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Slic3r/lib/Slic3r/Geometry.pm

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package Slic3r::Geometry;
use strict;
use warnings;
require Exporter;
our @ISA = qw(Exporter);
our @EXPORT_OK = qw(
PI X Y Z A B X1 Y1 X2 Y2 MIN MAX epsilon slope line_atan lines_parallel
line_point_belongs_to_segment points_coincide distance_between_points
chained_path_items chained_path_points normalize tan move_points_3D
line_length midpoint point_in_polygon point_in_segment segment_in_segment
point_is_on_left_of_segment polyline_lines polygon_lines
point_along_segment polygon_segment_having_point polygon_has_subsegment
polygon_has_vertex polyline_length can_connect_points deg2rad rad2deg
rotate_points move_points clip_segment_polygon
sum_vectors multiply_vector subtract_vectors dot perp polygon_points_visibility
line_intersection bounding_box bounding_box_intersect same_point same_line
longest_segment angle3points three_points_aligned line_direction
polyline_remove_parallel_continuous_edges polyline_remove_acute_vertices
polygon_remove_acute_vertices polygon_remove_parallel_continuous_edges
chained_path collinear scale unscale merge_collinear_lines
rad2deg_dir bounding_box_center line_intersects_any douglas_peucker
polyline_remove_short_segments normal triangle_normal polygon_is_convex
scaled_epsilon bounding_box_3D size_3D size_2D
);
use constant PI => 4 * atan2(1, 1);
use constant A => 0;
use constant B => 1;
use constant X => 0;
use constant Y => 1;
use constant Z => 2;
use constant X1 => 0;
use constant Y1 => 1;
use constant X2 => 2;
use constant Y2 => 3;
use constant MIN => 0;
use constant MAX => 1;
our $parallel_degrees_limit = abs(deg2rad(0.1));
sub epsilon () { 1E-4 }
sub scaled_epsilon () { epsilon / &Slic3r::SCALING_FACTOR }
sub scale ($) { $_[0] / &Slic3r::SCALING_FACTOR }
sub unscale ($) { $_[0] * &Slic3r::SCALING_FACTOR }
sub tan {
my ($angle) = @_;
return (sin $angle) / (cos $angle);
}
sub slope {
my ($line) = @_;
return undef if abs($line->[B][X] - $line->[A][X]) < epsilon; # line is vertical
return ($line->[B][Y] - $line->[A][Y]) / ($line->[B][X] - $line->[A][X]);
}
sub line_atan {
my ($line) = @_;
return atan2($line->[B][Y] - $line->[A][Y], $line->[B][X] - $line->[A][X]);
}
sub line_direction {
my ($line) = @_;
my $atan2 = line_atan($line);
return ($atan2 == PI) ? 0
: ($atan2 < 0) ? ($atan2 + PI)
: $atan2;
}
sub lines_parallel {
my ($line1, $line2) = @_;
return abs(line_direction($line1) - line_direction($line2)) < $parallel_degrees_limit;
}
sub three_points_aligned {
my ($p1, $p2, $p3) = @_;
return lines_parallel([$p1, $p2], [$p2, $p3]);
}
# this subroutine checks whether a given point may belong to a given
# segment given the hypothesis that it belongs to the line containing
# the segment
sub line_point_belongs_to_segment {
my ($point, $segment) = @_;
#printf " checking whether %f,%f may belong to segment %f,%f - %f,%f\n",
# @$point, map @$_, @$segment;
my @segment_extents = (
[ sort { $a <=> $b } map $_->[X], @$segment ],
[ sort { $a <=> $b } map $_->[Y], @$segment ],
);
return 0 if $point->[X] < ($segment_extents[X][0] - epsilon) || $point->[X] > ($segment_extents[X][1] + epsilon);
return 0 if $point->[Y] < ($segment_extents[Y][0] - epsilon) || $point->[Y] > ($segment_extents[Y][1] + epsilon);
return 1;
}
sub points_coincide {
my ($p1, $p2) = @_;
return 1 if abs($p2->[X] - $p1->[X]) < epsilon && abs($p2->[Y] - $p1->[Y]) < epsilon;
return 0;
}
sub same_point {
my ($p1, $p2) = @_;
return $p1->[X] == $p2->[X] && $p1->[Y] == $p2->[Y];
}
sub same_line {
my ($line1, $line2) = @_;
