1/////////////////////////////////////////////////////////////////////////////////////////////////// 2// OpenGL Mathematics Copyright (c) 2005 - 2012 G-Truc Creation (www.g-truc.net) 3/////////////////////////////////////////////////////////////////////////////////////////////////// 4// Based on the work of Stefan Gustavson and Ashima Arts on "webgl-noise": 5// https://github.com/ashima/webgl-noise 6// Following Stefan Gustavson's paper "Simplex noise demystified": 7// http://www.itn.liu.se/~stegu/simplexnoise/simplexnoise.pdf 8/////////////////////////////////////////////////////////////////////////////////////////////////// 9// Created : 2011-04-21 10// Updated : 2011-09-27 11// Licence : This source is under MIT License 12// File : glm/gtc/noise.inl 13/////////////////////////////////////////////////////////////////////////////////////////////////// 14// Dependency: 15// - GLM core 16/////////////////////////////////////////////////////////////////////////////////////////////////// 17 18namespace glm 19{ 20 template <typename T> 21 GLM_FUNC_QUALIFIER T mod289(T const & x) 22 { 23 return x - floor(x * T(1.0 / 289.0)) * T(289.0); 24 } 25 26 template <typename T> 27 GLM_FUNC_QUALIFIER T permute(T const & x) 28 { 29 return mod289(((x * T(34)) + T(1)) * x); 30 } 31 32 template <typename T, template<typename> class vecType> 33 GLM_FUNC_QUALIFIER vecType<T> permute(vecType<T> const & x) 34 { 35 return mod289(((x * T(34)) + T(1)) * x); 36 } 37 38 template <typename T> 39 GLM_FUNC_QUALIFIER T taylorInvSqrt(T const & r) 40 { 41 return T(1.79284291400159) - T(0.85373472095314) * r; 42 } 43 44 template <typename T, template<typename> class vecType> 45 GLM_FUNC_QUALIFIER vecType<T> taylorInvSqrt(vecType<T> const & r) 46 { 47 return T(1.79284291400159) - T(0.85373472095314) * r; 48 } 49 50 template <typename T, template <typename> class vecType> 51 GLM_FUNC_QUALIFIER vecType<T> fade(vecType<T> const & t) 52 { 53 return t * t * t * (t * (t * T(6) - T(15)) + T(10)); 54 } 55 56 template <typename T> 57 GLM_FUNC_QUALIFIER detail::tvec4<T> grad4(T const & j, detail::tvec4<T> const & ip) 58 { 59 detail::tvec3<T> pXYZ = floor(fract(detail::tvec3<T>(j) * detail::tvec3<T>(ip)) * T(7)) * ip[2] - T(1); 60 T pW = T(1.5) - dot(abs(pXYZ), detail::tvec3<T>(1)); 61 detail::tvec4<T> s = detail::tvec4<T>(lessThan(detail::tvec4<T>(pXYZ, pW), detail::tvec4<T>(0.0))); 62 pXYZ = pXYZ + (detail::tvec3<T>(s) * T(2) - T(1)) * s.w; 63 return detail::tvec4<T>(pXYZ, pW); 64 } 65 66 // Classic Perlin noise 67 template <typename T> 68 GLM_FUNC_QUALIFIER T perlin(detail::tvec2<T> const & P) 69 { 70 detail::tvec4<T> Pi = glm::floor(detail::tvec4<T>(P.x, P.y, P.x, P.y)) + detail::tvec4<T>(0.0, 0.0, 1.0, 1.0); 71 detail::tvec4<T> Pf = glm::fract(detail::tvec4<T>(P.x, P.y, P.x, P.y)) - detail::tvec4<T>(0.0, 0.0, 1.0, 1.0); 72 Pi = mod(Pi, T(289)); // To avoid truncation effects in permutation 73 detail::tvec4<T> ix(Pi.x, Pi.z, Pi.x, Pi.z); 74 detail::tvec4<T> iy(Pi.y, Pi.y, Pi.w, Pi.w); 75 detail::tvec4<T> fx(Pf.x, Pf.z, Pf.x, Pf.z); 76 detail::tvec4<T> fy(Pf.y, Pf.y, Pf.w, Pf.w); 77 78 detail::tvec4<T> i = glm::permute(glm::permute(ix) + iy); 79 80 detail::tvec4<T> gx = T(2) * glm::fract(i / T(41)) - T(1); 81 detail::tvec4<T> gy = glm::abs(gx) - T(0.5); 82 detail::tvec4<T> tx = glm::floor(gx + T(0.5)); 83 gx = gx - tx; 84 85 detail::tvec2<T> g00(gx.x, gy.x); 86 detail::tvec2<T> g10(gx.y, gy.y); 87 detail::tvec2<T> g01(gx.z, gy.z); 88 detail::tvec2<T> g11(gx.w, gy.w); 89 90 detail::tvec4<T> norm = taylorInvSqrt(detail::tvec4<T>(dot(g00, g00), dot(g01, g01), dot(g10, g10), dot(g11, g11))); 91 g00 *= norm.x; 92 g01 *= norm.y; 93 g10 *= norm.z; 94 g11 *= norm.w; 95 96 T n00 = dot(g00, detail::tvec2<T>(fx.x, fy.x)); 97 T n10 = dot(g10, detail::tvec2<T>(fx.y, fy.y)); 98 T n01 = dot(g01, detail::tvec2<T>(fx.z, fy.z)); 99 T n11 = dot(g11, detail::tvec2<T>(fx.w, fy.w)); 100 101 detail::tvec2<T> fade_xy = fade(detail::tvec2<T>(Pf.x, Pf.y)); 102 detail::tvec2<T> n_x = mix(detail::tvec2<T>(n00, n01), detail::tvec2<T>(n10, n11), fade_xy.x); 103 T n_xy = mix(n_x.x, n_x.y, fade_xy.y); 104 return T(2.3) * n_xy; 105 } 106 107 // Classic Perlin noise 108 template <typename T> 109 GLM_FUNC_QUALIFIER T perlin(detail::tvec3<T> const & P) 110 { 111 detail::tvec3<T> Pi0 = floor(P); // Integer part for indexing 112 detail::tvec3<T> Pi1 = Pi0 + T(1); // Integer part + 1 113 Pi0 = mod289(Pi0); 114 Pi1 = mod289(Pi1); 115 detail::tvec3<T> Pf0 = fract(P); // Fractional part for interpolation 116 detail::tvec3<T> Pf1 = Pf0 - T(1); // Fractional part - 1.0 117 detail::tvec4<T> ix(Pi0.x, Pi1.x, Pi0.x, Pi1.x); 118 detail::tvec4<T> iy = detail::tvec4<T>(detail::tvec2<T>(Pi0.y), detail::tvec2<T>(Pi1.y)); 