source: josm/trunk/src/org/openstreetmap/josm/data/projection/Ellipsoid.java@ 8345

Last change on this file since 8345 was 8255, checked in by bastiK, 9 years ago

fixed #11369 - Add EPSG:2019 projection
  • Property svn:eol-style set to native
File size: 9.5 KB
Line 
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 */
7
8package org.openstreetmap.josm.data.projection;
9
10import org.openstreetmap.josm.data.coor.LatLon;
11
12/**
13 * Reference ellipsoids.
14 */
15public final class Ellipsoid {
16
17 /**
18 * Clarke 1866 ellipsoid
19 */
20 public static final Ellipsoid clarke1866 = Ellipsoid.create_a_b(6378206.4, 6356583.8);
21
22 /**
23 * Clarke 1880 IGN (French national geographic institute)
24 */
25 public static final Ellipsoid clarkeIGN = Ellipsoid.create_a_b(6378249.2, 6356515.0);
26
27 /**
28 * Hayford's ellipsoid 1909 (ED50 system)<br>
29 * Proj.4 code: intl
30 */
31 public static final Ellipsoid hayford = Ellipsoid.create_a_rf(6378388.0, 297.0);
32
33 /**
34 * GRS67 ellipsoid
35 */
36 public static final Ellipsoid GRS67 = Ellipsoid.create_a_rf(6378160.0, 298.247167472);
37
38 /**
39 * GRS80 ellipsoid
40 */
41 public static final Ellipsoid GRS80 = Ellipsoid.create_a_rf(6378137.0, 298.257222101);
42
43 /**
44 * WGS84 ellipsoid
45 */
46 public static final Ellipsoid WGS84 = Ellipsoid.create_a_rf(6378137.0, 298.257223563);
47
48 /**
49 * Bessel 1841 ellipsoid
50 */
51 public static final Ellipsoid Bessel1841 = Ellipsoid.create_a_rf(6377397.155, 299.1528128);
52
53 /**
54 * half long axis
55 */
56 public final double a;
57
58 /**
59 * half short axis
60 */
61 public final double b;
62
63 /**
64 * first eccentricity
65 */
66 public final double e;
67
68 /**
69 * first eccentricity squared
70 */
71 public final double e2;
72
73 /**
74 * square of the second eccentricity
75 */
76 public final double eb2;
77
78 /**
79 * private constructur - use one of the create_* methods
80 *
81 * @param a semimajor radius of the ellipsoid axis
82 * @param b semiminor radius of the ellipsoid axis
83 * @param e first eccentricity of the ellipsoid ( = sqrt((a*a - b*b)/(a*a)))
84 * @param e2 first eccentricity squared
85 * @param eb2 square of the second eccentricity
86 */
87 private Ellipsoid(double a, double b, double e, double e2, double eb2) {
88 this.a = a;
89 this.b = b;
90 this.e = e;
91 this.e2 = e2;
92 this.eb2 = eb2;
93 }
94
95 /**
96 * create a new ellipsoid
97 *
98 * @param a semimajor radius of the ellipsoid axis (in meters)
99 * @param b semiminor radius of the ellipsoid axis (in meters)
100 * @return the new ellipsoid
101 */
102 public static Ellipsoid create_a_b(double a, double b) {
103 double e2 = (a*a - b*b) / (a*a);
104 double e = Math.sqrt(e2);
105 double eb2 = e2 / (1.0 - e2);
106 return new Ellipsoid(a, b, e, e2, eb2);
107 }
108
109 /**
110 * create a new ellipsoid
111 *
112 * @param a semimajor radius of the ellipsoid axis (in meters)
113 * @param es first eccentricity squared
114 * @return the new ellipsoid
115 */
116 public static Ellipsoid create_a_es(double a, double es) {
117 double b = a * Math.sqrt(1.0 - es);
118 double e = Math.sqrt(es);
119 double eb2 = es / (1.0 - es);
120 return new Ellipsoid(a, b, e, es, eb2);
121 }
122
123 /**
124 * create a new ellipsoid
125 *
126 * @param a semimajor radius of the ellipsoid axis (in meters)
127 * @param f flattening ( = (a - b) / a)
128 * @return the new ellipsoid
129 */
130 public static Ellipsoid create_a_f(double a, double f) {
131 double b = a * (1.0 - f);
132 double e2 = f * (2 - f);
133 double e = Math.sqrt(e2);
134 double eb2 = e2 / (1.0 - e2);
135 return new Ellipsoid(a, b, e, e2, eb2);
136 }
137
138 /**
139 * create a new ellipsoid
140 *
141 * @param a semimajor radius of the ellipsoid axis (in meters)
142 * @param rf inverse flattening
143 * @return the new ellipsoid
144 */
145 public static Ellipsoid create_a_rf(double a, double rf) {
146 return create_a_f(a, 1.0 / rf);
147 }
148
149 @Override
150 public String toString() {
151 return "Ellipsoid{a="+a+", b="+b+"}";
152 }
153
154 /**
155 * Returns the <i>radius of curvature in the prime vertical</i>
156 * for this reference ellipsoid at the specified latitude.
157 *
158 * @param phi The local latitude (radians).
159 * @return The radius of curvature in the prime vertical (meters).
160 */
161 public double verticalRadiusOfCurvature(final double phi) {
162 return a / Math.sqrt(1.0 - (e2 * sqr(Math.sin(phi))));
163 }
164
165 private static double sqr(final double x) {
166 return x * x;
167 }
168
169 /**
170 * Returns the meridional arc, the true meridional distance on the
171 * ellipsoid from the equator to the specified latitude, in meters.
172 *
173 * @param phi The local latitude (in radians).
174 * @return The meridional arc (in meters).
