268 lines
7.9 KiB
Perl
268 lines
7.9 KiB
Perl
package Slic3r::Geometry;
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use strict;
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use warnings;
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use Slic3r::Geometry::DouglasPeucker;
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use XXX;
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use constant PI => 4 * atan2(1, 1);
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use constant A => 0;
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use constant B => 1;
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use constant X => 0;
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use constant Y => 1;
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use constant epsilon => 1E-6;
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our $parallel_degrees_limit = abs(deg2rad(3));
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sub slope {
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my ($line) = @_;
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return undef if abs($line->[B][X] - $line->[A][X]) < epsilon; # line is vertical
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return ($line->[B][Y] - $line->[A][Y]) / ($line->[B][X] - $line->[A][X]);
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}
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sub line_atan {
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my ($line) = @_;
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return atan2($line->[B][Y] - $line->[A][Y], $line->[B][X] - $line->[A][X]);
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}
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sub lines_parallel {
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my ($line1, $line2) = @_;
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return abs(line_atan($line1) - line_atan($line2)) < $parallel_degrees_limit;
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}
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# this subroutine checks whether a given point may belong to a given
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# segment given the hypothesis that it belongs to the line containing
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# the segment
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sub line_point_belongs_to_segment {
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my ($point, $segment) = @_;
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#printf " checking whether %f,%f may belong to segment %f,%f - %f,%f\n",
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# @$point, map @$_, @$segment;
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my @segment_extents = (
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[ sort { $a <=> $b } map $_->[X], @$segment ],
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[ sort { $a <=> $b } map $_->[Y], @$segment ],
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);
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return 0 if $point->[X] < ($segment_extents[X][0] - epsilon) || $point->[X] > ($segment_extents[X][1] + epsilon);
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return 0 if $point->[Y] < ($segment_extents[Y][0] - epsilon) || $point->[Y] > ($segment_extents[Y][1] + epsilon);
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return 1;
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}
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sub points_coincide {
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my ($p1, $p2) = @_;
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return 1 if abs($p2->[X] - $p1->[X]) < epsilon && abs($p2->[Y] - $p1->[Y]) < epsilon;
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return 0;
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}
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sub distance_between_points {
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my ($p1, $p2) = @_;
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return sqrt((($p1->[X] - $p2->[X])**2) + ($p1->[Y] - $p2->[Y])**2);
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}
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sub point_in_polygon {
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my ($point, $polygon) = @_;
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my ($x, $y) = @$point;
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my @xy = map @$_, @$polygon;
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# Derived from the comp.graphics.algorithms FAQ,
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# courtesy of Wm. Randolph Franklin
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my $n = @xy / 2; # Number of points in polygon
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my @i = map { 2*$_ } 0..(@xy/2); # The even indices of @xy
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my @x = map { $xy[$_] } @i; # Even indices: x-coordinates
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my @y = map { $xy[$_ + 1] } @i; # Odd indices: y-coordinates
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my ($i, $j);
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my $side = 0; # 0 = outside; 1 = inside
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for ($i = 0, $j = $n - 1; $i < $n; $j = $i++) {
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if (
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# If the y is between the (y-) borders...
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($y[$i] <= $y && $y < $y[$j]) || ($y[$j] <= $y && $y < $y[$i])
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and
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# ...the (x,y) to infinity line crosses the edge
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# from the ith point to the jth point...
