From 2e5205e379ba0edc3de2682470ba45d6146e0151 Mon Sep 17 00:00:00 2001
From: Justin Kunimune <justinkunimune@gmail.com>
Date: Thu, 14 Dec 2023 14:08:14 -0800
Subject: [PATCH] attention to detail

I went thru and corrected numerus inspection warnings.  I'd say most of it is correcting typos.  I also removed a bunch of unused variables and methods (and even a cupple of files), adjusted varius stylings, improved a few docstrings, made local variables where one quantity was getting calculated multiple times, and cetera.  the spiciest thing was that I refatord the part where it saves a screenshot of the graphs in the MapAnalyzer; previusly it was bizzy-waiting for the GUI thread to finish taking the screenshot, which was probably fine, but now it uses FutureTask.get(), which is probably faster and definitely cleaner.  I also deleted the code for the two-point equalized projection because it was bad and didn't work very well (to be precise it wasn't in use after I removed it from the projection list a few days ago so this is just codifying that renunciation).  I also made AuthaGraph fixd instead of parameterized because I think that was just a mistake.
---
 input/Advanced/Template countries.svg         |   5 +-
 input/Advanced/Test.svg                       |   1 -
 input/Advanced/Tissot Wikipedia +0.svg        |   1 -
 input/Advanced/Tissot Wikipedia -20.svg       |   1 -
 input/Basic.svg                               |   1 -
 input/Compound.svg                            |   1 -
 input/Graticule.svg                           |   1 -
 input/Orthodromes.svg                         |   9 +-
 input/Political.svg                           |   1 -
 input/{Sillouette.png => Silhouette.png}      | Bin
 input/Simplified.svg                          |   1 -
 input/Tissot.svg                              |   1 -
 src/apps/MapAnalyzer.java                     |  28 +++--
 src/apps/MapApplication.java                  |  13 +--
 src/apps/MapConverter.java                    |  63 ++++++------
 src/apps/MapEvaluator.java                    |   4 +-
 src/apps/MapExplainer.java                    |  10 +-
 src/apps/MapOptimizer.java                    |  12 +--
 src/apps/MapPlotter.java                      |   2 +-
 src/dialogs/ProjectionSelectionDialog.java    |   4 +-
 src/image/ImageUtils.java                     |  11 +-
 src/image/SVGMap.java                         |  12 +--
 src/maps/CahillKeyes.java                     |   5 +-
 src/maps/Elastic.java                         |   8 +-
 src/maps/Misc.java                            |   4 +-
 src/maps/MyProjections.java                   |  92 -----------------
 src/maps/Octahedral.java                      |   2 +-
 src/maps/Polyhedral.java                      |  39 +++----
 src/maps/Projection.java                      |  72 ++++---------
 src/maps/Waterman.java                        |   7 +-
 src/maps/WinkelTripel.java                    |   2 +-
 src/utils/Dixon.java                          |   2 +-
 src/utils/Math2.java                          |  48 +--------
 src/utils/MutableDouble.java                  |   6 +-
 src/utils/SAXUtils.java                       |  46 ---------
 src/zupplemental/generate_graticule.py        |   4 +-
 src/zupplemental/generate_orthodromes.py      |   2 +-
 src/zupplemental/generate_political_shapes.py |  20 ++--
 src/zupplemental/generate_shapes.py           |   3 +-
 src/zupplemental/helpers.py                   |  96 +++++++++++-------
 40 files changed, 203 insertions(+), 437 deletions(-)
 rename input/{Sillouette.png => Silhouette.png} (100%)
 delete mode 100644 src/maps/MyProjections.java
 delete mode 100644 src/utils/SAXUtils.java

diff --git a/input/Advanced/Template countries.svg b/input/Advanced/Template countries.svg
index c1437cc..ad8cf61 100644
--- a/input/Advanced/Template countries.svg	
+++ b/input/Advanced/Template countries.svg	
@@ -3,7 +3,6 @@
 	 xmlns:dc="http://purl.org/dc/elements/1.1/"
 	 xmlns:cc="http://creativecommons.org/ns#"
 	 xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
-	 xmlns:svg="http://www.w3.org/2000/svg"
 	 xmlns="http://www.w3.org/2000/svg"
 	 width="2048"
 	 height="1024"
@@ -15,7 +14,7 @@
 				<rdf:Description
 					 about="https://github.com/jkunimune/Map-Projections/"
 					 dc:title="Blank world map (de facto country borders)"
-					 dc:description="A map of the world, showing all countries' defacto borders, with major lakes overlaid. Borders precise to 110km. Equirectangular projection."
+					 dc:description="A map of the world, showing all countries' de facto borders, with major lakes overlaid. Borders precise to 110km. Equirectangular projection."
 					 dc:creator="Justin Kunimune"
 					 dc:source="http://www.naturalearthdata.com/"
 					 dc:date="2018-02-04"
@@ -35,7 +34,7 @@
 	</metadata>
 	<title>Blank world map (de facto country borders)</title>
 	<desc>
-		A map of the world, showing all countries' defacto borders, with major lakes overlaid. Borders precise to 110km. Equirectangular projection.
+		A map of the world, showing all countries' de facto borders, with major lakes overlaid. Borders precise to 110km. Equirectangular projection.
 	</desc>
 	<style type="text/css">
 		.country {
diff --git a/input/Advanced/Test.svg b/input/Advanced/Test.svg
index 580080c..2d353ae 100644
--- a/input/Advanced/Test.svg
+++ b/input/Advanced/Test.svg
@@ -3,7 +3,6 @@
 	 xmlns:dc="http://purl.org/dc/elements/1.1/"
 	 xmlns:cc="http://creativecommons.org/ns#"
 	 xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
-	 xmlns:svg="http://www.w3.org/2000/svg"
 	 xmlns="http://www.w3.org/2000/svg"
 	 width="2048"
 	 height="1024"
diff --git a/input/Advanced/Tissot Wikipedia +0.svg b/input/Advanced/Tissot Wikipedia +0.svg
index 8ceddf1..1a4fcb0 100644
--- a/input/Advanced/Tissot Wikipedia +0.svg	
+++ b/input/Advanced/Tissot Wikipedia +0.svg	
@@ -3,7 +3,6 @@
 	 xmlns:dc="http://purl.org/dc/elements/1.1/"
 	 xmlns:cc="http://creativecommons.org/ns#"
 	 xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
-	 xmlns:svg="http://www.w3.org/2000/svg"
 	 xmlns="http://www.w3.org/2000/svg"
 	 width="1600"
 	 height="800"
diff --git a/input/Advanced/Tissot Wikipedia -20.svg b/input/Advanced/Tissot Wikipedia -20.svg
index f5b0662..c2ecf57 100644
--- a/input/Advanced/Tissot Wikipedia -20.svg	
+++ b/input/Advanced/Tissot Wikipedia -20.svg	
@@ -3,7 +3,6 @@
 	 xmlns:dc="http://purl.org/dc/elements/1.1/"
 	 xmlns:cc="http://creativecommons.org/ns#"
 	 xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
-	 xmlns:svg="http://www.w3.org/2000/svg"
 	 xmlns="http://www.w3.org/2000/svg"
 	 width="1600"
 	 height="800"
diff --git a/input/Basic.svg b/input/Basic.svg
index 01b43bc..775790d 100644
--- a/input/Basic.svg
+++ b/input/Basic.svg
@@ -3,7 +3,6 @@
 	 xmlns:dc="http://purl.org/dc/elements/1.1/"
 	 xmlns:cc="http://creativecommons.org/ns#"
 	 xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
-	 xmlns:svg="http://www.w3.org/2000/svg"
 	 xmlns="http://www.w3.org/2000/svg"
 	 width="2048"
 	 height="1024"
diff --git a/input/Compound.svg b/input/Compound.svg
index b359367..341addd 100644
--- a/input/Compound.svg
+++ b/input/Compound.svg
@@ -3,7 +3,6 @@
 	 xmlns:dc="http://purl.org/dc/elements/1.1/"
 	 xmlns:cc="http://creativecommons.org/ns#"
 	 xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
-	 xmlns:svg="http://www.w3.org/2000/svg"
 	 xmlns="http://www.w3.org/2000/svg"
 	 width="2048"
 	 height="1024"
diff --git a/input/Graticule.svg b/input/Graticule.svg
index caeb872..82e1ce4 100644
--- a/input/Graticule.svg
+++ b/input/Graticule.svg
@@ -3,7 +3,6 @@
 	 xmlns:dc="http://purl.org/dc/elements/1.1/"
 	 xmlns:cc="http://creativecommons.org/ns#"
 	 xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
-	 xmlns:svg="http://www.w3.org/2000/svg"
 	 xmlns="http://www.w3.org/2000/svg"
 	 width="2048"
 	 height="1024"
diff --git a/input/Orthodromes.svg b/input/Orthodromes.svg
index f40eea3..badc43e 100644
--- a/input/Orthodromes.svg
+++ b/input/Orthodromes.svg
@@ -3,7 +3,6 @@
 	 xmlns:dc="http://purl.org/dc/elements/1.1/"
 	 xmlns:cc="http://creativecommons.org/ns#"
 	 xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
-	 xmlns:svg="http://www.w3.org/2000/svg"
 	 xmlns="http://www.w3.org/2000/svg"
 	 width="2048"
 	 height="1024"
@@ -14,8 +13,8 @@
 			<cc:work>
 				<rdf:Description
 					 about="https://github.com/jkunimune/Map-Projections/"
-					 dc:title="Icosohedral orthodromic mesh - Equirectangular projection"
-					 dc:description="A mesh of great circles that intersect with 10-fold symmetry at 12 principal nodes and 6-fold symmetry at 20 minor nodes. Aligns with the edges of an icosohedron and its dual dodecahedron."
+					 dc:title="Icosahedral orthodromic mesh - Equirectangular projection"
+					 dc:description="A mesh of great circles that intersect with 10-fold symmetry at 12 principal nodes and 6-fold symmetry at 20 minor nodes. Aligns with the edges of an icosahedron and its dual dodecahedron."
 					 dc:creator="Justin Kunimune"
 					 dc:source="http://www.naturalearthdata.com/"
 					 dc:date="2018-02-04"
@@ -33,9 +32,9 @@
 			</cc:License>
 		</rdf:RDF>
 	</metadata>
-	<title>Icosohedral orthodromic mesh &#8211; Equirectangular projection</title>
+	<title>Icosahedral orthodromic mesh &#8211; Equirectangular projection</title>
 	<desc>
-		A mesh of great circles that intersect with 10-fold symmetry at 12 principal nodes and 6-fold symmetry at 20 minor nodes. Aligns with the edges of an icosohedron and its dual dodecahedron.
+		A mesh of great circles that intersect with 10-fold symmetry at 12 principal nodes and 6-fold symmetry at 20 minor nodes. Aligns with the edges of an icosahedron and its dual dodecahedron.
 	</desc>
 	<style type="text/css">
 		.lines {
diff --git a/input/Political.svg b/input/Political.svg
index 634c941..4edea15 100644
--- a/input/Political.svg
+++ b/input/Political.svg
@@ -3,7 +3,6 @@
 	 xmlns:dc="http://purl.org/dc/elements/1.1/"
 	 xmlns:cc="http://creativecommons.org/ns#"
 	 xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
-	 xmlns:svg="http://www.w3.org/2000/svg"
 	 xmlns="http://www.w3.org/2000/svg"
 	 width="2048"
 	 height="1024"
diff --git a/input/Sillouette.png b/input/Silhouette.png
similarity index 100%
rename from input/Sillouette.png
rename to input/Silhouette.png
diff --git a/input/Simplified.svg b/input/Simplified.svg
index c1b077f..dca8a8c 100644
--- a/input/Simplified.svg
+++ b/input/Simplified.svg
@@ -3,7 +3,6 @@
 	 xmlns:dc="http://purl.org/dc/elements/1.1/"
 	 xmlns:cc="http://creativecommons.org/ns#"
 	 xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
-	 xmlns:svg="http://www.w3.org/2000/svg"
 	 xmlns="http://www.w3.org/2000/svg"
 	 width="2048"
 	 height="1024"
diff --git a/input/Tissot.svg b/input/Tissot.svg
index 4b566f1..f8acc3a 100644
--- a/input/Tissot.svg
+++ b/input/Tissot.svg
@@ -3,7 +3,6 @@
 	 xmlns:dc="http://purl.org/dc/elements/1.1/"
 	 xmlns:cc="http://creativecommons.org/ns#"
 	 xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
-	 xmlns:svg="http://www.w3.org/2000/svg"
 	 xmlns="http://www.w3.org/2000/svg"
 	 width="2048"
 	 height="1024"
diff --git a/src/apps/MapAnalyzer.java b/src/apps/MapAnalyzer.java
index 44896de..02e1714 100644
--- a/src/apps/MapAnalyzer.java
+++ b/src/apps/MapAnalyzer.java
@@ -25,11 +25,11 @@ package apps;
 
