add voronoi and circles (chatgpt)

DelauneyTriangulation/ViewModels/MainWindowViewModel.cs

@@ -250,6 +250,80 @@ public partial class MainWindowViewModel : ViewModelBase
         }
     }
 
+    void BuildVoronoi(Geometries.Point sa, Geometries.Point sb, Geometries.Point sc)
+    {
+        VoronoiDiagram.Clear();
+
+        var center = new Dictionary<Geometries.Triangle, (double x, double y)>();
+        foreach (var t in Triangles)
+        {
+            if (UsesVertex(t, sa) || UsesVertex(t, sb) || UsesVertex(t, sc)) continue;
+            try
+            {
+                var cc = new Geometries.Circle(
+                    new Geometries.Point(t.X.X, t.X.Y),
+                    new Geometries.Point(t.Y.X, t.Y.Y),
+                    new Geometries.Point(t.Z.X, t.Z.Y));
+                center[t] = (cc.X, cc.Y);
+            }
+            catch (ArgumentException)
+            {
+            }
+        }
+
+        var map = new Dictionary<string, (Geometries.Edge edge, List<Geometries.Triangle> tris)>();
+        foreach (var t in Triangles)
+        {
+            if (UsesVertex(t, sa) || UsesVertex(t, sb) || UsesVertex(t, sc)) continue;
+            foreach (var e in ExtractTriangleEdges(t))
+            {
+                var k = CanonKey(e);
+                if (!map.TryGetValue(k, out var val)) val = (e, new List<Geometries.Triangle>());
+                val.tris.Add(t);
+                map[k] = val;
+            }
+        }
+
+        var far = 10 * Math.Max(Width, Height);
+        foreach (var kv in map.Values)
+        {
+            var e = kv.edge;
+            var tris = kv.tris;
+
+            if (tris.Count == 2 && center.TryGetValue(tris[0], out var c0) && center.TryGetValue(tris[1], out var c1))
+                VoronoiDiagram.Add(new Geometries.Edge(c0.x, c0.y, c1.x, c1.y));
+
+            else if (tris.Count == 1 && center.TryGetValue(tris[0], out var c))
+            {
+                double ex = e.X2 - e.X1, ey = e.Y2 - e.Y1;
+                double nx = -ey, ny = ex;
+                var nlen = Math.Sqrt(nx * nx + ny * ny);
+
+                if (nlen > 0)
+                {
+                    nx /= nlen;
+                    ny /= nlen;
+                }
+
+                var mx = 0.5 * (e.X1 + e.X2);
+                var my = 0.5 * (e.Y1 + e.Y2);
+
+                var t = tris[0];
+                var cx = (t.X.X + t.Y.X + t.Z.X) / 3.0;
+                var cy = (t.X.Y + t.Y.Y + t.Z.Y) / 3.0;
+                var dot = (cx - mx) * nx + (cy - my) * ny;
+
+                if (dot > 0)
+                {
+                    nx = -nx;
+                    ny = -ny;
+                }
+
+                VoronoiDiagram.Add(new Geometries.Edge(c.x, c.y, c.x + nx * far, c.y + ny * far));
+            }
+        }
+    }
+
     async Task BowyerWatson(CancellationToken ct)
     {
         Triangles.Clear();
@@ -324,6 +398,9 @@ public partial class MainWindowViewModel : ViewModelBase
 
         DrawCircles(Triangles, sa, sb, sc);
         await DelayAsync(ct);
+
+        BuildVoronoi(sa, sb, sc);
+        await DelayAsync(ct);
     }
 
     async Task DelaunayTriangulateAsync(CancellationToken ct)