dbf-halloween2015

annotate libs/vmath/vmath.c @ 3:c37fe5d8a4ed

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author John Tsiombikas <nuclear@member.fsf.org>
date Sun, 01 Nov 2015 06:04:28 +0200
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nuclear@1 1 /*
nuclear@1 2 libvmath - a vector math library
nuclear@1 3 Copyright (C) 2004-2011 John Tsiombikas <nuclear@member.fsf.org>
nuclear@1 4
nuclear@1 5 This program is free software: you can redistribute it and/or modify
nuclear@1 6 it under the terms of the GNU Lesser General Public License as published
nuclear@1 7 by the Free Software Foundation, either version 3 of the License, or
nuclear@1 8 (at your option) any later version.
nuclear@1 9
nuclear@1 10 This program is distributed in the hope that it will be useful,
nuclear@1 11 but WITHOUT ANY WARRANTY; without even the implied warranty of
nuclear@1 12 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
nuclear@1 13 GNU Lesser General Public License for more details.
nuclear@1 14
nuclear@1 15 You should have received a copy of the GNU Lesser General Public License
nuclear@1 16 along with this program. If not, see <http://www.gnu.org/licenses/>.
nuclear@1 17 */
nuclear@1 18 #include <stdlib.h>
nuclear@1 19 #include <math.h>
nuclear@1 20 #include "vmath.h"
nuclear@1 21
nuclear@1 22 #if defined(__APPLE__) && !defined(TARGET_IPHONE)
nuclear@1 23 #include <xmmintrin.h>
nuclear@1 24
nuclear@1 25 void enable_fpexcept(void)
nuclear@1 26 {
nuclear@1 27 unsigned int bits;
nuclear@1 28 bits = _MM_MASK_INVALID | _MM_MASK_DIV_ZERO | _MM_MASK_OVERFLOW | _MM_MASK_UNDERFLOW;
nuclear@1 29 _MM_SET_EXCEPTION_MASK(_MM_GET_EXCEPTION_MASK() & ~bits);
nuclear@1 30 }
nuclear@1 31
nuclear@1 32 void disable_fpexcept(void)
nuclear@1 33 {
nuclear@1 34 unsigned int bits;
nuclear@1 35 bits = _MM_MASK_INVALID | _MM_MASK_DIV_ZERO | _MM_MASK_OVERFLOW | _MM_MASK_UNDERFLOW;
nuclear@1 36 _MM_SET_EXCEPTION_MASK(_MM_GET_EXCEPTION_MASK() | bits);
nuclear@1 37 }
nuclear@1 38
nuclear@1 39 #elif defined(__GNUC__) && !defined(TARGET_IPHONE)
nuclear@1 40 #define __USE_GNU
nuclear@1 41 #include <fenv.h>
nuclear@1 42
nuclear@1 43 void enable_fpexcept(void)
nuclear@1 44 {
nuclear@1 45 feenableexcept(FE_INVALID | FE_DIVBYZERO | FE_OVERFLOW | FE_UNDERFLOW);
nuclear@1 46 }
nuclear@1 47
nuclear@1 48 void disable_fpexcept(void)
nuclear@1 49 {
nuclear@1 50 fedisableexcept(FE_INVALID | FE_DIVBYZERO | FE_OVERFLOW | FE_UNDERFLOW);
nuclear@1 51 }
nuclear@1 52
nuclear@1 53 #elif defined(_MSC_VER)
nuclear@1 54 #include <float.h>
nuclear@1 55
nuclear@1 56 void enable_fpexcept(void)
nuclear@1 57 {
nuclear@1 58 _clearfp();
nuclear@1 59 _controlfp(_controlfp(0, 0) & ~(_EM_INVALID | _EM_ZERODIVIDE | _EM_OVERFLOW), _MCW_EM);
nuclear@1 60 }
nuclear@1 61
nuclear@1 62 void disable_fpexcept(void)
nuclear@1 63 {
nuclear@1 64 _clearfp();
