SimplexNoiseRevised.cs

using UnityEngine;
using System.Collections;

namespace Gist {
/*
 * A speed-improved simplex noise algorithm for 2D, 3D and 4D in Java.
 *
 * Based on example code by Stefan Gustavson ([email protected]).
 * Optimisations by Peter Eastman ([email protected]).
 * Better rank ordering method by Stefan Gustavson in 2012.
 *
 * This could be speeded up even further, but it's useful as it is.
 *
 * Version 2012-03-09
 *
 * This code was placed in the public domain by its original author,
 * Stefan Gustavson. You may use it as you see fit, but
 * attribution is appreciated.
 *
 */
	
	public static class SimplexNoise {  // Simplex noise in 2D, 3D and 4D
		private static readonly Grad[] grad3 = new Grad[]{
			new Grad(1,1,0),new Grad(-1,1,0),new Grad(1,-1,0),new Grad(-1,-1,0),
			new Grad(1,0,1),new Grad(-1,0,1),new Grad(1,0,-1),new Grad(-1,0,-1),
			new Grad(0,1,1),new Grad(0,-1,1),new Grad(0,1,-1),new Grad(0,-1,-1)};
		
		private static readonly Grad[] grad4 = new Grad[]{
			new Grad(0,1,1,1),new Grad(0,1,1,-1),new Grad(0,1,-1,1),new Grad(0,1,-1,-1),
			new Grad(0,-1,1,1),new Grad(0,-1,1,-1),new Grad(0,-1,-1,1),new Grad(0,-1,-1,-1),
			new Grad(1,0,1,1),new Grad(1,0,1,-1),new Grad(1,0,-1,1),new Grad(1,0,-1,-1),
			new Grad(-1,0,1,1),new Grad(-1,0,1,-1),new Grad(-1,0,-1,1),new Grad(-1,0,-1,-1),
			new Grad(1,1,0,1),new Grad(1,1,0,-1),new Grad(1,-1,0,1),new Grad(1,-1,0,-1),
			new Grad(-1,1,0,1),new Grad(-1,1,0,-1),new Grad(-1,-1,0,1),new Grad(-1,-1,0,-1),
			new Grad(1,1,1,0),new Grad(1,1,-1,0),new Grad(1,-1,1,0),new Grad(1,-1,-1,0),
			new Grad(-1,1,1,0),new Grad(-1,1,-1,0),new Grad(-1,-1,1,0),new Grad(-1,-1,-1,0)};
		
		private static readonly short[] p = new short[]{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 readonly short[] perm = new short[512];
		private static readonly short[] permMod12 = new short[512];
		static SimplexNoise() {
			for(int i=0; i<512; i++)
			{
				perm[i]=p[i & 255];
				permMod12[i] = (short)(perm[i] % 12);
			}
		}
		
		// Skewing and unskewing factors for 2, 3, and 4 dimensions
		private const double SQRT3 = 1.73205080757;
		private const double SQRT5 = 2.2360679775;
		private const double F2 = 0.5*(SQRT3-1.0);
		private const double G2 = (3.0-SQRT3)/6.0;
		private const double F3 = 1.0/3.0;
		private const double G3 = 1.0/6.0;
		private const double F4 = (SQRT5-1.0)/4.0;
		private const double G4 = (5.0-SQRT5)/20.0;
		
		// This method is a *lot* faster than using (int)Math.floor(x)
		private static int fastfloor(double x) {
			int xi = (int)x;
			return x<xi ? xi-1 : xi;
		}
		
		private static double dot(Grad g, double x, double y) {
			return g.x*x + g.y*y; }
		
		private static double dot(Grad g, double x, double y, double z) {
			return g.x*x + g.y*y + g.z*z; }
		
		private static double dot(Grad g, double x, double y, double z, double w) {
			return g.x*x + g.y*y + g.z*z + g.w*w; }
		
