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Skeining algorithm totally rewritten

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This commit is contained in:
Alessandro Ranellucci 2011-10-08 19:02:05 +02:00
parent 3274f3978b
commit ad27f25c71
8 changed files with 180 additions and 144 deletions
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1
lib/Slic3r.pm
View file

@ -55,6 +55,7 @@ our $flow_width;
# print options # print options
our $perimeter_offsets = 3; our $perimeter_offsets = 3;
our $solid_layers = 3; our $solid_layers = 3;
our $bridge_overlap = 2; # mm
our $fill_type = 'rectilinear'; our $fill_type = 'rectilinear';
our $fill_density = 0.4; # 1 = 100% our $fill_density = 0.4; # 1 = 100%
our $fill_angle = 0; our $fill_angle = 0;

17
lib/Slic3r/Geometry.pm
View file

@ -5,7 +5,7 @@ use warnings;
require Exporter; require Exporter;
our @ISA = qw(Exporter); our @ISA = qw(Exporter);
our @EXPORT_OK = qw( our @EXPORT_OK = qw(
epsilon slope line_atan lines_parallel three_points_aligned PI epsilon slope line_atan lines_parallel three_points_aligned
line_point_belongs_to_segment points_coincide distance_between_points line_point_belongs_to_segment points_coincide distance_between_points
line_length midpoint point_in_polygon point_in_segment segment_in_segment line_length midpoint point_in_polygon point_in_segment segment_in_segment
point_is_on_left_of_segment polyline_lines polygon_lines nearest_point point_is_on_left_of_segment polyline_lines polygon_lines nearest_point
@ -14,10 +14,10 @@ our @EXPORT_OK = qw(
rotate_points move_points remove_coinciding_points clip_segment_polygon rotate_points move_points remove_coinciding_points clip_segment_polygon
sum_vectors multiply_vector subtract_vectors dot perp polygon_points_visibility sum_vectors multiply_vector subtract_vectors dot perp polygon_points_visibility
line_intersection bounding_box bounding_box_intersect line_intersection bounding_box bounding_box_intersect
clip_segment_complex_polygon longest_segment clip_segment_complex_polygon longest_segment angle3points
); );
use Slic3r::Geometry::DouglasPeucker; use Slic3r::Geometry::DouglasPeucker ();
use XXX; use XXX;
use constant PI => 4 * atan2(1, 1); use constant PI => 4 * atan2(1, 1);
@ -564,4 +564,15 @@ sub clip_segment_complex_polygon {
return [@lines]; return [@lines];
} }
sub angle3points {
my ($p1, $p2, $p3) = @_;
# p1 is the center
my $angle = atan2($p2->[X] - $p1->[X], $p2->[Y] - $p1->[Y])
- atan2($p3->[X] - $p1->[X], $p3->[Y] - $p1->[Y]);
# we only want to return only positive angles
return $angle <= 0 ? $angle + 2*PI() : $angle;
}
1; 1;

2
lib/Slic3r/Geometry/DouglasPeucker.pm
View file

@ -160,7 +160,7 @@ sub angle3points # Angle between three points in radians
{ {
my $p1 = shift ; my $p1 = shift ;
my $p2 = shift ; my $p2 = shift ;
return( sprintf("%0.6f",atan2( (@$p2[1] - @$p1[1]),( @$p2[0] - @$p1[0] ))) ) ; return atan2( (@$p2[1] - @$p1[1]),( @$p2[0] - @$p1[0] ));
} }
} }

