simplex.js

// https://gist.github.com/banksean/304522
//
// Ported from Stefan Gustavson's java implementation
// http://staffwww.itn.liu.se/~stegu/simplexnoise/simplexnoise.pdf
// Read Stefan's excellent paper for details on how this code works.
//
// Sean McCullough banksean@gmail.com

/**
 * You can pass in a random number generator object if you like.
 * It is assumed to have a random() method.
 */
const SimplexNoise = function (r) {
  if (r == undefined) r = Math;
  this.grad3 = [
    [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],
  ];

  const seed = [
    81, 8, 192, 189, 103, 142, 197, 204, 212, 122, 229, 251, 248, 100, 123, 154,
    159, 147, 61, 187, 88, 34, 43, 4, 129, 116, 25, 134, 131, 150, 215, 133,
    255, 60, 46, 107, 52, 108, 53, 183, 73, 3, 57, 124, 234, 238, 188, 15, 85,
    245, 149, 112, 185, 235, 190, 111, 144, 115, 48, 216, 7, 35, 114, 67, 225,
    38, 62, 130, 63, 83, 175, 44, 249, 231, 213, 182, 109, 151, 95, 31, 118, 56,
    186, 193, 47, 127, 241, 250, 64, 0, 237, 51, 194, 140, 220, 230, 96, 171,
    145, 104, 227, 14, 10, 17, 178, 113, 163, 80, 98, 199, 152, 164, 169, 240,
    143, 166, 59, 92, 93, 242, 232, 246, 165, 157, 65, 252, 11, 33, 27, 196, 84,
    90, 205, 91, 26, 21, 233, 87, 69, 121, 224, 126, 210, 105, 94, 50, 23, 162,
    39, 79, 198, 176, 89, 179, 208, 75, 82, 101, 6, 226, 156, 97, 1, 28, 206,
    19, 168, 155, 239, 207, 217, 5, 161, 40, 110, 158, 167, 45, 18, 209, 49,
    138, 66, 42, 153, 106, 148, 12, 29, 120, 228, 174, 86, 254, 117, 247, 136,
    160, 132, 170, 71, 200, 128, 37, 146, 135, 20, 54, 236, 70, 223, 172, 55,
    184, 139, 243, 219, 2, 16, 201, 102, 41, 13, 195, 177, 202, 58, 211, 72,
    203, 9, 244, 22, 214, 68, 74, 173, 218, 222, 36, 76, 125, 181, 191, 137, 24,
    253, 141, 119, 77, 99, 180, 30, 78, 221, 32,
  ];

  this.p = [];
  for (var i = 0; i < 256; i++) {
    this.p[i] = seed[i];
  }
  // To remove the need for index wrapping, double the permutation table length
  this.perm = [];
  for (var i = 0; i < 512; i++) {
    this.perm[i] = this.p[i & 255];
  }

  // 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.
  this.simplex = [
    [0, 1, 2, 3],
    [0, 1, 3, 2],
    [0, 0, 0, 0],
    [0, 2, 3, 1],
    [0, 0, 0, 0],
    [0, 0, 0, 0],
    [0, 0, 0, 0],
    [1, 2, 3, 0],
    [0, 2, 1, 3],
    [0, 0, 0, 0],
    [0, 3, 1, 2],
    [0, 3, 2, 1],
    [0, 0, 0, 0],
    [0, 0, 0, 0],
    [0, 0, 0, 0],
    [1, 3, 2, 0],
    [0, 0, 0, 0],
    [0, 0, 0, 0],
    [0, 0, 0, 0],
    [0, 0, 0, 0],
    [0, 0, 0, 0],
    [0, 0, 0, 0],
    [0, 0, 0, 0],
    [0, 0, 0, 0],
    [1, 2, 0, 3],
    [0, 0, 0, 0],
    [1, 3, 0, 2],
    [0, 0, 0, 0],
    [0, 0, 0, 0],
    [0, 0, 0, 0],
    [2, 3, 0, 1],
    [2, 3, 1, 0],
    [1, 0, 2, 3],
    [1, 0, 3, 2],
    [0, 0, 0, 0],
    [0, 0, 0, 0],
    [0, 0, 0, 0],
    [2, 0, 3, 1],
    [0, 0, 0, 0],
    [2, 1, 3, 0],
    [0, 0, 0, 0],
    [0, 0, 0, 0],
    [0, 0, 0, 0],
    [0, 0, 0, 0],
    [0, 0, 0, 0],
    [0, 0, 0, 0],
    [0, 0, 0, 0],
    [0, 0, 0, 0],
    [2, 0, 1, 3],
    [0, 0, 0, 0],
    [0, 0, 0, 0],
    [0, 0, 0, 0],
    [3, 0, 1, 2],
    [3, 0, 2, 1],
    [0, 0, 0, 0],
    [3, 1, 2, 0],
    [2, 1, 0, 3],
    [0, 0, 0, 0],
    [0, 0, 0, 0],
    [0, 0, 0, 0],
    [3, 1, 0, 2],
    [0, 0, 0, 0],
    [3, 2, 0, 1],
    [3, 2, 1, 0],
  ];
};

SimplexNoise.prototype.dot = function (g, x, y) {
  return g[0] * x + g[1] * y;
};

SimplexNoise.prototype.dot3 = function (g, x, y, z) {
  return g[0] * x + g[1] * y + g[2] * z;
};

