perlin-noise-classical.js

## perlin-noise-classical.js
// 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.
 */
var ClassicalNoise = function(r) { // Classic Perlin noise in 3D, for comparison
	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]];
  this.p = [];
  for (var i=0; i<256; i++) {
	  this.p[i] = Math.floor(r.random()*256);
  }
  // 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];
  }
};

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

ClassicalNoise.prototype.mix = function(a, b, t) {
    return (1.0-t)*a + t*b;
};

ClassicalNoise.prototype.fade = function(t) {
    return t*t*t*(t*(t*6.0-15.0)+10.0);
};

  // Classic Perlin noise, 3D version
ClassicalNoise.prototype.noise = function(x, y, z) {
  // Find unit grid cell containing point
  var X = Math.floor(x);
  var Y = Math.floor(y);
  var Z = Math.floor(z);

  // Get relative xyz coordinates of point within that cell
  x = x - X;
  y = y - Y;
  z = z - Z;

  // Wrap the integer cells at 255 (smaller integer period can be introduced here)
  X = X & 255;
  Y = Y & 255;
  Z = Z & 255;

  // Calculate a set of eight hashed gradient indices
  var gi000 = this.perm[X+this.perm[Y+this.perm[Z]]] % 12;
  var gi001 = this.perm[X+this.perm[Y+this.perm[Z+1]]] % 12;
  var gi010 = this.perm[X+this.perm[Y+1+this.perm[Z]]] % 12;
  var gi011 = this.perm[X+this.perm[Y+1+this.perm[Z+1]]] % 12;
  var gi100 = this.perm[X+1+this.perm[Y+this.perm[Z]]] % 12;
  var gi101 = this.perm[X+1+this.perm[Y+this.perm[Z+1]]] % 12;
  var gi110 = this.perm[X+1+this.perm[Y+1+this.perm[Z]]] % 12;
  var gi111 = this.perm[X+1+this.perm[Y+1+this.perm[Z+1]]] % 12;

  // The gradients of each corner are now:
  // g000 = grad3[gi000];
  // g001 = grad3[gi001];
  // g010 = grad3[gi010];
  // g011 = grad3[gi011];
  // g100 = grad3[gi100];
  // g101 = grad3[gi101];
  // g110 = grad3[gi110];
  // g111 = grad3[gi111];
  // Calculate noise contributions from each of the eight corners
  var n000= this.dot(this.grad3[gi000], x, y, z);
  var n100= this.dot(this.grad3[gi100], x-1, y, z);
  var n010= this.dot(this.grad3[gi010], x, y-1, z);
  var n110= this.dot(this.grad3[gi110], x-1, y-1, z);
  var n001= this.dot(this.grad3[gi001], x, y, z-1);
  var n101= this.dot(this.grad3[gi101], x-1, y, z-1);
  var n011= this.dot(this.grad3[gi011], x, y-1, z-1);
  var n111= this.dot(this.grad3[gi111], x-1, y-1, z-1);
  // Compute the fade curve value for each of x, y, z
  var u = this.fade(x);
  var v = this.fade(y);
  var w = this.fade(z);
   // Interpolate along x the contributions from each of the corners
  var nx00 = this.mix(n000, n100, u);
  var nx01 = this.mix(n001, n101, u);
  var nx10 = this.mix(n010, n110, u);
  var nx11 = this.mix(n011, n111, u);
  // Interpolate the four results along y
  var nxy0 = this.mix(nx00, nx10, v);
  var nxy1 = this.mix(nx01, nx11, v);
  // Interpolate the two last results along z
  var nxyz = this.mix(nxy0, nxy1, w);

  return nxyz;
};

## perlin-noise-simplex.js
// 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.
 */
var 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]];
  this.p = [];
  for (var i=0; i<256; i++) {
	  this.p[i] = Math.floor(r.random()*256);
  }
  // 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.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.dot(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.dot(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.dot(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.dot(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);
};