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annotate libs/vmath/vmath.c @ 0:b2f14e535253

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author John Tsiombikas <nuclear@member.fsf.org>
date Sat, 01 Feb 2014 19:58:19 +0200
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nuclear@0 1 /*
nuclear@0 2 libvmath - a vector math library
nuclear@0 3 Copyright (C) 2004-2011 John Tsiombikas <nuclear@member.fsf.org>
nuclear@0 4
nuclear@0 5 This program is free software: you can redistribute it and/or modify
nuclear@0 6 it under the terms of the GNU Lesser General Public License as published
nuclear@0 7 by the Free Software Foundation, either version 3 of the License, or
nuclear@0 8 (at your option) any later version.
nuclear@0 9
nuclear@0 10 This program is distributed in the hope that it will be useful,
nuclear@0 11 but WITHOUT ANY WARRANTY; without even the implied warranty of
nuclear@0 12 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
nuclear@0 13 GNU Lesser General Public License for more details.
nuclear@0 14
nuclear@0 15 You should have received a copy of the GNU Lesser General Public License
nuclear@0 16 along with this program. If not, see <http://www.gnu.org/licenses/>.
nuclear@0 17 */
nuclear@0 18 #include <stdlib.h>
nuclear@0 19 #include <math.h>
nuclear@0 20 #include "vmath.h"
nuclear@0 21
nuclear@0 22 #if defined(__APPLE__) && !defined(TARGET_IPHONE)
nuclear@0 23 #include <xmmintrin.h>
nuclear@0 24
nuclear@0 25 void enable_fpexcept(void)
nuclear@0 26 {
nuclear@0 27 unsigned int bits;
nuclear@0 28 bits = _MM_MASK_INVALID | _MM_MASK_DIV_ZERO | _MM_MASK_OVERFLOW | _MM_MASK_UNDERFLOW;
nuclear@0 29 _MM_SET_EXCEPTION_MASK(_MM_GET_EXCEPTION_MASK() & ~bits);
nuclear@0 30 }
nuclear@0 31
nuclear@0 32 void disable_fpexcept(void)
nuclear@0 33 {
nuclear@0 34 unsigned int bits;
nuclear@0 35 bits = _MM_MASK_INVALID | _MM_MASK_DIV_ZERO | _MM_MASK_OVERFLOW | _MM_MASK_UNDERFLOW;
nuclear@0 36 _MM_SET_EXCEPTION_MASK(_MM_GET_EXCEPTION_MASK() | bits);
nuclear@0 37 }
nuclear@0 38
nuclear@0 39 #elif defined(__GNUC__) && !defined(TARGET_IPHONE)
nuclear@0 40 #define __USE_GNU
nuclear@0 41 #include <fenv.h>
nuclear@0 42
nuclear@0 43 void enable_fpexcept(void)
nuclear@0 44 {
nuclear@0 45 feenableexcept(FE_INVALID | FE_DIVBYZERO | FE_OVERFLOW | FE_UNDERFLOW);
nuclear@0 46 }
nuclear@0 47
nuclear@0 48 void disable_fpexcept(void)
nuclear@0 49 {
nuclear@0 50 fedisableexcept(FE_INVALID | FE_DIVBYZERO | FE_OVERFLOW | FE_UNDERFLOW);
nuclear@0 51 }
nuclear@0 52
nuclear@0 53 #elif defined(_MSC_VER)
nuclear@0 54 #include <float.h>
nuclear@0 55
nuclear@0 56 void enable_fpexcept(void)
nuclear@0 57 {
nuclear@0 58 _clearfp();
nuclear@0 59 _controlfp(_controlfp(0, 0) & ~(_EM_INVALID | _EM_ZERODIVIDE | _EM_OVERFLOW), _MCW_EM);
nuclear@0 60 }
nuclear@0 61
nuclear@0 62 void disable_fpexcept(void)
nuclear@0 63 {
