// License: GPL. Copyright 2007 by Immanuel Scholz and others
package es.emergya.geo.util;
import static org.openstreetmap.josm.tools.I18n.tr;
import org.openstreetmap.josm.data.Bounds;
import org.openstreetmap.josm.data.coor.EastNorth;
import org.openstreetmap.josm.data.coor.LatLon;
/**
* Directly use latitude / longitude values as x/y.
*
* @author Dirk Stöcker
* code based on JavaScript from Chuck Taylor
*/
public class UTM implements Projection {
public UTM(int zone) {
super();
this.zone = zone;
}
public UTM() {
super();
}
final private double UTMScaleFactor = 0.9996;
private int zone = 30;
/*
* ArcLengthOfMeridian
*
* Computes the ellipsoidal distance from the equator to a point at a
* given latitude.
*
* Reference: Hoffmann-Wellenhof, B., Lichtenegger, H., and Collins, J.,
* GPS: Theory and Practice, 3rd ed. New York: Springer-Verlag Wien, 1994.
*
* Inputs:
* phi - Latitude of the point, in radians.
*
* Globals:
* Ellipsoid.GRS80.a - Ellipsoid model major axis.
* Ellipsoid.GRS80.b - Ellipsoid model minor axis.
*
* Returns:
* The ellipsoidal distance of the point from the equator, in meters.
*
*/
private double ArcLengthOfMeridian(double phi)
{
/* Precalculate n */
double n = (Ellipsoid.GRS80.a - Ellipsoid.GRS80.b) / (Ellipsoid.GRS80.a + Ellipsoid.GRS80.b);
/* Precalculate alpha */
double alpha = ((Ellipsoid.GRS80.a + Ellipsoid.GRS80.b) / 2.0)
* (1.0 + (Math.pow (n, 2.0) / 4.0) + (Math.pow (n, 4.0) / 64.0));
/* Precalculate beta */
double beta = (-3.0 * n / 2.0) + (9.0 * Math.pow (n, 3.0) / 16.0)
+ (-3.0 * Math.pow (n, 5.0) / 32.0);
/* Precalculate gamma */
double gamma = (15.0 * Math.pow (n, 2.0) / 16.0)
+ (-15.0 * Math.pow (n, 4.0) / 32.0);
/* Precalculate delta */
double delta = (-35.0 * Math.pow (n, 3.0) / 48.0)
+ (105.0 * Math.pow (n, 5.0) / 256.0);
/* Precalculate epsilon */
double epsilon = (315.0 * Math.pow (n, 4.0) / 512.0);
/* Now calculate the sum of the series and return */
return alpha
* (phi + (beta * Math.sin (2.0 * phi))
+ (gamma * Math.sin (4.0 * phi))
+ (delta * Math.sin (6.0 * phi))
+ (epsilon * Math.sin (8.0 * phi)));
}
/*
* UTMCentralMeridian
*
* Determines the central meridian for the given UTM zone.
*
* Inputs:
* zone - An integer value designating the UTM zone, range [1,60].
*
* Returns:
* The central meridian for the given UTM zone, in radians, or zero
* if the UTM zone parameter is outside the range [1,60].
* Range of the central meridian is the radian equivalent of [-177,+177].
*
*/
public double UTMCentralMeridian(int zone)
{
return Math.toRadians(-183.0 + (zone * 6.0));
}
private double UTMCentralMeridianDeg(int zone)
{
return -183.0 + (zone * 6.0);
}
/*
* FootpointLatitude
*
* Computes the footpoint latitude for use in converting transverse
* Mercator coordinates to ellipsoidal coordinates.
*
* Reference: Hoffmann-Wellenhof, B., Lichtenegger, H., and Collins, J.,
* GPS: Theory and Practice, 3rd ed. New York: Springer-Verlag Wien, 1994.
*
* Inputs:
* y - The UTM northing coordinate, in meters.
*
* Returns:
* The footpoint latitude, in radians.
*
*/
private double FootpointLatitude(double y)
{
/* Precalculate n (Eq. 10.18) */
double n = (Ellipsoid.GRS80.a - Ellipsoid.GRS80.b) / (Ellipsoid.GRS80.a + Ellipsoid.GRS80.b);
/* Precalculate alpha_ (Eq. 10.22) */
/* (Same as alpha in Eq. 10.17) */
double alpha_ = ((Ellipsoid.GRS80.a + Ellipsoid.GRS80.b) / 2.0)
* (1 + (Math.pow (n, 2.0) / 4) + (Math.pow (n, 4.0) / 64));
/* Precalculate y_ (Eq. 10.23) */
double y_ = y / alpha_;
/* Precalculate beta_ (Eq. 10.22) */
double beta_ = (3.0 * n / 2.0) + (-27.0 * Math.pow (n, 3.0) / 32.0)
+ (269.0 * Math.pow (n, 5.0) / 512.0);
/* Precalculate gamma_ (Eq. 10.22) */
double gamma_ = (21.0 * Math.pow (n, 2.0) / 16.0)
+ (-55.0 * Math.pow (n, 4.0) / 32.0);
/* Precalculate delta_ (Eq. 10.22) */
double delta_ = (151.0 * Math.pow (n, 3.0) / 96.0)
+ (-417.0 * Math.pow (n, 5.0) / 128.0);
/* Precalculate epsilon_ (Eq. 10.22) */
double epsilon_ = (1097.0 * Math.pow (n, 4.0) / 512.0);
/* Now calculate the sum of the series (Eq. 10.21) */
return y_ + (beta_ * Math.sin (2.0 * y_))
+ (gamma_ * Math.sin (4.0 * y_))
+ (delta_ * Math.sin (6.0 * y_))
+ (epsilon_ * Math.sin (8.0 * y_));
}
/*
* MapLatLonToXY
*
* Converts a latitude/longitude pair to x and y coordinates in the
* Transverse Mercator projection. Note that Transverse Mercator is not
* the same as UTM; a scale factor is required to convert between them.
