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 * Permission is hereby granted, free of charge, to any person obtaining a copy
7 * of this software and/or associated documentation files (the "Materials"), to
8 * deal in the Materials without restriction, including without limitation the
9 * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
10 * sell copies of the Materials, and to permit persons to whom the Materials are
11 * furnished to do so, subject to the following conditions:
12 *
13 * The above copyright notice(s) and this permission notice shall be included in
14 * all copies or substantial portions of the Materials.
15 *
16 * THE MATERIALS ARE PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
17 * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
18 * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
19 *
20 * IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM,
21 * DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR
22 * OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE MATERIALS OR THE
23 * USE OR OTHER DEALINGS IN THE MATERIALS.
24 *
25 * Relicensed from the WTFPL (http://www.wtfpl.net/faq/).
26 */
27
28 #ifndef LINMATH_H
29 #define LINMATH_H
30
31 #include <math.h>
32
33 // Converts degrees to radians.
34 #define degreesToRadians(angleDegrees) (angleDegrees * M_PI / 180.0)
35
36 // Converts radians to degrees.
37 #define radiansToDegrees(angleRadians) (angleRadians * 180.0 / M_PI)
38
39 typedef float vec3[3];
vec3_add(vec3 r,vec3 const a,vec3 const b)40 static inline void vec3_add(vec3 r, vec3 const a, vec3 const b) {
41 int i;
42 for (i = 0; i < 3; ++i)
43 r[i] = a[i] + b[i];
44 }
vec3_sub(vec3 r,vec3 const a,vec3 const b)45 static inline void vec3_sub(vec3 r, vec3 const a, vec3 const b) {
46 int i;
47 for (i = 0; i < 3; ++i)
48 r[i] = a[i] - b[i];
49 }
vec3_scale(vec3 r,vec3 const v,float const s)50 static inline void vec3_scale(vec3 r, vec3 const v, float const s) {
51 int i;
52 for (i = 0; i < 3; ++i)
53 r[i] = v[i] * s;
54 }
vec3_mul_inner(vec3 const a,vec3 const b)55 static inline float vec3_mul_inner(vec3 const a, vec3 const b) {
56 float p = 0.f;
57 int i;
58 for (i = 0; i < 3; ++i)
59 p += b[i] * a[i];
60 return p;
61 }
vec3_mul_cross(vec3 r,vec3 const a,vec3 const b)62 static inline void vec3_mul_cross(vec3 r, vec3 const a, vec3 const b) {
63 r[0] = a[1] * b[2] - a[2] * b[1];
64 r[1] = a[2] * b[0] - a[0] * b[2];
65 r[2] = a[0] * b[1] - a[1] * b[0];
66 }
vec3_len(vec3 const v)67 static inline float vec3_len(vec3 const v) {
68 return sqrtf(vec3_mul_inner(v, v));
69 }
