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];
vec3_add(vec3 r,vec3 const a,vec3 const b)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 }
vec3_sub(vec3 r,vec3 const a,vec3 const b)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 }
vec3_scale(vec3 r,vec3 const v,float const s)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 }
vec3_mul_inner(vec3 const a,vec3 const b)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 }
vec3_mul_cross(vec3 r,vec3 const a,vec3 const b)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 }
vec3_len(vec3 const v)56 static inline float vec3_len(vec3 const v) { return sqrtf(vec3_mul_inner(v, v)); }
vec3_norm(vec3 r,vec3 const 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 }
vec3_reflect(vec3 r,vec3 const v,vec3 const n)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];
vec4_add(vec4 r,vec4 const a,vec4 const b)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 }
vec4_sub(vec4 r,vec4 const a,vec4 const b)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 }
vec4_scale(vec4 r,vec4 v,float s)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 }
vec4_mul_inner(vec4 a,vec4 b)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 }
vec4_mul_cross(vec4 r,vec4 a,vec4 b)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 }
vec4_len(vec4 v)92 static inline float vec4_len(vec4 v) { return sqrtf(vec4_mul_inner(v, v)); }
vec4_norm(vec4 r,vec4 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 }
vec4_reflect(vec4 r,vec4 v,vec4 n)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];
mat4x4_identity(mat4x4 M)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 }
mat4x4_dup(mat4x4 M,mat4x4 N)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 }
mat4x4_row(vec4 r,mat4x4 M,int i)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 }
mat4x4_col(vec4 r,mat4x4 M,int i)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 }
mat4x4_transpose(mat4x4 M,mat4x4 N)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 }
mat4x4_add(mat4x4 M,mat4x4 a,mat4x4 b)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 }
mat4x4_sub(mat4x4 M,mat4x4 a,mat4x4 b)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 }
mat4x4_scale(mat4x4 M,mat4x4 a,float k)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 }
mat4x4_scale_aniso(mat4x4 M,mat4x4 a,float x,float y,float z)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 }
mat4x4_mul(mat4x4 M,mat4x4 a,mat4x4 b)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 }
mat4x4_mul_vec4(vec4 r,mat4x4 M,vec4 v)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 }
mat4x4_translate(mat4x4 T,float x,float y,float z)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 }
mat4x4_translate_in_place(mat4x4 M,float x,float y,float z)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 }
mat4x4_from_vec3_mul_outer(mat4x4 M,vec3 a,vec3 b)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 }
mat4x4_rotate(mat4x4 R,mat4x4 M,float x,float y,float z,float angle)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 }
mat4x4_rotate_X(mat4x4 Q,mat4x4 M,float angle)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 }
mat4x4_rotate_Y(mat4x4 Q,mat4x4 M,float angle)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 }
mat4x4_rotate_Z(mat4x4 Q,mat4x4 M,float angle)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 }
mat4x4_invert(mat4x4 T,mat4x4 M)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 }
mat4x4_orthonormalize(mat4x4 R,mat4x4 M)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
mat4x4_frustum(mat4x4 M,float l,float r,float b,float t,float n,float f)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 }
mat4x4_ortho(mat4x4 M,float l,float r,float b,float t,float n,float f)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 }
mat4x4_perspective(mat4x4 m,float y_fov,float aspect,float n,float f)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 }
mat4x4_look_at(mat4x4 m,vec3 eye,vec3 center,vec3 up)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];
quat_identity(quat q)389 static inline void quat_identity(quat q) {
390 q[0] = q[1] = q[2] = 0.f;
391 q[3] = 1.f;
392 }
quat_add(quat r,quat a,quat b)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 }
quat_sub(quat r,quat a,quat b)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 }
quat_mul(quat r,quat p,quat q)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 }
quat_scale(quat r,quat v,float s)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 }
quat_inner_product(quat a,quat b)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 }
quat_conj(quat r,quat q)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
quat_mul_vec3(vec3 r,quat q,vec3 v)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 }
mat4x4_from_quat(mat4x4 M,quat q)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
mat4x4o_mul_quat(mat4x4 R,mat4x4 M,quat q)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 }
quat_from_mat4x4(quat q,mat4x4 M)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