175 */
176 public double meridionalArc(final double phi) {
177 final double sin2Phi = Math.sin(2.0 * phi);
178 final double sin4Phi = Math.sin(4.0 * phi);
179 final double sin6Phi = Math.sin(6.0 * phi);
180 final double sin8Phi = Math.sin(8.0 * phi);
181 // TODO . calculate 'f'
182 //double f = 1.0 / 298.257222101; // GRS80
183 double f = 1.0 / 298.257223563; // WGS84
184 final double n = f / (2.0 - f);
185 final double n2 = n * n;
186 final double n3 = n2 * n;
187 final double n4 = n3 * n;
188 final double n5 = n4 * n;
189 final double n1n2 = n - n2;
190 final double n2n3 = n2 - n3;
191 final double n3n4 = n3 - n4;
192 final double n4n5 = n4 - n5;
193 final double ap = a * (1.0 - n + (5.0 / 4.0) * (n2n3) + (81.0 / 64.0) * (n4n5));
194 final double bp = (3.0 / 2.0) * a * (n1n2 + (7.0 / 8.0) * (n3n4) + (55.0 / 64.0) * n5);
195 final double cp = (15.0 / 16.0) * a * (n2n3 + (3.0 / 4.0) * (n4n5));
196 final double dp = (35.0 / 48.0) * a * (n3n4 + (11.0 / 16.0) * n5);
197 final double ep = (315.0 / 512.0) * a * (n4n5);
198 return ap * phi - bp * sin2Phi + cp * sin4Phi - dp * sin6Phi + ep * sin8Phi;
199 }
200
201 /**
202 * Returns the <i>radius of curvature in the meridian</i>
203 * for this reference ellipsoid at the specified latitude.
204 *
205 * @param phi The local latitude (in radians).
206 * @return The radius of curvature in the meridian (in meters).
207 */
208 public double meridionalRadiusOfCurvature(final double phi) {
209 return verticalRadiusOfCurvature(phi)
210 / (1.0 + eb2 * sqr(Math.cos(phi)));
211 }
212
213 /**
214 * Returns isometric latitude of phi on given first eccentricity (e)
215 * @param phi The local latitude (radians).
216 * @return isometric latitude of phi on first eccentricity (e)
217 */
218 public double latitudeIsometric(double phi, double e) {
219 double v1 = 1-e*Math.sin(phi);
220 double v2 = 1+e*Math.sin(phi);
221 return Math.log(Math.tan(Math.PI/4+phi/2)*Math.pow(v1/v2,e/2));
222 }
223
224 /**
225 * Returns isometric latitude of phi on first eccentricity (e)
226 * @param phi The local latitude (radians).
227 * @return isometric latitude of phi on first eccentricity (e)
228 */
229 public double latitudeIsometric(double phi) {
230 double v1 = 1-e*Math.sin(phi);
231 double v2 = 1+e*Math.sin(phi);
232 return Math.log(Math.tan(Math.PI/4+phi/2)*Math.pow(v1/v2,e/2));
233 }
234
235 /**
236 * Returns geographic latitude of isometric latitude of first eccentricity (e)
237 * and epsilon precision
238 * @return geographic latitude of isometric latitude of first eccentricity (e)
239 * and epsilon precision
240 */
241 public double latitude(double latIso, double e, double epsilon) {
242 double lat0 = 2*Math.atan(Math.exp(latIso))-Math.PI/2;
243 double lati = lat0;
244 double lati1 = 1.0; // random value to start the iterative processus
245 while(Math.abs(lati1-lati)>=epsilon) {
246 lati = lati1;
247 double v1 = 1+e*Math.sin(lati);
248 double v2 = 1-e*Math.sin(lati);
249 lati1 = 2*Math.atan(Math.pow(v1/v2,e/2)*Math.exp(latIso))-Math.PI/2;
250 }
251 return lati1;
252 }
253
254 /**
255 * convert cartesian coordinates to ellipsoidal coordinates
256 *
257 * @param xyz the coordinates in meters (X, Y, Z)
258 * @return The corresponding latitude and longitude in degrees
259 */
260 public LatLon cart2LatLon(double[] xyz) {
261 return cart2LatLon(xyz, 1e-11);
262 }
263
264 public LatLon cart2LatLon(double[] xyz, double epsilon) {
265 double norm = Math.sqrt(xyz[0] * xyz[0] + xyz[1] * xyz[1]);
266 double lg = 2.0 * Math.atan(xyz[1] / (xyz[0] + norm));
267 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])))));
268 double delta = 1.0;
269 while (delta > epsilon) {
270 double s2 = Math.sin(lt);
271 s2 *= s2;
272 double l = Math.atan((xyz[2] / norm)
273 / (1.0 - (a * e2 * Math.cos(lt) / (norm * Math.sqrt(1.0 - e2 * s2)))));
274 delta = Math.abs(l - lt);
275 lt = l;
276 }
277 return new LatLon(Math.toDegrees(lt), Math.toDegrees(lg));
278 }
279
280 /**
281 * convert ellipsoidal coordinates to cartesian coordinates
282 *
283 * @param coord The Latitude and longitude in degrees
284 * @return the corresponding (X, Y Z) cartesian coordinates in meters.
285 */
286 public double[] latLon2Cart(LatLon coord) {
287 double phi = Math.toRadians(coord.lat());
288 double lambda = Math.toRadians(coord.lon());
289
290 double Rn = a / Math.sqrt(1 - e2 * Math.pow(Math.sin(phi), 2));
291 double[] xyz = new double[3];
292 xyz[0] = Rn * Math.cos(phi) * Math.cos(lambda);
293 xyz[1] = Rn * Math.cos(phi) * Math.sin(lambda);
294 xyz[2] = Rn * (1 - e2) * Math.sin(phi);
295
296 return xyz;
297 }
298}
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