Merge pull request #1 from That-One-Nerd/canary

Version 1.1 is out.

Base/Base.csproj

@@ -12,9 +12,9 @@
     <GeneratePackageOnBuild>True</GeneratePackageOnBuild>
     <PackageId>ThatOneNerd.Graphing</PackageId>
     <Title>ThatOneNerd.Graphing</Title>
-    <Version>1.0.0</Version>
+    <Version>1.1.0</Version>
     <Authors>That_One_Nerd</Authors>
-    <Description>A fairly adept graphing calculator made in Windows Forms. </Description>
+    <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>
@@ -22,6 +22,8 @@
     <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/1.1.0</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 +16,8 @@
     <Compile Update="Forms\SetZoomForm.cs">
       <SubType>Form</SubType>
     </Compile>
+    <Compile Update="Forms\ViewCacheForm.cs">
+      <SubType>Form</SubType>
+    </Compile>
   </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/Forms/Controls/PieChart.Designer.cs

@@ -0,0 +1,44 @@
+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 = AutoScaleMode.Font;
+            Name = "PieChart";
+            Size = new Size(500, 500);
+            ResumeLayout(false);
+        }
+
+        #endregion
+    }
+}

Base/Forms/Controls/PieChart.cs

@@ -0,0 +1,59 @@
+using System.Drawing.Drawing2D;
+
+namespace Graphing.Forms.Controls;
+
+public partial class PieChart : UserControl
+{
+    public List<(Color, double)> Values { get; set; }
+
+    public PieChart()
+    {
+        SetStyle(ControlStyles.OptimizedDoubleBuffer, true);
+        SetStyle(ControlStyles.AllPaintingInWmPaint, true);
+        SetStyle(ControlStyles.UserPaint, true);
+
+        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.
+        Pen outlinePartsPen = new(Color.FromArgb(unchecked((int)0xFF_202020)), 3);
+        current = 0;
+        foreach ((Color, double value) item in Values)
+        {
+            double start = 360 * current / sum,
+                   end = 360 * (current + item.value) / sum;
+            g.DrawPie(outlinePartsPen, rect, (float)start, (float)(end - start));
+
+            current += item.value;
+        }
+
+        // Outline
+        Pen outlinePen = new(Color.FromArgb(unchecked((int)0xFF_202020)), 5);
+        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/GraphForm.Designer.cs

@@ -39,6 +39,8 @@
             MenuEquations = new ToolStripMenuItem();
             MenuEquationsDerivative = new ToolStripMenuItem();
             MenuEquationsIntegral = new ToolStripMenuItem();
+            MenuMisc = new ToolStripMenuItem();
+            MenuMiscCaches = new ToolStripMenuItem();
             GraphMenu.SuspendLayout();
             SuspendLayout();
             // 
@@ -58,7 +60,7 @@
             // GraphMenu
             // 
             GraphMenu.ImageScalingSize = new Size(32, 32);
-            GraphMenu.Items.AddRange(new ToolStripItem[] { MenuViewport, MenuColors, MenuEquations });
+            GraphMenu.Items.AddRange(new ToolStripItem[] { MenuViewport, MenuColors, MenuEquations, MenuMisc });
             GraphMenu.Location = new Point(0, 0);
             GraphMenu.Name = "GraphMenu";
             GraphMenu.Size = new Size(1449, 42);
@@ -125,6 +127,20 @@
             MenuEquationsIntegral.Size = new Size(360, 44);
             MenuEquationsIntegral.Text = "Compute Integral";
             // 
+            // MenuMisc
+            // 
+            MenuMisc.DropDownItems.AddRange(new ToolStripItem[] { MenuMiscCaches });
+            MenuMisc.Name = "MenuMisc";
+            MenuMisc.Size = new Size(83, 38);
+            MenuMisc.Text = "Misc";
+            // 
+            // MenuMiscCaches
+            // 
+            MenuMiscCaches.Name = "MenuMiscCaches";
+            MenuMiscCaches.Size = new Size(359, 44);
+            MenuMiscCaches.Text = "View Caches";
+            MenuMiscCaches.Click += MenuMiscCaches_Click;
+            // 
             // GraphForm
             // 
             AutoScaleDimensions = new SizeF(13F, 32F);
@@ -154,5 +170,7 @@
         private ToolStripMenuItem MenuEquations;
         private ToolStripMenuItem MenuEquationsDerivative;
         private ToolStripMenuItem MenuEquationsIntegral;
+        private ToolStripMenuItem MenuMisc;
+        private ToolStripMenuItem MenuMiscCaches;
     }
 }

