Merge remote-tracking branch 'origin/dev' into sla_base_pool

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
 }

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);
     }
 }
 

lib/Slic3r/GUI/Plater/ObjectPartsPanel.pm

@@ -378,6 +378,7 @@ sub on_btn_load {
         }
     }
 
+    $self->{model_object}->center_around_origin if $self->{parts_changed};
     $self->_parts_changed;
 }
 
@@ -480,6 +481,7 @@ sub on_btn_delete {
         $self->{parts_changed} = 1;
     }
 
+    $self->{model_object}->center_around_origin if $self->{parts_changed};
     $self->_parts_changed;
 }
 

xs/CMakeLists.txt

@@ -207,6 +207,8 @@ add_library(libslic3r_gui STATIC
     ${LIBDIR}/slic3r/GUI/GLGizmo.cpp
     ${LIBDIR}/slic3r/GUI/GLTexture.hpp
     ${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

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 },

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.
+    // If any two of the three vertices are found to be exactally the same, call them degenerate and remove the facet.
-    // When using a memcmp on raw floats, those numbers report to be different.
+    if (facet.vertex[0] == facet.vertex[1] ||
-    // Unify all +0 and -0 to +0 to make the floats equal under memcmp.
+        facet.vertex[1] == facet.vertex[2] ||
-    {
+        facet.vertex[0] == facet.vertex[2]) {
-      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))) {
       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],
+      stl_load_edge_exact(stl, &edge, &facet.vertex[j], &facet.vertex[(j + 1) % 3]);
-                          &facet.vertex[(j + 1) % 3]);
+      insert_hash_edge(stl, edge, stl_record_neighbors);
-
-      insert_hash_edge(stl, edge, stl_match_neighbors_exact);
     }
   }
   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);
+    stl_vertex diff = (*a - *b).cwiseAbs();
-    float diff_y = ABS(a->y - b->y);
+    float max_diff = std::max(diff(0), std::max(diff(1), diff(2)));
-    float diff_z = ABS(a->z - b->z);
+    stl->stats.shortest_edge = std::min(max_diff, stl->stats.shortest_edge);
-    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);
   }
 
   // Ensure identical vertex ordering of equal edges.
   // This method is numerically robust.
-  if ((a->x != b->x) ? 
+  if (stl_vertex_lower(*a, *b)) {
-        (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));
   } else {
-    memcpy(&edge->key[0], b, sizeof(stl_vertex));
+    std::swap(a, b);
-    memcpy(&edge->key[3], a, sizeof(stl_vertex));
     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
+static void insert_hash_edge(stl_file *stl, stl_hash_edge edge,
-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 *edge_a, stl_hash_edge *edge_b))
-  stl_hash_edge *link;
+{
-  stl_hash_edge *new_edge;
-  stl_hash_edge *temp;
-  int            chain_number;
-
   if (stl->error) return;
 
-  chain_number = stl_get_hash_for_edge(stl->M, &edge);
+  int            chain_number = edge.hash(stl->M);
-
+  stl_hash_edge *link = stl->heads[chain_number];
-  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,
   }
 }
 
-
+// Return 1 if the edges are not matched.
-static int
+static inline int stl_compare_function(stl_hash_edge *edge_a, stl_hash_edge *edge_b)
-stl_get_hash_for_edge(int M, stl_hash_edge *edge) {
+{
-  return ((edge->key[0] / 23 + edge->key[1] / 19 + edge->key[2] / 17
+    // Don't match edges of the same facet
-           + edge->key[3] /13  + edge->key[4] / 11 + edge->key[5] / 7 ) % M);
+    return (edge_a->facet_number == edge_b->facet_number) || (*edge_a != *edge_b);
 }
 
-static int
+void stl_check_facets_nearby(stl_file *stl, float tolerance)
-stl_compare_function(stl_hash_edge *edge_a, stl_hash_edge *edge_b) {
+{
-  if(edge_a->facet_number == edge_b->facet_number) {
+  if (stl->error)
-    return 1;			/* Don't match edges of the same facet */
+    return;
-  } 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;
 
   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++) {
+  for (int i = 0; i < stl->stats.number_of_facets; ++ i) {
-    facet = stl->facet_start[i];
+    //FIXME is the copy necessary?
-    // Positive and negative zeros are possible in the floats, which are considered equal by the FP unit.
+    stl_facet facet = stl->facet_start[i];
-    // When using a memcmp on raw floats, those numbers report to be different.
+    for (int j = 0; j < 3; j++) {
-    // 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++) {
       if(stl->neighbors_start[i].neighbor[j] == -1) {
-        edge[j].facet_number = i;
+        stl_hash_edge edge;
-        edge[j].which_edge = j;
+        edge.facet_number = i;
-        if(stl_load_edge_nearby(stl, &edge[j], &facet.vertex[j],
+        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
+static int stl_load_edge_nearby(stl_file *stl, stl_hash_edge *edge, stl_vertex *a, stl_vertex *b, float tolerance)
-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] = {
+  typedef Eigen::Matrix<int32_t,  3, 1, Eigen::DontAlign> Vec3i;
-    (uint32_t)((a->x - stl->stats.min.x) / tolerance),
+  Vec3i vertex1 = (*a / tolerance).cast<int32_t>();
-    (uint32_t)((a->y - stl->stats.min.y) / tolerance),
+  Vec3i vertex2 = (*b / tolerance).cast<int32_t>();
-    (uint32_t)((a->z - stl->stats.min.z) / tolerance)
+  static_assert(sizeof(Vec3i) == 12, "size of Vec3i incorrect");
-  };
-  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)
-  };
 
-  if(   (vertex1[0] == vertex2[0])
+  if (vertex1 == vertex2)
-        && (vertex1[1] == vertex2[1])
+    // Both vertices hash to the same value
-        && (vertex1[2] == vertex2[2])) {
-    /* 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[0],                  vertex1.data(), sizeof(stl_vertex));
-    memcpy(&edge->key[3], vertex2, 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[0],                  vertex2.data(), sizeof(stl_vertex));
-    memcpy(&edge->key[3], vertex1, 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
+static void stl_free_edges(stl_file *stl)
-stl_free_edges(stl_file *stl) {
+{
-  int i;
+  if (stl->error)
-  stl_hash_edge *temp;
+    return;
-
-  if (stl->error) return;
 
   if(stl->stats.malloced != stl->stats.freed) {
-    for(i = 0; i < stl->M; i++) {
+    for (int i = 0; i < stl->M; i++) {
-      for(temp = stl->heads[i]; stl->heads[i] != stl->tail;
+      for (stl_hash_edge *temp = stl->heads[i]; stl->heads[i] != stl->tail; temp = stl->heads[i]) {
-          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
+static void stl_initialize_facet_check_nearby(stl_file *stl)
-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
+static void stl_match_neighbors_nearby(stl_file *stl, stl_hash_edge *edge_a, stl_hash_edge *edge_b)
-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) {
   int facet1;
   int facet2;
   int vertex1;
@@ -517,9 +458,7 @@ stl_match_neighbors_nearby(stl_file *stl,
 }
 
 
-static void
+static void stl_change_vertices(stl_file *stl, int facet_num, int vnot, stl_vertex new_vertex) {
-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 &&
+    if (stl->facet_start[facet_num].vertex[pivot_vertex](0) == new_vertex(0) &&
-        stl->facet_start[facet_num].vertex[pivot_vertex].y == new_vertex.y &&
+        stl->facet_start[facet_num].vertex[pivot_vertex](1) == new_vertex(1) &&
-        stl->facet_start[facet_num].vertex[pivot_vertex].z == new_vertex.z)
+        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,
+          stl->facet_start[facet_num].vertex[pivot_vertex](0),
-          *reinterpret_cast<const int*>(&stl->facet_start[facet_num].vertex[pivot_vertex].x),
+          *reinterpret_cast<const int*>(&stl->facet_start[facet_num].vertex[pivot_vertex](0)),
-          new_vertex.x,
+          new_vertex(0),
-          *reinterpret_cast<const int*>(&new_vertex.x));
+          *reinterpret_cast<const int*>(&new_vertex(0)));
-      if (stl->facet_start[facet_num].vertex[pivot_vertex].y != new_vertex.y)
+      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,
+          stl->facet_start[facet_num].vertex[pivot_vertex](1),
-          *reinterpret_cast<const int*>(&stl->facet_start[facet_num].vertex[pivot_vertex].y),
+          *reinterpret_cast<const int*>(&stl->facet_start[facet_num].vertex[pivot_vertex](1)),
-          new_vertex.y,
+          new_vertex(1),
-          *reinterpret_cast<const int*>(&new_vertex.y));
+          *reinterpret_cast<const int*>(&new_vertex(1)));
-      if (stl->facet_start[facet_num].vertex[pivot_vertex].z != new_vertex.z)
+      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,
+          stl->facet_start[facet_num].vertex[pivot_vertex](2),
-          *reinterpret_cast<const int*>(&stl->facet_start[facet_num].vertex[pivot_vertex].z),
+          *reinterpret_cast<const int*>(&stl->facet_start[facet_num].vertex[pivot_vertex](2)),
-          new_vertex.z,
+          new_vertex(2),
-          *reinterpret_cast<const int*>(&new_vertex.z));
+          *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 */
+  // Of the first pair, which vertex, if any, should be changed
-  if(!memcmp(&stl->facet_start[edge_a->facet_number].vertex[v1a],
+  if(stl->facet_start[edge_a->facet_number].vertex[v1a] == 
-             &stl->facet_start[edge_b->facet_number].vertex[v1b],
+     stl->facet_start[edge_b->facet_number].vertex[v1b]) {
-             sizeof(stl_vertex))) {
+    // These facets are already equal.  No need to change.
-    /* 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],
+  if(stl->facet_start[edge_a->facet_number].vertex[v2a] == 
-             &stl->facet_start[edge_b->facet_number].vertex[v2b],
+     stl->facet_start[edge_b->facet_number].vertex[v2b]) {
-             sizeof(stl_vertex))) {
+    // These facets are already equal.  No need to change.
-    /* 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
+void stl_remove_unconnected_facets(stl_file *stl)
-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;
+  // remove degenerate facets
-
+  for (int i = 0; i < stl->stats.number_of_facets; ++ i) {
-  if (stl->error) return;
+    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] ||
-  /* remove degenerate facets */
+       stl->facet_start[i].vertex[1] == stl->facet_start[i].vertex[2]) {
-  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))) {
       stl_remove_degenerate(stl, i);
       i--;
     }
   }
 
