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; 008import org.openstreetmap.josm.tools.CheckParameterUtil; 009 010/** 011 * Transverse Mercator Projection (EPSG code 9807). This 012 * is a cylindrical projection, in which the cylinder has been rotated 90°. 013 * Instead of being tangent to the equator (or to an other standard latitude), 014 * it is tangent to a central meridian. Deformation are more important as we 015 * are going futher from the central meridian. The Transverse Mercator 016 * projection is appropriate for region wich have a greater extent north-south 017 * than east-west. 018 * <p> 019 * 020 * The elliptical equations used here are series approximations, and their accuracy 021 * decreases as points move farther from the central meridian of the projection. 022 * The forward equations here are accurate to a less than a mm ±10 degrees from 023 * the central meridian, a few mm ±15 degrees from the 024 * central meridian and a few cm ±20 degrees from the central meridian. 025 * The spherical equations are not approximations and should always give the 026 * correct values. 027 * <p> 028 * 029 * There are a number of versions of the transverse mercator projection 030 * including the Universal (UTM) and Modified (MTM) Transverses Mercator 031 * projections. In these cases the earth is divided into zones. For the UTM 032 * the zones are 6 degrees wide, numbered from 1 to 60 proceeding east from 033 * 180 degrees longitude, and between lats 84 degrees North and 80 034 * degrees South. The central meridian is taken as the center of the zone 035 * and the latitude of origin is the equator. A scale factor of 0.9996 and 036 * false easting of 500000m is used for all zones and a false northing of 10000000m 037 * is used for zones in the southern hemisphere. 038 * <p> 039 * 040 * NOTE: formulas used below are not those of Snyder, but rather those 041 * from the {@code proj4} package of the USGS survey, which 042 * have been reproduced verbatim. USGS work is acknowledged here. 043 * <p> 044 * 045 * This class has been derived from the implementation of the Geotools project; 046 * git 8cbf52d, org.geotools.referencing.operation.projection.TransverseMercator 047 * at the time of migration. 048 * <p> 049 * 050 * <b>References:</b> 051 * <ul> 052 * <li> Proj-4.4.6 available at <A HREF="http://www.remotesensing.org/proj">www.remotesensing.org/proj</A><br> 053 * Relevent files are: {@code PJ_tmerc.c}, {@code pj_mlfn.c}, {@code pj_fwd.c} and {@code pj_inv.c}.</li> 054 * <li> John P. Snyder (Map Projections - A Working Manual, 055 * U.S. Geological Survey Professional Paper 1395, 1987).</li> 056 * <li> "Coordinate Conversions and Transformations including Formulas", 057 * EPSG Guidence Note Number 7, Version 19.</li> 058 * </ul> 059 * 060 * @author André Gosselin 061 * @author Martin Desruisseaux (PMO, IRD) 062 * @author Rueben Schulz 063 * 064 * @see <A HREF="http://mathworld.wolfram.com/MercatorProjection.html">Transverse Mercator projection on MathWorld</A> 065 * @see <A HREF="http://www.remotesensing.org/geotiff/proj_list/transverse_mercator.html">"Transverse_Mercator" on RemoteSensing.org</A> 066 */ 067public class TransverseMercator extends AbstractProj { 068 069 /** 070 * Contants used for the forward and inverse transform for the eliptical 071 * case of the Transverse Mercator. 072 */ 073 private static final double FC1 = 1.00000000000000000000000, // 1/1 074 FC2 = 0.50000000000000000000000, // 1/2 075 FC3 = 0.16666666666666666666666, // 1/6 076 FC4 = 0.08333333333333333333333, // 1/12 077 FC5 = 0.05000000000000000000000, // 1/20 078 FC6 = 0.03333333333333333333333, // 1/30 079 FC7 = 0.02380952380952380952380, // 1/42 080 FC8 = 0.01785714285714285714285; // 1/56 081 082 /** 083 * Maximum difference allowed when comparing real numbers. 