linmath.h (12708B)
1 #ifndef LINMATH_H 2 #define LINMATH_H 3 4 #include <math.h> 5 6 #ifdef _MSC_VER 7 #define inline __inline 8 #endif 9 10 #define LINMATH_H_DEFINE_VEC(n) \ 11 typedef float vec##n[n]; \ 12 static inline void vec##n##_add(vec##n r, vec##n const a, vec##n const b) \ 13 { \ 14 int i; \ 15 for(i=0; i<n; ++i) \ 16 r[i] = a[i] + b[i]; \ 17 } \ 18 static inline void vec##n##_sub(vec##n r, vec##n const a, vec##n const b) \ 19 { \ 20 int i; \ 21 for(i=0; i<n; ++i) \ 22 r[i] = a[i] - b[i]; \ 23 } \ 24 static inline void vec##n##_scale(vec##n r, vec##n const v, float const s) \ 25 { \ 26 int i; \ 27 for(i=0; i<n; ++i) \ 28 r[i] = v[i] * s; \ 29 } \ 30 static inline float vec##n##_mul_inner(vec##n const a, vec##n const b) \ 31 { \ 32 float p = 0.; \ 33 int i; \ 34 for(i=0; i<n; ++i) \ 35 p += b[i]*a[i]; \ 36 return p; \ 37 } \ 38 static inline float vec##n##_len(vec##n const v) \ 39 { \ 40 return (float) sqrt(vec##n##_mul_inner(v,v)); \ 41 } \ 42 static inline void vec##n##_norm(vec##n r, vec##n const v) \ 43 { \ 44 float k = 1.f / vec##n##_len(v); \ 45 vec##n##_scale(r, v, k); \ 46 } 47 48 LINMATH_H_DEFINE_VEC(2) 49 LINMATH_H_DEFINE_VEC(3) 50 LINMATH_H_DEFINE_VEC(4) 51 52 static inline void vec3_mul_cross(vec3 r, vec3 const a, vec3 const b) 53 { 54 r[0] = a[1]*b[2] - a[2]*b[1]; 55 r[1] = a[2]*b[0] - a[0]*b[2]; 56 r[2] = a[0]*b[1] - a[1]*b[0]; 57 } 58 59 static inline void vec3_reflect(vec3 r, vec3 const v, vec3 const n) 60 { 61 float p = 2.f*vec3_mul_inner(v, n); 62 int i; 63 for(i=0;i<3;++i) 64 r[i] = v[i] - p*n[i]; 65 } 66 67 static inline void vec4_mul_cross(vec4 r, vec4 a, vec4 b) 68 { 69 r[0] = a[1]*b[2] - a[2]*b[1]; 70 r[1] = a[2]*b[0] - a[0]*b[2]; 71 r[2] = a[0]*b[1] - a[1]*b[0]; 72 r[3] = 1.f; 73 } 74 75 static inline void vec4_reflect(vec4 r, vec4 v, vec4 n) 76 { 77 float p = 2.f*vec4_mul_inner(v, n); 78 int i; 79 for(i=0;i<4;++i) 80 r[i] = v[i] - p*n[i]; 81 } 82 83 typedef vec4 mat4x4[4]; 84 static inline void mat4x4_identity(mat4x4 M) 85 { 86 int i, j; 87 for(i=0; i<4; ++i) 88 for(j=0; j<4; ++j) 89 M[i][j] = i==j ? 