Base class for quaternion expressions. More...

#include <Quaternion.h>

Public Types
enum	{ Flags = Eigen::internal::traits<Derived>::Flags }

typedef RotationBase< Derived, 3 >	Base

typedef internal::traits< Derived >::Scalar	Scalar

typedef NumTraits< Scalar >::Real	RealScalar

typedef internal::traits< Derived >::Coefficients	Coefficients

typedef Coefficients::CoeffReturnType	CoeffReturnType

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

typedef Matrix< Scalar, 3, 1 >	Vector3

typedef Matrix< Scalar, 3, 3 >	Matrix3

typedef AngleAxis< Scalar >	AngleAxisType

Public Member Functions
EIGEN_DEVICE_FUNC CoeffReturnType	x () const

EIGEN_DEVICE_FUNC CoeffReturnType	y () const

EIGEN_DEVICE_FUNC CoeffReturnType	z () const

EIGEN_DEVICE_FUNC CoeffReturnType	w () const

EIGEN_DEVICE_FUNC NonConstCoeffReturnType	x ()

EIGEN_DEVICE_FUNC NonConstCoeffReturnType	y ()

EIGEN_DEVICE_FUNC NonConstCoeffReturnType	z ()

EIGEN_DEVICE_FUNC NonConstCoeffReturnType	w ()

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

EIGEN_DEVICE_FUNC VectorBlock< Coefficients, 3 >	vec ()

EIGEN_DEVICE_FUNC const internal::traits< Derived >::Coefficients &	coeffs () const

EIGEN_DEVICE_FUNC internal::traits< Derived >::Coefficients &	coeffs ()

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE QuaternionBase< Derived > &	operator= (const QuaternionBase< Derived > &other)

template<class OtherDerived >
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived &	operator= (const QuaternionBase< OtherDerived > &other)

EIGEN_DEVICE_FUNC Derived &	operator= (const AngleAxisType &aa)

template<class OtherDerived >
EIGEN_DEVICE_FUNC Derived &	operator= (const MatrixBase< OtherDerived > &m)

EIGEN_DEVICE_FUNC QuaternionBase &	setIdentity ()

EIGEN_DEVICE_FUNC Scalar	squaredNorm () const

EIGEN_DEVICE_FUNC Scalar	norm () const

EIGEN_DEVICE_FUNC void	normalize ()

EIGEN_DEVICE_FUNC Quaternion< Scalar >	normalized () const

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

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

EIGEN_DEVICE_FUNC Matrix3	toRotationMatrix () const

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

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

template<class OtherDerived >
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived &	operator*= (const QuaternionBase< OtherDerived > &q)

EIGEN_DEVICE_FUNC Quaternion< Scalar >	inverse () const

EIGEN_DEVICE_FUNC Quaternion< Scalar >	conjugate () const

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

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

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

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

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Vector3	_transformVector (const Vector3 &v) const

template<typename NewScalarType >
EIGEN_DEVICE_FUNC internal::enable_if< internal::is_same< Scalar, NewScalarType >::value, const Derived & >::type	cast () const

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

template<class OtherDerived >
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Quaternion< typename internal::traits< Derived >::Scalar >	operator* (const QuaternionBase< OtherDerived > &other) const

template<class MatrixDerived >
EIGEN_DEVICE_FUNC Derived &	operator= (const MatrixBase< MatrixDerived > &xpr)

template<class OtherDerived >
EIGEN_DEVICE_FUNC internal::traits< Derived >::Scalar	angularDistance (const QuaternionBase< OtherDerived > &other) const

template<class OtherDerived >
EIGEN_DEVICE_FUNC Quaternion< typename internal::traits< Derived >::Scalar >	slerp (const Scalar &t, const QuaternionBase< OtherDerived > &other) 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

template<typename OtherDerived >
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE internal::rotation_base_generic_product_selector< Derived, OtherDerived, OtherDerived::IsVectorAtCompileTime >::ReturnType	operator* (const EigenBase< OtherDerived > &e) const

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

EIGEN_DEVICE_FUNC const Derived &	derived () const

EIGEN_DEVICE_FUNC Derived &	derived ()