return same_point($line1->[A], $line2->[A]) && same_point($line1->[B], $line2->[B]);
}
sub distance_between_points {
my ($p1, $p2) = @_;
return sqrt((($p1->[X] - $p2->[X])**2) + ($p1->[Y] - $p2->[Y])**2);
}
sub point_line_distance {
my ($point, $line) = @_;
return distance_between_points($point, $line->[A])
if same_point($line->[A], $line->[B]);
my $n = ($line->[B][X] - $line->[A][X]) * ($line->[A][Y] - $point->[Y])
- ($line->[A][X] - $point->[X]) * ($line->[B][Y] - $line->[A][Y]);
my $d = sqrt((($line->[B][X] - $line->[A][X]) ** 2) + (($line->[B][Y] - $line->[A][Y]) ** 2));
return abs($n) / $d;
}
sub line_length {
my ($line) = @_;
return distance_between_points(@$line[A, B]);
}
sub longest_segment {
my (@lines) = @_;
my ($longest, $maxlength);
foreach my $line (@lines) {
my $line_length = line_length($line);
if (!defined $longest || $line_length > $maxlength) {
$longest = $line;
$maxlength = $line_length;
}
}
return $longest;
}
sub midpoint {
my ($line) = @_;
return [ ($line->[B][X] + $line->[A][X]) / 2, ($line->[B][Y] + $line->[A][Y]) / 2 ];
}
# this will check whether a point is in a polygon regardless of polygon orientation
sub point_in_polygon {
my ($point, $polygon) = @_;
my ($x, $y) = @$point;
my $n = @$polygon;
my @x = map $_->[X], @$polygon;
my @y = map $_->[Y], @$polygon;
# Derived from the comp.graphics.algorithms FAQ,
# courtesy of Wm. Randolph Franklin
my ($i, $j);
my $side = 0; # 0 = outside; 1 = inside
for ($i = 0, $j = $n - 1; $i < $n; $j = $i++) {
if (
# If the y is between the (y-) borders...
($y[$i] <= $y && $y < $y[$j]) || ($y[$j] <= $y && $y < $y[$i])
and
# ...the (x,y) to infinity line crosses the edge
# from the ith point to the jth point...
($x < ($x[$j] - $x[$i]) * ($y - $y[$i]) / ($y[$j] - $y[$i]) + $x[$i])
) {
$side = not $side; # Jump the fence
}
}
# if point is not in polygon, let's check whether it belongs to the contour
if (!$side && 0) {
return 1 if polygon_segment_having_point($polygon, $point);
}
return $side;
}
sub point_in_segment {
my ($point, $line) = @_;
my ($x, $y) = @$point;
my $line_p = $line->pp;
my @line_x = sort { $a <=> $b } $line_p->[A][X], $line_p->[B][X];
my @line_y = sort { $a <=> $b } $line_p->[A][Y], $line_p->[B][Y];
# check whether the point is in the segment bounding box
return 0 unless $x >= ($line_x[0] - epsilon) && $x <= ($line_x[1] + epsilon)
&& $y >= ($line_y[0] - epsilon) && $y <= ($line_y[1] + epsilon);
# if line is vertical, check whether point's X is the same as the line
if ($line_p->[A][X] == $line_p->[B][X]) {
return abs($x - $line_p->[A][X]) < epsilon ? 1 : 0;
}
# calculate the Y in line at X of the point
my $y3 = $line_p->[A][Y] + ($line_p->[B][Y] - $line_p->[A][Y])
* ($x - $line_p->[A][X]) / ($line_p->[B][X] - $line_p->[A][X]);
return abs($y3 - $y) < epsilon ? 1 : 0;
}
sub segment_in_segment {
my ($needle, $haystack) = @_;
# a segment is contained in another segment if its endpoints are contained
return point_in_segment($needle->[A], $haystack) && point_in_segment($needle->[B], $haystack);
}
sub point_is_on_left_of_segment {
my ($point, $line) = @_;
return (($line->[B][X] - $line->[A][X])*($point->[Y] - $line->[A][Y])
- ($line->[B][Y] - $line->[A][Y])*($point->[X] - $line->[A][X])) > 0;
}
sub polyline_lines {
my ($polyline) = @_;
my @points = @$polyline;
return map Slic3r::Line->new(@points[$_, $_+1]), 0 .. $#points-1;
}
sub polygon_lines {
my ($polygon) = @_;
return polyline_lines([ @$polygon, $polygon->[0] ]);
}
# given a segment $p1-$p2, get the point at $distance from $p1 along segment
sub point_along_segment {
my ($p1, $p2, $distance) = @_;
my $point = [ @$p1 ];
my $line_length = sqrt( (($p2->[X] - $p1->[X])**2) + (($p2->[Y] - $p1->[Y])**2) );