nuclear@0 64 _clearfp();
nuclear@0 65 _controlfp(_controlfp(0, 0) | (_EM_INVALID | _EM_ZERODIVIDE | _EM_OVERFLOW), _MCW_EM);
nuclear@0 66 }
nuclear@0 67 #else
nuclear@0 68 void enable_fpexcept(void) {}
nuclear@0 69 void disable_fpexcept(void) {}
nuclear@0 70 #endif
nuclear@0 71
nuclear@0 72
nuclear@0 73 /** Numerical calculation of integrals using simpson's rule */
nuclear@0 74 scalar_t integral(scalar_t (*f)(scalar_t), scalar_t low, scalar_t high, int samples)
nuclear@0 75 {
nuclear@0 76 int i;
nuclear@0 77 scalar_t h = (high - low) / (scalar_t)samples;
nuclear@0 78 scalar_t sum = 0.0;
nuclear@0 79
nuclear@0 80 for(i=0; i<samples+1; i++) {
nuclear@0 81 scalar_t y = f((scalar_t)i * h + low);
nuclear@0 82 sum += ((!i || i == samples) ? y : ((i % 2) ? 4.0 * y : 2.0 * y)) * (h / 3.0);
nuclear@0 83 }
nuclear@0 84 return sum;
nuclear@0 85 }
nuclear@0 86
nuclear@0 87 /** Gaussuan function */
nuclear@0 88 scalar_t gaussian(scalar_t x, scalar_t mean, scalar_t sdev)
nuclear@0 89 {
nuclear@0 90 scalar_t exponent = -SQ(x - mean) / (2.0 * SQ(sdev));
nuclear@0 91 return 1.0 - -pow(M_E, exponent) / (sdev * sqrt(TWO_PI));
nuclear@0 92 }
nuclear@0 93
nuclear@0 94
nuclear@0 95 /** b-spline approximation */
nuclear@0 96 scalar_t bspline(scalar_t a, scalar_t b, scalar_t c, scalar_t d, scalar_t t)
nuclear@0 97 {
nuclear@0 98 vec4_t tmp;
nuclear@0 99 scalar_t tsq = t * t;
nuclear@0 100
nuclear@0 101 static mat4_t bspline_mat = {
nuclear@0 102 {-1, 3, -3, 1},
nuclear@0 103 {3, -6, 3, 0},
nuclear@0 104 {-3, 0, 3, 0},
nuclear@0 105 {1, 4, 1, 0}
nuclear@0 106 };
nuclear@0 107
nuclear@0 108 tmp = v4_scale(v4_transform(v4_cons(a, b, c, d), bspline_mat), 1.0 / 6.0);
nuclear@0 109 return v4_dot(v4_cons(tsq * t, tsq, t, 1.0), tmp);
nuclear@0 110 }
nuclear@0 111
nuclear@0 112 /** Catmull-rom spline interpolation */
nuclear@0 113 scalar_t spline(scalar_t a, scalar_t b, scalar_t c, scalar_t d, scalar_t t)
nuclear@0 114 {
nuclear@0 115 vec4_t tmp;
nuclear@0 116 scalar_t tsq = t * t;
nuclear@0 117
nuclear@0 118 static mat4_t crspline_mat = {
nuclear@0 119 {-1, 3, -3, 1},
nuclear@0 120 {2, -5, 4, -1},
nuclear@0 121 {-1, 0, 1, 0},
nuclear@0 122 {0, 2, 0, 0}
nuclear@0 123 };
nuclear@0 124
nuclear@0 125 tmp = v4_scale(v4_transform(v4_cons(a, b, c, d), crspline_mat), 0.5);
nuclear@0 126 return v4_dot(v4_cons(tsq * t, tsq, t, 1.0), tmp);
nuclear@0 127 }
nuclear@0 128
nuclear@0 129 /** Bezier interpolation */
nuclear@0 130 scalar_t bezier(scalar_t a, scalar_t b, scalar_t c, scalar_t d, scalar_t t)
nuclear@0 131 {
nuclear@0 132 scalar_t omt, omt3, t3, f;
nuclear@0 133 t3 = t * t * t;
nuclear@0 134 omt = 1.0f - t;
nuclear@0 135 omt3 = omt * omt * omt;
nuclear@0 136 f = 3 * t * omt;
nuclear@0 137
nuclear@0 138 return (a * omt3) + (b * f * omt) + (c * f * t) + (d * t3);
nuclear@0 139 }
nuclear@0 140
