Changeset 9112 in josm for trunk/src/org/openstreetmap/josm/data/projection/proj/TransverseMercator.java
- Timestamp:
- 2015-12-13T17:17:37+01:00 (8 years ago)
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trunk/src/org/openstreetmap/josm/data/projection/proj/TransverseMercator.java
r9073 r9112 2 2 package org.openstreetmap.josm.data.projection.proj; 3 3 4 import static java.lang.Math.cos;5 import static java.lang.Math.pow;6 import static java.lang.Math.sin;7 import static java.lang.Math.sqrt;8 import static java.lang.Math.tan;9 4 import static org.openstreetmap.josm.tools.I18n.tr; 10 5 … … 12 7 13 8 /** 14 * Transverse Mercator projection. 9 * Transverse Mercator Projection (EPSG code 9807). This 10 * is a cylindrical projection, in which the cylinder has been rotated 90°. 11 * Instead of being tangent to the equator (or to an other standard latitude), 12 * it is tangent to a central meridian. Deformation are more important as we 13 * are going futher from the central meridian. The Transverse Mercator 14 * projection is appropriate for region wich have a greater extent north-south 15 * than east-west. 16 * <p> 15 17 * 16 * @author Dirk Stöcker 17 * code based on JavaScript from Chuck Taylor 18 * The elliptical equations used here are series approximations, and their accuracy 19 * decreases as points move farther from the central meridian of the projection. 20 * The forward equations here are accurate to a less than a mm ±10 degrees from 21 * the central meridian, a few mm ±15 degrees from the 22 * central meridian and a few cm ±20 degrees from the central meridian. 23 * The spherical equations are not approximations and should always give the 24 * correct values. 25 * <p> 18 26 * 27 * There are a number of versions of the transverse mercator projection 28 * including the Universal (UTM) and Modified (MTM) Transverses Mercator 29 * projections. In these cases the earth is divided into zones. For the UTM 30 * the zones are 6 degrees wide, numbered from 1 to 60 proceeding east from 31 * 180 degrees longitude, and between lats 84 degrees North and 80 32 * degrees South. The central meridian is taken as the center of the zone 33 * and the latitude of origin is the equator. A scale factor of 0.9996 and 34 * false easting of 500000m is used for all zones and a false northing of 10000000m 35 * is used for zones in the southern hemisphere. 36 * <p> 37 * 38 * NOTE: formulas used below are not those of Snyder, but rather those 39 * from the {@code proj4} package of the USGS survey, which 40 * have been reproduced verbatim. USGS work is acknowledged here. 41 * <p> 42 * 43 * This class has been derived from the implementation of the Geotools project; 44 * git 8cbf52d, org.geotools.referencing.operation.projection.TransverseMercator 45 * at the time of migration. 46 * <p> 47 * 48 * <b>References:</b> 49 * <ul> 50 * <li> Proj-4.4.6 available at <A HREF="http://www.remotesensing.org/proj">www.remotesensing.org/proj</A><br> 51 * Relevent files are: {@code PJ_tmerc.c}, {@code pj_mlfn.c}, {@code pj_fwd.c} and {@code pj_inv.c}.</li> 52 * <li> John P. Snyder (Map Projections - A Working Manual, 53 * U.S. Geological Survey Professional Paper 1395, 1987).