#include <StarShaped2D.h>

Inheritance diagram for DGtal::StarShaped2D< TSpace >:

Public Types
typedef TSpace	Space
typedef Space::Point	Point
typedef Space::RealPoint	RealPoint

Public Member Functions
	StarShaped2D ()
	~StarShaped2D ()
virtual RealPoint	interiorPoint () const
virtual RealPoint	getLowerBound () const =0
virtual RealPoint	getUpperBound () const =0
virtual RealPoint	center () const =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
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
void	selfDisplay (std::ostream &out) const
bool	isValid () const

Private Member Functions
StarShaped2D &	operator= (const StarShaped2D &other)

Detailed Description

template<typename TSpace>
class DGtal::StarShaped2D< TSpace >

Description of template class 'StarShaped2D'

Aim: Abstract class that represents any star-shaped object in dimension 2. Such a shape as a center and any segment from this center to the shape boundary is included in the shape. These shapes can thus be parameterized by an angle 't' turning around the center.

StarShaped2D and its derived classes are models of CEuclideanBoundedShape and CEuclideanOrientedShape.

NB: A backport from ImaGene.

Template Parameters:

TSpace space in which the shape is defined.

Definition at line 73 of file StarShaped2D.h.

Member Typedef Documentation

template<typename TSpace>

typedef Space::Point DGtal::StarShaped2D< TSpace >::Point

Reimplemented in DGtal::AccFlower2D< TSpace >, DGtal::Ellipse2D< TSpace >, DGtal::Flower2D< TSpace >, DGtal::NGon2D< TSpace >, and DGtal::Ball2D< TSpace >.

Definition at line 78 of file StarShaped2D.h.

template<typename TSpace>

typedef Space::RealPoint DGtal::StarShaped2D< TSpace >::RealPoint

Definition at line 79 of file StarShaped2D.h.

template<typename TSpace>

typedef TSpace DGtal::StarShaped2D< TSpace >::Space

Reimplemented in DGtal::AccFlower2D< TSpace >, DGtal::Ellipse2D< TSpace >, DGtal::Flower2D< TSpace >, DGtal::NGon2D< TSpace >, and DGtal::Ball2D< TSpace >.

Definition at line 77 of file StarShaped2D.h.

Constructor & Destructor Documentation

template<typename TSpace>

DGtal::StarShaped2D< TSpace >::StarShaped2D ( )

inline

Constructor.

Definition at line 84 of file StarShaped2D.h.

{}

template<typename T >

DGtal::StarShaped2D< T >::~StarShaped2D ( )

inline

Destructor.

Definition at line 204 of file StarShaped2D.ih.

{

}

Member Function Documentation

template<typename TSpace >

double DGtal::StarShaped2D< TSpace >::arclength	(	double	t1,
		double	t2,
		unsigned int	nb
	)		const

inline

Parameters:

t1	any angle between 0 and 2*Pi.
t2	any angle between 0 and 2*Pi, further from [t1].
nb	the number of points used to estimate the arclength between x(t1) and x(t2).

Returns:: the estimated arclength.

Definition at line 179 of file StarShaped2D.ih.

References M_PI.

{
  while ( t2 < t1 ) t2 += 2.0*M_PI;
  RealPoint x0( x( t1 ) );
  double l = 0.0;
  // JOL 2008/08/28
  for ( unsigned int i = 1; i <= nb; ++i )
    {
      double t = ( ( t2 - t1 ) * i ) / nb;
      RealPoint x1( x( t1 + t ) );
      l += sqrt( ( x1[0] - x0[0] )*( x1[0] - x0[0] )
         + ( x1[1] - x0[1] )*( x1[1] - x0[1] ) );
      x0 = x1;
    }
  return l;
}

template<typename TSpace>

virtual RealPoint DGtal::StarShaped2D< TSpace >::center ( ) const

pure virtual

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

Implemented in DGtal::AccFlower2D< TSpace >, DGtal::Flower2D< TSpace >, DGtal::Ellipse2D< TSpace >, DGtal::NGon2D< TSpace >, and DGtal::Ball2D< TSpace >.

