/*
* Copyright 2010, Silvio Heuberger @ IFS www.ifs.hsr.ch
*
* This code is release under the LGPL license.
* You should have received a copy of the license
* in the LICENSE file. If you have not, see
* http://www.gnu.org/licenses/lgpl-3.0.txt
*/
package ch.hsr.geohash.util;
import ch.hsr.geohash.WGS84Point;
/**
* Ecapsulates Vincety's geodesy algorithm .
*/
public class VincentyGeodesy {
static final double equatorRadius = 6378137, poleRadius = 6356752.3142, f = 1 / 298.257223563;
public static final double degToRad = 0.0174532925199433;
static final double equatorRadiusSquared = equatorRadius * equatorRadius, poleRadiusSquared = poleRadius
* poleRadius;
public static final double EPSILON = 1e-12;
/**
* returns the {@link WGS84Point} that is in the given direction at the
* following distance of the given point.<br>
* Uses Vincenty's formula and the WGS84 ellipsoid.
*
* @param directionInDegrees
* : must be within 0 and 360
*/
public static WGS84Point moveInDirection(WGS84Point point, double bearingInDegrees, double distanceInMeters) {
if (bearingInDegrees < 0 || bearingInDegrees > 360) {
throw new IllegalArgumentException("direction must be in (0,360)");
}
double a = 6378137, b = 6356752.3142, f = 1 / 298.257223563; // WGS-84
// ellipsiod
double alpha1 = bearingInDegrees * degToRad;
double sinAlpha1 = Math.sin(alpha1), cosAlpha1 = Math.cos(alpha1);
double tanU1 = (1 - f) * Math.tan(point.getLatitude() * degToRad);
double cosU1 = 1 / Math.sqrt((1 + tanU1 * tanU1)), sinU1 = tanU1 * cosU1;
double sigma1 = Math.atan2(tanU1, cosAlpha1);
double sinAlpha = cosU1 * sinAlpha1;
double cosSqAlpha = 1 - sinAlpha * sinAlpha;
double uSq = cosSqAlpha * (a * a - b * b) / (b * b);
double A = 1 + uSq / 16384 * (4096 + uSq * (-768 + uSq * (320 - 175 * uSq)));
double B = uSq / 1024 * (256 + uSq * (-128 + uSq * (74 - 47 * uSq)));
double sinSigma = 0, cosSigma = 0, cos2SigmaM = 0;
double sigma = distanceInMeters / (b * A), sigmaP = 2 * Math.PI;
while (Math.abs(sigma - sigmaP) > 1e-12) {
cos2SigmaM = Math.cos(2 * sigma1 + sigma);
sinSigma = Math.sin(sigma);
cosSigma = Math.cos(sigma);
double deltaSigma = B
* sinSigma
* (cos2SigmaM + B
/ 4
* (cosSigma * (-1 + 2 * cos2SigmaM * cos2SigmaM) - B / 6 * cos2SigmaM
* (-3 + 4 * sinSigma * sinSigma) * (-3 + 4 * cos2SigmaM * cos2SigmaM)));
sigmaP = sigma;
sigma = distanceInMeters / (b * A) + deltaSigma;
}
double tmp = sinU1 * sinSigma - cosU1 * cosSigma * cosAlpha1;
double lat2 = Math.atan2(sinU1 * cosSigma + cosU1 * sinSigma * cosAlpha1, (1 - f)
* Math.sqrt(sinAlpha * sinAlpha + tmp * tmp));
double lambda = Math.atan2(sinSigma * sinAlpha1, cosU1 * cosSigma - sinU1 * sinSigma * cosAlpha1);
double C = f / 16 * cosSqAlpha * (4 + f * (4 - 3 * cosSqAlpha));
double L = lambda - (1 - C) * f * sinAlpha
* (sigma + C * sinSigma * (cos2SigmaM + C * cosSigma * (-1 + 2 * cos2SigmaM * cos2SigmaM)));
double newLat = lat2 / degToRad;
double newLon = point.getLongitude() + L / degToRad;
newLon = (newLon > 180.0 ? 360.0 - newLon : newLon);
newLon = (newLon < -180.0 ? 360.0 + newLon : newLon);
return new WGS84Point(newLat, newLon);
}
public static double distanceInMeters(WGS84Point foo, WGS84Point bar) {
double a = 6378137, b = 6356752.3142, f = 1 / 298.257223563; // WGS-84
// ellipsiod
double L = (bar.getLongitude() - foo.getLongitude()) * degToRad;
double U1 = Math.atan((1 - f) * Math.tan(foo.getLatitude() * degToRad));
double U2 = Math.atan((1 - f) * Math.tan(bar.getLatitude() * degToRad));
double sinU1 = Math.sin(U1), cosU1 = Math.cos(U1);
double sinU2 = Math.sin(U2), cosU2 = Math.cos(U2);
double cosSqAlpha, sinSigma, cos2SigmaM, cosSigma, sigma;
double lambda = L, lambdaP, iterLimit = 20;
do {
double sinLambda = Math.sin(lambda), cosLambda = Math.cos(lambda);
sinSigma = Math.sqrt((cosU2 * sinLambda) * (cosU2 * sinLambda)
+ (cosU1 * sinU2 - sinU1 * cosU2 * cosLambda) * (cosU1 * sinU2 - sinU1 * cosU2 * cosLambda));
if (sinSigma == 0) {
return 0; // co-incident points
}
cosSigma = sinU1 * sinU2 + cosU1 * cosU2 * cosLambda;
sigma = Math.atan2(sinSigma, cosSigma);
double sinAlpha = cosU1 * cosU2 * sinLambda / sinSigma;
cosSqAlpha = 1 - sinAlpha * sinAlpha;
cos2SigmaM = cosSigma - 2 * sinU1 * sinU2 / cosSqAlpha;
if (Double.isNaN(cos2SigmaM)) {
cos2SigmaM = 0; // equatorial line: cosSqAlpha=0
}
double C = f / 16 * cosSqAlpha * (4 + f * (4 - 3 * cosSqAlpha));
lambdaP = lambda;
lambda = L + (1 - C) * f * sinAlpha
* (sigma + C * sinSigma * (cos2SigmaM + C * cosSigma * (-1 + 2 * cos2SigmaM * cos2SigmaM)));
} while (Math.abs(lambda - lambdaP) > EPSILON && --iterLimit > 0);
if (iterLimit == 0) {
return Double.NaN;
}
double uSquared = cosSqAlpha * (a * a - b * b) / (b * b);
double A = 1 + uSquared / 16384 * (4096 + uSquared * (-768 + uSquared * (320 - 175 * uSquared)));
double B = uSquared / 1024 * (256 + uSquared * (-128 + uSquared * (74 - 47 * uSquared)));
double deltaSigma = B
* sinSigma
* (cos2SigmaM + B
/ 4
* (cosSigma * (-1 + 2 * cos2SigmaM * cos2SigmaM) - B / 6 * cos2SigmaM
* (-3 + 4 * sinSigma * sinSigma) * (-3 + 4 * cos2SigmaM * cos2SigmaM)));
double s = b * A * (sigma - deltaSigma);
return s;
}
}