SE2< T > Class Template Reference

Class representing a member of the \(SE(2)\) manifold, or a 2D rigid body transform. More...

#include <SE2.h>

Public Member Functions
	SE2 ()
	Create a transform (with garbage data).
	SE2 (const Ref< const Vec4T > &arr)
	Create a transform from an array representing all transform fields in \(\begin{bmatrix}\boldsymbol{t} & \boldsymbol{q}\end{bmatrix}^\top\).
	SE2 (const SE2 &x)
	Copy constructor from another transform.
	SE2 (const T *data)
	Create a transform from a pointer array representing all transform fields in \(\begin{bmatrix}\boldsymbol{t} & \boldsymbol{q}\end{bmatrix}^\top\).
T &	operator[] (int i)
	Access a field from \(\begin{bmatrix}\boldsymbol{t} & \boldsymbol{q}\end{bmatrix}^\top\).
const Map< Vec2T > &	t () const
	Access the translation vector \(\boldsymbol{t}\in\mathbb{R}^2\).
const SO2< T > &	q () const
	Access the rotation \(\boldsymbol{q}\in SO(2)\).
Map< Vec2T > &	t ()
	Access the translation vector \(\boldsymbol{t}\in\mathbb{R}^2\).
SO2< T > &	q ()
	Access the rotation \(\boldsymbol{q}\in SO(2)\).
const Vec4T	elements () const
	Access all elements of \(\begin{bmatrix}\boldsymbol{t} & \boldsymbol{q}\end{bmatrix}^\top\).
Vec4T	array () const
	Access all elements of \(\begin{bmatrix}\boldsymbol{t} & \boldsymbol{q}\end{bmatrix}^\top\).
T *	data ()
	Access pointer to all elements of \(\begin{bmatrix}\boldsymbol{t} & \boldsymbol{q}\end{bmatrix}^\top\).
const T *	data () const
	Access pointer to all elements of \(\begin{bmatrix}\boldsymbol{t} & \boldsymbol{q}\end{bmatrix}^\top\).
SE2	copy () const
	Get a deep copy of the current transform.
Mat3T	H () const
	Convert the transform to matrix representation \(\begin{bmatrix}\boldsymbol{R} & \boldsymbol{t} \\ \boldsymbol{0} & 1\end{bmatrix}\in\mathbb{R}^{3\times 3}\).
SE2	inverse () const
	Obtain the inverse transform \(\boldsymbol{T}_A^B\rightarrow \boldsymbol{T}_B^A\).
SE2 &	invert ()
	Invert the current transform \(\boldsymbol{T}_A^B\rightarrow \boldsymbol{T}_B^A\).
template<typename Tout = T, typename T2 >
SE2< Tout >	otimes (const SE2< T2 > &x) const
	Implementation of group composition: \(\boldsymbol{T}_B^C \otimes \boldsymbol{T}_A^B\rightarrow \boldsymbol{T}_A^C\).
template<typename Tout = T, typename T2 >
SE2< Tout >	oplus (const Matrix< T2, 3, 1 > &delta) const
	Implementation of tangent space group perturbations: \(\boldsymbol{T}_A^B\oplus \boldsymbol{t}_B^{B'} \rightarrow \boldsymbol{T}_A^{B'}\).
template<typename Tout = T, typename T2 >
Matrix< Tout, 3, 1 >	ominus (const SE2< T2 > &x) const
	Implementation of group subtraction: \(\boldsymbol{T}_A^B\ominus \boldsymbol{T}_A^{B'} \rightarrow \boldsymbol{t}_B^{B'}\).
SE2 &	operator= (const SE2 &x)
	Copy constructor.
template<typename T2 >
SE2	operator* (const SE2< T2 > &x) const
	Invocation of otimes via multiplication.
template<typename T2 >
SE2 &	operator*= (const SE2< T2 > &x)
	Invocation of otimes via multiplication.
SE2 &	operator*= (const double &s)
	Scale a transform by a scalar.
SE2 &	operator/= (const double &s)
	Scale a transform by a scalar.
SE2	operator/ (const double &s) const
	Scale a transform by a scalar.
template<typename Tout = T, typename T2 >
Matrix< Tout, 2, 1 >	operator* (const Matrix< T2, 2, 1 > &v) const
	Transform a vector via multiplication: \(\boldsymbol{T}_A^B\boldsymbol{t}^A \rightarrow \boldsymbol{t}^B\).
Vec2T	operator* (const Vec2T &v) const
	Transform a vector via multiplication: \(\boldsymbol{T}_A^B\boldsymbol{t}^A \rightarrow \boldsymbol{t}^B\).
SE2	operator+ (const Vec3T &v) const
	Invocation of oplus via addition.
SE2 &	operator+= (const Vec3T &v)
	Invocation of oplus via addition.
template<typename T2 >
Vec3T	operator- (const SE2< T2 > &x) const
	Invocation of ominus via subtraction.
template<typename T2 >
SE2< T2 >	cast () const
	Cast the underlying numeric type.

