1 /* 2 * Copyright (c) 2015-2016 The Khronos Group Inc. 3 * Copyright (c) 2015-2016 Valve Corporation 4 * Copyright (c) 2015-2016 LunarG, Inc. 5 * 6 * Licensed under the Apache License, Version 2.0 (the "License"); 7 * you may not use this file except in compliance with the License. 8 * You may obtain a copy of the License at 9 * 10 * http://www.apache.org/licenses/LICENSE-2.0 11 * 12 * Unless required by applicable law or agreed to in writing, software 13 * distributed under the License is distributed on an "AS IS" BASIS, 14 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 15 * See the License for the specific language governing permissions and 16 * limitations under the License. 17 * 18 * Relicensed from the WTFPL (http://www.wtfpl.net/faq/). 19 */ 20 21 #ifndef LINMATH_H 22 #define LINMATH_H 23 24 #include <math.h> 25 26 // Converts degrees to radians. 27 #define degreesToRadians(angleDegrees) (angleDegrees * M_PI / 180.0) 28 29 // Converts radians to degrees. 30 #define radiansToDegrees(angleRadians) (angleRadians * 180.0 / M_PI) 31 32 typedef float vec3[3]; 33 static inline void vec3_add(vec3 r, vec3 const a, vec3 const b) { 34 int i; 35 for (i = 0; i < 3; ++i) 36 r[i] = a[i] + b[i]; 37 } 38 static inline void vec3_sub(vec3 r, vec3 const a, vec3 const b) { 39 int i; 40 for (i = 0; i < 3; ++i) 41 r[i] = a[i] - b[i]; 42 } 43 static inline void vec3_scale(vec3 r, vec3 const v, float const s) { 44 int i; 45 for (i = 0; i < 3; ++i) 46 r[i] = v[i] * s; 47 } 48 static inline float vec3_mul_inner(vec3 const a, vec3 const b) { 49 float p = 0.f; 50 int i; 51 for (i = 0; i < 3; ++i) 52 p += b[i] * a[i]; 53 return p; 54 } 55 static inline void vec3_mul_cross(vec3 r, vec3 const a, vec3 const b) { 56 r[0] = a[1] * b[2] - a[2] * b[1]; 57 r[1] = a[2] * b[0] - a[0] * b[2]; 58 r[2] = a[0] * b[1] - a[1] * b[0]; 59 } 60 static inline float vec3_len(vec3 const v) { 61 return sqrtf(vec3_mul_inner(v, v)); 62 } 63 static inline void vec3_norm(vec3 r, vec3 const v) { 64 float k = 1.f / vec3_len(v); 65 vec3_scale(r, v, k); 66 } 67 static inline void vec3_reflect(vec3 r, vec3 const v, vec3 const n) { 68 float p = 2.f * vec3_mul_inner(v, n); 69 int i; 70 for (i = 0; i < 3; ++i) 71 r[i] = v[i] - p * n[i]; 72 } 73 74 typedef float vec4[4]; 75 static inline void vec4_add(vec4 r, vec4 const a, vec4 const b) { 76 int i; 77 for (i = 0; i < 4; ++i) 78 r[i] = a[i] + b[i]; 79 } 80 static inline void vec4_sub(vec4 r, vec4 const a, vec4 const b) { 81 int i; 82 for (i = 0; i < 4; ++i) 83 r[i] = a[i] - b[i]; 84 } 85 static inline