Eigen::QuaternionBase

template<class 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


typedef AngleAxis< Scalar >	AngleAxisType

typedef Matrix< Scalar, 3, 3 >	Matrix3

typedef Matrix< Scalar, 3, 1 >	Vector3

Public Types inherited from Eigen::RotationBase< Derived, 3 >
typedef Matrix< Scalar, Dim, Dim >	RotationMatrixType

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


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

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

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

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

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

VectorBlock< Coefficients, 3 >	vec ()

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

NonConstCoeffReturnType	w ()

CoeffReturnType	w () const

NonConstCoeffReturnType	x ()

CoeffReturnType	x () const

NonConstCoeffReturnType	y ()

CoeffReturnType	y () const

NonConstCoeffReturnType	z ()

CoeffReturnType	z () const

Public Member Functions inherited from Eigen::RotationBase< Derived, 3 >
Derived	inverse () const

RotationMatrixType	matrix () 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

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

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

RotationMatrixType	toRotationMatrix () const


static Quaternion< Scalar >	Identity ()

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

_transformVector()

template<class Derived >

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

(

const Vector3 &

)

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

angularDistance()

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()

cast()

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.

coeffs() [1/2]

template<class Derived >

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 >

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 >

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 >

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 Quaternion<Scalar> Eigen::QuaternionBase< Derived >::Identity

(

)

inlinestatic

Returns: a quaternion representing an identity rotation

See also: MatrixBase::Identity()

inverse()

template<class Derived >

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 >

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 >

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 >

void Eigen::QuaternionBase< Derived >::normalize

(

void

)

inline

Normalizes the quaternion *this

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

normalized()

template<class Derived >

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 >

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*()

template<class Derived >

template<class OtherDerived >

Quaternion<typename internal::traits<Derived>::Scalar> Eigen::QuaternionBase< Derived >::operator*

(

const QuaternionBase< OtherDerived > &

other

)

const

inline

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

operator*=()

template<class Derived >

template<class OtherDerived >

Derived & Eigen::QuaternionBase< Derived >::operator*=

(

const QuaternionBase< OtherDerived > &

other

)

inline

See also: operator*(Quaternion)

operator=() [1/2]

template<class Derived >

Derived & Eigen::QuaternionBase< Derived >::operator=

(

const AngleAxisType &

)

inline

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

operator=() [2/2]

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

operator==()

template<class Derived >

template<class OtherDerived >

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 >

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 >

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

(

)

inline

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

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 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 >

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 >

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 >

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 >

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 >

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 >

CoeffReturnType Eigen::QuaternionBase< Derived >::w

(

)

const

inline

Returns: the w coefficient

x() [1/2]

template<class Derived >

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 >

CoeffReturnType Eigen::QuaternionBase< Derived >::x

(

)

const

inline

Returns: the x coefficient

y() [1/2]

template<class Derived >

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 >

CoeffReturnType Eigen::QuaternionBase< Derived >::y

(

)

const

inline

Returns: the y coefficient

z() [1/2]

template<class Derived >

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 >

CoeffReturnType Eigen::QuaternionBase< Derived >::z

(

)

const

inline

Returns: the z coefficient

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

Quaternion.h

Eigen::QuaternionBase

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

AngleAxisType

Matrix3

Vector3

_transformVector()

angularDistance()

cast()

coeffs() [1/2]

coeffs() [2/2]

conjugate()

dot()

Identity()

inverse()

isApprox()

norm()

normalize()

normalized()

operator!=()

operator*()

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]

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