Various things. Added a tangent line system, allows for different graph parts, and more caching stuff.

Base/Forms/GraphForm.cs

@@ -1,5 +1,7 @@
 using Graphing.Extensions;
 using Graphing.Graphables;
+using Graphing.Parts;
+using System.Drawing.Drawing2D;
 using System.Text;
 
 namespace Graphing.Forms;
@@ -145,6 +147,7 @@ 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);
@@ -154,19 +157,9 @@ 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 (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);
-            }
+            foreach (IGraphPart gp in lines) gp.Render(this, g, graphBrush);
         }
 
         base.OnPaint(e);
@@ -375,24 +368,17 @@ public partial class GraphForm : Form
         long total = 0;
         foreach (Graphable able in ables)
         {
-            if (able is Equation equ)
-            {
-                long size = equ.GetCacheBytes();
+            long size = able.GetCacheBytes();
             message.AppendLine($"{able.Name}: {size.FormatAsBytes()}");
-
             total += size;
         }
-        }
 
-        message.AppendLine($"\nTotal: {total.FormatAsBytes()}\n\nClick \"No\" to erase caches.");
+        message.AppendLine($"\nTotal: {total.FormatAsBytes()}\n\nErase cache?");
 
         DialogResult result = MessageBox.Show(message.ToString(), "Graph Caches", MessageBoxButtons.YesNo, MessageBoxIcon.Information);
-        if (result == DialogResult.No)
+        if (result == DialogResult.Yes)
         {
-            foreach (Graphable able in ables)
-            {
-                if (able is Equation equ) equ.EraseCache();
-            }
+            foreach (Graphable able in ables) able.EraseCache();
         }
     }
 }

Base/Forms/SetZoomForm.cs

@@ -1,18 +1,7 @@
-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
 {
-    public partial class SetZoomForm : Form
-    {
     private double minZoomRange;
     private double maxZoomRange;
 
@@ -127,5 +116,4 @@ namespace Graphing.Forms
             ZoomMaxValue.Text = maxZoomRange.ToString("0.00");
         }
     }
-    }
 }

Base/Graphable.cs

@@ -1,4 +1,5 @@
 using Graphing.Forms;
+using Graphing.Parts;
 
 namespace Graphing;
 
@@ -26,5 +27,8 @@ 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 void EraseCache();
+    public abstract long GetCacheBytes();
 }

Base/Graphables/Equation.cs

@@ -1,4 +1,5 @@
 using Graphing.Forms;
+using Graphing.Parts;
 
 namespace Graphing.Graphables;
 
@@ -19,73 +20,73 @@ public class Equation : Graphable
         cache = [];
     }
 
-    public override IEnumerable<Line2d> GetItemsToRender(in GraphForm graph)
+    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;
 
-        List<Line2d> lines = [];
+        List<IGraphPart> lines = [];
 
-        bool addedToDictionary = false;
         double previousX = graph.MinVisibleGraph.x;
-        double previousY = GetFromCache(previousX, epsilon, ref addedToDictionary);
+        double previousY = GetFromCache(previousX, epsilon);
 
         for (int i = 1; i < graph.ClientRectangle.Width; i += step)
         {
             double currentX = graph.ScreenSpaceToGraphSpace(new Int2(i, 0)).x;
-            double currentY = GetFromCache(currentX, epsilon, ref addedToDictionary);
+            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;
         }
 
-        if (addedToDictionary) cache.Sort((a, b) => a.y.CompareTo(b.y));
+        // if (addedToDictionary) cache.Sort((a, b) => a.y.CompareTo(b.y)); todo: not required until binary search
 
         return lines;
     }
 
     public EquationDelegate GetDelegate() => equ;
 
-    public void EraseCache() => cache.Clear();
-    private double GetFromCache(double x, double epsilon, ref bool addedToDictionary)
+    public override void EraseCache() => cache.Clear();
+    private double GetFromCache(double x, double epsilon)
     {
-        (double dist, double nearest) = NearestCachedPoint(x);
+        (double dist, double nearest, int index) = NearestCachedPoint(x);
         if (dist < epsilon) return nearest;
         else
         {
-            addedToDictionary = true;
             double result = equ(x);
             cache.Add(new(x, result));
             // TODO: Rather than sorting the whole list when we add a single number,
-            //       we could just insert it.
+            //       we could just insert it in its proper place.
             return result;
         }
     }
 
