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| 1 | // Copyright Contributors to the OpenVDB Project | ||
| 2 | // SPDX-License-Identifier: MPL-2.0 | ||
| 3 | |||
| 4 | /// @file math/OpenSimplexNoise.cc | ||
| 5 | |||
| 6 | #include "OpenSimplexNoise.h" | ||
| 7 | |||
| 8 | #include <algorithm> | ||
| 9 | #include <cmath> | ||
| 10 | #include <type_traits> | ||
| 11 | |||
| 12 | // see OpenSimplexNoise.h for details about the origin on this code | ||
| 13 | |||
| 14 | namespace OSN { | ||
| 15 | |||
| 16 | namespace { | ||
| 17 | |||
| 18 | template <typename T> | ||
| 19 | inline T pow4 (T x) | ||
| 20 | { | ||
| 21 | 10836 | x *= x; | |
| 22 | 10836 | return x*x; | |
| 23 | } | ||
| 24 | |||
| 25 | template <typename T> | ||
| 26 | inline T pow2 (T x) | ||
| 27 | { | ||
| 28 | 2408 | return x*x; | |
| 29 | } | ||
| 30 | |||
| 31 | template <typename T> | ||
| 32 | inline OSNoise::inttype fastFloori (T x) | ||
| 33 | { | ||
| 34 | 3612 | OSNoise::inttype ip = (OSNoise::inttype)x; | |
| 35 | |||
| 36 |
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1204 | if (x < 0.0) --ip; |
| 37 | |||
| 38 | return ip; | ||
| 39 | } | ||
| 40 | |||
| 41 | inline void LCG_STEP (int64_t & x) | ||
| 42 | { | ||
| 43 | // Magic constants are attributed to Donald Knuth's MMIX implementation. | ||
| 44 | static const int64_t MULTIPLIER = 6364136223846793005LL; | ||
| 45 | static const int64_t INCREMENT = 1442695040888963407LL; | ||
| 46 | 14 | x = ((x * MULTIPLIER) + INCREMENT); | |
| 47 | } | ||
| 48 | |||
| 49 | } // anonymous namespace | ||
| 50 | |||
| 51 | // Array of gradient values for 3D. They approximate the directions to the | ||
| 52 | // vertices of a rhombicuboctahedron from its center, skewed so that the | ||
| 53 | // triangular and square facets can be inscribed in circles of the same radius. | ||
| 54 | // New gradient set 2014-10-06. | ||
| 55 | const int OSNoise::sGradients [] = { | ||
| 56 | -11, 4, 4, -4, 11, 4, -4, 4, 11, 11, 4, 4, 4, 11, 4, 4, 4, 11, | ||
| 57 | -11,-4, 4, -4,-11, 4, -4,-4, 11, 11,-4, 4, 4,-11, 4, 4,-4, 11, | ||
| 58 | -11, 4,-4, -4, 11,-4, -4, 4,-11, 11, 4,-4, 4, 11,-4, 4, 4,-11, | ||
| 59 | -11,-4,-4, -4,-11,-4, -4,-4,-11, 11,-4,-4, 4,-11,-4, 4,-4,-11 | ||
| 60 | }; | ||
| 61 | |||
| 62 | template <typename T> | ||
| 63 | ✗ | inline T OSNoise::extrapolate(const OSNoise::inttype xsb, | |
| 64 | const OSNoise::inttype ysb, | ||
| 65 | const OSNoise::inttype zsb, | ||
| 66 | const T dx, | ||
| 67 | const T dy, | ||
| 68 | const T dz) const | ||
| 69 | { | ||
| 70 | 2408 | unsigned int index = mPermGradIndex[(mPerm[(mPerm[xsb & 0xFF] + ysb) & 0xFF] + zsb) & 0xFF]; | |
| 71 | 2408 | return sGradients[index] * dx + | |
| 72 | 2408 | sGradients[index + 1] * dy + | |
| 73 | 2408 | sGradients[index + 2] * dz; | |
| 74 | |||
| 75 | } | ||
| 76 | |||
| 77 | template <typename T> | ||
| 78 | ✗ | inline T OSNoise::extrapolate(const OSNoise::inttype xsb, | |
| 79 | const OSNoise::inttype ysb, | ||
| 80 | const OSNoise::inttype zsb, | ||
| 81 | const T dx, | ||
| 82 | const T dy, | ||
| 83 | const T dz, | ||
| 84 | T (&de) [3]) const | ||
| 85 | { | ||
| 86 | ✗ | unsigned int index = mPermGradIndex[(mPerm[(mPerm[xsb & 0xFF] + ysb) & 0xFF] + zsb) & 0xFF]; | |
| 87 | ✗ | return (de[0] = sGradients[index]) * dx + | |
| 88 | ✗ | (de[1] = sGradients[index + 1]) * dy + | |
| 89 | ✗ | (de[2] = sGradients[index + 2]) * dz; | |
| 90 | } | ||
| 91 | |||
| 92 | 14 | OSNoise::OSNoise(OSNoise::inttype seed) | |
| 93 | { | ||
| 94 | int source [256]; | ||
| 95 |
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3598 | for (int i = 0; i < 256; ++i) { source[i] = i; } |
| 96 | LCG_STEP(seed); | ||
| 97 | LCG_STEP(seed); | ||
| 98 | LCG_STEP(seed); | ||
| 99 |
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3598 | for (int i = 255; i >= 0; --i) { |
| 100 | LCG_STEP(seed); | ||
| 101 | 3584 | int r = (int)((seed + 31) % (i + 1)); | |
| 102 |