186
lib/Slic3r/Layer.pm
View file

@ -3,9 +3,12 @@ use Moo;
use Math::Clipper ':all'; use Math::Clipper ':all';
use Math::ConvexHull qw(convex_hull); use Math::ConvexHull qw(convex_hull);
use Slic3r::Geometry qw(polygon_lines points_coincide angle3points polyline_lines);
use XXX; use XXX;
use constant PI => 4 * atan2(1, 1); use constant PI => 4 * atan2(1, 1);
use constant A => 0;
use constant B => 1;
# a sequential number of layer, starting at 0 # a sequential number of layer, starting at 0
has 'id' => ( has 'id' => (
@ -100,6 +103,7 @@ sub add_line {
my ($line) = @_; my ($line) = @_;
$line = Slic3r::Line->cast($line); $line = Slic3r::Line->cast($line);
return if $line->a->coincides_with($line->b);
push @{ $self->lines }, $line; push @{ $self->lines }, $line;
return $line; return $line;
@ -118,141 +122,78 @@ sub remove_surface {
} }
# build polylines of lines which do not already belong to a surface # build polylines of lines which do not already belong to a surface
# okay, this code is a mess. will need some refactoring. sorry.
sub make_polylines { sub make_polylines {
my $self = shift; my $self = shift;
# remove line duplicates my @lines = ();
if (0) { push @lines, map $_->p, @{$self->lines};
# this removes any couple of coinciding Slic3r::Line::FacetEdge
my %lines_map = ();
foreach my $line (grep $_->isa('Slic3r::Line::FacetEdge'), @{ $self->lines }) {
my $ordered_id = $line->ordered_id;
if (exists $lines_map{$ordered_id}) {
delete $lines_map{$ordered_id};
next;
}
$lines_map{$ordered_id} = $line;
}
@{ $self->lines } = (values(%lines_map), grep !$_->isa('Slic3r::Line::FacetEdge'), @{ $self->lines });
}
if (1) {
# this removes any duplicate, leaving one
my %lines_map = map { join(',', sort map $_->id, @{$_->points} ) => "$_" } @{ $self->lines };
%lines_map = reverse %lines_map;
@{ $self->lines } = grep $lines_map{"$_"}, @{ $self->lines };
}
# now remove lines that are already part of a surface #use Slic3r::SVG;
if (1) { #Slic3r::SVG::output(undef, "lines.svg",
my @lines = @{ $self->lines }; # lines => [ map $_->p, grep !$_->isa('Slic3r::Line::FacetEdge'), @{$self->lines} ],
@{ $self->lines } = (); # red_lines => [ map $_->p, grep $_->isa('Slic3r::Line::FacetEdge'), @{$self->lines} ],
LINE: foreach my $line (@lines) { #);
if (!$line->isa('Slic3r::Line::FacetEdge')) {
push @{ $self->lines }, $line; my $get_point_id = sub { sprintf "%d,%d", @{$_[0]} };
next LINE;
}
foreach my $surface (@{$self->surfaces}) {
if ($surface->surface_type eq $line->edge_type && $surface->contour->has_segment($line)) {
next LINE;
}
}
push @{ $self->lines }, $line;
}
}
# make a cache of line endpoints
my (%pointmap) = (); my (%pointmap) = ();
foreach my $line (@{ $self->lines }) { foreach my $line (@lines) {
for my $point (@{ $line->points }) { my $point_id = $get_point_id->($line->[A]);
$pointmap{$point->id} ||= []; $pointmap{$point_id} ||= [];
push @{ $pointmap{$point->id} }, $line; push @{ $pointmap{$point_id} }, $line;
}
}
foreach my $point_id (keys %pointmap) {
$pointmap{$point_id} = [
sort { $a->isa('Slic3r::Line::FacetEdge') <=> $b->isa('Slic3r::Line::FacetEdge') }
@{$pointmap{$point_id}} ];
} }
if (0) { my $n = 0;
# defensive programming my @polylines = ();
for (keys %pointmap) { while (my $first_line = shift @lines) {
next if @{$pointmap{$_}} == 2; my @points = @$first_line;
my %seen_points = map { $get_point_id->($points[$_]) => $_ } 0..1;
use Slic3r::SVG;
Slic3r::SVG::output(undef, "lines_and_points.svg",
lines => [ map $_->p, grep !$_->isa('Slic3r::Line::FacetEdge'), @{$self->lines} ],
red_lines => [ map $_->p, grep $_->isa('Slic3r::Line::FacetEdge'), @{$self->lines} ],
points => [ map [split /,/], keys %pointmap ],
red_points => [ [split /,/, $_ ] ],
);
YYY $pointmap{$_};
die sprintf "No point should be endpoint of less or more than 2 lines ($_ => %d)!", scalar(@{$pointmap{$_}});
}
while (my @single_line_points = grep @{$pointmap{$_}} == 1, keys %pointmap) { CYCLE: while (1) {
for my $point_id (@single_line_points) { my $next_lines = $pointmap{ $get_point_id->($points[-1]) }
foreach my $lines (values %pointmap) { or die sprintf "No lines start at point %d,%d. This shouldn't happen", @{$points[-1]};
next unless $pointmap{$point_id}->[0]; last CYCLE if !@$next_lines;
@$lines = grep $_ ne $pointmap{$point_id}->[0], @$lines;
} my @ordered_next_lines = sort
delete $pointmap{$point_id}; { angle3points($points[-1], $points[-2], $next_lines->[$a][B]) <=> angle3points($points[-1], $points[-2], $next_lines->[$b][B]) }
0..$#$next_lines;
#if (@$next_lines > 1) {
# Slic3r::SVG::output(undef, "next_line.svg",
# lines => $next_lines,
# red_lines => [ polyline_lines([@points]) ],
# green_lines => [ $next_lines->[ $ordered_next_lines[0] ] ],
# );
#}
