\geometry_module More...

#include <Quaternion.h>

Inheritance diagram for Eigen::Quaternion< _Scalar, _Options >:

Public Types
enum

typedef QuaternionBase< Quaternion< _Scalar, _Options > >	Base

typedef _Scalar	Scalar

typedef internal::traits< Quaternion >::Coefficients	Coefficients

typedef Base::AngleAxisType	AngleAxisType

Public Types inherited from Eigen::QuaternionBase< Quaternion< _Scalar, _Options > >
enum

typedef RotationBase< Quaternion< _Scalar, _Options >, 3 >	Base

typedef internal::traits< Quaternion< _Scalar, _Options > >::Scalar	Scalar

typedef NumTraits< Scalar >::Real	RealScalar

typedef internal::traits< Quaternion< _Scalar, _Options > >::Coefficients	Coefficients

typedef Matrix< Scalar, 3, 1 >	Vector3
	the type of a 3D vector

typedef Matrix< Scalar, 3, 3 >	Matrix3
	the equivalent rotation matrix type

typedef AngleAxis< Scalar >	AngleAxisType
	the equivalent angle-axis type

Public Types inherited from Eigen::RotationBase< Derived, _Dim >
enum	{ Dim = _Dim }

typedef internal::traits< Derived >::Scalar	Scalar
	the scalar type of the coefficients

typedef Matrix< Scalar, Dim, Dim >	RotationMatrixType
	corresponding linear transformation matrix type

typedef Matrix< Scalar, Dim, 1 >	VectorType

Public Member Functions
	Quaternion ()
	Default constructor leaving the quaternion uninitialized.

	Quaternion (const Scalar &w, const Scalar &x, const Scalar &y, const Scalar &z)
	Constructs and initializes the quaternion from its four coefficients w, x, y and z.

	Quaternion (const Scalar *data)
	Constructs and initialize a quaternion from the array data.

template<class Derived >
EIGEN_STRONG_INLINE	Quaternion (const QuaternionBase< Derived > &other)
	Copy constructor.

	Quaternion (const AngleAxisType &aa)
	Constructs and initializes a quaternion from the angle-axis aa.

template<typename Derived >
	Quaternion (const MatrixBase< Derived > &other)
	Constructs and initializes a quaternion from either:

template<typename OtherScalar , int OtherOptions>
	Quaternion (const Quaternion< OtherScalar, OtherOptions > &other)
	Explicit copy constructor with scalar conversion.

Coefficients &	coeffs ()

const Coefficients &	coeffs () const

template<typename Derived1 , typename Derived2 >
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.

Public Member Functions inherited from Eigen::QuaternionBase< Quaternion< _Scalar, _Options > >
Scalar	x () const

Scalar &	x ()

Scalar	y () const

Scalar &	y ()

Scalar	z () const

Scalar &	z ()

Scalar	w () const

Scalar &	w ()

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

VectorBlock< Coefficients, 3 >	vec ()

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

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

EIGEN_STRONG_INLINE QuaternionBase< Quaternion< _Scalar, _Options > > &	operator= (const QuaternionBase< Quaternion< _Scalar, _Options > > &other)

EIGEN_STRONG_INLINE Quaternion< _Scalar, _Options > &	operator= (const QuaternionBase< OtherDerived > &other)

Quaternion< _Scalar, _Options > &	operator= (const AngleAxisType &aa)
	Set `this` from an angle-axis aa and returns a reference to `this`.

Quaternion< _Scalar, _Options > &	operator= (const MatrixBase< OtherDerived > &m)

Quaternion< _Scalar, _Options > &	operator= (const MatrixBase< MatrixDerived > &xpr)
	Set `this` from the expression xpr:*

QuaternionBase &	setIdentity ()

Scalar	squaredNorm () const

Scalar	norm () const

void	normalize ()
	Normalizes the quaternion `*this`.

Quaternion< Scalar >	normalized () const

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

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

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

Matrix3	toRotationMatrix () const
	Convert the quaternion to a 3x3 rotation matrix.

Quaternion< _Scalar, _Options > &	setFromTwoVectors (const MatrixBase< Derived1 > &a, const MatrixBase< Derived2 > &b)
	Sets `*this` to be a quaternion representing a rotation between the two arbitrary vectors a and b.

EIGEN_STRONG_INLINE Quaternion< Scalar >	operator* (const QuaternionBase< OtherDerived > &q) const

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

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

Quaternion< Scalar >	inverse () const

Quaternion< Scalar >	conjugate () const

Quaternion< Scalar >	slerp (const Scalar &t, const QuaternionBase< OtherDerived > &other) const

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

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

EIGEN_STRONG_INLINE Vector3	_transformVector (const Vector3 &v) const
	return the result vector of v through the rotation

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

Public Member Functions inherited from Eigen::RotationBase< Derived, _Dim >
const Derived &	derived () const

Derived &	derived ()

RotationMatrixType	toRotationMatrix () const

RotationMatrixType	matrix () const

Derived	inverse () const

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

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

template<typename OtherDerived >
EIGEN_STRONG_INLINE 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

template<typename OtherVectorType >
VectorType	_transformVector (const OtherVectorType &v) const

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

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

Static Protected Member Functions
static EIGEN_STRONG_INLINE void	_check_template_params ()

Protected Attributes
Coefficients	m_coeffs

Detailed Description

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

\geometry_module

The quaternion class used to represent 3D orientations and rotations

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

Constructor & Destructor Documentation

◆ Quaternion() [1/2]

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() [2/2]

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.

Member Function Documentation

◆ 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.

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

External/Eigen/src/Core/util/ForwardDeclarations.h
External/Eigen/src/Geometry/Quaternion.h

Public Types

Public Member Functions

Static Public Member Functions

Static Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ Quaternion() [1/2]

◆ Quaternion() [2/2]

Member Function Documentation

◆ FromTwoVectors()