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 core 24 /// @file glm/core/func_noise.inl 25 /// @date 2008-08-01 / 2011-09-27 26 /// @author Christophe Riccio 27 /////////////////////////////////////////////////////////////////////////////////// 28 29 #include "../detail/_noise.hpp" 30 #include "./func_common.hpp" 31 32 namespace glm{ 33 namespace detail 34 { 35 template <typename T, precision P> 36 GLM_FUNC_QUALIFIER detail::tvec4<T, P> grad4(T const & j, detail::tvec4<T, P> const & ip) 37 { 38 detail::tvec3<T, P> pXYZ = floor(fract(detail::tvec3<T, P>(j) * detail::tvec3<T, P>(ip)) * T(7)) * ip[2] - T(1); 39 T pW = static_cast<T>(1.5) - dot(abs(pXYZ), detail::tvec3<T, P>(1)); 40 detail::tvec4<T, P> s = detail::tvec4<T, P>(lessThan(detail::tvec4<T, P>(pXYZ, pW), detail::tvec4<T, P>(0.0))); 41 pXYZ = pXYZ + (detail::tvec3<T, P>(s) * T(2) - T(1)) * s.w; 42 return detail::tvec4<T, P>(pXYZ, pW); 43 } 44 }//namespace detail 45 46 template <typename T> 47 GLM_FUNC_QUALIFIER T noise1(T const & x) 48 { 49 return noise1(detail::tvec2<T, defaultp>(x, T(0))); 50 } 51 52 template <typename T> 53 GLM_FUNC_QUALIFIER detail::tvec2<T, defaultp> noise2(T const & x) 54 { 55 return detail::tvec2<T, defaultp>( 56 noise1(x + T(0.0)), 57 noise1(x + T(1.0))); 58 } 59 60 template <typename T> 61 GLM_FUNC_QUALIFIER detail::tvec3<T, defaultp> noise3(T const & x) 62 { 63 return detail::tvec3<T, defaultp>( 64 noise1(x - T(1.0)), 65 noise1(x + T(0.0)), 66 noise1(x + T(1.0))); 67 } 68 69 template <typename T> 70 GLM_FUNC_QUALIFIER detail::tvec4<T, defaultp> noise4(T const & x) 71 { 72 return detail::tvec4<T, defaultp>( 73 noise1(x - T(1.0)), 74 noise1(x + T(0.0)), 75 noise1(x + T(1.0)), 76 noise1(x + T(2.0))); 77 } 78 79 template <typename T, precision P> 80 GLM_FUNC_QUALIFIER T noise1(detail::tvec2<T, P> const & v) 81 { 82 detail::tvec4<T, P> const C = detail::tvec4<T, P>( 83 T( 0.211324865405187), // (3.0 - sqrt(3.0)) / 6.0 84 T( 0.366025403784439), // 0.5 * (sqrt(3.0) - 1.0) 85 T(-0.577350269189626), // -1.0 + 2.0 * C.x 86 T( 0.024390243902439)); // 1.0 / 41.0 87 88 // First corner 89 detail::tvec2<T, P> i = floor(v + dot(v, detail::tvec2<T, P>(C[1]))); 90 detail::tvec2<T, P> x0 = v - i + dot(i, detail::tvec2<T, P>(C[0])); 91 92 // Other corners 93 //i1.x = step( x0.y, x0.x ); // x0.x > x0.y ? 