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