A Quaternion \( \mathbf{q}\in \mathbb{R}^4 \) a complex number used to describe rotations in 3-dimensional space. \( q_w+{\bf i}\ q_x+ {\bf j} q_y+ {\bf k}\ q_z \). More...

#include <Quaternion.hpp>

Inherits Rotation3DVector< double >.

Public Types
typedef T	value_type
	Value type.

Public Member Functions
	Quaternion ()
	constuct Quaterinion of {0,0,0,1}

	Quaternion (T qx, T qy, T qz, T qw)
	Creates a Quaternion. More...

	Quaternion (const Quaternion< T > &quat)
	Creates a Quaternion from another Quaternion. More...

	Quaternion (const rw::math::Rotation3DVector< T > &rot)
	Creates a Quaternion from another Rotation3DVector type. More...

	Quaternion (const rw::math::Rotation3D< T > &rot)
	Extracts a Quaternion from Rotation matrix using setRotation(const Rotation3D<R>& rot) More...

	Quaternion (const Eigen::Quaternion< T > &r)
	Creates a Quaternion from a Eigen quaternion. More...

template<class R >
	Quaternion (const Eigen::MatrixBase< R > &r)
	Creates a Quaternion from vector_expression. More...

T	getQx () const
	get method for the x component More...

T	getQy () const
	get method for the y component More...

T	getQz () const
	get method for the z component More...

T	getQw () const
	get method for the w component More...

T	operator() (size_t i) const
	Returns reference to Quaternion element. More...

T &	operator() (size_t i)
	Returns reference to Quaternion element. More...

T &	operator[] (size_t i)
	Returns reference to Quaternion element. More...

T	operator[] (size_t i) const
	Returns reference to Quaternion element. More...

const rw::math::Rotation3D< T >	toRotation3D () const
	Calculates the \( 3\times 3 \) Rotation matrix. More...

template<class R >
void	setRotation (const rw::math::Rotation3D< R > &rot)
	Converts a Rotation3D to a Quaternion and saves the Quaternion in this. More...

size_t	size () const
	The dimension of the quaternion (i.e. 4). This method is provided to help support generic algorithms using size() and operator[].

Eigen::Quaternion< T > &	e ()
	Convert to an Eigen Quaternion. More...

const Eigen::Quaternion< T > &	e () const
	Convert to an Eigen Quaternion. More...

Eigen::Matrix< T, 4, 1 >	toEigenVector () const
	convert to Eigen Vector More...

Quaternion< T >	operator- () const
	Unary minus.

Quaternion< T >	operator+ () const
	Unary plus.

const Quaternion< T >	operator- (const Quaternion< T > &v)
	Subtraction.

Quaternion< T >	operator* (const Quaternion< T > &r) const
	Multiply-from operator.

const Quaternion< T >	operator+ (const Quaternion< T > &v) const
	Addition of two quaternions.

const Quaternion< T >	operator* (T s) const
	Scalar multiplication.

const Quaternion< T >	operator/ (T s) const
	Scalar Devision.

Quaternion< T >	elemDivide (const T &lhs) const
	element whise division More...

T	getLength () const
	get length of quaternion \( \sqrt{q_x^2+q_y^2+q_z^2+q_w^2} \) More...

T	getLengthSquared () const
	get squared length of quaternion \( q_x^2+q_y^2+q_z^2+q_w^2 \) More...

void	normalize ()
	normalizes this quaternion so that \( normalze(Q)=\frac{Q}{\sqrt{q_x^2+q_y^2+q_z^2+q_w^2}} \)

const Quaternion< T >	slerp (const Quaternion< T > &v, const T t) const
	Calculates a slerp interpolation between this and v. More...

Quaternion< T >	exp () const

Quaternion< T >	inverse () const
	Calculate the inverse Quaternion. More...

Quaternion< T >	ln () const
	calculates the natural logerithm of this quaternion More...