vec3_norm(vec3 r,vec3 const v)70 static inline void vec3_norm(vec3 r, vec3 const v) {
71 float k = 1.f / vec3_len(v);
72 vec3_scale(r, v, k);
73 }
vec3_reflect(vec3 r,vec3 const v,vec3 const n)74 static inline void vec3_reflect(vec3 r, vec3 const v, vec3 const n) {
75 float p = 2.f * vec3_mul_inner(v, n);
76 int i;
77 for (i = 0; i < 3; ++i)
78 r[i] = v[i] - p * n[i];
79 }
80
81 typedef float vec4[4];
vec4_add(vec4 r,vec4 const a,vec4 const b)82 static inline void vec4_add(vec4 r, vec4 const a, vec4 const b) {
83 int i;
84 for (i = 0; i < 4; ++i)
85 r[i] = a[i] + b[i];
86 }
vec4_sub(vec4 r,vec4 const a,vec4 const b)87 static inline void vec4_sub(vec4 r, vec4 const a, vec4 const b) {
88 int i;
89 for (i = 0; i < 4; ++i)
90 r[i] = a[i] - b[i];
91 }
vec4_scale(vec4 r,vec4 v,float s)92 static inline void vec4_scale(vec4 r, vec4 v, float s) {
93 int i;
94 for (i = 0; i < 4; ++i)
95 r[i] = v[i] * s;
96 }
vec4_mul_inner(vec4 a,vec4 b)97 static inline float vec4_mul_inner(vec4 a, vec4 b) {
98 float p = 0.f;
99 int i;
100 for (i = 0; i < 4; ++i)
101 p += b[i] * a[i];
102 return p;
103 }
vec4_mul_cross(vec4 r,vec4 a,vec4 b)104 static inline void vec4_mul_cross(vec4 r, vec4 a, vec4 b) {
105 r[0] = a[1] * b[2] - a[2] * b[1];
106 r[1] = a[2] * b[0] - a[0] * b[2];
107 r[2] = a[0] * b[1] - a[1] * b[0];
108 r[3] = 1.f;
109 }
vec4_len(vec4 v)110 static inline float vec4_len(vec4 v) { return sqrtf(vec4_mul_inner(v, v)); }
vec4_norm(vec4 r,vec4 v)111 static inline void vec4_norm(vec4 r, vec4 v) {
112 float k = 1.f / vec4_len(v);
113 vec4_scale(r, v, k);
114 }
vec4_reflect(vec4 r,vec4 v,vec4 n)115 static inline void vec4_reflect(vec4 r, vec4 v, vec4 n) {
116 float p = 2.f * vec4_mul_inner(v, n);
117 int i;
118 for (i = 0; i < 4; ++i)
119 r[i] = v[i] - p * n[i];
120 }
121
122 typedef vec4 mat4x4[4];
mat4x4_identity(mat4x4 M)123 static inline void mat4x4_identity(mat4x4 M) {
124 int i, j;
125 for (i = 0; i < 4; ++i)
126 for (j = 0; j < 4; ++j)
127 M[i][j] = i == j ? 1.f : 0.f;
128 }
mat4x4_dup(mat4x4 M,mat4x4 N)129 static inline void mat4x4_dup(mat4x4 M, mat4x4 N) {
130 int i, j;
131 for (i = 0; i < 4; ++i)
132 for (j = 0; j < 4; ++j)
133 M[i][j] = N[i][j];
134 }
mat4x4_row(vec4 r,mat4x4 M,int i)135 static inline void mat4x4_row(vec4 r, mat4x4 M, int i) {
136 int k;
137 for (k = 0; k < 4; ++k)
138 r[k] = M[k][i];
139 }
mat4x4_col(vec4 r,mat4x4 M,int i)140 static inline void mat4x4_col(vec4 r, mat4x4 M, int i) {
141 int k;
142 for (k = 0; k < 4; ++k)
143 r[k] = M[i][k];
144 }
mat4x4_transpose(mat4x4 M,mat4x4 N)145 static inline void mat4x4_transpose(mat4x4 M, mat4x4 N) {
146 int i, j;
147 for (j = 0; j < 4; ++j)