   if(stl->stats.connected_facets_1_edge < stl->stats.number_of_facets) {
-    /* remove completely unconnected facets */
+    // remove completely unconnected facets
-    for(i = 0; i < stl->stats.number_of_facets; i++) {
+    for (int i = 0; i < stl->stats.number_of_facets; i++) {
-      if(   (stl->neighbors_start[i].neighbor[0] == -1)
+      if (stl->neighbors_start[i].neighbor[0] == -1 &&
-            && (stl->neighbors_start[i].neighbor[1] == -1)
+          stl->neighbors_start[i].neighbor[1] == -1 &&
-            && (stl->neighbors_start[i].neighbor[2] == -1)) {
+          stl->neighbors_start[i].neighbor[2] == -1) {
-        /* This facet is completely unconnected.  Remove it. */
+        // 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],
+  if (stl->facet_start[facet].vertex[0] == stl->facet_start[facet].vertex[1] &&
-                &stl->facet_start[facet].vertex[1], sizeof(stl_vertex))
+      stl->facet_start[facet].vertex[1] == stl->facet_start[facet].vertex[2]) {
-        && !memcmp(&stl->facet_start[facet].vertex[1],
-                   &stl->facet_start[facet].vertex[2], sizeof(stl_vertex))) {
     /* 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],
+  if (stl->facet_start[facet].vertex[0] == stl->facet_start[facet].vertex[1]) {
-             &stl->facet_start[facet].vertex[1], sizeof(stl_vertex))) {
     edge1 = 1;
     edge2 = 2;
     edge3 = 0;
-  } else if(!memcmp(&stl->facet_start[facet].vertex[1],
+  } else if (stl->facet_start[facet].vertex[1] == stl->facet_start[facet].vertex[2]) {
-                    &stl->facet_start[facet].vertex[2], sizeof(stl_vertex))) {
     edge1 = 0;
     edge2 = 2;
     edge3 = 1;
-  } else if(!memcmp(&stl->facet_start[facet].vertex[2],
+  } else if (stl->facet_start[facet].vertex[2] == stl->facet_start[facet].vertex[0]) {
-                    &stl->facet_start[facet].vertex[0], sizeof(stl_vertex))) {
     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 = stl_normal::Zero();
-  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->neighbors_start[stl->stats.number_of_facets].neighbor[0] = -1;
   stl->neighbors_start[stl->stats.number_of_facets].neighbor[1] = -1;

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)
+  const float eps = 0.001f;
-        && (ABS(normal[1] - facet->normal.y) < 0.001)
+  if (normal_dif(0) < eps && normal_dif(1) < eps && normal_dif(2) < eps) {
-        && (ABS(normal[2] - facet->normal.z) < 0.001)) {
     /* It is not really necessary to change the values here */
     /* but just for consistency, I will. */
-    facet->normal.x = normal[0];
+    facet->normal = normal;
-    facet->normal.y = normal[1];
-    facet->normal.z = normal[2];
     return 0;
   }
 
-  test_norm[0] = facet->normal.x;
+  stl_normal test_norm = facet->normal;
-  test_norm[1] = facet->normal.y;
-  test_norm[2] = facet->normal.z;
-
   stl_normalize_vector(test_norm);
-  if(   (ABS(normal[0] - test_norm[0]) < 0.001)
+  normal_dif = (normal - test_norm).cwiseAbs();
-        && (ABS(normal[1] - test_norm[1]) < 0.001)
+  if (normal_dif(0) < eps && normal_dif(1) < eps && normal_dif(2) < eps) {
-        && (ABS(normal[2] - test_norm[2]) < 0.001)) {
     if(normal_fix_flag) {
-      facet->normal.x = normal[0];
+      facet->normal = normal;
-      facet->normal.y = normal[1];
-      facet->normal.z = normal[2];
       stl->stats.normals_fixed += 1;
     }
     return 1;
   }
 
-  stl_reverse_vector(test_norm);
+  test_norm *= -1.f;
-  if(   (ABS(normal[0] - test_norm[0]) < 0.001)
+  normal_dif = (normal - test_norm).cwiseAbs();
-        && (ABS(normal[1] - test_norm[1]) < 0.001)
+  if (normal_dif(0) < eps && normal_dif(1) < eps && normal_dif(2) < eps) {
-        && (ABS(normal[2] - test_norm[2]) < 0.001)) {
+    // Facet is backwards.
-    /* Facet is backwards. */
     if(normal_fix_flag) {
-      facet->normal.x = normal[0];
+      facet->normal = normal;
-      facet->normal.y = normal[1];
-      facet->normal.z = normal[2];
       stl->stats.normals_fixed += 1;
     }
     return 2;
   }
   if(normal_fix_flag) {
-    facet->normal.x = normal[0];
+    facet->normal = normal;
-    facet->normal.y = normal[1];
-    facet->normal.z = normal[2];
     stl->stats.normals_fixed += 1;
   }
   return 4;
 }
 
-void stl_calculate_normal(float normal[], stl_facet *facet) {
+void stl_fix_normal_values(stl_file *stl) {
-  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) {
   int i;
 
   if (stl->error) return;
@@ -333,20 +277,16 @@ stl_fix_normal_values(stl_file *stl) {
   }
 }
 
-void
+void stl_reverse_all_facets(stl_file *stl)
-stl_reverse_all_facets(stl_file *stl) {
+{
-  int i;
+  if (stl->error)
-  float normal[3];
+  	return;
 
-  if (stl->error) return;
+  stl_normal normal;
-
+  for(int i = 0; i < stl->stats.number_of_facets; i++) {
-  for(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 = normal;
-    stl->facet_start[i].normal.y = normal[1];
-    stl->facet_start[i].normal.z = normal[2];
   }
 }
-

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);

xs/src/admesh/stl.h

@@ -27,9 +27,7 @@
 #include <stdint.h>
 #include <stddef.h>
 
-#define STL_MAX(A,B) ((A)>(B)? (A):(B))
+#include <Eigen/Geometry> 
-#define STL_MIN(A,B) ((A)<(B)? (A):(B))
-#define ABS(X)  ((X) < 0 ? -(X) : (X))
 
 // 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.
+  // Key of a hash edge: sorted vertices of the edge.
-  uint32_t       key[6];
+  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_versor(stl_file *stl, const stl_vertex &versor);
-extern void stl_scale(stl_file *stl, float factor);
+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);
+inline void stl_calculate_normal(stl_normal &normal, stl_facet *facet) {
-extern void stl_normalize_vector(float v[]);
+  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_read(stl_file *stl, int first_facet, bool first);
-extern void stl_facet_stats(stl_file *stl, stl_facet facet, int 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);

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(0), stl->edge_start[i].p1(1),
-            stl->edge_start[i].p1.z, stl->edge_start[i].p2.x,
+            stl->edge_start[i].p1(2), stl->edge_start[i].p2(0),
-            stl->edge_start[i].p2.y, stl->edge_start[i].p2.z);
+            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(0), stl->facet_start[i].normal(1),
-            stl->facet_start[i].normal.z);
+            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](0), stl->facet_start[i].vertex[0](1),
-            stl->facet_start[i].vertex[0].z);
+            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](0), stl->facet_start[i].vertex[1](1),
-            stl->facet_start[i].vertex[1].z);
+            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](0), stl->facet_start[i].vertex[2](1),
-            stl->facet_start[i].vertex[2].z);
+            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](0),
-         stl->facet_start[facet].vertex[vertex].y,
+         stl->facet_start[facet].vertex[vertex](1),
-         stl->facet_start[facet].vertex[vertex].z);
+         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 connect_color = stl_vertex::Zero();
-  stl_vertex uncon_1_color;
+  stl_vertex uncon_1_color = stl_vertex::Zero();
-  stl_vertex uncon_2_color;
+  stl_vertex uncon_2_color = stl_vertex::Zero();
-  stl_vertex uncon_3_color;
+  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](0),
-            stl->facet_start[i].vertex[0].y,
+            stl->facet_start[i].vertex[0](1),
-            stl->facet_start[i].vertex[0].z, color.x, color.y, color.z);
+            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](0),
-            stl->facet_start[i].vertex[1].y,
+            stl->facet_start[i].vertex[1](1),
-            stl->facet_start[i].vertex[1].z, color.x, color.y, color.z);
+            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](0),
-            stl->facet_start[i].vertex[2].y,
+            stl->facet_start[i].vertex[2](1),
-            stl->facet_start[i].vertex[2].z, color.x, color.y, color.z);
+            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](0),
-            stl->facet_start[i].vertex[2].y,
+            stl->facet_start[i].vertex[2](1),
-            stl->facet_start[i].vertex[2].z, color.x, color.y, color.z);
+            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](0), stl->facet_start[i].vertex[0](1),
-            stl->facet_start[i].vertex[0].z);
+            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](0), stl->facet_start[i].vertex[1](1),
-            stl->facet_start[i].vertex[1].z);
+            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](0), stl->facet_start[i].vertex[2](1),
-            stl->facet_start[i].vertex[2].z);
+            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](0), stl->facet_start[i].vertex[2](1),
-            stl->facet_start[i].vertex[2].z);
+            stl->facet_start[i].vertex[2](2));
   }
 
   fprintf(fp, "0\nENDSEC\n0\nEOF\n");