1.0 : 0.0 94 //i1.y = 1.0 - i1.x; 95 detail::tvec2<T, P> i1 = (x0.x > x0.y) ? detail::tvec2<T, P>(1, 0) : detail::tvec2<T, P>(0, 1); 96 97 // x0 = x0 - 0.0 + 0.0 * C.xx ; 98 // x1 = x0 - i1 + 1.0 * C.xx ; 99 // x2 = x0 - 1.0 + 2.0 * C.xx ; 100 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); 101 x12 = detail::tvec4<T, P>(detail::tvec2<T, P>(x12) - i1, x12.z, x12.w); 102 103 // Permutations 104 i = mod(i, T(289)); // Avoid truncation effects in permutation 105 detail::tvec3<T, P> p = detail::permute( 106 detail::permute(i.y + detail::tvec3<T, P>(T(0), i1.y, T(1))) + i.x + detail::tvec3<T, P>(T(0), i1.x, T(1))); 107 108 detail::tvec3<T, P> m = max(T(0.5) - detail::tvec3<T, P>( 109 dot(x0, x0), 110 dot(detail::tvec2<T, P>(x12.x, x12.y), detail::tvec2<T, P>(x12.x, x12.y)), 111 dot(detail::tvec2<T, P>(x12.z, x12.w), detail::tvec2<T, P>(x12.z, x12.w))), T(0)); 112 113 m = m * m; 114 m = m * m; 115 116 // Gradients: 41 points uniformly over a line, mapped onto a diamond. 117 // The ring size 17*17 = 289 is close to a multiple of 41 (41*7 = 287) 118 119 detail::tvec3<T, P> x = static_cast<T>(2) * fract(p * C.w) - T(1); 120 detail::tvec3<T, P> h = abs(x) - T(0.5); 121 detail::tvec3<T, P> ox = floor(x + T(0.5)); 122 detail::tvec3<T, P> a0 = x - ox; 123 124 // Normalise gradients implicitly by scaling m 125 // Inlined for speed: m *= taylorInvSqrt( a0*a0 + h*h ); 126 m *= static_cast<T>(1.79284291400159) - T(0.85373472095314) * (a0 * a0 + h * h); 127 128 // Compute final noise value at P 129 detail::tvec3<T, P> g; 130 g.x = a0.x * x0.x + h.x * x0.y; 131 //g.yz = a0.yz * x12.xz + h.yz * x12.yw; 132 g.y = a0.y * x12.x + h.y * x12.y; 133 g.z = a0.z * x12.z + h.z * x12.w; 134 return T(130) * dot(m, g); 135 } 136 137 template <typename T, precision P> 138 GLM_FUNC_QUALIFIER T noise1(detail::tvec3<T, P> const & v) 139 { 140 detail::tvec2<T, P> const C(1.0 / 6.0, 1.0 / 3.0); 141 detail::tvec4<T, P> const D(0.0, 0.5, 1.0, 2.0); 142 143 // First corner 144 detail::tvec3<T, P> i(floor(v + dot(v, detail::tvec3<T, P>(C.y)))); 145 detail::tvec3<T, P> x0(v - i + dot(i, detail::tvec3<T, P>(C.x))); 146 147 // Other corners 148 detail::tvec3<T, P> g(step(detail::tvec3<T, P>(x0.y, x0.z, x0.x), x0)); 149 detail::tvec3<T, P> l(T(1) - g); 150 detail::tvec3<T, P> i1(min(g, detail::tvec3<T, P>(l.z, l.x, l.y))); 151 detail::tvec3<T, P> i2(max(g, detail::tvec3<T, P>(l.z, l.x, l.y))); 152 153 // x0 = x0 - 0.0 + 0.0 * C.xxx; 154 // x1 = x0 - i1 + 1.0 * C.xxx; 155 // x2 = x0 - i2 + 2.0 * C.xxx; 156 // x3 = x0 - 1.0 + 3.0 * C.xxx; 157 detail::tvec3<T, P> x1(x0 - i1 + C.x); 158 detail::tvec3<T, P> x2(x0 - i2 + C.y); // 2.0*C.x = 1/3 = C.y 159 detail::tvec3<T, P> x3(x0 - D.y); // -1.0+3.0*C.x = -0.5 = -D.y 160 161 // Permutations 162 i = mod289(i); 163 detail::tvec4<T, P> p(detail::permute(detail::permute(detail::permute( 164 i.z + detail::tvec4<T, P>(T(0), i1.z, i2.z, T(1))) + 165 i.y + detail::tvec4<T, P>(T(0), i1.y, i2.y, T(1))) + 166 i.x + detail::tvec4<T, P>(T(0), i1.x, i2.x, T(1)))); 167 168 // Gradients: 7x7 points over a square, mapped onto an octahedron. 