001// License: GPL. For details, see LICENSE file.
002package org.openstreetmap.josm.data.projection.proj;
003
004import static org.openstreetmap.josm.tools.I18n.tr;
005
006import org.openstreetmap.josm.data.Bounds;
007import org.openstreetmap.josm.data.projection.ProjectionConfigurationException;
008
009/**
010 * The polar case of the stereographic projection.
011 * <p>
012 * In the proj.4 library, the code "stere" covers several variants of the
013 * Stereographic projection, depending on the latitude of natural origin
014 * (parameter lat_0).
015 * <p>
016 *
017 * In this file, only the polar case is implemented. This corresponds to
018 * EPSG:9810 (Polar Stereographic Variant A) and EPSG:9829 (Polar Stereographic
019 * Variant B).
020 * <p>
021 *
022 * It is required, that the latitude of natural origin has the value +/-90 degrees.
023 * <p>
024 *
025 * This class has been derived from the implementation of the Geotools project;
026 * git 8cbf52d, org.geotools.referencing.operation.projection.PolarStereographic
027 * at the time of migration.
028 * <p>
029 *
030 * <b>References:</b>
031 * <ul>
032 *   <li>John P. Snyder (Map Projections - A Working Manual,<br>
033 *       U.S. Geological Survey Professional Paper 1395, 1987)</li>
034 *   <li>"Coordinate Conversions and Transformations including Formulas",<br>
035 *       EPSG Guidence Note Number 7, Version 19.</li>
036 *   <li>Gerald Evenden. <A HREF="http://members.bellatlantic.net/~vze2hc4d/proj4/sterea.pdf">
037 *       "Supplementary PROJ.4 Notes - Oblique Stereographic Alternative"</A></li>
038 *   <li>Krakiwsky, E.J., D.B. Thomson, and R.R. Steeves. 1977. A Manual
039 *       For Geodetic Coordinate Transformations in the Maritimes.
040 *       Geodesy and Geomatics Engineering, UNB. Technical Report No. 48.</li>
041 *   <li>Thomson, D.B., M.P. Mepham and R.R. Steeves. 1977.
042 *       The Stereographic Double Projection.
043 *       Geodesy and Geomatics Engineereng, UNB. Technical Report No. 46.</li>
044 * </ul>
045 *
046 * @author André Gosselin
047 * @author Martin Desruisseaux (PMO, IRD)
048 * @author Rueben Schulz
049 *
050 * @see <A HREF="http://mathworld.wolfram.com/StereographicProjection.html">Stereographic projection on MathWorld</A>
051 * @see <A HREF="http://www.remotesensing.org/geotiff/proj_list/polar_stereographic.html">Polar_Stereographic</A>
052 * @see <A HREF="http://www.remotesensing.org/geotiff/proj_list/oblique_stereographic.html">Oblique_Stereographic</A>
053 * @see <A HREF="http://www.remotesensing.org/geotiff/proj_list/stereographic.html">Stereographic</A>
054 * @see <A HREF="http://www.remotesensing.org/geotiff/proj_list/random_issues.html#stereographic">Some Random Stereographic Issues</A>
055 *
056 * @see DoubleStereographic
057 * @since 9419
058 */
059public class PolarStereographic extends AbstractProj {
060    /**
061     * Maximum number of iterations for iterative computations.
062     */
063    private static final int MAXIMUM_ITERATIONS = 15;
064
065    /**
066     * Difference allowed in iterative computations.
067     */
068    private static final double ITERATION_TOLERANCE = 1E-10;
069
070    /**
071     * Maximum difference allowed when comparing real numbers.
072     */
073    private static final double EPSILON = 1E-8;
074
075    /**
076     * A constant used in the transformations.
077     */
078    private double k0;
079
080    /**
081     * Latitude of true scale, in radians
082     */
083    private double latitudeTrueScale;
084
085    /**
086     * {@code true} if this projection is for the south pole, or {@code false}
087     * if it is for the north pole.
088     */
089    boolean southPole;
090
091    @Override
092    public String getName() {
093        return tr("Polar Stereographic");
094    }
095
096    @Override
097    public String getProj4Id() {
098        return "stere";
099    }
100
101    @Override
102    public void initialize(ProjParameters params) throws ProjectionConfigurationException {
103        super.initialize(params);
104        if (params.lat0 == null)
105            throw new ProjectionConfigurationException(tr("Parameter ''{0}'' required.", "lat_0"));
106        if (params.lat0 != 90.0 && params.lat0 != -90.0)
107            throw new ProjectionConfigurationException(
108                    tr("Polar Stereographic: Parameter ''{0}'' must be 90 or -90.", "lat_0"));
109        if (params.lat_ts == null) {
110            latitudeTrueScale = (params.lat0 < 0) ? -Math.PI/2 : Math.PI/2;
111        } else {
112            latitudeTrueScale = Math.toRadians(params.lat_ts);
113        }
114        southPole = latitudeTrueScale < 0;
115
116        // Computes coefficients.
117        double latitudeTrueScaleAbs = Math.abs(latitudeTrueScale);
118        if (Math.abs(latitudeTrueScaleAbs - Math.PI/2) >= EPSILON) {
119            final double t = Math.sin(latitudeTrueScaleAbs);
120            k0 = msfn(t, Math.cos(latitudeTrueScaleAbs)) /
121                 tsfn(latitudeTrueScaleAbs, t); // Derives from (21-32 and 21-33)
122        } else {
123            // True scale at pole (part of (21-33))
124            k0 = 2.0 / Math.sqrt(Math.pow(1+e, 1+e)*
125                                 Math.pow(1-e, 1-e));
126        }
127    }
128
129    @Override
130    public double[] project(double y, double x) {
131        final double sinlat = Math.sin(y);
132        final double coslon = Math.cos(x);
133        final double sinlon = Math.sin(x);
134        if (southPole) {
135            final double rho = k0 * tsfn(-y, -sinlat);
136            x = rho * sinlon;
137            y = rho * coslon;
138        } else {
139            final double rho = k0 * tsfn(y, sinlat);
140            x =  rho * sinlon;
141            y = -rho * coslon;
142        }
143        return new double[] {x, y};
144    }
145
146    @Override
147    public double[] invproject(double x, double y) {
148        final double rho = Math.hypot(x, y);
149        if (southPole) {
150            y = -y;
151        }
152        /*
153         * Compute latitude using iterative technique.
154         */
155        final double t = rho/k0;
156        final double halfe = e/2.0;
157        double phi0 = 0;
158        for (int i = MAXIMUM_ITERATIONS;;) {
159            final double esinphi = e * Math.sin(phi0);
160            final double phi = (Math.PI/2) - 2.0*Math.atan(t*Math.pow((1-esinphi)/(1+esinphi), halfe));
161            if (Math.abs(phi-phi0) < ITERATION_TOLERANCE) {
162                x = (Math.abs(rho) < EPSILON) ? 0.0 : Math.atan2(x, -y);
163                y = southPole ? -phi : phi;
164                break;
165            }
166            phi0 = phi;
167            if (--i < 0) {
168                throw new RuntimeException("no convergence");
169            }
170        }
171        return new double[] {y, x};
172    }
173
174    @Override
175    public Bounds getAlgorithmBounds() {
176        final double CUT = 60;
177        if (southPole) {
178            return new Bounds(-90, -180, CUT, 180, false);
179        } else {
180            return new Bounds(-CUT, -180, 90, 180, false);
181        }
182    }
183}