Cylinder object. More...

#include <JCylinder3D.hh>

Inheritance diagram for JGEOMETRY3D::JCylinder3D:

Public Member Functions
	JCylinder3D ()
	Default constructor. More...

	JCylinder3D (const JCircle2D &circle, const double zmin, const double zmax)
	Constructor. More...

template<class T >
	JCylinder3D (T __begin, T __end)
	Constructor. More...

double	getZmin () const
	Get minimal z position. More...

double	getZmax () const
	Get maximal z position. More...

void	setZmin (const double zmin)
	Set minimal z position. More...

void	setZmax (const double zmax)
	Set maximal z position. More...

JCylinder3D &	add (const JVector3D &pos)
	Add position. More...

void	addMargin (const double D)
	Add (safety) margin. More...

double	getVolume () const
	Get volume. More...

JPosition3D	getCenter () const
	Get centre. More...

bool	is_inside (const JVector3D &pos) const
	Check whether given point is inside cylinder. More...

double	getDistance (const JVector3D &pos) const
	Get distance between cylinder wall and given position. More...

double	getDistanceSquared (const JVector3D &pos) const
	Get square of distance between cylinder wall and given position. More...

std::pair< double, double >	getIntersection (const JAxis3D &axis) const
	Get intersection points of axis with cylinder. More...

double	getRadius () const
	Get radius. More...

void	set (const JVector2D &p0, const JVector2D &p1)
	Set circle. More...

void	set (const JVector2D &p0, const JVector2D &p1, const JVector2D &p2)
	Set circle. More...

template<class T >
void	set (T __begin, T __end)
	Set circle. More...

bool	is_inside (const JVector2D &pos) const
	Check whether given point is inside circle. More...

const JPosition2D &	getPosition () const
	Get position. More...

JPosition2D &	getPosition ()
	Get position. More...

void	setPosition (const JVector2D &pos)
	Set position. More...

	operator JAngle2D () const
	Type conversion operator. More...

	operator JVersor2D () const
	Type conversion operator. More...

JPosition2D &	rotate (const JRotation2D &R)
	Rotate. More...

JPosition2D &	rotate_back (const JRotation2D &R)
	Rotate back. More...

double	getDot (const JAngle2D &angle) const
	Get dot product. More...

double	getDot (const JVersor2D &versor) const
	Get dot product. More...

double	getDot (const JVector2D &point) const
	Get dot product. More...

double	getPerpDot (const JAngle2D &angle) const
	Get perpendicular dot product. More...

double	getPerpDot (const JVersor2D &dir) const
	Get perpendicular dot product. More...

double	getPerpDot (const JVector2D &point) const
	Get perpendicular dot product. More...

double	getX () const
	Get x position. More...

double	getY () const
	Get y position. More...

JVector2D &	negate ()
	Negate vector. More...

JVector2D &	add (const JVector2D &vector)
	Add vector. More...

JVector2D &	sub (const JVector2D &vector)
	Subtract vector. More...

JVector2D &	mul (const double factor)
	Scale vector. More...

JVector2D &	mul (const JNullType &object)
	Multiply with object. More...

JVector2D &	div (const double factor)
	Scale vector. More...

JVector2D &	transform (const JMatrix2D &T)
	Transform. More...

bool	equals (const JVector2D &vector) const
	Check equality. More...

double	getLengthSquared () const
	Get length squared. More...

double	getLength () const
	Get length. More...

double	getDistanceSquared (const JVector2D &point) const
	Get squared of distance to point. More...

double	getDistance (const JVector2D &point) const
	Get distance to point. More...

Protected Attributes
double	zmin

double	zmax

double	__r

double	__x

double	__y

Friends
std::istream &	operator>> (std::istream &in, JCylinder3D &cylinder)
	Read cylinder from input stream. More...

std::ostream &	operator<< (std::ostream &out, const JCylinder3D &cylinder)
	Write cylinder to output stream. More...

JReader &	operator>> (JReader &in, JCylinder3D &cylinder)
	Read cylinder from input. More...

JWriter &	operator<< (JWriter &out, const JCylinder3D &cylinder)
	Write cylinder to output. More...

Detailed Description

Cylinder object.

A cylinder object consists of a 2D circle in (x,y) and a range in z.

Definition at line 37 of file JCylinder3D.hh.