169 // The ring size 17*17 = 289 is close to a multiple of 49 (49*6 = 294) 170 T n_ = static_cast<T>(0.142857142857); // 1.0/7.0 171 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)); 172 173 detail::tvec4<T, P> j(p - T(49) * floor(p * ns.z * ns.z)); // mod(p,7*7) 174 175 detail::tvec4<T, P> x_(floor(j * ns.z)); 176 detail::tvec4<T, P> y_(floor(j - T(7) * x_)); // mod(j,N) 177 178 detail::tvec4<T, P> x(x_ * ns.x + ns.y); 179 detail::tvec4<T, P> y(y_ * ns.x + ns.y); 180 detail::tvec4<T, P> h(T(1) - abs(x) - abs(y)); 181 182 detail::tvec4<T, P> b0(x.x, x.y, y.x, y.y); 183 detail::tvec4<T, P> b1(x.z, x.w, y.z, y.w); 184 185 // vec4 s0 = vec4(lessThan(b0,0.0))*2.0 - 1.0; 186 // vec4 s1 = vec4(lessThan(b1,0.0))*2.0 - 1.0; 187 detail::tvec4<T, P> s0(floor(b0) * T(2) + T(1)); 188 detail::tvec4<T, P> s1(floor(b1) * T(2) + T(1)); 189 detail::tvec4<T, P> sh(-step(h, detail::tvec4<T, P>(0.0))); 190 191 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); 192 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); 193 194 detail::tvec3<T, P> p0(a0.x, a0.y, h.x); 195 detail::tvec3<T, P> p1(a0.z, a0.w, h.y); 196 detail::tvec3<T, P> p2(a1.x, a1.y, h.z); 197 detail::tvec3<T, P> p3(a1.z, a1.w, h.w); 198 199 // Normalise gradients 200 detail::tvec4<T, P> norm = taylorInvSqrt(detail::tvec4<T, P>(dot(p0, p0), dot(p1, p1), dot(p2, p2), dot(p3, p3))); 201 p0 *= norm.x; 202 p1 *= norm.y; 203 p2 *= norm.z; 204 p3 *= norm.w; 205 206 // Mix final noise value 207 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)), T(0)); 208 m = m * m; 209 return T(42) * dot(m * m, detail::tvec4<T, P>(dot(p0, x0), dot(p1, x1), dot(p2, x2), dot(p3, x3))); 210 } 211 212 template <typename T, precision P> 213 GLM_FUNC_QUALIFIER T noise1(detail::tvec4<T, P> const & v) 214 { 215 detail::tvec4<T, P> const C( 216 0.138196601125011, // (5 - sqrt(5))/20 G4 217 0.276393202250021, // 2 * G4 218 0.414589803375032, // 3 * G4 219 -0.447213595499958); // -1 + 4 * G4 220 221 // (sqrt(5) - 1)/4 = F4, used once below 222 T const F4 = static_cast<T>(0.309016994374947451); 223 224 // First corner 225 detail::tvec4<T, P> i = floor(v + dot(v, detail::tvec4<T, P>(F4))); 226 detail::tvec4<T, P> x0 = v - i + dot(i, detail::tvec4<T, P>(C.x)); 227 228 // Other corners 229 230 // Rank sorting originally contributed by Bill Licea-Kane, AMD (formerly ATI) 231 detail::tvec4<T, P> i0; 232 detail::tvec3<T, P> isX = step(detail::tvec3<T, P>(x0.y, x0.z, x0.w), detail::tvec3<T, P>(x0.x)); 233 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)); 234 235 // i0.x = dot(isX, vec3(1.0)); 236 //i0.x = isX.x + isX.y + isX.z; 237 //i0.yzw = static_cast<T>(1) - isX; 238 i0 = detail::tvec4<T, P>(isX.x + isX.y + isX.z, T(1) - isX); 239 240 // i0.y += dot(isYZ.xy, vec2(1.0)); 241 i0.y += isYZ.x + isYZ.y; 242 243 //i0.zw += 1.0 - detail::tvec2<T, P>(isYZ.x, isYZ.y); 244 i0.z += static_cast<T>(1) - isYZ.x; 245 i0.w += static_cast<T>(1) - isYZ.y; 246 i0.z += isYZ.z; 247 i0.w += static_cast<T>(1) - isYZ.z; 248 249 // i0 now contains the unique values 0,1,2,3 in each channel 250 detail::tvec4<T, P> i3 = clamp(i0, T(0), T(1)); 251 detail::tvec4<T, P> i2 = clamp(i0 - T(1), T(0), T(1)); 252 detail::tvec4<T, P> i1 = clamp(i0 - T(2), T(0), T(1)); 253 254 // x0 = x0 - 0.0 + 0.0 * C.xxxx 255 // x1 = x0 - i1 + 0.0 * C.xxxx 256 // x2 = x0 - i2 + 0.0 * C.xxxx 257 // x3 = x0 - i3 + 0.0 * C.xxxx 258 // x4 = x0 - 1.0 + 4.0 * C.xxxx 259 detail::tvec4<T, P> x1 = x0 - i1 + C.x; 260 detail::tvec4<T, P> x2 = x0 - i2 + C.y; 261 detail::tvec4<T, P> x3 = x0 - i3 + C.z; 262 detail::tvec4<T, P> x4 = x0 + C.w; 263 264 // Permutations 265 i = mod(i, T(289)); 266 T j0 = detail::permute(detail::permute(detail::permute(detail::permute(i.w) + i.z) + i.y) + i.x); 267 detail::tvec4<T, P> j1 = detail::permute(detail::permute(detail::permute(detail::permute( 268 i.w + detail::tvec4<T, P>(i1.w, i2.w, i3.w, T(1))) + 269 i.z + detail::tvec4<T, P>(i1.z, i2.z, i3.z, T(1))) + 270 i.y + detail::tvec4<T, P>(i1.y, i2.y, i3.y, T(1))) + 271 i.x + detail::tvec4<T, P>(i1.x, i2.x, i3.x, T(1))); 272 273 // Gradients: 7x7x6 points over a cube, mapped onto a 4-cross polytope 274 // 7*7*6 = 294, which is close to the ring size 17*17 = 289. 275 detail::tvec4<T, P> ip = detail::tvec4<T, P>(T(1) / T(294), T(1) / T(49), T(1) / T(7), T(0)); 276 277 detail::tvec4<T, P> p0 = detail::grad4(j0, ip); 278 detail::tvec4<T, P> p1 = detail::grad4(j1.x, ip); 279 detail::tvec4<T, P> p2 = detail::grad4(j1.y, ip); 280 detail::tvec4<T, P> p3 = detail::grad4(j1.z, ip); 281 detail::tvec4<T, P> p4 = detail::grad4(j1.w, ip); 282 283 // Normalise gradients 284 detail::tvec4<T, P> norm = detail::taylorInvSqrt(detail::tvec4<T, P>(dot(p0, p0), dot(p1, p1), dot(p2, p2), dot(p3, p3))); 285 p0 *= norm.x; 286 p1 *= norm.y; 287 p2 *= norm.z; 288 p3 *= norm.w; 289 p4 *= taylorInvSqrt(dot(p4, p4)); 290 291 // Mix contributions from the five corners 292 detail::tvec3<T, P> m0 = max(T(0.6) - detail::tvec3<T, P>(dot(x0, x0), dot(x1, x1), dot(x2, x2)), T(0)); 293 detail::tvec2<T, P> m1 = max(T(0.6) - detail::tvec2<T, P>(dot(x3, x3), dot(x4, x4) ), T(0)); 294 m0 = m0 * m0; 295 m1 = m1 * m1; 296 297 return T(49) * ( 298 dot(m0 * m0, detail::tvec3<T, P>(dot(p0, x0), dot(p1, x1), dot(p2, x2))) + 299 dot(m1 * m1, detail::tvec2<T, P>(dot(p3, x3), dot(p4, x4)))); 