for (X, Y) {
if ($p1->[$_] != $p2->[$_]) {
$point->[$_] = $p1->[$_] + ($p2->[$_] - $p1->[$_]) * $distance / $line_length;
}
}
return Slic3r::Point->new(@$point);
}
# given a $polygon, return the (first) segment having $point
sub polygon_segment_having_point {
my ($polygon, $point) = @_;
foreach my $line (@{ $polygon->lines }) {
return $line if point_in_segment($point, $line);
}
return undef;
}
# return true if the given segment is contained in any edge of the polygon
sub polygon_has_subsegment {
my ($polygon, $segment) = @_;
foreach my $line (polygon_lines($polygon)) {
return 1 if segment_in_segment($segment, $line);
}
return 0;
}
sub polygon_has_vertex {
my ($polygon, $point) = @_;
foreach my $p (@$polygon) {
return 1 if points_coincide($p, $point);
}
return 0;
}
# polygon must be simple (non complex) and ccw
sub polygon_is_convex {
my ($points) = @_;
for (my $i = 0; $i <= $#$points; $i++) {
my $angle = angle3points($points->[$i-1], $points->[$i-2], $points->[$i]);
return 0 if $angle < PI;
}
return 1;
}
sub polyline_length {
my ($polyline) = @_;
my $length = 0;
$length += line_length($_) for polygon_lines($polyline);
return $length;
}
sub can_connect_points {
my ($p1, $p2, $polygons) = @_;
# check that the two points are visible from each other
return 0 if grep !polygon_points_visibility($_, $p1, $p2), @$polygons;
# get segment where $p1 lies
my $p1_segment;
for (@$polygons) {
$p1_segment = polygon_segment_having_point($_, $p1);
last if $p1_segment;
}
# defensive programming, this shouldn't happen
if (!$p1_segment) {
die sprintf "Point %f,%f wasn't found in polygon contour or holes!", @$p1;
}
# check whether $p2 is internal or external (internal = on the left)
return point_is_on_left_of_segment($p2, $p1_segment)
|| point_in_segment($p2, $p1_segment);
}
sub deg2rad {
my ($degrees) = @_;
return PI() * $degrees / 180;
}
sub rad2deg {
my ($rad) = @_;
return $rad / PI() * 180;
}
sub rad2deg_dir {
my ($rad) = @_;
$rad = ($rad < PI) ? (-$rad + PI/2) : ($rad + PI/2);
$rad += PI if $rad < 0;
return rad2deg($rad);
}
sub rotate_points {
my ($radians, $center, @points) = @_;
$center //= [0,0];
return map {
[
$center->[X] + cos($radians) * ($_->[X] - $center->[X]) - sin($radians) * ($_->[Y] - $center->[Y]),
$center->[Y] + cos($radians) * ($_->[Y] - $center->[Y]) + sin($radians) * ($_->[X] - $center->[X]),
]
} @points;
}
sub move_points {
my ($shift, @points) = @_;
return map {
my @p = @$_;
Slic3r::Point->new($shift->[X] + $p[X], $shift->[Y] + $p[Y]);
} @points;
}
sub move_points_3D {
my ($shift, @points) = @_;
return map [
$shift->[X] + $_->[X],
$shift->[Y] + $_->[Y],
$shift->[Z] + $_->[Z],
], @points;
}
# implementation of Liang-Barsky algorithm
# polygon must be convex and ccw
sub clip_segment_polygon {
my ($line, $polygon) = @_;
if (@$line == 1) {
# the segment is a point, check for inclusion
return point_in_polygon($line, $polygon);
}
my @V = (@$polygon, $polygon->[0]);
my $tE = 0; # the maximum entering segment parameter
my $tL = 1; # the minimum entering segment parameter
my $dS = subtract_vectors($line->[B], $line->[A]); # the segment direction vector
for (my $i = 0; $i < $#V; $i++) { # process polygon edge V[i]V[Vi+1]
my $e = subtract_vectors($V[$i+1], $V[$i]);
my $N = perp($e, subtract_vectors($line->[A], $V[$i]));
my $D = -perp($e, $dS);
if (abs($D) < epsilon) { # $line is nearly parallel to this edge
($N < 0) ? return : next; # P0 outside this edge ? $line is outside : $line cannot cross edge, thus ignoring
}
my $t = $N / $D;
if ($D < 0) { # $line is entering across this edge
if ($t > $tE) { # new max $tE
$tE = $t;
return if $tE > $tL; # $line enters after leaving polygon?
