isCheck= log_i(ints, "n", numInts/2, numInts, checkEvery);
+        SETtruncate_(ints, numInts/2);
+        checkSetContents("SETtruncate_ by half", ints, numInts/2, 0, -1, -1);
+    }
+    isCheck= log_i(ints, "n", 0, numInts, checkEvery);
+    SETtruncate_(ints, 0);
+    checkSetContents("SETtruncate_", ints, 0, -1, -1, -1);
+
+    qh_setfree(&ints);
+}/*testSetappendSettruncate*/
+
+void testSetdelSetadd(int numInts, int *intarray, int checkEvery)
+{
+    setT *ints=qh_setnew(1);
+    int i,j,isCheck;
+
+    qh_fprintf(stderr, 8003, "\n\nTesting qh_setdelnthsorted and qh_setaddnth 1..%d. Test", numInts-1);
+    for(j=1; j<numInts; j++){  /* size 0 not valid */
+        if(log_i(ints, "j", j, numInts, MAXint)){
+            for(i= qh_setsize(ints); i<j; i++){
+                qh_setappend(&ints, intarray+i);
+            }
+            checkSetContents("qh_setappend", ints, j, 0, -1, -1);
+            for(i= 0; i<j && i<100; i++){  /* otherwise too slow */
+                isCheck= log_i(ints, "", i, numInts, checkEvery);
+                (void)isCheck; /* unused */
+                qh_setdelnthsorted(ints, i);
+                qh_setaddnth(&ints, i, intarray+i);
+                if(checkEvery==1){
+                    checkSetContents("qh_setdelnthsorted qh_setaddnth", ints, j, 0, -1, -1);
+                }
+            }
+            checkSetContents("qh_setdelnthsorted qh_setaddnth 2", ints, j, 0, -1, -1);
+        }
+    }
+    qh_setfree(&ints);
+}/*testSetdelSetadd*/
+
+void testSetappendSet(int numInts, int *intarray, int checkEvery)
+{
+    setT *ints=qh_setnew(1);
+    setT *ints2;
+    int i,j,k;
+
+    qh_fprintf(stderr, 8016, "\n\nTesting qh_setappend_set 0..%d. Test", numInts-1);
+    for(j=0; j<numInts; j++){
+        if(log_i(ints, "j", j, numInts, numInts)){
+            for(i= qh_setsize(ints); i<j; i++){
+                qh_setappend(&ints, intarray+i);
+            }
+            if(checkEvery==1){
+                checkSetContents("qh_setappend", ints, j, 0, -1, -1);
+            }
+            ints2= qh_setnew(j==0 ? 0 : j-1);  /* One less than needed */
+            for(i= 0; i<=j && i<=20; i++){  /* otherwise too slow */
+                if(log_i(ints, "", i, numInts, numInts)){
+                    for(k= qh_setsize(ints2); k<i; k++){
+                        qh_setappend(&ints2, intarray+k);
+                    }
+                    if(checkEvery==1){
+                        checkSetContents("qh_setappend 2", ints2, i, 0, -1, -1);
+                    }
+                    qh_setappend_set(&ints, ints2);
+                    checkSetContents("qh_setappend_set", ints, i+j, 0, (j==0 ? -1 : 0), -1);
+                    qh_settruncate(ints, j);
+                    if(checkEvery==1){
+                        checkSetContents("qh_settruncate", ints, j, 0, -1, -1);
+                    }
+                }
+            }
+            qh_setfree(&ints2);
+        }
+    }
+    qh_setfree(&ints);
+}/*testSetappendSet*/
+
+void testSetcompactCopy(int numInts, int *intarray, int checkEvery)
+{
+    setT *ints= qh_setnew(20);
+    setT *ints2= NULL;
+    int i,j,k;
+
+    qh_fprintf(stderr, 8017, "\n\nTesting qh_setcompact and qh_setcopy 0..%d. Test", numInts-1);
+    for(j=0; j<numInts; j++){
+        if(log_i(ints, "j", j, numInts, checkEvery)){
+            for(i= qh_setsize(ints); i<j; i++){  /* Test i<j to test the empty set */
+                for(k= 0; k<i%7; k++){
+                    qh_setappend(&ints, NULL);
+                }
+                qh_setappend(&ints, intarray+i);
+            }
+            qh_setfree(&ints2);
+            ints2= qh_setcopy(ints, 0);
+            qh_setcompact(ints);
+            qh_setcompact(ints2);
+            checkSetContents("qh_setcompact", ints, j, 0, 0, -1);
+            checkSetContents("qh_setcompact", ints2, j, 0, 0, -1);
+            qh_setcompact(ints);
+            checkSetContents("qh_setcompact", ints, j, 0, 0, -1);
+        }
+    }
+    qh_setfree(&ints);
+    qh_setfree(&ints2);
+}/*testSetcompactCopy*/
+
+void testSetdelsortedEtc(int numInts, int *intarray, int checkEvery)
+{
+    setT *ints= qh_setnew(1);
+    setT *ints2= NULL;
+    int i,j;
+
+    qh_fprintf(stderr, 8018, "\n\nTesting qh_setdel*, qh_setaddsorted, and  0..%d. Test", numInts-1);
+    for(j=0; j<numInts; j++){
+        if(log_i(ints, "j", j, numInts, checkEvery)){
+            for(i= qh_setsize(ints); i<j; i++){  /* Test i<j to test the empty set */
+                qh_setaddsorted(&ints, intarray+i);
+            }
+            checkSetContents("qh_setaddsorted", ints, j, 0, 0, -1);
+            if(j>3){
+                qh_setdelsorted(ints, intarray+i/2);
+                checkSetContents("qh_setdelsorted", ints, j-1, 0, i/2+1, -1);
+                qh_setaddsorted(&ints, intarray+i/2);
+                checkSetContents("qh_setaddsorted i/2", ints, j, 0, 0, -1);
+            }
+            qh_setdellast(ints);
+            checkSetContents("qh_setdellast", ints, (j ? j-1 : 0), 0, -1, -1);
+            if(j>0){
+                qh_setaddsorted(&ints, intarray+j-1);
+                checkSetContents("qh_setaddsorted j-1", ints, j, 0, -1, -1);
+            }
+            if(j>4){
+                qh_setdelnthsorted(ints, i/2);
+                if (checkEvery==1)
+                  checkSetContents("qh_setdelnthsorted", ints, j-1, 0, i/2+1, -1);
+                /* test qh_setdelnth and move-to-front */
+                qh_setdelsorted(ints, intarray+i/2+1);
+                checkSetContents("qh_setdelsorted 2", ints, j-2, 0, i/2+2, -1);
+                qh_setaddsorted(&ints, intarray+i/2+1);
+                if (checkEvery==1)
+                  checkSetContents("qh_setaddsorted i/2+1", ints, j-1, 0, i/2+1, -1);
+                qh_setaddsorted(&ints, intarray+i/2);
+                checkSetContents("qh_setaddsorted i/2 again", ints, j, 0, -1, -1);
+            }
+            qh_setfree(&ints2);
+            ints2= qh_setcopy(ints, 0);
+            qh_setcompact(ints);
+            qh_setcompact(ints2);
+            checkSetContents("qh_setcompact", ints, j, 0, 0, -1);
+            checkSetContents("qh_setcompact 2", ints2, j, 0, 0, -1);
+            qh_setcompact(ints);
+            checkSetContents("qh_setcompact 3", ints, j, 0, 0, -1);
+            qh_setfree(&ints2);
+        }
+    }
+    qh_setfreelong(&ints);
+    if(ints){
+        qh_setfree(&ints); /* Was quick memory */
+    }
+}/*testSetdelsortedEtc*/
+
+void testSetequalInEtc(int numInts, int *intarray, int checkEvery)
+{
+    setT *ints= NULL;
+    setT *ints2= NULL;
+    setT *ints3= NULL;
+    int i,j,n;
+
+    qh_fprintf(stderr, 8019, "\n\nTesting qh_setequal*, qh_setin*, qh_setdel, qh_setdelnth, and qh_setlarger 0..%d. Test", numInts-1);
+    for(j=0; j<numInts; j++){
+        if(log_i(ints, "j", j, numInts, checkEvery)){
+            n= qh_setsize(ints);
+            qh_setlarger(&ints);
+            checkSetContents("qh_setlarger", ints, n, 0, -1, -1);
+            for(i= qh_setsize(ints); i<j; i++){  /* Test i<j to test the empty set */
+                qh_setappend(&ints, intarray+i);
+            }
+            checkSetContents("qh_setappend", ints, j, 0, -1, -1);
+            if(!qh_setequal(ints, ints)){
+                qh_fprintf(stderr, 6300, "testSetequalInEtc: set not equal to itself at length %d\n", j);
+                error_count++;
+            }
+            if(j==0 && !qh_setequal(ints, ints2)){
+                qh_fprintf(stderr, 6323, "testSetequalInEtc: empty set not equal to null set\n");
+                error_count++;
+            }
+            if(j>0){
+                if(qh_setequal(ints, ints2)){
+                    qh_fprintf(stderr, 6324, "testSetequalInEtc: non-empty set equal to empty set\n", j);
+                    error_count++;
+                }
+                qh_setfree(&ints3);
+                ints3= qh_setcopy(ints, 0);
+                checkSetContents("qh_setreplace", ints3, j, 0, -1, -1);
+                qh_setreplace(ints3, intarray+j/2, intarray+j/2+1);
+                if(j==1){
+                    checkSetContents("qh_setreplace 2", ints3, j, j/2+1, -1, -1);
+                }else if(j==2){
+                    checkSetContents("qh_setreplace 3", ints3, j, 0, j/2+1, -1);
+                }else{
+                    checkSetContents("qh_setreplace 3", ints3, j, 0, j/2+1, j/2+1);
+                }
+                if(qh_setequal(ints, ints3)){
+                    qh_fprintf(stderr, 6325, "testSetequalInEtc: modified set equal to original set at %d/2\n", j);
+                    error_count++;
+                }
+                if(!qh_setequal_except(ints, intarray+j/2, ints3, intarray+j/2+1)){
+                    qh_fprintf(stderr, 6326, "qh_setequal_except: modified set not equal to original set except modified\n", j);
+                    error_count++;
+                }
+                if(qh_setequal_except(ints, intarray+j/2, ints3, intarray)){
+                    qh_fprintf(stderr, 6327, "qh_setequal_except: modified set equal to original set with wrong excepts\n", j);
+                    error_count++;
+                }
+                if(!qh_setequal_skip(ints, j/2, ints3, j/2)){
+                    qh_fprintf(stderr, 6328, "qh_setequal_skip: modified set not equal to original set except modified\n", j);
+                    error_count++;
+                }
+                if(j>2 && qh_setequal_skip(ints, j/2, ints3, 0)){
+                    qh_fprintf(stderr, 6329, "qh_setequal_skip: modified set equal to original set with wrong excepts\n", j);
+                    error_count++;
+                }
+                if(intarray+j/2+1!=qh_setdel(ints3, intarray+j/2+1)){
+                    qh_fprintf(stderr, 6330, "qh_setdel: failed to find added element\n", j);
+                    error_count++;
+                }
+                checkSetContents("qh_setdel", ints3, j-1, 0, j-1, (j==1 ? -1 : j/2+1));  /* swaps last element with deleted element */
+                if(j>3){
+                    qh_setdelnth(ints3, j/2); /* Delete at the same location as the original replace, for only one out-of-order element */
+                    checkSetContents("qh_setdelnth", ints3, j-2, 0, j-2, (j==2 ? -1 : j/2+1));
+                }
+                if(qh_setin(ints3, intarray+j/2)){
+                    qh_fprintf(stderr, 6331, "qh_setin: found deleted element\n");
+                    error_count++;
+                }
+                if(j>4 && !qh_setin(ints3, intarray+1)){
+                    qh_fprintf(stderr, 6332, "qh_setin: did not find second element\n");
+                    error_count++;
+                }
+                if(j>4 && !qh_setin(ints3, intarray+j-2)){
+                    qh_fprintf(stderr, 6333, "qh_setin: did not find last element\n");
+                    error_count++;
+                }
+                if(-1!=qh_setindex(ints2, intarray)){
+                    qh_fprintf(stderr, 6334, "qh_setindex: found element in empty set\n");
+                    error_count++;
+                }
+                if(-1!=qh_setindex(ints3, intarray+j/2)){
+                    qh_fprintf(stderr, 6335, "qh_setindex: found deleted element in set\n");
+                    error_count++;
+                }
+                if(0!=qh_setindex(ints, intarray)){
+                    qh_fprintf(stderr, 6336, "qh_setindex: did not find first in set\n");
+                    error_count++;
+                }
+                if(j-1!=qh_setindex(ints, intarray+j-1)){
+                    qh_fprintf(stderr, 6337, "qh_setindex: did not find last in set\n");
+                    error_count++;
+                }
+            }
+            qh_setfree(&ints2);
+        }
+    }
+    qh_setfree(&ints3);
+    qh_setfreelong(&ints);
+    if(ints){
+        qh_setfree(&ints); /* Was quick memory */
+    }
+}/*testSetequalInEtc*/
+
+
+void testSetlastEtc(int numInts, int *intarray, int checkEvery)
+{
+    setT *ints= NULL;
+    setT *ints2= NULL;
+    int i,j,prepend;
+
+    qh_fprintf(stderr, 8020, "\n\nTesting qh_setlast, qh_setnew_delnthsorted, qh_setunique, and qh_setzero 0..%d. Test", numInts-1);
+    for(j=0; j<numInts; j++){
+        if(log_i(ints, "j", j, numInts, checkEvery)){
+            for(i= qh_setsize(ints); i<j; i++){  /* Test i<j to test the empty set */
+                if(!qh_setunique(&ints, intarray+i)){
+                    qh_fprintf(stderr, 6340, "qh_setunique: not able to append next element %d\n", i);
+                    error_count++;
+                }
+                if(checkEvery==1){
+                    checkSetContents("qh_setunique", ints, i+1, 0, -1, -1);
+                }
+                if(qh_setunique(&ints, intarray+i)){
+                    qh_fprintf(stderr, 6341, "qh_setunique: appended next element twice %d\n", i);
+                    error_count++;
+                }
+                if(qh_setunique(&ints, intarray+i/2)){
+                    qh_fprintf(stderr, 6346, "qh_setunique: appended middle element twice %d/2\n", i);
+                    error_count++;
+                }
+            }
+            checkSetContents("qh_setunique 2", ints, j, 0, -1, -1);
+            if(j==0 && NULL!=qh_setlast(ints)){
+                qh_fprintf(stderr, 6339, "qh_setlast: returned last element of empty set\n");
+                error_count++;
+            }
+            if(j>0){
+                if(intarray+j-1!=qh_setlast(ints)){
+                    qh_fprintf(stderr, 6338, "qh_setlast: wrong last element\n");
+                    error_count++;
+                }
+                prepend= (j<100 ? j/4 : 0);
+                ints2= qh_setnew_delnthsorted(ints, qh_setsize(ints), j/2, prepend);
+                if(qh_setsize(ints2)!=j+prepend-1){
+                    qh_fprintf(stderr, 6345, "qh_setnew_delnthsorted: Expecting %d elements, got %d\n", j+prepend-1, qh_setsize(ints2));
+                    error_count++;
+                }
+                /* Define prepended elements.  Otherwise qh_setdelnthsorted may fail */
+                for(i= 0; i<prepend; i++){
+                    void **p= &SETelem_(ints2, i);
+                    *p= intarray+0;
+                }
+                for(i= 0; i<prepend; i++){
+                    qh_setdelnthsorted(ints2, 0);  /* delete undefined prefix */
+                }
+                checkSetContents("qh_setnew_delnthsorted", ints2, j-1, 0, j/2+1, -1);
+                if(j>2){
+                    qh_setzero(ints2, j/2, j-1);  /* max size may be j-1 */
+                    if(qh_setsize(ints2)!=j-1){
+                        qh_fprintf(stderr, 6342, "qh_setzero: Expecting %d elements, got %d\n", j, qh_setsize(ints2));
+                        error_count++;
+                    }
+                    qh_setcompact(ints2);
+                    checkSetContents("qh_setzero", ints2, j/2, 0, -1, -1);
+                }
+            }
+            qh_setfree(&ints2);
+        }
+    }
+    qh_setfreelong(&ints);
+    if(ints){
+        qh_setfree(&ints); /* Was quick memory */
+    }
+}/*testSetlastEtc*/
+
+void testSettemp(int numInts, int *intarray, int checkEvery)
+{
+    setT *ints= NULL;
+    setT *ints2= NULL;
+    setT *ints3= NULL;
+    int i,j;
+
+    qh_fprintf(stderr, 8021, "\n\nTesting qh_settemp* 0..%d. Test", numInts-1);
+    for(j=0; j<numInts; j++){
+        if(log_i(ints, "j", j, numInts, checkEvery)){
+            if(j<20){
+                for(i=0; i<j; i++){
+                    ints2= qh_settemp(j);
+                }
+                qh_settempfree_all();
+            }
+            for(i= qh_setsize(ints); i<j; i++){  /* Test i<j to test the empty set */
+                qh_setappend(&ints, intarray+i);
+            }
+            ints2= qh_settemp(j);
+            if(j>0){
+                qh_settemppush(ints);
+                ints3= qh_settemppop();
+                if(ints!=ints3){
+                    qh_fprintf(stderr, 6343, "qh_settemppop: didn't pop the push\n");
+                    error_count++;
+                }
+            }
+            qh_settempfree(&ints2);
+        }
+    }
+    qh_setfreelong(&ints);
+    if(ints){
+        qh_setfree(&ints); /* Was quick memory */
+    }
+}/*testSettemp*/
+
+/* Check that a set contains count elements
+   Ranges are consecutive (e.g., 1,2,3,...) starting with first, mid, and last
+   Use -1 for missing ranges
+   Returns -1 if should check results
+*/
+int log_i(setT *set, const char *s, int i, int numInts, int checkEvery)
+{
+    int j= i;
+    int scale= 1;
+    int e= 0;
+    int *i2, **i2p;
+
+    if(*s || checkEvery==1){
+        if(i<10){
+            qh_fprintf(stderr, 8004, " %s%d", s, i);
+        }else{
+            if(i==11 && checkEvery==1){
+                qh_fprintf(stderr, 8005, "\nResults after 10: ");
+                FOREACHint_(set){
+                    qh_fprintf(stderr, 8006, " %d", *i2);
+                }
+                qh_fprintf(stderr, 8007, " Continue");
+            }
+            while((j= j/10)>=1){
+                scale *= 10;
+                e++;
+            }
+            if(i==numInts-1){
+                qh_fprintf(stderr, 8008, " %s%d", s, i);
+            }else if(i==scale){
+                if(i<=1000){
+                    qh_fprintf(stderr, 8010, " %s%d", s, i);
+                }else{
+                    qh_fprintf(stderr, 8009, " %s1e%d", s, e);
+                }
+            }
+        }
+    }
+    if(i<1000 || i%checkEvery==0 || i== scale || i==numInts-1){
+        return 1;
+    }
+    return 0;
+}/*log_i*/
+
+/* Check that a set contains count elements
+   Ranges are consecutive (e.g., 1,2,3,...) starting with first, mid, and last
+   Use -1 for missing ranges
+*/
+void checkSetContents(const char *name, setT *set, int count, int rangeA, int rangeB, int rangeC)
+{
+
+    i2T *i2, **i2p;
+    int i2_i, i2_n;
+    int prev= -1; /* avoid warning */
+    int i;
+    int first= -3;
+    int second= -3;
+    int rangeCount=1;
+    int actualSize= 0;
+
+    qh_setcheck(set, name, 0);
+    if(set){
+        SETreturnsize_(set, actualSize);  /* normally used only when speed is critical */
+        if(*qh_setendpointer(set)!=NULL){
+            qh_fprintf(stderr, 6344, "%s: qh_setendpointer(), 0x%x, is not NULL terminator of set 0x%x", name, qh_setendpointer(set), set);
+            error_count++;
+        }
+    }
+    if(actualSize!=qh_setsize(set)){
+        qh_fprintf(stderr, 6305, "%s: SETreturnsize_() returned %d while qh_setsize() returns %d\n", name, actualSize, qh_setsize(set));
+        error_count++;
+    }else if(actualSize!=count){
+        qh_fprintf(stderr, 6306, "%s: Expecting %d elements for set.  Got %d elements\n", name, count, actualSize);
+        error_count++;
+    }
+    if(SETempty_(set)){
+        if(count!=0){
+            qh_fprintf(stderr, 6307, "%s: Got empty set instead of count %d, rangeA %d, rangeB %d, rangeC %d\n", name, count, rangeA, rangeB, rangeC);
+            error_count++;
+        }
+    }else{
+        /* Must be first, otherwise trips msvc 8 */
+        i2T **p= SETaddr_(set, i2T);
+        if(*p!=SETfirstt_(set, i2T)){
+            qh_fprintf(stderr, 6309, "%s: SETaddr_(set, i2t) [%p] is not the same as SETfirst_(set) [%p]\n", name, SETaddr_(set, i2T), SETfirst_(set));
+            error_count++;
+        }
+        first= *(int *)SETfirst_(set);
+        if(SETfirst_(set)!=SETfirstt_(set, i2T)){
+            qh_fprintf(stderr, 6308, "%s: SETfirst_(set) [%p] is not the same as SETfirstt_(set, i2T [%p]\n", name, SETfirst_(set), SETfirstt_(set, i2T));
+            error_count++;
+        }
+        if(qh_setsize(set)>1){
+            second= *(int *)SETsecond_(set);
+            if(SETsecond_(set)!=SETsecondt_(set, i2T)){
+                qh_fprintf(stderr, 6310, "%s: SETsecond_(set) [%p] is not the same as SETsecondt_(set, i2T) [%p]\n", name, SETsecond_(set), SETsecondt_(set, i2T));
+                error_count++;
+            }
+        }
+    }
+    /* Test first run of ints in set*/
+    i= 0;
+    FOREACHint_(set){
+        if(i2!=SETfirst_(set) && *i2!=prev+1){
+            break;
+        }
+        prev= *i2;
+        if(SETindex_(set, i2)!=i){
+            qh_fprintf(stderr, 6311, "%s: Expecting SETIndex_(set, pointer-to-%d) to be %d.  Got %d\n", name, *i2, i, SETindex_(set, i2));
+            error_count++;;
+        }
+        if(i2!=SETref_(i2)){
+            qh_fprintf(stderr, 6312, "%s: SETref_(i2) [%p] does not point to i2 (the %d'th element)\n", name, SETref_(i2), i);
+            error_count++;;
+        }
+        i++;
+    }
+    FOREACHint_i_(set){
+        /* Must be first conditional, otherwise it trips up msvc 8 */
+        i2T **p= SETelemaddr_(set, i2_i, i2T);
+        if(i2!=*p){
+            qh_fprintf(stderr, 6320, "%s: SETelemaddr_(set, %d, i2T) [%p] does not point to i2\n", name, i2_i, SETelemaddr_(set, i2_i, int));
+            error_count++;;
+        }
+        if(i2_i==0){
+            if(first!=*i2){
+                qh_fprintf(stderr, 6314, "%s: First element is %d instead of SETfirst %d\n", name, *i2, first);
+                error_count++;;
+            }
+            if(rangeA!=*i2){
+                qh_fprintf(stderr, 6315, "%s: starts with %d instead of rangeA %d\n", name, *i2, rangeA);
+                error_count++;;
+            }
+            prev= rangeA;
+        }else{
+            if(i2_i==1 && second!=*i2){
+                qh_fprintf(stderr, 6316, "%s: Second element is %d instead of SETsecond %d\n", name, *i2, second);
+                error_count++;;
+            }
+            if(prev+1==*i2){
+                prev++;
+            }else{
+                if(*i2==rangeB){
+                    prev= rangeB;
+                    rangeB= -1;
+                    rangeCount++;
+                }else if(rangeB==-1 && *i2==rangeC){
+                    prev= rangeC;
+                    rangeC= -1;
+                    rangeCount++;
+                }else{
+                    prev++;
+                    qh_fprintf(stderr, 6317, "%s: Expecting %d'th element to be %d.  Got %d\n", name, i2_i, prev, *i2);
+                    error_count++;
+                }
+            }
+        }
+        if(i2!=SETelem_(set, i2_i)){
+            qh_fprintf(stderr, 6318, "%s: SETelem_(set, %d) [%p] is not i2 [%p] (the %d'th element)\n", name, i2_i, SETelem_(set, i2_i), i2, i2_i);
+            error_count++;;
+        }
+        if(SETelemt_(set, i2_i, i2T)!=SETelem_(set, i2_i)){   /* Normally SETelemt_ is used for generic sets */
+            qh_fprintf(stderr, 6319, "%s: SETelemt_(set, %d, i2T) [%p] is not SETelem_(set, %d) [%p] (the %d'th element)\n", name, i2_i, SETelemt_(set, i2_i, int), i2_i, SETelem_(set, i2_i), i2_i);
+            error_count++;;
+        }
+    }
+    if(error_count>=MAXerrorCount){
+        qh_fprintf(stderr, 8011, "testqset: Stop testing after %d errors\n", error_count);
+        exit(1);
+    }
+}/*checkSetContents*/
+
diff --git a/xs/src/qhull/src/testqset/testqset.pro b/xs/src/qhull/src/testqset/testqset.pro
new file mode 100644
index 0000000000..3f69048aac
--- /dev/null
+++ b/xs/src/qhull/src/testqset/testqset.pro
@@ -0,0 +1,30 @@
+# -------------------------------------------------
+# testqset.pro -- Qt project file for testqset.exe
+# -------------------------------------------------
+
+include(../qhull-warn.pri)
+
+TARGET = testqset
+
+DESTDIR = ../../bin
+TEMPLATE = app
+CONFIG += console warn_on
+CONFIG -= qt
+CONFIG += qhull_warn_conversion
+
+build_pass:CONFIG(debug, debug|release){
+   OBJECTS_DIR = Debug
+}else:build_pass:CONFIG(release, debug|release){
+   OBJECTS_DIR = Release
+}
+
+INCLUDEPATH += ..
+
+SOURCES += testqset.c
+SOURCES += ../libqhull/qset.c
+SOURCES += ../libqhull/mem.c
+SOURCES += ../libqhull/usermem.c
+
+HEADERS += ../libqhull/mem.h
+HEADERS += ../libqhull/qset.h
+
diff --git a/xs/src/qhull/src/testqset_r/testqset_r.c b/xs/src/qhull/src/testqset_r/testqset_r.c
new file mode 100644
index 0000000000..9a6d496e40
--- /dev/null
+++ b/xs/src/qhull/src/testqset_r/testqset_r.c
@@ -0,0 +1,890 @@
+/*<html><pre>  -<a                             href="../libqhull/index.htm#TOC"
+  >-------------------------------</a><a name="TOP">-</a>
+
+   testset.c -- test qset.c and its use of mem.c
+
+   The test sets are pointers to int.  Normally a set is a pointer to a type (e.g., facetT, ridgeT, etc.).
+   For consistency in notation, an "int" is typedef'd to i2T
+
+Functions and macros from qset.h.  Counts occurrences in this test.  Does not correspond to thoroughness.
+    qh_setaddsorted -- 4 tests
+    qh_setaddnth -- 1 test
+    qh_setappend -- 7 tests
+    qh_setappend_set -- 1 test
+    qh_setappend2ndlast -- 1 test
+    qh_setcheck -- lots of tests
+    qh_setcompact -- 7 tests
+    qh_setcopy -- 3 tests
+    qh_setdel -- 1 tests
+    qh_setdellast -- 1 tests
+    qh_setdelnth -- 2 tests
+    qh_setdelnthsorted -- 2 tests
+    qh_setdelsorted -- 1 test
+    qh_setduplicate -- not testable here
+    qh_setequal -- 4 tests
+    qh_setequal_except -- 2 tests
+    qh_setequal_skip -- 2 tests
+    qh_setfree -- 11+ tests
+    qh_setfree2 -- not testable here
+    qh_setfreelong -- 2 tests
+    qh_setin -- 3 tests
+    qh_setindex -- 4 tests
+    qh_setlarger -- 1 test
+    qh_setlast -- 2 tests
+    qh_setnew -- 6 tests
+    qh_setnew_delnthsorted
+    qh_setprint -- tested elsewhere
+    qh_setreplace -- 1 test
+    qh_setsize -- 9+ tests
+    qh_settemp -- 2 tests
+    qh_settempfree -- 1 test
+    qh_settempfree_all -- 1 test
+    qh_settemppop -- 1 test
+    qh_settemppush -- 1 test
+    qh_settruncate -- 3 tests
+    qh_setunique -- 3 tests
+    qh_setzero -- 1 test
+    FOREACHint_ -- 2 test
+    FOREACHint4_
+    FOREACHint_i_ -- 1 test
+    FOREACHintreverse_
+    FOREACHintreverse12_
+    FOREACHsetelement_ -- 1 test
+    FOREACHsetelement_i_ -- 1 test
+    FOREACHsetelementreverse_ -- 1 test
+    FOREACHsetelementreverse12_ -- 1 test
+    SETelem_ -- 3 tests
+    SETelemaddr_ -- 2 tests
+    SETelemt_ -- not tested (generic)
+    SETempty_ -- 1 test
+    SETfirst_ -- 4 tests
+    SETfirstt_ -- 2 tests
+    SETindex_ -- 2 tests
+    SETref_ -- 2 tests
+    SETreturnsize_ -- 2 tests
+    SETsecond_ -- 1 test
+    SETsecondt_ -- 2 tests
+    SETtruncate_ -- 2 tests
+
+    Copyright (c) 2012-2015 C.B. Barber. All rights reserved.
+    $Id: //main/2015/qhull/src/testqset_r/testqset_r.c#5 $$Change: 2064 $
+    $DateTime: 2016/01/18 12:36:08 $$Author: bbarber $
+*/
+
+#include "libqhull_r/user_r.h"  /* QHULL_CRTDBG */
+#include "libqhull_r/qset_r.h"
+#include "libqhull_r/mem_r.h"
+#include "libqhull_r/libqhull_r.h"
+
+#include <stdarg.h>
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+
+typedef int i2T;
+#define MAXerrorCount 100 /* quit after n errors */
+
+#define FOREACHint_( ints ) FOREACHsetelement_( i2T, ints, i2)
+#define FOREACHint4_( ints ) FOREACHsetelement_( i2T, ints, i4)
+#define FOREACHint_i_( qh, ints ) FOREACHsetelement_i_( qh, i2T, ints, i2)
+#define FOREACHintreverse_( qh, ints ) FOREACHsetelementreverse_( qh, i2T, ints, i2)
+#define FOREACHintreverse12_( ints ) FOREACHsetelementreverse12_( i2T, ints, i2)
+
+enum {
+    MAXint= 0x7fffffff,
+};
+
+char prompt[]= "testqset_r N [M] [T5] -- Test reentrant qset_r.c and mem_r.c\n\
+  \n\
+  If this test fails then reentrant Qhull will not work.\n\
+  \n\
+  Test qsets of 0..N integers with a check every M iterations (default ~log10)\n\
+  Additional checking and logging if M is 1\n\
+  \n\
+  T5 turns on memory logging (qset does not log)\n\
+  \n\
+  For example:\n\
+    testqset_r 10000\n\
+";
+
+int error_count= 0;  /* Global error_count.  checkSetContents(qh) keeps its own error count.  It exits on too many errors */
+
+/* Macros normally defined in geom.h */
+#define fmax_( a,b )  ( ( a ) < ( b ) ? ( b ) : ( a ) )
+
+/* Macros normally defined in QhullSet.h */
+
+/* Functions normally defined in user_r.h for usermem_r.c */
+
+void    qh_exit(int exitcode);
+void    qh_fprintf_stderr(int msgcode, const char *fmt, ... );
+void    qh_free(void *mem);
+void   *qh_malloc(size_t size);
+
+/* Normally defined in user_r.c */
+
+void    qh_errexit(qhT *qh, int exitcode, facetT *f, ridgeT *r)
+{
+    (void)f; /* unused */
+    (void)r; /* unused */
+    (void)qh; /* unused */
+    qh_exit(exitcode);
+}
+
+/* Normally defined in userprintf.c */
+
+void    qh_fprintf(qhT *qh, FILE *fp, int msgcode, const char *fmt, ... )
+{
+    static int needs_cr= 0;  /* True if qh_fprintf needs a CR. testqset_r is not itself reentrant */
+
+    size_t fmtlen= strlen(fmt);
+    va_list args;
+
+    if (!fp) {
+        /* Do not use qh_fprintf_stderr.  This is a standalone program */
+        if(!qh)
+            fprintf(stderr, "QH6241 qh_fprintf: fp and qh not defined for '%s'", fmt);
+        else
+            fprintf(stderr, "QH6232 qh_fprintf: fp is 0.  Was wrong qh_fprintf called for '%s'", fmt);
+        qh_errexit(qh, 6232, NULL, NULL);
+    }
+    if(fmtlen>0){
+        if(fmt[fmtlen-1]=='\n'){
+            if(needs_cr && fmtlen>1){
+                fprintf(fp, "\n");
+            }
+            needs_cr= 0;
+        }else{
+            needs_cr= 1;
+        }
+    }
+    if(msgcode>=6000 && msgcode<7000){
+        fprintf(fp, "Error TQ%d ", msgcode);
+    }
+    va_start(args, fmt);
+    vfprintf(fp, fmt, args);
+    va_end(args);
+}
+
+/* Defined below in order of use */
+int main(int argc, char **argv);
+void readOptions(qhT *qh, int argc, char **argv, const char *promptstr, int *numInts, int *checkEvery, int *traceLevel);
+void setupMemory(qhT *qh, int tracelevel, int numInts, int **intarray);
+
+void testSetappendSettruncate(qhT *qh, int numInts, int *intarray, int checkEvery);
+void testSetdelSetadd(qhT *qh, int numInts, int *intarray, int checkEvery);
+void testSetappendSet(qhT *qh, int numInts, int *intarray, int checkEvery);
+void testSetcompactCopy(qhT *qh, int numInts, int *intarray, int checkEvery);
+void testSetequalInEtc(qhT *qh, int numInts, int *intarray, int checkEvery);
+void testSettemp(qhT *qh, int numInts, int *intarray, int checkEvery);
+void testSetlastEtc(qhT *qh, int numInts, int *intarray, int checkEvery);
+void testSetdelsortedEtc(qhT *qh, int numInts, int *intarray, int checkEvery);
+
+int log_i(qhT *qh, setT *set, const char *s, int i, int numInts, int checkEvery);
+void checkSetContents(qhT *qh, const char *name, setT *set, int count, int rangeA, int rangeB, int rangeC);
+
+int main(int argc, char **argv) {
+    int *intarray= NULL;
+    int numInts;
+    int checkEvery= MAXint;
+    int curlong, totlong;
+    int traceLevel= 4; /* 4 normally, no tracing since qset does not log.  Option 'T5' for memory tracing */
+    qhT qh_qh;
+    qhT *qh= &qh_qh;
+
+#if defined(_MSC_VER) && defined(_DEBUG) && defined(QHULL_CRTDBG)  /* user_r.h */
+    _CrtSetDbgFlag( _CRTDBG_ALLOC_MEM_DF | _CRTDBG_DELAY_FREE_MEM_DF | _CRTDBG_LEAK_CHECK_DF | _CrtSetDbgFlag(_CRTDBG_REPORT_FLAG) );
+    _CrtSetReportMode( _CRT_ERROR, _CRTDBG_MODE_FILE | _CRTDBG_MODE_DEBUG );
+    _CrtSetReportFile( _CRT_ERROR, _CRTDBG_FILE_STDERR );
+#endif
+
+    readOptions(qh, argc, argv, prompt, &numInts, &checkEvery, &traceLevel);
+    setupMemory(qh, traceLevel, numInts, &intarray);
+
+    testSetappendSettruncate(qh, numInts, intarray, checkEvery);
+    testSetdelSetadd(qh, numInts, intarray, checkEvery);
+    testSetappendSet(qh, numInts, intarray, checkEvery);
+    testSetcompactCopy(qh, numInts, intarray, checkEvery);
+    testSetequalInEtc(qh, numInts, intarray, checkEvery);
+    testSettemp(qh, numInts, intarray, checkEvery);
+    testSetlastEtc(qh, numInts, intarray, checkEvery);
+    testSetdelsortedEtc(qh, numInts, intarray, checkEvery);
+    printf("\n\nNot testing qh_setduplicate and qh_setfree2.\n  These routines use heap-allocated set contents.  See qhull tests.\n");
+
+    qh_memstatistics(qh, stdout);
+    qh_memfreeshort(qh, &curlong, &totlong);
+    if (curlong || totlong){
+        qh_fprintf(qh, stderr, 8043, "qh_memfreeshort: did not free %d bytes of long memory(%d pieces)\n", totlong, curlong);
+        error_count++;
+    }
+    if(error_count){
+        qh_fprintf(qh, stderr, 8012, "testqset: %d errors\n\n", error_count);
+        exit(1);
+    }else{
+        printf("testqset_r: OK\n\n");
+    }
+    return 0;
+}/*main*/
+
+void readOptions(qhT *qh, int argc, char **argv, const char *promptstr, int *numInts, int *checkEvery, int *traceLevel)
+{
+    long numIntsArg;
+    long checkEveryArg;
+    char *endp;
+    int isTracing= 0;
+
+    if (argc < 2 || argc > 4) {
+        printf("%s", promptstr);
+        exit(0);
+    }
+    numIntsArg= strtol(argv[1], &endp, 10);
+    if(numIntsArg<1){
+        qh_fprintf(qh, stderr, 6301, "First argument should be 1 or greater.  Got '%s'\n", argv[1]);
+        exit(1);
+    }
+    if(numIntsArg>MAXint){
+        qh_fprintf(qh, stderr, 6302, "qset does not currently support 64-bit ints.  Maximum count is %d\n", MAXint);
+        exit(1);
+    }
+    *numInts= (int)numIntsArg;
+
+    if(argc==3 && argv[2][0]=='T' && argv[2][1]=='5' ){
+        isTracing= 1;
+        *traceLevel= 5;
+    }
+    if(argc==4 || (argc==3 && !isTracing)){
+        checkEveryArg= strtol(argv[2], &endp, 10);
+        if(checkEveryArg<1){
+            qh_fprintf(qh, stderr, 6321, "checkEvery argument should be 1 or greater.  Got '%s'\n", argv[2]);
+            exit(1);
+        }
+        if(checkEveryArg>MAXint){
+            qh_fprintf(qh, stderr, 6322, "qset does not currently support 64-bit ints.  Maximum checkEvery is %d\n", MAXint);
+            exit(1);
+        }
+        if(argc==4){
+            if(argv[3][0]=='T' && argv[3][1]=='5' ){
+                isTracing= 1;
+                *traceLevel= 5;
+            }else{
+                qh_fprintf(qh, stderr, 6242, "Optional third argument must be 'T5'.  Got '%s'\n", argv[3]);
+                exit(1);
+            }
+        }
+        *checkEvery= (int)checkEveryArg;
+    }
+}/*readOptions*/
+
+void setupMemory(qhT *qh, int tracelevel, int numInts, int **intarray)
+{
+    int i;
+    if(numInts<0 || numInts*(int)sizeof(int)<0){
+        qh_fprintf(qh, stderr, 6303, "qset does not currently support 64-bit ints.  Integer overflow\n");
+        exit(1);
+    }
+    *intarray= qh_malloc(numInts * sizeof(int));
+    if(!*intarray){
+        qh_fprintf(qh, stderr, 6304, "Failed to allocate %d bytes of memory\n", numInts * sizeof(int));
+        exit(1);
+    }
+    for(i= 0; i<numInts; i++){
+        (*intarray)[i] =i;
+    }
+
+    qh_meminit(qh, stderr);
+    qh_meminitbuffers(qh, tracelevel, qh_MEMalign, 4 /*sizes*/, qh_MEMbufsize, qh_MEMinitbuf);
+    qh_memsize(qh, 10);
+    qh_memsize(qh, 20);
+    qh_memsize(qh, 30);
+    qh_memsize(qh, 40);
+    qh_memsetup(qh);
+
+    qh_fprintf(qh, stderr, 8001, "SETelemsize is %d bytes for pointer-to-int\n", SETelemsize);
+}/*setupMemmory*/
+
+void testSetappendSettruncate(qhT *qh, int numInts, int *intarray, int checkEvery)
+{
+    setT *ints= qh_setnew(qh, 4);
+    int i, isCheck;
+
+    qh_fprintf(qh, stderr, 8002, "\n\nTesting qh_setappend 0..%d.  Test", numInts-1);
+    for(i= 0; i<numInts; i++){
+        isCheck= log_i(qh, ints, "i", i, numInts, checkEvery);
+        qh_setappend(qh, &ints, intarray+i);
+        if(isCheck){
+            checkSetContents(qh, "qh_setappend", ints, i+1, 0, -1, -1);
+        }
+    }
+
+    qh_fprintf(qh, stderr, 8014, "\n\nTesting qh_settruncate %d and 0.  Test", numInts/2);
+    if(numInts>=2){
+        isCheck= log_i(qh, ints, "n", numInts/2, numInts, checkEvery);
+        qh_settruncate(qh, ints, numInts/2);
+        checkSetContents(qh, "qh_settruncate by half", ints, numInts/2, 0, -1, -1);
+    }
+    isCheck= log_i(qh, ints, "n", 0, numInts, checkEvery);
+    qh_settruncate(qh, ints, 0);
+    checkSetContents(qh, "qh_settruncate", ints, 0, -1, -1, -1);
+
+    qh_fprintf(qh, stderr, 8003, "\n\nTesting qh_setappend2ndlast 0,0..%d.  Test 0", numInts-1);
+    qh_setfree(qh, &ints);
+    ints= qh_setnew(qh, 4);
+    qh_setappend(qh, &ints, intarray+0);
+    for(i= 0; i<numInts; i++){
+        isCheck= log_i(qh, ints, "i", i, numInts, checkEvery);
+        qh_setappend2ndlast(qh, &ints, intarray+i);
+        if(isCheck){
+            checkSetContents(qh, "qh_setappend2ndlast", ints, i+2, 0, 0, -1);
+        }
+    }
+    qh_fprintf(qh, stderr, 8015, "\n\nTesting SETtruncate_ %d and 0.  Test", numInts/2);
+    if(numInts>=2){
+        isCheck= log_i(qh, ints, "n", numInts/2, numInts, checkEvery);
+        SETtruncate_(ints, numInts/2);
+        checkSetContents(qh, "SETtruncate_ by half", ints, numInts/2, 0, -1, -1);
+    }
+    isCheck= log_i(qh, ints, "n", 0, numInts, checkEvery);
+    SETtruncate_(ints, 0);
+    checkSetContents(qh, "SETtruncate_", ints, 0, -1, -1, -1);
+
+    qh_setfree(qh, &ints);
+}/*testSetappendSettruncate*/
+
+void testSetdelSetadd(qhT *qh, int numInts, int *intarray, int checkEvery)
+{
+    setT *ints=qh_setnew(qh, 1);
+    int i,j,isCheck;
+
+    qh_fprintf(qh, stderr, 8003, "\n\nTesting qh_setdelnthsorted and qh_setaddnth 1..%d. Test", numInts-1);
+    for(j=1; j<numInts; j++){  /* size 0 not valid */
+        if(log_i(qh, ints, "j", j, numInts, MAXint)){
+            for(i= qh_setsize(qh, ints); i<j; i++){
+                qh_setappend(qh, &ints, intarray+i);
+            }
+            checkSetContents(qh, "qh_setappend", ints, j, 0, -1, -1);
+            for(i= 0; i<j && i<100; i++){  /* otherwise too slow */
+                isCheck= log_i(qh, ints, "", i, numInts, checkEvery);
+                (void)isCheck; /* unused */
+                qh_setdelnthsorted(qh, ints, i);
+                qh_setaddnth(qh, &ints, i, intarray+i);
+                if(checkEvery==1){
+                    checkSetContents(qh, "qh_setdelnthsorted qh_setaddnth", ints, j, 0, -1, -1);
+                }
+            }
+            checkSetContents(qh, "qh_setdelnthsorted qh_setaddnth 2", ints, j, 0, -1, -1);
+        }
+    }
+    qh_setfree(qh, &ints);
+}/*testSetdelSetadd*/
+
+void testSetappendSet(qhT *qh, int numInts, int *intarray, int checkEvery)
+{
+    setT *ints=qh_setnew(qh, 1);
+    setT *ints2;
+    int i,j,k;
+
+    qh_fprintf(qh, stderr, 8016, "\n\nTesting qh_setappend_set 0..%d. Test", numInts-1);
+    for(j=0; j<numInts; j++){
+        if(log_i(qh, ints, "j", j, numInts, numInts)){
+            for(i= qh_setsize(qh, ints); i<j; i++){
+                qh_setappend(qh, &ints, intarray+i);
+            }
+            if(checkEvery==1){
+                checkSetContents(qh, "qh_setappend", ints, j, 0, -1, -1);
+            }
+            ints2= qh_setnew(qh, j==0 ? 0 : j-1);  /* One less than needed */
+            for(i= 0; i<=j && i<=20; i++){  /* otherwise too slow */
+                if(log_i(qh, ints, "", i, numInts, numInts)){
+                    for(k= qh_setsize(qh, ints2); k<i; k++){
+                        qh_setappend(qh, &ints2, intarray+k);
+                    }
+                    if(checkEvery==1){
+                        checkSetContents(qh, "qh_setappend 2", ints2, i, 0, -1, -1);
+                    }
+                    qh_setappend_set(qh, &ints, ints2);
+                    checkSetContents(qh, "qh_setappend_set", ints, i+j, 0, (j==0 ? -1 : 0), -1);
+                    qh_settruncate(qh, ints, j);
+                    if(checkEvery==1){
+                        checkSetContents(qh, "qh_settruncate", ints, j, 0, -1, -1);
+                    }
+                }
+            }
+            qh_setfree(qh, &ints2);
+        }
+    }
+    qh_setfree(qh, &ints);
+}/*testSetappendSet*/
+
+void testSetcompactCopy(qhT *qh, int numInts, int *intarray, int checkEvery)
+{
+    setT *ints= qh_setnew(qh, 20);
+    setT *ints2= NULL;
+    int i,j,k;
+
+    qh_fprintf(qh, stderr, 8017, "\n\nTesting qh_setcompact and qh_setcopy 0..%d. Test", numInts-1);
+    for(j=0; j<numInts; j++){
+        if(log_i(qh, ints, "j", j, numInts, checkEvery)){
+            for(i= qh_setsize(qh, ints); i<j; i++){  /* Test i<j to test the empty set */
+                for(k= 0; k<i%7; k++){
+                    qh_setappend(qh, &ints, NULL);
+                }
+                qh_setappend(qh, &ints, intarray+i);
+            }
+            qh_setfree(qh, &ints2);
+            ints2= qh_setcopy(qh, ints, 0);
+            qh_setcompact(qh, ints);
+            qh_setcompact(qh, ints2);
+            checkSetContents(qh, "qh_setcompact", ints, j, 0, 0, -1);
+            checkSetContents(qh, "qh_setcompact", ints2, j, 0, 0, -1);
+            qh_setcompact(qh, ints);
+            checkSetContents(qh, "qh_setcompact", ints, j, 0, 0, -1);
+        }
+    }
+    qh_setfree(qh, &ints);
+    qh_setfree(qh, &ints2);
+}/*testSetcompactCopy*/
+
+void testSetdelsortedEtc(qhT *qh, int numInts, int *intarray, int checkEvery)
+{
+    setT *ints= qh_setnew(qh, 1);
+    setT *ints2= NULL;
+    int i,j;
+
+    qh_fprintf(qh, stderr, 8018, "\n\nTesting qh_setdel*, qh_setaddsorted, and  0..%d. Test", numInts-1);
+    for(j=0; j<numInts; j++){
+        if(log_i(qh, ints, "j", j, numInts, checkEvery)){
+            for(i= qh_setsize(qh, ints); i<j; i++){  /* Test i<j to test the empty set */
+                qh_setaddsorted(qh, &ints, intarray+i);
+            }
+            checkSetContents(qh, "qh_setaddsorted", ints, j, 0, 0, -1);
+            if(j>3){
+                qh_setdelsorted(ints, intarray+i/2);
+                checkSetContents(qh, "qh_setdelsorted", ints, j-1, 0, i/2+1, -1);
+                qh_setaddsorted(qh, &ints, intarray+i/2);
+                checkSetContents(qh, "qh_setaddsorted i/2", ints, j, 0, 0, -1);
+            }
+            qh_setdellast(ints);
+            checkSetContents(qh, "qh_setdellast", ints, (j ? j-1 : 0), 0, -1, -1);
+            if(j>0){
+                qh_setaddsorted(qh, &ints, intarray+j-1);
+                checkSetContents(qh, "qh_setaddsorted j-1", ints, j, 0, -1, -1);
+            }
+            if(j>4){
+                qh_setdelnthsorted(qh, ints, i/2);
+                if (checkEvery==1)
+                  checkSetContents(qh, "qh_setdelnthsorted", ints, j-1, 0, i/2+1, -1);
+                /* test qh_setdelnth and move-to-front */
+                qh_setdelsorted(ints, intarray+i/2+1);
+                checkSetContents(qh, "qh_setdelsorted 2", ints, j-2, 0, i/2+2, -1);
+                qh_setaddsorted(qh, &ints, intarray+i/2+1);
+                if (checkEvery==1)
+                  checkSetContents(qh, "qh_setaddsorted i/2+1", ints, j-1, 0, i/2+1, -1);
+                qh_setaddsorted(qh, &ints, intarray+i/2);
+                checkSetContents(qh, "qh_setaddsorted i/2 again", ints, j, 0, -1, -1);
+            }
+            qh_setfree(qh, &ints2);
+            ints2= qh_setcopy(qh, ints, 0);
+            qh_setcompact(qh, ints);
+            qh_setcompact(qh, ints2);
+            checkSetContents(qh, "qh_setcompact", ints, j, 0, 0, -1);
+            checkSetContents(qh, "qh_setcompact 2", ints2, j, 0, 0, -1);
+            qh_setcompact(qh, ints);
+            checkSetContents(qh, "qh_setcompact 3", ints, j, 0, 0, -1);
+            qh_setfree(qh, &ints2);
+        }
+    }
+    qh_setfreelong(qh, &ints);
+    if(ints){
+        qh_setfree(qh, &ints); /* Was quick memory */
+    }
+}/*testSetdelsortedEtc*/
+
+void testSetequalInEtc(qhT *qh, int numInts, int *intarray, int checkEvery)
+{
+    setT *ints= NULL;
+    setT *ints2= NULL;
+    setT *ints3= NULL;
+    int i,j,n;
+
+    qh_fprintf(qh, stderr, 8019, "\n\nTesting qh_setequal*, qh_setin*, qh_setdel, qh_setdelnth, and qh_setlarger 0..%d. Test", numInts-1);
+    for(j=0; j<numInts; j++){
+        if(log_i(qh, ints, "j", j, numInts, checkEvery)){
+            n= qh_setsize(qh, ints);
+            qh_setlarger(qh, &ints);
+            checkSetContents(qh, "qh_setlarger", ints, n, 0, -1, -1);
+            for(i= qh_setsize(qh, ints); i<j; i++){  /* Test i<j to test the empty set */
+                qh_setappend(qh, &ints, intarray+i);
+            }
+            checkSetContents(qh, "qh_setappend", ints, j, 0, -1, -1);
+            if(!qh_setequal(ints, ints)){
+                qh_fprintf(qh, stderr, 6300, "testSetequalInEtc: set not equal to itself at length %d\n", j);
+                error_count++;
+            }
+            if(j==0 && !qh_setequal(ints, ints2)){
+                qh_fprintf(qh, stderr, 6323, "testSetequalInEtc: empty set not equal to null set\n");
+                error_count++;
+            }
+            if(j>0){
+                if(qh_setequal(ints, ints2)){
+                    qh_fprintf(qh, stderr, 6324, "testSetequalInEtc: non-empty set equal to empty set\n", j);
+                    error_count++;
+                }
+                qh_setfree(qh, &ints3);
+                ints3= qh_setcopy(qh, ints, 0);
+                checkSetContents(qh, "qh_setreplace", ints3, j, 0, -1, -1);
+                qh_setreplace(qh, ints3, intarray+j/2, intarray+j/2+1);
+                if(j==1){
+                    checkSetContents(qh, "qh_setreplace 2", ints3, j, j/2+1, -1, -1);
+                }else if(j==2){
+                    checkSetContents(qh, "qh_setreplace 3", ints3, j, 0, j/2+1, -1);
+                }else{
+                    checkSetContents(qh, "qh_setreplace 3", ints3, j, 0, j/2+1, j/2+1);
+                }
+                if(qh_setequal(ints, ints3)){
+                    qh_fprintf(qh, stderr, 6325, "testSetequalInEtc: modified set equal to original set at %d/2\n", j);
+                    error_count++;
+                }
+                if(!qh_setequal_except(ints, intarray+j/2, ints3, intarray+j/2+1)){
+                    qh_fprintf(qh, stderr, 6326, "qh_setequal_except: modified set not equal to original set except modified\n", j);
+                    error_count++;
+                }
+                if(qh_setequal_except(ints, intarray+j/2, ints3, intarray)){
+                    qh_fprintf(qh, stderr, 6327, "qh_setequal_except: modified set equal to original set with wrong excepts\n", j);
+                    error_count++;
+                }
+                if(!qh_setequal_skip(ints, j/2, ints3, j/2)){
+                    qh_fprintf(qh, stderr, 6328, "qh_setequal_skip: modified set not equal to original set except modified\n", j);
+                    error_count++;
+                }
+                if(j>2 && qh_setequal_skip(ints, j/2, ints3, 0)){
+                    qh_fprintf(qh, stderr, 6329, "qh_setequal_skip: modified set equal to original set with wrong excepts\n", j);
+                    error_count++;
+                }
+                if(intarray+j/2+1!=qh_setdel(ints3, intarray+j/2+1)){
+                    qh_fprintf(qh, stderr, 6330, "qh_setdel: failed to find added element\n", j);
+                    error_count++;
+                }
+                checkSetContents(qh, "qh_setdel", ints3, j-1, 0, j-1, (j==1 ? -1 : j/2+1));  /* swaps last element with deleted element */
+                if(j>3){
+                    qh_setdelnth(qh, ints3, j/2); /* Delete at the same location as the original replace, for only one out-of-order element */
+                    checkSetContents(qh, "qh_setdelnth", ints3, j-2, 0, j-2, (j==2 ? -1 : j/2+1));
+                }
+                if(qh_setin(ints3, intarray+j/2)){
+                    qh_fprintf(qh, stderr, 6331, "qh_setin: found deleted element\n");
+                    error_count++;
+                }
+                if(j>4 && !qh_setin(ints3, intarray+1)){
+                    qh_fprintf(qh, stderr, 6332, "qh_setin: did not find second element\n");
+                    error_count++;
+                }
+                if(j>4 && !qh_setin(ints3, intarray+j-2)){
+                    qh_fprintf(qh, stderr, 6333, "qh_setin: did not find last element\n");
+                    error_count++;
+                }
+                if(-1!=qh_setindex(ints2, intarray)){
+                    qh_fprintf(qh, stderr, 6334, "qh_setindex: found element in empty set\n");
+                    error_count++;
+                }
+                if(-1!=qh_setindex(ints3, intarray+j/2)){
+                    qh_fprintf(qh, stderr, 6335, "qh_setindex: found deleted element in set\n");
+                    error_count++;
+                }
+                if(0!=qh_setindex(ints, intarray)){
+                    qh_fprintf(qh, stderr, 6336, "qh_setindex: did not find first in set\n");
+                    error_count++;
+                }
+                if(j-1!=qh_setindex(ints, intarray+j-1)){
+                    qh_fprintf(qh, stderr, 6337, "qh_setindex: did not find last in set\n");
+                    error_count++;
+                }
+            }
+            qh_setfree(qh, &ints2);
+        }
+    }
+    qh_setfree(qh, &ints3);
+    qh_setfreelong(qh, &ints);
+    if(ints){
+        qh_setfree(qh, &ints); /* Was quick memory */
+    }
+}/*testSetequalInEtc*/
+
+
+void testSetlastEtc(qhT *qh, int numInts, int *intarray, int checkEvery)
+{
+    setT *ints= NULL;
+    setT *ints2= NULL;
+    int i,j,prepend;
+
+    qh_fprintf(qh, stderr, 8020, "\n\nTesting qh_setlast, qh_setnew_delnthsorted, qh_setunique, and qh_setzero 0..%d. Test", numInts-1);
+    for(j=0; j<numInts; j++){
+        if(log_i(qh, ints, "j", j, numInts, checkEvery)){
+            for(i= qh_setsize(qh, ints); i<j; i++){  /* Test i<j to test the empty set */
+                if(!qh_setunique(qh, &ints, intarray+i)){
+                    qh_fprintf(qh, stderr, 6340, "qh_setunique: not able to append next element %d\n", i);
+                    error_count++;
+                }
+                if(checkEvery==1){
+                    checkSetContents(qh, "qh_setunique", ints, i+1, 0, -1, -1);
+                }
+                if(qh_setunique(qh, &ints, intarray+i)){
+                    qh_fprintf(qh, stderr, 6341, "qh_setunique: appended next element twice %d\n", i);
+                    error_count++;
+                }
+                if(qh_setunique(qh, &ints, intarray+i/2)){
+                    qh_fprintf(qh, stderr, 6346, "qh_setunique: appended middle element twice %d/2\n", i);
+                    error_count++;
+                }
+            }
+            checkSetContents(qh, "qh_setunique 2", ints, j, 0, -1, -1);
+            if(j==0 && NULL!=qh_setlast(ints)){
+                qh_fprintf(qh, stderr, 6339, "qh_setlast: returned last element of empty set\n");
+                error_count++;
+            }
+            if(j>0){
+                if(intarray+j-1!=qh_setlast(ints)){
+                    qh_fprintf(qh, stderr, 6338, "qh_setlast: wrong last element\n");
+                    error_count++;
+                }
+                prepend= (j<100 ? j/4 : 0);
+                ints2= qh_setnew_delnthsorted(qh, ints, qh_setsize(qh, ints), j/2, prepend);
+                if(qh_setsize(qh, ints2)!=j+prepend-1){
+                    qh_fprintf(qh, stderr, 6345, "qh_setnew_delnthsorted: Expecting %d elements, got %d\n", j+prepend-1, qh_setsize(qh, ints2));
+                    error_count++;
+                }
+                /* Define prepended elements.  Otherwise qh_setdelnthsorted may fail */
+                for(i= 0; i<prepend; i++){
+                    void **p= &SETelem_(ints2, i);
+                    *p= intarray+0;
+                }
+                for(i= 0; i<prepend; i++){
+                    qh_setdelnthsorted(qh, ints2, 0);  /* delete undefined prefix */
+                }
+                checkSetContents(qh, "qh_setnew_delnthsorted", ints2, j-1, 0, j/2+1, -1);
+                if(j>2){
+                    qh_setzero(qh, ints2, j/2, j-1);  /* max size may be j-1 */
+                    if(qh_setsize(qh, ints2)!=j-1){
+                        qh_fprintf(qh, stderr, 6342, "qh_setzero: Expecting %d elements, got %d\n", j, qh_setsize(qh, ints2));
+                        error_count++;
+                    }
+                    qh_setcompact(qh, ints2);
+                    checkSetContents(qh, "qh_setzero", ints2, j/2, 0, -1, -1);
+                }
+            }
+            qh_setfree(qh, &ints2);
+        }
+    }
+    qh_setfreelong(qh, &ints);
+    if(ints){
+        qh_setfree(qh, &ints); /* Was quick memory */
+    }
+}/*testSetlastEtc*/
+
+void testSettemp(qhT *qh, int numInts, int *intarray, int checkEvery)
+{
+    setT *ints= NULL;
+    setT *ints2= NULL;
+    setT *ints3= NULL;
+    int i,j;
+
+    qh_fprintf(qh, stderr, 8021, "\n\nTesting qh_settemp* 0..%d. Test", numInts-1);
+    for(j=0; j<numInts; j++){
+        if(log_i(qh, ints, "j", j, numInts, checkEvery)){
+            if(j<20){
+                for(i=0; i<j; i++){
+                    ints2= qh_settemp(qh, j);
+                }
+                qh_settempfree_all(qh);
+            }
+            for(i= qh_setsize(qh, ints); i<j; i++){  /* Test i<j to test the empty set */
+                qh_setappend(qh, &ints, intarray+i);
+            }
+            ints2= qh_settemp(qh, j);
+            if(j>0){
+                qh_settemppush(qh, ints);
+                ints3= qh_settemppop(qh);
+                if(ints!=ints3){
+                    qh_fprintf(qh, stderr, 6343, "qh_settemppop: didn't pop the push\n");
+                    error_count++;
+                }
+            }
+            qh_settempfree(qh, &ints2);
+        }
+    }
+    qh_setfreelong(qh, &ints);
+    if(ints){
+        qh_setfree(qh, &ints); /* Was quick memory */
+    }
+}/*testSettemp*/
+
+/* Check that a set contains count elements
+   Ranges are consecutive (e.g., 1,2,3,...) starting with first, mid, and last
+   Use -1 for missing ranges
+   Returns -1 if should check results
+*/
+int log_i(qhT *qh, setT *set, const char *s, int i, int numInts, int checkEvery)
+{
+    int j= i;
+    int scale= 1;
+    int e= 0;
+    int *i2, **i2p;
+
+    if(*s || checkEvery==1){
+        if(i<10){
+            qh_fprintf(qh, stderr, 8004, " %s%d", s, i);
+        }else{
+            if(i==11 && checkEvery==1){
+                qh_fprintf(qh, stderr, 8005, "\nResults after 10: ");
+                FOREACHint_(set){
+                    qh_fprintf(qh, stderr, 8006, " %d", *i2);
+                }
+                qh_fprintf(qh, stderr, 8007, " Continue");
+            }
+            while((j= j/10)>=1){
+                scale *= 10;
+                e++;
+            }
+            if(i==numInts-1){
+                qh_fprintf(qh, stderr, 8008, " %s%d", s, i);
+            }else if(i==scale){
+                if(i<=1000){
+                    qh_fprintf(qh, stderr, 8010, " %s%d", s, i);
+                }else{
+                    qh_fprintf(qh, stderr, 8009, " %s1e%d", s, e);
+                }
+            }
+        }
+    }
+    if(i<1000 || i%checkEvery==0 || i== scale || i==numInts-1){
+        return 1;
+    }
+    return 0;
+}/*log_i*/
+
+/* Check that a set contains count elements
+   Ranges are consecutive (e.g., 1,2,3,...) starting with first, mid, and last
+   Use -1 for missing ranges
+*/
+void checkSetContents(qhT *qh, const char *name, setT *set, int count, int rangeA, int rangeB, int rangeC)
+{
+
+    i2T *i2, **i2p;
+    int i2_i, i2_n;
+    int prev= -1; /* avoid warning */
+    int i;
+    int first= -3;
+    int second= -3;
+    int rangeCount=1;
+    int actualSize= 0;
+
+    qh_setcheck(qh, set, name, 0);
+    if(set){
+        SETreturnsize_(set, actualSize);  /* normally used only when speed is critical */
+        if(*qh_setendpointer(set)!=NULL){
+            qh_fprintf(qh, stderr, 6344, "%s: qh_setendpointer(set), 0x%x, is not NULL terminator of set 0x%x", name, qh_setendpointer(set), set);
+            error_count++;
+        }
+    }
+    if(actualSize!=qh_setsize(qh, set)){
+        qh_fprintf(qh, stderr, 6305, "%s: SETreturnsize_(qh) returned %d while qh_setsize(qh) returns %d\n", name, actualSize, qh_setsize(qh, set));
+        error_count++;
+    }else if(actualSize!=count){
+        qh_fprintf(qh, stderr, 6306, "%s: Expecting %d elements for set.  Got %d elements\n", name, count, actualSize);
+        error_count++;
+    }
+    if(SETempty_(set)){
+        if(count!=0){
+            qh_fprintf(qh, stderr, 6307, "%s: Got empty set instead of count %d, rangeA %d, rangeB %d, rangeC %d\n", name, count, rangeA, rangeB, rangeC);
+            error_count++;
+        }
+    }else{
+        /* Must be first, otherwise trips msvc 8 */
+        i2T **p= SETaddr_(set, i2T);
+        if(*p!=SETfirstt_(set, i2T)){
+            qh_fprintf(qh, stderr, 6309, "%s: SETaddr_(set, i2t) [%p] is not the same as SETfirst_(set) [%p]\n", name, SETaddr_(set, i2T), SETfirst_(set));
+            error_count++;
+        }
+        first= *(int *)SETfirst_(set);
+        if(SETfirst_(set)!=SETfirstt_(set, i2T)){
+            qh_fprintf(qh, stderr, 6308, "%s: SETfirst_(set) [%p] is not the same as SETfirstt_(set, i2T [%p]\n", name, SETfirst_(set), SETfirstt_(set, i2T));
+            error_count++;
+        }
+        if(qh_setsize(qh, set)>1){
+            second= *(int *)SETsecond_(set);
+            if(SETsecond_(set)!=SETsecondt_(set, i2T)){
+                qh_fprintf(qh, stderr, 6310, "%s: SETsecond_(set) [%p] is not the same as SETsecondt_(set, i2T) [%p]\n", name, SETsecond_(set), SETsecondt_(set, i2T));
+                error_count++;
+            }
+        }
+    }
+    /* Test first run of ints in set*/
+    i= 0;
+    FOREACHint_(set){
+        if(i2!=SETfirst_(set) && *i2!=prev+1){
+            break;
+        }
+        prev= *i2;
+        if(SETindex_(set, i2)!=i){
+            qh_fprintf(qh, stderr, 6311, "%s: Expecting SETindex_(set, pointer-to-%d) to be %d.  Got %d\n", name, *i2, i, SETindex_(set, i2));
+            error_count++;;
+        }
+        if(i2!=SETref_(i2)){
+            qh_fprintf(qh, stderr, 6312, "%s: SETref_(i2) [%p] does not point to i2 (the %d'th element)\n", name, SETref_(i2), i);
+            error_count++;;
+        }
+        i++;
+    }
+    FOREACHint_i_(qh, set){
+        /* Must be first conditional, otherwise it trips up msvc 8 */
+        i2T **p= SETelemaddr_(set, i2_i, i2T);
+        if(i2!=*p){
+            qh_fprintf(qh, stderr, 6320, "%s: SETelemaddr_(set, %d, i2T) [%p] does not point to i2\n", name, i2_i, SETelemaddr_(set, i2_i, int));
+            error_count++;;
+        }
+        if(i2_i==0){
+            if(first!=*i2){
+                qh_fprintf(qh, stderr, 6314, "%s: First element is %d instead of SETfirst %d\n", name, *i2, first);
+                error_count++;;
+            }
+            if(rangeA!=*i2){
+                qh_fprintf(qh, stderr, 6315, "%s: starts with %d instead of rangeA %d\n", name, *i2, rangeA);
+                error_count++;;
+            }
+            prev= rangeA;
+        }else{
+            if(i2_i==1 && second!=*i2){
+                qh_fprintf(qh, stderr, 6316, "%s: Second element is %d instead of SETsecond %d\n", name, *i2, second);
+                error_count++;;
+            }
+            if(prev+1==*i2){
+                prev++;
+            }else{
+                if(*i2==rangeB){
+                    prev= rangeB;
+                    rangeB= -1;
+                    rangeCount++;
+                }else if(rangeB==-1 && *i2==rangeC){
+                    prev= rangeC;
+                    rangeC= -1;
+                    rangeCount++;
+                }else{
+                    prev++;
+                    qh_fprintf(qh, stderr, 6317, "%s: Expecting %d'th element to be %d.  Got %d\n", name, i2_i, prev, *i2);
+                    error_count++;
+                }
+            }
+        }
+        if(i2!=SETelem_(set, i2_i)){
+            qh_fprintf(qh, stderr, 6318, "%s: SETelem_(set, %d) [%p] is not i2 [%p] (the %d'th element)\n", name, i2_i, SETelem_(set, i2_i), i2, i2_i);
+            error_count++;;
+        }
+        if(SETelemt_(set, i2_i, i2T)!=SETelem_(set, i2_i)){   /* Normally SETelemt_ is used for generic sets */
+            qh_fprintf(qh, stderr, 6319, "%s: SETelemt_(set, %d, i2T) [%p] is not SETelem_(set, %d) [%p] (the %d'th element)\n", name, i2_i, SETelemt_(set, i2_i, int), i2_i, SETelem_(set, i2_i), i2_i);
+            error_count++;;
+        }
+    }
+    if(error_count>=MAXerrorCount){
+        qh_fprintf(qh, stderr, 8011, "testqset: Stop testing after %d errors\n", error_count);
+        exit(1);
+    }
+}/*checkSetContents*/
+
diff --git a/xs/src/qhull/src/testqset_r/testqset_r.pro b/xs/src/qhull/src/testqset_r/testqset_r.pro
new file mode 100644
index 0000000000..951e0624e8
--- /dev/null
+++ b/xs/src/qhull/src/testqset_r/testqset_r.pro
@@ -0,0 +1,30 @@
+# -------------------------------------------------
+# testqset_r.pro -- Qt project file for testqset_r.exe
+# -------------------------------------------------
+
+include(../qhull-warn.pri)
+
+TARGET = testqset_r
+
+DESTDIR = ../../bin
+TEMPLATE = app
+CONFIG += console warn_on
+CONFIG -= qt
+CONFIG += qhull_warn_conversion
+
+build_pass:CONFIG(debug, debug|release){
+   OBJECTS_DIR = Debug
+}else:build_pass:CONFIG(release, debug|release){
+   OBJECTS_DIR = Release
+}
+
+INCLUDEPATH += ..
+
+SOURCES += testqset_r.c
+SOURCES += ../libqhull_r/qset_r.c
+SOURCES += ../libqhull_r/mem_r.c
+SOURCES += ../libqhull_r/usermem_r.c
+
+HEADERS += ../libqhull_r/mem_r.h
+HEADERS += ../libqhull_r/qset_r.h
+
diff --git a/xs/src/qhull/src/user_eg/user_eg.c b/xs/src/qhull/src/user_eg/user_eg.c
new file mode 100644
index 0000000000..9c5fee51b3
--- /dev/null
+++ b/xs/src/qhull/src/user_eg/user_eg.c
@@ -0,0 +1,330 @@
+/*<html><pre>  -<a                             href="../libqhull/qh-user.htm"
+  >-------------------------------</a><a name="TOP">-</a>
+
+  user_eg.c
+  sample code for calling qhull() from an application
+
+  call with:
+
+     user_eg "cube/diamond options" "delaunay options" "halfspace options"
+
+  for example:
+
+     user_eg                             # return summaries
+
+     user_eg "n" "o" "Fp"                # return normals, OFF, points
+
+     user_eg "n Qt" "o" "Fp"             # triangulated cube
+
+     user_eg "QR0 p" "QR0 v p" "QR0 Fp"  # rotate input and return points
+                                         # 'v' returns Voronoi
+                                         # transform is rotated for halfspaces
+
+   main() makes three runs of qhull.
+
+     1) compute the convex hull of a cube
+
+     2a) compute the Delaunay triangulation of random points
+
+     2b) find the Delaunay triangle closest to a point.
+
+     3) compute the halfspace intersection of a diamond
+
+ notes:
+
+   For another example, see main() in unix.c and user_eg2.c.
+   These examples, call qh_qhull() directly.  They allow
+   tighter control on the code loaded with Qhull.
+
+   For a C++ example, see user_eg3/user_eg3_r.cpp
+
+   Summaries are sent to stderr if other output formats are used
+
+   compiled by 'make bin/user_eg'
+
+   see libqhull.h for data structures, macros, and user-callable functions.
+*/
+
+#define qh_QHimport
+#include "libqhull/qhull_a.h"
+
+/*-------------------------------------------------
+-internal function prototypes
+*/
+void print_summary(void);
+void makecube(coordT *points, int numpoints, int dim);
+void makeDelaunay(coordT *points, int numpoints, int dim, int seed);
+void findDelaunay(int dim);
+void makehalf(coordT *points, int numpoints, int dim);
+
+/*-------------------------------------------------
+-print_summary()
+*/
+void print_summary(void) {
+  facetT *facet;
+  int k;
+
+  printf("\n%d vertices and %d facets with normals:\n",
+                 qh num_vertices, qh num_facets);
+  FORALLfacets {
+    for (k=0; k < qh hull_dim; k++)
+      printf("%6.2g ", facet->normal[k]);
+    printf("\n");
+  }
+}
+
+/*--------------------------------------------------
+-makecube- set points to vertices of cube
+  points is numpoints X dim
+*/
+void makecube(coordT *points, int numpoints, int dim) {
+  int j,k;
+  coordT *point;
+
+  for (j=0; j<numpoints; j++) {
+    point= points + j*dim;
+    for (k=dim; k--; ) {
+      if (j & ( 1 << k))
+        point[k]= 1.0;
+      else
+        point[k]= -1.0;
+    }
+  }
+} /*.makecube.*/
+
+/*--------------------------------------------------
+-makeDelaunay- set points for dim Delaunay triangulation of random points
+  points is numpoints X dim.
+notes:
+  makeDelaunay() in user_eg2.c uses qh_setdelaunay() to project points in place.
+*/
+void makeDelaunay(coordT *points, int numpoints, int dim, int seed) {
+  int j,k;
+  coordT *point, realr;
+
+  printf("seed: %d\n", seed);
+  qh_RANDOMseed_( seed);
+  for (j=0; j<numpoints; j++) {
+    point= points + j*dim;
+    for (k= 0; k < dim; k++) {
+      realr= qh_RANDOMint;
+      point[k]= 2.0 * realr/(qh_RANDOMmax+1) - 1.0;
+    }
+  }
+} /*.makeDelaunay.*/
+
+/*--------------------------------------------------
+-findDelaunay- find Delaunay triangle for [0.5,0.5,...]
+  assumes dim < 100
+notes:
+  calls qh_setdelaunay() to project the point to a parabaloid
+warning:
+  This is not implemented for tricoplanar facets ('Qt'),
+  See <a href="../html/qh-code.htm#findfacet">locate a facet with qh_findbestfacet()</a>
+*/
+void findDelaunay(int dim) {
+  int k;
+  coordT point[ 100];
+  boolT isoutside;
+  realT bestdist;
+  facetT *facet;
+  vertexT *vertex, **vertexp;
+
+  for (k= 0; k < dim; k++)
+    point[k]= 0.5;
+  qh_setdelaunay(dim+1, 1, point);
+  facet= qh_findbestfacet(point, qh_ALL, &bestdist, &isoutside);
+  if (facet->tricoplanar) {
+    fprintf(stderr, "findDelaunay: not implemented for triangulated, non-simplicial Delaunay regions (tricoplanar facet, f%d).\n",
+       facet->id);
+    qh_errexit(qh_ERRqhull, facet, NULL);
+  }
+  FOREACHvertex_(facet->vertices) {
+    for (k=0; k < dim; k++)
+      printf("%5.2f ", vertex->point[k]);
+    printf("\n");
+  }
+} /*.findDelaunay.*/
+
+/*--------------------------------------------------
+-makehalf- set points to halfspaces for a (dim)-dimensional diamond
+  points is numpoints X dim+1
+
+  each halfspace consists of dim coefficients followed by an offset
+*/
+void makehalf(coordT *points, int numpoints, int dim) {
+  int j,k;
+  coordT *point;
+
+  for (j=0; j<numpoints; j++) {
+    point= points + j*(dim+1);
+    point[dim]= -1.0; /* offset */
+    for (k=dim; k--; ) {
+      if (j & ( 1 << k))
+        point[k]= 1.0;
+      else
+        point[k]= -1.0;
+    }
+  }
+} /*.makehalf.*/
+
+#define DIM 3     /* dimension of points, must be < 31 for SIZEcube */
+#define SIZEcube (1<<DIM)
+#define SIZEdiamond (2*DIM)
+#define TOTpoints (SIZEcube + SIZEdiamond)
+
+/*--------------------------------------------------
+-main- derived from Qhull-template in user.c
+
+  see program header
+
+  this contains three runs of Qhull for convex hull, Delaunay
+  triangulation or Voronoi vertices, and halfspace intersection
+
+*/
+int main(int argc, char *argv[]) {
+  int dim= DIM;             /* dimension of points */
+  int numpoints;            /* number of points */
+  coordT points[(DIM+1)*TOTpoints]; /* array of coordinates for each point */
+  coordT *rows[TOTpoints];
+  boolT ismalloc= False;    /* True if qhull should free points in qh_freeqhull() or reallocation */
+  char flags[250];          /* option flags for qhull, see qh-quick.htm */
+  FILE *outfile= stdout;    /* output from qh_produce_output()
+                               use NULL to skip qh_produce_output() */
+  FILE *errfile= stderr;    /* error messages from qhull code */
+  int exitcode;             /* 0 if no error from qhull */
+  facetT *facet;            /* set by FORALLfacets */
+  int curlong, totlong;     /* memory remaining after qh_memfreeshort */
+  int i;
+
+  QHULL_LIB_CHECK
+
+  printf("This is the output from user_eg.c\n\n\
+It shows how qhull() may be called from an application using the qhull\n\
+shared library.  user_eg is not part of qhull itself.  If it appears\n\
+accidently, please remove user_eg.c from your project.  If it fails\n\
+immediately, user_eg.c was incorrectly linked to the reentrant library.\n\
+Also try 'user_eg T1 2>&1'\n\n");
+
+#if qh_QHpointer  /* see user.h */
+  if (qh_qh){
+      printf("QH6233: Qhull link error.  The global variable qh_qh was not initialized\n\
+to NULL by global.c.  Please compile user_eg.c with -Dqh_QHpointer_dllimport\n\
+as well as -Dqh_QHpointer, or use libqhullstatic, or use a different tool chain.\n\n");
+      return -1;
+  }
+#endif
+
+  /*
+    Run 1: convex hull
+  */
+  printf( "\ncompute convex hull of cube after rotating input\n");
+  sprintf(flags, "qhull s Tcv %s", argc >= 2 ? argv[1] : "");
+  numpoints= SIZEcube;
+  makecube(points, numpoints, DIM);
+  for (i=numpoints; i--; )
+    rows[i]= points+dim*i;
+  qh_printmatrix(outfile, "input", rows, numpoints, dim);
+  exitcode= qh_new_qhull(dim, numpoints, points, ismalloc,
+                      flags, outfile, errfile);
+  if (!exitcode) {                  /* if no error */
+    /* 'qh facet_list' contains the convex hull */
+    print_summary();
+    FORALLfacets {
+       /* ... your code ... */
+    }
+  }
+  qh_freeqhull(!qh_ALL);                   /* free long memory  */
+  qh_memfreeshort(&curlong, &totlong);    /* free short memory and memory allocator */
+  if (curlong || totlong)
+    fprintf(errfile, "qhull internal warning (user_eg, #1): did not free %d bytes of long memory (%d pieces)\n", totlong, curlong);
+
+  /*
+    Run 2: Delaunay triangulation
+  */
+
+  printf( "\ncompute %d-d Delaunay triangulation\n", dim);
+  sprintf(flags, "qhull s d Tcv %s", argc >= 3 ? argv[2] : "");
+  numpoints= SIZEcube;
+  makeDelaunay(points, numpoints, dim, (int)time(NULL));
+  for (i=numpoints; i--; )
+    rows[i]= points+dim*i;
+  qh_printmatrix(outfile, "input", rows, numpoints, dim);
+  exitcode= qh_new_qhull(dim, numpoints, points, ismalloc,
+                      flags, outfile, errfile);
+  if (!exitcode) {                  /* if no error */
+    /* 'qh facet_list' contains the convex hull */
+    /* If you want a Voronoi diagram ('v') and do not request output (i.e., outfile=NULL),
+       call qh_setvoronoi_all() after qh_new_qhull(). */
+    print_summary();
+    FORALLfacets {
+       /* ... your code ... */
+    }
+    printf( "\nfind %d-d Delaunay triangle closest to [0.5, 0.5, ...]\n", dim);
+    exitcode= setjmp(qh errexit);
+    if (!exitcode) {
+      /* Trap Qhull errors in findDelaunay().  Without the setjmp(), Qhull
+         will exit() after reporting an error */
+      qh NOerrexit= False;
+      findDelaunay(DIM);
+    }
+    qh NOerrexit= True;
+  }
+#if qh_QHpointer  /* see user.h */
+  {
+    qhT *oldqhA, *oldqhB;
+    coordT pointsB[DIM*TOTpoints]; /* array of coordinates for each point */
+
+    printf( "\nsave first triangulation and compute a new triangulation\n");
+    oldqhA= qh_save_qhull();
+    sprintf(flags, "qhull s d Tcv %s", argc >= 3 ? argv[2] : "");
+    numpoints= SIZEcube;
+    makeDelaunay(pointsB, numpoints, dim, (int)time(NULL)+1);
+    for (i=numpoints; i--; )
+      rows[i]= pointsB+dim*i;
+    qh_printmatrix(outfile, "input", rows, numpoints, dim);
+    exitcode= qh_new_qhull(dim, numpoints, pointsB, ismalloc,
+                      flags, outfile, errfile);
+    if (!exitcode)
+      print_summary();
+    printf( "\nsave second triangulation and restore first one\n");
+    oldqhB= qh_save_qhull();
+    qh_restore_qhull(&oldqhA);
+    print_summary();
+    printf( "\nfree first triangulation and restore second one.\n");
+    qh_freeqhull(qh_ALL);               /* free short and long memory used by first call */
+                                         /* do not use qh_memfreeshort */
+    qh_restore_qhull(&oldqhB);
+    print_summary();
+  }
+#endif
+  qh_freeqhull(!qh_ALL);                 /* free long memory */
+  qh_memfreeshort(&curlong, &totlong);  /* free short memory and memory allocator */
+  if (curlong || totlong)
+    fprintf(errfile, "qhull internal warning (user_eg, #2): did not free %d bytes of long memory (%d pieces)\n", totlong, curlong);
+
+  /*
+    Run 3: halfspace intersection about the origin
+  */
+  printf( "\ncompute halfspace intersection about the origin for a diamond\n");
+  sprintf(flags, "qhull H0 s Tcv %s", argc >= 4 ? argv[3] : "Fp");
+  numpoints= SIZEcube;
+  makehalf(points, numpoints, dim);
+  for (i=numpoints; i--; )
+    rows[i]= points+(dim+1)*i;
+  qh_printmatrix(outfile, "input as halfspace coefficients + offsets", rows, numpoints, dim+1);
+  /* use qh_sethalfspace_all to transform the halfspaces yourself.
+     If so, set 'qh feasible_point and do not use option 'Hn,...' [it would retransform the halfspaces]
+  */
+  exitcode= qh_new_qhull(dim+1, numpoints, points, ismalloc,
+                      flags, outfile, errfile);
+  if (!exitcode)
+    print_summary();
+  qh_freeqhull(!qh_ALL);
+  qh_memfreeshort(&curlong, &totlong);
+  if (curlong || totlong)  /* could also check previous runs */
+    fprintf(stderr, "qhull internal warning (user_eg, #3): did not free %d bytes of long memory (%d pieces)\n",
+       totlong, curlong);
+  return exitcode;
+} /* main */
+
diff --git a/xs/src/qhull/src/user_eg/user_eg.pro b/xs/src/qhull/src/user_eg/user_eg.pro
new file mode 100644
index 0000000000..9dda010099
--- /dev/null
+++ b/xs/src/qhull/src/user_eg/user_eg.pro
@@ -0,0 +1,11 @@
+# -------------------------------------------------
+# user_eg.pro -- Qt project for Qhull demonstration using shared Qhull library
+#
+# It uses reentrant Qhull
+# -------------------------------------------------
+
+include(../qhull-app-shared_r.pri)
+
+TARGET = user_eg
+
+SOURCES += user_eg_r.c
diff --git a/xs/src/qhull/src/user_eg/user_eg_r.c b/xs/src/qhull/src/user_eg/user_eg_r.c
new file mode 100644
index 0000000000..21b0ccf4e9
--- /dev/null
+++ b/xs/src/qhull/src/user_eg/user_eg_r.c
@@ -0,0 +1,326 @@
+/*<html><pre>  -<a                             href="../libqhull_r/qh-user_r.htm"
+  >-------------------------------</a><a name="TOP">-</a>
+
+  user_eg_r.c
+  sample code for calling qhull() from an application.  Uses reentrant libqhull_r
+
+  call with:
+
+     user_eg "cube/diamond options" "delaunay options" "halfspace options"
+
+  for example:
+
+     user_eg                             # return summaries
+
+     user_eg "n" "o" "Fp"                # return normals, OFF, points
+
+     user_eg "n Qt" "o" "Fp"             # triangulated cube
+
+     user_eg "QR0 p" "QR0 v p" "QR0 Fp"  # rotate input and return points
+                                         # 'v' returns Voronoi
+                                         # transform is rotated for halfspaces
+
+   main() makes three runs of qhull.
+
+     1) compute the convex hull of a cube
+
+     2a) compute the Delaunay triangulation of random points
+
+     2b) find the Delaunay triangle closest to a point.
+
+     3) compute the halfspace intersection of a diamond
+
+ notes:
+
+   For another example, see main() in unix_r.c and user_eg2_r.c.
+   These examples, call qh_qhull() directly.  They allow
+   tighter control on the code loaded with Qhull.
+
+   For a C++ example, see user_eg3/user_eg3_r.cpp
+
+   Summaries are sent to stderr if other output formats are used
+
+   compiled by 'make bin/user_eg'
+
+   see libqhull.h for data structures, macros, and user-callable functions.
+*/
+
+#define qh_QHimport
+#include "libqhull_r/qhull_ra.h"
+
+/*-------------------------------------------------
+-internal function prototypes
+*/
+void print_summary(qhT *qh);
+void makecube(coordT *points, int numpoints, int dim);
+void makeDelaunay(qhT *qh, coordT *points, int numpoints, int dim, int seed);
+void findDelaunay(qhT *qh, int dim);
+void makehalf(coordT *points, int numpoints, int dim);
+
+/*-------------------------------------------------
+-print_summary(qh)
+*/
+void print_summary(qhT *qh) {
+  facetT *facet;
+  int k;
+
+  printf("\n%d vertices and %d facets with normals:\n",
+                 qh->num_vertices, qh->num_facets);
+  FORALLfacets {
+    for (k=0; k < qh->hull_dim; k++)
+      printf("%6.2g ", facet->normal[k]);
+    printf("\n");
+  }
+}
+
+/*--------------------------------------------------
+-makecube- set points to vertices of cube
+  points is numpoints X dim
+*/
+void makecube(coordT *points, int numpoints, int dim) {
+  int j,k;
+  coordT *point;
+
+  for (j=0; j<numpoints; j++) {
+    point= points + j*dim;
+    for (k=dim; k--; ) {
+      if (j & ( 1 << k))
+        point[k]= 1.0;
+      else
+        point[k]= -1.0;
+    }
+  }
+} /*.makecube.*/
+
+/*--------------------------------------------------
+-makeDelaunay- set points for dim Delaunay triangulation of random points
+  points is numpoints X dim.
+notes:
+  makeDelaunay() in user_eg2.c uses qh_setdelaunay() to project points in place.
+*/
+void makeDelaunay(qhT *qh, coordT *points, int numpoints, int dim, int seed) {
+  int j,k;
+  coordT *point, realr;
+
+  printf("seed: %d\n", seed);
+  qh_RANDOMseed_(qh, seed);
+  for (j=0; j<numpoints; j++) {
+    point= points + j*dim;
+    for (k= 0; k < dim; k++) {
+      realr= qh_RANDOMint;
+      point[k]= 2.0 * realr/(qh_RANDOMmax+1) - 1.0;
+    }
+  }
+} /*.makeDelaunay.*/
+
+/*--------------------------------------------------
+-findDelaunay- find Delaunay triangle for [0.5,0.5,...]
+  assumes dim < 100
+notes:
+  calls qh_setdelaunay() to project the point to a parabaloid
+warning:
+  This is not implemented for tricoplanar facets ('Qt'),
+  See <a href="../html/qh-code.htm#findfacet">locate a facet with qh_findbestfacet()</a>
+*/
+void findDelaunay(qhT *qh, int dim) {
+  int k;
+  coordT point[ 100];
+  boolT isoutside;
+  realT bestdist;
+  facetT *facet;
+  vertexT *vertex, **vertexp;
+
+  for (k= 0; k < dim; k++)
+    point[k]= 0.5;
+  qh_setdelaunay(qh, dim+1, 1, point);
+  facet= qh_findbestfacet(qh, point, qh_ALL, &bestdist, &isoutside);
+  if (facet->tricoplanar) {
+    fprintf(stderr, "findDelaunay: not implemented for triangulated, non-simplicial Delaunay regions (tricoplanar facet, f%d).\n",
+       facet->id);
+    qh_errexit(qh, qh_ERRqhull, facet, NULL);
+  }
+  FOREACHvertex_(facet->vertices) {
+    for (k=0; k < dim; k++)
+      printf("%5.2f ", vertex->point[k]);
+    printf("\n");
+  }
+} /*.findDelaunay.*/
+
+/*--------------------------------------------------
+-makehalf- set points to halfspaces for a (dim)-dimensional diamond
+  points is numpoints X dim+1
+
+  each halfspace consists of dim coefficients followed by an offset
+*/
+void makehalf(coordT *points, int numpoints, int dim) {
+  int j,k;
+  coordT *point;
+
+  for (j=0; j<numpoints; j++) {
+    point= points + j*(dim+1);
+    point[dim]= -1.0; /* offset */
+    for (k=dim; k--; ) {
+      if (j & ( 1 << k))
+        point[k]= 1.0;
+      else
+        point[k]= -1.0;
+    }
+  }
+} /*.makehalf.*/
+
+#define DIM 3     /* dimension of points, must be < 31 for SIZEcube */
+#define SIZEcube (1<<DIM)
+#define SIZEdiamond (2*DIM)
+#define TOTpoints (SIZEcube + SIZEdiamond)
+
+/*--------------------------------------------------
+-main- derived from Qhull-template in user.c
+
+  see program header
+
+  this contains three runs of Qhull for convex hull, Delaunay
+  triangulation or Voronoi vertices, and halfspace intersection
+
+*/
+int main(int argc, char *argv[]) {
+  int dim= DIM;             /* dimension of points */
+  int numpoints;            /* number of points */
+  coordT points[(DIM+1)*TOTpoints]; /* array of coordinates for each point */
+  coordT *rows[TOTpoints];
+  boolT ismalloc= False;    /* True if qhull should free points in qh_freeqhull() or reallocation */
+  char flags[250];          /* option flags for qhull, see qh-quick.htm */
+  FILE *outfile= stdout;    /* output from qh_produce_output()
+                               use NULL to skip qh_produce_output() */
+  FILE *errfile= stderr;    /* error messages from qhull code */
+  int exitcode;             /* 0 if no error from qhull */
+  facetT *facet;            /* set by FORALLfacets */
+  int curlong, totlong;     /* memory remaining after qh_memfreeshort */
+  int i;
+
+  qhT qh_qh;                /* Qhull's data structure.  First argument of most calls */
+  qhT *qh= &qh_qh;
+
+  QHULL_LIB_CHECK
+
+  qh_zero(qh, errfile);
+
+  printf("This is the output from user_eg_r.c\n\n\
+It shows how qhull() may be called from an application using the qhull\n\
+reentrant library.  user_eg is not part of qhull itself.  If it appears\n\
+accidently, please remove user_eg_r.c from your project.  If it fails\n\
+immediately, user_eg_r.c was incorrectly linked to the non-reentrant library.\n\
+Also try 'user_eg T1 2>&1'\n\n");
+
+  /*
+    Run 1: convex hull
+  */
+  printf( "\ncompute convex hull of cube after rotating input\n");
+  sprintf(flags, "qhull s Tcv %s", argc >= 2 ? argv[1] : "");
+  numpoints= SIZEcube;
+  makecube(points, numpoints, DIM);
+  for (i=numpoints; i--; )
+    rows[i]= points+dim*i;
+  qh_printmatrix(qh, outfile, "input", rows, numpoints, dim);
+  exitcode= qh_new_qhull(qh, dim, numpoints, points, ismalloc,
+                      flags, outfile, errfile);
+  if (!exitcode) {                  /* if no error */
+    /* 'qh->facet_list' contains the convex hull */
+    print_summary(qh);
+    FORALLfacets {
+       /* ... your code ... */
+    }
+  }
+  qh_freeqhull(qh, !qh_ALL);                   /* free long memory  */
+  qh_memfreeshort(qh, &curlong, &totlong);    /* free short memory and memory allocator */
+  if (curlong || totlong)
+    fprintf(errfile, "qhull internal warning (user_eg, #1): did not free %d bytes of long memory (%d pieces)\n", totlong, curlong);
+
+  /*
+    Run 2: Delaunay triangulation, reusing the previous qh/qh_qh
+  */
+
+  printf( "\ncompute %d-d Delaunay triangulation\n", dim);
+  sprintf(flags, "qhull s d Tcv %s", argc >= 3 ? argv[2] : "");
+  numpoints= SIZEcube;
+  makeDelaunay(qh, points, numpoints, dim, (int)time(NULL));
+  for (i=numpoints; i--; )
+    rows[i]= points+dim*i;
+  qh_printmatrix(qh, outfile, "input", rows, numpoints, dim);
+  exitcode= qh_new_qhull(qh, dim, numpoints, points, ismalloc,
+                      flags, outfile, errfile);
+  if (!exitcode) {                  /* if no error */
+    /* 'qh->facet_list' contains the convex hull */
+    /* If you want a Voronoi diagram ('v') and do not request output (i.e., outfile=NULL),
+       call qh_setvoronoi_all() after qh_new_qhull(). */
+    print_summary(qh);
+    FORALLfacets {
+       /* ... your code ... */
+    }
+    printf( "\nfind %d-d Delaunay triangle closest to [0.5, 0.5, ...]\n", dim);
+    exitcode= setjmp(qh->errexit);
+    if (!exitcode) {
+      /* Trap Qhull errors in findDelaunay().  Without the setjmp(), Qhull
+         will exit() after reporting an error */
+      qh->NOerrexit= False;
+      findDelaunay(qh, DIM);
+    }
+    qh->NOerrexit= True;
+  }
+  {
+    coordT pointsB[DIM*TOTpoints]; /* array of coordinates for each point */
+
+    qhT qh_qhB;    /* Create a new instance of Qhull (qhB) */
+    qhT *qhB= &qh_qhB;
+    qh_zero(qhB, errfile);
+
+    printf( "\nCompute a new triangulation as a separate instance of Qhull\n");
+    sprintf(flags, "qhull s d Tcv %s", argc >= 3 ? argv[2] : "");
+    numpoints= SIZEcube;
+    makeDelaunay(qhB, pointsB, numpoints, dim, (int)time(NULL)+1);
+    for (i=numpoints; i--; )
+      rows[i]= pointsB+dim*i;
+    qh_printmatrix(qhB, outfile, "input", rows, numpoints, dim);
+    exitcode= qh_new_qhull(qhB, dim, numpoints, pointsB, ismalloc,
+                      flags, outfile, errfile);
+    if (!exitcode)
+      print_summary(qhB);
+    printf( "\nFree memory allocated by the new instance of Qhull, and redisplay the old results.\n");
+    qh_freeqhull(qhB, !qh_ALL);                 /* free long memory */
+    qh_memfreeshort(qhB, &curlong, &totlong);  /* free short memory and memory allocator */
+    if (curlong || totlong)
+        fprintf(errfile, "qhull internal warning (user_eg, #4): did not free %d bytes of long memory (%d pieces)\n", totlong, curlong);
+
+    printf( "\n\n");
+    print_summary(qh);  /* The other instance is unchanged */
+    /* Exiting the block frees qh_qhB */
+  }
+  qh_freeqhull(qh, !qh_ALL);                 /* free long memory */
+  qh_memfreeshort(qh, &curlong, &totlong);  /* free short memory and memory allocator */
+  if (curlong || totlong)
+    fprintf(errfile, "qhull internal warning (user_eg, #2): did not free %d bytes of long memory (%d pieces)\n", totlong, curlong);
+
+  /*
+    Run 3: halfspace intersection about the origin
+  */
+  printf( "\ncompute halfspace intersection about the origin for a diamond\n");
+  sprintf(flags, "qhull H0 s Tcv %s", argc >= 4 ? argv[3] : "Fp");
+  numpoints= SIZEcube;
+  makehalf(points, numpoints, dim);
+  for (i=numpoints; i--; )
+    rows[i]= points+(dim+1)*i;
+  qh_printmatrix(qh, outfile, "input as halfspace coefficients + offsets", rows, numpoints, dim+1);
+  /* use qh_sethalfspace_all to transform the halfspaces yourself.
+     If so, set 'qh->feasible_point and do not use option 'Hn,...' [it would retransform the halfspaces]
+  */
+  exitcode= qh_new_qhull(qh, dim+1, numpoints, points, ismalloc,
+                      flags, outfile, errfile);
+  if (!exitcode)
+    print_summary(qh);
+  qh_freeqhull(qh, !qh_ALL);
+  qh_memfreeshort(qh, &curlong, &totlong);
+  if (curlong || totlong)  /* could also check previous runs */
+    fprintf(stderr, "qhull internal warning (user_eg, #3): did not free %d bytes of long memory (%d pieces)\n",
+       totlong, curlong);
+  return exitcode;
+} /* main */
+
diff --git a/xs/src/qhull/src/user_eg2/user_eg2.c b/xs/src/qhull/src/user_eg2/user_eg2.c
new file mode 100644
index 0000000000..a455f025d1
--- /dev/null
+++ b/xs/src/qhull/src/user_eg2/user_eg2.c
@@ -0,0 +1,746 @@
+/*<html><pre>  -<a                             href="../libqhull/qh-user.htm"
+  >-------------------------------</a><a name="TOP">-</a>
+
+  user_eg2.c
+
+  sample code for calling qhull() from an application.
+
+  See user_eg.c for a simpler method using qh_new_qhull().
+  The method used here and in unix.c gives you additional
+  control over Qhull.
+
+  See user_eg3/user_eg3_r.cpp for a C++ example
+
+  call with:
+
+     user_eg2 "triangulated cube/diamond options" "delaunay options" "halfspace options"
+
+  for example:
+
+     user_eg2                             # return summaries
+
+     user_eg2 "n" "o" "Fp"                # return normals, OFF, points
+
+     user_eg2 "QR0 p" "QR0 v p" "QR0 Fp"  # rotate input and return points
+                                         # 'v' returns Voronoi
+                                         # transform is rotated for halfspaces
+
+   main() makes three runs of qhull.
+
+     1) compute the convex hull of a cube, and incrementally add a diamond
+
+     2a) compute the Delaunay triangulation of random points, and add points.
+
+     2b) find the Delaunay triangle closest to a point.
+
+     3) compute the halfspace intersection of a diamond, and add a cube
+
+ notes:
+
+   summaries are sent to stderr if other output formats are used
+
+   derived from unix.c and compiled by 'make bin/user_eg2'
+
+   see libqhull.h for data structures, macros, and user-callable functions.
+
+   If you want to control all output to stdio and input to stdin,
+   set the #if below to "1" and delete all lines that contain "io.c".
+   This prevents the loading of io.o.  Qhull will
+   still write to 'qh ferr' (stderr) for error reporting and tracing.
+
+   Defining #if 1, also prevents user.o from being loaded.
+*/
+
+#include "libqhull/qhull_a.h"
+
+/*-------------------------------------------------
+-internal function prototypes
+*/
+void print_summary(void);
+void makecube(coordT *points, int numpoints, int dim);
+void adddiamond(coordT *points, int numpoints, int numnew, int dim);
+void makeDelaunay(coordT *points, int numpoints, int dim);
+void addDelaunay(coordT *points, int numpoints, int numnew, int dim);
+void findDelaunay(int dim);
+void makehalf(coordT *points, int numpoints, int dim);
+void addhalf(coordT *points, int numpoints, int numnew, int dim, coordT *feasible);
+
+/*-------------------------------------------------
+-print_summary()
+*/
+void print_summary(void) {
+  facetT *facet;
+  int k;
+
+  printf("\n%d vertices and %d facets with normals:\n",
+                 qh num_vertices, qh num_facets);
+  FORALLfacets {
+    for (k=0; k < qh hull_dim; k++)
+      printf("%6.2g ", facet->normal[k]);
+    printf("\n");
+  }
+}
+
+/*--------------------------------------------------
+-makecube- set points to vertices of cube
+  points is numpoints X dim
+*/
+void makecube(coordT *points, int numpoints, int dim) {
+  int j,k;
+  coordT *point;
+
+  for (j=0; j<numpoints; j++) {
+    point= points + j*dim;
+    for (k=dim; k--; ) {
+      if (j & ( 1 << k))
+        point[k]= 1.0;
+      else
+        point[k]= -1.0;
+    }
+  }
+} /*.makecube.*/
+
+/*--------------------------------------------------
+-adddiamond- add diamond to convex hull
+  points is numpoints+numnew X dim.
+
+notes:
+  qh_addpoint() does not make a copy of the point coordinates.
+
+  For inside points and some outside points, qh_findbestfacet performs
+  an exhaustive search for a visible facet.  Algorithms that retain
+  previously constructed hulls should be faster for on-line construction
+  of the convex hull.
+*/
+void adddiamond(coordT *points, int numpoints, int numnew, int dim) {
+  int j,k;
+  coordT *point;
+  facetT *facet;
+  boolT isoutside;
+  realT bestdist;
+
+  for (j= 0; j < numnew ; j++) {
+    point= points + (numpoints+j)*dim;
+    if (points == qh first_point)  /* in case of 'QRn' */
+      qh num_points= numpoints+j+1;
+    /* qh.num_points sets the size of the points array.  You may
+       allocate the points elsewhere.  If so, qh_addpoint records
+       the point's address in qh other_points
+    */
+    for (k=dim; k--; ) {
+      if (j/2 == k)
+        point[k]= (j & 1) ? 2.0 : -2.0;
+      else
+        point[k]= 0.0;
+    }
+    facet= qh_findbestfacet(point, !qh_ALL, &bestdist, &isoutside);
+    if (isoutside) {
+      if (!qh_addpoint(point, facet, False))
+        break;  /* user requested an early exit with 'TVn' or 'TCn' */
+    }
+    printf("%d vertices and %d facets\n",
+                 qh num_vertices, qh num_facets);
+    /* qh_produce_output(); */
+  }
+  if (qh DOcheckmax)
+    qh_check_maxout();
+  else if (qh KEEPnearinside)
+    qh_nearcoplanar();
+} /*.adddiamond.*/
+
+/*--------------------------------------------------
+-makeDelaunay- set points for dim-1 Delaunay triangulation of random points
+  points is numpoints X dim.  Each point is projected to a paraboloid.
+*/
+void makeDelaunay(coordT *points, int numpoints, int dim) {
+  int j,k, seed;
+  coordT *point, realr;
+
+  seed= (int)time(NULL); /* time_t to int */
+  printf("seed: %d\n", seed);
+  qh_RANDOMseed_( seed);
+  for (j=0; j<numpoints; j++) {
+    point= points + j*dim;
+    for (k= 0; k < dim-1; k++) {
+      realr= qh_RANDOMint;
+      point[k]= 2.0 * realr/(qh_RANDOMmax+1) - 1.0;
+    }
+  }
+  qh_setdelaunay(dim, numpoints, points);
+} /*.makeDelaunay.*/
+
+/*--------------------------------------------------
+-addDelaunay- add points to dim-1 Delaunay triangulation
+  points is numpoints+numnew X dim.  Each point is projected to a paraboloid.
+notes:
+  qh_addpoint() does not make a copy of the point coordinates.
+
+  Since qh_addpoint() is not given a visible facet, it performs a directed
+  search of all facets.  Algorithms that retain previously
+  constructed hulls may be faster.
+*/
+void addDelaunay(coordT *points, int numpoints, int numnew, int dim) {
+  int j,k;
+  coordT *point, realr;
+  facetT *facet;
+  realT bestdist;
+  boolT isoutside;
+
+  for (j= 0; j < numnew ; j++) {
+    point= points + (numpoints+j)*dim;
+    if (points == qh first_point)  /* in case of 'QRn' */
+      qh num_points= numpoints+j+1;
+    /* qh.num_points sets the size of the points array.  You may
+       allocate the point elsewhere.  If so, qh_addpoint records
+       the point's address in qh other_points
+    */
+    for (k= 0; k < dim-1; k++) {
+      realr= qh_RANDOMint;
+      point[k]= 2.0 * realr/(qh_RANDOMmax+1) - 1.0;
+    }
+    qh_setdelaunay(dim, 1, point);
+    facet= qh_findbestfacet(point, !qh_ALL, &bestdist, &isoutside);
+    if (isoutside) {
+      if (!qh_addpoint(point, facet, False))
+        break;  /* user requested an early exit with 'TVn' or 'TCn' */
+    }
+    qh_printpoint(stdout, "added point", point);
+    printf("%d points, %d extra points, %d vertices, and %d facets in total\n",
+                  qh num_points, qh_setsize(qh other_points),
+                  qh num_vertices, qh num_facets);
+
+    /* qh_produce_output(); */
+  }
+  if (qh DOcheckmax)
+    qh_check_maxout();
+  else if (qh KEEPnearinside)
+    qh_nearcoplanar();
+} /*.addDelaunay.*/
+
+/*--------------------------------------------------
+-findDelaunay- find Delaunay triangle for [0.5,0.5,...]
+  assumes dim < 100
+notes:
+  calls qh_setdelaunay() to project the point to a parabaloid
+warning:
+  This is not implemented for tricoplanar facets ('Qt'),
+  See <a href="../html/qh-code.htm#findfacet">locate a facet with qh_findbestfacet()</a>
+*/
+void findDelaunay(int dim) {
+  int k;
+  coordT point[ 100];
+  boolT isoutside;
+  realT bestdist;
+  facetT *facet;
+  vertexT *vertex, **vertexp;
+
+  for (k= 0; k < dim-1; k++)
+    point[k]= 0.5;
+  qh_setdelaunay(dim, 1, point);
+  facet= qh_findbestfacet(point, qh_ALL, &bestdist, &isoutside);
+  if (facet->tricoplanar) {
+    fprintf(stderr, "findDelaunay: not implemented for triangulated, non-simplicial Delaunay regions (tricoplanar facet, f%d).\n",
+       facet->id);
+    qh_errexit(qh_ERRqhull, facet, NULL);
+  }
+  FOREACHvertex_(facet->vertices) {
+    for (k=0; k < dim-1; k++)
+      printf("%5.2f ", vertex->point[k]);
+    printf("\n");
+  }
+} /*.findDelaunay.*/
+
+/*--------------------------------------------------
+-makehalf- set points to halfspaces for a (dim)-d diamond
+  points is numpoints X dim+1
+
+  each halfspace consists of dim coefficients followed by an offset
+*/
+void makehalf(coordT *points, int numpoints, int dim) {
+  int j,k;
+  coordT *point;
+
+  for (j=0; j<numpoints; j++) {
+    point= points + j*(dim+1);
+    point[dim]= -1.0; /* offset */
+    for (k=dim; k--; ) {
+      if (j & ( 1 << k))
+        point[k]= 1.0;
+      else
+        point[k]= -1.0;
+    }
+  }
+} /*.makehalf.*/
+
+/*--------------------------------------------------
+-addhalf- add halfspaces for a (dim)-d cube to the intersection
+  points is numpoints+numnew X dim+1
+notes:
+  assumes dim < 100.
+
+  For makehalf(), points is the initial set of halfspaces with offsets.
+  It is transformed by qh_sethalfspace_all into a
+  (dim)-d set of newpoints.  Qhull computed the convex hull of newpoints -
+  this is equivalent to the halfspace intersection of the
+  orginal halfspaces.
+
+  For addhalf(), the remainder of points stores the transforms of
+  the added halfspaces.  Qhull computes the convex hull of newpoints
+  and the added points.  qh_addpoint() does not make a copy of these points.
+
+  Since halfspace intersection is equivalent to a convex hull,
+  qh_findbestfacet may perform an exhaustive search
+  for a visible facet.  Algorithms that retain previously constructed
+  intersections should be faster for on-line construction.
+*/
+void addhalf(coordT *points, int numpoints, int numnew, int dim, coordT *feasible) {
+  int j,k;
+  coordT *point, normal[100], offset, *next;
+  facetT *facet;
+  boolT isoutside;
+  realT bestdist;
+
+  for (j= 0; j < numnew ; j++) {
+    offset= -1.0;
+    for (k=dim; k--; ) {
+      if (j/2 == k) {
+        normal[k]= sqrt((coordT)dim);   /* to normalize as in makehalf */
+        if (j & 1)
+          normal[k]= -normal[k];
+      }else
+        normal[k]= 0.0;
+    }
+    point= points + (numpoints+j)* (dim+1);  /* does not use point[dim] */
+    qh_sethalfspace(dim, point, &next, normal, &offset, feasible);
+    facet= qh_findbestfacet(point, !qh_ALL, &bestdist, &isoutside);
+    if (isoutside) {
+      if (!qh_addpoint(point, facet, False))
+        break;  /* user requested an early exit with 'TVn' or 'TCn' */
+    }
+    qh_printpoint(stdout, "added offset -1 and normal", normal);
+    printf("%d points, %d extra points, %d vertices, and %d facets in total\n",
+                  qh num_points, qh_setsize(qh other_points),
+                  qh num_vertices, qh num_facets);
+    /* qh_produce_output(); */
+  }
+  if (qh DOcheckmax)
+    qh_check_maxout();
+  else if (qh KEEPnearinside)
+    qh_nearcoplanar();
+} /*.addhalf.*/
+
+#define DIM 3     /* dimension of points, must be < 31 for SIZEcube */
+#define SIZEcube (1<<DIM)
+#define SIZEdiamond (2*DIM)
+#define TOTpoints (SIZEcube + SIZEdiamond)
+
+/*--------------------------------------------------
+-main- derived from unix.c
+
+  see program header
+
+  this contains three runs of Qhull for convex hull, Delaunay
+  triangulation or Voronoi vertices, and halfspace intersection
+
+*/
+int main(int argc, char *argv[]) {
+  boolT ismalloc;
+  int curlong, totlong, exitcode;
+  char options [2000];
+
+  QHULL_LIB_CHECK
+
+  printf("This is the output from user_eg2.c\n\n\
+It shows how qhull() may be called from an application in the same way as\n\
+qconvex.  It is not part of qhull itself.  If it appears accidently,\n\
+please remove user_eg2.c from your project.\n\n");
+
+#if qh_QHpointer  /* see user.h */
+  if (qh_qh){
+      printf("QH6237: Qhull link error.  The global variable qh_qh was not initialized\n\
+              to NULL by global.c.  Please compile user_eg2.c with -Dqh_QHpointer_dllimport\n\
+              as well as -Dqh_QHpointer, or use libqhullstatic, or use a different tool chain.\n\n");
+      return -1;
+  }
+#endif
+
+
+  ismalloc= False;      /* True if qh_freeqhull should 'free(array)' */
+  /*
+    Run 1: convex hull
+  */
+  qh_init_A(stdin, stdout, stderr, 0, NULL);
+  exitcode= setjmp(qh errexit);
+  if (!exitcode) {
+    coordT array[TOTpoints][DIM];
+
+    strcat(qh rbox_command, "user_eg cube");
+    sprintf(options, "qhull s Tcv Q11 %s ", argc >= 2 ? argv[1] : "");
+    qh_initflags(options);
+    printf( "\ncompute triangulated convex hull of cube after rotating input\n");
+    makecube(array[0], SIZEcube, DIM);
+    qh_init_B(array[0], SIZEcube, DIM, ismalloc);
+    qh_qhull();
+    qh_check_output();
+    qh_triangulate();  /* requires option 'Q11' if want to add points */
+    print_summary();
+    if (qh VERIFYoutput && !qh STOPpoint && !qh STOPcone)
+      qh_check_points();
+    printf( "\nadd points in a diamond\n");
+    adddiamond(array[0], SIZEcube, SIZEdiamond, DIM);
+    qh_check_output();
+    print_summary();
+    qh_produce_output();  /* delete this line to help avoid io.c */
+    if (qh VERIFYoutput && !qh STOPpoint && !qh STOPcone)
+      qh_check_points();
+  }
+  qh NOerrexit= True;
+  qh_freeqhull(!qh_ALL);
+  qh_memfreeshort(&curlong, &totlong);
+  if (curlong || totlong)
+    fprintf(stderr, "qhull warning (user_eg, run 1): did not free %d bytes of long memory (%d pieces)\n",
+       totlong, curlong);
+
+  /*
+    Run 2: Delaunay triangulation
+  */
+  qh_init_A(stdin, stdout, stderr, 0, NULL);
+  exitcode= setjmp(qh errexit);
+  if (!exitcode) {
+    coordT array[TOTpoints][DIM];
+
+    strcat(qh rbox_command, "user_eg Delaunay");
+    sprintf(options, "qhull s d Tcv %s", argc >= 3 ? argv[2] : "");
+    qh_initflags(options);
+    printf( "\ncompute %d-d Delaunay triangulation\n", DIM-1);
+    makeDelaunay(array[0], SIZEcube, DIM);
+    /* Instead of makeDelaunay with qh_setdelaunay, you may
+       produce a 2-d array of points, set DIM to 2, and set
+       qh PROJECTdelaunay to True.  qh_init_B will call
+       qh_projectinput to project the points to the paraboloid
+       and add a point "at-infinity".
+    */
+    qh_init_B(array[0], SIZEcube, DIM, ismalloc);
+    qh_qhull();
+    /* If you want Voronoi ('v') without qh_produce_output(), call
+       qh_setvoronoi_all() after qh_qhull() */
+    qh_check_output();
+    print_summary();
+    qh_produce_output();  /* delete this line to help avoid io.c */
+    if (qh VERIFYoutput && !qh STOPpoint && !qh STOPcone)
+      qh_check_points();
+    printf( "\nadd points to triangulation\n");
+    addDelaunay(array[0], SIZEcube, SIZEdiamond, DIM);
+    qh_check_output();
+    qh_produce_output();  /* delete this line to help avoid io.c */
+    if (qh VERIFYoutput && !qh STOPpoint && !qh STOPcone)
+      qh_check_points();
+    printf( "\nfind Delaunay triangle closest to [0.5, 0.5, ...]\n");
+    findDelaunay(DIM);
+  }
+  qh NOerrexit= True;
+  qh_freeqhull(!qh_ALL);
+  qh_memfreeshort(&curlong, &totlong);
+  if (curlong || totlong)
+    fprintf(stderr, "qhull warning (user_eg, run 2): did not free %d bytes of long memory (%d pieces)\n",
+       totlong, curlong);
+
+  /*
+    Run 3: halfspace intersection
+  */
+  qh_init_A(stdin, stdout, stderr, 0, NULL);
+  exitcode= setjmp(qh errexit);
+  if (!exitcode) {
+    coordT array[TOTpoints][DIM+1];  /* +1 for halfspace offset */
+    pointT *points;
+
+    strcat(qh rbox_command, "user_eg halfspaces");
+    sprintf(options, "qhull H0 s Tcv %s", argc >= 4 ? argv[3] : "");
+    qh_initflags(options);
+    printf( "\ncompute halfspace intersection about the origin for a diamond\n");
+    makehalf(array[0], SIZEcube, DIM);
+    qh_setfeasible(DIM); /* from io.c, sets qh feasible_point from 'Hn,n' */
+    /* you may malloc and set qh feasible_point directly.  It is only used for
+       option 'Fp' */
+    points= qh_sethalfspace_all( DIM+1, SIZEcube, array[0], qh feasible_point);
+    qh_init_B(points, SIZEcube, DIM, True); /* qh_freeqhull frees points */
+    qh_qhull();
+    qh_check_output();
+    qh_produce_output();  /* delete this line to help avoid io.c */
+    if (qh VERIFYoutput && !qh STOPpoint && !qh STOPcone)
+      qh_check_points();
+    printf( "\nadd halfspaces for cube to intersection\n");
+    addhalf(array[0], SIZEcube, SIZEdiamond, DIM, qh feasible_point);
+    qh_check_output();
+    qh_produce_output();  /* delete this line to help avoid io.c */
+    if (qh VERIFYoutput && !qh STOPpoint && !qh STOPcone)
+      qh_check_points();
+  }
+  qh NOerrexit= True;
+  qh NOerrexit= True;
+  qh_freeqhull(!qh_ALL);
+  qh_memfreeshort(&curlong, &totlong);
+  if (curlong || totlong)
+    fprintf(stderr, "qhull warning (user_eg, run 3): did not free %d bytes of long memory (%d pieces)\n",
+       totlong, curlong);
+  return exitcode;
+} /* main */
+
+#if 1    /* use 1 to prevent loading of io.o and user.o */
+/*-------------------------------------------
+-errexit- return exitcode to system after an error
+  assumes exitcode non-zero
+  prints useful information
+  see qh_errexit2() in libqhull.c for 2 facets
+*/
+void qh_errexit(int exitcode, facetT *facet, ridgeT *ridge) {
+  QHULL_UNUSED(facet);
+  QHULL_UNUSED(ridge);
+
+  if (qh ERREXITcalled) {
+    fprintf(qh ferr, "qhull error while processing previous error.  Exit program\n");
+    exit(1);
+  }
+  qh ERREXITcalled= True;
+  if (!qh QHULLfinished)
+    qh hulltime= (unsigned)clock() - qh hulltime;
+  fprintf(qh ferr, "\nWhile executing: %s | %s\n", qh rbox_command, qh qhull_command);
+  fprintf(qh ferr, "Options selected:\n%s\n", qh qhull_options);
+  if (qh furthest_id >= 0) {
+    fprintf(qh ferr, "\nLast point added to hull was p%d", qh furthest_id);
+    if (zzval_(Ztotmerge))
+      fprintf(qh ferr, "  Last merge was #%d.", zzval_(Ztotmerge));
+    if (qh QHULLfinished)
+      fprintf(qh ferr, "\nQhull has finished constructing the hull.");
+    else if (qh POSTmerging)
+      fprintf(qh ferr, "\nQhull has started post-merging");
+    fprintf(qh ferr, "\n\n");
+  }
+  if (qh NOerrexit) {
+    fprintf(qh ferr, "qhull error while ending program.  Exit program\n");
+    exit(1);
+  }
+  if (!exitcode)
+    exitcode= qh_ERRqhull;
+  qh NOerrexit= True;
+  longjmp(qh errexit, exitcode);
+} /* errexit */
+
+
+/*-------------------------------------------
+-errprint- prints out the information of the erroneous object
+    any parameter may be NULL, also prints neighbors and geomview output
+*/
+void qh_errprint(const char *string, facetT *atfacet, facetT *otherfacet, ridgeT *atridge, vertexT *atvertex) {
+
+  fprintf(qh ferr, "%s facets f%d f%d ridge r%d vertex v%d\n",
+           string, getid_(atfacet), getid_(otherfacet), getid_(atridge),
+           getid_(atvertex));
+} /* errprint */
+
+
+void qh_printfacetlist(facetT *facetlist, setT *facets, boolT printall) {
+  facetT *facet, **facetp;
+
+  /* remove these calls to help avoid io.c */
+  qh_printbegin(qh ferr, qh_PRINTfacets, facetlist, facets, printall);/*io.c*/
+  FORALLfacet_(facetlist)                                              /*io.c*/
+    qh_printafacet(qh ferr, qh_PRINTfacets, facet, printall);          /*io.c*/
+  FOREACHfacet_(facets)                                                /*io.c*/
+    qh_printafacet(qh ferr, qh_PRINTfacets, facet, printall);          /*io.c*/
+  qh_printend(qh ferr, qh_PRINTfacets, facetlist, facets, printall);  /*io.c*/
+
+  FORALLfacet_(facetlist)
+    fprintf( qh ferr, "facet f%d\n", facet->id);
+} /* printfacetlist */
+
+/* qh_printhelp_degenerate( fp )
+    prints descriptive message for precision error
+
+  notes:
+    no message if qh_QUICKhelp
+*/
+void qh_printhelp_degenerate(FILE *fp) {
+
+  if (qh MERGEexact || qh PREmerge || qh JOGGLEmax < REALmax/2)
+    qh_fprintf(fp, 9368, "\n\
+A Qhull error has occurred.  Qhull should have corrected the above\n\
+precision error.  Please send the input and all of the output to\n\
+qhull_bug@qhull.org\n");
+  else if (!qh_QUICKhelp) {
+    qh_fprintf(fp, 9369, "\n\
+Precision problems were detected during construction of the convex hull.\n\
+This occurs because convex hull algorithms assume that calculations are\n\
+exact, but floating-point arithmetic has roundoff errors.\n\
+\n\
+To correct for precision problems, do not use 'Q0'.  By default, Qhull\n\
+selects 'C-0' or 'Qx' and merges non-convex facets.  With option 'QJ',\n\
+Qhull joggles the input to prevent precision problems.  See \"Imprecision\n\
+in Qhull\" (qh-impre.htm).\n\
+\n\
+If you use 'Q0', the output may include\n\
+coplanar ridges, concave ridges, and flipped facets.  In 4-d and higher,\n\
+Qhull may produce a ridge with four neighbors or two facets with the same \n\
+vertices.  Qhull reports these events when they occur.  It stops when a\n\
+concave ridge, flipped facet, or duplicate facet occurs.\n");
+#if REALfloat
+    qh_fprintf(fp, 9370, "\
+\n\
+Qhull is currently using single precision arithmetic.  The following\n\
+will probably remove the precision problems:\n\
+  - recompile qhull for realT precision(#define REALfloat 0 in user.h).\n");
+#endif
+    if (qh DELAUNAY && !qh SCALElast && qh MAXabs_coord > 1e4)
+      qh_fprintf(fp, 9371, "\
+\n\
+When computing the Delaunay triangulation of coordinates > 1.0,\n\
+  - use 'Qbb' to scale the last coordinate to [0,m] (max previous coordinate)\n");
+    if (qh DELAUNAY && !qh ATinfinity)
+      qh_fprintf(fp, 9372, "\
+When computing the Delaunay triangulation:\n\
+  - use 'Qz' to add a point at-infinity.  This reduces precision problems.\n");
+
+    qh_fprintf(fp, 9373, "\
+\n\
+If you need triangular output:\n\
+  - use option 'Qt' to triangulate the output\n\
+  - use option 'QJ' to joggle the input points and remove precision errors\n\
+  - use option 'Ft'.  It triangulates non-simplicial facets with added points.\n\
+\n\
+If you must use 'Q0',\n\
+try one or more of the following options.  They can not guarantee an output.\n\
+  - use 'QbB' to scale the input to a cube.\n\
+  - use 'Po' to produce output and prevent partitioning for flipped facets\n\
+  - use 'V0' to set min. distance to visible facet as 0 instead of roundoff\n\
+  - use 'En' to specify a maximum roundoff error less than %2.2g.\n\
+  - options 'Qf', 'Qbb', and 'QR0' may also help\n",
+               qh DISTround);
+    qh_fprintf(fp, 9374, "\
+\n\
+To guarantee simplicial output:\n\
+  - use option 'Qt' to triangulate the output\n\
+  - use option 'QJ' to joggle the input points and remove precision errors\n\
+  - use option 'Ft' to triangulate the output by adding points\n\
+  - use exact arithmetic (see \"Imprecision in Qhull\", qh-impre.htm)\n\
+");
+  }
+} /* printhelp_degenerate */
+
+
+/* qh_printhelp_narrowhull( minangle )
+     Warn about a narrow hull
+
+  notes:
+    Alternatively, reduce qh_WARNnarrow in user.h
+
+*/
+void qh_printhelp_narrowhull(FILE *fp, realT minangle) {
+
+    qh_fprintf(fp, 9375, "qhull precision warning: \n\
+The initial hull is narrow (cosine of min. angle is %.16f).\n\
+A coplanar point may lead to a wide facet.  Options 'QbB' (scale to unit box)\n\
+or 'Qbb' (scale last coordinate) may remove this warning.  Use 'Pp' to skip\n\
+this warning.  See 'Limitations' in qh-impre.htm.\n",
+          -minangle);   /* convert from angle between normals to angle between facets */
+} /* printhelp_narrowhull */
+
+/* qh_printhelp_singular
+      prints descriptive message for singular input
+*/
+void qh_printhelp_singular(FILE *fp) {
+  facetT *facet;
+  vertexT *vertex, **vertexp;
+  realT min, max, *coord, dist;
+  int i,k;
+
+  qh_fprintf(fp, 9376, "\n\
+The input to qhull appears to be less than %d dimensional, or a\n\
+computation has overflowed.\n\n\
+Qhull could not construct a clearly convex simplex from points:\n",
+           qh hull_dim);
+  qh_printvertexlist(fp, "", qh facet_list, NULL, qh_ALL);
+  if (!qh_QUICKhelp)
+    qh_fprintf(fp, 9377, "\n\
+The center point is coplanar with a facet, or a vertex is coplanar\n\
+with a neighboring facet.  The maximum round off error for\n\
+computing distances is %2.2g.  The center point, facets and distances\n\
+to the center point are as follows:\n\n", qh DISTround);
+  qh_printpointid(fp, "center point", qh hull_dim, qh interior_point, -1);
+  qh_fprintf(fp, 9378, "\n");
+  FORALLfacets {
+    qh_fprintf(fp, 9379, "facet");
+    FOREACHvertex_(facet->vertices)
+      qh_fprintf(fp, 9380, " p%d", qh_pointid(vertex->point));
+    zinc_(Zdistio);
+    qh_distplane(qh interior_point, facet, &dist);
+    qh_fprintf(fp, 9381, " distance= %4.2g\n", dist);
+  }
+  if (!qh_QUICKhelp) {
+    if (qh HALFspace)
+      qh_fprintf(fp, 9382, "\n\
+These points are the dual of the given halfspaces.  They indicate that\n\
+the intersection is degenerate.\n");
+    qh_fprintf(fp, 9383,"\n\
+These points either have a maximum or minimum x-coordinate, or\n\
+they maximize the determinant for k coordinates.  Trial points\n\
+are first selected from points that maximize a coordinate.\n");
+    if (qh hull_dim >= qh_INITIALmax)
+      qh_fprintf(fp, 9384, "\n\
+Because of the high dimension, the min x-coordinate and max-coordinate\n\
+points are used if the determinant is non-zero.  Option 'Qs' will\n\
+do a better, though much slower, job.  Instead of 'Qs', you can change\n\
+the points by randomly rotating the input with 'QR0'.\n");
+  }
+  qh_fprintf(fp, 9385, "\nThe min and max coordinates for each dimension are:\n");
+  for (k=0; k < qh hull_dim; k++) {
+    min= REALmax;
+    max= -REALmin;
+    for (i=qh num_points, coord= qh first_point+k; i--; coord += qh hull_dim) {
+      maximize_(max, *coord);
+      minimize_(min, *coord);
+    }
+    qh_fprintf(fp, 9386, "  %d:  %8.4g  %8.4g  difference= %4.4g\n", k, min, max, max-min);
+  }
+  if (!qh_QUICKhelp) {
+    qh_fprintf(fp, 9387, "\n\
+If the input should be full dimensional, you have several options that\n\
+may determine an initial simplex:\n\
+  - use 'QJ'  to joggle the input and make it full dimensional\n\
+  - use 'QbB' to scale the points to the unit cube\n\
+  - use 'QR0' to randomly rotate the input for different maximum points\n\
+  - use 'Qs'  to search all points for the initial simplex\n\
+  - use 'En'  to specify a maximum roundoff error less than %2.2g.\n\
+  - trace execution with 'T3' to see the determinant for each point.\n",
+                     qh DISTround);
+#if REALfloat
+    qh_fprintf(fp, 9388, "\
+  - recompile qhull for realT precision(#define REALfloat 0 in libqhull.h).\n");
+#endif
+    qh_fprintf(fp, 9389, "\n\
+If the input is lower dimensional:\n\
+  - use 'QJ' to joggle the input and make it full dimensional\n\
+  - use 'Qbk:0Bk:0' to delete coordinate k from the input.  You should\n\
+    pick the coordinate with the least range.  The hull will have the\n\
+    correct topology.\n\
+  - determine the flat containing the points, rotate the points\n\
+    into a coordinate plane, and delete the other coordinates.\n\
+  - add one or more points to make the input full dimensional.\n\
+");
+    if (qh DELAUNAY && !qh ATinfinity)
+      qh_fprintf(fp, 9390, "\n\n\
+This is a Delaunay triangulation and the input is co-circular or co-spherical:\n\
+  - use 'Qz' to add a point \"at infinity\" (i.e., above the paraboloid)\n\
+  - or use 'QJ' to joggle the input and avoid co-circular data\n");
+  }
+} /* printhelp_singular */
+
+
+/*-----------------------------------------
+-user_memsizes- allocate up to 10 additional, quick allocation sizes
+*/
+void qh_user_memsizes(void) {
+
+  /* qh_memsize(size); */
+} /* user_memsizes */
+
+#endif
diff --git a/xs/src/qhull/src/user_eg2/user_eg2.pro b/xs/src/qhull/src/user_eg2/user_eg2.pro
new file mode 100644
index 0000000000..c841bfe134
--- /dev/null
+++ b/xs/src/qhull/src/user_eg2/user_eg2.pro
@@ -0,0 +1,11 @@
+# -------------------------------------------------
+# user_eg2.pro -- Qt project for Qhull demonstration using the static Qhull library
+#
+# It uses reentrant Qhull
+# -------------------------------------------------
+
+include(../qhull-app-c_r.pri)
+
+TARGET = user_eg2
+
+SOURCES += user_eg2_r.c
diff --git a/xs/src/qhull/src/user_eg2/user_eg2_r.c b/xs/src/qhull/src/user_eg2/user_eg2_r.c
new file mode 100644
index 0000000000..2f8b4e6c76
--- /dev/null
+++ b/xs/src/qhull/src/user_eg2/user_eg2_r.c
@@ -0,0 +1,742 @@
+/*<html><pre>  -<a                             href="../libqhull_r/qh-user_r.htm"
+  >-------------------------------</a><a name="TOP">-</a>
+
+  user_eg2_r.c
+
+  sample code for calling qhull() from an application.
+
+  See user_eg_r.c for a simpler method using qh_new_qhull().
+  The method used here and in unix_r.c gives you additional
+  control over Qhull.
+
+  See user_eg3/user_eg3_r.cpp for a C++ example
+
+  call with:
+
+     user_eg2 "triangulated cube/diamond options" "delaunay options" "halfspace options"
+
+  for example:
+
+     user_eg2                             # return summaries
+
+     user_eg2 "n" "o" "Fp"                # return normals, OFF, points
+
+     user_eg2 "QR0 p" "QR0 v p" "QR0 Fp"  # rotate input and return points
+                                         # 'v' returns Voronoi
+                                         # transform is rotated for halfspaces
+
+   main() makes three runs of qhull.
+
+     1) compute the convex hull of a cube, and incrementally add a diamond
+
+     2a) compute the Delaunay triangulation of random points, and add points.
+
+     2b) find the Delaunay triangle closest to a point.
+
+     3) compute the halfspace intersection of a diamond, and add a cube
+
+ notes:
+
+   summaries are sent to stderr if other output formats are used
+
+   derived from unix.c and compiled by 'make bin/user_eg2'
+
+   see libqhull.h for data structures, macros, and user-callable functions.
+
+   If you want to control all output to stdio and input to stdin,
+   set the #if below to "1" and delete all lines that contain "io.c".
+   This prevents the loading of io.o.  Qhull will
+   still write to 'qh->ferr' (stderr) for error reporting and tracing.
+
+   Defining #if 1, also prevents user.o from being loaded.
+*/
+
+#include "libqhull_r/qhull_ra.h"
+
+/*-------------------------------------------------
+-internal function prototypes
+*/
+void print_summary(qhT *qh);
+void makecube(coordT *points, int numpoints, int dim);
+void adddiamond(qhT *qh, coordT *points, int numpoints, int numnew, int dim);
+void makeDelaunay(qhT *qh, coordT *points, int numpoints, int dim);
+void addDelaunay(qhT *qh, coordT *points, int numpoints, int numnew, int dim);
+void findDelaunay(qhT *qh, int dim);
+void makehalf(coordT *points, int numpoints, int dim);
+void addhalf(qhT *qh, coordT *points, int numpoints, int numnew, int dim, coordT *feasible);
+
+/*-------------------------------------------------
+-print_summary(qh)
+*/
+void print_summary(qhT *qh) {
+  facetT *facet;
+  int k;
+
+  printf("\n%d vertices and %d facets with normals:\n",
+                 qh->num_vertices, qh->num_facets);
+  FORALLfacets {
+    for (k=0; k < qh->hull_dim; k++)
+      printf("%6.2g ", facet->normal[k]);
+    printf("\n");
+  }
+}
+
+/*--------------------------------------------------
+-makecube- set points to vertices of cube
+  points is numpoints X dim
+*/
+void makecube(coordT *points, int numpoints, int dim) {
+  int j,k;
+  coordT *point;
+
+  for (j=0; j<numpoints; j++) {
+    point= points + j*dim;
+    for (k=dim; k--; ) {
+      if (j & ( 1 << k))
+        point[k]= 1.0;
+      else
+        point[k]= -1.0;
+    }
+  }
+} /*.makecube.*/
+
+/*--------------------------------------------------
+-adddiamond- add diamond to convex hull
+  points is numpoints+numnew X dim.
+
+notes:
+  qh_addpoint() does not make a copy of the point coordinates.
+
+  For inside points and some outside points, qh_findbestfacet performs
+  an exhaustive search for a visible facet.  Algorithms that retain
+  previously constructed hulls should be faster for on-line construction
+  of the convex hull.
+*/
+void adddiamond(qhT *qh, coordT *points, int numpoints, int numnew, int dim) {
+  int j,k;
+  coordT *point;
+  facetT *facet;
+  boolT isoutside;
+  realT bestdist;
+
+  for (j= 0; j < numnew ; j++) {
+    point= points + (numpoints+j)*dim;
+    if (points == qh->first_point)  /* in case of 'QRn' */
+      qh->num_points= numpoints+j+1;
+    /* qh.num_points sets the size of the points array.  You may
+       allocate the points elsewhere.  If so, qh_addpoint records
+       the point's address in qh->other_points
+    */
+    for (k=dim; k--; ) {
+      if (j/2 == k)
+        point[k]= (j & 1) ? 2.0 : -2.0;
+      else
+        point[k]= 0.0;
+    }
+    facet= qh_findbestfacet(qh, point, !qh_ALL, &bestdist, &isoutside);
+    if (isoutside) {
+      if (!qh_addpoint(qh, point, facet, False))
+        break;  /* user requested an early exit with 'TVn' or 'TCn' */
+    }
+    printf("%d vertices and %d facets\n",
+                 qh->num_vertices, qh->num_facets);
+    /* qh_produce_output(); */
+  }
+  if (qh->DOcheckmax)
+    qh_check_maxout(qh);
+  else if (qh->KEEPnearinside)
+    qh_nearcoplanar(qh);
+} /*.adddiamond.*/
+
+/*--------------------------------------------------
+-makeDelaunay- set points for dim-1 Delaunay triangulation of random points
+  points is numpoints X dim.  Each point is projected to a paraboloid.
+*/
+void makeDelaunay(qhT *qh, coordT *points, int numpoints, int dim) {
+  int j,k, seed;
+  coordT *point, realr;
+
+  seed= (int)time(NULL); /* time_t to int */
+  printf("seed: %d\n", seed);
+  qh_RANDOMseed_(qh, seed);
+  for (j=0; j<numpoints; j++) {
+    point= points + j*dim;
+    for (k= 0; k < dim-1; k++) {
+      realr= qh_RANDOMint;
+      point[k]= 2.0 * realr/(qh_RANDOMmax+1) - 1.0;
+    }
+  }
+  qh_setdelaunay(qh, dim, numpoints, points);
+} /*.makeDelaunay.*/
+
+/*--------------------------------------------------
+-addDelaunay- add points to dim-1 Delaunay triangulation
+  points is numpoints+numnew X dim.  Each point is projected to a paraboloid.
+notes:
+  qh_addpoint() does not make a copy of the point coordinates.
+
+  Since qh_addpoint() is not given a visible facet, it performs a directed
+  search of all facets.  Algorithms that retain previously
+  constructed hulls may be faster.
+*/
+void addDelaunay(qhT *qh, coordT *points, int numpoints, int numnew, int dim) {
+  int j,k;
+  coordT *point, realr;
+  facetT *facet;
+  realT bestdist;
+  boolT isoutside;
+
+  for (j= 0; j < numnew ; j++) {
+    point= points + (numpoints+j)*dim;
+    if (points == qh->first_point)  /* in case of 'QRn' */
+      qh->num_points= numpoints+j+1;
+    /* qh.num_points sets the size of the points array.  You may
+       allocate the point elsewhere.  If so, qh_addpoint records
+       the point's address in qh->other_points
+    */
+    for (k= 0; k < dim-1; k++) {
+      realr= qh_RANDOMint;
+      point[k]= 2.0 * realr/(qh_RANDOMmax+1) - 1.0;
+    }
+    qh_setdelaunay(qh, dim, 1, point);
+    facet= qh_findbestfacet(qh, point, !qh_ALL, &bestdist, &isoutside);
+    if (isoutside) {
+      if (!qh_addpoint(qh, point, facet, False))
+        break;  /* user requested an early exit with 'TVn' or 'TCn' */
+    }
+    qh_printpoint(qh, stdout, "added point", point);
+    printf("%d points, %d extra points, %d vertices, and %d facets in total\n",
+                  qh->num_points, qh_setsize(qh, qh->other_points),
+                  qh->num_vertices, qh->num_facets);
+
+    /* qh_produce_output(qh); */
+  }
+  if (qh->DOcheckmax)
+    qh_check_maxout(qh);
+  else if (qh->KEEPnearinside)
+    qh_nearcoplanar(qh);
+} /*.addDelaunay.*/
+
+/*--------------------------------------------------
+-findDelaunay- find Delaunay triangle for [0.5,0.5,...]
+  assumes dim < 100
+notes:
+  calls qh_setdelaunay() to project the point to a parabaloid
+warning:
+  This is not implemented for tricoplanar facets ('Qt'),
+  See <a href="../html/qh-code.htm#findfacet">locate a facet with qh_findbestfacet()</a>
+*/
+void findDelaunay(qhT *qh, int dim) {
+  int k;
+  coordT point[ 100];
+  boolT isoutside;
+  realT bestdist;
+  facetT *facet;
+  vertexT *vertex, **vertexp;
+
+  for (k= 0; k < dim-1; k++)
+    point[k]= 0.5;
+  qh_setdelaunay(qh, dim, 1, point);
+  facet= qh_findbestfacet(qh, point, qh_ALL, &bestdist, &isoutside);
+  if (facet->tricoplanar) {
+    fprintf(stderr, "findDelaunay: not implemented for triangulated, non-simplicial Delaunay regions (tricoplanar facet, f%d).\n",
+       facet->id);
+    qh_errexit(qh, qh_ERRqhull, facet, NULL);
+  }
+  FOREACHvertex_(facet->vertices) {
+    for (k=0; k < dim-1; k++)
+      printf("%5.2f ", vertex->point[k]);
+    printf("\n");
+  }
+} /*.findDelaunay.*/
+
+/*--------------------------------------------------
+-makehalf- set points to halfspaces for a (dim)-d diamond
+  points is numpoints X dim+1
+
+  each halfspace consists of dim coefficients followed by an offset
+*/
+void makehalf(coordT *points, int numpoints, int dim) {
+  int j,k;
+  coordT *point;
+
+  for (j=0; j<numpoints; j++) {
+    point= points + j*(dim+1);
+    point[dim]= -1.0; /* offset */
+    for (k=dim; k--; ) {
+      if (j & ( 1 << k))
+        point[k]= 1.0;
+      else
+        point[k]= -1.0;
+    }
+  }
+} /*.makehalf.*/
+
+/*--------------------------------------------------
+-addhalf- add halfspaces for a (dim)-d cube to the intersection
+  points is numpoints+numnew X dim+1
+notes:
+  assumes dim < 100.
+
+  For makehalf(), points is the initial set of halfspaces with offsets.
+  It is transformed by qh_sethalfspace_all into a
+  (dim)-d set of newpoints.  Qhull computed the convex hull of newpoints -
+  this is equivalent to the halfspace intersection of the
+  orginal halfspaces.
+
+  For addhalf(), the remainder of points stores the transforms of
+  the added halfspaces.  Qhull computes the convex hull of newpoints
+  and the added points.  qh_addpoint() does not make a copy of these points.
+
+  Since halfspace intersection is equivalent to a convex hull,
+  qh_findbestfacet may perform an exhaustive search
+  for a visible facet.  Algorithms that retain previously constructed
+  intersections should be faster for on-line construction.
+*/
+void addhalf(qhT *qh, coordT *points, int numpoints, int numnew, int dim, coordT *feasible) {
+  int j,k;
+  coordT *point, normal[100], offset, *next;
+  facetT *facet;
+  boolT isoutside;
+  realT bestdist;
+
+  for (j= 0; j < numnew ; j++) {
+    offset= -1.0;
+    for (k=dim; k--; ) {
+      if (j/2 == k) {
+        normal[k]= sqrt((coordT)dim);   /* to normalize as in makehalf */
+        if (j & 1)
+          normal[k]= -normal[k];
+      }else
+        normal[k]= 0.0;
+    }
+    point= points + (numpoints+j)* (dim+1);  /* does not use point[dim] */
+    qh_sethalfspace(qh, dim, point, &next, normal, &offset, feasible);
+    facet= qh_findbestfacet(qh, point, !qh_ALL, &bestdist, &isoutside);
+    if (isoutside) {
+      if (!qh_addpoint(qh, point, facet, False))
+        break;  /* user requested an early exit with 'TVn' or 'TCn' */
+    }
+    qh_printpoint(qh, stdout, "added offset -1 and normal", normal);
+    printf("%d points, %d extra points, %d vertices, and %d facets in total\n",
+                  qh->num_points, qh_setsize(qh, qh->other_points),
+                  qh->num_vertices, qh->num_facets);
+    /* qh_produce_output(qh); */
+  }
+  if (qh->DOcheckmax)
+    qh_check_maxout(qh);
+  else if (qh->KEEPnearinside)
+    qh_nearcoplanar(qh);
+} /*.addhalf.*/
+
+#define DIM 3     /* dimension of points, must be < 31 for SIZEcube */
+#define SIZEcube (1<<DIM)
+#define SIZEdiamond (2*DIM)
+#define TOTpoints (SIZEcube + SIZEdiamond)
+
+/*--------------------------------------------------
+-main- Similar to unix.c, the main program for qhull
+
+  see program header
+
+  this contains three runs of Qhull for convex hull, Delaunay
+  triangulation or Voronoi vertices, and halfspace intersection
+
+*/
+int main(int argc, char *argv[]) {
+  boolT ismalloc;
+  int curlong, totlong, exitcode;
+  char options [2000];
+  qhT qh_qh;
+  qhT *qh= &qh_qh;  /* Alternatively -- qhT *qh= (qhT*)malloc(sizeof(qhT)) */
+
+  QHULL_LIB_CHECK
+
+  printf("This is the output from user_eg2_r.c\n\n\
+It shows how qhull() may be called from an application using qhull's\n\
+static, reentrant library.  user_eg2 is not part of qhull itself.  If it\n\
+appears accidently, please remove user_eg2_r.c from your project.  If it fails\n\
+immediately, user_eg2_r.c was incorrectly linked to the non-reentrant library.\n\
+Also try 'user_eg2 T1 2>&1'\n\n");
+
+  ismalloc= False;      /* True if qh_freeqhull should 'free(array)' */
+  /*
+    Run 1: convex hull
+  */
+  qh_init_A(qh, stdin, stdout, stderr, 0, NULL);
+  exitcode= setjmp(qh->errexit);
+  if (!exitcode) {
+    coordT array[TOTpoints][DIM];
+
+    qh->NOerrexit= False;
+    strcat(qh->rbox_command, "user_eg2 cube example");
+    sprintf(options, "qhull s Tcv Q11 %s ", argc >= 2 ? argv[1] : "");
+    qh_initflags(qh, options);
+    printf( "\ncompute triangulated convex hull of cube after rotating input\n");
+    makecube(array[0], SIZEcube, DIM);
+    qh_init_B(qh, array[0], SIZEcube, DIM, ismalloc);
+    qh_qhull(qh);
+    qh_check_output(qh);
+    qh_triangulate(qh);  /* requires option 'Q11' if want to add points */
+    print_summary(qh);
+    if (qh->VERIFYoutput && !qh->STOPpoint && !qh->STOPcone)
+      qh_check_points(qh);
+    printf( "\nadd points in a diamond\n");
+    adddiamond(qh, array[0], SIZEcube, SIZEdiamond, DIM);
+    qh_check_output(qh);
+    print_summary(qh);
+    qh_produce_output(qh);  /* delete this line to help avoid io.c */
+    if (qh->VERIFYoutput && !qh->STOPpoint && !qh->STOPcone)
+      qh_check_points(qh);
+  }
+  qh->NOerrexit= True;
+  qh_freeqhull(qh, !qh_ALL);
+  qh_memfreeshort(qh, &curlong, &totlong);
+  if (curlong || totlong)
+      fprintf(stderr, "qhull warning (user_eg2, run 1): did not free %d bytes of long memory (%d pieces)\n",
+          totlong, curlong);
+  /*
+    Run 2: Delaunay triangulation
+  */
+  qh_init_A(qh, stdin, stdout, stderr, 0, NULL);
+  exitcode= setjmp(qh->errexit);
+  if (!exitcode) {
+    coordT array[TOTpoints][DIM];
+
+    qh->NOerrexit= False;
+    strcat(qh->rbox_command, "user_eg2 Delaunay example");
+    sprintf(options, "qhull s d Tcv %s", argc >= 3 ? argv[2] : "");
+    qh_initflags(qh, options);
+    printf( "\ncompute %d-d Delaunay triangulation\n", DIM-1);
+    makeDelaunay(qh, array[0], SIZEcube, DIM);
+    /* Instead of makeDelaunay with qh_setdelaunay, you may
+       produce a 2-d array of points, set DIM to 2, and set
+       qh->PROJECTdelaunay to True.  qh_init_B will call
+       qh_projectinput to project the points to the paraboloid
+       and add a point "at-infinity".
+    */
+    qh_init_B(qh, array[0], SIZEcube, DIM, ismalloc);
+    qh_qhull(qh);
+    /* If you want Voronoi ('v') without qh_produce_output(), call
+       qh_setvoronoi_all() after qh_qhull() */
+    qh_check_output(qh);
+    print_summary(qh);
+    qh_produce_output(qh);  /* delete this line to help avoid io.c */
+    if (qh->VERIFYoutput && !qh->STOPpoint && !qh->STOPcone)
+      qh_check_points(qh);
+    printf( "\nadd points to triangulation\n");
+    addDelaunay(qh, array[0], SIZEcube, SIZEdiamond, DIM);
+    qh_check_output(qh);
+    qh_produce_output(qh);  /* delete this line to help avoid io.c */
+    if (qh->VERIFYoutput && !qh->STOPpoint && !qh->STOPcone)
+      qh_check_points(qh);
+    printf( "\nfind Delaunay triangle closest to [0.5, 0.5, ...]\n");
+    findDelaunay(qh, DIM);
+  }
+  qh->NOerrexit= True;
+  qh_freeqhull(qh, !qh_ALL);
+  qh_memfreeshort(qh, &curlong, &totlong);
+  if (curlong || totlong) 
+      fprintf(stderr, "qhull warning (user_eg2, run 2): did not free %d bytes of long memory (%d pieces)\n",
+         totlong, curlong);
+  /*
+    Run 3: halfspace intersection
+  */
+  qh_init_A(qh, stdin, stdout, stderr, 0, NULL);
+  exitcode= setjmp(qh->errexit);
+  if (!exitcode) {
+    coordT array[TOTpoints][DIM+1];  /* +1 for halfspace offset */
+    pointT *points;
+
+    qh->NOerrexit= False;
+    strcat(qh->rbox_command, "user_eg2 halfspace example");
+    sprintf(options, "qhull H0 s Tcv %s", argc >= 4 ? argv[3] : "");
+    qh_initflags(qh, options);
+    printf( "\ncompute halfspace intersection about the origin for a diamond\n");
+    makehalf(array[0], SIZEcube, DIM);
+    qh_setfeasible(qh, DIM); /* from io.c, sets qh->feasible_point from 'Hn,n' */
+    /* you may malloc and set qh->feasible_point directly.  It is only used for
+       option 'Fp' */
+    points= qh_sethalfspace_all(qh, DIM+1, SIZEcube, array[0], qh->feasible_point);
+    qh_init_B(qh, points, SIZEcube, DIM, True); /* qh_freeqhull frees points */
+    qh_qhull(qh);
+    qh_check_output(qh);
+    qh_produce_output(qh);  /* delete this line to help avoid io.c */
+    if (qh->VERIFYoutput && !qh->STOPpoint && !qh->STOPcone)
+      qh_check_points(qh);
+    printf( "\nadd halfspaces for cube to intersection\n");
+    addhalf(qh, array[0], SIZEcube, SIZEdiamond, DIM, qh->feasible_point);
+    qh_check_output(qh);
+    qh_produce_output(qh);  /* delete this line to help avoid io.c */
+    if (qh->VERIFYoutput && !qh->STOPpoint && !qh->STOPcone)
+      qh_check_points(qh);
+  }
+  qh->NOerrexit= True;
+  qh->NOerrexit= True;
+  qh_freeqhull(qh, !qh_ALL);
+  qh_memfreeshort(qh, &curlong, &totlong);
+  if (curlong || totlong)
+      fprintf(stderr, "qhull warning (user_eg2, run 3): did not free %d bytes of long memory (%d pieces)\n",
+          totlong, curlong);
+  return exitcode;
+} /* main */
+
+#if 1    /* use 1 to prevent loading of io.o and user.o */
+/*-------------------------------------------
+-errexit- return exitcode to system after an error
+  assumes exitcode non-zero
+  prints useful information
+  see qh_errexit2() in libqhull.c for 2 facets
+*/
+void qh_errexit(qhT *qh, int exitcode, facetT *facet, ridgeT *ridge) {
+  QHULL_UNUSED(facet);
+  QHULL_UNUSED(ridge);
+
+  if (qh->ERREXITcalled) {
+    fprintf(qh->ferr, "qhull error while processing previous error.  Exit program\n");
+    exit(1);
+  }
+  qh->ERREXITcalled= True;
+  if (!qh->QHULLfinished)
+    qh->hulltime= (unsigned)clock() - qh->hulltime;
+  fprintf(qh->ferr, "\nWhile executing: %s | %s\n", qh->rbox_command, qh->qhull_command);
+  fprintf(qh->ferr, "Options selected:\n%s\n", qh->qhull_options);
+  if (qh->furthest_id >= 0) {
+    fprintf(qh->ferr, "\nLast point added to hull was p%d", qh->furthest_id);
+    if (zzval_(Ztotmerge))
+      fprintf(qh->ferr, "  Last merge was #%d.", zzval_(Ztotmerge));
+    if (qh->QHULLfinished)
+      fprintf(qh->ferr, "\nQhull has finished constructing the hull.");
+    else if (qh->POSTmerging)
+      fprintf(qh->ferr, "\nQhull has started post-merging");
+    fprintf(qh->ferr, "\n\n");
+  }
+  if (qh->NOerrexit) {
+    fprintf(qh->ferr, "qhull error while ending program.  Exit program\n");
+    exit(1);
+  }
+  if (!exitcode)
+    exitcode= qh_ERRqhull;
+  qh->NOerrexit= True;
+  longjmp(qh->errexit, exitcode);
+} /* errexit */
+
+
+/*-------------------------------------------
+-errprint- prints out the information of the erroneous object
+    any parameter may be NULL, also prints neighbors and geomview output
+*/
+void qh_errprint(qhT *qh, const char *string, facetT *atfacet, facetT *otherfacet, ridgeT *atridge, vertexT *atvertex) {
+
+  fprintf(qh->ferr, "%s facets f%d f%d ridge r%d vertex v%d\n",
+           string, getid_(atfacet), getid_(otherfacet), getid_(atridge),
+           getid_(atvertex));
+} /* errprint */
+
+
+void qh_printfacetlist(qhT *qh, facetT *facetlist, setT *facets, boolT printall) {
+  facetT *facet, **facetp;
+
+  /* remove these calls to help avoid io.c */
+  qh_printbegin(qh, qh->ferr, qh_PRINTfacets, facetlist, facets, printall);/*io.c*/
+  FORALLfacet_(facetlist)                                              /*io.c*/
+    qh_printafacet(qh, qh->ferr, qh_PRINTfacets, facet, printall);          /*io.c*/
+  FOREACHfacet_(facets)                                                /*io.c*/
+    qh_printafacet(qh, qh->ferr, qh_PRINTfacets, facet, printall);          /*io.c*/
+  qh_printend(qh, qh->ferr, qh_PRINTfacets, facetlist, facets, printall);  /*io.c*/
+
+  FORALLfacet_(facetlist)
+    fprintf( qh->ferr, "facet f%d\n", facet->id);
+} /* printfacetlist */
+
+/* qh_printhelp_degenerate( fp )
+    prints descriptive message for precision error
+
+  notes:
+    no message if qh_QUICKhelp
+*/
+void qh_printhelp_degenerate(qhT *qh, FILE *fp) {
+
+  if (qh->MERGEexact || qh->PREmerge || qh->JOGGLEmax < REALmax/2)
+    qh_fprintf(qh, fp, 9368, "\n\
+A Qhull error has occurred.  Qhull should have corrected the above\n\
+precision error.  Please send the input and all of the output to\n\
+qhull_bug@qhull.org\n");
+  else if (!qh_QUICKhelp) {
+    qh_fprintf(qh, fp, 9369, "\n\
+Precision problems were detected during construction of the convex hull.\n\
+This occurs because convex hull algorithms assume that calculations are\n\
+exact, but floating-point arithmetic has roundoff errors.\n\
+\n\
+To correct for precision problems, do not use 'Q0'.  By default, Qhull\n\
+selects 'C-0' or 'Qx' and merges non-convex facets.  With option 'QJ',\n\
+Qhull joggles the input to prevent precision problems.  See \"Imprecision\n\
+in Qhull\" (qh-impre.htm).\n\
+\n\
+If you use 'Q0', the output may include\n\
+coplanar ridges, concave ridges, and flipped facets.  In 4-d and higher,\n\
+Qhull may produce a ridge with four neighbors or two facets with the same \n\
+vertices.  Qhull reports these events when they occur.  It stops when a\n\
+concave ridge, flipped facet, or duplicate facet occurs.\n");
+#if REALfloat
+    qh_fprintf(qh, fp, 9370, "\
+\n\
+Qhull is currently using single precision arithmetic.  The following\n\
+will probably remove the precision problems:\n\
+  - recompile qhull for realT precision(#define REALfloat 0 in user.h).\n");
+#endif
+    if (qh->DELAUNAY && !qh->SCALElast && qh->MAXabs_coord > 1e4)
+      qh_fprintf(qh, fp, 9371, "\
+\n\
+When computing the Delaunay triangulation of coordinates > 1.0,\n\
+  - use 'Qbb' to scale the last coordinate to [0,m] (max previous coordinate)\n");
+    if (qh->DELAUNAY && !qh->ATinfinity)
+      qh_fprintf(qh, fp, 9372, "\
+When computing the Delaunay triangulation:\n\
+  - use 'Qz' to add a point at-infinity.  This reduces precision problems.\n");
+
+    qh_fprintf(qh, fp, 9373, "\
+\n\
+If you need triangular output:\n\
+  - use option 'Qt' to triangulate the output\n\
+  - use option 'QJ' to joggle the input points and remove precision errors\n\
+  - use option 'Ft'.  It triangulates non-simplicial facets with added points.\n\
+\n\
+If you must use 'Q0',\n\
+try one or more of the following options.  They can not guarantee an output.\n\
+  - use 'QbB' to scale the input to a cube.\n\
+  - use 'Po' to produce output and prevent partitioning for flipped facets\n\
+  - use 'V0' to set min. distance to visible facet as 0 instead of roundoff\n\
+  - use 'En' to specify a maximum roundoff error less than %2.2g.\n\
+  - options 'Qf', 'Qbb', and 'QR0' may also help\n",
+               qh->DISTround);
+    qh_fprintf(qh, fp, 9374, "\
+\n\
+To guarantee simplicial output:\n\
+  - use option 'Qt' to triangulate the output\n\
+  - use option 'QJ' to joggle the input points and remove precision errors\n\
+  - use option 'Ft' to triangulate the output by adding points\n\
+  - use exact arithmetic (see \"Imprecision in Qhull\", qh-impre.htm)\n\
+");
+  }
+} /* printhelp_degenerate */
+
+
+/* qh_printhelp_narrowhull( minangle )
+     Warn about a narrow hull
+
+  notes:
+    Alternatively, reduce qh_WARNnarrow in user.h
+
+*/
+void qh_printhelp_narrowhull(qhT *qh, FILE *fp, realT minangle) {
+
+    qh_fprintf(qh, fp, 9375, "qhull precision warning: \n\
+The initial hull is narrow (cosine of min. angle is %.16f).\n\
+A coplanar point may lead to a wide facet.  Options 'QbB' (scale to unit box)\n\
+or 'Qbb' (scale last coordinate) may remove this warning.  Use 'Pp' to skip\n\
+this warning.  See 'Limitations' in qh-impre.htm.\n",
+          -minangle);   /* convert from angle between normals to angle between facets */
+} /* printhelp_narrowhull */
+
+/* qh_printhelp_singular
+      prints descriptive message for singular input
+*/
+void qh_printhelp_singular(qhT *qh, FILE *fp) {
+  facetT *facet;
+  vertexT *vertex, **vertexp;
+  realT min, max, *coord, dist;
+  int i,k;
+
+  qh_fprintf(qh, fp, 9376, "\n\
+The input to qhull appears to be less than %d dimensional, or a\n\
+computation has overflowed.\n\n\
+Qhull could not construct a clearly convex simplex from points:\n",
+           qh->hull_dim);
+  qh_printvertexlist(qh, fp, "", qh->facet_list, NULL, qh_ALL);
+  if (!qh_QUICKhelp)
+    qh_fprintf(qh, fp, 9377, "\n\
+The center point is coplanar with a facet, or a vertex is coplanar\n\
+with a neighboring facet.  The maximum round off error for\n\
+computing distances is %2.2g.  The center point, facets and distances\n\
+to the center point are as follows:\n\n", qh->DISTround);
+  qh_printpointid(qh, fp, "center point", qh->hull_dim, qh->interior_point, -1);
+  qh_fprintf(qh, fp, 9378, "\n");
+  FORALLfacets {
+    qh_fprintf(qh, fp, 9379, "facet");
+    FOREACHvertex_(facet->vertices)
+      qh_fprintf(qh, fp, 9380, " p%d", qh_pointid(qh, vertex->point));
+    zinc_(Zdistio);
+    qh_distplane(qh, qh->interior_point, facet, &dist);
+    qh_fprintf(qh, fp, 9381, " distance= %4.2g\n", dist);
+  }
+  if (!qh_QUICKhelp) {
+    if (qh->HALFspace)
+      qh_fprintf(qh, fp, 9382, "\n\
+These points are the dual of the given halfspaces.  They indicate that\n\
+the intersection is degenerate.\n");
+    qh_fprintf(qh, fp, 9383,"\n\
+These points either have a maximum or minimum x-coordinate, or\n\
+they maximize the determinant for k coordinates.  Trial points\n\
+are first selected from points that maximize a coordinate.\n");
+    if (qh->hull_dim >= qh_INITIALmax)
+      qh_fprintf(qh, fp, 9384, "\n\
+Because of the high dimension, the min x-coordinate and max-coordinate\n\
+points are used if the determinant is non-zero.  Option 'Qs' will\n\
+do a better, though much slower, job.  Instead of 'Qs', you can change\n\
+the points by randomly rotating the input with 'QR0'.\n");
+  }
+  qh_fprintf(qh, fp, 9385, "\nThe min and max coordinates for each dimension are:\n");
+  for (k=0; k < qh->hull_dim; k++) {
+    min= REALmax;
+    max= -REALmin;
+    for (i=qh->num_points, coord= qh->first_point+k; i--; coord += qh->hull_dim) {
+      maximize_(max, *coord);
+      minimize_(min, *coord);
+    }
+    qh_fprintf(qh, fp, 9386, "  %d:  %8.4g  %8.4g  difference= %4.4g\n", k, min, max, max-min);
+  }
+  if (!qh_QUICKhelp) {
+    qh_fprintf(qh, fp, 9387, "\n\
+If the input should be full dimensional, you have several options that\n\
+may determine an initial simplex:\n\
+  - use 'QJ'  to joggle the input and make it full dimensional\n\
+  - use 'QbB' to scale the points to the unit cube\n\
+  - use 'QR0' to randomly rotate the input for different maximum points\n\
+  - use 'Qs'  to search all points for the initial simplex\n\
+  - use 'En'  to specify a maximum roundoff error less than %2.2g.\n\
+  - trace execution with 'T3' to see the determinant for each point.\n",
+                     qh->DISTround);
+#if REALfloat
+    qh_fprintf(qh, fp, 9388, "\
+  - recompile qhull for realT precision(#define REALfloat 0 in libqhull.h).\n");
+#endif
+    qh_fprintf(qh, fp, 9389, "\n\
+If the input is lower dimensional:\n\
+  - use 'QJ' to joggle the input and make it full dimensional\n\
+  - use 'Qbk:0Bk:0' to delete coordinate k from the input.  You should\n\
+    pick the coordinate with the least range.  The hull will have the\n\
+    correct topology.\n\
+  - determine the flat containing the points, rotate the points\n\
+    into a coordinate plane, and delete the other coordinates.\n\
+  - add one or more points to make the input full dimensional.\n\
+");
+    if (qh->DELAUNAY && !qh->ATinfinity)
+      qh_fprintf(qh, fp, 9390, "\n\n\
+This is a Delaunay triangulation and the input is co-circular or co-spherical:\n\
+  - use 'Qz' to add a point \"at infinity\" (i.e., above the paraboloid)\n\
+  - or use 'QJ' to joggle the input and avoid co-circular data\n");
+  }
+} /* printhelp_singular */
+
+
+/*-----------------------------------------
+-user_memsizes- allocate up to 10 additional, quick allocation sizes
+*/
+void qh_user_memsizes(qhT *qh) {
+
+  QHULL_UNUSED(qh);
+  /* qh_memsize(qh, size); */
+} /* user_memsizes */
+
+#endif
diff --git a/xs/src/qhull/src/user_eg3/user_eg3.pro b/xs/src/qhull/src/user_eg3/user_eg3.pro
new file mode 100644
index 0000000000..35372fbf92
--- /dev/null
+++ b/xs/src/qhull/src/user_eg3/user_eg3.pro
@@ -0,0 +1,12 @@
+# -------------------------------------------------
+# user_eg3.pro -- Qt project for cpp demonstration user_eg3.exe
+#
+# The C++ interface requires reentrant Qhull.
+# -------------------------------------------------
+
+include(../qhull-app-cpp.pri)
+
+TARGET = user_eg3
+CONFIG -= qt
+
+SOURCES += user_eg3_r.cpp
diff --git a/xs/src/qhull/src/user_eg3/user_eg3_r.cpp b/xs/src/qhull/src/user_eg3/user_eg3_r.cpp
new file mode 100644
index 0000000000..5257872ab8
--- /dev/null
+++ b/xs/src/qhull/src/user_eg3/user_eg3_r.cpp
@@ -0,0 +1,162 @@
+#//! user_eg3_r.cpp -- Invoke rbox and qhull from C++
+
+#include "libqhullcpp/RboxPoints.h"
+#include "libqhullcpp/QhullError.h"
+#include "libqhullcpp/QhullQh.h"
+#include "libqhullcpp/QhullFacet.h"
+#include "libqhullcpp/QhullFacetList.h"
+#include "libqhullcpp/QhullLinkedList.h"
+#include "libqhullcpp/QhullVertex.h"
+#include "libqhullcpp/Qhull.h"
+
+#include <cstdio>   /* for printf() of help message */
+#include <ostream>
+#include <stdexcept>
+
+using std::cerr;
+using std::cin;
+using std::cout;
+using std::endl;
+
+using orgQhull::Qhull;
+using orgQhull::QhullError;
+using orgQhull::QhullFacet;
+using orgQhull::QhullFacetList;
+using orgQhull::QhullQh;
+using orgQhull::RboxPoints;
+using orgQhull::QhullVertex;
+using orgQhull::QhullVertexSet;
+
+int main(int argc, char **argv);
+int user_eg3(int argc, char **argv);
+
+char prompt[]= "\n\
+user_eg3 -- demonstrate calling rbox and qhull from C++.\n\
+\n\
+user_eg3 is statically linked to reentrant qhull.  If user_eg3\n\
+fails immediately, it is probably linked to the non-reentrant qhull.\n\
+Try 'user_eg3 rbox qhull \"T1\"'\n\
+\n\
+  eg-100                       Run the example in qh-code.htm\n\
+  rbox \"200 D4\" ...            Generate points from rbox\n\
+  qhull \"d p\" ...              Run qhull and produce output\n\
+  qhull-cout \"o\" ...           Run qhull and produce output to cout\n\
+  qhull \"T1\" ...               Run qhull with level-1 trace to cerr\n\
+  facets                       Print facets when done\n\
+\n\
+For example\n\
+  user_eg3 rbox qhull\n\
+  user_eg3 rbox qhull d\n\
+  user_eg3 rbox \"10 D2\"  \"2 D2\" qhull  \"s p\" facets\n\
+\n\
+";
+
+
+/*--------------------------------------------
+-user_eg3-  main procedure of user_eg3 application
+*/
+int main(int argc, char **argv) {
+
+    QHULL_LIB_CHECK
+
+    if(argc==1){
+        cout << prompt;
+        return 1;
+    }
+    try{
+        return user_eg3(argc, argv);
+    }catch(QhullError &e){
+        cerr << e.what() << std::endl;
+        return e.errorCode();
+    }
+}//main
+
+int user_eg3(int argc, char **argv)
+{
+    if(strcmp(argv[1], "eg-100")==0){
+        RboxPoints rbox("100");
+        Qhull q(rbox, "");
+        QhullFacetList facets= q.facetList();
+        cout << facets;
+        return 0;
+    }
+    bool printFacets= false;
+    RboxPoints rbox;
+    Qhull qhull;
+    int readingRbox= 0;
+    int readingQhull= 0;
+    for(int i=1; i<argc; i++){
+        if(strcmp(argv[i], "rbox")==0){
+            if(readingRbox!=0 || readingQhull!=0){
+                cerr << "user_eg3 -- \"rbox\" must be first" << endl;
+                return 1;
+            }
+            readingRbox++;
+        }else if(strcmp(argv[i], "qhull")==0
+        || strcmp(argv[i], "qhull-cout")==0){
+            if(readingQhull){
+                cerr << "user_eg3 -- only one \"qhull\" or \"qhull-cout\" allowed." << endl;
+                return 1;
+            }
+            if(strcmp(argv[i], "qhull-cout")==0){
+                qhull.setOutputStream(&cout);
+            }
+            if(rbox.isEmpty()){
+                if(readingRbox){
+                    rbox.appendPoints("10 D2");
+                }else{
+                    cerr << "Enter dimension count coordinates.  End with ^Z (Windows) or ^D (Unix).\n";
+                    rbox.appendPoints(cin);
+                }
+            }
+            readingQhull++;
+            readingRbox= 0;
+        }else if(strcmp(argv[i], "facets")==0){
+            printFacets= true;
+        }else if(readingRbox){
+            readingRbox++;
+            cerr << "rbox " << argv[i] << endl;
+            rbox.appendPoints(argv[i]);
+            if(rbox.hasRboxMessage()){
+                cerr << "user_eg3 " << argv[i] << " -- " << rbox.rboxMessage();
+                return rbox.rboxStatus();
+            }
+        }else if(readingQhull){
+            if(readingQhull==1){
+                qhull.runQhull(rbox, argv[i]);
+                qhull.outputQhull();
+            }else{
+                qhull.outputQhull(argv[i]);
+            }
+            readingQhull++;
+            if(qhull.hasQhullMessage()){
+                cerr << "\nResults of " << argv[i] << "\n" << qhull.qhullMessage();
+                qhull.clearQhullMessage();
+            }
+        }else{
+            cerr << "user_eg3 error: Expecting qhull, qhull-cout, or rbox.  Got " << argv[i] << endl;
+            return 1;
+        }
+    }//foreach argv
+    if(readingRbox){
+        cout << rbox;
+        return 0;
+    }
+    if(readingQhull==1){ // e.g., rbox 10 qhull
+        qhull.runQhull(rbox, "");
+        qhull.outputQhull();
+        if(qhull.hasQhullMessage()){
+            cerr << "\nResults of qhull\n" << qhull.qhullMessage();
+            qhull.clearQhullMessage();
+        }
+    }
+    if(qhull.hasOutputStream()){
+        return 0;
+    }
+    if(printFacets){
+        QhullFacetList facets= qhull.facetList();
+        cout << "\nFacets created by Qhull::runQhull()\n" << facets;
+    }
+    return 0;
+}//user_eg3
+
diff --git a/xs/src/slic3r/GUI/2DBed.cpp b/xs/src/slic3r/GUI/2DBed.cpp
index 5f087a8816..e19f839cdd 100644
--- a/xs/src/slic3r/GUI/2DBed.cpp
+++ b/xs/src/slic3r/GUI/2DBed.cpp
@@ -32,7 +32,7 @@ void Bed_2D::repaint()
 	cw--;
 	ch--;
 