119 detail::tvec4<T> iz0(Pi0.z); 120 detail::tvec4<T> iz1(Pi1.z); 121 122 detail::tvec4<T> ixy = permute(permute(ix) + iy); 123 detail::tvec4<T> ixy0 = permute(ixy + iz0); 124 detail::tvec4<T> ixy1 = permute(ixy + iz1); 125 126 detail::tvec4<T> gx0 = ixy0 * T(1.0 / 7.0); 127 detail::tvec4<T> gy0 = fract(floor(gx0) * T(1.0 / 7.0)) - T(0.5); 128 gx0 = fract(gx0); 129 detail::tvec4<T> gz0 = detail::tvec4<T>(0.5) - abs(gx0) - abs(gy0); 130 detail::tvec4<T> sz0 = step(gz0, detail::tvec4<T>(0.0)); 131 gx0 -= sz0 * (step(T(0), gx0) - T(0.5)); 132 gy0 -= sz0 * (step(T(0), gy0) - T(0.5)); 133 134 detail::tvec4<T> gx1 = ixy1 * T(1.0 / 7.0); 135 detail::tvec4<T> gy1 = fract(floor(gx1) * T(1.0 / 7.0)) - T(0.5); 136 gx1 = fract(gx1); 137 detail::tvec4<T> gz1 = detail::tvec4<T>(0.5) - abs(gx1) - abs(gy1); 138 detail::tvec4<T> sz1 = step(gz1, detail::tvec4<T>(0.0)); 139 gx1 -= sz1 * (step(T(0), gx1) - T(0.5)); 140 gy1 -= sz1 * (step(T(0), gy1) - T(0.5)); 141 142 detail::tvec3<T> g000(gx0.x, gy0.x, gz0.x); 143 detail::tvec3<T> g100(gx0.y, gy0.y, gz0.y); 144 detail::tvec3<T> g010(gx0.z, gy0.z, gz0.z); 145 detail::tvec3<T> g110(gx0.w, gy0.w, gz0.w); 146 detail::tvec3<T> g001(gx1.x, gy1.x, gz1.x); 147 detail::tvec3<T> g101(gx1.y, gy1.y, gz1.y); 148 detail::tvec3<T> g011(gx1.z, gy1.z, gz1.z); 149 detail::tvec3<T> g111(gx1.w, gy1.w, gz1.w); 150 151 detail::tvec4<T> norm0 = taylorInvSqrt(detail::tvec4<T>(dot(g000, g000), dot(g010, g010), dot(g100, g100), dot(g110, g110))); 152 g000 *= norm0.x; 153 g010 *= norm0.y; 154 g100 *= norm0.z; 155 g110 *= norm0.w; 156 detail::tvec4<T> norm1 = taylorInvSqrt(detail::tvec4<T>(dot(g001, g001), dot(g011, g011), dot(g101, g101), dot(g111, g111))); 157 g001 *= norm1.x; 158 g011 *= norm1.y; 159 g101 *= norm1.z; 160 g111 *= norm1.w; 161 162 T n000 = dot(g000, Pf0); 163 T n100 = dot(g100, detail::tvec3<T>(Pf1.x, Pf0.y, Pf0.z)); 164 T n010 = dot(g010, detail::tvec3<T>(Pf0.x, Pf1.y, Pf0.z)); 165 T n110 = dot(g110, detail::tvec3<T>(Pf1.x, Pf1.y, Pf0.z)); 166 T n001 = dot(g001, detail::tvec3<T>(Pf0.x, Pf0.y, Pf1.z)); 167 T n101 = dot(g101, detail::tvec3<T>(Pf1.x, Pf0.y, Pf1.z)); 168 T n011 = dot(g011, detail::tvec3<T>(Pf0.x, Pf1.y, Pf1.z)); 169 T n111 = dot(g111, Pf1); 170 171 detail::tvec3<T> fade_xyz = fade(Pf0); 172 detail::tvec4<T> n_z = mix(detail::tvec4<T>(n000, n100, n010, n110), detail::tvec4<T>(n001, n101, n011, n111), fade_xyz.z); 173 detail::tvec2<T> n_yz = mix(detail::tvec2<T>(n_z.x, n_z.y), detail::tvec2<T>(n_z.z, n_z.w), fade_xyz.y); 174 T n_xyz = mix(n_yz.x, n_yz.y, fade_xyz.x); 175 return T(2.2) * n_xyz; 176 } 177 /* 178 // Classic Perlin noise 179 template <typename T> 180 GLM_FUNC_QUALIFIER T perlin(detail::tvec3<T> const & P) 181 { 182 detail::tvec3<T> Pi0 = floor(P); // Integer part for indexing 183 detail::tvec3<T> Pi1 = Pi0 + T(1); // Integer part + 1 184 Pi0 = mod(Pi0, T(289)); 185 Pi1 = mod(Pi1, T(289)); 186 detail::tvec3<T> Pf0 = fract(P); // Fractional part for interpolation 187 detail::tvec3<T> Pf1 = Pf0 - T(1); // Fractional part - 1.0 188 detail::tvec4<T> ix(Pi0.x, Pi1.x, Pi0.x, Pi1.x); 189 detail::tvec4<T> iy(Pi0.y, Pi0.y, Pi1.y, Pi1.y); 190 detail::tvec4<T> iz0(Pi0.z); 191 detail::tvec4<T> iz1(Pi1.z); 192 193 detail::tvec4<T> ixy = permute(permute(ix) + iy); 194 detail::tvec4<T> ixy0 = permute(ixy + iz0); 195 detail::tvec4<T> ixy1 = permute(ixy + iz1); 196 197 detail::tvec4<T> gx0 = ixy0 / T(7); 198 detail::tvec4<T> gy0 = fract(floor(gx0) / T(7)) - T(0.5); 199 gx0 = fract(gx0); 200 detail::tvec4<T> gz0 = detail::tvec4<T>(0.5) - abs(gx0) - abs(gy0); 201 detail::tvec4<T> sz0 = step(gz0, detail::tvec4<T>(0.0)); 202 gx0 -= sz0 * (step(0.0, gx0) - T(0.5)); 203 gy0 -= sz0 * (step(0.0, gy0) - T(0.5)); 204 205 detail::tvec4<T> gx1 = ixy1 / T(7); 206 detail::tvec4<T> gy1 = fract(floor(gx1) / T(7)) - T(0.5); 207 gx1 = fract(gx1); 208 detail::tvec4<T> gz1 = detail::tvec4<T>(0.5) - abs(gx1) - abs(gy1); 209 detail::tvec4<T> sz1 = step(gz1, detail::tvec4<T>(0.0)); 210 gx1 -= sz1 * (step(T(0), gx1) - T(0.5)); 211 gy1 -= sz1 * (step(T(0), gy1) - T(0.5)); 212 213 detail::tvec3<T> g000(gx0.x, gy0.x, gz0.x); 214 detail::tvec3<T> g100(gx0.y, gy0.y, gz0.y); 215 detail::tvec3<T> g010(gx0.z, gy0.z, gz0.z); 216 detail::tvec3<T> g110(gx0.w, gy0.w, gz0.w); 217 detail::tvec3<T> g001(gx1.x, gy1.x, gz1.x); 218 detail::tvec3<T> g101(gx1.y, gy1.y, gz1.y); 219 detail::tvec3<T> g011(gx1.z, gy1.z, gz1.z); 220 detail::tvec3<T> g111(gx1.w, gy1.w, gz1.w); 221 222 detail::tvec4<T> norm0 = taylorInvSqrt(detail::tvec4<T>(dot(g000, g000), dot(g010, g010), dot(g100, g100), dot(g110, g110))); 223 g000 *= norm0.x; 224 g010 *= norm0.y; 225 g100 *= norm0.z; 226 g110 *= norm0.w; 