Version 1.3 is ready.

Changelog written, release coming out soon.

.gitignore

@@ -1,4 +1,5 @@
 .vs/
+.github/
 
 Base/obj/
 Base/bin/

Base/Abstract/IConvertColumnTable.cs

@@ -0,0 +1,10 @@
+using Graphing.Graphables;
+
+namespace Graphing.Abstract;
+
+public interface IConvertColumnTable
+{
+    public bool UngraphWhenConvertedToColumnTable { get; }
+
+    public ColumnTable ToColumnTable(double start, double end, int detail);
+}

Base/Abstract/IConvertEquation.cs

@@ -0,0 +1,10 @@
+using Graphing.Graphables;
+
+namespace Graphing.Abstract;
+
+public interface IConvertEquation
+{
+    public bool UngraphWhenConvertedToEquation { get; }
+
+    public Equation ToEquation();
+}

Base/Abstract/IConvertSlopeField.cs

@@ -0,0 +1,10 @@
+using Graphing.Graphables;
+
+namespace Graphing.Abstract;
+
+public interface IConvertSlopeField
+{
+    public bool UngraphWhenConvertedToSlopeField { get; }
+
+    public SlopeField ToSlopeField(int detail);
+}

Base/Abstract/IDerivable.cs

@@ -0,0 +1,8 @@
+using Graphing.Graphables;
+
+namespace Graphing.Abstract;
+
+public interface IDerivable
+{
+    public Graphable Derive();
+}

Base/Abstract/IIntegrable.cs

@@ -0,0 +1,8 @@
+using Graphing.Graphables;
+
+namespace Graphing.Abstract;
+
+public interface IIntegrable
+{
+    public Graphable Integrate();
+}

Base/Abstract/ITranslatable.cs

@@ -0,0 +1,3 @@
+namespace Graphing.Abstract;
+
+public interface ITranslatable { }

Base/Abstract/ITranslatableX.cs

@@ -0,0 +1,6 @@
+namespace Graphing.Abstract;
+
+public interface ITranslatableX : ITranslatable
+{
+    public double OffsetX { get; set; }
+}

Base/Abstract/ITranslatableXY.cs

@@ -0,0 +1,3 @@
+namespace Graphing.Abstract;
+
+public interface ITranslatableXY : ITranslatableX, ITranslatableY { }

Base/Abstract/ITranslatableY.cs

@@ -0,0 +1,6 @@
+namespace Graphing.Abstract;
+
+public interface ITranslatableY : ITranslatable
+{
+    public double OffsetY { get; set; }
+}

Base/Base.csproj

@@ -5,23 +5,25 @@
     <TargetFramework>net8.0-windows</TargetFramework>
     <Nullable>enable</Nullable>
     <UseWindowsForms>true</UseWindowsForms>
-    <ImplicitUsings>enable</ImplicitUsings>
+    <ImplicitUsings>disable</ImplicitUsings>
     <RootNamespace>Graphing</RootNamespace>
     <AssemblyName>ThatOneNerd.Graphing</AssemblyName>
     <ProduceReferenceAssembly>True</ProduceReferenceAssembly>
     <GeneratePackageOnBuild>True</GeneratePackageOnBuild>
     <PackageId>ThatOneNerd.Graphing</PackageId>
     <Title>ThatOneNerd.Graphing</Title>
-    <Version>1.0.0</Version>
+    <Version>1.3.0</Version>
     <Authors>That_One_Nerd</Authors>
     <Description>A fairly adept graphing calculator made in Windows Forms.</Description>
     <Copyright>MIT</Copyright>
     <RepositoryUrl>https://github.com/That-One-Nerd/Graphing</RepositoryUrl>
     <PackageReadmeFile>README.md</PackageReadmeFile>
-    <PackageTags>graphing;graph;plot;math;calculus;visual;desmos</PackageTags>
+    <PackageTags>graphing;graph;plot;math;calculus;visual;desmos;slope field;slopefield;equation;visualizer;parametric equation;parametric;difference;tangent</PackageTags>
     <PackageLicenseExpression>MIT</PackageLicenseExpression>
     <IncludeSymbols>True</IncludeSymbols>
     <SymbolPackageFormat>snupkg</SymbolPackageFormat>
+    <PackageReleaseNotes>View the GitHub release for the changelog:
+https://github.com/That-One-Nerd/Graphing/releases/tag/1.3.0</PackageReleaseNotes>
   </PropertyGroup>
 
   <PropertyGroup Condition="'$(Configuration)|$(Platform)'=='Debug|AnyCPU'">

Base/Base.csproj.user

@@ -1,6 +1,12 @@
 <?xml version="1.0" encoding="utf-8"?>
 <Project ToolsVersion="Current" xmlns="http://schemas.microsoft.com/developer/msbuild/2003">
+  <PropertyGroup>
+    <_LastSelectedProfileId>C:\Users\kyley\Desktop\Coding\C#\Graphing\Base\Properties\PublishProfiles\FolderProfile.pubxml</_LastSelectedProfileId>
+  </PropertyGroup>
   <ItemGroup>
+    <Compile Update="Forms\Controls\PieChart.cs">
+      <SubType>UserControl</SubType>
+    </Compile>
     <Compile Update="Forms\GraphColorPickerForm.cs">
       <SubType>Form</SubType>
     </Compile>
@@ -10,5 +16,19 @@
     <Compile Update="Forms\SetZoomForm.cs">
       <SubType>Form</SubType>
     </Compile>
+    <Compile Update="Forms\SlopeFieldDetailForm.cs">
+      <SubType>Form</SubType>
+    </Compile>
+    <Compile Update="Forms\TranslateForm.cs">
+      <SubType>Form</SubType>
+    </Compile>
+    <Compile Update="Forms\ViewCacheForm.cs">
+      <SubType>Form</SubType>
+    </Compile>
+  </ItemGroup>
+  <ItemGroup>
+    <EmbeddedResource Update="Forms\ViewCacheForm.resx">
+      <SubType>Designer</SubType>
+    </EmbeddedResource>
   </ItemGroup>
 </Project>

Base/Extensions/FormattingExtensions.cs

@@ -0,0 +1,32 @@
+namespace Graphing.Extensions;
+
+public static class FormattingExtensions
+{
+    private static readonly string[] sizeUnits =
+    [
+        " bytes",
+        " KB",
+        " MB",
+        " GB",
+        " TB",
+        " PB",
+    ];
+
+    public static string FormatAsBytes(this long bytes)
+    {
+        double val = bytes;
+        int unitIndex = 0;
+
+        while (val > 1024)
+        {
+            unitIndex++;
+            val /= 1024;
+        }
+
+        string result;
+        if (unitIndex == 0) result = val.ToString("0");
+        else result = val.ToString("0.00");
+
+        return result + sizeUnits[unitIndex];
+    }
+}

Base/Float2.cs

@@ -1,4 +1,6 @@
-namespace Graphing;
+using System.Drawing;
+
+namespace Graphing;
 
 public record struct Float2
 {

Base/Forms/Controls/PieChart.Designer.cs

@@ -0,0 +1,46 @@
+using System.Drawing;
+
+namespace Graphing.Forms.Controls
+{
+    partial class PieChart
+    {
+        /// <summary> 
+        /// Required designer variable.
+        /// </summary>
+        private System.ComponentModel.IContainer components = null;
+
+        /// <summary> 
+        /// Clean up any resources being used.
+        /// </summary>
+        /// <param name="disposing">true if managed resources should be disposed; otherwise, false.</param>
+        protected override void Dispose(bool disposing)
+        {
+            if (disposing && (components != null))
+            {
+                components.Dispose();
+            }
+            base.Dispose(disposing);
+        }
+
+        #region Component Designer generated code
+
+        /// <summary> 
+        /// Required method for Designer support - do not modify 
+        /// the contents of this method with the code editor.
+        /// </summary>
+        private void InitializeComponent()
+        {
+            SuspendLayout();
+            // 
+            // PieChart
+            // 
+            AutoScaleDimensions = new SizeF(13F, 32F);
+            AutoScaleMode = System.Windows.Forms.AutoScaleMode.Font;
+            Name = "PieChart";
+            Size = new Size(500, 500);
+            ResumeLayout(false);
+        }
+
+        #endregion
+    }
+}

Base/Forms/Controls/PieChart.cs

@@ -0,0 +1,74 @@
+using System;
+using System.Collections.Generic;
+using System.Drawing;
+using System.Drawing.Drawing2D;
+using System.Windows.Forms;
+
+namespace Graphing.Forms.Controls;
+
+public partial class PieChart : UserControl
+{
+    public List<(Color, double)> Values { get; set; }
+
+    public float DpiFloat { get; private set; }
+
+    public PieChart()
+    {
+        SetStyle(ControlStyles.OptimizedDoubleBuffer, true);
+        SetStyle(ControlStyles.AllPaintingInWmPaint, true);
+        SetStyle(ControlStyles.UserPaint, true);
+
+        Graphics tempG = CreateGraphics();
+        DpiFloat = (tempG.DpiX + tempG.DpiY) / 2;
+        tempG.Dispose();
+
+        Values = [];
+        InitializeComponent();
+    }
+
+    protected override void OnPaint(PaintEventArgs e)
+    {
+        Graphics g = e.Graphics;
+        g.SmoothingMode = SmoothingMode.HighQuality;
+        int size = Math.Min(Width, Height);
+        Rectangle rect = new(5, 5, size - 10, size - 10);
+
+        double sum = 0;
+        foreach ((Color, double v) item in Values)
+            sum += item.v;
+
+        // Draw them.
+        double current = 0;
+        foreach ((Color color, double value) item in Values)
+        {
+            double start = 360 * current / sum,
+                   end = 360 * (current + item.value) / sum;
+
+            Brush filler = new SolidBrush(item.color);
+            g.FillPie(filler, rect, (float)start, (float)(end - start));
+
+            current += item.value;
+        }
+
+        // Draw the outline of each slice.
+        // Only done if there is more than one slice.
+        if (Values.Count > 1)
+        {
+            Pen outlinePartsPen = new(Color.FromArgb(unchecked((int)0xFF_202020)), DpiFloat * 3 / 192);
+            current = 0;
+            foreach ((Color, double value) item in Values)
+            {
+                double start = 360 * current / sum,
+                       end = 360 * (current + item.value) / sum;
+                if (item.value > 0)
+                    g.DrawPie(outlinePartsPen, rect, (float)start, (float)(end - start));
+
+                current += item.value;
+            }
+        }
+
+        // Outline
+        Pen outlinePen = new(Color.FromArgb(unchecked((int)0xFF_202020)), DpiFloat * 5 / 192);
+        g.DrawEllipse(outlinePen, rect);
+    }
+}

Base/Forms/Controls/PieChart.resx

@@ -0,0 +1,120 @@
+<?xml version="1.0" encoding="utf-8"?>
+<root>
+  <!--
+    Microsoft ResX Schema 
+
+    Version 2.0
+
+    The primary goals of this format is to allow a simple XML format
+    that is mostly human readable. The generation and parsing of the
+    various data types are done through the TypeConverter classes
+    associated with the data types.
+
+    Example:
+
+    ... ado.net/XML headers & schema ...
+    <resheader name="resmimetype">text/microsoft-resx</resheader>
+    <resheader name="version">2.0</resheader>
+    <resheader name="reader">System.Resources.ResXResourceReader, System.Windows.Forms, ...</resheader>
+    <resheader name="writer">System.Resources.ResXResourceWriter, System.Windows.Forms, ...</resheader>
+    <data name="Name1"><value>this is my long string</value><comment>this is a comment</comment></data>
+    <data name="Color1" type="System.Drawing.Color, System.Drawing">Blue</data>
+    <data name="Bitmap1" mimetype="application/x-microsoft.net.object.binary.base64">
+        <value>[base64 mime encoded serialized .NET Framework object]</value>
+    </data>
+    <data name="Icon1" type="System.Drawing.Icon, System.Drawing" mimetype="application/x-microsoft.net.object.bytearray.base64">
+        <value>[base64 mime encoded string representing a byte array form of the .NET Framework object]</value>
+        <comment>This is a comment</comment>
+    </data>
+
+    There are any number of "resheader" rows that contain simple
+    name/value pairs.
+
+    Each data row contains a name, and value. The row also contains a
+    type or mimetype. Type corresponds to a .NET class that support
+    text/value conversion through the TypeConverter architecture.
+    Classes that don't support this are serialized and stored with the
+    mimetype set.
+
+    The mimetype is used for serialized objects, and tells the
+    ResXResourceReader how to depersist the object. This is currently not
+    extensible. For a given mimetype the value must be set accordingly:
+
+    Note - application/x-microsoft.net.object.binary.base64 is the format
+    that the ResXResourceWriter will generate, however the reader can
+    read any of the formats listed below.
+
+    mimetype: application/x-microsoft.net.object.binary.base64
+    value   : The object must be serialized with
+            : System.Runtime.Serialization.Formatters.Binary.BinaryFormatter
+            : and then encoded with base64 encoding.
+    
+    mimetype: application/x-microsoft.net.object.soap.base64
+    value   : The object must be serialized with
+            : System.Runtime.Serialization.Formatters.Soap.SoapFormatter
+            : and then encoded with base64 encoding.
+
+    mimetype: application/x-microsoft.net.object.bytearray.base64
+    value   : The object must be serialized into a byte array
+            : using a System.ComponentModel.TypeConverter
+            : and then encoded with base64 encoding.
+    -->
+  <xsd:schema id="root" xmlns="" xmlns:xsd="http://www.w3.org/2001/XMLSchema" xmlns:msdata="urn:schemas-microsoft-com:xml-msdata">
+    <xsd:import namespace="http://www.w3.org/XML/1998/namespace" />
+    <xsd:element name="root" msdata:IsDataSet="true">
+      <xsd:complexType>
+        <xsd:choice maxOccurs="unbounded">
+          <xsd:element name="metadata">
+            <xsd:complexType>
+              <xsd:sequence>
+                <xsd:element name="value" type="xsd:string" minOccurs="0" />
+              </xsd:sequence>
+              <xsd:attribute name="name" use="required" type="xsd:string" />
+              <xsd:attribute name="type" type="xsd:string" />
+              <xsd:attribute name="mimetype" type="xsd:string" />
+              <xsd:attribute ref="xml:space" />
+            </xsd:complexType>
+          </xsd:element>
+          <xsd:element name="assembly">
+            <xsd:complexType>
+              <xsd:attribute name="alias" type="xsd:string" />
+              <xsd:attribute name="name" type="xsd:string" />
+            </xsd:complexType>
+          </xsd:element>
+          <xsd:element name="data">
+            <xsd:complexType>
+              <xsd:sequence>
+                <xsd:element name="value" type="xsd:string" minOccurs="0" msdata:Ordinal="1" />
+                <xsd:element name="comment" type="xsd:string" minOccurs="0" msdata:Ordinal="2" />
+              </xsd:sequence>
+              <xsd:attribute name="name" type="xsd:string" use="required" msdata:Ordinal="1" />
+              <xsd:attribute name="type" type="xsd:string" msdata:Ordinal="3" />
+              <xsd:attribute name="mimetype" type="xsd:string" msdata:Ordinal="4" />
+              <xsd:attribute ref="xml:space" />
+            </xsd:complexType>
+          </xsd:element>
+          <xsd:element name="resheader">
+            <xsd:complexType>
+              <xsd:sequence>
+                <xsd:element name="value" type="xsd:string" minOccurs="0" msdata:Ordinal="1" />
+              </xsd:sequence>
+              <xsd:attribute name="name" type="xsd:string" use="required" />
+            </xsd:complexType>
+          </xsd:element>
+        </xsd:choice>
+      </xsd:complexType>
+    </xsd:element>
+  </xsd:schema>
+  <resheader name="resmimetype">
+    <value>text/microsoft-resx</value>
+  </resheader>
+  <resheader name="version">
+    <value>2.0</value>
+  </resheader>
+  <resheader name="reader">
+    <value>System.Resources.ResXResourceReader, System.Windows.Forms, Version=4.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089</value>
+  </resheader>
+  <resheader name="writer">
+    <value>System.Resources.ResXResourceWriter, System.Windows.Forms, Version=4.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089</value>
+  </resheader>
+</root>

Base/Forms/GraphColorPickerForm.Designer.cs

@@ -1,4 +1,7 @@
-namespace Graphing.Forms
+using System.Drawing;
+using System.Windows.Forms;
+
+namespace Graphing.Forms
 {
     partial class GraphColorPickerForm
     {
@@ -40,7 +43,7 @@
             ResultView = new Panel();
             BottomPanel = new Panel();
             OkButton = new Button();
-            CancelButton = new Button();
+            CancellingButton = new Button();
             RgbSliders.SuspendLayout();
             ((System.ComponentModel.ISupportInitialize)BlueTrackBar).BeginInit();
             ((System.ComponentModel.ISupportInitialize)RedTrackBar).BeginInit();
@@ -169,7 +172,7 @@
             // 
             BottomPanel.BackColor = SystemColors.Window;
             BottomPanel.Controls.Add(OkButton);
-            BottomPanel.Controls.Add(CancelButton);
+            BottomPanel.Controls.Add(CancellingButton);
             BottomPanel.Dock = DockStyle.Bottom;
             BottomPanel.Location = new Point(0, 517);
             BottomPanel.Margin = new Padding(0);
@@ -191,15 +194,15 @@
             // 
             // CancelButton
             // 
-            CancelButton.Anchor = AnchorStyles.Right;
-            CancelButton.Location = new Point(384, 9);
-            CancelButton.Margin = new Padding(0);
-            CancelButton.Name = "CancelButton";
-            CancelButton.Size = new Size(150, 46);
-            CancelButton.TabIndex = 0;
-            CancelButton.Text = "Cancel";
-            CancelButton.UseVisualStyleBackColor = true;
-            CancelButton.Click += CancelButton_Click;
+            CancellingButton.Anchor = AnchorStyles.Right;
+            CancellingButton.Location = new Point(384, 9);
+            CancellingButton.Margin = new Padding(0);
+            CancellingButton.Name = "CancelButton";
+            CancellingButton.Size = new Size(150, 46);
+            CancellingButton.TabIndex = 0;
+            CancellingButton.Text = "Cancel";
+            CancellingButton.UseVisualStyleBackColor = true;
+            CancellingButton.Click += CancelButton_Click;
             // 
             // GraphColorPickerForm
             // 
@@ -234,7 +237,7 @@
         private TrackBar BlueTrackBar;
         private TrackBar RedTrackBar;
         private Panel BottomPanel;
-        private Button CancelButton;
+        private Button CancellingButton;
         private Button OkButton;
         private TextBox RedValueBox;
         private TextBox BlueValueBox;

Base/Forms/GraphColorPickerForm.cs

@@ -1,4 +1,8 @@
-namespace Graphing.Forms;
+using System;
+using System.Drawing;
+using System.Windows.Forms;
+
+namespace Graphing.Forms;
 
 public partial class GraphColorPickerForm : Form
 {
@@ -37,7 +41,7 @@ public partial class GraphColorPickerForm : Form
         MessageLabel.Text = $"Pick a color for {able.Name}.";
 
         // Add preset buttons.
-        const int size = 48;
+        int size = (int)(graph.DpiFloat * 48 / 192);
         int position = 0;
         foreach (uint cId in Graphable.DefaultColors)
         {