my ($next_line) = splice @$next_lines, $ordered_next_lines[0], 1;
push @points, $next_line->[B];
my $point_id = $get_point_id->($points[-1]);
if ($seen_points{$point_id}) {
splice @points, 0, $seen_points{$point_id};
last CYCLE;
} }
}
}
# make a subroutine to remove lines from pointmap
my $remove_line = sub {
my $line = shift;
foreach my $lines ($pointmap{$line->a->id}, $pointmap{$line->b->id}) {
@$lines = grep $_ ne $line, @$lines;
}
};
my $polylines = [];
# loop while we have spare lines
while (my ($first_line) = map @$_, values %pointmap) {
# add first line to a new polyline
my $points = [ $first_line->a, $first_line->b ];
$remove_line->($first_line);
my $last_point = $first_line->b;
# loop through connected lines until we return to the first point
while (my $next_line = $pointmap{$last_point->id}->[0]) {
# get next point $seen_points{$point_id} = $#points;
($last_point) = grep $_->id ne $last_point->id, @{$next_line->points};
# add point to polyline
push @$points, $last_point;
$remove_line->($next_line);
} }
# remove last point as it coincides with first one if (@points < 4 || !points_coincide($points[0], $points[-1])) {
pop @$points;
if (@$points == 1 && $first_line->isa('Slic3r::Line::FacetEdge')) {
Slic3r::debugf "Skipping spare facet edge";
next; next;
} }
die sprintf "Invalid polyline with only %d points\n", scalar(@$points) if @$points < 3; pop @points;
Slic3r::debugf "Discovered polyline of %d points\n", scalar(@points);
Slic3r::debugf "Discovered polyline of %d points (%s)\n", scalar @$points, push @polylines, [@points];
join ' - ', map $_->id, @$points;
push @$polylines, Slic3r::Polyline::Closed->new(points => $points);
# actually this is not needed, as Math::Clipper used in make_surfaces() also cleans contours
$polylines->[-1]->merge_continuous_lines;
#$polylines->[-1]->cleanup; # not proven to be actually useful
} }
return $polylines; #Slic3r::SVG::output(undef, "polylines.svg",
# polylines => [ @polylines ],
#);
return [ map Slic3r::Polyline::Closed->cast($_), @polylines ];
} }
sub make_surfaces { sub make_surfaces {
@ -336,7 +277,7 @@ sub merge_contiguous_surfaces {
Slic3r::debugf "Initial surfaces (%d):\n", scalar @{ $self->surfaces }; Slic3r::debugf "Initial surfaces (%d):\n", scalar @{ $self->surfaces };
Slic3r::debugf " [%s] %s (%s with %d holes)\n", $_->surface_type, $_->id, Slic3r::debugf " [%s] %s (%s with %d holes)\n", $_->surface_type, $_->id,
($_->contour->is_counter_clockwise ? 'ccw' : 'cw'), scalar @{$_->holes} for @{ $self->surfaces }; ($_->contour->is_counter_clockwise ? 'ccw' : 'cw'), scalar @{$_->holes} for @{ $self->surfaces };
#Slic3r::SVG::output_polygons($main::print, "polygons-before.svg", [ map $_->contour->p, @{$self->surfaces} ]); #Slic3r::SVG::output_polygons(undef, "polygons-before.svg", [ map $_->contour->p, @{$self->surfaces} ]);
} }
my %resulting_surfaces = (); my %resulting_surfaces = ();
@ -487,12 +428,13 @@ sub process_bridges {
# now connect the first point to the last of each polyline # now connect the first point to the last of each polyline
@supported_polylines = map [ $_->[0]->[0], $_->[-1]->[-1] ], @supported_polylines; @supported_polylines = map [ $_->[0]->[0], $_->[-1]->[-1] ], @supported_polylines;
# @supported_polylines becomes actually an array of lines
# if we got more than two supports, get the longest two # if we got more than two supports, get the longest two
if (@supported_polylines > 2) { if (@supported_polylines > 2) {
my %lengths = map { "$_" => Slic3r::Geometry::line_length($_) }, @supported_polylines; my %lengths = map { $_ => Slic3r::Geometry::line_length($_) } @supported_polylines;
@supported_polylines = sort { $lengths{"$a"} <=> $lengths{"$b"} } @supported_polylines; @supported_polylines = sort { $lengths{"$a"} <=> $lengths{"$b"} } @supported_polylines;
@supported_polylines = @supported_polylines[0,1]; @supported_polylines = @supported_polylines[-2,-1];
} }
# connect the midpoints, that will give the the optimal infill direction # connect the midpoints, that will give the the optimal infill direction
@ -517,8 +459,8 @@ sub process_bridges {
# now, extend our bridge by taking a portion of supporting surfaces # now, extend our bridge by taking a portion of supporting surfaces
{ {
# offset the bridge by 5mm # offset the bridge by the specified amount of mm
my $bridge_offset = ${ offset([$surface_p], 5 / $Slic3r::resolution, $Slic3r::resolution * 100, JT_MITER, 2) }[0]; my $bridge_offset = ${ offset([$surface_p], $Slic3r::bridge_overlap / $Slic3r::resolution, $Slic3r::resolution * 100, JT_MITER, 2) }[0];
# calculate the new bridge # calculate the new bridge
my $clipper = Math::Clipper->new; my $clipper = Math::Clipper->new;

