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Comparing deliantra/server/common/noise.C (file contents):
Revision 1.6 by root, Sat Apr 23 05:42:11 2011 UTC vs.
Revision 1.17 by root, Sun May 1 08:19:17 2011 UTC

… …
22 22
23#include "noise.h" 23#include "noise.h"
24 24
25///////////////////////////////////////////////////////////////////////////// 25/////////////////////////////////////////////////////////////////////////////
26 26
27// perl -e 'for(0..255) { $p = (atan2 1,0) / 64 * $_; printf " %10g, %10g,\n", sin $p, cos $p }' | sort -R
28static const float charges2[256][2] = {
29 -.975702, -.219101, .893224, .449611, .870087, -.492898, .595699, -.803208,
30 .14673, .989177, .995185, .0980171, .91421, -.405241, -.514103, .857729,
31 -.985278, -.170962, -.689541, -.724247, -.427555, .903989, .83147, -.55557,
32 .999699, -.0245412, .634393, .77301, -.514103, -.857729, -.0735646, -.99729,
33 .514103, -.857729, -.595699, -.803208, -.290285, .95694, .595699, .803208,
34 .266713, .963776, -.33689, .941544, .492898, -.870087, -.471397, -.881921,
35 -.99729, -.0735646, .615232, -.788346, -.91421, -.405241, -.575808, .817585,
36 .0980171, .995185, -.980785, .19509, -.122411, -.99248, .0735646, .99729,
37 -.634393, .77301, -.91421, .405241, .99248, .122411, .903989, -.427555,
38 -.24298, .970031, -.857729, .514103, -.359895, .932993, .382683, .92388,
39 .740951, -.671559, -.893224, .449611, -.95694, -.290285, -.975702, .219101,
40 -.970031, .24298, .999699, .0245412, -.405241, .91421, .985278, .170962,
41 .382683, -.92388, .95694, -.290285, .707107, -.707107, -.817585, -.575808,
42 -.989177, .14673, -.19509, -.980785, -.359895, -.932993, .313682, .949528,
43 -.0980171, .995185, 1, 6.12323e-17, .963776, -.266713, .998795, -.0490677,
44 -.998795, -.0490677, -.970031, -.24298, -.55557, .83147, -.14673, .989177,
45 -.83147, -.55557, -.995185, -.0980171, .870087, .492898, .941544, -.33689,
46 .575808, -.817585, .33689, .941544, .19509, -.980785, 0, 1,
47 .219101, -.975702, -.83147, .55557, .757209, -.653173, -.95694, .290285,
48 -.266713, .963776, -.0490677, .998795, .405241, .91421, -.405241, -.91421,
49 -.689541, .724247, -.534998, -.844854, -.99248, -.122411, .724247, .689541,
50 .492898, .870087, .817585, -.575808, .740951, .671559, -.33689, -.941544,
51 .95694, .290285, .77301, -.634393, .0245412, -.999699, -.77301, -.634393,
52 -.382683, .92388, -.24298, -.970031, -.893224, -.449611, .449611, .893224,
53 .975702, -.219101, -.382683, -.92388, .844854, .534998, -.803208, -.595699,
54 .941544, .33689, .963776, .266713, .932993, .359895, -.0735646, .99729,
55 .634393, -.77301, .405241, -.91421, .33689, -.941544, .99729, .0735646,
56 1.22465e-16, -1, -.941544, -.33689, .0490677, -.998795, -.313682, .949528,
57 .92388, .382683, -.999699, .0245412, .0245412, .999699, .653173, .757209,
58 -.803208, .595699, .980785, -.19509, .817585, .575808, .975702, .219101,
59 -.615232, -.788346, .99248, -.122411, .998795, .0490677, -.707107, .707107,
60 .803208, -.595699, .671559, .740951, -.757209, -.653173, -.949528, .313682,
61 -.989177, -.14673, -.817585, .575808, -.14673, -.989177, -1, -1.83697e-16,
62 .290285, .95694, -.932993, -.359895, .24298, -.970031, .170962, .985278,
63 -.671559, -.740951, .427555, .903989, .427555, -.903989, -.941544, .33689,
64 -.492898, -.870087, -.266713, -.963776, .857729, -.514103, -.724247, .689541,
65 .724247, -.689541, -.653173, .757209, .689541, -.724247, .949528, -.313682,
66 -.19509, .980785, -.740951, .671559, -.999699, -.0245412, .689541, .724247,
67 .803208, .595699, -.170962, .985278, .0735646, -.99729, .970031, -.24298,
68 -.170962, -.985278, .471397, .881921, .91421, .405241, .893224, -.449611,
69 .0490677, .998795, -.615232, .788346, -.998795, .0490677, -.427555, -.903989,
70 -.0245412, .999699, -.534998, .844854, -.313682, -.949528, -.55557, -.83147,
71 -.903989, -.427555, -.724247, -.689541, -.740951, -.671559, .985278, -.170962,
72 -.857729, -.514103, -.99729, .0735646, .881921, -.471397, .534998, .844854,
73 .359895, -.932993, .77301, .634393, .99729, -.0735646, .290285, -.95694,
74 .575808, .817585, .757209, .653173, .903989, .427555, -.995185, .0980171,
75 -.903989, .427555, -.844854, .534998, -.707107, -.707107, -.92388, .382683,
