Made preload functions for most of the other graphables.

Base/Forms/Controls/PieChart.cs

@@ -46,17 +46,22 @@ public partial class PieChart : UserControl
             current += item.value;
         }
 
-        // Draw the outline.
+        // 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);

Base/Forms/GraphForm.cs

@@ -466,12 +466,16 @@ public partial class GraphForm : Form
         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; //
+        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);
 
-        foreach (Graphable able in Graphables) able.Preload(xRange, yRange);
+        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);
     }
 }

Base/Graphable.cs

@@ -32,7 +32,7 @@ public abstract class Graphable
 
     public abstract void EraseCache();
     public abstract long GetCacheBytes();
-    public abstract void Preload(Float2 xRange, Float2 yRange);
+    public abstract void Preload(Float2 xRange, Float2 yRange, double step);
 
     public abstract bool ShouldSelectGraphable(in GraphForm graph, Float2 graphMousePos, double factor);
     public abstract Float2 GetSelectedPoint(in GraphForm graph, Float2 graphMousePos);

Base/Graphables/ColumnTable.cs

@@ -52,5 +52,6 @@ public class ColumnTable : Graphable
     public override bool ShouldSelectGraphable(in GraphForm graph, Float2 graphMousePos, double factor) => false;
     public override Float2 GetSelectedPoint(in GraphForm graph, Float2 graphMousePos) => default;
 
-    public override void Preload(Float2 xRange, Float2 yRange) { }
+    // Nothing to preload, everything is already cached.
+    public override void Preload(Float2 xRange, Float2 yRange, double step) { }
 }

Base/Graphables/Equation.cs

@@ -116,9 +116,9 @@ public class Equation : Graphable
         return new(graphMousePos.x, GetFromCache(graphMousePos.x, 0.001));
     }
 
-    public override void Preload(Float2 xRange, Float2 yRange)
+    public override void Preload(Float2 xRange, Float2 yRange, double step)
     {
-        for (double x = xRange.x; x <= xRange.y; x += 1e-3) GetFromCache(x, 1e-4);
+        for (double x = xRange.x; x <= xRange.y; x += step) GetFromCache(x, step);
     }
 }
 

Base/Graphables/SlopeField.cs

@@ -78,7 +78,16 @@ public class SlopeField : Graphable
     public override bool ShouldSelectGraphable(in GraphForm graph, Float2 graphMousePos, double factor) => false;
     public override Float2 GetSelectedPoint(in GraphForm graph, Float2 graphMousePos) => default;
 
-    public override void Preload(Float2 xRange, Float2 yRange) { }
+    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

@@ -5,17 +5,32 @@ namespace Graphing.Graphables;
 
 public class TangentLine : Graphable
 {
-    public double Position { get; set; }
+    public double Position
+    {
+        get => _position;
+        set
+        {
+            currentSlope = DerivativeAtPoint(value);
+            _position = value;
+        }
+    }
+    private double _position;
 
     protected readonly Equation parent;
     protected readonly EquationDelegate parentEqu;
 
     protected readonly double length;
 
+    protected double currentSlope;
+
+    // No binary search for this, I want it to be exact.
+    protected Dictionary<double, double> slopeCache;
+
     public TangentLine(double length, double position, Equation parent)
     {
         Name = $"Tangent Line of {parent.Name}";
 
+        slopeCache = [];
         parentEqu = parent.GetDelegate();
         Position = position;
         this.length = length;
@@ -25,7 +40,7 @@ public class TangentLine : Graphable
     public override IEnumerable<IGraphPart> GetItemsToRender(in GraphForm graph)
     {
         Float2 point = new(Position, parentEqu(Position));
-        return [MakeSlopeLine(point, DerivativeAtPoint(Position)),
+        return [MakeSlopeLine(point, currentSlope),
                 new GraphUiCircle(point, 8)];
     }
     protected GraphLine MakeSlopeLine(Float2 position, double slope)
@@ -40,17 +55,29 @@ public class TangentLine : Graphable
     }
     protected double DerivativeAtPoint(double x)
     {
+        // If value is already computed, return it.
+        if (slopeCache.TryGetValue(x, out double y)) return y;
+
         const double step = 1e-3;
-        return (parentEqu(x + step) - parentEqu(x)) / step;
+        double result = (parentEqu(x + step) - parentEqu(x)) / step;
+        slopeCache.Add(x, result);
+        return result;
     }
 
     public override Graphable DeepCopy() => new TangentLine(length, Position, parent);
 
-    public override void EraseCache() { }
+    public override void EraseCache() => slopeCache.Clear();
-    public override long GetCacheBytes() => 0;
+    public override long GetCacheBytes() => slopeCache.Count * 16;
 
     public override bool ShouldSelectGraphable(in GraphForm graph, Float2 graphMousePos, double factor) => false;
     public override Float2 GetSelectedPoint(in GraphForm graph, Float2 graphMousePos) => default;
 
-    public override void Preload(Float2 xRange, Float2 yRange) { }
+    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);
+    }
 }

Testing/Program.cs

@@ -14,10 +14,10 @@ internal static class Program
 
         GraphForm graph = new("One Of The Graphing Calculators Of All Time");
 
-        Equation equ1 = new(x => -x * x + 2);
+        Equation possibleA = new(x => x * x * x);
-        Equation equ2 = new(x => x);
+        SlopeField sf = new(2, (x, y) => 3 * x * x);
-        Equation equ3 = new(x => -Math.Sqrt(x));
+        TangentLine tl = new(5, 2, possibleA);
-        graph.Graph(equ1, equ2, equ3);
+        graph.Graph(possibleA, sf, tl);
 
         // You can also now view and reset caches in the UI by going to
         // Misc > View Caches.