Eigen  3.3.3
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:

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()
+ Inheritance diagram for Eigen::AngleAxis< _Scalar >:

List of all members.

Public Types

typedef _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 >
AngleAxisfromRotationMatrix (const MatrixBase< Derived > &m)
 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<class QuatDerived >
AngleAxisoperator= (const QuaternionBase< QuatDerived > &q)
template<typename Derived >
AngleAxisoperator= (const MatrixBase< Derived > &m)
Matrix3 toRotationMatrix (void) 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

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


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) [inline, explicit]

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) [inline, explicit]

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) [inline, explicit]

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

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

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.

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


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 file:
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