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324 lines
13 KiB
324 lines
13 KiB
// 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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// Added 4D noise
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// Joshua Koo zz85nus@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.grad4 = [[ 0,1,1,1 ], [ 0,1,1,-1 ], [ 0,1,-1,1 ], [ 0,1,-1,-1 ],
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[ 0,-1,1,1 ], [ 0,-1,1,-1 ], [ 0,-1,-1,1 ], [ 0,-1,-1,-1 ],
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[ 1,0,1,1 ], [ 1,0,1,-1 ], [ 1,0,-1,1 ], [ 1,0,-1,-1 ],
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[ -1,0,1,1 ], [ -1,0,1,-1 ], [ -1,0,-1,1 ], [ -1,0,-1,-1 ],
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[ 1,1,0,1 ], [ 1,1,0,-1 ], [ 1,-1,0,1 ], [ 1,-1,0,-1 ],
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[ -1,1,0,1 ], [ -1,1,0,-1 ], [ -1,-1,0,1 ], [ -1,-1,0,-1 ],
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[ 1,1,1,0 ], [ 1,1,-1,0 ], [ 1,-1,1,0 ], [ 1,-1,-1,0 ],
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[ -1,1,1,0 ], [ -1,1,-1,0 ], [ -1,-1,1,0 ], [ -1,-1,-1,0 ]];
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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.dot3 = function(g, x, y, z) {
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return g[0] * x + g[1] * y + g[2] * z;
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};
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SimplexNoise.prototype.dot4 = function(g, x, y, z, w) {
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return g[0] * x + g[1] * y + g[2] * z + g[3] * w;
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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.dot3(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.dot3(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.dot3(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.dot3(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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// 4D simplex noise
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SimplexNoise.prototype.noise4d = function( x, y, z, w ) {
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// For faster and easier lookups
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var grad4 = this.grad4;
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var simplex = this.simplex;
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var perm = this.perm;
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// The skewing and unskewing factors are hairy again for the 4D case
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var F4 = (Math.sqrt(5.0) - 1.0) / 4.0;
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var G4 = (5.0 - Math.sqrt(5.0)) / 20.0;
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var n0, n1, n2, n3, n4; // Noise contributions from the five corners
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// Skew the (x,y,z,w) space to determine which cell of 24 simplices we're in
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var s = (x + y + z + w) * F4; // Factor for 4D skewing
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var i = Math.floor(x + s);
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var j = Math.floor(y + s);
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var k = Math.floor(z + s);
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var l = Math.floor(w + s);
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var t = (i + j + k + l) * G4; // Factor for 4D unskewing
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var X0 = i - t; // Unskew the cell origin back to (x,y,z,w) space
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var Y0 = j - t;
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var Z0 = k - t;
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var W0 = l - t;
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var x0 = x - X0; // The x,y,z,w distances from the cell origin
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var y0 = y - Y0;
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var z0 = z - Z0;
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var w0 = w - W0;
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// For the 4D case, the simplex is a 4D shape I won't even try to describe.
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// To find out which of the 24 possible simplices we're in, we need to
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// determine the magnitude ordering of x0, y0, z0 and w0.
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// The method below is a good way of finding the ordering of x,y,z,w and
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// then find the correct traversal order for the simplex we’re in.
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// First, six pair-wise comparisons are performed between each possible pair
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// of the four coordinates, and the results are used to add up binary bits
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// for an integer index.
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var c1 = (x0 > y0) ? 32 : 0;
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var c2 = (x0 > z0) ? 16 : 0;
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var c3 = (y0 > z0) ? 8 : 0;
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var c4 = (x0 > w0) ? 4 : 0;
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var c5 = (y0 > w0) ? 2 : 0;
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var c6 = (z0 > w0) ? 1 : 0;
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var c = c1 + c2 + c3 + c4 + c5 + c6;
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var i1, j1, k1, l1; // The integer offsets for the second simplex corner
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var i2, j2, k2, l2; // The integer offsets for the third simplex corner
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var i3, j3, k3, l3; // The integer offsets for the fourth simplex corner
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// simplex[c] is a 4-vector with the numbers 0, 1, 2 and 3 in some order.