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
+void stl_read(stl_file *stl, int first_facet, bool first) {
-stl_read(stl_file *stl, int first_facet, int 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 ||
+	  if (sscanf(normal_buf[0], "%f", &facet.normal(0)) != 1 ||
-		  sscanf(normal_buf[1], "%f", &facet.normal.y) != 1 ||
+		  sscanf(normal_buf[1], "%f", &facet.normal(1)) != 1 ||
-		  sscanf(normal_buf[2], "%f", &facet.normal.z) != 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)
+        if (facet.vertex[j](0) > -1e-12f && facet.vertex[j](0) < 1e-12f)
-            printf("stl_read: facet %d.x = %e\r\n", j, facet.vertex[j].x);
+            printf("stl_read: facet %d(0) = %e\r\n", j, facet.vertex[j](0));
-        if (facet.vertex[j].y > -1e-12f && facet.vertex[j].y < 1e-12f)
+        if (facet.vertex[j](1) > -1e-12f && facet.vertex[j](1) < 1e-12f)
-            printf("stl_read: facet %d.y = %e\r\n", j, facet.vertex[j].y);
+            printf("stl_read: facet %d(1) = %e\r\n", j, facet.vertex[j](1));
-        if (facet.vertex[j].z > -1e-12f && facet.vertex[j].z < 1e-12f)
+        if (facet.vertex[j](2) > -1e-12f && facet.vertex[j](2) < 1e-12f)
-            printf("stl_read: facet %d.z = %e\r\n", j, facet.vertex[j].z);
+            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 = stl->stats.max - stl->stats.min;
-  stl->stats.size.y = stl->stats.max.y - stl->stats.min.y;
+  stl->stats.bounding_diameter = stl->stats.size.norm();
-  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
-                                 );
 }
 
-void
+void stl_facet_stats(stl_file *stl, stl_facet facet, bool &first)
-stl_facet_stats(stl_file *stl, stl_facet facet, int first) {
+{
-  float diff_x;
+  if (stl->error)
-  float diff_y;
+  	return;
-  float diff_z;
-  float max_diff;
 
-  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;
+	// Initialize the max and min values the first time through
-    stl->stats.min.x = facet.vertex[0].x;
+    stl->stats.min = facet.vertex[0];
-    stl->stats.max.y = facet.vertex[0].y;
+    stl->stats.max = facet.vertex[0];
-    stl->stats.min.y = facet.vertex[0].y;
+    stl_vertex diff = (facet.vertex[1] - facet.vertex[0]).cwiseAbs();
-    stl->stats.max.z = facet.vertex[0].z;
+    stl->stats.shortest_edge = std::max(diff(0), std::max(diff(1), diff(2)));
-    stl->stats.min.z = facet.vertex[0].z;
+    first = false;
-
-    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;
   }
 
-  /* now find the max and min values */
+  // Now find the max and min values.
-  stl->stats.max.x = STL_MAX(stl->stats.max.x, facet.vertex[0].x);
+  for (size_t i = 0; i < 3; ++ i) {
-  stl->stats.min.x = STL_MIN(stl->stats.min.x, facet.vertex[0].x);
+  	stl->stats.min = stl->stats.min.cwiseMin(facet.vertex[i]);
-  stl->stats.max.y = STL_MAX(stl->stats.max.y, facet.vertex[0].y);
+  	stl->stats.max = stl->stats.max.cwiseMax(facet.vertex[i]);
-  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);
 }
 
 void

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
+void stl_translate(stl_file *stl, float x, float y, float z)
-stl_translate(stl_file *stl, float x, float y, float z) {
+{
-  int i;
+  if (stl->error)
-  int j;
+  	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].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;
 
+  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
+void stl_translate_relative(stl_file *stl, float x, float y, float z)
-stl_translate_relative(stl_file *stl, float x, float y, float z) {
+{
-  int i;
+  if (stl->error)
-  int j;
+  	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].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;
 
+  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
+void stl_scale_versor(stl_file *stl, const stl_vertex &versor)
-stl_scale_versor(stl_file *stl, float versor[3]) {
+{
-  int i;
+  if (stl->error)
-  int j;
+  	return;
-
-  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];
-    }
-  }
 
+  // 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
+static void calculate_normals(stl_file *stl) 
-stl_scale(stl_file *stl, float factor) {
+{
-  float versor[3];
+  if (stl->error)
-
+  	return;
-  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;
 
+  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 = normal;
-    stl->facet_start[i].normal.y = normal[1];
-    stl->facet_start[i].normal.z = normal[2];
   }
 }
 
@@ -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(0) = trafo3x4[0] * v_src(0) + trafo3x4[1] * v_src(1) + trafo3x4[2]  * v_src(2) + trafo3x4[3];
-      v_dst.y = trafo3x4[4] * v_src.x + trafo3x4[5] * v_src.y + trafo3x4[6]  * v_src.z + trafo3x4[7];
+      v_dst(1) = trafo3x4[4] * v_src(0) + trafo3x4[5] * v_src(1) + trafo3x4[6]  * v_src(2) + trafo3x4[7];
-      v_dst.z = trafo3x4[8] * v_src.x + trafo3x4[9] * v_src.y + trafo3x4[10] * v_src.z + trafo3x4[11];
+      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_rotate(&stl->facet_start[i].vertex[j](1),
-                 &stl->facet_start[i].vertex[j].z, c, s);
+                 &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_rotate(&stl->facet_start[i].vertex[j](2),
-                 &stl->facet_start[i].vertex[j].x, c, s);
+                 &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_rotate(&stl->facet_start[i].vertex[j](0),
-                 &stl->facet_start[i].vertex[j].y, c, s);
+                 &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
+void stl_get_size(stl_file *stl)
-stl_get_size(stl_file *stl) {
+{
-  int i;
+  if (stl->error || stl->stats.number_of_facets == 0)
-  int j;
+  	return;
-
+  stl->stats.min = stl->facet_start[0].vertex[0];
-  if (stl->error) return;
+  stl->stats.max = stl->stats.min;
-  if (stl->stats.number_of_facets == 0) return;
+  for (int i = 0; i < stl->stats.number_of_facets; ++ i) {
-
+  	const stl_facet &face = stl->facet_start[i];
-  stl->stats.min.x = stl->facet_start[0].vertex[0].x;
+    for (int j = 0; j < 3; ++ j) {
-  stl->stats.min.y = stl->facet_start[0].vertex[0].y;
+      stl->stats.min = stl->stats.min.cwiseMin(face.vertex[j]);
-  stl->stats.min.z = stl->facet_start[0].vertex[0].z;
+      stl->stats.max = stl->stats.max.cwiseMax(face.vertex[j]);
-  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);
     }
   }
-  stl->stats.size.x = stl->stats.max.x - stl->stats.min.x;
+  stl->stats.size = stl->stats.max - stl->stats.min;
-  stl->stats.size.y = stl->stats.max.y - stl->stats.min.y;
+  stl->stats.bounding_diameter = stl->stats.size.norm();
-  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
-                                 );
 }
 
-void
+void stl_mirror_xy(stl_file *stl)
-stl_mirror_xy(stl_file *stl) {
+{
-  int i;
+  if (stl->error) 
-  int j;
+  	return;
-  float temp_size;
 
-  if (stl->error) return;
+  for(int i = 0; i < stl->stats.number_of_facets; i++) {
-
+    for(int j = 0; j < 3; j++) {
-  for(i = 0; i < stl->stats.number_of_facets; i++) {
+      stl->facet_start[i].vertex[j](2) *= -1.0;
-    for(j = 0; j < 3; j++) {
-      stl->facet_start[i].vertex[j].z *= -1.0;
     }
   }
-  temp_size = stl->stats.min.z;
+  float temp_size = stl->stats.min(2);
-  stl->stats.min.z = stl->stats.max.z;
+  stl->stats.min(2) = stl->stats.max(2);
-  stl->stats.max.z = temp_size;
+  stl->stats.max(2) = temp_size;
-  stl->stats.min.z *= -1.0;
+  stl->stats.min(2) *= -1.0;
-  stl->stats.max.z *= -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
+void stl_mirror_yz(stl_file *stl)
-stl_mirror_yz(stl_file *stl) {
+{
-  int i;
-  int j;
-  float temp_size;
-
   if (stl->error) return;
 