76 -.653173, -.757209, -.881921, -.471397, -.219101, .975702, -.595699, .803208,
77 .0980171, -.995185, -.788346, .615232, -.0980171, -.995185, -.985278, .170962,
78 .122411, .99248, -.449611, -.893224, .170962, -.985278, .788346, .615232,
79 -.492898, .870087, .671559, -.740951, .449611, -.893224, -.757209, .653173,
80 .83147, .55557, -.290285, -.95694, -.932993, .359895, -.870087, -.492898,
81 .266713, -.963776, -.881921, .471397, -.77301, .634393, -.471397, .881921,
82 .844854, -.534998, .707107, .707107, .534998, -.844854, .514103, .857729,
83 .14673, -.989177, .980785, .19509, -.122411, .99248, -.449611, .893224,
84 .995185, -.0980171, -.634393, -.77301, .857729, .514103, .55557, .83147,
85 -.92388, -.382683, -.844854, -.534998, -.963776, .266713, .989177, -.14673,
86 .313682, -.949528, .359895, .932993, .24298, .970031, -.949528, -.313682,
87 .932993, -.359895, .55557, -.83147, .615232, .788346, -.788346, -.615232,
88 -.0245412, -.999699, -.219101, -.975702, .788346, -.615232, -.99248, .122411,
89 -.671559, .740951, -.870087, .492898, .970031, .24298, .881921, .471397,
90 .122411, -.99248, .471397, -.881921, .19509, .980785, -.963776, -.266713,
91 .92388, -.382683, .989177, .14673, -.575808, -.817585, .219101, .975702,
92 -.0490677, -.998795, -.980785, -.19509, .949528, .313682, .653173, -.757209,
93};
94
27// http://www-wales.ch.cam.ac.uk/~wales/CCD/Thomson/table.html, random permutation 95// http://www-wales.ch.cam.ac.uk/~wales/CCD/Thomson/table.html, random permutation
28// used as gradient vectors for noise3d 96// used as gradient vectors for noise3d
29static const float charges[256][3] = { 97static const float charges3[256][3] = {
30 6.32096444e-01, -6.11406706e-01, 4.76062943e-01, 5.19172442e-01, 8.08229585e-01, -2.77893708e-01, 98 6.32096444e-01, -6.11406706e-01, 4.76062943e-01, 5.19172442e-01, 8.08229585e-01, -2.77893708e-01,
31 -8.81072422e-01, -4.68301230e-01, 6.63727731e-02, -1.92122323e-01, 9.81341519e-01, -7.60505942e-03, 99 -8.81072422e-01, -4.68301230e-01, 6.63727731e-02, -1.92122323e-01, 9.81341519e-01, -7.60505942e-03,
32 -2.57478265e-01, 9.34157733e-01, -2.47091628e-01, 8.75501090e-01, -1.48087600e-01, -4.59965112e-01, 100 -2.57478265e-01, 9.34157733e-01, -2.47091628e-01, 8.75501090e-01, -1.48087600e-01, -4.59965112e-01,
33 -6.44086082e-01, 3.21868600e-01, 6.93940720e-01, -4.42053435e-01, -1.94962529e-01, -8.75544615e-01, 101 -6.44086082e-01, 3.21868600e-01, 6.93940720e-01, -4.42053435e-01, -1.94962529e-01, -8.75544615e-01,
34 -6.86776297e-01, 5.34610386e-01, -4.92473403e-01, -8.45541961e-01, -2.41708225e-01, 4.76062943e-01, 102 -6.86776297e-01, 5.34610386e-01, -4.92473403e-01, -8.45541961e-01, -2.41708225e-01, 4.76062943e-01,
… …
158}; 226};
159 227
160///////////////////////////////////////////////////////////////////////////// 228/////////////////////////////////////////////////////////////////////////////
161 229
162template<int N, typename T> 230template<int N, typename T>
163template<class random_generator>
164void 231void
165permutation<N,T>::seed (random_generator &rng) 232permutation<N,T>::seed (seedable_rand_gen &rng)
166{ 233{
167 for (int i = 0; i < N; ++i) 234 for (int i = 0; i < N; ++i)
168 pmap[i] = i; 235 pmap[i] = i;
169 236
170 // fisher-yates to randomly perturb 237 // fisher-yates to randomly perturb
… …
174 241
175template class permutation<256, uint8_t>; 242template class permutation<256, uint8_t>;
176 243
177///////////////////////////////////////////////////////////////////////////// 244/////////////////////////////////////////////////////////////////////////////
178 245
179static vec2d 246template<class vec_t>
180floor (vec2d v) 247void
248noise_gen_base<vec_t>::seed (seedable_rand_gen &rng)
181{ 249{
182 return vec2d (std::floor (v[0]), std::floor (v[1])); 250 for (int i = 0; i < array_length (rvmap); ++i)
251 rvmap[i].seed (rng);
183} 252}
184 253
185static vec3d 254template<class vec_t>
186floor (vec3d v) 255void
187{ 256noise_gen_base<vec_t>::seed (seed_t seed)
188 return vec3d (std::floor (v[0]), std::floor (v[1]), std::floor (v[2]));
189}
190
191noise_gen<vec2d>::noise_gen (uint32_t seed)
192{ 257{
193 seedable_rand_gen rng (seed); 258 seedable_rand_gen rng (seed);
194 259
195#if 0 260 this->seed (rng);
196 for (int i = 0; i < 256; ++i)
197 {
198 vec2d rv (rng () - 0.5f, rng () - 0.5f);