-    private (double dist, double y) NearestCachedPoint(double x)
+    private (double dist, double y, int index) NearestCachedPoint(double x)
     {
         // TODO: Replace with a binary search system.
         double closestDist = double.PositiveInfinity;
         double closest = 0;
+        int closestIndex = -1;
 
-        foreach (Float2 p in cache)
+        for (int i = 0; i < cache.Count; i++)
         {
-            double dist = Math.Abs(x - p.x);
+            double dist = Math.Abs(x - cache[i].x);
             if (dist < closestDist)
             {
                 closestDist = dist;
-                closest = p.y;
+                closest = cache[i].y;
+                closestIndex = i;
             }
         }
 
-        return (closestDist, closest);
+        return (closestDist, closest, closestIndex);
     }
 
-    public long GetCacheBytes() => cache.Count * 16;
+    public override long GetCacheBytes() => cache.Count * 16;
 }
 
 public delegate double EquationDelegate(double x);

Base/Graphables/SlopeField.cs

@@ -1,4 +1,6 @@
 using Graphing.Forms;
+using Graphing.Parts;
+using static System.Windows.Forms.LinkLabel;
 
 namespace Graphing.Graphables;
 
@@ -9,6 +11,8 @@ public class SlopeField : Graphable
     private readonly SlopeFieldsDelegate equ;
     private readonly double detail;
 
+    private readonly List<(Float2, GraphLine)> cache;
+
     public SlopeField(int detail, SlopeFieldsDelegate equ)
     {
         slopeFieldNum++;
@@ -16,25 +20,26 @@ 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);
+        List<IGraphPart> lines = [];
 
         for (double x = Math.Ceiling(graph.MinVisibleGraph.x - 1); x < graph.MaxVisibleGraph.x + 1; x += 1 / detail)
         {
             for (double y = Math.Ceiling(graph.MinVisibleGraph.y - 1); y < graph.MaxVisibleGraph.y + 1; y += 1 / detail)
             {
-                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)
+    private GraphLine MakeSlopeLine(Float2 position, double slope)
     {
         double size = detail;
 
@@ -46,6 +51,28 @@ public class SlopeField : Graphable
 
         return new(new(position.x + dirX, position.y + dirY), new(position.x - dirX, position.y - dirY));
     }
+    private 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 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 +1,47 @@
+using Graphing.Forms;
+using Graphing.Parts;
+
+namespace Graphing.Graphables;
+
+public class TangentLine : Graphable
+{
+    public double Position { get; set; }
+
+    private readonly EquationDelegate parentEqu;
+
+    private 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;
+    }
+
+    public override IEnumerable<IGraphPart> GetItemsToRender(in GraphForm graph)
+    {
+        Float2 point = new(Position, parentEqu(Position));
+        return [MakeSlopeLine(point, DerivativeAtPoint(Position)),
+                new GraphCircle(point, 8)];
+    }
+    private 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));
+    }
+    private double DerivativeAtPoint(double x)
+    {
+        const double step = 1e-3;
+        return (parentEqu(x + step) - parentEqu(x)) / step;
+    }
+
+    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/GraphCircle.cs

@@ -0,0 +1,31 @@
+using Graphing.Forms;
+
+namespace Graphing.Parts;
+
+public record struct GraphCircle : IGraphPart
+{
+    public Float2 center;
+    public int radius;
+
+    public GraphCircle()
+    {
+        center = new();
+        radius = 1;
+    }
+    public GraphCircle(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.IsNormal(center.x) || !double.IsNormal(center.y) ||
+            !double.IsNormal(radius)) 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/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.IsNormal(a.x) || !double.IsNormal(a.y) ||
+            !double.IsNormal(b.x) || !double.IsNormal(b.y)) return;
+
+        Int2 start = form.GraphSpaceToScreenSpace(a),
+             end = form.GraphSpaceToScreenSpace(b);
+
+        Pen pen = new(brush, 3);
+        g.DrawLine(pen, start, end);
+    }
+}

Testing/Program.cs

@@ -10,12 +10,21 @@ 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(x => Math.Pow(2, x)));
-        graph.Graph(new Equation(Math.Log2));
+
+        Equation equ = new(x => x * x);
+        TangentLine tangent = new(5, 2, equ);
+
+        graph.Graph(equ);
+        graph.Graph(tangent);
 
         Application.Run(graph);
     }
+
+    private static double PopulationGraph(double max, double k, double A, double t)
+    {
+        return max / (1 + A * Math.Exp(-k * t));
+    }
 }