Detailed Description

Version:: 0.1

Author:: thomas.lemaire@laas.fr, ayman.zureiki@laas.fr, martial.sanfourche@laas.fr

The module geom contains 2D and 3D geometry tools.

History

0.2 (2006-04-20) - t3d can be loaded and saved from a file, add T3DIdentity type
0.1 (2006-03-30) - Import T3D from module cine

Requirements

module jmath, boost ublas
CGAL library CGAL (optionnal)

CGAL

chose the CGAL build you want to use according to the machine you are working on (for example i686_Linux-2.6.12-1.1381-FC3smp_g++-3.4.4)

add to your .login

setenv CGAL_OS_COMPILER i686_Linux-2.6.12-1.1381-FC3smp_g++-3.4.4
setenv LD_LIBRARY_PATH "${LD_LIBRARY_PATH}:/usr/local/CGAL-3.1/lib/$CGAL_OS_COMPILER"

configure jafar with the according options, for example:

./configure --with-cgal=/usr/local/CGAL-3.1 --with-cgallib=/usr/local/CGAL-3.1/lib/$CGAL_OS_COMPILER

T3D

Different T3D representations are available:

jafar::geom::T3DEuler represents the pose using 6 parameters, 3 parameters for the translation, and 3 parameters for orientation, the euler angles around z,y,x.
jafar::geom::T3DQuaternion represents the pose using 7 parameters, 3 parameters for the translation, and 4 parameters for orientation, the quaternion.
jafar::geom::T3DRotationVector represents the pose using 6 parameters, 3 parameters for the translation, and 3 parameters for orientation the rotation vector.

All the T3D representations share the same computation layer using homogeneous matrix.

A special attention is required for functions:

jafar::geom::t3d::pointFromFrameJac

Consider $ P_A = T3D P_B $ with $T3D = \left[ \begin{array} {cc} R & T \\ \end{array} \right]$ i.e.

$\left( \begin{array}{c} P_A\\ 1\\ \end{array} \right) = \left( \begin{array}{ccc} R & T \\ 0 & 1 \\ \end{array} \right) \left( \begin{array}{c} P_B\\ 1\\ \end{array} \right)$

then $ P_A = R P_B + T $

so

$JPtB = \frac {dP_A}{dP_B} = R$

and

$JT3D = \frac {dP_A}{dT3D} = \left( \begin{array}{cc} Id(3) & J \end{array} \right)$

with $ J $ the Jacobian of $ P_A $ with respect to the rotation part of the vectorized T3D.

jafar::geom::t3d::pointToFrameJac

Consider $P_B = T3D^{-1} P_A$ with $T3D = \left[ \begin{array} {cc} R & T \\ \end{array} \right]$ i.e.

$\left( \begin{array}{c} P_B\\ 1\\ \end{array} \right) = \left( \begin{array}{ccc} R^T & -R^TT \\ 0 & 1 \\ \end{array} \right) \left( \begin{array}{c} P_A\\ 1\\ \end{array} \right)$

then $ P_B = R^T P_A - R^TT = R^T(P_A - T)$

so

$JPtA = \frac {dP_B}{dP_A} = R^T$

and

$JT3D = \frac {dP_B}{dT3D} = \left( \begin{array}{cc} -R^T & J\\ \end{array} \right)$

with $ J $ the Jacobian of $ P_B $ with respect to the rotation part of the vectorized T3D.

Macro

Extra doc for macro can go here... (you can delete this section if not relevant)

Tcl interface (generated by swig)

The interface of the module is generated from the following files:

geom.i defines the wrapped classes and functions,
geomException.i defines the try { } catch block for this module.

