Represents a 3D rotation as a rotation angle around an arbitrary 3D axis. More...

#include <AngleAxis.h>

Public Types
enum	{ Dim = 3 }

typedef _Scalar	Scalar

typedef Matrix< Scalar, 3, 3 >	Matrix3

typedef Matrix< Scalar, 3, 1 >	Vector3

typedef Quaternion< Scalar >	QuaternionType

Public Member Functions
EIGEN_DEVICE_FUNC	AngleAxis ()

template<typename Derived >
EIGEN_DEVICE_FUNC	AngleAxis (const Scalar &angle, const MatrixBase< Derived > &axis)

template<typename QuatDerived >
EIGEN_DEVICE_FUNC	AngleAxis (const QuaternionBase< QuatDerived > &q)

template<typename Derived >
EIGEN_DEVICE_FUNC	AngleAxis (const MatrixBase< Derived > &m)

EIGEN_DEVICE_FUNC Scalar	angle () const

EIGEN_DEVICE_FUNC Scalar &	angle ()

EIGEN_DEVICE_FUNC const Vector3 &	axis () const

EIGEN_DEVICE_FUNC Vector3 &	axis ()

EIGEN_DEVICE_FUNC QuaternionType	operator* (const AngleAxis &other) const

EIGEN_DEVICE_FUNC QuaternionType	operator* (const QuaternionType &other) const

EIGEN_DEVICE_FUNC AngleAxis	inverse () const

template<class QuatDerived >
EIGEN_DEVICE_FUNC AngleAxis &	operator= (const QuaternionBase< QuatDerived > &q)

template<typename Derived >
EIGEN_DEVICE_FUNC AngleAxis &	operator= (const MatrixBase< Derived > &m)

template<typename Derived >
EIGEN_DEVICE_FUNC AngleAxis &	fromRotationMatrix (const MatrixBase< Derived > &m)

EIGEN_DEVICE_FUNC Matrix3	toRotationMatrix (void) const

template<typename NewScalarType >
EIGEN_DEVICE_FUNC internal::cast_return_type< AngleAxis, AngleAxis< NewScalarType > >::type	cast () const

template<typename OtherScalarType >
EIGEN_DEVICE_FUNC	AngleAxis (const AngleAxis< OtherScalarType > &other)

EIGEN_DEVICE_FUNC bool	isApprox (const AngleAxis &other, const typename NumTraits< Scalar >::Real &prec=NumTraits< Scalar >::dummy_precision()) const

template<typename QuatDerived >
EIGEN_DEVICE_FUNC AngleAxis< Scalar > &	operator= (const QuaternionBase< QuatDerived > &q)

template<typename Derived >
EIGEN_DEVICE_FUNC AngleAxis< Scalar > &	operator= (const MatrixBase< Derived > &mat)

template<typename Derived >
EIGEN_DEVICE_FUNC AngleAxis< Scalar > &	fromRotationMatrix (const MatrixBase< Derived > &mat)
	Sets `*this` from a 3x3 rotation matrix.

EIGEN_DEVICE_FUNC Transform< Scalar, Dim, Isometry >	operator* (const Translation< Scalar, Dim > &t) const

EIGEN_DEVICE_FUNC RotationMatrixType	operator* (const UniformScaling< Scalar > &s) const

template<typename OtherDerived >
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE internal::rotation_base_generic_product_selector< Derived, OtherDerived, OtherDerived::IsVectorAtCompileTime >::ReturnType	operator* (const EigenBase< OtherDerived > &e) const

template<int Mode, int Options>
EIGEN_DEVICE_FUNC Transform< Scalar, Dim, Mode >	operator* (const Transform< Scalar, Dim, Mode, Options > &t) const

Static Public Member Functions
static EIGEN_DEVICE_FUNC const AngleAxis	Identity ()

Protected Attributes
Vector3	m_axis

Scalar	m_angle

Friends
EIGEN_DEVICE_FUNC QuaternionType	operator* (const QuaternionType &a, const AngleAxis &b)

template<typename OtherDerived >
EIGEN_DEVICE_FUNC RotationMatrixType	operator* (const EigenBase< OtherDerived > &l, const Derived &r)

EIGEN_DEVICE_FUNC friend Transform< Scalar, Dim, Affine >	operator* (const DiagonalMatrix< Scalar, Dim > &l, const Derived &r)

Detailed Description

template<typename _Scalar>
class Eigen::AngleAxis< _Scalar >

Represents a 3D rotation as a rotation angle around an arbitrary 3D axis.

\geometry_module

Parameters

_Scalar the scalar type, i.e., the type of the coefficients.

Warning: When setting up an AngleAxis object, the axis vector must be normalized.

The following two typedefs are provided for convenience:

AngleAxisf for float
AngleAxisd for double

Combined with MatrixBase::Unit{X,Y,Z}, AngleAxis can be used to easily mimic Euler-angles. Here is an example:

Output:

Note: This class is not aimed to be used to store a rotation transformation, but rather to make easier the creation of other rotation (Quaternion, rotation Matrix) and transformation objects.

See also: class Quaternion, class Transform, MatrixBase::UnitX()

Member Typedef Documentation

◆ Scalar

template<typename _Scalar >

typedef _Scalar Eigen::AngleAxis< _Scalar >::Scalar

the scalar type of the coefficients

Constructor & Destructor Documentation

◆ AngleAxis() [1/5]

template<typename _Scalar >

EIGEN_DEVICE_FUNC Eigen::AngleAxis< _Scalar >::AngleAxis ( )

inline

Default constructor without initialization.

◆ AngleAxis() [2/5]

template<typename _Scalar >

template<typename Derived >

EIGEN_DEVICE_FUNC Eigen::AngleAxis< _Scalar >::AngleAxis	(	const Scalar &	angle,
		const MatrixBase< Derived > &	axis
	)

inline

Constructs and initialize the angle-axis rotation from an angle in radian and an axis which must be normalized.

Warning: If the axis vector is not normalized, then the angle-axis object represents an invalid rotation.

◆ AngleAxis() [3/5]

template<typename _Scalar >

template<typename QuatDerived >

EIGEN_DEVICE_FUNC Eigen::AngleAxis< _Scalar >::AngleAxis ( const QuaternionBase< QuatDerived > & q )

inlineexplicit

Constructs and initialize the angle-axis rotation from a quaternion q. This function implicitly normalizes the quaternion q.

◆ AngleAxis() [4/5]

template<typename _Scalar >

template<typename Derived >

EIGEN_DEVICE_FUNC Eigen::AngleAxis< _Scalar >::AngleAxis ( const MatrixBase< Derived > & m )

inlineexplicit

Constructs and initialize the angle-axis rotation from a 3x3 rotation matrix.

◆ AngleAxis() [5/5]

template<typename _Scalar >

template<typename OtherScalarType >

EIGEN_DEVICE_FUNC Eigen::AngleAxis< _Scalar >::AngleAxis ( const AngleAxis< OtherScalarType > & other )

inlineexplicit

Copy constructor with scalar type conversion

Member Function Documentation

◆ angle() [1/2]

template<typename _Scalar >

EIGEN_DEVICE_FUNC Scalar& Eigen::AngleAxis< _Scalar >::angle ( )

inline

Returns: a read-write reference to the stored angle in radian

◆ angle() [2/2]

template<typename _Scalar >

EIGEN_DEVICE_FUNC Scalar Eigen::AngleAxis< _Scalar >::angle ( ) const

inline

Returns: the value of the rotation angle in radian

◆ axis() [1/2]

template<typename _Scalar >

EIGEN_DEVICE_FUNC Vector3& Eigen::AngleAxis< _Scalar >::axis ( )

inline

Returns: a read-write reference to the stored rotation axis.

Warning: The rotation axis must remain a unit vector.

◆ axis() [2/2]

template<typename _Scalar >

EIGEN_DEVICE_FUNC const Vector3& Eigen::AngleAxis< _Scalar >::axis ( ) const

inline

Returns: the rotation axis

◆ cast()

template<typename _Scalar >

template<typename NewScalarType >

EIGEN_DEVICE_FUNC internal::cast_return_type<AngleAxis,AngleAxis<NewScalarType> >::type Eigen::AngleAxis< _Scalar >::cast ( ) const

inline

Returns: *this with scalar type casted to NewScalarType

Note that if NewScalarType is equal to the current scalar type of *this then this function smartly returns a const reference to *this.

◆ inverse()

template<typename _Scalar >

EIGEN_DEVICE_FUNC AngleAxis Eigen::AngleAxis< _Scalar >::inverse ( ) const

inline

Returns: the inverse rotation, i.e., an angle-axis with opposite rotation angle

◆ isApprox()

template<typename _Scalar >

EIGEN_DEVICE_FUNC bool Eigen::AngleAxis< _Scalar >::isApprox	(	const AngleAxis< _Scalar > &	other,
		const typename NumTraits< Scalar >::Real &	prec = `NumTraits<Scalar>::dummy_precision()`
	)		const

inline

Returns: true if *this is approximately equal to other, within the precision determined by prec.