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3584 | if (r < 0) { r += (i + 1); } |
| 103 | 3584 | mPerm[i] = source[r]; | |
| 104 | 3584 | mPermGradIndex[i] = (int)((mPerm[i] % (72 / 3)) * 3); | |
| 105 | 3584 | source[r] = source[i]; | |
| 106 | } | ||
| 107 | 14 | } | |
| 108 | |||
| 109 | ✗ | OSNoise::OSNoise(const int * p) | |
| 110 | { | ||
| 111 | // Copy the supplied permutation array into this instance. | ||
| 112 | ✗ | for (int i = 0; i < 256; ++i) { | |
| 113 | ✗ | mPerm[i] = p[i]; | |
| 114 | ✗ | mPermGradIndex[i] = (int)((mPerm[i] % (72 / 3)) * 3); | |
| 115 | } | ||
| 116 | } | ||
| 117 | |||
| 118 | template <typename T> | ||
| 119 | 1204 | T OSNoise::eval(const T x, const T y, const T z) const | |
| 120 | { | ||
| 121 | static_assert(std::is_floating_point<T>::value, "OpenSimplexNoise can only be used with floating-point types"); | ||
| 122 | |||
| 123 | static const T STRETCH_CONSTANT = (T)(-1.0 / 6.0); // (1 / sqrt(3 + 1) - 1) / 3 | ||
| 124 | static const T SQUISH_CONSTANT = (T)(1.0 / 3.0); // (sqrt(3 + 1) - 1) / 3 | ||
| 125 | static const T NORM_CONSTANT = (T)(1.0 / 103.0); | ||
| 126 | |||
| 127 | OSNoise::inttype xsb, ysb, zsb; | ||
| 128 | T dx0, dy0, dz0; | ||
| 129 | T xins, yins, zins; | ||
| 130 | |||
| 131 | // Parameters for the individual contributions | ||
| 132 | T contr_m [9], contr_ext [9]; | ||
| 133 | |||
| 134 | { | ||
| 135 | // Place input coordinates on simplectic lattice. | ||
| 136 | 1204 | T stretchOffset = (x + y + z) * STRETCH_CONSTANT; | |
| 137 | 1204 | T xs = x + stretchOffset; | |
| 138 | 1204 | T ys = y + stretchOffset; | |
| 139 |
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1204 | T zs = z + stretchOffset; |
| 140 | |||
| 141 | // Floor to get simplectic lattice coordinates of rhombohedron | ||
| 142 | // (stretched cube) super-cell. | ||
| 143 | #ifdef __FAST_MATH__ | ||
| 144 | T xsbd = std::floor(xs); | ||
| 145 | T ysbd = std::floor(ys); | ||
| 146 | T zsbd = std::floor(zs); | ||
| 147 | xsb = (OSNoise::inttype)xsbd; | ||
| 148 | ysb = (OSNoise::inttype)ysbd; | ||
| 149 | zsb = (OSNoise::inttype)zsbd; | ||
| 150 | #else | ||
| 151 | xsb = fastFloori(xs); | ||
| 152 | ysb = fastFloori(ys); | ||
| 153 | zsb = fastFloori(zs); | ||
| 154 | 1204 | T xsbd = (T)xsb; | |
| 155 | 1204 | T ysbd = (T)ysb; | |
| 156 | 1204 | T zsbd = (T)zsb; | |
| 157 | #endif | ||
| 158 | |||
| 159 | // Skew out to get actual coordinates of rhombohedron origin. | ||
| 160 | 1204 | T squishOffset = (xsbd + ysbd + zsbd) * SQUISH_CONSTANT; | |
| 161 | 1204 | T xb = xsbd + squishOffset; | |
| 162 | 1204 | T yb = ysbd + squishOffset; | |
| 163 | 1204 | T zb = zsbd + squishOffset; | |
| 164 | |||
| 165 | // Positions relative to origin point. | ||
| 166 | 1204 | dx0 = x - xb; | |
| 167 | 1204 | dy0 = y - yb; | |
| 168 | 1204 | dz0 = z - zb; | |
| 169 | |||
| 170 | // Compute simplectic lattice coordinates relative to rhombohedral origin. | ||
| 171 | 1204 | xins = xs - xsbd; | |
| 172 | 1204 | yins = ys - ysbd; | |
| 173 | 1204 | zins = zs - zsbd; | |
| 174 | } | ||
| 175 | |||
| 176 | // These are given values inside the next block, and used afterwards. | ||
| 177 | OSNoise::inttype xsv_ext0, ysv_ext0, zsv_ext0; | ||
| 178 | OSNoise::inttype xsv_ext1, ysv_ext1, zsv_ext1; | ||
| 179 | T dx_ext0, dy_ext0, dz_ext0; | ||
| 180 | T dx_ext1, dy_ext1, dz_ext1; | ||
| 181 | |||
| 182 | // Sum together to get a value that determines which cell we are in. | ||
| 183 | 1204 | T inSum = xins + yins + zins; | |
| 184 | |||
| 185 |
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1204 | if (inSum > (T)1.0 && inSum < (T)2.0) { |
| 186 | // The point is inside the octahedron (rectified 3-Simplex) inbetween. | ||
| 187 | |||
| 188 | T aScore; | ||
| 189 | uint_fast8_t aPoint; | ||
| 190 | bool aIsFurtherSide; | ||
| 191 | T bScore; | ||
| 192 | uint_fast8_t bPoint; | ||
| 193 | bool bIsFurtherSide; | ||
| 194 | |||
| 195 | // Decide between point (1,0,0) and (0,1,1) as closest. | ||
