protected function plotCubicSegment($gd, $x0, $y0, $x1, $y1, $x2, $y2, $x3, $y3)
{
/* plot limited anti-aliased cubic Bezier segment */
$f = 0;
$fx = 0;
$fy = 0;
$leg = 1;
$sx = $x0 < $x3 ? 1 : -1;
$sy = $y0 < $y3 ? 1 : -1;
/* step direction */
$xc = -abs($x0 + $x1 - $x2 - $x3);
$xa = $xc - 4 * $sx * ($x1 - $x2);
$xb = $sx * ($x0 - $x1 - $x2 + $x3);
$yc = -abs($y0 + $y1 - $y2 - $y3);
$ya = $yc - 4 * $sy * ($y1 - $y2);
$yb = $sy * ($y0 - $y1 - $y2 + $y3);
$ab = 0;
$ac = 0;
$bc = 0;
$ba = 0;
$xx = 0;
$xy = 0;
$yy = 0;
$dx = 0;
$dy = 0;
$ex = 0;
$px = 0;
$py = 0;
$ed = 0;
$ip = 0;
$EP = 0.01;
/* check for curve restrains */
/* slope P0-P1 == P2-P3 and (P0-P3 == P1-P2 or no slope change) */
assert(($x1 - $x0) * ($x2 - $x3) < $EP && (($x3 - $x0) * ($x1 - $x2) < $EP || $xb * $xb < $xa * $xc + $EP));
assert(($y1 - $y0) * ($y2 - $y3) < $EP && (($y3 - $y0) * ($y1 - $y2) < $EP || $yb * $yb < $ya * $yc + $EP));
if ($xa == 0 && $ya == 0) {
/* quadratic Bezier */
$sx = floor((3 * $x1 - $x0 + 1) / 2);
$sy = floor((3 * $y1 - $y0 + 1) / 2);
/* new midpoint */
$this->plotQuadSegment($gd, $x0, $y0, $sx, $sy, $x3, $y3);
return;
}
$x1 = ($x1 - $x0) * ($x1 - $x0) + ($y1 - $y0) * ($y1 - $y0) + 1;
/* line lengths */
$x2 = ($x2 - $x3) * ($x2 - $x3) + ($y2 - $y3) * ($y2 - $y3) + 1;
do {
/* loop over both ends */
$ab = $xa * $yb - $xb * $ya;
$ac = $xa * $yc - $xc * $ya;
$bc = $xb * $yc - $xc * $yb;
$ip = 4 * $ab * $bc - $ac * $ac;
/* self intersection loop at all? */
$ex = $ab * ($ab + $ac - 3 * $bc) + $ac * $ac;
/* P0 part of self-intersection loop? */
$f = $ex > 0 ? 1 : sqrt(1 + 1024 / $x1);
/* calculate resolution */
$ab *= $f;
$ac *= $f;
$bc *= $f;
$ex *= $f * $f;
/* increase resolution */
$xy = 9 * ($ab + $ac + $bc) / 8;
$ba = 8 * ($xa - $ya);
/* init differences of 1st degree */
$dx = 27 * (8 * $ab * ($yb * $yb - $ya * $yc) + $ex * ($ya + 2 * $yb + $yc)) / 64 - $ya * $ya * ($xy - $ya);
$dy = 27 * (8 * $ab * ($xb * $xb - $xa * $xc) - $ex * ($xa + 2 * $xb + $xc)) / 64 - $xa * $xa * ($xy + $xa);
/* init differences of 2nd degree */
$xx = 3 * (3 * $ab * (3 * $yb * $yb - $ya * $ya - 2 * $ya * $yc) - $ya * (3 * $ac * ($ya + $yb) + $ya * $ba)) / 4;
$yy = 3 * (3 * $ab * (3 * $xb * $xb - $xa * $xa - 2 * $xa * $xc) - $xa * (3 * $ac * ($xa + $xb) + $xa * $ba)) / 4;
$xy = $xa * $ya * (6 * $ab + 6 * $ac - 3 * $bc + $ba);
$ac = $ya * $ya;
$ba = $xa * $xa;
$xy = 3 * ($xy + 9 * $f * ($ba * $yb * $yc - $xb * $xc * $ac) - 18 * $xb * $yb * $ab) / 8;
