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;
010import org.openstreetmap.josm.tools.Utils;
011
012/**
013 * Reference ellipsoids.
014 */
015public final class Ellipsoid {
016
017    /**
018     * Airy 1830
019     */
020    public static final Ellipsoid Airy = Ellipsoid.createAb(6377563.396, 6356256.910);
021
022    /**
023     * Modified Airy 1849
024     */
025    public static final Ellipsoid AiryMod = Ellipsoid.createAb(6377340.189, 6356034.446);
026
027    /**
028     * Australian National Spheroid (Australian Natl & S. Amer. 1969)
029     * same as GRS67 Modified
030     */
031    public static final Ellipsoid AustSA = Ellipsoid.createArf(6378160.0, 298.25);
032
033    /**
034     * Bessel 1841 ellipsoid
035     */
036    public static final Ellipsoid Bessel1841 = Ellipsoid.createArf(6377397.155, 299.1528128);
037
038    /**
039     * Bessel 1841 (Namibia)
040     */
041    public static final Ellipsoid BesselNamibia = Ellipsoid.createArf(6377483.865, 299.1528128);
042
043    /**
044     * Clarke 1866 ellipsoid
045     */
046    public static final Ellipsoid Clarke1866 = Ellipsoid.createAb(6378206.4, 6356583.8);
047
048    /**
049     * Clarke 1880 (modified)
050     */
051    public static final Ellipsoid Clarke1880 = Ellipsoid.createArf(6378249.145, 293.4663);
052
053    /**
054     * Clarke 1880 IGN (French national geographic institute)
055     */
056    public static final Ellipsoid ClarkeIGN = Ellipsoid.createAb(6378249.2, 6356515.0);
057
058    /**
059     * Everest (Sabah & Sarawak)
060     */
061    public static final Ellipsoid EverestSabahSarawak = Ellipsoid.createArf(6377298.556, 300.8017);
062
063    /**
064     * Fischer (Mercury Datum) 1960
065     */
066    public static final Ellipsoid Fischer = Ellipsoid.createArf(6378166., 298.3);
067
068    /**
069     * Modified Fischer 1960
070     */
071    public static final Ellipsoid FischerMod = Ellipsoid.createArf(6378155., 298.3);
072
073    /**
074     * GRS67 ellipsoid
075     */
076    public static final Ellipsoid GRS67 = Ellipsoid.createArf(6378160.0, 298.247167427);
077
078    /**
079     * GRS80 ellipsoid
080     */
081    public static final Ellipsoid GRS80 = Ellipsoid.createArf(6378137.0, 298.257222101);
082
083    /**
084     * Hayford's ellipsoid 1909 (ED50 system)
085     * Also known as International 1924
086     * Proj.4 code: intl
087     */
088    public static final Ellipsoid Hayford = Ellipsoid.createArf(6378388.0, 297.0);
089
090    /**
091     * Helmert 1906
092     */
093    public static final Ellipsoid Helmert = Ellipsoid.createArf(6378200.0, 298.3);
094
095    /**
096     * Krassowsky 1940 ellipsoid
097     */
098    public static final Ellipsoid Krassowsky = Ellipsoid.createArf(6378245.0, 298.3);
099
100    /**
101     * WGS66 ellipsoid
102     */
103    public static final Ellipsoid WGS66 = Ellipsoid.createArf(6378145.0, 298.25);
104
105    /**
106     * WGS72 ellipsoid
107     */
108    public static final Ellipsoid WGS72 = Ellipsoid.createArf(6378135.0, 298.26);
109
110    /**
111     * WGS84 ellipsoid
112     */
113    public static final Ellipsoid WGS84 = Ellipsoid.createArf(6378137.0, 298.257223563);
114
115    /**
116     * half long axis
117     */
118    public final double a;
119
120    /**
121     * half short axis
122     */
123    public final double b;
124
125    /**
126     * first eccentricity:
127     * sqrt(a*a - b*b) / a
128     */
129    public final double e;
130
131    /**
132     * first eccentricity squared:
133     * (a*a - b*b) / (a*a)
134     */
135    public final double e2;
136
137    /**
138     * square of the second eccentricity:
139     * (a*a - b*b) / (b*b)
140     */
141    public final double eb2;
142
143    /**
144     * if ellipsoid is spherical, i.e. the major and minor semiaxis are
145     * the same
146     */
147    public final boolean spherical;
148
149    /**
150     * private constructur - use one of the create_* methods
151     *
152     * @param a semimajor radius of the ellipsoid axis
153     * @param b semiminor radius of the ellipsoid axis
154     * @param e first eccentricity of the ellipsoid ( = sqrt((a*a - b*b)/(a*a)))
155     * @param e2 first eccentricity squared
156     * @param eb2 square of the second eccentricity
157     * @param sperical if the ellipsoid is sphere
158     */
159    private Ellipsoid(double a, double b, double e, double e2, double eb2, boolean sperical) {