-  for(i = 0; i < stl->stats.number_of_facets; i++) {
+  for (int i = 0; i < stl->stats.number_of_facets; i++) {
-    for(j = 0; j < 3; j++) {
+    for (int j = 0; j < 3; j++) {
-      stl->facet_start[i].vertex[j].x *= -1.0;
+      stl->facet_start[i].vertex[j](0) *= -1.0;
     }
   }
-  temp_size = stl->stats.min.x;
+  float temp_size = stl->stats.min(0);
-  stl->stats.min.x = stl->stats.max.x;
+  stl->stats.min(0) = stl->stats.max(0);
-  stl->stats.max.x = temp_size;
+  stl->stats.max(0) = temp_size;
-  stl->stats.min.x *= -1.0;
+  stl->stats.min(0) *= -1.0;
-  stl->stats.max.x *= -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
+void stl_mirror_xz(stl_file *stl)
-stl_mirror_xz(stl_file *stl) {
+{
-  int i;
+  if (stl->error)
-  int j;
+  	return;
-  float temp_size;
 
-  if (stl->error) return;
+  for (int i = 0; i < stl->stats.number_of_facets; i++) {
-
+    for (int j = 0; j < 3; j++) {
-  for(i = 0; i < stl->stats.number_of_facets; i++) {
+      stl->facet_start[i].vertex[j](1) *= -1.0;
-    for(j = 0; j < 3; j++) {
-      stl->facet_start[i].vertex[j].y *= -1.0;
     }
   }
-  temp_size = stl->stats.min.y;
+  float temp_size = stl->stats.min(1);
-  stl->stats.min.y = stl->stats.max.y;
+  stl->stats.min(1) = stl->stats.max(1);
-  stl->stats.max.y = temp_size;
+  stl->stats.max(1) = temp_size;
-  stl->stats.min.y *= -1.0;
+  stl->stats.min(1) *= -1.0;
-  stl->stats.max.y *= -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) {
+static float get_volume(stl_file *stl)
-  stl_vertex p0;
+{
-  stl_vertex p;
+  if (stl->error)
-  stl_normal n;
+  	return 0;
-  float height;
-  float area;
-  float volume = 0.0;
 
-  if (stl->error) return 0;
+  // Choose a point, any point as the reference.
-
+  stl_vertex p0 = stl->facet_start[0].vertex[0];
-  /* Choose a point, any point as the reference */
+  float volume = 0.f;
-  p0.x = stl->facet_start[0].vertex[0].x;
+  for(uint32_t i = 0; i < stl->stats.number_of_facets; ++ i) {
-  p0.y = stl->facet_start[0].vertex[0].y;
+    // Do dot product to get distance from point to plane.
-  p0.z = stl->facet_start[0].vertex[0].z;
+    float height = stl->facet_start[i].normal.dot(stl->facet_start[i].vertex[0] - p0);
-
+    float area   = get_area(&stl->facet_start[i]);
-  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]);
     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) {
+static float get_area(stl_facet *facet)
-  double cross[3][3];
+{
-  float sum[3];
-  float n[3];
-  float area;
-  int i;
-
   /* 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++) {
+  double cross[3][3];
-    cross[i][0]=(((double)facet->vertex[i].y * (double)facet->vertex[(i + 1) % 3].z) -
+  for (int i = 0; i < 3; i++) {
-                 ((double)facet->vertex[i].z * (double)facet->vertex[(i + 1) % 3].y));
+    cross[i][0]=(((double)facet->vertex[i](1) * (double)facet->vertex[(i + 1) % 3](2)) -
-    cross[i][1]=(((double)facet->vertex[i].z * (double)facet->vertex[(i + 1) % 3].x) -
+                 ((double)facet->vertex[i](2) * (double)facet->vertex[(i + 1) % 3](1)));
-                 ((double)facet->vertex[i].x * (double)facet->vertex[(i + 1) % 3].z));
+    cross[i][1]=(((double)facet->vertex[i](2) * (double)facet->vertex[(i + 1) % 3](0)) -
-    cross[i][2]=(((double)facet->vertex[i].x * (double)facet->vertex[(i + 1) % 3].y) -
+                 ((double)facet->vertex[i](0) * (double)facet->vertex[(i + 1) % 3](2)));
-                 ((double)facet->vertex[i].y * (double)facet->vertex[(i + 1) % 3].x));
+    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];
+  stl_normal sum;
-  sum[1] = cross[0][1] + cross[1][1] + cross[2][1];
+  sum(0) = cross[0][0] + cross[1][0] + cross[2][0];
-  sum[2] = cross[0][2] + cross[1][2] + cross[2][2];
+  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);
-
+  return 0.5f * n.dot(sum);
-  area = 0.5 * (n[0] * sum[0] + n[1] * sum[1] + n[2] * sum[2]);
-  return area;
 }
 
 void stl_repair(stl_file *stl,

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
+void BoundingBox::polygon(Polygon* polygon) const
-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
+Polygon BoundingBox::polygon() const
-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<Vec2d>::scale(double factor);
-template void BoundingBoxBase<Pointf3>::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 = this->min.cwiseMin(point);
-        this->min(1) = std::min(point(1), this->min(1));
+        this->max = this->max.cwiseMax(point);
-        this->max(0) = std::max(point(0), this->max(0));
-        this->max(1) = std::max(point(1), this->max(1));
     } 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 = this->min.cwiseMin(bb.min);
-            this->min(1) = std::min(bb.min(1), this->min(1));
+            this->max = this->max.cwiseMax(bb.max);
-            this->max(0) = std::max(bb.max(0), this->max(0));
-            this->max(1) = std::max(bb.max(1), this->max(1));
         } 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->min = this->min.cwiseMin(point);
-        this->max(2) = std::max(point(2), this->max(2));
+        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->min = this->min.cwiseMin(bb.min);
-            this->max(2) = std::max(bb.max(2), this->max(2));
+            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(
+    return (this->min + this->max) / 2;
-        (this->max(0) + this->min(0))/2,
-        (this->max(1) + this->min(1))/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(
+    return (this->min + this->max) / 2;
-        (this->max(0) + this->min(0))/2,
-        (this->max(1) + this->min(1))/2,
-        (this->max(2) + this->min(2))/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 src_vertices;
-    vertices(0, 1) = (float)max(0); vertices(1, 1) = (float)min(1); vertices(2, 1) = (float)min(2);
+    src_vertices(0, 0) = min(0); src_vertices(1, 0) = min(1); src_vertices(2, 0) = min(2);
-    vertices(0, 2) = (float)max(0); vertices(1, 2) = (float)max(1); vertices(2, 2) = (float)min(2);
+    src_vertices(0, 1) = max(0); src_vertices(1, 1) = min(1); src_vertices(2, 1) = min(2);
-    vertices(0, 3) = (float)min(0); vertices(1, 3) = (float)max(1); vertices(2, 3) = (float)min(2);
+    src_vertices(0, 2) = max(0); src_vertices(1, 2) = max(1); src_vertices(2, 2) = min(2);
-    vertices(0, 4) = (float)min(0); vertices(1, 4) = (float)min(1); vertices(2, 4) = (float)max(2);
+    src_vertices(0, 3) = min(0); src_vertices(1, 3) = max(1); src_vertices(2, 3) = min(2);
-    vertices(0, 5) = (float)max(0); vertices(1, 5) = (float)min(1); vertices(2, 5) = (float)max(2);
+    src_vertices(0, 4) = min(0); src_vertices(1, 4) = min(1); src_vertices(2, 4) = max(2);
-    vertices(0, 6) = (float)max(0); vertices(1, 6) = (float)max(1); vertices(2, 6) = (float)max(2);
+    src_vertices(0, 5) = max(0); src_vertices(1, 5) = min(1); src_vertices(2, 5) = max(2);
-    vertices(0, 7) = (float)min(0); vertices(1, 7) = (float)max(1); vertices(2, 7) = (float)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);
+    Vec3d v_min(dst_vertices(0, 0), dst_vertices(1, 0), dst_vertices(2, 0));
-    float max_x = transf_vertices(0, 0);
+    Vec3d v_max = v_min;
-    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);
 
     for (int i = 1; i < 8; ++i)
     {
-        min_x = std::min(min_x, transf_vertices(0, i));
+        for (int j = 0; j < 3; ++j)
-        max_x = std::max(max_x, transf_vertices(0, i));
+        {
-        min_y = std::min(min_y, transf_vertices(1, i));
+            v_min(j) = std::min(v_min(j), dst_vertices(j, i));
-        max_y = std::max(max_y, transf_vertices(1, i));
+            v_max(j) = std::max(v_max(j), dst_vertices(j, i));
-        min_z = std::min(min_z, transf_vertices(2, i));
+        }
-        max_z = std::max(max_z, transf_vertices(2, 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);
 }
 
