Add class to split a polygon into triangles

Author: adamgraham

Runtime/Triangulator.cs

@@ -0,0 +1,158 @@
+using System.Collections.Generic;
+using UnityEngine;
+
+namespace Zigurous.Graphics
+{
+    /// <summary>
+    /// Splits a polygon into triangles.
+    /// </summary>
+    public static class Triangulator
+    {
+        /// <summary>
+        /// Splits a polygon into triangles. Supports concave polygons but not
+        /// polygons with holes.
+        /// </summary>
+        /// <param name="points">The points that form a polygon.</param>
+        /// <returns>The indices of the triangles.</returns>
+        public static int[] Triangulate(Vector2[] points)
+        {
+            int n = points.Length;
+
+            if (n < 3) {
+                return new int[0];
+            }
+
+            int[] V = new int[n];
+
+            if (Area(points) > 0f)
+            {
+                for (int v = 0; v < n; v++) {
+                    V[v] = v;
+                }
+            }
+            else
+            {
+                for (int v = 0; v < n; v++) {
+                    V[v] = (n - 1) - v;
+                }
+            }
+
+            List<int> indices = new List<int>();
+
+            int nv = n;
+            int count = 2 * nv;
+
+            for (int m = 0, v = nv - 1; nv > 2;)
+            {
+                if ((count--) <= 0) {
+                    return indices.ToArray();
+                }
+
+                int u = v;
+
+                if (nv <= u) {
+                    u = 0;
+                }
+
+                v = u + 1;
+
+                if (nv <= v) {
+                    v = 0;
+                }
+
+                int w = v + 1;
+
+                if (nv <= w) {
+                    w = 0;
+                }
+
+                if (Snip(points, u, v, w, nv, V))
+                {
+                    int a, b, c, s, t;
+
+                    a = V[u];
+                    b = V[v];
+                    c = V[w];
+
+                    indices.Add(a);
+                    indices.Add(b);
+                    indices.Add(c);
+
+                    m++;
+
+                    for (s = v, t = v + 1; t < nv; s++, t++) {
+                        V[s] = V[t];
+                    }
+
+                    nv--;
+                    count = 2 * nv;
+                }
+            }
+
+            indices.Reverse();
+            return indices.ToArray();
+        }
+
+        private static float Area(Vector2[] points)
+        {
+            int n = points.Length;
+            float A = 0f;
+
+            for (int p = n - 1, q = 0; q < n; p = q++)
+            {
+                Vector2 pval = points[p];
+                Vector2 qval = points[q];
+                A += pval.x * qval.y - qval.x * pval.y;
+            }
+
+            return (A * 0.5f);
+        }
+
+        private static bool Snip(Vector2[] points, int u, int v, int w, int n, int[] V)
+        {
+            Vector2 A = points[V[u]];
+            Vector2 B = points[V[v]];
+            Vector2 C = points[V[w]];
+
+            if (Mathf.Epsilon > (((B.x - A.x) * (C.y - A.y)) - ((B.y - A.y) * (C.x - A.x)))) {
+                return false;
+            }
+
+            for (int p = 0; p < n; p++)
+            {
+                if ((p == u) || (p == v) || (p == w)) {
+                    continue;
+                }
+
+                Vector2 P = points[V[p]];
+
+                if (InsideTriangle(A, B, C, P)) {
+                    return false;
+                }
+            }
+
+            return true;
+        }
+
+        private static bool InsideTriangle(Vector2 A, Vector2 B, Vector2 C, Vector2 P)
+        {
+            float ax, ay, bx, by, cx, cy, apx, apy, bpx, bpy, cpx, cpy;
+            float cCROSSap, bCROSScp, aCROSSbp;
+
+            ax = C.x - B.x; ay = C.y - B.y;
+            bx = A.x - C.x; by = A.y - C.y;
+            cx = B.x - A.x; cy = B.y - A.y;
+            apx = P.x - A.x; apy = P.y - A.y;
+            bpx = P.x - B.x; bpy = P.y - B.y;
+            cpx = P.x - C.x; cpy = P.y - C.y;
+
+            aCROSSbp = ax * bpy - ay * bpx;
+            cCROSSap = cx * apy - cy * apx;
+            bCROSScp = bx * cpy - by * cpx;
+
+            return ((aCROSSbp >= 0f) && (bCROSScp >= 0f) && (cCROSSap >= 0f));
+        }
+
+    }
+
+}