199
200 // normalise
201 float mag = 1.f / sqrtf (dot (rv, rv));
202
203 rv[0] *= mag;
204 rv[1] *= mag;
205
206 rvec[i] = rv;
207 }
208#endif
209
210#if 1
211 float offset = rng () * M_PI;
212
213 for (int i = 0; i < 256; ++i)
214 {
215 float phi = i * (M_PI * 2 / 256) + offset;
216
217 rvec[i][0] = sinf (phi);
218 rvec[i][1] = -cosf (phi);
219 }
220
221 // fisher-yates to randomly perturb
222 for (int i = 256; --i; )
223 ::swap (rvec [i], rvec [rng (i + 1)]);
224#endif
225
226 rvmap[0].seed (rng);
227 rvmap[1].seed (rng);
228} 261}
229 262
263template<>
230vec2d::T_numtype 264vec2d::T_numtype
231noise_gen<vec2d>::operator() (vec2d P) 265noise_gen_base<vec2d>::operator() (vec2d P, uint32_t seed)
232{ 266{
233 vec2d I = floor (P); 267 vec2d I = floor (P);
234 vec2d F = P - I; 268 vec2d F = P - I;
235 269
236 float v = 0; 270 value_t v = 0;
271
272 seed *= 3039177861;
273 uint8_t i1 = uint8_t (I[1]) + (seed >> 16);
274 uint8_t i0 = uint8_t (I[0]) + (seed >> 8);
275
276 uint8_t h2 = rvmap[2](seed);
237 277
238 for (int j = -1; j <= 2; ++j) 278 for (int j = -1; j <= 2; ++j)
279 {
280 uint8_t h1 = rvmap[1](i1 + j) ^ h2;
281
239 for (int i = -1; i <= 2; ++i) 282 for (int i = -1; i <= 2; ++i)
240 { 283 {
241 vec2d A = F - vec2d (i, j); 284 vec2d A = F - vec2d (i, j);
242
243 float d = dot (A, A); 285 value_t d = dot (A, A);
244 286
245 if (d < 4) 287 if (d < 4)
246 { 288 {
247 float t1 = 1 - d / 4; 289 value_t t1 = 1 - d / 4;
248 float t2 = t1 * t1; 290 value_t t2 = t1 * t1;
249 float t4 = t2 * t2; 291 value_t t4 = t2 * t2;
250 292
251 float p = (4 * t1 - 3) * t4; 293 value_t p = (4 * t1 - 3) * t4;
252 294
253 int h = rvmap [0](I[0] + i) ^ rvmap [1](I[1] + j); 295 uint8_t h = rvmap[0](i0 + i) ^ h1;
254 vec2d G = rvec [h & 0xff]; 296 vec2d G = charges2[h & 0xff];
255 297
256 v += dot (A, G) * p; 298 v += dot (A, G) * p;
257 } 299 }
258 } 300 }
301 }
259 302
260 return clamp (v, -.9999999f, .9999999f); 303 return v;
261} 304}
262 305
263///////////////////////////////////////////////////////////////////////////// 306/////////////////////////////////////////////////////////////////////////////
264 307
265noise_gen<vec3d>::noise_gen (uint32_t seed) 308template<>
266{
267 seedable_rand_gen rng (seed);
268
269 rvmap [0].seed (rng);
270 rvmap [1].seed (rng);
271 rvmap [2].seed (rng);
272}
273
274vec3d::T_numtype 309vec3d::T_numtype
275noise_gen<vec3d>::operator() (vec3d P) 310noise_gen_base<vec3d>::operator() (vec3d P, uint32_t seed)
276{ 311{
277 vec3d I = floor (P); 312 vec3d I = floor (P);
278 vec3d F = P - I; 313 vec3d F = P - I;
279 314
280 float v = 0; 315 seed *= 3039177861;
316 uint8_t i2 = uint8_t (I[2]) + (seed >> 24);
317 uint8_t i1 = uint8_t (I[1]) + (seed >> 16);
318 uint8_t i0 = uint8_t (I[0]) + (seed >> 8);
281 319
282 for (int j = -1; j <= 2; ++j) 320 uint8_t h3 = rvmap[3](seed);
283 for (int i = -1; i <= 2; ++i) 321
322 value_t v = 0;
323
284 for (int k = -1; k <= 2; ++k) 324 for (int k = -1; k <= 2; ++k)
325 {
326 uint8_t h2 = rvmap[2](i2 + k) ^ h3;
327
328 for (int j = -1; j <= 2; ++j)
285 { 329 {
286 vec3d A = F - vec3d (i, j, k); 330 uint8_t h1 = rvmap[1](i1 + j) ^ h2;
287 float d = dot (A, A);
288 331
289 if (d < 4) 332 for (int i = -1; i <= 2; ++i)
290 { 333 {
291 float t1 = 1 - d / 4;
292 float t2 = t1 * t1;
293 float t4 = t2 * t2;
294
295 // (4t⁵ - 3t⁴)
296 float p = (4 * t1 - 3) * t4;
297
298 int h = rvmap[0](I[0] + i) ^ rvmap[1](I[1] + j) ^ rvmap[2](I[2] + k);
299 const float *G = charges[h & 0xff];
300
301 v += dot (A, vec3d (G[0], G[1], G[2])) * p;
302 }
303 }
304
305 return clamp (v * 2, -.9999999f, .9999999f);
306}
307
308vec3d::T_numtype
309noise_gen<vec3d>::operator() (vec3d P, vec3d N)
310{
311 vec3d I = floor (P);
312 vec3d F = P - I;
313
314 float v = 0;
315
316 for (int j = -1; j <= 2; ++j)
317 for (int i = -1; i <= 2; ++i)
318 for (int k = -1; k <= 2; ++k)
319 {
320 vec3d D = F - vec3d (i, j, k); 334 vec3d A = F - vec3d (i, j, k);
321 float e = dot (D, N);
322 float o = 1 - abs (e);
323
324 if (o > 0)
325 {
326 vec3d A = D - e * N;
327 float d = dot (A, A); 335 value_t d = dot (A, A);
328 336
329 if (d < 4) 337 if (d < 4)
330 { 338 {
331 float t1 = 1 - d / 4; 339 value_t t1 = 1 - d / 4;
332 float t2 = t1 * t1; 340 value_t t2 = t1 * t1;
