#include <visp3/core/vpHomogeneousMatrix.h>

Inheritance diagram for vpHomogeneousMatrix:

Public Member Functions
	vpHomogeneousMatrix ()

	vpHomogeneousMatrix (const vpHomogeneousMatrix &M)

	vpHomogeneousMatrix (const vpTranslationVector &t, const vpRotationMatrix &R)

	vpHomogeneousMatrix (const vpTranslationVector &t, const vpThetaUVector &tu)

	vpHomogeneousMatrix (const vpTranslationVector &t, const vpQuaternionVector &q)

	vpHomogeneousMatrix (const vpPoseVector &p)

	vpHomogeneousMatrix (const std::vector< float > &v)

	vpHomogeneousMatrix (const std::vector< double > &v)

	vpHomogeneousMatrix (const double tx, const double ty, const double tz, const double tux, const double tuy, const double tuz)

virtual	~vpHomogeneousMatrix ()

void	buildFrom (const vpTranslationVector &t, const vpRotationMatrix &R)

void	buildFrom (const vpTranslationVector &t, const vpThetaUVector &tu)

void	buildFrom (const vpTranslationVector &t, const vpQuaternionVector &q)

void	buildFrom (const vpPoseVector &p)

void	buildFrom (const std::vector< float > &v)

void	buildFrom (const std::vector< double > &v)

void	buildFrom (const double tx, const double ty, const double tz, const double tux, const double tuy, const double tuz)

void	convert (std::vector< float > &M)

void	convert (std::vector< double > &M)

void	eye ()

vpColVector	getCol (const unsigned int j) const

vpRotationMatrix	getRotationMatrix ()

vpThetaUVector	getThetaUVector ()

vpTranslationVector	getTranslationVector ()

vpHomogeneousMatrix	inverse () const

void	inverse (vpHomogeneousMatrix &Mi) const

bool	isAnHomogeneousMatrix () const

void	insert (const vpRotationMatrix &R)

void	insert (const vpThetaUVector &tu)

void	insert (const vpTranslationVector &t)

void	insert (const vpQuaternionVector &t)

void	extract (vpRotationMatrix &R) const

void	extract (vpThetaUVector &tu) const

void	extract (vpTranslationVector &t) const

void	extract (vpQuaternionVector &q) const

void	load (std::ifstream &f)

void	save (std::ofstream &f) const

vpHomogeneousMatrix &	operator= (const vpHomogeneousMatrix &M)

vpHomogeneousMatrix	operator* (const vpHomogeneousMatrix &M) const

vpColVector	operator* (const vpColVector &v) const

vpPoint	operator* (const vpPoint &bP) const

void	print () const

void	resize (const unsigned int nrows, const unsigned int ncols, const bool flagNullify=true)

Deprecated functions
vp_deprecated void	init ()

vp_deprecated void	setIdentity ()

Inherited functionalities from vpArray2D
double	getMinValue () const

double	getMaxValue () const

unsigned int	getRows () const

unsigned int	getCols () const

unsigned int	size () const

double *	operator[] (unsigned int i)

double *	operator[] (unsigned int i) const

Static Public Member Functions
Inherited I/O from vpArray2D with Static Public Member Functions
static bool	load (const std::string &filename, vpArray2D< double > &A, const bool binary=false, char *header=NULL)

static bool	loadYAML (const std::string &filename, vpArray2D< double > &A, char *header=NULL)

static bool	save (const std::string &filename, const vpArray2D< double > &A, const bool binary=false, const char *header="")

static bool	saveYAML (const std::string &filename, const vpArray2D< double > &A, const char *header="")

Public Attributes
double *	data

Protected Attributes
unsigned int	rowNum

unsigned int	colNum

double **	rowPtrs

unsigned int	dsize

Related Functions
(Note that these are not member functions.)
enum	vpGEMMmethod

Detailed Description

Implementation of an homogeneous matrix and operations on such kind of matrices.

The class provides a data structure for the homogeneous matrices as well as a set of operations on these matrices.

The vpHomogeneousMatrix class is derived from vpArray2D<double>.

An homogeneous matrix is 4x4 matrix defines as

$^a{\bf M}_b = \left(\begin{array}{cc} ^a{\bf R}_b & ^a{\bf t}_b \\ {\bf 0}_{1\times 3} & 1 \end{array} \right)$

that defines the position of frame b in frame a

$^a{\bf R}_b$ is a rotation matrix and $^a{\bf t}_b$ is a translation vector.

