-
Notifications
You must be signed in to change notification settings - Fork 3
/
README_CQRlib.html
625 lines (473 loc) · 26.7 KB
/
README_CQRlib.html
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
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
<html>
<head>
<title>README CQRlib -- API for Quaternion Rotations</title>
</head>
<body bgcolor="FFFFFF">
<font face="Arial,Helevtica,Times" size=4>
<a href="http://sourceforge.net/projects/cqrlib"><img src="http://sflogo.sourceforge.net/sflogo.php?group_id=268743&type=13" width="120" height="30" alt="Get CQRlib at SourceForge.net. Fast, secure and Free Open Source software downloads" /></a><hr>
<h3 align="center">CQRlib -- ANSI C API for Quaternion Rotations</h3>
<P>
<center>
Release 1.1.4<br />
29 Apr 2018<br />
© 2008, 2009, 2010, 2014, 2018 Herbert J. Bernstein<br/>
<script language="javascript" type="text/javascript">
<!--
var name = "yayahjb";
var domain = "gmail";
var domext = "com";
document.write ("<a href=\"mailto:" + name + "@" + domain + "." + domext + "\"style=\"text-decoration:none\">" + name + " <b>at</b> " + domain + " <b>dot</b> " + domext+"</a>");
// -->
</script>
<noscript>
yayahjb <b>at</b> gmail <b>dot</b> com
</noscript><br />
You may distribute the CQRlib API under the <a href=lgpl.txt style="text-decoration:none">LGPL</a><br />
</center>
<P>
The 1.1.4 release is a documentation change to reflect a move of the source to github.
The 1.1.3 release parenthesized uses of *this that caused errors from OSX clang.
Thanks to Zack Settel for reporting the problem.
The 1.1.2 release improved the portability of the code for Visual Studio.
The 1.1.1 release relaxed some of the test constraints and parametrized the tests against DBL_EPSILON
and added the Dist and Distsq functions.
The 1.1 release added functions for log, exp, power and root, added a macro form of the
norm and fixed the macro for inverse.
The 1.0.6 release fixed an error in the CQRHLERPDist definition and comments.
The 1.0.5 release added SLERP/HLERP support in C++ and C, moved from the <a
href=http://sf.net/projects/vector>vector</a> project.
The 1.0.4 release added a version of L. Andrews adaptation to a C++ template.
The 1.0.3 release changed from use of a FAR macro to use of a CQR_FAR macro to avoid name conflicts.
the macros for malloc, free, memmove and memset were also changed.
The 1.0.2 release of 14 June 2009 corrected the Makefile for case-sensitive file systems and to include -lm in loading.
Release 1.0.1 of 23 February 2009 was a minor documentation update to the original 1.0 release of 22 February 2009.
<p>
CQRlib is an ANSI C implementation of a utility library for quaternion arithmetic and
quaternion rotation math. See
<ul>
<li>"Quaternions and spatial rotation", Wikipedia
<a href="http://en.wikipedia.org/wiki/Quaternions_and_spatial_rotation">http://en.wikipedia.org/wiki/Quaternions_and_spatial_rotation</a>
<li> K. Shoemake, "Quaternions", Department of Computer Science,
University of Pennsylvania, Philadelphia, PA 19104,
<a href="ftp://ftp.cis.upenn.edu/pub/graphics/shoemake/quatut.ps.Z">ftp://ftp.cis.upenn.edu/pub/graphics/shoemake/quatut.ps.Z</a>
<li>K. Shoemake, "Animating rotation with quaternion curves",
ACM SIGGRAPH Computer Graphics, Vol 19, No. 3, pp 245--254,
1985.
</ul>
<p>
Work supported in part by NIH NIGMS under grant 1R15GM078077-01 and DOE under grant ER63601-1021466-0009501.
Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the funding agencies.
<p>
<h4>Installation</h4>
<P>
The CQRlib package is available at <a href="https://github.com/yayahjb/cqrlib.git">https://github.com/yayahjb/cqrlib.git</a>.
