This class allows one to take all three types of frictional interactions into account. The sliding, rolling and torsional frictional interaction. See. More...

#include <FrictionInteraction.h>

Inheritance diagram for FrictionInteraction:

Public Types
typedef FrictionSpecies	SpeciesType
	An alias for FrictionSpecies. More...

Public Types inherited from SlidingFrictionInteraction
typedef SlidingFrictionSpecies	SpeciesType
	An alias name for SlidingFrictionSpecies data type. More...

Public Member Functions
	FrictionInteraction (BaseInteractable P, BaseInteractable I, Mdouble timeStamp)
	Constructor. More...

	FrictionInteraction (const FrictionInteraction &p)
	Copy constructor. More...

virtual	~FrictionInteraction ()
	Destructor. More...

void	computeFrictionForce ()
	Computes the forces arising due to all three types of friction, i.e., sliding, rolling and torsional. More...

void	read (std::istream &is)
	Interaction read function, which accepts an std::istream as input. More...

void	write (std::ostream &os) const
	Interaction print function, which accepts an std::ostream as input. More...

void	integrate (Mdouble timeStep)
	Computes the amount of compression in all the springs, i.e., increments the rollingSpring_, slidingSpring_ (see SlidingFrictionInteraction.cc) and torsionSpring_. More...

Mdouble	getElasticEnergy () const
	Returns the global amount of energy stored in all the springs (rolling, sliding and torsional). More...

std::string	getBaseName () const
	Returns interaction name/type. More...

const FrictionSpecies *	getSpecies () const
	Returns a const pointer of type FrictionSpecies*. More...

void	reverseHistory ()
	A useful feature if one wants to return to the initial state of the springs. However, reverse history decrements the current state to the state corresponding to previous time step. Decrements the state or value of rollingSpring_, torsionSpring_ and slidingSpring_. More...

void	rotateHistory (Matrix3D &rotationMatrix)
	When periodic particles are used, some interactions need certain history properties rotated (e.g. tangential springs). This is the function for that. More...

Vec3D	getRollingSpring () const

Public Member Functions inherited from SlidingFrictionInteraction
	SlidingFrictionInteraction (BaseInteractable P, BaseInteractable I, Mdouble timeStamp)
	Constructor. More...

	SlidingFrictionInteraction (const SlidingFrictionInteraction &p)
	Copy constructor. More...

virtual	~SlidingFrictionInteraction ()
	Destructor. More...

void	computeFrictionForce ()
	Computes the tangential force generated due to compression in the sliding spring. Does take into account if the interaction is between particle-particle or particle-wall. More...

void	read (std::istream &is)
	Interaction read function, which accepts an std::istream as input. More...

void	write (std::ostream &os) const
	Interaction write function, which accepts an std::ostream as input. More...

void	integrate (Mdouble timeStep)
	Increments the amount of compression in sliding spring. More...

Mdouble	getElasticEnergy () const
	Returns the amount of elastic energy stored in sliding spring. More...

Mdouble	getTangentialOverlap () const
	Returns the amount of tangential overlap which is needed by BaseInteraction::writeToFstat(). More...

std::string	getBaseName () const
	Returns the type/name of interaction (sliding friction interaction) More...

void	setSlidingSpring (const Vec3D slidingSpring)

Vec3D	getSlidingSpring () const

const Vec3D	getTangentialForce () const
	Returns the sliding friction force vector. More...

const SlidingFrictionSpecies *	getSpecies () const
	Returns a const pointer of type SlidingFrictionSpecies*. More...

void	reverseHistory ()
	A useful feature if one wants to return to the initial state of the spring. However, reverse history decrements the current state to the state corresponding to previous time step. Decrements the value of slidingSpring_. More...

void	rotateHistory (Matrix3D &rotationMatrix)
	When periodic particles are used, some interactions need certain history properties rotated (e.g. tangential springs). This is the function for that. More...

void	moveSlidingSpring (const Vec3D displacement)

Public Member Functions inherited from BaseInteraction
	BaseInteraction (BaseInteractable P, BaseInteractable I, Mdouble timeStamp)
	A constructor takes the BaseInteractable objects which are interacting (come into contact) and time the interaction starts. More...

	BaseInteraction (const BaseInteraction &p)
	Copy constructor. More...