333 float t4 = t2 * t2; 341 value_t t4 = t2 * t2;
334 342
335 float o2 = o * o;
336
337 // (4t⁵ - 3t⁴) * (3o³ - 2o²) 343 // (4t⁵ - 3t⁴)
338 // alternative? ((o * 6 - 15) * o + 10) * o³ 344 value_t p = (4 * t1 - 3) * t4;
339 float p = (4 * t1 - 3) * t4 * (3 * o2 - 2 * o2 * o);
340 345
341 int h = rvmap[0](I[0] + i) ^ rvmap[1](I[1] + j) ^ rvmap[2](I[2] + k); 346 uint8_t h = rvmap[0](i0 + i) ^ h1;
342 const float *G = charges[h & 0xff]; 347 const value_t *G = charges3[h & 0xff];
343 348
344 v += dot (A, vec3d (G[0], G[1], G[2])) * p; 349 v += dot (A, vec3d (G[0], G[1], G[2])) * p;
345 } 350 }
346 } 351 }
347 } 352 }
353 }
348 354
349 return clamp (v, -.9999999f, .9999999f); 355 return v * 2;
356}
357
358vec3d::T_numtype
359noise_gen<vec3d>::operator() (vec3d P, vec3d N, uint32_t seed)
360{
361 vec3d I = floor (P);
362 vec3d F = P - I;
363
364 seed *= 3039177861;
365 uint8_t i2 = uint8_t (I[2]) + (seed >> 24);
366 uint8_t i1 = uint8_t (I[1]) + (seed >> 16);
367 uint8_t i0 = uint8_t (I[0]) + (seed >> 8);
368
369 uint8_t h3 = rvmap[3](seed);
370
371 value_t v = 0;
372
373 for (int k = -1; k <= 2; ++k)
374 {
375 uint8_t h2 = rvmap[2](i2 + k) ^ h3;
376
377 for (int j = -1; j <= 2; ++j)
378 {
379 uint8_t h1 = rvmap[1](i1 + j) ^ h2;
380
381 for (int i = -1; i <= 2; ++i)
382 {
383 vec3d D = F - vec3d (i, j, k);
384 value_t e = dot (D, N);
385 value_t o = 1 - abs (e);
386
387 if (o > 0)
388 {
389 vec3d A = D - e * N;
390 value_t d = dot (A, A);
391
392 if (d < 4)
393 {
394 value_t t1 = 1 - d / 4;
395 value_t t2 = t1 * t1;
396 value_t t4 = t2 * t2;
397
398 value_t o2 = o * o;
399
400 // (4t⁵ - 3t⁴) * (3o³ - 2o²)
401 // alternative? ((o * 6 - 15) * o + 10) * o³
402 value_t p = (4 * t1 - 3) * t4 * (3 * o2 - 2 * o2 * o);
403
404 uint8_t h = rvmap[0](i0 + i) ^ h1;
405 const value_t *G = charges3[h & 0xff];
406
407 v += dot (A, vec3d (G[0], G[1], G[2])) * p;
408 }
409 }
410 }
411 }
412 }
413
414 return v;
350} 415}
351 416
352template class noise_gen<vec2d>; 417template class noise_gen<vec2d>;
353template class noise_gen<vec3d>; 418template class noise_gen<vec3d>;
354 419
355///////////////////////////////////////////////////////////////////////////// 420/////////////////////////////////////////////////////////////////////////////
356 421
357template<class vec_t> 422template<class vec_t>
358static vec_t 423frac_gen<vec_t>::frac_gen (int octaves, value_t lacunarity, value_t hurst_expo, seed_t seed)
359ith_octave (vec_t P, int i) 424: octaves (octaves), lac (lacunarity), h (hurst_expo)
360{ 425{
361 vec_t r = P; 426 this->seed (seed);
362 r[0] += i;
363 return r;
364}
365 427
366template<class vec_t>
367frac_gen<vec_t>::frac_gen (value_t hurst_expo, value_t lacunarity)
368: h (hurst_expo), lac (lacunarity), noise_gen<vec_t> (0)
369{
370 value_t exsum = 0; 428 value_t exsum = 0;
429 value_t phi = noise (vec_t (value_t (0))) * 0.5 + 1;
371 430
372 for (int i = 0; i < MAX_OCTAVES; ++i) 431 for (int i = 0; i < octaves; ++i)
373 { 432 {
374 ex [i] = powf (lac, -h * i); 433 ex [i] = pow (lac, -h * i);
375 exsum += ex [i]; 434 exsum += ex [i];
376 fbm_mul [i] = 0.5f / (exsum * 0.75f); // .75f is a heuristic 435 fbm_mul [i] = 0.5 / (exsum * 0.75); // .75 is a heuristic
377 rot [i].set (0.4488f * i); 436 rot [i].set (phi * i + 1);
378 } 437 }
379} 438}
380 439
381template<class vec_t> 440template<class vec_t>
382typename frac_gen<vec_t>::value_t 441typename frac_gen<vec_t>::value_t
383frac_gen<vec_t>::fBm (vec_t P, int octaves) 442frac_gen<vec_t>::fBm (vec_t P)
384{ 443{
385 value_t v = 0.f; 444 value_t v = 0;
386 445
387 for (int i = 0; i < octaves; ++i) 446 for (int i = 0; i < octaves; ++i)
388 { 447 {
389 rot [i](P); 448 rot [i](P);
390 v += noise (ith_octave (P, i)) * ex [i]; 449 v += noise (P, i) * ex [i];
391 P *= lac; 450 P *= lac;
392 } 451 }
393 452
394 return clamp (v * fbm_mul [octaves - 1] + 0.5f, 0.f, .9999999f); 453 return v * fbm_mul [octaves - 1];
395} 454}
396 455
397template<class vec_t> 456template<class vec_t>
398typename frac_gen<vec_t>::value_t 457typename frac_gen<vec_t>::value_t
399frac_gen<vec_t>::turbulence (vec_t P, int octaves) 458frac_gen<vec_t>::turbulence (vec_t P)
400{ 459{
401 value_t v = 0.f; 460 value_t v = 0;
402 461
403 for (int i = 0; i < octaves; ++i) 462 for (int i = 0; i < octaves; ++i)
404 { 463 {