}
} else { # $line is leaving across this edge
if ($t < $tL) { # new min $tL
$tL = $t;
return if $tL < $tE; # $line leaves before entering polygon?
}
}
}
# $tE <= $tL implies that there is a valid intersection subsegment
return [
sum_vectors($line->[A], multiply_vector($dS, $tE)), # = P(tE) = point where S enters polygon
sum_vectors($line->[A], multiply_vector($dS, $tL)), # = P(tE) = point where S enters polygon
];
}
sub sum_vectors {
my ($v1, $v2) = @_;
return [ $v1->[X] + $v2->[X], $v1->[Y] + $v2->[Y] ];
}
sub multiply_vector {
my ($line, $scalar) = @_;
return [ $line->[X] * $scalar, $line->[Y] * $scalar ];
}
sub subtract_vectors {
my ($line2, $line1) = @_;
return [ $line2->[X] - $line1->[X], $line2->[Y] - $line1->[Y] ];
}
sub normal {
my ($line1, $line2) = @_;
return [
($line1->[Y] * $line2->[Z]) - ($line1->[Z] * $line2->[Y]),
-($line2->[Z] * $line1->[X]) + ($line2->[X] * $line1->[Z]),
($line1->[X] * $line2->[Y]) - ($line1->[Y] * $line2->[X]),
];
}
sub triangle_normal {
my ($v1, $v2, $v3) = @_;
my $u = [ map +($v2->[$_] - $v1->[$_]), (X,Y,Z) ];
my $v = [ map +($v3->[$_] - $v1->[$_]), (X,Y,Z) ];
return normal($u, $v);
}
sub normalize {
my ($line) = @_;
my $len = sqrt( ($line->[X]**2) + ($line->[Y]**2) + ($line->[Z]**2) )
or return [0, 0, 0]; # to avoid illegal division by zero
return [ map $_ / $len, @$line ];
}
# 2D dot product
sub dot {
my ($u, $v) = @_;
return $u->[X] * $v->[X] + $u->[Y] * $v->[Y];
}
# 2D perp product
sub perp {
my ($u, $v) = @_;
return $u->[X] * $v->[Y] - $u->[Y] * $v->[X];
}
sub polygon_points_visibility {
my ($polygon, $p1, $p2) = @_;
my $our_line = [ $p1, $p2 ];
foreach my $line (polygon_lines($polygon)) {
my $intersection = line_intersection($our_line, $line, 1) // next;
next if grep points_coincide($intersection, $_), $p1, $p2;
return 0;
}
return 1;
}
sub line_intersects_any {
my ($line, $lines) = @_;
for (@$lines) {
return 1 if line_intersection($line, $_, 1);
}
return 0;
}
sub line_intersection {
my ($line1, $line2, $require_crossing) = @_;
$require_crossing ||= 0;
my $intersection = _line_intersection(map @$_, @$line1, @$line2);
return (ref $intersection && $intersection->[1] == $require_crossing)
? $intersection->[0]
: undef;
}
sub collinear {
my ($line1, $line2, $require_overlapping) = @_;
my $intersection = _line_intersection(map @$_, @$line1, @$line2);
return 0 unless !ref($intersection)
&& ($intersection eq 'parallel collinear'
|| ($intersection eq 'parallel vertical' && abs($line1->[A][X] - $line2->[A][X]) < epsilon));
if ($require_overlapping) {
my @box_a = bounding_box([ $line1->[0], $line1->[1] ]);
my @box_b = bounding_box([ $line2->[0], $line2->[1] ]);
return 0 unless bounding_box_intersect( 2, @box_a, @box_b );
}
return 1;
}
sub merge_collinear_lines {
my ($lines) = @_;
my $line_count = @$lines;
for (my $i = 0; $i <= $#$lines-1; $i++) {
for (my $j = $i+1; $j <= $#$lines; $j++) {
# lines are collinear and overlapping?
next unless collinear($lines->[$i], $lines->[$j], 1);
