content: /*
   * FXGL - JavaFX Game Library. The MIT License (MIT).
   * Copyright (c) AlmasB (almaslvl@gmail.com).
   * See LICENSE for details.
   */
  
  package com.almasb.fxgl.core.math;
  
  /**
   * Simplex Noise from https://github.com/shathor/SimplexNoise
   */
  public class SimplexNoise {
  
  	private static int[][] grad3 = {{1, 1, 0}, {-1, 1, 0}, {1, -1, 0}, {-1, -1, 0}, {1, 0, 1}, {-1, 0, 1}, {1, 0, -1}, {-1, 0, -1}, {0, 1, 1}, {0, -1, 1}, {0, 1, -1},
  			{0, -1, -1}};
  
  	private static int[] p = {151, 160, 137, 91, 90, 15, 131, 13, 201, 95, 96, 53, 194, 233, 7, 225, 140, 36, 103, 30, 69, 142, 8, 99, 37, 240, 21, 10, 23, 190, 6, 148, 247, 120, 234, 75, 0, 26, 197,
  			62, 94, 252, 219, 203, 117, 35, 11, 32, 57, 177, 33, 88, 237, 149, 56, 87, 174, 20, 125, 136, 171, 168, 68, 175, 74, 165, 71, 134, 139, 48, 27, 166, 77, 146, 158, 231, 83, 111, 229, 122,
  			60, 211, 133, 230, 220, 105, 92, 41, 55, 46, 245, 40, 244, 102, 143, 54, 65, 25, 63, 161, 1, 216, 80, 73, 209, 76, 132, 187, 208, 89, 18, 169, 200, 196, 135, 130, 116, 188, 159, 86, 164,
  			100, 109, 198, 173, 186, 3, 64, 52, 217, 226, 250, 124, 123, 5, 202, 38, 147, 118, 126, 255, 82, 85, 212, 207, 206, 59, 227, 47, 16, 58, 17, 182, 189, 28, 42, 223, 183, 170, 213, 119, 248,
  			152, 2, 44, 154, 163, 70, 221, 153, 101, 155, 167, 43, 172, 9, 129, 22, 39, 253, 19, 98, 108, 110, 79, 113, 224, 232, 178, 185, 112, 104, 218, 246, 97, 228, 251, 34, 242, 193, 238, 210,
  			144, 12, 191, 179, 162, 241, 81, 51, 145, 235, 249, 14, 239, 107, 49, 192, 214, 31, 181, 199, 106, 157, 184, 84, 204, 176, 115, 121, 50, 45, 127, 4, 150, 254, 138, 236, 205, 93, 222, 114,
  			67, 29, 24, 72, 243, 141, 128, 195, 78, 66, 215, 61, 156, 180};
  
  	// To remove the need for index wrapping, double the permutation table length
  	private static int[] perm = new int[512];
  
  	static {
  		for (int i = 0; i < 512; i++)
  			perm[i] = p[i & 255];
  	}
  
  	// This method is a *lot* faster than using (int)Math.floor(x)
  	private static int fastfloor(double x) {
  		return x > 0 ? (int) x : (int) x - 1;
  	}
  
  	private static double dot(int[] g, double x, double y) {
  		return g[0] * x + g[1] * y;
  	}
  
  	private static double dot(int[] g, double x, double y, double z) {
  		return g[0] * x + g[1] * y + g[2] * z;
  	}
  
