#include <Ellipse2D.h>

Inheritance diagram for DGtal::Ellipse2D< TSpace >:

Collaboration diagram for DGtal::Ellipse2D< TSpace >:

Public Types
typedef TSpace	Space
typedef Space::Point	Point
typedef Space::RealPoint	RealPoint2D
typedef Space::RealVector	RealVector2D
Public Types inherited from DGtal::StarShaped2D< TSpace >
typedef Space::RealPoint	RealPoint

Public Member Functions
	~Ellipse2D ()
	Ellipse2D (const double x0, const double y0, const double a0, const double a1, const double theta)
	Ellipse2D (const RealPoint2D &aPoint, const double a0, const double a1, const double theta)
	Ellipse2D (const Point &aPoint, const double a0, const double a1, const double theta)
RealPoint2D	getLowerBound () const
RealPoint2D	getUpperBound () const
RealPoint2D	center () const
double	parameter (const RealPoint2D &p) const
RealPoint2D	x (const double t) const
RealVector2D	xp (const double t) const
RealVector2D	xpp (const double t) const
void	selfDisplay (std::ostream &out) const
bool	isValid () const
Public Member Functions inherited from DGtal::StarShaped2D< TSpace >
	StarShaped2D ()
	~StarShaped2D ()
virtual RealPoint	interiorPoint () const
bool	isInside (const RealPoint &p) const
bool	isInside (const Point &p) const
Orientation	orientation (const RealPoint &p) const
RealPoint	tangent (double t) const
RealPoint	normal (double t) const
double	curvature (double t) const
double	arclength (double t1, double t2, unsigned int nb) const

Protected Member Functions
	Ellipse2D ()

Private Member Functions
Ellipse2D &	operator= (const Ellipse2D &other)

Private Attributes
RealPoint2D	myCenter
double	myAxis1
double	myAxis2
double	myTheta

Detailed Description

template<typename TSpace>
class DGtal::Ellipse2D< TSpace >

Aim: Model of the concept StarShaped represents any ellipse in the plane.

Description of template class 'Ellipse2D'

NB: A backport from ImaGene.

Definition at line 64 of file Ellipse2D.h.

Member Typedef Documentation

template<typename TSpace>

typedef Space::Point DGtal::Ellipse2D< TSpace >::Point

Reimplemented from DGtal::StarShaped2D< TSpace >.

Definition at line 70 of file Ellipse2D.h.

template<typename TSpace>

typedef Space::RealPoint DGtal::Ellipse2D< TSpace >::RealPoint2D

Definition at line 71 of file Ellipse2D.h.

template<typename TSpace>

typedef Space::RealVector DGtal::Ellipse2D< TSpace >::RealVector2D

Definition at line 72 of file Ellipse2D.h.

template<typename TSpace>

typedef TSpace DGtal::Ellipse2D< TSpace >::Space

Reimplemented from DGtal::StarShaped2D< TSpace >.

Definition at line 69 of file Ellipse2D.h.

Constructor & Destructor Documentation

template<typename T >

DGtal::Ellipse2D< T >::~Ellipse2D ( )

inline

Destructor.

Definition at line 48 of file Ellipse2D.ih.

{

}

template<typename T >

DGtal::Ellipse2D< T >::Ellipse2D	(	const double	x0,
		const double	y0,
		const double	a0,
		const double	a1,
		const double	theta
	)

inline

Constructor.

Parameters:

x0	the x-coordinate of the circle center.
y0	the y-coordinate of the circle center.
a1	the half big axis of the ellipse.
a2	the half small axis of the ellipse.
theta	the orientation of the ellipse.

Definition at line 54 of file Ellipse2D.ih.

: myCenter(x0,y0), myAxis1(a0),myAxis2(a1),myTheta(theta)

{}

template<typename T >

DGtal::Ellipse2D< T >::Ellipse2D	(	const RealPoint2D &	aPoint,
		const double	a0,
		const double	a1,
		const double	theta
	)

inline

Constructor.

Parameters:

aPoint	the circle center.
a1	the half big axis of the ellipse.
a2	the half small axis of the ellipse.
theta	the orientation of the ellipse.

Definition at line 62 of file Ellipse2D.ih.

: myCenter(aPoint), myAxis1(a0),myAxis2(a1),myTheta(theta)

{}

template<typename T >

DGtal::Ellipse2D< T >::Ellipse2D	(	const Point &	aPoint,
		const double	a0,
		const double	a1,
		const double	theta
	)

inline

Constructor.

