001/*
002 * Import from fr.geo.convert package, a geographic coordinates converter.
003 * (https://www.i3s.unice.fr/~johan/gps/)
004 * License: GPL. For details, see LICENSE file.
005 * Copyright (C) 2002 Johan Montagnat (johan@creatis.insa-lyon.fr)
006 */
007package org.openstreetmap.josm.data.projection;
008
009import org.openstreetmap.josm.data.coor.LatLon;
010
011/**
012 * Reference ellipsoids.
013 */
014public final class Ellipsoid {
015
016    /**
017     * Airy 1830
018     */
019    public static final Ellipsoid Airy = Ellipsoid.create_a_b(6377563.396, 6356256.910);
020
021    /**
022     * Modified Airy 1849
023     */
024    public static final Ellipsoid AiryMod = Ellipsoid.create_a_b(6377340.189, 6356034.446);
025
026    /**
027     * Australian National Spheroid (Australian Natl & S. Amer. 1969)
028     * same as GRS67 Modified
029     */
030    public static final Ellipsoid AustSA = Ellipsoid.create_a_rf(6378160.0, 298.25);
031
032    /**
033     * Bessel 1841 ellipsoid
034     */
035    public static final Ellipsoid Bessel1841 = Ellipsoid.create_a_rf(6377397.155, 299.1528128);
036
037    /**
038     * Bessel 1841 (Namibia)
039     */
040    public static final Ellipsoid BesselNamibia = Ellipsoid.create_a_rf(6377483.865, 299.1528128);
041
042    /**
043     * Clarke 1866 ellipsoid
044     */
045    public static final Ellipsoid Clarke1866 = Ellipsoid.create_a_b(6378206.4, 6356583.8);
046
047    /**
048     * Clarke 1880 (modified)
049     */
050    public static final Ellipsoid Clarke1880 = Ellipsoid.create_a_rf(6378249.145, 293.4663);
051
052    /**
053     * Clarke 1880 IGN (French national geographic institute)
054     */
055    public static final Ellipsoid ClarkeIGN = Ellipsoid.create_a_b(6378249.2, 6356515.0);
056
057    /**
058     * Everest (Sabah & Sarawak)
059     */
060    public static final Ellipsoid EverestSabahSarawak = Ellipsoid.create_a_rf(6377298.556, 300.8017);
061
062    /**
063     * GRS67 ellipsoid
064     */
065    public static final Ellipsoid GRS67 = Ellipsoid.create_a_rf(6378160.0, 298.247167427);
066
067    /**
068     * GRS80 ellipsoid
069     */
070    public static final Ellipsoid GRS80 = Ellipsoid.create_a_rf(6378137.0, 298.257222101);
071
072    /**
073     * Hayford's ellipsoid 1909 (ED50 system)
074     * Also known as International 1924
075     * Proj.4 code: intl
076     */
077    public static final Ellipsoid Hayford = Ellipsoid.create_a_rf(6378388.0, 297.0);
078
079    /**
080     * Helmert 1906
081     */
082    public static final Ellipsoid Helmert = Ellipsoid.create_a_rf(6378200.0, 298.3);
083
084    /**
085     * Krassowsky 1940 ellipsoid
086     */
087    public static final Ellipsoid Krassowsky = Ellipsoid.create_a_rf(6378245.0, 298.3);
088
089    /**
090     * WGS66 ellipsoid
091     */
092    public static final Ellipsoid WGS66 = Ellipsoid.create_a_rf(6378145.0, 298.25);
093
094    /**
095     * WGS72 ellipsoid
096     */
097    public static final Ellipsoid WGS72 = Ellipsoid.create_a_rf(6378135.0, 298.26);
098
099    /**
100     * WGS84 ellipsoid
101     */
102    public static final Ellipsoid WGS84 = Ellipsoid.create_a_rf(6378137.0, 298.257223563);
103
104
105    /**
106     * half long axis
107     */
108    public final double a;
109
110    /**
111     * half short axis
112     */
113    public final double b;
114
115    /**
116     * first eccentricity:
117     * sqrt(a*a - b*b) / a
118     */
119    public final double e;
120
121    /**
122     * first eccentricity squared:
123     * (a*a - b*b) / (a*a)
124     */
125    public final double e2;
126
127    /**
128     * square of the second eccentricity:
129     * (a*a - b*b) / (b*b)
130     */
131    public final double eb2;
132
133    /**
134     * if ellipsoid is spherical, i.e. the major and minor semiaxis are
135     * the same
136     */
137    public final boolean spherical;
138
139    /**
140     * private constructur - use one of the create_* methods
141     *
142     * @param a semimajor radius of the ellipsoid axis
143     * @param b semiminor radius of the ellipsoid axis
144     * @param e first eccentricity of the ellipsoid ( = sqrt((a*a - b*b)/(a*a)))
145     * @param e2 first eccentricity squared
146     * @param eb2 square of the second eccentricity
147     * @param sperical if the ellipsoid is sphere
148     */
149    private Ellipsoid(double a, double b, double e, double e2, double eb2, boolean sperical) {