 import image.ImageUtils;
 import image.SavableImage;
+import javafx.application.Platform;
 import javafx.concurrent.Task;
 import javafx.embed.swing.SwingFXUtils;
 import javafx.geometry.Insets;
 import javafx.geometry.Pos;
-import javafx.scene.SnapshotResult;
 import javafx.scene.chart.BarChart;
 import javafx.scene.chart.CategoryAxis;
 import javafx.scene.chart.NumberAxis;
@@ -38,6 +38,7 @@ import javafx.scene.chart.XYChart.Series;
 import javafx.scene.control.Label;
 import javafx.scene.control.Separator;
 import javafx.scene.image.ImageView;
+import javafx.scene.image.WritableImage;
 import javafx.scene.layout.HBox;
 import javafx.scene.layout.Region;
 import javafx.scene.layout.StackPane;
@@ -53,6 +54,7 @@ import utils.Procedure;
 import java.awt.Color;
 import java.awt.Graphics2D;
 import java.awt.image.BufferedImage;
+import java.util.concurrent.ExecutionException;
 import java.util.function.DoubleUnaryOperator;
 
 import static java.lang.Double.isFinite;
@@ -194,20 +196,16 @@ public class MapAnalyzer extends MapApplication {
 	
 	private Task<SavableImage> calculatePlotTask() {
 		Task<SavableImage> task = new Task<SavableImage>() {
-			private SnapshotResult snapRes = null;
-			
-			protected void running() {
-				charts.snapshot((snapRes) -> {
-					this.snapRes = snapRes;
-					return null;
-				}, null, null);
-			}
-			
-			protected SavableImage call() { //yeah, this is weird and dumb, but only because the
-				updateProgress(-1, 1); //snapshot method is dumb. Why does it have to be called on
-				updateMessage("Converting graph\u2026"); //the GUI thread? It's clearly doing Thread
-				while (!isCancelled() && snapRes == null) {} //things, judging by the fact that it
-				return SavableImage.savable(snapRes.getImage()); //_has_ a Callback version
+			protected SavableImage call() throws ExecutionException, InterruptedException {
+				updateProgress(-1, 1);
+				updateMessage("Converting graph\u2026");
+				Task<WritableImage> snapshotTask = new Task<>() {
+					protected WritableImage call() {
+						return charts.snapshot(null, null);
+					}
+				};
+				Platform.runLater(snapshotTask);
+				return SavableImage.savable(snapshotTask.get());
 			}
 		};
 		disableWhile(task.runningProperty(), ButtonType.SAVE_GRAPH);
diff --git a/src/apps/MapApplication.java b/src/apps/MapApplication.java
index 14b8ae0..090ab26 100644
--- a/src/apps/MapApplication.java
+++ b/src/apps/MapApplication.java
@@ -74,7 +74,6 @@ import maps.EqualEarth;
 import maps.Gyorffy;
 import maps.Lenticular;
 import maps.Misc;
-import maps.MyProjections;
 import maps.Octahedral;
 import maps.Polyhedral;
 import maps.Projection;
@@ -224,7 +223,7 @@ public abstract class MapApplication extends Application {
 			FileChooser.ExtensionFilter defaultExtension,
 			Function<File, Task<Void>> inputSetter) {
 		final Label label = new Label("Current input:");
-		final Text inputLabel = new Text("Basic"+defaultExtension.getExtensions().get(0).substring(1)); //this line kind of cheats, since it assumes the first input will be called "Basic", but I couldn't figure out a good way for this to update when the subclass programatically sets the input
+		final Text inputLabel = new Text("Basic"+defaultExtension.getExtensions().get(0).substring(1)); //this line kind of cheats, since it assumes the first input will be called "Basic", but I couldn't figure out a good way for this to update when the subclass programmatically sets the input
 		
 		final FileChooser inputChooser = new FileChooser();
 		inputChooser.setInitialDirectory(new File("input"));
@@ -415,9 +414,7 @@ public abstract class MapApplication extends Application {
 		final CheckBox cropBox = new CheckBox("Crop at antimeridian"); //the CheckBox for whether there should be shown imagery beyond += 180 degrees
 		cropBox.setSelected(cropAtIDL.isSet());
 		cropBox.setTooltip(new Tooltip("Hide points of extreme longitude."));
-		cropBox.selectedProperty().addListener((observable, old, now) -> {
-				cropAtIDL.set(now);
-			});
+		cropBox.selectedProperty().addListener((observable, old, now) -> cropAtIDL.set(now));
 		
 		final ObservableList<Double> factorsOf90 = FXCollections.observableArrayList();
 		for (double f = 1; f <= 90; f += 0.5)
@@ -533,9 +530,7 @@ public abstract class MapApplication extends Application {
 									"Could not access "+f.getAbsolutePath()+". It's possible that another program has it open.");
 						}
 						pBar.close();
-//						try {
-//							Desktop.getDesktop().open(f.getParentFile()); // TODO: show a popup here with a button to open the folder inste of of doing it automatically
-//						} catch (IOException e) {} //if you can't open the directory for some reason, don't worry about it.
+//						// TODO: show a popup here with a button to open the folder
 					});
 					disableWhile(task.runningProperty(), buttonType);
 					new Thread(task).start(); //now execute!
@@ -698,7 +693,7 @@ public abstract class MapApplication extends Application {
 	
 	
 	protected enum ButtonType {
-		LOAD_INPUT, UPDATE_MAP, SAVE_MAP, SAVE_GRAPH;
+		LOAD_INPUT, UPDATE_MAP, SAVE_MAP, SAVE_GRAPH
 	}
 }
 
diff --git a/src/apps/MapConverter.java b/src/apps/MapConverter.java
index 7536d1a..027329a 100644
--- a/src/apps/MapConverter.java
+++ b/src/apps/MapConverter.java
@@ -49,41 +49,42 @@ public class MapConverter {
 		// the desired map projection
 		Projection projection = Polyhedral.DYMAXION;
 