Parameters:

aPoint	the circle center.
a1	the half big axis of the ellipse.
a2	the half small axis of the ellipse.
theta	the orientation of the ellipse.

Definition at line 69 of file Ellipse2D.ih.

References DGtal::Ellipse2D< TSpace >::myCenter.

  : myAxis1(a0),myAxis2(a1),myTheta(theta)
{
  myCenter = aPoint;
}

template<typename TSpace>

DGtal::Ellipse2D< TSpace >::Ellipse2D ( )

protected

Constructor. Forbidden by default (protected to avoid g++ warnings).

Member Function Documentation

template<typename TSpace>

RealPoint2D DGtal::Ellipse2D< TSpace >::center ( ) const

inlinevirtual

Returns:: the center of the star-shaped object.

Implements DGtal::StarShaped2D< TSpace >.

Definition at line 135 of file Ellipse2D.h.

References DGtal::Ellipse2D< TSpace >::myCenter.

    {
      return myCenter;
    }

template<typename TSpace>

RealPoint2D DGtal::Ellipse2D< TSpace >::getLowerBound ( ) const

inlinevirtual

Returns:: the lower bound of the shape bounding box.

Implements DGtal::StarShaped2D< TSpace >.

Definition at line 118 of file Ellipse2D.h.

References DGtal::Ellipse2D< TSpace >::myAxis1, and DGtal::Ellipse2D< TSpace >::myCenter.

    {
      return RealPoint2D(myCenter[0] - myAxis1, myCenter[1] - myAxis1);
    }

template<typename TSpace>

RealPoint2D DGtal::Ellipse2D< TSpace >::getUpperBound ( ) const

inlinevirtual

Returns:: the upper bound of the shape bounding box.

Implements DGtal::StarShaped2D< TSpace >.

Definition at line 127 of file Ellipse2D.h.

References DGtal::Ellipse2D< TSpace >::myAxis1, and DGtal::Ellipse2D< TSpace >::myCenter.

    {
      return RealPoint2D(myCenter[0] + myAxis1, myCenter[1] + myAxis1);
    }

template<typename T >

bool DGtal::Ellipse2D< T >::isValid ( ) const

inline

Checks the validity/consistency of the object.

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

Reimplemented from DGtal::StarShaped2D< TSpace >.

Definition at line 223 of file Ellipse2D.ih.

{
    return true;
}

template<typename TSpace>

Ellipse2D& DGtal::Ellipse2D< TSpace >::operator= ( const Ellipse2D< TSpace > & other )

private

Copy constructor.

Parameters:

other	the object to clone. Forbidden by default. Assignment.
other	the object to copy.

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

template<typename T >

double DGtal::Ellipse2D< T >::parameter ( const RealPoint2D & pp ) const

inlinevirtual

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 >.

Definition at line 88 of file Ellipse2D.ih.

References M_PI.

{
  RealPoint2D v2d( pp );
  v2d -= myCenter;
  
  double angle; 
  if ( v2d[0] == 0.0 ) 
    {
      if ( v2d[1] >0 )
        angle = M_PI/2.0; 
      else 
        angle = 1.5*M_PI; 
    }
  else if (  ( v2d[0] > 0.0 ) && (   v2d[1] >= 0.0 ) )
    angle = atan(v2d[1]/v2d[0]);
  else if (  ( v2d[0] > 0.0 ) && (   v2d[1] <= 0.0 ) )
    angle = 2*M_PI + atan(v2d[1]/v2d[0]);
  else if (  ( v2d[0] < 0.0 ) && (   v2d[1] >= 0.0 ) )
    angle = atan(v2d[1]/v2d[0]) + M_PI;
  else // (  ( v2d[0] < 0.0 ) && (   v2d[1] <= 0.0 ) )
    angle = atan(v2d[1]/v2d[0]) + M_PI;
   return angle;
}

template<typename T >

void DGtal::Ellipse2D< T >::selfDisplay ( std::ostream & out ) const

inline

Writes/Displays the object on an output stream.

Parameters:

out	the output stream where the object is written.

Reimplemented from DGtal::StarShaped2D< TSpace >.

Definition at line 210 of file Ellipse2D.ih.

{
  out << "[Ellipse2D] center= "<<myCenter<<" big axis="<<myAxis1
      <<" small axis="<<myAxis2<<" phase="<<myTheta;
}

template<typename T >

DGtal::Ellipse2D< T >::RealPoint2D DGtal::Ellipse2D< T >::x ( const double t ) const

inlinevirtual

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 >.

