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// Ported from Stefan Gustavson's java implementation |
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// http://staffwww.itn.liu.se/~stegu/simplexnoise/simplexnoise.pdf |
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// Read Stefan's excellent paper for details on how this code works. |
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// |
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// Sean McCullough banksean@gmail.com |
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/** |
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* You can pass in a random number generator object if you like. |
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* It is assumed to have a random() method. |
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*/ |
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var SimplexNoise = function(r) { |
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if (r == undefined) r = Math; |
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this.grad3 = [[1,1,0],[-1,1,0],[1,-1,0],[-1,-1,0], |
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[1,0,1],[-1,0,1],[1,0,-1],[-1,0,-1], |
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[0,1,1],[0,-1,1],[0,1,-1],[0,-1,-1]]; |
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this.p = []; |
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for (var i=0; i<256; i++) { |
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this.p[i] = Math.floor(r.random()*256); |
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} |
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// To remove the need for index wrapping, double the permutation table length |
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this.perm = []; |
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for(var i=0; i<512; i++) { |
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this.perm[i]=this.p[i & 255]; |
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} |
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// A lookup table to traverse the simplex around a given point in 4D. |
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// Details can be found where this table is used, in the 4D noise method. |
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this.simplex = [ |
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[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], |
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[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], |
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[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], |
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[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], |
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[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], |
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[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], |
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[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], |
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[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]]; |
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}; |
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SimplexNoise.prototype.dot = function(g, x, y) { |
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return g[0]*x + g[1]*y; |
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}; |
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SimplexNoise.prototype.noise = function(xin, yin) { |
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var n0, n1, n2; // Noise contributions from the three corners |
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// Skew the input space to determine which simplex cell we're in |
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var F2 = 0.5*(Math.sqrt(3.0)-1.0); |
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var s = (xin+yin)*F2; // Hairy factor for 2D |
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var i = Math.floor(xin+s); |
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var j = Math.floor(yin+s); |
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var G2 = (3.0-Math.sqrt(3.0))/6.0; |
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var t = (i+j)*G2; |
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var X0 = i-t; // Unskew the cell origin back to (x,y) space |
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var Y0 = j-t; |
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var x0 = xin-X0; // The x,y distances from the cell origin |
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var y0 = yin-Y0; |
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// For the 2D case, the simplex shape is an equilateral triangle. |
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// Determine which simplex we are in. |
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var i1, j1; // Offsets for second (middle) corner of simplex in (i,j) coords |
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if(x0>y0) {i1=1; j1=0;} // lower triangle, XY order: (0,0)->(1,0)->(1,1) |
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else {i1=0; j1=1;} // upper triangle, YX order: (0,0)->(0,1)->(1,1) |
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// A step of (1,0) in (i,j) means a step of (1-c,-c) in (x,y), and |
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// a step of (0,1) in (i,j) means a step of (-c,1-c) in (x,y), where |
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// c = (3-sqrt(3))/6 |
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var x1 = x0 - i1 + G2; // Offsets for middle corner in (x,y) unskewed coords |
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var y1 = y0 - j1 + G2; |
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var x2 = x0 - 1.0 + 2.0 * G2; // Offsets for last corner in (x,y) unskewed coords |
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var y2 = y0 - 1.0 + 2.0 * G2; |
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// Work out the hashed gradient indices of the three simplex corners |
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var ii = i & 255; |
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var jj = j & 255; |
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var gi0 = this.perm[ii+this.perm[jj]] % 12; |
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var gi1 = this.perm[ii+i1+this.perm[jj+j1]] % 12; |
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var gi2 = this.perm[ii+1+this.perm[jj+1]] % 12; |
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// Calculate the contribution from the three corners |
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var t0 = 0.5 - x0*x0-y0*y0; |
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if(t0<0) n0 = 0.0; |
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else { |
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t0 *= t0; |
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n0 = t0 * t0 * this.dot(this.grad3[gi0], x0, y0); // (x,y) of grad3 used for 2D gradient |
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} |
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var t1 = 0.5 - x1*x1-y1*y1; |
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if(t1<0) n1 = 0.0; |
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else { |
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t1 *= t1; |
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n1 = t1 * t1 * this.dot(this.grad3[gi1], x1, y1); |
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} |
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var t2 = 0.5 - x2*x2-y2*y2; |
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if(t2<0) n2 = 0.0; |
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else { |
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t2 *= t2; |
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n2 = t2 * t2 * this.dot(this.grad3[gi2], x2, y2); |
