#include <Eigen/src/Geometry/Quaternion.h>

Detailed Description

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

Inheritance diagram for Eigen::Quaternion< Scalar_, Options_ >:

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

Quaternion &	operator= (Quaternion &&other) noexcept(std::is_nothrow_move_assignable< Scalar >::value)

	Quaternion ()

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

template<typename Derived >
	Quaternion (const Scalar &w, const Eigen::MatrixBase< Derived > &vec)

	Quaternion (const Scalar *data)

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

	Quaternion (const AngleAxisType &aa)

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

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

	Quaternion (Quaternion &&other) noexcept(std::is_nothrow_move_constructible< Scalar >::value)

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

const internal::traits< Quaternion< Scalar_, Options_ > >::Coefficients &	coeffs () const

internal::traits< Quaternion< Scalar_, Options_ > >::Coefficients &	coeffs ()

internal::traits< Quaternion< Scalar_, Options_ > >::Coefficients	coeffsScalarFirst () const

internal::traits< Quaternion< Scalar_, Options_ > >::Coefficients	coeffsScalarLast () 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

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

VectorBlock< Coefficients, 3 >	vec ()

constexpr CoeffReturnType	w () const

constexpr NonConstCoeffReturnType	w ()

constexpr CoeffReturnType	x () const

constexpr NonConstCoeffReturnType	x ()

constexpr CoeffReturnType	y () const

constexpr NonConstCoeffReturnType	y ()

constexpr CoeffReturnType	z () const

constexpr NonConstCoeffReturnType	z ()

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

RotationMatrixType	matrix () 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< Quaternion< Scalar_, Options_ >, 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

Static Public Member Functions
static Quaternion	FromCoeffsScalarFirst (const Scalar &w, const Scalar &x, const Scalar &y, const Scalar &z)

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

static Quaternion	UnitRandom ()

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

Additional Inherited Members
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< Quaternion< Scalar_, Options_ >, 3 >
typedef Matrix< Scalar, Dim, Dim >	RotationMatrixType

typedef internal::traits< Quaternion< Scalar_, Options_ > >::Scalar	Scalar

Constructor & Destructor Documentation

◆ Quaternion() [1/9]

template<typename Scalar_ , int Options_>

Eigen::Quaternion< Scalar_, Options_ >::Quaternion ( )

inline

Default constructor leaving the quaternion uninitialized.

◆ Quaternion() [2/9]

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() [3/9]

template<typename Scalar_ , int Options_>

template<typename Derived >

Eigen::Quaternion< Scalar_, Options_ >::Quaternion	(	const Scalar &	w,
		const Eigen::MatrixBase< Derived > &	vec
	)

inline

Constructs and initializes a quaternion from its real part as a scalar, and its imaginary part as a 3-vector [x, y, z]

◆ Quaternion() [4/9]

template<typename Scalar_ , int Options_>

Eigen::Quaternion< Scalar_, Options_ >::Quaternion ( const Scalar * data )

inlineexplicit

Constructs and initialize a quaternion from the array data

◆ Quaternion() [5/9]

template<typename Scalar_ , int Options_>

template<class Derived >

Eigen::Quaternion< Scalar_, Options_ >::Quaternion ( const QuaternionBase< Derived > & other )

inline

Copy constructor

◆ Quaternion() [6/9]

template<typename Scalar_ , int Options_>

Eigen::Quaternion< Scalar_, Options_ >::Quaternion ( const AngleAxisType & aa )

inlineexplicit

Constructs and initializes a quaternion from the angle-axis aa

◆ Quaternion() [7/9]

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 in the order [x, y, z, w].

◆ Quaternion() [8/9]

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

◆ Quaternion() [9/9]

template<typename Scalar_ , int Options_>

Eigen::Quaternion< Scalar_, Options_ >::Quaternion ( Quaternion< Scalar_, Options_ > && other )

inlinenoexcept

Default move constructor

Member Function Documentation

◆ FromCoeffsScalarFirst()

template<typename Scalar , int Options>

Quaternion< Scalar, Options > Eigen::Quaternion< Scalar, Options >::FromCoeffsScalarFirst	(	const Scalar &	w,
		const Scalar &	x,
		const Scalar &	y,
		const Scalar &	z
	)

static

Constructs a quaternion from its coefficients in the order [w, x, y, z], i.e. scalar part w FIRST, vector part [x, y, z] last.

This factory accepts the parameters in the same order as the constructor

Quaternion(const Scalar& w, const

Scalar& x, const Scalar& y, const Scalar& z)

. Consider using this factory function to make the parameter ordering explicit.

◆ FromCoeffsScalarLast()

template<typename Scalar , int Options>

Quaternion< Scalar, Options > Eigen::Quaternion< Scalar, Options >::FromCoeffsScalarLast	(	const Scalar &	x,
		const Scalar &	y,
		const Scalar &	z,
		const Scalar &	w
	)

static

Constructs a quaternion from its coefficients in the order [x, y, z, w], i.e. vector part [x, y, z] first, scalar part w LAST.

This factory accepts the parameters in the same order as the underlying coefficient vector. Consider using this factory function to make the parameter ordering explicit.

◆ 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.

◆ operator=()

template<typename Scalar_ , int Options_>

Quaternion& Eigen::Quaternion< Scalar_, Options_ >::operator= ( Quaternion< Scalar_, Options_ > && other )

inlinenoexcept

Default move assignment operator

◆ 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 files:

/builddir/build/BUILD/eigen-5.0.1/Eigen/src/Core/util/ForwardDeclarations.h
/builddir/build/BUILD/eigen-5.0.1/Eigen/src/Geometry/Quaternion.h

	Eigen 5.0.1-dev

Detailed Description

template<typename Scalar_, int Options_> class Eigen::Quaternion< Scalar_, Options_ >

Public Member Functions

Static Public Member Functions

Additional Inherited Members

Constructor & Destructor Documentation

◆ Quaternion() [1/9]

◆ Quaternion() [2/9]

◆ Quaternion() [3/9]

◆ Quaternion() [4/9]

◆ Quaternion() [5/9]

◆ Quaternion() [6/9]

◆ Quaternion() [7/9]

◆ Quaternion() [8/9]

◆ Quaternion() [9/9]

Member Function Documentation

◆ FromCoeffsScalarFirst()

◆ FromCoeffsScalarLast()

◆ FromTwoVectors()

◆ operator=()

◆ UnitRandom()

template<typename Scalar_, int Options_>
class Eigen::Quaternion< Scalar_, Options_ >