Static Public Member Functions
static EIGEN_DEVICE_FUNC Quaternion< Scalar >	Identity ()

Friends
std::ostream &	operator<< (std::ostream &s, const QuaternionBase< Derived > &q)

template<typename OtherDerived >
EIGEN_DEVICE_FUNC RotationMatrixType	operator* (const EigenBase< OtherDerived > &l, const Derived &r)

EIGEN_DEVICE_FUNC friend Transform< Scalar, Dim, Affine >	operator* (const DiagonalMatrix< Scalar, Dim > &l, const Derived &r)

Detailed Description

template<class Derived>
class Eigen::QuaternionBase< Derived >

Base class for quaternion expressions.

\geometry_module

Template Parameters

Derived derived type (CRTP)

See also: class Quaternion

Member Typedef Documentation

◆ AngleAxisType

template<class Derived >

typedef AngleAxis<Scalar> Eigen::QuaternionBase< Derived >::AngleAxisType

the equivalent angle-axis type

◆ Matrix3

template<class Derived >

typedef Matrix<Scalar,3,3> Eigen::QuaternionBase< Derived >::Matrix3

the equivalent rotation matrix type

◆ Vector3

template<class Derived >

typedef Matrix<Scalar,3,1> Eigen::QuaternionBase< Derived >::Vector3

the type of a 3D vector

Member Function Documentation

◆ _transformVector()

template<class Derived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE QuaternionBase< Derived >::Vector3 Eigen::QuaternionBase< Derived >::_transformVector ( const Vector3 & v ) const

return the result vector of v through the rotation

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:

Quaternion2: 30n
Via a Matrix3: 24 + 15n

◆ angularDistance()

template<class Derived >

template<class OtherDerived >

EIGEN_DEVICE_FUNC internal::traits<Derived>::Scalar Eigen::QuaternionBase< Derived >::angularDistance ( const QuaternionBase< OtherDerived > & other ) const

inline

Returns: the angle (in radian) between two rotations

See also: dot()

◆ coeffs() [1/2]

template<class Derived >

EIGEN_DEVICE_FUNC internal::traits<Derived>::Coefficients& Eigen::QuaternionBase< Derived >::coeffs ( )

inline

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

◆ coeffs() [2/2]

template<class Derived >

EIGEN_DEVICE_FUNC const internal::traits<Derived>::Coefficients& Eigen::QuaternionBase< Derived >::coeffs ( ) const

inline

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

◆ conjugate()

template<class Derived >

EIGEN_DEVICE_FUNC Quaternion< typename internal::traits< Derived >::Scalar > Eigen::QuaternionBase< Derived >::conjugate ( void ) const

inline

Returns: the conjugated quaternion; 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: Quaternion2::inverse()

◆ dot()

template<class Derived >

template<class OtherDerived >

EIGEN_DEVICE_FUNC Scalar Eigen::QuaternionBase< Derived >::dot ( const QuaternionBase< OtherDerived > & 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()

◆ Identity()

template<class Derived >

static EIGEN_DEVICE_FUNC Quaternion<Scalar> Eigen::QuaternionBase< Derived >::Identity ( )

inlinestatic

Returns: a quaternion representing an identity rotation

See also: MatrixBase::Identity()

◆ inverse()

template<class Derived >

EIGEN_DEVICE_FUNC Quaternion< typename internal::traits< Derived >::Scalar > Eigen::QuaternionBase< Derived >::inverse

inline

Returns: the quaternion describing the inverse rotation; 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: QuaternionBase::conjugate()

◆ isApprox()

template<class Derived >

template<class OtherDerived >

EIGEN_DEVICE_FUNC bool Eigen::QuaternionBase< Derived >::isApprox	(	const QuaternionBase< OtherDerived > &	other,
		const RealScalar &	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()

◆ norm()

template<class Derived >

EIGEN_DEVICE_FUNC Scalar Eigen::QuaternionBase< Derived >::norm ( ) const

inline

Returns: the norm of the quaternion's coefficients

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

◆ normalize()

template<class Derived >

EIGEN_DEVICE_FUNC void Eigen::QuaternionBase< Derived >::normalize ( void )

inline

Normalizes the quaternion *this

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

◆ normalized()

template<class Derived >

EIGEN_DEVICE_FUNC Quaternion<Scalar> Eigen::QuaternionBase< Derived >::normalized ( ) const

inline

Returns: a normalized copy of *this

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

◆ operator!=()

template<class Derived >

template<class OtherDerived >

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

inline

Returns: true if at least one pair of coefficients of *this and other are not exactly equal to each other.