  	public static double noise2D(double xin, double yin) {
  		double n0, n1, n2;
  		// Noise contributions from the three corners
  		// Skew the input space to determine which simplex cell we're in
  		final double F2 = 0.5 * (Math.sqrt(3.0) - 1.0);
  		double s = (xin + yin) * F2;
  		// Hairy factor for 2D
  		int i = fastfloor(xin + s);
  		int j = fastfloor(yin + s);
  		final double G2 = (3.0 - Math.sqrt(3.0)) / 6.0;
  		double t = (i + j) * G2;
  		double X0 = i - t;
  		// Unskew the cell origin back to (x,y) space
  		double Y0 = j - t;
  		double x0 = xin - X0;
  		// The x,y distances from the cell origin
  		double y0 = yin - Y0;
  		// For the 2D case, the simplex shape is an equilateral triangle.
  		// Determine which simplex we are in.
  		int i1, j1;
  		// Offsets for second (middle) corner of simplex in (i,j) coords
  		if (x0 > y0) {
  			i1 = 1;
  			j1 = 0;
  		}
  		// lower triangle, XY order: (0,0)->(1,0)->(1,1)
  		else {
  			i1 = 0;
  			j1 = 1;
  		}
  		// upper triangle, YX order: (0,0)->(0,1)->(1,1)
  		// A step of (1,0) in (i,j) means a step of (1-c,-c) in (x,y), and
  		// a step of (0,1) in (i,j) means a step of (-c,1-c) in (x,y), where
  		// c = (3-sqrt(3))/6
  		double x1 = x0 - i1 + G2;
  		// Offsets for middle corner in (x,y) unskewed coords
  		double y1 = y0 - j1 + G2;
  		double x2 = x0 - 1.0 + 2.0 * G2;
  		// Offsets for last corner in (x,y) unskewed coords
  		double y2 = y0 - 1.0 + 2.0 * G2;
  		// Work out the hashed gradient indices of the three simplex corners
  		int ii = i & 255;
  		int jj = j & 255;
  		int gi0 = perm[ii + perm[jj]] % 12;
  		int gi1 = perm[ii + i1 + perm[jj + j1]] % 12;
  		int gi2 = perm[ii + 1 + perm[jj + 1]] % 12;
  		// Calculate the contribution from the three corners
  		double t0 = 0.5 - x0 * x0 - y0 * y0;
  		if (t0 < 0)
  			n0 = 0.0;
  		else {
  			t0 *= t0;
  			n0 = t0 * t0 * dot(grad3[gi0], x0, y0);
  			// (x,y) of grad3 used for 2D gradient
  		}
  		double t1 = 0.5 - x1 * x1 - y1 * y1;
  		if (t1 < 0)
  			n1 = 0.0;
  		else {
  			t1 *= t1;
  			n1 = t1 * t1 * dot(grad3[gi1], x1, y1);
  		}
  		double t2 = 0.5 - x2 * x2 - y2 * y2;
  		if (t2 < 0)
  			n2 = 0.0;
  		else {
  			t2 *= t2;
  			n2 = t2 * t2 * dot(grad3[gi2], x2, y2);
  		}
  		// Add contributions from each corner to get the final noise value.
  		// The result is scaled to return values in the interval [-1,1].
  		return 70.0 * (n0 + n1 + n2);
  	}
  
  	public static double noise3D(double xin, double yin, double zin) {
  		double n0, n1, n2, n3;
  		// Noise contributions from the four corners
  		// Skew the input space to determine which simplex cell we're in
  		final double F3 = 1.0 / 3.0;
  		double s = (xin + yin + zin) * F3;
  		// Very nice and simple skew factor for 3D
  		int i = fastfloor(xin + s);
  		int j = fastfloor(yin + s);
  		int k = fastfloor(zin + s);
  		final double G3 = 1.0 / 6.0;
  		// Very nice and simple unskew factor, too
  		double t = (i + j + k) * G3;
  		double X0 = i - t;
  		// Unskew the cell origin back to (x,y,z) space
  		double Y0 = j - t;
  		double Z0 = k - t;
  		double x0 = xin - X0;
  		// The x,y,z distances from the cell origin
  		double y0 = yin - Y0;
  		double z0 = zin - Z0;
  		// For the 3D case, the simplex shape is a slightly irregular tetrahedron.
  		// Determine which simplex we are in.
  		int i1, j1, k1;
  		// Offsets for second corner of simplex in (i,j,k) coords
  		int i2, j2, k2;
  		// Offsets for third corner of simplex in (i,j,k) coords
  		if (x0 >= y0) {
  			if (y0 >= z0) {
  				i1 = 1;
  				j1 = 0;
  				k1 = 0;
  				i2 = 1;
  				j2 = 1;
  				k2 = 0;
  			}
  			// X Y Z order
  			else if (x0 >= z0) {
  				i1 = 1;
  				j1 = 0;
  				k1 = 0;
  				i2 = 1;
  				j2 = 0;
  				k2 = 1;
  			}
  			// X Z Y order
  			else {
  				i1 = 0;
  				j1 = 0;
  				k1 = 1;
  				i2 = 1;
  				j2 = 0;
  				k2 = 1;
  			}
  			// Z X Y order
  		}
  		else {
  			// x0<y0
  			if (y0 < z0) {
  				i1 = 0;
  				j1 = 0;
  				k1 = 1;
  				i2 = 0;
  				j2 = 1;
  				k2 = 1;
  			}
  			// Z Y X order
  			else if (x0 < z0) {
  				i1 = 0;
  				j1 = 1;
  				k1 = 0;
  				i2 = 0;
  				j2 = 1;
  				k2 = 1;
  			}
  			// Y Z X order
  			else {
  				i1 = 0;
  				j1 = 1;
  				k1 = 0;
  				i2 = 1;
  				j2 = 1;
  				k2 = 0;
  			}
  			// Y X Z order
  		}
  