See also: MatrixBase::isApprox()

◆ operator*() [1/6]

template<typename _Scalar >

EIGEN_DEVICE_FUNC QuaternionType Eigen::AngleAxis< _Scalar >::operator* ( const AngleAxis< _Scalar > & other ) const

inline

Concatenates two rotations

◆ operator*() [2/6]

template<typename _Scalar >

template<typename OtherDerived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE internal::rotation_base_generic_product_selector<Derived,OtherDerived,OtherDerived::IsVectorAtCompileTime>::ReturnType Eigen::RotationBase< Derived, _Dim >::operator* ( typename OtherDerived )

inline

Returns

the concatenation of the rotation *this with a generic expression e e can be:

a DimxDim linear transformation matrix
a DimxDim diagonal matrix (axis aligned scaling)
a vector of size Dim

◆ operator*() [3/6]

template<typename _Scalar >

EIGEN_DEVICE_FUNC QuaternionType Eigen::AngleAxis< _Scalar >::operator* ( const QuaternionType & other ) const

inline

Concatenates two rotations

◆ operator*() [4/6]

template<typename _Scalar >

template<int Mode, int Options>

EIGEN_DEVICE_FUNC Transform<Scalar,Dim,Mode> Eigen::RotationBase< Derived, _Dim >::operator*	(	int	Mode,
		int	Options
	)

inline

Returns: the concatenation of the rotation *this with a transformation t

◆ operator*() [5/6]

template<typename _Scalar >

EIGEN_DEVICE_FUNC Transform<Scalar,Dim,Isometry> Eigen::RotationBase< Derived, _Dim >::operator*

inline

Returns: the concatenation of the rotation *this with a translation t

◆ operator*() [6/6]

template<typename _Scalar >

EIGEN_DEVICE_FUNC RotationMatrixType Eigen::RotationBase< Derived, _Dim >::operator*

inline

Returns: the concatenation of the rotation *this with a uniform scaling s

◆ operator=() [1/2]

template<typename _Scalar >

template<typename Derived >

EIGEN_DEVICE_FUNC AngleAxis<Scalar>& Eigen::AngleAxis< _Scalar >::operator= ( const MatrixBase< Derived > & mat )

Set *this from a 3x3 rotation matrix mat.

◆ operator=() [2/2]

template<typename _Scalar >

template<typename QuatDerived >

EIGEN_DEVICE_FUNC AngleAxis<Scalar>& Eigen::AngleAxis< _Scalar >::operator= ( const QuaternionBase< QuatDerived > & q )

Set *this from a unit quaternion.

The resulting axis is normalized, and the computed angle is in the [0,pi] range.

This function implicitly normalizes the quaternion q.

◆ toRotationMatrix()

template<typename Scalar >

AngleAxis< Scalar >::Matrix3 EIGEN_DEVICE_FUNC Eigen::AngleAxis< Scalar >::toRotationMatrix ( void ) const

Constructs and

Returns: an equivalent 3x3 rotation matrix.

Friends And Related Function Documentation

◆ operator* [1/3]

template<typename _Scalar >

EIGEN_DEVICE_FUNC friend Transform<Scalar,Dim,Affine> operator*

friend

Returns: the concatenation of a scaling l with the rotation r

◆ operator* [2/3]

template<typename _Scalar >

template<typename OtherDerived >

EIGEN_DEVICE_FUNC RotationMatrixType operator* ( typename OtherDerived )

friend

Returns: the concatenation of a linear transformation l with the rotation r

◆ operator* [3/3]

template<typename _Scalar >

EIGEN_DEVICE_FUNC QuaternionType operator*	(	const QuaternionType &	a,
		const AngleAxis< _Scalar > &	b
	)

friend

Concatenates two rotations

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

Public Types

Public Member Functions

Static Public Member Functions

Protected Attributes

Friends

Detailed Description

template<typename _Scalar> class Eigen::AngleAxis< _Scalar >

Member Typedef Documentation

◆ Scalar

Constructor & Destructor Documentation

◆ AngleAxis() [1/5]

◆ AngleAxis() [2/5]

◆ AngleAxis() [3/5]

◆ AngleAxis() [4/5]

◆ AngleAxis() [5/5]

Member Function Documentation

◆ angle() [1/2]

◆ angle() [2/2]

◆ axis() [1/2]

◆ axis() [2/2]

◆ cast()

◆ inverse()

◆ isApprox()

◆ operator*() [1/6]

◆ operator*() [2/6]

◆ operator*() [3/6]

◆ operator*() [4/6]

◆ operator*() [5/6]

◆ operator*() [6/6]

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ toRotationMatrix()

Friends And Related Function Documentation

◆ operator* [1/3]

◆ operator* [2/3]

◆ operator* [3/3]

template<typename _Scalar>
class Eigen::AngleAxis< _Scalar >