227 detail::tvec4<T> norm1 = taylorInvSqrt(detail::tvec4<T>(dot(g001, g001), dot(g011, g011), dot(g101, g101), dot(g111, g111))); 228 g001 *= norm1.x; 229 g011 *= norm1.y; 230 g101 *= norm1.z; 231 g111 *= norm1.w; 232 233 T n000 = dot(g000, Pf0); 234 T n100 = dot(g100, detail::tvec3<T>(Pf1.x, Pf0.y, Pf0.z)); 235 T n010 = dot(g010, detail::tvec3<T>(Pf0.x, Pf1.y, Pf0.z)); 236 T n110 = dot(g110, detail::tvec3<T>(Pf1.x, Pf1.y, Pf0.z)); 237 T n001 = dot(g001, detail::tvec3<T>(Pf0.x, Pf0.y, Pf1.z)); 238 T n101 = dot(g101, detail::tvec3<T>(Pf1.x, Pf0.y, Pf1.z)); 239 T n011 = dot(g011, detail::tvec3<T>(Pf0.x, Pf1.y, Pf1.z)); 240 T n111 = dot(g111, Pf1); 241 242 detail::tvec3<T> fade_xyz = fade(Pf0); 243 detail::tvec4<T> n_z = mix(detail::tvec4<T>(n000, n100, n010, n110), detail::tvec4<T>(n001, n101, n011, n111), fade_xyz.z); 244 detail::tvec2<T> n_yz = mix( 245 detail::tvec2<T>(n_z.x, n_z.y), 246 detail::tvec2<T>(n_z.z, n_z.w), fade_xyz.y); 247 T n_xyz = mix(n_yz.x, n_yz.y, fade_xyz.x); 248 return T(2.2) * n_xyz; 249 } 250 */ 251 // Classic Perlin noise 252 template <typename T> 253 GLM_FUNC_QUALIFIER T perlin(detail::tvec4<T> const & P) 254 { 255 detail::tvec4<T> Pi0 = floor(P); // Integer part for indexing 256 detail::tvec4<T> Pi1 = Pi0 + T(1); // Integer part + 1 257 Pi0 = mod(Pi0, T(289)); 258 Pi1 = mod(Pi1, T(289)); 259 detail::tvec4<T> Pf0 = fract(P); // Fractional part for interpolation 260 detail::tvec4<T> Pf1 = Pf0 - T(1); // Fractional part - 1.0 261 detail::tvec4<T> ix(Pi0.x, Pi1.x, Pi0.x, Pi1.x); 262 detail::tvec4<T> iy(Pi0.y, Pi0.y, Pi1.y, Pi1.y); 263 detail::tvec4<T> iz0(Pi0.z); 264 detail::tvec4<T> iz1(Pi1.z); 265 detail::tvec4<T> iw0(Pi0.w); 266 detail::tvec4<T> iw1(Pi1.w); 267 268 detail::tvec4<T> ixy = permute(permute(ix) + iy); 269 detail::tvec4<T> ixy0 = permute(ixy + iz0); 270 detail::tvec4<T> ixy1 = permute(ixy + iz1); 271 detail::tvec4<T> ixy00 = permute(ixy0 + iw0); 272 detail::tvec4<T> ixy01 = permute(ixy0 + iw1); 273 detail::tvec4<T> ixy10 = permute(ixy1 + iw0); 274 detail::tvec4<T> ixy11 = permute(ixy1 + iw1); 275 276 detail::tvec4<T> gx00 = ixy00 / T(7); 277 detail::tvec4<T> gy00 = floor(gx00) / T(7); 278 detail::tvec4<T> gz00 = floor(gy00) / T(6); 279 gx00 = fract(gx00) - T(0.5); 280 gy00 = fract(gy00) - T(0.5); 281 gz00 = fract(gz00) - T(0.5); 282 detail::tvec4<T> gw00 = detail::tvec4<T>(0.75) - abs(gx00) - abs(gy00) - abs(gz00); 283 detail::tvec4<T> sw00 = step(gw00, detail::tvec4<T>(0.0)); 284 gx00 -= sw00 * (step(T(0), gx00) - T(0.5)); 285 gy00 -= sw00 * (step(T(0), gy00) - T(0.5)); 286 287 detail::tvec4<T> gx01 = ixy01 / T(7); 288 detail::tvec4<T> gy01 = floor(gx01) / T(7); 289 detail::tvec4<T> gz01 = floor(gy01) / T(6); 290 gx01 = fract(gx01) - T(0.5); 291 gy01 = fract(gy01) - T(0.5); 292 gz01 = fract(gz01) - T(0.5); 293 detail::tvec4<T> gw01 = detail::tvec4<T>(0.75) - abs(gx01) - abs(gy01) - abs(gz01); 294 detail::tvec4<T> sw01 = step(gw01, detail::tvec4<T>(0.0)); 295 gx01 -= sw01 * (step(T(0), gx01) - T(0.5)); 296 gy01 -= sw01 * (step(T(0), gy01) - T(0.5)); 297 298 detail::tvec4<T> gx10 = ixy10 / T(7); 299 detail::tvec4<T> gy10 = floor(gx10) / T(7); 300 detail::tvec4<T> gz10 = floor(gy10) / T(6); 301 gx10 = fract(gx10) - T(0.5); 302 gy10 = fract(gy10) - T(0.5); 303 gz10 = fract(gz10) - T(0.5); 304 detail::tvec4<T> gw10 = detail::tvec4<T>(0.75) - abs(gx10) - abs(gy10) - abs(gz10); 305 detail::tvec4<T> sw10 = step(gw10, detail::tvec4<T>(0)); 306 gx10 -= sw10 * (step(T(0), gx10) - T(0.5)); 307 gy10 -= sw10 * (step(T(0), gy10) - T(0.5)); 308 309 detail::tvec4<T> gx11 = ixy11 / T(7); 310 detail::tvec4<T> gy11 = floor(gx11) / T(7); 311 detail::tvec4<T> gz11 = floor(gy11) / T(6); 312 gx11 = fract(gx11) - T(0.5); 313 gy11 = fract(gy11) - T(0.5); 314 gz11 = fract(gz11) - T(0.5); 315 detail::tvec4<T> gw11 = detail::tvec4<T>(0.75) - abs(gx11) - abs(gy11) - abs(gz11); 316 detail::tvec4<T> sw11 = step(gw11, detail::tvec4<T>(0.0)); 317 gx11 -= sw11 * (step(T(0), gx11) - T(0.5)); 318 gy11 -= sw11 * (step(T(0), gy11) - T(0.5)); 319 320 detail::tvec4<T> g0000(gx00.x, gy00.x, gz00.x, gw00.x); 321 detail::tvec4<T> g1000(gx00.y, gy00.y, gz00.y, gw00.y); 322 detail::tvec4<T> g0100(gx00.z, gy00.z, gz00.z, gw00.z); 323 detail::tvec4<T> g1100(gx00.w, gy00.w, gz00.w, gw00.w); 324 detail::tvec4<T> g0010(gx10.x, gy10.x, gz10.x, gw10.x); 325 detail::tvec4<T> g1010(gx10.y, gy10.y, gz10.y, gw10.y); 326 detail::tvec4<T> g0110(gx10.z, gy10.z, gz10.z, gw10.z); 327 detail::tvec4<T> g1110(gx10.w, gy10.w, gz10.w, gw10.w); 328 detail::tvec4<T> g0001(gx01.x, gy01.x, gz01.x, gw01.x); 329 detail::tvec4<T> g1001(gx01.y, gy01.y, gz01.y, gw01.y); 330 detail::tvec4<T> g0101(gx01.z, gy01.z, gz01.z, gw01.z); 