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

#include <se2.h>

Public Member Functions
	SE2 ()
template<class A >
	SE2 (const SO2< Precision > &R, const Vector< 2, Precision, A > &T)
template<int S, class P , class A >
	SE2 (const Vector< S, P, A > &v)
SO2< Precision > &	get_rotation ()
const SO2< Precision > &	get_rotation () const
Vector< 2, Precision > &	get_translation ()
const Vector< 2, Precision > &	get_translation () const
Vector< 3, Precision >	ln () const
SE2	inverse () const
template<typename P >
SE2< typename Internal::MultiplyType < Precision, P >::type >	operator* (const SE2< P > &rhs) const
template<typename P >
SE2 &	operator*= (const SE2< P > &rhs)
template<typename Accessor >
Vector< 3, Precision >	adjoint (const Vector< 3, Precision, Accessor > &vect) const
template<typename Accessor >
Matrix< 3, 3, Precision >	adjoint (const Matrix< 3, 3, Precision, Accessor > &M) const
template<int S, typename PV , typename Accessor >
SE2< Precision >	exp (const Vector< S, PV, Accessor > &mu)
Static Public Member Functions
template<int S, typename P , typename A >
static SE2	exp (const Vector< S, P, A > &vect)
static Vector< 3, Precision >	ln (const SE2 &se2)
static Matrix< 3, 3, Precision >	generator (int i)
Related Functions
(Note that these are not member functions.)
template<class Precision >
std::ostream &	operator<< (std::ostream &os, const SE2< Precision > &rhs)
template<int S, typename P , typename PV , typename A >
Vector< 3, typename Internal::MultiplyType< P, PV > ::type >	operator* (const SE2< P > &lhs, const Vector< S, PV, A > &rhs)
template<typename P , typename PV , typename A >
Vector< 2, typename Internal::MultiplyType< P, PV > ::type >	operator* (const SE2< P > &lhs, const Vector< 2, PV, A > &rhs)
template<int S, typename P , typename PV , typename A >
Vector< 3, typename Internal::MultiplyType< PV, P > ::type >	operator* (const Vector< S, PV, A > &lhs, const SE2< P > &rhs)
template<int R, int Cols, typename PM , typename A , typename P >
Matrix< 3, Cols, typename Internal::MultiplyType< P, PM > ::type >	operator* (const SE2< P > &lhs, const Matrix< R, Cols, PM, A > &rhs)
template<int Rows, int C, typename PM , typename A , typename P >
Matrix< Rows, 3, typename Internal::MultiplyType< PM, P > ::type >	operator* (const Matrix< Rows, C, PM, A > &lhs, const SE2< P > &rhs)

Detailed Description

template<typename Precision = DefaultPrecision>
class TooN::SE2< Precision >

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

This can be represented by a $2\times 3$ matrix operating on a homogeneous co-ordinate, so that a vector $\underline{x}$ is transformed to a new location $\underline{x}'$ by

$\begin{aligned}\underline{x}' &= E\times\underline{x}\\ \begin{bmatrix}x'\\y'\end{bmatrix} &= \begin{pmatrix}r_{11} & r_{12} & t_1\\r_{21} & r_{22} & t_2\end{pmatrix}\begin{bmatrix}x\\y\\1\end{bmatrix}\end{aligned}$

This transformation is a member of the Special Euclidean Lie group SE2. These can be parameterised with three numbers (in the space of the Lie Algebra). In this class, the first two parameters are a translation vector while the third is the amount of rotation in the plane as for SO2.

Member Function Documentation

const SO2<Precision>& get_rotation ( ) const

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

const Vector<2, Precision>& get_translation ( ) const

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

static SE2 exp ( const Vector< S, P, A > & vect ) [static]

Exponentiate a Vector in the Lie Algebra to generate a new SE2.

See the Detailed Description for details of this vector.

Parameters:

vect	The Vector to exponentiate

static Vector<3, Precision> ln ( const SE2< Precision > & se2 ) [static]

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

See the Detailed Description for details of this vector.

Vector<3, Precision> ln ( ) const

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

Referenced by SE2< P >::ln().

SE2<typename Internal::MultiplyType<Precision,P>::type> operator* ( const SE2< P > & rhs ) const

Right-multiply by another SE2 (concatenate the two transformations)

Parameters:

rhs	The multipier

SE2& operator*= ( const SE2< P > & rhs )

Self right-multiply by another SE2 (concatenate the two transformations)

Parameters:

rhs	The multipier

static Matrix<3,3, Precision> generator ( int i ) [static]

returns the generators for the Lie group.

These are a set of matrices that form a basis for the vector space of the Lie algebra.

0 is translation in x
1 is translation in y
2 is rotation in the plane

Friends And Related Function Documentation

std::ostream & operator<<	(	std::ostream &	os,
		const SE2< Precision > &	rhs
	)		`[related]`

Write an SE2 to a stream.

Vector< 3, typename Internal::MultiplyType< P, PV >::type > operator*	(	const SE2< P > &	lhs,
		const Vector< S, PV, A > &	rhs
	)		`[related]`

Right-multiply with a Vector<3>

Vector< 2, typename Internal::MultiplyType< P, PV >::type > operator*	(	const SE2< P > &	lhs,
		const Vector< 2, PV, A > &	rhs
	)		`[related]`

Right-multiply with a Vector<2> (special case, extended to be a homogeneous vector)

References SE2< Precision >::get_rotation(), and SE2< Precision >::get_translation().

Vector< 3, typename Internal::MultiplyType< PV, P >::type > operator*	(	const Vector< S, PV, A > &	lhs,
		const SE2< P > &	rhs
	)		`[related]`

Left-multiply with a Vector<3>

Matrix< 3, Cols, typename Internal::MultiplyType< P, PM >::type > operator*	(	const SE2< P > &	lhs,
		const Matrix< R, Cols, PM, A > &	rhs
	)		`[related]`

Right-multiply with a Matrix<3>

Matrix< Rows, 3, typename Internal::MultiplyType< PM, P >::type > operator*	(	const Matrix< Rows, C, PM, A > &	lhs,
		const SE2< P > &	rhs
	)		`[related]`

Left-multiply with a Matrix<3>

Public Member Functions

Static Public Member Functions

Related Functions

Detailed Description

template<typename Precision = DefaultPrecision> class TooN::SE2< Precision >

Member Function Documentation

Friends And Related Function Documentation

template<typename Precision = DefaultPrecision>
class TooN::SE2< Precision >