 }

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 = *it;
-        this->min(1) = this->max(1) = (*it)(1);
+        this->max = *it;
-        for (++it; it != points.end(); ++it)
+        for (++ it; it != points.end(); ++ it) {
-        {
+            this->min = this->min.cwiseMin(*it);
-            this->min(0) = std::min((*it)(0), this->min(0));
+            this->max = this->max.cwiseMax(*it);
-            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->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);
+        this->min = *it;
-        for (++it; it != points.end(); ++it)
+        this->max = *it;
-        {
+        for (++ it; it != points.end(); ++ it) {
-            this->min(2) = std::min((*it)(2), this->min(2));
+            this->min = this->min.cwiseMin(*it);
-            this->max(2) = std::max((*it)(2), this->max(2));
+            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() : BoundingBox3Base<Vec3crd>() {};
-    BoundingBox3(const Point3 &pmin, const Point3 &pmax) : BoundingBox3Base<Point3>(pmin, pmax) {};
+    BoundingBox3(const Vec3crd &pmin, const Vec3crd &pmax) : BoundingBox3Base<Vec3crd>(pmin, pmax) {};
-    BoundingBox3(const Points3& points) : BoundingBox3Base<Point3>(points) {};
+    BoundingBox3(const Points3& points) : BoundingBox3Base<Vec3crd>(points) {};
 };
 
-class BoundingBoxf : public BoundingBoxBase<Pointf> 
+class BoundingBoxf : public BoundingBoxBase<Vec2d> 
 {
 public:
-    BoundingBoxf() : BoundingBoxBase<Pointf>() {};
+    BoundingBoxf() : BoundingBoxBase<Vec2d>() {};
-    BoundingBoxf(const Pointf &pmin, const Pointf &pmax) : BoundingBoxBase<Pointf>(pmin, pmax) {};
+    BoundingBoxf(const Vec2d &pmin, const Vec2d &pmax) : BoundingBoxBase<Vec2d>(pmin, pmax) {};
-    BoundingBoxf(const std::vector<Pointf> &points) : BoundingBoxBase<Pointf>(points) {};
+    BoundingBoxf(const std::vector<Vec2d> &points) : BoundingBoxBase<Vec2d>(points) {};
 };
 
-class BoundingBoxf3 : public BoundingBox3Base<Pointf3> 
+class BoundingBoxf3 : public BoundingBox3Base<Vec3d> 
 {
 public:
-    BoundingBoxf3() : BoundingBox3Base<Pointf3>() {};
+    BoundingBoxf3() : BoundingBox3Base<Vec3d>() {};
-    BoundingBoxf3(const Pointf3 &pmin, const Pointf3 &pmax) : BoundingBox3Base<Pointf3>(pmin, pmax) {};
+    BoundingBoxf3(const Vec3d &pmin, const Vec3d &pmax) : BoundingBox3Base<Vec3d>(pmin, pmax) {};
-    BoundingBoxf3(const std::vector<Pointf3> &points) : BoundingBox3Base<Pointf3>(points) {};
+    BoundingBoxf3(const std::vector<Vec3d> &points) : BoundingBox3Base<Vec3d>(points) {};
 
-    BoundingBoxf3 transformed(const Transform3f& matrix) const;
+    BoundingBoxf3 transformed(const Transform3d& matrix) const;
 };
 
 template<typename VT>

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)) {}
+    ConfigOptionPoint() : ConfigOptionSingle<Vec2d>(Vec2d(0,0)) {}
-    explicit ConfigOptionPoint(const Pointf &value) : ConfigOptionSingle<Pointf>(value) {}
+    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>() {}
+    ConfigOptionPoints() : ConfigOptionVector<Vec2d>() {}
-    explicit ConfigOptionPoints(size_t n, const Pointf &value) : ConfigOptionVector<Pointf>(n, value) {}
+    explicit ConfigOptionPoints(size_t n, const Vec2d &value) : ConfigOptionVector<Vec2d>(n, value) {}
-    explicit ConfigOptionPoints(std::initializer_list<Pointf> il) : ConfigOptionVector<Pointf>(std::move(il)) {}
+    explicit ConfigOptionPoints(std::initializer_list<Vec2d> il) : ConfigOptionVector<Vec2d>(std::move(il)) {}
-    explicit ConfigOptionPoints(const std::vector<Pointf> &values) : ConfigOptionVector<Pointf>(values) {}
+    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();
+        return from_string(str, this->value);
-        auto it = enum_keys_map.find(str);
-        if (it == enum_keys_map.end())
-            return false;
-        this->value = static_cast<T>(it->second);
-        return true;
     }
 
     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)

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;

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;
 }
 

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;

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)));
+            points.emplace_back(Vec2d(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
+            // 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
+            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

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(Vec2d(0, 0));
-    out.push_back(Pointf(1, 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(Vec2d( r,  0.));
-        out.push_back(Pointf( r2, rx));
+        out.push_back(Vec2d( r2, rx));
-        out.push_back(Pointf( rx, rx));
+        out.push_back(Vec2d( rx, rx));
-        out.push_back(Pointf( rx, r2));
+        out.push_back(Vec2d( rx, r2));
-        out.push_back(Pointf(0.,  r));
+        out.push_back(Vec2d(0.,  r));
-        out.push_back(Pointf(-rx, r2));
+        out.push_back(Vec2d(-rx, r2));
-        out.push_back(Pointf(-rx, rx));
+        out.push_back(Vec2d(-rx, rx));
-        out.push_back(Pointf(-r2, rx));
+        out.push_back(Vec2d(-r2, rx));
-        out.push_back(Pointf(-r,  0.));
+        out.push_back(Vec2d(-r,  0.));
-        out.push_back(Pointf(-r2, -rx));
+        out.push_back(Vec2d(-r2, -rx));
-        out.push_back(Pointf(-rx, -rx));
+        out.push_back(Vec2d(-rx, -rx));
-        out.push_back(Pointf(-rx, -r2));
+        out.push_back(Vec2d(-rx, -r2));
-        out.push_back(Pointf(0., -r));
+        out.push_back(Vec2d(0., -r));
-        out.push_back(Pointf( rx, -r2));
+        out.push_back(Vec2d( rx, -r2));
-        out.push_back(Pointf( rx, -rx));
+        out.push_back(Vec2d( rx, -rx));
-        out.push_back(Pointf( r2+r_inc, -rx));
+        out.push_back(Vec2d( r2+r_inc, -rx));
     }
     return out;
 }

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.

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.

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 Vec2d   p1(seg_start.cast<coordf_t>());
-    const Pointf   v1((seg_end - 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 Vec2d   p2(line->pos.cast<coordf_t>());
-    const Pointf   v2(line->dir.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.

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 << "x=\"" << stl.v_shared[i](0) << "\" ";
-                stream << "y=\"" << stl.v_shared[i].y << "\" ";
+                stream << "y=\"" << stl.v_shared[i](1) << "\" ";
-                stream << "z=\"" << stl.v_shared[i].z << "\" />\n";
+                stream << "z=\"" << stl.v_shared[i](2) << "\" />\n";
             }
         }
 

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 << "             <x>" << stl.v_shared[i](0) << "</x>\n";
-                stream << "             <y>" << stl.v_shared[i].y << "</y>\n";
+                stream << "             <y>" << stl.v_shared[i](1) << "</y>\n";
-                stream << "             <z>" << stl.v_shared[i].z << "</z>\n";
+                stream << "             <z>" << stl.v_shared[i](2) << "</z>\n";
                 stream << "           </coordinates>\n";
                 stream << "         </vertex>\n";
             }

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(0) += data.normals[vertex.normalIdx*3];
-                normal.y += data.normals[vertex.normalIdx*3+1];
+                normal(1) += data.normals[vertex.normalIdx*3+1];
-                normal.z += data.normals[vertex.normalIdx*3+2];
+                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(0) += data.normals[vertex.normalIdx*3];
-                normal.y += data.normals[vertex.normalIdx*3+1];
+                normal(1) += data.normals[vertex.normalIdx*3+1];
-                normal.z += data.normals[vertex.normalIdx*3+2];
+                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 /= len;
-                    normal.y /= len;
-                    normal.z /= 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);
+            float len = facet.normal.norm();
-            if (len > EPSILON) {
+            if (len > EPSILON)
-                normal.x /= len;
+                facet.normal = normal / len;
-                normal.y /= len;
-                normal.z /= len;
-                facet.normal = normal;
-            }
         }
 	}
     stl_get_size(&stl);

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)
+							if (std::abs(stl.stats.min(2)) < EPSILON)
-								stl.stats.min.z = 0.;
+								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 ||
+                        if (sscanf(normal_buf[0], "%f", &facet.normal(0)) != 1 ||
-                            sscanf(normal_buf[1], "%f", &facet.normal.y) != 1 ||
+                            sscanf(normal_buf[1], "%f", &facet.normal(1)) != 1 ||
-                            sscanf(normal_buf[2], "%f", &facet.normal.z) != 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));

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);
+    Vec2d extruder_offset = EXTRUDER_CONFIG(extruder_offset);
-    return Pointf(
+    return unscale(point) + m_origin - extruder_offset;
-        unscale(point(0)) + m_origin(0) - extruder_offset(0),
-        unscale(point(1)) + m_origin(1) - extruder_offset(1));
 }
 
 // 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.

