Detailed Description

template<typename _Scalar>
class Eigen::AngleAxis< _Scalar >

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

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:

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 63 of file Geometry.

Inheritance diagram for Eigen::AngleAxis< _Scalar >:

[legend]

List of all members.

Public Types
enum	{ Dim = 3 }
typedef _Scalar	Scalar
	the scalar type of the coefficients
typedef Matrix< Scalar, 3, 3 >	Matrix3
typedef Matrix< Scalar, 3, 1 >	Vector3
typedef Quaternion< Scalar >	QuaternionType
enum
typedef Matrix< Scalar, Dim, Dim >	RotationMatrixType
	corresponding linear transformation matrix type
typedef Matrix< Scalar, Dim, 1 >	VectorType
Public Member Functions
	AngleAxis ()
	Default constructor without initialization.
template<typename Derived >
	AngleAxis (Scalar angle, const MatrixBase< Derived > &axis)
	Constructs and initialize the angle-axis rotation from an angle in radian and an axis which must be normalized.
template<typename QuatDerived >
	AngleAxis (const QuaternionBase< QuatDerived > &q)
	Constructs and initialize the angle-axis rotation from a quaternion q.
template<typename Derived >
	AngleAxis (const MatrixBase< Derived > &m)
	Constructs and initialize the angle-axis rotation from a 3x3 rotation matrix.
Scalar	angle () const
Scalar &	angle ()
const Vector3 &	axis () const
Vector3 &	axis ()
QuaternionType	operator* (const AngleAxis &other) const
	Concatenates two rotations.
QuaternionType	operator* (const QuaternionType &other) const
	Concatenates two rotations.
AngleAxis	inverse () const
template<class QuatDerived >
AngleAxis &	operator= (const QuaternionBase< QuatDerived > &q)
	Set `this` from a unit* quaternion.
template<typename Derived >
AngleAxis &	operator= (const MatrixBase< Derived > &m)
	Set `this` from a 3x3 rotation matrix mat*.
template<typename Derived >
AngleAxis &	fromRotationMatrix (const MatrixBase< Derived > &m)
	Sets `*this` from a 3x3 rotation matrix.
Matrix3	toRotationMatrix (void) const
	Constructs and.
template<typename NewScalarType >
internal::cast_return_type < AngleAxis, AngleAxis < NewScalarType > >::type	cast () const
template<typename OtherScalarType >
	AngleAxis (const AngleAxis< OtherScalarType > &other)
	Copy constructor with scalar type conversion.
bool	isApprox (const AngleAxis &other, typename NumTraits< Scalar >::Real prec=NumTraits< Scalar >::dummy_precision()) const
const AngleAxis< _Scalar > &	derived () const
AngleAxis< _Scalar > &	derived ()
RotationMatrixType	matrix () const
Transform< Scalar, Dim, Isometry >	operator* (const Translation< Scalar, Dim > &t) const
RotationMatrixType	operator* (const UniformScaling< Scalar > &s) const
EIGEN_STRONG_INLINE 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
VectorType	_transformVector (const OtherVectorType &v) const
Static Public Member Functions
static const AngleAxis	Identity ()
Protected Attributes
Vector3	m_axis
Scalar	m_angle
Private Types
typedef RotationBase < AngleAxis< _Scalar >, 3 >	Base
Friends
QuaternionType	operator* (const QuaternionType &a, const AngleAxis &b)
	Concatenates two rotations.
RotationMatrixType	operator* (const EigenBase< OtherDerived > &l, const AngleAxis< _Scalar > &r)
Transform< Scalar, Dim, Affine >	operator* (const DiagonalMatrix< Scalar, Dim > &l, const AngleAxis< _Scalar > &r)

Member Typedef Documentation

template<typename _Scalar>

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

Definition at line 65 of file Geometry.

template<typename _Scalar>

typedef Matrix<Scalar,3,3> Eigen::AngleAxis< _Scalar >::Matrix3

Definition at line 74 of file Geometry.

template<typename _Scalar>

typedef Quaternion<Scalar> Eigen::AngleAxis< _Scalar >::QuaternionType

Definition at line 76 of file Geometry.

typedef Matrix<Scalar,Dim,Dim> Eigen::RotationBase< AngleAxis< _Scalar > , _Dim >::RotationMatrixType [inherited]

corresponding linear transformation matrix type

Definition at line 51 of file Geometry.

template<typename _Scalar>

typedef _Scalar Eigen::AngleAxis< _Scalar >::Scalar

the scalar type of the coefficients

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

Definition at line 73 of file Geometry.

template<typename _Scalar>

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

Definition at line 75 of file Geometry.

typedef Matrix<Scalar,Dim,1> Eigen::RotationBase< AngleAxis< _Scalar > , _Dim >::VectorType [inherited]

Definition at line 52 of file Geometry.

Member Enumeration Documentation

anonymous enum [inherited]

Definition at line 46 of file Geometry.

template<typename _Scalar>

anonymous enum

Enumerator:

Dim

Definition at line 71 of file Geometry.

Constructor & Destructor Documentation

template<typename _Scalar>

Eigen::AngleAxis< _Scalar >::AngleAxis ( ) [inline]

Default constructor without initialization.