-	auto cbb = BoundingBoxf(Pointf(0, 0),Pointf(cw, ch));
+	auto cbb = BoundingBoxf(Vec2d(0, 0),Vec2d(cw, ch));
 	// leave space for origin point
 	cbb.min(0) += 4;
 	cbb.max -= Vec2d(4., 4.);
@@ -50,19 +50,19 @@ void Bed_2D::repaint()
 	auto bed_shape = m_bed_shape;
 	auto bed_polygon = Polygon::new_scale(m_bed_shape);
 	auto bb = BoundingBoxf(m_bed_shape);
-	bb.merge(Pointf(0, 0));  // origin needs to be in the visible area
+	bb.merge(Vec2d(0, 0));  // origin needs to be in the visible area
 	auto bw = bb.size()(0);
 	auto bh = bb.size()(1);
 	auto bcenter = bb.center();
 
 	// calculate the scaling factor for fitting bed shape in canvas area
 	auto sfactor = std::min(cw/bw, ch/bh);
-	auto shift = Pointf(
+	auto shift = Vec2d(
 		ccenter(0) - bcenter(0) * sfactor,
 		ccenter(1) - bcenter(1) * sfactor
 		);
 	m_scale_factor = sfactor;
-	m_shift = Pointf(shift(0) + cbb.min(0),
+	m_shift = Vec2d(shift(0) + cbb.min(0),
 					shift(1) - (cbb.max(1) - GetSize().GetHeight()));
 
 	// draw bed fill
@@ -79,11 +79,10 @@ void Bed_2D::repaint()
 	auto step = 10;  // 1cm grid
 	Polylines polylines;
 	for (auto x = bb.min(0) - fmod(bb.min(0), step) + step; x < bb.max(0); x += step) {
-		Polyline pl = Polyline::new_scale({ Pointf(x, bb.min(1)), Pointf(x, bb.max(1)) });
-		polylines.push_back(pl);
+		polylines.push_back(Polyline::new_scale({ Vec2d(x, bb.min(1)), Vec2d(x, bb.max(1)) }));
 	}
 	for (auto y = bb.min(1) - fmod(bb.min(1), step) + step; y < bb.max(1); y += step) {
-		polylines.push_back(Polyline::new_scale({ Pointf(bb.min(0), y), Pointf(bb.max(0), y) }));
+		polylines.push_back(Polyline::new_scale({ Vec2d(bb.min(0), y), Vec2d(bb.max(0), y) }));
 	}
 	polylines = intersection_pl(polylines, bed_polygon);
 
@@ -91,8 +90,8 @@ void Bed_2D::repaint()
 	for (auto pl : polylines)
 	{
 		for (size_t i = 0; i < pl.points.size()-1; i++){
-			Point pt1 = to_pixels(Pointf::new_unscale(pl.points[i]));
-			Point pt2 = to_pixels(Pointf::new_unscale(pl.points[i+1]));
+			Point pt1 = to_pixels(unscale(pl.points[i]));
+			Point pt2 = to_pixels(unscale(pl.points[i+1]));
 			dc.DrawLine(pt1(0), pt1(1), pt2(0), pt2(1));
 		}
 	}
@@ -102,29 +101,25 @@ void Bed_2D::repaint()
 	dc.SetBrush(wxBrush(wxColour(0, 0, 0), wxTRANSPARENT));
 	dc.DrawPolygon(&pt_list, 0, 0);
 
-	auto origin_px = to_pixels(Pointf(0, 0));
+	auto origin_px = to_pixels(Vec2d(0, 0));
 
 	// draw axes
 	auto axes_len = 50;
 	auto arrow_len = 6;
 	auto arrow_angle = Geometry::deg2rad(45.0);
 	dc.SetPen(wxPen(wxColour(255, 0, 0), 2, wxSOLID));  // red
-	auto x_end = Pointf(origin_px(0) + axes_len, origin_px(1));
+	auto x_end = Vec2d(origin_px(0) + axes_len, origin_px(1));
 	dc.DrawLine(wxPoint(origin_px(0), origin_px(1)), wxPoint(x_end(0), x_end(1)));
 	for (auto angle : { -arrow_angle, arrow_angle }){
-		auto end = x_end;
-		end(0) -= arrow_len;
-		end.rotate(angle, x_end);
+		auto end = Eigen::Translation2d(x_end) * Eigen::Rotation2Dd(angle) * Eigen::Translation2d(- x_end) * Eigen::Vector2d(x_end(0) - arrow_len, x_end(1));
 		dc.DrawLine(wxPoint(x_end(0), x_end(1)), wxPoint(end(0), end(1)));
 	}
 
 	dc.SetPen(wxPen(wxColour(0, 255, 0), 2, wxSOLID));  // green
-	auto y_end = Pointf(origin_px(0), origin_px(1) - axes_len);
+	auto y_end = Vec2d(origin_px(0), origin_px(1) - axes_len);
 	dc.DrawLine(wxPoint(origin_px(0), origin_px(1)), wxPoint(y_end(0), y_end(1)));
 	for (auto angle : { -arrow_angle, arrow_angle }) {
-		auto end = y_end;
-		end(1) += arrow_len;
-		end.rotate(angle, y_end);
+		auto end = Eigen::Translation2d(y_end) * Eigen::Rotation2Dd(angle) * Eigen::Translation2d(- y_end) * Eigen::Vector2d(y_end(0), y_end(1) + arrow_len);
 		dc.DrawLine(wxPoint(y_end(0), y_end(1)), wxPoint(end(0), end(1)));
 	}
 
@@ -142,7 +137,7 @@ void Bed_2D::repaint()
 	dc.DrawText(origin_label, origin_label_x, origin_label_y);
 
 	// draw current position
-	if (m_pos!= Pointf(0, 0)) {
+	if (m_pos!= Vec2d(0, 0)) {
 		auto pos_px = to_pixels(m_pos);
 		dc.SetPen(wxPen(wxColour(200, 0, 0), 2, wxSOLID));
 		dc.SetBrush(wxBrush(wxColour(200, 0, 0), wxTRANSPARENT));
@@ -156,7 +151,7 @@ void Bed_2D::repaint()
 }
 
 // convert G - code coordinates into pixels
-Point Bed_2D::to_pixels(Pointf point){
+Point Bed_2D::to_pixels(Vec2d point){
 	auto p = point * m_scale_factor + m_shift;
 	return Point(p(0), GetSize().GetHeight() - p(1)); 
 }
@@ -175,11 +170,11 @@ void Bed_2D::mouse_event(wxMouseEvent event){
 }
 
 // convert pixels into G - code coordinates
-Pointf Bed_2D::to_units(Point point){
-	return (Pointf(point(0), GetSize().GetHeight() - point(1)) - m_shift) * (1. / m_scale_factor);
+Vec2d Bed_2D::to_units(Point point){
+	return (Vec2d(point(0), GetSize().GetHeight() - point(1)) - m_shift) * (1. / m_scale_factor);
 }
 
-void Bed_2D::set_pos(Pointf pos){
+void Bed_2D::set_pos(Vec2d pos){
 	m_pos = pos;
 	Refresh();
 }
diff --git a/xs/src/slic3r/GUI/2DBed.hpp b/xs/src/slic3r/GUI/2DBed.hpp
index 4b14986a2b..d7a7f4260e 100644
--- a/xs/src/slic3r/GUI/2DBed.hpp
+++ b/xs/src/slic3r/GUI/2DBed.hpp
@@ -14,15 +14,15 @@ class Bed_2D : public wxPanel
 	bool		m_painted = false;
 	bool		m_interactive = false;
 	double		m_scale_factor;
-	Pointf		m_shift;
-	Pointf		m_pos;
-	std::function<void(Pointf)>	m_on_move = nullptr;
+	Vec2d		m_shift = Vec2d::Zero();
+	Vec2d		m_pos = Vec2d::Zero();
+	std::function<void(Vec2d)>	m_on_move = nullptr;
 
-	Point		to_pixels(Pointf point);
-	Pointf		to_units(Point point);
+	Point		to_pixels(Vec2d point);
+	Vec2d		to_units(Point point);
 	void		repaint();
 	void		mouse_event(wxMouseEvent event);
-	void		set_pos(Pointf pos);
+	void		set_pos(Vec2d pos);
 
 public:
 	Bed_2D(wxWindow* parent) 
@@ -41,7 +41,7 @@ public:
 	}
 	~Bed_2D(){}
 
-	std::vector<Pointf>		m_bed_shape;
+	std::vector<Vec2d>		m_bed_shape;
 		
 };
 
diff --git a/xs/src/slic3r/GUI/3DScene.cpp b/xs/src/slic3r/GUI/3DScene.cpp
index 36952d230e..c9607ccf9c 100644
--- a/xs/src/slic3r/GUI/3DScene.cpp
+++ b/xs/src/slic3r/GUI/3DScene.cpp
@@ -39,7 +39,7 @@ void GLIndexedVertexArray::load_mesh_flat_shading(const TriangleMesh &mesh)
     for (int i = 0; i < mesh.stl.stats.number_of_facets; ++ i) {
         const stl_facet &facet = mesh.stl.facet_start[i];
         for (int j = 0; j < 3; ++ j)
-            this->push_geometry(facet.vertex[j].x, facet.vertex[j].y, facet.vertex[j].z, facet.normal.x, facet.normal.y, facet.normal.z);
+            this->push_geometry(facet.vertex[j](0), facet.vertex[j](1), facet.vertex[j](2), facet.normal(0), facet.normal(1), facet.normal(2));
     }
 }
 
@@ -55,7 +55,7 @@ void GLIndexedVertexArray::load_mesh_full_shading(const TriangleMesh &mesh)
     for (int i = 0; i < mesh.stl.stats.number_of_facets; ++i) {
         const stl_facet &facet = mesh.stl.facet_start[i];
         for (int j = 0; j < 3; ++j)
-            this->push_geometry(facet.vertex[j].x, facet.vertex[j].y, facet.vertex[j].z, facet.normal.x, facet.normal.y, facet.normal.z);
+            this->push_geometry(facet.vertex[j](0), facet.vertex[j](1), facet.vertex[j](2), facet.normal(0), facet.normal(1), facet.normal(2));
 
         this->push_triangle(vertices_count, vertices_count + 1, vertices_count + 2);
         vertices_count += 3;
@@ -195,9 +195,12 @@ const float GLVolume::OUTSIDE_COLOR[4] = { 0.0f, 0.38f, 0.8f, 1.0f };
 const float GLVolume::SELECTED_OUTSIDE_COLOR[4] = { 0.19f, 0.58f, 1.0f, 1.0f };
 
 GLVolume::GLVolume(float r, float g, float b, float a)
-    : m_angle_z(0.0f)
+    : m_origin(0, 0, 0)
+    , m_angle_z(0.0f)
     , m_scale_factor(1.0f)
-    , m_dirty(true)
+    , m_transformed_bounding_box_dirty(true)
+    , m_transformed_convex_hull_bounding_box_dirty(true)
+    , m_convex_hull(nullptr)
     , composite_id(-1)
     , select_group_id(-1)
     , drag_group_id(-1)
@@ -214,8 +217,6 @@ GLVolume::GLVolume(float r, float g, float b, float a)
     , tverts_range(0, size_t(-1))
     , qverts_range(0, size_t(-1))
 {
-    m_world_mat = Transform3f::Identity();
-
     color[0] = r;
     color[1] = g;
     color[2] = b;
@@ -252,51 +253,86 @@ void GLVolume::set_render_color()
         set_render_color(color, 4);
 }
 
-const Pointf3& GLVolume::get_origin() const
+const Vec3d& GLVolume::get_origin() const
 {
     return m_origin;
 }
 
-void GLVolume::set_origin(const Pointf3& origin)
+float GLVolume::get_angle_z()
 {
-    m_origin = origin;
-    m_dirty = true;
+    return m_angle_z;
+}
+
+void GLVolume::set_origin(const Vec3d& origin)
+{
+    if (m_origin != origin)
+    {
+        m_origin = origin;
+        m_transformed_bounding_box_dirty = true;
+        m_transformed_convex_hull_bounding_box_dirty = true;
+    }
 }
 
 void GLVolume::set_angle_z(float angle_z)
 {
-    m_angle_z = angle_z;
-    m_dirty = true;
+    if (m_angle_z != angle_z)
+    {
+        m_angle_z = angle_z;
+        m_transformed_bounding_box_dirty = true;
+        m_transformed_convex_hull_bounding_box_dirty = true;
+    }
 }
 
 void GLVolume::set_scale_factor(float scale_factor)
 {
-    m_scale_factor = scale_factor;
-    m_dirty = true;
+    if (m_scale_factor != scale_factor)
+    {
+        m_scale_factor = scale_factor;
+        m_transformed_bounding_box_dirty = true;
+        m_transformed_convex_hull_bounding_box_dirty = true;
+    }
 }
 
-const Transform3f& GLVolume::world_matrix() const
+void GLVolume::set_convex_hull(const TriangleMesh& convex_hull)
 {
-    if (m_dirty)
-    {
-        m_world_mat = Transform3f::Identity();
-        m_world_mat.translate(Vec3f(m_origin(0), m_origin(1), 0));
-        m_world_mat.rotate(Eigen::AngleAxisf(m_angle_z, Vec3f::UnitZ()));
-        m_world_mat.scale(m_scale_factor);
-        m_dirty = false;
-    }
+    m_convex_hull = &convex_hull;
+}
 
-    return m_world_mat;
+Transform3f GLVolume::world_matrix() const
+{
+    Transform3f matrix = Transform3f::Identity();
+    matrix.translate(Vec3f((float)m_origin(0), (float)m_origin(1), (float)m_origin(2)));
+    matrix.rotate(Eigen::AngleAxisf(m_angle_z, Vec3f::UnitZ()));
+    matrix.scale(m_scale_factor);
+    return matrix;
 }
 
 BoundingBoxf3 GLVolume::transformed_bounding_box() const
 {
-    if (m_dirty)
-        m_transformed_bounding_box = bounding_box.transformed(world_matrix());
+    if (m_transformed_bounding_box_dirty)
+    {
+        m_transformed_bounding_box = bounding_box.transformed(world_matrix().cast<double>());
+        m_transformed_bounding_box_dirty = false;
+    }
 
     return m_transformed_bounding_box;
 }
 
+BoundingBoxf3 GLVolume::transformed_convex_hull_bounding_box() const
+{
+    if (m_transformed_convex_hull_bounding_box_dirty)
+    {
+        if ((m_convex_hull != nullptr) && (m_convex_hull->stl.stats.number_of_facets > 0))
+            m_transformed_convex_hull_bounding_box = m_convex_hull->transformed_bounding_box(world_matrix().cast<double>());
+        else
+            m_transformed_convex_hull_bounding_box = bounding_box.transformed(world_matrix().cast<double>());
+
+        m_transformed_convex_hull_bounding_box_dirty = false;
+    }
+
+    return m_transformed_convex_hull_bounding_box;
+}
+
 void GLVolume::set_range(double min_z, double max_z)
 {
     this->qverts_range.first  = 0;
@@ -623,13 +659,14 @@ std::vector<int> GLVolumeCollection::load_object(
 
             if (!model_volume->modifier)
             {
+                v.set_convex_hull(model_volume->get_convex_hull());
                 v.layer_height_texture = layer_height_texture;
                 if (extruder_id != -1)
                     v.extruder_id = extruder_id;
             }
             v.is_modifier = model_volume->modifier;
             v.shader_outside_printer_detection_enabled = !model_volume->modifier;
-            v.set_origin(Pointf3(instance->offset(0), instance->offset(1), 0.0));
+            v.set_origin(Vec3d(instance->offset(0), instance->offset(1), 0.0));
             v.set_angle_z(instance->rotation);
             v.set_scale_factor(instance->scaling_factor);
         }
@@ -660,16 +697,16 @@ int GLVolumeCollection::load_wipe_tower_preview(
         // We'll now create the box with jagged edge. y-coordinates of the pre-generated model are shifted so that the front
         // edge has y=0 and centerline of the back edge has y=depth:
         Pointf3s points;
-        std::vector<Point3> facets;
+        std::vector<Vec3crd> facets;
         float out_points_idx[][3] = {{0, -depth, 0}, {0, 0, 0}, {38.453, 0, 0}, {61.547, 0, 0}, {100, 0, 0}, {100, -depth, 0}, {55.7735, -10, 0}, {44.2265, 10, 0},
                                      {38.453, 0, 1}, {0, 0, 1}, {0, -depth, 1}, {100, -depth, 1}, {100, 0, 1}, {61.547, 0, 1}, {55.7735, -10, 1}, {44.2265, 10, 1}};
         int out_facets_idx[][3] = {{0, 1, 2}, {3, 4, 5}, {6, 5, 0}, {3, 5, 6}, {6, 2, 7}, {6, 0, 2}, {8, 9, 10}, {11, 12, 13}, {10, 11, 14}, {14, 11, 13}, {15, 8, 14},
                                    {8, 10, 14}, {3, 12, 4}, {3, 13, 12}, {6, 13, 3}, {6, 14, 13}, {7, 14, 6}, {7, 15, 14}, {2, 15, 7}, {2, 8, 15}, {1, 8, 2}, {1, 9, 8},
                                    {0, 9, 1}, {0, 10, 9}, {5, 10, 0}, {5, 11, 10}, {4, 11, 5}, {4, 12, 11}};
         for (int i=0;i<16;++i)
-            points.push_back(Pointf3(out_points_idx[i][0] / (100.f/min_width), out_points_idx[i][1] + depth, out_points_idx[i][2]));
+            points.push_back(Vec3d(out_points_idx[i][0] / (100.f/min_width), out_points_idx[i][1] + depth, out_points_idx[i][2]));
         for (int i=0;i<28;++i)
-            facets.push_back(Point3(out_facets_idx[i][0], out_facets_idx[i][1], out_facets_idx[i][2]));
+            facets.push_back(Vec3crd(out_facets_idx[i][0], out_facets_idx[i][1], out_facets_idx[i][2]));
         TriangleMesh tooth_mesh(points, facets);
 
         // We have the mesh ready. It has one tooth and width of min_width. We will now append several of these together until we are close to
@@ -680,7 +717,7 @@ int GLVolumeCollection::load_wipe_tower_preview(
             tooth_mesh.translate(min_width, 0.f, 0.f);
         }
 
-        mesh.scale(Pointf3(width/(n*min_width), 1.f, height)); // Scaling to proper width
+        mesh.scale(Vec3d(width/(n*min_width), 1.f, height)); // Scaling to proper width
     }
     else
         mesh = make_cube(width, depth, height);
@@ -700,7 +737,7 @@ int GLVolumeCollection::load_wipe_tower_preview(
     else
         v.indexed_vertex_array.load_mesh_flat_shading(mesh);
 
-    v.set_origin(Pointf3(pos_x, pos_y, 0.));
+    v.set_origin(Vec3d(pos_x, pos_y, 0.));
 
     // finalize_geometry() clears the vertex arrays, therefore the bounding box has to be computed before finalize_geometry().
     v.bounding_box = v.indexed_vertex_array.bounding_box();
@@ -786,7 +823,7 @@ bool GLVolumeCollection::check_outside_state(const DynamicPrintConfig* config, M
         return false;
 
     BoundingBox bed_box_2D = get_extents(Polygon::new_scale(opt->values));
-    BoundingBoxf3 print_volume(Pointf3(unscale(bed_box_2D.min(0)), unscale(bed_box_2D.min(1)), 0.0), Pointf3(unscale(bed_box_2D.max(0)), unscale(bed_box_2D.max(1)), config->opt_float("max_print_height")));
+    BoundingBoxf3 print_volume(Vec3d(unscale<double>(bed_box_2D.min(0)), unscale<double>(bed_box_2D.min(1)), 0.0), Vec3d(unscale<double>(bed_box_2D.max(0)), unscale<double>(bed_box_2D.max(1)), config->opt_float("max_print_height")));
     // Allow the objects to protrude below the print bed
     print_volume.min(2) = -1e10;
 
@@ -795,9 +832,9 @@ bool GLVolumeCollection::check_outside_state(const DynamicPrintConfig* config, M
 
     for (GLVolume* volume : this->volumes)
     {
-        if ((volume != nullptr) && !volume->is_modifier)
+        if ((volume != nullptr) && !volume->is_modifier && (!volume->is_wipe_tower || (volume->is_wipe_tower && volume->shader_outside_printer_detection_enabled)))
         {
-            const BoundingBoxf3& bb = volume->transformed_bounding_box();
+            const BoundingBoxf3& bb = volume->transformed_convex_hull_bounding_box();
             bool contained = print_volume.contains(bb);
             all_contained &= contained;
 
@@ -951,8 +988,8 @@ static void thick_lines_to_indexed_vertex_array(
     // right, left, top, bottom
     int     idx_prev[4]      = { -1, -1, -1, -1 };
     double  bottom_z_prev    = 0.;
-    Pointf  b1_prev;
-    Vectorf v_prev;
+    Vec2d  b1_prev(Vec2d::Zero());
+    Vec2d v_prev(Vec2d::Zero());
     int     idx_initial[4]   = { -1, -1, -1, -1 };
     double  width_initial    = 0.;
     double  bottom_z_initial = 0.0;
@@ -962,7 +999,7 @@ static void thick_lines_to_indexed_vertex_array(
     for (size_t ii = 0; ii < lines_end; ++ ii) {
         size_t i = (ii == lines.size()) ? 0 : ii;
         const Line &line = lines[i];
-        double len = unscale(line.length());
+        double len = unscale<double>(line.length());
         double inv_len = 1.0 / len;
         double bottom_z = top_z - heights[i];
         double middle_z = 0.5 * (top_z + bottom_z);
@@ -972,28 +1009,28 @@ static void thick_lines_to_indexed_vertex_array(
         bool is_last = (ii == lines_end - 1);
         bool is_closing = closed && is_last;
 
-        Vectorf v = Vectorf::new_unscale(line.vector());
+        Vec2d v = unscale(line.vector());
         v *= inv_len;
 
-        Pointf a = Pointf::new_unscale(line.a);
-        Pointf b = Pointf::new_unscale(line.b);
-        Pointf a1 = a;
-        Pointf a2 = a;
-        Pointf b1 = b;
-        Pointf b2 = b;
+        Vec2d a = unscale(line.a);
+        Vec2d b = unscale(line.b);
+        Vec2d a1 = a;
+        Vec2d a2 = a;
+        Vec2d b1 = b;
+        Vec2d b2 = b;
         {
             double dist = 0.5 * width;  // scaled
             double dx = dist * v(0);
             double dy = dist * v(1);
-            a1 += Vectorf(+dy, -dx);
-            a2 += Vectorf(-dy, +dx);
-            b1 += Vectorf(+dy, -dx);
-            b2 += Vectorf(-dy, +dx);
+            a1 += Vec2d(+dy, -dx);
+            a2 += Vec2d(-dy, +dx);
+            b1 += Vec2d(+dy, -dx);
+            b2 += Vec2d(-dy, +dx);
         }
 
         // calculate new XY normals
         Vector n = line.normal();
-        Vectorf3 xy_right_normal = Vectorf3::new_unscale(n(0), n(1), 0);
+        Vec3d xy_right_normal = unscale(n(0), n(1), 0);
         xy_right_normal *= inv_len;
 
         int idx_a[4];
@@ -1063,7 +1100,7 @@ static void thick_lines_to_indexed_vertex_array(
                 {
                     // Create a sharp corner with an overshot and average the left / right normals.
                     // At the crease angle of 45 degrees, the overshot at the corner will be less than (1-1/cos(PI/8)) = 8.2% over an arc.
-                    Pointf intersection;
+                    Vec2d intersection(Vec2d::Zero());
                     Geometry::ray_ray_intersection(b1_prev, v_prev, a1, v, intersection);
                     a1 = intersection;
                     a2 = 2. * a - intersection;
@@ -1196,15 +1233,15 @@ static void thick_lines_to_indexed_vertex_array(const Lines3& lines,
     int      idx_initial[4] = { -1, -1, -1, -1 };
     int      idx_prev[4] = { -1, -1, -1, -1 };
     double   z_prev = 0.0;
-    Vectorf3 n_right_prev;
-    Vectorf3 n_top_prev;
-    Vectorf3 unit_v_prev;
+    Vec3d n_right_prev = Vec3d::Zero();
+    Vec3d n_top_prev = Vec3d::Zero();
+    Vec3d unit_v_prev = Vec3d::Zero();
     double   width_initial = 0.0;
 
     // new vertices around the line endpoints
     // left, right, top, bottom
-    Pointf3 a[4];
-    Pointf3 b[4];
+    Vec3d a[4] = { Vec3d::Zero(), Vec3d::Zero(), Vec3d::Zero(), Vec3d::Zero() };
+    Vec3d b[4] = { Vec3d::Zero(), Vec3d::Zero(), Vec3d::Zero(), Vec3d::Zero() };
 
     // loop once more in case of closed loops
     size_t lines_end = closed ? (lines.size() + 1) : lines.size();
@@ -1216,17 +1253,17 @@ static void thick_lines_to_indexed_vertex_array(const Lines3& lines,
         double height = heights[i];
         double width = widths[i];
 
-        Vectorf3 unit_v = Vectorf3::new_unscale(line.vector()).normalized();
+        Vec3d unit_v = unscale(line.vector()).normalized();
 
-        Vectorf3 n_top;
-        Vectorf3 n_right;
-        Vectorf3 unit_positive_z(0.0, 0.0, 1.0);
+        Vec3d n_top = Vec3d::Zero();
+        Vec3d n_right = Vec3d::Zero();
+        Vec3d unit_positive_z(0.0, 0.0, 1.0);
 
         if ((line.a(0) == line.b(0)) && (line.a(1) == line.b(1)))
         {
             // vertical segment
-            n_right = (line.a(2) < line.b(2)) ? Vectorf3(-1.0, 0.0, 0.0) : Vectorf3(1.0, 0.0, 0.0);
-            n_top = Vectorf3(0.0, 1.0, 0.0);
+            n_right = (line.a(2) < line.b(2)) ? Vec3d(-1.0, 0.0, 0.0) : Vec3d(1.0, 0.0, 0.0);
+            n_top = Vec3d(0.0, 1.0, 0.0);
         }
         else
         {
@@ -1235,10 +1272,10 @@ static void thick_lines_to_indexed_vertex_array(const Lines3& lines,
             n_top = n_right.cross(unit_v).normalized();
         }
 
-        Vectorf3 rl_displacement = 0.5 * width * n_right;
-        Vectorf3 tb_displacement = 0.5 * height * n_top;
-        Pointf3 l_a = Pointf3::new_unscale(line.a);
-        Pointf3 l_b = Pointf3::new_unscale(line.b);
+        Vec3d rl_displacement = 0.5 * width * n_right;
+        Vec3d tb_displacement = 0.5 * height * n_top;
+        Vec3d l_a = unscale(line.a);
+        Vec3d l_b = unscale(line.b);
 
         a[RIGHT] = l_a + rl_displacement;
         a[LEFT] = l_a - rl_displacement;
@@ -1249,8 +1286,8 @@ static void thick_lines_to_indexed_vertex_array(const Lines3& lines,
         b[TOP] = l_b + tb_displacement;
         b[BOTTOM] = l_b - tb_displacement;
 
-        Vectorf3 n_bottom = -n_top;
-        Vectorf3 n_left = -n_right;
+        Vec3d n_bottom = -n_top;
+        Vec3d n_left = -n_right;
 
         int idx_a[4];
         int idx_b[4];
@@ -1316,9 +1353,9 @@ static void thick_lines_to_indexed_vertex_array(const Lines3& lines,
                 // At the crease angle of 45 degrees, the overshot at the corner will be less than (1-1/cos(PI/8)) = 8.2% over an arc.
 