		
		// 2D simplex noise
		public static double Noise(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
			double s = (xin+yin)*F2; // Hairy factor for 2D
			int i = fastfloor(xin+s);
			int j = fastfloor(yin+s);
			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 = permMod12[ii+perm[jj]];
			int gi1 = permMod12[ii+i1+perm[jj+j1]];
			int gi2 = permMod12[ii+1+perm[jj+1]];
			// 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);
		}
		
		
		// 3D simplex noise
		public static double Noise(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
			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);
			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 = permMod12[ii+perm[jj+perm[kk]]];
			int gi1 = permMod12[ii+i1+perm[jj+j1+perm[kk+k1]]];
			int gi2 = permMod12[ii+i2+perm[jj+j2+perm[kk+k2]]];
			int gi3 = permMod12[ii+1+perm[jj+1+perm[kk+1]]];
			// Calculate the contribution from the four corners
			double t0 = 0.5 - 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 = 0.5 - 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 = 0.5 - 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 = 0.5 - 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);
		}
		
		
		// 4D simplex noise, better simplex rank ordering method 2012-03-09
		public static double Noise(double x, double y, double z, double w) {
			
			double n0, n1, n2, n3, n4; // Noise contributions from the five corners
			// Skew the (x,y,z,w) space to determine which cell of 24 simplices we're in
			double s = (x + y + z + w) * F4; // Factor for 4D skewing
			int i = fastfloor(x + s);
			int j = fastfloor(y + s);
			int k = fastfloor(z + s);
			int l = fastfloor(w + s);
			double t = (i + j + k + l) * G4; // Factor for 4D unskewing
			double X0 = i - t; // Unskew the cell origin back to (x,y,z,w) space
			double Y0 = j - t;
			double Z0 = k - t;
			double W0 = l - t;
			double x0 = x - X0;  // The x,y,z,w distances from the cell origin
			double y0 = y - Y0;
			double z0 = z - Z0;
			double w0 = w - W0;
			// For the 4D case, the simplex is a 4D shape I won't even try to describe.
			// To find out which of the 24 possible simplices we're in, we need to
			// determine the magnitude ordering of x0, y0, z0 and w0.
			// Six pair-wise comparisons are performed between each possible pair
			// of the four coordinates, and the results are used to rank the numbers.
			int rankx = 0;
			int ranky = 0;
			int rankz = 0;
			int rankw = 0;
			if(x0 > y0) rankx++; else ranky++;
			if(x0 > z0) rankx++; else rankz++;
			if(x0 > w0) rankx++; else rankw++;
			if(y0 > z0) ranky++; else rankz++;
			if(y0 > w0) ranky++; else rankw++;
			if(z0 > w0) rankz++; else rankw++;
			int i1, j1, k1, l1; // The integer offsets for the second simplex corner
			int i2, j2, k2, l2; // The integer offsets for the third simplex corner
			int i3, j3, k3, l3; // The integer offsets for the fourth simplex corner
			// simplex[c] is a 4-vector with the numbers 0, 1, 2 and 3 in some order.