1.f : 0.f; 90 } 91 static inline void mat4x4_dup(mat4x4 M, mat4x4 N) 92 { 93 int i, j; 94 for(i=0; i<4; ++i) 95 for(j=0; j<4; ++j) 96 M[i][j] = N[i][j]; 97 } 98 static inline void mat4x4_row(vec4 r, mat4x4 M, int i) 99 { 100 int k; 101 for(k=0; k<4; ++k) 102 r[k] = M[k][i]; 103 } 104 static inline void mat4x4_col(vec4 r, mat4x4 M, int i) 105 { 106 int k; 107 for(k=0; k<4; ++k) 108 r[k] = M[i][k]; 109 } 110 static inline void mat4x4_transpose(mat4x4 M, mat4x4 N) 111 { 112 int i, j; 113 for(j=0; j<4; ++j) 114 for(i=0; i<4; ++i) 115 M[i][j] = N[j][i]; 116 } 117 static inline void mat4x4_add(mat4x4 M, mat4x4 a, mat4x4 b) 118 { 119 int i; 120 for(i=0; i<4; ++i) 121 vec4_add(M[i], a[i], b[i]); 122 } 123 static inline void mat4x4_sub(mat4x4 M, mat4x4 a, mat4x4 b) 124 { 125 int i; 126 for(i=0; i<4; ++i) 127 vec4_sub(M[i], a[i], b[i]); 128 } 129 static inline void mat4x4_scale(mat4x4 M, mat4x4 a, float k) 130 { 131 int i; 132 for(i=0; i<4; ++i) 133 vec4_scale(M[i], a[i], k); 134 } 135 static inline void mat4x4_scale_aniso(mat4x4 M, mat4x4 a, float x, float y, float z) 136 { 137 int i; 138 vec4_scale(M[0], a[0], x); 139 vec4_scale(M[1], a[1], y); 140 vec4_scale(M[2], a[2], z); 141 for(i = 0; i < 4; ++i) { 142 M[3][i] = a[3][i]; 143 } 144 } 145 static inline void mat4x4_mul(mat4x4 M, mat4x4 a, mat4x4 b) 146 { 147 mat4x4 temp; 148 int k, r, c; 149 for(c=0; c<4; ++c) for(r=0; r<4; ++r) { 150 temp[c][r] = 0.f; 151 for(k=0; k<4; ++k) 152 temp[c][r] += a[k][r] * b[c][k]; 153 } 154 mat4x4_dup(M, temp); 155 } 156 static inline void mat4x4_mul_vec4(vec4 r, mat4x4 M, vec4 v) 157 { 158 int i, j; 159 for(j=0; j<4; ++j) { 160 r[j] = 0.f; 161 for(i=0; i<4; ++i) 162 r[j] += M[i][j] * v[i]; 163 } 164 } 165 static inline void mat4x4_translate(mat4x4 T, float x, float y, float z) 166 { 167 mat4x4_identity(T); 168 T[3][0] = x; 169 T[3][1] = y; 170 T[3][2] = z; 171 } 172 static inline void mat4x4_translate_in_place(mat4x4 M, float x, float y, float z) 173 { 174 vec4 t = {x, y, z, 0}; 175 vec4 r; 176 int i; 177 for (i = 0; i < 4; ++i) { 178 mat4x4_row(r, M, i); 179 M[3][i] += vec4_mul_inner(r, t); 180 } 181 } 182 static inline void mat4x4_from_vec3_mul_outer(mat4x4 M, vec3 a, vec3 b) 183 { 184 int i, j; 185 for(i=0; i<4; ++i) for(j=0; j<4; ++j) 186 M[i][j] = i<3 && j<3 ? a[i] * b[j] : 0.f; 187 } 188 static inline void mat4x4_rotate(mat4x4 R, mat4x4 M, float x, float y, float z, float angle) 189 { 190 float s = sinf(angle); 191 float c = cosf(angle); 192 vec3 u = {x, y, z}; 193 194 if(vec3_len(u) > 1e-4) { 195 mat4x4 T, C, S = {{0}}; 196 197 vec3_norm(u, u); 198 mat4x4_from_vec3_mul_outer(T, u, u); 199 200 S[1][2] = u[0]; 201 S[2][1] = -u[0]; 202 S[2][0] = u[1]; 203 S[0][2] = -u[1]; 204 