From b095d00ee67affff4acecd15e505f5d79bdf200a Mon Sep 17 00:00:00 2001
From: jkunimune <jkunimune@522MT32.olin.edu>
Date: Mon, 21 Nov 2016 15:39:18 -0500
Subject: [PATCH] Reinforced the North-Up Convention

So, it turns out that one of the reasons I was having such trouble with
AuthaGraph was that I had a sign convention where south was positive and
the international date line was zero. So, I fixed that, because that was
awful. It should be easier for me to figure out polyhedric projections
now. Mind you, AuthaGraph doesn't work at all right now. It's just not
even close right now. Don't worry - I'll work on that.
---
 bin/MapProjections.class | Bin 21502 -> 21710 bytes
 src/MapProjections.java  | 138 ++++++++++++++++++++++-----------------
 2 files changed, 78 insertions(+), 60 deletions(-)

diff --git a/bin/MapProjections.class b/bin/MapProjections.class
index ae52a132346f8a0bc788e2398c2955b78fb627b3..5dab5e0fa8ef37b396b5821ab3985bb078d063c5 100644
GIT binary patch
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diff --git a/src/MapProjections.java b/src/MapProjections.java
index baf8d24..2ab24d6 100644
--- a/src/MapProjections.java
+++ b/src/MapProjections.java
@@ -18,6 +18,7 @@ import javafx.scene.control.Label;
 import javafx.scene.control.MenuButton;
 import javafx.scene.control.MenuItem;
 import javafx.scene.control.Slider;
+import javafx.scene.control.Spinner;
 import javafx.scene.control.Tooltip;
 import javafx.scene.image.Image;
 import javafx.scene.image.ImageView;
@@ -57,7 +58,7 @@ public class MapProjections extends Application {
 			"Represents earth viewed from an infinite distance",
 			"Every straight line on the map is a straight line on the sphere", "A conformal conical map",
 			"The compromise map used by National Geographic (caution: very slow)", "A circular compromise map",
-			"An equal-area map shaped like an elipse", "An equal-area map shaped like an elipse",
+			"An equal-area map shaped like an ellipse", "An equal-area map shaped like an elipse",
 			"An equal-area map shaped like a sinusoid", "BURN LIFE'S HOUSE DOWN!",
 			"A conformal square map that uses complex math",
 			"A reorganized version of Pierce Quincuncial and actually the best map ever",
@@ -66,10 +67,10 @@ public class MapProjections extends Application {
 			"What happens when you apply a complex differentiable function to a stereographic projection?" };
 	
 	private static final String[] AXES = { "Standard", "Transverse", "Center of Mass", "Jerusalem", "Point Nemo",
-			"Longest Line", "Longest Line Transverse", "Cylindrical", "Conical", "Quincuncial", "Random" };
-	private static final double[] DEF_LATS = { 90, 0, 29.9792, 31.7833, 48.8767, -28.5217, -46.4883, -35, -10, 60, Double.NaN };
-	private static final double[] DEF_LONS = { 0, 0, 31.1344, 35.216, 56.6067, 141.451, 16.5305, -13.6064, 65, -6, Double.NaN };
-	private static final double[] DEF_THTS = { 0, 0, -32, -35, -45, 71.5, 137, 145, -150, -10, Double.NaN };
+			"Longest Line", "Longest Line Transverse", "Cylindrical", "Conical", "Quincuncial", "Antipode", "Random" };
+	private static final double[] DEF_LATS = { 90, 0, 29.9792, 31.7833, 48.8767, -28.5217, -46.4883, -35, -10, 60 };
+	private static final double[] DEF_LONS = { 0, 0, 31.1344, 35.216, 56.6067, 141.451, 16.5305, -13.6064, 65, -6 };
+	private static final double[] DEF_THTS = { 0, 0, -32, -35, -45, 161.5, 137, 145, -150, -10 };
 	
 	
 	private FileChooser inputChooser, saver;
@@ -138,14 +139,14 @@ public class MapProjections extends Application {
 			}
 		});
 		projectionChooser.setPrefWidth(200);
-		projectionChooser.setValue("Mercator");
+		projectionChooser.setValue(PROJ_ARR[1]);
 		layout.getChildren().add(new HBox(3, lbl, projectionChooser));
 		