405 rot [i](P); 464 rot [i](P);
406 v += abs (noise (ith_octave (P, i))) * ex [i]; 465 v += abs (noise (P, i)) * ex [i];
407 P *= lac; 466 P *= lac;
408 } 467 }
409 468
410 return clamp (v * fbm_mul [octaves - 1] * 2.f, 0.f, .9999999f); 469 return v * fbm_mul [octaves - 1] * (0.5 / noise_gen<vec_t>::abs_avg ());
411} 470}
412 471
413template<class vec_t> 472template<class vec_t>
414typename frac_gen<vec_t>::value_t 473typename frac_gen<vec_t>::value_t
415frac_gen<vec_t>::multifractal (vec_t P, int octaves, value_t offset) 474frac_gen<vec_t>::multifractal (vec_t P, value_t offset)
416{ 475{
417 value_t v = 1.f; 476 value_t v = 1;
418 477
419 for (int i = 0; i < octaves; ++i) 478 for (int i = 0; i < octaves; ++i)
420 { 479 {
421 rot [i](P); 480 rot [i](P);
422 v *= noise (P) * ex [i] + offset; 481 v *= noise (P) * ex [i] + offset;
423 P *= lac; 482 P *= lac;
424 } 483 }
425 484
426 return clamp (v * 0.5f, 0.f, .9999999f); 485 return v * value_t (0.5);
427} 486}
428 487
429template<class vec_t> 488template<class vec_t>
430typename frac_gen<vec_t>::value_t 489typename frac_gen<vec_t>::value_t
431frac_gen<vec_t>::heterofractal (vec_t P, int octaves, value_t offset) 490frac_gen<vec_t>::heterofractal (vec_t P, value_t offset)
432{ 491{
433 value_t v = noise (P) + offset; 492 value_t v = noise (P) + offset;
434 int i;
435 493
436 for (i = 1; i < octaves; ++i) 494 for (int i = 1; i < octaves; ++i)
437 { 495 {
438 rot [i](P); 496 rot [i](P);
439 P *= lac; 497 P *= lac;
440 v += v * (noise (P) * ex [i] + offset); 498 v += v * (noise (P) * ex [i] + offset);
441 } 499 }
442 500
443 return v / powf (2., octaves); 501 return v / (1 << octaves);
444} 502}
445 503
446template<class vec_t> 504template<class vec_t>
447typename frac_gen<vec_t>::value_t 505typename frac_gen<vec_t>::value_t
448frac_gen<vec_t>::hybridfractal (vec_t P, int octaves, value_t offset, value_t gain) 506frac_gen<vec_t>::hybridfractal (vec_t P, value_t offset, value_t gain)
449{ 507{
450 value_t v = (noise (P) + offset) * ex [0]; 508 value_t v = (noise (P) + offset) * ex [0];
451 value_t weight = v; 509 value_t weight = v;
452 int i;
453 510
454 for (i = 1; i < octaves; ++i) 511 for (int i = 1; i < octaves; ++i)
455 { 512 {
456 rot [i](P); 513 rot [i](P);
457 P *= lac; 514 P *= lac;
458 515
459 min_it (weight, 1.f); 516 min_it (weight, 1);
460 517
461 value_t sig = (noise (P) + offset) * ex [i]; 518 value_t sig = (noise (P) + offset) * ex [i];
462 v += weight * sig; 519 v += weight * sig;
463 weight *= gain * sig; 520 weight *= gain * sig;
464 } 521 }
465 522
466 return clamp (v * 0.5f + 0.5f, 0.f, .9999999f); 523 return v * value_t (0.5) + value_t (0.5);
467} 524}
468 525
469template<class vec_t> 526template<class vec_t>
470typename frac_gen<vec_t>::value_t 527typename frac_gen<vec_t>::value_t
471frac_gen<vec_t>::ridgedmultifractal (vec_t P, int octaves, value_t offset, value_t gain) 528frac_gen<vec_t>::ridgedmultifractal (vec_t P, value_t offset, value_t gain)
472{ 529{
473 value_t sig = offset - abs (noise (P)); 530 value_t sig = offset - abs (noise (P));
474 sig *= sig; 531 sig *= sig;
475 value_t v = sig; 532 value_t v = sig;
476 533
477 for (int i = 1; i < octaves; ++i) 534 for (int i = 1; i < octaves; ++i)
478 { 535 {
479 rot [i](P); 536 rot [i](P);
480 P *= lac; 537 P *= lac;
481 538
539 // weight higher octaves by previous signal
482 value_t w = clamp (sig * gain, 0.f, 1.f); 540 value_t w = clamp (sig * gain, 0, 1);
483 541
484 sig = offset - abs (noise (P)); 542 sig = offset - abs (noise (P));
485 sig *= sig; 543 sig *= sig;
486 sig *= w; 544 sig *= w;
487 545
488 v += sig * ex [i]; 546 v += sig * ex [i];
489 } 547 }
490 548
491 return clamp (v * 0.25f, 0.f, .9999999f); 549 return v * value_t (0.25);
550}
551
552template<class vec_t>
553typename frac_gen<vec_t>::value_t
554frac_gen<vec_t>::billowfractal (vec_t P, value_t offset, value_t gain)
555{
556 value_t v = 0;
557
558 offset += 2 * noise_gen<vec_t>::abs_avg () - 1;
559
560 for (int i = 0; i < octaves; ++i)
561 {
562 rot [i](P);
563 v += (abs (noise (P, i)) * gain - offset) * ex [i];
564 P *= lac;
565 }
566
567 return v;
492} 568}
493 569
494// http://www.gamasutra.com/view/feature/3098/a_realtime_procedural_universe_.php?page=2 570// http://www.gamasutra.com/view/feature/3098/a_realtime_procedural_universe_.php?page=2