148 for (i = 0; i < 4; ++i)
149 M[i][j] = N[j][i];
150 }
mat4x4_add(mat4x4 M,mat4x4 a,mat4x4 b)151 static inline void mat4x4_add(mat4x4 M, mat4x4 a, mat4x4 b) {
152 int i;
153 for (i = 0; i < 4; ++i)
154 vec4_add(M[i], a[i], b[i]);
155 }
mat4x4_sub(mat4x4 M,mat4x4 a,mat4x4 b)156 static inline void mat4x4_sub(mat4x4 M, mat4x4 a, mat4x4 b) {
157 int i;
158 for (i = 0; i < 4; ++i)
159 vec4_sub(M[i], a[i], b[i]);
160 }
mat4x4_scale(mat4x4 M,mat4x4 a,float k)161 static inline void mat4x4_scale(mat4x4 M, mat4x4 a, float k) {
162 int i;
163 for (i = 0; i < 4; ++i)
164 vec4_scale(M[i], a[i], k);
165 }
mat4x4_scale_aniso(mat4x4 M,mat4x4 a,float x,float y,float z)166 static inline void mat4x4_scale_aniso(mat4x4 M, mat4x4 a, float x, float y,
167 float z) {
168 int i;
169 vec4_scale(M[0], a[0], x);
170 vec4_scale(M[1], a[1], y);
171 vec4_scale(M[2], a[2], z);
172 for (i = 0; i < 4; ++i) {
173 M[3][i] = a[3][i];
174 }
175 }
mat4x4_mul(mat4x4 M,mat4x4 a,mat4x4 b)176 static inline void mat4x4_mul(mat4x4 M, mat4x4 a, mat4x4 b) {
177 int k, r, c;
178 for (c = 0; c < 4; ++c)
179 for (r = 0; r < 4; ++r) {
180 M[c][r] = 0.f;
181 for (k = 0; k < 4; ++k)
182 M[c][r] += a[k][r] * b[c][k];
183 }
184 }
mat4x4_mul_vec4(vec4 r,mat4x4 M,vec4 v)185 static inline void mat4x4_mul_vec4(vec4 r, mat4x4 M, vec4 v) {
186 int i, j;
187 for (j = 0; j < 4; ++j) {
188 r[j] = 0.f;
189 for (i = 0; i < 4; ++i)
190 r[j] += M[i][j] * v[i];
191 }
192 }
mat4x4_translate(mat4x4 T,float x,float y,float z)193 static inline void mat4x4_translate(mat4x4 T, float x, float y, float z) {
194 mat4x4_identity(T);
195 T[3][0] = x;
196 T[3][1] = y;
197 T[3][2] = z;
198 }
mat4x4_translate_in_place(mat4x4 M,float x,float y,float z)199 static inline void mat4x4_translate_in_place(mat4x4 M, float x, float y,
200 float z) {
201 vec4 t = {x, y, z, 0};
202 vec4 r;
203 int i;
204 for (i = 0; i < 4; ++i) {
205 mat4x4_row(r, M, i);
206 M[3][i] += vec4_mul_inner(r, t);
207 }
208 }
mat4x4_from_vec3_mul_outer(mat4x4 M,vec3 a,vec3 b)209 static inline void mat4x4_from_vec3_mul_outer(mat4x4 M, vec3 a, vec3 b) {
210 int i, j;
211 for (i = 0; i < 4; ++i)
212 for (j = 0; j < 4; ++j)
213 M[i][j] = i < 3 && j < 3 ? a[i] * b[j] : 0.f;
214 }
mat4x4_rotate(mat4x4 R,mat4x4 M,float x,float y,float z,float angle)215 static inline void mat4x4_rotate(mat4x4 R, mat4x4 M, float x, float y, float z,
216 float angle) {
217 float s = sinf(angle);
218 float c = cosf(angle);
219 vec3 u = {x, y, z};
220
221 if (vec3_len(u) > 1e-4) {
222 vec3_norm(u, u);
223 mat4x4 T;
224 mat4x4_from_vec3_mul_outer(T, u, u);
225
226 mat4x4 S = {{0, u[2], -u[1], 0},