| 196 | T p1 = xins + yins; | ||
| 197 |
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380 | if (p1 <= (T)1.0) { |
| 198 | 64 | aScore = (T)1.0 - p1; | |
| 199 | aPoint = 4; | ||
| 200 | aIsFurtherSide = false; | ||
| 201 | } else { | ||
| 202 | 316 | aScore = p1 - (T)1.0; | |
| 203 | aPoint = 3; | ||
| 204 | aIsFurtherSide = true; | ||
| 205 | } | ||
| 206 | |||
| 207 | // Decide between point (0,1,0) and (1,0,1) as closest. | ||
| 208 | 380 | T p2 = xins + zins; | |
| 209 |
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380 | if (p2 <= (T)1.0) { |
| 210 | 64 | bScore = (T)1.0 - p2; | |
| 211 | bPoint = 2; | ||
| 212 | bIsFurtherSide = false; | ||
| 213 | } else { | ||
| 214 | 316 | bScore = p2 - (T)1.0; | |
| 215 | bPoint = 5; | ||
| 216 | bIsFurtherSide = true; | ||
| 217 | } | ||
| 218 | |||
| 219 | // The closest out of the two (0,0,1) and (1,1,0) will replace the | ||
| 220 | // furthest out of the two decided above if closer. | ||
| 221 | 380 | T p3 = yins + zins; | |
| 222 |
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380 | if (p3 > (T)1.0) { |
| 223 | ✗ | T score = p3 - (T)1.0; | |
| 224 | ✗ | if (aScore > bScore && bScore < score) { | |
| 225 | bScore = score; | ||
| 226 | bPoint = 6; | ||
| 227 | bIsFurtherSide = true; | ||
| 228 | ✗ | } else if (aScore <= bScore && aScore < score) { | |
| 229 | aScore = score; | ||
| 230 | aPoint = 6; | ||
| 231 | aIsFurtherSide = true; | ||
| 232 | } | ||
| 233 | } else { | ||
| 234 | 380 | T score = (T)1.0 - p3; | |
| 235 |
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380 | if (aScore > bScore && bScore < score) { |
| 236 | bScore = score; | ||
| 237 | bPoint = 1; | ||
| 238 | bIsFurtherSide = false; | ||
| 239 |
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380 | } else if (aScore <= bScore && aScore < score) { |
| 240 | aScore = score; | ||
| 241 | aPoint = 1; | ||
| 242 | aIsFurtherSide = false; | ||
| 243 | } | ||
| 244 | } | ||
| 245 | |||
| 246 | // Where each of the two closest points are determines how the | ||
| 247 | // extra two vertices are calculated. | ||
| 248 |
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380 | if (aIsFurtherSide == bIsFurtherSide) { |
| 249 |
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380 | if (aIsFurtherSide) { |
| 250 | // Both closest points on (1,1,1) side. | ||
| 251 | |||
| 252 | // One of the two extra points is (1,1,1) | ||
| 253 | 316 | xsv_ext0 = xsb + 1; | |
| 254 | 316 | ysv_ext0 = ysb + 1; | |
| 255 | 316 | zsv_ext0 = zsb + 1; | |
| 256 | 316 | dx_ext0 = dx0 - (T)1.0 - (SQUISH_CONSTANT * (T)3.0); | |
| 257 | 316 | dy_ext0 = dy0 - (T)1.0 - (SQUISH_CONSTANT * (T)3.0); | |
| 258 | 316 | dz_ext0 = dz0 - (T)1.0 - (SQUISH_CONSTANT * (T)3.0); | |
| 259 | |||
| 260 | // Other extra point is based on the shared axis. | ||
| 261 | 316 | uint_fast8_t c = aPoint & bPoint; | |
| 262 |
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316 | if (c & 0x01) { |
| 263 | 316 | xsv_ext1 = xsb + 2; | |
| 264 | ysv_ext1 = ysb; | ||
| 265 | zsv_ext1 = zsb; | ||
| 266 | 316 | dx_ext1 = dx0 - (T)2.0 - (SQUISH_CONSTANT * (T)2.0); | |
| 267 | 316 | dy_ext1 = dy0 - (SQUISH_CONSTANT * (T)2.0); | |
| 268 | 316 | dz_ext1 = dz0 - (SQUISH_CONSTANT * (T)2.0); | |
| 269 | ✗ | } else if (c & 0x02) { | |
| 270 | xsv_ext1 = xsb; | ||
| 271 | ✗ | ysv_ext1 = ysb + 2; | |
| 272 | zsv_ext1 = zsb; | ||
| 273 | ✗ | dx_ext1 = dx0 - (SQUISH_CONSTANT * (T)2.0); | |
| 274 | ✗ | dy_ext1 = dy0 - (T)2.0 - (SQUISH_CONSTANT * (T)2.0); | |
| 275 | ✗ | dz_ext1 = dz0 - (SQUISH_CONSTANT * (T)2.0); | |
| 276 | } else { | ||
| 277 | xsv_ext1 = xsb; | ||
| 278 | ysv_ext1 = ysb; | ||
| 279 | ✗ | zsv_ext1 = zsb + 2; | |
| 280 | ✗ | dx_ext1 = dx0 - (SQUISH_CONSTANT * (T)2.0); | |
| 281 | ✗ | dy_ext1 = dy0 - (SQUISH_CONSTANT * (T)2.0); | |
| 282 | ✗ | dz_ext1 = dz0 - (T)2.0 - (SQUISH_CONSTANT * (T)2.0); | |
| 283 | } | ||
| 284 | } else { | ||
