simplex-noise.js

/*
 * A fast javascript implementation of simplex noise by Jonas Wagner

Based on a speed-improved simplex noise algorithm for 2D, 3D and 4D in Java.
Which is based on example code by Stefan Gustavson (stegu@itn.liu.se).
With Optimisations by Peter Eastman (peastman@drizzle.stanford.edu).
Better rank ordering method by Stefan Gustavson in 2012.

 Copyright (c) 2018 Jonas Wagner

 Permission is hereby granted, free of charge, to any person obtaining a copy
 of this software and associated documentation files (the "Software"), to deal
 in the Software without restriction, including without limitation the rights
 to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
 copies of the Software, and to permit persons to whom the Software is
 furnished to do so, subject to the following conditions:

 The above copyright notice and this permission notice shall be included in all
 copies or substantial portions of the Software.

 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
 SOFTWARE.
 */
(function() {
  'use strict';

  var F2 = 0.5 * (Math.sqrt(3.0) - 1.0);
  var G2 = (3.0 - Math.sqrt(3.0)) / 6.0;
  var F3 = 1.0 / 3.0;
  var G3 = 1.0 / 6.0;
  var F4 = (Math.sqrt(5.0) - 1.0) / 4.0;
  var G4 = (5.0 - Math.sqrt(5.0)) / 20.0;

  function SimplexNoise(randomOrSeed) {
    var random;
    if (typeof randomOrSeed == 'function') {
      random = randomOrSeed;
    }
    else if (randomOrSeed) {
      random = alea(randomOrSeed);
    } else {
      random = Math.random;
    }
    this.p = buildPermutationTable(random);
    this.perm = new Uint8Array(512);
    this.permMod12 = new Uint8Array(512);
    for (var i = 0; i < 512; i++) {
      this.perm[i] = this.p[i & 255];
      this.permMod12[i] = this.perm[i] % 12;
    }

  }
  SimplexNoise.prototype = {
    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]),
    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]),
    noise2D: function(xin, yin) {
      var permMod12 = this.permMod12;
      var perm = this.perm;
      var grad3 = this.grad3;
      var n0 = 0; // Noise contributions from the three corners
      var n1 = 0;
      var n2 = 0;
      // Skew the input space to determine which simplex cell we're in
      var s = (xin + yin) * F2; // Hairy factor for 2D
      var i = Math.floor(xin + s);
      var j = Math.floor(yin + s);
      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;
      // Calculate the contribution from the three corners
      var t0 = 0.5 - x0 * x0 - y0 * y0;
      if (t0 >= 0) {
        var gi0 = permMod12[ii + perm[jj]] * 3;
        t0 *= t0;
        n0 = t0 * t0 * (grad3[gi0] * x0 + grad3[gi0 + 1] * y0); // (x,y) of grad3 used for 2D gradient
      }
      var t1 = 0.5 - x1 * x1 - y1 * y1;
      if (t1 >= 0) {
        var gi1 = permMod12[ii + i1 + perm[jj + j1]] * 3;
        t1 *= t1;
        n1 = t1 * t1 * (grad3[gi1] * x1 + grad3[gi1 + 1] * y1);
      }
      var t2 = 0.5 - x2 * x2 - y2 * y2;
      if (t2 >= 0) {
        var 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
    noise3D: function(xin, yin, zin) {
      var permMod12 = this.permMod12;
      var perm = this.perm;
      var grad3 = this.grad3;
      var n0, n1, n2, n3; // Noise contributions from the four corners
      // Skew the input space to determine which simplex cell we're in
      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 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;
      // Calculate the contribution from the four corners
      var t0 = 0.6 - x0 * x0 - y0 * y0 - z0 * z0;
      if (t0 < 0) n0 = 0.0;
      else {
        var gi0 = permMod12[ii + perm[jj + perm[kk]]] * 3;
        t0 *= t0;
        n0 = t0 * t0 * (grad3[gi0] * x0 + grad3[gi0 + 1] * y0 + grad3[gi0 + 2] * z0);
      }
      var t1 = 0.6 - x1 * x1 - y1 * y1 - z1 * z1;
      if (t1 < 0) n1 = 0.0;
      else {
        var 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);
      }
      var t2 = 0.6 - x2 * x2 - y2 * y2 - z2 * z2;
      if (t2 < 0) n2 = 0.0;
      else {
        var 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);
      }
      var t3 = 0.6 - x3 * x3 - y3 * y3 - z3 * z3;
      if (t3 < 0) n3 = 0.0;
      else {
        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
    noise4D: function(x, y, z, w) {
      var perm = this.perm;
      var grad4 = this.grad4;

