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

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:

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_ >:

Public Types
typedef Scalar_	Scalar
Public Types inherited from Eigen::RotationBase< AngleAxis< Scalar_ >, 3 >
typedef Matrix< Scalar, Dim, Dim >	RotationMatrixType
typedef internal::traits< AngleAxis< Scalar_ > >::Scalar	Scalar

Public Member Functions
Scalar &	angle ()
Scalar	angle () const
	AngleAxis ()
template<typename OtherScalarType >
	AngleAxis (const AngleAxis< OtherScalarType > &other)
template<typename Derived >
	AngleAxis (const MatrixBase< Derived > &m)
template<typename QuatDerived >
	AngleAxis (const QuaternionBase< QuatDerived > &q)
template<typename Derived >
	AngleAxis (const Scalar &angle, const MatrixBase< Derived > &axis)
Vector3 &	axis ()
const Vector3 &	axis () const
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
QuaternionType	operator* (const AngleAxis &other) const
QuaternionType	operator* (const QuaternionType &other) const
template<typename Derived >
AngleAxis< Scalar > &	operator= (const MatrixBase< Derived > &mat)
template<typename QuatDerived >
AngleAxis< Scalar > &	operator= (const QuaternionBase< QuatDerived > &q)
Matrix3	toRotationMatrix (void) const
Public Member Functions inherited from Eigen::RotationBase< AngleAxis< Scalar_ >, 3 >
AngleAxis< Scalar_ >	inverse () const
RotationMatrixType	matrix () 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
Transform< Scalar, Dim, Isometry >	operator* (const Translation< Scalar, Dim > &t) const
RotationMatrixType	operator* (const UniformScaling< Scalar > &s) const
RotationMatrixType	toRotationMatrix () const

Member Typedef Documentation

Scalar

template<typename Scalar_ >

typedef Scalar_ Eigen::AngleAxis< Scalar_ >::Scalar

the scalar type of the coefficients

Constructor & Destructor Documentation

AngleAxis() [1/5]

template<typename Scalar_ >

Eigen::AngleAxis< Scalar_ >::AngleAxis ( )

inline

Default constructor without initialization.

AngleAxis() [2/5]

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.

AngleAxis() [3/5]

template<typename Scalar_ >

template<typename QuatDerived >

Eigen::AngleAxis< Scalar_ >::AngleAxis ( const QuaternionBase< QuatDerived > & q )

inlineexplicit

Constructs and initialize the angle-axis rotation from a quaternion q. This function implicitly normalizes the quaternion q.

AngleAxis() [4/5]

template<typename Scalar_ >

template<typename Derived >

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

inlineexplicit

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

AngleAxis() [5/5]

template<typename Scalar_ >

template<typename OtherScalarType >

Eigen::AngleAxis< Scalar_ >::AngleAxis ( const AngleAxis< OtherScalarType > & other )

inlineexplicit

Copy constructor with scalar type conversion

Member Function Documentation

angle() [1/2]

template<typename Scalar_ >

Scalar & Eigen::AngleAxis< Scalar_ >::angle ( )

inline

Returns

a read-write reference to the stored angle in radian

angle() [2/2]

template<typename Scalar_ >

Scalar Eigen::AngleAxis< Scalar_ >::angle ( ) const

inline

Returns

the value of the rotation angle in radian

axis() [1/2]

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.

axis() [2/2]

template<typename Scalar_ >

const Vector3 & Eigen::AngleAxis< Scalar_ >::axis ( ) const

inline

Returns

the rotation axis

cast()

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.

inverse()

template<typename Scalar_ >

AngleAxis Eigen::AngleAxis< Scalar_ >::inverse ( ) const

inline

Returns

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

isApprox()

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()

operator*() [1/2]

template<typename Scalar_ >

QuaternionType Eigen::AngleAxis< Scalar_ >::operator* ( const AngleAxis< Scalar_ > & other ) const

inline

Concatenates two rotations

operator*() [2/2]

template<typename Scalar_ >

QuaternionType Eigen::AngleAxis< Scalar_ >::operator* ( const QuaternionType & other ) const

inline

Concatenates two rotations

operator=() [1/2]

template<typename Scalar_ >

template<typename Derived >

AngleAxis< Scalar > & Eigen::AngleAxis< Scalar_ >::operator=

(

const MatrixBase< Derived > &

mat

)

Set *this from a 3x3 rotation matrix mat.

operator=() [2/2]

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.

toRotationMatrix()

template<typename Scalar >

AngleAxis< Scalar >::Matrix3 Eigen::AngleAxis< Scalar >::toRotationMatrix

(

void

)

const

Constructs and

Returns

an equivalent 3x3 rotation matrix.

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

• AngleAxis.h