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) r[i] = a[i] + b[i]; 36 } 37 static inline void vec3_sub(vec3 r, vec3 const a, vec3 const b) { 38 int i; 39 for (i = 0; i < 3; ++i) r[i] = a[i] - b[i]; 40 } 41 static inline void vec3_scale(vec3 r, vec3 const v, float const s) { 42 int i; 43 for (i = 0; i < 3; ++i) r[i] = v[i] * s; 44 } 45 static inline float vec3_mul_inner(vec3 const a, vec3 const b) { 46 float p = 0.f; 47 int i; 48 for (i = 0; i < 3; ++i) p += b[i] * a[i]; 49 return p; 50 } 51 static inline void vec3_mul_cross(vec3 r, vec3 const a, vec3 const b) { 52 r[0] = a[1] * b[2] - a[2] * b[1]; 53 r[1] = a[2] * b[0] - a[0] * b[2]; 54 r[2] = a[0] * b[1] - a[1] * b[0]; 55 } 56 static inline float vec3_len(vec3 const v) { return sqrtf(vec3_mul_inner(v, v)); } 57 static inline void vec3_norm(vec3 r, vec3 const v) { 58 float k = 1.f / vec3_len(v); 59 vec3_scale(r, v, k); 60 } 61 static inline void vec3_reflect(vec3 r, vec3 const v, vec3 const n) { 62 float p = 2.f * vec3_mul_inner(v, n); 63 int i; 64 for (i = 0; i < 3; ++i) r[i] = v[i] - p * n[i]; 65 } 66 67 typedef float vec4[4]; 68 static inline void vec4_add(vec4 r, vec4 const a, vec4 const b) { 69 int i; 70 for (i = 0; i < 4; ++i) r[i] = a[i] + b[i]; 71 } 72 static inline void vec4_sub(vec4 r, vec4 const a, vec4 const b) { 73 int i; 74 for (i = 0; i < 4; ++i) r[i] = a[i] - b[i]; 75 } 76 static inline void vec4_scale(vec4 r, vec4 v, float s) { 77 int i; 78 for (i = 0; i < 4; ++i) r[i] = v[i] * s; 79 } 80 static inline float vec4_mul_inner(vec4 a, vec4 b) { 81 float p = 0.f; 82 int i; 83 for (i = 0; i < 4; ++i) p += b[i] * a[i]; 84 return p; 85 } 86 static inline void vec4_mul_cross(vec4 r, vec4 a, vec4 b) { 87 r[0] = a[1] * b[2] - a[2] * b[1]; 88 r[1] = a[2] * b[0] - a[0] * b[2]; 89 r[2] = a[0] * b[1] - a[1] * b[0]; 90 r[3] = 1.f; 91 } 92 static inline float vec4_len(vec4 v) { return sqrtf(vec4_mul_inner(v, v)); } 93 static inline void vec4_norm(vec4 r, vec4 v) { 94 float k = 1.f / vec4_len(v); 95 vec4_scale(r, v, k); 96 } 97 static inline void vec4_reflect(vec4 r, vec4 v, vec4 n) { 98 float p = 2.f * vec4_mul_inner(v, n); 99 int i; 100 for (i = 0; i < 4; ++i) r[i] = v[i] - p * n[i]; 101 } 102 103 typedef vec4 mat4x4[4]; 104 static inline void mat4x4_identity(mat4x4 M) { 105 int i, j; 106 for (i = 0; i < 4; ++i) 107 for (j = 0; j < 4; ++j) M[i][j] = i == j ? 1.f : 0.f; 108 } 109 static inline void mat4x4_dup(mat4x4 M, mat4x4 N) { 110 int i, j; 111 for (i = 0; i < 4; ++i) 112 for (j = 0; j < 4; ++j) M[i][j] = N[i][j]; 113 } 114 static inline void mat4x4_row(vec4 r, mat4x4 M, int i) { 115 int k; 116 for (k = 0; k < 4; ++k) r[k] = M[k][i]; 117 } 118 static inline void mat4x4_col(vec4 r, mat4x4 M, int i) { 119 int k; 120 for (k = 0; k < 4; ++k) r[k] = M[i][k]; 121 } 122 static inline void mat4x4_transpose(mat4x4 