-		Stream<Path> paths = Files.walk(Paths.get(directory));
-		Iterable<Path> pathIterable = paths::iterator;
+		try (Stream<Path> paths = Files.walk(Paths.get(directory))) {
+			Iterable<Path> pathIterable = paths::iterator;
 
-		// iterate thru the directory
-		for (Path inputPath: pathIterable) {
-			// look for images that are not dymaxion projections
-			if (inputPath.toString().endsWith(".jpg") ||
-			    inputPath.toString().endsWith(".jpeg") ||
-			    inputPath.toString().endsWith(".tif") ||
-			    inputPath.toString().endsWith(".tiff") ||
-			    inputPath.toString().endsWith(".png") &&
-			    !inputPath.toString().endsWith(".dymaxion.png")) {
-				System.out.println(inputPath);
-				PixelMap inputImage = new PixelMap(inputPath.toFile());
+			// iterate thru the directory
+			for (Path inputPath : pathIterable) {
+				// look for images that are not dymaxion projections
+				if (inputPath.toString().endsWith(".jpg") ||
+				    inputPath.toString().endsWith(".jpeg") ||
+				    inputPath.toString().endsWith(".tif") ||
+				    inputPath.toString().endsWith(".tiff") ||
+				    inputPath.toString().endsWith(".png") &&
+				    !inputPath.toString().endsWith(".dymaxion.png")) {
+					System.out.println(inputPath);
+					PixelMap inputImage = new PixelMap(inputPath.toFile());
 
-				// reduce the area by 2 to avoid pixelation
-				double area = inputImage.getWidth() * inputImage.getHeight() / 2.;
-				// and calculate the new dimensions according to Dymaxion's aspect ratio
-				int width = (int) sqrt(area * projection.getShape().aspectRatio);
-				int height = (int) sqrt(area / projection.getShape().aspectRatio);
+					// reduce the area by 2 to avoid pixelation
+					double area = inputImage.getWidth()*inputImage.getHeight()/2.;
+					// and calculate the new dimensions according to Dymaxion's aspect ratio
+					int width = (int) sqrt(area*projection.getShape().aspectRatio);
+					int height = (int) sqrt(area/projection.getShape().aspectRatio);
 
-				// generate the new map
-				BufferedImage outputImage = MapDesignerRaster.calculate(
-					  width, height, 2, inputImage, projection,
-					  null, true, 0,
-					  null, null, null);
+					// generate the new map
+					BufferedImage outputImage = MapDesignerRaster.calculate(
+							width, height, 2, inputImage, projection,
+							null, true, 0,
+							null, null, null);
 
-				// update the filename and save to disk
-				String outputPath = inputPath.toString();
-				outputPath = outputPath.replace(".jpg", ".png");
-				outputPath = outputPath.replace(".jpeg", ".png");
-				outputPath = outputPath.replace(".tif", ".png");
-				outputPath = outputPath.replace(".tiff", ".png");
-				outputPath = outputPath.replace(".png", ".dymaxion.png");
-				SavableImage.savable(outputImage).save(new File(outputPath));
+					// update the filename and save to disk
+					String outputPath = inputPath.toString();
+					outputPath = outputPath.replace(".jpg", ".png");
+					outputPath = outputPath.replace(".jpeg", ".png");
+					outputPath = outputPath.replace(".tif", ".png");
+					outputPath = outputPath.replace(".tiff", ".png");
+					outputPath = outputPath.replace(".png", ".dymaxion.png");
+					SavableImage.savable(outputImage).save(new File(outputPath));
+				}
 			}
 		}
 
diff --git a/src/apps/MapEvaluator.java b/src/apps/MapEvaluator.java
index ff4805b..99c6737 100644
--- a/src/apps/MapEvaluator.java
+++ b/src/apps/MapEvaluator.java
@@ -69,7 +69,7 @@ public class MapEvaluator {
 			};
 
 	public static void main(String[] args) throws IOException {
-		BufferedImage img = ImageIO.read(new File("input/Sillouette.png")); // start by loading the mask
+		BufferedImage img = ImageIO.read(new File("input/Silhouette.png")); // start by loading the mask
 		boolean[][] land = new boolean[img.getHeight()][img.getWidth()];
 		for (int i = 0; i < land.length; i ++)
 			for (int j = 0; j < land[i].length; j ++)
@@ -142,7 +142,7 @@ public class MapEvaluator {
 			}
 			
 			System.out.printf("Usable area: %.6f sr\n", totalArea);
-			System.out.printf("Anglular:   %8.4f %%\n", 100*shearedArea/totalArea);
+			System.out.printf("Angular:    %8.4f %%\n", 100*shearedArea/totalArea);
 			System.out.printf("Areal:      %8.4f %%\n", 100*swollenArea/totalArea);
 			System.out.printf("Precision:  %8.4f %%\n", 100*maxArea/totalArea);
 			System.out.println();
diff --git a/src/apps/MapExplainer.java b/src/apps/MapExplainer.java
index 1700234..1787bbd 100644
--- a/src/apps/MapExplainer.java
+++ b/src/apps/MapExplainer.java
@@ -141,17 +141,17 @@ public class MapExplainer extends Application {
 					out.print("&#9734;");
 				out.println("</dt>");
 				out.println("      <dt>Geometry:&nbsp;</dt>");
-				out.println("      <dd>"+proj.getType().getName()+"</dd>");
+				out.println("      <dd>" + proj.getType().getName() + "</dd>");
 				out.println("      <dt>Property:&nbsp;</dt>");
-				out.println("      <dd>"+proj.getProperty().getName()+"</dd>");
+				out.println("      <dd>" + proj.getProperty().getName() + "</dd>");
 				out.println("      <dt>Uninterrupted:&nbsp;</dt>");
-				out.println("      <dd>"+ (proj.isContinuous() ? "Yes":"No") +"</dd>");
+				out.println("      <dd>" + (proj.isContinuous() ? "Yes":"No") + "</dd>");
 				out.println("      <dt>Shows entire world:&nbsp;</dt>");
 				out.println("      <dd>" + (proj.isComprehensive() ? "Yes" : "No") + "</dd>");
 				out.println("      <dt>Closed-form solution:&nbsp;</dt>");
-				out.println("      <dd>"+ (proj.isSolveable() ? "Yes":"No") +"</dd>");
+				out.println("      <dd>" + (proj.isSolvable() ? "Yes" : "No") + "</dd>");
 				out.println("      <dt>Closed-form inverse:&nbsp;</dt>");
-				out.println("      <dd>"+ (proj.isInvertable() ? "Yes":"No") +"</dd>");
+				out.println("      <dd>" + (proj.isInvertible() ? "Yes" : "No") + "</dd>");
 				out.println("    </dl>");
 				out.println("    <br>");
 				out.println("  </div>");
diff --git a/src/apps/MapOptimizer.java b/src/apps/MapOptimizer.java
index f7884f1..1cc2188 100644
--- a/src/apps/MapOptimizer.java
+++ b/src/apps/MapOptimizer.java
@@ -93,7 +93,7 @@ public class MapOptimizer extends Application {
 		chart.setCreateSymbols(true);
 		chart.setAxisSortingPolicy(SortingPolicy.NONE);
 		
-		PrintStream log = new PrintStream(new File("output/parameters.txt"));
+		PrintStream log = new PrintStream("output/parameters.txt");
 		
 		chart.getData().add(analyzeAll(EXISTING_PROJECTIONS));
 		for (Projection p: PROJECTIONS_TO_OPTIMIZE)
@@ -119,13 +119,13 @@ public class MapOptimizer extends Application {
 		
 		for (Projection proj : projs)
 			if (!proj.isParametrized())
-				output.getData().add(plotDistortion(proj, new double[0]));
+				output.getData().add(plotDistortion(proj));
 		
 		return output;
 	}
 	
 	
-	private static Data<Number, Number> plotDistortion(Projection proj, double[] params) {
+	private static Data<Number, Number> plotDistortion(Projection proj) {
 		double[] distortion = proj.avgDistortion(GLOBE, proj.getDefaultParameters());
 		return new Data<Number, Number>(distortion[0], distortion[1]);
 	}
@@ -193,8 +193,8 @@ public class MapOptimizer extends Application {
 				bestValue = avgDist;
 				bestParams = params.clone();
 			}
-			for (int i = 0; i < params.length; i ++)
-				System.out.print(params[i]+", ");
+			for (double param: params)
+				System.out.print(param + ", ");
 			System.out.println(avgDist+";");
 			
