The quaternion class used to represent 3D orientations and rotations. More...

#include <ForwardDeclarations.h>

Inheritance diagram for Eigen::Quaternion< _Scalar, _Options >:

Public Types
enum

typedef Base::AngleAxisType	AngleAxisType

typedef QuaternionBase< Quaternion< _Scalar, _Options > >	Base

typedef internal::traits< Quaternion >::Coefficients	Coefficients

typedef _Scalar	Scalar

Public Types inherited from Eigen::QuaternionBase< Quaternion< _Scalar, _Options > >
enum

typedef AngleAxis< Scalar >	AngleAxisType

typedef RotationBase< Quaternion< _Scalar, _Options >, 3 >	Base

typedef internal::traits< Quaternion< _Scalar, _Options > >::Coefficients	Coefficients

typedef Coefficients::CoeffReturnType	CoeffReturnType

typedef Matrix< Scalar, 3, 3 >	Matrix3

typedef internal::conditional< bool(internal::traits< Quaternion< _Scalar, _Options > >::Flags &LvalueBit), Scalar &, CoeffReturnType >::type	NonConstCoeffReturnType

typedef NumTraits< Scalar >::Real	RealScalar

typedef internal::traits< Quaternion< _Scalar, _Options > >::Scalar	Scalar

typedef Matrix< Scalar, 3, 1 >	Vector3

Public Types inherited from Eigen::RotationBase< Quaternion< _Scalar, _Options >, 3 >
enum

typedef Matrix< Scalar, Dim, Dim >	RotationMatrixType

typedef internal::traits< Quaternion< _Scalar, _Options > >::Scalar	Scalar

typedef Matrix< Scalar, Dim, 1 >	VectorType

Public Member Functions
EIGEN_DEVICE_FUNC Coefficients &	coeffs ()

EIGEN_DEVICE_FUNC const Coefficients &	coeffs () const

template<typename Derived1 , typename Derived2 >
EIGEN_DEVICE_FUNC Quaternion< Scalar, Options >	FromTwoVectors (const MatrixBase< Derived1 > &a, const MatrixBase< Derived2 > &b)

EIGEN_DEVICE_FUNC	Quaternion ()

EIGEN_DEVICE_FUNC	Quaternion (const Scalar &w, const Scalar &x, const Scalar &y, const Scalar &z)

EIGEN_DEVICE_FUNC	Quaternion (const Scalar *data)

template<class Derived >
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE	Quaternion (const QuaternionBase< Derived > &other)

EIGEN_DEVICE_FUNC	Quaternion (const AngleAxisType &aa)

template<typename Derived >
EIGEN_DEVICE_FUNC	Quaternion (const MatrixBase< Derived > &other)

template<typename OtherScalar , int OtherOptions>
EIGEN_DEVICE_FUNC	Quaternion (const Quaternion< OtherScalar, OtherOptions > &other)

Public Member Functions inherited from Eigen::QuaternionBase< Quaternion< _Scalar, _Options > >
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Vector3	_transformVector (const Vector3 &v) const

EIGEN_DEVICE_FUNC Scalar	angularDistance (const QuaternionBase< OtherDerived > &other) const

EIGEN_DEVICE_FUNC internal::traits< Quaternion< _Scalar, _Options > >::Scalar	angularDistance (const QuaternionBase< OtherDerived > &other) const

EIGEN_DEVICE_FUNC internal::enable_if< internal::is_same< Scalar, NewScalarType >::value, const Quaternion< _Scalar, _Options > &>::type	cast () const

EIGEN_DEVICE_FUNC internal::enable_if<!internal::is_same< Scalar, NewScalarType >::value, Quaternion< NewScalarType > >::type	cast () const

EIGEN_DEVICE_FUNC const internal::traits< Quaternion< _Scalar, _Options > >::Coefficients &	coeffs () const

EIGEN_DEVICE_FUNC internal::traits< Quaternion< _Scalar, _Options > >::Coefficients &	coeffs ()

EIGEN_DEVICE_FUNC Quaternion< Scalar >	conjugate () const

EIGEN_DEVICE_FUNC Scalar	dot (const QuaternionBase< OtherDerived > &other) const

EIGEN_DEVICE_FUNC Quaternion< Scalar >	inverse () const

EIGEN_DEVICE_FUNC bool	isApprox (const QuaternionBase< OtherDerived > &other, const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const

EIGEN_DEVICE_FUNC Scalar	norm () const

EIGEN_DEVICE_FUNC void	normalize ()

EIGEN_DEVICE_FUNC Quaternion< Scalar >	normalized () const

EIGEN_DEVICE_FUNC bool	operator!= (const QuaternionBase< OtherDerived > &other) const

