1/*
2 * A speed-improved perlin and simplex noise algorithms for 2D.
3 *
4 * Based on example code by Stefan Gustavson (stegu@itn.liu.se).
5 * Optimisations by Peter Eastman (peastman@drizzle.stanford.edu).
6 * Better rank ordering method by Stefan Gustavson in 2012.
7 * Converted to Javascript by Joseph Gentle.
8 *
9 * Version 2012-03-09
10 *
11 * This code was placed in the public domain by its original author,
12 * Stefan Gustavson. You may use it as you see fit, but
13 * attribution is appreciated.
14 *
15 */
16
17(function(global){
18 var module = global.noise = {};
19
20 function Grad(x, y, z) {
21 this.x = x; this.y = y; this.z = z;
22 }
23
24 Grad.prototype.dot2 = function(x, y) {
25 return this.x*x + this.y*y;
26 };
27
28 Grad.prototype.dot3 = function(x, y, z) {
29 return this.x*x + this.y*y + this.z*z;
30 };
31
32 var grad3 = [new Grad(1,1,0),new Grad(-1,1,0),new Grad(1,-1,0),new Grad(-1,-1,0),
33 new Grad(1,0,1),new Grad(-1,0,1),new Grad(1,0,-1),new Grad(-1,0,-1),
34 new Grad(0,1,1),new Grad(0,-1,1),new Grad(0,1,-1),new Grad(0,-1,-1)];
35
36 var p = [151,160,137,91,90,15,
37 131,13,201,95,96,53,194,233,7,225,140,36,103,30,69,142,8,99,37,240,21,10,23,
38 190, 6,148,247,120,234,75,0,26,197,62,94,252,219,203,117,35,11,32,57,177,33,
39 88,237,149,56,87,174,20,125,136,171,168, 68,175,74,165,71,134,139,48,27,166,
40 77,146,158,231,83,111,229,122,60,211,133,230,220,105,92,41,55,46,245,40,244,
41 102,143,54, 65,25,63,161, 1,216,80,73,209,76,132,187,208, 89,18,169,200,196,
42 135,130,116,188,159,86,164,100,109,198,173,186, 3,64,52,217,226,250,124,123,
43 5,202,38,147,118,126,255,82,85,212,207,206,59,227,47,16,58,17,182,189,28,42,
44 223,183,170,213,119,248,152, 2,44,154,163, 70,221,153,101,155,167, 43,172,9,
45 129,22,39,253, 19,98,108,110,79,113,224,232,178,185, 112,104,218,246,97,228,
46 251,34,242,193,238,210,144,12,191,179,162,241, 81,51,145,235,249,14,239,107,
47 49,192,214, 31,181,199,106,157,184, 84,204,176,115,121,50,45,127, 4,150,254,
48 138,236,205,93,222,114,67,29,24,72,243,141,128,195,78,66,215,61,156,180];
49 // To remove the need for index wrapping, double the permutation table length
50 var perm = new Array(512);
51 var gradP = new Array(512);
52
53 // This isn't a very good seeding function, but it works ok. It supports 2^16
54 // different seed values. Write something better if you need more seeds.
55 module.seed = function(seed) {
56 if(seed > 0 && seed < 1) {
57 // Scale the seed out
58 seed *= 65536;
59 }
60
61 seed = Math.floor(seed);
62 if(seed < 256) {
63 seed |= seed << 8;
64 }
65
66 for(var i = 0; i < 256; i++) {
67 var v;
68 if (i & 1) {
69 v = p[i] ^ (seed & 255);
70 } else {
71 v = p[i] ^ ((seed>>8) & 255);
72 }
73
74 perm[i] = perm[i + 256] = v;
75 gradP[i] = gradP[i + 256] = grad3[v % 12];
76 }
77 };
78
79 module.seed(0);
80
81 /*
82 for(var i=0; i<256; i++) {
83 perm[i] = perm[i + 256] = p[i];
84 gradP[i] = gradP[i + 256] = grad3[perm[i] % 12];
85 }*/
86
87 // Skewing and unskewing factors for 2, 3, and 4 dimensions
88 var F2 = 0.5*(Math.sqrt(3)-1);
89 var G2 = (3-Math.sqrt(3))/6;
90
91 var F3 = 1/3;
92 var G3 = 1/6;
93
94 // 2D simplex noise
95 module.simplex2 = function(xin, yin) {
96 var n0, n1, n2; // Noise contributions from the three corners
97 // Skew the input space to determine which simplex cell we're in
98 var s = (xin+yin)*F2; // Hairy factor for 2D
99 var i = Math.floor(xin+s);
100 var j = Math.floor(yin+s);
101 var t = (i+j)*G2;
102 var x0 = xin-i+t; // The x,y distances from the cell origin, unskewed.
103 var y0 = yin-j+t;
104 // For the 2D case, the simplex shape is an equilateral triangle.