160        this.a = a;
161        this.b = b;
162        this.e = e;
163        this.e2 = e2;
164        this.eb2 = eb2;
165        this.spherical = sperical;
166    }
167
168    /**
169     * create a new ellipsoid
170     *
171     * @param a semimajor radius of the ellipsoid axis (in meters)
172     * @param b semiminor radius of the ellipsoid axis (in meters)
173     * @return the new ellipsoid
174     */
175    public static Ellipsoid createAb(double a, double b) {
176        double e2 = (a*a - b*b) / (a*a);
177        double e = Math.sqrt(e2);
178        double eb2 = e2 / (1.0 - e2);
179        return new Ellipsoid(a, b, e, e2, eb2, a == b);
180    }
181
182    /**
183     * create a new ellipsoid
184     *
185     * @param a semimajor radius of the ellipsoid axis (in meters)
186     * @param es first eccentricity squared
187     * @return the new ellipsoid
188     */
189    public static Ellipsoid createAes(double a, double es) {
190        double b = a * Math.sqrt(1.0 - es);
191        double e = Math.sqrt(es);
192        double eb2 = es / (1.0 - es);
193        return new Ellipsoid(a, b, e, es, eb2, es == 0);
194    }
195
196    /**
197     * create a new ellipsoid
198     *
199     * @param a semimajor radius of the ellipsoid axis (in meters)
200     * @param f flattening ( = (a - b) / a)
201     * @return the new ellipsoid
202     */
203    public static Ellipsoid createAf(double a, double f) {
204        double b = a * (1.0 - f);
205        double e2 = f * (2 - f);
206        double e = Math.sqrt(e2);
207        double eb2 = e2 / (1.0 - e2);
208        return new Ellipsoid(a, b, e, e2, eb2, f == 0);
209    }
210
211    /**
212     * create a new ellipsoid
213     *
214     * @param a semimajor radius of the ellipsoid axis (in meters)
215     * @param rf inverse flattening
216     * @return the new ellipsoid
217     */
218    public static Ellipsoid createArf(double a, double rf) {
219        return createAf(a, 1.0 / rf);
220    }
221
222    @Override
223    public String toString() {
224        return "Ellipsoid{a="+a+", b="+b+'}';
225    }
226
227    /**
228     * Returns the <i>radius of curvature in the prime vertical</i>
229     * for this reference ellipsoid at the specified latitude.
230     *
231     * @param phi The local latitude (radians).
232     * @return The radius of curvature in the prime vertical (meters).
233     */
234    public double verticalRadiusOfCurvature(final double phi) {
235        return a / Math.sqrt(1.0 - (e2 * sqr(Math.sin(phi))));
236    }
237
238    private static double sqr(final double x) {
239        return x * x;
240    }
241
242    /**
243     *  Returns the meridional arc, the true meridional distance on the
244     * ellipsoid from the equator to the specified latitude, in meters.
245     *
246     * @param phi   The local latitude (in radians).
247     * @return  The meridional arc (in meters).
248     */
249    public double meridionalArc(final double phi) {
250        final double sin2Phi = Math.sin(2.0 * phi);
251        final double sin4Phi = Math.sin(4.0 * phi);
252        final double sin6Phi = Math.sin(6.0 * phi);
253        final double sin8Phi = Math.sin(8.0 * phi);
254        // TODO . calculate 'f'
255        //double f = 1.0 / 298.257222101; // GRS80
256        double f = 1.0 / 298.257223563; // WGS84
257        final double n = f / (2.0 - f);
258        final double n2 = n * n;
259        final double n3 = n2 * n;
260        final double n4 = n3 * n;
261        final double n5 = n4 * n;
262        final double n1n2 = n - n2;
263        final double n2n3 = n2 - n3;
264        final double n3n4 = n3 - n4;
265        final double n4n5 = n4 - n5;
266        final double ap = a * (1.0 - n + (5.0 / 4.0) * (n2n3) + (81.0 / 64.0) * (n4n5));
267        final double bp = (3.0 / 2.0) * a * (n1n2 + (7.0 / 8.0) * (n3n4) + (55.0 / 64.0) * n5);
268        final double cp = (15.0 / 16.0) * a * (n2n3 + (3.0 / 4.0) * (n4n5));
269        final double dp = (35.0 / 48.0) * a * (n3n4 + (11.0 / 16.0) * n5);
270        final double ep = (315.0 / 512.0) * a * (n4n5);
271        return ap * phi - bp * sin2Phi + cp * sin4Phi - dp * sin6Phi + ep * sin8Phi;
272    }
273
274    /**
275     *  Returns the <i>radius of curvature in the meridian</i>
276     *  for this reference ellipsoid at the specified latitude.
