//! \file examples/Minkowski_sum_2/exact_inset.cpp
// Computing the exact inner offset of a polygon.
#include <CGAL/basic.h>

#ifndef CGAL_USE_CORE
#include <iostream>
int main ()
{
  std::cout << "Sorry, this example needs CORE ..." << std::endl;
  return (0);
}
#else

#include <CGAL/Cartesian.h>
#include <CGAL/CORE_algebraic_number_traits.h>
#include <CGAL/Arr_conic_traits_2.h>
#include <CGAL/offset_polygon_2.h>
#include <CGAL/Timer.h>
#include <iostream>

typedef CGAL::CORE_algebraic_number_traits     Nt_traits;
typedef Nt_traits::Rational                    Rational;
typedef Nt_traits::Algebraic                   Algebraic;

struct Rat_kernel : public CGAL::Cartesian<Rational> {};
struct Alg_kernel : public CGAL::Cartesian<Algebraic> {};
struct Conic_traits_2 : public CGAL::Arr_conic_traits_2<Rat_kernel,
                                                        Alg_kernel,
                                                        Nt_traits> {};

typedef CGAL::Polygon_2<Rat_kernel>            Polygon_2;

typedef CGAL::Gps_traits_2<Conic_traits_2>     Gps_traits_2;
typedef Gps_traits_2::Polygon_2                Offset_polygon_2;

int main ()
{
  // Open the input file.
  std::ifstream    in_file ("tight.dat");

  if (! in_file.is_open())
  {
    std::cerr << "Failed to open the input file." << std::endl;
    return (1);
  }

  // Read the input polygon.
  Polygon_2        P;

  in_file >> P;
  in_file.close();

  std::cout << "Read an input polygon with "
            << P.size() << " vertices." << std::endl;

  // Compute the inner offset of the polygon.
  Conic_traits_2                         traits;
  const Rational                         radius = 1;
  std::list<Offset_polygon_2>            inset_polygons;
  std::list<Offset_polygon_2>::iterator  iit;
  CGAL::Timer                            timer;

  timer.start();
  inset_polygon_2 (P, radius, traits,
                   std::back_inserter (inset_polygons));
  timer.stop();

  std::cout << "The inset comprises " 
            << inset_polygons.size() << " polygon(s)." << std::endl;
  for (iit = inset_polygons.begin(); iit != inset_polygons.end(); ++iit)
  {
      std::cout << "    Polygon with "
                << iit->size() << " vertices." << std::endl;
  }
  std::cout << "Inset computation took "
            << timer.time() << " seconds." << std::endl;
  return (0);
}

#endif