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; }
+    const Vec2d&   origin() const { return m_origin; }
-    void            set_origin(const Pointf &pointf);
+    void            set_origin(const Vec2d &pointf);
-    void            set_origin(const coordf_t x, const coordf_t y) { this->set_origin(Pointf(x, y)); }
+    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;
+    Vec2d          point_to_gcode(const Point &point) const;
-    Point           gcode_to_point(const Pointf &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;

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(Vec3crd(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.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);
     }
 }

xs/src/libslic3r/GCode/Analyzer.hpp

@@ -75,12 +75,12 @@ public:
 
         EType type;
         Metadata data;
-        Pointf3 start_position;
+        Vec3d start_position;
-        Pointf3 end_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, 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 Pointf3& start_position, const Pointf3& 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);
+    void _set_start_position(const Vec3d& position);
-    const Pointf3& _get_start_position() const;
+    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);

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));

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)

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;

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.min = unscale(bbox.min);
-        bboxf.max = Pointf::new_unscale(bbox.max);
+        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.min = unscale(bbox.min);
-        bboxf.max = Pointf::new_unscale(bbox.max);
+        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.min = unscale(bbox.min);
-        bboxf.max = Pointf::new_unscale(bbox.max);
+        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);
+    Transform2d trafo =
-    float wipe_tower_angle = print.config.wipe_tower_rotation_angle.value;
+        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);
+                    Vec2d delta = 0.5 * Vec2d(e.width, e.width);
-                    Pointf  p2(e.pos.x, e.pos.y);
+                    Vec2d p1 = trafo * Vec2d((&e - 1)->pos.x, (&e - 1)->pos.y);
-                    p1.rotate(wipe_tower_angle);
+                    Vec2d p2 = trafo * Vec2d(e.pos.x, e.pos.y);
-                    p1 += wipe_tower_pos;
+                    bbox.merge(p1.cwiseMin(p2) - delta);
-                    p2.rotate(wipe_tower_angle);
+                    bbox.merge(p1.cwiseMax(p2) + delta);
-                    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);
                 }
             }
         }
@@ -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);
+                Vec2d  p1((&e - 1)->pos.x, (&e - 1)->pos.y);
-                Pointf  p2(e.pos.x, e.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);

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;

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_xy(const Vec2d &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_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_xy(const Vec2d &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_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);

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),
+            Vec2d(0, 0),
-            Pointf(cell_size(0) * num_parts, cell_size(1) * num_parts));
+            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);
+    Vec2d       cells_size(cellw * cell_size(0) - gap, cellh * cell_size(1) - gap);
-    Pointf       cells_offset(bed_bbox.center() - 0.5 * cells_size);
+    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:
+public:
-    Pointf pos;
+    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) {

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);
 

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);
 }
 
 }

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(const Point& a, const 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, 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() : a(Vec3crd::Zero()), b(Vec3crd::Zero()) {}
-    Line3(const Point3& _a, const Point3& _b) : a(_a), b(_b) {}
+    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;
+    Vec3crd a;
-    Point3 b;
+    Vec3crd b;
 };
 
 class Linef
 {
 public:
-    Linef() {}
+    Linef() : a(Vec2d::Zero()), b(Vec2d::Zero()) {}
-    explicit Linef(Pointf _a, Pointf _b): a(_a), b(_b) {}
+    Linef(const Vec2d& _a, const Vec2d& _b) : a(_a), b(_b) {}
 
-    Pointf a;
+    Vec2d a;
-    Pointf b;
+    Vec2d b;
 };
 
 class Linef3
 {
 public:
-    Linef3() {}
+    Linef3() : a(Vec3d::Zero()), b(Vec3d::Zero()) {}
-    explicit Linef3(Pointf3 _a, Pointf3 _b): a(_a), b(_b) {}
+    Linef3(const Vec3d& _a, const Vec3d& _b) : a(_a), b(_b) {}
-    Pointf3 intersect_plane(double z) const;
-    void    scale(double factor) { this->a *= factor; this->b *= factor; }
 
-    Pointf3 a;
+    Vec3d   intersect_plane(double z) const;
-    Pointf3 b;
+    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

xs/src/libslic3r/Model.cpp

@@ -235,15 +235,7 @@ BoundingBoxf3 Model::bounding_box() const
     return bb;
 }
 
-BoundingBoxf3 Model::transformed_bounding_box() const
+void Model::center_instances_around_point(const Vec2d &point)
-{
-    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)
 {
 //    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_sizes.emplace_back(to_2d(bbox.size()));
-            instance_centers.push_back(bbox.center().xy());
+            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
+    // First align to origin on XYZ, then center it on XY.
-    Vectorf3 vector(-bb.min(0), -bb.min(1), -bb.min(2));
+    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
+    this->translate(shift3);
-    Sizef3 size = bb.size();
+    this->origin_translation += shift3;
-    vector(0) -= size(0)/2;
-    vector(1) -= size(1)/2;
-    
-    this->translate(vector);
-    this->origin_translation += vector;
     
     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();
+            Eigen::Rotation2Dd rot(i->rotation);
-            v.rotate(i->rotation);
+            i->offset -= rot * shift2 * i->scaling_factor;
-            i->offset += v * 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));
+        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)
+    center_around_origin();
-    {
-        // 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);
-        }
-    }
 
-    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);
+    this->origin_translation = Vec3d::Zero();
-    invalidate_bounding_box();
+    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);
+                BoundingBoxf3 bb = vol->get_convex_hull().transformed_bounding_box(m);
-                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);
-                    }
-                }
 
                 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];
+            const stl_vertex &v = facet.vertex[j];
-            double xold = v.x;
+			bbox.merge(Vec3d(c * v(0) - s * v(1), s * v(0) + c * v(1), v(2)));
-            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));
         }
     }
     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 *= this->scaling_factor;
-            bbox.min(1) *= float(this->scaling_factor);
+			bbox.max *= 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);
         }
         // Translate the bounding box.
         if (! dont_translate) {
-            bbox.min(0) += float(this->offset(0));
+            Eigen::Map<Vec2d>(bbox.min.data()) += this->offset;
-            bbox.min(1) += float(this->offset(1));
+            Eigen::Map<Vec2d>(bbox.max.data()) += this->offset;
-            bbox.max(0) += float(this->offset(0));
-            bbox.max(1) += float(this->offset(1));
         }
     }
     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.translate(Vec3d(offset(0), offset(1), 0.0));
-    matrix.rotate(Eigen::AngleAxisf(rotation, Vec3f::UnitZ()));
+
+    matrix.rotate(Eigen::AngleAxisd(rotation, Vec3d::UnitZ()));
     matrix.scale(scaling_factor);
     return bbox.transformed(matrix);
 }

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, const TriangleMesh &mesh) : mesh(mesh), modifier(false), object(object)
-    ModelVolume(ModelObject *object, TriangleMesh &&mesh) : mesh(std::move(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), config(other.config), modifier(other.modifier), object(object)
+        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()); }
+    {
+        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
+    void center_instances_around_point(const Vec2d &point);
-    BoundingBoxf3 transformed_bounding_box() const;
-    void center_instances_around_point(const Pointf &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);

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

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;
     }

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);

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

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)

xs/src/libslic3r/Point.hpp

@@ -16,19 +16,7 @@ namespace Slic3r {
 class Line;
 class MultiPoint;
 class Point;
-class Point3;
+typedef Point Vector;
-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;
 
 // 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
+std::ostream& operator<<(std::ostream &stm, const Vec2d &pointf);
-{
-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)); }
-};
 
 } // namespace Slic3r
 

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)));

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) { 
+	static Polygon new_scale(const std::vector<Vec2d> &points) { 
-		Points int_points;
+        Polygon pgn;
-		for (auto pt : points)
+        pgn.points.reserve(points.size());
-			int_points.push_back(Point::new_scale(pt(0), pt(1)));
+        for (const Vec2d &pt : points)
-		return Polygon(int_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; }

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;
+		pl.points.reserve(points.size());
-		for (auto pt : points)
+		for (const Vec2d &pt : points)
-			int_points.push_back(Point::new_scale(pt(0), pt(1)));
+			pl.points.emplace_back(Point::new_scale(pt(0), pt(1)));
-		pl.append(int_points);
 		return pl;
     }
     

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)

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) {

xs/src/libslic3r/PrintConfig.cpp

@@ -18,8 +18,50 @@ namespace Slic3r {
 
 PrintConfigDef::PrintConfigDef()
 {
-    t_optiondef_map &Options = this->options;
+    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 = this->add("host_type", coEnum);
-    def->label = L("API Key");
+    def->label = L("Host Type");
-    def->tooltip = L("Slic3r can upload G-code files to OctoPrint. This field should contain "
+    def->tooltip = L("Slic3r can upload G-code files to a printer host. This field must contain "
-                   "the API Key required for authentication.");
+                   "the kind of the host.");
-    def->cli = "octoprint-apikey=s";
+    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 "
+    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 OctoPrint instance.");
+                   "the hostname, IP address or URL of the printer host instance.");
-    def->cli = "octoprint-host=s";
+    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;
+
 }

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;
+    ConfigOptionEnum<PrintHostType> host_type;
-    ConfigOptionString              octoprint_apikey;
+    ConfigOptionString              print_host;
-    ConfigOptionString              octoprint_cafile;
+    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(host_type);
-        OPT_PTR(octoprint_apikey);
+        OPT_PTR(print_host);
-        OPT_PTR(octoprint_cafile);
+        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