38
lib/Slic3r/STL.pm
View file

@ -3,6 +3,7 @@ use Moo;
use CAD::Format::STL; use CAD::Format::STL;
use Math::Clipper qw(integerize_coordinate_sets is_counter_clockwise); use Math::Clipper qw(integerize_coordinate_sets is_counter_clockwise);
use Slic3r::Geometry qw(three_points_aligned longest_segment);
use XXX; use XXX;
use constant X => 0; use constant X => 0;
@ -82,7 +83,7 @@ sub parse_file {
# round Z coordinates to the nearest multiple of layer height # round Z coordinates to the nearest multiple of layer height
# XY will be rounded automatically to integers with coercion # XY will be rounded automatically to integers with coercion
$vertex->[Z] = sprintf('%.0f', $vertex->[Z] * $Slic3r::resolution / $Slic3r::layer_height) $vertex->[Z] = int($vertex->[Z] * $Slic3r::resolution / $Slic3r::layer_height)
* $Slic3r::layer_height / $Slic3r::resolution; * $Slic3r::layer_height / $Slic3r::resolution;
} }
@ -118,12 +119,38 @@ sub _facet {
Slic3r::debugf "layers: min = %s, max = %s\n", $min_layer, $max_layer; Slic3r::debugf "layers: min = %s, max = %s\n", $min_layer, $max_layer;
# 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)
{
my @z_order = sort { $vertices[$a][Z] <=> $vertices[$b][Z] } 0..2;
@vertices = (splice(@vertices, $z_order[0]), splice(@vertices, 0, $z_order[0]));
}
# is the facet horizontal? # is the facet horizontal?
# (note that we can have $min_z == $max_z && $min_layer != $max_layer # (note that we can have $min_z == $max_z && $min_layer != $max_layer
# if $min_z % $layer_height != 0) # if $min_z % $layer_height != 0)
if ($min_z == $max_z) { if ($min_z == $max_z) {
Slic3r::debugf "Facet is horizontal\n";
my $layer = $print->layer($min_layer); my $layer = $print->layer($min_layer);
# if all vertices are aligned, then facet is not horizontal but vertical
# with a height less than layer height: that's why it was squashed on a
# single layer
##local $Slic3r::Geometry::parallel_degrees_limit = 1;
##if (three_points_aligned(@vertices)) {
if (0 && abs($normal->[Z]) == 0) {
Slic3r::debugf "Facet is vertical with a height less than layer height\n";
my ($p1, $p2, $p3) = @vertices;
$layer->add_line(Slic3r::Line::FacetEdge->cast(
$_,
edge_type => 'bottom',
)) for ([$p1, $p2], [$p2, $p3], [$p1, $p3], [$p2, $p1], [$p3, $p2], [$p3, $p1]);
return;
}
Slic3r::debugf "Facet is horizontal\n";
my $surface = $layer->add_surface(@vertices); my $surface = $layer->add_surface(@vertices);
# to determine whether the surface is a top or bottom let's recompute # to determine whether the surface is a top or bottom let's recompute
@ -147,6 +174,7 @@ sub _facet {
} }
if ($layer->id == 0 && !$clockwise) { if ($layer->id == 0 && !$clockwise) {
YYY $normal;
die "Right-hand rule gives bad result for facets on base layer!\n"; die "Right-hand rule gives bad result for facets on base layer!\n";
} }
@ -180,11 +208,13 @@ sub intersect_facet {
if ($a->[Z] == $b->[Z] && $a->[Z] == $z) { if ($a->[Z] == $b->[Z] && $a->[Z] == $z) {
# edge is horizontal and belongs to the current layer # edge is horizontal and belongs to the current layer
my $edge_type = (grep $_->[Z] > $z, @$vertices) ? 'bottom' : 'top';
($a, $b) = ($b, $a) if $edge_type eq 'bottom';
push @lines, Slic3r::Line::FacetEdge->cast( push @lines, Slic3r::Line::FacetEdge->cast(
[ [$a->[X], $a->[Y]], [$b->[X], $b->[Y]] ], [ [$a->[X], $a->[Y]], [$b->[X], $b->[Y]] ],
edge_type => (grep $_->[Z] > $z, @$vertices) ? 'bottom' : 'top', edge_type => $edge_type,
); );
#print "Horizontal!\n"; #print "Horizontal edge!\n";
} elsif (($a->[Z] < $z && $b->[Z] > $z) || ($b->[Z] < $z && $a->[Z] > $z)) { } elsif (($a->[Z] < $z && $b->[Z] > $z) || ($b->[Z] < $z && $a->[Z] > $z)) {
# edge intersects the current layer; calculate intersection # edge intersects the current layer; calculate intersection

