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<?php |
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/** |
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* PHPCoord. |
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* |
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* @author Doug Wright |
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*/ |
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declare(strict_types=1); |
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namespace PHPCoord; |
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use function abs; |
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use function asinh; |
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use function atan; |
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use function atan2; |
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use function atanh; |
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use function cos; |
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use function cosh; |
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use DateTime; |
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use DateTimeImmutable; |
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use DateTimeInterface; |
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use function get_class; |
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use function implode; |
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use InvalidArgumentException; |
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use function is_nan; |
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use function log; |
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use function max; |
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use PHPCoord\CoordinateOperation\AutoConversion; |
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use PHPCoord\CoordinateOperation\ComplexNumber; |
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use PHPCoord\CoordinateOperation\GeocentricValue; |
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use PHPCoord\CoordinateOperation\GeographicValue; |
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use PHPCoord\CoordinateReferenceSystem\Compound; |
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use PHPCoord\CoordinateReferenceSystem\Geocentric; |
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use PHPCoord\CoordinateReferenceSystem\Geographic; |
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use PHPCoord\CoordinateReferenceSystem\Geographic2D; |
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use PHPCoord\CoordinateReferenceSystem\Geographic3D; |
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use PHPCoord\CoordinateReferenceSystem\Projected; |
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use PHPCoord\CoordinateSystem\Axis; |
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use PHPCoord\Datum\Ellipsoid; |
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use PHPCoord\Exception\InvalidCoordinateReferenceSystemException; |
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use PHPCoord\Exception\UnknownAxisException; |
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use PHPCoord\UnitOfMeasure\Angle\Angle; |
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use PHPCoord\UnitOfMeasure\Angle\ArcSecond; |
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use PHPCoord\UnitOfMeasure\Angle\Degree; |
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use PHPCoord\UnitOfMeasure\Angle\Radian; |
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use PHPCoord\UnitOfMeasure\Length\Length; |
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use PHPCoord\UnitOfMeasure\Length\Metre; |
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use PHPCoord\UnitOfMeasure\Scale\Coefficient; |
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use PHPCoord\UnitOfMeasure\Scale\Scale; |
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use PHPCoord\UnitOfMeasure\Scale\Unity; |
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use function sin; |
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use function sinh; |
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use function sprintf; |
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use function sqrt; |
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use function tan; |
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use TypeError; |
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/** |
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* Coordinate representing a point on an ellipsoid. |
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*/ |
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class GeographicPoint extends Point |
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{ |
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use AutoConversion; |
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/** |
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* Latitude. |
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*/ |
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protected Angle $latitude; |
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/** |
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* Longitude. |
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*/ |
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protected Angle $longitude; |
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/** |
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* Height above ellipsoid (N.B. *not* height above ground, sea-level or anything else tangible). |
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*/ |
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protected ?Length $height; |
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/** |
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* Coordinate reference system. |
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*/ |
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protected Geographic $crs; |
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/** |
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* Coordinate epoch (date for which the specified coordinates represented this point). |
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*/ |
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protected ?DateTimeImmutable $epoch; |
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protected function __construct(Angle $latitude, Angle $longitude, ?Length $height, Geographic $crs, ?DateTimeInterface $epoch = null) |
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{ |
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if (!$crs instanceof Geographic2D && !$crs instanceof Geographic3D) { |
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throw new TypeError(sprintf("A geographic point must be associated with a geographic CRS, but a '%s' CRS was given", get_class($crs))); |
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} |
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if ($crs instanceof Geographic2D && $height !== null) { |
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throw new InvalidCoordinateReferenceSystemException('A 2D geographic point must not include a height'); |
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} |
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if ($crs instanceof Geographic3D && $height === null) { |
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throw new InvalidCoordinateReferenceSystemException('A 3D geographic point must include a height, none given'); |
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} |
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$this->crs = $crs; |
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$this->latitude = Angle::convert($latitude, $this->getAxisByName(Axis::GEODETIC_LATITUDE)->getUnitOfMeasureId()); |
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$this->longitude = Angle::convert($longitude, $this->getAxisByName(Axis::GEODETIC_LONGITUDE)->getUnitOfMeasureId()); |
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if ($height) { |
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$this->height = Length::convert($height, $this->getAxisByName(Axis::ELLIPSOIDAL_HEIGHT)->getUnitOfMeasureId()); |
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} else { |
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$this->height = null; |
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} |
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if ($epoch instanceof DateTime) { |
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$epoch = DateTimeImmutable::createFromMutable($epoch); |
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} |
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$this->epoch = $epoch; |
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} |
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/** |
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* @param Angle $latitude refer to CRS for preferred unit of measure, but any angle unit accepted |
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* @param Angle $longitude refer to CRS for preferred unit of measure, but any angle unit accepted |
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* @param ?Length $height refer to CRS for preferred unit of measure, but any length unit accepted |
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*/ |
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public static function create(Angle $latitude, Angle $longitude, ?Length $height, Geographic $crs, ?DateTimeInterface $epoch = null): self |
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{ |
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return new static($latitude, $longitude, $height, $crs, $epoch); |
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} |
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public function getLatitude(): Angle |
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{ |
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return $this->latitude; |
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} |
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public function getLongitude(): Angle |
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{ |
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return $this->longitude; |
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} |
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public function getHeight(): ?Length |
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{ |
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return $this->height; |
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} |
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public function getCRS(): Geographic |
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{ |
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return $this->crs; |
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} |
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public function getCoordinateEpoch(): ?DateTimeImmutable |
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{ |
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return $this->epoch; |
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} |
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/** |
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* Calculate surface distance between two points. |
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*/ |
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public function calculateDistance(Point $to): Length |
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{ |
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if ($to->getCRS()->getSRID() !== $this->crs->getSRID()) { |
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throw new InvalidArgumentException('Can only calculate distances between two points in the same CRS'); |
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} |
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//Mean radius definition taken from Wikipedia |
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/** @var Ellipsoid $ellipsoid */ |
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$ellipsoid = $this->getCRS()->getDatum()->getEllipsoid(); |
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$radius = ((2 * $ellipsoid->getSemiMajorAxis()->asMetres()->getValue()) + $ellipsoid->getSemiMinorAxis()->asMetres()->getValue()) / 3; |
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return new Metre(self::acos(sin($this->latitude->asRadians()->getValue()) * sin($to->latitude->asRadians()->getValue()) + cos($this->latitude->asRadians()->getValue()) * cos($to->latitude->asRadians()->getValue()) * cos($to->longitude->asRadians()->getValue() - $this->longitude->asRadians()->getValue())) * $radius); |
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} |
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public function __toString(): string |
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{ |
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$values = []; |
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foreach ($this->getCRS()->getCoordinateSystem()->getAxes() as $axis) { |
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if ($axis->getName() === Axis::GEODETIC_LATITUDE) { |
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$values[] = $this->latitude; |
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} elseif ($axis->getName() === Axis::GEODETIC_LONGITUDE) { |
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$values[] = $this->longitude; |
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} elseif ($axis->getName() === Axis::ELLIPSOIDAL_HEIGHT) { |
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$values[] = $this->height; |
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} else { |
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throw new UnknownAxisException(); // @codeCoverageIgnore |
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} |
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} |
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return '(' . implode(', ', $values) . ')'; |
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} |
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/** |
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* Geographic/geocentric conversions |
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* In applications it is often concatenated with the 3- 7- or 10-parameter transformations 9603, 9606, 9607 or |
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* 9636 to form a geographic to geographic transformation. |
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*/ |
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public function geographicGeocentric( |
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Geocentric $to |
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): GeocentricPoint { |
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$geographicValue = new GeographicValue($this->latitude, $this->longitude, $this->height, $this->crs->getDatum()); |
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$asGeocentric = $geographicValue->asGeocentricValue(); |
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return GeocentricPoint::create($asGeocentric->getX(), $asGeocentric->getY(), $asGeocentric->getZ(), $to, $this->epoch); |
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} |
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/** |
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* Coordinate Frame rotation (geog2D/geog3D domain) |
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* Note the analogy with the Position Vector tfm (codes 9606/1037) but beware of the differences! The Position Vector |
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* convention is used by IAG and recommended by ISO 19111. See methods 1032/1038/9607 for similar tfms operating |
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* between other CRS types. |
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*/ |
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public function coordinateFrameRotation( |
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Geographic $to, |
