simplex.js

/**
 * Based on Stefan Gustavson's (stegu@itn.liu.se) implementation and Peter
 * Eastman's optimization (peastman@drizzle.stanford.edu) in Java (09/03/2012).
 * 
 * Source: https://weber.itn.liu.se/~stegu/simplexnoise/SimplexNoise.java
 * 
 * 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.
 * 
 * JavaScript version by Leonardo de S.L.F, 17/10/2021 (http://leodeslf.com/).
 */

function dot2(g, x, y) {
  return g.x * x + g.y * y;
}

function dot3(g, x, y, z) {
  return g.x * x + g.y * y + g.z * z;
}

function dot4(g, x, y, z, w) {
  return g.x * x + g.y * y + g.z * z + g.w * w;
}

class Grad3 {
  constructor(x, y, z) {
    this.x = x;
    this.y = y;
    this.z = z;
  }
}

class Grad4 {
  constructor(x, y, z, w) {
    this.x = x;
    this.y = y;
    this.z = z;
    this.w = w;
  }
}

const grad3 = [
  new Grad3(+1, +1, +0), new Grad3(-1, +1, +0), new Grad3(+1, -1, +0),
  new Grad3(-1, -1, +0), new Grad3(+1, +0, +1), new Grad3(-1, +0, +1),
  new Grad3(+1, +0, -1), new Grad3(-1, +0, -1), new Grad3(+0, +1, +1),
  new Grad3(+0, -1, +1), new Grad3(+0, +1, -1), new Grad3(+0, -1, -1)
];

const grad4 = [
  new Grad4(+0, +1, +1, +1), new Grad4(+0, +1, +1, -1),
  new Grad4(+0, +1, -1, +1), new Grad4(+0, +1, -1, -1),
  new Grad4(+0, -1, +1, +1), new Grad4(+0, -1, +1, -1),
  new Grad4(+0, -1, -1, +1), new Grad4(+0, -1, -1, -1),
  new Grad4(+1, +0, +1, +1), new Grad4(+1, +0, +1, -1),
  new Grad4(+1, +0, -1, +1), new Grad4(+1, +0, -1, -1),
  new Grad4(-1, +0, +1, +1), new Grad4(-1, +0, +1, -1),
  new Grad4(-1, +0, -1, +1), new Grad4(-1, +0, -1, -1),
  new Grad4(+1, +1, +0, +1), new Grad4(+1, +1, +0, -1),
  new Grad4(+1, -1, +0, +1), new Grad4(+1, -1, +0, -1),
  new Grad4(-1, +1, +0, +1), new Grad4(-1, +1, +0, -1),
  new Grad4(-1, -1, +0, +1), new Grad4(-1, -1, +0, -1),
  new Grad4(+1, +1, +1, +0), new Grad4(+1, +1, -1, +0),
  new Grad4(+1, -1, +1, +0), new Grad4(+1, -1, -1, +0),
  new Grad4(-1, +1, +1, +0), new Grad4(-1, +1, -1, +0),
  new Grad4(-1, -1, +1, +0), new Grad4(-1, -1, -1, +0)
];

// Permutation table.
const 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.
const perm = [];
const permMod12 = [];
for (let i = 0; i < 512; i++) {
  perm[i] = p[i & 255];
  permMod12[i] = perm[i] % 12;
}

// Skewing and unskewing factors for 2, 3, and 4 dimensions.
const F2 = .5 * (Math.sqrt(3) - 1);
const G2 = (3 - Math.sqrt(3)) / 6;
const F3 = 1 / 3;
const G3 = 1 / 6;
const F4 = (Math.sqrt(5) - 1) / 4;
const G4 = (5 - Math.sqrt(5)) / 20;

// 2D simplex noise.
function simplex2D(x, y) {
  let n0, n1, n2; // Noise contributions from the three corners.

