More selection stuff. Do we really want to select tangent lines this way?

Base/Graphables/ColumnTable.cs

@@ -48,9 +48,6 @@ public class ColumnTable : Graphable
         return items;
     }
 
-    public override bool ShouldSelectGraphable(in GraphForm graph, Float2 graphMousePos, double factor) => false;
-    public override Float2 GetSelectedPoint(in GraphForm graph, Float2 graphMousePos) => default;
-
     // Nothing to preload, everything is already cached.
     public override void Preload(Float2 xRange, Float2 yRange, double step) { }
 }

Base/Graphables/SlopeField.cs

@@ -74,9 +74,46 @@ public class SlopeField : Graphable
 
     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);
 
-    public override bool ShouldSelectGraphable(in GraphForm graph, Float2 graphMousePos, double factor) => false;
+        double epsilon = 1 / (detail * 2.0);
-    public override Float2 GetSelectedPoint(in GraphForm graph, Float2 graphMousePos) => default;
+        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 Float2 GetSelectedPoint(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 point;
+    }
 
     public override void Preload(Float2 xRange, Float2 yRange, double step)
     {

Base/Graphables/TangentLine.cs

@@ -21,10 +21,12 @@ public class TangentLine : Graphable
 
     protected readonly double length;
 
-    protected double currentSlope;
+    // X is slope, Y is height.
+    protected Float2 currentSlope;
 
     // No binary search for this, I want it to be exact.
-    protected Dictionary<double, double> slopeCache;
+    // Value: X is slope, Y is height.
+    protected Dictionary<double, Float2> slopeCache;
 
     public TangentLine(double length, double position, Equation parent)
     {
@@ -39,27 +41,28 @@ public class TangentLine : Graphable
 
     public override IEnumerable<IGraphPart> GetItemsToRender(in GraphForm graph)
     {
-        Float2 point = new(Position, parentEqu(Position));
+        Float2 point = new(Position, currentSlope.y);
-        return [MakeSlopeLine(point, currentSlope),
+        return [MakeSlopeLine(), new GraphUiCircle(point, 8)];
-                new GraphUiCircle(point, 8)];
     }
-    protected GraphLine MakeSlopeLine(Float2 position, double slope)
+    protected GraphLine MakeSlopeLine()
     {
-        double dirX = length, dirY = slope * length;
+        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.x + dirX, position.y + dirY), new(position.x - dirX, position.y - dirY));
+        return new(new(Position + dirX, currentSlope.y + dirY), new(Position - dirX, currentSlope.y - dirY));
     }
-    protected double DerivativeAtPoint(double x)
+    protected Float2 DerivativeAtPoint(double x)
     {
         // If value is already computed, return it.
-        if (slopeCache.TryGetValue(x, out double y)) return y;
+        if (slopeCache.TryGetValue(x, out Float2 val)) return val;
 
         const double step = 1e-3;
-        double result = (parentEqu(x + step) - parentEqu(x)) / step;
+
+        double initial = parentEqu(x);
+        Float2 result = new((parentEqu(x + step) - initial) / step, initial);
         slopeCache.Add(x, result);
         return result;
     }
@@ -67,10 +70,37 @@ public class TangentLine : Graphable
     public override Graphable DeepCopy() => new TangentLine(length, Position, parent);
 
     public override void EraseCache() => slopeCache.Clear();
-    public override long GetCacheBytes() => slopeCache.Count * 16;
+    public override long GetCacheBytes() => slopeCache.Count * 24;
 
-    public override bool ShouldSelectGraphable(in GraphForm graph, Float2 graphMousePos, double factor) => false;
+    public override bool ShouldSelectGraphable(in GraphForm graph, Float2 graphMousePos, double factor)
-    public override Float2 GetSelectedPoint(in GraphForm graph, Float2 graphMousePos) => default;
+    {
+        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 Float2 GetSelectedPoint(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;
+        return new Float2(lineX, lineY);
+    }
 
     public override void Preload(Float2 xRange, Float2 yRange, double step)
     {

Testing/Program.cs

@@ -14,8 +14,8 @@ internal static class Program
 
         GraphForm graph = new("One Of The Graphing Calculators Of All Time");
 
-        Equation possibleA = new(x => Math.Sin(x));
+        Equation possibleA = new(x => x * x * x);
-        SlopeField sf = new(2, (x, y) => Math.Cos(x));
+        SlopeField sf = new(2, (x, y) => 1 / x);
         TangentLine tl = new(2, 2, possibleA);
         graph.Graph(possibleA, sf, tl);