1 /////////////////////////////////////////////////////////////////////////////////// 2 /// OpenGL Mathematics (glm.g-truc.net) 3 /// 4 /// Copyright (c) 2005 - 2014 G-Truc Creation (www.g-truc.net) 5 /// Permission is hereby granted, free of charge, to any person obtaining a copy 6 /// of this software and associated documentation files (the "Software"), to deal 7 /// in the Software without restriction, including without limitation the rights 8 /// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell 9 /// copies of the Software, and to permit persons to whom the Software is 10 /// furnished to do so, subject to the following conditions: 11 /// 12 /// The above copyright notice and this permission notice shall be included in 13 /// all copies or substantial portions of the Software. 14 /// 15 /// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR 16 /// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 17 /// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE 18 /// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER 19 /// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, 20 /// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN 21 /// THE SOFTWARE. 22 /// 23 /// @ref gtc_noise 24 /// @file glm/gtc/noise.inl 25 /// @date 2011-04-21 / 2012-04-07 26 /// @author Christophe Riccio 27 /////////////////////////////////////////////////////////////////////////////////// 28 // Based on the work of Stefan Gustavson and Ashima Arts on "webgl-noise": 29 // https://github.com/ashima/webgl-noise 30 // Following Stefan Gustavson's paper "Simplex noise demystified": 31 // http://www.itn.liu.se/~stegu/simplexnoise/simplexnoise.pdf 32 /////////////////////////////////////////////////////////////////////////////////// 33 34 #include "../geometric.hpp" 35 #include "../common.hpp" 36 #include "../vector_relational.hpp" 37 #include "../detail/_noise.hpp" 38 39 namespace glm{ 40 namespace gtc 41 { 42 template <typename T, precision P> 43 GLM_FUNC_QUALIFIER detail::tvec4<T, P> grad4(T const & j, detail::tvec4<T, P> const & ip) 44 { 45 detail::tvec3<T, P> pXYZ = floor(fract(detail::tvec3<T, P>(j) * detail::tvec3<T, P>(ip)) * T(7)) * ip[2] - T(1); 46 T pW = static_cast<T>(1.5) - dot(abs(pXYZ), detail::tvec3<T, P>(1)); 47 detail::tvec4<T, P> s = detail::tvec4<T, P>(lessThan(detail::tvec4<T, P>(pXYZ, pW), detail::tvec4<T, P>(0.0))); 48 pXYZ = pXYZ + (detail::tvec3<T, P>(s) * T(2) - T(1)) * s.w; 49 return detail::tvec4<T, P>(pXYZ, pW); 50 } 51 }//namespace gtc 52 53 // Classic Perlin noise 54 template <typename T, precision P> 55 GLM_FUNC_QUALIFIER T perlin(detail::tvec2<T, P> const & Position) 56 { 57 detail::tvec4<T, P> Pi = glm::floor(detail::tvec4<T, P>(Position.x, Position.y, Position.x, Position.y)) + detail::tvec4<T, P>(0.0, 0.0, 1.0, 1.0); 58 detail::tvec4<T, P> Pf = glm::fract(detail::tvec4<T, P>(Position.x, Position.y, Position.x, Position.y)) - detail::tvec4<T, P>(0.0, 0.0, 1.0, 1.0); 59 Pi = mod(Pi, detail::tvec4<T, P>(289)); // To avoid truncation effects in permutation 60 detail::tvec4<T, P> ix(Pi.x, Pi.z, Pi.x, Pi.z); 61 detail::tvec4<T, P> iy(Pi.y, Pi.y, Pi.w, Pi.w); 62 detail::tvec4<T, P> fx(Pf.x, Pf.z, Pf.x, Pf.z); 63 detail::tvec4<T, P> fy(Pf.y, Pf.y, Pf.w, Pf.w); 64 65 detail::tvec4<T, P> i = detail::permute(detail::permute(ix) + iy); 66 67 detail::tvec4<T, P> gx = static_cast<T>(2) * glm::fract(i / T(41)) - T(1); 68 detail::tvec4<T, P> gy = glm::abs(gx) - T(0.5); 69 detail::tvec4<T, P> tx = glm::floor(gx + T(0.5)); 70 gx = gx - tx; 71 72 detail::tvec2<T, P> g00(gx.x, gy.x); 73 detail::tvec2<T, P> g10(gx.y, gy.y); 74 detail::tvec2<T, P> g01(gx.z, gy.z); 75 detail::tvec2<T, P> g11(gx.w, gy.w); 76 77 detail::tvec4<T, P> norm = taylorInvSqrt(detail::tvec4<T, P>(dot(g00, g00), dot(g01, g01), dot(g10, g10), dot(g11, g11))); 78 g00 *= norm.x; 79 g01 *= norm.y; 80 g10 *= norm.z; 81 g11 *= norm.w; 82 83 T n00 = dot(g00, detail::tvec2<T, P>(fx.x, fy.x)); 84 T n10 = dot(g10, detail::tvec2<T, P>(fx.y, fy.y)); 85 T n01 = dot(g01, detail::tvec2<T, P>(fx.z, fy.z)); 86 T n11 = dot(g11, detail::tvec2<T, P>(fx.w, fy.w)); 87 88 detail::tvec2<T, P> fade_xy = fade(detail::tvec2<T, P>(Pf.x, Pf.y)); 89 detail::tvec2<T, P> n_x = mix(detail::tvec2<T, P>(n00, n01), detail::tvec2<T, P>(n10, n11), fade_xy.x); 90 T n_xy = mix(n_x.x, n_x.y, fade_xy.y); 91 return T(2.3) * n_xy; 92 } 93 94 // Classic Perlin noise 95 template <typename T, precision P> 96 GLM_FUNC_QUALIFIER T perlin(detail::tvec3<T, P> const & Position) 97 { 98 detail::tvec3<T, P> Pi0 = floor(Position); // Integer part for indexing 99 detail::tvec3<T, P> Pi1 = Pi0 + T(1); // Integer part + 1 100 Pi0 = mod289(Pi0); 101 Pi1 = mod289(Pi1); 102 detail::tvec3<T, P> Pf0 = fract(Position); // Fractional part for interpolation 103 detail::tvec3<T, P> Pf1 = Pf0 - T(1); // Fractional part - 1.0 104 detail::tvec4<T, P> ix(Pi0.x, Pi1.x, Pi0.x, Pi1.x); 105 detail::tvec4<T, P> iy = detail::tvec4<T, P>(detail::tvec2<T, P>(Pi0.y), detail::tvec2<T, P>(Pi1.y)); 106 detail::tvec4<T, P> iz0(Pi0.z); 107 