-		projectionDesc = new Text("Please choose a projection.");
+		projectionDesc = new Text(DESC[1]);
 		projectionDesc.setWrappingWidth(CONT_WIDTH);
 		layout.getChildren().add(projectionDesc);
 		
-		final MenuButton defAxes = new MenuButton("Axis Presets");
+		final MenuButton defAxes = new MenuButton("Aspect Presets");
 		for (String preset: AXES) {
 			MenuItem m = new MenuItem(preset);
 			m.setOnAction(new EventHandler<ActionEvent>() {
@@ -156,12 +157,16 @@ public class MapProjections extends Application {
 			defAxes.getItems().add(m);
 		}
 		defAxes.setTooltip(new Tooltip(
-				"Set the axis sliders based on a preset"));
+				"Set the aspect sliders based on a preset"));
 		layout.getChildren().add(defAxes);
 		
 		latSlider = new Slider(-90, 90, 90);
 		lonSlider = new Slider(-180,180,0);
 		thtSlider = new Slider(-180,180,0);
+		Tooltip aspTlTp = new Tooltip("Change the aspect of the map");
+		latSlider.setTooltip(aspTlTp);
+		lonSlider.setTooltip(aspTlTp);
+		thtSlider.setTooltip(aspTlTp);
 		
 		GridPane grid = new GridPane();
 		grid.addRow(0, new Text("Latitude:"), latSlider);
@@ -227,6 +232,12 @@ public class MapProjections extends Application {
 	
 	
 	private void setAxisByPreset(String preset) {
+		if (preset.equals("Antipode")) {
+			latSlider.setValue(-latSlider.getValue());
+			lonSlider.setValue((lonSlider.getValue()+360)%360-180);
+			thtSlider.setValue(-thtSlider.getValue());
+			return;
+		}
 		if (preset.equals("Random")) {
 			latSlider.setValue(Math.toDegrees(Math.asin(Math.random()*2-1)));
 			lonSlider.setValue(Math.random()*360-180);
@@ -273,7 +284,7 @@ public class MapProjections extends Application {
 		final int[] refDims = {(int)width, (int)height};
 		final String p = projectionChooser.getValue();
 		final double X = 2.0*x/outputWidth-1;
-		final double Y = 2.0*y/outputHeight-1;
+		final double Y = 1-2.0*y/outputHeight;
 		if (p.equals("Pierce Quincuncial"))
 			return quincuncial(pole, X, Y, refDims, input);
 		else if (p.equals("Equirectangular"))
@@ -327,8 +338,8 @@ public class MapProjections extends Application {
 		Complex k = new Complex(Math.sqrt(0.5)); // the rest comes from some fancy complex calculus
 		Complex ans = Jacobi.cn(u, k);
 		double p = 2 * Math.atan(ans.abs());
-		double theta = Math.atan2(ans.getRe(), ans.getIm()) + Math.PI;
-		double lambda = p - Math.PI / 2;
+		double theta = Math.atan2(ans.getIm(), ans.getRe()) - Math.PI/2;
+		double lambda = Math.PI/2 - p;
 		return getColor(pole, lambda, theta, refDims, ref);
 	}
 	
@@ -336,15 +347,15 @@ public class MapProjections extends Application {
 	private static int experiment(final double[] pole, double x, double y,
 			int[] refDims, Image ref) { // just some random complex plane stuff
 		Complex z = new Complex(x*3, y*3);
-		Complex ans = z.neg().exp().minus(1).neg().invert();
+		Complex ans = z;
 		double p = 2 * Math.atan(ans.abs());
-		double theta = Math.atan2(ans.getRe(), ans.getIm()) + Math.PI;
-		double lambda = p - Math.PI / 2;
+		double theta = Math.atan2(ans.getIm(), ans.getRe()) + Math.PI/2;
+		double lambda = Math.PI/2 - p;
 		return getColor(pole, lambda, theta, refDims, ref);
 	}
 	
 	private static int equirectangular(final double[] pole, double x, double y,
-			int[] refDims, Image ref) { // a basic scale
+			int[] refDims, Image ref) { // a linear scale
 		return getColor(pole, y*Math.PI/2, x*Math.PI, refDims, ref);
 	}
 	
