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<?php
/**
* Class PerspectiveTransform
*
* @created 17.01.2021
* @author ZXing Authors
* @author Smiley <smiley@chillerlan.net>
* @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;
}
/**
* @SuppressWarnings(PHPMD.ExcessiveParameterList)
*/
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 * $other->a33)
);
}
/**
* @return array[] [$xValues, $yValues]
*/
public function transformPoints(array $xValues, ?array $yValues = null):array{
$max = count($xValues);
if($yValues !== null){ // unused
for($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) / $denominator);
}
return [$xValues, $yValues];
}
for($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) / $denominator);
}
return [$xValues, []];
}
}
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