# lines have same orientation?
next unless ($lines->[$i][A][X] <=> $lines->[$i][B][X]) == ($lines->[$j][A][X] <=> $lines->[$j][B][X])
&& ($lines->[$i][A][Y] <=> $lines->[$i][B][Y]) == ($lines->[$j][A][Y] <=> $lines->[$j][B][Y]);
# resulting line
my @x = sort { $a <=> $b } ($lines->[$i][A][X], $lines->[$i][B][X], $lines->[$j][A][X], $lines->[$j][B][X]);
my @y = sort { $a <=> $b } ($lines->[$i][A][Y], $lines->[$i][B][Y], $lines->[$j][A][Y], $lines->[$j][B][Y]);
my $new_line = Slic3r::Line->new([$x[0], $y[0]], [$x[-1], $y[-1]]);
for (X, Y) {
($new_line->[A][$_], $new_line->[B][$_]) = ($new_line->[B][$_], $new_line->[A][$_])
if $lines->[$i][A][$_] > $lines->[$i][B][$_];
}
# save new line and remove found one
$lines->[$i] = $new_line;
splice @$lines, $j, 1;
$j--;
}
}
Slic3r::debugf " merging %d lines resulted in %d lines\n", $line_count, scalar(@$lines);
return $lines;
}
sub _line_intersection {
my ( $x0, $y0, $x1, $y1, $x2, $y2, $x3, $y3 ) = @_;
my ($x, $y); # The as-yet-undetermined intersection point.
my $dy10 = $y1 - $y0; # dyPQ, dxPQ are the coordinate differences
my $dx10 = $x1 - $x0; # between the points P and Q.
my $dy32 = $y3 - $y2;
my $dx32 = $x3 - $x2;
my $dy10z = abs( $dy10 ) < epsilon; # Is the difference $dy10 "zero"?
my $dx10z = abs( $dx10 ) < epsilon;
my $dy32z = abs( $dy32 ) < epsilon;
my $dx32z = abs( $dx32 ) < epsilon;
my $dyx10; # The slopes.
my $dyx32;
$dyx10 = $dy10 / $dx10 unless $dx10z;
$dyx32 = $dy32 / $dx32 unless $dx32z;
# Now we know all differences and the slopes;
# we can detect horizontal/vertical special cases.
# E.g., slope = 0 means a horizontal line.
unless ( defined $dyx10 or defined $dyx32 ) {
return "parallel vertical";
}
elsif ( $dy10z and not $dy32z ) { # First line horizontal.
$y = $y0;
$x = $x2 + ( $y - $y2 ) * $dx32 / $dy32;
}
elsif ( not $dy10z and $dy32z ) { # Second line horizontal.
$y = $y2;
$x = $x0 + ( $y - $y0 ) * $dx10 / $dy10;
}
elsif ( $dx10z and not $dx32z ) { # First line vertical.
$x = $x0;
$y = $y2 + $dyx32 * ( $x - $x2 );
}
elsif ( not $dx10z and $dx32z ) { # Second line vertical.
$x = $x2;
$y = $y0 + $dyx10 * ( $x - $x0 );
}
elsif ( abs( $dyx10 - $dyx32 ) < epsilon ) {
# The slopes are suspiciously close to each other.
# Either we have parallel collinear or just parallel lines.
# The bounding box checks have already weeded the cases
# "parallel horizontal" and "parallel vertical" away.
my $ya = $y0 - $dyx10 * $x0;
my $yb = $y2 - $dyx32 * $x2;
return "parallel collinear" if abs( $ya - $yb ) < epsilon;
return "parallel";
}
else {
# None of the special cases matched.
# We have a "honest" line intersection.
$x = ($y2 - $y0 + $dyx10*$x0 - $dyx32*$x2)/($dyx10 - $dyx32);
$y = $y0 + $dyx10 * ($x - $x0);
}
my $h10 = $dx10 ? ($x - $x0) / $dx10 : ($dy10 ? ($y - $y0) / $dy10 : 1);
my $h32 = $dx32 ? ($x - $x2) / $dx32 : ($dy32 ? ($y - $y2) / $dy32 : 1);
return [Slic3r::Point->new($x, $y), $h10 >= 0 && $h10 <= 1 && $h32 >= 0 && $h32 <= 1];
}
# http://paulbourke.net/geometry/lineline2d/
sub _line_intersection2 {
my ($line1, $line2) = @_;
my $denom = ($line2->[B][Y] - $line2->[A][Y]) * ($line1->[B][X] - $line1->[A][X])
- ($line2->[B][X] - $line2->[A][X]) * ($line1->[B][Y] - $line1->[A][Y]);
my $numerA = ($line2->[B][X] - $line2->[A][X]) * ($line1->[A][Y] - $line2->[A][Y])
- ($line2->[B][Y] - $line2->[A][Y]) * ($line1->[A][X] - $line2->[A][X]);
my $numerB = ($line1->[B][X] - $line1->[A][X]) * ($line1->[A][Y] - $line2->[A][Y])
- ($line1->[B][Y] - $line1->[A][Y]) * ($line1->[A][X] - $line2->[A][X]);
