Visual Servoing Platform version 3.7.0
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vpCircle Class Reference

#include <vpCircle.h>

Inheritance diagram for vpCircle:

Public Types

enum  vpForwardProjectionDeallocatorType { user , vpDisplayForwardProjection }

Public Member Functions

 vpCircle ()
VP_EXPLICIT vpCircle (const vpColVector &oP)
 vpCircle (double oA, double oB, double oC, double oX, double oY, double oZ, double R)
 vpCircle (const vpCircle &)=default
virtual ~vpCircle () VP_OVERRIDE=default
void changeFrame (const vpHomogeneousMatrix &noMo, vpColVector &noP) const VP_OVERRIDE
void changeFrame (const vpHomogeneousMatrix &cMo) VP_OVERRIDE
void display (const vpImage< unsigned char > &I, const vpCameraParameters &cam, const vpColor &color=vpColor::green, unsigned int thickness=1) VP_OVERRIDE
void display (const vpImage< unsigned char > &I, const vpHomogeneousMatrix &cMo, const vpCameraParameters &cam, const vpColor &color=vpColor::green, unsigned int thickness=1) VP_OVERRIDE
void display (const vpImage< vpRGBa > &I, const vpCameraParameters &cam, const vpColor &color=vpColor::green, unsigned int thickness=1)
void display (const vpImage< vpRGBa > &I, const vpHomogeneousMatrix &cMo, const vpCameraParameters &cam, const vpColor &color=vpColor::green, unsigned int thickness=1)
vpCircleduplicate () const VP_OVERRIDE
double get_x () const
double get_y () const
double get_n20 () const
double get_n11 () const
double get_n02 () const
double getA () const
double getB () const
double getC () const
double getX () const
double getY () const
double getZ () const
double getR () const
vpCircleoperator= (const vpCircle &)=default
void projection () VP_OVERRIDE
void projection (const vpColVector &cP, vpColVector &p) const VP_OVERRIDE
void setWorldCoordinates (const vpColVector &oP) VP_OVERRIDE
void setWorldCoordinates (double oA, double oB, double oC, double oX, double oY, double oZ, double R)
Public Member Functions Inherited from vpForwardProjection
vpColVector get_oP () const
vpForwardProjectionDeallocatorType getDeallocate ()
virtual void print () const
void project ()
void project (const vpHomogeneousMatrix &cMo)
void setDeallocate (vpForwardProjectionDeallocatorType d)
void track (const vpHomogeneousMatrix &cMo)
Public Member Functions Inherited from vpTracker
vpColVector get_p () const
vpColVector get_cP () const

Static Public Member Functions

static void computeIntersectionPoint (const vpCircle &circle, const vpCameraParameters &cam, const double &rho, const double &theta, double &i, double &j)

Public Attributes

Public Attributes Inherited from vpForwardProjection
vpColVector oP
Public Attributes Inherited from vpTracker
vpColVector p
vpColVector cP
bool cPAvailable

Deprecated functions

VP_DEPRECATED double get_mu20 () const
VP_DEPRECATED double get_mu11 () const
VP_DEPRECATED double get_mu02 () const
void init () VP_OVERRIDE

Detailed Description

Class that defines a 3D circle in the object frame and allows forward projection of a 3D circle in the camera frame and in the 2D image plane by perspective projection. All the parameters must be set in meter.

Note that a 3D circle is defined from the intersection between a 3D plane and a 3D sphere.

A 3D circle has the followings parameters:

Examples
manGeometricFeatures.cpp, servoSimuCircle2DCamVelocity.cpp, servoSimuCircle2DCamVelocityDisplay.cpp, simulateCircle2DCamVelocity.cpp, testCameraParametersConversion.cpp, and testPoseFeatures.cpp.

Definition at line 86 of file vpCircle.h.

Member Enumeration Documentation

◆ vpForwardProjectionDeallocatorType

Used for memory issue especially in the vpServo class.

Enumerator
user 
vpDisplayForwardProjection 

Definition at line 70 of file vpForwardProjection.h.

Constructor & Destructor Documentation

◆ vpCircle() [1/4]

vpCircle::vpCircle ( )

Default constructor that initialize internal vectors.

Definition at line 96 of file vpCircle.cpp.

References init().

Referenced by computeIntersectionPoint(), duplicate(), operator=(), vpCircle(), and ~vpCircle().

◆ vpCircle() [2/4]

vpCircle::vpCircle ( const vpColVector & oP_)

Construct the circle from the intersection of a plane and a sphere.