A source zip file is available at
<a href="https://github.com/yayahjb/cqrlib/archive/master.zip">https://github.com/yayahjb/cqrlib/archive/master.zip</a>
<P>
When the source is downloaded and unpacked, you should have a directory cqrlib or master. To build you may need to
install the libtool-bin package. To see the
current settings for a build execute
<p>
make
</p>
which should give the following information:
<p>
<pre><tt>
PLEASE READ README_CQRlib.txt and lgpl.txt
Before making the CQRlib library and example programs, check
that the chosen settings are correct
The current C and C++ compile commands are:
libtool --mode=compile gcc -g -O2 -Wall -ansi -pedantic -I. -c
libtool --mode=compile g++ -g -O2 -Wall -ansi -pedantic -DCQR_NOCCODE=1 -I. -c
The current library C and C++ link commands are:
libtool --mode=link gcc -version-info 3:0:1 -rpath /home/yaya/lib
libtool --mode=link g++ -version-info 3:0:1 -rpath /home/yaya/lib
The current C library local, dynamic and static build commands are:
libtool --mode=link gcc -g -O2 -Wall -ansi -pedantic -I.
libtool --mode=link gcc -g -O2 -Wall -ansi -pedantic -dynamic -I /home/yaya/include -L/home/yaya/lib
libtool --mode=link gcc -g -O2 -Wall -ansi -pedantic -static -I /home/yaya/include -L/home/yaya/lib
The current C++ template local, dynamic and static build commands are:
libtool --mode=link g++ -g -O2 -Wall -ansi -pedantic -DCQR_NOCCODE=1 -I.
libtool --mode=link g++ -g -O2 -Wall -ansi -pedantic -DCQR_NOCCODE=1 -dynamic -I /home/yaya/include -L/home/yaya/lib
libtool --mode=link g++ -g -O2 -Wall -ansi -pedantic -DCQR_NOCCODE=1 -static -I /home/yaya/include -L/home/yaya/lib
Before installing the CQRlib library and example programs, check
that the install directory and install commands are correct:
The current values are :
/home/yaya
libtool --mode=install cp
To compile the CQRlib library and example programs type:
make clean
make all
To run a set of tests type:
make tests
To clean up the directories type:
make clean
To install the library and binaries type:
make install
</tt>
</pre>
<p>
If these settings need to be changed, edit Makefile. On some systems, e.g. Mac OS X, the default
libtool is not appropriate. In that case you should install a recent version of libtool. The
CQRlib kit has been tested with libtool versions 1.3.5, 1.5.4 and 2.4.6. If the system libtool is
not to be used, define the variable LIBTOOL to be the path to the libtool executable, e.g.
in bash
<p>
export LIBTOOL=$HOME/bin/libtool
<p>
of in the Makefie
<p>
LIBTOOL = $(HOME)/bin/libtool
<p>
If you need to include local header files using #include "..." instead of #include <...>,
define the variable USE_LOCAL_HEADERS. This definition is forced if _MSC_VER is defined, meaning that
local headers will automatically be used for Visual Studio.
