sharpetronics/Map-Projections
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That's not how you integrate polynomials!

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I was able to get the Bat projection working without too much trouble.
It turned out that while I got my MacLaurin series right for the
conformal mapping from the disc to a hexagon, my integral was wrong. I
fixed that, but I still needed to do tho oblique trick to make it look
good enough. All in all, it works great. Now I just need an inverse.
Newton-Raphson, anyone?
This commit is contained in:
Justin Kunimune 2018-02-07 21:01:00 -10:00
parent c13f1a2608
commit cc6d7fcddf
2 changed files with 16 additions and 4 deletions
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2
src/apps/MapDesignerVector.java
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@ -87,9 +87,7 @@ public class MapDesignerVector extends MapApplication {
public void start(Stage root) {
super.start(root);
new Thread(() -> {
System.out.println("Check 0");
setInput(new File("input/Basic.svg")); //this automatically updates the map
System.out.println("Check 1");
}).start();
}

18
src/maps/Octohedral.java
View File

@ -105,11 +105,25 @@ public class Octohedral {
Math.sqrt(3)/2, 0, 0b1000, Property.CONFORMAL, 3, Configuration.BAT_SHAPE) {
protected double[] faceProject(double lat, double lon) {
double[] poleCoords = {lat, lon};
double[] vertCoords = obliquifySphc(lat, lon, new double[] {0, Math.PI/4, -3*Math.PI/4}); //look at an oblique aspect from the nearest vertex
if (poleCoords[0] > vertCoords[0]) { //if this point is closer to the pole
return fortyoctantProject(lat, lon); //project it as normal
}
else { //if it is closer to the vertex
double[] skewCoords = fortyoctantProject(vertCoords[0], vertCoords[1]); //use the maclaurin series centered there
return new double[] {
-1/2.*skewCoords[0] + Math.sqrt(3)/2*skewCoords[1] + Math.sqrt(3)/2,
-Math.sqrt(3)/2*skewCoords[0] - 1/2.*skewCoords[1] + 1/2. };
}
}
private double[] fortyoctantProject(double lat, double lon) { //an even finer projection than the half-octant
final Complex w = Complex.fromPolar(
Math.pow(Math.tan(Math.PI/4-lat/2), 2/3.), lon*2/3.-Math.PI/6);
Complex z = w.plus(w.pow(7).divide(3)).plus(w.pow(11).divide(9)).plus(w.pow(13).divide(99/16.));
Complex z = w.plus(w.pow(7).divide(21)).plus(w.pow(11).divide(99)).plus(w.pow(13).divide(1287/16.));
if (z.isInfinite() || z.isNaN()) z = new Complex(0);
z = z.times(new Complex(Math.sqrt(3)/2, 1/2.));
z = z.times(new Complex(Math.sqrt(3)/2, 1/2.)).divide(1.112913); //this number is 2^(2/3)/6*\int_0^\pi sin^(-1/3) x dx
return new double[] { z.getRe(), z.getIm() };
}