  // Skew the input space to determine which simplex cell we're in.
  const s = (x + y) * F2; // Hairy factor for 2D.

  const i = Math.floor(x + s);
  const j = Math.floor(y + s);

  const t = (i + j) * G2;

  const X0 = i - t; // Unskew the cell origin back to (x,y) space.
  const Y0 = j - t;

  const x0 = x - X0; // The x,y distances from the cell origin.
  const y0 = y - Y0;

  // For the 2D case, the simplex shape is an equilateral triangle.
  // Determine which simplex we are in.

  let 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.
   */

  const x1 = x0 - i1 + G2; // Offsets for middle corner in (x,y) unskewed coords.
  const y1 = y0 - j1 + G2;

  const x2 = x0 - 1.0 + 2.0 * G2; // Offsets for last corner in (x,y) unskewed coords.
  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;

  const gi0 = permMod12[ii + perm[jj]];
  const gi1 = permMod12[ii + i1 + perm[jj + j1]];
  const gi2 = permMod12[ii + 1 + perm[jj + 1]];

  // Calculate the contribution from the three corners.
  let t0 = 0.5 - x0 * x0 - y0 * y0;
  if (t0 < 0) n0 = 0.0;
  else {
    t0 *= t0;
    n0 = t0 * t0 * dot2(grad3[gi0], x0, y0); // (x,y) of grad3 used for 2D gradient.
  }

  let t1 = 0.5 - x1 * x1 - y1 * y1;
  if (t1 < 0) n1 = 0.0;
  else {
    t1 *= t1;
    n1 = t1 * t1 * dot2(grad3[gi1], x1, y1);
  }

  let t2 = 0.5 - x2 * x2 - y2 * y2;
  if (t2 < 0) n2 = 0.0;
  else {
    t2 *= t2;
    n2 = t2 * t2 * dot2(grad3[gi2], x2, y2);
  }

  // Add contributions from each corner to get the final noise2D value.
  // The result is scaled to return values in the interval [-1,1].
  return 70.0 * (n0 + n1 + n2);
}

// 3D simplex noise
function simplex3D(x, y, z) {
  let n0, n1, n2, n3; // Noise contributions from the four corners.

  // Skew the input space to determine which simplex cell we're in.
  const s = (x + y + z) * F3; // Very nice and simple skew factor for 3D.

  const i = Math.floor(x + s);
  const j = Math.floor(y + s);
  const k = Math.floor(z + s);

  const t = (i + j + k) * G3;

  const X0 = i - t; // Unskew the cell origin back to (x,y,z) space.
  const Y0 = j - t;
  const Z0 = k - t;

  const x0 = x - X0; // The x,y,z distances from the cell origin.
  const y0 = y - Y0;
  const z0 = z - Z0;

  // For the 3D case, the simplex shape is a slightly irregular tetrahedron.
  // Determine which simplex we are in.
  let i1, j1, k1; // Offsets for second corner of simplex in (i,j,k) coords.
  let 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 {
    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.
   */

  const x1 = x0 - i1 + G3; // Offsets for second corner in (x,y,z) coords.
  const y1 = y0 - j1 + G3;
  const z1 = z0 - k1 + G3;

  const x2 = x0 - i2 + 2.0 * G3; // Offsets for third corner in (x,y,z) coords.
  const y2 = y0 - j2 + 2.0 * G3;
  const z2 = z0 - k2 + 2.0 * G3;

  const x3 = x0 - 1.0 + 3.0 * G3; // Offsets for last corner in (x,y,z) coords.
  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;

  const gi0 = permMod12[ii + perm[jj + perm[kk]]];
  const gi1 = permMod12[ii + i1 + perm[jj + j1 + perm[kk + k1]]];
  const gi2 = permMod12[ii + i2 + perm[jj + j2 + perm[kk + k2]]];
  const gi3 = permMod12[ii + 1 + perm[jj + 1 + perm[kk + 1]]];

  // Calculate the contribution from the four corners.
  let t0 = 0.6 - x0 * x0 - y0 * y0 - z0 * z0;
  if (t0 < 0) n0 = 0.0;
  else {
    t0 *= t0;
    n0 = t0 * t0 * dot3(grad3[gi0], x0, y0, z0);
  }

  let t1 = 0.6 - x1 * x1 - y1 * y1 - z1 * z1;
  if (t1 < 0) n1 = 0.0;
  else {
    t1 *= t1;
    n1 = t1 * t1 * dot3(grad3[gi1], x1, y1, z1);
  }

  let t2 = 0.6 - x2 * x2 - y2 * y2 - z2 * z2;
  if (t2 < 0) n2 = 0.0;
  else {
    t2 *= t2;
    n2 = t2 * t2 * dot3(grad3[gi2], x2, y2, z2);
  }

  let t3 = 0.6 - x3 * x3 - y3 * y3 - z3 * z3;
  if (t3 < 0) n3 = 0.0;
  else {
    t3 *= t3;
    n3 = t3 * t3 * dot3(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.