Constructor & Destructor Documentation

JGEOMETRY3D::JCylinder3D::JCylinder3D ( )

inline

Default constructor.

Definition at line 44 of file JCylinder3D.hh.

                   :
       JCircle2D(),
       zmin(0.0),
       zmax(0.0)
     {}

JGEOMETRY3D::JCylinder3D::JCylinder3D	(	const JCircle2D &	circle,
		const double	zmin,
		const double	zmax
	)

inline

Constructor.

Parameters

circle	2D circle in (x,y)
zmin	minimal z
zmax	maximal z

Definition at line 58 of file JCylinder3D.hh.

                                        :
       JCircle2D(circle)
     {
       this->zmin = zmin;
       this->zmax = zmax;
     }

template<class T >

JGEOMETRY3D::JCylinder3D::JCylinder3D	(	T	__begin,
		T	__end
	)

inline

Constructor.

Determines smallest enclosing cylinder for any number of points.

Parameters

__begin	begin of data
__end	end of data

Definition at line 77 of file JCylinder3D.hh.

                          :
       JCircle2D(__begin, __end),
       zmin(0.0),
       zmax(0.0)
     {
       if (__begin != __end) {
 
         zmin = +std::numeric_limits<double>::max();
         zmax = -std::numeric_limits<double>::max();
         
         for (T i = __begin; i != __end; ++i) {
           if (i->getZ() < zmin) zmin = i->getZ();
           if (i->getZ() > zmax) zmax = i->getZ();
         }
       }
     }

Member Function Documentation

double JGEOMETRY3D::JCylinder3D::getZmin ( ) const

inline

Get minimal z position.

Returns: minimal z position

Definition at line 101 of file JCylinder3D.hh.

     { 
       return zmin;
     }

double JGEOMETRY3D::JCylinder3D::getZmax ( ) const

inline

Get maximal z position.

Returns: maximal z position

Definition at line 112 of file JCylinder3D.hh.

     { 
       return zmax;
     }

void JGEOMETRY3D::JCylinder3D::setZmin ( const double zmin )

inline

Set minimal z position.

Parameters

zmin	minimal z position

Definition at line 123 of file JCylinder3D.hh.

     { 
       this->zmin = zmin;
     }

void JGEOMETRY3D::JCylinder3D::setZmax ( const double zmax )

inline

Set maximal z position.

Parameters

zmax	maximal z position

Definition at line 134 of file JCylinder3D.hh.

     { 
       this->zmax = zmax;
     }

JCylinder3D& JGEOMETRY3D::JCylinder3D::add ( const JVector3D & pos )

inline

Add position.

Parameters

pos position

Returns: this cylinder

Definition at line 146 of file JCylinder3D.hh.

     {
       static_cast<JPosition2D&>(*this).add(JPosition2D(pos.getX(), pos.getY()));
 
       zmin += pos.getZ();
       zmax += pos.getZ();
                                            
       return *this;
     }

void JGEOMETRY3D::JCylinder3D::addMargin ( const double D )

inline

Add (safety) margin.

Parameters

D margin

Returns: this cylinder

Definition at line 163 of file JCylinder3D.hh.

     {
       __r  += D;
       zmin -= D;
       zmax += D;
     }

double JGEOMETRY3D::JCylinder3D::getVolume ( ) const

inline

Get volume.

Returns: volume

Definition at line 176 of file JCylinder3D.hh.

     {
       return (getZmax ()- getZmin()) * JTOOLS::PI * getRadius() * getRadius();
     }

JPosition3D JGEOMETRY3D::JCylinder3D::getCenter ( ) const

inline

Get centre.

Returns: centre

Definition at line 187 of file JCylinder3D.hh.

     {
       return JPosition3D(getPosition(), (getZmax() - getZmin())/2.0);
     }

bool JGEOMETRY3D::JCylinder3D::is_inside ( const JVector3D & pos ) const

inline

Check whether given point is inside cylinder.

Parameters

pos position

Returns: true if inside; else false

Definition at line 199 of file JCylinder3D.hh.

     {
       return (pos.getZ() >= getZmin() && 
               pos.getZ() <= getZmax() &&
               JCircle2D::is_inside(JVector2D(pos.getX(), pos.getY())));
     }

double JGEOMETRY3D::JCylinder3D::getDistance ( const JVector3D & pos ) const

inline

Get distance between cylinder wall and given position.