300 } 301 302 template <typename T, precision P> 303 GLM_FUNC_QUALIFIER detail::tvec2<T, P> noise2(detail::tvec2<T, P> const & x) 304 { 305 return detail::tvec2<T, P>( 306 noise1(x + detail::tvec2<T, P>(0.0)), 307 noise1(detail::tvec2<T, P>(0.0) - x)); 308 } 309 310 template <typename T, precision P> 311 GLM_FUNC_QUALIFIER detail::tvec2<T, P> noise2(detail::tvec3<T, P> const & x) 312 { 313 return detail::tvec2<T, P>( 314 noise1(x + detail::tvec3<T, P>(0.0)), 315 noise1(detail::tvec3<T, P>(0.0) - x)); 316 } 317 318 template <typename T, precision P> 319 GLM_FUNC_QUALIFIER detail::tvec2<T, P> noise2(detail::tvec4<T, P> const & x) 320 { 321 return detail::tvec2<T, P>( 322 noise1(x + detail::tvec4<T, P>(0)), 323 noise1(detail::tvec4<T, P>(0) - x)); 324 } 325 326 template <typename T, precision P> 327 GLM_FUNC_QUALIFIER detail::tvec3<T, P> noise3(detail::tvec2<T, P> const & x) 328 { 329 return detail::tvec3<T, P>( 330 noise1(x - detail::tvec2<T, P>(1.0)), 331 noise1(x + detail::tvec2<T, P>(0.0)), 332 noise1(x + detail::tvec2<T, P>(1.0))); 333 } 334 335 template <typename T, precision P> 336 GLM_FUNC_QUALIFIER detail::tvec3<T, P> noise3(detail::tvec3<T, P> const & x) 337 { 338 return detail::tvec3<T, P>( 339 noise1(x - detail::tvec3<T, P>(1.0)), 340 noise1(x + detail::tvec3<T, P>(0.0)), 341 noise1(x + detail::tvec3<T, P>(1.0))); 342 } 343 344 template <typename T, precision P> 345 GLM_FUNC_QUALIFIER detail::tvec3<T, P> noise3(detail::tvec4<T, P> const & x) 346 { 347 return detail::tvec3<T, P>( 348 noise1(x - detail::tvec4<T, P>(1)), 349 noise1(x + detail::tvec4<T, P>(0)), 350 noise1(x + detail::tvec4<T, P>(1))); 351 } 352 353 template <typename T, precision P> 354 GLM_FUNC_QUALIFIER detail::tvec4<T, P> noise4(detail::tvec2<T, P> const & x) 355 { 356 return detail::tvec4<T, P>( 357 noise1(x - detail::tvec2<T, P>(1)), 358 noise1(x + detail::tvec2<T, P>(0)), 359 noise1(x + detail::tvec2<T, P>(1)), 360 noise1(x + detail::tvec2<T, P>(2))); 361 } 362 363 364 template <typename T, precision P> 365 GLM_FUNC_QUALIFIER detail::tvec4<T, P> noise4(detail::tvec3<T, P> const & x) 366 { 367 return detail::tvec4<T, P>( 368 noise1(x - detail::tvec3<T, P>(1)), 369 noise1(x + detail::tvec3<T, P>(0)), 370 noise1(x + detail::tvec3<T, P>(1)), 371 noise1(x + detail::tvec3<T, P>(2))); 372 } 373 374 template <typename T, precision P> 375 GLM_FUNC_QUALIFIER detail::tvec4<T, P> noise4(detail::tvec4<T, P> const & x) 376 { 377 return detail::tvec4<T, P>( 378 noise1(x - detail::tvec4<T, P>(1)), 379 noise1(x + detail::tvec4<T, P>(0)), 380 noise1(x + detail::tvec4<T, P>(1)), 381 noise1(x + detail::tvec4<T, P>(2))); 382 } 383 384 }//namespace glm 385