			// Many values of c will never occur, since e.g. x>y>z>w makes x<z, y<w and x<w
			// impossible. Only the 24 indices which have non-zero entries make any sense.
			// We use a thresholding to set the coordinates in turn from the largest magnitude.
			// Rank 3 denotes the largest coordinate.
			i1 = rankx >= 3 ? 1 : 0;
			j1 = ranky >= 3 ? 1 : 0;
			k1 = rankz >= 3 ? 1 : 0;
			l1 = rankw >= 3 ? 1 : 0;
			// Rank 2 denotes the second largest coordinate.
			i2 = rankx >= 2 ? 1 : 0;
			j2 = ranky >= 2 ? 1 : 0;
			k2 = rankz >= 2 ? 1 : 0;
			l2 = rankw >= 2 ? 1 : 0;
			// Rank 1 denotes the second smallest coordinate.
			i3 = rankx >= 1 ? 1 : 0;
			j3 = ranky >= 1 ? 1 : 0;
			k3 = rankz >= 1 ? 1 : 0;
			l3 = rankw >= 1 ? 1 : 0;
			// The fifth corner has all coordinate offsets = 1, so no need to compute that.
			double x1 = x0 - i1 + G4; // Offsets for second corner in (x,y,z,w) coords
			double y1 = y0 - j1 + G4;
			double z1 = z0 - k1 + G4;
			double w1 = w0 - l1 + G4;
			double x2 = x0 - i2 + 2.0*G4; // Offsets for third corner in (x,y,z,w) coords
			double y2 = y0 - j2 + 2.0*G4;
			double z2 = z0 - k2 + 2.0*G4;
			double w2 = w0 - l2 + 2.0*G4;
			double x3 = x0 - i3 + 3.0*G4; // Offsets for fourth corner in (x,y,z,w) coords
			double y3 = y0 - j3 + 3.0*G4;
			double z3 = z0 - k3 + 3.0*G4;
			double w3 = w0 - l3 + 3.0*G4;
			double x4 = x0 - 1.0 + 4.0*G4; // Offsets for last corner in (x,y,z,w) coords
			double y4 = y0 - 1.0 + 4.0*G4;
			double z4 = z0 - 1.0 + 4.0*G4;
			double w4 = w0 - 1.0 + 4.0*G4;
			// Work out the hashed gradient indices of the five simplex corners
			int ii = i & 255;
			int jj = j & 255;
			int kk = k & 255;
			int ll = l & 255;
			int gi0 = perm[ii+perm[jj+perm[kk+perm[ll]]]] % 32;
			int gi1 = perm[ii+i1+perm[jj+j1+perm[kk+k1+perm[ll+l1]]]] % 32;
			int gi2 = perm[ii+i2+perm[jj+j2+perm[kk+k2+perm[ll+l2]]]] % 32;
			int gi3 = perm[ii+i3+perm[jj+j3+perm[kk+k3+perm[ll+l3]]]] % 32;
			int gi4 = perm[ii+1+perm[jj+1+perm[kk+1+perm[ll+1]]]] % 32;
			// Calculate the contribution from the five corners
			double t0 = 0.5 - x0*x0 - y0*y0 - z0*z0 - w0*w0;
			if(t0<0) n0 = 0.0;
			else {
				t0 *= t0;
				n0 = t0 * t0 * dot(grad4[gi0], x0, y0, z0, w0);
			}
			double t1 = 0.5 - x1*x1 - y1*y1 - z1*z1 - w1*w1;
			if(t1<0) n1 = 0.0;
			else {
				t1 *= t1;
				n1 = t1 * t1 * dot(grad4[gi1], x1, y1, z1, w1);
			}
			double t2 = 0.5 - x2*x2 - y2*y2 - z2*z2 - w2*w2;
			if(t2<0) n2 = 0.0;
			else {
				t2 *= t2;
				n2 = t2 * t2 * dot(grad4[gi2], x2, y2, z2, w2);
			}
			double t3 = 0.5 - x3*x3 - y3*y3 - z3*z3 - w3*w3;
			if(t3<0) n3 = 0.0;
			else {
				t3 *= t3;
				n3 = t3 * t3 * dot(grad4[gi3], x3, y3, z3, w3);
			}
			double t4 = 0.5 - x4*x4 - y4*y4 - z4*z4 - w4*w4;
			if(t4<0) n4 = 0.0;
			else {
				t4 *= t4;
				n4 = t4 * t4 * dot(grad4[gi4], x4, y4, z4, w4);
			}
			// Sum up and scale the result to cover the range [-1,1]
			return 27.0 * (n0 + n1 + n2 + n3 + n4);
		}
		