detail::tvec4<T, P> iz1(Pi1.z); 108 109 detail::tvec4<T, P> ixy = detail::permute(detail::permute(ix) + iy); 110 detail::tvec4<T, P> ixy0 = detail::permute(ixy + iz0); 111 detail::tvec4<T, P> ixy1 = detail::permute(ixy + iz1); 112 113 detail::tvec4<T, P> gx0 = ixy0 * T(1.0 / 7.0); 114 detail::tvec4<T, P> gy0 = fract(floor(gx0) * T(1.0 / 7.0)) - T(0.5); 115 gx0 = fract(gx0); 116 detail::tvec4<T, P> gz0 = detail::tvec4<T, P>(0.5) - abs(gx0) - abs(gy0); 117 detail::tvec4<T, P> sz0 = step(gz0, detail::tvec4<T, P>(0.0)); 118 gx0 -= sz0 * (step(T(0), gx0) - T(0.5)); 119 gy0 -= sz0 * (step(T(0), gy0) - T(0.5)); 120 121 detail::tvec4<T, P> gx1 = ixy1 * T(1.0 / 7.0); 122 detail::tvec4<T, P> gy1 = fract(floor(gx1) * T(1.0 / 7.0)) - T(0.5); 123 gx1 = fract(gx1); 124 detail::tvec4<T, P> gz1 = detail::tvec4<T, P>(0.5) - abs(gx1) - abs(gy1); 125 detail::tvec4<T, P> sz1 = step(gz1, detail::tvec4<T, P>(0.0)); 126 gx1 -= sz1 * (step(T(0), gx1) - T(0.5)); 127 gy1 -= sz1 * (step(T(0), gy1) - T(0.5)); 128 129 detail::tvec3<T, P> g000(gx0.x, gy0.x, gz0.x); 130 detail::tvec3<T, P> g100(gx0.y, gy0.y, gz0.y); 131 detail::tvec3<T, P> g010(gx0.z, gy0.z, gz0.z); 132 detail::tvec3<T, P> g110(gx0.w, gy0.w, gz0.w); 133 detail::tvec3<T, P> g001(gx1.x, gy1.x, gz1.x); 134 detail::tvec3<T, P> g101(gx1.y, gy1.y, gz1.y); 135 detail::tvec3<T, P> g011(gx1.z, gy1.z, gz1.z); 136 detail::tvec3<T, P> g111(gx1.w, gy1.w, gz1.w); 137 138 detail::tvec4<T, P> norm0 = detail::taylorInvSqrt(detail::tvec4<T, P>(dot(g000, g000), dot(g010, g010), dot(g100, g100), dot(g110, g110))); 139 g000 *= norm0.x; 140 g010 *= norm0.y; 141 g100 *= norm0.z; 142 g110 *= norm0.w; 143 detail::tvec4<T, P> norm1 = detail::taylorInvSqrt(detail::tvec4<T, P>(dot(g001, g001), dot(g011, g011), dot(g101, g101), dot(g111, g111))); 144 g001 *= norm1.x; 145 g011 *= norm1.y; 146 g101 *= norm1.z; 147 g111 *= norm1.w; 148 149 T n000 = dot(g000, Pf0); 150 T n100 = dot(g100, detail::tvec3<T, P>(Pf1.x, Pf0.y, Pf0.z)); 151 T n010 = dot(g010, detail::tvec3<T, P>(Pf0.x, Pf1.y, Pf0.z)); 152 T n110 = dot(g110, detail::tvec3<T, P>(Pf1.x, Pf1.y, Pf0.z)); 153 T n001 = dot(g001, detail::tvec3<T, P>(Pf0.x, Pf0.y, Pf1.z)); 154 T n101 = dot(g101, detail::tvec3<T, P>(Pf1.x, Pf0.y, Pf1.z)); 155 T n011 = dot(g011, detail::tvec3<T, P>(Pf0.x, Pf1.y, Pf1.z)); 156 T n111 = dot(g111, Pf1); 157 158 detail::tvec3<T, P> fade_xyz = fade(Pf0); 159 detail::tvec4<T, P> n_z = mix(detail::tvec4<T, P>(n000, n100, n010, n110), detail::tvec4<T, P>(n001, n101, n011, n111), fade_xyz.z); 160 detail::tvec2<T, P> n_yz = mix(detail::tvec2<T, P>(n_z.x, n_z.y), detail::tvec2<T, P>(n_z.z, n_z.w), fade_xyz.y); 161 T n_xyz = mix(n_yz.x, n_yz.y, fade_xyz.x); 162 return T(2.2) * n_xyz; 163 } 164 /* 165 // Classic Perlin noise 166 template <typename T, precision P> 167 GLM_FUNC_QUALIFIER T perlin(detail::tvec3<T, P> const & P) 168 { 169 detail::tvec3<T, P> Pi0 = floor(P); // Integer part for indexing 170 detail::tvec3<T, P> Pi1 = Pi0 + T(1); // Integer part + 1 171 Pi0 = mod(Pi0, T(289)); 172 Pi1 = mod(Pi1, T(289)); 173 detail::tvec3<T, P> Pf0 = fract(P); // Fractional part for interpolation 174 detail::tvec3<T, P> Pf1 = Pf0 - T(1); // Fractional part - 1.0 175 detail::tvec4<T, P> ix(Pi0.x, Pi1.x, Pi0.x, Pi1.x); 176 detail::tvec4<T, P> iy(Pi0.y, Pi0.y, Pi1.y, Pi1.y); 177 detail::tvec4<T, P> iz0(Pi0.z); 178 detail::tvec4<T, P> iz1(Pi1.z); 179 180 detail::tvec4<T, P> ixy = permute(permute(ix) + iy); 181 detail::tvec4<T, P> ixy0 = permute(ixy + iz0); 182 detail::tvec4<T, P> ixy1 = permute(ixy + iz1); 183 184 detail::tvec4<T, P> gx0 = ixy0 / T(7); 185 detail::tvec4<T, P> gy0 = fract(floor(gx0) / T(7)) - T(0.5); 186 gx0 = fract(gx0); 187 detail::tvec4<T, P> gz0 = detail::tvec4<T, P>(0.5) - abs(gx0) - abs(gy0); 188 detail::tvec4<T, P> sz0 = step(gz0, detail::tvec4<T, P>(0.0)); 189 gx0 -= sz0 * (step(0.0, gx0) - T(0.5)); 190 gy0 -= sz0 * (step(0.0, gy0) - T(0.5)); 191 192 detail::tvec4<T, P> gx1 = ixy1 / T(7); 193 detail::tvec4<T, P> gy1 = fract(floor(gx1) / T(7)) - T(0.5); 194 gx1 = fract(gx1); 195 detail::tvec4<T, P> gz1 = detail::tvec4<T, P>(0.5) - abs(gx1) - abs(gy1); 196 detail::tvec4<T, P> sz1 = step(gz1, detail::tvec4<T, P>(0.0)); 197 gx1 -= sz1 * (step(T(0), gx1) - T(0.5)); 198 gy1 -= sz1 * (step(T(0), gy1) - T(0.5)); 199 200 detail::tvec3<T, P> g000(gx0.x, gy0.x, gz0.x); 201 detail::tvec3<T, P> g100(gx0.y, gy0.y, gz0.y); 202 detail::tvec3<T, P> g010(gx0.z, gy0.z, gz0.z); 203 detail::tvec3<T, P> g110(gx0.w, gy0.w, gz0.w); 204 detail::tvec3<T, P> g001(gx1.x, gy1.x, gz1.x); 205 detail::tvec3<T, P> g101(gx1.y, gy1.y, gz1.y); 206 detail::tvec3<T, P> g011(gx1.z, gy1.z, gz1.z); 207 detail::tvec3<T, P> g111(gx1.w, gy1.w, gz1.w); 208 209 detail::tvec4<T, P> norm0 = taylorInvSqrt(detail::tvec4<T, P>(dot(g000, g000), dot(g010, g010), dot(g100, g100), dot(g110, g110))); 210 g000 *= norm0.x; 211 g010 *= norm0.y; 212 g100 *= norm0.z; 213 g110 *= norm0.w; 214 detail::tvec4<T, P> norm1 = taylorInvSqrt(detail::tvec4<T, P>(dot(g001, g001), dot(g011, g011), dot(g101, g101), dot(g111, g111))); 