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// Many values of c will never occur, since e.g. x>y>z>w makes x<z, y<w and x<w
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// impossible. Only the 24 indices which have non-zero entries make any sense.
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// We use a thresholding to set the coordinates in turn from the largest magnitude.
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// The number 3 in the "simplex" array is at the position of the largest coordinate.
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i1 = simplex[c][0] >= 3 ? 1 : 0;
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j1 = simplex[c][1] >= 3 ? 1 : 0;
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k1 = simplex[c][2] >= 3 ? 1 : 0;
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l1 = simplex[c][3] >= 3 ? 1 : 0;
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// The number 2 in the "simplex" array is at the second largest coordinate.
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i2 = simplex[c][0] >= 2 ? 1 : 0;
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j2 = simplex[c][1] >= 2 ? 1 : 0; k2 = simplex[c][2] >= 2 ? 1 : 0;
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l2 = simplex[c][3] >= 2 ? 1 : 0;
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// The number 1 in the "simplex" array is at the second smallest coordinate.
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i3 = simplex[c][0] >= 1 ? 1 : 0;
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j3 = simplex[c][1] >= 1 ? 1 : 0;
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k3 = simplex[c][2] >= 1 ? 1 : 0;
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l3 = simplex[c][3] >= 1 ? 1 : 0;
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// The fifth corner has all coordinate offsets = 1, so no need to look that up.
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var x1 = x0 - i1 + G4; // Offsets for second corner in (x,y,z,w) coords
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var y1 = y0 - j1 + G4;
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var z1 = z0 - k1 + G4;
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var w1 = w0 - l1 + G4;
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var x2 = x0 - i2 + 2.0 * G4; // Offsets for third corner in (x,y,z,w) coords
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var y2 = y0 - j2 + 2.0 * G4;
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var z2 = z0 - k2 + 2.0 * G4;
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var w2 = w0 - l2 + 2.0 * G4;
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var x3 = x0 - i3 + 3.0 * G4; // Offsets for fourth corner in (x,y,z,w) coords
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var y3 = y0 - j3 + 3.0 * G4;
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var z3 = z0 - k3 + 3.0 * G4;
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var w3 = w0 - l3 + 3.0 * G4;
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var x4 = x0 - 1.0 + 4.0 * G4; // Offsets for last corner in (x,y,z,w) coords
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var y4 = y0 - 1.0 + 4.0 * G4;
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var z4 = z0 - 1.0 + 4.0 * G4;
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var w4 = w0 - 1.0 + 4.0 * G4;
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// Work out the hashed gradient indices of the five 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 ll = l & 255;
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var gi0 = perm[ii + perm[jj + perm[kk + perm[ll]]]] % 32;
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var gi1 = perm[ii + i1 + perm[jj + j1 + perm[kk + k1 + perm[ll + l1]]]] % 32;
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var gi2 = perm[ii + i2 + perm[jj + j2 + perm[kk + k2 + perm[ll + l2]]]] % 32;
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var gi3 = perm[ii + i3 + perm[jj + j3 + perm[kk + k3 + perm[ll + l3]]]] % 32;
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var gi4 = perm[ii + 1 + perm[jj + 1 + perm[kk + 1 + perm[ll + 1]]]] % 32;
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// Calculate the contribution from the five corners
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var t0 = 0.6 - x0 * x0 - y0 * y0 - z0 * z0 - w0 * w0;
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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.dot4(grad4[gi0], x0, y0, z0, w0);
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}
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var t1 = 0.6 - x1 * x1 - y1 * y1 - z1 * z1 - w1 * w1;
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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.dot4(grad4[gi1], x1, y1, z1, w1);
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}
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var t2 = 0.6 - x2 * x2 - y2 * y2 - z2 * z2 - w2 * w2;
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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.dot4(grad4[gi2], x2, y2, z2, w2);
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} var t3 = 0.6 - x3 * x3 - y3 * y3 - z3 * z3 - w3 * w3;
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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.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);
|
|
};
|