| 285 | // Both closest points are on the (0,0,0) side. | ||
| 286 | |||
| 287 | // One of the two extra points is (0,0,0). | ||
| 288 | xsv_ext0 = xsb; | ||
| 289 | ysv_ext0 = ysb; | ||
| 290 | zsv_ext0 = zsb; | ||
| 291 | dx_ext0 = dx0; | ||
| 292 | dy_ext0 = dy0; | ||
| 293 | dz_ext0 = dz0; | ||
| 294 | |||
| 295 | // The other extra point is based on the omitted axis. | ||
| 296 | 64 | uint_fast8_t c = aPoint | bPoint; | |
| 297 |
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64 | if (!(c & 0x01)) { |
| 298 | 64 | xsv_ext1 = xsb - 1; | |
| 299 | 64 | ysv_ext1 = ysb + 1; | |
| 300 | 64 | zsv_ext1 = zsb + 1; | |
| 301 | 64 | dx_ext1 = dx0 + (T)1.0 - SQUISH_CONSTANT; | |
| 302 | 64 | dy_ext1 = dy0 - (T)1.0 - SQUISH_CONSTANT; | |
| 303 | 64 | dz_ext1 = dz0 - (T)1.0 - SQUISH_CONSTANT; | |
| 304 | ✗ | } else if (!(c & 0x02)) { | |
| 305 | ✗ | xsv_ext1 = xsb + 1; | |
| 306 | ✗ | ysv_ext1 = ysb - 1; | |
| 307 | ✗ | zsv_ext1 = zsb + 1; | |
| 308 | ✗ | dx_ext1 = dx0 - (T)1.0 - SQUISH_CONSTANT; | |
| 309 | ✗ | dy_ext1 = dy0 + (T)1.0 - SQUISH_CONSTANT; | |
| 310 | ✗ | dz_ext1 = dz0 - (T)1.0 - SQUISH_CONSTANT; | |
| 311 | } else { | ||
| 312 | ✗ | xsv_ext1 = xsb + 1; | |
| 313 | ✗ | ysv_ext1 = ysb + 1; | |
| 314 | ✗ | zsv_ext1 = zsb - 1; | |
| 315 | ✗ | dx_ext1 = dx0 - (T)1.0 - SQUISH_CONSTANT; | |
| 316 | ✗ | dy_ext1 = dy0 - (T)1.0 - SQUISH_CONSTANT; | |
| 317 | ✗ | dz_ext1 = dz0 + (T)1.0 - SQUISH_CONSTANT; | |
| 318 | } | ||
| 319 | } | ||
| 320 | } else { | ||
| 321 | // One point is on the (0,0,0) side, one point is on the (1,1,1) side. | ||
| 322 | |||
| 323 | uint_fast8_t c1, c2; | ||
| 324 | ✗ | if (aIsFurtherSide) { | |
| 325 | c1 = aPoint; | ||
| 326 | c2 = bPoint; | ||
| 327 | } else { | ||
| 328 | c1 = bPoint; | ||
| 329 | c2 = aPoint; | ||
| 330 | } | ||
| 331 | |||
| 332 | // One contribution is a permutation of (1,1,-1). | ||
| 333 | ✗ | if (!(c1 & 0x01)) { | |
| 334 | ✗ | xsv_ext0 = xsb - 1; | |
| 335 | ✗ | ysv_ext0 = ysb + 1; | |
| 336 | ✗ | zsv_ext0 = zsb + 1; | |
| 337 | ✗ | dx_ext0 = dx0 + (T)1.0 - SQUISH_CONSTANT; | |
| 338 | ✗ | dy_ext0 = dy0 - (T)1.0 - SQUISH_CONSTANT; | |
| 339 | ✗ | dz_ext0 = dz0 - (T)1.0 - SQUISH_CONSTANT; | |
| 340 | ✗ | } else if (!(c1 & 0x02)) { | |
| 341 | ✗ | xsv_ext0 = xsb + 1; | |
| 342 | ✗ | ysv_ext0 = ysb - 1; | |
| 343 | ✗ | zsv_ext0 = zsb + 1; | |
| 344 | ✗ | dx_ext0 = dx0 - (T)1.0 - SQUISH_CONSTANT; | |
| 345 | ✗ | dy_ext0 = dy0 + (T)1.0 - SQUISH_CONSTANT; | |
| 346 | ✗ | dz_ext0 = dz0 - (T)1.0 - SQUISH_CONSTANT; | |
| 347 | } else { | ||
| 348 | ✗ | xsv_ext0 = xsb + 1; | |
| 349 | ✗ | ysv_ext0 = ysb + 1; | |
| 350 | ✗ | zsv_ext0 = zsb - 1; | |
| 351 | ✗ | dx_ext0 = dx0 - (T)1.0 - SQUISH_CONSTANT; | |
| 352 | ✗ | dy_ext0 = dy0 - (T)1.0 - SQUISH_CONSTANT; | |
| 353 | ✗ | dz_ext0 = dz0 + (T)1.0 - SQUISH_CONSTANT; | |
| 354 | } | ||
| 355 | |||
| 356 | // One contribution is a permutation of (0,0,2). | ||
| 357 | ✗ | if (c2 & 0x01) { | |
| 358 | ✗ | xsv_ext1 = xsb + 2; | |
| 359 | ysv_ext1 = ysb; | ||
| 360 | zsv_ext1 = zsb; | ||
| 361 | ✗ | dx_ext1 = dx0 - (T)2.0 - (SQUISH_CONSTANT * (T)2.0); | |
| 362 | ✗ | dy_ext1 = dy0 - (SQUISH_CONSTANT * (T)2.0); | |
| 363 | ✗ | dz_ext1 = dz0 - (SQUISH_CONSTANT * (T)2.0); | |
| 364 | ✗ | } else if (c2 & 0x02) { | |
| 365 | xsv_ext1 = xsb; | ||
| 366 | ✗ | ysv_ext1 = ysb + 2; | |
| 367 | zsv_ext1 = zsb; | ||
| 368 | ✗ | dx_ext1 = dx0 - (SQUISH_CONSTANT * (T)2.0); | |
| 369 | ✗ | dy_ext1 = dy0 - (T)2.0 - (SQUISH_CONSTANT * (T)2.0); | |
| 370 | ✗ | dz_ext1 = dz0 - (SQUISH_CONSTANT * (T)2.0); | |
| 371 | } else { | ||
| 372 | xsv_ext1 = xsb; | ||
| 373 | ysv_ext1 = ysb; | ||
| 374 | ✗ | zsv_ext1 = zsb + 2; | |
| 375 | ✗ | dx_ext1 = dx0 - (SQUISH_CONSTANT * (T)2.0); | |
| 376 | ✗ | dy_ext1 = dy0 - (SQUISH_CONSTANT * (T)2.0); | |
| 377 | ✗ | dz_ext1 = dz0 - (T)2.0 - (SQUISH_CONSTANT * (T)2.0); | |
| 378 | } | ||
| 379 | } | ||
| 380 | |||
| 381 | 380 | contr_m[0] = contr_ext[0] = 0.0; | |
| 382 | |||