495template<class vec_t> 571template<class vec_t>
496typename frac_gen<vec_t>::value_t 572typename frac_gen<vec_t>::value_t
497frac_gen<vec_t>::terrain (vec_t P, int octaves) 573frac_gen<vec_t>::terrain (vec_t P)
498{ 574{
499 value_t v = 0.f; 575 value_t v = 0;
500 576
501 for (int i = 0; i < octaves; ++i) 577 for (int i = 0; i < octaves; ++i)
502 { 578 {
503 rot [i](P); 579 rot [i](P);
504 v += noise (P) * ex [i]; 580 v += noise (P) * ex [i];
505 P *= lac; 581 P *= lac;
506 } 582 }
507 583
508 v *= fbm_mul [octaves - 1]; 584 v *= fbm_mul [octaves - 1];
509 585
510 return v <= 0.f ? - powf (-v, 0.7f) : powf (v, 1. + noise (P) * v); 586 return v <= 0 ? - pow (-v, 0.7) : pow (v, 1 + noise (P) * v);
511} 587}
512 588
513template<class vec_t> 589template<class vec_t>
514typename frac_gen<vec_t>::value_t 590typename frac_gen<vec_t>::value_t
515frac_gen<vec_t>::terrain2 (vec_t P, int octaves) 591frac_gen<vec_t>::terrain2 (vec_t P)
516{ 592{
517 value_t a = fBm (P, octaves); 593 value_t a = fBm (P);
518 value_t b = ridgedmultifractal (P, octaves, 1, 8); 594 value_t b = ridgedmultifractal (P, 1, 8);
519 value_t fade = fBm (P + vec_t(10.3), octaves); 595 value_t fade = fBm (P + vec_t(10.3));
520 596
521 const value_t width = 0.05f; 597 const value_t width = 0.05;
522 598
523 if (fade > 0.5f + width) 599 if (fade > 0.5 + width)
524 return a; 600 return a;
525 else if (fade < 0.5f - width) 601 else if (fade < 0.5 - width)
526 return b; 602 return b;
527 603
528 fade = (fade - 0.5f + width) / (width * 2); 604 fade = (fade - 0.5 + width) / (width * 2);
529 605
530 // sigmoidal curve 606 // sigmoidal curve
531 fade = fade * fade * 2 * (1.5f - fade); 607 fade = fade * fade * 2 * (1.5 - fade);
532 608
533 return a * fade + b * (1 - fade); 609 return a * fade + b * (1 - fade);
534} 610}
535 611
536template class frac_gen<vec2d>; 612template class frac_gen<vec2d>;
537template class frac_gen<vec3d>; 613template class frac_gen<vec3d>;
538 614
539///////////////////////////////////////////////////////////////////////////// 615/////////////////////////////////////////////////////////////////////////////
540 616
617template<typename T, typename U>
618T
619inline border_blend (T a, T b, vec2d P, U N, U W)
620{
621 U border = W; // within n places of the border
622
623 min_it (border, P [0]);
624 min_it (border, N - P [0]);
625 min_it (border, P [1]);
626 min_it (border, N - P [1]);
627
628 return blend (a, b,border, U(0), W);
629}
630
631// highest mountains, deepest sea == 200 .. -200
632
633#define FANCY_GRAPHICS 1
634
635static void
636gen_quadspace (int x, int y, int z)
637{
638 vec2d P = vec2d (x, y);
639
640 const int deep_sea_z = -200;
641 const int mountain_z = 200;
642
643 static frac2d gen(13);
644
645 static frac2d vec_gen1 (6, 2, 0.5, 1);
646 static frac2d vec_gen2 (6, 2, 0.5, 2);
647
648 const float continent_scale = 0.00008;
649
650 vec2d perturb_pos = pow (P, 1.4) * 1e-5;
651
652 vec2d perturb (
653 vec_gen1.fBm (perturb_pos),
654 vec_gen2.fBm (perturb_pos)
655 );
656
657 float perturb_perturb = 1 - (P[1] - P[0]) * (1. / 25000 / 2);
658 perturb_perturb = perturb_perturb * perturb_perturb * 0.4;
659 perturb *= perturb_perturb;
660
661 vec2d P_continent = P * continent_scale + perturb;
662
663 static frac2d continent_gen (13, 2.13, 0.5);
664 float continent = continent_gen.fBm (P_continent) + 0.05f;
665
666 float x_gradient = P[0] * (1. / 25000);
667 float y_gradient = P[1] * (1. / 25000);
668 float xy_gradient = (P[0] + P[1]) * (0.5 / 25000);
669
670 const float N = (25000 - 1) * continent_scale;
671
672 // we clip a large border on the perturbed shape, to get irregular coastline
673 // and then clip a smaller border around the real shape
674 continent = border_blend (-1.f, continent, P_continent , N, 400 * continent_scale);
675 continent = border_blend (-1.f, continent, P * continent_scale + perturb * 0.1, N, 100 * continent_scale);
676
677 enum {
678 T_NONE,
679 T_OCEAN,
680 T_RIVER,
681 T_VALLEY,
682 T_MOUNTAIN,
683 T_UNDERGROUND,
684 T_ACQUIFER,
685 } t = T_NONE;
686
687 vec3d c;
688 int h = 1000000; // height form heightmap
689
690 // the continent increases in height from 0 to ~700 levels in the absence of anything else
691 // thats about one step every 7 maps.