Examples:: AROgre.cpp, AROgreBasic.cpp, calibrateTsai.cpp, exponentialMap.cpp, HelloWorldOgre.cpp, HelloWorldOgreAdvanced.cpp, homographyHartleyDLT2DObject.cpp, homographyHLM2DObject.cpp, homographyHLM3DObject.cpp, homographyRansac2DObject.cpp, manGeometricFeatures.cpp, manServo4PointsDisplay.cpp, manServoMomentsSimple.cpp, manSimu4Dots.cpp, manSimu4Points.cpp, mbtEdgeKltTracking.cpp, mbtEdgeTracking.cpp, mbtKltTracking.cpp, photometricVisualServoing.cpp, poseVirtualVS.cpp, servoAfma4Point2DArtVelocity.cpp, servoAfma62DhalfCamVelocity.cpp, servoAfma6Cylinder2DCamVelocity.cpp, servoAfma6Cylinder2DCamVelocitySecondaryTask.cpp, servoAfma6FourPoints2DCamVelocityInteractionCurrent.cpp, servoAfma6FourPoints2DCamVelocityInteractionDesired.cpp, servoAfma6Line2DCamVelocity.cpp, servoAfma6Point2DArtVelocity.cpp, servoAfma6Points2DCamVelocityEyeToHand.cpp, servoAfma6SquareLines2DCamVelocity.cpp, servoAfma6TwoLines2DCamVelocity.cpp, servoBiclopsPoint2DArtVelocity.cpp, servoMomentImage.cpp, servoMomentPoints.cpp, servoMomentPolygon.cpp, servoPioneerPanSegment3D.cpp, servoPtu46Point2DArtVelocity.cpp, servoSimu3D_cdMc_CamVelocity.cpp, servoSimu3D_cdMc_CamVelocityWithoutVpServo.cpp, servoSimu3D_cMcd_CamVelocity.cpp, servoSimu3D_cMcd_CamVelocityWithoutVpServo.cpp, servoSimu4Points.cpp, servoSimuAfma6FourPoints2DCamVelocity.cpp, servoSimuCircle2DCamVelocity.cpp, servoSimuCircle2DCamVelocityDisplay.cpp, servoSimuCylinder.cpp, servoSimuCylinder2DCamVelocityDisplay.cpp, servoSimuCylinder2DCamVelocityDisplaySecondaryTask.cpp, servoSimuFourPoints2DCamVelocity.cpp, servoSimuFourPoints2DCamVelocityDisplay.cpp, servoSimuFourPoints2DPolarCamVelocityDisplay.cpp, servoSimuLine2DCamVelocityDisplay.cpp, servoSimuPoint2DCamVelocity1.cpp, servoSimuPoint2DCamVelocity2.cpp, servoSimuPoint2DCamVelocity3.cpp, servoSimuPoint2DhalfCamVelocity1.cpp, servoSimuPoint2DhalfCamVelocity2.cpp, servoSimuPoint2DhalfCamVelocity3.cpp, servoSimuPoint3DCamVelocity.cpp, servoSimuSphere.cpp, servoSimuSphere2DCamVelocity.cpp, servoSimuSphere2DCamVelocitySecondaryTask.cpp, servoSimuSquareLine2DCamVelocityDisplay.cpp, servoSimuThetaUCamVelocity.cpp, servoSimuViper850FourPoints2DCamVelocity.cpp, servoViper650FourPoints2DArtVelocityInteractionCurrent.cpp, servoViper650FourPoints2DCamVelocityInteractionCurrent.cpp, servoViper850FourPoints2DArtVelocityInteractionCurrent.cpp, servoViper850FourPoints2DCamVelocityInteractionCurrent.cpp, servoViper850FourPointsKinect.cpp, servoViper850Point2DArtVelocity.cpp, simulateCircle2DCamVelocity.cpp, simulateFourPoints2DCartesianCamVelocity.cpp, simulateFourPoints2DPolarCamVelocity.cpp, testDisplacement.cpp, testFeatureSegment.cpp, testFindMatch.cpp, testKeyPoint-2.cpp, testKeyPoint-4.cpp, testPose.cpp, testPoseFeatures.cpp, testPoseRansac.cpp, testPoseVector.cpp, testRobotAfma6Pose.cpp, testRobotViper850.cpp, testRobotViper850Pose.cpp, testViper850.cpp, tutorial-detection-object-mbt.cpp, tutorial-detection-object-mbt2.cpp, tutorial-homography-from-points.cpp, tutorial-ibvs-4pts-display.cpp, tutorial-ibvs-4pts-image-tracking.cpp, tutorial-ibvs-4pts-ogre-tracking.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-wireframe-camera.cpp, tutorial-ibvs-4pts-wireframe-robot-afma6.cpp, tutorial-ibvs-4pts-wireframe-robot-viper.cpp, tutorial-ibvs-4pts.cpp, tutorial-image-simulator.cpp, tutorial-mb-edge-tracker.cpp, tutorial-mb-hybrid-tracker.cpp, tutorial-mb-klt-tracker.cpp, tutorial-mb-tracker-full.cpp, tutorial-mb-tracker.cpp, tutorial-pose-from-points-image.cpp, tutorial-pose-from-points-tracking.cpp, tutorial-simu-pioneer-continuous-gain-adaptive.cpp, tutorial-simu-pioneer-continuous-gain-constant.cpp, tutorial-simu-pioneer-pan.cpp, tutorial-simu-pioneer.cpp, and wireframeSimulator.cpp.

Definition at line 93 of file vpHomogeneousMatrix.h.

Constructor & Destructor Documentation

vpHomogeneousMatrix::vpHomogeneousMatrix ( )

Default constructor that initialize an homogeneous matrix as identity.

Definition at line 66 of file vpHomogeneousMatrix.cpp.

References eye().

vpHomogeneousMatrix::vpHomogeneousMatrix ( const vpHomogeneousMatrix & M )

Copy constructor that initialize an homogeneous matrix from another homogeneous matrix.

Definition at line 75 of file vpHomogeneousMatrix.cpp.

vpHomogeneousMatrix::vpHomogeneousMatrix	(	const vpTranslationVector &	t,
		const vpRotationMatrix &	R
	)

Construct an homogeneous matrix from a translation vector and a rotation matrix.

Definition at line 95 of file vpHomogeneousMatrix.cpp.

References insert().

vpHomogeneousMatrix::vpHomogeneousMatrix	(	const vpTranslationVector &	t,
		const vpThetaUVector &	tu
	)

Construct an homogeneous matrix from a translation vector and $\theta {\bf u}$ rotation vector.

Definition at line 84 of file vpHomogeneousMatrix.cpp.

References buildFrom().

vpHomogeneousMatrix::vpHomogeneousMatrix	(	const vpTranslationVector &	t,
		const vpQuaternionVector &	q
	)

Construct an homogeneous matrix from a translation vector and quaternion rotation vector.

Definition at line 55 of file vpHomogeneousMatrix.cpp.

References buildFrom().

vpHomogeneousMatrix::vpHomogeneousMatrix ( const vpPoseVector & p )

Construct an homogeneous matrix from a pose vector.

Definition at line 107 of file vpHomogeneousMatrix.cpp.

References buildFrom().

vpHomogeneousMatrix::vpHomogeneousMatrix ( const std::vector< float > & v )

Construct an homogeneous matrix from a vector of float.

Parameters

v	: Vector of 12 or 16 values corresponding to the values of the homogeneous matrix.

The following example shows how to use this function:

#include <visp3/core/vpHomogeneousMatrix.h>
int main()
{
  std::vector<float> v(12, 0);
  v[1]  = -1.; // ry=-90
  v[4]  =  1.; // rx=90
  v[10] = -1.; // rz=-90
  v[3]  = 0.3; // tx
  v[7]  = 0.4; // ty
  v[11] = 0.5; // tz
  std::cout << "v: ";
  for(unsigned int i=0; i<v.size(); i++)
    std::cout << v[i] << " ";
  std::cout << std::endl;
  vpHomogeneousMatrix M(v);
  std::cout << "M:\n" << M << std::endl;
}

It produces the following printings:

v: 0 -1 0 0.3 1 0 0 0.4 0 0 -1 0.5
M:
0  -1  0  0.3000000119
1  0  0  0.400000006
0  0  -1  0.5
0  0  0  1

Definition at line 152 of file vpHomogeneousMatrix.cpp.