Static Public Member Functions
static SE2	random ()
	Obtain a random \(SE(2)\) transform.
static SE2	identity ()
	Obtain an identity \(SE(2)\) transform.
static SE2	nans ()
	Obtain a transform full of NaNs.
static SE2	fromH (const Mat3T &m)
	Convert a transform matrix \(\begin{bmatrix}\boldsymbol{R} & \boldsymbol{t} \\ \boldsymbol{0} & 1\end{bmatrix}\) into a \(SE(2)\) transform.
static SE2	fromVecAndRot (const T tx, const T ty, const T qw, const T qx)
	Construct a transform from the individual fields.
static SE2	fromVecAndRot (const Vec2T &tvec, const Vec2T &qvec)
	Construct a transform from a translation vector and rotation fields vector.
static SE2	fromVecAndRot (const Vec2T &t, const SO2< T > &q)
	Construct a transform from a translation vector and a rotation object.
static Mat3T	hat (const Vec3T &omega)
	Hat operator implementation, which coverts the tangent-space vector representation to the corresponding Lie algebra: \(\mathbb{R}^3\rightarrow \mathfrak{se}(2)\).
static Vec3T	vee (const Mat3T &Omega)
	Vee operator implementation, which coverts the Lie algebra representation to a tangent-space vector representation: \(\mathfrak{se}(2) \rightarrow \mathbb{R}^3\).
static Mat3T	log (const SE2 &x)
	Logarithmic chart map implementation: \(SE(2) \rightarrow \mathfrak{se}(2)\).
static Vec3T	Log (const SE2 &x)
	Logarithmic chart map implementation: \(SE(2) \rightarrow \mathbb{R}^3\).
static SE2	exp (const Mat3T &Omega)
	Exponential chart map implementation: \(\mathfrak{se}(2) \rightarrow SE(2)\).
static SE2	Exp (const Vec3T &omega)
	Exponential chart map implementation: \(\mathbb{R}^3 \rightarrow SE(2)\).

Public Attributes
EIGEN_MAKE_ALIGNED_OPERATOR_NEW Map< Vec4T >	arr_
	Memory-mapped array representing all transform fields in \(\begin{bmatrix}\boldsymbol{t} & \boldsymbol{q}\end{bmatrix}^\top\).
Map< Vec2T >	t_
	Memory-mapped array representing only the translation component of the transform \(\boldsymbol{t}\).
SO2< T >	q_
	Memory-mapped array representing only the rotation component of the transform \(\boldsymbol{q}\).

Detailed Description

template<typename T>
class SE2< T >

Class representing a member of the \(SE(2)\) manifold, or a 2D rigid body transform.

Constructor & Destructor Documentation

SE2() [1/4]

template<typename T >

SE2< T >::SE2 ( )

inline

Create a transform (with garbage data).

SE2() [2/4]

template<typename T >

SE2< T >::SE2 ( const Ref< const Vec4T > & arr )

inline

Create a transform from an array representing all transform fields in \(\begin{bmatrix}\boldsymbol{t} & \boldsymbol{q}\end{bmatrix}^\top\).

SE2() [3/4]

template<typename T >

SE2< T >::SE2 ( const SE2< T > & x )

inline

Copy constructor from another transform.

SE2() [4/4]

template<typename T >

SE2< T >::SE2 ( const T * data )

inline

Create a transform from a pointer array representing all transform fields in \(\begin{bmatrix}\boldsymbol{t} & \boldsymbol{q}\end{bmatrix}^\top\).

Member Function Documentation

array()

template<typename T >

Vec4T SE2< T >::array ( ) const

inline

Access all elements of \(\begin{bmatrix}\boldsymbol{t} & \boldsymbol{q}\end{bmatrix}^\top\).

cast()

template<typename T >

template<typename T2 >

SE2< T2 > SE2< T >::cast ( ) const

inline

Cast the underlying numeric type.

copy()

template<typename T >

SE2 SE2< T >::copy ( ) const

inline

Get a deep copy of the current transform.

data() [1/2]

template<typename T >

T * SE2< T >::data ( )

inline

Access pointer to all elements of \(\begin{bmatrix}\boldsymbol{t} & \boldsymbol{q}\end{bmatrix}^\top\).

data() [2/2]

template<typename T >

const T * SE2< T >::data ( ) const

inline

Access pointer to all elements of \(\begin{bmatrix}\boldsymbol{t} & \boldsymbol{q}\end{bmatrix}^\top\).

elements()

template<typename T >

const Vec4T SE2< T >::elements ( ) const

inline

Access all elements of \(\begin{bmatrix}\boldsymbol{t} & \boldsymbol{q}\end{bmatrix}^\top\).

exp()

template<typename T >

static SE2 SE2< T >::exp ( const Mat3T & Omega )

inlinestatic

Exponential chart map implementation: \(\mathfrak{se}(2) \rightarrow SE(2)\).

