001// License: GPL. For details, see LICENSE file.
002package org.openstreetmap.josm.data.projection.proj;
003
004import static java.lang.Math.PI;
005import static java.lang.Math.abs;
006import static java.lang.Math.asin;
007import static java.lang.Math.atan;
008import static java.lang.Math.cos;
009import static java.lang.Math.exp;
010import static java.lang.Math.log;
011import static java.lang.Math.pow;
012import static java.lang.Math.sin;
013import static java.lang.Math.sqrt;
014import static java.lang.Math.tan;
015import static java.lang.Math.toRadians;
016import static org.openstreetmap.josm.tools.I18n.tr;
017
018import org.openstreetmap.josm.data.Bounds;
019import org.openstreetmap.josm.data.projection.Ellipsoid;
020import org.openstreetmap.josm.data.projection.ProjectionConfigurationException;
021
022/**
023 * Implementation of the stereographic double projection,
024 * also known as Oblique Stereographic and the Schreiber double stereographic projection.
025 *
026 * @author vholten
027 *
028 * Source: IOGP Publication 373-7-2 – Geomatics Guidance Note number 7, part 2,
029 * Sec. 1.3.7.1 Oblique and Equatorial Stereographic, http://www.epsg.org/GuidanceNotes
030 */
031public class DoubleStereographic extends AbstractProj {
032
033    private Ellipsoid ellps;
034    private double n;
035    private double c;
036    private double chi0;
037    private double r;
038
039    private static final double EPSILON = 1e-12;
040
041    @Override
042    public String getName() {
043        return tr("Double Stereographic");
044    }
045
046    @Override
047    public String getProj4Id() {
048        return "sterea";
049    }
050
051    @Override
052    public void initialize(ProjParameters params) throws ProjectionConfigurationException {
053        super.initialize(params);
054        if (params.lat0 == null)
055            throw new ProjectionConfigurationException(tr("Parameter ''{0}'' required.", "lat_0"));
056        ellps = params.ellps;
057        initialize(params.lat0);
058    }
059
060    private void initialize(double lat_0) {
061        double phi0 = toRadians(lat_0);
062        double e2 = ellps.e2;
063        r = sqrt(1-e2) / (1 - e2*pow(sin(phi0), 2));
064        n = sqrt(1 + ellps.eb2 * pow(cos(phi0), 4));
065        double S1 = (1 + sin(phi0)) / (1 - sin(phi0));
066        double S2 = (1 - e * sin(phi0)) / (1 + e * sin(phi0));
067        double w1 = pow(S1 * pow(S2, e), n);
068        double sinchi00 = (w1 - 1) / (w1 + 1);
069        c = (n + sin(phi0)) * (1 - sinchi00) / ((n - sin(phi0)) * (1 + sinchi00));
070        double w2 = c * w1;
071        chi0 = asin((w2 - 1) / (w2 + 1));
072    }
073
074    @Override
075    public double[] project(double phi, double lambda) {
076        double Lambda = n * lambda;
077        double Sa = (1 + sin(phi)) / (1 - sin(phi));
078        double Sb = (1 - e * sin(phi)) / (1 + e * sin(phi));
079        double w = c * pow(Sa * pow(Sb, e), n);
080        double chi = asin((w - 1) / (w + 1));
081        double B = 1 + sin(chi) * sin(chi0) + cos(chi) * cos(chi0) * cos(Lambda);
082        double x = 2 * r * cos(chi) * sin(Lambda) / B;
083        double y = 2 * r * (sin(chi) * cos(chi0) - cos(chi) * sin(chi0) * cos(Lambda)) / B;
084        return new double[] {x, y};
085    }
086
087    @Override
088    public double[] invproject(double x, double y) {
089        double e2 = ellps.e2;
090        double g = 2 * r * tan(PI/4 - chi0/2);
091        double h = 4 * r * tan(chi0) + g;
092        double i = atan(x/(h + y));
093        double j = atan(x/(g - y)) - i;
094        double chi = chi0 + 2 * atan((y - x * tan(j/2)) / (2 * r));
095        double Lambda = j + 2*i;
096        double lambda = Lambda / n;
097        double psi = 0.5 * log((1 + sin(chi)) / (c*(1 - sin(chi)))) / n;
098        double phiprev = -1000;
099        int iteration = 0;
100        double phi = 2 * atan(exp(psi)) - PI/2;
101        while (abs(phi - phiprev) > EPSILON) {
102            if (++iteration > 10)
103                throw new RuntimeException("Too many iterations");
104            phiprev = phi;
105            double psii = log(tan(phi/2 + PI/4) * pow((1 - e * sin(phi)) / (1 + e * sin(phi)), e/2));
106            phi = phi - (psii - psi) * cos(phi) * (1 - e2 * pow(sin(phi), 2)) / (1 - e2);
107        }
108        return new double[] {phi, lambda};
109    }
110
111    @Override
112    public Bounds getAlgorithmBounds() {
113        return new Bounds(-89, -87, 89, 87, false);
114    }
115}