215 g001 *= norm1.x; 216 g011 *= norm1.y; 217 g101 *= norm1.z; 218 g111 *= norm1.w; 219 220 T n000 = dot(g000, Pf0); 221 T n100 = dot(g100, detail::tvec3<T, P>(Pf1.x, Pf0.y, Pf0.z)); 222 T n010 = dot(g010, detail::tvec3<T, P>(Pf0.x, Pf1.y, Pf0.z)); 223 T n110 = dot(g110, detail::tvec3<T, P>(Pf1.x, Pf1.y, Pf0.z)); 224 T n001 = dot(g001, detail::tvec3<T, P>(Pf0.x, Pf0.y, Pf1.z)); 225 T n101 = dot(g101, detail::tvec3<T, P>(Pf1.x, Pf0.y, Pf1.z)); 226 T n011 = dot(g011, detail::tvec3<T, P>(Pf0.x, Pf1.y, Pf1.z)); 227 T n111 = dot(g111, Pf1); 228 229 detail::tvec3<T, P> fade_xyz = fade(Pf0); 230 detail::tvec4<T, P> n_z = mix(detail::tvec4<T, P>(n000, n100, n010, n110), detail::tvec4<T, P>(n001, n101, n011, n111), fade_xyz.z); 231 detail::tvec2<T, P> n_yz = mix( 232 detail::tvec2<T, P>(n_z.x, n_z.y), 233 detail::tvec2<T, P>(n_z.z, n_z.w), fade_xyz.y); 234 T n_xyz = mix(n_yz.x, n_yz.y, fade_xyz.x); 235 return T(2.2) * n_xyz; 236 } 237 */ 238 // Classic Perlin noise 239 template <typename T, precision P> 240 GLM_FUNC_QUALIFIER T perlin(detail::tvec4<T, P> const & Position) 241 { 242 detail::tvec4<T, P> Pi0 = floor(Position); // Integer part for indexing 243 detail::tvec4<T, P> Pi1 = Pi0 + T(1); // Integer part + 1 244 Pi0 = mod(Pi0, detail::tvec4<T, P>(289)); 245 Pi1 = mod(Pi1, detail::tvec4<T, P>(289)); 246 detail::tvec4<T, P> Pf0 = fract(Position); // Fractional part for interpolation 247 detail::tvec4<T, P> Pf1 = Pf0 - T(1); // Fractional part - 1.0 248 detail::tvec4<T, P> ix(Pi0.x, Pi1.x, Pi0.x, Pi1.x); 249 detail::tvec4<T, P> iy(Pi0.y, Pi0.y, Pi1.y, Pi1.y); 250 detail::tvec4<T, P> iz0(Pi0.z); 251 detail::tvec4<T, P> iz1(Pi1.z); 252 detail::tvec4<T, P> iw0(Pi0.w); 253 detail::tvec4<T, P> iw1(Pi1.w); 254 255 detail::tvec4<T, P> ixy = detail::permute(detail::permute(ix) + iy); 256 detail::tvec4<T, P> ixy0 = detail::permute(ixy + iz0); 257 detail::tvec4<T, P> ixy1 = detail::permute(ixy + iz1); 258 detail::tvec4<T, P> ixy00 = detail::permute(ixy0 + iw0); 259 detail::tvec4<T, P> ixy01 = detail::permute(ixy0 + iw1); 260 detail::tvec4<T, P> ixy10 = detail::permute(ixy1 + iw0); 261 detail::tvec4<T, P> ixy11 = detail::permute(ixy1 + iw1); 262 263 detail::tvec4<T, P> gx00 = ixy00 / T(7); 264 detail::tvec4<T, P> gy00 = floor(gx00) / T(7); 265 detail::tvec4<T, P> gz00 = floor(gy00) / T(6); 266 gx00 = fract(gx00) - T(0.5); 267 gy00 = fract(gy00) - T(0.5); 268 gz00 = fract(gz00) - T(0.5); 269 detail::tvec4<T, P> gw00 = detail::tvec4<T, P>(0.75) - abs(gx00) - abs(gy00) - abs(gz00); 270 detail::tvec4<T, P> sw00 = step(gw00, detail::tvec4<T, P>(0.0)); 271 gx00 -= sw00 * (step(T(0), gx00) - T(0.5)); 272 gy00 -= sw00 * (step(T(0), gy00) - T(0.5)); 273 274 detail::tvec4<T, P> gx01 = ixy01 / T(7); 275 detail::tvec4<T, P> gy01 = floor(gx01) / T(7); 276 detail::tvec4<T, P> gz01 = floor(gy01) / T(6); 277 gx01 = fract(gx01) - T(0.5); 278 gy01 = fract(gy01) - T(0.5); 279 gz01 = fract(gz01) - T(0.5); 280 detail::tvec4<T, P> gw01 = detail::tvec4<T, P>(0.75) - abs(gx01) - abs(gy01) - abs(gz01); 281 detail::tvec4<T, P> sw01 = step(gw01, detail::tvec4<T, P>(0.0)); 282 gx01 -= sw01 * (step(T(0), gx01) - T(0.5)); 283 gy01 -= sw01 * (step(T(0), gy01) - T(0.5)); 284 285 detail::tvec4<T, P> gx10 = ixy10 / T(7); 286 detail::tvec4<T, P> gy10 = floor(gx10) / T(7); 287 detail::tvec4<T, P> gz10 = floor(gy10) / T(6); 288 gx10 = fract(gx10) - T(0.5); 289 gy10 = fract(gy10) - T(0.5); 290 gz10 = fract(gz10) - T(0.5); 291 detail::tvec4<T, P> gw10 = detail::tvec4<T, P>(0.75) - abs(gx10) - abs(gy10) - abs(gz10); 292 detail::tvec4<T, P> sw10 = step(gw10, detail::tvec4<T, P>(0)); 293 gx10 -= sw10 * (step(T(0), gx10) - T(0.5)); 294 gy10 -= sw10 * (step(T(0), gy10) - T(0.5)); 295 296 detail::tvec4<T, P> gx11 = ixy11 / T(7); 297 detail::tvec4<T, P> gy11 = floor(gx11) / T(7); 298 detail::tvec4<T, P> gz11 = floor(gy11) / T(6); 299 gx11 = fract(gx11) - T(0.5); 300 gy11 = fract(gy11) - T(0.5); 301 gz11 = fract(gz11) - T(0.5); 302 detail::tvec4<T, P> gw11 = detail::tvec4<T, P>(0.75) - abs(gx11) - abs(gy11) - abs(gz11); 303 detail::tvec4<T, P> sw11 = step(gw11, detail::tvec4<T, P>(0.0)); 304 gx11 -= sw11 * (step(T(0), gx11) - T(0.5)); 305 gy11 -= sw11 * (step(T(0), gy11) - T(0.5)); 306 307 detail::tvec4<T, P> g0000(gx00.x, gy00.x, gz00.x, gw00.x); 308 detail::tvec4<T, P> g1000(gx00.y, gy00.y, gz00.y, gw00.y); 309 detail::tvec4<T, P> g0100(gx00.z, gy00.z, gz00.z, gw00.z); 310 detail::tvec4<T, P> g1100(gx00.w, gy00.w, gz00.w, gw00.w); 311 detail::tvec4<T, P> g0010(gx10.x, gy10.x, gz10.x, gw10.x); 312 detail::tvec4<T, P> g1010(gx10.y, gy10.y, gz10.y, gw10.y); 313 detail::tvec4<T, P> g0110(gx10.z, gy10.z, gz10.z, gw10.z); 314 detail::tvec4<T, P> g1110(gx10.w, gy10.w, gz10.w, gw10.w); 315 detail::tvec4<T, P> g0001(gx01.x, gy01.x, gz01.x, gw01.x); 316 detail::tvec4<T, P> g1001(gx01.y, gy01.y, gz01.y, gw01.y); 317 detail::tvec4<T, P> g0101(gx01.z, gy01.z, gz01.z, gw01.z); 318 detail::tvec4<T, P> g1101(gx01.w, gy01.w, gz01.w, gw01.w); 319 detail::tvec4<T, P> g0011(gx11.x, gy11.x, gz11.x, gw11.x); 320 