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 * Clarke 1866 ellipsoid 039 */ 040 public static final Ellipsoid Clarke1866 = Ellipsoid.create_a_b(6378206.4, 6356583.8); 041 042 /** 043 * Clarke 1880 IGN (French national geographic institute) 044 */ 045 public static final Ellipsoid ClarkeIGN = Ellipsoid.create_a_b(6378249.2, 6356515.0); 046 047 /** 048 * GRS67 ellipsoid 049 */ 050 public static final Ellipsoid GRS67 = Ellipsoid.create_a_rf(6378160.0, 298.247167427); 051 052 /** 053 * GRS80 ellipsoid 054 */ 055 public static final Ellipsoid GRS80 = Ellipsoid.create_a_rf(6378137.0, 298.257222101); 056 057 /** 058 * Hayford's ellipsoid 1909 (ED50 system) 059 * Also known as International 1924 060 * Proj.4 code: intl 061 */ 062 public static final Ellipsoid Hayford = Ellipsoid.create_a_rf(6378388.0, 297.0); 063 064 /** 065 * Helmert 1906 066 */ 067 public static final Ellipsoid Helmert = Ellipsoid.create_a_rf(6378200.0, 298.3); 068 069 /** 070 * Krassowsky 1940 ellipsoid 071 */ 072 public static final Ellipsoid Krassowsky = Ellipsoid.create_a_rf(6378245.0, 298.3); 073 074 /** 075 * WGS72 ellipsoid 076 */ 077 public static final Ellipsoid WGS72 = Ellipsoid.create_a_rf(6378135.0, 298.26); 078 079 /** 080 * WGS84 ellipsoid 081 */ 082 public static final Ellipsoid WGS84 = Ellipsoid.create_a_rf(6378137.0, 298.257223563); 083 084 085 /** 086 * half long axis 087 */ 088 public final double a; 089 090 /** 091 * half short axis 092 */ 093 public final double b; 094 095 /** 096 * first eccentricity 097 */ 098 public final double e; 099 100 /** 101 * first eccentricity squared 102 */ 103 public final double e2; 104 105 /** 106 * square of the second eccentricity 107 */ 108 public final double eb2; 109 110 /** 111 * private constructur - use one of the create_* methods 112 * 113 * @param a semimajor radius of the ellipsoid axis 114 * @param b semiminor radius of the ellipsoid axis 115 * @param e first eccentricity of the ellipsoid ( = sqrt((a*a - b*b)/(a*a))) 116 * @param e2 first eccentricity squared 117 * @param eb2 square of the second eccentricity 118 */ 119 private Ellipsoid(double a, double b, double e, double e2, double eb2) { 120 this.a = a; 121 this.b = b; 122 this.e = e; 123 this.e2 = e2; 124 this.eb2 = eb2; 125 } 126 127 /** 128 * create a new ellipsoid 129 * 130 * @param a semimajor radius of the ellipsoid axis (in meters) 131 * @param b semiminor radius of the ellipsoid axis (in meters) 132 * @return the new ellipsoid 133 */ 134 public static Ellipsoid create_a_b(double a, double b) { 135 double e2 = (a*a - b*b) / (a*a); 136 double e = Math.sqrt(e2); 137 double eb2 = e2 / (1.0 - e2); 138 return new Ellipsoid(a, b, e, e2, eb2); 139 } 140 141 /** 142 * create a new ellipsoid 143 * 144 * @param a semimajor radius of the ellipsoid axis (in meters) 145 * @param es first eccentricity squared 146 * @return the new ellipsoid 147 */ 148 public static Ellipsoid create_a_es(double a, double es) { 149 double b = a * Math.sqrt(1.0 - es); 150 double e = Math.sqrt(es); 151 double eb2 = es / (1.0 - es); 152 return new Ellipsoid(a, b, e, es, eb2); 153 } 154 155 /** 156 * create a new ellipsoid 157 * 158 * @param a semimajor radius of the ellipsoid axis (in meters) 159 * @param f flattening ( = (a - b) / a) 160 * @return the new ellipsoid 161 */ 162 public static Ellipsoid create_a_f(double a, double f) { 163 double b = a * (1.0 - f); 164 double e2 = f * (2 - f); 165 double e = Math.sqrt(e2); 166 double eb2 = e2 / (1.0 - e2); 167 return new Ellipsoid(a, b, e, e2, eb2); 168 } 169 170 /** 171 * create a new ellipsoid 172 * 173 * @param a semimajor radius of the ellipsoid axis (in meters) 174 * @param rf inverse flattening 175 * @return the new ellipsoid 176 */ 177 public static Ellipsoid create_a_rf(double a, double rf) { 178 return create_a_f(a, 1.0 / rf); 179 } 180 181 @Override 182 public String toString() { 183 return "Ellipsoid{a="+a+", b="+b+'}'; 184 } 185 186 /** 187 * Returns the <i>radius of curvature in the prime vertical</i> 188 * for this reference ellipsoid at the specified latitude. 189 * 190 * @param phi The local latitude (radians). 191 * @return The radius of curvature in the prime vertical (meters). 192 */ 193 public double verticalRadiusOfCurvature(final double phi) { 194 return a / Math.sqrt(1.0 - (e2 * sqr(Math.sin(phi)))); 195 } 196 197 private static double sqr(final double x) { 198 return x * x; 199 } 200 201 /** 202 * Returns the meridional arc, the true meridional distance on the 203 * ellipsoid from the equator to the specified latitude, in meters. 204 * 205 * @param phi The local latitude (in radians). 