Parameters
oP_: This 7-dim vector defines the parameters oP[0], oP[1], oP[2] corresponding to parameters oA, oB, oC of the plane with equation oA*(X-oX)+oB*(Y-oY)+oC*(Z-oZ)=0 passing through the 3D sphere center. oP[3], oP[4], oP[5] correspond to oX, oY, oZ the coordinates of the center of the sphere. oP[6] corresponds to the radius of the sphere.
See also
setWorldCoordinates()

Definition at line 109 of file vpCircle.cpp.

References init(), and setWorldCoordinates().

◆ vpCircle() [3/4]

vpCircle::vpCircle ( double oA,
double oB,
double oC,
double oX,
double oY,
double oZ,
double R )

Construct the 3D circle from the intersection of a plane and a sphere with coordinates expressed in the object frame.

The equation of the plane which contains the 3D circle is the following:

\‍[ oA*(X-oX)+oB*(Y-oY)+oC*(Z-oZ)=0 \‍]

where $ (oA, oB, oC) $ are the coordinates of the vector normal to the plane, and $ (oX, oY, oZ) $ are the 3D coordinates of the circle center.

Parameters
oA: Coordinate along X-axis of the vector normal to the plane.
oB: Coordinate along Y-axis of the vector normal to the plane.
oC: Coordinate along Z-axis of the vector normal to the plane.
oX: Coordinate of the center of the sphere along X-axis in the object frame.
oY: Coordinate of the center of the sphere along Y-axis in the object frame.
oZ: Coordinate of the center of the sphere along Z-axis in the object frame.
R: Radius of the sphere.
See also
setWorldCoordinates()

Definition at line 134 of file vpCircle.cpp.

References init(), and setWorldCoordinates().

◆ vpCircle() [4/4]

vpCircle::vpCircle ( const vpCircle & )
default

References vpCircle().

◆ ~vpCircle()

virtual vpCircle::~vpCircle ( )
virtualdefault

References vpCircle().

Member Function Documentation

◆ changeFrame() [1/2]

void vpCircle::changeFrame ( const vpHomogeneousMatrix & cMo)
virtual

Perspective projection of the circle. Internal circle parameters are modified in cP.

Parameters
cMo: Homogeneous transformation from camera frame to object frame.

Implements vpForwardProjection.

Definition at line 313 of file vpCircle.cpp.

References vpTracker::cP, and vpForwardProjection::oP.

◆ changeFrame() [2/2]

void vpCircle::changeFrame ( const vpHomogeneousMatrix & noMo,
vpColVector & noP ) const
virtual

From the 3D coordinates of the circle in the object frame oP that are set using for example vpCircle(double oA, double oB, double oC, double oX, double oY, double oZ, double R) or setWorldCoordinates(), compute the 3D coordinates of the circle in a new object frame noP = noMo * oP. Internal parameters of the circle remain unchanged.

Parameters
noMo: Transformation from camera to object frame.
noP: 3D normalized coordinates of the circle in the a new ojbect frame noP = (noA, noB, noC, noX, noY, noZ, R).

Implements vpForwardProjection.

Examples
testCameraParametersConversion.cpp.

Definition at line 273 of file vpCircle.cpp.

References vpForwardProjection::oP, and vpColVector::resize().

Referenced by display(), and display().

◆ computeIntersectionPoint()

void vpCircle::computeIntersectionPoint ( const vpCircle & circle,
const vpCameraParameters & cam,
const double & rho,
const double & theta,
double & i,
double & j )
static

Computes the coordinates of the point corresponding to the intersection between a circle and a line.

Warning
This functions assumes changeFrame() and projection() have already been called.
See also
changeFrame(), projection()
Parameters
circle: Circle to consider for the intersection.
cam: Camera parameters that have to be used for the intersection computation.
rho: The rho parameter of the line.
theta: The theta parameter of the line.
i: resulting i-coordinate of the intersection point.
j: resulting j-coordinate of the intersection point.

Definition at line 458 of file vpCircle.cpp.

References vpTracker::p, vpMath::sqr(), and vpCircle().

Referenced by vpMbtDistanceCylinder::getModelForDisplay(), vpMbtDistanceKltCylinder::getModelForDisplay(), vpMbtDistanceCylinder::initMovingEdge(), operator=(), and vpMbtDistanceCylinder::updateMovingEdge().