                 // averages normals
-                Vectorf3 average_n_right = 0.5 * (n_right + n_right_prev).normalized();
-                Vectorf3 average_n_left = -average_n_right;
-                Vectorf3 average_rl_displacement = 0.5 * width * average_n_right;
+                Vec3d average_n_right = 0.5 * (n_right + n_right_prev).normalized();
+                Vec3d average_n_left = -average_n_right;
+                Vec3d average_rl_displacement = 0.5 * width * average_n_right;
 
                 // updates vertices around a
                 a[RIGHT] = l_a + average_rl_displacement;
@@ -1441,14 +1478,14 @@ static void thick_lines_to_indexed_vertex_array(const Lines3& lines,
 #undef BOTTOM
 }
 
-static void point_to_indexed_vertex_array(const Point3& point,
+static void point_to_indexed_vertex_array(const Vec3crd& point,
     double width,
     double height,
     GLIndexedVertexArray& volume)
 {
     // builds a double piramid, with vertices on the local axes, around the point
 
-    Pointf3 center = Pointf3::new_unscale(point);
+    Vec3d center = unscale(point);
 
     double scale_factor = 1.0;
     double w = scale_factor * width;
@@ -1462,13 +1499,13 @@ static void point_to_indexed_vertex_array(const Point3& point,
         idxs[i] = idx_last + i;
     }
 
-    Vectorf3 displacement_x(w, 0.0, 0.0);
-    Vectorf3 displacement_y(0.0, w, 0.0);
-    Vectorf3 displacement_z(0.0, 0.0, h);
+    Vec3d displacement_x(w, 0.0, 0.0);
+    Vec3d displacement_y(0.0, w, 0.0);
+    Vec3d displacement_z(0.0, 0.0, h);
 
-    Vectorf3 unit_x(1.0, 0.0, 0.0);
-    Vectorf3 unit_y(0.0, 1.0, 0.0);
-    Vectorf3 unit_z(0.0, 0.0, 1.0);
+    Vec3d unit_x(1.0, 0.0, 0.0);
+    Vec3d unit_y(0.0, 1.0, 0.0);
+    Vec3d unit_z(0.0, 0.0, 1.0);
 
     // vertices
     volume.push_geometry(center - displacement_x, -unit_x); // idxs[0]
@@ -1511,7 +1548,7 @@ void _3DScene::thick_lines_to_verts(const Lines3& lines,
     thick_lines_to_indexed_vertex_array(lines, widths, heights, closed, volume.indexed_vertex_array);
 }
 
-static void thick_point_to_verts(const Point3& point,
+static void thick_point_to_verts(const Vec3crd& point,
     double width,
     double height,
     GLVolume& volume)
@@ -1617,7 +1654,7 @@ void _3DScene::polyline3_to_verts(const Polyline3& polyline, double width, doubl
     thick_lines_to_verts(lines, widths, heights, false, volume);
 }
 
-void _3DScene::point3_to_verts(const Point3& point, double width, double height, GLVolume& volume)
+void _3DScene::point3_to_verts(const Vec3crd& point, double width, double height, GLVolume& volume)
 {
     thick_point_to_verts(point, width, height, volume);
 }
@@ -1814,6 +1851,11 @@ void _3DScene::enable_gizmos(wxGLCanvas* canvas, bool enable)
     s_canvas_mgr.enable_gizmos(canvas, enable);
 }
 
+void _3DScene::enable_toolbar(wxGLCanvas* canvas, bool enable)
+{
+    s_canvas_mgr.enable_toolbar(canvas, enable);
+}
+
 void _3DScene::enable_shader(wxGLCanvas* canvas, bool enable)
 {
     s_canvas_mgr.enable_shader(canvas, enable);
@@ -1834,6 +1876,16 @@ void _3DScene::allow_multisample(wxGLCanvas* canvas, bool allow)
     s_canvas_mgr.allow_multisample(canvas, allow);
 }
 
+void _3DScene::enable_toolbar_item(wxGLCanvas* canvas, const std::string& name, bool enable)
+{
+    s_canvas_mgr.enable_toolbar_item(canvas, name, enable);
+}
+
+bool _3DScene::is_toolbar_item_pressed(wxGLCanvas* canvas, const std::string& name)
+{
+    return s_canvas_mgr.is_toolbar_item_pressed(canvas, name);
+}
+
 void _3DScene::zoom_to_bed(wxGLCanvas* canvas)
 {
     s_canvas_mgr.zoom_to_bed(canvas);
@@ -1969,6 +2021,56 @@ void _3DScene::register_on_update_geometry_info_callback(wxGLCanvas* canvas, voi
     s_canvas_mgr.register_on_update_geometry_info_callback(canvas, callback);
 }
 
+void _3DScene::register_action_add_callback(wxGLCanvas* canvas, void* callback)
+{
+    s_canvas_mgr.register_action_add_callback(canvas, callback);
+}
+
+void _3DScene::register_action_delete_callback(wxGLCanvas* canvas, void* callback)
+{
+    s_canvas_mgr.register_action_delete_callback(canvas, callback);
+}
+
+void _3DScene::register_action_deleteall_callback(wxGLCanvas* canvas, void* callback)
+{
+    s_canvas_mgr.register_action_deleteall_callback(canvas, callback);
+}
+
+void _3DScene::register_action_arrange_callback(wxGLCanvas* canvas, void* callback)
+{
+    s_canvas_mgr.register_action_arrange_callback(canvas, callback);
+}
+
+void _3DScene::register_action_more_callback(wxGLCanvas* canvas, void* callback)
+{
+    s_canvas_mgr.register_action_more_callback(canvas, callback);
+}
+
+void _3DScene::register_action_fewer_callback(wxGLCanvas* canvas, void* callback)
+{
+    s_canvas_mgr.register_action_fewer_callback(canvas, callback);
+}
+
+void _3DScene::register_action_split_callback(wxGLCanvas* canvas, void* callback)
+{
+    s_canvas_mgr.register_action_split_callback(canvas, callback);
+}
+
+void _3DScene::register_action_cut_callback(wxGLCanvas* canvas, void* callback)
+{
+    s_canvas_mgr.register_action_cut_callback(canvas, callback);
+}
+
+void _3DScene::register_action_settings_callback(wxGLCanvas* canvas, void* callback)
+{
+    s_canvas_mgr.register_action_settings_callback(canvas, callback);
+}
+
+void _3DScene::register_action_layersediting_callback(wxGLCanvas* canvas, void* callback)
+{
+    s_canvas_mgr.register_action_layersediting_callback(canvas, callback);
+}
+
 static inline int hex_digit_to_int(const char c)
 {
     return 
diff --git a/xs/src/slic3r/GUI/3DScene.hpp b/xs/src/slic3r/GUI/3DScene.hpp
index 41839a3404..b4aa6ce955 100644
--- a/xs/src/slic3r/GUI/3DScene.hpp
+++ b/xs/src/slic3r/GUI/3DScene.hpp
@@ -119,7 +119,7 @@ public:
         push_geometry(float(x), float(y), float(z), float(nx), float(ny), float(nz));
     }
 
-    inline void push_geometry(const Pointf3& p, const Vectorf3& n) {
+    inline void push_geometry(const Vec3d& p, const Vec3d& n) {
         push_geometry(p(0), p(1), p(2), n(0), n(1), n(2));
     }
 
@@ -255,17 +255,21 @@ public:
 
 private:
     // Offset of the volume to be rendered.
-    Pointf3               m_origin;
+    Vec3d                 m_origin;
     // Rotation around Z axis of the volume to be rendered.
     float                 m_angle_z;
     // Scale factor of the volume to be rendered.
     float                 m_scale_factor;
-    // World matrix of the volume to be rendered.
-    mutable Transform3f   m_world_mat;
     // Bounding box of this volume, in unscaled coordinates.
     mutable BoundingBoxf3 m_transformed_bounding_box;
-    // Whether or not is needed to recalculate the world matrix.
-    mutable bool          m_dirty;
+    // Whether or not is needed to recalculate the transformed bounding box.
+    mutable bool          m_transformed_bounding_box_dirty;
+    // Pointer to convex hull of the original mesh, if any.
+    const TriangleMesh*   m_convex_hull;
+    // Bounding box of this volume, in unscaled coordinates.
+    mutable BoundingBoxf3 m_transformed_convex_hull_bounding_box;
+    // Whether or not is needed to recalculate the transformed convex hull bounding box.
+    mutable bool          m_transformed_convex_hull_bounding_box_dirty;
 
 public:
 
@@ -319,17 +323,20 @@ public:
     // Sets render color in dependence of current state
     void set_render_color();
 
-    const Pointf3& get_origin() const;
-    void set_origin(const Pointf3& origin);
+    float get_angle_z();
+    const Vec3d& get_origin() const;
+    void set_origin(const Vec3d& origin);
     void set_angle_z(float angle_z);
     void set_scale_factor(float scale_factor);
+    void set_convex_hull(const TriangleMesh& convex_hull);
 
     int                 object_idx() const { return this->composite_id / 1000000; }
     int                 volume_idx() const { return (this->composite_id / 1000) % 1000; }
     int                 instance_idx() const { return this->composite_id % 1000; }
 
-    const Transform3f&  world_matrix() const;
+    Transform3f         world_matrix() const;
     BoundingBoxf3       transformed_bounding_box() const;
+    BoundingBoxf3       transformed_convex_hull_bounding_box() const;
 
     bool                empty() const { return this->indexed_vertex_array.empty(); }
     bool                indexed() const { return this->indexed_vertex_array.indexed(); }
@@ -497,11 +504,15 @@ public:
     static void enable_picking(wxGLCanvas* canvas, bool enable);
     static void enable_moving(wxGLCanvas* canvas, bool enable);
     static void enable_gizmos(wxGLCanvas* canvas, bool enable);
+    static void enable_toolbar(wxGLCanvas* canvas, bool enable);
     static void enable_shader(wxGLCanvas* canvas, bool enable);
     static void enable_force_zoom_to_bed(wxGLCanvas* canvas, bool enable);
     static void enable_dynamic_background(wxGLCanvas* canvas, bool enable);
     static void allow_multisample(wxGLCanvas* canvas, bool allow);
 
+    static void enable_toolbar_item(wxGLCanvas* canvas, const std::string& name, bool enable);
+    static bool is_toolbar_item_pressed(wxGLCanvas* canvas, const std::string& name);
+
     static void zoom_to_bed(wxGLCanvas* canvas);
     static void zoom_to_volumes(wxGLCanvas* canvas);
     static void select_view(wxGLCanvas* canvas, const std::string& direction);
@@ -534,6 +545,17 @@ public:
     static void register_on_gizmo_rotate_callback(wxGLCanvas* canvas, void* callback);
     static void register_on_update_geometry_info_callback(wxGLCanvas* canvas, void* callback);
 
+    static void register_action_add_callback(wxGLCanvas* canvas, void* callback);
+    static void register_action_delete_callback(wxGLCanvas* canvas, void* callback);
+    static void register_action_deleteall_callback(wxGLCanvas* canvas, void* callback);
+    static void register_action_arrange_callback(wxGLCanvas* canvas, void* callback);
+    static void register_action_more_callback(wxGLCanvas* canvas, void* callback);
+    static void register_action_fewer_callback(wxGLCanvas* canvas, void* callback);
+    static void register_action_split_callback(wxGLCanvas* canvas, void* callback);
+    static void register_action_cut_callback(wxGLCanvas* canvas, void* callback);
+    static void register_action_settings_callback(wxGLCanvas* canvas, void* callback);
+    static void register_action_layersediting_callback(wxGLCanvas* canvas, void* callback);
+
     static std::vector<int> load_object(wxGLCanvas* canvas, const ModelObject* model_object, int obj_idx, std::vector<int> instance_idxs);
     static std::vector<int> load_object(wxGLCanvas* canvas, const Model* model, int obj_idx);
 
@@ -553,7 +575,7 @@ public:
     static void extrusionentity_to_verts(const ExtrusionEntityCollection& extrusion_entity_collection, float print_z, const Point& copy, GLVolume& volume);
     static void extrusionentity_to_verts(const ExtrusionEntity* extrusion_entity, float print_z, const Point& copy, GLVolume& volume);
     static void polyline3_to_verts(const Polyline3& polyline, double width, double height, GLVolume& volume);
-    static void point3_to_verts(const Point3& point, double width, double height, GLVolume& volume);
+    static void point3_to_verts(const Vec3crd& point, double width, double height, GLVolume& volume);
 };
 
 }
diff --git a/xs/src/slic3r/GUI/AppConfig.cpp b/xs/src/slic3r/GUI/AppConfig.cpp
index 2a33cd7331..0f77b1953c 100644
--- a/xs/src/slic3r/GUI/AppConfig.cpp
+++ b/xs/src/slic3r/GUI/AppConfig.cpp
@@ -233,6 +233,7 @@ void AppConfig::reset_selections()
     if (it != m_storage.end()) {
         it->second.erase("print");
         it->second.erase("filament");
+        it->second.erase("sla_material");
         it->second.erase("printer");
         m_dirty = true;
     }
diff --git a/xs/src/slic3r/GUI/BedShapeDialog.cpp b/xs/src/slic3r/GUI/BedShapeDialog.cpp
index f021e1b96a..e04f2b3700 100644
--- a/xs/src/slic3r/GUI/BedShapeDialog.cpp
+++ b/xs/src/slic3r/GUI/BedShapeDialog.cpp
@@ -48,14 +48,14 @@ void BedShapePanel::build_panel(ConfigOptionPoints* default_pt)
 	auto optgroup = init_shape_options_page(_(L("Rectangular")));
 		ConfigOptionDef def;
 		def.type = coPoints;
-		def.default_value = new ConfigOptionPoints{ Pointf(200, 200) };
+		def.default_value = new ConfigOptionPoints{ Vec2d(200, 200) };
 		def.label = L("Size");
 		def.tooltip = L("Size in X and Y of the rectangular plate.");
 		Option option(def, "rect_size");
 		optgroup->append_single_option_line(option);
 
 		def.type = coPoints;
-		def.default_value = new ConfigOptionPoints{ Pointf(0, 0) };
+		def.default_value = new ConfigOptionPoints{ Vec2d(0, 0) };
 		def.label = L("Origin");
 		def.tooltip = L("Distance of the 0,0 G-code coordinate from the front left corner of the rectangle.");
 		option = Option(def, "rect_origin");
@@ -159,11 +159,11 @@ void BedShapePanel::set_shape(ConfigOptionPoints* points)
                 y_max = std::max(y_max, pt(1));
             }
 
-            auto origin = new ConfigOptionPoints{ Pointf(-x_min, -y_min) };
+            auto origin = new ConfigOptionPoints{ Vec2d(-x_min, -y_min) };
 
 			m_shape_options_book->SetSelection(SHAPE_RECTANGULAR);
 			auto optgroup = m_optgroups[SHAPE_RECTANGULAR];
-			optgroup->set_value("rect_size", new ConfigOptionPoints{ Pointf(x_max - x_min, y_max - y_min) });//[x_max - x_min, y_max - y_min]);
+			optgroup->set_value("rect_size", new ConfigOptionPoints{ Vec2d(x_max - x_min, y_max - y_min) });//[x_max - x_min, y_max - y_min]);
 			optgroup->set_value("rect_origin", origin);
 			update_shape();
 			return;
@@ -195,7 +195,7 @@ void BedShapePanel::set_shape(ConfigOptionPoints* points)
 			// all vertices are equidistant to center
 			m_shape_options_book->SetSelection(SHAPE_CIRCULAR);
 			auto optgroup = m_optgroups[SHAPE_CIRCULAR];
-			boost::any ret = wxNumberFormatter::ToString(unscale(avg_dist * 2), 0);
+			boost::any ret = wxNumberFormatter::ToString(unscale<double>(avg_dist * 2), 0);
  			optgroup->set_value("diameter", ret);
 			update_shape();
 			return;
@@ -206,8 +206,8 @@ void BedShapePanel::set_shape(ConfigOptionPoints* points)
 		// Invalid polygon.Revert to default bed dimensions.
 		m_shape_options_book->SetSelection(SHAPE_RECTANGULAR);
 		auto optgroup = m_optgroups[SHAPE_RECTANGULAR];
-		optgroup->set_value("rect_size", new ConfigOptionPoints{ Pointf(200, 200) });
-		optgroup->set_value("rect_origin", new ConfigOptionPoints{ Pointf(0, 0) });
+		optgroup->set_value("rect_size", new ConfigOptionPoints{ Vec2d(200, 200) });
+		optgroup->set_value("rect_origin", new ConfigOptionPoints{ Vec2d(0, 0) });
 		update_shape();
 		return;
 	}
@@ -230,13 +230,15 @@ void BedShapePanel::update_shape()
 {
 	auto page_idx = m_shape_options_book->GetSelection();
 	if (page_idx == SHAPE_RECTANGULAR) {
-		Pointf rect_size, rect_origin;
+		Vec2d rect_size(Vec2d::Zero());
+		Vec2d rect_origin(Vec2d::Zero());
 		try{
-			rect_size = boost::any_cast<Pointf>(m_optgroups[SHAPE_RECTANGULAR]->get_value("rect_size")); }
+			rect_size = boost::any_cast<Vec2d>(m_optgroups[SHAPE_RECTANGULAR]->get_value("rect_size")); }
 		catch (const std::exception &e){
-			return;}
+			return;
+		}
 		try{
-			rect_origin = boost::any_cast<Pointf>(m_optgroups[SHAPE_RECTANGULAR]->get_value("rect_origin"));
+			rect_origin = boost::any_cast<Vec2d>(m_optgroups[SHAPE_RECTANGULAR]->get_value("rect_origin"));
 		}
 		catch (const std::exception &e){
 			return;}
@@ -257,10 +259,10 @@ void BedShapePanel::update_shape()
 		x1 -= dx;
 		y0 -= dy;
 		y1 -= dy;
-		m_canvas->m_bed_shape = {	Pointf(x0, y0),
-									Pointf(x1, y0),
-									Pointf(x1, y1),
-									Pointf(x0, y1)};
+		m_canvas->m_bed_shape = {	Vec2d(x0, y0),
+									Vec2d(x1, y0),
+									Vec2d(x1, y1),
+									Vec2d(x0, y1)};
 	} 
 	else if(page_idx == SHAPE_CIRCULAR) {
 		double diameter;
@@ -274,10 +276,10 @@ void BedShapePanel::update_shape()
 		auto r = diameter / 2;
 		auto twopi = 2 * PI;
 		auto edges = 60;
-		std::vector<Pointf> points;
+		std::vector<Vec2d> points;
 		for (size_t i = 1; i <= 60; ++i){
 			auto angle = i * twopi / edges;
-			points.push_back(Pointf(r*cos(angle), r*sin(angle)));
+			points.push_back(Vec2d(r*cos(angle), r*sin(angle)));
 		}
 		m_canvas->m_bed_shape = points;
 	}
@@ -330,9 +332,9 @@ void BedShapePanel::load_stl()
 	}
 
 	auto polygon = expolygons[0].contour;
-	std::vector<Pointf> points;
+	std::vector<Vec2d> points;
 	for (auto pt : polygon.points)
-		points.push_back(Pointf::new_unscale(pt));
+		points.push_back(unscale(pt));
 	m_canvas->m_bed_shape = points;
 	update_preview();
 }
diff --git a/xs/src/slic3r/GUI/BedShapeDialog.hpp b/xs/src/slic3r/GUI/BedShapeDialog.hpp
index 5ff4880637..d8ba5a9128 100644
--- a/xs/src/slic3r/GUI/BedShapeDialog.hpp
+++ b/xs/src/slic3r/GUI/BedShapeDialog.hpp
@@ -34,7 +34,7 @@ public:
 	void		load_stl();
 	
 	// Returns the resulting bed shape polygon. This value will be stored to the ini file.
-	std::vector<Pointf>	GetValue() { return m_canvas->m_bed_shape; }
+	std::vector<Vec2d>	GetValue() { return m_canvas->m_bed_shape; }
 };
 
 class BedShapeDialog : public wxDialog
@@ -46,7 +46,7 @@ public:
 	~BedShapeDialog(){  }
 
 	void		build_dialog(ConfigOptionPoints* default_pt);
-	std::vector<Pointf>	GetValue() { return m_panel->GetValue(); }
+	std::vector<Vec2d>	GetValue() { return m_panel->GetValue(); }
 };
 
 } // GUI
diff --git a/xs/src/slic3r/GUI/Field.cpp b/xs/src/slic3r/GUI/Field.cpp
index 942b134400..4043a44572 100644
--- a/xs/src/slic3r/GUI/Field.cpp
+++ b/xs/src/slic3r/GUI/Field.cpp
@@ -132,7 +132,11 @@ namespace Slic3r { namespace GUI {
 				break;
 			}
 			double val;
-			str.ToCDouble(&val);
+			if(!str.ToCDouble(&val))
+			{
+				show_error(m_parent, _(L("Input value contains incorrect symbol(s).\nUse, please, only digits")));
+				set_value(double_to_string(val), true);
+			}
 			if (m_opt.min > val || val > m_opt.max)
 			{
 				show_error(m_parent, _(L("Input value is out of range")));
@@ -274,7 +278,7 @@ void CheckBox::BUILD() {
 
 	bool check_value =	m_opt.type == coBool ? 
 						m_opt.default_value->getBool() : m_opt.type == coBools ? 
-						static_cast<ConfigOptionBools*>(m_opt.default_value)->get_at(m_opt_idx) : 
+						static_cast<const ConfigOptionBools*>(m_opt.default_value)->get_at(m_opt_idx) : 
     					false;
 
 	auto temp = new wxCheckBox(m_parent, wxID_ANY, wxString(""), wxDefaultPosition, size); 
@@ -330,9 +334,7 @@ void SpinCtrl::BUILD() {
 		break;
 	}
 
-	const int min_val = m_opt_id == "standby_temperature_delta" ? 
-						-500 : m_opt.min > 0 ? 
-						m_opt.min : 0;
+    const int min_val = m_opt.min == INT_MIN ? 0: m_opt.min;
 	const int max_val = m_opt.max < 2147483647 ? m_opt.max : 2147483647;
 
 	auto temp = new wxSpinCtrl(m_parent, wxID_ANY, text_value, wxDefaultPosition, size,
@@ -558,8 +560,11 @@ boost::any& Choice::get_value()
 // 	boost::any m_value;
 	wxString ret_str = static_cast<wxComboBox*>(window)->GetValue();	
 
-	if (m_opt_id == "support")
-		return m_value = boost::any(ret_str);//ret_str;
+	// options from right panel
+	std::vector <std::string> right_panel_options{ "support", "scale_unit" };
+	for (auto rp_option: right_panel_options)
+		if (m_opt_id == rp_option)
+			return m_value = boost::any(ret_str);
 
 	if (m_opt.type != coEnum)
 		/*m_value = */get_value_by_opt_type(ret_str);
@@ -586,6 +591,8 @@ boost::any& Choice::get_value()
 			m_value = static_cast<SupportMaterialPattern>(ret_enum);
 		else if (m_opt_id.compare("seam_position") == 0)
 			m_value = static_cast<SeamPosition>(ret_enum);
+		else if (m_opt_id.compare("host_type") == 0)
+			m_value = static_cast<PrintHostType>(ret_enum);
 	}	
 
 	return m_value;
@@ -597,7 +604,7 @@ void ColourPicker::BUILD()
 	if (m_opt.height >= 0) size.SetHeight(m_opt.height);
 	if (m_opt.width >= 0) size.SetWidth(m_opt.width);
 
-	wxString clr(static_cast<ConfigOptionStrings*>(m_opt.default_value)->get_at(m_opt_idx));
+	wxString clr(static_cast<const ConfigOptionStrings*>(m_opt.default_value)->get_at(m_opt_idx));
 	auto temp = new wxColourPickerCtrl(m_parent, wxID_ANY, clr, wxDefaultPosition, size);
 		
 	// 	// recast as a wxWindow to fit the calling convention
@@ -629,7 +636,7 @@ void PointCtrl::BUILD()
 	// 
 	wxSize field_size(40, -1);
 
-	auto default_pt = static_cast<ConfigOptionPoints*>(m_opt.default_value)->values.at(0);
+	auto default_pt = static_cast<const ConfigOptionPoints*>(m_opt.default_value)->values.at(0);
 	double val = default_pt(0);
 	wxString X = val - int(val) == 0 ? wxString::Format(_T("%i"), int(val)) : wxNumberFormatter::ToString(val, 2, wxNumberFormatter::Style_None);
 	val = default_pt(1);
@@ -653,7 +660,7 @@ void PointCtrl::BUILD()
 	y_textctrl->SetToolTip(get_tooltip_text(X+", "+Y));
 }
 
-void PointCtrl::set_value(const Pointf& value, bool change_event)
+void PointCtrl::set_value(const Vec2d& value, bool change_event)
 {
 	m_disable_change_event = !change_event;
 
@@ -667,8 +674,8 @@ void PointCtrl::set_value(const Pointf& value, bool change_event)
 
 void PointCtrl::set_value(const boost::any& value, bool change_event)
 {
-	Pointf pt;
-	const Pointf *ptf = boost::any_cast<Pointf>(&value);
+	Vec2d pt(Vec2d::Zero());
+	const Vec2d *ptf = boost::any_cast<Vec2d>(&value);
 	if (!ptf)
 	{
 		ConfigOptionPoints* pts = boost::any_cast<ConfigOptionPoints*>(value);
@@ -681,13 +688,10 @@ void PointCtrl::set_value(const boost::any& value, bool change_event)
 
 boost::any& PointCtrl::get_value()
 {
-	Pointf ret_point;
-	double val;
-	x_textctrl->GetValue().ToDouble(&val);
-	ret_point(0) = val;
-	y_textctrl->GetValue().ToDouble(&val);
-	ret_point(1) = val;
-	return m_value = ret_point;
+	double x, y;
+	x_textctrl->GetValue().ToDouble(&x);
+	y_textctrl->GetValue().ToDouble(&y);
+	return m_value = Vec2d(x, y);
 }
 
 void StaticText::BUILD()
@@ -696,7 +700,7 @@ void StaticText::BUILD()
 	if (m_opt.height >= 0) size.SetHeight(m_opt.height);
 	if (m_opt.width >= 0) size.SetWidth(m_opt.width);
 
-	wxString legend(static_cast<ConfigOptionString*>(m_opt.default_value)->value);
+	wxString legend(static_cast<const ConfigOptionString*>(m_opt.default_value)->value);
 	auto temp = new wxStaticText(m_parent, wxID_ANY, legend, wxDefaultPosition, size);
 	temp->SetFont(bold_font());
 
@@ -706,6 +710,69 @@ void StaticText::BUILD()
 	temp->SetToolTip(get_tooltip_text(legend));
 }
 
+void SliderCtrl::BUILD()
+{
+	auto size = wxSize(wxDefaultSize);
+	if (m_opt.height >= 0) size.SetHeight(m_opt.height);
+	if (m_opt.width >= 0) size.SetWidth(m_opt.width);
+
+	auto temp = new wxBoxSizer(wxHORIZONTAL);
+
+	auto def_val = static_cast<const ConfigOptionInt*>(m_opt.default_value)->value;
+	auto min = m_opt.min == INT_MIN ? 0 : m_opt.min;
+	auto max = m_opt.max == INT_MAX ? 100 : m_opt.max;
+
+	m_slider = new wxSlider(m_parent, wxID_ANY, def_val * m_scale,
+							min * m_scale, max * m_scale,
+							wxDefaultPosition, size);
+ 	wxSize field_size(40, -1);
+
+	m_textctrl = new wxTextCtrl(m_parent, wxID_ANY, wxString::Format("%d", m_slider->GetValue()/m_scale), 
+								wxDefaultPosition, field_size);
+
+	temp->Add(m_slider, 1, wxEXPAND | wxALIGN_CENTER_VERTICAL, 0);
+	temp->Add(m_textctrl, 0, wxALIGN_CENTER_VERTICAL, 0);
+
+	m_slider->Bind(wxEVT_SLIDER, ([this](wxCommandEvent e) {
+		if (!m_disable_change_event){
+			int val = boost::any_cast<int>(get_value());
+			m_textctrl->SetLabel(wxString::Format("%d", val));
+			on_change_field();
+		}
+	}), m_slider->GetId());
+
+	m_textctrl->Bind(wxEVT_TEXT, ([this](wxCommandEvent e) {
+		std::string value = e.GetString().utf8_str().data();
+		if (is_matched(value, "^-?\\d+(\\.\\d*)?$")){
+			m_disable_change_event = true;
+			m_slider->SetValue(stoi(value)*m_scale);
+			m_disable_change_event = false;
+			on_change_field();
+		}
+	}), m_textctrl->GetId());
+
+	m_sizer = dynamic_cast<wxSizer*>(temp);
+}
+
+void SliderCtrl::set_value(const boost::any& value, bool change_event)
+{
+	m_disable_change_event = !change_event;
+
+	m_slider->SetValue(boost::any_cast<int>(value)*m_scale);
+	int val = boost::any_cast<int>(get_value());
+	m_textctrl->SetLabel(wxString::Format("%d", val));
+
+	m_disable_change_event = false;
+}
+
+boost::any& SliderCtrl::get_value()
+{
+// 	int ret_val;
+// 	x_textctrl->GetValue().ToDouble(&val);
+	return m_value = int(m_slider->GetValue()/m_scale);
+}
+
+
 } // GUI
 } // Slic3r
 
diff --git a/xs/src/slic3r/GUI/Field.hpp b/xs/src/slic3r/GUI/Field.hpp
index db8d2a4085..e305f1e530 100644
--- a/xs/src/slic3r/GUI/Field.hpp
+++ b/xs/src/slic3r/GUI/Field.hpp
@@ -38,6 +38,7 @@ wxString double_to_string(double const value);
 
 class MyButton : public wxButton
 {
+    bool hidden = false; // never show button if it's hidden ones
 public:
 	MyButton() {}
 	MyButton(wxWindow* parent, wxWindowID id, const wxString& label = wxEmptyString,
@@ -52,6 +53,12 @@ public:
 	// overridden from wxWindow base class
 	virtual bool
 		AcceptsFocusFromKeyboard() const { return false; }
+
+    virtual bool Show(bool show = true) override {
+        if (!show)
+            hidden = true;
+        return wxButton::Show(!hidden);
+	}
 };
 
 class Field {
@@ -189,6 +196,10 @@ public:
 		return false;
 	}
 
+	void	set_side_text_ptr(wxStaticText* side_text) {
+		m_side_text = side_text;
+    }
+
 protected:
 	MyButton*			m_Undo_btn = nullptr;
 	// Bitmap and Tooltip text for m_Undo_btn. The wxButton will be updated only if the new wxBitmap pointer differs from the currently rendered one.
@@ -203,6 +214,8 @@ protected:
 	// Color for Label. The wxColour will be updated only if the new wxColour pointer differs from the currently rendered one.
 	const wxColour*		m_label_color = nullptr;
 
+	wxStaticText*		m_side_text = nullptr;
+
 	// current value
 	boost::any			m_value;
 
@@ -214,7 +227,7 @@ protected:
 inline bool is_bad_field(const t_field& obj) { return obj->getSizer() == nullptr && obj->getWindow() == nullptr; }
 
 /// Covenience function to determine whether this field is a valid window field.
-inline bool is_window_field(const t_field& obj) { return !is_bad_field(obj) && obj->getWindow() != nullptr; }
+inline bool is_window_field(const t_field& obj) { return !is_bad_field(obj) && obj->getWindow() != nullptr && obj->getSizer() == nullptr; }
 
 /// Covenience function to determine whether this field is a valid sizer field.
 inline bool is_sizer_field(const t_field& obj) { return !is_bad_field(obj) && obj->getSizer() != nullptr; }
@@ -372,7 +385,7 @@ public:
 
 	void			BUILD()  override;
 
-	void			set_value(const Pointf& value, bool change_event = false);
+	void			set_value(const Vec2d& value, bool change_event = false);
 	void			set_value(const boost::any& value, bool change_event = false);
 	boost::any&		get_value() override;
 
@@ -408,11 +421,44 @@ public:
 
 	boost::any&		get_value()override { return m_value; }
 
-	void			enable() override { dynamic_cast<wxColourPickerCtrl*>(window)->Enable(); };
-	void			disable() override{ dynamic_cast<wxColourPickerCtrl*>(window)->Disable(); };
+	void			enable() override { dynamic_cast<wxStaticText*>(window)->Enable(); };
+	void			disable() override{ dynamic_cast<wxStaticText*>(window)->Disable(); };
 	wxWindow*		getWindow() override { return window; }
 };
 
+class SliderCtrl : public Field {
+	using Field::Field;
+public:
+	SliderCtrl(const ConfigOptionDef& opt, const t_config_option_key& id) : Field(opt, id) {}
+	SliderCtrl(wxWindow* parent, const ConfigOptionDef& opt, const t_config_option_key& id) : Field(parent, opt, id) {}
+	~SliderCtrl() {}
+
+	wxSizer*		m_sizer{ nullptr };
+	wxTextCtrl*		m_textctrl{ nullptr };
+	wxSlider*		m_slider{ nullptr };
+
+	int				m_scale = 10;
+
+	void			BUILD()  override;
+
+	void			set_value(const int value, bool change_event = false);
+	void			set_value(const boost::any& value, bool change_event = false);
+	boost::any&		get_value() override;
+
+	void			enable() override {
+		m_slider->Enable();
+		m_textctrl->Enable();
+		m_textctrl->SetEditable(true);
+	}
+	void			disable() override{
+		m_slider->Disable();
+		m_textctrl->Disable();
+		m_textctrl->SetEditable(false);
+	}
+	wxSizer*		getSizer() override { return m_sizer; }
+	wxWindow*		getWindow() override { return dynamic_cast<wxWindow*>(m_slider); }
+};
+
 } // GUI
 } // Slic3r
 
diff --git a/xs/src/slic3r/GUI/GLCanvas3D.cpp b/xs/src/slic3r/GUI/GLCanvas3D.cpp
index d380c4bfc0..14c3bffa72 100644
--- a/xs/src/slic3r/GUI/GLCanvas3D.cpp
+++ b/xs/src/slic3r/GUI/GLCanvas3D.cpp
@@ -71,8 +71,8 @@ bool GeometryBuffer::set_from_triangles(const Polygons& triangles, float z, bool
     if (generate_tex_coords)
         m_tex_coords = std::vector<float>(t_size, 0.0f);
 
-    float min_x = (float)unscale(triangles[0].points[0](0));
-    float min_y = (float)unscale(triangles[0].points[0](1));
+    float min_x = unscale<float>(triangles[0].points[0](0));
+    float min_y = unscale<float>(triangles[0].points[0](1));
     float max_x = min_x;
     float max_y = min_y;
 
@@ -83,8 +83,8 @@ bool GeometryBuffer::set_from_triangles(const Polygons& triangles, float z, bool
         for (unsigned int v = 0; v < 3; ++v)
         {
             const Point& p = t.points[v];
-            float x = (float)unscale(p(0));
-            float y = (float)unscale(p(1));
+            float x = unscale<float>(p(0));
+            float y = unscale<float>(p(1));
 
             m_vertices[v_coord++] = x;
             m_vertices[v_coord++] = y;
@@ -137,11 +137,11 @@ bool GeometryBuffer::set_from_lines(const Lines& lines, float z)
     unsigned int coord = 0;
     for (const Line& l : lines)
     {
-        m_vertices[coord++] = (float)unscale(l.a(0));
-        m_vertices[coord++] = (float)unscale(l.a(1));
+        m_vertices[coord++] = unscale<float>(l.a(0));
+        m_vertices[coord++] = unscale<float>(l.a(1));
         m_vertices[coord++] = z;
-        m_vertices[coord++] = (float)unscale(l.b(0));
-        m_vertices[coord++] = (float)unscale(l.b(1));
+        m_vertices[coord++] = unscale<float>(l.b(0));
+        m_vertices[coord++] = unscale<float>(l.b(1));
         m_vertices[coord++] = z;
     }
 
@@ -317,7 +317,7 @@ bool GLCanvas3D::Bed::set_shape(const Pointfs& shape)
     _calc_bounding_box();
 
     ExPolygon poly;
-    for (const Pointf& p : m_shape)
+    for (const Vec2d& p : m_shape)
     {
         poly.contour.append(Point(scale_(p(0)), scale_(p(1))));
     }
@@ -373,9 +373,9 @@ void GLCanvas3D::Bed::render(float theta) const
 void GLCanvas3D::Bed::_calc_bounding_box()
 {
     m_bounding_box = BoundingBoxf3();
-    for (const Pointf& p : m_shape)
+    for (const Vec2d& p : m_shape)
     {
-        m_bounding_box.merge(Pointf3(p(0), p(1), 0.0));
+        m_bounding_box.merge(Vec3d(p(0), p(1), 0.0));
     }
 }
 
@@ -507,6 +507,7 @@ void GLCanvas3D::Bed::_render_prusa(float theta) const
     if (triangles_vcount > 0)
     {
         ::glEnable(GL_DEPTH_TEST);
+        ::glDepthMask(GL_FALSE);
 
         ::glEnable(GL_BLEND);
         ::glBlendFunc(GL_SRC_ALPHA, GL_ONE_MINUS_SRC_ALPHA);
@@ -535,6 +536,7 @@ void GLCanvas3D::Bed::_render_prusa(float theta) const
         ::glDisable(GL_TEXTURE_2D);
 
         ::glDisable(GL_BLEND);
+        ::glDepthMask(GL_TRUE);
     }
 }
 
@@ -591,7 +593,7 @@ bool GLCanvas3D::Bed::_are_equal(const Pointfs& bed_1, const Pointfs& bed_2)
 }
 
 GLCanvas3D::Axes::Axes()
-    : length(0.0f)
+    : origin(0, 0, 0), length(0.0f)
 {
 }
 
@@ -1040,7 +1042,7 @@ void GLCanvas3D::LayersEditing::_render_profile(const PrintObject& print_object,
     // Make the vertical bar a bit wider so the layer height curve does not touch the edge of the bar region.
     layer_height_max *= 1.12;
 
-    coordf_t max_z = unscale(print_object.size(2));
+    double max_z = unscale<double>(print_object.size(2));
     double layer_height = dynamic_cast<const ConfigOptionFloat*>(print_object.config.option("layer_height"))->value;
     float l = bar_rect.get_left();
     float w = bar_rect.get_right() - l;
@@ -1062,7 +1064,7 @@ void GLCanvas3D::LayersEditing::_render_profile(const PrintObject& print_object,
     const ModelObject* model_object = print_object.model_object();
     if (model_object->layer_height_profile_valid)
     {
-        const std::vector<coordf_t>& profile = model_object->layer_height_profile;
+        const std::vector<double>& profile = model_object->layer_height_profile;
 
         ::glColor3f(0.0f, 0.0f, 1.0f);
         ::glBegin(GL_LINE_STRIP);
@@ -1075,11 +1077,12 @@ void GLCanvas3D::LayersEditing::_render_profile(const PrintObject& print_object,
 }
 
 const Point GLCanvas3D::Mouse::Drag::Invalid_2D_Point(INT_MAX, INT_MAX);
-const Pointf3 GLCanvas3D::Mouse::Drag::Invalid_3D_Point(DBL_MAX, DBL_MAX, DBL_MAX);
+const Vec3d GLCanvas3D::Mouse::Drag::Invalid_3D_Point(DBL_MAX, DBL_MAX, DBL_MAX);
 
 GLCanvas3D::Mouse::Drag::Drag()
     : start_position_2D(Invalid_2D_Point)
     , start_position_3D(Invalid_3D_Point)
+    , volume_center_offset(0, 0, 0)
     , move_with_shift(false)
     , move_volume_idx(-1)
     , gizmo_volume_idx(-1)
@@ -1128,9 +1131,13 @@ GLCanvas3D::Gizmos::~Gizmos()
     _reset();
 }
 
-bool GLCanvas3D::Gizmos::init()
+bool GLCanvas3D::Gizmos::init(GLCanvas3D& parent)
 {
-    GLGizmoBase* gizmo = new GLGizmoScale;
+#if ENABLE_GIZMOS_3D
+    GLGizmoBase* gizmo = new GLGizmoScale3D(parent);
+#else
+    GLGizmoBase* gizmo = new GLGizmoScale(parent);
+#endif // ENABLE_GIZMOS_3D
     if (gizmo == nullptr)
         return false;
 
@@ -1139,7 +1146,11 @@ bool GLCanvas3D::Gizmos::init()
 
     m_gizmos.insert(GizmosMap::value_type(Scale, gizmo));
 
-    gizmo = new GLGizmoRotate;
+#if ENABLE_GIZMOS_3D
+    gizmo = new GLGizmoRotate3D(parent);
+#else
+    gizmo = new GLGizmoRotate(parent, GLGizmoRotate::Z);
+#endif // ENABLE_GIZMOS_3D
     if (gizmo == nullptr)
     {
         _reset();
@@ -1167,7 +1178,7 @@ void GLCanvas3D::Gizmos::set_enabled(bool enable)
     m_enabled = enable;
 }
 
-void GLCanvas3D::Gizmos::update_hover_state(const GLCanvas3D& canvas, const Pointf& mouse_pos)
+void GLCanvas3D::Gizmos::update_hover_state(const GLCanvas3D& canvas, const Vec2d& mouse_pos)
 {
     if (!m_enabled)
         return;
@@ -1186,14 +1197,14 @@ void GLCanvas3D::Gizmos::update_hover_state(const GLCanvas3D& canvas, const Poin
         // we currently use circular icons for gizmo, so we check the radius
         if (it->second->get_state() != GLGizmoBase::On)
         {
-            bool inside = (mouse_pos - Pointf(OverlayOffsetX + half_tex_size, top_y + half_tex_size)).norm() < half_tex_size;
+            bool inside = (mouse_pos - Vec2d(OverlayOffsetX + half_tex_size, top_y + half_tex_size)).norm() < half_tex_size;
             it->second->set_state(inside ? GLGizmoBase::Hover : GLGizmoBase::Off);
         }
         top_y += (tex_size + OverlayGapY);
     }
 }
 
-void GLCanvas3D::Gizmos::update_on_off_state(const GLCanvas3D& canvas, const Pointf& mouse_pos)
+void GLCanvas3D::Gizmos::update_on_off_state(const GLCanvas3D& canvas, const Vec2d& mouse_pos)
 {
     if (!m_enabled)
         return;
@@ -1210,7 +1221,7 @@ void GLCanvas3D::Gizmos::update_on_off_state(const GLCanvas3D& canvas, const Poi
         float half_tex_size = 0.5f * tex_size;
 
         // we currently use circular icons for gizmo, so we check the radius
-        if ((mouse_pos - Pointf(OverlayOffsetX + half_tex_size, top_y + half_tex_size)).norm() < half_tex_size)
+        if ((mouse_pos - Vec2d(OverlayOffsetX + half_tex_size, top_y + half_tex_size)).norm() < half_tex_size)
         {
             if ((it->second->get_state() == GLGizmoBase::On))
             {
@@ -1259,7 +1270,7 @@ void GLCanvas3D::Gizmos::set_hover_id(int id)
     }
 }
 
-bool GLCanvas3D::Gizmos::overlay_contains_mouse(const GLCanvas3D& canvas, const Pointf& mouse_pos) const
+bool GLCanvas3D::Gizmos::overlay_contains_mouse(const GLCanvas3D& canvas, const Vec2d& mouse_pos) const
 {
     if (!m_enabled)
         return false;
@@ -1276,7 +1287,7 @@ bool GLCanvas3D::Gizmos::overlay_contains_mouse(const GLCanvas3D& canvas, const
         float half_tex_size = 0.5f * tex_size;
 
         // we currently use circular icons for gizmo, so we check the radius
-        if ((mouse_pos - Pointf(OverlayOffsetX + half_tex_size, top_y + half_tex_size)).norm() < half_tex_size)
+        if ((mouse_pos - Vec2d(OverlayOffsetX + half_tex_size, top_y + half_tex_size)).norm() < half_tex_size)
             return true;
 
         top_y += (tex_size + OverlayGapY);
@@ -1294,14 +1305,14 @@ bool GLCanvas3D::Gizmos::grabber_contains_mouse() const
     return (curr != nullptr) ? (curr->get_hover_id() != -1) : false;
 }
 
-void GLCanvas3D::Gizmos::update(const Pointf& mouse_pos)
+void GLCanvas3D::Gizmos::update(const Linef3& mouse_ray)
 {
     if (!m_enabled)
         return;
 
     GLGizmoBase* curr = _get_current();
     if (curr != nullptr)
-        curr->update(mouse_pos);
+        curr->update(mouse_ray);
 }
 
 void GLCanvas3D::Gizmos::refresh()
@@ -1355,7 +1366,11 @@ float GLCanvas3D::Gizmos::get_scale() const
         return 1.0f;
 
     GizmosMap::const_iterator it = m_gizmos.find(Scale);
+#if ENABLE_GIZMOS_3D
+    return (it != m_gizmos.end()) ? reinterpret_cast<GLGizmoScale3D*>(it->second)->get_scale_x() : 1.0f;
+#else
     return (it != m_gizmos.end()) ? reinterpret_cast<GLGizmoScale*>(it->second)->get_scale() : 1.0f;
+#endif // ENABLE_GIZMOS_3D
 }
 
 void GLCanvas3D::Gizmos::set_scale(float scale)
@@ -1365,7 +1380,11 @@ void GLCanvas3D::Gizmos::set_scale(float scale)
 
     GizmosMap::const_iterator it = m_gizmos.find(Scale);
     if (it != m_gizmos.end())
+#if ENABLE_GIZMOS_3D
+        reinterpret_cast<GLGizmoScale3D*>(it->second)->set_scale(scale);
+#else
         reinterpret_cast<GLGizmoScale*>(it->second)->set_scale(scale);
+#endif // ENABLE_GIZMOS_3D
 }
 
 float GLCanvas3D::Gizmos::get_angle_z() const
@@ -1374,7 +1393,11 @@ float GLCanvas3D::Gizmos::get_angle_z() const
         return 0.0f;
 
     GizmosMap::const_iterator it = m_gizmos.find(Rotate);
-    return (it != m_gizmos.end()) ? reinterpret_cast<GLGizmoRotate*>(it->second)->get_angle_z() : 0.0f;
+#if ENABLE_GIZMOS_3D
+    return (it != m_gizmos.end()) ? reinterpret_cast<GLGizmoRotate3D*>(it->second)->get_angle_z() : 0.0f;
+#else
+    return (it != m_gizmos.end()) ? reinterpret_cast<GLGizmoRotate*>(it->second)->get_angle() : 0.0f;
+#endif // ENABLE_GIZMOS_3D
 }
 
 void GLCanvas3D::Gizmos::set_angle_z(float angle_z)
@@ -1384,25 +1407,20 @@ void GLCanvas3D::Gizmos::set_angle_z(float angle_z)
 
     GizmosMap::const_iterator it = m_gizmos.find(Rotate);
     if (it != m_gizmos.end())
-        reinterpret_cast<GLGizmoRotate*>(it->second)->set_angle_z(angle_z);
+#if ENABLE_GIZMOS_3D
+reinterpret_cast<GLGizmoRotate3D*>(it->second)->set_angle_z(angle_z);
+#else
+        reinterpret_cast<GLGizmoRotate*>(it->second)->set_angle(angle_z);
+#endif // ENABLE_GIZMOS_3D
 }
 
-void GLCanvas3D::Gizmos::render(const GLCanvas3D& canvas, const BoundingBoxf3& box) const
+void GLCanvas3D::Gizmos::render_current_gizmo(const BoundingBoxf3& box) const
 {
     if (!m_enabled)
         return;
 
-    ::glDisable(GL_DEPTH_TEST);
-
     if (box.radius() > 0.0)
         _render_current_gizmo(box);
-
-    ::glPushMatrix();
-    ::glLoadIdentity();
-
-    _render_overlay(canvas);
-
-    ::glPopMatrix();
 }
 
 void GLCanvas3D::Gizmos::render_current_gizmo_for_picking_pass(const BoundingBoxf3& box) const
@@ -1410,13 +1428,26 @@ void GLCanvas3D::Gizmos::render_current_gizmo_for_picking_pass(const BoundingBox
     if (!m_enabled)
         return;
 
-    ::glDisable(GL_DEPTH_TEST);
-
     GLGizmoBase* curr = _get_current();
     if (curr != nullptr)
         curr->render_for_picking(box);
 }
 
+void GLCanvas3D::Gizmos::render_overlay(const GLCanvas3D& canvas) const
+{
+    if (!m_enabled)
+        return;
+
+    ::glDisable(GL_DEPTH_TEST);
+
+    ::glPushMatrix();
+    ::glLoadIdentity();
+
+    _render_overlay(canvas);
+
+    ::glPopMatrix();
+}
+
 void GLCanvas3D::Gizmos::_reset()
 {
     for (GizmosMap::value_type& gizmo : m_gizmos)
@@ -1473,6 +1504,13 @@ float GLCanvas3D::Gizmos::_get_total_overlay_height() const
 const unsigned char GLCanvas3D::WarningTexture::Background_Color[3] = { 9, 91, 134 };
 const unsigned char GLCanvas3D::WarningTexture::Opacity = 255;
 
+GLCanvas3D::WarningTexture::WarningTexture()
+    : GUI::GLTexture()
+    , m_original_width(0)
+    , m_original_height(0)
+{
+}
+
 bool GLCanvas3D::WarningTexture::generate(const std::string& msg)
 {
     reset();
@@ -1482,13 +1520,21 @@ bool GLCanvas3D::WarningTexture::generate(const std::string& msg)
 
     wxMemoryDC memDC;
     // select default font
-    memDC.SetFont(wxSystemSettings::GetFont(wxSYS_DEFAULT_GUI_FONT));
+    wxFont font = wxSystemSettings::GetFont(wxSYS_DEFAULT_GUI_FONT);
+    font.MakeLarger();
+    font.MakeBold();
+    memDC.SetFont(font);
 
     // calculates texture size
     wxCoord w, h;
     memDC.GetTextExtent(msg, &w, &h);
-    m_width = (int)w;
-    m_height = (int)h;
+
+    int pow_of_two_size = next_highest_power_of_2((int)std::max(w, h));
+
+    m_original_width = (int)w;
+    m_original_height = (int)h;
+    m_width = pow_of_two_size;
+    m_height = pow_of_two_size;
 
     // generates bitmap
     wxBitmap bitmap(m_width, m_height);
@@ -1540,10 +1586,51 @@ bool GLCanvas3D::WarningTexture::generate(const std::string& msg)
     return true;
 }
 
+void GLCanvas3D::WarningTexture::render(const GLCanvas3D& canvas) const
+{
+    if ((m_id > 0) && (m_original_width > 0) && (m_original_height > 0) && (m_width > 0) && (m_height > 0))
+    {
+        ::glDisable(GL_DEPTH_TEST);
+        ::glPushMatrix();
+        ::glLoadIdentity();
+
+        const Size& cnv_size = canvas.get_canvas_size();
+        float zoom = canvas.get_camera_zoom();
+        float inv_zoom = (zoom != 0.0f) ? 1.0f / zoom : 0.0f;
+        float left = (-0.5f * (float)m_original_width) * inv_zoom;
+        float top = (-0.5f * (float)cnv_size.get_height() + (float)m_original_height + 2.0f) * inv_zoom;
+        float right = left + (float)m_original_width * inv_zoom;
+        float bottom = top - (float)m_original_height * inv_zoom;
+
+        float uv_left = 0.0f;
+        float uv_top = 0.0f;
+        float uv_right = (float)m_original_width / (float)m_width;
+        float uv_bottom = (float)m_original_height / (float)m_height;
+
+        GLTexture::Quad_UVs uvs;
+        uvs.left_top = { uv_left, uv_top };
+        uvs.left_bottom = { uv_left, uv_bottom };
+        uvs.right_bottom = { uv_right, uv_bottom };
+        uvs.right_top = { uv_right, uv_top };
+
+        GLTexture::render_sub_texture(m_id, left, right, bottom, top, uvs);
+
+        ::glPopMatrix();
+        ::glEnable(GL_DEPTH_TEST);
+    }
+}
+
 const unsigned char GLCanvas3D::LegendTexture::Squares_Border_Color[3] = { 64, 64, 64 };
 const unsigned char GLCanvas3D::LegendTexture::Background_Color[3] = { 9, 91, 134 };
 const unsigned char GLCanvas3D::LegendTexture::Opacity = 255;
 
+GLCanvas3D::LegendTexture::LegendTexture()
+    : GUI::GLTexture()
+    , m_original_width(0)
+    , m_original_height(0)
+{
+}
+
 bool GLCanvas3D::LegendTexture::generate(const GCodePreviewData& preview_data, const std::vector<float>& tool_colors)
 {
     reset();
@@ -1576,10 +1663,15 @@ bool GLCanvas3D::LegendTexture::generate(const GCodePreviewData& preview_data, c
         max_text_height = std::max(max_text_height, (int)h);
     }
 
-    m_width = std::max(2 * Px_Border + title_width, 2 * (Px_Border + Px_Square_Contour) + Px_Square + Px_Text_Offset + max_text_width);
-    m_height = 2 * (Px_Border + Px_Square_Contour) + title_height + Px_Title_Offset + items_count * Px_Square;
+    m_original_width = std::max(2 * Px_Border + title_width, 2 * (Px_Border + Px_Square_Contour) + Px_Square + Px_Text_Offset + max_text_width);
+    m_original_height = 2 * (Px_Border + Px_Square_Contour) + title_height + Px_Title_Offset + items_count * Px_Square;
     if (items_count > 1)
-        m_height += (items_count - 1) * Px_Square_Contour;
+        m_original_height += (items_count - 1) * Px_Square_Contour;
+
+    int pow_of_two_size = next_highest_power_of_2(std::max(m_original_width, m_original_height));
+
+    m_width = pow_of_two_size;
+    m_height = pow_of_two_size;
 
     // generates bitmap
     wxBitmap bitmap(m_width, m_height);
@@ -1688,6 +1780,40 @@ bool GLCanvas3D::LegendTexture::generate(const GCodePreviewData& preview_data, c
     return true;
 }
 
+void GLCanvas3D::LegendTexture::render(const GLCanvas3D& canvas) const
+{
+    if ((m_id > 0) && (m_original_width > 0) && (m_original_height > 0) && (m_width > 0) && (m_height > 0))
+    {
+        ::glDisable(GL_DEPTH_TEST);
+        ::glPushMatrix();
+        ::glLoadIdentity();
+
+        const Size& cnv_size = canvas.get_canvas_size();
+        float zoom = canvas.get_camera_zoom();
+        float inv_zoom = (zoom != 0.0f) ? 1.0f / zoom : 0.0f;
+        float left = (-0.5f * (float)cnv_size.get_width()) * inv_zoom;
+        float top = (0.5f * (float)cnv_size.get_height()) * inv_zoom;
+        float right = left + (float)m_original_width * inv_zoom;
+        float bottom = top - (float)m_original_height * inv_zoom;
+
+        float uv_left = 0.0f;
+        float uv_top = 0.0f;
+        float uv_right = (float)m_original_width / (float)m_width;
+        float uv_bottom = (float)m_original_height / (float)m_height;
+
+        GLTexture::Quad_UVs uvs;
+        uvs.left_top = { uv_left, uv_top };
+        uvs.left_bottom = { uv_left, uv_bottom };
+        uvs.right_bottom = { uv_right, uv_bottom };
+        uvs.right_top = { uv_right, uv_top };
+
+        GLTexture::render_sub_texture(m_id, left, right, bottom, top, uvs);
+
+        ::glPopMatrix();
+        ::glEnable(GL_DEPTH_TEST);
+    }
+}
+
 GLGizmoBase* GLCanvas3D::Gizmos::_get_current() const
 {
     GizmosMap::const_iterator it = m_gizmos.find(m_current);
@@ -1698,6 +1824,7 @@ GLCanvas3D::GLCanvas3D(wxGLCanvas* canvas)
     : m_canvas(canvas)
     , m_context(nullptr)
     , m_timer(nullptr)
+    , m_toolbar(*this)
     , m_config(nullptr)
     , m_print(nullptr)
     , m_model(nullptr)
@@ -1707,6 +1834,7 @@ GLCanvas3D::GLCanvas3D(wxGLCanvas* canvas)
     , m_force_zoom_to_bed_enabled(false)
     , m_apply_zoom_to_volumes_filter(false)
     , m_hover_volume_id(-1)
+    , m_toolbar_action_running(false)
     , m_warning_texture_enabled(false)
     , m_legend_texture_enabled(false)
     , m_picking_enabled(false)
@@ -1810,7 +1938,10 @@ bool GLCanvas3D::init(bool useVBOs, bool use_legacy_opengl)
     if (!m_volumes.empty())
         m_volumes.finalize_geometry(m_use_VBOs);
 
-    if (m_gizmos.is_enabled() && !m_gizmos.init())
+    if (m_gizmos.is_enabled() && !m_gizmos.init(*this))
+        return false;
+
+    if (!_init_toolbar())
         return false;
 
     m_initialized = true;
@@ -1950,7 +2081,7 @@ void GLCanvas3D::set_bed_shape(const Pointfs& shape)
     bool new_shape = m_bed.set_shape(shape);
 
     // Set the origin and size for painting of the coordinate system axes.
-    m_axes.origin = Pointf3(0.0, 0.0, (coordf_t)GROUND_Z);
+    m_axes.origin = Vec3d(0.0, 0.0, (double)GROUND_Z);
     set_axes_length(0.3f * (float)m_bed.get_bounding_box().max_size());
 
     if (new_shape)
@@ -1969,8 +2100,8 @@ void GLCanvas3D::set_auto_bed_shape()
 {
     // draw a default square bed around object center
     const BoundingBoxf3& bbox = volumes_bounding_box();
-    coordf_t max_size = bbox.max_size();
-    const Pointf3 center = bbox.center();
+    double max_size = bbox.max_size();
+    const Vec3d center = bbox.center();
 
     Pointfs bed_shape;
     bed_shape.reserve(4);
@@ -1982,7 +2113,7 @@ void GLCanvas3D::set_auto_bed_shape()
     set_bed_shape(bed_shape);
 
     // Set the origin for painting of the coordinate system axes.
-    m_axes.origin = Pointf3(center(0), center(1), (coordf_t)GROUND_Z);
+    m_axes.origin = Vec3d(center(0), center(1), (double)GROUND_Z);
 }
 
 void GLCanvas3D::set_axes_length(float length)
@@ -2076,6 +2207,11 @@ void GLCanvas3D::enable_gizmos(bool enable)
     m_gizmos.set_enabled(enable);
 }
 
+void GLCanvas3D::enable_toolbar(bool enable)
+{
+    m_toolbar.set_enabled(enable);
+}
+
 void GLCanvas3D::enable_shader(bool enable)
 {
     m_shader_enabled = enable;
@@ -2096,6 +2232,19 @@ void GLCanvas3D::allow_multisample(bool allow)
     m_multisample_allowed = allow;
 }
 
+void GLCanvas3D::enable_toolbar_item(const std::string& name, bool enable)
+{
+    if (enable)
+        m_toolbar.enable_item(name);
+    else
+        m_toolbar.disable_item(name);
+}
+
+bool GLCanvas3D::is_toolbar_item_pressed(const std::string& name) const
+{
+    return m_toolbar.is_item_pressed(name);
+}
+
 void GLCanvas3D::zoom_to_bed()
 {
     _zoom_to_bounding_box(m_bed.get_bounding_box());
@@ -2205,26 +2354,34 @@ void GLCanvas3D::render()
     float theta = m_camera.get_theta();
     bool is_custom_bed = m_bed.is_custom();
 
+    // picking pass
     _picking_pass();
+
+    // draw scene
     _render_background();
-    // untextured bed needs to be rendered before objects
-    if (is_custom_bed)
+
+    if (is_custom_bed) // untextured bed needs to be rendered before objects
     {
         _render_bed(theta);
         // disable depth testing so that axes are not covered by ground
         _render_axes(false);
     }
     _render_objects();
-    // textured bed needs to be rendered after objects
-    if (!is_custom_bed)
+
+    if (!is_custom_bed) // textured bed needs to be rendered after objects
     {
         _render_axes(true);
         _render_bed(theta);
     }
+
+    _render_current_gizmo();
     _render_cutting_plane();
+
+    // draw overlays
+    _render_gizmos_overlay();
     _render_warning_texture();
     _render_legend_texture();
-    _render_gizmo();
+    _render_toolbar();
     _render_layer_editing_overlay();
 
     m_canvas->SwapBuffers();
@@ -2311,7 +2468,7 @@ void GLCanvas3D::reload_scene(bool force)
         if ((extruders_count > 1) && semm && wt && !co)
         {
             // Height of a print (Show at least a slab)
-            coordf_t height = std::max(m_model->bounding_box().max(2), 10.0);
+            double height = std::max(m_model->bounding_box().max(2), 10.0);
 
             float x = dynamic_cast<const ConfigOptionFloat*>(m_config->option("wipe_tower_x"))->value;
             float y = dynamic_cast<const ConfigOptionFloat*>(m_config->option("wipe_tower_y"))->value;
@@ -2527,6 +2684,66 @@ void GLCanvas3D::register_on_update_geometry_info_callback(void* callback)
         m_on_update_geometry_info_callback.register_callback(callback);
 }
 
+void GLCanvas3D::register_action_add_callback(void* callback)
+{
+    if (callback != nullptr)
+        m_action_add_callback.register_callback(callback);
+}
+
+void GLCanvas3D::register_action_delete_callback(void* callback)
+{
+    if (callback != nullptr)
+        m_action_delete_callback.register_callback(callback);
+}
+
+void GLCanvas3D::register_action_deleteall_callback(void* callback)
+{
+    if (callback != nullptr)
+        m_action_deleteall_callback.register_callback(callback);
+}
+
+void GLCanvas3D::register_action_arrange_callback(void* callback)
+{
+    if (callback != nullptr)
+        m_action_arrange_callback.register_callback(callback);
+}
+
+void GLCanvas3D::register_action_more_callback(void* callback)
+{
+    if (callback != nullptr)
+        m_action_more_callback.register_callback(callback);
+}
+
+void GLCanvas3D::register_action_fewer_callback(void* callback)
+{
+    if (callback != nullptr)
+        m_action_fewer_callback.register_callback(callback);
+}
+
+void GLCanvas3D::register_action_split_callback(void* callback)
+{
+    if (callback != nullptr)
+        m_action_split_callback.register_callback(callback);
+}
+
+void GLCanvas3D::register_action_cut_callback(void* callback)
+{
+    if (callback != nullptr)
+        m_action_cut_callback.register_callback(callback);
+}
+
+void GLCanvas3D::register_action_settings_callback(void* callback)
+{
+    if (callback != nullptr)
+        m_action_settings_callback.register_callback(callback);
+}
+
+void GLCanvas3D::register_action_layersediting_callback(void* callback)
+{
+    if (callback != nullptr)
+        m_action_layersediting_callback.register_callback(callback);
+}
+
 void GLCanvas3D::bind_event_handlers()
 {
     if (m_canvas != nullptr)
@@ -2704,6 +2921,7 @@ void GLCanvas3D::on_mouse(wxMouseEvent& evt)
     int layer_editing_object_idx = is_layers_editing_enabled() ? selected_object_idx : -1;
     m_layers_editing.last_object_id = layer_editing_object_idx;
     bool gizmos_overlay_contains_mouse = m_gizmos.overlay_contains_mouse(*this, m_mouse.position);
+    int toolbar_contains_mouse = m_toolbar.contains_mouse(m_mouse.position);
 
     if (evt.Entering())
     {
@@ -2714,15 +2932,20 @@ void GLCanvas3D::on_mouse(wxMouseEvent& evt)
 
         m_mouse.set_start_position_2D_as_invalid();
 #endif
-    } 
+    }
     else if (evt.Leaving())
     {
         // to remove hover on objects when the mouse goes out of this canvas
-        m_mouse.position = Pointf(-1.0, -1.0);
+        m_mouse.position = Vec2d(-1.0, -1.0);
         m_dirty = true;
     }
     else if (evt.LeftDClick() && (m_hover_volume_id != -1))
         m_on_double_click_callback.call();
+    else if (evt.LeftDClick() && (toolbar_contains_mouse != -1))
+    {
+        m_toolbar_action_running = true;
+        m_toolbar.do_action((unsigned int)toolbar_contains_mouse);
+    }
     else if (evt.LeftDown() || evt.RightDown())
     {
         // If user pressed left or right button we first check whether this happened
@@ -2761,6 +2984,11 @@ void GLCanvas3D::on_mouse(wxMouseEvent& evt)
             m_mouse.drag.gizmo_volume_idx = _get_first_selected_volume_id(selected_object_idx);
             m_dirty = true;
         }
+        else if (toolbar_contains_mouse != -1)
+        {
+            m_toolbar_action_running = true;
+            m_toolbar.do_action((unsigned int)toolbar_contains_mouse);
+        }
         else
         {
             // Select volume in this 3D canvas.
@@ -2799,7 +3027,7 @@ void GLCanvas3D::on_mouse(wxMouseEvent& evt)
                 {
                     // The mouse_to_3d gets the Z coordinate from the Z buffer at the screen coordinate pos x, y,
                     // an converts the screen space coordinate to unscaled object space.
-                    Pointf3 pos3d = (volume_idx == -1) ? Pointf3(DBL_MAX, DBL_MAX, DBL_MAX) : _mouse_to_3d(pos);
+                    Vec3d pos3d = (volume_idx == -1) ? Vec3d(DBL_MAX, DBL_MAX, DBL_MAX) : _mouse_to_3d(pos);
 
                     // Only accept the initial position, if it is inside the volume bounding box.
                     BoundingBoxf3 volume_bbox = m_volumes.volumes[volume_idx]->transformed_bounding_box();
@@ -2817,9 +3045,16 @@ void GLCanvas3D::on_mouse(wxMouseEvent& evt)
                 }
                 else if (evt.RightDown())
                 {
-                    // if right clicking on volume, propagate event through callback
-                    if (m_volumes.volumes[volume_idx]->hover)
-                        m_on_right_click_callback.call(pos(0), pos(1));
+                    // forces a frame render to ensure that m_hover_volume_id is updated even when the user right clicks while
+                    // the context menu is already shown, ensuring it to disappear if the mouse is outside any volume
+                    m_mouse.position = Vec2d((double)pos(0), (double)pos(1));
+                    render();
+                    if (m_hover_volume_id != -1)
+                    {
+                        // if right clicking on volume, propagate event through callback (shows context menu)
+                        if (m_volumes.volumes[volume_idx]->hover)
+                            m_on_right_click_callback.call(pos(0), pos(1));
+                    }
                 }
             }
         }
@@ -2831,7 +3066,7 @@ void GLCanvas3D::on_mouse(wxMouseEvent& evt)
         // Get new position at the same Z of the initial click point.
         float z0 = 0.0f;
         float z1 = 1.0f;
-        Pointf3 cur_pos = Linef3(_mouse_to_3d(pos, &z0), _mouse_to_3d(pos, &z1)).intersect_plane(m_mouse.drag.start_position_3D(2));
+        Vec3d cur_pos = Linef3(_mouse_to_3d(pos, &z0), _mouse_to_3d(pos, &z1)).intersect_plane(m_mouse.drag.start_position_3D(2));
 
         // Clip the new position, so the object center remains close to the bed.
         cur_pos += m_mouse.drag.volume_center_offset;
@@ -2839,13 +3074,13 @@ void GLCanvas3D::on_mouse(wxMouseEvent& evt)
         if (!m_bed.contains(cur_pos2))
         {
             Point ip = m_bed.point_projection(cur_pos2);
-            cur_pos(0) = unscale(ip(0));
-            cur_pos(1) = unscale(ip(1));
+            cur_pos(0) = unscale<double>(ip(0));
+            cur_pos(1) = unscale<double>(ip(1));
         }
         cur_pos -= m_mouse.drag.volume_center_offset;
 
         // Calculate the translation vector.
-        Vectorf3 vector = cur_pos - m_mouse.drag.start_position_3D;
+        Vec3d vector = cur_pos - m_mouse.drag.start_position_3D;
         // Get the volume being dragged.
         GLVolume* volume = m_volumes.volumes[m_mouse.drag.move_volume_idx];
         // Get all volumes belonging to the same group, if any.
@@ -2867,7 +3102,7 @@ void GLCanvas3D::on_mouse(wxMouseEvent& evt)
 
         // Apply new temporary volume origin and ignore Z.
         for (GLVolume* v : volumes)
-            v->set_origin(v->get_origin() + Vectorf3(vector(0), vector(1), 0.0));
+            v->set_origin(v->get_origin() + Vec3d(vector(0), vector(1), 0.0));
 
         m_mouse.drag.start_position_3D = cur_pos;
         m_gizmos.refresh();
@@ -2876,10 +3111,10 @@ void GLCanvas3D::on_mouse(wxMouseEvent& evt)
     }
     else if (evt.Dragging() && m_gizmos.is_dragging())
     {
-        m_mouse.dragging = true;
+        m_canvas->CaptureMouse();
 
-        const Pointf3& cur_pos = _mouse_to_bed_3d(pos);
-        m_gizmos.update(Pointf(cur_pos(0), cur_pos(1)));
+        m_mouse.dragging = true;
+        m_gizmos.update(mouse_ray(pos));
 
         std::vector<GLVolume*> volumes;
         if (m_mouse.drag.gizmo_volume_idx != -1)
@@ -2931,8 +3166,10 @@ void GLCanvas3D::on_mouse(wxMouseEvent& evt)
             {
                 bb.merge(volume->transformed_bounding_box());
             }
-            const Pointf3& size = bb.size();
+            const Vec3d& size = bb.size();
             m_on_update_geometry_info_callback.call(size(0), size(1), size(2), m_gizmos.get_scale());
+            update_scale_values(size, m_gizmos.get_scale());
+            update_rotation_value(volumes[0]->get_angle_z(), "z");
         }
 
         if ((m_gizmos.get_current_type() != Gizmos::Rotate) && (volumes.size() > 1))
@@ -2954,7 +3191,7 @@ void GLCanvas3D::on_mouse(wxMouseEvent& evt)
             // if dragging over blank area with left button, rotate
             if (m_mouse.is_start_position_3D_defined())
             {
-                const Pointf3& orig = m_mouse.drag.start_position_3D;
+                const Vec3d& orig = m_mouse.drag.start_position_3D;
                 m_camera.phi += (((float)pos(0) - (float)orig(0)) * TRACKBALLSIZE);
                 m_camera.set_theta(m_camera.get_theta() - ((float)pos(1) - (float)orig(1)) * TRACKBALLSIZE);
 
@@ -2962,7 +3199,7 @@ void GLCanvas3D::on_mouse(wxMouseEvent& evt)
 
                 m_dirty = true;
             }
-            m_mouse.drag.start_position_3D = Pointf3((coordf_t)pos(0), (coordf_t)pos(1), 0.0);
+            m_mouse.drag.start_position_3D = Vec3d((double)pos(0), (double)pos(1), 0.0);
         }
         else if (evt.MiddleIsDown() || evt.RightIsDown())
         {
@@ -2971,8 +3208,8 @@ void GLCanvas3D::on_mouse(wxMouseEvent& evt)
             {
                 // get point in model space at Z = 0
                 float z = 0.0f;
-                const Pointf3& cur_pos = _mouse_to_3d(pos, &z);
-                Pointf3 orig = _mouse_to_3d(m_mouse.drag.start_position_2D, &z);
+                const Vec3d& cur_pos = _mouse_to_3d(pos, &z);
+                Vec3d orig = _mouse_to_3d(m_mouse.drag.start_position_2D, &z);
                 m_camera.target += orig - cur_pos;
 
                 m_on_viewport_changed_callback.call();
@@ -3011,11 +3248,15 @@ void GLCanvas3D::on_mouse(wxMouseEvent& evt)
             }
             
             _on_move(volume_idxs);
+
+            // force re-selection of the wipe tower, if needed
+            if ((volume_idxs.size() == 1) && m_volumes.volumes[volume_idxs[0]]->is_wipe_tower)
+                select_volume(volume_idxs[0]);
         }
-        else if (!m_mouse.dragging && (m_hover_volume_id == -1) && !gizmos_overlay_contains_mouse && !m_gizmos.is_dragging() && !is_layers_editing_enabled())
+        else if (evt.LeftUp() && !m_mouse.dragging && (m_hover_volume_id == -1) && !gizmos_overlay_contains_mouse && !m_gizmos.is_dragging() && !is_layers_editing_enabled())
         {
             // deselect and propagate event through callback
-            if (m_picking_enabled)
+            if (m_picking_enabled && !m_toolbar_action_running)
             {
                 deselect_volumes();
                 _on_select(-1);
@@ -3029,6 +3270,7 @@ void GLCanvas3D::on_mouse(wxMouseEvent& evt)
             case Gizmos::Scale:
             {
                 m_on_gizmo_scale_uniformly_callback.call((double)m_gizmos.get_scale());
+                Slic3r::GUI::update_settings_value();
                 break;
             }
             case Gizmos::Rotate:
@@ -3047,11 +3289,15 @@ void GLCanvas3D::on_mouse(wxMouseEvent& evt)
         m_mouse.set_start_position_3D_as_invalid();
         m_mouse.set_start_position_2D_as_invalid();
         m_mouse.dragging = false;
+        m_toolbar_action_running = false;
         m_dirty = true;
+
+        if (m_canvas->HasCapture())
+            m_canvas->ReleaseMouse();
     }
     else if (evt.Moving())
     {
-        m_mouse.position = Pointf((coordf_t)pos(0), (coordf_t)pos(1));
+        m_mouse.position = Vec2d((double)pos(0), (double)pos(1));
         // Only refresh if picking is enabled, in that case the objects may get highlighted if the mouse cursor hovers over.
         if (m_picking_enabled)
             m_dirty = true;
@@ -3113,6 +3359,12 @@ void GLCanvas3D::reset_legend_texture()
     m_legend_texture.reset();
 }
 
+void GLCanvas3D::set_tooltip(const std::string& tooltip)
+{
+    if (m_canvas != nullptr)
+        m_canvas->SetToolTip(tooltip);
+}
+
 bool GLCanvas3D::_is_shown_on_screen() const
 {
     return (m_canvas != nullptr) ? m_canvas->IsShownOnScreen() : false;
@@ -3124,6 +3376,119 @@ void GLCanvas3D::_force_zoom_to_bed()
     m_force_zoom_to_bed_enabled = false;
 }
 
+bool GLCanvas3D::_init_toolbar()
+{
+    if (!m_toolbar.is_enabled())
+        return true;
+
+    if (!m_toolbar.init("toolbar.png", 36, 1, 1))
+    {
+        // unable to init the toolbar texture, disable it
+        m_toolbar.set_enabled(false);
+        return true;
+    }
+
+//    m_toolbar.set_layout_type(GLToolbar::Layout::Vertical);
+    m_toolbar.set_layout_type(GLToolbar::Layout::Horizontal);
+    m_toolbar.set_separator_size(5);
+    m_toolbar.set_gap_size(2);
+
+    GLToolbarItem::Data item;
+
+    item.name = "add";
+    item.tooltip = GUI::L_str("Add...");
+    item.sprite_id = 0;
+    item.is_toggable = false;
+    item.action_callback = &m_action_add_callback;
+    if (!m_toolbar.add_item(item))
+        return false;
+
+    item.name = "delete";
+    item.tooltip = GUI::L_str("Delete");
+    item.sprite_id = 1;
+    item.is_toggable = false;
+    item.action_callback = &m_action_delete_callback;
+    if (!m_toolbar.add_item(item))
+        return false;
+
+    item.name = "deleteall";
+    item.tooltip = GUI::L_str("Delete all");
+    item.sprite_id = 2;
+    item.is_toggable = false;
+    item.action_callback = &m_action_deleteall_callback;
+    if (!m_toolbar.add_item(item))
+        return false;
+
+    item.name = "arrange";
+    item.tooltip = GUI::L_str("Arrange");
+    item.sprite_id = 3;
+    item.is_toggable = false;
+    item.action_callback = &m_action_arrange_callback;
+    if (!m_toolbar.add_item(item))
+        return false;
+
+    if (!m_toolbar.add_separator())
+        return false;
+
+    item.name = "more";
+    item.tooltip = GUI::L_str("Add instance");
+    item.sprite_id = 4;
+    item.is_toggable = false;
+    item.action_callback = &m_action_more_callback;
+    if (!m_toolbar.add_item(item))
+        return false;
+
+    item.name = "fewer";
+    item.tooltip = GUI::L_str("Remove instance");
+    item.sprite_id = 5;
+    item.is_toggable = false;
+    item.action_callback = &m_action_fewer_callback;
+    if (!m_toolbar.add_item(item))
+        return false;
+
+    if (!m_toolbar.add_separator())
+        return false;
+
+    item.name = "split";
+    item.tooltip = GUI::L_str("Split");
+    item.sprite_id = 6;
+    item.is_toggable = false;
+    item.action_callback = &m_action_split_callback;
+    if (!m_toolbar.add_item(item))
+        return false;
+
+    item.name = "cut";
+    item.tooltip = GUI::L_str("Cut...");
+    item.sprite_id = 7;
+    item.is_toggable = false;
+    item.action_callback = &m_action_cut_callback;
+    if (!m_toolbar.add_item(item))
+        return false;
+
+    if (!m_toolbar.add_separator())
+        return false;
+
+    item.name = "settings";
+    item.tooltip = GUI::L_str("Settings...");
+    item.sprite_id = 8;
+    item.is_toggable = false;
+    item.action_callback = &m_action_settings_callback;
+    if (!m_toolbar.add_item(item))
+        return false;
+
+    item.name = "layersediting";
+    item.tooltip = GUI::L_str("Layers editing");
+    item.sprite_id = 9;
+    item.is_toggable = true;
+    item.action_callback = &m_action_layersediting_callback;
+    if (!m_toolbar.add_item(item))
+        return false;
+
+    enable_toolbar_item("add", true);
+
+    return true;
+}
+
 void GLCanvas3D::_resize(unsigned int w, unsigned int h)
 {
     if ((m_canvas == nullptr) && (m_context == nullptr))
@@ -3231,13 +3596,13 @@ BoundingBoxf3 GLCanvas3D::_selected_volumes_bounding_box() const
             bb.merge(volume->bounding_box);
         }
 
-        bb = bb.transformed(selected_volumes[0]->world_matrix());
+        bb = bb.transformed(selected_volumes[0]->world_matrix().cast<double>());
     }
     else
     {
         for (const GLVolume* volume : selected_volumes)
         {
-            bb.merge(volume->transformed_bounding_box());
+            bb.merge(volume->transformed_convex_hull_bounding_box());
         }
     }
 
@@ -3277,16 +3642,16 @@ float GLCanvas3D::_get_zoom_to_bounding_box_factor(const BoundingBoxf3& bbox) co
     ::glGetFloatv(GL_MODELVIEW_MATRIX, matrix);
 
     // camera axes
-    Pointf3 right((coordf_t)matrix[0], (coordf_t)matrix[4], (coordf_t)matrix[8]);
-    Pointf3 up((coordf_t)matrix[1], (coordf_t)matrix[5], (coordf_t)matrix[9]);
-    Pointf3 forward((coordf_t)matrix[2], (coordf_t)matrix[6], (coordf_t)matrix[10]);
+    Vec3d right((double)matrix[0], (double)matrix[4], (double)matrix[8]);
+    Vec3d up((double)matrix[1], (double)matrix[5], (double)matrix[9]);
+    Vec3d forward((double)matrix[2], (double)matrix[6], (double)matrix[10]);
 
-    Pointf3 bb_min = bbox.min;
-    Pointf3 bb_max = bbox.max;
-    Pointf3 bb_center = bbox.center();
+    Vec3d bb_min = bbox.min;
+    Vec3d bb_max = bbox.max;
+    Vec3d bb_center = bbox.center();
 
     // bbox vertices in world space
-    std::vector<Pointf3> vertices;
+    std::vector<Vec3d> vertices;
     vertices.reserve(8);
     vertices.push_back(bb_min);
     vertices.emplace_back(bb_max(0), bb_min(1), bb_min(2));
@@ -3297,21 +3662,21 @@ float GLCanvas3D::_get_zoom_to_bounding_box_factor(const BoundingBoxf3& bbox) co
     vertices.push_back(bb_max);
     vertices.emplace_back(bb_min(0), bb_max(1), bb_max(2));
 
-    coordf_t max_x = 0.0;
-    coordf_t max_y = 0.0;
+    double max_x = 0.0;
+    double max_y = 0.0;
 
     // margin factor to give some empty space around the bbox
-    coordf_t margin_factor = 1.25;
+    double margin_factor = 1.25;
 
-    for (const Pointf3 v : vertices)
+    for (const Vec3d v : vertices)
     {
         // project vertex on the plane perpendicular to camera forward axis
-        Pointf3 pos(v(0) - bb_center(0), v(1) - bb_center(1), v(2) - bb_center(2));
-        Pointf3 proj_on_plane = pos - pos.dot(forward) * forward;
+        Vec3d pos(v(0) - bb_center(0), v(1) - bb_center(1), v(2) - bb_center(2));
+        Vec3d proj_on_plane = pos - pos.dot(forward) * forward;
 
         // calculates vertex coordinate along camera xy axes
-        coordf_t x_on_plane = proj_on_plane.dot(right);
-        coordf_t y_on_plane = proj_on_plane.dot(up);
+        double x_on_plane = proj_on_plane.dot(right);
+        double y_on_plane = proj_on_plane.dot(up);
 
         max_x = std::max(max_x, margin_factor * std::abs(x_on_plane));
         max_y = std::max(max_y, margin_factor * std::abs(y_on_plane));
@@ -3324,7 +3689,7 @@ float GLCanvas3D::_get_zoom_to_bounding_box_factor(const BoundingBoxf3& bbox) co
     max_y *= 2.0;
 
     const Size& cnv_size = get_canvas_size();
-    return (float)std::min((coordf_t)cnv_size.get_width() / max_x, (coordf_t)cnv_size.get_height() / max_y);
+    return (float)std::min((double)cnv_size.get_width() / max_x, (double)cnv_size.get_height() / max_y);
 }
 
 void GLCanvas3D::_deregister_callbacks()
@@ -3347,6 +3712,17 @@ void GLCanvas3D::_deregister_callbacks()
     m_on_gizmo_scale_uniformly_callback.deregister_callback();
     m_on_gizmo_rotate_callback.deregister_callback();
     m_on_update_geometry_info_callback.deregister_callback();
+
+    m_action_add_callback.deregister_callback();
+    m_action_delete_callback.deregister_callback();
+    m_action_deleteall_callback.deregister_callback();
+    m_action_arrange_callback.deregister_callback();
+    m_action_more_callback.deregister_callback();
+    m_action_fewer_callback.deregister_callback();
+    m_action_split_callback.deregister_callback();
+    m_action_cut_callback.deregister_callback();
+    m_action_settings_callback.deregister_callback();
+    m_action_layersediting_callback.deregister_callback();
 }
 
 void GLCanvas3D::_mark_volumes_for_layer_height() const
@@ -3389,15 +3765,15 @@ void GLCanvas3D::_camera_tranform() const
     ::glRotatef(-m_camera.get_theta(), 1.0f, 0.0f, 0.0f); // pitch
     ::glRotatef(m_camera.phi, 0.0f, 0.0f, 1.0f);          // yaw
 
-    Pointf3 neg_target = - m_camera.target;
+    Vec3d neg_target = - m_camera.target;
     ::glTranslatef((GLfloat)neg_target(0), (GLfloat)neg_target(1), (GLfloat)neg_target(2));
 }
 
 void GLCanvas3D::_picking_pass() const
 {
-    const Pointf& pos = m_mouse.position;
+    const Vec2d& pos = m_mouse.position;
 
-    if (m_picking_enabled && !m_mouse.dragging && (pos != Pointf(DBL_MAX, DBL_MAX)))
+    if (m_picking_enabled && !m_mouse.dragging && (pos != Vec2d(DBL_MAX, DBL_MAX)))
     {
         // Render the object for picking.
         // FIXME This cannot possibly work in a multi - sampled context as the color gets mangled by the anti - aliasing.
@@ -3458,6 +3834,8 @@ void GLCanvas3D::_picking_pass() const
             m_gizmos.update_hover_state(*this, pos);
         else
             m_gizmos.reset_all_states();
+
+        m_toolbar.update_hover_state(pos);
     }
 }
 
@@ -3511,6 +3889,7 @@ void GLCanvas3D::_render_objects() const
         return;
 
     ::glEnable(GL_LIGHTING);
+    ::glEnable(GL_DEPTH_TEST);
 
     if (!m_shader_enabled)
         _render_volumes(false);
@@ -3562,32 +3941,7 @@ void GLCanvas3D::_render_warning_texture() const
     if (!m_warning_texture_enabled)
         return;
 
-    // If the warning texture has not been loaded into the GPU, do it now.
-    unsigned int tex_id = m_warning_texture.get_id();
-    if (tex_id > 0)
-    {
-        int w = m_warning_texture.get_width();
-        int h = m_warning_texture.get_height();
-        if ((w > 0) && (h > 0))
-        {
-            ::glDisable(GL_DEPTH_TEST);
-            ::glPushMatrix();
-            ::glLoadIdentity();
-
-            const Size& cnv_size = get_canvas_size();
-            float zoom = get_camera_zoom();
-            float inv_zoom = (zoom != 0.0f) ? 1.0f / zoom : 0.0f;
-            float l = (-0.5f * (float)w) * inv_zoom;
-            float t = (-0.5f * (float)cnv_size.get_height() + (float)h) * inv_zoom;
-            float r = l + (float)w * inv_zoom;
-            float b = t - (float)h * inv_zoom;
-
-            GLTexture::render_texture(tex_id, l, r, b, t);
-
-            ::glPopMatrix();
-            ::glEnable(GL_DEPTH_TEST);
-        }
-    }
+    m_warning_texture.render(*this);
 }
 
 void GLCanvas3D::_render_legend_texture() const
@@ -3595,32 +3949,7 @@ void GLCanvas3D::_render_legend_texture() const
     if (!m_legend_texture_enabled)
         return;
 
-    // If the legend texture has not been loaded into the GPU, do it now.
-    unsigned int tex_id = m_legend_texture.get_id();
-    if (tex_id > 0)
-    {
-        int w = m_legend_texture.get_width();
-        int h = m_legend_texture.get_height();
-        if ((w > 0) && (h > 0))
-        {
-            ::glDisable(GL_DEPTH_TEST);
-            ::glPushMatrix();
-            ::glLoadIdentity();
-
-            const Size& cnv_size = get_canvas_size();
-            float zoom = get_camera_zoom();
-            float inv_zoom = (zoom != 0.0f) ? 1.0f / zoom : 0.0f;
-            float l = (-0.5f * (float)cnv_size.get_width()) * inv_zoom;
-            float t = (0.5f * (float)cnv_size.get_height()) * inv_zoom;
-            float r = l + (float)w * inv_zoom;
-            float b = t - (float)h * inv_zoom;
-
-            GLTexture::render_texture(tex_id, l, r, b, t);
-
-            ::glPopMatrix();
-            ::glEnable(GL_DEPTH_TEST);
-        }
-    }
+    m_legend_texture.render(*this);
 }
 
 void GLCanvas3D::_render_layer_editing_overlay() const
@@ -3702,9 +4031,20 @@ void GLCanvas3D::_render_volumes(bool fake_colors) const
         ::glDisable(GL_LIGHTING);
 }
 
-void GLCanvas3D::_render_gizmo() const
+void GLCanvas3D::_render_current_gizmo() const
 {
-    m_gizmos.render(*this, _selected_volumes_bounding_box());
+    m_gizmos.render_current_gizmo(_selected_volumes_bounding_box());
+}
+
+void GLCanvas3D::_render_gizmos_overlay() const
+{
+    m_gizmos.render_overlay(*this);
+}
+
+void GLCanvas3D::_render_toolbar() const
+{
+    _resize_toolbar();
+    m_toolbar.render();
 }
 
 float GLCanvas3D::_get_layers_editing_cursor_z_relative() const
@@ -3730,7 +4070,7 @@ void GLCanvas3D::_perform_layer_editing_action(wxMouseEvent* evt)
     {
         const Rect& rect = LayersEditing::get_bar_rect_screen(*this);
         float b = rect.get_bottom();
-        m_layers_editing.last_z = unscale(selected_obj->size(2)) * (b - evt->GetY() - 1.0f) / (b - rect.get_top());
+        m_layers_editing.last_z = unscale<double>(selected_obj->size(2)) * (b - evt->GetY() - 1.0f) / (b - rect.get_top());
         m_layers_editing.last_action = evt->ShiftDown() ? (evt->RightIsDown() ? 3 : 2) : (evt->RightIsDown() ? 0 : 1);
     }
 
@@ -3760,10 +4100,10 @@ void GLCanvas3D::_perform_layer_editing_action(wxMouseEvent* evt)
     _start_timer();
 }
 
-Pointf3 GLCanvas3D::_mouse_to_3d(const Point& mouse_pos, float* z)
+Vec3d GLCanvas3D::_mouse_to_3d(const Point& mouse_pos, float* z)
 {
     if (m_canvas == nullptr)
-        return Pointf3(DBL_MAX, DBL_MAX, DBL_MAX);
+        return Vec3d(DBL_MAX, DBL_MAX, DBL_MAX);
 
     _camera_tranform();
 
@@ -3783,14 +4123,19 @@ Pointf3 GLCanvas3D::_mouse_to_3d(const Point& mouse_pos, float* z)
 
     GLdouble out_x, out_y, out_z;
     ::gluUnProject((GLdouble)mouse_pos(0), (GLdouble)y, (GLdouble)mouse_z, modelview_matrix, projection_matrix, viewport, &out_x, &out_y, &out_z);
-    return Pointf3((coordf_t)out_x, (coordf_t)out_y, (coordf_t)out_z);
+    return Vec3d((double)out_x, (double)out_y, (double)out_z);
 }
 
-Pointf3 GLCanvas3D::_mouse_to_bed_3d(const Point& mouse_pos)
+Vec3d GLCanvas3D::_mouse_to_bed_3d(const Point& mouse_pos)
+{
+    return mouse_ray(mouse_pos).intersect_plane(0.0);
+}
+
+Linef3 GLCanvas3D::mouse_ray(const Point& mouse_pos)
 {
     float z0 = 0.0f;
     float z1 = 1.0f;
-    return Linef3(_mouse_to_3d(mouse_pos, &z0), _mouse_to_3d(mouse_pos, &z1)).intersect_plane(0.0);
+    return Linef3(_mouse_to_3d(mouse_pos, &z0), _mouse_to_3d(mouse_pos, &z1));
 }
 
 void GLCanvas3D::_start_timer()
@@ -4501,7 +4846,7 @@ bool GLCanvas3D::_travel_paths_by_type(const GCodePreviewData& preview_data)
         TypesList::iterator type = std::find(types.begin(), types.end(), Type(polyline.type));
         if (type != types.end())
         {
-            type->volume->print_zs.push_back(unscale(polyline.polyline.bounding_box().min(2)));
+            type->volume->print_zs.push_back(unscale<double>(polyline.polyline.bounding_box().min(2)));
             type->volume->offsets.push_back(type->volume->indexed_vertex_array.quad_indices.size());
             type->volume->offsets.push_back(type->volume->indexed_vertex_array.triangle_indices.size());
 
@@ -4567,7 +4912,7 @@ bool GLCanvas3D::_travel_paths_by_feedrate(const GCodePreviewData& preview_data)
         FeedratesList::iterator feedrate = std::find(feedrates.begin(), feedrates.end(), Feedrate(polyline.feedrate));
         if (feedrate != feedrates.end())
         {
-            feedrate->volume->print_zs.push_back(unscale(polyline.polyline.bounding_box().min(2)));
+            feedrate->volume->print_zs.push_back(unscale<double>(polyline.polyline.bounding_box().min(2)));
             feedrate->volume->offsets.push_back(feedrate->volume->indexed_vertex_array.quad_indices.size());
             feedrate->volume->offsets.push_back(feedrate->volume->indexed_vertex_array.triangle_indices.size());
 
@@ -4633,7 +4978,7 @@ bool GLCanvas3D::_travel_paths_by_tool(const GCodePreviewData& preview_data, con
         ToolsList::iterator tool = std::find(tools.begin(), tools.end(), Tool(polyline.extruder_id));
         if (tool != tools.end())
         {
-            tool->volume->print_zs.push_back(unscale(polyline.polyline.bounding_box().min(2)));
+            tool->volume->print_zs.push_back(unscale<double>(polyline.polyline.bounding_box().min(2)));
             tool->volume->offsets.push_back(tool->volume->indexed_vertex_array.quad_indices.size());
             tool->volume->offsets.push_back(tool->volume->indexed_vertex_array.triangle_indices.size());
 
@@ -4662,7 +5007,7 @@ void GLCanvas3D::_load_gcode_retractions(const GCodePreviewData& preview_data)
 
         for (const GCodePreviewData::Retraction::Position& position : copy)
         {
-            volume->print_zs.push_back(unscale(position.position(2)));
+            volume->print_zs.push_back(unscale<double>(position.position(2)));
             volume->offsets.push_back(volume->indexed_vertex_array.quad_indices.size());
             volume->offsets.push_back(volume->indexed_vertex_array.triangle_indices.size());
 
@@ -4693,7 +5038,7 @@ void GLCanvas3D::_load_gcode_unretractions(const GCodePreviewData& preview_data)
 
         for (const GCodePreviewData::Retraction::Position& position : copy)
         {
-            volume->print_zs.push_back(unscale(position.position(2)));
+            volume->print_zs.push_back(unscale<double>(position.position(2)));
             volume->offsets.push_back(volume->indexed_vertex_array.quad_indices.size());
             volume->offsets.push_back(volume->indexed_vertex_array.triangle_indices.size());
 
@@ -4733,7 +5078,7 @@ void GLCanvas3D::_load_shells()
     }
 
     // adds wipe tower's volume
-    coordf_t max_z = m_print->objects[0]->model_object()->get_model()->bounding_box().max(2);
+    double max_z = m_print->objects[0]->model_object()->get_model()->bounding_box().max(2);
     const PrintConfig& config = m_print->config;
     unsigned int extruders_count = config.nozzle_diameter.size();
     if ((extruders_count > 1) && config.single_extruder_multi_material && config.wipe_tower && !config.complete_objects) {
@@ -4806,8 +5151,8 @@ void GLCanvas3D::_update_gcode_volumes_visibility(const GCodePreviewData& previe
 void GLCanvas3D::_update_toolpath_volumes_outside_state()
 {
     // tolerance to avoid false detection at bed edges
-    static const coordf_t tolerance_x = 0.05;
-    static const coordf_t tolerance_y = 0.05;
+    static const double tolerance_x = 0.05;
+    static const double tolerance_y = 0.05;
 
