Add cubic bezier functions.

Assets/Cryville/Common/Math/CubicBezier.cs

@@ -0,0 +1,44 @@
+using SMath = System.Math;
+
+namespace Cryville.Common.Math {
+	// Ported from https://github.com/arian/cubic-bezier/blob/master/index.js
+	public static class CubicBezier {
+		public static float Evaluate(float t, float x1, float y1, float x2, float y2, float epsilon) {
+			float x = t, t0, t1, t2, tx, d2, i;
+			for (t2 = x, i = 0; i < 8; i++) {
+				tx = CurveX(t2, x1, x2) - x;
+				if (SMath.Abs(tx) < epsilon) return CurveY(t2, y1, y2);
+				d2 = DerivativeCurveX(t2, x1, x2);
+				if (SMath.Abs(d2) < 1e-6) break;
+				t2 -= tx / d2;
+			}
+
+			t0 = 0; t1 = 1; t2 = x;
+
+			if (t2 < t0) return CurveY(t0, y1, y2);
+			if (t2 > t1) return CurveY(t1, y1, y2);
+
+			while (t0 < t1) {
+				tx = CurveX(t2, x1, x2);
+				if (SMath.Abs(tx - x) < epsilon) return CurveY(t2, y1, y2);
+				if (x > tx) t0 = t2;
+				else t1 = t2;
+				t2 = (t1 - t0) * .5f + t0;
+			}
+
+			return CurveY(t2, y1, y2);
+		}
+		static float CurveX(float t, float x1, float x2) {
+			float v = 1 - t;
+			return 3 * v * v * t * x1 + 3 * v * t * t * x2 + t * t * t;
+		}
+		static float CurveY(float t, float y1, float y2) {
+			float v = 1 - t;
+			return 3 * v * v * t * y1 + 3 * v * t * t * y2 + t * t * t;
+		}
+		static float DerivativeCurveX(float t, float x1, float x2) {
+			float v = 1 - t;
+			return 3 * (2 * (t - 1) * t + v * v) * x1 + 3 * (-t * t * t + 2 * v * t) * x2;
+		}
+	}
+}