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AngleAxis< _Scalar > Class Template Reference
Public Types | Public Member Functions | Friends

AngleAxis< _Scalar > Class Template Reference
[Geometry module]

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#include <AngleAxis.h>

Inherits RotationBase< AngleAxis< _Scalar >, 3 >.

Public Types

typedef _Scalar Scalar
 the scalar type of the coefficients
typedef Matrix< Scalar, Dim, Dim > RotationMatrixType
 corresponding linear transformation matrix type

Public Member Functions

 AngleAxis ()
 Default constructor without initialization.
template<typename Derived >
 AngleAxis (const Scalar &angle, const MatrixBase< Derived > &axis)
 Constructs and initialize the angle-axis rotation from an angle in radian and an axis which must be normalized.
template<typename QuatDerived >
 AngleAxis (const QuaternionBase< QuatDerived > &q)
 Constructs and initialize the angle-axis rotation from a quaternion q.
template<typename Derived >
 AngleAxis (const MatrixBase< Derived > &m)
 Constructs and initialize the angle-axis rotation from a 3x3 rotation matrix.
Scalar angle () const
Scalar & angle ()
const Vector3 & axis () const
Vector3 & axis ()
QuaternionType operator* (const AngleAxis &other) const
 Concatenates two rotations.
QuaternionType operator* (const QuaternionType &other) const
 Concatenates two rotations.
AngleAxis inverse () const
template<class QuatDerived >
AngleAxis & operator= (const QuaternionBase< QuatDerived > &q)
 Set *this from a unit quaternion.
template<typename Derived >
AngleAxis & operator= (const MatrixBase< Derived > &m)
 Set *this from a 3x3 rotation matrix mat.
template<typename Derived >
AngleAxis & fromRotationMatrix (const MatrixBase< Derived > &m)
 Sets *this from a 3x3 rotation matrix.
Matrix3 toRotationMatrix (void) const
 Constructs and.
template<typename NewScalarType >
internal::cast_return_type
< AngleAxis, AngleAxis
< NewScalarType > >::type 		cast () const
template<typename OtherScalarType >
 AngleAxis (const AngleAxis< OtherScalarType > &other)
 Copy constructor with scalar type conversion.
bool isApprox (const AngleAxis &other, const typename NumTraits< Scalar >::Real &prec=NumTraits< Scalar >::dummy_precision()) const
RotationMatrixType matrix () const
Transform< Scalar, Dim, Isometry > operator* (const Translation< Scalar, Dim > &t) const
RotationMatrixType operator* (const UniformScaling< Scalar > &s) const
EIGEN_STRONG_INLINE
internal::rotation_base_generic_product_selector
< AngleAxis< _Scalar >
, OtherDerived,
OtherDerived::IsVectorAtCompileTime >
::ReturnType 		operator* (const EigenBase< OtherDerived > &e) const
Transform< Scalar, Dim, Mode > operator* (const Transform< Scalar, Dim, Mode, Options > &t) const

Friends

QuaternionType operator* (const QuaternionType &a, const AngleAxis &b)
 Concatenates two rotations.
RotationMatrixType operator* (const EigenBase< OtherDerived > &l, const AngleAxis< _Scalar > &r)
Transform< Scalar, Dim, Affine > operator* (const DiagonalMatrix< Scalar, Dim > &l, const AngleAxis< _Scalar > &r)

Detailed Description

template<typename _Scalar>
class Eigen::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.
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: 

 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 49 of file AngleAxis.h.


Member Typedef Documentation






      

        

          typedef Matrix<Scalar,Dim,Dim> RotationMatrixType [inherited]
        

      







corresponding linear transformation matrix type 



Definition at line 37 of file RotationBase.h.











      

        

          typedef _Scalar Scalar
        

      







the scalar type of the coefficients 



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



Definition at line 59 of file AngleAxis.h.







Constructor & Destructor Documentation






      

        

          AngleAxis 
          (
           )
          
        

      







Default constructor without initialization. 



Definition at line 72 of file AngleAxis.h.











      

        

          AngleAxis 
          (
          const Scalar & 
           angle, 
        

        

          
          
          const MatrixBase< Derived > & 
           axis 
        

        

          
          )
          
        

      







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 79 of file AngleAxis.h.











      

        

          AngleAxis 
          (
          const QuaternionBase< QuatDerived > & 
           q )
           [explicit]
        

      







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



Definition at line 81 of file AngleAxis.h.











