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;
		}
	}
}