◆ display() [1/4]

void vpCircle::display ( const vpImage< unsigned char > & I,
const vpCameraParameters & cam,
const vpColor & color = vpColor::green,
unsigned int thickness = 1 )
virtual

Display the projection of a 3D circle in image I using internal coordinates in the image plane (x,y,n20,n11,n02) available in p vector. These coordinates may be updated using projection().

Parameters
I: Image used as background.
cam: Camera parameters.
color: Color used to draw the circle.
thickness: Thickness used to draw the circle.

Implements vpForwardProjection.

Examples
manGeometricFeatures.cpp.

Definition at line 353 of file vpCircle.cpp.

References vpFeatureDisplay::displayEllipse(), and vpTracker::p.

◆ display() [2/4]

void vpCircle::display ( const vpImage< unsigned char > & I,
const vpHomogeneousMatrix & cMo,
const vpCameraParameters & cam,
const vpColor & color = vpColor::green,
unsigned int thickness = 1 )
virtual

Display the projection of a sphere in image I. This method is non destructive wrt. cP and p internal circle parameters.

Parameters
I: Image used as background.
cMo: Homogeneous transformation from camera frame to object frame. The circle is considered as viewed from this camera position.
cam: Camera parameters.
color: Color used to draw the sphere.
thickness: Thickness used to draw the circle.

Implements vpForwardProjection.

Definition at line 395 of file vpCircle.cpp.

References changeFrame(), vpFeatureDisplay::displayEllipse(), and projection().

◆ display() [3/4]

void vpCircle::display ( const vpImage< vpRGBa > & I,
const vpCameraParameters & cam,
const vpColor & color = vpColor::green,
unsigned int thickness = 1 )

Display the projection of a 3D circle in image I using internal coordinates in the image plane (x,y,n20,n11,n02) available in p vector. These coordinates may be updated using projection().

Parameters
I: Image used as background.
cam: Camera parameters.
color: Color used to draw the circle.
thickness: Thickness used to draw the circle.

Definition at line 373 of file vpCircle.cpp.

References vpFeatureDisplay::displayEllipse(), and vpTracker::p.

◆ display() [4/4]

void vpCircle::display ( const vpImage< vpRGBa > & I,
const vpHomogeneousMatrix & cMo,
const vpCameraParameters & cam,
const vpColor & color = vpColor::green,
unsigned int thickness = 1 )

Display the projection of a sphere in image I. This method is non destructive wrt. cP and p internal circle parameters.

Parameters
I: Image used as background.
cMo: Homogeneous transformation from camera frame to object frame. The circle is considered as viewed from this camera position.
cam: Camera parameters.
color: Color used to draw the sphere.
thickness: Thickness used to draw the circle.

Definition at line 420 of file vpCircle.cpp.

References changeFrame(), vpFeatureDisplay::displayEllipse(), and projection().

◆ duplicate()

vpCircle * vpCircle::duplicate ( ) const
virtual

For memory issue (used by the vpServo class only).

Implements vpForwardProjection.

Definition at line 435 of file vpCircle.cpp.

References vpCircle().

◆ get_cP()

vpColVector vpTracker::get_cP ( ) const
inlineinherited

Return object parameters expressed in the 3D camera frame.

Definition at line 95 of file vpTracker.h.

References cP.

◆ get_mu02()

VP_DEPRECATED double vpCircle::get_mu02 ( ) const
inline
Deprecated
You should rather use get_n02(). This function is incorrectly named and is confusing since it returns second order centered moments of the ellipse normalized by its area that corresponds to $n_02 = mu_02/a$.

Definition at line 172 of file vpCircle.h.

References vpTracker::p.

◆ get_mu11()

VP_DEPRECATED double vpCircle::get_mu11 ( ) const
inline
Deprecated
You should rather use get_n11(). This function is incorrectly named and is confusing since it returns second order centered moments of the ellipse normalized by its area that corresponds to $n_11 = mu@name Deprecated functions_11/a$.

Definition at line 165 of file vpCircle.h.

References vpTracker::p.

◆ get_mu20()

VP_DEPRECATED double vpCircle::get_mu20 ( ) const
inline
Deprecated
You should rather use get_n20(). This function is incorrectly named and is confusing since it returns second order centered moments of the ellipse normalized by its area that corresponds to $n_20 = mu_20/a$.

Definition at line 158 of file vpCircle.h.

References vpTracker::p.

◆ get_n02()

double vpCircle::get_n02 ( ) const
inline

Definition at line 119 of file vpCircle.h.

References vpTracker::p.

◆ get_n11()

double vpCircle::get_n11 ( ) const
inline

Definition at line 118 of file vpCircle.h.