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Length $xAxisTranslation, |
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Length $yAxisTranslation, |
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Length $zAxisTranslation, |
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Angle $xAxisRotation, |
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Angle $yAxisRotation, |
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Angle $zAxisRotation, |
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Scale $scaleDifference |
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): self { |
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return $this->coordinateFrameMolodenskyBadekas( |
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$to, |
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$xAxisTranslation, |
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$yAxisTranslation, |
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$zAxisTranslation, |
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$xAxisRotation, |
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$yAxisRotation, |
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$zAxisRotation, |
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$scaleDifference, |
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new Metre(0), |
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2 |
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new Metre(0), |
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new Metre(0) |
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); |
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} |
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/** |
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* Molodensky-Badekas (CF geog2D/geog3D domain) |
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* See method codes 1034 and 1039/9636 for this operation in other coordinate domains and method code 1062/1063 for the |
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* opposite rotation convention in geographic 2D domain. |
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*/ |
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4 |
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public function coordinateFrameMolodenskyBadekas( |
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Geographic $to, |
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Length $xAxisTranslation, |
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Length $yAxisTranslation, |
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Length $zAxisTranslation, |
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Angle $xAxisRotation, |
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Angle $yAxisRotation, |
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Angle $zAxisRotation, |
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Scale $scaleDifference, |
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Length $ordinate1OfEvaluationPoint, |
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Length $ordinate2OfEvaluationPoint, |
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Length $ordinate3OfEvaluationPoint |
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): self { |
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$geographicValue = new GeographicValue($this->latitude, $this->longitude, $this->height, $this->crs->getDatum()); |
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4 |
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$asGeocentric = $geographicValue->asGeocentricValue(); |
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255
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256
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4 |
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$xs = $asGeocentric->getX()->asMetres()->getValue(); |
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4 |
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$ys = $asGeocentric->getY()->asMetres()->getValue(); |
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4 |
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$zs = $asGeocentric->getZ()->asMetres()->getValue(); |
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4 |
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$tx = $xAxisTranslation->asMetres()->getValue(); |
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4 |
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$ty = $yAxisTranslation->asMetres()->getValue(); |
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4 |
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$tz = $zAxisTranslation->asMetres()->getValue(); |
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4 |
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$rx = $xAxisRotation->asRadians()->getValue(); |
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4 |
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$ry = $yAxisRotation->asRadians()->getValue(); |
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4 |
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$rz = $zAxisRotation->asRadians()->getValue(); |
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4 |
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$M = 1 + $scaleDifference->asUnity()->getValue(); |
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4 |
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$xp = $ordinate1OfEvaluationPoint->asMetres()->getValue(); |
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4 |
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$yp = $ordinate2OfEvaluationPoint->asMetres()->getValue(); |
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4 |
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$zp = $ordinate3OfEvaluationPoint->asMetres()->getValue(); |
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270
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4 |
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$xt = $M * ((($xs - $xp) * 1) + (($ys - $yp) * $rz) + (($zs - $zp) * -$ry)) + $tx + $xp; |
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4 |
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$yt = $M * ((($xs - $xp) * -$rz) + (($ys - $yp) * 1) + (($zs - $zp) * $rx)) + $ty + $yp; |
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4 |
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$zt = $M * ((($xs - $xp) * $ry) + (($ys - $yp) * -$rx) + (($zs - $zp) * 1)) + $tz + $zp; |
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4 |
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$newGeocentric = new GeocentricValue(new Metre($xt), new Metre($yt), new Metre($zt), $to->getDatum()); |
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4 |
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$newGeographic = $newGeocentric->asGeographicValue(); |
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276
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4 |
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return static::create($newGeographic->getLatitude(), $newGeographic->getLongitude(), $to instanceof Geographic3D ? $newGeographic->getHeight() : null, $to, $this->epoch); |
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} |
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278
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279
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/** |
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280
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* Position Vector transformation (geog2D/geog3D domain) |
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281
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* Note the analogy with the Coordinate Frame rotation (code 9607/1038) but beware of the differences! The Position |
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* Vector convention is used by IAG and recommended by ISO 19111. See methods 1033/1037/9606 for similar tfms |
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* operating between other CRS types. |
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284
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*/ |
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285
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4 |
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public function positionVectorTransformation( |
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286
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Geographic $to, |
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287
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Length $xAxisTranslation, |
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288
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Length $yAxisTranslation, |
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289
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Length $zAxisTranslation, |
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290
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Angle $xAxisRotation, |
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Angle $yAxisRotation, |
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292
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Angle $zAxisRotation, |
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293
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Scale $scaleDifference |
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294
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): self { |
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295
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4 |
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return $this->positionVectorMolodenskyBadekas( |
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296
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4 |
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$to, |
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297
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|
|
$xAxisTranslation, |
|
298
|
|
|
$yAxisTranslation, |
|
299
|
|
|
$zAxisTranslation, |
|
300
|
|
|
$xAxisRotation, |
|
301
|
|
|
$yAxisRotation, |
|
302
|
|
|
$zAxisRotation, |
|
303
|
|
|
$scaleDifference, |
|
304
|
4 |
|
new Metre(0), |
|
305
|
4 |
|
new Metre(0), |
|
306
|
4 |
|
new Metre(0) |
|
307
|
|
|
); |
|
308
|
|
|
} |
|
309
|
|
|
|
|
310
|
|
|
/** |
|
311
|
|
|
* Molodensky-Badekas (PV geog2D/geog3D domain) |
|
312
|
|
|
* See method codes 1061 and 1062/1063 for this operation in other coordinate domains and method code 1039/9636 for opposite |
|
313
|
|
|
* rotation in geographic 2D/3D domain. |
|
314
|
|
|
*/ |
|
315
|
6 |
|
public function positionVectorMolodenskyBadekas( |
|
316
|
|
|
Geographic $to, |
|
317
|
|
|
Length $xAxisTranslation, |
|
318
|
|
|
Length $yAxisTranslation, |
|
319
|
|
|
Length $zAxisTranslation, |
|
320
|
|
|
Angle $xAxisRotation, |
|
321
|
|
|
Angle $yAxisRotation, |
|
322
|
|
|
Angle $zAxisRotation, |
|
323
|
|
|
Scale $scaleDifference, |
|
324
|
|
|
Length $ordinate1OfEvaluationPoint, |
|
325
|
|
|
Length $ordinate2OfEvaluationPoint, |
|
326
|
|
|
Length $ordinate3OfEvaluationPoint |
|
327
|
|
|
): self { |
|
328
|
6 |
|
$geographicValue = new GeographicValue($this->latitude, $this->longitude, $this->height, $this->crs->getDatum()); |
|
329
|
6 |
|
$asGeocentric = $geographicValue->asGeocentricValue(); |
|
330
|
|
|
|
|
331
|
6 |
|
$xs = $asGeocentric->getX()->asMetres()->getValue(); |
|
332
|
6 |
|
$ys = $asGeocentric->getY()->asMetres()->getValue(); |
|
333
|
6 |
|
$zs = $asGeocentric->getZ()->asMetres()->getValue(); |
|
334
|
6 |
|
$tx = $xAxisTranslation->asMetres()->getValue(); |
|
335
|
6 |
|
$ty = $yAxisTranslation->asMetres()->getValue(); |
|
336
|
6 |
|
$tz = $zAxisTranslation->asMetres()->getValue(); |
|
337
|
6 |
|
$rx = $xAxisRotation->asRadians()->getValue(); |
|
338
|
6 |
|
$ry = $yAxisRotation->asRadians()->getValue(); |
|
339
|
6 |
|
$rz = $zAxisRotation->asRadians()->getValue(); |
|
340
|
6 |
|
$M = 1 + $scaleDifference->asUnity()->getValue(); |
|
341
|
6 |
|
$xp = $ordinate1OfEvaluationPoint->asMetres()->getValue(); |
|
342
|
6 |
|
$yp = $ordinate2OfEvaluationPoint->asMetres()->getValue(); |
|
343
|
6 |
|
$zp = $ordinate3OfEvaluationPoint->asMetres()->getValue(); |
|
344
|
|
|
|
|
345
|
6 |
|
$xt = $M * ((($xs - $xp) * 1) + (($ys - $yp) * -$rz) + (($zs - $zp) * $ry)) + $tx + $xp; |
|
346
|
6 |
|
$yt = $M * ((($xs - $xp) * $rz) + (($ys - $yp) * 1) + (($zs - $zp) * -$rx)) + $ty + $yp; |
|
347
|
6 |
|
$zt = $M * ((($xs - $xp) * -$ry) + (($ys - $yp) * $rx) + (($zs - $zp) * 1)) + $tz + $zp; |
|
348
|
6 |
|
$newGeocentric = new GeocentricValue(new Metre($xt), new Metre($yt), new Metre($zt), $to->getDatum()); |
|
349
|
6 |
|
$newGeographic = $newGeocentric->asGeographicValue(); |
|
350
|
|
|
|
|
351
|
6 |
|
return static::create($newGeographic->getLatitude(), $newGeographic->getLongitude(), $to instanceof Geographic3D ? $newGeographic->getHeight() : null, $to, $this->epoch); |
|
352
|
|
|
} |
|
353
|
|
|
|
|
354
|
|
|
/** |
|
355
|
|
|
* Geocentric translations |
|
356
|
|
|
* This method allows calculation of geocentric coords in the target system by adding the parameter values to the |
|
357
|
|
|
* corresponding coordinates of the point in the source system. See methods 1031 and 1035 for similar tfms |
|
358
|
|
|
* operating between other CRSs types. |
|
359
|
|
|
*/ |
|
360
|
1 |
|
public function geocentricTranslation( |
|
361
|
|
|
Geographic $to, |
|
362
|
|
|
Length $xAxisTranslation, |
|
363
|
|
|
Length $yAxisTranslation, |
|
364
|
|
|
Length $zAxisTranslation |
|
365
|
|
|
): self { |
|
366
|
1 |
|
return $this->positionVectorTransformation( |
|
367
|
1 |
|
$to, |
|
368
|
|
|
$xAxisTranslation, |
|
369
|
|
|
$yAxisTranslation, |
|
370
|
|
|
$zAxisTranslation, |
|
371
|
1 |
|
new Radian(0), |
|
372
|
1 |
|
new Radian(0), |
|
373
|
1 |
|
new Radian(0), |
|
374
|
1 |
|
new Unity(0) |
|
375
|
|
|
); |
|
376
|
|
|
} |
|
377
|
|
|
|
|
378
|
|
|
/** |
|
379
|
|
|
* Abridged Molodensky |
|
380
|
|
|
* This transformation is a truncated Taylor series expansion of a transformation between two geographic coordinate |
|
381
|
|
|
* systems, modelled as a set of geocentric translations. |
|
382
|
|
|
*/ |
|
383
|
2 |
|
public function abridgedMolodensky( |
|
384
|
|
|
Geographic $to, |
|
385
|
|
|
Length $xAxisTranslation, |
|
386
|
|
|
Length $yAxisTranslation, |
|
387
|
|
|
Length $zAxisTranslation, |
|
388
|
|
|
Length $differenceInSemiMajorAxis, |
|
389
|
|
|
Scale $differenceInFlattening |
|
390
|
|
|
): self { |
|
391
|
2 |
|
$latitude = $this->latitude->asRadians()->getValue(); |
|
392
|
2 |
|
$longitude = $this->longitude->asRadians()->getValue(); |
|
393
|
2 |
|
$fromHeight = $this->height ? $this->height->asMetres()->getValue() : 0; |
|
394
|
2 |
|
$tx = $xAxisTranslation->asMetres()->getValue(); |
|
395
|
2 |
|
$ty = $yAxisTranslation->asMetres()->getValue(); |
|
396
|
2 |
|
$tz = $zAxisTranslation->asMetres()->getValue(); |
|
397
|
2 |
|
$da = $differenceInSemiMajorAxis->asMetres()->getValue(); |
|
398
|
2 |
|
$df = $differenceInFlattening->asUnity()->getValue(); |
|
399
|
|
|
|
|
400
|
2 |
|
$a = $this->crs->getDatum()->getEllipsoid()->getSemiMajorAxis()->asMetres()->getValue(); |
|
401
|
2 |
|
$e2 = $this->crs->getDatum()->getEllipsoid()->getEccentricitySquared(); |
|
402
|
|
|
|
|
403
|
2 |
|
$rho = $a * (1 - $e2) / (1 - $e2 * sin($latitude) ** 2) ** (3 / 2); |
|
404
|
2 |
|
$nu = $a / sqrt(1 - $e2 * (sin($latitude) ** 2)); |
|
405
|
|
|
|
|
406
|
2 |
|
$f = $this->crs->getDatum()->getEllipsoid()->getInverseFlattening(); |
|
407
|
|
|
|
|
408
|
2 |
|
$dLatitude = ((-$tx * sin($latitude) * cos($longitude)) - ($ty * sin($latitude) * sin($longitude)) + ($tz * cos($latitude)) + ((($a * $df) + ($this->crs->getDatum()->getEllipsoid()->getInverseFlattening() * $da)) * sin(2 * $latitude))) / ($rho * sin((new ArcSecond(1))->asRadians()->getValue())); |
|
409
|
2 |
|
$dLongitude = (-$tx * sin($longitude) + $ty * cos($longitude)) / (($nu * cos($latitude)) * sin((new ArcSecond(1))->asRadians()->getValue())); |
|
410
|
2 |
|
$dHeight = ($tx * cos($latitude) * cos($longitude)) + ($ty * cos($latitude) * sin($longitude)) + ($tz * sin($latitude)) + (($a * $df + $f * $da) * (sin($latitude) ** 2)) - $da; |
|
411
|
|
|
|
|
412
|
2 |
|
$toLatitude = $latitude + (new ArcSecond($dLatitude))->asRadians()->getValue(); |
|
413
|
2 |
|
$toLongitude = $longitude + (new ArcSecond($dLongitude))->asRadians()->getValue(); |
|
414
|
2 |
|
$toHeight = $fromHeight + $dHeight; |
|
415
|
|
|
|
|
416
|
2 |
|
return static::create(new Radian($toLatitude), new Radian($toLongitude), $to instanceof Geographic3D ? new Metre($toHeight) : null, $to, $this->epoch); |
|
417
|
|
|
} |
|
418
|
|
|
|
|
419
|
|
|
/** |
|
420
|
|
|
* Molodensky |
|
421
|
|
|
* See Abridged Molodensky. |
|
422
|
|
|
*/ |
|
423
|
2 |
|
public function molodensky( |
|
424
|
|
|
Geographic $to, |
|
425
|
|
|
Length $xAxisTranslation, |
|
426
|
|
|
Length $yAxisTranslation, |
|
427
|
|
|
Length $zAxisTranslation, |
|
428
|
|
|
Length $differenceInSemiMajorAxis, |
|
429
|
|
|
Scale $differenceInFlattening |
|
430
|
|
|
): self { |
|
431
|
2 |
|
$latitude = $this->latitude->asRadians()->getValue(); |
|
432
|
2 |
|
$longitude = $this->longitude->asRadians()->getValue(); |
|
433
|
2 |
|
$fromHeight = $this->height ? $this->height->asMetres()->getValue() : 0; |
|
434
|
2 |
|
$tx = $xAxisTranslation->asMetres()->getValue(); |
|
435
|
2 |
|
$ty = $yAxisTranslation->asMetres()->getValue(); |
|
436
|
2 |
|
$tz = $zAxisTranslation->asMetres()->getValue(); |
|
437
|
2 |
|
$da = $differenceInSemiMajorAxis->asMetres()->getValue(); |
|
438
|
2 |
|
$df = $differenceInFlattening->asUnity()->getValue(); |
|
439
|
|
|
|
|
440
|
2 |
|
$a = $this->crs->getDatum()->getEllipsoid()->getSemiMajorAxis()->asMetres()->getValue(); |
|
441
|
2 |
|
$b = $this->crs->getDatum()->getEllipsoid()->getSemiMinorAxis()->asMetres()->getValue(); |
|
442
|
2 |
|
$e2 = $this->crs->getDatum()->getEllipsoid()->getEccentricitySquared(); |
|
443
|
|
|
|
|
444
|
2 |
|
$rho = $a * (1 - $e2) / (1 - $e2 * sin($latitude) ** 2) ** (3 / 2); |
|
445
|
2 |
|
$nu = $a / sqrt(1 - $e2 * (sin($latitude) ** 2)); |
|
446
|
|
|
|
|
447
|
2 |
|
$f = $this->crs->getDatum()->getEllipsoid()->getInverseFlattening(); |
|
|
|
|
|
|
448
|
|
|
|
|
449
|
2 |
|
$dLatitude = ((-$tx * sin($latitude) * cos($longitude)) - ($ty * sin($latitude) * sin($longitude)) + ($tz * cos($latitude)) + ($da * ($nu * $e2 * sin($latitude) * cos($latitude)) / $a + $df * ($rho * ($a / $b) + $nu * ($b / $a)) * sin($latitude) * cos($latitude))) / (($rho + $fromHeight) * sin((new ArcSecond(1))->asRadians()->getValue())); |
|
450
|
2 |
|
$dLongitude = (-$tx * sin($longitude) + $ty * cos($longitude)) / ((($nu + $fromHeight) * cos($latitude)) * sin((new ArcSecond(1))->asRadians()->getValue())); |
|
451
|
2 |
|
$dHeight = ($tx * cos($latitude) * cos($longitude)) + ($ty * cos($latitude) * sin($longitude)) + ($tz * sin($latitude)) - $da * $a / $nu + $df * $b / $a * $nu * sin($latitude) ** 2; |
|
452
|
|
|
|
|
453
|
2 |
|
$toLatitude = $latitude + (new ArcSecond($dLatitude))->asRadians()->getValue(); |
|
454
|
2 |
|
$toLongitude = $longitude + (new ArcSecond($dLongitude))->asRadians()->getValue(); |
|
455
|
2 |
|
$toHeight = $fromHeight + $dHeight; |
|
456
|
|
|
|
|
457
|
2 |
|
return static::create(new Radian($toLatitude), new Radian($toLongitude), $to instanceof Geographic3D ? new Metre($toHeight) : null, $to, $this->epoch); |
|
458
|
|
|
} |
|
459
|
|
|
|
|
460
|
|
|
/** |
|
461
|
|
|
* Albers Equal Area. |
|
462
|
|
|
*/ |
|
463
|
2 |
|
public function albersEqualArea( |
|
464
|
|
|
Projected $to, |
|
465
|
|
|
Angle $latitudeOfFalseOrigin, |
|
466
|
|
|
Angle $longitudeOfFalseOrigin, |
|
467
|
|
|
Angle $latitudeOf1stStandardParallel, |
|
468
|
|
|
Angle $latitudeOf2ndStandardParallel, |
|
469
|
|
|
Length $eastingAtFalseOrigin, |
|
470
|
|
|
Length $northingAtFalseOrigin |
|
471
|
|
|
): ProjectedPoint { |
|
472
|
2 |
|
$latitude = $this->latitude->asRadians()->getValue(); |
|
473
|
2 |
|
$longitude = $this->longitude->asRadians()->getValue(); |
|
474
|
2 |
|
$phiOrigin = $latitudeOfFalseOrigin->asRadians()->getValue(); |
|
475
|
2 |
|
$phi1 = $latitudeOf1stStandardParallel->asRadians()->getValue(); |
|
476
|
2 |
|
$phi2 = $latitudeOf2ndStandardParallel->asRadians()->getValue(); |
|
477
|
2 |
|
$a = $this->crs->getDatum()->getEllipsoid()->getSemiMajorAxis()->asMetres()->getValue(); |
|
478
|
2 |
|
$e = $this->crs->getDatum()->getEllipsoid()->getEccentricity(); |
|
479
|
2 |
|
$e2 = $this->crs->getDatum()->getEllipsoid()->getEccentricitySquared(); |
|
480
|
|
|
|
|
481
|
2 |
|
$centralMeridianFirstParallel = cos($phi1) / sqrt(1 - ($e2 * sin($phi1) ** 2)); |
|
482
|
2 |
|
$centralMeridianSecondParallel = cos($phi2) / sqrt(1 - ($e2 * sin($phi2) ** 2)); |
|
483
|
|
|
|
|
484
|
2 |
|
$alpha = (1 - $e2) * (sin($latitude) / (1 - $e2 * sin($latitude) ** 2) - (1 / 2 / $e) * log((1 - $e * sin($latitude)) / (1 + $e * sin($latitude)))); |
|
485
|
2 |
|
$alphaOrigin = (1 - $e2) * (sin($phiOrigin) / (1 - $e2 * sin($phiOrigin) ** 2) - (1 / 2 / $e) * log((1 - $e * sin($phiOrigin)) / (1 + $e * sin($phiOrigin)))); |
|
486
|
2 |
|
$alphaFirstParallel = (1 - $e2) * (sin($phi1) / (1 - $e2 * sin($phi1) ** 2) - (1 / 2 / $e) * log((1 - $e * sin($phi1)) / (1 + $e * sin($phi1)))); |
|
487
|
2 |
|
$alphaSecondParallel = (1 - $e2) * (sin($phi2) / (1 - $e2 * sin($phi2) ** 2) - (1 / 2 / $e) * log((1 - $e * sin($phi2)) / (1 + $e * sin($phi2)))); |
|
488
|
|
|
|
|
489
|
2 |
|
$n = ($centralMeridianFirstParallel ** 2 - $centralMeridianSecondParallel ** 2) / ($alphaSecondParallel - $alphaFirstParallel); |
|
490
|
2 |
|
$C = $centralMeridianFirstParallel ** 2 + $n * $alphaFirstParallel; |
|
491
|
2 |
|
$theta = $n * ($longitude - $longitudeOfFalseOrigin->asRadians()->getValue()); |
|
492
|
2 |
|
$rho = $a * sqrt($C - $n * $alpha) / $n; |
|
493
|
2 |
|
$rhoOrigin = ($a * sqrt($C - $n * $alphaOrigin)) / $n; |
|
494
|
|
|
|
|
495
|
2 |
|
$easting = $eastingAtFalseOrigin->asMetres()->getValue() + ($rho * sin($theta)); |
|
496
|
2 |
|
$northing = $northingAtFalseOrigin->asMetres()->getValue() + $rhoOrigin - ($rho * cos($theta)); |
|
497
|
|
|
|
|
498
|
2 |
|
return ProjectedPoint::create(new Metre($easting), new Metre($northing), new Metre(-$easting), new Metre(-$northing), $to, $this->epoch); |
|
499
|
|
|
} |
|
500
|
|
|
|
|
501
|
|
|
/** |
|
502
|
|
|
* American Polyconic. |
|
503
|
|
|
*/ |
|
504
|
1 |
|
public function americanPolyconic( |
|
505
|
|
|
Projected $to, |
|
506
|
|
|
Angle $latitudeOfNaturalOrigin, |
|
507
|
|
|
Angle $longitudeOfNaturalOrigin, |
|
508
|
|
|
Length $falseEasting, |
|
509
|
|
|
Length $falseNorthing |
|
510
|
|
|
): ProjectedPoint { |
|
511
|
1 |
|
$latitude = $this->latitude->asRadians()->getValue(); |
|
512
|
1 |
|
$longitude = $this->longitude->asRadians()->getValue(); |
|
513
|
1 |
|
$latitudeOrigin = $latitudeOfNaturalOrigin->asRadians()->getValue(); |
|
514
|
1 |
|
$longitudeOrigin = $longitudeOfNaturalOrigin->asRadians()->getValue(); |
|
515
|
1 |
|
$a = $this->crs->getDatum()->getEllipsoid()->getSemiMajorAxis()->asMetres()->getValue(); |
|
516
|
1 |
|
$e = $this->crs->getDatum()->getEllipsoid()->getEccentricity(); |
|
517
|
1 |
|
$e2 = $this->crs->getDatum()->getEllipsoid()->getEccentricitySquared(); |
|
518
|
1 |
|
$e4 = $e ** 4; |
|
519
|
1 |
|
$e6 = $e ** 6; |
|
520
|
|
|
|
|
521
|
1 |
|
$M = $a * ((1 - $e2 / 4 - 3 * $e4 / 64 - 5 * $e6 / 256) * $latitude - (3 * $e2 / 8 + 3 * $e4 / 32 + 45 * $e6 / 1024) * sin(2 * $latitude) + (15 * $e4 / 256 + 45 * $e6 / 1024) * sin(4 * $latitude) - (35 * $e6 / 3072) * sin(6 * $latitude)); |
|
522
|
1 |
|
$MO = $a * ((1 - $e2 / 4 - 3 * $e4 / 64 - 5 * $e6 / 256) * $latitudeOrigin - (3 * $e2 / 8 + 3 * $e4 / 32 + 45 * $e6 / 1024) * sin(2 * $latitudeOrigin) + (15 * $e4 / 256 + 45 * $e6 / 1024) * sin(4 * $latitudeOrigin) - (35 * $e6 / 3072) * sin(6 * $latitudeOrigin)); |
|
523
|
|
|
|
|
524
|
1 |
|
if ($latitude === 0.0) { |
|
|
|
|
|
|
525
|
|
|
$easting = $falseEasting->asMetres()->getValue() + $a * ($longitude - $longitudeOrigin); |
|
526
|
|
|
$northing = $falseNorthing->asMetres()->getValue() - $MO; |
|
527
|
|
|
} else { |
|
528
|
1 |
|
$L = ($longitude - $longitudeOrigin) * sin($latitude); |
|
529
|
1 |
|
$nu = $a / sqrt(1 - $e2 * sin($latitude) ** 2); |
|
530
|
|
|
|
|
531
|
1 |
|
$easting = $falseEasting->asMetres()->getValue() + $nu * 1 / tan($latitude) * sin($L); |
|
532
|
1 |
|
$northing = $falseNorthing->asMetres()->getValue() + $M - $MO + $nu * 1 / tan($latitude) * (1 - cos($L)); |
|
533
|
|
|
} |
|
534
|
|
|
|
|
535
|
1 |
|
return ProjectedPoint::create(new Metre($easting), new Metre($northing), new Metre(-$easting), new Metre(-$northing), $to, $this->epoch); |
|
536
|
|
|
} |
|
537
|
|
|
|
|
538
|
|
|
/** |
|
539
|
|
|
* Bonne. |
|
540
|
|
|
*/ |
|
541
|
1 |
|
public function bonne( |
|
542
|
|
|
Projected $to, |
|
543
|
|
|
Angle $latitudeOfNaturalOrigin, |
|
544
|
|
|
Angle $longitudeOfNaturalOrigin, |
|
545
|
|
|
Length $falseEasting, |
|
546
|
|
|
Length $falseNorthing |
|
547
|
|
|
): ProjectedPoint { |
|
548
|
1 |
|
$latitude = $this->latitude->asRadians()->getValue(); |
|
549
|
1 |
|
$longitude = $this->longitude->asRadians()->getValue(); |
|
550
|
1 |
|
$latitudeOrigin = $latitudeOfNaturalOrigin->asRadians()->getValue(); |
|
551
|
1 |
|
$longitudeOrigin = $longitudeOfNaturalOrigin->asRadians()->getValue(); |
|
552
|
1 |
|
$a = $this->crs->getDatum()->getEllipsoid()->getSemiMajorAxis()->asMetres()->getValue(); |
|
553
|
1 |
|
$e = $this->crs->getDatum()->getEllipsoid()->getEccentricity(); |
|
554
|
1 |
|
$e2 = $this->crs->getDatum()->getEllipsoid()->getEccentricitySquared(); |
|
555
|
1 |
|
$e4 = $e ** 4; |
|
556
|
1 |
|
$e6 = $e ** 6; |
|
557
|
|
|
|
|
558
|
1 |
|
$m = cos($latitude) / sqrt(1 - $e2 * sin($latitude) ** 2); |
|
559
|
1 |
|
$mO = cos($latitudeOrigin) / sqrt(1 - $e2 * sin($latitudeOrigin) ** 2); |
|
560
|
|
|
|
|
561
|
1 |
|
$M = $a * ((1 - $e2 / 4 - 3 * $e4 / 64 - 5 * $e6 / 256) * $latitude - (3 * $e2 / 8 + 3 * $e4 / 32 + 45 * $e6 / 1024) * sin(2 * $latitude) + (15 * $e4 / 256 + 45 * $e6 / 1024) * sin(4 * $latitude) - (35 * $e6 / 3072) * sin(6 * $latitude)); |
|
562
|
1 |
|
$MO = $a * ((1 - $e2 / 4 - 3 * $e4 / 64 - 5 * $e6 / 256) * $latitudeOrigin - (3 * $e2 / 8 + 3 * $e4 / 32 + 45 * $e6 / 1024) * sin(2 * $latitudeOrigin) + (15 * $e4 / 256 + 45 * $e6 / 1024) * sin(4 * $latitudeOrigin) - (35 * $e6 / 3072) * sin(6 * $latitudeOrigin)); |
|
563
|
|
|
|
|
564
|
1 |
|
$rho = $a * $mO / sin($latitudeOrigin) + $MO - $M; |
|
565
|
1 |
|
$tau = $a * $m * ($longitude - $longitudeOrigin) / $rho; |
|
566
|
|
|
|
|
567
|
1 |
|
$easting = $falseEasting->asMetres()->getValue() + ($rho * sin($tau)); |
|
568
|
1 |
|
$northing = $falseNorthing->asMetres()->getValue() + (($a * $mO / sin($latitudeOrigin) - $rho * cos($tau))); |
|
569
|
|
|
|
|
570
|
1 |
|
return ProjectedPoint::create(new Metre($easting), new Metre($northing), new Metre(-$easting), new Metre(-$northing), $to, $this->epoch); |
|
571
|
|
|
} |
|
572
|
|
|
|
|
573
|
|
|
/** |
|
574
|
|
|
* Bonne South Orientated. |
|
575
|
|
|
*/ |
|
576
|
1 |
|
public function bonneSouthOrientated( |
|
577
|
|
|
Projected $to, |
|
578
|
|
|
Angle $latitudeOfNaturalOrigin, |
|
579
|
|
|
Angle $longitudeOfNaturalOrigin, |
|
580
|
|
|
Length $falseEasting, |
|
581
|
|
|
Length $falseNorthing |
|
582
|
|
|
): ProjectedPoint { |
|
583
|
1 |
|
$latitude = $this->latitude->asRadians()->getValue(); |
|
584
|
1 |
|
$longitude = $this->longitude->asRadians()->getValue(); |
|
585
|
1 |
|
$latitudeOrigin = $latitudeOfNaturalOrigin->asRadians()->getValue(); |
|
586
|
1 |
|
$longitudeOrigin = $longitudeOfNaturalOrigin->asRadians()->getValue(); |
|
587
|
1 |
|
$a = $this->crs->getDatum()->getEllipsoid()->getSemiMajorAxis()->asMetres()->getValue(); |
|
588
|
1 |
|
$e = $this->crs->getDatum()->getEllipsoid()->getEccentricity(); |
|
589
|
1 |
|
$e2 = $this->crs->getDatum()->getEllipsoid()->getEccentricitySquared(); |
|
590
|
1 |
|
$e4 = $e ** 4; |
|
591
|
1 |
|
$e6 = $e ** 6; |
|
592
|
|
|
|
|
593
|
1 |
|
$m = cos($latitude) / sqrt(1 - $e2 * sin($latitude) ** 2); |
|
594
|
1 |
|
$mO = cos($latitudeOrigin) / sqrt(1 - $e2 * sin($latitudeOrigin) ** 2); |
|
595
|
|
|
|
|
596
|
1 |
|
$M = $a * ((1 - $e2 / 4 - 3 * $e4 / 64 - 5 * $e6 / 256) * $latitude - (3 * $e2 / 8 + 3 * $e4 / 32 + 45 * $e6 / 1024) * sin(2 * $latitude) + (15 * $e4 / 256 + 45 * $e6 / 1024) * sin(4 * $latitude) - (35 * $e6 / 3072) * sin(6 * $latitude)); |
|
597
|
1 |
|
$MO = $a * ((1 - $e2 / 4 - 3 * $e4 / 64 - 5 * $e6 / 256) * $latitudeOrigin - (3 * $e2 / 8 + 3 * $e4 / 32 + 45 * $e6 / 1024) * sin(2 * $latitudeOrigin) + (15 * $e4 / 256 + 45 * $e6 / 1024) * sin(4 * $latitudeOrigin) - (35 * $e6 / 3072) * sin(6 * $latitudeOrigin)); |
|
598
|
|
|
|
|
599
|
1 |
|
$rho = $a * $mO / sin($latitudeOrigin) + $MO - $M; |
|
600
|
1 |
|
$tau = $a * $m * ($longitude - $longitudeOrigin) / $rho; |
|
601
|
|
|
|
|
602
|
1 |
|
$westing = $falseEasting->asMetres()->getValue() - ($rho * sin($tau)); |
|
603
|
1 |
|
$southing = $falseNorthing->asMetres()->getValue() - (($a * $mO / sin($latitudeOrigin) - $rho * cos($tau))); |
|
604
|
|
|
|
|
605
|
1 |
|
return ProjectedPoint::create(new Metre(-$westing), new Metre(-$southing), new Metre($westing), new Metre($southing), $to, $this->epoch); |
|
606
|
|
|
} |
|
607
|
|
|
|
|
608
|
|
|
/** |
|
609
|
|
|
* Cassini-Soldner. |
|
610
|
|
|
*/ |
|
611
|
1 |
|
public function cassiniSoldner( |
|
612
|
|
|
Projected $to, |
|
613
|
|
|
Angle $latitudeOfNaturalOrigin, |
|
614
|
|
|
Angle $longitudeOfNaturalOrigin, |
|
615
|
|
|
Length $falseEasting, |
|
616
|
|
|
Length $falseNorthing |
|
617
|
|
|
): ProjectedPoint { |
|
618
|
1 |
|
$latitude = $this->latitude->asRadians()->getValue(); |
|
619
|
1 |
|
$longitude = $this->longitude->asRadians()->getValue(); |
|
620
|
1 |
|
$latitudeOrigin = $latitudeOfNaturalOrigin->asRadians()->getValue(); |
|
621
|
1 |
|
$longitudeOrigin = $longitudeOfNaturalOrigin->asRadians()->getValue(); |
|
622
|
1 |
|
$a = $this->crs->getDatum()->getEllipsoid()->getSemiMajorAxis()->asMetres()->getValue(); |
|
623
|
1 |
|
$e = $this->crs->getDatum()->getEllipsoid()->getEccentricity(); |
|
624
|
1 |
|
$e2 = $this->crs->getDatum()->getEllipsoid()->getEccentricitySquared(); |
|
625
|
1 |
|
$e4 = $e ** 4; |
|
626
|
1 |
|
$e6 = $e ** 6; |
|
627
|
|
|
|
|
628
|
1 |
|
$M = $a * ((1 - $e2 / 4 - 3 * $e4 / 64 - 5 * $e6 / 256) * $latitude - (3 * $e2 / 8 + 3 * $e4 / 32 + 45 * $e6 / 1024) * sin(2 * $latitude) + (15 * $e4 / 256 + 45 * $e6 / 1024) * sin(4 * $latitude) - (35 * $e6 / 3072) * sin(6 * $latitude)); |
|
629
|
1 |
|
$MO = $a * ((1 - $e2 / 4 - 3 * $e4 / 64 - 5 * $e6 / 256) * $latitudeOrigin - (3 * $e2 / 8 + 3 * $e4 / 32 + 45 * $e6 / 1024) * sin(2 * $latitudeOrigin) + (15 * $e4 / 256 + 45 * $e6 / 1024) * sin(4 * $latitudeOrigin) - (35 * $e6 / 3072) * sin(6 * $latitudeOrigin)); |
|
630
|
|
|
|
|
631
|
1 |
|
$A = ($longitude - $longitudeOrigin) * cos($latitude); |
|
632
|
1 |
|
$T = tan($latitude) ** 2; |
|
633
|
1 |
|
$C = $e2 * cos($latitude) ** 2 / (1 - $e2); |
|
634
|
1 |
|
$nu = $a / sqrt(1 - $e2 * (sin($latitude) ** 2)); |
|
635
|
1 |
|
$X = $M - $MO + $nu * tan($latitude) * ($A ** 2 / 2 + (5 - $T + 6 * $C) * $A ** 4 / 24); |
|
636
|
|
|
|
|
637
|
1 |
|
$easting = $falseEasting->asMetres()->getValue() + $nu * ($A - $T * $A ** 3 / 6 - (8 - $T + 8 * $C) * $T * $A ** 5 / 120); |
|
638
|
1 |
|
$northing = $falseNorthing->asMetres()->getValue() + $X; |
|
639
|
|
|
|
|
640
|
1 |
|
return ProjectedPoint::create(new Metre($easting), new Metre($northing), new Metre(-$easting), new Metre(-$northing), $to, $this->epoch); |
|
641
|
|
|
} |
|
642
|
|
|
|
|
643
|
|
|
/** |
|
644
|
|
|
* Hyperbolic Cassini-Soldner. |
|
645
|
|
|
*/ |
|
646
|
2 |
|
public function hyperbolicCassiniSoldner( |
|
647
|
|
|
Projected $to, |
|
648
|
|
|
Angle $latitudeOfNaturalOrigin, |
|
649
|
|
|
Angle $longitudeOfNaturalOrigin, |
|
650
|
|
|
Length $falseEasting, |
|
651
|
|
|
Length $falseNorthing |
|
652
|
|
|
): ProjectedPoint { |
|
653
|
2 |
|
$latitude = $this->latitude->asRadians()->getValue(); |
|
654
|
2 |
|
$longitude = $this->longitude->asRadians()->getValue(); |
|
655
|
2 |
|
$latitudeOrigin = $latitudeOfNaturalOrigin->asRadians()->getValue(); |
|
656
|
2 |
|
$longitudeOrigin = $longitudeOfNaturalOrigin->asRadians()->getValue(); |
|
657
|
2 |
|
$a = $this->crs->getDatum()->getEllipsoid()->getSemiMajorAxis()->asMetres()->getValue(); |
|
658
|
2 |
|
$e = $this->crs->getDatum()->getEllipsoid()->getEccentricity(); |
|
659
|
2 |
|
$e2 = $this->crs->getDatum()->getEllipsoid()->getEccentricitySquared(); |
|
660
|
2 |
|
$e4 = $e ** 4; |
|
661
|
2 |
|
$e6 = $e ** 6; |
|
662
|
|
|
|
|
663
|
2 |
|
$M = $a * ((1 - $e2 / 4 - 3 * $e4 / 64 - 5 * $e6 / 256) * $latitude - (3 * $e2 / 8 + 3 * $e4 / 32 + 45 * $e6 / 1024) * sin(2 * $latitude) + (15 * $e4 / 256 + 45 * $e6 / 1024) * sin(4 * $latitude) - (35 * $e6 / 3072) * sin(6 * $latitude)); |