Parameters

pos position

Returns: distance

Definition at line 213 of file JCylinder3D.hh.

     {
       JVector2D D(pos);
 
       D.sub(*this);
 
       double R = D.getLength();
     
       if (R > this->getRadius()) {
 
         R -= this->getRadius();
 
         double dz = 0.0;
 
         if      (pos.getZ() > this->getZmax())
           dz = pos.getZ() - this->getZmax();
         else if (pos.getZ() < this->getZmin())
           dz = this->getZmin() - pos.getZ();
         else 
           return R;
 
         return sqrt(R*R + dz*dz);
 
       } else {
 
         if      (pos.getZ() > this->getZmax())
           return  pos.getZ() - this->getZmax();
         else if (pos.getZ() < this->getZmin())
           return this->getZmin() - pos.getZ();
         else 
           return 0.0;
       }
     }

double JGEOMETRY3D::JCylinder3D::getDistanceSquared ( const JVector3D & pos ) const

inline

Get square of distance between cylinder wall and given position.

Parameters

pos position

Returns: square of distance

Definition at line 254 of file JCylinder3D.hh.

     {
       const double d = getDistance(pos);
 
       return d*d;
     }

std::pair<double, double> JGEOMETRY3D::JCylinder3D::getIntersection ( const JAxis3D & axis ) const

inline

Get intersection points of axis with cylinder.

Parameters

axis axis

Returns: up and down stream positions along axis

Definition at line 268 of file JCylinder3D.hh.

     {
       double path[] = { 0.0, 0.0 };
 
       if (fabs(axis.getDZ()) != 0.0) {
 
         // intersection with bottom or top surface
 
         const double Z[] = { 
           axis.getDZ() > 0 ? this->getZmin() : this->getZmax(),
           axis.getDZ() > 0 ? this->getZmax() : this->getZmin()
         };
 
         for (int i = 0; i != 2; ++i) {
 
           const double u = (Z[i] - axis.getZ()) / axis.getDZ();
           const double x =  axis.getX() + u * axis.getDX() - this->getX();
           const double y =  axis.getY() + u * axis.getDY() - this->getY();
       
           if (x*x + y*y <= this->getRadius() * this->getRadius()) {
             path[i] = u;
           }
         }
       }
   
       if (fabs(axis.getDZ()) != 1.0) {
     
         // intersection with cylinder wall
 
         const double x  = axis.getX() - this->getX();
         const double y  = axis.getY() - this->getY();
         const double dx = axis.getDX();
         const double dy = axis.getDY();
         const double R  = this->getRadius();
 
         const double a  =   (dx * dx +  dy * dy);
         const double b  = 2*(dx * x  +  dy * y);
         const double c  =   (x  * x  +  y  * y)  -  R * R;
     
         const double q  = b*b - 4*a*c;
     
         if (q >= 0) {
       
           const double u[] = {
             (-b - sqrt(q)) / (2*a),
             (-b + sqrt(q)) / (2*a)
           };
       
           for (int i = 0; i != 2; ++i) {
         
             const double z = axis.getZ() + u[i] * axis.getDZ();
         
             if (z >= this->getZmin() && z <= this->getZmax()) {
               path[i] = u[i];
             }
           }
         }
       }
 
       return std::make_pair(path[0], path[1]);
     }

double JGEOMETRY2D::JCircle2D::getRadius ( ) const

inlineinherited

Get radius.

Returns: radius

Definition at line 121 of file JCircle2D.hh.

     { 
       return __r;
     }

void JGEOMETRY2D::JCircle2D::set	(	const JVector2D &	p0,
		const JVector2D &	p1
	)

inlineinherited

Set circle.

Determines circle through two points.

Parameters

p0	first point
p1	second point

Definition at line 134 of file JCircle2D.hh.

     {
       __x = 0.5 * (p0.getX() + p1.getX());
       __y = 0.5 * (p0.getY() + p1.getY());      
       __r = this->getDistance(p0);
     }

void JGEOMETRY2D::JCircle2D::set	(	const JVector2D &	p0,
		const JVector2D &	p1,
		const JVector2D &	p2
	)

inlineinherited

Set circle.

Determines circle through three points.