References vpTracker::p.

◆ get_n20()

double vpCircle::get_n20 ( ) const
inline

Definition at line 117 of file vpCircle.h.

References vpTracker::p.

◆ get_oP()

vpColVector vpForwardProjection::get_oP ( ) const
inlineinherited

Return object parameters expressed in the 3D object frame.

Definition at line 155 of file vpForwardProjection.h.

References oP.

◆ get_p()

vpColVector vpTracker::get_p ( ) const
inlineinherited

Return object parameters expressed in the 2D image plane computed by perspective projection.

Definition at line 93 of file vpTracker.h.

References p.

◆ get_x()

double vpCircle::get_x ( ) const
inline

Definition at line 114 of file vpCircle.h.

References get_x(), and vpTracker::p.

Referenced by get_x().

◆ get_y()

double vpCircle::get_y ( ) const
inline

Definition at line 115 of file vpCircle.h.

References vpTracker::p.

◆ getA()

double vpCircle::getA ( ) const
inline

Definition at line 121 of file vpCircle.h.

References vpTracker::cP.

◆ getB()

double vpCircle::getB ( ) const
inline

Definition at line 122 of file vpCircle.h.

References vpTracker::cP.

◆ getC()

double vpCircle::getC ( ) const
inline

Definition at line 123 of file vpCircle.h.

References vpTracker::cP.

◆ getDeallocate()

vpForwardProjectionDeallocatorType vpForwardProjection::getDeallocate ( )
inlineinherited

Definition at line 157 of file vpForwardProjection.h.

◆ getR()

double vpCircle::getR ( ) const
inline

Definition at line 129 of file vpCircle.h.

References vpTracker::cP.

◆ getX()

double vpCircle::getX ( ) const
inline

Definition at line 125 of file vpCircle.h.

References vpTracker::cP.

◆ getY()

double vpCircle::getY ( ) const
inline

Definition at line 126 of file vpCircle.h.

References vpTracker::cP.

◆ getZ()

double vpCircle::getZ ( ) const
inline

Definition at line 127 of file vpCircle.h.

References vpTracker::cP.

◆ init()

BEGIN_VISP_NAMESPACE void vpCircle::init ( )
protectedvirtual

Default initialisation of the feature parameters:

  • in the object frame: oP
  • in the camera frame: cP
  • in the image plane: p.

Implements vpForwardProjection.

Definition at line 39 of file vpCircle.cpp.

References vpTracker::cP, vpForwardProjection::oP, and vpTracker::p.

Referenced by vpCircle(), vpCircle(), and vpCircle().

◆ operator=()

◆ print()

BEGIN_VISP_NAMESPACE void vpForwardProjection::print ( ) const
virtualinherited

Print to stdout the feature parameters in:

  • the object frame
  • the camera frame
  • the image plane.
Examples
servoSimuCircle2DCamVelocityDisplay.cpp, servoSimuLine2DCamVelocityDisplay.cpp, and servoSimuSquareLine2DCamVelocityDisplay.cpp.

Definition at line 48 of file vpForwardProjection.cpp.

References vpTracker::cP, oP, and vpTracker::p.

◆ project() [1/2]

◆ project() [2/2]

void vpForwardProjection::project ( const vpHomogeneousMatrix & cMo)
inherited

Compute the feature parameters in the camera frame (vpTracker::cP) and than compute the projection of these parameters in the image plane (vpTracker::p).

Warning
The feature parameters in the object frame (vpForwardProjection:oP) need to be set prior the use of this method. To initialize these parameters see setWorldCoordinates().
Parameters
cMo: The homogeneous matrix corresponding to the pose between the camera frame and the object frame.

Definition at line 79 of file vpForwardProjection.cpp.

References changeFrame(), and projection().

◆ projection() [1/2]

void vpCircle::projection ( )
virtual

Perspective projection of the circle.

From the 3D parameters of the circle in the camera frame available in cP, computes the 2D parameters of the ellipse resulting from the perspective projection in the image plane. Those 2D parameters are available in p vector.

See vpCircle::projection(const vpColVector &, vpColVector &) const for a more detailed description of the parameters.

Implements vpForwardProjection.

Examples
testCameraParametersConversion.cpp.

Definition at line 151 of file vpCircle.cpp.

References vpTracker::cP, vpTracker::p, and projection().

Referenced by display(), display(), operator=(), and projection().

◆ projection() [2/2]

void vpCircle::projection ( const vpColVector & cP_,
vpColVector & p_ ) const
virtual

Perspective projection of the circle.

