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<?php |
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declare(strict_types=1); |
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namespace Location\Bearing; |
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use InvalidArgumentException; |
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use Location\Coordinate; |
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use Location\Exception\NotConvergingException; |
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/** |
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* Calculation of bearing between two points using a |
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* ellipsoidal model of the earth. |
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* |
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* This class is based on the awesome work Chris Veness |
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* has done. For more information visit the following URL. |
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* |
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* @see http://www.movable-type.co.uk/scripts/latlong-vincenty.html |
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* |
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* @author Marcus Jaschen <[email protected]> |
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*/ |
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class BearingEllipsoidal implements BearingInterface |
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{ |
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/** |
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* This method calculates the initial bearing between the |
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* two points. |
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* |
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* If the two points share the same location, the bearing |
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* value will be 0.0. |
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* |
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* @param Coordinate $point1 |
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* @param Coordinate $point2 |
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* |
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* @return float Bearing Angle |
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*/ |
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public function calculateBearing(Coordinate $point1, Coordinate $point2): float |
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{ |
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if ($point1->hasSameLocation($point2)) { |
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return 0.0; |
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} |
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return $this->inverseVincenty($point1, $point2)->getBearingInitial(); |
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} |
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/** |
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* Calculates the final bearing between the two points. |
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* |
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* @param Coordinate $point1 |
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* @param Coordinate $point2 |
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* |
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* @return float |
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*/ |
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public function calculateFinalBearing(Coordinate $point1, Coordinate $point2): float |
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{ |
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return $this->inverseVincenty($point1, $point2)->getBearingFinal(); |
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} |
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/** |
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* Calculates a destination point for the given point, bearing angle, |
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* and distance. |
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* |
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* @param Coordinate $point |
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* @param float $bearing the bearing angle between 0 and 360 degrees |
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* @param float $distance the distance to the destination point in meters |
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* |
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* @return Coordinate |
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*/ |
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public function calculateDestination(Coordinate $point, float $bearing, float $distance): Coordinate |
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{ |
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return $this->directVincenty($point, $bearing, $distance)->getDestination(); |
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} |
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/** |
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* Calculates the final bearing angle for a destination point. |
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* The method expects a starting point point, the bearing angle, |
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* and the distance to destination. |
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* |
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* @param Coordinate $point |
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* @param float $bearing |
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* @param float $distance |
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* |
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* @return float |
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* |
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* @throws NotConvergingException |
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*/ |
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public function calculateDestinationFinalBearing(Coordinate $point, float $bearing, float $distance): float |
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{ |
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return $this->directVincenty($point, $bearing, $distance)->getBearingFinal(); |
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} |
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/** |
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* @param Coordinate $point |
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* @param float $bearing |
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* @param float $distance |
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* |
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* @return DirectVincentyBearing |
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* |
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* @throws NotConvergingException |
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*/ |
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private function directVincenty(Coordinate $point, float $bearing, float $distance): DirectVincentyBearing |
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{ |
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$phi1 = deg2rad($point->getLat()); |
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$lambda1 = deg2rad($point->getLng()); |
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$alpha1 = deg2rad($bearing); |
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$a = $point->getEllipsoid()->getA(); |
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$b = $point->getEllipsoid()->getB(); |
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$f = 1 / $point->getEllipsoid()->getF(); |
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$sinAlpha1 = sin($alpha1); |
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$cosAlpha1 = cos($alpha1); |
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$tanU1 = (1 - $f) * tan($phi1); |
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$cosU1 = 1 / sqrt(1 + $tanU1 * $tanU1); |
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$sinU1 = $tanU1 * $cosU1; |
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$sigma1 = atan2($tanU1, $cosAlpha1); |
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$sinAlpha = $cosU1 * $sinAlpha1; |
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$cosSquAlpha = 1 - $sinAlpha * $sinAlpha; |
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$uSq = $cosSquAlpha * ($a * $a - $b * $b) / ($b * $b); |
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$A = 1 + $uSq / 16384 * (4096 + $uSq * (-768 + $uSq * (320 - 175 * $uSq))); |
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$B = $uSq / 1024 * (256 + $uSq * (-128 + $uSq * (74 - 47 * $uSq))); |
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$sigmaS = $distance / ($b * $A); |
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$sigma = $sigmaS; |
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$iterations = 0; |