Quaternion< T >	pow (double power) const
	calculates the quaternion lifted to the power of power More...

void	operator= (const Eigen::Quaternion< T > &r)
	copy a boost quaternion to this Quaternion More...

const Quaternion< T >	operator*= (T s)
	Scalar multiplication.

const Quaternion< T >	operator*= (const Quaternion< T > &r)
	Multiply with operator.

const Quaternion< T >	operator+= (const Quaternion< T > &r)
	Add-to operator.

const Quaternion< T >	operator-= (const Quaternion< T > &r)
	Subtract-from operator.

Quaternion< T > &	operator= (const rw::math::Rotation3D<> &rhs)
	copyfrom rotaion matrix, same as setRotation. More...

bool	operator== (const Quaternion< T > &r) const
	Comparison (equals) operator.

bool	operator!= (const Quaternion< T > &r) const
	Comparison (not equals) operator.

Public Member Functions inherited from Rotation3DVector< double >
virtual	~Rotation3DVector ()
	Virtual destructor.

Friends
const Quaternion< T >	operator* (T s, const Quaternion< T > &v)
	Scalar multiplication.

Related Functions
(Note that these are not member functions.)
template<class T >
std::ostream &	operator<< (std::ostream &out, const Quaternion< T > &v)
	Streaming operator.

template<>
void	write (const rw::math::Quaternion< double > &sobject, rw::common::OutputArchive &oarchive, const std::string &id)

template<>
void	write (const rw::math::Quaternion< float > &sobject, rw::common::OutputArchive &oarchive, const std::string &id)

template<>
void	read (rw::math::Quaternion< double > &sobject, rw::common::InputArchive &iarchive, const std::string &id)

template<>
void	read (rw::math::Quaternion< float > &sobject, rw::common::InputArchive &iarchive, const std::string &id)

Additional Inherited Members
Protected Member Functions inherited from Rotation3DVector< double >
	Rotation3DVector (const Rotation3DVector &)
	Copy Constructor. More...

	Rotation3DVector ()
	Default Constructor.

Rotation3DVector &	operator= (const Rotation3DVector &)
	Assignment operator is protected to force subclasses to implement it by themself.

Detailed Description

template<class T = double>
class rw::math::Quaternion< T >

A Quaternion \( \mathbf{q}\in \mathbb{R}^4 \) a complex number used to describe rotations in 3-dimensional space. \( q_w+{\bf i}\ q_x+ {\bf j} q_y+ {\bf k}\ q_z \).

Quaternions can be added and multiplied in a similar way as usual algebraic numbers. Though there are differences. Quaternion multiplication is not commutative which means \( Q\cdot P \neq P\cdot Q \)

Constructor & Destructor Documentation

◆ Quaternion() [1/6]

Quaternion	(	T	qx,
		T	qy,
		T	qz,
		T	qw
	)

inline

Creates a Quaternion.

Parameters

qx	[in] \( q_x \)
qy	[in] \( q_y \)
qz	[in] \( q_z \)
qw	[in] \( q_w \)

◆ Quaternion() [2/6]

Quaternion ( const Quaternion< T > & quat )

inline

Creates a Quaternion from another Quaternion.

Parameters

quat	[in] Quaternion

◆ Quaternion() [3/6]

Quaternion ( const rw::math::Rotation3DVector< T > & rot )

inline

Creates a Quaternion from another Rotation3DVector type.

Parameters

rot	[in] The Rotation3DVector type

◆ Quaternion() [4/6]

Quaternion ( const rw::math::Rotation3D< T > & rot )

inline

Extracts a Quaternion from Rotation matrix using setRotation(const Rotation3D<R>& rot)

Parameters

rot	[in] A 3x3 rotation matrix \( \mathbf{rot} \)

◆ Quaternion() [5/6]

Quaternion ( const Eigen::Quaternion< T > & r )

inline

Creates a Quaternion from a Eigen quaternion.

Parameters

r	[in] a boost quaternion

◆ Quaternion() [6/6]

Quaternion ( const Eigen::MatrixBase< R > & r )

inlineexplicit

Creates a Quaternion from vector_expression.

Parameters

r	[in] an Eigen Vector

Member Function Documentation

◆ e() [1/2]

Eigen::Quaternion<T>& e ( )

inline

Convert to an Eigen Quaternion.