Warning: When using floating point scalar values you probably should rather use a fuzzy comparison such as isApprox()

See also: isApprox(), operator==

◆ operator*() [1/5]

template<class Derived >

template<typename OtherDerived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE internal::rotation_base_generic_product_selector<Derived,OtherDerived,OtherDerived::IsVectorAtCompileTime>::ReturnType Eigen::RotationBase< Derived, _Dim >::operator* ( typename OtherDerived )

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*() [2/5]

template<class Derived >

template<class OtherDerived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Quaternion<typename internal::traits<Derived>::Scalar> Eigen::QuaternionBase< Derived >::operator* ( const QuaternionBase< OtherDerived > & other ) const

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

◆ operator*() [3/5]

template<class Derived >

template<int Mode, int Options>

EIGEN_DEVICE_FUNC Transform<Scalar,Dim,Mode> Eigen::RotationBase< Derived, _Dim >::operator*	(	int	Mode,
		int	Options
	)

inline

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

◆ operator*() [4/5]

template<class Derived >

EIGEN_DEVICE_FUNC Transform<Scalar,Dim,Isometry> Eigen::RotationBase< Derived, _Dim >::operator*

inline

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

◆ operator*() [5/5]

template<class Derived >

EIGEN_DEVICE_FUNC RotationMatrixType Eigen::RotationBase< Derived, _Dim >::operator*

inline

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

◆ operator*=()

template<class Derived >

template<class OtherDerived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived & Eigen::QuaternionBase< Derived >::operator*= ( const QuaternionBase< OtherDerived > & other )

See also: operator*(Quaternion)

◆ operator=() [1/2]

template<class Derived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived & Eigen::QuaternionBase< Derived >::operator= ( const AngleAxisType & aa )

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

◆ operator=() [2/2]

template<class Derived >

template<class MatrixDerived >

EIGEN_DEVICE_FUNC Derived& Eigen::QuaternionBase< Derived >::operator= ( const MatrixBase< MatrixDerived > & 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

◆ operator==()

template<class Derived >

template<class OtherDerived >

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

inline

Returns: true if each coefficients of *this and other are all exactly equal.

Warning: When using floating point scalar values you probably should rather use a fuzzy comparison such as isApprox()

See also: isApprox(), operator!=

◆ setFromTwoVectors()

template<class Derived >

template<typename Derived1 , typename Derived2 >

EIGEN_DEVICE_FUNC Derived & Eigen::QuaternionBase< Derived >::setFromTwoVectors	(	const MatrixBase< Derived1 > &	a,
		const MatrixBase< Derived2 > &	b
	)

inline

Returns: the quaternion which transform a into b through a rotation

Sets *this to be 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: a reference to *this.

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

◆ setIdentity()

template<class Derived >

EIGEN_DEVICE_FUNC QuaternionBase& Eigen::QuaternionBase< Derived >::setIdentity ( )

inline

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

◆ slerp()

template<class Derived >

template<class OtherDerived >

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

Returns: the spherical linear interpolation between the two quaternions *this and other at the parameter t in [0;1].

This represents an interpolation for a constant motion between *this and other, see also http://en.wikipedia.org/wiki/Slerp.

◆ squaredNorm()

template<class Derived >

EIGEN_DEVICE_FUNC Scalar Eigen::QuaternionBase< Derived >::squaredNorm ( ) const

inline

Returns: the squared norm of the quaternion's coefficients

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

◆ toRotationMatrix()

template<class Derived >

EIGEN_DEVICE_FUNC QuaternionBase< Derived >::Matrix3 Eigen::QuaternionBase< Derived >::toRotationMatrix ( void ) const

inline

Returns: an equivalent 3x3 rotation matrix

Convert the quaternion to a 3x3 rotation matrix. The quaternion is required to be normalized, otherwise the result is undefined.

