source: josm/trunk/src/org/openstreetmap/josm/data/projection/Ellipsoid.java @ 5241

/*
 * 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;

import org.openstreetmap.josm.data.coor.LatLon;

/**
 * the reference ellipsoids
 */
public class Ellipsoid {
    /**
     * Clarke 1880 IGN (French national geographic institute)
     */
    public static final Ellipsoid clarkeIGN = Ellipsoid.create_a_b(6378249.2, 6356515.0);
    /**
     * Hayford's ellipsoid 1909 (ED50 system)
     * Proj.4 code: intl
     */
    public static final Ellipsoid hayford = Ellipsoid.create_a_rf(6378388.0, 297.0);
    /**
     * GRS80 ellipsoid
     */
    public static final Ellipsoid GRS80 = Ellipsoid.create_a_rf(6378137.0, 298.257222101);

    /**
     * WGS84 ellipsoid
     */
    public static final Ellipsoid WGS84 = Ellipsoid.create_a_rf(6378137.0, 298.257223563);

    /**
     * Bessel 1841 ellipsoid
     */
    public static final Ellipsoid Bessel1841 = Ellipsoid.create_a_rf(6377397.155, 299.1528128);

    /**
     * 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;

    /**
     * private constructur - use one of the create_* methods
     *
     * @param a semimajor radius of the ellipsoid axis
     * @param b semiminor radius of the ellipsoid axis
     * @param e first eccentricity of the ellipsoid ( = sqrt((a*a - b*b)/(a*a)))
     * @param e2 first eccentricity squared
     * @param eb2 square of the second eccentricity
     */
    private Ellipsoid(double a, double b, double e, double e2, double eb2) {
        this.a = a;
        this.b = b;
        this.e = e;
        this.e2 = e2;
        this.eb2 = eb2;
    }

    /**
     * create a new ellipsoid
     *
     * @param a semimajor radius of the ellipsoid axis (in meters)
     * @param b semiminor radius of the ellipsoid axis (in meters)
     */
    public static Ellipsoid create_a_b(double a, double b) {
        double e2 = (a*a - b*b) / (a*a);
        double e = Math.sqrt(e2);
        double eb2 = e2 / (1.0 - e2);
        return new Ellipsoid(a, b, e, e2, eb2);
    }

    /**
     * create a new ellipsoid
     *
     * @param a semimajor radius of the ellipsoid axis (in meters)
     * @param es first eccentricity squared
     */
    public static Ellipsoid create_a_es(double a, double es) {
        double b = a * Math.sqrt(1.0 - es);
        double e = Math.sqrt(es);
        double eb2 = es / (1.0 - es);
        return new Ellipsoid(a, b, e, es, eb2);
    }

    /**
     * create a new ellipsoid
     *
     * @param a semimajor radius of the ellipsoid axis (in meters)
     * @param f flattening ( = (a - b) / a)
     */
    public static Ellipsoid create_a_f(double a, double f) {
        double b = a * (1.0 - f);
        double e2 = f * (2 - f);
        double e = Math.sqrt(e2);
        double eb2 = e2 / (1.0 - e2);
        return new Ellipsoid(a, b, e, e2, eb2);
    }

    /**
     * create a new ellipsoid
     *
     * @param a semimajor radius of the ellipsoid axis (in meters)
     * @param rf inverse flattening
     */
    public static Ellipsoid create_a_rf(double a, double rf) {
        return create_a_f(a, 1.0 / rf);
    }

    @Override
    public String toString() {
        return "Ellipsoid{a="+a+", b="+b+"}";
    }

    /**
     * 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;
    }

    /**
     * convert cartesian coordinates to ellipsoidal coordinates
     *
     * @param XYZ the coordinates in meters (X, Y, Z)
     * @return The corresponding latitude and longitude in degrees
     */
    public LatLon cart2LatLon(double[] XYZ) {
        return cart2LatLon(XYZ, 1e-11);
    }
    public LatLon cart2LatLon(double[] XYZ, double epsilon) {
        double norm = Math.sqrt(XYZ[0] * XYZ[0] + XYZ[1] * XYZ[1]);
        double lg = 2.0 * Math.atan(XYZ[1] / (XYZ[0] + norm));
        double lt = Math.atan(XYZ[2] / (norm * (1.0 - (a * e2 / Math.sqrt(XYZ[0] * XYZ[0] + XYZ[1] * XYZ[1] + XYZ[2] * XYZ[2])))));
        double delta = 1.0;
        while (delta > epsilon) {
            double s2 = Math.sin(lt);
            s2 *= s2;
            double l = Math.atan((XYZ[2] / norm)
                    / (1.0 - (a * e2 * Math.cos(lt) / (norm * Math.sqrt(1.0 - e2 * s2)))));
            delta = Math.abs(l - lt);
            lt = l;
        }
        return new LatLon(Math.toDegrees(lt), Math.toDegrees(lg));
    }

    /**
     * convert ellipsoidal coordinates to cartesian coordinates
     *
     * @param coord The Latitude and longitude in degrees
     * @return the corresponding (X, Y Z) cartesian coordinates in meters.
     */
    public double[] latLon2Cart(LatLon coord) {
        double phi = Math.toRadians(coord.lat());
        double lambda = Math.toRadians(coord.lon());

        double Rn = a / Math.sqrt(1 - e2 * Math.pow(Math.sin(phi), 2));
        double[] XYZ = new double[3];
        XYZ[0] = Rn * Math.cos(phi) * Math.cos(lambda);
        XYZ[1] = Rn * Math.cos(phi) * Math.sin(lambda);
        XYZ[2] = Rn * (1 - e2) * Math.sin(phi);

        return XYZ;
    }
}