Returns: Eigen Quaternion representation.

◆ e() [2/2]

const Eigen::Quaternion<T>& e ( ) const

inline

Convert to an Eigen Quaternion.

Returns: Eigen Quaternion representation.

◆ elemDivide()

Quaternion<T> elemDivide ( const T & lhs ) const

element whise division

Parameters

lhs	[in] the scalar to devide with

Returns: the result of elementwise devision

◆ getLength()

T getLength ( ) const

inline

get length of quaternion \( \sqrt{q_x^2+q_y^2+q_z^2+q_w^2} \)

Returns: the length og this quaternion

◆ getLengthSquared()

T getLengthSquared ( ) const

inline

get squared length of quaternion \( q_x^2+q_y^2+q_z^2+q_w^2 \)

Returns: the length og this quaternion

◆ getQw()

T getQw ( ) const

inline

get method for the w component

Returns: the w component of the quaternion

◆ getQx()

T getQx ( ) const

inline

get method for the x component

Returns: the x component of the quaternion

◆ getQy()

T getQy ( ) const

inline

get method for the y component

Returns: the y component of the quaternion

◆ getQz()

T getQz ( ) const

inline

get method for the z component

Returns: the z component of the quaternion

◆ inverse()

Quaternion<T> inverse ( ) const

Calculate the inverse Quaternion.

Returns: the inverse quaternion

◆ ln()

Quaternion<T> ln ( ) const

calculates the natural logerithm of this quaternion

Returns: natural logetihm

◆ operator()() [1/2]

T& operator() ( size_t i )

inline

Returns reference to Quaternion element.

Parameters

i	[in] index in the quaternion \(i\in \{0,1,2,3\} \)

Returns: reference to element

◆ operator()() [2/2]

T operator() ( size_t i ) const

inline

Returns reference to Quaternion element.

Parameters

i	[in] index in the quaternion \(i\in \{0,1,2,3\} \)

Returns: const reference to element

◆ operator=() [1/2]

void operator= ( const Eigen::Quaternion< T > & r )

inline

copy a boost quaternion to this Quaternion

Parameters

r	[in] - boost quaternion

◆ operator=() [2/2]

Quaternion<T>& operator= ( const rw::math::Rotation3D<> & rhs )

inline

copyfrom rotaion matrix, same as setRotation.

Parameters

rhs	[in] the rotation that will be copyed

◆ operator[]() [1/2]

T& operator[] ( size_t i )

inline

Returns reference to Quaternion element.

Parameters

i	[in] index in the quaternion \(i\in \{0,1,2,3\} \)

Returns: reference to element

◆ operator[]() [2/2]

T operator[] ( size_t i ) const

inline

Returns reference to Quaternion element.

Parameters

i	[in] index in the quaternion \(i\in \{0,1,2,3\} \)

Returns: reference to element

◆ pow()

Quaternion<T> pow ( double power ) const

calculates the quaternion lifted to the power of power

Parameters

power [in] the power the quaternion is lifted to

Returns: \( Quaternion^power \)

◆ setRotation()

void setRotation ( const rw::math::Rotation3D< R > & rot )

inline

Converts a Rotation3D to a Quaternion and saves the Quaternion in this.

Parameters

rot	[in] A 3x3 rotation matrix \( \mathbf{R} \)

\( \begin{array}{c} q_x\\ q_y\\ q_z\\ q_w \end{array} = \left[ \begin{array}{c} \\ \\ \end{array} \right] \)

The conversion method is proposed by Henrik Gordon Petersen. The switching between different cases occur well before numerical instabilities, hence the solution should be more robust, than many of the methods proposed elsewhere.

◆ slerp()

const Quaternion<T> slerp	(	const Quaternion< T > &	v,
		const T	t
	)		const

inline

Calculates a slerp interpolation between this and v.

The slerp interpolation ensures a constant velocity across the interpolation. For \( t=0\) the result is this and for \( t=1\) it is v.