void vec4_scale(vec4 r, vec4 v, float s) { 86 int i; 87 for (i = 0; i < 4; ++i) 88 r[i] = v[i] * s; 89 } 90 static inline float vec4_mul_inner(vec4 a, vec4 b) { 91 float p = 0.f; 92 int i; 93 for (i = 0; i < 4; ++i) 94 p += b[i] * a[i]; 95 return p; 96 } 97 static inline void vec4_mul_cross(vec4 r, vec4 a, vec4 b) { 98 r[0] = a[1] * b[2] - a[2] * b[1]; 99 r[1] = a[2] * b[0] - a[0] * b[2]; 100 r[2] = a[0] * b[1] - a[1] * b[0]; 101 r[3] = 1.f; 102 } 103 static inline float vec4_len(vec4 v) { return sqrtf(vec4_mul_inner(v, v)); } 104 static inline void vec4_norm(vec4 r, vec4 v) { 105 float k = 1.f / vec4_len(v); 106 vec4_scale(r, v, k); 107 } 108 static inline void vec4_reflect(vec4 r, vec4 v, vec4 n) { 109 float p = 2.f * vec4_mul_inner(v, n); 110 int i; 111 for (i = 0; i < 4; ++i) 112 r[i] = v[i] - p * n[i]; 113 } 114 115 typedef vec4 mat4x4[4]; 116 static inline void mat4x4_identity(mat4x4 M) { 117 int i, j; 118 for (i = 0; i < 4; ++i) 119 for (j = 0; j < 4; ++j) 120 M[i][j] = i == j ? 1.f : 0.f; 121 } 122 static inline void mat4x4_dup(mat4x4 M, mat4x4 N) { 123 int i, j; 124 for (i = 0; i < 4; ++i) 125 for (j = 0; j < 4; ++j) 126 M[i][j] = N[i][j]; 127 } 128 static inline void mat4x4_row(vec4 r, mat4x4 M, int i) { 129 int k; 130 for (k = 0; k < 4; ++k) 131 r[k] = M[k][i]; 132 } 133 static inline void mat4x4_col(vec4 r, mat4x4 M, int i) { 134 int k; 135 for (k = 0; k < 4; ++k) 136 r[k] = M[i][k]; 137 } 138 static inline void mat4x4_transpose(mat4x4 M, mat4x4 N) { 139 int i, j; 140 for (j = 0; j < 4; ++j) 141 for (i = 0; i < 4; ++i) 142 M[i][j] = N[j][i]; 143 } 144 static inline void mat4x4_add(mat4x4 M, mat4x4 a, mat4x4 b) { 145 int i; 146 for (i = 0; i < 4; ++i) 147 vec4_add(M[i], a[i], b[i]); 148 } 149 static inline void mat4x4_sub(mat4x4 M, mat4x4 a, mat4x4 b) { 150 int i; 151 for (i = 0; i < 4; ++i) 152 vec4_sub(M[i], a[i], b[i]); 153 } 154 static inline void mat4x4_scale(mat4x4 M, mat4x4 a, float k) { 155 int i; 156 for (i = 0; i < 4; ++i) 157 vec4_scale(M[i], a[i], k); 158 } 159 static inline void mat4x4_scale_aniso(mat4x4 M, mat4x4 a, float x, float y, 160 float z) { 161 int i; 162 vec4_scale(M[0], a[0], x); 163 vec4_scale(M[1], a[1], y); 164 vec4_scale(M[2], a[2], z); 165 for (i = 0; i < 4; ++i) { 166 M[3][i] = a[3][i]; 167 } 168 } 169 static inline void mat4x4_mul(mat4x4 M, mat4x4 a, mat4x4 b) { 170 int k, r, c; 171 for (c = 0; c < 4; ++c) 172 for (r = 0; r < 4; ++r) { 173 M[c][r] = 0.f; 174 for (k = 0; k < 4; ++k) 175 M[c][r] += a[k][r] * b[c][k]; 176 } 177 } 178 static inline void mat4x4_mul_vec4(vec4 r, mat4x4 M, vec4 v) { 179 int i, j; 180 for (j = 0; j < 4; ++j) { 181 r[j] = 0.f; 182 for (i = 0; i < 4; ++i) 183 r[j] += M[i][j] * v[i]; 184 } 185 } 186 static inline void mat4x4_translate(mat4x4 T, float x, float y, float z) { 187 mat4x4_identity(T); 188 T[3][0] = x; 189 T[3][1] = y; 190 T[3][2] = z; 191 } 192 static inline void mat4x4_translate_in_place(mat4x4 M, float x, float y, 193 float z) { 194 vec4 t = {x, y, z, 0}; 195 vec4 r; 196 int i; 197 for (i = 0; i < 4; ++i) { 198 mat4x4_row(r, M, i); 199 M[3][i] += vec4_mul_inner(r, t); 200 } 201 } 202 static inline void mat4x4_from_vec3_mul_outer(mat4x4 M, vec3 a, vec3 b) { 203 int i, j; 204 for (i = 0; i < 4; ++i) 205 for (j = 0; j < 4; ++j) 206 M[i][j] = i < 3 && j < 3 ? a[i] * b[j] : 0.f; 207 } 208 static inline void mat4x4_rotate(mat4x4 R, mat4x4 M, float x, float y, float z, 209 float angle) { 210 float s = sinf(angle); 211 float c = cosf(angle); 212 vec3 u = {x, y, z}; 213 214 if (vec3_len(u) > 1e-4) { 215 vec3_norm(u, u); 216 mat4x4 T; 217 mat4x4_from_vec3_mul_outer(T, u, u); 218 219 mat4x4 S = {{0, u[2], -u[1], 0}, 220 {-u[2], 0, u[0], 0}, 221 {u[1], -u[0], 0, 0}, 222 {0, 0, 0, 0}}; 223 mat4x4_scale(S, S, s); 224 225 mat4x4 C; 226 mat4x4_identity(C); 227 mat4x4_sub(C, C, T); 228 229 mat4x4_scale(C, C, c); 230 231 mat4x4_add(T, T, C); 232 mat4x4_add(T, T, S); 233 234 T[3][3] = 1.; 235 mat4x4_mul(R, M, T); 236 } else { 237 mat4x4_dup(R, M); 238 } 239 } 240 static inline void mat4x4_rotate_X(mat4x4 Q, mat4x4 M, float angle) { 241 float s = sinf(angle); 242 float c = cosf(angle); 243 mat4x4 R = {{1.f, 0.f, 0.f, 0.f}, 244 {0.f, c, s, 0.f}, 245 {0.f, -s, c, 0.f}, 246 {0.f, 0.f, 0.f, 1.f}}; 247 mat4x4_mul(Q, M, R); 248 } 249 static inline void mat4x4_rotate_Y(mat4x4 Q, mat4x4 M, float angle) { 250 float s = sinf(angle); 251 float c = cosf(angle); 252 mat4x4 R = {{c, 0.f, s, 0.f}, 253 {0.f, 1.f, 0.f, 0.f}, 254 {-s, 0.f, c, 0.f}, 255 {0.f, 0.f, 0.f, 1.f}}; 256 mat4x4_mul(Q, M, R); 257 } 258 static inline void mat4x4_rotate_Z(mat4x4 Q, mat4x4 M, float angle) { 259 float s = sinf(angle); 260 float c = cosf(angle); 261 mat4x4 R = {{c, s, 0.f, 0.f}, 262 {-s, c, 0.f, 0.f}, 263 {0.f, 0.f, 1.f, 0.f}, 264 {0.f, 0.f, 0.f, 1.f}}; 265 mat4x4_mul(Q, M, R); 266 } 267 static inline void mat4x4_invert(mat4x4 T, mat4x4 M) { 268 float s[6]; 269 float c[6]; 270 s[0] = M[0][0] * M[1][1] - M[1][0] * M[0][1]; 271 s[1] = M[0][0] * M[1][2] - M[1][0] * M[0][2]; 272 s[2] = M[0][0] * M[1][3] - M[1][0] * M[0][3]; 273 s[3] = M[0][1] * M[1][2] - M[1][1] * M[0][2]; 