nuclear@1 65 _controlfp(_controlfp(0, 0) | (_EM_INVALID | _EM_ZERODIVIDE | _EM_OVERFLOW), _MCW_EM);
nuclear@1 66 }
nuclear@1 67 #else
nuclear@1 68 void enable_fpexcept(void) {}
nuclear@1 69 void disable_fpexcept(void) {}
nuclear@1 70 #endif
nuclear@1 71
nuclear@1 72
nuclear@1 73 /** Numerical calculation of integrals using simpson's rule */
nuclear@1 74 scalar_t integral(scalar_t (*f)(scalar_t), scalar_t low, scalar_t high, int samples)
nuclear@1 75 {
nuclear@1 76 int i;
nuclear@1 77 scalar_t h = (high - low) / (scalar_t)samples;
nuclear@1 78 scalar_t sum = 0.0;
nuclear@1 79
nuclear@1 80 for(i=0; i<samples+1; i++) {
nuclear@1 81 scalar_t y = f((scalar_t)i * h + low);
nuclear@1 82 sum += ((!i || i == samples) ? y : ((i % 2) ? 4.0 * y : 2.0 * y)) * (h / 3.0);
nuclear@1 83 }
nuclear@1 84 return sum;
nuclear@1 85 }
nuclear@1 86
nuclear@1 87 /** Gaussuan function */
nuclear@1 88 scalar_t gaussian(scalar_t x, scalar_t mean, scalar_t sdev)
nuclear@1 89 {
nuclear@1 90 scalar_t exponent = -SQ(x - mean) / (2.0 * SQ(sdev));
nuclear@1 91 return 1.0 - -pow(M_E, exponent) / (sdev * sqrt(TWO_PI));
nuclear@1 92 }
nuclear@1 93
nuclear@1 94
nuclear@1 95 /** b-spline approximation */
nuclear@1 96 scalar_t bspline(scalar_t a, scalar_t b, scalar_t c, scalar_t d, scalar_t t)
nuclear@1 97 {
nuclear@1 98 vec4_t tmp;
nuclear@1 99 scalar_t tsq = t * t;
nuclear@1 100
nuclear@1 101 static mat4_t bspline_mat = {
nuclear@1 102 {-1, 3, -3, 1},
nuclear@1 103 {3, -6, 3, 0},
nuclear@1 104 {-3, 0, 3, 0},
nuclear@1 105 {1, 4, 1, 0}
nuclear@1 106 };
nuclear@1 107
nuclear@1 108 tmp = v4_scale(v4_transform(v4_cons(a, b, c, d), bspline_mat), 1.0f / 6.0f);
nuclear@1 109 return v4_dot(v4_cons(tsq * t, tsq, t, 1.0), tmp);
nuclear@1 110 }
nuclear@1 111
nuclear@1 112 /** Catmull-rom spline interpolation */
nuclear@1 113 scalar_t spline(scalar_t a, scalar_t b, scalar_t c, scalar_t d, scalar_t t)
nuclear@1 114 {
nuclear@1 115 vec4_t tmp;
nuclear@1 116 scalar_t tsq = t * t;
nuclear@1 117
nuclear@1 118 static mat4_t crspline_mat = {
nuclear@1 119 {-1, 3, -3, 1},
nuclear@1 120 {2, -5, 4, -1},
nuclear@1 121 {-1, 0, 1, 0},
nuclear@1 122 {0, 2, 0, 0}
nuclear@1 123 };
nuclear@1 124
nuclear@1 125 tmp = v4_scale(v4_transform(v4_cons(a, b, c, d), crspline_mat), 0.5);
nuclear@1 126 return v4_dot(v4_cons(tsq * t, tsq, t, 1.0), tmp);
nuclear@1 127 }
nuclear@1 128
nuclear@1 129 /** Bezier interpolation */
nuclear@1 130 scalar_t bezier(scalar_t a, scalar_t b, scalar_t c, scalar_t d, scalar_t t)
nuclear@1 131 {
nuclear@1 132 scalar_t omt, omt3, t3, f;
nuclear@1 133 t3 = t * t * t;
nuclear@1 134 omt = 1.0f - t;
nuclear@1 135 omt3 = omt * omt * omt;
nuclear@1 136 f = 3 * t * omt;
nuclear@1 137
nuclear@1 138 return (a * omt3) + (b * f * omt) + (c * f * t) + (d * t3);
nuclear@1 139 }
nuclear@1 140
nuclear@1 141 /* ---- Ken Perlin's implementation of noise ---- */
