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

#include <Quaternion.h>

Inheritance diagram for Eigen::Quaternion< _Scalar >:

Public Types
typedef AngleAxis< Scalar >	AngleAxisType

typedef Base::AngleAxisType	AngleAxisType

typedef Matrix< Scalar, 4, 1 >	Coefficients

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

typedef Matrix< Scalar, 3, 3 >	Matrix3

typedef _Scalar	Scalar

typedef _Scalar	Scalar

typedef Matrix< Scalar, 3, 1 >	Vector3

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

typedef AngleAxis< Scalar >	AngleAxisType

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

typedef Matrix< Scalar, 3, 3 >	Matrix3

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

enum

typedef Matrix< Scalar, Dim, Dim >	RotationMatrixType

typedef Matrix< Scalar, Dim, Dim >	RotationMatrixType

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

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

typedef Matrix< Scalar, Dim, 1 >	VectorType

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

enum

typedef Matrix< Scalar, Dim, Dim >	RotationMatrixType

typedef Matrix< Scalar, Dim, Dim >	RotationMatrixType

typedef ei_traits< Quaternion< _Scalar > >::Scalar	Scalar

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

typedef Matrix< Scalar, Dim, 1 >	VectorType

Public Member Functions
Scalar	angularDistance (const Quaternion &other) const

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

const Coefficients &	coeffs () const

Coefficients &	coeffs ()

Coefficients &	coeffs ()

const Coefficients &	coeffs () const

Quaternion	conjugate (void) const

Scalar	eigen2_dot (const Quaternion &other) const

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

Quaternion	inverse (void) const

bool	isApprox (const Quaternion &other, typename NumTraits< Scalar >::Real prec=precision< Scalar >()) const

Scalar	norm () const

void	normalize ()

Quaternion	normalized () const

Quaternion	operator* (const Quaternion &q) const

template<typename Derived >
Vector3	operator* (const MatrixBase< Derived > &vec) const

Quaternion &	operator*= (const Quaternion &q)

Quaternion &	operator= (const Quaternion &other)

Quaternion &	operator= (const AngleAxisType &aa)

template<typename Derived >
Quaternion &	operator= (const MatrixBase< Derived > &m)

template<typename Derived >
Quaternion< Scalar > &	operator= (const MatrixBase< Derived > &xpr)

	Quaternion ()

	Quaternion (Scalar w, Scalar x, Scalar y, Scalar z)

	Quaternion (const Quaternion &other)

	Quaternion (const AngleAxisType &aa)

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

template<typename OtherScalarType >
	Quaternion (const Quaternion< OtherScalarType > &other)

	Quaternion ()

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

	Quaternion (const Scalar *data)

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

	Quaternion (const AngleAxisType &aa)

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

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

template<typename Derived1 , typename Derived2 >
Quaternion &	setFromTwoVectors (const MatrixBase< Derived1 > &a, const MatrixBase< Derived2 > &b)

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

Quaternion &	setIdentity ()

Quaternion	slerp (Scalar t, const Quaternion &other) const

Scalar	squaredNorm () const

Matrix3	toRotationMatrix (void) const

const Block< const Coefficients, 3, 1 >	vec () const

Block< Coefficients, 3, 1 >	vec ()

Scalar	w () const

Scalar &	w ()

Scalar	x () const

Scalar &	x ()

Scalar	y () const

Scalar &	y ()

Scalar	z () const

Scalar &	z ()

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

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

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

internal::cast_return_type< Quaternion< _Scalar, _Options >, Quaternion< NewScalarType > >::type	cast () const

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

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

Quaternion< Scalar >	conjugate () const

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

Quaternion< Scalar >	inverse () const

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

Scalar	norm () const

void	normalize ()

Quaternion< Scalar >	normalized () const

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

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

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

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

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

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

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

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

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

QuaternionBase &	setIdentity ()

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

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

Scalar	squaredNorm () const

Matrix3	toRotationMatrix () const

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

VectorBlock< Coefficients, 3 >	vec ()

Scalar	w () const

Scalar &	w ()

Scalar	x () const

Scalar &	x ()

Scalar	y () const

Scalar &	y ()

Scalar	z () const

Scalar &	z ()

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

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

Quaternion< _Scalar, _Options > &	derived ()

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

Quaternion< _Scalar, _Options > &	derived ()

