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+package Math::Bezier::Convert;
+# This program is free software; you can redistribute it and/or
+# modify it under the terms of the GNU LGPL Libray General Public License
+# as published by the Free Software Foundation; either version 2
+# of the License, or (at your option) any later version.
+#
+# This program is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+# GNU Library General Public License for more details.
+#
+# You should have received a copy of the GNU Library General Public License
+# along with this program; if not, write to the Free Software
+# Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA,
+# or refer to http://www.gnu.org/copyleft/lgpl.html
+#
+##################################################################
+
+require 5.005_62;
+use strict;
+use warnings;
+use Carp;
+
+require Exporter;
+
+our @ISA = qw(Exporter);
+
+our %EXPORT_TAGS = ( 'all' => [ qw(
+ divide_cubic
+ divide_quadratic
+ cubic_to_quadratic
+ quadratic_to_cubic
+ cubic_to_lines
+ quadratic_to_lines
+) ] );
+
+our @EXPORT_OK = ( @{ $EXPORT_TAGS{'all'} } );
+
+our @EXPORT = qw(
+
+);
+our $VERSION = '0.01';
+
+# Globals
+
+our $APPROX_QUADRATIC_TOLERANCE = 1;
+our $APPROX_LINE_TOLERANCE = 1;
+our $CTRL_PT_TOLERANCE = 3;
+
+sub divide_cubic {
+ my ($p0x, $p0y, $p1x, $p1y, $p2x, $p2y, $p3x, $p3y, $sep) = @_;
+ my ($p10x, $p10y, $p11x, $p11y, $p12x, $p12y, $p20x, $p20y, $p21x, $p21y, $p30x, $p30y);
+
+ $p10x = $p0x + $sep * ($p1x - $p0x);
+ $p10y = $p0y + $sep * ($p1y - $p0y);
+ $p11x = $p1x + $sep * ($p2x - $p1x);
+ $p11y = $p1y + $sep * ($p2y - $p1y);
+ $p12x = $p2x + $sep * ($p3x - $p2x);
+ $p12y = $p2y + $sep * ($p3y - $p2y);
+ $p20x = $p10x+ $sep * ($p11x-$p10x);
+ $p20y = $p10y+ $sep * ($p11y-$p10y);
+ $p21x = $p11x+ $sep * ($p12x-$p11x);
+ $p21y = $p11y+ $sep * ($p12y-$p11y);
+ $p30x = $p20x+ $sep * ($p21x-$p20x);
+ $p30y = $p20y+ $sep * ($p21y-$p20y);
+
+ return ($p0x, $p0y, $p10x, $p10y, $p20x, $p20y, $p30x, $p30y, $p21x, $p21y, $p12x, $p12y, $p3x, $p3y);
+}
+
+sub divide_quadratic {
+ my ($p0x, $p0y, $p1x, $p1y, $p2x, $p2y, $sep) = @_;
+ my ($p10x, $p10y, $p11x, $p11y, $p20x, $p20y);
+
+ $p10x = $p0x + $sep * ($p1x - $p0x);
+ $p10y = $p0y + $sep * ($p1y - $p0y);
+ $p11x = $p1x + $sep * ($p2x - $p1x);
+ $p11y = $p1y + $sep * ($p2y - $p1y);
+ $p20x = $p10x+ $sep * ($p11x-$p10x);
