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Eigen  3.3.71
Eigen::AngleAxis Class Reference

Detailed Description

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:

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:

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()

Public Types

typedef _Scalar Scalar
 

Public Member Functions

Scalarangle ()
 
Scalar angle () const
 
 AngleAxis ()
 
template<typename OtherScalarType >
 AngleAxis (const AngleAxis< OtherScalarType > &other)
 
template<typename Derived >
 AngleAxis (const MatrixBase< Derived > &m)
 
template<typename QuatDerived >
 AngleAxis (const QuaternionBase< QuatDerived > &q)
 
template<typename Derived >
 AngleAxis (const Scalar &angle, const MatrixBase< Derived > &axis)
 
Vector3axis ()
 
const Vector3axis () const
 
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
 
template<typename OtherDerived >
internal::rotation_base_generic_product_selector< Derived, OtherDerived, OtherDerived::IsVectorAtCompileTime >::ReturnType operator* (const EigenBase< OtherDerived > &e) const
 
QuaternionType operator* (const QuaternionType &other) const
 
template<int Mode, int Options>
Transform< Scalar, Dim, Mode > operator* (const Transform< Scalar, Dim, Mode, Options > &t) const
 
Transform< Scalar, Dim, Isometryoperator* (const Translation< Scalar, Dim > &t) const
 
RotationMatrixType operator* (const UniformScaling< Scalar > &s) const
 
template<typename Derived >
AngleAxis< Scalar > & operator= (const MatrixBase< Derived > &mat)
 
template<typename QuatDerived >
AngleAxis< Scalar > & operator= (const QuaternionBase< QuatDerived > &q)
 
Matrix3 toRotationMatrix (void) const
 

Member Typedef Documentation

◆ Scalar

typedef _Scalar Eigen::AngleAxis::Scalar

the scalar type of the coefficients

Constructor & Destructor Documentation

◆ AngleAxis() [1/5]

Eigen::AngleAxis::AngleAxis ( )
inline

Default constructor without initialization.

◆ AngleAxis() [2/5]

template<typename Derived >
Eigen::AngleAxis::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() [3/5]

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

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

◆ AngleAxis() [4/5]

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

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

◆ AngleAxis() [5/5]

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

Copy constructor with scalar type conversion

Member Function Documentation

◆ angle() [1/2]

Scalar& Eigen::AngleAxis::angle ( )
inline
Returns
a read-write reference to the stored angle in radian

◆ angle() [2/2]

Scalar Eigen::AngleAxis::angle ( ) const
inline
Returns
the value of the rotation angle in radian

◆ axis() [1/2]

Vector3& Eigen::AngleAxis::axis ( )
inline
Returns
a read-write reference to the stored rotation axis.
Warning
The rotation axis must remain a unit vector.

◆ axis() [2/2]

const Vector3& Eigen::AngleAxis::axis ( ) const
inline
Returns
the rotation axis

◆ cast()

template<typename NewScalarType >
internal::cast_return_type<AngleAxis,AngleAxis<NewScalarType> >::type Eigen::AngleAxis::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.

◆ inverse()

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

◆ isApprox()

bool Eigen::AngleAxis::isApprox ( const AngleAxis 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()

◆ operator*() [1/6]

QuaternionType Eigen::AngleAxis::operator* ( const AngleAxis other) const
inline

Concatenates two rotations

◆ operator*() [2/6]

template<typename OtherDerived >
internal::rotation_base_generic_product_selector<Derived,OtherDerived,OtherDerived::IsVectorAtCompileTime>::ReturnType Eigen::RotationBase::operator* ( typename OtherDerived  )
inline
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

◆ operator*() [3/6]

QuaternionType Eigen::AngleAxis::operator* ( const QuaternionType other) const
inline

Concatenates two rotations

◆ operator*() [4/6]

template<int Mode, int Options>
Transform<Scalar,Dim,Mode> Eigen::RotationBase::operator* ( int  Mode,
int  Options 
)
inline
Returns
the concatenation of the rotation *this with a transformation t

◆ operator*() [5/6]

Transform<Scalar,Dim,Isometry> Eigen::RotationBase::operator*
inline
Returns
the concatenation of the rotation *this with a translation t

◆ operator*() [6/6]

RotationMatrixType Eigen::RotationBase::operator*
inline
Returns
the concatenation of the rotation *this with a uniform scaling s

◆ operator=() [1/2]

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

Set *this from a 3x3 rotation matrix mat.

◆ operator=() [2/2]

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

◆ toRotationMatrix()

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

Constructs and

Returns
an equivalent 3x3 rotation matrix.

The documentation for this class was generated from the following files:
Eigen::MatrixBase::UnitZ
static const BasisReturnType UnitZ()
Definition: CwiseNullaryOp.h:851
Eigen::MatrixBase::UnitX
static const BasisReturnType UnitX()
Definition: CwiseNullaryOp.h:831
Eigen::AngleAxisf
AngleAxis< float > AngleAxisf
Definition: AngleAxis.h:157
Eigen::MatrixBase::UnitY
static const BasisReturnType UnitY()
Definition: CwiseNullaryOp.h:841