*
* Reference: Hoffmann-Wellenhof, B., Lichtenegger, H., and Collins, J.,
* GPS: Theory and Practice, 3rd ed. New York: Springer-Verlag Wien, 1994.
*
* Inputs:
* phi - Latitude of the point, in radians.
* lambda - Longitude of the point, in radians.
* lambda0 - Longitude of the central meridian to be used, in radians.
*
* Outputs:
* xy - A 2-element array containing the x and y coordinates
* of the computed point.
*
* Returns:
* The function does not return a value.
*
*/
public EastNorth MapLatLonToXY(double phi, double lambda, double lambda0)
{
/* Precalculate ep2 */
double ep2 = (Math.pow (Ellipsoid.GRS80.a, 2.0) - Math.pow (Ellipsoid.GRS80.b, 2.0)) / Math.pow (Ellipsoid.GRS80.b, 2.0);
/* Precalculate nu2 */
double nu2 = ep2 * Math.pow (Math.cos (phi), 2.0);
/* Precalculate N */
double N = Math.pow (Ellipsoid.GRS80.a, 2.0) / (Ellipsoid.GRS80.b * Math.sqrt (1 + nu2));
/* Precalculate t */
double t = Math.tan (phi);
double t2 = t * t;
double tmp = (t2 * t2 * t2) - Math.pow (t, 6.0);
/* Precalculate l */
double l = lambda - lambda0;
/* Precalculate coefficients for l**n in the equations below
so a normal human being can read the expressions for easting
and northing
-- l**1 and l**2 have coefficients of 1.0 */
double l3coef = 1.0 - t2 + nu2;
double l4coef = 5.0 - t2 + 9 * nu2 + 4.0 * (nu2 * nu2);
double l5coef = 5.0 - 18.0 * t2 + (t2 * t2) + 14.0 * nu2
- 58.0 * t2 * nu2;
double l6coef = 61.0 - 58.0 * t2 + (t2 * t2) + 270.0 * nu2
- 330.0 * t2 * nu2;
double l7coef = 61.0 - 479.0 * t2 + 179.0 * (t2 * t2) - (t2 * t2 * t2);
double l8coef = 1385.0 - 3111.0 * t2 + 543.0 * (t2 * t2) - (t2 * t2 * t2);
return new EastNorth(
/* Calculate easting (x) */
N * Math.cos (phi) * l
+ (N / 6.0 * Math.pow (Math.cos (phi), 3.0) * l3coef * Math.pow (l, 3.0))
+ (N / 120.0 * Math.pow (Math.cos (phi), 5.0) * l5coef * Math.pow (l, 5.0))
+ (N / 5040.0 * Math.pow (Math.cos (phi), 7.0) * l7coef * Math.pow (l, 7.0)),
/* Calculate northing (y) */
ArcLengthOfMeridian (phi)
+ (t / 2.0 * N * Math.pow (Math.cos (phi), 2.0) * Math.pow (l, 2.0))
+ (t / 24.0 * N * Math.pow (Math.cos (phi), 4.0) * l4coef * Math.pow (l, 4.0))
+ (t / 720.0 * N * Math.pow (Math.cos (phi), 6.0) * l6coef * Math.pow (l, 6.0))
+ (t / 40320.0 * N * Math.pow (Math.cos (phi), 8.0) * l8coef * Math.pow (l, 8.0)));
}
/*
* MapXYToLatLon
*
* Converts x and y coordinates in the Transverse Mercator projection to
* a latitude/longitude pair. Note that Transverse Mercator is not
* the same as UTM; a scale factor is required to convert between them.
*
* Reference: Hoffmann-Wellenhof, B., Lichtenegger, H., and Collins, J.,
* GPS: Theory and Practice, 3rd ed. New York: Springer-Verlag Wien, 1994.
*
* Inputs:
* x - The easting of the point, in meters.
* y - The northing of the point, in meters.
* lambda0 - Longitude of the central meridian to be used, in radians.
*
* Outputs:
* philambda - A 2-element containing the latitude and longitude
* in radians.
*
* Returns:
* The function does not return a value.
*
* Remarks:
* The local variables Nf, nuf2, tf, and tf2 serve the same purpose as
* N, nu2, t, and t2 in MapLatLonToXY, but they are computed with respect
* to the footpoint latitude phif.
