three.js/examples/js/SimplexNoise.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 [email protected]
//
// Added 4D noise
// Joshua Koo [email protected] 

/**
 * 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.grad4 = [[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]];

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

SimplexNoise.prototype.dot4 = function(g, x, y, z, w) {
  return g[0]*x + g[1]*y + g[2]*z + g[3]*w;
};

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); 
};

// 4D simplex noise
SimplexNoise.prototype.noise4d = function( x, y, z, w ) {
	// For faster and easier lookups
	var grad4 = this.grad4;
	var simplex = this.simplex;
	var perm = this.perm;
	
   // The skewing and unskewing factors are hairy again for the 4D case
   var F4 = (Math.sqrt(5.0)-1.0)/4.0;
   var G4 = (5.0-Math.sqrt(5.0))/20.0;
   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.
   // The method below is a good way of finding the ordering of x,y,z,w and
   // then find the correct traversal order for the simplex we’re in.
   // First, six pair-wise comparisons are performed between each possible pair
   // of the four coordinates, and the results are used to add up binary bits
   // for an integer index.
   var c1 = (x0 > y0) ? 32 : 0;
   var c2 = (x0 > z0) ? 16 : 0;
   var c3 = (y0 > z0) ? 8 : 0;
   var c4 = (x0 > w0) ? 4 : 0;
   var c5 = (y0 > w0) ? 2 : 0;
   var c6 = (z0 > w0) ? 1 : 0;
   var c = c1 + c2 + c3 + c4 + c5 + c6;
   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.
   // The number 3 in the "simplex" array is at the position of the largest coordinate.
   i1 = simplex[c][0]>=3 ? 1 : 0;
   j1 = simplex[c][1]>=3 ? 1 : 0;
   k1 = simplex[c][2]>=3 ? 1 : 0;
   l1 = simplex[c][3]>=3 ? 1 : 0;
   // The number 2 in the "simplex" array is at the second largest coordinate.
   i2 = simplex[c][0]>=2 ? 1 : 0;
   j2 = simplex[c][1]>=2 ? 1 : 0;    k2 = simplex[c][2]>=2 ? 1 : 0;
   l2 = simplex[c][3]>=2 ? 1 : 0;
   // The number 1 in the "simplex" array is at the second smallest coordinate.
   i3 = simplex[c][0]>=1 ? 1 : 0;
   j3 = simplex[c][1]>=1 ? 1 : 0;
   k3 = simplex[c][2]>=1 ? 1 : 0;
   l3 = simplex[c][3]>=1 ? 1 : 0;
   // The fifth corner has all coordinate offsets = 1, so no need to look that up.
   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;
   var gi0 = perm[ii+perm[jj+perm[kk+perm[ll]]]] % 32;
   var gi1 = perm[ii+i1+perm[jj+j1+perm[kk+k1+perm[ll+l1]]]] % 32;
   var gi2 = perm[ii+i2+perm[jj+j2+perm[kk+k2+perm[ll+l2]]]] % 32;
   var gi3 = perm[ii+i3+perm[jj+j3+perm[kk+k3+perm[ll+l3]]]] % 32;
   var gi4 = perm[ii+1+perm[jj+1+perm[kk+1+perm[ll+1]]]] % 32;
   // 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 {
     t0 *= t0;
     n0 = t0 * t0 * this.dot4(grad4[gi0], x0, y0, z0, w0);
   }
  var t1 = 0.6 - x1*x1 - y1*y1 - z1*z1 - w1*w1;
   if(t1<0) n1 = 0.0;
   else {
     t1 *= t1;
     n1 = t1 * t1 * this.dot4(grad4[gi1], x1, y1, z1, w1);
   }
  var t2 = 0.6 - x2*x2 - y2*y2 - z2*z2 - w2*w2;
   if(t2<0) n2 = 0.0;
   else {
     t2 *= t2;
     n2 = t2 * t2 * this.dot4(grad4[gi2], x2, y2, z2, w2);
   }   var t3 = 0.6 - x3*x3 - y3*y3 - z3*z3 - w3*w3;
   if(t3<0) n3 = 0.0;
   else {
     t3 *= t3;
     n3 = t3 * t3 * this.dot4(grad4[gi3], x3, y3, z3, w3);
   }
  var t4 = 0.6 - x4*x4 - y4*y4 - z4*z4 - w4*w4;
   if(t4<0) n4 = 0.0;
   else {
     t4 *= t4;
     n4 = t4 * t4 * this.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);
};