@@ -356,9 +367,10 @@ public class MapProjections extends Application {
 	
 	private static int polar(final double[] pole, double x, double y,
 			int[] refDims, Image ref) { // the projection used on the UN flag
-		double phi = Math.PI * Math.hypot(x, y) - Math.PI/2;
+		double phi = Math.PI/2 - Math.PI * Math.hypot(x, y);
 		if (Math.abs(phi) < Math.PI/2)
-			return getColor(pole, phi, Math.atan2(x, y), refDims, ref);
+			return getColor(pole, phi, Math.atan2(y, x) + Math.PI/2,
+					refDims, ref);
 		else
 			return 0;
 	}
@@ -376,21 +388,21 @@ public class MapProjections extends Application {
 	
 	private static int stereographic(final double[] pole, double x, double y,
 			int[] refDims, Image ref) { // a shape-preserving infinite map
-		return getColor(pole, 2*Math.atan(2*Math.hypot(x, y)) - Math.PI/2,
-				Math.atan2(x, y), refDims, ref);
+		return getColor(pole, Math.PI/2 - 2*Math.atan(2*Math.hypot(x, y)),
+				Math.atan2(y, x) + Math.PI/2, refDims, ref);
 	}
 	
 	private static int gnomonic(final double[] pole, double x, double y,
 			int[] refDims, Image ref) { // map where straight lines are straight
-		return getColor(pole, Math.atan(2*Math.hypot(x, y)) - Math.PI/2,
-				Math.atan2(x, y), refDims, ref);
+		return getColor(pole, Math.PI/2 - Math.atan(2*Math.hypot(x, y)),
+				Math.atan2(y, x) + Math.PI/2, refDims, ref);
 	}
 	
 	private static int orthographic(final double[] pole, double x, double y,
 			int[] refDims, Image ref) { // a map that mimics the view from space
 		double R = Math.hypot(x, y);
 		if (R <= 1)
-			return getColor(pole, -Math.acos(R), Math.atan2(x, y),
+			return getColor(pole, Math.acos(R), Math.atan2(y, x) + Math.PI/2,
 					refDims, ref);
 		else
 			return 0;
@@ -403,10 +415,10 @@ public class MapProjections extends Application {
 	
 	private static int lambert(final double[] pole, double x, double y,
 			int[] refDims, Image ref) { // a conical projection
-		y = (y+1)/2;
+		y = (y-1)/2;
 		return getColor(pole,
-				2*Math.atan(Math.pow(1.5*Math.hypot(x, y), 2)) - Math.PI/2,
-				2*Math.atan2(x, y), refDims, ref);
+				Math.PI/2 - 2*Math.atan(Math.pow(1.5*Math.hypot(x, y), 2)),
+				2*(Math.atan2(y, x) + Math.PI/2), refDims, ref);
 	}
 	
 	private static int lemons(final double[] pole, double x, double y,
@@ -427,8 +439,8 @@ public class MapProjections extends Application {
 			final int[] refDims, Image ref) { // the lambert azimuthal equal area projection
 		double R = Math.hypot(x, y);
 		if (R <= 1)
-			return getColor(pole, Math.asin(2*R*R - 1), Math.atan2(x, y),
-					refDims, ref);
+			return getColor(pole, Math.asin(1 - 2*R*R),
+					Math.atan2(y, x) + Math.PI/2, refDims, ref);
 		else
 			return 0;
 	}
@@ -439,8 +451,8 @@ public class MapProjections extends Application {
 		Complex k = new Complex(Math.sqrt(0.5)); // the rest comes from some fancy complex calculus
 		Complex ans = Jacobi.cn(u, k);
 		double p = 2 * Math.atan(ans.abs());
-		double theta = Math.atan2(ans.getRe(), ans.getIm());
-		double lambda = p - Math.PI / 2;
+		double theta = Math.atan2(ans.getIm(), ans.getRe());
+		double lambda = Math.PI/2 - p;
 		return getColor(pole, lambda, theta, refDims, ref);
 	}
 	