331 detail::tvec4<T> g1101(gx01.w, gy01.w, gz01.w, gw01.w); 332 detail::tvec4<T> g0011(gx11.x, gy11.x, gz11.x, gw11.x); 333 detail::tvec4<T> g1011(gx11.y, gy11.y, gz11.y, gw11.y); 334 detail::tvec4<T> g0111(gx11.z, gy11.z, gz11.z, gw11.z); 335 detail::tvec4<T> g1111(gx11.w, gy11.w, gz11.w, gw11.w); 336 337 detail::tvec4<T> norm00 = taylorInvSqrt(detail::tvec4<T>(dot(g0000, g0000), dot(g0100, g0100), dot(g1000, g1000), dot(g1100, g1100))); 338 g0000 *= norm00.x; 339 g0100 *= norm00.y; 340 g1000 *= norm00.z; 341 g1100 *= norm00.w; 342 343 detail::tvec4<T> norm01 = taylorInvSqrt(detail::tvec4<T>(dot(g0001, g0001), dot(g0101, g0101), dot(g1001, g1001), dot(g1101, g1101))); 344 g0001 *= norm01.x; 345 g0101 *= norm01.y; 346 g1001 *= norm01.z; 347 g1101 *= norm01.w; 348 349 detail::tvec4<T> norm10 = taylorInvSqrt(detail::tvec4<T>(dot(g0010, g0010), dot(g0110, g0110), dot(g1010, g1010), dot(g1110, g1110))); 350 g0010 *= norm10.x; 351 g0110 *= norm10.y; 352 g1010 *= norm10.z; 353 g1110 *= norm10.w; 354 355 detail::tvec4<T> norm11 = taylorInvSqrt(detail::tvec4<T>(dot(g0011, g0011), dot(g0111, g0111), dot(g1011, g1011), dot(g1111, g1111))); 356 g0011 *= norm11.x; 357 g0111 *= norm11.y; 358 g1011 *= norm11.z; 359 g1111 *= norm11.w; 360 361 T n0000 = dot(g0000, Pf0); 362 T n1000 = dot(g1000, detail::tvec4<T>(Pf1.x, Pf0.y, Pf0.z, Pf0.w)); 363 T n0100 = dot(g0100, detail::tvec4<T>(Pf0.x, Pf1.y, Pf0.z, Pf0.w)); 364 T n1100 = dot(g1100, detail::tvec4<T>(Pf1.x, Pf1.y, Pf0.z, Pf0.w)); 365 T n0010 = dot(g0010, detail::tvec4<T>(Pf0.x, Pf0.y, Pf1.z, Pf0.w)); 366 T n1010 = dot(g1010, detail::tvec4<T>(Pf1.x, Pf0.y, Pf1.z, Pf0.w)); 367 T n0110 = dot(g0110, detail::tvec4<T>(Pf0.x, Pf1.y, Pf1.z, Pf0.w)); 368 T n1110 = dot(g1110, detail::tvec4<T>(Pf1.x, Pf1.y, Pf1.z, Pf0.w)); 369 T n0001 = dot(g0001, detail::tvec4<T>(Pf0.x, Pf0.y, Pf0.z, Pf1.w)); 370 T n1001 = dot(g1001, detail::tvec4<T>(Pf1.x, Pf0.y, Pf0.z, Pf1.w)); 371 T n0101 = dot(g0101, detail::tvec4<T>(Pf0.x, Pf1.y, Pf0.z, Pf1.w)); 372 T n1101 = dot(g1101, detail::tvec4<T>(Pf1.x, Pf1.y, Pf0.z, Pf1.w)); 373 T n0011 = dot(g0011, detail::tvec4<T>(Pf0.x, Pf0.y, Pf1.z, Pf1.w)); 374 T n1011 = dot(g1011, detail::tvec4<T>(Pf1.x, Pf0.y, Pf1.z, Pf1.w)); 375 T n0111 = dot(g0111, detail::tvec4<T>(Pf0.x, Pf1.y, Pf1.z, Pf1.w)); 376 T n1111 = dot(g1111, Pf1); 377 378 detail::tvec4<T> fade_xyzw = fade(Pf0); 379 detail::tvec4<T> n_0w = mix(detail::tvec4<T>(n0000, n1000, n0100, n1100), detail::tvec4<T>(n0001, n1001, n0101, n1101), fade_xyzw.w); 380 detail::tvec4<T> n_1w = mix(detail::tvec4<T>(n0010, n1010, n0110, n1110), detail::tvec4<T>(n0011, n1011, n0111, n1111), fade_xyzw.w); 381 detail::tvec4<T> n_zw = mix(n_0w, n_1w, fade_xyzw.z); 382 detail::tvec2<T> n_yzw = mix(detail::tvec2<T>(n_zw.x, n_zw.y), detail::tvec2<T>(n_zw.z, n_zw.w), fade_xyzw.y); 383 T n_xyzw = mix(n_yzw.x, n_yzw.y, fade_xyzw.x); 384 return T(2.2) * n_xyzw; 385 } 386 387 // Classic Perlin noise, periodic variant 388 template <typename T> 389 GLM_FUNC_QUALIFIER T perlin(detail::tvec2<T> const & P, detail::tvec2<T> const & rep) 390 { 391 detail::tvec4<T> Pi = floor(detail::tvec4<T>(P.x, P.y, P.x, P.y)) + detail::tvec4<T>(0.0, 0.0, 1.0, 1.0); 392 detail::tvec4<T> Pf = fract(detail::tvec4<T>(P.x, P.y, P.x, P.y)) - detail::tvec4<T>(0.0, 0.0, 1.0, 1.0); 393 Pi = mod(Pi, detail::tvec4<T>(rep.x, rep.y, rep.x, rep.y)); // To create noise with explicit period 394 Pi = mod(Pi, T(289)); // To avoid truncation effects in permutation 395 detail::tvec4<T> ix(Pi.x, Pi.z, Pi.x, Pi.z); 396 detail::tvec4<T> iy(Pi.y, Pi.y, Pi.w, Pi.w); 397 detail::tvec4<T> fx(Pf.x, Pf.z, Pf.x, Pf.z); 398 detail::tvec4<T> fy(Pf.y, Pf.y, Pf.w, Pf.w); 399 400 detail::tvec4<T> i = permute(permute(ix) + iy); 401 402 detail::tvec4<T> gx = T(2) * fract(i / T(41)) - T(1); 403 detail::tvec4<T> gy = abs(gx) - T(0.5); 404 detail::tvec4<T> tx = floor(gx + T(0.5)); 405 gx = gx - tx; 406 407 detail::tvec2<T> g00(gx.x, gy.x); 408 detail::tvec2<T> g10(gx.y, gy.y); 409 detail::tvec2<T> g01(gx.z, gy.z); 410 detail::tvec2<T> g11(gx.w, gy.w); 411 412 detail::tvec4<T> norm = taylorInvSqrt(detail::tvec4<T>(dot(g00, g00), dot(g01, g01), dot(g10, g10), dot(g11, g11))); 413 g00 *= norm.x; 414 g01 *= norm.y; 415 g10 *= norm.z; 416 g11 *= norm.w; 417 418 T n00 = dot(g00, detail::tvec2<T>(fx.x, fy.x)); 419 T n10 = dot(g10, detail::tvec2<T>(fx.y, fy.y)); 420 T n01 = dot(g01, detail::tvec2<T>(fx.z, fy.z)); 421 T n11 = dot(g11, detail::tvec2<T>(fx.w, fy.w)); 422 423 detail::tvec2<T> fade_xy = fade(detail::tvec2<T>(Pf.x, Pf.y)); 424 detail::tvec2<T> n_x = mix(detail::tvec2<T>(n00, n01), detail::tvec2<T>(n10, n11), fade_xy.x); 425 T n_xy = mix(n_x.x, n_x.y, fade_xy.y); 426 return