| /* |
| * A fast javascript implementation of simplex noise by Jonas Wagner |
| * |
| * Based on a speed-improved simplex noise algorithm for 2D, 3D and 4D in Java. |
| * Which is based on example code by Stefan Gustavson (stegu@itn.liu.se). |
| * With Optimisations by Peter Eastman (peastman@drizzle.stanford.edu). |
| * Better rank ordering method by Stefan Gustavson in 2012. |
| * |
| * |
| * Copyright (C) 2016 Jonas Wagner |
| * |
| * Permission is hereby granted, free of charge, to any person obtaining |
| * a copy of this software and associated documentation files (the |
| * "Software"), to deal in the Software without restriction, including |
| * without limitation the rights to use, copy, modify, merge, publish, |
| * distribute, sublicense, and/or sell copies of the Software, and to |
| * permit persons to whom the Software is furnished to do so, subject to |
| * the following conditions: |
| * |
| * The above copyright notice and this permission notice shall be |
| * included in all copies or substantial portions of the Software. |
| * |
| * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, |
| * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF |
| * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND |
| * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE |
| * LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION |
| * OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION |
| * WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. |
| * |
| */ |
| (function() { |
| 'use strict'; |
| |
| var F2 = 0.5 * (Math.sqrt(3.0) - 1.0); |
| var G2 = (3.0 - Math.sqrt(3.0)) / 6.0; |
| var F3 = 1.0 / 3.0; |
| var G3 = 1.0 / 6.0; |
| var F4 = (Math.sqrt(5.0) - 1.0) / 4.0; |
| var G4 = (5.0 - Math.sqrt(5.0)) / 20.0; |
| |
| function SimplexNoise(random) { |
| if (!random) random = Math.random; |
| this.p = buildPermutationTable(random); |
| this.perm = new Uint8Array(512); |
| this.permMod12 = new Uint8Array(512); |
| for (var i = 0; i < 512; i++) { |
| this.perm[i] = this.p[i & 255]; |
| this.permMod12[i] = this.perm[i] % 12; |
| } |
| |
| } |
| SimplexNoise.prototype = { |
| grad3: new Float32Array([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]), |
| grad4: new Float32Array([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]), |
| noise2D: function(xin, yin) { |
| var permMod12 = this.permMod12; |
| var perm = this.perm; |
| var grad3 = this.grad3; |
| var n0 = 0; // Noise contributions from the three corners |
| var n1 = 0; |
| var n2 = 0; |
| // Skew the input space to determine which simplex cell we're in |
| var s = (xin + yin) * F2; // Hairy factor for 2D |
| var i = Math.floor(xin + s); |
| var j = Math.floor(yin + s); |
| 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; |
| // Calculate the contribution from the three corners |
| var t0 = 0.5 - x0 * x0 - y0 * y0; |
| if (t0 >= 0) { |
| var gi0 = permMod12[ii + perm[jj]] * 3; |
| t0 *= t0; |
| n0 = t0 * t0 * (grad3[gi0] * x0 + grad3[gi0 + 1] * y0); // (x,y) of grad3 used for 2D gradient |
| } |
| var t1 = 0.5 - x1 * x1 - y1 * y1; |
| if (t1 >= 0) { |
| var gi1 = permMod12[ii + i1 + perm[jj + j1]] * 3; |
| t1 *= t1; |
| n1 = t1 * t1 * (grad3[gi1] * x1 + grad3[gi1 + 1] * y1); |
| } |
| var t2 = 0.5 - x2 * x2 - y2 * y2; |
| if (t2 >= 0) { |
| var gi2 = permMod12[ii + 1 + perm[jj + 1]] * 3; |
| t2 *= t2; |
| n2 = t2 * t2 * (grad3[gi2] * x2 + grad3[gi2 + 1] * 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 |
| noise3D: function(xin, yin, zin) { |
| var permMod12 = this.permMod12; |
| var perm = this.perm; |
| var grad3 = this.grad3; |
| var n0, n1, n2, n3; // Noise contributions from the four corners |
| // Skew the input space to determine which simplex cell we're in |
| 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 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; |
| // Calculate the contribution from the four corners |
| var t0 = 0.6 - x0 * x0 - y0 * y0 - z0 * z0; |
| if (t0 < 0) n0 = 0.0; |
| else { |
| var gi0 = permMod12[ii + perm[jj + perm[kk]]] * 3; |
| t0 *= t0; |
| n0 = t0 * t0 * (grad3[gi0] * x0 + grad3[gi0 + 1] * y0 + grad3[gi0 + 2] * z0); |
| } |
| var t1 = 0.6 - x1 * x1 - y1 * y1 - z1 * z1; |
| if (t1 < 0) n1 = 0.0; |
| else { |
| var gi1 = permMod12[ii + i1 + perm[jj + j1 + perm[kk + k1]]] * 3; |
| t1 *= t1; |
| n1 = t1 * t1 * (grad3[gi1] * x1 + grad3[gi1 + 1] * y1 + grad3[gi1 + 2] * z1); |
