SE3< T > Class Template Reference

Class representing a member of the \(SE(3)\) manifold, or a 3D rigid body transform. More...

#include <SE3.h>

Public Member Functions
	SE3 ()
	Create a transform (with garbage data).
	SE3 (const Ref< const Vec7T > &arr)
	Create a transform from an array representing all transform fields in \(\begin{bmatrix}\boldsymbol{t} & \boldsymbol{q}\end{bmatrix}^\top\).
	SE3 (const SE3 &x)
	Copy constructor from another transform.
	SE3 (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< Vec3T > &	t () const
	Access the translation vector \(\boldsymbol{t}\in\mathbb{R}^3\).
const SO3< T > &	q () const
	Access the rotation \(\boldsymbol{q}\in SO(3)\).
Map< Vec3T > &	t ()
	Access the translation vector \(\boldsymbol{t}\in\mathbb{R}^3\).
SO3< T > &	q ()
	Access the rotation \(\boldsymbol{q}\in SO(3)\).
const Vec7T	elements () const
	Access all elements of \(\begin{bmatrix}\boldsymbol{t} & \boldsymbol{q}\end{bmatrix}^\top\).
Vec7T	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 \(\begin{bmatrix}\boldsymbol{t} & \boldsymbol{q}\end{bmatrix}^\top\).
SE3	copy () const
	Get a deep copy of the current transform.
Mat4T	H () const
	Convert the transform to matrix representation \(\begin{bmatrix}\boldsymbol{R} & \boldsymbol{t} \\ \boldsymbol{0} & 1\end{bmatrix}\in\mathbb{R}^{4\times 4}\).
SE3	inverse () const
	Obtain the inverse transform \(\boldsymbol{T}_A^B\rightarrow \boldsymbol{T}_B^A\).
SE3 &	invert ()
	Invert the current transform \(\boldsymbol{T}_A^B\rightarrow \boldsymbol{T}_B^A\).
template<typename Tout = T, typename T2 >
SE3< Tout >	otimes (const SE3< 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 >
SE3< Tout >	oplus (const Matrix< T2, 6, 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, 6, 1 >	ominus (const SE3< T2 > &x) const
	Implementation of group subtraction: \(\boldsymbol{T}_A^B\ominus \boldsymbol{T}_A^{B'} \rightarrow \boldsymbol{t}_B^{B'}\).
SE3 &	operator= (const SE3 &x)
	Copy constructor.
template<typename T2 >
SE3	operator* (const SE3< T2 > &x) const
	Invocation of otimes via multiplication.
template<typename T2 >
SE3 &	operator*= (const SE3< T2 > &x)
	Invocation of otimes via multiplication.
SE3 &	operator*= (const double &s)
	Scale a transform by a scalar.
SE3 &	operator/= (const double &s)
	Scale a transform by a scalar.
SE3	operator/ (const double &s) const
	Scale a transform by a scalar.
template<typename Tout = T, typename T2 >
Matrix< Tout, 3, 1 >	operator* (const Matrix< T2, 3, 1 > &v) const
	Transform a vector via multiplication: \(\boldsymbol{T}_A^B\boldsymbol{t}^A \rightarrow \boldsymbol{t}^B\).
Vec3T	operator* (const Vec3T &v) const
	Transform a vector via multiplication: \(\boldsymbol{T}_A^B\boldsymbol{t}^A \rightarrow \boldsymbol{t}^B\).
SE3	operator+ (const Vec6T &v) const
	Invocation of oplus via addition.
SE3 &	operator+= (const Vec6T &v)
	Invocation of oplus via addition.
template<typename T2 >
Vec6T	operator- (const SE3< T2 > &x) const
	Invocation of ominus via subtraction.
template<typename T2 >
SE3< T2 >	cast () const
	Cast the underlying numeric type.

Static Public Member Functions
static SE3	random ()
	Obtain a random rigid body transform.
static SE3	identity ()
	Obtain an identity \(SE(3)\) transform.
static SE3	nans ()
	Obtain a transform full of NaNs.
static SE3	fromH (const Mat4T &m)
	Convert a transform matrix \(\begin{bmatrix}\boldsymbol{R} & \boldsymbol{t} \\ \boldsymbol{0} & 1\end{bmatrix}\) into a \(SE(3)\) transform.
static SE3	fromVecAndQuat (const T tx, const T ty, const T tz, const T qw, const T qx, const T qy, const T qz)
	Construct a transform from the individual fields.
static SE3	fromVecAndQuat (const Vec3T &tvec, const Vec4T &qvec)
	Construct a transform from a translation vector and rotation fields vector.
static SE3	fromVecAndQuat (const Vec3T &t, const SO3< T > &q)
	Construct a transform from a translation vector and a rotation object.
static SE3	fromVecAndQuat (const Vec3T &tvec, const Quaternion< T > quat)
	Construct a transform from a translation vector and an Eigen Quaternion object.
static Mat4T	hat (const Vec6T &omega)
	Hat operator implementation, which coverts the tangent-space vector representation to the corresponding Lie algebra: \(\mathbb{R}^6\rightarrow \mathfrak{se}(3)\).
static Vec6T	vee (const Mat4T &Omega)
	Vee operator implementation, which coverts the Lie algebra representation to a tangent-space vector representation: \(\mathfrak{se}(3) \rightarrow \mathbb{R}^6\).
static Mat4T	log (const SE3 &x)
	Logarithmic chart map implementation: \(SE(3) \rightarrow \mathfrak{se}(3)\).
static Vec6T	Log (const SE3 &x)
	Logarithmic chart map implementation: \(SE(3) \rightarrow \mathbb{R}^6\).
static SE3	exp (const Mat4T &Omega)
	Exponential chart map implementation: \(\mathfrak{se}(3) \rightarrow SE(3)\).
static SE3	Exp (const Vec6T &omega)
	Exponential chart map implementation: \(\mathbb{R}^6 \rightarrow SE(3)\).

