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AngleAxis< _Scalar > Class Template Reference

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

Public Types

enum  { Dim }
typedef Matrix< Scalar, 3, 3 > Matrix3
typedef Quaternion< ScalarQuaternionType
typedef _Scalar Scalar
typedef Matrix< Scalar, 3, 1 > Vector3
- Public Types inherited from RotationBase< AngleAxis< _Scalar >, 3 >
enum  
typedef Matrix< Scalar, Dim, Dim > RotationMatrixType
typedef ei_traits< AngleAxis
< _Scalar > >::Scalar 
Scalar

Public Member Functions

Scalar angle () const
Scalarangle ()
 AngleAxis ()
template<typename Derived >
 AngleAxis (Scalar angle, const MatrixBase< Derived > &axis)
 AngleAxis (const QuaternionType &q)
template<typename Derived >
 AngleAxis (const MatrixBase< Derived > &m)
template<typename OtherScalarType >
 AngleAxis (const AngleAxis< OtherScalarType > &other)
const Vector3axis () const
Vector3axis ()
template<typename NewScalarType >
ei_cast_return_type< AngleAxis,
AngleAxis< NewScalarType >
>::type 
cast () const
template<typename Derived >
AngleAxisfromRotationMatrix (const MatrixBase< Derived > &m)
AngleAxis inverse () const
bool isApprox (const AngleAxis &other, typename NumTraits< Scalar >::Real prec=precision< Scalar >()) const
QuaternionType operator* (const AngleAxis &other) const
QuaternionType operator* (const QuaternionType &other) const
Matrix3 operator* (const Matrix3 &other) const
Vector3 operator* (const Vector3 &other) const
AngleAxisoperator= (const QuaternionType &q)
template<typename Derived >
AngleAxisoperator= (const MatrixBase< Derived > &m)
Matrix3 toRotationMatrix (void) const
- Public Member Functions inherited from RotationBase< AngleAxis< _Scalar >, 3 >
const AngleAxis< _Scalar > & derived () const
AngleAxis< _Scalar > & derived ()
Transform< Scalar, Dim > operator* (const Translation< Scalar, Dim > &t) const
RotationMatrixType operator* (const Scaling< Scalar, Dim > &s) const
Transform< Scalar, Dim > operator* (const Transform< Scalar, Dim > &t) const

Protected Attributes

Scalar m_angle
Vector3 m_axis

Friends

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

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.

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:

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()

Member Typedef Documentation

typedef _Scalar Scalar

the scalar type of the coefficients

Constructor & Destructor Documentation

AngleAxis ( )
inline

Default constructor without initialization.

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.

AngleAxis ( const QuaternionType q)
inline

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

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

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

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

Concatenates two rotations

QuaternionType operator* ( const QuaternionType other) const
inline

Concatenates two rotations

Matrix3 operator* ( const Matrix3 other) const
inline

Concatenates two rotations

Vector3 operator* ( const Vector3 other) const
inline

Applies rotation to vector

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

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

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.

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

Friends And Related Function Documentation

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

Concatenates two rotations

Matrix3 operator* ( const Matrix3 a,
const AngleAxis< _Scalar > &  b 
)
friend

Concatenates two rotations


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