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ShaderPlayground / deps / glm / glm / gtc / noise.inl
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1/// @ref gtc_noise
2///
3// Based on the work of Stefan Gustavson and Ashima Arts on "webgl-noise":
4// https://github.com/ashima/webgl-noise
5// Following Stefan Gustavson's paper "Simplex noise demystified":
6// http://www.itn.liu.se/~stegu/simplexnoise/simplexnoise.pdf
7
8namespace glm{
9namespace gtc
10{
11 template<typename T, qualifier Q>
12 GLM_FUNC_QUALIFIER vec<4, T, Q> grad4(T const& j, vec<4, T, Q> const& ip)
13 {
14 vec<3, T, Q> pXYZ = floor(fract(vec<3, T, Q>(j) * vec<3, T, Q>(ip)) * T(7)) * ip[2] - T(1);
15 T pW = static_cast<T>(1.5) - dot(abs(pXYZ), vec<3, T, Q>(1));
16 vec<4, T, Q> s = vec<4, T, Q>(lessThan(vec<4, T, Q>(pXYZ, pW), vec<4, T, Q>(0.0)));
17 pXYZ = pXYZ + (vec<3, T, Q>(s) * T(2) - T(1)) * s.w;
18 return vec<4, T, Q>(pXYZ, pW);
19 }
20}//namespace gtc
21
22 // Classic Perlin noise
23 template<typename T, qualifier Q>
24 GLM_FUNC_QUALIFIER T perlin(vec<2, T, Q> const& Position)
25 {
26 vec<4, T, Q> Pi = glm::floor(vec<4, T, Q>(Position.x, Position.y, Position.x, Position.y)) + vec<4, T, Q>(0.0, 0.0, 1.0, 1.0);
27 vec<4, T, Q> Pf = glm::fract(vec<4, T, Q>(Position.x, Position.y, Position.x, Position.y)) - vec<4, T, Q>(0.0, 0.0, 1.0, 1.0);
28 Pi = mod(Pi, vec<4, T, Q>(289)); // To avoid truncation effects in permutation
29 vec<4, T, Q> ix(Pi.x, Pi.z, Pi.x, Pi.z);
30 vec<4, T, Q> iy(Pi.y, Pi.y, Pi.w, Pi.w);
31 vec<4, T, Q> fx(Pf.x, Pf.z, Pf.x, Pf.z);
32 vec<4, T, Q> fy(Pf.y, Pf.y, Pf.w, Pf.w);
33
34 vec<4, T, Q> i = detail::permute(detail::permute(ix) + iy);
35
36 vec<4, T, Q> gx = static_cast<T>(2) * glm::fract(i / T(41)) - T(1);
37 vec<4, T, Q> gy = glm::abs(gx) - T(0.5);
38 vec<4, T, Q> tx = glm::floor(gx + T(0.5));
39 gx = gx - tx;
40
41 vec<2, T, Q> g00(gx.x, gy.x);
42 vec<2, T, Q> g10(gx.y, gy.y);
43 vec<2, T, Q> g01(gx.z, gy.z);
44 vec<2, T, Q> g11(gx.w, gy.w);
45
46 vec<4, T, Q> norm = detail::taylorInvSqrt(vec<4, T, Q>(dot(g00, g00), dot(g01, g01), dot(g10, g10), dot(g11, g11)));
47 g00 *= norm.x;
48 g01 *= norm.y;
49 g10 *= norm.z;
50 g11 *= norm.w;
51
52 T n00 = dot(g00, vec<2, T, Q>(fx.x, fy.x));
53 T n10 = dot(g10, vec<2, T, Q>(fx.y, fy.y));
54 T n01 = dot(g01, vec<2, T, Q>(fx.z, fy.z));
55 T n11 = dot(g11, vec<2, T, Q>(fx.w, fy.w));
56
57 vec<2, T, Q> fade_xy = detail::fade(vec<2, T, Q>(Pf.x, Pf.y));
58 vec<2, T, Q> n_x = mix(vec<2, T, Q>(n00, n01), vec<2, T, Q>(n10, n11), fade_xy.x);
59 T n_xy = mix(n_x.x, n_x.y, fade_xy.y);
60 return T(2.3) * n_xy;
61 }
62
63 // Classic Perlin noise
64 template<typename T, qualifier Q>
65 GLM_FUNC_QUALIFIER T perlin(vec<3, T, Q> const& Position)
66 {
67 vec<3, T, Q> Pi0 = floor(Position); // Integer part for indexing
68 vec<3, T, Q> Pi1 = Pi0 + T(1); // Integer part + 1
69 Pi0 = detail::mod289(Pi0);
70 Pi1 = detail::mod289(Pi1);
71 vec<3, T, Q> Pf0 = fract(Position); // Fractional part for interpolation
72 vec<3, T, Q> Pf1 = Pf0 - T(1); // Fractional part - 1.0
73 vec<4, T, Q> ix(Pi0.x, Pi1.x, Pi0.x, Pi1.x);
74 vec<4, T, Q> iy = vec<4, T, Q>(vec<2, T, Q>(Pi0.y), vec<2, T, Q>(Pi1.y));
75 vec<4, T, Q> iz0(Pi0.z);
76 vec<4, T, Q> iz1(Pi1.z);
77
78 vec<4, T, Q> ixy = detail::permute(detail::permute(ix) + iy);
79 vec<4, T, Q> ixy0 = detail::permute(ixy + iz0);
80 vec<4, T, Q> ixy1 = detail::permute(ixy + iz1);
81
82 vec<4, T, Q> gx0 = ixy0 * T(1.0 / 7.0);
83 vec<4, T, Q> gy0 = fract(floor(gx0) * T(1.0 / 7.0)) - T(0.5);
84 gx0 = fract(gx0);
85 vec<4, T, Q> gz0 = vec<4, T, Q>(0.5) - abs(gx0) - abs(gy0);
86 vec<4, T, Q> sz0 = step(gz0, vec<4, T, Q>(0.0));
87 gx0 -= sz0 * (step(T(0), gx0) - T(0.5));
88 gy0 -= sz0 * (step(T(0), gy0) - T(0.5));
89
90 vec<4, T, Q> gx1 = ixy1 * T(1.0 / 7.0);
91 vec<4, T, Q> gy1 = fract(floor(gx1) * T(1.0 / 7.0)) - T(0.5);
92 gx1 = fract(gx1);
93 vec<4, T, Q> gz1 = vec<4, T, Q>(0.5) - abs(gx1) - abs(gy1);
94 vec<4, T, Q> sz1 = step(gz1, vec<4, T, Q>(0.0));
95 gx1 -= sz1 * (step(T(0), gx1) - T(0.5));
96 gy1 -= sz1 * (step(T(0), gy1) - T(0.5));
97
98 vec<3, T, Q> g000(gx0.x, gy0.x, gz0.x);
99 vec<3, T, Q> g100(gx0.y, gy0.y, gz0.y);
100 vec<3, T, Q> g010(gx0.z, gy0.z, gz0.z);
101 vec<3, T, Q> g110(gx0.w, gy0.w, gz0.w);
