Base class for rigid transformation. More...

#include <pinocchio/spatial/se3-base.hpp>

Inheritance diagram for SE3Base< Derived >:

Collaboration diagram for SE3Base< Derived >:

Public Member Functions
template<typename D>
SE3GroupAction< D >::ReturnType	act (const D &d) const
	ay = aXb.act(by)
template<typename D>
SE3GroupAction< D >::ReturnType	actInv (const D &d) const
	by = aXb.actInv(ay)
Derived &	const_cast_derived () const
Derived &	derived ()
const Derived &	derived () const
void	disp (std::ostream &os) const
bool	isApprox (const Derived &other, const Scalar &prec=Eigen::NumTraits< Scalar >::dummy_precision()) const
bool	isIdentity (const typename traits< Derived >::Scalar &prec=Eigen::NumTraits< typename traits< Derived >::Scalar >::dummy_precision()) const
bool	isNormalized (const Scalar &prec=Eigen::NumTraits< Scalar >::dummy_precision()) const
void	normalize ()
	Normalize this in such a way the rotation part of this lies on SO(3).
PlainType	normalized () const
	operator ActionMatrixType () const
	operator HomogeneousMatrixType () const
bool	operator!= (const Derived &other) const
SE3GroupAction< Derived >::ReturnType	operator* (const Derived &m2) const
bool	operator== (const Derived &other) const
	PINOCCHIO_SE3_TYPEDEF_TPL (Derived)
AngularRef	rotation ()
ConstAngularRef	rotation () const
void	rotation (const AngularType &R)
ActionMatrixType	toActionMatrix () const
	The action matrix ${}^aX_b$ of ${}^aM_b$ .
template<typename Matrix6Like>
void	toActionMatrix (const Eigen::MatrixBase< Matrix6Like > &action_matrix) const
ActionMatrixType	toActionMatrixInverse () const
	The action matrix ${}^bX_a$ of ${}^aM_b$ .
template<typename Matrix6Like>
void	toActionMatrixInverse (const Eigen::MatrixBase< Matrix6Like > &action_matrix_inverse) const
ActionMatrixType	toDualActionMatrix () const
template<typename Matrix6Like>
void	toDualActionMatrix (const Eigen::MatrixBase< Matrix6Like > &dual_action_matrix) const
HomogeneousMatrixType	toHomogeneousMatrix () const
LinearRef	translation ()
ConstLinearRef	translation () const
void	translation (const LinearType &t)

Friends
std::ostream &	operator<< (std::ostream &os, const SE3Base< Derived > &X)

Additional Inherited Members
Public Types inherited from NumericalBase< Derived >
typedef traits< Derived >::Scalar	Scalar

Detailed Description

template<class Derived>
struct pinocchio::SE3Base< Derived >

Base class for rigid transformation.

The rigid transform aMb can be seen in two ways:

given a point p expressed in frame B by its coordinate vector , computes its coordinates in frame A by $^ap = {}^aM_b {}^bp$ .
displaces a solid S centered at frame A into the solid centered in B. In particular, the origin of A is displaced at the origin of B: $^aM_b {}^aA = {}^aB$ .

The rigid displacement is stored as a rotation matrix and translation vector by: $^aM_b x = {}^aR_b x + {}^aAB$ where $^aAB$ is the vector from origin A to origin B expressed in coordinates A.

Remarkable identity: ${}^aM_c = {}^aM_b {}^bM_c$

Definition at line 30 of file se3-base.hpp.

Member Function Documentation

◆ act()

template<class Derived>

template<typename D>

SE3GroupAction< D >::ReturnType act ( const D & d ) const

inline

ay = aXb.act(by)

Definition at line 145 of file se3-base.hpp.

◆ actInv()

template<class Derived>

template<typename D>

SE3GroupAction< D >::ReturnType actInv ( const D & d ) const

inline

by = aXb.actInv(ay)

Definition at line 152 of file se3-base.hpp.

◆ const_cast_derived()

template<class Derived>

Derived & const_cast_derived ( ) const

inline

Definition at line 43 of file se3-base.hpp.

◆ derived() [1/2]

template<class Derived>

Derived & derived ( )

inline

Definition at line 34 of file se3-base.hpp.

◆ derived() [2/2]

template<class Derived>

const Derived & derived ( ) const

inline

Definition at line 38 of file se3-base.hpp.

◆ disp()

template<class Derived>

void disp ( std::ostream & os ) const

inline

Definition at line 127 of file se3-base.hpp.

◆ isApprox()

template<class Derived>

bool isApprox	(	const Derived &	other,
		const Scalar &	prec = Eigen::NumTraits<Scalar>::dummy_precision() ) const

inline

Definition at line 167 of file se3-base.hpp.

◆ isIdentity()

template<class Derived>

bool isIdentity ( const typename traits< Derived >::Scalar & prec = Eigen::NumTraits<typename traits<Derived>::Scalar>::dummy_precision() ) const

inline

Returns: true if *this is approximately equal to the identity placement, within the precision given by prec.

Definition at line 184 of file se3-base.hpp.

◆ isNormalized()

template<class Derived>

bool isNormalized ( const Scalar & prec = Eigen::NumTraits<Scalar>::dummy_precision() ) const

inline

Returns: true if the rotational part of *this is a rotation matrix (normalized columns), within the precision given by prec.

Definition at line 195 of file se3-base.hpp.