function simplex4D(x, y, z, w) {
  let 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.
  const s = (x + y + z + w) * F4; // Factor for 4D skewing.

  const i = Math.floor(x + s);
  const j = Math.floor(y + s);
  const k = Math.floor(z + s);
  const l = Math.floor(w + s);

  const t = (i + j + k + l) * G4; // Factor for 4D unskewing.

  const X0 = i - t; // Unskew the cell origin back to (x,y,z,w) space.
  const Y0 = j - t;
  const Z0 = k - t;
  const W0 = l - t;

  const x0 = x - X0; // The x,y,z,w distances from the cell origin.
  const y0 = y - Y0;
  const z0 = z - Z0;
  const 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.
   */

  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.

  /**
   * [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.
  const x1 = x0 - i1 + G4; // Offsets for second corner in (x,y,z,w) coords.
  const y1 = y0 - j1 + G4;
  const z1 = z0 - k1 + G4;
  const w1 = w0 - l1 + G4;

  const x2 = x0 - i2 + 2.0 * G4; // Offsets for third corner in (x,y,z,w) coords.
  const y2 = y0 - j2 + 2.0 * G4;
  const z2 = z0 - k2 + 2.0 * G4;
  const w2 = w0 - l2 + 2.0 * G4;

  const x3 = x0 - i3 + 3.0 * G4; // Offsets for fourth corner in (x,y,z,w) coords.
  const y3 = y0 - j3 + 3.0 * G4;
  const z3 = z0 - k3 + 3.0 * G4;
  const w3 = w0 - l3 + 3.0 * G4;

  const x4 = x0 - 1.0 + 4.0 * G4; // Offsets for last corner in (x,y,z,w) coords.
  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;

  const gi0 = perm[ii + perm[jj + perm[kk + perm[ll]]]] % 32;
  const gi1 = perm[ii + i1 + perm[jj + j1 + perm[kk + k1 + perm[ll + l1]]]] % 32;
  const gi2 = perm[ii + i2 + perm[jj + j2 + perm[kk + k2 + perm[ll + l2]]]] % 32;
  const gi3 = perm[ii + i3 + perm[jj + j3 + perm[kk + k3 + perm[ll + l3]]]] % 32;
  const gi4 = perm[ii + 1 + perm[jj + 1 + perm[kk + 1 + perm[ll + 1]]]] % 32;

  // Calculate the contribution from the five corners.
  let t0 = 0.6 - x0 * x0 - y0 * y0 - z0 * z0 - w0 * w0;
  if (t0 < 0) n0 = 0.0;
  else {
    t0 *= t0;
    n0 = t0 * t0 * dot4(grad4[gi0], x0, y0, z0, w0);
  }

  let t1 = 0.6 - x1 * x1 - y1 * y1 - z1 * z1 - w1 * w1;
  if (t1 < 0) n1 = 0.0;
  else {
    t1 *= t1;
    n1 = t1 * t1 * dot4(grad4[gi1], x1, y1, z1, w1);
  }

  let t2 = 0.6 - x2 * x2 - y2 * y2 - z2 * z2 - w2 * w2;
  if (t2 < 0) n2 = 0.0;
  else {
    t2 *= t2;
    n2 = t2 * t2 * dot4(grad4[gi2], x2, y2, z2, w2);
  }

  let t3 = 0.6 - x3 * x3 - y3 * y3 - z3 * z3 - w3 * w3;
  if (t3 < 0) n3 = 0.0;
  else {
    t3 *= t3;
    n3 = t3 * t3 * dot4(grad4[gi3], x3, y3, z3, w3);
  }

  let t4 = 0.6 - x4 * x4 - y4 * y4 - z4 * z4 - w4 * w4;
  if (t4 < 0) n4 = 0.0;
  else {
    t4 *= t4;
    n4 = t4 * t4 * dot4(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);
}

export { simplex2D, simplex3D, simplex4D };