source: josm/trunk/src/org/openstreetmap/josm/data/projection/Ellipsoid.java@ 12795

Last change on this file since 12795 was 12171, checked in by michael2402, 7 years ago

Fixed checkstyle warnings.
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1/*
2 * Import from fr.geo.convert package, a geographic coordinates converter.
3 * (https://www.i3s.unice.fr/~johan/gps/)
4 * License: GPL. For details, see LICENSE file.
5 * Copyright (C) 2002 Johan Montagnat (johan@creatis.insa-lyon.fr)
6 */
7package org.openstreetmap.josm.data.projection;
8
9import org.openstreetmap.josm.data.coor.LatLon;
10import org.openstreetmap.josm.tools.Utils;
11
12/**
13 * Reference ellipsoids.
14 */
15public final class Ellipsoid {
16
17 /**
18 * Airy 1830
19 */
20 public static final Ellipsoid Airy = Ellipsoid.createAb(6377563.396, 6356256.910);
21
22 /**
23 * Modified Airy 1849
24 */
25 public static final Ellipsoid AiryMod = Ellipsoid.createAb(6377340.189, 6356034.446);
26
27 /**
28 * Australian National Spheroid (Australian Natl & S. Amer. 1969)
29 * same as GRS67 Modified
30 */
31 public static final Ellipsoid AustSA = Ellipsoid.createArf(6378160.0, 298.25);
32
33 /**
34 * Bessel 1841 ellipsoid
35 */
36 public static final Ellipsoid Bessel1841 = Ellipsoid.createArf(6377397.155, 299.1528128);
37
38 /**
39 * Bessel 1841 (Namibia)
40 */
41 public static final Ellipsoid BesselNamibia = Ellipsoid.createArf(6377483.865, 299.1528128);
42
43 /**
44 * Clarke 1866 ellipsoid
45 */
46 public static final Ellipsoid Clarke1866 = Ellipsoid.createAb(6378206.4, 6356583.8);
47
48 /**
49 * Clarke 1880 (modified)
50 */
51 public static final Ellipsoid Clarke1880 = Ellipsoid.createArf(6378249.145, 293.4663);
52
53 /**
54 * Clarke 1880 IGN (French national geographic institute)
55 */
56 public static final Ellipsoid ClarkeIGN = Ellipsoid.createAb(6378249.2, 6356515.0);
57
58 /**
59 * Everest (Sabah & Sarawak)
60 */
61 public static final Ellipsoid EverestSabahSarawak = Ellipsoid.createArf(6377298.556, 300.8017);
62
63 /**
64 * GRS67 ellipsoid
65 */
66 public static final Ellipsoid GRS67 = Ellipsoid.createArf(6378160.0, 298.247167427);
67
68 /**
69 * GRS80 ellipsoid
70 */
71 public static final Ellipsoid GRS80 = Ellipsoid.createArf(6378137.0, 298.257222101);
72
73 /**
74 * Hayford's ellipsoid 1909 (ED50 system)
75 * Also known as International 1924
76 * Proj.4 code: intl
77 */
78 public static final Ellipsoid Hayford = Ellipsoid.createArf(6378388.0, 297.0);
79
80 /**
81 * Helmert 1906
82 */
83 public static final Ellipsoid Helmert = Ellipsoid.createArf(6378200.0, 298.3);
84
85 /**
86 * Krassowsky 1940 ellipsoid
87 */
88 public static final Ellipsoid Krassowsky = Ellipsoid.createArf(6378245.0, 298.3);
89
90 /**
91 * WGS66 ellipsoid
92 */
93 public static final Ellipsoid WGS66 = Ellipsoid.createArf(6378145.0, 298.25);
94
95 /**
96 * WGS72 ellipsoid
97 */
98 public static final Ellipsoid WGS72 = Ellipsoid.createArf(6378135.0, 298.26);
99
100 /**
101 * WGS84 ellipsoid
102 */
103 public static final Ellipsoid WGS84 = Ellipsoid.createArf(6378137.0, 298.257223563);
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 createAb(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 createAes(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 createAf(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 createArf(double a, double rf) {
209 return createAf(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(Utils.toDegrees(lt), Utils.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 = Utils.toRadians(coord.lat());
353 double lambda = Utils.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}
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