◆ vec() [1/2]

template<class Derived >

EIGEN_DEVICE_FUNC VectorBlock<Coefficients,3> Eigen::QuaternionBase< Derived >::vec ( )

inline

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

◆ vec() [2/2]

template<class Derived >

EIGEN_DEVICE_FUNC const VectorBlock<const Coefficients,3> Eigen::QuaternionBase< Derived >::vec ( ) const

inline

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

◆ w() [1/2]

template<class Derived >

EIGEN_DEVICE_FUNC NonConstCoeffReturnType Eigen::QuaternionBase< Derived >::w ( )

inline

Returns: a reference to the w coefficient (if Derived is a non-const lvalue)

◆ w() [2/2]

template<class Derived >

EIGEN_DEVICE_FUNC CoeffReturnType Eigen::QuaternionBase< Derived >::w ( ) const

inline

Returns: the w coefficient

◆ x() [1/2]

template<class Derived >

EIGEN_DEVICE_FUNC NonConstCoeffReturnType Eigen::QuaternionBase< Derived >::x ( )

inline

Returns: a reference to the x coefficient (if Derived is a non-const lvalue)

◆ x() [2/2]

template<class Derived >

EIGEN_DEVICE_FUNC CoeffReturnType Eigen::QuaternionBase< Derived >::x ( ) const

inline

Returns: the x coefficient

◆ y() [1/2]

template<class Derived >

EIGEN_DEVICE_FUNC NonConstCoeffReturnType Eigen::QuaternionBase< Derived >::y ( )

inline

Returns: a reference to the y coefficient (if Derived is a non-const lvalue)

◆ y() [2/2]

template<class Derived >

EIGEN_DEVICE_FUNC CoeffReturnType Eigen::QuaternionBase< Derived >::y ( ) const

inline

Returns: the y coefficient

◆ z() [1/2]

template<class Derived >

EIGEN_DEVICE_FUNC NonConstCoeffReturnType Eigen::QuaternionBase< Derived >::z ( )

inline

Returns: a reference to the z coefficient (if Derived is a non-const lvalue)

◆ z() [2/2]

template<class Derived >

EIGEN_DEVICE_FUNC CoeffReturnType Eigen::QuaternionBase< Derived >::z ( ) const

inline

Returns: the z coefficient

Friends And Related Function Documentation

◆ operator* [1/2]

template<class Derived >

EIGEN_DEVICE_FUNC friend Transform<Scalar,Dim,Affine> operator*

friend

Returns: the concatenation of a scaling l with the rotation r

◆ operator* [2/2]

template<class Derived >

template<typename OtherDerived >

EIGEN_DEVICE_FUNC RotationMatrixType operator* ( typename OtherDerived )

friend

Returns: the concatenation of a linear transformation l with the rotation r

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

Public Types

Public Member Functions

Static Public Member Functions

Friends

Detailed Description

template<class Derived> class Eigen::QuaternionBase< Derived >

Member Typedef Documentation

◆ AngleAxisType

◆ Matrix3

◆ Vector3

Member Function Documentation

◆ _transformVector()

◆ angularDistance()

◆ coeffs() [1/2]

◆ coeffs() [2/2]

◆ conjugate()

◆ dot()

◆ Identity()

◆ inverse()

◆ isApprox()

◆ norm()

◆ normalize()

◆ normalized()

◆ operator!=()

◆ operator*() [1/5]

◆ operator*() [2/5]

◆ operator*() [3/5]

◆ operator*() [4/5]

◆ operator*() [5/5]

◆ operator*=()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ operator==()

◆ setFromTwoVectors()

◆ 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]

Friends And Related Function Documentation

◆ operator* [1/2]

◆ operator* [2/2]

template<class Derived>
class Eigen::QuaternionBase< Derived >