Public Types | Public Member Functions | Static Public Member Functions | Protected Attributes | Private Types | Friends
AngleAxis< _Scalar > Class Template Reference

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

#include <AngleAxis.h>

Inheritance diagram for AngleAxis< _Scalar >:
Inheritance graph
[legend]

List of all members.

Public Types

enum  { Dim = 3 }
enum  { Dim = 3 }
typedef Matrix< Scalar, 3, 3 > Matrix3
typedef Matrix< Scalar, 3, 3 > Matrix3
typedef Quaternion< ScalarQuaternionType
typedef Quaternion< ScalarQuaternionType
typedef _Scalar Scalar
typedef _Scalar Scalar
typedef Matrix< Scalar, 3, 1 > Vector3
typedef Matrix< Scalar, 3, 1 > Vector3

Public Member Functions

Scalar angle () const
Scalarangle ()
Scalar angle () const
Scalarangle ()
 AngleAxis ()
 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 Derived >
 AngleAxis (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 OtherScalarType >
 AngleAxis (const AngleAxis< OtherScalarType > &other)
const Vector3axis () const
Vector3axis ()
const Vector3axis () const
Vector3axis ()
template<typename NewScalarType >
internal::cast_return_type
< AngleAxis, AngleAxis
< NewScalarType > >::type 
cast () const
template<typename NewScalarType >
internal::cast_return_type
< AngleAxis, AngleAxis
< NewScalarType > >::type 
cast () const
template<typename Derived >
AngleAxisfromRotationMatrix (const MatrixBase< Derived > &m)
template<typename Derived >
AngleAxisfromRotationMatrix (const MatrixBase< Derived > &m)
 Sets *this from a 3x3 rotation matrix.
AngleAxis inverse () const
AngleAxis inverse () const
bool isApprox (const AngleAxis &other, typename NumTraits< Scalar >::Real prec=NumTraits< Scalar >::dummy_precision()) 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
QuaternionType operator* (const AngleAxis &other) const
QuaternionType operator* (const QuaternionType &other) const
Matrix3 operator* (const Matrix3 &other) const
Vector3 operator* (const Vector3 &other) const
template<class QuatDerived >
AngleAxisoperator= (const QuaternionBase< QuatDerived > &q)
template<typename Derived >
AngleAxisoperator= (const MatrixBase< Derived > &m)
AngleAxisoperator= (const QuaternionType &q)
template<typename Derived >
AngleAxisoperator= (const MatrixBase< Derived > &m)
Matrix3 toRotationMatrix (void) const
Matrix3 toRotationMatrix (void) const

Static Public Member Functions

static const AngleAxis Identity ()

Protected Attributes

Scalar m_angle
Vector3 m_axis

Private Types

typedef RotationBase
< AngleAxis< _Scalar >, 3 > 
Base
typedef RotationBase
< AngleAxis< _Scalar >, 3 > 
Base

Friends

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

Detailed Description

template<typename _Scalar>
class AngleAxis< _Scalar >

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

Parameters:
_Scalarthe scalar type, i.e., the type of the coefficients.

The following two typedefs are provided for convenience:

AngleAxisForEuler How to define a rotation from Euler-angles

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:

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()
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:

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:

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()

Definition at line 60 of file Eigen2Support/Geometry/AngleAxis.h.


Member Typedef Documentation

template<typename _Scalar>
typedef RotationBase<AngleAxis<_Scalar>,3> AngleAxis< _Scalar >::Base [private]

Definition at line 62 of file Eigen2Support/Geometry/AngleAxis.h.

template<typename _Scalar>
typedef RotationBase<AngleAxis<_Scalar>,3> AngleAxis< _Scalar >::Base [private]

Definition at line 64 of file Geometry/AngleAxis.h.

template<typename _Scalar>
typedef Matrix<Scalar,3,3> AngleAxis< _Scalar >::Matrix3

Definition at line 71 of file Eigen2Support/Geometry/AngleAxis.h.

template<typename _Scalar>
typedef Matrix<Scalar,3,3> AngleAxis< _Scalar >::Matrix3

Definition at line 73 of file Geometry/AngleAxis.h.

template<typename _Scalar>
typedef Quaternion<Scalar> AngleAxis< _Scalar >::QuaternionType

Definition at line 73 of file Eigen2Support/Geometry/AngleAxis.h.

template<typename _Scalar>
typedef Quaternion<Scalar> AngleAxis< _Scalar >::QuaternionType

Definition at line 75 of file Geometry/AngleAxis.h.

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

the scalar type of the coefficients

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

Definition at line 70 of file Eigen2Support/Geometry/AngleAxis.h.