References buildFrom().

vpHomogeneousMatrix::vpHomogeneousMatrix ( const std::vector< double > & v )

Construct an homogeneous matrix from a vector of double.

Parameters

v	: Vector of 12 or 16 values corresponding to the values of the homogeneous matrix.

The following example shows how to use this function:

#include <visp3/core/vpHomogeneousMatrix.h>
int main()
{
  std::vector<double> v(12, 0);
  v[1]  = -1.; // ry=-90
  v[4]  =  1.; // rx=90
  v[10] = -1.; // rz=-90
  v[3]  = 0.3; // tx
  v[7]  = 0.4; // ty
  v[11] = 0.5; // tz
  std::cout << "v: ";
  for(unsigned int i=0; i<v.size(); i++)
    std::cout << v[i] << " ";
  std::cout << std::endl;
  vpHomogeneousMatrix M(v);
  std::cout << "M:\n" << M << std::endl;
}

It produces the following printings:

v: 0 -1 0 0.3 1 0 0 0.4 0 0 -1 0.5
M:
0  -1  0  0.3
1  0  0  0.4
0  0  -1  0.5
0  0  0  1

Definition at line 197 of file vpHomogeneousMatrix.cpp.

References buildFrom().

vpHomogeneousMatrix::vpHomogeneousMatrix	(	const double	tx,
		const double	ty,
		const double	tz,
		const double	tux,
		const double	tuy,
		const double	tuz
	)

Construct an homogeneous matrix from a translation vector ${\bf t}=(t_x, t_y, t_z)^T$ and a $\theta {\bf u}=(\theta u_x, \theta u_y, \theta u_z)^T$ rotation vector.

Definition at line 208 of file vpHomogeneousMatrix.cpp.

References buildFrom().

virtual vpHomogeneousMatrix::~vpHomogeneousMatrix ( )

inlinevirtual

Destructor.

Definition at line 109 of file vpHomogeneousMatrix.h.

Member Function Documentation

void vpHomogeneousMatrix::buildFrom	(	const vpTranslationVector &	t,
		const vpRotationMatrix &	R
	)

Build an homogeneous matrix from a translation vector and a rotation matrix.

Examples:: calibrateTsai.cpp, mbtEdgeKltTracking.cpp, mbtEdgeTracking.cpp, mbtKltTracking.cpp, photometricVisualServoing.cpp, servoAfma6FourPoints2DCamVelocityInteractionCurrent.cpp, servoAfma6FourPoints2DCamVelocityInteractionDesired.cpp, servoSimu3D_cdMc_CamVelocity.cpp, servoSimu3D_cMcd_CamVelocity.cpp, servoSimuPoint2DhalfCamVelocity1.cpp, servoSimuPoint2DhalfCamVelocity2.cpp, servoSimuPoint2DhalfCamVelocity3.cpp, servoSimuThetaUCamVelocity.cpp, servoViper650FourPoints2DArtVelocityInteractionCurrent.cpp, servoViper650FourPoints2DCamVelocityInteractionCurrent.cpp, servoViper850FourPoints2DArtVelocityInteractionCurrent.cpp, servoViper850FourPoints2DCamVelocityInteractionCurrent.cpp, servoViper850FourPointsKinect.cpp, testKeyPoint-2.cpp, testRobotAfma6Pose.cpp, and testRobotViper850Pose.cpp.

Definition at line 237 of file vpHomogeneousMatrix.cpp.

References insert().

Referenced by vpHomography::buildFrom(), vpViper850::init(), vpViper650::init(), vpAfma6::init(), vpSimulatorAfma6::init(), vpSimulatorViper850::init(), vpMbTracker::initClick(), vpMbTracker::initFromPose(), vpWireFrameSimulator::navigation(), vpViper850::parseConfigFile(), vpAfma6::parseConfigFile(), vpPioneerPan::set_cMe(), vpViper::set_eMc(), vpWireFrameSimulator::setExternalCameraPosition(), vpSimulatorPioneer::setVelocity(), vpSimulatorPioneerPan::setVelocity(), vpAfma4::vpAfma4(), vpHomogeneousMatrix(), vpKinect::vpKinect(), and vpWireFrameSimulator::vpWireFrameSimulator().

void vpHomogeneousMatrix::buildFrom	(	const vpTranslationVector &	t,
		const vpThetaUVector &	tu
	)

Build an homogeneous matrix from a translation vector and a $\theta {\bf u}$ rotation vector.

Definition at line 225 of file vpHomogeneousMatrix.cpp.

References insert().

void vpHomogeneousMatrix::buildFrom	(	const vpTranslationVector &	t,
		const vpQuaternionVector &	q
	)

Build an homogeneous matrix from a translation vector and a quaternion rotation vector.

Definition at line 261 of file vpHomogeneousMatrix.cpp.

References insert().

void vpHomogeneousMatrix::buildFrom ( const vpPoseVector & p )

Build an homogeneous matrix from a pose vector.

Definition at line 248 of file vpHomogeneousMatrix.cpp.

References insert().

void vpHomogeneousMatrix::buildFrom ( const std::vector< float > & v )

Build an homogeneous matrix from a vector of float.

Parameters

v	: Vector of 12 or 16 values corresponding to the values of the homogeneous matrix.

The following example shows how to use this function:

#include <visp3/core/vpHomogeneousMatrix.h>
int main()
{
  std::vector<float> v(12, 0);
  v[1]  = -1.; // ry=-90
  v[4]  =  1.; // rx=90
  v[10] = -1.; // rz=-90
  v[3]  = 0.3; // tx
  v[7]  = 0.4; // ty
  v[11] = 0.5; // tz
  std::cout << "v: ";
  for(unsigned int i=0; i<v.size(); i++)
    std::cout << v[i] << " ";
  std::cout << std::endl;
  vpHomogeneousMatrix M;
  M.buildFrom(v);
  std::cout << "M:\n" << M << std::endl;
}

It produces the following printings:

v: 0 -1 0 0.3 1 0 0 0.4 0 0 -1 0.5
M:
0  -1  0  0.3000000119
1  0  0  0.400000006
0  0  -1  0.5
0  0  0  1

Definition at line 327 of file vpHomogeneousMatrix.cpp.

