diff --git a/Scripts/ShapeEditor/Decomposition/Bayazit/BayazitDecomposer.cs b/Scripts/ShapeEditor/Decomposition/Bayazit/BayazitDecomposer.cs
index c038e9e..3529b31 100644
--- a/Scripts/ShapeEditor/Decomposition/Bayazit/BayazitDecomposer.cs
+++ b/Scripts/ShapeEditor/Decomposition/Bayazit/BayazitDecomposer.cs
@@ -22,6 +22,8 @@ namespace AeternumGames.ShapeEditor
     public static class BayazitDecomposer
     {
         private static int MaxPolygonVertices = 1024; // henry: used to be 8, but we want less CSG brushes / meshes.
+        private const float SingularityEpsilon = 1e-4f;
+        private const float SingularityEpsilonSqr = SingularityEpsilon * SingularityEpsilon;
 
         /// <summary>
         /// [2D] Decompose the polygon into several smaller non-concave polygon. If the polygon is
@@ -32,6 +34,14 @@ public static List<Polygon> ConvexPartition(Polygon vertices)
             Debug.Assert(vertices.Count >= 3);
             Debug.Assert(vertices.IsCounterClockWise2D());
 
+            if (TrySplitAtSingularity(vertices, out var splitPolygons))
+            {
+                var splitResult = new List<Polygon>();
+                for (int i = 0; i < splitPolygons.Count; i++)
+                    splitResult.AddRange(ConvexPartition(splitPolygons[i]));
+                return splitResult;
+            }
+
             var depth = 800;
             var result = TriangulatePolygon(vertices, ref depth);
 
@@ -41,6 +51,164 @@ public static List<Polygon> ConvexPartition(Polygon vertices)
             return result;
         }
 