T(2.3) * n_xy; 427 } 428 429 // Classic Perlin noise, periodic variant 430 template <typename T> 431 GLM_FUNC_QUALIFIER T perlin(detail::tvec3<T> const & P, detail::tvec3<T> const & rep) 432 { 433 detail::tvec3<T> Pi0 = mod(floor(P), rep); // Integer part, modulo period 434 detail::tvec3<T> Pi1 = mod(Pi0 + detail::tvec3<T>(1.0), rep); // Integer part + 1, mod period 435 Pi0 = mod(Pi0, T(289)); 436 Pi1 = mod(Pi1, T(289)); 437 detail::tvec3<T> Pf0 = fract(P); // Fractional part for interpolation 438 detail::tvec3<T> Pf1 = Pf0 - detail::tvec3<T>(1.0); // Fractional part - 1.0 439 detail::tvec4<T> ix = detail::tvec4<T>(Pi0.x, Pi1.x, Pi0.x, Pi1.x); 440 detail::tvec4<T> iy = detail::tvec4<T>(Pi0.y, Pi0.y, Pi1.y, Pi1.y); 441 detail::tvec4<T> iz0(Pi0.z); 442 detail::tvec4<T> iz1(Pi1.z); 443 444 detail::tvec4<T> ixy = permute(permute(ix) + iy); 445 detail::tvec4<T> ixy0 = permute(ixy + iz0); 446 detail::tvec4<T> ixy1 = permute(ixy + iz1); 447 448 detail::tvec4<T> gx0 = ixy0 / T(7); 449 detail::tvec4<T> gy0 = fract(floor(gx0) / T(7)) - T(0.5); 450 gx0 = fract(gx0); 451 detail::tvec4<T> gz0 = detail::tvec4<T>(0.5) - abs(gx0) - abs(gy0); 452 detail::tvec4<T> sz0 = step(gz0, detail::tvec4<T>(0)); 453 gx0 -= sz0 * (step(0.0, gx0) - T(0.5)); 454 gy0 -= sz0 * (step(0.0, gy0) - T(0.5)); 455 456 detail::tvec4<T> gx1 = ixy1 / T(7); 457 detail::tvec4<T> gy1 = fract(floor(gx1) / T(7)) - T(0.5); 458 gx1 = fract(gx1); 459 detail::tvec4<T> gz1 = detail::tvec4<T>(0.5) - abs(gx1) - abs(gy1); 460 detail::tvec4<T> sz1 = step(gz1, detail::tvec4<T>(0.0)); 461 gx1 -= sz1 * (step(0.0, gx1) - T(0.5)); 462 gy1 -= sz1 * (step(0.0, gy1) - T(0.5)); 463 464 detail::tvec3<T> g000 = detail::tvec3<T>(gx0.x, gy0.x, gz0.x); 465 detail::tvec3<T> g100 = detail::tvec3<T>(gx0.y, gy0.y, gz0.y); 466 detail::tvec3<T> g010 = detail::tvec3<T>(gx0.z, gy0.z, gz0.z); 467 detail::tvec3<T> g110 = detail::tvec3<T>(gx0.w, gy0.w, gz0.w); 468 detail::tvec3<T> g001 = detail::tvec3<T>(gx1.x, gy1.x, gz1.x); 469 detail::tvec3<T> g101 = detail::tvec3<T>(gx1.y, gy1.y, gz1.y); 470 detail::tvec3<T> g011 = detail::tvec3<T>(gx1.z, gy1.z, gz1.z); 471 detail::tvec3<T> g111 = detail::tvec3<T>(gx1.w, gy1.w, gz1.w); 472 473 detail::tvec4<T> norm0 = taylorInvSqrt(detail::tvec4<T>(dot(g000, g000), dot(g010, g010), dot(g100, g100), dot(g110, g110))); 474 g000 *= norm0.x; 475 g010 *= norm0.y; 476 g100 *= norm0.z; 477 g110 *= norm0.w; 478 detail::tvec4<T> norm1 = taylorInvSqrt(detail::tvec4<T>(dot(g001, g001), dot(g011, g011), dot(g101, g101), dot(g111, g111))); 479 g001 *= norm1.x; 480 g011 *= norm1.y; 481 g101 *= norm1.z; 482 g111 *= norm1.w; 483 484 T n000 = dot(g000, Pf0); 485 T n100 = dot(g100, detail::tvec3<T>(Pf1.x, Pf0.y, Pf0.z)); 486 T n010 = dot(g010, detail::tvec3<T>(Pf0.x, Pf1.y, Pf0.z)); 487 T n110 = dot(g110, detail::tvec3<T>(Pf1.x, Pf1.y, Pf0.z)); 488 T n001 = dot(g001, detail::tvec3<T>(Pf0.x, Pf0.y, Pf1.z)); 489 T n101 = dot(g101, detail::tvec3<T>(Pf1.x, Pf0.y, Pf1.z)); 490 T n011 = dot(g011, detail::tvec3<T>(Pf0.x, Pf1.y, Pf1.z)); 491 T n111 = dot(g111, Pf1); 492 493 detail::tvec3<T> fade_xyz = fade(Pf0); 494 detail::tvec4<T> n_z = mix(detail::tvec4<T>(n000, n100, n010, n110), detail::tvec4<T>(n001, n101, n011, n111), fade_xyz.z); 495 detail::tvec2<T> n_yz = mix(detail::tvec2<T>(n_z.x, n_z.y), detail::tvec2<T>(n_z.z, n_z.w), fade_xyz.y); 496 T n_xyz = mix(n_yz.x, n_yz.y, fade_xyz.x); 497 return T(2.2) * n_xyz; 498 } 499 500 // Classic Perlin noise, periodic version 501 template <typename T> 502 GLM_FUNC_QUALIFIER T perlin(detail::tvec4<T> const & P, detail::tvec4<T> const & rep) 503 { 504 detail::tvec4<T> Pi0 = mod(floor(P), rep); // Integer part modulo rep 505 detail::tvec4<T> Pi1 = mod(Pi0 + T(1), rep); // Integer part + 1 mod rep 506 detail::tvec4<T> Pf0 = fract(P); // Fractional part for interpolation 507 detail::tvec4<T> Pf1 = Pf0 - T(1); // Fractional part - 1.0 508 detail::tvec4<T> ix = detail::tvec4<T>(Pi0.x, Pi1.x, Pi0.x, Pi1.x); 509 detail::tvec4<T> iy = detail::tvec4<T>(Pi0.y, Pi0.y, Pi1.y, Pi1.y); 510 detail::tvec4<T> iz0(Pi0.z); 511 detail::tvec4<T> iz1(Pi1.z); 512 detail::tvec4<T> iw0(Pi0.w); 513 detail::tvec4<T> iw1(Pi1.w); 514 515 detail::tvec4<T> ixy = permute(permute(ix) + iy); 516 detail::tvec4<T> ixy0 = permute(ixy + iz0); 517 detail::tvec4<T> ixy1 = permute(ixy + iz1); 518 detail::tvec4<T> ixy00 = permute(ixy0 + iw0); 519 detail::tvec4<T> ixy01 = permute(ixy0 + iw1); 520 detail::tvec4<T> ixy10 = permute(ixy1 + iw0); 521 detail::tvec4<T> ixy11 = permute(ixy1 + iw1); 522 523 detail::tvec4<T> gx00 = ixy00 / T(7); 524 detail::tvec4<T> gy00 = floor(gx00) / T(7); 525 detail::tvec4<T> gz00 = floor(gy00) / T(6); 526 gx00 = fract(gx00) - T(0.5); 527 gy00 = fract(gy00) - T(0.5); 528 gz00 = fract(gz00) - T(0.5); 529 detail::tvec4<T> gw00 = detail::tvec4<T>(0.75) - abs(gx00) - abs(gy00) - abs(gz00); 530 detail::tvec4<T> sw00 = step(gw00, detail::tvec4<T>(0)); 531 gx00 -= sw00 * (step(0.0, gx00) - T(0.5)); 532 gy00 -= sw00 * (step(0.0, gy00) - T(0.5)); 533 534 detail::tvec4<T> gx01 = ixy01 / T(7); 535 detail::tvec4<T> gy01 = floor(gx01) / T(7); 536 detail::tvec4<T> gz01 = floor(gy01) / T(6); 537 gx01 = fract(gx01) - T(0.5); 538 gy01 = fract(gy01) - T(0.5); 539 gz01 = fract(gz01) - T(0.5); 540 detail::tvec4<T> gw01 = detail::tvec4<T>(0.75) - abs(gx01) - abs(gy01) - abs(gz01); 541 detail::tvec4<T> sw01 = step(gw01, detail::tvec4<T>(0.0)); 542 gx01 -= sw01 * (step(0.0, gx01) - T(0.5)); 543 gy01 -= sw01 * (step(0.0, gy01) - T(0.5)); 544 545 detail::tvec4<T> gx10 = ixy10 / T(7); 546 detail::tvec4<T> gy10 = floor(gx10) / T(7); 547 detail::tvec4<T> gz10 = floor(gy10) / T(6); 548 gx10 = fract(gx10) - T(0.5); 549 gy10 = fract(gy10) - T(0.5); 550 gz10 = fract(gz10) - T(0.5); 551 detail::tvec4<T> gw10 = detail::tvec4<T>(0.75) - abs(gx10) - abs(gy10) - abs(gz10); 552 detail::tvec4<T> sw10 = step(gw10, detail::tvec4<T>(0.0)); 553 gx10 -= sw10 * (step(0.0, gx10) - T(0.5)); 554 gy10 -= sw10 * (step(0.0, gy10) - T(0.5)); 555 556 detail::tvec4<T> gx11 = ixy11 / T(7); 557 detail::tvec4<T> gy11 = floor(gx11) / T(7); 558 detail::tvec4<T> gz11 = floor(gy11) / T(6); 559 gx11 = fract(gx11) - T(0.5); 560 gy11 = fract(gy11) - T(0.5); 561 gz11 = fract(gz11) - T(0.5); 562 detail::tvec4<T> gw11 = detail::tvec4<T>(0.75) - abs(gx11) - abs(gy11) - abs(gz11); 563 detail::tvec4<T> sw11 = step(gw11, detail::tvec4<T>(0.0)); 564 gx11 -= sw11 * (step(0.0, gx11) - T(0.5)); 565 gy11 -= sw11 * (step(0.0, gy11) - T(0.5)); 566 567 detail::tvec4<T> g0000(gx00.x, gy00.x, gz00.x, gw00.x); 568 detail::tvec4<T> g1000(gx00.y, gy00.y, gz00.y, gw00.y); 569 detail::tvec4<T> g0100(gx00.z, gy00.z, gz00.z, gw00.z); 570 detail::tvec4<T> g1100(gx00.w, gy00.w, gz00.w, gw00.w); 571 detail::tvec4<T> g0010(gx10.x, gy10.x, gz10.x, gw10.x); 572 detail::tvec4<T> g1010(gx10.y, gy10.y, gz10.y, gw10.y); 573 detail::tvec4<T> g0110(gx10.z, gy10.z, gz10.z, gw10.z); 574 detail::tvec4<T> g1110(gx10.w, gy10.w, gz10.w, gw10.w); 575 detail::tvec4<T> g0001(gx01.x, gy01.x, gz01.x, gw01.x); 576 detail::tvec4<T> g1001(gx01.y, gy01.y, gz01.y, gw01.y); 577 detail::tvec4<T> g0101(gx01.z, gy01.z, gz01.z, gw01.z); 578 detail::tvec4<T> g1101(gx01.w, gy01.w, gz01.w, gw01.w); 579 detail::tvec4<T> g0011(gx11.x, gy11.x, gz11.x, gw11.x); 580 detail::tvec4<T> g1011(gx11.y, gy11.y, gz11.y, gw11.y); 581 detail::tvec4<T> g0111(gx11.z, gy11.z, gz11.z, gw11.z); 582 detail::tvec4<T> g1111(gx11.w, gy11.w, gz11.w, gw11.w); 583 584 detail::tvec4<T> norm00 = taylorInvSqrt(detail::tvec4<T>(dot(g0000, g0000), dot(g0100, g0100), dot(g1000, g1000), dot(g1100, g1100))); 585 g0000 *= norm00.x; 586 g0100 *= norm00.y; 587 g1000 *= norm00.z; 588 g1100 *= norm00.w; 589 590 detail::tvec4<T> norm01 = taylorInvSqrt(detail::tvec4<T>(dot(g0001, g0001), dot(g0101, g0101), dot(g1001, g1001), dot(g1101, g1101))); 591 g0001 *= norm01.x; 592 g0101 *= norm01.y; 593 g1001 *= norm01.z; 594 g1101 *= norm01.w; 595 596 detail::tvec4<T> norm10 = taylorInvSqrt(detail::tvec4<T>(dot(g0010, g0010), dot(g0110, g0110), dot(g1010, g1010), dot(g1110, g1110))); 597 g0010 *= norm10.x; 598 g0110 *= norm10.y; 599 g1010 *= norm10.z; 600 g1110 *= norm10.w; 601 602 detail::tvec4<T> norm11 = taylorInvSqrt(detail::tvec4<T>(dot(g0011, g0011), dot(g0111, g0111), dot(g1011, g1011), dot(g1111, g1111))); 603 g0011 *= norm11.x; 604 g0111 *= norm11.y; 605 g1011 *= norm11.z; 606 g1111 *= norm11.w; 607 608 T n0000 = dot(g0000, Pf0); 609 T n1000 = dot(g1000, detail::tvec4<T>(Pf1.x, Pf0.y, Pf0.z, Pf0.w)); 610 T n0100 = dot(g0100, detail::tvec4<T>(Pf0.x, Pf1.y, Pf0.z, Pf0.w)); 611 T n1100 = dot(g1100, detail::tvec4<T>(Pf1.x, Pf1.y, Pf0.z, Pf0.w)); 612 T n0010 = dot(g0010, detail::tvec4<T>(Pf0.x, Pf0.y, Pf1.z, Pf0.w)); 613 T n1010 = dot(g1010, detail::tvec4<T>(Pf1.x, Pf0.y, Pf1.z, Pf0.w)); 614 T n0110 = dot(g0110, detail::tvec4<T>(Pf0.x, Pf1.y, Pf1.z, Pf0.w)); 615 T n1110 = dot(g1110, detail::tvec4<T>(Pf1.x, Pf1.y, Pf1.z, Pf0.w)); 616 T n0001 = dot(g0001, detail::tvec4<T>(Pf0.x, Pf0.y, Pf0.z, Pf1.w)); 617 T n1001 = dot(g1001, detail::tvec4<T>(Pf1.x, Pf0.y, Pf0.z, Pf1.w)); 618 T n0101 = dot(g0101, detail::tvec4<T>(Pf0.x, Pf1.y, Pf0.z, Pf1.w)); 619 T n1101 = dot(g1101, detail::tvec4<T>(Pf1.x, Pf1.y, Pf0.z, Pf1.w)); 620 T n0011 = dot(g0011, detail::tvec4<T>(Pf0.x, Pf0.y, Pf1.z, Pf1.w)); 621 T n1011 = dot(g1011, detail::tvec4<T>(Pf1.x, Pf0.y, Pf1.z, Pf1.w)); 622 T n0111 = dot(g0111, detail::tvec4<T>(Pf0.x, Pf1.y, Pf1.z, Pf1.w)); 