150        this.a = a;
151        this.b = b;
152        this.e = e;
153        this.e2 = e2;
154        this.eb2 = eb2;
155        this.spherical = sperical;
156    }
157
158    /**
159     * create a new ellipsoid
160     *
161     * @param a semimajor radius of the ellipsoid axis (in meters)
162     * @param b semiminor radius of the ellipsoid axis (in meters)
163     * @return the new ellipsoid
164     */
165    public static Ellipsoid create_a_b(double a, double b) {
166        double e2 = (a*a - b*b) / (a*a);
167        double e = Math.sqrt(e2);
168        double eb2 = e2 / (1.0 - e2);
169        return new Ellipsoid(a, b, e, e2, eb2, a == b);
170    }
171
172    /**
173     * create a new ellipsoid
174     *
175     * @param a semimajor radius of the ellipsoid axis (in meters)
176     * @param es first eccentricity squared
177     * @return the new ellipsoid
178     */
179    public static Ellipsoid create_a_es(double a, double es) {
180        double b = a * Math.sqrt(1.0 - es);
181        double e = Math.sqrt(es);
182        double eb2 = es / (1.0 - es);
183        return new Ellipsoid(a, b, e, es, eb2, es == 0);
184    }
185
186    /**
187     * create a new ellipsoid
188     *
189     * @param a semimajor radius of the ellipsoid axis (in meters)
190     * @param f flattening ( = (a - b) / a)
191     * @return the new ellipsoid
192     */
193    public static Ellipsoid create_a_f(double a, double f) {
194        double b = a * (1.0 - f);
195        double e2 = f * (2 - f);
196        double e = Math.sqrt(e2);
197        double eb2 = e2 / (1.0 - e2);
198        return new Ellipsoid(a, b, e, e2, eb2, f == 0);
199    }
200
201    /**
202     * create a new ellipsoid
203     *
204     * @param a semimajor radius of the ellipsoid axis (in meters)
205     * @param rf inverse flattening
206     * @return the new ellipsoid
207     */
208    public static Ellipsoid create_a_rf(double a, double rf) {
209        return create_a_f(a, 1.0 / rf);
210    }
211
212    @Override
213    public String toString() {
214        return "Ellipsoid{a="+a+", b="+b+'}';
215    }
216
217    /**
218     * Returns the <i>radius of curvature in the prime vertical</i>
219     * for this reference ellipsoid at the specified latitude.
220     *
221     * @param phi The local latitude (radians).
222     * @return The radius of curvature in the prime vertical (meters).
223     */
224    public double verticalRadiusOfCurvature(final double phi) {
225        return a / Math.sqrt(1.0 - (e2 * sqr(Math.sin(phi))));
226    }
227
228    private static double sqr(final double x) {
229        return x * x;
230    }
231
232    /**
233     *  Returns the meridional arc, the true meridional distance on the
234     * ellipsoid from the equator to the specified latitude, in meters.
235     *
236     * @param phi   The local latitude (in radians).
237     * @return  The meridional arc (in meters).
238     */
239    public double meridionalArc(final double phi) {
240        final double sin2Phi = Math.sin(2.0 * phi);
241        final double sin4Phi = Math.sin(4.0 * phi);
242        final double sin6Phi = Math.sin(6.0 * phi);
243        final double sin8Phi = Math.sin(8.0 * phi);
244        // TODO . calculate 'f'
245        //double f = 1.0 / 298.257222101; // GRS80
246        double f = 1.0 / 298.257223563; // WGS84
247        final double n = f / (2.0 - f);
248        final double n2 = n * n;
249        final double n3 = n2 * n;
250        final double n4 = n3 * n;
251        final double n5 = n4 * n;
252        final double n1n2 = n - n2;
253        final double n2n3 = n2 - n3;
254        final double n3n4 = n3 - n4;
255        final double n4n5 = n4 - n5;
256        final double ap = a * (1.0 - n + (5.0 / 4.0) * (n2n3) + (81.0 / 64.0) * (n4n5));
257        final double bp = (3.0 / 2.0) * a * (n1n2 + (7.0 / 8.0) * (n3n4) + (55.0 / 64.0) * n5);
258        final double cp = (15.0 / 16.0) * a * (n2n3 + (3.0 / 4.0) * (n4n5));
259        final double dp = (35.0 / 48.0) * a * (n3n4 + (11.0 / 16.0) * n5);
260        final double ep = (315.0 / 512.0) * a * (n4n5);
261        return ap * phi - bp * sin2Phi + cp * sin4Phi - dp * sin6Phi + ep * sin8Phi;
262    }
263
264    /**
265     *  Returns the <i>radius of curvature in the meridian</i>
266     *  for this reference ellipsoid at the specified latitude.