105 // Determine which simplex we are in.
106 var i1, j1; // Offsets for second (middle) corner of simplex in (i,j) coords
107 if(x0>y0) { // lower triangle, XY order: (0,0)->(1,0)->(1,1)
108 i1=1; j1=0;
109 } else { // upper triangle, YX order: (0,0)->(0,1)->(1,1)
110 i1=0; j1=1;
111 }
112 // A step of (1,0) in (i,j) means a step of (1-c,-c) in (x,y), and
113 // a step of (0,1) in (i,j) means a step of (-c,1-c) in (x,y), where
114 // c = (3-sqrt(3))/6
115 var x1 = x0 - i1 + G2; // Offsets for middle corner in (x,y) unskewed coords
116 var y1 = y0 - j1 + G2;
117 var x2 = x0 - 1 + 2 * G2; // Offsets for last corner in (x,y) unskewed coords
118 var y2 = y0 - 1 + 2 * G2;
119 // Work out the hashed gradient indices of the three simplex corners
120 i &= 255;
121 j &= 255;
122 var gi0 = gradP[i+perm[j]];
123 var gi1 = gradP[i+i1+perm[j+j1]];
124 var gi2 = gradP[i+1+perm[j+1]];
125 // Calculate the contribution from the three corners
126 var t0 = 0.5 - x0*x0-y0*y0;
127 if(t0<0) {
128 n0 = 0;
129 } else {
130 t0 *= t0;
131 n0 = t0 * t0 * gi0.dot2(x0, y0); // (x,y) of grad3 used for 2D gradient
132 }
133 var t1 = 0.5 - x1*x1-y1*y1;
134 if(t1<0) {
135 n1 = 0;
136 } else {
137 t1 *= t1;
138 n1 = t1 * t1 * gi1.dot2(x1, y1);
139 }
140 var t2 = 0.5 - x2*x2-y2*y2;
141 if(t2<0) {
142 n2 = 0;
143 } else {
144 t2 *= t2;
145 n2 = t2 * t2 * gi2.dot2(x2, y2);
146 }
147 // Add contributions from each corner to get the final noise value.
148 // The result is scaled to return values in the interval [-1,1].
149 return 70 * (n0 + n1 + n2);
150 };
151
152 // 3D simplex noise
153 module.simplex3 = function(xin, yin, zin) {
154 var n0, n1, n2, n3; // Noise contributions from the four corners
155
156 // Skew the input space to determine which simplex cell we're in
157 var s = (xin+yin+zin)*F3; // Hairy factor for 2D
158 var i = Math.floor(xin+s);
159 var j = Math.floor(yin+s);
160 var k = Math.floor(zin+s);
161
162 var t = (i+j+k)*G3;
163 var x0 = xin-i+t; // The x,y distances from the cell origin, unskewed.
164 var y0 = yin-j+t;
165 var z0 = zin-k+t;
166
167 // For the 3D case, the simplex shape is a slightly irregular tetrahedron.
168 // Determine which simplex we are in.
169 var i1, j1, k1; // Offsets for second corner of simplex in (i,j,k) coords
170 var i2, j2, k2; // Offsets for third corner of simplex in (i,j,k) coords
171 if(x0 >= y0) {
172 if(y0 >= z0) { i1=1; j1=0; k1=0; i2=1; j2=1; k2=0; }
173 else if(x0 >= z0) { i1=1; j1=0; k1=0; i2=1; j2=0; k2=1; }
174 else { i1=0; j1=0; k1=1; i2=1; j2=0; k2=1; }
175 } else {
176 if(y0 < z0) { i1=0; j1=0; k1=1; i2=0; j2=1; k2=1; }
177 else if(x0 < z0) { i1=0; j1=1; k1=0; i2=0; j2=1; k2=1; }
178 else { i1=0; j1=1; k1=0; i2=1; j2=1; k2=0; }
179 }
180 // A step of (1,0,0) in (i,j,k) means a step of (1-c,-c,-c) in (x,y,z),
181 // a step of (0,1,0) in (i,j,k) means a step of (-c,1-c,-c) in (x,y,z), and
182 // a step of (0,0,1) in (i,j,k) means a step of (-c,-c,1-c) in (x,y,z), where
183 // c = 1/6.
