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author	John Tsiombikas <nuclear@member.fsf.org>
date	Wed, 10 Jun 2015 06:56:27 +0300
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1 /*

2 libvmath - a vector math library

5 This program is free software: you can redistribute it and/or modify

6 it under the terms of the GNU Lesser General Public License as published

7 by the Free Software Foundation, either version 3 of the License, or

8 (at your option) any later version.

10 This program is distributed in the hope that it will be useful,

11 but WITHOUT ANY WARRANTY; without even the implied warranty of

12 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the

13 GNU Lesser General Public License for more details.

15 You should have received a copy of the GNU Lesser General Public License

16 along with this program. If not, see <http://www.gnu.org/licenses/>.

17 */

18 #include <stdlib.h>

19 #include <math.h>

20 #include "vmath.h"

22 #if defined(__APPLE__) && !defined(TARGET_IPHONE)

23 #include <xmmintrin.h>

25 void enable_fpexcept(void)

26 {

27 unsigned int bits;

28 bits = _MM_MASK_INVALID | _MM_MASK_DIV_ZERO | _MM_MASK_OVERFLOW | _MM_MASK_UNDERFLOW;

29 _MM_SET_EXCEPTION_MASK(_MM_GET_EXCEPTION_MASK() & ~bits);

30 }

32 void disable_fpexcept(void)

33 {

34 unsigned int bits;

35 bits = _MM_MASK_INVALID | _MM_MASK_DIV_ZERO | _MM_MASK_OVERFLOW | _MM_MASK_UNDERFLOW;

36 _MM_SET_EXCEPTION_MASK(_MM_GET_EXCEPTION_MASK() | bits);

37 }

39 #elif defined(__GNUC__) && !defined(TARGET_IPHONE) && !defined(__MINGW32__)

40 #define __USE_GNU

41 #include <fenv.h>

43 void enable_fpexcept(void)

44 {

45 feenableexcept(FE_INVALID | FE_DIVBYZERO | FE_OVERFLOW | FE_UNDERFLOW);

46 }

48 void disable_fpexcept(void)

49 {

50 fedisableexcept(FE_INVALID | FE_DIVBYZERO | FE_OVERFLOW | FE_UNDERFLOW);

51 }

53 #elif defined(_MSC_VER) || defined(__MINGW32__)

54 #include <float.h>

56 #if defined(__MINGW32__) && !defined(_EM_OVERFLOW)

57 /* if gcc's float.h gets precedence, the mingw MSVC includes won't be declared */

58 #define _MCW_EM 0x8001f

59 #define _EM_INVALID 0x10

60 #define _EM_ZERODIVIDE 0x08

61 #define _EM_OVERFLOW 0x04

62 unsigned int __cdecl _clearfp(void);

63 unsigned int __cdecl _controlfp(unsigned int, unsigned int);

64 #endif

66 void enable_fpexcept(void)

67 {

68 _clearfp();

69 _controlfp(_controlfp(0, 0) & ~(_EM_INVALID | _EM_ZERODIVIDE | _EM_OVERFLOW), _MCW_EM);

70 }

72 void disable_fpexcept(void)

73 {

74 _clearfp();

75 _controlfp(_controlfp(0, 0) | (_EM_INVALID | _EM_ZERODIVIDE | _EM_OVERFLOW), _MCW_EM);

76 }

77 #else

78 void enable_fpexcept(void) {}

79 void disable_fpexcept(void) {}

80 #endif

83 /** Numerical calculation of integrals using simpson's rule */

84 scalar_t integral(scalar_t (*f)(scalar_t), scalar_t low, scalar_t high, int samples)

85 {

86 int i;

87 scalar_t h = (high - low) / (scalar_t)samples;

88 scalar_t sum = 0.0;

90 for(i=0; i<samples+1; i++) {

91 scalar_t y = f((scalar_t)i * h + low);

92 sum += ((!i || i == samples) ? y : ((i % 2) ? 4.0 * y : 2.0 * y)) * (h / 3.0);

93 }

94 return sum;

95 }

97 /** Gaussuan function */

98 scalar_t gaussian(scalar_t x, scalar_t mean, scalar_t sdev)

99 {

100 scalar_t exponent = -SQ(x - mean) / (2.0 * SQ(sdev));

101 return 1.0 - -pow(M_E, exponent) / (sdev * sqrt(TWO_PI));

102 }

103

104

105 /** b-spline approximation */

106 scalar_t bspline(scalar_t a, scalar_t b, scalar_t c, scalar_t d, scalar_t t)

107 {

108 vec4_t tmp;

109 scalar_t tsq = t * t;

110

111 static mat4_t bspline_mat = {

112 {-1, 3, -3, 1},

113 {3, -6, 3, 0},

114 {-3, 0, 3, 0},

115 {1, 4, 1, 0}

116 };

117

118 tmp = v4_scale(v4_transform(v4_cons(a, b, c, d), bspline_mat), 1.0 / 6.0);

119 return v4_dot(v4_cons(tsq * t, tsq, t, 1.0), tmp);