102 vec<3, T, Q> g001(gx1.x, gy1.x, gz1.x);
103 vec<3, T, Q> g101(gx1.y, gy1.y, gz1.y);
104 vec<3, T, Q> g011(gx1.z, gy1.z, gz1.z);
105 vec<3, T, Q> g111(gx1.w, gy1.w, gz1.w);
106
107 vec<4, T, Q> norm0 = detail::taylorInvSqrt(vec<4, T, Q>(dot(g000, g000), dot(g010, g010), dot(g100, g100), dot(g110, g110)));
108 g000 *= norm0.x;
109 g010 *= norm0.y;
110 g100 *= norm0.z;
111 g110 *= norm0.w;
112 vec<4, T, Q> norm1 = detail::taylorInvSqrt(vec<4, T, Q>(dot(g001, g001), dot(g011, g011), dot(g101, g101), dot(g111, g111)));
113 g001 *= norm1.x;
114 g011 *= norm1.y;
115 g101 *= norm1.z;
116 g111 *= norm1.w;
117
118 T n000 = dot(g000, Pf0);
119 T n100 = dot(g100, vec<3, T, Q>(Pf1.x, Pf0.y, Pf0.z));
120 T n010 = dot(g010, vec<3, T, Q>(Pf0.x, Pf1.y, Pf0.z));
121 T n110 = dot(g110, vec<3, T, Q>(Pf1.x, Pf1.y, Pf0.z));
122 T n001 = dot(g001, vec<3, T, Q>(Pf0.x, Pf0.y, Pf1.z));
123 T n101 = dot(g101, vec<3, T, Q>(Pf1.x, Pf0.y, Pf1.z));
124 T n011 = dot(g011, vec<3, T, Q>(Pf0.x, Pf1.y, Pf1.z));
125 T n111 = dot(g111, Pf1);
126
127 vec<3, T, Q> fade_xyz = detail::fade(Pf0);
128 vec<4, T, Q> n_z = mix(vec<4, T, Q>(n000, n100, n010, n110), vec<4, T, Q>(n001, n101, n011, n111), fade_xyz.z);
129 vec<2, T, Q> n_yz = mix(vec<2, T, Q>(n_z.x, n_z.y), vec<2, T, Q>(n_z.z, n_z.w), fade_xyz.y);
130 T n_xyz = mix(n_yz.x, n_yz.y, fade_xyz.x);
131 return T(2.2) * n_xyz;
132 }
133 /*
134 // Classic Perlin noise
135 template<typename T, qualifier Q>
136 GLM_FUNC_QUALIFIER T perlin(vec<3, T, Q> const& P)
137 {
138 vec<3, T, Q> Pi0 = floor(P); // Integer part for indexing
139 vec<3, T, Q> Pi1 = Pi0 + T(1); // Integer part + 1
140 Pi0 = mod(Pi0, T(289));
141 Pi1 = mod(Pi1, T(289));
142 vec<3, T, Q> Pf0 = fract(P); // Fractional part for interpolation
143 vec<3, T, Q> Pf1 = Pf0 - T(1); // Fractional part - 1.0
144 vec<4, T, Q> ix(Pi0.x, Pi1.x, Pi0.x, Pi1.x);
145 vec<4, T, Q> iy(Pi0.y, Pi0.y, Pi1.y, Pi1.y);
146 vec<4, T, Q> iz0(Pi0.z);
147 vec<4, T, Q> iz1(Pi1.z);
148
149 vec<4, T, Q> ixy = permute(permute(ix) + iy);
150 vec<4, T, Q> ixy0 = permute(ixy + iz0);
151 vec<4, T, Q> ixy1 = permute(ixy + iz1);
152
153 vec<4, T, Q> gx0 = ixy0 / T(7);
154 vec<4, T, Q> gy0 = fract(floor(gx0) / T(7)) - T(0.5);
155 gx0 = fract(gx0);
156 vec<4, T, Q> gz0 = vec<4, T, Q>(0.5) - abs(gx0) - abs(gy0);
157 vec<4, T, Q> sz0 = step(gz0, vec<4, T, Q>(0.0));
158 gx0 -= sz0 * (step(0.0, gx0) - T(0.5));
159 gy0 -= sz0 * (step(0.0, gy0) - T(0.5));
160
161 vec<4, T, Q> gx1 = ixy1 / T(7);
162 vec<4, T, Q> gy1 = fract(floor(gx1) / T(7)) - T(0.5);
163 gx1 = fract(gx1);
164 vec<4, T, Q> gz1 = vec<4, T, Q>(0.5) - abs(gx1) - abs(gy1);
165 vec<4, T, Q> sz1 = step(gz1, vec<4, T, Q>(0.0));
166 gx1 -= sz1 * (step(T(0), gx1) - T(0.5));
167 gy1 -= sz1 * (step(T(0), gy1) - T(0.5));
168
169 vec<3, T, Q> g000(gx0.x, gy0.x, gz0.x);
170 vec<3, T, Q> g100(gx0.y, gy0.y, gz0.y);
171 vec<3, T, Q> g010(gx0.z, gy0.z, gz0.z);
172 vec<3, T, Q> g110(gx0.w, gy0.w, gz0.w);
173 vec<3, T, Q> g001(gx1.x, gy1.x, gz1.x);
174 vec<3, T, Q> g101(gx1.y, gy1.y, gz1.y);
175 vec<3, T, Q> g011(gx1.z, gy1.z, gz1.z);
176 vec<3, T, Q> g111(gx1.w, gy1.w, gz1.w);
177
178 vec<4, T, Q> norm0 = taylorInvSqrt(vec<4, T, Q>(dot(g000, g000), dot(g010, g010), dot(g100, g100), dot(g110, g110)));
179 g000 *= norm0.x;
180 g010 *= norm0.y;
181 g100 *= norm0.z;
182 g110 *= norm0.w;
183 vec<4, T, Q> norm1 = taylorInvSqrt(vec<4, T, Q>(dot(g001, g001), dot(g011, g011), dot(g101, g101), dot(g111, g111)));
184 g001 *= norm1.x;
185 g011 *= norm1.y;
186 g101 *= norm1.z;
187 g111 *= norm1.w;
188
189 T n000 = dot(g000, Pf0);
190 T n100 = dot(g100, vec<3, T, Q>(Pf1.x, Pf0.y, Pf0.z));
191 T n010 = dot(g010, vec<3, T, Q>(Pf0.x, Pf1.y, Pf0.z));
192 T n110 = dot(g110, vec<3, T, Q>(Pf1.x, Pf1.y, Pf0.z));
193 T n001 = dot(g001, vec<3, T, Q>(Pf0.x, Pf0.y, Pf1.z));
194 T n101 = dot(g101, vec<3, T, Q>(Pf1.x, Pf0.y, Pf1.z));
195 T n011 = dot(g011, vec<3, T, Q>(Pf0.x, Pf1.y, Pf1.z));
196 T n111 = dot(g111, Pf1);
197
198 vec<3, T, Q> fade_xyz = fade(Pf0);
199 vec<4, T, Q> n_z = mix(vec<4, T, Q>(n000, n100, n010, n110), vec<4, T, Q>(n001, n101, n011, n111), fade_xyz.z);
200 vec<2, T, Q> n_yz = mix(
201 vec<2, T, Q>(n_z.x, n_z.y),
202 vec<2, T, Q>(n_z.z, n_z.w), fade_xyz.y);
203 T n_xyz = mix(n_yz.x, n_yz.y, fade_xyz.x);
