Eigen::AngleAxis

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()


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


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

Scalar

template<typename _Scalar >

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

the scalar type of the coefficients

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 > &

)

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 > &

)

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

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 > &

)

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.

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

AngleAxis.h

Eigen::AngleAxis

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

Scalar

AngleAxis() [1/5]

AngleAxis() [2/5]

AngleAxis() [3/5]

AngleAxis() [4/5]

AngleAxis() [5/5]

angle() [1/2]

angle() [2/2]

axis() [1/2]

axis() [2/2]

cast()

inverse()

isApprox()

operator*() [1/2]

operator*() [2/2]

operator=() [1/2]

operator=() [2/2]

toRotationMatrix()

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