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

#include <ForwardDeclarations.h>

Inheritance diagram for Eigen::AngleAxis< _Scalar >:

Public Types
enum	{ Dim = 3 }

typedef Matrix< Scalar, 3, 3 >	Matrix3

typedef Quaternion< Scalar >	QuaternionType

typedef _Scalar	Scalar

typedef Matrix< Scalar, 3, 1 >	Vector3

Public Types inherited from Eigen::RotationBase< AngleAxis< _Scalar >, 3 >
enum

typedef Matrix< Scalar, Dim, Dim >	RotationMatrixType

typedef internal::traits< AngleAxis< _Scalar > >::Scalar	Scalar

typedef Matrix< Scalar, Dim, 1 >	VectorType

Public Member Functions
EIGEN_DEVICE_FUNC Scalar	angle () const

EIGEN_DEVICE_FUNC Scalar &	angle ()

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)

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

EIGEN_DEVICE_FUNC const Vector3 &	axis () const

EIGEN_DEVICE_FUNC Vector3 &	axis ()

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

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

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

EIGEN_DEVICE_FUNC AngleAxis	inverse () const

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

EIGEN_DEVICE_FUNC QuaternionType	operator* (const AngleAxis &other) const

EIGEN_DEVICE_FUNC QuaternionType	operator* (const QuaternionType &other) 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 QuatDerived >
EIGEN_DEVICE_FUNC AngleAxis< Scalar > &	operator= (const QuaternionBase< QuatDerived > &q)

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

EIGEN_DEVICE_FUNC Matrix3	toRotationMatrix (void) const

Public Member Functions inherited from Eigen::RotationBase< AngleAxis< _Scalar >, 3 >
EIGEN_DEVICE_FUNC VectorType	_transformVector (const OtherVectorType &v) const

EIGEN_DEVICE_FUNC const AngleAxis< _Scalar > &	derived () const

EIGEN_DEVICE_FUNC AngleAxis< _Scalar > &	derived ()

EIGEN_DEVICE_FUNC AngleAxis< _Scalar >	inverse () const

EIGEN_DEVICE_FUNC RotationMatrixType	matrix () const

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

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

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE internal::rotation_base_generic_product_selector< AngleAxis< _Scalar >, OtherDerived, OtherDerived::IsVectorAtCompileTime >::ReturnType	operator* (const EigenBase< OtherDerived > &e) const

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

EIGEN_DEVICE_FUNC RotationMatrixType	toRotationMatrix () const

Static Public Member Functions
static EIGEN_DEVICE_FUNC const AngleAxis	Identity ()

Protected Attributes
Scalar	m_angle

Vector3	m_axis

Private Types
typedef RotationBase< AngleAxis< _Scalar >, 3 >	Base

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

Detailed Description

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

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

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:

Matrix3f m;
m = AngleAxisf(0.25*M_PI, Vector3f::UnitX())
  * AngleAxisf(0.5*M_PI,  Vector3f::UnitY())
  * AngleAxisf(0.33*M_PI, Vector3f::UnitZ());
cout << m << endl << "is unitary: " << m.isUnitary() << endl;

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()

Definition at line 290 of file ForwardDeclarations.h.

Member Typedef Documentation

◆ Base

template<typename _Scalar>

typedef RotationBase<AngleAxis<_Scalar>,3> Eigen::AngleAxis< _Scalar >::Base

private

Definition at line 51 of file AngleAxis.h.

◆ Matrix3

template<typename _Scalar>

typedef Matrix<Scalar,3,3> Eigen::AngleAxis< _Scalar >::Matrix3

Definition at line 60 of file AngleAxis.h.

◆ QuaternionType

template<typename _Scalar>

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

Definition at line 62 of file AngleAxis.h.

◆ Scalar

template<typename _Scalar>

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

the scalar type of the coefficients

Definition at line 59 of file AngleAxis.h.

◆ Vector3

template<typename _Scalar>

typedef Matrix<Scalar,3,1> Eigen::AngleAxis< _Scalar >::Vector3

Definition at line 61 of file AngleAxis.h.

Member Enumeration Documentation

◆ anonymous enum

template<typename _Scalar>

anonymous enum

Enumerator
Dim

Definition at line 57 of file AngleAxis.h.

Constructor & Destructor Documentation

◆ AngleAxis() [1/5]

template<typename _Scalar>

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

inline

Default constructor without initialization.

Definition at line 72 of file AngleAxis.h.

◆ 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.

Definition at line 80 of file AngleAxis.h.

◆ 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.

Definition at line 85 of file AngleAxis.h.

◆ 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.

Definition at line 88 of file AngleAxis.h.

◆ 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

Definition at line 139 of file AngleAxis.h.

Member Function Documentation

◆ angle() [1/2]

template<typename _Scalar>

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

inline

Returns: the value of the rotation angle in radian

Definition at line 91 of file AngleAxis.h.

◆ angle() [2/2]

template<typename _Scalar>

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

inline

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

Definition at line 93 of file AngleAxis.h.

◆ axis() [1/2]

template<typename _Scalar>

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

inline

Returns: the rotation axis

Definition at line 96 of file AngleAxis.h.

◆ axis() [2/2]

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.

Definition at line 101 of file AngleAxis.h.

◆ 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.

Definition at line 134 of file AngleAxis.h.

◆ fromRotationMatrix() [1/2]

template<typename _Scalar>

template<typename Derived >

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

◆ fromRotationMatrix() [2/2]

template<typename _Scalar>

template<typename Derived >

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

Sets *this from a 3x3 rotation matrix.

Definition at line 209 of file AngleAxis.h.

◆ Identity()

template<typename _Scalar>

static EIGEN_DEVICE_FUNC const AngleAxis Eigen::AngleAxis< _Scalar >::Identity ( )

inlinestatic

Definition at line 145 of file AngleAxis.h.

◆ 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

Definition at line 116 of file AngleAxis.h.

◆ 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()

Definition at line 151 of file AngleAxis.h.

◆ operator*() [1/2]

template<typename _Scalar>

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

inline

Concatenates two rotations

Definition at line 104 of file AngleAxis.h.

◆ operator*() [2/2]

template<typename _Scalar>

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

inline

Concatenates two rotations

Definition at line 108 of file AngleAxis.h.

◆ operator=() [1/4]

template<typename _Scalar>

template<class QuatDerived >

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

◆ operator=() [2/4]

template<typename _Scalar>

template<typename Derived >

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

◆ operator=() [3/4]

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.

Definition at line 170 of file AngleAxis.h.

◆ operator=() [4/4]

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.

Definition at line 197 of file AngleAxis.h.

◆ toRotationMatrix()

template<typename Scalar >

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

Constructs and

Returns: an equivalent 3x3 rotation matrix.

Definition at line 218 of file AngleAxis.h.

Friends And Related Function Documentation

◆ operator*

template<typename _Scalar>

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

friend

Concatenates two rotations

Definition at line 112 of file AngleAxis.h.

Member Data Documentation

◆ m_angle

template<typename _Scalar>

Scalar Eigen::AngleAxis< _Scalar >::m_angle

protected

Definition at line 67 of file AngleAxis.h.

◆ m_axis

template<typename _Scalar>

Vector3 Eigen::AngleAxis< _Scalar >::m_axis

protected

Definition at line 66 of file AngleAxis.h.

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

Public Types

Public Member Functions

Static Public Member Functions

Protected Attributes

Private Types

Friends

Detailed Description

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

Member Typedef Documentation

◆ Base

◆ Matrix3

◆ QuaternionType

◆ Scalar

◆ Vector3

Member Enumeration Documentation

◆ anonymous enum

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()

◆ fromRotationMatrix() [1/2]

◆ fromRotationMatrix() [2/2]

◆ Identity()

◆ inverse()

◆ isApprox()

◆ operator*() [1/2]

◆ operator*() [2/2]

◆ operator=() [1/4]

◆ operator=() [2/4]

◆ operator=() [3/4]

◆ operator=() [4/4]

◆ toRotationMatrix()

Friends And Related Function Documentation

◆ operator*

Member Data Documentation

◆ m_angle

◆ m_axis

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