References vpArray2D< double >::data, and vpException::dimensionError.

void vpHomogeneousMatrix::buildFrom ( const std::vector< double > & v )

Build an homogeneous matrix from a vector of double.

Parameters

v	: Vector of 12 or 16 values corresponding to the values of the homogeneous matrix.

The following example shows how to use this function:

#include <visp3/core/vpHomogeneousMatrix.h>
int main()
{
  std::vector<double> v(12, 0);
  v[1]  = -1.; // ry=-90
  v[4]  =  1.; // rx=90
  v[10] = -1.; // rz=-90
  v[3]  = 0.3; // tx
  v[7]  = 0.4; // ty
  v[11] = 0.5; // tz
  std::cout << "v: ";
  for(unsigned int i=0; i<v.size(); i++)
    std::cout << v[i] << " ";
  std::cout << std::endl;
  vpHomogeneousMatrix M;
  M.buildFrom(v);
  std::cout << "M:\n" << M << std::endl;
}

It produces the following printings:

v: 0 -1 0 0.3 1 0 0 0.4 0 0 -1 0.5
M:
0  -1  0  0.3
1  0  0  0.4
0  0  -1  0.5
0  0  0  1

Definition at line 377 of file vpHomogeneousMatrix.cpp.

References vpArray2D< double >::data, and vpException::dimensionError.

void vpHomogeneousMatrix::buildFrom	(	const double	tx,
		const double	ty,
		const double	tz,
		const double	tux,
		const double	tuy,
		const double	tuz
	)

Build an homogeneous matrix from a translation vector ${\bf t}=(t_x, t_y, t_z)^T$ and a $\theta {\bf u}=(\theta u_x, \theta u_y, \theta u_z)^T$ rotation vector.

Definition at line 273 of file vpHomogeneousMatrix.cpp.

References insert().

void vpHomogeneousMatrix::convert ( std::vector< float > & M )

Converts an homogeneous matrix to a vector of 12 floats.

Parameters

M	: Converted matrix.

Definition at line 774 of file vpHomogeneousMatrix.cpp.

References vpArray2D< double >::data.

void vpHomogeneousMatrix::convert ( std::vector< double > & M )

Converts an homogeneous matrix to a vector of 12 doubles.

Parameters

M	: Converted matrix.

Definition at line 785 of file vpHomogeneousMatrix.cpp.

References vpArray2D< double >::data.

void vpHomogeneousMatrix::extract ( vpRotationMatrix & R ) const

Extract the rotational matrix from the homogeneous matrix.

Parameters

R	: rotational component as a rotation matrix.

Examples:: calibrateTsai.cpp, exponentialMap.cpp, servoAfma6FourPoints2DCamVelocityInteractionCurrent.cpp, servoMomentImage.cpp, servoMomentPoints.cpp, servoMomentPolygon.cpp, servoSimu3D_cdMc_CamVelocityWithoutVpServo.cpp, servoSimu3D_cMcd_CamVelocityWithoutVpServo.cpp, servoViper650FourPoints2DArtVelocityInteractionCurrent.cpp, servoViper650FourPoints2DCamVelocityInteractionCurrent.cpp, servoViper850FourPoints2DArtVelocityInteractionCurrent.cpp, servoViper850FourPoints2DCamVelocityInteractionCurrent.cpp, servoViper850FourPointsKinect.cpp, testRobotAfma6Pose.cpp, testRobotViper850.cpp, testRobotViper850Pose.cpp, and testViper850.cpp.

Definition at line 531 of file vpHomogeneousMatrix.cpp.

Referenced by vpTranslationVector::buildFrom(), vpPoseVector::buildFrom(), vpForceTwistMatrix::buildFrom(), vpVelocityTwistMatrix::buildFrom(), vpThetaUVector::buildFrom(), vpFeatureThetaU::buildFrom(), vpMbtDistanceKltPoints::computeHomography(), vpViper::get_eJe(), vpViper::get_fJe(), vpRobotAfma6::getDisplacement(), vpSimulatorCamera::getPosition(), vpRobotCamera::getPosition(), vpSimulatorPioneer::getPosition(), vpSimulatorPioneerPan::getPosition(), vpSimulatorAfma6::getPosition(), vpSimulatorViper850::getPosition(), vpRobotAfma4::getPosition(), vpRobotAfma6::getPosition(), getRotationMatrix(), getThetaUVector(), getTranslationVector(), vpRobotAfma6::getVelocity(), vpRobotViper850::getVelocity(), vpRobotViper650::getVelocity(), vpExponentialMap::inverse(), inverse(), isAnHomogeneousMatrix(), operator*(), vpPose::poseLowe(), vpViper::set_eMc(), vpImageSimulator::setCameraPosition(), vpWireFrameSimulator::setExternalCameraPosition(), vpMbKltTracker::setPose(), vpAROgre::setPosition(), vpSimulatorAfma6::setPosition(), vpRobotAfma4::setVelocity(), vpFeatureThetaU::vpFeatureThetaU(), and vpTranslationVector::vpTranslationVector().

void vpHomogeneousMatrix::extract ( vpThetaUVector & tu ) const

Extract the rotation as a $\theta \bf u$ vector.

Definition at line 552 of file vpHomogeneousMatrix.cpp.

References vpThetaUVector::buildFrom().

void vpHomogeneousMatrix::extract ( vpTranslationVector & t ) const

Extract the translation vector from the homogeneous matrix.

Definition at line 542 of file vpHomogeneousMatrix.cpp.

void vpHomogeneousMatrix::extract ( vpQuaternionVector & q ) const

Extract the rotation as a quaternion.

Definition at line 563 of file vpHomogeneousMatrix.cpp.

References vpQuaternionVector::buildFrom().

void vpHomogeneousMatrix::eye ( )

Set transformation to identity.

Examples:: calibrateTsai.cpp.

Definition at line 650 of file vpHomogeneousMatrix.cpp.