| 383 | // Contribution (0,0,1). | ||
| 384 | 380 | T dx1 = dx0 - (T)1.0 - SQUISH_CONSTANT; | |
| 385 | 380 | T dy1 = dy0 - SQUISH_CONSTANT; | |
| 386 | 380 | T dz1 = dz0 - SQUISH_CONSTANT; | |
| 387 | 380 | contr_m[1] = pow2(dx1) + pow2(dy1) + pow2(dz1); | |
| 388 | 380 | contr_ext[1] = extrapolate(xsb + 1, ysb, zsb, dx1, dy1, dz1); | |
| 389 | |||
| 390 | // Contribution (0,1,0). | ||
| 391 | 380 | T dx2 = dx0 - SQUISH_CONSTANT; | |
| 392 | 380 | T dy2 = dy0 - (T)1.0 - SQUISH_CONSTANT; | |
| 393 | T dz2 = dz1; | ||
| 394 | 380 | contr_m[2] = pow2(dx2) + pow2(dy2) + pow2(dz2); | |
| 395 | 380 | contr_ext[2] = extrapolate(xsb, ysb + 1, zsb, dx2, dy2, dz2); | |
| 396 | |||
| 397 | // Contribution (1,0,0). | ||
| 398 | T dx3 = dx2; | ||
| 399 | T dy3 = dy1; | ||
| 400 | 380 | T dz3 = dz0 - (T)1.0 - SQUISH_CONSTANT; | |
| 401 | 380 | contr_m[3] = pow2(dx3) + pow2(dy3) + pow2(dz3); | |
| 402 | 380 | contr_ext[3] = extrapolate(xsb, ysb, zsb + 1, dx3, dy3, dz3); | |
| 403 | |||
| 404 | // Contribution (1,1,0). | ||
| 405 | 380 | T dx4 = dx0 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0); | |
| 406 | 380 | T dy4 = dy0 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0); | |
| 407 | 380 | T dz4 = dz0 - (SQUISH_CONSTANT * (T)2.0); | |
| 408 | 380 | contr_m[4] = pow2(dx4) + pow2(dy4) + pow2(dz4); | |
| 409 | 380 | contr_ext[4] = extrapolate(xsb + 1, ysb + 1, zsb, dx4, dy4, dz4); | |
| 410 | |||
| 411 | // Contribution (1,0,1). | ||
| 412 | T dx5 = dx4; | ||
| 413 | 380 | T dy5 = dy0 - (SQUISH_CONSTANT * (T)2.0); | |
| 414 | 380 | T dz5 = dz0 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0); | |
| 415 | 380 | contr_m[5] = pow2(dx5) + pow2(dy5) + pow2(dz5); | |
| 416 | 380 | contr_ext[5] = extrapolate(xsb + 1, ysb, zsb + 1, dx5, dy5, dz5); | |
| 417 | |||
| 418 | // Contribution (0,1,1). | ||
| 419 | 380 | T dx6 = dx0 - (SQUISH_CONSTANT * (T)2.0); | |
| 420 | T dy6 = dy4; | ||
| 421 | T dz6 = dz5; | ||
| 422 | 380 | contr_m[6] = pow2(dx6) + pow2(dy6) + pow2(dz6); | |
| 423 | 380 | contr_ext[6] = extrapolate(xsb, ysb + 1, zsb + 1, dx6, dy6, dz6); | |
| 424 | |||
| 425 |
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824 | } else if (inSum <= (T)1.0) { |
| 426 | // The point is inside the tetrahedron (3-Simplex) at (0,0,0) | ||
| 427 | |||
| 428 | // Determine which of (0,0,1), (0,1,0), (1,0,0) are closest. | ||
| 429 | uint_fast8_t aPoint = 1; | ||
| 430 | T aScore = xins; | ||
| 431 | uint_fast8_t bPoint = 2; | ||
| 432 | T bScore = yins; | ||
| 433 |
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696 | if (aScore < bScore && zins > aScore) { |
| 434 | aScore = zins; | ||
| 435 | aPoint = 4; | ||
| 436 |
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380 | } else if (aScore >= bScore && zins > bScore) { |
| 437 | bScore = zins; | ||
| 438 | bPoint = 4; | ||
| 439 | } | ||
| 440 | |||
| 441 | // Determine the two lattice points not part of the tetrahedron that may contribute. | ||
| 442 | // This depends on the closest two tetrahedral vertices, including (0,0,0). | ||
| 443 | 696 | T wins = (T)1.0 - inSum; | |
| 444 |
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696 | if (wins > aScore || wins > bScore) { |
| 445 | // (0,0,0) is one of the closest two tetrahedral vertices. | ||
| 446 | |||
| 447 | // The other closest vertex is the closer of a and b. | ||
| 448 |
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64 | uint_fast8_t c = ((bScore > aScore) ? bPoint : aPoint); |
| 449 | |||
| 450 |
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64 | if (c != 1) { |
| 451 | ✗ | xsv_ext0 = xsb - 1; | |
| 452 | xsv_ext1 = xsb; | ||
| 453 | ✗ | dx_ext0 = dx0 + (T)1.0; | |
| 454 | dx_ext1 = dx0; | ||
| 455 | } else { | ||
| 456 | 64 | xsv_ext0 = xsv_ext1 = xsb + 1; | |
| 457 | 64 | dx_ext0 = dx_ext1 = dx0 - (T)1.0; | |
| 458 | } | ||
| 459 | |||
| 460 |
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64 | if (c != 2) { |