nuclear@0 141 /* ---- Ken Perlin's implementation of noise ---- */
nuclear@0 142
nuclear@0 143 #define B 0x100
nuclear@0 144 #define BM 0xff
nuclear@0 145 #define N 0x1000
nuclear@0 146 #define NP 12 /* 2^N */
nuclear@0 147 #define NM 0xfff
nuclear@0 148
nuclear@0 149 #define s_curve(t) (t * t * (3.0f - 2.0f * t))
nuclear@0 150
nuclear@0 151 #define setup(elem, b0, b1, r0, r1) \
nuclear@0 152 do { \
nuclear@0 153 scalar_t t = elem + N; \
nuclear@0 154 b0 = ((int)t) & BM; \
nuclear@0 155 b1 = (b0 + 1) & BM; \
nuclear@0 156 r0 = t - (int)t; \
nuclear@0 157 r1 = r0 - 1.0f; \
nuclear@0 158 } while(0)
nuclear@0 159
nuclear@0 160
nuclear@0 161 static int perm[B + B + 2]; /* permuted index from g_n onto themselves */
nuclear@0 162 static vec3_t grad3[B + B + 2]; /* 3D random gradients */
nuclear@0 163 static vec2_t grad2[B + B + 2]; /* 2D random gradients */
nuclear@0 164 static scalar_t grad1[B + B + 2]; /* 1D random ... slopes */
nuclear@0 165 static int tables_valid;
nuclear@0 166
nuclear@0 167 static void init_noise()
nuclear@0 168 {
nuclear@0 169 int i;
nuclear@0 170
nuclear@0 171 /* calculate random gradients */
nuclear@0 172 for(i=0; i<B; i++) {
nuclear@0 173 perm[i] = i; /* .. and initialize permutation mapping to identity */
nuclear@0 174
nuclear@0 175 grad1[i] = (scalar_t)((rand() % (B + B)) - B) / B;
nuclear@0 176
nuclear@0 177 grad2[i].x = (scalar_t)((rand() % (B + B)) - B) / B;
nuclear@0 178 grad2[i].y = (scalar_t)((rand() % (B + B)) - B) / B;
nuclear@0 179 grad2[i] = v2_normalize(grad2[i]);
nuclear@0 180
nuclear@0 181 grad3[i].x = (scalar_t)((rand() % (B + B)) - B) / B;
nuclear@0 182 grad3[i].y = (scalar_t)((rand() % (B + B)) - B) / B;
nuclear@0 183 grad3[i].z = (scalar_t)((rand() % (B + B)) - B) / B;
nuclear@0 184 grad3[i] = v3_normalize(grad3[i]);
nuclear@0 185 }
nuclear@0 186
nuclear@0 187 /* permute indices by swapping them randomly */
nuclear@0 188 for(i=0; i<B; i++) {
nuclear@0 189 int rand_idx = rand() % B;
nuclear@0 190
nuclear@0 191 int tmp = perm[i];
nuclear@0 192 perm[i] = perm[rand_idx];
nuclear@0 193 perm[rand_idx] = tmp;
nuclear@0 194 }
nuclear@0 195
nuclear@0 196 /* fill up the rest of the arrays by duplicating the existing gradients */
nuclear@0 197 /* and permutations */
nuclear@0 198 for(i=0; i<B+2; i++) {
nuclear@0 199 perm[B + i] = perm[i];
nuclear@0 200 grad1[B + i] = grad1[i];
nuclear@0 201 grad2[B + i] = grad2[i];
nuclear@0 202 grad3[B + i] = grad3[i];
nuclear@0 203 }
nuclear@0 204 }
nuclear@0 205
nuclear@0 206 scalar_t noise1(scalar_t x)
nuclear@0 207 {
nuclear@0 208 int bx0, bx1;
nuclear@0 209 scalar_t rx0, rx1, sx, u, v;
nuclear@0 210
nuclear@0 211 if(!tables_valid) {
nuclear@0 212 init_noise();
nuclear@0 213 tables_valid = 1;
nuclear@0 214 }
nuclear@0 215
nuclear@0 216 setup(x, bx0, bx1, rx0, rx1);
nuclear@0 217 sx = s_curve(rx0);
nuclear@0 218 u = rx0 * grad1[perm[bx0]];
