001 /* 002 * Import from fr.geo.convert package, a geographic coordinates converter. 003 * (http://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 */ 007 008 package org.openstreetmap.josm.data.projection; 009 010 import org.openstreetmap.josm.data.coor.LatLon; 011 012 /** 013 * the reference ellipsoids 014 */ 015 public class Ellipsoid { 016 /** 017 * Clarke 1880 IGN (French national geographic institute) 018 */ 019 public static final Ellipsoid clarkeIGN = Ellipsoid.create_a_b(6378249.2, 6356515.0); 020 /** 021 * Hayford's ellipsoid 1909 (ED50 system) 022 * Proj.4 code: intl 023 */ 024 public static final Ellipsoid hayford = Ellipsoid.create_a_rf(6378388.0, 297.0); 025 /** 026 * GRS80 ellipsoid 027 */ 028 public static final Ellipsoid GRS80 = Ellipsoid.create_a_rf(6378137.0, 298.257222101); 029 030 /** 031 * WGS84 ellipsoid 032 */ 033 public static final Ellipsoid WGS84 = Ellipsoid.create_a_rf(6378137.0, 298.257223563); 034 035 /** 036 * Bessel 1841 ellipsoid 037 */ 038 public static final Ellipsoid Bessel1841 = Ellipsoid.create_a_rf(6377397.155, 299.1528128); 039 040 /** 041 * half long axis 042 */ 043 public final double a; 044 /** 045 * half short axis 046 */ 047 public final double b; 048 /** 049 * first eccentricity 050 */ 051 public final double e; 052 /** 053 * first eccentricity squared 054 */ 055 public final double e2; 056 057 /** 058 * square of the second eccentricity 059 */ 060 public final double eb2; 061 062 /** 063 * private constructur - use one of the create_* methods 064 * 065 * @param a semimajor radius of the ellipsoid axis 066 * @param b semiminor radius of the ellipsoid axis 067 * @param e first eccentricity of the ellipsoid ( = sqrt((a*a - b*b)/(a*a))) 068 * @param e2 first eccentricity squared 069 * @param eb2 square of the second eccentricity 070 */ 071 private Ellipsoid(double a, double b, double e, double e2, double eb2) { 072 this.a = a; 073 this.b = b; 074 this.e = e; 075 this.e2 = e2; 076 this.eb2 = eb2; 077 } 078 079 /** 080 * create a new ellipsoid 081 * 082 * @param a semimajor radius of the ellipsoid axis (in meters) 083 * @param b semiminor radius of the ellipsoid axis (in meters) 084 */ 085 public static Ellipsoid create_a_b(double a, double b) { 086 double e2 = (a*a - b*b) / (a*a); 087 double e = Math.sqrt(e2); 088 double eb2 = e2 / (1.0 - e2); 089 return new Ellipsoid(a, b, e, e2, eb2); 090 } 091 092 /** 093 * create a new ellipsoid 094 * 095 * @param a semimajor radius of the ellipsoid axis (in meters) 096 * @param es first eccentricity squared 097 */ 098 public static Ellipsoid create_a_es(double a, double es) { 099 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 }