204 return T(2.2) * n_xyz;
205 }
206 */
207 // Classic Perlin noise
208 template<typename T, qualifier Q>
209 GLM_FUNC_QUALIFIER T perlin(vec<4, T, Q> const& Position)
210 {
211 vec<4, T, Q> Pi0 = floor(Position); // Integer part for indexing
212 vec<4, T, Q> Pi1 = Pi0 + T(1); // Integer part + 1
213 Pi0 = mod(Pi0, vec<4, T, Q>(289));
214 Pi1 = mod(Pi1, vec<4, T, Q>(289));
215 vec<4, T, Q> Pf0 = fract(Position); // Fractional part for interpolation
216 vec<4, T, Q> Pf1 = Pf0 - T(1); // Fractional part - 1.0
217 vec<4, T, Q> ix(Pi0.x, Pi1.x, Pi0.x, Pi1.x);
218 vec<4, T, Q> iy(Pi0.y, Pi0.y, Pi1.y, Pi1.y);
219 vec<4, T, Q> iz0(Pi0.z);
220 vec<4, T, Q> iz1(Pi1.z);
221 vec<4, T, Q> iw0(Pi0.w);
222 vec<4, T, Q> iw1(Pi1.w);
223
224 vec<4, T, Q> ixy = detail::permute(detail::permute(ix) + iy);
225 vec<4, T, Q> ixy0 = detail::permute(ixy + iz0);
226 vec<4, T, Q> ixy1 = detail::permute(ixy + iz1);
227 vec<4, T, Q> ixy00 = detail::permute(ixy0 + iw0);
228 vec<4, T, Q> ixy01 = detail::permute(ixy0 + iw1);
229 vec<4, T, Q> ixy10 = detail::permute(ixy1 + iw0);
230 vec<4, T, Q> ixy11 = detail::permute(ixy1 + iw1);
231
232 vec<4, T, Q> gx00 = ixy00 / T(7);
233 vec<4, T, Q> gy00 = floor(gx00) / T(7);
234 vec<4, T, Q> gz00 = floor(gy00) / T(6);
235 gx00 = fract(gx00) - T(0.5);
236 gy00 = fract(gy00) - T(0.5);
237 gz00 = fract(gz00) - T(0.5);
238 vec<4, T, Q> gw00 = vec<4, T, Q>(0.75) - abs(gx00) - abs(gy00) - abs(gz00);
239 vec<4, T, Q> sw00 = step(gw00, vec<4, T, Q>(0.0));
240 gx00 -= sw00 * (step(T(0), gx00) - T(0.5));
241 gy00 -= sw00 * (step(T(0), gy00) - T(0.5));
242
243 vec<4, T, Q> gx01 = ixy01 / T(7);
244 vec<4, T, Q> gy01 = floor(gx01) / T(7);
245 vec<4, T, Q> gz01 = floor(gy01) / T(6);
246 gx01 = fract(gx01) - T(0.5);
247 gy01 = fract(gy01) - T(0.5);
248 gz01 = fract(gz01) - T(0.5);
249 vec<4, T, Q> gw01 = vec<4, T, Q>(0.75) - abs(gx01) - abs(gy01) - abs(gz01);
250 vec<4, T, Q> sw01 = step(gw01, vec<4, T, Q>(0.0));
251 gx01 -= sw01 * (step(T(0), gx01) - T(0.5));
252 gy01 -= sw01 * (step(T(0), gy01) - T(0.5));
253
254 vec<4, T, Q> gx10 = ixy10 / T(7);
255 vec<4, T, Q> gy10 = floor(gx10) / T(7);
256 vec<4, T, Q> gz10 = floor(gy10) / T(6);
257 gx10 = fract(gx10) - T(0.5);
258 gy10 = fract(gy10) - T(0.5);
259 gz10 = fract(gz10) - T(0.5);
260 vec<4, T, Q> gw10 = vec<4, T, Q>(0.75) - abs(gx10) - abs(gy10) - abs(gz10);
261 vec<4, T, Q> sw10 = step(gw10, vec<4, T, Q>(0));
262 gx10 -= sw10 * (step(T(0), gx10) - T(0.5));
263 gy10 -= sw10 * (step(T(0), gy10) - T(0.5));
264
265 vec<4, T, Q> gx11 = ixy11 / T(7);
266 vec<4, T, Q> gy11 = floor(gx11) / T(7);
267 vec<4, T, Q> gz11 = floor(gy11) / T(6);
268 gx11 = fract(gx11) - T(0.5);
269 gy11 = fract(gy11) - T(0.5);
270 gz11 = fract(gz11) - T(0.5);
271 vec<4, T, Q> gw11 = vec<4, T, Q>(0.75) - abs(gx11) - abs(gy11) - abs(gz11);
272 vec<4, T, Q> sw11 = step(gw11, vec<4, T, Q>(0.0));
273 gx11 -= sw11 * (step(T(0), gx11) - T(0.5));
274 gy11 -= sw11 * (step(T(0), gy11) - T(0.5));
275
276 vec<4, T, Q> g0000(gx00.x, gy00.x, gz00.x, gw00.x);
277 vec<4, T, Q> g1000(gx00.y, gy00.y, gz00.y, gw00.y);
278 vec<4, T, Q> g0100(gx00.z, gy00.z, gz00.z, gw00.z);
279 vec<4, T, Q> g1100(gx00.w, gy00.w, gz00.w, gw00.w);
280 vec<4, T, Q> g0010(gx10.x, gy10.x, gz10.x, gw10.x);
281 vec<4, T, Q> g1010(gx10.y, gy10.y, gz10.y, gw10.y);
282 vec<4, T, Q> g0110(gx10.z, gy10.z, gz10.z, gw10.z);
283 vec<4, T, Q> g1110(gx10.w, gy10.w, gz10.w, gw10.w);
284 vec<4, T, Q> g0001(gx01.x, gy01.x, gz01.x, gw01.x);
285 vec<4, T, Q> g1001(gx01.y, gy01.y, gz01.y, gw01.y);
286 vec<4, T, Q> g0101(gx01.z, gy01.z, gz01.z, gw01.z);
287 vec<4, T, Q> g1101(gx01.w, gy01.w, gz01.w, gw01.w);
288 vec<4, T, Q> g0011(gx11.x, gy11.x, gz11.x, gw11.x);
289 vec<4, T, Q> g1011(gx11.y, gy11.y, gz11.y, gw11.y);
290 vec<4, T, Q> g0111(gx11.z, gy11.z, gz11.z, gw11.z);
291 vec<4, T, Q> g1111(gx11.w, gy11.w, gz11.w, gw11.w);
292
293 vec<4, T, Q> norm00 = detail::taylorInvSqrt(vec<4, T, Q>(dot(g0000, g0000), dot(g0100, g0100), dot(g1000, g1000), dot(g1100, g1100)));
294 g0000 *= norm00.x;
295 g0100 *= norm00.y;
296 g1000 *= norm00.z;
297 g1100 *= norm00.w;
298
299 vec<4, T, Q> norm01 = detail::taylorInvSqrt(vec<4, T, Q>(dot(g0001, g0001), dot(g0101, g0101), dot(g1001, g1001), dot(g1101, g1101)));