*
* x1frac, x2frac, x2poly, x3poly, etc. are to enhance readability and
* to optimize computations.
*
*/
public LatLon MapXYToLatLon(double x, double y, double lambda0)
{
/* Get the value of phif, the footpoint latitude. */
double phif = FootpointLatitude (y);
/* Precalculate ep2 */
double ep2 = (Math.pow (Ellipsoid.GRS80.a, 2.0) - Math.pow (Ellipsoid.GRS80.b, 2.0))
/ Math.pow (Ellipsoid.GRS80.b, 2.0);
/* Precalculate cos (phif) */
double cf = Math.cos (phif);
/* Precalculate nuf2 */
double nuf2 = ep2 * Math.pow (cf, 2.0);
/* Precalculate Nf and initialize Nfpow */
double Nf = Math.pow (Ellipsoid.GRS80.a, 2.0) / (Ellipsoid.GRS80.b * Math.sqrt (1 + nuf2));
double Nfpow = Nf;
/* Precalculate tf */
double tf = Math.tan (phif);
double tf2 = tf * tf;
double tf4 = tf2 * tf2;
/* Precalculate fractional coefficients for x**n in the equations
below to simplify the expressions for latitude and longitude. */
double x1frac = 1.0 / (Nfpow * cf);
Nfpow *= Nf; /* now equals Nf**2) */
double x2frac = tf / (2.0 * Nfpow);
Nfpow *= Nf; /* now equals Nf**3) */
double x3frac = 1.0 / (6.0 * Nfpow * cf);
Nfpow *= Nf; /* now equals Nf**4) */
double x4frac = tf / (24.0 * Nfpow);
Nfpow *= Nf; /* now equals Nf**5) */
double x5frac = 1.0 / (120.0 * Nfpow * cf);
Nfpow *= Nf; /* now equals Nf**6) */
double x6frac = tf / (720.0 * Nfpow);
Nfpow *= Nf; /* now equals Nf**7) */
double x7frac = 1.0 / (5040.0 * Nfpow * cf);
Nfpow *= Nf; /* now equals Nf**8) */
double x8frac = tf / (40320.0 * Nfpow);
/* Precalculate polynomial coefficients for x**n.
-- x**1 does not have a polynomial coefficient. */
double x2poly = -1.0 - nuf2;
double x3poly = -1.0 - 2 * tf2 - nuf2;
double x4poly = 5.0 + 3.0 * tf2 + 6.0 * nuf2 - 6.0 * tf2 * nuf2 - 3.0 * (nuf2 *nuf2) - 9.0 * tf2 * (nuf2 * nuf2);
double x5poly = 5.0 + 28.0 * tf2 + 24.0 * tf4 + 6.0 * nuf2 + 8.0 * tf2 * nuf2;
double x6poly = -61.0 - 90.0 * tf2 - 45.0 * tf4 - 107.0 * nuf2 + 162.0 * tf2 * nuf2;
double x7poly = -61.0 - 662.0 * tf2 - 1320.0 * tf4 - 720.0 * (tf4 * tf2);
double x8poly = 1385.0 + 3633.0 * tf2 + 4095.0 * tf4 + 1575 * (tf4 * tf2);
return new LatLon(
/* Calculate latitude */
Math.toDegrees(
phif + x2frac * x2poly * (x * x)
+ x4frac * x4poly * Math.pow (x, 4.0)
+ x6frac * x6poly * Math.pow (x, 6.0)
+ x8frac * x8poly * Math.pow (x, 8.0)),
Math.toDegrees(
/* Calculate longitude */
lambda0 + x1frac * x
+ x3frac * x3poly * Math.pow (x, 3.0)
+ x5frac * x5poly * Math.pow (x, 5.0)
+ x7frac * x7poly * Math.pow (x, 7.0)));
}
public EastNorth latlon2eastNorth(LatLon p) {
EastNorth a = MapLatLonToXY(Math.toRadians(p.lat()), Math.toRadians(p.lon()), UTMCentralMeridian(getzone()));
return new EastNorth(a.east() * UTMScaleFactor + 500000.0, a.north() * UTMScaleFactor);
}
public LatLon eastNorth2latlon(EastNorth p) {
return MapXYToLatLon((p.east()-500000.0)/UTMScaleFactor, p.north()/UTMScaleFactor, UTMCentralMeridian(getzone()));
}
@Override public String toString() {
return tr("UTM Zone {0}", getzone());
}
/* TODO - support all UTM's not only zone 33 */
public int getzone()
{
return zone;
}
public String toCode() {
return "EPSG:325837";
}
public String getCacheDirectoryName() {
return "epsg325837";
}
public ProjectionBounds getWorldBounds()
{
Bounds b = getWorldBoundsLatLon();
return new ProjectionBounds(latlon2eastNorth(b.min), latlon2eastNorth(b.max));
}
public Bounds getWorldBoundsLatLon()
{
return new Bounds(
new LatLon(-85.0, UTMCentralMeridianDeg(getzone())-5.0),
new LatLon(85.0, UTMCentralMeridianDeg(getzone())+5.0));
}
}