1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
|
.. default-domain:: C
quaternions
===========
Header: cglm/quat.h
**Important:** *cglm* stores quaternion as **[x, y, z, w]** in memory
since **v0.4.0** it was **[w, x, y, z]**
before v0.4.0 ( **v0.3.5 and earlier** ). w is real part.
What you can do with quaternions with existing functions is (Some of them):
- You can rotate transform matrix using quaterion
- You can rotate vector using quaterion
- You can create view matrix using quaterion
- You can create a lookrotation (from source point to dest)
Table of contents (click to go):
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Macros:
1. GLM_QUAT_IDENTITY_INIT
#. GLM_QUAT_IDENTITY
Functions:
1. :c:func:`glm_quat_identity`
#. :c:func:`glm_quat_identity_array`
#. :c:func:`glm_quat_init`
#. :c:func:`glm_quat`
#. :c:func:`glm_quatv`
#. :c:func:`glm_quat_copy`
#. :c:func:`glm_quat_from_vecs`
#. :c:func:`glm_quat_norm`
#. :c:func:`glm_quat_normalize`
#. :c:func:`glm_quat_normalize_to`
#. :c:func:`glm_quat_dot`
#. :c:func:`glm_quat_conjugate`
#. :c:func:`glm_quat_inv`
#. :c:func:`glm_quat_add`
#. :c:func:`glm_quat_sub`
#. :c:func:`glm_quat_real`
#. :c:func:`glm_quat_imag`
#. :c:func:`glm_quat_imagn`
#. :c:func:`glm_quat_imaglen`
#. :c:func:`glm_quat_angle`
#. :c:func:`glm_quat_axis`
#. :c:func:`glm_quat_mul`
#. :c:func:`glm_quat_mat4`
#. :c:func:`glm_quat_mat4t`
#. :c:func:`glm_quat_mat3`
#. :c:func:`glm_quat_mat3t`
#. :c:func:`glm_quat_lerp`
#. :c:func:`glm_quat_nlerp`
#. :c:func:`glm_quat_slerp`
#. :c:func:`glm_quat_look`
#. :c:func:`glm_quat_for`
#. :c:func:`glm_quat_forp`
#. :c:func:`glm_quat_rotatev`
#. :c:func:`glm_quat_rotate`
#. :c:func:`glm_quat_rotate_at`
#. :c:func:`glm_quat_rotate_atm`
Functions documentation
~~~~~~~~~~~~~~~~~~~~~~~
.. c:function:: void glm_quat_identity(versor q)
| makes given quat to identity
Parameters:
| *[in, out]* **q** quaternion
.. c:function:: void glm_quat_identity_array(versor * __restrict q, size_t count)
| make given quaternion array's each element identity quaternion
Parameters:
| *[in, out]* **q** quat array (must be aligned (16) if alignment is not disabled)
| *[in]* **count** count of quaternions
.. c:function:: void glm_quat_init(versor q, float x, float y, float z, float w)
| inits quaternion with given values
Parameters:
| *[out]* **q** quaternion
| *[in]* **x** imag.x
| *[in]* **y** imag.y
| *[in]* **z** imag.z
| *[in]* **w** w (real part)
.. c:function:: void glm_quat(versor q, float angle, float x, float y, float z)
| creates NEW quaternion with individual axis components
| given axis will be normalized
Parameters:
| *[out]* **q** quaternion
| *[in]* **angle** angle (radians)
| *[in]* **x** axis.x
| *[in]* **y** axis.y
| *[in]* **z** axis.z
.. c:function:: void glm_quatv(versor q, float angle, vec3 axis)
| creates NEW quaternion with axis vector
| given axis will be normalized
Parameters:
| *[out]* **q** quaternion
| *[in]* **angle** angle (radians)
| *[in]* **axis** axis (will be normalized)
.. c:function:: void glm_quat_copy(versor q, versor dest)
| copy quaternion to another one
Parameters:
| *[in]* **q** source quaternion
| *[out]* **dest** destination quaternion
.. c:function:: void glm_quat_from_vecs(vec3 a, vec3 b, versor dest)
| compute unit quaternion needed to rotate a into b
References:
* `Finding quaternion representing the rotation from one vector to another <https://stackoverflow.com/a/11741520/183120>`_
* `Quaternion from two vectors <http://lolengine.net/blog/2014/02/24/quaternion-from-two-vectors-final>`_
* `Angle between vectors <http://www.euclideanspace.com/maths/algebra/vectors/angleBetween/minorlogic.htm>`_
Parameters:
| *[in]* **a** unit vector
| *[in]* **b** unit vector
| *[in]* **dest** unit quaternion
.. c:function:: float glm_quat_norm(versor q)
| returns norm (magnitude) of quaternion
Parameters:
| *[in]* **a** quaternion
Returns:
norm (magnitude)
.. c:function:: void glm_quat_normalize_to(versor q, versor dest)
| normalize quaternion and store result in dest, original one will not be normalized
Parameters:
| *[in]* **q** quaternion to normalize into
| *[out]* **dest** destination quaternion
.. c:function:: void glm_quat_normalize(versor q)
| normalize quaternion
Parameters:
| *[in, out]* **q** quaternion
.. c:function:: float glm_quat_dot(versor p, versor q)
dot product of two quaternion
Parameters:
| *[in]* **p** quaternion 1
| *[in]* **q** quaternion 2
Returns:
dot product
.. c:function:: void glm_quat_conjugate(versor q, versor dest)
conjugate of quaternion
Parameters:
| *[in]* **q** quaternion
| *[in]* **dest** conjugate
.. c:function:: void glm_quat_inv(versor q, versor dest)
inverse of non-zero quaternion
Parameters:
| *[in]* **q** quaternion
| *[in]* **dest** inverse quaternion
.. c:function:: void glm_quat_add(versor p, versor q, versor dest)
add (componentwise) two quaternions and store result in dest
Parameters:
| *[in]* **p** quaternion 1
| *[in]* **q** quaternion 2
| *[in]* **dest** result quaternion
.. c:function:: void glm_quat_sub(versor p, versor q, versor dest)
subtract (componentwise) two quaternions and store result in dest
Parameters:
| *[in]* **p** quaternion 1
| *[in]* **q** quaternion 2
| *[in]* **dest** result quaternion
.. c:function:: float glm_quat_real(versor q)
returns real part of quaternion
Parameters:
| *[in]* **q** quaternion
Returns:
real part (quat.w)
.. c:function:: void glm_quat_imag(versor q, vec3 dest)
returns imaginary part of quaternion
Parameters:
| *[in]* **q** quaternion
| *[out]* **dest** imag
.. c:function:: void glm_quat_imagn(versor q, vec3 dest)
returns normalized imaginary part of quaternion
Parameters:
| *[in]* **q** quaternion
| *[out]* **dest** imag
.. c:function:: float glm_quat_imaglen(versor q)
returns length of imaginary part of quaternion
Parameters:
| *[in]* **q** quaternion
Returns:
norm of imaginary part
.. c:function:: float glm_quat_angle(versor q)
returns angle of quaternion
Parameters:
| *[in]* **q** quaternion
Returns:
angles of quat (radians)
.. c:function:: void glm_quat_axis(versor q, versor dest)
axis of quaternion
Parameters:
| *[in]* **p** quaternion
| *[out]* **dest** axis of quaternion
.. c:function:: void glm_quat_mul(versor p, versor q, versor dest)
| multiplies two quaternion and stores result in dest
| this is also called Hamilton Product
| According to WikiPedia:
| The product of two rotation quaternions [clarification needed] will be
equivalent to the rotation q followed by the rotation p
Parameters:
| *[in]* **p** quaternion 1 (first rotation)
| *[in]* **q** quaternion 2 (second rotation)
| *[out]* **dest** result quaternion
.. c:function:: void glm_quat_mat4(versor q, mat4 dest)
| convert quaternion to mat4
Parameters:
| *[in]* **q** quaternion
| *[out]* **dest** result matrix
.. c:function:: void glm_quat_mat4t(versor q, mat4 dest)
| convert quaternion to mat4 (transposed). This is transposed version of glm_quat_mat4
Parameters:
| *[in]* **q** quaternion
| *[out]* **dest** result matrix
.. c:function:: void glm_quat_mat3(versor q, mat3 dest)
| convert quaternion to mat3
Parameters:
| *[in]* **q** quaternion
| *[out]* **dest** result matrix
.. c:function:: void glm_quat_mat3t(versor q, mat3 dest)
| convert quaternion to mat3 (transposed). This is transposed version of glm_quat_mat3
Parameters:
| *[in]* **q** quaternion
| *[out]* **dest** result matrix
.. c:function:: void glm_quat_lerp(versor from, versor to, float t, versor dest)
| interpolates between two quaternions
| using spherical linear interpolation (LERP)
Parameters:
| *[in]* **from** from
| *[in]* **to** to
| *[in]* **t** interpolant (amount) clamped between 0 and 1
| *[out]* **dest** result quaternion
.. c:function:: void glm_quat_nlerp(versor q, versor r, float t, versor dest)
| interpolates between two quaternions
| taking the shortest rotation path using
| normalized linear interpolation (NLERP)
| This is a cheaper alternative to slerp; most games use nlerp
| for animations as it visually makes little difference.