     BoundingBoxf3 print_volume;
     if (m_config != nullptr)
@@ -4816,7 +5161,7 @@ void GLCanvas3D::_update_toolpath_volumes_outside_state()
         if (opt != nullptr)
         {
             BoundingBox bed_box_2D = get_extents(Polygon::new_scale(opt->values));
-            print_volume = BoundingBoxf3(Pointf3(unscale(bed_box_2D.min(0)) - tolerance_x, unscale(bed_box_2D.min(1)) - tolerance_y, 0.0), Pointf3(unscale(bed_box_2D.max(0)) + tolerance_x, unscale(bed_box_2D.max(1)) + tolerance_y, m_config->opt_float("max_print_height")));
+            print_volume = BoundingBoxf3(Vec3d(unscale<double>(bed_box_2D.min(0)) - tolerance_x, unscale<double>(bed_box_2D.min(1)) - tolerance_y, 0.0), Vec3d(unscale<double>(bed_box_2D.max(0)) + tolerance_x, unscale<double>(bed_box_2D.max(1)) + tolerance_y, m_config->opt_float("max_print_height")));
             // Allow the objects to protrude below the print bed
             print_volume.min(2) = -1e10;
         }
@@ -4849,7 +5194,7 @@ void GLCanvas3D::_on_move(const std::vector<int>& volume_idxs)
 
     std::set<std::string> done;  // prevent moving instances twice
     bool object_moved = false;
-    Pointf3 wipe_tower_origin(0.0, 0.0, 0.0);
+    Vec3d wipe_tower_origin(0.0, 0.0, 0.0);
     for (int volume_idx : volume_idxs)
     {
         GLVolume* volume = m_volumes.volumes[volume_idx];
@@ -4868,8 +5213,8 @@ void GLCanvas3D::_on_move(const std::vector<int>& volume_idxs)
         {
             // Move a regular object.
             ModelObject* model_object = m_model->objects[obj_idx];
-            const Pointf3& origin = volume->get_origin();
-            model_object->instances[instance_idx]->offset = Pointf(origin(0), origin(1));
+            const Vec3d& origin = volume->get_origin();
+            model_object->instances[instance_idx]->offset = Vec2d(origin(0), origin(1));
             model_object->invalidate_bounding_box();
             object_moved = true;
         }
@@ -4881,7 +5226,7 @@ void GLCanvas3D::_on_move(const std::vector<int>& volume_idxs)
     if (object_moved)
         m_on_instance_moved_callback.call();
 
-    if (wipe_tower_origin != Pointf3(0.0, 0.0, 0.0))
+    if (wipe_tower_origin != Vec3d(0.0, 0.0, 0.0))
         m_on_wipe_tower_moved_callback.call(wipe_tower_origin(0), wipe_tower_origin(1));
 }
 
@@ -4958,5 +5303,36 @@ bool GLCanvas3D::_is_any_volume_outside() const
     return false;
 }
 
+void GLCanvas3D::_resize_toolbar() const
+{
+    Size cnv_size = get_canvas_size();
+    float zoom = get_camera_zoom();
+    float inv_zoom = (zoom != 0.0f) ? 1.0f / zoom : 0.0f;
+
+    switch (m_toolbar.get_layout_type())
+    {
+    default:
+    case GLToolbar::Layout::Horizontal:
+    {
+        // centers the toolbar on the top edge of the 3d scene
+        unsigned int toolbar_width = m_toolbar.get_width();
+        float top = (0.5f * (float)cnv_size.get_height() - 2.0f) * inv_zoom;
+        float left = -0.5f * (float)toolbar_width * inv_zoom;
+        m_toolbar.set_position(top, left);
+        break;
+    }
+    case GLToolbar::Layout::Vertical:
+    {
+        // centers the toolbar on the right edge of the 3d scene
+        unsigned int toolbar_width = m_toolbar.get_width();
+        unsigned int toolbar_height = m_toolbar.get_height();
+        float top = 0.5f * (float)toolbar_height * inv_zoom;
+        float left = (0.5f * (float)cnv_size.get_width() - toolbar_width - 2.0f) * inv_zoom;
+        m_toolbar.set_position(top, left);
+        break;
+    }
+    }
+}
+
 } // namespace GUI
 } // namespace Slic3r
diff --git a/xs/src/slic3r/GUI/GLCanvas3D.hpp b/xs/src/slic3r/GUI/GLCanvas3D.hpp
index ae20882fc6..2334fe0927 100644
--- a/xs/src/slic3r/GUI/GLCanvas3D.hpp
+++ b/xs/src/slic3r/GUI/GLCanvas3D.hpp
@@ -2,7 +2,7 @@
 #define slic3r_GLCanvas3D_hpp_
 
 #include "../../slic3r/GUI/3DScene.hpp"
-#include "../../slic3r/GUI/GLTexture.hpp"
+#include "../../slic3r/GUI/GLToolbar.hpp"
 
 class wxTimer;
 class wxSizeEvent;
@@ -120,7 +120,7 @@ public:
         float zoom;
         float phi;
 //        float distance;
-        Pointf3 target;
+        Vec3d target;
 
     private:
         float m_theta;
@@ -185,7 +185,7 @@ public:
 
     struct Axes
     {
-        Pointf3 origin;
+        Vec3d origin;
         float length;
 
         Axes();
@@ -299,11 +299,11 @@ public:
         struct Drag
         {
             static const Point Invalid_2D_Point;
-            static const Pointf3 Invalid_3D_Point;
+            static const Vec3d Invalid_3D_Point;
 
             Point start_position_2D;
-            Pointf3 start_position_3D;
-            Vectorf3 volume_center_offset;
+            Vec3d start_position_3D;
+            Vec3d volume_center_offset;
 
             bool move_with_shift;
             int move_volume_idx;
@@ -314,7 +314,7 @@ public:
         };
 
         bool dragging;
-        Pointf position;
+        Vec2d position;
         Drag drag;
 
         Mouse();
@@ -352,20 +352,20 @@ public:
         Gizmos();
         ~Gizmos();
 
-        bool init();
+        bool init(GLCanvas3D& parent);
 
         bool is_enabled() const;
         void set_enabled(bool enable);
 
-        void update_hover_state(const GLCanvas3D& canvas, const Pointf& mouse_pos);
-        void update_on_off_state(const GLCanvas3D& canvas, const Pointf& mouse_pos);
+        void update_hover_state(const GLCanvas3D& canvas, const Vec2d& mouse_pos);
+        void update_on_off_state(const GLCanvas3D& canvas, const Vec2d& mouse_pos);
         void reset_all_states();
 
         void set_hover_id(int id);
 
-        bool overlay_contains_mouse(const GLCanvas3D& canvas, const Pointf& mouse_pos) const;
+        bool overlay_contains_mouse(const GLCanvas3D& canvas, const Vec2d& mouse_pos) const;
         bool grabber_contains_mouse() const;
-        void update(const Pointf& mouse_pos);
+        void update(const Linef3& mouse_ray);
         void refresh();
 
         EType get_current_type() const;
@@ -382,8 +382,9 @@ public:
         float get_angle_z() const;
         void set_angle_z(float angle_z);
 
-        void render(const GLCanvas3D& canvas, const BoundingBoxf3& box) const;
+        void render_current_gizmo(const BoundingBoxf3& box) const;
         void render_current_gizmo_for_picking_pass(const BoundingBoxf3& box) const;
+        void render_overlay(const GLCanvas3D& canvas) const;
 
     private:
         void _reset();
@@ -400,8 +401,15 @@ public:
         static const unsigned char Background_Color[3];
         static const unsigned char Opacity;
 
+        int m_original_width;
+        int m_original_height;
+
     public:
+        WarningTexture();
+
         bool generate(const std::string& msg);
+
+        void render(const GLCanvas3D& canvas) const;
     };
 
     class LegendTexture : public GUI::GLTexture
@@ -415,8 +423,15 @@ public:
         static const unsigned char Background_Color[3];
         static const unsigned char Opacity;
 
+        int m_original_width;
+        int m_original_height;
+
     public:
+        LegendTexture();
+
         bool generate(const GCodePreviewData& preview_data, const std::vector<float>& tool_colors);
+
+        void render(const GLCanvas3D& canvas) const;
     };
 
 private:
@@ -433,6 +448,7 @@ private:
     Shader m_shader;
     Mouse m_mouse;
     mutable Gizmos m_gizmos;
+    mutable GLToolbar m_toolbar;
 
     mutable GLVolumeCollection m_volumes;
     DynamicPrintConfig* m_config;
@@ -445,6 +461,7 @@ private:
     bool m_force_zoom_to_bed_enabled;
     bool m_apply_zoom_to_volumes_filter;
     mutable int m_hover_volume_id;
+    bool m_toolbar_action_running;
     bool m_warning_texture_enabled;
     bool m_legend_texture_enabled;
     bool m_picking_enabled;
@@ -482,6 +499,17 @@ private:
     PerlCallback m_on_gizmo_rotate_callback;
     PerlCallback m_on_update_geometry_info_callback;
 
+    PerlCallback m_action_add_callback;
+    PerlCallback m_action_delete_callback;
+    PerlCallback m_action_deleteall_callback;
+    PerlCallback m_action_arrange_callback;
+    PerlCallback m_action_more_callback;
+    PerlCallback m_action_fewer_callback;
+    PerlCallback m_action_split_callback;
+    PerlCallback m_action_cut_callback;
+    PerlCallback m_action_settings_callback;
+    PerlCallback m_action_layersediting_callback;
+
 public:
     GLCanvas3D(wxGLCanvas* canvas);
     ~GLCanvas3D();
@@ -539,11 +567,15 @@ public:
     void enable_picking(bool enable);
     void enable_moving(bool enable);
     void enable_gizmos(bool enable);
+    void enable_toolbar(bool enable);
     void enable_shader(bool enable);
     void enable_force_zoom_to_bed(bool enable);
     void enable_dynamic_background(bool enable);
     void allow_multisample(bool allow);
 
+    void enable_toolbar_item(const std::string& name, bool enable);
+    bool is_toolbar_item_pressed(const std::string& name) const;
+
     void zoom_to_bed();
     void zoom_to_volumes();
     void select_view(const std::string& direction);
@@ -584,6 +616,17 @@ public:
     void register_on_gizmo_rotate_callback(void* callback);
     void register_on_update_geometry_info_callback(void* callback);
 
+    void register_action_add_callback(void* callback);
+    void register_action_delete_callback(void* callback);
+    void register_action_deleteall_callback(void* callback);
+    void register_action_arrange_callback(void* callback);
+    void register_action_more_callback(void* callback);
+    void register_action_fewer_callback(void* callback);
+    void register_action_split_callback(void* callback);
+    void register_action_cut_callback(void* callback);
+    void register_action_settings_callback(void* callback);
+    void register_action_layersediting_callback(void* callback);
+
     void bind_event_handlers();
     void unbind_event_handlers();
 
@@ -601,10 +644,14 @@ public:
 
     void reset_legend_texture();
 
+    void set_tooltip(const std::string& tooltip);
+
 private:
     bool _is_shown_on_screen() const;
     void _force_zoom_to_bed();
 
+    bool _init_toolbar();
+
     void _resize(unsigned int w, unsigned int h);
 
     BoundingBoxf3 _max_bounding_box() const;
@@ -629,17 +676,22 @@ private:
     void _render_legend_texture() const;
     void _render_layer_editing_overlay() const;
     void _render_volumes(bool fake_colors) const;
-    void _render_gizmo() const;
+    void _render_current_gizmo() const;
+    void _render_gizmos_overlay() const;
+    void _render_toolbar() const;
 
     float _get_layers_editing_cursor_z_relative() const;
     void _perform_layer_editing_action(wxMouseEvent* evt = nullptr);
 
     // Convert the screen space coordinate to an object space coordinate.
     // If the Z screen space coordinate is not provided, a depth buffer value is substituted.
-    Pointf3 _mouse_to_3d(const Point& mouse_pos, float* z = nullptr);
+    Vec3d _mouse_to_3d(const Point& mouse_pos, float* z = nullptr);
 
     // Convert the screen space coordinate to world coordinate on the bed.
-    Pointf3 _mouse_to_bed_3d(const Point& mouse_pos);
+    Vec3d _mouse_to_bed_3d(const Point& mouse_pos);
+
+    // Returns the view ray line, in world coordinate, at the given mouse position.
+    Linef3 mouse_ray(const Point& mouse_pos);
 
     void _start_timer();
     void _stop_timer();
@@ -687,6 +739,8 @@ private:
 
     bool _is_any_volume_outside() const;
 
+    void _resize_toolbar() const;
+
     static std::vector<float> _parse_colors(const std::vector<std::string>& colors);
 };
 
diff --git a/xs/src/slic3r/GUI/GLCanvas3DManager.cpp b/xs/src/slic3r/GUI/GLCanvas3DManager.cpp
index 5249f6dc4f..57a49d7ab4 100644
--- a/xs/src/slic3r/GUI/GLCanvas3DManager.cpp
+++ b/xs/src/slic3r/GUI/GLCanvas3DManager.cpp
@@ -404,6 +404,13 @@ void GLCanvas3DManager::enable_gizmos(wxGLCanvas* canvas, bool enable)
         it->second->enable_gizmos(enable);
 }
 
+void GLCanvas3DManager::enable_toolbar(wxGLCanvas* canvas, bool enable)
+{
+    CanvasesMap::iterator it = _get_canvas(canvas);
+    if (it != m_canvases.end())
+        it->second->enable_toolbar(enable);
+}
+
 void GLCanvas3DManager::enable_shader(wxGLCanvas* canvas, bool enable)
 {
     CanvasesMap::iterator it = _get_canvas(canvas);
@@ -432,6 +439,19 @@ void GLCanvas3DManager::allow_multisample(wxGLCanvas* canvas, bool allow)
         it->second->allow_multisample(allow);
 }
 
+void GLCanvas3DManager::enable_toolbar_item(wxGLCanvas* canvas, const std::string& name, bool enable)
+{
+    CanvasesMap::iterator it = _get_canvas(canvas);
+    if (it != m_canvases.end())
+        it->second->enable_toolbar_item(name, enable);
+}
+
+bool GLCanvas3DManager::is_toolbar_item_pressed(wxGLCanvas* canvas, const std::string& name) const
+{
+    CanvasesMap::const_iterator it = _get_canvas(canvas);
+    return (it != m_canvases.end()) ? it->second->is_toolbar_item_pressed(name) : false;
+}
+
 void GLCanvas3DManager::zoom_to_bed(wxGLCanvas* canvas)
 {
     CanvasesMap::iterator it = _get_canvas(canvas);
@@ -675,6 +695,76 @@ void GLCanvas3DManager::register_on_update_geometry_info_callback(wxGLCanvas* ca
         it->second->register_on_update_geometry_info_callback(callback);
 }
 
+void GLCanvas3DManager::register_action_add_callback(wxGLCanvas* canvas, void* callback)
+{
+    CanvasesMap::iterator it = _get_canvas(canvas);
+    if (it != m_canvases.end())
+        it->second->register_action_add_callback(callback);
+}
+
+void GLCanvas3DManager::register_action_delete_callback(wxGLCanvas* canvas, void* callback)
+{
+    CanvasesMap::iterator it = _get_canvas(canvas);
+    if (it != m_canvases.end())
+        it->second->register_action_delete_callback(callback);
+}
+
+void GLCanvas3DManager::register_action_deleteall_callback(wxGLCanvas* canvas, void* callback)
+{
+    CanvasesMap::iterator it = _get_canvas(canvas);
+    if (it != m_canvases.end())
+        it->second->register_action_deleteall_callback(callback);
+}
+
+void GLCanvas3DManager::register_action_arrange_callback(wxGLCanvas* canvas, void* callback)
+{
+    CanvasesMap::iterator it = _get_canvas(canvas);
+    if (it != m_canvases.end())
+        it->second->register_action_arrange_callback(callback);
+}
+
+void GLCanvas3DManager::register_action_more_callback(wxGLCanvas* canvas, void* callback)
+{
+    CanvasesMap::iterator it = _get_canvas(canvas);
+    if (it != m_canvases.end())
+        it->second->register_action_more_callback(callback);
+}
+
+void GLCanvas3DManager::register_action_fewer_callback(wxGLCanvas* canvas, void* callback)
+{
+    CanvasesMap::iterator it = _get_canvas(canvas);
+    if (it != m_canvases.end())
+        it->second->register_action_fewer_callback(callback);
+}
+
+void GLCanvas3DManager::register_action_split_callback(wxGLCanvas* canvas, void* callback)
+{
+    CanvasesMap::iterator it = _get_canvas(canvas);
+    if (it != m_canvases.end())
+        it->second->register_action_split_callback(callback);
+}
+
+void GLCanvas3DManager::register_action_cut_callback(wxGLCanvas* canvas, void* callback)
+{
+    CanvasesMap::iterator it = _get_canvas(canvas);
+    if (it != m_canvases.end())
+        it->second->register_action_cut_callback(callback);
+}
+
+void GLCanvas3DManager::register_action_settings_callback(wxGLCanvas* canvas, void* callback)
+{
+    CanvasesMap::iterator it = _get_canvas(canvas);
+    if (it != m_canvases.end())
+        it->second->register_action_settings_callback(callback);
+}
+
+void GLCanvas3DManager::register_action_layersediting_callback(wxGLCanvas* canvas, void* callback)
+{
+    CanvasesMap::iterator it = _get_canvas(canvas);
+    if (it != m_canvases.end())
+        it->second->register_action_layersediting_callback(callback);
+}
+
 GLCanvas3DManager::CanvasesMap::iterator GLCanvas3DManager::_get_canvas(wxGLCanvas* canvas)
 {
     return (canvas == nullptr) ? m_canvases.end() : m_canvases.find(canvas);
diff --git a/xs/src/slic3r/GUI/GLCanvas3DManager.hpp b/xs/src/slic3r/GUI/GLCanvas3DManager.hpp
index 55c42fda69..f7705a56c6 100644
--- a/xs/src/slic3r/GUI/GLCanvas3DManager.hpp
+++ b/xs/src/slic3r/GUI/GLCanvas3DManager.hpp
@@ -110,11 +110,15 @@ public:
     void enable_picking(wxGLCanvas* canvas, bool enable);
     void enable_moving(wxGLCanvas* canvas, bool enable);
     void enable_gizmos(wxGLCanvas* canvas, bool enable);
+    void enable_toolbar(wxGLCanvas* canvas, bool enable);
     void enable_shader(wxGLCanvas* canvas, bool enable);
     void enable_force_zoom_to_bed(wxGLCanvas* canvas, bool enable);
     void enable_dynamic_background(wxGLCanvas* canvas, bool enable);
     void allow_multisample(wxGLCanvas* canvas, bool allow);
 
+    void enable_toolbar_item(wxGLCanvas* canvas, const std::string& name, bool enable);
+    bool is_toolbar_item_pressed(wxGLCanvas* canvas, const std::string& name) const;
+
     void zoom_to_bed(wxGLCanvas* canvas);
     void zoom_to_volumes(wxGLCanvas* canvas);
     void select_view(wxGLCanvas* canvas, const std::string& direction);
@@ -157,6 +161,17 @@ public:
     void register_on_gizmo_rotate_callback(wxGLCanvas* canvas, void* callback);
     void register_on_update_geometry_info_callback(wxGLCanvas* canvas, void* callback);
 
+    void register_action_add_callback(wxGLCanvas* canvas, void* callback);
+    void register_action_delete_callback(wxGLCanvas* canvas, void* callback);
+    void register_action_deleteall_callback(wxGLCanvas* canvas, void* callback);
+    void register_action_arrange_callback(wxGLCanvas* canvas, void* callback);
+    void register_action_more_callback(wxGLCanvas* canvas, void* callback);
+    void register_action_fewer_callback(wxGLCanvas* canvas, void* callback);
+    void register_action_split_callback(wxGLCanvas* canvas, void* callback);
+    void register_action_cut_callback(wxGLCanvas* canvas, void* callback);
+    void register_action_settings_callback(wxGLCanvas* canvas, void* callback);
+    void register_action_layersediting_callback(wxGLCanvas* canvas, void* callback);
+
 private:
     CanvasesMap::iterator _get_canvas(wxGLCanvas* canvas);
     CanvasesMap::const_iterator _get_canvas(wxGLCanvas* canvas) const;
diff --git a/xs/src/slic3r/GUI/GLGizmo.cpp b/xs/src/slic3r/GUI/GLGizmo.cpp
index f4f947d9c2..39ba440c3c 100644
--- a/xs/src/slic3r/GUI/GLGizmo.cpp
+++ b/xs/src/slic3r/GUI/GLGizmo.cpp
@@ -1,23 +1,34 @@
 #include "GLGizmo.hpp"
 
 #include "../../libslic3r/Utils.hpp"
-#include "../../libslic3r/BoundingBox.hpp"
+#include "../../slic3r/GUI/GLCanvas3D.hpp"
+
+#include <Eigen/Dense>
 
 #include <GL/glew.h>
 
 #include <iostream>
 
+static const float DEFAULT_BASE_COLOR[3] = { 0.625f, 0.625f, 0.625f };
+static const float DEFAULT_DRAG_COLOR[3] = { 1.0f, 1.0f, 1.0f };
+static const float DEFAULT_HIGHLIGHT_COLOR[3] = { 1.0f, 0.38f, 0.0f };
+
+static const float RED[3] = { 1.0f, 0.0f, 0.0f };
+static const float GREEN[3] = { 0.0f, 1.0f, 0.0f };
+static const float BLUE[3] = { 0.0f, 0.0f, 1.0f };
+
 namespace Slic3r {
 namespace GUI {
 
 const float GLGizmoBase::Grabber::HalfSize = 2.0f;
-const float GLGizmoBase::Grabber::HoverOffset = 0.5f;
-const float GLGizmoBase::BaseColor[3] = { 1.0f, 1.0f, 1.0f };
-const float GLGizmoBase::HighlightColor[3] = { 1.0f, 0.38f, 0.0f };
+const float GLGizmoBase::Grabber::DraggingScaleFactor = 1.25f;
 
 GLGizmoBase::Grabber::Grabber()
-    : center(Pointf(0.0, 0.0))
+    : center(0.0, 0.0, 0.0)
+    , angle_x(0.0f)
+    , angle_y(0.0f)
     , angle_z(0.0f)
+    , dragging(false)
 {
     color[0] = 1.0f;
     color[1] = 1.0f;
@@ -26,18 +37,92 @@ GLGizmoBase::Grabber::Grabber()
 
 void GLGizmoBase::Grabber::render(bool hover) const
 {
-    float min_x = -HalfSize;
-    float max_x = +HalfSize;
-    float min_y = -HalfSize;
-    float max_y = +HalfSize;
+    float render_color[3];
+    if (hover)
+    {
+        render_color[0] = 1.0f - color[0];
+        render_color[1] = 1.0f - color[1];
+        render_color[2] = 1.0f - color[2];
+    }
+    else
+        ::memcpy((void*)render_color, (const void*)color, 3 * sizeof(float));
 
-    ::glColor3f((GLfloat)color[0], (GLfloat)color[1], (GLfloat)color[2]);
+#if ENABLE_GIZMOS_3D
+    render(render_color, true);
+#else
+    render(render_color);
+#endif // ENABLE_GIZMOS_3D
+}
+
+#if ENABLE_GIZMOS_3D
+void GLGizmoBase::Grabber::render(const float* render_color, bool use_lighting) const
+#else
+void GLGizmoBase::Grabber::render(const float* render_color) const
+#endif // ENABLE_GIZMOS_3D
+{
+    float half_size = dragging ? HalfSize * DraggingScaleFactor : HalfSize;
+#if ENABLE_GIZMOS_3D
+    if (use_lighting)
+        ::glEnable(GL_LIGHTING);
+#else
+    float min_x = -half_size;
+    float max_x = +half_size;
+    float min_y = -half_size;
+    float max_y = +half_size;
+#endif // !ENABLE_GIZMOS_3D
+
+    ::glColor3f((GLfloat)render_color[0], (GLfloat)render_color[1], (GLfloat)render_color[2]);
 
-    float angle_z_in_deg = angle_z * 180.0f / (float)PI;
     ::glPushMatrix();
-    ::glTranslatef((GLfloat)center(0), (GLfloat)center(1), 0.0f);
-    ::glRotatef((GLfloat)angle_z_in_deg, 0.0f, 0.0f, 1.0f);
+    ::glTranslatef((GLfloat)center(0), (GLfloat)center(1), (GLfloat)center(2));
 
+    float rad_to_deg = 180.0f / (GLfloat)PI;
+    ::glRotatef((GLfloat)angle_x * rad_to_deg, 1.0f, 0.0f, 0.0f);
+    ::glRotatef((GLfloat)angle_y * rad_to_deg, 0.0f, 1.0f, 0.0f);
+    ::glRotatef((GLfloat)angle_z * rad_to_deg, 0.0f, 0.0f, 1.0f);
+
+#if ENABLE_GIZMOS_3D
+    // face min x
+    ::glPushMatrix();
+    ::glTranslatef(-(GLfloat)half_size, 0.0f, 0.0f);
+    ::glRotatef(-90.0f, 0.0f, 1.0f, 0.0f);
+    render_face(half_size);
+    ::glPopMatrix();
+
+    // face max x
+    ::glPushMatrix();
+    ::glTranslatef((GLfloat)half_size, 0.0f, 0.0f);
+    ::glRotatef(90.0f, 0.0f, 1.0f, 0.0f);
+    render_face(half_size);
+    ::glPopMatrix();
+
+    // face min y
+    ::glPushMatrix();
+    ::glTranslatef(0.0f, -(GLfloat)half_size, 0.0f);
+    ::glRotatef(90.0f, 1.0f, 0.0f, 0.0f);
+    render_face(half_size);
+    ::glPopMatrix();
+
+    // face max y
+    ::glPushMatrix();
+    ::glTranslatef(0.0f, (GLfloat)half_size, 0.0f);
+    ::glRotatef(-90.0f, 1.0f, 0.0f, 0.0f);
+    render_face(half_size);
+    ::glPopMatrix();
+
+    // face min z
+    ::glPushMatrix();
+    ::glTranslatef(0.0f, 0.0f, -(GLfloat)half_size);
+    ::glRotatef(180.0f, 1.0f, 0.0f, 0.0f);
+    render_face(half_size);
+    ::glPopMatrix();
+
+    // face max z
+    ::glPushMatrix();
+    ::glTranslatef(0.0f, 0.0f, (GLfloat)half_size);
+    render_face(half_size);
+    ::glPopMatrix();
+#else
     ::glDisable(GL_CULL_FACE);
     ::glBegin(GL_TRIANGLES);
     ::glVertex3f((GLfloat)min_x, (GLfloat)min_y, 0.0f);
@@ -48,121 +133,93 @@ void GLGizmoBase::Grabber::render(bool hover) const
     ::glVertex3f((GLfloat)min_x, (GLfloat)min_y, 0.0f);
     ::glEnd();
     ::glEnable(GL_CULL_FACE);
-
-    if (hover)
-    {
-        min_x -= HoverOffset;
-        max_x += HoverOffset;
-        min_y -= HoverOffset;
-        max_y += HoverOffset;
-
-        ::glBegin(GL_LINE_LOOP);
-        ::glVertex3f((GLfloat)min_x, (GLfloat)min_y, 0.0f);
-        ::glVertex3f((GLfloat)max_x, (GLfloat)min_y, 0.0f);
-        ::glVertex3f((GLfloat)max_x, (GLfloat)max_y, 0.0f);
-        ::glVertex3f((GLfloat)min_x, (GLfloat)max_y, 0.0f);
-        ::glEnd();
-    }
+#endif // ENABLE_GIZMOS_3D
 
     ::glPopMatrix();
+
+#if ENABLE_GIZMOS_3D
+    if (use_lighting)
+        ::glDisable(GL_LIGHTING);
+#endif // ENABLE_GIZMOS_3D
 }
 
-GLGizmoBase::GLGizmoBase()
-    : m_state(Off)
+#if ENABLE_GIZMOS_3D
+void GLGizmoBase::Grabber::render_face(float half_size) const
+{
+    ::glBegin(GL_TRIANGLES);
+    ::glNormal3f(0.0f, 0.0f, 1.0f);
+    ::glVertex3f(-(GLfloat)half_size, -(GLfloat)half_size, 0.0f);
+    ::glVertex3f((GLfloat)half_size, -(GLfloat)half_size, 0.0f);
+    ::glVertex3f((GLfloat)half_size, (GLfloat)half_size, 0.0f);
+    ::glVertex3f((GLfloat)half_size, (GLfloat)half_size, 0.0f);
+    ::glVertex3f(-(GLfloat)half_size, (GLfloat)half_size, 0.0f);
+    ::glVertex3f(-(GLfloat)half_size, -(GLfloat)half_size, 0.0f);
+    ::glEnd();
+}
+#endif // ENABLE_GIZMOS_3D
+
+GLGizmoBase::GLGizmoBase(GLCanvas3D& parent)
+    : m_parent(parent)
+    , m_group_id(-1)
+    , m_state(Off)
     , m_hover_id(-1)
+    , m_is_container(false)
 {
-}
-
-GLGizmoBase::~GLGizmoBase()
-{
-}
-
-bool GLGizmoBase::init()
-{
-    return on_init();
-}
-
-GLGizmoBase::EState GLGizmoBase::get_state() const
-{
-    return m_state;
-}
-
-void GLGizmoBase::set_state(GLGizmoBase::EState state)
-{
-    m_state = state;
-    on_set_state();
-}
-
-unsigned int GLGizmoBase::get_texture_id() const
-{
-    return m_textures[m_state].get_id();
-}
-
-int GLGizmoBase::get_textures_size() const
-{
-    return m_textures[Off].get_width();
-}
-
-int GLGizmoBase::get_hover_id() const
-{
-    return m_hover_id;
+    ::memcpy((void*)m_base_color, (const void*)DEFAULT_BASE_COLOR, 3 * sizeof(float));
+    ::memcpy((void*)m_drag_color, (const void*)DEFAULT_DRAG_COLOR, 3 * sizeof(float));
+    ::memcpy((void*)m_highlight_color, (const void*)DEFAULT_HIGHLIGHT_COLOR, 3 * sizeof(float));
 }
 
 void GLGizmoBase::set_hover_id(int id)
 {
-    if (id < (int)m_grabbers.size())
+    if (m_is_container || (id < (int)m_grabbers.size()))
+    {
         m_hover_id = id;
+        on_set_hover_id();
+    }
+}
+
+void GLGizmoBase::set_highlight_color(const float* color)
+{
+    if (color != nullptr)
+        ::memcpy((void*)m_highlight_color, (const void*)color, 3 * sizeof(float));
 }
 
 void GLGizmoBase::start_dragging()
 {
+    for (int i = 0; i < (int)m_grabbers.size(); ++i)
+    {
+        m_grabbers[i].dragging = (m_hover_id == i);
+    }
+
     on_start_dragging();
 }
 
 void GLGizmoBase::stop_dragging()
 {
+    set_tooltip("");
+
+    for (int i = 0; i < (int)m_grabbers.size(); ++i)
+    {
+        m_grabbers[i].dragging = false;
+    }
+
     on_stop_dragging();
 }
 
-void GLGizmoBase::update(const Pointf& mouse_pos)
+void GLGizmoBase::update(const Linef3& mouse_ray)
 {
     if (m_hover_id != -1)
-        on_update(mouse_pos);
+        on_update(mouse_ray);
 }
 
-void GLGizmoBase::refresh()
+float GLGizmoBase::picking_color_component(unsigned int id) const
 {
-    on_refresh();
-}
+    int color = 254 - (int)id;
+    if (m_group_id > -1)
+        color -= m_group_id;
 
-void GLGizmoBase::render(const BoundingBoxf3& box) const
-{
-    on_render(box);
-}
-
-void GLGizmoBase::render_for_picking(const BoundingBoxf3& box) const
-{
-    on_render_for_picking(box);
-}
-
-void GLGizmoBase::on_set_state()
-{
-    // do nothing
-}
-
-void GLGizmoBase::on_start_dragging()
-{
-    // do nothing
-}
-
-void GLGizmoBase::on_stop_dragging()
-{
-    // do nothing
-}
-
-void GLGizmoBase::on_refresh()
-{
-    // do nothing
+    return (float)color / 255.0f;
 }
 
 void GLGizmoBase::render_grabbers() const
@@ -173,41 +230,394 @@ void GLGizmoBase::render_grabbers() const
     }
 }
 
+void GLGizmoBase::render_grabbers_for_picking() const
+{
+    for (int i = 0; i < (int)m_grabbers.size(); ++i)
+    {
+        m_grabbers[i].render_for_picking();
+    }
+}
+
+void GLGizmoBase::set_tooltip(const std::string& tooltip) const
+{
+    m_parent.set_tooltip(tooltip);
+}
+
+std::string GLGizmoBase::format(float value, unsigned int decimals) const
+{
+    char buf[1024];
+    ::sprintf(buf, "%.*f", decimals, value);
+    return buf;
+}
+
 const float GLGizmoRotate::Offset = 5.0f;
 const unsigned int GLGizmoRotate::CircleResolution = 64;
 const unsigned int GLGizmoRotate::AngleResolution = 64;
-const unsigned int GLGizmoRotate::ScaleStepsCount = 60;
+const unsigned int GLGizmoRotate::ScaleStepsCount = 72;
 const float GLGizmoRotate::ScaleStepRad = 2.0f * (float)PI / GLGizmoRotate::ScaleStepsCount;
-const unsigned int GLGizmoRotate::ScaleLongEvery = 5;
+const unsigned int GLGizmoRotate::ScaleLongEvery = 2;
 const float GLGizmoRotate::ScaleLongTooth = 2.0f;
 const float GLGizmoRotate::ScaleShortTooth = 1.0f;
 const unsigned int GLGizmoRotate::SnapRegionsCount = 8;
 const float GLGizmoRotate::GrabberOffset = 5.0f;
 
-GLGizmoRotate::GLGizmoRotate()
-    : GLGizmoBase()
-    , m_angle_z(0.0f)
-    , m_center(Pointf(0.0, 0.0))
+GLGizmoRotate::GLGizmoRotate(GLCanvas3D& parent, GLGizmoRotate::Axis axis)
+    : GLGizmoBase(parent)
+    , m_axis(axis)
+    , m_angle(0.0f)
+    , m_center(0.0, 0.0, 0.0)
     , m_radius(0.0f)
-    , m_keep_radius(false)
+    , m_keep_initial_values(false)
 {
 }
 
-float GLGizmoRotate::get_angle_z() const
+void GLGizmoRotate::set_angle(float angle)
 {
-    return m_angle_z;
-}
+    if (std::abs(angle - 2.0f * PI) < EPSILON)
+        angle = 0.0f;
 
-void GLGizmoRotate::set_angle_z(float angle_z)
-{
-    if (std::abs(angle_z - 2.0f * PI) < EPSILON)
-        angle_z = 0.0f;
-
-    m_angle_z = angle_z;
+    m_angle = angle;
 }
 
 bool GLGizmoRotate::on_init()
 {
+#if !ENABLE_GIZMOS_3D
+    std::string path = resources_dir() + "/icons/overlay/";
+
+    std::string filename = path + "rotate_off.png";
+    if (!m_textures[Off].load_from_file(filename, false))
+        return false;
+    
+    filename = path + "rotate_hover.png";
+    if (!m_textures[Hover].load_from_file(filename, false))
+        return false;
+    
+    filename = path + "rotate_on.png";
+    if (!m_textures[On].load_from_file(filename, false))
+        return false;
+#endif // !ENABLE_GIZMOS_3D
+
+    m_grabbers.push_back(Grabber());
+
+    return true;
+}
+
+void GLGizmoRotate::on_update(const Linef3& mouse_ray)
+{ 
+    Vec2d mouse_pos = to_2d(mouse_position_in_local_plane(mouse_ray));
+
+    Vec2d orig_dir = Vec2d::UnitX();
+    Vec2d new_dir = mouse_pos.normalized();
+
+    double theta = ::acos(clamp(-1.0, 1.0, new_dir.dot(orig_dir)));
+    if (cross2(orig_dir, new_dir) < 0.0)
+        theta = 2.0 * (double)PI - theta;
+
+    double len = mouse_pos.norm();
+
+    // snap to snap region
+    double in_radius = (double)m_radius / 3.0;
+    double out_radius = 2.0 * (double)in_radius;
+    if ((in_radius <= len) && (len <= out_radius))
+    {
+        double step = 2.0 * (double)PI / (double)SnapRegionsCount;
+        theta = step * (double)std::round(theta / step);
+    }
+    else
+    {
+        // snap to scale
+        in_radius = (double)m_radius;
+        out_radius = in_radius + (double)ScaleLongTooth;
+        if ((in_radius <= len) && (len <= out_radius))
+        {
+            double step = 2.0 * (double)PI / (double)ScaleStepsCount;
+            theta = step * (double)std::round(theta / step);
+        }
+    }
+
+    if (theta == 2.0 * (double)PI)
+        theta = 0.0;
+
+    m_angle = (float)theta;
+}
+
+void GLGizmoRotate::on_render(const BoundingBoxf3& box) const
+{
+    if (m_grabbers[0].dragging)
+        set_tooltip(format(m_angle * 180.0f / (float)PI, 4));
+
+#if ENABLE_GIZMOS_3D
+    ::glEnable(GL_DEPTH_TEST);
+#else
+    ::glDisable(GL_DEPTH_TEST);
+#endif // ENABLE_GIZMOS_3D
+
+    if (!m_keep_initial_values)
+    {
+        m_center = box.center();
+#if !ENABLE_GIZMOS_3D
+        const Vec3d& size = box.size();
+        m_center(2) = 0.0;
+#endif // !ENABLE_GIZMOS_3D
+
+#if ENABLE_GIZMOS_3D
+        m_radius = Offset + box.radius();
+#else
+        m_radius = Offset + ::sqrt(sqr(0.5f * (float)size(0)) + sqr(0.5f * (float)size(1)));
+#endif // ENABLE_GIZMOS_3D
+        m_keep_initial_values = true;
+    }
+
+    ::glPushMatrix();
+    transform_to_local();
+
+#if ENABLE_GIZMOS_3D
+    ::glLineWidth((m_hover_id != -1) ? 2.0f : 1.5f);
+    ::glColor3fv((m_hover_id != -1) ? m_drag_color : m_highlight_color);
+#else
+    ::glLineWidth(2.0f);
+    ::glColor3fv(m_drag_color);
+#endif // ENABLE_GIZMOS_3D
+
+    render_circle();
+#if ENABLE_GIZMOS_3D
+    if (m_hover_id != -1)
+    {
+#endif // ENABLE_GIZMOS_3D
+        render_scale();
+        render_snap_radii();
+        render_reference_radius();
+#if ENABLE_GIZMOS_3D
+    }
+#endif // ENABLE_GIZMOS_3D
+
+    ::glColor3fv(m_highlight_color);
+#if ENABLE_GIZMOS_3D
+    if (m_hover_id != -1)
+#endif // ENABLE_GIZMOS_3D
+        render_angle();
+
+    render_grabber();
+
+    ::glPopMatrix();
+}
+
+void GLGizmoRotate::on_render_for_picking(const BoundingBoxf3& box) const
+{
+    ::glDisable(GL_DEPTH_TEST);
+
+    ::glPushMatrix();
+    transform_to_local();
+
+    m_grabbers[0].color[0] = 1.0f;
+    m_grabbers[0].color[1] = 1.0f;
+    m_grabbers[0].color[2] = picking_color_component(0);
+
+    render_grabbers_for_picking();
+
+    ::glPopMatrix();
+}
+
+void GLGizmoRotate::render_circle() const
+{
+    ::glBegin(GL_LINE_LOOP);
+    for (unsigned int i = 0; i < ScaleStepsCount; ++i)
+    {
+        float angle = (float)i * ScaleStepRad;
+        float x = ::cos(angle) * m_radius;
+        float y = ::sin(angle) * m_radius;
+        float z = 0.0f;
+        ::glVertex3f((GLfloat)x, (GLfloat)y, (GLfloat)z);
+    }
+    ::glEnd();
+}
+
+void GLGizmoRotate::render_scale() const
+{
+    float out_radius_long = m_radius + ScaleLongTooth;
+    float out_radius_short = m_radius + ScaleShortTooth;
+
+    ::glBegin(GL_LINES);
+    for (unsigned int i = 0; i < ScaleStepsCount; ++i)
+    {
+        float angle = (float)i * ScaleStepRad;
+        float cosa = ::cos(angle);
+        float sina = ::sin(angle);
+        float in_x = cosa * m_radius;
+        float in_y = sina * m_radius;
+        float in_z = 0.0f;
+        float out_x = (i % ScaleLongEvery == 0) ? cosa * out_radius_long : cosa * out_radius_short;
+        float out_y = (i % ScaleLongEvery == 0) ? sina * out_radius_long : sina * out_radius_short;
+        float out_z = 0.0f;
+        ::glVertex3f((GLfloat)in_x, (GLfloat)in_y, (GLfloat)in_z);
+        ::glVertex3f((GLfloat)out_x, (GLfloat)out_y, (GLfloat)out_z);
+    }
+    ::glEnd();
+}
+
+void GLGizmoRotate::render_snap_radii() const
+{
+    float step = 2.0f * (float)PI / (float)SnapRegionsCount;
+
+    float in_radius = m_radius / 3.0f;
+    float out_radius = 2.0f * in_radius;
+
+    ::glBegin(GL_LINES);
+    for (unsigned int i = 0; i < SnapRegionsCount; ++i)
+    {
+        float angle = (float)i * step;
+        float cosa = ::cos(angle);
+        float sina = ::sin(angle);
+        float in_x = cosa * in_radius;
+        float in_y = sina * in_radius;
+        float in_z = 0.0f;
+        float out_x = cosa * out_radius;
+        float out_y = sina * out_radius;
+        float out_z = 0.0f;
+        ::glVertex3f((GLfloat)in_x, (GLfloat)in_y, (GLfloat)in_z);
+        ::glVertex3f((GLfloat)out_x, (GLfloat)out_y, (GLfloat)out_z);
+    }
+    ::glEnd();
+}
+
+void GLGizmoRotate::render_reference_radius() const
+{
+    ::glBegin(GL_LINES);
+    ::glVertex3f(0.0f, 0.0f, 0.0f);
+    ::glVertex3f((GLfloat)(m_radius + GrabberOffset), 0.0f, 0.0f);
+    ::glEnd();
+}
+
+void GLGizmoRotate::render_angle() const
+{
+    float step_angle = m_angle / AngleResolution;
+    float ex_radius = m_radius + GrabberOffset;
+
+    ::glBegin(GL_LINE_STRIP);
+    for (unsigned int i = 0; i <= AngleResolution; ++i)
+    {
+        float angle = (float)i * step_angle;
+        float x = ::cos(angle) * ex_radius;
+        float y = ::sin(angle) * ex_radius;
+        float z = 0.0f;
+        ::glVertex3f((GLfloat)x, (GLfloat)y, (GLfloat)z);
+    }
+    ::glEnd();
+}
+
+void GLGizmoRotate::render_grabber() const
+{
+    float grabber_radius = m_radius + GrabberOffset;
+    m_grabbers[0].center = Vec3d(::cos(m_angle) * grabber_radius, ::sin(m_angle) * grabber_radius, 0.0);
+    m_grabbers[0].angle_z = m_angle;
+
+#if ENABLE_GIZMOS_3D
+    ::glColor3fv((m_hover_id != -1) ? m_drag_color : m_highlight_color);
+#else
+    ::glColor3fv(m_drag_color);
+#endif // ENABLE_GIZMOS_3D
+
+    ::glBegin(GL_LINES);
+    ::glVertex3f(0.0f, 0.0f, 0.0f);
+    ::glVertex3f((GLfloat)m_grabbers[0].center(0), (GLfloat)m_grabbers[0].center(1), (GLfloat)m_grabbers[0].center(2));
+    ::glEnd();
+
+    ::memcpy((void*)m_grabbers[0].color, (const void*)m_highlight_color, 3 * sizeof(float));
+    render_grabbers();
+}
+
+void GLGizmoRotate::transform_to_local() const
+{
+    ::glTranslatef((GLfloat)m_center(0), (GLfloat)m_center(1), (GLfloat)m_center(2));
+
+    switch (m_axis)
+    {
+    case X:
+    {
+        ::glRotatef(90.0f, 0.0f, 1.0f, 0.0f);
+        ::glRotatef(90.0f, 0.0f, 0.0f, 1.0f);
+        break;
+    }
+    case Y:
+    {
+        ::glRotatef(-90.0f, 1.0f, 0.0f, 0.0f);
+        ::glRotatef(180.0f, 0.0f, 0.0f, 1.0f);
+        break;
+    }
+    default:
+    case Z:
+    {
+        // no rotation
+        break;
+    }
+    }
+}
+
+Vec3d GLGizmoRotate::mouse_position_in_local_plane(const Linef3& mouse_ray) const
+{
+    double half_pi = 0.5 * (double)PI;
+
+    Transform3d m = Transform3d::Identity();
+
+    switch (m_axis)
+    {
+    case X:
+    {
+        m.rotate(Eigen::AngleAxisd(-half_pi, Vec3d::UnitZ()));
+        m.rotate(Eigen::AngleAxisd(-half_pi, Vec3d::UnitY()));
+        break;
+    }
+    case Y:
+    {
+        m.rotate(Eigen::AngleAxisd(-(double)PI, Vec3d::UnitZ()));
+        m.rotate(Eigen::AngleAxisd(half_pi, Vec3d::UnitX()));
+        break;
+    }
+    default:
+    case Z:
+    {
+        // no rotation applied
+        break;
+    }
+    }
+
+    m.translate(-m_center);
+
+    Eigen::Matrix<double, 3, 2> world_ray;
+    Eigen::Matrix<double, 3, 2> local_ray;
+    world_ray(0, 0) = mouse_ray.a(0);
+    world_ray(1, 0) = mouse_ray.a(1);
+    world_ray(2, 0) = mouse_ray.a(2);
+    world_ray(0, 1) = mouse_ray.b(0);
+    world_ray(1, 1) = mouse_ray.b(1);
+    world_ray(2, 1) = mouse_ray.b(2);
+    local_ray = m * world_ray.colwise().homogeneous();
+
+    return Linef3(Vec3d(local_ray(0, 0), local_ray(1, 0), local_ray(2, 0)), Vec3d(local_ray(0, 1), local_ray(1, 1), local_ray(2, 1))).intersect_plane(0.0);
+}
+
+GLGizmoRotate3D::GLGizmoRotate3D(GLCanvas3D& parent)
+    : GLGizmoBase(parent)
+    , m_x(parent, GLGizmoRotate::X)
+    , m_y(parent, GLGizmoRotate::Y)
+    , m_z(parent, GLGizmoRotate::Z)
+{
+    m_is_container = true;
+
+    m_x.set_group_id(0);
+    m_y.set_group_id(1);
+    m_z.set_group_id(2);
+}
+
+bool GLGizmoRotate3D::on_init()
+{
+    if (!m_x.init() || !m_y.init() || !m_z.init())
+        return false;
+
+    m_x.set_highlight_color(RED);
+    m_y.set_highlight_color(GREEN);
+    m_z.set_highlight_color(BLUE);
+
     std::string path = resources_dir() + "/icons/overlay/";
 
     std::string filename = path + "rotate_off.png";
@@ -222,194 +632,82 @@ bool GLGizmoRotate::on_init()
     if (!m_textures[On].load_from_file(filename, false))
         return false;
 
-    m_grabbers.push_back(Grabber());
-
     return true;
 }
 
-void GLGizmoRotate::on_set_state()
+void GLGizmoRotate3D::on_start_dragging()
 {
-    m_keep_radius = (m_state == On) ? false : true;
-}
-
-void GLGizmoRotate::on_update(const Pointf& mouse_pos)
-{
-    Vectorf orig_dir(1.0, 0.0);
-    Vectorf new_dir = (mouse_pos - m_center).normalized();
-    coordf_t theta = ::acos(clamp(-1.0, 1.0, new_dir.dot(orig_dir)));
-    if (cross2(orig_dir, new_dir) < 0.0)
-        theta = 2.0 * (coordf_t)PI - theta;
-
-    // snap
-    if ((mouse_pos - m_center).norm() < 2.0 * (double)m_radius / 3.0)
+    switch (m_hover_id)
     {
-        coordf_t step = 2.0 * (coordf_t)PI / (coordf_t)SnapRegionsCount;
-        theta = step * (coordf_t)std::round(theta / step);
-    }
-
-    if (theta == 2.0 * (coordf_t)PI)
-        theta = 0.0;
-
-    m_angle_z = (float)theta;
-}
-
-void GLGizmoRotate::on_refresh()
-{
-    m_keep_radius = false;
-}
-
-void GLGizmoRotate::on_render(const BoundingBoxf3& box) const
-{
-    ::glDisable(GL_DEPTH_TEST);
-
-    const Pointf size = box.size().xy();
-    m_center = box.center().xy();
-    if (!m_keep_radius)
+    case 0:
     {
-        m_radius = Offset + ::sqrt(sqr(0.5f * size(0)) + sqr(0.5f * size(1)));
-        m_keep_radius = true;
+        m_x.start_dragging();
+        break;
     }
-
-    ::glLineWidth(2.0f);
-    ::glColor3fv(BaseColor);
-
-    _render_circle();
-    _render_scale();
-    _render_snap_radii();
-    _render_reference_radius();
-
-    ::glColor3fv(HighlightColor);
-    _render_angle_z();
-    _render_grabber();
-}
-
-void GLGizmoRotate::on_render_for_picking(const BoundingBoxf3& box) const
-{
-    ::glDisable(GL_DEPTH_TEST);
-
-    m_grabbers[0].color[0] = 1.0f;
-    m_grabbers[0].color[1] = 1.0f;
-    m_grabbers[0].color[2] = 254.0f / 255.0f;
-    render_grabbers();
-}
-
-void GLGizmoRotate::_render_circle() const
-{
-    ::glBegin(GL_LINE_LOOP);
-    for (unsigned int i = 0; i < ScaleStepsCount; ++i)
+    case 1:
     {
-        float angle = (float)i * ScaleStepRad;
-        float x = m_center(0) + ::cos(angle) * m_radius;
-        float y = m_center(1) + ::sin(angle) * m_radius;
-        ::glVertex3f((GLfloat)x, (GLfloat)y, 0.0f);
+        m_y.start_dragging();
+        break;
     }
-    ::glEnd();
-}
-
-void GLGizmoRotate::_render_scale() const
-{
-    float out_radius_long = m_radius + ScaleLongTooth;
-    float out_radius_short = m_radius + ScaleShortTooth;
-
-    ::glBegin(GL_LINES);
-    for (unsigned int i = 0; i < ScaleStepsCount; ++i)
+    case 2:
     {
-        float angle = (float)i * ScaleStepRad;
-        float cosa = ::cos(angle);
-        float sina = ::sin(angle);
-        float in_x = m_center(0) + cosa * m_radius;
-        float in_y = m_center(1) + sina * m_radius;
-        float out_x = (i % ScaleLongEvery == 0) ? m_center(0) + cosa * out_radius_long : m_center(0) + cosa * out_radius_short;
-        float out_y = (i % ScaleLongEvery == 0) ? m_center(1) + sina * out_radius_long : m_center(1) + sina * out_radius_short;
-        ::glVertex3f((GLfloat)in_x, (GLfloat)in_y, 0.0f);
-        ::glVertex3f((GLfloat)out_x, (GLfloat)out_y, 0.0f);
+        m_z.start_dragging();
+        break;
     }
-    ::glEnd();
-}
-
-void GLGizmoRotate::_render_snap_radii() const
-{
-    float step = 2.0f * (float)PI / (float)SnapRegionsCount;
-
-    float in_radius = m_radius / 3.0f;
-    float out_radius = 2.0f * in_radius;
-
-    ::glBegin(GL_LINES);
-    for (unsigned int i = 0; i < SnapRegionsCount; ++i)
+    default:
     {
-        float angle = (float)i * step;
-        float cosa = ::cos(angle);
-        float sina = ::sin(angle);
-        float in_x = m_center(0) + cosa * in_radius;
-        float in_y = m_center(1) + sina * in_radius;
-        float out_x = m_center(0) + cosa * out_radius;
-        float out_y = m_center(1) + sina * out_radius;
-        ::glVertex3f((GLfloat)in_x, (GLfloat)in_y, 0.0f);
-        ::glVertex3f((GLfloat)out_x, (GLfloat)out_y, 0.0f);
+        break;
+    }
     }
-    ::glEnd();
 }
 
-void GLGizmoRotate::_render_reference_radius() const
+void GLGizmoRotate3D::on_stop_dragging()
 {
-    ::glBegin(GL_LINES);
-    ::glVertex3f((GLfloat)m_center(0), (GLfloat)m_center(1), 0.0f);
-    ::glVertex3f((GLfloat)m_center(0) + m_radius + GrabberOffset, (GLfloat)m_center(1), 0.0f);
-    ::glEnd();
-}
-
-void GLGizmoRotate::_render_angle_z() const
-{
-    float step_angle = m_angle_z / AngleResolution;
-    float ex_radius = m_radius + GrabberOffset;
-
-    ::glBegin(GL_LINE_STRIP);
-    for (unsigned int i = 0; i <= AngleResolution; ++i)
+    switch (m_hover_id)
     {
-        float angle = (float)i * step_angle;
-        float x = m_center(0) + ::cos(angle) * ex_radius;
-        float y = m_center(1) + ::sin(angle) * ex_radius;
-        ::glVertex3f((GLfloat)x, (GLfloat)y, 0.0f);
+    case 0:
+    {
+        m_x.stop_dragging();
+        break;
+    }
+    case 1:
+    {
+        m_y.stop_dragging();
+        break;
+    }
+    case 2:
+    {
+        m_z.stop_dragging();
+        break;
+    }
+    default:
+    {
+        break;
+    }
     }
-    ::glEnd();
 }
 
-void GLGizmoRotate::_render_grabber() const
+void GLGizmoRotate3D::on_render(const BoundingBoxf3& box) const
 {
-    float grabber_radius = m_radius + GrabberOffset;
-    m_grabbers[0].center(0) = m_center(0) + ::cos(m_angle_z) * grabber_radius;
-    m_grabbers[0].center(1) = m_center(1) + ::sin(m_angle_z) * grabber_radius;
-    m_grabbers[0].angle_z = m_angle_z;
+    if ((m_hover_id == -1) || (m_hover_id == 0))
+        m_x.render(box);
 
-    ::glColor3fv(BaseColor);
-    ::glBegin(GL_LINES);
-    ::glVertex3f((GLfloat)m_center(0), (GLfloat)m_center(1), 0.0f);
-    ::glVertex3f((GLfloat)m_grabbers[0].center(0), (GLfloat)m_grabbers[0].center(1), 0.0f);
-    ::glEnd();
+    if ((m_hover_id == -1) || (m_hover_id == 1))
+        m_y.render(box);
 
-    ::memcpy((void*)m_grabbers[0].color, (const void*)HighlightColor, 3 * sizeof(float));
-    render_grabbers();
+    if ((m_hover_id == -1) || (m_hover_id == 2))
+        m_z.render(box);
 }
 
 const float GLGizmoScale::Offset = 5.0f;
 
-GLGizmoScale::GLGizmoScale()
-    : GLGizmoBase()
+GLGizmoScale::GLGizmoScale(GLCanvas3D& parent)
+    : GLGizmoBase(parent)
     , m_scale(1.0f)
     , m_starting_scale(1.0f)
 {
 }
 
-float GLGizmoScale::get_scale() const
-{
-    return m_scale;
-}
-
-void GLGizmoScale::set_scale(float scale)
-{
-    m_starting_scale = scale;
-}
-
 bool GLGizmoScale::on_init()
 {
     std::string path = resources_dir() + "/icons/overlay/";
@@ -437,40 +735,41 @@ bool GLGizmoScale::on_init()
 void GLGizmoScale::on_start_dragging()
 {
     if (m_hover_id != -1)
-        m_starting_drag_position = m_grabbers[m_hover_id].center;
+        m_starting_drag_position = to_2d(m_grabbers[m_hover_id].center);
 }
 
-void GLGizmoScale::on_update(const Pointf& mouse_pos)
+void GLGizmoScale::on_update(const Linef3& mouse_ray)
 {
-    Pointf center(0.5 * (m_grabbers[1].center(0) + m_grabbers[0].center(0)), 0.5 * (m_grabbers[3].center(1) + m_grabbers[0].center(1)));
+    Vec2d mouse_pos = to_2d(mouse_ray.intersect_plane(0.0));
+    Vec2d center(0.5 * (m_grabbers[1].center(0) + m_grabbers[0].center(0)), 0.5 * (m_grabbers[3].center(1) + m_grabbers[0].center(1)));
 
-    coordf_t orig_len = (m_starting_drag_position - center).norm();
-    coordf_t new_len = (mouse_pos - center).norm();
-    coordf_t ratio = (orig_len != 0.0) ? new_len / orig_len : 1.0;
+    double orig_len = (m_starting_drag_position - center).norm();
+    double new_len = (mouse_pos - center).norm();
+    double ratio = (orig_len != 0.0) ? new_len / orig_len : 1.0;
 
     m_scale = m_starting_scale * (float)ratio;
 }
 
 void GLGizmoScale::on_render(const BoundingBoxf3& box) const
 {
+    if (m_grabbers[0].dragging || m_grabbers[1].dragging || m_grabbers[2].dragging || m_grabbers[3].dragging)
+        set_tooltip(format(100.0f * m_scale, 4) + "%");
+
     ::glDisable(GL_DEPTH_TEST);
 
-    coordf_t min_x = box.min(0) - (coordf_t)Offset;
-    coordf_t max_x = box.max(0) + (coordf_t)Offset;
-    coordf_t min_y = box.min(1) - (coordf_t)Offset;
-    coordf_t max_y = box.max(1) + (coordf_t)Offset;
+    double min_x = box.min(0) - (double)Offset;
+    double max_x = box.max(0) + (double)Offset;
+    double min_y = box.min(1) - (double)Offset;
+    double max_y = box.max(1) + (double)Offset;
 
-    m_grabbers[0].center(0) = min_x;
-    m_grabbers[0].center(1) = min_y;
-    m_grabbers[1].center(0) = max_x;
-    m_grabbers[1].center(1) = min_y;
-    m_grabbers[2].center(0) = max_x;
-    m_grabbers[2].center(1) = max_y;
-    m_grabbers[3].center(0) = min_x;
-    m_grabbers[3].center(1) = max_y;
+    m_grabbers[0].center = Vec3d(min_x, min_y, 0.0);
+    m_grabbers[1].center = Vec3d(max_x, min_y, 0.0);
+    m_grabbers[2].center = Vec3d(max_x, max_y, 0.0);
+    m_grabbers[3].center = Vec3d(min_x, max_y, 0.0);
 
     ::glLineWidth(2.0f);
-    ::glColor3fv(BaseColor);
+    ::glColor3fv(m_drag_color);
+
     // draw outline
     ::glBegin(GL_LINE_LOOP);
     for (unsigned int i = 0; i < 4; ++i)
@@ -482,24 +781,388 @@ void GLGizmoScale::on_render(const BoundingBoxf3& box) const
     // draw grabbers
     for (unsigned int i = 0; i < 4; ++i)
     {
-        ::memcpy((void*)m_grabbers[i].color, (const void*)HighlightColor, 3 * sizeof(float));
+        ::memcpy((void*)m_grabbers[i].color, (const void*)m_highlight_color, 3 * sizeof(float));
     }
     render_grabbers();
 }
 
 void GLGizmoScale::on_render_for_picking(const BoundingBoxf3& box) const
 {
-    static const GLfloat INV_255 = 1.0f / 255.0f;
-
     ::glDisable(GL_DEPTH_TEST);
 
     for (unsigned int i = 0; i < 4; ++i)
     {
         m_grabbers[i].color[0] = 1.0f;
         m_grabbers[i].color[1] = 1.0f;
-        m_grabbers[i].color[2] = (254.0f - (float)i) * INV_255;
+        m_grabbers[i].color[2] = picking_color_component(i);
     }
-    render_grabbers();
+    render_grabbers_for_picking();
+}
+
+const float GLGizmoScale3D::Offset = 5.0f;
+
+GLGizmoScale3D::GLGizmoScale3D(GLCanvas3D& parent)
+    : GLGizmoBase(parent)
+    , m_scale_x(1.0f)
+    , m_scale_y(1.0f)
+    , m_scale_z(1.0f)
+    , m_starting_scale_x(1.0f)
+    , m_starting_scale_y(1.0f)
+    , m_starting_scale_z(1.0f)
+{
+}
+
+bool GLGizmoScale3D::on_init()
+{
+    std::string path = resources_dir() + "/icons/overlay/";
+
+    std::string filename = path + "scale_off.png";
+    if (!m_textures[Off].load_from_file(filename, false))
+        return false;
+
+    filename = path + "scale_hover.png";
+    if (!m_textures[Hover].load_from_file(filename, false))
+        return false;
+
+    filename = path + "scale_on.png";
+    if (!m_textures[On].load_from_file(filename, false))
+        return false;
+
+    for (int i = 0; i < 10; ++i)
+    {
+        m_grabbers.push_back(Grabber());
+    }
+
+    float half_pi = 0.5f * (float)PI;
+
+    // x axis
+    m_grabbers[0].angle_y = half_pi;
+    m_grabbers[1].angle_y = half_pi;
+
+    // y axis
+    m_grabbers[2].angle_x = half_pi;
+    m_grabbers[3].angle_x = half_pi;
+
+    return true;
+}
+
+void GLGizmoScale3D::on_start_dragging()
+{
+    if (m_hover_id != -1)
+    {
+        m_starting_drag_position = m_grabbers[m_hover_id].center;
+        m_starting_center = m_box.center();
+    }
+}
+
+void GLGizmoScale3D::on_update(const Linef3& mouse_ray)
+{
+    if ((m_hover_id == 0) || (m_hover_id == 1))
+        do_scale_x(mouse_ray);
+    else if ((m_hover_id == 2) || (m_hover_id == 3))
+        do_scale_y(mouse_ray);
+    else if ((m_hover_id == 4) || (m_hover_id == 5))
+        do_scale_z(mouse_ray);
+    else if (m_hover_id >= 6)
+        do_scale_uniform(mouse_ray);
+}
+
+void GLGizmoScale3D::on_render(const BoundingBoxf3& box) const
+{
+    if (m_grabbers[0].dragging || m_grabbers[1].dragging)
+        set_tooltip("X: " + format(100.0f * m_scale_x, 4) + "%");
+    else if (m_grabbers[2].dragging || m_grabbers[3].dragging)
+        set_tooltip("Y: " + format(100.0f * m_scale_y, 4) + "%");
+    else if (m_grabbers[4].dragging || m_grabbers[5].dragging)
+        set_tooltip("Z: " + format(100.0f * m_scale_z, 4) + "%");
+    else if (m_grabbers[6].dragging || m_grabbers[7].dragging || m_grabbers[8].dragging || m_grabbers[9].dragging)
+    {
+        std::string tooltip = "X: " + format(100.0f * m_scale_x, 4) + "%\n";
+        tooltip += "Y: " + format(100.0f * m_scale_y, 4) + "%\n";
+        tooltip += "Z: " + format(100.0f * m_scale_z, 4) + "%";
+        set_tooltip(tooltip);
+    }
+
+    ::glEnable(GL_DEPTH_TEST);
+
+    Vec3d offset_vec = (double)Offset * Vec3d::Ones();
+
+    m_box = BoundingBoxf3(box.min - offset_vec, box.max + offset_vec);
+    const Vec3d& center = m_box.center();
+
+    // x axis
+    m_grabbers[0].center = Vec3d(m_box.min(0), center(1), center(2));
+    m_grabbers[1].center = Vec3d(m_box.max(0), center(1), center(2));
+    ::memcpy((void*)m_grabbers[0].color, (const void*)RED, 3 * sizeof(float));
+    ::memcpy((void*)m_grabbers[1].color, (const void*)RED, 3 * sizeof(float));
+
+    // y axis
+    m_grabbers[2].center = Vec3d(center(0), m_box.min(1), center(2));
+    m_grabbers[3].center = Vec3d(center(0), m_box.max(1), center(2));
+    ::memcpy((void*)m_grabbers[2].color, (const void*)GREEN, 3 * sizeof(float));
+    ::memcpy((void*)m_grabbers[3].color, (const void*)GREEN, 3 * sizeof(float));
+
+    // z axis
+    m_grabbers[4].center = Vec3d(center(0), center(1), m_box.min(2));
+    m_grabbers[5].center = Vec3d(center(0), center(1), m_box.max(2));
+    ::memcpy((void*)m_grabbers[4].color, (const void*)BLUE, 3 * sizeof(float));
+    ::memcpy((void*)m_grabbers[5].color, (const void*)BLUE, 3 * sizeof(float));
+
+    // uniform
+    m_grabbers[6].center = Vec3d(m_box.min(0), m_box.min(1), m_box.min(2));
+    m_grabbers[7].center = Vec3d(m_box.max(0), m_box.min(1), m_box.min(2));
+    m_grabbers[8].center = Vec3d(m_box.max(0), m_box.max(1), m_box.min(2));
+    m_grabbers[9].center = Vec3d(m_box.min(0), m_box.max(1), m_box.min(2));
+    for (int i = 6; i < 10; ++i)
+    {
+        ::memcpy((void*)m_grabbers[i].color, (const void*)m_highlight_color, 3 * sizeof(float));
+    }
+
+    ::glLineWidth((m_hover_id != -1) ? 2.0f : 1.5f);
+
+    if (m_hover_id == -1)
+    {
+        ::glColor3fv(m_base_color);
+        // draw box
+        render_box();
+        // draw grabbers
+        render_grabbers();
+    }
+    else if ((m_hover_id == 0) || (m_hover_id == 1))
+    {
+        ::glColor3fv(m_grabbers[0].color);
+        // draw connection
+        render_grabbers_connection(0, 1);
+        // draw grabbers
+        m_grabbers[0].render(true);
+        m_grabbers[1].render(true);
+    }
+    else if ((m_hover_id == 2) || (m_hover_id == 3))
+    {
+        ::glColor3fv(m_grabbers[2].color);
+        // draw connection
+        render_grabbers_connection(2, 3);
+        // draw grabbers
+        m_grabbers[2].render(true);
+        m_grabbers[3].render(true);
+    }
+    else if ((m_hover_id == 4) || (m_hover_id == 5))
+    {
+        ::glColor3fv(m_grabbers[4].color);
+        // draw connection
+        render_grabbers_connection(4, 5);
+        // draw grabbers
+        m_grabbers[4].render(true);
+        m_grabbers[5].render(true);
+    }
+    else if (m_hover_id >= 6)
+    {
+        ::glColor3fv(m_drag_color);
+        // draw box
+        render_box();
+        // draw grabbers
+        for (int i = 6; i < 10; ++i)
+        {
+            m_grabbers[i].render(true);
+        }
+    }
+}
+
+void GLGizmoScale3D::on_render_for_picking(const BoundingBoxf3& box) const
+{
+    ::glDisable(GL_DEPTH_TEST);
+
+    for (unsigned int i = 0; i < (unsigned int)m_grabbers.size(); ++i)
+    {
+        m_grabbers[i].color[0] = 1.0f;
+        m_grabbers[i].color[1] = 1.0f;
+        m_grabbers[i].color[2] = picking_color_component(i);
+    }
+
+    render_grabbers_for_picking();
+}
+
+void GLGizmoScale3D::render_box() const
+{
+    // bottom face
+    ::glBegin(GL_LINE_LOOP);
+    ::glVertex3f((GLfloat)m_box.min(0), (GLfloat)m_box.min(1), (GLfloat)m_box.min(2));
+    ::glVertex3f((GLfloat)m_box.min(0), (GLfloat)m_box.max(1), (GLfloat)m_box.min(2));
+    ::glVertex3f((GLfloat)m_box.max(0), (GLfloat)m_box.max(1), (GLfloat)m_box.min(2));
+    ::glVertex3f((GLfloat)m_box.max(0), (GLfloat)m_box.min(1), (GLfloat)m_box.min(2));
+    ::glEnd();
+
+    // top face
+    ::glBegin(GL_LINE_LOOP);
+    ::glVertex3f((GLfloat)m_box.min(0), (GLfloat)m_box.min(1), (GLfloat)m_box.max(2));
+    ::glVertex3f((GLfloat)m_box.min(0), (GLfloat)m_box.max(1), (GLfloat)m_box.max(2));
+    ::glVertex3f((GLfloat)m_box.max(0), (GLfloat)m_box.max(1), (GLfloat)m_box.max(2));
+    ::glVertex3f((GLfloat)m_box.max(0), (GLfloat)m_box.min(1), (GLfloat)m_box.max(2));
+    ::glEnd();
+
+    // vertical edges
+    ::glBegin(GL_LINES);
+    ::glVertex3f((GLfloat)m_box.min(0), (GLfloat)m_box.min(1), (GLfloat)m_box.min(2)); ::glVertex3f((GLfloat)m_box.min(0), (GLfloat)m_box.min(1), (GLfloat)m_box.max(2));
+    ::glVertex3f((GLfloat)m_box.min(0), (GLfloat)m_box.max(1), (GLfloat)m_box.min(2)); ::glVertex3f((GLfloat)m_box.min(0), (GLfloat)m_box.max(1), (GLfloat)m_box.max(2));
+    ::glVertex3f((GLfloat)m_box.max(0), (GLfloat)m_box.max(1), (GLfloat)m_box.min(2)); ::glVertex3f((GLfloat)m_box.max(0), (GLfloat)m_box.max(1), (GLfloat)m_box.max(2));
+    ::glVertex3f((GLfloat)m_box.max(0), (GLfloat)m_box.min(1), (GLfloat)m_box.min(2)); ::glVertex3f((GLfloat)m_box.max(0), (GLfloat)m_box.min(1), (GLfloat)m_box.max(2));
+    ::glEnd();
+}
+
+void GLGizmoScale3D::render_grabbers_connection(unsigned int id_1, unsigned int id_2) const
+{
+    unsigned int grabbers_count = (unsigned int)m_grabbers.size();
+    if ((id_1 < grabbers_count) && (id_2 < grabbers_count))
+    {
+        ::glBegin(GL_LINES);
+        ::glVertex3f((GLfloat)m_grabbers[id_1].center(0), (GLfloat)m_grabbers[id_1].center(1), (GLfloat)m_grabbers[id_1].center(2));
+        ::glVertex3f((GLfloat)m_grabbers[id_2].center(0), (GLfloat)m_grabbers[id_2].center(1), (GLfloat)m_grabbers[id_2].center(2));
+        ::glEnd();
+    }
+}
+
+Linef3 transform(const Linef3& line, const Transform3d& t)
+{
+    Eigen::Matrix<double, 3, 2> world_line;
+    Eigen::Matrix<double, 3, 2> local_line;
+    world_line(0, 0) = line.a(0);
+    world_line(1, 0) = line.a(1);
+    world_line(2, 0) = line.a(2);
+    world_line(0, 1) = line.b(0);
+    world_line(1, 1) = line.b(1);
+    world_line(2, 1) = line.b(2);
+    local_line = t * world_line.colwise().homogeneous();
+
+    return Linef3(Vec3d(local_line(0, 0), local_line(1, 0), local_line(2, 0)), Vec3d(local_line(0, 1), local_line(1, 1), local_line(2, 1)));
+}
+
+void GLGizmoScale3D::do_scale_x(const Linef3& mouse_ray)
+{
+    double ratio = calc_ratio(1, mouse_ray, m_starting_center);
+
+    if (ratio > 0.0)
+        m_scale_x = m_starting_scale_x * (float)ratio;
+}
+
+void GLGizmoScale3D::do_scale_y(const Linef3& mouse_ray)
+{
+    double ratio = calc_ratio(2, mouse_ray, m_starting_center);
+
+    if (ratio > 0.0)
+        m_scale_x = m_starting_scale_y * (float)ratio; // << this is temporary
+//        m_scale_y = m_starting_scale_y * (float)ratio;
+}
+
+void GLGizmoScale3D::do_scale_z(const Linef3& mouse_ray)
+{
+    double ratio = calc_ratio(1, mouse_ray, m_starting_center);
+
+    if (ratio > 0.0)
+        m_scale_x = m_starting_scale_z * (float)ratio; // << this is temporary
+//        m_scale_z = m_starting_scale_z * (float)ratio;
+}
+
+void GLGizmoScale3D::do_scale_uniform(const Linef3& mouse_ray)
+{
+    Vec3d center = m_starting_center;
+    center(2) = m_box.min(2);
+    double ratio = calc_ratio(0, mouse_ray, center);
+
+    if (ratio > 0.0)
+    {
+        m_scale_x = m_starting_scale_x * (float)ratio;
+        m_scale_y = m_starting_scale_y * (float)ratio;
+        m_scale_z = m_starting_scale_z * (float)ratio;
+    }
+}
+
+double GLGizmoScale3D::calc_ratio(unsigned int preferred_plane_id, const Linef3& mouse_ray, const Vec3d& center) const
+{
+    double ratio = 0.0;
+
+    Vec3d starting_vec = m_starting_drag_position - center;
+    double len_starting_vec = starting_vec.norm();
+    if (len_starting_vec == 0.0)
+        return ratio;
+
+    Vec3d starting_vec_dir = starting_vec.normalized();
+    Vec3d mouse_dir = mouse_ray.unit_vector();
+    unsigned int plane_id = preferred_plane_id;
+
+    // 1st try to see if the mouse direction is close enough to the preferred plane normal
+    double dot_to_normal = 0.0;
+    switch (plane_id)
+    {
+    case 0:
+    {
+        dot_to_normal = std::abs(mouse_dir.dot(Vec3d::UnitZ()));
+        break;
+    }
+    case 1:
+    {
+        dot_to_normal = std::abs(mouse_dir.dot(-Vec3d::UnitY()));
+        break;
+    }
+    case 2:
+    {
+        dot_to_normal = std::abs(mouse_dir.dot(Vec3d::UnitX()));
+        break;
+    }
+    }
+
+    if (dot_to_normal < 0.1)
+    {
+        // if not, select the plane who's normal is closest to the mouse direction
+
+        typedef std::map<double, unsigned int> ProjsMap;
+        ProjsMap projs_map;
+
+        projs_map.insert(ProjsMap::value_type(std::abs(mouse_dir.dot(Vec3d::UnitZ())), 0));  // plane xy
+        projs_map.insert(ProjsMap::value_type(std::abs(mouse_dir.dot(-Vec3d::UnitY())), 1)); // plane xz
+        projs_map.insert(ProjsMap::value_type(std::abs(mouse_dir.dot(Vec3d::UnitX())), 2));  // plane yz
+        plane_id = projs_map.rbegin()->second;
+    }
+
+    switch (plane_id)
+    {
+    case 0:
+    {
+        // calculates the intersection of the mouse ray with the plane parallel to plane XY and passing through the given center
+        Transform3d m = Transform3d::Identity();
+        m.translate(-center);
+        Vec2d mouse_pos_2d = to_2d(transform(mouse_ray, m).intersect_plane(0.0));
+
+        // ratio is given by the projection of the calculated intersection on the starting vector divided by the starting vector length
+        ratio = starting_vec_dir.dot(Vec3d(mouse_pos_2d(0), mouse_pos_2d(1), 0.0)) / len_starting_vec;
+        break;
+    }
+    case 1:
+    {
+        // calculates the intersection of the mouse ray with the plane parallel to plane XZ and passing through the given center
+        Transform3d m = Transform3d::Identity();
+        m.rotate(Eigen::AngleAxisd(-0.5 * (double)PI, Vec3d::UnitX()));
+        m.translate(-center);
+        Vec2d mouse_pos_2d = to_2d(transform(mouse_ray, m).intersect_plane(0.0));
+
+        // ratio is given by the projection of the calculated intersection on the starting vector divided by the starting vector length
+        ratio = starting_vec_dir.dot(Vec3d(mouse_pos_2d(0), 0.0, mouse_pos_2d(1))) / len_starting_vec;
+        break;
+    }
+    case 2:
+    {
+        // calculates the intersection of the mouse ray with the plane parallel to plane YZ and passing through the given center
+        Transform3d m = Transform3d::Identity();
+        m.rotate(Eigen::AngleAxisd(-0.5f * (double)PI, Vec3d::UnitY()));
+        m.translate(-center);
+        Vec2d mouse_pos_2d = to_2d(transform(mouse_ray, m).intersect_plane(0.0));
+
+        // ratio is given by the projection of the calculated intersection on the starting vector divided by the starting vector length
+        ratio = starting_vec_dir.dot(Vec3d(0.0, mouse_pos_2d(1), -mouse_pos_2d(0))) / len_starting_vec;
+        break;
+    }
+    }
+
+    return ratio;
 }
 
 } // namespace GUI
diff --git a/xs/src/slic3r/GUI/GLGizmo.hpp b/xs/src/slic3r/GUI/GLGizmo.hpp
index 506b3972e7..50bb333e5c 100644
--- a/xs/src/slic3r/GUI/GLGizmo.hpp
+++ b/xs/src/slic3r/GUI/GLGizmo.hpp
@@ -3,33 +3,54 @@
 
 #include "../../slic3r/GUI/GLTexture.hpp"
 #include "../../libslic3r/Point.hpp"
+#include "../../libslic3r/BoundingBox.hpp"
 
 #include <vector>
 
+#define ENABLE_GIZMOS_3D 1
+
 namespace Slic3r {
 
 class BoundingBoxf3;
-class Pointf3;
+class Linef3;
 
 namespace GUI {
 
+class GLCanvas3D;
+
 class GLGizmoBase
 {
 protected:
-    static const float BaseColor[3];
-    static const float HighlightColor[3];
-
     struct Grabber
     {
         static const float HalfSize;
-        static const float HoverOffset;
+        static const float DraggingScaleFactor;
 
-        Pointf center;
+        Vec3d center;
+        float angle_x;
+        float angle_y;
         float angle_z;
         float color[3];
+        bool dragging;
 
         Grabber();
+
         void render(bool hover) const;
+#if ENABLE_GIZMOS_3D
+        void render_for_picking() const { render(color, false); }
+#else
+        void render_for_picking() const { render(color); }
+#endif // ENABLE_GIZMOS_3D
+
+    private:
+#if ENABLE_GIZMOS_3D
+        void render(const float* render_color, bool use_lighting) const;
+#else
+        void render(const float* render_color) const;
+#endif // ENABLE_GIZMOS_3D
+#if ENABLE_GIZMOS_3D
+        void render_face(float half_size) const;
+#endif // ENABLE_GIZMOS_3D
     };
 
 public:
@@ -42,46 +63,64 @@ public:
     };
 
 protected:
+    GLCanvas3D& m_parent;
+
+    int m_group_id;
     EState m_state;
     // textures are assumed to be square and all with the same size in pixels, no internal check is done
     GLTexture m_textures[Num_States];
     int m_hover_id;
+    float m_base_color[3];
+    float m_drag_color[3];
+    float m_highlight_color[3];
     mutable std::vector<Grabber> m_grabbers;
+    bool m_is_container;
 
 public:
-    GLGizmoBase();
-    virtual ~GLGizmoBase();
+    explicit GLGizmoBase(GLCanvas3D& parent);
+    virtual ~GLGizmoBase() {}
 
-    bool init();
+    bool init() { return on_init(); }
 
-    EState get_state() const;
-    void set_state(EState state);
+    int get_group_id() const { return m_group_id; }
+    void set_group_id(int id) { m_group_id = id; }
 
-    unsigned int get_texture_id() const;
-    int get_textures_size() const;
+    EState get_state() const { return m_state; }
+    void set_state(EState state) { m_state = state; on_set_state(); }
 
-    int get_hover_id() const;
+    unsigned int get_texture_id() const { return m_textures[m_state].get_id(); }
+    int get_textures_size() const { return m_textures[Off].get_width(); }
+
+    int get_hover_id() const { return m_hover_id; }
     void set_hover_id(int id);
 
+    void set_highlight_color(const float* color);
+
     void start_dragging();
     void stop_dragging();
-    void update(const Pointf& mouse_pos);
-    void refresh();
+    void update(const Linef3& mouse_ray);
+    void refresh() { on_refresh(); }
 
-    void render(const BoundingBoxf3& box) const;
-    void render_for_picking(const BoundingBoxf3& box) const;
+    void render(const BoundingBoxf3& box) const { on_render(box); }
+    void render_for_picking(const BoundingBoxf3& box) const { on_render_for_picking(box); }
 
 protected:
     virtual bool on_init() = 0;
-    virtual void on_set_state();
-    virtual void on_start_dragging();
-    virtual void on_stop_dragging();
-    virtual void on_update(const Pointf& mouse_pos) = 0;
-    virtual void on_refresh();
+    virtual void on_set_state() {}
+    virtual void on_set_hover_id() {}
+    virtual void on_start_dragging() {}
+    virtual void on_stop_dragging() {}
+    virtual void on_update(const Linef3& mouse_ray) = 0;
+    virtual void on_refresh() {}
     virtual void on_render(const BoundingBoxf3& box) const = 0;
     virtual void on_render_for_picking(const BoundingBoxf3& box) const = 0;
 
+    float picking_color_component(unsigned int id) const;
     void render_grabbers() const;
+    void render_grabbers_for_picking() const;
+
+    void set_tooltip(const std::string& tooltip) const;
+    std::string format(float value, unsigned int decimals) const;
 };
 
 class GLGizmoRotate : public GLGizmoBase
@@ -97,33 +136,102 @@ class GLGizmoRotate : public GLGizmoBase
     static const unsigned int SnapRegionsCount;
     static const float GrabberOffset;
 
-    float m_angle_z;
+public:
+    enum Axis : unsigned char
+    {
+        X,
+        Y,
+        Z
+    };
 
-    mutable Pointf m_center;
+private:
+    Axis m_axis;
+    float m_angle;
+
+    mutable Vec3d m_center;
     mutable float m_radius;
-    mutable bool m_keep_radius;
+    mutable bool m_keep_initial_values;
 
 public:
-    GLGizmoRotate();
+    GLGizmoRotate(GLCanvas3D& parent, Axis axis);
 
-    float get_angle_z() const;
-    void set_angle_z(float angle_z);
+    float get_angle() const { return m_angle; }
+    void set_angle(float angle);
 
 protected:
     virtual bool on_init();
-    virtual void on_set_state();
-    virtual void on_update(const Pointf& mouse_pos);
-    virtual void on_refresh();
+    virtual void on_set_state() { m_keep_initial_values = (m_state == On) ? false : true; }
+    virtual void on_update(const Linef3& mouse_ray);
+    virtual void on_refresh() { m_keep_initial_values = false; }
     virtual void on_render(const BoundingBoxf3& box) const;
     virtual void on_render_for_picking(const BoundingBoxf3& box) const;
 
 private:
-    void _render_circle() const;
-    void _render_scale() const;
-    void _render_snap_radii() const;
-    void _render_reference_radius() const;
-    void _render_angle_z() const;
-    void _render_grabber() const;
+    void render_circle() const;
+    void render_scale() const;
+    void render_snap_radii() const;
+    void render_reference_radius() const;
+    void render_angle() const;
+    void render_grabber() const;
+
+    void transform_to_local() const;
+    // returns the intersection of the mouse ray with the plane perpendicular to the gizmo axis, in local coordinate
+    Vec3d mouse_position_in_local_plane(const Linef3& mouse_ray) const;
+};
+
+class GLGizmoRotate3D : public GLGizmoBase
+{
+    GLGizmoRotate m_x;
+    GLGizmoRotate m_y;
+    GLGizmoRotate m_z;
+
+public:
+    explicit GLGizmoRotate3D(GLCanvas3D& parent);
+
+    float get_angle_x() const { return m_x.get_angle(); }
+    void set_angle_x(float angle) { m_x.set_angle(angle); }
+
+    float get_angle_y() const { return m_y.get_angle(); }
+    void set_angle_y(float angle) { m_y.set_angle(angle); }
+
+    float get_angle_z() const { return m_z.get_angle(); }
+    void set_angle_z(float angle) { m_z.set_angle(angle); }
+
+protected:
+    virtual bool on_init();
+    virtual void on_set_state()
+    {
+        m_x.set_state(m_state);
+        m_y.set_state(m_state);
+        m_z.set_state(m_state);
+    }
+    virtual void on_set_hover_id()
+    {
+        m_x.set_hover_id(m_hover_id == 0 ? 0 : -1);
+        m_y.set_hover_id(m_hover_id == 1 ? 0 : -1);
+        m_z.set_hover_id(m_hover_id == 2 ? 0 : -1);
+    }
+    virtual void on_start_dragging();
+    virtual void on_stop_dragging();
+    virtual void on_update(const Linef3& mouse_ray)
+    {
+        m_x.update(mouse_ray);
+        m_y.update(mouse_ray);
+        m_z.update(mouse_ray);
+    }
+    virtual void on_refresh()
+    {
+        m_x.refresh();
+        m_y.refresh();
+        m_z.refresh();
+    }
+    virtual void on_render(const BoundingBoxf3& box) const;
+    virtual void on_render_for_picking(const BoundingBoxf3& box) const
+    {
+        m_x.render_for_picking(box);
+        m_y.render_for_picking(box);
+        m_z.render_for_picking(box);
+    }
 };
 
 class GLGizmoScale : public GLGizmoBase
@@ -133,22 +241,77 @@ class GLGizmoScale : public GLGizmoBase
     float m_scale;
     float m_starting_scale;
 
-    Pointf m_starting_drag_position;
+    Vec2d m_starting_drag_position;
 
 public:
-    GLGizmoScale();
+    explicit GLGizmoScale(GLCanvas3D& parent);
 
-    float get_scale() const;
-    void set_scale(float scale);
+    float get_scale() const { return m_scale; }
+    void set_scale(float scale) { m_starting_scale = scale; }
 
 protected:
     virtual bool on_init();
     virtual void on_start_dragging();
-    virtual void on_update(const Pointf& mouse_pos);
+    virtual void on_update(const Linef3& mouse_ray);
     virtual void on_render(const BoundingBoxf3& box) const;
     virtual void on_render_for_picking(const BoundingBoxf3& box) const;
 };
 
+class GLGizmoScale3D : public GLGizmoBase
+{
+    static const float Offset;
+
+    mutable BoundingBoxf3 m_box;
+
+    float m_scale_x;
+    float m_scale_y;
+    float m_scale_z;
+
+    float m_starting_scale_x;
+    float m_starting_scale_y;
+    float m_starting_scale_z;
+
+    Vec3d m_starting_drag_position;
+    Vec3d m_starting_center;
+
+public:
+    explicit GLGizmoScale3D(GLCanvas3D& parent);
+
+    float get_scale_x() const { return m_scale_x; }
+    void set_scale_x(float scale) { m_starting_scale_x = scale; }
+
+    float get_scale_y() const { return m_scale_y; }
+    void set_scale_y(float scale) { m_starting_scale_y = scale; }
+
+    float get_scale_z() const { return m_scale_z; }
+    void set_scale_z(float scale) { m_starting_scale_z = scale; }
+
+    void set_scale(float scale)
+    {
+        m_starting_scale_x = scale;
+        m_starting_scale_y = scale;
+        m_starting_scale_z = scale;
+    }
+
+protected:
+    virtual bool on_init();
+    virtual void on_start_dragging();
+    virtual void on_update(const Linef3& mouse_ray);
+    virtual void on_render(const BoundingBoxf3& box) const;
+    virtual void on_render_for_picking(const BoundingBoxf3& box) const;
+
+private:
+    void render_box() const;
+    void render_grabbers_connection(unsigned int id_1, unsigned int id_2) const;
+
+    void do_scale_x(const Linef3& mouse_ray);
+    void do_scale_y(const Linef3& mouse_ray);
+    void do_scale_z(const Linef3& mouse_ray);
+    void do_scale_uniform(const Linef3& mouse_ray);
+
+    double calc_ratio(unsigned int preferred_plane_id, const Linef3& mouse_ray, const Vec3d& center) const;
+};
+
 } // namespace GUI
 } // namespace Slic3r
 
diff --git a/xs/src/slic3r/GUI/GLTexture.cpp b/xs/src/slic3r/GUI/GLTexture.cpp
index 18c9f5dea0..235e3d93b6 100644
--- a/xs/src/slic3r/GUI/GLTexture.cpp
+++ b/xs/src/slic3r/GUI/GLTexture.cpp
@@ -12,6 +12,8 @@
 namespace Slic3r {
 namespace GUI {
 
+GLTexture::Quad_UVs GLTexture::FullTextureUVs = { { 0.0f, 1.0f }, { 1.0f, 1.0f }, { 1.0f, 0.0f }, { 0.0f, 0.0f } };
+
 GLTexture::GLTexture()
     : m_id(0)
     , m_width(0)
@@ -128,6 +130,11 @@ const std::string& GLTexture::get_source() const
 }
 
 void GLTexture::render_texture(unsigned int tex_id, float left, float right, float bottom, float top)
+{
+    render_sub_texture(tex_id, left, right, bottom, top, FullTextureUVs);
+}
+
+void GLTexture::render_sub_texture(unsigned int tex_id, float left, float right, float bottom, float top, const GLTexture::Quad_UVs& uvs)
 {
     ::glEnable(GL_BLEND);
     ::glBlendFunc(GL_SRC_ALPHA, GL_ONE_MINUS_SRC_ALPHA);
@@ -138,10 +145,10 @@ void GLTexture::render_texture(unsigned int tex_id, float left, float right, flo
     ::glBindTexture(GL_TEXTURE_2D, (GLuint)tex_id);
 
     ::glBegin(GL_QUADS);
-    ::glTexCoord2f(0.0f, 1.0f); ::glVertex2f(left, bottom);
-    ::glTexCoord2f(1.0f, 1.0f); ::glVertex2f(right, bottom);
-    ::glTexCoord2f(1.0f, 0.0f); ::glVertex2f(right, top);
-    ::glTexCoord2f(0.0f, 0.0f); ::glVertex2f(left, top);
+    ::glTexCoord2f(uvs.left_bottom.u, uvs.left_bottom.v); ::glVertex2f(left, bottom);
+    ::glTexCoord2f(uvs.right_bottom.u, uvs.right_bottom.v); ::glVertex2f(right, bottom);
+    ::glTexCoord2f(uvs.right_top.u, uvs.right_top.v); ::glVertex2f(right, top);
+    ::glTexCoord2f(uvs.left_top.u, uvs.left_top.v); ::glVertex2f(left, top);
     ::glEnd();
 