      

        

          AngleAxis 
          (
          const MatrixBase< Derived > & 
           m )
           [explicit]
        

      







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



Definition at line 84 of file AngleAxis.h.











      

        

          AngleAxis 
          (
          const AngleAxis< OtherScalarType > & 
           other )
           [explicit]
        

      







Copy constructor with scalar type conversion. 



Definition at line 135 of file AngleAxis.h.







Member Function Documentation






      

        

          Scalar angle 
          (
           )
           const
        

      






Returns:
the value of the rotation angle in radian 



Definition at line 87 of file AngleAxis.h.











      

        

          Scalar& angle 
          (
           )
          
        

      






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



Definition at line 89 of file AngleAxis.h.











      

        

          Vector3& axis 
          (
           )
          
        

      






Returns:
a read-write reference to the stored rotation axis.


Warning:
The rotation axis must remain a unit vector. 



Definition at line 97 of file AngleAxis.h.











      

        

          const Vector3& axis 
          (
           )
           const
        

      






Returns:
the rotation axis 



Definition at line 92 of file AngleAxis.h.











      

        

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

      






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 130 of file AngleAxis.h.











      

        

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

      







Sets *this from a 3x3 rotation matrix. 



Definition at line 202 of file AngleAxis.h.











      

        

          AngleAxis inverse 
          (
           )
           const
        

      






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



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



Definition at line 112 of file AngleAxis.h.











      

        

          bool isApprox 
          (
          const AngleAxis< _Scalar > & 
           other, 
        

        

          
          
          const typename NumTraits< Scalar >::Real & 
           prec = NumTraits<Scalar>::dummy_precision() 
        

        

          
          )
           const
        

      






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


See also:
MatrixBase::isApprox() 



Definition at line 147 of file AngleAxis.h.











      

        

          RotationMatrixType matrix 
          (
           )
           const [inherited]
        

      






Returns:
an equivalent rotation matrix This function is added to be conform with the Transform class' naming scheme. 



Definition at line 50 of file RotationBase.h.











      

        

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

      







Concatenates two rotations. 



Definition at line 100 of file AngleAxis.h.











      

        

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

      






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.











      

        

          Transform<Scalar,Dim,Isometry> operator* 
          (
          const Translation< Scalar, Dim > & 
           t )
           const [inherited]
        

      






Returns:
the concatenation of the rotation *this with a translation t 



Definition at line 56 of file RotationBase.h.











      

        

          RotationMatrixType operator* 
          (
          const UniformScaling< Scalar > & 
           s )
           const [inherited]
        

      






Returns:
the concatenation of the rotation *this with a uniform scaling s 



Definition at line 60 of file RotationBase.h.











      

        

          Transform<Scalar,Dim,Mode> operator* 
          (
          const Transform< Scalar, Dim, Mode, Options > & 
           t )
           const [inherited]
        

      






Returns:
the concatenation of the rotation *this with a transformation t 



Definition at line 89 of file RotationBase.h.











      

        

          QuaternionType operator* 
          (
          const QuaternionType & 
           other )
           const
        

      







Concatenates two rotations. 



Definition at line 104 of file AngleAxis.h.











      

        

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

      







Set *this from a 3x3 rotation matrix mat. 



Definition at line 190 of file AngleAxis.h.











      

        

          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 166 of file AngleAxis.h.











      

        

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

      







Constructs and. 


Returns:
an equivalent 3x3 rotation matrix. 



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



Definition at line 211 of file AngleAxis.h.







Friends And Related Function Documentation






      

        

          QuaternionType operator* 
          (
          const QuaternionType & 
           a, 
        

        

          
          
          const AngleAxis< _Scalar > & 
           b 
        

        

          
          )
           [friend]
        

      







Concatenates two rotations. 



Definition at line 108 of file AngleAxis.h.











      

        

          Transform<Scalar,Dim,Affine> operator* 
          (
          const DiagonalMatrix< Scalar, Dim > & 
           l, 
        

        

          
          
          const AngleAxis< _Scalar >  & 
           r 
        

        

          
          )
           [friend, inherited]
        

      






Returns:
the concatenation of a scaling l with the rotation r 



Definition at line 80 of file RotationBase.h.











      

        

          RotationMatrixType operator* 
          (
          const EigenBase< OtherDerived > & 
           l, 
        

        

          
          
          const AngleAxis< _Scalar >  & 
           r 
        

        

          
          )
           [friend, inherited]
        

      






Returns:
the concatenation of a linear transformation l with the rotation r 



Definition at line 76 of file RotationBase.h.









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