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Stefan Gustavson's "Simplex noise demystified" in C# + Unity3d Mathf methods.
using UnityEngine;
using System.Collections;
// copied and modified from http://webstaff.itn.liu.se/~stegu/simplexnoise/simplexnoise.pdf
public class SimplexNoise { // Simplex noise in 2D, 3D and 4D
private static int[][] grad3 = new int[][] {
new int[] {1,1,0}, new int[] {-1,1,0}, new int[] {1,-1,0}, new int[] {-1,-1,0},
new int[] {1,0,1}, new int[] {-1,0,1}, new int[] {1,0,-1}, new int[] {-1,0,-1},
new int[] {0,1,1}, new int[] {0,-1,1}, new int[] {0,1,-1}, new int[] {0,-1,-1}};
private static int[][] grad4 = new int[][] {
new int[] {0,1,1,1}, new int[] {0,1,1,-1}, new int[] {0,1,-1,1}, new int[] {0,1,-1,-1},
new int[] {0,-1,1,1}, new int[] {0,-1,1,-1}, new int[] {0,-1,-1,1}, new int[] {0,-1,-1,-1},
new int[] {1,0,1,1}, new int[] {1,0,1,-1}, new int[] {1,0,-1,1}, new int[] {1,0,-1,-1},
new int[] {-1,0,1,1}, new int[] {-1,0,1,-1}, new int[] {-1,0,-1,1}, new int[] {-1,0,-1,-1},
new int[] {1,1,0,1}, new int[] {1,1,0,-1}, new int[] {1,-1,0,1}, new int[] {1,-1,0,-1},
new int[] {-1,1,0,1}, new int[] {-1,1,0,-1}, new int[] {-1,-1,0,1}, new int[] {-1,-1,0,-1},
new int[] {1,1,1,0}, new int[] {1,1,-1,0}, new int[] {1,-1,1,0}, new int[] {1,-1,-1,0},
new int[] {-1,1,1,0}, new int[] {-1,1,-1,0}, new int[] {-1,-1,1,0}, new int[] {-1,-1,-1,0}};
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 SimplexNoise() { for(int i=0; i<512; i++) perm[i]=p[i & 255]; } // moved to constructor
// A lookup table to traverse the simplex around a given point in 4D.
// Details can be found where this table is used, in the 4D noise method.
private static int[][] simplex = new int[][] {
new int[] {0,1,2,3}, new int[] {0,1,3,2}, new int[] {0,0,0,0}, new int[] {0,2,3,1}, new int[] {0,0,0,0}, new int[] {0,0,0,0}, new int[] {0,0,0,0}, new int[] {1,2,3,0},
new int[] {0,2,1,3}, new int[] {0,0,0,0}, new int[] {0,3,1,2}, new int[] {0,3,2,1}, new int[] {0,0,0,0}, new int[] {0,0,0,0}, new int[] {0,0,0,0}, new int[] {1,3,2,0},
new int[] {0,0,0,0}, new int[] {0,0,0,0}, new int[] {0,0,0,0}, new int[] {0,0,0,0}, new int[] {0,0,0,0}, new int[] {0,0,0,0}, new int[] {0,0,0,0}, new int[] {0,0,0,0},
new int[] {1,2,0,3}, new int[] {0,0,0,0}, new int[] {1,3,0,2}, new int[] {0,0,0,0}, new int[] {0,0,0,0}, new int[] {0,0,0,0}, new int[] {2,3,0,1}, new int[] {2,3,1,0},
new int[] {1,0,2,3}, new int[] {1,0,3,2}, new int[] {0,0,0,0}, new int[] {0,0,0,0}, new int[] {0,0,0,0}, new int[] {2,0,3,1}, new int[] {0,0,0,0}, new int[] {2,1,3,0},
new int[] {0,0,0,0}, new int[] {0,0,0,0}, new int[] {0,0,0,0}, new int[] {0,0,0,0}, new int[] {0,0,0,0}, new int[] {0,0,0,0}, new int[] {0,0,0,0}, new int[] {0,0,0,0},
new int[] {2,0,1,3}, new int[] {0,0,0,0}, new int[] {0,0,0,0}, new int[] {0,0,0,0}, new int[] {3,0,1,2}, new int[] {3,0,2,1}, new int[] {0,0,0,0}, new int[] {3,1,2,0},
new int[] {2,1,0,3}, new int[] {0,0,0,0}, new int[] {0,0,0,0}, new int[] {0,0,0,0}, new int[] {3,1,0,2}, new int[] {0,0,0,0}, new int[] {3,2,0,1}, new int[] {3,2,1,0}};
// This method is a *lot* faster than using (int)Mathf.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; }
