The 1.0.5 release added SLERP/HLERP support in C++ and C, moved from the vector 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.
CQRlib is an ANSI C implementation of a utility library for quaternion arithmetic and quaternion rotation math. See
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.
The CQRlib package is available at www.sourceforge.net/projects/cqrlib. A source tarball is available at downloads.sourceforge.net/cqrlib/CQRlib-1.0.5.tar.gz. Later tarballs may be available.
When the source tarball is downloaded and unpacked, you should have a directory CQRlib-1.0.5. To see the current settings for a build execute
make
which should give the following information:
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:
/Users/yaya/bin/libtool --mode=compile gcc -g -O2 -Wall -ansi -pedantic -I. -c
/Users/yaya/bin/libtool --mode=compile g++ -g -O2 -Wall -ansi -pedantic -DCQR_NOCCODE=1 -I. -c
The current library C and C++ link commands are:
/Users/yaya/bin/libtool --mode=link gcc -version-info 2:0:0 -rpath /Users/yaya/lib
/Users/yaya/bin/libtool --mode=link g++ -version-info 2:0:0 -rpath /Users/yaya/lib
The current C library local, dynamic and static build commands are:
/Users/yaya/bin/libtool --mode=link gcc -g -O2 -Wall -ansi -pedantic -I.
/Users/yaya/bin/libtool --mode=link gcc -g -O2 -Wall -ansi -pedantic -dynamic -I /Users/yaya/include -L/Users/yaya/lib
/Users/yaya/bin/libtool --mode=link gcc -g -O2 -Wall -ansi -pedantic -static -I /Users/yaya/include -L/Users/yaya/lib
The current C++ template local, dynamic and static build commands are:
/Users/yaya/bin/libtool --mode=link g++ -g -O2 -Wall -ansi -pedantic -DCQR_NOCCODE=1 -I.
/Users/yaya/bin/libtool --mode=link g++ -g -O2 -Wall -ansi -pedantic -DCQR_NOCCODE=1 -dynamic -I /Users/yaya/include -L/Users/yaya/lib
/Users/yaya/bin/libtool --mode=link g++ -g -O2 -Wall -ansi -pedantic -DCQR_NOCCODE=1 -static -I /Users/yaya/include -L/Users/yaya/lib
Before installing the CQRlib library and example programs, check
that the install directory and install commands are correct:
The current values are :
/usr/local
/usr/local/bin/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
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 and 1.5.4. 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
export LIBTOOL=$HOME/bin/libtool
of in the Makefie
LIBTOOL = $(HOME)/bin/libtool
If you need to include local header files using #include "..." instead of #include <...>, define the variable USE_LOCAL_HEADERS
#include <cqrlib.h>
/* 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);
/* 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 ) ;
/* 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);
/* SLERPDist -- Spherical Linear Interpolation distance */
int CQRSLERPDist (double CQR_FAR * dist, const CQRQuaternionHandle q1, const CQRQuaternionHandle q2);
/* HLERPDist -- Hemispherical Linear Interpolation distance */
int HLERPDist (double CQR_FAR * dist, const CQRQuaternionHandle q1, const CQRQuaternionHandle q2);
and for C++
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;
/* 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;
/* Inverse -- Form the inverse of a quaternion */
inline CPPQR Inverse ( void ) 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
The cqrlib.h header file defines the CQRQuaternionHandle type as a pointer to a struct of the CQRQuaternion type:
typedef struct {
double w;
double x;
double y;
double z; } CQRQuaternion;
representing w + xi +yj + zk. A quaternion may be declared directly using the CQRQuaternion 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.
The rules of quaternion arithmetic are applied:
-1 = i*i = j*j = k*k, i*j=k=-j*i, j*k=i=-j*k, k*i=j=-i*k
by CQRAdd, CQRSubtract, CQRMultiply and CQRDivide. CQRScalarMultiply multiplies a quaternion by a scalar.
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.
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.
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.
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.
The CQRlib functions return 0 for normal completion, or the sum of one or more of the following non-zero error codes:
Error Return Numeric Value Meaning CQR_BAD_ARGUMENT 1 /* An argument is not valid */ CQR_NO_MEMORY 2 /* A call to allocate memory failed */ CQR_FAILED 4 /* Operation failed */
To create a quaternion dynamically from memory, initialized as the x vector with a zero scalar value, reporting failure to stderr:
#include <cqrlib.h>
#include <stdio.h>
...
CQRQuaternionHandle quathandle;
...
if (CQRCreateQuaternion(&quathandle,0.,1.,0.,0.)) fprintf(stderr," CQRCreateQuaternion failed!!\n");
To create an x vector quaternion, a y vector quaternion, add then together and multiply by a z-vector, and print the result :
#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);
The output should be "Result = ((i+j)*k) = 0 +1i -1j +0k".
To rotate the 3D vector [-1.,0.,1.] 90 degrees clockwise around the vector [1.,1.,1.]:
#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]);
The output should be "[-1.,0.,1.] rotated 90 degrees clockwise around the vector [1.,1.,1.] = [0.57735, -1.1547, 0.57735]".
See the test program CQRlibTest.c.
For examples of the use of the CPPQR template, see the C++ test program CPPQRTest.cpp.