<h4>Synopsis</h4>
<P>
<b>#include <cqrlib.h></b>
<pre>
<tt>
/* CQRCreateQuaternion -- create a quaternion = w +ix+jy+kz */
int CQRCreateQuaternion(CQRQuaternionHandle * quaternion, double w, double x, double y, double z);
/* CQRCreateEmptyQuaternion -- create a quaternion = 0 +i0+j0+k0 */
int CQRCreateEmptyQuaternion(CQRQuaternionHandle * quaternion) ;
/* CQRFreeQuaternion -- free a quaternion */
int CQRFreeQuaternion(CQRQuaternionHandle * quaternion);
/* CQRSetQuaternion -- create an existing quaternion = w +ix+jy+kz */
int CQRSetQuaternion( CQRQuaternionHandle quaternion, double w, double x, double y, double z);
/* CQRGetQuaternionW -- get the w component of a quaternion */
int CQRGetQuaternionW( double CQR_FAR * qw, CQRQuaternionHandle q );
/* CQRGetQuaternionX -- get the x component of a quaternion */
int CQRGetQuaternionX( double CQR_FAR * qx, CQRQuaternionHandle q );
/* CQRGetQuaternionY -- get the y component of a quaternion */
int CQRGetQuaternionY( double CQR_FAR * qy, CQRQuaternionHandle q );
/* CQRGetQuaternionZ -- get the z component of a quaternion */
int CQRGetQuaternionZ( double CQR_FAR * qz, CQRQuaternionHandle q );
/* CQRGetQuaternionIm -- get the imaginary component of a quaternion */
int CQRGetQuaternionIm( CQRQuaternionHandle quaternion, CQRQuaternionHandle q );
/* CQRGetQuaternionAxis -- get the axis for the polar representation of a quaternion */
int CQRGetQuaternionAxis( CQRQuaternionHandle quaternion, CQRQuaternionHandle q );
/* CQRGetQuaternionAngle -- get the angular component of the polar representation
of aquaternion */
int CQRGetQuaternionAngle( double CQR_FAR * angle, CQRQuaternionHandle q );
/* CQRLog -- get the natural logarithm of a quaternion */
int CQRLog( CQRQuaternionHandle quaternion, CQRQuaternionHandle q );
/* CQRExp -- get the exponential (exp) of a quaternion */
int CQRExp( CQRQuaternionHandle quaternion, CQRQuaternionHandle q );
/* CQRQuaternionPower -- take a quarernion to a quaternion power */
int CQRQuaternionPower( CQRQuaternionHandle quaternion, CQRQuaternionHandle q, CQRQuaternionHandle p);
/* CQRDoublePower -- take a quarernion to a double power */
int CQRDoublePower( CQRQuaternionHandle quaternion, CQRQuaternionHandle q, double p);
/* CQRIntegerPower -- take a quaternion to an integer power */
int CQRIntegerPower( CQRQuaternionHandle quaternion, CQRQuaternionHandle q, int p);
/* CQRIntegerRoot -- take the given integer root of a quaternion, returning
the indicated mth choice from among multiple roots.
For reals the cycle runs through first the i-based
roots, then the j-based roots and then the k-based roots,
out of the infinite number of possible roots of reals. */
int CQRIntegerRoot( CQRQuaternionHandle quaternion, CQRQuaternionHandle q, int r, int m);
/* CQRAdd -- add a quaternion (q1) to a quaternion (q2) */
int CQRAdd (CQRQuaternionHandle quaternion, CQRQuaternionHandle q1, CQRQuaternionHandle q2 );
/* CQRSubtract -- subtract a quaternion (q2) from a quaternion (q1) */
int CQRSubtract (CQRQuaternionHandle quaternion, CQRQuaternionHandle q1, CQRQuaternionHandle q2 );
/* CQRMultiply -- multiply a quaternion (q1) by quaternion (q2) */
int CQRMultiply (CQRQuaternionHandle quaternion, CQRQuaternionHandle q1, CQRQuaternionHandle q2 );
/* CQRDot -- dot product of quaternion (q1) by quaternion (q2) as 4-vectors */
int CQRDot (double CQR_FAR * dotprod, CQRQuaternionHandle q1, CQRQuaternionHandle q2 );
/* CQRDivide -- Divide a quaternion (q1) by quaternion (q2) */
int CQRDivide (CQRQuaternionHandle quaternion, CQRQuaternionHandle q1, CQRQuaternionHandle q2 );
/* CQRScalarMultiply -- multiply a quaternion (q) by scalar (s) */
int CQRScalarMultiply (CQRQuaternionHandle quaternion, CQRQuaternionHandle q, double s );
/* CQREqual -- return 0 if quaternion q1 == q2 */
int CQREqual (CQRQuaternionHandle q1, CQRQuaternionHandle q2 );
/* CQRConjugate -- Form the conjugate of a quaternion qconj */