Base/Forms/GraphForm.Designer.cs

@@ -1,4 +1,7 @@
-namespace Graphing.Forms
+using System.Drawing;
+using System.Windows.Forms;
+
+namespace Graphing.Forms
 {
     partial class GraphForm
     {
@@ -35,30 +38,45 @@
             ButtonViewportSetCenter = new ToolStripMenuItem();
             ButtonViewportReset = new ToolStripMenuItem();
             ButtonViewportResetWindow = new ToolStripMenuItem();
-            MenuColors = new ToolStripMenuItem();
-            MenuEquations = new ToolStripMenuItem();
-            MenuEquationsDerivative = new ToolStripMenuItem();
-            MenuEquationsIntegral = new ToolStripMenuItem();
+            MenuElements = new ToolStripMenuItem();
+            MenuElementsColors = new ToolStripMenuItem();
+            MenuElementsRemove = new ToolStripMenuItem();
+            MenuOperations = new ToolStripMenuItem();
+            MenuOperationsDerivative = new ToolStripMenuItem();
+            MenuOperationsIntegral = new ToolStripMenuItem();
+            MenuOperationsTranslate = new ToolStripMenuItem();
+            MenuConvert = new ToolStripMenuItem();
+            MenuConvertEquation = new ToolStripMenuItem();
+            MenuConvertSlopeField = new ToolStripMenuItem();
+            MenuMisc = new ToolStripMenuItem();
+            MenuMiscCaches = new ToolStripMenuItem();
+            MiscMenuPreload = new ToolStripMenuItem();
+            UpdaterPopup = new Panel();
+            UpdaterPopupDownloadButton = new Button();
+            UpdaterPopupCloseButton = new Button();
+            UpdaterPopupMessage = new Label();
+            MenuElementsDetail = new ToolStripMenuItem();
             GraphMenu.SuspendLayout();
+            UpdaterPopup.SuspendLayout();
             SuspendLayout();
             // 
             // ResetViewportButton
             // 
             ResetViewportButton.Anchor = AnchorStyles.Top | AnchorStyles.Right;
-            ResetViewportButton.Font = new Font("Segoe UI Emoji", 13.875F, FontStyle.Regular, GraphicsUnit.Point, 0);
-            ResetViewportButton.Location = new Point(1373, 43);
+            ResetViewportButton.Font = new Font("Segoe UI Emoji", 12F, FontStyle.Regular, GraphicsUnit.Point, 0);
+            ResetViewportButton.Location = new Point(1372, 43);
+            ResetViewportButton.Margin = new Padding(4, 2, 4, 2);
             ResetViewportButton.Name = "ResetViewportButton";
-            ResetViewportButton.Size = new Size(64, 64);
+            ResetViewportButton.Size = new Size(63, 64);
             ResetViewportButton.TabIndex = 0;
-            ResetViewportButton.Text = "⌂";
-            ResetViewportButton.TextAlign = ContentAlignment.TopRight;
+            ResetViewportButton.Text = "🏠";
             ResetViewportButton.UseVisualStyleBackColor = true;
             ResetViewportButton.Click += ResetViewportButton_Click;
             // 
             // GraphMenu
             // 
             GraphMenu.ImageScalingSize = new Size(32, 32);
-            GraphMenu.Items.AddRange(new ToolStripItem[] { MenuViewport, MenuColors, MenuEquations });
+            GraphMenu.Items.AddRange(new ToolStripItem[] { MenuViewport, MenuElements, MenuOperations, MenuConvert, MenuMisc });
             GraphMenu.Location = new Point(0, 0);
             GraphMenu.Name = "GraphMenu";
             GraphMenu.Size = new Size(1449, 42);
@@ -75,68 +93,185 @@
             // ButtonViewportSetZoom
             // 
             ButtonViewportSetZoom.Name = "ButtonViewportSetZoom";
-            ButtonViewportSetZoom.Size = new Size(350, 44);
+            ButtonViewportSetZoom.Size = new Size(359, 44);
             ButtonViewportSetZoom.Text = "Set Zoom";
             ButtonViewportSetZoom.Click += ButtonViewportSetZoom_Click;
             // 
             // ButtonViewportSetCenter
             // 
             ButtonViewportSetCenter.Name = "ButtonViewportSetCenter";
-            ButtonViewportSetCenter.Size = new Size(350, 44);
+            ButtonViewportSetCenter.Size = new Size(359, 44);
             ButtonViewportSetCenter.Text = "Set Center Position";
             ButtonViewportSetCenter.Click += ButtonViewportSetCenter_Click;
             // 
             // ButtonViewportReset
             // 
             ButtonViewportReset.Name = "ButtonViewportReset";
-            ButtonViewportReset.Size = new Size(350, 44);
+            ButtonViewportReset.Size = new Size(359, 44);
             ButtonViewportReset.Text = "Reset Viewport";
             ButtonViewportReset.Click += ButtonViewportReset_Click;
             // 
             // ButtonViewportResetWindow
             // 
             ButtonViewportResetWindow.Name = "ButtonViewportResetWindow";
-            ButtonViewportResetWindow.Size = new Size(350, 44);
+            ButtonViewportResetWindow.Size = new Size(359, 44);
             ButtonViewportResetWindow.Text = "Reset Window Size";
             ButtonViewportResetWindow.Click += ButtonViewportResetWindow_Click;
             // 
-            // MenuColors
+            // MenuElements
             // 
-            MenuColors.Name = "MenuColors";
-            MenuColors.Size = new Size(101, 38);
-            MenuColors.Text = "Colors";
+            MenuElements.DropDownItems.AddRange(new ToolStripItem[] { MenuElementsColors, MenuElementsDetail, MenuElementsRemove });
+            MenuElements.Name = "MenuElements";
+            MenuElements.Size = new Size(131, 38);
+            MenuElements.Text = "Elements";
             // 
-            // MenuEquations
+            // MenuElementsColors
             // 
-            MenuEquations.DropDownItems.AddRange(new ToolStripItem[] { MenuEquationsDerivative, MenuEquationsIntegral });
-            MenuEquations.Name = "MenuEquations";
-            MenuEquations.Size = new Size(138, 38);
-            MenuEquations.Text = "Equations";
+            MenuElementsColors.Name = "MenuElementsColors";
+            MenuElementsColors.Size = new Size(359, 44);
+            MenuElementsColors.Text = "Colors";
             // 
-            // MenuEquationsDerivative
+            // MenuElementsRemove
             // 
-            MenuEquationsDerivative.Name = "MenuEquationsDerivative";
-            MenuEquationsDerivative.Size = new Size(360, 44);
-            MenuEquationsDerivative.Text = "Compute Derivative";
+            MenuElementsRemove.Name = "MenuElementsRemove";
+            MenuElementsRemove.Size = new Size(359, 44);
+            MenuElementsRemove.Text = "Remove";
             // 
-            // MenuEquationsIntegral
+            // MenuOperations
             // 
-            MenuEquationsIntegral.Name = "MenuEquationsIntegral";
-            MenuEquationsIntegral.Size = new Size(360, 44);
-            MenuEquationsIntegral.Text = "Compute Integral";
+            MenuOperations.DropDownItems.AddRange(new ToolStripItem[] { MenuOperationsDerivative, MenuOperationsIntegral, MenuOperationsTranslate });
+            MenuOperations.Name = "MenuOperations";
+            MenuOperations.Size = new Size(151, 38);
+            MenuOperations.Text = "Operations";
+            // 
+            // MenuOperationsDerivative
+            // 
+            MenuOperationsDerivative.Name = "MenuOperationsDerivative";
+            MenuOperationsDerivative.Size = new Size(360, 44);
+            MenuOperationsDerivative.Text = "Compute Derivative";
+            // 
+            // MenuOperationsIntegral
+            // 
+            MenuOperationsIntegral.Name = "MenuOperationsIntegral";
+            MenuOperationsIntegral.Size = new Size(360, 44);
+            MenuOperationsIntegral.Text = "Compute Integral";
+            // 
+            // MenuOperationsTranslate
+            // 
+            MenuOperationsTranslate.Name = "MenuOperationsTranslate";
+            MenuOperationsTranslate.Size = new Size(360, 44);
+            MenuOperationsTranslate.Text = "Translate";
+            // 
+            // MenuConvert
+            // 
+            MenuConvert.DropDownItems.AddRange(new ToolStripItem[] { MenuConvertEquation, MenuConvertSlopeField });
+            MenuConvert.Name = "MenuConvert";
+            MenuConvert.Size = new Size(118, 38);
+            MenuConvert.Text = "Convert";
+            // 
+            // MenuConvertEquation
+            // 
+            MenuConvertEquation.Name = "MenuConvertEquation";
+            MenuConvertEquation.Size = new Size(297, 44);
+            MenuConvertEquation.Text = "To Equation";
+            // 
+            // MenuConvertSlopeField
+            // 
+            MenuConvertSlopeField.Name = "MenuConvertSlopeField";
+            MenuConvertSlopeField.Size = new Size(297, 44);
+            MenuConvertSlopeField.Text = "To Slope Field";
+            // 
+            // MenuMisc
+            // 
+            MenuMisc.DropDownItems.AddRange(new ToolStripItem[] { MenuMiscCaches, MiscMenuPreload });
+            MenuMisc.Name = "MenuMisc";
+            MenuMisc.Size = new Size(83, 38);
+            MenuMisc.Text = "Misc";
+            // 
+            // MenuMiscCaches
+            // 
+            MenuMiscCaches.Name = "MenuMiscCaches";
+            MenuMiscCaches.Size = new Size(299, 44);
+            MenuMiscCaches.Text = "View Caches";
+            MenuMiscCaches.Click += MenuMiscCaches_Click;
+            // 
+            // MiscMenuPreload
+            // 
+            MiscMenuPreload.Name = "MiscMenuPreload";
+            MiscMenuPreload.Size = new Size(299, 44);
+            MiscMenuPreload.Text = "Preload Cache";
+            MiscMenuPreload.Click += MiscMenuPreload_Click;
+            // 
+            // UpdaterPopup
+            // 
+            UpdaterPopup.Anchor = AnchorStyles.Bottom | AnchorStyles.Right;
+            UpdaterPopup.BackColor = SystemColors.HighlightText;
+            UpdaterPopup.BorderStyle = BorderStyle.FixedSingle;
+            UpdaterPopup.Controls.Add(UpdaterPopupDownloadButton);
+            UpdaterPopup.Controls.Add(UpdaterPopupCloseButton);
+            UpdaterPopup.Controls.Add(UpdaterPopupMessage);
+            UpdaterPopup.Location = new Point(966, 791);
+            UpdaterPopup.Margin = new Padding(6, 6, 6, 6);
+            UpdaterPopup.Name = "UpdaterPopup";
+            UpdaterPopup.Size = new Size(483, 115);
+            UpdaterPopup.TabIndex = 2;
+            UpdaterPopup.Visible = false;
+            // 
+            // UpdaterPopupDownloadButton
+            // 
+            UpdaterPopupDownloadButton.Anchor = AnchorStyles.Bottom | AnchorStyles.Right;
+            UpdaterPopupDownloadButton.Location = new Point(336, 58);
+            UpdaterPopupDownloadButton.Margin = new Padding(6, 6, 6, 6);
+            UpdaterPopupDownloadButton.Name = "UpdaterPopupDownloadButton";
+            UpdaterPopupDownloadButton.Size = new Size(139, 49);
+            UpdaterPopupDownloadButton.TabIndex = 2;
+            UpdaterPopupDownloadButton.Text = "Visit";
+            UpdaterPopupDownloadButton.UseVisualStyleBackColor = true;
+            // 
+            // UpdaterPopupCloseButton
+            // 
+            UpdaterPopupCloseButton.Anchor = AnchorStyles.Top | AnchorStyles.Right;
+            UpdaterPopupCloseButton.Location = new Point(435, 2);
+            UpdaterPopupCloseButton.Margin = new Padding(2, 2, 2, 2);
+            UpdaterPopupCloseButton.Name = "UpdaterPopupCloseButton";
+            UpdaterPopupCloseButton.Size = new Size(45, 51);
+            UpdaterPopupCloseButton.TabIndex = 1;
+            UpdaterPopupCloseButton.Text = "X";
+            UpdaterPopupCloseButton.UseVisualStyleBackColor = true;
+            UpdaterPopupCloseButton.Click += UpdaterPopupCloseButton_Click;
+            // 
+            // UpdaterPopupMessage
+            // 
+            UpdaterPopupMessage.Anchor = AnchorStyles.Top | AnchorStyles.Bottom | AnchorStyles.Left;
+            UpdaterPopupMessage.Font = new Font("Segoe UI", 9.75F, FontStyle.Bold, GraphicsUnit.Point, 0);
+            UpdaterPopupMessage.Location = new Point(6, 6);
+            UpdaterPopupMessage.Margin = new Padding(6, 6, 6, 6);
+            UpdaterPopupMessage.Name = "UpdaterPopupMessage";
+            UpdaterPopupMessage.Size = new Size(423, 100);
+            UpdaterPopupMessage.TabIndex = 0;
+            UpdaterPopupMessage.Text = "A <type> update is available!\r\nA.B.C → E.F.G";
+            // 
+            // MenuElementsDetail
+            // 
+            MenuElementsDetail.Name = "MenuElementsDetail";
+            MenuElementsDetail.Size = new Size(359, 44);
+            MenuElementsDetail.Text = "Detail";
             // 
             // GraphForm
             // 
             AutoScaleDimensions = new SizeF(13F, 32F);
             AutoScaleMode = AutoScaleMode.Font;
             ClientSize = new Size(1449, 907);
+            Controls.Add(UpdaterPopup);
             Controls.Add(ResetViewportButton);
             Controls.Add(GraphMenu);
             MainMenuStrip = GraphMenu;
+            Margin = new Padding(4, 2, 4, 2);
             Name = "GraphForm";
             Text = "GraphFormBase";
             GraphMenu.ResumeLayout(false);
             GraphMenu.PerformLayout();
+            UpdaterPopup.ResumeLayout(false);
             ResumeLayout(false);
             PerformLayout();
         }
@@ -145,14 +280,28 @@
 
         private Button ResetViewportButton;
         private MenuStrip GraphMenu;
-        private ToolStripMenuItem MenuColors;
         private ToolStripMenuItem MenuViewport;
         private ToolStripMenuItem ButtonViewportSetZoom;
         private ToolStripMenuItem ButtonViewportSetCenter;
         private ToolStripMenuItem ButtonViewportReset;
         private ToolStripMenuItem ButtonViewportResetWindow;
-        private ToolStripMenuItem MenuEquations;
-        private ToolStripMenuItem MenuEquationsDerivative;
-        private ToolStripMenuItem MenuEquationsIntegral;
+        private ToolStripMenuItem MenuOperations;
+        private ToolStripMenuItem MenuOperationsDerivative;
+        private ToolStripMenuItem MenuOperationsIntegral;
+        private ToolStripMenuItem MenuMisc;
+        private ToolStripMenuItem MenuMiscCaches;
+        private ToolStripMenuItem MiscMenuPreload;
+        private ToolStripMenuItem MenuConvert;
+        private ToolStripMenuItem MenuConvertEquation;
+        private ToolStripMenuItem MenuElements;
+        private ToolStripMenuItem MenuElementsColors;
+        private ToolStripMenuItem MenuElementsRemove;
+        private ToolStripMenuItem MenuOperationsTranslate;
+        private ToolStripMenuItem MenuConvertSlopeField;
+        private Panel UpdaterPopup;
+        private Label UpdaterPopupMessage;
+        private Button UpdaterPopupCloseButton;
+        private Button UpdaterPopupDownloadButton;
+        private ToolStripMenuItem MenuElementsDetail;
     }
 }

Base/Forms/GraphForm.cs

@@ -1,32 +1,71 @@
-using Graphing.Graphables;
+using Graphing.Abstract;
+using Graphing.Graphables;
+using System;
+using System.Collections.Generic;
+using System.Diagnostics;
+using System.Drawing;
+using System.Drawing.Drawing2D;
+using System.Linq;
+using System.Net.Http;
+using System.Reflection;
+using System.Text.Json;
+using System.Text.Json.Nodes;
+using System.Windows.Forms;
 
 namespace Graphing.Forms;
 
 public partial class GraphForm : Form
 {
-    public Float2 ScreenCenter { get; private set; }
+    public static readonly Color BackgroundColor = Color.White;
+    public static readonly Color MainAxisColor = Color.Black;
+    public static readonly Color SemiAxisColor = Color.FromArgb(unchecked((int)0xFF_999999));    // Grayish
+    public static readonly Color QuarterAxisColor = Color.FromArgb(unchecked((int)0xFF_E0E0E0)); // Lighter grayish
+    public static readonly Color UnitsTextColor = Color.Black;
+    public static readonly Color ZoomBoxColor = Color.Black;
+
+    public static readonly Color MajorUpdateColor = Color.FromArgb(unchecked((int)0xFF_F74434)); // Red
+    public static readonly Color MinorUpdateColor = Color.FromArgb(unchecked((int)0xFF_FCA103)); // Orange
+
+    public Float2 ScreenCenter { get; set; }
     public Float2 Dpi { get; private set; }
 
-    public double ZoomLevel
+    public float DpiFloat { get; private set; }
+
+    public Float2 ZoomLevel
     {
         get => _zoomLevel;
         set
         {
-            double oldZoom = ZoomLevel;
+            _zoomLevel = new(Math.Clamp(value.x, 1e-5, 1e3),
+                             Math.Clamp(value.y, 1e-5, 1e3));
+            OnZoomLevelChanged(this, new());
+            Invalidate(false);
+        }
+    }
+    private Float2 _zoomLevel;
 
-            _zoomLevel = Math.Clamp(value, 1e-2, 1e3);
-
-            int totalSegments = 0;
-            foreach (Graphable able in ables) totalSegments += able.GetItemsToRender(this).Count();
-
-            if (totalSegments > 10_000)
+    public bool ViewportLocked
     {
-                _zoomLevel = oldZoom;
-                return; // Too many segments, stop.
+        get => _viewportLocked;
+        set
+        {
+            if (value)
+            {
+                FormBorderStyle = FormBorderStyle.FixedSingle;
+                ResetViewportButton.Text = "🔒";
+            }
+            else
+            {
+                FormBorderStyle = FormBorderStyle.Sizable;
+                ResetViewportButton.Text = "🏠";
+            }
+            MaximizeBox = !value;
+            ResetViewportButton.Enabled = !value;
+
+            _viewportLocked = value;
         }
     }
-    }
-    private double _zoomLevel;
+    private bool _viewportLocked;
 
     private readonly Point initialWindowPos;
     private readonly Size initialWindowSize;
@@ -38,6 +77,8 @@ public partial class GraphForm : Form
 
     private readonly List<Graphable> ables;
 
+    public event EventHandler OnZoomLevelChanged = delegate { };
+
     public GraphForm(string title)
     {
         SetStyle(ControlStyles.OptimizedDoubleBuffer, true);
@@ -50,10 +91,15 @@ public partial class GraphForm : Form
         Graphics tempG = CreateGraphics();
         Dpi = new(tempG.DpiX, tempG.DpiY);
         tempG.Dispose();
+
+        DpiFloat = (float)((Dpi.x + Dpi.y) / 2);
+
         ables = [];
-        ZoomLevel = 1;
+        ZoomLevel = new(1, 1);
         initialWindowPos = Location;
         initialWindowSize = Size;
+
+        RunUpdateChecker();
     }
 
     public Int2 GraphSpaceToScreenSpace(Float2 graphPoint)
@@ -63,8 +109,8 @@ public partial class GraphForm : Form
         graphPoint.x -= ScreenCenter.x;
         graphPoint.y -= ScreenCenter.y;
 
-        graphPoint.x *= Dpi.x / ZoomLevel;
-        graphPoint.y *= Dpi.y / ZoomLevel;
+        graphPoint.x *= Dpi.x / ZoomLevel.x;
+        graphPoint.y *= Dpi.y / ZoomLevel.y;
 
         graphPoint.x += ClientRectangle.Width / 2.0;
         graphPoint.y += ClientRectangle.Height / 2.0;
@@ -78,8 +124,8 @@ public partial class GraphForm : Form
         result.x -= ClientRectangle.Width / 2.0;
         result.y -= ClientRectangle.Height / 2.0;
 
-        result.x /= Dpi.x / ZoomLevel;
-        result.y /= Dpi.y / ZoomLevel;
+        result.x /= Dpi.x / ZoomLevel.x;
+        result.y /= Dpi.y / ZoomLevel.y;
 
         result.x += ScreenCenter.x;
         result.y += ScreenCenter.y;
@@ -91,19 +137,20 @@ public partial class GraphForm : Form
 
     protected virtual void PaintGrid(Graphics g)
     {
-        double axisScale = Math.Pow(2, Math.Round(Math.Log2(ZoomLevel)));
+        double axisScaleX = Math.Pow(2, Math.Round(Math.Log2(ZoomLevel.x))),
+               axisScaleY = Math.Pow(2, Math.Round(Math.Log2(ZoomLevel.y)));
 
         // Draw horizontal/vertical quarter-axis.
-        Brush quarterBrush = new SolidBrush(Color.FromArgb(unchecked((int)0xFF_E0E0E0)));
-        Pen quarterPen = new(quarterBrush, 2);
+        Brush quarterBrush = new SolidBrush(QuarterAxisColor);
+        Pen quarterPen = new(quarterBrush, DpiFloat * 2 / 192);
 
-        for (double x = Math.Ceiling(MinVisibleGraph.x * 4 / axisScale) * axisScale / 4; x <= Math.Floor(MaxVisibleGraph.x * 4 / axisScale) * axisScale / 4; x += axisScale / 4)
+        for (double x = Math.Ceiling(MinVisibleGraph.x * 4 / axisScaleX) * axisScaleX / 4; x <= Math.Floor(MaxVisibleGraph.x * 4 / axisScaleX) * axisScaleX / 4; x += axisScaleX / 4)
         {
             Int2 startPos = GraphSpaceToScreenSpace(new Float2(x, MinVisibleGraph.y)),
                  endPos = GraphSpaceToScreenSpace(new Float2(x, MaxVisibleGraph.y));
             g.DrawLine(quarterPen, startPos, endPos);
         }
-        for (double y = Math.Ceiling(MinVisibleGraph.y * 4 / axisScale) * axisScale / 4; y <= Math.Floor(MaxVisibleGraph.y * 4 / axisScale) * axisScale / 4; y += axisScale / 4)
+        for (double y = Math.Ceiling(MinVisibleGraph.y * 4 / axisScaleY) * axisScaleY / 4; y <= Math.Floor(MaxVisibleGraph.y * 4 / axisScaleY) * axisScaleY / 4; y += axisScaleY / 4)
         {
             Int2 startPos = GraphSpaceToScreenSpace(new Float2(MinVisibleGraph.x, y)),
                  endPos = GraphSpaceToScreenSpace(new Float2(MaxVisibleGraph.x, y));
@@ -111,24 +158,24 @@ public partial class GraphForm : Form
         }
 
         // Draw horizontal/vertical semi-axis.
-        Brush semiBrush = new SolidBrush(Color.FromArgb(unchecked((int)0xFF_999999)));
-        Pen semiPen = new(semiBrush, 2);
+        Brush semiBrush = new SolidBrush(SemiAxisColor);
+        Pen semiPen = new(semiBrush, DpiFloat * 2 / 192);
 
-        for (double x = Math.Ceiling(MinVisibleGraph.x / axisScale) * axisScale; x <= Math.Floor(MaxVisibleGraph.x / axisScale) * axisScale; x += axisScale)
+        for (double x = Math.Ceiling(MinVisibleGraph.x / axisScaleX) * axisScaleX; x <= Math.Floor(MaxVisibleGraph.x / axisScaleX) * axisScaleX; x += axisScaleX)
         {
             Int2 startPos = GraphSpaceToScreenSpace(new Float2(x, MinVisibleGraph.y)),
                  endPos = GraphSpaceToScreenSpace(new Float2(x, MaxVisibleGraph.y));
             g.DrawLine(semiPen, startPos, endPos);
         }
-        for (double y = Math.Ceiling(MinVisibleGraph.y / axisScale) * axisScale; y <= Math.Floor(MaxVisibleGraph.y / axisScale) * axisScale; y += axisScale)
+        for (double y = Math.Ceiling(MinVisibleGraph.y / axisScaleY) * axisScaleY; y <= Math.Floor(MaxVisibleGraph.y / axisScaleY) * axisScaleY; y += axisScaleY)
         {
             Int2 startPos = GraphSpaceToScreenSpace(new Float2(MinVisibleGraph.x, y)),
                  endPos = GraphSpaceToScreenSpace(new Float2(MaxVisibleGraph.x, y));
             g.DrawLine(semiPen, startPos, endPos);
         }
 
-        Brush mainLineBrush = new SolidBrush(Color.Black);
-        Pen mainLinePen = new(mainLineBrush, 3);
+        Brush mainLineBrush = new SolidBrush(MainAxisColor);
+        Pen mainLinePen = new(mainLineBrush, DpiFloat * 3 / 192);
 
         // Draw the main axis (on top of the semi axis).
         Int2 startCenterY = GraphSpaceToScreenSpace(new Float2(0, MinVisibleGraph.y)),
@@ -139,32 +186,98 @@ public partial class GraphForm : Form
         g.DrawLine(mainLinePen, startCenterX, endCenterX);
         g.DrawLine(mainLinePen, startCenterY, endCenterY);
     }
+    protected virtual void PaintUnits(Graphics g)
+    {
+        double axisScaleX = Math.Pow(2, Math.Round(Math.Log2(ZoomLevel.x))),
+               axisScaleY = Math.Pow(2, Math.Round(Math.Log2(ZoomLevel.y)));
+        Brush textBrush = new SolidBrush(UnitsTextColor);
+        Font textFont = new(Font.Name, 9, FontStyle.Regular);
+
+        // X-axis
+        int minX = (int)(DpiFloat * 50 / 192),
+            maxX = ClientRectangle.Height - (int)(DpiFloat * 40 / 192);
+        for (double x = Math.Ceiling(MinVisibleGraph.x / axisScaleX) * axisScaleX; x <= MaxVisibleGraph.x; x += axisScaleX)
+        {
+            if (x == 0) x = 0; // Fixes -0
+
+            Int2 screenPos = GraphSpaceToScreenSpace(new Float2(x, 0));
+
+            if (screenPos.y < minX) screenPos.y = minX;
+            else if (screenPos.y > maxX) screenPos.y = maxX;
+
+            g.DrawString($"{x}", textFont, textBrush, screenPos.x, screenPos.y);
+        }
+
+        // Y-axis
+        int minY = (int)(DpiFloat * 10 / 192);
+        for (double y = Math.Ceiling(MinVisibleGraph.y / axisScaleY) * axisScaleY; y <= MaxVisibleGraph.y; y += axisScaleY)
+        {
+            if (y == 0) continue;
+
+            Int2 screenPos = GraphSpaceToScreenSpace(new Float2(0, y));
+
+            string result = y.ToString();
+            int maxY = ClientRectangle.Width - (int)(DpiFloat * (textFont.Height * result.Length * 0.40 + 15) / 192);
+
+            if (screenPos.x < minY) screenPos.x = minY;
+            else if (screenPos.x > maxY) screenPos.x = maxY;
+
+            g.DrawString($"{y}", textFont, textBrush, screenPos.x, screenPos.y);
+        }
+    }
 
     protected override void OnPaint(PaintEventArgs e)
     {
         Graphics g = e.Graphics;
+        g.SmoothingMode = SmoothingMode.HighQuality;
 
-        Brush background = new SolidBrush(Color.White);
+        Brush background = new SolidBrush(BackgroundColor);
         g.FillRectangle(background, e.ClipRectangle);
 
         PaintGrid(g);
+        PaintUnits(g);
+
+        Point clientMousePos = PointToClient(Cursor.Position);
+        Float2 graphMousePos = ScreenSpaceToGraphSpace(new(clientMousePos.X,
+                                                           clientMousePos.Y));
 
         // Draw the actual graphs.
+        Pen[] graphPens = new Pen[ables.Count];
         for (int i = 0; i < ables.Count; i++)
         {
-            IEnumerable<Line2d> lines = ables[i].GetItemsToRender(this);
+            IEnumerable<IGraphPart> lines = ables[i].GetItemsToRender(this);
             Brush graphBrush = new SolidBrush(ables[i].Color);
-            Pen penBrush = new(graphBrush, 3);
-
-            foreach (Line2d l in lines)
-            {
-                if (!double.IsNormal(l.a.x) || !double.IsNormal(l.a.y) ||
-                    !double.IsNormal(l.b.x) || !double.IsNormal(l.b.y)) continue;
-
-                Int2 start = GraphSpaceToScreenSpace(l.a),
-                     end = GraphSpaceToScreenSpace(l.b);
-                g.DrawLine(penBrush, start, end);
+            Pen graphPen = new(graphBrush, DpiFloat * 3 / 192);
+            graphPens[i] = graphPen;
+            foreach (IGraphPart gp in lines) gp.Render(this, g, graphPen);
         }
+
+        // Equation selection detection.
+        // This system lets you select multiple graphs, and that's cool by me.
+        if (selectState == SelectionState.GraphSelect)
+        {
+            for (int i = 0; i < ables.Count; i++)
+            {
+                if (ables[i].ShouldSelectGraphable(this, graphMousePos, 2.5))
+                {
+                    IEnumerable<IGraphPart> selectionParts = ables[i].GetSelectionItemsToRender(this, graphMousePos);
+                    foreach (IGraphPart selPart in selectionParts) selPart.Render(this, g, graphPens[i]);
+                }
+            }
+        }
+        else if (selectState == SelectionState.ZoomBox)
+        {
+            // Draw the current box selection.
+            Int2 boxPosA = GraphSpaceToScreenSpace(boxSelectA),
+                 boxPosB = GraphSpaceToScreenSpace(boxSelectB);
+
+            if (boxPosA.x > boxPosB.x) (boxPosA.x, boxPosB.x) = (boxPosB.x, boxPosA.x);
+            if (boxPosA.y > boxPosB.y) (boxPosA.y, boxPosB.y) = (boxPosB.y, boxPosA.y);
+
+            Pen boxPen = new(ZoomBoxColor, 2 * DpiFloat / 192);
+            g.DrawRectangle(boxPen, new(boxPosA.x, boxPosA.y,
+                                        boxPosB.x - boxPosA.x,
+                                        boxPosB.y - boxPosA.y));
         }
 
         base.OnPaint(e);
@@ -175,60 +288,153 @@ public partial class GraphForm : Form
         Invalidate(false);
     }
 
-    public void Graph(Graphable able)
+    public void Graph(params Graphable[] newAbles)
     {
-        ables.Add(able);
+        ables.AddRange(newAbles);
+        RegenerateMenuItems();
+        Invalidate(false);
+    }
+    public void Ungraph(params Graphable[] ables)
+    {
+        this.ables.RemoveAll(x => ables.Contains(x));
         RegenerateMenuItems();
         Invalidate(false);
     }
 
-    private bool mouseDrag = false;
+    public bool IsGraphPointVisible(Float2 point)
+    {
+        Int2 pixelPos = GraphSpaceToScreenSpace(point);
+        return pixelPos.x >= 0 && pixelPos.x < ClientRectangle.Width &&
+               pixelPos.y >= 0 && pixelPos.y < ClientRectangle.Height;
+    }
+
+    private SelectionState selectState = SelectionState.None;
+    internal bool canBoxSelect;
+    private SetZoomForm? setZoomForm;
+
     private Int2 initialMouseLocation;
     private Float2 initialScreenCenter;
+
+    private Float2 boxSelectA, boxSelectB;
+
     protected override void OnMouseDown(MouseEventArgs e)
     {
-        mouseDrag = true;
+        if (selectState == SelectionState.None && canBoxSelect)
+        {
+            Point clientMousePos = PointToClient(Cursor.Position);
+            Float2 graphMousePos = ScreenSpaceToGraphSpace(new(clientMousePos.X,
+                                                               clientMousePos.Y));
+
+            boxSelectA = graphMousePos;
+            boxSelectB = graphMousePos;
+
+            selectState = SelectionState.ZoomBox;
+        }
+
+        if (selectState == SelectionState.None)
+        {
+            Point clientMousePos = PointToClient(Cursor.Position);
+            Float2 graphMousePos = ScreenSpaceToGraphSpace(new(clientMousePos.X,
+                                                               clientMousePos.Y));
+            foreach (Graphable able in Graphables)
+            {
+                if (able.ShouldSelectGraphable(this, graphMousePos, 1))
+                    selectState = SelectionState.GraphSelect;
+            }
+            if (selectState == SelectionState.GraphSelect) Invalidate(false);
+        }
+
+        if (selectState == SelectionState.None && !ViewportLocked)
+        {
+            selectState = SelectionState.ViewportDrag;
             initialMouseLocation = new Int2(Cursor.Position.X, Cursor.Position.Y);
             initialScreenCenter = ScreenCenter;
         }
+    }
     protected override void OnMouseUp(MouseEventArgs e)
     {
-        if (mouseDrag)
+        if (selectState == SelectionState.None) return;
+        else if (selectState == SelectionState.ViewportDrag)
         {
             Int2 pixelDiff = new(initialMouseLocation.x - Cursor.Position.X,
                              initialMouseLocation.y - Cursor.Position.Y);
-            Float2 graphDiff = new(pixelDiff.x * ZoomLevel / Dpi.x, pixelDiff.y * ZoomLevel / Dpi.y);
+            Float2 graphDiff = new(pixelDiff.x * ZoomLevel.x / Dpi.x, pixelDiff.y * ZoomLevel.y / Dpi.y);
             ScreenCenter = new(initialScreenCenter.x + graphDiff.x,
                                initialScreenCenter.y + graphDiff.y);
-            Invalidate(false);
         }
-        mouseDrag = false;
+        else if (selectState == SelectionState.ZoomBox)
+        {
+            Point clientMousePos = PointToClient(Cursor.Position);
+            Float2 graphMousePos = ScreenSpaceToGraphSpace(new(clientMousePos.X,
+                                                               clientMousePos.Y));
+            boxSelectB = graphMousePos;
+
+            // Set center.
+            ScreenCenter = new((boxSelectA.x + boxSelectB.x) * 0.5,
+                              -(boxSelectA.y + boxSelectB.y) * 0.5);
+
+            // Set zoom. Kind of weird but it works.
+            Float2 minGraph = MinVisibleGraph, maxGraph = MaxVisibleGraph;
+            Float2 oldDist = new(maxGraph.x - minGraph.x,
+                                 maxGraph.y - minGraph.y);
+            Float2 newDist = new(Math.Abs(boxSelectB.x - boxSelectA.x),
+                                 Math.Abs(boxSelectB.y - boxSelectA.y));
+            ZoomLevel = new(ZoomLevel.x * newDist.x / oldDist.x,
+                            ZoomLevel.y * newDist.y / oldDist.y);
+
+            setZoomForm!.CompleteBoxSelection();
+
+            boxSelectA = new(0, 0);
+            boxSelectB = new(0, 0);
+        }
+        selectState = SelectionState.None;
+        Invalidate(false);
     }
     protected override void OnMouseMove(MouseEventArgs e)
     {
-        if (mouseDrag)
+        if (selectState == SelectionState.None) return;
+        else if (selectState == SelectionState.ViewportDrag)
         {
             Int2 pixelDiff = new(initialMouseLocation.x - Cursor.Position.X,
                              initialMouseLocation.y - Cursor.Position.Y);
-            Float2 graphDiff = new(pixelDiff.x * ZoomLevel / Dpi.x, pixelDiff.y * ZoomLevel / Dpi.y);
+            Float2 graphDiff = new(pixelDiff.x * ZoomLevel.x / Dpi.x, pixelDiff.y * ZoomLevel.y / Dpi.y);
             ScreenCenter = new(initialScreenCenter.x + graphDiff.x,
                                initialScreenCenter.y + graphDiff.y);
-            Invalidate(false);
         }
+        else if (selectState == SelectionState.ZoomBox)
+        {
+            Point clientMousePos = PointToClient(Cursor.Position);
+            Float2 graphMousePos = ScreenSpaceToGraphSpace(new(clientMousePos.X,
+                                                               clientMousePos.Y));
+            boxSelectB = graphMousePos;
+        }
+        Invalidate(false);
     }
     protected override void OnMouseWheel(MouseEventArgs e)
     {
-        ZoomLevel *= 1 - e.Delta * 0.00075; // Zoom factor.
+        if (ViewportLocked) return;
+
+        Point clientMousePos = PointToClient(Cursor.Position);
+        Int2 mousePos = new(clientMousePos.X, clientMousePos.Y);
+        Float2 mouseOver = ScreenSpaceToGraphSpace(mousePos);
+
+        Float2 newZoom = ZoomLevel;
+        newZoom.x *= 1 - e.Delta * 0.00075; // Zoom factor.
+        newZoom.y *= 1 - e.Delta * 0.00075;
+        ZoomLevel = newZoom;
+
+        // Keep the mouse as the zoom hotspot.
+        Float2 newOver = ScreenSpaceToGraphSpace(mousePos);
+        Float2 delta = new(newOver.x - mouseOver.x, newOver.y - mouseOver.y);
+        ScreenCenter = new(ScreenCenter.x - delta.x, ScreenCenter.y + delta.y);
+
         Invalidate(false);
     }
 
     private void ResetViewportButton_Click(object? sender, EventArgs e)
     {
-        ScreenCenter = new Float2(0, 0);
-        ZoomLevel = 1;
-        Invalidate(false);
+        ResetAllViewport();
     }
-
     private void GraphColorPickerButton_Click(Graphable able)
     {
         GraphColorPickerForm picker = new(this, able)
@@ -237,15 +443,57 @@ public partial class GraphForm : Form
         };
         picker.Location = new Point(Location.X + ClientRectangle.Width + 10,
                                     Location.Y + (ClientRectangle.Height - picker.ClientRectangle.Height) / 2);
+
+        if (picker.Location.X + picker.Width > Screen.FromControl(this).WorkingArea.Width)
+        {
+            picker.StartPosition = FormStartPosition.WindowsDefaultLocation;
+        }
+
+        picker.TopMost = true;
         picker.ShowDialog();
         RegenerateMenuItems();
     }
 
+    private readonly Dictionary<SlopeField, SlopeFieldDetailForm> sfDetailForms = [];
+    private void ChangeSlopeFieldDetail(SlopeField sf)
+    {
+        if (sfDetailForms.TryGetValue(sf, out SlopeFieldDetailForm? preexistingForm))
+        {
+            preexistingForm.Focus();
+            return;
+        }
+
+        SlopeFieldDetailForm detailForm = new(this, sf)
+        {
+            StartPosition = FormStartPosition.Manual
+        };
+        sfDetailForms.Add(sf, detailForm);
+
+        detailForm.Location = new Point(Location.X + ClientRectangle.Width + 10,
+                                        Location.Y + (ClientRectangle.Height - detailForm.ClientRectangle.Height) / 2);
+
+        if (detailForm.Location.X + detailForm.Width > Screen.FromControl(this).WorkingArea.Width)
+        {
+            detailForm.StartPosition = FormStartPosition.WindowsDefaultLocation;
+        }
+        detailForm.TopMost = true;
+        detailForm.Show();
+
+        detailForm.FormClosed += (o, e) => sfDetailForms.Remove(sf);
+    }
+
     private void RegenerateMenuItems()
     {
-        MenuColors.DropDownItems.Clear();
-        MenuEquationsDerivative.DropDownItems.Clear();
-        MenuEquationsIntegral.DropDownItems.Clear();
+        MenuElementsColors.DropDownItems.Clear();
+        MenuElementsDetail.DropDownItems.Clear();
+        MenuElementsRemove.DropDownItems.Clear();
+        MenuOperationsDerivative.DropDownItems.Clear();
+        MenuOperationsIntegral.DropDownItems.Clear();
+        MenuConvertEquation.DropDownItems.Clear();
+        MenuConvertSlopeField.DropDownItems.Clear();
+        MenuOperationsTranslate.DropDownItems.Clear();
+        // At some point, we'll have a Convert To Column Table button,
+        // but I'll need to make a form for the ranges when I do that.
 
         foreach (Graphable able in ables)
         {
@@ -255,52 +503,126 @@ public partial class GraphForm : Form
                 Text = able.Name
             };
             colorItem.Click += (o, e) => GraphColorPickerButton_Click(able);
-            MenuColors.DropDownItems.Add(colorItem);
+            MenuElementsColors.DropDownItems.Add(colorItem);
 
-            if (able is Equation)
+            ToolStripMenuItem removeItem = new()
+            {
+                ForeColor = able.Color,
+                Text = able.Name
+            };
+            removeItem.Click += (o, e) => Ungraph(able);
+            MenuElementsRemove.DropDownItems.Add(removeItem);
+
+            if (able is SlopeField sf)
+            {
+                ToolStripMenuItem sfDetailItem = new()
+                {
+                    ForeColor = able.Color,
+                    Text = able.Name
+                };
+                sfDetailItem.Click += (o, e) => ChangeSlopeFieldDetail(sf);
+                MenuElementsDetail.DropDownItems.Add(sfDetailItem);
+            }
+
+            if (able is IDerivable derivable)
             {
                 ToolStripMenuItem derivativeItem = new()
                 {
                     ForeColor = able.Color,
                     Text = able.Name
                 };
-                derivativeItem.Click += (o, e) => EquationComputeDerivative_Click((able as Equation)!);
-                MenuEquationsDerivative.DropDownItems.Add(derivativeItem);
-
+                derivativeItem.Click += (o, e) => Graph(derivable.Derive());
+                MenuOperationsDerivative.DropDownItems.Add(derivativeItem);
+            }
+            if (able is IIntegrable integrable)
+            {
                 ToolStripMenuItem integralItem = new()
                 {
                     ForeColor = able.Color,
                     Text = able.Name
                 };
-                integralItem.Click += (o, e) => EquationComputeIntegral_Click((able as Equation)!);
-                MenuEquationsIntegral.DropDownItems.Add(integralItem);
+                integralItem.Click += (o, e) => Graph(integrable.Integrate());
+                MenuOperationsIntegral.DropDownItems.Add(integralItem);
+            }
+            if (able is IConvertEquation equConvert)
+            {
+                ToolStripMenuItem equItem = new()
+                {
+                    ForeColor = able.Color,
+                    Text = able.Name
+                };
+                equItem.Click += (o, e) =>
+                {
+                    if (equConvert.UngraphWhenConvertedToEquation) Ungraph(able);
+                    Graph(equConvert.ToEquation());
+                };
+                MenuConvertEquation.DropDownItems.Add(equItem);
+            }
+            if (able is IConvertSlopeField sfConvert)
+            {
+                ToolStripMenuItem sfItem = new()
+                {
+                    ForeColor = able.Color,
+                    Text = able.Name
+                };
+                sfItem.Click += (o, e) =>
+                {
+                    if (sfConvert.UngraphWhenConvertedToSlopeField) Ungraph(able);
+                    Graph(sfConvert.ToSlopeField(2));
+                };
+                MenuConvertSlopeField.DropDownItems.Add(sfItem);
+            }
+            if (able is ITranslatable translatable)
+            {
+                ToolStripMenuItem transItem = new()
+                {
+                    ForeColor = able.Color,
+                    Text = able.Name
+                };
+                transItem.Click += (o, e) => ElementsOperationsTranslate_Click(able, translatable);
+                MenuOperationsTranslate.DropDownItems.Add(transItem);
             }
         }
     }
 
     private void ButtonViewportSetZoom_Click(object? sender, EventArgs e)
     {
-        SetZoomForm picker = new(this)
+        if (setZoomForm is not null)
+        {
+            setZoomForm.Focus();
+            return;
+        }
+
+        SetZoomForm zoomForm = new(this)
         {
             StartPosition = FormStartPosition.Manual,
         };
-        picker.Location = new Point(Location.X + ClientRectangle.Width + 10,
-                                    Location.Y + (ClientRectangle.Height - picker.ClientRectangle.Height) / 2);
-        picker.ShowDialog();
+        zoomForm.Location = new Point(Location.X + ClientRectangle.Width + 10,
+                                    Location.Y + (ClientRectangle.Height - zoomForm.ClientRectangle.Height) / 2);
+
+        if (zoomForm.Location.X + zoomForm.Width > Screen.FromControl(this).WorkingArea.Width)
+        {
+            zoomForm.StartPosition = FormStartPosition.WindowsDefaultLocation;
         }
 
+        setZoomForm = zoomForm;
+        zoomForm.Show();
+        zoomForm.FormClosing += (o, e) =>
+        {
+            zoomForm.CompleteBoxSelection();
+            setZoomForm = null;
+        };
+    }
     private void ButtonViewportSetCenter_Click(object? sender, EventArgs e)
     {
         MessageBox.Show("TODO", "Set Center Position", MessageBoxButtons.OK, MessageBoxIcon.Error);
     }
-
     private void ButtonViewportReset_Click(object? sender, EventArgs e)
     {
         ScreenCenter = new Float2(0, 0);
-        ZoomLevel = 1;
+        ZoomLevel = new(1, 1);
         Invalidate(false);
     }
-
     private void ButtonViewportResetWindow_Click(object? sender, EventArgs e)
     {
         Location = initialWindowPos;
@@ -308,60 +630,147 @@ public partial class GraphForm : Form
         WindowState = FormWindowState.Normal;
     }
 
-    private void EquationComputeDerivative_Click(Equation equation)
+    public void ResetAllViewport()
     {
-        EquationDelegate equ = equation.GetDelegate();
-        string oldName = equation.Name, newName;
-        if (oldName.StartsWith("Derivative of ")) newName = "Second Derivative of " + oldName[14..];
-        else if (oldName.StartsWith("Second Derivative of ")) newName = "Third Derivative of " + oldName[21..];
-        else newName = "Derivative of " + oldName;
-        // TODO: anti-integrate (maybe).
+        ScreenCenter = new Float2(0, 0);
+        ZoomLevel = new(1, 1);
+        Location = initialWindowPos;
+        Size = initialWindowSize;
+        WindowState = FormWindowState.Normal;
+        Invalidate(false);
+    }
 
-        Graph(new Equation(DerivativeAtPoint(equ))
+    private ViewCacheForm? cacheForm;
+    private void MenuMiscCaches_Click(object? sender, EventArgs e)
     {
-            Name = newName
-        });
+        if (this.cacheForm is not null)
+        {
+            this.cacheForm.Focus();
+            return;
+        }
 
-        static EquationDelegate DerivativeAtPoint(EquationDelegate e)
+        ViewCacheForm cacheForm = new(this)
         {
-            const double step = 1e-3;
-            return x => (e(x + step) - e(x)) / step;
+            StartPosition = FormStartPosition.Manual
+        };
+        this.cacheForm = cacheForm;
+
+        cacheForm.Location = new Point(Location.X + ClientRectangle.Width + 10,
+                                       Location.Y + (ClientRectangle.Height - cacheForm.ClientRectangle.Height) / 2);
+
+        if (cacheForm.Location.X + cacheForm.Width > Screen.FromControl(this).WorkingArea.Width)
+        {
+            cacheForm.StartPosition = FormStartPosition.WindowsDefaultLocation;
+        }
+        cacheForm.TopMost = true;
+        cacheForm.Show();
+    }
+    private void MiscMenuPreload_Click(object? sender, EventArgs e)
+    {
+        Float2 min = MinVisibleGraph, max = MaxVisibleGraph;
+        Float2 add = new(max.x - min.x, max.y - min.y);
+        add.x *= 0.75; // Expansion
+        add.y *= 0.75; // Screen + 75%
+
+        Float2 xRange = new(min.x - add.x, max.x + add.x),
+               yRange = new(min.y - add.y, max.y + add.y);
+
+        double step = ScreenSpaceToGraphSpace(new Int2(1, 0)).x
+                    - ScreenSpaceToGraphSpace(new Int2(0, 0)).x;
+        step /= 10;
+
+        foreach (Graphable able in Graphables) able.Preload(xRange, yRange, step);
+        Invalidate(false);
+    }
+    private void UpdaterPopupCloseButton_Click(object? sender, EventArgs e)
+    {
+        UpdaterPopup.Dispose();
+    }
+
+    private void ElementsOperationsTranslate_Click(Graphable ableRaw, ITranslatable ableTrans)
+    {
+        TranslateForm shifter = new(this, ableRaw, ableTrans)
+        {
+            StartPosition = FormStartPosition.Manual,
+        };
+        shifter.Location = new Point(Location.X + ClientRectangle.Width + 10,
+                                     Location.Y + (ClientRectangle.Height - shifter.ClientRectangle.Height) / 2);
+        if (shifter.Location.X + shifter.Width > Screen.FromControl(this).WorkingArea.Width)
+        {
+            shifter.StartPosition = FormStartPosition.WindowsDefaultLocation;
+        }
+        shifter.Show();
+    }
+
+    private async void RunUpdateChecker()
+    {
+        try
+        {
+            HttpClient http = new();
+            HttpRequestMessage request = new(HttpMethod.Get, "https://api.github.com/repos/That-One-Nerd/Graphing/releases");
+            request.Headers.Add("User-Agent", "ThatOneNerd.Graphing-Update-Checker");
+
+            HttpResponseMessage result = await http.SendAsync(request);
+            if (!result.IsSuccessStatusCode)
+            {
+                Console.WriteLine($"Failed to check for updates.");
+                return;
+            }
+
+            JsonArray arr = JsonSerializer.Deserialize<JsonArray>(await result.Content.ReadAsStreamAsync())!;
+            JsonObject latest = arr[0]!.AsObject();
+
+            Version curVersion = Version.Parse(Assembly.GetAssembly(typeof(GraphForm))!.FullName!.Split(',')[1].Trim()[8..^2]);
+            Version newVersion = Version.Parse(latest["tag_name"]!.GetValue<string>());
+
+            if (newVersion > curVersion)
+            {
+                string type;
+
+                if (newVersion.Major > curVersion.Major || // x.0.0
+                    newVersion.Minor > curVersion.Minor)   // 0.x.0
+                {
+                    type = "major";
+                    UpdaterPopupMessage.ForeColor = MajorUpdateColor;
+                }
+                else                                       // 0.0.x
+                {
+                    type = "minor";
+                    UpdaterPopupMessage.ForeColor = MinorUpdateColor;
+                }
+
+                UpdaterPopupMessage.Text = $"A {type} update is available!\n{curVersion} → {newVersion}";
+                UpdaterPopup.Visible = true;
+
+                string url = latest["html_url"]!.GetValue<string>();
+                Console.WriteLine($"An update is available! {curVersion} -> {newVersion}\n{url}");
+                UpdaterPopupDownloadButton.Click += (o, e) =>
+                {
+                    ProcessStartInfo website = new()
+                    {
+                        FileName = url,
+                        UseShellExecute = true
+                    };
+                    Process.Start(website);
+                };
+            }
+            else
+            {
+                Console.WriteLine("Up-to-date.");
+                UpdaterPopup.Dispose();
+            }
+        }
+        catch (Exception ex)
+        {
+            Console.WriteLine($"Failed to check for updates:\n{ex}");
         }
     }
 
-    private void EquationComputeIntegral_Click(Equation equation)
+    private enum SelectionState
     {
-        EquationDelegate equ = equation.GetDelegate();
-        string oldName = equation.Name, newName;
-        if (oldName.StartsWith("Integral of ")) newName = "Second Integral of " + oldName[12..];
-        else if (oldName.StartsWith("Second Integral of ")) newName = "Third Integral of " + oldName[19..];
-        else newName = "Integral of " + oldName;
-        // TODO: anti-derive (maybe)
-
-        Graph(new Equation(x => Integrate(equ, 0, x))
-        {
-            Name = newName
-        });
-
-        static double Integrate(EquationDelegate e, double lower, double upper)
-        {
-            // TODO: a better rendering method could make this much faster.
-            const double step = 1e-1;
-
-            double factor = 1;
-            if (upper < lower)
-            {
-                factor = -1;
-                (lower, upper) = (upper, lower);
-            }
-
-            double sum = 0;
-            for (double x = lower; x <= upper; x += step)
-            {
-                sum += e(x) * step;
-            }
-
-            return sum * factor;
-        }
+        None = 0,
+        ViewportDrag,
+        GraphSelect,
+        ZoomBox,
     }
 }

Base/Forms/SetZoomForm.Designer.cs

@@ -28,90 +28,157 @@
         /// </summary>
         private void InitializeComponent()
         {
-            MessageLabel = new Label();
-            ZoomTrackBar = new TrackBar();
-            ValueLabel = new Label();
-            ZoomMinValue = new TextBox();
-            ZoomMaxValue = new TextBox();
-            ((System.ComponentModel.ISupportInitialize)ZoomTrackBar).BeginInit();
+            EnableBoxSelect = new System.Windows.Forms.Button();
+            MatchAspectButton = new System.Windows.Forms.Button();
+            ResetButton = new System.Windows.Forms.Button();
+            NormalizeButton = new System.Windows.Forms.Button();
+            MinBoxX = new System.Windows.Forms.TextBox();
+            TextX = new System.Windows.Forms.Label();
+            MaxBoxX = new System.Windows.Forms.TextBox();
+            MaxBoxY = new System.Windows.Forms.TextBox();
+            TextY = new System.Windows.Forms.Label();
+            MinBoxY = new System.Windows.Forms.TextBox();
+            ViewportLock = new System.Windows.Forms.CheckBox();
             SuspendLayout();
             // 
-            // MessageLabel
+            // EnableBoxSelect
             // 
-            MessageLabel.Anchor = AnchorStyles.Top | AnchorStyles.Left | AnchorStyles.Right;
-            MessageLabel.Location = new Point(52, 20);
-            MessageLabel.Name = "MessageLabel";
-            MessageLabel.Size = new Size(413, 35);
-            MessageLabel.TabIndex = 0;
-            MessageLabel.Text = "Set the zoom level for the graph.";
-            MessageLabel.TextAlign = ContentAlignment.MiddleCenter;
+            EnableBoxSelect.Location = new System.Drawing.Point(12, 12);
+            EnableBoxSelect.Name = "EnableBoxSelect";
+            EnableBoxSelect.Size = new System.Drawing.Size(187, 46);
+            EnableBoxSelect.TabIndex = 0;
+            EnableBoxSelect.Text = "Box Select";
+            EnableBoxSelect.UseVisualStyleBackColor = true;
+            EnableBoxSelect.Click += EnableBoxSelect_Click;
             // 
-            // ZoomTrackBar
+            // MatchAspectButton
             // 
-            ZoomTrackBar.Anchor = AnchorStyles.Top | AnchorStyles.Left | AnchorStyles.Right;
-            ZoomTrackBar.LargeChange = 1000;
-            ZoomTrackBar.Location = new Point(12, 127);
-            ZoomTrackBar.Maximum = 10000;
-            ZoomTrackBar.Name = "ZoomTrackBar";
-            ZoomTrackBar.Size = new Size(489, 90);
-            ZoomTrackBar.TabIndex = 1;
-            ZoomTrackBar.TickStyle = TickStyle.None;
-            ZoomTrackBar.Scroll += ZoomTrackBar_Scroll;
+            MatchAspectButton.Location = new System.Drawing.Point(12, 64);
+            MatchAspectButton.Name = "MatchAspectButton";
+            MatchAspectButton.Size = new System.Drawing.Size(187, 46);
+            MatchAspectButton.TabIndex = 1;
+            MatchAspectButton.Text = "Match Aspect";
+            MatchAspectButton.UseVisualStyleBackColor = true;
+            MatchAspectButton.Click += MatchAspectButton_Click;
             // 
-            // ValueLabel
+            // ResetButton
             // 
-            ValueLabel.Anchor = AnchorStyles.Top | AnchorStyles.Left | AnchorStyles.Right;
-            ValueLabel.Location = new Point(52, 91);
-            ValueLabel.Name = "ValueLabel";
-            ValueLabel.Size = new Size(413, 33);
-            ValueLabel.TabIndex = 2;
-            ValueLabel.Text = "1.00x";
-            ValueLabel.TextAlign = ContentAlignment.TopCenter;
+            ResetButton.Location = new System.Drawing.Point(12, 168);
+            ResetButton.Name = "ResetButton";
+            ResetButton.Size = new System.Drawing.Size(187, 46);
+            ResetButton.TabIndex = 2;
+            ResetButton.Text = "Reset";
+            ResetButton.UseVisualStyleBackColor = true;
+            ResetButton.Click += ResetButton_Click;
             // 
-            // ZoomMinValue
+            // NormalizeButton
             // 
-            ZoomMinValue.Location = new Point(12, 178);
-            ZoomMinValue.Name = "ZoomMinValue";
-            ZoomMinValue.Size = new Size(83, 39);
-            ZoomMinValue.TabIndex = 3;
-            ZoomMinValue.Text = "0.50";
-            ZoomMinValue.TextChanged += ZoomMinValue_TextChanged;
+            NormalizeButton.Location = new System.Drawing.Point(12, 116);
+            NormalizeButton.Name = "NormalizeButton";
+            NormalizeButton.Size = new System.Drawing.Size(187, 46);
+            NormalizeButton.TabIndex = 3;
+            NormalizeButton.Text = "Normalize";
+            NormalizeButton.UseVisualStyleBackColor = true;
+            NormalizeButton.Click += NormalizeButton_Click;
             // 
-            // ZoomMaxValue
+            // MinBoxX
             // 
-            ZoomMaxValue.Anchor = AnchorStyles.Top | AnchorStyles.Right;
-            ZoomMaxValue.Location = new Point(418, 178);
-            ZoomMaxValue.Name = "ZoomMaxValue";
-            ZoomMaxValue.Size = new Size(83, 39);
-            ZoomMaxValue.TabIndex = 4;
-            ZoomMaxValue.Text = "2.00";
-            ZoomMaxValue.TextAlign = HorizontalAlignment.Right;
-            ZoomMaxValue.TextChanged += ZoomMaxValue_TextChanged;
+            MinBoxX.Location = new System.Drawing.Point(227, 49);
+            MinBoxX.Margin = new System.Windows.Forms.Padding(25, 3, 0, 3);
+            MinBoxX.Name = "MinBoxX";
+            MinBoxX.Size = new System.Drawing.Size(108, 39);
+            MinBoxX.TabIndex = 4;
+            // 
+            // TextX
+            // 
+            TextX.Location = new System.Drawing.Point(335, 49);
+            TextX.Margin = new System.Windows.Forms.Padding(0);
+            TextX.Name = "TextX";
+            TextX.Size = new System.Drawing.Size(77, 39);
+            TextX.TabIndex = 5;
+            TextX.Text = "≤ x ≤";
+            TextX.TextAlign = System.Drawing.ContentAlignment.MiddleCenter;
+            // 
+            // MaxBoxX
+            // 
+            MaxBoxX.Location = new System.Drawing.Point(412, 49);
+            MaxBoxX.Margin = new System.Windows.Forms.Padding(0, 3, 25, 3);
+            MaxBoxX.Name = "MaxBoxX";
+            MaxBoxX.Size = new System.Drawing.Size(108, 39);
+            MaxBoxX.TabIndex = 6;
+            // 
+            // MaxBoxY
+            // 
+            MaxBoxY.Location = new System.Drawing.Point(412, 94);
+            MaxBoxY.Margin = new System.Windows.Forms.Padding(0, 3, 25, 3);
+            MaxBoxY.Name = "MaxBoxY";
+            MaxBoxY.Size = new System.Drawing.Size(108, 39);
+            MaxBoxY.TabIndex = 9;
+            // 
+            // TextY
+            // 
+            TextY.Location = new System.Drawing.Point(335, 94);
+            TextY.Margin = new System.Windows.Forms.Padding(0);
+            TextY.Name = "TextY";
+            TextY.Size = new System.Drawing.Size(77, 39);
+            TextY.TabIndex = 8;
+            TextY.Text = "≤ y ≤";
+            TextY.TextAlign = System.Drawing.ContentAlignment.MiddleCenter;
+            // 
+            // MinBoxY
+            // 
+            MinBoxY.Location = new System.Drawing.Point(227, 94);
+            MinBoxY.Margin = new System.Windows.Forms.Padding(25, 3, 0, 3);
+            MinBoxY.Name = "MinBoxY";
+            MinBoxY.Size = new System.Drawing.Size(108, 39);
+            MinBoxY.TabIndex = 7;
+            // 
+            // ViewportLock
+            // 
+            ViewportLock.Location = new System.Drawing.Point(227, 139);
+            ViewportLock.Name = "ViewportLock";
+            ViewportLock.Size = new System.Drawing.Size(293, 39);
+            ViewportLock.TabIndex = 10;
+            ViewportLock.Text = "Lock Viewport";
+            ViewportLock.TextAlign = System.Drawing.ContentAlignment.MiddleCenter;
+            ViewportLock.UseVisualStyleBackColor = true;
+            ViewportLock.CheckedChanged += ViewportLock_CheckedChanged;
             // 
             // SetZoomForm
             // 
-            AutoScaleDimensions = new SizeF(13F, 32F);
-            AutoScaleMode = AutoScaleMode.Font;
-            ClientSize = new Size(513, 230);
-            Controls.Add(ZoomMaxValue);
-            Controls.Add(ZoomMinValue);
-            Controls.Add(ValueLabel);
-            Controls.Add(ZoomTrackBar);
-            Controls.Add(MessageLabel);
-            FormBorderStyle = FormBorderStyle.FixedToolWindow;
+            AutoScaleDimensions = new System.Drawing.SizeF(13F, 32F);
+            AutoScaleMode = System.Windows.Forms.AutoScaleMode.Font;
+            ClientSize = new System.Drawing.Size(533, 227);
+            Controls.Add(ViewportLock);
+            Controls.Add(MaxBoxY);
+            Controls.Add(TextY);
+            Controls.Add(MinBoxY);
+            Controls.Add(MaxBoxX);
+            Controls.Add(TextX);
+            Controls.Add(MinBoxX);
+            Controls.Add(NormalizeButton);
+            Controls.Add(ResetButton);
+            Controls.Add(MatchAspectButton);
+            Controls.Add(EnableBoxSelect);
+            FormBorderStyle = System.Windows.Forms.FormBorderStyle.FixedToolWindow;
             Name = "SetZoomForm";
-            Text = "Zoom Level";
-            ((System.ComponentModel.ISupportInitialize)ZoomTrackBar).EndInit();
+            Text = "Set Viewport Zoom";
             ResumeLayout(false);
             PerformLayout();
         }
 
         #endregion
 
-        private Label MessageLabel;
-        private TrackBar ZoomTrackBar;
-        private Label ValueLabel;
-        private TextBox ZoomMinValue;
-        private TextBox ZoomMaxValue;
+        private System.Windows.Forms.Button EnableBoxSelect;
+        private System.Windows.Forms.Button MatchAspectButton;
+        private System.Windows.Forms.Button ResetButton;
+        private System.Windows.Forms.Button NormalizeButton;
+        private System.Windows.Forms.TextBox MinBoxX;
+        private System.Windows.Forms.Label TextX;
+        private System.Windows.Forms.TextBox MaxBoxX;
+        private System.Windows.Forms.TextBox MaxBoxY;
+        private System.Windows.Forms.Label TextY;
+        private System.Windows.Forms.TextBox MinBoxY;
+        private System.Windows.Forms.CheckBox ViewportLock;
     }
 }

Base/Forms/SetZoomForm.cs

@@ -1,131 +1,227 @@
 using System;
-using System.Collections.Generic;
-using System.ComponentModel;
-using System.Data;
-using System.Drawing;
-using System.Linq;
-using System.Numerics;
-using System.Text;
-using System.Threading.Tasks;
 using System.Windows.Forms;
 
-namespace Graphing.Forms
-{
+namespace Graphing.Forms;
+
 public partial class SetZoomForm : Form
 {
-        private double minZoomRange;
-        private double maxZoomRange;
+    private readonly GraphForm refForm;
 
-        private double zoomLevel;
+    private bool boxSelectEnabled;
 
-        private readonly GraphForm form;
-
-        public SetZoomForm(GraphForm form)
+    public SetZoomForm(GraphForm refForm)
     {
         InitializeComponent();
+        this.refForm = refForm;
 
-            minZoomRange = 1 / (form.ZoomLevel * 2);
-            maxZoomRange = 2 / form.ZoomLevel;
-            zoomLevel = 1 / form.ZoomLevel;
+        refForm.Paint += (o, e) => RedeclareValues();
+        RedeclareValues();
 
-            ZoomTrackBar.Value = (int)(ZoomToFactor(zoomLevel) * (ZoomTrackBar.Maximum - ZoomTrackBar.Minimum) + ZoomTrackBar.Minimum);
+        MinBoxX.Leave += MinBoxX_Finish;
+        MinBoxX.KeyDown += (o, e) =>
+        {
+            if (e.KeyCode == Keys.Enter) MinBoxX_Finish(o, e);
+        };
+        MaxBoxX.Leave += MaxBoxX_Finish;
+        MaxBoxX.KeyDown += (o, e) =>
+        {
+            if (e.KeyCode == Keys.Enter) MaxBoxX_Finish(o, e);
+        };
 
-            this.form = form;
+        MinBoxY.Leave += MinBoxY_Finish;
+        MinBoxY.KeyDown += (o, e) =>
+        {
+            if (e.KeyCode == Keys.Enter) MinBoxY_Finish(o, e);
+        };
+        MaxBoxY.Leave += MaxBoxY_Finish;
+        MaxBoxY.KeyDown += (o, e) =>
+        {
+            if (e.KeyCode == Keys.Enter) MaxBoxY_Finish(o, e);
+        };
     }
 
-        protected override void OnPaint(PaintEventArgs e)
+    private void EnableBoxSelect_Click(object? sender, EventArgs e)
     {
-            ZoomMaxValue.Text = maxZoomRange.ToString("0.00");
-            ZoomMinValue.Text = minZoomRange.ToString("0.00");
+        boxSelectEnabled = !boxSelectEnabled;
+        refForm.canBoxSelect = boxSelectEnabled;
 
-            ValueLabel.Text = $"{zoomLevel:0.00}x";
-
-            base.OnPaint(e);
-
-            form.ZoomLevel = 1 / zoomLevel;
-            form.Invalidate(false);
-        }
-
-        private double FactorToZoom(double factor)
+        if (boxSelectEnabled)
         {
-            return minZoomRange + (factor * factor) * (maxZoomRange - minZoomRange);
-        }
-        private double ZoomToFactor(double zoom)
-        {
-            double sqrValue = (zoom - minZoomRange) / (maxZoomRange - minZoomRange);
-            return Math.Sign(sqrValue) * Math.Sqrt(Math.Abs(sqrValue));
-        }
-
-        private void ZoomTrackBar_Scroll(object? sender, EventArgs e)
-        {
-            double factor = (ZoomTrackBar.Value - ZoomTrackBar.Minimum) / (double)(ZoomTrackBar.Maximum - ZoomTrackBar.Minimum);
-            zoomLevel = FactorToZoom(factor);
-
-            Invalidate(true);
-        }
-
-        private void ZoomMinValue_TextChanged(object? sender, EventArgs e)
-        {
-            double original = minZoomRange;
-            try
-            {
-                double value;
-                if (string.IsNullOrWhiteSpace(ZoomMinValue.Text) ||
-                    ZoomMinValue.Text.EndsWith('.'))
-                {
-                    return;
+            EnableBoxSelect.Text = $"Cancel ...";
+            refForm.Focus();
         }
         else
         {
-                    value = double.Parse(ZoomMinValue.Text);
-                    if (value < 1e-2 || value > 1e3 || value > maxZoomRange) throw new();
+            EnableBoxSelect.Text = "Box Select";
+        }
+    }
+    private void MatchAspectButton_Click(object? sender, EventArgs e)
+    {
+        double zoomXFactor = refForm.ZoomLevel.x / refForm.ZoomLevel.y;
+        double actualXFactor = refForm.ClientRectangle.Width / refForm.ClientRectangle.Height;
+
+        double diff = actualXFactor / zoomXFactor;
+        int newWidth = (int)(refForm.Width / diff);
+        refForm.ZoomLevel = new(refForm.ZoomLevel.x * diff, refForm.ZoomLevel.y);
+
+        int maxScreenWidth = Screen.FromControl(refForm).WorkingArea.Width;
+        if (newWidth >= maxScreenWidth)
+        {
+            refForm.Location = new(0, refForm.Location.Y);
+
+            double xScaleFactor = (double)maxScreenWidth / newWidth;
+            newWidth = maxScreenWidth;
+            refForm.Height = (int)(refForm.Height * xScaleFactor);
+            refForm.ZoomLevel = new(refForm.ZoomLevel.x * xScaleFactor, refForm.ZoomLevel.y * xScaleFactor);
         }
 
-                minZoomRange = value;
-                ZoomTrackBar.Value = (int)Math.Clamp(ZoomToFactor(zoomLevel) * (ZoomTrackBar.Maximum - ZoomTrackBar.Minimum) + ZoomTrackBar.Minimum, ZoomTrackBar.Minimum, ZoomTrackBar.Maximum);
-                double factor = (ZoomTrackBar.Value - ZoomTrackBar.Minimum) / (double)(ZoomTrackBar.Maximum - ZoomTrackBar.Minimum);
-                double newZoom = FactorToZoom(factor);
-
-                zoomLevel = newZoom;
-                if (newZoom != factor) Invalidate(true);
+        refForm.Width = newWidth;
     }
-            catch
+    private void NormalizeButton_Click(object? sender, EventArgs e)
     {
-                minZoomRange = original;
-                ZoomMinValue.Text = minZoomRange.ToString("0.00");
+        double factor = 1 / Math.Min(refForm.ZoomLevel.x, refForm.ZoomLevel.y);
+        refForm.ZoomLevel = new(factor * refForm.ZoomLevel.x, factor * refForm.ZoomLevel.y);
     }
+    private void ResetButton_Click(object? sender, EventArgs e)
+    {
+        refForm.ResetAllViewport();
+    }
+    private void ViewportLock_CheckedChanged(object? sender, EventArgs e)
+    {
+        refForm.ViewportLocked = ViewportLock.Checked;
+        RedeclareValues();
     }
 
-        private void ZoomMaxValue_TextChanged(object sender, EventArgs e)
+    private void MinBoxX_Finish(object? sender, EventArgs e)
     {
-            double original = maxZoomRange;
-            try
+        if (double.TryParse(MinBoxX.Text, out double minX))
         {
-                double value;
-                if (string.IsNullOrWhiteSpace(ZoomMaxValue.Text) ||
-                    ZoomMaxValue.Text.EndsWith('.'))
+            Float2 min = refForm.MinVisibleGraph, max = refForm.MaxVisibleGraph;
+
+            if (minX > max.x)
             {
-                    return;
-                }
-                else
-                {
-                    value = double.Parse(ZoomMaxValue.Text);
-                    if (value < 1e-2 || value > 1e3 || value < minZoomRange) throw new();
+                MaxBoxX.Text = MinBoxX.Text;
+                MaxBoxX_Finish(sender, e);
+                minX = max.x;
+
+                // Redefine bounds.
+                min = refForm.MinVisibleGraph;
+                max = refForm.MaxVisibleGraph;
             }
 
-                maxZoomRange = value;
-                ZoomTrackBar.Value = (int)Math.Clamp(ZoomToFactor(zoomLevel) * (ZoomTrackBar.Maximum - ZoomTrackBar.Minimum) + ZoomTrackBar.Minimum, ZoomTrackBar.Minimum, ZoomTrackBar.Maximum);
-                double factor = (ZoomTrackBar.Value - ZoomTrackBar.Minimum) / (double)(ZoomTrackBar.Maximum - ZoomTrackBar.Minimum);
-                double newZoom = FactorToZoom(factor);
+            double newCenterX = (minX + max.x) / 2,
+                   zoomFactorX = (max.x - minX) / (max.x - min.x);
 
-                zoomLevel = newZoom;
-                if (newZoom != factor) Invalidate(true);
+            refForm.ScreenCenter = new(newCenterX, refForm.ScreenCenter.y);
+            refForm.ZoomLevel = new(refForm.ZoomLevel.x * zoomFactorX, refForm.ZoomLevel.y);
         }
-            catch
+
+        refForm.Invalidate(false);
+    }
+    private void MaxBoxX_Finish(object? sender, EventArgs e)
     {
-                maxZoomRange = original;
-                ZoomMaxValue.Text = maxZoomRange.ToString("0.00");
-            }
-        }
+        if (double.TryParse(MaxBoxX.Text, out double maxX))
+        {
+            Float2 min = refForm.MinVisibleGraph, max = refForm.MaxVisibleGraph;
+
+            if (maxX < min.x)
+            {
+                MinBoxX.Text = MaxBoxX.Text;
+                MinBoxX_Finish(sender, e);
+                maxX = min.x;
+
+                // Redefine bounds.
+                min = refForm.MinVisibleGraph;
+                max = refForm.MaxVisibleGraph;
+            }
+
+            double newCenterX = (min.x + maxX) / 2,
+                   zoomFactorX = (maxX - min.x) / (max.x - min.x);
+
+            refForm.ScreenCenter = new(newCenterX, refForm.ScreenCenter.y);
+            refForm.ZoomLevel = new(refForm.ZoomLevel.x * zoomFactorX, refForm.ZoomLevel.y);
+        }
+
+        refForm.Invalidate(false);
+    }
+    private void MinBoxY_Finish(object? sender, EventArgs e)
+    {
+        if (double.TryParse(MinBoxY.Text, out double minY))
+        {
+            Float2 min = refForm.MinVisibleGraph, max = refForm.MaxVisibleGraph;
+
+            if (minY > max.y)
+            {
+                MaxBoxY.Text = MinBoxY.Text;
+                MaxBoxY_Finish(sender, e);
+                minY = max.y;
+
+                // Redefine bounds.
+                min = refForm.MinVisibleGraph;
+                max = refForm.MaxVisibleGraph;
+            }
+
+            double newCenterY = -(minY + max.y) / 2, // Keeping it positive flips it for some reason ???
+                   zoomFactorY = (max.y - minY) / (max.y - min.y);
+
+            refForm.ScreenCenter = new(refForm.ScreenCenter.x, newCenterY);
+            refForm.ZoomLevel = new(refForm.ZoomLevel.x, refForm.ZoomLevel.y * zoomFactorY);
+        }
+
+        refForm.Invalidate(false);
+    }
+    private void MaxBoxY_Finish(object? sender, EventArgs e)
+    {
+        if (double.TryParse(MaxBoxY.Text, out double maxY))
+        {
+            Float2 min = refForm.MinVisibleGraph, max = refForm.MaxVisibleGraph;
+
+            if (maxY < min.y)
+            {
+                MinBoxY.Text = MaxBoxY.Text;
+                MinBoxY_Finish(sender, e);
+                maxY = min.y;
+
+                // Redefine bounds.
+                min = refForm.MinVisibleGraph;
+                max = refForm.MaxVisibleGraph;
+            }
+
+            double newCenterY = -(min.y + maxY) / 2, // Keeping it positive flips it for some reason ???
+                   zoomFactorY = (maxY - min.y) / (max.y - min.y);
+
+            refForm.ScreenCenter = new(refForm.ScreenCenter.x, newCenterY);
+            refForm.ZoomLevel = new(refForm.ZoomLevel.x, refForm.ZoomLevel.y * zoomFactorY);
+        }
+
+        refForm.Invalidate(false);
+    }
+
+    public void RedeclareValues()
+    {
+        bool enabled = !refForm.ViewportLocked;
+
+        Float2 minGraph = refForm.MinVisibleGraph,
+               maxGraph = refForm.MaxVisibleGraph;
+
+        MinBoxX.Text = $"{minGraph.x:0.000}";
+        MaxBoxX.Text = $"{maxGraph.x:0.000}";
+        MinBoxY.Text = $"{minGraph.y:0.000}";
+        MaxBoxY.Text = $"{maxGraph.y:0.000}";
+
+        ViewportLock.Checked = !enabled;
+        EnableBoxSelect.Enabled = enabled;
+        MatchAspectButton.Enabled = enabled;
+        NormalizeButton.Enabled = enabled;
+        ResetButton.Enabled = enabled;
+        MinBoxX.Enabled = enabled;
+        MaxBoxX.Enabled = enabled;
+        MinBoxY.Enabled = enabled;
+        MaxBoxY.Enabled = enabled;
+    }
+
+    internal void CompleteBoxSelection()
+    {
+        if (boxSelectEnabled) EnableBoxSelect_Click(null, new());
     }
 }

Base/Forms/SlopeFieldDetailForm.Designer.cs

@@ -0,0 +1,147 @@
+namespace Graphing.Forms
+{
+    partial class SlopeFieldDetailForm
+    {
+        /// <summary>
+        /// Required designer variable.
+        /// </summary>
+        private System.ComponentModel.IContainer components = null;
+
+        /// <summary>
+        /// Clean up any resources being used.
+        /// </summary>
+        /// <param name="disposing">true if managed resources should be disposed; otherwise, false.</param>
+        protected override void Dispose(bool disposing)
+        {
+            if (disposing && (components != null))
+            {
+                components.Dispose();
+            }
+            base.Dispose(disposing);
+        }
+
+        #region Windows Form Designer generated code
+
+        /// <summary>
+        /// Required method for Designer support - do not modify
+        /// the contents of this method with the code editor.
+        /// </summary>
+        private void InitializeComponent()
+        {
+            Message = new System.Windows.Forms.Label();
+            TrackSlopeDetail = new System.Windows.Forms.TrackBar();
+            MinDetailBox = new System.Windows.Forms.TextBox();
+            MaxDetailBox = new System.Windows.Forms.TextBox();
+            CurrentDetailBox = new System.Windows.Forms.TextBox();
+            IncrementButton = new System.Windows.Forms.Button();
+            DecrementButton = new System.Windows.Forms.Button();
+            ((System.ComponentModel.ISupportInitialize)TrackSlopeDetail).BeginInit();
+            SuspendLayout();
+            // 
+            // Message
+            // 
+            Message.Anchor = System.Windows.Forms.AnchorStyles.Top | System.Windows.Forms.AnchorStyles.Left | System.Windows.Forms.AnchorStyles.Right;
+            Message.Location = new System.Drawing.Point(119, 25);
+            Message.Margin = new System.Windows.Forms.Padding(110);
+            Message.Name = "Message";
+            Message.Size = new System.Drawing.Size(516, 109);
+            Message.TabIndex = 1;
+            Message.Text = "Change the Detail of %name%\r\nA higher value means more lines per unit.";
+            Message.TextAlign = System.Drawing.ContentAlignment.MiddleCenter;
+            // 
+            // TrackSlopeDetail
+            // 
+            TrackSlopeDetail.Anchor = System.Windows.Forms.AnchorStyles.Left | System.Windows.Forms.AnchorStyles.Right;
+            TrackSlopeDetail.LargeChange = 250;
+            TrackSlopeDetail.Location = new System.Drawing.Point(59, 158);
+            TrackSlopeDetail.Margin = new System.Windows.Forms.Padding(50);
+            TrackSlopeDetail.Maximum = 1000;
+            TrackSlopeDetail.Name = "TrackSlopeDetail";
+            TrackSlopeDetail.Size = new System.Drawing.Size(636, 90);
+            TrackSlopeDetail.SmallChange = 0;
+            TrackSlopeDetail.TabIndex = 0;
+            TrackSlopeDetail.TickFrequency = 0;
+            TrackSlopeDetail.TickStyle = System.Windows.Forms.TickStyle.Both;
+            TrackSlopeDetail.Scroll += TrackSlopeDetail_Scroll;
+            // 
+            // MinDetailBox
+            // 
+            MinDetailBox.Anchor = System.Windows.Forms.AnchorStyles.Left;
+            MinDetailBox.Location = new System.Drawing.Point(12, 228);
+            MinDetailBox.Name = "MinDetailBox";
+            MinDetailBox.Size = new System.Drawing.Size(100, 39);
+            MinDetailBox.TabIndex = 2;
+            // 
+            // MaxDetailBox
+            // 
+            MaxDetailBox.Anchor = System.Windows.Forms.AnchorStyles.Right;
+            MaxDetailBox.Location = new System.Drawing.Point(642, 228);
+            MaxDetailBox.Name = "MaxDetailBox";
+            MaxDetailBox.Size = new System.Drawing.Size(100, 39);
+            MaxDetailBox.TabIndex = 3;
+            MaxDetailBox.TextAlign = System.Windows.Forms.HorizontalAlignment.Right;
+            // 
+            // CurrentDetailBox
+            // 
+            CurrentDetailBox.Anchor = System.Windows.Forms.AnchorStyles.None;
+            CurrentDetailBox.Location = new System.Drawing.Point(330, 228);
+            CurrentDetailBox.Name = "CurrentDetailBox";
+            CurrentDetailBox.Size = new System.Drawing.Size(100, 39);
+            CurrentDetailBox.TabIndex = 4;
+            CurrentDetailBox.TextAlign = System.Windows.Forms.HorizontalAlignment.Center;
+            // 
+            // IncrementButton
+            // 
+            IncrementButton.Anchor = System.Windows.Forms.AnchorStyles.None;
+            IncrementButton.Font = new System.Drawing.Font("Segoe UI", 7.875F, System.Drawing.FontStyle.Regular, System.Drawing.GraphicsUnit.Point, 0);
+            IncrementButton.Location = new System.Drawing.Point(436, 228);
+            IncrementButton.Name = "IncrementButton";
+            IncrementButton.Size = new System.Drawing.Size(40, 40);
+            IncrementButton.TabIndex = 5;
+            IncrementButton.Text = "+";
+            IncrementButton.UseVisualStyleBackColor = true;
+            IncrementButton.Click += IncrementButton_Click;
+            // 
+            // DecrementButton
+            // 
+            DecrementButton.Anchor = System.Windows.Forms.AnchorStyles.None;
+            DecrementButton.Font = new System.Drawing.Font("Segoe UI", 7.875F, System.Drawing.FontStyle.Regular, System.Drawing.GraphicsUnit.Point, 0);
+            DecrementButton.Location = new System.Drawing.Point(284, 228);
+            DecrementButton.Name = "DecrementButton";
+            DecrementButton.Size = new System.Drawing.Size(40, 40);
+            DecrementButton.TabIndex = 6;
+            DecrementButton.Text = "-";
+            DecrementButton.UseVisualStyleBackColor = true;
+            DecrementButton.Click += DecrementButton_Click;
+            // 
+            // SlopeFieldDetailForm
+            // 
+            AutoScaleDimensions = new System.Drawing.SizeF(13F, 32F);
+            AutoScaleMode = System.Windows.Forms.AutoScaleMode.Font;
+            ClientSize = new System.Drawing.Size(754, 282);
+            Controls.Add(DecrementButton);
+            Controls.Add(IncrementButton);
+            Controls.Add(CurrentDetailBox);
+            Controls.Add(MaxDetailBox);
+            Controls.Add(MinDetailBox);
+            Controls.Add(Message);
+            Controls.Add(TrackSlopeDetail);
+            FormBorderStyle = System.Windows.Forms.FormBorderStyle.FixedToolWindow;
+            Name = "SlopeFieldDetailForm";
+            Text = "Change Slope Field Detail";
+            ((System.ComponentModel.ISupportInitialize)TrackSlopeDetail).EndInit();
+            ResumeLayout(false);
+            PerformLayout();
+        }
+
+        #endregion
+
+        private System.Windows.Forms.Label Message;
+        private System.Windows.Forms.TrackBar TrackSlopeDetail;
+        private System.Windows.Forms.TextBox MinDetailBox;
+        private System.Windows.Forms.TextBox MaxDetailBox;
+        private System.Windows.Forms.TextBox CurrentDetailBox;
+        private System.Windows.Forms.Button IncrementButton;
+        private System.Windows.Forms.Button DecrementButton;
+    }
+}

Base/Forms/SlopeFieldDetailForm.cs

@@ -0,0 +1,130 @@
+using Graphing.Graphables;
+using System;
+using System.Windows.Forms;
+
+namespace Graphing.Forms;
+
+public partial class SlopeFieldDetailForm : Form
+{
+    private readonly GraphForm refForm;
+    private readonly SlopeField slopeField;
+
+    private double minDetail, maxDetail;
+
+    public SlopeFieldDetailForm(GraphForm form, SlopeField sf)
+    {
+        InitializeComponent();
+
+        refForm = form;
+        slopeField = sf;
+
+        refForm.Paint += (o, e) => RedeclareValues();
+        RedeclareValues();
+
+        TrackSlopeDetail.KeyDown += (o, e) =>
+        {
+            if (e.KeyCode == Keys.Right) IncrementButton_Click(o, e);
+            else if (e.KeyCode == Keys.Left) DecrementButton_Click(o, e);
+        };
+
+        MinDetailBox.Leave += MinDetailBox_Finish;
+        MinDetailBox.KeyDown += (o, e) =>
+        {
+            if (e.KeyCode == Keys.Enter) MinDetailBox_Finish(o, e);
+        };
+        MaxDetailBox.Leave += MaxDetailBox_Finish;
+        MaxDetailBox.KeyDown += (o, e) =>
+        {
+            if (e.KeyCode == Keys.Enter) MaxDetailBox_Finish(o, e);
+        };
+        CurrentDetailBox.Leave += CurrentDetailBox_Finish;
+        CurrentDetailBox.KeyDown += (o, e) =>
+        {
+            if (e.KeyCode == Keys.Enter) CurrentDetailBox_Finish(o, e);
+        };
+
+        minDetail = sf.Detail / 2;
+        maxDetail = sf.Detail * 2;
+
+        Message.Text = Message.Text.Replace("%name%", sf.Name);
+    }
+
+    // Exponential interpolations are better than simple lerps here since
+    // we're scaling a multiple rather than an additive.
+    private double Interp(double t)
+    {
+        // This is weird. I don't like the +1s and -1s, I don't think I wrote this right.
+        // But it seems to get the job done.
+        return minDetail + Math.Pow(2, t * Math.Log2(maxDetail - minDetail + 1)) - 1;
+    }
+    private double InverseInterp(double c)
+    {
+        return Math.Log2(c - minDetail + 1) / Math.Log2(maxDetail - minDetail + 1);
+    }
+
+    private void RedeclareValues()
+    {
+        double detail = slopeField.Detail;
+        if (detail < minDetail) minDetail = detail;
+        else if (detail > maxDetail) maxDetail = detail;
+
+        double t = InverseInterp(detail);
+        TrackSlopeDetail.Value = (int)(TrackSlopeDetail.Minimum + t * (TrackSlopeDetail.Maximum - TrackSlopeDetail.Minimum));
+
+        MinDetailBox.Text = $"{minDetail:0.00}";
+        MaxDetailBox.Text = $"{maxDetail:0.00}";
+        CurrentDetailBox.Text = $"{detail:0.00}";
+    }
+
+    private void TrackSlopeDetail_Scroll(object? sender, EventArgs e)
+    {
+        double t = (double)(TrackSlopeDetail.Value - TrackSlopeDetail.Minimum) / (TrackSlopeDetail.Maximum - TrackSlopeDetail.Minimum);
+        double newDetail = Interp(t);
+
+        slopeField.Detail = newDetail;
+        refForm.Invalidate(false);
+    }
+    private void MinDetailBox_Finish(object? sender, EventArgs e)
+    {
+        if (double.TryParse(MinDetailBox.Text, out double newMinDetail))
+        {
+            minDetail = newMinDetail;
+            if (minDetail > slopeField.Detail) slopeField.Detail = newMinDetail;
+        }
+        refForm.Invalidate(false);
+    }
+    private void MaxDetailBox_Finish(object? sender, EventArgs e)
+    {
+        if (double.TryParse(MaxDetailBox.Text, out double newMaxDetail))
+        {
+            maxDetail = newMaxDetail;
+            if (maxDetail < slopeField.Detail) slopeField.Detail = newMaxDetail;
+        }
+        refForm.Invalidate(false);
+    }
+    private void CurrentDetailBox_Finish(object? sender, EventArgs e)
+    {
+        if (double.TryParse(CurrentDetailBox.Text, out double newDetail))
+        {
+            if (newDetail < minDetail) minDetail = newDetail;
+            else if (newDetail > maxDetail) maxDetail = newDetail;
+            slopeField.Detail = newDetail;
+        }
+        refForm.Invalidate(false);
+    }
+
+    private void IncrementButton_Click(object? sender, EventArgs e)
+    {
+        double newDetail = slopeField.Detail * 1.0625f;
+        if (newDetail > maxDetail) maxDetail = newDetail;
+        slopeField.Detail = newDetail;
+        refForm.Invalidate(false);
+    }
+    private void DecrementButton_Click(object? sender, EventArgs e)
+    {
+        double newDetail = slopeField.Detail / 1.0625f;
+        if (newDetail < minDetail) minDetail = newDetail;
+        slopeField.Detail = newDetail;
+        refForm.Invalidate(false);
+    }
+}

Base/Forms/SlopeFieldDetailForm.resx

@@ -0,0 +1,120 @@
+<?xml version="1.0" encoding="utf-8"?>
+<root>
+  <!--
+    Microsoft ResX Schema 
+
+    Version 2.0
+
+    The primary goals of this format is to allow a simple XML format
+    that is mostly human readable. The generation and parsing of the
+    various data types are done through the TypeConverter classes
+    associated with the data types.
+
+    Example:
+
+    ... ado.net/XML headers & schema ...
+    <resheader name="resmimetype">text/microsoft-resx</resheader>
+    <resheader name="version">2.0</resheader>
+    <resheader name="reader">System.Resources.ResXResourceReader, System.Windows.Forms, ...</resheader>
+    <resheader name="writer">System.Resources.ResXResourceWriter, System.Windows.Forms, ...</resheader>
+    <data name="Name1"><value>this is my long string</value><comment>this is a comment</comment></data>
+    <data name="Color1" type="System.Drawing.Color, System.Drawing">Blue</data>
+    <data name="Bitmap1" mimetype="application/x-microsoft.net.object.binary.base64">
+        <value>[base64 mime encoded serialized .NET Framework object]</value>
+    </data>
+    <data name="Icon1" type="System.Drawing.Icon, System.Drawing" mimetype="application/x-microsoft.net.object.bytearray.base64">
+        <value>[base64 mime encoded string representing a byte array form of the .NET Framework object]</value>
+        <comment>This is a comment</comment>
+    </data>
+
+    There are any number of "resheader" rows that contain simple
+    name/value pairs.
+
+    Each data row contains a name, and value. The row also contains a
+    type or mimetype. Type corresponds to a .NET class that support
+    text/value conversion through the TypeConverter architecture.
+    Classes that don't support this are serialized and stored with the
+    mimetype set.
+
+    The mimetype is used for serialized objects, and tells the
+    ResXResourceReader how to depersist the object. This is currently not
+    extensible. For a given mimetype the value must be set accordingly:
+
+    Note - application/x-microsoft.net.object.binary.base64 is the format
+    that the ResXResourceWriter will generate, however the reader can
+    read any of the formats listed below.
+
+    mimetype: application/x-microsoft.net.object.binary.base64
+    value   : The object must be serialized with
+            : System.Runtime.Serialization.Formatters.Binary.BinaryFormatter
+            : and then encoded with base64 encoding.
+    
+    mimetype: application/x-microsoft.net.object.soap.base64
+    value   : The object must be serialized with
+            : System.Runtime.Serialization.Formatters.Soap.SoapFormatter
+            : and then encoded with base64 encoding.
+
+    mimetype: application/x-microsoft.net.object.bytearray.base64
+    value   : The object must be serialized into a byte array
+            : using a System.ComponentModel.TypeConverter
+            : and then encoded with base64 encoding.
+    -->
+  <xsd:schema id="root" xmlns="" xmlns:xsd="http://www.w3.org/2001/XMLSchema" xmlns:msdata="urn:schemas-microsoft-com:xml-msdata">
+    <xsd:import namespace="http://www.w3.org/XML/1998/namespace" />
+    <xsd:element name="root" msdata:IsDataSet="true">
+      <xsd:complexType>
+        <xsd:choice maxOccurs="unbounded">
+          <xsd:element name="metadata">
+            <xsd:complexType>
+              <xsd:sequence>
+                <xsd:element name="value" type="xsd:string" minOccurs="0" />
+              </xsd:sequence>
+              <xsd:attribute name="name" use="required" type="xsd:string" />
+              <xsd:attribute name="type" type="xsd:string" />
+              <xsd:attribute name="mimetype" type="xsd:string" />
+              <xsd:attribute ref="xml:space" />
+            </xsd:complexType>
+          </xsd:element>
+          <xsd:element name="assembly">
+            <xsd:complexType>
+              <xsd:attribute name="alias" type="xsd:string" />
+              <xsd:attribute name="name" type="xsd:string" />
+            </xsd:complexType>
+          </xsd:element>
+          <xsd:element name="data">
+            <xsd:complexType>
+              <xsd:sequence>
+                <xsd:element name="value" type="xsd:string" minOccurs="0" msdata:Ordinal="1" />
+                <xsd:element name="comment" type="xsd:string" minOccurs="0" msdata:Ordinal="2" />
+              </xsd:sequence>
+              <xsd:attribute name="name" type="xsd:string" use="required" msdata:Ordinal="1" />
+              <xsd:attribute name="type" type="xsd:string" msdata:Ordinal="3" />
+              <xsd:attribute name="mimetype" type="xsd:string" msdata:Ordinal="4" />
+              <xsd:attribute ref="xml:space" />
+            </xsd:complexType>
+          </xsd:element>
+          <xsd:element name="resheader">
+            <xsd:complexType>
+              <xsd:sequence>
+                <xsd:element name="value" type="xsd:string" minOccurs="0" msdata:Ordinal="1" />
+              </xsd:sequence>
+              <xsd:attribute name="name" type="xsd:string" use="required" />
+            </xsd:complexType>
+          </xsd:element>
+        </xsd:choice>
+      </xsd:complexType>
+    </xsd:element>
+  </xsd:schema>
+  <resheader name="resmimetype">
+    <value>text/microsoft-resx</value>
+  </resheader>
+  <resheader name="version">
+    <value>2.0</value>
+  </resheader>
+  <resheader name="reader">
+    <value>System.Resources.ResXResourceReader, System.Windows.Forms, Version=4.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089</value>
+  </resheader>
+  <resheader name="writer">
+    <value>System.Resources.ResXResourceWriter, System.Windows.Forms, Version=4.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089</value>
+  </resheader>
+</root>

Base/Forms/TranslateForm.Designer.cs

@@ -0,0 +1,204 @@
+namespace Graphing.Forms
+{
+    partial class TranslateForm
+    {
+        /// <summary>
+        /// Required designer variable.
+        /// </summary>
+        private System.ComponentModel.IContainer components = null;
+
+        /// <summary>
+        /// Clean up any resources being used.
+        /// </summary>
+        /// <param name="disposing">true if managed resources should be disposed; otherwise, false.</param>
+        protected override void Dispose(bool disposing)
+        {
+            if (disposing && (components != null))
+            {
+                components.Dispose();
+            }
+            base.Dispose(disposing);
+        }
+
+        #region Windows Form Designer generated code
+
+        /// <summary>
+        /// Required method for Designer support - do not modify
+        /// the contents of this method with the code editor.
+        /// </summary>
+        private void InitializeComponent()
+        {
+            TrackX = new System.Windows.Forms.TrackBar();
+            LabelX = new System.Windows.Forms.Label();
+            MinBoxX = new System.Windows.Forms.TextBox();
+            MaxBoxX = new System.Windows.Forms.TextBox();
+            ThisValueX = new System.Windows.Forms.TextBox();
+            ThisValueY = new System.Windows.Forms.TextBox();
+            MaxBoxY = new System.Windows.Forms.TextBox();
+            MinBoxY = new System.Windows.Forms.TextBox();
+            LabelY = new System.Windows.Forms.Label();
+            TrackY = new System.Windows.Forms.TrackBar();
+            TitleLabel = new System.Windows.Forms.Label();
+            ((System.ComponentModel.ISupportInitialize)TrackX).BeginInit();
+            ((System.ComponentModel.ISupportInitialize)TrackY).BeginInit();
+            SuspendLayout();
+            // 
+            // TrackX
+            // 
+            TrackX.Anchor = System.Windows.Forms.AnchorStyles.Top | System.Windows.Forms.AnchorStyles.Left | System.Windows.Forms.AnchorStyles.Right;
+            TrackX.LargeChange = 250;
+            TrackX.Location = new System.Drawing.Point(15, 193);
+            TrackX.Margin = new System.Windows.Forms.Padding(0);
+            TrackX.Maximum = 1000;
+            TrackX.Name = "TrackX";
+            TrackX.Size = new System.Drawing.Size(644, 90);
+            TrackX.SmallChange = 50;
+            TrackX.TabIndex = 0;
+            TrackX.TabStop = false;
+            TrackX.TickFrequency = 50;
+            TrackX.TickStyle = System.Windows.Forms.TickStyle.Both;
+            TrackX.Value = 1;
+            TrackX.Scroll += TrackX_Scroll;
+            // 
+            // LabelX
+            // 
+            LabelX.Anchor = System.Windows.Forms.AnchorStyles.Top | System.Windows.Forms.AnchorStyles.Left | System.Windows.Forms.AnchorStyles.Right;
+            LabelX.Location = new System.Drawing.Point(15, 157);
+            LabelX.Name = "LabelX";
+            LabelX.Size = new System.Drawing.Size(644, 36);
+            LabelX.TabIndex = 1;
+            LabelX.Text = "X Offset";
+            LabelX.TextAlign = System.Drawing.ContentAlignment.MiddleCenter;
+            // 
+            // MinBoxX
+            // 
+            MinBoxX.Location = new System.Drawing.Point(15, 259);
+            MinBoxX.Name = "MinBoxX";
+            MinBoxX.Size = new System.Drawing.Size(100, 39);
+            MinBoxX.TabIndex = 2;
+            // 
+            // MaxBoxX
+            // 
+            MaxBoxX.Anchor = System.Windows.Forms.AnchorStyles.Top | System.Windows.Forms.AnchorStyles.Right;
+            MaxBoxX.Location = new System.Drawing.Point(556, 259);
+            MaxBoxX.Name = "MaxBoxX";
+            MaxBoxX.Size = new System.Drawing.Size(100, 39);
+            MaxBoxX.TabIndex = 3;
+            MaxBoxX.TextAlign = System.Windows.Forms.HorizontalAlignment.Right;
+            // 
+            // ThisValueX
+            // 
+            ThisValueX.Anchor = System.Windows.Forms.AnchorStyles.Top;
+            ThisValueX.Location = new System.Drawing.Point(289, 259);
+            ThisValueX.Name = "ThisValueX";
+            ThisValueX.Size = new System.Drawing.Size(100, 39);
+            ThisValueX.TabIndex = 4;
+            ThisValueX.TextAlign = System.Windows.Forms.HorizontalAlignment.Center;
+            // 
+            // ThisValueY
+            // 
+            ThisValueY.Anchor = System.Windows.Forms.AnchorStyles.Top;
+            ThisValueY.Location = new System.Drawing.Point(289, 449);
+            ThisValueY.Name = "ThisValueY";
+            ThisValueY.Size = new System.Drawing.Size(100, 39);
+            ThisValueY.TabIndex = 9;
+            ThisValueY.TextAlign = System.Windows.Forms.HorizontalAlignment.Center;
+            // 
+            // MaxBoxY
+            // 
+            MaxBoxY.Anchor = System.Windows.Forms.AnchorStyles.Top | System.Windows.Forms.AnchorStyles.Right;
+            MaxBoxY.Location = new System.Drawing.Point(556, 449);
+            MaxBoxY.Name = "MaxBoxY";
+            MaxBoxY.Size = new System.Drawing.Size(100, 39);
+            MaxBoxY.TabIndex = 8;
+            MaxBoxY.TextAlign = System.Windows.Forms.HorizontalAlignment.Right;
+            // 
+            // MinBoxY
+            // 
+            MinBoxY.Location = new System.Drawing.Point(15, 449);
+            MinBoxY.Name = "MinBoxY";
+            MinBoxY.Size = new System.Drawing.Size(100, 39);
+            MinBoxY.TabIndex = 7;
+            // 
+            // LabelY
+            // 
+            LabelY.Anchor = System.Windows.Forms.AnchorStyles.Top | System.Windows.Forms.AnchorStyles.Left | System.Windows.Forms.AnchorStyles.Right;
+            LabelY.Location = new System.Drawing.Point(15, 347);
+            LabelY.Name = "LabelY";
+            LabelY.Size = new System.Drawing.Size(644, 36);
+            LabelY.TabIndex = 6;
+            LabelY.Text = "Y Offset";
+            LabelY.TextAlign = System.Drawing.ContentAlignment.MiddleCenter;
+            // 
+            // TrackY
+            // 
+            TrackY.Anchor = System.Windows.Forms.AnchorStyles.Top | System.Windows.Forms.AnchorStyles.Left | System.Windows.Forms.AnchorStyles.Right;
+            TrackY.LargeChange = 250;
+            TrackY.Location = new System.Drawing.Point(15, 383);
+            TrackY.Margin = new System.Windows.Forms.Padding(0);
+            TrackY.Maximum = 1000;
+            TrackY.Name = "TrackY";
+            TrackY.Size = new System.Drawing.Size(644, 90);
+            TrackY.SmallChange = 50;
+            TrackY.TabIndex = 5;
+            TrackY.TabStop = false;
+            TrackY.TickFrequency = 50;
+            TrackY.TickStyle = System.Windows.Forms.TickStyle.Both;
+            TrackY.Value = 1;
+            TrackY.Scroll += TrackY_Scroll;
+            // 
+            // TitleLabel
+            // 
+            TitleLabel.Anchor = System.Windows.Forms.AnchorStyles.Top | System.Windows.Forms.AnchorStyles.Left | System.Windows.Forms.AnchorStyles.Right;
+            TitleLabel.Location = new System.Drawing.Point(12, 39);
+            TitleLabel.Name = "TitleLabel";
+            TitleLabel.Padding = new System.Windows.Forms.Padding(0, 0, 0, 18);
+            TitleLabel.Size = new System.Drawing.Size(644, 89);
+            TitleLabel.TabIndex = 10;
+            TitleLabel.Text = "Change the Location of %name%";
+            TitleLabel.TextAlign = System.Drawing.ContentAlignment.MiddleCenter;
+            // 
+            // TranslateForm
+            // 
+            AutoScaleDimensions = new System.Drawing.SizeF(13F, 32F);
+            AutoScaleMode = System.Windows.Forms.AutoScaleMode.Font;
+            AutoSize = true;
+            AutoSizeMode = System.Windows.Forms.AutoSizeMode.GrowAndShrink;
+            ClientSize = new System.Drawing.Size(674, 531);
+            Controls.Add(TitleLabel);
+            Controls.Add(ThisValueY);
+            Controls.Add(MaxBoxY);
+            Controls.Add(MinBoxY);
+            Controls.Add(LabelY);
+            Controls.Add(TrackY);
+            Controls.Add(ThisValueX);
+            Controls.Add(MaxBoxX);
+            Controls.Add(MinBoxX);
+            Controls.Add(LabelX);
+            Controls.Add(TrackX);
+            FormBorderStyle = System.Windows.Forms.FormBorderStyle.FixedToolWindow;
+            Name = "TranslateForm";
+            Padding = new System.Windows.Forms.Padding(15);
+            Text = "Herm";
+            TopMost = true;
+            ((System.ComponentModel.ISupportInitialize)TrackX).EndInit();
+            ((System.ComponentModel.ISupportInitialize)TrackY).EndInit();
+            ResumeLayout(false);
+            PerformLayout();
+        }
+
+        #endregion
+
+        private System.Windows.Forms.TrackBar TrackX;
+        private System.Windows.Forms.Label LabelX;
+        private System.Windows.Forms.TextBox MinBoxX;
+        private System.Windows.Forms.TextBox MaxBoxX;
+        private System.Windows.Forms.TextBox ThisValueX;
+        private System.Windows.Forms.TextBox ThisValueY;
+        private System.Windows.Forms.TextBox MaxBoxY;
+        private System.Windows.Forms.TextBox MinBoxY;
+        private System.Windows.Forms.Label LabelY;
+        private System.Windows.Forms.TrackBar TrackY;
+        private System.Windows.Forms.Label TitleLabel;
+    }
+}

Base/Forms/TranslateForm.cs

@@ -0,0 +1,285 @@
+using Graphing.Abstract;
+using System;
+using System.Windows.Forms;
+
+namespace Graphing.Forms;
+
+public partial class TranslateForm : Form
+{
+    private readonly GraphForm refForm;
+
+    // These variables both represent the same graphable.
+    private readonly ITranslatableX? ableTransX;
+    private readonly ITranslatableY? ableTransY;
+
+    private readonly bool useX;
+    private readonly bool useY;
+
+    private double minX, maxX, curX, minY, maxY, curY;
+
+    public TranslateForm(GraphForm graph, Graphable ableRaw, ITranslatable ableTrans)
+    {
+        InitializeComponent();
+
+        Text = $"Translate {ableRaw.Name}";
+        TitleLabel.Text = $"Adjust Location for {ableRaw.Name}";
+
+        MinBoxX.Leave += (o, e) => UpdateFromMinBoxX();
+        MinBoxX.KeyDown += (o, e) =>
+        {
+            if (e.KeyCode == Keys.Enter) UpdateFromMinBoxX();
+        };
+        MaxBoxX.Leave += (o, e) => UpdateFromMaxBoxX();
+        MaxBoxX.KeyDown += (o, e) =>
+        {
+            if (e.KeyCode == Keys.Enter) UpdateFromMaxBoxX();
+        };
+        ThisValueX.Leave += (o, e) => UpdateFromThisBoxX();
+        ThisValueX.KeyDown += (o, e) =>
+        {
+            if (e.KeyCode == Keys.Enter) UpdateFromThisBoxX();
+        };
+
+        MinBoxY.Leave += (o, e) => UpdateFromMinBoxY();
+        MinBoxY.KeyDown += (o, e) =>
+        {
+            if (e.KeyCode == Keys.Enter) UpdateFromMinBoxY();
+        };
+        MaxBoxY.Leave += (o, e) => UpdateFromMaxBoxY();
+        MaxBoxY.KeyDown += (o, e) =>
+        {
+            if (e.KeyCode == Keys.Enter) UpdateFromMaxBoxY();
+        };
+        ThisValueY.Leave += (o, e) => UpdateFromThisBoxY();
+        ThisValueY.KeyDown += (o, e) =>
+        {
+            if (e.KeyCode == Keys.Enter) UpdateFromThisBoxY();
+        };
+
+        refForm = graph;
+
+        double curX = 0, curY = 0;
+        if (ableTrans is ITranslatableX transX)
+        {
+            useX = true;
+            ableTransX = transX;
+            curX = transX.OffsetX;
+        }
+        else
+        {
+            LabelY.Location = LabelX.Location;
+            TrackY.Location = TrackX.Location;
+            MinBoxY.Location = MinBoxX.Location;
+            MaxBoxY.Location = MaxBoxX.Location;
+            ThisValueY.Location = ThisValueX.Location;
+
+            LabelX.Dispose();
+            TrackX.Dispose();
+            MinBoxX.Dispose();
+            MaxBoxX.Dispose();
+            ThisValueX.Dispose();
+        }
+
+        if (ableTrans is ITranslatableY transY)
+        {
+            useY = true;
+            ableTransY = transY;
+            curY = transY.OffsetY;
+        }
+        else
+        {
+            LabelY.Dispose();
+            TrackY.Dispose();
+            MinBoxY.Dispose();
+            MaxBoxY.Dispose();
+            ThisValueY.Dispose();
+        }
+
+        if (!useX && !useY)
+        {
+            TitleLabel.Text = $"There doesn't seem to be anything you can translate for {ableRaw.Name}.";
+        }
+
+        // TODO: Maybe replace these default limits with what's visible on screen?
+        //       Tried it and it got a bit confusing so maybe not.
+        minX = -10;
+        maxX = 10;
+        minY = -10;
+        maxY = 10;
+
+        UpdateFromCurX(curX, false);
+        UpdateFromCurY(curY, false);
+    }
+
+    private void UpdateFromCurX(double newCurX, bool invalidate)
+    {
+        curX = newCurX;
+        if (curX < minX) minX = curX;
+        else if (curX > maxX) maxX = curX;
+
+        int step = (int)(1000 * InverseLerp(minX, maxX, curX));
+        TrackX.Value = step;
+        MinBoxX.Text = $"{minX:0.00}";
+        MaxBoxX.Text = $"{maxX:0.00}";
+        ThisValueX.Text = $"{curX:0.00}";
+
+        if (invalidate) refForm.Invalidate(false);
+    }
+    private void UpdateFromSliderX(bool invalidate)
+    {
+        double t = InverseLerp(0, 1000, TrackX.Value);
+        curX = Lerp(minX, maxX, t);
+
+        ThisValueX.Text = $"{curX:0.00}";
+        ableTransX!.OffsetX = curX;
+
+        if (invalidate) refForm.Invalidate(false);
+    }
+    private void UpdateFromMinBoxX()
+    {
+        if (!double.TryParse(MinBoxX.Text, out double newMin))
+        {
+            MinBoxX.Text = $"{minX:0.00}";
+            return;
+        }
+        minX = newMin;
+        MinBoxX.Text = $"{minX:0.00}";
+
+        if (minX > curX)
+        {
+            curX = minX;
+            ThisValueX.Text = $"{curX:0.00}";
+            ableTransX!.OffsetX = curX;
+        }
+
+        int step = (int)(1000 * InverseLerp(minX, maxX, curX));
+        TrackX.Value = step;
+
+        refForm.Invalidate(false);
+    }
+    private void UpdateFromMaxBoxX()
+    {
+        if (!double.TryParse(MaxBoxX.Text, out double newMax))
+        {
+            MaxBoxX.Text = $"{maxX:0.00}";
+            return;
+        }
+
+        maxX = newMax;
+        MaxBoxX.Text = $"{maxX:0.00}";
+
+        if (maxX < curX)
+        {
+            curX = maxX;
+            ThisValueX.Text = $"{curX:0.00}";
+            ableTransX!.OffsetX = curX;
+        }
+
+        int step = (int)(1000 * InverseLerp(minX, maxX, curX));
+        TrackX.Value = step;
+
+        refForm.Invalidate(false);
+    }
+    private void UpdateFromThisBoxX()
+    {
+        if (!double.TryParse(ThisValueX.Text, out double newCur))
+        {
+            ThisValueX.Text = $"{curX:0.00}";
+            return;
+        }
+        ableTransX!.OffsetX = newCur;
+        UpdateFromCurX(newCur, true);
+    }
+
+    private void UpdateFromCurY(double newCurY, bool invalidate)
+    {
+        curY = newCurY;
+        if (curY < minY) minY = curY;
+        else if (curY > maxY) maxY = curY;
+
+        int step = (int)(1000 * InverseLerp(minY, maxY, curY));
+        TrackY.Value = step;
+        MinBoxY.Text = $"{minY:0.00}";
+        MaxBoxY.Text = $"{maxY:0.00}";
+        ThisValueY.Text = $"{curY:0.00}";
+
+        if (invalidate) refForm.Invalidate(false);
+    }
+    private void UpdateFromSliderY(bool invalidate)
+    {
+        double t = InverseLerp(0, 1000, TrackY.Value);
+        curY = Lerp(minY, maxY, t);
+
+        ThisValueY.Text = $"{curY:0.00}";
+        ableTransY!.OffsetY = curY;
+
+        if (invalidate) refForm.Invalidate(false);
+    }
+    private void UpdateFromMinBoxY()
+    {
+        if (!double.TryParse(MinBoxY.Text, out double newMin))
+        {
+            MinBoxY.Text = $"{minY:0.00}";
+            return;
+        }
+        minY = newMin;
+        MinBoxY.Text = $"{minY:0.00}";
+
+        if (minY > curY)
+        {
+            curY = minY;
+            ThisValueY.Text = $"{curY:0.00}";
+            ableTransY!.OffsetY = curY;
+        }
+
+        int step = (int)(1000 * InverseLerp(minY, maxY, curY));
+        TrackY.Value = step;
+
+        refForm.Invalidate(false);
+    }
+    private void UpdateFromMaxBoxY()
+    {
+        if (!double.TryParse(MaxBoxY.Text, out double newMax))
+        {
+            MaxBoxY.Text = $"{maxY:0.00}";
+            return;
+        }
+
+        maxY = newMax;
+        MaxBoxY.Text = $"{maxY:0.00}";
+
+        if (maxY < curY)
+        {
+            curY = maxY;
+            ThisValueY.Text = $"{curY:0.00}";
+            ableTransY!.OffsetY = curY;
+        }
+
+        int step = (int)(1000 * InverseLerp(minY, maxY, curY));
+        TrackY.Value = step;
+
+        refForm.Invalidate(false);
+    }
+    private void UpdateFromThisBoxY()
+    {
+        if (!double.TryParse(ThisValueY.Text, out double newCur))
+        {
+            ThisValueY.Text = $"{curY:0.00}";
+            return;
+        }
+        ableTransY!.OffsetY = newCur;
+        UpdateFromCurY(newCur, true);
+    }
+
+    private static double Lerp(double a, double b, double t) => a + t * (b - a);
+    private static double InverseLerp(double a, double b, double c) => (c - a) / (b - a);
+
+    private void TrackX_Scroll(object sender, EventArgs e)
+    {
+        UpdateFromSliderX(true);
+    }
+    private void TrackY_Scroll(object sender, EventArgs e)
+    {
+        UpdateFromSliderY(true);
+    }
+}