| 461 | ysv_ext0 = ysv_ext1 = ysb; | ||
| 462 | dy_ext0 = dy_ext1 = dy0; | ||
| 463 |
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64 | if (c == 1) { |
| 464 | 64 | ysv_ext0 -= 1; | |
| 465 | 64 | dy_ext0 += (T)1.0; | |
| 466 | } else { | ||
| 467 | ✗ | ysv_ext1 -= 1; | |
| 468 | ✗ | dy_ext1 += (T)1.0; | |
| 469 | } | ||
| 470 | } else { | ||
| 471 | ✗ | ysv_ext0 = ysv_ext1 = ysb + 1; | |
| 472 | ✗ | dy_ext0 = dy_ext1 = dy0 - (T)1.0; | |
| 473 | } | ||
| 474 | |||
| 475 |
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64 | if (c != 4) { |
| 476 | zsv_ext0 = zsb; | ||
| 477 | 64 | zsv_ext1 = zsb - 1; | |
| 478 | dz_ext0 = dz0; | ||
| 479 | 64 | dz_ext1 = dz0 + (T)1.0; | |
| 480 | } else { | ||
| 481 | ✗ | zsv_ext0 = zsv_ext1 = zsb + 1; | |
| 482 | ✗ | dz_ext0 = dz_ext1 = dz0 - (T)1.0; | |
| 483 | } | ||
| 484 | } else { | ||
| 485 | // (0,0,0) is not one of the closest two tetrahedral vertices. | ||
| 486 | |||
| 487 | // The two extra vertices are determined by the closest two. | ||
| 488 | 632 | uint_fast8_t c = (aPoint | bPoint); | |
| 489 | |||
| 490 |
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632 | if (c & 0x01) { |
| 491 | 316 | xsv_ext0 = xsv_ext1 = xsb + 1; | |
| 492 | 316 | dx_ext0 = dx0 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0); | |
| 493 | 316 | dx_ext1 = dx0 - (T)1.0 - SQUISH_CONSTANT; | |
| 494 | } else { | ||
| 495 | xsv_ext0 = xsb; | ||
| 496 | 316 | xsv_ext1 = xsb - 1; | |
| 497 | 316 | dx_ext0 = dx0 - (SQUISH_CONSTANT * (T)2.0); | |
| 498 | 316 | dx_ext1 = dx0 + (T)1.0 - SQUISH_CONSTANT; | |
| 499 | } | ||
| 500 | |||
| 501 |
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632 | if (c & 0x02) { |
| 502 | 316 | ysv_ext0 = ysv_ext1 = ysb + 1; | |
| 503 | 316 | dy_ext0 = dy0 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0); | |
| 504 | 316 | dy_ext1 = dy0 - (T)1.0 - SQUISH_CONSTANT; | |
| 505 | } else { | ||
| 506 | ysv_ext0 = ysb; | ||
| 507 | 316 | ysv_ext1 = ysb - 1; | |
| 508 | 316 | dy_ext0 = dy0 - (SQUISH_CONSTANT * (T)2.0); | |
| 509 | 316 | dy_ext1 = dy0 + (T)1.0 - SQUISH_CONSTANT; | |
| 510 | } | ||
| 511 | |||
| 512 |
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632 | if (c & 0x04) { |
| 513 | 632 | zsv_ext0 = zsv_ext1 = zsb + 1; | |
| 514 | 632 | dz_ext0 = dz0 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0); | |
| 515 | 632 | dz_ext1 = dz0 - (T)1.0 - SQUISH_CONSTANT; | |
| 516 | } else { | ||
| 517 | zsv_ext0 = zsb; | ||
| 518 | ✗ | zsv_ext1 = zsb - 1; | |
| 519 | ✗ | dz_ext0 = dz0 - (SQUISH_CONSTANT * (T)2.0); | |
| 520 | ✗ | dz_ext1 = dz0 + (T)1.0 - SQUISH_CONSTANT; | |
| 521 | } | ||
| 522 | } | ||
| 523 | |||
| 524 | // Contribution (0,0,0) | ||
| 525 | { | ||
| 526 | 696 | contr_m[0] = pow2(dx0) + pow2(dy0) + pow2(dz0); | |
| 527 | 696 | contr_ext[0] = extrapolate(xsb, ysb, zsb, dx0, dy0, dz0); | |
| 528 | } | ||
| 529 | |||
| 530 | // Contribution (0,0,1) | ||
| 531 | 696 | T dx1 = dx0 - (T)1.0 - SQUISH_CONSTANT; | |
| 532 | 696 | T dy1 = dy0 - SQUISH_CONSTANT; | |
| 533 | 696 | T dz1 = dz0 - SQUISH_CONSTANT; | |
| 534 | 696 | contr_m[1] = pow2(dx1) + pow2(dy1) + pow2(dz1); | |
| 535 | 696 | contr_ext[1] = extrapolate(xsb + 1, ysb, zsb, dx1, dy1, dz1); | |
| 536 | |||
| 537 | // Contribution (0,1,0) | ||
| 538 | 696 | T dx2 = dx0 - SQUISH_CONSTANT; | |
| 539 | 696 | T dy2 = dy0 - (T)1.0 - SQUISH_CONSTANT; | |
| 540 | T dz2 = dz1; | ||
| 541 | 696 | contr_m[2] = pow2(dx2) + pow2(dy2) + pow2(dz2); | |
| 542 | 696 | contr_ext[2] = extrapolate(xsb, ysb + 1, zsb, dx2, dy2, dz2); | |
| 543 | |||
| 544 | // Contribution (1,0,0) | ||
| 545 | T dx3 = dx2; | ||
| 546 | T dy3 = dy1; | ||
| 547 | 696 | T dz3 = dz0 - (T)1.0 - SQUISH_CONSTANT; | |
| 548 | 696 | contr_m[3] = pow2(dx3) + pow2(dy3) + pow2(dz3); | |
| 549 | 696 | contr_ext[3] = extrapolate(xsb, ysb, zsb + 1, dx3, dy3, dz3); | |
| 550 | |||
| 551 | 696 | contr_m[4] = contr_m[5] = contr_m[6] = 0.0; | |
| 552 | 696 | contr_ext[4] = contr_ext[5] = contr_ext[6] = 0.0; | |