692 int base_height = blend (0, 300, xy_gradient, 0.2f, 0.9f);
693 int river_height = base_height * 9 / 10;
694
695 // add this to rivers to "dry them out"
696 float dry_out = max (0.f, lerp (xy_gradient, 0.7f, 1.f, 0.f, 0.3f));
697
698 static frac2d river_gen (2);
699 float river1 = abs (river_gen.fBm (P * 0.001 + perturb * 4)) + dry_out;
700 float river2 = river_gen.ridgedmultifractal (P * 0.04, 0.8, 10) - y_gradient * 0.2 - 0.16 - dry_out;
701
702 float valley = river1 - 0.2f;
703
704 static frac2d mountain_gen (8, 2.14, 0.5);
705 float mountain = mountain_gen.ridgedmultifractal (P * 0.004);
706
707 t = valley < 0 ? T_VALLEY : T_MOUNTAIN;
708 c = blend0 (vec3d (0, 0.8, 0), vec3d (0.8, 0, 0), valley, 0.1f);
709 h = blend0 (base_height + continent * 300, base_height + mountain * xy_gradient * 400, valley, 0.1f);
710
711 if (river1 < 0.01f)
712 {
713 // main rivers - they cut deeply into the mountains (base_height * 0.9f)
714 t = T_RIVER;
715 c = vec3d (0.2, 0.2, 1);
716 min_it (h, river_height + lerp<float> (river1, 0.f, 0.01f, -20, -1));
717 }
718
719 if (river2 > 0)
720 {
721 t = T_RIVER;
722 c = vec3d (0.2, 0.2, 1);
723 min_it (h, river_height + lerp<float> (river1, 0.f, 0.01f, -5, -1));
724 }
725
726 if (continent < 0)
727 {
728 t = T_OCEAN;
729 min_it (h, min (continent * 200, -1));
730 c = vec3d (0, 0, 1);
731 }
732
733 // now we have the base height, and base terrain
734
735#if FANCY_GRAPHICS
736 z = h; // show the surface, not the given z layer
737#endif
738
739 // everything below the surface is underground, or a variant
740 if (z < h)
741 {
742 t = T_UNDERGROUND;
743 }
744
745 // put acquifers a bit below the surface, to reduce them leaking out (will still happen)
746 if (z < h - 3)
747 {
748 static frac3d acquifer_gen (4);
749 float acquifer = acquifer_gen.ridgedmultifractal (vec3d (x * 0.001, y * 0.001, z * 0.01), 1.003, 2);
750
751 if (acquifer > 0.48)
752 {
753 t = T_ACQUIFER;
754 c = vec3d (1,1,1);
755 }
756 }
757
758 // TODO: caves
759 // TODO: chees areas
760 // TODO: minerals
761 // TODO: monsters
762
763#if FANCY_GRAPHICS
764 float v = clamp (lerp<float> (h, deep_sea_z, mountain_z*0+800, 0.f, 1.f), 0.f, 1.f);
765 c *= v;
766
767 putc (clamp<int> (255 * c[0], 0, 255), stdout);
768 putc (clamp<int> (255 * c[1], 0, 255), stdout);
769 putc (clamp<int> (255 * c[2], 0, 255), stdout);
770#endif
771}
772
773void noise_test ();
774void noise_test ()
775{
541#if 0 776#if 0
542void hack(); void hack()
543{
544 frac_gen<vec2d> gen (0.5, 2);
545 frac_gen<vec3d> gen3;
546
547#if 0
548 int N = 1024; 777 int Nw = 700;
549 778
550 printf ("P5 %d %d 255\n", N, N); 779 printf ("P6 %d %d 255\n", Nw * 3, Nw * 2);
551 // pmake&&server/deliantra-server >x&&convert -depth 8 -size 512xx512 gray:x x.ppm&& cv x.ppm 780 // pmake&&server/deliantra-server >x&&convert -depth 8 -size 512xx512 gray:x x.ppm&& cv x.ppm
552 for (int y = 0; y < N; ++y) 781 for (int y = 0; y < Nw; ++y)
553 { 782 {
554 if (!(y&63))fprintf (stderr, "y %d\n", y);//D 783 if (!(y&63))fprintf (stderr, "y %d\n", y * 50 / Nw);//D
784
785 for (int x = 0; x < Nw; ++x) gen_quadspace (x * 25000 / Nw, y * 25000 / Nw, 0);
786
787 for (int x = 0; x < Nw; ++x) gen_quadspace (x + 400, y, 0);
788 for (int x = 0; x < Nw; ++x) gen_quadspace (x + 22000, y + 2000, 0);