  		// A step of (1,0,0) in (i,j,k) means a step of (1-c,-c,-c) in (x,y,z),
  		// a step of (0,1,0) in (i,j,k) means a step of (-c,1-c,-c) in (x,y,z), and
  		// a step of (0,0,1) in (i,j,k) means a step of (-c,-c,1-c) in (x,y,z), where
  		// c = 1/6.
  		double x1 = x0 - i1 + G3;
  
  		// Offsets for second corner in (x,y,z) coords
  		double y1 = y0 - j1 + G3;
  		double z1 = z0 - k1 + G3;
  		double x2 = x0 - i2 + 2.0 * G3;
  
  		// Offsets for third corner in (x,y,z) coords
  		double y2 = y0 - j2 + 2.0 * G3;
  		double z2 = z0 - k2 + 2.0 * G3;
  		double x3 = x0 - 1.0 + 3.0 * G3;
  
  		// Offsets for last corner in (x,y,z) coords
  		double y3 = y0 - 1.0 + 3.0 * G3;
  		double z3 = z0 - 1.0 + 3.0 * G3;
  
  		// Work out the hashed gradient indices of the four simplex corners
  		int ii = i & 255;
  		int jj = j & 255;
  		int kk = k & 255;
  		int gi0 = perm[ii + perm[jj + perm[kk]]] % 12;
  		int gi1 = perm[ii + i1 + perm[jj + j1 + perm[kk + k1]]] % 12;
  		int gi2 = perm[ii + i2 + perm[jj + j2 + perm[kk + k2]]] % 12;
  		int gi3 = perm[ii + 1 + perm[jj + 1 + perm[kk + 1]]] % 12;
  
  		// Calculate the contribution from the four corners
  		double t0 = 0.6 - x0 * x0 - y0 * y0 - z0 * z0;
  		if (t0 < 0)
  			n0 = 0.0;
  		else {
  			t0 *= t0;
  			n0 = t0 * t0 * dot(grad3[gi0], x0, y0, z0);
  		}
  		double t1 = 0.6 - x1 * x1 - y1 * y1 - z1 * z1;
  		if (t1 < 0)
  			n1 = 0.0;
  		else {
  			t1 *= t1;
  			n1 = t1 * t1 * dot(grad3[gi1], x1, y1, z1);
  		}
  		double t2 = 0.6 - x2 * x2 - y2 * y2 - z2 * z2;
  		if (t2 < 0)
  			n2 = 0.0;
  		else {
  			t2 *= t2;
  			n2 = t2 * t2 * dot(grad3[gi2], x2, y2, z2);
  		}
  		double t3 = 0.6 - x3 * x3 - y3 * y3 - z3 * z3;
  		if (t3 < 0)
  			n3 = 0.0;
  		else {
  			t3 *= t3;
  			n3 = t3 * t3 * dot(grad3[gi3], x3, y3, z3);
  		}
  		// Add contributions from each corner to get the final noise value.
  		// The result is scaled to stay just inside [-1,1]
  		return 32.0 * (n0 + n1 + n2 + n3);
  	}
  }