org.osgeo.proj4j.proj.VanDerGrintenProjection Maven / Gradle / Ivy

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Proj4J is a Java library to transform point coordinates from one geographic coordinate system to another, including datum transformations.
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/*
Copyright 2006 Jerry Huxtable

Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at

   http://www.apache.org/licenses/LICENSE-2.0

Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*/

/*
 * This file was semi-automatically converted from the public-domain USGS PROJ source.
 */
package org.osgeo.proj4j.proj;

import org.osgeo.proj4j.ProjCoordinate;
import org.osgeo.proj4j.ProjectionException;
import org.osgeo.proj4j.util.ProjectionMath;

public class VanDerGrintenProjection extends Projection {

	private final static double TOL = 1.e-10;
	private final static double THIRD = .33333333333333333333;
	private final static double TWO_THRD = .66666666666666666666;
	private final static double C2_27 = .07407407407407407407;
	private final static double PI4_3 = 4.18879020478639098458;
	private final static double PISQ = 9.86960440108935861869;
	private final static double TPISQ = 19.73920880217871723738;
	private final static double HPISQ = 4.93480220054467930934;

	public ProjCoordinate project(double lplam, double lpphi, ProjCoordinate out) {
		double  al, al2, g, g2, p2;

		p2 = Math.abs(lpphi / ProjectionMath.HALFPI);
		if ((p2 - TOL) > 1.) throw new ProjectionException("F");
		if (p2 > 1.)
			p2 = 1.;
		if (Math.abs(lpphi) <= TOL) {
			out.x = lplam;
			out.y = 0.;
		} else if (Math.abs(lplam) <= TOL || Math.abs(p2 - 1.) < TOL) {
			out.x = 0.;
			out.y = Math.PI * Math.tan(.5 * Math.asin(p2));
			if (lpphi < 0.) out.y = -out.y;
		} else {
			al = .5 * Math.abs(Math.PI / lplam - lplam / Math.PI);
			al2 = al * al;
			g = Math.sqrt(1. - p2 * p2);
			g = g / (p2 + g - 1.);
			g2 = g * g;
			p2 = g * (2. / p2 - 1.);
			p2 = p2 * p2;
			out.x = g - p2; g = p2 + al2;
			out.x = Math.PI * (al * out.x + Math.sqrt(al2 * out.x * out.x - g * (g2 - p2))) / g;
			if (lplam < 0.) out.x = -out.x;
			out.y = Math.abs(out.x / Math.PI);
			out.y = 1. - out.y * (out.y + 2. * al);
			if (out.y < -TOL) throw new ProjectionException("F");
			if (out.y < 0.)
				out.y = 0.;
			else
				out.y = Math.sqrt(out.y) * (lpphi < 0. ? -Math.PI : Math.PI);
		}
		return out;
	}

	public ProjCoordinate projectInverse(double xyx, double xyy, ProjCoordinate out) {
		double t, c0, c1, c2, c3, al, r2, r, m, d, ay, x2, y2;

		x2 = xyx * xyx;
		if ((ay = Math.abs(xyy)) < TOL) {
			out.y = 0.;
			t = x2 * x2 + TPISQ * (x2 + HPISQ);
			out.x = Math.abs(xyx) <= TOL ? 0. :
			   .5 * (x2 - PISQ + Math.sqrt(t)) / xyx;
			return out;
		}
		y2 = xyy * xyy;
		r = x2 + y2;	r2 = r * r;
		c1 = - Math.PI * ay * (r + PISQ);
		c3 = r2 + ProjectionMath.TWOPI * (ay * r + Math.PI * (y2 + Math.PI * (ay + ProjectionMath.HALFPI)));
		c2 = c1 + PISQ * (r - 3. *  y2);
		c0 = Math.PI * ay;
		c2 /= c3;
		al = c1 / c3 - THIRD * c2 * c2;
		m = 2. * Math.sqrt(-THIRD * al);
		d = C2_27 * c2 * c2 * c2 + (c0 * c0 - THIRD * c2 * c1) / c3;
		if (((t = Math.abs(d = 3. * d / (al * m))) - TOL) <= 1.) {
			d = t > 1. ? (d > 0. ? 0. : Math.PI) : Math.acos(d);
			out.y = Math.PI * (m * Math.cos(d * THIRD + PI4_3) - THIRD * c2);
			if (xyy < 0.) out.y = -out.y;
			t = r2 + TPISQ * (x2 - y2 + HPISQ);
			out.x = Math.abs(xyx) <= TOL ? 0. :
			   .5 * (r - PISQ + (t <= 0. ? 0. : Math.sqrt(t))) / xyx;
		} else
			throw new ProjectionException("I");
		return out;
	}

	public boolean hasInverse() {
		return true;
	}

	public String toString() {
		return "van der Grinten (I)";
	}

}