Parameters
cP_: 3D cercle input parameters expressed in the camera frame. This 7-dim vector contains the following parameters: cA, cB, cC, cX, cY, cZ, R where
  • cA, cB, cC are the parameters of the plane with equation cA*(x-cX)+cB*(y-cY)+cC*(z-cZ)=0 passing through the 3D sphere center.
  • cX, cY, cZ are the 3D coordinates of the circle in the camera frame
  • R is the circle radius in [m].
p_: 2D circle output parameters. This is a 5 dimension vector. It contains the following parameters: x, y, n20, n11, n02 where:
  • x, y are the normalized coordinates of the ellipse centroid (ie the perspective projection of a 3D circle becomes a 2D ellipse in the image) in the image plane.
  • n20, n11, n02 which are the second order centered moments of the ellipse normalized by its area (i.e., such that $n_{ij} = \mu_{ij}/a$ where $\mu_{ij}$ are the centered moments and a the area).

Implements vpForwardProjection.

Definition at line 171 of file vpCircle.cpp.

References vpException::divideByZeroError, vpColVector::resize(), and vpMath::sqr().

◆ setDeallocate()

void vpForwardProjection::setDeallocate ( vpForwardProjectionDeallocatorType d)
inlineinherited

Definition at line 185 of file vpForwardProjection.h.

◆ setWorldCoordinates() [1/2]

void vpCircle::setWorldCoordinates ( const vpColVector & oP_)
virtual

Set the parameters of the 3D circle in the object frame.

Parameters
oP_: This 7-dim vector defines the parameters oP[0], oP[1], oP[2] corresponding to parameters oA, oB, oC of the plane with equation oA*(X-oX)+oB*(Y-oY)+oC*(Z-oZ)=0 passing through the 3D sphere center. oP[3], oP[4], oP[5] correspond to oX, oY, oZ the coordinates of the center of the sphere. oP[6] corresponds to the radius of the sphere.

Implements vpForwardProjection.

Examples
manGeometricFeatures.cpp, servoSimuCircle2DCamVelocity.cpp, servoSimuCircle2DCamVelocityDisplay.cpp, simulateCircle2DCamVelocity.cpp, testCameraParametersConversion.cpp, and testPoseFeatures.cpp.

Definition at line 58 of file vpCircle.cpp.

References vpForwardProjection::oP.

Referenced by operator=(), vpCircle(), and vpCircle().

◆ setWorldCoordinates() [2/2]

void vpCircle::setWorldCoordinates ( double oA,
double oB,
double oC,
double oX,
double oY,
double oZ,
double R )

Set the 3D circle parameters in the object frame. The equation of the plane which contains the 3D circle is the following:

\‍[ oA*(X-oX)+oB*(Y-oY)+oC*(Z-oZ)=0 \‍]

where $ (oA, oB, oC) $ are the coordinates of the vector normal to the plane, and $ (oX, oY, oZ) $ are the 3D coordinates of the circle center.

Parameters
oA: Coordinate along X-axis of the vector normal to the plane.
oB: Coordinate along Y-axis of the vector normal to the plane.
oC: Coordinate along Z-axis of the vector normal to the plane.
oX: Coordinate of the center of the sphere along X-axis in the object frame.
oY: Coordinate of the center of the sphere along Y-axis in the object frame.
oZ: Coordinate of the center of the sphere along Z-axis in the object frame.
R: Radius of the sphere.

Definition at line 75 of file vpCircle.cpp.

References vpForwardProjection::oP.

◆ track()

void vpForwardProjection::track ( const vpHomogeneousMatrix & cMo)
inherited

Track the feature parameters in the camera frame (vpTracker::cP) and than compute the projection of these parameters in the image plane (vpTracker::p).

This method is similar to project(const vpHomogeneousMatrix &).