227 {-u[2], 0, u[0], 0},
228 {u[1], -u[0], 0, 0},
229 {0, 0, 0, 0}};
230 mat4x4_scale(S, S, s);
231
232 mat4x4 C;
233 mat4x4_identity(C);
234 mat4x4_sub(C, C, T);
235
236 mat4x4_scale(C, C, c);
237
238 mat4x4_add(T, T, C);
239 mat4x4_add(T, T, S);
240
241 T[3][3] = 1.;
242 mat4x4_mul(R, M, T);
243 } else {
244 mat4x4_dup(R, M);
245 }
246 }
mat4x4_rotate_X(mat4x4 Q,mat4x4 M,float angle)247 static inline void mat4x4_rotate_X(mat4x4 Q, mat4x4 M, float angle) {
248 float s = sinf(angle);
249 float c = cosf(angle);
250 mat4x4 R = {{1.f, 0.f, 0.f, 0.f},
251 {0.f, c, s, 0.f},
252 {0.f, -s, c, 0.f},
253 {0.f, 0.f, 0.f, 1.f}};
254 mat4x4_mul(Q, M, R);
255 }
mat4x4_rotate_Y(mat4x4 Q,mat4x4 M,float angle)256 static inline void mat4x4_rotate_Y(mat4x4 Q, mat4x4 M, float angle) {
257 float s = sinf(angle);
258 float c = cosf(angle);
259 mat4x4 R = {{c, 0.f, s, 0.f},
260 {0.f, 1.f, 0.f, 0.f},
261 {-s, 0.f, c, 0.f},
262 {0.f, 0.f, 0.f, 1.f}};
263 mat4x4_mul(Q, M, R);
264 }
mat4x4_rotate_Z(mat4x4 Q,mat4x4 M,float angle)265 static inline void mat4x4_rotate_Z(mat4x4 Q, mat4x4 M, float angle) {
266 float s = sinf(angle);
267 float c = cosf(angle);
268 mat4x4 R = {{c, s, 0.f, 0.f},
269 {-s, c, 0.f, 0.f},
270 {0.f, 0.f, 1.f, 0.f},
271 {0.f, 0.f, 0.f, 1.f}};
272 mat4x4_mul(Q, M, R);
273 }
mat4x4_invert(mat4x4 T,mat4x4 M)274 static inline void mat4x4_invert(mat4x4 T, mat4x4 M) {
275 float s[6];
276 float c[6];
277 s[0] = M[0][0] * M[1][1] - M[1][0] * M[0][1];
278 s[1] = M[0][0] * M[1][2] - M[1][0] * M[0][2];
279 s[2] = M[0][0] * M[1][3] - M[1][0] * M[0][3];
280 s[3] = M[0][1] * M[1][2] - M[1][1] * M[0][2];
281 s[4] = M[0][1] * M[1][3] - M[1][1] * M[0][3];
282 s[5] = M[0][2] * M[1][3] - M[1][2] * M[0][3];
283
284 c[0] = M[2][0] * M[3][1] - M[3][0] * M[2][1];
285 c[1] = M[2][0] * M[3][2] - M[3][0] * M[2][2];
286 c[2] = M[2][0] * M[3][3] - M[3][0] * M[2][3];
287 c[3] = M[2][1] * M[3][2] - M[3][1] * M[2][2];
288 c[4] = M[2][1] * M[3][3] - M[3][1] * M[2][3];
289 c[5] = M[2][2] * M[3][3] - M[3][2] * M[2][3];
290
291 /* Assumes it is invertible */
292 float idet = 1.0f / (s[0] * c[5] - s[1] * c[4] + s[2] * c[3] + s[3] * c[2] -
293 s[4] * c[1] + s[5] * c[0]);
294
295 T[0][0] = (M[1][1] * c[5] - M[1][2] * c[4] + M[1][3] * c[3]) * idet;
296 T[0][1] = (-M[0][1] * c[5] + M[0][2] * c[4] - M[0][3] * c[3]) * idet;
297 T[0][2] = (M[3][1] * s[5] - M[3][2] * s[4] + M[3][3] * s[3]) * idet;
298 T[0][3] = (-M[2][1] * s[5] + M[2][2] * s[4] - M[2][3] * s[3]) * idet;
299
300 T[1][0] = (-M[1][0] * c[5] + M[1][2] * c[2] - M[1][3] * c[1]) * idet;
301 T[1][1] = (M[0][0] * c[5] - M[0][2] * c[2] + M[0][3] * c[1]) * idet;