300 g0001 *= norm01.x;
301 g0101 *= norm01.y;
302 g1001 *= norm01.z;
303 g1101 *= norm01.w;
304
305 vec<4, T, Q> norm10 = detail::taylorInvSqrt(vec<4, T, Q>(dot(g0010, g0010), dot(g0110, g0110), dot(g1010, g1010), dot(g1110, g1110)));
306 g0010 *= norm10.x;
307 g0110 *= norm10.y;
308 g1010 *= norm10.z;
309 g1110 *= norm10.w;
310
311 vec<4, T, Q> norm11 = detail::taylorInvSqrt(vec<4, T, Q>(dot(g0011, g0011), dot(g0111, g0111), dot(g1011, g1011), dot(g1111, g1111)));
312 g0011 *= norm11.x;
313 g0111 *= norm11.y;
314 g1011 *= norm11.z;
315 g1111 *= norm11.w;
316
317 T n0000 = dot(g0000, Pf0);
318 T n1000 = dot(g1000, vec<4, T, Q>(Pf1.x, Pf0.y, Pf0.z, Pf0.w));
319 T n0100 = dot(g0100, vec<4, T, Q>(Pf0.x, Pf1.y, Pf0.z, Pf0.w));
320 T n1100 = dot(g1100, vec<4, T, Q>(Pf1.x, Pf1.y, Pf0.z, Pf0.w));
321 T n0010 = dot(g0010, vec<4, T, Q>(Pf0.x, Pf0.y, Pf1.z, Pf0.w));
322 T n1010 = dot(g1010, vec<4, T, Q>(Pf1.x, Pf0.y, Pf1.z, Pf0.w));
323 T n0110 = dot(g0110, vec<4, T, Q>(Pf0.x, Pf1.y, Pf1.z, Pf0.w));
324 T n1110 = dot(g1110, vec<4, T, Q>(Pf1.x, Pf1.y, Pf1.z, Pf0.w));
325 T n0001 = dot(g0001, vec<4, T, Q>(Pf0.x, Pf0.y, Pf0.z, Pf1.w));
326 T n1001 = dot(g1001, vec<4, T, Q>(Pf1.x, Pf0.y, Pf0.z, Pf1.w));
327 T n0101 = dot(g0101, vec<4, T, Q>(Pf0.x, Pf1.y, Pf0.z, Pf1.w));
328 T n1101 = dot(g1101, vec<4, T, Q>(Pf1.x, Pf1.y, Pf0.z, Pf1.w));
329 T n0011 = dot(g0011, vec<4, T, Q>(Pf0.x, Pf0.y, Pf1.z, Pf1.w));
330 T n1011 = dot(g1011, vec<4, T, Q>(Pf1.x, Pf0.y, Pf1.z, Pf1.w));
331 T n0111 = dot(g0111, vec<4, T, Q>(Pf0.x, Pf1.y, Pf1.z, Pf1.w));
332 T n1111 = dot(g1111, Pf1);
333
334 vec<4, T, Q> fade_xyzw = detail::fade(Pf0);
335 vec<4, T, Q> n_0w = mix(vec<4, T, Q>(n0000, n1000, n0100, n1100), vec<4, T, Q>(n0001, n1001, n0101, n1101), fade_xyzw.w);
336 vec<4, T, Q> n_1w = mix(vec<4, T, Q>(n0010, n1010, n0110, n1110), vec<4, T, Q>(n0011, n1011, n0111, n1111), fade_xyzw.w);
337 vec<4, T, Q> n_zw = mix(n_0w, n_1w, fade_xyzw.z);
338 vec<2, T, Q> n_yzw = mix(vec<2, T, Q>(n_zw.x, n_zw.y), vec<2, T, Q>(n_zw.z, n_zw.w), fade_xyzw.y);
339 T n_xyzw = mix(n_yzw.x, n_yzw.y, fade_xyzw.x);
340 return T(2.2) * n_xyzw;
341 }
342
343 // Classic Perlin noise, periodic variant
344 template<typename T, qualifier Q>
345 GLM_FUNC_QUALIFIER T perlin(vec<2, T, Q> const& Position, vec<2, T, Q> const& rep)
346 {
347 vec<4, T, Q> Pi = floor(vec<4, T, Q>(Position.x, Position.y, Position.x, Position.y)) + vec<4, T, Q>(0.0, 0.0, 1.0, 1.0);
348 vec<4, T, Q> Pf = fract(vec<4, T, Q>(Position.x, Position.y, Position.x, Position.y)) - vec<4, T, Q>(0.0, 0.0, 1.0, 1.0);
349 Pi = mod(Pi, vec<4, T, Q>(rep.x, rep.y, rep.x, rep.y)); // To create noise with explicit period
350 Pi = mod(Pi, vec<4, T, Q>(289)); // To avoid truncation effects in permutation
351 vec<4, T, Q> ix(Pi.x, Pi.z, Pi.x, Pi.z);
352 vec<4, T, Q> iy(Pi.y, Pi.y, Pi.w, Pi.w);
353 vec<4, T, Q> fx(Pf.x, Pf.z, Pf.x, Pf.z);
354 vec<4, T, Q> fy(Pf.y, Pf.y, Pf.w, Pf.w);
355
356 vec<4, T, Q> i = detail::permute(detail::permute(ix) + iy);
357
358 vec<4, T, Q> gx = static_cast<T>(2) * fract(i / T(41)) - T(1);
359 vec<4, T, Q> gy = abs(gx) - T(0.5);
360 vec<4, T, Q> tx = floor(gx + T(0.5));
361 gx = gx - tx;
362
363 vec<2, T, Q> g00(gx.x, gy.x);
364 vec<2, T, Q> g10(gx.y, gy.y);
365 vec<2, T, Q> g01(gx.z, gy.z);
366 vec<2, T, Q> g11(gx.w, gy.w);
367
368 vec<4, T, Q> norm = detail::taylorInvSqrt(vec<4, T, Q>(dot(g00, g00), dot(g01, g01), dot(g10, g10), dot(g11, g11)));
369 g00 *= norm.x;
370 g01 *= norm.y;
371 g10 *= norm.z;
372 g11 *= norm.w;
373
374 T n00 = dot(g00, vec<2, T, Q>(fx.x, fy.x));
375 T n10 = dot(g10, vec<2, T, Q>(fx.y, fy.y));
376 T n01 = dot(g01, vec<2, T, Q>(fx.z, fy.z));
377 T n11 = dot(g11, vec<2, T, Q>(fx.w, fy.w));
378
379 vec<2, T, Q> fade_xy = detail::fade(vec<2, T, Q>(Pf.x, Pf.y));
380 vec<2, T, Q> n_x = mix(vec<2, T, Q>(n00, n01), vec<2, T, Q>(n10, n11), fade_xy.x);
381 T n_xy = mix(n_x.x, n_x.y, fade_xy.y);
382 return T(2.3) * n_xy;
383 }
384
385 // Classic Perlin noise, periodic variant
386 template<typename T, qualifier Q>
387 GLM_FUNC_QUALIFIER T perlin(vec<3, T, Q> const& Position, vec<3, T, Q> const& rep)
388 {
389 vec<3, T, Q> Pi0 = mod(floor(Position), rep); // Integer part, modulo period
390 vec<3, T, Q> Pi1 = mod(Pi0 + vec<3, T, Q>(T(1)), rep); // Integer part + 1, mod period