	BaseInteraction ()
	Empty constructor. More...

virtual	~BaseInteraction ()
	The default destructor. More...

virtual void	actionsOnErase ()
	If an interaction needs to do something before it gets erased, add it here. E.g. Liquid bridges rupture at the end of their lifetime, and the liquid bridge volume has to be redistributed. The reason this action is not done in the destructor is that this action should not be taken when erasing ghost interactions. More...

virtual void	computeForce ()
	Virtual function that contains the force law between the two objects interacting. More...

void	writeToFStat (std::ostream &os) const
	Writes forces data to the FStat file. More...

virtual std::string	getName () const
	Virtual function which allows interactions to be named. More...

void	setDistance (Mdouble distance)
	Sets the interaction distance between the two interacting objects. More...

void	setNormal (Vec3D normal)
	Sets the normal vector between the two interacting objects. More...

void	setOverlap (Mdouble overlap)
	Set the overlap between the two interacting object. More...

void	setContactPoint (Vec3D contactPoint)
	Set the location of the contact point between the two interacting objects. More...

void	setTimeStamp (Mdouble timeStamp)
	Updates the time step of the interacting. Note, timesteps used to find completed interactions. More...

void	setSpecies (BaseSpecies *species)
	Set the Species of the interaction; note this can either be a Species or MixedSpecies. More...

void	setP (BaseInteractable *P)
	Sets the first object involved in the interaction (normally a particle). More...

void	setI (BaseInteractable *I)
	Sets the second object involved in the interaction (often particle or wall). More...

void	setHandler (InteractionHandler *handler)
	Sets the pointer to the interaction hander which is storing this interaction. More...

InteractionHandler *	getHandler () const
	Gets a point to the interaction handlers to which this interaction belongs. More...

const Vec3D &	getForce () const
	Gets the current force (vector) between the two interacting objects. More...

const Vec3D &	getTorque () const
	Gets the current torque (vector) between the two interacting objects. More...

const Vec3D &	getNormal () const
	Gets the normal vector between the two interacting objects. More...

const Vec3D &	getContactPoint () const
	Gets constant reference to contact point (vector). More...

Mdouble	getOverlap () const
	Returns a Mdouble with the current overlap between the two interacting objects. More...

Mdouble	getContactRadius () const
	Returns a Mdouble with the current contact between the two interacting objects. More...

void	removeFromHandler ()
	Removes this interaction from its interaction hander. More...

void	copySwitchPointer (const BaseInteractable original, BaseInteractable ghost) const
	This copies the interactions of the original particle and replaces the original with the ghost copy. More...

void	gatherContactStatistics ()

BaseInteractable *	getP ()
	Returns a pointer to first object involved in the interaction (normally a particle). More...

BaseInteractable *	getI ()

const BaseInteractable *	getP () const

const BaseInteractable *	getI () const
	Returns a constant pointer to the second object involved in the interaction. More...

Mdouble	getTimeStamp () const
	Returns an Mdouble which is the time stamp of the interaction. More...

Mdouble	getDistance () const
	Returns an Mdouble which is the norm (length) of distance vector. More...

const Vec3D &	getRelativeVelocity () const
	Returns a constant reference to a vector of relative velocity. More...

Mdouble	getNormalRelativeVelocity () const
	Returns a double which is the norm (length) of the relative velocity vector. More...

Mdouble	getAbsoluteNormalForce () const
	Returns the absolute value of the norm (length) of the Normal force vector. More...

virtual BaseInteraction *	copy () const =0
	Makes a copy of the interaction and returns a pointer to the copy. More...

unsigned int	getMultiContactIdentifier () const

void	setMultiContactIdentifier (unsigned int multiContactIdentifier_)

virtual void	actionsAfterTimeStep ()

virtual unsigned	getNumberOfFieldsVTK () const

virtual std::string	getTypeVTK (unsigned i) const

virtual std::string	getNameVTK (unsigned i) const

virtual std::vector< Mdouble >	getFieldVTK (unsigned i) const

void	setForce (Vec3D force)
	set total force (this is used by the normal force, tangential forces are added use addForce) More...

Public Member Functions inherited from BaseObject
	BaseObject ()
	Default constructor. More...

