DGtal  1.1.0
Public Types | Public Member Functions | Private Member Functions | Private Attributes
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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Collaboration 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  }

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.

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

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.

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

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

◆ isAlmostEqual()

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

Equality test using relative tolerance.

Definition at line 222 of file Lemniscate2D.h.

223  {
224  return std::abs(x - y) <= std::numeric_limits<T>::epsilon();
225  }

◆ 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  {
150  myCenter = newCenter;
151  }

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

◆ 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.

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

◆ myCenter

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

The documentation for this class was generated from the following file:
DGtal::Lemniscate2D::myCenter
RealPoint myCenter
Definition: Lemniscate2D.h:191
DGtal::Lemniscate2D::myA
double myA
Definition: Lemniscate2D.h:196
DGtal::Lemniscate2D::RealPoint
Space::RealPoint RealPoint
Definition: Lemniscate2D.h:67