084 */ 085 private static final double EPSILON = 1E-6; 086 087 /** 088 * A derived quantity of excentricity, computed by <code>e'² = (a²-b²)/b² = es/(1-es)</code> 089 * where <var>a</var> is the semi-major axis length and <var>b</var> is the semi-minor axis 090 * length. 091 */ 092 private double eb2; 093 094 /** 095 * Latitude of origin in <u>radians</u>. Default value is 0, the equator. 096 * This is called '<var>phi0</var>' in Snyder. 097 * <p> 098 * <strong>Consider this field as final</strong>. It is not final only 099 * because some classes need to modify it at construction time. 100 */ 101 protected double latitudeOfOrigin; 102 103 /** 104 * Meridian distance at the {@code latitudeOfOrigin}. 105 * Used for calculations for the ellipsoid. 106 */ 107 private double ml0; 108 109 @Override 110 public String getName() { 111 return tr("Transverse Mercator"); 112 } 113 114 @Override 115 public String getProj4Id() { 116 return "tmerc"; 117 } 118 119 @Override 120 public void initialize(ProjParameters params) throws ProjectionConfigurationException { 121 super.initialize(params); 122 CheckParameterUtil.ensureParameterNotNull(params, "params"); 123 CheckParameterUtil.ensureParameterNotNull(params.ellps, "params.ellps"); 124 eb2 = params.ellps.eb2; 125 latitudeOfOrigin = params.lat0 == null ? 0 : Math.toRadians(params.lat0); 126 ml0 = mlfn(latitudeOfOrigin, Math.sin(latitudeOfOrigin), Math.cos(latitudeOfOrigin)); 127 } 128 129 @Override 130 public double[] project(double y, double x) { 131 double sinphi = Math.sin(y); 132 double cosphi = Math.cos(y); 133 134 double t = (Math.abs(cosphi) > EPSILON) ? sinphi/cosphi : 0; 135 t *= t; 136 double al = cosphi*x; 137 double als = al*al; 138 al /= Math.sqrt(1.0 - e2 * sinphi*sinphi); 139 double n = eb2 * cosphi*cosphi; 140 141 /* NOTE: meridinal distance at latitudeOfOrigin is always 0 */ 142 y = mlfn(y, sinphi, cosphi) - ml0 + 143 sinphi * al * x * 144 FC2 * (1.0 + 145 FC4 * als * (5.0 - t + n*(9.0 + 4.0*n) + 146 FC6 * als * (61.0 + t * (t - 58.0) + n*(270.0 - 330.0*t) + 147 FC8 * als * (1385.0 + t * (t*(543.0 - t) - 3111.0))))); 148 149 x = al*(FC1 + FC3 * als*(1.0 - t + n + 150 FC5 * als * (5.0 + t*(t - 18.0) + n*(14.0 - 58.0*t) + 151 FC7 * als * (61.0+ t*(t*(179.0 - t) - 479.0))))); 152 153 return new double[] {x, y}; 154 } 155 156 @Override 157 public double[] invproject(double x, double y) { 158 double phi = inv_mlfn(ml0 + y); 159 160 if (Math.abs(phi) >= Math.PI/2) { 161 y = y < 0.0 ? -(Math.PI/2) : (Math.PI/2); 162 x = 0.0; 163 } else { 164 double sinphi = Math.sin(phi); 165 double cosphi = Math.cos(phi); 166 double t = (Math.abs(cosphi) > EPSILON) ? sinphi/cosphi : 0.0; 167 double n = eb2 * cosphi*cosphi; 168 double con = 1.0 - e2 * sinphi*sinphi; 169 double d = x * Math.sqrt(con); 170 con *= t; 171 t *= t; 172 double ds = d*d; 173 174 y = phi - (con*ds / (1.0 - e2)) * 175 FC2 * (1.0 - ds * 176 FC4 * (5.0 + t*(3.0 - 9.0*n) + n*(1.0 - 4*n) - ds * 177 FC6 * (61.0 + t*(90.0 - 252.0*n + 45.0*t) + 46.0*n - ds * 178 FC8 * (1385.0 + t*(3633.0 + t*(4095.0 + 1574.0*t)))))); 179 180 x = d*(FC1 - ds * FC3 * (1.0 + 2.0*t + n - 181 ds*FC5*(5.0 + t*(28.0 + 24* t + 8.0*n) + 6.0*n - 182 ds*FC7*(61.0 + t*(662.0 + t*(1320.0 + 720.0*t))))))/cosphi; 183 } 184 return new double[] {y, x}; 185 } 186 187 @Override 188 public Bounds getAlgorithmBounds() { 189 return new Bounds(-89, -7, 89, 7, false); 190 } 191}