* * The elliptical equations used here are series approximations, and their accuracy * decreases as points move farther from the central meridian of the projection. * The forward equations here are accurate to a less than a mm ±10 degrees from * the central meridian, a few mm ±15 degrees from the * central meridian and a few cm ±20 degrees from the central meridian. * The spherical equations are not approximations and should always give the * correct values. *
* * There are a number of versions of the transverse mercator projection * including the Universal (UTM) and Modified (MTM) Transverses Mercator * projections. In these cases the earth is divided into zones. For the UTM * the zones are 6 degrees wide, numbered from 1 to 60 proceeding east from * 180 degrees longitude, and between lats 84 degrees North and 80 * degrees South. The central meridian is taken as the center of the zone * and the latitude of origin is the equator. A scale factor of 0.9996 and * false easting of 500000m is used for all zones and a false northing of 10000000m * is used for zones in the southern hemisphere. *
* * NOTE: formulas used below are not those of Snyder, but rather those * from the {@code proj4} package of the USGS survey, which * have been reproduced verbatim. USGS work is acknowledged here. *
* * This class has been derived from the implementation of the Geotools project; * git 8cbf52d, org.geotools.referencing.operation.projection.TransverseMercator * at the time of migration. *
* The non-standard parameter gamma has been added as a method
* to rotate the projected coordinates by a certain angle (clockwise, see
* {@link ObliqueMercator}).
*
* References: *
e'² = (a²-b²)/b² = es/(1-es)
* where a is the semi-major axis length and b is the semi-minor axis
* length.
*/
private double eb2;
/**
* Latitude of origin in radians. Default value is 0, the equator.
* This is called 'phi0' in Snyder.
* * Consider this field as final. It is not final only * because some classes need to modify it at construction time. */ protected double latitudeOfOrigin; /** * Meridian distance at the {@code latitudeOfOrigin}. * Used for calculations for the ellipsoid. */ private double ml0; /** * The rectified bearing of the central line, in radians. */ protected double rectifiedGridAngle; /** * Sine and Cosine values for the coordinate system rotation angle */ private double sinrot, cosrot; @Override public String getName() { return tr("Transverse Mercator"); } @Override public String getProj4Id() { return "tmerc"; } @Override public void initialize(ProjParameters params) throws ProjectionConfigurationException { super.initialize(params); CheckParameterUtil.ensureParameterNotNull(params, "params"); CheckParameterUtil.ensureParameterNotNull(params.ellps, "params.ellps"); eb2 = params.ellps.eb2; latitudeOfOrigin = params.lat0 == null ? 0 : Math.toRadians(params.lat0); ml0 = mlfn(latitudeOfOrigin, Math.sin(latitudeOfOrigin), Math.cos(latitudeOfOrigin)); if (params.gamma != null) { rectifiedGridAngle = Math.toRadians(params.gamma); } else { rectifiedGridAngle = 0.0; } sinrot = Math.sin(rectifiedGridAngle); cosrot = Math.cos(rectifiedGridAngle); } @Override public double[] project(double y, double x) { double sinphi = Math.sin(y); double cosphi = Math.cos(y); double u, v; double t = (Math.abs(cosphi) > EPSILON) ? sinphi/cosphi : 0; t *= t; double al = cosphi*x; double als = al*al; al /= Math.sqrt(1.0 - e2 * sinphi*sinphi); double n = eb2 * cosphi*cosphi; /* NOTE: meridinal distance at latitudeOfOrigin is always 0 */ y = mlfn(y, sinphi, cosphi) - ml0 + sinphi * al * x * FC2 * (1.0 + FC4 * als * (5.0 - t + n*(9.0 + 4.0*n) + FC6 * als * (61.0 + t * (t - 58.0) + n*(270.0 - 330.0*t) + FC8 * als * (1385.0 + t * (t*(543.0 - t) - 3111.0))))); x = al*(FC1 + FC3 * als*(1.0 - t + n + FC5 * als * (5.0 + t*(t - 18.0) + n*(14.0 - 58.0*t) + FC7 * als * (61.0+ t*(t*(179.0 - t) - 479.0))))); u = y; v = x; x = v * cosrot + u * sinrot; y = u * cosrot - v * sinrot; return new double[] {x, y}; } @Override public double[] invproject(double x, double y) { double v = x * cosrot - y * sinrot; double u = y * cosrot + x * sinrot; x = v; y = u; double phi = invMlfn(ml0 + y); if (Math.abs(phi) >= Math.PI/2) { y = y < 0.0 ? -(Math.PI/2) : (Math.PI/2); x = 0.0; } else { double sinphi = Math.sin(phi); double cosphi = Math.cos(phi); double t = (Math.abs(cosphi) > EPSILON) ? sinphi/cosphi : 0.0; double n = eb2 * cosphi*cosphi; double con = 1.0 - e2 * sinphi*sinphi; double d = x * Math.sqrt(con); con *= t; t *= t; double ds = d*d; y = phi - (con*ds / (1.0 - e2)) * FC2 * (1.0 - ds * FC4 * (5.0 + t*(3.0 - 9.0*n) + n*(1.0 - 4*n) - ds * FC6 * (61.0 + t*(90.0 - 252.0*n + 45.0*t) + 46.0*n - ds * FC8 * (1385.0 + t*(3633.0 + t*(4095.0 + 1574.0*t)))))); x = d*(FC1 - ds * FC3 * (1.0 + 2.0*t + n - ds*FC5*(5.0 + t*(28.0 + 24* t + 8.0*n) + 6.0*n - ds*FC7*(61.0 + t*(662.0 + t*(1320.0 + 720.0*t))))))/cosphi; } return new double[] {y, x}; } @Override public Bounds getAlgorithmBounds() { return new Bounds(-89, -7, 89, 7, false); } }