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<?php |
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namespace Samsara\Fermat\Coordinates\Values; |
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use ReflectionException; |
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use Samsara\Exceptions\SystemError\LogicalError\IncompatibleObjectState; |
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use Samsara\Exceptions\UsageError\IntegrityConstraint; |
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use Samsara\Exceptions\UsageError\OptionalExit; |
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use Samsara\Fermat\Core\Numbers; |
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use Samsara\Fermat\Coordinates\Types\Base\Interfaces\Coordinates\CoordinateInterface; |
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use Samsara\Fermat\Coordinates\Types\Base\Interfaces\Coordinates\ThreeDCoordinateInterface; |
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use Samsara\Fermat\Coordinates\Types\Base\Interfaces\Coordinates\TwoDCoordinateInterface; |
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use Samsara\Fermat\Coordinates\Types\Coordinate; |
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use Samsara\Fermat\Core\Values\ImmutableDecimal; |
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class CartesianCoordinate extends Coordinate implements TwoDCoordinateInterface, ThreeDCoordinateInterface |
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{ |
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/** |
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* CartesianCoordinate constructor. |
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* |
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* @param $x |
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* @param null $y |
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* @param null $z |
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*/ |
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public function __construct($x, $y = null, $z = null) |
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{ |
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$data = [ |
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'x' => $x |
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]; |
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if (!is_null($y)) { |
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$data['y'] = $y; |
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if (!is_null($z)) { |
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$data['z'] = $z; |
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} |
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} else if (!is_null($z)) { |
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$data['y'] = $z; |
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} |
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parent::__construct($data); |
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if (!array_key_exists('y', $this->parameters)) { |
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$this->parameters['y'] = 1; |
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} |
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if (!array_key_exists('z', $this->parameters)) { |
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$this->parameters['z'] = 2; |
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} |
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} |
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/** |
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* @param $axis |
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* |
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* @return ImmutableDecimal |
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* @throws ReflectionException |
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* @throws IntegrityConstraint |
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*/ |
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public function getAxis($axis): ImmutableDecimal |
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{ |
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if (is_int($axis)) { |
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$axisIndex = $axis; |
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} else { |
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$axisIndex = $this->parameters[$axis]; |
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} |
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if (!$this->values->hasIndex($axisIndex)) { |
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return Numbers::makeZero(); |
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} |
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return $this->getAxisByIndex($axisIndex); |
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} |
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/** |
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* @return ImmutableDecimal |
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*/ |
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public function getDistanceFromOrigin(?int $scale = null): ImmutableDecimal |
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{ |
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$scale = $scale ?? 10; |
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$intScale = $scale + 2; |
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$x = 0; |
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if ($this->numberOfDimensions() > 1) { |
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$y = 0; |
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} else { |
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$y = null; |
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} |
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if ($this->numberOfDimensions() > 2) { |
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$z = 0; |
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} else { |
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$z = null; |
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} |
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return $this->distanceTo(new CartesianCoordinate($x, $y, $z), $intScale)->roundToScale($scale); |
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} |
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/** |
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* @param CoordinateInterface $coordinate |
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* |
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* @return ImmutableDecimal |
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* @throws IntegrityConstraint |
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* @throws ReflectionException |
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*/ |
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public function distanceTo(CoordinateInterface $coordinate, ?int $scale = null): ImmutableDecimal |
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{ |
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$scale = $scale ?? 10; |
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$intScale = $scale + 2; |
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if (!($coordinate instanceof CartesianCoordinate)) { |
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$coordinate = $coordinate->asCartesian(); |
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} |
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$n = Numbers::makeZero($intScale); |
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$firstValues = ($this->numberOfDimensions() >= $coordinate->numberOfDimensions()) ? $this->axesValues() : $coordinate->axesValues(); |
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$secondValues = ($this->numberOfDimensions() >= $coordinate->numberOfDimensions()) ? $coordinate->axesValues() : $this->axesValues(); |
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foreach ($firstValues as $index => $value) { |
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$n = $n->add($secondValues[$index]->subtract($value)->pow(2)); |
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} |
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return $n->sqrt($intScale)->roundToScale($scale); |
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} |
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/** |
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* @return CartesianCoordinate |
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*/ |
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public function asCartesian(): CartesianCoordinate |
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{ |
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return $this; |
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} |
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/** |
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* @return ImmutableDecimal |
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* @throws IncompatibleObjectState |
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*/ |
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public function getPolarAngle(): ImmutableDecimal |
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{ |
