Eigen: Eigen::AngleAxis< Scalar_ > Class Template Reference

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#include <Eigen/src/Geometry/AngleAxis.h>

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 * EIGEN_PI, Vector3f::UnitX()) * AngleAxisf(0.5 * EIGEN_PI, Vector3f::UnitY()) *
    AngleAxisf(0.33 * EIGEN_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 Eigen::AngleAxis< Scalar_ >:

Public Types
typedef Scalar_	Scalar

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

typedef Matrix< Scalar, Dim, Dim >	RotationMatrixType

typedef internal::traits< AngleAxis< Scalar_ > >::Scalar	Scalar

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

internal::rotation_base_generic_product_selector< AngleAxis< Scalar_ >, OtherDerived, OtherDerived::IsVectorAtCompileTime >::ReturnType	operator* (const EigenBase< OtherDerived > &e) const

QuaternionType	operator* (const QuaternionType &other) 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

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

AngleAxis< Scalar_ >	inverse () const

RotationMatrixType	matrix () const

RotationMatrixType	matrix () const

internal::rotation_base_generic_product_selector< AngleAxis< Scalar_ >, OtherDerived, OtherDerived::IsVectorAtCompileTime >::ReturnType	operator* (const EigenBase< OtherDerived > &e) 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, Mode >	operator* (const Transform< Scalar, Dim, Mode, Options > &t) const

Transform< Scalar, Dim, Isometry >	operator* (const Translation< Scalar, Dim > &t) const

Transform< Scalar, Dim, Isometry >	operator* (const Translation< Scalar, Dim > &t) const

RotationMatrixType	operator* (const UniformScaling< Scalar > &s) const

RotationMatrixType	operator* (const UniformScaling< Scalar > &s) const

RotationMatrixType	toRotationMatrix () 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*() [1/6]

template<typename Scalar_>

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

inline

Concatenates two rotations

◆ operator*() [2/6]

template<typename Scalar_>

internal::rotation_base_generic_product_selector< AngleAxis< Scalar_ >, OtherDerived, OtherDerived::IsVectorAtCompileTime >::ReturnType Eigen::RotationBase< AngleAxis< Scalar_ >, Dim_ >::operator* ( const EigenBase< OtherDerived > & e ) const

inline

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

◆ operator*() [3/6]

template<typename Scalar_>

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

inline

Concatenates two rotations

◆ operator*() [4/6]

template<typename Scalar_>

Transform< Scalar, Dim, Mode > Eigen::RotationBase< AngleAxis< Scalar_ >, Dim_ >::operator* ( const Transform< Scalar, Dim, Mode, Options > & t ) const

inline

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

◆ operator*() [5/6]

template<typename Scalar_>

Transform< Scalar, Dim, Isometry > Eigen::RotationBase< AngleAxis< Scalar_ >, Dim_ >::operator* ( const Translation< Scalar, Dim > & t ) const

inline

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

◆ operator*() [6/6]

template<typename Scalar_>

RotationMatrixType Eigen::RotationBase< AngleAxis< Scalar_ >, Dim_ >::operator* ( const UniformScaling< Scalar > & s ) const

inline

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

◆ 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.

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

/usr/local/google/home/cantonios/dev/eigen/Eigen/src/Core/util/ForwardDeclarations.h
/usr/local/google/home/cantonios/dev/eigen/Eigen/src/Geometry/AngleAxis.h

Detailed Description

Public Types

Public Member Functions

Member Typedef Documentation

◆ Scalar

Constructor & Destructor Documentation

◆ AngleAxis() [1/5]

◆ AngleAxis() [2/5]

◆ AngleAxis() [3/5]

◆ AngleAxis() [4/5]

◆ AngleAxis() [5/5]

Member Function Documentation

◆ angle() [1/2]

◆ angle() [2/2]

◆ axis() [1/2]

◆ axis() [2/2]

◆ cast()

◆ inverse()

◆ isApprox()

◆ operator*() [1/6]

◆ operator*() [2/6]

◆ operator*() [3/6]

◆ operator*() [4/6]

◆ operator*() [5/6]

◆ operator*() [6/6]

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ toRotationMatrix()