|
664
|
2 |
|
$MO = $a * ((1 - $e2 / 4 - 3 * $e4 / 64 - 5 * $e6 / 256) * $latitudeOrigin - (3 * $e2 / 8 + 3 * $e4 / 32 + 45 * $e6 / 1024) * sin(2 * $latitudeOrigin) + (15 * $e4 / 256 + 45 * $e6 / 1024) * sin(4 * $latitudeOrigin) - (35 * $e6 / 3072) * sin(6 * $latitudeOrigin)); |
|
665
|
|
|
|
|
666
|
2 |
|
$A = ($longitude - $longitudeOrigin) * cos($latitude); |
|
667
|
2 |
|
$T = tan($latitude) ** 2; |
|
668
|
2 |
|
$C = $e2 * cos($latitude) ** 2 / (1 - $e2); |
|
669
|
2 |
|
$nu = $a / sqrt(1 - $e2 * (sin($latitude) ** 2)); |
|
670
|
2 |
|
$rho = $a * (1 - $e2) / (1 - $e2 * sin($latitude) ** 2) ** (3 / 2); |
|
671
|
2 |
|
$X = $M - $MO + $nu * tan($latitude) * ($A ** 2 / 2 + (5 - $T + 6 * $C) * $A ** 4 / 24); |
|
672
|
|
|
|
|
673
|
2 |
|
$easting = $falseEasting->asMetres()->getValue() + $nu * ($A - $T * $A ** 3 / 6 - (8 - $T + 8 * $C) * $T * $A ** 5 / 120); |
|
674
|
2 |
|
$northing = $falseNorthing->asMetres()->getValue() + $X - ($X ** 3 / (6 * $rho * $nu)); |
|
675
|
|
|
|
|
676
|
2 |
|
return ProjectedPoint::create(new Metre($easting), new Metre($northing), new Metre(-$easting), new Metre(-$northing), $to, $this->epoch); |
|
677
|
|
|
} |
|
678
|
|
|
|
|
679
|
|
|
/** |
|
680
|
|
|
* Colombia Urban. |
|
681
|
|
|
*/ |
|
682
|
1 |
|
public function columbiaUrban( |
|
683
|
|
|
Projected $to, |
|
684
|
|
|
Angle $latitudeOfNaturalOrigin, |
|
685
|
|
|
Angle $longitudeOfNaturalOrigin, |
|
686
|
|
|
Length $falseEasting, |
|
687
|
|
|
Length $falseNorthing, |
|
688
|
|
|
Length $projectionPlaneOriginHeight |
|
689
|
|
|
): ProjectedPoint { |
|
690
|
1 |
|
$latitude = $this->latitude->asRadians()->getValue(); |
|
691
|
1 |
|
$longitude = $this->longitude->asRadians()->getValue(); |
|
692
|
1 |
|
$latitudeOrigin = $latitudeOfNaturalOrigin->asRadians()->getValue(); |
|
693
|
1 |
|
$longitudeOrigin = $longitudeOfNaturalOrigin->asRadians()->getValue(); |
|
694
|
1 |
|
$heightOrigin = $projectionPlaneOriginHeight->asMetres()->getValue(); |
|
695
|
1 |
|
$a = $this->crs->getDatum()->getEllipsoid()->getSemiMajorAxis()->asMetres()->getValue(); |
|
696
|
1 |
|
$e2 = $this->crs->getDatum()->getEllipsoid()->getEccentricitySquared(); |
|
697
|
|
|
|
|
698
|
1 |
|
$rho = $a * (1 - $e2) / (1 - $e2 * sin($latitude) ** 2) ** (3 / 2); |
|
|
|
|
|
|
699
|
1 |
|
$rhoOrigin = $a * (1 - $e2) / (1 - $e2 * sin($latitudeOrigin) ** 2) ** (3 / 2); |
|
700
|
1 |
|
$rhoMid = $a * (1 - $e2) / (1 - $e2 * sin(($latitude + $latitudeOrigin) / 2) ** 2) ** (3 / 2); |
|
701
|
|
|
|
|
702
|
1 |
|
$nu = $a / sqrt(1 - $e2 * (sin($latitude) ** 2)); |
|
703
|
1 |
|
$nuOrigin = $a / sqrt(1 - $e2 * (sin($latitudeOrigin) ** 2)); |
|
704
|
|
|
|
|
705
|
1 |
|
$A = 1 + $heightOrigin / $nuOrigin; |
|
706
|
1 |
|
$B = tan($latitudeOrigin) / (2 * $rhoOrigin * $nuOrigin); |
|
707
|
1 |
|
$G = 1 + $heightOrigin / $rhoMid; |
|
708
|
|
|
|
|
709
|
1 |
|
$easting = $falseEasting->asMetres()->getValue() + $A * $nu * cos($latitude) * ($longitude - $longitudeOrigin); |
|
710
|
1 |
|
$northing = $falseNorthing->asMetres()->getValue() + $G * $rhoOrigin * (($latitude - $latitudeOrigin) + ($B * ($longitude - $longitudeOrigin) ** 2 * $nu ** 2 * cos($latitude) ** 2)); |
|
711
|
|
|
|
|
712
|
1 |
|
return ProjectedPoint::create(new Metre($easting), new Metre($northing), new Metre(-$easting), new Metre(-$northing), $to, $this->epoch); |
|
713
|
|
|
} |
|
714
|
|
|
|
|
715
|
|
|
/** |
|
716
|
|
|
* Equal Earth. |
|
717
|
|
|
*/ |
|
718
|
1 |
|
public function equalEarth( |
|
719
|
|
|
Projected $to, |
|
720
|
|
|
Angle $longitudeOfNaturalOrigin, |
|
721
|
|
|
Length $falseEasting, |
|
722
|
|
|
Length $falseNorthing |
|
723
|
|
|
): ProjectedPoint { |
|
724
|
1 |
|
$latitude = $this->latitude->asRadians()->getValue(); |
|
725
|
1 |
|
$longitude = $this->longitude->asRadians()->getValue(); |
|
726
|
1 |
|
$longitudeOrigin = $longitudeOfNaturalOrigin->asRadians()->getValue(); |
|
727
|
1 |
|
$a = $this->crs->getDatum()->getEllipsoid()->getSemiMajorAxis()->asMetres()->getValue(); |
|
728
|
1 |
|
$e = $this->crs->getDatum()->getEllipsoid()->getEccentricity(); |
|
729
|
1 |
|
$e2 = $this->crs->getDatum()->getEllipsoid()->getEccentricitySquared(); |
|
730
|
|
|
|
|
731
|
1 |
|
$q = (1 - $e2) * ((sin($latitude) / (1 - $e2 * sin($latitude) ** 2)) - (1 / (2 * $e) * log((1 - $e * sin($latitude)) / (1 + $e * sin($latitude))))); |
|
732
|
1 |
|
$qP = (1 - $e2) * ((1 / (1 - $e2)) - (1 / (2 * $e) * log((1 - $e) / (1 + $e)))); |
|
733
|
1 |
|
$beta = self::asin($q / $qP); |
|
734
|
1 |
|
$theta = self::asin(sin($beta) * sqrt(3) / 2); |
|
735
|
1 |
|
$Rq = $a * sqrt($qP / 2); |
|
736
|
|
|
|
|
737
|
1 |
|
$easting = $falseEasting->asMetres()->getValue() + ($Rq * 2 * ($longitude - $longitudeOrigin) * cos($theta)) / (sqrt(3) * (1.340264 - 0.243318 * $theta ** 2 + $theta ** 6 * (0.006251 + 0.034164 * $theta ** 2))); |
|
738
|
1 |
|
$northing = $falseNorthing->asMetres()->getValue() + $Rq * $theta * (1.340264 - 0.081106 * $theta ** 2 + $theta ** 6 * (0.000893 + 0.003796 * $theta ** 2)); |
|
739
|
|
|
|
|
740
|
1 |
|
return ProjectedPoint::create(new Metre($easting), new Metre($northing), new Metre(-$easting), new Metre(-$northing), $to, $this->epoch); |
|
741
|
|
|
} |
|
742
|
|
|
|
|
743
|
|
|
/** |
|
744
|
|
|
* Equidistant Cylindrical |
|
745
|
|
|
* See method code 1029 for spherical development. See also Pseudo Plate Carree, method code 9825. |
|
746
|
|
|
*/ |
|
747
|
1 |
|
public function equidistantCylindrical( |
|
748
|
|
|
Projected $to, |
|
749
|
|
|
Angle $latitudeOf1stStandardParallel, |
|
750
|
|
|
Angle $longitudeOfNaturalOrigin, |
|
751
|
|
|
Length $falseEasting, |
|
752
|
|
|
Length $falseNorthing |
|
753
|
|
|
): ProjectedPoint { |
|
754
|
1 |
|
$latitude = $this->latitude->asRadians()->getValue(); |
|
755
|
1 |
|
$longitude = $this->longitude->asRadians()->getValue(); |
|
756
|
1 |
|
$latitudeFirstParallel = $latitudeOf1stStandardParallel->asRadians()->getValue(); |
|
757
|
1 |
|
$longitudeOrigin = $longitudeOfNaturalOrigin->asRadians()->getValue(); |
|
758
|
1 |
|
$a = $this->crs->getDatum()->getEllipsoid()->getSemiMajorAxis()->asMetres()->getValue(); |
|
759
|
1 |
|
$e = $this->crs->getDatum()->getEllipsoid()->getEccentricity(); |
|
760
|
1 |
|
$e2 = $this->crs->getDatum()->getEllipsoid()->getEccentricitySquared(); |
|
761
|
1 |
|
$e4 = $e ** 4; |
|
762
|
1 |
|
$e6 = $e ** 6; |
|
763
|
1 |
|
$e8 = $e ** 8; |
|
764
|
1 |
|
$e10 = $e ** 10; |
|
765
|
1 |
|
$e12 = $e ** 12; |
|
766
|
1 |
|
$e14 = $e ** 14; |
|
767
|
|
|
|
|
768
|
1 |
|
$nu1 = $a / sqrt(1 - $e2 * sin($latitudeFirstParallel) ** 2); |
|
769
|
|
|
|
|
770
|
|
|
$M = $a * ( |
|
771
|
1 |
|
(1 - 1 / 4 * $e2 - 3 / 64 * $e4 - 5 / 256 * $e6 - 175 / 16384 * $e8 - 441 / 65536 * $e10 - 4851 / 1048576 * $e12 - 14157 / 4194304 * $e14) * $latitude + |
|
772
|
1 |
|
(-3 / 8 * $e2 - 3 / 32 * $e4 - 45 / 1024 * $e6 - 105 / 4096 * $e8 - 2205 / 131072 * $e10 - 6237 / 524288 * $e12 - 297297 / 33554432 * $e14) * sin(2 * $latitude) + |
|
773
|
1 |
|
(15 / 256 * $e4 + 45 / 1024 * $e ** 6 + 525 / 16384 * $e ** 8 + 1575 / 65536 * $e10 + 155925 / 8388608 * $e12 + 495495 / 33554432 * $e14) * sin(4 * $latitude) + |
|
774
|
1 |
|
(-35 / 3072 * $e6 - 175 / 12288 * $e8 - 3675 / 262144 * $e10 - 13475 / 1048576 * $e12 - 385385 / 33554432 * $e14) * sin(6 * $latitude) + |
|
775
|
1 |
|
(315 / 131072 * $e8 + 2205 / 524288 * $e10 + 43659 / 8388608 * $e12 + 189189 / 33554432 * $e14) * sin(8 * $latitude) + |
|
776
|
1 |
|
(-693 / 1310720 * $e10 - 6537 / 5242880 * $e12 - 297297 / 167772160 * $e14) * sin(10 * $latitude) + |
|
777
|
1 |
|
(1001 / 8388608 * $e12 + 11011 / 33554432 * $e14) * sin(12 * $latitude) + |
|
778
|
1 |
|
(-6435 / 234881024 * $e ** 14) * sin(14 * $latitude) |
|
779
|
|
|
); |
|
780
|
|
|
|
|
781
|
1 |
|
$easting = $falseEasting->asMetres()->getValue() + $nu1 * cos($latitudeFirstParallel) * ($longitude - $longitudeOrigin); |
|
782
|
1 |
|
$northing = $falseNorthing->asMetres()->getValue() + $M; |
|
783
|
|
|
|
|
784
|
1 |
|
return ProjectedPoint::create(new Metre($easting), new Metre($northing), new Metre(-$easting), new Metre(-$northing), $to, $this->epoch); |
|
785
|
|
|
} |
|
786
|
|
|
|
|
787
|
|
|
/** |
|
788
|
|
|
* Guam Projection |
|
789
|
|
|
* Simplified form of Oblique Azimuthal Equidistant projection method. |
|
790
|
|
|
*/ |
|
791
|
1 |
|
public function guamProjection( |
|
792
|
|
|
Projected $to, |
|
793
|
|
|
Angle $latitudeOfNaturalOrigin, |
|
794
|
|
|
Angle $longitudeOfNaturalOrigin, |
|
795
|
|
|
Length $falseEasting, |
|
796
|
|
|
Length $falseNorthing |
|
797
|
|
|
): ProjectedPoint { |
|
798
|
1 |
|
$latitude = $this->latitude->asRadians()->getValue(); |
|
799
|
1 |
|
$longitude = $this->longitude->asRadians()->getValue(); |
|
800
|
1 |
|
$latitudeOrigin = $latitudeOfNaturalOrigin->asRadians()->getValue(); |
|
801
|
1 |
|
$longitudeOrigin = $longitudeOfNaturalOrigin->asRadians()->getValue(); |
|
802
|
1 |
|
$a = $this->crs->getDatum()->getEllipsoid()->getSemiMajorAxis()->asMetres()->getValue(); |
|
803
|
1 |
|
$e = $this->crs->getDatum()->getEllipsoid()->getEccentricity(); |
|
804
|
1 |
|
$e2 = $this->crs->getDatum()->getEllipsoid()->getEccentricitySquared(); |
|
805
|
1 |
|
$e4 = $e ** 4; |
|
806
|
1 |
|
$e6 = $e ** 6; |
|
807
|
|
|
|
|
808
|
1 |
|
$M = $a * ((1 - $e2 / 4 - 3 * $e4 / 64 - 5 * $e6 / 256) * $latitude - (3 * $e2 / 8 + 3 * $e4 / 32 + 45 * $e6 / 1024) * sin(2 * $latitude) + (15 * $e4 / 256 + 45 * $e6 / 1024) * sin(4 * $latitude) - (35 * $e6 / 3072) * sin(6 * $latitude)); |
|
809
|
1 |
|
$MO = $a * ((1 - $e2 / 4 - 3 * $e4 / 64 - 5 * $e6 / 256) * $latitudeOrigin - (3 * $e2 / 8 + 3 * $e4 / 32 + 45 * $e6 / 1024) * sin(2 * $latitudeOrigin) + (15 * $e4 / 256 + 45 * $e6 / 1024) * sin(4 * $latitudeOrigin) - (35 * $e6 / 3072) * sin(6 * $latitudeOrigin)); |
|
810
|
1 |
|
$x = ($a * ($longitude - $longitudeOrigin) * cos($latitude)) / sqrt(1 - $e2 * sin($latitude) ** 2); |
|
811
|
|
|
|
|
812
|
1 |
|
$easting = $falseEasting->asMetres()->getValue() + $x; |
|
813
|
1 |
|
$northing = $falseNorthing->asMetres()->getValue() + $M - $MO + ($x ** 2 * tan($latitude) * sqrt(1 - $e2 * sin($latitude) ** 2) / (2 * $a)); |
|
814
|
|
|
|
|
815
|
1 |
|
return ProjectedPoint::create(new Metre($easting), new Metre($northing), new Metre(-$easting), new Metre(-$northing), $to, $this->epoch); |
|
816
|
|
|
} |
|
817
|
|
|
|
|
818
|
|
|
/** |
|
819
|
|
|
* Krovak. |
|
820
|
|
|
*/ |
|
821
|
4 |
|
public function krovak( |
|
822
|
|
|
Projected $to, |
|
823
|
|
|
Angle $latitudeOfProjectionCentre, |
|
824
|
|
|
Angle $longitudeOfOrigin, |
|
825
|
|
|
Angle $coLatitudeOfConeAxis, |
|
826
|
|
|
Angle $latitudeOfPseudoStandardParallel, |
|
827
|
|
|
Scale $scaleFactorOnPseudoStandardParallel, |
|
828
|
|
|
Length $falseEasting, |
|
829
|
|
|
Length $falseNorthing |
|
830
|
|
|
): ProjectedPoint { |
|
831
|
4 |
|
$longitudeOffset = $to->getDatum()->getPrimeMeridian()->getGreenwichLongitude()->asRadians()->getValue() - $this->getCRS()->getDatum()->getPrimeMeridian()->getGreenwichLongitude()->asRadians()->getValue(); |
|
832
|
4 |
|
$latitude = $this->latitude->asRadians()->getValue(); |
|
833
|
4 |
|
$longitude = $this->longitude->asRadians()->getValue() - $longitudeOffset; |
|
834
|
4 |
|
$latitudeC = $latitudeOfProjectionCentre->asRadians()->getValue(); |
|
835
|
4 |
|
$longitudeO = $longitudeOfOrigin->asRadians()->getValue(); |
|
836
|
4 |
|
$alphaC = $coLatitudeOfConeAxis->asRadians()->getValue(); |
|
837
|
4 |
|
$latitudeP = $latitudeOfPseudoStandardParallel->asRadians()->getValue(); |
|
838
|
4 |
|
$kP = $scaleFactorOnPseudoStandardParallel->asUnity()->getValue(); |
|
839
|
4 |
|
$a = $this->crs->getDatum()->getEllipsoid()->getSemiMajorAxis()->asMetres()->getValue(); |
|
840
|
4 |
|
$e = $this->crs->getDatum()->getEllipsoid()->getEccentricity(); |
|
841
|
4 |
|
$e2 = $this->crs->getDatum()->getEllipsoid()->getEccentricitySquared(); |
|
842
|
|
|
|
|
843
|
4 |
|
$A = $a * sqrt(1 - $e2) / (1 - $e2 * sin($latitudeC) ** 2); |
|
844
|
4 |
|
$B = sqrt(1 + $e2 * cos($latitudeC) ** 4 / (1 - $e2)); |
|
845
|
4 |
|
$upsilonO = self::asin(sin($latitudeC) / $B); |
|
846
|
4 |
|
$tO = tan(M_PI / 4 + $upsilonO / 2) * ((1 + $e * sin($latitudeC)) / (1 - $e * sin($latitudeC))) ** ($e * $B / 2) / (tan(M_PI / 4 + $latitudeC / 2) ** $B); |
|
847
|
4 |
|
$n = sin($latitudeP); |
|
848
|
4 |
|
$rO = $kP * $A / tan($latitudeP); |
|
849
|
|
|
|
|
850
|
4 |
|
$U = 2 * (atan($tO * tan($latitude / 2 + M_PI / 4) ** $B / ((1 + $e * sin($latitude)) / (1 - $e * sin($latitude))) ** ($e * $B / 2)) - M_PI / 4); |
|
851
|
4 |
|
$V = $B * ($longitudeO - $longitude); |
|
852
|
4 |
|
$T = self::asin(cos($alphaC) * sin($U) + sin($alphaC) * cos($U) * cos($V)); |
|
853
|
4 |
|
$D = atan2(cos($U) * sin($V) / cos($T), ((cos($alphaC) * sin($T) - sin($U)) / (sin($alphaC) * cos($T)))); |
|
854
|
4 |
|
$theta = $n * $D; |
|
855
|
4 |
|
$r = $rO * tan(M_PI / 4 + $latitudeP / 2) ** $n / tan($T / 2 + M_PI / 4) ** $n; |
|
856
|
4 |
|
$X = $r * cos($theta); |
|
857
|
4 |
|
$Y = $r * sin($theta); |
|
858
|
|
|
|
|
859
|
4 |
|
$westing = $Y + $falseEasting->asMetres()->getValue(); |
|
860
|
4 |
|
$southing = $X + $falseNorthing->asMetres()->getValue(); |
|
861
|
|
|
|
|
862
|
4 |
|
return ProjectedPoint::create(new Metre(-$westing), new Metre(-$southing), new Metre($westing), new Metre($southing), $to, $this->epoch); |
|
863
|
|
|
} |
|
864
|
|
|
|
|
865
|
|
|
/** |
|
866
|
|
|
* Krovak Modified |
|
867
|
|
|
* Incorporates a polynomial transformation which is defined to be exact and for practical purposes is considered |
|
868
|
|
|
* to be a map projection. |
|
869
|
|
|
*/ |
|
870
|
2 |
|
public function krovakModified( |
|
871
|
|
|
Projected $to, |
|
872
|
|
|
Angle $latitudeOfProjectionCentre, |
|
873
|
|
|
Angle $longitudeOfOrigin, |
|
874
|
|
|
Angle $coLatitudeOfConeAxis, |
|
875
|
|
|
Angle $latitudeOfPseudoStandardParallel, |
|
876
|
|
|
Scale $scaleFactorOnPseudoStandardParallel, |
|
877
|
|
|
Length $falseEasting, |
|
878
|
|
|
Length $falseNorthing, |
|
879
|
|
|
Length $ordinate1OfEvaluationPoint, |
|
880
|
|
|
Length $ordinate2OfEvaluationPoint, |
|
881
|
|
|
Coefficient $C1, |
|
882
|
|
|
Coefficient $C2, |
|
883
|
|
|
Coefficient $C3, |
|
884
|
|
|
Coefficient $C4, |
|
885
|
|
|
Coefficient $C5, |
|
886
|
|
|
Coefficient $C6, |
|
887
|
|
|
Coefficient $C7, |
|
888
|
|
|
Coefficient $C8, |
|
889
|
|
|
Coefficient $C9, |
|
890
|
|
|
Coefficient $C10 |
|
891
|
|
|
): ProjectedPoint { |
|
892
|
2 |
|
$asKrovak = $this->krovak($to, $latitudeOfProjectionCentre, $longitudeOfOrigin, $coLatitudeOfConeAxis, $latitudeOfPseudoStandardParallel, $scaleFactorOnPseudoStandardParallel, new Metre(0), new Metre(0)); |
|
893
|
|
|
|
|
894
|
2 |
|
$westing = $asKrovak->getWesting()->asMetres()->getValue(); |
|
895
|
2 |
|
$southing = $asKrovak->getSouthing()->asMetres()->getValue(); |
|
896
|
2 |
|
$c1 = $C1->asUnity()->getValue(); |
|
897
|
2 |
|
$c2 = $C2->asUnity()->getValue(); |
|
898
|
2 |
|
$c3 = $C3->asUnity()->getValue(); |
|
899
|
2 |
|
$c4 = $C4->asUnity()->getValue(); |
|
900
|
2 |
|
$c5 = $C5->asUnity()->getValue(); |
|
901
|
2 |
|
$c6 = $C6->asUnity()->getValue(); |
|
902
|
2 |
|
$c7 = $C7->asUnity()->getValue(); |
|
903
|
2 |
|
$c8 = $C8->asUnity()->getValue(); |
|
904
|
2 |
|
$c9 = $C9->asUnity()->getValue(); |
|
905
|
2 |
|
$c10 = $C10->asUnity()->getValue(); |
|
906
|
|
|
|
|
907
|
2 |
|
$Xr = $southing - $ordinate1OfEvaluationPoint->asMetres()->getValue(); |
|
908
|
2 |
|
$Yr = $westing - $ordinate2OfEvaluationPoint->asMetres()->getValue(); |
|
909
|
|
|
|
|
910
|
2 |
|
$dX = $c1 + $c3 * $Xr - $c4 * $Yr - 2 * $c6 * $Xr * $Yr + $c5 * ($Xr ** 2 - $Yr ** 2) + $c7 * $Xr * ($Xr ** 2 - 3 * $Yr ** 2) - $c8 * $Yr * (3 * $Xr ** 2 - $Yr ** 2) + 4 * $c9 * $Xr * $Yr * ($Xr ** 2 - $Yr ** 2) + $c10 * ($Xr ** 4 + $Yr ** 4 - 6 * $Xr ** 2 * $Yr ** 2); |
|
911
|
2 |
|
$dY = $c2 + $c3 * $Yr + $c4 * $Xr + 2 * $c5 * $Xr * $Yr + $c6 * ($Xr ** 2 - $Yr ** 2) + $c8 * $Xr * ($Xr ** 2 - 3 * $Yr ** 2) + $c7 * $Yr * (3 * $Xr ** 2 - $Yr ** 2) - 4 * $c10 * $Xr * $Yr * ($Xr ** 2 - $Yr ** 2) + $c9 * ($Xr ** 4 + $Yr ** 4 - 6 * $Xr ** 2 * $Yr ** 2); |
|
912
|
|
|
|
|
913
|
2 |
|
$westing += $falseEasting->asMetres()->getValue() - $dY; |
|
914
|
2 |
|
$southing += $falseNorthing->asMetres()->getValue() - $dX; |
|
915
|
|
|
|
|
916
|
2 |
|
return ProjectedPoint::create(new Metre(-$westing), new Metre(-$southing), new Metre($westing), new Metre($southing), $to, $this->epoch); |
