// Copyright (c) 2003,2004  INRIA Sophia-Antipolis (France).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org).
//
// $URL: https://github.com/CGAL/cgal/blob/v6.1/Apollonius_graph_2/include/CGAL/Hyperbola_2.h $
// $Id: include/CGAL/Hyperbola_2.h b26b07a1242 $
// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
//
//
// Author(s)     : Menelaos Karavelas <mkaravel@iacm.forth.gr>



#ifndef CGAL_HYPERBOLA_2_H
#define CGAL_HYPERBOLA_2_H

#include <CGAL/license/Apollonius_graph_2.h>


#include <CGAL/enum.h>
#include <CGAL/determinant.h>

#include <CGAL/Apollonius_site_2.h>
#include <CGAL/Kernel_traits.h>

namespace CGAL {

template < class Gt >
class Hyperbola_2
{
public:
  typedef Gt                Geom_traits;
  typedef typename Gt::Site_2     Site_2;
  typedef typename Gt::Segment_2  Segment_2;
  typedef typename Gt::Point_2    Point_2;
  typedef typename Gt::FT         FT;
#if 0
  typedef typename Kernel_traits<Point>::Kernel   Kernel;
  typedef CGAL::Apollonius_site_2<Kernel>         Site_2;
  typedef typename Kernel::Segment_2              Segment_2;
  typedef Point                                   Point_2;
  typedef typename Kernel::FT                     FT;
#endif
  //  typedef typename R::RT          FT;
  //  typedef double                                  FT;
  //  typedef CGAL::Point_2< Cartesian<double>  >     Point_2;
  //  typedef CGAL::Segment_2< Cartesian< double > >  Segment_2;

protected:
  FT STEP;

  Point_2 f1, f2;
  FT r;
  Point_2 o;

  inline
  Point_2 lchain(const FT &t) const
  {
    std::vector< Point_2 > p = compute_points(t);
    if ( right(p[0]) )  return p[1];
    return p[0];
  }

  inline
  Point_2 rchain(const FT &t) const
  {
    std::vector< Point_2 > p = compute_points(t);
    if ( right(p[0]) )  return p[0];
    return p[1];
  }

  inline
  FT norm2(const Point_2& p) const
  {
    return (CGAL::square(p.x()) + CGAL::square(p.y()));
  }

  inline
  FT distance2(const Point_2& p1, const Point_2& p2) const
  {
    FT dx = p1.x()-p2.x();
    FT dy = p1.y()-p2.y();
    return (CGAL::square(dx) + CGAL::square(dy));
  }

  inline
  FT distance(const Point_2& p1, const Point_2& p2) const
  {
    return CGAL::sqrt( distance2(p1, p2) );
  }

  void compute_origin()
  {
    FT dx = f2.x() - f1.x();
    FT dy = f2.y() - f1.y();
    FT a = CGAL::sqrt(CGAL::square(dx) + CGAL::square(dy));
    FT t = (FT(1) + r / a) / FT(2);

    o = Point_2(dx * t + f1.x(), dy * t + f1.y());
  }

  std::vector< Point_2 > compute_points(const FT &d) const {
      FT d1 = distance(o, f1) + d;
      FT d2 = distance(o, f2) + d;
      d1 *= d1;
      d2 *= d2;

      Point_2 df = Point_2(f2.x() - f1.x(), f2.y()-f1.y());

      std::vector< Point_2 > p;

      if ( CGAL::is_negative(d) ) return p;

      if ( CGAL::is_zero(df.x()) ) {
        FT y = (d1 - d2 + norm2(f2) - norm2(f1)) / (FT(2) * df.y());

        FT D = d1 - CGAL::square(y - f1.y());

        D = CGAL::abs(D);

        FT x1 = CGAL::sqrt(D) + f1.x();
        FT x2 = -CGAL::sqrt(D) + f1.x();

        p.push_back(Point_2(x1, y));
        p.push_back(Point_2(x2, y));

        return p;
      }

      FT gamma = (d1 - d2 + norm2(f2) - norm2(f1)) / (FT(2) * df.x());
      FT gamma1 = gamma - f1.x();
      FT beta = df.y() / df.x();

      FT a = FT(1) + CGAL::square(beta);
      FT b = -FT(2) * (gamma1 * beta + f1.y());
      FT c = CGAL::square(f1.y()) + CGAL::square(gamma1) - d1;

      FT D = CGAL::square(b) - FT(4) * a * c;

      D = CGAL::abs(D);