Base/Forms/TranslateForm.resx

@@ -0,0 +1,120 @@
+<?xml version="1.0" encoding="utf-8"?>
+<root>
+  <!--
+    Microsoft ResX Schema 
+
+    Version 2.0
+
+    The primary goals of this format is to allow a simple XML format
+    that is mostly human readable. The generation and parsing of the
+    various data types are done through the TypeConverter classes
+    associated with the data types.
+
+    Example:
+
+    ... ado.net/XML headers & schema ...
+    <resheader name="resmimetype">text/microsoft-resx</resheader>
+    <resheader name="version">2.0</resheader>
+    <resheader name="reader">System.Resources.ResXResourceReader, System.Windows.Forms, ...</resheader>
+    <resheader name="writer">System.Resources.ResXResourceWriter, System.Windows.Forms, ...</resheader>
+    <data name="Name1"><value>this is my long string</value><comment>this is a comment</comment></data>
+    <data name="Color1" type="System.Drawing.Color, System.Drawing">Blue</data>
+    <data name="Bitmap1" mimetype="application/x-microsoft.net.object.binary.base64">
+        <value>[base64 mime encoded serialized .NET Framework object]</value>
+    </data>
+    <data name="Icon1" type="System.Drawing.Icon, System.Drawing" mimetype="application/x-microsoft.net.object.bytearray.base64">
+        <value>[base64 mime encoded string representing a byte array form of the .NET Framework object]</value>
+        <comment>This is a comment</comment>
+    </data>
+
+    There are any number of "resheader" rows that contain simple
+    name/value pairs.
+
+    Each data row contains a name, and value. The row also contains a
+    type or mimetype. Type corresponds to a .NET class that support
+    text/value conversion through the TypeConverter architecture.
+    Classes that don't support this are serialized and stored with the
+    mimetype set.
+
+    The mimetype is used for serialized objects, and tells the
+    ResXResourceReader how to depersist the object. This is currently not
+    extensible. For a given mimetype the value must be set accordingly:
+
+    Note - application/x-microsoft.net.object.binary.base64 is the format
+    that the ResXResourceWriter will generate, however the reader can
+    read any of the formats listed below.
+
+    mimetype: application/x-microsoft.net.object.binary.base64
+    value   : The object must be serialized with
+            : System.Runtime.Serialization.Formatters.Binary.BinaryFormatter
+            : and then encoded with base64 encoding.
+    
+    mimetype: application/x-microsoft.net.object.soap.base64
+    value   : The object must be serialized with
+            : System.Runtime.Serialization.Formatters.Soap.SoapFormatter
+            : and then encoded with base64 encoding.
+
+    mimetype: application/x-microsoft.net.object.bytearray.base64
+    value   : The object must be serialized into a byte array
+            : using a System.ComponentModel.TypeConverter
+            : and then encoded with base64 encoding.
+    -->
+  <xsd:schema id="root" xmlns="" xmlns:xsd="http://www.w3.org/2001/XMLSchema" xmlns:msdata="urn:schemas-microsoft-com:xml-msdata">
+    <xsd:import namespace="http://www.w3.org/XML/1998/namespace" />
+    <xsd:element name="root" msdata:IsDataSet="true">
+      <xsd:complexType>
+        <xsd:choice maxOccurs="unbounded">
+          <xsd:element name="metadata">
+            <xsd:complexType>
+              <xsd:sequence>
+                <xsd:element name="value" type="xsd:string" minOccurs="0" />
+              </xsd:sequence>
+              <xsd:attribute name="name" use="required" type="xsd:string" />
+              <xsd:attribute name="type" type="xsd:string" />
+              <xsd:attribute name="mimetype" type="xsd:string" />
+              <xsd:attribute ref="xml:space" />
+            </xsd:complexType>
+          </xsd:element>
+          <xsd:element name="assembly">
+            <xsd:complexType>
+              <xsd:attribute name="alias" type="xsd:string" />
+              <xsd:attribute name="name" type="xsd:string" />
+            </xsd:complexType>
+          </xsd:element>
+          <xsd:element name="data">
+            <xsd:complexType>
+              <xsd:sequence>
+                <xsd:element name="value" type="xsd:string" minOccurs="0" msdata:Ordinal="1" />
+                <xsd:element name="comment" type="xsd:string" minOccurs="0" msdata:Ordinal="2" />
+              </xsd:sequence>
+              <xsd:attribute name="name" type="xsd:string" use="required" msdata:Ordinal="1" />
+              <xsd:attribute name="type" type="xsd:string" msdata:Ordinal="3" />
+              <xsd:attribute name="mimetype" type="xsd:string" msdata:Ordinal="4" />
+              <xsd:attribute ref="xml:space" />
+            </xsd:complexType>
+          </xsd:element>
+          <xsd:element name="resheader">
+            <xsd:complexType>
+              <xsd:sequence>
+                <xsd:element name="value" type="xsd:string" minOccurs="0" msdata:Ordinal="1" />
+              </xsd:sequence>
+              <xsd:attribute name="name" type="xsd:string" use="required" />
+            </xsd:complexType>
+          </xsd:element>
+        </xsd:choice>
+      </xsd:complexType>
+    </xsd:element>
+  </xsd:schema>
+  <resheader name="resmimetype">
+    <value>text/microsoft-resx</value>
+  </resheader>
+  <resheader name="version">
+    <value>2.0</value>
+  </resheader>
+  <resheader name="reader">
+    <value>System.Resources.ResXResourceReader, System.Windows.Forms, Version=4.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089</value>
+  </resheader>
+  <resheader name="writer">
+    <value>System.Resources.ResXResourceWriter, System.Windows.Forms, Version=4.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089</value>
+  </resheader>
+</root>

Base/Forms/ViewCacheForm.Designer.cs

@@ -0,0 +1,100 @@
+using System.Drawing;
+using System.Windows.Forms;
+
+namespace Graphing.Forms
+{
+    partial class ViewCacheForm
+    {
+        /// <summary>
+        /// Required designer variable.
+        /// </summary>
+        private System.ComponentModel.IContainer components = null;
+
+        /// <summary>
+        /// Clean up any resources being used.
+        /// </summary>
+        /// <param name="disposing">true if managed resources should be disposed; otherwise, false.</param>
+        protected override void Dispose(bool disposing)
+        {
+            if (disposing && (components != null))
+            {
+                components.Dispose();
+            }
+            base.Dispose(disposing);
+        }
+
+        #region Windows Form Designer generated code
+
+        /// <summary>
+        /// Required method for Designer support - do not modify
+        /// the contents of this method with the code editor.
+        /// </summary>
+        private void InitializeComponent()
+        {
+            System.ComponentModel.ComponentResourceManager resources = new System.ComponentModel.ComponentResourceManager(typeof(ViewCacheForm));
+            CachePie = new Controls.PieChart();
+            TotalCacheText = new Label();
+            EraseAllCacheButton = new Button();
+            SpecificCachePanel = new Panel();
+            SuspendLayout();
+            // 
+            // CachePie
+            // 
+            CachePie.Location = new Point(50, 50);
+            CachePie.Name = "CachePie";
+            CachePie.Size = new Size(450, 450);
+            CachePie.TabIndex = 0;
+            // 
+            // TotalCacheText
+            // 
+            TotalCacheText.Font = new Font("Segoe UI Semibold", 10.125F, FontStyle.Bold, GraphicsUnit.Point, 0);
+            TotalCacheText.Location = new Point(62, 540);
+            TotalCacheText.Name = "TotalCacheText";
+            TotalCacheText.Size = new Size(425, 45);
+            TotalCacheText.TabIndex = 1;
+            TotalCacheText.Text = "Total Cache: Something";
+            TotalCacheText.TextAlign = ContentAlignment.TopCenter;
+            // 
+            // EraseAllCacheButton
+            // 
+            EraseAllCacheButton.Location = new Point(200, 580);
+            EraseAllCacheButton.Name = "EraseAllCacheButton";
+            EraseAllCacheButton.Size = new Size(150, 46);
+            EraseAllCacheButton.TabIndex = 2;
+            EraseAllCacheButton.Text = "Erase All";
+            EraseAllCacheButton.UseVisualStyleBackColor = true;
+            EraseAllCacheButton.Click += EraseAllCacheButton_Click;
+            // 
+            // SpecificCachePanel
+            // 
+            SpecificCachePanel.Anchor = AnchorStyles.Top | AnchorStyles.Bottom | AnchorStyles.Left | AnchorStyles.Right;
+            SpecificCachePanel.AutoScroll = true;
+            SpecificCachePanel.Location = new Point(520, 12);
+            SpecificCachePanel.Name = "SpecificCachePanel";
+            SpecificCachePanel.Size = new Size(542, 657);
+            SpecificCachePanel.TabIndex = 3;
+            // 
+            // ViewCacheForm
+            // 
+            AutoScaleDimensions = new SizeF(13F, 32F);
+            AutoScaleMode = AutoScaleMode.Font;
+            ClientSize = new Size(1074, 679);
+            Controls.Add(SpecificCachePanel);
+            Controls.Add(EraseAllCacheButton);
+            Controls.Add(TotalCacheText);
+            Controls.Add(CachePie);
+            FormBorderStyle = FormBorderStyle.SizableToolWindow;
+            MinimumSize = new Size(885, 750);
+            Name = "ViewCacheForm";
+            Text = "Graph Caches";
+            ResumeLayout(false);
+        }
+
+        #endregion
+
+        private Controls.PieChart CachePie;
+        private Label TotalCacheText;
+        private Button EraseAllCacheButton;
+        private Panel SpecificCachePanel;
+    }
+}

Base/Forms/ViewCacheForm.cs

@@ -0,0 +1,98 @@
+using Graphing.Extensions;
+using System;
+using System.Collections.Generic;
+using System.Drawing;
+using System.Windows.Forms;
+
+namespace Graphing.Forms;
+
+public partial class ViewCacheForm : Form
+{
+    private readonly GraphForm refForm;
+
+    private readonly List<Label> labelCache;
+    private readonly List<Button> buttonCache;
+
+    public ViewCacheForm(GraphForm thisForm)
+    {
+        InitializeComponent();
+
+        refForm = thisForm;
+        refForm.Paint += (o, e) => UpdatePieChart();
+        labelCache = [];
+        buttonCache = [];
+        UpdatePieChart();
+    }
+
+    private void UpdatePieChart()
+    {
+        CachePie.Values.Clear();
+
+        long totalBytes = 0;
+        int index = 0;
+        foreach (Graphable able in refForm.Graphables)
+        {
+            long thisBytes = able.GetCacheBytes();
+            if (thisBytes == 0) continue;
+            CachePie.Values.Add((able.Color, thisBytes));
+            totalBytes += thisBytes;
+
+            int buttonHeight = (int)(refForm.DpiFloat * 46 / 192),
+                buttonWidth = (int)(refForm.DpiFloat * 92 / 192),
+                buttonSpaced = (int)(refForm.DpiFloat * 98 / 192);
+
+            if (index < labelCache.Count)
+            {
+                Label reuseLabel = labelCache[index];
+                reuseLabel.ForeColor = able.Color;
+                reuseLabel.Text = $"{able.Name}: {thisBytes.FormatAsBytes()}";
+            }
+            else
+            {
+                Label newText = new()
+                {
+                    Anchor = AnchorStyles.Left | AnchorStyles.Top | AnchorStyles.Right,
+                    AutoEllipsis = true,
+                    ForeColor = able.Color,
+                    Location = new Point(0, labelCache.Count * buttonHeight),
+                    Parent = SpecificCachePanel,
+                    Size = new Size(SpecificCachePanel.Width - buttonSpaced, buttonHeight),
+                    Text = $"{able.Name}: {thisBytes.FormatAsBytes()}",
+                    TextAlign = ContentAlignment.MiddleLeft,
+                };
+                labelCache.Add(newText);
+            }
+
+            if (index >= buttonCache.Count)
+            {
+                Button newButton = new()
+                {
+                    Anchor = AnchorStyles.Top | AnchorStyles.Right,
+                    Location = new Point(SpecificCachePanel.Width - buttonWidth, buttonCache.Count * buttonHeight),
+                    Parent = SpecificCachePanel,
+                    Size = new Size(buttonWidth, buttonHeight),
+                    Text = "Clear"
+                };
+                newButton.Click += (o, e) => EraseSpecificGraphable_Click(able);
+                buttonCache.Add(newButton);
+            }
+
+            index++;
+        }
+
+        TotalCacheText.Text = $"Total Cache: {totalBytes.FormatAsBytes()}";
+
+        Invalidate(true);
+    }
+
+    private void EraseAllCacheButton_Click(object? sender, EventArgs e)
+    {
+        foreach (Graphable able in refForm.Graphables) able.EraseCache();
+        refForm.Invalidate(false);
+    }
+    private void EraseSpecificGraphable_Click(Graphable able)
+    {
+        able.EraseCache();
+        refForm.Invalidate(false);
+    }
+}

Base/Forms/ViewCacheForm.resx

@@ -0,0 +1,139 @@
+<?xml version="1.0" encoding="utf-8"?>
+<root>
+  <!--
+    Microsoft ResX Schema 
+
+    Version 2.0
+
+    The primary goals of this format is to allow a simple XML format
+    that is mostly human readable. The generation and parsing of the
+    various data types are done through the TypeConverter classes
+    associated with the data types.
+
+    Example:
+
+    ... ado.net/XML headers & schema ...
+    <resheader name="resmimetype">text/microsoft-resx</resheader>
+    <resheader name="version">2.0</resheader>
+    <resheader name="reader">System.Resources.ResXResourceReader, System.Windows.Forms, ...</resheader>
+    <resheader name="writer">System.Resources.ResXResourceWriter, System.Windows.Forms, ...</resheader>
+    <data name="Name1"><value>this is my long string</value><comment>this is a comment</comment></data>
+    <data name="Color1" type="System.Drawing.Color, System.Drawing">Blue</data>
+    <data name="Bitmap1" mimetype="application/x-microsoft.net.object.binary.base64">
+        <value>[base64 mime encoded serialized .NET Framework object]</value>
+    </data>
+    <data name="Icon1" type="System.Drawing.Icon, System.Drawing" mimetype="application/x-microsoft.net.object.bytearray.base64">
+        <value>[base64 mime encoded string representing a byte array form of the .NET Framework object]</value>
+        <comment>This is a comment</comment>
+    </data>
+
+    There are any number of "resheader" rows that contain simple
+    name/value pairs.
+
+    Each data row contains a name, and value. The row also contains a
+    type or mimetype. Type corresponds to a .NET class that support
+    text/value conversion through the TypeConverter architecture.
+    Classes that don't support this are serialized and stored with the
+    mimetype set.
+
+    The mimetype is used for serialized objects, and tells the
+    ResXResourceReader how to depersist the object. This is currently not
+    extensible. For a given mimetype the value must be set accordingly:
+
+    Note - application/x-microsoft.net.object.binary.base64 is the format
+    that the ResXResourceWriter will generate, however the reader can
+    read any of the formats listed below.
+
+    mimetype: application/x-microsoft.net.object.binary.base64
+    value   : The object must be serialized with
+            : System.Runtime.Serialization.Formatters.Binary.BinaryFormatter
+            : and then encoded with base64 encoding.
+    
+    mimetype: application/x-microsoft.net.object.soap.base64
+    value   : The object must be serialized with
+            : System.Runtime.Serialization.Formatters.Soap.SoapFormatter
+            : and then encoded with base64 encoding.
+
+    mimetype: application/x-microsoft.net.object.bytearray.base64
+    value   : The object must be serialized into a byte array
+            : using a System.ComponentModel.TypeConverter
+            : and then encoded with base64 encoding.
+    -->
+  <xsd:schema id="root" xmlns="" xmlns:xsd="http://www.w3.org/2001/XMLSchema" xmlns:msdata="urn:schemas-microsoft-com:xml-msdata">
+    <xsd:import namespace="http://www.w3.org/XML/1998/namespace" />
+    <xsd:element name="root" msdata:IsDataSet="true">
+      <xsd:complexType>
+        <xsd:choice maxOccurs="unbounded">
+          <xsd:element name="metadata">
+            <xsd:complexType>
+              <xsd:sequence>
+                <xsd:element name="value" type="xsd:string" minOccurs="0" />
+              </xsd:sequence>
+              <xsd:attribute name="name" use="required" type="xsd:string" />
+              <xsd:attribute name="type" type="xsd:string" />
+              <xsd:attribute name="mimetype" type="xsd:string" />
+              <xsd:attribute ref="xml:space" />
+            </xsd:complexType>
+          </xsd:element>
+          <xsd:element name="assembly">
+            <xsd:complexType>
+              <xsd:attribute name="alias" type="xsd:string" />
+              <xsd:attribute name="name" type="xsd:string" />
+            </xsd:complexType>
+          </xsd:element>
+          <xsd:element name="data">
+            <xsd:complexType>
+              <xsd:sequence>
+                <xsd:element name="value" type="xsd:string" minOccurs="0" msdata:Ordinal="1" />
+                <xsd:element name="comment" type="xsd:string" minOccurs="0" msdata:Ordinal="2" />
+              </xsd:sequence>
+              <xsd:attribute name="name" type="xsd:string" use="required" msdata:Ordinal="1" />
+              <xsd:attribute name="type" type="xsd:string" msdata:Ordinal="3" />
+              <xsd:attribute name="mimetype" type="xsd:string" msdata:Ordinal="4" />
+              <xsd:attribute ref="xml:space" />
+            </xsd:complexType>
+          </xsd:element>
+          <xsd:element name="resheader">
+            <xsd:complexType>
+              <xsd:sequence>
+                <xsd:element name="value" type="xsd:string" minOccurs="0" msdata:Ordinal="1" />
+              </xsd:sequence>
+              <xsd:attribute name="name" type="xsd:string" use="required" />
+            </xsd:complexType>
+          </xsd:element>
+        </xsd:choice>
+      </xsd:complexType>
+    </xsd:element>
+  </xsd:schema>
+  <resheader name="resmimetype">
+    <value>text/microsoft-resx</value>
+  </resheader>
+  <resheader name="version">
+    <value>2.0</value>
+  </resheader>
+  <resheader name="reader">
+    <value>System.Resources.ResXResourceReader, System.Windows.Forms, Version=4.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089</value>
+  </resheader>
+  <resheader name="writer">
+    <value>System.Resources.ResXResourceWriter, System.Windows.Forms, Version=4.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089</value>
+  </resheader>
+  <data name="CachePie.Values" mimetype="application/x-microsoft.net.object.binary.base64">
+    <value>
+        AAEAAAD/////AQAAAAAAAAAEAQAAAM0CU3lzdGVtLkNvbGxlY3Rpb25zLkdlbmVyaWMuTGlzdGAxW1tT
+        eXN0ZW0uVmFsdWVUdXBsZWAyW1tTeXN0ZW0uRHJhd2luZy5Db2xvciwgU3lzdGVtLkRyYXdpbmcsIFZl
+        cnNpb249NC4wLjAuMCwgQ3VsdHVyZT1uZXV0cmFsLCBQdWJsaWNLZXlUb2tlbj1iMDNmNWY3ZjExZDUw
+        YTNhXSxbU3lzdGVtLkRvdWJsZSwgbXNjb3JsaWIsIFZlcnNpb249NC4wLjAuMCwgQ3VsdHVyZT1uZXV0
+        cmFsLCBQdWJsaWNLZXlUb2tlbj1iNzdhNWM1NjE5MzRlMDg5XV0sIG1zY29ybGliLCBWZXJzaW9uPTQu
+        MC4wLjAsIEN1bHR1cmU9bmV1dHJhbCwgUHVibGljS2V5VG9rZW49Yjc3YTVjNTYxOTM0ZTA4OV1dAwAA
+        AAZfaXRlbXMFX3NpemUIX3ZlcnNpb24DAADdAVN5c3RlbS5WYWx1ZVR1cGxlYDJbW1N5c3RlbS5EcmF3
+        aW5nLkNvbG9yLCBTeXN0ZW0uRHJhd2luZywgVmVyc2lvbj00LjAuMC4wLCBDdWx0dXJlPW5ldXRyYWws
+        IFB1YmxpY0tleVRva2VuPWIwM2Y1ZjdmMTFkNTBhM2FdLFtTeXN0ZW0uRG91YmxlLCBtc2NvcmxpYiwg
+        VmVyc2lvbj00LjAuMC4wLCBDdWx0dXJlPW5ldXRyYWwsIFB1YmxpY0tleVRva2VuPWI3N2E1YzU2MTkz
+        NGUwODldXVtdCAgJAgAAAAAAAAAAAAAABwIAAAAAAQAAAAAAAAAD2wFTeXN0ZW0uVmFsdWVUdXBsZWAy
+        W1tTeXN0ZW0uRHJhd2luZy5Db2xvciwgU3lzdGVtLkRyYXdpbmcsIFZlcnNpb249NC4wLjAuMCwgQ3Vs
+        dHVyZT1uZXV0cmFsLCBQdWJsaWNLZXlUb2tlbj1iMDNmNWY3ZjExZDUwYTNhXSxbU3lzdGVtLkRvdWJs
+        ZSwgbXNjb3JsaWIsIFZlcnNpb249NC4wLjAuMCwgQ3VsdHVyZT1uZXV0cmFsLCBQdWJsaWNLZXlUb2tl
+        bj1iNzdhNWM1NjE5MzRlMDg5XV0L
+</value>
+  </data>
+</root>

Base/Graphable.cs

@@ -1,4 +1,6 @@
 using Graphing.Forms;
+using System.Collections.Generic;
+using System.Drawing;
 
 namespace Graphing;
 
@@ -7,12 +9,12 @@ public abstract class Graphable
     private static int defaultColorsUsed;
     public static readonly uint[] DefaultColors =
     [
-        0xEF_B34D47, // Red
-        0xEF_4769B3, // Blue
-        0xEF_50B347, // Green
-        0xEF_7047B3, // Purple
-        0xEF_B38B47, // Orange
-        0xEF_5B5B5B  // Black
+        0xFF_B34D47, // Red
+        0xFF_4769B3, // Blue
+        0xFF_50B347, // Green
+        0xFF_7047B3, // Purple
+        0xFF_B38B47, // Orange
+        0xFF_5B5B5B  // Black
     ];
 
     public Color Color { get; set; }
@@ -26,5 +28,14 @@ public abstract class Graphable
         Name = "Unnamed Graphable.";
     }
 
-    public abstract IEnumerable<Line2d> GetItemsToRender(in GraphForm graph);
+    public abstract IEnumerable<IGraphPart> GetItemsToRender(in GraphForm graph);
+
+    public abstract Graphable ShallowCopy();
+
+    public virtual void EraseCache() { }
+    public virtual long GetCacheBytes() => 0;
+    public virtual void Preload(Float2 xRange, Float2 yRange, double step) { }
+
+    public virtual bool ShouldSelectGraphable(in GraphForm graph, Float2 graphMousePos, double factor) => false;
+    public virtual IEnumerable<IGraphPart> GetSelectionItemsToRender(in GraphForm graph, Float2 graphMousePos) => [];
 }