267     *
268     * @param phi The local latitude (in radians).
269     * @return  The radius of curvature in the meridian (in meters).
270     */
271    public double meridionalRadiusOfCurvature(final double phi) {
272        return verticalRadiusOfCurvature(phi)
273        / (1.0 + eb2 * sqr(Math.cos(phi)));
274    }
275
276    /**
277     * Returns isometric latitude of phi on given first eccentricity (e)
278     * @param phi The local latitude (radians).
279     * @param e first eccentricity
280     * @return isometric latitude of phi on first eccentricity (e)
281     */
282    public double latitudeIsometric(double phi, double e) {
283        double v1 = 1-e*Math.sin(phi);
284        double v2 = 1+e*Math.sin(phi);
285        return Math.log(Math.tan(Math.PI/4+phi/2)*Math.pow(v1/v2, e/2));
286    }
287
288    /**
289     * Returns isometric latitude of phi on first eccentricity (e)
290     * @param phi The local latitude (radians).
291     * @return isometric latitude of phi on first eccentricity (e)
292     */
293    public double latitudeIsometric(double phi) {
294        double v1 = 1-e*Math.sin(phi);
295        double v2 = 1+e*Math.sin(phi);
296        return Math.log(Math.tan(Math.PI/4+phi/2)*Math.pow(v1/v2, e/2));
297    }
298
299    /**
300     * Returns geographic latitude of isometric latitude of first eccentricity (e) and epsilon precision
301     * @param latIso isometric latitude
302     * @param e first eccentricity
303     * @param epsilon epsilon precision
304     * @return geographic latitude of isometric latitude of first eccentricity (e) and epsilon precision
305     */
306    public double latitude(double latIso, double e, double epsilon) {
307        double lat0 = 2*Math.atan(Math.exp(latIso))-Math.PI/2;
308        double lati = lat0;
309        double lati1 = 1.0; // random value to start the iterative processus
310        while (Math.abs(lati1-lati) >= epsilon) {
311            lati = lati1;
312            double v1 = 1+e*Math.sin(lati);
313            double v2 = 1-e*Math.sin(lati);
314            lati1 = 2*Math.atan(Math.pow(v1/v2, e/2)*Math.exp(latIso))-Math.PI/2;
315        }
316        return lati1;
317    }
318
319    /**
320     * convert cartesian coordinates to ellipsoidal coordinates
321     *
322     * @param xyz the coordinates in meters (X, Y, Z)
323     * @return The corresponding latitude and longitude in degrees
324     */
325    public LatLon cart2LatLon(double[] xyz) {
326        return cart2LatLon(xyz, 1e-11);
327    }
328
329    public LatLon cart2LatLon(double[] xyz, double epsilon) {
330        double norm = Math.sqrt(xyz[0] * xyz[0] + xyz[1] * xyz[1]);
331        double lg = 2.0 * Math.atan(xyz[1] / (xyz[0] + norm));
332        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])))));
333        double delta = 1.0;
334        while (delta > epsilon) {
335            double s2 = Math.sin(lt);
336            s2 *= s2;
337            double l = Math.atan((xyz[2] / norm)
338                    / (1.0 - (a * e2 * Math.cos(lt) / (norm * Math.sqrt(1.0 - e2 * s2)))));
339            delta = Math.abs(l - lt);
340            lt = l;
341        }
342        return new LatLon(Math.toDegrees(lt), Math.toDegrees(lg));
343    }
344
345    /**
346     * convert ellipsoidal coordinates to cartesian coordinates
347     *
348     * @param coord The Latitude and longitude in degrees
349     * @return the corresponding (X, Y Z) cartesian coordinates in meters.
350     */
351    public double[] latLon2Cart(LatLon coord) {
352        double phi = Math.toRadians(coord.lat());
353        double lambda = Math.toRadians(coord.lon());
354
355        double Rn = a / Math.sqrt(1 - e2 * Math.pow(Math.sin(phi), 2));
356        double[] xyz = new double[3];
357        xyz[0] = Rn * Math.cos(phi) * Math.cos(lambda);
358        xyz[1] = Rn * Math.cos(phi) * Math.sin(lambda);
359        xyz[2] = Rn * (1 - e2) * Math.sin(phi);
360
361        return xyz;
362    }
363}