S[0][1] = u[2]; 205 S[1][0] = -u[2]; 206 207 mat4x4_scale(S, S, s); 208 209 mat4x4_identity(C); 210 mat4x4_sub(C, C, T); 211 212 mat4x4_scale(C, C, c); 213 214 mat4x4_add(T, T, C); 215 mat4x4_add(T, T, S); 216 217 T[3][3] = 1.; 218 mat4x4_mul(R, M, T); 219 } else { 220 mat4x4_dup(R, M); 221 } 222 } 223 static inline void mat4x4_rotate_X(mat4x4 Q, mat4x4 M, float angle) 224 { 225 float s = sinf(angle); 226 float c = cosf(angle); 227 mat4x4 R = { 228 {1.f, 0.f, 0.f, 0.f}, 229 {0.f, c, s, 0.f}, 230 {0.f, -s, c, 0.f}, 231 {0.f, 0.f, 0.f, 1.f} 232 }; 233 mat4x4_mul(Q, M, R); 234 } 235 static inline void mat4x4_rotate_Y(mat4x4 Q, mat4x4 M, float angle) 236 { 237 float s = sinf(angle); 238 float c = cosf(angle); 239 mat4x4 R = { 240 { c, 0.f, -s, 0.f}, 241 { 0.f, 1.f, 0.f, 0.f}, 242 { s, 0.f, c, 0.f}, 243 { 0.f, 0.f, 0.f, 1.f} 244 }; 245 mat4x4_mul(Q, M, R); 246 } 247 static inline void mat4x4_rotate_Z(mat4x4 Q, mat4x4 M, float angle) 248 { 249 float s = sinf(angle); 250 float c = cosf(angle); 251 mat4x4 R = { 252 { c, s, 0.f, 0.f}, 253 { -s, c, 0.f, 0.f}, 254 { 0.f, 0.f, 1.f, 0.f}, 255 { 0.f, 0.f, 0.f, 1.f} 256 }; 257 mat4x4_mul(Q, M, R); 258 } 259 static inline void mat4x4_invert(mat4x4 T, mat4x4 M) 260 { 261 float idet; 262 float s[6]; 263 float c[6]; 264 s[0] = M[0][0]*M[1][1] - M[1][0]*M[0][1]; 265 s[1] = M[0][0]*M[1][2] - M[1][0]*M[0][2]; 266 s[2] = M[0][0]*M[1][3] - M[1][0]*M[0][3]; 267 s[3] = M[0][1]*M[1][2] - M[1][1]*M[0][2]; 268 s[4] = M[0][1]*M[1][3] - M[1][1]*M[0][3]; 269 s[5] = M[0][2]*M[1][3] - M[1][2]*M[0][3]; 270 271 c[0] = M[2][0]*M[3][1] - M[3][0]*M[2][1]; 272 c[1] = M[2][0]*M[3][2] - M[3][0]*M[2][2]; 273 c[2] = M[2][0]*M[3][3] - M[3][0]*M[2][3]; 274 c[3] = M[2][1]*M[3][2] - M[3][1]*M[2][2]; 275 c[4] = M[2][1]*M[3][3] - M[3][1]*M[2][3]; 276 c[5] = M[2][2]*M[3][3] - M[3][2]*M[2][3]; 277 278 /* Assumes it is invertible */ 279 idet = 1.0f/( s[0]*c[5]-s[1]*c[4]+s[2]*c[3]+s[3]*c[2]-s[4]*c[1]+s[5]*c[0] ); 280 281 T[0][0] = ( M[1][1] * c[5] - M[1][2] * c[4] + M[1][3] * c[3]) * idet; 282 T[0][1] = (-M[0][1] * c[5] + M[0][2] * c[4] - M[0][3] * c[3]) * idet; 283 T[0][2] = ( M[3][1] * s[5] - M[3][2] * s[4] + M[3][3] * s[3]) * idet; 284 T[0][3] = (-M[2][1] * s[5] + M[2][2] * s[4] - M[2][3] * s[3]) * idet; 285 286 T[1][0] = (-M[1][0] * c[5] + M[1][2] * c[2] - M[1][3] * c[1]) * idet; 287 T[1][1] = ( M[0][0] * c[5] - M[0][2] * c[2] + M[0][3] * c[1]) * idet; 