Note: Algorithm and implementation is thanks to euclideanspace.com

◆ toEigenVector()

Eigen::Matrix<T, 4, 1> toEigenVector ( ) const

inline

convert to Eigen Vector

Returns: eigen Vector of quaternion

◆ toRotation3D()

const rw::math::Rotation3D<T> toRotation3D ( ) const

inlinevirtual

Calculates the \( 3\times 3 \) Rotation matrix.

Returns: A 3x3 rotation matrix \( \mathbf{rot} \) \( \mathbf{rot} = \left[ \begin{array}{ccc} 1-2(q_y^2-q_z^2) & 2(q_x\ q_y+q_z\ q_w)& 2(q_x\ q_z-q_y\ q_w) \\ 2(q_x\ q_y-q_z\ q_w) & 1-2(q_x^2-q_z^2) & 2(q_y\ q_z+q_x\ q_w)\\ 2(q_x\ q_z+q_y\ q_w) & 2(q_y\ q_z-q_x\ q_z) & 1-2(q_x^2-q_y^2) \end{array} \right] \)

Implements Rotation3DVector< double >.

Friends And Related Function Documentation

◆ read() [1/2]

void read	(	rw::math::Quaternion< double > &	sobject,
		rw::common::InputArchive &	iarchive,
		const std::string &	id
	)

Parameters

sobject	[out] the object in which the data should be streamed into
iarchive	[in] the InputArchive from which to read data.
id	[in] The id of the serialized sobject.

Note: the id can be empty in which case the overloaded method should provide a default identifier. E.g. the Vector3D class defined "Vector3D" as its default id.

◆ read() [2/2]

void read	(	rw::math::Quaternion< float > &	sobject,
		rw::common::InputArchive &	iarchive,
		const std::string &	id
	)

Parameters

sobject	[out] the object in which the data should be streamed into
iarchive	[in] the InputArchive from which to read data.
id	[in] The id of the serialized sobject.

Note: the id can be empty in which case the overloaded method should provide a default identifier. E.g. the Vector3D class defined "Vector3D" as its default id.

◆ write() [1/2]

void write	(	const rw::math::Quaternion< double > &	sobject,
		rw::common::OutputArchive &	oarchive,
		const std::string &	id
	)

Parameters

sobject	[in] the object from which the data should be streamed.
oarchive	[out] the OutputArchive in which data should be written.
id	[in] The id of the serialized sobject.

Note: the id can be empty in which case the overloaded method should provide a default identifier. E.g. the Vector3D class defined "Vector3D" as its default id.

◆ write() [2/2]

void write	(	const rw::math::Quaternion< float > &	sobject,
		rw::common::OutputArchive &	oarchive,
		const std::string &	id
	)

Parameters

sobject	[in] the object from which the data should be streamed.
oarchive	[out] the OutputArchive in which data should be written.
id	[in] The id of the serialized sobject.

Note: the id can be empty in which case the overloaded method should provide a default identifier. E.g. the Vector3D class defined "Vector3D" as its default id.

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

core/math_fwd.hpp
Quaternion.hpp

Public Types

Public Member Functions

Friends

Related Functions

Additional Inherited Members

Detailed Description

template<class T = double> class rw::math::Quaternion< T >

Constructor & Destructor Documentation

◆ Quaternion() [1/6]

◆ Quaternion() [2/6]

◆ Quaternion() [3/6]

◆ Quaternion() [4/6]

◆ Quaternion() [5/6]

◆ Quaternion() [6/6]

Member Function Documentation

◆ e() [1/2]

◆ e() [2/2]

◆ elemDivide()

◆ getLength()

◆ getLengthSquared()

◆ getQw()

◆ getQx()

◆ getQy()

◆ getQz()

◆ inverse()

◆ ln()

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ pow()

◆ setRotation()

◆ slerp()

◆ toEigenVector()

◆ toRotation3D()

Friends And Related Function Documentation

◆ read() [1/2]

◆ read() [2/2]

◆ write() [1/2]

◆ write() [2/2]

template<class T = double>
class rw::math::Quaternion< T >