+ $p20y = $p10y+ $sep * ($p11y-$p10y);
+
+ return ($p0x, $p0y, $p10x, $p10y, $p20x, $p20y, $p11x, $p11y, $p2x, $p2y);
+}
+
+sub cubic_to_quadratic {
+ my ($p0x, $p0y, @cp) = @_;
+ my ($p1x, $p1y, $p2x, $p2y, $p3x, $p3y);
+ my ($a1, $b1, $a2, $b2, $cx, $cy) = (undef) x 6;
+ my @qp = ($p0x, $p0y);
+ my @p;
+
+ croak '$CTRL_PT_TOLERANCE must be more than 1.5 ' unless $CTRL_PT_TOLERANCE > 1.5;
+
+CURVE:
+ while (@cp and @p = ($p1x, $p1y, $p2x, $p2y, $p3x, $p3y) = splice(@cp, 0, 6)) {
+
+ my $step = 0.5;
+ my $sep = 1;
+ my @qp1 = ();
+ my @cp1 = ();
+ my ($cp3x, $cp3y);
+
+ while ($step > 0.0000001) {
+
+ my ($v01x, $v01y) = ($p1x-$p0x, $p1y-$p0y);
+ my ($v02x, $v02y) = ($p2x-$p0x, $p2y-$p0y);
+ my ($v03x, $v03y) = ($p3x-$p0x, $p3y-$p0y);
+ my ($v32x, $v32y) = ($p2x-$p3x, $p2y-$p3y);
+
+ next CURVE if (abs($v01x)<0.0001 and abs($v02x)<0.0001 and abs($v03x)<0.0001 and
+ abs($v01y)<0.0001 and abs($v02y)<0.0001 and abs($v03y)<0.0001);
+
+
+ if (abs($v01x)<0.0001 and abs($v32x)<0.0001 and
+ abs($v01y)<0.0001 and abs($v32y)<0.0001) {
+
+ @qp1 = (($p0x+$p3x)/2, ($p0y+$p3y)/2);
+ last;
+ }
+
+ my $n = $v01y*$v32x - $v01x*$v32y;
+ if ($n == 0) {
+ if ($v02x*$v32y - $v02y*$v32x == 0) {
+ @qp1 = (($p0x+$p3x)/2, ($p0y+$p3y)/2);
+ last;
+ } else {
+ $sep -= $step;
+ $step /= 2;
+ next;
+ }
+ }
+ my $m1 = $v01x*$v03y - $v01y*$v03x;
+ my $m2 = $v02x*$v03y - $v03x*$v02y;
+ if ($m1/$n < 1 or $m2/$n < 1 or $m1/$n >$CTRL_PT_TOLERANCE or $m2/$n > $CTRL_PT_TOLERANCE) {
+ $sep -= $step;
+ $step /= 2;
+ next;
+ }
+ $cx = $p0x + $m2 * $v01x / $n;
+ $cy = $p0y + $m2 * $v01y / $n;
+
+ if (defined $cx and _q_c_check($p0x, $p0y, $p1x, $p1y, $p2x, $p2y, $p3x, $p3y, $cx, $cy)) {
+ @qp1 = ($cx, $cy);
+ last if $sep>=1;
+ $sep += $step;
+ } else {
+ $sep -= $step;
+ }
+ $step /= 2;
+ } continue {
+ (undef, undef, $p1x, $p1y, $p2x, $p2y, $p3x, $p3y, @cp1) = divide_cubic($p0x, $p0y, @p, $sep);
+ }
+ unless (@qp1) {
+ die "Can't approx @p";
+# return @qp;
+ }
+ push @qp, @qp1, $p3x, $p3y;
+ $p0x = $p3x;
+ $p0y = $p3y;
+ if (@cp1) {
+ @p = ($p1x, $p1y, $p2x, $p2y, $p3x, $p3y) = @cp1;
+ redo;
+ }
+ }
+ return @qp;
+}
+
+sub _q_c_check {
+ my ($cx0, $cy0, $cx1, $cy1, $cx2, $cy2, $cx3, $cy3, $qx1, $qy1) = @_;
+ my ($a, $b, $c, $d, $sep);
+
+ $a = (($cx0-$cx3)*($cy1-$cy3)-($cy0-$cy3)*($cx1-$cx3)<=>0);
+ $b = (($cx0-$cx3)*($cy2-$cy3)-($cy0-$cy3)*($cx2-$cx3)<=>0);