Referenced by DGtal::StarShaped2D< TSpace >::interiorPoint().

template<typename TSpace >

double DGtal::StarShaped2D< TSpace >::curvature ( double t ) const

inline

Parameters:

t	any angle between 0 and 2*Pi.

Returns:: the algebraic curvature at point (x(t),y(t)), positive is convex, negative is concave when shape is to the left and the shape boundary is followed counterclockwise.

Definition at line 160 of file StarShaped2D.ih.

{
  RealPoint tgt( xp( t ) );
  RealPoint dt( xpp( t ) );
  double norm = tgt.norm();
  double curv = ( dt[0] * tgt[1] - dt[1] * tgt[0] ) / ( norm * norm * norm );
  return - curv;
}

template<typename TSpace>

virtual RealPoint DGtal::StarShaped2D< TSpace >::getLowerBound ( ) const

pure virtual

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

Implemented in DGtal::AccFlower2D< TSpace >, DGtal::Flower2D< TSpace >, DGtal::Ellipse2D< TSpace >, DGtal::NGon2D< TSpace >, and DGtal::Ball2D< TSpace >.

template<typename TSpace>

virtual RealPoint DGtal::StarShaped2D< TSpace >::getUpperBound ( ) const

pure virtual

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

Implemented in DGtal::AccFlower2D< TSpace >, DGtal::Flower2D< TSpace >, DGtal::Ellipse2D< TSpace >, DGtal::NGon2D< TSpace >, and DGtal::Ball2D< TSpace >.

template<typename TSpace>

virtual RealPoint DGtal::StarShaped2D< TSpace >::interiorPoint ( ) const

inlinevirtual

Returns:: a point p such that 'isInside(p)' returns 'true'.

Definition at line 97 of file StarShaped2D.h.

References DGtal::StarShaped2D< TSpace >::center().

    {
      return center();
    }

template<typename TSpace >

bool DGtal::StarShaped2D< TSpace >::isInside ( const RealPoint & p ) const

inline

Parameters:

p	any point in the plane.

Returns:: 'true' if the point is inside the shape, 'false' if it is strictly outside.

Parameters:

p	any point in the plane.

Returns:: 'true' if the point is inside or on the shape, 'false' if it is strictly outside.

Definition at line 74 of file StarShaped2D.ih.

{
  double t = parameter( p );
  RealPoint x_rel = x( t );
  x_rel -= center();
  double d_x = x_rel[0]*x_rel[0] + x_rel[1]*x_rel[1];
  RealPoint p_rel( p );
  p_rel -= center();
  double d_p = p_rel[0]*p_rel[0] + p_rel[1]*p_rel[1];
   
  return d_p <= d_x;
}

template<typename TSpace >

bool DGtal::StarShaped2D< TSpace >::isInside ( const Point & p ) const

inline

Parameters:

p	any point in the digital plane.

Returns:: 'true' if the point is inside the shape, 'false' if it is strictly outside.

Parameters:

p	any point in the plane.

Returns:: 'true' if the point is inside the shape, 'false' if it is strictly outside.

Definition at line 55 of file StarShaped2D.ih.

{
  RealPoint prel(NumberTraits<typename Point::Component>::castToDouble(p[0]),
     NumberTraits<typename Point::Component>::castToDouble(p[1]));
  
  return this->isInside(prel);
}

template<typename T >

bool DGtal::StarShaped2D< T >::isValid ( ) const

inline

Checks the validity/consistency of the object.

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

Reimplemented in DGtal::AccFlower2D< TSpace >, DGtal::Flower2D< TSpace >, DGtal::Ellipse2D< TSpace >, DGtal::NGon2D< TSpace >, and DGtal::Ball2D< TSpace >.

Definition at line 230 of file StarShaped2D.ih.

{
  return true;
}

template<typename TSpace >

DGtal::StarShaped2D< TSpace >::RealPoint DGtal::StarShaped2D< TSpace >::normal ( double t ) const

inline

Parameters:

t	any angle between 0 and 2*Pi.

Returns:: the vector (x''(t),y''(t)) made unitary which is the unit normal to the shape boundary looking inside the shape.

Parameters:

t	any angle between 0 and 2*Pi.

