Base class for quaternion expressions. More...

#include <ForwardDeclarations.h>

Inheritance diagram for Eigen::QuaternionBase< Derived >:

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

typedef AngleAxis< Scalar >	AngleAxisType

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

typedef Matrix< Scalar, 3, 3 >	Matrix3

typedef NumTraits< Scalar >::Real	RealScalar

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

typedef Matrix< Scalar, 3, 1 >	Vector3

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

enum

typedef Matrix< Scalar, Dim, Dim >	RotationMatrixType

typedef Matrix< Scalar, Dim, Dim >	RotationMatrixType

typedef ei_traits< Derived >::Scalar	Scalar

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

typedef Matrix< Scalar, Dim, 1 >	VectorType

Public Member Functions
EIGEN_STRONG_INLINE Vector3	_transformVector (Vector3 v) const

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

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

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

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

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

Quaternion< Scalar >	conjugate () const

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

Quaternion< Scalar >	inverse () const

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

Scalar	norm () const

void	normalize ()

Quaternion< Scalar >	normalized () const

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

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

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

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

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

Derived &	operator= (const AngleAxisType &aa)

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

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

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

QuaternionBase &	setIdentity ()

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

template<class OtherDerived >
Quaternion< typename internal::traits< Derived >::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< Derived, 3 >
VectorType	_transformVector (const OtherVectorType &v) const

const Derived &	derived () const

Derived &	derived ()

const Derived &	derived () const

Derived &	derived ()

Derived	inverse () const

Derived	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< Derived, 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
static Quaternion< Scalar >	Identity ()

Private Types
typedef RotationBase< Derived, 3 >	Base

Detailed Description

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

Base class for quaternion expressions.

Template Parameters

Derived derived type (CRTP)

See also: class Quaternion

Definition at line 233 of file ForwardDeclarations.h.

Member Typedef Documentation

template<class Derived>

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

the equivalent angle-axis type

Definition at line 55 of file Geometry/Quaternion.h.

template<class Derived>

typedef RotationBase<Derived, 3> Eigen::QuaternionBase< Derived >::Base

private

Definition at line 37 of file Geometry/Quaternion.h.

template<class Derived>

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

Definition at line 44 of file Geometry/Quaternion.h.

template<class Derived>

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

the equivalent rotation matrix type

Definition at line 53 of file Geometry/Quaternion.h.

template<class Derived>

typedef NumTraits<Scalar>::Real Eigen::QuaternionBase< Derived >::RealScalar

Definition at line 43 of file Geometry/Quaternion.h.

template<class Derived>

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

Definition at line 42 of file Geometry/Quaternion.h.

template<class Derived>

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

the type of a 3D vector

Definition at line 51 of file Geometry/Quaternion.h.

Member Enumeration Documentation

template<class Derived>

anonymous enum

Enumerator
Flags

Definition at line 45 of file Geometry/Quaternion.h.

Member Function Documentation

template<class Derived >

EIGEN_STRONG_INLINE QuaternionBase< Derived >::Vector3 Eigen::QuaternionBase< Derived >::_transformVector ( 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

Definition at line 466 of file Geometry/Quaternion.h.

template<class Derived>

template<class OtherDerived >

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

template<class Derived>

template<class OtherDerived >

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()

Definition at line 670 of file Geometry/Quaternion.h.

template<class Derived>

template<typename NewScalarType >

internal::cast_return_type<Derived,Quaternion<NewScalarType> >::type Eigen::QuaternionBase< Derived >::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 176 of file Geometry/Quaternion.h.

template<class Derived>

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

inline

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

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

template<class Derived>

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

inline

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

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

template<class Derived >

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()

Definition at line 659 of file Geometry/Quaternion.h.

template<class Derived>

template<class OtherDerived >

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()

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

template<class Derived>

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

inlinestatic

Returns: a quaternion representing an identity rotation

See also: MatrixBase::Identity()

Definition at line 105 of file Geometry/Quaternion.h.

template<class Derived >

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

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()

Definition at line 638 of file Geometry/Quaternion.h.

template<class Derived>

template<class OtherDerived >

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()

Definition at line 164 of file Geometry/Quaternion.h.

template<class Derived>

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

inline

Returns: the norm of the quaternion's coefficients

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

Definition at line 119 of file Geometry/Quaternion.h.

template<class Derived>

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

inline

Normalizes the quaternion *this

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

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

template<class Derived>

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

inline

Returns: a normalized copy of *this

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

Definition at line 126 of file Geometry/Quaternion.h.

template<class Derived>

template<class OtherDerived >

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

template<class Derived>

template<class OtherDerived >

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

Definition at line 439 of file Geometry/Quaternion.h.

template<class Derived >

template<class OtherDerived >

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

See also: operator*(Quaternion)

Definition at line 451 of file Geometry/Quaternion.h.

template<class Derived>

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

Definition at line 479 of file Geometry/Quaternion.h.

template<class Derived >

template<class OtherDerived >

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

Definition at line 487 of file Geometry/Quaternion.h.

template<class Derived>

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

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

Definition at line 496 of file Geometry/Quaternion.h.

template<class Derived>

template<class OtherDerived >

Derived& Eigen::QuaternionBase< Derived >::operator= ( const MatrixBase< OtherDerived > & m )

template<class Derived>

template<class MatrixDerived >

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

Definition at line 514 of file Geometry/Quaternion.h.

template<class Derived >

template<typename Derived1 , typename Derived2 >

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.

Definition at line 573 of file Geometry/Quaternion.h.

template<class Derived>

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

inline

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

Definition at line 109 of file Geometry/Quaternion.h.

template<class Derived>

template<class OtherDerived >

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

Returns: an interpolation for a constant motion between other and *this t in [0;1] see http://en.wikipedia.org/wiki/Slerp

template<class Derived>

template<class OtherDerived >

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

Definition at line 686 of file Geometry/Quaternion.h.

template<class Derived>

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

inline

Returns: the squared norm of the quaternion's coefficients

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

Definition at line 114 of file Geometry/Quaternion.h.

template<class Derived >

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.

Definition at line 527 of file Geometry/Quaternion.h.

template<class Derived>

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

inline

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

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

template<class Derived>

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

inline

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

Definition at line 81 of file Geometry/Quaternion.h.

template<class Derived>

Scalar Eigen::QuaternionBase< Derived >::w ( ) const

inline

Returns: the w coefficient

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

template<class Derived>

Scalar& Eigen::QuaternionBase< Derived >::w ( )

inline

Returns: a reference to the w coefficient

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

template<class Derived>

Scalar Eigen::QuaternionBase< Derived >::x ( ) const

inline

Returns: the x coefficient

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

template<class Derived>

Scalar& Eigen::QuaternionBase< Derived >::x ( )

inline

Returns: a reference to the x coefficient

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

template<class Derived>

Scalar Eigen::QuaternionBase< Derived >::y ( ) const

inline

Returns: the y coefficient

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

template<class Derived>

Scalar& Eigen::QuaternionBase< Derived >::y ( )

inline

Returns: a reference to the y coefficient

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

template<class Derived>

Scalar Eigen::QuaternionBase< Derived >::z ( ) const

inline

Returns: the z coefficient

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

template<class Derived>

Scalar& Eigen::QuaternionBase< Derived >::z ( )

inline

Returns: a reference to the z coefficient

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

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

Public Types

Public Member Functions

Static Public Member Functions

Private Types

Detailed Description

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

Member Typedef Documentation

Member Enumeration Documentation

Member Function Documentation

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