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File Content: EllipticArc.php

<?php
declare(strict_types = 1);

namespace BaconQrCode\Renderer\Path;

final class EllipticArc implements OperationInterface
{
    private const ZERO_TOLERANCE = 1e-05;

/**
     * @var float
     */
    private $xRadius;

/**
     * @var float
     */
    private $yRadius;

/**
     * @var float
     */
    private $xAxisAngle;

/**
     * @var bool
     */
    private $largeArc;

/**
     * @var bool
     */
    private $sweep;

/**
     * @var float
     */
    private $x;

/**
     * @var float
     */
    private $y;

public function __construct(
        float $xRadius,
        float $yRadius,
        float $xAxisAngle,
        bool $largeArc,
        bool $sweep,
        float $x,
        float $y
    ) {
        $this->xRadius = abs($xRadius);
        $this->yRadius = abs($yRadius);
        $this->xAxisAngle = $xAxisAngle % 360;
        $this->largeArc = $largeArc;
        $this->sweep = $sweep;
        $this->x = $x;
        $this->y = $y;
    }

public function getXRadius() : float
    {
        return $this->xRadius;
    }

public function getYRadius() : float
    {
        return $this->yRadius;
    }

public function getXAxisAngle() : float
    {
        return $this->xAxisAngle;
    }

public function isLargeArc() : bool
    {
        return $this->largeArc;
    }

public function isSweep() : bool
    {
        return $this->sweep;
    }

public function getX() : float
    {
        return $this->x;
    }

public function getY() : float
    {
        return $this->y;
    }

/**
     * @return self
     */
    public function translate(float $x, float $y) : OperationInterface
    {
        return new self(
            $this->xRadius,
            $this->yRadius,
            $this->xAxisAngle,
            $this->largeArc,
            $this->sweep,
            $this->x + $x,
            $this->y + $y
        );
    }

/**
     * Converts the elliptic arc to multiple curves.
     *
     * Since not all image back ends support elliptic arcs, this method allows to convert the arc into multiple curves
     * resembling the same result.
     *
     * @see https://mortoray.com/2017/02/16/rendering-an-svg-elliptical-arc-as-bezier-curves/
     * @return array<Curve|Line>
     */
    public function toCurves(float $fromX, float $fromY) : array
    {
        if (sqrt(($fromX - $this->x) ** 2 + ($fromY - $this->y) ** 2) < self::ZERO_TOLERANCE) {
            return [];
        }

if ($this->xRadius < self::ZERO_TOLERANCE || $this->yRadius < self::ZERO_TOLERANCE) {
            return [new Line($this->x, $this->y)];
        }

return $this->createCurves($fromX, $fromY);
    }

/**
     * @return Curve[]
     */
    private function createCurves(float $fromX, float $fromY) : array
    {
        $xAngle = deg2rad($this->xAxisAngle);
        list($centerX, $centerY, $radiusX, $radiusY, $startAngle, $deltaAngle) =
            $this->calculateCenterPointParameters($fromX, $fromY, $xAngle);

$s = $startAngle;
        $e = $s + $deltaAngle;
        $sign = ($e < $s) ? -1 : 1;
        $remain = abs($e - $s);
        $p1 = self::point($centerX, $centerY, $radiusX, $radiusY, $xAngle, $s);
        $curves = [];

while ($remain > self::ZERO_TOLERANCE) {
            $step = min($remain, pi() / 2);
            $signStep = $step * $sign;
            $p2 = self::point($centerX, $centerY, $radiusX, $radiusY, $xAngle, $s + $signStep);

$alphaT = tan($signStep / 2);
            $alpha = sin($signStep) * (sqrt(4 + 3 * $alphaT ** 2) - 1) / 3;
            $d1 = self::derivative($radiusX, $radiusY, $xAngle, $s);
            $d2 = self::derivative($radiusX, $radiusY, $xAngle, $s + $signStep);

$curves[] = new Curve(
                $p1[0] + $alpha * $d1[0],
                $p1[1] + $alpha * $d1[1],
                $p2[0] - $alpha * $d2[0],
                $p2[1] - $alpha * $d2[1],
                $p2[0],
                $p2[1]
            );

