This class implements a perspective transform in two dimensions. Given four source and four * destination points, it will compute the transformation implied between them. The code is based * directly upon section 3.4.2 of George Wolberg's "Digital Image Warping"; see pages 54-56.

* * @author Sean Owen */ final class PerspectiveTransform { private $a11; private $a12; private $a13; private $a21; private $a22; private $a23; private $a31; private $a32; private $a33; private function __construct( $a11, $a21, $a31, $a12, $a22, $a32, $a13, $a23, $a33 ) { $this->a11 = $a11; $this->a12 = $a12; $this->a13 = $a13; $this->a21 = $a21; $this->a22 = $a22; $this->a23 = $a23; $this->a31 = $a31; $this->a32 = $a32; $this->a33 = $a33; } public static function quadrilateralToQuadrilateral( $x0, $y0, $x1, $y1, $x2, $y2, $x3, $y3, $x0p, $y0p, $x1p, $y1p, $x2p, $y2p, $x3p, $y3p ) { $qToS = self::quadrilateralToSquare($x0, $y0, $x1, $y1, $x2, $y2, $x3, $y3); $sToQ = self::squareToQuadrilateral($x0p, $y0p, $x1p, $y1p, $x2p, $y2p, $x3p, $y3p); return $sToQ->times($qToS); } public static function quadrilateralToSquare( $x0, $y0, $x1, $y1, $x2, $y2, $x3, $y3 ) { // Here, the adjoint serves as the inverse: return self::squareToQuadrilateral($x0, $y0, $x1, $y1, $x2, $y2, $x3, $y3)->buildAdjoint(); } public function buildAdjoint() { // Adjoint is the transpose of the cofactor matrix: return new PerspectiveTransform($this->a22 * $this->a33 - $this->a23 * $this->a32, $this->a23 * $this->a31 - $this->a21 * $this->a33, $this->a21 * $this->a32 - $this->a22 * $this->a31, $this->a13 * $this->a32 - $this->a12 * $this->a33, $this->a11 * $this->a33 - $this->a13 * $this->a31, $this->a12 * $this->a31 - $this->a11 * $this->a32, $this->a12 * $this->a23 - $this->a13 * $this->a22, $this->a13 * $this->a21 - $this->a11 * $this->a23, $this->a11 * $this->a22 - $this->a12 * $this->a21); } public static function squareToQuadrilateral( $x0, $y0, $x1, $y1, $x2, $y2, $x3, $y3 ) { $dx3 = $x0 - $x1 + $x2 - $x3; $dy3 = $y0 - $y1 + $y2 - $y3; if ($dx3 == 0.0 && $dy3 == 0.0) { // Affine return new PerspectiveTransform($x1 - $x0, $x2 - $x1, $x0, $y1 - $y0, $y2 - $y1, $y0, 0.0, 0.0, 1.0); } else { $dx1 = $x1 - $x2; $dx2 = $x3 - $x2; $dy1 = $y1 - $y2; $dy2 = $y3 - $y2; $denominator = $dx1 * $dy2 - $dx2 * $dy1; $a13 = ($dx3 * $dy2 - $dx2 * $dy3) / $denominator; $a23 = ($dx1 * $dy3 - $dx3 * $dy1) / $denominator; return new PerspectiveTransform($x1 - $x0 + $a13 * $x1, $x3 - $x0 + $a23 * $x3, $x0, $y1 - $y0 + $a13 * $y1, $y3 - $y0 + $a23 * $y3, $y0, $a13, $a23, 1.0); } } public function times($other) { return new PerspectiveTransform($this->a11 * $other->a11 + $this->a21 * $other->a12 + $this->a31 * $other->a13, $this->a11 * $other->a21 + $this->a21 * $other->a22 + $this->a31 * $other->a23, $this->a11 * $other->a31 + $this->a21 * $other->a32 + $this->a31 * $other->a33, $this->a12 * $other->a11 + $this->a22 * $other->a12 + $this->a32 * $other->a13, $this->a12 * $other->a21 + $this->a22 * $other->a22 + $this->a32 * $other->a23, $this->a12 * $other->a31 + $this->a22 * $other->a32 + $this->a32 * $other->a33, $this->a13 * $other->a11 + $this->a23 * $other->a12 + $this->a33 * $other->a13, $this->a13 * $other->a21 + $this->a23 * $other->a22 + $this->a33 * $other->a23, $this->a13 * $other->a31 + $this->a23 * $other->a32 + $this->a33 * $other->a33); } public function transformPoints(&$points, &$yValues = 0) { if ($yValues) { $this->transformPoints_($points, $yValues); return; } $max = count($points); $a11 = $this->a11; $a12 = $this->a12; $a13 = $this->a13; $a21 = $this->a21; $a22 = $this->a22; $a23 = $this->a23; $a31 = $this->a31; $a32 = $this->a32; $a33 = $this->a33; for ($i = 0; $i < $max; $i += 2) { $x = $points[$i]; $y = $points[$i + 1]; $denominator = $a13 * $x + $a23 * $y + $a33; $points[$i] = ($a11 * $x + $a21 * $y + $a31) / $denominator; $points[$i + 1] = ($a12 * $x + $a22 * $y + $a32) / $denominator; } } public function transformPoints_(&$xValues, &$yValues) { $n = count($xValues); for ($i = 0; $i < $n; $i++) { $x = $xValues[$i]; $y = $yValues[$i]; $denominator = $this->a13 * $x + $this->a23 * $y + $this->a33; $xValues[$i] = ($this->a11 * $x + $this->a21 * $y + $this->a31) / $denominator; $yValues[$i] = ($this->a12 * $x + $this->a22 * $y + $this->a32) / $denominator; } } }