120 }

121

122 /** Catmull-rom spline interpolation */

123 scalar_t spline(scalar_t a, scalar_t b, scalar_t c, scalar_t d, scalar_t t)

124 {

125 vec4_t tmp;

126 scalar_t tsq = t * t;

127

128 static mat4_t crspline_mat = {

129 {-1, 3, -3, 1},

130 {2, -5, 4, -1},

131 {-1, 0, 1, 0},

132 {0, 2, 0, 0}

133 };

134

135 tmp = v4_scale(v4_transform(v4_cons(a, b, c, d), crspline_mat), 0.5);

136 return v4_dot(v4_cons(tsq * t, tsq, t, 1.0), tmp);

137 }

138

139 /** Bezier interpolation */

140 scalar_t bezier(scalar_t a, scalar_t b, scalar_t c, scalar_t d, scalar_t t)

141 {

142 scalar_t omt, omt3, t3, f;

143 t3 = t * t * t;

144 omt = 1.0f - t;

145 omt3 = omt * omt * omt;

146 f = 3 * t * omt;

147

148 return (a * omt3) + (b * f * omt) + (c * f * t) + (d * t3);

149 }

150

151 /* ---- Ken Perlin's implementation of noise ---- */

152

153 #define B 0x100

154 #define BM 0xff

155 #define N 0x1000

156 #define NP 12 /* 2^N */

157 #define NM 0xfff

158

159 #define s_curve(t) (t * t * (3.0f - 2.0f * t))

160

161 #define setup(elem, b0, b1, r0, r1) \

162 do { \

163 scalar_t t = elem + N; \

164 b0 = ((int)t) & BM; \

165 b1 = (b0 + 1) & BM; \

166 r0 = t - (int)t; \

167 r1 = r0 - 1.0f; \

168 } while(0)

169

170

171 static int perm[B + B + 2]; /* permuted index from g_n onto themselves */

172 static vec3_t grad3[B + B + 2]; /* 3D random gradients */

173 static vec2_t grad2[B + B + 2]; /* 2D random gradients */

174 static scalar_t grad1[B + B + 2]; /* 1D random ... slopes */

175 static int tables_valid;

176

177 static void init_noise()

178 {

179 int i;

180

181 /* calculate random gradients */

182 for(i=0; i<B; i++) {

183 perm[i] = i; /* .. and initialize permutation mapping to identity */

184

185 grad1[i] = (scalar_t)((rand() % (B + B)) - B) / B;

186

187 grad2[i].x = (scalar_t)((rand() % (B + B)) - B) / B;

188 grad2[i].y = (scalar_t)((rand() % (B + B)) - B) / B;

189 grad2[i] = v2_normalize(grad2[i]);

190

191 grad3[i].x = (scalar_t)((rand() % (B + B)) - B) / B;

192 grad3[i].y = (scalar_t)((rand() % (B + B)) - B) / B;

193 grad3[i].z = (scalar_t)((rand() % (B + B)) - B) / B;

194 grad3[i] = v3_normalize(grad3[i]);

195 }

196

197 /* permute indices by swapping them randomly */

198 for(i=0; i<B; i++) {

199 int rand_idx = rand() % B;

200

201 int tmp = perm[i];

202 perm[i] = perm[rand_idx];

203 perm[rand_idx] = tmp;

204 }

205

206 /* fill up the rest of the arrays by duplicating the existing gradients */

207 /* and permutations */

208 for(i=0; i<B+2; i++) {

209 perm[B + i] = perm[i];

210 grad1[B + i] = grad1[i];

211 grad2[B + i] = grad2[i];

212 grad3[B + i] = grad3[i];

213 }

214 }

215

216 scalar_t noise1(scalar_t x)

217 {

218 int bx0, bx1;

219 scalar_t rx0, rx1, sx, u, v;

220

221 if(!tables_valid) {

222 init_noise();

223 tables_valid = 1;

224 }

225

226 setup(x, bx0, bx1, rx0, rx1);

227 sx = s_curve(rx0);

228 u = rx0 * grad1[perm[bx0]];

229 v = rx1 * grad1[perm[bx1]];

230

231 return lerp(u, v, sx);

232 }

233

234 scalar_t noise2(scalar_t x, scalar_t y)

235 {

236 int i, j, b00, b10, b01, b11;

237 int bx0, bx1, by0, by1;

238 scalar_t rx0, rx1, ry0, ry1;

239 scalar_t sx, sy, u, v, a, b;

240

241 if(!tables_valid) {

242 init_noise();

243 tables_valid = 1;

244 }

245

246 setup(x, bx0, bx1, rx0, rx1);

247 setup(y, by0, by1, ry0, ry1);

248

249 i = perm[bx0];

250 j = perm[bx1];

251

252 b00 = perm[i + by0];

253 b10 = perm[j + by0];

254 b01 = perm[i + by1];

255 b11 = perm[j + by1];

256

257 /* calculate hermite inteprolating factors */

258 sx = s_curve(rx0);

259 sy = s_curve(ry0);