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 = (modobj_bbox.size() * (1. / SCALING_FACTOR)).cast<coord_t>();
-        this->size = Point3::new_scale(size(0), size(1), size(2));
     }
     
     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);

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));
+    Vec2d dir(line.b(0)-line.a(0), line.b(1)-line.a(1));
-    Pointf perp(-dir(1), dir(0));
+    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;

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;
+    std::vector<Vec3crd> palette_raw;
-    palette_raw.push_back(Point3(0x01A, 0x098, 0x050));
+    palette_raw.push_back(Vec3crd(0x01A, 0x098, 0x050));
-    palette_raw.push_back(Point3(0x066, 0x0BD, 0x063));
+    palette_raw.push_back(Vec3crd(0x066, 0x0BD, 0x063));
-    palette_raw.push_back(Point3(0x0A6, 0x0D9, 0x06A));
+    palette_raw.push_back(Vec3crd(0x0A6, 0x0D9, 0x06A));
-    palette_raw.push_back(Point3(0x0D9, 0x0F1, 0x0EB));
+    palette_raw.push_back(Vec3crd(0x0D9, 0x0F1, 0x0EB));
-    palette_raw.push_back(Point3(0x0FE, 0x0E6, 0x0EB));
+    palette_raw.push_back(Vec3crd(0x0FE, 0x0E6, 0x0EB));
-    palette_raw.push_back(Point3(0x0FD, 0x0AE, 0x061));
+    palette_raw.push_back(Vec3crd(0x0FD, 0x0AE, 0x061));
-    palette_raw.push_back(Point3(0x0F4, 0x06D, 0x043));
+    palette_raw.push_back(Vec3crd(0x0F4, 0x06D, 0x043));
-    palette_raw.push_back(Point3(0x0D7, 0x030, 0x027));
+    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 Vec3crd &color1 = palette_raw[idx1];
-            const Point3 &color2 = palette_raw[idx2];
+            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 Vec3crd &color1 = palette_raw[idx1];
-                const Point3 &color2 = palette_raw[idx2];
+                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));

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::min(std::min(f->vertex[0](2), f->vertex[1](2)), f->vertex[2](2)),
-		std::max(std::max(f->vertex[0].z, f->vertex[1].z), f->vertex[2].z));
+		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)

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 Vec2d 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_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;

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()
+TriangleMesh::TriangleMesh(const Pointf3s &points, const std::vector<Vec3crd>& facets )
-    : repaired(false)
-{
-    stl_initialize(&this->stl);
-}
-
-TriangleMesh::TriangleMesh(const Pointf3s &points, const std::vector<Point3>& 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;
-
+        facet.vertex[0] = points[facets[i](0)].cast<float>();
-        const Pointf3& ref_f1 = points[facets[i](0)];
+        facet.vertex[1] = points[facets[i](1)].cast<float>();
-        facet.vertex[0].x = ref_f1(0);
+        facet.vertex[2] = points[facets[i](2)].cast<float>();
-        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.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 = normal;
-        facet.normal.y = normal[1];
-        facet.normal.z = normal[2];
 
         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
+void TriangleMesh::reset_repair_stats() {
-{
-    return this->stl.stats.connected_facets_3_edge == this->stl.stats.number_of_facets;
-}
-
-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
+bool TriangleMesh::needed_repair() const
-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
+void TriangleMesh::WriteOBJFile(char* output_file)
-TriangleMesh::facets_count() const
 {
-    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];
+    stl_scale_versor(&this->stl, versor.cast<float>());
-    fversor[0] = versor(0);
-    fversor[1] = versor(1);
-    fversor[2] = versor(2);
-    stl_scale_versor(&this->stl, fversor);
     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(0),
-        -(this->stl.stats.min.y),
+        - this->stl.stats.min(1),
-        -(this->stl.stats.min.z)
+        - 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
+TriangleMeshPtrs TriangleMesh::split() const
-TriangleMesh::split() const
 {
-    TriangleMeshPtrs meshes;
+    TriangleMeshPtrs            meshes;
-    std::set<int> seen_facets;
+    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 (;;) {
@@ -491,23 +379,24 @@ 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;
+        if (facet_queue.empty())
+            break;
 
-        while (!facet_queue.empty()) {
+        while (! facet_queue.empty()) {
             int facet_idx = facet_queue.front();
             facet_queue.pop();
-            if (seen_facets.find(facet_idx) != seen_facets.end()) continue;
+            if (! facet_visited[facet_idx]) {
-            facets.emplace_back(facet_idx);
+                facets.emplace_back(facet_idx);
-            for (int j = 0; j <= 2; j++) {
+                for (int j = 0; j < 3; ++ j)
-                facet_queue.push(this->stl.neighbors_start[facet_idx].neighbor[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;
@@ -518,19 +407,17 @@ TriangleMesh::split() const
         stl_clear_error(&mesh->stl);
         stl_allocate(&mesh->stl);
         
-        int first = 1;
+        bool first = true;
-        for (std::deque<int>::const_iterator facet = facets.begin(); facet != facets.end(); ++facet) {
+        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
+void TriangleMesh::merge(const TriangleMesh &mesh)
-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[0] = Point::new_scale(facet->vertex[0](0), facet->vertex[0](1));
-        p.points[1] = Point::new_scale(facet->vertex[1].x, facet->vertex[1].y);
+        p.points[1] = Point::new_scale(facet->vertex[1](0), facet->vertex[1](1));
-        p.points[2] = Point::new_scale(facet->vertex[2].x, facet->vertex[2].y);
+        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];
+        const stl_vertex &v = this->stl.v_shared[i];
-        pp.emplace_back(Point::new_scale(v->x, v->y));
+        pp.emplace_back(Point::new_scale(v(0), v(1)));
     }
     return Slic3r::Geometry::convex_hull(pp);
 }
 
-BoundingBoxf3
+BoundingBoxf3 TriangleMesh::bounding_box() const
-TriangleMesh::bounding_box() const
 {
     BoundingBoxf3 bb;
     bb.defined = true;
-    bb.min(0) = this->stl.stats.min.x;
+    bb.min = this->stl.stats.min.cast<double>();
-    bb.min(1) = this->stl.stats.min.y;
+    bb.max = this->stl.stats.max.cast<double>();
-    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;
     return bb;
 }
 
-void
+BoundingBoxf3 TriangleMesh::transformed_bounding_box(const Transform3d& t) const
-TriangleMesh::require_shared_vertices()
+{
+    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) {
+    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] *= float(1. / SCALING_FACTOR);
-        this->v_scaled_shared[i].y /= float(SCALING_FACTOR);
-        this->v_scaled_shared[i].z /= float(SCALING_FACTOR);
-    }
 
     // Create a mapping from triangle edge into face.
     struct EdgeToFace {
@@ -697,8 +695,7 @@ TriangleMeshSlicer::TriangleMeshSlicer(TriangleMesh* _mesh) :
     }
 }
 