Referenced by vpViper::get_wMe(), vpMbTracker::initClick(), vpMbKltTracker::reinit(), vpMbKltTracker::reInitModel(), vpMbEdgeTracker::reInitModel(), vpMbKltTracker::resetTracker(), vpMbEdgeTracker::resetTracker(), setIdentity(), vpMbKltTracker::setPose(), vpAfma6::vpAfma6(), vpHomogeneousMatrix(), and vpViper::vpViper().

vpColVector vpHomogeneousMatrix::getCol ( const unsigned int j ) const

Extract a column vector from an homogeneous matrix.

Warning: All the indexes start from 0 in this function.

Parameters

j	: Index of the column to extract. If j=0, the first column is extracted.

Returns: The extracted column vector.

The following example shows how to use this function:

#include <visp3/core/vpColVector.h>
#include <visp3/core/vpHomogeneousMatrix.h>
int main()
{
  vpHomogeneousMatrix M;
  vpColVector t = M.getCol(3);
  std::cout << "Last column: \n" << t << std::endl;
}

It produces the following output:

Last column:
0
0
1
0

Definition at line 852 of file vpHomogeneousMatrix.cpp.

References vpException::dimensionError, vpArray2D< double >::getCols(), and vpArray2D< double >::getRows().

unsigned int vpArray2D< double >::getCols ( ) const

inlineinherited

Return the number of columns of the 2D array.

Examples:: servoViper850Point2DArtVelocity-jointAvoidance-basic.cpp, testColVector.cpp, testDisplacement.cpp, testMatrix.cpp, testMatrixInverse.cpp, testPoseVector.cpp, testRowVector.cpp, testSvd.cpp, and testTranslationVector.cpp.

Definition at line 154 of file vpArray2D.h.

References vpArray2D< Type >::colNum.

Referenced by vpMatrix::csvPrint(), vpRotationMatrix::getCol(), getCol(), vpMatrix::getCol(), vpMatrix::getRow(), vpMatrix::inverseByQRLapack(), vpMatrix::kernel(), vpMatrix::maplePrint(), vpRowVector::operator*(), vpRowVector::operator+(), vpRowVector::operator+=(), vpRowVector::operator-(), vpRowVector::operator-=(), vpForceTwistMatrix::print(), vpVelocityTwistMatrix::print(), vpRowVector::print(), vpMatrix::print(), vpMatrix::pseudoInverse(), and vpMatrix::svd().

double vpArray2D< double >::getMaxValue ( ) const

inherited

Return the array max value.

Examples:: servoMomentImage.cpp.

double vpArray2D< double >::getMinValue ( ) const

inherited

Return the array min value.

Examples:: servoMomentImage.cpp.

vpRotationMatrix vpHomogeneousMatrix::getRotationMatrix ( )

Return the rotation matrix from the homogeneous transformation matrix.

Definition at line 805 of file vpHomogeneousMatrix.cpp.

References extract().

unsigned int vpArray2D< double >::getRows ( ) const

inlineinherited

Return the number of rows of the 2D array.

Examples:: testColVector.cpp, testDisplacement.cpp, testMatrix.cpp, testMatrixInverse.cpp, testPoseVector.cpp, testRowVector.cpp, testSvd.cpp, and testTranslationVector.cpp.

Definition at line 152 of file vpArray2D.h.

References vpArray2D< Type >::rowNum.

Referenced by vpMatrix::cppPrint(), vpMatrix::csvPrint(), vpRotationMatrix::getCol(), getCol(), vpMatrix::getCol(), vpMatrix::getRow(), vpMatrix::inverseByCholeskyLapack(), vpMatrix::inverseByQRLapack(), vpMatrix::kernel(), vpMatrix::maplePrint(), vpMatrix::matlabPrint(), vpColVector::operator+(), vpColVector::operator+=(), vpColVector::operator-(), vpColVector::operator-=(), vpForceTwistMatrix::print(), vpVelocityTwistMatrix::print(), vpPoseVector::print(), vpColVector::print(), vpMatrix::print(), and vpMatrix::pseudoInverse().

vpThetaUVector vpHomogeneousMatrix::getThetaUVector ( )

Return the $\theta {\bf u}$ vector that corresponds to the rotation part of the homogeneous transformation.

Definition at line 816 of file vpHomogeneousMatrix.cpp.

References extract().

vpTranslationVector vpHomogeneousMatrix::getTranslationVector ( )

Return the translation vector from the homogeneous transformation matrix.

Definition at line 795 of file vpHomogeneousMatrix.cpp.

References extract().

vp_deprecated void vpHomogeneousMatrix::init ( )

inline

Deprecated:: Provided only for compat with previous releases. This function does nothing.

Examples:: HelloWorldOgreAdvanced.cpp.

Definition at line 186 of file vpHomogeneousMatrix.h.

void vpHomogeneousMatrix::insert ( const vpRotationMatrix & R )

Insert the rotational component of the homogeneous matrix.

Examples:: testDisplacement.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 574 of file vpHomogeneousMatrix.cpp.

Referenced by buildFrom(), vpCalibration::calibrationTsai(), vpExponentialMap::direct(), insert(), inverse(), operator*(), vpPose::poseLowe(), and vpHomogeneousMatrix().

void vpHomogeneousMatrix::insert ( const vpThetaUVector & tu )

Insert the rotational component of the homogeneous matrix from a $theta {\bf u}$ rotation vector.

Definition at line 588 of file vpHomogeneousMatrix.cpp.

References insert().

void vpHomogeneousMatrix::insert ( const vpTranslationVector & t )

Insert the translational component in a homogeneous matrix.

Definition at line 598 of file vpHomogeneousMatrix.cpp.

void vpHomogeneousMatrix::insert ( const vpQuaternionVector & q )

Insert the rotational component of the homogeneous matrix from a quaternion rotation vector.

Definition at line 612 of file vpHomogeneousMatrix.cpp.