detail::tvec4<T, P> g1011(gx11.y, gy11.y, gz11.y, gw11.y); 321 detail::tvec4<T, P> g0111(gx11.z, gy11.z, gz11.z, gw11.z); 322 detail::tvec4<T, P> g1111(gx11.w, gy11.w, gz11.w, gw11.w); 323 324 detail::tvec4<T, P> norm00 = detail::taylorInvSqrt(detail::tvec4<T, P>(dot(g0000, g0000), dot(g0100, g0100), dot(g1000, g1000), dot(g1100, g1100))); 325 g0000 *= norm00.x; 326 g0100 *= norm00.y; 327 g1000 *= norm00.z; 328 g1100 *= norm00.w; 329 330 detail::tvec4<T, P> norm01 = detail::taylorInvSqrt(detail::tvec4<T, P>(dot(g0001, g0001), dot(g0101, g0101), dot(g1001, g1001), dot(g1101, g1101))); 331 g0001 *= norm01.x; 332 g0101 *= norm01.y; 333 g1001 *= norm01.z; 334 g1101 *= norm01.w; 335 336 detail::tvec4<T, P> norm10 = detail::taylorInvSqrt(detail::tvec4<T, P>(dot(g0010, g0010), dot(g0110, g0110), dot(g1010, g1010), dot(g1110, g1110))); 337 g0010 *= norm10.x; 338 g0110 *= norm10.y; 339 g1010 *= norm10.z; 340 g1110 *= norm10.w; 341 342 detail::tvec4<T, P> norm11 = detail::taylorInvSqrt(detail::tvec4<T, P>(dot(g0011, g0011), dot(g0111, g0111), dot(g1011, g1011), dot(g1111, g1111))); 343 g0011 *= norm11.x; 344 g0111 *= norm11.y; 345 g1011 *= norm11.z; 346 g1111 *= norm11.w; 347 348 T n0000 = dot(g0000, Pf0); 349 T n1000 = dot(g1000, detail::tvec4<T, P>(Pf1.x, Pf0.y, Pf0.z, Pf0.w)); 350 T n0100 = dot(g0100, detail::tvec4<T, P>(Pf0.x, Pf1.y, Pf0.z, Pf0.w)); 351 T n1100 = dot(g1100, detail::tvec4<T, P>(Pf1.x, Pf1.y, Pf0.z, Pf0.w)); 352 T n0010 = dot(g0010, detail::tvec4<T, P>(Pf0.x, Pf0.y, Pf1.z, Pf0.w)); 353 T n1010 = dot(g1010, detail::tvec4<T, P>(Pf1.x, Pf0.y, Pf1.z, Pf0.w)); 354 T n0110 = dot(g0110, detail::tvec4<T, P>(Pf0.x, Pf1.y, Pf1.z, Pf0.w)); 355 T n1110 = dot(g1110, detail::tvec4<T, P>(Pf1.x, Pf1.y, Pf1.z, Pf0.w)); 356 T n0001 = dot(g0001, detail::tvec4<T, P>(Pf0.x, Pf0.y, Pf0.z, Pf1.w)); 357 T n1001 = dot(g1001, detail::tvec4<T, P>(Pf1.x, Pf0.y, Pf0.z, Pf1.w)); 358 T n0101 = dot(g0101, detail::tvec4<T, P>(Pf0.x, Pf1.y, Pf0.z, Pf1.w)); 359 T n1101 = dot(g1101, detail::tvec4<T, P>(Pf1.x, Pf1.y, Pf0.z, Pf1.w)); 360 T n0011 = dot(g0011, detail::tvec4<T, P>(Pf0.x, Pf0.y, Pf1.z, Pf1.w)); 361 T n1011 = dot(g1011, detail::tvec4<T, P>(Pf1.x, Pf0.y, Pf1.z, Pf1.w)); 362 T n0111 = dot(g0111, detail::tvec4<T, P>(Pf0.x, Pf1.y, Pf1.z, Pf1.w)); 363 T n1111 = dot(g1111, Pf1); 364 365 detail::tvec4<T, P> fade_xyzw = fade(Pf0); 366 detail::tvec4<T, P> n_0w = mix(detail::tvec4<T, P>(n0000, n1000, n0100, n1100), detail::tvec4<T, P>(n0001, n1001, n0101, n1101), fade_xyzw.w); 367 detail::tvec4<T, P> n_1w = mix(detail::tvec4<T, P>(n0010, n1010, n0110, n1110), detail::tvec4<T, P>(n0011, n1011, n0111, n1111), fade_xyzw.w); 368 detail::tvec4<T, P> n_zw = mix(n_0w, n_1w, fade_xyzw.z); 369 detail::tvec2<T, P> n_yzw = mix(detail::tvec2<T, P>(n_zw.x, n_zw.y), detail::tvec2<T, P>(n_zw.z, n_zw.w), fade_xyzw.y); 370 T n_xyzw = mix(n_yzw.x, n_yzw.y, fade_xyzw.x); 371 return T(2.2) * n_xyzw; 372 } 373 374 // Classic Perlin noise, periodic variant 375 template <typename T, precision P> 376 GLM_FUNC_QUALIFIER T perlin(detail::tvec2<T, P> const & Position, detail::tvec2<T, P> const & rep) 377 { 378 detail::tvec4<T, P> Pi = floor(detail::tvec4<T, P>(Position.x, Position.y, Position.x, Position.y)) + detail::tvec4<T, P>(0.0, 0.0, 1.0, 1.0); 379 detail::tvec4<T, P> Pf = fract(detail::tvec4<T, P>(Position.x, Position.y, Position.x, Position.y)) - detail::tvec4<T, P>(0.0, 0.0, 1.0, 1.0); 380 Pi = mod(Pi, detail::tvec4<T, P>(rep.x, rep.y, rep.x, rep.y)); // To create noise with explicit period 381 Pi = mod(Pi, detail::tvec4<T, P>(289)); // To avoid truncation effects in permutation 382 detail::tvec4<T, P> ix(Pi.x, Pi.z, Pi.x, Pi.z); 383 detail::tvec4<T, P> iy(Pi.y, Pi.y, Pi.w, Pi.w); 384 detail::tvec4<T, P> fx(Pf.x, Pf.z, Pf.x, Pf.z); 385 detail::tvec4<T, P> fy(Pf.y, Pf.y, Pf.w, Pf.w); 386 387 detail::tvec4<T, P> i = detail::permute(detail::permute(ix) + iy); 388 389 detail::tvec4<T, P> gx = static_cast<T>(2) * fract(i / T(41)) - T(1); 390 detail::tvec4<T, P> gy = abs(gx) - T(0.5); 391 detail::tvec4<T, P> tx = floor(gx + T(0.5)); 392 gx = gx - tx; 393 394 detail::tvec2<T, P> g00(gx.x, gy.x); 395 detail::tvec2<T, P> g10(gx.y, gy.y); 396 detail::tvec2<T, P> g01(gx.z, gy.z); 397 detail::tvec2<T, P> g11(gx.w, gy.w); 398 399 detail::tvec4<T, P> norm = detail::taylorInvSqrt(detail::tvec4<T, P>(dot(g00, g00), dot(g01, g01), dot(g10, g10), dot(g11, g11))); 400 g00 *= norm.x; 401 g01 *= norm.y; 402 g10 *= norm.z; 403 g11 *= norm.w; 404 405 T n00 = dot(g00, detail::tvec2<T, P>(fx.x, fy.x)); 406 T n10 = dot(g10, detail::tvec2<T, P>(fx.y, fy.y)); 407 T n01 = dot(g01, detail::tvec2<T, P>(fx.z, fy.z)); 408 T n11 = dot(g11, detail::tvec2<T, P>(fx.w, fy.w)); 409 410 detail::tvec2<T, P> fade_xy = fade(detail::tvec2<T, P>(Pf.x, Pf.y)); 411 detail::tvec2<T, P> n_x = mix(detail::tvec2<T, P>(n00, n01), detail::tvec2<T, P>(n10, n11), fade_xy.x); 412 T n_xy = mix(n_x.x, n_x.y, fade_xy.y); 413 return T(2.3) * n_xy; 414 } 415 416 // Classic Perlin noise, periodic variant 417 template <typename T, precision P> 418 GLM_FUNC_QUALIFIER