27
lib/Slic3r/SVG.pm
View file

@ -14,7 +14,24 @@ sub factor {
sub svg { sub svg {
my ($print) = @_; my ($print) = @_;
$print ||= Slic3r::Print->new(x_length => 200 / $Slic3r::resolution, y_length => 200 / $Slic3r::resolution); $print ||= Slic3r::Print->new(x_length => 200 / $Slic3r::resolution, y_length => 200 / $Slic3r::resolution);
return SVG->new(width => $print->max_length * factor(), height => $print->max_length * factor()); my $svg = SVG->new(width => $print->max_length * factor(), height => $print->max_length * factor());
my $marker_end = $svg->marker(
id => "endArrow",
viewBox => "0 0 10 10",
refX => "1",
refY => "5",
markerUnits => "strokeWidth",
orient => "auto",
markerWidth => "10",
markerHeight => "8",
);
$marker_end->polyline(
points => "0,0 10,5 0,10 1,5",
fill => "darkblue",
);
return $svg;
} }
sub output { sub output {
@ -40,6 +57,7 @@ sub output {
); );
$g->$method( $g->$method(
%$path, %$path,
'marker-end' => "url(#endArrow)",
); );
} }
} }
@ -65,9 +83,9 @@ sub output {
} }
} }
foreach my $type (qw(lines red_lines)) { foreach my $type (qw(lines red_lines green_lines)) {
if ($things{$type}) { if ($things{$type}) {
my ($colour) = $type eq 'lines' ? ('black') : ('red'); my ($colour) = $type =~ /^(red|green)_/;
my $g = $svg->group( my $g = $svg->group(
style => { style => {
'stroke-width' => 2, 'stroke-width' => 2,
@ -80,8 +98,9 @@ sub output {
x2 => $line->[1][X] * factor(), x2 => $line->[1][X] * factor(),
y2 => $line->[1][Y] * factor(), y2 => $line->[1][Y] * factor(),
style => { style => {
'stroke' => $colour, 'stroke' => $colour || 'black',
}, },
'marker-end' => "url(#endArrow)",
); );
} }
} }