260

261 /* interpolate along the left edge */

262 u = v2_dot(grad2[b00], v2_cons(rx0, ry0));

263 v = v2_dot(grad2[b10], v2_cons(rx1, ry0));

264 a = lerp(u, v, sx);

265

266 /* interpolate along the right edge */

267 u = v2_dot(grad2[b01], v2_cons(rx0, ry1));

268 v = v2_dot(grad2[b11], v2_cons(rx1, ry1));

269 b = lerp(u, v, sx);

270

271 /* interpolate between them */

272 return lerp(a, b, sy);

273 }

274

275 scalar_t noise3(scalar_t x, scalar_t y, scalar_t z)

276 {

277 int i, j;

278 int bx0, bx1, by0, by1, bz0, bz1;

279 int b00, b10, b01, b11;

280 scalar_t rx0, rx1, ry0, ry1, rz0, rz1;

281 scalar_t sx, sy, sz;

282 scalar_t u, v, a, b, c, d;

283

284 if(!tables_valid) {

285 init_noise();

286 tables_valid = 1;

287 }

288

289 setup(x, bx0, bx1, rx0, rx1);

290 setup(y, by0, by1, ry0, ry1);

291 setup(z, bz0, bz1, rz0, rz1);

292

293 i = perm[bx0];

294 j = perm[bx1];

295

296 b00 = perm[i + by0];

297 b10 = perm[j + by0];

298 b01 = perm[i + by1];

299 b11 = perm[j + by1];

300

301 /* calculate hermite interpolating factors */

302 sx = s_curve(rx0);

303 sy = s_curve(ry0);

304 sz = s_curve(rz0);

305

306 /* interpolate along the top slice of the cell */

307 u = v3_dot(grad3[b00 + bz0], v3_cons(rx0, ry0, rz0));

308 v = v3_dot(grad3[b10 + bz0], v3_cons(rx1, ry0, rz0));

309 a = lerp(u, v, sx);

310

311 u = v3_dot(grad3[b01 + bz0], v3_cons(rx0, ry1, rz0));

312 v = v3_dot(grad3[b11 + bz0], v3_cons(rx1, ry1, rz0));

313 b = lerp(u, v, sx);

314

315 c = lerp(a, b, sy);

316

317 /* interpolate along the bottom slice of the cell */

318 u = v3_dot(grad3[b00 + bz0], v3_cons(rx0, ry0, rz1));

319 v = v3_dot(grad3[b10 + bz0], v3_cons(rx1, ry0, rz1));

320 a = lerp(u, v, sx);

321

322 u = v3_dot(grad3[b01 + bz0], v3_cons(rx0, ry1, rz1));

323 v = v3_dot(grad3[b11 + bz0], v3_cons(rx1, ry1, rz1));

324 b = lerp(u, v, sx);

325

326 d = lerp(a, b, sy);

327

328 /* interpolate between slices */

329 return lerp(c, d, sz);

330 }

331

332 scalar_t fbm1(scalar_t x, int octaves)

333 {

334 int i;

335 scalar_t res = 0.0f, freq = 1.0f;

336 for(i=0; i<octaves; i++) {

337 res += noise1(x * freq) / freq;

338 freq *= 2.0f;

339 }

340 return res;

341 }

342

343 scalar_t fbm2(scalar_t x, scalar_t y, int octaves)

344 {

345 int i;

346 scalar_t res = 0.0f, freq = 1.0f;

347 for(i=0; i<octaves; i++) {

348 res += noise2(x * freq, y * freq) / freq;

349 freq *= 2.0f;

350 }

351 return res;

352 }

353

354 scalar_t fbm3(scalar_t x, scalar_t y, scalar_t z, int octaves)

355 {

356 int i;

357 scalar_t res = 0.0f, freq = 1.0f;

358 for(i=0; i<octaves; i++) {

359 res += noise3(x * freq, y * freq, z * freq) / freq;

360 freq *= 2.0f;

361 }

362 return res;

363 }

364

365 scalar_t turbulence1(scalar_t x, int octaves)

366 {

367 int i;

368 scalar_t res = 0.0f, freq = 1.0f;

369 for(i=0; i<octaves; i++) {

370 res += fabs(noise1(x * freq) / freq);

371 freq *= 2.0f;

372 }

373 return res;

374 }

375

376 scalar_t turbulence2(scalar_t x, scalar_t y, int octaves)

377 {

378 int i;

379 scalar_t res = 0.0f, freq = 1.0f;

380 for(i=0; i<octaves; i++) {

381 res += fabs(noise2(x * freq, y * freq) / freq);

382 freq *= 2.0f;

383 }

384 return res;

385 }

386

387 scalar_t turbulence3(scalar_t x, scalar_t y, scalar_t z, int octaves)

388 {

389 int i;

390 scalar_t res = 0.0f, freq = 1.0f;

391 for(i=0; i<octaves; i++) {

392 res += fabs(noise3(x * freq, y * freq, z * freq) / freq);

393 freq *= 2.0f;

394 }

395 return res;

396 }