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Quaternion< Scalar >	operator* (const QuaternionBase< OtherDerived > &q) const

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Quaternion< typename internal::traits< Quaternion< _Scalar, _Options > >::Scalar >	operator* (const QuaternionBase< OtherDerived > &other) const

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Quaternion< _Scalar, _Options > &	operator*= (const QuaternionBase< OtherDerived > &q)

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE QuaternionBase< Quaternion< _Scalar, _Options > > &	operator= (const QuaternionBase< Quaternion< _Scalar, _Options > > &other)

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Quaternion< _Scalar, _Options > &	operator= (const QuaternionBase< OtherDerived > &other)

EIGEN_DEVICE_FUNC Quaternion< _Scalar, _Options > &	operator= (const AngleAxisType &aa)

EIGEN_DEVICE_FUNC Quaternion< _Scalar, _Options > &	operator= (const MatrixBase< OtherDerived > &m)

EIGEN_DEVICE_FUNC Quaternion< _Scalar, _Options > &	operator= (const MatrixBase< MatrixDerived > &xpr)

EIGEN_DEVICE_FUNC bool	operator== (const QuaternionBase< OtherDerived > &other) const

EIGEN_DEVICE_FUNC Quaternion< _Scalar, _Options > &	setFromTwoVectors (const MatrixBase< Derived1 > &a, const MatrixBase< Derived2 > &b)

EIGEN_DEVICE_FUNC QuaternionBase &	setIdentity ()

EIGEN_DEVICE_FUNC Quaternion< Scalar >	slerp (const Scalar &t, const QuaternionBase< OtherDerived > &other) const

EIGEN_DEVICE_FUNC Quaternion< typename internal::traits< Quaternion< _Scalar, _Options > >::Scalar >	slerp (const Scalar &t, const QuaternionBase< OtherDerived > &other) const

EIGEN_DEVICE_FUNC Scalar	squaredNorm () const

EIGEN_DEVICE_FUNC Matrix3	toRotationMatrix () const

EIGEN_DEVICE_FUNC const VectorBlock< const Coefficients, 3 >	vec () const

EIGEN_DEVICE_FUNC VectorBlock< Coefficients, 3 >	vec ()

EIGEN_DEVICE_FUNC CoeffReturnType	w () const

EIGEN_DEVICE_FUNC NonConstCoeffReturnType	w ()

EIGEN_DEVICE_FUNC CoeffReturnType	x () const

EIGEN_DEVICE_FUNC NonConstCoeffReturnType	x ()

EIGEN_DEVICE_FUNC CoeffReturnType	y () const

EIGEN_DEVICE_FUNC NonConstCoeffReturnType	y ()

EIGEN_DEVICE_FUNC CoeffReturnType	z () const

EIGEN_DEVICE_FUNC NonConstCoeffReturnType	z ()

Public Member Functions inherited from Eigen::RotationBase< Quaternion< _Scalar, _Options >, 3 >
EIGEN_DEVICE_FUNC VectorType	_transformVector (const OtherVectorType &v) const

EIGEN_DEVICE_FUNC const Quaternion< _Scalar, _Options > &	derived () const

EIGEN_DEVICE_FUNC Quaternion< _Scalar, _Options > &	derived ()

EIGEN_DEVICE_FUNC Quaternion< _Scalar, _Options >	inverse () const

EIGEN_DEVICE_FUNC RotationMatrixType	matrix () const

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

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

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE internal::rotation_base_generic_product_selector< Quaternion< _Scalar, _Options >, OtherDerived, OtherDerived::IsVectorAtCompileTime >::ReturnType	operator* (const EigenBase< OtherDerived > &e) const

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

EIGEN_DEVICE_FUNC RotationMatrixType	toRotationMatrix () const

Static Public Member Functions
template<typename Derived1 , typename Derived2 >
static EIGEN_DEVICE_FUNC Quaternion	FromTwoVectors (const MatrixBase< Derived1 > &a, const MatrixBase< Derived2 > &b)

static EIGEN_DEVICE_FUNC Quaternion	UnitRandom ()

Static Public Member Functions inherited from Eigen::QuaternionBase< Quaternion< _Scalar, _Options > >
static EIGEN_DEVICE_FUNC Quaternion< Scalar >	Identity ()

Static Protected Member Functions
static EIGEN_STRONG_INLINE void	_check_template_params ()

Protected Attributes
Coefficients	m_coeffs

Detailed Description

template<typename _Scalar, int _Options>
class Eigen::Quaternion< _Scalar, _Options >

The quaternion class used to represent 3D orientations and rotations.