Quaternion< _Scalar, _Options >	inverse () const

Quaternion< _Scalar, _Options >	inverse () const

RotationMatrixType	matrix () const

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

RotationMatrixType	operator* (const Scaling< Scalar, Dim > &s) const

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

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

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

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

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

RotationMatrixType	toRotationMatrix () const

RotationMatrixType	toRotationMatrix () const

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

const Quaternion< _Scalar > &	derived () const

Quaternion< _Scalar > &	derived ()

const Quaternion< _Scalar > &	derived () const

Quaternion< _Scalar > &	derived ()

Quaternion< _Scalar >	inverse () const

Quaternion< _Scalar >	inverse () const

RotationMatrixType	matrix () const

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

RotationMatrixType	operator* (const Scaling< Scalar, Dim > &s) const

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

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

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

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

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

RotationMatrixType	toRotationMatrix () const

RotationMatrixType	toRotationMatrix () const

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

static Quaternion	Identity ()

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

Static Protected Member Functions
static EIGEN_STRONG_INLINE void	_check_template_params ()

Protected Attributes
Coefficients	m_coeffs

Private Types
enum	{ IsAligned = internal::traits<Quaternion>::IsAligned }

typedef RotationBase< Quaternion< _Scalar >, 3 >	Base

typedef QuaternionBase< Quaternion< _Scalar, _Options > >	Base

Detailed Description

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

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

Parameters

_Scalar the scalar type, i.e., the type of the coefficients

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, quatertions 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

See also: class AngleAxis, class Transform

Template Parameters

_Scalar	the scalar type, i.e., the type of the coefficients
_Options	controls the memory alignement of the coeffecients. 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, quatertions 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

See also: class AngleAxis, class Transform

Definition at line 47 of file Eigen2Support/Geometry/Quaternion.h.

Member Typedef Documentation

◆ AngleAxisType [1/2]

template<typename _Scalar>

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

the equivalent angle-axis type

Definition at line 66 of file Eigen2Support/Geometry/Quaternion.h.

◆ AngleAxisType [2/2]

template<typename _Scalar>

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

Definition at line 240 of file Geometry/Quaternion.h.

◆ Base [1/2]

template<typename _Scalar>

typedef RotationBase<Quaternion<_Scalar>,3> Eigen::Quaternion< _Scalar >::Base

private

Definition at line 49 of file Eigen2Support/Geometry/Quaternion.h.

◆ Base [2/2]

template<typename _Scalar>

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

private

Definition at line 230 of file Geometry/Quaternion.h.

◆ Coefficients [1/2]

template<typename _Scalar>

typedef Matrix<Scalar, 4, 1> Eigen::Quaternion< _Scalar >::Coefficients

the type of the Coefficients 4-vector

Definition at line 60 of file Eigen2Support/Geometry/Quaternion.h.

◆ Coefficients [2/2]

template<typename _Scalar>

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

Definition at line 239 of file Geometry/Quaternion.h.

◆ Matrix3

template<typename _Scalar>

typedef Matrix<Scalar,3,3> Eigen::Quaternion< _Scalar >::Matrix3

the equivalent rotation matrix type

Definition at line 64 of file Eigen2Support/Geometry/Quaternion.h.

◆ Scalar [1/2]

template<typename _Scalar>

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

the scalar type of the coefficients

Definition at line 57 of file Eigen2Support/Geometry/Quaternion.h.

◆ Scalar [2/2]

template<typename _Scalar>

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

Definition at line 234 of file Geometry/Quaternion.h.

◆ Vector3

template<typename _Scalar>

typedef Matrix<Scalar,3,1> Eigen::Quaternion< _Scalar >::Vector3

the type of a 3D vector

Definition at line 62 of file Eigen2Support/Geometry/Quaternion.h.

Member Enumeration Documentation

◆ anonymous enum

template<typename _Scalar>

anonymous enum

private

Enumerator
IsAligned

Definition at line 231 of file Geometry/Quaternion.h.

Constructor & Destructor Documentation

◆ Quaternion() [1/13]

template<typename _Scalar>

Eigen::Quaternion< _Scalar >::Quaternion ( )

inline

Default constructor leaving the quaternion uninitialized.

Definition at line 99 of file Eigen2Support/Geometry/Quaternion.h.

◆ Quaternion() [2/13]

template<typename _Scalar>

Eigen::Quaternion< _Scalar >::Quaternion	(	Scalar	w,
		Scalar	x,
		Scalar	y,
		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 108 of file Eigen2Support/Geometry/Quaternion.h.