+ return if ($a == 0 or $b == 0 or $a != $b);
+
+ my ($cx, $cy) = (divide_cubic($cx0,$cy0,$cx1,$cy1,$cx2,$cy2,$cx3,$cy3, 0.5))[6,7];
+ $a = $cx0-2*$qx1+$cx3;
+ $b = 2*$qx1-2*$cx0;
+ $c = $cx0-$cx;
+ $d = $b*$b-4*$a*$c;
+ return if ($d<0);
+ my ($qx, $qy);
+ if ($a!=0) {
+ $sep = (-$b-sqrt($d))/2/$a;
+ $sep = (-$b+sqrt($d))/2/$a if ($sep<=0 or $sep>=1);
+ return if ($sep<=0 or $sep>=1);
+ ($qx, $qy) = (divide_quadratic($cx0,$cy0,$qx1,$qy1,$cx3,$cy3, $sep))[4, 5];
+ } else {
+ ($qx, $qy) = ($qx1, $qy1);
+ }
+ return ($cx-$qx)*($cx-$qx)+($cy-$qy)*($cy-$qy) < $APPROX_QUADRATIC_TOLERANCE;
+}
+
+sub quadratic_to_cubic {
+ my ($p0x, $p0y, @qp) = @_;
+ my @cp = ($p0x, $p0y);
+ my ($p1x, $p1y, $p2x, $p2y);
+
+ while (@qp and ($p1x, $p1y, $p2x, $p2y) = splice(@qp, 0, 4)) {
+ push @cp, $p0x+($p1x-$p0x)*2/3, $p0y+($p1y-$p0y)*2/3, $p1x+($p2x-$p1x)/3, $p1y+($p2y-$p1y)/3, $p2x, $p2y;
+ $p0x = $p2x;
+ $p0y = $p2y;
+ }
+ return @cp;
+}
+
+sub cubic_to_lines {
+ my @cp = @_;
+ my @p;
+ my @last = splice(@cp, 0, 2);
+ my @lp = @last;
+
+ while (@cp and @p = splice(@cp, 0, 6)) {
+ push @lp, _c2lsub(@last, @p);
+ push @lp, @last = @p[4,5];
+ }
+ return @lp;
+}
+
+sub _c2lsub {
+ my @p = @_;
+ my ($p0x, $p0y, $p10x, $p10y, $p20x, $p20y, $p30x, $p30y, $p21x, $p21y, $p12x, $p12y, $p3x, $p3y) =
+ divide_cubic(@p[0..7], 0.5);
+ my ($cx, $cy) = (($p0x+$p3x)/2, ($p0y+$p3y)/2);
+ return () if (($p30x-$cx)*($p30x-$cx)+($p30y-$cy)*($p30y-$cy) < $APPROX_LINE_TOLERANCE);
+ return (_c2lsub($p0x, $p0y, $p10x, $p10y, $p20x, $p20y, $p30x, $p30y), $p30x, $p30y, _c2lsub($p30x, $p30y, $p21x, $p21y, $p12x, $p12y, $p3x, $p3y));
+}
+
+sub quadratic_to_lines {
+ my @qp = @_;
+ my @p;
+ my @last = splice(@qp, 0, 2);
+ my @lp = @last;
+
+ while (@qp and @p = splice(@qp, 0, 4)) {
+ push @lp, _q2lsub(@last, @p);
+ push @lp, @last = @p[2,3];
+ }
+ return @lp;
+}
+
+sub _q2lsub {
+ my @p = @_;
+ my ($p0x, $p0y, $p10x, $p10y, $p20x, $p20y, $p11x, $p11y, $p2x, $p2y) =
+ divide_quadratic(@p[0..5], 0.5);
+ my ($cx, $cy) = (($p0x+$p2x)/2, ($p0y+$p2y)/2);
+ return () if (($p20x-$cx)*($p20x-$cx)+($p20y-$cy)*($p20y-$cy) < $APPROX_LINE_TOLERANCE);
+ return (_q2lsub($p0x, $p0y, $p10x, $p10y, $p20x, $p20y), $p20x, $p20y, _q2lsub($p20x, $p20y, $p11x, $p11y, $p2x, $p2y));
+}
+
+1;
+__END__
+
+=head1 NAME
+
+Math::Bezier::Convert - Convert cubic and quadratic bezier each other.