Classes
struct	jafar::geom::Box< T >
class	jafar::geom::OGSensorModel
class	jafar::geom::DenseOG
class	jafar::geom::SparseOG
class	jafar::geom::Atom< dimension >
	class Atom Atom is the base class of geometric objects. More...
class	jafar::geom::BoundingBox< dimension >
	A BoundingBox is the smallest box that contains an Atom . More...
class	jafar::geom::Facet< dimension >
class	jafar::geom::GeomException
	Base class for all exceptions defined in the module geom. More...
class	jafar::geom::HyperPlane< dimension >
	An HyperPlane is a space of dimension (n-1), this correspond to a Plan in dimension 3 and to a Line in dimension 2. More...
class	jafar::geom::InterestPoint
	This class represents an interest point. More...
class	jafar::geom::Line< dimension >
	This class defines a line (which is a space of dimension 1). More...
class	jafar::geom::OrientedPlan< dimension >
	This class represent an hyperplan associated to a repere. More...
class	jafar::geom::Point< dimension >
	class Point This class represents a point. More...
class	jafar::geom::Point< dimension >::Driver
	class Driver Base class for driver of a point More...
class	jafar::geom::Point< dimension >::EuclideanDriver
	class EuclideanDriver Euclidean Driver for a point that is defined by its absolute coordinates. More...
class	jafar::geom::Rectangle< _T_ >
	This class is used to represent a rectangle on an image. More...
class	jafar::geom::Repere< dimension >
	This class represent a Repere which can be used as a reference for other. More...
class	jafar::geom::Repere3D
	3D Reference More...
class	jafar::geom::Segment< dimension >
	This class defines a segment (which is a bounded space of dimension 1). More...
class	jafar::geom::T3D
	A generic 3D transformation, support for uncertain transformation. More...
class	jafar::geom::T3DEuler
	A 3D transformation, the rotation is represented with Euler angles. More...
class	jafar::geom::T3DQuaternion
	A 3D transformation where the rotation is represented with a quaternion. More...
class	jafar::geom::T3DRotationVector
	A 3D transformation the rotation is represented with a quaternion. More...
class	jafar::stereo::StereoOGSensorModel
Namespaces
namespace	jafar::geom::t3d
	This namespace contains free functions related to T3D class.
Typedefs
typedef boost::numeric::ublas::bounded_vector < double, 3 >	jafar::geom::VoxelCoord
Functions
template<int dimension>
void	jafar::geom::cosAngleCov (const typename Atom< dimension >::HomogenousVecD &v1, const typename Atom< dimension >::HomogenousSymMatrixD &v1Cov, const typename Atom< dimension >::HomogenousVecD &v2, const typename Atom< dimension >::HomogenousSymMatrixD &v2Cov, double &angle, double &cov)
	Compute the cosinus of the angle between two vectors and the associated covariance.
template<int dimension>
bool	jafar::geom::intersection (const Line< dimension > &l1, const HyperPlane< dimension > &hyp, typename Atom< dimension >::HomogenousVecD &vec)
	Compute the interesection between a line and an hyperplane.
template<int dimension>
bool	jafar::geom::intersection (const Line< dimension > &l1, const Line< dimension > &l2, typename Atom< dimension >::HomogenousVecD &vec)
	Compute the interesection between two lines.
void	jafar::geom::t3d::invJacEuler (const jblas::vec &v, jblas::mat &J)
	Compute jacobian of inverse fonction (Euler).
void	jafar::geom::t3d::composeJacEuler (jblas::vec const &v1_, jblas::vec const &v2_, jblas::mat &J1, jblas::mat &J2)
	Compute jacobian of compose fonction (Euler).
template<class VecT , class VecPt , class MatJT , class MatJPt >
void	jafar::geom::t3d::pointFromFrameJacEuler (VecT const &t, VecPt const &pt, MatJT &JT, MatJPt &JPt)
	Compute jacobian of t3d::pointFromFrame() (Euler).
template<class VecT , class VecPt , class MatJT , class MatJPt >
void	jafar::geom::t3d::pointToFrameJacEuler (VecT const &t, VecPt const &pt, MatJT &JT, MatJPt &JPt)
	Compute jacobian of t3d::pointToFrame() (Euler).
template<class VecPtB , class VecPtA >
void	jafar::geom::t3d::pointFromFrame (T3D const &aToB, VecPtB const &ptB, VecPtA &ptA)
	Apply transformation aToB to ptB in order to obtain coordinate of the vector in frame A vA.
template<class VecPtB , class MatJT3D , class MatJPtB >
void	jafar::geom::t3d::pointFromFrameJac (T3D const &aToB, VecPtB const &ptB, MatJT3D &JT3D, MatJPtB &JPtB)
	Compute jacobian of pointFromFrame()
template<class VecPtB , class MatJT3D , class MatJPtB >
void	jafar::geom::t3d::pointFromFrameJac (T3D const &aToB, VecPtB const &ptB, VecPtB &ptA, MatJT3D &JT3D, MatJPtB &JPtB)
	Compute pointFromFrame() and its jacobians.
template<class VecPtB , class VecPtA >
void	jafar::geom::t3d::pointToFrame (T3D const &aToB, VecPtA const &ptA, VecPtB &ptB)
	Apply transformation aToB to ptA in order to obtain coordinate of the vector in frame B ptB.
template<class VecPtB , class MatJT3D , class MatJPtA >
void	jafar::geom::t3d::pointToFrameJac (T3D const &aToB, VecPtB const &ptA, MatJT3D &JT3D, MatJPtA &JPtA)
	Compute jacobian of pointToFrame()
template<class VecPtB , class MatJT3D , class MatJPtA >
void	jafar::geom::t3d::pointToFrameJac (T3D const &aToB, VecPtB const &ptA, VecPtB &ptB, MatJT3D &JT3D, MatJPtA &JPtA)
	Compute pointToFrame() and its jacobians.
template<class VecT , class VecPt , class MatJT , class MatJPt >
void	jafar::geom::t3d::pointFromFrameJacQuaternion (VecT const &t, VecPt const &pt, MatJT &JT, MatJPt &JPt)
	Compute jacobian of pointFromFrame()
template<class VecT , class VecPt , class MatJT , class MatJPt >
void	jafar::geom::t3d::pointToFrameJacQuaternion (VecT const &t, VecPt const &pt, MatJT &JT, MatJPt &JPt)
	Compute jacobian of pointToFrame()