|
917
|
|
|
} |
|
918
|
|
|
|
|
919
|
|
|
/** |
|
920
|
|
|
* Lambert Azimuthal Equal Area |
|
921
|
|
|
* This is the ellipsoidal form of the projection. |
|
922
|
|
|
*/ |
|
923
|
1 |
|
public function lambertAzimuthalEqualArea( |
|
924
|
|
|
Projected $to, |
|
925
|
|
|
Angle $latitudeOfNaturalOrigin, |
|
926
|
|
|
Angle $longitudeOfNaturalOrigin, |
|
927
|
|
|
Length $falseEasting, |
|
928
|
|
|
Length $falseNorthing |
|
929
|
|
|
): ProjectedPoint { |
|
930
|
1 |
|
$latitude = $this->latitude->asRadians()->getValue(); |
|
931
|
1 |
|
$longitude = $this->longitude->asRadians()->getValue(); |
|
932
|
1 |
|
$latitudeOrigin = $latitudeOfNaturalOrigin->asRadians()->getValue(); |
|
933
|
1 |
|
$longitudeOrigin = $longitudeOfNaturalOrigin->asRadians()->getValue(); |
|
934
|
1 |
|
$a = $this->crs->getDatum()->getEllipsoid()->getSemiMajorAxis()->asMetres()->getValue(); |
|
935
|
1 |
|
$e = $this->crs->getDatum()->getEllipsoid()->getEccentricity(); |
|
936
|
1 |
|
$e2 = $this->crs->getDatum()->getEllipsoid()->getEccentricitySquared(); |
|
937
|
|
|
|
|
938
|
1 |
|
$q = (1 - $e2) * ((sin($latitude) / (1 - $e2 * sin($latitude) ** 2)) - ((1 / (2 * $e)) * log((1 - $e * sin($latitude)) / (1 + $e * sin($latitude))))); |
|
939
|
1 |
|
$qO = (1 - $e2) * ((sin($latitudeOrigin) / (1 - $e2 * sin($latitudeOrigin) ** 2)) - ((1 / (2 * $e)) * log((1 - $e * sin($latitudeOrigin)) / (1 + $e * sin($latitudeOrigin))))); |
|
940
|
1 |
|
$qP = (1 - $e2) * ((1 / (1 - $e2)) - ((1 / (2 * $e)) * log((1 - $e) / (1 + $e)))); |
|
941
|
1 |
|
$beta = self::asin($q / $qP); |
|
942
|
1 |
|
$betaO = self::asin($qO / $qP); |
|
943
|
1 |
|
$Rq = $a * sqrt($qP / 2); |
|
944
|
1 |
|
$B = $Rq * sqrt(2 / (1 + sin($betaO) * sin($beta) + (cos($betaO) * cos($beta) * cos($longitude - $longitudeOrigin)))); |
|
945
|
1 |
|
$D = $a * (cos($latitudeOrigin) / sqrt(1 - $e2 * sin($latitudeOrigin) ** 2)) / ($Rq * cos($betaO)); |
|
946
|
|
|
|
|
947
|
1 |
|
$easting = $falseEasting->asMetres()->getValue() + (($B * $D) * (cos($beta) * sin($longitude - $longitudeOrigin))); |
|
948
|
1 |
|
$northing = $falseNorthing->asMetres()->getValue() + ($B / $D) * ((cos($betaO) * sin($beta)) - (sin($betaO) * cos($beta) * cos($longitude - $longitudeOrigin))); |
|
949
|
|
|
|
|
950
|
1 |
|
return ProjectedPoint::create(new Metre($easting), new Metre($northing), new Metre(-$easting), new Metre(-$northing), $to, $this->epoch); |
|
951
|
|
|
} |
|
952
|
|
|
|
|
953
|
|
|
/** |
|
954
|
|
|
* Lambert Azimuthal Equal Area (Spherical) |
|
955
|
|
|
* This is the spherical form of the projection. See coordinate operation method Lambert Azimuthal Equal Area |
|
956
|
|
|
* (code 9820) for ellipsoidal form. Differences of several tens of metres result from comparison of the two |
|
957
|
|
|
* methods. |
|
958
|
|
|
*/ |
|
959
|
1 |
|
public function lambertAzimuthalEqualAreaSpherical( |
|
960
|
|
|
Projected $to, |
|
961
|
|
|
Angle $latitudeOfNaturalOrigin, |
|
962
|
|
|
Angle $longitudeOfNaturalOrigin, |
|
963
|
|
|
Length $falseEasting, |
|
964
|
|
|
Length $falseNorthing |
|
965
|
|
|
): ProjectedPoint { |
|
966
|
1 |
|
$latitude = $this->latitude->asRadians()->getValue(); |
|
967
|
1 |
|
$longitude = $this->longitude->asRadians()->getValue(); |
|
968
|
1 |
|
$latitudeOrigin = $latitudeOfNaturalOrigin->asRadians()->getValue(); |
|
969
|
1 |
|
$longitudeOrigin = $longitudeOfNaturalOrigin->asRadians()->getValue(); |
|
970
|
1 |
|
$a = $this->crs->getDatum()->getEllipsoid()->getSemiMajorAxis()->asMetres()->getValue(); |
|
971
|
|
|
|
|
972
|
1 |
|
$k = sqrt(2 / (1 + sin($latitudeOrigin) * sin($latitude) + cos($latitudeOrigin) * cos($latitude) * cos($longitude - $longitudeOrigin))); |
|
973
|
|
|
|
|
974
|
1 |
|
$easting = $falseEasting->asMetres()->getValue() + ($a * $k * cos($latitude) * sin($longitude - $longitudeOrigin)); |
|
975
|
1 |
|
$northing = $falseNorthing->asMetres()->getValue() + ($a * $k * (cos($latitudeOrigin) * sin($latitude) - sin($latitudeOrigin) * cos($latitude) * cos($longitude - $longitudeOrigin))); |
|
976
|
|
|
|
|
977
|
1 |
|
return ProjectedPoint::create(new Metre($easting), new Metre($northing), new Metre(-$easting), new Metre(-$northing), $to, $this->epoch); |
|
978
|
|
|
} |
|
979
|
|
|
|
|
980
|
|
|
/** |
|
981
|
|
|
* Lambert Conic Conformal (1SP). |
|
982
|
|
|
*/ |
|
983
|
1 |
|
public function lambertConicConformal1SP( |
|
984
|
|
|
Projected $to, |
|
985
|
|
|
Angle $latitudeOfNaturalOrigin, |
|
986
|
|
|
Angle $longitudeOfNaturalOrigin, |
|
987
|
|
|
Scale $scaleFactorAtNaturalOrigin, |
|
988
|
|
|
Length $falseEasting, |
|
989
|
|
|
Length $falseNorthing |
|
990
|
|
|
): ProjectedPoint { |
|
991
|
1 |
|
$latitude = $this->latitude->asRadians()->getValue(); |
|
992
|
1 |
|
$longitude = $this->longitude->asRadians()->getValue(); |
|
993
|
1 |
|
$latitudeOrigin = $latitudeOfNaturalOrigin->asRadians()->getValue(); |
|
994
|
1 |
|
$longitudeOrigin = $longitudeOfNaturalOrigin->asRadians()->getValue(); |
|
995
|
1 |
|
$kO = $scaleFactorAtNaturalOrigin->asUnity()->getValue(); |
|
996
|
1 |
|
$a = $this->crs->getDatum()->getEllipsoid()->getSemiMajorAxis()->asMetres()->getValue(); |
|
997
|
1 |
|
$e = $this->crs->getDatum()->getEllipsoid()->getEccentricity(); |
|
998
|
1 |
|
$e2 = $this->crs->getDatum()->getEllipsoid()->getEccentricitySquared(); |
|
999
|
|
|
|
|
1000
|
1 |
|
$mO = cos($latitudeOrigin) / sqrt(1 - $e2 * sin($latitudeOrigin) ** 2); |
|
1001
|
1 |
|
$tO = tan(M_PI / 4 - $latitudeOrigin / 2) / ((1 - $e * sin($latitudeOrigin)) / (1 + $e * sin($latitudeOrigin))) ** ($e / 2); |
|
1002
|
1 |
|
$t = tan(M_PI / 4 - $latitude / 2) / ((1 - $e * sin($latitude)) / (1 + $e * sin($latitude))) ** ($e / 2); |
|
1003
|
1 |
|
$n = sin($latitudeOrigin); |
|
1004
|
1 |
|
$F = $mO / ($n * $tO ** $n); |
|
1005
|
1 |
|
$rO = $a * $F * $tO ** $n * $kO; |
|
1006
|
1 |
|
$r = $a * $F * $t ** $n * $kO; |
|
1007
|
1 |
|
$theta = $n * ($longitude - $longitudeOrigin); |
|
1008
|
|
|
|
|
1009
|
1 |
|
$easting = $falseEasting->asMetres()->getValue() + $r * sin($theta); |
|
1010
|
1 |
|
$northing = $falseNorthing->asMetres()->getValue() + $rO - $r * cos($theta); |
|
1011
|
|
|
|
|
1012
|
1 |
|
return ProjectedPoint::create(new Metre($easting), new Metre($northing), new Metre(-$easting), new Metre(-$northing), $to, $this->epoch); |
|
1013
|
|
|
} |
|
1014
|
|
|
|
|
1015
|
|
|
/** |
|
1016
|
|
|
* Lambert Conic Conformal (2SP Belgium) |
|
1017
|
|
|
* In 2000 this modification was replaced through use of the regular Lambert Conic Conformal (2SP) method [9802] |
|
1018
|
|
|
* with appropriately modified parameter values. |
|
1019
|
|
|
*/ |
|
1020
|
1 |
|
public function lambertConicConformal2SPBelgium( |
|
1021
|
|
|
Projected $to, |
|
1022
|
|
|
Angle $latitudeOfFalseOrigin, |
|
1023
|
|
|
Angle $longitudeOfFalseOrigin, |
|
1024
|
|
|
Angle $latitudeOf1stStandardParallel, |
|
1025
|
|
|
Angle $latitudeOf2ndStandardParallel, |
|
1026
|
|
|
Length $eastingAtFalseOrigin, |
|
1027
|
|
|
Length $northingAtFalseOrigin |
|
1028
|
|
|
): ProjectedPoint { |
|
1029
|
1 |
|
$latitude = $this->latitude->asRadians()->getValue(); |
|
1030
|
1 |
|
$longitude = $this->longitude->asRadians()->getValue(); |
|
1031
|
1 |
|
$lambdaF = $longitudeOfFalseOrigin->asRadians()->getValue(); |
|
1032
|
1 |
|
$phiF = $latitudeOfFalseOrigin->asRadians()->getValue(); |
|
1033
|
1 |
|
$phi1 = $latitudeOf1stStandardParallel->asRadians()->getValue(); |
|
1034
|
1 |
|
$phi2 = $latitudeOf2ndStandardParallel->asRadians()->getValue(); |
|
1035
|
1 |
|
$a = $this->crs->getDatum()->getEllipsoid()->getSemiMajorAxis()->asMetres()->getValue(); |
|
1036
|
1 |
|
$e = $this->crs->getDatum()->getEllipsoid()->getEccentricity(); |
|
1037
|
1 |
|
$e2 = $this->crs->getDatum()->getEllipsoid()->getEccentricitySquared(); |
|
1038
|
|
|
|
|
1039
|
1 |
|
$m1 = cos($phi1) / sqrt(1 - $e2 * sin($phi1) ** 2); |
|
1040
|
1 |
|
$m2 = cos($phi2) / sqrt(1 - $e2 * sin($phi2) ** 2); |
|
1041
|
1 |
|
$t = tan(M_PI / 4 - $latitude / 2) / ((1 - $e * sin($latitude)) / (1 + $e * sin($latitude))) ** ($e / 2); |
|
1042
|
1 |
|
$t1 = tan(M_PI / 4 - $phi1 / 2) / ((1 - $e * sin($phi1)) / (1 + $e * sin($phi1))) ** ($e / 2); |
|
1043
|
1 |
|
$t2 = tan(M_PI / 4 - $phi2 / 2) / ((1 - $e * sin($phi2)) / (1 + $e * sin($phi2))) ** ($e / 2); |
|
1044
|
1 |
|
$tF = tan(M_PI / 4 - $phiF / 2) / ((1 - $e * sin($phiF)) / (1 + $e * sin($phiF))) ** ($e / 2); |
|
1045
|
1 |
|
$n = (log($m1) - log($m2)) / (log($t1) - log($t2)); |
|
1046
|
1 |
|
$F = $m1 / ($n * $t1 ** $n); |
|
1047
|
1 |
|
$r = $a * $F * $t ** $n; |
|
1048
|
1 |
|
$rF = $a * $F * $tF ** $n; |
|
1049
|
1 |
|
if (is_nan($rF)) { |
|
1050
|
1 |
|
$rF = 0; |
|
1051
|
|
|
} |
|
1052
|
1 |
|
$theta = ($n * ($longitude - $lambdaF)) - (new ArcSecond(29.2985))->asRadians()->getValue(); |
|
1053
|
|
|
|
|
1054
|
1 |
|
$easting = $eastingAtFalseOrigin->asMetres()->getValue() + $r * sin($theta); |
|
1055
|
1 |
|
$northing = $northingAtFalseOrigin->asMetres()->getValue() + $rF - $r * cos($theta); |
|
1056
|
|
|
|
|
1057
|
1 |
|
return ProjectedPoint::create(new Metre($easting), new Metre($northing), new Metre(-$easting), new Metre(-$northing), $to, $this->epoch); |
|
1058
|
|
|
} |
|
1059
|
|
|
|
|
1060
|
|
|
/** |
|
1061
|
|
|
* Lambert Conic Conformal (2SP Michigan). |
|
1062
|
|
|
*/ |
|
1063
|
1 |
|
public function lambertConicConformal2SPMichigan( |
|
1064
|
|
|
Projected $to, |
|
1065
|
|
|
Angle $latitudeOfFalseOrigin, |
|
1066
|
|
|
Angle $longitudeOfFalseOrigin, |
|
1067
|
|
|
Angle $latitudeOf1stStandardParallel, |
|
1068
|
|
|
Angle $latitudeOf2ndStandardParallel, |
|
1069
|
|
|
Length $eastingAtFalseOrigin, |
|
1070
|
|
|
Length $northingAtFalseOrigin, |
|
1071
|
|
|
Scale $ellipsoidScalingFactor |
|
1072
|
|
|
): ProjectedPoint { |
|
1073
|
1 |
|
$latitude = $this->latitude->asRadians()->getValue(); |
|
1074
|
1 |
|
$longitude = $this->longitude->asRadians()->getValue(); |
|
1075
|
1 |
|
$lambdaF = $longitudeOfFalseOrigin->asRadians()->getValue(); |
|
1076
|
1 |
|
$phiF = $latitudeOfFalseOrigin->asRadians()->getValue(); |
|
1077
|
1 |
|
$phi1 = $latitudeOf1stStandardParallel->asRadians()->getValue(); |
|
1078
|
1 |
|
$phi2 = $latitudeOf2ndStandardParallel->asRadians()->getValue(); |
|
1079
|
1 |
|
$K = $ellipsoidScalingFactor->asUnity()->getValue(); |
|
1080
|
1 |
|
$a = $this->crs->getDatum()->getEllipsoid()->getSemiMajorAxis()->asMetres()->getValue(); |
|
1081
|
1 |
|
$e = $this->crs->getDatum()->getEllipsoid()->getEccentricity(); |
|
1082
|
1 |
|
$e2 = $this->crs->getDatum()->getEllipsoid()->getEccentricitySquared(); |
|
1083
|
|
|
|
|
1084
|
1 |
|
$m1 = cos($phi1) / sqrt(1 - $e2 * sin($phi1) ** 2); |
|
1085
|
1 |
|
$m2 = cos($phi2) / sqrt(1 - $e2 * sin($phi2) ** 2); |
|
1086
|
1 |
|
$t = tan(M_PI / 4 - $latitude / 2) / ((1 - $e * sin($latitude)) / (1 + $e * sin($latitude))) ** ($e / 2); |
|
1087
|
1 |
|
$t1 = tan(M_PI / 4 - $phi1 / 2) / ((1 - $e * sin($phi1)) / (1 + $e * sin($phi1))) ** ($e / 2); |
|
1088
|
1 |
|
$t2 = tan(M_PI / 4 - $phi2 / 2) / ((1 - $e * sin($phi2)) / (1 + $e * sin($phi2))) ** ($e / 2); |
|
1089
|
1 |
|
$tF = tan(M_PI / 4 - $phiF / 2) / ((1 - $e * sin($phiF)) / (1 + $e * sin($phiF))) ** ($e / 2); |
|
1090
|
1 |
|
$n = (log($m1) - log($m2)) / (log($t1) - log($t2)); |
|
1091
|
1 |
|
$F = $m1 / ($n * $t1 ** $n); |
|
1092
|
1 |
|
$r = $a * $K * $F * $t ** $n; |
|
1093
|
1 |
|
$rF = $a * $K * $F * $tF ** $n; |
|
1094
|
1 |
|
$theta = $n * ($longitude - $lambdaF); |
|
1095
|
|
|
|
|
1096
|
1 |
|
$easting = $eastingAtFalseOrigin->asMetres()->getValue() + $r * sin($theta); |
|
1097
|
1 |
|
$northing = $northingAtFalseOrigin->asMetres()->getValue() + $rF - $r * cos($theta); |
|
1098
|
|
|
|
|
1099
|
1 |
|
return ProjectedPoint::create(new Metre($easting), new Metre($northing), new Metre(-$easting), new Metre(-$northing), $to, $this->epoch); |
|
1100
|
|
|
} |
|
1101
|
|
|
|
|
1102
|
|
|
/** |
|
1103
|
|
|
* Lambert Conic Conformal (2SP). |
|
1104
|
|
|
*/ |
|
1105
|
1 |
|
public function lambertConicConformal2SP( |
|
1106
|
|
|
Projected $to, |
|
1107
|
|
|
Angle $latitudeOfFalseOrigin, |
|
1108
|
|
|
Angle $longitudeOfFalseOrigin, |
|
1109
|
|
|
Angle $latitudeOf1stStandardParallel, |
|
1110
|
|
|
Angle $latitudeOf2ndStandardParallel, |
|
1111
|
|
|
Length $eastingAtFalseOrigin, |
|
1112
|
|
|
Length $northingAtFalseOrigin |
|
1113
|
|
|
): ProjectedPoint { |
|
1114
|
1 |
|
$latitude = $this->latitude->asRadians()->getValue(); |
|
1115
|
1 |
|
$longitude = $this->longitude->asRadians()->getValue(); |
|
1116
|
1 |
|
$lambdaF = $longitudeOfFalseOrigin->asRadians()->getValue(); |
|
1117
|
1 |
|
$phiF = $latitudeOfFalseOrigin->asRadians()->getValue(); |
|
1118
|
1 |
|
$phi1 = $latitudeOf1stStandardParallel->asRadians()->getValue(); |
|
1119
|
1 |
|
$phi2 = $latitudeOf2ndStandardParallel->asRadians()->getValue(); |
|
1120
|
1 |
|
$a = $this->crs->getDatum()->getEllipsoid()->getSemiMajorAxis()->asMetres()->getValue(); |
|
1121
|
1 |
|
$e = $this->crs->getDatum()->getEllipsoid()->getEccentricity(); |
|
1122
|
1 |
|
$e2 = $this->crs->getDatum()->getEllipsoid()->getEccentricitySquared(); |
|
1123
|
|
|
|
|
1124
|
1 |
|
$m1 = cos($phi1) / sqrt(1 - $e2 * sin($phi1) ** 2); |
|
1125
|
1 |
|
$m2 = cos($phi2) / sqrt(1 - $e2 * sin($phi2) ** 2); |
|
1126
|
1 |
|
$t = tan(M_PI / 4 - $latitude / 2) / ((1 - $e * sin($latitude)) / (1 + $e * sin($latitude))) ** ($e / 2); |
|
1127
|
1 |
|
$t1 = tan(M_PI / 4 - $phi1 / 2) / ((1 - $e * sin($phi1)) / (1 + $e * sin($phi1))) ** ($e / 2); |
|
1128
|
1 |
|
$t2 = tan(M_PI / 4 - $phi2 / 2) / ((1 - $e * sin($phi2)) / (1 + $e * sin($phi2))) ** ($e / 2); |
|
1129
|
1 |
|
$tF = tan(M_PI / 4 - $phiF / 2) / ((1 - $e * sin($phiF)) / (1 + $e * sin($phiF))) ** ($e / 2); |
|
1130
|
1 |
|
$n = (log($m1) - log($m2)) / (log($t1) - log($t2)); |
|
1131
|
1 |
|
$F = $m1 / ($n * $t1 ** $n); |
|
1132
|
1 |
|
$r = $a * $F * $t ** $n; |
|
1133
|
1 |
|
$rF = $a * $F * $tF ** $n; |
|
1134
|
1 |
|
$theta = $n * ($longitude - $lambdaF); |
|
1135
|
|
|
|
|
1136
|
1 |
|
$easting = $eastingAtFalseOrigin->asMetres()->getValue() + $r * sin($theta); |
|
1137
|
1 |
|
$northing = $northingAtFalseOrigin->asMetres()->getValue() + $rF - $r * cos($theta); |
|
1138
|
|
|
|
|
1139
|
1 |
|
return ProjectedPoint::create(new Metre($easting), new Metre($northing), new Metre(-$easting), new Metre(-$northing), $to, $this->epoch); |
|
1140
|
|
|
} |
|
1141
|
|
|
|
|
1142
|
|
|
/** |
|
1143
|
|
|
* Lambert Conic Conformal (West Orientated). |
|
1144
|
|
|
*/ |
|
1145
|
|
|
public function lambertConicConformalWestOrientated( |
|
1146
|
|
|
Projected $to, |
|
1147
|
|
|
Angle $latitudeOfNaturalOrigin, |
|
1148
|
|
|
Angle $longitudeOfNaturalOrigin, |
|
1149
|
|
|
Scale $scaleFactorAtNaturalOrigin, |
|
1150
|
|
|
Length $falseEasting, |
|
1151
|
|
|
Length $falseNorthing |
|
1152
|
|
|
): ProjectedPoint { |
|
1153
|
|
|
$latitude = $this->latitude->asRadians()->getValue(); |
|
1154
|
|
|
$longitude = $this->longitude->asRadians()->getValue(); |
|
1155
|
|
|
$latitudeOrigin = $latitudeOfNaturalOrigin->asRadians()->getValue(); |
|
1156
|
|
|
$longitudeOrigin = $longitudeOfNaturalOrigin->asRadians()->getValue(); |
|
1157
|
|
|
$kO = $scaleFactorAtNaturalOrigin->asUnity()->getValue(); |
|
1158
|
|
|
$a = $this->crs->getDatum()->getEllipsoid()->getSemiMajorAxis()->asMetres()->getValue(); |
|
1159
|
|
|
$e = $this->crs->getDatum()->getEllipsoid()->getEccentricity(); |
|
1160
|
|
|
$e2 = $this->crs->getDatum()->getEllipsoid()->getEccentricitySquared(); |
|
1161
|
|
|
|
|
1162
|
|
|
$mO = cos($latitudeOrigin) / sqrt(1 - $e2 * sin($latitudeOrigin) ** 2); |
|
1163
|
|
|
$tO = tan(M_PI / 4 - $latitudeOrigin / 2) / ((1 - $e * sin($latitudeOrigin)) / (1 + $e * sin($latitudeOrigin))) ** ($e / 2); |
|
1164
|
|
|
$t = tan(M_PI / 4 - $latitude / 2) / ((1 - $e * sin($latitude)) / (1 + $e * sin($latitude))) ** ($e / 2); |
|
1165
|
|
|
$n = sin($latitudeOrigin); |
|
1166
|
|
|
$F = $mO / ($n * $tO ** $n); |
|
1167
|
|
|
$rO = $a * $F * $tO ** $n ** $kO; |
|
1168
|
|
|
$r = $a * $F * $t ** $n ** $kO; |
|
1169
|
|
|
$theta = $n * ($longitude - $longitudeOrigin); |
|
1170
|
|
|
|
|
1171
|
|
|
$westing = $falseEasting->asMetres()->getValue() - $r * sin($theta); |
|
1172
|
|
|
$northing = $falseNorthing->asMetres()->getValue() + $rO - $r * cos($theta); |
|
1173
|
|
|
|
|
1174
|
|
|
return ProjectedPoint::create(new Metre(-$westing), new Metre($northing), new Metre($westing), new Metre(-$northing), $to, $this->epoch); |
|
1175
|
|
|
} |
|
1176
|
|
|
|
|
1177
|
|
|
/** |
|
1178
|
|
|
* Lambert Conic Near-Conformal |
|
1179
|