	BaseObject (const BaseObject &p)
	Copy constructor, copies all the objects BaseObject contains. More...

virtual	~BaseObject ()
	virtual destructor More...

virtual void	moveInHandler (const unsigned int index)
	Except that it is virtual, it does the same thing as setIndex() does. More...

void	setIndex (const unsigned int index)
	Allows one to assign an index to an object in the handler/container. More...

void	setId (const unsigned int id)
	Assigns a unique identifier to each object in the handler (container) which remains constant even after the object is deleted from the container/handler. More...

unsigned int	getIndex () const
	Returns the index of the object in the handler. More...

unsigned int	getId () const
	Returns the unique identifier of any particular object. More...

Private Attributes
Vec3D	rollingSpring_
	Stores the amount of rolling spring compression. Set in integrate(), used in computing frictional force due to rolling. More...

Vec3D	rollingSpringVelocity_
	Stores the rate at which the rolling spring compresses or relaxes. Set in computeFrictionForce(), used in computing the amount of compression in rolling spring. Used in integrate(). More...

Vec3D	torsionSpring_
	Stores the amount of torsional spring compression. Set in integrate(), used in computing frictional force due to torsion. More...

Vec3D	torsionSpringVelocity_
	Stores the rate at which the torsional spring compresses or relaxes. Set in computeFrictionForce(), used in computing the amount of compression in torsion spring. Used in integrate(). More...

Additional Inherited Members
Protected Member Functions inherited from BaseInteraction
Mdouble	getEffectiveRadius () const
	Returns a Mdouble to the effective radius of the interaction. (Not corrected for the overlap) More...

Mdouble	getEffectiveMass () const
	Returns a Mdouble to the effective radius of the interaction. (Not corrected for the overlap) More...

Mdouble	getEffectiveCorrectedRadius ()
	Returns a Mdouble to the effective radius corrected for the overlaps of the particles. More...

void	addForce (Vec3D force)
	add an force increment to the total force. More...

void	addTorque (Vec3D torque)

void	setTorque (Vec3D torque)
	set the total force (this is used by the normal force, tangential torques are added use addTorque) More...

void	setRelativeVelocity (Vec3D relativeVelocity)
	set the relative velocity of the current of the interactions. More...

void	setNormalRelativeVelocity (Mdouble normalRelativeVelocit)
	set the normal component of the relative velocity. More...

void	setAbsoluteNormalForce (Mdouble absoluteNormalForce)
	the absolute values of the norm (length) of the normal force More...

const BaseSpecies *	getBaseSpecies () const
	Return a constant point to BaseSpecies of the interaction. More...

virtual Mdouble	getElasticEnergyAtEquilibrium (Mdouble adhesiveForce) const

Detailed Description

This class allows one to take all three types of frictional interactions into account. The sliding, rolling and torsional frictional interaction. See.

Definition at line 41 of file FrictionInteraction.h.

Member Typedef Documentation

typedef FrictionSpecies FrictionInteraction::SpeciesType

An alias for FrictionSpecies.

Definition at line 47 of file FrictionInteraction.h.

Constructor & Destructor Documentation

FrictionInteraction::FrictionInteraction	(	BaseInteractable *	P,
		BaseInteractable *	I,
		Mdouble	timeStamp
	)

Constructor.

Parameters

[in]	P
[in]	I
[in]	timeStamp

Definition at line 40 of file FrictionInteraction.cc.

References rollingSpring_, Vec3D::setZero(), and torsionSpring_.

     : BaseInteraction(P, I, timeStamp), SlidingFrictionInteraction(P, I, timeStamp)
 {
     rollingSpring_.setZero();
     torsionSpring_.setZero();
 #ifdef DEBUG_CONSTRUCTOR
     std::cout<<"FrictionInteraction::FrictionInteraction() finished"<<std::endl;
 #endif
 }

FrictionInteraction::FrictionInteraction ( const FrictionInteraction & p )

Copy constructor.

Parameters

[in] p

Definition at line 52 of file FrictionInteraction.cc.

References rollingSpring_, and torsionSpring_.

     : BaseInteraction(p), SlidingFrictionInteraction(p)
 {
     rollingSpring_=p.rollingSpring_;
     torsionSpring_=p.torsionSpring_;
 #ifdef DEBUG_CONSTRUCTOR
     std::cout<<"FrictionInteraction::FrictionInteraction(const FrictionInteraction& p) finished"<<std::endl;
 #endif
 }

FrictionInteraction::~FrictionInteraction ( )

virtual

Destructor.