Template Parameters

_Scalar	the scalar type, i.e., the type of the coefficients
_Options	controls the memory alignment of the coefficients. Can be # AutoAlign or # DontAlign. Default is AutoAlign.

This class represents a quaternion $ w+xi+yj+zk $ that is a convenient representation of orientations and rotations of objects in three dimensions. Compared to other representations like Euler angles or 3x3 matrices, quaternions offer the following advantages:

compact storage (4 scalars)
efficient to compose (28 flops),
stable spherical interpolation

The following two typedefs are provided for convenience:

Quaternionf for float
Quaterniond for double

Warning: Operations interpreting the quaternion as rotation have undefined behavior if the quaternion is not normalized.

See also: class AngleAxis, class Transform

Definition at line 293 of file ForwardDeclarations.h.

Member Typedef Documentation

◆ AngleAxisType

template<typename _Scalar, int _Options>

typedef Base::AngleAxisType Eigen::Quaternion< _Scalar, _Options >::AngleAxisType

Definition at line 285 of file 3rdparty/Eigen/Eigen/src/Geometry/Quaternion.h.

◆ Base

template<typename _Scalar, int _Options>

typedef QuaternionBase<Quaternion<_Scalar,_Options> > Eigen::Quaternion< _Scalar, _Options >::Base

Definition at line 276 of file 3rdparty/Eigen/Eigen/src/Geometry/Quaternion.h.

◆ Coefficients

template<typename _Scalar, int _Options>

typedef internal::traits<Quaternion>::Coefficients Eigen::Quaternion< _Scalar, _Options >::Coefficients

Definition at line 284 of file 3rdparty/Eigen/Eigen/src/Geometry/Quaternion.h.

◆ Scalar

template<typename _Scalar, int _Options>

typedef _Scalar Eigen::Quaternion< _Scalar, _Options >::Scalar

Definition at line 279 of file 3rdparty/Eigen/Eigen/src/Geometry/Quaternion.h.

Member Enumeration Documentation

◆ anonymous enum

template<typename _Scalar, int _Options>

anonymous enum

Definition at line 277 of file 3rdparty/Eigen/Eigen/src/Geometry/Quaternion.h.

Constructor & Destructor Documentation

◆ Quaternion() [1/7]

template<typename _Scalar, int _Options>

EIGEN_DEVICE_FUNC Eigen::Quaternion< _Scalar, _Options >::Quaternion ( )

inline

Default constructor leaving the quaternion uninitialized.

Definition at line 288 of file 3rdparty/Eigen/Eigen/src/Geometry/Quaternion.h.

◆ Quaternion() [2/7]

template<typename _Scalar, int _Options>

EIGEN_DEVICE_FUNC Eigen::Quaternion< _Scalar, _Options >::Quaternion	(	const Scalar &	w,
		const Scalar &	x,
		const Scalar &	y,
		const Scalar &	z
	)

inline

Constructs and initializes the quaternion $ w+xi+yj+zk $ from its four coefficients w, x, y and z.

Warning: Note the order of the arguments: the real w coefficient first, while internally the coefficients are stored in the following order: [x, y, z, w]

Definition at line 297 of file 3rdparty/Eigen/Eigen/src/Geometry/Quaternion.h.

◆ Quaternion() [3/7]

template<typename _Scalar, int _Options>

EIGEN_DEVICE_FUNC Eigen::Quaternion< _Scalar, _Options >::Quaternion ( const Scalar * data )

inlineexplicit

Constructs and initialize a quaternion from the array data

Definition at line 300 of file 3rdparty/Eigen/Eigen/src/Geometry/Quaternion.h.

◆ Quaternion() [4/7]

template<typename _Scalar, int _Options>

template<class Derived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Eigen::Quaternion< _Scalar, _Options >::Quaternion ( const QuaternionBase< Derived > & other )

inline

Copy constructor

Definition at line 303 of file 3rdparty/Eigen/Eigen/src/Geometry/Quaternion.h.

◆ Quaternion() [5/7]

template<typename _Scalar, int _Options>

EIGEN_DEVICE_FUNC Eigen::Quaternion< _Scalar, _Options >::Quaternion ( const AngleAxisType & aa )

inlineexplicit

Constructs and initializes a quaternion from the angle-axis aa

Definition at line 306 of file 3rdparty/Eigen/Eigen/src/Geometry/Quaternion.h.

◆ Quaternion() [6/7]

template<typename _Scalar, int _Options>

template<typename Derived >

EIGEN_DEVICE_FUNC Eigen::Quaternion< _Scalar, _Options >::Quaternion ( const MatrixBase< Derived > & other )

inlineexplicit

Constructs and initializes a quaternion from either:

a rotation matrix expression,
a 4D vector expression representing quaternion coefficients.