|
|
* The Lambert Near-Conformal projection is derived from the Lambert Conformal Conic projection by truncating the |
|
1180
|
|
|
* series expansion of the projection formulae. |
|
1181
|
|
|
*/ |
|
1182
|
1 |
|
public function lambertConicNearConformal( |
|
1183
|
|
|
Projected $to, |
|
1184
|
|
|
Angle $latitudeOfNaturalOrigin, |
|
1185
|
|
|
Angle $longitudeOfNaturalOrigin, |
|
1186
|
|
|
Scale $scaleFactorAtNaturalOrigin, |
|
1187
|
|
|
Length $falseEasting, |
|
1188
|
|
|
Length $falseNorthing |
|
1189
|
|
|
): ProjectedPoint { |
|
1190
|
1 |
|
$latitude = $this->latitude->asRadians()->getValue(); |
|
1191
|
1 |
|
$longitude = $this->longitude->asRadians()->getValue(); |
|
1192
|
1 |
|
$latitudeOrigin = $latitudeOfNaturalOrigin->asRadians()->getValue(); |
|
1193
|
1 |
|
$longitudeOrigin = $longitudeOfNaturalOrigin->asRadians()->getValue(); |
|
1194
|
1 |
|
$kO = $scaleFactorAtNaturalOrigin->asUnity()->getValue(); |
|
1195
|
1 |
|
$a = $this->crs->getDatum()->getEllipsoid()->getSemiMajorAxis()->asMetres()->getValue(); |
|
1196
|
1 |
|
$e2 = $this->crs->getDatum()->getEllipsoid()->getEccentricitySquared(); |
|
1197
|
1 |
|
$f = $this->crs->getDatum()->getEllipsoid()->getInverseFlattening(); |
|
1198
|
|
|
|
|
1199
|
1 |
|
$n = $f / (2 - $f); |
|
1200
|
1 |
|
$rhoO = $a * (1 - $e2) / (1 - $e2 * sin($latitudeOrigin) ** 2) ** (3 / 2); |
|
1201
|
1 |
|
$nuO = $a / sqrt(1 - $e2 * (sin($latitudeOrigin) ** 2)); |
|
1202
|
1 |
|
$A = 1 / (6 * $rhoO * $nuO); |
|
1203
|
1 |
|
$APrime = $a * (1 - $n + 5 * ($n ** 2 - $n ** 3) / 4 + 81 * ($n ** 4 - $n ** 5) / 64); |
|
1204
|
1 |
|
$BPrime = 3 * $a * ($n - $n ** 2 + 7 * ($n ** 3 - $n ** 4) / 8 + 55 * $n ** 5 / 64) / 2; |
|
1205
|
1 |
|
$CPrime = 15 * $a * ($n ** 2 - $n ** 3 + 3 * ($n ** 4 - $n ** 5) / 4) / 16; |
|
1206
|
1 |
|
$DPrime = 35 * $a * ($n ** 3 - $n ** 4 + 11 * $n ** 5 / 16) / 48; |
|
1207
|
1 |
|
$EPrime = 315 * $a * ($n ** 4 - $n ** 5) / 512; |
|
1208
|
1 |
|
$rO = $kO * $nuO / tan($latitudeOrigin); |
|
1209
|
1 |
|
$sO = $APrime * $latitudeOrigin - $BPrime * sin(2 * $latitudeOrigin) + $CPrime * sin(4 * $latitudeOrigin) - $DPrime * sin(6 * $latitudeOrigin) + $EPrime * sin(8 * $latitudeOrigin); |
|
1210
|
1 |
|
$s = $APrime * $latitude - $BPrime * sin(2 * $latitude) + $CPrime * sin(4 * $latitude) - $DPrime * sin(6 * $latitude) + $EPrime * sin(8 * $latitude); |
|
1211
|
1 |
|
$m = $s - $sO; |
|
1212
|
1 |
|
$M = $kO * ($m + $A * $m ** 3); |
|
1213
|
1 |
|
$r = $rO - $M; |
|
1214
|
1 |
|
$theta = ($longitude - $longitudeOrigin) * sin($latitudeOrigin); |
|
1215
|
|
|
|
|
1216
|
1 |
|
$easting = $falseEasting->asMetres()->getValue() + $r * sin($theta); |
|
1217
|
1 |
|
$northing = $falseNorthing->asMetres()->getValue() + $M + $r * sin($theta) * tan($theta / 2); |
|
1218
|
|
|
|
|
1219
|
1 |
|
return ProjectedPoint::create(new Metre($easting), new Metre($northing), new Metre(-$easting), new Metre(-$northing), $to, $this->epoch); |
|
1220
|
|
|
} |
|
1221
|
|
|
|
|
1222
|
|
|
/** |
|
1223
|
|
|
* Lambert Cylindrical Equal Area |
|
1224
|
|
|
* This is the ellipsoidal form of the projection. |
|
1225
|
|
|
*/ |
|
1226
|
1 |
|
public function lambertCylindricalEqualArea( |
|
1227
|
|
|
Projected $to, |
|
1228
|
|
|
Angle $latitudeOf1stStandardParallel, |
|
1229
|
|
|
Angle $longitudeOfNaturalOrigin, |
|
1230
|
|
|
Length $falseEasting, |
|
1231
|
|
|
Length $falseNorthing |
|
1232
|
|
|
): ProjectedPoint { |
|
1233
|
1 |
|
$latitude = $this->latitude->asRadians()->getValue(); |
|
1234
|
1 |
|
$longitude = $this->longitude->asRadians()->getValue(); |
|
1235
|
1 |
|
$latitudeFirstParallel = $latitudeOf1stStandardParallel->asRadians()->getValue(); |
|
1236
|
1 |
|
$longitudeOrigin = $longitudeOfNaturalOrigin->asRadians()->getValue(); |
|
1237
|
1 |
|
$a = $this->crs->getDatum()->getEllipsoid()->getSemiMajorAxis()->asMetres()->getValue(); |
|
1238
|
1 |
|
$e = $this->crs->getDatum()->getEllipsoid()->getEccentricity(); |
|
1239
|
1 |
|
$e2 = $this->crs->getDatum()->getEllipsoid()->getEccentricitySquared(); |
|
1240
|
|
|
|
|
1241
|
1 |
|
$k = cos($latitudeFirstParallel) / sqrt(1 - $e2 * sin($latitudeFirstParallel) ** 2); |
|
1242
|
1 |
|
$q = (1 - $e2) * ((sin($latitude) / (1 - $e2 * sin($latitude) ** 2)) - (1 / (2 * $e)) * log((1 - $e * sin($latitude)) / (1 + $e * sin($latitude)))); |
|
1243
|
|
|
|
|
1244
|
1 |
|
$x = $a * $k * ($longitude - $longitudeOrigin); |
|
1245
|
1 |
|
$y = $a * $q / (2 * $k); |
|
1246
|
|
|
|
|
1247
|
1 |
|
$easting = $falseEasting->asMetres()->getValue() + $x; |
|
1248
|
1 |
|
$northing = $falseNorthing->asMetres()->getValue() + $y; |
|
1249
|
|
|
|
|
1250
|
1 |
|
return ProjectedPoint::create(new Metre($easting), new Metre($northing), new Metre(-$easting), new Metre(-$northing), $to, $this->epoch); |
|
1251
|
|
|
} |
|
1252
|
|
|
|
|
1253
|
|
|
/** |
|
1254
|
|
|
* Modified Azimuthal Equidistant |
|
1255
|
|
|
* Modified form of Oblique Azimuthal Equidistant projection method developed for Polynesian islands. For the |
|
1256
|
|
|
* distances over which these projections are used (under 800km) this modification introduces no significant error. |
|
1257
|
|
|
*/ |
|
1258
|
1 |
|
public function modifiedAzimuthalEquidistant( |
|
1259
|
|
|
Projected $to, |
|
1260
|
|
|
Angle $latitudeOfNaturalOrigin, |
|
1261
|
|
|
Angle $longitudeOfNaturalOrigin, |
|
1262
|
|
|
Length $falseEasting, |
|
1263
|
|
|
Length $falseNorthing |
|
1264
|
|
|
): ProjectedPoint { |
|
1265
|
1 |
|
$latitude = $this->latitude->asRadians()->getValue(); |
|
1266
|
1 |
|
$longitude = $this->longitude->asRadians()->getValue(); |
|
1267
|
1 |
|
$latitudeOrigin = $latitudeOfNaturalOrigin->asRadians()->getValue(); |
|
1268
|
1 |
|
$longitudeOrigin = $longitudeOfNaturalOrigin->asRadians()->getValue(); |
|
1269
|
1 |
|
$a = $this->crs->getDatum()->getEllipsoid()->getSemiMajorAxis()->asMetres()->getValue(); |
|
1270
|
1 |
|
$e = $this->crs->getDatum()->getEllipsoid()->getEccentricity(); |
|
1271
|
1 |
|
$e2 = $this->crs->getDatum()->getEllipsoid()->getEccentricitySquared(); |
|
1272
|
|
|
|
|
1273
|
1 |
|
$nuO = $a / sqrt(1 - $e2 * sin($latitudeOrigin) ** 2); |
|
1274
|
1 |
|
$nu = $a / sqrt(1 - $e2 * sin($latitude) ** 2); |
|
1275
|
1 |
|
$psi = atan((1 - $e2) * tan($latitude) + ($e2 * $nuO * sin($latitudeOrigin)) / ($nu * cos($latitude))); |
|
1276
|
1 |
|
$alpha = atan2(sin($longitude - $longitudeOrigin), (cos($latitudeOrigin) * tan($psi) - sin($latitudeOrigin) * cos($longitude - $longitudeOrigin))); |
|
1277
|
1 |
|
$G = $e * sin($latitudeOrigin) / sqrt(1 - $e2); |
|
1278
|
1 |
|
$H = $e * cos($latitudeOrigin) * cos($alpha) / sqrt(1 - $e2); |
|
1279
|
|
|
|
|
1280
|
1 |
|
if (sin($alpha) === 0.0) { |
|
1281
|
|
|
$s = self::asin(cos($latitudeOrigin) * sin($psi) - sin($latitudeOrigin) * cos($alpha)) * cos($alpha) / abs(cos($alpha)); |
|
1282
|
|
|
} else { |
|
1283
|
1 |
|
$s = self::asin(sin($longitude - $longitudeOrigin) * cos($psi) / sin($alpha)); |
|
1284
|
|
|
} |
|
1285
|
|
|
|
|
1286
|
1 |
|
$c = $nuO * $s * ((1 - $s ** 2 * $H ** 2 * (1 - $H ** 2) / 6) + (($s ** 3 / 8) * $G * $H * (1 - 2 * $H ** 2)) + ($s ** 4 / 120) * ($H ** 2 * (4 - 7 * $H ** 2) - 3 * $G ** 2 * (1 - 7 * $H ** 2)) - (($s ** 5 / 48) * $G * $H)); |
|
1287
|
|
|
|
|
1288
|
1 |
|
$easting = $falseEasting->asMetres()->getValue() + $c * sin($alpha); |
|
1289
|
1 |
|
$northing = $falseNorthing->asMetres()->getValue() + $c * cos($alpha); |
|
1290
|
|
|
|
|
1291
|
1 |
|
return ProjectedPoint::create(new Metre($easting), new Metre($northing), new Metre(-$easting), new Metre(-$northing), $to, $this->epoch); |
|
1292
|
|
|
} |
|
1293
|
|
|
|
|
1294
|
|
|
/** |
|
1295
|
|
|
* Oblique Stereographic |
|
1296
|
|
|
* This is not the same as the projection method of the same name in USGS Professional Paper no. 1395, "Map |
|
1297
|
|
|
* Projections - A Working Manual" by John P. Snyder. |
|
1298
|
|
|
*/ |
|
1299
|
1 |
|
public function obliqueStereographic( |
|
1300
|
|
|
Projected $to, |
|
1301
|
|
|
Angle $latitudeOfNaturalOrigin, |
|
1302
|
|
|
Angle $longitudeOfNaturalOrigin, |
|
1303
|
|
|
Scale $scaleFactorAtNaturalOrigin, |
|
1304
|
|
|
Length $falseEasting, |
|
1305
|
|
|
Length $falseNorthing |
|
1306
|
|
|
): ProjectedPoint { |
|
1307
|
1 |
|
$latitude = $this->latitude->asRadians()->getValue(); |
|
1308
|
1 |
|
$longitude = $this->longitude->asRadians()->getValue(); |
|
1309
|
1 |
|
$latitudeOrigin = $latitudeOfNaturalOrigin->asRadians()->getValue(); |
|
1310
|
1 |
|
$longitudeOrigin = $longitudeOfNaturalOrigin->asRadians()->getValue(); |
|
1311
|
1 |
|
$kO = $scaleFactorAtNaturalOrigin->asUnity()->getValue(); |
|
1312
|
1 |
|
$a = $this->crs->getDatum()->getEllipsoid()->getSemiMajorAxis()->asMetres()->getValue(); |
|
1313
|
1 |
|
$e = $this->crs->getDatum()->getEllipsoid()->getEccentricity(); |
|
1314
|
1 |
|
$e2 = $this->crs->getDatum()->getEllipsoid()->getEccentricitySquared(); |
|
1315
|
|
|
|
|
1316
|
1 |
|
$rhoOrigin = $a * (1 - $e2) / (1 - $e2 * sin($latitudeOrigin) ** 2) ** (3 / 2); |
|
1317
|
1 |
|
$nuOrigin = $a / sqrt(1 - $e2 * (sin($latitudeOrigin) ** 2)); |
|
1318
|
1 |
|
$R = sqrt($rhoOrigin * $nuOrigin); |
|
1319
|
|
|
|
|
1320
|
1 |
|
$n = sqrt(1 + ($e2 * cos($latitudeOrigin) ** 4 / (1 - $e2))); |
|
1321
|
1 |
|
$S1 = (1 + sin($latitudeOrigin)) / (1 - sin($latitudeOrigin)); |
|
1322
|
1 |
|
$S2 = (1 - $e * sin($latitudeOrigin)) / (1 + $e * sin($latitudeOrigin)); |
|
1323
|
1 |
|
$w1 = ($S1 * ($S2 ** $e)) ** $n; |
|
1324
|
1 |
|
$c = (($n + sin($latitudeOrigin)) * (1 - ($w1 - 1) / ($w1 + 1))) / (($n - sin($latitudeOrigin)) * (1 + ($w1 - 1) / ($w1 + 1))); |
|
1325
|
1 |
|
$w2 = $c * $w1; |
|
1326
|
1 |
|
$chiOrigin = self::asin(($w2 - 1) / ($w2 + 1)); |
|
1327
|
|
|
|
|
1328
|
1 |
|
$lambda = $n * ($longitude - $longitudeOrigin) + $longitudeOrigin; |
|
1329
|
|
|
|
|
1330
|
1 |
|
$Sa = (1 + sin($latitude)) / (1 - sin($latitude)); |
|
1331
|
1 |
|
$Sb = (1 - $e * sin($latitude)) / (1 + $e * sin($latitude)); |
|
1332
|
1 |
|
$w = $c * ($Sa * ($Sb ** $e)) ** $n; |
|
1333
|
1 |
|
$chi = self::asin(($w - 1) / ($w + 1)); |
|
1334
|
|
|
|
|
1335
|
1 |
|
$B = (1 + sin($chi) * sin($chiOrigin) + cos($chi) * cos($chiOrigin) * cos($lambda - $longitudeOrigin)); |
|
1336
|
|
|
|
|
1337
|
1 |
|
$easting = $falseEasting->asMetres()->getValue() + 2 * $R * $kO * cos($chi) * sin($lambda - $longitudeOrigin) / $B; |
|
1338
|
1 |
|
$northing = $falseNorthing->asMetres()->getValue() + 2 * $R * $kO * (sin($chi) * cos($chiOrigin) - cos($chi) * sin($chiOrigin) * cos($lambda - $longitudeOrigin)) / $B; |
|
1339
|
|
|
|
|
1340
|
1 |
|
return ProjectedPoint::create(new Metre($easting), new Metre($northing), new Metre(-$easting), new Metre(-$northing), $to, $this->epoch); |
|
1341
|
|
|
} |
|
1342
|
|
|
|
|
1343
|
|
|
/** |
|
1344
|
|
|
* Polar Stereographic (variant A) |
|
1345
|
|
|
* Latitude of natural origin must be either 90 degrees or -90 degrees (or equivalent in alternative angle unit). |
|
1346
|
|
|
*/ |
|
1347
|
1 |
|
public function polarStereographicVariantA( |
|
1348
|
|
|
Projected $to, |
|
1349
|
|
|
Angle $latitudeOfNaturalOrigin, |
|
1350
|
|
|
Angle $longitudeOfNaturalOrigin, |
|
1351
|
|
|
Scale $scaleFactorAtNaturalOrigin, |
|
1352
|
|
|
Length $falseEasting, |
|
1353
|
|
|
Length $falseNorthing |
|
1354
|
|
|
): ProjectedPoint { |
|
1355
|
1 |
|
$latitude = $this->latitude->asRadians()->getValue(); |
|
1356
|
1 |
|
$longitude = $this->longitude->asRadians()->getValue(); |
|
1357
|
1 |
|
$latitudeOrigin = $latitudeOfNaturalOrigin->asRadians()->getValue(); |
|
1358
|
1 |
|
$longitudeOrigin = $longitudeOfNaturalOrigin->asRadians()->getValue(); |
|
1359
|
1 |
|
$kO = $scaleFactorAtNaturalOrigin->asUnity()->getValue(); |
|
1360
|
1 |
|
$a = $this->crs->getDatum()->getEllipsoid()->getSemiMajorAxis()->asMetres()->getValue(); |
|
1361
|
1 |
|
$e = $this->crs->getDatum()->getEllipsoid()->getEccentricity(); |
|
1362
|
|
|
|
|
1363
|
1 |
|
if ($latitudeOrigin < 0) { |
|
1364
|
|
|
$t = tan(M_PI / 4 + $latitude / 2) / (((1 + $e * sin($latitude)) / (1 - $e * sin($latitude))) ** ($e / 2)); |
|
1365
|
|
|
} else { |
|
1366
|
1 |
|
$t = tan(M_PI / 4 - $latitude / 2) * (((1 + $e * sin($latitude)) / (1 - $e * sin($latitude))) ** ($e / 2)); |
|
1367
|
|
|
} |
|
1368
|
1 |
|
$rho = 2 * $a * $kO * $t / sqrt((1 + $e) ** (1 + $e) * (1 - $e) ** (1 - $e)); |
|
1369
|
|
|
|
|
1370
|
1 |
|
$theta = $longitude - $longitudeOrigin; |
|
1371
|
1 |
|
$dE = $rho * sin($theta); |
|
1372
|
1 |
|
$dN = $rho * cos($theta); |
|
1373
|
|
|
|
|
1374
|
1 |
|
$easting = $falseEasting->asMetres()->getValue() + $dE; |
|
1375
|
1 |
|
if ($latitudeOrigin < 0) { |
|
1376
|
|
|
$northing = $falseNorthing->asMetres()->getValue() + $dN; |
|
1377
|
|
|
} else { |
|
1378
|
1 |
|
$northing = $falseNorthing->asMetres()->getValue() - $dN; |
|
1379
|
|
|
} |
|
1380
|
|
|
|
|
1381
|
1 |
|
return ProjectedPoint::create(new Metre($easting), new Metre($northing), new Metre(-$easting), new Metre(-$northing), $to, $this->epoch); |
|
1382
|
|
|
} |
|
1383
|
|
|
|
|
1384
|
|
|
/** |
|
1385
|
|
|
* Polar Stereographic (variant B). |
|
1386
|
|
|
*/ |
|
1387
|
1 |
|
public function polarStereographicVariantB( |
|
1388
|
|
|
Projected $to, |
|
1389
|
|
|
Angle $latitudeOfStandardParallel, |
|
1390
|
|
|
Angle $longitudeOfOrigin, |
|
1391
|
|
|
Length $falseEasting, |
|
1392
|
|
|
Length $falseNorthing |
|
1393
|
|
|
): ProjectedPoint { |
|
1394
|
1 |
|
$latitude = $this->latitude->asRadians()->getValue(); |
|
1395
|
1 |
|
$longitude = $this->longitude->asRadians()->getValue(); |
|
1396
|
1 |
|
$firstStandardParallel = $latitudeOfStandardParallel->asRadians()->getValue(); |
|
1397
|
1 |
|
$longitudeOrigin = $longitudeOfOrigin->asRadians()->getValue(); |
|
1398
|
1 |
|
$a = $this->crs->getDatum()->getEllipsoid()->getSemiMajorAxis()->asMetres()->getValue(); |
|
1399
|
1 |
|
$e = $this->crs->getDatum()->getEllipsoid()->getEccentricity(); |
|
1400
|
1 |
|
$e2 = $this->crs->getDatum()->getEllipsoid()->getEccentricitySquared(); |
|
1401
|
|
|
|
|
1402
|
1 |
|
if ($firstStandardParallel < 0) { |
|
1403
|
1 |
|
$tF = tan(M_PI / 4 + $firstStandardParallel / 2) / (((1 + $e * sin($firstStandardParallel)) / (1 - $e * sin($firstStandardParallel))) ** ($e / 2)); |
|
1404
|
1 |
|
$t = tan(M_PI / 4 + $latitude / 2) / (((1 + $e * sin($latitude)) / (1 - $e * sin($latitude))) ** ($e / 2)); |
|
1405
|
|
|
} else { |
|
1406
|
|
|
$tF = tan(M_PI / 4 - $firstStandardParallel / 2) * (((1 + $e * sin($firstStandardParallel)) / (1 - $e * sin($firstStandardParallel))) ** ($e / 2)); |
|
1407
|
|
|
$t = tan(M_PI / 4 - $latitude / 2) * (((1 + $e * sin($latitude)) / (1 - $e * sin($latitude))) ** ($e / 2)); |
|
1408
|
|
|
} |
|
1409
|
1 |
|
$mF = cos($firstStandardParallel) / sqrt(1 - $e2 * sin($firstStandardParallel) ** 2); |
|
1410
|
1 |
|
$kO = $mF * sqrt((1 + $e) ** (1 + $e) * (1 - $e) ** (1 - $e)) / (2 * $tF); |
|
1411
|
|
|
|
|
1412
|
1 |
|
$rho = 2 * $a * $kO * $t / sqrt((1 + $e) ** (1 + $e) * (1 - $e) ** (1 - $e)); |
|
1413
|
|
|
|
|
1414
|
1 |
|
$theta = $longitude - $longitudeOrigin; |
|
1415
|
1 |
|
$dE = $rho * sin($theta); |
|
1416
|
1 |
|
$dN = $rho * cos($theta); |
|
1417
|
|
|
|
|
1418
|
1 |
|
$easting = $falseEasting->asMetres()->getValue() + $dE; |
|
1419
|
1 |
|
if ($firstStandardParallel < 0) { |
|
1420
|
1 |
|
$northing = $falseNorthing->asMetres()->getValue() + $dN; |
|
1421
|
|
|
} else { |
|
1422
|
|
|
$northing = $falseNorthing->asMetres()->getValue() - $dN; |
|
1423
|
|
|
} |
|
1424
|
|
|
|
|
1425
|
1 |
|
return ProjectedPoint::create(new Metre($easting), new Metre($northing), new Metre(-$easting), new Metre(-$northing), $to, $this->epoch); |
|
1426
|
|
|
} |
|
1427
|
|
|
|
|
1428
|
|
|
/** |
|
1429
|
|
|
* Polar Stereographic (variant C). |
|
1430
|
|
|
*/ |
|
1431
|
1 |
|
public function polarStereographicVariantC( |
|
1432
|
|
|
Projected $to, |
|
1433
|
|
|
Angle $latitudeOfStandardParallel, |
|
1434
|
|
|
Angle $longitudeOfOrigin, |
|
1435
|
|
|
Length $eastingAtFalseOrigin, |
|
1436
|
|
|
Length $northingAtFalseOrigin |
|
1437
|
|
|
): ProjectedPoint { |
|
1438
|
1 |
|
$latitude = $this->latitude->asRadians()->getValue(); |
|
1439
|
1 |
|
$longitude = $this->longitude->asRadians()->getValue(); |
|
1440
|
1 |
|
$firstStandardParallel = $latitudeOfStandardParallel->asRadians()->getValue(); |
|
1441
|
1 |
|
$longitudeOrigin = $longitudeOfOrigin->asRadians()->getValue(); |
|
1442
|
1 |
|
$a = $this->crs->getDatum()->getEllipsoid()->getSemiMajorAxis()->asMetres()->getValue(); |
|
1443
|
1 |
|
$e = $this->crs->getDatum()->getEllipsoid()->getEccentricity(); |
