Detailed Description

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

Base class for quaternion expressions.

This is defined in the Geometry module.

#include <Eigen/Geometry>

Template Parameters

Derived derived type (CRTP)

See Also: class Quaternion

Inheritance diagram for QuaternionBase< Derived >:

Public Types
typedef AngleAxis< Scalar >	AngleAxisType

typedef Matrix< Scalar, 3, 3 >	Matrix3

typedef Matrix< Scalar, Dim, Dim >	RotationMatrixType

typedef Matrix< Scalar, 3, 1 >	Vector3

Public Member Functions
Vector3	_transformVector (const Vector3 &v) 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

RotationMatrixType	matrix () const

Scalar	norm () const

void	normalize ()

Quaternion< Scalar >	normalized () const

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

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

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

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

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

Derived &	operator= (const AngleAxisType &aa)

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< 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 ()

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

Member Typedef Documentation

typedef AngleAxis<Scalar> AngleAxisType

the equivalent angle-axis type

typedef Matrix<Scalar,3,3> Matrix3

the equivalent rotation matrix type

typedef Matrix<Scalar,Dim,Dim> RotationMatrixType

inherited

corresponding linear transformation matrix type

typedef Matrix<Scalar,3,1> Vector3

the type of a 3D vector

Member Function Documentation

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

inline

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

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

inline

Returns: the angle (in radian) between two rotations

See Also: dot()

internal::cast_return_type<Derived,Quaternion<NewScalarType> >::type 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.

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

inline

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

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

inline

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

Quaternion< typename internal::traits< Derived >::Scalar > conjugate ( ) 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()

Scalar 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()

static Quaternion<Scalar> Identity ( )

inlinestatic

Returns: a quaternion representing an identity rotation

See Also: MatrixBase::Identity()

Quaternion< typename internal::traits< Derived >::Scalar > inverse ( ) 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()

bool 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()

RotationMatrixType matrix ( ) const

inlineinherited

Returns: an equivalent rotation matrix This function is added to be conform with the Transform class' naming scheme.

Scalar norm ( ) const

inline

Returns: the norm of the quaternion's coefficients

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

void normalize ( void )

inline

Normalizes the quaternion *this

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

Quaternion<Scalar> normalized ( ) const

inline

Returns: a normalized copy of *this

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

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

inlineinherited

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

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

inlineinherited

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

References RotationBase< Derived, _Dim >::toRotationMatrix().

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

inlineinherited

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

References EigenBase< Derived >::derived().

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

inlineinherited

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

References RotationBase< Derived, _Dim >::toRotationMatrix().

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

inline

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

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

inline

See Also: operator*(Quaternion)

Derived & operator= ( const AngleAxisType & aa )

inline

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

References AngleAxis< Scalar >::angle(), and AngleAxis< Scalar >::axis().

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

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.

References Eigen::ComputeFullV, JacobiSVD< MatrixType, QRPreconditioner >::matrixV(), and MatrixBase< Derived >::normalized().

QuaternionBase& setIdentity ( )

inline

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

Quaternion<typename internal::traits<Derived>::Scalar> 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.

Scalar squaredNorm ( ) const

inline

Returns: the squared norm of the quaternion's coefficients

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

QuaternionBase< Derived >::Matrix3 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.

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

inline

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

Referenced by AngleAxis< Scalar >::operator=().

VectorBlock<Coefficients,3> vec ( )

inline

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

Scalar w ( ) const

inline

Returns: the w coefficient

Referenced by AngleAxis< Scalar >::operator=().

Scalar& w ( )

inline

Returns: a reference to the w coefficient

Scalar x ( ) const

inline

Returns: the x coefficient

Scalar& x ( )

inline

Returns: a reference to the x coefficient

Scalar y ( ) const

inline

Returns: the y coefficient

Scalar& y ( )

inline

Returns: a reference to the y coefficient

Scalar z ( ) const

inline

Returns: the z coefficient

Scalar& z ( )

inline

Returns: a reference to the z coefficient

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

Detailed Description

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

Public Types

Public Member Functions

Static Public Member Functions

Member Typedef Documentation

Member Function Documentation

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