Definition at line 313 of file 3rdparty/Eigen/Eigen/src/Geometry/Quaternion.h.

◆ Quaternion() [7/7]

template<typename _Scalar, int _Options>

template<typename OtherScalar , int OtherOptions>

EIGEN_DEVICE_FUNC Eigen::Quaternion< _Scalar, _Options >::Quaternion ( const Quaternion< OtherScalar, OtherOptions > & other )

inlineexplicit

Explicit copy constructor with scalar conversion

Definition at line 317 of file 3rdparty/Eigen/Eigen/src/Geometry/Quaternion.h.

Member Function Documentation

◆ _check_template_params()

template<typename _Scalar, int _Options>

static EIGEN_STRONG_INLINE void Eigen::Quaternion< _Scalar, _Options >::_check_template_params ( )

inlinestaticprotected

Definition at line 353 of file 3rdparty/Eigen/Eigen/src/Geometry/Quaternion.h.

◆ coeffs() [1/2]

template<typename _Scalar, int _Options>

EIGEN_DEVICE_FUNC Coefficients& Eigen::Quaternion< _Scalar, _Options >::coeffs ( )

inline

Definition at line 340 of file 3rdparty/Eigen/Eigen/src/Geometry/Quaternion.h.

◆ coeffs() [2/2]

template<typename _Scalar, int _Options>

EIGEN_DEVICE_FUNC const Coefficients& Eigen::Quaternion< _Scalar, _Options >::coeffs ( ) const

inline

Definition at line 341 of file 3rdparty/Eigen/Eigen/src/Geometry/Quaternion.h.

◆ FromTwoVectors() [1/2]

template<typename _Scalar, int _Options>

template<typename Derived1 , typename Derived2 >

static EIGEN_DEVICE_FUNC Quaternion Eigen::Quaternion< _Scalar, _Options >::FromTwoVectors	(	const MatrixBase< Derived1 > &	a,
		const MatrixBase< Derived2 > &	b
	)

static

◆ FromTwoVectors() [2/2]

template<typename _Scalar, int _Options>

template<typename Derived1 , typename Derived2 >

EIGEN_DEVICE_FUNC Quaternion<Scalar,Options> Eigen::Quaternion< _Scalar, _Options >::FromTwoVectors	(	const MatrixBase< Derived1 > &	a,
		const MatrixBase< Derived2 > &	b
	)

Returns a quaternion representing a rotation between the two arbitrary vectors a and b. In other words, the built rotation represent a rotation sending the line of direction a to the line of direction b, both lines passing through the origin.

Returns: resulting quaternion

Note that the two input vectors do not have to be normalized, and do not need to have the same norm.

Definition at line 705 of file 3rdparty/Eigen/Eigen/src/Geometry/Quaternion.h.

◆ UnitRandom()

template<typename Scalar , int Options>

EIGEN_DEVICE_FUNC Quaternion< Scalar, Options > Eigen::Quaternion< Scalar, Options >::UnitRandom ( )

static

Returns: a random unit quaternion following a uniform distribution law on SO(3)

Note: The implementation is based on http://planning.cs.uiuc.edu/node198.html

Definition at line 679 of file 3rdparty/Eigen/Eigen/src/Geometry/Quaternion.h.

Member Data Documentation

◆ m_coeffs

template<typename _Scalar, int _Options>

Coefficients Eigen::Quaternion< _Scalar, _Options >::m_coeffs

protected

Definition at line 350 of file 3rdparty/Eigen/Eigen/src/Geometry/Quaternion.h.

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

Public Types

Public Member Functions

Static Public Member Functions

Static Protected Member Functions

Protected Attributes

Detailed Description

template<typename _Scalar, int _Options> class Eigen::Quaternion< _Scalar, _Options >

Member Typedef Documentation

◆ AngleAxisType

◆ Base

◆ Coefficients

◆ Scalar

Member Enumeration Documentation

◆ anonymous enum

Constructor & Destructor Documentation

◆ Quaternion() [1/7]

◆ Quaternion() [2/7]

◆ Quaternion() [3/7]

◆ Quaternion() [4/7]

◆ Quaternion() [5/7]

◆ Quaternion() [6/7]

◆ Quaternion() [7/7]

Member Function Documentation

◆ _check_template_params()

◆ coeffs() [1/2]

◆ coeffs() [2/2]

◆ FromTwoVectors() [1/2]

◆ FromTwoVectors() [2/2]

◆ UnitRandom()

Member Data Documentation

◆ m_coeffs

template<typename _Scalar, int _Options>
class Eigen::Quaternion< _Scalar, _Options >