Warning
The feature parameters in the object frame (vpForwardProjection:oP) need to be set prior the use of this method. To initialize these parameters see setWorldCoordinates().
Parameters
cMo: The homogeneous matrix corresponding to the pose between the camera frame and the object frame.
Examples
servoSimu4Points.cpp, servoSimuAfma6FourPoints2DCamVelocity.cpp, servoSimuCircle2DCamVelocity.cpp, servoSimuCircle2DCamVelocityDisplay.cpp, servoSimuFourPoints2DCamVelocity.cpp, servoSimuFourPoints2DCamVelocityDisplay.cpp, servoSimuFourPoints2DPolarCamVelocityDisplay.cpp, servoSimuLine2DCamVelocityDisplay.cpp, servoSimuSphere.cpp, servoSimuSphere2DCamVelocity.cpp, servoSimuSphere2DCamVelocityDisplay.cpp, servoSimuSphere2DCamVelocityDisplaySecondaryTask.cpp, servoSimuSquareLine2DCamVelocityDisplay.cpp, servoSimuViper850FourPoints2DCamVelocity.cpp, simulateCircle2DCamVelocity.cpp, simulateFourPoints2DCartesianCamVelocity.cpp, simulateFourPoints2DPolarCamVelocity.cpp, testPoint.cpp, tutorial-ibvs-4pts-json.cpp, tutorial-ibvs-4pts-ogre.cpp, tutorial-ibvs-4pts-plotter-continuous-gain-adaptive.cpp, tutorial-ibvs-4pts-plotter-gain-adaptive.cpp, tutorial-ibvs-4pts-plotter.cpp, tutorial-ibvs-4pts.cpp, tutorial-simu-pioneer-continuous-gain-adaptive.cpp, tutorial-simu-pioneer-continuous-gain-constant.cpp, tutorial-simu-pioneer-pan.cpp, and tutorial-simu-pioneer.cpp.

Definition at line 101 of file vpForwardProjection.cpp.

References project().

Referenced by vpPose::computeResidual(), vpPose::computeResidual(), vpImageDraw::drawFrame(), vpImageDraw::drawFrame(), vpPose::poseVirtualVS(), vpPose::poseVirtualVSrobust(), vpWireFrameSimulator::projectCameraTrajectory(), vpWireFrameSimulator::projectCameraTrajectory(), vpWireFrameSimulator::projectCameraTrajectory(), vpWireFrameSimulator::projectCameraTrajectory(), setWorldCoordinates(), vpSimulatorAfma6::updateArticularPosition(), and vpSimulatorViper850::updateArticularPosition().

Member Data Documentation

◆ cP

◆ cPAvailable

bool vpTracker::cPAvailable
inherited

Flag used to indicate if the feature parameters cP expressed in the camera frame are available.

Definition at line 79 of file vpTracker.h.

Referenced by init(), operator=(), vpTracker(), and vpTracker().

◆ oP

◆ p

vpColVector vpTracker::p
inherited

Feature coordinates expressed in the image plane p. They correspond to 2D normalized coordinates expressed in meters.

Definition at line 69 of file vpTracker.h.

Referenced by vpCircle::computeIntersectionPoint(), vpMeterPixelConversion::convertEllipse(), vpMeterPixelConversion::convertEllipse(), vpMeterPixelConversion::convertEllipse(), vpMeterPixelConversion::convertEllipse(), vpCircle::display(), vpCircle::display(), vpCylinder::display(), vpCylinder::display(), vpLine::display(), vpLine::display(), vpPoint::display(), vpPoint::display(), vpSphere::display(), vpSphere::display(), vpFeatureDisplay::displayEllipse(), vpFeatureDisplay::displayEllipse(), vpPose::displayModel(), vpPose::displayModel(), vpImageDraw::drawFrame(), vpImageDraw::drawFrame(), vpCircle::get_mu02(), vpSphere::get_mu02(), vpCircle::get_mu11(), vpSphere::get_mu11(), vpCircle::get_mu20(), vpSphere::get_mu20(), vpCircle::get_n02(), vpSphere::get_n02(), vpCircle::get_n11(), vpSphere::get_n11(), vpCircle::get_n20(), vpSphere::get_n20(), get_p(), vpPoint::get_w(), vpCircle::get_x(), vpPoint::get_x(), vpSphere::get_x(), vpCircle::get_y(), vpPoint::get_y(), vpSphere::get_y(), vpLine::getRho(), vpCylinder::getRho1(), vpCylinder::getRho2(), vpLine::getTheta(), vpCylinder::getTheta1(), vpCylinder::getTheta2(), vpCircle::init(), vpCylinder::init(), vpLine::init(), vpMeTracker::init(), vpPoint::init(), vpSphere::init(), vpCircle::operator=(), operator=(), vpForwardProjection::print(), vpPose::printPoint(), vpForwardProjection::project(), vpCircle::projection(), vpCylinder::projection(), vpForwardProjection::projection(), vpLine::projection(), vpPoint::projection(), vpSphere::projection(), vpPoint::set_w(), vpPoint::set_x(), vpPoint::set_y(), vpLine::setRho(), vpLine::setTheta(), vpTracker(), and vpTracker().