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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:

-2.38e-07  5.96e-08         1
    0.969    -0.249  5.96e-08
    0.249     0.969 -2.38e-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 AngleAxis< Scalar >:

Public Types

typedef Matrix< Scalar, Dim, Dim > RotationMatrixType
 
typedef _Scalar Scalar
 

Public Member Functions

 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)
 
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
 
RotationMatrixType matrix () const
 
Transform< Scalar, Dim, Isometryoperator* (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
 
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
 

Friends

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

Member Typedef Documentation

typedef Matrix<Scalar,Dim,Dim> RotationMatrixType
inherited

corresponding linear transformation matrix type

typedef _Scalar Scalar

the scalar type of the coefficients

Constructor & Destructor Documentation

AngleAxis ( )
inline

Default constructor without initialization.

Referenced by AngleAxis< Scalar >::inverse().

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.
AngleAxis ( const QuaternionBase< QuatDerived > &  q)
inlineexplicit

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

AngleAxis ( const MatrixBase< Derived > &  m)
inlineexplicit

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

AngleAxis ( const AngleAxis< OtherScalarType > &  other)
inlineexplicit

Copy constructor with scalar type conversion

Member Function Documentation

internal::cast_return_type<AngleAxis,AngleAxis<NewScalarType> >::type 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.

AngleAxis inverse ( ) const
inline
Returns
the inverse rotation, i.e., an angle-axis with opposite rotation angle

References AngleAxis< Scalar >::AngleAxis().

bool 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()
RotationMatrixType matrix ( ) const
inlineinherited
Returns
an equivalent rotation matrix This function is added to be conform with the Transform class' naming scheme.
Transform<Scalar,Dim,Isometry> operator* ( const Translation< Scalar, Dim > &  t) const
inlineinherited
Returns
the concatenation of the rotation *this with a translation t
RotationMatrixType operator* ( const UniformScaling< Scalar > &  s) const
inlineinherited
Returns
the concatenation of the rotation *this with a uniform scaling s
internal::rotation_base_generic_product_selector<AngleAxis< _Scalar > ,OtherDerived,OtherDerived::IsVectorAtCompileTime>::ReturnType operator* ( const EigenBase< OtherDerived > &  e) const
inlineinherited
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
Transform<Scalar,Dim,Mode> operator* ( const Transform< Scalar, Dim, Mode, Options > &  t) const
inlineinherited
Returns
the concatenation of the rotation *this with a transformation t
QuaternionType operator* ( const AngleAxis< Scalar > &  other) const
inline

Concatenates two rotations

QuaternionType operator* ( const QuaternionType other) const
inline

Concatenates two rotations

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.

References QuaternionBase< Derived >::vec(), and QuaternionBase< Derived >::w().

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

Set *this from a 3x3 rotation matrix mat.

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

Constructs and

Returns
an equivalent 3x3 rotation matrix.

References MatrixBase< Derived >::diagonal().

Friends And Related Function Documentation

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

Concatenates two rotations


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