SE3Base< Derived > Struct Template Reference

Base class for rigid transformation. More...

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

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

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 \( ^bp \), \( ^aM_b \) computes its coordinates in frame A by \( ^ap = {}^aM_b {}^bp \).
• \( ^aM_b \) 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

isIdentity()

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 122 of file se3-base.hpp.

isNormalized()

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 130 of file se3-base.hpp.

normalized()

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 146 of file se3-base.hpp.

toActionMatrix()

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 60 of file se3-base.hpp.

toActionMatrixInverse()

ActionMatrixType toActionMatrixInverse ( ) const

inline

The action matrix \( {}^bX_a \) of \( {}^aM_b \).

See also

toActionMatrix()

Definition at line 70 of file se3-base.hpp.

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

• include/pinocchio/spatial/se3-base.hpp