◆ Quaternion() [3/13]

template<typename _Scalar>

Eigen::Quaternion< _Scalar >::Quaternion ( const Quaternion< _Scalar > & other )

inline

Copy constructor

Definition at line 112 of file Eigen2Support/Geometry/Quaternion.h.

◆ Quaternion() [4/13]

template<typename _Scalar>

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

inlineexplicit

Constructs and initializes a quaternion from the angle-axis aa

Definition at line 115 of file Eigen2Support/Geometry/Quaternion.h.

◆ Quaternion() [5/13]

template<typename _Scalar>

template<typename Derived >

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

inlineexplicit

Constructs and initializes a quaternion from either:

a rotation matrix expression,
a 4D vector expression representing quaternion coefficients.
See also
operator=(MatrixBase<Derived>)

Definition at line 123 of file Eigen2Support/Geometry/Quaternion.h.

◆ Quaternion() [6/13]

template<typename _Scalar>

template<typename OtherScalarType >

Eigen::Quaternion< _Scalar >::Quaternion ( const Quaternion< OtherScalarType > & other )

inlineexplicit

Copy constructor with scalar type conversion

Definition at line 192 of file Eigen2Support/Geometry/Quaternion.h.

◆ Quaternion() [7/13]

template<typename _Scalar>

Eigen::Quaternion< _Scalar >::Quaternion ( )

inline

Default constructor leaving the quaternion uninitialized.

Definition at line 243 of file Geometry/Quaternion.h.

◆ Quaternion() [8/13]

template<typename _Scalar>

Eigen::Quaternion< _Scalar >::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 252 of file Geometry/Quaternion.h.

◆ Quaternion() [9/13]

template<typename _Scalar>

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

inline

Constructs and initialize a quaternion from the array data

Definition at line 255 of file Geometry/Quaternion.h.

◆ Quaternion() [10/13]

template<typename _Scalar>

template<class Derived >

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

inline

Copy constructor

Definition at line 258 of file Geometry/Quaternion.h.

◆ Quaternion() [11/13]

template<typename _Scalar>

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

inlineexplicit

Constructs and initializes a quaternion from the angle-axis aa

Definition at line 261 of file Geometry/Quaternion.h.

◆ Quaternion() [12/13]

template<typename _Scalar>

template<typename Derived >

Eigen::Quaternion< _Scalar >::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 268 of file Geometry/Quaternion.h.

◆ Quaternion() [13/13]

template<typename _Scalar>

template<typename OtherScalar , int OtherOptions>

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

inlineexplicit

Explicit copy constructor with scalar conversion

Definition at line 272 of file Geometry/Quaternion.h.

Member Function Documentation

◆ _check_template_params()

template<typename _Scalar>

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

inlinestaticprotected

Definition at line 287 of file Geometry/Quaternion.h.

◆ angularDistance()

template<typename Scalar >

Scalar Quaternion::angularDistance ( const Quaternion< _Scalar > & other ) const

inline

Returns: the angle (in radian) between two rotations

See also: eigen2_dot()

Definition at line 404 of file Eigen2Support/Geometry/Quaternion.h.

◆ cast()

template<typename _Scalar>

template<typename NewScalarType >

internal::cast_return_type<Quaternion,Quaternion<NewScalarType> >::type Eigen::Quaternion< _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.

Definition at line 187 of file Eigen2Support/Geometry/Quaternion.h.

◆ coeffs() [1/4]

template<typename _Scalar>

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

inline

Returns: a read-only vector expression of the coefficients (x,y,z,w)

Definition at line 93 of file Eigen2Support/Geometry/Quaternion.h.

◆ coeffs() [2/4]

template<typename _Scalar>

Coefficients& Eigen::Quaternion< _Scalar >::coeffs ( )

inline

Returns: a vector expression of the coefficients (x,y,z,w)

Definition at line 96 of file Eigen2Support/Geometry/Quaternion.h.

◆ coeffs() [3/4]

template<typename _Scalar>

Coefficients& Eigen::Quaternion< _Scalar >::coeffs ( )

inline

Definition at line 278 of file Geometry/Quaternion.h.

◆ coeffs() [4/4]

template<typename _Scalar>

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

inline

Definition at line 279 of file Geometry/Quaternion.h.