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} |
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// Add contributions from each corner to get the final noise value. |
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// The result is scaled to return values in the interval [-1,1]. |
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return 70.0 * (n0 + n1 + n2); |
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}; |
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// 3D simplex noise |
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SimplexNoise.prototype.noise3d = function(xin, yin, zin) { |
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var n0, n1, n2, n3; // Noise contributions from the four corners |
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// Skew the input space to determine which simplex cell we're in |
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var F3 = 1.0/3.0; |
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var s = (xin+yin+zin)*F3; // Very nice and simple skew factor for 3D |
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var i = Math.floor(xin+s); |
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var j = Math.floor(yin+s); |
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var k = Math.floor(zin+s); |
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var G3 = 1.0/6.0; // Very nice and simple unskew factor, too |
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var t = (i+j+k)*G3; |
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var X0 = i-t; // Unskew the cell origin back to (x,y,z) space |
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var Y0 = j-t; |
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var Z0 = k-t; |
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var x0 = xin-X0; // The x,y,z distances from the cell origin |
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var y0 = yin-Y0; |
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var z0 = zin-Z0; |
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// For the 3D case, the simplex shape is a slightly irregular tetrahedron. |
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// Determine which simplex we are in. |
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var i1, j1, k1; // Offsets for second corner of simplex in (i,j,k) coords |
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var i2, j2, k2; // Offsets for third corner of simplex in (i,j,k) coords |
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if(x0>=y0) { |
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if(y0>=z0) |
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{ i1=1; j1=0; k1=0; i2=1; j2=1; k2=0; } // X Y Z order |
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else if(x0>=z0) { i1=1; j1=0; k1=0; i2=1; j2=0; k2=1; } // X Z Y order |
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else { i1=0; j1=0; k1=1; i2=1; j2=0; k2=1; } // Z X Y order |
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} |
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else { // x0<y0 |
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if(y0<z0) { i1=0; j1=0; k1=1; i2=0; j2=1; k2=1; } // Z Y X order |
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else if(x0<z0) { i1=0; j1=1; k1=0; i2=0; j2=1; k2=1; } // Y Z X order |
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else { i1=0; j1=1; k1=0; i2=1; j2=1; k2=0; } // Y X Z order |
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} |
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// A step of (1,0,0) in (i,j,k) means a step of (1-c,-c,-c) in (x,y,z), |
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// a step of (0,1,0) in (i,j,k) means a step of (-c,1-c,-c) in (x,y,z), and |
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// a step of (0,0,1) in (i,j,k) means a step of (-c,-c,1-c) in (x,y,z), where |
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// c = 1/6. |
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var x1 = x0 - i1 + G3; // Offsets for second corner in (x,y,z) coords |
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var y1 = y0 - j1 + G3; |
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var z1 = z0 - k1 + G3; |
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var x2 = x0 - i2 + 2.0*G3; // Offsets for third corner in (x,y,z) coords |
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var y2 = y0 - j2 + 2.0*G3; |
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var z2 = z0 - k2 + 2.0*G3; |
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var x3 = x0 - 1.0 + 3.0*G3; // Offsets for last corner in (x,y,z) coords |
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var y3 = y0 - 1.0 + 3.0*G3; |
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var z3 = z0 - 1.0 + 3.0*G3; |
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// Work out the hashed gradient indices of the four simplex corners |
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var ii = i & 255; |
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var jj = j & 255; |
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var kk = k & 255; |
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var gi0 = this.perm[ii+this.perm[jj+this.perm[kk]]] % 12; |
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var gi1 = this.perm[ii+i1+this.perm[jj+j1+this.perm[kk+k1]]] % 12; |
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var gi2 = this.perm[ii+i2+this.perm[jj+j2+this.perm[kk+k2]]] % 12; |
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var gi3 = this.perm[ii+1+this.perm[jj+1+this.perm[kk+1]]] % 12; |
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// Calculate the contribution from the four corners |
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var t0 = 0.6 - x0*x0 - y0*y0 - z0*z0; |
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if(t0<0) n0 = 0.0; |
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else { |
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t0 *= t0; |
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n0 = t0 * t0 * this.dot(this.grad3[gi0], x0, y0, z0); |
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} |
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var t1 = 0.6 - x1*x1 - y1*y1 - z1*z1; |
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if(t1<0) n1 = 0.0; |
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else { |
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t1 *= t1; |
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n1 = t1 * t1 * this.dot(this.grad3[gi1], x1, y1, z1); |
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} |
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var t2 = 0.6 - x2*x2 - y2*y2 - z2*z2; |
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if(t2<0) n2 = 0.0; |
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else { |
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t2 *= t2; |
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n2 = t2 * t2 * this.dot(this.grad3[gi2], x2, y2, z2); |
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} |
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var t3 = 0.6 - x3*x3 - y3*y3 - z3*z3; |
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if(t3<0) n3 = 0.0; |
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else { |
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t3 *= t3; |
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n3 = t3 * t3 * this.dot(this.grad3[gi3], x3, y3, z3); |
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} |
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// Add contributions from each corner to get the final noise value. |
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// The result is scaled to stay just inside [-1,1] |
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return 32.0*(n0 + n1 + n2 + n3); |
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}; |
This comment has been minimized.
Thanks for sharing! I found the Classical function to be noticeably faster than the Simplex3D while polling large numbers of points. (Chrome 28.0.1500.95)