		// Inner class to speed upp gradient computations
		// (array access is a lot slower than member access)
		public struct Grad {
			public double x, y, z, w;
			
			public Grad(double x, double y, double z) : this(x, y, z, 0) {}			
			public Grad(double x, double y, double z, double w)
			{
				this.x = x;
				this.y = y;
				this.z = z;
				this.w = w;
			}
		}
	}
}
 * Optimisations by Peter Eastman ([email protected]).
 * Better rank ordering method by Stefan Gustavson in 2012.
 *
 * This could be speeded up even further, but it's useful as it is.
 *
 * Version 2012-03-09
 *
 * This code was placed in the public domain by its original author,
 * Stefan Gustavson. You may use it as you see fit, but
 * attribution is appreciated.
 *
 */
	
	public static class SimplexNoise {  // Simplex noise in 2D, 3D and 4D
		private static readonly Grad[] grad3 = new Grad[]{
			new Grad(1,1,0),new Grad(-1,1,0),new Grad(1,-1,0),new Grad(-1,-1,0),
			new Grad(1,0,1),new Grad(-1,0,1),new Grad(1,0,-1),new Grad(-1,0,-1),
			new Grad(0,1,1),new Grad(0,-1,1),new Grad(0,1,-1),new Grad(0,-1,-1)};
		
		private static readonly Grad[] grad4 = new Grad[]{
			new Grad(0,1,1,1),new Grad(0,1,1,-1),new Grad(0,1,-1,1),new Grad(0,1,-1,-1),
			new Grad(0,-1,1,1),new Grad(0,-1,1,-1),new Grad(0,-1,-1,1),new Grad(0,-1,-1,-1),
			new Grad(1,0,1,1),new Grad(1,0,1,-1),new Grad(1,0,-1,1),new Grad(1,0,-1,-1),
			new Grad(-1,0,1,1),new Grad(-1,0,1,-1),new Grad(-1,0,-1,1),new Grad(-1,0,-1,-1),
			new Grad(1,1,0,1),new Grad(1,1,0,-1),new Grad(1,-1,0,1),new Grad(1,-1,0,-1),
			new Grad(-1,1,0,1),new Grad(-1,1,0,-1),new Grad(-1,-1,0,1),new Grad(-1,-1,0,-1),
			new Grad(1,1,1,0),new Grad(1,1,-1,0),new Grad(1,-1,1,0),new Grad(1,-1,-1,0),
			new Grad(-1,1,1,0),new Grad(-1,1,-1,0),new Grad(-1,-1,1,0),new Grad(-1,-1,-1,0)};
		
		private static readonly short[] p = new short[]{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 readonly short[] perm = new short[512];
		private static readonly short[] permMod12 = new short[512];
		static SimplexNoise() {
			for(int i=0; i<512; i++)
			{
				perm[i]=p[i & 255];
				permMod12[i] = (short)(perm[i] % 12);
			}
		}
		
		// Skewing and unskewing factors for 2, 3, and 4 dimensions
		private const double SQRT3 = 1.73205080757;
		private const double SQRT5 = 2.2360679775;
		private const double F2 = 0.5*(SQRT3-1.0);
		private const double G2 = (3.0-SQRT3)/6.0;
		private const double F3 = 1.0/3.0;
		private const double G3 = 1.0/6.0;
		private const double F4 = (SQRT5-1.0)/4.0;
		private const double G4 = (5.0-SQRT5)/20.0;
		
		// This method is a *lot* faster than using (int)Math.floor(x)
		private static int fastfloor(double x) {
			int xi = (int)x;
			return x<xi ? xi-1 : xi;
		}
		
		private static double dot(Grad g, double x, double y) {
			return g.x*x + g.y*y; }
		
		private static double dot(Grad g, double x, double y, double z) {
			return g.x*x + g.y*y + g.z*z; }
		
		private static double dot(Grad g, double x, double y, double z, double w) {
			return g.x*x + g.y*y + g.z*z + g.w*w; }
		