206 * @return The meridional arc (in meters). 207 */ 208 public double meridionalArc(final double phi) { 209 final double sin2Phi = Math.sin(2.0 * phi); 210 final double sin4Phi = Math.sin(4.0 * phi); 211 final double sin6Phi = Math.sin(6.0 * phi); 212 final double sin8Phi = Math.sin(8.0 * phi); 213 // TODO . calculate 'f' 214 //double f = 1.0 / 298.257222101; // GRS80 215 double f = 1.0 / 298.257223563; // WGS84 216 final double n = f / (2.0 - f); 217 final double n2 = n * n; 218 final double n3 = n2 * n; 219 final double n4 = n3 * n; 220 final double n5 = n4 * n; 221 final double n1n2 = n - n2; 222 final double n2n3 = n2 - n3; 223 final double n3n4 = n3 - n4; 224 final double n4n5 = n4 - n5; 225 final double ap = a * (1.0 - n + (5.0 / 4.0) * (n2n3) + (81.0 / 64.0) * (n4n5)); 226 final double bp = (3.0 / 2.0) * a * (n1n2 + (7.0 / 8.0) * (n3n4) + (55.0 / 64.0) * n5); 227 final double cp = (15.0 / 16.0) * a * (n2n3 + (3.0 / 4.0) * (n4n5)); 228 final double dp = (35.0 / 48.0) * a * (n3n4 + (11.0 / 16.0) * n5); 229 final double ep = (315.0 / 512.0) * a * (n4n5); 230 return ap * phi - bp * sin2Phi + cp * sin4Phi - dp * sin6Phi + ep * sin8Phi; 231 } 232 233 /** 234 * Returns the <i>radius of curvature in the meridian</i> 235 * for this reference ellipsoid at the specified latitude. 236 * 237 * @param phi The local latitude (in radians). 238 * @return The radius of curvature in the meridian (in meters). 239 */ 240 public double meridionalRadiusOfCurvature(final double phi) { 241 return verticalRadiusOfCurvature(phi) 242 / (1.0 + eb2 * sqr(Math.cos(phi))); 243 } 244 245 /** 246 * Returns isometric latitude of phi on given first eccentricity (e) 247 * @param phi The local latitude (radians). 248 * @return isometric latitude of phi on first eccentricity (e) 249 */ 250 public double latitudeIsometric(double phi, double e) { 251 double v1 = 1-e*Math.sin(phi); 252 double v2 = 1+e*Math.sin(phi); 253 return Math.log(Math.tan(Math.PI/4+phi/2)*Math.pow(v1/v2, e/2)); 254 } 255 256 /** 257 * Returns isometric latitude of phi on first eccentricity (e) 258 * @param phi The local latitude (radians). 259 * @return isometric latitude of phi on first eccentricity (e) 260 */ 261 public double latitudeIsometric(double phi) { 262 double v1 = 1-e*Math.sin(phi); 263 double v2 = 1+e*Math.sin(phi); 264 return Math.log(Math.tan(Math.PI/4+phi/2)*Math.pow(v1/v2, e/2)); 265 } 266 267 /** 268 * Returns geographic latitude of isometric latitude of first eccentricity (e) 269 * and epsilon precision 270 * @return geographic latitude of isometric latitude of first eccentricity (e) 271 * and epsilon precision 272 */ 273 public double latitude(double latIso, double e, double epsilon) { 274 double lat0 = 2*Math.atan(Math.exp(latIso))-Math.PI/2; 275 double lati = lat0; 276 double lati1 = 1.0; // random value to start the iterative processus 277 while (Math.abs(lati1-lati) >= epsilon) { 278 lati = lati1; 279 double v1 = 1+e*Math.sin(lati); 280 double v2 = 1-e*Math.sin(lati); 281 lati1 = 2*Math.atan(Math.pow(v1/v2, e/2)*Math.exp(latIso))-Math.PI/2; 282 } 283 return lati1; 284 } 285 286 /** 287 * convert cartesian coordinates to ellipsoidal coordinates 288 * 289 * @param xyz the coordinates in meters (X, Y, Z) 290 * @return The corresponding latitude and longitude in degrees 291 */ 292 public LatLon cart2LatLon(double[] xyz) { 293 return cart2LatLon(xyz, 1e-11); 294 } 295 296 public LatLon cart2LatLon(double[] xyz, double epsilon) { 297 double norm = Math.sqrt(xyz[0] * xyz[0] + xyz[1] * xyz[1]); 298 double lg = 2.0 * Math.atan(xyz[1] / (xyz[0] + norm)); 299 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]))))); 300 double delta = 1.0; 301 while (delta > epsilon) { 302 double s2 = Math.sin(lt); 303 s2 *= s2; 304 double l = Math.atan((xyz[2] / norm) 305 / (1.0 - (a * e2 * Math.cos(lt) / (norm * Math.sqrt(1.0 - e2 * s2))))); 306 delta = Math.abs(l - lt); 307 lt = l; 308 } 309 return new LatLon(Math.toDegrees(lt), Math.toDegrees(lg)); 310 } 311 312 /** 313 * convert ellipsoidal coordinates to cartesian coordinates 314 * 315 * @param coord The Latitude and longitude in degrees 316 * @return the corresponding (X, Y Z) cartesian coordinates in meters. 317 */ 318 public double[] latLon2Cart(LatLon coord) { 319 double phi = Math.toRadians(coord.lat()); 320 double lambda = Math.toRadians(coord.lon()); 321 322 double Rn = a / Math.sqrt(1 - e2 * Math.pow(Math.sin(phi), 2)); 323 double[] xyz = new double[3]; 324 xyz[0] = Rn * Math.cos(phi) * Math.cos(lambda); 325 xyz[1] = Rn * Math.cos(phi) * Math.sin(lambda); 326 xyz[2] = Rn * (1 - e2) * Math.sin(phi); 327 328 return xyz; 329 } 330}