     ::glBindTexture(GL_TEXTURE_2D, 0);
diff --git a/xs/src/slic3r/GUI/GLTexture.hpp b/xs/src/slic3r/GUI/GLTexture.hpp
index 3113fcab20..e027bd152f 100644
--- a/xs/src/slic3r/GUI/GLTexture.hpp
+++ b/xs/src/slic3r/GUI/GLTexture.hpp
@@ -10,6 +10,23 @@ namespace GUI {
 
     class GLTexture
     {
+    public:
+        struct UV
+        {
+            float u;
+            float v;
+        };
+
+        struct Quad_UVs
+        {
+            UV left_bottom;
+            UV right_bottom;
+            UV right_top;
+            UV left_top;
+        };
+
+        static Quad_UVs FullTextureUVs;
+
     protected:
         unsigned int m_id;
         int m_width;
@@ -30,6 +47,7 @@ namespace GUI {
         const std::string& get_source() const;
 
         static void render_texture(unsigned int tex_id, float left, float right, float bottom, float top);
+        static void render_sub_texture(unsigned int tex_id, float left, float right, float bottom, float top, const Quad_UVs& uvs);
 
     protected:
         unsigned int _generate_mipmaps(wxImage& image);
diff --git a/xs/src/slic3r/GUI/GLToolbar.cpp b/xs/src/slic3r/GUI/GLToolbar.cpp
new file mode 100644
index 0000000000..388868b12f
--- /dev/null
+++ b/xs/src/slic3r/GUI/GLToolbar.cpp
@@ -0,0 +1,722 @@
+#include "../../libslic3r/Point.hpp"
+#include "GLToolbar.hpp"
+
+#include "../../libslic3r/libslic3r.h"
+#include "../../slic3r/GUI/GLCanvas3D.hpp"
+
+#include <GL/glew.h>
+
+#include <wx/bitmap.h>
+#include <wx/dcmemory.h>
+#include <wx/settings.h>
+
+namespace Slic3r {
+namespace GUI {
+
+GLToolbarItem::Data::Data()
+    : name("")
+    , tooltip("")
+    , sprite_id(-1)
+    , is_toggable(false)
+    , action_callback(nullptr)
+{
+}
+
+GLToolbarItem::GLToolbarItem(GLToolbarItem::EType type, const GLToolbarItem::Data& data)
+    : m_type(type)
+    , m_state(Disabled)
+    , m_data(data)
+{
+}
+
+GLToolbarItem::EState GLToolbarItem::get_state() const
+{
+    return m_state;
+}
+
+void GLToolbarItem::set_state(GLToolbarItem::EState state)
+{
+    m_state = state;
+}
+
+const std::string& GLToolbarItem::get_name() const
+{
+    return m_data.name;
+}
+
+const std::string& GLToolbarItem::get_tooltip() const
+{
+    return m_data.tooltip;
+}
+
+void GLToolbarItem::do_action()
+{
+    if (m_data.action_callback != nullptr)
+        m_data.action_callback->call();
+}
+
+bool GLToolbarItem::is_enabled() const
+{
+    return m_state != Disabled;
+}
+
+bool GLToolbarItem::is_hovered() const
+{
+    return (m_state == Hover) || (m_state == HoverPressed);
+}
+
+bool GLToolbarItem::is_pressed() const
+{
+    return (m_state == Pressed) || (m_state == HoverPressed);
+}
+
+bool GLToolbarItem::is_toggable() const
+{
+    return m_data.is_toggable;
+}
+
+bool GLToolbarItem::is_separator() const
+{
+    return m_type == Separator;
+}
+
+void GLToolbarItem::render(unsigned int tex_id, float left, float right, float bottom, float top, unsigned int texture_size, unsigned int border_size, unsigned int icon_size, unsigned int gap_size) const
+{
+    GLTexture::render_sub_texture(tex_id, left, right, bottom, top, get_uvs(texture_size, border_size, icon_size, gap_size));
+}
+
+GLTexture::Quad_UVs GLToolbarItem::get_uvs(unsigned int texture_size, unsigned int border_size, unsigned int icon_size, unsigned int gap_size) const
+{
+    GLTexture::Quad_UVs uvs;
+
+    float inv_texture_size = (texture_size != 0) ? 1.0f / (float)texture_size : 0.0f;
+
+    float scaled_icon_size = (float)icon_size * inv_texture_size;
+    float scaled_border_size = (float)border_size * inv_texture_size;
+    float scaled_gap_size = (float)gap_size * inv_texture_size;
+    float stride = scaled_icon_size + scaled_gap_size;
+
+    float left = scaled_border_size + (float)m_state * stride;
+    float right = left + scaled_icon_size;
+    float top = scaled_border_size + (float)m_data.sprite_id * stride;
+    float bottom = top + scaled_icon_size;
+
+    uvs.left_top = { left, top };
+    uvs.left_bottom = { left, bottom };
+    uvs.right_bottom = { right, bottom };
+    uvs.right_top = { right, top };
+    
+    return uvs;
+}
+
+GLToolbar::ItemsIconsTexture::ItemsIconsTexture()
+    : items_icon_size(0)
+    , items_icon_border_size(0)
+    , items_icon_gap_size(0)
+{
+}
+
+GLToolbar::Layout::Layout()
+    : type(Horizontal)
+    , top(0.0f)
+    , left(0.0f)
+    , separator_size(0.0f)
+    , gap_size(0.0f)
+{
+}
+
+GLToolbar::GLToolbar(GLCanvas3D& parent)
+    : m_parent(parent)
+    , m_enabled(false)
+{
+}
+
+bool GLToolbar::init(const std::string& icons_texture_filename, unsigned int items_icon_size, unsigned int items_icon_border_size, unsigned int items_icon_gap_size)
+{
+    std::string path = resources_dir() + "/icons/";
+    bool res = !icons_texture_filename.empty() && m_icons_texture.texture.load_from_file(path + icons_texture_filename, false);
+    if (res)
+    {
+        m_icons_texture.items_icon_size = items_icon_size;
+        m_icons_texture.items_icon_border_size = items_icon_border_size;
+        m_icons_texture.items_icon_gap_size = items_icon_gap_size;
+    }
+
+    return res;
+}
+
+GLToolbar::Layout::Type GLToolbar::get_layout_type() const
+{
+    return m_layout.type;
+}
+
+void GLToolbar::set_layout_type(GLToolbar::Layout::Type type)
+{
+    m_layout.type = type;
+}
+
+void GLToolbar::set_position(float top, float left)
+{
+    m_layout.top = top;
+    m_layout.left = left;
+}
+
+void GLToolbar::set_separator_size(float size)
+{
+    m_layout.separator_size = size;
+}
+
+void GLToolbar::set_gap_size(float size)
+{
+    m_layout.gap_size = size;
+}
+
+bool GLToolbar::is_enabled() const
+{
+    return m_enabled;
+}
+
+void GLToolbar::set_enabled(bool enable)
+{
+    m_enabled = true;
+}
+
+bool GLToolbar::add_item(const GLToolbarItem::Data& data)
+{
+    GLToolbarItem* item = new GLToolbarItem(GLToolbarItem::Action, data);
+    if (item == nullptr)
+        return false;
+
+    m_items.push_back(item);
+    return true;
+}
+
+bool GLToolbar::add_separator()
+{
+    GLToolbarItem::Data data;
+    GLToolbarItem* item = new GLToolbarItem(GLToolbarItem::Separator, data);
+    if (item == nullptr)
+        return false;
+
+    m_items.push_back(item);
+    return true;
+}
+
+float GLToolbar::get_width() const
+{
+    switch (m_layout.type)
+    {
+    default:
+    case Layout::Horizontal:
+    {
+        return get_width_horizontal();
+    }
+    case Layout::Vertical:
+    {
+        return get_width_vertical();
+    }
+    }
+}
+
+float GLToolbar::get_height() const
+{
+    switch (m_layout.type)
+    {
+    default:
+    case Layout::Horizontal:
+    {
+        return get_height_horizontal();
+    }
+    case Layout::Vertical:
+    {
+        return get_height_vertical();
+    }
+    }
+}
+
+void GLToolbar::enable_item(const std::string& name)
+{
+    for (GLToolbarItem* item : m_items)
+    {
+        if ((item->get_name() == name) && (item->get_state() == GLToolbarItem::Disabled))
+        {
+            item->set_state(GLToolbarItem::Normal);
+            return;
+        }
+    }
+}
+
+void GLToolbar::disable_item(const std::string& name)
+{
+    for (GLToolbarItem* item : m_items)
+    {
+        if (item->get_name() == name)
+        {
+            item->set_state(GLToolbarItem::Disabled);
+            return;
+        }
+    }
+}
+
+bool GLToolbar::is_item_pressed(const std::string& name) const
+{
+    for (GLToolbarItem* item : m_items)
+    {
+        if (item->get_name() == name)
+            return item->is_pressed();
+    }
+
+    return false;
+}
+
+void GLToolbar::update_hover_state(const Vec2d& mouse_pos)
+{
+    if (!m_enabled)
+        return;
+
+    switch (m_layout.type)
+    {
+    default:
+    case Layout::Horizontal:
+    {
+        update_hover_state_horizontal(mouse_pos);
+        break;
+    }
+    case Layout::Vertical:
+    {
+        update_hover_state_vertical(mouse_pos);
+        break;
+    }
+    }
+}
+
+int GLToolbar::contains_mouse(const Vec2d& mouse_pos) const
+{
+    if (!m_enabled)
+        return -1;
+
+    switch (m_layout.type)
+    {
+    default:
+    case Layout::Horizontal:
+    {
+        return contains_mouse_horizontal(mouse_pos);
+    }
+    case Layout::Vertical:
+    {
+        return contains_mouse_vertical(mouse_pos);
+    }
+    }
+}
+
+void GLToolbar::do_action(unsigned int item_id)
+{
+    if (item_id < (unsigned int)m_items.size())
+    {
+        GLToolbarItem* item = m_items[item_id];
+        if ((item != nullptr) && !item->is_separator() && item->is_hovered())
+        {
+            if (item->is_toggable())
+            {
+                GLToolbarItem::EState state = item->get_state();
+                if (state == GLToolbarItem::Hover)
+                    item->set_state(GLToolbarItem::HoverPressed);
+                else if (state == GLToolbarItem::HoverPressed)
+                    item->set_state(GLToolbarItem::Hover);
+
+                m_parent.render();
+                item->do_action();
+            }
+            else
+            {
+                item->set_state(GLToolbarItem::HoverPressed);
+                m_parent.render();
+                item->do_action();
+                if (item->get_state() != GLToolbarItem::Disabled)
+                {
+                    // the item may get disabled during the action, if not, set it back to hover state
+                    item->set_state(GLToolbarItem::Hover);
+                    m_parent.render();
+                }
+            }
+        }
+    }
+}
+
+void GLToolbar::render() const
+{
+    if (!m_enabled || m_items.empty())
+        return;
+
+    ::glDisable(GL_DEPTH_TEST);
+
+    ::glPushMatrix();
+    ::glLoadIdentity();
+
+    switch (m_layout.type)
+    {
+    default:
+    case Layout::Horizontal:
+    {
+        render_horizontal();
+        break;
+    }
+    case Layout::Vertical:
+    {
+        render_vertical();
+        break;
+    }
+    }
+
+    ::glPopMatrix();
+}
+
+float GLToolbar::get_width_horizontal() const
+{
+    return get_main_size();
+}
+
+float GLToolbar::get_width_vertical() const
+{
+    return m_icons_texture.items_icon_size;
+}
+
+float GLToolbar::get_height_horizontal() const
+{
+    return m_icons_texture.items_icon_size;
+}
+
+float GLToolbar::get_height_vertical() const
+{
+    return get_main_size();
+}
+
+float GLToolbar::get_main_size() const
+{
+    float size = 0.0f;
+    for (unsigned int i = 0; i < (unsigned int)m_items.size(); ++i)
+    {
+        if (m_items[i]->is_separator())
+            size += m_layout.separator_size;
+        else
+            size += (float)m_icons_texture.items_icon_size;
+    }
+
+    if (m_items.size() > 1)
+        size += ((float)m_items.size() - 1.0f) * m_layout.gap_size;
+
+    return size;
+}
+
+void GLToolbar::update_hover_state_horizontal(const Vec2d& mouse_pos)
+{
+    float zoom = m_parent.get_camera_zoom();
+    float inv_zoom = (zoom != 0.0f) ? 1.0f / zoom : 0.0f;
+
+    Size cnv_size = m_parent.get_canvas_size();
+    Vec2d scaled_mouse_pos((mouse_pos(0) - 0.5 * (double)cnv_size.get_width()) * inv_zoom, (0.5 * (double)cnv_size.get_height() - mouse_pos(1)) * inv_zoom);
+
+    float scaled_icons_size = (float)m_icons_texture.items_icon_size * inv_zoom;
+    float scaled_separator_size = m_layout.separator_size * inv_zoom;
+    float scaled_gap_size = m_layout.gap_size * inv_zoom;
+
+    float separator_stride = scaled_separator_size + scaled_gap_size;
+    float icon_stride = scaled_icons_size + scaled_gap_size;
+
+    float left = m_layout.left;
+    float top = m_layout.top;
+
+    std::string tooltip = "";
+        
+    for (GLToolbarItem* item : m_items)
+    {
+        if (item->is_separator())
+            left += separator_stride;
+        else
+        {
+            float right = left + scaled_icons_size;
+            float bottom = top - scaled_icons_size;
+
+            GLToolbarItem::EState state = item->get_state();
+            bool inside = (left <= (float)scaled_mouse_pos(0)) && ((float)scaled_mouse_pos(0) <= right) && (bottom <= (float)scaled_mouse_pos(1)) && ((float)scaled_mouse_pos(1) <= top);
+
+            switch (state)
+            {
+            case GLToolbarItem::Normal:
+            {
+                if (inside)
+                    item->set_state(GLToolbarItem::Hover);
+
+                break;
+            }
+            case GLToolbarItem::Hover:
+            {
+                if (inside)
+                    tooltip = item->get_tooltip();
+                else
+                    item->set_state(GLToolbarItem::Normal);
+                
+                break;
+            }
+            case GLToolbarItem::Pressed:
+            {
+                if (inside)
+                    item->set_state(GLToolbarItem::HoverPressed);
+                
+                break;
+            }
+            case GLToolbarItem::HoverPressed:
+            {
+                if (inside)
+                    tooltip = item->get_tooltip();
+                else
+                    item->set_state(GLToolbarItem::Pressed);
+                
+                break;
+            }
+            default:
+            case GLToolbarItem::Disabled:
+            {
+                break;
+            }
+            }
+
+            left += icon_stride;
+        }
+    }
+
+    m_parent.set_tooltip(tooltip);
+}
+
+void GLToolbar::update_hover_state_vertical(const Vec2d& mouse_pos)
+{
+    float zoom = m_parent.get_camera_zoom();
+    float inv_zoom = (zoom != 0.0f) ? 1.0f / zoom : 0.0f;
+
+    Size cnv_size = m_parent.get_canvas_size();
+    Vec2d scaled_mouse_pos((mouse_pos(0) - 0.5 * (double)cnv_size.get_width()) * inv_zoom, (0.5 * (double)cnv_size.get_height() - mouse_pos(1)) * inv_zoom);
+
+    float scaled_icons_size = (float)m_icons_texture.items_icon_size * inv_zoom;
+    float scaled_separator_size = m_layout.separator_size * inv_zoom;
+    float scaled_gap_size = m_layout.gap_size * inv_zoom;
+
+    float separator_stride = scaled_separator_size + scaled_gap_size;
+    float icon_stride = scaled_icons_size + scaled_gap_size;
+
+    float left = m_layout.left;
+    float top = m_layout.top;
+
+    std::string tooltip = "";
+
+    for (GLToolbarItem* item : m_items)
+    {
+        if (item->is_separator())
+            top -= separator_stride;
+        else
+        {
+            float right = left + scaled_icons_size;
+            float bottom = top - scaled_icons_size;
+
+            GLToolbarItem::EState state = item->get_state();
+            bool inside = (left <= (float)scaled_mouse_pos(0)) && ((float)scaled_mouse_pos(0) <= right) && (bottom <= (float)scaled_mouse_pos(1)) && ((float)scaled_mouse_pos(1) <= top);
+
+            switch (state)
+            {
+            case GLToolbarItem::Normal:
+            {
+                if (inside)
+                    item->set_state(GLToolbarItem::Hover);
+
+                break;
+            }
+            case GLToolbarItem::Hover:
+            {
+                if (inside)
+                    tooltip = item->get_tooltip();
+                else
+                    item->set_state(GLToolbarItem::Normal);
+
+                break;
+            }
+            case GLToolbarItem::Pressed:
+            {
+                if (inside)
+                    item->set_state(GLToolbarItem::HoverPressed);
+
+                break;
+            }
+            case GLToolbarItem::HoverPressed:
+            {
+                if (inside)
+                    tooltip = item->get_tooltip();
+                else
+                    item->set_state(GLToolbarItem::Pressed);
+
+                break;
+            }
+            default:
+            case GLToolbarItem::Disabled:
+            {
+                break;
+            }
+            }
+
+            top -= icon_stride;
+        }
+    }
+
+    m_parent.set_tooltip(tooltip);
+}
+
+int GLToolbar::contains_mouse_horizontal(const Vec2d& mouse_pos) const
+{
+    float zoom = m_parent.get_camera_zoom();
+    float inv_zoom = (zoom != 0.0f) ? 1.0f / zoom : 0.0f;
+
+    Size cnv_size = m_parent.get_canvas_size();
+    Vec2d scaled_mouse_pos((mouse_pos(0) - 0.5 * (double)cnv_size.get_width()) * inv_zoom, (0.5 * (double)cnv_size.get_height() - mouse_pos(1)) * inv_zoom);
+
+    float scaled_icons_size = (float)m_icons_texture.items_icon_size * inv_zoom;
+    float scaled_separator_size = m_layout.separator_size * inv_zoom;
+    float scaled_gap_size = m_layout.gap_size * inv_zoom;
+
+    float separator_stride = scaled_separator_size + scaled_gap_size;
+    float icon_stride = scaled_icons_size + scaled_gap_size;
+
+    float left = m_layout.left;
+    float top = m_layout.top;
+
+    int id = -1;
+    
+    for (GLToolbarItem* item : m_items)
+    {
+        ++id;
+        
+        if (item->is_separator())
+            left += separator_stride;
+        else
+        {
+            float right = left + scaled_icons_size;
+            float bottom = top - scaled_icons_size;
+            
+            if ((left <= (float)scaled_mouse_pos(0)) && ((float)scaled_mouse_pos(0) <= right) && (bottom <= (float)scaled_mouse_pos(1)) && ((float)scaled_mouse_pos(1) <= top))
+                return id;
+            
+            left += icon_stride;
+        }
+    }
+    
+    return -1;
+}
+
+int GLToolbar::contains_mouse_vertical(const Vec2d& mouse_pos) const
+{
+    float zoom = m_parent.get_camera_zoom();
+    float inv_zoom = (zoom != 0.0f) ? 1.0f / zoom : 0.0f;
+
+    Size cnv_size = m_parent.get_canvas_size();
+    Vec2d scaled_mouse_pos((mouse_pos(0) - 0.5 * (double)cnv_size.get_width()) * inv_zoom, (0.5 * (double)cnv_size.get_height() - mouse_pos(1)) * inv_zoom);
+
+    float scaled_icons_size = (float)m_icons_texture.items_icon_size * inv_zoom;
+    float scaled_separator_size = m_layout.separator_size * inv_zoom;
+    float scaled_gap_size = m_layout.gap_size * inv_zoom;
+
+    float separator_stride = scaled_separator_size + scaled_gap_size;
+    float icon_stride = scaled_icons_size + scaled_gap_size;
+
+    float left = m_layout.left;
+    float top = m_layout.top;
+
+    int id = -1;
+
+    for (GLToolbarItem* item : m_items)
+    {
+        ++id;
+
+        if (item->is_separator())
+            top -= separator_stride;
+        else
+        {
+            float right = left + scaled_icons_size;
+            float bottom = top - scaled_icons_size;
+
+            if ((left <= (float)scaled_mouse_pos(0)) && ((float)scaled_mouse_pos(0) <= right) && (bottom <= (float)scaled_mouse_pos(1)) && ((float)scaled_mouse_pos(1) <= top))
+                return id;
+
+            top -= icon_stride;
+        }
+    }
+
+    return -1;
+}
+
+void GLToolbar::render_horizontal() const
+{
+    unsigned int tex_id = m_icons_texture.texture.get_id();
+    int tex_size = m_icons_texture.texture.get_width();
+
+    if ((tex_id == 0) || (tex_size <= 0))
+        return;
+
+    float zoom = m_parent.get_camera_zoom();
+    float inv_zoom = (zoom != 0.0f) ? 1.0f / zoom : 0.0f;
+
+    float scaled_icons_size = (float)m_icons_texture.items_icon_size * inv_zoom;
+    float scaled_separator_size = m_layout.separator_size * inv_zoom;
+    float scaled_gap_size = m_layout.gap_size * inv_zoom;
+
+    float separator_stride = scaled_separator_size + scaled_gap_size;
+    float icon_stride = scaled_icons_size + scaled_gap_size;
+
+    float left = m_layout.left;
+    float top = m_layout.top;
+
+    // renders icons
+    for (const GLToolbarItem* item : m_items)
+    {
+        if (item->is_separator())
+            left += separator_stride;
+        else
+        {
+            item->render(tex_id, left, left + scaled_icons_size, top - scaled_icons_size, top, (unsigned int)tex_size, m_icons_texture.items_icon_border_size, m_icons_texture.items_icon_size, m_icons_texture.items_icon_gap_size);
+            left += icon_stride;
+        }
+    }
+}
+
+void GLToolbar::render_vertical() const
+{
+    unsigned int tex_id = m_icons_texture.texture.get_id();
+    int tex_size = m_icons_texture.texture.get_width();
+
+    if ((tex_id == 0) || (tex_size <= 0))
+        return;
+
+    float zoom = m_parent.get_camera_zoom();
+    float inv_zoom = (zoom != 0.0f) ? 1.0f / zoom : 0.0f;
+
+    float scaled_icons_size = (float)m_icons_texture.items_icon_size * inv_zoom;
+    float scaled_separator_size = m_layout.separator_size * inv_zoom;
+    float scaled_gap_size = m_layout.gap_size * inv_zoom;
+
+    float separator_stride = scaled_separator_size + scaled_gap_size;
+    float icon_stride = scaled_icons_size + scaled_gap_size;
+
+    float left = m_layout.left;
+    float top = m_layout.top;
+
+    // renders icons
+    for (const GLToolbarItem* item : m_items)
+    {
+        if (item->is_separator())
+            top -= separator_stride;
+        else
+        {
+            item->render(tex_id, left, left + scaled_icons_size, top - scaled_icons_size, top, (unsigned int)tex_size, m_icons_texture.items_icon_border_size, m_icons_texture.items_icon_size, m_icons_texture.items_icon_gap_size);
+            top -= icon_stride;
+        }
+    }
+}
+
+} // namespace GUI
+} // namespace Slic3r
diff --git a/xs/src/slic3r/GUI/GLToolbar.hpp b/xs/src/slic3r/GUI/GLToolbar.hpp
new file mode 100644
index 0000000000..c1501b10c2
--- /dev/null
+++ b/xs/src/slic3r/GUI/GLToolbar.hpp
@@ -0,0 +1,175 @@
+#ifndef slic3r_GLToolbar_hpp_
+#define slic3r_GLToolbar_hpp_
+
+#include "../../slic3r/GUI/GLTexture.hpp"
+#include "../../libslic3r/Utils.hpp"
+
+#include <string>
+#include <vector>
+
+namespace Slic3r {
+namespace GUI {
+
+class GLCanvas3D;
+
+class GLToolbarItem
+{
+public:
+    enum EType : unsigned char
+    {
+        Action,
+        Separator,
+        Num_Types
+    };
+
+    enum EState : unsigned char
+    {
+        Normal,
+        Pressed,
+        Disabled,
+        Hover,
+        HoverPressed,
+        Num_States
+    };
+
+    struct Data
+    {
+        std::string name;
+        std::string tooltip;
+        unsigned int sprite_id;
+        bool is_toggable;
+        PerlCallback* action_callback;
+
+        Data();
+    };
+
+private:
+    EType m_type;
+    EState m_state;
+    Data m_data;
+
+public:
+    GLToolbarItem(EType type, const Data& data);
+
+    EState get_state() const;
+    void set_state(EState state);
+
+    const std::string& get_name() const;
+    const std::string& get_tooltip() const;
+
+    void do_action();
+
+    bool is_enabled() const;
+    bool is_hovered() const;
+    bool is_pressed() const;
+
+    bool is_toggable() const;
+    bool is_separator() const;
+
+    void render(unsigned int tex_id, float left, float right, float bottom, float top, unsigned int texture_size, unsigned int border_size, unsigned int icon_size, unsigned int gap_size) const;
+
+private:
+    GLTexture::Quad_UVs get_uvs(unsigned int texture_size, unsigned int border_size, unsigned int icon_size, unsigned int gap_size) const;
+};
+
+class GLToolbar
+{
+public:
+    // items icon textures are assumed to be square and all with the same size in pixels, no internal check is done
+    // icons are layed-out into the texture starting from the top-left corner in the same order as enum GLToolbarItem::EState
+    // from left to right
+    struct ItemsIconsTexture
+    {
+        GLTexture texture;
+        // size of the square icons, in pixels
+        unsigned int items_icon_size;
+        // distance from the border, in pixels
+        unsigned int items_icon_border_size;
+        // distance between two adjacent icons (to avoid filtering artifacts), in pixels
+        unsigned int items_icon_gap_size;
+
+        ItemsIconsTexture();
+    };
+
+    struct Layout
+    {
+        enum Type : unsigned char
+        {
+            Horizontal,
+            Vertical,
+            Num_Types
+        };
+
+        Type type;
+        float top;
+        float left;
+        float separator_size;
+        float gap_size;
+
+        Layout();
+    };
+
+private:
+    typedef std::vector<GLToolbarItem*> ItemsList;
+
+    GLCanvas3D& m_parent;
+    bool m_enabled;
+    ItemsIconsTexture m_icons_texture;
+    Layout m_layout;
+
+    ItemsList m_items;
+
+public:
+    explicit GLToolbar(GLCanvas3D& parent);
+
+    bool init(const std::string& icons_texture_filename, unsigned int items_icon_size, unsigned int items_icon_border_size, unsigned int items_icon_gap_size);
+    
+    Layout::Type get_layout_type() const;
+    void set_layout_type(Layout::Type type);
+
+    void set_position(float top, float left);
+    void set_separator_size(float size);
+    void set_gap_size(float size);
+
+    bool is_enabled() const;
+    void set_enabled(bool enable);
+
+    bool add_item(const GLToolbarItem::Data& data);
+    bool add_separator();
+
+    float get_width() const;
+    float get_height() const;
+
+    void enable_item(const std::string& name);
+    void disable_item(const std::string& name);
+
+    bool is_item_pressed(const std::string& name) const;
+
+    void update_hover_state(const Vec2d& mouse_pos);
+
+    // returns the id of the item under the given mouse position or -1 if none
+    int contains_mouse(const Vec2d& mouse_pos) const;
+
+    void do_action(unsigned int item_id);
+
+    void render() const;
+
+private:
+    float get_width_horizontal() const;
+    float get_width_vertical() const;
+    float get_height_horizontal() const;
+    float get_height_vertical() const;
+    float get_main_size() const;
+    void update_hover_state_horizontal(const Vec2d& mouse_pos);
+    void update_hover_state_vertical(const Vec2d& mouse_pos);
+    int contains_mouse_horizontal(const Vec2d& mouse_pos) const;
+    int contains_mouse_vertical(const Vec2d& mouse_pos) const;
+
+    void render_horizontal() const;
+    void render_vertical() const;
+};
+
+} // namespace GUI
+} // namespace Slic3r
+
+#endif // slic3r_GLToolbar_hpp_
diff --git a/xs/src/slic3r/GUI/GUI.cpp b/xs/src/slic3r/GUI/GUI.cpp
index e5dca948c9..9e28de04a5 100644
--- a/xs/src/slic3r/GUI/GUI.cpp
+++ b/xs/src/slic3r/GUI/GUI.cpp
@@ -38,6 +38,8 @@
 #include <wx/msgdlg.h>
 #include <wx/settings.h>
 #include <wx/display.h>
+#include <wx/collpane.h>
+#include <wx/wupdlock.h>
 
 #include "wxExtensions.hpp"
 
@@ -53,12 +55,15 @@
 #include "PresetBundle.hpp"
 #include "UpdateDialogs.hpp"
 #include "FirmwareDialog.hpp"
+#include "GUI_ObjectParts.hpp"
 
 #include "../Utils/PresetUpdater.hpp"
 #include "../Config/Snapshot.hpp"
 
 #include "3DScene.hpp"
 #include "libslic3r/I18N.hpp"
+#include "Model.hpp"
+#include "LambdaObjectDialog.hpp"
 
 namespace Slic3r { namespace GUI {
 
@@ -123,10 +128,26 @@ wxLocale*	g_wxLocale;
 wxFont		g_small_font;
 wxFont		g_bold_font;
 
-std::shared_ptr<ConfigOptionsGroup>	m_optgroup;
-double m_brim_width = 0.0;
+std::vector <std::shared_ptr<ConfigOptionsGroup>> m_optgroups;
+double		m_brim_width = 0.0;
+size_t		m_label_width = 100;
 wxButton*	g_wiping_dialog_button = nullptr;
 
+//showed/hided controls according to the view mode
+wxWindow	*g_right_panel = nullptr;
+wxBoxSizer	*g_frequently_changed_parameters_sizer = nullptr;
+wxBoxSizer	*g_expert_mode_part_sizer = nullptr;
+wxBoxSizer	*g_scrolled_window_sizer = nullptr;
+wxBoxSizer	*g_object_list_sizer = nullptr;
+wxButton	*g_btn_export_gcode = nullptr;
+wxButton	*g_btn_export_stl = nullptr;
+wxButton	*g_btn_reslice = nullptr;
+wxButton	*g_btn_print = nullptr;
+wxButton	*g_btn_send_gcode = nullptr;
+wxStaticBitmap	*g_manifold_warning_icon = nullptr;
+bool		g_show_print_info = false;
+bool		g_show_manifold_warning_icon = false;
+
 static void init_label_colours()
 {
 	auto luma = get_colour_approx_luma(wxSystemSettings::GetColour(wxSYS_COLOUR_WINDOW));
@@ -206,6 +227,39 @@ void set_3DScene(_3DScene *scene)
 	g_3DScene = scene;
 }
 
+void set_objects_from_perl(	wxWindow* parent, wxBoxSizer *frequently_changed_parameters_sizer,
+							wxBoxSizer *expert_mode_part_sizer, wxBoxSizer *scrolled_window_sizer,
+							wxButton *btn_export_gcode,
+							wxButton *btn_export_stl, wxButton *btn_reslice, 
+							wxButton *btn_print, wxButton *btn_send_gcode,
+							wxStaticBitmap *manifold_warning_icon)
+{
+	g_right_panel = parent;
+	g_frequently_changed_parameters_sizer = frequently_changed_parameters_sizer;
+	g_expert_mode_part_sizer = expert_mode_part_sizer;
+	g_scrolled_window_sizer = scrolled_window_sizer;
+	g_btn_export_gcode = btn_export_gcode;
+	g_btn_export_stl = btn_export_stl;
+	g_btn_reslice = btn_reslice;
+	g_btn_print = btn_print;
+	g_btn_send_gcode = btn_send_gcode;
+	g_manifold_warning_icon = manifold_warning_icon;
+}
+
+void set_show_print_info(bool show)
+{
+	g_show_print_info = show;
+}
+
+void set_show_manifold_warning_icon(bool show)
+{
+	g_show_manifold_warning_icon = show;
+}
+
+void set_objects_list_sizer(wxBoxSizer *objects_list_sizer){
+	g_object_list_sizer = objects_list_sizer;
+}
+
 std::vector<Tab *>& get_tabs_list()
 {
 	return g_tabs_list;
@@ -332,10 +386,21 @@ enum ConfigMenuIDs {
 	ConfigMenuTakeSnapshot,
 	ConfigMenuUpdate,
 	ConfigMenuPreferences,
+	ConfigMenuModeSimple,
+	ConfigMenuModeExpert,
 	ConfigMenuLanguage,
 	ConfigMenuFlashFirmware,
 	ConfigMenuCnt,
 };
+	
+ConfigMenuIDs get_view_mode()
+{
+	if (!g_AppConfig->has("view_mode"))
+		return ConfigMenuModeSimple;
+
+	const auto mode = g_AppConfig->get("view_mode");
+	return mode == "expert" ? ConfigMenuModeExpert : ConfigMenuModeSimple;
+}
 
 static wxString dots("…", wxConvUTF8);
 
@@ -353,8 +418,15 @@ void add_config_menu(wxMenuBar *menu, int event_preferences_changed, int event_l
 // 	local_menu->Append(config_id_base + ConfigMenuUpdate, 		_(L("Check for updates")), 					_(L("Check for configuration updates")));
    	local_menu->AppendSeparator();
    	local_menu->Append(config_id_base + ConfigMenuPreferences, 	_(L("Preferences"))+dots+"\tCtrl+,", 		_(L("Application preferences")));
-   	local_menu->Append(config_id_base + ConfigMenuLanguage, 	_(L("Change Application Language")));
+	local_menu->AppendSeparator();
+	auto mode_menu = new wxMenu();
+	mode_menu->AppendRadioItem(config_id_base + ConfigMenuModeSimple,	_(L("&Simple")),					_(L("Simple View Mode")));
+	mode_menu->AppendRadioItem(config_id_base + ConfigMenuModeExpert,	_(L("&Expert")),					_(L("Expert View Mode")));
+	mode_menu->Check(config_id_base + get_view_mode(), true);
+	local_menu->AppendSubMenu(mode_menu,						_(L("&Mode")), 								_(L("Slic3r View Mode")));
    	local_menu->AppendSeparator();
+	local_menu->Append(config_id_base + ConfigMenuLanguage,		_(L("Change Application Language")));
+	local_menu->AppendSeparator();
 	local_menu->Append(config_id_base + ConfigMenuFlashFirmware, _(L("Flash printer firmware")), _(L("Upload a firmware image into an Arduino based printer")));
 	// TODO: for when we're able to flash dictionaries
 	// local_menu->Append(config_id_base + FirmwareMenuDict,  _(L("Flash language file")),    _(L("Upload a language dictionary file into a Prusa printer")));
@@ -421,6 +493,13 @@ void add_config_menu(wxMenuBar *menu, int event_preferences_changed, int event_l
 			break;
 		}
 	});
+	mode_menu->Bind(wxEVT_MENU, [config_id_base](wxEvent& event) {
+		std::string mode =	event.GetId() - config_id_base == ConfigMenuModeExpert ?
+							"expert" : "simple";
+		g_AppConfig->set("view_mode", mode);
+		g_AppConfig->save();
+		update_mode();
+	});
 	menu->Append(local_menu, _(L("&Configuration")));
 }
 
@@ -429,6 +508,26 @@ void add_menus(wxMenuBar *menu, int event_preferences_changed, int event_languag
     add_config_menu(menu, event_preferences_changed, event_language_change);
 }
 
+void open_model(wxWindow *parent, wxArrayString& input_files){
+	t_file_wild_card vec_FILE_WILDCARDS = get_file_wild_card();
+	std::vector<std::string> file_types = { "known", "stl", "obj", "amf", "3mf", "prusa" };
+	wxString MODEL_WILDCARD;
+	for (auto file_type : file_types)
+		MODEL_WILDCARD += vec_FILE_WILDCARDS.at(file_type) + "|";
+
+	auto dlg_title = _(L("Choose one or more files (STL/OBJ/AMF/3MF/PRUSA):"));
+	auto dialog = new wxFileDialog(parent /*? parent : GetTopWindow(g_wxMainFrame)*/, dlg_title, 
+		g_AppConfig->get_last_dir(), "",
+		MODEL_WILDCARD, wxFD_OPEN | wxFD_MULTIPLE | wxFD_FILE_MUST_EXIST);
+	if (dialog->ShowModal() != wxID_OK) {
+		dialog->Destroy();
+		return ;
+	}
+	
+	dialog->GetPaths(input_files);
+	dialog->Destroy();
+}
+
 // This is called when closing the application, when loading a config file or when starting the config wizard
 // to notify the user whether he is aware that some preset changes will be lost.
 bool check_unsaved_changes()
@@ -496,20 +595,33 @@ void open_preferences_dialog(int event_preferences)
 void create_preset_tabs(bool no_controller, int event_value_change, int event_presets_changed)
 {	
 	update_label_colours_from_appconfig();
-	add_created_tab(new TabPrint	(g_wxTabPanel, no_controller));
-	add_created_tab(new TabFilament	(g_wxTabPanel, no_controller));
-	add_created_tab(new TabPrinter	(g_wxTabPanel, no_controller));
-	for (size_t i = 0; i < g_wxTabPanel->GetPageCount(); ++ i) {
-		Tab *tab = dynamic_cast<Tab*>(g_wxTabPanel->GetPage(i));
-		if (! tab)
-			continue;
-		tab->set_event_value_change(wxEventType(event_value_change));
-		tab->set_event_presets_changed(wxEventType(event_presets_changed));
-	}
+	add_created_tab(new TabPrint	    (g_wxTabPanel, no_controller), event_value_change, event_presets_changed);
+	add_created_tab(new TabFilament	    (g_wxTabPanel, no_controller), event_value_change, event_presets_changed);
+	add_created_tab(new TabSLAMaterial  (g_wxTabPanel, no_controller), event_value_change, event_presets_changed);
+	add_created_tab(new TabPrinter	    (g_wxTabPanel, no_controller), event_value_change, event_presets_changed);
+}
+
+std::vector<PresetTab> preset_tabs = {
+    { "print",        nullptr, ptFFF },
+    { "filament",     nullptr, ptFFF },
+    { "sla_material", nullptr, ptSLA }
+};
+const std::vector<PresetTab>& get_preset_tabs() {
+    return preset_tabs;
+}
+
+Tab* get_tab(const std::string& name)
+{
+    std::vector<PresetTab>::iterator it = std::find_if(preset_tabs.begin(), preset_tabs.end(),
+                                                       [name](PresetTab& tab){ return name == tab.name; });
+    return it != preset_tabs.end() ? it->panel : nullptr;
 }
 
 TabIface* get_preset_tab_iface(char *name)
 {
+    Tab* tab = get_tab(name);
+    if (tab) return new TabIface(tab);
+
 	for (size_t i = 0; i < g_wxTabPanel->GetPageCount(); ++ i) {
 		Tab *tab = dynamic_cast<Tab*>(g_wxTabPanel->GetPage(i));
 		if (! tab)
@@ -604,14 +716,16 @@ void change_opt_value(DynamicPrintConfig& config, const t_config_option_key& opt
 				config.set_key_value(opt_key, new ConfigOptionEnum<SupportMaterialPattern>(boost::any_cast<SupportMaterialPattern>(value)));
 			else if (opt_key.compare("seam_position") == 0)
 				config.set_key_value(opt_key, new ConfigOptionEnum<SeamPosition>(boost::any_cast<SeamPosition>(value)));
+			else if (opt_key.compare("host_type") == 0)
+				config.set_key_value(opt_key, new ConfigOptionEnum<PrintHostType>(boost::any_cast<PrintHostType>(value)));
 			}
 			break;
 		case coPoints:{
 			if (opt_key.compare("bed_shape") == 0){
-				config.option<ConfigOptionPoints>(opt_key)->values = boost::any_cast<std::vector<Pointf>>(value);
+				config.option<ConfigOptionPoints>(opt_key)->values = boost::any_cast<std::vector<Vec2d>>(value);
 				break;
 			}
-			ConfigOptionPoints* vec_new = new ConfigOptionPoints{ boost::any_cast<Pointf>(value) };
+			ConfigOptionPoints* vec_new = new ConfigOptionPoints{ boost::any_cast<Vec2d>(value) };
 			config.option<ConfigOptionPoints>(opt_key)->set_at(vec_new, opt_index, 0);
 			}
 			break;
@@ -627,13 +741,28 @@ void change_opt_value(DynamicPrintConfig& config, const t_config_option_key& opt
 	}
 }
 
-void add_created_tab(Tab* panel)
+void add_created_tab(Tab* panel, int event_value_change, int event_presets_changed)
 {
 	panel->create_preset_tab(g_PresetBundle);
 
 	// Load the currently selected preset into the GUI, update the preset selection box.
 	panel->load_current_preset();
-	g_wxTabPanel->AddPage(panel, panel->title());
+
+    panel->set_event_value_change(wxEventType(event_value_change));
+    panel->set_event_presets_changed(wxEventType(event_presets_changed));
+
+    const wxString& tab_name = panel->GetName();
+    bool add_panel = true;
+
+    auto it = std::find_if( preset_tabs.begin(), preset_tabs.end(), 
+                           [tab_name](PresetTab& tab){return tab.name == tab_name; });
+    if (it != preset_tabs.end()) {
+        it->panel = panel;
+        add_panel = it->technology == g_PresetBundle->printers.get_edited_preset().printer_technology();
+    }
+
+    if (add_panel)
+	    g_wxTabPanel->AddPage(panel, panel->title());
 }
 
 void load_current_presets()
@@ -723,6 +852,22 @@ unsigned get_colour_approx_luma(const wxColour &colour)
 	));
 }
 
+wxWindow* get_right_panel(){
+	return g_right_panel;
+}
+
+wxFrame* get_main_frame() {
+	return g_wxMainFrame;
+}
+
+wxNotebook * get_tab_panel() {
+	return g_wxTabPanel;
+}
+
+const size_t& label_width(){
+	return m_label_width;
+}
+
 void create_combochecklist(wxComboCtrl* comboCtrl, std::string text, std::string items, bool initial_value)
 {
     if (comboCtrl == nullptr)
@@ -791,14 +936,37 @@ wxString from_u8(const std::string &str)
 	return wxString::FromUTF8(str.c_str());
 }
 
+void add_expert_mode_part(	wxWindow* parent, wxBoxSizer* sizer, 
+							Model &model,
+							int event_object_selection_changed,
+							int event_object_settings_changed,
+							int event_remove_object, 
+							int event_update_scene)
+{
+	set_event_object_selection_changed(event_object_selection_changed);
+	set_event_object_settings_changed(event_object_settings_changed);
+	set_event_remove_object(event_remove_object);
+	set_event_update_scene(event_update_scene);
+	set_objects_from_model(model);
+	init_mesh_icons();
+
+// 	wxWindowUpdateLocker noUpdates(parent);
+
+// 	add_objects_list(parent, sizer);
+
+// 	add_collapsible_panes(parent, sizer);
+}
 
 void add_frequently_changed_parameters(wxWindow* parent, wxBoxSizer* sizer, wxFlexGridSizer* preset_sizer)
 {
 	DynamicPrintConfig*	config = &g_PresetBundle->prints.get_edited_preset().config;
-	m_optgroup = std::make_shared<ConfigOptionsGroup>(parent, "", config);
+	std::shared_ptr<ConfigOptionsGroup> optgroup = std::make_shared<ConfigOptionsGroup>(parent, "", config);
 	const wxArrayInt& ar = preset_sizer->GetColWidths();
-	m_optgroup->label_width = ar.IsEmpty() ? 100 : ar.front()-4; // doesn't work
-	m_optgroup->m_on_change = [config](t_config_option_key opt_key, boost::any value){
+	m_label_width = ar.IsEmpty() ? 100 : ar.front()-4;
+	optgroup->label_width = m_label_width;
+
+	//Frequently changed parameters
+	optgroup->m_on_change = [config](t_config_option_key opt_key, boost::any value){
 		TabPrint* tab_print = nullptr;
 		for (size_t i = 0; i < g_wxTabPanel->GetPageCount(); ++i) {
 			Tab *tab = dynamic_cast<Tab*>(g_wxTabPanel->GetPage(i));
@@ -813,7 +981,7 @@ void add_frequently_changed_parameters(wxWindow* parent, wxBoxSizer* sizer, wxFl
 			return;
 
 		if (opt_key == "fill_density"){
-			value = m_optgroup->get_config_value(*config, opt_key);
+			value = m_optgroups[ogFrequentlyChangingParameters]->get_config_value(*config, opt_key);
 			tab_print->set_value(opt_key, value);
 			tab_print->update();
 		}
@@ -836,14 +1004,14 @@ void add_frequently_changed_parameters(wxWindow* parent, wxBoxSizer* sizer, wxFl
 			}
 			else{ //(opt_key == "support")
 				const wxString& selection = boost::any_cast<wxString>(value);
-				
+
 				auto support_material = selection == _("None") ? false : true;
 				new_conf.set_key_value("support_material", new ConfigOptionBool(support_material));
 
 				if (selection == _("Everywhere"))
 					new_conf.set_key_value("support_material_buildplate_only", new ConfigOptionBool(false));
 				else if (selection == _("Support on build plate only"))
-					new_conf.set_key_value("support_material_buildplate_only", new ConfigOptionBool(true));				
+					new_conf.set_key_value("support_material_buildplate_only", new ConfigOptionBool(true));
 			}
 			tab_print->load_config(new_conf);
 		}
@@ -851,10 +1019,10 @@ void add_frequently_changed_parameters(wxWindow* parent, wxBoxSizer* sizer, wxFl
 		tab_print->update_dirty();
 	};
 
-	Option option = m_optgroup->get_option("fill_density");
+	Option option = optgroup->get_option("fill_density");
 	option.opt.sidetext = "";
 	option.opt.full_width = true;
-	m_optgroup->append_single_option_line(option);
+	optgroup->append_single_option_line(option);
 
 	ConfigOptionDef def;
 
@@ -873,7 +1041,7 @@ void add_frequently_changed_parameters(wxWindow* parent, wxBoxSizer* sizer, wxFl
 	def.default_value = new ConfigOptionStrings { selection };
 	option = Option(def, "support");
 	option.opt.full_width = true;
-	m_optgroup->append_single_option_line(option);
+	optgroup->append_single_option_line(option);
 
 	m_brim_width = config->opt_float("brim_width");
 	def.label = L("Brim");
@@ -882,7 +1050,7 @@ void add_frequently_changed_parameters(wxWindow* parent, wxBoxSizer* sizer, wxFl
 	def.gui_type = "";
 	def.default_value = new ConfigOptionBool{ m_brim_width > 0.0 ? true : false };
 	option = Option(def, "brim");
-	m_optgroup->append_single_option_line(option);
+	optgroup->append_single_option_line(option);
 
 
     Line line = { "", "" };
@@ -908,16 +1076,95 @@ void add_frequently_changed_parameters(wxWindow* parent, wxBoxSizer* sizer, wxFl
 			}));
 			return sizer;
 		};
-		m_optgroup->append_line(line);
+		optgroup->append_line(line);
 
+	sizer->Add(optgroup->sizer, 0, wxEXPAND | wxBOTTOM, 2);
 
+	m_optgroups.push_back(optgroup);// ogFrequentlyChangingParameters
 
-	sizer->Add(m_optgroup->sizer, 1, wxEXPAND | wxBOTTOM, 2);
+	// Object List
+	add_objects_list(parent, sizer);
+
+	// Frequently Object Settings
+	add_object_settings(parent, sizer);
 }
 
-ConfigOptionsGroup* get_optgroup()
+void show_frequently_changed_parameters(bool show)
 {
-	return m_optgroup.get();
+	g_frequently_changed_parameters_sizer->Show(show);
+	if (!show) return;
+
+	for (size_t i = 0; i < g_wxTabPanel->GetPageCount(); ++i) {
+		Tab *tab = dynamic_cast<Tab*>(g_wxTabPanel->GetPage(i));
+		if (!tab)
+			continue;
+		tab->update_wiping_button_visibility();
+		break;
+	}
+}
+
+void show_buttons(bool show)
+{
+	g_btn_export_stl->Show(show);
+	g_btn_reslice->Show(show);
+	for (size_t i = 0; i < g_wxTabPanel->GetPageCount(); ++i) {
+		TabPrinter *tab = dynamic_cast<TabPrinter*>(g_wxTabPanel->GetPage(i));
+		if (!tab)
+			continue;
+        if (g_PresetBundle->printers.get_selected_preset().printer_technology() == ptFFF) {
+            g_btn_print->Show(show && !tab->m_config->opt_string("serial_port").empty());
+            g_btn_send_gcode->Show(show && !tab->m_config->opt_string("print_host").empty());
+        }
+		break;
+	}
+}
+
+void show_info_sizer(bool show)
+{
+	g_scrolled_window_sizer->Show(static_cast<size_t>(0), show); 
+	g_scrolled_window_sizer->Show(1, show && g_show_print_info);
+	g_manifold_warning_icon->Show(show && g_show_manifold_warning_icon);
+}
+
+void update_mode()
+{
+	wxWindowUpdateLocker noUpdates(g_right_panel);
+
+	// TODO There is a not the best place of it!
+	//*** Update style of the "Export G-code" button****
+	if (g_btn_export_gcode->GetFont() != bold_font()){
+		g_btn_export_gcode->SetBackgroundColour(wxColour(252, 77, 1));
+		g_btn_export_gcode->SetFont(bold_font());
+	}
+	// ***********************************
+
+	ConfigMenuIDs mode = get_view_mode();
+
+// 	show_frequently_changed_parameters(mode >= ConfigMenuModeRegular);
+// 	g_expert_mode_part_sizer->Show(mode == ConfigMenuModeExpert);
+	g_object_list_sizer->Show(mode == ConfigMenuModeExpert);
+	show_info_sizer(mode == ConfigMenuModeExpert);
+	show_buttons(mode == ConfigMenuModeExpert);
+
+	// TODO There is a not the best place of it!
+	// *** Update showing of the collpane_settings
+// 	show_collpane_settings(mode == ConfigMenuModeExpert);
+	// *************************
+	g_right_panel->GetParent()->Layout();
+	g_right_panel->Layout();
+}
+
+bool is_expert_mode(){
+	return get_view_mode() == ConfigMenuModeExpert;
+}
+
+ConfigOptionsGroup* get_optgroup(size_t i)
+{
+	return m_optgroups[i].get();
+}
+
+std::vector <std::shared_ptr<ConfigOptionsGroup>>& get_optgroups() {
+	return m_optgroups;
 }
 
 wxButton* get_wiping_dialog_button()
diff --git a/xs/src/slic3r/GUI/GUI.hpp b/xs/src/slic3r/GUI/GUI.hpp
index 165288819b..69e83eaabb 100644
--- a/xs/src/slic3r/GUI/GUI.hpp
+++ b/xs/src/slic3r/GUI/GUI.hpp
@@ -3,8 +3,9 @@
 
 #include <string>
 #include <vector>
-#include "Config.hpp"
+#include "PrintConfig.hpp"
 #include "../../libslic3r/Utils.hpp"
+#include "GUI_ObjectParts.hpp"
 
 #include <wx/intl.h>
 #include <wx/string.h>
@@ -12,7 +13,6 @@
 class wxApp;
 class wxWindow;
 class wxFrame;
-class wxFont;
 class wxMenuBar;
 class wxNotebook;
 class wxComboCtrl;
@@ -24,6 +24,8 @@ class wxBoxSizer;
 class wxFlexGridSizer;
 class wxButton;
 class wxFileDialog;
+class wxStaticBitmap;
+class wxFont;
 
 namespace Slic3r { 
 
@@ -67,19 +69,26 @@ typedef std::map<std::string, std::string> t_file_wild_card;
 inline t_file_wild_card& get_file_wild_card() {
 	static t_file_wild_card FILE_WILDCARDS;
 	if (FILE_WILDCARDS.empty()){
-		FILE_WILDCARDS["known"] = "Known files (*.stl, *.obj, *.amf, *.xml, *.prusa)|*.stl;*.STL;*.obj;*.OBJ;*.amf;*.AMF;*.xml;*.XML;*.prusa;*.PRUSA";
-		FILE_WILDCARDS["stl"] = "STL files (*.stl)|*.stl;*.STL";
-		FILE_WILDCARDS["obj"] = "OBJ files (*.obj)|*.obj;*.OBJ";
-        FILE_WILDCARDS["amf"] = "AMF files (*.amf)|*.zip.amf;*.amf;*.AMF;*.xml;*.XML";
-        FILE_WILDCARDS["3mf"] = "3MF files (*.3mf)|*.3mf;*.3MF;";
-        FILE_WILDCARDS["prusa"] = "Prusa Control files (*.prusa)|*.prusa;*.PRUSA";
-		FILE_WILDCARDS["ini"] = "INI files *.ini|*.ini;*.INI";
+		FILE_WILDCARDS["known"]	= "Known files (*.stl, *.obj, *.amf, *.xml, *.prusa)|*.stl;*.STL;*.obj;*.OBJ;*.amf;*.AMF;*.xml;*.XML;*.prusa;*.PRUSA";
+		FILE_WILDCARDS["stl"]	= "STL files (*.stl)|*.stl;*.STL";
+		FILE_WILDCARDS["obj"]	= "OBJ files (*.obj)|*.obj;*.OBJ";
+        FILE_WILDCARDS["amf"]	= "AMF files (*.amf)|*.zip.amf;*.amf;*.AMF;*.xml;*.XML";
+        FILE_WILDCARDS["3mf"]	= "3MF files (*.3mf)|*.3mf;*.3MF;";
+        FILE_WILDCARDS["prusa"]	= "Prusa Control files (*.prusa)|*.prusa;*.PRUSA";
+		FILE_WILDCARDS["ini"]	= "INI files *.ini|*.ini;*.INI";
 		FILE_WILDCARDS["gcode"] = "G-code files (*.gcode, *.gco, *.g, *.ngc)|*.gcode;*.GCODE;*.gco;*.GCO;*.g;*.G;*.ngc;*.NGC";
-		FILE_WILDCARDS["svg"] = "SVG files *.svg|*.svg;*.SVG";
+		FILE_WILDCARDS["svg"]	= "SVG files *.svg|*.svg;*.SVG";
 	}
 	return FILE_WILDCARDS;
 }
 
+struct PresetTab {
+    std::string       name;
+    Tab*              panel;
+    PrinterTechnology technology;
+};
+
+
 void disable_screensaver();
 void enable_screensaver();
 bool debugged();
@@ -93,10 +102,26 @@ void set_app_config(AppConfig *app_config);
 void set_preset_bundle(PresetBundle *preset_bundle);
 void set_preset_updater(PresetUpdater *updater);
 void set_3DScene(_3DScene *scene);
+void set_objects_from_perl(	wxWindow* parent,
+							wxBoxSizer *frequently_changed_parameters_sizer,
+							wxBoxSizer *expert_mode_part_sizer,
+							wxBoxSizer *scrolled_window_sizer,
+							wxButton *btn_export_gcode,
+							wxButton *btn_export_stl,
+							wxButton *btn_reslice,
+							wxButton *btn_print,
+							wxButton *btn_send_gcode,
+							wxStaticBitmap *manifold_warning_icon);
+void set_show_print_info(bool show);
+void set_show_manifold_warning_icon(bool show);
+void set_objects_list_sizer(wxBoxSizer *objects_list_sizer);
 
-AppConfig*	get_app_config();
-wxApp*		get_app();
-PresetBundle* get_preset_bundle();
+AppConfig*		get_app_config();
+wxApp*			get_app();
+PresetBundle*	get_preset_bundle();
+wxFrame*		get_main_frame();
+wxNotebook *	get_tab_panel();
+wxNotebook*		get_tab_panel();
 
 const wxColour& get_label_clr_modified();
 const wxColour& get_label_clr_sys();
@@ -108,6 +133,14 @@ void set_label_clr_sys(const wxColour& clr);
 const wxFont& small_font();
 const wxFont& bold_font();
 
+void open_model(wxWindow *parent, wxArrayString& input_files);
+
+wxWindow*			get_right_panel();
+const size_t&		label_width();
+
+Tab*         get_tab(const std::string& name);
+const std::vector<PresetTab>& get_preset_tabs();
+
 extern void add_menus(wxMenuBar *menu, int event_preferences_changed, int event_language_change);
 
 // This is called when closing the application, when loading a config file or when starting the config wizard
@@ -130,7 +163,7 @@ void create_preset_tabs(bool no_controller, int event_value_change, int event_pr
 TabIface* get_preset_tab_iface(char *name);
 
 // add it at the end of the tab panel.
-void add_created_tab(Tab* panel);
+void add_created_tab(Tab* panel, int event_value_change, int event_presets_changed);
 // Change option value in config
 void change_opt_value(DynamicPrintConfig& config, const t_config_option_key& opt_key, const boost::any& value, int opt_index = 0);
 
@@ -150,6 +183,8 @@ void save_language();
 void get_installed_languages(wxArrayString & names, wxArrayLong & identifiers);
 // select language from the list of installed languages
 bool select_language(wxArrayString & names, wxArrayLong & identifiers);
+// update right panel of the Plater according to view mode
+void update_mode();
 
 std::vector<Tab *>& get_tabs_list();
 bool checked_tab(Tab* tab);
@@ -169,13 +204,22 @@ wxString	L_str(const std::string &str);
 // Return wxString from std::string in UTF8
 wxString	from_u8(const std::string &str);
 
-
+void add_expert_mode_part(	wxWindow* parent, wxBoxSizer* sizer, 
+							Model &model,
+							int event_object_selection_changed,
+							int event_object_settings_changed,
+							int event_remove_object, 
+							int event_update_scene);
 void add_frequently_changed_parameters(wxWindow* parent, wxBoxSizer* sizer, wxFlexGridSizer* preset_sizer);
+// Update view mode according to selected menu 
+void update_mode();
+bool is_expert_mode();
 
 // Callback to trigger a configuration update timer on the Plater.
 static PerlCallback g_on_request_update_callback;
  
-ConfigOptionsGroup* get_optgroup();
+ConfigOptionsGroup* get_optgroup(size_t i); 
+std::vector <std::shared_ptr<ConfigOptionsGroup>>& get_optgroups();
 wxButton*			get_wiping_dialog_button();
 
 void add_export_option(wxFileDialog* dlg, const std::string& format);
diff --git a/xs/src/slic3r/GUI/GUI_ObjectParts.cpp b/xs/src/slic3r/GUI/GUI_ObjectParts.cpp
new file mode 100644
index 0000000000..50b1a1f5a3
--- /dev/null
+++ b/xs/src/slic3r/GUI/GUI_ObjectParts.cpp
@@ -0,0 +1,1644 @@
+#include "GUI.hpp"
+#include "OptionsGroup.hpp"
+#include "PresetBundle.hpp"
+#include "GUI_ObjectParts.hpp"
+#include "Model.hpp"
+#include "wxExtensions.hpp"
+#include "LambdaObjectDialog.hpp"
+#include "../../libslic3r/Utils.hpp"
+
+#include <wx/msgdlg.h>
+#include <boost/filesystem.hpp>
+#include <boost/algorithm/string.hpp>
+#include "Geometry.hpp"
+#include "slic3r/Utils/FixModelByWin10.hpp"
+
+namespace Slic3r
+{
+namespace GUI
+{
+wxSizer		*m_sizer_object_buttons = nullptr;
+wxSizer		*m_sizer_part_buttons = nullptr;
+wxSizer		*m_sizer_object_movers = nullptr;
+wxDataViewCtrl				*m_objects_ctrl = nullptr;
+PrusaObjectDataViewModel	*m_objects_model = nullptr;
+wxCollapsiblePane			*m_collpane_settings = nullptr;
+
+wxIcon		m_icon_modifiermesh;
+wxIcon		m_icon_solidmesh;
+wxIcon		m_icon_manifold_warning;
+wxBitmap	m_bmp_cog;
+wxBitmap	m_bmp_split;
+
+wxSlider*	m_mover_x = nullptr;
+wxSlider*	m_mover_y = nullptr;
+wxSlider*	m_mover_z = nullptr;
+wxButton*	m_btn_move_up = nullptr;
+wxButton*	m_btn_move_down = nullptr;
+Vec3d		m_move_options;
+Vec3d		m_last_coords;
+int			m_selected_object_id = -1;
+
+bool		g_prevent_list_events = false;		// We use this flag to avoid circular event handling Select() 
+												// happens to fire a wxEVT_LIST_ITEM_SELECTED on OSX, whose event handler 
+												// calls this method again and again and again
+bool        g_is_percent_scale = false;         // It indicates if scale unit is percentage
+int         g_rotation_x = 0;                   // Last value of the rotation around the X axis
+int         g_rotation_y = 0;                   // Last value of the rotation around the Y axis
+ModelObjectPtrs*			m_objects;
+std::shared_ptr<DynamicPrintConfig*> m_config;
+std::shared_ptr<DynamicPrintConfig> m_default_config;
+wxBoxSizer*					m_option_sizer = nullptr;
+
+// option groups for settings
+std::vector <std::shared_ptr<ConfigOptionsGroup>> m_og_settings;
+
+int			m_event_object_selection_changed = 0;
+int			m_event_object_settings_changed = 0;
+int			m_event_remove_object = 0;
+int			m_event_update_scene = 0;
+
+bool m_parts_changed = false;
+bool m_part_settings_changed = false;
+
+#ifdef __WXOSX__
+    wxString g_selected_extruder = "";
+#endif //__WXOSX__
+
+// typedef std::map<std::string, std::string> t_category_icon;
+typedef std::map<std::string, wxBitmap> t_category_icon;
+inline t_category_icon& get_category_icon() {
+	static t_category_icon CATEGORY_ICON;
+	if (CATEGORY_ICON.empty()){
+		CATEGORY_ICON[L("Layers and Perimeters")]	= wxBitmap(from_u8(Slic3r::var("layers.png")), wxBITMAP_TYPE_PNG);
+		CATEGORY_ICON[L("Infill")]					= wxBitmap(from_u8(Slic3r::var("infill.png")), wxBITMAP_TYPE_PNG);
+		CATEGORY_ICON[L("Support material")]		= wxBitmap(from_u8(Slic3r::var("building.png")), wxBITMAP_TYPE_PNG);
+		CATEGORY_ICON[L("Speed")]					= wxBitmap(from_u8(Slic3r::var("time.png")), wxBITMAP_TYPE_PNG);
+		CATEGORY_ICON[L("Extruders")]				= wxBitmap(from_u8(Slic3r::var("funnel.png")), wxBITMAP_TYPE_PNG);
+		CATEGORY_ICON[L("Extrusion Width")]			= wxBitmap(from_u8(Slic3r::var("funnel.png")), wxBITMAP_TYPE_PNG);
+// 		CATEGORY_ICON[L("Skirt and brim")]			= wxBitmap(from_u8(Slic3r::var("box.png")), wxBITMAP_TYPE_PNG);
+// 		CATEGORY_ICON[L("Speed > Acceleration")]	= wxBitmap(from_u8(Slic3r::var("time.png")), wxBITMAP_TYPE_PNG);
+		CATEGORY_ICON[L("Advanced")]				= wxBitmap(from_u8(Slic3r::var("wand.png")), wxBITMAP_TYPE_PNG);
+	}
+	return CATEGORY_ICON;
+}
+
+std::vector<std::string> get_options(const bool is_part)
+{
+	PrintRegionConfig reg_config;
+	auto options = reg_config.keys();
+	if (!is_part) {
+		PrintObjectConfig obj_config;
+		std::vector<std::string> obj_options = obj_config.keys();
+		options.insert(options.end(), obj_options.begin(), obj_options.end());
+	}
+	return options;
+}
+
+//				  category ->		vector 			 ( option	;  label )
+typedef std::map< std::string, std::vector< std::pair<std::string, std::string> > > settings_menu_hierarchy;
+void get_options_menu(settings_menu_hierarchy& settings_menu, bool is_part)
+{
+	auto options = get_options(is_part);
+
+    auto extruders_cnt = get_preset_bundle()->printers.get_selected_preset().printer_technology() == ptSLA ? 1 :
+                         get_preset_bundle()->printers.get_edited_preset().config.option<ConfigOptionFloats>("nozzle_diameter")->values.size();
+
+	DynamicPrintConfig config;
+	for (auto& option : options)
+	{
+		auto const opt = config.def()->get(option);
+		auto category = opt->category;
+        if (category.empty() ||
+            (category == "Extruders" && extruders_cnt == 1)) continue;
+
+		std::pair<std::string, std::string> option_label(option, opt->label);
+		std::vector< std::pair<std::string, std::string> > new_category;
+		auto& cat_opt_label = settings_menu.find(category) == settings_menu.end() ? new_category : settings_menu.at(category);
+		cat_opt_label.push_back(option_label);
+		if (cat_opt_label.size() == 1)
+			settings_menu[category] = cat_opt_label;
+	}
+}
+
+void set_event_object_selection_changed(const int& event){
+	m_event_object_selection_changed = event;
+}
+void set_event_object_settings_changed(const int& event){
+	m_event_object_settings_changed = event;
+}
+void set_event_remove_object(const int& event){
+	m_event_remove_object = event;
+}
+void set_event_update_scene(const int& event){
+	m_event_update_scene = event;
+}
+
+void set_objects_from_model(Model &model) {
+	m_objects = &(model.objects);
+}
+
+void init_mesh_icons(){
+	m_icon_modifiermesh = wxIcon(Slic3r::GUI::from_u8(Slic3r::var("lambda.png")), wxBITMAP_TYPE_PNG);//(Slic3r::var("plugin.png")), wxBITMAP_TYPE_PNG);
+	m_icon_solidmesh = wxIcon(Slic3r::GUI::from_u8(Slic3r::var("object.png")), wxBITMAP_TYPE_PNG);//(Slic3r::var("package.png")), wxBITMAP_TYPE_PNG);
+
+	// init icon for manifold warning
+	m_icon_manifold_warning = wxIcon(Slic3r::GUI::from_u8(Slic3r::var("exclamation_mark_.png")), wxBITMAP_TYPE_PNG);//(Slic3r::var("error.png")), wxBITMAP_TYPE_PNG);
+
+	// init bitmap for "Split to sub-objects" context menu
+    m_bmp_split = wxBitmap(Slic3r::GUI::from_u8(Slic3r::var("split.png")), wxBITMAP_TYPE_PNG);
+
+	// init bitmap for "Add Settings" context menu
+	m_bmp_cog = wxBitmap(Slic3r::GUI::from_u8(Slic3r::var("cog.png")), wxBITMAP_TYPE_PNG);
+}
+
+bool is_parts_changed(){return m_parts_changed;}
+bool is_part_settings_changed(){ return m_part_settings_changed; }
+
+static wxString dots("…", wxConvUTF8);
+
+void set_tooltip_for_item(const wxPoint& pt)
+{
+    wxDataViewItem item;
+    wxDataViewColumn* col;
+    m_objects_ctrl->HitTest(pt, item, col);
+    if (!item) return;
+
+    if (col->GetTitle() == " ")
+        m_objects_ctrl->GetMainWindow()->SetToolTip(_(L("Right button click the icon to change the object settings")));
+    else if (col->GetTitle() == _("Name") &&
+        m_objects_model->GetIcon(item).GetRefData() == m_icon_manifold_warning.GetRefData()) {
+        int obj_idx = m_objects_model->GetIdByItem(item);
+        auto& stats = (*m_objects)[obj_idx]->volumes[0]->mesh.stl.stats;
+        int errors = stats.degenerate_facets + stats.edges_fixed + stats.facets_removed +
+            stats.facets_added + stats.facets_reversed + stats.backwards_edges;
+
+        wxString tooltip = wxString::Format(_(L("Auto-repaired (%d errors):\n")), errors);
+
+        std::map<std::string, int> error_msg;
+        error_msg[L("degenerate facets")] = stats.degenerate_facets;
+        error_msg[L("edges fixed")] = stats.edges_fixed;
+        error_msg[L("facets removed")] = stats.facets_removed;
+        error_msg[L("facets added")] = stats.facets_added;
+        error_msg[L("facets reversed")] = stats.facets_reversed;
+        error_msg[L("backwards edges")] = stats.backwards_edges;
+
+        for (auto error : error_msg)
+        {
+            if (error.second > 0)
+                tooltip += wxString::Format(_("\t%d %s\n"), error.second, error.first);
+        }
+// OR
+//             tooltip += wxString::Format(_(L("%d degenerate facets, %d edges fixed, %d facets removed, "
+//                                             "%d facets added, %d facets reversed, %d backwards edges")),
+//                                             stats.degenerate_facets, stats.edges_fixed, stats.facets_removed,
+//                                             stats.facets_added, stats.facets_reversed, stats.backwards_edges);
+
+        if (is_windows10())
+            tooltip += _(L("Right button click the icon to fix STL through Netfabb"));
+
+        m_objects_ctrl->GetMainWindow()->SetToolTip(tooltip);
+    }
+    else
+        m_objects_ctrl->GetMainWindow()->SetToolTip(""); // hide tooltip
+}
+
+wxPoint get_mouse_position_in_control() {
+    const wxPoint& pt = wxGetMousePosition();
+    wxWindow* win = m_objects_ctrl->GetMainWindow();
+    return wxPoint(pt.x - win->GetScreenPosition().x, 
+                   pt.y - win->GetScreenPosition().y);
+}
+
+bool is_mouse_position_in_control(wxPoint& pt) {
+    pt = get_mouse_position_in_control();
+    const wxSize& cz = m_objects_ctrl->GetSize();
+    if (pt.x > 0 && pt.x < cz.x &&
+        pt.y > 0 && pt.y < cz.y)
+        return true;
+    return false;
+}
+
+wxDataViewColumn* object_ctrl_create_extruder_column(int extruders_count)
+{
+    wxArrayString choices;
+    choices.Add("default");
+    for (int i = 1; i <= extruders_count; ++i)
+        choices.Add(wxString::Format("%d", i));
+    wxDataViewChoiceRenderer *c =
+        new wxDataViewChoiceRenderer(choices, wxDATAVIEW_CELL_EDITABLE, wxALIGN_CENTER_HORIZONTAL);
+    wxDataViewColumn* column = new wxDataViewColumn(_(L("Extruder")), c, 3, 60, wxALIGN_CENTER_HORIZONTAL, wxDATAVIEW_COL_RESIZABLE);
+    return column;
+}
+
+void create_objects_ctrl(wxWindow* win, wxBoxSizer*& objects_sz)
+{
+	m_objects_ctrl = new wxDataViewCtrl(win, wxID_ANY, wxDefaultPosition, wxDefaultSize);
+	m_objects_ctrl->SetInitialSize(wxSize(-1, 150)); // TODO - Set correct height according to the opened/closed objects
+
+	objects_sz = new wxBoxSizer(wxVERTICAL);
+	objects_sz->Add(m_objects_ctrl, 1, wxGROW | wxLEFT, 20);
+
+	m_objects_model = new PrusaObjectDataViewModel;
+	m_objects_ctrl->AssociateModel(m_objects_model);
+#if wxUSE_DRAG_AND_DROP && wxUSE_UNICODE
+	m_objects_ctrl->EnableDragSource(wxDF_UNICODETEXT);
+	m_objects_ctrl->EnableDropTarget(wxDF_UNICODETEXT);
+#endif // wxUSE_DRAG_AND_DROP && wxUSE_UNICODE
+
+	// column 0(Icon+Text) of the view control:
+	m_objects_ctrl->AppendIconTextColumn(_(L("Name")), 0, wxDATAVIEW_CELL_INERT, 120,
+		wxALIGN_LEFT, wxDATAVIEW_COL_RESIZABLE);
+
+	// column 1 of the view control:
+	m_objects_ctrl->AppendTextColumn(_(L("Copy")), 1, wxDATAVIEW_CELL_INERT, 45,
+		wxALIGN_CENTER_HORIZONTAL, wxDATAVIEW_COL_RESIZABLE);
+
+	// column 2 of the view control:
+	m_objects_ctrl->AppendTextColumn(_(L("Scale")), 2, wxDATAVIEW_CELL_INERT, 55,
+		wxALIGN_CENTER_HORIZONTAL, wxDATAVIEW_COL_RESIZABLE);
+
+	// column 3 of the view control:
+    m_objects_ctrl->AppendColumn(object_ctrl_create_extruder_column(4));
+
+	// column 4 of the view control:
+	m_objects_ctrl->AppendBitmapColumn(" ", 4, wxDATAVIEW_CELL_INERT, 25,
+		wxALIGN_CENTER_HORIZONTAL, wxDATAVIEW_COL_RESIZABLE);
+}
+
+// ****** from GUI.cpp
+wxBoxSizer* create_objects_list(wxWindow *win)
+{
+    wxBoxSizer* objects_sz;
+    // create control
+    create_objects_ctrl(win, objects_sz);
+
+    // describe control behavior 
+    m_objects_ctrl->Bind(wxEVT_DATAVIEW_SELECTION_CHANGED, [](wxEvent& event) {
+		object_ctrl_selection_changed();
+#ifndef __WXMSW__
+        set_tooltip_for_item(get_mouse_position_in_control());
+#endif //__WXMSW__        
+	});
+
+    m_objects_ctrl->Bind(wxEVT_DATAVIEW_ITEM_CONTEXT_MENU, [](wxDataViewEvent& event) {
+        object_ctrl_context_menu();
+		event.Skip();
+	});
+
+    m_objects_ctrl->Bind(wxEVT_CHAR, [](wxKeyEvent& event) { object_ctrl_key_event(event); }); // doesn't work on OSX
+
+#ifdef __WXMSW__
+    // Extruder value changed
+	m_objects_ctrl->Bind(wxEVT_CHOICE, [](wxCommandEvent& event) { update_extruder_in_config(event.GetString()); });
+
+    m_objects_ctrl->GetMainWindow()->Bind(wxEVT_MOTION, [](wxMouseEvent& event) {
+         set_tooltip_for_item(event.GetPosition());
+         event.Skip();
+    });
+#else
+    // equivalent to wxEVT_CHOICE on __WXMSW__
+    m_objects_ctrl->Bind(wxEVT_DATAVIEW_ITEM_VALUE_CHANGED, [](wxDataViewEvent& event) { object_ctrl_item_value_change(event); });
+#endif //__WXMSW__
+
+    m_objects_ctrl->Bind(wxEVT_DATAVIEW_ITEM_BEGIN_DRAG,    [](wxDataViewEvent& e) {on_begin_drag(e);});
+    m_objects_ctrl->Bind(wxEVT_DATAVIEW_ITEM_DROP_POSSIBLE, [](wxDataViewEvent& e) {on_drop_possible(e); });
+    m_objects_ctrl->Bind(wxEVT_DATAVIEW_ITEM_DROP,          [](wxDataViewEvent& e) {on_drop(e);});
+	return objects_sz;
+}
+
+wxBoxSizer* create_edit_object_buttons(wxWindow* win)
+{
+	auto sizer = new wxBoxSizer(wxVERTICAL);
+
+	auto btn_load_part = new wxButton(win, wxID_ANY, /*Load */"part" + dots, wxDefaultPosition, wxDefaultSize, wxBU_EXACTFIT | wxNO_BORDER/*wxBU_LEFT*/);
+	auto btn_load_modifier = new wxButton(win, wxID_ANY, /*Load */"modifier" + dots, wxDefaultPosition, wxDefaultSize, wxBU_EXACTFIT | wxNO_BORDER/*wxBU_LEFT*/);
+	auto btn_load_lambda_modifier = new wxButton(win, wxID_ANY, /*Load */"generic" + dots, wxDefaultPosition, wxDefaultSize, wxBU_EXACTFIT | wxNO_BORDER/*wxBU_LEFT*/);
+	auto btn_delete = new wxButton(win, wxID_ANY, "Delete"/*" part"*/, wxDefaultPosition, wxDefaultSize, wxBU_EXACTFIT | wxNO_BORDER/*wxBU_LEFT*/);
+	auto btn_split = new wxButton(win, wxID_ANY, "Split"/*" part"*/, wxDefaultPosition, wxDefaultSize, wxBU_EXACTFIT | wxNO_BORDER/*wxBU_LEFT*/);
+	m_btn_move_up = new wxButton(win, wxID_ANY, "", wxDefaultPosition, wxDefaultSize/*wxSize(30, -1)*/, wxBU_LEFT);
+	m_btn_move_down = new wxButton(win, wxID_ANY, "", wxDefaultPosition, wxDefaultSize/*wxSize(30, -1)*/, wxBU_LEFT);
+
+	//*** button's functions
+	btn_load_part->Bind(wxEVT_BUTTON, [win](wxEvent&) {
+		on_btn_load(win);
+	});
+
+	btn_load_modifier->Bind(wxEVT_BUTTON, [win](wxEvent&) {
+		on_btn_load(win, true);
+	});
+
+	btn_load_lambda_modifier->Bind(wxEVT_BUTTON, [win](wxEvent&) {
+		on_btn_load(win, true, true);
+	});
+
+	btn_delete		->Bind(wxEVT_BUTTON, [](wxEvent&) { on_btn_del(); });
+	btn_split		->Bind(wxEVT_BUTTON, [](wxEvent&) { on_btn_split(true); });
+	m_btn_move_up	->Bind(wxEVT_BUTTON, [](wxEvent&) { on_btn_move_up(); });
+	m_btn_move_down	->Bind(wxEVT_BUTTON, [](wxEvent&) { on_btn_move_down(); });
+	//***
+
+	m_btn_move_up->SetMinSize(wxSize(20, -1));
+	m_btn_move_down->SetMinSize(wxSize(20, -1));
+	btn_load_part->SetBitmap(wxBitmap(from_u8(Slic3r::var("brick_add.png")), wxBITMAP_TYPE_PNG));
+	btn_load_modifier->SetBitmap(wxBitmap(from_u8(Slic3r::var("brick_add.png")), wxBITMAP_TYPE_PNG));
+	btn_load_lambda_modifier->SetBitmap(wxBitmap(from_u8(Slic3r::var("brick_add.png")), wxBITMAP_TYPE_PNG));
+	btn_delete->SetBitmap(wxBitmap(from_u8(Slic3r::var("brick_delete.png")), wxBITMAP_TYPE_PNG));
+	btn_split->SetBitmap(wxBitmap(from_u8(Slic3r::var("shape_ungroup.png")), wxBITMAP_TYPE_PNG));
+	m_btn_move_up->SetBitmap(wxBitmap(from_u8(Slic3r::var("bullet_arrow_up.png")), wxBITMAP_TYPE_PNG));
+	m_btn_move_down->SetBitmap(wxBitmap(from_u8(Slic3r::var("bullet_arrow_down.png")), wxBITMAP_TYPE_PNG));
+
+	m_sizer_object_buttons = new wxGridSizer(1, 3, 0, 0);
+	m_sizer_object_buttons->Add(btn_load_part, 0, wxEXPAND);
+	m_sizer_object_buttons->Add(btn_load_modifier, 0, wxEXPAND);
+	m_sizer_object_buttons->Add(btn_load_lambda_modifier, 0, wxEXPAND);
+	m_sizer_object_buttons->Show(false);
+
+	m_sizer_part_buttons = new wxGridSizer(1, 3, 0, 0);
+	m_sizer_part_buttons->Add(btn_delete, 0, wxEXPAND);
+	m_sizer_part_buttons->Add(btn_split, 0, wxEXPAND);
+	{
+		auto up_down_sizer = new wxGridSizer(1, 2, 0, 0);
+		up_down_sizer->Add(m_btn_move_up, 1, wxEXPAND);
+		up_down_sizer->Add(m_btn_move_down, 1, wxEXPAND);
+		m_sizer_part_buttons->Add(up_down_sizer, 0, wxEXPAND);
+	}
+	m_sizer_part_buttons->Show(false);
+
+	btn_load_part->SetFont(Slic3r::GUI::small_font());
+	btn_load_modifier->SetFont(Slic3r::GUI::small_font());
+	btn_load_lambda_modifier->SetFont(Slic3r::GUI::small_font());
+	btn_delete->SetFont(Slic3r::GUI::small_font());
+	btn_split->SetFont(Slic3r::GUI::small_font());
+	m_btn_move_up->SetFont(Slic3r::GUI::small_font());
+	m_btn_move_down->SetFont(Slic3r::GUI::small_font());
+
+	sizer->Add(m_sizer_object_buttons, 0, wxEXPAND | wxLEFT, 20);
+	sizer->Add(m_sizer_part_buttons, 0, wxEXPAND | wxLEFT, 20);
+	return sizer;
+}
+
+void update_after_moving()
+{
+	auto item = m_objects_ctrl->GetSelection();
+	if (!item || m_selected_object_id<0)
+		return;
+
+	auto volume_id = m_objects_model->GetVolumeIdByItem(item);
+	if (volume_id < 0)
+		return;
+
+	Vec3d m = m_move_options;
+	Vec3d l = m_last_coords;
+
+    auto d = Vec3d(m(0) - l(0), m(1) - l(1), m(2) - l(2));
+	auto volume = (*m_objects)[m_selected_object_id]->volumes[volume_id];
+    volume->mesh.translate(d(0), d(1), d(2));
+	m_last_coords = m;
+
+	m_parts_changed = true;
+	parts_changed(m_selected_object_id);
+}
+
+wxSizer* object_movers(wxWindow *win)
+{
+// 	DynamicPrintConfig* config = &get_preset_bundle()->/*full_config();//*/printers.get_edited_preset().config; // TODO get config from Model_volume
+	std::shared_ptr<ConfigOptionsGroup> optgroup = std::make_shared<ConfigOptionsGroup>(win, "Move"/*, config*/);
+	optgroup->label_width = 20;
+	optgroup->m_on_change = [](t_config_option_key opt_key, boost::any value){
+		int val = boost::any_cast<int>(value);
+		bool update = false;
+        if (opt_key == "x" && m_move_options(0) != val){
+			update = true;
+            m_move_options(0) = val;
+		}
+        else if (opt_key == "y" && m_move_options(1) != val){
+			update = true;
+            m_move_options(1) = val;
+		}
+        else if (opt_key == "z" && m_move_options(2) != val){
+			update = true;
+            m_move_options(2) = val;
+		}
+		if (update) update_after_moving();
+	};
+
+	ConfigOptionDef def;
+	def.label = L("X");
+	def.type = coInt;
+	def.gui_type = "slider";
+	def.default_value = new ConfigOptionInt(0);
+
+	Option option = Option(def, "x");
+	option.opt.full_width = true;
+	optgroup->append_single_option_line(option);
+	m_mover_x = dynamic_cast<wxSlider*>(optgroup->get_field("x")->getWindow());
+
+	def.label = L("Y");
+	option = Option(def, "y");
+	optgroup->append_single_option_line(option);
+	m_mover_y = dynamic_cast<wxSlider*>(optgroup->get_field("y")->getWindow());
+
+	def.label = L("Z");
+	option = Option(def, "z");
+	optgroup->append_single_option_line(option);
+	m_mover_z = dynamic_cast<wxSlider*>(optgroup->get_field("z")->getWindow());
+
+	get_optgroups().push_back(optgroup);  // ogObjectMovers
+
+	m_sizer_object_movers = optgroup->sizer;
+	m_sizer_object_movers->Show(false);
+
+	m_move_options = Vec3d(0, 0, 0);
+	m_last_coords = Vec3d(0, 0, 0);
+
+	return optgroup->sizer;
+}
+
+wxBoxSizer* content_settings(wxWindow *win)
+{
+	DynamicPrintConfig* config = &get_preset_bundle()->/*full_config();//*/printers.get_edited_preset().config; // TODO get config from Model_volume
+	std::shared_ptr<ConfigOptionsGroup> optgroup = std::make_shared<ConfigOptionsGroup>(win, "Extruders", config);
+	optgroup->label_width = label_width();
+
+	Option option = optgroup->get_option("extruder");
+	option.opt.default_value = new ConfigOptionInt(1);
+	optgroup->append_single_option_line(option);
+
+	get_optgroups().push_back(optgroup);  // ogObjectSettings
+
+	auto sizer = new wxBoxSizer(wxVERTICAL);
+	sizer->Add(create_edit_object_buttons(win), 0, wxEXPAND, 0); // *** Edit Object Buttons***
+
+	sizer->Add(optgroup->sizer, 1, wxEXPAND | wxLEFT, 20);
+
+	auto add_btn = new wxButton(win, wxID_ANY, "", wxDefaultPosition, wxDefaultSize, wxBU_EXACTFIT | wxNO_BORDER);
+	if (wxMSW) add_btn->SetBackgroundColour(wxSystemSettings::GetColour(wxSYS_COLOUR_WINDOW));
+	add_btn->SetBitmap(wxBitmap(from_u8(Slic3r::var("add.png")), wxBITMAP_TYPE_PNG));
+	sizer->Add(add_btn, 0, wxALIGN_LEFT | wxLEFT, 20);
+
+	sizer->Add(object_movers(win), 0, wxEXPAND | wxLEFT, 20);
+
+	return sizer;
+}
+
+void add_objects_list(wxWindow* parent, wxBoxSizer* sizer)
+{
+	const auto ol_sizer = create_objects_list(parent);
+	sizer->Add(ol_sizer, 1, wxEXPAND | wxTOP, 20);
+	set_objects_list_sizer(ol_sizer);
+}
+
+Line add_og_to_object_settings(const std::string& option_name, const std::string& sidetext, int def_value = 0)
+{
+	Line line = { _(option_name), "" };
+
+	ConfigOptionDef def;
+	def.type = coInt;
+	def.default_value = new ConfigOptionInt(def_value);
+	def.sidetext = sidetext;
+	def.width = 70;
+
+    if (option_name == "Rotation")
+        def.min = -360;
+
+	const std::string lower_name = boost::algorithm::to_lower_copy(option_name);
+
+	std::vector<std::string> axes{ "x", "y", "z" };
+	for (auto axis : axes) {
+		def.label = boost::algorithm::to_upper_copy(axis);
+		Option option = Option(def, lower_name + "_" + axis);
+		option.opt.full_width = true;
+		line.append_option(option);
+	}
+
+	if (option_name == "Scale")
+	{
+		def.label = L("Units");
+		def.type = coStrings;
+		def.gui_type = "select_open";
+		def.enum_labels.push_back(L("%"));
+		def.enum_labels.push_back(L("mm"));
+		def.default_value = new ConfigOptionStrings{ "%" };
+		def.sidetext = " ";
+
+		Option option = Option(def, lower_name + "_unit");
+		line.append_option(option);
+	}
+
+	return line;
+}
+
+void add_object_settings(wxWindow* parent, wxBoxSizer* sizer)
+{
+	auto optgroup = std::make_shared<ConfigOptionsGroup>(parent, _(L("Object Settings")));
+	optgroup->label_width = 100;
+	optgroup->set_grid_vgap(5);
+
+	optgroup->m_on_change = [](t_config_option_key opt_key, boost::any value){
+		if (opt_key == "scale_unit"){
+			const wxString& selection = boost::any_cast<wxString>(value);
+			std::vector<std::string> axes{ "x", "y", "z" };
+			for (auto axis : axes) {
+				std::string key = "scale_" + axis;
+				get_optgroup(ogFrequentlyObjectSettings)->set_side_text(key, selection);
+			}
+
+            g_is_percent_scale = selection == _("%");
+            update_scale_values();
+		}
+	};
+
+// 	def.label = L("Name");
+// 	def.type = coString;
+// 	def.tooltip = L("Object name");
+// 	def.full_width = true;
+// 	def.default_value = new ConfigOptionString{ "BlaBla_object.stl" };
+// 	optgroup->append_single_option_line(Option(def, "object_name"));
+
+	ConfigOptionDef def;
+
+	def.label = L("Name");
+// 	def.type = coString;
+    def.gui_type = "legend";
+	def.tooltip = L("Object name");
+	def.full_width = true;
+	def.default_value = new ConfigOptionString{ " " };
+	optgroup->append_single_option_line(Option(def, "object_name"));
+
+	optgroup->set_flag(ogSIDE_OPTIONS_VERTICAL);
+	optgroup->sidetext_width = 25;
+
+	optgroup->append_line(add_og_to_object_settings(L("Position"), L("mm")));
+	optgroup->append_line(add_og_to_object_settings(L("Rotation"), "°"));
+	optgroup->append_line(add_og_to_object_settings(L("Scale"), "%"));
+
+	optgroup->set_flag(ogDEFAULT);
+
+	def.label = L("Place on bed");
+	def.type = coBool;
+	def.tooltip = L("Automatic placing of models on printing bed in Y axis");
+	def.gui_type = "";
+	def.sidetext = "";
+	def.default_value = new ConfigOptionBool{ false };
+	optgroup->append_single_option_line(Option(def, "place_on_bed"));
+
+	m_option_sizer = new wxBoxSizer(wxVERTICAL);
+	optgroup->sizer->Add(m_option_sizer, 1, wxEXPAND | wxLEFT, 5);
+
+	sizer->Add(optgroup->sizer, 0, wxEXPAND | wxLEFT | wxTOP, 20);
+
+	optgroup->disable();
+
+	get_optgroups().push_back(optgroup);  // ogFrequentlyObjectSettings
+
+// 	add_current_settings();
+}
+
+
+// add Collapsible Pane to sizer
+wxCollapsiblePane* add_collapsible_pane(wxWindow* parent, wxBoxSizer* sizer_parent, const wxString& name, std::function<wxSizer *(wxWindow *)> content_function)
+{
+#ifdef __WXMSW__
+	auto *collpane = new PrusaCollapsiblePaneMSW(parent, wxID_ANY, name);
+#else
+	auto *collpane = new PrusaCollapsiblePane/*wxCollapsiblePane*/(parent, wxID_ANY, name);
+#endif // __WXMSW__
+	// add the pane with a zero proportion value to the sizer which contains it
+	sizer_parent->Add(collpane, 0, wxGROW | wxALL, 0);
+
+	wxWindow *win = collpane->GetPane();
+
+	wxSizer *sizer = content_function(win);
+
+	wxSizer *sizer_pane = new wxBoxSizer(wxVERTICAL);
+	sizer_pane->Add(sizer, 1, wxGROW | wxEXPAND | wxBOTTOM, 2);
+	win->SetSizer(sizer_pane);
+	// 	sizer_pane->SetSizeHints(win);
+	return collpane;
+}
+
+void add_collapsible_panes(wxWindow* parent, wxBoxSizer* sizer)
+{
+	// *** Objects List ***	
+	auto collpane = add_collapsible_pane(parent, sizer, "Objects List:", create_objects_list);
+	collpane->Bind(wxEVT_COLLAPSIBLEPANE_CHANGED, ([collpane](wxCommandEvent& e){
+		// 		wxWindowUpdateLocker noUpdates(g_right_panel);
+		if (collpane->IsCollapsed()) {
+			m_sizer_object_buttons->Show(false);
+			m_sizer_part_buttons->Show(false);
+			m_sizer_object_movers->Show(false);
+			if (!m_objects_ctrl->HasSelection())
+				m_collpane_settings->Show(false);
+		}
+	}));
+
+	// *** Object/Part Settings ***
+	m_collpane_settings = add_collapsible_pane(parent, sizer, "Object Settings", content_settings);
+}
+
+void show_collpane_settings(bool expert_mode)
+{
+	m_collpane_settings->Show(expert_mode && !m_objects_model->IsEmpty());
+}
+
+void add_object_to_list(const std::string &name, ModelObject* model_object)
+{
+	wxString item_name = name;
+	int scale = model_object->instances[0]->scaling_factor * 100;
+	auto item = m_objects_model->Add(item_name, model_object->instances.size(), scale);
+	m_objects_ctrl->Select(item);
+
+	// Add error icon if detected auto-repaire
+	auto stats = model_object->volumes[0]->mesh.stl.stats;
+	int errors =	stats.degenerate_facets + stats.edges_fixed + stats.facets_removed + 
+					stats.facets_added + stats.facets_reversed + stats.backwards_edges;
+	if (errors > 0)		{
+		const wxDataViewIconText data(item_name, m_icon_manifold_warning);
+		wxVariant variant;
+		variant << data;
+		m_objects_model->SetValue(variant, item, 0);
+	}
+
+    if (model_object->volumes.size() > 1) {
+        for (auto id = 0; id < model_object->volumes.size(); id++)
+            m_objects_model->AddChild(item, 
+                                      model_object->volumes[id]->name, 
+                                      m_icon_solidmesh, 
+                                      model_object->volumes[id]->config.option<ConfigOptionInt>("extruder")->value,
+                                      false);
+        m_objects_ctrl->Expand(item);
+    }
+
+#ifndef __WXOSX__ 
+	object_ctrl_selection_changed();
+#endif //__WXMSW__
+}
+
+void delete_object_from_list()
+{
+	auto item = m_objects_ctrl->GetSelection();
+	if (!item || m_objects_model->GetParent(item) != wxDataViewItem(0))
+		return;
+// 	m_objects_ctrl->Select(m_objects_model->Delete(item));
+	m_objects_model->Delete(item);
+
+// 	if (m_objects_model->IsEmpty())
+// 		m_collpane_settings->Show(false);
+}
+
+void delete_all_objects_from_list()
+{
+	m_objects_model->DeleteAll();
+// 	m_collpane_settings->Show(false);
+}
+
+void set_object_count(int idx, int count)
+{
+	m_objects_model->SetValue(wxString::Format("%d", count), idx, 1);
+	m_objects_ctrl->Refresh();
+}
+
+void set_object_scale(int idx, int scale)
+{
+	m_objects_model->SetValue(wxString::Format("%d%%", scale), idx, 2);
+	m_objects_ctrl->Refresh();
+}
+
+void unselect_objects()
+{
+    if (!m_objects_ctrl->GetSelection())
+        return;
+
+    g_prevent_list_events = true;
+    m_objects_ctrl->UnselectAll();
+    part_selection_changed();
+    g_prevent_list_events = false;
+}
+
+void select_current_object(int idx)
+{
+	g_prevent_list_events = true;
+	m_objects_ctrl->UnselectAll();
+	if (idx < 0) {
+		g_prevent_list_events = false;
+		return;
+	}
+	m_objects_ctrl->Select(m_objects_model->GetItemById(idx));
+	part_selection_changed();
+	g_prevent_list_events = false;
+}
+
+void remove()
+{
+	auto item = m_objects_ctrl->GetSelection();
+	if (!item)
+		return;
+	
+	if (m_objects_model->GetParent(item) == wxDataViewItem(0)) {
+		if (m_event_remove_object > 0) {
+			wxCommandEvent event(m_event_remove_object);
+			get_main_frame()->ProcessWindowEvent(event);
+		}
+// 		delete_object_from_list();
+	}
+	else
+		on_btn_del();
+}
+
+void object_ctrl_selection_changed()
+{
+	if (g_prevent_list_events) return;
+
+	part_selection_changed();
+
+	if (m_event_object_selection_changed > 0) {
+		wxCommandEvent event(m_event_object_selection_changed);
+		event.SetInt(int(m_objects_model->GetParent(m_objects_ctrl->GetSelection()) != wxDataViewItem(0)));
+		event.SetId(m_selected_object_id);
+		get_main_frame()->ProcessWindowEvent(event);
+	}
+
+#ifdef __WXOSX__
+    update_extruder_in_config(g_selected_extruder);
+#endif //__WXOSX__        
+}
+
+void object_ctrl_context_menu()
+{
+    wxDataViewItem item;
+    wxDataViewColumn* col;
+    m_objects_ctrl->HitTest(get_mouse_position_in_control(), item, col);
+    wxString title = col->GetTitle();
+    if (!item) return;
+
+    if (title == " ")
+        show_context_menu();
+// ys_FIXME
+//         else if (title == _("Name") && pt.x >15 &&
+//                     m_objects_model->GetIcon(item).GetRefData() == m_icon_manifold_warning.GetRefData())
+//         {
+//             if (is_windows10())
+//                 fix_through_netfabb();
+//         }
+#ifndef __WXMSW__
+    m_objects_ctrl->GetMainWindow()->SetToolTip(""); // hide tooltip
+#endif //__WXMSW__
+}
+
+void object_ctrl_key_event(wxKeyEvent& event)
+{
+    if (event.GetKeyCode() == WXK_TAB)
+        m_objects_ctrl->Navigate(event.ShiftDown() ? wxNavigationKeyEvent::IsBackward : wxNavigationKeyEvent::IsForward);
+    else if (event.GetKeyCode() == WXK_DELETE
+#ifdef __WXOSX__
+        || event.GetKeyCode() == WXK_BACK
+#endif //__WXOSX__
+        ){
+        printf("WXK_BACK\n");
+        remove();
+    }
+    else
+        event.Skip();
+}
+
+void object_ctrl_item_value_change(wxDataViewEvent& event)
+{
+    if (event.GetColumn() == 3)
+    {
+        wxVariant variant;
+        m_objects_model->GetValue(variant, event.GetItem(), 3);
+#ifdef __WXOSX__
+        g_selected_extruder = variant.GetString();
+#else // --> for Linux
+        update_extruder_in_config(variant.GetString());
+#endif //__WXOSX__  
+    }
+}
+
+//update_optgroup
+void update_settings_list()
+{
+#ifdef __WXGTK__
+    auto parent = get_optgroup(ogFrequentlyObjectSettings)->get_parent();
+#else
+    auto parent = get_optgroup(ogFrequentlyObjectSettings)->parent();
+#endif /* __WXGTK__ */
+    
+// There is a bug related to Ubuntu overlay scrollbars, see https://github.com/prusa3d/Slic3r/issues/898 and https://github.com/prusa3d/Slic3r/issues/952.
+// The issue apparently manifests when Show()ing a window with overlay scrollbars while the UI is frozen. For this reason,
+// we will Thaw the UI prematurely on Linux. This means destroing the no_updates object prematurely.
+#ifdef __linux__
+	std::unique_ptr<wxWindowUpdateLocker> no_updates(new wxWindowUpdateLocker(parent));
+#else
+	wxWindowUpdateLocker noUpdates(parent);
+#endif
+
+	m_option_sizer->Clear(true);
+
+	if (m_config) 
+	{
+        auto extra_column = [](wxWindow* parent, const Line& line)
+		{
+			auto opt_key = (line.get_options())[0].opt_id;  //we assume that we have one option per line
+
+			auto btn = new wxBitmapButton(parent, wxID_ANY, wxBitmap(Slic3r::GUI::from_u8(Slic3r::var("erase.png")), wxBITMAP_TYPE_PNG),
+				wxDefaultPosition, wxDefaultSize, wxBORDER_NONE);
+			btn->Bind(wxEVT_BUTTON, [opt_key](wxEvent &event){
+				(*m_config)->erase(opt_key);
+				wxTheApp->CallAfter([]() { update_settings_list(); });
+			});
+			return btn;
+		};
+
+		std::map<std::string, std::vector<std::string>> cat_options;
+		auto opt_keys = (*m_config)->keys();
+		if (opt_keys.size() == 1 && opt_keys[0] == "extruder")
+			return;
+
+        auto extruders_cnt = get_preset_bundle()->printers.get_selected_preset().printer_technology() == ptSLA ? 1 :
+                             get_preset_bundle()->printers.get_edited_preset().config.option<ConfigOptionFloats>("nozzle_diameter")->values.size();
+
+		for (auto& opt_key : opt_keys) {
+			auto category = (*m_config)->def()->get(opt_key)->category;
+			if (category.empty() ||
+                (category == "Extruders" && extruders_cnt==1)) continue;
+
+			std::vector< std::string > new_category;
+
+			auto& cat_opt = cat_options.find(category) == cat_options.end() ? new_category : cat_options.at(category);
+			cat_opt.push_back(opt_key);
+			if (cat_opt.size() == 1)
+				cat_options[category] = cat_opt;
+		}
+
+
+		m_og_settings.resize(0);
+		for (auto& cat : cat_options) {
+			if (cat.second.size() == 1 && cat.second[0] == "extruder")
+				continue;
+
+			auto optgroup = std::make_shared<ConfigOptionsGroup>(parent, cat.first, *m_config, false, ogDEFAULT, extra_column);
+			optgroup->label_width = 100;
+			optgroup->sidetext_width = 70;
+
+			for (auto& opt : cat.second)
+			{
+				if (opt == "extruder")
+					continue;
+				Option option = optgroup->get_option(opt);
+				option.opt.width = 70;
+				optgroup->append_single_option_line(option);
+			}
+			optgroup->reload_config();
+			m_option_sizer->Add(optgroup->sizer, 0, wxEXPAND | wxALL, 0);
+			m_og_settings.push_back(optgroup);
+		}
+	}
+
+#ifdef __linux__
+	no_updates.reset(nullptr);
+#endif
+
+    get_right_panel()->Layout();
+	get_right_panel()->GetParent()->Layout();
+}
+
+void get_settings_choice(wxMenu *menu, int id, bool is_part)
+{
+	auto category_name = menu->GetLabel(id);
+
+	wxArrayString names;
+	wxArrayInt selections;
+
+	settings_menu_hierarchy settings_menu;
+	get_options_menu(settings_menu, is_part);
+	std::vector< std::pair<std::string, std::string> > *settings_list = nullptr;
+
+	auto opt_keys = (*m_config)->keys();
+
+	for (auto& cat : settings_menu)
+	{
+		if (_(cat.first) == category_name) {
+			int sel = 0;
+			for (auto& pair : cat.second) {
+				names.Add(_(pair.second));
+				if (find(opt_keys.begin(), opt_keys.end(), pair.first) != opt_keys.end())
+					selections.Add(sel);
+				sel++;
+			}
+			settings_list = &cat.second;
+			break;
+		}
+	} 
+
+	if (!settings_list)
+		return;
+
+	if (wxGetMultipleChoices(selections, _(L("Select showing settings")), category_name, names) ==0 )
+		return;
+
+	std::vector <std::string> selected_options;
+	for (auto sel : selections)
+		selected_options.push_back((*settings_list)[sel].first);
+
+	for (auto& setting:(*settings_list) )
+	{
+		auto& opt_key = setting.first;
+		if (find(opt_keys.begin(), opt_keys.end(), opt_key) != opt_keys.end() &&
+			find(selected_options.begin(), selected_options.end(), opt_key) == selected_options.end())
+			(*m_config)->erase(opt_key);
+		
+		if(find(opt_keys.begin(), opt_keys.end(), opt_key) == opt_keys.end() &&
+				find(selected_options.begin(), selected_options.end(), opt_key) != selected_options.end())
+			(*m_config)->set_key_value(opt_key, m_default_config.get()->option(opt_key)->clone());
+	}
+
+	update_settings_list();
+}
+
+bool cur_item_hase_children()
+{
+    wxDataViewItemArray children;
+    if (m_objects_model->GetChildren(m_objects_ctrl->GetSelection(), children) > 0)
+        return true;
+    return false;
+}
+
+wxMenuItem* menu_item_split(wxMenu* menu, int id) {
+    auto menu_item = new wxMenuItem(menu, id, _(L("Split to parts")));
+    menu_item->SetBitmap(m_bmp_split);
+    return menu_item;
+}
+
+wxMenuItem* menu_item_settings(wxMenu* menu, int id) {
+    auto  menu_item = new wxMenuItem(menu, id, _(L("Add settings")));
+    menu_item->SetBitmap(m_bmp_cog);
+
+    auto sub_menu = create_add_settings_popupmenu(false);
+    menu_item->SetSubMenu(sub_menu);
+    return menu_item;
+}
+
+wxMenu *create_add_part_popupmenu()
+{
+	wxMenu *menu = new wxMenu;
+	std::vector<std::string> menu_items = { L("Add part"), L("Add modifier"), L("Add generic") };
+
+	wxWindowID config_id_base = wxWindow::NewControlId(menu_items.size()+2);
+
+	int i = 0;
+	for (auto& item : menu_items) {
+		auto menu_item = new wxMenuItem(menu, config_id_base + i, _(item));
+		menu_item->SetBitmap(i == 0 ? m_icon_solidmesh : m_icon_modifiermesh);
+		menu->Append(menu_item);
+		i++;
+    }
+
+    menu->AppendSeparator();
+    auto menu_item = menu_item_split(menu, config_id_base + i);
+    menu->Append(menu_item);
+    menu_item->Enable(!cur_item_hase_children());
+
+    menu->AppendSeparator();
+    // Append settings popupmenu
+    menu->Append(menu_item_settings(menu, config_id_base + i + 1));
+
+	wxWindow* win = get_tab_panel()->GetPage(0);
+
+	menu->Bind(wxEVT_MENU, [config_id_base, win, menu](wxEvent &event){
+		switch (event.GetId() - config_id_base) {
+		case 0:
+			on_btn_load(win);
+			break;
+		case 1:
+			on_btn_load(win, true);
+			break;
+		case 2:
+			on_btn_load(win, true, true);
+			break;
+		case 3:
+			on_btn_split(false);
+			break;
+		default:{
+			get_settings_choice(menu, event.GetId(), false);
+			break;}
+		}
+	});
+
+	return menu;
+}
+
+wxMenu *create_part_settings_popupmenu()
+{
+    wxMenu *menu = new wxMenu;
+    wxWindowID config_id_base = wxWindow::NewControlId(2);
+
+    menu->Append(menu_item_split(menu, config_id_base));
+
+    menu->AppendSeparator();
+    // Append settings popupmenu
+    menu->Append(menu_item_settings(menu, config_id_base + 1));
+
+    menu->Bind(wxEVT_MENU, [config_id_base, menu](wxEvent &event){
+        switch (event.GetId() - config_id_base) {
+        case 0:
+            on_btn_split(true);
+            break;
+        default:{
+            get_settings_choice(menu, event.GetId(), true);
+            break; }
+        }
+    });
+
+    return menu;
+}
+
+wxMenu *create_add_settings_popupmenu(bool is_part)
+{
+	wxMenu *menu = new wxMenu;
+
+ 	auto categories = get_category_icon();
+
+	settings_menu_hierarchy settings_menu;
+	get_options_menu(settings_menu, is_part);
+
+	for (auto cat : settings_menu)
+	{
+		auto menu_item = new wxMenuItem(menu, wxID_ANY, _(cat.first));
+		menu_item->SetBitmap(categories.find(cat.first) == categories.end() ? 
+								wxNullBitmap : categories.at(cat.first));
+		menu->Append(menu_item);
+	}
+
+	menu->Bind(wxEVT_MENU, [menu](wxEvent &event) {
+		get_settings_choice(menu, event.GetId(), true);
+	});
+
+	return menu;
+}
+
+void show_context_menu()
+{
+    auto item = m_objects_ctrl->GetSelection();
+    if (item)
+    {
+        if (m_objects_model->GetParent(item) == wxDataViewItem(0))				{
+            auto menu = create_add_part_popupmenu();
+            get_tab_panel()->GetPage(0)->PopupMenu(menu);
+        }
+        else {
+            auto menu = create_part_settings_popupmenu();
+            get_tab_panel()->GetPage(0)->PopupMenu(menu);
+        }
+    }
+}
+
+// ******
+
+void load_part(	wxWindow* parent, ModelObject* model_object, 
+				wxArrayString& part_names, const bool is_modifier)
+{
+	wxArrayString input_files;
+	open_model(parent, input_files);
+	for (int i = 0; i < input_files.size(); ++i) {
+		std::string input_file = input_files.Item(i).ToStdString();
+
+		Model model;
+		try {
+			model = Model::read_from_file(input_file);
+		}
+		catch (std::exception &e) {
+			auto msg = _(L("Error! ")) + input_file + " : " + e.what() + ".";
+			show_error(parent, msg);
+			exit(1);
+		}
+
+		for ( auto object : model.objects) {
+			for (auto volume : object->volumes) {
+				auto new_volume = model_object->add_volume(*volume);
+				new_volume->modifier = is_modifier;
+				boost::filesystem::path(input_file).filename().string();
+				new_volume->name = boost::filesystem::path(input_file).filename().string();
+
+				part_names.Add(new_volume->name);
+
+				// apply the same translation we applied to the object
+				new_volume->mesh.translate( model_object->origin_translation(0),
+											model_object->origin_translation(1), 
+											model_object->origin_translation(2) );
+				// set a default extruder value, since user can't add it manually
+				new_volume->config.set_key_value("extruder", new ConfigOptionInt(0));
+
+				m_parts_changed = true;
+			}
+		}
+	}
+}
+
+void load_lambda(	wxWindow* parent, ModelObject* model_object,
+					wxArrayString& part_names, const bool is_modifier)
+{
+	auto dlg = new LambdaObjectDialog(parent);
+	if (dlg->ShowModal() == wxID_CANCEL) {
+		return;
+	}
+
+	std::string name = "lambda-";
+	TriangleMesh mesh;
+
+	auto params = dlg->ObjectParameters();
+	switch (params.type)
+	{
+	case LambdaTypeBox:{
+		mesh = make_cube(params.dim[0], params.dim[1], params.dim[2]);
+		name += "Box";
+		break;}
+	case LambdaTypeCylinder:{
+		mesh = make_cylinder(params.cyl_r, params.cyl_h);
+		name += "Cylinder";
+		break;}
+	case LambdaTypeSphere:{
+		mesh = make_sphere(params.sph_rho);
+		name += "Sphere";
+		break;}
+	case LambdaTypeSlab:{
+		const auto& size = model_object->bounding_box().size();
+        mesh = make_cube(size(0)*1.5, size(1)*1.5, params.slab_h);
+		// box sets the base coordinate at 0, 0, move to center of plate and move it up to initial_z
+        mesh.translate(-size(0)*1.5 / 2.0, -size(1)*1.5 / 2.0, params.slab_z);
+		name += "Slab";
+		break; }
+	default:
+		break;
+	}
+	mesh.repair();
+
+	auto new_volume = model_object->add_volume(mesh);
+	new_volume->modifier = is_modifier;
+	new_volume->name = name;
+	// set a default extruder value, since user can't add it manually
+	new_volume->config.set_key_value("extruder", new ConfigOptionInt(0));
+
+	part_names.Add(name);
+
+	m_parts_changed = true;
+}
+
+void on_btn_load(wxWindow* parent, bool is_modifier /*= false*/, bool is_lambda/* = false*/)
+{
+	auto item = m_objects_ctrl->GetSelection();
+	if (!item)
+		return;
+	int obj_idx = -1;
+	if (m_objects_model->GetParent(item) == wxDataViewItem(0))
+		obj_idx = m_objects_model->GetIdByItem(item);
+	else
+		return;
+
+	if (obj_idx < 0) return;
+	wxArrayString part_names;
+	if (is_lambda)
+		load_lambda(parent, (*m_objects)[obj_idx], part_names, is_modifier);
+	else
+		load_part(parent, (*m_objects)[obj_idx], part_names, is_modifier);
+
+	parts_changed(obj_idx);
+
+	for (int i = 0; i < part_names.size(); ++i)
+		m_objects_ctrl->Select(	m_objects_model->AddChild(item, part_names.Item(i), 
+								is_modifier ? m_icon_modifiermesh : m_icon_solidmesh));
+// 	part_selection_changed();
+#ifdef __WXMSW__
+	object_ctrl_selection_changed();
+#endif //__WXMSW__
+}
+
+void on_btn_del()
+{
+	auto item = m_objects_ctrl->GetSelection();
+	if (!item) return;
+
+	auto volume_id = m_objects_model->GetVolumeIdByItem(item);
+	if (volume_id < 0)
+		return;
+	auto volume = (*m_objects)[m_selected_object_id]->volumes[volume_id];
+
+	// if user is deleting the last solid part, throw error
+	int solid_cnt = 0;
+	for (auto vol : (*m_objects)[m_selected_object_id]->volumes)
+		if (!vol->modifier)
+			++solid_cnt;
+	if (!volume->modifier && solid_cnt == 1) {
+		Slic3r::GUI::show_error(nullptr, _(L("You can't delete the last solid part from this object.")));
+		return;
+	}
+
+	(*m_objects)[m_selected_object_id]->delete_volume(volume_id);
+	m_parts_changed = true;
+
+	parts_changed(m_selected_object_id);
+
+	m_objects_ctrl->Select(m_objects_model->Delete(item));
+	part_selection_changed();
+// #ifdef __WXMSW__
+// 	object_ctrl_selection_changed();
+// #endif //__WXMSW__
+}
+
+void on_btn_split(const bool split_part)
+{
+	auto item = m_objects_ctrl->GetSelection();
+	if (!item || m_selected_object_id<0)
+		return;
+	auto volume_id = m_objects_model->GetVolumeIdByItem(item);
+    ModelVolume* volume;
+    if (volume_id < 0) {
+        if (split_part) return;
+        else
+            volume = (*m_objects)[m_selected_object_id]->volumes[0]; }
+    else
+	    volume = (*m_objects)[m_selected_object_id]->volumes[volume_id];
+ 	DynamicPrintConfig&	config = get_preset_bundle()->printers.get_edited_preset().config;
+    auto nozzle_dmrs_cnt = config.option<ConfigOptionFloats>("nozzle_diameter")->values.size();
+    auto split_rez = volume->split(nozzle_dmrs_cnt);
+    if (split_rez == 1) {
+        wxMessageBox(_(L("The selected object couldn't be split because it contains only one part.")));
+        return;
+    }
+
+    auto model_object = (*m_objects)[m_selected_object_id];
+
+    if (split_part) {
+        auto parent = m_objects_model->GetParent(item);
+        m_objects_model->DeleteChildren(parent);
+
+        for (auto id = 0; id < model_object->volumes.size(); id++)
+            m_objects_model->AddChild(parent, model_object->volumes[id]->name,
+                                      model_object->volumes[id]->modifier ? m_icon_modifiermesh : m_icon_solidmesh,
+                                      model_object->volumes[id]->config.option<ConfigOptionInt>("extruder")->value, 
+                                      false);
+
+        m_objects_ctrl->Expand(parent);
+    }
+    else {
+        for (auto id = 0; id < model_object->volumes.size(); id++)
+            m_objects_model->AddChild(item, model_object->volumes[id]->name, 
+                                      m_icon_solidmesh,
+                                      model_object->volumes[id]->config.option<ConfigOptionInt>("extruder")->value, 
+                                      false);
+        m_objects_ctrl->Expand(item);
+    }
+}
+
+void on_btn_move_up(){
+	auto item = m_objects_ctrl->GetSelection();
+	if (!item)
+		return;
+	auto volume_id = m_objects_model->GetVolumeIdByItem(item);
+	if (volume_id < 0)
+		return;
+	auto& volumes = (*m_objects)[m_selected_object_id]->volumes;
+	if (0 < volume_id && volume_id < volumes.size()) {
+		std::swap(volumes[volume_id - 1], volumes[volume_id]);
+		m_parts_changed = true;
+		m_objects_ctrl->Select(m_objects_model->MoveChildUp(item));
+		part_selection_changed();
+// #ifdef __WXMSW__
+// 		object_ctrl_selection_changed();
+// #endif //__WXMSW__
+	}
+}
+
+void on_btn_move_down(){
+	auto item = m_objects_ctrl->GetSelection();
+	if (!item)
+		return;
+	auto volume_id = m_objects_model->GetVolumeIdByItem(item);
+	if (volume_id < 0)
+		return;
+	auto& volumes = (*m_objects)[m_selected_object_id]->volumes;
+	if (0 <= volume_id && volume_id+1 < volumes.size()) {
+		std::swap(volumes[volume_id + 1], volumes[volume_id]);
+		m_parts_changed = true;
+		m_objects_ctrl->Select(m_objects_model->MoveChildDown(item));
+		part_selection_changed();
+// #ifdef __WXMSW__
+// 		object_ctrl_selection_changed();
+// #endif //__WXMSW__
+	}
+}
+
+void parts_changed(int obj_idx)
+{ 
+	if (m_event_object_settings_changed <= 0) return;
+
+	wxCommandEvent e(m_event_object_settings_changed);
+	auto event_str = wxString::Format("%d %d %d", obj_idx,
+		is_parts_changed() ? 1 : 0,
+		is_part_settings_changed() ? 1 : 0);
+	e.SetString(event_str);
+	get_main_frame()->ProcessWindowEvent(e);
+}
+	
+void update_settings_value()
+{
+	auto og = get_optgroup(ogFrequentlyObjectSettings);
+	if (m_selected_object_id < 0 || m_objects->size() <= m_selected_object_id) {
+		og->set_value("scale_x", 0);
+		og->set_value("scale_y", 0);
+		og->set_value("scale_z", 0);
+        og->disable();
+		return;
+	}
+    g_is_percent_scale = boost::any_cast<wxString>(og->get_value("scale_unit")) == _("%");
+    update_scale_values();
+    update_rotation_values();
+    og->enable();
+}
+
+void part_selection_changed()
+{
+	auto item = m_objects_ctrl->GetSelection();
+	int obj_idx = -1;
+	auto og = get_optgroup(ogFrequentlyObjectSettings);
+	if (item)
+	{
+		bool is_part = false;
+		if (m_objects_model->GetParent(item) == wxDataViewItem(0)) {
+			obj_idx = m_objects_model->GetIdByItem(item);
+			og->set_name(" " + _(L("Object Settings")) + " ");
+			m_config = std::make_shared<DynamicPrintConfig*>(&(*m_objects)[obj_idx]->config);
+		}
+		else {
+			auto parent = m_objects_model->GetParent(item);
+			// Take ID of the parent object to "inform" perl-side which object have to be selected on the scene
+			obj_idx = m_objects_model->GetIdByItem(parent);
+			og->set_name(" " + _(L("Part Settings")) + " ");
+			is_part = true;
+			auto volume_id = m_objects_model->GetVolumeIdByItem(item);
+			m_config = std::make_shared<DynamicPrintConfig*>(&(*m_objects)[obj_idx]->volumes[volume_id]->config);
+		}
+
+		auto config = m_config;
+        og->set_value("object_name", m_objects_model->GetName(item));
+		m_default_config = std::make_shared<DynamicPrintConfig>(*DynamicPrintConfig::new_from_defaults_keys(get_options(is_part)));
+	}
+    else {
+        wxString empty_str = wxEmptyString;
+        og->set_value("object_name", empty_str);
+        m_config = nullptr;
+    }
+
+	update_settings_list();
+
+	m_selected_object_id = obj_idx;
+
+	update_settings_value();
+
+/*	wxWindowUpdateLocker noUpdates(get_right_panel());
+
+	m_move_options = Point3(0, 0, 0);
+	m_last_coords = Point3(0, 0, 0);
+	// reset move sliders
+	std::vector<std::string> opt_keys = {"x", "y", "z"};
+	auto og = get_optgroup(ogObjectMovers);
+	for (auto opt_key: opt_keys)
+		og->set_value(opt_key, int(0));
+
+// 	if (!item || m_selected_object_id < 0){
+	if (m_selected_object_id < 0){
+		m_sizer_object_buttons->Show(false);
+		m_sizer_part_buttons->Show(false);
+		m_sizer_object_movers->Show(false);
+		m_collpane_settings->Show(false);
+		return;
+	}
+
+	m_collpane_settings->Show(true);
+
+	auto volume_id = m_objects_model->GetVolumeIdByItem(item);
+	if (volume_id < 0){
+		m_sizer_object_buttons->Show(true);
+		m_sizer_part_buttons->Show(false);
+		m_sizer_object_movers->Show(false);
+		m_collpane_settings->SetLabelText(_(L("Object Settings")) + ":");
+
+// 		elsif($itemData->{type} eq 'object') {
+// 			# select nothing in 3D preview
+// 
+// 			# attach object config to settings panel
+// 			$self->{optgroup_movers}->disable;
+// 			$self->{staticbox}->SetLabel('Object Settings');
+// 			@opt_keys = (map @{$_->get_keys}, Slic3r::Config::PrintObject->new, Slic3r::Config::PrintRegion->new);
+// 			$config = $self->{model_object}->config;
+// 		}
+
+		return;
+	}
+
+	m_collpane_settings->SetLabelText(_(L("Part Settings")) + ":");
+	
+	m_sizer_object_buttons->Show(false);
+	m_sizer_part_buttons->Show(true);
+	m_sizer_object_movers->Show(true);
+
+	auto bb_size = m_objects[m_selected_object_id]->bounding_box().size();
+	int scale = 10; //??
+
+	m_mover_x->SetMin(-bb_size.x * 4 * scale);
+	m_mover_x->SetMax(bb_size.x * 4 * scale);
+
+	m_mover_y->SetMin(-bb_size.y * 4 * scale);
+	m_mover_y->SetMax(bb_size.y * 4 * scale);
+
+	m_mover_z->SetMin(-bb_size.z * 4 * scale);
+	m_mover_z->SetMax(bb_size.z * 4 * scale);
+
+
+	
+//	my ($config, @opt_keys);
+	m_btn_move_up->Enable(volume_id > 0);
+	m_btn_move_down->Enable(volume_id + 1 < m_objects[m_selected_object_id]->volumes.size());
+
+	// attach volume config to settings panel
+	auto volume = m_objects[m_selected_object_id]->volumes[volume_id];
+
+	if (volume->modifier) 
+		og->enable();
+	else 
+		og->disable();
+
+//	auto config = volume->config;
+
+	// get default values
+// 	@opt_keys = @{Slic3r::Config::PrintRegion->new->get_keys};
+// 	} 
+/*	
+	# get default values
+	my $default_config = Slic3r::Config::new_from_defaults_keys(\@opt_keys);
+
+	# append default extruder
+	push @opt_keys, 'extruder';
+	$default_config->set('extruder', 0);
+	$config->set_ifndef('extruder', 0);
+	$self->{settings_panel}->set_default_config($default_config);
+	$self->{settings_panel}->set_config($config);
+	$self->{settings_panel}->set_opt_keys(\@opt_keys);
+	$self->{settings_panel}->set_fixed_options([qw(extruder)]);
+	$self->{settings_panel}->enable;
+	}
+	 */
+}
+
+void set_extruder_column_hidden(bool hide)
+{
+	m_objects_ctrl->GetColumn(3)->SetHidden(hide);
+}
+
+void update_extruder_in_config(const wxString& selection)
+{
+    if (!m_config || selection.empty())
+        return;
+
+    int extruder = selection.size() > 1 ? 0 : atoi(selection.c_str());
+    (*m_config)->set_key_value("extruder", new ConfigOptionInt(extruder));
+
+    if (m_event_update_scene > 0) {
+        wxCommandEvent e(m_event_update_scene);
+        get_main_frame()->ProcessWindowEvent(e);
+    }
+}
+
+void update_scale_values()
+{
+    update_scale_values((*m_objects)[m_selected_object_id]->instance_bounding_box(0).size(),
+                        (*m_objects)[m_selected_object_id]->instances[0]->scaling_factor);
+}
+
+void update_scale_values(const Vec3d& size, float scaling_factor)
+{
+    auto og = get_optgroup(ogFrequentlyObjectSettings);
+
+    if (g_is_percent_scale) {
+        auto scale = scaling_factor * 100;
+        og->set_value("scale_x", int(scale));
+        og->set_value("scale_y", int(scale));
+        og->set_value("scale_z", int(scale));
+    }
+    else {
+        og->set_value("scale_x", int(size(0) + 0.5));
+        og->set_value("scale_y", int(size(1) + 0.5));
+        og->set_value("scale_z", int(size(2) + 0.5));
+    }
+}
+
+void update_rotation_values()
+{
+    auto og = get_optgroup(ogFrequentlyObjectSettings);
+
+    og->set_value("rotation_x", 0);
+    og->set_value("rotation_y", 0);
+
+    auto rotation_z = (*m_objects)[m_selected_object_id]->instances[0]->rotation;
+    auto deg = int(Geometry::rad2deg(rotation_z));
+//     if (deg > 180) deg -= 360;
+
+    og->set_value("rotation_z", deg);
+}
+
+void update_rotation_value(const double angle, const std::string& axis)
+{
+    auto og = get_optgroup(ogFrequentlyObjectSettings);
+    
+    int deg = int(Geometry::rad2deg(angle));
+//     if (deg>180) deg -= 360;
+
+    og->set_value("rotation_"+axis, deg);
+}
+
+void on_begin_drag(wxDataViewEvent &event)
+{
+    wxDataViewItem item(event.GetItem());
+
+    // only allow drags for item, not containers
+    if (m_objects_model->GetParent(item) == wxDataViewItem(0)) {
+        event.Veto();
+        return;
+    }
+
+    /* Under MSW or OSX, DnD moves an item to the place of another selected item
+     * But under GTK, DnD moves an item between another two items.
+     * And as a result - call EVT_CHANGE_SELECTION to unselect all items.
+     * To prevent such behavior use g_prevent_list_events
+    **/
+    g_prevent_list_events = true;//it's needed for GTK
+
+    wxTextDataObject *obj = new wxTextDataObject;
+    obj->SetText(wxString::Format("%d", m_objects_model->GetVolumeIdByItem(item)));
+    event.SetDataObject(obj);
+    event.SetDragFlags(/*wxDrag_AllowMove*/wxDrag_DefaultMove); // allows both copy and move;
+}
+
+void on_drop_possible(wxDataViewEvent &event)
+{
+    wxDataViewItem item(event.GetItem());
+
+    // only allow drags for item or background, not containers
+    if (item.IsOk() && m_objects_model->GetParent(item) == wxDataViewItem(0) ||
+        event.GetDataFormat() != wxDF_UNICODETEXT)
+        event.Veto();
+}
+
+void on_drop(wxDataViewEvent &event)
+{
+    wxDataViewItem item(event.GetItem());
+
+    // only allow drops for item, not containers
+    if (item.IsOk() && m_objects_model->GetParent(item) == wxDataViewItem(0) ||
+        event.GetDataFormat() != wxDF_UNICODETEXT) {
+        event.Veto();
+        return;
+    }    
+
+    wxTextDataObject obj;
+    obj.SetData(wxDF_UNICODETEXT, event.GetDataSize(), event.GetDataBuffer());
+
+    int from_volume_id = std::stoi(obj.GetText().ToStdString());
+    int to_volume_id = m_objects_model->GetVolumeIdByItem(item);
+
+#ifdef __WXGTK__
+    /* Under GTK, DnD moves an item between another two items.
+     * And event.GetItem() return item, which is under "insertion line"
+     * So, if we move item down we should to decrease the to_volume_id value
+    **/
+    if (to_volume_id > from_volume_id) to_volume_id--;
+#endif // __WXGTK__
+
+    m_objects_ctrl->Select(m_objects_model->ReorganizeChildren(from_volume_id, to_volume_id,
+                                                               m_objects_model->GetParent(item)));
+
+    auto& volumes = (*m_objects)[m_selected_object_id]->volumes;
+    auto delta = to_volume_id < from_volume_id ? -1 : 1;
+    int cnt = 0;
+    for (int id = from_volume_id; cnt < abs(from_volume_id - to_volume_id); id+=delta, cnt++)
+        std::swap(volumes[id], volumes[id +delta]);
+
+    g_prevent_list_events = false;
+}
+
+void update_objects_list_extruder_column(int extruders_count)
+{
+    if (get_preset_bundle()->printers.get_selected_preset().printer_technology() == ptSLA)
+        extruders_count = 1;
+
+    // delete old 3rd column
+    m_objects_ctrl->DeleteColumn(m_objects_ctrl->GetColumn(3));
+    // insert new created 3rd column
+    m_objects_ctrl->InsertColumn(3, object_ctrl_create_extruder_column(extruders_count));
+    // set show/hide for this column 
+    set_extruder_column_hidden(extruders_count <= 1);
+}
+
+} //namespace GUI
+} //namespace Slic3r 
\ No newline at end of file
diff --git a/xs/src/slic3r/GUI/GUI_ObjectParts.hpp b/xs/src/slic3r/GUI/GUI_ObjectParts.hpp
new file mode 100644
index 0000000000..40dfb92797
--- /dev/null
+++ b/xs/src/slic3r/GUI/GUI_ObjectParts.hpp
@@ -0,0 +1,126 @@
+#ifndef slic3r_GUI_ObjectParts_hpp_
+#define slic3r_GUI_ObjectParts_hpp_
+
+class wxWindow;
+class wxSizer;
+class wxBoxSizer;
+class wxString;
+class wxArrayString;
+class wxMenu;
+class wxDataViewEvent;
+class wxKeyEvent;
+
+namespace Slic3r {
+class ModelObject;
+class Model;
+
+namespace GUI {
+
+enum ogGroup{
+	ogFrequentlyChangingParameters,
+	ogFrequentlyObjectSettings,
+	ogCurrentSettings
+// 	ogObjectSettings,
+// 	ogObjectMovers,
+// 	ogPartSettings
+};
+
+enum LambdaTypeIDs{
+	LambdaTypeBox,
+	LambdaTypeCylinder,
+	LambdaTypeSphere,
+	LambdaTypeSlab
+};
+
+struct OBJECT_PARAMETERS
+{
+	LambdaTypeIDs	type = LambdaTypeBox;
+	double			dim[3];// = { 1.0, 1.0, 1.0 };
+	int				cyl_r = 1;
+	int				cyl_h = 1;
+	double			sph_rho = 1.0;
+	double			slab_h = 1.0;
+	double			slab_z = 0.0;
+};
+
+void add_collapsible_panes(wxWindow* parent, wxBoxSizer* sizer);
+void add_objects_list(wxWindow* parent, wxBoxSizer* sizer);
+void add_object_settings(wxWindow* parent, wxBoxSizer* sizer);
+void show_collpane_settings(bool expert_mode);
+
+wxMenu *create_add_settings_popupmenu(bool is_part);
+wxMenu *create_add_part_popupmenu();
+wxMenu *create_part_settings_popupmenu();
+
+// Add object to the list
+//void add_object(const std::string &name);
+void add_object_to_list(const std::string &name, ModelObject* model_object);
+// Delete object from the list
+void delete_object_from_list();
+// Delete all objects from the list
+void delete_all_objects_from_list();
+// Set count of object on c++ side
+void set_object_count(int idx, int count);
+// Set object scale on c++ side
+void set_object_scale(int idx, int scale);
+// Unselect all objects in the list on c++ side
+void unselect_objects();
+// Select current object in the list on c++ side
+void select_current_object(int idx);
+// Remove objects/sub-object from the list
+void remove();
+
+void object_ctrl_selection_changed();
+void object_ctrl_context_menu();
+void object_ctrl_key_event(wxKeyEvent& event);
+void object_ctrl_item_value_change(wxDataViewEvent& event);
+void show_context_menu();
+
+void init_mesh_icons();
+void set_event_object_selection_changed(const int& event);
+void set_event_object_settings_changed(const int& event); 
+void set_event_remove_object(const int& event);
+void set_event_update_scene(const int& event);
+void set_objects_from_model(Model &model);
+
+bool is_parts_changed();
+bool is_part_settings_changed();
+
+void load_part(	wxWindow* parent, ModelObject* model_object, 
+				wxArrayString& part_names, const bool is_modifier); 
+
+void load_lambda(wxWindow* parent, ModelObject* model_object, 
+				wxArrayString& part_names, const bool is_modifier);
+
+void on_btn_load(wxWindow* parent, bool is_modifier = false, bool is_lambda = false);
+void on_btn_del();
+void on_btn_split(const bool split_part);
+void on_btn_move_up();
+void on_btn_move_down();
+
+void parts_changed(int obj_idx);
+void part_selection_changed();
+
+void update_settings_value();
+// show/hide "Extruder" column for Objects List
+void set_extruder_column_hidden(bool hide);
+// update extruder in current config
+void update_extruder_in_config(const wxString& selection);
+// update scale values after scale unit changing or "gizmos"
+void update_scale_values();
+void update_scale_values(const Vec3d& size, float scale);
+// update rotation values object selection changing
+void update_rotation_values();
+// update rotation value after "gizmos"
+void update_rotation_value(const double angle, const std::string& axis);
+
+void on_begin_drag(wxDataViewEvent &event);
+void on_drop_possible(wxDataViewEvent &event);
+void on_drop(wxDataViewEvent &event);
+
+// update extruder column for objects_ctrl according to extruders count
+void update_objects_list_extruder_column(int extruders_count);
+
+} //namespace GUI
+} //namespace Slic3r 
+#endif  //slic3r_GUI_ObjectParts_hpp_
\ No newline at end of file
diff --git a/xs/src/slic3r/GUI/LambdaObjectDialog.cpp b/xs/src/slic3r/GUI/LambdaObjectDialog.cpp
new file mode 100644
index 0000000000..7543821c0e
--- /dev/null
+++ b/xs/src/slic3r/GUI/LambdaObjectDialog.cpp
@@ -0,0 +1,176 @@
+#include "LambdaObjectDialog.hpp"
+
+#include <wx/window.h>
+#include <wx/button.h>
+#include "OptionsGroup.hpp"
+
+namespace Slic3r
+{
+namespace GUI
+{
+static wxString dots("…", wxConvUTF8);
+
+LambdaObjectDialog::LambdaObjectDialog(wxWindow* parent)
+{
+	Create(parent, wxID_ANY, _(L("Lambda Object")),
+		wxDefaultPosition, wxDefaultSize,
+		wxDEFAULT_DIALOG_STYLE | wxRESIZE_BORDER);
+
+	// instead of double dim[3] = { 1.0, 1.0, 1.0 };
+	object_parameters.dim[0] = 1.0;
+	object_parameters.dim[1] = 1.0;
+	object_parameters.dim[2] = 1.0;
+
+	sizer = new wxBoxSizer(wxVERTICAL);
+
+	// modificator options
+	m_modificator_options_book = new wxChoicebook(	this, wxID_ANY, wxDefaultPosition, 
+													wxDefaultSize, wxCHB_TOP);
+	sizer->Add(m_modificator_options_book, 1, wxEXPAND| wxALL, 10);
+
+	auto optgroup = init_modificator_options_page(_(L("Box")));
+		optgroup->m_on_change = [this](t_config_option_key opt_key, boost::any value){
+			int opt_id =	opt_key == "l" ? 0 :
+							opt_key == "w" ? 1 : 
+							opt_key == "h" ? 2 : -1;
+			if (opt_id < 0) return;
+			object_parameters.dim[opt_id] = boost::any_cast<double>(value);
+		};
+
+		ConfigOptionDef def;
+		def.width = 70;
+		def.type = coFloat;
+		def.default_value = new ConfigOptionFloat{ 1.0 };
+		def.label = L("L");
+		Option option(def, "l");
+		optgroup->append_single_option_line(option);
+		
+		def.label = L("W");
+		option = Option(def, "w");
+		optgroup->append_single_option_line(option);
+		
+		def.label = L("H");
+		option = Option(def, "h");
+		optgroup->append_single_option_line(option);
+
+	optgroup = init_modificator_options_page(_(L("Cylinder")));
+		optgroup->m_on_change = [this](t_config_option_key opt_key, boost::any value){
+			int val = boost::any_cast<int>(value);
+			if (opt_key == "cyl_r")
+				object_parameters.cyl_r = val;
+			else if (opt_key == "cyl_h")
+				object_parameters.cyl_h = val;
+			else return;
+		};
+
+		def.type = coInt;
+		def.default_value = new ConfigOptionInt{ 1 };
+		def.label = L("Radius");
+		option = Option(def, "cyl_r");
+		optgroup->append_single_option_line(option);
+
+		def.label = L("Height");
+		option = Option(def, "cyl_h");
+		optgroup->append_single_option_line(option);
+
+	optgroup = init_modificator_options_page(_(L("Sphere")));
+		optgroup->m_on_change = [this](t_config_option_key opt_key, boost::any value){
+			if (opt_key == "sph_rho")
+				object_parameters.sph_rho = boost::any_cast<double>(value);
+			else return;
+		};
+
+		def.type = coFloat;
+		def.default_value = new ConfigOptionFloat{ 1.0 };
+		def.label = L("Rho");
+		option = Option(def, "sph_rho");
+		optgroup->append_single_option_line(option);
+
+	optgroup = init_modificator_options_page(_(L("Slab")));
+		optgroup->m_on_change = [this](t_config_option_key opt_key, boost::any value){
+			double val = boost::any_cast<double>(value);
+			if (opt_key == "slab_z")
+				object_parameters.slab_z = val;
+			else if (opt_key == "slab_h")
+				object_parameters.slab_h = val;
+			else return;
+		};
+
+		def.label = L("H");
+		option = Option(def, "slab_h");
+		optgroup->append_single_option_line(option);
+
+		def.label = L("Initial Z");
+		option = Option(def, "slab_z");
+		optgroup->append_single_option_line(option);
+
+	Bind(wxEVT_CHOICEBOOK_PAGE_CHANGED, ([this](wxCommandEvent e)
+	{
+		auto page_idx = m_modificator_options_book->GetSelection();
+		if (page_idx < 0) return;
+		switch (page_idx)
+		{
+		case 0:
+			object_parameters.type = LambdaTypeBox;
+			break;
+		case 1:
+			object_parameters.type = LambdaTypeCylinder;
+			break;
+		case 2:
+			object_parameters.type = LambdaTypeSphere;
+			break;
+		case 3:
+			object_parameters.type = LambdaTypeSlab;
+			break;
+		default:
+			break;
+		}
+	}));
+
+
+	auto button_sizer = CreateStdDialogButtonSizer(wxOK | wxCANCEL);
+
+	wxButton* btn_OK = static_cast<wxButton*>(FindWindowById(wxID_OK, this));
+	btn_OK->Bind(wxEVT_BUTTON, [this](wxCommandEvent&) {
+		// validate user input
+		if (!CanClose())return;
+		EndModal(wxID_OK);
+		Destroy();
+	});
+
+	wxButton* btn_CANCEL = static_cast<wxButton*>(FindWindowById(wxID_CANCEL, this));
+	btn_CANCEL->Bind(wxEVT_BUTTON, [this](wxCommandEvent&) {
+		// validate user input
+		if (!CanClose())return;
+		EndModal(wxID_CANCEL);
+		Destroy();
+	});
+
+	sizer->Add(button_sizer, 0, wxALIGN_CENTER_HORIZONTAL | wxBOTTOM, 10);
+
+	SetSizer(sizer);
+	sizer->Fit(this);
+	sizer->SetSizeHints(this);
+}
+
+// Called from the constructor.
+// Create a panel for a rectangular / circular / custom bed shape.
+ConfigOptionsGroupShp LambdaObjectDialog::init_modificator_options_page(wxString title){
+
+	auto panel = new wxPanel(m_modificator_options_book);
+
+	ConfigOptionsGroupShp optgroup;
+	optgroup = std::make_shared<ConfigOptionsGroup>(panel, _(L("Add")) + " " +title + " " +dots);
+	optgroup->label_width = 100;
+
+	m_optgroups.push_back(optgroup);
+
+	panel->SetSizerAndFit(optgroup->sizer);
+	m_modificator_options_book->AddPage(panel, title);
+
+	return optgroup;
+}
+
+
+} //namespace GUI
+} //namespace Slic3r 
diff --git a/xs/src/slic3r/GUI/LambdaObjectDialog.hpp b/xs/src/slic3r/GUI/LambdaObjectDialog.hpp
new file mode 100644
index 0000000000..a70c124490
--- /dev/null
+++ b/xs/src/slic3r/GUI/LambdaObjectDialog.hpp
@@ -0,0 +1,35 @@
+#ifndef slic3r_LambdaObjectDialog_hpp_
+#define slic3r_LambdaObjectDialog_hpp_
+
+#include "GUI.hpp"
+
+#include <wx/dialog.h>
+#include <wx/sizer.h>
+#include <wx/choicebk.h>
+
+namespace Slic3r
+{
+namespace GUI
+{
+using ConfigOptionsGroupShp = std::shared_ptr<ConfigOptionsGroup>;
+class LambdaObjectDialog : public wxDialog
+{
+	wxChoicebook*	m_modificator_options_book;
+	std::vector <ConfigOptionsGroupShp>	m_optgroups;
+public:
+	LambdaObjectDialog(wxWindow* parent);
+	~LambdaObjectDialog(){}
+
+	bool CanClose() { return true; }	// ???
+	OBJECT_PARAMETERS& ObjectParameters(){ return object_parameters; }
+
+	ConfigOptionsGroupShp init_modificator_options_page(wxString title);
+	
+	// Note whether the window was already closed, so a pending update is not executed.
+	bool m_already_closed = false;
+	OBJECT_PARAMETERS object_parameters;
+	wxBoxSizer* sizer = nullptr;
+};
+} //namespace GUI
+} //namespace Slic3r 
+#endif  //slic3r_LambdaObjectDialog_hpp_
diff --git a/xs/src/slic3r/GUI/OptionsGroup.cpp b/xs/src/slic3r/GUI/OptionsGroup.cpp
index d5cc29e19f..453a2f3f74 100644
--- a/xs/src/slic3r/GUI/OptionsGroup.cpp
+++ b/xs/src/slic3r/GUI/OptionsGroup.cpp
@@ -30,6 +30,7 @@ const t_field& OptionsGroup::build_field(const t_config_option_key& id, const Co
                 opt.gui_type.compare("i_enum_closed") == 0) {
 		m_fields.emplace(id, STDMOVE(Choice::Create<Choice>(parent(), opt, id)));
     } else if (opt.gui_type.compare("slider") == 0) {
+		m_fields.emplace(id, STDMOVE(SliderCtrl::Create<SliderCtrl>(parent(), opt, id)));
     } else if (opt.gui_type.compare("i_spin") == 0) { // Spinctrl
     } else if (opt.gui_type.compare("legend") == 0) { // StaticText
 		m_fields.emplace(id, STDMOVE(StaticText::Create<StaticText>(parent(), opt, id)));
@@ -88,17 +89,23 @@ const t_field& OptionsGroup::build_field(const t_config_option_key& id, const Co
 		if (!this->m_disabled)
 			this->back_to_sys_value(opt_id);
 	};
-	if (!m_show_modified_btns) {
-		field->m_Undo_btn->Hide();
-		field->m_Undo_to_sys_btn->Hide();
-	}
-//	if (nonsys_btn_icon != nullptr)
-//		field->set_nonsys_btn_icon(*nonsys_btn_icon);
     
