* * 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.
*/
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 : Utils.toRadians(params.lat0);
ml0 = mlfn(latitudeOfOrigin, Math.sin(latitudeOfOrigin), Math.cos(latitudeOfOrigin));
if (params.gamma != null) {
rectifiedGridAngle = Utils.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 + 1575.0*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);
}
/**
* Determines the UTM zone of a given lat/lon.
* @param ll lat/lon to locate in the UTM grid.
* @return the UTM zone of {@code ll}
* @since 13167
*/
public static Pair