001// License: GPL. For details, see LICENSE file. 002package org.openstreetmap.josm.data.projection.proj; 003 004import static org.openstreetmap.josm.tools.I18n.tr; 005 006import org.openstreetmap.josm.data.Bounds; 007import org.openstreetmap.josm.data.projection.ProjectionConfigurationException; 008 009/** 010 * Transverse Mercator Projection (EPSG code 9807). This 011 * is a cylindrical projection, in which the cylinder has been rotated 90°. 012 * Instead of being tangent to the equator (or to an other standard latitude), 013 * it is tangent to a central meridian. Deformation are more important as we 014 * are going futher from the central meridian. The Transverse Mercator 015 * projection is appropriate for region wich have a greater extent north-south 016 * than east-west. 017 * <p> 018 * 019 * The elliptical equations used here are series approximations, and their accuracy 020 * decreases as points move farther from the central meridian of the projection. 021 * The forward equations here are accurate to a less than a mm ±10 degrees from 022 * the central meridian, a few mm ±15 degrees from the 023 * central meridian and a few cm ±20 degrees from the central meridian. 024 * The spherical equations are not approximations and should always give the 025 * correct values. 026 * <p> 027 * 028 * There are a number of versions of the transverse mercator projection 029 * including the Universal (UTM) and Modified (MTM) Transverses Mercator 030 * projections. In these cases the earth is divided into zones. For the UTM 031 * the zones are 6 degrees wide, numbered from 1 to 60 proceeding east from 032 * 180 degrees longitude, and between lats 84 degrees North and 80 033 * degrees South. The central meridian is taken as the center of the zone 034 * and the latitude of origin is the equator. A scale factor of 0.9996 and 035 * false easting of 500000m is used for all zones and a false northing of 10000000m 036 * is used for zones in the southern hemisphere. 037 * <p> 038 * 039 * NOTE: formulas used below are not those of Snyder, but rather those 040 * from the {@code proj4} package of the USGS survey, which 041 * have been reproduced verbatim. USGS work is acknowledged here. 042 * <p> 043 * 044 * This class has been derived from the implementation of the Geotools project; 045 * git 8cbf52d, org.geotools.referencing.operation.projection.TransverseMercator 046 * at the time of migration. 047 * <p> 048 * 049 * <b>References:</b> 050 * <ul> 051 * <li> Proj-4.4.6 available at <A HREF="http://www.remotesensing.org/proj">www.remotesensing.org/proj</A><br> 052 * Relevent files are: {@code PJ_tmerc.c}, {@code pj_mlfn.c}, {@code pj_fwd.c} and {@code pj_inv.c}.</li> 053 * <li> John P. Snyder (Map Projections - A Working Manual, 054 * U.S. Geological Survey Professional Paper 1395, 1987).</li> 055 * <li> "Coordinate Conversions and Transformations including Formulas", 056 * EPSG Guidence Note Number 7, Version 19.</li> 057 * </ul> 058 * 059 * @author André Gosselin 060 * @author Martin Desruisseaux (PMO, IRD) 061 * @author Rueben Schulz 062 * 063 * @see <A HREF="http://mathworld.wolfram.com/MercatorProjection.html">Transverse Mercator projection on MathWorld</A> 064 * @see <A HREF="http://www.remotesensing.org/geotiff/proj_list/transverse_mercator.html">"Transverse_Mercator" on RemoteSensing.org</A> 065 */ 066public class TransverseMercator extends AbstractProj { 067 068 /** 069 * Contants used for the forward and inverse transform for the eliptical 070 * case of the Transverse Mercator. 