if ($ex < 0) {
/* negate values if inside self-intersection loop */
$dx = -$dx;
$dy = -$dy;
$xx = -$xx;
$yy = -$yy;
$xy = -$xy;
$ac = -$ac;
$ba = -$ba;
}
/* init differences of 3rd degree */
$ab = 6 * $ya * $ac;
$ac = -6 * $xa * $ac;
$bc = 6 * $ya * $ba;
$ba = -6 * $xa * $ba;
$dx += $xy;
$ex = $dx + $dy;
$dy += $xy;
/* error of 1st step */
for ($fx = $fy = $f; $x0 != $x3 && $y0 != $y3;) {
$y1 = min($xy - $dx, $dy - $xy);
$ed = max($xy - $dx, $dy - $xy);
/* approximate error distance */
$ed = $f * ($ed + 2 * $ed * $y1 * $y1 / (4 * $ed * $ed + $y1 * $y1));
$y1 = 255 * abs($ex - ($f - $fx + 1) * $dx - ($f - $fy + 1) * $dy + $f * $xy) / $ed;
if ($y1 < 256) {
$this->setPixel($gd, $x0, $y0, $y1 / 255);
}
/* plot curve */
$px = abs($ex - ($f - $fx + 1) * $dx + ($fy - 1) * $dy);
/* pixel intensity x move */
$py = abs($ex + ($fx - 1) * $dx - ($f - $fy + 1) * $dy);
/* pixel intensity y move */
$y2 = $y0;
do {
/* move sub-steps of one pixel */
if ($ip >= -$EP) {
if ($dx + $xx > $xy || $dy + $yy < $xy) {
goto exits;
}
}
/* two x or y steps */
$y1 = 2 * $ex + $dx;
/* save value for test of y step */
if (2 * $ex + $dy > 0) {
/* x sub-step */
$fx--;
$ex += $dx += $xx;
$dy += $xy += $ac;
$yy += $bc;
$xx += $ab;
} else {
if ($y1 > 0) {
goto exits;
}
}
/* tiny nearly cusp */
if ($y1 <= 0) {
/* y sub-step */
$fy--;
$ex += $dy += $yy;
$dx += $xy += $bc;
$xx += $ac;
$yy += $ba;
}
} while ($fx > 0 && $fy > 0);
/* pixel complete? */
if (2 * $fy <= $f) {
/* x+ anti-aliasing pixel */
if ($py < $ed) {
$this->setPixel($gd, $x0 + $sx, $y0, $py / $ed);
}
/* plot curve */
$y0 += $sy;
$fy += $f;
/* y step */
}
if (2 * $fx <= $f) {
/* y+ anti-aliasing pixel */
if ($px < $ed) {
$this->setPixel($gd, $x0, $y2 + $sy, $px / $ed);
}
/* plot curve */
$x0 += $sx;
$fx += $f;
/* x step */
}
}
break;
/* finish curve by line */
exits:
if (2 * $ex < $dy && 2 * $fy <= $f + 2) {
/* round x+ approximation pixel */
if ($py < $ed) {
$this->setPixel($gd, $x0 + $sx, $y0, $py / $ed);
}
/* plot curve */
$y0 += $sy;
}
if (2 * $ex > $dx && 2 * $fx <= $f + 2) {
/* round y+ approximation pixel */
if ($px < $ed) {
$this->setPixel($gd, $x0, $y2 + $sy, $px / $ed);
}
/* plot curve */
$x0 += $sx;
}
$xx = $x0;
$x0 = $x3;
$x3 = $xx;
$sx = -$sx;
$xb = -$xb;
/* swap legs */
$yy = $y0;
$y0 = $y3;
$y3 = $yy;
$sy = -$sy;
$yb = -$yb;
$x1 = $x2;
} while ($leg--);
/* try other end */
$this->plotLine($gd, $x0, $y0, $x3, $y3);
/* remaining part in case of cusp or crunode */
}