 	// assign function objects for callbacks, etc.
     return field;
 }
 
+void OptionsGroup::add_undo_buttuns_to_sizer(wxSizer* sizer, const t_field& field)
+{
+	if (!m_show_modified_btns) {
+		field->m_Undo_btn->Hide();
+		field->m_Undo_to_sys_btn->Hide();
+		return;
+	}
+
+	sizer->Add(field->m_Undo_to_sys_btn, 0, wxALIGN_CENTER_VERTICAL);
+	sizer->Add(field->m_Undo_btn, 0, wxALIGN_CENTER_VERTICAL);
+}
+
 void OptionsGroup::append_line(const Line& line, wxStaticText**	colored_Label/* = nullptr*/) {
 //!    if (line.sizer != nullptr || (line.widget != nullptr && line.full_width > 0)){
 	if ( (line.sizer != nullptr || line.widget != nullptr) && line.full_width){
@@ -133,8 +140,7 @@ void OptionsGroup::append_line(const Line& line, wxStaticText**	colored_Label/*
 		const auto& field = build_field(option);
 
 		auto btn_sizer = new wxBoxSizer(wxHORIZONTAL);
-		btn_sizer->Add(field->m_Undo_to_sys_btn);
-		btn_sizer->Add(field->m_Undo_btn);
+		add_undo_buttuns_to_sizer(btn_sizer, field);
 		tmp_sizer->Add(btn_sizer, 0, wxEXPAND | wxALL, 0);
 		if (is_window_field(field))
 			tmp_sizer->Add(field->getWindow(), 0, wxEXPAND | wxALL, wxOSX ? 0 : 5);
@@ -149,6 +155,18 @@ void OptionsGroup::append_line(const Line& line, wxStaticText**	colored_Label/*
         m_panel->Layout();
 #endif /* __WXGTK__ */
 
+	// if we have an extra column, build it
+	if (extra_column) {
+		if (extra_column) {
+			grid_sizer->Add(extra_column(parent(), line), 0, wxALIGN_CENTER_VERTICAL, 0);
+		}
+		else {
+			// if the callback provides no sizer for the extra cell, put a spacer
+			grid_sizer->AddSpacer(1);
+		}
+	}
+
+
     // Build a label if we have it
 	wxStaticText* label=nullptr;
     if (label_width != 0) {
@@ -163,7 +181,8 @@ void OptionsGroup::append_line(const Line& line, wxStaticText**	colored_Label/*
 							wxDefaultPosition, wxSize(label_width, -1), label_style);
         label->SetFont(label_font);
         label->Wrap(label_width); // avoid a Linux/GTK bug
-		grid_sizer->Add(label, 0, (staticbox ? 0 : wxALIGN_RIGHT | wxRIGHT) | wxALIGN_CENTER_VERTICAL, 5);
+		grid_sizer->Add(label, 0, (staticbox ? 0 : wxALIGN_RIGHT | wxRIGHT) | 
+						(m_flag == ogSIDE_OPTIONS_VERTICAL ? wxTOP : wxALIGN_CENTER_VERTICAL), 5);
 		if (line.label_tooltip.compare("") != 0)
 			label->SetToolTip(line.label_tooltip);
     }
@@ -177,28 +196,35 @@ void OptionsGroup::append_line(const Line& line, wxStaticText**	colored_Label/*
 		return;
 	}
 	
-	// if we have a single option with no sidetext just add it directly to the grid sizer
-	auto sizer = new wxBoxSizer(wxHORIZONTAL);
-	grid_sizer->Add(sizer, 0, wxEXPAND | (staticbox ? wxALL : wxBOTTOM|wxTOP|wxLEFT), staticbox ? 0 : 1);
+	// If we're here, we have more than one option or a single option with sidetext
+    // so we need a horizontal sizer to arrange these things
+	auto sizer = new wxBoxSizer(m_flag == ogSIDE_OPTIONS_VERTICAL ? wxVERTICAL : wxHORIZONTAL);
+	grid_sizer->Add(sizer, 0, wxEXPAND | (staticbox ? wxALL : wxBOTTOM | wxTOP | wxLEFT), staticbox ? 0 : 1);
+	// If we have a single option with no sidetext just add it directly to the grid sizer
 	if (option_set.size() == 1 && option_set.front().opt.sidetext.size() == 0 &&
 		option_set.front().side_widget == nullptr && line.get_extra_widgets().size() == 0) {
 		const auto& option = option_set.front();
 		const auto& field = build_field(option, label);
 
-		sizer->Add(field->m_Undo_to_sys_btn, 0, wxALIGN_CENTER_VERTICAL); 
-		sizer->Add(field->m_Undo_btn, 0, wxALIGN_CENTER_VERTICAL);
+		add_undo_buttuns_to_sizer(sizer, field);
 		if (is_window_field(field)) 
 			sizer->Add(field->getWindow(), option.opt.full_width ? 1 : 0, (option.opt.full_width ? wxEXPAND : 0) |
 							wxBOTTOM | wxTOP | wxALIGN_CENTER_VERTICAL, (wxOSX||!staticbox) ? 0 : 2);
 		if (is_sizer_field(field)) 
-			sizer->Add(field->getSizer(), 0, (option.opt.full_width ? wxEXPAND : 0) | wxALIGN_CENTER_VERTICAL, 0);
+			sizer->Add(field->getSizer(), 1, (option.opt.full_width ? wxEXPAND : 0) | wxALIGN_CENTER_VERTICAL, 0);
 		return;
 	}
 
-    // if we're here, we have more than one option or a single option with sidetext
-    // so we need a horizontal sizer to arrange these things
-	for (auto opt : option_set) {
+    for (auto opt : option_set) {
 		ConfigOptionDef option = opt.opt;
+		wxSizer* sizer_tmp;
+		if (m_flag == ogSIDE_OPTIONS_VERTICAL){
+			auto sz = new wxFlexGridSizer(1, 3, 2, 2);
+			sz->RemoveGrowableCol(2);
+			sizer_tmp = sz;
+		}
+    	else
+    		sizer_tmp = sizer;
 		// add label if any
 		if (option.label != "") {
 			wxString str_label = _(option.label);
@@ -208,34 +234,38 @@ void OptionsGroup::append_line(const Line& line, wxStaticText**	colored_Label/*
 // 								L_str(option.label);
 			label = new wxStaticText(parent(), wxID_ANY, str_label + ":", wxDefaultPosition, wxDefaultSize);
 			label->SetFont(label_font);
-			sizer->Add(label, 0, wxALIGN_CENTER_VERTICAL, 0);
+			sizer_tmp->Add(label, 0, wxALIGN_RIGHT | wxALIGN_CENTER_VERTICAL, 0);
 		}
 
 		// add field
 		const Option& opt_ref = opt;
 		auto& field = build_field(opt_ref, label);
-		sizer->Add(field->m_Undo_to_sys_btn, 0, wxALIGN_CENTER_VERTICAL);
-		sizer->Add(field->m_Undo_btn, 0, wxALIGN_CENTER_VERTICAL, 0);
+		add_undo_buttuns_to_sizer(sizer_tmp, field);
 		is_sizer_field(field) ? 
-			sizer->Add(field->getSizer(), 0, wxALIGN_CENTER_VERTICAL, 0) :
-			sizer->Add(field->getWindow(), 0, wxALIGN_CENTER_VERTICAL, 0);
+			sizer_tmp->Add(field->getSizer(), 0, wxALIGN_CENTER_VERTICAL, 0) :
+			sizer_tmp->Add(field->getWindow(), 0, wxALIGN_CENTER_VERTICAL, 0);
 		
 		// add sidetext if any
 		if (option.sidetext != "") {
-			auto sidetext = new wxStaticText(parent(), wxID_ANY, _(option.sidetext), wxDefaultPosition, wxDefaultSize);
+			auto sidetext = new wxStaticText(	parent(), wxID_ANY, _(option.sidetext), wxDefaultPosition, 
+												wxSize(sidetext_width, -1)/*wxDefaultSize*/, wxALIGN_LEFT);
 			sidetext->SetFont(sidetext_font);
-			sizer->Add(sidetext, 0, wxLEFT | wxALIGN_CENTER_VERTICAL, 4);
+			sizer_tmp->Add(sidetext, 0, wxLEFT | wxALIGN_CENTER_VERTICAL, m_flag == ogSIDE_OPTIONS_VERTICAL ? 0 : 4);
+			field->set_side_text_ptr(sidetext);
 		}
 
 		// add side widget if any
 		if (opt.side_widget != nullptr) {
-			sizer->Add(opt.side_widget(parent())/*!.target<wxWindow>()*/, 0, wxLEFT | wxALIGN_CENTER_VERTICAL, 1);	//! requires verification
+			sizer_tmp->Add(opt.side_widget(parent())/*!.target<wxWindow>()*/, 0, wxLEFT | wxALIGN_CENTER_VERTICAL, 1);	//! requires verification
 		}
 
-		if (opt.opt_id != option_set.back().opt_id) //! istead of (opt != option_set.back())
+		if (opt.opt_id != option_set.back().opt_id && m_flag != ogSIDE_OPTIONS_VERTICAL) //! istead of (opt != option_set.back())
 		{
-			sizer->AddSpacer(6);
+			sizer_tmp->AddSpacer(6);
 	    }
+
+		if (m_flag == ogSIDE_OPTIONS_VERTICAL)
+			sizer->Add(sizer_tmp, 0, wxALIGN_RIGHT|wxALL, 0);
 	}
 	// add extra sizers if any
 	for (auto extra_widget : line.get_extra_widgets()) {
@@ -259,7 +289,7 @@ void OptionsGroup::on_change_OG(const t_config_option_key& opt_id, const boost::
 Option ConfigOptionsGroup::get_option(const std::string& opt_key, int opt_index /*= -1*/)
 {
 	if (!m_config->has(opt_key)) {
-		std::cerr << "No " << opt_key << " in ConfigOptionsGroup config.";
+		std::cerr << "No " << opt_key << " in ConfigOptionsGroup config.\n";
 	}
 
 	std::string opt_id = opt_index == -1 ? opt_key : opt_key + "#" + std::to_string(opt_index);
@@ -459,8 +489,12 @@ boost::any ConfigOptionsGroup::get_config_value(const DynamicPrintConfig& config
 		else if (opt_key.compare("support_material_pattern") == 0){
 			ret = static_cast<int>(config.option<ConfigOptionEnum<SupportMaterialPattern>>(opt_key)->value);
 		}
-		else if (opt_key.compare("seam_position") == 0)
+		else if (opt_key.compare("seam_position") == 0){
 			ret = static_cast<int>(config.option<ConfigOptionEnum<SeamPosition>>(opt_key)->value);
+		}
+		else if (opt_key.compare("host_type") == 0){
+			ret = static_cast<int>(config.option<ConfigOptionEnum<PrintHostType>>(opt_key)->value);
+		}
 	}
 		break;
 	case coPoints:
diff --git a/xs/src/slic3r/GUI/OptionsGroup.hpp b/xs/src/slic3r/GUI/OptionsGroup.hpp
index 422e1afd9e..4f263f5e3c 100644
--- a/xs/src/slic3r/GUI/OptionsGroup.hpp
+++ b/xs/src/slic3r/GUI/OptionsGroup.hpp
@@ -26,9 +26,13 @@
 
 namespace Slic3r { namespace GUI {
 
+enum ogDrawFlag{
+	ogDEFAULT,
+	ogSIDE_OPTIONS_VERTICAL
+};
+
 /// Widget type describes a function object that returns a wxWindow (our widget) and accepts a wxWidget (parent window).
 using widget_t = std::function<wxSizer*(wxWindow*)>;//!std::function<wxWindow*(wxWindow*)>;
-using column_t = std::function<wxSizer*(const Line&)>;
 
 //auto default_label_clr = wxSystemSettings::GetColour(wxSYS_COLOUR_3DLIGHT); //GetSystemColour
 //auto modified_label_clr = *new wxColour(254, 189, 101);
@@ -71,10 +75,13 @@ private:
     std::vector<widget_t>	m_extra_widgets;//! {std::vector<widget_t>()};
 };
 
+using column_t = std::function<wxWindow*(wxWindow* parent, const Line&)>;//std::function<wxSizer*(const Line&)>;
+
 using t_optionfield_map = std::map<t_config_option_key, t_field>;
 using t_opt_map = std::map< std::string, std::pair<std::string, int> >;
 
 class OptionsGroup {
+	wxStaticBox*	stb;
 public:
     const bool		staticbox {true};
     const wxString	title {wxString("")};
@@ -88,8 +95,7 @@ public:
 
     wxFont			sidetext_font {wxSystemSettings::GetFont(wxSYS_DEFAULT_GUI_FONT) };
     wxFont			label_font {wxSystemSettings::GetFont(wxSYS_DEFAULT_GUI_FONT) };
-
-//	std::function<const wxBitmap&()>	nonsys_btn_icon{ nullptr };
+	int				sidetext_width{ -1 };
 
     /// Returns a copy of the pointer of the parent wxWindow.
     /// Accessor function is because users are not allowed to change the parent
@@ -101,6 +107,11 @@ public:
 		return m_parent;
 #endif /* __WXGTK__ */
     }
+#ifdef __WXGTK__
+    wxWindow* get_parent() const {
+        return m_parent;
+    }
+#endif /* __WXGTK__ */
 
 	void		append_line(const Line& line, wxStaticText** colored_Label = nullptr);
     Line		create_single_option_line(const Option& option) const;
@@ -124,23 +135,39 @@ public:
 							return out;
     }
 
+	bool			set_side_text(const t_config_option_key& opt_key, const wxString& side_text) {
+							if (m_fields.find(opt_key) == m_fields.end()) return false;
+							auto st = m_fields.at(opt_key)->m_side_text;
+							if (!st) return false;
+							st->SetLabel(side_text);
+							return true;
+    }
+
+	void			set_name(const wxString& new_name) {
+							stb->SetLabel(new_name);
+    }
+
 	inline void		enable() { for (auto& field : m_fields) field.second->enable(); }
     inline void		disable() { for (auto& field : m_fields) field.second->disable(); }
+	void			set_flag(ogDrawFlag flag) { m_flag = flag; }
+	void			set_grid_vgap(int gap) { m_grid_sizer->SetVGap(gap); }
 
 	void set_show_modified_btns_val(bool show) {
 		m_show_modified_btns = show;
     }
 
-    OptionsGroup(wxWindow* _parent, const wxString& title, bool is_tab_opt=false) : 
-		m_parent(_parent), title(title), m_show_modified_btns(is_tab_opt), staticbox(title!="") {
-		auto stb = new wxStaticBox(_parent, wxID_ANY, title);
+	OptionsGroup(	wxWindow* _parent, const wxString& title, bool is_tab_opt = false, 
+					ogDrawFlag flag = ogDEFAULT, column_t extra_clmn = nullptr) :
+					m_parent(_parent), title(title), m_show_modified_btns(is_tab_opt),
+					staticbox(title!=""), m_flag(flag), extra_column(extra_clmn){
+		stb = new wxStaticBox(_parent, wxID_ANY, title);
 		stb->SetFont(bold_font());
-		sizer = (staticbox ? new wxStaticBoxSizer(stb/*new wxStaticBox(_parent, wxID_ANY, title)*/, wxVERTICAL) : new wxBoxSizer(wxVERTICAL));
+        sizer = (staticbox ? new wxStaticBoxSizer(stb, wxVERTICAL) : new wxBoxSizer(wxVERTICAL));
         auto num_columns = 1U;
         if (label_width != 0) num_columns++;
         if (extra_column != nullptr) num_columns++;
-        m_grid_sizer = new wxFlexGridSizer(0, num_columns, 0,0);
-        static_cast<wxFlexGridSizer*>(m_grid_sizer)->SetFlexibleDirection(wxHORIZONTAL);
+        m_grid_sizer = new wxFlexGridSizer(0, num_columns, 1,0);
+        static_cast<wxFlexGridSizer*>(m_grid_sizer)->SetFlexibleDirection(wxBOTH/*wxHORIZONTAL*/);
         static_cast<wxFlexGridSizer*>(m_grid_sizer)->AddGrowableCol(label_width != 0);
 #ifdef __WXGTK__
         m_panel = new wxPanel( _parent, wxID_ANY, wxDefaultPosition, wxDefaultSize, wxTAB_TRAVERSAL );
@@ -164,6 +191,8 @@ protected:
 	// "true" if option is created in preset tabs
 	bool					m_show_modified_btns{ false };
 
+	ogDrawFlag				m_flag{ ogDEFAULT };
+
 	// This panel is needed for correct showing of the ToolTips for Button, StaticText and CheckBox
 	// Tooltips on GTK doesn't work inside wxStaticBoxSizer unless you insert a panel 
 	// inside it before you insert the other controls.
@@ -177,6 +206,7 @@ protected:
 	const t_field&		build_field(const t_config_option_key& id, const ConfigOptionDef& opt, wxStaticText* label = nullptr);
 	const t_field&		build_field(const t_config_option_key& id, wxStaticText* label = nullptr);
 	const t_field&		build_field(const Option& opt, wxStaticText* label = nullptr);
+	void				add_undo_buttuns_to_sizer(wxSizer* sizer, const t_field& field);
 
     virtual void		on_kill_focus (){};
 	virtual void		on_change_OG(const t_config_option_key& opt_id, const boost::any& value);
@@ -186,8 +216,9 @@ protected:
 
 class ConfigOptionsGroup: public OptionsGroup {
 public:
-	ConfigOptionsGroup(wxWindow* parent, const wxString& title, DynamicPrintConfig* _config = nullptr, bool is_tab_opt = false) :
-		OptionsGroup(parent, title, is_tab_opt), m_config(_config) {}
+	ConfigOptionsGroup(	wxWindow* parent, const wxString& title, DynamicPrintConfig* _config = nullptr, 
+						bool is_tab_opt = false, ogDrawFlag flag = ogDEFAULT, column_t extra_clmn = nullptr) :
+		OptionsGroup(parent, title, is_tab_opt, flag, extra_clmn), m_config(_config) {}
 
     /// reference to libslic3r config, non-owning pointer (?).
     DynamicPrintConfig*		m_config {nullptr};
diff --git a/xs/src/slic3r/GUI/Preset.cpp b/xs/src/slic3r/GUI/Preset.cpp
index effe9f4fbb..675e06c60f 100644
--- a/xs/src/slic3r/GUI/Preset.cpp
+++ b/xs/src/slic3r/GUI/Preset.cpp
@@ -120,6 +120,11 @@ VendorProfile VendorProfile::from_ini(const ptree &tree, const boost::filesystem
             VendorProfile::PrinterModel model;
             model.id = section.first.substr(printer_model_key.size());
             model.name = section.second.get<std::string>("name", model.id);
+            auto technology_field = section.second.get<std::string>("technology", "FFF");
+            if (! ConfigOptionEnum<PrinterTechnology>::from_string(technology_field, model.technology)) {
+                BOOST_LOG_TRIVIAL(error) << boost::format("Vendor bundle: `%1%`: Invalid printer technology field: `%2%`") % id % technology_field;
+                model.technology = ptFFF;
+            }
             section.second.get<std::string>("variants", "");
             const auto variants_field = section.second.get<std::string>("variants", "");
             std::vector<std::string> variants;
@@ -177,7 +182,7 @@ void Preset::normalize(DynamicPrintConfig &config)
 {
     auto *nozzle_diameter = dynamic_cast<const ConfigOptionFloats*>(config.option("nozzle_diameter"));
     if (nozzle_diameter != nullptr)
-        // Loaded the Printer settings. Verify, that all extruder dependent values have enough values.
+        // Loaded the FFF Printer settings. Verify, that all extruder dependent values have enough values.
         set_num_extruders(config, (unsigned int)nozzle_diameter->values.size());
     if (config.option("filament_diameter") != nullptr) {
         // This config contains single or multiple filament presets.
@@ -204,12 +209,9 @@ void Preset::normalize(DynamicPrintConfig &config)
     }
 }
 
-// Load a config file, return a C++ class Slic3r::DynamicPrintConfig with $keys initialized from the config file.
-// In case of a "default" config item, return the default values.
-DynamicPrintConfig& Preset::load(const std::vector<std::string> &keys)
+DynamicPrintConfig& Preset::load(const std::vector<std::string> &keys, const StaticPrintConfig &defaults)
 {
     // Set the configuration from the defaults.
-    Slic3r::FullPrintConfig defaults;
     this->config.apply_only(defaults, keys.empty() ? defaults.keys() : keys);
     if (! this->is_default) {
         // Load the preset file, apply preset values on top of defaults.
@@ -260,8 +262,9 @@ bool Preset::is_compatible_with_printer(const Preset &active_printer) const
 {
     DynamicPrintConfig config;
     config.set_key_value("printer_preset", new ConfigOptionString(active_printer.name));
-    config.set_key_value("num_extruders", new ConfigOptionInt(
-        (int)static_cast<const ConfigOptionFloats*>(active_printer.config.option("nozzle_diameter"))->values.size()));
+	const ConfigOption *opt = active_printer.config.option("nozzle_diameter");
+	if (opt)
+		config.set_key_value("num_extruders", new ConfigOptionInt((int)static_cast<const ConfigOptionFloats*>(opt)->values.size()));
     return this->is_compatible_with_printer(active_printer, &config);
 }
 
@@ -329,8 +332,10 @@ const std::vector<std::string>& Preset::printer_options()
     static std::vector<std::string> s_opts;
     if (s_opts.empty()) {
         s_opts = {
+            "printer_technology",
             "bed_shape", "z_offset", "gcode_flavor", "use_relative_e_distances", "serial_port", "serial_speed", 
-            "octoprint_host", "octoprint_apikey", "octoprint_cafile", "use_firmware_retraction", "use_volumetric_e", "variable_layer_height",
+            "use_firmware_retraction", "use_volumetric_e", "variable_layer_height",
+            "host_type", "print_host", "printhost_apikey", "printhost_cafile",
             "single_extruder_multi_material", "start_gcode", "end_gcode", "before_layer_gcode", "layer_gcode", "toolchange_gcode",
             "between_objects_gcode", "printer_vendor", "printer_model", "printer_variant", "printer_notes", "cooling_tube_retraction",
             "cooling_tube_length", "parking_pos_retraction", "extra_loading_move", "max_print_height", "default_print_profile", "inherits",
@@ -360,7 +365,39 @@ const std::vector<std::string>& Preset::nozzle_options()
     return s_opts;
 }
 
-PresetCollection::PresetCollection(Preset::Type type, const std::vector<std::string> &keys) :
+const std::vector<std::string>& Preset::sla_printer_options()
+{    
+    static std::vector<std::string> s_opts;
+    if (s_opts.empty()) {
+        s_opts = {
+            "printer_technology",
+            "bed_shape", "max_print_height",
+            "display_width", "display_height", "display_pixels_x", "display_pixels_y",
+            "printer_correction",
+            "printer_notes",
+            "inherits"
+        };
+    }
+    return s_opts;
+}
+
+const std::vector<std::string>& Preset::sla_material_options()
+{    
+    static std::vector<std::string> s_opts;
+    if (s_opts.empty()) {
+        s_opts = {
+            "layer_height", "initial_layer_height",
+            "exposure_time", "initial_exposure_time",
+            "material_correction_printing", "material_correction_curing",
+            "material_notes",
+            "compatible_printers",
+            "compatible_printers_condition", "inherits"
+        };
+    }
+    return s_opts;
+}
+
+PresetCollection::PresetCollection(Preset::Type type, const std::vector<std::string> &keys, const Slic3r::StaticPrintConfig &defaults, const std::string &default_name) :
     m_type(type),
     m_edited_preset(type, "", false),
     m_idx_selected(0),
@@ -368,8 +405,7 @@ PresetCollection::PresetCollection(Preset::Type type, const std::vector<std::str
 	m_bitmap_cache(new GUI::BitmapCache)
 {
     // Insert just the default preset.
-    m_presets.emplace_back(Preset(type, "- default -", true));
-    m_presets.front().load(keys);
+    this->add_default_preset(keys, defaults, default_name);
     m_edited_preset.config.apply(m_presets.front().config);
 }
 
@@ -383,7 +419,7 @@ PresetCollection::~PresetCollection()
 
 void PresetCollection::reset(bool delete_files)
 {
-    if (m_presets.size() > 1) {
+    if (m_presets.size() > m_num_default_presets) {
         if (delete_files) {
             // Erase the preset files.
             for (Preset &preset : m_presets)
@@ -391,11 +427,19 @@ void PresetCollection::reset(bool delete_files)
                     boost::nowide::remove(preset.file.c_str());
         }
         // Don't use m_presets.resize() here as it requires a default constructor for Preset.
-        m_presets.erase(m_presets.begin() + 1, m_presets.end());
+        m_presets.erase(m_presets.begin() + m_num_default_presets, m_presets.end());
         this->select_preset(0);
     }
 }
 
+void PresetCollection::add_default_preset(const std::vector<std::string> &keys, const Slic3r::StaticPrintConfig &defaults, const std::string &preset_name)
+{
+    // Insert just the default preset.
+    m_presets.emplace_back(Preset(this->type(), preset_name, true));
+    m_presets.back().load(keys, defaults);
+    ++ m_num_default_presets;
+}
+
 // Load all presets found in dir_path.
 // Throws an exception on error.
 void PresetCollection::load_presets(const std::string &dir_path, const std::string &subdir)
@@ -418,14 +462,15 @@ void PresetCollection::load_presets(const std::string &dir_path, const std::stri
             try {
                 Preset preset(m_type, name, false);
                 preset.file = dir_entry.path().string();
-                preset.load(keys);
+                //FIXME One should initialize with SLAFullPrintConfig for the SLA profiles!
+                preset.load(keys, static_cast<const HostConfig&>(FullPrintConfig::defaults()));
                 m_presets.emplace_back(preset);
             } catch (const std::runtime_error &err) {
                 errors_cummulative += err.what();
                 errors_cummulative += "\n";
 			}
         }
-    std::sort(m_presets.begin() + 1, m_presets.end());
+    std::sort(m_presets.begin() + m_num_default_presets, m_presets.end());
     this->select_preset(first_visible_idx());
     if (! errors_cummulative.empty())
         throw std::runtime_error(errors_cummulative);
@@ -643,7 +688,7 @@ Preset* PresetCollection::find_preset(const std::string &name, bool first_visibl
 // Return index of the first visible preset. Certainly at least the '- default -' preset shall be visible.
 size_t PresetCollection::first_visible_idx() const
 {
-    size_t idx = m_default_suppressed ? 1 : 0;
+    size_t idx = m_default_suppressed ? m_num_default_presets : 0;
     for (; idx < this->m_presets.size(); ++ idx)
         if (m_presets[idx].is_visible)
             break;
@@ -656,7 +701,7 @@ void PresetCollection::set_default_suppressed(bool default_suppressed)
 {
     if (m_default_suppressed != default_suppressed) {
         m_default_suppressed = default_suppressed;
-        m_presets.front().is_visible = ! default_suppressed || (m_presets.size() > 1 && m_idx_selected > 0);
+        m_presets.front().is_visible = ! default_suppressed || (m_presets.size() > m_num_default_presets && m_idx_selected > 0);
     }
 }
 
@@ -664,9 +709,10 @@ size_t PresetCollection::update_compatible_with_printer_internal(const Preset &a
 {
     DynamicPrintConfig config;
     config.set_key_value("printer_preset", new ConfigOptionString(active_printer.name));
-    config.set_key_value("num_extruders", new ConfigOptionInt(
-        (int)static_cast<const ConfigOptionFloats*>(active_printer.config.option("nozzle_diameter"))->values.size()));
-    for (size_t idx_preset = 1; idx_preset < m_presets.size(); ++ idx_preset) {
+    const ConfigOption *opt = active_printer.config.option("nozzle_diameter");
+    if (opt)
+        config.set_key_value("num_extruders", new ConfigOptionInt((int)static_cast<const ConfigOptionFloats*>(opt)->values.size()));
+    for (size_t idx_preset = m_num_default_presets; idx_preset < m_presets.size(); ++ idx_preset) {
         bool    selected        = idx_preset == m_idx_selected;
         Preset &preset_selected = m_presets[idx_preset];
         Preset &preset_edited   = selected ? m_edited_preset : preset_selected;
@@ -707,7 +753,7 @@ void PresetCollection::update_platter_ui(wxBitmapComboBox *ui)
 	wxString selected = "";
 	if (!this->m_presets.front().is_visible)
 		ui->Append("------- " +_(L("System presets")) + " -------", wxNullBitmap);
-	for (size_t i = this->m_presets.front().is_visible ? 0 : 1; i < this->m_presets.size(); ++i) {
+	for (size_t i = this->m_presets.front().is_visible ? 0 : m_num_default_presets; i < this->m_presets.size(); ++i) {
         const Preset &preset = this->m_presets[i];
         if (! preset.is_visible || (! preset.is_compatible && i != m_idx_selected))
             continue;
@@ -745,7 +791,7 @@ void PresetCollection::update_platter_ui(wxBitmapComboBox *ui)
 			if (i == m_idx_selected)
 				selected = wxString::FromUTF8((preset.name + (preset.is_dirty ? g_suffix_modified : "")).c_str());
 		}
-		if (preset.is_default)
+		if (i + 1 == m_num_default_presets)
 			ui->Append("------- " + _(L("System presets")) + " -------", wxNullBitmap);
 	}
 	if (!nonsys_presets.empty())
@@ -775,7 +821,7 @@ size_t PresetCollection::update_tab_ui(wxBitmapComboBox *ui, bool show_incompati
 	wxString selected = "";
 	if (!this->m_presets.front().is_visible)
 		ui->Append("------- " + _(L("System presets")) + " -------", wxNullBitmap);
-	for (size_t i = this->m_presets.front().is_visible ? 0 : 1; i < this->m_presets.size(); ++i) {
+	for (size_t i = this->m_presets.front().is_visible ? 0 : m_num_default_presets; i < this->m_presets.size(); ++i) {
         const Preset &preset = this->m_presets[i];
         if (! preset.is_visible || (! show_incompatible && ! preset.is_compatible && i != m_idx_selected))
             continue;
@@ -805,7 +851,7 @@ size_t PresetCollection::update_tab_ui(wxBitmapComboBox *ui, bool show_incompati
 			if (i == m_idx_selected)
 				selected = wxString::FromUTF8((preset.name + (preset.is_dirty ? g_suffix_modified : "")).c_str());
 		}
-		if (preset.is_default)
+        if (i + 1 == m_num_default_presets)
 			ui->Append("------- " + _(L("System presets")) + " -------", wxNullBitmap);
     }
 	if (!nonsys_presets.empty())
@@ -853,11 +899,11 @@ bool PresetCollection::update_dirty_ui(wxBitmapComboBox *ui)
     return was_dirty != is_dirty;
 }
 
-std::vector<std::string> PresetCollection::dirty_options(const Preset *edited, const Preset *reference, const bool is_printer_type /*= false*/)
+std::vector<std::string> PresetCollection::dirty_options(const Preset *edited, const Preset *reference, const bool deep_compare /*= false*/)
 {
     std::vector<std::string> changed;
 	if (edited != nullptr && reference != nullptr) {
-        changed = is_printer_type  ? 
+        changed = deep_compare ?
 				reference->config.deep_diff(edited->config) :
 				reference->config.diff(edited->config);
         // The "compatible_printers" option key is handled differently from the others:
@@ -897,7 +943,7 @@ bool PresetCollection::select_preset_by_name(const std::string &name_w_suffix, b
         idx = it - m_presets.begin();
     else {
         // Find the first visible preset.
-        for (size_t i = m_default_suppressed ? 1 : 0; i < m_presets.size(); ++ i)
+        for (size_t i = m_default_suppressed ? m_num_default_presets : 0; i < m_presets.size(); ++ i)
             if (m_presets[i].is_visible) {
                 idx = i;
                 break;
@@ -939,7 +985,7 @@ std::vector<std::string> PresetCollection::merge_presets(PresetCollection &&othe
         if (preset.is_default || preset.is_external)
             continue;
         Preset key(m_type, preset.name);
-        auto it = std::lower_bound(m_presets.begin() + 1, m_presets.end(), key);
+        auto it = std::lower_bound(m_presets.begin() + m_num_default_presets, m_presets.end(), key);
         if (it == m_presets.end() || it->name != preset.name) {
             if (preset.vendor != nullptr) {
                 // Re-assign a pointer to the vendor structure in the new PresetBundle.
diff --git a/xs/src/slic3r/GUI/Preset.hpp b/xs/src/slic3r/GUI/Preset.hpp
index 0d00cae485..821d7dc543 100644
--- a/xs/src/slic3r/GUI/Preset.hpp
+++ b/xs/src/slic3r/GUI/Preset.hpp
@@ -52,6 +52,7 @@ public:
         PrinterModel() {}
         std::string                 id;
         std::string                 name;
+        PrinterTechnology           technology;
         std::vector<PrinterVariant> variants;
         PrinterVariant*       variant(const std::string &name) {
             for (auto &v : this->variants)
@@ -83,6 +84,7 @@ public:
         TYPE_INVALID,
         TYPE_PRINT,
         TYPE_FILAMENT,
+        TYPE_SLA_MATERIAL,
         TYPE_PRINTER,
     };
 
@@ -123,8 +125,7 @@ public:
     DynamicPrintConfig  config;
 
     // Load this profile for the following keys only.
-    // Throws std::runtime_error in case the file cannot be read.
-    DynamicPrintConfig& load(const std::vector<std::string> &keys);
+    DynamicPrintConfig& load(const std::vector<std::string> &keys, const StaticPrintConfig &defaults);
 
     void                save();
 
@@ -149,6 +150,10 @@ public:
     std::string&        compatible_printers_condition() { return Preset::compatible_printers_condition(this->config); }
     const std::string&  compatible_printers_condition() const { return Preset::compatible_printers_condition(const_cast<Preset*>(this)->config); }
 
+    static PrinterTechnology& printer_technology(DynamicPrintConfig &cfg) { return cfg.option<ConfigOptionEnum<PrinterTechnology>>("printer_technology", true)->value; }
+    PrinterTechnology&        printer_technology() { return Preset::printer_technology(this->config); }
+    const PrinterTechnology&  printer_technology() const { return Preset::printer_technology(const_cast<Preset*>(this)->config); }
+
     // Mark this preset as compatible if it is compatible with active_printer.
     bool                update_compatible_with_printer(const Preset &active_printer, const DynamicPrintConfig *extra_config);
 
@@ -167,6 +172,10 @@ public:
     static const std::vector<std::string>&  printer_options();
     // Nozzle options of the printer options.
     static const std::vector<std::string>&  nozzle_options();
+
+    static const std::vector<std::string>&  sla_printer_options();
+    static const std::vector<std::string>&  sla_material_options();
+
 	static void update_suffix_modified();
 
 protected:
@@ -184,15 +193,15 @@ class PresetCollection
 {
 public:
     // Initialize the PresetCollection with the "- default -" preset.
-    PresetCollection(Preset::Type type, const std::vector<std::string> &keys);
+    PresetCollection(Preset::Type type, const std::vector<std::string> &keys, const Slic3r::StaticPrintConfig &defaults, const std::string &default_name = "- default -");
     ~PresetCollection();
 
     typedef std::deque<Preset>::iterator Iterator;
     typedef std::deque<Preset>::const_iterator ConstIterator;
-    Iterator begin() { return m_presets.begin() + 1; }
-    ConstIterator begin() const { return m_presets.begin() + 1; }
-    Iterator end() { return m_presets.end(); }
-    ConstIterator end() const { return m_presets.end(); }
+    Iterator        begin() { return m_presets.begin() + m_num_default_presets; }
+    ConstIterator   begin() const { return m_presets.begin() + m_num_default_presets; }
+    Iterator        end() { return m_presets.end(); }
+    ConstIterator   end() const { return m_presets.end(); }
 
     void            reset(bool delete_files);
 
@@ -200,6 +209,9 @@ public:
     std::string     name() const;
     const std::deque<Preset>& operator()() const { return m_presets; }
 
+    // Add default preset at the start of the collection, increment the m_default_preset counter.
+    void            add_default_preset(const std::vector<std::string> &keys, const Slic3r::StaticPrintConfig &defaults, const std::string &preset_name);
+
     // Load ini files of the particular type from the provided directory path.
     void            load_presets(const std::string &dir_path, const std::string &subdir);
 
@@ -247,6 +259,8 @@ public:
     Preset&         get_selected_preset()       { return m_presets[m_idx_selected]; }
     const Preset&   get_selected_preset() const { return m_presets[m_idx_selected]; }
     int             get_selected_idx()    const { return m_idx_selected; }
+    // Returns the name of the selected preset, or an empty string if no preset is selected.
+    std::string     get_selected_preset_name() const { return (m_idx_selected == -1) ? std::string() : this->get_selected_preset().name; }
     // For the current edited preset, return the parent preset if there is one.
     // If there is no parent preset, nullptr is returned.
     // The parent preset may be a system preset or a user preset, which will be
@@ -283,7 +297,7 @@ public:
     template<typename PreferedCondition>
     size_t          first_compatible_idx(PreferedCondition prefered_condition) const
     {
-        size_t i = m_default_suppressed ? 1 : 0;
+        size_t i = m_default_suppressed ? m_num_default_presets : 0;
         size_t n = this->m_presets.size();
         size_t i_compatible = n;
         for (; i < n; ++ i)
@@ -309,7 +323,8 @@ public:
     const Preset&   first_compatible() const    { return this->preset(this->first_compatible_idx()); }
 
     // Return number of presets including the "- default -" preset.
-    size_t          size() const                { return this->m_presets.size(); }
+    size_t          size() const                { return m_presets.size(); }
+    bool            has_defaults_only() const   { return m_presets.size() <= m_num_default_presets; }
 
     // For Print / Filament presets, disable those, which are not compatible with the printer.
     template<typename PreferedCondition>
@@ -327,11 +342,11 @@ public:
     // Compare the content of get_selected_preset() with get_edited_preset() configs, return true if they differ.
     bool                        current_is_dirty() const { return ! this->current_dirty_options().empty(); }
     // Compare the content of get_selected_preset() with get_edited_preset() configs, return the list of keys where they differ.
-    std::vector<std::string>    current_dirty_options(const bool is_printer_type = false) const
-        { return dirty_options(&this->get_edited_preset(), &this->get_selected_preset(), is_printer_type); }
+    std::vector<std::string>    current_dirty_options(const bool deep_compare = false) const
+        { return dirty_options(&this->get_edited_preset(), &this->get_selected_preset(), deep_compare); }
     // Compare the content of get_selected_preset() with get_edited_preset() configs, return the list of keys where they differ.
-    std::vector<std::string>    current_different_from_parent_options(const bool is_printer_type = false) const
-        { return dirty_options(&this->get_edited_preset(), this->get_selected_preset_parent(), is_printer_type); }
+    std::vector<std::string>    current_different_from_parent_options(const bool deep_compare = false) const
+        { return dirty_options(&this->get_edited_preset(), this->get_selected_preset_parent(), deep_compare); }
 
     // Update the choice UI from the list of presets.
     // If show_incompatible, all presets are shown, otherwise only the compatible presets are shown.
@@ -374,8 +389,16 @@ private:
     std::deque<Preset>::iterator find_preset_internal(const std::string &name)
     {
         Preset key(m_type, name);
-        auto it = std::lower_bound(m_presets.begin() + 1, m_presets.end(), key);
-        return ((it == m_presets.end() || it->name != name) && m_presets.front().name == name) ? m_presets.begin() : it;
+        auto it = std::lower_bound(m_presets.begin() + m_num_default_presets, m_presets.end(), key);
+        if (it == m_presets.end() || it->name != name) {
+            // Preset has not been not found in the sorted list of non-default presets. Try the defaults.
+            for (size_t i = 0; i < m_num_default_presets; ++ i)
+                if (m_presets[i].name == name) {
+                    it = m_presets.begin() + i;
+                    break;
+                }
+        }
+        return it;
     }
     std::deque<Preset>::const_iterator find_preset_internal(const std::string &name) const
         { return const_cast<PresetCollection*>(this)->find_preset_internal(name); }
@@ -395,7 +418,8 @@ private:
     // Selected preset.
     int                     m_idx_selected;
     // Is the "- default -" preset suppressed?
-    bool                    m_default_suppressed = true;
+    bool                    m_default_suppressed  = true;
+    size_t                  m_num_default_presets = 0;
     // Compatible & incompatible marks, to be placed at the wxBitmapComboBox items of a Platter.
     // These bitmaps are not owned by PresetCollection, but by a PresetBundle.
     const wxBitmap         *m_bitmap_compatible   = nullptr;
diff --git a/xs/src/slic3r/GUI/PresetBundle.cpp b/xs/src/slic3r/GUI/PresetBundle.cpp
index 94baa0e0ef..cd3924dd0a 100644
--- a/xs/src/slic3r/GUI/PresetBundle.cpp
+++ b/xs/src/slic3r/GUI/PresetBundle.cpp
@@ -40,9 +40,10 @@ static std::vector<std::string> s_project_options {
 };
 
 PresetBundle::PresetBundle() :
-    prints(Preset::TYPE_PRINT, Preset::print_options()), 
-    filaments(Preset::TYPE_FILAMENT, Preset::filament_options()), 
-    printers(Preset::TYPE_PRINTER, Preset::printer_options()),
+    prints(Preset::TYPE_PRINT, Preset::print_options(), static_cast<const HostConfig&>(FullPrintConfig::defaults())), 
+    filaments(Preset::TYPE_FILAMENT, Preset::filament_options(), static_cast<const HostConfig&>(FullPrintConfig::defaults())), 
+    sla_materials(Preset::TYPE_SLA_MATERIAL, Preset::sla_material_options(), static_cast<const SLAMaterialConfig&>(SLAFullPrintConfig::defaults())), 
+    printers(Preset::TYPE_PRINTER, Preset::printer_options(), static_cast<const HostConfig&>(FullPrintConfig::defaults()), "- default FFF -"),
     m_bitmapCompatible(new wxBitmap),
     m_bitmapIncompatible(new wxBitmap),
     m_bitmapLock(new wxBitmap),
@@ -69,24 +70,35 @@ PresetBundle::PresetBundle() :
     this->filaments.default_preset().compatible_printers_condition();
     this->filaments.default_preset().inherits();
 
-    this->printers.default_preset().config.optptr("printer_settings_id", true);
-    this->printers.default_preset().config.optptr("printer_vendor", true);
-    this->printers.default_preset().config.optptr("printer_model", true);
-    this->printers.default_preset().config.optptr("printer_variant", true);
-    this->printers.default_preset().config.optptr("default_print_profile", true);
-    this->printers.default_preset().config.option<ConfigOptionStrings>("default_filament_profile", true)->values = { "" };
-	this->printers.default_preset().inherits();
+    this->sla_materials.default_preset().config.optptr("sla_material_settings_id", true);
+    this->sla_materials.default_preset().compatible_printers_condition();
+    this->sla_materials.default_preset().inherits();
+
+    this->printers.add_default_preset(Preset::sla_printer_options(), static_cast<const SLAMaterialConfig&>(SLAFullPrintConfig::defaults()), "- default SLA -");
+    this->printers.preset(1).printer_technology() = ptSLA;
+    for (size_t i = 0; i < 2; ++ i) {
+        Preset &preset = this->printers.preset(i);
+        preset.config.optptr("printer_settings_id", true);
+        preset.config.optptr("printer_vendor", true);
+        preset.config.optptr("printer_model", true);
+        preset.config.optptr("printer_variant", true);
+        preset.config.optptr("default_print_profile", true);
+        preset.config.option<ConfigOptionStrings>("default_filament_profile", true)->values = { "" };
+        preset.inherits();
+    }
 
 	// Load the default preset bitmaps.
-    this->prints   .load_bitmap_default("cog.png");
-    this->filaments.load_bitmap_default("spool.png");
-    this->printers .load_bitmap_default("printer_empty.png");
+    this->prints       .load_bitmap_default("cog.png");
+    this->filaments    .load_bitmap_default("spool.png");
+    this->sla_materials.load_bitmap_default("package_green.png");
+    this->printers     .load_bitmap_default("printer_empty.png");
     this->load_compatible_bitmaps();
 
     // Re-activate the default presets, so their "edited" preset copies will be updated with the additional configuration values above.
-    this->prints   .select_preset(0);
-    this->filaments.select_preset(0);
-    this->printers .select_preset(0);
+    this->prints       .select_preset(0);
+    this->filaments    .select_preset(0);
+    this->sla_materials.select_preset(0);
+    this->printers     .select_preset(0);
 
     this->project_config.apply_only(FullPrintConfig::defaults(), s_project_options);
 }
@@ -113,13 +125,15 @@ void PresetBundle::reset(bool delete_files)
 {
     // Clear the existing presets, delete their respective files.
     this->vendors.clear();
-    this->prints   .reset(delete_files);
-    this->filaments.reset(delete_files);
-    this->printers .reset(delete_files);
+    this->prints       .reset(delete_files);
+    this->filaments    .reset(delete_files);
+    this->sla_materials.reset(delete_files);
+    this->printers     .reset(delete_files);
     this->filament_presets.clear();
-    this->filament_presets.emplace_back(this->filaments.get_selected_preset().name);
+    this->filament_presets.emplace_back(this->filaments.get_selected_preset_name());
     this->obsolete_presets.prints.clear();
     this->obsolete_presets.filaments.clear();
+    this->obsolete_presets.sla_materials.clear();
     this->obsolete_presets.printers.clear();
 }
 
@@ -135,11 +149,13 @@ void PresetBundle::setup_directories()
         data_dir / "presets", 
         data_dir / "presets" / "print", 
         data_dir / "presets" / "filament", 
+        data_dir / "presets" / "sla_material", 
         data_dir / "presets" / "printer" 
 #else
         // Store the print/filament/printer presets at the same location as the upstream Slic3r.
         data_dir / "print", 
         data_dir / "filament", 
+        data_dir / "sla_material", 
         data_dir / "printer" 
 #endif
     };
@@ -175,6 +191,11 @@ void PresetBundle::load_presets(const AppConfig &config)
     } catch (const std::runtime_error &err) {
         errors_cummulative += err.what();
     }
+    try {
+        this->sla_materials.load_presets(dir_user_presets, "sla_material");
+    } catch (const std::runtime_error &err) {
+        errors_cummulative += err.what();
+    }
     try {
         this->printers.load_presets(dir_user_presets, "printer");
     } catch (const std::runtime_error &err) {
@@ -238,13 +259,16 @@ std::string PresetBundle::load_system_presets()
 std::vector<std::string> PresetBundle::merge_presets(PresetBundle &&other)
 {
     this->vendors.insert(other.vendors.begin(), other.vendors.end());
-    std::vector<std::string> duplicate_prints    = this->prints   .merge_presets(std::move(other.prints),    this->vendors);
-    std::vector<std::string> duplicate_filaments = this->filaments.merge_presets(std::move(other.filaments), this->vendors);
-    std::vector<std::string> duplicate_printers  = this->printers .merge_presets(std::move(other.printers),  this->vendors);
-	append(this->obsolete_presets.prints,    std::move(other.obsolete_presets.prints));
-	append(this->obsolete_presets.filaments, std::move(other.obsolete_presets.filaments));
-	append(this->obsolete_presets.printers,  std::move(other.obsolete_presets.printers));
+    std::vector<std::string> duplicate_prints        = this->prints       .merge_presets(std::move(other.prints),        this->vendors);
+    std::vector<std::string> duplicate_filaments     = this->filaments    .merge_presets(std::move(other.filaments),     this->vendors);
+    std::vector<std::string> duplicate_sla_materials = this->sla_materials.merge_presets(std::move(other.sla_materials), this->vendors);
+    std::vector<std::string> duplicate_printers      = this->printers     .merge_presets(std::move(other.printers),      this->vendors);
+	append(this->obsolete_presets.prints,        std::move(other.obsolete_presets.prints));
+	append(this->obsolete_presets.filaments,     std::move(other.obsolete_presets.filaments));
+    append(this->obsolete_presets.sla_materials, std::move(other.obsolete_presets.sla_materials));
+	append(this->obsolete_presets.printers,      std::move(other.obsolete_presets.printers));
 	append(duplicate_prints, std::move(duplicate_filaments));
+    append(duplicate_prints, std::move(duplicate_sla_materials));
     append(duplicate_prints, std::move(duplicate_printers));
     return duplicate_prints;
 }
@@ -275,9 +299,10 @@ void PresetBundle::load_selections(const AppConfig &config)
 	this->load_installed_printers(config);
 
     // Parse the initial print / filament / printer profile names.
-    std::string initial_print_profile_name    = remove_ini_suffix(config.get("presets", "print"));
-    std::string initial_filament_profile_name = remove_ini_suffix(config.get("presets", "filament"));
-	std::string initial_printer_profile_name  = remove_ini_suffix(config.get("presets", "printer"));
+    std::string initial_print_profile_name        = remove_ini_suffix(config.get("presets", "print"));
+    std::string initial_filament_profile_name     = remove_ini_suffix(config.get("presets", "filament"));
+    std::string initial_sla_material_profile_name = remove_ini_suffix(config.get("presets", "sla_material"));
+	std::string initial_printer_profile_name      = remove_ini_suffix(config.get("presets", "printer"));
 
 	// Activate print / filament / printer profiles from the config.
 	// If the printer profile enumerated by the config are not visible, select an alternate preset.
@@ -285,21 +310,24 @@ void PresetBundle::load_selections(const AppConfig &config)
     // will be selected by the following call of this->update_compatible_with_printer(true).
     prints.select_preset_by_name_strict(initial_print_profile_name);
     filaments.select_preset_by_name_strict(initial_filament_profile_name);
+    sla_materials.select_preset_by_name_strict(initial_sla_material_profile_name);
     printers.select_preset_by_name(initial_printer_profile_name, true);
 
-    // Load the names of the other filament profiles selected for a multi-material printer.
-    auto   *nozzle_diameter = dynamic_cast<const ConfigOptionFloats*>(printers.get_selected_preset().config.option("nozzle_diameter"));
-    size_t  num_extruders = nozzle_diameter->values.size();
-    this->filament_presets = { initial_filament_profile_name };
-    for (unsigned int i = 1; i < (unsigned int)num_extruders; ++ i) {
-        char name[64];
-        sprintf(name, "filament_%d", i);
-        if (! config.has("presets", name))
-            break;
-        this->filament_presets.emplace_back(remove_ini_suffix(config.get("presets", name)));
+    if (printers.get_selected_preset().printer_technology() == ptFFF){
+        // Load the names of the other filament profiles selected for a multi-material printer.
+        auto   *nozzle_diameter = dynamic_cast<const ConfigOptionFloats*>(printers.get_selected_preset().config.option("nozzle_diameter"));
+        size_t  num_extruders = nozzle_diameter->values.size();
+        this->filament_presets = { initial_filament_profile_name };
+        for (unsigned int i = 1; i < (unsigned int)num_extruders; ++i) {
+            char name[64];
+            sprintf(name, "filament_%d", i);
+            if (!config.has("presets", name))
+                break;
+            this->filament_presets.emplace_back(remove_ini_suffix(config.get("presets", name)));
+        }
+        // Do not define the missing filaments, so that the update_compatible_with_printer() will use the preferred filaments.
+        this->filament_presets.resize(num_extruders, "");
     }
-    // Do not define the missing filaments, so that the update_compatible_with_printer() will use the preferred filaments.
-    this->filament_presets.resize(num_extruders, "");
 
     // Update visibility of presets based on their compatibility with the active printer.
     // Always try to select a compatible print and filament preset to the current printer preset,
@@ -313,25 +341,33 @@ void PresetBundle::load_selections(const AppConfig &config)
 void PresetBundle::export_selections(AppConfig &config)
 {
     assert(filament_presets.size() >= 1);
-    assert(filament_presets.size() > 1 || filaments.get_selected_preset().name == filament_presets.front());
+    assert(filament_presets.size() > 1 || filaments.get_selected_preset_name() == filament_presets.front());
     config.clear_section("presets");
-    config.set("presets", "print",    prints.get_selected_preset().name);
-    config.set("presets", "filament", filament_presets.front());
+    config.set("presets", "print",        prints.get_selected_preset_name());
+    config.set("presets", "filament",     filament_presets.front());
 	for (int i = 1; i < filament_presets.size(); ++i) {
         char name[64];
         sprintf(name, "filament_%d", i);
         config.set("presets", name, filament_presets[i]);
     }
-    config.set("presets", "printer",  printers.get_selected_preset().name);
+    config.set("presets", "sla_material", sla_materials.get_selected_preset_name());
+    config.set("presets", "printer",  printers.get_selected_preset_name());
 }
 
 void PresetBundle::export_selections(PlaceholderParser &pp)
 {
     assert(filament_presets.size() >= 1);
-    assert(filament_presets.size() > 1 || filaments.get_selected_preset().name == filament_presets.front());
-    pp.set("print_preset",    prints.get_selected_preset().name);
-    pp.set("filament_preset", filament_presets);
-    pp.set("printer_preset",  printers.get_selected_preset().name);
+    assert(filament_presets.size() > 1 || filaments.get_selected_preset_name() == filament_presets.front());
+    switch (printers.get_edited_preset().printer_technology()) {
+    case ptFFF:
+        pp.set("print_preset",        prints.get_selected_preset().name);
+        pp.set("filament_preset",     filament_presets);
+        break;
+    case ptSLA:
+        pp.set("sla_material_preset", sla_materials.get_selected_preset().name);
+        break;
+    }
+    pp.set("printer_preset",      printers.get_selected_preset().name);
 }
 
 bool PresetBundle::load_compatible_bitmaps()
@@ -349,32 +385,43 @@ bool PresetBundle::load_compatible_bitmaps()
     bool loaded_lock_open = m_bitmapLockOpen->LoadFile(
         wxString::FromUTF8(Slic3r::var(path_bitmap_lock_open).c_str()), wxBITMAP_TYPE_PNG);
     if (loaded_compatible) {
-        prints   .set_bitmap_compatible(m_bitmapCompatible);
-        filaments.set_bitmap_compatible(m_bitmapCompatible);
+        prints       .set_bitmap_compatible(m_bitmapCompatible);
+        filaments    .set_bitmap_compatible(m_bitmapCompatible);
+        sla_materials.set_bitmap_compatible(m_bitmapCompatible);
 //        printers .set_bitmap_compatible(m_bitmapCompatible);
     }
     if (loaded_incompatible) {
-        prints   .set_bitmap_incompatible(m_bitmapIncompatible);
-        filaments.set_bitmap_incompatible(m_bitmapIncompatible);
-//        printers .set_bitmap_incompatible(m_bitmapIncompatible);        
+        prints       .set_bitmap_incompatible(m_bitmapIncompatible);
+        filaments    .set_bitmap_incompatible(m_bitmapIncompatible);
+        sla_materials.set_bitmap_incompatible(m_bitmapIncompatible);
+//        printers .set_bitmap_incompatible(m_bitmapIncompatible);
     }
     if (loaded_lock) {
-        prints   .set_bitmap_lock(m_bitmapLock);
-        filaments.set_bitmap_lock(m_bitmapLock);
-        printers .set_bitmap_lock(m_bitmapLock);
+        prints       .set_bitmap_lock(m_bitmapLock);
+        filaments    .set_bitmap_lock(m_bitmapLock);
+        sla_materials.set_bitmap_lock(m_bitmapLock);
+        printers     .set_bitmap_lock(m_bitmapLock);
     }
     if (loaded_lock_open) {
-        prints   .set_bitmap_lock_open(m_bitmapLock);
-        filaments.set_bitmap_lock_open(m_bitmapLock);
-        printers .set_bitmap_lock_open(m_bitmapLock);
+        prints       .set_bitmap_lock_open(m_bitmapLock);
+        filaments    .set_bitmap_lock_open(m_bitmapLock);
+        sla_materials.set_bitmap_lock_open(m_bitmapLock);
+        printers     .set_bitmap_lock_open(m_bitmapLock);
     }
     return loaded_compatible && loaded_incompatible && loaded_lock && loaded_lock_open;
 }
 
 DynamicPrintConfig PresetBundle::full_config() const
+{
+    return (this->printers.get_edited_preset().printer_technology() == ptFFF) ?
+        this->full_fff_config() :
+        this->full_sla_config();
+}
+
+DynamicPrintConfig PresetBundle::full_fff_config() const
 {    
     DynamicPrintConfig out;
-    out.apply(FullPrintConfig());
+    out.apply(FullPrintConfig::defaults());
     out.apply(this->prints.get_edited_preset().config);
     // Add the default filament preset to have the "filament_preset_id" defined.
 	out.apply(this->filaments.default_preset().config);
@@ -466,6 +513,48 @@ DynamicPrintConfig PresetBundle::full_config() const
     return out;
 }
 
+DynamicPrintConfig PresetBundle::full_sla_config() const
+{    
+    DynamicPrintConfig out;
+    out.apply(SLAFullPrintConfig::defaults());
+    out.apply(this->sla_materials.get_edited_preset().config);
+    out.apply(this->printers.get_edited_preset().config);
+    // There are no project configuration values as of now, the project_config is reserved for FFF printers.
+//    out.apply(this->project_config);
+
+    // Collect the "compatible_printers_condition" and "inherits" values over all presets (sla_materials, printers) into a single vector.
+    std::vector<std::string> compatible_printers_condition;
+    std::vector<std::string> inherits;
+    compatible_printers_condition.emplace_back(this->/*prints*/sla_materials.get_edited_preset().compatible_printers_condition());
+    inherits                     .emplace_back(this->/*prints*/sla_materials.get_edited_preset().inherits());
+    inherits                     .emplace_back(this->printers.get_edited_preset().inherits());
+
+    // These two value types clash between the print and filament profiles. They should be renamed.
+    out.erase("compatible_printers");
+    out.erase("compatible_printers_condition");
+    out.erase("inherits");
+    
+    out.option<ConfigOptionString >("sla_material_settings_id", true)->value  = this->sla_materials.get_selected_preset().name;
+    out.option<ConfigOptionString >("printer_settings_id",      true)->value  = this->printers.get_selected_preset().name;
+
+    // Serialize the collected "compatible_printers_condition" and "inherits" fields.
+    // There will be 1 + num_exturders fields for "inherits" and 2 + num_extruders for "compatible_printers_condition" stored.
+    // The vector will not be stored if all fields are empty strings.
+    auto add_if_some_non_empty = [&out](std::vector<std::string> &&values, const std::string &key) {
+        bool nonempty = false;
+        for (const std::string &v : values)
+            if (! v.empty()) {
+                nonempty = true;
+                break;
+            }
+        if (nonempty)
+            out.set_key_value(key, new ConfigOptionStrings(std::move(values)));
+    };
+    add_if_some_non_empty(std::move(compatible_printers_condition), "compatible_printers_condition_cummulative");
+    add_if_some_non_empty(std::move(inherits),                      "inherits_cummulative");
+    return out;
+}
+
 // Load an external config file containing the print, filament and printer presets.
 // Instead of a config file, a G-code may be loaded containing the full set of parameters.
 // In the future the configuration will likely be read from an AMF file as well.
@@ -530,6 +619,8 @@ void PresetBundle::load_config_string(const char* str, const char* source_filena
 // Load a config file from a boost property_tree. This is a private method called from load_config_file.
 void PresetBundle::load_config_file_config(const std::string &name_or_path, bool is_external, DynamicPrintConfig &&config)
 {
+    PrinterTechnology printer_technology = Preset::printer_technology(config);
+
     // The "compatible_printers" field should not have been exported into a config.ini or a G-code anyway, 
     // but some of the alpha versions of Slic3r did.
     {
@@ -541,8 +632,10 @@ void PresetBundle::load_config_file_config(const std::string &name_or_path, bool
         }
     }
 