Base/Forms/GraphForm.cs

@@ -1,9 +1,16 @@
-using Graphing.Graphables;
+using Graphing.Extensions;
+using Graphing.Graphables;
+using System.Drawing.Drawing2D;
+using System.Text;
 
 namespace Graphing.Forms;
 
 public partial class GraphForm : Form
 {
+    public static readonly Color MainAxisColor = Color.Black;
+    public static readonly Color SemiAxisColor = Color.FromArgb(unchecked((int)0xFF_999999));
+    public static readonly Color QuarterAxisColor = Color.FromArgb(unchecked((int)0xFF_E0E0E0));
+
     public Float2 ScreenCenter { get; private set; }
     public Float2 Dpi { get; private set; }
 
@@ -94,7 +101,7 @@ public partial class GraphForm : Form
         double axisScale = Math.Pow(2, Math.Round(Math.Log2(ZoomLevel)));
 
         // Draw horizontal/vertical quarter-axis.
-        Brush quarterBrush = new SolidBrush(Color.FromArgb(unchecked((int)0xFF_E0E0E0)));
+        Brush quarterBrush = new SolidBrush(QuarterAxisColor);
         Pen quarterPen = new(quarterBrush, 2);
 
         for (double x = Math.Ceiling(MinVisibleGraph.x * 4 / axisScale) * axisScale / 4; x <= Math.Floor(MaxVisibleGraph.x * 4 / axisScale) * axisScale / 4; x += axisScale / 4)
@@ -111,7 +118,7 @@ public partial class GraphForm : Form
         }
 
         // Draw horizontal/vertical semi-axis.
-        Brush semiBrush = new SolidBrush(Color.FromArgb(unchecked((int)0xFF_999999)));
+        Brush semiBrush = new SolidBrush(SemiAxisColor);
         Pen semiPen = new(semiBrush, 2);
 
         for (double x = Math.Ceiling(MinVisibleGraph.x / axisScale) * axisScale; x <= Math.Floor(MaxVisibleGraph.x / axisScale) * axisScale; x += axisScale)
@@ -127,7 +134,7 @@ public partial class GraphForm : Form
             g.DrawLine(semiPen, startPos, endPos);
         }
 
-        Brush mainLineBrush = new SolidBrush(Color.Black);
+        Brush mainLineBrush = new SolidBrush(MainAxisColor);
         Pen mainLinePen = new(mainLineBrush, 3);
 
         // Draw the main axis (on top of the semi axis).
@@ -143,6 +150,7 @@ public partial class GraphForm : Form
     protected override void OnPaint(PaintEventArgs e)
     {
         Graphics g = e.Graphics;
+        g.SmoothingMode = SmoothingMode.HighQuality;
 
         Brush background = new SolidBrush(Color.White);
         g.FillRectangle(background, e.ClipRectangle);
@@ -152,19 +160,9 @@ public partial class GraphForm : Form
         // Draw the actual graphs.
         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 (IGraphPart gp in lines) gp.Render(this, g, graphBrush);
-
-            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);
-            }
         }
 
         base.OnPaint(e);
@@ -175,9 +173,9 @@ public partial class GraphForm : Form
         Invalidate(false);
     }
 
-    public void Graph(Graphable able)
+    public void Graph(params Graphable[] able)
     {
-        ables.Add(able);
+        ables.AddRange(able);
         RegenerateMenuItems();
         Invalidate(false);
     }
@@ -257,14 +255,14 @@ public partial class GraphForm : Form
             colorItem.Click += (o, e) => GraphColorPickerButton_Click(able);
             MenuColors.DropDownItems.Add(colorItem);
 
-            if (able is Equation)
+            if (able is Equation equ)
             {
                 ToolStripMenuItem derivativeItem = new()
                 {
                     ForeColor = able.Color,
                     Text = able.Name
                 };
-                derivativeItem.Click += (o, e) => EquationComputeDerivative_Click((able as Equation)!);
+                derivativeItem.Click += (o, e) => EquationComputeDerivative_Click(equ);
                 MenuEquationsDerivative.DropDownItems.Add(derivativeItem);
 
                 ToolStripMenuItem integralItem = new()
@@ -272,7 +270,7 @@ public partial class GraphForm : Form
                     ForeColor = able.Color,
                     Text = able.Name
                 };
-                integralItem.Click += (o, e) => EquationComputeIntegral_Click((able as Equation)!);
+                integralItem.Click += (o, e) => EquationComputeIntegral_Click(equ);
                 MenuEquationsIntegral.DropDownItems.Add(integralItem);
             }
         }
@@ -346,7 +344,7 @@ public partial class GraphForm : Form
         static double Integrate(EquationDelegate e, double lower, double upper)
         {
             // TODO: a better rendering method could make this much faster.
-            const double step = 1e-1;
+            const double step = 1e-2;
 
             double factor = 1;
             if (upper < lower)
@@ -364,4 +362,16 @@ public partial class GraphForm : Form
             return sum * factor;
         }
     }
+
+    private void MenuMiscCaches_Click(object? sender, EventArgs e)
+    {
+        ViewCacheForm cacheForm = new(this)
+        {
+            StartPosition = FormStartPosition.Manual
+        };
+
+        cacheForm.Location = new Point(Location.X + ClientRectangle.Width + 10,
+                                       Location.Y + (ClientRectangle.Height - cacheForm.ClientRectangle.Height) / 2);
+        cacheForm.Show();
+    }
 }

Base/Forms/SetZoomForm.cs

@@ -1,131 +1,119 @@
-using System;
+namespace Graphing.Forms;
-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
+public partial class SetZoomForm : Form
 {
-    public partial class SetZoomForm : Form
+    private double minZoomRange;
+    private double maxZoomRange;
+
+    private double zoomLevel;
+
+    private readonly GraphForm form;
+
+    public SetZoomForm(GraphForm form)
     {
-        private double minZoomRange;
+        InitializeComponent();
-        private double maxZoomRange;
 
-        private double zoomLevel;
+        minZoomRange = 1 / (form.ZoomLevel * 2);
+        maxZoomRange = 2 / form.ZoomLevel;
+        zoomLevel = 1 / form.ZoomLevel;
 
-        private readonly GraphForm form;
+        ZoomTrackBar.Value = (int)(ZoomToFactor(zoomLevel) * (ZoomTrackBar.Maximum - ZoomTrackBar.Minimum) + ZoomTrackBar.Minimum);
 
-        public SetZoomForm(GraphForm form)
+        this.form = form;
+    }
+
+    protected override void OnPaint(PaintEventArgs e)
+    {
+        ZoomMaxValue.Text = maxZoomRange.ToString("0.00");
+        ZoomMinValue.Text = minZoomRange.ToString("0.00");
+
+        ValueLabel.Text = $"{zoomLevel:0.00}x";
+
+        base.OnPaint(e);
+
+        form.ZoomLevel = 1 / zoomLevel;
+        form.Invalidate(false);
+    }
+
+    private double FactorToZoom(double factor)
+    {
+        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
         {
-            InitializeComponent();
+            double value;
+            if (string.IsNullOrWhiteSpace(ZoomMinValue.Text) ||
+                ZoomMinValue.Text.EndsWith('.'))
+            {
+                return;
+            }
+            else
+            {
+                value = double.Parse(ZoomMinValue.Text);
+                if (value < 1e-2 || value > 1e3 || value > maxZoomRange) throw new();
+            }
 
-            minZoomRange = 1 / (form.ZoomLevel * 2);
+            minZoomRange = value;
-            maxZoomRange = 2 / form.ZoomLevel;
+            ZoomTrackBar.Value = (int)Math.Clamp(ZoomToFactor(zoomLevel) * (ZoomTrackBar.Maximum - ZoomTrackBar.Minimum) + ZoomTrackBar.Minimum, ZoomTrackBar.Minimum, ZoomTrackBar.Maximum);
-            zoomLevel = 1 / form.ZoomLevel;
-
-            ZoomTrackBar.Value = (int)(ZoomToFactor(zoomLevel) * (ZoomTrackBar.Maximum - ZoomTrackBar.Minimum) + ZoomTrackBar.Minimum);
-
-            this.form = form;
-        }
-
-        protected override void OnPaint(PaintEventArgs e)
-        {
-            ZoomMaxValue.Text = maxZoomRange.ToString("0.00");
-            ZoomMinValue.Text = minZoomRange.ToString("0.00");
-
-            ValueLabel.Text = $"{zoomLevel:0.00}x";
-
-            base.OnPaint(e);
-
-            form.ZoomLevel = 1 / zoomLevel;
-            form.Invalidate(false);
-        }
-
-        private double FactorToZoom(double factor)
-        {
-            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);
+            double newZoom = FactorToZoom(factor);
 
-            Invalidate(true);
+            zoomLevel = newZoom;
+            if (newZoom != factor) Invalidate(true);
         }
-
+        catch
-        private void ZoomMinValue_TextChanged(object? sender, EventArgs e)
         {
-            double original = minZoomRange;
+            minZoomRange = original;
-            try
+            ZoomMinValue.Text = minZoomRange.ToString("0.00");
-            {
-                double value;
-                if (string.IsNullOrWhiteSpace(ZoomMinValue.Text) ||
-                    ZoomMinValue.Text.EndsWith('.'))
-                {
-                    return;
-                }
-                else
-                {
-                    value = double.Parse(ZoomMinValue.Text);
-                    if (value < 1e-2 || value > 1e3 || value > maxZoomRange) throw new();
-                }
-
-                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);
-            }
-            catch
-            {
-                minZoomRange = original;
-                ZoomMinValue.Text = minZoomRange.ToString("0.00");
-            }
         }
+    }
 
-        private void ZoomMaxValue_TextChanged(object sender, EventArgs e)
+    private void ZoomMaxValue_TextChanged(object sender, EventArgs e)
+    {
+        double original = maxZoomRange;
+        try
         {
-            double original = maxZoomRange;
+            double value;
-            try
+            if (string.IsNullOrWhiteSpace(ZoomMaxValue.Text) ||
+                ZoomMaxValue.Text.EndsWith('.'))
             {
-                double value;
+                return;
-                if (string.IsNullOrWhiteSpace(ZoomMaxValue.Text) ||
-                    ZoomMaxValue.Text.EndsWith('.'))
-                {
-                    return;
-                }
-                else
-                {
-                    value = double.Parse(ZoomMaxValue.Text);
-                    if (value < 1e-2 || value > 1e3 || value < minZoomRange) throw new();
-                }
-
-                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);
-
-                zoomLevel = newZoom;
-                if (newZoom != factor) Invalidate(true);
             }
-            catch
+            else
             {
-                maxZoomRange = original;
+                value = double.Parse(ZoomMaxValue.Text);
-                ZoomMaxValue.Text = maxZoomRange.ToString("0.00");
+                if (value < 1e-2 || value > 1e3 || value < minZoomRange) throw new();
             }
+
+            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);
+
+            zoomLevel = newZoom;
+            if (newZoom != factor) Invalidate(true);
+        }
+        catch
+        {
+            maxZoomRange = original;
+            ZoomMaxValue.Text = maxZoomRange.ToString("0.00");
         }
     }
 }