Definition at line 64 of file FrictionInteraction.cc.

 {
 #ifdef DEBUG_DESTRUCTOR
     std::cout<<"FrictionInteraction::~FrictionInteraction() finished"<<std::endl;
 #endif
 }

Member Function Documentation

void FrictionInteraction::computeFrictionForce ( )

Computes the forces arising due to all three types of friction, i.e., sliding, rolling and torsional.

Calls the slidingFrictionInteraction::computeFrictionForce() as well, see slidingFrictionInteraction.cc.

Todo:: TW: Why do we not use the corrected diameter here, as in the rolling case? And check if Stefan uses radius or diameter

Definition at line 92 of file FrictionInteraction.cc.

 {
     SlidingFrictionInteraction::computeFrictionForce();
 
     const FrictionSpecies* species = getSpecies();
     //If tangential forces are present
     if (getAbsoluteNormalForce() == 0.0) return;
 
 
     if (species->getRollingFrictionCoefficient() != 0.0)
     {
         if (species->getRollingStiffness() != 0.0)
         {
             Mdouble effectiveDiameter = 2.0*getEffectiveRadius();
 
             //From Luding2008, objective rolling velocity (eq 15) w/o 2.0!
             Vec3D rollingRelativeVelocity = -effectiveDiameter *
              Vec3D::cross(getNormal(), getP()->getAngularVelocity() - getI()->getAngularVelocity());
 
             if (dynamic_cast<BaseParticle*>(getI())==0)  //if particle-wall
                 rollingSpringVelocity_= rollingRelativeVelocity;
             else //if particle-particle
             {
                 const Vec3D relativeVelocity = getP()->getVelocity() - getI()->getVelocity();
                 rollingSpringVelocity_ = rollingRelativeVelocity
                                          - Vec3D::dot(rollingSpring_, relativeVelocity) / getDistance() * getNormal();
             }
 
             //used to Integrate the spring
             //rollingSpringVelocity_= rollingRelativeVelocity;
             //integrate(getHandler()->timeStep_);
             rollingSpring_ += rollingSpringVelocity_ * getHandler()->getDPMBase()->getTimeStep();
             
             //Calculate test force acting on P including viscous force
             Vec3D rollingForce = - species->getRollingStiffness() * rollingSpring_ - species->getRollingDissipation() * rollingRelativeVelocity;
 
             //tangential forces are modelled by a spring-damper of elasticity kt and viscosity dispt (sticking),
             //but the force is limited by Coulomb friction (rolling):
             Mdouble rollingForceSquared = rollingForce.getLengthSquared();
             if (rollingForceSquared <= mathsFunc::square(species->getRollingFrictionCoefficientStatic() * getAbsoluteNormalForce()))
             {
                 //if sticking (|ft|<=mu*|fn|), apply the force
             }
             else
             {
                 //if rolling, resize the tangential force such that |ft|=mu*|fn|
                 rollingForce *= species->getRollingFrictionCoefficient() * getAbsoluteNormalForce() / std::sqrt(rollingForceSquared);
                 //resize the tangential spring accordingly such ft=-k*delta-nu*relVel
                 rollingSpring_ = -(rollingForce + species->getRollingDissipation() * rollingRelativeVelocity) / species->getRollingStiffness();
             }
             //Add (virtual) rolling force to torque
             addTorque(effectiveDiameter * Vec3D::cross(getNormal(), rollingForce));
         }
         else //if no spring stiffness is set
         {
             std::cerr << "FrictionInteraction::computeFrictionForce(): Rolling stiffness is zero" << std::endl;
             exit(-1);
         }
     } //end if rolling force
 
     if (species->getTorsionFrictionCoefficient() != 0.0)
     {
         if (species->getTorsionStiffness() != 0.0)
         {
             Mdouble effectiveDiameter = 2.0*getEffectiveRadius();
 
             //From Luding2008, spin velocity (eq 16) w/o 2.0!
             Vec3D torsionRelativeVelocity = effectiveDiameter * Vec3D::dot(getNormal(), getP()->getAngularVelocity() - getI()->getAngularVelocity()) * getNormal();
 
