Base class for quaternion expressions. More...

#include <Quaternion.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 Member Functions
EIGEN_STRONG_INLINE Vector3	_transformVector (Vector3 v) const
template<class OtherDerived >
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, 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 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 (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 ()
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 35 of file Geometry/Quaternion.h.

Member Typedef Documentation

template<class Derived>

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

the equivalent angle-axis type

Reimplemented in Eigen::Quaternion< _Scalar >, and Eigen::Quaternion< _Scalar >.

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

template<class Derived>

typedef RotationBase<Derived, 3> Eigen::QuaternionBase< Derived >::Base [private]

Reimplemented in Eigen::Map< Quaternion< _Scalar >, _Options >, Eigen::Map< const Quaternion< _Scalar >, _Options >, Eigen::Quaternion< _Scalar >, and Eigen::Quaternion< _Scalar >.

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

template<class Derived>

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

Reimplemented in Eigen::Map< Quaternion< _Scalar >, _Options >, Eigen::Map< const Quaternion< _Scalar >, _Options >, Eigen::Quaternion< _Scalar >, and Eigen::Quaternion< _Scalar >.

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

Reimplemented in Eigen::Quaternion< _Scalar >.

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

the scalar type of the coefficients

Reimplemented from Eigen::RotationBase< Derived, 3 >.

Reimplemented in Eigen::Map< Quaternion< _Scalar >, _Options >, Eigen::Map< const Quaternion< _Scalar >, _Options >, Eigen::Quaternion< _Scalar >, and Eigen::Quaternion< _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

Reimplemented in Eigen::Quaternion< _Scalar >.

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 476 of file Geometry/Quaternion.h.

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 677 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.

Reimplemented in Eigen::Quaternion< _Scalar >.

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)

Reimplemented in Eigen::Map< Quaternion< _Scalar >, _Options >, Eigen::Map< const Quaternion< _Scalar >, _Options >, Eigen::Quaternion< _Scalar >, and Eigen::Quaternion< _Scalar >.

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)

Reimplemented in Eigen::Map< Quaternion< _Scalar >, _Options >, Eigen::Quaternion< _Scalar >, and Eigen::Quaternion< _Scalar >.

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()

Reimplemented in Eigen::Quaternion< _Scalar >.

Definition at line 666 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 ( ) [inline, static]

Returns:: a quaternion representing an identity rotation

See also:: MatrixBase::Identity()

Reimplemented in Eigen::Quaternion< _Scalar >.

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()

Reimplemented from Eigen::RotationBase< Derived, 3 >.

Reimplemented in Eigen::Quaternion< _Scalar >.

Definition at line 645 of file Geometry/Quaternion.h.

template<class Derived>

template<class OtherDerived >

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

Reimplemented in Eigen::Quaternion< _Scalar >.

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()

Reimplemented in Eigen::Quaternion< _Scalar >.

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()

Reimplemented in Eigen::Quaternion< _Scalar >.

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

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 449 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 461 of file Geometry/Quaternion.h.

template<class Derived>

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

Definition at line 489 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 497 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

Reimplemented in Eigen::Quaternion< _Scalar >.

Definition at line 506 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 522 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.

Reimplemented in Eigen::Quaternion< _Scalar >.

Definition at line 581 of file Geometry/Quaternion.h.

template<class Derived>

QuaternionBase& Eigen::QuaternionBase< Derived >::setIdentity ( ) [inline]

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

Reimplemented in Eigen::Quaternion< _Scalar >.

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

template<class Derived >

template<class OtherDerived >

Quaternion< typename internal::traits< Derived >::Scalar > Eigen::QuaternionBase< Derived >::slerp	(	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; the spherical linear interpolation between the two quaternions *this and other at the parameter t

Definition at line 692 of file Geometry/Quaternion.h.

template<class Derived>

Scalar Eigen::QuaternionBase< Derived >::squaredNorm ( ) const [inline]