T perlin(detail::tvec3<T, P> const & Position, detail::tvec3<T, P> const & rep) 419 { 420 detail::tvec3<T, P> Pi0 = mod(floor(Position), rep); // Integer part, modulo period 421 detail::tvec3<T, P> Pi1 = mod(Pi0 + detail::tvec3<T, P>(T(1)), rep); // Integer part + 1, mod period 422 Pi0 = mod(Pi0, detail::tvec3<T, P>(289)); 423 Pi1 = mod(Pi1, detail::tvec3<T, P>(289)); 424 detail::tvec3<T, P> Pf0 = fract(Position); // Fractional part for interpolation 425 detail::tvec3<T, P> Pf1 = Pf0 - detail::tvec3<T, P>(T(1)); // Fractional part - 1.0 426 detail::tvec4<T, P> ix = detail::tvec4<T, P>(Pi0.x, Pi1.x, Pi0.x, Pi1.x); 427 detail::tvec4<T, P> iy = detail::tvec4<T, P>(Pi0.y, Pi0.y, Pi1.y, Pi1.y); 428 detail::tvec4<T, P> iz0(Pi0.z); 429 detail::tvec4<T, P> iz1(Pi1.z); 430 431 detail::tvec4<T, P> ixy = detail::permute(detail::permute(ix) + iy); 432 detail::tvec4<T, P> ixy0 = detail::permute(ixy + iz0); 433 detail::tvec4<T, P> ixy1 = detail::permute(ixy + iz1); 434 435 detail::tvec4<T, P> gx0 = ixy0 / T(7); 436 detail::tvec4<T, P> gy0 = fract(floor(gx0) / T(7)) - T(0.5); 437 gx0 = fract(gx0); 438 detail::tvec4<T, P> gz0 = detail::tvec4<T, P>(0.5) - abs(gx0) - abs(gy0); 439 detail::tvec4<T, P> sz0 = step(gz0, detail::tvec4<T, P>(0)); 440 gx0 -= sz0 * (step(T(0), gx0) - T(0.5)); 441 gy0 -= sz0 * (step(T(0), gy0) - T(0.5)); 442 443 detail::tvec4<T, P> gx1 = ixy1 / T(7); 444 detail::tvec4<T, P> gy1 = fract(floor(gx1) / T(7)) - T(0.5); 445 gx1 = fract(gx1); 446 detail::tvec4<T, P> gz1 = detail::tvec4<T, P>(0.5) - abs(gx1) - abs(gy1); 447 detail::tvec4<T, P> sz1 = step(gz1, detail::tvec4<T, P>(T(0))); 448 gx1 -= sz1 * (step(T(0), gx1) - T(0.5)); 449 gy1 -= sz1 * (step(T(0), gy1) - T(0.5)); 450 451 detail::tvec3<T, P> g000 = detail::tvec3<T, P>(gx0.x, gy0.x, gz0.x); 452 detail::tvec3<T, P> g100 = detail::tvec3<T, P>(gx0.y, gy0.y, gz0.y); 453 detail::tvec3<T, P> g010 = detail::tvec3<T, P>(gx0.z, gy0.z, gz0.z); 454 detail::tvec3<T, P> g110 = detail::tvec3<T, P>(gx0.w, gy0.w, gz0.w); 455 detail::tvec3<T, P> g001 = detail::tvec3<T, P>(gx1.x, gy1.x, gz1.x); 456 detail::tvec3<T, P> g101 = detail::tvec3<T, P>(gx1.y, gy1.y, gz1.y); 457 detail::tvec3<T, P> g011 = detail::tvec3<T, P>(gx1.z, gy1.z, gz1.z); 458 detail::tvec3<T, P> g111 = detail::tvec3<T, P>(gx1.w, gy1.w, gz1.w); 459 460 detail::tvec4<T, P> norm0 = detail::taylorInvSqrt(detail::tvec4<T, P>(dot(g000, g000), dot(g010, g010), dot(g100, g100), dot(g110, g110))); 461 g000 *= norm0.x; 462 g010 *= norm0.y; 463 g100 *= norm0.z; 464 g110 *= norm0.w; 465 detail::tvec4<T, P> norm1 = detail::taylorInvSqrt(detail::tvec4<T, P>(dot(g001, g001), dot(g011, g011), dot(g101, g101), dot(g111, g111))); 466 g001 *= norm1.x; 467 g011 *= norm1.y; 468 g101 *= norm1.z; 469 g111 *= norm1.w; 470 471 T n000 = dot(g000, Pf0); 472 T n100 = dot(g100, detail::tvec3<T, P>(Pf1.x, Pf0.y, Pf0.z)); 473 T n010 = dot(g010, detail::tvec3<T, P>(Pf0.x, Pf1.y, Pf0.z)); 474 T n110 = dot(g110, detail::tvec3<T, P>(Pf1.x, Pf1.y, Pf0.z)); 475 T n001 = dot(g001, detail::tvec3<T, P>(Pf0.x, Pf0.y, Pf1.z)); 476 T n101 = dot(g101, detail::tvec3<T, P>(Pf1.x, Pf0.y, Pf1.z)); 477 T n011 = dot(g011, detail::tvec3<T, P>(Pf0.x, Pf1.y, Pf1.z)); 478 T n111 = dot(g111, Pf1); 479 480 detail::tvec3<T, P> fade_xyz = fade(Pf0); 481 detail::tvec4<T, P> n_z = mix(detail::tvec4<T, P>(n000, n100, n010, n110), detail::tvec4<T, P>(n001, n101, n011, n111), fade_xyz.z); 482 detail::tvec2<T, P> n_yz = mix(detail::tvec2<T, P>(n_z.x, n_z.y), detail::tvec2<T, P>(n_z.z, n_z.w), fade_xyz.y); 483 T n_xyz = mix(n_yz.x, n_yz.y, fade_xyz.x); 484 return T(2.2) * n_xyz; 485 } 486 487 // Classic Perlin noise, periodic version 488 template <typename T, precision P> 489 GLM_FUNC_QUALIFIER T perlin(detail::tvec4<T, P> const & Position, detail::tvec4<T, P> const & rep) 490 { 491 detail::tvec4<T, P> Pi0 = mod(floor(Position), rep); // Integer part modulo rep 492 detail::tvec4<T, P> Pi1 = mod(Pi0 + T(1), rep); // Integer part + 1 mod rep 493 detail::tvec4<T, P> Pf0 = fract(Position); // Fractional part for interpolation 494 detail::tvec4<T, P> Pf1 = Pf0 - T(1); // Fractional part - 1.0 495 detail::tvec4<T, P> ix = detail::tvec4<T, P>(Pi0.x, Pi1.x, Pi0.x, Pi1.x); 496 detail::tvec4<T, P> iy = detail::tvec4<T, P>(Pi0.y, Pi0.y, Pi1.y, Pi1.y); 497 detail::tvec4<T, P> iz0(Pi0.z); 498 detail::tvec4<T, P> iz1(Pi1.z); 499 detail::tvec4<T, P> iw0(Pi0.w); 500 detail::tvec4<T, P> iw1(Pi1.w); 501 502 detail::tvec4<T, P> ixy = detail::permute(detail::permute(ix) + iy); 503 detail::tvec4<T, P> ixy0 = detail::permute(ixy + iz0); 504 detail::tvec4<T, P> ixy1 = detail::permute(ixy + iz1); 505 detail::tvec4<T, P> ixy00 = detail::permute(ixy0 + iw0); 506 detail::tvec4<T, P> ixy01 = detail::permute(ixy0 + iw1); 507 detail::tvec4<T, P> ixy10 = detail::permute(ixy1 + iw0); 508 detail::tvec4<T, P> ixy11 = detail::permute(ixy1 + iw1); 509 510 detail::tvec4<T, P> gx00 = ixy00 / T(7); 511 detail::tvec4<T, P> gy00 = floor(gx00) / T(7); 512 detail::tvec4<T, P> gz00 = floor(gy00) / T(6); 513 gx00 = fract(gx00) - T(0.5); 