Hah! Aitoff _does_ have an inverse solution!

I tweaked MapExplainer to be a little bit better, corrected some minor issues with the Projection metadata, added real descriptions to my custom parameterised projections, and fixed a critical bug with WinkelTripel's inverse solution.

src/apps/MapExplainer.java

@@ -64,7 +64,7 @@ public class MapExplainer {
 					Tetrahedral.TETRAGRAPH, Tetrahedral.AUTHAGRAPH, Pseudocylindrical.SINUSOIDAL,
 					Pseudocylindrical.MOLLWEIDE, Tobler.TOBLER, Misc.HAMMER, Misc.AITOFF,
 					Misc.VAN_DER_GRINTEN, Robinson.ROBINSON, WinkelTripel.WINKEL_TRIPEL,
-					Misc.PEIRCE_QUINCUNCIAL.transverse(), Misc.GUYOU, Misc.TWO_POINT_EQUIDISTANT,
+					Misc.PEIRCE_QUINCUNCIAL.transverse(), Misc.TWO_POINT_EQUIDISTANT,
 					Misc.HAMMER_RETROAZIMUTHAL },
 
 			{ MyProjections.PSEUDOSTEREOGRAPHIC, MyProjections.HYPERELLIPOWER,
@@ -117,6 +117,7 @@ public static void main(String[] args) throws IOException {
 						"title=\"TODO\">");
 				out.println("  </div>");
 				out.println("</div>");
+				out.println("<br>");
 
 				out.println();
 			}

src/maps/Azimuthal.java

@@ -45,7 +45,8 @@ public double[] inverse(double x, double y) {
 
 
 	public static final Projection POLAR =
-			new Projection("Polar", 1., 0b1111, Type.AZIMUTHAL, Property.EQUIDISTANT) {
+			new Projection(
+					"Azimuthal Equidistant", 1., 0b1111, Type.AZIMUTHAL, Property.EQUIDISTANT) {
 
 		public double[] project(double lat, double lon) {
 			final double r = .5 - lat/Math.PI;

src/maps/Misc.java

@@ -39,7 +39,7 @@ public class Misc {
 
 	public static final Projection AITOFF =
 			new Projection("Aitoff", "A compromise projection shaped like an ellipse",
-					2., 0b1011, Type.PSEUDOAZIMUTHAL, Property.COMPROMISE) {
+					2., 0b1111, Type.PSEUDOAZIMUTHAL, Property.COMPROMISE) {
 
 		public double[] project(double lat, double lon) {
 			final double a = Math.acos(Math.cos(lat)*Math.cos(lon/2));

src/maps/MyProjections.java

@@ -85,7 +85,8 @@ public double[] inverse(double x, double y) {
 
 
 	public static final Projection PSEUDOSTEREOGRAPHIC =
-			new Projection("Pseudostereographic", "The logical next step after Aitoff and Hammer",
+			new Projection(
+					"Pseudostereographic", "The logical next step after Aitoff and Hammer",
 					2, 0b1111, Type.PSEUDOAZIMUTHAL, Property.COMPROMISE) {
 
 		public double[] project(double lat, double lon) {
@@ -106,7 +107,8 @@ public double[] inverse(double x, double y) {
 
 
 	public static final Projection HYPERELLIPOWER =
-			new Projection("Hyperellipower", "A parametric projection that I'm still testing",
+			new Projection(
+					"Hyperellipower", "A parametrised pseudocylindrical projection that I invented",
 					2., 0b1111, Type.PSEUDOCYLINDRICAL, Property.COMPROMISE,
 					new String[] {"k","n","a"},
 					new double[][] {{1,3,5},{.5,2.,1.20},{.5,2.,1.13}}) {
@@ -136,7 +138,8 @@ public double[] inverse(double x, double y) {
 
 
 	public static final Projection TWO_POINT_EQUALIZED =
-			new Projection("Two-Point Equalized", "A parametric projection that I'm still testing",
+			new Projection("Two-Point Equalized",
+					"A projection I invented specifically for viewing small elliptical regions of the Earth",
 					0, 0b1111, Type.OTHER, Property.EQUIDISTANT, new String[] {"Width"},
 					new double[][] { {0, 180, 120} }) {
 

src/maps/Tetrahedral.java

@@ -78,7 +78,7 @@ public double[] innerInverse(double r, double tht) {
 
 	public static final Projection TETRAPOWER =
 			new TetrahedralProjection(
-					"Tetrapower", "A parametric projection that I'm still testing",
+					"Tetrapower", "A parameterised tetrahedral projection that I invented.",
 					Math.sqrt(3), 0b1111, Property.COMPROMISE, new String[] {"k1","k2","k3"},
 					new double[][] {{.01,2.,.98},{.01,2.,1.2},{.01,2.,.98}}) {
 