References insert().

vpHomogeneousMatrix vpHomogeneousMatrix::inverse ( ) const

Invert the homogeneous matrix

Returns: $\left[\begin{array}{cc} {\bf R} & {\bf t} \\ {\bf 0}_{1\times 3} & 1 \end{array} \right]^{-1} = \left[\begin{array}{cc} {\bf R}^T & -{\bf R}^T {\bf t} \\ {\bf 0}_{1\times 3} & 1 \end{array} \right]$

Examples:: calibrateTsai.cpp, manServo4PointsDisplay.cpp, manServoMomentsSimple.cpp, manSimu4Dots.cpp, manSimu4Points.cpp, photometricVisualServoing.cpp, servoAfma62DhalfCamVelocity.cpp, servoMomentImage.cpp, servoSimu3D_cdMc_CamVelocity.cpp, servoSimu3D_cdMc_CamVelocityWithoutVpServo.cpp, servoSimu3D_cMcd_CamVelocity.cpp, servoSimu3D_cMcd_CamVelocityWithoutVpServo.cpp, servoSimu4Points.cpp, servoSimuCircle2DCamVelocity.cpp, servoSimuCircle2DCamVelocityDisplay.cpp, servoSimuCylinder.cpp, servoSimuCylinder2DCamVelocityDisplay.cpp, servoSimuCylinder2DCamVelocityDisplaySecondaryTask.cpp, servoSimuFourPoints2DCamVelocity.cpp, servoSimuFourPoints2DCamVelocityDisplay.cpp, servoSimuFourPoints2DPolarCamVelocityDisplay.cpp, servoSimuLine2DCamVelocityDisplay.cpp, servoSimuPoint2DCamVelocity1.cpp, servoSimuPoint2DCamVelocity2.cpp, servoSimuPoint2DCamVelocity3.cpp, servoSimuPoint2DhalfCamVelocity1.cpp, servoSimuPoint2DhalfCamVelocity2.cpp, servoSimuPoint2DhalfCamVelocity3.cpp, servoSimuPoint3DCamVelocity.cpp, servoSimuSphere.cpp, servoSimuSphere2DCamVelocity.cpp, servoSimuSphere2DCamVelocitySecondaryTask.cpp, servoSimuSquareLine2DCamVelocityDisplay.cpp, servoSimuThetaUCamVelocity.cpp, simulateCircle2DCamVelocity.cpp, simulateFourPoints2DCartesianCamVelocity.cpp, simulateFourPoints2DPolarCamVelocity.cpp, testFeatureSegment.cpp, tutorial-ibvs-4pts-display.cpp, tutorial-ibvs-4pts-image-tracking.cpp, tutorial-ibvs-4pts-ogre-tracking.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-wireframe-camera.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 631 of file vpHomogeneousMatrix.cpp.

References extract(), insert(), and vpRotationMatrix::t().

Referenced by vpKeyPoint::compute3D(), vpSimulatorViper850::compute_fMi(), vpPtu46::computeMGD(), vpBiclops::computeMGD(), vpMbEdgeKltTracker::computeVVS(), vpMbKltTracker::computeVVS(), vpMbEdgeTracker::computeVVS(), vpProjectionDisplay::displayCamera(), vpPtu46::get_cMe(), vpViper::get_cMe(), vpAfma4::get_cMe(), vpAfma6::get_cMe(), vpRobotWireFrameSimulator::get_cMo(), vpAfma4::get_cVf(), vpViper::get_eJe(), vpViper::get_fJe(), vpBiclops::get_fMc(), vpRobotBiclops::getDisplacement(), vpRobotAfma6::getDisplacement(), vpSimulator::getExternalCameraPosition(), vpSimulatorAfma6::getExternalImage(), vpSimulatorViper850::getExternalImage(), vpWireFrameSimulator::getExternalImage(), vpWireFrameSimulator::getInternalImage(), vpRobotWireFrameSimulator::getInternalView(), vpViper::getInverseKinematics(), vpAfma6::getInverseKinematics(), vpRobotAfma4::getVelocity(), vpRobotAfma6::getVelocity(), vpRobotViper850::getVelocity(), vpRobotViper650::getVelocity(), vpSimulatorAfma6::initialiseCameraRelativeToObject(), vpSimulatorViper850::initialiseCameraRelativeToObject(), inverse(), vpSimulator::moveInternalCamera(), vpPose::poseVirtualVS(), vpPose::poseVirtualVSrobust(), vpWireFrameSimulator::projectCameraTrajectory(), vpPioneerPan::set_cMe(), vpBiclops::set_cMe(), vpWireFrameSimulator::setCameraPositionRelObj(), vpWireFrameSimulator::setCameraPositionRelWorld(), vpWireFrameSimulator::setExternalCameraPosition(), vpMbKltTracker::setPose(), vpSimulatorAfma6::setPosition(), vpSimulatorPioneer::setVelocity(), vpRobotCamera::setVelocity(), vpSimulatorPioneerPan::setVelocity(), and vpKinect::vpKinect().

void vpHomogeneousMatrix::inverse ( vpHomogeneousMatrix & M ) const

Invert the homogeneous matrix.

Parameters

M	: The inverted homogeneous matrix: $\left[\begin{array}{cc} {\bf R} & {\bf t} \\ {\bf 0}_{1\times 3} & 1 \end{array} \right]^{-1} = \left[\begin{array}{cc} {\bf R}^T & -{\bf R}^T {\bf t} \\ {\bf 0}_{1\times 3} & 1 \end{array} \right]$

Definition at line 678 of file vpHomogeneousMatrix.cpp.

References inverse().

bool vpHomogeneousMatrix::isAnHomogeneousMatrix ( ) const

Test if the 3x3 rotational part of the homogeneous matrix is really a rotation matrix.

Definition at line 518 of file vpHomogeneousMatrix.cpp.

References extract(), and vpRotationMatrix::isARotationMatrix().

void vpHomogeneousMatrix::load ( std::ifstream & f )

Read an homogeneous matrix from an input file stream. The homogeneous matrix is considered as a 4 by 4 matrix.

Parameters

f	: Input file stream.

The code below shows how to get an homogeneous matrix from a file.

vpHomogeneousMatrix M;
std::ifstream f("homogeneous.dat");
M.load(f);

See also: save()

Examples:: servoAfma6Points2DCamVelocityEyeToHand.cpp.

Definition at line 738 of file vpHomogeneousMatrix.cpp.

References vpException::ioError.

static bool vpArray2D< double >::load	(	const std::string &	filename,
		vpArray2D< double > &	A,
		const bool	binary = `false`,
		char *	header = `NULL`
	)

inlinestaticinherited

Load a matrix from a file.