514 gy00 = fract(gy00) - T(0.5); 515 gz00 = fract(gz00) - T(0.5); 516 detail::tvec4<T, P> gw00 = detail::tvec4<T, P>(0.75) - abs(gx00) - abs(gy00) - abs(gz00); 517 detail::tvec4<T, P> sw00 = step(gw00, detail::tvec4<T, P>(0)); 518 gx00 -= sw00 * (step(T(0), gx00) - T(0.5)); 519 gy00 -= sw00 * (step(T(0), gy00) - T(0.5)); 520 521 detail::tvec4<T, P> gx01 = ixy01 / T(7); 522 detail::tvec4<T, P> gy01 = floor(gx01) / T(7); 523 detail::tvec4<T, P> gz01 = floor(gy01) / T(6); 524 gx01 = fract(gx01) - T(0.5); 525 gy01 = fract(gy01) - T(0.5); 526 gz01 = fract(gz01) - T(0.5); 527 detail::tvec4<T, P> gw01 = detail::tvec4<T, P>(0.75) - abs(gx01) - abs(gy01) - abs(gz01); 528 detail::tvec4<T, P> sw01 = step(gw01, detail::tvec4<T, P>(0.0)); 529 gx01 -= sw01 * (step(T(0), gx01) - T(0.5)); 530 gy01 -= sw01 * (step(T(0), gy01) - T(0.5)); 531 532 detail::tvec4<T, P> gx10 = ixy10 / T(7); 533 detail::tvec4<T, P> gy10 = floor(gx10) / T(7); 534 detail::tvec4<T, P> gz10 = floor(gy10) / T(6); 535 gx10 = fract(gx10) - T(0.5); 536 gy10 = fract(gy10) - T(0.5); 537 gz10 = fract(gz10) - T(0.5); 538 detail::tvec4<T, P> gw10 = detail::tvec4<T, P>(0.75) - abs(gx10) - abs(gy10) - abs(gz10); 539 detail::tvec4<T, P> sw10 = step(gw10, detail::tvec4<T, P>(0.0)); 540 gx10 -= sw10 * (step(T(0), gx10) - T(0.5)); 541 gy10 -= sw10 * (step(T(0), gy10) - T(0.5)); 542 543 detail::tvec4<T, P> gx11 = ixy11 / T(7); 544 detail::tvec4<T, P> gy11 = floor(gx11) / T(7); 545 detail::tvec4<T, P> gz11 = floor(gy11) / T(6); 546 gx11 = fract(gx11) - T(0.5); 547 gy11 = fract(gy11) - T(0.5); 548 gz11 = fract(gz11) - T(0.5); 549 detail::tvec4<T, P> gw11 = detail::tvec4<T, P>(0.75) - abs(gx11) - abs(gy11) - abs(gz11); 550 detail::tvec4<T, P> sw11 = step(gw11, detail::tvec4<T, P>(T(0))); 551 gx11 -= sw11 * (step(T(0), gx11) - T(0.5)); 552 gy11 -= sw11 * (step(T(0), gy11) - T(0.5)); 553 554 detail::tvec4<T, P> g0000(gx00.x, gy00.x, gz00.x, gw00.x); 555 detail::tvec4<T, P> g1000(gx00.y, gy00.y, gz00.y, gw00.y); 556 detail::tvec4<T, P> g0100(gx00.z, gy00.z, gz00.z, gw00.z); 557 detail::tvec4<T, P> g1100(gx00.w, gy00.w, gz00.w, gw00.w); 558 detail::tvec4<T, P> g0010(gx10.x, gy10.x, gz10.x, gw10.x); 559 detail::tvec4<T, P> g1010(gx10.y, gy10.y, gz10.y, gw10.y); 560 detail::tvec4<T, P> g0110(gx10.z, gy10.z, gz10.z, gw10.z); 561 detail::tvec4<T, P> g1110(gx10.w, gy10.w, gz10.w, gw10.w); 562 detail::tvec4<T, P> g0001(gx01.x, gy01.x, gz01.x, gw01.x); 563 detail::tvec4<T, P> g1001(gx01.y, gy01.y, gz01.y, gw01.y); 564 detail::tvec4<T, P> g0101(gx01.z, gy01.z, gz01.z, gw01.z); 565 detail::tvec4<T, P> g1101(gx01.w, gy01.w, gz01.w, gw01.w); 566 detail::tvec4<T, P> g0011(gx11.x, gy11.x, gz11.x, gw11.x); 567 detail::tvec4<T, P> g1011(gx11.y, gy11.y, gz11.y, gw11.y); 568 detail::tvec4<T, P> g0111(gx11.z, gy11.z, gz11.z, gw11.z); 569 detail::tvec4<T, P> g1111(gx11.w, gy11.w, gz11.w, gw11.w); 570 571 detail::tvec4<T, P> norm00 = detail::taylorInvSqrt(detail::tvec4<T, P>(dot(g0000, g0000), dot(g0100, g0100), dot(g1000, g1000), dot(g1100, g1100))); 572 g0000 *= norm00.x; 573 g0100 *= norm00.y; 574 g1000 *= norm00.z; 575 g1100 *= norm00.w; 576 577 detail::tvec4<T, P> norm01 = detail::taylorInvSqrt(detail::tvec4<T, P>(dot(g0001, g0001), dot(g0101, g0101), dot(g1001, g1001), dot(g1101, g1101))); 578 g0001 *= norm01.x; 579 g0101 *= norm01.y; 580 g1001 *= norm01.z; 581 g1101 *= norm01.w; 582 583 detail::tvec4<T, P> norm10 = taylorInvSqrt(detail::tvec4<T, P>(dot(g0010, g0010), dot(g0110, g0110), dot(g1010, g1010), dot(g1110, g1110))); 584 g0010 *= norm10.x; 585 g0110 *= norm10.y; 586 g1010 *= norm10.z; 587 g1110 *= norm10.w; 588 589 detail::tvec4<T, P> norm11 = taylorInvSqrt(detail::tvec4<T, P>(dot(g0011, g0011), dot(g0111, g0111), dot(g1011, g1011), dot(g1111, g1111))); 590 g0011 *= norm11.x; 591 g0111 *= norm11.y; 592 g1011 *= norm11.z; 593 g1111 *= norm11.w; 594 595 T n0000 = dot(g0000, Pf0); 596 T n1000 = dot(g1000, detail::tvec4<T, P>(Pf1.x, Pf0.y, Pf0.z, Pf0.w)); 597 T n0100 = dot(g0100, detail::tvec4<T, P>(Pf0.x, Pf1.y, Pf0.z, Pf0.w)); 598 T n1100 = dot(g1100, detail::tvec4<T, P>(Pf1.x, Pf1.y, Pf0.z, Pf0.w)); 599 T n0010 = dot(g0010, detail::tvec4<T, P>(Pf0.x, Pf0.y, Pf1.z, Pf0.w)); 600 T n1010 = dot(g1010, detail::tvec4<T, P>(Pf1.x, Pf0.y, Pf1.z, Pf0.w)); 601 T n0110 = dot(g0110, detail::tvec4<T, P>(Pf0.x, Pf1.y, Pf1.z, Pf0.w)); 602 T n1110 = dot(g1110, detail::tvec4<T, P>(Pf1.x, Pf1.y, Pf1.z, Pf0.w)); 603 T n0001 = dot(g0001, detail::tvec4<T, P>(Pf0.x, Pf0.y, Pf0.z, Pf1.w)); 604 T n1001 = dot(g1001, detail::tvec4<T, P>(Pf1.x, Pf0.y, Pf0.z, Pf1.w)); 605 T n0101 = dot(g0101, detail::tvec4<T, P>(Pf0.x, Pf1.y, Pf0.z, Pf1.w)); 606 T n1101 = dot(g1101, detail::tvec4<T, P>(Pf1.x, Pf1.y, Pf0.z, Pf1.w)); 607 T n0011 = dot(g0011, detail::tvec4<T, P>(Pf0.x, Pf0.y, Pf1.z, Pf1.w)); 608 T n1011 = dot(g1011, detail::tvec4<T, P>(Pf1.x, Pf0.y, Pf1.z, Pf1.w)); 609 T n0111 = dot(g0111, detail::tvec4<T, P>(Pf0.x, Pf1.y, Pf1.z, Pf1.w)); 610 T n1111 = dot(g1111, Pf1); 611 612 detail::tvec4<T, P> fade_xyzw = fade(Pf0); 613 detail::tvec4<T, P> n_0w = mix(detail::tvec4<T, P>(n0000, n1000, n0100, n1100), detail::tvec4<T, P>(n0001, n1001, n0101, n1101), fade_xyzw.w); 614 detail::tvec4<T, P> n_1w = mix(detail::tvec4<T, P>(n0010, n1010, n0110, n1110), detail::tvec4<T, P>(n0011, n1011, n0111, n1111), fade_xyzw.w); 615 detail::tvec4<T, P> n_zw = mix(n_0w, n_1w, fade_xyzw.z); 616 detail::tvec2<T, P> n_yzw = mix(detail::tvec2<T, P>(n_zw.x, n_zw.y), detail::tvec2<T, P>(n_zw.z, n_zw.w), fade_xyzw.y); 617 T n_xyzw = mix(n_yzw.x, n_yzw.y, fade_xyzw.x); 618 return T(2.2) * n_xyzw; 619 } 620 621 template <typename T, precision P> 622 GLM_FUNC_QUALIFIER T simplex(glm::detail::tvec2<T, P> const & v) 623 { 624 detail::tvec4<T, P> const C = detail::tvec4<T, P>( 625 T( 0.211324865405187), // (3.0 - sqrt(3.0)) / 6.0 626 T( 0.366025403784439), // 0.5 * (sqrt(3.0) - 1.0) 627 T(-0.577350269189626), // -1.0 + 2.0 * C.x 628 T( 0.024390243902439)); // 1.0 / 41.0 629 630 // First corner 631 detail::tvec2<T, P> i = floor(v + dot(v, detail::tvec2<T, P>(C[1]))); 632 detail::tvec2<T, P> x0 = v - i + dot(i, detail::tvec2<T, P>(C[0])); 633 634 // Other corners 635 //i1.x = step( x0.y, x0.x ); // x0.x > x0.y ? 1.0 : 0.0 636 //i1.y = 1.0 - i1.x; 637 detail::tvec2<T, P> i1 = (x0.x > x0.y) ? detail::tvec2<T, P>(1, 0) : detail::tvec2<T, P>(0, 1); 638 // x0 = x0 - 0.0 + 0.0 * C.xx ; 639 // x1 = x0 - i1 + 1.0 * C.xx ; 640 // x2 = x0 - 1.0 + 2.0 * C.xx ; 641 detail::tvec4<T, P> x12 = detail::tvec4<T, P>(x0.x, x0.y, x0.x, x0.y) + detail::tvec4<T, P>(C.x, C.x, C.z, C.z); 642 x12 = detail::tvec4<T, P>(detail::tvec2<T, P>(x12) - i1, x12.z, x12.w); 643 644 // Permutations 645 i = mod(i, detail::tvec2<T, P>(289)); // Avoid truncation effects in permutation 646 detail::tvec3<T, P> p = detail::permute( 647 detail::permute(i.y + detail::tvec3<T, P>(T(0), i1.y, T(1))) 648 + i.x + detail::tvec3<T, P>(T(0), i1.x, T(1))); 649 650 detail::tvec3<T, P> m = max(detail::tvec3<T, P>(0.5) - detail::tvec3<T, P>( 651 dot(x0, x0), 652 dot(detail::tvec2<T, P>(x12.x, x12.y), detail::tvec2<T, P>(x12.x, x12.y)), 653 dot(detail::tvec2<T, P>(x12.z, x12.w), detail::tvec2<T, P>(x12.z, x12.w))), detail::tvec3<T, P>(0)); 654 m = m * m ; 655 m = m * m ; 656 657 // Gradients: 41 points uniformly over a line, mapped onto a diamond. 658 // The ring size 17*17 = 289 is close to a multiple of 41 (41*7 = 287) 659 660 detail::tvec3<T, P> x = static_cast<T>(2) * fract(p * C.w) - T(1); 661 detail::tvec3<T, P> h = abs(x) - T(0.5); 662 detail::tvec3<T, P> ox = floor(x + T(0.5)); 663 detail::tvec3<T, P> a0 = x - ox; 664 665 // Normalise gradients implicitly by scaling m 666 // Inlined for speed: m *= taylorInvSqrt( a0*a0 + h*h ); 667 m *= static_cast<T>(1.79284291400159) - T(0.85373472095314) * (a0 * a0 + h * h); 668 669 // Compute final noise value at P 670 detail::tvec3<T, P> g; 671 g.x = a0.x * x0.x + h.x * x0.y; 672 //g.yz = a0.yz * x12.xz + h.yz * x12.yw; 673 g.y = a0.y * x12.x + h.y * x12.y; 674 g.z = a0.z * x12.z + h.z * x12.w; 675 return T(130) * dot(m, g); 676 } 677 678 template <typename T, precision P> 679 GLM_FUNC_QUALIFIER T simplex(detail::tvec3<T, P> const & v) 680 { 681 detail::tvec2<T, P> const C(1.0 / 6.0, 1.0 / 3.0); 682 detail::tvec4<T, P> const D(0.0, 0.5, 1.0, 2.0); 683 684 // First corner 685 detail::tvec3<T, P> i(floor(v + dot(v, detail::tvec3<T, P>(C.y)))); 686 detail::tvec3<T, P> x0(v - i + dot(i, detail::tvec3<T, P>(C.x))); 687 688 // Other corners 689 detail::tvec3<T, P> g(step(detail::tvec3<T, P>(x0.y, x0.z, x0.x), x0)); 690 detail::tvec3<T, P> l(T(1) - g); 691 detail::tvec3<T, P> i1(min(g, detail::tvec3<T, P>(l.z, l.x, l.y))); 692 detail::tvec3<T, P> i2(max(g, detail::tvec3<T, P>(l.z, l.x, l.y))); 693 694 // x0 = x0 - 0.0 + 0.0 * C.xxx; 695 // x1 = x0 - i1 + 1.0 * C.xxx; 696 // x2 = x0 - i2 + 2.0 * C.xxx; 697 // x3 = x0 - 1.0 + 3.0 * C.xxx; 698 detail::tvec3<T, P> x1(x0 - i1 + C.x); 699 detail::tvec3<T, P> x2(x0 - i2 + C.y); // 2.0*C.x = 1/3 = C.y 700 detail::tvec3<T, P> x3(x0 - D.y); // -1.0+3.0*C.x = -0.5 = -D.y 701 702 // Permutations 703 i = mod289(i); 704 detail::tvec4<T, P> p(detail::permute(detail::permute(detail::permute( 705 i.z + detail::tvec4<T, P>(T(0), i1.z, i2.z, T(1))) + 706 i.y + detail::tvec4<T, P>(T(0), i1.y, i2.y, T(1))) + 707 i.x + detail::tvec4<T, P>(T(0), i1.x, i2.x, T(1)))); 708 709 // Gradients: 7x7 points over a square, mapped onto an octahedron. 