A 3x3 rotation matrix \( \mathbf{R}\in SO(3) \). More...

#include <Rotation3D.hpp>

Public Types
typedef T	value_type
	Value type.

typedef Eigen::Matrix< T, 3, 3 >	EigenMatrix3x3
	The type of the internal Eigen matrix implementation.

Public Member Functions
	Rotation3D ()
	A rotation matrix with uninitialized storage.

	Rotation3D (T r11, T r12, T r13, T r21, T r22, T r23, T r31, T r32, T r33)
	Constructs an initialized 3x3 rotation matrix. More...

	Rotation3D (const rw::math::Vector3D< T > &i, const rw::math::Vector3D< T > &j, const rw::math::Vector3D< T > &k)
	Constructs an initialized 3x3 rotation matrix \( \robabx{a}{b}{\mathbf{R}} = \left[ \begin{array}{ccc} \robabx{a}{b}{\mathbf{i}} & \robabx{a}{b}{\mathbf{j}} & \robabx{a}{b}{\mathbf{k}} \end{array} \right] \). More...

	Rotation3D (const Rotation3DVector< T > &rotVec)
	Initialize Rotation3D from other rotation types. More...

void	normalize ()
	Normalizes the rotation matrix to satisfy SO(3). More...

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...

const rw::math::Vector3D< T >	getRow (size_t i) const
	Returns the i'th row of the rotation matrix. More...

const rw::math::Vector3D< T >	getCol (size_t i) const
	Returns the i'th column of the rotation matrix. More...

bool	operator== (const Rotation3D< T > &rhs) const
	Comparison operator. More...

bool	operator!= (const Rotation3D< T > &rhs) const
	Comparison operator. More...

bool	equal (const Rotation3D< T > &rot, const T precision=std::numeric_limits< T >::epsilon()) const
	Compares rotations with a given precision. More...

bool	isProperRotation () const
	Verify that this rotation is a proper rotation. More...

bool	isProperRotation (T precision) const
	Verify that this rotation is a proper rotation. More...

const EigenMatrix3x3 &	e () const
	Returns a Eigen 3x3 matrix \( \mathbf{M}\in SO(3) \) that represents this rotation. More...

EigenMatrix3x3 &	e ()
	Returns a Eigen 3x3 matrix \( \mathbf{M}\in SO(3) \) that represents this rotation. More...

const Rotation3D	operator* (const Rotation3D &bRc) const
	Calculates \( \robabx{a}{c}{\mathbf{R}} = \robabx{a}{b}{\mathbf{R}} \robabx{b}{c}{\mathbf{R}} \). More...

template<class R >
const Rotation3D	operator* (const Eigen::MatrixBase< R > &rhs) const
	Calculates \( \robabx{a}{c}{\mathbf{R}} = \robabx{a}{b}{\mathbf{R}} \robabx{b}{c}{\mathbf{R}} \). More...

const rw::math::Vector3D< T >	operator* (const rw::math::Vector3D< T > &bVc) const
	Calculates \( \robabx{a}{c}{\mathbf{v}} = \robabx{a}{b}{\mathbf{R}} \robabx{b}{c}{\mathbf{v}} \). More...

template<class R >
	Rotation3D (const EigenMatrix3x3 &r)
	Construct a rotation matrix from a 3x3 Eigen matrix It is the responsibility of the user that 3x3 matrix is indeed a rotation matrix.

template<class R >
	Rotation3D (const Eigen::MatrixBase< R > &m)
	Construct a rotation matrix from a 3x3 Eigen matrix It is the responsibility of the user that 3x3 matrix is indeed a rotation matrix.

Rotation3D< T > &	inverse ()
	Calculate the inverse. More...

Rotation3D< T >	inverse (bool copy)
	Calculate the inverse. More...

const Rotation3D< T >	inverse (bool copy) const
	Calculate the inverse. of a const Rotation3D. For this function copy is always true. More...

T	tr () const

Rotation3D< T > &	operator= (const Rotation3DVector< T > &rot)
	Assignment of RotationVector to Rotation3D. More...