Base/Forms/ViewCacheForm.Designer.cs

@@ -0,0 +1,97 @@
+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 +1,89 @@
+using Graphing.Extensions;
+
+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();
+            CachePie.Values.Add((able.Color, thisBytes));
+            totalBytes += thisBytes;
+
+            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 * 46),
+                    Parent = SpecificCachePanel,
+                    Size = new Size(SpecificCachePanel.Width - 98, 46),
+                    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 - 92, buttonCache.Count * 46),
+                    Parent = SpecificCachePanel,
+                    Size = new Size(92, 46),
+                    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 +1,5 @@
 using Graphing.Forms;
+using Graphing.Parts;
 
 namespace Graphing;
 
@@ -26,5 +27,10 @@ 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 DeepCopy();
+
+    public abstract void EraseCache();
+    public abstract long GetCacheBytes();
 }

Base/Graphables/ColumnTable.cs

@@ -0,0 +1,51 @@
+using Graphing.Forms;
+using Graphing.Parts;
+
+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)
+    {
+        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 void EraseCache() { }
+    public override long GetCacheBytes() => 16 * tableXY.Count;
+
+    public override Graphable DeepCopy() => new ColumnTable(width / 0.75, tableXY.ToArray().ToDictionary());
+
+    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)));
+        }
+
+        return items;
+    }
+}

Base/Graphables/Equation.cs

@@ -1,4 +1,5 @@
 using Graphing.Forms;
+using Graphing.Parts;
 
 namespace Graphing.Graphables;
 
@@ -6,7 +7,8 @@ public class Equation : Graphable
 {
     private static int equationNum;
 
-    private readonly EquationDelegate equ;
+    protected readonly EquationDelegate equ;
+    protected readonly List<Float2> cache;
 
     public Equation(EquationDelegate equ)
     {
@@ -14,20 +16,27 @@ public class Equation : Graphable
         Name = $"Equation {equationNum}";
 
         this.equ = equ;
+        cache = [];
     }
 
-    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;
+
+        List<IGraphPart> lines = [];
+
         double previousX = graph.MinVisibleGraph.x;
-        double previousY = equ(previousX);
+        double previousY = GetFromCache(previousX, epsilon);
-        for (int i = 1; i < graph.ClientRectangle.Width; i += 10)
+
+        for (int i = 1; i < graph.ClientRectangle.Width; 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;
@@ -36,6 +45,57 @@ public class Equation : Graphable
     }
 
     public EquationDelegate GetDelegate() => equ;
+
+    public override void EraseCache() => cache.Clear();
+    protected double GetFromCache(double x, double epsilon)
+    {
+        (double dist, double nearest, int index) = NearestCachedPoint(x);
+        if (dist < epsilon) return nearest;
+        else
+        {
+            double result = equ(x);
+            cache.Insert(index + 1, new(x, result));
+            return result;
+        }
+    }
+
+    // Pretty sure this works. Certainly works pretty well with "hard-to-compute"
+    // equations.
+    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 DeepCopy() => new Equation(equ);
+
+    public override long GetCacheBytes() => cache.Count * 16;
 }
 
 public delegate double EquationDelegate(double x);

Base/Graphables/SlopeField.cs

@@ -1,4 +1,5 @@
 using Graphing.Forms;
+using Graphing.Parts;
 
 namespace Graphing.Graphables;
 
@@ -6,8 +7,10 @@ public class SlopeField : Graphable
 {
     private static int slopeFieldNum;
 
-    private readonly SlopeFieldsDelegate equ;
+    protected readonly SlopeFieldsDelegate equ;
-    private readonly double detail;
+    protected readonly int detail;
+
+    protected readonly List<(Float2, GraphLine)> cache;
 
     public SlopeField(int detail, SlopeFieldsDelegate equ)
     {
@@ -16,25 +19,26 @@ public class SlopeField : Graphable
 
         this.equ = equ;
         this.detail = detail;
+        cache = [];
     }
 
-    public override IEnumerable<Line2d> GetItemsToRender(in GraphForm graph)
+    public override IEnumerable<IGraphPart> GetItemsToRender(in GraphForm graph)
     {
-        List<Line2d> lines = [];
+        double epsilon = 1 / (detail * 2.0);
+        List<IGraphPart> lines = [];
 
-        for (double x = Math.Ceiling(graph.MinVisibleGraph.x - 1); x < graph.MaxVisibleGraph.x + 1; x += 1 / detail)
+        for (double x = Math.Ceiling(graph.MinVisibleGraph.x - 1); x < graph.MaxVisibleGraph.x + 1; x += 1.0 / detail)
         {
-            for (double y = Math.Ceiling(graph.MinVisibleGraph.y - 1); y < graph.MaxVisibleGraph.y + 1; y += 1 / detail)
+            for (double y = Math.Ceiling(graph.MinVisibleGraph.y - 1); y < graph.MaxVisibleGraph.y + 1; y += 1.0 / detail)
             {
-                double slope = equ(x, y);
+                lines.Add(GetFromCache(epsilon, x, y));
-                lines.Add(MakeSlopeLine(new Float2(x, y), slope));
             }
         }
 
         return lines;
     }
 
-    private Line2d MakeSlopeLine(Float2 position, double slope)
+    protected GraphLine MakeSlopeLine(Float2 position, double slope)
     {
         double size = detail;
 
@@ -46,6 +50,30 @@ 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 DeepCopy() => new SlopeField(detail, equ);
+
+    public override void EraseCache() => cache.Clear();
+    public override long GetCacheBytes() => cache.Count * 48;
 }
 
 public delegate double SlopeFieldsDelegate(double x, double y);

Base/Graphables/TangentLine.cs

@@ -0,0 +1,51 @@
+using Graphing.Forms;
+using Graphing.Parts;
+
+namespace Graphing.Graphables;
+
+public class TangentLine : Graphable
+{
+    public double Position { get; set; }
+
+    protected readonly Equation parent;
+    protected readonly EquationDelegate parentEqu;
+
+    protected readonly double length;
+
+    public TangentLine(double length, double position, Equation parent)
+    {
+        Name = $"Tangent Line of {parent.Name}";
+
+        parentEqu = parent.GetDelegate();
+        Position = position;
+        this.length = length;
+        this.parent = parent;
+    }
+
+    public override IEnumerable<IGraphPart> GetItemsToRender(in GraphForm graph)
+    {
+        Float2 point = new(Position, parentEqu(Position));
+        return [MakeSlopeLine(point, DerivativeAtPoint(Position)),
+                new GraphUiCircle(point, 8)];
+    }
+    protected GraphLine MakeSlopeLine(Float2 position, double slope)
+    {
+        double dirX = length, dirY = slope * length;
+        double magnitude = Math.Sqrt(dirX * dirX + dirY * dirY);
+
+        dirX /= magnitude * 2 / length;
+        dirY /= magnitude * 2 / length;
+
+        return new(new(position.x + dirX, position.y + dirY), new(position.x - dirX, position.y - dirY));
+    }
+    protected double DerivativeAtPoint(double x)
+    {
+        const double step = 1e-3;
+        return (parentEqu(x + step) - parentEqu(x)) / step;
+    }
+
+    public override Graphable DeepCopy() => new TangentLine(length, Position, parent);
+
+    public override void EraseCache() { }
+    public override long GetCacheBytes() => 0;
+}

Base/IGraphPart.cs

@@ -0,0 +1,8 @@
+using Graphing.Forms;
+
+namespace Graphing;
+
+public interface IGraphPart
+{
+    public void Render(in GraphForm form, in Graphics g, in Brush brush);
+}

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 +1,32 @@
+using Graphing.Forms;
+
+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 Brush brush)
+    {
+        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);
+
+        Pen pen = new(brush, 3);
+        g.DrawLine(pen, start, end);
+    }
+}

Base/Parts/GraphRectangle.cs

@@ -0,0 +1,45 @@
+using Graphing.Forms;
+
+namespace Graphing.Parts;
+
+public record struct GraphRectangle : IGraphPart
+{
+    public Float2 min, max;
+
+    public GraphRectangle()
+    {
+        min = new();
+        max = new();
+    }
+    
+    public static GraphRectangle FromSize(Float2 center, Float2 size) => 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)
+    };
+    public static GraphRectangle FromRange(Float2 min, Float2 max) => new()
+    {
+        min = min,
+        max = max
+    };
+
+    public void Render(in GraphForm form, in Graphics g, in Brush brush)
+    {
+        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;
+        g.FillRectangle(brush, new Rectangle(start.x, end.y, size.x, size.y));
+    }
+}

Base/Parts/GraphUiCircle.cs

@@ -0,0 +1,31 @@
+using Graphing.Forms;
+
+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)
+    {
+        this.center = center;
+        this.radius = radius;
+    }
+
+    public readonly void Render(in GraphForm form, in Graphics g, in Brush brush)
+    {
+        if (!double.IsFinite(center.x) || !double.IsFinite(center.y) ||
+            !double.IsFinite(radius) || radius == 0) return;
+
+        Int2 centerPix = form.GraphSpaceToScreenSpace(center);
+        g.FillEllipse(brush, new Rectangle(new Point(centerPix.x - radius,
+                                                     centerPix.y - radius),
+                                            new Size(radius * 2, radius * 2)));
+    }
+}

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|2024-03-13T14:31:43.4569441Z;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;
-}

Testing/Program.cs

@@ -10,10 +10,31 @@ internal static class Program
     {
         Application.EnableVisualStyles();
         Application.SetCompatibleTextRenderingDefault(false);
-        Application.SetHighDpiMode(HighDpiMode.PerMonitorV2);
+        Application.SetHighDpiMode(HighDpiMode.SystemAware);
 
         GraphForm graph = new("One Of The Graphing Calculators Of All Time");
-        graph.Graph(new Equation(Math.Cos));
+
+        Equation equ1 = new(x =>
+        {
+            // Demonstrate the caching abilities of the software.
+            // This extra waiting is done every time the form requires a
+            // calculation done. At the start, it'll be laggy, but as you
+            // move around and zoom in, more pieces are cached, and when
+            // you reset, the viewport will be a lot less laggy.
+
+            // Remove this loop to make the equation fast again. I didn't
+            // slow the engine down much more with this improvement, so any
+            // speed decrease you might notice is likely this function.
+            for (int i = 0; i < 1_000_000; i++) ;
+            return -x * x + 2;
+        });
+        Equation equ2 = new(x => x);
+        Equation equ3 = new(x => -Math.Sqrt(x));
+        SlopeField sf = new(2, (x, y) => (x * x - y * y) / x);
+        graph.Graph(equ1, equ2, equ3, sf);
+
+        // You can also now view and reset caches in the UI by going to
+        // Misc > View Caches.
 
         Application.Run(graph);
     }

Testing/Testing.csproj

@@ -1,7 +1,6 @@
 <Project Sdk="Microsoft.NET.Sdk">
 
   <PropertyGroup>
-    <OutputType>WinExe</OutputType>
     <TargetFramework>net8.0-windows</TargetFramework>
     <Nullable>enable</Nullable>
     <UseWindowsForms>true</UseWindowsForms>
@@ -10,6 +9,14 @@
     <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>