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

#include <AngleAxis.h>

Inheritance diagram for AngleAxis< _Scalar >:

Public Types
enum	{ Dim }
enum
typedef Matrix< Scalar, 3, 3 >	Matrix3
typedef Quaternion< Scalar >	QuaternionType
typedef Matrix< Scalar, Dim, Dim >	RotationMatrixType
typedef _Scalar	Scalar
typedef Matrix< Scalar, 3, 1 >	Vector3
typedef Matrix< Scalar, Dim, 1 >	VectorType

Public Member Functions
VectorType	_transformVector (const OtherVectorType &v) const
Scalar	angle () const
Scalar &	angle ()
	AngleAxis ()
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)
const Vector3 &	axis () const
Vector3 &	axis ()
template<typename NewScalarType >
internal::cast_return_type < AngleAxis, AngleAxis < NewScalarType > >::type	cast () const
const AngleAxis< _Scalar > &	derived () const
AngleAxis< _Scalar > &	derived ()
template<typename Derived >
AngleAxis &	fromRotationMatrix (const MatrixBase< Derived > &m)
	Sets `*this` from a 3x3 rotation matrix.
AngleAxis	inverse () const
bool	isApprox (const AngleAxis &other, typename NumTraits< Scalar >::Real prec=NumTraits< Scalar >::dummy_precision()) const
RotationMatrixType	matrix () const
Transform< Scalar, Dim, Isometry >	operator* (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<class QuatDerived >
AngleAxis &	operator= (const QuaternionBase< QuatDerived > &q)
template<typename Derived >
AngleAxis &	operator= (const MatrixBase< Derived > &m)
Matrix3	toRotationMatrix (void) const

Static Public Member Functions
static const AngleAxis	Identity ()

Protected Attributes
Scalar	m_angle
Vector3	m_axis

Friends
QuaternionType	operator* (const QuaternionType &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:

_Scalar the 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()

Member Typedef Documentation

typedef Matrix<Scalar,3,3> Matrix3

typedef Quaternion<Scalar> QuaternionType

typedef Matrix<Scalar,Dim,Dim> RotationMatrixType

inherited

corresponding linear transformation matrix type

typedef _Scalar Scalar

the scalar type of the coefficients

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

typedef Matrix<Scalar,3,1> Vector3

typedef Matrix<Scalar,Dim,1> VectorType

inherited

Member Enumeration Documentation

anonymous enum

Enumerator:

Dim

anonymous enum

inherited

Constructor & Destructor Documentation

AngleAxis ( )

inline

Default constructor without initialization.

Referenced by AngleAxis< _Scalar >::Identity(), and AngleAxis< _Scalar >::inverse().

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.

AngleAxis ( const QuaternionBase< QuatDerived > & q )

inlineexplicit

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

References 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

References AngleAxis< _Scalar >::angle(), AngleAxis< _Scalar >::axis(), AngleAxis< _Scalar >::m_angle, and AngleAxis< _Scalar >::m_axis.

Member Function Documentation

VectorType _transformVector ( const OtherVectorType & v ) const

inlineinherited

Scalar angle ( ) const

inline

References AngleAxis< _Scalar >::m_angle.

Referenced by AngleAxis< _Scalar >::AngleAxis(), and QuaternionBase< Derived >::operator=().

Scalar& angle ( )

inline

References AngleAxis< _Scalar >::m_angle.

const Vector3& axis ( ) const

inline

References AngleAxis< _Scalar >::m_axis.

Referenced by AngleAxis< _Scalar >::AngleAxis(), and QuaternionBase< Derived >::operator=().

Vector3& axis ( )

inline

References AngleAxis< _Scalar >::m_axis.

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.

const AngleAxis< _Scalar > & derived ( ) const

inlineinherited

AngleAxis< _Scalar > & derived ( )

inlineinherited

AngleAxis< Scalar > & fromRotationMatrix ( const MatrixBase< Derived > & m )

Sets *this from a 3x3 rotation matrix.

static const AngleAxis Identity ( )

inlinestatic

References AngleAxis< _Scalar >::AngleAxis().

AngleAxis inverse ( ) const

inline

Returns:: the inverse rotation, i.e., an angle-axis with opposite rotation angle

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

References AngleAxis< _Scalar >::AngleAxis(), AngleAxis< _Scalar >::m_angle, and AngleAxis< _Scalar >::m_axis.

bool 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()

References AngleAxis< _Scalar >::m_angle, and AngleAxis< _Scalar >::m_axis.

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