679 lines
21 KiB
Perl
679 lines
21 KiB
Perl
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 epsilon slope line_atan lines_parallel
|
|
line_point_belongs_to_segment points_coincide distance_between_points
|
|
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_along_segment polygon_segment_having_point polygon_has_subsegment
|
|
polygon_has_vertex polyline_length can_connect_points deg2rad rad2deg
|
|
rotate_points move_points remove_coinciding_points clip_segment_polygon
|
|
sum_vectors multiply_vector subtract_vectors dot perp polygon_points_visibility
|
|
line_intersection bounding_box bounding_box_intersect same_point
|
|
longest_segment angle3points three_points_aligned
|
|
polyline_remove_parallel_continuous_edges polyline_remove_acute_vertices
|
|
polygon_remove_acute_vertices polygon_remove_parallel_continuous_edges
|
|
shortest_path collinear scale unscale merge_collinear_lines
|
|
);
|
|
|
|
use Slic3r::Geometry::DouglasPeucker qw(Douglas_Peucker);
|
|
use XXX;
|
|
|
|
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;
|
|
our $parallel_degrees_limit = abs(deg2rad(3));
|
|
|
|
our $epsilon = 1E-6;
|
|
sub epsilon () { $epsilon }
|
|
|
|
sub scale ($) { $_[0] / $Slic3r::resolution }
|
|
sub unscale ($) { $_[0] * $Slic3r::resolution }
|
|
|
|
sub slope {
|
|
my ($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] - $line->[A][X]);
|
|
}
|
|
|
|
sub lines_parallel {
|
|
my ($line1, $line2) = @_;
|
|
|
|
return abs(line_atan($line1) - line_atan($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] == $p2->[Y];
|
|
}
|
|
|
|
sub distance_between_points {
|
|
my ($p1, $p2) = @_;
|
|
return sqrt((($p1->[X] - $p2->[X])**2) + ($p1->[Y] - $p2->[Y])**2);
|
|
}
|
|
|
|
sub line_length {
|
|
my ($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 @xy = map @$_, @$polygon;
|
|
|
|
# Derived from the comp.graphics.algorithms FAQ,
|
|
# courtesy of Wm. Randolph Franklin
|
|
my $n = @xy / 2; # Number of points in polygon
|
|
my @i = map { 2*$_ } 0..(@xy/2); # The even indices of @xy
|
|
my @x = map { $xy[$_] } @i; # Even indices: x-coordinates
|
|
my @y = map { $xy[$_ + 1] } @i; # Odd indices: y-coordinates
|
|
|
|
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_x = sort { $a <=> $b } $line->[A][X], $line->[B][X];
|
|
my @line_y = sort { $a <=> $b } $line->[A][Y], $line->[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->[A][X] == $line->[B][X]) {
|
|
return abs($x - $line->[A][X]) < epsilon ? 1 : 0;
|
|
}
|
|
|
|
# calculate the Y in line at X of the point
|
|
my $y3 = $line->[A][Y] + ($line->[B][Y] - $line->[A][Y])
|
|
* ($x - $line->[A][X]) / ($line->[B][X] - $line->[A][X]);
|
|
return abs($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] - $line->[A][X])) > 0;
|
|
}
|
|
|
|
sub polyline_lines {
|
|
my ($polygon) = @_;
|
|
|
|
my @lines = ();
|
|
my $last_point;
|
|
foreach my $point (@$polygon) {
|
|
push @lines, [ $last_point, $point ] if $last_point;
|
|
$last_point = $point;
|
|
}
|
|
|
|
return @lines;
|
|
}
|
|
|
|
sub polygon_lines {
|
|
my ($polygon) = @_;
|
|
return polyline_lines([ @$polygon, $polygon->[0] ]);
|
|
}
|
|
|
|
sub nearest_point {
|
|
my ($point, $points) = @_;
|
|
|
|
my ($nearest_point, $distance) = ();
|
|
foreach my $p (@$points) {
|
|
my $d = distance_between_points($point, $p);
|
|
if (!defined $distance || $d < $distance) {
|
|
$nearest_point = $p;
|
|
$distance = $d;
|
|
return $p if $distance < epsilon;
|
|
}
|
|
}
|
|
return $nearest_point;
|
|
}
|
|
|
|
# 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 $point;
|
|
}
|
|
|
|
# given a $polygon, return the (first) segment having $point
|
|
