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, vec<4, T, Q>(F4))); 736 vec<4, T, Q> x0 = v - i + dot(i, vec<4, T, Q>(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 808