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Convex desktop GUI and test applications
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package convex.gui.utils;

import java.awt.geom.Point2D;

public class RobinsonProjection {
	public static final double HALFPI = Math.PI * 0.5;

	private final static double X[] = { 1, -5.67239e-12, -7.15511e-05, 3.11028e-06, 0.9986, -0.000482241, -2.4897e-05,
			-1.33094e-06, 0.9954, -0.000831031, -4.4861e-05, -9.86588e-07, 0.99, -0.00135363, -5.96598e-05, 3.67749e-06,
			0.9822, -0.00167442, -4.4975e-06, -5.72394e-06, 0.973, -0.00214869, -9.03565e-05, 1.88767e-08, 0.96,
			-0.00305084, -9.00732e-05, 1.64869e-06, 0.9427, -0.00382792, -6.53428e-05, -2.61493e-06, 0.9216,
			-0.00467747, -0.000104566, 4.8122e-06, 0.8962, -0.00536222, -3.23834e-05, -5.43445e-06, 0.8679, -0.00609364,
			-0.0001139, 3.32521e-06, 0.835, -0.00698325, -6.40219e-05, 9.34582e-07, 0.7986, -0.00755337, -5.00038e-05,
			9.35532e-07, 0.7597, -0.00798325, -3.59716e-05, -2.27604e-06, 0.7186, -0.00851366, -7.0112e-05,
			-8.63072e-06, 0.6732, -0.00986209, -0.000199572, 1.91978e-05, 0.6213, -0.010418, 8.83948e-05, 6.24031e-06,
			0.5722, -0.00906601, 0.000181999, 6.24033e-06, 0.5322, 0., 0., 0. };

	private final static double Y[] = { 0, 0.0124, 3.72529e-10, 1.15484e-09, 0.062, 0.0124001, 1.76951e-08,
			-5.92321e-09, 0.124, 0.0123998, -7.09668e-08, 2.25753e-08, 0.186, 0.0124008, 2.66917e-07, -8.44523e-08,
			0.248, 0.0123971, -9.99682e-07, 3.15569e-07, 0.31, 0.0124108, 3.73349e-06, -1.1779e-06, 0.372, 0.0123598,
			-1.3935e-05, 4.39588e-06, 0.434, 0.0125501, 5.20034e-05, -1.00051e-05, 0.4968, 0.0123198, -9.80735e-05,
			9.22397e-06, 0.5571, 0.0120308, 4.02857e-05, -5.2901e-06, 0.6176, 0.0120369, -3.90662e-05, 7.36117e-07,
			0.6769, 0.0117015, -2.80246e-05, -8.54283e-07, 0.7346, 0.0113572, -4.08389e-05, -5.18524e-07, 0.7903,
			0.0109099, -4.86169e-05, -1.0718e-06, 0.8435, 0.0103433, -6.46934e-05, 5.36384e-09, 0.8936, 0.00969679,
			-6.46129e-05, -8.54894e-06, 0.9394, 0.00840949, -0.000192847, -4.21023e-06, 0.9761, 0.00616525,
			-0.000256001, -4.21021e-06, 1., 0., 0., 0 };

	private final int NODES = 18;
	private final static double FXC = 0.8487;
	private final static double FYC = 1.3523;
	private final static double C1 = 11.45915590261646417544;
	private final static double RC1 = 0.08726646259971647884;
	private final static double EPS = 1e-8;

	private RobinsonProjection() {
	}

	private static final RobinsonProjection INSTANCE = new RobinsonProjection();

	public static Point2D getPoint(double latitude, double longitude) {
		Point2D.Double pt = new Point2D.Double();

		double lam = longitude / 360.0 * Math.PI;
		double phi = latitude / 90.0;
		INSTANCE.project(lam, phi, pt);
		pt.x = 0.45 + (pt.x * 0.357);
		pt.y = 0.5 - (pt.y * 0.56);
		return pt;
	}

	private double poly(double[] array, int offset, double z) {
		return (array[offset] + z * (array[offset + 1] + z * (array[offset + 2] + z * array[offset + 3])));
	}

	public Point2D.Double project(double lplam, double lpphi, Point2D.Double xy) {
		double phi = Math.abs(lpphi);
		int i = (int) Math.floor(phi * C1);
		if (i >= NODES) i = NODES - 1;
		phi = Math.toDegrees(phi - RC1 * i);
		i *= 4;
		xy.x = poly(X, i, phi) * FXC * lplam;
		xy.y = poly(Y, i, phi) * FYC;
		if (lpphi < 0.0) xy.y = -xy.y;
		return xy;
	}

	public Point2D.Double projectInverse(double x, double y, Point2D.Double lp) {
		int i;
		double t, t1;

		lp.x = x / FXC;
		lp.y = Math.abs(y / FYC);
		if (lp.y >= 1.0) {
			if (lp.y > 1.000001) {
				throw new Error("Out of range y?");
			} else {
				lp.y = y < 0. ? -HALFPI : HALFPI;
				lp.x /= X[4 * NODES];
			}
		} else {
			for (i = 4 * (int) Math.floor(lp.y * NODES);;) {
				if (Y[i] > lp.y) i -= 4;
				else if (Y[i + 4] <= lp.y) i += 4;
				else break;
			}
			t = 5. * (lp.y - Y[i]) / (Y[i + 4] - Y[i]);
			double Tc0 = Y[i];
			double Tc1 = Y[i + 1];
			double Tc2 = Y[i + 2];
			double Tc3 = Y[i + 3];
			t = 5. * (lp.y - Tc0) / (Y[i + 1] - Tc0);
			Tc0 -= lp.y;
			for (;;) { // Newton-Raphson
				t -= t1 = (Tc0 + t * (Tc1 + t * (Tc2 + t * Tc3))) / (Tc1 + t * (Tc2 + Tc2 + t * 3. * Tc3));
				if (Math.abs(t1) < EPS) break;
			}
			lp.y = Math.toRadians(5 * i + t);
			if (y < 0.) lp.y = -lp.y;
			lp.x /= poly(X, i, t);
		}
		return lp;
	}

	public boolean hasInverse() {
		return true;
	}

	public String toString() {
		return "Robinson";
	}

}