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($x < ($x[$j] - $x[$i]) * ($y - $y[$i]) / ($y[$j] - $y[$i]) + $x[$i])
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) {
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$side = not $side; # Jump the fence
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}
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}
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# if point is not in polygon, let's check whether it belongs to the contour
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if (!$side && 0) {
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foreach my $line (polygon_lines($polygon)) {
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return 1 if point_in_segment($point, $line);
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}
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}
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return $side;
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}
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sub point_in_segment {
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my ($point, $line) = @_;
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my ($x, $y) = @$point;
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my @line_x = sort { $a <=> $b } $line->[A][X], $line->[B][X];
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my @line_y = sort { $a <=> $b } $line->[A][Y], $line->[B][Y];
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# check whether the point is in the segment bounding box
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return 0 unless $x >= ($line_x[0] - epsilon) && $x <= ($line_x[1] + epsilon)
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&& $y >= ($line_y[0] - epsilon) && $y <= ($line_y[1] + epsilon);
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# if line is vertical, check whether point's X is the same as the line
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if ($line->[A][X] == $line->[B][X]) {
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return 1 if abs($x - $line->[A][X]) < epsilon;
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}
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# calculate the Y in line at X of the point
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my $y3 = $line->[A][Y] + ($line->[B][Y] - $line->[A][Y])
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* ($x - $line->[A][X]) / ($line->[B][X] - $line->[A][X]);
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return abs($y3 - $y) < epsilon ? 1 : 0;
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}
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sub polygon_lines {
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my ($polygon) = @_;
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my @lines = ();
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my $last_point = $polygon->[-1];
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foreach my $point (@$polygon) {
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push @lines, [ $last_point, $point ];
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$last_point = $point;
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}
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return @lines;
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}
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sub nearest_point {
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my ($point, $points) = @_;
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my ($nearest_point, $distance);
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foreach my $p (@$points) {
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my $d = distance_between_points($point, $p);
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if (!defined $distance || $d < $distance) {
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$nearest_point = $p;
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$distance = $d;
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return $p if $distance < epsilon;
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}
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}
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return $nearest_point;
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}
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sub point_along_segment {
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my ($p1, $p2, $distance) = @_;
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my $point = [ @$p1 ];
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my $line_length = sqrt( (($p2->[X] - $p1->[X])**2) + (($p2->[Y] - $p1->[Y])**2) );
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for (X, Y) {
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if ($p1->[$_] != $p2->[$_]) {
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$point->[$_] = $p1->[$_] + ($p2->[$_] - $p1->[$_]) * $distance / $line_length;
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}
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}
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return $point;
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}
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sub deg2rad {
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my ($degrees) = @_;
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return PI() * $degrees / 180;
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}
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sub rotate_points {
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my ($radians, $center, @points) = @_;
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$center ||= [0,0];
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return map {
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[
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$center->[X] + cos($radians) * ($_->[X] - $center->[X]) - sin($radians) * ($_->[Y] - $center->[Y]),
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$center->[Y] + cos($radians) * ($_->[Y] - $center->[Y]) + sin($radians) * ($_->[X] - $center->[X]),
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]
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} @points;
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}
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sub move_points {
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my ($shift, @points) = @_;
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return map [ $shift->[X] + $_->[X], $shift->[Y] + $_->[Y] ], @points;
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}
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# preserves order
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sub remove_coinciding_points {
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my ($points) = @_;
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my %p = map { sprintf('%f,%f', @$_) => "$_" } @$points;
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%p = reverse %p;
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@$points = grep $p{"$_"}, @$points;
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}
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# implementation of Liang-Barsky algorithm
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# polygon must be convex and ccw
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sub clip_segment_polygon {
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my ($line, $polygon) = @_;
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if (@$line == 1) {
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# the segment is a point, check for inclusion
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return point_in_polygon($line, $polygon);
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}
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my @V = (@$polygon, $polygon->[0]);
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my $tE = 0; # the maximum entering segment parameter
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my $tL = 1; # the minimum entering segment parameter
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my $dS = subtract_vectors($line->[B], $line->[A]); # the segment direction vector
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for (my $i = 0; $i < $#V; $i++) { # process polygon edge V[i]V[Vi+1]
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my $e = subtract_vectors($V[$i+1], $V[$i]);
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my $N = perp($e, subtract_vectors($line->[A], $V[$i]));
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my $D = -perp($e, $dS);
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if (abs($D) < epsilon) { # $line is nearly parallel to this edge
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($N < 0) ? return : next; # P0 outside this edge ? $line is outside : $line cannot cross edge, thus ignoring
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}
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my $t = $N / $D;
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if ($D < 0) { # $line is entering across this edge
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if ($t > $tE) { # new max $tE
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$tE = $t;
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return if $tE > $tL; # $line enters after leaving polygon?
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}
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} else { # $line is leaving across this edge
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if ($t < $tL) { # new min $tL
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$tL = $t;
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return if $tL < $tE; # $line leaves before entering polygon?
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}
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}
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}
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# $tE <= $tL implies that there is a valid intersection subsegment
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return [
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sum_vectors($line->[A], multiply_vector($dS, $tE)), # = P(tE) = point where S enters polygon
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sum_vectors($line->[A], multiply_vector($dS, $tL)), # = P(tE) = point where S enters polygon
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];
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}
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sub sum_vectors {
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my ($v1, $v2) = @_;
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return [ $v1->[X] + $v2->[X], $v1->[Y] + $v2->[Y] ];
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}
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sub multiply_vector {
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my ($line, $scalar) = @_;
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return [ $line->[X] * $scalar, $line->[Y] * $scalar ];
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}
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sub subtract_vectors {
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my ($line2, $line1) = @_;
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return [ $line2->[X] - $line1->[X], $line2->[Y] - $line1->[Y] ];
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}
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# 2D dot product
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sub dot {
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my ($u, $v) = @_;
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return $u->[X] * $v->[X] + $u->[Y] * $v->[Y];
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}
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# 2D perp product
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sub perp {
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my ($u, $v) = @_;
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return $u->[X] * $v->[Y] - $u->[Y] * $v->[X];
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}
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1;
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