Function Documentation

template<int dimension>

bool jafar::geom::intersection	(	const Line< dimension > &	l1,
		const HyperPlane< dimension > &	hyp,
		typename Atom< dimension >::HomogenousVecD &	vec
	)		`[inline]`

Compute the interesection between a line and an hyperplane.

The result, is undefined if l1 and hyp are parallel.

Returns:: false if the line are parallel

Definition at line 6 of file IntersectionImpl.hpp.

References jafar::geom::HyperPlane< dimension >::normal(), jafar::geom::HyperPlane< dimension >::origin(), jafar::geom::Line< dimension >::origin(), and jafar::geom::Line< dimension >::pointAt().

template<int dimension>

bool jafar::geom::intersection	(	const Line< dimension > &	l1,
		const Line< dimension > &	l2,
		typename Atom< dimension >::HomogenousVecD &	vec
	)		`[inline]`

Compute the interesection between two lines.

The result, is undefined if l1 and l2 are parallel lines.

Returns:: false if the line are parallel

template<class VecPtB , class MatJT3D , class MatJPtB >

void jafar::geom::t3d::pointFromFrameJac	(	T3D const &	aToB,
		VecPtB const &	ptB,
		MatJT3D &	JT3D,
		MatJPtB &	JPtB
	)

Compute jacobian of pointFromFrame()

Parameters:

JT3D	Jacobian matrix with respect to the T3D.
JPtB	Jacobian matrix with respect to the input point.

Definition at line 47 of file t3dPointTools.hpp.

References jafar::geom::T3D::EULER, JFR_PRECOND, JFR_RUN_TIME, JFR_TRACE_END, jafar::geom::t3d::pointFromFrameJacEuler(), jafar::geom::t3d::pointFromFrameJacQuaternion(), jafar::geom::T3D::QUATERNION, and jafar::geom::T3D::type().

template<class VecPtB , class MatJT3D , class MatJPtB >

void jafar::geom::t3d::pointFromFrameJac	(	T3D const &	aToB,
		VecPtB const &	ptB,
		VecPtB &	ptA,
		MatJT3D &	JT3D,
		MatJPtB &	JPtB
	)

Compute pointFromFrame() and its jacobians.

Parameters:

aToB	input T3D from frame A to frame B
ptB	input point expressed in frame B
ptA	output point expressed in frame A
JT3D	output Jacobian matrix with respect to the T3D.
JPtB	output Jacobian matrix with respect to the input point.

Definition at line 82 of file t3dPointTools.hpp.