391 Pi0 = mod(Pi0, vec<3, T, Q>(289));
392 Pi1 = mod(Pi1, vec<3, T, Q>(289));
393 vec<3, T, Q> Pf0 = fract(Position); // Fractional part for interpolation
394 vec<3, T, Q> Pf1 = Pf0 - vec<3, T, Q>(T(1)); // Fractional part - 1.0
395 vec<4, T, Q> ix = vec<4, T, Q>(Pi0.x, Pi1.x, Pi0.x, Pi1.x);
396 vec<4, T, Q> iy = vec<4, T, Q>(Pi0.y, Pi0.y, Pi1.y, Pi1.y);
397 vec<4, T, Q> iz0(Pi0.z);
398 vec<4, T, Q> iz1(Pi1.z);
399
400 vec<4, T, Q> ixy = detail::permute(detail::permute(ix) + iy);
401 vec<4, T, Q> ixy0 = detail::permute(ixy + iz0);
402 vec<4, T, Q> ixy1 = detail::permute(ixy + iz1);
403
404 vec<4, T, Q> gx0 = ixy0 / T(7);
405 vec<4, T, Q> gy0 = fract(floor(gx0) / T(7)) - T(0.5);
406 gx0 = fract(gx0);
407 vec<4, T, Q> gz0 = vec<4, T, Q>(0.5) - abs(gx0) - abs(gy0);
408 vec<4, T, Q> sz0 = step(gz0, vec<4, T, Q>(0));
409 gx0 -= sz0 * (step(T(0), gx0) - T(0.5));
410 gy0 -= sz0 * (step(T(0), gy0) - T(0.5));
411
412 vec<4, T, Q> gx1 = ixy1 / T(7);
413 vec<4, T, Q> gy1 = fract(floor(gx1) / T(7)) - T(0.5);
414 gx1 = fract(gx1);
415 vec<4, T, Q> gz1 = vec<4, T, Q>(0.5) - abs(gx1) - abs(gy1);
416 vec<4, T, Q> sz1 = step(gz1, vec<4, T, Q>(T(0)));
417 gx1 -= sz1 * (step(T(0), gx1) - T(0.5));
418 gy1 -= sz1 * (step(T(0), gy1) - T(0.5));
419
420 vec<3, T, Q> g000 = vec<3, T, Q>(gx0.x, gy0.x, gz0.x);
421 vec<3, T, Q> g100 = vec<3, T, Q>(gx0.y, gy0.y, gz0.y);
422 vec<3, T, Q> g010 = vec<3, T, Q>(gx0.z, gy0.z, gz0.z);
423 vec<3, T, Q> g110 = vec<3, T, Q>(gx0.w, gy0.w, gz0.w);
424 vec<3, T, Q> g001 = vec<3, T, Q>(gx1.x, gy1.x, gz1.x);
425 vec<3, T, Q> g101 = vec<3, T, Q>(gx1.y, gy1.y, gz1.y);
426 vec<3, T, Q> g011 = vec<3, T, Q>(gx1.z, gy1.z, gz1.z);
427 vec<3, T, Q> g111 = vec<3, T, Q>(gx1.w, gy1.w, gz1.w);
428
429 vec<4, T, Q> norm0 = detail::taylorInvSqrt(vec<4, T, Q>(dot(g000, g000), dot(g010, g010), dot(g100, g100), dot(g110, g110)));
430 g000 *= norm0.x;
431 g010 *= norm0.y;
432 g100 *= norm0.z;
433 g110 *= norm0.w;
434 vec<4, T, Q> norm1 = detail::taylorInvSqrt(vec<4, T, Q>(dot(g001, g001), dot(g011, g011), dot(g101, g101), dot(g111, g111)));
435 g001 *= norm1.x;
436 g011 *= norm1.y;
437 g101 *= norm1.z;
438 g111 *= norm1.w;
439
440 T n000 = dot(g000, Pf0);
441 T n100 = dot(g100, vec<3, T, Q>(Pf1.x, Pf0.y, Pf0.z));
442 T n010 = dot(g010, vec<3, T, Q>(Pf0.x, Pf1.y, Pf0.z));
443 T n110 = dot(g110, vec<3, T, Q>(Pf1.x, Pf1.y, Pf0.z));
444 T n001 = dot(g001, vec<3, T, Q>(Pf0.x, Pf0.y, Pf1.z));
445 T n101 = dot(g101, vec<3, T, Q>(Pf1.x, Pf0.y, Pf1.z));
446 T n011 = dot(g011, vec<3, T, Q>(Pf0.x, Pf1.y, Pf1.z));
447 T n111 = dot(g111, Pf1);
448
449 vec<3, T, Q> fade_xyz = detail::fade(Pf0);
450 vec<4, T, Q> n_z = mix(vec<4, T, Q>(n000, n100, n010, n110), vec<4, T, Q>(n001, n101, n011, n111), fade_xyz.z);
451 vec<2, T, Q> n_yz = mix(vec<2, T, Q>(n_z.x, n_z.y), vec<2, T, Q>(n_z.z, n_z.w), fade_xyz.y);
452 T n_xyz = mix(n_yz.x, n_yz.y, fade_xyz.x);
453 return T(2.2) * n_xyz;
454 }
455
456 // Classic Perlin noise, periodic version
457 template<typename T, qualifier Q>
458 GLM_FUNC_QUALIFIER T perlin(vec<4, T, Q> const& Position, vec<4, T, Q> const& rep)
459 {
460 vec<4, T, Q> Pi0 = mod(floor(Position), rep); // Integer part modulo rep
461 vec<4, T, Q> Pi1 = mod(Pi0 + T(1), rep); // Integer part + 1 mod rep
462 vec<4, T, Q> Pf0 = fract(Position); // Fractional part for interpolation
463 vec<4, T, Q> Pf1 = Pf0 - T(1); // Fractional part - 1.0
464 vec<4, T, Q> ix = vec<4, T, Q>(Pi0.x, Pi1.x, Pi0.x, Pi1.x);
465 vec<4, T, Q> iy = vec<4, T, Q>(Pi0.y, Pi0.y, Pi1.y, Pi1.y);
466 vec<4, T, Q> iz0(Pi0.z);
467 vec<4, T, Q> iz1(Pi1.z);
468 vec<4, T, Q> iw0(Pi0.w);
469 vec<4, T, Q> iw1(Pi1.w);
470
471 vec<4, T, Q> ixy = detail::permute(detail::permute(ix) + iy);
472 vec<4, T, Q> ixy0 = detail::permute(ixy + iz0);
473 vec<4, T, Q> ixy1 = detail::permute(ixy + iz1);
474 vec<4, T, Q> ixy00 = detail::permute(ixy0 + iw0);
475 vec<4, T, Q> ixy01 = detail::permute(ixy0 + iw1);
476 vec<4, T, Q> ixy10 = detail::permute(ixy1 + iw0);
477 vec<4, T, Q> ixy11 = detail::permute(ixy1 + iw1);
478
479 vec<4, T, Q> gx00 = ixy00 / T(7);
480 vec<4, T, Q> gy00 = floor(gx00) / T(7);
481 vec<4, T, Q> gz00 = floor(gy00) / T(6);
482 gx00 = fract(gx00) - T(0.5);
483 gy00 = fract(gy00) - T(0.5);