-void
+void TriangleMeshSlicer::slice(const std::vector<float> &z, std::vector<Polygons>* layers) const
-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 min_z = fminf(facet.vertex[0](2), fminf(facet.vertex[1](2), facet.vertex[2](2)));
-    const float max_z = fmaxf(facet.vertex[0].z, fmaxf(facet.vertex[1].z, facet.vertex[2].z));
+    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[0].x, facet.vertex[0].y, facet.vertex[0](2),
-        facet.vertex[1].x, facet.vertex[1].y, facet.vertex[1].z,
+        facet.vertex[1].x, facet.vertex[1].y, facet.vertex[1](2),
-        facet.vertex[2].x, facet.vertex[2].y, facet.vertex[2].z);
+        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 &a = this->v_scaled_shared[a_id];
-                    const stl_vertex *b = &this->v_scaled_shared[b_id];
+                    const stl_vertex &b = this->v_scaled_shared[b_id];
-                    il.a(0)    = a->x;
+                    il.a(0)    = a(0);
-                    il.a(1)    = a->y;
+                    il.a(1)    = a(1);
-                    il.b(0)    = b->x;
+                    il.b(0)    = b(0);
-                    il.b(1)    = b->y;
+                    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 &a = this->v_scaled_shared[a_id];
-        const stl_vertex *b = &this->v_scaled_shared[b_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);
+                    swap = true;
-                    std::swap(a_id, b_id);
                 }
-            } 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);
+                swap = true;
-                std::swap(a_id, b_id);
             } 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 = to_2d(swap ? b : a).cast<coord_t>();
-            line_out->a(1)  = a->y;
+            line_out->b = to_2d(swap ? a : b).cast<coord_t>();
-            line_out->b(0)  = b->x;
+            line_out->a_id = swap ? b_id : a_id;
-            line_out->b(1)  = b->y;
+            line_out->b_id = swap ? a_id : b_id;
-            line_out->a_id   = a_id;
-            line_out->b_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(0)       = a(0);
-            point(1)       = a->y;
+            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(0)       = b(0);
-            point(1)       = b->y;
+            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(0)       = b(0) + (a(0) - b(0)) * (slice_z - b(2)) / (a(2) - b(2));
-            point(1)       = b->y + (a->y - b->y) * (slice_z - b->z) / (a->z - b->z);
+            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 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].z, std::max(facet->vertex[1].z, facet->vertex[2].z));
+        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];
+            const stl_vertex &v0 = facet->vertex[isolated_vertex];
-            stl_vertex* v1 = &facet->vertex[(isolated_vertex+1) % 3];
+            const stl_vertex &v1 = facet->vertex[(isolated_vertex+1) % 3];
-            stl_vertex* v2 = &facet->vertex[(isolated_vertex+2) % 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(0) = v1(0) + (v0(0) - v1(0)) * (z - v1(2)) / (v0(2) - v1(2));
-            v0v1.y = v1->y + (v0->y - v1->y) * (z - v1->z) / (v0->z - v1->z);
+            v0v1(1) = v1(1) + (v0(1) - v1(1)) * (z - v1(2)) / (v0(2) - v1(2));
-            v0v1.z = z;
+            v0v1(2) = z;
-            v2v0.x = v2->x + (v0->x - v2->x) * (z - v2->z) / (v0->z - v2->z);
+            v2v0(0) = v2(0) + (v0(0) - v2(0)) * (z - v2(2)) / (v0(2) - v2(2));
-            v2v0.y = v2->y + (v0->y - v2->y) * (z - v2->z) / (v0->z - v2->z);
+            v2v0(1) = v2(1) + (v0(1) - v2(1)) * (z - v2(2)) / (v0(2) - v2(2));
-            v2v0.z = z;
+            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[0] = v1;
-            quadrilateral[0].vertex[1] = *v2;
+            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 = stl_normal(0, 0, -1.f);
-            facet.normal.y = 0;
-            facet.normal.z = -1;
             for (size_t i = 0; i <= 2; ++i) {
-                facet.vertex[i].x = unscale(p.points[i](0));
+                facet.vertex[i](0) = unscale<float>(p.points[i](0));
-                facet.vertex[i].y = unscale(p.points[i](1));
+                facet.vertex[i](1) = unscale<float>(p.points[i](1));
-                facet.vertex[i].z = z;
+                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 = stl_normal(0, 0, 1.f);
-            facet.normal.y = 0;
-            facet.normal.z = 1;
             for (size_t i = 0; i <= 2; ++i) {
-                facet.vertex[i].x = unscale(polygon->points[i](0));
+                facet.vertex[i](0) = unscale<float>(polygon->points[i](0));
-                facet.vertex[i].y = unscale(polygon->points[i](1));
+                facet.vertex[i](1) = unscale<float>(polygon->points[i](1));
-                facet.vertex[i].z = z;
+                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] = { 
+    Vec3d pv[8] = { 
-        Pointf3(x, y, 0), Pointf3(x, 0, 0), Pointf3(0, 0, 0), 
+        Vec3d(x, y, 0), Vec3d(x, 0, 0), Vec3d(0, 0, 0), 
-        Pointf3(0, y, 0), Pointf3(x, y, z), Pointf3(0, y, z), 
+        Vec3d(0, y, 0), Vec3d(x, y, z), Vec3d(0, y, z), 
-        Pointf3(0, 0, z), Pointf3(x, 0, z) 
+        Vec3d(0, 0, z), Vec3d(x, 0, z) 
     };
-    Point3 fv[12] = { 
+    Vec3crd fv[12] = { 
-        Point3(0, 1, 2), Point3(0, 2, 3), Point3(4, 5, 6), 
+        Vec3crd(0, 1, 2), Vec3crd(0, 2, 3), Vec3crd(4, 5, 6), 
-        Point3(4, 6, 7), Point3(0, 4, 7), Point3(0, 7, 1), 
+        Vec3crd(4, 6, 7), Vec3crd(0, 4, 7), Vec3crd(0, 7, 1), 
-        Point3(1, 7, 6), Point3(1, 6, 2), Point3(2, 6, 5), 
+        Vec3crd(1, 7, 6), Vec3crd(1, 6, 2), Vec3crd(2, 6, 5), 
-        Point3(2, 5, 3), Point3(4, 0, 3), Point3(4, 3, 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(Vec3d(0.0, 0.0, 0.0));
-    vertices.emplace_back(Pointf3(0.0, 0.0, h));
+    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(Vec3d(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, h));
     for (double i = 0; i < 2*PI; i+=angle) {
-        Pointf p(0, r);
+        Vec2d p = Eigen::Rotation2Dd(i) * Eigen::Vector2d(0, r);
-        p.rotate(i);
+        vertices.emplace_back(Vec3d(p(0), p(1), 0.));
-        vertices.emplace_back(Pointf3(p(0), p(1), 0.));
+        vertices.emplace_back(Vec3d(p(0), p(1), h));
-        vertices.emplace_back(Pointf3(p(0), p(1), h));
         id = vertices.size() - 1;
-        facets.emplace_back(Point3( 0, id - 1, id - 3)); // top
+        facets.emplace_back(Vec3crd( 0, id - 1, id - 3)); // top
-        facets.emplace_back(Point3(id,      1, id - 2)); // bottom
+        facets.emplace_back(Vec3crd(id,      1, id - 2)); // bottom
-        facets.emplace_back(Point3(id, id - 2, id - 3)); // upper-right of side
+        facets.emplace_back(Vec3crd(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(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(Vec3crd( 2, 0, id - 1));
-    facets.emplace_back(Point3( 1, 3,     id));
+    facets.emplace_back(Vec3crd( 1, 3,     id));
-    facets.emplace_back(Point3(id, 3,      2));
+    facets.emplace_back(Vec3crd(id, 3,      2));
-    facets.emplace_back(Point3(id, 2, id - 1));
+    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);
+        Vec2d b = Eigen::Rotation2Dd(ring[i]) * Eigen::Vector2d(0, r);
-        b.rotate(ring[i]);
+        vertices.emplace_back(Vec3d(b(0), b(1), z));
-        vertices.emplace_back(Pointf3(b(0), b(1), z));
+        facets.emplace_back((i == 0) ? Vec3crd(1, 0, ring.size()) : Vec3crd(id, 0, id - 1));
-        facets.emplace_back((i == 0) ? Point3(1, 0, ring.size()) : Point3(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);
+            Vec2d b = Eigen::Rotation2Dd(ring[i]) * Eigen::Vector2d(0, r);
-            b.rotate(ring[i]); 
+            vertices.emplace_back(Vec3d(b(0), b(1), z));
-            vertices.emplace_back(Pointf3(b(0), b(1), z));
             if (i == 0) {
                 // wrap around
-                facets.emplace_back(Point3(id + ring.size() - 1 , id, id - 1)); 
+                facets.emplace_back(Vec3crd(id + ring.size() - 1 , id, id - 1)); 
-                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(), (id - 1) - ring.size())); 
+                facets.emplace_back(Vec3crd(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 - 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++;

xs/src/libslic3r/TriangleMesh.hpp

@@ -20,33 +20,33 @@ typedef std::vector<TriangleMesh*> TriangleMeshPtrs;
 class TriangleMesh
 {
 public:
-    TriangleMesh();
+    TriangleMesh() : repaired(false) { stl_initialize(&this->stl); }
-    TriangleMesh(const Pointf3s &points, const std::vector<Point3> &facets);
+    TriangleMesh(const Pointf3s &points, const std::vector<Vec3crd> &facets);
-    TriangleMesh(const TriangleMesh &other);
+    TriangleMesh(const TriangleMesh &other) : repaired(false) { stl_initialize(&this->stl); *this = other; }
-    TriangleMesh(TriangleMesh &&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);
+    TriangleMesh& operator=(TriangleMesh &&other) { this->swap(other); return *this; }
-    void swap(TriangleMesh &other);
+    void swap(TriangleMesh &other) { std::swap(this->stl, other.stl); std::swap(this->repaired, other.repaired); }
-    ~TriangleMesh();
+    void ReadSTLFile(const char* input_file) { stl_open(&stl, input_file); }
-    void ReadSTLFile(const char* input_file);
+    void write_ascii(const char* output_file) { stl_write_ascii(&this->stl, output_file, ""); }
-    void write_ascii(const char* output_file);
+    void write_binary(const char* output_file) { stl_write_binary(&this->stl, output_file, ""); }
-    void write_binary(const char* 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_x(float angle) { this->rotate(angle, X); }
-    void rotate_y(float angle);
+    void rotate_y(float angle) { this->rotate(angle, Y); }
-    void rotate_z(float angle);
+    void rotate_z(float angle) { this->rotate(angle, Z); }
     void mirror(const Axis &axis);
-    void mirror_x();
+    void mirror_x() { this->mirror(X); }
-    void mirror_y();
+    void mirror_y() { this->mirror(Y); }
-    void mirror_z();
+    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:

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>

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(Vec2d, "Pointf");
-REGISTER_CLASS(Pointf, "Pointf");
+__REGISTER_CLASS(Vec3d, "Pointf3");
-REGISTER_CLASS(Pointf3, "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);

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.

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)

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.

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.

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!

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>
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+href="http://www.qhull.org/news">News</a> about Qhull<br>
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+<b>To:</b> <a href="#TOC">Qhull manual</a>: Table of Contents<br>
+<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
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+<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>

xs/src/qhull/html/qconvex.htm

@@ -0,0 +1,630 @@
+<!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>
+<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>

xs/src/qhull/html/qdelau_f.htm

@@ -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>
+&#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>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>
+&#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>
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+&#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
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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>

xs/src/qhull/html/qdelaun.htm

@@ -0,0 +1,628 @@
+<!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>
+<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>
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+&#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>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>
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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>
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