M, mat4x4 N) { 123 int i, j; 124 for (j = 0; j < 4; ++j) 125 for (i = 0; i < 4; ++i) M[i][j] = N[j][i]; 126 } 127 static inline void mat4x4_add(mat4x4 M, mat4x4 a, mat4x4 b) { 128 int i; 129 for (i = 0; i < 4; ++i) vec4_add(M[i], a[i], b[i]); 130 } 131 static inline void mat4x4_sub(mat4x4 M, mat4x4 a, mat4x4 b) { 132 int i; 133 for (i = 0; i < 4; ++i) vec4_sub(M[i], a[i], b[i]); 134 } 135 static inline void mat4x4_scale(mat4x4 M, mat4x4 a, float k) { 136 int i; 137 for (i = 0; i < 4; ++i) vec4_scale(M[i], a[i], k); 138 } 139 static inline void mat4x4_scale_aniso(mat4x4 M, mat4x4 a, float x, float y, float z) { 140 int i; 141 vec4_scale(M[0], a[0], x); 142 vec4_scale(M[1], a[1], y); 143 vec4_scale(M[2], a[2], z); 144 for (i = 0; i < 4; ++i) { 145 M[3][i] = a[3][i]; 146 } 147 } 148 static inline void mat4x4_mul(mat4x4 M, mat4x4 a, mat4x4 b) { 149 int k, r, c; 150 for (c = 0; c < 4; ++c) 151 for (r = 0; r < 4; ++r) { 152 M[c][r] = 0.f; 153 for (k = 0; k < 4; ++k) M[c][r] += a[k][r] * b[c][k]; 154 } 155 } 156 static inline void mat4x4_mul_vec4(vec4 r, mat4x4 M, vec4 v) { 157 int i, j; 158 for (j = 0; j < 4; ++j) { 159 r[j] = 0.f; 160 for (i = 0; i < 4; ++i) r[j] += M[i][j] * v[i]; 161 } 162 } 163 static inline void mat4x4_translate(mat4x4 T, float x, float y, float z) { 164 mat4x4_identity(T); 165 T[3][0] = x; 166 T[3][1] = y; 167 T[3][2] = z; 168 } 169 static inline void mat4x4_translate_in_place(mat4x4 M, float x, float y, float z) { 170 vec4 t = {x, y, z, 0}; 171 vec4 r; 172 int i; 173 for (i = 0; i < 4; ++i) { 174 mat4x4_row(r, M, i); 175 M[3][i] += vec4_mul_inner(r, t); 176 } 177 } 178 static inline void mat4x4_from_vec3_mul_outer(mat4x4 M, vec3 a, vec3 b) { 179 int i, j; 180 for (i = 0; i < 4; ++i) 181 for (j = 0; j < 4; ++j) M[i][j] = i < 3 && j < 3 ? a[i] * b[j] : 0.f; 182 } 183 static inline void mat4x4_rotate(mat4x4 R, mat4x4 M, float x, float y, float z, float angle) { 184 float s = sinf(angle); 185 float c = cosf(angle); 186 vec3 u = {x, y, z}; 187 188 if (vec3_len(u) > 1e-4) { 189 vec3_norm(u, u); 190 mat4x4 T; 191 mat4x4_from_vec3_mul_outer(T, u, u); 192 193 mat4x4 S = {{0, u[2], -u[1], 0}, {-u[2], 0, u[0], 0}, {u[1], -u[0], 0, 0}, {0, 0, 0, 0}}; 194 mat4x4_scale(S, S, s); 195 196 mat4x4 C; 197 mat4x4_identity(C); 198 mat4x4_sub(C, C, T); 199 200 mat4x4_scale(C, C, c); 201 202 mat4x4_add(T, T, C); 203 mat4x4_add(T, T, S); 204 205 T[3][3] = 1.; 206 mat4x4_mul(R, M, T); 207 } else { 208 mat4x4_dup(R, M); 209 } 210 } 211 static inline void mat4x4_rotate_X(mat4x4 Q, mat4x4 M, float angle) { 212 float s = sinf(angle); 213 float c = cosf(angle); 214 mat4x4 R = {{1.f, 0.f, 0.f, 0.f}, {0.f, c, s, 0.f}, {0.f, -s, c, 0.f}, {0.f, 0.f, 0.f, 1.f}}; 215 mat4x4_mul(Q, M, R); 216 } 217 static inline void mat4x4_rotate_Y(mat4x4 Q, mat4x4 M, float angle) { 218 float s = sinf(angle); 219 float c = cosf(angle); 220 mat4x4 R = {{c, 0.f, s, 0.f}, {0.f, 1.f, 0.f, 0.f}, {-s, 0.f, c, 0.f}, {0.f, 0.f, 0.f, 1.f}}; 221 mat4x4_mul(Q, M, R); 222 } 223 static inline void mat4x4_rotate_Z(mat4x4 Q, mat4x4 M, float angle) { 224 float s = sinf(angle); 225 float c = cosf(angle); 226 mat4x4 R = {{c, s, 0.f, 0.f}, {-s, c, 0.f, 0.f}, {0.f, 0.f, 1.f, 0.f}, {0.f, 0.f, 0.f, 1.f}}; 227 mat4x4_mul(Q, M, R); 228 } 229 static inline void mat4x4_invert(mat4x4 T, mat4x4 M) { 230 float s[6]; 231 float c[6]; 232 s[0] = M[0][0] * M[1][1] - M[1][0] * M[0][1]; 233 s[1] = M[0][0] * M[1][2] - M[1][0] * M[0][2]; 234 s[2] = M[0][0] * M[1][3] - M[1][0] * M[0][3]; 235 s[3] = M[0][1] * M[1][2] - M[1][1] * M[0][2]; 236 s[4] = M[0][1] * M[1][3] - M[1][1] * M[0][3]; 237 s[5] = M[0][2] * M[1][3] - M[1][2] * M[0][3]; 238 239 c[0] = M[2][0] * M[3][1] - M[3][0] * M[2][1]; 240 c[1] = M[2][0] * M[3][2] - M[3][0] * M[2][2]; 241 c[2] = M[2][0] * M[3][3] - M[3][0] * M[2][3]; 242 c[3] = M[2][1] * M[3][2] - M[3][1] * M[2][2]; 243 c[4] = M[2][1] * M[3][3] - M[3][1] * M[2][3]; 244 c[5] = M[2][2] * M[3][3] - M[3][2] * M[2][3]; 245 246 /* Assumes it is invertible */ 247 float 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]); 248 249 T[0][0] = (M[1][1] * c[5] - M[1][2] * c[4] + M[1][3] * c[3]) * idet; 250 T[0][1] = (-M[0][1] * c[5] + M[0][2] * c[4] - M[0][3] * c[3]) * idet; 251 T[0][2] = (M[3][1] * s[5] - M[3][2] * s[4] + M[3][3] * s[3]) * idet; 252 T[0][3] = (-M[2][1] * s[5] + M[2][2] * s[4] - M[2][3] * s[3]) * idet; 253 254 T[1][0] = (-M[1][0] * c[5] + M[1][2] * c[2] - M[1][3] * c[1]) * idet; 255 T[1][1] = (M[0][0] * c[5] - M[0][2] * c[2] + M[0][3] * c[1]) * idet; 256 T[1][2] = (-M[3][0] * s[5] + M[3][2] * s[2] - M[3][3] * s[1]) * idet; 257 T[1][3] = (M[2][0] * s[5] - M[2][2] * s[2] + M[2][3] * s[1]) * idet; 258 259 T[2][0] = (M[1][0] * c[4] - M[1][1] * c[2] + M[1][3] * c[0]) * idet; 260 T[2][1] = (-M[0][0] * c[4] + M[0][1] * c[2] - M[0][3] * c[0]) * idet; 261 T[2][2] = (M[3][0] * s[4] - M[3][1] * s[2] + M[3][3] * s[0]) * idet; 262 T[2][3] = (-M[2][0] * s[4] + M[2][1] * s[2] - M[2][3] * s[0]) * idet; 263 264 T[3][0] = (-M[1][0] * c[3] + M[1][1] * c[1] - M[1][2] * c[0]) * idet; 265 T[3][1] = (M[0][0] * c[3] - M[0][1] * c[1] + M[0][2] * c[0]) * idet; 266 T[3][2] = (-M[3][0] * s[3] + M[3][1] * s[1] - M[3][2] * s[0]) * idet; 267 T[3][3] = (M[2][0] * s[3] - M[2][1] * s[1] + M[2][2] * s[0]) * idet; 268 } 269 static inline void mat4x4_orthonormalize(mat4x4 R, mat4x4 M) { 270 mat4x4_dup(R, M); 271 float s = 1.; 272 vec3 h; 273 274 vec3_norm(R[2], R[2]); 275 276 s = vec3_mul_inner(R[1], R[2]); 277 vec3_scale(h, R[2], s); 278 vec3_sub(R[1], R[1], h); 279 vec3_norm(R[2], R[2]); 280 281 s = vec3_mul_inner(R[1], R[2]); 282 vec3_scale(h, R[2], s); 283 vec3_sub(R[1], R[1], h); 284 vec3_norm(R[1], R[1]); 