SimplexNoise.prototype.noise = function (xin, yin) {
  var n0, n1, n2; // Noise contributions from the three corners
  // Skew the input space to determine which simplex cell we're in
  var F2 = 0.5 * (Math.sqrt(3.0) - 1.0);
  var s = (xin + yin) * F2; // Hairy factor for 2D
  var i = Math.floor(xin + s);
  var j = Math.floor(yin + s);
  var G2 = (3.0 - Math.sqrt(3.0)) / 6.0;
  var t = (i + j) * G2;
  var X0 = i - t; // Unskew the cell origin back to (x,y) space
  var Y0 = j - t;
  var x0 = xin - X0; // The x,y distances from the cell origin
  var y0 = yin - Y0;
  // For the 2D case, the simplex shape is an equilateral triangle.
  // Determine which simplex we are in.
  var 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
  var x1 = x0 - i1 + G2; // Offsets for middle corner in (x,y) unskewed coords
  var y1 = y0 - j1 + G2;
  var x2 = x0 - 1.0 + 2.0 * G2; // Offsets for last corner in (x,y) unskewed coords
  var y2 = y0 - 1.0 + 2.0 * G2;
  // Work out the hashed gradient indices of the three simplex corners
  var ii = i & 255;
  var jj = j & 255;
  var gi0 = this.perm[ii + this.perm[jj]] % 12;
  var gi1 = this.perm[ii + i1 + this.perm[jj + j1]] % 12;
  var gi2 = this.perm[ii + 1 + this.perm[jj + 1]] % 12;
  // Calculate the contribution from the three corners
  var t0 = 0.5 - x0 * x0 - y0 * y0;
  if (t0 < 0) n0 = 0.0;
  else {
    t0 *= t0;
    n0 = t0 * t0 * this.dot(this.grad3[gi0], x0, y0); // (x,y) of grad3 used for 2D gradient
  }
  var t1 = 0.5 - x1 * x1 - y1 * y1;
  if (t1 < 0) n1 = 0.0;
  else {
    t1 *= t1;
    n1 = t1 * t1 * this.dot(this.grad3[gi1], x1, y1);
  }
  var t2 = 0.5 - x2 * x2 - y2 * y2;
  if (t2 < 0) n2 = 0.0;
  else {
    t2 *= t2;
    n2 = t2 * t2 * this.dot(this.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
SimplexNoise.prototype.noise3d = function (xin, yin, zin) {
  var n0, n1, n2, n3; // Noise contributions from the four corners
  // Skew the input space to determine which simplex cell we're in
  var F3 = 1.0 / 3.0;
  var s = (xin + yin + zin) * F3; // Very nice and simple skew factor for 3D
  var i = Math.floor(xin + s);
  var j = Math.floor(yin + s);
  var k = Math.floor(zin + s);
  var G3 = 1.0 / 6.0; // Very nice and simple unskew factor, too
  var t = (i + j + k) * G3;
  var X0 = i - t; // Unskew the cell origin back to (x,y,z) space
  var Y0 = j - t;
  var Z0 = k - t;
  var x0 = xin - X0; // The x,y,z distances from the cell origin
  var y0 = yin - Y0;
  var z0 = zin - Z0;
  // For the 3D case, the simplex shape is a slightly irregular tetrahedron.
  // Determine which simplex we are in.
  var i1, j1, k1; // Offsets for second corner of simplex in (i,j,k) coords
  var 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.
  var x1 = x0 - i1 + G3; // Offsets for second corner in (x,y,z) coords
  var y1 = y0 - j1 + G3;
  var z1 = z0 - k1 + G3;
  var x2 = x0 - i2 + 2.0 * G3; // Offsets for third corner in (x,y,z) coords
  var y2 = y0 - j2 + 2.0 * G3;
  var z2 = z0 - k2 + 2.0 * G3;
  var x3 = x0 - 1.0 + 3.0 * G3; // Offsets for last corner in (x,y,z) coords
  var y3 = y0 - 1.0 + 3.0 * G3;
  var z3 = z0 - 1.0 + 3.0 * G3;
  // Work out the hashed gradient indices of the four simplex corners
  var ii = i & 255;
  var jj = j & 255;
  var kk = k & 255;
  var gi0 = this.perm[ii + this.perm[jj + this.perm[kk]]] % 12;
  var gi1 = this.perm[ii + i1 + this.perm[jj + j1 + this.perm[kk + k1]]] % 12;
  var gi2 = this.perm[ii + i2 + this.perm[jj + j2 + this.perm[kk + k2]]] % 12;
  var gi3 = this.perm[ii + 1 + this.perm[jj + 1 + this.perm[kk + 1]]] % 12;
  // Calculate the contribution from the four corners
  var t0 = 0.6 - x0 * x0 - y0 * y0 - z0 * z0;
  if (t0 < 0) n0 = 0.0;
  else {
    t0 *= t0;
    n0 = t0 * t0 * this.dot3(this.grad3[gi0], x0, y0, z0);
  }
  var t1 = 0.6 - x1 * x1 - y1 * y1 - z1 * z1;
  if (t1 < 0) n1 = 0.0;
  else {
    t1 *= t1;
    n1 = t1 * t1 * this.dot3(this.grad3[gi1], x1, y1, z1);
  }
  var t2 = 0.6 - x2 * x2 - y2 * y2 - z2 * z2;
  if (t2 < 0) n2 = 0.0;
  else {
    t2 *= t2;
    n2 = t2 * t2 * this.dot3(this.grad3[gi2], x2, y2, z2);
  }
  var t3 = 0.6 - x3 * x3 - y3 * y3 - z3 * z3;
  if (t3 < 0) n3 = 0.0;
  else {
    t3 *= t3;
    n3 = t3 * t3 * this.dot3(this.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);
};

window.SimplexNoise = SimplexNoise;