mirror of
https://github.com/csharpee/Map-Projections.git
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5e01e339b9
I tidied up the documentation on the BFGS stuff and updated my maps and defaults to be informed by the new optimizations.
93 lines
3.3 KiB
Java
93 lines
3.3 KiB
Java
/**
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* MIT License
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*
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* Copyright (c) 2017 Justin Kunimune
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*
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* Permission is hereby granted, free of charge, to any person obtaining a copy
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* of this software and associated documentation files (the "Software"), to deal
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* in the Software without restriction, including without limitation the rights
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* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
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* copies of the Software, and to permit persons to whom the Software is
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* furnished to do so, subject to the following conditions:
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*
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* The above copyright notice and this permission notice shall be included in all
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* copies or substantial portions of the Software.
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*
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* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
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* SOFTWARE.
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*/
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package maps;
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import java.util.Arrays;
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import maps.Projection.Property;
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import maps.Projection.Type;
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import utils.Math2;
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import utils.NumericalAnalysis;
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/**
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* A class of values and functions used to approximate the Tobler projection
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*
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* @author jkunimune
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*/
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public class Tobler {
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public static final Projection TOBLER =
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new Projection(
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"Tobler Hyperelliptical", "An equal-area projection shaped like a hyperellipse.",
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2*Math.PI, 0, 0b1001, Type.PSEUDOCYLINDRICAL, Property.EQUAL_AREA, 4,
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new String[]{"Std. Parallel","alpha","K"},
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new double[][] {{0,89,30}, {0,1,.46}, {1,5,3.7}}) { //optimal parameters are 30.6,.50,3.63, but these defaults are more recognizably Tobler
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private static final int N = 20000;
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private double alpha, kappa, epsilon; //epsilon is related to gamma, but defined somewhat differently
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private double[] Z; //Z[i] = sin(phi) when y = i/(Z.length-1)
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public void setParameters(double... params) {
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this.height = 2/Math.pow(Math.cos(Math.toRadians(params[0])),2);
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this.alpha = params[1];
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this.kappa = params[2];
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this.epsilon = NumericalAnalysis.simpsonIntegrate(
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0, 1, this::hyperEllipse, 1./N);
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this.Z = NumericalAnalysis.simpsonODESolve(
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1, N, this::dZdY, 1./N);
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}
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public double[] project(double lat, double lon) {
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final double z0 = Math.abs(Math.sin(lat));
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final int i = Arrays.binarySearch(Z, z0);
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final double y;
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if (i >= 0)
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y = i/(Z.length-1.);
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else if (-i-1 >= Z.length)
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y = Z[Z.length-1];
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else
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y = Math2.linInterp(z0, Z[-i-2], Z[-i-1], -i-2, -i-1)/
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(Z.length-1.);
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return new double[] {
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lon * Math.abs(alpha + (1-alpha)*hyperEllipse(y)),
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y * Math.signum(lat)*height/2 };
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}
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public double[] inverse(double x, double y) {
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return new double[] {
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Math.asin(Z[(int)Math.round(Math.abs(2*y/height)*(Z.length-1))])*Math.signum(y),
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x / Math.abs(alpha + (1-alpha)*hyperEllipse(2*y/height)) };
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}
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public double dZdY(double y) {
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return Math.abs((alpha + (1-alpha)*hyperEllipse(y))/
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(alpha + (1-alpha)*epsilon));
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}
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public double hyperEllipse(double y) {
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return Math.pow(1 - Math.pow(Math.abs(y),kappa), 1/kappa);
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}
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};
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}
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