* @copyright 2021 Smiley * @license Apache-2.0 */ namespace chillerlan\QRCode\Detector; use function count; /** *

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 float $a11; private float $a12; private float $a13; private float $a21; private float $a22; private float $a23; private float $a31; private float $a32; private float $a33; private function set( float $a11, float $a21, float $a31, float $a12, float $a22, float $a32, float $a13, float $a23, float $a33 ):self{ $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; return $this; } public function quadrilateralToQuadrilateral( float $x0, float $y0, float $x1, float $y1, float $x2, float $y2, float $x3, float $y3, float $x0p, float $y0p, float $x1p, float $y1p, float $x2p, float $y2p, float $x3p, float $y3p ):self{ return (new self) ->squareToQuadrilateral($x0p, $y0p, $x1p, $y1p, $x2p, $y2p, $x3p, $y3p) ->times($this->quadrilateralToSquare($x0, $y0, $x1, $y1, $x2, $y2, $x3, $y3)); } private function quadrilateralToSquare( float $x0, float $y0, float $x1, float $y1, float $x2, float $y2, float $x3, float $y3 ):self{ // Here, the adjoint serves as the inverse: return $this ->squareToQuadrilateral($x0, $y0, $x1, $y1, $x2, $y2, $x3, $y3) ->buildAdjoint(); } private function buildAdjoint():self{ // Adjoint is the transpose of the cofactor matrix: return $this->set( $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 ); } private function squareToQuadrilateral( float $x0, float $y0, float $x1, float $y1, float $x2, float $y2, float $x3, float $y3 ):self{ $dx3 = $x0 - $x1 + $x2 - $x3; $dy3 = $y0 - $y1 + $y2 - $y3; if($dx3 === 0.0 && $dy3 === 0.0){ // Affine return $this->set($x1 - $x0, $x2 - $x1, $x0, $y1 - $y0, $y2 - $y1, $y0, 0.0, 0.0, 1.0); } $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 $this->set( $x1 - $x0 + $a13 * $x1, $x3 - $x0 + $a23 * $x3, $x0, $y1 - $y0 + $a13 * $y1, $y3 - $y0 + $a23 * $y3, $y0, $a13, $a23, 1.0 ); } private function times(PerspectiveTransform $other):self{ return $this->set( $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 * $other->a33 ); } public function transformPoints(array &$xValues, array &$yValues = null):void{ $max = count($xValues); if($yValues !== null){ for($i = 0; $i < $max; $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) / $denominator; } return; } for($i = 0; $i < $max; $i += 2){ $x = $xValues[$i]; $y = $xValues[$i + 1]; $denominator = $this->a13 * $x + $this->a23 * $y + $this->a33; $xValues[$i] = ($this->a11 * $x + $this->a21 * $y + $this->a31) / $denominator; $xValues[$i + 1] = ($this->a12 * $x + $this->a22 * $y + $this->a32) / $denominator; } } }