Parameters

p0	first point
p1	second point
p2	third point

Definition at line 151 of file JCircle2D.hh.

     {
       const double x0 = p2.getX() - p1.getX();
       const double x1 = p0.getX() - p2.getX();
       const double x2 = p1.getX() - p0.getX();
 
       const double y0 = p1.getY() - p2.getY();
       const double y1 = p2.getY() - p0.getY();
       const double y2 = p0.getY() - p1.getY();
 
       const double D  = 2.0 * (p0.getX()*y0 + p1.getX()*y1 + p2.getX()*y2);
 
       if (D != 0.0) {
 
         const double a = p0.getLengthSquared();
         const double b = p1.getLengthSquared();
         const double c = p2.getLengthSquared();
 
         __x = (a*y0 + b*y1 + c*y2) / D;
         __y = (a*x0 + b*x1 + c*x2) / D;
         __r = this->getDistance(p0);
 
       } else {
 
         set(p0, p1);
 
         const JCircle2D c1(p1, p2);
         const JCircle2D c2(p0, p2);
 
         if (c1.getRadius() > this->getRadius()) { *this = c1; }
         if (c2.getRadius() > this->getRadius()) { *this = c2; }
       }
     }

template<class T >

void JGEOMETRY2D::JCircle2D::set	(	T	__begin,
		T	__end
	)

inlineinherited

Set circle.

Determines smallest enclosing circle around set of points.

    double getX();   // x coordinate
    double getY();   // y coordinate

Parameters

__begin	begin of data
__end	end of data

Definition at line 200 of file JCircle2D.hh.

     {
       if        (std::distance(__begin,__end) == 1) {
 
         __x = __begin->getX();
         __y = __begin->getY();
         __r = 0.0;
 
       } else if (std::distance(__begin,__end) >  1) {
 
         T j = __begin;
         
         const JVector2D p0(j->getX(), j->getY());
 
         ++j;
 
         const JVector2D p1(j->getX(), j->getY());
 
         set(p0, p1);
 
         while (++j != __end) {
 
           const JVector2D p2(j->getX(), j->getY());
 
           if (this->getDistance(p2) > this->getRadius()) {
             configure(__begin, j, p2);
           }
         }
       }
     }

bool JGEOMETRY2D::JCircle2D::is_inside ( const JVector2D & pos ) const

inlineinherited

Check whether given point is inside circle.

Parameters

pos position

Returns: true if inside; else false

Definition at line 239 of file JCircle2D.hh.

     {
       return (this->getDistance(pos) <= this->getRadius());
     }

const JPosition2D& JGEOMETRY2D::JPosition2D::getPosition ( ) const

inlineinherited

Get position.

Returns: position

Definition at line 97 of file JPosition2D.hh.

     {
       return static_cast<const JPosition2D&>(*this);
     }

JPosition2D& JGEOMETRY2D::JPosition2D::getPosition ( )

inlineinherited

Get position.

Returns: position

Definition at line 108 of file JPosition2D.hh.

     {
       return static_cast<JPosition2D&>(*this);
     }

void JGEOMETRY2D::JPosition2D::setPosition ( const JVector2D & pos )

inlineinherited

Set position.

Parameters

pos position

Definition at line 119 of file JPosition2D.hh.

     {
       static_cast<JVector2D&>(*this) = pos;
     }

JGEOMETRY2D::JPosition2D::operator JAngle2D ( ) const

inlineinherited

Type conversion operator.

Returns: angle

Definition at line 130 of file JPosition2D.hh.

     {
       return JAngle2D(getX(), getY());
     }

JGEOMETRY2D::JPosition2D::operator JVersor2D ( ) const

inlineinherited

Type conversion operator.

Returns: direction

Definition at line 141 of file JPosition2D.hh.

     {
       return JVersor2D(getX(), getY());
     }

JPosition2D& JGEOMETRY2D::JPosition2D::rotate ( const JRotation2D & R )

inlineinherited

Rotate.

Parameters

R	rotation matrix

Returns: this position

Definition at line 153 of file JPosition2D.hh.

     {
       R.rotate(__x, __y);
 
       return *this;
     }

JPosition2D& JGEOMETRY2D::JPosition2D::rotate_back ( const JRotation2D & R )

inlineinherited

Rotate back.

