/*
* Import from fr.geo.convert package, a geographic coordinates converter.
* (http://www.i3s.unice.fr/~johan/gps/)
* License: GPL. For details, see LICENSE file.
* Copyright (C) 2002 Johan Montagnat (johan@creatis.insa-lyon.fr)
*/
package org.openstreetmap.josm.data.projection;
/**
* the reference ellipsoids
*/
public class Ellipsoid {
/**
* Clarke's ellipsoid (NTF system)
*/
public static final Ellipsoid clarke = new Ellipsoid(6378249.2, 6356515.0);
/**
* Hayford's ellipsoid (ED50 system)
*/
public static final Ellipsoid hayford =
new Ellipsoid(6378388.0, 6356911.9461);
/**
* GRS80 ellipsoid
*/
public static final Ellipsoid GRS80 = new Ellipsoid(6378137.0, 6356752.3141);
/**
* WGS84 ellipsoid
*/
public static final Ellipsoid WGS84 = new Ellipsoid(6378137.0, 6356752.3142);
/**
* half long axis
*/
public final double a;
/**
* half short axis
*/
public final double b;
/**
* first eccentricity
*/
public final double e;
/**
* first eccentricity squared
*/
public final double e2;
/**
* square of the second eccentricity
*/
public final double eb2;
/**
* create a new ellipsoid and precompute its parameters
*
* @param a ellipsoid long axis (in meters)
* @param b ellipsoid short axis (in meters)
*/
public Ellipsoid(double a, double b) {
this.a = a;
this.b = b;
e2 = (a*a - b*b) / (a*a);
e = Math.sqrt(e2);
eb2 = e2 / (1.0 - e2);
}
/**
* Returns the <i>radius of curvature in the prime vertical</i>
* for this reference ellipsoid at the specified latitude.
*
* @param phi The local latitude (radians).
* @return The radius of curvature in the prime vertical (meters).
*/
public double verticalRadiusOfCurvature(final double phi) {
return a / Math.sqrt(1.0 - (e2 * sqr(Math.sin(phi))));
}
private static double sqr(final double x) {
return x * x;
}
/**
* Returns the meridional arc, the true meridional distance on the
* ellipsoid from the equator to the specified latitude, in meters.
*
* @param phi The local latitude (in radians).
* @return The meridional arc (in meters).
*/
public double meridionalArc(final double phi) {
final double sin2Phi = Math.sin(2.0 * phi);
final double sin4Phi = Math.sin(4.0 * phi);
final double sin6Phi = Math.sin(6.0 * phi);
final double sin8Phi = Math.sin(8.0 * phi);
// TODO . calculate 'f'
//double f = 1.0 / 298.257222101; // GRS80
double f = 1.0 / 298.257223563; // WGS84
final double n = f / (2.0 - f);
final double n2 = n * n;
final double n3 = n2 * n;
final double n4 = n3 * n;
final double n5 = n4 * n;
final double n1n2 = n - n2;
final double n2n3 = n2 - n3;
final double n3n4 = n3 - n4;
final double n4n5 = n4 - n5;
final double ap = a * (1.0 - n + (5.0 / 4.0) * (n2n3) + (81.0 / 64.0) * (n4n5));
final double bp = (3.0 / 2.0) * a * (n1n2 + (7.0 / 8.0) * (n3n4) + (55.0 / 64.0) * n5);
final double cp = (15.0 / 16.0) * a * (n2n3 + (3.0 / 4.0) * (n4n5));
final double dp = (35.0 / 48.0) * a * (n3n4 + (11.0 / 16.0) * n5);
final double ep = (315.0 / 512.0) * a * (n4n5);
return ap * phi - bp * sin2Phi + cp * sin4Phi - dp * sin6Phi + ep * sin8Phi;
}
/**
* Returns the <i>radius of curvature in the meridian<i>
* for this reference ellipsoid at the specified latitude.
*
* @param phi The local latitude (in radians).
* @return The radius of curvature in the meridian (in meters).
*/
public double meridionalRadiusOfCurvature(final double phi) {
return verticalRadiusOfCurvature(phi)
/ (1.0 + eb2 * sqr(Math.cos(phi)));
}
/**
* Returns isometric latitude of phi on given first eccentricity (e)
* @param phi The local latitude (radians).
* @return isometric latitude of phi on first eccentricity (e)
*/
public double latitudeIsometric(double phi, double e) {
double v1 = 1-e*Math.sin(phi);
double v2 = 1+e*Math.sin(phi);
return Math.log(Math.tan(Math.PI/4+phi/2)*Math.pow(v1/v2,e/2));
}
/**
* Returns isometric latitude of phi on first eccentricity (e)
* @param phi The local latitude (radians).
* @return isometric latitude of phi on first eccentricity (e)
*/
public double latitudeIsometric(double phi) {
double v1 = 1-e*Math.sin(phi);
double v2 = 1+e*Math.sin(phi);
return Math.log(Math.tan(Math.PI/4+phi/2)*Math.pow(v1/v2,e/2));
}
/*
* Returns geographic latitude of isometric latitude of first eccentricity (e)
* and epsilon precision
*/
public double latitude(double latIso, double e, double epsilon) {
double lat0 = 2*Math.atan(Math.exp(latIso))-Math.PI/2;
double lati = lat0;
double lati1 = 1.0; // random value to start the iterative processus
while(Math.abs(lati1-lati)>=epsilon) {
lati = lati1;
double v1 = 1+e*Math.sin(lati);
double v2 = 1-e*Math.sin(lati);
lati1 = 2*Math.atan(Math.pow(v1/v2,e/2)*Math.exp(latIso))-Math.PI/2;
}
return lati1;
}
}