274 s[4] = M[0][1] * M[1][3] - M[1][1] * M[0][3]; 275 s[5] = M[0][2] * M[1][3] - M[1][2] * M[0][3]; 276 277 c[0] = M[2][0] * M[3][1] - M[3][0] * M[2][1]; 278 c[1] = M[2][0] * M[3][2] - M[3][0] * M[2][2]; 279 c[2] = M[2][0] * M[3][3] - M[3][0] * M[2][3]; 280 c[3] = M[2][1] * M[3][2] - M[3][1] * M[2][2]; 281 c[4] = M[2][1] * M[3][3] - M[3][1] * M[2][3]; 282 c[5] = M[2][2] * M[3][3] - M[3][2] * M[2][3]; 283 284 /* Assumes it is invertible */ 285 float idet = 1.0f / (s[0] * c[5] - s[1] * c[4] + s[2] * c[3] + s[3] * c[2] - 286 s[4] * c[1] + s[5] * c[0]); 287 288 T[0][0] = (M[1][1] * c[5] - M[1][2] * c[4] + M[1][3] * c[3]) * idet; 289 T[0][1] = (-M[0][1] * c[5] + M[0][2] * c[4] - M[0][3] * c[3]) * idet; 290 T[0][2] = (M[3][1] * s[5] - M[3][2] * s[4] + M[3][3] * s[3]) * idet; 291 T[0][3] = (-M[2][1] * s[5] + M[2][2] * s[4] - M[2][3] * s[3]) * idet; 292 293 T[1][0] = (-M[1][0] * c[5] + M[1][2] * c[2] - M[1][3] * c[1]) * idet; 294 T[1][1] = (M[0][0] * c[5] - M[0][2] * c[2] + M[0][3] * c[1]) * idet; 295 T[1][2] = (-M[3][0] * s[5] + M[3][2] * s[2] - M[3][3] * s[1]) * idet; 296 T[1][3] = (M[2][0] * s[5] - M[2][2] * s[2] + M[2][3] * s[1]) * idet; 297 298 T[2][0] = (M[1][0] * c[4] - M[1][1] * c[2] + M[1][3] * c[0]) * idet; 299 T[2][1] = (-M[0][0] * c[4] + M[0][1] * c[2] - M[0][3] * c[0]) * idet; 300 T[2][2] = (M[3][0] * s[4] - M[3][1] * s[2] + M[3][3] * s[0]) * idet; 301 T[2][3] = (-M[2][0] * s[4] + M[2][1] * s[2] - M[2][3] * s[0]) * idet; 302 303 T[3][0] = (-M[1][0] * c[3] + M[1][1] * c[1] - M[1][2] * c[0]) * idet; 304 T[3][1] = (M[0][0] * c[3] - M[0][1] * c[1] + M[0][2] * c[0]) * idet; 305 T[3][2] = (-M[3][0] * s[3] + M[3][1] * s[1] - M[3][2] * s[0]) * idet; 306 T[3][3] = (M[2][0] * s[3] - M[2][1] * s[1] + M[2][2] * s[0]) * idet; 307 } 308 static inline void mat4x4_orthonormalize(mat4x4 R, mat4x4 M) { 309 mat4x4_dup(R, M); 310 float s = 1.; 311 vec3 h; 312 313 vec3_norm(R[2], R[2]); 314 315 s = vec3_mul_inner(R[1], R[2]); 316 vec3_scale(h, R[2], s); 317 vec3_sub(R[1], R[1], h); 318 vec3_norm(R[2], R[2]); 319 320 s = vec3_mul_inner(R[1], R[2]); 321 vec3_scale(h, R[2], s); 322 vec3_sub(R[1], R[1], h); 323 vec3_norm(R[1], R[1]); 324 325 s = vec3_mul_inner(R[0], R[1]); 326 vec3_scale(h, R[1], s); 327 vec3_sub(R[0], R[0], h); 328 vec3_norm(R[0], R[0]); 329 } 330 331 static inline void mat4x4_frustum(mat4x4 M, float l, float r, float b, float t, 332 float n, float f) { 333 M[0][0] = 2.f * n / (r - l); 334 M[0][1] = M[0][2] = M[0][3] = 0.f; 335 336 M[1][1] = 2.f * n / (t - b); 337 M[1][0] = M[1][2] = M[1][3] = 