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Eigen::AngleAxis Class Reference

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

#include <ForwardDeclarations.h>

Public Types

enum  { Dim = 3 }
 
typedef Matrix< Scalar, 3, 3 > Matrix3
 
typedef Quaternion< ScalarQuaternionType
 
typedef _Scalar Scalar
 
typedef Matrix< Scalar, 3, 1 > Vector3
 

Public Member Functions

EIGEN_DEVICE_FUNC Scalarangle ()
 
EIGEN_DEVICE_FUNC Scalar angle () const
 
EIGEN_DEVICE_FUNC AngleAxis ()
 
template<typename OtherScalarType >
EIGEN_DEVICE_FUNC AngleAxis (const AngleAxis< OtherScalarType > &other)
 
template<typename Derived >
EIGEN_DEVICE_FUNC AngleAxis (const MatrixBase< Derived > &m)
 
template<typename QuatDerived >
EIGEN_DEVICE_FUNC AngleAxis (const QuaternionBase< QuatDerived > &q)
 
template<typename Derived >
EIGEN_DEVICE_FUNC AngleAxis (const Scalar &angle, const MatrixBase< Derived > &axis)
 
EIGEN_DEVICE_FUNC Vector3axis ()
 
const EIGEN_DEVICE_FUNC Vector3axis () const
 
template<typename NewScalarType >
EIGEN_DEVICE_FUNC internal::cast_return_type< AngleAxis, AngleAxis< NewScalarType > >::type cast () const
 
template<typename Derived >
EIGEN_DEVICE_FUNC AngleAxisfromRotationMatrix (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
 
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
 
EIGEN_DEVICE_FUNC QuaternionType operator* (const QuaternionType &other) const
 
template<int Mode, int Options>
EIGEN_DEVICE_FUNC Transform< Scalar, Dim, Mode > operator* (const Transform< Scalar, Dim, Mode, Options > &t) const
 
EIGEN_DEVICE_FUNC Transform< Scalar, Dim, Isometryoperator* (const Translation< Scalar, Dim > &t) const
 
EIGEN_DEVICE_FUNC RotationMatrixType operator* (const UniformScaling< Scalar > &s) const
 
template<typename Derived >
EIGEN_DEVICE_FUNC AngleAxisoperator= (const MatrixBase< Derived > &m)
 
template<typename Derived >
EIGEN_DEVICE_FUNC AngleAxis< Scalar > & operator= (const MatrixBase< Derived > &mat)
 
template<class QuatDerived >
EIGEN_DEVICE_FUNC AngleAxisoperator= (const QuaternionBase< QuatDerived > &q)
 
template<typename QuatDerived >
EIGEN_DEVICE_FUNC AngleAxis< Scalar > & operator= (const QuaternionBase< QuatDerived > &q)
 
EIGEN_DEVICE_FUNC Matrix3 toRotationMatrix (void) const
 

Static Public Member Functions

static const EIGEN_DEVICE_FUNC AngleAxis Identity ()
 

Protected Attributes

Scalar m_angle
 
Vector3 m_axis
 

Private Types

typedef RotationBase< AngleAxis< _Scalar >, 3 > Base
 

Friends

EIGEN_DEVICE_FUNC friend Transform< Scalar, Dim, Affineoperator* (const DiagonalMatrix< Scalar, Dim > &l, const Derived &r)
 
template<typename OtherDerived >
EIGEN_DEVICE_FUNC RotationMatrixType operator* (const EigenBase< OtherDerived > &l, const Derived &r)
 
EIGEN_DEVICE_FUNC QuaternionType operator* (const QuaternionType &a, const AngleAxis &b)
 

Detailed Description

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

\geometry_module

Parameters
_Scalarthe 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:

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

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

Definition at line 51 of file AngleAxis.h.

◆ Matrix3

Definition at line 60 of file AngleAxis.h.

◆ QuaternionType

Definition at line 62 of file AngleAxis.h.

◆ Scalar

typedef _Scalar Eigen::AngleAxis::Scalar

the scalar type of the coefficients

Definition at line 59 of file AngleAxis.h.

◆ Vector3

Definition at line 61 of file AngleAxis.h.

Member Enumeration Documentation

◆ anonymous enum

anonymous enum
Enumerator
Dim 

Definition at line 57 of file AngleAxis.h.

Constructor & Destructor Documentation

◆ AngleAxis() [1/5]

EIGEN_DEVICE_FUNC Eigen::AngleAxis::AngleAxis ( )
inline

Default constructor without initialization.

Definition at line 72 of file AngleAxis.h.

◆ AngleAxis() [2/5]

template<typename Derived >
EIGEN_DEVICE_FUNC Eigen::AngleAxis::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 QuatDerived >
EIGEN_DEVICE_FUNC Eigen::AngleAxis::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 Derived >
EIGEN_DEVICE_FUNC Eigen::AngleAxis::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 OtherScalarType >
EIGEN_DEVICE_FUNC Eigen::AngleAxis::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]

EIGEN_DEVICE_FUNC Scalar& Eigen::AngleAxis::angle ( )
inline
Returns
a read-write reference to the stored angle in radian

Definition at line 93 of file AngleAxis.h.

◆ angle() [2/2]

EIGEN_DEVICE_FUNC Scalar Eigen::AngleAxis::angle ( ) const
inline
Returns
the value of the rotation angle in radian

Definition at line 91 of file AngleAxis.h.

◆ axis() [1/2]

EIGEN_DEVICE_FUNC Vector3& Eigen::AngleAxis::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.

◆ axis() [2/2]

const EIGEN_DEVICE_FUNC Vector3& Eigen::AngleAxis::axis ( ) const
inline
Returns
the rotation axis

Definition at line 96 of file AngleAxis.h.

◆ cast()

template<typename NewScalarType >
EIGEN_DEVICE_FUNC internal::cast_return_type<AngleAxis,AngleAxis<NewScalarType> >::type Eigen::AngleAxis::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 Derived >
EIGEN_DEVICE_FUNC AngleAxis& Eigen::AngleAxis::fromRotationMatrix ( const MatrixBase< Derived > &  m)

◆ fromRotationMatrix() [2/2]

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

Sets *this from a 3x3 rotation matrix.

Definition at line 209 of file AngleAxis.h.

◆ Identity()

static const EIGEN_DEVICE_FUNC AngleAxis Eigen::AngleAxis::Identity ( )
inlinestatic

Definition at line 145 of file AngleAxis.h.

◆ inverse()

EIGEN_DEVICE_FUNC AngleAxis Eigen::AngleAxis::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()

EIGEN_DEVICE_FUNC bool Eigen::AngleAxis::isApprox ( const AngleAxis 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*() [1/6]

EIGEN_DEVICE_FUNC QuaternionType Eigen::AngleAxis::operator* ( const AngleAxis other) const
inline

Concatenates two rotations

Definition at line 104 of file AngleAxis.h.

◆ operator*() [2/6]

template<typename OtherDerived >
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE internal::rotation_base_generic_product_selector<Derived,OtherDerived,OtherDerived::IsVectorAtCompileTime>::ReturnType Eigen::RotationBase::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

Definition at line 71 of file RotationBase.h.

◆ operator*() [3/6]

EIGEN_DEVICE_FUNC QuaternionType Eigen::AngleAxis::operator* ( const QuaternionType other) const
inline

Concatenates two rotations

Definition at line 108 of file AngleAxis.h.

◆ operator*() [4/6]

template<int Mode, int Options>
EIGEN_DEVICE_FUNC Transform<Scalar,Dim,Mode> Eigen::RotationBase::operator* ( int  Mode,
int  Options 
)
inline
Returns
the concatenation of the rotation *this with a transformation t

Definition at line 89 of file RotationBase.h.

◆ operator*() [5/6]

EIGEN_DEVICE_FUNC Transform<Scalar,Dim,Isometry> Eigen::RotationBase::operator*
inline
Returns
the concatenation of the rotation *this with a translation t

Definition at line 56 of file RotationBase.h.

◆ operator*() [6/6]

EIGEN_DEVICE_FUNC RotationMatrixType Eigen::RotationBase::operator*
inline
Returns
the concatenation of the rotation *this with a uniform scaling s

Definition at line 60 of file RotationBase.h.

◆ operator=() [1/4]

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

◆ operator=() [2/4]

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

Set *this from a 3x3 rotation matrix mat.

Definition at line 197 of file AngleAxis.h.

◆ operator=() [3/4]

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

◆ operator=() [4/4]

template<typename QuatDerived >
EIGEN_DEVICE_FUNC AngleAxis<Scalar>& Eigen::AngleAxis::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.

◆ toRotationMatrix()

AngleAxis< Scalar >::Matrix3 EIGEN_DEVICE_FUNC Eigen::AngleAxis::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* [1/3]

EIGEN_DEVICE_FUNC friend Transform<Scalar,Dim,Affine> operator*
friend
Returns
the concatenation of a scaling l with the rotation r

Definition at line 80 of file RotationBase.h.

◆ operator* [2/3]

template<typename OtherDerived >
EIGEN_DEVICE_FUNC RotationMatrixType operator* ( typename OtherDerived  )
friend
Returns
the concatenation of a linear transformation l with the rotation r

Definition at line 76 of file RotationBase.h.

◆ operator* [3/3]

EIGEN_DEVICE_FUNC QuaternionType operator* ( const QuaternionType a,
const AngleAxis b 
)
friend

Concatenates two rotations

Definition at line 112 of file AngleAxis.h.

Member Data Documentation

◆ m_angle

Scalar Eigen::AngleAxis::m_angle
protected

Definition at line 67 of file AngleAxis.h.

◆ m_axis

Vector3 Eigen::AngleAxis::m_axis
protected

Definition at line 66 of file AngleAxis.h.


The documentation for this class was generated from the following files:
m
Matrix3f m
Definition: AngleAxis_mimic_euler.cpp:1
Eigen::AngleAxisf
AngleAxis< float > AngleAxisf
Definition: AngleAxis.h:157
M_PI
#define M_PI
Definition: mconf.h:117


gtsam
Author(s):
autogenerated on Sat Nov 16 2024 04:10:18