623 T n1111 = dot(g1111, Pf1); 624 625 detail::tvec4<T> fade_xyzw = fade(Pf0); 626 detail::tvec4<T> n_0w = mix(detail::tvec4<T>(n0000, n1000, n0100, n1100), detail::tvec4<T>(n0001, n1001, n0101, n1101), fade_xyzw.w); 627 detail::tvec4<T> n_1w = mix(detail::tvec4<T>(n0010, n1010, n0110, n1110), detail::tvec4<T>(n0011, n1011, n0111, n1111), fade_xyzw.w); 628 detail::tvec4<T> n_zw = mix(n_0w, n_1w, fade_xyzw.z); 629 detail::tvec2<T> n_yzw = mix(detail::tvec2<T>(n_zw.x, n_zw.y), detail::tvec2<T>(n_zw.z, n_zw.w), fade_xyzw.y); 630 T n_xyzw = mix(n_yzw.x, n_yzw.y, fade_xyzw.x); 631 return T(2.2) * n_xyzw; 632 } 633 634 template <typename T> 635 GLM_FUNC_QUALIFIER T simplex(glm::detail::tvec2<T> const & v) 636 { 637 detail::tvec4<T> const C = detail::tvec4<T>( 638 T( 0.211324865405187), // (3.0 - sqrt(3.0)) / 6.0 639 T( 0.366025403784439), // 0.5 * (sqrt(3.0) - 1.0) 640 T(-0.577350269189626), // -1.0 + 2.0 * C.x 641 T( 0.024390243902439)); // 1.0 / 41.0 642 643 // First corner 644 detail::tvec2<T> i = floor(v + dot(v, detail::tvec2<T>(C[1]))); 645 detail::tvec2<T> x0 = v - i + dot(i, detail::tvec2<T>(C[0])); 646 647 // Other corners 648 //i1.x = step( x0.y, x0.x ); // x0.x > x0.y ? 1.0 : 0.0 649 //i1.y = 1.0 - i1.x; 650 detail::tvec2<T> i1 = (x0.x > x0.y) ? detail::tvec2<T>(1, 0) : detail::tvec2<T>(0, 1); 651 // x0 = x0 - 0.0 + 0.0 * C.xx ; 652 // x1 = x0 - i1 + 1.0 * C.xx ; 653 // x2 = x0 - 1.0 + 2.0 * C.xx ; 654 detail::tvec4<T> x12 = detail::tvec4<T>(x0.x, x0.y, x0.x, x0.y) + detail::tvec4<T>(C.x, C.x, C.z, C.z); 655 x12 = detail::tvec4<T>(detail::tvec2<T>(x12) - i1, x12.z, x12.w); 656 657 // Permutations 658 i = mod(i, T(289)); // Avoid truncation effects in permutation 659 detail::tvec3<T> p = permute( 660 permute(i.y + detail::tvec3<T>(T(0), i1.y, T(1))) 661 + i.x + detail::tvec3<T>(T(0), i1.x, T(1))); 662 663 detail::tvec3<T> m = max(T(0.5) - detail::tvec3<T>( 664 dot(x0, x0), 665 dot(detail::tvec2<T>(x12.x, x12.y), detail::tvec2<T>(x12.x, x12.y)), 666 dot(detail::tvec2<T>(x12.z, x12.w), detail::tvec2<T>(x12.z, x12.w))), T(0)); 667 m = m * m ; 668 m = m * m ; 669 670 // Gradients: 41 points uniformly over a line, mapped onto a diamond. 671 // The ring size 17*17 = 289 is close to a multiple of 41 (41*7 = 287) 672 673 detail::tvec3<T> x = T(2) * fract(p * C.w) - T(1); 674 detail::tvec3<T> h = abs(x) - T(0.5); 675 detail::tvec3<T> ox = floor(x + T(0.5)); 676 detail::tvec3<T> a0 = x - ox; 677 678 // Normalise gradients implicitly by scaling m 679 // Inlined for speed: m *= taylorInvSqrt( a0*a0 + h*h ); 680 m *= T(1.79284291400159) - T(0.85373472095314) * (a0 * a0 + h * h); 681 682 // Compute final noise value at P 683 detail::tvec3<T> g; 684 g.x = a0.x * x0.x + h.x * x0.y; 685 //g.yz = a0.yz * x12.xz + h.yz * x12.yw; 686 g.y = a0.y * x12.x + h.y * x12.y; 687 g.z = a0.z * x12.z + h.z * x12.w; 688 return T(130) * dot(m, g); 689 } 690 691 template <typename T> 692 GLM_FUNC_QUALIFIER T simplex(detail::tvec3<T> const & v) 693 { 694 detail::tvec2<T> const C(1.0 / 6.0, 1.0 / 3.0); 695 detail::tvec4<T> const D(0.0, 0.5, 1.0, 2.0); 696 697 // First corner 698 detail::tvec3<T> i(floor(v + dot(v, detail::tvec3<T>(C.y)))); 699 detail::tvec3<T> x0(v - i + dot(i, detail::tvec3<T>(C.x))); 700 701 // Other corners 702 detail::tvec3<T> g(step(detail::tvec3<T>(x0.y, x0.z, x0.x), x0)); 703 detail::tvec3<T> l(T(1) - g); 704 detail::tvec3<T> i1(min(g, detail::tvec3<T>(l.z, l.x, l.y))); 705 detail::tvec3<T> i2(max(g, detail::tvec3<T>(l.z, l.x, l.y))); 706 707 // x0 = x0 - 0.0 + 0.0 * C.xxx; 708 // x1 = x0 - i1 + 1.0 * C.xxx; 709 // x2 = x0 - i2 + 2.0 * C.xxx; 710 // x3 = x0 - 1.0 + 3.0 * C.xxx; 711 detail::tvec3<T> x1(x0 - i1 + C.x); 712 detail::tvec3<T> x2(x0 - i2 + C.y); // 2.0*C.x = 1/3 = C.y 713 detail::tvec3<T> x3(x0 - D.y); // -1.0+3.0*C.x = -0.5 = -D.y 714 715 // Permutations 716 i = mod289(i); 717 detail::tvec4<T> p(permute(permute(permute( 718 i.z + detail::tvec4<T>(T(0), i1.z, i2.z, T(1))) + 719 i.y + detail::tvec4<T>(T(0), i1.y, i2.y, T(1))) + 720 i.x + detail::tvec4<T>(T(0), i1.x, i2.x, T(1)))); 721 722 // Gradients: 7x7 points over a square, mapped onto an octahedron. 