Aim: Model of the concept StarShaped represents a lemniscate. More...

#include <DGtal/shapes/parametric/Lemniscate2D.h>

Inheritance diagram for DGtal::Lemniscate2D< TSpace >:

Public Types
typedef TSpace	Space

typedef Space::RealPoint	RealPoint

typedef Space::RealVector	RealVector

Public Types inherited from DGtal::StarShaped2D< TSpace >
typedef TSpace	Space

typedef Space::RealPoint	RealPoint

Public Member Functions
	Lemniscate2D ()=delete

	Lemniscate2D (const double x0, const double y0, const double a)

	Lemniscate2D (const RealPoint &aPoint, const double a)

	Lemniscate2D (const Lemniscate2D &other)

Lemniscate2D &	operator= (const Lemniscate2D &other)=delete

	~Lemniscate2D ()=default

RealPoint	getLowerBound () const

RealPoint	getUpperBound () const

RealPoint	center () const

void	moveTo (const RealPoint &newCenter)

double	parameter (const RealPoint &p) const

RealPoint	x (const double t) const

RealVector	xp (const double t) const

RealVector	xpp (const double t) const

void	selfDisplay (std::ostream &out) const

bool	isValid () const

Public Member Functions inherited from DGtal::StarShaped2D< TSpace >
	StarShaped2D ()=default

	StarShaped2D (const StarShaped2D &other)=delete

StarShaped2D &	operator= (const StarShaped2D &other)=delete

virtual	~StarShaped2D ()=default

virtual RealPoint	interiorPoint () const

virtual RealPoint	getLowerBound () const =0

virtual RealPoint	getUpperBound () const =0

virtual RealPoint	center () const =0

virtual void	moveTo (const RealPoint &newCenter)=0

virtual double	parameter (const RealPoint &p) const =0

virtual RealPoint	x (const double t) const =0

virtual RealPoint	xp (const double t) const =0

virtual RealPoint	xpp (const double t) const =0

Orientation	orientation (const RealPoint &p) const

RealPoint	tangent (const double t) const

RealPoint	normal (const double t) const

double	curvature (const double t) const

double	arclength (const double t1, double t2, const unsigned int nb) const

RealPoint	findIntersection (const RealPoint &inner, const RealPoint &outer, const double epsilon) const

RealPoint	closestPointWithWitnesses (const RealPoint &p, const RealPoint &left, const RealPoint &right, const int step) const

void	selfDisplay (std::ostream &out) const

bool	isValid () const

Private Member Functions
template<typename T >
bool	isAlmostEqual (T x, T y) const

Private Attributes
RealPoint	myCenter

double	myA

Detailed Description

template<typename TSpace>
class DGtal::Lemniscate2D< TSpace >

Aim: Model of the concept StarShaped represents a lemniscate.

Description of template class 'Lemniscate'

Definition at line 61 of file Lemniscate2D.h.

Member Typedef Documentation

◆ RealPoint

template<typename TSpace >

typedef Space::RealPoint DGtal::Lemniscate2D< TSpace >::RealPoint

Definition at line 67 of file Lemniscate2D.h.

◆ RealVector

template<typename TSpace >

typedef Space::RealVector DGtal::Lemniscate2D< TSpace >::RealVector

Definition at line 68 of file Lemniscate2D.h.

◆ Space

template<typename TSpace >

typedef TSpace DGtal::Lemniscate2D< TSpace >::Space

Definition at line 66 of file Lemniscate2D.h.

Constructor & Destructor Documentation

◆ Lemniscate2D() [1/4]

template<typename TSpace >

DGtal::Lemniscate2D< TSpace >::Lemniscate2D ( )

delete

Constructor. Forbidden by default.

◆ Lemniscate2D() [2/4]

template<typename TSpace >

DGtal::Lemniscate2D< TSpace >::Lemniscate2D	(	const double	x0,
		const double	y0,
		const double	a
	)

Constructor. The absolute value of parameter a is used.

Parameters

x0	the x-coordinate of the lemniscate center.
y0	the y-coordinate of the lemniscate center.
a	semi-axis length along x-axis

◆ Lemniscate2D() [3/4]

template<typename TSpace >

DGtal::Lemniscate2D< TSpace >::Lemniscate2D	(	const RealPoint &	aPoint,
		const double	a
	)

Constructor. The absolute value of parameter a is used. The absolute value of a parameters is used.

Parameters

aPoint	the lemniscate center
a	semi-axis length along x-axis

◆ Lemniscate2D() [4/4]

template<typename TSpace >

DGtal::Lemniscate2D< TSpace >::Lemniscate2D ( const Lemniscate2D< TSpace > & other )

Copy constructor.

Parameters

other the object to clone.

◆ ~Lemniscate2D()

template<typename TSpace >

DGtal::Lemniscate2D< TSpace >::~Lemniscate2D ( )

default

Destructor.

Member Function Documentation

◆ center()

template<typename TSpace >

RealPoint DGtal::Lemniscate2D< TSpace >::center ( ) const

inlinevirtual

Returns: the center of the star-shaped object.

Implements DGtal::StarShaped2D< TSpace >.

Definition at line 138 of file Lemniscate2D.h.

    {
      return myCenter;
    }

References DGtal::Lemniscate2D< TSpace >::myCenter.

◆ getLowerBound()

template<typename TSpace >

RealPoint DGtal::Lemniscate2D< TSpace >::getLowerBound ( ) const

inlinevirtual

Returns: the lower bound of the shape bounding box.

