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Eigen::AngleAxis< Scalar > Class Template Reference

Detailed Description

template<typename Scalar>
class Eigen::AngleAxis< Scalar >

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

This is defined in the Geometry module.

#include <Eigen/Geometry>
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:

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:

1.19e-07        0        1
   0.969   -0.249        0
   0.249    0.969 1.19e-07
is unitary: 1
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()
+ Inheritance diagram for Eigen::AngleAxis< Scalar >:

Public Types

typedef _Scalar Scalar
 
- Public Types inherited from Eigen::RotationBase< AngleAxis< _Scalar >, 3 >
typedef Matrix< Scalar, Dim, Dim > RotationMatrixType
 
typedef internal::traits
< AngleAxis< _Scalar >
>::Scalar 
Scalar
 

Public Member Functions

Scalar angle () const
 
Scalarangle ()
 
 AngleAxis ()
 
template<typename Derived >
 AngleAxis (const 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)
 
const Vector3axis () const
 
Vector3axis ()
 
template<typename NewScalarType >
internal::cast_return_type
< AngleAxis, AngleAxis
< NewScalarType > >::type 
cast () const
 
template<typename Derived >
AngleAxis< Scalar > & fromRotationMatrix (const MatrixBase< Derived > &mat)
 Sets *this from a 3x3 rotation matrix.
 
AngleAxis inverse () const
 
bool isApprox (const AngleAxis &other, const typename NumTraits< Scalar >::Real &prec=NumTraits< Scalar >::dummy_precision()) const
 
QuaternionType operator* (const AngleAxis &other) const
 
QuaternionType operator* (const QuaternionType &other) const
 
template<typename QuatDerived >
AngleAxis< Scalar > & operator= (const QuaternionBase< QuatDerived > &q)
 
template<typename Derived >
AngleAxis< Scalar > & operator= (const MatrixBase< Derived > &mat)
 
Matrix3 toRotationMatrix (void) const
 
- Public Member Functions inherited from Eigen::RotationBase< AngleAxis< _Scalar >, 3 >
AngleAxis< _Scalar > inverse () const
 
RotationMatrixType matrix () const
 
Transform< Scalar, Dim, Isometry > operator* (const Translation< Scalar, Dim > &t) const
 
RotationMatrixType operator* (const UniformScaling< Scalar > &s) const
 
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
 
RotationMatrixType toRotationMatrix () const
 

Friends

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

Member Typedef Documentation

template<typename Scalar >
typedef _Scalar Eigen::AngleAxis< Scalar >::Scalar

the scalar type of the coefficients

Constructor & Destructor Documentation

template<typename Scalar >
Eigen::AngleAxis< Scalar >::AngleAxis ( )
inline

Default constructor without initialization.

template<typename Scalar >
template<typename Derived >
Eigen::AngleAxis< Scalar >::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.
template<typename Scalar >
template<typename QuatDerived >
Eigen::AngleAxis< Scalar >::AngleAxis ( const QuaternionBase< QuatDerived > &  q)
inlineexplicit

Constructs and initialize the angle-axis rotation from a quaternion q. This function implicitly normalizes the quaternion q.

template<typename Scalar >
template<typename Derived >
Eigen::AngleAxis< Scalar >::AngleAxis ( const MatrixBase< Derived > &  m)
inlineexplicit

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

template<typename Scalar >
template<typename OtherScalarType >
Eigen::AngleAxis< Scalar >::AngleAxis ( const AngleAxis< OtherScalarType > &  other)
inlineexplicit

Copy constructor with scalar type conversion

Member Function Documentation

template<typename Scalar >
Scalar Eigen::AngleAxis< Scalar >::angle ( ) const
inline
Returns
the value of the rotation angle in radian
template<typename Scalar >
Scalar& Eigen::AngleAxis< Scalar >::angle ( )
inline
Returns
a read-write reference to the stored angle in radian
template<typename Scalar >
const Vector3& Eigen::AngleAxis< Scalar >::axis ( ) const
inline
Returns
the rotation axis
template<typename Scalar >
Vector3& Eigen::AngleAxis< Scalar >::axis ( )
inline
Returns
a read-write reference to the stored rotation axis.
Warning
The rotation axis must remain a unit vector.
template<typename Scalar >
template<typename NewScalarType >
internal::cast_return_type<AngleAxis,AngleAxis<NewScalarType> >::type Eigen::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 >
AngleAxis Eigen::AngleAxis< Scalar >::inverse ( ) const
inline
Returns
the inverse rotation, i.e., an angle-axis with opposite rotation angle
template<typename Scalar >
bool Eigen::AngleAxis< Scalar >::isApprox ( const AngleAxis< Scalar > &  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()
template<typename Scalar >
QuaternionType Eigen::AngleAxis< Scalar >::operator* ( const AngleAxis< Scalar > &  other) const
inline

Concatenates two rotations

template<typename Scalar >
QuaternionType Eigen::AngleAxis< Scalar >::operator* ( const QuaternionType other) const
inline

Concatenates two rotations

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

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

Set *this from a 3x3 rotation matrix mat.

template<typename Scalar >
AngleAxis< Scalar >::Matrix3 Eigen::AngleAxis< Scalar >::toRotationMatrix ( void  ) const

Constructs and

Returns
an equivalent 3x3 rotation matrix.

Friends And Related Function Documentation

template<typename Scalar >
QuaternionType operator* ( const QuaternionType a,
const AngleAxis< Scalar > &  b 
)
friend

Concatenates two rotations


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