@spissvinkel/simplex-noise
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Simplex noise generator for JS/TS
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JavaScript
/**
* Initialize a new simplex noise generator using the provided PRNG
*
* @param random a PRNG function like `Math.random` or `AleaPRNG.random`
* @returns an initialized simplex noise generator
*/
export const mkSimplexNoise = (random) => {
const tables = buildPermutationTables(random);
return {
noise2D: (x, y) => noise2D(tables, x, y),
noise3D: (x, y, z) => noise3D(tables, x, y, z),
noise4D: (x, y, z, w) => noise4D(tables, x, y, z, w)
};
};
// 2D simplex noise
/** @internal */
const noise2D = (tables, x, y) => {
const { perm, permMod12 } = tables;
// Noise contributions from the three corners
let n0 = 0.0, n1 = 0.0, n2 = 0.0;
// Skew the input space to determine which simplex cell we're in
var s = (x + y) * F2; // Hairy factor for 2D
var i = Math.floor(x + s);
var j = Math.floor(y + s);
var t = (i + j) * G2;
// Unskew the cell origin back to (x, y) space
const x00 = i - t;
const y00 = j - t;
// The x, y distances from the cell origin
const x0 = x - x00;
const y0 = y - y00;
// For the 2D case, the simplex shape is an equilateral triangle.
// Determine which simplex we are in.
// Offsets for second (middle) corner of simplex in (i, j) coords
// lower triangle, XY order (0, 0) -> (1, 0) -> (1, 1) - or upper triangle, YX order (0, 0) -> (0, 1) -> (1, 1)
const i1 = x0 > y0 ? 1 : 0;
const j1 = x0 > y0 ? 0 : 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
// Offsets for middle corner in (x, y) unskewed coords
const x1 = x0 - i1 + G2;
const y1 = y0 - j1 + G2;
// Offsets for last corner in (x, y) unskewed coords
const x2 = x0 - 1.0 + 2.0 * G2;
const y2 = y0 - 1.0 + 2.0 * G2;
// Work out the hashed gradient indices of the three simplex corners
const ii = i & 255;
const jj = j & 255;
// Calculate the contribution from the three corners
let t0 = 0.5 - x0 * x0 - y0 * y0;
if (t0 >= 0) {
const gi0 = permMod12[ii + perm[jj]] * 3;
t0 *= t0;
// (x, y) of GRAD3 used for 2D gradient
n0 = t0 * t0 * (GRAD3[gi0] * x0 + GRAD3[gi0 + 1] * y0);
}
let t1 = 0.5 - x1 * x1 - y1 * y1;
if (t1 >= 0) {
const gi1 = permMod12[ii + i1 + perm[jj + j1]] * 3;
t1 *= t1;
n1 = t1 * t1 * (GRAD3[gi1] * x1 + GRAD3[gi1 + 1] * y1);
}
let t2 = 0.5 - x2 * x2 - y2 * y2;
if (t2 >= 0) {
const gi2 = permMod12[ii + 1 + perm[jj + 1]] * 3;
t2 *= t2;
n2 = t2 * t2 * (GRAD3[gi2] * x2 + GRAD3[gi2 + 1] * 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
/** @internal */
const noise3D = (tables, x, y, z) => {
const { perm, permMod12 } = tables;
// Noise contributions from the four corners
let n0 = 0.0, n1 = 0.0, n2 = 0.0, n3 = 0.0;
// Skew the input space to determine which simplex cell we're in
// Very nice and simple skew factor for 3D
const s = (x + y + z) * F3;
const i = Math.floor(x + s);
const j = Math.floor(y + s);
const k = Math.floor(z + s);
const t = (i + j + k) * G3;
// Unskew the cell origin back to (x, y, z) space
const x00 = i - t;
const y00 = j - t;
const z00 = k - t;
// The x, y, z distances from the cell origin
const x0 = x - x00;
const y0 = y - y00;
const z0 = z - z00;
// For the 3D case, the simplex shape is a slightly irregular tetrahedron.
// Determine which simplex we are in.
// Offsets for second corner of simplex in (i, j, k) coords
let i1, j1, k1;
// Offsets for third corner of simplex in (i, j, k) coords
let i2, j2, k2;
if (x0 >= y0) {
if (y0 >= z0) { // X Y Z order
i1 = 1;
j1 = 0;
k1 = 0;
i2 = 1;
j2 = 1;
k2 = 0;
}
else if (x0 >= z0) { // X Z Y order
i1 = 1;
j1 = 0;
k1 = 0;
i2 = 1;
j2 = 0;
k2 = 1;
}
else { // Z X Y order
i1 = 0;
j1 = 0;
k1 = 1;
i2 = 1;
j2 = 0;
k2 = 1;
}
}
else { // x0 < y0
if (y0 < z0) { // Z Y X order
i1 = 0;
j1 = 0;
k1 = 1;
i2 = 0;
j2 = 1;
k2 = 1;
}
else if (x0 < z0) { // Y Z X order
i1 = 0;
j1 = 1;
k1 = 0;
i2 = 0;
j2 = 1;
k2 = 1;
}
else { // Y X Z order
i1 = 0;
j1 = 1;
k1 = 0;
i2 = 1;
j2 = 1;
k2 = 0;
}
}
// 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.