277     *
278     * @param phi The local latitude (in radians).
279     * @return  The radius of curvature in the meridian (in meters).
280     */
281    public double meridionalRadiusOfCurvature(final double phi) {
282        return verticalRadiusOfCurvature(phi)
283        / (1.0 + eb2 * sqr(Math.cos(phi)));
284    }
285
286    /**
287     * Returns isometric latitude of phi on given first eccentricity (e)
288     * @param phi The local latitude (radians).
289     * @param e first eccentricity
290     * @return isometric latitude of phi on first eccentricity (e)
291     */
292    public double latitudeIsometric(double phi, double e) {
293        double v1 = 1-e*Math.sin(phi);
294        double v2 = 1+e*Math.sin(phi);
295        return Math.log(Math.tan(Math.PI/4+phi/2)*Math.pow(v1/v2, e/2));
296    }
297
298    /**
299     * Returns isometric latitude of phi on first eccentricity (e)
300     * @param phi The local latitude (radians).
301     * @return isometric latitude of phi on first eccentricity (e)
302     */
303    public double latitudeIsometric(double phi) {
304        double v1 = 1-e*Math.sin(phi);
305        double v2 = 1+e*Math.sin(phi);
306        return Math.log(Math.tan(Math.PI/4+phi/2)*Math.pow(v1/v2, e/2));
307    }
308
309    /**
310     * Returns geographic latitude of isometric latitude of first eccentricity (e) and epsilon precision
311     * @param latIso isometric latitude
312     * @param e first eccentricity
313     * @param epsilon epsilon precision
314     * @return geographic latitude of isometric latitude of first eccentricity (e) and epsilon precision
315     */
316    public double latitude(double latIso, double e, double epsilon) {
317        double lat0 = 2*Math.atan(Math.exp(latIso))-Math.PI/2;
318        double lati = lat0;
319        double lati1 = 1.0; // random value to start the iterative processus
320        while (Math.abs(lati1-lati) >= epsilon) {
321            lati = lati1;
322            double v1 = 1+e*Math.sin(lati);
323            double v2 = 1-e*Math.sin(lati);
324            lati1 = 2*Math.atan(Math.pow(v1/v2, e/2)*Math.exp(latIso))-Math.PI/2;
325        }
326        return lati1;
327    }
328
329    /**
330     * convert cartesian coordinates to ellipsoidal coordinates
331     *
332     * @param xyz the coordinates in meters (X, Y, Z)
333     * @return The corresponding latitude and longitude in degrees
334     */
335    public LatLon cart2LatLon(double... xyz) {
336        return cart2LatLon(xyz, 1e-11);
337    }
338
339    public LatLon cart2LatLon(double[] xyz, double epsilon) {
340        double norm = Math.sqrt(xyz[0] * xyz[0] + xyz[1] * xyz[1]);
341        double lg = 2.0 * Math.atan(xyz[1] / (xyz[0] + norm));
342        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])))));
343        double delta = 1.0;
344        while (delta > epsilon) {
345            double s2 = Math.sin(lt);
346            s2 *= s2;
347            double l = Math.atan((xyz[2] / norm)
348                    / (1.0 - (a * e2 * Math.cos(lt) / (norm * Math.sqrt(1.0 - e2 * s2)))));
349            delta = Math.abs(l - lt);
350            lt = l;
351        }
352        return new LatLon(Utils.toDegrees(lt), Utils.toDegrees(lg));
353    }
354
355    /**
356     * convert ellipsoidal coordinates to cartesian coordinates
357     *
358     * @param coord The Latitude and longitude in degrees
359     * @return the corresponding (X, Y Z) cartesian coordinates in meters.
360     */
361    public double[] latLon2Cart(LatLon coord) {
362        double phi = Utils.toRadians(coord.lat());
363        double lambda = Utils.toRadians(coord.lon());
364
365        double rn = a / Math.sqrt(1 - e2 * Math.pow(Math.sin(phi), 2));
366        double[] xyz = new double[3];
367        xyz[0] = rn * Math.cos(phi) * Math.cos(lambda);
368        xyz[1] = rn * Math.cos(phi) * Math.sin(lambda);
369        xyz[2] = rn * (1 - e2) * Math.sin(phi);
370
371        return xyz;
372    }
373}