Parameters

filename	: Absolute file name.
A	: Array to be loaded
binary	: If true the matrix is loaded from a binary file, else from a text file.
header	: Header of the file is loaded in this parameter.

Returns: Returns true if success.

See also: save()

Definition at line 308 of file vpArray2D.h.

References vpException::badValue, and vpArray2D< Type >::resize().

static bool vpArray2D< double >::loadYAML	(	const std::string &	filename,
		vpArray2D< double > &	A,
		char *	header = `NULL`
	)

inlinestaticinherited

Load an array from a YAML-formatted file.

Parameters

filename	: absolute file name.
A	: array to be loaded from the file.
header	: header of the file is loaded in this parameter.

Returns: Returns true on success.

See also: saveYAML()

Definition at line 392 of file vpArray2D.h.

References vpArray2D< Type >::resize().

vpHomogeneousMatrix vpHomogeneousMatrix::operator* ( const vpHomogeneousMatrix & M ) const

Operator that allow to multiply an homogeneous matrix by an other one.

#include <visp3/core/vpHomogeneousMatrix.h>
int main()
{
  vpHomogeneousMatrix aMb, bMc;
  // Initialize aMb and bMc...
  // Compute aMc * bMc
  vpHomogeneousMatrix aMc = aMb * bMc;  
}

Definition at line 421 of file vpHomogeneousMatrix.cpp.

References extract(), and insert().

vpColVector vpHomogeneousMatrix::operator* ( const vpColVector & v ) const

Operator that allow to multiply an homogeneous matrix by a 4-dimension column vector.

Exceptions

vpException::dimensionError : If the vector v is not a 4-dimension vector.

Definition at line 450 of file vpHomogeneousMatrix.cpp.

References vpException::dimensionError, vpArray2D< Type >::getRows(), vpArray2D< double >::rowNum, and vpArray2D< double >::rowPtrs.

vpPoint vpHomogeneousMatrix::operator* ( const vpPoint & bP ) const

From the coordinates of the point in camera frame b and the transformation between camera frame a and camera frame b computes the coordinates of the point in camera frame a.

Parameters

bP	: 3D coordinates of the point in camera frame bP.

Returns: A point with 3D coordinates in the camera frame a. The coordinates in the world or object frame are set to the same coordinates than the one in the camera frame.

Definition at line 479 of file vpHomogeneousMatrix.cpp.

References vpPoint::get_W(), vpPoint::get_X(), vpPoint::get_Y(), vpPoint::get_Z(), vpPoint::set_oW(), vpPoint::set_oX(), vpPoint::set_oY(), vpPoint::set_oZ(), vpPoint::set_W(), vpPoint::set_X(), vpPoint::set_Y(), and vpPoint::set_Z().

vpHomogeneousMatrix & vpHomogeneousMatrix::operator= ( const vpHomogeneousMatrix & M )

Copy operator that allows to set an homogeneous matrix from an other one.

Parameters

M	: Matrix to copy.

Definition at line 393 of file vpHomogeneousMatrix.cpp.

References vpArray2D< double >::rowPtrs, and vpArray2D< Type >::rowPtrs.

double * vpArray2D< double >::operator[] ( unsigned int i )

inlineinherited

Set element $A_{ij} = x$ using A[i][j] = x.

Definition at line 259 of file vpArray2D.h.

double * vpArray2D< double >::operator[] ( unsigned int i ) const

inlineinherited

Get element $x = A_{ij}$ using x = A[i][j].

Definition at line 261 of file vpArray2D.h.

void vpHomogeneousMatrix::print ( ) const

Print the matrix as a pose vector $({\bf t}^T \theta {\bf u}^T)$ .

Examples:: servoAfma6Points2DCamVelocityEyeToHand.cpp, servoSimuAfma6FourPoints2DCamVelocity.cpp, and servoSimuViper850FourPoints2DCamVelocity.cpp.

Definition at line 755 of file vpHomogeneousMatrix.cpp.

References vpPoseVector::t().

void vpHomogeneousMatrix::resize	(	const unsigned int	nrows,
		const unsigned int	ncols,
		const bool	flagNullify = `true`
	)

inline

This function is not applicable to an homogeneous matrix that is always a 4-by-4 matrix.

Exceptions

vpException::fatalError When this function is called.

Definition at line 168 of file vpHomogeneousMatrix.h.

References vpException::fatalError.

void vpHomogeneousMatrix::save ( std::ofstream & f ) const

Write an homogeneous matrix in an output file stream.

Parameters

f	: Output file stream. The homogeneous matrix is saved as a 4 by 4 matrix.

The code below shows how to save an homogeneous matrix in a file.

// Contruct an homogeneous matrix
vpTranslationVector t(1,2,3);
vpRxyzVector r(M_PI, 0, -M_PI/4.);
vpRotationMatrix R(r);
vpHomogeneousMatrix M(t, R);
// Save the content of the matrix in "homogeneous.dat"
std::ofstream f("homogeneous.dat");  
M.save(f);

See also: load()

Examples:: servoAfma6Points2DCamVelocityEyeToHand.cpp.

Definition at line 707 of file vpHomogeneousMatrix.cpp.

References vpException::ioError.

static bool vpArray2D< double >::save	(	const std::string &	filename,
		const vpArray2D< double > &	A,
		const bool	binary = `false`,
		const char *	header = `""`
	)

inlinestaticinherited

Save a matrix to a file.

Parameters

filename	: Absolute file name.
A	: Array to be saved.
binary	: If true the matrix is saved in a binary file, else a text file.
header	: Optional line that will be saved at the beginning of the file.

Returns: Returns true if success.

Warning : If you save the matrix as in a text file the precision is less than if you save it in a binary file.

See also: load()

Definition at line 468 of file vpArray2D.h.

References vpArray2D< Type >::getCols(), and vpArray2D< Type >::getRows().

static bool vpArray2D< double >::saveYAML	(	const std::string &	filename,
		const vpArray2D< double > &	A,
		const char *	header = `""`
	)

inlinestaticinherited

Save an array in a YAML-formatted file.

Parameters

filename	: absolute file name.
A	: array to be saved in the file.
header	: optional lines that will be saved at the beginning of the file. Should be YAML-formatted and will adapt to the indentation if any.