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

the scalar type of the coefficients

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

Definition at line 72 of file Geometry/AngleAxis.h.

template<typename _Scalar>
typedef Matrix<Scalar,3,1> AngleAxis< _Scalar >::Vector3

Definition at line 72 of file Eigen2Support/Geometry/AngleAxis.h.

template<typename _Scalar>
typedef Matrix<Scalar,3,1> AngleAxis< _Scalar >::Vector3

Definition at line 74 of file Geometry/AngleAxis.h.


Member Enumeration Documentation

template<typename _Scalar>
anonymous enum
Enumerator:
Dim 

Definition at line 68 of file Eigen2Support/Geometry/AngleAxis.h.

template<typename _Scalar>
anonymous enum
Enumerator:
Dim 

Definition at line 70 of file Geometry/AngleAxis.h.


Constructor & Destructor Documentation

template<typename _Scalar>
AngleAxis< _Scalar >::AngleAxis ( ) [inline]

Default constructor without initialization.

Definition at line 83 of file Eigen2Support/Geometry/AngleAxis.h.

template<typename _Scalar>
template<typename Derived >
AngleAxis< _Scalar >::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.

Definition at line 87 of file Eigen2Support/Geometry/AngleAxis.h.

template<typename _Scalar>
AngleAxis< _Scalar >::AngleAxis ( const QuaternionType q) [inline]

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

Definition at line 89 of file Eigen2Support/Geometry/AngleAxis.h.

template<typename _Scalar>
template<typename Derived >
AngleAxis< _Scalar >::AngleAxis ( const MatrixBase< Derived > &  m) [inline, explicit]

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

Definition at line 92 of file Eigen2Support/Geometry/AngleAxis.h.

template<typename _Scalar>
template<typename OtherScalarType >
AngleAxis< _Scalar >::AngleAxis ( const AngleAxis< OtherScalarType > &  other) [inline, explicit]

Copy constructor with scalar type conversion

Definition at line 147 of file Eigen2Support/Geometry/AngleAxis.h.

template<typename _Scalar>
AngleAxis< _Scalar >::AngleAxis ( ) [inline]

Default constructor without initialization.

Definition at line 85 of file Geometry/AngleAxis.h.

template<typename _Scalar>
template<typename Derived >
AngleAxis< _Scalar >::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.

Warning:
If the axis vector is not normalized, then the angle-axis object represents an invalid rotation.

Definition at line 92 of file Geometry/AngleAxis.h.

template<typename _Scalar>
template<typename QuatDerived >
AngleAxis< _Scalar >::AngleAxis ( const QuaternionBase< QuatDerived > &  q) [inline, explicit]

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

Definition at line 94 of file Geometry/AngleAxis.h.

template<typename _Scalar>
template<typename Derived >
AngleAxis< _Scalar >::AngleAxis ( const MatrixBase< Derived > &  m) [inline, explicit]

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

Definition at line 97 of file Geometry/AngleAxis.h.

template<typename _Scalar>
template<typename OtherScalarType >
AngleAxis< _Scalar >::AngleAxis ( const AngleAxis< OtherScalarType > &  other) [inline, explicit]

Copy constructor with scalar type conversion

Definition at line 141 of file Geometry/AngleAxis.h.


Member Function Documentation

template<typename _Scalar>
Scalar AngleAxis< _Scalar >::angle ( ) const [inline]

Definition at line 94 of file Eigen2Support/Geometry/AngleAxis.h.

template<typename _Scalar>
Scalar& AngleAxis< _Scalar >::angle ( ) [inline]

Definition at line 95 of file Eigen2Support/Geometry/AngleAxis.h.

template<typename _Scalar>
Scalar AngleAxis< _Scalar >::angle ( ) const [inline]

Definition at line 99 of file Geometry/AngleAxis.h.

template<typename _Scalar>
Scalar& AngleAxis< _Scalar >::angle ( ) [inline]

Definition at line 100 of file Geometry/AngleAxis.h.

template<typename _Scalar>
const Vector3& AngleAxis< _Scalar >::axis ( ) const [inline]

Definition at line 97 of file Eigen2Support/Geometry/AngleAxis.h.

template<typename _Scalar>
Vector3& AngleAxis< _Scalar >::axis ( ) [inline]

Definition at line 98 of file Eigen2Support/Geometry/AngleAxis.h.

template<typename _Scalar>
const Vector3& AngleAxis< _Scalar >::axis ( ) const [inline]

Definition at line 102 of file Geometry/AngleAxis.h.

template<typename _Scalar>
Vector3& AngleAxis< _Scalar >::axis ( ) [inline]

Definition at line 103 of file Geometry/AngleAxis.h.

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

Definition at line 136 of file Geometry/AngleAxis.h.