Definition at line 86 of file Geometry.

template<typename _Scalar>

template<typename Derived >

Eigen::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 93 of file Geometry.

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.

Definition at line 95 of file Geometry.

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.

Definition at line 98 of file Geometry.

template<typename _Scalar>

template<typename OtherScalarType >

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

Copy constructor with scalar type conversion.

Definition at line 142 of file Geometry.

Member Function Documentation

VectorType Eigen::RotationBase< AngleAxis< _Scalar > , _Dim >::_transformVector ( const OtherVectorType & v ) const [inline, inherited]

Definition at line 107 of file Geometry.

template<typename _Scalar>

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

Definition at line 100 of file Geometry.

template<typename _Scalar>

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

Definition at line 101 of file Geometry.

template<typename _Scalar>

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

Definition at line 104 of file Geometry.

template<typename _Scalar>

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

Definition at line 103 of file Geometry.

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.

Definition at line 137 of file Geometry.

AngleAxis< _Scalar > & Eigen::RotationBase< AngleAxis< _Scalar > , _Dim >::derived ( ) [inline, inherited]

Definition at line 56 of file Geometry.

const AngleAxis< _Scalar > & Eigen::RotationBase< AngleAxis< _Scalar > , _Dim >::derived ( ) const [inline, inherited]

Definition at line 55 of file Geometry.

template<typename Scalar >

template<typename Derived >

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

Sets *this from a 3x3 rotation matrix.

Definition at line 208 of file Geometry.

template<typename _Scalar>

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

Definition at line 148 of file Geometry.

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 >.

Definition at line 119 of file Geometry.

template<typename _Scalar>

bool Eigen::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 154 of file Geometry.

RotationMatrixType Eigen::RotationBase< AngleAxis< _Scalar > , _Dim >::matrix ( ) const [inline, inherited]

Returns:: an equivalent rotation matrix This function is added to be conform with the Transform class' naming scheme.

Definition at line 64 of file Geometry.

template<typename _Scalar>

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

Concatenates two rotations.

Definition at line 107 of file Geometry.

EIGEN_STRONG_INLINE internal::rotation_base_generic_product_selector<AngleAxis< _Scalar > ,OtherDerived,OtherDerived::IsVectorAtCompileTime>::ReturnType Eigen::RotationBase< AngleAxis< _Scalar > , _Dim >::operator* ( const EigenBase< OtherDerived > & e ) const [inline, inherited]

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

Definition at line 85 of file Geometry.

Transform<Scalar,Dim,Isometry> Eigen::RotationBase< AngleAxis< _Scalar > , _Dim >::operator* ( const Translation< Scalar, Dim > & t ) const [inline, inherited]

Returns:: the concatenation of the rotation *this with a translation t

Definition at line 70 of file Geometry.

RotationMatrixType Eigen::RotationBase< AngleAxis< _Scalar > , _Dim >::operator* ( const UniformScaling< Scalar > & s ) const [inline, inherited]

Returns:: the concatenation of the rotation *this with a uniform scaling s

Definition at line 74 of file Geometry.

Transform<Scalar,Dim,Mode> Eigen::RotationBase< AngleAxis< _Scalar > , _Dim >::operator* ( const Transform< Scalar, Dim, Mode, Options > & t ) const [inline, inherited]

Returns:: the concatenation of the rotation *this with a transformation t

Definition at line 103 of file Geometry.

template<typename _Scalar>

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

Concatenates two rotations.

Definition at line 111 of file Geometry.

template<typename Scalar >

template<typename Derived >

AngleAxis< Scalar > & Eigen::AngleAxis< Scalar >::operator= ( const MatrixBase< Derived > & m )

Set *this from a 3x3 rotation matrix mat.

Definition at line 196 of file Geometry.

template<typename Scalar >

template<typename QuatDerived >

AngleAxis< Scalar > & Eigen::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 173 of file Geometry.

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 >.

Definition at line 217 of file Geometry.

Friends And Related Function Documentation

template<typename _Scalar>

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

Concatenates two rotations.

Definition at line 115 of file Geometry.

Transform<Scalar,Dim,Affine> operator*	(	const DiagonalMatrix< Scalar, Dim > &	l,
		const AngleAxis< _Scalar > &	r
	)		`[friend, inherited]`

Returns:: the concatenation of a scaling l with the rotation r

Definition at line 94 of file Geometry.

RotationMatrixType operator*	(	const EigenBase< OtherDerived > &	l,
		const AngleAxis< _Scalar > &	r
	)		`[friend, inherited]`

Returns:: the concatenation of a linear transformation l with the rotation r

Definition at line 90 of file Geometry.

Member Data Documentation

template<typename _Scalar>

Scalar Eigen::AngleAxis< _Scalar >::m_angle [protected]

Definition at line 81 of file Geometry.

template<typename _Scalar>

Vector3 Eigen::AngleAxis< _Scalar >::m_axis [protected]

Definition at line 80 of file Geometry.

Detailed Description

template<typename _Scalar> class Eigen::AngleAxis< _Scalar >

Public Types

Public Member Functions

Static Public Member Functions

Protected Attributes

Private Types

Friends

Member Typedef Documentation

Member Enumeration Documentation

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

Member Data Documentation

template<typename _Scalar>
class Eigen::AngleAxis< _Scalar >