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Eigen::Quaternion

template<typename _Scalar, int _Options>
class Eigen::Quaternion< _Scalar, _Options >

The quaternion class used to represent 3D orientations and rotations.

This is defined in the Geometry module.

#include <Eigen/Geometry>

Template Parameters

_Scalar	the scalar type, i.e., the type of the coefficients
_Options	controls the memory alignment of the coefficients. Can be # AutoAlign or # DontAlign. Default is AutoAlign.

This class represents a quaternion \( w+xi+yj+zk \) that is a convenient representation of orientations and rotations of objects in three dimensions. Compared to other representations like Euler angles or 3x3 matrices, quaternions offer the following advantages:

compact storage (4 scalars)
efficient to compose (28 flops),
stable spherical interpolation

The following two typedefs are provided for convenience:

Quaternionf for float
Quaterniond for double

Warning: Operations interpreting the quaternion as rotation have undefined behavior if the quaternion is not normalized.

See also: class AngleAxis, class Transform


template<typename Derived1 , typename Derived2 >
Quaternion< Scalar, Options >	FromTwoVectors (const MatrixBase< Derived1 > &a, const MatrixBase< Derived2 > &b)

	Quaternion ()

	Quaternion (const AngleAxisType &aa)

template<typename Derived >
	Quaternion (const MatrixBase< Derived > &other)

template<typename OtherScalar , int OtherOptions>
	Quaternion (const Quaternion< OtherScalar, OtherOptions > &other)

template<class Derived >
	Quaternion (const QuaternionBase< Derived > &other)

	Quaternion (const Scalar &w, const Scalar &x, const Scalar &y, const Scalar &z)

	Quaternion (const Scalar *data)

Public Member Functions inherited from Eigen::QuaternionBase< Quaternion< _Scalar, _Options > >
Vector3	_transformVector (const Vector3 &v) const

internal::traits< Quaternion< _Scalar, _Options > >::Scalar	angularDistance (const QuaternionBase< OtherDerived > &other) const

internal::cast_return_type< Quaternion< _Scalar, _Options >, Quaternion< NewScalarType > >::type	cast () const

internal::traits< Quaternion< _Scalar, _Options > >::Coefficients &	coeffs ()

const internal::traits< Quaternion< _Scalar, _Options > >::Coefficients &	coeffs () const

Quaternion< Scalar >	conjugate () const

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

Quaternion< Scalar >	inverse () const

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

Scalar	norm () const

void	normalize ()

Quaternion< Scalar >	normalized () const

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

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

Quaternion< _Scalar, _Options > &	operator*= (const QuaternionBase< OtherDerived > &q)

Quaternion< _Scalar, _Options > &	operator= (const AngleAxisType &aa)

Quaternion< _Scalar, _Options > &	operator= (const MatrixBase< MatrixDerived > &xpr)

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

Quaternion< _Scalar, _Options > &	setFromTwoVectors (const MatrixBase< Derived1 > &a, const MatrixBase< Derived2 > &b)

QuaternionBase &	setIdentity ()

Quaternion< typename internal::traits< Quaternion< _Scalar, _Options > >::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, _Dim >
Derived	inverse () const

RotationMatrixType	matrix () const

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

template<int Mode, int Options>
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	UnitRandom ()

Static Public Member Functions inherited from Eigen::QuaternionBase< Quaternion< _Scalar, _Options > >
static Quaternion< Scalar >	Identity ()


Public Types inherited from Eigen::QuaternionBase< Quaternion< _Scalar, _Options > >
typedef AngleAxis< Scalar >	AngleAxisType

typedef Matrix< Scalar, 3, 3 >	Matrix3

typedef Matrix< Scalar, 3, 1 >	Vector3

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

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

Quaternion() [1/7]

template<typename _Scalar , int _Options>

Eigen::Quaternion< _Scalar, _Options >::Quaternion

(

)

inline

Default constructor leaving the quaternion uninitialized.

Quaternion() [2/7]

template<typename _Scalar , int _Options>

Eigen::Quaternion< _Scalar, _Options >::Quaternion	(	const Scalar &	w,
		const Scalar &	x,
		const Scalar &	y,
		const Scalar &	z
	)

inline

Constructs and initializes the quaternion \( w+xi+yj+zk \) from its four coefficients w, x, y and z.

Warning: Note the order of the arguments: the real w coefficient first, while internally the coefficients are stored in the following order: [x, y, z, w]

Quaternion() [3/7]

template<typename _Scalar , int _Options>

Eigen::Quaternion< _Scalar, _Options >::Quaternion

(

const Scalar *

data

)

inlineexplicit

Constructs and initialize a quaternion from the array data

Quaternion() [4/7]

template<typename _Scalar , int _Options>

template<class Derived >

Eigen::Quaternion< _Scalar, _Options >::Quaternion

(

const QuaternionBase< Derived > &

other

)

inline

Copy constructor

Quaternion() [5/7]

template<typename _Scalar , int _Options>

Eigen::Quaternion< _Scalar, _Options >::Quaternion

(

const AngleAxisType &

)

inlineexplicit

Constructs and initializes a quaternion from the angle-axis aa

Quaternion() [6/7]

template<typename _Scalar , int _Options>

template<typename Derived >

Eigen::Quaternion< _Scalar, _Options >::Quaternion

(

const MatrixBase< Derived > &

other

)

inlineexplicit

Constructs and initializes a quaternion from either:

a rotation matrix expression,
a 4D vector expression representing quaternion coefficients.

Quaternion() [7/7]

template<typename _Scalar , int _Options>

template<typename OtherScalar , int OtherOptions>

Eigen::Quaternion< _Scalar, _Options >::Quaternion

(

const Quaternion< OtherScalar, OtherOptions > &

other

)

inlineexplicit

Explicit copy constructor with scalar conversion

FromTwoVectors()

template<typename _Scalar , int _Options>

template<typename Derived1 , typename Derived2 >

Quaternion<Scalar,Options> Eigen::Quaternion< _Scalar, _Options >::FromTwoVectors	(	const MatrixBase< Derived1 > &	a,
		const MatrixBase< Derived2 > &	b
	)

Returns 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: resulting quaternion

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

UnitRandom()

template<typename Scalar , int Options>

Quaternion< Scalar, Options > Eigen::Quaternion< Scalar, Options >::UnitRandom

static

Returns: a random unit quaternion following a uniform distribution law on SO(3)

Note: The implementation is based on http://planning.cs.uiuc.edu/node198.html

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

Quaternion.h

Eigen::Quaternion

template<typename _Scalar, int _Options> class Eigen::Quaternion< _Scalar, _Options >

Quaternion() [1/7]

Quaternion() [2/7]

Quaternion() [3/7]

Quaternion() [4/7]

Quaternion() [5/7]

Quaternion() [6/7]

Quaternion() [7/7]

FromTwoVectors()

UnitRandom()

template<typename _Scalar, int _Options>
class Eigen::Quaternion< _Scalar, _Options >