 			int i;
@@ -222,7 +222,7 @@ public class MapOptimizer extends Application {
 	 * a backtracking line search.
 	 * @param arrFunction - The function that takes a parameter array and returns a double value.
 	 * @param x0 - The initial guess.
-	 * @return The array of parameters that mimimise arrFunction.
+	 * @return The array of parameters that minimise arrFunction.
 	 */
 	private static double[] bfgsMinimise(Function<double[], Double> arrFunction, double[] x0) { //The Broyden-Fletcher-Goldfarb-Shanno algorithm
 		System.out.println("BFGS = [");
diff --git a/src/apps/MapPlotter.java b/src/apps/MapPlotter.java
index 46f2e7b..f8e4217 100644
--- a/src/apps/MapPlotter.java
+++ b/src/apps/MapPlotter.java
@@ -155,7 +155,7 @@ public class MapPlotter extends Application {
 		for (Projection projection: projections) {
 			System.out.print(projection+": ");
 			final double[] params = projection.getDefaultParameters();
-			final double distortion[] = projection.avgDistortion(points, params);
+			final double[] distortion = projection.avgDistortion(points, params);
 			final Data<Number, Number> datum = new Data<Number, Number>(
 					distortion[0]/DECIBEL, distortion[1]/DECIBEL);
 			series.getData().add(datum);
diff --git a/src/dialogs/ProjectionSelectionDialog.java b/src/dialogs/ProjectionSelectionDialog.java
index 22a95b9..ad746ff 100644
--- a/src/dialogs/ProjectionSelectionDialog.java
+++ b/src/dialogs/ProjectionSelectionDialog.java
@@ -144,8 +144,8 @@ public class ProjectionSelectionDialog extends Dialog<Projection> {
 		text.addRow(1, new Label("Property:"), new Label(p.getProperty().getName()));
 		text.addRow(2, new Label("Uninterrupted:"), new Label(p.isContinuous() ? "Yes" : "No"));
 		text.addRow(3, new Label("Shows entire world:"), new Label(p.isComprehensive() ? "Yes" : "No"));
-		text.addRow(4, new Label("Closed-form solution:"), new Label(p.isSolveable() ? "Yes" : "No"));
-		text.addRow(5, new Label("Closed-form inverse:"), new Label(p.isInvertable() ? "Yes" : "No"));
+		text.addRow(4, new Label("Closed-form solution:"), new Label(p.isSolvable() ? "Yes" : "No"));
+		text.addRow(5, new Label("Closed-form inverse:"), new Label(p.isInvertible() ? "Yes" : "No"));
 		for (Node label: text.getChildren())
 			((Label)label).setFont(body.getFont());
 	}
diff --git a/src/image/ImageUtils.java b/src/image/ImageUtils.java
index 3198214..fc570f7 100644
--- a/src/image/ImageUtils.java
+++ b/src/image/ImageUtils.java
@@ -77,14 +77,9 @@ public class ImageUtils {
 		Path2D awtPath = new Path2D.Double(Path2D.WIND_NON_ZERO, path.size());
 		for (Path.Command svgCmd: path) {
 			switch (svgCmd.type) {
-			case 'M':
-				awtPath.moveTo(svgCmd.args[0], svgCmd.args[1]);
-				break;
-			case 'L':
-				awtPath.lineTo(svgCmd.args[0], svgCmd.args[1]);
-				break;
-			case 'Z':
-				awtPath.closePath();
+				case 'M' -> awtPath.moveTo(svgCmd.args[0], svgCmd.args[1]);
+				case 'L' -> awtPath.lineTo(svgCmd.args[0], svgCmd.args[1]);
+				case 'Z' -> awtPath.closePath();
 			}
 		}
 		g.draw(awtPath);
diff --git a/src/image/SVGMap.java b/src/image/SVGMap.java
index 063d942..96aa958 100644
--- a/src/image/SVGMap.java
+++ b/src/image/SVGMap.java
@@ -243,7 +243,7 @@ public class SVGMap implements Iterable<SVGMap.SVGElement>, SavableImage {
 				y = y*transform[1] + transform[3];
 				width = width*transform[0];
 				height = height*transform[1];
-				// check if it exactly covers the viewbox (it's okay if it's vertically inverted)
+				// check if it exactly covers the viewBox (it's okay if it's vertically inverted)
 				if ((x == header.vbMinX && y == header.vbMinY && width == header.vbWidth && height == header.vbHeight) ||
 				    (x == header.vbMinX && y == header.vbMinY + header.vbHeight && width == header.vbWidth && height == -header.vbHeight)) {
 					// if so, remove the dimensions and stick the remainder in a Background Object
@@ -516,7 +516,7 @@ public class SVGMap implements Iterable<SVGMap.SVGElement>, SavableImage {
 						partI.remove(0); //remove the useless moveto
 						partJ.addAll(partI); //combine them
 						partI = partJ;
-						parts.remove(j); //don't look at J anymone; it has been absorbed.
+						parts.remove(j); //don't look at J anymore; it has been absorbed.
 						break;
 					}
 				}
@@ -553,10 +553,6 @@ public class SVGMap implements Iterable<SVGMap.SVGElement>, SavableImage {
 			this.content = content;
 		}
 
-		public Content projected() {
-			return this;
-		}
-
 		public String toString() {
 			return this.content;
 		}
@@ -623,10 +619,6 @@ public class SVGMap implements Iterable<SVGMap.SVGElement>, SavableImage {
 			this.y = y;
 		}
 
-		public GeographicPoint projected() {
-			return this;
-		}
-
 		public String toString() {
 			return format(formatSpecifier, x, y);
 		}
diff --git a/src/maps/CahillKeyes.java b/src/maps/CahillKeyes.java
index 7aa2778..365a708 100644
--- a/src/maps/CahillKeyes.java
+++ b/src/maps/CahillKeyes.java
@@ -42,7 +42,8 @@ import static utils.Math2.tand;
 /**
  * A truncated octahedral map. The projection is Cahill-Keyes, because it was invented after Cahill,
  * so it is presumably better (not that Tobler World in a Square wasn't invented after Lambert EAC).
- * http://www.genekeyes.com/CKOG-OOo/7-CKOG-illus-&-coastline.html
+ *
+ * <a href="http://www.genekeyes.com/CKOG-OOo/7-CKOG-illus-&-coastline.html">genekeyes.com/CKOG-OOo/7-CKOG-illus-&-coastline</a>
  *
  * @author jkunimune
  */
@@ -74,7 +75,7 @@ public class CahillKeyes {
 	public static final double POLE_OFFSET = lMA*SCALE_FACTOR; //lMA expressed in output coordinates
 	
