Tetris3D/js/libs/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);
};