Implements DGtal::StarShaped2D< TSpace >.

Definition at line 121 of file Lemniscate2D.h.

    {
      return RealPoint( myCenter[0] - myA, myCenter[1] - myA * 0.5 );
    }

References DGtal::Lemniscate2D< TSpace >::myA, and DGtal::Lemniscate2D< TSpace >::myCenter.

◆ getUpperBound()

template<typename TSpace >

RealPoint DGtal::Lemniscate2D< TSpace >::getUpperBound ( ) const

inlinevirtual

Returns: the upper bound of the shape bounding box.

Implements DGtal::StarShaped2D< TSpace >.

Definition at line 130 of file Lemniscate2D.h.

    {
      return RealPoint( myCenter[0] + myA, myCenter[1] + myA * 0.5 );
    }

References DGtal::Lemniscate2D< TSpace >::myA, and DGtal::Lemniscate2D< TSpace >::myCenter.

◆ isAlmostEqual()

template<typename TSpace >

template<typename T >

bool DGtal::Lemniscate2D< TSpace >::isAlmostEqual	(	T	x,
		T	y
	)		const

inlineprivate

Equality test using relative tolerance.

Definition at line 222 of file Lemniscate2D.h.

    {
      return std::abs(x - y) <= std::numeric_limits<T>::epsilon();
    }

◆ isValid()

template<typename TSpace >

bool DGtal::Lemniscate2D< TSpace >::isValid ( ) const

Checks the validity/consistency of the object.

Returns: 'true' if the object is valid, 'false' otherwise.

◆ moveTo()

template<typename TSpace >

void DGtal::Lemniscate2D< TSpace >::moveTo ( const RealPoint & newCenter )

inlinevirtual

Modify the shape center

Parameters

newCenter the new center position

Implements DGtal::StarShaped2D< TSpace >.

Definition at line 148 of file Lemniscate2D.h.

    {
      myCenter = newCenter;
    }

References DGtal::Lemniscate2D< TSpace >::myCenter.

◆ operator=()

template<typename TSpace >

Lemniscate2D & DGtal::Lemniscate2D< TSpace >::operator= ( const Lemniscate2D< TSpace > & other )

delete

Assignment.

Parameters

other the object to copy.

Returns: a reference on 'this'. Forbidden by default.

◆ parameter()

template<typename TSpace >

double DGtal::Lemniscate2D< TSpace >::parameter ( const RealPoint & p ) const

virtual

Parameters

p	any point in the plane.

Returns: the angle parameter between 0 and 2*Pi corresponding to this point for the shape.

Implements DGtal::StarShaped2D< TSpace >.

◆ selfDisplay()

template<typename TSpace >

void DGtal::Lemniscate2D< TSpace >::selfDisplay ( std::ostream & out ) const

Writes/Displays the object on an output stream.

Parameters

out	the output stream where the object is written.

◆ x()

template<typename TSpace >

RealPoint DGtal::Lemniscate2D< TSpace >::x ( const double t ) const

virtual

Parameters

t	any angle between 0 and 2*Pi.

Returns: the vector (x(t),y(t)) which is the position on the shape boundary.

Implements DGtal::StarShaped2D< TSpace >.

◆ xp()

template<typename TSpace >

RealVector DGtal::Lemniscate2D< TSpace >::xp ( const double t ) const

virtual

Parameters

t	any angle between 0 and 2*Pi.

Returns: the vector (x'(t),y'(t)) which is the tangent to the shape boundary.

Implements DGtal::StarShaped2D< TSpace >.

◆ xpp()

template<typename TSpace >

RealVector DGtal::Lemniscate2D< TSpace >::xpp ( const double t ) const

virtual

Parameters

t	any angle between 0 and 2*Pi.

Returns: the vector (x''(t),y''(t)).

Implements DGtal::StarShaped2D< TSpace >.

Field Documentation

◆ myA

template<typename TSpace >

double DGtal::Lemniscate2D< TSpace >::myA

private

Semi-axis length along x-axis

Definition at line 196 of file Lemniscate2D.h.

Referenced by DGtal::Lemniscate2D< TSpace >::getLowerBound(), and DGtal::Lemniscate2D< TSpace >::getUpperBound().

◆ myCenter

template<typename TSpace >

RealPoint DGtal::Lemniscate2D< TSpace >::myCenter

private

Center of the circle.

Definition at line 191 of file Lemniscate2D.h.

Referenced by DGtal::Lemniscate2D< TSpace >::center(), DGtal::Lemniscate2D< TSpace >::getLowerBound(), DGtal::Lemniscate2D< TSpace >::getUpperBound(), and DGtal::Lemniscate2D< TSpace >::moveTo().

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

Lemniscate2D.h

Public Types

Public Member Functions

Private Member Functions

Private Attributes

Detailed Description

Member Typedef Documentation

◆ RealPoint

◆ RealVector

◆ Space

Constructor & Destructor Documentation

◆ Lemniscate2D() [1/4]

◆ Lemniscate2D() [2/4]

◆ Lemniscate2D() [3/4]

◆ Lemniscate2D() [4/4]

◆ ~Lemniscate2D()

Member Function Documentation

◆ center()

◆ getLowerBound()

◆ getUpperBound()

◆ isAlmostEqual()

◆ isValid()

◆ moveTo()

◆ operator=()

◆ parameter()

◆ selfDisplay()

◆ x()

◆ xp()

◆ xpp()

Field Documentation

◆ myA

◆ myCenter