Returns: Returns true if success.

Here is an example of outputs.

vpArray2D<double> M(3,4);
vpArray2D::saveYAML("matrix.yml", M, "example: a YAML-formatted header");
vpArray2D::saveYAML("matrixIndent.yml", M, "example:\n    - a YAML-formatted header\n    - with inner indentation");

Content of matrix.yml:

example: a YAML-formatted header
rows: 3
cols: 4
data:
  - [0, 0, 0, 0]
  - [0, 0, 0, 0]
  - [0, 0, 0, 0]

Content of matrixIndent.yml:

example:
    - a YAML-formatted header
    - with inner indentation
rows: 3
cols: 4
data:
    - [0, 0, 0, 0]
    - [0, 0, 0, 0]
    - [0, 0, 0, 0]

See also: loadYAML()

Definition at line 560 of file vpArray2D.h.

References vpArray2D< Type >::getCols(), and vpArray2D< Type >::getRows().

void vpHomogeneousMatrix::setIdentity ( )

Deprecated:: You should rather use eye().

Set homogeneous matrix to identity.

See also: eye()

Definition at line 765 of file vpHomogeneousMatrix.cpp.

References eye().

unsigned int vpArray2D< double >::size ( ) const

inlineinherited

Return the number of elements of the 2D array.

Examples:: testColVector.cpp, testDisplacement.cpp, testMatrix.cpp, testPoseVector.cpp, testRowVector.cpp, testTranslationVector.cpp, tutorial-ibvs-4pts-wireframe-robot-afma6.cpp, and tutorial-ibvs-4pts-wireframe-robot-viper.cpp.

Definition at line 156 of file vpArray2D.h.

References vpArray2D< Type >::rowNum.

Referenced by vpRowVector::insert(), vpColVector::insert(), and vpColVector::operator*().

Friends And Related Function Documentation

enum vpGEMMmethod

Operations are :

VP_GEMM_A_T to use the transpose matrix of A instead of the matrix A
VP_GEMM_B_T to use the transpose matrix of B instead of the matrix B
VP_GEMM_C_T to use the transpose matrix of C instead of the matrix C

Definition at line 57 of file vpGEMM.h.

Member Data Documentation

unsigned int vpArray2D< double >::colNum

protectedinherited

Number of columns in the array.

Definition at line 76 of file vpArray2D.h.

double * vpArray2D< double >::data

inherited

Address of the first element of the data array.

Examples:: testDisplacement.cpp, testMatrix.cpp, testPoseVector.cpp, and testTranslationVector.cpp.

Definition at line 84 of file vpArray2D.h.

Referenced by vpMatrix::AtA(), buildFrom(), vpRzyxVector::buildFrom(), vpRzyzVector::buildFrom(), vpRxyzVector::buildFrom(), vpThetaUVector::buildFrom(), vpSubColVector::checkParentStatus(), vpSubRowVector::checkParentStatus(), vpSubMatrix::checkParentStatus(), vpColVector::clear(), convert(), vpTranslationVector::euclideanNorm(), vpRowVector::euclideanNorm(), vpColVector::euclideanNorm(), vpMatrix::euclideanNorm(), vpMatrix::expm(), vpThetaUVector::extract(), vpSubColVector::init(), vpSubRowVector::init(), vpSubMatrix::init(), vpTranslationVector::operator*(), vpRowVector::operator*(), vpColVector::operator*(), vpHomography::operator*(), vpTranslationVector::operator-(), vpRowVector::operator-(), vpColVector::operator-(), vpTranslationVector::operator/(), vpRowVector::operator/(), vpColVector::operator/(), vpHomography::operator/(), vpHomography::operator/=(), vpSubColVector::operator=(), vpSubRowVector::operator=(), vpTranslationVector::operator=(), vpRowVector::operator=(), vpColVector::operator=(), vpRzyxVector::operator=(), vpRzyzVector::operator=(), vpRxyzVector::operator=(), vpMatrix::operator=(), vpThetaUVector::operator=(), vpColVector::operator[](), vpRowVector::reshape(), vpColVector::reshape(), vpQuaternionVector::set(), vpMatrix::stackRows(), vpRotationVector::t(), vpTranslationVector::t(), vpPoseVector::t(), vpRowVector::t(), vpColVector::t(), vpQuaternionVector::w(), vpQuaternionVector::x(), vpQuaternionVector::y(), vpQuaternionVector::z(), vpSubColVector::~vpSubColVector(), vpSubMatrix::~vpSubMatrix(), and vpSubRowVector::~vpSubRowVector().

unsigned int vpArray2D< double >::dsize

protectedinherited

unsigned int vpArray2D< double >::rowNum

protectedinherited

Number of rows in the array.

Definition at line 74 of file vpArray2D.h.

double ** vpArray2D< double >::rowPtrs

protectedinherited

Address of the first element of each rows.

Definition at line 78 of file vpArray2D.h.

Referenced by vpMatrix::AAt(), vpColVector::clear(), vpMatrix::infinityNorm(), vpSubColVector::init(), vpSubRowVector::init(), vpSubMatrix::init(), vpRowVector::init(), vpColVector::init(), vpMatrix::init(), vpRotationMatrix::operator*(), vpForceTwistMatrix::operator*(), vpVelocityTwistMatrix::operator*(), operator*(), vpMatrix::operator*(), vpRotationMatrix::operator*=(), vpMatrix::operator*=(), vpMatrix::operator+=(), vpMatrix::operator-=(), vpMatrix::operator/(), vpMatrix::operator/=(), vpMatrix::operator<<(), vpColVector::operator<<(), vpSubMatrix::operator=(), vpRotationMatrix::operator=(), vpForceTwistMatrix::operator=(), vpVelocityTwistMatrix::operator=(), operator=(), vpRowVector::operator=(), vpMatrix::operator=(), vpMatrix::stackColumns(), vpMatrix::sum(), vpRotationVector::sumSquare(), vpTranslationVector::sumSquare(), vpRowVector::sumSquare(), vpColVector::sumSquare(), vpMatrix::sumSquare(), and vpMatrix::transpose().

Public Member Functions

Static Public Member Functions

Public Attributes

Protected Attributes

Related Functions

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

Member Data Documentation