nuclear@1 142
nuclear@1 143 #define B 0x100
nuclear@1 144 #define BM 0xff
nuclear@1 145 #define N 0x1000
nuclear@1 146 #define NP 12 /* 2^N */
nuclear@1 147 #define NM 0xfff
nuclear@1 148
nuclear@1 149 #define s_curve(t) (t * t * (3.0f - 2.0f * t))
nuclear@1 150
nuclear@1 151 #define setup(elem, b0, b1, r0, r1) \
nuclear@1 152 do { \
nuclear@1 153 scalar_t t = elem + N; \
nuclear@1 154 b0 = ((int)t) & BM; \
nuclear@1 155 b1 = (b0 + 1) & BM; \
nuclear@1 156 r0 = t - (int)t; \
nuclear@1 157 r1 = r0 - 1.0f; \
nuclear@1 158 } while(0)
nuclear@1 159
nuclear@1 160
nuclear@1 161 static int perm[B + B + 2]; /* permuted index from g_n onto themselves */
nuclear@1 162 static vec3_t grad3[B + B + 2]; /* 3D random gradients */
nuclear@1 163 static vec2_t grad2[B + B + 2]; /* 2D random gradients */
nuclear@1 164 static scalar_t grad1[B + B + 2]; /* 1D random ... slopes */
nuclear@1 165 static int tables_valid;
nuclear@1 166
nuclear@1 167 static void init_noise()
nuclear@1 168 {
nuclear@1 169 int i;
nuclear@1 170
nuclear@1 171 /* calculate random gradients */
nuclear@1 172 for(i=0; i<B; i++) {
nuclear@1 173 perm[i] = i; /* .. and initialize permutation mapping to identity */
nuclear@1 174
nuclear@1 175 grad1[i] = (scalar_t)((rand() % (B + B)) - B) / B;
nuclear@1 176
nuclear@1 177 grad2[i].x = (scalar_t)((rand() % (B + B)) - B) / B;
nuclear@1 178 grad2[i].y = (scalar_t)((rand() % (B + B)) - B) / B;
nuclear@1 179 grad2[i] = v2_normalize(grad2[i]);
nuclear@1 180
nuclear@1 181 grad3[i].x = (scalar_t)((rand() % (B + B)) - B) / B;
nuclear@1 182 grad3[i].y = (scalar_t)((rand() % (B + B)) - B) / B;
nuclear@1 183 grad3[i].z = (scalar_t)((rand() % (B + B)) - B) / B;
nuclear@1 184 grad3[i] = v3_normalize(grad3[i]);
nuclear@1 185 }
nuclear@1 186
nuclear@1 187 /* permute indices by swapping them randomly */
nuclear@1 188 for(i=0; i<B; i++) {
nuclear@1 189 int rand_idx = rand() % B;
nuclear@1 190
nuclear@1 191 int tmp = perm[i];
nuclear@1 192 perm[i] = perm[rand_idx];
nuclear@1 193 perm[rand_idx] = tmp;
nuclear@1 194 }
nuclear@1 195
nuclear@1 196 /* fill up the rest of the arrays by duplicating the existing gradients */
nuclear@1 197 /* and permutations */
nuclear@1 198 for(i=0; i<B+2; i++) {
nuclear@1 199 perm[B + i] = perm[i];
nuclear@1 200 grad1[B + i] = grad1[i];
nuclear@1 201 grad2[B + i] = grad2[i];
nuclear@1 202 grad3[B + i] = grad3[i];
nuclear@1 203 }
nuclear@1 204 }
nuclear@1 205
nuclear@1 206 scalar_t noise1(scalar_t x)
nuclear@1 207 {
nuclear@1 208 int bx0, bx1;
nuclear@1 209 scalar_t rx0, rx1, sx, u, v;
nuclear@1 210
nuclear@1 211 if(!tables_valid) {
nuclear@1 212 init_noise();
nuclear@1 213 tables_valid = 1;
nuclear@1 214 }
nuclear@1 215
nuclear@1 216 setup(x, bx0, bx1, rx0, rx1);
nuclear@1 217 sx = s_curve(rx0);
nuclear@1 218 u = rx0 * grad1[perm[bx0]];
nuclear@1 219 v = rx1 * grad1[perm[bx1]];