		
		// 2D simplex noise
		public static double Noise(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
			double s = (xin+yin)*F2; // Hairy factor for 2D
			int i = fastfloor(xin+s);
			int j = fastfloor(yin+s);
			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 = permMod12[ii+perm[jj]];
			int gi1 = permMod12[ii+i1+perm[jj+j1]];
			int gi2 = permMod12[ii+1+perm[jj+1]];
			// 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);
		}
		
		
		// 3D simplex noise
		public static double Noise(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
			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);
			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 = permMod12[ii+perm[jj+perm[kk]]];
			int gi1 = permMod12[ii+i1+perm[jj+j1+perm[kk+k1]]];
			int gi2 = permMod12[ii+i2+perm[jj+j2+perm[kk+k2]]];
			int gi3 = permMod12[ii+1+perm[jj+1+perm[kk+1]]];
			// Calculate the contribution from the four corners
			double t0 = 0.5 - 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 = 0.5 - 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 = 0.5 - 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 = 0.5 - 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);
		}
		
		
		// 4D simplex noise, better simplex rank ordering method 2012-03-09
		public static double Noise(double x, double y, double z, double w) {
			
			double n0, n1, n2, n3, n4; // Noise contributions from the five corners
			// Skew the (x,y,z,w) space to determine which cell of 24 simplices we're in
			double s = (x + y + z + w) * F4; // Factor for 4D skewing
			int i = fastfloor(x + s);
			int j = fastfloor(y + s);
			int k = fastfloor(z + s);
			int l = fastfloor(w + s);
			double t = (i + j + k + l) * G4; // Factor for 4D unskewing
			double X0 = i - t; // Unskew the cell origin back to (x,y,z,w) space
			double Y0 = j - t;
			double Z0 = k - t;
			double W0 = l - t;
			double x0 = x - X0;  // The x,y,z,w distances from the cell origin
			double y0 = y - Y0;
			double z0 = z - Z0;
			double w0 = w - W0;
			// For the 4D case, the simplex is a 4D shape I won't even try to describe.
			// To find out which of the 24 possible simplices we're in, we need to
			// determine the magnitude ordering of x0, y0, z0 and w0.
			// Six pair-wise comparisons are performed between each possible pair
			// of the four coordinates, and the results are used to rank the numbers.
			int rankx = 0;
			int ranky = 0;
			int rankz = 0;
			int rankw = 0;
			if(x0 > y0) rankx++; else ranky++;
			if(x0 > z0) rankx++; else rankz++;
			if(x0 > w0) rankx++; else rankw++;
			if(y0 > z0) ranky++; else rankz++;
			if(y0 > w0) ranky++; else rankw++;
			if(z0 > w0) rankz++; else rankw++;
			int i1, j1, k1, l1; // The integer offsets for the second simplex corner
			int i2, j2, k2, l2; // The integer offsets for the third simplex corner
			int i3, j3, k3, l3; // The integer offsets for the fourth simplex corner
			// simplex[c] is a 4-vector with the numbers 0, 1, 2 and 3 in some order.
			// Many values of c will never occur, since e.g. x>y>z>w makes x<z, y<w and x<w
			// impossible. Only the 24 indices which have non-zero entries make any sense.
