/**
* Get the distance between two Latitude/Longitude objects using the Vincenty formula
*
* The Vincenty Formula calculates the distance to your destination point based on the specified ellipsoid
*
* @param LatLong $endPoint The destination point
* @param ReferenceEllipsoid $ellipsoid
* @return Distance The great circle distance between this Lat/Long and the $endpoint Lat/Long
* @throws Exception
*/
public function getDistanceVincenty(LatLong $endPoint, ReferenceEllipsoid $ellipsoid = null)
{
if (is_null($ellipsoid)) {
$ellipsoid = new ReferenceEllipsoid(ReferenceEllipsoid::WGS_84);
}
$semiMinor = $ellipsoid->getSemiMinorAxis();
$flattening = $ellipsoid->getFlattening();
$lDifference = $this->longitude->getValue(Angle::RADIANS) - $endPoint->getLongitude()->getValue(Angle::RADIANS);
$U1Value = atan((1 - $flattening) * tan($endPoint->getLatitude()->getValue(Angle::RADIANS)));
$U2Value = atan((1 - $flattening) * tan($this->latitude->getValue(Angle::RADIANS)));
$sinU1 = sin($U1Value);
$cosU1 = cos($U1Value);
$sinU2 = sin($U2Value);
$cosU2 = cos($U2Value);
$lambda = $lDifference;
$lambdaP = 2 * M_PI;
$iterLimit = 20;
while (abs($lambda - $lambdaP) > 1.0E-12 && $iterLimit > 0) {
$sinLambda = sin($lambda);
$cosLambda = cos($lambda);
$sinSigma = sqrt($cosU2 * $sinLambda * ($cosU2 * $sinLambda) + ($cosU1 * $sinU2 - $sinU1 * $cosU2 * $cosLambda) * ($cosU1 * $sinU2 - $sinU1 * $cosU2 * $cosLambda));
if ($sinSigma == 0.0) {
// co-incident points
return new Distance();
}
$cosSigma = $sinU1 * $sinU2 + $cosU1 * $cosU2 * $cosLambda;
$sigma = atan2($sinSigma, $cosSigma);
$alpha = asin($cosU1 * $cosU2 * $sinLambda / $sinSigma);
$cosSqAlpha = cos($alpha) * cos($alpha);
$cos2SigmaM = $cosSigma - 2 * $sinU1 * $sinU2 / $cosSqAlpha;
$cValue = $flattening / 16 * $cosSqAlpha * (4 + $flattening * (4 - 3 * $cosSqAlpha));
$lambdaP = $lambda;
$lambda = $lDifference + (1 - $cValue) * $flattening * sin($alpha) * ($sigma + $cValue * $sinSigma * ($cos2SigmaM + $cValue * $cosSigma * (-1 + 2 * $cos2SigmaM * $cos2SigmaM)));
}
$uSq = $cosSqAlpha * $ellipsoid->getSecondEccentricitySquared();
$aValue = 1 + $uSq / 16384 * (4096 + $uSq * (-768 + $uSq * (320 - 175 * $uSq)));
$bValue = $uSq / 1024 * (256 + $uSq * (-128 + $uSq * (74 - 47 * $uSq)));
$deltaSigma = $bValue * $sinSigma * ($cos2SigmaM + $bValue / 4 * ($cosSigma * (-1 + 2 * $cos2SigmaM * $cos2SigmaM) - $bValue / 6 * $cos2SigmaM * (-3 + 4 * $sinSigma * $sinSigma) * (-3 + 4 * $cos2SigmaM * $cos2SigmaM)));
return new Distance($semiMinor * $aValue * ($sigma - $deltaSigma));
}
public function testGetEllipsoidNames()
{
$referenceEllipsoidNames = ReferenceEllipsoid::getEllipsoidNames();
$this->assertGreaterThan(0, count($referenceEllipsoidNames));
$this->assertTrue(in_array('Airy (1830)', $referenceEllipsoidNames));
}
/**
* Get the Area of this region
*
* The algorithm used here is derived from the algorithm used by the GRASS GIS package
*
* @param ReferenceEllipsoid|null $ellipsoid Reference Ellipsoid to use for this calculation
* If null, then the WGS 1984 Ellipsoid will be used
* @return Area The area of this region
*/
public function getArea(ReferenceEllipsoid $ellipsoid = null)
{
$pointCount = count($this->nodePoints);
if ($pointCount == 0) {
return new Area();
} elseif (is_null($ellipsoid)) {
$ellipsoid = new ReferenceEllipsoid(ReferenceEllipsoid::WGS_1984);
}
$semiMajorAxis = $ellipsoid->getSemiMajorAxis();
$eccentricitySquared = $ellipsoid->getFirstEccentricitySquared();
$eccentricity4 = $eccentricitySquared * $eccentricitySquared;
$eccentricity6 = $eccentricity4 * $eccentricitySquared;
$AE = $semiMajorAxis * $semiMajorAxis * (1 - $eccentricitySquared);
$this->QA = 2.0 / 3.0 * $eccentricitySquared;
$this->QB = 3.0 / 5.0 * $eccentricity4;
$this->QC = 4.0 / 7.0 * $eccentricity6;
$this->QbarA = -1.0 - 2.0 / 3.0 * $eccentricitySquared - 3.0 / 5.0 * $eccentricity4 - 4.0 / 7.0 * $eccentricity6;
$this->QbarB = 2.0 / 9.0 * $eccentricitySquared + 2.0 / 5.0 * $eccentricity4 + 4.0 / 7.0 * $eccentricity6;
$this->QbarC = -(3.0 / 25.0) * $eccentricity4 - 12.0 / 35.0 * $eccentricity6;
$this->QbarD = 4.0 / 49.0 * $eccentricity6;
$Qp = $this->_Q(M_PI_2);
$pointCount--;
$longitude2 = $this->nodePoints[$pointCount]->getLongitude()->getValue(Angle::RADIANS);
$latitude2 = $this->nodePoints[$pointCount]->getLatitude()->getValue(Angle::RADIANS);
$Qbar2 = $this->_Qbar($latitude2);
$area = 0.0;
$n = 0;
while ($n++ < $pointCount) {
$longitude1 = $longitude2;
$latitude1 = $latitude2;
$Qbar1 = $Qbar2;
$longitude2 = $this->nodePoints[$n]->getLongitude()->getValue(Angle::RADIANS);
$latitude2 = $this->nodePoints[$n]->getLatitude()->getValue(Angle::RADIANS);
$Qbar2 = $this->_Qbar($latitude2);
self::datelineAdjust($longitude1, $longitude2);
$deltaLongitude = $longitude2 - $longitude1;
$area += $deltaLongitude * ($Qp - $this->_Q($latitude2));
if (($deltaLatitude = $latitude2 - $latitude1) != 0.0) {
$area += $deltaLongitude * $this->_Q($latitude2) - $deltaLongitude / $deltaLatitude * ($Qbar2 - $Qbar1);
}
}
$area = self::polarAdjust($area, $AE, $Qp);
return new Area($area);
}
