<3

I added the Bonne projection, which is a generalized form of Sinusoidal and Werner (I don't have Werner). As it turns out, this was one of the go-to map projections back in the days before Albers and Van der Grinten had been invented.

src/maps/Conic.java

@@ -197,9 +197,11 @@ public class Conic {
 				lat = -lat;
 				lon = -lon;
 			}
-			final double s = reversed ? -1 : 1;
 			final double r = Math.sqrt(C - 2*n*Math.sin(lat));
-			return new double[] { s*r*Math.sin(n*lon), s*(y0 - r*Math.cos(n*lon)) };
+			final double x = r*Math.sin(n*lon);
+			final double y = -r*Math.cos(n*lon);
+			if (reversed) 	return new double[] {-x,-y};
+			else 			return new double[] { x, y};
 		}
 		
 		public double[] inverse(double x, double y) {
@@ -219,7 +221,6 @@ public class Conic {
 	};
 	
 	
-	
 	/**
 	 * A base for all conic projections
 	 * @author jkunimune

src/maps/Misc.java

@@ -233,6 +233,89 @@ public class Misc {
 	};
 	
 	
+	public static final Projection BONNE =
+			new Projection(
+					"Bonne", "A traditional pseudoconic projection, also known as the Sylvanus projection.",
+					10, 10, 0b1111, Type.PSEUDOCONIC, Property.EQUAL_AREA, 1,
+					new String[] {"Std. Parallel"}, new double[][] {{-90, 90, 45}}) {
+		
+		private double r0;
+		private double yC; // the y coordinate of the centers of the parallels
+		private boolean reversed; // if the standard parallel is southern
+		
+		public void setParameters(double... params) {
+			double lat0 = Math.toRadians(params[0]);
+			this.reversed = (lat0 < 0);
+			if (reversed)
+				lat0 = -lat0;
+			this.r0 = 1/Math.tan(lat0) + lat0;
+			if (Double.isInfinite(r0)) {
+				this.width = Pseudocylindrical.SINUSOIDAL.getWidth();
+				this.height = Pseudocylindrical.SINUSOIDAL.getHeight();
+			}
+			else { // for such a simple map projection...
+				double argmaxX = NumericalAnalysis.bisectionFind(
+						(p) -> (Math.PI*(1/(r0-p)*Math.cos(p) - Math.sin(p))*Math.cos(Math.PI/(r0-p)*Math.cos(p)) - Math.sin(Math.PI/(r0-p)*Math.cos(p))),
+						-Math.PI/2, 0, 1e-3); // it sure is complicated to find its dimensions!
+				double maxX = (r0 - argmaxX)*Math.sin(Math.PI/(r0 - argmaxX)*Math.cos(argmaxX));
+				this.width = 2*maxX;
+				double argmaxY;
+				try {
+					argmaxY = NumericalAnalysis.bisectionFind(
+							(p) -> (Math.PI*(1/(r0-p)*Math.cos(p) - Math.sin(p))*Math.sin(Math.PI/(r0-p)*Math.cos(p)) + Math.cos(Math.PI/(r0-p)*Math.cos(p))),
+							0, Math.PI/4, 1e-3);
+				} catch (IllegalArgumentException e) {
+					argmaxY = Math.PI/2;
+				}
+				double maxY = Math.max(-r0 + Math.PI/2,
+						-(r0 - argmaxY)*Math.cos(Math.PI/(r0 - argmaxY)*Math.cos(argmaxY)));
+				this.height = r0 + Math.PI/2 + maxY;
+				this.yC = (r0 + Math.PI/2 - maxY)/2;
+			}
+		}
+		
+		public double[] project(double lat, double lon) {
+			if (Double.isInfinite(r0))
+				return Pseudocylindrical.SINUSOIDAL.project(lat, lon);
+			if (reversed) {
+				lat = -lat;
+				lon = -lon;
+			}
+			
+			double r = r0 - lat;
+			double th = lon*Math.cos(lat)/r;
+			double x = r*Math.sin(th);
+			double y = yC - r*Math.cos(th);
+			
+			if (reversed)
+				return new double[] {-x,-y};
+			else
+				return new double[] { x, y};
+		}
+		
+		public double[] inverse(double x, double y) {
+			if (Double.isInfinite(r0))
+				return Pseudocylindrical.SINUSOIDAL.inverse(x, y);
+			if (reversed) {
+				x = -x;
+				y = -y;
+			}
+			
+			double r = Math.hypot(x,  y-yC);
+			if (r < r0 - Math.PI/2 || r > r0 + Math.PI/2)
+				return null;
+			double th = Math.atan2(x, -(y-yC));
+			double lat = r0 - r;
+			double lon = th*r/Math.cos(lat);
+			
+			if (reversed)
+				return new double[] {-lat,-lon};
+			else
+				return new double[] { lat, lon};
+		}
+	};
+	
+	
 	public static final Projection T_SHIRT =
 			new Projection(
 					"T-Shirt", "A conformal projection onto a torso.",