private static double dot(int[] g, double x, double y, double z, double w) {
return g[0]*x + g[1]*y + g[2]*z + g[3]*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 F2 = 0.5*(Mathf.Sqrt(3.0f)-1.0);
double s = (xin+yin)*F2; // Hairy factor for 2D
int i = fastfloor(xin+s);
int j = fastfloor(yin+s);
double G2 = (3.0-Mathf.Sqrt(3.0f))/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);
}
// 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 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);
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);
} // 4D simplex noise
double noise(double x, double y, double z, double w) {
// The skewing and unskewing factors are hairy again for the 4D case
double F4 = (Mathf.Sqrt(5.0f)-1.0)/4.0;
double G4 = (5.0-Mathf.Sqrt(5.0f))/20.0;
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.
// The method below is a good way of finding the ordering of x,y,z,w and
// then find the correct traversal order for the simplex we’re in.
// First, six pair-wise comparisons are performed between each possible pair
// of the four coordinates, and the results are used to add up binary bits
// for an integer index.
int c1 = (x0 > y0) ? 32 : 0;
int c2 = (x0 > z0) ? 16 : 0;
int c3 = (y0 > z0) ? 8 : 0;
int c4 = (x0 > w0) ? 4 : 0;
int c5 = (y0 > w0) ? 2 : 0;
int c6 = (z0 > w0) ? 1 : 0;
int c = c1 + c2 + c3 + c4 + c5 + c6;
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.
// The number 3 in the "simplex" array is at the position of the largest coordinate.
i1 = simplex[c][0]>=3 ? 1 : 0;
j1 = simplex[c][1]>=3 ? 1 : 0;
k1 = simplex[c][2]>=3 ? 1 : 0;
l1 = simplex[c][3]>=3 ? 1 : 0;
// The number 2 in the "simplex" array is at the second largest coordinate.
i2 = simplex[c][0]>=2 ? 1 : 0;
j2 = simplex[c][1]>=2 ? 1 : 0; k2 = simplex[c][2]>=2 ? 1 : 0;
l2 = simplex[c][3]>=2 ? 1 : 0;
// The number 1 in the "simplex" array is at the second smallest coordinate.
i3 = simplex[c][0]>=1 ? 1 : 0;
j3 = simplex[c][1]>=1 ? 1 : 0;
k3 = simplex[c][2]>=1 ? 1 : 0;
l3 = simplex[c][3]>=1 ? 1 : 0;
// The fifth corner has all coordinate offsets = 1, so no need to look that up.
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 = 0.6 - 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 = 0.6 - 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 = 0.6 - 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 = 0.6 - 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 = 0.6 - 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);
}
}
@tinjaw

I have tried using this and I am getting zeros when x and y are opposite values. (0,0) (1,-1) (2, -2) (-3,3) (-5,-5).

I have no idea how to debug this. I am a beginner and just Googled for Simplex Noise.

Have you noticed this and corrected this code?

@sgeos

Returning zero for whole number inputs is not necessarily a bug.
(3, 0, 0) -> 0.0
(3, 1, 2) -> 0.0

The noise function is typically called with fractional inputs. Results from a version written in Elixir.
(0/3, 0, 0) -> 0.0
(1/3, 0, 0) -> 0.25921480465376207
(2/3, 0, 0) -> 2.0322105370121734e-4
(3/3, 0, 0) -> -0.3215020576131685

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