@@ -508,8 +520,8 @@ public class MapProjections extends Application {
 			int[] refDims, Image ref) { // a novelty map that magnifies the center profusely
 		double R = Math.hypot(x, y);
 		if (R <= 1)
-			return getColor(pole, Math.PI/2 * (R*R*R*1.8 + R*.2 - 1),
-					Math.atan2(x, y), refDims, ref);
+			return getColor(pole, Math.PI/2 * (1 - R*.2 - R*R*R*1.8),
+					Math.atan2(y, x) + Math.PI/2, refDims, ref);
 		else
 			return 0;
 	}
@@ -529,43 +541,46 @@ public class MapProjections extends Application {
 		final double[] faceCenter = new double[3];
 		final double localX, localY;
 		if (y+1 > 4*x && y+1 > -4*x) {
-			faceCenter[0] = Math.PI/2-Math.asin(Math.sqrt(8)/3);
-			faceCenter[1] = Math.PI;
+			//faceCenter[0] = Math.asin(Math.sqrt(8)/3)-Math.PI/2;
+			faceCenter[0] = -1;
+			faceCenter[1] = 0;
 			faceCenter[2] = 0;
 			localX = 2*x;
 			localY = y-1/3.0;
 		}
 		else if (y+1 > 4*(x+1)) {
-			faceCenter[0] = -Math.PI/2;
+			faceCenter[0] = Math.PI/2;
 			faceCenter[1] = 0;
 			faceCenter[2] = 0;
 			localX = 2*(x+1);
 			localY = y-1/3.0;
 		}
 		else if (y+1 > -4*(x-1)) {
-			faceCenter[0] = -Math.PI/2;
+			faceCenter[0] = Math.PI/2;
 			faceCenter[1] = 0;
 			faceCenter[2] = 0;
 			localX = 2*(x-1);
 			localY = y-1/3.0;
 		}
 		else if (x < 0) {
-			faceCenter[0] = Math.PI/2-Math.asin(Math.sqrt(8)/3);
-			faceCenter[1] = Math.PI/3;
+			faceCenter[0] = Math.asin(Math.sqrt(8)/3)-Math.PI/2;
+			faceCenter[1] = 4*Math.PI/3;
 			faceCenter[2] = Math.PI/3;
 			localX = 2*(x+0.5);
 			localY = y+1/3.0;
 		}
 		else {
-			faceCenter[0] = Math.PI/2-Math.asin(Math.sqrt(8)/3);
-			faceCenter[1] =5*Math.PI/3;
+			faceCenter[0] = Math.asin(Math.sqrt(8)/3)-Math.PI/2;
+			faceCenter[1] =2*Math.PI/3;
 			faceCenter[2] = -Math.PI/3;
 			localX = 2*(x-0.5);
 			localY = y+1/3.0;
 		}
 		
 		double[] newPole = obliquify(pole, faceCenter);
-		return gnomonic(newPole, localX, localY, refDims, ref);
+		return getColor(newPole,
+				Math.PI/2 - Math.atan(2.35*Math.hypot(localX, localY)),
+				Math.atan2(localY, localX) + Math.PI/2, refDims, ref);
 	}
 	
