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Rotation2D< T > Class Template Reference

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 ( r11,
r12,
r21,
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)
related

The inverse \( \robabx{b}{a}{\mathbf{R}} = \robabx{a}{b}{\mathbf{R}}^{-1} \) of a rotation matrix.

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 
)
related

Enable read-serialization of class T by overloading this method. Data is read from iarchive and filled into sobject.

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 
)
related

Enable read-serialization of class T by overloading this method. Data is read from iarchive and filled into sobject.

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 
)
related

Boost serialization.

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 
)
related

Enable write-serialization of class T by overloading this method. Data is written to oarchive from the sobject.

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 
)
related

Enable write-serialization of class T by overloading this method. Data is written to oarchive from the sobject.

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: