Represent a three-dimensional Euclidean transformation (a rotation and a translation). More...

#include <se3.h>

Public Member Functions
	SE3 ()
	Default constructor. Initialises the the rotation to zero (the identity) and the translation to zero.

template<int S, typename P , typename A >
	SE3 (const SO3< Precision > &R, const Vector< S, P, A > &T)

template<int S, typename P , typename A >
	SE3 (const Vector< S, P, A > &v)

template<class IP , int S, typename P , typename A >
	SE3 (const Operator< Internal::Identity< IP > > &, const Vector< S, P, A > &T)

SO3< Precision > &	get_rotation ()
	Returns the rotation part of the transformation as a SO3.

const SO3< Precision > &	get_rotation () const

Vector< 3, Precision > &	get_translation ()
	Returns the translation part of the transformation as a Vector.

const Vector< 3, Precision > &	get_translation () const

Vector< 6, Precision >	ln () const

SE3	inverse () const

template<typename P >
SE3 &	operator*= (const SE3< P > &rhs)
	Right-multiply by another SE3 (concatenate the two transformations) More...

template<typename P >
SE3< typename Internal::MultiplyType< Precision, P >::type >	operator* (const SE3< P > &rhs) const
	Right-multiply by another SE3 (concatenate the two transformations) More...

SE3 &	left_multiply_by (const SE3 &left)

template<int S, typename P2 , typename Accessor >
Vector< 6, Precision >	adjoint (const Vector< S, P2, Accessor > &vect) const
	Transfer a matrix in the Lie Algebra from one co-ordinate frame to another. More...

template<int S, typename P2 , typename Accessor >
Vector< 6, Precision >	trinvadjoint (const Vector< S, P2, Accessor > &vect) const
	Transfer covectors between frames (using the transpose of the inverse of the adjoint) so that trinvadjoint(vect1) * adjoint(vect2) = vect1 * vect2.

template<int R, int C, typename P2 , typename Accessor >
Matrix< 6, 6, Precision >	adjoint (const Matrix< R, C, P2, Accessor > &M) const

template<int R, int C, typename P2 , typename Accessor >
Matrix< 6, 6, Precision >	trinvadjoint (const Matrix< R, C, P2, Accessor > &M) const

template<int S, typename P , typename VA >
SE3< Precision >	exp (const Vector< S, P, VA > &mu)

Static Public Member Functions
template<int S, typename P , typename A >
static SE3	exp (const Vector< S, P, A > &vect)
	Exponentiate a Vector in the Lie Algebra to generate a new SE3. More...

static Vector< 6, Precision >	ln (const SE3 &se3)
	Take the logarithm of the matrix, generating the corresponding vector in the Lie Algebra. More...

static Matrix< 4, 4, Precision >	generator (int i)

template<typename Base >
static Vector< 4, Precision >	generator_field (int i, const Vector< 4, Precision, Base > &pos)
	Returns the i-th generator times pos.

Related Functions
(Note that these are not member functions.)
template<typename Precision >
std::ostream &	operator<< (std::ostream &os, const SE3< Precision > &rhs)
	Write an SE3 to a stream. More...

template<typename Precision >
std::istream &	operator>> (std::istream &is, SE3< Precision > &rhs)
	Reads an SE3 from a stream. More...

template<int S, typename PV , typename A , typename P >
Vector< 4, typename Internal::MultiplyType< P, PV >::type >	operator* (const SE3< P > &lhs, const Vector< S, PV, A > &rhs)
	Right-multiply by a Vector. More...

template<typename PV , typename A , typename P >
Vector< 3, typename Internal::MultiplyType< P, PV >::type >	operator* (const SE3< P > &lhs, const Vector< 3, PV, A > &rhs)
	Right-multiply by a Vector. More...

template<int S, typename PV , typename A , typename P >
Vector< 4, typename Internal::MultiplyType< P, PV >::type >	operator* (const Vector< S, PV, A > &lhs, const SE3< P > &rhs)
	Left-multiply by a Vector. More...

template<int R, int Cols, typename PM , typename A , typename P >
Matrix< 4, Cols, typename Internal::MultiplyType< P, PM >::type >	operator* (const SE3< P > &lhs, const Matrix< R, Cols, PM, A > &rhs)
	Right-multiply by a Matrix. More...

template<int Rows, int C, typename PM , typename A , typename P >
Matrix< Rows, 4, typename Internal::MultiplyType< PM, P >::type >	operator* (const Matrix< Rows, C, PM, A > &lhs, const SE3< P > &rhs)
	Left-multiply by a Matrix. More...

Detailed Description

template<typename Precision = DefaultPrecision>
class TooN::SE3< Precision >

Represent a three-dimensional Euclidean transformation (a rotation and a translation).

This can be represented by a matrix operating on a homogeneous co-ordinate, so that a vector \(\underline{x}\) is transformed to a new location \(\underline{x}'\) by

\[\begin{aligned}\underline{x}' &= E\times\underline{x}\\ \begin{bmatrix}x'\\y'\\z'\end{bmatrix} &= \begin{pmatrix}r_{11} & r_{12} & r_{13} & t_1\\r_{21} & r_{22} & r_{23} & t_2\\r_{31} & r_{32} & r_{33} & t_3\end{pmatrix}\begin{bmatrix}x\\y\\z\\1\end{bmatrix}\end{aligned}\]

This transformation is a member of the Special Euclidean Lie group SE3. These can be parameterised six numbers (in the space of the Lie Algebra). In this class, the first three parameters are a translation vector while the second three are a rotation vector, whose direction is the axis of rotation and length the amount of rotation (in radians), as for SO3

Member Function Documentation

◆ adjoint() [1/2]

template<typename Precision >

template<int S, typename P2 , typename Accessor >

Vector< 6, Precision > TooN::SE3< Precision >::adjoint ( const Vector< S, P2, Accessor > & vect ) const

inline

Transfer a matrix in the Lie Algebra from one co-ordinate frame to another.

This is the operation such that for a matrix \( B \), \( e^{\text{Adj}(v)} = Be^{v}B^{-1} \)

Parameters

M	The Matrix to transfer

◆ adjoint() [2/2]

template<typename Precision >

template<int R, int C, typename P2 , typename Accessor >

Matrix< 6, 6, Precision > TooN::SE3< Precision >::adjoint ( const Matrix< R, C, P2, Accessor > & M ) const

inline

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

◆ exp()

template<typename Precision = DefaultPrecision>

template<int S, typename P , typename A >

static SE3 TooN::SE3< Precision >::exp ( const Vector< S, P, A > & vect )

inlinestatic

Exponentiate a Vector in the Lie Algebra to generate a new SE3.

See the Detailed Description for details of this vector.

Parameters

vect	The Vector to exponentiate

◆ get_rotation()

template<typename Precision = DefaultPrecision>

const SO3<Precision>& TooN::SE3< Precision >::get_rotation ( ) const

inline

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

◆ get_translation()

template<typename Precision = DefaultPrecision>

const Vector<3, Precision>& TooN::SE3< Precision >::get_translation ( ) const

inline

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

◆ ln() [1/2]

template<typename Precision >

Vector< 6, Precision > TooN::SE3< Precision >::ln ( const SE3< Precision > & se3 )

inlinestatic

Take the logarithm of the matrix, generating the corresponding vector in the Lie Algebra.

See the Detailed Description for details of this vector.

◆ ln() [2/2]

template<typename Precision = DefaultPrecision>

Vector<6, Precision> TooN::SE3< Precision >::ln ( ) const

inline

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

◆ operator*()

template<typename Precision = DefaultPrecision>

template<typename P >

SE3<typename Internal::MultiplyType<Precision, P>::type> TooN::SE3< Precision >::operator* ( const SE3< P > & rhs ) const

inline

Right-multiply by another SE3 (concatenate the two transformations)

Parameters

rhs	The multipier

◆ operator*=()

template<typename Precision = DefaultPrecision>

template<typename P >

SE3& TooN::SE3< Precision >::operator*= ( const SE3< P > & rhs )

inline

Right-multiply by another SE3 (concatenate the two transformations)

Parameters

rhs	The multipier

◆ trinvadjoint()

template<typename Precision >

template<int R, int C, typename P2 , typename Accessor >

Matrix< 6, 6, Precision > TooN::SE3< Precision >::trinvadjoint ( const Matrix< R, C, P2, Accessor > & M ) const

inline

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Friends And Related Function Documentation

◆ operator*() [1/5]

template<int S, typename PV , typename A , typename P >

Vector< 4, typename Internal::MultiplyType< P, PV >::type > operator*	(	const SE3< P > &	lhs,
		const Vector< S, PV, A > &	rhs
	)

◆ operator*() [2/5]

template<typename PV , typename A , typename P >

Vector< 3, typename Internal::MultiplyType< P, PV >::type > operator*	(	const SE3< P > &	lhs,
		const Vector< 3, PV, A > &	rhs
	)

◆ operator*() [3/5]

template<int S, typename PV , typename A , typename P >

Vector< 4, typename Internal::MultiplyType< P, PV >::type > operator*	(	const Vector< S, PV, A > &	lhs,
		const SE3< P > &	rhs
	)

◆ operator*() [4/5]

template<int R, int Cols, typename PM , typename A , typename P >

Matrix< 4, Cols, typename Internal::MultiplyType< P, PM >::type > operator*	(	const SE3< P > &	lhs,
		const Matrix< R, Cols, PM, A > &	rhs
	)

◆ operator*() [5/5]

template<int Rows, int C, typename PM , typename A , typename P >

Matrix< Rows, 4, typename Internal::MultiplyType< PM, P >::type > operator*	(	const Matrix< Rows, C, PM, A > &	lhs,
		const SE3< P > &	rhs
	)

◆ operator<<()

template<typename Precision >

std::ostream & operator<<	(	std::ostream &	os,
		const SE3< Precision > &	rhs
	)

◆ operator>>()

template<typename Precision >

std::istream & operator>>	(	std::istream &	is,
		SE3< Precision > &	rhs
	)

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

TooN/se3.h

Public Member Functions

Static Public Member Functions

Related Functions

Detailed Description

template<typename Precision = DefaultPrecision> class TooN::SE3< Precision >

Member Function Documentation

◆ adjoint() [1/2]

◆ adjoint() [2/2]

◆ exp()

◆ get_rotation()

◆ get_translation()

◆ ln() [1/2]

◆ ln() [2/2]

◆ operator*()

◆ operator*=()

◆ trinvadjoint()

Friends And Related Function Documentation

◆ operator*() [1/5]

◆ operator*() [2/5]

◆ operator*() [3/5]

◆ operator*() [4/5]

◆ operator*() [5/5]

◆ operator<<()

◆ operator>>()

template<typename Precision = DefaultPrecision>
class TooN::SE3< Precision >