nuclear@0 219 v = rx1 * grad1[perm[bx1]];
nuclear@0 220
nuclear@0 221 return lerp(u, v, sx);
nuclear@0 222 }
nuclear@0 223
nuclear@0 224 scalar_t noise2(scalar_t x, scalar_t y)
nuclear@0 225 {
nuclear@0 226 int i, j, b00, b10, b01, b11;
nuclear@0 227 int bx0, bx1, by0, by1;
nuclear@0 228 scalar_t rx0, rx1, ry0, ry1;
nuclear@0 229 scalar_t sx, sy, u, v, a, b;
nuclear@0 230
nuclear@0 231 if(!tables_valid) {
nuclear@0 232 init_noise();
nuclear@0 233 tables_valid = 1;
nuclear@0 234 }
nuclear@0 235
nuclear@0 236 setup(x, bx0, bx1, rx0, rx1);
nuclear@0 237 setup(y, by0, by1, ry0, ry1);
nuclear@0 238
nuclear@0 239 i = perm[bx0];
nuclear@0 240 j = perm[bx1];
nuclear@0 241
nuclear@0 242 b00 = perm[i + by0];
nuclear@0 243 b10 = perm[j + by0];
nuclear@0 244 b01 = perm[i + by1];
nuclear@0 245 b11 = perm[j + by1];
nuclear@0 246
nuclear@0 247 /* calculate hermite inteprolating factors */
nuclear@0 248 sx = s_curve(rx0);
nuclear@0 249 sy = s_curve(ry0);
nuclear@0 250
nuclear@0 251 /* interpolate along the left edge */
nuclear@0 252 u = v2_dot(grad2[b00], v2_cons(rx0, ry0));
nuclear@0 253 v = v2_dot(grad2[b10], v2_cons(rx1, ry0));
nuclear@0 254 a = lerp(u, v, sx);
nuclear@0 255
nuclear@0 256 /* interpolate along the right edge */
nuclear@0 257 u = v2_dot(grad2[b01], v2_cons(rx0, ry1));
nuclear@0 258 v = v2_dot(grad2[b11], v2_cons(rx1, ry1));
nuclear@0 259 b = lerp(u, v, sx);
nuclear@0 260
nuclear@0 261 /* interpolate between them */
nuclear@0 262 return lerp(a, b, sy);
nuclear@0 263 }
nuclear@0 264
nuclear@0 265 scalar_t noise3(scalar_t x, scalar_t y, scalar_t z)
nuclear@0 266 {
nuclear@0 267 int i, j;
nuclear@0 268 int bx0, bx1, by0, by1, bz0, bz1;
nuclear@0 269 int b00, b10, b01, b11;
nuclear@0 270 scalar_t rx0, rx1, ry0, ry1, rz0, rz1;
nuclear@0 271 scalar_t sx, sy, sz;
nuclear@0 272 scalar_t u, v, a, b, c, d;
nuclear@0 273
nuclear@0 274 if(!tables_valid) {
nuclear@0 275 init_noise();
nuclear@0 276 tables_valid = 1;
nuclear@0 277 }
nuclear@0 278
nuclear@0 279 setup(x, bx0, bx1, rx0, rx1);
nuclear@0 280 setup(y, by0, by1, ry0, ry1);
nuclear@0 281 setup(z, bz0, bz1, rz0, rz1);
nuclear@0 282
nuclear@0 283 i = perm[bx0];
nuclear@0 284 j = perm[bx1];
nuclear@0 285
nuclear@0 286 b00 = perm[i + by0];
nuclear@0 287 b10 = perm[j + by0];
nuclear@0 288 b01 = perm[i + by1];
nuclear@0 289 b11 = perm[j + by1];
nuclear@0 290
nuclear@0 291 /* calculate hermite interpolating factors */
nuclear@0 292 sx = s_curve(rx0);
nuclear@0 293 sy = s_curve(ry0);
nuclear@0 294 sz = s_curve(rz0);
nuclear@0 295
nuclear@0 296 /* interpolate along the top slice of the cell */
nuclear@0 297 u = v3_dot(grad3[b00 + bz0], v3_cons(rx0, ry0, rz0));
nuclear@0 298 v = v3_dot(grad3[b10 + bz0], v3_cons(rx1, ry0, rz0));
nuclear@0 299 a = lerp(u, v, sx);
nuclear@0 300
nuclear@0 301 u = v3_dot(grad3[b01 + bz0], v3_cons(rx0, ry1, rz0));