</li> 54 * <li> "Coordinate Conversions and Transformations including Formulas", 55 * EPSG Guidence Note Number 7, Version 19.</li> 56 * </ul> 57 * 58 * @see <A HREF="http://mathworld.wolfram.com/MercatorProjection.html">Transverse Mercator projection on MathWorld</A> 59 * @see <A HREF="http://www.remotesensing.org/geotiff/proj_list/transverse_mercator.html">"Transverse_Mercator" on RemoteSensing.org</A> 60 * 61 * @author André Gosselin 62 * @author Martin Desruisseaux (PMO, IRD) 63 * @author Rueben Schulz 19 64 */ 20 public class TransverseMercator implementsProj {65 public class TransverseMercator extends AbstractProj { 21 66 22 protected double a, b; 67 /** 68 * Contants used for the forward and inverse transform for the eliptical 69 * case of the Transverse Mercator. 70 */ 71 private static final double FC1= 1.00000000000000000000000, // 1/1 72 FC2= 0.50000000000000000000000, // 1/2 73 FC3= 0.16666666666666666666666, // 1/6 74 FC4= 0.08333333333333333333333, // 1/12 75 FC5= 0.05000000000000000000000, // 1/20 76 FC6= 0.03333333333333333333333, // 1/30 77 FC7= 0.02380952380952380952380, // 1/42 78 FC8= 0.01785714285714285714285; // 1/56 79 80 /** 81 * Maximum difference allowed when comparing real numbers. 82 */ 83 private static final double EPSILON = 1E-6; 84 85 /** 86 * A derived quantity of excentricity, computed by <code>e'² = (a²-b²)/b² = es/(1-es)</code> 87 * where <var>a</var> is the semi-major axis length and <var>b</bar> is the semi-minor axis 88 * length. 89 */ 90 private double eb2; 91 92 /** 93 * Latitude of origin in <u>radians</u>. Default value is 0, the equator. 94 * This is called '<var>phi0</var>' in Snyder. 95 * <p> 96 * <strong>Consider this field as final</strong>. It is not final only 97 * because some classes need to modify it at construction time. 98 */ 99 protected double latitudeOfOrigin; 100 101 /** 102 * Meridian distance at the {@code latitudeOfOrigin}. 103 * Used for calculations for the ellipsoid. 104 */ 105 private double ml0; 23 106 24 107 @Override … … 34 117 @Override 35 118 public void initialize(ProjParameters params) throws ProjectionConfigurationException { 36 this.a = params.ellps.a; 37 this.b = params.ellps.b; 119 super.initialize(params); 120 eb2 = params.ellps.eb2; 121 latitudeOfOrigin = params.lat0 == null ? 0 : Math.toRadians(params.lat0); 122 ml0 = mlfn(latitudeOfOrigin, Math.sin(latitudeOfOrigin), Math.cos(latitudeOfOrigin)); 38 123 } 39 124 40 /**41 * Converts a latitude/longitude pair to x and y coordinates in the42 * Transverse Mercator projection. Note that Transverse Mercator is not43 * the same as UTM; a scale factor is required to convert between them.44 *45 * Reference: Hoffmann-Wellenhof, B., Lichtenegger, H., and Collins, J.,46 * GPS: Theory and Practice, 3rd ed. New York: Springer-Verlag Wien, 1994.47 *48 * @param phi Latitude of the point, in radians49 * @param lambda Longitude of the point, in radians50 * @return A 2-element array containing the x and y coordinates51 * of the computed point52 */53 125 @Override 54 public double[] project(double phi, double lambda) { 126 public double[] project(double y, double x) { 127 double sinphi = Math.sin(y); 128 double cosphi = Math.cos(y); 55 129 56 /* Precalculate ep2 */ 57 