             //Integrate the spring
             torsionSpringVelocity_= torsionRelativeVelocity;
             //integrate(getHandler()->timeStep_);
             torsionSpring_ += Vec3D::dot(torsionSpring_ + torsionSpringVelocity_ * getHandler()->getDPMBase()->getTimeStep(), getNormal()) * getNormal();
 
             //Calculate test force acting on P including viscous force
             Vec3D torsionForce = - species->getTorsionStiffness() * torsionSpring_ - species->getTorsionDissipation() * torsionRelativeVelocity;
 
             //tangential forces are modelled by a spring-damper of elasticity kt and viscosity dispt (sticking),
             //but the force is limited by Coulomb friction (torsion):
             Mdouble torsionForceSquared = torsionForce.getLengthSquared();
             if (torsionForceSquared <= mathsFunc::square(species->getTorsionFrictionCoefficientStatic() * getAbsoluteNormalForce()))
             {
                 //if sticking (|ft|<=mu*|fn|), apply the force
             }
             else
             {
                 //if torsion, resize the tangential force such that |ft|=mu*|fn|
                 torsionForce *= species->getTorsionFrictionCoefficient() * getAbsoluteNormalForce() / std::sqrt(torsionForceSquared);
                 //resize the tangential spring accordingly such ft=-k*delta-nu*relVel
                 torsionSpring_ = -(torsionForce + species->getTorsionDissipation() * torsionRelativeVelocity) / species->getTorsionStiffness();
             }
             //Add (virtual) rolling force to torque
             addTorque(effectiveDiameter * torsionForce);
         }
         else //if no spring stiffness is set
         {
             std::cerr << "FrictionInteraction::computeFrictionForce(): Torsion stiffness is zero" << std::endl;
             exit(-1);
         }
     } //end if torsion force
 }

std::string FrictionInteraction::getBaseName ( ) const

Returns interaction name/type.

Returns: std::string

Definition at line 222 of file FrictionInteraction.cc.

 {
     return "Friction";
 }

Mdouble FrictionInteraction::getElasticEnergy ( ) const

virtual

Returns the global amount of energy stored in all the springs (rolling, sliding and torsional).

Returns: Mdouble

Reimplemented from BaseInteraction.

Definition at line 206 of file FrictionInteraction.cc.

References SlidingFrictionInteraction::getElasticEnergy(), Vec3D::getLengthSquared(), FrictionSpecies::getRollingStiffness(), getSpecies(), FrictionSpecies::getTorsionStiffness(), rollingSpring_, and torsionSpring_.

 {
     return SlidingFrictionInteraction::getElasticEnergy()
         +  0.5 * getSpecies()->getRollingStiffness() * rollingSpring_.getLengthSquared()
         +  0.5 * getSpecies()->getTorsionStiffness() * torsionSpring_.getLengthSquared();
 }

Vec3D FrictionInteraction::getRollingSpring ( ) const

Definition at line 250 of file FrictionInteraction.cc.

References rollingSpring_.

 {
     return rollingSpring_;
 }

const FrictionSpecies * FrictionInteraction::getSpecies ( ) const

Returns a const pointer of type FrictionSpecies*.

Returns: const FrictionSpecies*

Definition at line 215 of file FrictionInteraction.cc.

References BaseInteraction::getBaseSpecies().

Referenced by computeFrictionForce(), and getElasticEnergy().

 {
     return dynamic_cast<const FrictionSpecies*>(getBaseSpecies());
 }

void FrictionInteraction::integrate ( Mdouble timeStep )

virtual

Computes the amount of compression in all the springs, i.e., increments the rollingSpring_, slidingSpring_ (see SlidingFrictionInteraction.cc) and torsionSpring_.

Parameters

[in] timeStep

Reimplemented from BaseInteraction.

Definition at line 197 of file FrictionInteraction.cc.

References Vec3D::dot(), BaseInteraction::getNormal(), SlidingFrictionInteraction::integrate(), rollingSpring_, rollingSpringVelocity_, torsionSpring_, and torsionSpringVelocity_.

 {
     SlidingFrictionInteraction::integrate(timeStep);
     rollingSpring_ += rollingSpringVelocity_ * timeStep;
     torsionSpring_ += Vec3D::dot(torsionSpring_ + torsionSpringVelocity_ * timeStep, getNormal()) * getNormal();
 }

void FrictionInteraction::read ( std::istream & is )

virtual

Interaction read function, which accepts an std::istream as input.