285 286 s = vec3_mul_inner(R[0], R[1]); 287 vec3_scale(h, R[1], s); 288 vec3_sub(R[0], R[0], h); 289 vec3_norm(R[0], R[0]); 290 } 291 292 static inline void mat4x4_frustum(mat4x4 M, float l, float r, float b, float t, float n, float f) { 293 M[0][0] = 2.f * n / (r - l); 294 M[0][1] = M[0][2] = M[0][3] = 0.f; 295 296 M[1][1] = 2.f * n / (t - b); 297 M[1][0] = M[1][2] = M[1][3] = 0.f; 298 299 M[2][0] = (r + l) / (r - l); 300 M[2][1] = (t + b) / (t - b); 301 M[2][2] = -(f + n) / (f - n); 302 M[2][3] = -1.f; 303 304 M[3][2] = -2.f * (f * n) / (f - n); 305 M[3][0] = M[3][1] = M[3][3] = 0.f; 306 } 307 static inline void mat4x4_ortho(mat4x4 M, float l, float r, float b, float t, float n, float f) { 308 M[0][0] = 2.f / (r - l); 309 M[0][1] = M[0][2] = M[0][3] = 0.f; 310 311 M[1][1] = 2.f / (t - b); 312 M[1][0] = M[1][2] = M[1][3] = 0.f; 313 314 M[2][2] = -2.f / (f - n); 315 M[2][0] = M[2][1] = M[2][3] = 0.f; 316 317 M[3][0] = -(r + l) / (r - l); 318 M[3][1] = -(t + b) / (t - b); 319 M[3][2] = -(f + n) / (f - n); 320 M[3][3] = 1.f; 321 } 322 static inline void mat4x4_perspective(mat4x4 m, float y_fov, float aspect, float n, float f) { 323 /* NOTE: Degrees are an unhandy unit to work with. 324 * linmath.h uses radians for everything! */ 325 float const a = (float)(1.f / tan(y_fov / 2.f)); 326 327 m[0][0] = a / aspect; 328 m[0][1] = 0.f; 329 m[0][2] = 0.f; 330 m[0][3] = 0.f; 331 332 m[1][0] = 0.f; 333 m[1][1] = a; 334 m[1][2] = 0.f; 335 m[1][3] = 0.f; 336 337 m[2][0] = 0.f; 338 m[2][1] = 0.f; 339 m[2][2] = -((f + n) / (f - n)); 340 m[2][3] = -1.f; 341 342 m[3][0] = 0.f; 343 m[3][1] = 0.f; 344 m[3][2] = -((2.f * f * n) / (f - n)); 345 m[3][3] = 0.f; 346 } 347 static inline void mat4x4_look_at(mat4x4 m, vec3 eye, vec3 center, vec3 up) { 348 /* Adapted from Android's OpenGL Matrix.java. */ 349 /* See the OpenGL GLUT documentation for gluLookAt for a description */ 350 /* of the algorithm. We implement it in a straightforward way: */ 351 352 /* TODO: The negation of of can be spared by swapping the order of 353 * operands in the following cross products in the right way. */ 354 vec3 f; 355 vec3_sub(f, center, eye); 356 vec3_norm(f, f); 357 358 vec3 s; 359 vec3_mul_cross(s, f, up); 360 vec3_norm(s, s); 361 362 vec3 t; 363 vec3_mul_cross(t, s, f); 364 365 m[0][0] = s[0]; 366 m[0][1] = t[0]; 367 m[0][2] = -f[0]; 368 m[0][3] = 0.f; 369 370 m[1][0] = s[1]; 371 m[1][1] = t[1]; 372 m[1][2] = -f[1]; 373 m[1][3] = 0.f; 374 375 m[2][0] = s[2]; 376 m[2][1] = t[2]; 377 m[2][2] = -f[2]; 378 m[2][3] = 0.f; 379 380 m[3][0] = 0.f; 381 m[3][1] = 0.f; 382 m[3][2] = 0.f; 383 m[3][3] = 1.f; 384 385 mat4x4_translate_in_place(m, -eye[0], -eye[1], -eye[2]); 386 } 387 388 typedef float quat[4]; 389 static inline void quat_identity(quat q) { 390 q[0] = q[1] = q[2] = 0.f; 391 q[3] = 1.f; 392 } 393 static inline