int CQRConjugate (CQRQuaternionHandle qconjugate, CQRQuaternionHandle quaternion);
/* CQRNormsq -- Form the normsquared of a quaternion */
int CQRNormsq (double * normsq, CQRQuaternionHandle quaternion ) ;
/* CQRNorm -- Form the norm of a quaternion */
int CQRNorm (double * norm, CQRQuaternionHandle quaternion ) ;
/* CQRDistsq -- Form the distance squared between two quaternions */
int CQRDistsq (double CQR_FAR * distsq, CQRQuaternionHandle q1, CQRQuaternionHandle q2) ;
/* CQRDist -- Form the distance between two quaternions */
int CQRDist (double CQR_FAR * dist, CQRQuaternionHandle q1, CQRQuaternionHandle q2 ) ;
/* CQRInverse -- Form the inverse of a quaternion */
int CQRInverse (CQRQuaternionHandle inversequaternion, CQRQuaternionHandle quaternion );
/* CQRRotateByQuaternion -- Rotate a vector by a Quaternion, w = qvq* */
int CQRRotateByQuaternion(double * w, CQRQuaternionHandle rotquaternion, double * v);
/* CQRAxis2Quaternion -- Form the quaternion for a rotation around axis v by angle theta */
int CQRAxis2Quaternion (CQRQuaternionHandle rotquaternion, double * v, double theta);
/* CQRMatrix2Quaterion -- Form the quaternion from a 3x3 rotation matrix R */
int CQRMatrix2Quaternion (CQRQuaternionHandle rotquaternion, double R[3][3]);
/* CQRQuaternion2Matrix -- Form the 3x3 rotation matrix from a quaternion */
int CQRQuaternion2Matrix (double R[3][3], CQRQuaternionHandle rotquaternion);
/* CQRQuaternion2Angles -- Convert a Quaternion into Euler Angles for Rz(Ry(Rx))) convention */
int CQRQuaternion2Angles (double * RotX, double * RotY, double * RotZ, CQRQuaternionHandle rotquaternion);
/* CQRAngles2Quaternion -- Convert Euler Angles for Rz(Ry(Rx))) convention into a quaternion */
int CQRAngles2Quaternion (CQRQuaternionHandle rotquaternion, double RotX, double RotY, double RotZ );
/* Represent a 3-vector as a quaternion with w=0 */
int CQRPoint2Quaternion( CQRQuaternionHandle quaternion, double v[3] );
/* SLERP -- Spherical Linear Interpolation */
int CQRSLERP (CQRQuaternionHandle quaternion, const CQRQuaternionHandle q1, const CQRQuaternionHandle q2,
const double w1, const double w2);
/* HLERP -- Hemispherical Linear Interpolation */
int CQRHLERP (CQRQuaternionHandle quaternion, const CQRQuaternionHandle q1, const CQRQuaternionHandle q2,
const double w1, const double w2);
/* CQRSLERPDist -- Spherical Linear Interpolation distance */
int CQRSLERPDist (double CQR_FAR * dist, const CQRQuaternionHandle q1, const CQRQuaternionHandle q2);
/* CQRHLERPDist -- Hemispherical Linear Interpolation distance */
int CQRHLERPDist (double CQR_FAR * dist, const CQRQuaternionHandle q1, const CQRQuaternionHandle q2);
</tt>
</pre>
and for C++
<pre>
<tt>
template< typename DistanceType=double, typename VectorType=double[3], typename MatrixType=double[9] >
class CPPQR
{
public:
/* Constructors */
inline CPPQR( ); // default constructor
inline CPPQR( const CPPQR& q ); // copy constructor
inline CPPQR( const DistanceType& wi, const DistanceType& xi, const DistanceType& yi, const DistanceType& zi );
/* Set -- set the values of an existing quaternion = w +ix+jy+kz */
inline void Set ( const DistanceType& wi, const DistanceType& xi, const DistanceType& yi, const DistanceType& zi );
/* Accessors */
inline DistanceType GetW( void ) const;
inline DistanceType GetX( void ) const;
inline DistanceType GetY( void ) const;
inline DistanceType GetZ( void ) const;
inline CPPQR GetIm( void ) const;
inline CPPQR GetAxis( void ) const;
inline double GetAngle( void ) const;
/* Operators */
inline CPPQR operator+ ( const CPPQR& q ) const;
inline CPPQR& operator+= ( const CPPQR& q );
inline CPPQR& operator-= ( const CPPQR& q );
inline CPPQR operator- ( const CPPQR& q ) const;
inline CPPQR operator* ( const CPPQR& q ) const;
inline CPPQR operator/ ( const CPPQR& q2 ) const;
inline CPPQR operator* ( const DistanceType& d ) const;
inline CPPQR operator/ ( const DistanceType& d ) const;