| 553 | |||
| 554 | } else { | ||
| 555 | // The point is inside the tetrahedron (3-Simplex) at (1,1,1) | ||
| 556 | |||
| 557 | // Determine which two tetrahedral vertices are the closest | ||
| 558 | // out of (1,1,0), (1,0,1), and (0,1,1), but not (1,1,1). | ||
| 559 | uint_fast8_t aPoint = 6; | ||
| 560 | T aScore = xins; | ||
| 561 | uint_fast8_t bPoint = 5; | ||
| 562 | T bScore = yins; | ||
| 563 |
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128 | if (aScore <= bScore && zins < bScore) { |
| 564 | bScore = zins; | ||
| 565 | bPoint = 3; | ||
| 566 |
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64 | } else if (aScore > bScore && zins < aScore) { |
| 567 | aScore = zins; | ||
| 568 | aPoint = 3; | ||
| 569 | } | ||
| 570 | |||
| 571 | // Determine the two lattice points not part of the tetrahedron that may contribute. | ||
| 572 | // This depends on the closest two tetrahedral vertices, including (1,1,1). | ||
| 573 | 128 | T wins = 3.0 - inSum; | |
| 574 |
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128 | if (wins < aScore || wins < bScore) { |
| 575 | // (1,1,1) is one of the closest two tetrahedral vertices. | ||
| 576 | |||
| 577 | // The other closest vertex is the closest of a and b. | ||
| 578 |
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64 | uint_fast8_t c = ((bScore < aScore) ? bPoint : aPoint); |
| 579 | |||
| 580 |
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64 | if (c & 0x01) { |
| 581 | ✗ | xsv_ext0 = xsb + 2; | |
| 582 | ✗ | xsv_ext1 = xsb + 1; | |
| 583 | ✗ | dx_ext0 = dx0 - (T)2.0 - (SQUISH_CONSTANT * (T)3.0); | |
| 584 | ✗ | dx_ext1 = dx0 - (T)1.0 - (SQUISH_CONSTANT * (T)3.0); | |
| 585 | } else { | ||
| 586 | xsv_ext0 = xsv_ext1 = xsb; | ||
| 587 | 64 | dx_ext0 = dx_ext1 = dx0 - (SQUISH_CONSTANT * (T)3.0); | |
| 588 | } | ||
| 589 | |||
| 590 |
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64 | if (c & 0x02) { |
| 591 | 64 | ysv_ext0 = ysv_ext1 = ysb + 1; | |
| 592 | 64 | dy_ext0 = dy_ext1 = dy0 - (T)1.0 - (SQUISH_CONSTANT * (T)3.0); | |
| 593 |
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64 | if (c & 0x01) { |
| 594 | ✗ | ysv_ext1 += 1; | |
| 595 | ✗ | dy_ext1 -= (T)1.0; | |
| 596 | } else { | ||
| 597 | 64 | ysv_ext0 += 1; | |
| 598 | 64 | dy_ext0 -= (T)1.0; | |
| 599 | } | ||
| 600 | } else { | ||
| 601 | ysv_ext0 = ysv_ext1 = ysb; | ||
| 602 | ✗ | dy_ext0 = dy_ext1 = dy0 - (SQUISH_CONSTANT * (T)3.0); | |
| 603 | } | ||
| 604 | |||
| 605 |
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64 | if (c & 0x04) { |
| 606 | 64 | zsv_ext0 = zsb + 1; | |
| 607 | 64 | zsv_ext1 = zsb + 2; | |
| 608 | 64 | dz_ext0 = dz0 - (T)1.0 - (SQUISH_CONSTANT * (T)3.0); | |
| 609 | 64 | dz_ext1 = dz0 - (T)2.0 - (SQUISH_CONSTANT * (T)3.0); | |
| 610 | } else { | ||
| 611 | zsv_ext0 = zsv_ext1 = zsb; | ||
| 612 | ✗ | dz_ext0 = dz_ext1 = dz0 - (SQUISH_CONSTANT * (T)3.0); | |
| 613 | } | ||
| 614 | } else { | ||
| 615 | // (1,1,1) is not one of the closest two tetrahedral vertices. | ||
| 616 | |||
| 617 | // The two extra vertices are determined by the closest two. | ||
| 618 | 64 | uint_fast8_t c = aPoint & bPoint; | |
| 619 | |||
| 620 |
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64 | if (c & 0x01) { |
| 621 | ✗ | xsv_ext0 = xsb + 1; | |
| 622 | ✗ | xsv_ext1 = xsb + 2; | |
| 623 | ✗ | dx_ext0 = dx0 - (T)1.0 - SQUISH_CONSTANT; | |
| 624 | ✗ | dx_ext1 = dx0 - (T)2.0 - (SQUISH_CONSTANT * (T)2.0); | |
| 625 | } else { | ||
| 626 | xsv_ext0 = xsv_ext1 = xsb; | ||
| 627 | 64 | dx_ext0 = dx0 - SQUISH_CONSTANT; | |
| 628 | 64 | dx_ext1 = dx0 - (SQUISH_CONSTANT * (T)2.0); | |
| 629 | } | ||
| 630 | |||
| 631 |
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64 | if (c & 0x02) { |
| 632 | 64 | ysv_ext0 = ysb + 1; | |
| 633 | 64 | ysv_ext1 = ysb + 2; | |
| 634 | 64 | dy_ext0 = dy0 - (T)1.0 - SQUISH_CONSTANT; | |
| 635 | 64 | dy_ext1 = dy0 - (T)2.0 - (SQUISH_CONSTANT * (T)2.0); | |