 	
@@ -573,8 +588,8 @@ public class MapProjections extends Application {
 			int[] refDims, Image input) { // returns the color of any coordinate on earth
 		final double[] coords = {lat, lon};
 		final double[] convCoords = obliquify(pole, coords);
-		double x = convCoords[1] / (2*Math.PI);
-		double y = convCoords[0] * refDims[1] / Math.PI + refDims[1]/2.0;
+		double x = convCoords[1]/(2*Math.PI) + refDims[0]/2.0;
+		double y = refDims[1]/2.0 - convCoords[0]*refDims[1]/Math.PI;
 		
 		x = (x - Math.floor(x)) * refDims[0];
 		if (y < 0)
@@ -593,29 +608,32 @@ public class MapProjections extends Application {
 		double lat1 = coords[0];
 		double lon1 = coords[1];
 		lon1 += tht0;
-		double latitude = Math.asin(Math.sin(lat0) * Math.sin(lat1) + Math.cos(lat0) * Math.cos(lon1) * Math.cos(lat1));
-		double longitude;
-		double innerFunc = Math.sin(lat1) / Math.cos(lat0) / Math.cos(latitude) - Math.tan(lat0) * Math.tan(latitude);
+		double latf = Math.asin(Math.sin(lat0)*Math.sin(lat1) - Math.cos(lat0)*Math.cos(lon1)*Math.cos(lat1));
+		double lonf;
+		double innerFunc = Math.sin(lat1)/Math.cos(lat0)/Math.cos(latf) - Math.tan(lat0)*Math.tan(latf);
 		if (lat0 == Math.PI / 2) // accounts for special case when lat0 = pi/2
-			longitude = lon1+lon0 + Math.PI;
+			lonf = lon1+lon0+Math.PI;
 		else if (lat0 == -Math.PI / 2) // accounts for special case when lat0 = -pi/2
-			longitude = -lon1+lon0;
-		else if (Math.abs(innerFunc) > 1) { // accounts for special case when
-											// cos(lat) = --> 0
-			if ((lon1 == Math.PI && lat1 < -lat0) || (lon1 != Math.PI && lat1 < lat0))
-				longitude = Math.PI + lon0;
+			lonf = -lon1+lon0;
+		else if (Math.abs(innerFunc) > 1) { // accounts for special case when cos(lat1) = --> 0
+			if ((lon1 == 0 && lat1 < -lat0) || (lon1 != 0 && lat1 < lat0))
+				lonf = lon0;
 			else
-				longitude = lon0;
-		} else if (Math.sin(lon1) < 0)
-			longitude = lon0 + Math
-					.acos(Math.sin(lat1) / Math.cos(lat0) / Math.cos(latitude) - Math.tan(lat0) * Math.tan(latitude));
+				lonf = lon0 + Math.PI;
+		} else if (Math.sin(lon1) > 0)
+			lonf = Math.PI + lon0 +
+					Math.acos(Math.sin(lat1) / Math.cos(lat0)/Math.cos(latf) - Math.tan(lat0)*Math.tan(latf));
 		else
-			longitude = lon0 - Math.acos(Math.sin(lat1) / Math.cos(lat0) / Math.cos(latitude) - Math.tan(lat0) * Math.tan(latitude));
-		double orientation = (Math.cos(lat0)*Math.sin(lat0)-Math.tan(latitude)*Math.sin(lat1)+Math.tan(latitude)*Math.sin(latitude)*Math.sin(lat0))/Math.cos(lat1);
+			lonf = Math.PI + lon0 -
+					Math.acos(Math.sin(lat1)/Math.cos(lat0)/Math.cos(latf) - Math.tan(lat0)*Math.tan(latf));
 		
-		double[] output = {latitude, longitude, orientation};
+		double P = Math.sin(lat0)*Math.cos(latf)-Math.cos(lat0)*Math.sin(latf)*Math.cos(lonf-lon0);
+		double thtf = Math.acos(P/Math.cos(lat1));
+		thtf = 0;
 		if (coords.length >= 3)
-			output[2] += coords[2];	// carry forward some information if necessary
+			thtf += coords[2];
+		
+		double[] output = {latf, lonf, thtf};
 		return output;
 	}
 }
\ No newline at end of file