Public Attributes
EIGEN_MAKE_ALIGNED_OPERATOR_NEW Map< Vec7T >	arr_
	Memory-mapped array representing all transform fields in \(\begin{bmatrix}\boldsymbol{t} & \boldsymbol{q}\end{bmatrix}^\top\).
Map< Vec3T >	t_
	Memory-mapped array representing only the translation component of the transform \(\boldsymbol{t}\).
SO3< T >	q_
	Memory-mapped array representing only the rotation component of the transform \(\boldsymbol{q}\).

Detailed Description

template<typename T>
class SE3< T >

Class representing a member of the \(SE(3)\) manifold, or a 3D rigid body transform.

Constructor & Destructor Documentation

SE3() [1/4]

template<typename T >

SE3< T >::SE3 ( )

inline

Create a transform (with garbage data).

SE3() [2/4]

template<typename T >

SE3< T >::SE3 ( const Ref< const Vec7T > & arr )

inline

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

SE3() [3/4]

template<typename T >

SE3< T >::SE3 ( const SE3< T > & x )

inline

Copy constructor from another transform.

SE3() [4/4]

template<typename T >

SE3< T >::SE3 ( 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 >

Vec7T SE3< T >::array ( ) const

inline

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

cast()

template<typename T >

template<typename T2 >

SE3< T2 > SE3< T >::cast ( ) const

inline

Cast the underlying numeric type.

copy()

template<typename T >

SE3 SE3< T >::copy ( ) const

inline

Get a deep copy of the current transform.

data() [1/2]

template<typename T >

T * SE3< 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 * SE3< T >::data ( ) const

inline

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

elements()

template<typename T >

const Vec7T SE3< T >::elements ( ) const

inline

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

exp()

template<typename T >

static SE3 SE3< T >::exp ( const Mat4T & Omega )

inlinestatic

Exponential chart map implementation: \(\mathfrak{se}(3) \rightarrow SE(3)\).

Exp()

template<typename T >

static SE3 SE3< T >::Exp ( const Vec6T & omega )

inlinestatic

Exponential chart map implementation: \(\mathbb{R}^6 \rightarrow SE(3)\).

fromH()

template<typename T >

static SE3 SE3< T >::fromH ( const Mat4T & m )

inlinestatic

Convert a transform matrix \(\begin{bmatrix}\boldsymbol{R} & \boldsymbol{t} \\ \boldsymbol{0} & 1\end{bmatrix}\) into a \(SE(3)\) transform.

fromVecAndQuat() [1/4]

template<typename T >

static SE3 SE3< T >::fromVecAndQuat ( const T tx, const T ty, const T tz, const T qw, const T qx, const T qy, const T qz )

inlinestatic

Construct a transform from the individual fields.

Parameters

tx	First component of the translation \(\boldsymbol{t}\in\mathbb{R}^3\).
ty	Second component of the translation \(\boldsymbol{t}\in\mathbb{R}^3\).
tz	Third component of the translation \(\boldsymbol{t}\in\mathbb{R}^3\).
qw	Real component of the rotation \(\boldsymbol{q}\in SO(3)\).
qx	First imaginary component of the rotation \(\boldsymbol{q}\in SO(3)\).
qy	Second imaginary component of the rotation \(\boldsymbol{q}\in SO(3)\).
qz	Third imaginary component of the rotation \(\boldsymbol{q}\in SO(3)\).

fromVecAndQuat() [2/4]

template<typename T >

static SE3 SE3< T >::fromVecAndQuat ( const Vec3T & t, const SO3< T > & q )

inlinestatic

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

Parameters

t	The translation vector \(\boldsymbol{t}\in\mathbb{R}^3\).
q	The rotation \(\boldsymbol{q}\in SO(3)\).

fromVecAndQuat() [3/4]

template<typename T >

static SE3 SE3< T >::fromVecAndQuat ( const Vec3T & tvec, const Quaternion< T > quat )

inlinestatic

Construct a transform from a translation vector and an Eigen Quaternion object.