| 636 | } else { | ||
| 637 | ysv_ext0 = ysv_ext1 = ysb; | ||
| 638 | ✗ | dy_ext0 = dy0 - SQUISH_CONSTANT; | |
| 639 | ✗ | dy_ext1 = dy0 - (SQUISH_CONSTANT * (T)2.0); | |
| 640 | } | ||
| 641 | |||
| 642 |
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64 | if (c & 0x04) { |
| 643 | ✗ | zsv_ext0 = zsb + 1; | |
| 644 | ✗ | zsv_ext1 = zsb + 2; | |
| 645 | ✗ | dz_ext0 = dz0 - (T)1.0 - SQUISH_CONSTANT; | |
| 646 | ✗ | dz_ext1 = dz0 - (T)2.0 - (SQUISH_CONSTANT * (T)2.0); | |
| 647 | } else { | ||
| 648 | zsv_ext0 = zsv_ext1 = zsb; | ||
| 649 | 64 | dz_ext0 = dz0 - SQUISH_CONSTANT; | |
| 650 | 64 | dz_ext1 = dz0 - (SQUISH_CONSTANT * (T)2.0); | |
| 651 | } | ||
| 652 | } | ||
| 653 | |||
| 654 | // Contribution (1,1,0) | ||
| 655 | 128 | T dx3 = dx0 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0); | |
| 656 | 128 | T dy3 = dy0 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0); | |
| 657 | 128 | T dz3 = dz0 - (SQUISH_CONSTANT * (T)2.0); | |
| 658 | 128 | contr_m[3] = pow2(dx3) + pow2(dy3) + pow2(dz3); | |
| 659 | 128 | contr_ext[3] = extrapolate(xsb + 1, ysb + 1, zsb, dx3, dy3, dz3); | |
| 660 | |||
| 661 | // Contribution (1,0,1) | ||
| 662 | T dx2 = dx3; | ||
| 663 | 128 | T dy2 = dy0 - (SQUISH_CONSTANT * (T)2.0); | |
| 664 | 128 | T dz2 = dz0 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0); | |
| 665 | 128 | contr_m[2] = pow2(dx2) + pow2(dy2) + pow2(dz2); | |
| 666 | 128 | contr_ext[2] = extrapolate(xsb + 1, ysb, zsb + 1, dx2, dy2, dz2); | |
| 667 | |||
| 668 | // Contribution (0,1,1) | ||
| 669 | { | ||
| 670 | 128 | T dx1 = dx0 - (SQUISH_CONSTANT * (T)2.0); | |
| 671 | T dy1 = dy3; | ||
| 672 | T dz1 = dz2; | ||
| 673 | 128 | contr_m[1] = pow2(dx1) + pow2(dy1) + pow2(dz1); | |
| 674 | 128 | contr_ext[1] = extrapolate(xsb, ysb + 1, zsb + 1, dx1, dy1, dz1); | |
| 675 | } | ||
| 676 | |||
| 677 | // Contribution (1,1,1) | ||
| 678 | { | ||
| 679 | 128 | dx0 = dx0 - (T)1.0 - (SQUISH_CONSTANT * (T)3.0); | |
| 680 | 128 | dy0 = dy0 - (T)1.0 - (SQUISH_CONSTANT * (T)3.0); | |
| 681 | 128 | dz0 = dz0 - (T)1.0 - (SQUISH_CONSTANT * (T)3.0); | |
| 682 | 128 | contr_m[0] = pow2(dx0) + pow2(dy0) + pow2(dz0); | |
| 683 | 128 | contr_ext[0] = extrapolate(xsb + 1, ysb + 1, zsb + 1, dx0, dy0, dz0); | |
| 684 | } | ||
| 685 | |||
| 686 | 128 | contr_m[4] = contr_m[5] = contr_m[6] = 0.0; | |
| 687 | 128 | contr_ext[4] = contr_ext[5] = contr_ext[6] = 0.0; | |
| 688 | |||
| 689 | } | ||
| 690 | |||
| 691 | // First extra vertex. | ||
| 692 | 1204 | contr_m[7] = pow2(dx_ext0) + pow2(dy_ext0) + pow2(dz_ext0); | |
| 693 | 1204 | contr_ext[7] = extrapolate(xsv_ext0, ysv_ext0, zsv_ext0, dx_ext0, dy_ext0, dz_ext0); | |
| 694 | |||
| 695 | // Second extra vertex. | ||
| 696 | 1204 | contr_m[8] = pow2(dx_ext1) + pow2(dy_ext1) + pow2(dz_ext1); | |
| 697 | 1204 | contr_ext[8] = extrapolate(xsv_ext1, ysv_ext1, zsv_ext1, dx_ext1, dy_ext1, dz_ext1); | |
| 698 | |||
| 699 | T value = 0.0; | ||
| 700 |
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12040 | for (int i=0; i<9; ++i) { |
| 701 |
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12104 | value += pow4(std::max((T)2.0 - contr_m[i], (T)0.0)) * contr_ext[i]; |
| 702 | } | ||
| 703 | |||
| 704 | 1204 | return (value * NORM_CONSTANT); | |
| 705 | } | ||
| 706 | |||
| 707 | template OPENVDB_AX_API double OSNoise::extrapolate(const OSNoise::inttype xsb, const OSNoise::inttype ysb, const OSNoise::inttype zsb, | ||
| 708 | const double dx, const double dy, const double dz) const; | ||
| 709 | template OPENVDB_AX_API double OSNoise::extrapolate(const OSNoise::inttype xsb, const OSNoise::inttype ysb, const OSNoise::inttype zsb, | ||
| 710 | const double dx, const double dy, const double dz, | ||
| 711 | double (&de) [3]) const; | ||
| 712 | |||
| 713 | template OPENVDB_AX_API double OSNoise::eval(const double x, const double y, const double z) const; | ||
| 714 | |||
| 715 | } // namespace OSN | ||
| 716 |