References jafar::geom::T3D::EULER, JFR_PRECOND, JFR_RUN_TIME, JFR_TRACE_END, jafar::geom::t3d::pointFromFrame(), jafar::geom::t3d::pointFromFrameJacEuler(), jafar::geom::t3d::pointFromFrameJacQuaternion(), jafar::geom::T3D::QUATERNION, and jafar::geom::T3D::type().

template<class VecT , class VecPt , class MatJT , class MatJPt >

void jafar::geom::t3d::pointFromFrameJacQuaternion	(	VecT const &	t,
		VecPt const &	pt,
		MatJT &	JT,
		MatJPt &	JPt
	)

Compute jacobian of pointFromFrame()

Parameters:

t	vectorized T3DQuaternion must be of size 7.
pt	3D point must be of size 3.
JT	Jacobian matrix with respect to the T3D must be 3x7.
JPt	Jacobian matrix with respect to the input point must be 3x3.

Definition at line 65 of file t3dQuaternion.hpp.

References JFR_PRECOND.

Referenced by jafar::geom::t3d::pointFromFrameJac().

template<class VecPtB , class VecPtA >

void jafar::geom::t3d::pointToFrame	(	T3D const &	aToB,
		VecPtA const &	ptA,
		VecPtB &	ptB
	)

Apply transformation aToB to ptA in order to obtain coordinate of the vector in frame B ptB.

This operation requires the invertion of aToB.

Definition at line 118 of file t3dPointTools.hpp.

References JFR_PRECOND.

Referenced by jafar::geom::t3d::pointToFrameJac().

template<class VecPtB , class MatJT3D , class MatJPtA >

void jafar::geom::t3d::pointToFrameJac	(	T3D const &	aToB,
		VecPtB const &	ptA,
		MatJT3D &	JT3D,
		MatJPtA &	JPtA
	)

Compute jacobian of pointToFrame()

Parameters:

JT3D	Jacobian matrix with respect to the T3D.
JPtA	Jacobian matrix with respect to the input point.

Definition at line 168 of file t3dPointTools.hpp.

References jafar::geom::T3D::EULER, JFR_PRECOND, JFR_RUN_TIME, JFR_TRACE_END, jafar::geom::t3d::pointToFrameJacEuler(), jafar::geom::t3d::pointToFrameJacQuaternion(), jafar::geom::T3D::QUATERNION, and jafar::geom::T3D::type().

template<class VecPtB , class MatJT3D , class MatJPtA >

void jafar::geom::t3d::pointToFrameJac	(	T3D const &	aToB,
		VecPtB const &	ptA,
		VecPtB &	ptB,
		MatJT3D &	JT3D,
		MatJPtA &	JPtA
	)

Compute pointToFrame() and its jacobians.

Parameters:

aToB	input T3D from frame A to frame B
ptA	input point expressed in frame A
ptB	output point expressed in frame B
JT3D	output Jacobian matrix with respect to the T3D.
JPtA	output Jacobian matrix with respect to the input point.

Definition at line 203 of file t3dPointTools.hpp.

References jafar::geom::T3D::EULER, JFR_PRECOND, JFR_RUN_TIME, JFR_TRACE_END, jafar::geom::t3d::pointToFrame(), jafar::geom::t3d::pointToFrameJacEuler(), jafar::geom::t3d::pointToFrameJacQuaternion(), jafar::geom::T3D::QUATERNION, and jafar::geom::T3D::type().

template<class VecT , class VecPt , class MatJT , class MatJPt >

void jafar::geom::t3d::pointToFrameJacQuaternion	(	VecT const &	t,
		VecPt const &	pt,
		MatJT &	JT,
		MatJPt &	JPt
	)

Compute jacobian of pointToFrame()

Parameters:

t	vectorized T3DQuaternion must be of size 7.
pt	3D point must be of size 3.
JT	Jacobian matrix with respect to the T3D must be 3x7.
JPt	Jacobian matrix with respect to the input point must be 3x3.

Definition at line 120 of file t3dQuaternion.hpp.

References JFR_PRECOND.

Referenced by jafar::geom::t3d::pointToFrameJac().

Detailed Description

History

Requirements

CGAL

T3D

Macro

Tcl interface (generated by swig)

Classes

Namespaces

Typedefs

Functions

Function Documentation