484 gz00 = fract(gz00) - T(0.5);
485 vec<4, T, Q> gw00 = vec<4, T, Q>(0.75) - abs(gx00) - abs(gy00) - abs(gz00);
486 vec<4, T, Q> sw00 = step(gw00, vec<4, T, Q>(0));
487 gx00 -= sw00 * (step(T(0), gx00) - T(0.5));
488 gy00 -= sw00 * (step(T(0), gy00) - T(0.5));
489
490 vec<4, T, Q> gx01 = ixy01 / T(7);
491 vec<4, T, Q> gy01 = floor(gx01) / T(7);
492 vec<4, T, Q> gz01 = floor(gy01) / T(6);
493 gx01 = fract(gx01) - T(0.5);
494 gy01 = fract(gy01) - T(0.5);
495 gz01 = fract(gz01) - T(0.5);
496 vec<4, T, Q> gw01 = vec<4, T, Q>(0.75) - abs(gx01) - abs(gy01) - abs(gz01);
497 vec<4, T, Q> sw01 = step(gw01, vec<4, T, Q>(0.0));
498 gx01 -= sw01 * (step(T(0), gx01) - T(0.5));
499 gy01 -= sw01 * (step(T(0), gy01) - T(0.5));
500
501 vec<4, T, Q> gx10 = ixy10 / T(7);
502 vec<4, T, Q> gy10 = floor(gx10) / T(7);
503 vec<4, T, Q> gz10 = floor(gy10) / T(6);
504 gx10 = fract(gx10) - T(0.5);
505 gy10 = fract(gy10) - T(0.5);
506 gz10 = fract(gz10) - T(0.5);
507 vec<4, T, Q> gw10 = vec<4, T, Q>(0.75) - abs(gx10) - abs(gy10) - abs(gz10);
508 vec<4, T, Q> sw10 = step(gw10, vec<4, T, Q>(0.0));
509 gx10 -= sw10 * (step(T(0), gx10) - T(0.5));
510 gy10 -= sw10 * (step(T(0), gy10) - T(0.5));
511
512 vec<4, T, Q> gx11 = ixy11 / T(7);
513 vec<4, T, Q> gy11 = floor(gx11) / T(7);
514 vec<4, T, Q> gz11 = floor(gy11) / T(6);
515 gx11 = fract(gx11) - T(0.5);
516 gy11 = fract(gy11) - T(0.5);
517 gz11 = fract(gz11) - T(0.5);
518 vec<4, T, Q> gw11 = vec<4, T, Q>(0.75) - abs(gx11) - abs(gy11) - abs(gz11);
519 vec<4, T, Q> sw11 = step(gw11, vec<4, T, Q>(T(0)));
520 gx11 -= sw11 * (step(T(0), gx11) - T(0.5));
521 gy11 -= sw11 * (step(T(0), gy11) - T(0.5));
522
523 vec<4, T, Q> g0000(gx00.x, gy00.x, gz00.x, gw00.x);
524 vec<4, T, Q> g1000(gx00.y, gy00.y, gz00.y, gw00.y);
525 vec<4, T, Q> g0100(gx00.z, gy00.z, gz00.z, gw00.z);
526 vec<4, T, Q> g1100(gx00.w, gy00.w, gz00.w, gw00.w);
527 vec<4, T, Q> g0010(gx10.x, gy10.x, gz10.x, gw10.x);
528 vec<4, T, Q> g1010(gx10.y, gy10.y, gz10.y, gw10.y);
529 vec<4, T, Q> g0110(gx10.z, gy10.z, gz10.z, gw10.z);
530 vec<4, T, Q> g1110(gx10.w, gy10.w, gz10.w, gw10.w);
531 vec<4, T, Q> g0001(gx01.x, gy01.x, gz01.x, gw01.x);
532 vec<4, T, Q> g1001(gx01.y, gy01.y, gz01.y, gw01.y);
533 vec<4, T, Q> g0101(gx01.z, gy01.z, gz01.z, gw01.z);
534 vec<4, T, Q> g1101(gx01.w, gy01.w, gz01.w, gw01.w);
535 vec<4, T, Q> g0011(gx11.x, gy11.x, gz11.x, gw11.x);
536 vec<4, T, Q> g1011(gx11.y, gy11.y, gz11.y, gw11.y);
537 vec<4, T, Q> g0111(gx11.z, gy11.z, gz11.z, gw11.z);
538 vec<4, T, Q> g1111(gx11.w, gy11.w, gz11.w, gw11.w);
539
540 vec<4, T, Q> norm00 = detail::taylorInvSqrt(vec<4, T, Q>(dot(g0000, g0000), dot(g0100, g0100), dot(g1000, g1000), dot(g1100, g1100)));
541 g0000 *= norm00.x;
542 g0100 *= norm00.y;
543 g1000 *= norm00.z;
544 g1100 *= norm00.w;
545
546 vec<4, T, Q> norm01 = detail::taylorInvSqrt(vec<4, T, Q>(dot(g0001, g0001), dot(g0101, g0101), dot(g1001, g1001), dot(g1101, g1101)));
547 g0001 *= norm01.x;
548 g0101 *= norm01.y;
549 g1001 *= norm01.z;
550 g1101 *= norm01.w;
551
552 vec<4, T, Q> norm10 = detail::taylorInvSqrt(vec<4, T, Q>(dot(g0010, g0010), dot(g0110, g0110), dot(g1010, g1010), dot(g1110, g1110)));
553 g0010 *= norm10.x;
554 g0110 *= norm10.y;
555 g1010 *= norm10.z;
556 g1110 *= norm10.w;
557
558 vec<4, T, Q> norm11 = detail::taylorInvSqrt(vec<4, T, Q>(dot(g0011, g0011), dot(g0111, g0111), dot(g1011, g1011), dot(g1111, g1111)));
559 g0011 *= norm11.x;
560 g0111 *= norm11.y;
561 g1011 *= norm11.z;
562 g1111 *= norm11.w;
563
564 T n0000 = dot(g0000, Pf0);
565 T n1000 = dot(g1000, vec<4, T, Q>(Pf1.x, Pf0.y, Pf0.z, Pf0.w));
566 T n0100 = dot(g0100, vec<4, T, Q>(Pf0.x, Pf1.y, Pf0.z, Pf0.w));
567 T n1100 = dot(g1100, vec<4, T, Q>(Pf1.x, Pf1.y, Pf0.z, Pf0.w));
568 T n0010 = dot(g0010, vec<4, T, Q>(Pf0.x, Pf0.y, Pf1.z, Pf0.w));
569 T n1010 = dot(g1010, vec<4, T, Q>(Pf1.x, Pf0.y, Pf1.z, Pf0.w));
570 T n0110 = dot(g0110, vec<4, T, Q>(Pf0.x, Pf1.y, Pf1.z, Pf0.w));
571 T n1110 = dot(g1110, vec<4, T, Q>(Pf1.x, Pf1.y, Pf1.z, Pf0.w));
572 T n0001 = dot(g0001, vec<4, T, Q>(Pf0.x, Pf0.y, Pf0.z, Pf1.w));
573 T n1001 = dot(g1001, vec<4, T, Q>(Pf1.x, Pf0.y, Pf0.z, Pf1.w));
574 T n0101 = dot(g0101, vec<4, T, Q>(Pf0.x, Pf1.y, Pf0.z, Pf1.w));
575 T n1101 = dot(g1101, vec<4, T, Q>(Pf1.x, Pf1.y, Pf0.z, Pf1.w));