Exp()

template<typename T >

static SE2 SE2< T >::Exp ( const Vec3T & omega )

inlinestatic

Exponential chart map implementation: \(\mathbb{R}^3 \rightarrow SE(2)\).

fromH()

template<typename T >

static SE2 SE2< T >::fromH ( const Mat3T & m )

inlinestatic

Convert a transform matrix \(\begin{bmatrix}\boldsymbol{R} & \boldsymbol{t} \\ \boldsymbol{0} & 1\end{bmatrix}\) into a \(SE(2)\) transform.

fromVecAndRot() [1/3]

template<typename T >

static SE2 SE2< T >::fromVecAndRot ( const T tx, const T ty, const T qw, const T qx )

inlinestatic

Construct a transform from the individual fields.

Parameters

tx	First component of the translation \(\boldsymbol{t}\in\mathbb{R}^2\).
ty	Second component of the translation \(\boldsymbol{t}\in\mathbb{R}^2\).
qw	Real component of the rotation \(\boldsymbol{q}\in SO(2)\).
qx	Imaginary component of the rotation \(\boldsymbol{q}\in SO(2)\).

fromVecAndRot() [2/3]

template<typename T >

static SE2 SE2< T >::fromVecAndRot ( const Vec2T & t, const SO2< T > & q )

inlinestatic

Construct a transform from a translation vector and a rotation object.

Parameters

t	The translation vector \(\boldsymbol{t}\in\mathbb{R}^2\).
q	The rotation \(\boldsymbol{q}\in SO(2)\).

fromVecAndRot() [3/3]

template<typename T >

static SE2 SE2< T >::fromVecAndRot ( const Vec2T & tvec, const Vec2T & qvec )

inlinestatic

Construct a transform from a translation vector and rotation fields vector.

Parameters

tvec	The translation vector \(\boldsymbol{t}\in\mathbb{R}^2\).
qvec	The rotation represented as an array \(\boldsymbol{q}\in\mathbb{R}^2\).

H()

template<typename T >

Mat3T SE2< T >::H ( ) const

inline

Convert the transform to matrix representation \(\begin{bmatrix}\boldsymbol{R} & \boldsymbol{t} \\ \boldsymbol{0} & 1\end{bmatrix}\in\mathbb{R}^{3\times 3}\).

hat()

template<typename T >

static Mat3T SE2< T >::hat ( const Vec3T & omega )

inlinestatic

Hat operator implementation, which coverts the tangent-space vector representation to the corresponding Lie algebra: \(\mathbb{R}^3\rightarrow \mathfrak{se}(2)\).

identity()

template<typename T >

static SE2 SE2< T >::identity ( )

inlinestatic

Obtain an identity \(SE(2)\) transform.

inverse()

template<typename T >

SE2 SE2< T >::inverse ( ) const

inline

Obtain the inverse transform \(\boldsymbol{T}_A^B\rightarrow \boldsymbol{T}_B^A\).

invert()

template<typename T >

SE2 & SE2< T >::invert ( )

inline

Invert the current transform \(\boldsymbol{T}_A^B\rightarrow \boldsymbol{T}_B^A\).

log()

template<typename T >

static Mat3T SE2< T >::log ( const SE2< T > & x )

inlinestatic

Logarithmic chart map implementation: \(SE(2) \rightarrow \mathfrak{se}(2)\).

Log()

template<typename T >

static Vec3T SE2< T >::Log ( const SE2< T > & x )

inlinestatic

Logarithmic chart map implementation: \(SE(2) \rightarrow \mathbb{R}^3\).

nans()

template<typename T >

static SE2 SE2< T >::nans ( )

inlinestatic

Obtain a transform full of NaNs.

ominus()

template<typename T >

template<typename Tout = T, typename T2 >

Matrix< Tout, 3, 1 > SE2< T >::ominus ( const SE2< T2 > & x ) const

inline

Implementation of group subtraction: \(\boldsymbol{T}_A^B\ominus \boldsymbol{T}_A^{B'} \rightarrow \boldsymbol{t}_B^{B'}\).

operator*() [1/3]

template<typename T >

template<typename Tout = T, typename T2 >

Matrix< Tout, 2, 1 > SE2< T >::operator* ( const Matrix< T2, 2, 1 > & v ) const

inline

Transform a vector via multiplication: \(\boldsymbol{T}_A^B\boldsymbol{t}^A \rightarrow \boldsymbol{t}^B\).

operator*() [2/3]

template<typename T >

template<typename T2 >

SE2 SE2< T >::operator* ( const SE2< T2 > & x ) const

inline

Invocation of otimes via multiplication.

operator*() [3/3]

template<typename T >

Vec2T SE2< T >::operator* ( const Vec2T & v ) const

inline

Transform a vector via multiplication: \(\boldsymbol{T}_A^B\boldsymbol{t}^A \rightarrow \boldsymbol{t}^B\).

operator*=() [1/2]

template<typename T >

SE2 & SE2< T >::operator*= ( const double & s )

inline

Scale a transform by a scalar.

