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| − | If you want to understand how this program works Yo will have to spend a good number of hours going through it. This code is here not to show you how something works but rather what is possible. It seems unfathomable, but nevertheless someone wrote it. It has 350 lines of code, each component does something small and understandable. Working together they can achieve an almost magical result. | + | If you want to understand how this program works, you will have to spend a good number of hours going through it. This code is here not to show you how something works but rather what is possible. It seems unfathomable, but nevertheless someone wrote it. It has 180 lines of code, each component does something small and understandable. Working together they can achieve an almost magical result. |
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| − | <edcode>function noise2() { return 0.5}; | + | <edcode> |
| | function drawEye() { | | function drawEye() { |
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| | var fue = [1,1,1]; | | var fue = [1,1,1]; |
| − | var ven = noise2(24*x,24*y,256,256); | + | var ven = noise2d(24*x,24*y,128,128); |
| | ven = smoothStep(ven,0-0.2,0) - smoothStep(ven,0,0.2); | | ven = smoothStep(ven,0-0.2,0) - smoothStep(ven,0,0.2); |
| − | ven+=x + x*x*x*x*x*x*7; | + | ven+=x + x*x*x*x*x*x*10; |
| | fue[0]+=0.04 - 0.00*ven; | | fue[0]+=0.04 - 0.00*ven; |
| | fue[1]+=0.04 - 0.05*ven; | | fue[1]+=0.04 - 0.05*ven; |
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| | | | |
| | var den = [0.3,0.7,0.4+e]; | | var den = [0.3,0.7,0.4+e]; |
| − | var no = 0.8+0.2*noise2(4*r,32*a/Math.PI,32,32); | + | var no = 0.8+0.2*noise2(4*r,32*a/Math.PI,256,256); |
| | den=colsca(den,no); | | den=colsca(den,no); |
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| | //reflection | | //reflection |
| | var r3=Math.sqrt(r*r*r); | | var r3=Math.sqrt(r*r*r); |
| − | var re=noise2(2+4*r3*Math.cos(a),4*r3*Math.sin(a),256,256); | + | var re=noise2(2+4*r3*Math.cos(a),4*r3*Math.sin(a),128,128); |
| | re=0.4*smoothStep(re,0.1,0.5); | | re=0.4*smoothStep(re,0.1,0.5); |
| | mixed[0]+=re*(1-mixed[0]); | | mixed[0]+=re*(1-mixed[0]); |
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| | } | | } |
| | } | | } |
| − | // This bit 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
| |
| − | 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 = [];
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| − | 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
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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];
| |
| − | }
| |
| | | | |
| − | // A lookup table to traverse the simplex around a given point in 4D.
| + | function noise2(x,y,a,b) {return noise2d(x*a/256,y*b/256)}; |
| − | // Details can be found where this table is used, in the 4D noise method.
| + | |
| − | this.simplex = [
| + | drawEye(); |
| − | [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) {
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| − | return g[0]*x + g[1]*y;
| |
| − | };
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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
| |
| − | // 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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| − | 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);
| |
| − | }
| |
| − | // 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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| − |
| |
| − | // 3D simplex noise
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| − | SimplexNoise.prototype.noise3d = function(xin, yin, zin) {
| |
| − | 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
| |
| − | }
| |
| − | 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
| |
| − | 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
| |
| − | }
| |
| − | // 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
| |
| − | // 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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| − | };
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| − |
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| − | DefaultNoise = new SimplexNoise(Math);
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| − |
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| − | function noise2(x,y,p,q) {
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| − | return DefaultNoise.noise(x,y);
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| − | }
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| − |
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| − | drawEye();
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| | | | |
| | </edcode> | | </edcode> |
If you want to understand how this program works, you will have to spend a good number of hours going through it. This code is here not to show you how something works but rather what is possible. It seems unfathomable, but nevertheless someone wrote it. It has 180 lines of code, each component does something small and understandable. Working together they can achieve an almost magical result.