◆ conjugate()

template<typename Scalar >

Quaternion< Scalar > Quaternion::conjugate ( void ) const

inline

Returns: the conjugate of the *this which is equal to the multiplicative inverse if the quaternion is normalized. The conjugate of a quaternion represents the opposite rotation.

See also: Quaternion::inverse()

Definition at line 395 of file Eigen2Support/Geometry/Quaternion.h.

◆ eigen2_dot()

template<typename _Scalar>

Scalar Eigen::Quaternion< _Scalar >::eigen2_dot ( const Quaternion< _Scalar > & other ) const

inline

Returns: the dot product of *this and other Geometrically speaking, the dot product of two unit quaternions corresponds to the cosine of half the angle between the two rotations.

See also: angularDistance()

Definition at line 161 of file Eigen2Support/Geometry/Quaternion.h.

◆ FromTwoVectors() [1/2]

template<typename _Scalar>

template<typename Derived1 , typename Derived2 >

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

static

◆ FromTwoVectors() [2/2]

template<typename _Scalar>

template<typename Derived1 , typename Derived2 >

Quaternion<Scalar,Options> Eigen::Quaternion< _Scalar >::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 623 of file Geometry/Quaternion.h.

◆ Identity()

template<typename _Scalar>

static Quaternion Eigen::Quaternion< _Scalar >::Identity ( )

inlinestatic

Returns: a quaternion representing an identity rotation

See also: MatrixBase::Identity()

Definition at line 133 of file Eigen2Support/Geometry/Quaternion.h.

◆ inverse()

template<typename Scalar >

Quaternion< Scalar > Quaternion::inverse ( void ) const

inline

Returns: the multiplicative inverse of *this Note that in most cases, i.e., if you simply want the opposite rotation, and/or the quaternion is normalized, then it is enough to use the conjugate.

See also: Quaternion::conjugate()

Definition at line 375 of file Eigen2Support/Geometry/Quaternion.h.

◆ isApprox()

template<typename _Scalar>

bool Eigen::Quaternion< _Scalar >::isApprox	(	const Quaternion< _Scalar > &	other,
		typename NumTraits< Scalar >::Real	prec = `precision<Scalar>()`
	)		const

inline

Returns: true if *this is approximately equal to other, within the precision determined by prec.

See also: MatrixBase::isApprox()

Definition at line 199 of file Eigen2Support/Geometry/Quaternion.h.

◆ norm()

template<typename _Scalar>

Scalar Eigen::Quaternion< _Scalar >::norm ( ) const

inline

Returns: the norm of the quaternion's coefficients

See also: Quaternion::squaredNorm(), MatrixBase::norm()

Definition at line 147 of file Eigen2Support/Geometry/Quaternion.h.

◆ normalize()

template<typename _Scalar>

void Eigen::Quaternion< _Scalar >::normalize ( void )

inline

Normalizes the quaternion *this

See also: normalized(), MatrixBase::normalize()

Definition at line 151 of file Eigen2Support/Geometry/Quaternion.h.

◆ normalized()

template<typename _Scalar>

Quaternion Eigen::Quaternion< _Scalar >::normalized ( ) const

inline

Returns: a normalized version of *this

See also: normalize(), MatrixBase::normalized()

Definition at line 154 of file Eigen2Support/Geometry/Quaternion.h.

◆ operator*() [1/2]

template<typename Scalar >

Quaternion< Scalar > Quaternion::operator* ( const Quaternion< _Scalar > & other ) const

inline

Returns: the concatenation of two rotations as a quaternion-quaternion product

Definition at line 228 of file Eigen2Support/Geometry/Quaternion.h.

◆ operator*() [2/2]

template<typename Scalar >

template<typename Derived >

Quaternion< Scalar >::Vector3 Quaternion::operator* ( const MatrixBase< Derived > & v ) const

inline

Rotation of a vector by a quaternion.

Remarks

If the quaternion is used to rotate several points (>1) then it is much more efficient to first convert it to a 3x3 Matrix. Comparison of the operation cost for n transformations:

Quaternion: 30n
Via a Matrix3: 24 + 15n

Definition at line 250 of file Eigen2Support/Geometry/Quaternion.h.

◆ operator*=()

template<typename Scalar >

Quaternion< Scalar > & Quaternion::operator*= ( const Quaternion< _Scalar > & other )

inline

See also: operator*(Quaternion)

Definition at line 235 of file Eigen2Support/Geometry/Quaternion.h.