inline CPPQR Conjugate ( void ) const;
inline CPPQR& operator= ( const CPPQR& q );
inline bool operator== ( const CPPQR& q ) const;
inline bool operator!= ( const CPPQR& q ) const;
inline VectorType& operator* ( const VectorType& v );
DistanceType operator[] ( const int k ) const;
/* Dot -- Dot product of 2 quaternions as 4-vectors */
inline DistanceType Dot( const CPPQR& q) const;
/* Normsq -- Form the normsquared of a quaternion */
inline DistanceType Normsq ( void ) const;
/* Norm -- Form the norm of a quaternion */
inline DistanceType Norm ( void ) const;
/* Distsq -- Form the distance squared from a quaternion */
inline DistanceType Distsq ( const CPPQR& q ) const;
/* Dist -- Form the distance from a quaternion */
inline DistanceType Dist ( const CPPQR& q ) const;
/* Inverse -- Form the inverse of a quaternion */
inline CPPQR Inverse ( void ) const;
/* log -- Get the natural logarithm of a quaternion */
inline CPPQR log( void ) const;
/* exp -- Get the exponential of a quaternion */
inline CPPQR exp( void ) const;
/* pow -- Take a power of a quaternion */
template <typename powertype>
inline CPPQR pow( const powertype p) const;
inline CPPQR pow( const int p) const;
/* root -- Take an integer root of a quaternion */
inline CPPQR root( const int r, const int m) const;
/* RotateByQuaternion -- Rotate a vector by a Quaternion, w = qvq* */
inline void RotateByQuaternion(VectorType &w, const VectorType v );
inline VectorType& RotateByQuaternion( const VectorType v );
/* Axis2Quaternion -- Form the quaternion for a rotation around axis v by angle theta */
static inline CPPQR Axis2Quaternion ( const DistanceType& angle, const VectorType v );
static inline CPPQR Axis2Quaternion ( const VectorType v, const DistanceType& angle );
/* Matrix2Quaterion -- Form the quaternion from a 3x3 rotation matrix R */
static inline void Matrix2Quaternion ( CPPQR& rotquaternion, const MatrixType m );
static inline void Matrix2Quaternion ( CPPQR& rotquaternion, const DistanceType R[3][3] );
/* Quaternion2Matrix -- Form the 3x3 rotation matrix from a quaternion */
static inline void Quaternion2Matrix( MatrixType& m, const CPPQR q );
static inline void Quaternion2Matrix( DistanceType m[3][3], const CPPQR q );
/* Get a unit quaternion from a general one */
inline CPPQR UnitQ( void ) const;
/* Quaternion2Angles -- Convert a Quaternion into Euler Angles for Rz(Ry(Rx))) convention */
inline bool Quaternion2Angles ( DistanceType& rotX, DistanceType& rotY, DistanceType& rotZ ) const;
/* Angles2Quaternion -- Convert Euler Angles for Rz(Ry(Rx))) convention into a quaternion */
static inline CPPQR Angles2Quaternion ( const DistanceType& rotX, const DistanceType& rotY, const DistanceType& rotZ );
static inline CPPQR Point2Quaternion( const DistanceType v[3] );
/* SLERP -- Spherical Linear Interpolation */
inline CPPQR SLERP (const CPPQR& q, DistanceType w1, DistanceType w2) const;
/* HLERP -- Hemispherical Linear Interpolation */
inline CPPQR HLERP (const CPPQR& q, DistanceType w1, DistanceType w2) const;
/* SLERPDist -- Spherical Linear Interpolation distance */
inline DistanceType SLERPDist (const CPPQR& q) const;
/* HLERPDist -- Hemispherical Linear Interpolation distance */
inline DistanceType HLERPDist (const CPPQR& q) const;
}; // end class CPPQR
</tt>
</pre>
<p>
<h4>Description</h4>
<P>
The cqrlib.h header file defines the <b>CQRQuaternionHandle</b> type as a pointer to a struct of the <b>CQRQuaternion</b> type:
<p>
<pre><tt>
typedef struct {
double w;
double x;
double y;
double z; } CQRQuaternion;
</tt>
</pre>
representing w + xi +yj + zk. A quaternion may be declared directly using the <b>CQRQuaternion</b> type or dynamically
allocated by CQRCreateQuaternion or CQRCreateEmptyQuaternion, in which case it is a user responsibility to eventually
free the allocated memory with CQRFreeQuaternion. The components of an existing quaternion may be set by
CQRSetQuaternion.
<p>
The rules of quaternion arithmetic are applied:
<p>
-1 = i*i = j*j = k*k, i*j=k=-j*i, j*k=i=-j*k, k*i=j=-i*k
<p>
by CQRAdd, CQRSubtract, CQRMultiply and CQRDivide. CQRScalarMultiply multiplies a quaternion by a scalar.
<p>
CQREqual returns 0 if quaternion q1 == q2, component by component. CQRConjugate computes a quaternion with
the same scalar component and the negative of the vector component. CQRNormsq computes the sum of
the squares of the components. CQRInverse computes the inverse of a non-zero quaternion.
<p>
The functions CQRGetQuaternionW, CQRGetQuaternionX, CQRGetQuaternionY and CQRGetQuaternionZ extract the 4 components of a
quaternion. The function CQRGetQuaternionIm extract the imaginary part of a
quaternion as a quaternion with w=0. The function CQRQGetQuaternion extracts the
imaginary part and normalizes it to a unit vector. The function CQRGetQuaternionAngle
extracts the angle for the polar representation of a quaternion as an exponential (see below).
<p>
In handling rotations, a right-handed system is assumed.
CQRRotateByQuaternion rotates a vector by a quaternion, w = qvq*.
CQRAxis2Quaternion forms the quaternion for a rotation around axis v by angle theta.
CQRMatrix2Quaterion forms the quaternion equivalent a 3x3 rotation matrix R.
CQRQuaternion2Matrix forms a 3x3 rotation matrix from a quaternion.
CQRQuaternion2Angles converts a quaternion into Euler Angles for the Rz(Ry(Rx))) convention.
CQRAngles2Quaternion convert Euler angles for the Rz(Ry(Rx))) convention into a quaternion.
<p>
The logarithm of a quaternion in CQRLog is based on the polar representation
<p>
q = r*cos(theta) + r*sin(theta) [ i*axis_x + j*axis_y +k*axis_z]<br />
= r*exp(theta*[ i*axis_x + j*axis_y +k*axis_z])
<p>
with a unit axis. Then the natural logarithm is given by
<p>
log(q) = log(r) + theta*[ i*axis_x + j*axis_y +k*axis_z])
<p>
Note than any integer multiple of 2*PI could have been added to theta, so the
logarithm is multivalued. The code only returns one of these values. The
exponential in CQRExp is created by reversing the transformation. Taking
a quaternion to a quaternion power is done by taking the log, multiplying
by the power and then taking the exponential. Only one representative power
is returned by CQRQuaternionPower. CQRDoublePower takes a quaternion to
a double power by the same log-multiply-exp approach. CQRIntegerPower applies
positive and negative integer powers by multiplication withou taking any
logs or exponentials. CQRIntegerRoot applies the log-multiply-exp approach
for integer roots. The second integer argument allow selection of one of the
multiple roots. For roots of quaternions with a non-zero imaginary part, there
are r roots, so m = 0, 1, 2, ... r-1 are meaningful. For roots of reals,
there can be infinitely many alternate roots. In the case, m will cycle first
through the i-based roots, then the j-based roots and then the k-based roots.
<p>
The SLERP and HLERP functions combine quaternions by speherical linear interpolation. SLERP
take two quaternions and two weights and combine them following a great circle on the unit quaternion 4-D
sphere and linear interpolation between the radii. SLERP keeps a quaternion separate from the negative
of the same quaternion and is not appropriate for quaternions representing rotations. Use HLERP
to apply SLERP to quaternions representing rotations.
