Public Types | Public Member Functions | Static Public Member Functions | Protected Attributes | 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 >:
RotationBase< AngleAxis< _Scalar >, 3 > RotationBase< AngleAxis< _Scalar >, 3 >

List of all members.

Public Types

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

Public Member Functions

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

Static Public Member Functions

static const AngleAxis Identity ()

Protected Attributes

Vector3 m_axis
Scalar m_angle

Friends

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

 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:

  

    
_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: 



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








template<typename _Scalar> 

      

        

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

      

















template<typename _Scalar> 

      

        

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

      

















template<typename _Scalar> 

      

        

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

      

















template<typename _Scalar> 

      

        

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

      

















template<typename _Scalar> 

      

        

          typedef _Scalar AngleAxis< _Scalar >::Scalar
        

      






the scalar type of the coefficients 



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













template<typename _Scalar> 

      

        

          typedef _Scalar AngleAxis< _Scalar >::Scalar
        

      






the scalar type of the coefficients 



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













template<typename _Scalar> 

      

        

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

      

















template<typename _Scalar> 

      

        

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

      











Member Enumeration Documentation








template<typename _Scalar> 

      

        

          anonymous enum
        

      






Enumerator: 


Dim 




















template<typename _Scalar> 

      

        

          anonymous enum
        

      






Enumerator: 


Dim 














Constructor & Destructor Documentation








template<typename _Scalar> 

      

        

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

      






Default constructor without initialization. 













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. 













template<typename _Scalar> 

      

        

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

      






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













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. 













template<typename _Scalar> 



template<typename OtherScalarType > 

      

        

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

      






Copy constructor with scalar type conversion 













template<typename _Scalar> 

      

        

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

      






Default constructor without initialization. 













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. 













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. 













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. 













template<typename _Scalar> 



template<typename OtherScalarType > 

      

        

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

      






Copy constructor with scalar type conversion 







Member Function Documentation








template<typename _Scalar> 

      

        

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

      

















template<typename _Scalar> 

      

        

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

      

















template<typename _Scalar> 

      

        

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

      

















template<typename _Scalar> 

      

        

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

      

















template<typename _Scalar> 

      

        

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

      

















template<typename _Scalar> 

      

        

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

      

















template<typename _Scalar> 

      

        

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

      

















template<typename _Scalar> 

      

        

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

      

















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. 













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. 













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. 













template<typename _Scalar> 

      

        

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

      

















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 >.













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 >.













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() 













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() 













template<typename _Scalar> 

      

        

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

      






Applies rotation to vector 













template<typename _Scalar> 

      

        

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

      






Concatenates two rotations 













template<typename _Scalar> 

      

        

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

      






Concatenates two rotations 













template<typename _Scalar> 

      

        

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

      






Concatenates two rotations 













template<typename _Scalar> 

      

        

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

      






Concatenates two rotations 













template<typename _Scalar> 

      

        

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

      






Concatenates two rotations 













template<typename Scalar > 



template<typename Derived > 

      

        

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

      






Set *this from a 3x3 rotation matrix mat. 













template<typename Scalar > 

      

        

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

      






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













template<typename _Scalar> 



template<typename Derived > 

      

        

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

      

















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. 













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 >.













template<typename _Scalar> 

      

        

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

      






Returns:
an equivalent rotation matrix 



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







Friends And Related Function Documentation








template<typename _Scalar> 

      

        

          QuaternionType operator* 
          (
          const QuaternionType & 
           a, 
        

        

          
          
          const AngleAxis< _Scalar > & 
           b 
        

        

          
          )
           [friend]
        

      






Concatenates two rotations 













template<typename _Scalar> 

      

        

          QuaternionType operator* 
          (
          const QuaternionType & 
           a, 
        

        

          
          
          const AngleAxis< _Scalar > & 
           b 
        

        

          
          )
           [friend]
        

      






Concatenates two rotations 













template<typename _Scalar> 

      

        

          Matrix3 operator* 
          (
          const Matrix3 & 
           a, 
        

        

          
          
          const AngleAxis< _Scalar > & 
           b 
        

        

          
          )
           [friend]
        

      






Concatenates two rotations 







Member Data Documentation








template<typename _Scalar> 

      

        

          Scalar AngleAxis< _Scalar >::m_angle [protected]
        

      

















template<typename _Scalar> 

      

        

          Vector3 AngleAxis< _Scalar >::m_axis [protected]
        

      











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



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