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Eigen::AngleAxis Class Reference
Geometry » Reference » Geometry_Module

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< Scalar > QuaternionType
 
typedef _Scalar Scalar
 
typedef Matrix< Scalar, 3, 1 > Vector3
 

Public Member Functions

EIGEN_DEVICE_FUNC Scalar & angle ()
 
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 Vector3 & axis ()
 
const EIGEN_DEVICE_FUNC Vector3 & axis () const
 
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
 
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, Isometry > operator* (const Translation< Scalar, Dim > &t) const
 
EIGEN_DEVICE_FUNC RotationMatrixType operator* (const UniformScaling< Scalar > &s) const
 
template<typename Derived >
EIGEN_DEVICE_FUNC AngleAxis & operator= (const MatrixBase< Derived > &m)
 
template<typename Derived >
EIGEN_DEVICE_FUNC AngleAxis< Scalar > & operator= (const MatrixBase< Derived > &mat)
 
template<class QuatDerived >
EIGEN_DEVICE_FUNC AngleAxis & operator= (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, Affine > operator* (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






      

        

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

      





Definition at line 60 of file AngleAxis.h.








◆ QuaternionType






      

        

          typedef Quaternion<Scalar> Eigen::AngleAxis::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






      

        

          typedef Matrix<Scalar,3,1> Eigen::AngleAxis::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 Wed May 15 2024 15:27:35