From 5cf6bcd6e237c66b4565ee93773b9d82a1fba85c Mon Sep 17 00:00:00 2001
From: Justin Kunimune <justinkunimune@gmail.com>
Date: Tue, 15 Oct 2019 22:41:17 -0400
Subject: [PATCH] So many cones

I fixed up American polyconic, and I'm kind of glad I have it, even though it's a terrible map projection whose only application is making gores and Cassini is better for that, anyway.
---
 src/apps/MapApplication.java |  5 +++--
 src/maps/Lenticular.java     | 18 ++++++++++++++++--
 2 files changed, 19 insertions(+), 4 deletions(-)

diff --git a/src/apps/MapApplication.java b/src/apps/MapApplication.java
index 37ec021..2bd8e9b 100644
--- a/src/apps/MapApplication.java
+++ b/src/apps/MapApplication.java
@@ -145,8 +145,9 @@ public abstract class MapApplication extends Application {
 					Pseudocylindrical.MOLLWEIDE, ArbitraryPseudocylindrical.NATURAL_EARTH,
 					ArbitraryPseudocylindrical.ROBINSON, Pseudocylindrical.SINUSOIDAL,
 					Tobler.TOBLER, Pseudocylindrical.WAGNER_II, Pseudocylindrical.WAGNER_V },
-			{ Lenticular.EISENLOHR, Gyorffy.E, Lenticular.HAMMER, Lenticular.LAGRANGE,
-					Lenticular.STREBE_95, Lenticular.VAN_DER_GRINTEN, Lenticular.WAGNER_VIII,
+			{ Lenticular.AITOFF, Lenticular.POLYCONIC, Lenticular.EISENLOHR, Gyorffy.E,
+					Lenticular.HAMMER, Lenticular.LAGRANGE, Lenticular.STREBE_95,
+					Lenticular.VAN_DER_GRINTEN, Lenticular.WAGNER_VIII,
 					WinkelTripel.WINKEL_TRIPEL },
 			{ Misc.BONNE, Snyder.GS50, Misc.GUYOU, Misc.HAMMER_RETROAZIMUTHAL,
 					Pseudocylindrical.LEMONS, Misc.PEIRCE_QUINCUNCIAL, Misc.T_SHIRT,
diff --git a/src/maps/Lenticular.java b/src/maps/Lenticular.java
index 1bdeadd..b1f43d9 100644
--- a/src/maps/Lenticular.java
+++ b/src/maps/Lenticular.java
@@ -286,7 +286,7 @@ public class Lenticular {
 	
 	public static final Projection POLYCONIC = new Projection(
 			"American polyconic", "A map made for narrow strips of longitude that was really popular with the USGS for a while.",
-			2*Math.PI, 3.5, 0b1011, Type.OTHER, Property.EQUIDISTANT, 3) {
+			2*Math.PI, 4.81527, 0b1011, Type.OTHER, Property.EQUIDISTANT, 3) {
 		
 		public double[] project(double lat, double lon) {
 			if (lat == 0)
@@ -296,7 +296,21 @@ public class Lenticular {
 		}
 		
 		public double[] inverse(double x, double y) {
-			return null;
+			if (y < 0) { // the math gets inconvenient in the Southern Hemisphere
+				double[] refl = inverse(x, -y);
+				return new double[] {-refl[0], refl[1]};
+			}
+			else if (y == 0)
+				return new double[] {0, x};
+			
+			double logitLatGuess = Math.log(Math.hypot(x, y+Math.PI/2)/Math.hypot(x, y-Math.PI/2));
+			double lat = NumericalAnalysis.bisectionFind(
+					(ph)->(Math.pow(x, 2) + Math.pow(y - ph, 2) - 2*(y - ph)/Math.tan(ph)),
+					0, Math.PI/2*(Math.exp(logitLatGuess) - 1)/(Math.exp(logitLatGuess) + 1), // this guess is pretty complicated, but I'm proud of it
+					1e-4);
+			if (Double.isNaN(lat))
+				return null;
+			return new double[] { lat, Math.atan2(x, -(y - lat - 1/Math.tan(lat)))/Math.sin(lat) };
 		}
 	};