double ep2 = (pow(a, 2.0) - pow(b, 2.0)) / pow(b, 2.0); 130 double t = (Math.abs(cosphi) > EPSILON) ? sinphi/cosphi : 0; 131 t *= t; 132 double al = cosphi*x; 133 double als = al*al; 134 al /= Math.sqrt(1.0 - e2 * sinphi*sinphi); 135 double n = eb2 * cosphi*cosphi; 58 136 59 /* Precalculate nu2 */ 60 double nu2 = ep2 * pow(cos(phi), 2.0); 137 /* NOTE: meridinal distance at latitudeOfOrigin is always 0 */ 138 y = (mlfn(y, sinphi, cosphi) - ml0 + 139 sinphi * al * x * 140 FC2 * ( 1.0 + 141 FC4 * als * (5.0 - t + n*(9.0 + 4.0*n) + 142 FC6 * als * (61.0 + t * (t - 58.0) + n*(270.0 - 330.0*t) + 143 FC8 * als * (1385.0 + t * ( t*(543.0 - t) - 3111.0)))))); 61 144 62 /* Precalculate N / a */ 63 double N_a = a / (b * sqrt(1 + nu2)); 145 x = al*(FC1 + FC3 * als*(1.0 - t + n + 146 FC5 * als * (5.0 + t*(t - 18.0) + n*(14.0 - 58.0*t) + 147 FC7 * als * (61.0+ t*(t*(179.0 - t) - 479.0 ))))); 64 148 65 /* Precalculate t */ 66 double t = tan(phi); 67 double t2 = t * t; 68 69 /* Precalculate l */ 70 double l = lambda; 71 72 /* Precalculate coefficients for l**n in the equations below 73 so a normal human being can read the expressions for easting 74 and northing 75 -- l**1 and l**2 have coefficients of 1.0 */ 76 double l3coef = 1.0 - t2 + nu2; 77 78 double l4coef = 5.0 - t2 + 9 * nu2 + 4.0 * (nu2 * nu2); 79 80 double l5coef = 5.0 - 18.0 * t2 + (t2 * t2) + 14.0 * nu2 81 - 58.0 * t2 * nu2; 82 83 double l6coef = 61.0 - 58.0 * t2 + (t2 * t2) + 270.0 * nu2 84 - 330.0 * t2 * nu2; 85 86 double l7coef = 61.0 - 479.0 * t2 + 179.0 * (t2 * t2) - (t2 * t2 * t2); 87 88 double l8coef = 1385.0 - 3111.0 * t2 + 543.0 * (t2 * t2) - (t2 * t2 * t2); 89 90 return new double[] { 91 /* Calculate easting (x) */ 92 N_a * cos(phi) * l 93 + (N_a / 6.0 * pow(cos(phi), 3.0) * l3coef * pow(l, 3.0)) 94 + (N_a / 120.0 * pow(cos(phi), 5.0) * l5coef * pow(l, 5.0)) 95 + (N_a / 5040.0 * pow(cos(phi), 7.0) * l7coef * pow(l, 7.0)), 96 /* Calculate northing (y) */ 97 ArcLengthOfMeridian(phi) / a 98 + (t / 2.0 * N_a * pow(cos(phi), 2.0) * pow(l, 2.0)) 99 + (t / 24.0 * N_a * pow(cos(phi), 4.0) * l4coef * pow(l, 4.0)) 100 + (t / 720.0 * N_a * pow(cos(phi), 6.0) * l6coef * pow(l, 6.0)) 101 + (t / 40320.0 * N_a * pow(cos(phi), 8.0) * l8coef * pow(l, 8.0)) }; 149 return new double[] { x, y }; 102 150 } 103 151 104 /**105 * Converts x and y coordinates in the Transverse Mercator projection to106 * a latitude/longitude pair. Note that Transverse Mercator is not107 * the same as UTM; a scale factor is required to convert between them.108 *109 * Reference: Hoffmann-Wellenhof, B., Lichtenegger, H., and Collins, J.,110 * GPS: Theory and Practice, 3rd ed. New York: Springer-Verlag Wien, 1994.111 *112 * Remarks:113 * The local variables Nf, nuf2, tf, and tf2 serve the same purpose as114 * N, nu2, t, and t2 in MapLatLonToXY, but they are computed with respect115 * to the footpoint latitude phif.116 *117 * x1frac, x2frac, x2poly, x3poly, etc. are to enhance readability and118 * to optimize computations.119 *120 * @param x The easting of the point, in meters, divided by the semi major axis of the ellipsoid121 * @param y The northing of the point, in meters, divided by the semi major axis of the ellipsoid122 * @return A 2-element