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

Definition at line 142 of file Eigen2Support/Geometry/AngleAxis.h.

template<typename _Scalar>
template<typename Derived >
AngleAxis& AngleAxis< _Scalar >::fromRotationMatrix ( const MatrixBase< Derived > &  m)
template<typename Scalar >
template<typename Derived >
AngleAxis< Scalar > & AngleAxis< Scalar >::fromRotationMatrix ( const MatrixBase< Derived > &  m)

Sets *this from a 3x3 rotation matrix.

Definition at line 207 of file Geometry/AngleAxis.h.

template<typename _Scalar>
static const AngleAxis AngleAxis< _Scalar >::Identity ( ) [inline, static]

Definition at line 147 of file Geometry/AngleAxis.h.

template<typename _Scalar>
AngleAxis AngleAxis< _Scalar >::inverse ( void  ) const [inline]
Returns:
the inverse rotation, i.e., an angle-axis with opposite rotation angle

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

Definition at line 118 of file Geometry/AngleAxis.h.

template<typename _Scalar>
AngleAxis AngleAxis< _Scalar >::inverse ( ) const [inline]
Returns:
the inverse rotation, i.e., an angle-axis with opposite rotation angle

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

Definition at line 125 of file Eigen2Support/Geometry/AngleAxis.h.

template<typename _Scalar>
bool AngleAxis< _Scalar >::isApprox ( const AngleAxis< _Scalar > &  other,
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()

Definition at line 153 of file Geometry/AngleAxis.h.

template<typename _Scalar>
bool AngleAxis< _Scalar >::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()

Definition at line 157 of file Eigen2Support/Geometry/AngleAxis.h.

template<typename _Scalar>
QuaternionType AngleAxis< _Scalar >::operator* ( const AngleAxis< _Scalar > &  other) const [inline]

Concatenates two rotations

Definition at line 101 of file Eigen2Support/Geometry/AngleAxis.h.

template<typename _Scalar>
QuaternionType AngleAxis< _Scalar >::operator* ( const QuaternionType other) const [inline]

Concatenates two rotations

Definition at line 105 of file Eigen2Support/Geometry/AngleAxis.h.

template<typename _Scalar>
QuaternionType AngleAxis< _Scalar >::operator* ( const AngleAxis< _Scalar > &  other) const [inline]

Concatenates two rotations

Definition at line 106 of file Geometry/AngleAxis.h.

template<typename _Scalar>
QuaternionType AngleAxis< _Scalar >::operator* ( const QuaternionType other) const [inline]

Concatenates two rotations

Definition at line 110 of file Geometry/AngleAxis.h.

template<typename _Scalar>
Matrix3 AngleAxis< _Scalar >::operator* ( const Matrix3 other) const [inline]

Concatenates two rotations

Definition at line 113 of file Eigen2Support/Geometry/AngleAxis.h.

template<typename _Scalar>
Vector3 AngleAxis< _Scalar >::operator* ( const Vector3 other) const [inline]

Applies rotation to vector

Definition at line 121 of file Eigen2Support/Geometry/AngleAxis.h.

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

Definition at line 172 of file Geometry/AngleAxis.h.

template<typename _Scalar>
template<typename Derived >
AngleAxis& AngleAxis< _Scalar >::operator= ( const MatrixBase< Derived > &  m)
template<typename Scalar >
AngleAxis< Scalar > & AngleAxis< Scalar >::operator= ( const QuaternionType q)

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

Definition at line 172 of file Eigen2Support/Geometry/AngleAxis.h.

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

Set *this from a 3x3 rotation matrix mat.

Definition at line 192 of file Eigen2Support/Geometry/AngleAxis.h.

template<typename _Scalar>
Matrix3 AngleAxis< _Scalar >::toRotationMatrix ( void  ) const
Returns:
an equivalent rotation matrix

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

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

Constructs and

Returns:
an equivalent 3x3 rotation matrix.

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

Definition at line 203 of file Eigen2Support/Geometry/AngleAxis.h.


Friends And Related Function Documentation

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

Concatenates two rotations

Definition at line 109 of file Eigen2Support/Geometry/AngleAxis.h.

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

Concatenates two rotations

Definition at line 114 of file Geometry/AngleAxis.h.

template<typename _Scalar>
Matrix3 operator* ( const Matrix3 a,
const AngleAxis< _Scalar > &  b 
) [friend]

Concatenates two rotations

Definition at line 117 of file Eigen2Support/Geometry/AngleAxis.h.


Member Data Documentation

template<typename _Scalar>
Scalar AngleAxis< _Scalar >::m_angle [protected]

Definition at line 78 of file Eigen2Support/Geometry/AngleAxis.h.

template<typename _Scalar>
Vector3 AngleAxis< _Scalar >::m_axis [protected]

Definition at line 77 of file Eigen2Support/Geometry/AngleAxis.h.


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


libicr
Author(s): Robert Krug
autogenerated on Mon Jan 6 2014 11:34:09