Parameters

t	The translation vector \(\boldsymbol{t}\in\mathbb{R}^3\).
q	The Eigen Quaternion \(\boldsymbol{q}\in SO(3)\).

fromVecAndQuat() [4/4]

template<typename T >

static SE3 SE3< T >::fromVecAndQuat ( const Vec3T & tvec, const Vec4T & qvec )

inlinestatic

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

Parameters

tvec	The translation vector \(\boldsymbol{t}\in\mathbb{R}^3\).
qvec	The rotation represented as an array \(\boldsymbol{q}\in\mathbb{R}^4\).

H()

template<typename T >

Mat4T SE3< T >::H ( ) const

inline

Convert the transform to matrix representation \(\begin{bmatrix}\boldsymbol{R} & \boldsymbol{t} \\ \boldsymbol{0} & 1\end{bmatrix}\in\mathbb{R}^{4\times 4}\).

hat()

template<typename T >

static Mat4T SE3< T >::hat ( const Vec6T & omega )

inlinestatic

Hat operator implementation, which coverts the tangent-space vector representation to the corresponding Lie algebra: \(\mathbb{R}^6\rightarrow \mathfrak{se}(3)\).

identity()

template<typename T >

static SE3 SE3< T >::identity ( )

inlinestatic

Obtain an identity \(SE(3)\) transform.

inverse()

template<typename T >

SE3 SE3< T >::inverse ( ) const

inline

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

invert()

template<typename T >

SE3 & SE3< T >::invert ( )

inline

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

log()

template<typename T >

static Mat4T SE3< T >::log ( const SE3< T > & x )

inlinestatic

Logarithmic chart map implementation: \(SE(3) \rightarrow \mathfrak{se}(3)\).

Log()

template<typename T >

static Vec6T SE3< T >::Log ( const SE3< T > & x )

inlinestatic

Logarithmic chart map implementation: \(SE(3) \rightarrow \mathbb{R}^6\).

nans()

template<typename T >

static SE3 SE3< T >::nans ( )

inlinestatic

Obtain a transform full of NaNs.

ominus()

template<typename T >

template<typename Tout = T, typename T2 >

Matrix< Tout, 6, 1 > SE3< T >::ominus ( const SE3< 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, 3, 1 > SE3< T >::operator* ( const Matrix< T2, 3, 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 >

SE3 SE3< T >::operator* ( const SE3< T2 > & x ) const

inline

Invocation of otimes via multiplication.

operator*() [3/3]

template<typename T >

Vec3T SE3< T >::operator* ( const Vec3T & 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 >

SE3 & SE3< 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 >

SE3 & SE3< T >::operator*= ( const SE3< T2 > & x )

inline

Invocation of otimes via multiplication.

operator+()

template<typename T >

SE3 SE3< T >::operator+ ( const Vec6T & v ) const

inline

Invocation of oplus via addition.

operator+=()

template<typename T >

SE3 & SE3< T >::operator+= ( const Vec6T & v )

inline

Invocation of oplus via addition.

operator-()

template<typename T >

template<typename T2 >

Vec6T SE3< T >::operator- ( const SE3< T2 > & x ) const

inline

Invocation of ominus via subtraction.

operator/()

template<typename T >

SE3 SE3< 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 >

SE3 & SE3< 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 >

SE3 & SE3< T >::operator= ( const SE3< T > & x )

inline

Copy constructor.

operator[]()

template<typename T >

T & SE3< 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 >

SE3< Tout > SE3< T >::oplus ( const Matrix< T2, 6, 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 >

SE3< Tout > SE3< T >::otimes ( const SE3< 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 >

SO3< T > & SE3< T >::q ( )

inline

Access the rotation \(\boldsymbol{q}\in SO(3)\).

q() [2/2]

template<typename T >

const SO3< T > & SE3< T >::q ( ) const

inline

Access the rotation \(\boldsymbol{q}\in SO(3)\).

random()

template<typename T >

static SE3 SE3< T >::random ( )

inlinestatic

Obtain a random rigid body transform.

Returns

A random rigid body transform \(\mathbf{X}_B^W\in SE(3)\).

The rotation component \(\mathbf{q}_B^W\) will be normalized, but the translation component \(\mathbf{t}_{B/W}^W\) will not (each component will be between 0 and 1).

t() [1/2]

template<typename T >

Map< Vec3T > & SE3< T >::t ( )

inline

Access the translation vector \(\boldsymbol{t}\in\mathbb{R}^3\).

t() [2/2]

template<typename T >

const Map< Vec3T > & SE3< T >::t ( ) const

inline

Access the translation vector \(\boldsymbol{t}\in\mathbb{R}^3\).

vee()

template<typename T >

static Vec6T SE3< T >::vee ( const Mat4T & Omega )

inlinestatic

Vee operator implementation, which coverts the Lie algebra representation to a tangent-space vector representation: \(\mathfrak{se}(3) \rightarrow \mathbb{R}^6\).

Member Data Documentation

arr_

template<typename T >

EIGEN_MAKE_ALIGNED_OPERATOR_NEW Map<Vec7T> SE3< T >::arr_

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

q_

template<typename T >

SO3<T> SE3< T >::q_

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

t_

template<typename T >

Map<Vec3T> SE3< 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/SE3.h