710 // The ring size 17*17 = 289 is close to a multiple of 49 (49*6 = 294) 711 T n_ = static_cast<T>(0.142857142857); // 1.0/7.0 712 detail::tvec3<T, P> ns(n_ * detail::tvec3<T, P>(D.w, D.y, D.z) - detail::tvec3<T, P>(D.x, D.z, D.x)); 713 714 detail::tvec4<T, P> j(p - T(49) * floor(p * ns.z * ns.z)); // mod(p,7*7) 715 716 detail::tvec4<T, P> x_(floor(j * ns.z)); 717 detail::tvec4<T, P> y_(floor(j - T(7) * x_)); // mod(j,N) 718 719 detail::tvec4<T, P> x(x_ * ns.x + ns.y); 720 detail::tvec4<T, P> y(y_ * ns.x + ns.y); 721 detail::tvec4<T, P> h(T(1) - abs(x) - abs(y)); 722 723 detail::tvec4<T, P> b0(x.x, x.y, y.x, y.y); 724 detail::tvec4<T, P> b1(x.z, x.w, y.z, y.w); 725 726 // vec4 s0 = vec4(lessThan(b0,0.0))*2.0 - 1.0; 727 // vec4 s1 = vec4(lessThan(b1,0.0))*2.0 - 1.0; 728 detail::tvec4<T, P> s0(floor(b0) * T(2) + T(1)); 729 detail::tvec4<T, P> s1(floor(b1) * T(2) + T(1)); 730 detail::tvec4<T, P> sh(-step(h, detail::tvec4<T, P>(0.0))); 731 732 detail::tvec4<T, P> a0 = detail::tvec4<T, P>(b0.x, b0.z, b0.y, b0.w) + detail::tvec4<T, P>(s0.x, s0.z, s0.y, s0.w) * detail::tvec4<T, P>(sh.x, sh.x, sh.y, sh.y); 733 detail::tvec4<T, P> a1 = detail::tvec4<T, P>(b1.x, b1.z, b1.y, b1.w) + detail::tvec4<T, P>(s1.x, s1.z, s1.y, s1.w) * detail::tvec4<T, P>(sh.z, sh.z, sh.w, sh.w); 734 735 detail::tvec3<T, P> p0(a0.x, a0.y, h.x); 736 detail::tvec3<T, P> p1(a0.z, a0.w, h.y); 737 detail::tvec3<T, P> p2(a1.x, a1.y, h.z); 738 detail::tvec3<T, P> p3(a1.z, a1.w, h.w); 739 740 // Normalise gradients 741 detail::tvec4<T, P> norm = detail::taylorInvSqrt(detail::tvec4<T, P>(dot(p0, p0), dot(p1, p1), dot(p2, p2), dot(p3, p3))); 742 p0 *= norm.x; 743 p1 *= norm.y; 744 p2 *= norm.z; 745 p3 *= norm.w; 746 747 // Mix final noise value 748 detail::tvec4<T, P> m = max(T(0.6) - detail::tvec4<T, P>(dot(x0, x0), dot(x1, x1), dot(x2, x2), dot(x3, x3)), detail::tvec4<T, P>(0)); 749 m = m * m; 750 return T(42) * dot(m * m, detail::tvec4<T, P>(dot(p0, x0), dot(p1, x1), dot(p2, x2), dot(p3, x3))); 751 } 752 753 template <typename T, precision P> 754 GLM_FUNC_QUALIFIER T simplex(detail::tvec4<T, P> const & v) 755 { 756 detail::tvec4<T, P> const C( 757 0.138196601125011, // (5 - sqrt(5))/20 G4 758 0.276393202250021, // 2 * G4 759 0.414589803375032, // 3 * G4 760 -0.447213595499958); // -1 + 4 * G4 761 762 // (sqrt(5) - 1)/4 = F4, used once below 763 T const F4 = static_cast<T>(0.309016994374947451); 764 765 // First corner 766 detail::tvec4<T, P> i = floor(v + dot(v, vec4(F4))); 767 detail::tvec4<T, P> x0 = v - i + dot(i, vec4(C.x)); 768 769 // Other corners 770 771 // Rank sorting originally contributed by Bill Licea-Kane, AMD (formerly ATI) 772 detail::tvec4<T, P> i0; 773 detail::tvec3<T, P> isX = step(detail::tvec3<T, P>(x0.y, x0.z, x0.w), detail::tvec3<T, P>(x0.x)); 774 detail::tvec3<T, P> isYZ = step(detail::tvec3<T, P>(x0.z, x0.w, x0.w), detail::tvec3<T, P>(x0.y, x0.y, x0.z)); 775 // i0.x = dot(isX, vec3(1.0)); 776 //i0.x = isX.x + isX.y + isX.z; 777 //i0.yzw = static_cast<T>(1) - isX; 778 i0 = detail::tvec4<T, P>(isX.x + isX.y + isX.z, T(1) - isX); 779 // i0.y += dot(isYZ.xy, vec2(1.0)); 780 i0.y += isYZ.x + isYZ.y; 781 //i0.zw += 1.0 - detail::tvec2<T, P>(isYZ.x, isYZ.y); 782 i0.z += static_cast<T>(1) - isYZ.x; 783 i0.w += static_cast<T>(1) - isYZ.y; 784 i0.z += isYZ.z; 785 i0.w += static_cast<T>(1) - isYZ.z; 786 787 // i0 now contains the unique values 0,1,2,3 in each channel 788 detail::tvec4<T, P> i3 = clamp(i0, T(0), T(1)); 789 detail::tvec4<T, P> i2 = clamp(i0 - T(1), T(0), T(1)); 790 detail::tvec4<T, P> i1 = clamp(i0 - T(2), T(0), T(1)); 791 792 // x0 = x0 - 0.0 + 0.0 * C.xxxx 793 // x1 = x0 - i1 + 0.0 * C.xxxx 794 // x2 = x0 - i2 + 0.0 * C.xxxx 795 // x3 = x0 - i3 + 0.0 * C.xxxx 796 // x4 = x0 - 1.0 + 4.0 * C.xxxx 797 detail::tvec4<T, P> x1 = x0 - i1 + C.x; 798 detail::tvec4<T, P> x2 = x0 - i2 + C.y; 799 detail::tvec4<T, P> x3 = x0 - i3 + C.z; 800 detail::tvec4<T, P> x4 = x0 + C.w; 801 802 // Permutations 803 i = mod(i, detail::tvec4<T, P>(289)); 804 T j0 = detail::permute(detail::permute(detail::permute(detail::permute(i.w) + i.z) + i.y) + i.x); 805 detail::tvec4<T, P> j1 = detail::permute(detail::permute(detail::permute(detail::permute( 806 i.w + detail::tvec4<T, P>(i1.w, i2.w, i3.w, T(1))) + 807 i.z + detail::tvec4<T, P>(i1.z, i2.z, i3.z, T(1))) + 808 i.y + detail::tvec4<T, P>(i1.y, i2.y, i3.y, T(1))) + 809 i.x + detail::tvec4<T, P>(i1.x, i2.x, i3.x, T(1))); 810 811 // Gradients: 7x7x6 points over a cube, mapped onto a 4-cross polytope 812 // 7*7*6 = 294, which is close to the ring size 17*17 = 289. 813 detail::tvec4<T, P> ip = detail::tvec4<T, P>(T(1) / T(294), T(1) / T(49), T(1) / T(7), T(0)); 814 815 detail::tvec4<T, P> p0 = gtc::grad4(j0, ip); 816 detail::tvec4<T, P> p1 = gtc::grad4(j1.x, ip); 817 detail::tvec4<T, P> p2 = gtc::grad4(j1.y, ip); 818 detail::tvec4<T, P> p3 = gtc::grad4(j1.z, ip); 819 detail::tvec4<T, P> p4 = gtc::grad4(j1.w, ip); 820 821 // Normalise gradients 822 detail::tvec4<T, P> norm = detail::taylorInvSqrt(detail::tvec4<T, P>(dot(p0, p0), dot(p1, p1), dot(p2, p2), dot(p3, p3))); 823 p0 *= norm.x; 824 p1 *= norm.y; 825 p2 *= norm.z; 826 p3 *= norm.w; 827 p4 *= detail::taylorInvSqrt(dot(p4, p4)); 828 829 // Mix contributions from the five corners 830 detail::tvec3<T, P> m0 = max(T(0.6) - detail::tvec3<T, P>(dot(x0, x0), dot(x1, x1), dot(x2, x2)), detail::tvec3<T, P>(0)); 831 detail::tvec2<T, P> m1 = max(T(0.6) - detail::tvec2<T, P>(dot(x3, x3), dot(x4, x4) ), detail::tvec2<T, P>(0)); 832 m0 = m0 * m0; 833 m1 = m1 * m1; 834 return T(49) * 835 (dot(m0 * m0, detail::tvec3<T, P>(dot(p0, x0), dot(p1, x1), dot(p2, x2))) + 836 dot(m1 * m1, detail::tvec2<T, P>(dot(p3, x3), dot(p4, x4)))); 837 } 838 }//namespace glm 839
