fix(geometry): stabilize triangulation winding at large coordinates

OpenNest.Core/Geometry/ConvexDecomposition.cs

@@ -148,14 +148,12 @@ namespace OpenNest.Geometry
         /// </summary>
         private static double SignedArea(List<Vector> verts)
         {
+            // World-coordinate products can erase the sign of a small polygon's area
+            // far from the origin, leaving CW outlines/holes untriangulated. Measure
+            // relative to a vertex, just as the clipping kernel measures its fragments.
             var area = 0.0;
-
+            for (var i = 1; i + 1 < verts.Count; i++)
-            for (var i = 0; i < verts.Count; i++)
+                area += Cross(verts[0], verts[i], verts[i + 1]);
-            {
-                var j = (i + 1) % verts.Count;
-                area += verts[i].X * verts[j].Y;
-                area -= verts[j].X * verts[i].Y;
-            }
 
             return area * 0.5;
         }

OpenNest.Tests/Geometry/CollisionTranslationTests.cs

@@ -0,0 +1,70 @@
+using OpenNest.Geometry;
+
+namespace OpenNest.Tests.Geometry;
+
+public class CollisionTranslationTests
+{
+    [Theory]
+    [InlineData(false)]
+    [InlineData(true)]
+    public void Check_ContainedClockwisePolygonFarFromOriginDoesNotDependOnOperandOrder(bool swap)
+    {
+        var outer = Square(0, 0, 1e9);
+        var small = Square(999999998, 999999998, 1);
+        small.Reverse();
+
+        var result = swap ? Collision.Check(small, outer) : Collision.Check(outer, small);
+
+        Assert.True(result.Overlaps);
+        // Do not use Polygon.Area here: this test isolates triangulation, not that legacy API.
+        Assert.Equal(1, result.OverlapRegions.Sum(StableArea), 8);
+    }
+
+    [Fact]
+    public void Check_ClockwiseHoleFarFromOriginIsSubtracted()
+    {
+        var outer = Square(0, 0, 1e9);
+        var hole = Square(999999998, 999999998, 1);
+        hole.Reverse();
+        var insert = Square(999999998.25, 999999998.25, 0.5);
+
+        var result = Collision.Check(outer, insert, new List<Polygon> { hole });
+
+        Assert.False(result.Overlaps);
+        Assert.Empty(result.OverlapRegions);
+    }
+
+    [Theory]
+    [InlineData(1000000000)]
+    [InlineData(-1000000000)]
+    public void Triangulate_ClockwiseTranslatedUnitSquareHasFullArea(double offset)
+    {
+        var polygon = Square(offset, offset, 1);
+        polygon.Reverse();
+        var triangles = ConvexDecomposition.Triangulate(polygon);
+        Assert.Equal(2, triangles.Count);
+        Assert.Equal(1, triangles.Sum(StableArea), 8);
+    }
+
+    private static Polygon Square(double x, double y, double size)
+    {
+        var polygon = new Polygon();
+        polygon.Vertices.AddRange(new[] { new Vector(x, y), new Vector(x + size, y),
+            new Vector(x + size, y + size), new Vector(x, y + size), new Vector(x, y) });
+        polygon.UpdateBounds();
+        return polygon;
+    }
+
+    private static double StableArea(Polygon polygon)
+    {
+        var area = 0.0;
+        var origin = polygon.Vertices[0];
+        for (var i = 1; i + 1 < polygon.Vertices.Count; i++)
+        {
+            var a = polygon.Vertices[i] - origin;
+            var b = polygon.Vertices[i + 1] - origin;
+            area += a.X * b.Y - a.Y * b.X;
+        }
+        return System.Math.Abs(area) / 2;
+    }
+}