      var 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
      var s = (x + y + z + w) * F4; // Factor for 4D skewing
      var i = Math.floor(x + s);
      var j = Math.floor(y + s);
      var k = Math.floor(z + s);
      var l = Math.floor(w + s);
      var t = (i + j + k + l) * G4; // Factor for 4D unskewing
      var X0 = i - t; // Unskew the cell origin back to (x,y,z,w) space
      var Y0 = j - t;
      var Z0 = k - t;
      var W0 = l - t;
      var x0 = x - X0; // The x,y,z,w distances from the cell origin
      var y0 = y - Y0;
      var z0 = z - Z0;
      var 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.
      var rankx = 0;
      var ranky = 0;
      var rankz = 0;
      var 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++;
      var i1, j1, k1, l1; // The integer offsets for the second simplex corner
      var i2, j2, k2, l2; // The integer offsets for the third simplex corner
      var 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.
      var x1 = x0 - i1 + G4; // Offsets for second corner in (x,y,z,w) coords
      var y1 = y0 - j1 + G4;
      var z1 = z0 - k1 + G4;
      var w1 = w0 - l1 + G4;
      var x2 = x0 - i2 + 2.0 * G4; // Offsets for third corner in (x,y,z,w) coords
      var y2 = y0 - j2 + 2.0 * G4;
      var z2 = z0 - k2 + 2.0 * G4;
      var w2 = w0 - l2 + 2.0 * G4;
      var x3 = x0 - i3 + 3.0 * G4; // Offsets for fourth corner in (x,y,z,w) coords
      var y3 = y0 - j3 + 3.0 * G4;
      var z3 = z0 - k3 + 3.0 * G4;
      var w3 = w0 - l3 + 3.0 * G4;
      var x4 = x0 - 1.0 + 4.0 * G4; // Offsets for last corner in (x,y,z,w) coords
      var y4 = y0 - 1.0 + 4.0 * G4;
      var z4 = z0 - 1.0 + 4.0 * G4;
      var w4 = w0 - 1.0 + 4.0 * G4;
      // Work out the hashed gradient indices of the five simplex corners
      var ii = i & 255;
      var jj = j & 255;
      var kk = k & 255;
      var ll = l & 255;
      // Calculate the contribution from the five corners
      var t0 = 0.6 - x0 * x0 - y0 * y0 - z0 * z0 - w0 * w0;
      if (t0 < 0) n0 = 0.0;
      else {
        var 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);
      }
      var t1 = 0.6 - x1 * x1 - y1 * y1 - z1 * z1 - w1 * w1;
      if (t1 < 0) n1 = 0.0;
      else {
        var 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);
      }
      var t2 = 0.6 - x2 * x2 - y2 * y2 - z2 * z2 - w2 * w2;
      if (t2 < 0) n2 = 0.0;
      else {
        var 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);
      }
      var t3 = 0.6 - x3 * x3 - y3 * y3 - z3 * z3 - w3 * w3;
      if (t3 < 0) n3 = 0.0;
      else {
        var 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);
      }
      var t4 = 0.6 - x4 * x4 - y4 * y4 - z4 * z4 - w4 * w4;
      if (t4 < 0) n4 = 0.0;
      else {
        var 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);
    }
  };

  function buildPermutationTable(random) {
    var i;
    var p = new Uint8Array(256);
    for (i = 0; i < 256; i++) {
      p[i] = i;
    }
    for (i = 0; i < 255; i++) {
      var r = i + ~~(random() * (256 - i));
      var aux = p[i];
      p[i] = p[r];
      p[r] = aux;
    }
    return p;
  }
  SimplexNoise._buildPermutationTable = buildPermutationTable;

  /*
  The ALEA PRNG and masher code used by simplex-noise.js
  is based on code by Johannes Baagøe, modified by Jonas Wagner.
  See alea.md for the full license.
  */
  function alea() {
    var s0 = 0;
    var s1 = 0;
    var s2 = 0;
    var c = 1;

    var mash = masher();
    s0 = mash(' ');
    s1 = mash(' ');
    s2 = mash(' ');

    for (var i = 0; i < arguments.length; i++) {
      s0 -= mash(arguments[i]);
      if (s0 < 0) {
        s0 += 1;
      }
      s1 -= mash(arguments[i]);
      if (s1 < 0) {
        s1 += 1;
      }
      s2 -= mash(arguments[i]);
      if (s2 < 0) {
        s2 += 1;
      }
    }
    mash = null;
    return function() {
      var t = 2091639 * s0 + c * 2.3283064365386963e-10; // 2^-32
      s0 = s1;
      s1 = s2;
      return s2 = t - (c = t | 0);
    };
  }
  function masher() {
    var n = 0xefc8249d;
    return function(data) {
      data = data.toString();
      for (var i = 0; i < data.length; i++) {
        n += data.charCodeAt(i);
        var h = 0.02519603282416938 * n;
        n = h >>> 0;
        h -= n;
        h *= n;
        n = h >>> 0;
        h -= n;
        n += h * 0x100000000; // 2^32
      }
      return (n >>> 0) * 2.3283064365386963e-10; // 2^-32
    };
  }

  // amd
  if (typeof define !== 'undefined' && define.amd) define(function() {return SimplexNoise;});
  // common js
  if (typeof exports !== 'undefined') exports.SimplexNoise = SimplexNoise;
  // browser
  else if (typeof window !== 'undefined') window.SimplexNoise = SimplexNoise;
  // nodejs
  if (typeof module !== 'undefined') {
    module.exports = SimplexNoise;
  }

})();