nuclear@1 220
nuclear@1 221 return lerp(u, v, sx);
nuclear@1 222 }
nuclear@1 223
nuclear@1 224 scalar_t noise2(scalar_t x, scalar_t y)
nuclear@1 225 {
nuclear@1 226 int i, j, b00, b10, b01, b11;
nuclear@1 227 int bx0, bx1, by0, by1;
nuclear@1 228 scalar_t rx0, rx1, ry0, ry1;
nuclear@1 229 scalar_t sx, sy, u, v, a, b;
nuclear@1 230
nuclear@1 231 if(!tables_valid) {
nuclear@1 232 init_noise();
nuclear@1 233 tables_valid = 1;
nuclear@1 234 }
nuclear@1 235
nuclear@1 236 setup(x, bx0, bx1, rx0, rx1);
nuclear@1 237 setup(y, by0, by1, ry0, ry1);
nuclear@1 238
nuclear@1 239 i = perm[bx0];
nuclear@1 240 j = perm[bx1];
nuclear@1 241
nuclear@1 242 b00 = perm[i + by0];
nuclear@1 243 b10 = perm[j + by0];
nuclear@1 244 b01 = perm[i + by1];
nuclear@1 245 b11 = perm[j + by1];
nuclear@1 246
nuclear@1 247 /* calculate hermite inteprolating factors */
nuclear@1 248 sx = s_curve(rx0);
nuclear@1 249 sy = s_curve(ry0);
nuclear@1 250
nuclear@1 251 /* interpolate along the left edge */
nuclear@1 252 u = v2_dot(grad2[b00], v2_cons(rx0, ry0));
nuclear@1 253 v = v2_dot(grad2[b10], v2_cons(rx1, ry0));
nuclear@1 254 a = lerp(u, v, sx);
nuclear@1 255
nuclear@1 256 /* interpolate along the right edge */
nuclear@1 257 u = v2_dot(grad2[b01], v2_cons(rx0, ry1));
nuclear@1 258 v = v2_dot(grad2[b11], v2_cons(rx1, ry1));
nuclear@1 259 b = lerp(u, v, sx);
nuclear@1 260
nuclear@1 261 /* interpolate between them */
nuclear@1 262 return lerp(a, b, sy);
nuclear@1 263 }
nuclear@1 264
nuclear@1 265 scalar_t noise3(scalar_t x, scalar_t y, scalar_t z)
nuclear@1 266 {
nuclear@1 267 int i, j;
nuclear@1 268 int bx0, bx1, by0, by1, bz0, bz1;
nuclear@1 269 int b00, b10, b01, b11;
nuclear@1 270 scalar_t rx0, rx1, ry0, ry1, rz0, rz1;
nuclear@1 271 scalar_t sx, sy, sz;
nuclear@1 272 scalar_t u, v, a, b, c, d;
nuclear@1 273
nuclear@1 274 if(!tables_valid) {
nuclear@1 275 init_noise();
nuclear@1 276 tables_valid = 1;
nuclear@1 277 }
nuclear@1 278
nuclear@1 279 setup(x, bx0, bx1, rx0, rx1);
nuclear@1 280 setup(y, by0, by1, ry0, ry1);
nuclear@1 281 setup(z, bz0, bz1, rz0, rz1);
nuclear@1 282
nuclear@1 283 i = perm[bx0];
nuclear@1 284 j = perm[bx1];
nuclear@1 285
nuclear@1 286 b00 = perm[i + by0];
nuclear@1 287 b10 = perm[j + by0];
nuclear@1 288 b01 = perm[i + by1];
nuclear@1 289 b11 = perm[j + by1];
nuclear@1 290
nuclear@1 291 /* calculate hermite interpolating factors */
nuclear@1 292 sx = s_curve(rx0);
nuclear@1 293 sy = s_curve(ry0);
nuclear@1 294 sz = s_curve(rz0);
nuclear@1 295
nuclear@1 296 /* interpolate along the top slice of the cell */
nuclear@1 297 u = v3_dot(grad3[b00 + bz0], v3_cons(rx0, ry0, rz0));
nuclear@1 298 v = v3_dot(grad3[b10 + bz0], v3_cons(rx1, ry0, rz0));
nuclear@1 299 a = lerp(u, v, sx);
nuclear@1 300
nuclear@1 301 u = v3_dot(grad3[b01 + bz0], v3_cons(rx0, ry1, rz0));