      FT y1 = (-b + CGAL::sqrt(D)) / (FT(2) * a);
      FT y2 = (-b - CGAL::sqrt(D)) / (FT(2) * a);

      FT x1 = gamma - beta * y1;
      FT x2 = gamma - beta * y2;

      p.push_back(Point_2(x1, y1));
      p.push_back(Point_2(x2, y2));

      return p;
  }

  bool right(const Point_2& p) const
  {
    return
      CGAL::is_negative( determinant<FT>(f1.x(), f1.y(), 1,
                                               f2.x(), f2.y(), 1,
                                               p.x(),   p.y(), 1) );
  }

  inline
  Point_2 midpoint(const Point_2& p1, const Point_2& p2) const
  {
    FT t1 = t(p1);
    FT t2 = t(p2);
    FT midt = (t1+t2)/2;
    return f(midt);
  }

  inline
  Point_2 f(FT t) const
  {
    if ( CGAL::is_negative(t) )  return rchain(-t);
    return lchain(t);
  }

  inline
  FT t(const Point_2 &p) const
  {
    FT tt = distance(f1, p) - distance(f1, o);
    if ( right(p) )  return -tt;
    return tt;
  }

public:
  Hyperbola_2()  { STEP = FT(2); }

  Hyperbola_2(const Site_2 &ff1, const Site_2 &ff2)
  {
    STEP = FT(2);
    this->r = ff1.weight() - ff2.weight();

    this->f1 = ff1.point();
    this->f2 = ff2.point();

    compute_origin();
  }

  Oriented_side
  side_of_hyperbola(const Point_2 &p) const
  {
    double dist = distance(p, f1) - distance(p, f2) - r;
    if ( dist < 0 )  return ON_NEGATIVE_SIDE;
    if ( dist > 0 )  return ON_POSITIVE_SIDE;
    return ON_ORIENTED_BOUNDARY;
  }


  template<class QTWIDGET>
  void generate_points_qt(const QTWIDGET& W,
                          std::vector<Point_2>& pleft,
                          std::vector<Point_2>& pright) const
    {
      std::vector< Point_2 > p;

      pleft.push_back(o);
      pright.push_back(o);

      double width = W.x_max() - W.x_min();
      double height = W.y_max() - W.y_min();

      FT STEP;
      if ( width < height ) {
        STEP = width / 500.0;
      } else {
        STEP = height / 500.0;
      }
      //    double mind = distance(o, f1) - r1;
      for (int i = 1; i <= 100; i++) {
        p = compute_points(FT(i * i) * STEP);

        if ( p.size() > 0 ) {
          if ( right(p[0]) ) {
            pright.push_back(p[0]);
            pleft.push_back(p[1]);
          } else {
            pright.push_back(p[1]);
            pleft.push_back(p[0]);
          }
        }
      }
    }

  template<class QTWIDGET>
  void draw_qt(QTWIDGET& W) const
    {
      std::vector< Point_2 > pleft, pright;
      generate_points_qt(pleft, pright);

      for (unsigned int i = 0; i < pleft.size() - 1; i++) {
        W << Segment_2(pleft[i], pleft[i+1]);
      }

      for (unsigned int i = 0; i < pright.size() - 1; i++) {
        W << Segment_2(pright[i], pright[i+1]);
      }
    }

  void generate_points(std::vector<Point_2>& pleft,
                       std::vector<Point_2>& pright) const
  {
    std::vector< Point_2 > p;

    pleft.push_back(o);
    pright.push_back(o);

    //    double mind = distance(o, f1) - r1;
    for (int i = 1; i <= 100; i++) {
      p = compute_points(FT(i * i) * STEP);

      if ( p.size() > 0 ) {
        if ( right(p[0]) ) {
          pright.push_back(p[0]);
          pleft.push_back(p[1]);
        } else {
          pright.push_back(p[1]);
          pleft.push_back(p[0]);
        }
      }
    }
  }

  template< class Stream >
  void draw(Stream &W) const
  {
    std::vector< Point_2 > pleft, pright;
    generate_points(pleft,pright);

    for (unsigned int i = 0; i < pleft.size() - 1; i++) {
      W << Segment_2(pleft[i], pleft[i+1]);
    }

    for (unsigned int i = 0; i < pright.size() - 1; i++) {
      W << Segment_2(pright[i], pright[i+1]);
    }
  }

};

template< class Stream, class Gt >
inline
Stream& operator<<(Stream& s, const Hyperbola_2<Gt> &H)
{
  H.draw(s);
  return s;
}


} //namespace CGAL

#endif // CGAL_HYPERBOLA_2_H

