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DGtal 2.0.0
DGtal::Lemniscate2D< TSpace > Class Template Reference

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

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

Inheritance diagram for DGtal::Lemniscate2D< TSpace >:
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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)
Lemniscate2Doperator= (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
StarShaped2Doperator= (const StarShaped2D &other)=delete
virtual ~StarShaped2D ()=default
virtual RealPoint interiorPoint () const
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
x0the x-coordinate of the lemniscate center.
y0the y-coordinate of the lemniscate center.
asemi-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
aPointthe lemniscate center
asemi-axis length along x-axis

◆ Lemniscate2D() [4/4]

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

Copy constructor.

Parameters
otherthe 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.

139 {
140 return myCenter;
141 }

◆ 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.

122 {
123 return RealPoint( myCenter[0] - myA, myCenter[1] - myA * 0.5 );
124 }
Space::RealPoint RealPoint

◆ 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.

131 {
132 return RealPoint( myCenter[0] + myA, myCenter[1] + myA * 0.5 );
133 }

◆ 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.

223 {
225 }
Aim: Model of the concept StarShaped represents a lemniscate.
RealPoint x(const double t) const

◆ 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
newCenterthe new center position

Implements DGtal::StarShaped2D< TSpace >.

Definition at line 148 of file Lemniscate2D.h.

149 {
151 }

◆ operator=()

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

Assignment.

Parameters
otherthe 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
pany 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
outthe output stream where the object is written.

◆ x()

template<typename TSpace>
RealPoint DGtal::Lemniscate2D< TSpace >::x ( const double t) const
virtual
Parameters
tany 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
tany 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
tany 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.

◆ myCenter

template<typename TSpace>
RealPoint DGtal::Lemniscate2D< TSpace >::myCenter
private

Center of the circle.

Definition at line 191 of file Lemniscate2D.h.


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