|
1444
|
1 |
|
$e2 = $this->crs->getDatum()->getEllipsoid()->getEccentricitySquared(); |
|
1445
|
|
|
|
|
1446
|
1 |
|
if ($firstStandardParallel < 0) { |
|
1447
|
1 |
|
$tF = tan(M_PI / 4 + $firstStandardParallel / 2) / (((1 + $e * sin($firstStandardParallel)) / (1 - $e * sin($firstStandardParallel))) ** ($e / 2)); |
|
1448
|
1 |
|
$t = tan(M_PI / 4 + $latitude / 2) / (((1 + $e * sin($latitude)) / (1 - $e * sin($latitude))) ** ($e / 2)); |
|
1449
|
|
|
} else { |
|
1450
|
|
|
$tF = tan(M_PI / 4 - $firstStandardParallel / 2) * (((1 + $e * sin($firstStandardParallel)) / (1 - $e * sin($firstStandardParallel))) ** ($e / 2)); |
|
1451
|
|
|
$t = tan(M_PI / 4 - $latitude / 2) * (((1 + $e * sin($latitude)) / (1 - $e * sin($latitude))) ** ($e / 2)); |
|
1452
|
|
|
} |
|
1453
|
1 |
|
$mF = cos($firstStandardParallel) / sqrt(1 - $e2 * sin($firstStandardParallel) ** 2); |
|
1454
|
|
|
|
|
1455
|
1 |
|
$rhoF = $a * $mF; |
|
1456
|
1 |
|
$rho = $rhoF * $t / $tF; |
|
1457
|
|
|
|
|
1458
|
1 |
|
$theta = $longitude - $longitudeOrigin; |
|
1459
|
1 |
|
$dE = $rho * sin($theta); |
|
1460
|
1 |
|
$dN = $rho * cos($theta); |
|
1461
|
|
|
|
|
1462
|
1 |
|
$easting = $eastingAtFalseOrigin->asMetres()->getValue() + $dE; |
|
1463
|
1 |
|
if ($firstStandardParallel < 0) { |
|
1464
|
1 |
|
$northing = $northingAtFalseOrigin->asMetres()->getValue() - $rhoF + $dN; |
|
1465
|
|
|
} else { |
|
1466
|
|
|
$northing = $northingAtFalseOrigin->asMetres()->getValue() + $rhoF - $dN; |
|
1467
|
|
|
} |
|
1468
|
|
|
|
|
1469
|
1 |
|
return ProjectedPoint::create(new Metre($easting), new Metre($northing), new Metre(-$easting), new Metre(-$northing), $to, $this->epoch); |
|
1470
|
|
|
} |
|
1471
|
|
|
|
|
1472
|
|
|
/** |
|
1473
|
|
|
* Popular Visualisation Pseudo Mercator |
|
1474
|
|
|
* Applies spherical formulas to the ellipsoid. As such does not have the properties of a true Mercator projection. |
|
1475
|
|
|
*/ |
|
1476
|
1 |
|
public function popularVisualisationPseudoMercator( |
|
1477
|
|
|
Projected $to, |
|
1478
|
|
|
Angle $latitudeOfNaturalOrigin, |
|
1479
|
|
|
Angle $longitudeOfNaturalOrigin, |
|
1480
|
|
|
Length $falseEasting, |
|
1481
|
|
|
Length $falseNorthing |
|
1482
|
|
|
): ProjectedPoint { |
|
1483
|
1 |
|
$latitude = $this->latitude->asRadians()->getValue(); |
|
1484
|
1 |
|
$longitude = $this->longitude->asRadians()->getValue(); |
|
1485
|
1 |
|
$latitudeOrigin = $latitudeOfNaturalOrigin->asRadians()->getValue(); |
|
|
|
|
|
|
1486
|
1 |
|
$longitudeOrigin = $longitudeOfNaturalOrigin->asRadians()->getValue(); |
|
1487
|
1 |
|
$a = $this->crs->getDatum()->getEllipsoid()->getSemiMajorAxis()->asMetres()->getValue(); |
|
1488
|
|
|
|
|
1489
|
1 |
|
$easting = $falseEasting->asMetres()->getValue() + $a * ($longitude - $longitudeOrigin); |
|
1490
|
1 |
|
$northing = $falseNorthing->asMetres()->getValue() + $a * log(tan(M_PI / 4 + $latitude / 2)); |
|
1491
|
|
|
|
|
1492
|
1 |
|
return ProjectedPoint::create(new Metre($easting), new Metre($northing), new Metre(-$easting), new Metre(-$northing), $to, $this->epoch); |
|
1493
|
|
|
} |
|
1494
|
|
|
|
|
1495
|
|
|
/** |
|
1496
|
|
|
* Mercator (variant A) |
|
1497
|
|
|
* Note that in these formulas the parameter latitude of natural origin (latO) is not used. However for this |
|
1498
|
|
|
* Mercator (variant A) method the EPSG dataset includes this parameter, which must have a value of zero, for |
|
1499
|
|
|
* completeness in CRS labelling. |
|
1500
|
|
|
*/ |
|
1501
|
1 |
|
public function mercatorVariantA( |
|
1502
|
|
|
Projected $to, |
|
1503
|
|
|
Angle $latitudeOfNaturalOrigin, |
|
1504
|
|
|
Angle $longitudeOfNaturalOrigin, |
|
1505
|
|
|
Scale $scaleFactorAtNaturalOrigin, |
|
1506
|
|
|
Length $falseEasting, |
|
1507
|
|
|
Length $falseNorthing |
|
1508
|
|
|
): ProjectedPoint { |
|
1509
|
1 |
|
$latitude = $this->latitude->asRadians()->getValue(); |
|
1510
|
1 |
|
$longitude = $this->longitude->asRadians()->getValue(); |
|
1511
|
|
|
|
|
1512
|
1 |
|
$latitudeOrigin = $latitudeOfNaturalOrigin->asRadians()->getValue(); |
|
|
|
|
|
|
1513
|
1 |
|
$longitudeOrigin = $longitudeOfNaturalOrigin->asRadians()->getValue(); |
|
1514
|
1 |
|
$kO = $scaleFactorAtNaturalOrigin->asUnity()->getValue(); |
|
1515
|
|
|
|
|
1516
|
1 |
|
$a = $this->crs->getDatum()->getEllipsoid()->getSemiMajorAxis()->asMetres()->getValue(); |
|
1517
|
1 |
|
$e = $this->crs->getDatum()->getEllipsoid()->getEccentricity(); |
|
1518
|
|
|
|
|
1519
|
1 |
|
$easting = $falseEasting->asMetres()->getValue() + $a * $kO * ($longitude - $longitudeOrigin); |
|
1520
|
1 |
|
$northing = $falseNorthing->asMetres()->getValue() + $a * $kO * log(tan(M_PI / 4 + $latitude / 2) * ((1 - $e * sin($latitude)) / (1 + $e * sin($latitude))) ** ($e / 2)); |
|
1521
|
|
|
|
|
1522
|
1 |
|
return ProjectedPoint::create(new Metre($easting), new Metre($northing), new Metre(-$easting), new Metre(-$northing), $to, $this->epoch); |
|
1523
|
|
|
} |
|
1524
|
|
|
|
|
1525
|
|
|
/** |
|
1526
|
|
|
* Mercator (variant B) |
|
1527
|
|
|
* Used for most nautical charts. |
|
1528
|
|
|
*/ |
|
1529
|
1 |
|
public function mercatorVariantB( |
|
1530
|
|
|
Projected $to, |
|
1531
|
|
|
Angle $latitudeOf1stStandardParallel, |
|
1532
|
|
|
Angle $longitudeOfNaturalOrigin, |
|
1533
|
|
|
Length $falseEasting, |
|
1534
|
|
|
Length $falseNorthing |
|
1535
|
|
|
): ProjectedPoint { |
|
1536
|
1 |
|
$latitude = $this->latitude->asRadians()->getValue(); |
|
1537
|
1 |
|
$longitude = $this->longitude->asRadians()->getValue(); |
|
1538
|
1 |
|
$longitudeOrigin = $longitudeOfNaturalOrigin->asRadians()->getValue(); |
|
1539
|
1 |
|
$firstStandardParallel = $latitudeOf1stStandardParallel->asRadians()->getValue(); |
|
1540
|
1 |
|
$a = $this->crs->getDatum()->getEllipsoid()->getSemiMajorAxis()->asMetres()->getValue(); |
|
1541
|
1 |
|
$e = $this->crs->getDatum()->getEllipsoid()->getEccentricity(); |
|
1542
|
1 |
|
$e2 = $this->crs->getDatum()->getEllipsoid()->getEccentricitySquared(); |
|
1543
|
|
|
|
|
1544
|
1 |
|
$kO = cos($firstStandardParallel) / sqrt(1 - $e2 * sin($firstStandardParallel) ** 2); |
|
1545
|
|
|
|
|
1546
|
1 |
|
$easting = $falseEasting->asMetres()->getValue() + $a * $kO * ($longitude - $longitudeOrigin); |
|
1547
|
1 |
|
$northing = $falseNorthing->asMetres()->getValue() + $a * $kO * log(tan(M_PI / 4 + $latitude / 2) * ((1 - $e * sin($latitude)) / (1 + $e * sin($latitude))) ** ($e / 2)); |
|
1548
|
|
|
|
|
1549
|
1 |
|
return ProjectedPoint::create(new Metre($easting), new Metre($northing), new Metre(-$easting), new Metre(-$northing), $to, $this->epoch); |
|
1550
|
|
|
} |
|
1551
|
|
|
|
|
1552
|
|
|
/** |
|
1553
|
|
|
* Longitude rotation |
|
1554
|
|
|
* This transformation allows calculation of the longitude of a point in the target system by adding the parameter |
|
1555
|
|
|
* value to the longitude value of the point in the source system. |
|
1556
|
|
|
*/ |
|
1557
|
1 |
|
public function longitudeRotation( |
|
1558
|
|
|
Geographic $to, |
|
1559
|
|
|
Angle $longitudeOffset |
|
1560
|
|
|
): self { |
|
1561
|
1 |
|
$newLongitude = $this->longitude->add($longitudeOffset); |
|
1562
|
1 |
|
if ($newLongitude->asDegrees()->getValue() < -180) { |
|
1563
|
|
|
$newLongitude = $newLongitude->add(new Degree(360)); |
|
1564
|
|
|
} |
|
1565
|
|
|
|
|
1566
|
1 |
|
return static::create($this->latitude, $newLongitude, $this->height, $to, $this->epoch); |
|
1567
|
|
|
} |
|
1568
|
|
|
|
|
1569
|
|
|
/** |
|
1570
|
|
|
* Hotine Oblique Mercator (variant A). |
|
1571
|
|
|
*/ |
|
1572
|
1 |
|
public function obliqueMercatorHotineVariantA( |
|
1573
|
|
|
Projected $to, |
|
1574
|
|
|
Angle $latitudeOfProjectionCentre, |
|
1575
|
|
|
Angle $longitudeOfProjectionCentre, |
|
1576
|
|
|
Angle $azimuthOfInitialLine, |
|
1577
|
|
|
Angle $angleFromRectifiedToSkewGrid, |
|
1578
|
|
|
Scale $scaleFactorOnInitialLine, |
|
1579
|
|
|
Length $falseEasting, |
|
1580
|
|
|
Length $falseNorthing |
|
1581
|
|
|
): ProjectedPoint { |
|
1582
|
1 |
|
$latitude = $this->latitude->asRadians()->getValue(); |
|
1583
|
1 |
|
$longitude = $this->longitude->asRadians()->getValue(); |
|
1584
|
1 |
|
$latC = $latitudeOfProjectionCentre->asRadians()->getValue(); |
|
1585
|
1 |
|
$lonC = $longitudeOfProjectionCentre->asRadians()->getValue(); |
|
1586
|
1 |
|
$alphaC = $azimuthOfInitialLine->asRadians()->getValue(); |
|
1587
|
1 |
|
$kC = $scaleFactorOnInitialLine->asUnity()->getValue(); |
|
1588
|
1 |
|
$gammaC = $angleFromRectifiedToSkewGrid->asRadians()->getValue(); |
|
1589
|
1 |
|
$a = $this->crs->getDatum()->getEllipsoid()->getSemiMajorAxis()->asMetres()->getValue(); |
|
1590
|
1 |
|
$e = $this->crs->getDatum()->getEllipsoid()->getEccentricity(); |
|
1591
|
1 |
|
$e2 = $this->crs->getDatum()->getEllipsoid()->getEccentricitySquared(); |
|
1592
|
|
|
|
|
1593
|
1 |
|
$B = sqrt(1 + ($e2 * cos($latC) ** 4 / (1 - $e2))); |
|
1594
|
1 |
|
$A = $a * $B * $kC * sqrt(1 - $e2) / (1 - $e2 * sin($latC) ** 2); |
|
1595
|
1 |
|
$tO = tan(M_PI / 4 - $latC / 2) / ((1 - $e * sin($latC)) / (1 + $e * sin($latC))) ** ($e / 2); |
|
1596
|
1 |
|
$D = $B * sqrt((1 - $e2)) / (cos($latC) * sqrt(1 - $e2 * sin($latC) ** 2)); |
|
1597
|
1 |
|
$DD = max(1, $D ** 2); |
|
1598
|
1 |
|
$F = $D + sqrt($DD - 1) * static::sign($latC); |
|
1599
|
1 |
|
$H = $F * ($tO) ** $B; |
|
1600
|
1 |
|
$G = ($F - 1 / $F) / 2; |
|
1601
|
1 |
|
$gammaO = self::asin(sin($alphaC) / $D); |
|
1602
|
1 |
|
$lonO = $lonC - (self::asin($G * tan($gammaO))) / $B; |
|
1603
|
|
|
|
|
1604
|
1 |
|
$t = tan(M_PI / 4 - $latitude / 2) / ((1 - $e * sin($latitude)) / (1 + $e * sin($latitude))) ** ($e / 2); |
|
1605
|
1 |
|
$Q = $H / $t ** $B; |
|
1606
|
1 |
|
$S = ($Q - 1 / $Q) / 2; |
|
1607
|
1 |
|
$T = ($Q + 1 / $Q) / 2; |
|
1608
|
1 |
|
$V = sin($B * ($longitude - $lonO)); |
|
1609
|
1 |
|
$U = (-$V * cos($gammaO) + $S * sin($gammaO)) / $T; |
|
1610
|
1 |
|
$v = $A * log((1 - $U) / (1 + $U)) / (2 * $B); |
|
1611
|
1 |
|
$u = $A * atan2(($S * cos($gammaO) + $V * sin($gammaO)), cos($B * ($longitude - $lonO))) / $B; |
|
1612
|
|
|
|
|
1613
|
1 |
|
$easting = $v * cos($gammaC) + $u * sin($gammaC) + $falseEasting->asMetres()->getValue(); |
|
1614
|
1 |
|
$northing = $u * cos($gammaC) - $v * sin($gammaC) + $falseNorthing->asMetres()->getValue(); |
|
1615
|
|
|
|
|
1616
|
1 |
|
return ProjectedPoint::create(new Metre($easting), new Metre($northing), new Metre(-$easting), new Metre(-$northing), $to, $this->epoch); |
|
1617
|
|
|
} |
|
1618
|
|
|
|
|
1619
|
|
|
/** |
|
1620
|
|
|
* Hotine Oblique Mercator (variant B). |
|
1621
|
|
|
*/ |
|
1622
|
1 |
|
public function obliqueMercatorHotineVariantB( |
|
1623
|
|
|
Projected $to, |
|
1624
|
|
|
Angle $latitudeOfProjectionCentre, |
|
1625
|
|
|
Angle $longitudeOfProjectionCentre, |
|
1626
|
|
|
Angle $azimuthOfInitialLine, |
|
1627
|
|
|
Angle $angleFromRectifiedToSkewGrid, |
|
1628
|
|
|
Scale $scaleFactorOnInitialLine, |
|
1629
|
|
|
Length $eastingAtProjectionCentre, |
|
1630
|
|
|
Length $northingAtProjectionCentre |
|
1631
|
|
|
): ProjectedPoint { |
|
1632
|
1 |
|
$latitude = $this->latitude->asRadians()->getValue(); |
|
1633
|
1 |
|
$longitude = $this->longitude->asRadians()->getValue(); |
|
1634
|
1 |
|
$latC = $latitudeOfProjectionCentre->asRadians()->getValue(); |
|
1635
|
1 |
|
$lonC = $longitudeOfProjectionCentre->asRadians()->getValue(); |
|
1636
|
1 |
|
$alphaC = $azimuthOfInitialLine->asRadians()->getValue(); |
|
1637
|
1 |
|
$kC = $scaleFactorOnInitialLine->asUnity()->getValue(); |
|
1638
|
1 |
|
$gammaC = $angleFromRectifiedToSkewGrid->asRadians()->getValue(); |
|
1639
|
1 |
|
$a = $this->crs->getDatum()->getEllipsoid()->getSemiMajorAxis()->asMetres()->getValue(); |
|
1640
|
1 |
|
$e = $this->crs->getDatum()->getEllipsoid()->getEccentricity(); |
|
1641
|
1 |
|
$e2 = $this->crs->getDatum()->getEllipsoid()->getEccentricitySquared(); |
|
1642
|
|
|
|
|
1643
|
1 |
|
$B = sqrt(1 + ($e2 * cos($latC) ** 4 / (1 - $e2))); |
|
1644
|
1 |
|
$A = $a * $B * $kC * sqrt(1 - $e2) / (1 - $e2 * sin($latC) ** 2); |
|
1645
|
1 |
|
$tO = tan(M_PI / 4 - $latC / 2) / ((1 - $e * sin($latC)) / (1 + $e * sin($latC))) ** ($e / 2); |
|
1646
|
1 |
|
$D = $B * sqrt((1 - $e2)) / (cos($latC) * sqrt(1 - $e2 * sin($latC) ** 2)); |
|
1647
|
1 |
|
$DD = max(1, $D ** 2); |
|
1648
|
1 |
|
$F = $D + sqrt($DD - 1) * static::sign($latC); |
|
1649
|
1 |
|
$H = $F * ($tO) ** $B; |
|
1650
|
1 |
|
$G = ($F - 1 / $F) / 2; |
|
1651
|
1 |
|
$gammaO = self::asin(sin($alphaC) / $D); |
|
1652
|
1 |
|
$lonO = $lonC - (self::asin($G * tan($gammaO))) / $B; |
|
1653
|
1 |
|
$vC = 0; |
|
|
|
|
|
|
1654
|
1 |
|
if ($alphaC === M_PI / 2) { |
|
1655
|
|
|
$uC = $A * ($lonC - $lonO); |
|
1656
|
|
|
} else { |
|
1657
|
1 |
|
$uC = ($A / $B) * atan2(sqrt($DD - 1), cos($alphaC)) * static::sign($latC); |
|
1658
|
|
|
} |
|
1659
|
|
|
|
|
1660
|
1 |
|
$t = tan(M_PI / 4 - $latitude / 2) / ((1 - $e * sin($latitude)) / (1 + $e * sin($latitude))) ** ($e / 2); |
|
1661
|
1 |
|
$Q = $H / $t ** $B; |
|
1662
|
1 |
|
$S = ($Q - 1 / $Q) / 2; |
|
1663
|
1 |
|
$T = ($Q + 1 / $Q) / 2; |
|
1664
|
1 |
|
$V = sin($B * ($longitude - $lonO)); |
|
1665
|
1 |
|
$U = (-$V * cos($gammaO) + $S * sin($gammaO)) / $T; |
|
1666
|
1 |
|
$v = $A * log((1 - $U) / (1 + $U)) / (2 * $B); |
|
1667
|
|
|
|
|
1668
|
1 |
|
if ($alphaC === M_PI / 2) { |
|
1669
|
|
|
if ($longitude === $lonC) { |
|
1670
|
|
|
$u = 0; |
|
1671
|
|
|
} else { |
|
1672
|
|
|
$u = ($A * atan(($S * cos($gammaO) + $V * sin($gammaO)) / cos($B * ($longitude - $lonO))) / $B) - (abs($uC) * static::sign($latC) * static::sign($lonC - $longitude)); |
|
1673
|
|
|
} |
|
1674
|
|
|
} else { |
|
1675
|
1 |
|
$u = ($A * atan2(($S * cos($gammaO) + $V * sin($gammaO)), cos($B * ($longitude - $lonO))) / $B) - (abs($uC) * static::sign($latC)); |
|
1676
|
|
|
} |
|
1677
|
|
|
|
|
1678
|
1 |
|
$easting = $v * cos($gammaC) + $u * sin($gammaC) + $eastingAtProjectionCentre->asMetres()->getValue(); |
|
1679
|
1 |
|
$northing = $u * cos($gammaC) - $v * sin($gammaC) + $northingAtProjectionCentre->asMetres()->getValue(); |
|
1680
|
|
|
|
|
1681
|
1 |
|
return ProjectedPoint::create(new Metre($easting), new Metre($northing), new Metre(-$easting), new Metre(-$northing), $to, $this->epoch); |
|
1682
|
|
|
} |
|
1683
|
|
|
|
|
1684
|
|
|
/** |
|
1685
|
|
|
* Laborde Oblique Mercator. |
|
1686
|
|
|
*/ |
|
1687
|
1 |
|
public function obliqueMercatorLaborde( |
|
1688
|
|
|
Projected $to, |
|
1689
|
|
|
Angle $latitudeOfProjectionCentre, |
|
1690
|
|
|
Angle $longitudeOfProjectionCentre, |
|
1691
|
|
|
Angle $azimuthOfInitialLine, |
|
1692
|
|
|
Scale $scaleFactorOnInitialLine, |
|
1693
|
|
|
Length $falseEasting, |
|
1694
|
|
|
Length $falseNorthing |
|
1695
|
|
|
): ProjectedPoint { |
|
1696
|
1 |
|
$latitude = $this->latitude->asRadians()->getValue(); |
|
1697
|
1 |
|
$longitude = $this->longitude->asRadians()->getValue(); |
|
1698
|
1 |
|
$latC = $latitudeOfProjectionCentre->asRadians()->getValue(); |
|
1699
|
1 |
|
$lonC = $longitudeOfProjectionCentre->asRadians()->getValue(); |
|
1700
|
1 |
|
$alphaC = $azimuthOfInitialLine->asRadians()->getValue(); |
|
1701
|
1 |
|
$kC = $scaleFactorOnInitialLine->asUnity()->getValue(); |
|
1702
|
1 |
|
$a = $this->crs->getDatum()->getEllipsoid()->getSemiMajorAxis()->asMetres()->getValue(); |
|
1703
|
1 |
|
$e = $this->crs->getDatum()->getEllipsoid()->getEccentricity(); |
|
1704
|
1 |
|
$e2 = $this->crs->getDatum()->getEllipsoid()->getEccentricitySquared(); |
|
1705
|
|
|
|
|
1706
|
1 |
|
$B = sqrt(1 + ($e2 * cos($latC) ** 4 / (1 - $e2))); |
|
1707
|
1 |
|
$latS = self::asin(sin($latC) / $B); |
|
1708
|
1 |
|
$R = $a * $kC * (sqrt(1 - $e2) / (1 - $e2 * sin($latC) ** 2)); |
|
1709
|
1 |
|
$C = log(tan(M_PI / 4 + $latS / 2)) - $B * log(tan(M_PI / 4 + $latC / 2) * ((1 - $e * sin($latC)) / (1 + $e * sin($latC))) ** ($e / 2)); |
|
1710
|
|
|
|
|
1711
|
1 |
|
$L = $B * ($longitude - $lonC); |
|
1712
|
1 |
|
$q = $C + $B * log(tan(M_PI / 4 + $latitude / 2) * ((1 - $e * sin($latitude)) / (1 + $e * sin($latitude))) ** ($e / 2)); |
|
1713
|
1 |
|
$P = 2 * atan(M_E ** $q) - M_PI / 2; |
|
1714
|
1 |
|
$U = cos($P) * cos($L) * cos($latS) + sin($P) * sin($latS); |
|
1715
|
1 |
|
$V = cos($P) * cos($L) * sin($latS) - sin($P) * cos($latS); |
|
1716
|
1 |
|
$W = cos($P) * sin($L); |
|
1717
|
1 |
|
$d = sqrt($U ** 2 + $V ** 2); |
|
1718
|
1 |
|
if ($d === 0.0) { |
|
1719
|
|
|
$LPrime = 0; |
|
1720
|
|
|
$PPrime = static::sign($W) * M_PI / 2; |
|
1721
|
|
|
} else { |
|
1722
|
1 |
|
$LPrime = 2 * atan($V / ($U + $d)); |
|
1723
|
1 |
|
$PPrime = atan($W / $d); |
|
1724
|
|