 	
-	public static Projection FACE = new Projection(
+	public static final Projection FACE = new Projection(
 			"Cahill–Keyes (face)", "A single face of Gene Keyes's octahedral projection",
 			Shape.polygon(new double[][] {{0., 0.}, {0., -sqrt(3)/2.}, {1/2., -sqrt(3)/2.}}),
 			true, true, true, false, Projection.Type.OTHER, Projection.Property.COMPROMISE, 2) {
diff --git a/src/maps/Elastic.java b/src/maps/Elastic.java
index 1081e40..868aa4e 100644
--- a/src/maps/Elastic.java
+++ b/src/maps/Elastic.java
@@ -189,7 +189,9 @@ public class Elastic {
 		/**
 		 * convert a location on the map plane to a location on the globe by iteratively searching
 		 * for the coordinates that project to x and y on a given section.  the algorithm is
-		 * Levenberg-Marquardt; see <i>J. Res. NIST</i> 103, p. 633 (1998).
+		 * Levenberg-Marquardt; see <i>J. Res. NIST</i> 103, p. 633 (1998).  this procedure could
+		 * probably be a lot simpler (or omitted entirely) depending on how high quality an inverse
+		 * you want.
 		 * @param x the x value, in the same units as this.width
 		 * @param y the y value, in the same units as this.height
 		 * @param section_index the index of the section to search
@@ -484,7 +486,7 @@ public class Elastic {
 		/**
 		 * determine whether the given point falls within this polygon or not. the method used is a typical even/odd
 		 * algorithm, with the caveat that the directionality of the polygon is significant.  if the vertices go
-		 * counterclockwise, the contianed points are everything inside the polygon as one would expect, but if the
+		 * counterclockwise, the contained points are everything inside the polygon as one would expect, but if the
 		 * vertices go clockwise, the contained points are actually everything <i>outside</i> the polygon.
 		 * @param ф the latitude of the point
 		 * @param λ the longitude of the point
@@ -681,7 +683,7 @@ public class Elastic {
 		 * recenter a set of spherical coordinates so that the latitude is in the range [-PI/2, PI/2]
 		 * and the longitude is in the range [-PI, PI].  if it's outside of the latitude bounds, it
 		 * will get reflected about the poles until it isn't.  if it's out of the longitude bounds,
-		 * it will get modulused such that it isn't.
+		 * it will get moduloed such that it isn't.
 		 * @param ф the latitude (radians)
 		 * @param λ the longitude (radians)
 		 * @return the equivalent in-bounds latitude and longitude in an array
diff --git a/src/maps/Misc.java b/src/maps/Misc.java
index d304f23..b857ce2 100644
--- a/src/maps/Misc.java
+++ b/src/maps/Misc.java
@@ -170,7 +170,9 @@ public class Misc {
 			double phi1 = PI/2 - hypot(x, y);
 			if (phi1 < -PI/2) 	return null;
 			double lam1 = atan2(x, -y);
-			double phiP = asin(sin(phi0)/hypot(sin(phi1),cos(phi1)*cos(lam1))) - atan2(cos(phi1)*cos(lam1),sin(phi1));
+			double y1 = cos(phi1)*cos(lam1);
+			double z1 = sin(phi1);
+			double phiP = asin(sin(phi0)/hypot(z1, y1)) - atan2(y1, z1);
 			if (abs(phiP) > PI/2)
 				phiP = signum(phiP)*PI - phiP;
 			double delL = acos(sin(phi1)/cos(phiP)/cos(phi0) - tan(phiP)*tan(phi0));
diff --git a/src/maps/MyProjections.java b/src/maps/MyProjections.java
deleted file mode 100644
index 113d349..0000000
--- a/src/maps/MyProjections.java
+++ /dev/null
@@ -1,92 +0,0 @@
-/**
- * MIT License
- * 
- * Copyright (c) 2017 Justin Kunimune
- * 
- * Permission is hereby granted, free of charge, to any person obtaining a copy
- * of this software and associated documentation files (the "Software"), to deal
- * in the Software without restriction, including without limitation the rights
- * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
- * copies of the Software, and to permit persons to whom the Software is
- * furnished to do so, subject to the following conditions:
- * 
- * The above copyright notice and this permission notice shall be included in all
- * copies or substantial portions of the Software.
- * 
- * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
- * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
- * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
- * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
- * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
- * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
- * SOFTWARE.
- */
-package maps;
-
-import maps.Projection.Property;
-import maps.Projection.Type;
-import utils.Shape;
-
-import static java.lang.Math.PI;
-import static java.lang.Math.acos;
-import static java.lang.Math.asin;
-import static java.lang.Math.cos;
-import static java.lang.Math.hypot;
-import static java.lang.Math.pow;
-import static java.lang.Math.signum;
-import static java.lang.Math.sin;
-import static java.lang.Math.sqrt;
-import static java.lang.Math.tan;
-import static java.lang.Math.toRadians;
-
-/**
- * All of the projections I invented, save the tetrahedral ones, because
- * those have so much in common with other tetrahedral projections.
- * 
- * @author jkunimune
- */
-public class MyProjections {
-
-	public static final Projection TWO_POINT_EQUALIZED = new Projection("Two-Point Equalized",
-			"A projection I invented specifically for viewing small elliptical regions of the Earth",
-			null, true, true, true, true, Type.OTHER, Property.EQUIDISTANT, 2,
-			new String[] {"Width"}, new double[][] { {0, 180, 120} }) {
-		
-		private double theta;
-		
-		public void initialize(double... params) {
-			theta = toRadians(params[0])/2;
-			if (theta != 0)
-				this.shape = Shape.ellipse(
-						sqrt(pow(PI - theta, 2) - pow(theta, 2))*
-						sqrt(tan(theta)/theta), //minor axis
-						PI - theta //major axis
-				);
-			else
-				this.shape = Shape.circle(PI);
-		}
-		
-		public double[] project(double lat, double lon) {
-			if (theta == 0) 	return Azimuthal.POLAR.project(lat, lon);
-			final double d1 = acos(
-					sin(lat)*cos(theta) - cos(lat)*sin(theta)*cos(lon));
-			final double d2 = acos(
-					sin(lat)*cos(theta) + cos(lat)*sin(theta)*cos(lon));
-			final double k = signum(lon)*sqrt(tan(theta)/theta);
-			return new double[] {
-					k*sqrt(d1*d1 - pow((d1*d1-d2*d2+4*theta*theta)/(4*theta), 2)),
-					(d2*d2-d1*d1)/(4*theta) };
-		}
-		
-		public double[] inverse(double x, double y) {
-			if (theta == 0) 	return Azimuthal.POLAR.inverse(x, y);
-			final double d1 = hypot(x/sqrt(tan(theta)/theta), y - theta);
-			final double d2 = hypot(x/sqrt(tan(theta)/theta), y + theta);
-			if (d1 + d2 > 2*shape.yMax) 	return null;
-			final double phi = asin((cos(d1)+cos(d2))/(2*cos(theta)));
-			final double lam = signum(x)*acos(
-					(sin(phi)*cos(theta) - cos(d1))/(cos(phi)*sin(theta)));
-			return new double[] { phi, lam };
-		}
-	};
-}
diff --git a/src/maps/Octahedral.java b/src/maps/Octahedral.java
index c6a005f..b110764 100644
--- a/src/maps/Octahedral.java
+++ b/src/maps/Octahedral.java
@@ -182,7 +182,7 @@ public class Octahedral {
 		
 		public OctahedralProjection(String name, String desc, int rating, double tipOffset,
 		                            Projection faceProj, Configuration config) {
-			super(name, desc, null, false, config.comprehensive, faceProj.isSolveable(), faceProj.isInvertable(),
+			super(name, desc, null, false, config.comprehensive, faceProj.isSolvable(), faceProj.isInvertible(),
 			      (tipOffset == 0) ? Type.OCTAHEDRAL : Type.TETRADECAHEDRAL, faceProj.getProperty(), rating,
 			      new String[] {}, new double[][] {}, config.hasAspect);
 			this.octants = config.placeOctants(tipOffset);
diff --git a/src/maps/Polyhedral.java b/src/maps/Polyhedral.java
index 07779d5..e31a978 100644
--- a/src/maps/Polyhedral.java
+++ b/src/maps/Polyhedral.java
@@ -113,18 +113,14 @@ public class Polyhedral {
 	
 	public static final PolyhedralProjection AUTHAGRAPH = new PolyhedralProjection(
 			"IMAGO (AuthaGraph)",
-			"Authagraph is a hip new Japanese map that would be super great if they actually " +
+			"AuthaGraph is a hip new Japanese map that would be super great if they actually " +
 			"published their equations. This is technically just an approximation, also known as " +
-			"the Infinitessimal Mutated AuthaGraph Offspring.",
+			"the Infinitesimal Mutated AuthaGraph Offspring.",
 			true, true, false, Polyhedron.AUTHAGRAPH, Property.COMPROMISE, 3,
 			new String[] {"Power"}, new double[][] {{.5,1,.68}}) {
 		
 		private final double[] POLE = {toRadians(77), toRadians(143), toRadians(17)};
-		private double k;
-		
-		public void initialize(double... params) {
-				this.k = params[0];
-		}
+		private final double k = .68;
 		
 		@Override
 		public double[] project(double lat, double lon) { //apply a pole shift to AuthaGraph
@@ -137,21 +133,14 @@ public class Polyhedral {
 			return transformToOblique(super.inverse(x, y), POLE);
 		}
 		
-		
 		public double[] faceProject(double lat, double lon) {
-			final double tht = atan((lon - asin(sin(lon)/sqrt(3)))/PI*sqrt(12));
-			final double p = (PI/2 - lat) / atan(sqrt(2)/cos(lon));
-			return new double[] { pow(p,k)*sqrt(3)/cos(tht), tht };
+			AUTHAPOWER.initialize(k);
+			return AUTHAPOWER.faceProject(lat, lon);
 		}
 		
-		protected double[] faceInverse(double r, double th) {
-			final double lon = NumericalAnalysis.newtonRaphsonApproximation(th, th*2,
-					(l) -> atan((l - asin(sin(l)/sqrt(3)))/PI*sqrt(12)),
-					(l) -> (1-1/sqrt(1+2*pow(cos(l),-2)))/sqrt(pow(PI,2)/12+pow(l-asin(sin(l)/sqrt(3)),2)),
-					.001);
-			final double R = r / (sqrt(3)/cos(th));
-			return new double[] {
-					PI/2 - pow(R,1/k)*atan(sqrt(2)/cos(lon)), lon };
+		public double[] faceInverse(double r, double th) {
+			AUTHAPOWER.initialize(k);
+			return AUTHAPOWER.faceInverse(r, th);
 		}
 	};
 	
@@ -173,7 +162,7 @@ public class Polyhedral {
 			return new double[] { pow(p,k)*sqrt(3)/cos(tht), tht };
 		}
 		
-		protected double[] faceInverse(double r, double th) {
+		public double[] faceInverse(double r, double th) {
 			final double lon = NumericalAnalysis.newtonRaphsonApproximation(th, th*2,
 					(l) -> atan((l - asin(sin(l)/sqrt(3)))/PI*sqrt(12)),
 					(l) -> (1-1/sqrt(1+2*pow(cos(l),-2)))/sqrt(pow(PI,2)/12+pow(l-asin(sin(l)/sqrt(3)),2)),
@@ -310,9 +299,9 @@ public class Polyhedral {
 			double y = r*sin(th)*atan(2);
 			double a = sqrt(3)*x + y; //angular distance up each side of the triangle
 			double b = sqrt(3)*x - y;
-			double xG = cos36*(sin(a) + sin(b))/(1 + cos(a) + cos(b)); //unnormalised gnomonic coordinates
-			double yG = sin36*
-					(sin(a) - sin(b) + 2*sin(a-b))/(1 + cos(a) + cos(b));
+			double correction = 1 + cos(a) + cos(b);
+			double xG = cos36*(sin(a) + sin(b))/correction; //unnormalised gnomonic coordinates
+			double yG = sin36*(sin(a) - sin(b) + 2*sin(a-b))/correction;
 			return new double[] {atan(1/hypot(xG, yG)), atan2(yG, xG)}; //inverse gnomonic projection
 		}
 	};
@@ -530,7 +519,7 @@ public class Polyhedral {
 				new Facet(-0.5, -0.5*sqrt(3),    PI/2,       -PI/2,     0  , -3*PI/5,   -PI/5, 2*PI/5), //West Pacific O.
 				new Facet(-1.5, -0.5*sqrt(3),    PI/2,       -PI/2,     0  ,   -PI/5,     0  , 3*PI/5), //Melanesia
 		});
-		/** the number of the rotational spmmetry in the spherical coordinate system */
+		/** the number of the rotational symmetry in the spherical coordinate system */
 		public final int sphereSym;
 		/** the number of the rotational symmetry in the planar coordinate system */
 		public final int planarSym;
@@ -549,7 +538,7 @@ public class Polyhedral {
 			if (sphereSym == 3)
 				this.type = Type.TETRAHEDRAL;
 			else
-				this.type = Type.ICOSOHEDRAL;
+				this.type = Type.ICOSAHEDRAL;
 		}
 		
