Detailed Description

A quaternion, which can represent a 3D rotation as pair $(r,\mathbf{u})$ , with a real part "r" and a 3D vector $\mathbf{u} = (x,y,z)$ , or alternatively, q = r + ix + jy + kz.

The elements of the quaternion can be accessed by either:

r(), x(), y(), z(), or
the operator [] with indices running from 0 (=r) to 3 (=z).

Users will usually employ the typedef "CQuaternionDouble" instead of this template.

For more information about quaternions, see:

See also:: mrpt::poses::CPose3D

#include <mrpt/math/CQuaternion.h>

Inheritance diagram for mrpt::math::CQuaternion:

[legend]

List of all members.

Public Member Functions

	CQuaternion (TConstructorFlags_Quaternions constructor_dummy_param)
	Can be used with UNINITIALIZED_QUATERNION as argument, does not initialize the 4 elements of the quaternion (use this constructor when speed is critical).
	CQuaternion ()
	Default constructor: construct a (1, (0,0,0) ) quaternion representing no rotation.
	CQuaternion (const T r, const T x, const T y, const T z)
	Construct a quaternion from its parameters 'r', 'x', 'y', 'z', with q = r + ix + jy + kz.
T	r () const
	Return r coordinate of the quaternion.
T	x () const
	Return x coordinate of the quaternion.
T	y () const
	Return y coordinate of the quaternion.
T	z () const
	Return z coordinate of the quaternion.
void	r (const T r)
	Set r coordinate of the quaternion.
void	x (const T x)
	Set x coordinate of the quaternion.
void	y (const T y)
	Set y coordinate of the quaternion.
void	z (const T z)
	Set z coordinate of the quaternion.
template<class ARRAYLIKE >
void	fromRodriguesVector (const ARRAYLIKE &in)
	Set this quaternion to the rotation described by a 3D Rodrigues rotation vector.
void	crossProduct (const CQuaternion &q1, const CQuaternion &q2)
	Calculate the "cross" product (or "composed rotation") of two quaternion: this = q1 x q2 After the operation, "this" will represent the composed rotations of q1 and q2 (q2 applied "after" q1).
void	rotatePoint (const double lx, const double ly, const double lz, double &gx, double &gy, double &gz) const
	Rotate a 3D point (lx,ly,lz) -> (gx,gy,gz) as described by this quaternion.
void	inverseRotatePoint (const double lx, const double ly, const double lz, double &gx, double &gy, double &gz) const
	Rotate a 3D point (lx,ly,lz) -> (gx,gy,gz) as described by the inverse (conjugate) of this quaternion.
double	normSqr () const
	Return the squared norm of the quaternion.
void	normalize ()
	Normalize this quaternion, so its norm becomes the unitity.
template<class MATRIXLIKE >
void	normalizationJacobian (MATRIXLIKE &J) const
	Calculate the 4x4 Jacobian of the normalization operation of this quaternion.
template<class MATRIXLIKE >
void	rotationJacobian (MATRIXLIKE &J) const
	Compute the Jacobian of the rotation composition operation $p = f(\cdot) = q_{this} \times r$ , that is the 4x4 matrix $\frac{\partial f}{\partial q_{this} }$ .
template<class MATRIXLIKE >
void	rotationMatrix (MATRIXLIKE &M) const
	Calculate the 3x3 rotation matrix associated to this quaternion.
template<class MATRIXLIKE >
void	rotationMatrixNoResize (MATRIXLIKE &M) const
	Fill out the top-left 3x3 block of the given matrix with the rotation matrix associated to this quaternion (does not resize the matrix, for that, see rotationMatrix)
void	conj (CQuaternion &q_out) const
	Return the conjugate quaternion.
CQuaternion	conj () const
	Return the conjugate quaternion.
void	rpy (T &roll, T &pitch, T &yaw) const
	Return the yaw, pitch & roll angles associated to quaternion.
template<class MATRIXLIKE >
void	rpy_and_jacobian (T &roll, T &pitch, T &yaw, MATRIXLIKE *out_dr_dq=NULL, bool resize_out_dr_dq_to3x4=true) const
	Return the yaw, pitch & roll angles associated to quaternion, and (optionally) the 3x4 Jacobian of the transformation.
CQuaternion	operator* (const T &factor)
Private Types
typedef CArrayNumeric< T, 4 >	Base

Member Typedef Documentation

typedef CArrayNumeric<T,4> mrpt::math::CQuaternion::Base [private]

Reimplemented from mrpt::math::CArrayNumeric< T, 4 >.

Definition at line 63 of file CQuaternion.h.

Constructor & Destructor Documentation

mrpt::math::CQuaternion::CQuaternion ( TConstructorFlags_Quaternions constructor_dummy_param ) [inline]

Can be used with UNINITIALIZED_QUATERNION as argument, does not initialize the 4 elements of the quaternion (use this constructor when speed is critical).

Definition at line 69 of file CQuaternion.h.

mrpt::math::CQuaternion::CQuaternion ( ) [inline]

Default constructor: construct a (1, (0,0,0) ) quaternion representing no rotation.

Definition at line 72 of file CQuaternion.h.

mrpt::math::CQuaternion::CQuaternion	(	const T	r,
		const T	x,
		const T	y,
		const T	z
	)		`[inline]`

Construct a quaternion from its parameters 'r', 'x', 'y', 'z', with q = r + ix + jy + kz.

Definition at line 81 of file CQuaternion.h.