Under the hood, this converts the transform into a tangent-space vector, scales the vector, then converts the scaled vector back to a transform.

operator*=() [2/2]

template<typename T >

template<typename T2 >

SE2 & SE2< T >::operator*= ( const SE2< T2 > & x )

inline

Invocation of otimes via multiplication.

operator+()

template<typename T >

SE2 SE2< T >::operator+ ( const Vec3T & v ) const

inline

Invocation of oplus via addition.

operator+=()

template<typename T >

SE2 & SE2< T >::operator+= ( const Vec3T & v )

inline

Invocation of oplus via addition.

operator-()

template<typename T >

template<typename T2 >

Vec3T SE2< T >::operator- ( const SE2< T2 > & x ) const

inline

Invocation of ominus via subtraction.

operator/()

template<typename T >

SE2 SE2< T >::operator/ ( const double & s ) const

inline

Scale a transform by a scalar.

Under the hood, this converts the transform into a tangent-space vector, scales the vector, then converts the scaled vector back to a transform.

operator/=()

template<typename T >

SE2 & SE2< T >::operator/= ( const double & s )

inline

Scale a transform by a scalar.

Under the hood, this converts the transform into a tangent-space vector, scales the vector, then converts the scaled vector back to a transform.

operator=()

template<typename T >

SE2 & SE2< T >::operator= ( const SE2< T > & x )

inline

Copy constructor.

operator[]()

template<typename T >

T & SE2< T >::operator[] ( int i )

inline

Access a field from \(\begin{bmatrix}\boldsymbol{t} & \boldsymbol{q}\end{bmatrix}^\top\).

oplus()

template<typename T >

template<typename Tout = T, typename T2 >

SE2< Tout > SE2< T >::oplus ( const Matrix< T2, 3, 1 > & delta ) const

inline

Implementation of tangent space group perturbations: \(\boldsymbol{T}_A^B\oplus \boldsymbol{t}_B^{B'} \rightarrow \boldsymbol{T}_A^{B'}\).

otimes()

template<typename T >

template<typename Tout = T, typename T2 >

SE2< Tout > SE2< T >::otimes ( const SE2< T2 > & x ) const

inline

Implementation of group composition: \(\boldsymbol{T}_B^C \otimes \boldsymbol{T}_A^B\rightarrow \boldsymbol{T}_A^C\).

q() [1/2]

template<typename T >

SO2< T > & SE2< T >::q ( )

inline

Access the rotation \(\boldsymbol{q}\in SO(2)\).

q() [2/2]

template<typename T >

const SO2< T > & SE2< T >::q ( ) const

inline

Access the rotation \(\boldsymbol{q}\in SO(2)\).

random()

template<typename T >

static SE2 SE2< T >::random ( )

inlinestatic

Obtain a random \(SE(2)\) transform.

\(\boldsymbol{q}\) is normalized and \(0\leq t_i \leq 1\).

t() [1/2]

template<typename T >

Map< Vec2T > & SE2< T >::t ( )

inline

Access the translation vector \(\boldsymbol{t}\in\mathbb{R}^2\).

t() [2/2]

template<typename T >

const Map< Vec2T > & SE2< T >::t ( ) const

inline

Access the translation vector \(\boldsymbol{t}\in\mathbb{R}^2\).

vee()

template<typename T >

static Vec3T SE2< T >::vee ( const Mat3T & Omega )

inlinestatic

Vee operator implementation, which coverts the Lie algebra representation to a tangent-space vector representation: \(\mathfrak{se}(2) \rightarrow \mathbb{R}^3\).

Member Data Documentation

arr_

template<typename T >

EIGEN_MAKE_ALIGNED_OPERATOR_NEW Map<Vec4T> SE2< T >::arr_

Memory-mapped array representing all transform fields in \(\begin{bmatrix}\boldsymbol{t} & \boldsymbol{q}\end{bmatrix}^\top\).

q_

template<typename T >

SO2<T> SE2< T >::q_

Memory-mapped array representing only the rotation component of the transform \(\boldsymbol{q}\).

t_

template<typename T >

Map<Vec2T> SE2< T >::t_

Memory-mapped array representing only the translation component of the transform \(\boldsymbol{t}\).

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

• include/SE2.h