A 2x2 rotation matrix \( \mathbf{R}\in SO(2) \). More...

#include <Rotation2D.hpp>

Public Types
typedef T	value_type
	Value type.

typedef Eigen::Rotation2D< T >	EigenMatrix2x2
	The type of the internal Eigen matrix implementation.

Public Member Functions
	Rotation2D ()
	A rotation matrix with uninitialized storage.

	Rotation2D (T r11, T r12, T r21, T r22)
	Constructs an initialized 2x2 rotation matrix. More...

	Rotation2D (const rw::math::Vector2D< T > &i, const rw::math::Vector2D< T > &j)
	Constructs an initialized 2x2 rotation matrix \( \robabx{a}{b}{\mathbf{R}} = \left[ \begin{array}{cc} \robabx{a}{b}{\mathbf{i}} & \robabx{a}{b}{\mathbf{j}} \end{array} \right] \). More...

	Rotation2D (const T theta)
	Constructs an initialized 2x2 rotation matrix \( \robabx{a}{b}{\mathbf{R}} = \left[ \begin{array}{cc} \robabx{a}{b}{\mathbf{i}} & \robabx{a}{b}{\mathbf{j}} \end{array} \right] \). More...

	Rotation2D (const rw::math::Vector2D< T > &i)
	Construct an initialized 2x2 rotation matrix. More...

template<class R >
	Rotation2D (const EigenMatrix2x2 &m)
	Construct a rotation matrix from an Eigen matrix.

T &	operator() (size_t row, size_t column)
	Returns reference to matrix element. More...

const T &	operator() (size_t row, size_t column) const
	Returns reference to matrix element. More...

bool	operator== (const Rotation2D< T > &rhs) const
	Comparison operator. More...

bool	operator!= (const Rotation2D< T > &rhs) const
	Comparison operator. More...

EigenMatrix2x2	e () const
	Returns a Eigen 2x2 matrix \( \mathbf{M}\in SO(2) \) that represents this rotation. More...

const Rotation2D	operator* (const Rotation2D &bRc) const
	Calculates \( \robabx{a}{c}{\mathbf{R}} = \robabx{a}{b}{\mathbf{R}} \robabx{b}{c}{\mathbf{R}} \) where this object is \( \robabx{a}{b}{\mathbf{R}} \). More...

const rw::math::Vector2D< T >	operator* (const rw::math::Vector2D< T > &bVc) const
	Calculates \( \robabx{a}{c}{\mathbf{v}} = \robabx{a}{b}{\mathbf{R}} \robabx{b}{c}{\mathbf{v}} \) where this object is \( \robabx{a}{b}{\mathbf{R}} \). More...

Static Public Member Functions
static const Rotation2D	identity ()
	Constructs a 2x2 rotation matrix set to identity. More...

Friends
std::ostream &	operator<< (std::ostream &os, const Rotation2D &r)
	Writes rotation matrix to stream. More...

Related Functions
(Note that these are not member functions.)
template<class T >
const Rotation2D< T >	inverse (const Rotation2D< T > &aRb)
	The inverse \( \robabx{b}{a}{\mathbf{R}} = \robabx{a}{b}{\mathbf{R}}^{-1} \) of a rotation matrix. More...

template<>
void	write (const rw::math::Rotation2D< double > &sobject, rw::common::OutputArchive &oarchive, const std::string &id)

template<>
void	write (const rw::math::Rotation2D< float > &sobject, rw::common::OutputArchive &oarchive, const std::string &id)

template<>
void	read (rw::math::Rotation2D< double > &sobject, rw::common::InputArchive &iarchive, const std::string &id)

template<>
void	read (rw::math::Rotation2D< float > &sobject, rw::common::InputArchive &iarchive, const std::string &id)

template<class Archive , class T >
void	serialize (Archive &archive, rw::math::Rotation2D< T > &R, const unsigned int version)
	Boost serialization. More...

Detailed Description

template<class T = double>
class rw::math::Rotation2D< T >

A 2x2 rotation matrix \( \mathbf{R}\in SO(2) \).

\( \mathbf{R}= \left[ \begin{array}{cc} {}^A\hat{X}_B & {}^A\hat{Y}_B \end{array} \right] = \left[ \begin{array}{cc} r_{11} & r_{12} \\ r_{21} & r_{22} \end{array} \right] \)

Constructor & Destructor Documentation

◆ Rotation2D() [1/4]

Rotation2D	(	T	r11,
		T	r12,
		T	r21,
		T	r22
	)

inline

Constructs an initialized 2x2 rotation matrix.

Parameters

r11	\( r_{11} \)
r12	\( r_{12} \)
r21	\( r_{21} \)
r22	\( r_{22} \)

\( \mathbf{R} = \left[ \begin{array}{cc} r_{11} & r_{12} \\ r_{21} & r_{22} \end{array} \right] \)

◆ Rotation2D() [2/4]

Rotation2D	(	const rw::math::Vector2D< T > &	i,
		const rw::math::Vector2D< T > &	j
	)

inline

Constructs an initialized 2x2 rotation matrix \( \robabx{a}{b}{\mathbf{R}} = \left[ \begin{array}{cc} \robabx{a}{b}{\mathbf{i}} & \robabx{a}{b}{\mathbf{j}} \end{array} \right] \).