src/maps/Projection.java

@@ -560,6 +560,14 @@ public abstract class Projection {
 		return this.property;
 	}
 	
+	/**
+	 * @return the rating:
+	 * 0 if I hate it with a burning passion;
+	 * 1 if it is bad and you shouldn't use it;;
+	 * 2 if it has its use cases but isn't very good outside of them;
+	 * 3 if it is a solid, defensible choice; and
+	 * 4 if I love it with a burning passion.
+	 */
 	public final int getRating() {
 		return this.rating;
 	}
@@ -612,10 +620,10 @@ public abstract class Projection {
 	public static enum Type {
 		CYLINDRICAL("Cylindrical"), CONIC("Conic"), AZIMUTHAL("Azimuthal"),
 		PSEUDOCYLINDRICAL("Pseudocylindrical"), PSEUDOCONIC("Pseudoconic"),
-		PSEUDOAZIMUTHAL("Pseudoazimuthal"), QUASIAZIMUTHAL("Quasiazimuthal"),
+		PSEUDOAZIMUTHAL("Pseudoazimuthal"),
 		TETRAHEDRAL("Tetrahedral"), OCTOHEDRAL("Octohedral"),
 		TETRADECAHEDRAL("Truncated Octohedral"), ICOSOHEDRAL("Icosohedral"),
-		POLYNOMIAL("Polynomial"), STREBE("Strebe Blend"), PLANAR("Planar"), OTHER("Other");
+		POLYNOMIAL("Polynomial"), STREBE("Strebe blend"), PLANAR("Planar"), OTHER("Other");
 		
 		private String name;
 		

src/utils/NumericalAnalysis.java

@@ -138,6 +138,36 @@ public class NumericalAnalysis {
 	}
 	
 	
+	/**
+	 * Applies a bisection zero-finding scheme to find x such that f(x)=y
+	 * @param f The function whose zero must be found
+	 * @param xMin The lower bound for the zero
+	 * @param xMax The upper bound for the zero
+	 * @param tolerence The maximum error in x that this can return
+	 * @return The value of x that sets f to zero
+	 */
+	public static final double bisectionFind(DoubleUnaryOperator f,
+			double xMin, double xMax, double tolerance) {
+		double yMin = f.applyAsDouble(xMin);
+		double yMax = f.applyAsDouble(xMax);
+		if ((yMin < 0) == (yMax < 0))
+			throw new IllegalArgumentException("Bisection failed; bounds "+xMin+" and "+xMax+" do not necessarily straddle a zero.");
+		while (Math.abs(xMax - xMin) > tolerance) {
+			double x = (xMax + xMin)/2;
+			double y = f.applyAsDouble(x);
+			if ((y < 0) == (yMin < 0)) {
+				xMin = x;
+				yMin = y;
+			}
+			else {
+				xMax = x;
+				yMax = y;
+			}
+		}
+		return (xMax + xMin)/2;
+	}
+	
+	
 	/**
 	 * Applies Newton's method in one dimension to solve for x such that f(x)=y
 	 * @param y Desired value for f
@@ -145,7 +175,7 @@ public class NumericalAnalysis {
 	 * @param f The error in terms of x
 	 * @param dfdx The derivative of f with respect to x
 	 * @param tolerance The maximum error that this can return
-	 * @return The value of x that puts f near 0, or NaN if it does not converge in 5 iterations
+	 * @return The value of x that puts f near y, or NaN if it does not converge in 5 iterations
 	 */
 	public static final double newtonRaphsonApproximation(
 			double y, double x0, DoubleUnaryOperator f, DoubleUnaryOperator dfdx, double tolerance) {