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do { |
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$cos2SigmaM = cos(2 * $sigma1 + $sigma); |
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$sinSigma = sin($sigma); |
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$cosSigma = cos($sigma); |
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$deltaSigma = $B * $sinSigma |
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* ($cos2SigmaM + $B / 4 |
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* ($cosSigma |
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* (-1 + 2 * $cos2SigmaM * $cos2SigmaM) - $B / 6 |
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* $cos2SigmaM * (-3 + 4 * $sinSigma * $sinSigma) |
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* (-3 + 4 * $cos2SigmaM * $cos2SigmaM) |
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) |
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); |
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$sigmaS = $sigma; |
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$sigma = $distance / ($b * $A) + $deltaSigma; |
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} while (abs($sigma - $sigmaS) > 1e-12 && ++$iterations < 200); |
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if ($iterations >= 200) { |
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throw new NotConvergingException('Inverse Vincenty Formula did not converge'); |
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} |
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$tmp = $sinU1 * $sinSigma - $cosU1 * $cosSigma * $cosAlpha1; |
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$phi2 = atan2( |
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$sinU1 * $cosSigma + $cosU1 * $sinSigma * $cosAlpha1, |
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(1 - $f) * sqrt($sinAlpha * $sinAlpha + $tmp * $tmp) |
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); |
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$lambda = atan2($sinSigma * $sinAlpha1, $cosU1 * $cosSigma - $sinU1 * $sinSigma * $cosAlpha1); |
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$C = $f / 16 * $cosSquAlpha * (4 + $f * (4 - 3 * $cosSquAlpha)); |
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$L = $lambda |
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- (1 - $C) * $f * $sinAlpha |
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* ($sigma + $C * $sinSigma * ($cos2SigmaM + $C * $cosSigma * (-1 + 2 * $cos2SigmaM ** 2))); |
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$lambda2 = fmod($lambda1 + $L + 3 * M_PI, 2 * M_PI) - M_PI; |
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$alpha2 = atan2($sinAlpha, -$tmp); |
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$alpha2 = fmod($alpha2 + 2 * M_PI, 2 * M_PI); |
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return new DirectVincentyBearing( |
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new Coordinate(rad2deg($phi2), rad2deg($lambda2), $point->getEllipsoid()), |
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rad2deg($alpha2) |
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); |
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} |
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/** |
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* @param Coordinate $point1 |
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* @param Coordinate $point2 |
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* |
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* @return InverseVincentyBearing |
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* |
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* @throws NotConvergingException |
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*/ |
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private function inverseVincenty(Coordinate $point1, Coordinate $point2): InverseVincentyBearing |
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{ |
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$φ1 = deg2rad($point1->getLat()); |
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$φ2 = deg2rad($point2->getLat()); |
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$λ1 = deg2rad($point1->getLng()); |
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$λ2 = deg2rad($point2->getLng()); |
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$a = $point1->getEllipsoid()->getA(); |
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$b = $point1->getEllipsoid()->getB(); |
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$f = 1 / $point1->getEllipsoid()->getF(); |
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$L = $λ2 - $λ1; |
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$tanU1 = (1 - $f) * tan($φ1); |
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$cosU1 = 1 / sqrt(1 + $tanU1 * $tanU1); |
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$sinU1 = $tanU1 * $cosU1; |
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$tanU2 = (1 - $f) * tan($φ2); |
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$cosU2 = 1 / sqrt(1 + $tanU2 * $tanU2); |
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$sinU2 = $tanU2 * $cosU2; |
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$λ = $L; |
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$iterations = 0; |
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do { |
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$sinλ = sin($λ); |
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$cosλ = cos($λ); |
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$sinSqσ = ($cosU2 * $sinλ) * ($cosU2 * $sinλ) |
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+ ($cosU1 * $sinU2 - $sinU1 * $cosU2 * $cosλ) * ($cosU1 * $sinU2 - $sinU1 * $cosU2 * $cosλ); |
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$sinσ = sqrt($sinSqσ); |
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if ($sinσ == 0) { |
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new InverseVincentyBearing(0, 0, 0); |
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} |
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$cosσ = $sinU1 * $sinU2 + $cosU1 * $cosU2 * $cosλ; |
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$σ = atan2($sinσ, $cosσ); |
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$sinα = $cosU1 * $cosU2 * $sinλ / $sinσ; |
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$cosSqα = 1 - $sinα * $sinα; |
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$cos2σM = 0; |
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if ($cosSqα !== 0.0) { |
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$cos2σM = $cosσ - 2 * $sinU1 * $sinU2 / $cosSqα; |
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} |
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$C = $f / 16 * $cosSqα * (4 + $f * (4 - 3 * $cosSqα)); |
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$λp = $λ; |
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$λ = $L + (1 - $C) * $f * $sinα |
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* ($σ + $C * $sinσ * ($cos2σM + $C * $cosσ * (-1 + 2 * $cos2σM * $cos2σM))); |
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} while (abs($λ - $λp) > 1e-12 && ++$iterations < 200); |
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if ($iterations >= 200) { |
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throw new NotConvergingException('Inverse Vincenty Formula did not converge'); |
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} |
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$uSq = $cosSqα * ($a * $a - $b * $b) / ($b * $b); |
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$A = 1 + $uSq / 16384 * (4096 + $uSq * (-768 + $uSq * (320 - 175 * $uSq))); |
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$B = $uSq / 1024 * (256 + $uSq * (-128 + $uSq * (74 - 47 * $uSq))); |
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$Δσ = $B * $sinσ |
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* ($cos2σM + $B / 4 |
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* ($cosσ * (-1 + 2 * $cos2σM * $cos2σM) - $B / 6 |
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* $cos2σM * (-3 + 4 * $sinσ * $sinσ) |
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* (-3 + 4 * $cos2σM * $cos2σM) |
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) |
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); |
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$s = $b * $A * ($σ - $Δσ); |
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$α1 = atan2($cosU2 * $sinλ, $cosU1 * $sinU2 - $sinU1 * $cosU2 * $cosλ); |
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$α2 = atan2($cosU1 * $sinλ, -$sinU1 * $cosU2 + $cosU1 * $sinU2 * $cosλ); |
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$α1 = fmod($α1 + 2 * M_PI, 2 * M_PI); |
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$α2 = fmod($α2 + 2 * M_PI, 2 * M_PI); |
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$s = round($s, 3); |
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return new InverseVincentyBearing($s, rad2deg($α1), rad2deg($α2)); |
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} |
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} |
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