Member Function Documentation

void mrpt::math::CQuaternion::conj ( CQuaternion & q_out ) const [inline]

Return the conjugate quaternion.

Definition at line 240 of file CQuaternion.h.

CQuaternion mrpt::math::CQuaternion::conj ( ) const [inline]

Return the conjugate quaternion.

Definition at line 249 of file CQuaternion.h.

Referenced by mrpt::math::CQuaternion< double >::conj().

void mrpt::math::CQuaternion::crossProduct	(	const CQuaternion &	q1,
		const CQuaternion &	q2
	)		`[inline]`

Calculate the "cross" product (or "composed rotation") of two quaternion: this = q1 x q2 After the operation, "this" will represent the composed rotations of q1 and q2 (q2 applied "after" q1).

Definition at line 135 of file CQuaternion.h.

template<class ARRAYLIKE >

void mrpt::math::CQuaternion::fromRodriguesVector ( const ARRAYLIKE & in ) [inline]

Set this quaternion to the rotation described by a 3D Rodrigues rotation vector.

Definition at line 106 of file CQuaternion.h.

void mrpt::math::CQuaternion::inverseRotatePoint	(	const double	lx,
		const double	ly,
		const double	lz,
		double &	gx,
		double &	gy,
		double &	gz
	)		const `[inline]`

Rotate a 3D point (lx,ly,lz) -> (gx,gy,gz) as described by the inverse (conjugate) of this quaternion.

Definition at line 157 of file CQuaternion.h.

template<class MATRIXLIKE >

void mrpt::math::CQuaternion::normalizationJacobian ( MATRIXLIKE & J ) const [inline]

Calculate the 4x4 Jacobian of the normalization operation of this quaternion.

The output matrix can be a dynamic or fixed size (4x4) matrix.

Definition at line 182 of file CQuaternion.h.

void mrpt::math::CQuaternion::normalize ( ) [inline]

Normalize this quaternion, so its norm becomes the unitity.

Definition at line 171 of file CQuaternion.h.

Referenced by mrpt::math::CQuaternion< double >::crossProduct().

double mrpt::math::CQuaternion::normSqr ( ) const [inline]

Return the squared norm of the quaternion.

Definition at line 167 of file CQuaternion.h.

Referenced by mrpt::math::CQuaternion< double >::CQuaternion(), mrpt::math::CQuaternion< double >::normalize(), and mrpt::math::CQuaternion< double >::normalizationJacobian().

CQuaternion mrpt::math::CQuaternion::operator* ( const T & factor ) [inline]

Definition at line 341 of file CQuaternion.h.

T mrpt::math::CQuaternion::r ( ) const [inline]

Return r coordinate of the quaternion.

Definition at line 94 of file CQuaternion.h.

void mrpt::math::CQuaternion::r ( const T r ) [inline]

Set r coordinate of the quaternion.

Definition at line 98 of file CQuaternion.h.

Referenced by mrpt::math::CQuaternion< double >::r().

void mrpt::math::CQuaternion::rotatePoint	(	const double	lx,
		const double	ly,
		const double	lz,
		double &	gx,
		double &	gy,
		double &	gz
	)		const `[inline]`

Rotate a 3D point (lx,ly,lz) -> (gx,gy,gz) as described by this quaternion.

Definition at line 146 of file CQuaternion.h.

template<class MATRIXLIKE >

void mrpt::math::CQuaternion::rotationJacobian ( MATRIXLIKE & J ) const [inline]

Compute the Jacobian of the rotation composition operation $p = f(\cdot) = q_{this} \times r$ , that is the 4x4 matrix $\frac{\partial f}{\partial q_{this} }$ .

The output matrix can be a dynamic or fixed size (4x4) matrix.

Definition at line 212 of file CQuaternion.h.

template<class MATRIXLIKE >

void mrpt::math::CQuaternion::rotationMatrix ( MATRIXLIKE & M ) const [inline]

Calculate the 3x3 rotation matrix associated to this quaternion.

Definition at line 223 of file CQuaternion.h.

template<class MATRIXLIKE >

void mrpt::math::CQuaternion::rotationMatrixNoResize ( MATRIXLIKE & M ) const [inline]

Fill out the top-left 3x3 block of the given matrix with the rotation matrix associated to this quaternion (does not resize the matrix, for that, see rotationMatrix)

Definition at line 231 of file CQuaternion.h.

Referenced by mrpt::math::CQuaternion< double >::rotationMatrix().

void mrpt::math::CQuaternion::rpy	(	T &	roll,
		T &	pitch,
		T &	yaw
	)		const `[inline]`

Return the yaw, pitch & roll angles associated to quaternion.

See also:: For the equations, see The MRPT Book, or see http://www.euclideanspace.com/maths/geometry/rotations/conversions/quaternionToEuler/Quaternions.pdf; rpy_and_jacobian

Definition at line 260 of file CQuaternion.h.

template<class MATRIXLIKE >

void mrpt::math::CQuaternion::rpy_and_jacobian	(	T &	roll,
		T &	pitch,
		T &	yaw,
		MATRIXLIKE *	out_dr_dq = `NULL`,
		bool	resize_out_dr_dq_to3x4 = `true`
	)		const `[inline]`

Return the yaw, pitch & roll angles associated to quaternion, and (optionally) the 3x4 Jacobian of the transformation.

Note that both the angles and the Jacobian have one set of normal equations, plus other special formulas for the degenerated cases of |pitch|=90 degrees.