add Solid Earth projection

there was also a bug where the Liquid Earth projection threw an error if you tried to use a map with points on the pole or antimeridian.  but that's fixd now.  I also fixed a minor issue where it said that the Equal Earth projection had a closed-form inverse when it in fact does not.  I also renamed the liquid earth mesh files.

src/apps/MapApplication.java

@@ -75,7 +75,7 @@ import maps.EqualEarth;
 import maps.Gyorffy;
 import maps.HammerRetroazimuthal;
 import maps.Lenticular;
-import maps.Liquid;
+import maps.Sargent;
 import maps.Misc;
 import maps.Octahedral;
 import maps.Polyhedral;
@@ -161,7 +161,7 @@ public abstract class MapApplication extends Application {
 			  Lenticular.HAMMER, Lenticular.LAGRANGE, Lenticular.STREBE_95,
 			  Lenticular.VAN_DER_GRINTEN, Lenticular.WAGNER_VIII, WinkelTripel.WINKEL_TRIPEL },
 			{ Elastic.ELASTIC_I, Elastic.ELASTIC_II, Elastic.ELASTIC_III,
-			  Liquid.LIQUID_EARTH,
+			  Sargent.LIQUID_EARTH, Sargent.SOLID_EARTH,
 			  Danseiji.DANSEIJI_N, Danseiji.DANSEIJI_I, Danseiji.DANSEIJI_II, Danseiji.DANSEIJI_III,
 			  Danseiji.DANSEIJI_IV, Danseiji.DANSEIJI_V, Danseiji.DANSEIJI_VI },
 			{ Misc.BONNE, Misc.CASSINI, Snyder.GS50, Misc.GUYOU, HammerRetroazimuthal.FULL,

src/maps/EqualEarth.java

@@ -49,8 +49,8 @@ public class EqualEarth {
 	
 	
 	public static final Projection EQUAL_EARTH = new Projection(
-			"Equal Earth", "B. Savric, T. Patterson, and B. Jenny", "An equal-area pseudocylindrical projection specifically designed to woo Gall-Peters supporters away from that horrid thing",
-			null, true, true, true, true, Type.PSEUDOCYLINDRICAL, Property.EQUAL_AREA, 3) {
+			"Equal Earth", "B. Savric, Tom Patterson, and B. Jenny", "An equal-area pseudocylindrical projection specifically designed to woo Gall-Peters supporters away from that horrid thing",
+			null, true, true, true, false, Type.PSEUDOCYLINDRICAL, Property.EQUAL_AREA, 3) {
 		
 		public double[] project(double lat, double lon) {
 			double th = asin(B*sin(lat));
@@ -69,6 +69,31 @@ public class EqualEarth {
 	};
 	
 	
+	public static final Projection SARGENT_EQUIVALENT_EARTH = new Projection(
+			"Equivalent Earth", "R. Sargent", "An equal-area pseudocylindrical projection based on the Equal Earth projection and the cylindrical equal area projection, used as the base of the Solid Earth projection",
+			null, true, true, true, false, Type.PSEUDOCYLINDRICAL, Property.EQUAL_AREA, 2) {
+		
+		public double[] project(double lat, double lon) {
+			double th = asin(B*sin(lat));
+			return new double[] {
+					lon/(0.3*B*poly8(th)/cos(th) + 0.7*1.4),
+					0.3*poly9(th) + 0.7*1.4*sin(th)/B };
+		}
+		
+		public double[] inverse(double x, double y) {
+			double th = NumericalAnalysis.newtonRaphsonApproximation(
+					y, y/Y_SCALE,
+					(double th_) -> 0.3*poly9(th_) + 0.7*1.4*sin(th_)/B,
+					(double th_) -> 0.3*poly8(th_) + 0.7*1.4*cos(th_)/B, 1e-6);
+			return new double[] { asin(sin(th)/B), x*(0.3*B*poly8(th)/cos(th) + 0.7*1.4) };
+		}
+		
+		public void initialize(double... params) throws IllegalArgumentException {
+			this.shape = Shape.meridianEnvelope(this);
+		}
+	};
+	
+	
 	
 	private static double poly9(double x) {
 		return   A[3]*pow(x,9) +   A[2]*pow(x,7) +   A[1]*pow(x,3) + A[0]*x;

src/maps/Misc.java

@@ -606,9 +606,6 @@ public class Misc {
 			// for polar latitudes, switch to an azimuthal projection centered on the pole
 			else {
 				double sign = signum(φ0);
-				if (φ0 < -φMax) {
-					System.out.println(sign);
-				}
 				return new double[] {
 						sign*(PI/2 - hypot(x - sign*xPole, y - sign*yPole)),
 						sign*coerceAngle(θPole - atan2(xPole - sign*x, yPole - sign*y)) };