 		public double[] rotateOOB(double x, double y, double xCen, double yCen) { //move points that are out of bounds for project()
diff --git a/src/maps/Projection.java b/src/maps/Projection.java
index bc2abae..74c7fb0 100644
--- a/src/maps/Projection.java
+++ b/src/maps/Projection.java
@@ -70,8 +70,8 @@ public abstract class Projection {
 	
 	private final boolean continuous; //is the interruption kept to no more than one meridian's equivalent?
 	private final boolean comprehensive; //does it display the entire world?
-	private final boolean solveable; //is the solution closed-form?
-	private final boolean invertable; //is the inverse solution closed-form?
+	private final boolean solvable; //is the solution closed-form?
+	private final boolean invertible; //is the inverse solution closed-form?
 	private final Type type; //the geometry of the projection
 	private final Property property; //what it is good for
 	private final int rating; //how good I think it is
@@ -87,15 +87,15 @@ public abstract class Projection {
 	
 	protected Projection(
 			String name, String description, Shape shape, boolean continuous, boolean comprehensive,
-			boolean solveable, boolean invertable, Type type, Property property, int rating,
+			boolean solvable, boolean invertible, Type type, Property property, int rating,
 			String[] paramNames, double[][] paramValues) {
-		this(name, description, shape, continuous, comprehensive, solveable, invertable, type, property, rating,
+		this(name, description, shape, continuous, comprehensive, solvable, invertible, type, property, rating,
 		     paramNames, paramValues, true);
 	}
 	
 	protected Projection (
 			String name, String description, Shape shape, boolean continuous, boolean comprehensive,
-			boolean solveable, boolean invertable, Type type, Property property, int rating,
+			boolean solvable, boolean invertible, Type type, Property property, int rating,
 			String[] paramNames, double[][] paramValues, boolean hasAspect) {
 		this.name = name;
 		this.description = description;
@@ -105,16 +105,16 @@ public abstract class Projection {
 		this.shape = shape;
 		this.continuous = continuous;
 		this.comprehensive = comprehensive;
-		this.solveable = solveable;
-		this.invertable = invertable;
+		this.solvable = solvable;
+		this.invertible = invertible;
 		this.type = type;
 		this.property = property;
 		this.rating = rating;
 	}
 	
 	protected Projection(String name, Projection base) {
-		this(name, base.description, base.shape, base.comprehensive, base.invertable,
-		     base.solveable, base.continuous, base.type, base.property, base.rating,
+		this(name, base.description, base.shape, base.comprehensive, base.invertible,
+		     base.solvable, base.continuous, base.type, base.property, base.rating,
 		     base.paramNames, base.paramValues, base.hasAspect);
 	}
 
@@ -188,30 +188,7 @@ public abstract class Projection {
 	public double[] inverse(double[] coords) {
 		return inverse(coords[0], coords[1]);
 	}
-
-	/**
-	 * convert a location on the map plane to a location on the rotated globe
-	 * @param coords the x and y value, in the same units as this.bounds
-	 * @param pole the desired aspect: the latitude and longitude of the location that should appear as the North Pole
-	 *             and the angle to rotate the globe about its new axis
-	 * @return the latitude and longitude in radians
-	 */
-	public double[] inverse(double[] coords, double[] pole) {
-		return inverse(coords[0], coords[1], pole);
-	}
-
-	/**
-	 * convert a location on the map plane to a location on the rotated globe
-	 * @param x the x value in the same units as this.bounds
-	 * @param y the y value in the same units as this.bounds
-	 * @param pole the desired aspect: the latitude and longitude of the location that should appear as the North Pole
-	 *             and the angle to rotate the globe about its new axis
-	 * @return the latitude and longitude in radians
-	 */
-	public double[] inverse(double x, double y, double[] pole) {
-		return inverse(x, y, pole, false);
-	}
-
+	
 	/**
 	 * convert a location on the map plane to a location on the rotated globe
 	 * @param x the x value in the same units as this.bounds
@@ -233,19 +210,8 @@ public abstract class Projection {
 		else
 			return transformToOblique(relCoords, hasAspect ? pole : null);
 	}
-
-
-	/**
-	 * perform the inverse projection on a 2D array of points
-	 * @param size the maximum linear dimension of the 2D array
-	 * @return an array of latitude-longitude pairs, where each row is at a particular x value,
-	 *         and each column is at a particular y value.  y decreases with increasing row index.
-	 *         elements corresponding to points not on the map will be set to zero.
-	 */
-	public double[][][] map(int size) {
-		return map(size, false);
-	}
-
+	
+	
 	/**
 	 * perform the inverse projection on a 2D array of points
 	 * @param size the maximum linear dimension of the 2D array
@@ -431,11 +397,11 @@ public abstract class Projection {
 	}
 	
 	public double[][][] calculateDistortion(double[][][] points,
-			BooleanSupplier cancelation, DoubleConsumer progressTracker) { //calculate both kinds of distortion over the given region
+			BooleanSupplier cancellation, DoubleConsumer progressTracker) { //calculate both kinds of distortion over the given region
 		double[][][] output = new double[2][points.length][points[0].length]; //the distortion matrix
 		
 		for (int y = 0; y < points.length; y ++) {
-			if (cancelation.getAsBoolean()) 	return null;
+			if (cancellation.getAsBoolean()) 	return null;
 			progressTracker.accept((double)y/points.length);
 			for (int x = 0; x < points[y].length; x ++) {
 				if (points[y][x] != null) {
@@ -632,12 +598,12 @@ public abstract class Projection {
 		return this.comprehensive;
 	}
 	
-	public final boolean isInvertable() {
-		return this.invertable;
+	public final boolean isInvertible() {
+		return this.invertible;
 	}
 	
-	public final boolean isSolveable() {
-		return this.solveable;
+	public final boolean isSolvable() {
+		return this.solvable;
 	}
 	
 	public final boolean isContinuous() {
@@ -692,7 +658,7 @@ public abstract class Projection {
 		PSEUDOCYLINDRICAL("Pseudocylindrical"), PSEUDOCONIC("Pseudoconic"),
 		PSEUDOAZIMUTHAL("Pseudoazimuthal"),
 		TETRAHEDRAL("Tetrahedral"), OCTAHEDRAL("Octahedral"),
-		TETRADECAHEDRAL("Truncated Octahedral"), ICOSOHEDRAL("Icosohedral"),
+		TETRADECAHEDRAL("Truncated Octahedral"), ICOSAHEDRAL("Icosahedral"),
 		POLYNOMIAL("Polynomial"), STREBE("Strebe blend"), PLANAR("Planar"), OTHER("Other");
 		
 		private final String name;
diff --git a/src/maps/Waterman.java b/src/maps/Waterman.java
index 70671fe..ba982d8 100644
--- a/src/maps/Waterman.java
+++ b/src/maps/Waterman.java
@@ -35,8 +35,9 @@ import static utils.Math2.linInterp;
 
 /**
  * A class of methods pertaining to the Waterman projection.
- * http://www.watermanpolyhedron.com/methodp.html
- * 
+ *
+ * <a href="http://www.watermanpolyhedron.com/methodp.html">watermanpolyhedron.com/methodp</a>
+ *
  * @author jkunimune
  */
 public class Waterman {
@@ -50,7 +51,7 @@ public class Waterman {
 	private static final double cos15 = (sqrt(3)+1)/sqrt(8);  // cos(15°)
 	
 	
-	public static Projection FACE = new Projection(
+	public static final Projection FACE = new Projection(
 			"Waterman (face)", "A single face of Waterman's octahedral projection",
 			Shape.polygon(new double[][] {{0., 0.}, {0., -sqrt(3)/2.}, {1/2., -sqrt(3)/2.}}),
 			true, true, true, false, Type.OTHER, Property.COMPROMISE, 2) {
diff --git a/src/maps/WinkelTripel.java b/src/maps/WinkelTripel.java
index 9b1cc04..7338111 100644
--- a/src/maps/WinkelTripel.java
+++ b/src/maps/WinkelTripel.java
@@ -74,7 +74,7 @@ public final class WinkelTripel {
 		public double[] inverse(double x, double y) {
 			return NumericalAnalysis.newtonRaphsonApproximation(
 					x, y,
-					y/2, x*(1 + cos(y*PI/2))/(2 + 2*cos(stdParallel)), //inital guess is Eckert V
+					y/2, x*(1 + cos(y*PI/2))/(2 + 2*cos(stdParallel)), //initial guess is Eckert V
 					this::f1pX, this::f2pY,
 					this::df1dphi, this::df1dlam, this::df2dphi, this::df2dlam, .001);
 		}
diff --git a/src/utils/Dixon.java b/src/utils/Dixon.java
index 8315c0c..69b7bce 100644
--- a/src/utils/Dixon.java
+++ b/src/utils/Dixon.java
@@ -41,7 +41,7 @@ public class Dixon {
 	/**
 	 * One third of the period of a dixon sm or cm function
 	 */
-	public static double PERIOD_THIRD = 1.7666387503;
+	public static final double PERIOD_THIRD = 1.7666387503;
 	