$s += $signStep;
            $remain -= $step;
            $p1 = $p2;
        }

return $curves;
    }

/**
     * @return float[]
     */
    private function calculateCenterPointParameters(float $fromX, float $fromY, float $xAngle)
    {
        $rX = $this->xRadius;
        $rY = $this->yRadius;

// F.6.5.1
        $dx2 = ($fromX - $this->x) / 2;
        $dy2 = ($fromY - $this->y) / 2;
        $x1p = cos($xAngle) * $dx2 + sin($xAngle) * $dy2;
        $y1p = -sin($xAngle) * $dx2 + cos($xAngle) * $dy2;

// F.6.5.2
        $rxs = $rX ** 2;
        $rys = $rY ** 2;
        $x1ps = $x1p ** 2;
        $y1ps = $y1p ** 2;
        $cr = $x1ps / $rxs + $y1ps / $rys;

if ($cr > 1) {
            $s = sqrt($cr);
            $rX *= $s;
            $rY *= $s;
            $rxs = $rX ** 2;
            $rys = $rY ** 2;
        }

$dq = ($rxs * $y1ps + $rys * $x1ps);
        $pq = ($rxs * $rys - $dq) / $dq;
        $q = sqrt(max(0, $pq));

if ($this->largeArc === $this->sweep) {
            $q = -$q;
        }

$cxp = $q * $rX * $y1p / $rY;
        $cyp = -$q * $rY * $x1p / $rX;

// F.6.5.3
        $cx = cos($xAngle) * $cxp - sin($xAngle) * $cyp + ($fromX + $this->x) / 2;
        $cy = sin($xAngle) * $cxp + cos($xAngle) * $cyp + ($fromY + $this->y) / 2;

// F.6.5.5
        $theta = self::angle(1, 0, ($x1p - $cxp) / $rX, ($y1p - $cyp) / $rY);

// F.6.5.6
        $delta = self::angle(($x1p - $cxp) / $rX, ($y1p - $cyp) / $rY, (-$x1p - $cxp) / $rX, (-$y1p - $cyp) / $rY);
        $delta = fmod($delta, pi() * 2);

if (! $this->sweep) {
            $delta -= 2 * pi();
        }

return [$cx, $cy, $rX, $rY, $theta, $delta];
    }

private static function angle(float $ux, float $uy, float $vx, float $vy) : float
    {
        // F.6.5.4
        $dot = $ux * $vx + $uy * $vy;
        $length = sqrt($ux ** 2 + $uy ** 2) * sqrt($vx ** 2 + $vy ** 2);
        $angle = acos(min(1, max(-1, $dot / $length)));

if (($ux * $vy - $uy * $vx) < 0) {
            return -$angle;
        }

return $angle;
    }

/**
     * @return float[]
     */
    private static function point(
        float $centerX,
        float $centerY,
        float $radiusX,
        float $radiusY,
        float $xAngle,
        float $angle
    ) : array {
        return [
            $centerX + $radiusX * cos($xAngle) * cos($angle) - $radiusY * sin($xAngle) * sin($angle),
            $centerY + $radiusX * sin($xAngle) * cos($angle) + $radiusY * cos($xAngle) * sin($angle),
        ];
    }

/**
     * @return float[]
     */
    private static function derivative(float $radiusX, float $radiusY, float $xAngle, float $angle) : array
    {
        return [
            -$radiusX * cos($xAngle) * sin($angle) - $radiusY * sin($xAngle) * cos($angle),
            -$radiusX * sin($xAngle) * sin($angle) + $radiusY * cos($xAngle) * cos($angle),
        ];
    }
}

Name	Size	Permission
Close.php	504 bytes	0644
Curve.php	1469 bytes	0644
EllipticArc.php	6995 bytes	0644
Line.php	656 bytes	0644
Move.php	656 bytes	0644
OperationInterface.php	226 bytes	0644
Path.php	2468 bytes	0644