302 T[1][2] = (-M[3][0] * s[5] + M[3][2] * s[2] - M[3][3] * s[1]) * idet;
303 T[1][3] = (M[2][0] * s[5] - M[2][2] * s[2] + M[2][3] * s[1]) * idet;
304
305 T[2][0] = (M[1][0] * c[4] - M[1][1] * c[2] + M[1][3] * c[0]) * idet;
306 T[2][1] = (-M[0][0] * c[4] + M[0][1] * c[2] - M[0][3] * c[0]) * idet;
307 T[2][2] = (M[3][0] * s[4] - M[3][1] * s[2] + M[3][3] * s[0]) * idet;
308 T[2][3] = (-M[2][0] * s[4] + M[2][1] * s[2] - M[2][3] * s[0]) * idet;
309
310 T[3][0] = (-M[1][0] * c[3] + M[1][1] * c[1] - M[1][2] * c[0]) * idet;
311 T[3][1] = (M[0][0] * c[3] - M[0][1] * c[1] + M[0][2] * c[0]) * idet;
312 T[3][2] = (-M[3][0] * s[3] + M[3][1] * s[1] - M[3][2] * s[0]) * idet;
313 T[3][3] = (M[2][0] * s[3] - M[2][1] * s[1] + M[2][2] * s[0]) * idet;
314 }
mat4x4_orthonormalize(mat4x4 R,mat4x4 M)315 static inline void mat4x4_orthonormalize(mat4x4 R, mat4x4 M) {
316 mat4x4_dup(R, M);
317 float s = 1.;
318 vec3 h;
319
320 vec3_norm(R[2], R[2]);
321
322 s = vec3_mul_inner(R[1], R[2]);
323 vec3_scale(h, R[2], s);
324 vec3_sub(R[1], R[1], h);
325 vec3_norm(R[2], R[2]);
326
327 s = vec3_mul_inner(R[1], R[2]);
328 vec3_scale(h, R[2], s);
329 vec3_sub(R[1], R[1], h);
330 vec3_norm(R[1], R[1]);
331
332 s = vec3_mul_inner(R[0], R[1]);
333 vec3_scale(h, R[1], s);
334 vec3_sub(R[0], R[0], h);
335 vec3_norm(R[0], R[0]);
336 }
337
mat4x4_frustum(mat4x4 M,float l,float r,float b,float t,float n,float f)338 static inline void mat4x4_frustum(mat4x4 M, float l, float r, float b, float t,
339 float n, float f) {
340 M[0][0] = 2.f * n / (r - l);
341 M[0][1] = M[0][2] = M[0][3] = 0.f;
342
343 M[1][1] = 2.f * n / (t - b);
344 M[1][0] = M[1][2] = M[1][3] = 0.f;
345
346 M[2][0] = (r + l) / (r - l);
347 M[2][1] = (t + b) / (t - b);
348 M[2][2] = -(f + n) / (f - n);
349 M[2][3] = -1.f;
350
351 M[3][2] = -2.f * (f * n) / (f - n);
352 M[3][0] = M[3][1] = M[3][3] = 0.f;
353 }
mat4x4_ortho(mat4x4 M,float l,float r,float b,float t,float n,float f)354 static inline void mat4x4_ortho(mat4x4 M, float l, float r, float b, float t,
355 float n, float f) {
356 M[0][0] = 2.f / (r - l);
357 M[0][1] = M[0][2] = M[0][3] = 0.f;
358
359 M[1][1] = 2.f / (t - b);
360 M[1][0] = M[1][2] = M[1][3] = 0.f;
361
362 M[2][2] = -2.f / (f - n);
363 M[2][0] = M[2][1] = M[2][3] = 0.f;
364
365 M[3][0] = -(r + l) / (r - l);
366 M[3][1] = -(t + b) / (t - b);
367 M[3][2] = -(f + n) / (f - n);
368 M[3][3] = 1.f;
369 }
mat4x4_perspective(mat4x4 m,float y_fov,float aspect,float n,float f)370 static inline void mat4x4_perspective(mat4x4 m, float y_fov, float aspect,
371 float n, float f) {
372 /* NOTE: Degrees are an unhandy unit to work with.