 	private static final double[] COEF = { 1.000000e0, .625000e-1, .223214e-2, .069754e-3,
 			.020121e-4/*, .005539e-5, .001477e-6, .000385e-7, .000099e-8, .000025e-9*/ };
diff --git a/src/utils/Math2.java b/src/utils/Math2.java
index ed94ccd..f864a15 100644
--- a/src/utils/Math2.java
+++ b/src/utils/Math2.java
@@ -154,52 +154,8 @@ public class Math2 {
 	public static double linInterp(double x, double a0, double a1, double b0, double b1) {
 		return (x-a0)*(b1-b0)/(a1-a0) + b0;
 	}
-
-	public static double[] linInterp(double[] xs, double[][] A, double[][] B) {
-		double[] out = new double[xs.length];
-		for (int i = 0; i < xs.length; i ++)
-			out[i] = linInterp(xs[i], A[0][i], A[1][i], B[0][i], B[1][i]);
-		return out;
-	}
-
-	public static boolean outOfBoundsInSameDirection(double[][] range, double[]... xs) {
-		boolean allOutOnLeft = true;
-		for (double[] x : xs)
-			if (x[0] >= range[0][0]) {
-				allOutOnLeft = false;
-				break;
-			}
-		if (allOutOnLeft)
-			return true;
-
-		boolean allOutOnRight = true;
-		for (double[] x : xs)
-			if (x[0] <= range[1][0]) {
-				allOutOnRight = false;
-				break;
-			}
-		if (allOutOnRight)
-			return true;
-
-		boolean allOutOnBottom = true;
-		for (double[] x : xs)
-			if (x[1] >= range[0][1]) {
-				allOutOnBottom = false;
-				break;
-			}
-		if (allOutOnBottom)
-			return true;
-
-		boolean allOutOnTop = true;
-		for (double[] x : xs)
-			if (x[1] <= range[1][1]) {
-				allOutOnTop = false;
-				break;
-			}
-		return allOutOnTop;
-	}
-
-
+	
+	
 	public static double hypot(double[] a, double[] b) {
 		return Math.hypot(a[0] - b[0], a[1] - b[1]);
 	}
diff --git a/src/utils/MutableDouble.java b/src/utils/MutableDouble.java
index 7fd238b..720b1fe 100644
--- a/src/utils/MutableDouble.java
+++ b/src/utils/MutableDouble.java
@@ -44,11 +44,7 @@ public class MutableDouble {
 	public double get() {
 		return this.value;
 	}
-
-	public boolean isNaN() {
-		return Double.isNaN(this.value);
-	}
-
+	
 	public void set(double value) {
 		this.value = value;
 	}
diff --git a/src/utils/SAXUtils.java b/src/utils/SAXUtils.java
deleted file mode 100644
index f75ac38..0000000
--- a/src/utils/SAXUtils.java
+++ /dev/null
@@ -1,46 +0,0 @@
-/**
- * MIT License
- * 
- * Copyright (c) 2017 Justin Kunimune
- * 
- * Permission is hereby granted, free of charge, to any person obtaining a copy
- * of this software and associated documentation files (the "Software"), to deal
- * in the Software without restriction, including without limitation the rights
- * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
- * copies of the Software, and to permit persons to whom the Software is
- * furnished to do so, subject to the following conditions:
- * 
- * The above copyright notice and this permission notice shall be included in all
- * copies or substantial portions of the Software.
- * 
- * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
- * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
- * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
- * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
- * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
- * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
- * SOFTWARE.
- */
-package utils;
-
-/**
- * A class for working with and manipulating XML stuff.
- * 
- * @author jkunimune
- */
-public class SAXUtils {
-	
-	public static String encode(String s0) { //encode with the ampersand notation
-		StringBuilder s1 = new StringBuilder();
-		for (int i = 0; i < s0.length(); i ++) {
-			if (s0.charAt(i) >= 128)
-				s1.append("&#").append((int) s0.charAt(i)).append(";");
-			else if (s0.charAt(i) == '&')
-				s1.append("&amp;");
-			else
-				s1.append(s0.charAt(i));
-		}
-		return s1.toString();
-	}
-
-}
diff --git a/src/zupplemental/generate_graticule.py b/src/zupplemental/generate_graticule.py
index 9c430c8..e2d8c8f 100644
--- a/src/zupplemental/generate_graticule.py
+++ b/src/zupplemental/generate_graticule.py
@@ -2,7 +2,7 @@ import math
 
 
 AXIAL_TILT = 23.43694
-ANTI_TILT = 66.56306 #I have both of these because it's the easiest way to deal with roundoff
+ANTI_TILT = 66.56306 # I have both of these because it's the easiest way to deal with roundoff
 
 
 def plot_meridian(lamd, granularity, cut=0, clazz=None) -> str:
@@ -27,7 +27,7 @@ def generate_graticule(spacing, granularity, include_tropics=False, adjust_poles
 	result = ""
 	NUM_BASE = 90//spacing
 	cuts = [0]*(4*NUM_BASE)
-	if adjust_poles: #if this is True, reduce the number of meridians as you approach the pole
+	if adjust_poles: # if this is True, reduce the number of meridians as you approach the pole
 		old_num = 1
 		for p in range(0, 90, spacing):
 			new_num = old_num*int(1/math.cos(math.radians(p+spacing/2))/old_num)
diff --git a/src/zupplemental/generate_orthodromes.py b/src/zupplemental/generate_orthodromes.py
index f69cd64..e1662c0 100644
--- a/src/zupplemental/generate_orthodromes.py
+++ b/src/zupplemental/generate_orthodromes.py
@@ -15,7 +15,7 @@ def plot_orthodrome(phi0, lam0, tht0) -> str:
 	
 
 def generate_orthodromes() -> str:
-	"""generate an icosohedral orthodromic mesh, like the Brilliant logo (#notsponsored)"""
+	"""generate an icosahedral orthodromic mesh, like the Brilliant logo (#notsponsored)"""
 	result = ""
 	for l in range(-180, 180, 36):
 		result += plot_orthodrome(pi/2, 0, radians(l))
diff --git a/src/zupplemental/generate_political_shapes.py b/src/zupplemental/generate_political_shapes.py
index 9701d0e..64afc7d 100644
--- a/src/zupplemental/generate_political_shapes.py
+++ b/src/zupplemental/generate_political_shapes.py
@@ -67,7 +67,7 @@ def plot_political_shapes(filename, mode="normal",
 	else:
 		regions = load_shapes_from_one_place_and_records_from_another(filename, include_circles_from)
 	# go thru the records and sort them into a dictionary by ISO 3166 codes
-	hierarchially_arranged_regions: dict[tuple[tuple[str, ...], str], ShapeRecord] = {}
+	hierarchically_arranged_regions: dict[tuple[tuple[str, ...], str], ShapeRecord] = {}
 	for shape, record in regions:
 		# if it Antarctica, trim it
 		if trim_antarctica:
@@ -84,25 +84,25 @@ def plot_political_shapes(filename, mode="normal",
 			if province_code.endswith("~"):
 				province_code = province_code[:-1]
 			country_code = province_code[:province_code.index("-")]
-			hierarchial_identifier = (sovereign_code, country_code, province_code)
+			hierarchical_identifier = (sovereign_code, country_code, province_code)
 			unique_identifier = record["adm1_code"]
 		else:  # or by sovereign, admin0
 			country_code = record["adm0_a3"]
-			hierarchial_identifier = (sovereign_code, country_code)
+			hierarchical_identifier = (sovereign_code, country_code)
 			unique_identifier = country_code
-		if hierarchial_identifier[0] == hierarchial_identifier[1]:  # remove duplicate layers
-			hierarchial_identifier = hierarchial_identifier[1:]
-		key = (hierarchial_identifier, unique_identifier)
-		hierarchially_arranged_regions[key] = (shape, record)
+		if hierarchical_identifier[0] == hierarchical_identifier[1]:  # remove duplicate layers
+			hierarchical_identifier = hierarchical_identifier[1:]
+		key = (hierarchical_identifier, unique_identifier)
+		hierarchically_arranged_regions[key] = (shape, record)
 
 	# next, go thru and plot the borders
 	current_state = []
 	result = ""
 	already_titled = set()
 	# for each item
-	for key in sorted(hierarchially_arranged_regions.keys()):
+	for key in sorted(hierarchically_arranged_regions.keys()):
 		hierarchy, identifier = key
-		shape, record = hierarchially_arranged_regions[key]
+		shape, record = hierarchically_arranged_regions[key]
 
 		# decide whether it's "small"
 		is_small = True
@@ -179,7 +179,7 @@ def plot_political_shapes(filename, mode="normal",
 		current_state.pop()
 
 	# remove any groups with no elements
-	for i in range(3):
+	for _ in range(3):
 		result = re.sub(r'(\t)*<g class="([A-Za-z_-]+)">(\s*)</g>\n',
 		                '', result)
 	# simplify any groups with only a single element
diff --git a/src/zupplemental/generate_shapes.py b/src/zupplemental/generate_shapes.py
index 01bef9f..794b6ff 100644
--- a/src/zupplemental/generate_shapes.py
+++ b/src/zupplemental/generate_shapes.py
@@ -6,10 +6,11 @@ from helpers import plot, trim_edges, lengthen_edges, load_shaperecords
 def plot_shapes(
 		filename, max_rank=float('inf'), clazz=None,
 		trim_antarctica=False, flesh_out_antarctica=False, mark_antarctica=False,
-		filter_field=None, filter_values=['']) -> str:
+		filter_field=None, filter_values=None) -> str:
 	result = ""
 	for shape, record in load_shaperecords(filename):
 		if filter_field is not None:
+			assert filter_values is not None
 			filter_value = record[filter_field]
 			if filter_value not in filter_values:
 				continue  # skip it if it is filtered out
diff --git a/src/zupplemental/helpers.py b/src/zupplemental/helpers.py
index 8801f8e..ff82f39 100644
--- a/src/zupplemental/helpers.py
+++ b/src/zupplemental/helpers.py
@@ -1,10 +1,10 @@
 from __future__ import annotations
 