Parameters

R	rotation matrix

Returns: this position

Definition at line 167 of file JPosition2D.hh.

     {
       R.rotate_back(__x, __y);
 
       return *this;
     }

double JGEOMETRY2D::JPosition2D::getDot ( const JAngle2D & angle ) const

inlineinherited

Get dot product.

Parameters

angle angle

Returns: dot product

Definition at line 181 of file JPosition2D.hh.

     {
       return
         getX() * angle.getDX() +
         getY() * angle.getDY();
     }

double JGEOMETRY2D::JPosition2D::getDot ( const JVersor2D & versor ) const

inlineinherited

Get dot product.

Parameters

versor versor

Returns: dot product

Definition at line 195 of file JPosition2D.hh.

     {
       return
         getX() * versor.getDX() +
         getY() * versor.getDY();
     }

double JGEOMETRY2D::JVector2D::getDot ( const JVector2D & point ) const

inlineinherited

Get dot product.

Parameters

point vector

Returns: dot product

Definition at line 231 of file JVector2D.hh.

     {
       return
         getX() * point.getX() + 
         getY() * point.getY();
     }

double JGEOMETRY2D::JPosition2D::getPerpDot ( const JAngle2D & angle ) const

inlineinherited

Get perpendicular dot product.

Parameters

angle angle

Returns: perpendicular dot product

Definition at line 209 of file JPosition2D.hh.

     {
       return
         getX() * angle.getDY() -
         getY() * angle.getDX();
     }

double JGEOMETRY2D::JPosition2D::getPerpDot ( const JVersor2D & dir ) const

inlineinherited

Get perpendicular dot product.

Parameters

dir direction

Returns: perpendicular dot product

Definition at line 223 of file JPosition2D.hh.

     {
       return
         getX() * dir.getDY() -
         getY() * dir.getDX();
     }

double JGEOMETRY2D::JVector2D::getPerpDot ( const JVector2D & point ) const

inlineinherited

Get perpendicular dot product.

Parameters

point vector

Returns: perpendicular dot product

Definition at line 245 of file JVector2D.hh.

     {
       return
         getX() * point.getY() - 
         getY() * point.getX();
     }

double JGEOMETRY2D::JVector2D::getX ( ) const

inlineinherited

Get x position.

Returns: x position

Definition at line 61 of file JVector2D.hh.

     { 
       return __x;
     }

double JGEOMETRY2D::JVector2D::getY ( ) const

inlineinherited

Get y position.

Returns: y position

Definition at line 72 of file JVector2D.hh.

     { 
       return __y;
     }

JVector2D& JGEOMETRY2D::JVector2D::negate ( )

inlineinherited

Negate vector.

Returns: this vector

Definition at line 83 of file JVector2D.hh.

     {
       __x = -__x;
       __y = -__y;
 
       return *this;
     }

JVector2D& JGEOMETRY2D::JVector2D::add ( const JVector2D & vector )

inlineinherited

Add vector.

Parameters

vector vector

Returns: this vector

Definition at line 98 of file JVector2D.hh.

     {
       __x += vector.getX();
       __y += vector.getY();
 
       return *this;
     }

JVector2D& JGEOMETRY2D::JVector2D::sub ( const JVector2D & vector )

inlineinherited

Subtract vector.

Parameters

vector vector

Returns: this vector

Definition at line 113 of file JVector2D.hh.

     {
       __x -= vector.getX();
       __y -= vector.getY();
 
       return *this;
     }

JVector2D& JGEOMETRY2D::JVector2D::mul ( const double factor )

inlineinherited

Scale vector.

Parameters

factor multiplication factor

Returns: this vector

Definition at line 128 of file JVector2D.hh.

     {
       __x *= factor;
       __y *= factor;
 
       return *this;
     }

JVector2D & JMATH::JMath< JVector2D , JNullType >::mul ( const JNullType & object )

inlineinherited

Multiply with object.

Parameters

object object

Returns: result object

Definition at line 273 of file JMath.hh.

     {
       return static_cast<JFirst_t&>(*this) = JCalculator<JFirst_t>::calculator.mul(static_cast<const JFirst_t&>(*this), object);
     }

JVector2D& JGEOMETRY2D::JVector2D::div ( const double factor )

inlineinherited

Scale vector.