@@ -118,7 +118,8 @@ public double[] innerInverse(double r, double tht) {
 
 
 	public static final Projection TETRAFILLET =
-			new TetrahedralProjection("TetraFillet", "A parametric projection that I'm still testing",
+			new TetrahedralProjection("TetraFillet",
+					"A parameterised tetrahedral projection I invented with the corners filleted off",
 					Math.sqrt(3), 0b1110, Property.COMPROMISE, new String[] {"k1","k2","k3"},
 					new double[][] {{.01,2.,.78},{.01,2.,.99},{.01,2.,1.3}}) {
 
@@ -165,8 +166,9 @@ public double[] innerInverse(double r, double tht) {
 
 	public static final Projection TETRACHAMFER =
 			new TetrahedralProjection(
-					"TetraChamfer", "A parametric projection that I'm still testing", Math.sqrt(3),
-					0b1110, Property.COMPROMISE, new String[] {"k1","k2","k3"},
+					"TetraChamfer",
+					"A parameterised tetrahedral projection I invented with the corners chamfered off",
+					Math.sqrt(3), 0b1110, Property.COMPROMISE, new String[] {"k1","k2","k3"},
 					new double[][] {{.01,2.,.78},{.01,2.,.99},{.01,2.,1.3}}) {
 
 		private double k1, k2, k3;

src/maps/Tobler.java

@@ -42,7 +42,7 @@ public class Tobler {
 					"Tobler", "An equal-area projection shaped like a hyperellipse (in case you're wondering about gamma, it's calculated automatically)",
 					2., 0b1001, Type.PSEUDOCYLINDRICAL, Property.EQUAL_AREA,
 					new String[]{"Std. Parallel","alpha","K"},
-					new double[][] {{0,89,30.6}, {0,1,.5}, {1,8,3.63}}) {
+					new double[][] {{0,89,37}, {0,1,0}, {1,8,3.6}}) { //optimal parameters are 30.6,.50,3.63, but these defaults are more recognizably Tobler
 
 		private static final int N = 10000;
 		private double alpha, kappa, epsilon; //epsilon is related to gamma, but defined somewhat differently

src/maps/WinkelTripel.java

@@ -55,27 +55,28 @@ public void setParameters(double... params) {
 		}
 
 		public double[] project(double lat, double lon) {
-			return new double[] { f1pX(lat,lon)/aspectRatio, f2pY(lat,lon)/aspectRatio };
+			return new double[] {
+					f1pX(lat,lon)/aspectRatio/Math.PI, f2pY(lat,lon)/aspectRatio/Math.PI };
 		}
 
 		public double[] inverse(double x, double y) {
 			return NumericalAnalysis.newtonRaphsonApproximation(
-					x*aspectRatio, y, y/2, x*(1 + Math.cos(y*Math.PI/2))/2,
+					x*Math.PI*aspectRatio, y*Math.PI,
+					y*Math.PI/2, x*Math.PI*(1 + Math.cos(y*Math.PI/2))/2,
 					this::f1pX, this::f2pY,
 					this::df1dphi, this::df1dlam, this::df2dphi, this::df2dlam, .002);
 		}
 
 		private double f1pX(double phi, double lam) {
 			final double d = D(phi,lam);
 			final double c = C(phi,lam);
-			return 2/Math.PI*d/Math.sqrt(c)*Math.cos(phi)*Math.sin(lam/2)
-					+ lam/Math.PI*(aspectRatio-1);
+			return 2*d/Math.sqrt(c)*Math.cos(phi)*Math.sin(lam/2) + lam*(aspectRatio-1);
 		}
 
 		private double f2pY(double phi, double lam) {
 			final double d = D(phi,lam);
 			final double c = C(phi,lam);
-			return d/Math.sqrt(c)*Math.sin(phi)/Math.PI + phi/Math.PI;
+			return d/Math.sqrt(c)*Math.sin(phi) + phi;
 		}
 
 		private double df1dphi(double phi, double lam) {