Parameters

in/out] is

Reimplemented from BaseInteraction.

Definition at line 82 of file FrictionInteraction.cc.

References SlidingFrictionInteraction::read(), rollingSpring_, and torsionSpring_.

 {
     SlidingFrictionInteraction::read(is);
     std::string dummy;
     is >> dummy >> rollingSpring_;
     is >> dummy >> torsionSpring_;
 }

void FrictionInteraction::reverseHistory ( )

virtual

A useful feature if one wants to return to the initial state of the springs. However, reverse history decrements the current state to the state corresponding to previous time step. Decrements the state or value of rollingSpring_, torsionSpring_ and slidingSpring_.

Reimplemented from BaseInteraction.

Definition at line 229 of file FrictionInteraction.cc.

References SlidingFrictionInteraction::reverseHistory(), torsionSpring_, and torsionSpringVelocity_.

 {
     SlidingFrictionInteraction::reverseHistory();
     //rollingSpring_=-rollingSpring_;
     //rollingSpringVelocity_=-rollingSpringVelocity_;
     torsionSpring_=-torsionSpring_;
     torsionSpringVelocity_=-torsionSpringVelocity_;
 }

void FrictionInteraction::rotateHistory ( Matrix3D & rotationMatrix )

virtual

When periodic particles are used, some interactions need certain history properties rotated (e.g. tangential springs). This is the function for that.

Todo:: some of these might be unneccesary

Reimplemented from BaseInteraction.

Definition at line 241 of file FrictionInteraction.cc.

References rollingSpring_, rollingSpringVelocity_, SlidingFrictionInteraction::rotateHistory(), torsionSpring_, and torsionSpringVelocity_.

 {
     SlidingFrictionInteraction::rotateHistory(rotationMatrix);
     rollingSpring_=rotationMatrix*rollingSpring_;
     rollingSpringVelocity_=rotationMatrix*rollingSpringVelocity_;
     torsionSpring_=rotationMatrix*torsionSpring_;
     torsionSpringVelocity_=rotationMatrix*torsionSpringVelocity_;
 }

void FrictionInteraction::write ( std::ostream & os ) const

virtual

Interaction print function, which accepts an std::ostream as input.

Parameters

in/out] os

Reimplemented from BaseInteraction.

Definition at line 73 of file FrictionInteraction.cc.

References rollingSpring_, torsionSpring_, and SlidingFrictionInteraction::write().

 {
     SlidingFrictionInteraction::write(os);
     os << " rollingSpring " << rollingSpring_;
     os << " torsionSpring " << torsionSpring_;
 }

Member Data Documentation

Vec3D FrictionInteraction::rollingSpring_

private

Stores the amount of rolling spring compression. Set in integrate(), used in computing frictional force due to rolling.

Definition at line 106 of file FrictionInteraction.h.

Referenced by computeFrictionForce(), FrictionInteraction(), getElasticEnergy(), getRollingSpring(), integrate(), read(), rotateHistory(), and write().

Vec3D FrictionInteraction::rollingSpringVelocity_

private

Stores the rate at which the rolling spring compresses or relaxes. Set in computeFrictionForce(), used in computing the amount of compression in rolling spring. Used in integrate().

Definition at line 111 of file FrictionInteraction.h.

Referenced by computeFrictionForce(), integrate(), and rotateHistory().

Vec3D FrictionInteraction::torsionSpring_

private

Stores the amount of torsional spring compression. Set in integrate(), used in computing frictional force due to torsion.

Definition at line 116 of file FrictionInteraction.h.

Referenced by computeFrictionForce(), FrictionInteraction(), getElasticEnergy(), integrate(), read(), reverseHistory(), rotateHistory(), and write().

Vec3D FrictionInteraction::torsionSpringVelocity_

private

Stores the rate at which the torsional spring compresses or relaxes. Set in computeFrictionForce(), used in computing the amount of compression in torsion spring. Used in integrate().

Definition at line 121 of file FrictionInteraction.h.

Referenced by computeFrictionForce(), integrate(), reverseHistory(), and rotateHistory().

The documentation for this class was generated from the following files:

Interactions/FrictionForceInteractions/FrictionInteraction.h
Interactions/FrictionForceInteractions/FrictionInteraction.cc

Public Types

Public Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation