Public Types | Public Member Functions | Static Public Member Functions | Protected Attributes | Private Types | Friends
AngleAxis< _Scalar > Class Template Reference
Geometry_Module

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

#include <AngleAxis.h>

Inheritance diagram for AngleAxis< _Scalar >:
Inheritance graph
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List of all members.

Public Types

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

Public Member Functions

Scalar angle () const
Scalar & angle ()
Scalar angle () const
Scalar & angle ()
 AngleAxis ()
 AngleAxis ()
template<typename Derived >
 AngleAxis (Scalar angle, const MatrixBase< Derived > &axis)
 AngleAxis (const QuaternionType &q)
template<typename Derived >
 AngleAxis (const MatrixBase< Derived > &m)
template<typename Derived >
 AngleAxis (Scalar angle, const MatrixBase< Derived > &axis)
template<typename QuatDerived >
 AngleAxis (const QuaternionBase< QuatDerived > &q)
template<typename Derived >
 AngleAxis (const MatrixBase< Derived > &m)
template<typename OtherScalarType >
 AngleAxis (const AngleAxis< OtherScalarType > &other)
template<typename OtherScalarType >
 AngleAxis (const AngleAxis< OtherScalarType > &other)
const Vector3 & axis () const
Vector3 & axis ()
const Vector3 & axis () const
Vector3 & axis ()
template<typename NewScalarType >
internal::cast_return_type
< AngleAxis, AngleAxis
< NewScalarType > >::type 		cast () const
template<typename NewScalarType >
internal::cast_return_type
< AngleAxis, AngleAxis
< NewScalarType > >::type 		cast () const
template<typename Derived >
AngleAxis & fromRotationMatrix (const MatrixBase< Derived > &m)
template<typename Derived >
AngleAxis & fromRotationMatrix (const MatrixBase< Derived > &m)
 Sets *this from a 3x3 rotation matrix.
AngleAxis inverse () const
AngleAxis inverse () const
bool isApprox (const AngleAxis &other, typename NumTraits< Scalar >::Real prec=NumTraits< Scalar >::dummy_precision()) const
bool isApprox (const AngleAxis &other, typename NumTraits< Scalar >::Real prec=precision< Scalar >()) const
QuaternionType operator* (const AngleAxis &other) const
QuaternionType operator* (const QuaternionType &other) const
QuaternionType operator* (const AngleAxis &other) const
QuaternionType operator* (const QuaternionType &other) const
Matrix3 operator* (const Matrix3 &other) const
Vector3 operator* (const Vector3 &other) const
template<class QuatDerived >
AngleAxis & operator= (const QuaternionBase< QuatDerived > &q)
template<typename Derived >
AngleAxis & operator= (const MatrixBase< Derived > &m)
AngleAxis & operator= (const QuaternionType &q)
template<typename Derived >
AngleAxis & operator= (const MatrixBase< Derived > &m)
Matrix3 toRotationMatrix (void) const
Matrix3 toRotationMatrix (void) const

Static Public Member Functions

static const AngleAxis Identity ()

Protected Attributes

Scalar m_angle
Vector3 m_axis

Private Types

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

Friends

QuaternionType operator* (const QuaternionType &a, const AngleAxis &b)
QuaternionType operator* (const QuaternionType &a, const AngleAxis &b)
Matrix3 operator* (const Matrix3 &a, const AngleAxis &b)

Detailed Description

template<typename _Scalar>
class AngleAxis< _Scalar >

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

Parameters:
_Scalarthe scalar type, i.e., the type of the coefficients.

The following two typedefs are provided for convenience:

AngleAxisForEuler How to define a rotation from Euler-angles

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()


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 60 of file Eigen2Support/Geometry/AngleAxis.h.


Member Typedef Documentation








template<typename _Scalar> 

      

        

          typedef RotationBase<AngleAxis<_Scalar>,3> AngleAxis< _Scalar >::Base [private]
        

      







Definition at line 62 of file Eigen2Support/Geometry/AngleAxis.h.













template<typename _Scalar> 

      

        

          typedef RotationBase<AngleAxis<_Scalar>,3> AngleAxis< _Scalar >::Base [private]
        

      







Definition at line 64 of file Geometry/AngleAxis.h.













template<typename _Scalar> 

      

        

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

      







Definition at line 71 of file Eigen2Support/Geometry/AngleAxis.h.













template<typename _Scalar> 

      

        

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

      







Definition at line 73 of file Geometry/AngleAxis.h.













template<typename _Scalar> 

      

        

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

      







Definition at line 73 of file Eigen2Support/Geometry/AngleAxis.h.













template<typename _Scalar> 

      

        

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

      







Definition at line 75 of file Geometry/AngleAxis.h.













template<typename _Scalar> 

      

        

          typedef _Scalar AngleAxis< _Scalar >::Scalar
        

      






the scalar type of the coefficients 



Reimplemented from RotationBase< AngleAxis< _Scalar >, 3 >.



Definition at line 70 of file Eigen2Support/Geometry/AngleAxis.h.













template<typename _Scalar> 

      

        

          typedef _Scalar AngleAxis< _Scalar >::Scalar
        

      






the scalar type of the coefficients 



Reimplemented from RotationBase< AngleAxis< _Scalar >, 3 >.



Definition at line 72 of file Geometry/AngleAxis.h.













template<typename _Scalar> 

      

        

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

      







Definition at line 72 of file Eigen2Support/Geometry/AngleAxis.h.













template<typename _Scalar> 

      

        

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

      







Definition at line 74 of file Geometry/AngleAxis.h.







Member Enumeration Documentation








template<typename _Scalar> 

      

        

          anonymous enum
        

      






Enumerator: 


Dim 










Definition at line 68 of file Eigen2Support/Geometry/AngleAxis.h.













template<typename _Scalar> 

      

        

          anonymous enum
        

      






Enumerator: 


Dim 










Definition at line 70 of file Geometry/AngleAxis.h.







Constructor & Destructor Documentation








template<typename _Scalar> 

      

        

          AngleAxis< _Scalar >::AngleAxis 
          (
          )
           [inline]
        

      






Default constructor without initialization. 



Definition at line 83 of file Eigen2Support/Geometry/AngleAxis.h.













template<typename _Scalar> 



template<typename Derived > 

      

        

          AngleAxis< _Scalar >::AngleAxis 
          (
          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. 



Definition at line 87 of file Eigen2Support/Geometry/AngleAxis.h.













template<typename _Scalar> 

      

        

          AngleAxis< _Scalar >::AngleAxis 
          (
          const QuaternionType & 
          q)
           [inline]
        

      






Constructs and initialize the angle-axis rotation from a quaternion q. 



Definition at line 89 of file Eigen2Support/Geometry/AngleAxis.h.













template<typename _Scalar> 



template<typename Derived > 

      

        

          AngleAxis< _Scalar >::AngleAxis 
          (
          const MatrixBase< Derived > & 
          m)
           [inline, explicit]
        

      






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



Definition at line 92 of file Eigen2Support/Geometry/AngleAxis.h.













template<typename _Scalar> 



template<typename OtherScalarType > 

      

        

          AngleAxis< _Scalar >::AngleAxis 
          (
          const AngleAxis< OtherScalarType > & 
          other)
           [inline, explicit]
        

      






Copy constructor with scalar type conversion 



Definition at line 147 of file Eigen2Support/Geometry/AngleAxis.h.













template<typename _Scalar> 

      

        

          AngleAxis< _Scalar >::AngleAxis 
          (
          )
           [inline]
        

      






Default constructor without initialization. 



Definition at line 85 of file Geometry/AngleAxis.h.













template<typename _Scalar> 



template<typename Derived > 

      

        

          AngleAxis< _Scalar >::AngleAxis 
          (
          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 92 of file Geometry/AngleAxis.h.













template<typename _Scalar> 



template<typename QuatDerived > 

      

        

          AngleAxis< _Scalar >::AngleAxis 
          (
          const QuaternionBase< QuatDerived > & 
          q)
           [inline, explicit]
        

      






Constructs and initialize the angle-axis rotation from a quaternion q. 



Definition at line 94 of file Geometry/AngleAxis.h.













template<typename _Scalar> 



template<typename Derived > 

      

        

          AngleAxis< _Scalar >::AngleAxis 
          (
          const MatrixBase< Derived > & 
          m)
           [inline, explicit]
        

      






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



Definition at line 97 of file Geometry/AngleAxis.h.













template<typename _Scalar> 



template<typename OtherScalarType > 

      

        

          AngleAxis< _Scalar >::AngleAxis 
          (
          const AngleAxis< OtherScalarType > & 
          other)
           [inline, explicit]
        

      






Copy constructor with scalar type conversion 



Definition at line 141 of file Geometry/AngleAxis.h.







Member Function Documentation








template<typename _Scalar> 

      

        

          Scalar AngleAxis< _Scalar >::angle 
          (
          )
           const [inline]
        

      







Definition at line 94 of file Eigen2Support/Geometry/AngleAxis.h.













template<typename _Scalar> 

      

        

          Scalar& AngleAxis< _Scalar >::angle 
          (
          )
           [inline]
        

      







Definition at line 95 of file Eigen2Support/Geometry/AngleAxis.h.













template<typename _Scalar> 

      

        

          Scalar AngleAxis< _Scalar >::angle 
          (
          )
           const [inline]
        

      







Definition at line 99 of file Geometry/AngleAxis.h.













template<typename _Scalar> 

      

        

          Scalar& AngleAxis< _Scalar >::angle 
          (
          )
           [inline]
        

      







Definition at line 100 of file Geometry/AngleAxis.h.













template<typename _Scalar> 

      

        

          const Vector3& AngleAxis< _Scalar >::axis 
          (
          )
           const [inline]
        

      







Definition at line 97 of file Eigen2Support/Geometry/AngleAxis.h.













template<typename _Scalar> 

      

        

          Vector3& AngleAxis< _Scalar >::axis 
          (
          )
           [inline]
        

      







Definition at line 98 of file Eigen2Support/Geometry/AngleAxis.h.













template<typename _Scalar> 

      

        

          const Vector3& AngleAxis< _Scalar >::axis 
          (
          )
           const [inline]
        

      







Definition at line 102 of file Geometry/AngleAxis.h.













template<typename _Scalar> 

      

        

          Vector3& AngleAxis< _Scalar >::axis 
          (
          )
           [inline]
        

      







Definition at line 103 of file Geometry/AngleAxis.h.













template<typename _Scalar> 



template<typename NewScalarType > 

      

        

          internal::cast_return_type<AngleAxis,AngleAxis<NewScalarType> >::type 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 136 of file Geometry/AngleAxis.h.













template<typename _Scalar> 



template<typename NewScalarType > 

      

        

          internal::cast_return_type<AngleAxis,AngleAxis<NewScalarType> >::type 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 142 of file Eigen2Support/Geometry/AngleAxis.h.













template<typename _Scalar> 



template<typename Derived > 

      

        

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

      

















template<typename Scalar > 



template<typename Derived > 

      

        

          AngleAxis< Scalar > & AngleAxis< Scalar >::fromRotationMatrix 
          (
          const MatrixBase< Derived > & 
          m)
          
        

      







Sets *this from a 3x3 rotation matrix. 



Definition at line 207 of file Geometry/AngleAxis.h.













template<typename _Scalar> 

      

        

          static const AngleAxis AngleAxis< _Scalar >::Identity 
          (
          )
           [inline, static]
        

      







Definition at line 147 of file Geometry/AngleAxis.h.













template<typename _Scalar> 

      

        

          AngleAxis AngleAxis< _Scalar >::inverse 
          (
          void 
          )
           const [inline]
        

      






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



Reimplemented from RotationBase< AngleAxis< _Scalar >, 3 >.



Definition at line 118 of file Geometry/AngleAxis.h.













template<typename _Scalar> 

      

        

          AngleAxis AngleAxis< _Scalar >::inverse 
          (
          )
           const [inline]
        

      






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



Reimplemented from RotationBase< AngleAxis< _Scalar >, 3 >.



Definition at line 125 of file Eigen2Support/Geometry/AngleAxis.h.













template<typename _Scalar> 

      

        

          bool AngleAxis< _Scalar >::isApprox 
          (
          const AngleAxis< _Scalar > & 
          other, 
        

        

          
          
          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 153 of file Geometry/AngleAxis.h.













template<typename _Scalar> 

      

        

          bool AngleAxis< _Scalar >::isApprox 
          (
          const AngleAxis< _Scalar > & 
          other, 
        

        

          
          
          typename NumTraits< Scalar >::Real 
          prec = precision<Scalar>() 
        

        

          
          )
           const [inline]
        

      






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


See also:
MatrixBase::isApprox() 



Definition at line 157 of file Eigen2Support/Geometry/AngleAxis.h.













template<typename _Scalar> 

      

        

          QuaternionType AngleAxis< _Scalar >::operator* 
          (
          const AngleAxis< _Scalar > & 
          other)
           const [inline]
        

      






Concatenates two rotations 



Definition at line 101 of file Eigen2Support/Geometry/AngleAxis.h.













template<typename _Scalar> 

      

        