47
t/geometry.t
View file

@ -2,7 +2,7 @@ use Test::More;
use strict; use strict;
use warnings; use warnings;
plan tests => 6; plan tests => 15;
BEGIN { BEGIN {
use FindBin; use FindBin;
@ -10,6 +10,7 @@ BEGIN {
} }
use Slic3r; use Slic3r;
use Slic3r::Geometry qw(PI);
#========================================================== #==========================================================
@ -43,15 +44,19 @@ is_deeply Slic3r::Geometry::polygon_segment_having_point($polyline, $point),
#========================================================== #==========================================================
$point = [ 736310778.185108, 5017423926.8924 ]; {
my $line = [ [627484000, 3695776000], [750000000, 3720147000] ]; my $point = [ 736310778.185108, 5017423926.8924 ];
is Slic3r::Geometry::point_in_segment($point, $line), 0, 'point_in_segment'; my $line = [ [627484000, 3695776000], [750000000, 3720147000] ];
is Slic3r::Geometry::point_in_segment($point, $line), 0, 'point_in_segment';
}
#========================================================== #==========================================================
$point = [ 736310778.185108, 5017423926.8924 ]; {
my $line = [ [627484000, 3695776000], [750000000, 3720147000] ]; my $point = [ 736310778.185108, 5017423926.8924 ];
is Slic3r::Geometry::point_in_segment($point, $line), 0, 'point_in_segment'; my $line = [ [627484000, 3695776000], [750000000, 3720147000] ];
is Slic3r::Geometry::point_in_segment($point, $line), 0, 'point_in_segment';
}
#========================================================== #==========================================================
@ -81,3 +86,31 @@ my $points = [
is Slic3r::Geometry::can_connect_points(@$points, $polygons), 0, 'can_connect_points'; is Slic3r::Geometry::can_connect_points(@$points, $polygons), 0, 'can_connect_points';
#========================================================== #==========================================================
{
my $p1 = [10, 10];
my $p2 = [10, 20];
my $p3 = [10, 30];
my $p4 = [20, 20];
my $p5 = [0, 20];
is Slic3r::Geometry::angle3points($p2, $p3, $p1), PI(), 'angle3points';
is Slic3r::Geometry::angle3points($p2, $p1, $p3), PI(), 'angle3points';
is Slic3r::Geometry::angle3points($p2, $p3, $p4), PI()/2*3, 'angle3points';
is Slic3r::Geometry::angle3points($p2, $p4, $p3), PI()/2, 'angle3points';
is Slic3r::Geometry::angle3points($p2, $p1, $p4), PI()/2, 'angle3points';
is Slic3r::Geometry::angle3points($p2, $p1, $p5), PI()/2*3, 'angle3points';
}
{
my $p1 = [30, 30];
my $p2 = [20, 20];
my $p3 = [10, 10];
my $p4 = [30, 10];
is Slic3r::Geometry::angle3points($p2, $p1, $p3), PI(), 'angle3points';
is Slic3r::Geometry::angle3points($p2, $p1, $p4), PI()/2*3, 'angle3points';
is Slic3r::Geometry::angle3points($p2, $p1, $p1), 2*PI(), 'angle3points';
}
#==========================================================

6
t/stl.t
View file

@ -21,12 +21,12 @@ is_deeply lines(20, 20, 20), [
[ $points[2], $points[0] ], [ $points[2], $points[0] ],
], 'horizontal'; ], 'horizontal';
is_deeply lines(22, 20, 20), [ [ $points[1], $points[2] ] ], 'lower edge on layer'; is_deeply lines(22, 20, 20), [ [ $points[2], $points[1] ] ], 'lower edge on layer';
is_deeply lines(20, 20, 10), [ [ $points[0], $points[1] ] ], 'upper edge on layer'; is_deeply lines(20, 20, 10), [ [ $points[0], $points[1] ] ], 'upper edge on layer';
is_deeply lines(20, 15, 10), [ ], 'upper vertex on layer'; is_deeply lines(20, 15, 10), [ ], 'upper vertex on layer';
is_deeply lines(28, 20, 30), [ ], 'lower vertex on layer'; is_deeply lines(28, 20, 30), [ ], 'lower vertex on layer';
is_deeply lines(24, 10, 16), [ [ [4, 4], [2, 6] ] ], 'two edges intersect'; is_deeply lines(24, 10, 16), [ [ [2, 6], [4, 4] ] ], 'two edges intersect';
is_deeply lines(24, 10, 20), [ [ [4, 4], [1, 9] ] ], 'one vertex on plane and one edge intersects'; is_deeply lines(24, 10, 20), [ [ [1, 9], [4, 4] ] ], 'one vertex on plane and one edge intersects';
my @lower = $stl->intersect_facet(vertices(22, 20, 20), $z, $dz); my @lower = $stl->intersect_facet(vertices(22, 20, 20), $z, $dz);
my @upper = $stl->intersect_facet(vertices(20, 20, 10), $z, $dz); my @upper = $stl->intersect_facet(vertices(20, 20, 10), $z, $dz);