/*
* A speed-improved simplex noise algorithm for 2D, 3D and 4D in Java.
*
* Based on example code by Stefan Gustavson (stegu@itn.liu.se).
* Optimisations by Peter Eastman (peastman@drizzle.stanford.edu).
* Better rank ordering method for 4D 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.
*
*/
package monkstone.noise;
/**
*
* @author Martin Prout
*/
public class SimplexNoise { // Simplex noise in 2D, 3D and 4D
private static Grad grad3[] = {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 Grad grad4[] = {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 short 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
static short[] PERM = new short[512];
static short[] PERM_MOD_12 = new short[512];
static {
for (int i = 0; i < 512; i++) {
PERM[i] = p[i & 255];
PERM_MOD_12[i] = (short) (PERM[i] % 12);
}
}
// Skewing and unskewing factors for 2, 3, and 4 dimensions
private static final double F2 = 0.5 * (Math.sqrt(3.0) - 1.0);
private static final double G2 = (3.0 - Math.sqrt(3.0)) / 6.0;
private static final double F3 = 1.0 / 3.0;
private static final double G3 = 1.0 / 6.0;
private static final double F4 = (Math.sqrt(5.0) - 1.0) / 4.0;
private static final double G4 = (5.0 - Math.sqrt(5.0)) / 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
/**
*
* @param xin
* @param yin
* @return noise double
*/
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 = PERM_MOD_12[ii + PERM[jj]];
int gi1 = PERM_MOD_12[ii + i1 + PERM[jj + j1]];
int gi2 = PERM_MOD_12[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
/**
*
* @param xin
* @param yin
* @param zin
* @return
*/
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 = PERM_MOD_12[ii + PERM[jj + PERM[kk]]];
int gi1 = PERM_MOD_12[ii + i1 + PERM[jj + j1 + PERM[kk + k1]]];
int gi2 = PERM_MOD_12[ii + i2 + PERM[jj + j2 + PERM[kk + k2]]];
int gi3 = PERM_MOD_12[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
/**
*
* @param x
* @param y
* @param z
* @param w
* @return noise double
*/
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
// [rankx, ranky, rankz, rankw] is a 4-vector with the numbers 0, 1, 2 and 3
// in some order. We use a thresholding to set the coordinates in turn.
// 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
// (In Java, array access is a lot slower than member access)
private static class Grad {
double x, y, z, w;
Grad(double x, double y, double z) {
this.x = x;
this.y = y;
this.z = z;
}
Grad(double x, double y, double z, double w) {
this.x = x;
this.y = y;
this.z = z;
this.w = w;
}
}
}