◆ operator=() [1/4]

template<typename Scalar >

Quaternion< Scalar > & Quaternion::operator= ( const Quaternion< _Scalar > & other )

inline

Definition at line 263 of file Eigen2Support/Geometry/Quaternion.h.

◆ operator=() [2/4]

template<typename Scalar >

Quaternion< Scalar > & Quaternion::operator= ( const AngleAxisType & aa )

inline

Set *this from an angle-axis aa and returns a reference to *this

Definition at line 272 of file Eigen2Support/Geometry/Quaternion.h.

◆ operator=() [3/4]

template<typename _Scalar>

template<typename Derived >

Quaternion& Eigen::Quaternion< _Scalar >::operator= ( const MatrixBase< Derived > & m )

◆ operator=() [4/4]

template<typename _Scalar>

template<typename Derived >

Quaternion<Scalar>& Eigen::Quaternion< _Scalar >::operator= ( const MatrixBase< Derived > & xpr )

inline

Set *this from the expression xpr:

if xpr is a 4x1 vector, then xpr is assumed to be a quaternion
if xpr is a 3x3 matrix, then xpr is assumed to be rotation matrix and xpr is converted to a quaternion

Definition at line 287 of file Eigen2Support/Geometry/Quaternion.h.

◆ setFromTwoVectors() [1/2]

template<typename _Scalar>

template<typename Derived1 , typename Derived2 >

Quaternion& Eigen::Quaternion< _Scalar >::setFromTwoVectors	(	const MatrixBase< Derived1 > &	a,
		const MatrixBase< Derived2 > &	b
	)

◆ setFromTwoVectors() [2/2]

template<typename _Scalar>

template<typename Derived1 , typename Derived2 >

Quaternion<Scalar>& Eigen::Quaternion< _Scalar >::setFromTwoVectors	(	const MatrixBase< Derived1 > &	a,
		const MatrixBase< Derived2 > &	b
	)

inline

Sets *this to be a quaternion representing a rotation sending the vector a to the vector b.

Returns: a reference to *this.

Note that the two input vectors do not have to be normalized.

Definition at line 338 of file Eigen2Support/Geometry/Quaternion.h.

◆ setIdentity()

template<typename _Scalar>

Quaternion& Eigen::Quaternion< _Scalar >::setIdentity ( )

inline

See also: Quaternion::Identity(), MatrixBase::setIdentity()

Definition at line 137 of file Eigen2Support/Geometry/Quaternion.h.

◆ slerp()

template<typename Scalar >

Quaternion< Scalar > Quaternion::slerp	(	Scalar	t,
		const Quaternion< _Scalar > &	other
	)		const

Returns: the spherical linear interpolation between the two quaternions *this and other at the parameter t

Definition at line 416 of file Eigen2Support/Geometry/Quaternion.h.

◆ squaredNorm()

template<typename _Scalar>

Scalar Eigen::Quaternion< _Scalar >::squaredNorm ( ) const

inline

Returns: the squared norm of the quaternion's coefficients

See also: Quaternion::norm(), MatrixBase::squaredNorm()

Definition at line 142 of file Eigen2Support/Geometry/Quaternion.h.

◆ toRotationMatrix()

template<typename Scalar >

Quaternion< Scalar >::Matrix3 Quaternion::toRotationMatrix ( void ) const

inline

Convert the quaternion to a 3x3 rotation matrix

Definition at line 296 of file Eigen2Support/Geometry/Quaternion.h.

◆ vec() [1/2]

template<typename _Scalar>

const Block<const Coefficients,3,1> Eigen::Quaternion< _Scalar >::vec ( ) const

inline

Returns: a read-only vector expression of the imaginary part (x,y,z)

Definition at line 87 of file Eigen2Support/Geometry/Quaternion.h.

◆ vec() [2/2]

template<typename _Scalar>

Block<Coefficients,3,1> Eigen::Quaternion< _Scalar >::vec ( )

inline

Returns: a vector expression of the imaginary part (x,y,z)

Definition at line 90 of file Eigen2Support/Geometry/Quaternion.h.

◆ w() [1/2]

template<typename _Scalar>

Scalar Eigen::Quaternion< _Scalar >::w ( ) const

inline

Returns: the w coefficient

Definition at line 75 of file Eigen2Support/Geometry/Quaternion.h.

