Base class for rigid transformation. More...

#include <se3-base.hpp>

Inheritance diagram for pinocchio::SE3Base< Derived >:

Public Member Functions
template<typename D >
SE3GroupAction< D >::ReturnType	act (const D &d) const
	ay = aXb.act(by) More...

template<typename D >
SE3GroupAction< D >::ReturnType	actInv (const D &d) const
	by = aXb.actInv(ay) More...

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). More...

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 ${}^aM_b$ . More...

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

ActionMatrixType	toActionMatrixInverse () const
	The action matrix ${}^bX_a$ of ${}^aM_b$ . More...

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 pinocchio::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.

\cheatsheet ${}^aM_c = {}^aM_b {}^bM_c$

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

Member Function Documentation

◆ act()

template<class Derived >

template<typename D >

SE3GroupAction<D>::ReturnType pinocchio::SE3Base< Derived >::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 pinocchio::SE3Base< Derived >::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& pinocchio::SE3Base< Derived >::const_cast_derived ( ) const

inline

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

◆ derived() [1/2]

template<class Derived >

Derived& pinocchio::SE3Base< Derived >::derived ( )

inline

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

◆ derived() [2/2]

template<class Derived >

const Derived& pinocchio::SE3Base< Derived >::derived ( ) const

inline

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

◆ disp()

template<class Derived >

void pinocchio::SE3Base< Derived >::disp ( std::ostream & os ) const

inline

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

◆ isApprox()

template<class Derived >

bool pinocchio::SE3Base< Derived >::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 pinocchio::SE3Base< Derived >::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 pinocchio::SE3Base< Derived >::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 pinocchio::SE3Base< Derived >::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 pinocchio::SE3Base< Derived >::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 >

pinocchio::SE3Base< Derived >::operator ActionMatrixType ( ) const

inline

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

◆ operator HomogeneousMatrixType()

template<class Derived >

pinocchio::SE3Base< Derived >::operator HomogeneousMatrixType ( ) const

inline

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

◆ operator!=()

template<class Derived >

bool pinocchio::SE3Base< Derived >::operator!= ( const Derived & other ) const

inline

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

◆ operator*()

template<class Derived >

SE3GroupAction<Derived>::ReturnType pinocchio::SE3Base< Derived >::operator* ( const Derived & m2 ) const

inline

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

◆ operator==()

template<class Derived >

bool pinocchio::SE3Base< Derived >::operator== ( const Derived & other ) const

inline

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

◆ PINOCCHIO_SE3_TYPEDEF_TPL()

template<class Derived >

pinocchio::SE3Base< Derived >::PINOCCHIO_SE3_TYPEDEF_TPL ( Derived )

◆ rotation() [1/3]

template<class Derived >

AngularRef pinocchio::SE3Base< Derived >::rotation ( )

inline

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

◆ rotation() [2/3]

template<class Derived >

ConstAngularRef pinocchio::SE3Base< Derived >::rotation ( ) const

inline

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

◆ rotation() [3/3]

template<class Derived >

void pinocchio::SE3Base< Derived >::rotation ( const AngularType & R )

inline

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

◆ toActionMatrix() [1/2]

template<class Derived >

ActionMatrixType pinocchio::SE3Base< Derived >::toActionMatrix ( ) const

inline

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

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

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

\cheatsheet ${}^a\nu_c = {}^aX_b {}^b\nu_c$

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

◆ toActionMatrix() [2/2]

template<class Derived >

template<typename Matrix6Like >

void pinocchio::SE3Base< Derived >::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 pinocchio::SE3Base< Derived >::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 pinocchio::SE3Base< Derived >::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 pinocchio::SE3Base< Derived >::toDualActionMatrix ( ) const

inline

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

◆ toDualActionMatrix() [2/2]

template<class Derived >

template<typename Matrix6Like >

void pinocchio::SE3Base< Derived >::toDualActionMatrix ( const Eigen::MatrixBase< Matrix6Like > & dual_action_matrix ) const

inline

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

◆ toHomogeneousMatrix()

template<class Derived >

HomogeneousMatrixType pinocchio::SE3Base< Derived >::toHomogeneousMatrix ( ) const

inline

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

◆ translation() [1/3]

template<class Derived >

LinearRef pinocchio::SE3Base< Derived >::translation ( )

inline

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

◆ translation() [2/3]

template<class Derived >

ConstLinearRef pinocchio::SE3Base< Derived >::translation ( ) const

inline

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

◆ translation() [3/3]

template<class Derived >

void pinocchio::SE3Base< Derived >::translation ( const LinearType & t )

inline

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

Friends And Related Function Documentation

◆ 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:

se3-base.hpp

Public Member Functions

Friends

Additional Inherited Members

Detailed Description

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

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==()

◆ PINOCCHIO_SE3_TYPEDEF_TPL()

◆ 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 Function Documentation

◆ operator<<

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