071 */ 072 private static final double FC1 = 1.00000000000000000000000, // 1/1 073 FC2 = 0.50000000000000000000000, // 1/2 074 FC3 = 0.16666666666666666666666, // 1/6 075 FC4 = 0.08333333333333333333333, // 1/12 076 FC5 = 0.05000000000000000000000, // 1/20 077 FC6 = 0.03333333333333333333333, // 1/30 078 FC7 = 0.02380952380952380952380, // 1/42 079 FC8 = 0.01785714285714285714285; // 1/56 080 081 /** 082 * Maximum difference allowed when comparing real numbers. 083 */ 084 private static final double EPSILON = 1E-6; 085 086 /** 087 * A derived quantity of excentricity, computed by <code>e'² = (a²-b²)/b² = es/(1-es)</code> 088 * where <var>a</var> is the semi-major axis length and <var>b</var> is the semi-minor axis 089 * length. 090 */ 091 private double eb2; 092 093 /** 094 * Latitude of origin in <u>radians</u>. Default value is 0, the equator. 095 * This is called '<var>phi0</var>' in Snyder. 096 * <p> 097 * <strong>Consider this field as final</strong>. It is not final only 098 * because some classes need to modify it at construction time. 099 */ 100 protected double latitudeOfOrigin; 101 102 /** 103 * Meridian distance at the {@code latitudeOfOrigin}. 104 * Used for calculations for the ellipsoid. 105 */ 106 private double ml0; 107 108 @Override 109 public String getName() { 110 return tr("Transverse Mercator"); 111 } 112 113 @Override 114 public String getProj4Id() { 115 return "tmerc"; 116 } 117 118 @Override 119 public void initialize(ProjParameters params) throws ProjectionConfigurationException { 120 super.initialize(params); 121 eb2 = params.ellps.eb2; 122 latitudeOfOrigin = params.lat0 == null ? 0 : Math.toRadians(params.lat0); 123 ml0 = mlfn(latitudeOfOrigin, Math.sin(latitudeOfOrigin), Math.cos(latitudeOfOrigin)); 124 } 125 126 @Override 127 public double[] project(double y, double x) { 128 double sinphi = Math.sin(y); 129 double cosphi = Math.cos(y); 130 131 double t = (Math.abs(cosphi) > EPSILON) ? sinphi/cosphi : 0; 132 t *= t; 133 double al = cosphi*x; 134 double als = al*al; 135 al /= Math.sqrt(1.0 - e2 * sinphi*sinphi); 136 double n = eb2 * cosphi*cosphi; 137 138 /* NOTE: meridinal distance at latitudeOfOrigin is always 0 */ 139 y = mlfn(y, sinphi, cosphi) - ml0 + 140 sinphi * al * x * 141 FC2 * (1.0 + 142 FC4 * als * (5.0 - t + n*(9.0 + 4.0*n) + 143 FC6 * als * (61.0 + t * (t - 58.0) + n*(270.0 - 330.0*t) + 144 FC8 * als * (1385.0 + t * (t*(543.0 - t) - 3111.0))))); 145 146 x = al*(FC1 + FC3 * als*(1.0 - t + n + 147 FC5 * als * (5.0 + t*(t - 18.0) + n*(14.0 - 58.0*t) + 148 FC7 * als * (61.0+ t*(t*(179.0 - t) - 479.0))))); 149 150 return new double[] {x, y}; 151 } 152 153 @Override 154 public double[] invproject(double x, double y) { 155 double phi = inv_mlfn(ml0 + y); 156 157 if (Math.abs(phi) >= Math.PI/2) { 158 y = y < 0.0 ? -(Math.PI/2) : (Math.PI/2); 159 x = 0.0; 160 } else { 161 double sinphi = Math.sin(phi); 162 double cosphi = Math.cos(phi); 163 double t = (Math.abs(cosphi) > EPSILON) ? sinphi/cosphi : 0.0; 164 double n = eb2 * cosphi*cosphi; 165 double con = 1.0 - e2 * sinphi*sinphi; 166 double d = x * Math.sqrt(con); 167 con *= t; 168 t *= t; 169 double ds = d*d; 170 171 y = phi - (con*ds / (1.0 - e2)) * 172 FC2 * (1.0 - ds * 173 FC4 * (5.0 + t*(3.0 - 9.0*n) + n*(1.0 - 4*n) - ds * 174 FC6 * (61.0 + t*(90.0 - 252.0*n + 45.0*t) + 46.0*n - ds * 175 FC8 * (1385.0 + t*(3633.0 + t*(4095.0 + 1574.0*t)))))); 176 177 x = d*(FC1 - ds * FC3 * (1.0 + 2.0*t + n - 178 ds*FC5*(5.0 + t*(28.0 + 24* t + 8.0*n) + 6.0*n - 179 ds*FC7*(61.0 + t*(662.0 + t*(1320.0 + 720.0*t))))))/cosphi; 180 } 181 return new double[] {y, x}; 182 } 183 184 @Override 185 public Bounds getAlgorithmBounds() { 186 return new Bounds(-89, -7, 89, 7, false); 187 } 188}