◆ w() [2/2]

template<typename _Scalar>

Scalar& Eigen::Quaternion< _Scalar >::w ( )

inline

Returns: a reference to the w coefficient

Definition at line 84 of file Eigen2Support/Geometry/Quaternion.h.

◆ x() [1/2]

template<typename _Scalar>

Scalar Eigen::Quaternion< _Scalar >::x ( ) const

inline

Returns: the x coefficient

Definition at line 69 of file Eigen2Support/Geometry/Quaternion.h.

◆ x() [2/2]

template<typename _Scalar>

Scalar& Eigen::Quaternion< _Scalar >::x ( )

inline

Returns: a reference to the x coefficient

Definition at line 78 of file Eigen2Support/Geometry/Quaternion.h.

◆ y() [1/2]

template<typename _Scalar>

Scalar Eigen::Quaternion< _Scalar >::y ( ) const

inline

Returns: the y coefficient

Definition at line 71 of file Eigen2Support/Geometry/Quaternion.h.

◆ y() [2/2]

template<typename _Scalar>

Scalar& Eigen::Quaternion< _Scalar >::y ( )

inline

Returns: a reference to the y coefficient

Definition at line 80 of file Eigen2Support/Geometry/Quaternion.h.

◆ z() [1/2]

template<typename _Scalar>

Scalar Eigen::Quaternion< _Scalar >::z ( ) const

inline

Returns: the z coefficient

Definition at line 73 of file Eigen2Support/Geometry/Quaternion.h.

◆ z() [2/2]

template<typename _Scalar>

Scalar& Eigen::Quaternion< _Scalar >::z ( )

inline

Returns: a reference to the z coefficient

Definition at line 82 of file Eigen2Support/Geometry/Quaternion.h.

Member Data Documentation

◆ m_coeffs

template<typename _Scalar>

Coefficients Quaternion::m_coeffs

protected

Definition at line 203 of file Eigen2Support/Geometry/Quaternion.h.

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

Eigen2Support/Geometry/Quaternion.h

Public Types

Public Member Functions

Static Public Member Functions

Static Protected Member Functions

Protected Attributes

Private Types

Detailed Description

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

Member Typedef Documentation

◆ AngleAxisType [1/2]

◆ AngleAxisType [2/2]

◆ Base [1/2]

◆ Base [2/2]

◆ Coefficients [1/2]

◆ Coefficients [2/2]

◆ Matrix3

◆ Scalar [1/2]

◆ Scalar [2/2]

◆ Vector3

Member Enumeration Documentation

◆ anonymous enum

Constructor & Destructor Documentation

◆ Quaternion() [1/13]

◆ Quaternion() [2/13]

◆ Quaternion() [3/13]

◆ Quaternion() [4/13]

◆ Quaternion() [5/13]

◆ Quaternion() [6/13]

◆ Quaternion() [7/13]

◆ Quaternion() [8/13]

◆ Quaternion() [9/13]

◆ Quaternion() [10/13]

◆ Quaternion() [11/13]

◆ Quaternion() [12/13]

◆ Quaternion() [13/13]

Member Function Documentation

◆ _check_template_params()

◆ angularDistance()

◆ cast()

◆ coeffs() [1/4]

◆ coeffs() [2/4]

◆ coeffs() [3/4]

◆ coeffs() [4/4]

◆ conjugate()

◆ eigen2_dot()

◆ FromTwoVectors() [1/2]

◆ FromTwoVectors() [2/2]

◆ Identity()

◆ inverse()

◆ isApprox()

◆ norm()

◆ normalize()

◆ normalized()

◆ operator*() [1/2]

◆ operator*() [2/2]

◆ operator*=()

◆ operator=() [1/4]

◆ operator=() [2/4]

◆ operator=() [3/4]

◆ operator=() [4/4]

◆ setFromTwoVectors() [1/2]

◆ setFromTwoVectors() [2/2]

◆ setIdentity()

◆ slerp()

◆ squaredNorm()

◆ toRotationMatrix()

◆ vec() [1/2]

◆ vec() [2/2]

◆ w() [1/2]

◆ w() [2/2]

◆ x() [1/2]

◆ x() [2/2]

◆ y() [1/2]

◆ y() [2/2]

◆ z() [1/2]

◆ z() [2/2]

Member Data Documentation

◆ m_coeffs

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