Base/Graphables/ColumnTable.cs

@@ -0,0 +1,133 @@
+using Graphing.Forms;
+using Graphing.Parts;
+using System;
+using System.Collections.Generic;
+using System.Drawing;
+using System.Linq;
+
+namespace Graphing.Graphables;
+
+public class ColumnTable : Graphable
+{
+    private static int tableNum;
+
+    protected readonly Dictionary<double, double> tableXY;
+    protected readonly double width;
+
+    public ColumnTable(double width, Dictionary<double, double> tableXY)
+    {
+        tableNum++;
+        Name = $"Column Table {tableNum}";
+
+        this.tableXY = tableXY;
+        this.width = width;
+    }
+    public ColumnTable(double step, Equation equation, double min, double max)
+    {
+        Color = equation.Color;
+        Name = $"Column Table for {equation.Name}";
+
+        tableXY = [];
+        EquationDelegate equ = equation.GetDelegate();
+        width = 0.75 * step;
+
+        double minRounded = Math.Round(min / step) * step,
+               maxRounded = Math.Round(max / step) * step;
+        for (double x = minRounded; x <= maxRounded; x += step)
+            tableXY.Add(x, equ(x));
+    }
+
+    public override long GetCacheBytes() => 16 * tableXY.Count;
+
+    public override Graphable ShallowCopy() => new ColumnTable(width / 0.75, tableXY);
+
+    public override IEnumerable<IGraphPart> GetItemsToRender(in GraphForm graph)
+    {
+        List<IGraphPart> items = [];
+        foreach (KeyValuePair<double, double> col in tableXY)
+        {
+            items.Add(GraphRectangle.FromSize(new Float2(col.Key, col.Value / 2),
+                                              new Float2(width, col.Value), 0.625));
+        }
+
+        return items;
+    }
+
+    public override bool ShouldSelectGraphable(in GraphForm graph, Float2 graphMousePos, double factor)
+    {
+        // Get closest value to mouse pos.
+        double closestDist = double.PositiveInfinity, closestX = 0, closestY = 0;
+        foreach (KeyValuePair<double, double> points in tableXY)
+        {
+            double dist = Math.Abs(points.Key - graphMousePos.x);
+            if (dist < closestDist)
+            {
+                closestDist = dist;
+                closestX = points.Key;
+                closestY = points.Value;
+            }
+        }
+
+        Int2 screenMousePos = graph.GraphSpaceToScreenSpace(graphMousePos);
+        Int2 minBox = graph.GraphSpaceToScreenSpace(new(closestX - width / 2, 0)),
+             maxBox = graph.GraphSpaceToScreenSpace(new(closestX + width / 2, closestY));
+
+        int distX, distY;
+        if (screenMousePos.x < minBox.x) distX = minBox.x - screenMousePos.x; // On left side.
+        else if (screenMousePos.x > maxBox.x) distX = screenMousePos.x - maxBox.x; // On right side.
+        else distX = 0; // Inside.
+
+        if (closestY > 0)
+        {
+            if (screenMousePos.y > minBox.y) distY = screenMousePos.y - minBox.y; // Underneath.
+            else if (screenMousePos.y < maxBox.y) distY = maxBox.y - screenMousePos.y; // Above.
+            else distY = 0; // Inside.
+        }
+        else
+        {
+            if (screenMousePos.y < minBox.y) distY = minBox.y - screenMousePos.y; // Underneath.
+            else if (screenMousePos.y > maxBox.y) distY = screenMousePos.y - maxBox.y; // Above.
+            else distY = 0; // Inside.
+        }
+
+        int totalDist = (int)Math.Sqrt(distX * distX + distY * distY);
+        return totalDist < 50 * factor * graph.DpiFloat / 192;
+    }
+    public override IEnumerable<IGraphPart> GetSelectionItemsToRender(in GraphForm graph, Float2 graphMousePos)
+    {
+        // Get closest value to mouse pos.
+        double closestDist = double.PositiveInfinity, closestX = 0, closestY = 0;
+        foreach (KeyValuePair<double, double> points in tableXY)
+        {
+            double dist = Math.Abs(points.Key - graphMousePos.x);
+            if (dist < closestDist)
+            {
+                closestDist = dist;
+                closestX = points.Key;
+                closestY = points.Value;
+            }
+        }
+
+        Float2 textPoint = new(closestX, closestY);
+        Int2 offset;
+        ContentAlignment alignment;
+        if (textPoint.y >= 0)
+        {
+            offset = new(0, -5);
+            alignment = ContentAlignment.BottomCenter;
+        }
+        else
+        {
+            offset = new(0, 5);
+            alignment = ContentAlignment.TopCenter;
+        }
+
+        return
+        [
+            new GraphUiText($"{closestY:0.00}", textPoint, alignment, offsetPix: offset)
+        ];
+    }
+
+    // Nothing to preload, everything is already cached.
+    public override void Preload(Float2 xRange, Float2 yRange, double step) { }
+}

Base/Graphables/Equation.cs

@@ -1,12 +1,27 @@
-using Graphing.Forms;
+using Graphing.Abstract;
+using Graphing.Forms;
+using Graphing.Parts;
+using System;
+using System.Collections.Generic;
+using System.Drawing;
 
 namespace Graphing.Graphables;
 
-public class Equation : Graphable
+public class Equation : Graphable, IIntegrable, IDerivable, ITranslatableXY, IConvertSlopeField,
+                                   IConvertColumnTable
 {
     private static int equationNum;
 
-    private readonly EquationDelegate equ;
+    public bool UngraphWhenConvertedToColumnTable => false;
+    public bool UngraphWhenConvertedToSlopeField => false;
+
+    public double OffsetX { get; set; }
+    public double OffsetY { get; set; }
+
+    protected readonly EquationDelegate equ;
+    protected readonly List<Float2> cache;
+
+    public event Action<GraphForm> OnInvalidate;
 
     public Equation(EquationDelegate equ)
     {
@@ -14,28 +29,140 @@ public class Equation : Graphable
         Name = $"Equation {equationNum}";
 
         this.equ = equ;
+        cache = [];
+
+        OffsetX = 0;
+        OffsetY = 0;
+
+        OnInvalidate = delegate { };
     }
 
-    public override IEnumerable<Line2d> GetItemsToRender(in GraphForm graph)
+    public override IEnumerable<IGraphPart> GetItemsToRender(in GraphForm graph)
     {
-        List<Line2d> lines = [];
+        const int step = 10;
+
+        double epsilon = Math.Abs(graph.ScreenSpaceToGraphSpace(new Int2(0, 0)).x
+                                - graph.ScreenSpaceToGraphSpace(new Int2(step / 2, 0)).x) / 5;
+        epsilon *= graph.DpiFloat / 192;
+
+        List<IGraphPart> lines = [];
+
         double previousX = graph.MinVisibleGraph.x;
-        double previousY = equ(previousX);
-        for (int i = 1; i < graph.ClientRectangle.Width; i += 10)
+        double previousY = GetFromCache(previousX, epsilon);
+
+        for (int i = 0; i < graph.ClientRectangle.Width + step; i += step)
         {
             double currentX = graph.ScreenSpaceToGraphSpace(new Int2(i, 0)).x;
-            double currentY = equ(currentX);
+            double currentY = GetFromCache(currentX, epsilon);
             if (Math.Abs(currentY - previousY) <= 10)
             {
-                lines.Add(new Line2d(new Float2(previousX, previousY), new Float2(currentX, currentY)));
+                lines.Add(new GraphLine(new Float2(previousX, previousY), new Float2(currentX, currentY)));
             }
             previousX = currentX;
             previousY = currentY;
         }
+        OnInvalidate.Invoke(graph);
         return lines;
     }
 
+    protected double DerivativeAtPoint(double x)
+    {
+        const double step = 1e-3;
+        return (equ(x + step - OffsetX) - equ(x - OffsetX)) / step;
+    }
+
+    public Graphable Derive() => new Equation(DerivativeAtPoint);
+    public Graphable Integrate() => new IntegralEquation(this);
+
     public EquationDelegate GetDelegate() => equ;
+
+    public SlopeField ToSlopeField(int detail) => new(detail, (x, y) => DerivativeAtPoint(x))
+    {
+        Color = Color,
+        Name = $"Slope Field of {Name}"
+    };
+    public ColumnTable ToColumnTable(double start, double end, int detail)
+        => new(1.0 / detail, this, start, end);
+
+    public override void EraseCache() => cache.Clear();
+    protected double GetFromCache(double x, double epsilon)
+    {
+        (double dist, double nearest, int index) = NearestCachedPoint(x - OffsetX);
+        if (dist < epsilon) return nearest + OffsetY;
+        else
+        {
+            double result = equ(x - OffsetX);
+            cache.Insert(index + 1, new(x - OffsetX, result));
+            return result + OffsetY;
+        }
+    }
+
+    public double GetValueAt(double x) => GetFromCache(x, 0);
+
+    protected (double dist, double y, int index) NearestCachedPoint(double x)
+    {
+        if (cache.Count == 0) return (double.PositiveInfinity, double.NaN, -1);
+        else if (cache.Count == 1)
+        {
+            Float2 single = cache[0];
+            return (Math.Abs(single.x - x), single.y, 0);
+        }
+        else
+        {
+            int boundA = 0, boundB = cache.Count;
+            do
+            {
+                int boundC = (boundA + boundB) / 2;
+                Float2 pointC = cache[boundC];
+
+                if (pointC.x == x) return (0, pointC.y, boundC);
+                else if (pointC.x > x)
+                {
+                    boundA = boundC;
+                }
+                else // pointC.x < x
+                {
+                    boundB = boundC;
+                }
+
+            } while (boundB - boundA > 1);
+
+            return (Math.Abs(cache[boundA].x - x), cache[boundA].y, boundA);
+        }
+    }
+
+    public override Graphable ShallowCopy() => new Equation(equ);
+
+    public override long GetCacheBytes() => cache.Count * 16;
+
+    public override bool ShouldSelectGraphable(in GraphForm graph, Float2 graphMousePos, double factor)
+    {
+        Int2 screenMousePos = graph.GraphSpaceToScreenSpace(graphMousePos);
+
+        (_, _, int index) = NearestCachedPoint(graphMousePos.x);
+        Int2 screenCachePos = graph.GraphSpaceToScreenSpace(cache[index]);
+
+        double allowedDist = factor * graph.DpiFloat * 80 / 192;
+
+        Int2 dist = new(screenCachePos.x - screenMousePos.x,
+                        screenCachePos.y - screenMousePos.y);
+        double totalDist = Math.Sqrt(dist.x * dist.x + dist.y * dist.y);
+        return totalDist <= allowedDist;
+    }
+    public override IEnumerable<IGraphPart> GetSelectionItemsToRender(in GraphForm graph, Float2 graphMousePos)
+    {
+        Float2 point = new(graphMousePos.x, GetFromCache(graphMousePos.x, 1e-3));
+        return
+        [
+            new GraphUiText($"({point.x:0.00}, {point.y:0.00})", point, ContentAlignment.BottomLeft),
+            new GraphUiCircle(point),
+        ];
+    }
+
+    public override void Preload(Float2 xRange, Float2 yRange, double step)
+    {
+        for (double x = xRange.x; x <= xRange.y; x += step) GetFromCache(x, step);
+    }
 }
 
 public delegate double EquationDelegate(double x);

Base/Graphables/EquationDifference.cs

@@ -0,0 +1,96 @@
+using Graphing.Abstract;
+using Graphing.Forms;
+using Graphing.Parts;
+using System;
+using System.Collections.Generic;
+using System.Drawing;
+
+namespace Graphing.Graphables;
+
+public class EquationDifference : Graphable, ITranslatableX, IConvertEquation
+{
+    public bool UngraphWhenConvertedToEquation => true;
+
+    public double Position
+    {
+        get => _position;
+        set
+        {
+            _position = value;
+            points = new Float2(equA.GetValueAt(value), equB.GetValueAt(value));
+        }
+    }
+    private double _position;
+
+    public double OffsetX
+    {
+        get => Position;
+        set => Position = value;
+    }
+
+    protected readonly Equation equA, equB;
+    protected Float2 points; // X represents equA.y, Y represents equB.y
+
+    public EquationDifference(double position, Equation equA, Equation equB)
+    {
+        this.equA = equA;
+        this.equB = equB;
+
+        Name = $"Difference between {equA.Name} and {equB.Name}";
+
+        Position = position;
+    }
+
+    public override IEnumerable<IGraphPart> GetItemsToRender(in GraphForm graph)
+    {
+        Float2 pA = new(Position, points.x),
+               pB = new(Position, points.y);
+        return
+        [
+            new GraphUiCircle(pA),
+            new GraphUiCircle(pB),
+            new GraphLine(pA, pB)
+        ];
+    }
+
+    public double DistanceAtPoint(double x) => equA.GetValueAt(x) - equB.GetValueAt(x);
+
+    public override Graphable ShallowCopy() => new EquationDifference(Position, equA, equB);
+
+    public override bool ShouldSelectGraphable(in GraphForm graph, Float2 graphMousePos, double factor)
+    {
+        Float2 nearestPoint = new(Position, graphMousePos.y);
+        double upper = double.Max(points.x, points.y),
+               lower = double.Min(points.x, points.y);
+        if (nearestPoint.y > upper) nearestPoint.y = upper;
+        else if (nearestPoint.y < lower) nearestPoint.y = lower;
+
+        Int2 nearestPixelPoint = graph.GraphSpaceToScreenSpace(nearestPoint);
+        Int2 screenMousePos = graph.GraphSpaceToScreenSpace(graphMousePos);
+
+        Int2 diff = new(screenMousePos.x - nearestPixelPoint.x,
+                        screenMousePos.y - nearestPixelPoint.y);
+        int dist = (int)Math.Sqrt(diff.x * diff.x + diff.y * diff.y);
+        return dist < 50 * factor * graph.DpiFloat / 192;
+    }
+    public override IEnumerable<IGraphPart> GetSelectionItemsToRender(in GraphForm graph, Float2 graphMousePos)
+    {
+        Float2 nearestPoint = new(Position, graphMousePos.y);
+        double upper = double.Max(points.x, points.y),
+               lower = double.Min(points.x, points.y);
+        if (nearestPoint.y > upper) nearestPoint.y = upper;
+        else if (nearestPoint.y < lower) nearestPoint.y = lower;
+
+        return
+        [
+            new GraphUiText($"Δ = {points.x - points.y:0.000}", nearestPoint, ContentAlignment.MiddleLeft, offsetPix: new Int2(15, 0)),
+            new GraphUiCircle(nearestPoint)
+        ];
+    }
+
+    public Equation ToEquation() => new(DistanceAtPoint)
+    {
+        Color = Color,
+        Name = Name
+    };
+}

Base/Graphables/IntegralEquation.cs

@@ -0,0 +1,239 @@
+using Graphing.Abstract;
+using Graphing.Forms;
+using Graphing.Parts;
+using System;
+using System.Collections.Generic;
+using System.ComponentModel.Design;
+
+namespace Graphing.Graphables;
+
+public class IntegralEquation : Graphable, IIntegrable, IDerivable
+{
+    protected readonly Equation? baseEqu;
+    protected readonly EquationDelegate? baseEquDel;
+
+    protected readonly IntegralEquation? altBaseEqu;
+
+    protected readonly bool usingAlt;
+
+    public IntegralEquation(Equation baseEquation)
+    {
+        string oldName = baseEquation.Name, newName;
+        if (oldName.StartsWith("Integral of ")) newName = "Second Integral of " + oldName[12..];
+        else if (oldName.StartsWith("Second Integral of ")) newName = "Third Integral of " + oldName[19..];
+        else newName = "Integral of " + oldName;
+
+        Name = newName;
+
+        baseEqu = baseEquation;
+        baseEquDel = baseEquation.GetDelegate();
+
+        altBaseEqu = null;
+        usingAlt = false;
+    }
+    public IntegralEquation(IntegralEquation baseEquation)
+    {
+        string oldName = baseEquation.Name, newName;
+        if (oldName.StartsWith("Integral of ")) newName = "Second Integral of " + oldName[12..];
+        else if (oldName.StartsWith("Second Integral of ")) newName = "Third Integral of " + oldName[19..];
+        else newName = "Integral of " + oldName;
+
+        Name = newName;
+
+        baseEqu = null;
+        baseEquDel = null;
+
+        altBaseEqu = baseEquation;
+        usingAlt = true;
+    }
+
+    public override Graphable ShallowCopy() => new IntegralEquation(this);
+
+    public override IEnumerable<IGraphPart> GetItemsToRender(in GraphForm graph)
+    {
+        const int step = 10;
+        double epsilon = Math.Abs(graph.ScreenSpaceToGraphSpace(new Int2(0, 0)).x
+                                - graph.ScreenSpaceToGraphSpace(new Int2(step / 2, 0)).x) / 5;
+        epsilon *= graph.DpiFloat / 192;
+        List<IGraphPart> lines = [];
+
+        Int2 originLocation = graph.GraphSpaceToScreenSpace(new Float2(0, 0));
+        if (originLocation.x < 0)
+        {
+            // Origin is off the left side of the screen.
+            // Get to the left side from the origin.
+            double start = graph.MinVisibleGraph.x, end = graph.MaxVisibleGraph.x;
+            SetInternalStepper(start, epsilon);
+
+            // Now we can start.
+            double previousX = stepX;
+            double previousY = stepY;
+            for (double x = start; x <= end; x += epsilon)
+            {
+                MoveInternalStepper(epsilon);
+                lines.Add(new GraphLine(new Float2(previousX, previousY),
+                                        new Float2(stepX, stepY)));
+                previousX = stepX;
+                previousY = stepY;
+            }
+        }
+        else if (originLocation.x > graph.ClientRectangle.Width)
+        {
+            // Origin is off the right side of the screen.
+            // Get to the right side of the origin.
+            double start = graph.MaxVisibleGraph.x, end = graph.MinVisibleGraph.x;
+            SetInternalStepper(start, epsilon);
+
+            // Now we can start.
+            double previousX = stepX;
+            double previousY = stepY;
+            for (double x = start; x >= end; x -= epsilon)
+            {
+                MoveInternalStepper(-epsilon);
+                lines.Add(new GraphLine(new Float2(previousX, previousY),
+                                        new Float2(stepX, stepY)));
+                previousX = stepX;
+                previousY = stepY;
+            }
+        }
+        else
+        {
+            // Origin is on-screen.
+            // We need to do two cycles.
+
+            // Start with right.
+            double start = 0, end = graph.MaxVisibleGraph.x;
+            SetInternalStepper(start, epsilon);
+
+            double previousX = stepX;
+            double previousY = stepY;
+            for (double x = start; x <= end; x += epsilon)
+            {
+                MoveInternalStepper(epsilon);
+                lines.Add(new GraphLine(new Float2(previousX, previousY),
+                                        new Float2(stepX, stepY)));
+                previousX = stepX;
+                previousY = stepY;
+            }
+
+            // Now do left.
+            start = 0;
+            end = graph.MinVisibleGraph.x;
+            SetInternalStepper(start, epsilon);
+
+            previousX = stepX;
+            previousY = stepY;
+
+            for (double x = start; x >= end; x -= epsilon)
+            {
+                MoveInternalStepper(-epsilon);
+                lines.Add(new GraphLine(new Float2(previousX, previousY),
+                                        new Float2(stepX, stepY)));
+                previousX = stepX;
+                previousY = stepY;
+            }
+        }
+
+        return lines;
+    }
+
+    private double stepX = 0;
+    private double stepY = 0;
+    private void SetInternalStepper(double x, double dX)
+    {
+        stepX = 0;
+        stepY = 0;
+        if (usingAlt) altBaseEqu!.SetInternalStepper(0, dX);
+
+        if (x > 0)
+        {
+            while (stepX < x) MoveInternalStepper(dX);
+        }
+        else if (x < 0)
+        {
+            while (x < stepX) MoveInternalStepper(-dX);
+        }
+    }
+    private void MoveInternalStepper(double dX)
+    {
+        stepX += dX;
+        if (usingAlt)
+        {
+            altBaseEqu!.MoveInternalStepper(dX);
+            stepY += altBaseEqu!.stepY * dX;
+        }
+        else
+        {
+            stepY += (baseEquDel!(stepX - baseEqu!.OffsetX) + baseEqu.OffsetY) * dX;
+        }
+    }
+
+    // Try to avoid using this, as it converts the integral into a
+    // far less efficient format (uses the `IntegralAtPoint` method).
+    public Equation AsEquation() => new(IntegralAtPoint)
+    {
+        Name = Name,
+        Color = Color
+    };
+
+    public Graphable Derive()
+    {
+        if (usingAlt) return altBaseEqu!.ShallowCopy();
+        else return (Equation)baseEqu!.ShallowCopy();
+    }
+    public Graphable Integrate() => new IntegralEquation(this);
+
+    // Standard integral method.
+    // Inefficient for successive calls.
+    public double IntegralAtPoint(double x)
+    {
+        if (x > 0)
+        {
+            double start = Math.Min(0, x), end = Math.Max(0, x);
+            const double step = 1e-3;
+            double sum = 0;
+
+            SetInternalStepper(start, step);
+            for (double t = start; t <= end; t += step)
+            {
+                MoveInternalStepper(step);
+                sum += stepY * step;
+            }
+
+            return sum;
+        }
+        else if (x < 0)
+        {
+            double start = Math.Max(0, x), end = Math.Min(0, x);
+            const double step = 1e-3;
+            double sum = 0;
+
+            SetInternalStepper(start, step);
+            for (double t = start; t >= end; t -= step)
+            {
+                MoveInternalStepper(-step);
+                sum -= stepY * step;
+            }
+
+            return sum;
+        }
+        else return 0;
+    }
+
+    public override bool ShouldSelectGraphable(in GraphForm graph, Float2 graphMousePos, double factor)
+    {
+        Int2 screenMousePos = graph.GraphSpaceToScreenSpace(graphMousePos);
+
+        Int2 screenPos = graph.GraphSpaceToScreenSpace(new Float2(graphMousePos.x,
+                                                                  IntegralAtPoint(graphMousePos.x)));
+
+        double allowedDist = factor * graph.DpiFloat * 80 / 192;
+
+        Int2 dist = new(screenPos.x - screenMousePos.x,
+                        screenPos.y - screenMousePos.y);
+        double totalDist = Math.Sqrt(dist.x * dist.x + dist.y * dist.y);
+        return totalDist <= allowedDist;
+    }
+    public override IEnumerable<IGraphPart> GetSelectionItemsToRender(in GraphForm graph, Float2 graphMousePos) =>
+        [new GraphUiCircle(new(graphMousePos.x, IntegralAtPoint(graphMousePos.x)))];
+}

Base/Graphables/ParametricEquation.cs

@@ -0,0 +1,134 @@
+using Graphing.Abstract;
+using Graphing.Forms;
+using Graphing.Parts;
+using System;
+using System.Collections.Generic;
+
+namespace Graphing.Graphables;
+
+public class ParametricEquation : Graphable, IDerivable, ITranslatableXY
+{
+    private static int equationNum;
+
+    public double OffsetX { get; set; }
+    public double OffsetY { get; set; }
+
+    public double InitialT { get; set; }
+    public double FinalT { get; set; }
+
+    protected readonly ParametricDelegate equX, equY;
+    protected readonly List<(double t, Float2 point)> cache;
+
+    public ParametricEquation(double initialT, double finalT,
+                              ParametricDelegate equX, ParametricDelegate equY)
+    {
+        equationNum++;
+        Name = $"Parametric Equation {equationNum}";
+
+        InitialT = initialT;
+        FinalT = finalT;
+
+        this.equX = equX;
+        this.equY = equY;
+        cache = [];
+    }
+
+    public override Graphable ShallowCopy() => new ParametricEquation(InitialT, FinalT, equX, equY);
+
+    public override IEnumerable<IGraphPart> GetItemsToRender(in GraphForm graph)
+    {
+        const int step = 10;
+
+        double epsilon = Math.Abs(graph.ScreenSpaceToGraphSpace(new Int2(0, 0)).x
+                                - graph.ScreenSpaceToGraphSpace(new Int2(step, 0)).x);
+
+        List<IGraphPart> lines = [];
+
+        Float2 previousPoint = GetFromCache(InitialT, epsilon);
+        for (double t = InitialT; t <= FinalT; t += epsilon)
+        {
+            Float2 currentPoint = GetFromCache(t, epsilon);
+            if (graph.IsGraphPointVisible(currentPoint) ||
+                graph.IsGraphPointVisible(previousPoint))
+                    lines.Add(new GraphLine(previousPoint, currentPoint));
+            previousPoint = currentPoint;
+        }
+
+        return lines;
+    }
+
+    public Graphable Derive() =>
+        new ParametricEquation(InitialT, FinalT, GetDerivativeAtPointX, GetDerivativeAtPointY);
+
+    public ParametricDelegate GetXDelegate() => equX;
+    public ParametricDelegate GetYDelegate() => equY;
+
+    public double GetDerivativeAtPointX(double t)
+    {
+        const double step = 1e-3;
+        return (equX(t + step) - equX(t)) / step;
+    }
+    public double GetDerivativeAtPointY(double t)
+    {
+        const double step = 1e-3;
+        return (equY(t + step) - equY(t)) / step;
+    }
+    public Float2 GetDerivativeAtPoint(double t) =>
+        new(GetDerivativeAtPointX(t), GetDerivativeAtPointY(t));
+
+    public Float2 GetPointAt(double t) => GetFromCache(t, 0);
+
+    public override void EraseCache() => cache.Clear();
+    protected Float2 GetFromCache(double t, double epsilon)
+    {
+        (double dist, Float2 nearest, int index) = NearestCachedPoint(t);
+        if (dist < epsilon) return new(nearest.x + OffsetX, nearest.y + OffsetY);
+        else
+        {
+            Float2 result = new(equX(t), equY(t));
+            cache.Insert(index + 1, (t, result));
+            return new(result.x + OffsetX, result.y + OffsetY);
+        }
+    }
+    public override long GetCacheBytes() => cache.Count * 24;
+
+    protected (double dist, Float2 point, int index) NearestCachedPoint(double t)
+    {
+        if (cache.Count <= 1) return (double.PositiveInfinity, new(double.NaN, double.NaN), -1);
+        else if (cache.Count == 1)
+        {
+            (double resultT, Float2 resultPoint) = cache[0];
+            return (Math.Abs(resultT - t), resultPoint, 0);
+        }
+        else
+        {
+            int boundA = 0, boundB = cache.Count;
+            do
+            {
+                int boundC = (boundA + boundB) / 2;
+
+                (double thisT, Float2 thisPoint) = cache[boundC];
+                if (thisT == t) return (0, thisPoint, boundC);
+                else if (thisT > t)
+                {
+                    boundA = boundC;
+                }
+                else // thisT < t
+                {
+                    boundB = boundC;
+                }
+
+            } while (boundB - boundA > 1);
+
+            (double resultT, Float2 resultPoint) = cache[boundA];
+            return (Math.Abs(resultT - t), resultPoint, boundA);
+        }
+    }
+
+    public override void Preload(Float2 xRange, Float2 yRange, double step)
+    {
+        for (double t = InitialT; t <= FinalT; t += step) GetFromCache(t, step);
+    }
+}
+
+public delegate double ParametricDelegate(double t);

Base/Graphables/SlopeField.cs

@@ -1,4 +1,8 @@
 using Graphing.Forms;
+using Graphing.Parts;
+using System;
+using System.Collections.Generic;
+using System.Drawing;
 
 namespace Graphing.Graphables;
 
@@ -6,37 +10,61 @@ public class SlopeField : Graphable
 {
     private static int slopeFieldNum;
 
-    private readonly SlopeFieldsDelegate equ;
-    private readonly double detail;
+    public double Detail
+    {
+        get => _detail;
+        set
+        {
+            if (Math.Abs(value - Detail) >= 1e-4)
+            {
+                // When changing detail, we need to regenerate all
+                // the lines. Inefficient, I know. Might be optimized
+                // in a future update.
+                EraseCache();
+            }
+            _detail = value;
+        }
+    }
+    private double _detail;
 
-    public SlopeField(int detail, SlopeFieldsDelegate equ)
+    protected readonly SlopeFieldsDelegate equ;
+    protected readonly List<(Float2, GraphLine)> cache;
+
+    public SlopeField(double detail, SlopeFieldsDelegate equ)
     {
         slopeFieldNum++;
         Name = $"Slope Field {slopeFieldNum}";
 
         this.equ = equ;
-        this.detail = detail;
+        _detail = detail;
+        cache = [];
     }
 
-    public override IEnumerable<Line2d> GetItemsToRender(in GraphForm graph)
+    public override IEnumerable<IGraphPart> GetItemsToRender(in GraphForm graph)
     {
-        List<Line2d> lines = [];
+        double step = 1 / _detail;
+        double epsilon = step * 0.5;
+        List<IGraphPart> lines = [];
 
-        for (double x = Math.Ceiling(graph.MinVisibleGraph.x - 1); x < graph.MaxVisibleGraph.x + 1; x += 1 / detail)
+        double minX = Math.Round((graph.MinVisibleGraph.x - 1) / step) * step,
+               maxX = Math.Round((graph.MaxVisibleGraph.x + 1) / step) * step,
+               minY = Math.Round((graph.MinVisibleGraph.y - 1) / step) * step,
+               maxY = Math.Round((graph.MaxVisibleGraph.y + 1) / step) * step;
+
+        for (double x = minX; x < maxX; x += step)
         {
-            for (double y = Math.Ceiling(graph.MinVisibleGraph.y - 1); y < graph.MaxVisibleGraph.y + 1; y += 1 / detail)
+            for (double y = minY; y < maxY; y += step)
             {
-                double slope = equ(x, y);
-                lines.Add(MakeSlopeLine(new Float2(x, y), slope));
+                lines.Add(GetFromCache(epsilon, x, y));
             }
         }
 
         return lines;
     }
 
-    private Line2d MakeSlopeLine(Float2 position, double slope)
+    protected GraphLine MakeSlopeLine(Float2 position, double slope)
     {
-        double size = detail;
+        double size = _detail;
 
         double dirX = size, dirY = slope * size;
         double magnitude = Math.Sqrt(dirX * dirX + dirY * dirY);
@@ -46,6 +74,85 @@ public class SlopeField : Graphable
 
         return new(new(position.x + dirX, position.y + dirY), new(position.x - dirX, position.y - dirY));
     }
+    protected GraphLine GetFromCache(double epsilon, double x, double y)
+    {
+        // Probably no binary search here, though maybe it could be done
+        // in terms of just one axis.
+
+        foreach ((Float2 p, GraphLine l) in cache)
+        {
+            double diffX = Math.Abs(p.x - x),
+                   diffY = Math.Abs(p.y - y);
+
+            if (diffX < epsilon && diffY < epsilon) return l;
+        }
+
+        // Create a new value.
+        double slope = equ(x, y);
+        GraphLine result = MakeSlopeLine(new Float2(x, y), slope);
+        cache.Add((new Float2(x, y), result));
+        return result;
+    }
+
+    public override Graphable ShallowCopy() => new SlopeField(_detail, equ);
+
+    public override void EraseCache() => cache.Clear();
+    public override long GetCacheBytes() => cache.Count * 48;
+    
+    public override bool ShouldSelectGraphable(in GraphForm graph, Float2 graphMousePos, double factor)
+    {
+        Float2 nearestPos = new(Math.Round(graphMousePos.x * _detail) / _detail,
+                                Math.Round(graphMousePos.y * _detail) / _detail);
+
+        double epsilon = 1 / (_detail * 2.0);
+        GraphLine line = GetFromCache(epsilon, nearestPos.x, nearestPos.y);
+        double slope = (line.b.y - line.a.y) / (line.b.x - line.a.x);
+
+        if (graphMousePos.x < Math.Min(line.a.x, line.b.x) ||
+            graphMousePos.x > Math.Max(line.a.x, line.b.x)) return false;
+
+        double allowedDist = factor * graph.DpiFloat * 10 / 192;
+
+        double lineX = graphMousePos.x,
+               lineY = slope * (lineX - nearestPos.x) + nearestPos.y;
+
+        Int2 pointScreen = graph.GraphSpaceToScreenSpace(new Float2(lineX, lineY));
+        Int2 mouseScreen = graph.GraphSpaceToScreenSpace(graphMousePos);
+        Int2 dist = new(pointScreen.x - mouseScreen.x,
+                        pointScreen.y - mouseScreen.y);
+        double totalDist = Math.Sqrt(dist.x * dist.x + dist.y * dist.y);
+        return totalDist <= allowedDist;
+    }
+    public override IEnumerable<IGraphPart> GetSelectionItemsToRender(in GraphForm graph, Float2 graphMousePos)
+    {
+        Float2 nearestPos = new(Math.Round(graphMousePos.x * _detail) / _detail,
+                                Math.Round(graphMousePos.y * _detail) / _detail);
+
+        double epsilon = 1 / (_detail * 2.0);
+        GraphLine line = GetFromCache(epsilon, nearestPos.x, nearestPos.y);
+        double slope = (line.b.y - line.a.y) / (line.b.x - line.a.x);
+
+        double lineX = graphMousePos.x,
+               lineY = slope * (lineX - nearestPos.x) + nearestPos.y;
+        Float2 point = new(lineX, lineY);
+
+        return
+        [
+            new GraphUiText($"M = {slope:0.000}", point, ContentAlignment.BottomLeft),
+            new GraphUiCircle(point)
+        ];
+    }
+
+    public override void Preload(Float2 xRange, Float2 yRange, double step)
+    {
+        for (double x = Math.Ceiling(xRange.x - 1); x < xRange.y + 1; x += 1.0 / _detail)
+        {
+            for (double y = Math.Ceiling(yRange.x - 1); y < yRange.y + 1; y += 1.0 / _detail)
+            {
+                GetFromCache(step, x, y);
+            }
+        }
+    }
 }
 
 public delegate double SlopeFieldsDelegate(double x, double y);

Base/Graphables/TangentLine.cs

@@ -0,0 +1,152 @@
+using Graphing.Abstract;
+using Graphing.Forms;
+using Graphing.Parts;
+using System;
+using System.Collections.Generic;
+using System.Drawing;
+
+namespace Graphing.Graphables;
+
+public class TangentLine : Graphable, IConvertEquation, ITranslatableX
+{
+    public bool UngraphWhenConvertedToEquation => true;
+
+    public double Position
+    {
+        get => _position;
+        set
+        {
+            currentSlope = DerivativeAtPoint(value);
+            _position = value;
+        }
+    }
+    private double _position; // Private because it has exactly the same functionality as `Position`.
+
+    public double OffsetX
+    {
+        get => Position;
+        set => Position = value;
+    }
+
+    protected readonly Equation parent;
+
+    protected readonly double length;
+
+    // X is slope, Y is height.
+    protected Float2 currentSlope;
+
+    // No binary search for this, I want it to be exact.
+    // Value: X is slope, Y is height.
+    protected Dictionary<double, Float2> slopeCache;
+
+    public TangentLine(double length, double position, Equation parent)
+    {
+        Name = $"Tangent Line of {parent.Name}";
+
+        slopeCache = [];
+        this.length = length;
+        this.parent = parent;
+        Position = position;
+
+        parent.OnInvalidate += (graph) =>
+        {
+            // I don't love this but it works.
+            EraseCache();
+            Position = _position; // Done for side effects.
+        };
+    }
+
+    public override IEnumerable<IGraphPart> GetItemsToRender(in GraphForm graph)
+    {
+        Float2 point = new(Position, currentSlope.y);
+        return
+        [
+            MakeSlopeLine(),
+            new GraphUiCircle(point)
+        ];
+    }
+    protected GraphLine MakeSlopeLine()
+    {
+        double dirX = length, dirY = currentSlope.x * length;
+        double magnitude = Math.Sqrt(dirX * dirX + dirY * dirY);
+
+        dirX /= magnitude * 2 / length;
+        dirY /= magnitude * 2 / length;
+
+        return new(new(Position + dirX, currentSlope.y + dirY), new(Position - dirX, currentSlope.y - dirY));
+    }
+    protected Float2 DerivativeAtPoint(double x)
+    {
+        // If value is already computed, return it.
+        if (slopeCache.TryGetValue(x, out Float2 val)) return val;
+
+        const double step = 1e-3;
+
+        double initial = parent.GetValueAt(x);
+        Float2 result = new((parent.GetValueAt(x + step) - initial) / step, initial);
+        slopeCache.Add(x, result);
+        return result;
+    }
+
+    public override Graphable ShallowCopy() => new TangentLine(length, Position, parent);
+
+    public override void EraseCache() => slopeCache.Clear();
+    public override long GetCacheBytes() => slopeCache.Count * 24;
+
+    public override bool ShouldSelectGraphable(in GraphForm graph, Float2 graphMousePos, double factor)
+    {
+        GraphLine line = MakeSlopeLine();
+
+        if (graphMousePos.x < Math.Min(line.a.x - 0.25, line.b.x - 0.25) ||
+            graphMousePos.x > Math.Max(line.a.x + 0.25, line.b.x + 0.25)) return false;
+
+        double allowedDist = factor * graph.DpiFloat * 80 / 192;
+
+        double lineX = graphMousePos.x,
+               lineY = currentSlope.x * (lineX - Position) + currentSlope.y;
+
+        Int2 pointScreen = graph.GraphSpaceToScreenSpace(new Float2(lineX, lineY));
+        Int2 mouseScreen = graph.GraphSpaceToScreenSpace(graphMousePos);
+        Int2 dist = new(pointScreen.x - mouseScreen.x,
+                        pointScreen.y - mouseScreen.y);
+        double totalDist = Math.Sqrt(dist.x * dist.x + dist.y * dist.y);
+        return totalDist <= allowedDist;
+    }
+    public override IEnumerable<IGraphPart> GetSelectionItemsToRender(in GraphForm graph, Float2 graphMousePos)
+    {
+        GraphLine line = MakeSlopeLine();
+
+        double lineX = Math.Clamp(graphMousePos.x,
+                                  Math.Min(line.a.x, line.b.x),
+                                  Math.Max(line.a.x, line.b.x)),
+               lineY = currentSlope.x * (lineX - Position) + currentSlope.y;
+
+        double slope = currentSlope.x;
+        Float2 point = new(lineX, lineY);
+
+        return
+        [
+            new GraphUiText($"M = {slope:0.000}", point, ContentAlignment.BottomLeft),
+            new GraphUiCircle(new(lineX, lineY))
+        ];
+    }
+
+    public override void Preload(Float2 xRange, Float2 yRange, double step)
+    {
+        // Despite the tangent line barely using any data, when preloaded it
+        // will always take as much memory as an equation. Seems like a bit much,
+        // but may be used when the tangent line is moved. Not sure there's much
+        // that can be changed.
+        for (double x = xRange.x; x <= xRange.y; x += step) DerivativeAtPoint(x);
+    }
+
+    public Equation ToEquation()
+    {
+        double slope = currentSlope.x, x1 = Position, y1 = currentSlope.y;
+        return new(x => slope * (x - x1) + y1)
+        {
+            Name = Name,
+            Color = Color
+        };
+    }
+}

Base/IGraphPart.cs

@@ -0,0 +1,9 @@
+using Graphing.Forms;
+using System.Drawing;
+
+namespace Graphing;
+
+public interface IGraphPart
+{
+    public void Render(in GraphForm form, in Graphics g, in Pen pen);
+}

Base/Int2.cs

@@ -1,4 +1,6 @@
-namespace Graphing;
+using System.Drawing;
+
+namespace Graphing;
 
 public record struct Int2
 {

Base/Line2d.cs

@@ -1,18 +0,0 @@
-namespace Graphing;
-
-public record struct Line2d
-{
-    public Float2 a;
-    public Float2 b;
-
-    public Line2d()
-    {
-        a = new();
-        b = new();
-    }
-    public Line2d(Float2 a, Float2 b)
-    {
-        this.a = a;
-        this.b = b;
-    }
-}

Base/Parts/GraphLine.cs

@@ -0,0 +1,31 @@
+using Graphing.Forms;
+using System.Drawing;
+
+namespace Graphing.Parts;
+
+public record struct GraphLine : IGraphPart
+{
+    public Float2 a;
+    public Float2 b;
+
+    public GraphLine()
+    {
+        a = new();
+        b = new();
+    }
+    public GraphLine(Float2 a, Float2 b)
+    {
+        this.a = a;
+        this.b = b;
+    }
+
+    public readonly void Render(in GraphForm form, in Graphics g, in Pen pen)
+    {
+        if (!double.IsFinite(a.x) || !double.IsFinite(a.y) ||
+            !double.IsFinite(b.x) || !double.IsFinite(b.y)) return;
+
+        Int2 start = form.GraphSpaceToScreenSpace(a),
+             end = form.GraphSpaceToScreenSpace(b);
+        g.DrawLine(pen, start, end);
+    }
+}

Base/Parts/GraphRectangle.cs

@@ -0,0 +1,53 @@
+using Graphing.Forms;
+using System.Drawing;
+
+namespace Graphing.Parts;
+
+public record struct GraphRectangle : IGraphPart
+{
+    public Float2 min, max;
+    public double opacity;
+
+    public GraphRectangle()
+    {
+        min = new();
+        max = new();
+        opacity = 1;
+    }
+    
+    public static GraphRectangle FromSize(Float2 center, Float2 size, double opacity = 1) => new()
+    {
+        min = new(center.x - size.x / 2,
+                  center.y - size.y / 2),
+        max = new(center.x + size.x / 2,
+                  center.y + size.y / 2),
+        opacity = opacity,
+    };
+    public static GraphRectangle FromRange(Float2 min, Float2 max, double opacity = 1) => new()
+    {
+        min = min,
+        max = max,
+        opacity = opacity,
+    };
+
+    public void Render(in GraphForm form, in Graphics g, in Pen pen)
+    {
+        if (!double.IsFinite(max.x) || !double.IsFinite(max.y) ||
+            !double.IsFinite(min.x) || !double.IsFinite(min.y)) return;
+
+        if (min.x > max.x) (min.x, max.x) = (max.x, min.x);
+        if (min.y > max.y) (min.y, max.y) = (max.y, min.y);
+
+        Int2 start = form.GraphSpaceToScreenSpace(min),
+             end = form.GraphSpaceToScreenSpace(max);
+
+        Int2 size = new(end.x - start.x + 1,
+                        start.y - end.y);
+
+        if (size.x == 0 || size.y == 0) return;
+        Color initialColor = pen.Color;
+        pen.Color = Color.FromArgb((int)(opacity * 255), pen.Color);
+        g.FillRectangle(pen.Brush, new Rectangle(start.x, end.y, size.x, size.y));
+        pen.Color = initialColor;
+    }
+}

Base/Parts/GraphUiCircle.cs

@@ -0,0 +1,34 @@
+using Graphing.Forms;
+using System.Drawing;
+
+namespace Graphing.Parts;
+
+public record struct GraphUiCircle : IGraphPart
+{
+    public Float2 center;
+    public int radius;
+
+    public GraphUiCircle()
+    {
+        center = new();
+        radius = 1;
+    }
+    public GraphUiCircle(Float2 center, int radius = 8)
+    {
+        this.center = center;
+        this.radius = radius;
+    }
+
+    public readonly void Render(in GraphForm form, in Graphics g, in Pen pen)
+    {
+        if (!double.IsFinite(center.x) || !double.IsFinite(center.y) ||
+            !double.IsFinite(radius) || radius == 0) return;
+
+        int rad = (int)(form.DpiFloat * radius / 192);
+
+        Int2 centerPix = form.GraphSpaceToScreenSpace(center);
+        g.FillEllipse(pen.Brush, new Rectangle(new Point(centerPix.x - rad,
+                                                         centerPix.y - rad),
+                                               new Size(rad * 2, rad * 2)));
+    }
+}

Base/Parts/GraphUiText.cs

@@ -0,0 +1,87 @@
+using Graphing.Forms;
+using System.Drawing;
+
+namespace Graphing.Parts;
+
+public record struct GraphUiText : IGraphPart
+{
+    public string text;
+    public Float2 position;
+    public bool background;
+
+    public ContentAlignment alignment;
+    public Int2 offsetPix;
+
+    private readonly Font font;
+    private readonly Brush? backgroundBrush;
+
+    public GraphUiText(string text, Float2 position, ContentAlignment alignment,
+                       bool background = true, Int2? offsetPix = null)
+    {
+        font = new Font("Segoe UI", 8, FontStyle.Bold);
+
+        this.text = text;
+        this.position = position;
+        this.background = background;
+        this.alignment = alignment;
+        this.offsetPix = offsetPix ?? new();
+
+        if (background) backgroundBrush = new SolidBrush(GraphForm.BackgroundColor);
+    }
+
+    public readonly void Render(in GraphForm form, in Graphics g, in Pen p)
+    {
+        Int2 posScreen = form.GraphSpaceToScreenSpace(position);
+        SizeF size = g.MeasureString(text, font);
+
+        // Adjust X position based on alignment.
+        switch (alignment)
+        {
+            case ContentAlignment.TopLeft or
+                 ContentAlignment.MiddleLeft or
+                 ContentAlignment.BottomLeft: break; // Nothing to offset.
+
+            case ContentAlignment.TopCenter or
+                 ContentAlignment.MiddleCenter or
+                 ContentAlignment.BottomCenter:
+                posScreen.x -= (int)(size.Width / 2);
+                break;
+
+            case ContentAlignment.TopRight or
+                 ContentAlignment.MiddleRight or
+                 ContentAlignment.BottomRight:
+                posScreen.x -= (int)size.Width;
+                break;
+        }
+
+        // Adjust Y position based on alignment.
+        switch (alignment)
+        {
+            case ContentAlignment.TopLeft or
+                 ContentAlignment.TopCenter or
+                 ContentAlignment.TopRight: break; // Nothing to offset.
+
+            case ContentAlignment.MiddleLeft or
+                 ContentAlignment.MiddleCenter or
+                 ContentAlignment.MiddleRight:
+                posScreen.y -= (int)(size.Height / 2);
+                break;
+
+            case ContentAlignment.BottomLeft or
+                 ContentAlignment.BottomCenter or
+                 ContentAlignment.BottomRight:
+                posScreen.y -= (int)size.Height; 
+                break;
+        }
+
+        posScreen.x += (int)(offsetPix.x * form.DpiFloat / 192);
+        posScreen.y += (int)(offsetPix.y * form.DpiFloat / 192);
+
+        if (background)
+        {
+            g.FillRectangle(backgroundBrush!, new Rectangle(posScreen.x, posScreen.y,
+                                                            (int)size.Width, (int)size.Height));
+        }
+        g.DrawString(text, font, p.Brush, new Point(posScreen.x, posScreen.y));
+    }
+}

Base/Properties/PublishProfiles/FolderProfile.pubxml

@@ -0,0 +1,13 @@
+<?xml version="1.0" encoding="utf-8"?>
+<!--
+https://go.microsoft.com/fwlink/?LinkID=208121.
+-->
+<Project>
+  <PropertyGroup>
+    <Configuration>Release</Configuration>
+    <Platform>Any CPU</Platform>
+    <PublishDir>bin\Release\net8.0-windows\publish\</PublishDir>
+    <PublishProtocol>FileSystem</PublishProtocol>
+    <_TargetId>Folder</_TargetId>
+  </PropertyGroup>
+</Project>

Base/Properties/PublishProfiles/FolderProfile.pubxml.user

@@ -0,0 +1,10 @@
+<?xml version="1.0" encoding="utf-8"?>
+<!--
+https://go.microsoft.com/fwlink/?LinkID=208121.
+-->
+<Project>
+  <PropertyGroup>
+    <History>True|2024-03-20T12:48:45.8740885Z;True|2024-03-20T08:48:35.6948867-04:00;True|2024-03-20T08:39:01.6402921-04:00;True|2024-03-13T10:31:43.4569441-04:00;False|2024-03-13T10:30:01.4347009-04:00;False|2024-03-13T10:27:31.9554551-04:00;</History>
+    <LastFailureDetails />
+  </PropertyGroup>
+</Project>

Base/Range2d.cs

@@ -1,27 +0,0 @@
-namespace Graphing;
-
-public record struct Range2d
-{
-    public double minX;
-    public double minY;
-    public double maxX;
-    public double maxY;
-
-    public Range2d()
-    {
-        minX = 0;
-        minY = 0;
-        maxX = 0;
-        maxY = 0;
-    }
-    public Range2d(double minX, double minY, double maxX, double maxY)
-    {
-        this.minX = minX;
-        this.minY = minY;
-        this.maxX = maxX;
-        this.maxY = maxY;
-    }
-
-    public readonly bool Contains(Float2 p) =>
-        p.x >= minX && p.x <= maxX && p.y >= minY && p.y <= maxY;
-}

README.md

@@ -3,9 +3,15 @@
 This is a graphing calculator I made initially for a Calculus project in a day or so. I've written a basic rendering system in Windows Forms that runs on .NET 8.0.
 
 Currently, it doesn't have a whole lot of features, but I'll be adding more in the future. Here's currently what it can do:
-- Graph an equation (duh).
+- Graph standard equations (duh).
     - There are currently some rendering issues with asymptotes which will be focused on at some point.
+- Graph parametric equations.
+- Integrate and derive equations.
 - Graph a slope field of a `dy/dx =` style equation.
+- View a tangent line of an equation.
+- Display a vertical bar graph.
+
+However, you can develop your own features as well.
 
 The system does not and likely will not (at least for a while) support text-to-equation parsing. You must import this project as a library and add graphs that way.
 
@@ -70,7 +76,7 @@ An equation requires a delegate such as the one you see. Alternatively, you can
 graph.Graph(new Equation(x => Math.Pow(2, x))
 {
     Color = Color.Green,
-    Name = "2^x"
+    Name = "Exponential Base 2"
 });
 ```
 

Testing/Program.cs

@@ -1,5 +1,7 @@
 using Graphing.Forms;
 using Graphing.Graphables;
+using System;
+using System.Windows.Forms;
 
 namespace Graphing.Testing;
 
@@ -13,7 +15,13 @@ internal static class Program
         Application.SetHighDpiMode(HighDpiMode.PerMonitorV2);
         
         GraphForm graph = new("One Of The Graphing Calculators Of All Time");
-        graph.Graph(new Equation(Math.Cos));
+
+        Equation equA = new(Math.Sin),
+                 equB = new(Math.Cos);
+        EquationDifference diff = new(2, equA, equB);
+        ParametricEquation equC = new(0, 20, t => 0.0375 * t * Math.Cos(t), t => 0.0625 * t * Math.Sin(t) + 3);
+        TangentLine tanA = new(2, 2, equA);
+        graph.Graph(equA, equB, diff, equC, equB.ToColumnTable(-3, 3, 2), tanA);
 
         Application.Run(graph);
     }

Testing/Testing.csproj

@@ -1,15 +1,22 @@
 <Project Sdk="Microsoft.NET.Sdk">
 
   <PropertyGroup>
-    <OutputType>WinExe</OutputType>
     <TargetFramework>net8.0-windows</TargetFramework>
     <Nullable>enable</Nullable>
     <UseWindowsForms>true</UseWindowsForms>
-    <ImplicitUsings>enable</ImplicitUsings>
+    <ImplicitUsings>disable</ImplicitUsings>
     <RootNamespace>Graphing.Testing</RootNamespace>
     <AssemblyName>ThatOneNerd.Graphing.Testing</AssemblyName>
   </PropertyGroup>
     
+  <PropertyGroup Condition="'$(Configuration)|$(Platform)'=='Debug|AnyCPU'">
+    <OutputType>Exe</OutputType>
+  </PropertyGroup>
+
+  <PropertyGroup Condition="'$(Configuration)|$(Platform)'=='Release|AnyCPU'">
+    <OutputType>WinExe</OutputType>
+  </PropertyGroup>
+
   <ItemGroup>
     <ProjectReference Include="..\Base\Base.csproj" />
   </ItemGroup>