-    size_t num_extruders = std::min(config.option<ConfigOptionFloats>("nozzle_diameter"  )->values.size(), 
-                                    config.option<ConfigOptionFloats>("filament_diameter")->values.size());
+    size_t num_extruders = (printer_technology == ptFFF) ?
+        std::min(config.option<ConfigOptionFloats>("nozzle_diameter"  )->values.size(), 
+                 config.option<ConfigOptionFloats>("filament_diameter")->values.size()) :
+        0;
     // Make a copy of the "compatible_printers_condition_cummulative" and "inherits_cummulative" vectors, which 
     // accumulate values over all presets (print, filaments, printers).
     // These values will be distributed into their particular presets when loading.
@@ -553,7 +646,8 @@ void PresetBundle::load_config_file_config(const std::string &name_or_path, bool
     compatible_printers_condition_values.resize(num_extruders + 2, std::string());
     inherits_values.resize(num_extruders + 2, std::string());
     // The "default_filament_profile" will be later extracted into the printer profile.
-    config.option<ConfigOptionStrings>("default_filament_profile", true)->values.resize(num_extruders, std::string());
+    if (printer_technology == ptFFF)
+        config.option<ConfigOptionStrings>("default_filament_profile", true)->values.resize(num_extruders, std::string());
 
     // 1) Create a name from the file name.
     // Keep the suffix (.ini, .gcode, .amf, .3mf etc) to differentiate it from the normal profiles.
@@ -562,81 +656,83 @@ void PresetBundle::load_config_file_config(const std::string &name_or_path, bool
     // 2) If the loading succeeded, split and load the config into print / filament / printer settings.
     // First load the print and printer presets.
     for (size_t i_group = 0; i_group < 2; ++ i_group) {
-        PresetCollection &presets = (i_group == 0) ? this->prints : this->printers;
+        PresetCollection &presets = (i_group == 0) ? ((printer_technology == ptFFF) ? this->prints : this->sla_materials) : this->printers;
         // Split the "compatible_printers_condition" and "inherits" values one by one from a single vector to the print & printer profiles.
         size_t idx = (i_group == 0) ? 0 : num_extruders + 1;
         inherits                      = inherits_values[idx];
         compatible_printers_condition = compatible_printers_condition_values[idx];
 		if (is_external)
             presets.load_external_preset(name_or_path, name,
-                config.opt_string((i_group == 0) ? "print_settings_id" : "printer_settings_id", true), 
+                config.opt_string((i_group == 0) ? ((printer_technology == ptFFF) ? "print_settings_id" : "sla_material_id") :  "printer_settings_id", true),
                 config);
         else
             presets.load_preset(presets.path_from_name(name), name, config).save();
     }
 
-    // 3) Now load the filaments. If there are multiple filament presets, split them and load them.
-    auto old_filament_profile_names = config.option<ConfigOptionStrings>("filament_settings_id", true);
-	old_filament_profile_names->values.resize(num_extruders, std::string());
+    if (Preset::printer_technology(config) == ptFFF) {
+        // 3) Now load the filaments. If there are multiple filament presets, split them and load them.
+        auto old_filament_profile_names = config.option<ConfigOptionStrings>("filament_settings_id", true);
+    	old_filament_profile_names->values.resize(num_extruders, std::string());
 
-    if (num_extruders <= 1) {
-        // Split the "compatible_printers_condition" and "inherits" from the cummulative vectors to separate filament presets.
-        inherits                      = inherits_values[1];
-        compatible_printers_condition = compatible_printers_condition_values[1];
-        if (is_external)
-            this->filaments.load_external_preset(name_or_path, name, old_filament_profile_names->values.front(), config);
-        else
-            this->filaments.load_preset(this->filaments.path_from_name(name), name, config).save();
-        this->filament_presets.clear();
-        this->filament_presets.emplace_back(name);
-    } else {
-        // Split the filament presets, load each of them separately.
-        std::vector<DynamicPrintConfig> configs(num_extruders, this->filaments.default_preset().config);
-        // loop through options and scatter them into configs.
-        for (const t_config_option_key &key : this->filaments.default_preset().config.keys()) {
-            const ConfigOption *other_opt = config.option(key);
-            if (other_opt == nullptr)
-                continue;
-            if (other_opt->is_scalar()) {
-                for (size_t i = 0; i < configs.size(); ++ i)
-                    configs[i].option(key, false)->set(other_opt);
-            } else if (key != "compatible_printers") {
-                for (size_t i = 0; i < configs.size(); ++ i)
-                    static_cast<ConfigOptionVectorBase*>(configs[i].option(key, false))->set_at(other_opt, 0, i);
-            }
-        }
-        // Load the configs into this->filaments and make them active.
-        this->filament_presets.clear();
-        for (size_t i = 0; i < configs.size(); ++ i) {
-            DynamicPrintConfig &cfg = configs[i];
+        if (num_extruders <= 1) {
             // Split the "compatible_printers_condition" and "inherits" from the cummulative vectors to separate filament presets.
-            cfg.opt_string("compatible_printers_condition", true) = compatible_printers_condition_values[i + 1];
-            cfg.opt_string("inherits", true)                      = inherits_values[i + 1];
-            // Load all filament presets, but only select the first one in the preset dialog.
-            Preset *loaded = nullptr;
+            inherits                      = inherits_values[1];
+            compatible_printers_condition = compatible_printers_condition_values[1];
             if (is_external)
-                loaded = &this->filaments.load_external_preset(name_or_path, name,
-                    (i < old_filament_profile_names->values.size()) ? old_filament_profile_names->values[i] : "",
-                    std::move(cfg), i == 0);
-            else {
-                // Used by the config wizard when creating a custom setup.
-                // Therefore this block should only be called for a single extruder.
-                char suffix[64];
-                if (i == 0)
-                    suffix[0] = 0;
-                else
-                    sprintf(suffix, "%d", i);
-                std::string new_name = name + suffix;
-                loaded = &this->filaments.load_preset(this->filaments.path_from_name(new_name),
-                    new_name, std::move(cfg), i == 0);
-                loaded->save();
+                this->filaments.load_external_preset(name_or_path, name, old_filament_profile_names->values.front(), config);
+            else
+                this->filaments.load_preset(this->filaments.path_from_name(name), name, config).save();
+            this->filament_presets.clear();
+            this->filament_presets.emplace_back(name);
+        } else {
+            // Split the filament presets, load each of them separately.
+            std::vector<DynamicPrintConfig> configs(num_extruders, this->filaments.default_preset().config);
+            // loop through options and scatter them into configs.
+            for (const t_config_option_key &key : this->filaments.default_preset().config.keys()) {
+                const ConfigOption *other_opt = config.option(key);
+                if (other_opt == nullptr)
+                    continue;
+                if (other_opt->is_scalar()) {
+                    for (size_t i = 0; i < configs.size(); ++ i)
+                        configs[i].option(key, false)->set(other_opt);
+                } else if (key != "compatible_printers") {
+                    for (size_t i = 0; i < configs.size(); ++ i)
+                        static_cast<ConfigOptionVectorBase*>(configs[i].option(key, false))->set_at(other_opt, 0, i);
+                }
+            }
+            // Load the configs into this->filaments and make them active.
+            this->filament_presets.clear();
+            for (size_t i = 0; i < configs.size(); ++ i) {
+                DynamicPrintConfig &cfg = configs[i];
+                // Split the "compatible_printers_condition" and "inherits" from the cummulative vectors to separate filament presets.
+                cfg.opt_string("compatible_printers_condition", true) = compatible_printers_condition_values[i + 1];
+                cfg.opt_string("inherits", true)                      = inherits_values[i + 1];
+                // Load all filament presets, but only select the first one in the preset dialog.
+                Preset *loaded = nullptr;
+                if (is_external)
+                    loaded = &this->filaments.load_external_preset(name_or_path, name,
+                        (i < old_filament_profile_names->values.size()) ? old_filament_profile_names->values[i] : "",
+                        std::move(cfg), i == 0);
+                else {
+                    // Used by the config wizard when creating a custom setup.
+                    // Therefore this block should only be called for a single extruder.
+                    char suffix[64];
+                    if (i == 0)
+                        suffix[0] = 0;
+                    else
+                        sprintf(suffix, "%d", i);
+                    std::string new_name = name + suffix;
+                    loaded = &this->filaments.load_preset(this->filaments.path_from_name(new_name),
+                        new_name, std::move(cfg), i == 0);
+                    loaded->save();
+                }
+                this->filament_presets.emplace_back(loaded->name);
             }
-            this->filament_presets.emplace_back(loaded->name);
         }
-    }
 
-    // 4) Load the project config values (the per extruder wipe matrix etc).
-    this->project_config.apply_only(config, s_project_options);
+        // 4) Load the project config values (the per extruder wipe matrix etc).
+        this->project_config.apply_only(config, s_project_options);
+    }
 
     this->update_compatible_with_printer(false);
 }
@@ -691,9 +787,10 @@ void PresetBundle::load_config_file_config_bundle(const std::string &path, const
         collection_dst.load_preset(path, preset_name_dst, std::move(preset_src->config), activate).is_external = true;
         return preset_name_dst;
     };
-    load_one(this->prints,    tmp_bundle.prints,    tmp_bundle.prints   .get_selected_preset().name, true);
-    load_one(this->filaments, tmp_bundle.filaments, tmp_bundle.filaments.get_selected_preset().name, true);
-    load_one(this->printers,  tmp_bundle.printers,  tmp_bundle.printers .get_selected_preset().name, true);
+    load_one(this->prints,        tmp_bundle.prints,        tmp_bundle.prints       .get_selected_preset().name, true);
+    load_one(this->filaments,     tmp_bundle.filaments,     tmp_bundle.filaments    .get_selected_preset().name, true);
+    load_one(this->sla_materials, tmp_bundle.sla_materials, tmp_bundle.sla_materials.get_selected_preset().name, true);
+    load_one(this->printers,      tmp_bundle.printers,      tmp_bundle.printers     .get_selected_preset().name, true);
     this->update_multi_material_filament_presets();
     for (size_t i = 1; i < std::min(tmp_bundle.filament_presets.size(), this->filament_presets.size()); ++ i)
         this->filament_presets[i] = load_one(this->filaments, tmp_bundle.filaments, tmp_bundle.filament_presets[i], false);
@@ -817,6 +914,7 @@ static void flatten_configbundle_hierarchy(boost::property_tree::ptree &tree)
 {
     flatten_configbundle_hierarchy(tree, "print");
     flatten_configbundle_hierarchy(tree, "filament");
+    flatten_configbundle_hierarchy(tree, "sla_material");
     flatten_configbundle_hierarchy(tree, "printer");
 }
 
@@ -853,9 +951,11 @@ size_t PresetBundle::load_configbundle(const std::string &path, unsigned int fla
     // Parse the obsolete preset names, to be deleted when upgrading from the old configuration structure.
     std::vector<std::string> loaded_prints;
     std::vector<std::string> loaded_filaments;
+    std::vector<std::string> loaded_sla_materials;
     std::vector<std::string> loaded_printers;
     std::string              active_print;
     std::vector<std::string> active_filaments;
+    std::string              active_sla_material;
     std::string              active_printer;
     size_t                   presets_loaded = 0;
     for (const auto &section : tree) {
@@ -870,6 +970,10 @@ size_t PresetBundle::load_configbundle(const std::string &path, unsigned int fla
             presets = &this->filaments;
             loaded  = &loaded_filaments;
             preset_name = section.first.substr(9);
+        } else if (boost::starts_with(section.first, "sla_material:")) {
+            presets = &this->sla_materials;
+            loaded  = &loaded_sla_materials;
+            preset_name = section.first.substr(9);
         } else if (boost::starts_with(section.first, "printer:")) {
             presets = &this->printers;
             loaded  = &loaded_printers;
@@ -886,6 +990,8 @@ size_t PresetBundle::load_configbundle(const std::string &path, unsigned int fla
                             active_filaments.resize(idx + 1, std::string());
                         active_filaments[idx] = kvp.second.data();
                     }
+                } else if (kvp.first == "sla_material") {
+                    active_sla_material = kvp.second.data();
                 } else if (kvp.first == "printer") {
                     active_printer = kvp.second.data();
                 }
@@ -899,6 +1005,8 @@ size_t PresetBundle::load_configbundle(const std::string &path, unsigned int fla
                     dst = &this->obsolete_presets.prints;
                 else if (kvp.first == "filament")
                     dst = &this->obsolete_presets.filaments;
+                else if (kvp.first == "sla_material")
+                    dst = &this->obsolete_presets.sla_materials;
                 else if (kvp.first == "printer")
                     dst = &this->obsolete_presets.printers;
                 if (dst)
@@ -999,6 +1107,8 @@ size_t PresetBundle::load_configbundle(const std::string &path, unsigned int fla
     if ((flags & LOAD_CFGBNDLE_SYSTEM) == 0) {
         if (! active_print.empty()) 
             prints.select_preset_by_name(active_print, true);
+        if (! active_sla_material.empty()) 
+            sla_materials.select_preset_by_name(active_sla_material, true);
         if (! active_printer.empty())
             printers.select_preset_by_name(active_printer, true);
         // Activate the first filament preset.
@@ -1015,6 +1125,9 @@ size_t PresetBundle::load_configbundle(const std::string &path, unsigned int fla
 
 void PresetBundle::update_multi_material_filament_presets()
 {
+    if (printers.get_edited_preset().printer_technology() != ptFFF)
+        return;
+
     // Verify and select the filament presets.
     auto   *nozzle_diameter = static_cast<const ConfigOptionFloats*>(printers.get_edited_preset().config.option("nozzle_diameter"));
     size_t  num_extruders   = nozzle_diameter->values.size();
@@ -1055,36 +1168,51 @@ void PresetBundle::update_multi_material_filament_presets()
 void PresetBundle::update_compatible_with_printer(bool select_other_if_incompatible)
 {
     const Preset                   &printer_preset             = this->printers.get_edited_preset();
-    const std::string              &prefered_print_profile     = printer_preset.config.opt_string("default_print_profile");
-    const std::vector<std::string> &prefered_filament_profiles = printer_preset.config.option<ConfigOptionStrings>("default_filament_profile")->values;
-    prefered_print_profile.empty() ?
-        this->prints.update_compatible_with_printer(printer_preset, select_other_if_incompatible) :
-        this->prints.update_compatible_with_printer(printer_preset, select_other_if_incompatible,
-            [&prefered_print_profile](const std::string& profile_name){ return profile_name == prefered_print_profile; });
-    prefered_filament_profiles.empty() ?
-        this->filaments.update_compatible_with_printer(printer_preset, select_other_if_incompatible) :
-        this->filaments.update_compatible_with_printer(printer_preset, select_other_if_incompatible,
-            [&prefered_filament_profiles](const std::string& profile_name)
-                { return std::find(prefered_filament_profiles.begin(), prefered_filament_profiles.end(), profile_name) != prefered_filament_profiles.end(); });
-    if (select_other_if_incompatible) {
-        // Verify validity of the current filament presets.
-        this->filament_presets.front() = this->filaments.get_edited_preset().name;
-        for (size_t idx = 1; idx < this->filament_presets.size(); ++ idx) {
-            std::string &filament_name = this->filament_presets[idx];
-            Preset      *preset        = this->filaments.find_preset(filament_name, false);
-            if (preset == nullptr || ! preset->is_compatible) {
-                // Pick a compatible profile. If there are prefered_filament_profiles, use them.
-                if (prefered_filament_profiles.empty())
-                    filament_name = this->filaments.first_compatible().name;
-                else {
-                    const std::string &preferred = (idx < prefered_filament_profiles.size()) ? 
-                        prefered_filament_profiles[idx] : prefered_filament_profiles.front();
-                    filament_name = this->filaments.first_compatible(
-                        [&preferred](const std::string& profile_name){ return profile_name == preferred; }).name;
+
+    switch (printers.get_edited_preset().printer_technology()) {
+    case ptFFF:
+    {
+        const std::string              &prefered_print_profile     = printer_preset.config.opt_string("default_print_profile");
+        const std::vector<std::string> &prefered_filament_profiles = printer_preset.config.option<ConfigOptionStrings>("default_filament_profile")->values;
+        prefered_print_profile.empty() ?
+            this->prints.update_compatible_with_printer(printer_preset, select_other_if_incompatible) :
+            this->prints.update_compatible_with_printer(printer_preset, select_other_if_incompatible,
+                [&prefered_print_profile](const std::string& profile_name){ return profile_name == prefered_print_profile; });
+        prefered_filament_profiles.empty() ?
+            this->filaments.update_compatible_with_printer(printer_preset, select_other_if_incompatible) :
+            this->filaments.update_compatible_with_printer(printer_preset, select_other_if_incompatible,
+                [&prefered_filament_profiles](const std::string& profile_name)
+                    { return std::find(prefered_filament_profiles.begin(), prefered_filament_profiles.end(), profile_name) != prefered_filament_profiles.end(); });
+        if (select_other_if_incompatible) {
+            // Verify validity of the current filament presets.
+            this->filament_presets.front() = this->filaments.get_edited_preset().name;
+            for (size_t idx = 1; idx < this->filament_presets.size(); ++ idx) {
+                std::string &filament_name = this->filament_presets[idx];
+                Preset      *preset        = this->filaments.find_preset(filament_name, false);
+                if (preset == nullptr || ! preset->is_compatible) {
+                    // Pick a compatible profile. If there are prefered_filament_profiles, use them.
+                    if (prefered_filament_profiles.empty())
+                        filament_name = this->filaments.first_compatible().name;
+                    else {
+                        const std::string &preferred = (idx < prefered_filament_profiles.size()) ? 
+                            prefered_filament_profiles[idx] : prefered_filament_profiles.front();
+                        filament_name = this->filaments.first_compatible(
+                            [&preferred](const std::string& profile_name){ return profile_name == preferred; }).name;
+                    }
                 }
             }
         }
     }
+    case ptSLA:
+    {
+        const std::string              &prefered_print_profile     = printer_preset.config.opt_string("default_print_profile");
+        const std::vector<std::string> &prefered_filament_profiles = printer_preset.config.option<ConfigOptionStrings>("default_filament_profile")->values;
+        prefered_print_profile.empty() ?
+            this->sla_materials.update_compatible_with_printer(printer_preset, select_other_if_incompatible) :
+			this->sla_materials.update_compatible_with_printer(printer_preset, select_other_if_incompatible,
+                [&prefered_print_profile](const std::string& profile_name){ return profile_name == prefered_print_profile; });        
+    }
+    }
 }
 
 void PresetBundle::export_configbundle(const std::string &path) //, const DynamicPrintConfig &settings
@@ -1111,6 +1239,7 @@ void PresetBundle::export_configbundle(const std::string &path) //, const Dynami
     // Export the names of the active presets.
     c << std::endl << "[presets]" << std::endl;
     c << "print = " << this->prints.get_selected_preset().name << std::endl;
+    c << "sla_material = " << this->sla_materials.get_selected_preset().name << std::endl;
     c << "printer = " << this->printers.get_selected_preset().name << std::endl;
     for (size_t i = 0; i < this->filament_presets.size(); ++ i) {
         char suffix[64];
@@ -1170,7 +1299,7 @@ bool PresetBundle::parse_color(const std::string &scolor, unsigned char *rgb_out
 
 void PresetBundle::update_platter_filament_ui(unsigned int idx_extruder, wxBitmapComboBox *ui)
 {
-    if (ui == nullptr)
+    if (ui == nullptr || this->printers.get_edited_preset().printer_technology() == ptSLA)
         return;
 
     unsigned char rgb[3];
@@ -1265,6 +1394,7 @@ void PresetBundle::set_default_suppressed(bool default_suppressed)
 {
     prints.set_default_suppressed(default_suppressed);
     filaments.set_default_suppressed(default_suppressed);
+    sla_materials.set_default_suppressed(default_suppressed);
     printers.set_default_suppressed(default_suppressed);
 }
 
diff --git a/xs/src/slic3r/GUI/PresetBundle.hpp b/xs/src/slic3r/GUI/PresetBundle.hpp
index a5c5682f94..68ec534dae 100644
--- a/xs/src/slic3r/GUI/PresetBundle.hpp
+++ b/xs/src/slic3r/GUI/PresetBundle.hpp
@@ -40,6 +40,7 @@ public:
 
     PresetCollection            prints;
     PresetCollection            filaments;
+    PresetCollection            sla_materials;
     PresetCollection            printers;
     // Filament preset names for a multi-extruder or multi-material print.
     // extruders.size() should be the same as printers.get_edited_preset().config.nozzle_diameter.size()
@@ -57,12 +58,13 @@ public:
     struct ObsoletePresets {
         std::vector<std::string> prints;
         std::vector<std::string> filaments;
+        std::vector<std::string> sla_materials;
         std::vector<std::string> printers;
     };
     ObsoletePresets             obsolete_presets;
 
     bool                        has_defauls_only() const 
-        { return prints.size() <= 1 && filaments.size() <= 1 && printers.size() <= 1; }
+        { return prints.has_defaults_only() && filaments.has_defaults_only() && printers.has_defaults_only(); }
 
     DynamicPrintConfig          full_config() const;
 
@@ -146,6 +148,9 @@ private:
     void                        load_config_file_config_bundle(const std::string &path, const boost::property_tree::ptree &tree);
     bool                        load_compatible_bitmaps();
 
+    DynamicPrintConfig          full_fff_config() const;
+    DynamicPrintConfig          full_sla_config() const;
+
     // Indicator, that the preset is compatible with the selected printer.
     wxBitmap                            *m_bitmapCompatible;
     // Indicator, that the preset is NOT compatible with the selected printer.
diff --git a/xs/src/slic3r/GUI/Tab.cpp b/xs/src/slic3r/GUI/Tab.cpp
index 7c4322c5a0..111b2b933d 100644
--- a/xs/src/slic3r/GUI/Tab.cpp
+++ b/xs/src/slic3r/GUI/Tab.cpp
@@ -5,7 +5,7 @@
 #include "../../libslic3r/Utils.hpp"
 
 #include "slic3r/Utils/Http.hpp"
-#include "slic3r/Utils/OctoPrint.hpp"
+#include "slic3r/Utils/PrintHost.hpp"
 #include "slic3r/Utils/Serial.hpp"
 #include "BonjourDialog.hpp"
 #include "WipeTowerDialog.hpp"
@@ -214,7 +214,7 @@ void Tab::load_initial_data()
 	m_tt_non_system = m_presets->get_selected_preset_parent() ? &m_tt_value_unlock : &m_ttg_white_bullet_ns;
 }
 
-PageShp Tab::add_options_page(const wxString& title, const std::string& icon, bool is_extruder_pages/* = false*/)
+Slic3r::GUI::PageShp Tab::add_options_page(const wxString& title, const std::string& icon, bool is_extruder_pages /*= false*/)
 {
 	// Index of icon in an icon list $self->{icons}.
 	auto icon_idx = 0;
@@ -238,7 +238,8 @@ PageShp Tab::add_options_page(const wxString& title, const std::string& icon, bo
 	page->SetScrollbars(1, 1, 1, 1);
 	page->Hide();
 	m_hsizer->Add(page.get(), 1, wxEXPAND | wxLEFT, 5);
-	if (!is_extruder_pages) 
+
+    if (!is_extruder_pages) 
 		m_pages.push_back(page);
 
 	page->set_config(m_config);
@@ -313,10 +314,10 @@ void Tab::update_changed_ui()
 	if (m_postpone_update_ui) 
 		return;
 
-	const bool is_printer_type = (name() == "printer");
-	auto dirty_options = m_presets->current_dirty_options(is_printer_type);
-	auto nonsys_options = m_presets->current_different_from_parent_options(is_printer_type);
-	if (is_printer_type){
+	const bool deep_compare = (m_name == "printer" || m_name == "sla_material");
+	auto dirty_options = m_presets->current_dirty_options(deep_compare);
+	auto nonsys_options = m_presets->current_different_from_parent_options(deep_compare);
+    if (name() == "printer"){
 		TabPrinter* tab = static_cast<TabPrinter*>(this);
 		if (tab->m_initial_extruders_count != tab->m_extruders_count)
 			dirty_options.emplace_back("extruders_count");
@@ -397,7 +398,7 @@ void Tab::init_options_list()
 }
 
 template<class T>
-void add_correct_opts_to_options_list(const std::string &opt_key, std::map<std::string, int>& map, TabPrinter *tab, const int& value)
+void add_correct_opts_to_options_list(const std::string &opt_key, std::map<std::string, int>& map, Tab *tab, const int& value)
 {
 	T *opt_cur = static_cast<T*>(tab->m_config->option(opt_key));
 	for (int i = 0; i < opt_cur->values.size(); i++)
@@ -429,6 +430,30 @@ void TabPrinter::init_options_list()
 	m_options_list.emplace("extruders_count", m_opt_status_value);
 }
 
+void TabSLAMaterial::init_options_list()
+{
+    if (!m_options_list.empty())
+        m_options_list.clear();
+
+    for (const auto opt_key : m_config->keys())
+    {
+        if (opt_key == "compatible_printers"){
+            m_options_list.emplace(opt_key, m_opt_status_value);
+            continue;
+        }
+        switch (m_config->option(opt_key)->type())
+        {
+        case coInts:	add_correct_opts_to_options_list<ConfigOptionInts		>(opt_key, m_options_list, this, m_opt_status_value);	break;
+        case coBools:	add_correct_opts_to_options_list<ConfigOptionBools		>(opt_key, m_options_list, this, m_opt_status_value);	break;
+        case coFloats:	add_correct_opts_to_options_list<ConfigOptionFloats		>(opt_key, m_options_list, this, m_opt_status_value);	break;
+        case coStrings:	add_correct_opts_to_options_list<ConfigOptionStrings	>(opt_key, m_options_list, this, m_opt_status_value);	break;
+        case coPercents:add_correct_opts_to_options_list<ConfigOptionPercents	>(opt_key, m_options_list, this, m_opt_status_value);	break;
+        case coPoints:	add_correct_opts_to_options_list<ConfigOptionPoints		>(opt_key, m_options_list, this, m_opt_status_value);	break;
+        default:		m_options_list.emplace(opt_key, m_opt_status_value);		break;
+        }
+    }
+}
+
 void Tab::get_sys_and_mod_flags(const std::string& opt_key, bool& sys_page, bool& modified_page)
 {
 	auto opt = m_options_list.find(opt_key);
@@ -649,12 +674,21 @@ void Tab::on_value_change(const std::string& opt_key, const boost::any& value)
 			int val = boost::any_cast<size_t>(value);
 			event.SetInt(val);
 		}
+
+        if (opt_key == "printer_technology")
+        {
+            int val = boost::any_cast<PrinterTechnology>(value);
+            event.SetInt(val);
+            g_wxMainFrame->ProcessWindowEvent(event);
+            return;
+        }
+        
 		g_wxMainFrame->ProcessWindowEvent(event);
 	}
 	if (opt_key == "fill_density")
 	{
-		boost::any val = get_optgroup()->get_config_value(*m_config, opt_key);
-		get_optgroup()->set_value(opt_key, val);
+		boost::any val = get_optgroup(ogFrequentlyChangingParameters)->get_config_value(*m_config, opt_key);
+		get_optgroup(ogFrequentlyChangingParameters)->set_value(opt_key, val);
 	}
 	if (opt_key == "support_material" || opt_key == "support_material_buildplate_only")
 	{
@@ -663,12 +697,12 @@ void Tab::on_value_change(const std::string& opt_key, const boost::any& value)
 								m_config->opt_bool("support_material_buildplate_only") ?
 									_("Support on build plate only") :
 									_("Everywhere");
-		get_optgroup()->set_value("support", new_selection);
+		get_optgroup(ogFrequentlyChangingParameters)->set_value("support", new_selection);
 	}
 	if (opt_key == "brim_width")
 	{
 		bool val = m_config->opt_float("brim_width") > 0.0 ? true : false;
-		get_optgroup()->set_value("brim", val);
+		get_optgroup(ogFrequentlyChangingParameters)->set_value("brim", val);
 	}
 
     if (opt_key == "wipe_tower" || opt_key == "single_extruder_multi_material" || opt_key == "extruders_count" )
@@ -677,17 +711,16 @@ void Tab::on_value_change(const std::string& opt_key, const boost::any& value)
 	update();
 }
 
-
 // Show/hide the 'purging volumes' button
 void Tab::update_wiping_button_visibility() {
+    if (get_preset_bundle()->printers.get_selected_preset().printer_technology() == ptSLA)
+        return; // ys_FIXME
     bool wipe_tower_enabled = dynamic_cast<ConfigOptionBool*>(  (m_preset_bundle->prints.get_edited_preset().config  ).option("wipe_tower"))->value;
     bool multiple_extruders = dynamic_cast<ConfigOptionFloats*>((m_preset_bundle->printers.get_edited_preset().config).option("nozzle_diameter"))->values.size() > 1;
     bool single_extruder_mm = dynamic_cast<ConfigOptionBool*>(  (m_preset_bundle->printers.get_edited_preset().config).option("single_extruder_multi_material"))->value;
 
-    if (wipe_tower_enabled && multiple_extruders && single_extruder_mm)
-        get_wiping_dialog_button()->Show();
-    else get_wiping_dialog_button()->Hide();
-
+	get_wiping_dialog_button()->Show(wipe_tower_enabled && multiple_extruders && single_extruder_mm);
+	
     (get_wiping_dialog_button()->GetParent())->Layout();
 }
 
@@ -754,18 +787,18 @@ void Tab::update_preset_description_line()
 
 void Tab::update_frequently_changed_parameters()
 {
-	boost::any value = get_optgroup()->get_config_value(*m_config, "fill_density");
-	get_optgroup()->set_value("fill_density", value);
+	boost::any value = get_optgroup(ogFrequentlyChangingParameters)->get_config_value(*m_config, "fill_density");
+	get_optgroup(ogFrequentlyChangingParameters)->set_value("fill_density", value);
 
 	wxString new_selection = !m_config->opt_bool("support_material") ?
 							_("None") :
 							m_config->opt_bool("support_material_buildplate_only") ?
 								_("Support on build plate only") :
 								_("Everywhere");
-	get_optgroup()->set_value("support", new_selection);
+	get_optgroup(ogFrequentlyChangingParameters)->set_value("support", new_selection);
 
 	bool val = m_config->opt_float("brim_width") > 0.0 ? true : false;
-	get_optgroup()->set_value("brim", val);
+	get_optgroup(ogFrequentlyChangingParameters)->set_value("brim", val);
 
 	update_wiping_button_visibility();
 }
@@ -1007,6 +1040,9 @@ void TabPrint::reload_config(){
 
 void TabPrint::update()
 {
+    if (get_preset_bundle()->printers.get_selected_preset().printer_technology() == ptSLA)
+        return; // ys_FIXME
+
 	Freeze();
 
 	double fill_density = m_config->option<ConfigOptionPercent>("fill_density")->value;
@@ -1366,6 +1402,9 @@ void TabFilament::reload_config(){
 
 void TabFilament::update()
 {
+    if (get_preset_bundle()->printers.get_selected_preset().printer_technology() == ptSLA)
+        return; // ys_FIXME
+
 	Freeze();
 	wxString text = from_u8(PresetHints::cooling_description(m_presets->get_edited_preset()));
 	m_cooling_description_line->SetText(text);
@@ -1411,6 +1450,17 @@ void TabPrinter::build()
 	m_presets = &m_preset_bundle->printers;
 	load_initial_data();
 
+    m_printer_technology = m_presets->get_selected_preset().printer_technology();
+
+    m_presets->get_selected_preset().printer_technology() == ptSLA ? build_sla() : build_fff();
+
+//     on_value_change("printer_technology", m_printer_technology); // to update show/hide preset ComboBoxes
+}
+
+void TabPrinter::build_fff()
+{
+    if (!m_pages.empty())
+        m_pages.resize(0);
 	// to avoid redundant memory allocation / deallocation during extruders count changing
 	m_pages.reserve(30);
 
@@ -1426,7 +1476,7 @@ void TabPrinter::build()
 		Line line{ _(L("Bed shape")), "" };
 		line.widget = [this](wxWindow* parent){
 			auto btn = new wxButton(parent, wxID_ANY, _(L(" Set "))+dots, wxDefaultPosition, wxDefaultSize, wxBU_LEFT | wxBU_EXACTFIT);
-			//			btn->SetFont(Slic3r::GUI::small_font);
+			btn->SetFont(Slic3r::GUI::small_font());
 			btn->SetBitmap(wxBitmap(from_u8(Slic3r::var("printer_empty.png")), wxBITMAP_TYPE_PNG));
 
 			auto sizer = new wxBoxSizer(wxHORIZONTAL);
@@ -1494,7 +1544,7 @@ void TabPrinter::build()
 			auto serial_test = [this](wxWindow* parent){
 				auto btn = m_serial_test_btn = new wxButton(parent, wxID_ANY,
 					_(L("Test")), wxDefaultPosition, wxDefaultSize, wxBU_LEFT | wxBU_EXACTFIT);
-//				btn->SetFont($Slic3r::GUI::small_font);
+				btn->SetFont(Slic3r::GUI::small_font());
 				btn->SetBitmap(wxBitmap(from_u8(Slic3r::var("wrench.png")), wxBITMAP_TYPE_PNG));
 				auto sizer = new wxBoxSizer(wxHORIZONTAL);
 				sizer->Add(btn);
@@ -1521,10 +1571,12 @@ void TabPrinter::build()
 			optgroup->append_line(line);
 		}
 
-		optgroup = page->new_optgroup(_(L("OctoPrint upload")));
+		optgroup = page->new_optgroup(_(L("Printer Host upload")));
 
-		auto octoprint_host_browse = [this, optgroup] (wxWindow* parent) {
-			auto btn = new wxButton(parent, wxID_ANY, _(L(" Browse "))+dots, wxDefaultPosition, wxDefaultSize, wxBU_LEFT);
+		optgroup->append_single_option_line("host_type");
+
+		auto printhost_browse = [this, optgroup] (wxWindow* parent) {
+			auto btn = m_printhost_browse_btn = new wxButton(parent, wxID_ANY, _(L(" Browse "))+dots, wxDefaultPosition, wxDefaultSize, wxBU_LEFT);
 			btn->SetBitmap(wxBitmap(from_u8(Slic3r::var("zoom.png")), wxBITMAP_TYPE_PNG));
 			auto sizer = new wxBoxSizer(wxHORIZONTAL);
 			sizer->Add(btn);
@@ -1532,47 +1584,50 @@ void TabPrinter::build()
 			btn->Bind(wxEVT_BUTTON, [this, parent, optgroup](wxCommandEvent e) {
 				BonjourDialog dialog(parent);
 				if (dialog.show_and_lookup()) {
-					optgroup->set_value("octoprint_host", std::move(dialog.get_selected()), true);
+					optgroup->set_value("print_host", std::move(dialog.get_selected()), true);
 				}
 			});
 
 			return sizer;
 		};
 
-		auto octoprint_host_test = [this](wxWindow* parent) {
-			auto btn = m_octoprint_host_test_btn = new wxButton(parent, wxID_ANY, _(L("Test")), 
+		auto print_host_test = [this](wxWindow* parent) {
+			auto btn = m_print_host_test_btn = new wxButton(parent, wxID_ANY, _(L("Test")), 
 				wxDefaultPosition, wxDefaultSize, wxBU_LEFT | wxBU_EXACTFIT);
 			btn->SetBitmap(wxBitmap(from_u8(Slic3r::var("wrench.png")), wxBITMAP_TYPE_PNG));
 			auto sizer = new wxBoxSizer(wxHORIZONTAL);
 			sizer->Add(btn);
 
 			btn->Bind(wxEVT_BUTTON, [this](wxCommandEvent e) {
-				OctoPrint octoprint(m_config);
-				wxString msg;
-				if (octoprint.test(msg)) {
-					show_info(this, _(L("Connection to OctoPrint works correctly.")), _(L("Success!")));
-				} else {
-					const auto text = wxString::Format("%s: %s\n\n%s",
-						_(L("Could not connect to OctoPrint")), msg, _(L("Note: OctoPrint version at least 1.1.0 is required."))
-					);
+				std::unique_ptr<PrintHost> host(PrintHost::get_print_host(m_config));
+				if (! host) {
+					const auto text = wxString::Format("%s",
+						_(L("Could not get a valid Printer Host reference")));
 					show_error(this, text);
+					return;
+				}
+				wxString msg;
+				if (host->test(msg)) {
+					show_info(this, host->get_test_ok_msg(), _(L("Success!")));
+				} else {
+					show_error(this, host->get_test_failed_msg(msg));
 				}
 			});
 
 			return sizer;
 		};
 
-		Line host_line = optgroup->create_single_option_line("octoprint_host");
-		host_line.append_widget(octoprint_host_browse);
-		host_line.append_widget(octoprint_host_test);
+		Line host_line = optgroup->create_single_option_line("print_host");
+		host_line.append_widget(printhost_browse);
+		host_line.append_widget(print_host_test);
 		optgroup->append_line(host_line);
-		optgroup->append_single_option_line("octoprint_apikey");
+		optgroup->append_single_option_line("printhost_apikey");
 
 		if (Http::ca_file_supported()) {
 
-			Line cafile_line = optgroup->create_single_option_line("octoprint_cafile");
+			Line cafile_line = optgroup->create_single_option_line("printhost_cafile");
 
-			auto octoprint_cafile_browse = [this, optgroup] (wxWindow* parent) {
+			auto printhost_cafile_browse = [this, optgroup] (wxWindow* parent) {
 				auto btn = new wxButton(parent, wxID_ANY, _(L(" Browse "))+dots, wxDefaultPosition, wxDefaultSize, wxBU_LEFT);
 				btn->SetBitmap(wxBitmap(from_u8(Slic3r::var("zoom.png")), wxBITMAP_TYPE_PNG));
 				auto sizer = new wxBoxSizer(wxHORIZONTAL);
@@ -1582,17 +1637,17 @@ void TabPrinter::build()
 					static const auto filemasks = _(L("Certificate files (*.crt, *.pem)|*.crt;*.pem|All files|*.*"));
 					wxFileDialog openFileDialog(this, _(L("Open CA certificate file")), "", "", filemasks, wxFD_OPEN | wxFD_FILE_MUST_EXIST);
 					if (openFileDialog.ShowModal() != wxID_CANCEL) {
-						optgroup->set_value("octoprint_cafile", std::move(openFileDialog.GetPath()), true);
+						optgroup->set_value("printhost_cafile", std::move(openFileDialog.GetPath()), true);
 					}
 				});
 
 				return sizer;
 			};
 
-			cafile_line.append_widget(octoprint_cafile_browse);
+			cafile_line.append_widget(printhost_cafile_browse);
 			optgroup->append_line(cafile_line);
 
-			auto octoprint_cafile_hint = [this, optgroup] (wxWindow* parent) {
+			auto printhost_cafile_hint = [this, optgroup] (wxWindow* parent) {
 				auto txt = new wxStaticText(parent, wxID_ANY, 
 					_(L("HTTPS CA file is optional. It is only needed if you use HTTPS with a self-signed certificate.")));
 				auto sizer = new wxBoxSizer(wxHORIZONTAL);
@@ -1602,7 +1657,7 @@ void TabPrinter::build()
 
 			Line cafile_hint { "", "" };
 			cafile_hint.full_width = 1;
-			cafile_hint.widget = std::move(octoprint_cafile_hint);
+			cafile_hint.widget = std::move(printhost_cafile_hint);
 			optgroup->append_line(cafile_hint);
 
 		}
@@ -1692,6 +1747,76 @@ void TabPrinter::build()
 		update_serial_ports();
 }
 
+void TabPrinter::build_sla()
+{
+    if (!m_pages.empty())
+        m_pages.resize(0);
+    auto page = add_options_page(_(L("General")), "printer_empty.png");
+    auto optgroup = page->new_optgroup(_(L("Size and coordinates")));
+
+    Line line{ _(L("Bed shape")), "" };
+    line.widget = [this](wxWindow* parent){
+        auto btn = new wxButton(parent, wxID_ANY, _(L(" Set ")) + dots, wxDefaultPosition, wxDefaultSize, wxBU_LEFT | wxBU_EXACTFIT);
+        //			btn->SetFont(Slic3r::GUI::small_font);
+        btn->SetBitmap(wxBitmap(from_u8(Slic3r::var("printer_empty.png")), wxBITMAP_TYPE_PNG));
+
+        auto sizer = new wxBoxSizer(wxHORIZONTAL);
+        sizer->Add(btn);
+
+        btn->Bind(wxEVT_BUTTON, ([this](wxCommandEvent e)
+        {
+            auto dlg = new BedShapeDialog(this);
+            dlg->build_dialog(m_config->option<ConfigOptionPoints>("bed_shape"));
+            if (dlg->ShowModal() == wxID_OK){
+                load_key_value("bed_shape", dlg->GetValue());
+                update_changed_ui();
+            }
+        }));
+
+        return sizer;
+    };
+    optgroup->append_line(line, &m_colored_Label);
+    optgroup->append_single_option_line("max_print_height");
+
+    optgroup = page->new_optgroup(_(L("Display")));
+    optgroup->append_single_option_line("display_width");
+    optgroup->append_single_option_line("display_height");
+
+    auto option = optgroup->get_option("display_pixels_x");
+    line = { _(option.opt.full_label), "" };
+    line.append_option(option);
+    line.append_option(optgroup->get_option("display_pixels_y"));
+    optgroup->append_line(line);
+
+    optgroup = page->new_optgroup(_(L("Corrections")));
+    line = Line{ m_config->def()->get("printer_correction")->full_label, "" };
+    std::vector<std::string> axes{ "X", "Y", "Z" };
+    int id = 0;
+    for (auto& axis : axes) {
+        auto opt = optgroup->get_option("printer_correction", id);
+        opt.opt.label = axis;
+        line.append_option(opt);
+        ++id;
+    }
+    optgroup->append_line(line);
+
+    page = add_options_page(_(L("Notes")), "note.png");
+    optgroup = page->new_optgroup(_(L("Notes")), 0);
+    option = optgroup->get_option("printer_notes");
+    option.opt.full_width = true;
+    option.opt.height = 250;
+    optgroup->append_single_option_line(option);
+
+    page = add_options_page(_(L("Dependencies")), "wrench.png");
+    optgroup = page->new_optgroup(_(L("Profile dependencies")));
+    line = Line{ "", "" };
+    line.full_width = 1;
+    line.widget = [this](wxWindow* parent) {
+        return description_line_widget(parent, &m_parent_preset_description_line);
+    };
+    optgroup->append_line(line);
+}
+
 void TabPrinter::update_serial_ports(){
 	Field *field = get_field("serial_port");
 	Choice *choice = static_cast<Choice *>(field);
@@ -1705,6 +1830,7 @@ void TabPrinter::extruders_count_changed(size_t extruders_count){
 	build_extruder_pages();
 	reload_config();
 	on_value_change("extruders_count", extruders_count);
+    update_objects_list_extruder_column(extruders_count);
 }
 
 void TabPrinter::append_option_line(ConfigOptionsGroupShp optgroup, const std::string opt_key)
@@ -1883,7 +2009,38 @@ void TabPrinter::on_preset_loaded()
 	extruders_count_changed(extruders_count);
 }
 
-void TabPrinter::update(){
+void TabPrinter::update_pages()
+{
+    // update m_pages ONLY if printer technology is changed
+    if (m_presets->get_edited_preset().printer_technology() == m_printer_technology)
+        return;
+
+    // hide all old pages
+    for (auto& el : m_pages)
+        el.get()->Hide();
+
+    // set m_pages to m_pages_(technology before changing)
+    m_printer_technology == ptFFF ? m_pages.swap(m_pages_fff) : m_pages.swap(m_pages_sla);
+
+    // build Tab according to the technology, if it's not exist jet OR
+    // set m_pages_(technology after changing) to m_pages
+    if (m_presets->get_edited_preset().printer_technology() == ptFFF)
+        m_pages_fff.empty() ? build_fff() : m_pages.swap(m_pages_fff);
+    else 
+        m_pages_sla.empty() ? build_sla() : m_pages.swap(m_pages_sla);
+
+    rebuild_page_tree(true);
+
+    on_value_change("printer_technology", m_presets->get_edited_preset().printer_technology()); // to update show/hide preset ComboBoxes
+}
+
+void TabPrinter::update()
+{
+    m_presets->get_edited_preset().printer_technology() == ptFFF ? update_fff() : update_sla();
+}
+
+void TabPrinter::update_fff()
+{
 	Freeze();
 
 	bool en;
@@ -1897,8 +2054,12 @@ void TabPrinter::update(){
 			m_serial_test_btn->Disable();
 	}
 
-	m_octoprint_host_test_btn->Enable(!m_config->opt_string("octoprint_host").empty());
-	
+	{
+		std::unique_ptr<PrintHost> host(PrintHost::get_print_host(m_config));
+		m_print_host_test_btn->Enable(!m_config->opt_string("print_host").empty() && host->can_test());
+		m_printhost_browse_btn->Enable(host->has_auto_discovery());
+	}
+
 	bool have_multiple_extruders = m_extruders_count > 1;
 	get_field("toolchange_gcode")->toggle(have_multiple_extruders);
 	get_field("single_extruder_multi_material")->toggle(have_multiple_extruders);
@@ -1982,20 +2143,25 @@ void TabPrinter::update(){
 	Thaw();
 }
 
+void TabPrinter::update_sla(){ ; }
+
 // Initialize the UI from the current preset
 void Tab::load_current_preset()
 {
 	auto preset = m_presets->get_edited_preset();
 
 	(preset.is_default || preset.is_system) ? m_btn_delete_preset->Disable() : m_btn_delete_preset->Enable(true);
-	update();
-	// For the printer profile, generate the extruder pages.
-	on_preset_loaded();
-	// Reload preset pages with the new configuration values.
-	reload_config();
+
+    update();
+    // For the printer profile, generate the extruder pages.
+    if (preset.printer_technology() == ptFFF)
+        on_preset_loaded();
+    // Reload preset pages with the new configuration values.
+    reload_config();
+
 	m_bmp_non_system = m_presets->get_selected_preset_parent() ? &m_bmp_value_unlock : &m_bmp_white_bullet;
 	m_ttg_non_system = m_presets->get_selected_preset_parent() ? &m_ttg_value_unlock : &m_ttg_white_bullet_ns;
-	m_tt_non_system = m_presets->get_selected_preset_parent() ? &m_tt_value_unlock : &m_ttg_white_bullet_ns;
+	m_tt_non_system = m_presets->get_selected_preset_parent()  ? &m_tt_value_unlock  : &m_ttg_white_bullet_ns;
 
 	m_undo_to_sys_btn->Enable(!preset.is_default);
 
@@ -2008,6 +2174,27 @@ void Tab::load_current_preset()
 		if (!checked_tab(this))
 			return;
 		update_tab_ui();
+
+        // update show/hide tabs
+        if (m_name == "printer"){
+            PrinterTechnology& printer_technology = m_presets->get_edited_preset().printer_technology();
+            if (printer_technology != static_cast<TabPrinter*>(this)->m_printer_technology)
+            {
+                for (auto& tab : get_preset_tabs()){
+                    if (tab.technology != printer_technology)
+                    {
+                        int page_id = get_tab_panel()->FindPage(tab.panel);
+                        get_tab_panel()->GetPage(page_id)->Show(false);
+                        get_tab_panel()->RemovePage(page_id);
+                    }
+                    else
+                        get_tab_panel()->InsertPage(get_tab_panel()->FindPage(this), tab.panel, tab.panel->title());
+                }
+
+                static_cast<TabPrinter*>(this)->m_printer_technology = printer_technology;
+            }
+        }
+
 		on_presets_changed();
 
 		if (name() == "print")
@@ -2025,7 +2212,7 @@ void Tab::load_current_preset()
 }
 
 //Regerenerate content of the page tree.
-void Tab::rebuild_page_tree()
+void Tab::rebuild_page_tree(bool tree_sel_change_event /*= false*/)
 {
 	Freeze();
 	// get label of the currently selected item
@@ -2040,9 +2227,9 @@ void Tab::rebuild_page_tree()
 		m_treectrl->SetItemTextColour(itemId, p->get_item_colour());
 		if (p->title() == selected) {
 			if (!(p->title() == _(L("Machine limits")) || p->title() == _(L("Single extruder MM setup")))) // These Pages have to be updated inside OnTreeSelChange
-				m_disable_tree_sel_changed_event = 1;
+				m_disable_tree_sel_changed_event = !tree_sel_change_event;
 			m_treectrl->SelectItem(itemId);
-			m_disable_tree_sel_changed_event = 0;
+			m_disable_tree_sel_changed_event = false;
 			have_selection = 1;
 		}
 	}
@@ -2057,48 +2244,53 @@ void Tab::rebuild_page_tree()
 // Called by the UI combo box when the user switches profiles.
 // Select a preset by a name.If !defined(name), then the default preset is selected.
 // If the current profile is modified, user is asked to save the changes.
-void Tab::select_preset(const std::string& preset_name /*= ""*/)
+void Tab::select_preset(std::string preset_name /*= ""*/)
 {
-	std::string name = preset_name;
-	auto force = false;
-	auto presets = m_presets;
 	// If no name is provided, select the "-- default --" preset.
-	if (name.empty())
-		name= presets->default_preset().name;
-	auto current_dirty = presets->current_is_dirty();
-	auto canceled = false;
-	auto printer_tab = presets->name().compare("printer")==0;
+	if (preset_name.empty())
+		preset_name = m_presets->default_preset().name;
+	auto current_dirty = m_presets->current_is_dirty();
+	auto printer_tab   = m_presets->name() == "printer";
+	auto canceled      = false;
 	m_reload_dependent_tabs = {};
-	if (!force && current_dirty && !may_discard_current_dirty_preset()) {
+	if (current_dirty && !may_discard_current_dirty_preset()) {
 		canceled = true;
-	} else if(printer_tab) {
+	} else if (printer_tab) {
 		// Before switching the printer to a new one, verify, whether the currently active print and filament
 		// are compatible with the new printer.
 		// If they are not compatible and the current print or filament are dirty, let user decide
 		// whether to discard the changes or keep the current printer selection.
-		auto new_printer_preset = presets->find_preset(name, true);
-		auto print_presets = &m_preset_bundle->prints;
-		bool print_preset_dirty = print_presets->current_is_dirty();
-		bool print_preset_compatible = print_presets->get_edited_preset().is_compatible_with_printer(*new_printer_preset);
-		canceled = !force && print_preset_dirty && !print_preset_compatible &&
-			!may_discard_current_dirty_preset(print_presets, name);
-		auto filament_presets = &m_preset_bundle->filaments;
-		bool filament_preset_dirty = filament_presets->current_is_dirty();
-		bool filament_preset_compatible = filament_presets->get_edited_preset().is_compatible_with_printer(*new_printer_preset);
-		if (!canceled && !force) {
-			canceled = filament_preset_dirty && !filament_preset_compatible &&
-				!may_discard_current_dirty_preset(filament_presets, name);
+		//
+		// With the introduction of the SLA printer types, we need to support switching between
+		// the FFF and SLA printers.
+		const Preset 		&new_printer_preset     = *m_presets->find_preset(preset_name, true);
+		PrinterTechnology    old_printer_technology = m_presets->get_edited_preset().printer_technology();
+		PrinterTechnology    new_printer_technology = new_printer_preset.printer_technology();
+		struct PresetUpdate {
+			std::string          name;
+			PresetCollection 	*presets;
+			PrinterTechnology    technology;
+			bool    	         old_preset_dirty;
+			bool         	     new_preset_compatible;
+		};
+		std::vector<PresetUpdate> updates = {
+			{ "print",			&m_preset_bundle->prints,			ptFFF },
+			{ "filament",		&m_preset_bundle->filaments,		ptFFF },
+ 			{ "sla_material",	&m_preset_bundle->sla_materials,	ptSLA }
+		};
+		for (PresetUpdate &pu : updates) {
+			pu.old_preset_dirty      = (old_printer_technology == pu.technology) && pu.presets->current_is_dirty();
+			pu.new_preset_compatible = (new_printer_technology == pu.technology) && pu.presets->get_edited_preset().is_compatible_with_printer(new_printer_preset);
+			if (! canceled)
+				canceled = pu.old_preset_dirty && ! pu.new_preset_compatible && ! may_discard_current_dirty_preset(pu.presets, preset_name);
 		}
-		if (!canceled) {
-			if (!print_preset_compatible) {
+		if (! canceled) {
+			for (PresetUpdate &pu : updates) {
 				// The preset will be switched to a different, compatible preset, or the '-- default --'.
-				m_reload_dependent_tabs.push_back("print");
-				if (print_preset_dirty) print_presets->discard_current_changes();
-			}
-			if (!filament_preset_compatible) {
-				// The preset will be switched to a different, compatible preset, or the '-- default --'.
-				m_reload_dependent_tabs.push_back("filament");
-				if (filament_preset_dirty) filament_presets->discard_current_changes();
+                if (pu.technology == new_printer_technology)
+				    m_reload_dependent_tabs.emplace_back(pu.name);
+				if (pu.old_preset_dirty)
+					pu.presets->discard_current_changes();
 			}
 		}
 	}
@@ -2107,19 +2299,20 @@ void Tab::select_preset(const std::string& preset_name /*= ""*/)
 		// Trigger the on_presets_changed event so that we also restore the previous value in the plater selector,
 		// if this action was initiated from the platter.
 		on_presets_changed();
-	}
-	else {
-		if (current_dirty) presets->discard_current_changes() ;
-		presets->select_preset_by_name(name, force);
+	} else {
+		if (current_dirty)
+			m_presets->discard_current_changes() ;
+		m_presets->select_preset_by_name(preset_name, false);
 		// Mark the print & filament enabled if they are compatible with the currently selected preset.
 		// The following method should not discard changes of current print or filament presets on change of a printer profile,
 		// if they are compatible with the current printer.
 		if (current_dirty || printer_tab)
 			m_preset_bundle->update_compatible_with_printer(true);
 		// Initialize the UI from the current preset.
+        if (printer_tab)
+            static_cast<TabPrinter*>(this)->update_pages();
 		load_current_preset();
 	}
-
 }
 
 // If the current preset is dirty, the user is asked whether the changes may be discarded.
@@ -2761,5 +2954,71 @@ void SavePresetWindow::accept()
 	}
 }
 
+void TabSLAMaterial::build()
+{
+    m_presets = &m_preset_bundle->sla_materials;
+    load_initial_data();
+
+    auto page = add_options_page(_(L("Material")), "package_green.png");
+
+    auto optgroup = page->new_optgroup(_(L("Layers")));
+    optgroup->append_single_option_line("layer_height");
+    optgroup->append_single_option_line("initial_layer_height");
+
+    optgroup = page->new_optgroup(_(L("Exposure")));
+    optgroup->append_single_option_line("exposure_time");
+    optgroup->append_single_option_line("initial_exposure_time");
+
+    optgroup = page->new_optgroup(_(L("Corrections")));
+    optgroup->label_width = 190;
+    std::vector<std::string> corrections = { "material_correction_printing", "material_correction_curing" };
+    std::vector<std::string> axes{ "X", "Y", "Z" };
+    for (auto& opt_key : corrections){
+        auto line = Line{ m_config->def()->get(opt_key)->full_label, "" };
+        int id = 0;
+        for (auto& axis : axes) {
+            auto opt = optgroup->get_option(opt_key, id);
+            opt.opt.label = axis;
+            opt.opt.width = 60;
+            line.append_option(opt);
+            ++id;
+        }
+        optgroup->append_line(line);
+    }
+
+    page = add_options_page(_(L("Notes")), "note.png");
+    optgroup = page->new_optgroup(_(L("Notes")), 0);
+    optgroup->label_width = 0;
+    Option option = optgroup->get_option("material_notes");
+    option.opt.full_width = true;
+    option.opt.height = 250;
+    optgroup->append_single_option_line(option);
+
+    page = add_options_page(_(L("Dependencies")), "wrench.png");
+    optgroup = page->new_optgroup(_(L("Profile dependencies")));
+    auto line = Line { _(L("Compatible printers")), "" };
+    line.widget = [this](wxWindow* parent){
+        return compatible_printers_widget(parent, &m_compatible_printers_checkbox, &m_compatible_printers_btn);
+    };
+    optgroup->append_line(line, &m_colored_Label);
+
+    option = optgroup->get_option("compatible_printers_condition");
+    option.opt.full_width = true;
+    optgroup->append_single_option_line(option);
+
+    line = Line{ "", "" };
+    line.full_width = 1;
+    line.widget = [this](wxWindow* parent) {
+        return description_line_widget(parent, &m_parent_preset_description_line);
+    };
+    optgroup->append_line(line);
+}
+
+void TabSLAMaterial::update()
+{
+    if (get_preset_bundle()->printers.get_selected_preset().printer_technology() == ptFFF)
+        return; // ys_FIXME
+}
+
 } // GUI
 } // Slic3r
diff --git a/xs/src/slic3r/GUI/Tab.hpp b/xs/src/slic3r/GUI/Tab.hpp
index 8b4eae7de5..a1214465ea 100644
--- a/xs/src/slic3r/GUI/Tab.hpp
+++ b/xs/src/slic3r/GUI/Tab.hpp
@@ -218,8 +218,8 @@ public:
 	
 	void		create_preset_tab(PresetBundle *preset_bundle);
 	void		load_current_preset();
-	void		rebuild_page_tree();
-	void		select_preset(const std::string& preset_name = "");
+	void        rebuild_page_tree(bool tree_sel_change_event = false);
+	void		select_preset(std::string preset_name = "");
 	bool		may_discard_current_dirty_preset(PresetCollection* presets = nullptr, const std::string& new_printer_name = "");
 	wxSizer*	compatible_printers_widget(wxWindow* parent, wxCheckBox** checkbox, wxButton** btn);
 
@@ -267,11 +267,11 @@ public:
 
 	void			on_value_change(const std::string& opt_key, const boost::any& value);
 
+    void            update_wiping_button_visibility();
 protected:
 	void			on_presets_changed();
 	void			update_preset_description_line();
 	void			update_frequently_changed_parameters();
-    void            update_wiping_button_visibility();
 	void			update_tab_presets(wxComboCtrl* ui, bool show_incompatible);
 	void			fill_icon_descriptions();
 	void			set_tooltips_text();
@@ -319,21 +319,32 @@ class TabPrinter : public Tab
 	bool		m_use_silent_mode = false;
 	void		append_option_line(ConfigOptionsGroupShp optgroup, const std::string opt_key);
 	bool		m_rebuild_kinematics_page = false;
+
+    std::vector<PageShp>			m_pages_fff;
+    std::vector<PageShp>			m_pages_sla;
 public:
 	wxButton*	m_serial_test_btn;
-	wxButton*	m_octoprint_host_test_btn;
+	wxButton*	m_print_host_test_btn;
+	wxButton*	m_printhost_browse_btn;
 
 	size_t		m_extruders_count;
 	size_t		m_extruders_count_old = 0;
 	size_t		m_initial_extruders_count;
 	size_t		m_sys_extruders_count;
 
+    PrinterTechnology               m_printer_technology = ptFFF;
+
 	TabPrinter() {}
 	TabPrinter(wxNotebook* parent, bool no_controller) : Tab(parent, _(L("Printer Settings")), "printer", no_controller) {}
 	~TabPrinter(){}
 
 	void		build() override;
-	void		update() override;
+    void		build_fff();
+    void		build_sla();
+    void		update() override;
+    void		update_fff();
+    void		update_sla();
+    void        update_pages(); // update m_pages according to printer technology
 	void		update_serial_ports();
 	void		extruders_count_changed(size_t extruders_count);
 	PageShp		build_kinematics_page();
@@ -342,6 +353,19 @@ public:
 	void		init_options_list() override;
 };
 
+class TabSLAMaterial : public Tab
+{
+public:
+    TabSLAMaterial() {}
+    TabSLAMaterial(wxNotebook* parent, bool no_controller) :
+		Tab(parent, _(L("SLA Material Settings")), "sla_material", no_controller) {}
+    ~TabSLAMaterial(){}
+
+	void		build() override;
+	void		update() override;
+    void		init_options_list() override;
+};
+
 class SavePresetWindow :public wxDialog
 {
 public:
diff --git a/xs/src/slic3r/GUI/wxExtensions.cpp b/xs/src/slic3r/GUI/wxExtensions.cpp
index 5949efb377..7fcad9e656 100644
--- a/xs/src/slic3r/GUI/wxExtensions.cpp
+++ b/xs/src/slic3r/GUI/wxExtensions.cpp
@@ -1,5 +1,13 @@
 #include "wxExtensions.hpp"
 
+#include "GUI.hpp"
+#include "../../libslic3r/Utils.hpp"
+
+#include <wx/sizer.h>
+#include <wx/statline.h>
+#include <wx/dcclient.h>
+#include <wx/numformatter.h>
+
 const unsigned int wxCheckListBoxComboPopup::DefaultWidth = 200;
 const unsigned int wxCheckListBoxComboPopup::DefaultHeight = 200;
 const unsigned int wxCheckListBoxComboPopup::DefaultItemHeight = 18;
@@ -182,3 +190,1216 @@ void wxDataViewTreeCtrlComboPopup::OnDataViewTreeCtrlSelection(wxCommandEvent& e
 	auto selected = GetItemText(GetSelection());
 	cmb->SetText(selected);
 }
+
+// ----------------------------------------------------------------------------
+// ***  PrusaCollapsiblePane  ***    
+// ----------------------------------------------------------------------------
+void PrusaCollapsiblePane::OnStateChange(const wxSize& sz)
+{
+#ifdef __WXOSX__
+	wxCollapsiblePane::OnStateChange(sz);
+#else
+	SetSize(sz);
+
+	if (this->HasFlag(wxCP_NO_TLW_RESIZE))
+	{
+		// the user asked to explicitly handle the resizing itself...
+		return;
+	}
+
+	auto top = GetParent(); //right_panel
+	if (!top)
+		return;
+
+	wxSizer *sizer = top->GetSizer();
+	if (!sizer)
+		return;
+
+	const wxSize newBestSize = sizer->ComputeFittingClientSize(top);
+	top->SetMinClientSize(newBestSize);
+
+	wxWindowUpdateLocker noUpdates_p(top->GetParent());
+	// we shouldn't attempt to resize a maximized window, whatever happens
+	// 	if (!top->IsMaximized())
+	// 		top->SetClientSize(newBestSize);
+	top->GetParent()->Layout();
+	top->Refresh();
+#endif //__WXOSX__
+}
+
+// ----------------------------------------------------------------------------
+// ***  PrusaCollapsiblePaneMSW  ***    used only #ifdef __WXMSW__
+// ----------------------------------------------------------------------------
+#ifdef __WXMSW__
+bool PrusaCollapsiblePaneMSW::Create(wxWindow *parent, wxWindowID id, const wxString& label, 
+	const wxPoint& pos, const wxSize& size, long style, const wxValidator& val, const wxString& name)
+{
+	if (!wxControl::Create(parent, id, pos, size, style, val, name))
+		return false;
+	m_pStaticLine = NULL;
+	m_strLabel = label;
+
+	// sizer containing the expand button and possibly a static line
+	m_sz = new wxBoxSizer(wxHORIZONTAL);
+
+	m_bmp_close.LoadFile(Slic3r::GUI::from_u8(Slic3r::var("disclosure_triangle_close.png")), wxBITMAP_TYPE_PNG);
+	m_bmp_open.LoadFile(Slic3r::GUI::from_u8(Slic3r::var("disclosure_triangle_open.png")), wxBITMAP_TYPE_PNG);
+
+	m_pDisclosureTriangleButton = new wxButton(this, wxID_ANY, m_strLabel, wxPoint(0, 0),
+		wxDefaultSize, wxBU_EXACTFIT | wxNO_BORDER);
+	UpdateBtnBmp();
+	m_pDisclosureTriangleButton->Bind(wxEVT_BUTTON, [this](wxCommandEvent& event)
+	{
+		if (event.GetEventObject() != m_pDisclosureTriangleButton)
+		{
+			event.Skip();
+			return;
+		}
+
+		Collapse(!IsCollapsed());
+
+		// this change was generated by the user - send the event
+		wxCollapsiblePaneEvent ev(this, GetId(), IsCollapsed());
+		GetEventHandler()->ProcessEvent(ev);
+	});
+
+	m_sz->Add(m_pDisclosureTriangleButton, 0, wxLEFT | wxTOP | wxBOTTOM, GetBorder());
+
+	// do not set sz as our sizers since we handle the pane window without using sizers
+	m_pPane = new wxPanel(this, wxID_ANY, wxDefaultPosition, wxDefaultSize,
+		wxTAB_TRAVERSAL | wxNO_BORDER, wxT("wxCollapsiblePanePane"));
+
+	wxColour& clr = wxSystemSettings::GetColour(wxSYS_COLOUR_WINDOW);
+	m_pDisclosureTriangleButton->SetBackgroundColour(clr);
+	this->SetBackgroundColour(clr);
+	m_pPane->SetBackgroundColour(clr);
+
+	// start as collapsed:
+	m_pPane->Hide();
+
+	return true;
+}
+
+void PrusaCollapsiblePaneMSW::UpdateBtnBmp()
+{
+	if (IsCollapsed())
+		m_pDisclosureTriangleButton->SetBitmap(m_bmp_close);
+	else{
+		m_pDisclosureTriangleButton->SetBitmap(m_bmp_open);
+		// To updating button bitmap it's needed to lost focus on this button, so
+		// we set focus to mainframe 
+		//GetParent()->GetParent()->GetParent()->SetFocus();
+		//or to pane
+		GetPane()->SetFocus();
+	}
+	Layout();
+}
+
+void PrusaCollapsiblePaneMSW::SetLabel(const wxString &label)
+{
+	m_strLabel = label;
+	m_pDisclosureTriangleButton->SetLabel(m_strLabel);
+	Layout();
+}
+
+bool PrusaCollapsiblePaneMSW::Layout()
+{
+	if (!m_pDisclosureTriangleButton || !m_pPane || !m_sz)
+		return false;     // we need to complete the creation first!
+
+	wxSize oursz(GetSize());
+
+	// move & resize the button and the static line
+	m_sz->SetDimension(0, 0, oursz.GetWidth(), m_sz->GetMinSize().GetHeight());
+	m_sz->Layout();
+
+	if (IsExpanded())
+	{
+		// move & resize the container window
+		int yoffset = m_sz->GetSize().GetHeight() + GetBorder();
+		m_pPane->SetSize(0, yoffset,
+			oursz.x, oursz.y - yoffset);
+
+		// this is very important to make the pane window layout show correctly
+		m_pPane->Layout();
+	}
+
+	return true;
+}
+
+void PrusaCollapsiblePaneMSW::Collapse(bool collapse)
+{
+	// optimization
+	if (IsCollapsed() == collapse)
+		return;
+
+	InvalidateBestSize();
+
+	// update our state
+	m_pPane->Show(!collapse);
+
+	// update button bitmap
+	UpdateBtnBmp();
+
+	OnStateChange(GetBestSize());
+}
+#endif //__WXMSW__
+
+// *****************************************************************************
+// ----------------------------------------------------------------------------
+// PrusaObjectDataViewModelNode
+// ----------------------------------------------------------------------------
+
+void PrusaObjectDataViewModelNode::set_object_action_icon() {
+	m_action_icon = wxBitmap(Slic3r::GUI::from_u8(Slic3r::var("add_object.png")), wxBITMAP_TYPE_PNG);
+}
+void  PrusaObjectDataViewModelNode::set_part_action_icon() {
+	m_action_icon = wxBitmap(Slic3r::GUI::from_u8(Slic3r::var("cog.png")), wxBITMAP_TYPE_PNG);
+}
+
+// *****************************************************************************
+// ----------------------------------------------------------------------------
+// PrusaObjectDataViewModel
+// ----------------------------------------------------------------------------
+
+wxDataViewItem PrusaObjectDataViewModel::Add(wxString &name)
+{
+	auto root = new PrusaObjectDataViewModelNode(name);
+	m_objects.push_back(root);
+	// notify control
+	wxDataViewItem child((void*)root);
+	wxDataViewItem parent((void*)NULL);
+	ItemAdded(parent, child);
+	return child;
+}
+
+wxDataViewItem PrusaObjectDataViewModel::Add(wxString &name, int instances_count, int scale)
+{
+	auto root = new PrusaObjectDataViewModelNode(name, instances_count, scale);
+	m_objects.push_back(root);
+	// notify control
+	wxDataViewItem child((void*)root);
+	wxDataViewItem parent((void*)NULL);
+	ItemAdded(parent, child);
+	return child;
+}
+
+wxDataViewItem PrusaObjectDataViewModel::AddChild(	const wxDataViewItem &parent_item,
+													const wxString &name,
+													const wxIcon& icon,
+                                                    const int extruder/* = 0*/,
+                                                    const bool create_frst_child/* = true*/)
+{
+	PrusaObjectDataViewModelNode *root = (PrusaObjectDataViewModelNode*)parent_item.GetID();
+	if (!root) return wxDataViewItem(0);
+
+    wxString extruder_str = extruder == 0 ? "default" : wxString::Format("%d", extruder);
+
+    if (root->GetChildren().Count() == 0 && create_frst_child)
+	{
+		auto icon_solid_mesh = wxIcon(Slic3r::GUI::from_u8(Slic3r::var("object.png")), wxBITMAP_TYPE_PNG);//(Slic3r::var("package.png")), wxBITMAP_TYPE_PNG);
+		auto node = new PrusaObjectDataViewModelNode(root, root->m_name, icon_solid_mesh, extruder_str, 0);
+		root->Append(node);
+		// notify control
+		wxDataViewItem child((void*)node);
+		ItemAdded(parent_item, child);
+	}
+
+	auto volume_id = root->GetChildCount();
+	auto node = new PrusaObjectDataViewModelNode(root, name, icon, extruder_str, volume_id);
+	root->Append(node);
+	// notify control
+	wxDataViewItem child((void*)node);
+	ItemAdded(parent_item, child);
+	return child;
+}
+
+wxDataViewItem PrusaObjectDataViewModel::Delete(const wxDataViewItem &item)
+{
+	auto ret_item = wxDataViewItem(0);
+	PrusaObjectDataViewModelNode *node = (PrusaObjectDataViewModelNode*)item.GetID();
+	if (!node)      // happens if item.IsOk()==false
+		return ret_item;
+
+	auto node_parent = node->GetParent();
+	wxDataViewItem parent(node_parent);
+
+	// first remove the node from the parent's array of children;
+	// NOTE: MyObjectTreeModelNodePtrArray is only an array of _pointers_
+	//       thus removing the node from it doesn't result in freeing it
+	if (node_parent){
+		auto id = node_parent->GetChildren().Index(node);
+		auto v_id = node->GetVolumeId();
+		node_parent->GetChildren().Remove(node);
+		if (id > 0){ 
+			if(id == node_parent->GetChildCount()) id--;
+			ret_item = wxDataViewItem(node_parent->GetChildren().Item(id));
+		}
+
+		//update volume_id value for remaining child-nodes
+		auto children = node_parent->GetChildren();
+		for (size_t i = 0; i < node_parent->GetChildCount(); i++)
+		{
+			auto volume_id = children[i]->GetVolumeId();
+			if (volume_id > v_id)
+				children[i]->SetVolumeId(volume_id-1);
+		}
+	}
+	else
+	{
+		auto it = find(m_objects.begin(), m_objects.end(), node);
+		auto id = it - m_objects.begin();
+		if (it != m_objects.end())
+			m_objects.erase(it);
+		if (id > 0){ 
+			if(id == m_objects.size()) id--;
+			ret_item = wxDataViewItem(m_objects[id]);
+		}
+	}
+	// free the node
+	delete node;
+
+	// set m_containet to FALSE if parent has no child
+	if (node_parent && node_parent->GetChildCount() == 0){
+#ifndef __WXGTK__
+		node_parent->m_container = false;
+#endif //__WXGTK__
+		ret_item = parent;
+	}
+
+	// notify control
+	ItemDeleted(parent, item);
+	return ret_item;
+}
+
+void PrusaObjectDataViewModel::DeleteAll()
+{
+	while (!m_objects.empty())
+	{
+		auto object = m_objects.back();
+// 		object->RemoveAllChildren();
+		Delete(wxDataViewItem(object));	
+	}
+}
+
+void PrusaObjectDataViewModel::DeleteChildren(wxDataViewItem& parent)
+{
+    PrusaObjectDataViewModelNode *root = (PrusaObjectDataViewModelNode*)parent.GetID();
+    if (!root)      // happens if item.IsOk()==false
+        return;
+
+    // first remove the node from the parent's array of children;
+    // NOTE: MyObjectTreeModelNodePtrArray is only an array of _pointers_
+    //       thus removing the node from it doesn't result in freeing it
+    auto& children = root->GetChildren();
+    for (int id = root->GetChildCount() - 1; id >= 0; --id)
+    {
+        auto node = children[id];
+        auto item = wxDataViewItem(node);
+        children.RemoveAt(id);
+
+        // free the node
+        delete node;
+
+        // notify control
+        ItemDeleted(parent, item);
+    }
+
+    // set m_containet to FALSE if parent has no child
+#ifndef __WXGTK__
+        root->m_container = false;
+#endif //__WXGTK__
+}
+
+wxDataViewItem PrusaObjectDataViewModel::GetItemById(int obj_idx)
+{
+	if (obj_idx >= m_objects.size())
+	{
+		printf("Error! Out of objects range.\n");
+		return wxDataViewItem(0);
+	}
+	return wxDataViewItem(m_objects[obj_idx]);
+}
+
+
+int PrusaObjectDataViewModel::GetIdByItem(wxDataViewItem& item)
+{
+	wxASSERT(item.IsOk());
+
+	PrusaObjectDataViewModelNode *node = (PrusaObjectDataViewModelNode*)item.GetID();
+	auto it = find(m_objects.begin(), m_objects.end(), node);
+	if (it == m_objects.end())
+		return -1;
+
+	return it - m_objects.begin();
+}
+
+int PrusaObjectDataViewModel::GetVolumeIdByItem(wxDataViewItem& item)
+{
+	wxASSERT(item.IsOk());
+
+	PrusaObjectDataViewModelNode *node = (PrusaObjectDataViewModelNode*)item.GetID();
+	if (!node)      // happens if item.IsOk()==false
+		return -1;
+	return node->GetVolumeId();
+}
+
+wxString PrusaObjectDataViewModel::GetName(const wxDataViewItem &item) const
+{
+	PrusaObjectDataViewModelNode *node = (PrusaObjectDataViewModelNode*)item.GetID();
+	if (!node)      // happens if item.IsOk()==false
+		return wxEmptyString;
+
+	return node->m_name;
+}
+
+wxString PrusaObjectDataViewModel::GetCopy(const wxDataViewItem &item) const
+{
+	PrusaObjectDataViewModelNode *node = (PrusaObjectDataViewModelNode*)item.GetID();
+	if (!node)      // happens if item.IsOk()==false
+		return wxEmptyString;
+
+	return node->m_copy;
+}
+
+wxString PrusaObjectDataViewModel::GetScale(const wxDataViewItem &item) const
+{
+	PrusaObjectDataViewModelNode *node = (PrusaObjectDataViewModelNode*)item.GetID();
+	if (!node)      // happens if item.IsOk()==false
+		return wxEmptyString;
+
+	return node->m_scale;
+}
+
+wxIcon& PrusaObjectDataViewModel::GetIcon(const wxDataViewItem &item) const
+{
+    PrusaObjectDataViewModelNode *node = (PrusaObjectDataViewModelNode*)item.GetID();
+    return node->m_icon;
+}
+
+void PrusaObjectDataViewModel::GetValue(wxVariant &variant, const wxDataViewItem &item, unsigned int col) const
+{
+	wxASSERT(item.IsOk());
+
+	PrusaObjectDataViewModelNode *node = (PrusaObjectDataViewModelNode*)item.GetID();
+	switch (col)
+	{
+	case 0:{
+		const wxDataViewIconText data(node->m_name, node->m_icon);
+		variant << data;
+		break;}
+	case 1:
+		variant = node->m_copy;
+		break;
+	case 2:
+		variant = node->m_scale;
+		break;
+	case 3:
+		variant = node->m_extruder;
+		break;
+	case 4:
+		variant << node->m_action_icon;
+		break;
+	default:
+		;
+	}
+}
+
+bool PrusaObjectDataViewModel::SetValue(const wxVariant &variant, const wxDataViewItem &item, unsigned int col)
+{
+	wxASSERT(item.IsOk());
+
+	PrusaObjectDataViewModelNode *node = (PrusaObjectDataViewModelNode*)item.GetID();
+	return node->SetValue(variant, col);
+}
+
+bool PrusaObjectDataViewModel::SetValue(const wxVariant &variant, const int item_idx, unsigned int col)
+{
+	if (item_idx < 0 || item_idx >= m_objects.size())
+		return false;
+
+	return m_objects[item_idx]->SetValue(variant, col);
+}
+
+wxDataViewItem PrusaObjectDataViewModel::MoveChildUp(const wxDataViewItem &item)
+{
+	auto ret_item = wxDataViewItem(0);
+	wxASSERT(item.IsOk());
+	PrusaObjectDataViewModelNode *node = (PrusaObjectDataViewModelNode*)item.GetID();
+	if (!node)      // happens if item.IsOk()==false
+		return ret_item;
+
+	auto node_parent = node->GetParent();
+	if (!node_parent) // If isn't part, but object
+		return ret_item;
+
+	auto volume_id = node->GetVolumeId();
+	if (0 < volume_id && volume_id < node_parent->GetChildCount()){
+		node_parent->SwapChildrens(volume_id - 1, volume_id);
+		ret_item = wxDataViewItem(node_parent->GetNthChild(volume_id - 1));
+		ItemChanged(item);
+		ItemChanged(ret_item);
+	}
+	else
+		ret_item = wxDataViewItem(node_parent->GetNthChild(0));
+	return ret_item;
+}
+
+wxDataViewItem PrusaObjectDataViewModel::MoveChildDown(const wxDataViewItem &item)
+{
+	auto ret_item = wxDataViewItem(0);
+	wxASSERT(item.IsOk());
+	PrusaObjectDataViewModelNode *node = (PrusaObjectDataViewModelNode*)item.GetID();
+	if (!node)      // happens if item.IsOk()==false
+		return ret_item;
+
+	auto node_parent = node->GetParent();
+	if (!node_parent) // If isn't part, but object
+		return ret_item;
+
+	auto volume_id = node->GetVolumeId();
+	if (0 <= volume_id && volume_id+1 < node_parent->GetChildCount()){
+		node_parent->SwapChildrens(volume_id + 1, volume_id);
+		ret_item = wxDataViewItem(node_parent->GetNthChild(volume_id + 1));
+		ItemChanged(item);
+		ItemChanged(ret_item);
+	}
+	else
+		ret_item = wxDataViewItem(node_parent->GetNthChild(node_parent->GetChildCount()-1));
+	return ret_item;
+}
+
+wxDataViewItem PrusaObjectDataViewModel::ReorganizeChildren(int current_volume_id, int new_volume_id, const wxDataViewItem &parent)
+{
+    auto ret_item = wxDataViewItem(0);
+    if (current_volume_id == new_volume_id)
+        return ret_item;
+    wxASSERT(parent.IsOk());
+    PrusaObjectDataViewModelNode *node_parent = (PrusaObjectDataViewModelNode*)parent.GetID();
+    if (!node_parent)      // happens if item.IsOk()==false
+        return ret_item;
+
+    PrusaObjectDataViewModelNode *deleted_node = node_parent->GetNthChild(current_volume_id);
+    node_parent->GetChildren().Remove(deleted_node);
+    ItemDeleted(parent, wxDataViewItem(deleted_node));
+    node_parent->Insert(deleted_node, new_volume_id);
+    ItemAdded(parent, wxDataViewItem(deleted_node));
+
+    //update volume_id value for child-nodes
+    auto children = node_parent->GetChildren();
+    int id_frst = current_volume_id < new_volume_id ? current_volume_id : new_volume_id;
+    int id_last = current_volume_id > new_volume_id ? current_volume_id : new_volume_id;
+    for (int id = id_frst; id <= id_last; ++id)
+        children[id]->SetVolumeId(id);
+
+    return wxDataViewItem(node_parent->GetNthChild(new_volume_id));
+}
+
+// bool MyObjectTreeModel::IsEnabled(const wxDataViewItem &item, unsigned int col) const
+// {
+// 
+// }
+
+wxDataViewItem PrusaObjectDataViewModel::GetParent(const wxDataViewItem &item) const
+{
+	// the invisible root node has no parent
+	if (!item.IsOk())
+		return wxDataViewItem(0);
+
+	PrusaObjectDataViewModelNode *node = (PrusaObjectDataViewModelNode*)item.GetID();
+
+	// objects nodes has no parent too
+	if (find(m_objects.begin(), m_objects.end(),node) != m_objects.end())
+		return wxDataViewItem(0);
+
+	return wxDataViewItem((void*)node->GetParent());
+}
+
+bool PrusaObjectDataViewModel::IsContainer(const wxDataViewItem &item) const
+{
+	// the invisible root node can have children
+	if (!item.IsOk())
+		return true;
+
+	PrusaObjectDataViewModelNode *node = (PrusaObjectDataViewModelNode*)item.GetID();
+	return node->IsContainer();
+}
+
+unsigned int PrusaObjectDataViewModel::GetChildren(const wxDataViewItem &parent, wxDataViewItemArray &array) const
+{
+	PrusaObjectDataViewModelNode *node = (PrusaObjectDataViewModelNode*)parent.GetID();
+	if (!node)
+	{
+		for (auto object : m_objects)
+			array.Add(wxDataViewItem((void*)object));
+		return m_objects.size();
+	}
+
+	if (node->GetChildCount() == 0)
+	{
+		return 0;
+	}
+
+	unsigned int count = node->GetChildren().GetCount();
+	for (unsigned int pos = 0; pos < count; pos++)
+	{
+		PrusaObjectDataViewModelNode *child = node->GetChildren().Item(pos);
+		array.Add(wxDataViewItem((void*)child));
+	}
+
+	return count;
+}
+
+// ************************************** EXPERIMENTS ***************************************
+PrusaDoubleSlider::PrusaDoubleSlider(   wxWindow *parent,
+                                        wxWindowID id,
+                                        int lowerValue, 
+                                        int higherValue, 
+                                        int minValue, 
+                                        int maxValue,
+                                        const wxPoint& pos,
+                                        const wxSize& size,
+                                        long style,
+                                        const wxValidator& val,
+                                        const wxString& name) : 
+    wxControl(parent, id, pos, size, wxWANTS_CHARS | wxBORDER_NONE),
+    m_lower_value(lowerValue), m_higher_value (higherValue), 
+    m_min_value(minValue), m_max_value(maxValue),
+    m_style(style == wxSL_HORIZONTAL || style == wxSL_VERTICAL ? style: wxSL_HORIZONTAL)
+{
+#ifndef __WXOSX__ // SetDoubleBuffered exists on Win and Linux/GTK, but is missing on OSX
+    SetDoubleBuffered(true);
+#endif //__WXOSX__
+
+    m_bmp_thumb_higher = wxBitmap(style == wxSL_HORIZONTAL ? Slic3r::GUI::from_u8(Slic3r::var("right_half_circle.png")) :
+                                                             Slic3r::GUI::from_u8(Slic3r::var("up_half_circle.png")), wxBITMAP_TYPE_PNG);
+    m_bmp_thumb_lower  = wxBitmap(style == wxSL_HORIZONTAL ? Slic3r::GUI::from_u8(Slic3r::var("left_half_circle.png")) :
+                                                             Slic3r::GUI::from_u8(Slic3r::var("down_half_circle.png")), wxBITMAP_TYPE_PNG);
+    m_thumb_size = m_bmp_thumb_lower.GetSize();
+
+    m_bmp_add_tick_on  = wxBitmap(Slic3r::GUI::from_u8(Slic3r::var("colorchange_add_on.png")), wxBITMAP_TYPE_PNG);
+    m_bmp_add_tick_off = wxBitmap(Slic3r::GUI::from_u8(Slic3r::var("colorchange_add_off.png")), wxBITMAP_TYPE_PNG);
+    m_bmp_del_tick_on  = wxBitmap(Slic3r::GUI::from_u8(Slic3r::var("colorchange_delete_on.png")), wxBITMAP_TYPE_PNG);
+    m_bmp_del_tick_off = wxBitmap(Slic3r::GUI::from_u8(Slic3r::var("colorchange_delete_off.png")), wxBITMAP_TYPE_PNG);
+    m_tick_icon_dim = m_bmp_add_tick_on.GetSize().x;
+
+    m_bmp_one_layer_lock_on    = wxBitmap(Slic3r::GUI::from_u8(Slic3r::var("one_layer_lock_on.png")), wxBITMAP_TYPE_PNG);
+    m_bmp_one_layer_lock_off   = wxBitmap(Slic3r::GUI::from_u8(Slic3r::var("one_layer_lock_off.png")), wxBITMAP_TYPE_PNG);
+    m_bmp_one_layer_unlock_on  = wxBitmap(Slic3r::GUI::from_u8(Slic3r::var("one_layer_unlock_on.png")), wxBITMAP_TYPE_PNG);
+    m_bmp_one_layer_unlock_off = wxBitmap(Slic3r::GUI::from_u8(Slic3r::var("one_layer_unlock_off.png")), wxBITMAP_TYPE_PNG);
+    m_lock_icon_dim = m_bmp_one_layer_lock_on.GetSize().x;
+
+    m_selection = ssUndef;
+
+    // slider events
+    Bind(wxEVT_PAINT,       &PrusaDoubleSlider::OnPaint,    this);
+    Bind(wxEVT_LEFT_DOWN,   &PrusaDoubleSlider::OnLeftDown, this);
+    Bind(wxEVT_MOTION,      &PrusaDoubleSlider::OnMotion,   this);
+    Bind(wxEVT_LEFT_UP,     &PrusaDoubleSlider::OnLeftUp,   this);
+    Bind(wxEVT_MOUSEWHEEL,  &PrusaDoubleSlider::OnWheel,    this);
+    Bind(wxEVT_ENTER_WINDOW,&PrusaDoubleSlider::OnEnterWin, this);
+    Bind(wxEVT_LEAVE_WINDOW,&PrusaDoubleSlider::OnLeaveWin, this);
+    Bind(wxEVT_KEY_DOWN,    &PrusaDoubleSlider::OnKeyDown,  this);
+    Bind(wxEVT_KEY_UP,      &PrusaDoubleSlider::OnKeyUp,    this);
+    Bind(wxEVT_RIGHT_DOWN,  &PrusaDoubleSlider::OnRightDown,this);
+    Bind(wxEVT_RIGHT_UP,    &PrusaDoubleSlider::OnRightUp,  this);
+
+    // control's view variables
+    SLIDER_MARGIN     = 4 + (style == wxSL_HORIZONTAL ? m_bmp_thumb_higher.GetWidth() : m_bmp_thumb_higher.GetHeight());
+
+    DARK_ORANGE_PEN   = wxPen(wxColour(253, 84, 2));
+    ORANGE_PEN        = wxPen(wxColour(253, 126, 66));
+    LIGHT_ORANGE_PEN  = wxPen(wxColour(254, 177, 139));
+
+    DARK_GREY_PEN     = wxPen(wxColour(128, 128, 128));
+    GREY_PEN          = wxPen(wxColour(164, 164, 164));
+    LIGHT_GREY_PEN    = wxPen(wxColour(204, 204, 204));
+
+    line_pens = { &DARK_GREY_PEN, &GREY_PEN, &LIGHT_GREY_PEN };
+    segm_pens = { &DARK_ORANGE_PEN, &ORANGE_PEN, &LIGHT_ORANGE_PEN };
+}
+
+int PrusaDoubleSlider::GetActiveValue() const
+{
+    return m_selection == ssLower ?
+    m_lower_value : m_selection == ssHigher ?
+                m_higher_value : -1;
+}
+
+wxSize PrusaDoubleSlider::DoGetBestSize() const
+{
+    const wxSize size = wxControl::DoGetBestSize();
+    if (size.x > 1 && size.y > 1)
+        return size;
+    const int new_size = is_horizontal() ? 80 : 120;
+    return wxSize(new_size, new_size);
+}
+
+void PrusaDoubleSlider::SetLowerValue(const int lower_val)
+{
+    m_lower_value = lower_val;
+    Refresh();
+    Update();
+}
+
+void PrusaDoubleSlider::SetHigherValue(const int higher_val)
+{
+    m_higher_value = higher_val;
+    Refresh();
+    Update();
+}
+
+void PrusaDoubleSlider::SetMaxValue(const int max_value)
+{
+    m_max_value = max_value;
+    Refresh();
+    Update();
+}
+
+void PrusaDoubleSlider::draw_scroll_line(wxDC& dc, const int lower_pos, const int higher_pos)
+{
+    int width;
+    int height;
+    get_size(&width, &height);
+
+    wxCoord line_beg_x = is_horizontal() ? SLIDER_MARGIN : width*0.5 - 1;
+    wxCoord line_beg_y = is_horizontal() ? height*0.5 - 1 : SLIDER_MARGIN;
+    wxCoord line_end_x = is_horizontal() ? width - SLIDER_MARGIN + 1 : width*0.5 - 1;
+    wxCoord line_end_y = is_horizontal() ? height*0.5 - 1 : height - SLIDER_MARGIN + 1;
+
+    wxCoord segm_beg_x = is_horizontal() ? lower_pos : width*0.5 - 1;
+    wxCoord segm_beg_y = is_horizontal() ? height*0.5 - 1 : lower_pos-1;
+    wxCoord segm_end_x = is_horizontal() ? higher_pos : width*0.5 - 1;
+    wxCoord segm_end_y = is_horizontal() ? height*0.5 - 1 : higher_pos-1;
+
+    for (int id = 0; id < line_pens.size(); id++)
+    {
+        dc.SetPen(*line_pens[id]);
+        dc.DrawLine(line_beg_x, line_beg_y, line_end_x, line_end_y);
+        dc.SetPen(*segm_pens[id]);
+        dc.DrawLine(segm_beg_x, segm_beg_y, segm_end_x, segm_end_y);
+        if (is_horizontal())
+            line_beg_y = line_end_y = segm_beg_y = segm_end_y += 1;
+        else
+            line_beg_x = line_end_x = segm_beg_x = segm_end_x += 1;
+    }
+}
+
+double PrusaDoubleSlider::get_scroll_step()
+{
+    const wxSize sz = get_size();
+    const int& slider_len = m_style == wxSL_HORIZONTAL ? sz.x : sz.y;
+    return double(slider_len - SLIDER_MARGIN * 2) / (m_max_value - m_min_value);
+}
+
+// get position on the slider line from entered value
+wxCoord PrusaDoubleSlider::get_position_from_value(const int value)
+{
+    const double step = get_scroll_step();
+    const int val = is_horizontal() ? value : m_max_value - value;
+    return wxCoord(SLIDER_MARGIN + int(val*step + 0.5));
+}
+
+wxSize PrusaDoubleSlider::get_size()
+{
+    int w, h;
+    get_size(&w, &h);
+    return wxSize(w, h);
+}
+
+void PrusaDoubleSlider::get_size(int *w, int *h)
+{
+    GetSize(w, h);
+    is_horizontal() ? *w -= m_lock_icon_dim : *h -= m_lock_icon_dim;
+}
+
+void PrusaDoubleSlider::get_lower_and_higher_position(int& lower_pos, int& higher_pos)
+{
+    const double step = get_scroll_step();
+    if (is_horizontal()) {
+        lower_pos = SLIDER_MARGIN + int(m_lower_value*step + 0.5);
+        higher_pos = SLIDER_MARGIN + int(m_higher_value*step + 0.5);
+    }
+    else {
+        lower_pos = SLIDER_MARGIN + int((m_max_value - m_lower_value)*step + 0.5);
+        higher_pos = SLIDER_MARGIN + int((m_max_value - m_higher_value)*step + 0.5);
+    }
+}
+
+void PrusaDoubleSlider::draw_focus_rect()
+{
+    if (!m_is_focused) 
+        return;
+    const wxSize sz = GetSize();
+    wxPaintDC dc(this);
+    const wxPen pen = wxPen(wxColour(128, 128, 10), 1, wxPENSTYLE_DOT);
+    dc.SetPen(pen);
+    dc.SetBrush(wxBrush(wxColour(0, 0, 0), wxBRUSHSTYLE_TRANSPARENT));
+    dc.DrawRectangle(1, 1, sz.x - 2, sz.y - 2);
+}
+
+void PrusaDoubleSlider::render()
+{
+    SetBackgroundColour(GetParent()->GetBackgroundColour());
+    draw_focus_rect();
+
+    wxPaintDC dc(this);
+    wxFont font = dc.GetFont();
+    const wxFont smaller_font = font.Smaller();
+    dc.SetFont(smaller_font);
+
+    const wxCoord lower_pos = get_position_from_value(m_lower_value);
+    const wxCoord higher_pos = get_position_from_value(m_higher_value);
+
+    // draw line
+    draw_scroll_line(dc, lower_pos, higher_pos);
+
+//     //lower slider:
+//     draw_thumb(dc, lower_pos, ssLower);
+//     //higher slider:
+//     draw_thumb(dc, higher_pos, ssHigher);
+
+    // draw both sliders
+    draw_thumbs(dc, lower_pos, higher_pos);
+
+    //draw color print ticks
+    draw_ticks(dc);
+
+    //draw color print ticks
+    draw_one_layer_icon(dc);
+}
+
+void PrusaDoubleSlider::draw_action_icon(wxDC& dc, const wxPoint pt_beg, const wxPoint pt_end)
+{
+    const int tick = m_selection == ssLower ? m_lower_value : m_higher_value;
+    wxBitmap* icon = m_is_action_icon_focesed ? &m_bmp_add_tick_off : &m_bmp_add_tick_on;
+    if (m_ticks.find(tick) != m_ticks.end())
+        icon = m_is_action_icon_focesed ? &m_bmp_del_tick_off : &m_bmp_del_tick_on;
+
+    wxCoord x_draw, y_draw;
+    is_horizontal() ? x_draw = pt_beg.x - 0.5*m_tick_icon_dim : y_draw = pt_beg.y - 0.5*m_tick_icon_dim;
+    if (m_selection == ssLower)
+        is_horizontal() ? y_draw = pt_end.y + 3 : x_draw = pt_beg.x - m_tick_icon_dim-2;
+    else
+        is_horizontal() ? y_draw = pt_beg.y - m_tick_icon_dim-2 : x_draw = pt_end.x + 3;
+
+    dc.DrawBitmap(*icon, x_draw, y_draw);
+
+    //update rect of the tick action icon
+    m_rect_tick_action = wxRect(x_draw, y_draw, m_tick_icon_dim, m_tick_icon_dim);
+}
+
+void PrusaDoubleSlider::draw_info_line_with_icon(wxDC& dc, const wxPoint& pos, const SelectedSlider selection)
+{
+    if (m_selection == selection) {
+        //draw info line
+        dc.SetPen(DARK_ORANGE_PEN);
+        const wxPoint pt_beg = is_horizontal() ? wxPoint(pos.x, pos.y - m_thumb_size.y) : wxPoint(pos.x - m_thumb_size.x, pos.y - 1);
+        const wxPoint pt_end = is_horizontal() ? wxPoint(pos.x, pos.y + m_thumb_size.y) : wxPoint(pos.x + m_thumb_size.x, pos.y - 1);
+        dc.DrawLine(pt_beg, pt_end);
+
+        //draw action icon
+        draw_action_icon(dc, pt_beg, pt_end);
+    }
+}
+
+wxString PrusaDoubleSlider::get_label(const SelectedSlider& selection) const
+{
+    const int value = selection == ssLower ? m_lower_value : m_higher_value;
+
+    if (m_label_koef == 1.0 && m_values.empty())
+        return wxString::Format("%d", value);
+
+    const wxString str = m_values.empty() ? 
+                         wxNumberFormatter::ToString(m_label_koef*value, 2, wxNumberFormatter::Style_None) :
+                         wxNumberFormatter::ToString(m_values[value], 2, wxNumberFormatter::Style_None);
+    return wxString::Format("%s\n(%d)", str, value);
+}
+
+void PrusaDoubleSlider::draw_thumb_text(wxDC& dc, const wxPoint& pos, const SelectedSlider& selection) const
+{
+    if (m_is_one_layer && selection != m_selection || !selection) 
+        return;
+    wxCoord text_width, text_height;
+    const wxString label = get_label(selection);
+    dc.GetMultiLineTextExtent(label, &text_width, &text_height);
+    wxPoint text_pos;
+    if (selection ==ssLower)
+        text_pos = is_horizontal() ? wxPoint(pos.x + 1, pos.y + m_thumb_size.x) :
+                           wxPoint(pos.x + m_thumb_size.x+1, pos.y - 0.5*text_height - 1);
+    else
+        text_pos = is_horizontal() ? wxPoint(pos.x - text_width - 1, pos.y - m_thumb_size.x - text_height) :
+                    wxPoint(pos.x - text_width - 1 - m_thumb_size.x, pos.y - 0.5*text_height + 1);
+    dc.DrawText(label, text_pos);
+}
+
+void PrusaDoubleSlider::draw_thumb_item(wxDC& dc, const wxPoint& pos, const SelectedSlider& selection)
+{
+    wxCoord x_draw, y_draw;
+    if (selection == ssLower) {
+        if (is_horizontal()) {
+            x_draw = pos.x - m_thumb_size.x;
+            y_draw = pos.y - int(0.5*m_thumb_size.y);
+        }
+        else {
+            x_draw = pos.x - int(0.5*m_thumb_size.x);
+            y_draw = pos.y;
+        }
+    }
+    else{
+        if (is_horizontal()) {
+            x_draw = pos.x;
+            y_draw = pos.y - int(0.5*m_thumb_size.y);
+        }
+        else {
+            x_draw = pos.x - int(0.5*m_thumb_size.x);
+            y_draw = pos.y - m_thumb_size.y;
+        }
+    }
+    dc.DrawBitmap(selection == ssLower ? m_bmp_thumb_lower : m_bmp_thumb_higher, x_draw, y_draw);
+
+    // Update thumb rect
+    update_thumb_rect(x_draw, y_draw, selection);
+}
+
+void PrusaDoubleSlider::draw_thumb(wxDC& dc, const wxCoord& pos_coord, const SelectedSlider& selection)
+{
+    //calculate thumb position on slider line
+    int width, height;
+    get_size(&width, &height);
+    const wxPoint pos = is_horizontal() ? wxPoint(pos_coord, height*0.5) : wxPoint(0.5*width, pos_coord);
+
+    // Draw thumb
+    draw_thumb_item(dc, pos, selection);
+
+    // Draw info_line
+    draw_info_line_with_icon(dc, pos, selection);
+
+    // Draw thumb text
+    draw_thumb_text(dc, pos, selection);
+}
+
+void PrusaDoubleSlider::draw_thumbs(wxDC& dc, const wxCoord& lower_pos, const wxCoord& higher_pos)
+{
+    //calculate thumb position on slider line
+    int width, height;
+    get_size(&width, &height);
+    const wxPoint pos_l = is_horizontal() ? wxPoint(lower_pos, height*0.5) : wxPoint(0.5*width, lower_pos);
+    const wxPoint pos_h = is_horizontal() ? wxPoint(higher_pos, height*0.5) : wxPoint(0.5*width, higher_pos);
+
+    // Draw lower thumb
+    draw_thumb_item(dc, pos_l, ssLower);
+    // Draw lower info_line
+    draw_info_line_with_icon(dc, pos_l, ssLower);
+
+    // Draw higher thumb
+    draw_thumb_item(dc, pos_h, ssHigher);
+    // Draw higher info_line
+    draw_info_line_with_icon(dc, pos_h, ssHigher);
+    // Draw higher thumb text
+    draw_thumb_text(dc, pos_h, ssHigher);
+
+    // Draw lower thumb text
+    draw_thumb_text(dc, pos_l, ssLower);
+}
+
+void PrusaDoubleSlider::draw_ticks(wxDC& dc)
+{
+    dc.SetPen(DARK_GREY_PEN);
+    int height, width;
+    get_size(&width, &height);
+    const wxCoord mid = is_horizontal() ? 0.5*height : 0.5*width;
+    for (auto tick : m_ticks)
+    {
+        const wxCoord pos = get_position_from_value(tick);
+
+        is_horizontal() ?   dc.DrawLine(pos, mid-14, pos, mid-9) :
+                            dc.DrawLine(mid - 14, pos - 1, mid - 9, pos - 1);
+        is_horizontal() ?   dc.DrawLine(pos, mid+14, pos, mid+9) :
+                            dc.DrawLine(mid + 14, pos - 1, mid + 9, pos - 1);
+    }
+}
+
+void PrusaDoubleSlider::draw_one_layer_icon(wxDC& dc)
+{
+    wxBitmap* icon = m_is_one_layer ?
+                     m_is_one_layer_icon_focesed ? &m_bmp_one_layer_lock_off : &m_bmp_one_layer_lock_on :
+                     m_is_one_layer_icon_focesed ? &m_bmp_one_layer_unlock_off : &m_bmp_one_layer_unlock_on;
+
+    int width, height;
+    get_size(&width, &height);
+
+    wxCoord x_draw, y_draw;
+    is_horizontal() ? x_draw = width-2 : x_draw = 0.5*width - 0.5*m_lock_icon_dim;
+    is_horizontal() ? y_draw = 0.5*height - 0.5*m_lock_icon_dim : y_draw = height-2;
+
+    dc.DrawBitmap(*icon, x_draw, y_draw);
+
+    //update rect of the lock/unlock icon
+    m_rect_one_layer_icon = wxRect(x_draw, y_draw, m_lock_icon_dim, m_lock_icon_dim);
+}
+
+void PrusaDoubleSlider::update_thumb_rect(const wxCoord& begin_x, const wxCoord& begin_y, const SelectedSlider& selection)
+{
+    const wxRect& rect = wxRect(begin_x, begin_y, m_thumb_size.x, m_thumb_size.y);
+    if (selection == ssLower)
+        m_rect_lower_thumb = rect;
+    else
+        m_rect_higher_thumb = rect;
+}
+
+int PrusaDoubleSlider::get_value_from_position(const wxCoord x, const wxCoord y)
+{
+    const int height = get_size().y;
+    const double step = get_scroll_step();
+    
+    if (is_horizontal()) 
+        return int(double(x - SLIDER_MARGIN) / step + 0.5);
+    else 
+        return int(m_min_value + double(height - SLIDER_MARGIN - y) / step + 0.5);
+}
+
+void PrusaDoubleSlider::detect_selected_slider(const wxPoint& pt, const bool is_mouse_wheel /*= false*/)
+{
+    if (is_mouse_wheel)
+    {
+        if (is_horizontal()) {
+            m_selection = pt.x <= m_rect_lower_thumb.GetRight() ? ssLower :
+                          pt.x >= m_rect_higher_thumb.GetLeft() ? ssHigher : ssUndef;
+        }
+        else {
+            m_selection = pt.y >= m_rect_lower_thumb.GetTop() ? ssLower :
+                          pt.y <= m_rect_higher_thumb.GetBottom() ? ssHigher : ssUndef;            
+        }
+        return;
+    }
+
+    m_selection = is_point_in_rect(pt, m_rect_lower_thumb) ? ssLower :
+                  is_point_in_rect(pt, m_rect_higher_thumb) ? ssHigher : ssUndef;
+}
+
+bool PrusaDoubleSlider::is_point_in_rect(const wxPoint& pt, const wxRect& rect)
+{
+    if (rect.GetLeft() <= pt.x && pt.x <= rect.GetRight() && 
+        rect.GetTop()  <= pt.y && pt.y <= rect.GetBottom())
+        return true;
+    return false;
+}
+
+void PrusaDoubleSlider::OnLeftDown(wxMouseEvent& event)
+{
+    this->CaptureMouse();
+    wxClientDC dc(this);
+    wxPoint pos = event.GetLogicalPosition(dc);
+    if (is_point_in_rect(pos, m_rect_tick_action)) {
+        action_tick(taOnIcon);
+        return;
+    }
+
+    m_is_left_down = true;
+    if (is_point_in_rect(pos, m_rect_one_layer_icon)){
+        m_is_one_layer = !m_is_one_layer;
+        m_selection == ssLower ? correct_lower_value() : correct_higher_value();
+        if (!m_selection) m_selection = ssHigher;
+    }
+    else
+        detect_selected_slider(pos);
+
+    Refresh();
+    Update();
+    event.Skip();
+}
+
+void PrusaDoubleSlider::correct_lower_value()
+{
+    if (m_lower_value < m_min_value)
+        m_lower_value = m_min_value;
+    else if (m_lower_value > m_max_value)
+        m_lower_value = m_max_value;
+    
+    if (m_lower_value >= m_higher_value && m_lower_value <= m_max_value || m_is_one_layer)
+        m_higher_value = m_lower_value;
+}
+
+void PrusaDoubleSlider::correct_higher_value()
+{
+    if (m_higher_value > m_max_value)
+        m_higher_value = m_max_value;
+    else if (m_higher_value < m_min_value)
+        m_higher_value = m_min_value;
+    
+    if (m_higher_value <= m_lower_value && m_higher_value >= m_min_value || m_is_one_layer)
+        m_lower_value = m_higher_value;
+}
+
+void PrusaDoubleSlider::OnMotion(wxMouseEvent& event)
+{
+    const wxClientDC dc(this);
+    const wxPoint pos = event.GetLogicalPosition(dc);
+    m_is_one_layer_icon_focesed = is_point_in_rect(pos, m_rect_one_layer_icon);
+    if (!m_is_left_down && !m_is_one_layer){
+        m_is_action_icon_focesed = is_point_in_rect(pos, m_rect_tick_action);
+    }
+    else if (m_is_left_down || m_is_right_down){
+        if (m_selection == ssLower) {
+            m_lower_value = get_value_from_position(pos.x, pos.y);
+            correct_lower_value();
+        }
+        else if (m_selection == ssHigher) {
+            m_higher_value = get_value_from_position(pos.x, pos.y);
+            correct_higher_value();
+        }
+    }
+    Refresh();
+    Update();
+    event.Skip();
+}
+
+void PrusaDoubleSlider::OnLeftUp(wxMouseEvent& event)
+{
+    this->ReleaseMouse();
+    m_is_left_down = false;
+    Refresh();
+    Update();
+    event.Skip();
+
+    wxCommandEvent e(wxEVT_SCROLL_CHANGED);
+    e.SetEventObject(this);
+    ProcessWindowEvent(e);
+}
+
+void PrusaDoubleSlider::enter_window(wxMouseEvent& event, const bool enter)
+{
+    m_is_focused = enter;
+    Refresh();
+    Update();
+    event.Skip();
+}
+
+// "condition" have to be true for:
+//    -  value increase (if wxSL_VERTICAL)
+//    -  value decrease (if wxSL_HORIZONTAL) 
+void PrusaDoubleSlider::move_current_thumb(const bool condition)
+{
+    m_is_one_layer = wxGetKeyState(WXK_CONTROL);
+    int delta = condition ? -1 : 1;
+    if (is_horizontal())
+        delta *= -1;
+
+    if (m_selection == ssLower) {
+        m_lower_value -= delta;
+        correct_lower_value();
+    }
+    else if (m_selection == ssHigher) {
+        m_higher_value -= delta;
+        correct_higher_value();
+    }
+    Refresh();
+    Update();
+
+    wxCommandEvent e(wxEVT_SCROLL_CHANGED);
+    e.SetEventObject(this);
+    ProcessWindowEvent(e);
+}
+
+void PrusaDoubleSlider::action_tick(const TicksAction action)
+{
+    if (m_selection == ssUndef)
+        return;
+
+    const int tick = m_selection == ssLower ? m_lower_value : m_higher_value;
+
+    if (action == taOnIcon && !m_ticks.insert(tick).second)
+        m_ticks.erase(tick);
+    else {
+        const auto it = m_ticks.find(tick);
+        if (it == m_ticks.end() && action == taAdd)
+            m_ticks.insert(tick);
+        else if (it != m_ticks.end() && action == taDel)
+            m_ticks.erase(tick);
+        else
+            return;
+    }
+
+    Refresh();
+    Update();
+}
+
+void PrusaDoubleSlider::OnWheel(wxMouseEvent& event)
+{
+    wxClientDC dc(this);
+    wxPoint pos = event.GetLogicalPosition(dc);
+    detect_selected_slider(pos, true);
+
+    if (m_selection == ssUndef)
+        return;
+
+    move_current_thumb(event.GetWheelRotation() > 0);
+}
+
+void PrusaDoubleSlider::OnKeyDown(wxKeyEvent &event)
+{
+    const int key = event.GetKeyCode();
+    if (key == '+' || key == WXK_NUMPAD_ADD)
+        action_tick(taAdd);
+    else if (key == '-' || key == 390 || key == WXK_DELETE || key == WXK_BACK)
+        action_tick(taDel);
+    else if (is_horizontal())
+    {
+        if (key == WXK_LEFT || key == WXK_RIGHT)
+            move_current_thumb(key == WXK_LEFT); 
+        else if (key == WXK_UP || key == WXK_DOWN){
+            m_selection = key == WXK_UP ? ssHigher : ssLower;
+            Refresh();
+        }
+    }
+    else {
+        if (key == WXK_LEFT || key == WXK_RIGHT) {
+            m_selection = key == WXK_LEFT ? ssHigher : ssLower;
+            Refresh();
+        }
+        else if (key == WXK_UP || key == WXK_DOWN)
+            move_current_thumb(key == WXK_UP);
+    }
+}
+
+void PrusaDoubleSlider::OnKeyUp(wxKeyEvent &event)
+{
+    if (event.GetKeyCode() == WXK_CONTROL)
+        m_is_one_layer = false;
+    Refresh();
+    Update();
+    event.Skip();
+}
+
+void PrusaDoubleSlider::OnRightDown(wxMouseEvent& event)
+{
+    this->CaptureMouse();
+    const wxClientDC dc(this);
+    detect_selected_slider(event.GetLogicalPosition(dc));
+    if (!m_selection)
+        return;
+
+    if (m_selection == ssLower)
+        m_higher_value = m_lower_value;
+    else
+        m_lower_value = m_higher_value;
+
+    m_is_right_down = m_is_one_layer = true;
+
+    Refresh();
+    Update();
+    event.Skip();
+}
+
+void PrusaDoubleSlider::OnRightUp(wxMouseEvent& event)
+{
+    this->ReleaseMouse();
+    m_is_right_down = m_is_one_layer = false;
+
+    Refresh();
+    Update();
+    event.Skip();
+}
+
+// *****************************************************************************
diff --git a/xs/src/slic3r/GUI/wxExtensions.hpp b/xs/src/slic3r/GUI/wxExtensions.hpp
index 3667c7905b..064ce10389 100644
--- a/xs/src/slic3r/GUI/wxExtensions.hpp
+++ b/xs/src/slic3r/GUI/wxExtensions.hpp
@@ -4,6 +4,14 @@
 #include <wx/checklst.h>
 #include <wx/combo.h>
 #include <wx/dataview.h>
+#include <wx/dc.h>
+#include <wx/collpane.h>
+#include <wx/wupdlock.h>
+#include <wx/button.h>
+#include <wx/slider.h>
+
+#include <vector>
+#include <set>
 
 class wxCheckListBoxComboPopup : public wxCheckListBox, public wxComboPopup
 {
@@ -65,4 +73,568 @@ public:
 	void				SetItemsCnt(int cnt) { m_cnt_open_items = cnt; }
 };
 