288 T[1][2] = (-M[3][0] * s[5] + M[3][2] * s[2] - M[3][3] * s[1]) * idet; 289 T[1][3] = ( M[2][0] * s[5] - M[2][2] * s[2] + M[2][3] * s[1]) * idet; 290 291 T[2][0] = ( M[1][0] * c[4] - M[1][1] * c[2] + M[1][3] * c[0]) * idet; 292 T[2][1] = (-M[0][0] * c[4] + M[0][1] * c[2] - M[0][3] * c[0]) * idet; 293 T[2][2] = ( M[3][0] * s[4] - M[3][1] * s[2] + M[3][3] * s[0]) * idet; 294 T[2][3] = (-M[2][0] * s[4] + M[2][1] * s[2] - M[2][3] * s[0]) * idet; 295 296 T[3][0] = (-M[1][0] * c[3] + M[1][1] * c[1] - M[1][2] * c[0]) * idet; 297 T[3][1] = ( M[0][0] * c[3] - M[0][1] * c[1] + M[0][2] * c[0]) * idet; 298 T[3][2] = (-M[3][0] * s[3] + M[3][1] * s[1] - M[3][2] * s[0]) * idet; 299 T[3][3] = ( M[2][0] * s[3] - M[2][1] * s[1] + M[2][2] * s[0]) * idet; 300 } 301 static inline void mat4x4_orthonormalize(mat4x4 R, mat4x4 M) 302 { 303 float s = 1.; 304 vec3 h; 305 306 mat4x4_dup(R, M); 307 vec3_norm(R[2], R[2]); 308 309 s = vec3_mul_inner(R[1], R[2]); 310 vec3_scale(h, R[2], s); 311 vec3_sub(R[1], R[1], h); 312 vec3_norm(R[2], R[2]); 313 314 s = vec3_mul_inner(R[1], R[2]); 315 vec3_scale(h, R[2], s); 316 vec3_sub(R[1], R[1], h); 317 vec3_norm(R[1], R[1]); 318 319 s = vec3_mul_inner(R[0], R[1]); 320 vec3_scale(h, R[1], s); 321 vec3_sub(R[0], R[0], h); 322 vec3_norm(R[0], R[0]); 323 } 324 325 static inline void mat4x4_frustum(mat4x4 M, float l, float r, float b, float t, float n, float f) 326 { 327 M[0][0] = 2.f*n/(r-l); 328 M[0][1] = M[0][2] = M[0][3] = 0.f; 329 330 M[1][1] = 2.f*n/(t-b); 331 M[1][0] = M[1][2] = M[1][3] = 0.f; 332 333 M[2][0] = (r+l)/(r-l); 334 M[2][1] = (t+b)/(t-b); 335 M[2][2] = -(f+n)/(f-n); 336 M[2][3] = -1.f; 337 338 M[3][2] = -2.f*(f*n)/(f-n); 339 M[3][0] = M[3][1] = M[3][3] = 0.f; 340 } 341 static inline void mat4x4_ortho(mat4x4 M, float l, float r, float b, float t, float n, float f) 342 { 343 M[0][0] = 2.f/(r-l); 344 M[0][1] = M[0][2] = M[0][3] = 0.f; 345 346 M[1][1] = 2.f/(t-b); 347 M[1][0] = M[1][2] = M[1][3] = 0.f; 348 349 M[2][2] = -2.f/(f-n); 350 M[2][0] = M[2][1] = M[2][3] = 0.f; 351 352 M[3][0] = -(r+l)/(r-l); 353 M[3][1] = -(t+b)/(t-b); 354 M[3][2] = -(f+n)/(f-n); 355 M[3][3] = 1.f; 356 } 357 static inline void mat4x4_perspective(mat4x4 m, float y_fov, float aspect, float n, float f) 358 { 359 /* NOTE: Degrees are an unhandy unit to work with. 360 * linmath.h uses radians for everything! */ 361 float const a = 1.f / (float) tan(y_fov / 2.f); 362 363 m[0][0] = a / aspect; 364 m[0][1] = 0.f; 365 m[0][2] = 0.f; 366 m[0][3] = 0.f; 367 368 m[1][0] = 0.f; 369 m[1][1] = a; 370 m[1][2] = 0.f; 371 m[1][3] = 0.f; 372 373 m[2][0] = 0.f; 374 m[2][1] = 0.f; 375 m[2][2] = -((f + n) / (f - n)); 376 m[2][3] = -1.f; 377 378 m[3][0] = 0.f; 379 m[3][1] = 0.f; 380 m[3][2] = -((2.f * f * n) / (f - n)); 381 m[3][3] = 0.f; 382 } 383 static inline void mat4x4_look_at(mat4x4 m, vec3 eye, vec3 center, vec3 up) 384 { 385 /* Adapted from Android's OpenGL Matrix.java. */ 386 /* See the OpenGL GLUT documentation for gluLookAt for a description */ 387 /* of the algorithm. We implement it in a straightforward way: */ 388 389 /* TODO: The negation of of can be spared by swapping the order of 390 * operands in the following cross products in the right way. */ 391 vec3 f; 392 vec3 s; 393 vec3 t; 394 395 vec3_sub(f, center, eye); 396 vec3_norm(f, f); 397 398 vec3_mul_cross(s, f, up); 399 vec3_norm(s, s); 400 401 vec3_mul_cross(t, s, f); 402 403 m[0][0] = s[0]; 404 m[0][1] = t[0]; 405 m[0][2] = -f[0]; 406 m[0][3] = 0.f; 407 408 m[1][0] = s[1]; 409 m[1][1] = t[1]; 410 m[1][2] = -f[1]; 411 m[1][3] = 0.f; 412 413 m[2][0] = s[2]; 414 m[2][1] = t[2]; 415 m[2][2] = -f[2]; 416 m[2][3] = 0.f; 417 418 m[3][0] = 0.f; 419 m[3][1] = 0.f; 420 m[3][2] = 0.f; 421 m[3][3] = 1.f; 422 423 mat4x4_translate_in_place(m, -eye[0], -eye[1], -eye[2]); 424 } 425 426 typedef float quat[4]; 427 static inline void quat_identity(quat q) 428 { 429 q[0] = q[1] = q[2] = 0.f; 430 q[3] = 1.f; 431 } 432 static inline void quat_add(quat r, quat a, quat b) 433 { 434 int i; 435 for(i=0; i<4; ++i) 436 r[i] = a[i] + b[i]; 437 } 438 static inline void quat_sub(quat r, quat a, quat b) 439 { 440 int i; 441 for(i=0; i<4; ++i) 442 r[i] = a[i] - b[i]; 443 } 444 static inline void quat_mul(quat r, quat p, quat q) 445 { 446 vec3 w; 447 vec3_mul_cross(r, p, q); 448 vec3_scale(w, p, q[3]); 449 vec3_add(r, r, w); 450 vec3_scale(w, q, p[3]); 451 vec3_add(r, r, w); 452 r[3] = p[3]*q[3] - vec3_mul_inner(p, q); 453 } 454 static inline void quat_scale(quat r, quat v, float s) 455 { 456 int i; 457 for(i=0; i<4; ++i) 458 r[i] = v[i] * s; 459 } 460 static inline float quat_inner_product(quat a, quat b) 461 { 462 float p = 0.f; 463 int i; 464 for(i=0; i<4; ++i) 465 p += b[i]*a[i]; 466 return p; 467 } 468 static inline void quat_conj(quat r, quat q) 469 { 470 int i; 471 for(i=0; i<3; ++i) 472 r[i] = -q[i]; 473 r[3] = q[3]; 474 } 475 static inline void quat_rotate(quat r, float angle, vec3 axis) { 476 int i; 477 vec3 v; 478 vec3_scale(v, axis, sinf(angle / 2)); 479 for(i=0; i<3; ++i) 480 r[i] = v[i]; 481 r[3] = cosf(angle / 2); 482 } 483 #define quat_norm vec4_norm 484 static inline void quat_mul_vec3(vec3 r, quat q, vec3 v) 485 { 486 /* 487 * Method by Fabian 'ryg' Giessen (of Farbrausch) 488 t = 2 * cross(q.xyz, v) 489 v' = v + q.w * t + cross(q.xyz, t) 490 */ 491 vec3 t = {q[0], q[1], q[2]}; 492 vec3 u = {q[0], q[1], q[2]}; 493 494 vec3_mul_cross(t, t, v); 495 vec3_scale(t, t, 2); 496 497 vec3_mul_cross(u, u, t); 498 vec3_scale(t, t, q[3]); 499 500 vec3_add(r, v, t); 501 vec3_add(r, r, u); 502 } 503 static inline void mat4x4_from_quat(mat4x4 M, quat q) 504 { 505 float a = q[3]; 506 float b = q[0]; 507 float c = q[1]; 508 float d = q[2]; 509 float a2 = a*a; 510 float b2 = b*b; 511 float c2 = c*c; 512 float d2 = d*d; 513 514 M[0][0] = a2 + b2 - c2 - d2; 515 M[0][1] = 2.f*(b*c + a*d); 516 M[0][2] = 2.f*(b*d - a*c); 517 M[0][3] = 0.f; 518 519 M[1][0] = 2*(b*c - a*d); 520 M[1][1] = a2 - b2 + c2 - d2; 521 M[1][2] = 2.f*(c*d + a*b); 522 M[1][3] = 0.f; 523 524 M[2][0] = 2.f*(b*d + a*c); 525 M[2][1] = 2.f*(c*d - a*b); 526 M[2][2] = a2 - b2 - c2 + d2; 527 M[2][3] = 0.f; 528 529 M[3][0] = M[3][1] = M[3][2] = 0.f; 530 M[3][3] = 1.f; 531 } 532 533 static inline void mat4x4o_mul_quat(mat4x4 R, mat4x4 M, quat q) 534 { 535 /* XXX: The way this is written only works for othogonal matrices. */ 536 /* TODO: Take care of non-orthogonal case. */ 537 quat_mul_vec3(R[0], q, M[0]); 538 quat_mul_vec3(R[1], q, M[1]); 539 quat_mul_vec3(R[2], q, M[2]); 540 541 R[3][0] = R[3][1] = R[3][2] = 0.f; 542 R[3][3] = 1.f; 543 } 544 static inline void quat_from_mat4x4(quat q, mat4x4 M) 545 { 546 float r=0.f; 547 int i; 548 549 int perm[] = { 0, 1, 2, 0, 1 }; 550 int *p = perm; 551 552 for(i = 0; i<3; i++) { 553 float m = M[i][i]; 554 if( m < r ) 555 continue; 556 m = r; 557 p = &perm[i]; 558 } 559 560 r = (float) sqrt(1.f + M[p[0]][p[0]] - M[p[1]][p[1]] - M[p[2]][p[2]] ); 561 562 if(r < 1e-6) { 563 q[0] = 1.f; 564 q[1] = q[2] = q[3] = 0.f; 565 return; 566 } 567 568 q[0] = r/2.f; 569 q[1] = (M[p[0]][p[1]] - M[p[1]][p[0]])/(2.f*r); 570 q[2] = (M[p[2]][p[0]] - M[p[0]][p[2]])/(2.f*r); 571 q[3] = (M[p[2]][p[1]] - M[p[1]][p[2]])/(2.f*r); 572 } 573 574 #endif