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if ($this->numberOfDimensions() === 2) { |
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return $this->asPolar()->getPolarAngle(); |
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} |
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if ($this->numberOfDimensions() === 3) { |
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return $this->asSpherical()->getPolarAngle(); |
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} |
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throw new IncompatibleObjectState( |
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'Can only get a polar angle for a CartesianCoordinate of 2 or 3 dimensions.', |
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'Ensure the CartesianCoordinate has 2 or 3 dimensions.', |
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'Cannot get the polar angle for a CartesianCoordinate unless it has exactly 2 or 3 dimensions.' |
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); |
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} |
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/** |
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* @return ImmutableDecimal |
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* @throws IncompatibleObjectState |
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*/ |
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public function getPlanarAngle(): ImmutableDecimal |
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{ |
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if ($this->numberOfDimensions() === 2) { |
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return $this->getPolarAngle(); |
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} |
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if ($this->numberOfDimensions() === 3) { |
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return $this->asSpherical()->getPlanarAngle(); |
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} |
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throw new IncompatibleObjectState( |
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'Can only get a polar angle for a CartesianCoordinate of 2 or 3 dimensions.', |
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'Ensure the CartesianCoordinate has 2 or 3 dimensions.', |
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'Cannot get the polar angle for a CartesianCoordinate unless it has exactly 2 or 3 dimensions.' |
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); |
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} |
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/** |
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* @return SphericalCoordinate |
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* @throws IncompatibleObjectState |
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*/ |
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public function asSpherical(): SphericalCoordinate |
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{ |
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if ($this->numberOfDimensions() !== 3) { |
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throw new IncompatibleObjectState( |
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'Can only get SphericalCoordinate for a CartesianCoordinate of 3 dimensions.', |
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'Ensure the CartesianCoordinate has 3 dimensions.', |
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'Cannot get the SphericalCoordinate for a CartesianCoordinate unless it has exactly 3 dimensions.' |
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); |
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} |
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$rho = $this->getDistanceFromOrigin(); |
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$theta = $this->getAxis('y')->divide($this->getAxis('x'))->arctan(); |
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$phi = $this->getAxis('z')->divide($rho)->arccos(); |
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return new SphericalCoordinate($rho, $theta, $phi); |
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} |
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/** |
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* @return CylindricalCoordinate |
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* @throws IncompatibleObjectState |
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* @throws IntegrityConstraint |
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* @throws ReflectionException |
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*/ |
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public function asCylindrical(): CylindricalCoordinate |
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{ |
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if ($this->numberOfDimensions() !== 3) { |
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throw new IncompatibleObjectState( |
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'Can only get CylindricalCoordinate for a CartesianCoordinate of 3 dimensions.', |
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'Ensure the CartesianCoordinate has 3 dimensions.', |
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'Cannot get the CylindricalCoordinate for a CartesianCoordinate unless it has exactly 3 dimensions.' |
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); |
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} |
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$z = $this->getAxis('z'); |
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$r = $this->distanceTo(new CartesianCoordinate(0, 0, $z)); |
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$theta = $this->getAxis('y')->divide($this->getAxis('x'))->arctan(); |
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return new CylindricalCoordinate($r, $theta, $z); |
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} |
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/** |
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* @param int|null $scale |
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* @return PolarCoordinate |
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* @throws IncompatibleObjectState |
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* @throws IntegrityConstraint |
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* @throws OptionalExit |
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*/ |
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public function asPolar(?int $scale = null): PolarCoordinate |
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{ |
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$scale = $scale ?? 10; |
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$intScale = $scale + 3; |
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if ($this->numberOfDimensions() !== 2) { |
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throw new IncompatibleObjectState( |
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'Can only get PolarCoordinate for a CartesianCoordinate of 2 dimensions.', |
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'Ensure the CartesianCoordinate has 2 dimensions.', |
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'Cannot get the PolarCoordinate for a CartesianCoordinate unless it has exactly 2 dimensions.' |
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); |
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} |
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$rho = $this->getDistanceFromOrigin($intScale); |
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if ($rho->isEqual(0)) { |
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throw new OptionalExit( |
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'Attempted to convert a CartesianCoordinate at the origin into PolarCoordinate', |
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'Do not attempt to do this.', |
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'The origin has an undefined polar angle in the polar coordinate system.' |
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); |
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} |
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if ($this->getAxis('x')->isEqual(0)) { |
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$theta = Numbers::makePi($intScale)->divide(2); |
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if ($this->getAxis('y')->isNegative()) { |
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$theta = $theta->multiply(-1); |
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} |
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} else { |
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/** @var ImmutableDecimal $theta */ |
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$theta = $this->getAxis('y')->divide($this->getAxis('x'), $intScale)->arctan($intScale); |
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} |
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return new PolarCoordinate($rho->roundToScale($scale), $theta->roundToScale($scale)); |
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} |
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} |