Returns:: the vector (x''(t),y''(t)) made unitary which is the unit normal to the shape boundary looking inside the shape. b

Definition at line 143 of file StarShaped2D.ih.

{
  RealPoint tgt( tangent( t ) );
  return RealPoint( -tgt[1], tgt[0]);
}

template<typename TSpace>

StarShaped2D& DGtal::StarShaped2D< TSpace >::operator= ( const StarShaped2D< TSpace > & other )

private

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

DGtal::Orientation DGtal::StarShaped2D< TSpace >::orientation ( const RealPoint & p ) const

inline

Return the orienatation of a point with respect to a shape.

Parameters:

p	input point

Returns:: the orientation of the point (<0 means inside, ...)

Parameters:

p	any point in the plane.

Returns:: 'true' if the point is inside the shape, 'false' if it is strictly outside.

Definition at line 96 of file StarShaped2D.ih.

References DGtal::INSIDE, DGtal::ON, and DGtal::OUTSIDE.

{
  double t = parameter( p );
  RealPoint x_rel = x( t );
  x_rel -= center();
  double d_x = x_rel[0]*x_rel[0] + x_rel[1]*x_rel[1];
  RealPoint p_rel( p );
  p_rel -= center();
  double d_p = p_rel[0]*p_rel[0] + p_rel[1]*p_rel[1];
  if (d_p - d_x > 0.0)
    return OUTSIDE;
  else
    if (d_p - d_x < 0.0)
      return  INSIDE;
    else
      return ON;
}

template<typename TSpace>

virtual double DGtal::StarShaped2D< TSpace >::parameter ( const RealPoint & p ) const

pure virtual

Parameters:

p	any point in the plane.

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

Implemented in DGtal::AccFlower2D< TSpace >, DGtal::Flower2D< TSpace >, DGtal::Ellipse2D< TSpace >, DGtal::NGon2D< TSpace >, and DGtal::Ball2D< TSpace >.

template<typename T >

void DGtal::StarShaped2D< 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 in DGtal::AccFlower2D< TSpace >, DGtal::Flower2D< TSpace >, DGtal::Ellipse2D< TSpace >, DGtal::NGon2D< TSpace >, and DGtal::Ball2D< TSpace >.

Definition at line 218 of file StarShaped2D.ih.

{
  out << "[StarShaped2D]";
}

template<typename TSpace >

DGtal::StarShaped2D< TSpace >::RealPoint DGtal::StarShaped2D< TSpace >::tangent ( double t ) const

inline

Parameters:

t	any angle between 0 and 2*Pi.

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

Definition at line 125 of file StarShaped2D.ih.

{
  RealPoint tgt( xp( t ) );
  double norm = tgt.norm();
  tgt /= norm;
  return tgt;
}

template<typename TSpace>

virtual RealPoint DGtal::StarShaped2D< TSpace >::x ( const double t ) const

pure 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.

Implemented in DGtal::AccFlower2D< TSpace >, DGtal::Flower2D< TSpace >, DGtal::Ellipse2D< TSpace >, DGtal::NGon2D< TSpace >, and DGtal::Ball2D< TSpace >.

template<typename TSpace>

virtual RealPoint DGtal::StarShaped2D< TSpace >::xp ( const double t ) const

pure 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.

Implemented in DGtal::AccFlower2D< TSpace >, DGtal::Flower2D< TSpace >, DGtal::Ellipse2D< TSpace >, DGtal::NGon2D< TSpace >, and DGtal::Ball2D< TSpace >.

template<typename TSpace>

virtual RealPoint DGtal::StarShaped2D< TSpace >::xpp ( const double t ) const

pure virtual

Parameters:

t	any angle between 0 and 2*Pi.

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

Implemented in DGtal::AccFlower2D< TSpace >, DGtal::Flower2D< TSpace >, DGtal::Ellipse2D< TSpace >, DGtal::NGon2D< TSpace >, and DGtal::Ball2D< TSpace >.

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

Public Types

Public Member Functions

Private Member Functions

Detailed Description

template<typename TSpace> class DGtal::StarShaped2D< TSpace >

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

template<typename TSpace>
class DGtal::StarShaped2D< TSpace >