0.f; 338 339 M[2][0] = (r + l) / (r - l); 340 M[2][1] = (t + b) / (t - b); 341 M[2][2] = -(f + n) / (f - n); 342 M[2][3] = -1.f; 343 344 M[3][2] = -2.f * (f * n) / (f - n); 345 M[3][0] = M[3][1] = M[3][3] = 0.f; 346 } 347 static inline void mat4x4_ortho(mat4x4 M, float l, float r, float b, float t, 348 float n, float f) { 349 M[0][0] = 2.f / (r - l); 350 M[0][1] = M[0][2] = M[0][3] = 0.f; 351 352 M[1][1] = 2.f / (t - b); 353 M[1][0] = M[1][2] = M[1][3] = 0.f; 354 355 M[2][2] = -2.f / (f - n); 356 M[2][0] = M[2][1] = M[2][3] = 0.f; 357 358 M[3][0] = -(r + l) / (r - l); 359 M[3][1] = -(t + b) / (t - b); 360 M[3][2] = -(f + n) / (f - n); 361 M[3][3] = 1.f; 362 } 363 static inline void mat4x4_perspective(mat4x4 m, float y_fov, float aspect, 364 float n, float f) { 365 /* NOTE: Degrees are an unhandy unit to work with. 366 * linmath.h uses radians for everything! */ 367 float const a = (float)(1.f / tan(y_fov / 2.f)); 368 369 m[0][0] = a / aspect; 370 m[0][1] = 0.f; 371 m[0][2] = 0.f; 372 m[0][3] = 0.f; 373 374 m[1][0] = 0.f; 375 m[1][1] = a; 376 m[1][2] = 0.f; 377 m[1][3] = 0.f; 378 379 m[2][0] = 0.f; 380 m[2][1] = 0.f; 381 m[2][2] = -((f + n) / (f - n)); 382 m[2][3] = -1.f; 383 384 m[3][0] = 0.f; 385 m[3][1] = 0.f; 386 m[3][2] = -((2.f * f * n) / (f - n)); 387 m[3][3] = 0.f; 388 } 389 static inline void mat4x4_look_at(mat4x4 m, vec3 eye, vec3 center, vec3 up) { 390 /* Adapted from Android's OpenGL Matrix.java. */ 391 /* See the OpenGL GLUT documentation for gluLookAt for a description */ 392 /* of the algorithm. We implement it in a straightforward way: */ 393 394 /* TODO: The negation of of can be spared by swapping the order of 395 * operands in the following cross products in the right way. */ 396 vec3 f; 397 vec3_sub(f, center, eye); 398 vec3_norm(f, f); 399 400 vec3 s; 401 vec3_mul_cross(s, f, up); 402 vec3_norm(s, s); 403 404 vec3 t; 405 vec3_mul_cross(t, s, f); 406 407 m[0][0] = s[0]; 408 m[0][1] = t[0]; 409 m[0][2] = -f[0]; 410 m[0][3] = 0.f; 411 412 m[1][0] = s[1]; 413 m[1][1] = t[1]; 414 m[1][2] = -f[1]; 415 m[1][3] = 0.f; 416 417 m[2][0] = s[2]; 418 m[2][1] = t[2]; 419 m[2][2] = -f[2]; 420 m[2][3] = 0.f; 421 422 m[3][0] = 0.f; 423 m[3][1] = 0.f; 424 m[3][2] = 0.f; 425 m[3][3] = 1.f; 426 427 mat4x4_translate_in_place(m, -eye[0], -eye[1], -eye[2]); 428 } 429 430 typedef float quat[4]; 431 static inline void quat_identity(quat q) { 432 q[0] = q[1] = q[2] = 0.f; 433 q[3] = 1.f; 434 } 435 static inline void quat_add(quat r, quat a, quat b) { 436 int i; 437 for (i = 0; i < 4; ++i) 438 