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()

Inheritance diagram for AngleAxis< Scalar >:

Public Types
typedef Matrix< Scalar, Dim, Dim >	RotationMatrixType

typedef _Scalar	Scalar

Public Member Functions
Scalar	angle () const

Scalar &	angle ()

	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 Vector3 &	axis () const

Vector3 &	axis ()

template<typename NewScalarType >
internal::cast_return_type < AngleAxis, AngleAxis < NewScalarType > >::type	cast () const

template<typename Derived >
AngleAxis< Scalar > &	fromRotationMatrix (const MatrixBase< Derived > &mat)
	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

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<typename QuatDerived >
AngleAxis< Scalar > &	operator= (const QuaternionBase< QuatDerived > &q)

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

Matrix3	toRotationMatrix (void) const

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

Member Typedef Documentation

typedef Matrix<Scalar,Dim,Dim> RotationMatrixType

inherited

corresponding linear transformation matrix type

typedef _Scalar Scalar

the scalar type of the coefficients

Constructor & Destructor Documentation

AngleAxis ( )

inline

Default constructor without initialization.

Referenced by AngleAxis< Scalar >::inverse().

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.

AngleAxis ( const QuaternionBase< QuatDerived > & q )

inlineexplicit

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

Scalar angle ( ) const

inline

Returns: the value of the rotation angle in radian

Referenced by QuaternionBase< Derived >::operator=().

Scalar& angle ( )

inline

Returns: a read-write reference to the stored angle in radian

const Vector3& axis ( ) const

inline

Returns: the rotation axis

Referenced by QuaternionBase< Derived >::operator=().

Vector3& axis ( )

inline

Returns: a read-write reference to the stored rotation axis.

Warning: The rotation axis must remain a unit vector.

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.

AngleAxis inverse ( ) const

inline

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

References AngleAxis< Scalar >::AngleAxis().

bool 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()

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

inlineinherited

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

Transform<Scalar,Dim,Mode> operator* ( const Transform< Scalar, Dim, Mode, Options > & t ) const

inlineinherited

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

QuaternionType operator* ( const AngleAxis< Scalar > & other ) const

inline

Concatenates two rotations

QuaternionType operator* ( const QuaternionType & other ) const

inline

Concatenates two rotations

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.

References QuaternionBase< Derived >::vec(), and QuaternionBase< Derived >::w().

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.

References MatrixBase< Derived >::diagonal().

Friends And Related Function Documentation

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

friend

Concatenates two rotations

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

Detailed Description

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

Public Types

Public Member Functions

Friends

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

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