Static Public Member Functions
static const Rotation3D< T >	identity ()
	Constructs a 3x3 rotation matrix set to identity. More...

static void	multiply (const Rotation3D< T > &a, const Rotation3D< T > &b, Rotation3D< T > &result)
	Write to result the product a * b.

static void	multiply (const Rotation3D< T > &a, const rw::math::Vector3D< T > &b, rw::math::Vector3D< T > &result)
	Write to result the product a * b.

static const Rotation3D< T >	multiply (const Rotation3D< T > &aRb, const Rotation3D< T > &bRc)
	Calculates \( \robabx{a}{c}{\mathbf{R}} = \robabx{a}{b}{\mathbf{R}} \robabx{b}{c}{\mathbf{R}} \). More...

static const rw::math::Vector3D< T >	multiply (const Rotation3D< T > &aRb, const rw::math::Vector3D< T > &bVc)
	Calculates \( \robabx{a}{c}{\mathbf{v}} = \robabx{a}{b}{\mathbf{R}} \robabx{b}{c}{\mathbf{v}} \). More...

Friends
template<class R >
Rotation3D	operator* (const Eigen::MatrixBase< R > &lhs, const Rotation3D< T > &rhs)
	Calculates \( \robabx{a}{c}{\mathbf{R}} = \robabx{a}{b}{\mathbf{R}} \robabx{b}{c}{\mathbf{R}} \). More...

Related Functions
(Note that these are not member functions.)
static Rotation3D< T >	skew (const rw::math::Vector3D< T > &v)
	Creates a skew symmetric matrix from a Vector3D. Also known as the cross product matrix of v. More...

template<class S , class T >
const Rotation3D< S >	cast (const Rotation3D< T > &rot)
	Casts Rotation3D<T> to Rotation3D More...

template<class T >
const rw::math::Rotation3D< T >	inverse (const rw::math::Rotation3D< T > &aRb)
	Calculates the inverse \( \robabx{b}{a}{\mathbf{R}} = \robabx{a}{b}{\mathbf{R}}^{-1} \) of a rotation matrix. More...

template<class T >
std::ostream &	operator<< (std::ostream &os, const Rotation3D< T > &r)
	Writes rotation matrix to stream. More...

template<>
void	write (const rw::math::Rotation3D< double > &sobject, rw::common::OutputArchive &oarchive, const std::string &id)

template<>
void	write (const rw::math::Rotation3D< float > &sobject, rw::common::OutputArchive &oarchive, const std::string &id)

template<>
void	read (rw::math::Rotation3D< double > &sobject, rw::common::InputArchive &iarchive, const std::string &id)

template<>
void	read (rw::math::Rotation3D< float > &sobject, rw::common::InputArchive &iarchive, const std::string &id)

template<class Archive , class T >
void	serialize (Archive &archive, rw::math::Rotation3D< T > &R, const unsigned int version)
	Boost serialization. More...

Detailed Description

template<class T = double>
class rw::math::Rotation3D< T >

A 3x3 rotation matrix \( \mathbf{R}\in SO(3) \).

\( \mathbf{R}= \left[ \begin{array}{ccc} {}^A\hat{X}_B & {}^A\hat{Y}_B & {}^A\hat{Z}_B \end{array} \right] = \left[ \begin{array}{ccc} r_{11} & r_{12} & r_{13} \\ r_{21} & r_{22} & r_{23} \\ r_{31} & r_{32} & r_{33} \end{array} \right] \)

Constructor & Destructor Documentation

◆ Rotation3D() [1/3]

Rotation3D	(	T	r11,
		T	r12,
		T	r13,
		T	r21,
		T	r22,
		T	r23,
		T	r31,
		T	r32,
		T	r33
	)

inline

Constructs an initialized 3x3 rotation matrix.

Parameters

r11	\( r_{11} \)
r12	\( r_{12} \)
r13	\( r_{13} \)
r21	\( r_{21} \)
r22	\( r_{22} \)
r23	\( r_{23} \)
r31	\( r_{31} \)
r32	\( r_{32} \)
r33	\( r_{33} \)

\( \mathbf{R} = \left[ \begin{array}{ccc} r_{11} & r_{12} & r_{13} \\ r_{21} & r_{22} & r_{23} \\ r_{31} & r_{32} & r_{33} \end{array} \right] \)

◆ Rotation3D() [2/3]

Rotation3D	(	const rw::math::Vector3D< T > &	i,
		const rw::math::Vector3D< T > &	j,
		const rw::math::Vector3D< T > &	k
	)

inline

Constructs an initialized 3x3 rotation matrix \( \robabx{a}{b}{\mathbf{R}} = \left[ \begin{array}{ccc} \robabx{a}{b}{\mathbf{i}} & \robabx{a}{b}{\mathbf{j}} & \robabx{a}{b}{\mathbf{k}} \end{array} \right] \).

Parameters

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

◆ Rotation3D() [3/3]

Rotation3D ( const Rotation3DVector< T > & rotVec )

explicit

Initialize Rotation3D from other rotation types.

Parameters

rotVec [in] rotation type such as EAA, RPY, or Quaternion

Member Function Documentation

◆ e() [1/2]

EigenMatrix3x3& e ( )

inline

Returns a Eigen 3x3 matrix \( \mathbf{M}\in SO(3) \) that represents this rotation.

Returns: \( \mathbf{M}\in SO(3) \)

◆ e() [2/2]

const EigenMatrix3x3& e ( ) const

inline

Returns a Eigen 3x3 matrix \( \mathbf{M}\in SO(3) \) that represents this rotation.

Returns: \( \mathbf{M}\in SO(3) \)

◆ equal()

bool equal	(	const Rotation3D< T > &	rot,
		const T	precision = `std::numeric_limits<T>::epsilon()`
	)		const

inline

Compares rotations with a given precision.

Performs an element wise comparison. Two elements are considered equal if the difference are less than precision.

Parameters

rot	[in] Rotation to compare with
precision	[in] The precision to use for testing

Returns: True if all elements are less than precision apart.

◆ getCol()

const rw::math::Vector3D<T> getCol ( size_t i ) const

inline

Returns the i'th column of the rotation matrix.

Parameters

i	[in] Index of the column to return. Only valid indices are 0, 1 and 2.

◆ getRow()

const rw::math::Vector3D<T> getRow ( size_t i ) const

inline

Returns the i'th row of the rotation matrix.

Parameters

i	[in] Index of the row to return. Only valid indices are 0, 1 and 2.

◆ identity()

static const Rotation3D<T> identity ( )

inlinestatic

Constructs a 3x3 rotation matrix set to identity.

Returns: a 3x3 identity rotation matrix

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

◆ inverse() [1/3]

Rotation3D<T>& inverse ( )

inline

Calculate the inverse.

Note: This function changes the object that it is invoked on, but this is about x5 faster than rot = inverse( rot )

See also: rw::math::inverse(const rw::math::Rotation3D< T > &) for the (slower) version that does not change the rotation object itself.

Returns: the inverse rotation.

◆ inverse() [2/3]

Rotation3D<T> inverse ( bool copy )

Calculate the inverse.

Parameters

copy	[in] if coopy is false, This function changes the object that it is invoked on, but this is about x5 faster than rot = inverse( rot ). else it changes the object, making it a bit slower.

Returns: the inverse rotation.

◆ inverse() [3/3]

const Rotation3D<T> inverse ( bool copy ) const

Calculate the inverse. of a const Rotation3D. For this function copy is always true.

Parameters

copy	[in] always true

Returns: the inverse rotation.

◆ isProperRotation() [1/2]

bool isProperRotation ( ) const

Verify that this rotation is a proper rotation.

Returns: True if this rotation is considered a proper rotation

◆ isProperRotation() [2/2]

bool isProperRotation ( T precision ) const

Verify that this rotation is a proper rotation.

Returns: True if this rotation is considered a proper rotation

◆ multiply() [1/2]

static const Rotation3D<T> multiply	(	const Rotation3D< T > &	aRb,
		const Rotation3D< T > &	bRc
	)

static

Calculates \( \robabx{a}{c}{\mathbf{R}} = \robabx{a}{b}{\mathbf{R}} \robabx{b}{c}{\mathbf{R}} \).

Parameters

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

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

◆ multiply() [2/2]

static const rw::math::Vector3D<T> multiply	(	const Rotation3D< T > &	aRb,
		const rw::math::Vector3D< T > &	bVc
	)

static

Calculates \( \robabx{a}{c}{\mathbf{v}} = \robabx{a}{b}{\mathbf{R}} \robabx{b}{c}{\mathbf{v}} \).