r[i] = a[i] + b[i]; 439 } 440 static inline void quat_sub(quat r, quat a, quat b) { 441 int i; 442 for (i = 0; i < 4; ++i) 443 r[i] = a[i] - b[i]; 444 } 445 static inline void quat_mul(quat r, quat p, quat q) { 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 int i; 456 for (i = 0; i < 4; ++i) 457 r[i] = v[i] * s; 458 } 459 static inline float quat_inner_product(quat a, quat b) { 460 float p = 0.f; 461 int i; 462 for (i = 0; i < 4; ++i) 463 p += b[i] * a[i]; 464 return p; 465 } 466 static inline void quat_conj(quat r, quat q) { 467 int i; 468 for (i = 0; i < 3; ++i) 469 r[i] = -q[i]; 470 r[3] = q[3]; 471 } 472 #define quat_norm vec4_norm 473 static inline void quat_mul_vec3(vec3 r, quat q, vec3 v) { 474 quat v_ = {v[0], v[1], v[2], 0.f}; 475 476 quat_conj(r, q); 477 quat_norm(r, r); 478 quat_mul(r, v_, r); 479 quat_mul(r, q, r); 480 } 481 static inline void mat4x4_from_quat(mat4x4 M, quat q) { 482 float a = q[3]; 483 float b = q[0]; 484 float c = q[1]; 485 float d = q[2]; 486 float a2 = a * a; 487 float b2 = b * b; 488 float c2 = c * c; 489 float d2 = d * d; 490 491 M[0][0] = a2 + b2 - c2 - d2; 492 M[0][1] = 2.f * (b * c + a * d); 493 M[0][2] = 2.f * (b * d - a * c); 494 M[0][3] = 0.f; 495 496 M[1][0] = 2 * (b * c - a * d); 497 M[1][1] = a2 - b2 + c2 - d2; 498 M[1][2] = 2.f * (c * d + a * b); 499 M[1][3] = 0.f; 500 501 M[2][0] = 2.f * (b * d + a * c); 502 M[2][1] = 2.f * (c * d - a * b); 503 M[2][2] = a2 - b2 - c2 + d2; 504 M[2][3] = 0.f; 505 506 M[3][0] = M[3][1] = M[3][2] = 0.f; 507 M[3][3] = 1.f; 508 } 509 510 static inline void mat4x4o_mul_quat(mat4x4 R, mat4x4 M, quat q) { 511 /* XXX: The way this is written only works for othogonal matrices. */ 512 /* TODO: Take care of non-orthogonal case. */ 513 quat_mul_vec3(R[0], q, M[0]); 514 quat_mul_vec3(R[1], q, M[1]); 515 quat_mul_vec3(R[2], q, M[2]); 516 517 R[3][0] = R[3][1] = R[3][2] = 0.f; 518 R[3][3] = 1.f; 519 } 520 static inline void quat_from_mat4x4(quat q, mat4x4 M) { 521 float r = 0.f; 522 int i; 523 524 int perm[] = {0, 1, 2, 0, 1}; 525 int *p = perm; 526 527 for (i = 0; i < 3; i++) { 528 float m = M[i][i]; 529 if (m < r) 530 continue; 531 m = r; 532 p = &perm[i]; 533 } 534 535 r = sqrtf(1.f + M[p[0]][p[0]] - M[p[1]][p[1]] - M[p[2]][p[2]]); 536 537 if (r < 1e-6) { 538 q[0] = 1.f; 539 q[1] = q[2] = q[3] = 0.f; 540 return; 541 } 542 543 q[0] = r / 2.f; 544 q[1] = (M[p[0]][p[1]] - M[p[1]][p[0]]) / (2.f * r); 545 q[2] = (M[p[2]][p[0]] - M[p[0]][p[2]]) / (2.f * r); 546 q[3] = (M[p[2]][p[1]] - M[p[1]][p[2]]) / (2.f * r); 547 } 548 549 #endif 550