184 var x1 = x0 - i1 + G3; // Offsets for second corner
185 var y1 = y0 - j1 + G3;
186 var z1 = z0 - k1 + G3;
187
188 var x2 = x0 - i2 + 2 * G3; // Offsets for third corner
189 var y2 = y0 - j2 + 2 * G3;
190 var z2 = z0 - k2 + 2 * G3;
191
192 var x3 = x0 - 1 + 3 * G3; // Offsets for fourth corner
193 var y3 = y0 - 1 + 3 * G3;
194 var z3 = z0 - 1 + 3 * G3;
195
196 // Work out the hashed gradient indices of the four simplex corners
197 i &= 255;
198 j &= 255;
199 k &= 255;
200 var gi0 = gradP[i+ perm[j+ perm[k ]]];
201 var gi1 = gradP[i+i1+perm[j+j1+perm[k+k1]]];
202 var gi2 = gradP[i+i2+perm[j+j2+perm[k+k2]]];
203 var gi3 = gradP[i+ 1+perm[j+ 1+perm[k+ 1]]];
204
205 // Calculate the contribution from the four corners
206 var t0 = 0.6 - x0*x0 - y0*y0 - z0*z0;
207 if(t0<0) {
208 n0 = 0;
209 } else {
210 t0 *= t0;
211 n0 = t0 * t0 * gi0.dot3(x0, y0, z0); // (x,y) of grad3 used for 2D gradient
212 }
213 var t1 = 0.6 - x1*x1 - y1*y1 - z1*z1;
214 if(t1<0) {
215 n1 = 0;
216 } else {
217 t1 *= t1;
218 n1 = t1 * t1 * gi1.dot3(x1, y1, z1);
219 }
220 var t2 = 0.6 - x2*x2 - y2*y2 - z2*z2;
221 if(t2<0) {
222 n2 = 0;
223 } else {
224 t2 *= t2;
225 n2 = t2 * t2 * gi2.dot3(x2, y2, z2);
226 }
227 var t3 = 0.6 - x3*x3 - y3*y3 - z3*z3;
228 if(t3<0) {
229 n3 = 0;
230 } else {
231 t3 *= t3;
232 n3 = t3 * t3 * gi3.dot3(x3, y3, z3);
233 }
234 // Add contributions from each corner to get the final noise value.
235 // The result is scaled to return values in the interval [-1,1].
236 return 32 * (n0 + n1 + n2 + n3);
237
238 };
239
240 // ##### Perlin noise stuff
241
242 function fade(t) {
243 return t*t*t*(t*(t*6-15)+10);
244 }
245
246 function lerp(a, b, t) {
247 return (1-t)*a + t*b;
248 }
249
250 // 2D Perlin Noise
251 module.perlin2 = function(x, y) {
252 // Find unit grid cell containing point
253 var X = Math.floor(x), Y = Math.floor(y);
254 // Get relative xy coordinates of point within that cell
255 x = x - X; y = y - Y;
256 // Wrap the integer cells at 255 (smaller integer period can be introduced here)
257 X = X & 255; Y = Y & 255;
258
259 // Calculate noise contributions from each of the four corners
260 var n00 = gradP[X+perm[Y]].dot2(x, y);
261 var n01 = gradP[X+perm[Y+1]].dot2(x, y-1);
262 var n10 = gradP[X+1+perm[Y]].dot2(x-1, y);
263 var n11 = gradP[X+1+perm[Y+1]].dot2(x-1, y-1);
264
265 // Compute the fade curve value for x
266 var u = fade(x);
267
268 // Interpolate the four results
269 return lerp(
270 lerp(n00, n10, u),
271 lerp(n01, n11, u),
272 fade(y));
273 };
274
275 // 3D Perlin Noise
276 module.perlin3 = function(x, y, z) {
277 // Find unit grid cell containing point
278 var X = Math.floor(x), Y = Math.floor(y), Z = Math.floor(z);
279 // Get relative xyz coordinates of point within that cell
280 x = x - X; y = y - Y; z = z - Z;
281 // Wrap the integer cells at 255 (smaller integer period can be introduced here)
282 X = X & 255; Y = Y & 255; Z = Z & 255;
283
284 // Calculate noise contributions from each of the eight corners
285 var n000 = gradP[X+ perm[Y+ perm[Z ]]].dot3(x, y, z);
286 var n001 = gradP[X+ perm[Y+ perm[Z+1]]].dot3(x, y, z-1);
287 var n010 = gradP[X+ perm[Y+1+perm[Z ]]].dot3(x, y-1, z);
288 var n011 = gradP[X+ perm[Y+1+perm[Z+1]]].dot3(x, y-1, z-1);
289 var n100 = gradP[X+1+perm[Y+ perm[Z ]]].dot3(x-1, y, z);
290 var n101 = gradP[X+1+perm[Y+ perm[Z+1]]].dot3(x-1, y, z-1);
291 var n110 = gradP[X+1+perm[Y+1+perm[Z ]]].dot3(x-1, y-1, z);
292 var n111 = gradP[X+1+perm[Y+1+perm[Z+1]]].dot3(x-1, y-1, z-1);
293
294 // Compute the fade curve value for x, y, z
295 var u = fade(x);
296 var v = fade(y);
297 var w = fade(z);
298
299 // Interpolate
300 return lerp(
301 lerp(
302 lerp(n000, n100, u),
303 lerp(n001, n101, u), w),
304 lerp(
305 lerp(n010, n110, u),
306 lerp(n011, n111, u), w),
307 v);
308 };
309
310})(this);