			// We use a thresholding to set the coordinates in turn from the largest magnitude.
			// Rank 3 denotes the largest coordinate.
			i1 = rankx >= 3 ? 1 : 0;
			j1 = ranky >= 3 ? 1 : 0;
			k1 = rankz >= 3 ? 1 : 0;
			l1 = rankw >= 3 ? 1 : 0;
			// Rank 2 denotes the second largest coordinate.
			i2 = rankx >= 2 ? 1 : 0;
			j2 = ranky >= 2 ? 1 : 0;
			k2 = rankz >= 2 ? 1 : 0;
			l2 = rankw >= 2 ? 1 : 0;
			// Rank 1 denotes the second smallest coordinate.
			i3 = rankx >= 1 ? 1 : 0;
			j3 = ranky >= 1 ? 1 : 0;
			k3 = rankz >= 1 ? 1 : 0;
			l3 = rankw >= 1 ? 1 : 0;
			// The fifth corner has all coordinate offsets = 1, so no need to compute that.
			double x1 = x0 - i1 + G4; // Offsets for second corner in (x,y,z,w) coords
			double y1 = y0 - j1 + G4;
			double z1 = z0 - k1 + G4;
			double w1 = w0 - l1 + G4;
			double x2 = x0 - i2 + 2.0*G4; // Offsets for third corner in (x,y,z,w) coords
			double y2 = y0 - j2 + 2.0*G4;
			double z2 = z0 - k2 + 2.0*G4;
			double w2 = w0 - l2 + 2.0*G4;
			double x3 = x0 - i3 + 3.0*G4; // Offsets for fourth corner in (x,y,z,w) coords
			double y3 = y0 - j3 + 3.0*G4;
			double z3 = z0 - k3 + 3.0*G4;
			double w3 = w0 - l3 + 3.0*G4;
			double x4 = x0 - 1.0 + 4.0*G4; // Offsets for last corner in (x,y,z,w) coords
			double y4 = y0 - 1.0 + 4.0*G4;
			double z4 = z0 - 1.0 + 4.0*G4;
			double w4 = w0 - 1.0 + 4.0*G4;
			// Work out the hashed gradient indices of the five simplex corners
			int ii = i & 255;
			int jj = j & 255;
			int kk = k & 255;
			int ll = l & 255;
			int gi0 = perm[ii+perm[jj+perm[kk+perm[ll]]]] % 32;
			int gi1 = perm[ii+i1+perm[jj+j1+perm[kk+k1+perm[ll+l1]]]] % 32;
			int gi2 = perm[ii+i2+perm[jj+j2+perm[kk+k2+perm[ll+l2]]]] % 32;
			int gi3 = perm[ii+i3+perm[jj+j3+perm[kk+k3+perm[ll+l3]]]] % 32;
			int gi4 = perm[ii+1+perm[jj+1+perm[kk+1+perm[ll+1]]]] % 32;
			// Calculate the contribution from the five corners
			double t0 = 0.5 - x0*x0 - y0*y0 - z0*z0 - w0*w0;
			if(t0<0) n0 = 0.0;
			else {
				t0 *= t0;
				n0 = t0 * t0 * dot(grad4[gi0], x0, y0, z0, w0);
			}
			double t1 = 0.5 - x1*x1 - y1*y1 - z1*z1 - w1*w1;
			if(t1<0) n1 = 0.0;
			else {
				t1 *= t1;
				n1 = t1 * t1 * dot(grad4[gi1], x1, y1, z1, w1);
			}
			double t2 = 0.5 - x2*x2 - y2*y2 - z2*z2 - w2*w2;
			if(t2<0) n2 = 0.0;
			else {
				t2 *= t2;
				n2 = t2 * t2 * dot(grad4[gi2], x2, y2, z2, w2);
			}
			double t3 = 0.5 - x3*x3 - y3*y3 - z3*z3 - w3*w3;
			if(t3<0) n3 = 0.0;
			else {
				t3 *= t3;
				n3 = t3 * t3 * dot(grad4[gi3], x3, y3, z3, w3);
			}
			double t4 = 0.5 - x4*x4 - y4*y4 - z4*z4 - w4*w4;
			if(t4<0) n4 = 0.0;
			else {
				t4 *= t4;
				n4 = t4 * t4 * dot(grad4[gi4], x4, y4, z4, w4);
			}
			// Sum up and scale the result to cover the range [-1,1]
			return 27.0 * (n0 + n1 + n2 + n3 + n4);
		}
		
		// Inner class to speed upp gradient computations
		// (array access is a lot slower than member access)
		public struct Grad {
			public double x, y, z, w;
			
			public Grad(double x, double y, double z) : this(x, y, z, 0) {}			
			public Grad(double x, double y, double z, double w)
			{
				this.x = x;
				this.y = y;
				this.z = z;
				this.w = w;
			}
		}
	}
}