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SquidLib platform-independent logic and utility code. Please refer to
https://github.com/SquidPony/SquidLib .
/*
* MIT License
*
* Copyright (c) 2017 Justin Kunimune
*
* Permission is hereby granted, free of charge, to any person obtaining a copy
* of this software and associated documentation files (the "Software"), to deal
* in the Software without restriction, including without limitation the rights
* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
* copies of the Software, and to permit persons to whom the Software is
* furnished to do so, subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included in all
* copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
* SOFTWARE.
*/
package squidpony.squidgrid.mapping;
/**
* Added to SquidLib by Tommy Ettinger on 7/4/2018, using MIT-licensed work by Justin Kunimune from
* his Map-Projections repo.
* @author jkunimune
* @author Tommy Ettinger
*/
public class ProjectionTools {
/**
* Performs a definite integral using Simpson's rule and a constant step size; hard-coded to integrate a
* hyperellipse function.
* @param a The start of the integration region
* @param b The end of the integration region (must be greater than a)
* @param h The step size (must be positive)
* @param kappa the kappa value of the hyperellipse
* @return some magic stuff needed for Tobler Hyperelliptical maps
*/
public static double simpsonIntegrateHyperellipse(double a, double b, double h, double kappa) {
double sum = 0, ik = 1/kappa;
for (double x = a; x < b; x += h) {
if (x+h > b) h = b-x;
sum += h/6*(Math.pow(1 - Math.pow(Math.abs(x), kappa), ik)
+ 4*Math.pow(1 - Math.pow(Math.abs(x + h * 0.5), kappa), ik)
+ Math.pow(1 - Math.pow(Math.abs(x + h), kappa), ik));
}
return sum;
}
/**
* Solves a simple ODE using Simpson's rule and a constant step size; hard-coded to solve a hyperelliptical map
* projection task.
* @param T The maximum time value at which to sample (must be positive)
* @param y the double array to fill with samples; must not be null and must have length 1 or greater
* @param h The internal step size (must be positive)
* @param alpha part of the hyperelliptical projection's parameters
* @param kappa part of the hyperelliptical projection's parameters
* @param epsilon calculated beforehand using {@link #simpsonIntegrateHyperellipse(double, double, double, double)}
* @return y, after modifications
*/
public static double[] simpsonODESolveHyperellipse(final double T, final double[] y, final double h, final double alpha, final double kappa, final double epsilon)
{
final int n = y.length - 1;
double t = 0;
double sum = 0;
for (int i = 0; i <= n; i++) {
while (t < i * T / n) {
final double tph = Math.min(t + h, i * T / n);
sum += (tph - t) / 6 * (Math.abs((alpha + (1-alpha)*Math.pow(1 - Math.pow(Math.abs(t), kappa), 1.0/kappa)) / (alpha + (1-alpha)*epsilon))
+ 4 * Math.abs((alpha + (1-alpha)*Math.pow(1 - Math.pow(Math.abs((t + tph) * 0.5), kappa), 1.0/kappa)) / (alpha + (1-alpha)*epsilon))
+ Math.abs((alpha + (1-alpha)*Math.pow(1 - Math.pow(Math.abs(tph), kappa), 1.0/kappa)) / (alpha + (1-alpha)*epsilon)));
t = tph;
}
y[i] = sum;
}
return y;
}
/**
* Part of computing a hyperellipse; takes only a y parameter corresponding to the y on a map and a kappa parameter
* used by Tobler's hyperelliptical projection to determine shape.
* @param y y on a map, usually -1.0 to 1.0
* @param kappa one of the Tobler parameters
* @return I'm guessing the actual y used after hyperelliptical distortion; not sure
*/
public static double hyperellipse(double y, double kappa) {
return Math.pow(1 - Math.pow(Math.abs(y),kappa), 1/kappa);
}
}