789 }
555 for (int x = 0; x < N; ++x) 790 for (int y = 0; y < Nw; ++y)
556 { 791 {
792 if (!(y&63))fprintf (stderr, "y %d\n", y * 50 / Nw+50);//D
793
794 for (int x = 0; x < Nw; ++x) gen_quadspace (x + 1000, y + 22000, 0);
795 for (int x = 0; x < Nw; ++x) gen_quadspace (x + 12500, y + 12500, 0);
796 for (int x = 0; x < Nw; ++x) gen_quadspace (x + 22000, y + 22500, 0);
797 }
798
557 //putc (127 * n.noise (x * 0.1, y * 0.1, 0, 0,0,1) + 128, stdout); 799 //putc (127 * gen.noise (vec2d (x * 0.01, y * 0.01)) + 128, stdout);
558 //putc (256 * gen.terrain2 (x * 0.004, y * 0.004, 8), stdout); 800 //putc (256 * gen.terrain2 (x * 0.004, y * 0.004, 8), stdout);
559 //putc (256 * gen.fBm (x * 0.01, y * 0.01, 3), stdout); 801 //putc (256 * gen.fBm (vec2d(x * 0.01, y * 0.01), 16), stdout);
560 //putc (256 * gen.turbulence (x * 0.004 - 1, y * 0.004 - 1, 8), stdout); 802 //putc (256 * gen.turbulence (vec2d (x * 0.004 - 1, y * 0.004 - 1), 10), stdout);
561 //putc (256 * gen.heterofractal (x * 0.008, y * 0.008, 8, 0.9), stdout); 803 //putc (256 * gen.heterofractal (vec2d (x * 0.008, y * 0.008), 8, 0.9), stdout);
562
563 // mountais or somesuch(?)
564 //putc (256 * gen.hybridfractal (x * 0.01, y * 0.01, 8, -.4, -4), stdout); 804 //putc (256 * gen.hybridfractal (vec2d (x * 0.01, y * 0.01), 8, -.4, -4), stdout);
565
566 // temperature
567 //putc (256 * gen.fBm (x * 0.002, y * 0.002, 2), stdout); 805 //putc (256 * gen.fBm (vec2d (x * 0.002, y * 0.002), 2), stdout);
568 // rain 806 //putc (127.49 * gen.billowfractal (vec2d (x * 0.01, y * 0.01), 9) + 128, stdout);
569 //putc (256 * gen.ridgedmultifractal (x * 0.01, y * 0.01, 3, 1.03, 2), stdout);
570 }
571 }
572#else 807#else
573 int N = 512; 808 int N = 200;
574 809
575 //printf ("P6 %d %d 255\n", N, N); 810 //printf ("P6 %d %d 255\n", N, N);
576 // pmake&&server/deliantra-server >x&&convert -depth 8 -size 512xx512 gray:x x.ppm&& cv x.ppm 811 // pmake&&server/deliantra-server >x&&convert -depth 8 -size 512xx512 gray:x x.ppm&& cv x.ppm
577 for (int z = 0; z < N; ++z) 812 for (int z = 0; z < N; ++z)
578 { 813 {
579 if (!(z&7))fprintf (stderr, "z %d\n", z);//D 814 if (!(z&7))fprintf (stderr, "z %d\n", z);//D
580 for (int y = 0; y < N; ++y) 815 for (int y = 0; y < N; ++y)
581 for (int x = 0; x < N; ++x) 816 for (int x = 0; x < N; ++x)
582 { 817 {
583 float v = gen3.ridgedmultifractal (vec3d (x * 0.01 + 0.2, y * 0.01 + 0.2, z * 0.01 + 0.2), 3, 1.03, 2) * 2;
584
585#if 0 818#if 0
819 float v = gen3.ridgedmultifractal (vec3d (x * 0.001 + 0.2, y * 0.001 + 0.2, z * 0.01 + 0.2), 1.03, 2) * 2;
820
586 if (z < 64) 821 if (z < 64)
587 v = v * (z * z) / (64 * 64); 822 v = v * (z * z) / (64 * 64);
823
824 if (v <= 0.9)
825 continue;
588#endif 826#endif
827 static frac3d gen3 (10);
828 //float v = gen3.turbulence (vec3d (x * 0.01, y * 0.01, z * 0.01));
829 float v = gen3.ridgedmultifractal (vec3d (x * 0.001, y * 0.001, z * 0.001), 1.003, 2);
589 830
590 if (v <= 0.9999) 831 if (v <= 0.48) continue;
591 continue;
592 832
593 float r[4]; 833 float r[4];
594 int i[4]; 834 int i[4];
595 835
596 r[0] = x; 836 r[0] = x;
… …
610 } 850 }
611#endif 851#endif
612 852
613 exit (0); 853 exit (0);
614} 854}
615#endif

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