// License: GPL. For details, see LICENSE file.
package org.openstreetmap.josm.data.projection.proj;
import static org.openstreetmap.josm.tools.I18n.tr;
import org.openstreetmap.josm.data.Bounds;
import org.openstreetmap.josm.data.projection.ProjectionConfigurationException;
/**
* Cassini-Soldner Projection (EPSG code 9806).
* The Cassini-Soldner Projection is the ellipsoidal version of the Cassini
* projection for the sphere. It is not conformal but as it is relatively simple
* to construct it was extensively used in the last century and is still useful
* for mapping areas with limited longitudinal extent. It has now largely
* been replaced by the conformal Transverse Mercator which it resembles. Like this,
* it has a straight central meridian along which the scale is true, all other
* meridians and parallels are curved, and the scale distortion increases
* rapidly with increasing distance from the central meridian.
* <p>
*
* This class has been derived from the implementation of the Geotools project;
* git 8cbf52d, org.geotools.referencing.operation.projection.CassiniSoldner
* at the time of migration.
*/
public class CassiniSoldner extends AbstractProj {
/**
* Meridian distance at the {@code latitudeOfOrigin}.
* Used for calculations for the ellipsoid.
*/
private double ml0;
/**
* Contants used for the forward and inverse transform for the eliptical
* case of the Cassini-Soldner.
*/
private static final double C1 = 0.16666666666666666666;
private static final double C2 = 0.008333333333333333333;
private static final double C3 = 0.041666666666666666666;
private static final double C4 = 0.33333333333333333333;
private static final double C5 = 0.066666666666666666666;
@Override
public String getName() {
return tr("Cassini-Soldner");
}
@Override
public String getProj4Id() {
return "cass";
}
@Override
public void initialize(ProjParameters params) throws ProjectionConfigurationException {
super.initialize(params);
if (params.lat0 == null)
throw new ProjectionConfigurationException(tr("Parameter ''{0}'' required.", "lat_0"));
double latitudeOfOrigin = Math.toRadians(params.lat0);
ml0 = mlfn(latitudeOfOrigin, Math.sin(latitudeOfOrigin), Math.cos(latitudeOfOrigin));
}
@Override
public double[] project(double phi, double lam) {
double sinphi = Math.sin(phi);
double cosphi = Math.cos(phi);
double n = 1.0 / (Math.sqrt(1.0 - e2 * sinphi * sinphi));
double tn = Math.tan(phi);
double t = tn * tn;
double a1 = lam * cosphi;
double c = cosphi * cosphi * e2 / (1 - e2);
double a2 = a1 * a1;
double x = n * a1 * (1.0 - a2 * t * (C1 - (8.0 - t + 8.0 * c) * a2 * C2));
double y = mlfn(phi, sinphi, cosphi) - ml0 + n * tn * a2 * (0.5 + (5.0 - t + 6.0 * c) * a2 * C3);
return new double[] {x, y};
}
@Override
public double[] invproject(double x, double y) {
double ph1 = invMlfn(ml0 + y);
double tn = Math.tan(ph1);
double t = tn * tn;
double n = Math.sin(ph1);
double r = 1.0 / (1.0 - e2 * n * n);
n = Math.sqrt(r);
r *= (1.0 - e2) * n;
double dd = x / n;
double d2 = dd * dd;
double phi = ph1 - (n * tn / r) * d2 * (0.5 - (1.0 + 3.0 * t) * d2 * C3);
double lam = dd * (1.0 + t * d2 * (-C4 + (1.0 + 3.0 * t) * d2 * C5)) / Math.cos(ph1);
return new double[] {phi, lam};
}
@Override
public Bounds getAlgorithmBounds() {
return new Bounds(-89, -1.0, 89, 1.0, false);
}
}