Parameters

i	\( \robabx{a}{b}{\mathbf{i}} \)
j	\( \robabx{a}{b}{\mathbf{j}} \)

◆ Rotation2D() [3/4]

Rotation2D ( const T theta )

inline

Constructs an initialized 2x2 rotation matrix \( \robabx{a}{b}{\mathbf{R}} = \left[ \begin{array}{cc} \robabx{a}{b}{\mathbf{i}} & \robabx{a}{b}{\mathbf{j}} \end{array} \right] \).

Parameters

theta

◆ Rotation2D() [4/4]

Rotation2D ( const rw::math::Vector2D< T > & i )

inline

Construct an initialized 2x2 rotation matrix.

The second of column of the matrix is deduced from the first column.

Parameters

i	[in] The first column of the rotation matrix.

Member Function Documentation

◆ e()

EigenMatrix2x2 e ( ) const

inline

Returns a Eigen 2x2 matrix \( \mathbf{M}\in SO(2) \) that represents this rotation.

Returns: \( \mathbf{M}\in SO(2) \)

◆ identity()

static const Rotation2D identity ( )

inlinestatic

Constructs a 2x2 rotation matrix set to identity.

Returns: a 2x2 identity rotation matrix

\( \mathbf{R} = \left[ \begin{array}{cc} 1 & 0\\ 0 & 1 \end{array} \right] \)

◆ operator!=()

bool operator!= ( const Rotation2D< T > & rhs ) const

inline

Comparison operator.

The comparison operator makes a element wise comparison. Returns true if any of the elements are different.

Parameters

rhs	[in] Rotation2D to compare with

Returns: True if not equal.

◆ operator()() [1/2]

T& operator()	(	size_t	row,
		size_t	column
	)

inline

Returns reference to matrix element.

Parameters

row	[in] row
column	[in] column

Returns: reference to the element

◆ operator()() [2/2]

const T& operator()	(	size_t	row,
		size_t	column
	)		const

inline

Returns reference to matrix element.

Parameters

row	[in] row
column	[in] column

Returns: reference to the element

◆ operator*() [1/2]

const Rotation2D operator* ( const Rotation2D< T > & bRc ) const

inline

Calculates \( \robabx{a}{c}{\mathbf{R}} = \robabx{a}{b}{\mathbf{R}} \robabx{b}{c}{\mathbf{R}} \) where this object is \( \robabx{a}{b}{\mathbf{R}} \).

Parameters

bRc	[in] \( \robabx{b}{c}{\mathbf{R}} \)

Returns: \( \robabx{a}{c}{\mathbf{R}} \)

◆ operator*() [2/2]

const rw::math::Vector2D<T> operator* ( const rw::math::Vector2D< T > & bVc ) const

inline

Calculates \( \robabx{a}{c}{\mathbf{v}} = \robabx{a}{b}{\mathbf{R}} \robabx{b}{c}{\mathbf{v}} \) where this object is \( \robabx{a}{b}{\mathbf{R}} \).

Parameters

bVc	[in] \( \robabx{b}{c}{\mathbf{v}} \)

Returns: \( \robabx{a}{c}{\mathbf{v}} \)

◆ operator==()

bool operator== ( const Rotation2D< T > & rhs ) const

inline

Comparison operator.

The comparison operator makes a element wise comparison. Returns true only if all elements are equal.

Parameters

rhs	[in] Rotation2D to compare with

Returns: True if equal.

Friends And Related Function Documentation

◆ inverse()

const Rotation2D< T > inverse ( const Rotation2D< T > & aRb )

Parameters

aRb	[in] the rotation matrix \( \robabx{a}{b}{\mathbf{R}} \)

Returns: the matrix inverse \( \robabx{b}{a}{\mathbf{R}} = \robabx{a}{b}{\mathbf{R}}^{-1} \)

\( \robabx{b}{a}{\mathbf{R}} = \robabx{a}{b}{\mathbf{R}}^{-1} = \robabx{a}{b}{\mathbf{R}}^T \)

◆ operator<<

std::ostream& operator<<	(	std::ostream &	os,
		const Rotation2D< T > &	r
	)

friend

Writes rotation matrix to stream.

Parameters

os	[in/out] output stream to use
r	[in] rotation matrix to print

Returns: the updated output stream

◆ read() [1/2]

void read	(	rw::math::Rotation2D< 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::Rotation2D< 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.

◆ serialize()

void serialize	(	Archive &	archive,
		rw::math::Rotation2D< T > &	R,
		const unsigned int	version
	)

Parameters

archive	[in] the boost archive to read from or write to.
R	[in/out] the rotation matrix to read/write.
version	[in] class version (currently version 0).

◆ write() [1/2]

void write	(	const rw::math::Rotation2D< 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::Rotation2D< 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
Rotation2D.hpp

Public Types

Public Member Functions

Static Public Member Functions

Friends

Related Functions

Detailed Description

template<class T = double> class rw::math::Rotation2D< T >

Constructor & Destructor Documentation

◆ Rotation2D() [1/4]

◆ Rotation2D() [2/4]

◆ Rotation2D() [3/4]

◆ Rotation2D() [4/4]

Member Function Documentation

◆ e()

◆ identity()

◆ operator!=()

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ operator*() [1/2]

◆ operator*() [2/2]

◆ operator==()

Friends And Related Function Documentation

◆ inverse()

◆ operator<<

◆ read() [1/2]

◆ read() [2/2]

◆ serialize()

◆ write() [1/2]

◆ write() [2/2]

template<class T = double>
class rw::math::Rotation2D< T >