containing the latitude and longitude123 * in radians124 */125 152 @Override 126 153 public double[] invproject(double x, double y) { 127 /* Get the value of phif, the footpoint latitude. */ 128 double phif = footpointLatitude(y); 154 double phi = inv_mlfn(ml0 + y); 129 155 130 /* Precalculate ep2 */ 131 double ep2 = (a*a - b*b) 132 / (b*b); 156 if (Math.abs(phi) >= Math.PI/2) { 157 y = y<0.0 ? -(Math.PI/2) : (Math.PI/2); 158 x = 0.0; 159 } else { 160 double sinphi = Math.sin(phi); 161 double cosphi = Math.cos(phi); 162 double t = (Math.abs(cosphi) > EPSILON) ? sinphi/cosphi : 0.0; 163 double n = eb2 * cosphi*cosphi; 164 double con = 1.0 - e2 * sinphi*sinphi; 165 double d = x * Math.sqrt(con); 166 con *= t; 167 t *= t; 168 double ds = d*d; 133 169 134 /* Precalculate cos(phif) */ 135 double cf = cos(phif); 170 y = phi - (con*ds / (1.0 - e2)) * 171 FC2 * (1.0 - ds * 172 FC4 * (5.0 + t*(3.0 - 9.0*n) + n*(1.0 - 4*n) - ds * 173 FC6 * (61.0 + t*(90.0 - 252.0*n + 45.0*t) + 46.0*n - ds * 174 FC8 * (1385.0 + t*(3633.0 + t*(4095.0 + 1574.0*t)))))); 136 175 137 /* Precalculate nuf2 */ 138 double nuf2 = ep2 * pow(cf, 2.0); 139 140 /* Precalculate Nf / a and initialize Nfpow */ 141 double Nf_a = a / (b * sqrt(1 + nuf2)); 142 double Nfpow = Nf_a; 143 144 /* Precalculate tf */ 145 double tf = tan(phif); 146 double tf2 = tf * tf; 147 double tf4 = tf2 * tf2; 148 149 /* Precalculate fractional coefficients for x**n in the equations 150 below to simplify the expressions for latitude and longitude. */ 151 double x1frac = 1.0 / (Nfpow * cf); 152 153 Nfpow *= Nf_a; /* now equals Nf**2) */ 154 double x2frac = tf / (2.0 * Nfpow); 155 156 Nfpow *= Nf_a; /* now equals Nf**3) */ 157 double x3frac = 1.0 / (6.0 * Nfpow * cf); 158 159 Nfpow *= Nf_a; /* now equals Nf**4) */ 160 double x4frac = tf / (24.0 * Nfpow); 161 162 Nfpow *= Nf_a; /* now equals Nf**5) */ 163 double x5frac = 1.0 / (120.0 * Nfpow * cf); 164 165 Nfpow *= Nf_a; /* now equals Nf**6) */ 166 double x6frac = tf / (720.0 * Nfpow); 167 168 Nfpow *= Nf_a; /* now equals Nf**7) */ 169 double x7frac = 1.0 / (5040.0 * Nfpow * cf); 170 171 Nfpow *= Nf_a; /* now equals Nf**8) */ 172 double x8frac = tf / (40320.0 * Nfpow); 173 174 /* Precalculate polynomial coefficients for x**n. 175 -- x**1 does not have a polynomial coefficient. */ 176 double x2poly = -1.0 - nuf2; 177 double x3poly = -1.0 - 2 * tf2 - nuf2; 178 double x4poly = 5.0 + 3.0 * tf2 + 6.0 * nuf2 - 6.0 * tf2 * nuf2 - 3.0 * (nuf2 *nuf2) - 9.0 * tf2 * (nuf2 * nuf2); 179 double x5poly = 5.0 + 28.0 * tf2 + 24.0 * tf4 + 6.0 * nuf2 + 8.0 * tf2 * nuf2; 180 double x6poly = -61.0 - 90.0 * tf2 - 45.0 * tf4 - 107.0 * nuf2 + 162.0 * tf2 * nuf2; 181 double x7poly = -61.0 - 662.0 * tf2 - 1320.0 * tf4 - 720.0 * (tf4 * tf2); 182 double x8poly = 1385.0 + 3633.0 * tf2 + 4095.0 * tf4 + 1575 * (tf4 * tf2); 183 184 return new double[] { 185 /* Calculate latitude */ 186 phif + x2frac * x2poly * (x * x) 187 + x4frac * x4poly * pow(x, 4.0) 188 + x6frac * x6poly * pow(x, 6.0) 189 + x8frac * x8poly * pow(x, 8.0), 190 /* Calculate longitude */ 191 x1frac * x 192 + x3frac * x3poly * pow(x, 3.0) 193 + x5frac * x5poly * pow(x, 5.0) 194 + x7frac * x7poly * pow(x, 7.0) }; 195 } 196 197 /** 198 * ArcLengthOfMeridian 199 * 200 * Computes the ellipsoidal distance from the equator to a point at a 201 * given latitude. 