723 // The ring size 17*17 = 289 is close to a multiple of 49 (49*6 = 294) 724 T n_ = T(0.142857142857); // 1.0/7.0 725 detail::tvec3<T> ns(n_ * detail::tvec3<T>(D.w, D.y, D.z) - detail::tvec3<T>(D.x, D.z, D.x)); 726 727 detail::tvec4<T> j(p - T(49) * floor(p * ns.z * ns.z)); // mod(p,7*7) 728 729 detail::tvec4<T> x_(floor(j * ns.z)); 730 detail::tvec4<T> y_(floor(j - T(7) * x_)); // mod(j,N) 731 732 detail::tvec4<T> x(x_ * ns.x + ns.y); 733 detail::tvec4<T> y(y_ * ns.x + ns.y); 734 detail::tvec4<T> h(T(1) - abs(x) - abs(y)); 735 736 detail::tvec4<T> b0(x.x, x.y, y.x, y.y); 737 detail::tvec4<T> b1(x.z, x.w, y.z, y.w); 738 739 // vec4 s0 = vec4(lessThan(b0,0.0))*2.0 - 1.0; 740 // vec4 s1 = vec4(lessThan(b1,0.0))*2.0 - 1.0; 741 detail::tvec4<T> s0(floor(b0) * T(2) + T(1)); 742 detail::tvec4<T> s1(floor(b1) * T(2) + T(1)); 743 detail::tvec4<T> sh(-step(h, detail::tvec4<T>(0.0))); 744 745 detail::tvec4<T> a0 = detail::tvec4<T>(b0.x, b0.z, b0.y, b0.w) + detail::tvec4<T>(s0.x, s0.z, s0.y, s0.w) * detail::tvec4<T>(sh.x, sh.x, sh.y, sh.y); 746 detail::tvec4<T> a1 = detail::tvec4<T>(b1.x, b1.z, b1.y, b1.w) + detail::tvec4<T>(s1.x, s1.z, s1.y, s1.w) * detail::tvec4<T>(sh.z, sh.z, sh.w, sh.w); 747 748 detail::tvec3<T> p0(a0.x, a0.y, h.x); 749 detail::tvec3<T> p1(a0.z, a0.w, h.y); 750 detail::tvec3<T> p2(a1.x, a1.y, h.z); 751 detail::tvec3<T> p3(a1.z, a1.w, h.w); 752 753 // Normalise gradients 754 detail::tvec4<T> norm = taylorInvSqrt(detail::tvec4<T>(dot(p0, p0), dot(p1, p1), dot(p2, p2), dot(p3, p3))); 755 p0 *= norm.x; 756 p1 *= norm.y; 757 p2 *= norm.z; 758 p3 *= norm.w; 759 760 // Mix final noise value 761 detail::tvec4<T> m = max(T(0.6) - detail::tvec4<T>(dot(x0, x0), dot(x1, x1), dot(x2, x2), dot(x3, x3)), T(0)); 762 m = m * m; 763 return T(42) * dot(m * m, detail::tvec4<T>(dot(p0, x0), dot(p1, x1), dot(p2, x2), dot(p3, x3))); 764 } 765 766 template <typename T> 767 GLM_FUNC_QUALIFIER T simplex(detail::tvec4<T> const & v) 768 { 769 detail::tvec4<T> const C( 770 0.138196601125011, // (5 - sqrt(5))/20 G4 771 0.276393202250021, // 2 * G4 772 0.414589803375032, // 3 * G4 773 -0.447213595499958); // -1 + 4 * G4 774 775 // (sqrt(5) - 1)/4 = F4, used once below 776 T const F4 = T(0.309016994374947451); 777 778 // First corner 779 detail::tvec4<T> i = floor(v + dot(v, vec4(F4))); 780 detail::tvec4<T> x0 = v - i + dot(i, vec4(C.x)); 781 782 // Other corners 783 784 // Rank sorting originally contributed by Bill Licea-Kane, AMD (formerly ATI) 785 detail::tvec4<T> i0; 786 detail::tvec3<T> isX = step(detail::tvec3<T>(x0.y, x0.z, x0.w), detail::tvec3<T>(x0.x)); 787 detail::tvec3<T> isYZ = step(detail::tvec3<T>(x0.z, x0.w, x0.w), detail::tvec3<T>(x0.y, x0.y, x0.z)); 788 // i0.x = dot(isX, vec3(1.0)); 789 //i0.x = isX.x + isX.y + isX.z; 790 //i0.yzw = T(1) - isX; 791 i0 = detail::tvec4<T>(isX.x + isX.y + isX.z, T(1) - isX); 792 // i0.y += dot(isYZ.xy, vec2(1.0)); 793 i0.y += isYZ.x + isYZ.y; 794 //i0.zw += 1.0 - detail::tvec2<T>(isYZ.x, isYZ.y); 795 i0.z += T(1) - isYZ.x; 796 i0.w += T(1) - isYZ.y; 797 i0.z += isYZ.z; 798 i0.w += T(1) - isYZ.z; 799 800 // i0 now contains the unique values 0,1,2,3 in each channel 801 detail::tvec4<T> i3 = clamp(i0, 0.0, 1.0); 802 detail::tvec4<T> i2 = clamp(i0 - 1.0, 0.0, 1.0); 803 detail::tvec4<T> i1 = clamp(i0 - 2.0, 0.0, 1.0); 804 805 // x0 = x0 - 0.0 + 0.0 * C.xxxx 806 // x1 = x0 - i1 + 0.0 * C.xxxx 807 // x2 = x0 - i2 + 0.0 * C.xxxx 808 // x3 = x0 - i3 + 0.0 * C.xxxx 809 // x4 = x0 - 1.0 + 4.0 * C.xxxx 810 detail::tvec4<T> x1 = x0 - i1 + C.x; 811 detail::tvec4<T> x2 = x0 - i2 + C.y; 812 detail::tvec4<T> x3 = x0 - i3 + C.z; 813 detail::tvec4<T> x4 = x0 + C.w; 814 815 // Permutations 816 i = mod(i, T(289)); 817 T j0 = permute(permute(permute(permute(i.w) + i.z) + i.y) + i.x); 818 detail::tvec4<T> j1 = permute(permute(permute(permute( 819 i.w + detail::tvec4<T>(i1.w, i2.w, i3.w, T(1))) 820 + i.z + detail::tvec4<T>(i1.z, i2.z, i3.z, T(1))) 821 + i.y + detail::tvec4<T>(i1.y, i2.y, i3.y, T(1))) 822 + i.x + detail::tvec4<T>(i1.x, i2.x, i3.x, T(1))); 823 824 // Gradients: 7x7x6 points over a cube, mapped onto a 4-cross polytope 825 // 7*7*6 = 294, which is close to the ring size 17*17 = 289. 826 detail::tvec4<T> ip = detail::tvec4<T>(T(1) / T(294), T(1) / T(49), T(1) / T(7), T(0)); 827 828 detail::tvec4<T> p0 = grad4(j0, ip); 829 detail::tvec4<T> p1 = grad4(j1.x, ip); 830 detail::tvec4<T> p2 = grad4(j1.y, ip); 831 detail::tvec4<T> p3 = grad4(j1.z, ip); 832 detail::tvec4<T> p4 = grad4(j1.w, ip); 833 834 // Normalise gradients 835 detail::tvec4<T> norm = taylorInvSqrt(detail::tvec4<T>(dot(p0, p0), dot(p1, p1), dot(p2, p2), dot(p3, p3))); 836 p0 *= norm.x; 837 p1 *= norm.y; 838 p2 *= norm.z; 839 p3 *= norm.w; 840 p4 *= taylorInvSqrt(dot(p4, p4)); 841 842 // Mix contributions from the five corners 843 detail::tvec3<T> m0 = max(T(0.6) - detail::tvec3<T>(dot(x0, x0), dot(x1, x1), dot(x2, x2)), T(0)); 844 detail::tvec2<T> m1 = max(T(0.6) - detail::tvec2<T>(dot(x3, x3), dot(x4, x4) ), T(0)); 845 m0 = m0 * m0; 846 m1 = m1 * m1; 847 return T(49) * 848 (dot(m0 * m0, detail::tvec3<T>(dot(p0, x0), dot(p1, x1), dot(p2, x2))) + 849 dot(m1 * m1, detail::tvec2<T>(dot(p3, x3), dot(p4, x4)))); 850 } 851}//namespace glm 852