576 T n0011 = dot(g0011, vec<4, T, Q>(Pf0.x, Pf0.y, Pf1.z, Pf1.w));
577 T n1011 = dot(g1011, vec<4, T, Q>(Pf1.x, Pf0.y, Pf1.z, Pf1.w));
578 T n0111 = dot(g0111, vec<4, T, Q>(Pf0.x, Pf1.y, Pf1.z, Pf1.w));
579 T n1111 = dot(g1111, Pf1);
580
581 vec<4, T, Q> fade_xyzw = detail::fade(Pf0);
582 vec<4, T, Q> n_0w = mix(vec<4, T, Q>(n0000, n1000, n0100, n1100), vec<4, T, Q>(n0001, n1001, n0101, n1101), fade_xyzw.w);
583 vec<4, T, Q> n_1w = mix(vec<4, T, Q>(n0010, n1010, n0110, n1110), vec<4, T, Q>(n0011, n1011, n0111, n1111), fade_xyzw.w);
584 vec<4, T, Q> n_zw = mix(n_0w, n_1w, fade_xyzw.z);
585 vec<2, T, Q> n_yzw = mix(vec<2, T, Q>(n_zw.x, n_zw.y), vec<2, T, Q>(n_zw.z, n_zw.w), fade_xyzw.y);
586 T n_xyzw = mix(n_yzw.x, n_yzw.y, fade_xyzw.x);
587 return T(2.2) * n_xyzw;
588 }
589
590 template<typename T, qualifier Q>
591 GLM_FUNC_QUALIFIER T simplex(glm::vec<2, T, Q> const& v)
592 {
593 vec<4, T, Q> const C = vec<4, T, Q>(
594 T( 0.211324865405187), // (3.0 - sqrt(3.0)) / 6.0
595 T( 0.366025403784439), // 0.5 * (sqrt(3.0) - 1.0)
596 T(-0.577350269189626), // -1.0 + 2.0 * C.x
597 T( 0.024390243902439)); // 1.0 / 41.0
598
599 // First corner
600 vec<2, T, Q> i = floor(v + dot(v, vec<2, T, Q>(C[1])));
601 vec<2, T, Q> x0 = v - i + dot(i, vec<2, T, Q>(C[0]));
602
603 // Other corners
604 //i1.x = step( x0.y, x0.x ); // x0.x > x0.y ? 1.0 : 0.0
605 //i1.y = 1.0 - i1.x;
606 vec<2, T, Q> i1 = (x0.x > x0.y) ? vec<2, T, Q>(1, 0) : vec<2, T, Q>(0, 1);
607 // x0 = x0 - 0.0 + 0.0 * C.xx ;
608 // x1 = x0 - i1 + 1.0 * C.xx ;
609 // x2 = x0 - 1.0 + 2.0 * C.xx ;
610 vec<4, T, Q> x12 = vec<4, T, Q>(x0.x, x0.y, x0.x, x0.y) + vec<4, T, Q>(C.x, C.x, C.z, C.z);
611 x12 = vec<4, T, Q>(vec<2, T, Q>(x12) - i1, x12.z, x12.w);
612
613 // Permutations
614 i = mod(i, vec<2, T, Q>(289)); // Avoid truncation effects in permutation
615 vec<3, T, Q> p = detail::permute(
616 detail::permute(i.y + vec<3, T, Q>(T(0), i1.y, T(1)))
617 + i.x + vec<3, T, Q>(T(0), i1.x, T(1)));
618
619 vec<3, T, Q> m = max(vec<3, T, Q>(0.5) - vec<3, T, Q>(
620 dot(x0, x0),
621 dot(vec<2, T, Q>(x12.x, x12.y), vec<2, T, Q>(x12.x, x12.y)),
622 dot(vec<2, T, Q>(x12.z, x12.w), vec<2, T, Q>(x12.z, x12.w))), vec<3, T, Q>(0));
623 m = m * m ;
624 m = m * m ;
625
626 // Gradients: 41 points uniformly over a line, mapped onto a diamond.
627 // The ring size 17*17 = 289 is close to a multiple of 41 (41*7 = 287)
628
629 vec<3, T, Q> x = static_cast<T>(2) * fract(p * C.w) - T(1);
630 vec<3, T, Q> h = abs(x) - T(0.5);
631 vec<3, T, Q> ox = floor(x + T(0.5));
632 vec<3, T, Q> a0 = x - ox;
633
634 // Normalise gradients implicitly by scaling m
635 // Inlined for speed: m *= taylorInvSqrt( a0*a0 + h*h );
636 m *= static_cast<T>(1.79284291400159) - T(0.85373472095314) * (a0 * a0 + h * h);
637
638 // Compute final noise value at P
639 vec<3, T, Q> g;
640 g.x = a0.x * x0.x + h.x * x0.y;
641 //g.yz = a0.yz * x12.xz + h.yz * x12.yw;
642 g.y = a0.y * x12.x + h.y * x12.y;
643 g.z = a0.z * x12.z + h.z * x12.w;
644 return T(130) * dot(m, g);
645 }
646
647 template<typename T, qualifier Q>
648 GLM_FUNC_QUALIFIER T simplex(vec<3, T, Q> const& v)
649 {
650 vec<2, T, Q> const C(1.0 / 6.0, 1.0 / 3.0);
651 vec<4, T, Q> const D(0.0, 0.5, 1.0, 2.0);
652
653 // First corner
654 vec<3, T, Q> i(floor(v + dot(v, vec<3, T, Q>(C.y))));
655 vec<3, T, Q> x0(v - i + dot(i, vec<3, T, Q>(C.x)));
656
657 // Other corners
658 vec<3, T, Q> g(step(vec<3, T, Q>(x0.y, x0.z, x0.x), x0));
659 vec<3, T, Q> l(T(1) - g);
660 vec<3, T, Q> i1(min(g, vec<3, T, Q>(l.z, l.x, l.y)));
661 vec<3, T, Q> i2(max(g, vec<3, T, Q>(l.z, l.x, l.y)));
662
663 // x0 = x0 - 0.0 + 0.0 * C.xxx;
664 // x1 = x0 - i1 + 1.0 * C.xxx;
665 // x2 = x0 - i2 + 2.0 * C.xxx;
666 // x3 = x0 - 1.0 + 3.0 * C.xxx;
667 vec<3, T, Q> x1(x0 - i1 + C.x);
668 vec<3, T, Q> x2(x0 - i2 + C.y); // 2.0*C.x = 1/3 = C.y
669 vec<3, T, Q> x3(x0 - D.y); // -1.0+3.0*C.x = -0.5 = -D.y
670
671 // Permutations
672 i = detail::mod289(i);
673 vec<4, T, Q> p(detail::permute(detail::permute(detail::permute(
674 i.z + vec<4, T, Q>(T(0), i1.z, i2.z, T(1))) +
675 i.y + vec<4, T, Q>(T(0), i1.y, i2.y, T(1))) +
676 i.x + vec<4, T, Q>(T(0), i1.x, i2.x, T(1))));
677
678 // Gradients: 7x7 points over a square, mapped onto an octahedron.