sub polygon_segment_having_point {
|
|
my ($polygon, $point) = @_;
|
|
|
|
foreach my $line (polygon_lines($polygon)) {
|
|
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, $point);
|
|
}
|
|
return 0;
|
|
}
|
|
|
|
sub polyline_length {
|
|
my ($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 $rad / PI() * 180;
|
|
}
|
|
|
|
sub rotate_points {
|
|
my ($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 Slic3r::Point->new($shift->[X] + $_->[X], $shift->[Y] + $_->[Y]), @points;
|
|
}
|
|
|
|
# preserves order
|
|
sub remove_coinciding_points {
|
|
my ($points) = @_;
|
|
|
|
my %p = map { sprintf('%f,%f', @$_) => "$_" } @$points;
|
|
%p = reverse %p;
|
|
@$points = grep $p{"$_"}, @$points;
|
|
}
|
|
|
|
# implementation of Liang-Barsky algorithm
|
|
# polygon must be convex and ccw
|
|
sub clip_segment_polygon {
|
|
my ($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] - $line1->[Y] ];
|
|
}
|
|
|
|
# 2D dot product
|
|
sub dot {
|
|
my ($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, $line, 1) or next;
|
|
next if grep points_coincide($intersection, $_), $p1, $p2;
|
|
return 0;
|
|
}
|
|
|
|
return 1;
|
|
}
|
|
|
|
sub line_intersection {
|
|
my ($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 );
|
|
|
|
if ( @_ == 8 ) {
|
|
( $x0, $y0, $x1, $y1, $x2, $y2, $x3, $y3 ) = @_;
|
|
|
|
# The bounding boxes chop the lines into line segments.
|
|
# bounding_box() is defined later in this chapter.
|
|
my @box_a = bounding_box([ [$x0, $y0], [$x1, $y1] ]);
|
|
my @box_b = bounding_box([ [$x2, $y2], [$x3, $y3] ]);
|
|
|
|
# Take this test away and the line segments are
|
|
# turned into lines going from infinite to another.
|
|
# bounding_box_intersect() defined later in this chapter.
|
|
###return "out of bounding box" unless bounding_box_intersect( 2, @box_a, @box_b );
|
|
}
|
|
elsif ( @_ == 4 ) { # The parametric form.
|
|
$x0 = $x2 = 0;
|
|
( $y0, $y2 ) = @_[ 1, 3 ];
|
|
# Need to multiply by 'enough' to get 'far enough'.
|
|
my $abs_y0 = abs $y0;
|
|
my $abs_y2 = abs $y2;
|
|
my $enough = 10 * ( $abs_y0 > $abs_y2 ? $abs_y0 : $abs_y2 );
|
|
$x1 = $x3 = $enough;
|
|
$y1 = $_[0] * $x1 + $y0;
|
|
$y3 = $_[2] * $x2 + $y2;
|
|
}
|
|
|
|
my ($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 && $h32 <= 1];
|
|
}
|
|
|
|
# 2D
|
|
sub bounding_box {
|
|
my ($points) = @_;
|
|
|
|
my @x = sort { $a <=> $b } map $_->[X], @$points;
|
|
my @y = sort { $a <=> $b } map $_->[Y], @$points;
|
|
|
|
return ($x[0], $y[0], $x[-1], $y[-1]);
|
|
}
|
|
|
|
# bounding_box_intersect($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[ $i_min ];
|
|
}
|
|
|
|
return 1;
|
|
}
|
|
|
|
sub angle3points {
|
|
my ($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; $i++) {
|
|
if (Slic3r::Geometry::lines_parallel([$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($points, 1);
|
|
}
|
|
|
|
# accepts an arrayref; each item should be an arrayref whose first
|
|
# item is the point to be used for the shortest path, and the second
|
|
# one is the value to be returned in output (if the second item
|
|
# is not provided, the point will be returned)
|
|
sub shortest_path {
|
|
my ($items, $start_near) = @_;
|
|
|
|
my %values = map +($_->[0] => $_->[1] || $_->[0]), @$items;
|
|
my @points = map $_->[0], @$items;
|
|
|
|
my $result = [];
|
|
my $last_point;
|
|
if (!$start_near) {
|
|
$start_near = shift @points;
|
|
push @$result, $values{$start_near} if $start_near;
|
|
}
|
|
while (@points) {
|
|
$start_near = nearest_point($start_near, [@points]);
|
|
@points = grep $_ ne $start_near, @points;
|
|
push @$result, $values{$start_near};
|
|
}
|
|
|
|
return $result;
|
|
}
|
|
|
|
1;
|