/*!
 * SimplexNoise Object
 * 	Code more or less directly used from:
 * 	 Sean McCullough's javascript noise generators
 * 		http://gist.github.com/304522
 * 	 Stefan Gustavson's Simplex Noise Demystified
 * 		http://staffwww.itn.liu.se/~stegu/simplexnoise/simplexnoise.pdf
 * 
 * @class Star
 * @param {Object} rng - Random number generator, must have 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];
	}
};
// There's a way to do this with a single function in js, but not wasting time on it now
SimplexNoise.prototype.dot2 = 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.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]];
//2D simplex noise
SimplexNoise.prototype.noise2d = 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.dot2(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.dot2(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.dot2(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 from gist.github.com
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);
};


// A lookup table to traverse the simplex around a given povar in 4D.
// Details can be found where this table is used, in the 4D noise method.
SimplexNoise.prototype.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]];

// 4d gradient vectors
SimplexNoise.prototype.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]];

//4D simplex noise from Stefan Gustavson's Simplex Noise Demystified
SimplexNoise.prototype.noise4d = function(x, y, z, w) {
	// 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 vareger 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 vareger offsets for the second simplex corner
	var i2, j2, k2, l2; // The vareger offsets for the third simplex corner
	var i3, j3, k3, l3; // The vareger 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 = this.simplex[c][0] >= 3 ? 1 : 0;
	j1 = this.simplex[c][1] >= 3 ? 1 : 0;
	k1 = this.simplex[c][2] >= 3 ? 1 : 0;
	l1 = this.simplex[c][3] >= 3 ? 1 : 0;
	// The number 2 in the "this.simplex" array is at the second largest
	// coordinate.
	i2 = this.simplex[c][0] >= 2 ? 1 : 0;
	j2 = this.simplex[c][1] >= 2 ? 1 : 0;
	k2 = this.simplex[c][2] >= 2 ? 1 : 0;
	l2 = this.simplex[c][3] >= 2 ? 1 : 0;
	// The number 1 in the "this.simplex" array is at the second smallest
	// coordinate.
	i3 = this.simplex[c][0] >= 1 ? 1 : 0;
	j3 = this.simplex[c][1] >= 1 ? 1 : 0;
	k3 = this.simplex[c][2] >= 1 ? 1 : 0;
	l3 = this.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 = this.perm[ii + this.perm[jj + this.perm[kk + this.perm[ll]]]] % 32;
	var gi1 = this.perm[ii + i1
			+ this.perm[jj + j1 + this.perm[kk + k1 + this.perm[ll + l1]]]] % 32;
	var gi2 = this.perm[ii + i2
			+ this.perm[jj + j2 + this.perm[kk + k2 + this.perm[ll + l2]]]] % 32;
	var gi3 = this.perm[ii + i3
			+ this.perm[jj + j3 + this.perm[kk + k3 + this.perm[ll + l3]]]] % 32;
	var gi4 = this.perm[ii + 1
			+ this.perm[jj + 1 + this.perm[kk + 1 + this.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(this.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(this.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(this.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(this.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(this.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);
};