373 * linmath.h uses radians for everything! */
374 float const a = (float)(1.f / tan(y_fov / 2.f));
375
376 m[0][0] = a / aspect;
377 m[0][1] = 0.f;
378 m[0][2] = 0.f;
379 m[0][3] = 0.f;
380
381 m[1][0] = 0.f;
382 m[1][1] = a;
383 m[1][2] = 0.f;
384 m[1][3] = 0.f;
385
386 m[2][0] = 0.f;
387 m[2][1] = 0.f;
388 m[2][2] = -((f + n) / (f - n));
389 m[2][3] = -1.f;
390
391 m[3][0] = 0.f;
392 m[3][1] = 0.f;
393 m[3][2] = -((2.f * f * n) / (f - n));
394 m[3][3] = 0.f;
395 }
mat4x4_look_at(mat4x4 m,vec3 eye,vec3 center,vec3 up)396 static inline void mat4x4_look_at(mat4x4 m, vec3 eye, vec3 center, vec3 up) {
397 /* Adapted from Android's OpenGL Matrix.java. */
398 /* See the OpenGL GLUT documentation for gluLookAt for a description */
399 /* of the algorithm. We implement it in a straightforward way: */
400
401 /* TODO: The negation of of can be spared by swapping the order of
402 * operands in the following cross products in the right way. */
403 vec3 f;
404 vec3_sub(f, center, eye);
405 vec3_norm(f, f);
406
407 vec3 s;
408 vec3_mul_cross(s, f, up);
409 vec3_norm(s, s);
410
411 vec3 t;
412 vec3_mul_cross(t, s, f);
413
414 m[0][0] = s[0];
415 m[0][1] = t[0];
416 m[0][2] = -f[0];
417 m[0][3] = 0.f;
418
419 m[1][0] = s[1];
420 m[1][1] = t[1];
421 m[1][2] = -f[1];
422 m[1][3] = 0.f;
423
424 m[2][0] = s[2];
425 m[2][1] = t[2];
426 m[2][2] = -f[2];
427 m[2][3] = 0.f;
428
429 m[3][0] = 0.f;
430 m[3][1] = 0.f;
431 m[3][2] = 0.f;
432 m[3][3] = 1.f;
433
434 mat4x4_translate_in_place(m, -eye[0], -eye[1], -eye[2]);
435 }
436
437 typedef float quat[4];
quat_identity(quat q)438 static inline void quat_identity(quat q) {
439 q[0] = q[1] = q[2] = 0.f;
440 q[3] = 1.f;
441 }
quat_add(quat r,quat a,quat b)442 static inline void quat_add(quat r, quat a, quat b) {
443 int i;
444 for (i = 0; i < 4; ++i)
445 r[i] = a[i] + b[i];
446 }
quat_sub(quat r,quat a,quat b)447 static inline void quat_sub(quat r, quat a, quat b) {
448 int i;
449 for (i = 0; i < 4; ++i)
450 r[i] = a[i] - b[i];
451 }
quat_mul(quat r,quat p,quat q)452 static inline void quat_mul(quat r, quat p, quat q) {
453 vec3 w;
454 vec3_mul_cross(r, p, q);
455 vec3_scale(w, p, q[3]);
456 vec3_add(r, r, w);
457 vec3_scale(w, q, p[3]);
458 vec3_add(r, r, w);
459 r[3] = p[3] * q[3] - vec3_mul_inner(p, q);
460 }
quat_scale(quat r,quat v,float s)461 static inline void quat_scale(quat r, quat v, float s) {
462 int i;
463 for (i = 0; i < 4; ++i)
464 r[i] = v[i] * s;