<p>
If operating with __cplusplus defined, then the CPPQR template is defined allowing the creation of CPPQR quaternion
objects. The template has three typename arguments: DistanceType, VectorType and MatrixType that default to double,
double[3] and double[9]. Specializations are provided to support a double[3][3] MatrixType.
<p>
<h4>Returns</h4>
<p>
The CQRlib functions return 0 for normal completion, or the sum of one or more of the following non-zero error codes:
<p>
<blockquote>
<table border="0">
<tr><td>Error Return </td><td>Numeric Value </td><td> Meaning</td></tr>
<tr><td>CQR_BAD_ARGUMENT </td><td> 1 </td><td> /* An argument is not valid */</td></tr>
<tr><td>CQR_NO_MEMORY </td><td> 2 </td><td> /* A call to allocate memory failed */</td></tr>
<tr><td>CQR_FAILED </td><td> 4 </td><td> /* Operation failed */</td></tr>
</table>
</blockquote>
</p>
<p>
<h4>Examples</h4>
<p>
To create a quaternion dynamically from memory, initialized as the x vector with a zero scalar value, reporting failure to stderr:
<P>
<pre><tt>
#include <cqrlib.h>
#include <stdio.h>
...
CQRQuaternionHandle quathandle;
...
if (CQRCreateQuaternion(&quathandle,0.,1.,0.,0.)) fprintf(stderr," CQRCreateQuaternion failed!!\n");
</tt></pre>
<P>
To create an x vector quaternion, a y vector quaternion, add then together and multiply by a z-vector,
and print the result :
<P>
<pre><tt>
#include <cqrlib.h>
#include <stdio.h>
...
CQRQuaternion qx, qy, qz, qresult1, qresult2;
...
if (CQRSetQuaternion(&qx,0.,1.,0.,0.)
||CQRSetQuaternion(&qy,0.,0.,1.,0.)
||CQRSetQuaternion(&qz,0.,0.,0.,1.)) fprintf(stderr," CQRSetQuaternion failed!!\n");
if (CQRAdd(&qresult1,&qx,&qy)||CQRMultiply(&qresult2,&qresult1,&qz))
fprintf(stderr," CQR Add or Multiply failed!!\n");
fprintf(stdout,"Result = ((i+j)*k) = %g %+gi %+gj + %+gk\n",
qresult2.w, qresult2.x, qresult2.y, qresult2.z);
</tt></pre>
<p>The output should be "Result = ((i+j)*k) = 0 +1i -1j +0k".
<p>
To rotate the 3D vector [-1.,0.,1.] 90 degrees clockwise around the vector [1.,1.,1.]:
<p>
<pre><tt>
#include <cqrlib.h>
#include <math.h>
#include <stdio.h>
...
double axis[3] = {1.,1.,1.};
double vector[3] = {-1.,0.,1.};
double result[3];
CQRQuaternion rotquat;
double PI;
PI = 4.*atan2(1.,1.);
CQRAxis2Quaternion(&rotquat,axis,PI/2);
CQRRotateByQuaternion(result, &rotquat, vector);
...
fprintf(stdout," [-1.,0.,1.] rotated 90 degrees clockwise"
" around the vector [1.,1.,1.] = [%g, %g, %g]\n",
result[0], result[1], result[2]);
</tt></pre>
<p>The output should be "[-1.,0.,1.] rotated 90 degrees clockwise around the vector [1.,1.,1.] = [0.57735, -1.1547, 0.57735]".
<p>
See the test program <a href="CQRlibTest.c">CQRlibTest.c</a>.
<p>
For examples of the use of the CPPQR template, see the C++ test program <a href="CPPQRTest.cpp">CPPQRTest.cpp</a>.
<hr>
<font size="2">
Updated 29 April 2018<br />
<script language="javascript" type="text/javascript">
<!--
var name = "yayahjb";
var domain = "gmail";
var domext = "com";
document.write ("<a href=\"mailto:" + name + "@" + domain + "." + domext + "\" style=\"text-decoration:none\">" + name + " <b>at</b> " + domain + " <b>dot</b> " + domext+"</a>");
// -->
</script>
<noscript>
yayahjb <b>at</b> gmail <b>dot</b> com
</noscript>
</font>
</font>
</body>
</html>