Parameters

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

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

◆ normalize()

void normalize ( )

Normalizes the rotation matrix to satisfy SO(3).

Makes a normalization of the rotation matrix such that the columns are normalized and othogonal s.t. it belongs to SO(3).

◆ operator!=()

bool operator!= ( const Rotation3D< 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] Rotation 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*() [1/3]

const Rotation3D operator* ( const Eigen::MatrixBase< R > & rhs ) const

inline

Calculates \( \robabx{a}{c}{\mathbf{R}} = \robabx{a}{b}{\mathbf{R}} \robabx{b}{c}{\mathbf{R}} \).

Parameters

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

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

◆ operator*() [2/3]

const Rotation3D operator* ( const Rotation3D< T > & bRc ) const

inline

Calculates \( \robabx{a}{c}{\mathbf{R}} = \robabx{a}{b}{\mathbf{R}} \robabx{b}{c}{\mathbf{R}} \).

Parameters

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

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

◆ operator*() [3/3]

const rw::math::Vector3D<T> operator* ( const rw::math::Vector3D< T > & bVc ) const

inline

Calculates \( \robabx{a}{c}{\mathbf{v}} = \robabx{a}{b}{\mathbf{R}} \robabx{b}{c}{\mathbf{v}} \).

Parameters

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

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

◆ operator=()

Rotation3D<T>& operator= ( const Rotation3DVector< T > & rot )

Assignment of RotationVector to Rotation3D.

Parameters

rot	[in] Rotation input

◆ operator==()

bool operator== ( const Rotation3D< 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] Rotation to compare with

Returns: True if equal.

Friends And Related Function Documentation

◆ cast()

const Rotation3D< S > cast ( const Rotation3D< T > & rot )

Parameters

rot	[in] Rotation3D with type T

Returns: Rotation3D with type S

◆ inverse()

const rw::math::Rotation3D< T > inverse ( const rw::math::Rotation3D< T > & aRb )

See also: Rotation3D::inverse() for a faster version that modifies the existing rotation object instead of allocating a new one.

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*

Rotation3D operator*	(	const Eigen::MatrixBase< R > &	lhs,
		const Rotation3D< T > &	rhs
	)

friend

Calculates \( \robabx{a}{c}{\mathbf{R}} = \robabx{a}{b}{\mathbf{R}} \robabx{b}{c}{\mathbf{R}} \).

Parameters

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

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

◆ operator<<()

std::ostream & operator<<	(	std::ostream &	os,
		const Rotation3D< T > &	r
	)

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::Rotation3D< 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::Rotation3D< 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::Rotation3D< 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).

◆ skew()

static Rotation3D<T> skew ( const rw::math::Vector3D< T > & v )

Parameters

v	[in] vector to create Skew matrix from

◆ write() [1/2]

void write	(	const rw::math::Rotation3D< 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::Rotation3D< 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
Rotation3D.hpp

Public Types

Public Member Functions

Static Public Member Functions

Friends

Related Functions

Detailed Description

template<class T = double> class rw::math::Rotation3D< T >

Constructor & Destructor Documentation

◆ Rotation3D() [1/3]

◆ Rotation3D() [2/3]

◆ Rotation3D() [3/3]

Member Function Documentation

◆ e() [1/2]

◆ e() [2/2]

◆ equal()

◆ getCol()

◆ getRow()

◆ identity()

◆ inverse() [1/3]

◆ inverse() [2/3]

◆ inverse() [3/3]

◆ isProperRotation() [1/2]

◆ isProperRotation() [2/2]

◆ multiply() [1/2]

◆ multiply() [2/2]

◆ normalize()

◆ operator!=()

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ operator*() [1/3]

◆ operator*() [2/3]

◆ operator*() [3/3]

◆ operator=()

◆ operator==()

Friends And Related Function Documentation

◆ cast()

◆ inverse()

◆ operator*

◆ operator<<()

◆ read() [1/2]

◆ read() [2/2]

◆ serialize()

◆ skew()

◆ write() [1/2]

◆ write() [2/2]

template<class T = double>
class rw::math::Rotation3D< T >