// Implementation of 1D, 2D and 3D Perlin noise based on Ken Perlin's improved version https://mrl.nyu.edu/~perlin/noise/
// (See Random3.tps for additional third party software info.)
namespace FMathPerlinHelpers
{
	// random permutation of 256 numbers, repeated 2x
	static const int32 Permutation[512] = {
		63, 9, 212, 205, 31, 128, 72, 59, 137, 203, 195, 170, 181, 115, 165, 40, 116, 139, 175, 225, 132, 99, 222, 2, 41, 15, 197, 93, 169, 90, 228, 43, 221, 38, 206, 204, 73, 17, 97, 10, 96, 47, 32, 138, 136, 30, 219,
		78, 224, 13, 193, 88, 134, 211, 7, 112, 176, 19, 106, 83, 75, 217, 85, 0, 98, 140, 229, 80, 118, 151, 117, 251, 103, 242, 81, 238, 172, 82, 110, 4, 227, 77, 243, 46, 12, 189, 34, 188, 200, 161, 68, 76, 171, 194,
		57, 48, 247, 233, 51, 105, 5, 23, 42, 50, 216, 45, 239, 148, 249, 84, 70, 125, 108, 241, 62, 66, 64, 240, 173, 185, 250, 49, 6, 37, 26, 21, 244, 60, 223, 255, 16, 145, 27, 109, 58, 102, 142, 253, 120, 149, 160,
		124, 156, 79, 186, 135, 127, 14, 121, 22, 65, 54, 153, 91, 213, 174, 24, 252, 131, 192, 190, 202, 208, 35, 94, 231, 56, 95, 183, 163, 111, 147, 25, 67, 36, 92, 236, 71, 166, 1, 187, 100, 130, 143, 237, 178, 158,
		104, 184, 159, 177, 52, 214, 230, 119, 87, 114, 201, 179, 198, 3, 248, 182, 39, 11, 152, 196, 113, 20, 232, 69, 141, 207, 234, 53, 86, 180, 226, 74, 150, 218, 29, 133, 8, 44, 123, 28, 146, 89, 101, 154, 220, 126,
		155, 122, 210, 168, 254, 162, 129, 33, 18, 209, 61, 191, 199, 157, 245, 55, 164, 167, 215, 246, 144, 107, 235, 

		63, 9, 212, 205, 31, 128, 72, 59, 137, 203, 195, 170, 181, 115, 165, 40, 116, 139, 175, 225, 132, 99, 222, 2, 41, 15, 197, 93, 169, 90, 228, 43, 221, 38, 206, 204, 73, 17, 97, 10, 96, 47, 32, 138, 136, 30, 219,
		78, 224, 13, 193, 88, 134, 211, 7, 112, 176, 19, 106, 83, 75, 217, 85, 0, 98, 140, 229, 80, 118, 151, 117, 251, 103, 242, 81, 238, 172, 82, 110, 4, 227, 77, 243, 46, 12, 189, 34, 188, 200, 161, 68, 76, 171, 194,
		57, 48, 247, 233, 51, 105, 5, 23, 42, 50, 216, 45, 239, 148, 249, 84, 70, 125, 108, 241, 62, 66, 64, 240, 173, 185, 250, 49, 6, 37, 26, 21, 244, 60, 223, 255, 16, 145, 27, 109, 58, 102, 142, 253, 120, 149, 160,
		124, 156, 79, 186, 135, 127, 14, 121, 22, 65, 54, 153, 91, 213, 174, 24, 252, 131, 192, 190, 202, 208, 35, 94, 231, 56, 95, 183, 163, 111, 147, 25, 67, 36, 92, 236, 71, 166, 1, 187, 100, 130, 143, 237, 178, 158,
		104, 184, 159, 177, 52, 214, 230, 119, 87, 114, 201, 179, 198, 3, 248, 182, 39, 11, 152, 196, 113, 20, 232, 69, 141, 207, 234, 53, 86, 180, 226, 74, 150, 218, 29, 133, 8, 44, 123, 28, 146, 89, 101, 154, 220, 126,
		155, 122, 210, 168, 254, 162, 129, 33, 18, 209, 61, 191, 199, 157, 245, 55, 164, 167, 215, 246, 144, 107, 235
	};

	// Gradient functions for 1D, 2D and 3D Perlin noise

	FORCEINLINE float Grad1(int32 Hash, float X)
	{
		// Slicing Perlin's 3D improved noise would give us only scales of -1, 0 and 1; this looks pretty bad so let's use a different sampling
		static const float Grad1Scales[16] = {-8/8, -7/8., -6/8., -5/8., -4/8., -3/8., -2/8., -1/8., 1/8., 2/8., 3/8., 4/8., 5/8., 6/8., 7/8., 8/8};
		return Grad1Scales[Hash & 15] * X;
	}

	// Note: If you change the Grad2 or Grad3 functions, check that you don't change the range of the resulting noise as well; it should be (within floating point error) in the range of (-1, 1)
	FORCEINLINE float Grad2(int32 Hash, float X, float Y)
	{
		// corners and major axes (similar to the z=0 projection of the cube-edge-midpoint sampling from improved Perlin noise)
		switch (Hash & 7)
		{
		case 0: return X;
		case 1: return X + Y;
		case 2: return Y;
		case 3: return -X + Y;
		case 4: return -X;
		case 5: return -X - Y;
		case 6: return -Y;
		case 7: return X - Y;
		// can't happen
		default: return 0;
		}
	}

	FORCEINLINE float Grad3(int32 Hash, float X, float Y, float Z)
	{
		switch (Hash & 15)
		{
		// 12 cube midpoints
		case 0: return X + Z;
		case 1: return X + Y;
		case 2: return Y + Z;
		case 3: return -X + Y;
		case 4: return -X + Z;
		case 5: return -X - Y;
		case 6: return -Y + Z;
		case 7: return X - Y;
		case 8: return X - Z;
		case 9: return Y - Z;
		case 10: return -X - Z;
		case 11: return -Y - Z;
		// 4 vertices of regular tetrahedron
		case 12: return X + Y;
		case 13: return -X + Y;
		case 14: return -Y + Z;
		case 15: return -Y - Z;
		// can't happen
		default: return 0;
		}
	}

	// Curve w/ second derivative vanishing at 0 and 1, from Perlin's improved noise paper
	FORCEINLINE float SmoothCurve(float X)
	{
		return X * X * X * (X * (X * 6.0f - 15.0f) + 10.0f);
	}
};