References:
* `Understanding Slerp, Then Not Using it <http://number-none.com/product/Understanding%20Slerp,%20Then%20Not%20Using%20It>`_
* `Lerp, Slerp and Nlerp <https://keithmaggio.wordpress.com/2011/02/15/math-magician-lerp-slerp-and-nlerp/>`_
Parameters:
| *[in]* **from** from
| *[in]* **to** to
| *[in]* **t** interpolant (amount) clamped between 0 and 1
| *[out]* **dest** result quaternion
.. c:function:: void glm_quat_slerp(versor q, versor r, float t, versor dest)
| interpolates between two quaternions
| using spherical linear interpolation (SLERP)
Parameters:
| *[in]* **from** from
| *[in]* **to** to
| *[in]* **t** interpolant (amount) clamped between 0 and 1
| *[out]* **dest** result quaternion
.. c:function:: void glm_quat_look(vec3 eye, versor ori, mat4 dest)
| creates view matrix using quaternion as camera orientation
Parameters:
| *[in]* **eye** eye
| *[in]* **ori** orientation in world space as quaternion
| *[out]* **dest** result matrix
.. c:function:: void glm_quat_for(vec3 dir, vec3 up, versor dest)
| creates look rotation quaternion
Parameters:
| *[in]* **dir** direction to look
| *[in]* **up** up vector
| *[out]* **dest** result matrix
.. c:function:: void glm_quat_forp(vec3 from, vec3 to, vec3 up, versor dest)
| creates look rotation quaternion using source and destination positions p suffix stands for position
| this is similar to glm_quat_for except this computes direction for glm_quat_for for you.
Parameters:
| *[in]* **from** source point
| *[in]* **to** destination point
| *[in]* **up** up vector
| *[out]* **dest** result matrix
.. c:function:: void glm_quat_rotatev(versor q, vec3 v, vec3 dest)
| crotate vector using using quaternion
Parameters:
| *[in]* **q** quaternion
| *[in]* **v** vector to rotate
| *[out]* **dest** rotated vector
.. c:function:: void glm_quat_rotate(mat4 m, versor q, mat4 dest)
| rotate existing transform matrix using quaternion
instead of passing identity matrix, consider to use quat_mat4 functions
Parameters:
| *[in]* **m** existing transform matrix to rotate
| *[in]* **q** quaternion
| *[out]* **dest** rotated matrix/transform
.. c:function:: void glm_quat_rotate_at(mat4 m, versor q, vec3 pivot)
| rotate existing transform matrix using quaternion at pivot point
Parameters:
| *[in, out]* **m** existing transform matrix to rotate
| *[in]* **q** quaternion
| *[in]* **pivot** pivot
.. c:function:: void glm_quat_rotate_atm(mat4 m, versor q, vec3 pivot)
| rotate NEW transform matrix using quaternion at pivot point
| this creates rotation matrix, it assumes you don't have a matrix
| this should work faster than glm_quat_rotate_at because it reduces one glm_translate.
Parameters:
| *[in, out]* **m** existing transform matrix to rotate
| *[in]* **q** quaternion
| *[in]* **pivot** pivot
|