202 * 203 * Reference: Hoffmann-Wellenhof, B., Lichtenegger, H., and Collins, J., 204 * GPS: Theory and Practice, 3rd ed. New York: Springer-Verlag Wien, 1994. 205 * 206 * @param phi Latitude of the point, in radians 207 * @return The ellipsoidal distance of the point from the equator 208 * (in meters, divided by the semi major axis of the ellipsoid) 209 */ 210 private double ArcLengthOfMeridian(double phi) { 211 /* Precalculate n */ 212 double n = (a - b) / (a + b); 213 214 /* Precalculate alpha */ 215 double alpha = ((a + b) / 2.0) 216 * (1.0 + (pow(n, 2.0) / 4.0) + (pow(n, 4.0) / 64.0)); 217 218 /* Precalculate beta */ 219 double beta = (-3.0 * n / 2.0) + (9.0 * pow(n, 3.0) / 16.0) 220 + (-3.0 * pow(n, 5.0) / 32.0); 221 222 /* Precalculate gamma */ 223 double gamma = (15.0 * pow(n, 2.0) / 16.0) 224 + (-15.0 * pow(n, 4.0) / 32.0); 225 226 /* Precalculate delta */ 227 double delta = (-35.0 * pow(n, 3.0) / 48.0) 228 + (105.0 * pow(n, 5.0) / 256.0); 229 230 /* Precalculate epsilon */ 231 double epsilon = 315.0 * pow(n, 4.0) / 512.0; 232 233 /* Now calculate the sum of the series and return */ 234 return alpha 235 * (phi + (beta * sin(2.0 * phi)) 236 + (gamma * sin(4.0 * phi)) 237 + (delta * sin(6.0 * phi)) 238 + (epsilon * sin(8.0 * phi))); 239 } 240 241 /** 242 * FootpointLatitude 243 * 244 * Computes the footpoint latitude for use in converting transverse 245 * Mercator coordinates to ellipsoidal coordinates. 246 * 247 * Reference: Hoffmann-Wellenhof, B., Lichtenegger, H., and Collins, J., 248 * GPS: Theory and Practice, 3rd ed. New York: Springer-Verlag Wien, 1994. 249 * 250 * @param y northing coordinate, in meters, divided by the semi major axis of the ellipsoid 251 * @return The footpoint latitude, in radians 252 */ 253 private double footpointLatitude(double y) { 254 /* Precalculate n (Eq. 10.18) */ 255 double n = (a - b) / (a + b); 256 257 /* Precalculate alpha_ (Eq. 10.22) */ 258 /* (Same as alpha in Eq. 10.17) */ 259 double alpha_ = ((a + b) / 2.0) 260 * (1 + (pow(n, 2.0) / 4) + (pow(n, 4.0) / 64)); 261 262 /* Precalculate y_ (Eq. 10.23) */ 263 double y_ = y / alpha_ * a; 264 265 /* Precalculate beta_ (Eq. 10.22) */ 266 double beta_ = (3.0 * n / 2.0) + (-27.0 * pow(n, 3.0) / 32.0) 267 + (269.0 * pow(n, 5.0) / 512.0); 268 269 /* Precalculate gamma_ (Eq. 10.22) */ 270 double gamma_ = (21.0 * pow(n, 2.0) / 16.0) 271 + (-55.0 * pow(n, 4.0) / 32.0); 272 273 /* Precalculate delta_ (Eq. 10.22) */ 274 double delta_ = (151.0 * pow(n, 3.0) / 96.0) 275 + (-417.0 * pow(n, 5.0) / 128.0); 276 277 /* Precalculate epsilon_ (Eq. 10.22) */ 278 double epsilon_ = 1097.0 * pow(n, 4.0) / 512.0; 279 280 /* Now calculate the sum of the series (Eq. 10.21) */ 281 return y_ + (beta_ * sin(2.0 * y_)) 282 + (gamma_ * sin(4.0 * y_)) 283 + (delta_ * sin(6.0 * y_)) 284 + (epsilon_ * sin(8.0 * y_)); 176 x = d*(FC1 - ds * FC3 * (1.0 + 2.0*t + n - 177 ds*FC5*(5.0 + t*(28.0 + 24* t + 8.0*n) + 6.0*n - 178 ds*FC7*(61.0 + t*(662.0 + t*(1320.0 + 720.0*t))))))/cosphi; 179 } 180 return new double[] { y, x }; 285 181 } 286 182 }
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