# are the lines coincident?
if (abs($numerA) < epsilon && abs($numerB) < epsilon && abs($denom) < epsilon) {
return Slic3r::Point->new(
($line1->[A][X] + $line1->[B][X]) / 2,
($line1->[A][Y] + $line1->[B][Y]) / 2,
);
}
# are the lines parallel?
if (abs($denom) < epsilon) {
return undef;
}
# is the intersection along the segments?
my $muA = $numerA / $denom;
my $muB = $numerB / $denom;
if ($muA < 0 || $muA > 1 || $muB < 0 || $muB > 1) {
return undef;
}
return Slic3r::Point->new(
$line1->[A][X] + $muA * ($line1->[B][X] - $line1->[A][X]),
$line1->[A][Y] + $muA * ($line1->[B][Y] - $line1->[A][Y]),
);
}
# 2D
sub bounding_box {
my ($points) = @_;
use XXX; ZZZ "not" if ref($points->[0]) eq 'ARRAY';
my @x = map $_->x, @$points;
my @y = map $_->y, @$points; #,,
my @bb = (undef, undef, undef, undef);
for (0..$#x) {
$bb[X1] = $x[$_] if !defined $bb[X1] || $x[$_] < $bb[X1];
$bb[X2] = $x[$_] if !defined $bb[X2] || $x[$_] > $bb[X2];
$bb[Y1] = $y[$_] if !defined $bb[Y1] || $y[$_] < $bb[Y1];
$bb[Y2] = $y[$_] if !defined $bb[Y2] || $y[$_] > $bb[Y2];
}
return @bb[X1,Y1,X2,Y2];
}
sub bounding_box_center {
my ($bounding_box) = @_;
return Slic3r::Point->new(
($bounding_box->[X2] + $bounding_box->[X1]) / 2,
($bounding_box->[Y2] + $bounding_box->[Y1]) / 2,
);
}
sub size_2D {
my @bounding_box = bounding_box(@_);
return (
($bounding_box[X2] - $bounding_box[X1]),
($bounding_box[Y2] - $bounding_box[Y1]),
);
}
# bounding_box_intersect($d, @a, @b)
# Return true if the given bounding boxes @a and @b intersect
# in $d dimensions. Used by line_intersection().
sub bounding_box_intersect {
my ( $d, @bb ) = @_; # Number of dimensions and box coordinates.
my @aa = splice( @bb, 0, 2 * $d ); # The first box.
# (@bb is the second one.)
# Must intersect in all dimensions.
for ( my $i_min = 0; $i_min < $d; $i_min++ ) {
my $i_max = $i_min + $d; # The index for the maximum.
return 0 if ( $aa[ $i_max ] + epsilon ) < $bb[ $i_min ];
return 0 if ( $bb[ $i_max ] + epsilon ) < $aa[ $i_min ];
}
return 1;
}
# 3D
sub bounding_box_3D {
my ($points) = @_;
my @extents = (map [undef, undef], X,Y,Z);
foreach my $point (@$points) {
for (X,Y,Z) {
$extents[$_][MIN] = $point->[$_] if !defined $extents[$_][MIN] || $point->[$_] < $extents[$_][MIN];
$extents[$_][MAX] = $point->[$_] if !defined $extents[$_][MAX] || $point->[$_] > $extents[$_][MAX];
}
}
return @extents;
}
sub size_3D {
my ($points) = @_;
my @extents = bounding_box_3D($points);
return map $extents[$_][MAX] - $extents[$_][MIN], (X,Y,Z);
}
# this assumes a CCW rotation from $p2 to $p3 around $p1
sub angle3points {
my ($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() : $angle;
}
sub polyline_remove_parallel_continuous_edges {
my ($points, $isPolygon) = @_;
for (my $i = $isPolygon ? 0 : 2; $i <= $#$points && @$points >= 3; $i++) {
if (Slic3r::Geometry::lines_parallel([$points->[$i-2], $points->[$i-1]], [$points->[$i-1], $points->[$i]])) {
# we can remove $points->[$i-1]
splice @$points, $i-1, 1;
$i--;
}
}
}
sub polygon_remove_parallel_continuous_edges {
my ($points) = @_;
return polyline_remove_parallel_continuous_edges($points, 1);
}
sub polyline_remove_acute_vertices {
my ($points, $isPolygon) = @_;
for (my $i = $isPolygon ? -1 : 1; $i < $#$points; $i++) {
my $angle = angle3points($points->[$i], $points->[$i-1], $points->[$i+1]);
if ($angle < 0.01 || $angle >= 2*PI - 0.01) {
# we can remove $points->[$i]
splice @$points, $i, 1;
$i--;
}
}
}