◆ normalize()

template<class Derived>

void normalize ( )

inline

Normalize *this in such a way the rotation part of *this lies on SO(3).

Definition at line 203 of file se3-base.hpp.

◆ normalized()

template<class Derived>

PlainType normalized ( ) const

inline

Returns: a Normalized version of *this, in such a way the rotation part of the returned transformation lies on SO(3).

Definition at line 212 of file se3-base.hpp.

◆ operator ActionMatrixType()

template<class Derived>

operator ActionMatrixType ( ) const

inline

Definition at line 96 of file se3-base.hpp.

◆ operator HomogeneousMatrixType()

template<class Derived>

operator HomogeneousMatrixType ( ) const

inline

Definition at line 77 of file se3-base.hpp.

◆ operator!=()

template<class Derived>

bool operator!= ( const Derived & other ) const

inline

Definition at line 162 of file se3-base.hpp.

◆ operator*()

template<class Derived>

SE3GroupAction< Derived >::ReturnType operator* ( const Derived & m2 ) const

inline

Definition at line 138 of file se3-base.hpp.

◆ operator==()

template<class Derived>

bool operator== ( const Derived & other ) const

inline

Definition at line 157 of file se3-base.hpp.

◆ rotation() [1/3]

template<class Derived>

AngularRef rotation ( )

inline

Definition at line 56 of file se3-base.hpp.

◆ rotation() [2/3]

template<class Derived>

ConstAngularRef rotation ( ) const

inline

Definition at line 48 of file se3-base.hpp.

◆ rotation() [3/3]

template<class Derived>

void rotation ( const AngularType & R )

inline

Definition at line 64 of file se3-base.hpp.

◆ toActionMatrix() [1/2]

template<class Derived>

ActionMatrixType toActionMatrix ( ) const

inline

The action matrix ${}^aX_b$ of ${}^aM_b$ .

With ${}^aM_b = \left( \begin{array}{cc} R & t \\ 0 & 1 \\ \end{array} \right)$ ,

${}^aX_b = \left( \begin{array}{cc} R & \hat{t} R \\ 0 & R \\ \end{array} \right)$

Remarkable identity: ${}^a\nu_c = {}^aX_b {}^b\nu_c$

Definition at line 92 of file se3-base.hpp.

◆ toActionMatrix() [2/2]

template<class Derived>

template<typename Matrix6Like>

void toActionMatrix ( const Eigen::MatrixBase< Matrix6Like > & action_matrix ) const

inline

Definition at line 102 of file se3-base.hpp.

◆ toActionMatrixInverse() [1/2]

template<class Derived>

ActionMatrixType toActionMatrixInverse ( ) const

inline

The action matrix ${}^bX_a$ of ${}^aM_b$ .

See also: toActionMatrix()

Definition at line 111 of file se3-base.hpp.

◆ toActionMatrixInverse() [2/2]

template<class Derived>

template<typename Matrix6Like>

void toActionMatrixInverse ( const Eigen::MatrixBase< Matrix6Like > & action_matrix_inverse ) const

inline

Definition at line 117 of file se3-base.hpp.

◆ toDualActionMatrix() [1/2]

template<class Derived>

ActionMatrixType toDualActionMatrix ( ) const

inline

Definition at line 122 of file se3-base.hpp.

◆ toDualActionMatrix() [2/2]

template<class Derived>

template<typename Matrix6Like>

void toDualActionMatrix ( const Eigen::MatrixBase< Matrix6Like > & dual_action_matrix ) const

inline

Definition at line 133 of file se3-base.hpp.

◆ toHomogeneousMatrix()

template<class Derived>

HomogeneousMatrixType toHomogeneousMatrix ( ) const

inline

Definition at line 73 of file se3-base.hpp.

◆ translation() [1/3]

template<class Derived>

LinearRef translation ( )

inline

Definition at line 60 of file se3-base.hpp.

◆ translation() [2/3]

template<class Derived>

ConstLinearRef translation ( ) const

inline

Definition at line 52 of file se3-base.hpp.

◆ translation() [3/3]

template<class Derived>

void translation ( const LinearType & t )

inline

Definition at line 68 of file se3-base.hpp.

◆ operator<<

template<class Derived>

std::ostream & operator<<	(	std::ostream &	os,
		const SE3Base< Derived > &	X )

friend

Definition at line 174 of file se3-base.hpp.

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

include/pinocchio/spatial/se3-base.hpp

Public Member Functions

Friends

Additional Inherited Members

Detailed Description

Member Function Documentation

◆ act()

◆ actInv()

◆ const_cast_derived()

◆ derived() [1/2]

◆ derived() [2/2]

◆ disp()

◆ isApprox()

◆ isIdentity()

◆ isNormalized()

◆ normalize()

◆ normalized()

◆ operator ActionMatrixType()

◆ operator HomogeneousMatrixType()

◆ operator!=()

◆ operator*()

◆ operator==()

◆ rotation() [1/3]

◆ rotation() [2/3]

◆ rotation() [3/3]

◆ toActionMatrix() [1/2]

◆ toActionMatrix() [2/2]

◆ toActionMatrixInverse() [1/2]

◆ toActionMatrixInverse() [2/2]

◆ toDualActionMatrix() [1/2]

◆ toDualActionMatrix() [2/2]

◆ toHomogeneousMatrix()

◆ translation() [1/3]

◆ translation() [2/3]

◆ translation() [3/3]

Friends And Related Symbol Documentation

◆ operator<<