void quat_add(quat r, quat a, quat b) { 394 int i; 395 for (i = 0; i < 4; ++i) r[i] = a[i] + b[i]; 396 } 397 static inline void quat_sub(quat r, quat a, quat b) { 398 int i; 399 for (i = 0; i < 4; ++i) r[i] = a[i] - b[i]; 400 } 401 static inline void quat_mul(quat r, quat p, quat q) { 402 vec3 w; 403 vec3_mul_cross(r, p, q); 404 vec3_scale(w, p, q[3]); 405 vec3_add(r, r, w); 406 vec3_scale(w, q, p[3]); 407 vec3_add(r, r, w); 408 r[3] = p[3] * q[3] - vec3_mul_inner(p, q); 409 } 410 static inline void quat_scale(quat r, quat v, float s) { 411 int i; 412 for (i = 0; i < 4; ++i) r[i] = v[i] * s; 413 } 414 static inline float quat_inner_product(quat a, quat b) { 415 float p = 0.f; 416 int i; 417 for (i = 0; i < 4; ++i) p += b[i] * a[i]; 418 return p; 419 } 420 static inline void quat_conj(quat r, quat q) { 421 int i; 422 for (i = 0; i < 3; ++i) r[i] = -q[i]; 423 r[3] = q[3]; 424 } 425 #define quat_norm vec4_norm 426 static inline void quat_mul_vec3(vec3 r, quat q, vec3 v) { 427 quat v_ = {v[0], v[1], v[2], 0.f}; 428 429 quat_conj(r, q); 430 quat_norm(r, r); 431 quat_mul(r, v_, r); 432 quat_mul(r, q, r); 433 } 434 static inline void mat4x4_from_quat(mat4x4 M, quat q) { 435 float a = q[3]; 436 float b = q[0]; 437 float c = q[1]; 438 float d = q[2]; 439 float a2 = a * a; 440 float b2 = b * b; 441 float c2 = c * c; 442 float d2 = d * d; 443 444 M[0][0] = a2 + b2 - c2 - d2; 445 M[0][1] = 2.f * (b * c + a * d); 446 M[0][2] = 2.f * (b * d - a * c); 447 M[0][3] = 0.f; 448 449 M[1][0] = 2 * (b * c - a * d); 450 M[1][1] = a2 - b2 + c2 - d2; 451 M[1][2] = 2.f * (c * d + a * b); 452 M[1][3] = 0.f; 453 454 M[2][0] = 2.f * (b * d + a * c); 455 M[2][1] = 2.f * (c * d - a * b); 456 M[2][2] = a2 - b2 - c2 + d2; 457 M[2][3] = 0.f; 458 459 M[3][0] = M[3][1] = M[3][2] = 0.f; 460 M[3][3] = 1.f; 461 } 462 463 static inline void mat4x4o_mul_quat(mat4x4 R, mat4x4 M, quat q) { 464 /* XXX: The way this is written only works for othogonal matrices. */ 465 /* TODO: Take care of non-orthogonal case. */ 466 quat_mul_vec3(R[0], q, M[0]); 467 quat_mul_vec3(R[1], q, M[1]); 468 quat_mul_vec3(R[2], q, M[2]); 469 470 R[3][0] = R[3][1] = R[3][2] = 0.f; 471 R[3][3] = 1.f; 472 } 473 static inline void quat_from_mat4x4(quat q, mat4x4 M) { 474 float r = 0.f; 475 int i; 476 477 int perm[] = {0, 1, 2, 0, 1}; 478 int *p = perm; 479 480 for (i = 0; i < 3; i++) { 481 float m = M[i][i]; 482 if (m < r) continue; 483 m = r; 484 p = &perm[i]; 485 } 486 487 r = sqrtf(1.f + M[p[0]][p[0]] - M[p[1]][p[1]] - M[p[2]][p[2]]); 488 489 if (r < 1e-6) { 490 q[0] = 1.f; 491 q[1] = q[2] = q[3] = 0.f; 492 return; 493 } 494 495 q[0] = r / 2.f; 496 q[1] = (M[p[0]][p[1]] - M[p[1]][p[0]]) / (2.f * r); 497 q[2] = (M[p[2]][p[0]] - M[p[0]][p[2]]) / (2.f * r); 498 q[3] = (M[p[2]][p[1]] - M[p[1]][p[2]]) / (2.f * r); 499 } 500 501 #endif 502