// Offsets for second corner in (x, y, z) coords
const x1 = x0 - i1 + G3;
const y1 = y0 - j1 + G3;
const z1 = z0 - k1 + G3;
// Offsets for third corner in (x, y, z) coords
const x2 = x0 - i2 + 2.0 * G3;
const y2 = y0 - j2 + 2.0 * G3;
const z2 = z0 - k2 + 2.0 * G3;
// Offsets for last corner in (x, y, z) coords
const x3 = x0 - 1.0 + 3.0 * G3;
const y3 = y0 - 1.0 + 3.0 * G3;
const z3 = z0 - 1.0 + 3.0 * G3;
// Work out the hashed gradient indices of the four simplex corners
const ii = i & 255;
const jj = j & 255;
const kk = k & 255;
// Calculate the contribution from the four corners
let t0 = 0.6 - x0 * x0 - y0 * y0 - z0 * z0;
if (t0 >= 0) {
const gi0 = permMod12[ii + perm[jj + perm[kk]]] * 3;
t0 *= t0;
n0 = t0 * t0 * (GRAD3[gi0] * x0 + GRAD3[gi0 + 1] * y0 + GRAD3[gi0 + 2] * z0);
}
let t1 = 0.6 - x1 * x1 - y1 * y1 - z1 * z1;
if (t1 >= 0) {
const gi1 = permMod12[ii + i1 + perm[jj + j1 + perm[kk + k1]]] * 3;
t1 *= t1;
n1 = t1 * t1 * (GRAD3[gi1] * x1 + GRAD3[gi1 + 1] * y1 + GRAD3[gi1 + 2] * z1);
}
let t2 = 0.6 - x2 * x2 - y2 * y2 - z2 * z2;
if (t2 >= 0) {
const gi2 = permMod12[ii + i2 + perm[jj + j2 + perm[kk + k2]]] * 3;
t2 *= t2;
n2 = t2 * t2 * (GRAD3[gi2] * x2 + GRAD3[gi2 + 1] * y2 + GRAD3[gi2 + 2] * z2);
}
let t3 = 0.6 - x3 * x3 - y3 * y3 - z3 * z3;
if (t3 >= 0) {
var gi3 = permMod12[ii + 1 + perm[jj + 1 + perm[kk + 1]]] * 3;
t3 *= t3;
n3 = t3 * t3 * (GRAD3[gi3] * x3 + GRAD3[gi3 + 1] * y3 + GRAD3[gi3 + 2] * 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
/** @internal */
const noise4D = (tables, x, y, z, w) => {
const { perm } = tables;
// Noise contributions from the five corners
let n0 = 0.0, n1 = 0.0, n2 = 0.0, n3 = 0.0, n4 = 0.0;
// Skew the (x, y, z, w) space to determine which cell of 24 simplices we're in
// Factor for 4D skewing
const s = (x + y + z + w) * F4;
const i = Math.floor(x + s);
const j = Math.floor(y + s);
const k = Math.floor(z + s);
const l = Math.floor(w + s);
// Factor for 4D unskewing
const t = (i + j + k + l) * G4;
// Unskew the cell origin back to (x, y, z, w) space
const x00 = i - t;
const y00 = j - t;
const z00 = k - t;
const w00 = l - t;
// The x, y, z, w distances from the cell origin
const x0 = x - x00;
const y0 = y - y00;
const z0 = z - z00;
const w0 = w - w00;
// 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.
let rankx = 0;
let ranky = 0;
let rankz = 0;
let 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++;
let i1, j1, k1, l1; // The integer offsets for the second simplex corner
let i2, j2, k2, l2; // The integer offsets for the third simplex corner
let 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.