sub polygon_remove_acute_vertices {
my ($points) = @_;
return polyline_remove_acute_vertices($points, 1);
}
sub polyline_remove_short_segments {
my ($points, $min_length, $isPolygon) = @_;
for (my $i = $isPolygon ? 0 : 1; $i < $#$points; $i++) {
if (distance_between_points($points->[$i-1], $points->[$i]) < $min_length) {
# we can remove $points->[$i]
splice @$points, $i, 1;
$i--;
}
}
}
# accepts an arrayref of points; it returns a list of indices
# according to a nearest-neighbor walk
sub chained_path {
my ($items, $start_near) = @_;
my @points = @$items;
my %indices = map { $points[$_] => $_ } 0 .. $#points;
my @result = ();
if (!$start_near && @points) {
$start_near = shift @points;
push @result, $indices{$start_near};
}
while (@points) {
my $idx = $start_near->nearest_point_index(\@points);
my ($start_near) = splice @points, $idx, 1;
push @result, $indices{$start_near};
}
return @result;
}
# accepts an arrayref; each item should be an arrayref whose first
# item is the point to be used for the shortest path, and the second
# one is the value to be returned in output (if the second item
# is not provided, the point will be returned)
sub chained_path_items {
my ($items, $start_near) = @_;
my @indices = chained_path([ map $_->[0], @$items ], $start_near);
return [ map $_->[1], @$items[@indices] ];
}
sub chained_path_points {
my ($points, $start_near) = @_;
return [ @$points[ chained_path($points, $start_near) ] ];
}
sub douglas_peucker {
my ($points, $tolerance) = @_;
no warnings "recursion";
my $results = [];
my $dmax = 0;
my $index = 0;
for my $i (1..$#$points) {
my $d = point_line_distance($points->[$i], [ $points->[0], $points->[-1] ]);
if ($d > $dmax) {
$index = $i;
$dmax = $d;
}
}
if ($dmax >= $tolerance) {
my $dp1 = douglas_peucker([ @$points[0..$index] ], $tolerance);
$results = [
@$dp1[0..($#$dp1-1)],
@{douglas_peucker([ @$points[$index..$#$points] ], $tolerance)},
];
} else {
$results = [ $points->[0], $points->[-1] ];
}
return $results;
}
sub douglas_peucker2 {
my ($points, $tolerance) = @_;
my $anchor = 0;
my $floater = $#$points;
my @stack = ();
my %keep = ();
push @stack, [$anchor, $floater];
while (@stack) {
($anchor, $floater) = @{pop @stack};
# initialize line segment
my ($anchor_x, $anchor_y, $seg_len);
if (grep $points->[$floater][$_] != $points->[$anchor][$_], X, Y) {
$anchor_x = $points->[$floater][X] - $points->[$anchor][X];
$anchor_y = $points->[$floater][Y] - $points->[$anchor][Y];
$seg_len = sqrt(($anchor_x ** 2) + ($anchor_y ** 2));
# get the unit vector
$anchor_x /= $seg_len;
$anchor_y /= $seg_len;
} else {
$anchor_x = $anchor_y = $seg_len = 0;
}
# inner loop:
my $max_dist = 0;
my $farthest = $anchor + 1;
for my $i (($anchor + 1) .. $floater) {
my $dist_to_seg = 0;
# compare to anchor
my $vecX = $points->[$i][X] - $points->[$anchor][X];
my $vecY = $points->[$i][Y] - $points->[$anchor][Y];
$seg_len = sqrt(($vecX ** 2) + ($vecY ** 2));
# dot product:
my $proj = $vecX * $anchor_x + $vecY * $anchor_y;
if ($proj < 0) {
$dist_to_seg = $seg_len;
} else {
# compare to floater
$vecX = $points->[$i][X] - $points->[$floater][X];
$vecY = $points->[$i][Y] - $points->[$floater][Y];
$seg_len = sqrt(($vecX ** 2) + ($vecY ** 2));
# dot product:
$proj = $vecX * (-$anchor_x) + $vecY * (-$anchor_y);
if ($proj < 0) {
$dist_to_seg = $seg_len
} else { # calculate perpendicular distance to line (pythagorean theorem):