Parameters

factor division factor

Returns: this vector

Definition at line 143 of file JVector2D.hh.

     {
       __x /= factor;
       __y /= factor;
 
       return *this;
     }

JVector2D& JGEOMETRY2D::JVector2D::transform ( const JMatrix2D & T )

inlineinherited

Transform.

Parameters

T matrix

Returns: this vector

Definition at line 158 of file JVector2D.hh.

     {
       T.transform(__x, __y);
 
       return *this;
     }

bool JGEOMETRY2D::JVector2D::equals ( const JVector2D & vector ) const

inlineinherited

Check equality.

Parameters

vector vector

Returns: true if vectors are equal; else false

Definition at line 172 of file JVector2D.hh.

     {
       return (getX() == vector.getX() && 
               getY() == vector.getY());
     }

double JGEOMETRY2D::JVector2D::getLengthSquared ( ) const

inlineinherited

Get length squared.

Returns: square of length

Definition at line 184 of file JVector2D.hh.

     { 
       return getX()*getX() + getY()*getY();
     }

double JGEOMETRY2D::JVector2D::getLength ( ) const

inlineinherited

Get length.

Returns: length

Definition at line 195 of file JVector2D.hh.

     { 
       return sqrt(getLengthSquared());
     }

double JGEOMETRY2D::JVector2D::getDistanceSquared ( const JVector2D & point ) const

inlineinherited

Get squared of distance to point.

Parameters

point point

Returns: square of distance

Definition at line 207 of file JVector2D.hh.

     {
       return JVector2D(point).sub(*this).getLengthSquared();
     }

double JGEOMETRY2D::JVector2D::getDistance ( const JVector2D & point ) const

inlineinherited

Get distance to point.

Parameters

point point

Returns: distance

Definition at line 219 of file JVector2D.hh.

     {
       return sqrt(getDistanceSquared(point));
     }

Friends And Related Function Documentation

std::istream& operator>>	(	std::istream &	in,
		JCylinder3D &	cylinder
	)

friend

Read cylinder from input stream.

Parameters

in	input stream
cylinder	cylinder

Returns: input stream

Definition at line 338 of file JCylinder3D.hh.

     {
       in >> static_cast<JCircle2D&>(cylinder);
       in >> cylinder.zmin >> cylinder.zmax;
       
       return in;
     }

std::ostream& operator<<	(	std::ostream &	out,
		const JCylinder3D &	cylinder
	)

friend

Write cylinder to output stream.

Parameters

out	output stream
cylinder	cylinder

Returns: output stream

Definition at line 354 of file JCylinder3D.hh.

     {
       out << static_cast<const JCircle2D&>(cylinder);
       out << ' ';
       out << cylinder.zmin;
       out << ' ';
       out << cylinder.zmax;
 
       return out;
     }

JReader& operator>>	(	JReader &	in,
		JCylinder3D &	cylinder
	)

friend

Read cylinder from input.

Parameters

in	reader
cylinder	cylinder

Returns: reader

Definition at line 373 of file JCylinder3D.hh.

     {
       in >> static_cast<JCircle2D&>(cylinder);
       in >> cylinder.zmin >> cylinder.zmax;
 
       return in;
     }

JWriter& operator<<	(	JWriter &	out,
		const JCylinder3D &	cylinder
	)

friend

Write cylinder to output.

Parameters

out	writer
cylinder	cylinder

Returns: writer

Definition at line 389 of file JCylinder3D.hh.

     {
       out << static_cast<const JCircle2D&>(cylinder);
       out << cylinder.zmin << cylinder.zmax;
 
       return out;
     }

Member Data Documentation

double JGEOMETRY3D::JCylinder3D::zmin

protected

Definition at line 399 of file JCylinder3D.hh.

double JGEOMETRY3D::JCylinder3D::zmax

protected

Definition at line 400 of file JCylinder3D.hh.

double JGEOMETRY2D::JCircle2D::__r

protectedinherited

Definition at line 311 of file JCircle2D.hh.

double JGEOMETRY2D::JVector2D::__x

protectedinherited

Definition at line 253 of file JVector2D.hh.

double JGEOMETRY2D::JVector2D::__y

protectedinherited

Definition at line 254 of file JVector2D.hh.

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

JCylinder3D.hh

Public Member Functions

Protected Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

Member Data Documentation