// Offsets for second corner in (x,y,z,w) coords
const x1 = x0 - i1 + G4;
const y1 = y0 - j1 + G4;
const z1 = z0 - k1 + G4;
const w1 = w0 - l1 + G4;
// Offsets for third corner in (x, y, z, w) coords
const x2 = x0 - i2 + 2.0 * G4;
const y2 = y0 - j2 + 2.0 * G4;
const z2 = z0 - k2 + 2.0 * G4;
const w2 = w0 - l2 + 2.0 * G4;
// Offsets for fourth corner in (x, y, z, w) coords
const x3 = x0 - i3 + 3.0 * G4;
const y3 = y0 - j3 + 3.0 * G4;
const z3 = z0 - k3 + 3.0 * G4;
const w3 = w0 - l3 + 3.0 * G4;
// Offsets for last corner in (x, y, z, w) coords
const x4 = x0 - 1.0 + 4.0 * G4;
const y4 = y0 - 1.0 + 4.0 * G4;
const z4 = z0 - 1.0 + 4.0 * G4;
const w4 = w0 - 1.0 + 4.0 * G4;
// Work out the hashed gradient indices of the five simplex corners
const ii = i & 255;
const jj = j & 255;
const kk = k & 255;
const ll = l & 255;
// Calculate the contribution from the five corners
let t0 = 0.6 - x0 * x0 - y0 * y0 - z0 * z0 - w0 * w0;
if (t0 >= 0) {
const gi0 = (perm[ii + perm[jj + perm[kk + perm[ll]]]] % 32) * 4;
t0 *= t0;
n0 = t0 * t0 * (GRAD4[gi0] * x0 + GRAD4[gi0 + 1] * y0 + GRAD4[gi0 + 2] * z0 + GRAD4[gi0 + 3] * w0);
}
let t1 = 0.6 - x1 * x1 - y1 * y1 - z1 * z1 - w1 * w1;
if (t1 >= 0) {
const gi1 = (perm[ii + i1 + perm[jj + j1 + perm[kk + k1 + perm[ll + l1]]]] % 32) * 4;
t1 *= t1;
n1 = t1 * t1 * (GRAD4[gi1] * x1 + GRAD4[gi1 + 1] * y1 + GRAD4[gi1 + 2] * z1 + GRAD4[gi1 + 3] * w1);
}
let t2 = 0.6 - x2 * x2 - y2 * y2 - z2 * z2 - w2 * w2;
if (t2 >= 0) {
const gi2 = (perm[ii + i2 + perm[jj + j2 + perm[kk + k2 + perm[ll + l2]]]] % 32) * 4;
t2 *= t2;
n2 = t2 * t2 * (GRAD4[gi2] * x2 + GRAD4[gi2 + 1] * y2 + GRAD4[gi2 + 2] * z2 + GRAD4[gi2 + 3] * w2);
}
let t3 = 0.6 - x3 * x3 - y3 * y3 - z3 * z3 - w3 * w3;
if (t3 >= 0) {
const gi3 = (perm[ii + i3 + perm[jj + j3 + perm[kk + k3 + perm[ll + l3]]]] % 32) * 4;
t3 *= t3;
n3 = t3 * t3 * (GRAD4[gi3] * x3 + GRAD4[gi3 + 1] * y3 + GRAD4[gi3 + 2] * z3 + GRAD4[gi3 + 3] * w3);
}
let t4 = 0.6 - x4 * x4 - y4 * y4 - z4 * z4 - w4 * w4;
if (t4 >= 0) {
const gi4 = (perm[ii + 1 + perm[jj + 1 + perm[kk + 1 + perm[ll + 1]]]] % 32) * 4;
t4 *= t4;
n4 = t4 * t4 * (GRAD4[gi4] * x4 + GRAD4[gi4 + 1] * y4 + GRAD4[gi4 + 2] * z4 + GRAD4[gi4 + 3] * w4);
}
// Sum up and scale the result to cover the range [-1,1]
return 27.0 * (n0 + n1 + n2 + n3 + n4);
};
/** @internal */
const buildPermutationTables = (random) => {
const perm = new Uint8Array(512);
const permMod12 = new Uint8Array(512);
const tmp = new Uint8Array(256);
for (let i = 0; i < 256; i++)
tmp[i] = i;
for (let i = 0; i < 255; i++) {
const r = i + ~~(random() * (256 - i));
const v = tmp[r];
tmp[r] = tmp[i];
perm[i] = perm[i + 256] = v;
permMod12[i] = permMod12[i + 256] = v % 12;
}
const v = tmp[255];
perm[255] = perm[511] = v;
permMod12[255] = permMod12[511] = v % 12;
return { perm, permMod12 };
};
/** @internal */
const F2 = 0.5 * (Math.sqrt(3.0) - 1.0);
/** @internal */
const G2 = (3.0 - Math.sqrt(3.0)) / 6.0;
/** @internal */
const F3 = 1.0 / 3.0;
/** @internal */
const G3 = 1.0 / 6.0;
/** @internal */
const F4 = (Math.sqrt(5.0) - 1.0) / 4.0;
/** @internal */
const G4 = (5.0 - Math.sqrt(5.0)) / 20.0;
/** @internal */
const GRAD3 = new Float32Array([
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
]);
/** @internal */
const GRAD4 = new Float32Array([
0, 1, 1, 1,
0, 1, 1, -1,
0, 1, -1, 1,
0, 1, -1, -1,
0, -1, 1, 1,
0, -1, 1, -1,
0, -1, -1, 1,
0, -1, -1, -1,
1, 0, 1, 1,
1, 0, 1, -1,
1, 0, -1, 1,
1, 0, -1, -1,
-1, 0, 1, 1,
-1, 0, 1, -1,
-1, 0, -1, 1,
-1, 0, -1, -1,
1, 1, 0, 1,
1, 1, 0, -1,
1, -1, 0, 1,
1, -1, 0, -1,
-1, 1, 0, 1,
-1, 1, 0, -1,
-1, -1, 0, 1,
-1, -1, 0, -1,
1, 1, 1, 0,
1, 1, -1, 0,
1, -1, 1, 0,
1, -1, -1, 0,
-1, 1, 1, 0,
-1, 1, -1, 0,
-1, -1, 1, 0,
-1, -1, -1, 0
]);
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