465 }
quat_inner_product(quat a,quat b)466 static inline float quat_inner_product(quat a, quat b) {
467 float p = 0.f;
468 int i;
469 for (i = 0; i < 4; ++i)
470 p += b[i] * a[i];
471 return p;
472 }
quat_conj(quat r,quat q)473 static inline void quat_conj(quat r, quat q) {
474 int i;
475 for (i = 0; i < 3; ++i)
476 r[i] = -q[i];
477 r[3] = q[3];
478 }
479 #define quat_norm vec4_norm
quat_mul_vec3(vec3 r,quat q,vec3 v)480 static inline void quat_mul_vec3(vec3 r, quat q, vec3 v) {
481 quat v_ = {v[0], v[1], v[2], 0.f};
482
483 quat_conj(r, q);
484 quat_norm(r, r);
485 quat_mul(r, v_, r);
486 quat_mul(r, q, r);
487 }
mat4x4_from_quat(mat4x4 M,quat q)488 static inline void mat4x4_from_quat(mat4x4 M, quat q) {
489 float a = q[3];
490 float b = q[0];
491 float c = q[1];
492 float d = q[2];
493 float a2 = a * a;
494 float b2 = b * b;
495 float c2 = c * c;
496 float d2 = d * d;
497
498 M[0][0] = a2 + b2 - c2 - d2;
499 M[0][1] = 2.f * (b * c + a * d);
500 M[0][2] = 2.f * (b * d - a * c);
501 M[0][3] = 0.f;
502
503 M[1][0] = 2 * (b * c - a * d);
504 M[1][1] = a2 - b2 + c2 - d2;
505 M[1][2] = 2.f * (c * d + a * b);
506 M[1][3] = 0.f;
507
508 M[2][0] = 2.f * (b * d + a * c);
509 M[2][1] = 2.f * (c * d - a * b);
510 M[2][2] = a2 - b2 - c2 + d2;
511 M[2][3] = 0.f;
512
513 M[3][0] = M[3][1] = M[3][2] = 0.f;
514 M[3][3] = 1.f;
515 }
516
mat4x4o_mul_quat(mat4x4 R,mat4x4 M,quat q)517 static inline void mat4x4o_mul_quat(mat4x4 R, mat4x4 M, quat q) {
518 /* XXX: The way this is written only works for othogonal matrices. */
519 /* TODO: Take care of non-orthogonal case. */
520 quat_mul_vec3(R[0], q, M[0]);
521 quat_mul_vec3(R[1], q, M[1]);
522 quat_mul_vec3(R[2], q, M[2]);
523
524 R[3][0] = R[3][1] = R[3][2] = 0.f;
525 R[3][3] = 1.f;
526 }
quat_from_mat4x4(quat q,mat4x4 M)527 static inline void quat_from_mat4x4(quat q, mat4x4 M) {
528 float r = 0.f;
529 int i;
530
531 int perm[] = {0, 1, 2, 0, 1};
532 int *p = perm;
533
534 for (i = 0; i < 3; i++) {
535 float m = M[i][i];
536 if (m < r)
537 continue;
538 m = r;
539 p = &perm[i];
540 }
541
542 r = sqrtf(1.f + M[p[0]][p[0]] - M[p[1]][p[1]] - M[p[2]][p[2]]);
543
544 if (r < 1e-6) {
545 q[0] = 1.f;
546 q[1] = q[2] = q[3] = 0.f;
547 return;
548 }
549
550 q[0] = r / 2.f;
551 q[1] = (M[p[0]][p[1]] - M[p[1]][p[0]]) / (2.f * r);
552 q[2] = (M[p[2]][p[0]] - M[p[0]][p[2]]) / (2.f * r);
553 q[3] = (M[p[2]][p[1]] - M[p[1]][p[2]]) / (2.f * r);
554 }
555
556 #endif
557