+
+=head1 SYNOPSIS
+
+ use Math::Bezier::Convert;
+
+ @new_cubic = divide_cubic($cx1, $cy1, $cx2, $cy2, $cx3, $cy3, $cx4, $cy4, $t);
+ @new_quad = divide_quadratic($cx1, $cy1, $cx2, $cy2, $cx3, $cy3, $t);
+ @quad = cubic_to_quadratic(@cubic);
+ @cubic = quadratic_to_cubic(@quad);
+ @lines = cubic_to_lines(@cubic);
+ @lines = quadratic_to_lines(@cubic);
+
+=head1 DESCRIPTION
+
+Math::Bezier::Convert provides functions to convert quadratic bezier to cubic,
+to approximate cubic bezier to quadratic, and to approximate cubic and quadratic
+bezier to polyline.
+
+Each function takes an array of the coordinates of control points of the bezier curve.
+Cubic bezier consists of one I<ANCHOR> control point, two I<DIRECTOR> control points, one I<ANCHOR>, two I<DIRECTORS>, ... and the last I<ANCHOR>.
+Quadratic bezier consists of one I<ANCHOR>, one I<DIRECTOR>, ... and the last I<ANCHOR>.
+The curve pass over the I<ANCHOR> point, but dose not the I<DIRECTOR> point.
+Each point consists of X and Y coordinates. Both are flatly listed in the
+array of the curve, like ($x1, $y1, $x2, $y2, ...).
+
+=over 4
+
+=item divide_cubic( $cx1, $cy1, $cx2, $cy2, $cx3, $cy3, $cx4, $cy4, $t )
+
+divides one segment of the cubic bezier curve at ratio $t, and returns
+new cubic bezier which has two segment (7 points).
+
+=item divide_quadratic( $cx1, $cy1, $cx2, $cy2, $cx3, $cy3, $t )
+
+divides one segment of the quadratic bezier curve at ratio $t, and returns
+new quadratic bezier which has two segment (5 points).
+
+=item cubic_to_quadratic( @cubic )
+
+approximates cubic bezier to quadratic bezier, and returns an array of the
+control points of the quadratic bezier curve.
+
+=item quadratic_to_cubic( @quadratic )
+
+converts quadratic bezier to cubic bezier, and returns an array of the
+control points of the cubic bezier curve.
+
+=item cubic_to_lines( @cubic )
+
+approximates cubic bezier to polyline, and returns an array of endpoints.
+
+=item quadratic_to_lines( @cubic )
+
+approximates quadratic bezier to polyline, and returns an array of endpoints.
+
+=back
+
+=head2 GLOBALS
+
+=over 4
+
+=item $Math::Bezier::Convert::APPROX_QUADRATIC_TOLERANCE
+
+=item $Math::Bezier::Convert::APPROX_LINE_TOLERANCE
+
+Tolerance of the distance between the half point of the cubic bezier and the approximation point.
+Default is 1.
+
+=item $Math::Bezier::Convert::CTRL_PT_TOLERANCE
+
+Tolerance of the I<ANCHOR-DIRECTOR> distance ratio of quadratic to cubic.
+Default is 3. It must be specified more than 1.5.
+
+=back
+
+=head2 EXPORT
+
+None by default.
+All functions described above are exported when ':all' tag is specified.
+All global variables are not exported in any case.
+
+=head1 COPYRIGHT
+
+Copyright 2000 Yasuhiro Sasama (ySas), <ysas@nmt.ne.jp>
+
+This library is free software; you can redistribute it
+and/or modify it under the same terms as Perl itself.
+
+=head1 SEE ALSO
+
+perl(1).
+
+=cut
+
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