/Users/mourrain/Devel/mmx/shape/include/shape/voronoi_site2d.hpp

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/*****************************************************************************
 * M a t h e m a g i x
 *****************************************************************************
 * Voronoi_site2d
 * 2010-04-05 
* Angelos Mantzaflaris
 *****************************************************************************
 *               Copyright (C) 2010 INRIA Sophia-Antipolis
 *****************************************************************************
 * Comments :
 ****************************************************************************/

# ifndef shape_voronoi_site2d_hpp
# define shape_voronoi_site2d_hpp

# include <realroot/GMP.hpp>
# include <shape/point.hpp>
# include <realroot/polynomial_sparse.hpp>
# include <shape/algebraic_set.hpp>
# include <shape/viewer_axel.hpp>

# define TMPL template<class C, class V>
# define SELF voronoi_site2d<C,V>
# define REF REF_OF(V)
# define AlgebraicCurve algebraic_curve<C,V>
# define Point point<double>
# define Viewer viewer<V>
//====================================================================
namespace mmx {
namespace shape {
//====================================================================

template<class C, class V=default_env>
class voronoi_site2d 
{

public:

  typedef typename algebraic_set<C,V>::Polynomial Polynomial;
    //typedef polynomial<C, with<Sparse, DegRevLex> > Polynomial;

  voronoi_site2d(void) {} ;
  voronoi_site2d(const Point & p);
  voronoi_site2d(const Point & p, double a11, double a22,double a12);
  voronoi_site2d(const double & w, const Point & p);
  voronoi_site2d(const Point & p, const char * s);
  voronoi_site2d(const Point & p, const Polynomial &) ;
  ~voronoi_site2d(void) {};

  Polynomial distfunc() const  { return this->func ; }
  Point      coordinates() const { return this->coords ; }
  double      x() const { return this->coords.x() ; }
  double      y() const { return this->coords.y() ; } 
  double      z() const { return this->coords.z() ; }

private:
  Point coords;

  Polynomial func;

} ;

TMPL
SELF::voronoi_site2d(const Point & p, const char * s)
 { 
  typedef typename use<numeric_def,V>::Rational Coefficients;
  polynomial<Coefficients, with<Sparse,DegRevLex> >t(s, variables("x y"));
  Polynomial e; let::assign(func,t);

  coords= p; 
}

TMPL// Anisotropic site
SELF::voronoi_site2d(const Point & p, double a11,double a22,double a12)
{

  func= ( a11*( Polynomial(1,1,0)-p.x() ) + a12*( Polynomial(1,1,1)-p.y() ) ) * ( Polynomial(1,1,0) - p.x() ) + 
      ( a12*( Polynomial(1,1,0)-p.x() ) + a22*( Polynomial(1,1,1)-p.y() ) ) * ( Polynomial(1,1,1) - p.y() );

  coords= p; 
}

TMPL
SELF::voronoi_site2d(const Point & p)
{ 
  func= Polynomial(1,2,0)+Polynomial(1,2,1);
  func
    += ( p.x()!=0? Polynomial(-2*p.x(),1,0):0) //0 produces erroneous coeff
    +  ( p.y()!=0? Polynomial(-2*p.y(),1,1):0)
    +  Polynomial(p.x()*p.x()+p.y()*p.y(),0,0);

  //std::cout<<"site "<< func <<std::endl;
  coords= p;
}

TMPL
SELF::voronoi_site2d(const double & w, const Point & p)
{ 
  func= Polynomial(1,2,0)+Polynomial(1,2,1);

  func += Polynomial(-2*p.x(),1,0) // (coeff,degree,variable)
    +  Polynomial(-2*p.y(),1,1)
    +  Polynomial(p.x()*p.x()+p.y()*p.y(),0,0)
    -  Polynomial( w*w ,0,0);//adding weight 

  coords= p;
}

TMPL
SELF::voronoi_site2d(const Point& p, const Polynomial& f) 
    {
      func  = f;
      coords= p; 
    }


//====================================================================
} ; // namespace shape
} ; // namespace mmx
//====================================================================
# undef TMPL 
# undef SELF
# undef Point
# undef Viewer
# endif // shape_voronoi_site2d_hpp

// 
// voronoi_site2d.hpp ends here