+        private static bool TrySplitAtSingularity(Polygon vertices, out List<Polygon> polygons)
+        {
+            polygons = null;
+
+            if (vertices.Count < 4)
+                return false;
+
+            if (TrySplitAtCoincidentVertex(vertices, out polygons))
+                return true;
+
+            return TrySplitAtVertexOnEdge(vertices, out polygons);
+        }
+
+        private static bool TrySplitAtCoincidentVertex(Polygon vertices, out List<Polygon> polygons)
+        {
+            polygons = null;
+            var count = vertices.Count;
+
+            for (int i = 0; i < count; i++)
+            {
+                for (int j = i + 1; j < count; j++)
+                {
+                    if (AreAdjacent(i, j, count))
+                        continue;
+
+                    if (!SamePosition((Vector2)vertices[i].position, (Vector2)vertices[j].position))
+                        continue;
+
+                    var first = CopyRange(i, j, vertices);
+                    var second = CopyRange(j, i, vertices);
+                    if (TryCreateSplitResult(vertices, first, second, out polygons))
+                        return true;
+                }
+            }
+
+            return false;
+        }
+
+        private static bool TrySplitAtVertexOnEdge(Polygon vertices, out List<Polygon> polygons)
+        {
+            polygons = null;
+            var count = vertices.Count;
+
+            for (int vertexIndex = 0; vertexIndex < count; vertexIndex++)
+            {
+                var point = (Vector2)vertices[vertexIndex].position;
+
+                for (int edgeStartIndex = 0; edgeStartIndex < count; edgeStartIndex++)
+                {
+                    var edgeEndIndex = (edgeStartIndex + 1) % count;
+                    if (vertexIndex == edgeStartIndex || vertexIndex == edgeEndIndex)
+                        continue;
+
+                    var edgeStart = (Vector2)vertices[edgeStartIndex].position;
+                    var edgeEnd = (Vector2)vertices[edgeEndIndex].position;
+                    if (!PointIsInsideEdge(point, edgeStart, edgeEnd))
+                        continue;
+
+                    var first = CopyRange(vertexIndex, edgeStartIndex, vertices);
+                    first.Add(CreateSplitVertex(vertices[vertexIndex], point));
+
+                    var second = new Polygon();
+                    second.Add(CreateSplitVertex(vertices[vertexIndex], point));
+                    second.AddRange(CopyRange(edgeEndIndex, vertexIndex, vertices));
+
+                    if (TryCreateSplitResult(vertices, first, second, out polygons))
+                        return true;
+                }
+            }
+
+            return false;
+        }
+
+        private static bool TryCreateSplitResult(Polygon source, Polygon first, Polygon second, out List<Polygon> polygons)
+        {
+            polygons = null;
+
+            if (!PrepareSplitPolygon(source, first) || !PrepareSplitPolygon(source, second))
+                return false;
+
+            polygons = new List<Polygon> { first, second };
+            return true;
+        }
+
+        private static bool PrepareSplitPolygon(Polygon source, Polygon polygon)
+        {
+            RemoveDuplicateVertices(polygon);
+            polygon.CollinearSimplify(SingularityEpsilon);
+
+            if (polygon.Count < 3 || Mathf.Abs(polygon.GetSignedArea2D()) <= SingularityEpsilon)
+                return false;
+
+            polygon.ForceCounterClockWise2D();
+            polygon.booleanOperator = source.booleanOperator;
+            return true;
+        }
+
+        private static Polygon CopyRange(int start, int end, Polygon vertices)
+        {
+            var count = vertices.Count;
+            while (end < start)
+                end += count;
+
+            var result = new Polygon(end - start + 1);
+            for (int i = start; i <= end; i++)
+            {
+                var vertex = vertices[i % count];
+                result.Add(new Vertex(vertex.position, vertex.uv0, vertex.hidden, vertex.material));
+            }
+            return result;
+        }
+
+        private static void RemoveDuplicateVertices(Polygon polygon)
+        {
+            for (int i = polygon.Count - 1; i > 0; i--)
+            {
+                if (SamePosition((Vector2)polygon[i].position, (Vector2)polygon[i - 1].position))
+                    polygon.RemoveAt(i);
+            }
+
+            if (polygon.Count > 1 && SamePosition((Vector2)polygon[0].position, (Vector2)polygon[polygon.Count - 1].position))
+                polygon.RemoveAt(polygon.Count - 1);
+        }
+
+        private static Vertex CreateSplitVertex(Vertex template, Vector2 position)
+        {
+            return new Vertex(new Vector3(position.x, position.y, template.position.z), template.uv0, template.hidden, template.material);
+        }
+
+        private static bool AreAdjacent(int first, int second, int count)
+        {
+            return Mathf.Abs(first - second) == 1 || Mathf.Abs(first - second) == count - 1;
+        }
+
+        private static bool SamePosition(Vector2 first, Vector2 second)
+        {
+            return SquareDist(first, second) <= SingularityEpsilonSqr;
+        }
+
+        private static bool PointIsInsideEdge(Vector2 point, Vector2 edgeStart, Vector2 edgeEnd)
+        {
+            if (SquareDist(point, edgeStart) <= SingularityEpsilonSqr || SquareDist(point, edgeEnd) <= SingularityEpsilonSqr)
+                return false;
+
+            var edge = edgeEnd - edgeStart;
+            var pointOffset = point - edgeStart;
+            var edgeLengthSqr = edge.sqrMagnitude;
+            if (edgeLengthSqr <= SingularityEpsilonSqr)
+                return false;
+
+            var t = Vector2.Dot(pointOffset, edge) / edgeLengthSqr;
+            if (t <= 0f || t >= 1f)
+                return false;
+
+            var closestPoint = edgeStart + edge * t;
+            return SquareDist(point, closestPoint) <= SingularityEpsilonSqr;
+        }
+
         private static List<Polygon> TriangulatePolygon(Polygon vertices, ref int depth)
         {
             if (depth-- <= 0) return new List<Polygon> { vertices };
@@ -365,4 +533,4 @@ private static bool FloatEquals(float value1, float value2)
     }
 }
 
-#endif
\ No newline at end of file
+#endif