$dist_to_seg = sqrt(abs(($seg_len ** 2) - ($proj ** 2)));
}
if ($max_dist < $dist_to_seg) {
$max_dist = $dist_to_seg;
$farthest = $i;
}
}
}
if ($max_dist <= $tolerance) { # use line segment
$keep{$_} = 1 for $anchor, $floater;
} else {
push @stack, [$anchor, $farthest];
push @stack, [$farthest, $floater];
}
}
return [ map $points->[$_], sort keys %keep ];
}
sub arrange {
my ($total_parts, $partx, $party, $areax, $areay, $dist, $Config) = @_;
my $linint = sub {
my ($value, $oldmin, $oldmax, $newmin, $newmax) = @_;
return ($value - $oldmin) * ($newmax - $newmin) / ($oldmax - $oldmin) + $newmin;
};
# use actual part size (the largest) plus separation distance (half on each side) in spacing algorithm
$partx += $dist;
$party += $dist;
# margin needed for the skirt
my $skirt_margin;
if ($Config->skirts > 0) {
my $flow = Slic3r::Flow->new(
layer_height => $Config->get_value('first_layer_height'),
nozzle_diameter => $Config->nozzle_diameter->[0], # TODO: actually look for the extruder used for skirt
width => $Config->get_value('first_layer_extrusion_width'),
);
$skirt_margin = ($flow->spacing * $Config->skirts + $Config->skirt_distance) * 2;
} else {
$skirt_margin = 0;
}
# this is how many cells we have available into which to put parts
my $cellw = int(($areax - $skirt_margin + $dist) / $partx);
my $cellh = int(($areay - $skirt_margin + $dist) / $party);
die "$total_parts parts won't fit in your print area!\n" if $total_parts > ($cellw * $cellh);
# width and height of space used by cells
my $w = $cellw * $partx;
my $h = $cellh * $party;
# left and right border positions of space used by cells
my $l = ($areax - $w) / 2;
my $r = $l + $w;
# top and bottom border positions
my $t = ($areay - $h) / 2;
my $b = $t + $h;
# list of cells, sorted by distance from center
my @cellsorder;
# work out distance for all cells, sort into list
for my $i (0..$cellw-1) {
for my $j (0..$cellh-1) {
my $cx = $linint->($i + 0.5, 0, $cellw, $l, $r);
my $cy = $linint->($j + 0.5, 0, $cellh, $t, $b);
my $xd = abs(($areax / 2) - $cx);
my $yd = abs(($areay / 2) - $cy);
my $c = {
location => [$cx, $cy],
index => [$i, $j],
distance => $xd * $xd + $yd * $yd - abs(($cellw / 2) - ($i + 0.5)),
};
BINARYINSERTIONSORT: {
my $index = $c->{distance};
my $low = 0;
my $high = @cellsorder;
while ($low < $high) {
my $mid = ($low + (($high - $low) / 2)) | 0;
my $midval = $cellsorder[$mid]->[0];
if ($midval < $index) {
$low = $mid + 1;
} elsif ($midval > $index) {
$high = $mid;
} else {
splice @cellsorder, $mid, 0, [$index, $c];
last BINARYINSERTIONSORT;
}
}
splice @cellsorder, $low, 0, [$index, $c];
}
}
}
# the extents of cells actually used by objects
my ($lx, $ty, $rx, $by) = (0, 0, 0, 0);
# now find cells actually used by objects, map out the extents so we can position correctly
for my $i (1..$total_parts) {
my $c = $cellsorder[$i - 1];
my $cx = $c->[1]->{index}->[0];
my $cy = $c->[1]->{index}->[1];
if ($i == 1) {
$lx = $rx = $cx;
$ty = $by = $cy;
} else {
$rx = $cx if $cx > $rx;
$lx = $cx if $cx < $lx;
$by = $cy if $cy > $by;
$ty = $cy if $cy < $ty;
}
}
# now we actually place objects into cells, positioned such that the left and bottom borders are at 0
my @positions = ();
for (1..$total_parts) {
my $c = shift @cellsorder;
my $cx = $c->[1]->{index}->[0] - $lx;
my $cy = $c->[1]->{index}->[1] - $ty;
push @positions, [$cx * $partx, $cy * $party];
}
return @positions;
}
1;
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