nuclear@0 302 v = v3_dot(grad3[b11 + bz0], v3_cons(rx1, ry1, rz0));
nuclear@0 303 b = lerp(u, v, sx);
nuclear@0 304
nuclear@0 305 c = lerp(a, b, sy);
nuclear@0 306
nuclear@0 307 /* interpolate along the bottom slice of the cell */
nuclear@0 308 u = v3_dot(grad3[b00 + bz0], v3_cons(rx0, ry0, rz1));
nuclear@0 309 v = v3_dot(grad3[b10 + bz0], v3_cons(rx1, ry0, rz1));
nuclear@0 310 a = lerp(u, v, sx);
nuclear@0 311
nuclear@0 312 u = v3_dot(grad3[b01 + bz0], v3_cons(rx0, ry1, rz1));
nuclear@0 313 v = v3_dot(grad3[b11 + bz0], v3_cons(rx1, ry1, rz1));
nuclear@0 314 b = lerp(u, v, sx);
nuclear@0 315
nuclear@0 316 d = lerp(a, b, sy);
nuclear@0 317
nuclear@0 318 /* interpolate between slices */
nuclear@0 319 return lerp(c, d, sz);
nuclear@0 320 }
nuclear@0 321
nuclear@0 322 scalar_t fbm1(scalar_t x, int octaves)
nuclear@0 323 {
nuclear@0 324 int i;
nuclear@0 325 scalar_t res = 0.0f, freq = 1.0f;
nuclear@0 326 for(i=0; i<octaves; i++) {
nuclear@0 327 res += noise1(x * freq) / freq;
nuclear@0 328 freq *= 2.0f;
nuclear@0 329 }
nuclear@0 330 return res;
nuclear@0 331 }
nuclear@0 332
nuclear@0 333 scalar_t fbm2(scalar_t x, scalar_t y, int octaves)
nuclear@0 334 {
nuclear@0 335 int i;
nuclear@0 336 scalar_t res = 0.0f, freq = 1.0f;
nuclear@0 337 for(i=0; i<octaves; i++) {
nuclear@0 338 res += noise2(x * freq, y * freq) / freq;
nuclear@0 339 freq *= 2.0f;
nuclear@0 340 }
nuclear@0 341 return res;
nuclear@0 342 }
nuclear@0 343
nuclear@0 344 scalar_t fbm3(scalar_t x, scalar_t y, scalar_t z, int octaves)
nuclear@0 345 {
nuclear@0 346 int i;
nuclear@0 347 scalar_t res = 0.0f, freq = 1.0f;
nuclear@0 348 for(i=0; i<octaves; i++) {
nuclear@0 349 res += noise3(x * freq, y * freq, z * freq) / freq;
nuclear@0 350 freq *= 2.0f;
nuclear@0 351 }
nuclear@0 352 return res;
nuclear@0 353 }
nuclear@0 354
nuclear@0 355 scalar_t turbulence1(scalar_t x, int octaves)
nuclear@0 356 {
nuclear@0 357 int i;
nuclear@0 358 scalar_t res = 0.0f, freq = 1.0f;
nuclear@0 359 for(i=0; i<octaves; i++) {
nuclear@0 360 res += fabs(noise1(x * freq) / freq);
nuclear@0 361 freq *= 2.0f;
nuclear@0 362 }
nuclear@0 363 return res;
nuclear@0 364 }
nuclear@0 365
nuclear@0 366 scalar_t turbulence2(scalar_t x, scalar_t y, int octaves)
nuclear@0 367 {
nuclear@0 368 int i;
nuclear@0 369 scalar_t res = 0.0f, freq = 1.0f;
nuclear@0 370 for(i=0; i<octaves; i++) {
nuclear@0 371 res += fabs(noise2(x * freq, y * freq) / freq);
nuclear@0 372 freq *= 2.0f;
nuclear@0 373 }
nuclear@0 374 return res;
nuclear@0 375 }
nuclear@0 376
nuclear@0 377 scalar_t turbulence3(scalar_t x, scalar_t y, scalar_t z, int octaves)
nuclear@0 378 {
nuclear@0 379 int i;
nuclear@0 380 scalar_t res = 0.0f, freq = 1.0f;
nuclear@0 381 for(i=0; i<octaves; i++) {
nuclear@0 382 res += fabs(noise3(x * freq, y * freq, z * freq) / freq);
nuclear@0 383 freq *= 2.0f;
nuclear@0 384 }
nuclear@0 385 return res;
nuclear@0 386 }