Eigen::Quaternion< _Scalar, _Options > Class Template Reference

The quaternion class used to represent 3D orientations and rotations. More...

#include <Quaternion.h>

Public Types
enum
typedef QuaternionBase< Quaternion< _Scalar, _Options > >	Base
typedef _Scalar	Scalar
typedef internal::traits< Quaternion >::Coefficients	Coefficients
typedef Base::AngleAxisType	AngleAxisType

Public Member Functions
EIGEN_DEVICE_FUNC	Quaternion ()
EIGEN_DEVICE_FUNC	Quaternion (const Scalar &w, const Scalar &x, const Scalar &y, const Scalar &z)
EIGEN_DEVICE_FUNC	Quaternion (const Scalar *data)
template<class Derived >
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE	Quaternion (const QuaternionBase< Derived > &other)
EIGEN_DEVICE_FUNC	Quaternion (const AngleAxisType &aa)
template<typename Derived >
EIGEN_DEVICE_FUNC	Quaternion (const MatrixBase< Derived > &other)
template<typename OtherScalar , int OtherOptions>
EIGEN_DEVICE_FUNC	Quaternion (const Quaternion< OtherScalar, OtherOptions > &other)
EIGEN_DEVICE_FUNC Coefficients &	coeffs ()
EIGEN_DEVICE_FUNC const Coefficients &	coeffs () const
template<typename Derived1 , typename Derived2 >
EIGEN_DEVICE_FUNC Quaternion< Scalar, Options >	FromTwoVectors (const MatrixBase< Derived1 > &a, const MatrixBase< Derived2 > &b)
template<class OtherDerived >
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived &	operator*= (const QuaternionBase< OtherDerived > &q)

Static Public Member Functions
static EIGEN_DEVICE_FUNC Quaternion	UnitRandom ()
template<typename Derived1 , typename Derived2 >
static EIGEN_DEVICE_FUNC Quaternion	FromTwoVectors (const MatrixBase< Derived1 > &a, const MatrixBase< Derived2 > &b)

Static Protected Member Functions
static EIGEN_STRONG_INLINE void	_check_template_params ()

Protected Attributes
Coefficients	m_coeffs

Detailed Description

template<typename _Scalar, int _Options>
class Eigen::Quaternion< _Scalar, _Options >

The quaternion class used to represent 3D orientations and rotations.

\geometry_module

Template Parameters

_Scalar	the scalar type, i.e., the type of the coefficients
_Options	controls the memory alignment of the coefficients. Can be # AutoAlign or # DontAlign. Default is AutoAlign.

This class represents a quaternion that is a convenient representation of orientations and rotations of objects in three dimensions. Compared to other representations like Euler angles or 3x3 matrices, quaternions offer the following advantages:

• compact storage (4 scalars)
• efficient to compose (28 flops),
• stable spherical interpolation

The following two typedefs are provided for convenience:

• Quaternionf for float
• Quaterniond for double

Warning

Operations interpreting the quaternion as rotation have undefined behavior if the quaternion is not normalized.

See also

class AngleAxis, class Transform

Constructor & Destructor Documentation

Quaternion() [1/7]

template<typename _Scalar , int _Options>

EIGEN_DEVICE_FUNC Eigen::Quaternion< _Scalar, _Options >::Quaternion ( )

inline

Default constructor leaving the quaternion uninitialized.

Quaternion() [2/7]

template<typename _Scalar , int _Options>

EIGEN_DEVICE_FUNC Eigen::Quaternion< _Scalar, _Options >::Quaternion ( const Scalar &  w, const Scalar &  x, const Scalar &  y, const Scalar &  z  )

inline

Constructs and initializes the quaternion from its four coefficients w, x, y and z.

Warning

Note the order of the arguments: the real w coefficient first, while internally the coefficients are stored in the following order: [x, y, z, w]

Quaternion() [3/7]

template<typename _Scalar , int _Options>

EIGEN_DEVICE_FUNC Eigen::Quaternion< _Scalar, _Options >::Quaternion ( const Scalar *  data )

inlineexplicit

Constructs and initialize a quaternion from the array data

Quaternion() [4/7]

template<typename _Scalar , int _Options>

template<class Derived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Eigen::Quaternion< _Scalar, _Options >::Quaternion ( const QuaternionBase< Derived > &  other )

inline

Copy constructor

Quaternion() [5/7]

template<typename _Scalar , int _Options>

EIGEN_DEVICE_FUNC Eigen::Quaternion< _Scalar, _Options >::Quaternion ( const AngleAxisType &  aa )

inlineexplicit

Constructs and initializes a quaternion from the angle-axis aa

Quaternion() [6/7]

template<typename _Scalar , int _Options>

template<typename Derived >

EIGEN_DEVICE_FUNC Eigen::Quaternion< _Scalar, _Options >::Quaternion ( const MatrixBase< Derived > &  other )

inlineexplicit

Constructs and initializes a quaternion from either:

• a rotation matrix expression,
• a 4D vector expression representing quaternion coefficients.

Quaternion() [7/7]

template<typename _Scalar , int _Options>

template<typename OtherScalar , int OtherOptions>

EIGEN_DEVICE_FUNC Eigen::Quaternion< _Scalar, _Options >::Quaternion ( const Quaternion< OtherScalar, OtherOptions > &  other )

inlineexplicit

Explicit copy constructor with scalar conversion

Member Function Documentation

FromTwoVectors()

template<typename _Scalar , int _Options>

template<typename Derived1 , typename Derived2 >

EIGEN_DEVICE_FUNC Quaternion<Scalar,Options> Eigen::Quaternion< _Scalar, _Options >::FromTwoVectors	(	const MatrixBase< Derived1 > &	a,
		const MatrixBase< Derived2 > &	b
	)

Returns a quaternion representing a rotation between the two arbitrary vectors a and b. In other words, the built rotation represent a rotation sending the line of direction a to the line of direction b, both lines passing through the origin.

Returns

resulting quaternion

Note that the two input vectors do not have to be normalized, and do not need to have the same norm.

operator*=()

template<typename _Scalar , int _Options>

template<class OtherDerived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived & Eigen::QuaternionBase< Derived >::operator*=

(

class OtherDerived

)

See also

operator*(Quaternion)

UnitRandom()

template<typename Scalar , int Options>

EIGEN_DEVICE_FUNC Quaternion< Scalar, Options > Eigen::Quaternion< Scalar, Options >::UnitRandom

static

Returns

a random unit quaternion following a uniform distribution law on SO(3)

Note

The implementation is based on http://planning.cs.uiuc.edu/node198.html

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The documentation for this class was generated from the following files:

• ForwardDeclarations.h
• Quaternion.h