|
} |
|
1725
|
1 |
|
$H = new ComplexNumber(-$LPrime, log(tan(M_PI / 4 + $PPrime / 2))); |
|
1726
|
1 |
|
$G = (new ComplexNumber(1 - cos(2 * $alphaC), sin(2 * $alphaC)))->divide(new ComplexNumber(12, 0)); |
|
1727
|
|
|
|
|
1728
|
1 |
|
$easting = $falseEasting->asMetres()->getValue() + $R * $H->pow(3)->multiply($G)->add($H)->getImaginary(); |
|
1729
|
1 |
|
$northing = $falseNorthing->asMetres()->getValue() + $R * $H->pow(3)->multiply($G)->add($H)->getReal(); |
|
1730
|
|
|
|
|
1731
|
1 |
|
return ProjectedPoint::create(new Metre($easting), new Metre($northing), new Metre(-$easting), new Metre(-$northing), $to, $this->epoch); |
|
1732
|
|
|
} |
|
1733
|
|
|
|
|
1734
|
|
|
/** |
|
1735
|
|
|
* Transverse Mercator. |
|
1736
|
|
|
*/ |
|
1737
|
7 |
|
public function transverseMercator( |
|
1738
|
|
|
Projected $to, |
|
1739
|
|
|
Angle $latitudeOfNaturalOrigin, |
|
1740
|
|
|
Angle $longitudeOfNaturalOrigin, |
|
1741
|
|
|
Scale $scaleFactorAtNaturalOrigin, |
|
1742
|
|
|
Length $falseEasting, |
|
1743
|
|
|
Length $falseNorthing |
|
1744
|
|
|
): ProjectedPoint { |
|
1745
|
7 |
|
$latitude = $this->latitude->asRadians()->getValue(); |
|
1746
|
7 |
|
$longitude = $this->longitude->asRadians()->getValue(); |
|
1747
|
7 |
|
$latitudeOrigin = $latitudeOfNaturalOrigin->asRadians()->getValue(); |
|
1748
|
7 |
|
$longitudeOrigin = $longitudeOfNaturalOrigin->asRadians()->getValue(); |
|
1749
|
7 |
|
$kO = $scaleFactorAtNaturalOrigin->asUnity()->getValue(); |
|
1750
|
7 |
|
$a = $this->crs->getDatum()->getEllipsoid()->getSemiMajorAxis()->asMetres()->getValue(); |
|
1751
|
7 |
|
$e = $this->crs->getDatum()->getEllipsoid()->getEccentricity(); |
|
1752
|
7 |
|
$f = $this->crs->getDatum()->getEllipsoid()->getInverseFlattening(); |
|
1753
|
|
|
|
|
1754
|
7 |
|
$n = $f / (2 - $f); |
|
1755
|
7 |
|
$B = ($a / (1 + $n)) * (1 + $n ** 2 / 4 + $n ** 4 / 64); |
|
1756
|
|
|
|
|
1757
|
7 |
|
$h1 = $n / 2 - (2 / 3) * $n ** 2 + (5 / 16) * $n ** 3 + (41 / 180) * $n ** 4; |
|
1758
|
7 |
|
$h2 = (13 / 48) * $n ** 2 - (3 / 5) * $n ** 3 + (557 / 1440) * $n ** 4; |
|
1759
|
7 |
|
$h3 = (61 / 240) * $n ** 3 - (103 / 140) * $n ** 4; |
|
1760
|
7 |
|
$h4 = (49561 / 161280) * $n ** 4; |
|
1761
|
|
|
|
|
1762
|
7 |
|
if ($latitudeOrigin === 0.0) { |
|
|
|
|
|
|
1763
|
5 |
|
$mO = 0; |
|
1764
|
2 |
|
} elseif ($latitudeOrigin === M_PI / 2) { |
|
1765
|
|
|
$mO = $B * M_PI / 2; |
|
1766
|
2 |
|
} elseif ($latitudeOrigin === -M_PI / 2) { |
|
1767
|
|
|
$mO = $B * -M_PI / 2; |
|
1768
|
|
|
} else { |
|
1769
|
2 |
|
$qO = asinh(tan($latitudeOrigin)) - ($e * atanh($e * sin($latitudeOrigin))); |
|
1770
|
2 |
|
$betaO = atan(sinh($qO)); |
|
1771
|
2 |
|
$xiO0 = self::asin(sin($betaO)); |
|
1772
|
2 |
|
$xiO1 = $h1 * sin(2 * $xiO0); |
|
1773
|
2 |
|
$xiO2 = $h2 * sin(4 * $xiO0); |
|
1774
|
2 |
|
$xiO3 = $h3 * sin(6 * $xiO0); |
|
1775
|
2 |
|
$xiO4 = $h4 * sin(8 * $xiO0); |
|
1776
|
2 |
|
$xiO = $xiO0 + $xiO1 + $xiO2 + $xiO3 + $xiO4; |
|
1777
|
2 |
|
$mO = $B * $xiO; |
|
1778
|
|
|
} |
|
1779
|
|
|
|
|
1780
|
7 |
|
$Q = asinh(tan($latitude)) - ($e * atanh($e * sin($latitude))); |
|
1781
|
7 |
|
$beta = atan(sinh($Q)); |
|
1782
|
7 |
|
$eta0 = atanh(cos($beta) * sin($longitude - $longitudeOrigin)); |
|
1783
|
7 |
|
$xi0 = self::asin(sin($beta) * cosh($eta0)); |
|
1784
|
7 |
|
$xi1 = $h1 * sin(2 * $xi0) * cosh(2 * $eta0); |
|
1785
|
7 |
|
$eta1 = $h1 * cos(2 * $xi0) * sinh(2 * $eta0); |
|
1786
|
7 |
|
$xi2 = $h2 * sin(4 * $xi0) * cosh(4 * $eta0); |
|
1787
|
7 |
|
$eta2 = $h2 * cos(4 * $xi0) * sinh(4 * $eta0); |
|
1788
|
7 |
|
$xi3 = $h3 * sin(6 * $xi0) * cosh(6 * $eta0); |
|
1789
|
7 |
|
$eta3 = $h3 * cos(6 * $xi0) * sinh(6 * $eta0); |
|
1790
|
7 |
|
$xi4 = $h4 * sin(8 * $xi0) * cosh(8 * $eta0); |
|
1791
|
7 |
|
$eta4 = $h4 * cos(8 * $xi0) * sinh(8 * $eta0); |
|
1792
|
7 |
|
$xi = $xi0 + $xi1 + $xi2 + $xi3 + $xi4; |
|
1793
|
7 |
|
$eta = $eta0 + $eta1 + $eta2 + $eta3 + $eta4; |
|
1794
|
|
|
|
|
1795
|
7 |
|
$easting = $falseEasting->asMetres()->getValue() + $kO * $B * $eta; |
|
1796
|
7 |
|
$northing = $falseNorthing->asMetres()->getValue() + $kO * ($B * $xi - $mO); |
|
1797
|
|
|
|
|
1798
|
7 |
|
return ProjectedPoint::create(new Metre($easting), new Metre($northing), new Metre(-$easting), new Metre(-$northing), $to, $this->epoch); |
|
1799
|
|
|
} |
|
1800
|
|
|
|
|
1801
|
|
|
/** |
|
1802
|
|
|
* Transverse Mercator Zoned Grid System |
|
1803
|
|
|
* If locations fall outwith the fixed zones the general Transverse Mercator method (code 9807) must be used for |
|
1804
|
|
|
* each zone. |
|
1805
|
|
|
*/ |
|
1806
|
3 |
|
public function transverseMercatorZonedGrid( |
|
1807
|
|
|
Projected $to, |
|
1808
|
|
|
Angle $latitudeOfNaturalOrigin, |
|
1809
|
|
|
Angle $initialLongitude, |
|
1810
|
|
|
Angle $zoneWidth, |
|
1811
|
|
|
Scale $scaleFactorAtNaturalOrigin, |
|
1812
|
|
|
Length $falseEasting, |
|
1813
|
|
|
Length $falseNorthing |
|
1814
|
|
|
): ProjectedPoint { |
|
1815
|
3 |
|
$W = $zoneWidth->asDegrees()->getValue(); |
|
1816
|
3 |
|
$Z = ($this->longitude->subtract($initialLongitude)->asDegrees()->getValue() / $W) % (360 / $W) + 1; |
|
1817
|
|
|
|
|
1818
|
3 |
|
$longitudeOrigin = $initialLongitude->add(new Degree($Z * $W - $W / 2)); |
|
1819
|
3 |
|
$falseEasting = $falseEasting->add(new Metre($Z * 1000000)); |
|
1820
|
|
|
|
|
1821
|
3 |
|
return $this->transverseMercator($to, $latitudeOfNaturalOrigin, $longitudeOrigin, $scaleFactorAtNaturalOrigin, $falseEasting, $falseNorthing); |
|
1822
|
|
|
} |
|
1823
|
|
|
|
|
1824
|
|
|
/** |
|
1825
|
|
|
* New Zealand Map Grid. |
|
1826
|
|
|
*/ |
|
1827
|
3 |
|
public function newZealandMapGrid( |
|
1828
|
|
|
Projected $to, |
|
1829
|
|
|
Angle $latitudeOfNaturalOrigin, |
|
1830
|
|
|
Angle $longitudeOfNaturalOrigin, |
|
1831
|
|
|
Length $falseEasting, |
|
1832
|
|
|
Length $falseNorthing |
|
1833
|
|
|
): ProjectedPoint { |
|
1834
|
3 |
|
$a = $this->crs->getDatum()->getEllipsoid()->getSemiMajorAxis()->asMetres()->getValue(); |
|
1835
|
|
|
|
|
1836
|
3 |
|
$deltaLatitudeToOrigin = Angle::convert($this->latitude->subtract($latitudeOfNaturalOrigin), Angle::EPSG_ARC_SECOND)->getValue(); |
|
1837
|
3 |
|
$deltaLongitudeToOrigin = $this->longitude->subtract($longitudeOfNaturalOrigin)->asRadians(); |
|
1838
|
|
|
|
|
1839
|
3 |
|
$deltaPsi = 0; |
|
1840
|
3 |
|
$deltaPsi += 0.6399175073 * ($deltaLatitudeToOrigin * 0.00001) ** 1; |
|
1841
|
3 |
|
$deltaPsi += -0.1358797613 * ($deltaLatitudeToOrigin * 0.00001) ** 2; |
|
1842
|
3 |
|
$deltaPsi += 0.063294409 * ($deltaLatitudeToOrigin * 0.00001) ** 3; |
|
1843
|
3 |
|
$deltaPsi += -0.02526853 * ($deltaLatitudeToOrigin * 0.00001) ** 4; |
|
1844
|
3 |
|
$deltaPsi += 0.0117879 * ($deltaLatitudeToOrigin * 0.00001) ** 5; |
|
1845
|
3 |
|
$deltaPsi += -0.0055161 * ($deltaLatitudeToOrigin * 0.00001) ** 6; |
|
1846
|
3 |
|
$deltaPsi += 0.0026906 * ($deltaLatitudeToOrigin * 0.00001) ** 7; |
|
1847
|
3 |
|
$deltaPsi += -0.001333 * ($deltaLatitudeToOrigin * 0.00001) ** 8; |
|
1848
|
3 |
|
$deltaPsi += 0.00067 * ($deltaLatitudeToOrigin * 0.00001) ** 9; |
|
1849
|
3 |
|
$deltaPsi += -0.00034 * ($deltaLatitudeToOrigin * 0.00001) ** 10; |
|
1850
|
|
|
|
|
1851
|
3 |
|
$zeta = new ComplexNumber($deltaPsi, $deltaLongitudeToOrigin->getValue()); |
|
1852
|
|
|
|
|
1853
|
3 |
|
$B1 = new ComplexNumber(0.7557853228, 0.0); |
|
1854
|
3 |
|
$B2 = new ComplexNumber(0.249204646, 0.003371507); |
|
1855
|
3 |
|
$B3 = new ComplexNumber(-0.001541739, 0.041058560); |
|
1856
|
3 |
|
$B4 = new ComplexNumber(-0.10162907, 0.01727609); |
|
1857
|
3 |
|
$B5 = new ComplexNumber(-0.26623489, -0.36249218); |
|
1858
|
3 |
|
$B6 = new ComplexNumber(-0.6870983, -1.1651967); |
|
1859
|
3 |
|
$z = new ComplexNumber(0, 0); |
|
1860
|
3 |
|
$z = $z->add($B1->multiply($zeta->pow(1))); |
|
1861
|
3 |
|
$z = $z->add($B2->multiply($zeta->pow(2))); |
|
1862
|
3 |
|
$z = $z->add($B3->multiply($zeta->pow(3))); |
|
1863
|
3 |
|
$z = $z->add($B4->multiply($zeta->pow(4))); |
|
1864
|
3 |
|
$z = $z->add($B5->multiply($zeta->pow(5))); |
|
1865
|
3 |
|
$z = $z->add($B6->multiply($zeta->pow(6))); |
|
1866
|
|
|
|
|
1867
|
3 |
|
$easting = $falseEasting->asMetres()->getValue() + $z->getImaginary() * $a; |
|
1868
|
3 |
|
$northing = $falseNorthing->asMetres()->getValue() + $z->getReal() * $a; |
|
1869
|
|
|
|
|
1870
|
3 |
|
return ProjectedPoint::create(new Metre($easting), new Metre($northing), new Metre(-$easting), new Metre(-$northing), $to, $this->epoch); |
|
1871
|
|
|
} |
|
1872
|
|
|
|
|
1873
|
|
|
/** |
|
1874
|
|
|
* Madrid to ED50 polynomial. |
|
1875
|
|
|
*/ |
|
1876
|
1 |
|
public function madridToED50Polynomial( |
|
1877
|
|
|
Geographic2D $to, |
|
1878
|
|
|
Scale $A0, |
|
1879
|
|
|
Scale $A1, |
|
1880
|
|
|
Scale $A2, |
|
1881
|
|
|
Scale $A3, |
|
1882
|
|
|
Angle $B00, |
|
1883
|
|
|
Scale $B0, |
|
1884
|
|
|
Scale $B1, |
|
1885
|
|
|
Scale $B2, |
|
1886
|
|
|
Scale $B3 |
|
1887
|
|
|
): self { |
|
1888
|
1 |
|
$dLatitude = new ArcSecond($A0->add($A1->multiply($this->latitude->getValue()))->add($A2->multiply($this->longitude->getValue()))->add($A3->multiply($this->height ? $this->height->getValue() : 0))->getValue()); |
|
1889
|
1 |
|
$dLongitude = $B00->add(new ArcSecond($B0->add($B1->multiply($this->latitude->getValue()))->add($B2->multiply($this->longitude->getValue()))->add($B3->multiply($this->height ? $this->height->getValue() : 0))->getValue())); |
|
1890
|
|
|
|
|
1891
|
1 |
|
return self::create($this->latitude->add($dLatitude), $this->longitude->add($dLongitude), null, $to, $this->epoch); |
|
1892
|
|
|
} |
|
1893
|
|
|
|
|
1894
|
|
|
/** |
|
1895
|
|
|
* Geographic3D to 2D conversion. |
|
1896
|
|
|
*/ |
|
1897
|
1 |
|
public function threeDToTwoD( |
|
1898
|
|
|
Geographic $to |
|
1899
|
|
|
): self { |
|
1900
|
1 |
|
if ($to instanceof Geographic2D) { |
|
1901
|
1 |
|
return static::create($this->latitude, $this->longitude, null, $to, $this->epoch); |
|
1902
|
|
|
} |
|
1903
|
|
|
|
|
1904
|
|
|
return static::create($this->latitude, $this->longitude, new Metre(0), $to, $this->epoch); |
|
1905
|
|
|
} |
|
1906
|
|
|
|
|
1907
|
|
|
/** |
|
1908
|
|
|
* Geographic2D offsets. |
|
1909
|
|
|
* This transformation allows calculation of coordinates in the target system by adding the parameter value to the |
|
1910
|
|
|
* coordinate values of the point in the source system. |
|
1911
|
|
|
*/ |
|
1912
|
1 |
|
public function geographic2DOffsets( |
|
1913
|
|
|
Geographic $to, |
|
1914
|
|
|
Angle $latitudeOffset, |
|
1915
|
|
|
Angle $longitudeOffset |
|
1916
|
|
|
): self { |
|
1917
|
1 |
|
$toLatitude = $this->latitude->add($latitudeOffset); |
|
1918
|
1 |
|
$toLongitude = $this->longitude->add($longitudeOffset); |
|
1919
|
|
|
|
|
1920
|
1 |
|
return static::create($toLatitude, $toLongitude, null, $to, $this->epoch); |
|
1921
|
|
|
} |
|
1922
|
|
|
|
|
1923
|
|
|
/* |
|
1924
|
|
|
* Geographic2D with Height Offsets. |
|
1925
|
|
|
* This transformation allows calculation of coordinates in the target system by adding the parameter value to the |
|
1926
|
|
|
* coordinate values of the point in the source system. |
|
1927
|
|
|
*/ |
|
1928
|
|
|
public function geographic2DWithHeightOffsets( |
|
1929
|
|
|
Compound $to, |
|
1930
|
|
|
Angle $latitudeOffset, |
|
1931
|
|
|
Angle $longitudeOffset, |
|
1932
|
|
|
Length $geoidUndulation |
|
1933
|
|
|
): CompoundPoint { |
|
1934
|
|
|
$toLatitude = $this->latitude->add($latitudeOffset); |
|
1935
|
|
|
$toLongitude = $this->longitude->add($longitudeOffset); |
|
1936
|
|
|
$toHeight = $this->height->add($geoidUndulation); |
|
|
|
|
|
|
1937
|
|
|
|
|
1938
|
|
|
$horizontal = static::create($toLatitude, $toLongitude, null, $to->getHorizontal(), $this->epoch); |
|
1939
|
|
|
$vertical = VerticalPoint::create($toHeight, $to->getVertical(), $this->epoch); |
|
|
|
|
|
|
1940
|
|
|
|
|
1941
|
|
|
return CompoundPoint::create($horizontal, $vertical, $to, $this->epoch); |
|
1942
|
|
|
} |
|
1943
|
|
|
|
|
1944
|
|
|
/** |
|
1945
|
|
|
* General polynomial of degree. |
|
1946
|
|
|
* @param Coefficient[] $powerCoefficients |
|
1947
|
|
|
*/ |
|
1948
|
2 |
|
public function generalPolynomial( |
|
1949
|
|
|
Geographic $to, |
|
1950
|
|
|
Angle $ordinate1OfEvaluationPointInSourceCRS, |
|
1951
|
|
|
Angle $ordinate2OfEvaluationPointInSourceCRS, |
|
1952
|
|
|
Angle $ordinate1OfEvaluationPointInTargetCRS, |
|
1953
|
|
|
Angle $ordinate2OfEvaluationPointInTargetCRS, |
|
1954
|
|
|
Scale $scalingFactorForSourceCRSCoordDifferences, |
|
1955
|
|
|
Scale $scalingFactorForTargetCRSCoordDifferences, |
|
1956
|
|
|
Scale $A0, |
|
1957
|
|
|
Scale $B0, |
|
1958
|
|
|
array $powerCoefficients |
|
1959
|
|
|
): self { |
|
1960
|
2 |
|
$xs = $this->latitude->getValue(); |
|
1961
|
2 |
|
$ys = $this->longitude->getValue(); |
|
1962
|
|
|
|
|
1963
|
2 |
|
$t = $this->generalPolynomialUnitless( |
|
1964
|
2 |
|
$xs, |
|
1965
|
|
|
$ys, |
|
1966
|
|
|
$ordinate1OfEvaluationPointInSourceCRS, |
|
1967
|
|
|
$ordinate2OfEvaluationPointInSourceCRS, |
|
1968
|
|
|
$ordinate1OfEvaluationPointInTargetCRS, |
|
1969
|
|
|
$ordinate2OfEvaluationPointInTargetCRS, |
|
1970
|
|
|
$scalingFactorForSourceCRSCoordDifferences, |
|
1971
|
|
|
$scalingFactorForTargetCRSCoordDifferences, |
|
1972
|
|
|
$A0, |
|
1973
|
|
|
$B0, |
|
1974
|
|
|
$powerCoefficients |
|
1975
|
|
|
); |
|
1976
|
|
|
|
|
1977
|
2 |
|
$xtUnit = $to->getCoordinateSystem()->getAxes()[0]->getUnitOfMeasureId(); |
|
1978
|
2 |
|
if ($xtUnit === Angle::EPSG_DEGREE_SUPPLIER_TO_DEFINE_REPRESENTATION) { |
|
1979
|
2 |
|
$xtUnit = Angle::EPSG_DEGREE; |
|
1980
|
|
|
} |
|
1981
|
2 |
|
$ytUnit = $to->getCoordinateSystem()->getAxes()[1]->getUnitOfMeasureId(); |
|
1982
|
2 |
|
if ($ytUnit === Angle::EPSG_DEGREE_SUPPLIER_TO_DEFINE_REPRESENTATION) { |
|
1983
|
2 |
|
$ytUnit = Angle::EPSG_DEGREE; |
|
1984
|
|
|
} |
|
1985
|
|
|
|
|
1986
|
2 |
|
return static::create( |
|
1987
|
2 |
|
Angle::makeUnit($t['xt'], $xtUnit), |
|
1988
|
2 |
|
Angle::makeUnit($t['yt'], $ytUnit), |
|
1989
|
2 |
|
$this->height, |
|
1990
|
|
|
$to, |
|
1991
|
2 |
|
$this->epoch |
|
1992
|
|
|
); |
|
1993
|
|
|
} |
|
1994
|
|
|
|
|
1995
|
|
|
/** |
|
1996
|
|
|
* Reversible polynomial. |
|
1997
|
|
|
* @param Coefficient[] $powerCoefficients |
|
1998
|
|
|
*/ |
|
1999
|
4 |
|
public function reversiblePolynomial( |
|
2000
|
|
|
Geographic $to, |
|
2001
|
|
|
Angle $ordinate1OfEvaluationPoint, |
|
2002
|
|
|
Angle $ordinate2OfEvaluationPoint, |
|
2003
|
|
|
Scale $scalingFactorForCoordDifferences, |
|
2004
|
|
|
Scale $A0, |
|
2005
|
|
|
Scale $B0, |
|
2006
|
|
|
$powerCoefficients |
|
2007
|
|
|
): self { |
|
2008
|
4 |
|
$xs = $this->latitude->getValue(); |
|
2009
|
4 |
|
$ys = $this->longitude->getValue(); |
|
2010
|
|
|
|
|
2011
|
4 |
|
$t = $this->reversiblePolynomialUnitless( |
|
2012
|
4 |
|
$xs, |
|
2013
|
|
|
$ys, |
|
2014
|
|
|
$ordinate1OfEvaluationPoint, |
|
2015
|
|
|
$ordinate2OfEvaluationPoint, |
|
2016
|
|
|
$scalingFactorForCoordDifferences, |
|
2017
|
|
|
$A0, |
|
2018
|
|
|
$B0, |
|
2019
|
|
|
$powerCoefficients |
|
2020
|
|
|
); |
|
2021
|
|
|
|
|
2022
|
4 |
|
$xtUnit = $to->getCoordinateSystem()->getAxes()[0]->getUnitOfMeasureId(); |
|
2023
|
4 |
|
if ($xtUnit === Angle::EPSG_DEGREE_SUPPLIER_TO_DEFINE_REPRESENTATION) { |
|
2024
|
4 |
|
$xtUnit = Angle::EPSG_DEGREE; |
|
2025
|
|
|
} |
|
2026
|
4 |
|
$ytUnit = $to->getCoordinateSystem()->getAxes()[1]->getUnitOfMeasureId(); |
|
2027
|
4 |
|
if ($ytUnit === Angle::EPSG_DEGREE_SUPPLIER_TO_DEFINE_REPRESENTATION) { |
|
2028
|
4 |
|
$ytUnit = Angle::EPSG_DEGREE; |
|
2029
|
|
|
} |
|
2030
|
|
|
|
|
2031
|
4 |
|
return static::create( |
|
2032
|
4 |
|
Angle::makeUnit($t['xt'], $xtUnit), |
|
2033
|
4 |
|
Angle::makeUnit($t['yt'], $ytUnit), |
|
2034
|
4 |
|
$this->height, |
|
2035
|
|
|
$to, |
|
2036
|
4 |
|
$this->epoch |
|
2037
|
|
|
); |
|
2038
|
|
|
} |
|
2039
|
|
|
|
|
2040
|
|
|
/** |
|
2041
|
|
|
* Axis Order Reversal. |
|
2042
|
|
|
*/ |
|
2043
|
|
|
public function axisReversal( |
|
2044
|
|
|
Geographic $to |
|
2045
|
|
|
) { |
|
2046
|
|
|
// axes are read in from the CRS, this is a book-keeping adjustment only |
|
2047
|
|
|
return static::create($this->latitude, $this->longitude, $this->height, $to, $this->epoch); |
|
2048
|
|
|
} |
|
2049
|
|
|
|
|
2050
|
10 |
|
public function asGeographicValue(): GeographicValue |
|
2051
|
|
|
{ |
|
2052
|
10 |
|
return new GeographicValue($this->latitude, $this->longitude, $this->height, $this->crs->getDatum()); |
|
2053
|
|
|
} |
|
2054
|
|
|
} |
|
2055
|
|
|
|
dvdoug /
PHPCoord
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