          QuaternionType AngleAxis< _Scalar >::operator* 
          (
          const QuaternionType & 
          other)
           const [inline]
        

      






Concatenates two rotations 



Definition at line 105 of file Eigen2Support/Geometry/AngleAxis.h.













template<typename _Scalar> 

      

        

          QuaternionType AngleAxis< _Scalar >::operator* 
          (
          const AngleAxis< _Scalar > & 
          other)
           const [inline]
        

      






Concatenates two rotations 



Definition at line 106 of file Geometry/AngleAxis.h.













template<typename _Scalar> 

      

        

          QuaternionType AngleAxis< _Scalar >::operator* 
          (
          const QuaternionType & 
          other)
           const [inline]
        

      






Concatenates two rotations 



Definition at line 110 of file Geometry/AngleAxis.h.













template<typename _Scalar> 

      

        

          Matrix3 AngleAxis< _Scalar >::operator* 
          (
          const Matrix3 & 
          other)
           const [inline]
        

      






Concatenates two rotations 



Definition at line 113 of file Eigen2Support/Geometry/AngleAxis.h.













template<typename _Scalar> 

      

        

          Vector3 AngleAxis< _Scalar >::operator* 
          (
          const Vector3 & 
          other)
           const [inline]
        

      






Applies rotation to vector 



Definition at line 121 of file Eigen2Support/Geometry/AngleAxis.h.













template<typename Scalar > 



template<typename QuatDerived > 

      

        

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

      






Set *this from a unit quaternion. The axis is normalized.


Warning:
As any other method dealing with quaternion, if the input quaternion is not normalized then the result is undefined. 



Definition at line 172 of file Geometry/AngleAxis.h.













template<typename _Scalar> 



template<typename Derived > 

      

        

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

      

















template<typename Scalar > 

      

        

          AngleAxis< Scalar > & AngleAxis< Scalar >::operator= 
          (
          const QuaternionType & 
          q)
          
        

      






Set *this from a quaternion. The axis is normalized. 



Definition at line 172 of file Eigen2Support/Geometry/AngleAxis.h.













template<typename Scalar > 



template<typename Derived > 

      

        

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

      






Set *this from a 3x3 rotation matrix mat. 



Definition at line 192 of file Eigen2Support/Geometry/AngleAxis.h.













template<typename _Scalar> 

      

        

          Matrix3 AngleAxis< _Scalar >::toRotationMatrix 
          (
          void 
          )
           const
        

      






Returns:
an equivalent rotation matrix 



Reimplemented from RotationBase< AngleAxis< _Scalar >, 3 >.













template<typename Scalar > 

      

        

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

      






Constructs and 


Returns:
an equivalent 3x3 rotation matrix. 



Reimplemented from RotationBase< AngleAxis< _Scalar >, 3 >.



Definition at line 203 of file Eigen2Support/Geometry/AngleAxis.h.







Friends And Related Function Documentation








template<typename _Scalar> 

      

        

          QuaternionType operator* 
          (
          const QuaternionType & 
          a, 
        

        

          
          
          const AngleAxis< _Scalar > & 
          b 
        

        

          
          )
           [friend]
        

      






Concatenates two rotations 



Definition at line 109 of file Eigen2Support/Geometry/AngleAxis.h.













template<typename _Scalar> 

      

        

          QuaternionType operator* 
          (
          const QuaternionType & 
          a, 
        

        

          
          
          const AngleAxis< _Scalar > & 
          b 
        

        

          
          )
           [friend]
        

      






Concatenates two rotations 



Definition at line 114 of file Geometry/AngleAxis.h.













template<typename _Scalar> 

      

        

          Matrix3 operator* 
          (
          const Matrix3 & 
          a, 
        

        

          
          
          const AngleAxis< _Scalar > & 
          b 
        

        

          
          )
           [friend]
        

      






Concatenates two rotations 



Definition at line 117 of file Eigen2Support/Geometry/AngleAxis.h.







Member Data Documentation








template<typename _Scalar> 

      

        

          Scalar AngleAxis< _Scalar >::m_angle [protected]
        

      







Definition at line 78 of file Eigen2Support/Geometry/AngleAxis.h.













template<typename _Scalar> 

      

        

          Vector3 AngleAxis< _Scalar >::m_axis [protected]
        

      







Definition at line 77 of file Eigen2Support/Geometry/AngleAxis.h.







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







re_vision

Author(s): Dorian Galvez-Lopez

autogenerated on Sun Jan 5 2014 11:33:52