679 // The ring size 17*17 = 289 is close to a multiple of 49 (49*6 = 294)
680 T n_ = static_cast<T>(0.142857142857); // 1.0/7.0
681 vec<3, T, Q> ns(n_ * vec<3, T, Q>(D.w, D.y, D.z) - vec<3, T, Q>(D.x, D.z, D.x));
682
683 vec<4, T, Q> j(p - T(49) * floor(p * ns.z * ns.z)); // mod(p,7*7)
684
685 vec<4, T, Q> x_(floor(j * ns.z));
686 vec<4, T, Q> y_(floor(j - T(7) * x_)); // mod(j,N)
687
688 vec<4, T, Q> x(x_ * ns.x + ns.y);
689 vec<4, T, Q> y(y_ * ns.x + ns.y);
690 vec<4, T, Q> h(T(1) - abs(x) - abs(y));
691
692 vec<4, T, Q> b0(x.x, x.y, y.x, y.y);
693 vec<4, T, Q> b1(x.z, x.w, y.z, y.w);
694
695 // vec4 s0 = vec4(lessThan(b0,0.0))*2.0 - 1.0;
696 // vec4 s1 = vec4(lessThan(b1,0.0))*2.0 - 1.0;
697 vec<4, T, Q> s0(floor(b0) * T(2) + T(1));
698 vec<4, T, Q> s1(floor(b1) * T(2) + T(1));
699 vec<4, T, Q> sh(-step(h, vec<4, T, Q>(0.0)));
700
701 vec<4, T, Q> a0 = vec<4, T, Q>(b0.x, b0.z, b0.y, b0.w) + vec<4, T, Q>(s0.x, s0.z, s0.y, s0.w) * vec<4, T, Q>(sh.x, sh.x, sh.y, sh.y);
702 vec<4, T, Q> a1 = vec<4, T, Q>(b1.x, b1.z, b1.y, b1.w) + vec<4, T, Q>(s1.x, s1.z, s1.y, s1.w) * vec<4, T, Q>(sh.z, sh.z, sh.w, sh.w);
703
704 vec<3, T, Q> p0(a0.x, a0.y, h.x);
705 vec<3, T, Q> p1(a0.z, a0.w, h.y);
706 vec<3, T, Q> p2(a1.x, a1.y, h.z);
707 vec<3, T, Q> p3(a1.z, a1.w, h.w);
708
709 // Normalise gradients
710 vec<4, T, Q> norm = detail::taylorInvSqrt(vec<4, T, Q>(dot(p0, p0), dot(p1, p1), dot(p2, p2), dot(p3, p3)));
711 p0 *= norm.x;
712 p1 *= norm.y;
713 p2 *= norm.z;
714 p3 *= norm.w;
715
716 // Mix final noise value
717 vec<4, T, Q> m = max(T(0.6) - vec<4, T, Q>(dot(x0, x0), dot(x1, x1), dot(x2, x2), dot(x3, x3)), vec<4, T, Q>(0));
718 m = m * m;
719 return T(42) * dot(m * m, vec<4, T, Q>(dot(p0, x0), dot(p1, x1), dot(p2, x2), dot(p3, x3)));
720 }
721
722 template<typename T, qualifier Q>
723 GLM_FUNC_QUALIFIER T simplex(vec<4, T, Q> const& v)
724 {
725 vec<4, T, Q> const C(
726 0.138196601125011, // (5 - sqrt(5))/20 G4
727 0.276393202250021, // 2 * G4
728 0.414589803375032, // 3 * G4
729 -0.447213595499958); // -1 + 4 * G4
730
731 // (sqrt(5) - 1)/4 = F4, used once below
732 T const F4 = static_cast<T>(0.309016994374947451);
733
734 // First corner
735 vec<4, T, Q> i = floor(v + dot(v, vec4(F4)));
736 vec<4, T, Q> x0 = v - i + dot(i, vec4(C.x));
737
738 // Other corners
739
740 // Rank sorting originally contributed by Bill Licea-Kane, AMD (formerly ATI)
741 vec<4, T, Q> i0;
742 vec<3, T, Q> isX = step(vec<3, T, Q>(x0.y, x0.z, x0.w), vec<3, T, Q>(x0.x));
743 vec<3, T, Q> isYZ = step(vec<3, T, Q>(x0.z, x0.w, x0.w), vec<3, T, Q>(x0.y, x0.y, x0.z));
744 // i0.x = dot(isX, vec3(1.0));
745 //i0.x = isX.x + isX.y + isX.z;
746 //i0.yzw = static_cast<T>(1) - isX;
747 i0 = vec<4, T, Q>(isX.x + isX.y + isX.z, T(1) - isX);
748 // i0.y += dot(isYZ.xy, vec2(1.0));
749 i0.y += isYZ.x + isYZ.y;
750 //i0.zw += 1.0 - vec<2, T, Q>(isYZ.x, isYZ.y);
751 i0.z += static_cast<T>(1) - isYZ.x;
752 i0.w += static_cast<T>(1) - isYZ.y;
753 i0.z += isYZ.z;
754 i0.w += static_cast<T>(1) - isYZ.z;
755
756 // i0 now contains the unique values 0,1,2,3 in each channel
757 vec<4, T, Q> i3 = clamp(i0, T(0), T(1));
758 vec<4, T, Q> i2 = clamp(i0 - T(1), T(0), T(1));
759 vec<4, T, Q> i1 = clamp(i0 - T(2), T(0), T(1));
760
761 // x0 = x0 - 0.0 + 0.0 * C.xxxx
762 // x1 = x0 - i1 + 0.0 * C.xxxx
763 // x2 = x0 - i2 + 0.0 * C.xxxx
764 // x3 = x0 - i3 + 0.0 * C.xxxx
765 // x4 = x0 - 1.0 + 4.0 * C.xxxx
766 vec<4, T, Q> x1 = x0 - i1 + C.x;
767 vec<4, T, Q> x2 = x0 - i2 + C.y;
768 vec<4, T, Q> x3 = x0 - i3 + C.z;
769 vec<4, T, Q> x4 = x0 + C.w;
770
771 // Permutations
772 i = mod(i, vec<4, T, Q>(289));
773 T j0 = detail::permute(detail::permute(detail::permute(detail::permute(i.w) + i.z) + i.y) + i.x);
774 vec<4, T, Q> j1 = detail::permute(detail::permute(detail::permute(detail::permute(
775 i.w + vec<4, T, Q>(i1.w, i2.w, i3.w, T(1))) +
776 i.z + vec<4, T, Q>(i1.z, i2.z, i3.z, T(1))) +
777 i.y + vec<4, T, Q>(i1.y, i2.y, i3.y, T(1))) +
778 i.x + vec<4, T, Q>(i1.x, i2.x, i3.x, T(1)));
779
780 // Gradients: 7x7x6 points over a cube, mapped onto a 4-cross polytope
781 // 7*7*6 = 294, which is close to the ring size 17*17 = 289.
782 vec<4, T, Q> ip = vec<4, T, Q>(T(1) / T(294), T(1) / T(49), T(1) / T(7), T(0));
783
784 vec<4, T, Q> p0 = gtc::grad4(j0, ip);
785 vec<4, T, Q> p1 = gtc::grad4(j1.x, ip);
786 vec<4, T, Q> p2 = gtc::grad4(j1.y, ip);
787 vec<4, T, Q> p3 = gtc::grad4(j1.z, ip);
788 vec<4, T, Q> p4 = gtc::grad4(j1.w, ip);
789
790 // Normalise gradients
791 vec<4, T, Q> norm = detail::taylorInvSqrt(vec<4, T, Q>(dot(p0, p0), dot(p1, p1), dot(p2, p2), dot(p3, p3)));
792 p0 *= norm.x;
793 p1 *= norm.y;
794 p2 *= norm.z;
795 p3 *= norm.w;
796 p4 *= detail::taylorInvSqrt(dot(p4, p4));
797
798 // Mix contributions from the five corners
799 vec<3, T, Q> m0 = max(T(0.6) - vec<3, T, Q>(dot(x0, x0), dot(x1, x1), dot(x2, x2)), vec<3, T, Q>(0));
800 vec<2, T, Q> m1 = max(T(0.6) - vec<2, T, Q>(dot(x3, x3), dot(x4, x4) ), vec<2, T, Q>(0));
801 m0 = m0 * m0;
802 m1 = m1 * m1;
803 return T(49) *
804 (dot(m0 * m0, vec<3, T, Q>(dot(p0, x0), dot(p1, x1), dot(p2, x2))) +
805 dot(m1 * m1, vec<2, T, Q>(dot(p3, x3), dot(p4, x4))));
806 }
807}//namespace glm