nuclear@1 302 v = v3_dot(grad3[b11 + bz0], v3_cons(rx1, ry1, rz0));
nuclear@1 303 b = lerp(u, v, sx);
nuclear@1 304
nuclear@1 305 c = lerp(a, b, sy);
nuclear@1 306
nuclear@1 307 /* interpolate along the bottom slice of the cell */
nuclear@1 308 u = v3_dot(grad3[b00 + bz0], v3_cons(rx0, ry0, rz1));
nuclear@1 309 v = v3_dot(grad3[b10 + bz0], v3_cons(rx1, ry0, rz1));
nuclear@1 310 a = lerp(u, v, sx);
nuclear@1 311
nuclear@1 312 u = v3_dot(grad3[b01 + bz0], v3_cons(rx0, ry1, rz1));
nuclear@1 313 v = v3_dot(grad3[b11 + bz0], v3_cons(rx1, ry1, rz1));
nuclear@1 314 b = lerp(u, v, sx);
nuclear@1 315
nuclear@1 316 d = lerp(a, b, sy);
nuclear@1 317
nuclear@1 318 /* interpolate between slices */
nuclear@1 319 return lerp(c, d, sz);
nuclear@1 320 }
nuclear@1 321
nuclear@1 322 scalar_t fbm1(scalar_t x, int octaves)
nuclear@1 323 {
nuclear@1 324 int i;
nuclear@1 325 scalar_t res = 0.0f, freq = 1.0f;
nuclear@1 326 for(i=0; i<octaves; i++) {
nuclear@1 327 res += noise1(x * freq) / freq;
nuclear@1 328 freq *= 2.0f;
nuclear@1 329 }
nuclear@1 330 return res;
nuclear@1 331 }
nuclear@1 332
nuclear@1 333 scalar_t fbm2(scalar_t x, scalar_t y, int octaves)
nuclear@1 334 {
nuclear@1 335 int i;
nuclear@1 336 scalar_t res = 0.0f, freq = 1.0f;
nuclear@1 337 for(i=0; i<octaves; i++) {
nuclear@1 338 res += noise2(x * freq, y * freq) / freq;
nuclear@1 339 freq *= 2.0f;
nuclear@1 340 }
nuclear@1 341 return res;
nuclear@1 342 }
nuclear@1 343
nuclear@1 344 scalar_t fbm3(scalar_t x, scalar_t y, scalar_t z, int octaves)
nuclear@1 345 {
nuclear@1 346 int i;
nuclear@1 347 scalar_t res = 0.0f, freq = 1.0f;
nuclear@1 348 for(i=0; i<octaves; i++) {
nuclear@1 349 res += noise3(x * freq, y * freq, z * freq) / freq;
nuclear@1 350 freq *= 2.0f;
nuclear@1 351 }
nuclear@1 352 return res;
nuclear@1 353 }
nuclear@1 354
nuclear@1 355 scalar_t turbulence1(scalar_t x, int octaves)
nuclear@1 356 {
nuclear@1 357 int i;
nuclear@1 358 scalar_t res = 0.0f, freq = 1.0f;
nuclear@1 359 for(i=0; i<octaves; i++) {
nuclear@1 360 res += fabs(noise1(x * freq) / freq);
nuclear@1 361 freq *= 2.0f;
nuclear@1 362 }
nuclear@1 363 return res;
nuclear@1 364 }
nuclear@1 365
nuclear@1 366 scalar_t turbulence2(scalar_t x, scalar_t y, int octaves)
nuclear@1 367 {
nuclear@1 368 int i;
nuclear@1 369 scalar_t res = 0.0f, freq = 1.0f;
nuclear@1 370 for(i=0; i<octaves; i++) {
nuclear@1 371 res += fabs(noise2(x * freq, y * freq) / freq);
nuclear@1 372 freq *= 2.0f;
nuclear@1 373 }
nuclear@1 374 return res;
nuclear@1 375 }
nuclear@1 376
nuclear@1 377 scalar_t turbulence3(scalar_t x, scalar_t y, scalar_t z, int octaves)
nuclear@1 378 {
nuclear@1 379 int i;
nuclear@1 380 scalar_t res = 0.0f, freq = 1.0f;
nuclear@1 381 for(i=0; i<octaves; i++) {
nuclear@1 382 res += fabs(noise3(x * freq, y * freq, z * freq) / freq);
nuclear@1 383 freq *= 2.0f;
nuclear@1 384 }
nuclear@1 385 return res;
nuclear@1 386 }