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nstdio/Bezier.php

Last active January 21, 2017 14:27
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Bezier curves bounding box.
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Bezier.php
<?php
/**
* Class Bezier
*
* @package nstdio\svg\util
* @author Edgar Asatryan <nstdio@gmail.com>
*/
class Bezier
{
const EPSILON = 0.00001;
public static function quadraticBBox($p0x, $p0y, $p1x, $p1y, $p2x, $p2y)
{
$devx = $p0x + $p2x - 2 * $p1x;
$devy = $p0y + $p2y - 2 * $p1y;
self::avoidDivisionByZero($devy);
self::avoidDivisionByZero($devx);
$tx = ($p0x - $p1x) / $devx;
$ty = ($p0y - $p1y) / $devy;
self::checkBezierInterval($tx);
self::checkBezierInterval($ty);
$txByTX = self::getQuadraticValue($tx, $p0x, $p1x, $p2x);
$tyByTX = self::getQuadraticValue($tx, $p0y, $p1y, $p2y);
$txByTY = self::getQuadraticValue($ty, $p0x, $p1x, $p2x);
$tyByTY = self::getQuadraticValue($ty, $p0y, $p1y, $p2y);
$x1 = min($txByTX, $p0x, $p2x, $txByTY);
$y1 = min($tyByTX, $p0y, $p2y, $tyByTY);
$x2 = max($txByTX, $p0x, $p2x, $txByTY);
$y2 = max($tyByTX, $p0y, $p2y, $tyByTY);
return [
'width' => $x2 - min($x2, $x1),
'height' => max($y2, $y1) - min($y2, $y1),
'x' => min($x2, $x1),
'y' => min($y2, $y1),
];
}
public static function cubicBBox($p0x, $p0y, $p1x, $p1y, $p2x, $p2y, $p3x, $p3y)
{
$ax = $p3x - $p0x + 3 * ($p1x - $p2x);
$bx = 2 * ($p0x - 2 * $p1x + $p2x);
$cx = $p1x - $p0x;
$ay = $p3y - $p0y + 3 * ($p1y - $p2y);
$by = 2 * ($p0y - 2 * $p1y + $p2y);
$cy = $p1y - $p0y;
$txRoots = self::getRoots($ax, $bx, $cx);
$tyRoots = self::getRoots($ay, $by, $cy);
$tv0x = self::getCubicValue(0, $p0x, $p1x, $p2x, $p3x);
$tv1x = self::getCubicValue($txRoots[0], $p0x, $p1x, $p2x, $p3x);
$tv2x = self::getCubicValue($txRoots[1], $p0x, $p1x, $p2x, $p3x);
$tv3x = self::getCubicValue(1, $p0x, $p1x, $p2x, $p3x);
$tv0y = self::getCubicValue(0, $p0y, $p1y, $p2y, $p3y);
$tv1y = self::getCubicValue($tyRoots[0], $p0y, $p1y, $p2y, $p3y);
$tv2y = self::getCubicValue($tyRoots[1], $p0y, $p1y, $p2y, $p3y);
$tv3y = self::getCubicValue(1, $p0y, $p1y, $p2y, $p3y);
$x1 = min($tv0x, $tv1x, $tv2x, $tv3x, $p0x, $p3x);
$y1 = min($tv0y, $tv1y, $tv2y, $tv3y, $p0y, $p3y);
$x2 = max($tv0x, $tv1x, $tv2x, $tv3x, $p0x, $p3x);
$y2 = max($tv0y, $tv1y, $tv2y, $tv3y, $p0y, $p3y);
return [
'width' => $x2 - min($x2, $x1),
'height' => max($y2, $y1) - min($y2, $y1),
'x' => min($x2, $x1),
'y' => min($y2, $y1),
];
}
private static function getRoots($a, $b, $c)
{
$dis = $b * $b - 4 * $a * $c;
if ($dis < 0) {
return null;
}
self::avoidDivisionByZero($a);
$disSqrt = sqrt($dis);
$root1 = (-$b + $disSqrt) / (2 * $a);
$root2 = (-$b - $disSqrt) / (2 * $a);
self::checkBezierInterval($root1);
self::checkBezierInterval($root2);
return [$root1, $root2];
}
private static function getCubicValue($t, $p0, $p1, $p2, $p3)
{
$omt = 1 - $t;
$value = $p0 * $omt * $omt *$omt +
3 * $p1 * $t * $omt * $omt +
3 * $p2 * $t * $t * $omt +
$p3 * $t * $t * $t;
return $value;
}
/**
* @param $value
*/
private static function avoidDivisionByZero(&$value)
{
if ($value === 0) {
$value = self::EPSILON;
}
}
/**
* @param $t
*/
private static function checkBezierInterval(&$t)
{
if ($t > 1 || $t < 0) {
$t = 0;
}
}
/**
* @param $t
* @param $p0x
* @param $p1x
* @param $p2x
*
* @return mixed
*/
private static function getQuadraticValue($t, $p0x, $p1x, $p2x)
{
$omt = 1 - $t;
return $p0x * $omt * $omt + 2 * $t * $p1x * $omt + $p2x * $t * $t;
}
}
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