src/maps/Sargent.java

@@ -56,16 +56,19 @@ import static utils.Math2.coerceAngle;
  *
  * @author Justin Kunimune
  */
-public class Liquid {
-
-	public static final LiquidProjection LIQUID_EARTH = new LiquidProjection(
+public class Sargent {
+	
+	public static final SargentProjection LIQUID_EARTH = new SargentProjection(
 			"Liquid Earth", "An equal-area map in the shape of the Equal Earth projection, optimized around the continents",
-			EqualEarth.EQUAL_EARTH, toRadians(11), true, "liquid");
-
-
-	private static class LiquidProjection extends Projection {
+			EqualEarth.EQUAL_EARTH, toRadians(11), true);
+	
+	public static final SargentProjection SOLID_EARTH = new SargentProjection(
+			"Solid Earth", "A map optimised to show off the continents by compressing the oceans",
+			EqualEarth.SARGENT_EQUIVALENT_EARTH, toRadians(11), true);
+	
+	
+	private static class SargentProjection extends Projection {
 		
-		private final String filename; // the data filename
 		private final Projection baseProjection;
 		private final double centralMeridian;
 		private int[][] triangles;
@@ -77,14 +80,13 @@ public class Liquid {
 		private List<int[]>[][] lookupTableTransformed;
 		
 		
-		public LiquidProjection(
+		public SargentProjection(
 				String title, String description, Projection baseProjection,
-				double centralMeridian, boolean based_on_land, String filename) {
+				double centralMeridian, boolean based_on_land) {
 			super(title, "Robert C. Sargent", description, null,
 			      baseProjection.isContinuous(), baseProjection.isComprehensive(), true, true,
 			      Type.OTHER, baseProjection.getProperty(), 4,
 			      new String[0], new double[0][], !based_on_land);
-			this.filename = filename;
 			this.baseProjection = baseProjection;
 			this.centralMeridian = centralMeridian;
 		}
@@ -142,13 +144,17 @@ public class Liquid {
 		}
 		
 		
+		/**
+		 * find the triangle (represented as an array of three vertex indices) that contains the given point, using a
+		 * table of cached triangle locations to do so efficiently.
+		 */
 		private static int[] findContainingTriangle(
 				double[] фBins, double[] λBins, List<int[]>[][] lookupTable,
 				Vector[] vertices, double ф, double λ) {
 			λ = coerceAngle(λ);
 			Vector point = new Vector(cos(ф)*cos(λ), cos(ф)*sin(λ), sin(ф));
-			int i = (int) floor((ф - фBins[0])/(фBins[1] - фBins[0]));
-			int j = (int) floor((λ - λBins[0])/(λBins[1] - λBins[0]));
+			int i = min((int) floor((ф - фBins[0])/(фBins[1] - фBins[0])), фBins.length - 2);
+			int j = min((int) floor((λ - λBins[0])/(λBins[1] - λBins[0])), λBins.length - 2);
 			triangleLoop:
 			for (int[] triangle: lookupTable[i][j]) {
 				for (int k = 0; k < 3; k ++) {
@@ -216,14 +222,15 @@ public class Liquid {
 				return;
 			
 			// load the files
+			String filename = "res/" + this.getName().replace(" ", "_") + "_mesh";
 			double[][] verticesInitial, verticesTransformed;
 			int[][] triangles;
 			try {
-				verticesInitial = readNumpyFloatArray("res/" + this.filename + "_vertices_initial.npy");
-				verticesTransformed = readNumpyFloatArray("res/" + this.filename + "_vertices_transformed.npy");
-				triangles = readNumpyIntArray("res/" + this.filename + "_triangles.npy");
+				verticesInitial = readNumpyFloatArray(filename + "_verts_initial.npy");
+				verticesTransformed = readNumpyFloatArray(filename + "_verts_transformed.npy");
+				triangles = readNumpyIntArray(filename + "_tris.npy");
 			} catch (IOException e) {
-				throw new IllegalArgumentException("couldn't read the config file for this Liquid Projection: " + e);
+				throw new IllegalArgumentException("couldn't read the config file for this Sargent Projection: " + e);
 			}
 			if (verticesInitial.length != verticesTransformed.length)
 				throw new IllegalArgumentException("the initial vertices file and the transformed vertices files don't match.");
@@ -251,6 +258,15 @@ public class Liquid {
 		}
 		
 		
+		/**
+		 * build a table that will allow us to efficiently determine which triangles might contain a given pixel.
+		 * the output will be a table with фBins.length - 1 rows and λBins.length - 1 collums.  each entry i,j will be
+		 * a list of triangles that contact at least one point in the range
+		 *     фBins[i] <= ф <= фBins[i + 1] && λBins[j] <= λ <= λBins[j]
+		 * thus, if you need to find the triangle that contains a given point, you can find a cell of the table that
+		 * contains that point, and then you only need to check the contained triangles rather than every triangle in
+		 * the mesh.
+		 */
 		private static List<int[]>[][] cacheTriangleLocations(
 				int[][] triangles, Vector[] vertices, double[] фBins, double[] λBins) {
 			@SuppressWarnings("unchecked")