+
+
+// ***  PrusaCollapsiblePane  *** 
+// ----------------------------------------------------------------------------
+class PrusaCollapsiblePane : public wxCollapsiblePane
+{
+public:
+	PrusaCollapsiblePane() {}
+	PrusaCollapsiblePane(wxWindow *parent,
+		wxWindowID winid,
+		const wxString& label,
+		const wxPoint& pos = wxDefaultPosition,
+		const wxSize& size = wxDefaultSize,
+		long style = wxCP_DEFAULT_STYLE,
+		const wxValidator& val = wxDefaultValidator,
+		const wxString& name = wxCollapsiblePaneNameStr)
+	{
+		Create(parent, winid, label, pos, size, style, val, name);
+	}
+	~PrusaCollapsiblePane() {}
+
+	void OnStateChange(const wxSize& sz); //override/hide of OnStateChange from wxCollapsiblePane
+	virtual bool Show(bool show = true) override {
+		wxCollapsiblePane::Show(show);
+		OnStateChange(GetBestSize());
+		return true;
+	}
+};
+
+
+// ***  PrusaCollapsiblePaneMSW  ***  used only #ifdef __WXMSW__
+// ----------------------------------------------------------------------------
+#ifdef __WXMSW__
+class PrusaCollapsiblePaneMSW : public PrusaCollapsiblePane//wxCollapsiblePane
+{
+	wxButton*	m_pDisclosureTriangleButton = nullptr;
+	wxBitmap	m_bmp_close;
+	wxBitmap	m_bmp_open;
+public:
+	PrusaCollapsiblePaneMSW() {}
+	PrusaCollapsiblePaneMSW(	wxWindow *parent,
+							wxWindowID winid,
+							const wxString& label,
+							const wxPoint& pos = wxDefaultPosition,
+							const wxSize& size = wxDefaultSize,
+							long style = wxCP_DEFAULT_STYLE,
+							const wxValidator& val = wxDefaultValidator,
+							const wxString& name = wxCollapsiblePaneNameStr)
+	{
+		Create(parent, winid, label, pos, size, style, val, name);
+	}
+
+	~PrusaCollapsiblePaneMSW() {}
+
+	bool Create(wxWindow *parent,
+				wxWindowID id,
+				const wxString& label,
+				const wxPoint& pos,
+				const wxSize& size,
+				long style,
+				const wxValidator& val,
+				const wxString& name);
+
+	void UpdateBtnBmp();
+	void SetLabel(const wxString &label) override;
+	bool Layout() override;
+	void Collapse(bool collapse) override;
+};
+#endif //__WXMSW__
+
+// *****************************************************************************
+// ----------------------------------------------------------------------------
+// PrusaObjectDataViewModelNode: a node inside PrusaObjectDataViewModel
+// ----------------------------------------------------------------------------
+
+class PrusaObjectDataViewModelNode;
+WX_DEFINE_ARRAY_PTR(PrusaObjectDataViewModelNode*, MyObjectTreeModelNodePtrArray);
+
+class PrusaObjectDataViewModelNode
+{
+	PrusaObjectDataViewModelNode*	m_parent;
+	MyObjectTreeModelNodePtrArray   m_children;
+    wxIcon                          m_empty_icon; 
+public:
+	PrusaObjectDataViewModelNode(const wxString &name, int instances_count=1, int scale=100) {
+		m_parent	= NULL;
+		m_name		= name;
+		m_copy		= wxString::Format("%d", instances_count);
+		m_scale		= wxString::Format("%d%%", scale);
+		m_type		= "object";
+		m_volume_id	= -1;
+#ifdef __WXGTK__
+        // it's necessary on GTK because of control have to know if this item will be container
+        // in another case you couldn't to add subitem for this item
+        // it will be produce "segmentation fault"
+        m_container = true;
+#endif  //__WXGTK__
+		set_object_action_icon();
+	}
+
+	PrusaObjectDataViewModelNode(	PrusaObjectDataViewModelNode* parent,
+									const wxString& sub_obj_name, 
+									const wxIcon& icon, 
+                                    const wxString& extruder, 
+									const int volume_id=-1) {
+		m_parent	= parent;
+		m_name		= sub_obj_name;
+		m_copy		= wxEmptyString;
+		m_scale		= wxEmptyString;
+		m_icon		= icon;
+		m_type		= "volume";
+		m_volume_id = volume_id;
+        m_extruder  = extruder;
+		set_part_action_icon();
+	}
+
+	~PrusaObjectDataViewModelNode()
+	{
+		// free all our children nodes
+		size_t count = m_children.GetCount();
+		for (size_t i = 0; i < count; i++)
+		{
+			PrusaObjectDataViewModelNode *child = m_children[i];
+			delete child;
+		}
+	}
+	
+	wxString				m_name;
+	wxIcon&					m_icon = m_empty_icon;
+	wxString				m_copy;
+	wxString				m_scale;
+	std::string				m_type;
+	int						m_volume_id;
+	bool					m_container = false;
+	wxString				m_extruder = "default";
+	wxBitmap				m_action_icon;
+
+	bool IsContainer() const
+	{
+		return m_container;
+	}
+
+	PrusaObjectDataViewModelNode* GetParent()
+	{
+		return m_parent;
+	}
+	MyObjectTreeModelNodePtrArray& GetChildren()
+	{
+		return m_children;
+	}
+	PrusaObjectDataViewModelNode* GetNthChild(unsigned int n)
+	{
+		return m_children.Item(n);
+	}
+	void Insert(PrusaObjectDataViewModelNode* child, unsigned int n)
+	{
+		m_children.Insert(child, n);
+	}
+	void Append(PrusaObjectDataViewModelNode* child)
+	{
+		if (!m_container)
+			m_container = true;
+		m_children.Add(child);
+	}
+	void RemoveAllChildren()
+	{
+		if (GetChildCount() == 0)
+			return;
+		for (size_t id = GetChildCount() - 1; id >= 0; --id)
+		{
+			if (m_children.Item(id)->GetChildCount() > 0)
+				m_children[id]->RemoveAllChildren();
+			auto node = m_children[id];
+			m_children.RemoveAt(id);
+			delete node;
+		}
+	}
+
+	size_t GetChildCount() const
+	{
+		return m_children.GetCount();
+	}
+
+	bool SetValue(const wxVariant &variant, unsigned int col)
+	{
+		switch (col)
+		{
+		case 0:{
+			wxDataViewIconText data;
+			data << variant;
+			m_icon = data.GetIcon();
+			m_name = data.GetText();
+			return true;}
+		case 1:
+			m_copy = variant.GetString();
+			return true;
+		case 2:
+			m_scale = variant.GetString();
+			return true;
+		case 3:
+			m_extruder = variant.GetString();
+			return true;
+		case 4:
+			m_action_icon << variant;
+			return true;
+		default:
+			printf("MyObjectTreeModel::SetValue: wrong column");
+		}
+		return false;
+	}
+	void SetIcon(const wxIcon &icon)
+	{
+		m_icon = icon;
+	}
+	
+	void SetType(const std::string& type){
+		m_type = type;
+	}	
+	const std::string& GetType(){
+		return m_type;
+	}
+
+	void SetVolumeId(const int& volume_id){
+		m_volume_id = volume_id;
+	}
+	const int& GetVolumeId(){
+		return m_volume_id;
+	}
+
+	// use this function only for childrens
+	void AssignAllVal(PrusaObjectDataViewModelNode& from_node)
+	{
+		// ! Don't overwrite other values because of equality of this values for all children --
+		m_name = from_node.m_name;
+		m_icon = from_node.m_icon;
+		m_volume_id = from_node.m_volume_id;
+		m_extruder = from_node.m_extruder;
+	}
+
+	bool SwapChildrens(int frst_id, int scnd_id) {
+		if (GetChildCount() < 2 || 
+			frst_id < 0 || frst_id >= GetChildCount() || 
+			scnd_id < 0 || scnd_id >= GetChildCount())
+			return false;
+
+		PrusaObjectDataViewModelNode new_scnd = *GetNthChild(frst_id);
+		PrusaObjectDataViewModelNode new_frst = *GetNthChild(scnd_id);
+
+		new_scnd.m_volume_id = m_children.Item(scnd_id)->m_volume_id;
+		new_frst.m_volume_id = m_children.Item(frst_id)->m_volume_id;
+
+		m_children.Item(frst_id)->AssignAllVal(new_frst);
+		m_children.Item(scnd_id)->AssignAllVal(new_scnd);
+		return true;
+	}
+
+	// Set action icons for node
+	void set_object_action_icon();
+	void set_part_action_icon();
+};
+
+// ----------------------------------------------------------------------------
+// PrusaObjectDataViewModel
+// ----------------------------------------------------------------------------
+
+class PrusaObjectDataViewModel :public wxDataViewModel
+{
+	std::vector<PrusaObjectDataViewModelNode*> m_objects;
+public:
+	PrusaObjectDataViewModel(){}
+	~PrusaObjectDataViewModel()
+	{
+		for (auto object : m_objects)
+			delete object;		
+	}
+
+	wxDataViewItem Add(wxString &name);
+	wxDataViewItem Add(wxString &name, int instances_count, int scale);
+	wxDataViewItem AddChild(const wxDataViewItem &parent_item, 
+							const wxString &name, 
+                            const wxIcon& icon,
+                            const int = 0,
+                            const bool create_frst_child = true);
+	wxDataViewItem Delete(const wxDataViewItem &item);
+	void DeleteAll();
+    void DeleteChildren(wxDataViewItem& parent);
+	wxDataViewItem GetItemById(int obj_idx);
+	int GetIdByItem(wxDataViewItem& item);
+	int GetVolumeIdByItem(wxDataViewItem& item);
+	bool IsEmpty() { return m_objects.empty(); }
+
+	// helper method for wxLog
+
+	wxString GetName(const wxDataViewItem &item) const;
+	wxString GetCopy(const wxDataViewItem &item) const;
+	wxString GetScale(const wxDataViewItem &item) const;
+	wxIcon&  GetIcon(const wxDataViewItem &item) const;
+
+	// helper methods to change the model
+
+	virtual unsigned int GetColumnCount() const override { return 3;}
+	virtual wxString GetColumnType(unsigned int col) const override{ return wxT("string"); }
+
+	virtual void GetValue(wxVariant &variant,
+		const wxDataViewItem &item, unsigned int col) const override;
+	virtual bool SetValue(const wxVariant &variant,
+		const wxDataViewItem &item, unsigned int col) override;
+	bool SetValue(const wxVariant &variant, const int item_idx, unsigned int col);
+
+	wxDataViewItem MoveChildUp(const wxDataViewItem &item);
+	wxDataViewItem MoveChildDown(const wxDataViewItem &item);
+    // For parent move child from cur_volume_id place to new_volume_id 
+    // Remaining items will moved up/down accordingly
+    wxDataViewItem ReorganizeChildren(int cur_volume_id, 
+                                      int new_volume_id,
+                                      const wxDataViewItem &parent);
+
+// 	virtual bool IsEnabled(const wxDataViewItem &item,
+// 		unsigned int col) const override;
+
+	virtual wxDataViewItem GetParent(const wxDataViewItem &item) const override;
+	virtual bool IsContainer(const wxDataViewItem &item) const override;
+	virtual unsigned int GetChildren(const wxDataViewItem &parent,
+		wxDataViewItemArray &array) const override;
+
+	// Is the container just a header or an item with all columns
+	// In our case it is an item with all columns 
+	virtual bool HasContainerColumns(const wxDataViewItem& WXUNUSED(item)) const override {	return true; }
+};
+
+
+
+// ----------------------------------------------------------------------------
+// MyCustomRenderer
+// ----------------------------------------------------------------------------
+
+class MyCustomRenderer : public wxDataViewCustomRenderer
+{
+public:
+	// This renderer can be either activatable or editable, for demonstration
+	// purposes. In real programs, you should select whether the user should be
+	// able to activate or edit the cell and it doesn't make sense to switch
+	// between the two -- but this is just an example, so it doesn't stop us.
+	explicit MyCustomRenderer(wxDataViewCellMode mode)
+		: wxDataViewCustomRenderer("string", mode, wxALIGN_CENTER)
+	{ }
+
+	virtual bool Render(wxRect rect, wxDC *dc, int state) override/*wxOVERRIDE*/
+	{
+		dc->SetBrush(*wxLIGHT_GREY_BRUSH);
+		dc->SetPen(*wxTRANSPARENT_PEN);
+
+		rect.Deflate(2);
+		dc->DrawRoundedRectangle(rect, 5);
+
+		RenderText(m_value,
+			0, // no offset
+			wxRect(dc->GetTextExtent(m_value)).CentreIn(rect),
+			dc,
+			state);
+		return true;
+	}
+
+		virtual bool ActivateCell(const wxRect& WXUNUSED(cell),
+		wxDataViewModel *WXUNUSED(model),
+		const wxDataViewItem &WXUNUSED(item),
+		unsigned int WXUNUSED(col),
+		const wxMouseEvent *mouseEvent) override/*wxOVERRIDE*/
+	{
+		wxString position;
+		if (mouseEvent)
+			position = wxString::Format("via mouse at %d, %d", mouseEvent->m_x, mouseEvent->m_y);
+		else
+			position = "from keyboard";
+//		wxLogMessage("MyCustomRenderer ActivateCell() %s", position);
+		return false;
+	}
+
+		virtual wxSize GetSize() const override/*wxOVERRIDE*/
+	{
+		return wxSize(60, 20);
+	}
+
+		virtual bool SetValue(const wxVariant &value) override/*wxOVERRIDE*/
+	{
+		m_value = value.GetString();
+		return true;
+	}
+
+		virtual bool GetValue(wxVariant &WXUNUSED(value)) const override/*wxOVERRIDE*/{ return true; }
+
+		virtual bool HasEditorCtrl() const override/*wxOVERRIDE*/{ return true; }
+
+		virtual wxWindow*
+		CreateEditorCtrl(wxWindow* parent,
+		wxRect labelRect,
+		const wxVariant& value) override/*wxOVERRIDE*/
+	{
+		wxTextCtrl* text = new wxTextCtrl(parent, wxID_ANY, value,
+		labelRect.GetPosition(),
+		labelRect.GetSize(),
+		wxTE_PROCESS_ENTER);
+		text->SetInsertionPointEnd();
+
+		return text;
+	}
+
+		virtual bool
+			GetValueFromEditorCtrl(wxWindow* ctrl, wxVariant& value) override/*wxOVERRIDE*/
+	{
+		wxTextCtrl* text = wxDynamicCast(ctrl, wxTextCtrl);
+		if (!text)
+			return false;
+
+		value = text->GetValue();
+
+		return true;
+	}
+
+private:
+	wxString m_value;
+};
+// ******************************* EXPERIMENTS **********************************************
+enum SelectedSlider {
+    ssUndef,
+    ssLower,
+    ssHigher
+};
+enum TicksAction{
+    taOnIcon,
+    taAdd,
+    taDel
+};
+class PrusaDoubleSlider : public wxControl
+{
+public:
+    PrusaDoubleSlider(
+        wxWindow *parent,
+        wxWindowID id,
+        int lowerValue, 
+        int higherValue, 
+        int minValue, 
+        int maxValue,
+        const wxPoint& pos = wxDefaultPosition,
+        const wxSize& size = wxDefaultSize,
+        long style = wxSL_HORIZONTAL,
+        const wxValidator& val = wxDefaultValidator,
+        const wxString& name = wxEmptyString);
+
+    int GetLowerValue() const {
+        return m_lower_value;
+    }
+    int GetHigherValue() const {
+        return m_higher_value;
+    }
+    int GetActiveValue() const;
+    wxSize DoGetBestSize() const override;
+    void SetLowerValue(const int lower_val);
+    void SetHigherValue(const int higher_val);
+    void SetMaxValue(const int max_value);
+    void SetKoefForLabels(const double koef) {
+        m_label_koef = koef;
+    }
+    void SetSliderValues(const std::vector<double>& values) {
+        m_values = values;
+    }
+
+    void OnPaint(wxPaintEvent& ){ render();}
+    void OnLeftDown(wxMouseEvent& event);
+    void OnMotion(wxMouseEvent& event);
+    void OnLeftUp(wxMouseEvent& event);
+    void OnEnterWin(wxMouseEvent& event){ enter_window(event, true); }
+    void OnLeaveWin(wxMouseEvent& event){ enter_window(event, false); }
+    void OnWheel(wxMouseEvent& event);
+    void OnKeyDown(wxKeyEvent &event);
+    void OnKeyUp(wxKeyEvent &event);
+    void OnRightDown(wxMouseEvent& event);
+    void OnRightUp(wxMouseEvent& event);
+
+protected:
+ 
+    void    render();
+    void    draw_focus_rect();
+    void    draw_action_icon(wxDC& dc, const wxPoint pt_beg, const wxPoint pt_end);
+    void    draw_scroll_line(wxDC& dc, const int lower_pos, const int higher_pos);
+    void    draw_thumb(wxDC& dc, const wxCoord& pos_coord, const SelectedSlider& selection);
+    void    draw_thumbs(wxDC& dc, const wxCoord& lower_pos, const wxCoord& higher_pos);
+    void    draw_ticks(wxDC& dc);
+    void    draw_one_layer_icon(wxDC& dc);
+    void    draw_thumb_item(wxDC& dc, const wxPoint& pos, const SelectedSlider& selection);
+    void    draw_info_line_with_icon(wxDC& dc, const wxPoint& pos, SelectedSlider selection);
+    void    draw_thumb_text(wxDC& dc, const wxPoint& pos, const SelectedSlider& selection) const;
+
+    void    update_thumb_rect(const wxCoord& begin_x, const wxCoord& begin_y, const SelectedSlider& selection);
+    void    detect_selected_slider(const wxPoint& pt, const bool is_mouse_wheel = false);
+    void    correct_lower_value();
+    void    correct_higher_value();
+    void    move_current_thumb(const bool condition);
+    void    action_tick(const TicksAction action);
+    void    enter_window(wxMouseEvent& event, const bool enter);
+
+    bool    is_point_in_rect(const wxPoint& pt, const wxRect& rect);
+    bool    is_horizontal() const { return m_style == wxSL_HORIZONTAL; }
+
+    double      get_scroll_step();
+    wxString    get_label(const SelectedSlider& selection) const;
+    void        get_lower_and_higher_position(int& lower_pos, int& higher_pos);
+    int         get_value_from_position(const wxCoord x, const wxCoord y);
+    wxCoord     get_position_from_value(const int value);
+    wxSize      get_size();
+    void        get_size(int *w, int *h);
+
+private:
+    int         m_min_value;
+    int         m_max_value;
+    int         m_lower_value;
+    int         m_higher_value;
+    wxBitmap    m_bmp_thumb_higher;
+    wxBitmap    m_bmp_thumb_lower;
+    wxBitmap    m_bmp_add_tick_on;
+    wxBitmap    m_bmp_add_tick_off;
+    wxBitmap    m_bmp_del_tick_on;
+    wxBitmap    m_bmp_del_tick_off;
+    wxBitmap    m_bmp_one_layer_lock_on;
+    wxBitmap    m_bmp_one_layer_lock_off;
+    wxBitmap    m_bmp_one_layer_unlock_on;
+    wxBitmap    m_bmp_one_layer_unlock_off;
+    SelectedSlider  m_selection;
+    bool        m_is_left_down = false;
+    bool        m_is_right_down = false;
+    bool        m_is_one_layer = false;
+    bool        m_is_focused = false;
+    bool        m_is_action_icon_focesed = false;
+    bool        m_is_one_layer_icon_focesed = false;
+
+    wxRect      m_rect_lower_thumb;
+    wxRect      m_rect_higher_thumb;
+    wxRect      m_rect_tick_action;
+    wxRect      m_rect_one_layer_icon;
+    wxSize      m_thumb_size;
+    int         m_tick_icon_dim;
+    int         m_lock_icon_dim = 16;
+    long        m_style;
+    float       m_label_koef = 1.0;
+
+// control's view variables
+    wxCoord SLIDER_MARGIN; // margin around slider
+
+    wxPen   DARK_ORANGE_PEN;
+    wxPen   ORANGE_PEN;
+    wxPen   LIGHT_ORANGE_PEN;
+
+    wxPen   DARK_GREY_PEN;
+    wxPen   GREY_PEN;
+    wxPen   LIGHT_GREY_PEN;
+
+    std::vector<wxPen*> line_pens;
+    std::vector<wxPen*> segm_pens;
+    std::set<int>       m_ticks;
+    std::vector<double> m_values;
+};
+// ******************************************************************************************
+
+
 #endif // slic3r_GUI_wxExtensions_hpp_
diff --git a/xs/src/slic3r/Utils/Duet.cpp b/xs/src/slic3r/Utils/Duet.cpp
new file mode 100644
index 0000000000..865d2b4187
--- /dev/null
+++ b/xs/src/slic3r/Utils/Duet.cpp
@@ -0,0 +1,279 @@
+#include "Duet.hpp"
+#include "PrintHostSendDialog.hpp"
+
+#include <algorithm>
+#include <ctime>
+#include <boost/filesystem/path.hpp>
+#include <boost/format.hpp>
+#include <boost/log/trivial.hpp>
+#include <boost/property_tree/ptree.hpp>
+#include <boost/property_tree/json_parser.hpp>
+
+#include <wx/frame.h>
+#include <wx/event.h>
+#include <wx/progdlg.h>
+#include <wx/sizer.h>
+#include <wx/stattext.h>
+#include <wx/textctrl.h>
+#include <wx/checkbox.h>
+
+#include "libslic3r/PrintConfig.hpp"
+#include "slic3r/GUI/GUI.hpp"
+#include "slic3r/GUI/MsgDialog.hpp"
+#include "Http.hpp"
+
+namespace fs = boost::filesystem;
+namespace pt = boost::property_tree;
+
+namespace Slic3r {
+
+Duet::Duet(DynamicPrintConfig *config) :
+	host(config->opt_string("print_host")),
+	password(config->opt_string("printhost_apikey"))
+{}
+
+Duet::~Duet() {}
+
+bool Duet::test(wxString &msg) const
+{
+	bool connected = connect(msg);
+	if (connected) {
+		disconnect();
+	}
+
+	return connected;
+}
+
+wxString Duet::get_test_ok_msg () const
+{
+	return wxString::Format("%s", _(L("Connection to Duet works correctly.")));
+}
+
+wxString Duet::get_test_failed_msg (wxString &msg) const
+{
+	return wxString::Format("%s: %s", _(L("Could not connect to Duet")), msg);
+}
+
+bool Duet::send_gcode(const std::string &filename) const
+{
+	enum { PROGRESS_RANGE = 1000 };
+
+	const auto errortitle = _(L("Error while uploading to the Duet"));
+	fs::path filepath(filename);
+
+	PrintHostSendDialog send_dialog(filepath.filename(), true);
+	if (send_dialog.ShowModal() != wxID_OK) { return false; }
+
+	const bool print = send_dialog.print(); 
+	const auto upload_filepath = send_dialog.filename();
+	const auto upload_filename = upload_filepath.filename();
+	const auto upload_parent_path = upload_filepath.parent_path();
+
+	wxProgressDialog progress_dialog(
+	 	_(L("Duet upload")),
+	 	_(L("Sending G-code file to Duet...")),
+		PROGRESS_RANGE, nullptr, wxPD_AUTO_HIDE | wxPD_APP_MODAL | wxPD_CAN_ABORT);
+	progress_dialog.Pulse();
+
+	wxString connect_msg;
+	if (!connect(connect_msg)) {
+		auto errormsg = wxString::Format("%s: %s", errortitle, connect_msg);
+		GUI::show_error(&progress_dialog, std::move(errormsg));
+		return false;
+	}
+
+	bool res = true;
+
+	auto upload_cmd = get_upload_url(upload_filepath.string());
+	BOOST_LOG_TRIVIAL(info) << boost::format("Duet: Uploading file %1%, filename: %2%, path: %3%, print: %4%, command: %5%")
+		% filepath.string()
+		% upload_filename.string()
+		% upload_parent_path.string()
+		% print
+		% upload_cmd;
+
+	auto http = Http::post(std::move(upload_cmd));
+	http.set_post_body(filename)
+		.on_complete([&](std::string body, unsigned status) {
+			BOOST_LOG_TRIVIAL(debug) << boost::format("Duet: File uploaded: HTTP %1%: %2%") % status % body;
+			progress_dialog.Update(PROGRESS_RANGE);
+
+			int err_code = get_err_code_from_body(body);
+			if (err_code != 0) {
+				auto msg = format_error(body, L("Unknown error occured"), 0);
+				GUI::show_error(&progress_dialog, std::move(msg));
+				res = false;
+			} else if (print) {
+				wxString errormsg;
+				res = start_print(errormsg, upload_filepath.string());
+				if (!res) {
+					GUI::show_error(&progress_dialog, std::move(errormsg));
+				}
+			}
+		})
+		.on_error([&](std::string body, std::string error, unsigned status) {
+			BOOST_LOG_TRIVIAL(error) << boost::format("Duet: Error uploading file: %1%, HTTP %2%, body: `%3%`") % error % status % body;
+			auto errormsg = wxString::Format("%s: %s", errortitle, format_error(body, error, status));
+			GUI::show_error(&progress_dialog, std::move(errormsg));
+			res = false;
+		})
+		.on_progress([&](Http::Progress progress, bool &cancel) {
+			if (cancel) {
+				// Upload was canceled
+				res = false;
+			} else if (progress.ultotal > 0) {
+				int value = PROGRESS_RANGE * progress.ulnow / progress.ultotal;
+				cancel = !progress_dialog.Update(std::min(value, PROGRESS_RANGE - 1));    // Cap the value to prevent premature dialog closing
+			} else {
+				cancel = !progress_dialog.Pulse();
+			}
+		})
+		.perform_sync();
+
+	disconnect();
+
+	return res;
+}
+
+bool Duet::has_auto_discovery() const
+{
+	return false;
+}
+
+bool Duet::can_test() const
+{
+	return true;
+}
+
+bool Duet::connect(wxString &msg) const
+{
+	bool res = false;
+	auto url = get_connect_url();
+
+	auto http = Http::get(std::move(url));
+	http.on_error([&](std::string body, std::string error, unsigned status) {
+			BOOST_LOG_TRIVIAL(error) << boost::format("Duet: Error connecting: %1%, HTTP %2%, body: `%3%`") % error % status % body;
+			msg = format_error(body, error, status);
+		})
+		.on_complete([&](std::string body, unsigned) {
+			BOOST_LOG_TRIVIAL(debug) << boost::format("Duet: Got: %1%") % body;
+
+			int err_code = get_err_code_from_body(body);
+			switch (err_code) {
+				case 0:
+					res = true;
+					break;
+				case 1:
+					msg = format_error(body, L("Wrong password"), 0);
+					break;
+				case 2:
+					msg = format_error(body, L("Could not get resources to create a new connection"), 0);
+					break;
+				default:
+					msg = format_error(body, L("Unknown error occured"), 0);
+					break;
+			}
+
+		})
+		.perform_sync();
+
+	return res;
+}
+
+void Duet::disconnect() const
+{
+	auto url =  (boost::format("%1%rr_disconnect")
+			% get_base_url()).str();
+
+	auto http = Http::get(std::move(url));
+	http.on_error([&](std::string body, std::string error, unsigned status) {
+		// we don't care about it, if disconnect is not working Duet will disconnect automatically after some time
+		BOOST_LOG_TRIVIAL(error) << boost::format("Duet: Error disconnecting: %1%, HTTP %2%, body: `%3%`") % error % status % body;
+	})
+	.perform_sync();
+}
+
+std::string Duet::get_upload_url(const std::string &filename) const
+{
+	return (boost::format("%1%rr_upload?name=0:/gcodes/%2%&%3%")
+			% get_base_url()
+			% filename 
+			% timestamp_str()).str();
+}
+
+std::string Duet::get_connect_url() const
+{
+	return (boost::format("%1%rr_connect?password=%2%&%3%")
+			% get_base_url()
+			% (password.empty() ? "reprap" : password)
+			% timestamp_str()).str();
+}
+
+std::string Duet::get_base_url() const
+{
+	if (host.find("http://") == 0 || host.find("https://") == 0) {
+		if (host.back() == '/') {
+			return host;
+		} else {
+			return (boost::format("%1%/") % host).str();
+		}
+	} else {
+		return (boost::format("http://%1%/") % host).str();
+	}
+}
+
+std::string Duet::timestamp_str() const
+{
+	enum { BUFFER_SIZE = 32 };
+
+	auto t = std::time(nullptr);
+	auto tm = *std::localtime(&t);
+
+	char buffer[BUFFER_SIZE];
+	std::strftime(buffer, BUFFER_SIZE, "time=%Y-%d-%mT%H:%M:%S", &tm);
+
+	return std::string(buffer);
+}
+
+wxString Duet::format_error(const std::string &body, const std::string &error, unsigned status)
+{
+	if (status != 0) {
+		auto wxbody = wxString::FromUTF8(body.data());
+		return wxString::Format("HTTP %u: %s", status, wxbody);
+	} else {
+		return wxString::FromUTF8(error.data());
+	}
+}
+
+bool Duet::start_print(wxString &msg, const std::string &filename) const 
+{
+	bool res = false;
+	auto url = (boost::format("%1%rr_gcode?gcode=M32%%20\"%2%\"")
+			% get_base_url()
+			% filename).str();
+
+	auto http = Http::get(std::move(url));
+	http.on_error([&](std::string body, std::string error, unsigned status) {
+			BOOST_LOG_TRIVIAL(error) << boost::format("Duet: Error starting print: %1%, HTTP %2%, body: `%3%`") % error % status % body;
+			msg = format_error(body, error, status);
+		})
+		.on_complete([&](std::string body, unsigned) {
+			BOOST_LOG_TRIVIAL(debug) << boost::format("Duet: Got: %1%") % body;
+			res = true;
+		})
+		.perform_sync();
+
+	return res;
+}
+
+int Duet::get_err_code_from_body(const std::string &body) const
+{
+	pt::ptree root;
+	std::istringstream iss (body); // wrap returned json to istringstream
+	pt::read_json(iss, root);
+
+	return root.get<int>("err", 0);
+}
+
+
+}
diff --git a/xs/src/slic3r/Utils/Duet.hpp b/xs/src/slic3r/Utils/Duet.hpp
new file mode 100644
index 0000000000..bc210d7a45
--- /dev/null
+++ b/xs/src/slic3r/Utils/Duet.hpp
@@ -0,0 +1,47 @@
+#ifndef slic3r_Duet_hpp_
+#define slic3r_Duet_hpp_
+
+#include <string>
+#include <wx/string.h>
+
+#include "PrintHost.hpp"
+
+
+namespace Slic3r {
+
+
+class DynamicPrintConfig;
+class Http;
+
+class Duet : public PrintHost
+{
+public:
+	Duet(DynamicPrintConfig *config);
+	virtual ~Duet();
+
+	bool test(wxString &curl_msg) const;
+	wxString get_test_ok_msg () const;
+	wxString get_test_failed_msg (wxString &msg) const;
+	// Send gcode file to duet, filename is expected to be in UTF-8
+	bool send_gcode(const std::string &filename) const;
+	bool has_auto_discovery() const;
+	bool can_test() const;
+private:
+	std::string host;
+	std::string password;
+
+	std::string get_upload_url(const std::string &filename) const;
+	std::string get_connect_url() const;
+	std::string get_base_url() const;
+	std::string timestamp_str() const;
+	bool connect(wxString &msg) const;
+	void disconnect() const;
+	bool start_print(wxString &msg, const std::string &filename) const;
+	int get_err_code_from_body(const std::string &body) const;
+	static wxString format_error(const std::string &body, const std::string &error, unsigned status);
+};
+
+
+}
+
+#endif
diff --git a/xs/src/slic3r/Utils/Http.cpp b/xs/src/slic3r/Utils/Http.cpp
index 37eb59a00f..a92e399a08 100644
--- a/xs/src/slic3r/Utils/Http.cpp
+++ b/xs/src/slic3r/Utils/Http.cpp
@@ -4,6 +4,7 @@
 #include <functional>
 #include <thread>
 #include <deque>
+#include <sstream>
 #include <boost/filesystem/fstream.hpp>
 #include <boost/format.hpp>
 
@@ -42,6 +43,7 @@ struct Http::priv
 	// Used for storing file streams added as multipart form parts
 	// Using a deque here because unlike vector it doesn't ivalidate pointers on insertion
 	std::deque<fs::ifstream> form_files;
+	std::string postfields;
 	size_t limit;
 	bool cancel;
 
@@ -60,6 +62,7 @@ struct Http::priv
 	static size_t form_file_read_cb(char *buffer, size_t size, size_t nitems, void *userp);
 
 	void form_add_file(const char *name, const fs::path &path, const char* filename);
+	void set_post_body(const fs::path &path);
 
 	std::string curl_error(CURLcode curlcode);
 	std::string body_size_error();
@@ -187,6 +190,13 @@ void Http::priv::form_add_file(const char *name, const fs::path &path, const cha
 	}
 }
 
+void Http::priv::set_post_body(const fs::path &path)
+{
+	std::ifstream file(path.string());
+	std::string file_content { std::istreambuf_iterator<char>(file), std::istreambuf_iterator<char>() };
+	postfields = file_content;
+}
+
 std::string Http::priv::curl_error(CURLcode curlcode)
 {
 	return (boost::format("%1% (%2%)")
@@ -229,6 +239,11 @@ void Http::priv::http_perform()
 		::curl_easy_setopt(curl, CURLOPT_HTTPPOST, form);
 	}
 
+	if (!postfields.empty()) {
+		::curl_easy_setopt(curl, CURLOPT_POSTFIELDS, postfields.c_str());
+		::curl_easy_setopt(curl, CURLOPT_POSTFIELDSIZE_LARGE, postfields.size());
+	}
+
 	CURLcode res = ::curl_easy_perform(curl);
 
 	if (res != CURLE_OK) {
@@ -338,6 +353,12 @@ Http& Http::form_add_file(const std::string &name, const fs::path &path, const s
 	return *this;
 }
 
+Http& Http::set_post_body(const fs::path &path)
+{
+	if (p) { p->set_post_body(path);}
+	return *this;
+}
+
 Http& Http::on_complete(CompleteFn fn)
 {
 	if (p) { p->completefn = std::move(fn); }
diff --git a/xs/src/slic3r/Utils/Http.hpp b/xs/src/slic3r/Utils/Http.hpp
index ce4e438cad..f1302b0ed9 100644
--- a/xs/src/slic3r/Utils/Http.hpp
+++ b/xs/src/slic3r/Utils/Http.hpp
@@ -73,6 +73,11 @@ public:
 	// Same as above except also override the file's filename with a custom one
 	Http& form_add_file(const std::string &name, const boost::filesystem::path &path, const std::string &filename);
 
+	// Set the file contents as a POST request body.
+	// The data is used verbatim, it is not additionally encoded in any way.
+	// This can be used for hosts which do not support multipart requests.
+	Http& set_post_body(const boost::filesystem::path &path);
+
 	// Callback called on HTTP request complete
 	Http& on_complete(CompleteFn fn);
 	// Callback called on an error occuring at any stage of the requests: Url parsing, DNS lookup,
diff --git a/xs/src/slic3r/Utils/OctoPrint.cpp b/xs/src/slic3r/Utils/OctoPrint.cpp
index 97b4123d44..db86d76974 100644
--- a/xs/src/slic3r/Utils/OctoPrint.cpp
+++ b/xs/src/slic3r/Utils/OctoPrint.cpp
@@ -1,21 +1,11 @@
 #include "OctoPrint.hpp"
+#include "PrintHostSendDialog.hpp"
 
 #include <algorithm>
-#include <boost/filesystem/path.hpp>
 #include <boost/format.hpp>
 #include <boost/log/trivial.hpp>
 
-#include <wx/frame.h>
-#include <wx/event.h>
-#include <wx/progdlg.h>
-#include <wx/sizer.h>
-#include <wx/stattext.h>
-#include <wx/textctrl.h>
-#include <wx/checkbox.h>
-
 #include "libslic3r/PrintConfig.hpp"
-#include "slic3r/GUI/GUI.hpp"
-#include "slic3r/GUI/MsgDialog.hpp"
 #include "Http.hpp"
 
 namespace fs = boost::filesystem;
@@ -23,49 +13,14 @@ namespace fs = boost::filesystem;
 
 namespace Slic3r {
 
-
-struct SendDialog : public GUI::MsgDialog
-{
-	wxTextCtrl *txt_filename;
-	wxCheckBox *box_print;
-
-	SendDialog(const fs::path &path) :
-		MsgDialog(nullptr, _(L("Send G-Code to printer")), _(L("Upload to OctoPrint with the following filename:")), wxID_NONE),
-		txt_filename(new wxTextCtrl(this, wxID_ANY, path.filename().wstring())),
-		box_print(new wxCheckBox(this, wxID_ANY, _(L("Start printing after upload"))))
-	{
-		auto *label_dir_hint = new wxStaticText(this, wxID_ANY, _(L("Use forward slashes ( / ) as a directory separator if needed.")));
-		label_dir_hint->Wrap(CONTENT_WIDTH);
-
-		content_sizer->Add(txt_filename, 0, wxEXPAND);
-		content_sizer->Add(label_dir_hint);
-		content_sizer->AddSpacer(VERT_SPACING);
-		content_sizer->Add(box_print, 0, wxBOTTOM, 2*VERT_SPACING);
-
-		btn_sizer->Add(CreateStdDialogButtonSizer(wxOK | wxCANCEL));
-
-		txt_filename->SetFocus();
-		wxString stem(path.stem().wstring());
-		txt_filename->SetSelection(0, stem.Length());
-
-		Fit();
-	}
-
-	fs::path filename() const {
-		return fs::path(txt_filename->GetValue().wx_str());
-	}
-
-	bool print() const { return box_print->GetValue(); }
-};
-
-
-
 OctoPrint::OctoPrint(DynamicPrintConfig *config) :
-	host(config->opt_string("octoprint_host")),
-	apikey(config->opt_string("octoprint_apikey")),
-	cafile(config->opt_string("octoprint_cafile"))
+	host(config->opt_string("print_host")),
+	apikey(config->opt_string("printhost_apikey")),
+	cafile(config->opt_string("printhost_cafile"))
 {}
 
+OctoPrint::~OctoPrint() {}
+
 bool OctoPrint::test(wxString &msg) const
 {
 	// Since the request is performed synchronously here,
@@ -91,6 +46,17 @@ bool OctoPrint::test(wxString &msg) const
 	return res;
 }
 
+wxString OctoPrint::get_test_ok_msg () const
+{
+	return wxString::Format("%s", _(L("Connection to OctoPrint works correctly.")));
+}
+
+wxString OctoPrint::get_test_failed_msg (wxString &msg) const
+{
+	return wxString::Format("%s: %s\n\n%s",
+						_(L("Could not connect to OctoPrint")), msg, _(L("Note: OctoPrint version at least 1.1.0 is required.")));
+}
+
 bool OctoPrint::send_gcode(const std::string &filename) const
 {
 	enum { PROGRESS_RANGE = 1000 };
@@ -98,7 +64,7 @@ bool OctoPrint::send_gcode(const std::string &filename) const
 	const auto errortitle = _(L("Error while uploading to the OctoPrint server"));
 	fs::path filepath(filename);
 
-	SendDialog send_dialog(filepath.filename());
+	PrintHostSendDialog send_dialog(filepath.filename(), true);
 	if (send_dialog.ShowModal() != wxID_OK) { return false; }
 
 	const bool print = send_dialog.print();
@@ -161,6 +127,16 @@ bool OctoPrint::send_gcode(const std::string &filename) const
 	return res;
 }
 
+bool OctoPrint::has_auto_discovery() const
+{
+	return true;
+}
+
+bool OctoPrint::can_test() const
+{
+	return true;
+}
+
 void OctoPrint::set_auth(Http &http) const
 {
 	http.header("X-Api-Key", apikey);
diff --git a/xs/src/slic3r/Utils/OctoPrint.hpp b/xs/src/slic3r/Utils/OctoPrint.hpp
index 1e2098ae3f..f6c4d58c87 100644
--- a/xs/src/slic3r/Utils/OctoPrint.hpp
+++ b/xs/src/slic3r/Utils/OctoPrint.hpp
@@ -4,6 +4,8 @@
 #include <string>
 #include <wx/string.h>
 
+#include "PrintHost.hpp"
+
 
 namespace Slic3r {
 
@@ -11,14 +13,19 @@ namespace Slic3r {
 class DynamicPrintConfig;
 class Http;
 
-class OctoPrint
+class OctoPrint : public PrintHost
 {
 public:
 	OctoPrint(DynamicPrintConfig *config);
+	virtual ~OctoPrint();
 
 	bool test(wxString &curl_msg) const;
+	wxString get_test_ok_msg () const;
+	wxString get_test_failed_msg (wxString &msg) const;
 	// Send gcode file to octoprint, filename is expected to be in UTF-8
 	bool send_gcode(const std::string &filename) const;
+	bool has_auto_discovery() const;
+	bool can_test() const;
 private:
 	std::string host;
 	std::string apikey;
diff --git a/xs/src/slic3r/Utils/PresetUpdater.cpp b/xs/src/slic3r/Utils/PresetUpdater.cpp
index 6e23ab4219..2e423dc5ee 100644
--- a/xs/src/slic3r/Utils/PresetUpdater.cpp
+++ b/xs/src/slic3r/Utils/PresetUpdater.cpp
@@ -447,6 +447,7 @@ void PresetUpdater::priv::perform_updates(Updates &&updates, bool snapshot) cons
 
 			for (const auto &name : bundle.obsolete_presets.prints)    { obsolete_remover("print", name); }
 			for (const auto &name : bundle.obsolete_presets.filaments) { obsolete_remover("filament", name); }
+			for (const auto &name : bundle.obsolete_presets.filaments) { obsolete_remover("sla_material", name); }
 			for (const auto &name : bundle.obsolete_presets.printers)  { obsolete_remover("printer", name); }
 		}
 	}
diff --git a/xs/src/slic3r/Utils/PrintHost.cpp b/xs/src/slic3r/Utils/PrintHost.cpp
new file mode 100644
index 0000000000..dd72bae40f
--- /dev/null
+++ b/xs/src/slic3r/Utils/PrintHost.cpp
@@ -0,0 +1,23 @@
+#include "OctoPrint.hpp"
+#include "Duet.hpp"
+
+#include "libslic3r/PrintConfig.hpp"
+
+namespace Slic3r {
+
+
+PrintHost::~PrintHost() {}
+
+PrintHost* PrintHost::get_print_host(DynamicPrintConfig *config)
+{
+	PrintHostType kind = config->option<ConfigOptionEnum<PrintHostType>>("host_type")->value;
+	if (kind == htOctoPrint) {
+		return new OctoPrint(config);
+	} else if (kind == htDuet) {
+		return new Duet(config);
+	}
+	return nullptr;
+}
+
+
+}
diff --git a/xs/src/slic3r/Utils/PrintHost.hpp b/xs/src/slic3r/Utils/PrintHost.hpp
new file mode 100644
index 0000000000..bc828ea469
--- /dev/null
+++ b/xs/src/slic3r/Utils/PrintHost.hpp
@@ -0,0 +1,35 @@
+#ifndef slic3r_PrintHost_hpp_
+#define slic3r_PrintHost_hpp_
+
+#include <memory>
+#include <string>
+#include <wx/string.h>
+
+
+namespace Slic3r {
+
+
+class DynamicPrintConfig;
+
+class PrintHost
+{
+public:
+	virtual ~PrintHost();
+
+	virtual bool test(wxString &curl_msg) const = 0;
+	virtual wxString get_test_ok_msg () const = 0;
+	virtual wxString get_test_failed_msg (wxString &msg) const = 0;
+	// Send gcode file to print host, filename is expected to be in UTF-8
+	virtual bool send_gcode(const std::string &filename) const = 0;
+	virtual bool has_auto_discovery() const = 0;
+	virtual bool can_test() const = 0;
+
+	static PrintHost* get_print_host(DynamicPrintConfig *config);
+};
+
+
+
+
+}
+
+#endif
diff --git a/xs/src/slic3r/Utils/PrintHostSendDialog.cpp b/xs/src/slic3r/Utils/PrintHostSendDialog.cpp
new file mode 100644
index 0000000000..c5d441f876
--- /dev/null
+++ b/xs/src/slic3r/Utils/PrintHostSendDialog.cpp
@@ -0,0 +1,52 @@
+#include "PrintHostSendDialog.hpp"
+
+#include <wx/frame.h>
+#include <wx/event.h>
+#include <wx/progdlg.h>
+#include <wx/sizer.h>
+#include <wx/stattext.h>
+#include <wx/textctrl.h>
+#include <wx/checkbox.h>
+
+#include "slic3r/GUI/GUI.hpp"
+#include "slic3r/GUI/MsgDialog.hpp"
+
+
+namespace fs = boost::filesystem;
+
+namespace Slic3r {
+
+PrintHostSendDialog::PrintHostSendDialog(const fs::path &path, bool can_start_print) :
+	MsgDialog(nullptr, _(L("Send G-Code to printer host")), _(L("Upload to Printer Host with the following filename:")), wxID_NONE),
+	txt_filename(new wxTextCtrl(this, wxID_ANY, path.filename().wstring())),
+	box_print(new wxCheckBox(this, wxID_ANY, _(L("Start printing after upload")))),
+	can_start_print(can_start_print)
+{
+	auto *label_dir_hint = new wxStaticText(this, wxID_ANY, _(L("Use forward slashes ( / ) as a directory separator if needed.")));
+	label_dir_hint->Wrap(CONTENT_WIDTH);
+
+	content_sizer->Add(txt_filename, 0, wxEXPAND);
+	content_sizer->Add(label_dir_hint);
+	content_sizer->AddSpacer(VERT_SPACING);
+	content_sizer->Add(box_print, 0, wxBOTTOM, 2*VERT_SPACING);
+
+	btn_sizer->Add(CreateStdDialogButtonSizer(wxOK | wxCANCEL));
+
+	txt_filename->SetFocus();
+	wxString stem(path.stem().wstring());
+	txt_filename->SetSelection(0, stem.Length());
+
+	box_print->Enable(can_start_print);
+
+	Fit();
+}
+
+fs::path PrintHostSendDialog::filename() const 
+{
+	return fs::path(txt_filename->GetValue().wx_str());
+}
+
+bool PrintHostSendDialog::print() const 
+{ 
+	return box_print->GetValue(); }
+}
diff --git a/xs/src/slic3r/Utils/PrintHostSendDialog.hpp b/xs/src/slic3r/Utils/PrintHostSendDialog.hpp
new file mode 100644
index 0000000000..dc4a8d6f7c
--- /dev/null
+++ b/xs/src/slic3r/Utils/PrintHostSendDialog.hpp
@@ -0,0 +1,38 @@
+#ifndef slic3r_PrintHostSendDialog_hpp_
+#define slic3r_PrintHostSendDialog_hpp_
+
+#include <string>
+
+#include <boost/filesystem/path.hpp>
+
+#include <wx/string.h>
+#include <wx/frame.h>
+#include <wx/event.h>
+#include <wx/progdlg.h>
+#include <wx/sizer.h>
+#include <wx/stattext.h>
+#include <wx/textctrl.h>
+#include <wx/checkbox.h>
+
+#include "slic3r/GUI/GUI.hpp"
+#include "slic3r/GUI/MsgDialog.hpp"
+
+
+namespace Slic3r {
+
+class PrintHostSendDialog : public GUI::MsgDialog
+{
+private:
+	wxTextCtrl *txt_filename;
+	wxCheckBox *box_print;
+	bool can_start_print;
+
+public:
+	PrintHostSendDialog(const boost::filesystem::path &path, bool can_start_print);
+	boost::filesystem::path filename() const;
+	bool print() const;
+};
+
+}
+
+#endif
diff --git a/xs/src/xsinit.h b/xs/src/xsinit.h
index e32717532b..c9e3636027 100644
--- a/xs/src/xsinit.h
+++ b/xs/src/xsinit.h
@@ -197,9 +197,9 @@ void from_SV_check(SV* poly_sv, Polyline* THIS);
 SV* to_SV_pureperl(const Point* THIS);
 void from_SV(SV* point_sv, Point* point);
 void from_SV_check(SV* point_sv, Point* point);
-SV* to_SV_pureperl(const Pointf* point);
-bool from_SV(SV* point_sv, Pointf* point);
-bool from_SV_check(SV* point_sv, Pointf* point);
+SV* to_SV_pureperl(const Vec2d* point);
+bool from_SV(SV* point_sv, Vec2d* point);
+bool from_SV_check(SV* point_sv, Vec2d* point);
 void from_SV_check(SV* surface_sv, Surface* THIS);
 SV* to_SV(TriangleMesh* THIS);
 
diff --git a/xs/xsp/BoundingBox.xsp b/xs/xsp/BoundingBox.xsp
index d65f8a5237..a34cad0bc8 100644
--- a/xs/xsp/BoundingBox.xsp
+++ b/xs/xsp/BoundingBox.xsp
@@ -56,15 +56,15 @@ new_from_points(CLASS, points)
     Clone<BoundingBoxf> clone()
         %code{% RETVAL = THIS; %};
     void merge(BoundingBoxf* bb) %code{% THIS->merge(*bb); %};
-    void merge_point(Pointf* point) %code{% THIS->merge(*point); %};
+    void merge_point(Vec2d* point) %code{% THIS->merge(*point); %};
     void scale(double factor);
     void translate(double x, double y);
-    Clone<Pointf> size();
-    Clone<Pointf> center();
+    Clone<Vec2d> size();
+    Clone<Vec2d> center();
     double radius();
     bool empty() %code{% RETVAL = empty(*THIS); %};
-    Clone<Pointf> min_point() %code{% RETVAL = THIS->min; %};
-    Clone<Pointf> max_point() %code{% RETVAL = THIS->max; %};
+    Clone<Vec2d> min_point() %code{% RETVAL = THIS->min; %};
+    Clone<Vec2d> max_point() %code{% RETVAL = THIS->max; %};
     double x_min() %code{% RETVAL = THIS->min(0); %};
     double x_max() %code{% RETVAL = THIS->max(0); %};
     double y_min() %code{% RETVAL = THIS->min(1); %};
@@ -96,17 +96,17 @@ new_from_points(CLASS, points)
     Clone<BoundingBoxf3> clone()
         %code{% RETVAL = THIS; %};
     void merge(BoundingBoxf3* bb) %code{% THIS->merge(*bb); %};
-    void merge_point(Pointf3* point) %code{% THIS->merge(*point); %};
+    void merge_point(Vec3d* point) %code{% THIS->merge(*point); %};
     void scale(double factor);
     void translate(double x, double y, double z);
     void offset(double delta);
-    bool contains_point(Pointf3* point) %code{% RETVAL = THIS->contains(*point); %};
-    Clone<Pointf3> size();
-    Clone<Pointf3> center();
+    bool contains_point(Vec3d* point) %code{% RETVAL = THIS->contains(*point); %};
+    Clone<Vec3d> size();
+    Clone<Vec3d> center();
     double radius();
     bool empty() %code{% RETVAL = empty(*THIS); %};
-    Clone<Pointf3> min_point() %code{% RETVAL = THIS->min; %};
-    Clone<Pointf3> max_point() %code{% RETVAL = THIS->max; %};
+    Clone<Vec3d> min_point() %code{% RETVAL = THIS->min; %};
+    Clone<Vec3d> max_point() %code{% RETVAL = THIS->max; %};
     double x_min() %code{% RETVAL = THIS->min(0); %};
     double x_max() %code{% RETVAL = THIS->max(0); %};
     double y_min() %code{% RETVAL = THIS->min(1); %};
diff --git a/xs/xsp/GCode.xsp b/xs/xsp/GCode.xsp
index c1856ccf7b..9e04edd4c6 100644
--- a/xs/xsp/GCode.xsp
+++ b/xs/xsp/GCode.xsp
@@ -35,9 +35,9 @@
             }
         %};
 
-    Ref<Pointf> origin()
+    Ref<Vec2d> origin()
         %code{% RETVAL = &(THIS->origin()); %};
-    void set_origin(Pointf* pointf)
+    void set_origin(Vec2d* pointf)
         %code{% THIS->set_origin(*pointf); %};
     Ref<Point> last_pos()
         %code{% RETVAL = &(THIS->last_pos()); %};
diff --git a/xs/xsp/GUI.xsp b/xs/xsp/GUI.xsp
index c6eead1ad5..b9183af1de 100644
--- a/xs/xsp/GUI.xsp
+++ b/xs/xsp/GUI.xsp
@@ -87,6 +87,80 @@ void add_frequently_changed_parameters(SV *ui_parent, SV *ui_sizer, SV *ui_p_siz
                                                            (wxBoxSizer*)wxPli_sv_2_object(aTHX_ ui_sizer, "Wx::BoxSizer"),
                                                            (wxFlexGridSizer*)wxPli_sv_2_object(aTHX_ ui_p_sizer, "Wx::FlexGridSizer")); %};
 
+void add_expert_mode_part(  SV *ui_parent, SV *ui_sizer, 
+                            Model *model,
+                            int event_object_selection_changed,
+                            int event_object_settings_changed,
+                            int event_remove_object, 
+                            int event_update_scene)
+    %code%{ Slic3r::GUI::add_expert_mode_part(  (wxWindow*)wxPli_sv_2_object(aTHX_ ui_parent, "Wx::Window"),
+                                                (wxBoxSizer*)wxPli_sv_2_object(aTHX_ ui_sizer, "Wx::BoxSizer"), 
+                                                *model,  
+                                                event_object_selection_changed,
+                                                event_object_settings_changed,
+                                                event_remove_object, 
+                                                event_update_scene); %};
+
+void set_objects_from_perl( SV *ui_parent, 
+                            SV *frequently_changed_parameters_sizer,
+                            SV *expert_mode_part_sizer,
+                            SV *scrolled_window_sizer,
+                            SV *btn_export_gcode,
+                            SV *btn_export_stl,
+                            SV *btn_reslice,
+                            SV *btn_print,
+                            SV *btn_send_gcode,
+                            SV *manifold_warning_icon)
+    %code%{ Slic3r::GUI::set_objects_from_perl(
+                            (wxWindow *)wxPli_sv_2_object(aTHX_ ui_parent, "Wx::Window"),
+                            (wxBoxSizer *)wxPli_sv_2_object(aTHX_ frequently_changed_parameters_sizer, "Wx::BoxSizer"),
+                            (wxBoxSizer *)wxPli_sv_2_object(aTHX_ expert_mode_part_sizer, "Wx::BoxSizer"),
+                            (wxBoxSizer *)wxPli_sv_2_object(aTHX_ scrolled_window_sizer, "Wx::BoxSizer"),
+                            (wxButton *)wxPli_sv_2_object(aTHX_ btn_export_gcode, "Wx::Button"),
+                            (wxButton *)wxPli_sv_2_object(aTHX_ btn_export_stl, "Wx::Button"),
+                            (wxButton *)wxPli_sv_2_object(aTHX_ btn_reslice, "Wx::Button"),
+                            (wxButton *)wxPli_sv_2_object(aTHX_ btn_print, "Wx::Button"),
+                            (wxButton *)wxPli_sv_2_object(aTHX_ btn_send_gcode, "Wx::Button"),
+                            (wxStaticBitmap *)wxPli_sv_2_object(aTHX_ manifold_warning_icon, "Wx::StaticBitmap")); %};
+
+void set_show_print_info(bool show)
+    %code%{ Slic3r::GUI::set_show_print_info(show); %};
+
+void set_show_manifold_warning_icon(bool show)
+    %code%{ Slic3r::GUI::set_show_manifold_warning_icon(show); %};
+
+void update_mode()
+    %code%{ Slic3r::GUI::update_mode(); %};
+
+void add_object_to_list(const char *name, SV *object_model)
+    %code%{ Slic3r::GUI::add_object_to_list(
+                    name, 
+                    (ModelObject *)wxPli_sv_2_object(aTHX_ object_model, "Slic3r::Model::Object") ); %};
+
+void delete_object_from_list()
+    %code%{ Slic3r::GUI::delete_object_from_list(); %};
+
+void delete_all_objects_from_list()
+    %code%{ Slic3r::GUI::delete_all_objects_from_list(); %};
+
+void set_object_count(int idx, int count)
+    %code%{ Slic3r::GUI::set_object_count(idx, count); %};
+
+void set_object_scale(int idx, int scale)
+    %code%{ Slic3r::GUI::set_object_scale(idx, scale); %};
+
+void unselect_objects()
+    %code%{ Slic3r::GUI::unselect_objects(); %};
+
+void select_current_object(int idx)
+    %code%{ Slic3r::GUI::select_current_object(idx); %};
+
+void remove_obj()
+    %code%{ Slic3r::GUI::remove(); %};
+
+void update_rotation_value(double angle, const char *axis)
+    %code%{ Slic3r::GUI::update_rotation_value(angle, axis); %};
+
 std::string fold_utf8_to_ascii(const char *src)
     %code%{ RETVAL = Slic3r::fold_utf8_to_ascii(src); %};
 
diff --git a/xs/xsp/GUI_3DScene.xsp b/xs/xsp/GUI_3DScene.xsp
index 6349a7c766..c15fdc196f 100644
--- a/xs/xsp/GUI_3DScene.xsp
+++ b/xs/xsp/GUI_3DScene.xsp
@@ -55,13 +55,12 @@
     int                 object_idx() const;
     int                 volume_idx() const;
     int                 instance_idx() const;
-    Clone<Pointf3>      origin() const
+    Clone<Vec3d>        origin() const
         %code%{ RETVAL = THIS->get_origin(); %};
     void                translate(double x, double y, double z)
-        %code%{ THIS->set_origin(THIS->get_origin() + Pointf3(x, y, z)); %};
+        %code%{ THIS->set_origin(THIS->get_origin() + Vec3d(x, y, z)); %};
     Clone<BoundingBoxf3> bounding_box() const
         %code%{ RETVAL = THIS->bounding_box; %};
-    Clone<BoundingBoxf3> transformed_bounding_box() const;
 
     bool                empty() const;
     bool                indexed() const;
@@ -419,6 +418,13 @@ enable_shader(canvas, enable)
     CODE:
         _3DScene::enable_shader((wxGLCanvas*)wxPli_sv_2_object(aTHX_ canvas, "Wx::GLCanvas"), enable);
 
+void
+enable_toolbar(canvas, enable)
+        SV   *canvas;
+        bool enable;
+    CODE:
+        _3DScene::enable_toolbar((wxGLCanvas*)wxPli_sv_2_object(aTHX_ canvas, "Wx::GLCanvas"), enable);
+
 void
 enable_force_zoom_to_bed(canvas, enable)
         SV   *canvas;
@@ -440,6 +446,23 @@ allow_multisample(canvas, allow)
     CODE:
         _3DScene::allow_multisample((wxGLCanvas*)wxPli_sv_2_object(aTHX_ canvas, "Wx::GLCanvas"), allow);
 
+void
+enable_toolbar_item(canvas, item, enable)
+        SV          *canvas;
+        std::string item;
+        bool        enable;
+    CODE:
+        _3DScene::enable_toolbar_item((wxGLCanvas*)wxPli_sv_2_object(aTHX_ canvas, "Wx::GLCanvas"), item, enable);
+
+bool
+is_toolbar_item_pressed(canvas, item)
+        SV          *canvas;
+        std::string item;
+    CODE:
+        RETVAL = _3DScene::is_toolbar_item_pressed((wxGLCanvas*)wxPli_sv_2_object(aTHX_ canvas, "Wx::GLCanvas"), item);
+    OUTPUT:
+        RETVAL
+
 void
 zoom_to_bed(canvas)
         SV *canvas;
@@ -626,7 +649,77 @@ register_on_update_geometry_info_callback(canvas, callback)
         SV *callback;
     CODE:
         _3DScene::register_on_update_geometry_info_callback((wxGLCanvas*)wxPli_sv_2_object(aTHX_ canvas, "Wx::GLCanvas"), (void*)callback);
-             
+
+void
+register_action_add_callback(canvas, callback)
+        SV *canvas;
+        SV *callback;
+    CODE:
+        _3DScene::register_action_add_callback((wxGLCanvas*)wxPli_sv_2_object(aTHX_ canvas, "Wx::GLCanvas"), (void*)callback);
+
+void
+register_action_delete_callback(canvas, callback)
+        SV *canvas;
+        SV *callback;
+    CODE:
+        _3DScene::register_action_delete_callback((wxGLCanvas*)wxPli_sv_2_object(aTHX_ canvas, "Wx::GLCanvas"), (void*)callback);
+
+void
+register_action_deleteall_callback(canvas, callback)
+        SV *canvas;
+        SV *callback;
+    CODE:
+        _3DScene::register_action_deleteall_callback((wxGLCanvas*)wxPli_sv_2_object(aTHX_ canvas, "Wx::GLCanvas"), (void*)callback);
+
+void
+register_action_arrange_callback(canvas, callback)
+        SV *canvas;
+        SV *callback;
+    CODE:
+        _3DScene::register_action_arrange_callback((wxGLCanvas*)wxPli_sv_2_object(aTHX_ canvas, "Wx::GLCanvas"), (void*)callback);
+
+void
+register_action_more_callback(canvas, callback)
+        SV *canvas;
+        SV *callback;
+    CODE:
+        _3DScene::register_action_more_callback((wxGLCanvas*)wxPli_sv_2_object(aTHX_ canvas, "Wx::GLCanvas"), (void*)callback);
+
+void
+register_action_fewer_callback(canvas, callback)
+        SV *canvas;
+        SV *callback;
+    CODE:
+        _3DScene::register_action_fewer_callback((wxGLCanvas*)wxPli_sv_2_object(aTHX_ canvas, "Wx::GLCanvas"), (void*)callback);
+
+void
+register_action_split_callback(canvas, callback)
+        SV *canvas;
+        SV *callback;
+    CODE:
+        _3DScene::register_action_split_callback((wxGLCanvas*)wxPli_sv_2_object(aTHX_ canvas, "Wx::GLCanvas"), (void*)callback);
+
+void
+register_action_cut_callback(canvas, callback)
+        SV *canvas;
+        SV *callback;
+    CODE:
+        _3DScene::register_action_cut_callback((wxGLCanvas*)wxPli_sv_2_object(aTHX_ canvas, "Wx::GLCanvas"), (void*)callback);
+
+void
+register_action_settings_callback(canvas, callback)
+        SV *canvas;
+        SV *callback;
+    CODE:
+        _3DScene::register_action_settings_callback((wxGLCanvas*)wxPli_sv_2_object(aTHX_ canvas, "Wx::GLCanvas"), (void*)callback);
+
+void
+register_action_layersediting_callback(canvas, callback)
+        SV *canvas;
+        SV *callback;
+    CODE:
+        _3DScene::register_action_layersediting_callback((wxGLCanvas*)wxPli_sv_2_object(aTHX_ canvas, "Wx::GLCanvas"), (void*)callback);
+
 void
 reset_legend_texture()
     CODE:
diff --git a/xs/xsp/GUI_Preset.xsp b/xs/xsp/GUI_Preset.xsp
index 2c63db10c4..99d23a1421 100644
--- a/xs/xsp/GUI_Preset.xsp
+++ b/xs/xsp/GUI_Preset.xsp
@@ -32,7 +32,6 @@
 %name{Slic3r::GUI::PresetCollection} class PresetCollection {
 
     Ref<Preset>             preset(size_t idx) %code%{ RETVAL = &THIS->preset(idx); %};
-    Ref<Preset>             default_preset() %code%{ RETVAL = &THIS->default_preset(); %};
     size_t                  size() const;
     size_t                  num_visible() const;
     std::string             name() const;
@@ -133,6 +132,7 @@ PresetCollection::arrayref()
 
     Ref<PresetCollection>       print()    %code%{ RETVAL = &THIS->prints;   %};
     Ref<PresetCollection>       filament() %code%{ RETVAL = &THIS->filaments; %};
+    Ref<PresetCollection>       sla_material() %code%{ RETVAL = &THIS->sla_materials; %};
     Ref<PresetCollection>       printer()  %code%{ RETVAL = &THIS->printers;  %};
     Ref<DynamicPrintConfig>     project_config() %code%{ RETVAL = &THIS->project_config; %};
 
diff --git a/xs/xsp/Geometry.xsp b/xs/xsp/Geometry.xsp
index b23bbeffa9..b7e92ba695 100644
--- a/xs/xsp/Geometry.xsp
+++ b/xs/xsp/Geometry.xsp
@@ -8,7 +8,7 @@
 
 %package{Slic3r::Geometry};
 
-Pointfs arrange(size_t total_parts, Pointf* part, coordf_t dist, BoundingBoxf* bb = NULL)
+Pointfs arrange(size_t total_parts, Vec2d* part, coordf_t dist, BoundingBoxf* bb = NULL)
     %code{% 
         Pointfs points;
         if (! Slic3r::Geometry::arrange(total_parts, *part, dist, bb, points))
diff --git a/xs/xsp/Line.xsp b/xs/xsp/Line.xsp
index f7437de01c..777dc41fa7 100644
--- a/xs/xsp/Line.xsp
+++ b/xs/xsp/Line.xsp
@@ -78,15 +78,15 @@ Line::coincides_with(line_sv)
 
 
 %name{Slic3r::Linef3} class Linef3 {
-    Linef3(Pointf3* a, Pointf3* b)
+    Linef3(Vec3d* a, Vec3d* b)
         %code{% RETVAL = new Linef3(*a, *b); %};
     ~Linef3();
     Clone<Linef3> clone()
         %code{% RETVAL = THIS; %};
-    Ref<Pointf3> a()
+    Ref<Vec3d> a()
         %code{% RETVAL = &THIS->a; %};
-    Ref<Pointf3> b()
+    Ref<Vec3d> b()
         %code{% RETVAL = &THIS->b; %};
-    Clone<Pointf3> intersect_plane(double z);
+    Clone<Vec3d> intersect_plane(double z);
     void scale(double factor);
 };
diff --git a/xs/xsp/Model.xsp b/xs/xsp/Model.xsp
index 25c26c3804..ac265a3b36 100644
--- a/xs/xsp/Model.xsp
+++ b/xs/xsp/Model.xsp
@@ -81,7 +81,7 @@
 
     bool add_default_instances();
     Clone<BoundingBoxf3> bounding_box();
-    void center_instances_around_point(Pointf* point)
+    void center_instances_around_point(Vec2d* point)
         %code%{ THIS->center_instances_around_point(*point); %};
     void translate(double x, double y, double z);
     Clone<TriangleMesh> mesh();
@@ -289,9 +289,9 @@ ModelMaterial::attributes()
     void set_layer_height_profile(std::vector<double> profile)
         %code%{ THIS->layer_height_profile = profile; THIS->layer_height_profile_valid = true; %};
 
-    Ref<Pointf3> origin_translation()
+    Ref<Vec3d> origin_translation()
         %code%{ RETVAL = &THIS->origin_translation; %};
-    void set_origin_translation(Pointf3* point)
+    void set_origin_translation(Vec3d* point)
         %code%{ THIS->origin_translation = *point; %};
     
     bool needed_repair() const;
@@ -299,7 +299,7 @@ ModelMaterial::attributes()
     int facets_count();
     void center_around_origin();
     void translate(double x, double y, double z);
-    void scale_xyz(Pointf3* versor)
+    void scale_xyz(Vec3d* versor)
         %code{% THIS->scale(*versor); %};
     void rotate(float angle, Axis axis);
     void mirror(Axis axis);
@@ -357,14 +357,14 @@ ModelMaterial::attributes()
         %code%{ RETVAL = THIS->rotation; %};
     double scaling_factor()
         %code%{ RETVAL = THIS->scaling_factor; %};
-    Ref<Pointf> offset()
+    Ref<Vec2d> offset()
         %code%{ RETVAL = &THIS->offset; %};
 
     void set_rotation(double val)
         %code%{ THIS->rotation = val; THIS->get_object()->invalidate_bounding_box(); %};
     void set_scaling_factor(double val)
         %code%{ THIS->scaling_factor = val; THIS->get_object()->invalidate_bounding_box(); %};
-    void set_offset(Pointf *offset)
+    void set_offset(Vec2d *offset)
         %code%{ THIS->offset = *offset; %};
     
     void transform_mesh(TriangleMesh* mesh, bool dont_translate = false) const;
diff --git a/xs/xsp/Point.xsp b/xs/xsp/Point.xsp
index 2a98f9c396..beefc62494 100644
--- a/xs/xsp/Point.xsp
+++ b/xs/xsp/Point.xsp
@@ -77,24 +77,10 @@ Point::coincides_with(point_sv)
 
 };
 
-%name{Slic3r::Point3} class Point3 {
-    Point3(int _x = 0, int _y = 0, int _z = 0);
-    ~Point3();
-    Clone<Point3> clone()
-        %code{% RETVAL = THIS; %};
-    int x()
-        %code{% RETVAL = (*THIS)(0); %};
-    int y()
-        %code{% RETVAL = (*THIS)(1); %};
-    int z()
-        %code{% RETVAL = (*THIS)(2); %};
-    std::string serialize() %code{% char buf[2048]; sprintf(buf, "%ld,%ld,%ld", (*THIS)(0), (*THIS)(1), (*THIS)(2)); RETVAL = buf; %};
-};
-
-%name{Slic3r::Pointf} class Pointf {
-    Pointf(double _x = 0, double _y = 0);
-    ~Pointf();
-    Clone<Pointf> clone()
+%name{Slic3r::Pointf} class Vec2d {
+    Vec2d(double _x = 0, double _y = 0);
+    ~Vec2d();
+    Clone<Vec2d> clone()
         %code{% RETVAL = THIS; %};
     SV* arrayref()
         %code{% RETVAL = to_SV_pureperl(THIS); %};
@@ -109,22 +95,22 @@ Point::coincides_with(point_sv)
     void set_y(double val)
         %code{% (*THIS)(1) = val; %};
     void translate(double x, double y)
-        %code{% *THIS += Pointf(x, y); %};
+        %code{% *THIS += Vec2d(x, y); %};
     void scale(double factor)
         %code{% *THIS *= factor; %};
-    void rotate(double angle, Pointf* center)
-        %code{% THIS->rotate(angle, *center); %};
-    Pointf* negative()
-        %code{% RETVAL = new Pointf(- *THIS); %};
-    Pointf* vector_to(Pointf* point)
-        %code{% RETVAL = new Pointf(*point - *THIS); %};
+    void rotate(double angle, Vec2d* center)
+        %code{% *THIS = Eigen::Translation2d(*center) * Eigen::Rotation2Dd(angle) * Eigen::Translation2d(- *center) * Eigen::Vector2d((*THIS)(0), (*THIS)(1)); %};
+    Vec2d* negative()
+        %code{% RETVAL = new Vec2d(- *THIS); %};
+    Vec2d* vector_to(Vec2d* point)
+        %code{% RETVAL = new Vec2d(*point - *THIS); %};
     std::string serialize() %code{% char buf[2048]; sprintf(buf, "%lf,%lf", (*THIS)(0), (*THIS)(1)); RETVAL = buf; %};
 };
 
-%name{Slic3r::Pointf3} class Pointf3 {
-    Pointf3(double _x = 0, double _y = 0, double _z = 0);
-    ~Pointf3();
-    Clone<Pointf3> clone()
+%name{Slic3r::Pointf3} class Vec3d {
+    Vec3d(double _x = 0, double _y = 0, double _z = 0);
+    ~Vec3d();
+    Clone<Vec3d> clone()
         %code{% RETVAL = THIS; %};
     double x()
         %code{% RETVAL = (*THIS)(0); %};
@@ -139,14 +125,14 @@ Point::coincides_with(point_sv)
     void set_z(double val)
         %code{% (*THIS)(2) = val; %};
     void translate(double x, double y, double z)
-        %code{% *THIS += Pointf3(x, y, z); %};
+        %code{% *THIS += Vec3d(x, y, z); %};
     void scale(double factor)
         %code{% *THIS *= factor; %};
-    double distance_to(Pointf3* point)
+    double distance_to(Vec3d* point)
         %code{% RETVAL = (*point - *THIS).norm(); %};
-    Pointf3* negative()
-        %code{% RETVAL = new Pointf3(- *THIS); %};
-    Pointf3* vector_to(Pointf3* point)
-        %code{% RETVAL = new Pointf3(*point - *THIS); %};
+    Vec3d* negative()
+        %code{% RETVAL = new Vec3d(- *THIS); %};
+    Vec3d* vector_to(Vec3d* point)
+        %code{% RETVAL = new Vec3d(*point - *THIS); %};
     std::string serialize() %code{% char buf[2048]; sprintf(buf, "%lf,%lf,%lf", (*THIS)(0), (*THIS)(1), (*THIS)(2)); RETVAL = buf; %};
 };
diff --git a/xs/xsp/Print.xsp b/xs/xsp/Print.xsp
index 361e8a2bcb..96004d1a50 100644
--- a/xs/xsp/Print.xsp
+++ b/xs/xsp/Print.xsp
@@ -63,8 +63,6 @@ _constant()
         %code%{ RETVAL = THIS->layer_height_ranges; %};
     std::vector<double> layer_height_profile()
         %code%{ RETVAL = THIS->layer_height_profile; %};
-    Ref<Point3> size()
-        %code%{ RETVAL = &THIS->size; %};
     Clone<BoundingBox> bounding_box();
     
     Points _shifted_copies()
@@ -72,7 +70,7 @@ _constant()
     void set_shifted_copies(Points value)
         %code%{ THIS->_shifted_copies = value; %};
 
-    bool add_copy(Pointf* point)
+    bool add_copy(Vec2d* point)
         %code%{ RETVAL = THIS->add_copy(*point); %};
     bool delete_last_copy();
     bool delete_all_copies();
diff --git a/xs/xsp/TriangleMesh.xsp b/xs/xsp/TriangleMesh.xsp
index 1691066a50..2bc20da3a0 100644
--- a/xs/xsp/TriangleMesh.xsp
+++ b/xs/xsp/TriangleMesh.xsp
@@ -16,7 +16,7 @@
     void repair();
     void WriteOBJFile(char* output_file);
     void scale(float factor);
-    void scale_xyz(Pointf3* versor)
+    void scale_xyz(Vec3d* versor)
         %code{% THIS->scale(*versor); %};
     void translate(float x, float y, float z);
     void rotate_x(float angle);
@@ -33,7 +33,7 @@
     ExPolygons horizontal_projection();
     Clone<Polygon> convex_hull();
     Clone<BoundingBoxf3> bounding_box();
-    Clone<Pointf3> center()
+    Clone<Vec3d> center()
         %code{% RETVAL = THIS->bounding_box().center(); %};
     int facets_count();
     void reset_repair_stats();
@@ -60,14 +60,14 @@ TriangleMesh::ReadFromPerl(vertices, facets)
         for (int i = 0; i < stl.stats.number_of_facets; i++) {
             AV* facet_av = (AV*)SvRV(*av_fetch(facets_av, i, 0));
             stl_facet facet;
-            facet.normal.x = 0;
-            facet.normal.y = 0;
-            facet.normal.z = 0;
+            facet.normal(0) = 0;
+            facet.normal(1) = 0;
+            facet.normal(2) = 0;
             for (unsigned int v = 0; v <= 2; v++) {
                 AV* vertex_av = (AV*)SvRV(*av_fetch(vertices_av, SvIV(*av_fetch(facet_av, v, 0)), 0));
-                facet.vertex[v].x = SvNV(*av_fetch(vertex_av, 0, 0));
-                facet.vertex[v].y = SvNV(*av_fetch(vertex_av, 1, 0));
-                facet.vertex[v].z = SvNV(*av_fetch(vertex_av, 2, 0));
+                facet.vertex[v](0) = SvNV(*av_fetch(vertex_av, 0, 0));
+                facet.vertex[v](1) = SvNV(*av_fetch(vertex_av, 1, 0));
+                facet.vertex[v](2) = SvNV(*av_fetch(vertex_av, 2, 0));
             }
             facet.extra[0] = 0;
             facet.extra[1] = 0;
@@ -110,9 +110,9 @@ TriangleMesh::vertices()
             AV* vertex = newAV();
             av_store(vertices, i, newRV_noinc((SV*)vertex));
             av_extend(vertex, 2);
-            av_store(vertex, 0, newSVnv(THIS->stl.v_shared[i].x));
-            av_store(vertex, 1, newSVnv(THIS->stl.v_shared[i].y));
-            av_store(vertex, 2, newSVnv(THIS->stl.v_shared[i].z));
+            av_store(vertex, 0, newSVnv(THIS->stl.v_shared[i](0)));
+            av_store(vertex, 1, newSVnv(THIS->stl.v_shared[i](1)));
+            av_store(vertex, 2, newSVnv(THIS->stl.v_shared[i](2)));
         }
         
         RETVAL = newRV_noinc((SV*)vertices);
@@ -155,9 +155,9 @@ TriangleMesh::normals()
             AV* facet = newAV();
             av_store(normals, i, newRV_noinc((SV*)facet));
             av_extend(facet, 2);
-            av_store(facet, 0, newSVnv(THIS->stl.facet_start[i].normal.x));
-            av_store(facet, 1, newSVnv(THIS->stl.facet_start[i].normal.y));
-            av_store(facet, 2, newSVnv(THIS->stl.facet_start[i].normal.z));
+            av_store(facet, 0, newSVnv(THIS->stl.facet_start[i].normal(0)));
+            av_store(facet, 1, newSVnv(THIS->stl.facet_start[i].normal(1)));
+            av_store(facet, 2, newSVnv(THIS->stl.facet_start[i].normal(2)));
         }
         
         RETVAL = newRV_noinc((SV*)normals);
@@ -169,9 +169,9 @@ TriangleMesh::size()
     CODE:
         AV* size = newAV();
         av_extend(size, 2);
-        av_store(size, 0, newSVnv(THIS->stl.stats.size.x));
-        av_store(size, 1, newSVnv(THIS->stl.stats.size.y));
-        av_store(size, 2, newSVnv(THIS->stl.stats.size.z));
+        av_store(size, 0, newSVnv(THIS->stl.stats.size(0)));
+        av_store(size, 1, newSVnv(THIS->stl.stats.size(1)));
+        av_store(size, 2, newSVnv(THIS->stl.stats.size(2)));
         RETVAL = newRV_noinc((SV*)size);
     OUTPUT:
         RETVAL
@@ -216,12 +216,12 @@ TriangleMesh::cut(z, upper, lower)
 std::vector<double>
 TriangleMesh::bb3()
     CODE:
-        RETVAL.push_back(THIS->stl.stats.min.x);
-        RETVAL.push_back(THIS->stl.stats.min.y);
-        RETVAL.push_back(THIS->stl.stats.max.x);
-        RETVAL.push_back(THIS->stl.stats.max.y);
-        RETVAL.push_back(THIS->stl.stats.min.z);
-        RETVAL.push_back(THIS->stl.stats.max.z);
+        RETVAL.push_back(THIS->stl.stats.min(0));
+        RETVAL.push_back(THIS->stl.stats.min(1));
+        RETVAL.push_back(THIS->stl.stats.max(0));
+        RETVAL.push_back(THIS->stl.stats.max(1));
+        RETVAL.push_back(THIS->stl.stats.min(2));
+        RETVAL.push_back(THIS->stl.stats.max(2));
     OUTPUT:
         RETVAL
 
diff --git a/xs/xsp/Utils_OctoPrint.xsp b/xs/xsp/Utils_OctoPrint.xsp
deleted file mode 100644
index 28610cb01e..0000000000
--- a/xs/xsp/Utils_OctoPrint.xsp
+++ /dev/null
@@ -1,13 +0,0 @@
-%module{Slic3r::XS};
-
-%{
-#include <xsinit.h>
-#include "slic3r/Utils/OctoPrint.hpp"
-%}
-
-%name{Slic3r::OctoPrint} class OctoPrint {
-    OctoPrint(DynamicPrintConfig *config);
-    ~OctoPrint();
-
-    bool send_gcode(std::string filename) const;
-};
diff --git a/xs/xsp/Utils_PrintHost.xsp b/xs/xsp/Utils_PrintHost.xsp
new file mode 100644
index 0000000000..59c09c4317
--- /dev/null
+++ b/xs/xsp/Utils_PrintHost.xsp
@@ -0,0 +1,12 @@
+%module{Slic3r::XS};
+
+%{
+#include <xsinit.h>
+#include "slic3r/Utils/PrintHost.hpp"
+%}
+
+%name{Slic3r::PrintHost} class PrintHost {
+	bool send_gcode(std::string filename) const;
+
+	static PrintHost* get_print_host(DynamicPrintConfig *config);
+};
diff --git a/xs/xsp/my.map b/xs/xsp/my.map
index 4a14f483fc..d857340863 100644
--- a/xs/xsp/my.map
+++ b/xs/xsp/my.map
@@ -66,13 +66,13 @@ Point3*                    O_OBJECT_SLIC3R
 Ref<Point3>                O_OBJECT_SLIC3R_T
 Clone<Point3>              O_OBJECT_SLIC3R_T
 
-Pointf*                    O_OBJECT_SLIC3R
-Ref<Pointf>                O_OBJECT_SLIC3R_T
-Clone<Pointf>              O_OBJECT_SLIC3R_T
+Vec2d*                     O_OBJECT_SLIC3R
+Ref<Vec2d>                 O_OBJECT_SLIC3R_T
+Clone<Vec2d>               O_OBJECT_SLIC3R_T
 
-Pointf3*                   O_OBJECT_SLIC3R
-Ref<Pointf3>               O_OBJECT_SLIC3R_T
-Clone<Pointf3>             O_OBJECT_SLIC3R_T
+Vec3d*                     O_OBJECT_SLIC3R
+Ref<Vec3d>                 O_OBJECT_SLIC3R_T
+Clone<Vec3d>               O_OBJECT_SLIC3R_T
 
 Line*                      O_OBJECT_SLIC3R
 Ref<Line>                  O_OBJECT_SLIC3R_T
@@ -239,9 +239,7 @@ Ref<TabIface> 				O_OBJECT_SLIC3R_T
 PresetUpdater*              O_OBJECT_SLIC3R
 Ref<PresetUpdater>          O_OBJECT_SLIC3R_T
 
-OctoPrint*                  O_OBJECT_SLIC3R
-Ref<OctoPrint>              O_OBJECT_SLIC3R_T
-Clone<OctoPrint>            O_OBJECT_SLIC3R_T
+PrintHost*                  O_OBJECT_SLIC3R
 
 Axis                  T_UV
 ExtrusionLoopRole     T_UV
diff --git a/xs/xsp/typemap.xspt b/xs/xsp/typemap.xspt
index b576b1373e..b3d73b9b33 100644
--- a/xs/xsp/typemap.xspt
+++ b/xs/xsp/typemap.xspt
@@ -22,12 +22,12 @@
 %typemap{Point3*};
 %typemap{Ref<Point3>}{simple};
 %typemap{Clone<Point3>}{simple};
-%typemap{Pointf*};
-%typemap{Ref<Pointf>}{simple};
-%typemap{Clone<Pointf>}{simple};
-%typemap{Pointf3*};
-%typemap{Ref<Pointf3>}{simple};
-%typemap{Clone<Pointf3>}{simple};
+%typemap{Vec2d*};
+%typemap{Ref<Vec2d>}{simple};
+%typemap{Clone<Vec2d>}{simple};
+%typemap{Vec3d*};
+%typemap{Ref<Vec3d>}{simple};
+%typemap{Clone<Vec3d>}{simple};
 %typemap{BoundingBox*};
 %typemap{Ref<BoundingBox>}{simple};
 %typemap{Clone<BoundingBox>}{simple};
@@ -270,3 +270,4 @@
 };
 %typemap{AppController*};
 %typemap{PrintController*};
+%typemap{PrintHost*};