| } |
| var t2 = 0.6 - x2 * x2 - y2 * y2 - z2 * z2; |
| if (t2 < 0) n2 = 0.0; |
| else { |
| var gi2 = permMod12[ii + i2 + perm[jj + j2 + perm[kk + k2]]] * 3; |
| t2 *= t2; |
| n2 = t2 * t2 * (grad3[gi2] * x2 + grad3[gi2 + 1] * y2 + grad3[gi2 + 2] * z2); |
| } |
| var t3 = 0.6 - x3 * x3 - y3 * y3 - z3 * z3; |
| if (t3 < 0) n3 = 0.0; |
| else { |
| var gi3 = permMod12[ii + 1 + perm[jj + 1 + perm[kk + 1]]] * 3; |
| t3 *= t3; |
| n3 = t3 * t3 * (grad3[gi3] * x3 + grad3[gi3 + 1] * y3 + grad3[gi3 + 2] * 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, better simplex rank ordering method 2012-03-09 |
| noise4D: function(x, y, z, w) { |
| var permMod12 = this.permMod12; |
| var perm = this.perm; |
| var grad4 = this.grad4; |
| |
| 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. |
| // Six pair-wise comparisons are performed between each possible pair |
| // of the four coordinates, and the results are used to rank the numbers. |
| var rankx = 0; |
| var ranky = 0; |
| var rankz = 0; |
| var rankw = 0; |
| if (x0 > y0) rankx++; |
| else ranky++; |
| if (x0 > z0) rankx++; |
| else rankz++; |
| if (x0 > w0) rankx++; |
| else rankw++; |
| if (y0 > z0) ranky++; |
| else rankz++; |
| if (y0 > w0) ranky++; |
| else rankw++; |
| if (z0 > w0) rankz++; |
| else rankw++; |
| 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. |
| // Rank 3 denotes the largest coordinate. |
| i1 = rankx >= 3 ? 1 : 0; |
| j1 = ranky >= 3 ? 1 : 0; |
| k1 = rankz >= 3 ? 1 : 0; |
| l1 = rankw >= 3 ? 1 : 0; |
| // Rank 2 denotes the second largest coordinate. |
| i2 = rankx >= 2 ? 1 : 0; |
| j2 = ranky >= 2 ? 1 : 0; |
| k2 = rankz >= 2 ? 1 : 0; |
| l2 = rankw >= 2 ? 1 : 0; |
| // Rank 1 denotes the second smallest coordinate. |
| i3 = rankx >= 1 ? 1 : 0; |
| j3 = ranky >= 1 ? 1 : 0; |
| k3 = rankz >= 1 ? 1 : 0; |
| l3 = rankw >= 1 ? 1 : 0; |
| // The fifth corner has all coordinate offsets = 1, so no need to compute that. |
| 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; |
| // 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 { |
| var gi0 = (perm[ii + perm[jj + perm[kk + perm[ll]]]] % 32) * 4; |
| t0 *= t0; |
| n0 = t0 * t0 * (grad4[gi0] * x0 + grad4[gi0 + 1] * y0 + grad4[gi0 + 2] * z0 + grad4[gi0 + 3] * w0); |
| } |
| var t1 = 0.6 - x1 * x1 - y1 * y1 - z1 * z1 - w1 * w1; |
| if (t1 < 0) n1 = 0.0; |
| else { |
| var gi1 = (perm[ii + i1 + perm[jj + j1 + perm[kk + k1 + perm[ll + l1]]]] % 32) * 4; |
| t1 *= t1; |
| n1 = t1 * t1 * (grad4[gi1] * x1 + grad4[gi1 + 1] * y1 + grad4[gi1 + 2] * z1 + grad4[gi1 + 3] * w1); |
| } |
| var t2 = 0.6 - x2 * x2 - y2 * y2 - z2 * z2 - w2 * w2; |
| if (t2 < 0) n2 = 0.0; |
| else { |
| var gi2 = (perm[ii + i2 + perm[jj + j2 + perm[kk + k2 + perm[ll + l2]]]] % 32) * 4; |
| t2 *= t2; |
| n2 = t2 * t2 * (grad4[gi2] * x2 + grad4[gi2 + 1] * y2 + grad4[gi2 + 2] * z2 + grad4[gi2 + 3] * w2); |
| } |
| var t3 = 0.6 - x3 * x3 - y3 * y3 - z3 * z3 - w3 * w3; |
| if (t3 < 0) n3 = 0.0; |
| else { |
| var gi3 = (perm[ii + i3 + perm[jj + j3 + perm[kk + k3 + perm[ll + l3]]]] % 32) * 4; |
| t3 *= t3; |
| n3 = t3 * t3 * (grad4[gi3] * x3 + grad4[gi3 + 1] * y3 + grad4[gi3 + 2] * z3 + grad4[gi3 + 3] * w3); |
| } |
| var t4 = 0.6 - x4 * x4 - y4 * y4 - z4 * z4 - w4 * w4; |
| if (t4 < 0) n4 = 0.0; |
| else { |
| var gi4 = (perm[ii + 1 + perm[jj + 1 + perm[kk + 1 + perm[ll + 1]]]] % 32) * 4; |
| t4 *= t4; |
| n4 = t4 * t4 * (grad4[gi4] * x4 + grad4[gi4 + 1] * y4 + grad4[gi4 + 2] * z4 + grad4[gi4 + 3] * w4); |
| } |
| // Sum up and scale the result to cover the range [-1,1] |
| return 27.0 * (n0 + n1 + n2 + n3 + n4); |
| } |
| }; |
| |
| function buildPermutationTable(random) { |
| var i; |
| var p = new Uint8Array(256); |
| for (i = 0; i < 256; i++) { |
| p[i] = i; |
| } |
| for (i = 0; i < 255; i++) { |
| var r = i + ~~(random() * (256 - i)); |
| var aux = p[i]; |
| p[i] = p[r]; |
| p[r] = aux; |
| } |
| return p; |
| } |
| SimplexNoise._buildPermutationTable = buildPermutationTable; |
| |
| // amd |
| if (typeof define !== 'undefined' && define.amd) define(function() {return SimplexNoise;}); |
| // common js |
| if (typeof exports !== 'undefined') exports.SimplexNoise = SimplexNoise; |
| // browser |
| else if (typeof window !== 'undefined') window.SimplexNoise = SimplexNoise; |
| // nodejs |
| if (typeof module !== 'undefined') { |
| module.exports = SimplexNoise; |
| } |
| |
| })(); |