Definition at line 123 of file Ellipse2D.ih.

{
  double a2 = myAxis1*myAxis1;
  double b2 = myAxis2*myAxis2;
  double costth = cos( t - myTheta );
  //  double sintth = sin( t - myTheta );
  double cost = cos( t );
  double sint = sin( t );
  double rho = myAxis2 / sqrt( 1.0 - ((a2-b2)/a2)*costth*costth);
    //myAxis2*myAxis1 / sqrt( a2 - (a2-b2)*costth*costth);
  RealPoint2D v( rho*cost, 
     rho*sint );
  v += myCenter;
  return v;
}

template<typename T >

DGtal::Ellipse2D< T >::RealVector2D DGtal::Ellipse2D< T >::xp ( const double t ) const

inlinevirtual

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 >.

Definition at line 149 of file Ellipse2D.ih.

{
  double a2 = myAxis1*myAxis1;
  double b2 = myAxis2*myAxis2;
  double costth = cos( t - myTheta );
  double sintth = sin( t - myTheta );
  double cost = cos( t );
  double sint = sin( t );
  double rho = myAxis2 / sqrt( 1.0 - ((a2-b2)/a2)*costth*costth);
  double a = myAxis1; 
  double b = myAxis2;
  double rhod= a*b*(b2-a2)*sintth*costth
    / std::pow( a2*sintth*sintth + b2*costth*costth, 1.5 );
  RealPoint2D v( rhod*cost - rho*sint, rhod*sint + rho*cost );
  
  return v;
}

template<typename T >

DGtal::Ellipse2D< T >::RealVector2D DGtal::Ellipse2D< T >::xpp ( const double t ) const

inlinevirtual

Parameters:

t	any angle between 0 and 2*Pi.

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

Implements DGtal::StarShaped2D< TSpace >.

Definition at line 175 of file Ellipse2D.ih.

{
  double a2 = myAxis1*myAxis1;
  double b2 = myAxis2*myAxis2;
  double costth = cos( t - myTheta );
  double sintth = sin( t - myTheta );
  double cost = cos( t );
  double sint = sin( t );
  double rho = myAxis2 / sqrt( 1.0 - ((a2-b2)/a2)*costth*costth);
  double a = myAxis1; 
  double b = myAxis2;
  double rhod = a*b*(b2-a2)*sintth*costth
    / std::pow( a2*sintth*sintth + b2*costth*costth, 1.5 );
  double rhodd = a*b*(b2-a2)
    / std::pow( a2*sintth*sintth + b2*costth*costth, 2.5 )
    * ( (costth*costth - sintth*sintth) * (a2*sintth*sintth + b2*costth*costth)
  + 3.0*(b2-a2)*sintth*sintth*costth*costth );
  
  RealPoint2D v( rhodd*cost - 2.0*rhod*sint - rho*cost, 
     rhodd*sint + 2.0*rhod*cost - rho*sint );
  return v;
}

Field Documentation

template<typename TSpace>

double DGtal::Ellipse2D< TSpace >::myAxis1

private

First axis.

Definition at line 184 of file Ellipse2D.h.

Referenced by DGtal::Ellipse2D< TSpace >::getLowerBound(), and DGtal::Ellipse2D< TSpace >::getUpperBound().

template<typename TSpace>

double DGtal::Ellipse2D< TSpace >::myAxis2

private

Second axis.

Definition at line 190 of file Ellipse2D.h.

template<typename TSpace>

RealPoint2D DGtal::Ellipse2D< TSpace >::myCenter

private

Center of the circle.

Definition at line 179 of file Ellipse2D.h.

Referenced by DGtal::Ellipse2D< TSpace >::center(), DGtal::Ellipse2D< TSpace >::Ellipse2D(), DGtal::Ellipse2D< TSpace >::getLowerBound(), and DGtal::Ellipse2D< TSpace >::getUpperBound().

template<typename TSpace>

double DGtal::Ellipse2D< TSpace >::myTheta

private

Orientation (radian).

Definition at line 195 of file Ellipse2D.h.

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

Public Types

Public Member Functions

Protected Member Functions

Private Member Functions

Private Attributes

Detailed Description

template<typename TSpace> class DGtal::Ellipse2D< TSpace >

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

Field Documentation

template<typename TSpace>
class DGtal::Ellipse2D< TSpace >