Nice progress. Some of it is bodged a bit but that's okay.

Base/Forms/GraphForm.cs

@@ -11,6 +11,7 @@ namespace Graphing.Forms;
 
 public partial class GraphForm : Form
 {
+    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));
     public static readonly Color QuarterAxisColor = Color.FromArgb(unchecked((int)0xFF_E0E0E0));
@@ -200,7 +201,7 @@ public partial class GraphForm : Form
         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);
@@ -231,7 +232,7 @@ public partial class GraphForm : Form
                 if (ables[i].ShouldSelectGraphable(this, graphMousePos, 2.5))
                 {
                     Float2 selectedPoint = ables[i].GetSelectedPoint(this, graphMousePos);
-                    GraphUiCircle select = new(selectedPoint, 8);
+                    GraphUiCircle select = new(selectedPoint);
 
                     Int2 textPos = GraphSpaceToScreenSpace(select.center);
                     textPos.y -= (int)(DpiFloat * 32 / 192);

Base/Graphable.cs

@@ -30,7 +30,7 @@ public abstract class Graphable
 
     public abstract IEnumerable<IGraphPart> GetItemsToRender(in GraphForm graph);
 
-    public abstract Graphable DeepCopy();
+    public abstract Graphable ShallowCopy();
 
     public virtual void EraseCache() { }
     public virtual long GetCacheBytes() => 0;

Base/Graphables/ColumnTable.cs

@@ -37,7 +37,7 @@ public class ColumnTable : Graphable
 
     public override long GetCacheBytes() => 16 * tableXY.Count;
 
-    public override Graphable DeepCopy() => new ColumnTable(width / 0.75, tableXY.ToArray().ToDictionary());
+    public override Graphable ShallowCopy() => new ColumnTable(width / 0.75, tableXY);
 
     public override IEnumerable<IGraphPart> GetItemsToRender(in GraphForm graph)
     {

Base/Graphables/Equation.cs

@@ -116,7 +116,7 @@ public class Equation : Graphable, IIntegrable, IDerivable, ITranslatableXY
         }
     }
 
-    public override Graphable DeepCopy() => new Equation(equ);
+    public override Graphable ShallowCopy() => new Equation(equ);
 
     public override long GetCacheBytes() => cache.Count * 16;
 

Base/Graphables/EquationDifference.cs

@@ -0,0 +1,58 @@
+using Graphing.Abstract;
+using Graphing.Forms;
+using Graphing.Parts;
+using System.Collections.Generic;
+
+namespace Graphing.Graphables;
+
+public class EquationDifference : Graphable, ITranslatableX, IEquationConvertible
+{
+    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 = $"Difference between {equA.Name} and {equB.Name}";
+
+        Position = position;
+    }
+
+    public override IEnumerable<IGraphPart> GetItemsToRender(in GraphForm graph)
+    {
+        Float2 pA = new(Position, points.x),
+               pB = new(Position, points.y),
+               pC = new(Position, (points.x + points.y) / 2);
+        return [new GraphUiText($"{points.x - points.y:0.00}", pC),
+                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 Equation ToEquation() => new(DistanceAtPoint)
+    {
+        Color = Color,
+        Name = Name
+    };
+}

Base/Graphables/IntegralEquation.cs

@@ -47,7 +47,7 @@ public class IntegralEquation : Graphable, IIntegrable, IDerivable
         usingAlt = true;
     }
 
-    public override Graphable DeepCopy() => new IntegralEquation(this);
+    public override Graphable ShallowCopy() => new IntegralEquation(this);
 
     public override IEnumerable<IGraphPart> GetItemsToRender(in GraphForm graph)
     {
@@ -178,8 +178,8 @@ public class IntegralEquation : Graphable, IIntegrable, IDerivable
 
     public Graphable Derive()
     {
-        if (usingAlt) return altBaseEqu!.DeepCopy();
-        else return (Equation)baseEqu!.DeepCopy();
+        if (usingAlt) return altBaseEqu!.ShallowCopy();
+        else return (Equation)baseEqu!.ShallowCopy();
     }
     public Graphable Integrate() => new IntegralEquation(this);
 

Base/Graphables/SlopeField.cs

@@ -72,7 +72,7 @@ public class SlopeField : Graphable
         return result;
     }
 
-    public override Graphable DeepCopy() => new SlopeField(detail, equ);
+    public override Graphable ShallowCopy() => new SlopeField(detail, equ);
 
     public override void EraseCache() => cache.Clear();
     public override long GetCacheBytes() => cache.Count * 48;

Base/Graphables/TangentLine.cs

@@ -56,7 +56,7 @@ public class TangentLine : Graphable, IEquationConvertible, ITranslatableX
     public override IEnumerable<IGraphPart> GetItemsToRender(in GraphForm graph)
     {
         Float2 point = new(Position, currentSlope.y);
-        return [MakeSlopeLine(), new GraphUiCircle(point, 8)];
+        return [MakeSlopeLine(), new GraphUiCircle(point)];
     }
     protected GraphLine MakeSlopeLine()
     {
@@ -81,7 +81,7 @@ public class TangentLine : Graphable, IEquationConvertible, ITranslatableX
         return result;
     }
 
-    public override Graphable DeepCopy() => new TangentLine(length, Position, parent);
+    public override Graphable ShallowCopy() => new TangentLine(length, Position, parent);
 
     public override void EraseCache() => slopeCache.Clear();
     public override long GetCacheBytes() => slopeCache.Count * 24;

Base/Parts/GraphUiCircle.cs

@@ -13,7 +13,7 @@ public record struct GraphUiCircle : IGraphPart
         center = new();
         radius = 1;
     }
-    public GraphUiCircle(Float2 center, int radius)
+    public GraphUiCircle(Float2 center, int radius = 8)
     {
         this.center = center;
         this.radius = radius;

Base/Parts/GraphUiText.cs

@@ -0,0 +1,38 @@
+using Graphing.Forms;
+using System.Drawing;
+
+namespace Graphing.Parts;
+
+public record struct GraphUiText : IGraphPart
+{
+    public string text;
+    public Float2 position;
+    public bool background;
+
+    private readonly Font font;
+    private readonly Brush? backgroundBrush;
+
+    public GraphUiText(string text, Float2 position, bool background = true)
+    {
+        font = new Font("Segoe UI", 8, FontStyle.Bold);
+
+        this.text = text;
+        this.position = position;
+        this.background = background;
+
+        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);
+        posScreen.y -= (int)(form.DpiFloat * font.Size * 2 / 192);
+        if (background)
+        {
+            SizeF size = g.MeasureString(text, font);
+            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));
+    }
+}

Testing/Program.cs

@@ -16,15 +16,10 @@ internal static class Program
 
         GraphForm graph = new("One Of The Graphing Calculators Of All Time");
 
-        Equation equ = new(Math.Sin);
-        SlopeField sf = new(2, (x, y) => Math.Cos(x));
-        TangentLine tl = new(2, 2, equ);
-        graph.Graph(equ, sf, tl);
-
-        // Now, when integrating equations, the result is much less jagged
-        // and much faster. Try it out! You can also select points along
-        // equations and such as well. Click on an equation to see for
-        // yourself!
+        Equation equA = new(Math.Sin),
+                 equB = new(Math.Cos);
+        EquationDifference diff = new(2, equA, equB);
+        graph.Graph(equA, equB, diff);
 
         Application.Run(graph);
     }