-import math
 import random as rng
-from typing import Any, Iterable
+from typing import Any, Iterable, Optional
 
 import shapefile
+from numpy import pi, sin, cos, tan, arcsin, arccos, degrees, ceil, radians, arctan2, hypot
 
 
 def load_shaperecords(filename) -> Iterable[ShapeRecord]:
@@ -49,31 +49,46 @@ def load_shapes_from_one_place_and_records_from_another(shape_filename, record_f
 
 def obliquify(lat1, lon1, lat0, lon0):
 	""" go from relative to absolute coordinates """
-	latf = math.asin(math.sin(lat0)*math.sin(lat1) - math.cos(lat0)*math.cos(lon1)*math.cos(lat1))
-	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
+	latf = arcsin(sin(lat0)*sin(lat1) - cos(lat0)*cos(lon1)*cos(lat1))
+	innerFunc = sin(lat1)/cos(lat0)/cos(latf) - tan(lat0)*tan(latf)
+	if lat0 == pi/2: # accounts for special case when lat0 = pi/2
 		lonf = lon1+lon0
-	elif lat0 == -math.pi/2: # accounts for special case when lat0 = -pi/2
-		lonf = -lon1+lon0 + math.pi
+	elif lat0 == -pi/2: # accounts for special case when lat0 = -pi/2
+		lonf = -lon1+lon0 + pi
 	elif abs(innerFunc) > 1: # accounts for special case when cos(lat1) -> 0
 		if (lon1 == 0 and lat1 < -lat0) or (lon1 != 0 and lat1 < lat0):
-			lonf = lon0 + math.pi
+			lonf = lon0 + pi
 		else:
 			lonf = lon0
-	elif math.sin(lon1) > 0:
-		lonf = lon0 + math.acos(innerFunc)
+	elif sin(lon1) > 0:
+		lonf = lon0 + arccos(innerFunc)
 	else:
-		lonf = lon0 - math.acos(innerFunc)
+		lonf = lon0 - arccos(innerFunc)
 
-	while lonf > math.pi:
-		lonf -= 2*math.pi
-	while lonf < -math.pi:
-		lonf += 2*math.pi
+	while lonf > pi:
+		lonf -= 2*pi
+	while lonf < -pi:
+		lonf += 2*pi
 		
 	return latf, lonf
 
 
-def plot(coords, midx=[0], close=True, fourmat='pr', clazz=None, ident=None, tabs=3) -> str:
+def plot(coords: list[tuple[float, float]], midx: Optional[list[int]] = None, close=True, fourmat='pr', clazz=None, ident=None, tabs=3) -> str:
+	"""
+	express a list of 2D points as an SVG <path> tag
+	:param coords: the coordinate pairs of the vertices
+	:param midx: the indices at which each part of the path starts (that is, the indices of the movetos in the path)
+	:param close: whether to toss a Z on the end of the path string
+	:param fourmat: the order and units of the coordinates in each pair.  probably "pr" if it's (ф,λ) coordinates in
+	                radians, or "xd" if it's (λ,ф) in degrees.  the output will always be expressed as (λ,ф) in degrees,
+	                so that's why I ask.
+	:param clazz: the class attribute to give the <path>, if any
+	:param ident: the id attribute to give the <path>, if any
+	:param tabs: the number of tab characters to prepend to the <path> element
+	:return: a string describing the <path> in SVG syntax, including some tab characters on the front and a newline on the back
+	"""
+	if midx is None:
+		midx = [0]
 	class_attr = f'class="{clazz}" ' if clazz is not None else ''
 	ident_attr = f'id="{ident}" ' if ident is not None else ''
 	tag = '\t'*tabs + f'<path {class_attr}{ident_attr}d="'
@@ -92,11 +107,13 @@ def plot(coords, midx=[0], close=True, fourmat='pr', clazz=None, ident=None, tab
 			letter = 'L'
 
 		if 'r' in fourmat:
-			coord = (math.degrees(c) for c in coord)
+			coord = (degrees(c) for c in coord)
 		if 'p' in fourmat:
 			y, x = coord
 		elif 'x' in fourmat:
 			x, y = coord
+		else:
+			raise ValueError(f"unrecognized format string: '{fourmat}'")
 
 		tag += '{}{:.3f},{:.3f} '.format(letter, x, y)
 	if close:
@@ -126,11 +143,11 @@ def lengthen_edges(coast):
 		x1, y1 = coast[i+1]
 		if x0 == x1 and abs(y1-y0) > 1:
 			step = 1 if y0 > y1 else -1
-			for j in range(math.ceil(abs(y1-y0))-1):
+			for j in range(int(ceil(abs(y1-y0))-1)):
 				coast.insert(i+1, (x1, y1+step*(j+1)))
 		elif y0 == y1 and abs(x1-x0) > 1:
 			step = 1 if x0 > x1 else -1
-			for j in range(math.ceil(abs(x1-x0))-1):
+			for j in range(int(ceil(abs(x1-x0))-1)):
 				coast.insert(i+1, (x1+step*(j+1), y1))
 	return coast
 
@@ -143,10 +160,10 @@ def get_centroid(points, parts=None):
 	maxP = max([p[1] for p in points])
 
 	if maxL-minL < 15 and maxP-minP < 60:
-		return ((maxL+minL)/2, (maxP+minP)/2)
-	elif parts: #if there are multiple parts, try guessing the centroid of just one; the biggest one by bounding box
+		return (maxL + minL)/2, (maxP + minP)/2
+	elif parts: # if there are multiple parts, try guessing the centroid of just one; the biggest one by bounding box
 		parts.append(len(points))
-		max_area = 0
+		max_area, best_part = 0, None
 		for i in range(1, len(parts)):
 			part = points[parts[i-1]:parts[i]]
 			minL = min([p[0] for p in part])
@@ -156,7 +173,10 @@ def get_centroid(points, parts=None):
 			if (maxL-minL)*(maxP-minP) > max_area:
 				max_area = (maxL-minL)*(maxP-minP)
 				best_part = (parts[i-1], parts[i])
-		return get_centroid(points[best_part[0]:best_part[1]])
+		if best_part is not None:
+			return get_centroid(points[best_part[0]:best_part[1]])
+		else:
+			raise ValueError("no parts from which to take the centroid were found")
 
 	lines = []
 	for i in range(1, len(points)):
@@ -164,30 +184,30 @@ def get_centroid(points, parts=None):
 	xc, yc, zc = 0, 0, 0
 	j = 0
 	num_in = 0
-	min_latnum = math.sin(math.radians(minP))
-	max_latnum = math.sin(math.radians(maxP))
-	min_lonnum = math.radians(minL)
-	max_lonnum = math.radians(maxL)
+	min_latnum = sin(radians(minP))
+	max_latnum = sin(radians(maxP))
+	min_lonnum = radians(minL)
+	max_lonnum = radians(maxL)
 	rng.seed(0)
-	while j < 4000 or num_in < 10: #monte carlo
+	while j < 4000 or num_in < 10: # monte carlo
 		j += 1
-		latr = math.asin(rng.random()*(max_latnum-min_latnum)+min_latnum)
+		latr = arcsin(rng.random()*(max_latnum-min_latnum)+min_latnum)
 		lonr = rng.random()*(max_lonnum-min_lonnum) + min_lonnum
-		latd, lond = math.degrees(latr), math.degrees(lonr)
+		latd, lond = degrees(latr), degrees(lonr)
 		num_crosses = 0
-		for l1, p1, l2, p2 in lines: #count the lines a northward ray crosses
+		for l1, p1, l2, p2 in lines: # count the lines a northward ray crosses
 			if ((l1 <= lond and l2 > lond) or (l2 <= lond and l1 > lond)) and (p1*(l2-lond)/(l2-l1) + p2*(l1-lond)/(l1-l2) > latd):
 				num_crosses += 1
 
-		if num_crosses%2 == 1: #if odd,
+		if num_crosses%2 == 1: # if odd,
 			num_in += 1
-			xc += math.cos(latr)*math.cos(lonr) #this point is in.
-			yc += math.cos(latr)*math.sin(lonr) #update the centroid
-			zc += math.sin(latr)
+			xc += cos(latr)*cos(lonr) # this point is in.
+			yc += cos(latr)*sin(lonr) # update the centroid
+			zc += sin(latr)
 
-	loncr = math.atan2(yc, xc)
-	latcr = math.atan2(zc, math.hypot(xc, yc))
-	return (math.degrees(loncr), math.degrees(latcr))
+	loncr = arctan2(yc, xc)
+	latcr = arctan2(zc, hypot(xc, yc))
+	return degrees(loncr), degrees(latcr)
 
 
 def normalize_shaperecord(shaperecord: shapefile.ShapeRecord) -> ShapeRecord: