function_objects.h

很多二维 三维几何计算算法 C++ 类库

    }
  };

  template <typename K>
  class Compute_xmax_2
  {
    typedef typename K::FT              FT;
    typedef typename K::Iso_rectangle_2 Iso_rectangle_2;
    typedef FT                          Cartesian_coordinate_type;
    //typedef typename K::Cartesian_coordinate_type  Cartesian_coordinate_type;

  public:
    typedef FT               result_type;
    typedef Arity_tag< 1 >   Arity;

    Cartesian_coordinate_type
    operator()(const Iso_rectangle_2& r) const
    {
      return (r.max)().x();
    }
  };

  template <typename K>
  class Compute_xmax_3
  {
    typedef typename K::FT              FT;
    typedef typename K::Iso_cuboid_3    Iso_cuboid_3;
    typedef FT                          Cartesian_coordinate_type;
    //typedef typename K::Cartesian_coordinate_type  Cartesian_coordinate_type;

  public:
    typedef FT               result_type;
    typedef Arity_tag< 1 >   Arity;

    Cartesian_coordinate_type
    operator()(const Iso_cuboid_3& r) const
    {
      return (r.max)().x();
    }
  };

  template <typename K>
  class Compute_ymin_2
  {
    typedef typename K::FT              FT;
    typedef typename K::Iso_rectangle_2 Iso_rectangle_2;
    typedef FT                          Cartesian_coordinate_type;
    //typedef typename K::Cartesian_coordinate_type  Cartesian_coordinate_type;

  public:
    typedef FT               result_type;
    typedef Arity_tag< 1 >   Arity;

    Cartesian_coordinate_type
    operator()(const Iso_rectangle_2& r) const
    {
      return (r.min)().y();
    }
  };

  template <typename K>
  class Compute_ymin_3
  {
    typedef typename K::FT              FT;
    typedef typename K::Iso_cuboid_3    Iso_cuboid_3;
    typedef FT                          Cartesian_coordinate_type;
    //typedef typename K::Cartesian_coordinate_type  Cartesian_coordinate_type;

  public:
    typedef FT               result_type;
    typedef Arity_tag< 1 >   Arity;

    Cartesian_coordinate_type
    operator()(const Iso_cuboid_3& r) const
    {
      return (r.min)().y();
    }
  };

  template <typename K>
  class Compute_ymax_2
  {
    typedef typename K::FT              FT;
    typedef typename K::Iso_rectangle_2 Iso_rectangle_2;
    typedef FT                          Cartesian_coordinate_type;
    //typedef typename K::Cartesian_coordinate_type  Cartesian_coordinate_type;

  public:
    typedef FT               result_type;
    typedef Arity_tag< 1 >   Arity;

    Cartesian_coordinate_type
    operator()(const Iso_rectangle_2& r) const
    {
      return (r.max)().y();
    }
  };

  template <typename K>
  class Compute_ymax_3
  {
    typedef typename K::FT              FT;
    typedef typename K::Iso_cuboid_3    Iso_cuboid_3;
    typedef FT                          Cartesian_coordinate_type;
    //typedef typename K::Cartesian_coordinate_type  Cartesian_coordinate_type;

  public:
    typedef FT               result_type;
    typedef Arity_tag< 1 >   Arity;

    Cartesian_coordinate_type
    operator()(const Iso_cuboid_3& r) const
    {
      return (r.max)().y();
    }
  };

  template <typename K>
  class Compute_zmin_3
  {
    typedef typename K::FT              FT;
    typedef typename K::Iso_cuboid_3    Iso_cuboid_3;
    typedef FT                          Cartesian_coordinate_type;
    //typedef typename K::Cartesian_coordinate_type  Cartesian_coordinate_type;

  public:
    typedef FT               result_type;
    typedef Arity_tag< 1 >   Arity;

    Cartesian_coordinate_type
    operator()(const Iso_cuboid_3& r) const
    {
      return (r.min)().z();
    }
  };

  template <typename K>
  class Compute_zmax_3
  {
    typedef typename K::FT              FT;
    typedef typename K::Iso_cuboid_3    Iso_cuboid_3;
    typedef FT                          Cartesian_coordinate_type;
    //typedef typename K::Cartesian_coordinate_type  Cartesian_coordinate_type;

  public:
    typedef FT               result_type;
    typedef Arity_tag< 1 >   Arity;

    Cartesian_coordinate_type
    operator()(const Iso_cuboid_3& r) const
    {
      return (r.max)().z();
    }
  };

  template <typename K>
  class Construct_center_2 : Has_qrt
  {
    typedef typename K::Point_2   Point_2;
    typedef typename K::Circle_2  Circle_2;
  public:
    typedef Point_2          result_type;
    typedef Arity_tag< 1 >   Arity;

    const Point_2 &
    operator()(const Circle_2& c) const
    { return c.rep().center(); }
  };

  template <typename K>
  class Construct_center_3 : Has_qrt
  {
    typedef typename K::Point_3   Point_3;
    typedef typename K::Sphere_3  Sphere_3;
  public:
    typedef Point_3          result_type;
    typedef Arity_tag< 1 >   Arity;

    const Point_3 &
    operator()(const Sphere_3& s) const
    { return s.rep().center(); }
  };

  template <typename K>
  class Construct_circle_2
  {
    typedef typename K::FT          FT;
    typedef typename K::Point_2     Point_2;
    typedef typename K::Circle_2    Circle_2;
    typedef typename Circle_2::Rep  Rep;
  public:
    typedef Circle_2         result_type;
    typedef Arity_tag< 3 >   Arity;

    Rep // Circle_2
    operator()( Return_base_tag,
                const Point_2& center, const FT& squared_radius,
	        Orientation orientation = COUNTERCLOCKWISE) const
    { return Rep(center, squared_radius, orientation); }

    Rep // Circle_2
    operator()( Return_base_tag,
                const Point_2& p, const Point_2& q, const Point_2& r) const
    {
      typename K::Orientation_2 orientation;
      typename K::Compute_squared_distance_2 squared_distance;
      typename K::Construct_circumcenter_2 circumcenter;
      Orientation orient = orientation(p, q, r);
      CGAL_kernel_precondition( orient != COLLINEAR);

      Point_2 center = circumcenter(p, q, r);

      return Rep(center, squared_distance(p, center), orient);
    }

    Rep // Circle_2
    operator()( Return_base_tag,
                const Point_2& p, const Point_2& q,
	        Orientation orientation = COUNTERCLOCKWISE) const
    {
      CGAL_kernel_precondition( orientation != COLLINEAR);

      typename K::Compute_squared_distance_2 squared_distance;
      typename K::Construct_midpoint_2 midpoint;
      if (p != q) {
        Point_2 center = midpoint(p, q);
        return Rep(center, squared_distance(p, center), orientation);
      } else
        return Rep(p, FT(0), orientation);
    }

    Rep // Circle_2
    operator()( Return_base_tag,
                const Point_2& p, const Point_2& q,
	        const FT& bulge) const
    {
     
      typename K::Compute_squared_distance_2 squared_distance;
      const FT sqr_bulge = CGAL::square(bulge);
      const FT common = (FT(1) - sqr_bulge) / (FT(4)*bulge);
      const FT x_coord = (p.x() + q.x())/FT(2)
	                 + common*(p.y() - q.y());
      const FT y_coord = (p.y() + q.y())/FT(2)
                          + common*(q.x() - p.x());
      
      const FT sqr_rad = squared_distance(p, q) 
	                 * (FT(1)/sqr_bulge + FT(2) + sqr_bulge) / FT(16); 

      return Rep(Point_2(x_coord, y_coord), sqr_rad); 
    }


    Rep // Circle_2
    operator()( Return_base_tag, const Point_2& center,
	        Orientation orientation = COUNTERCLOCKWISE) const
    {
      CGAL_kernel_precondition( orientation != COLLINEAR );

      return Rep(center, FT(0), orientation);
    }


    Circle_2
    operator()( const Point_2& center, const FT& squared_radius,
	        Orientation orientation = COUNTERCLOCKWISE) const
    {
      return this->operator()(Return_base_tag(),
                              center, squared_radius, orientation);
    }

    Circle_2
    operator()( const Point_2& p, const Point_2& q, const Point_2& r) const
    {
      return this->operator()(Return_base_tag(), p, q, r);
    }

    Circle_2
    operator()( const Point_2& p, const Point_2& q,
	        Orientation orientation = COUNTERCLOCKWISE) const
    {
      return this->operator()(Return_base_tag(), p, q, orientation);
    }

    Circle_2
    operator()( const Point_2& p, const Point_2& q,
	        const FT& bulge) const
    {
      return this->operator()(Return_base_tag(), p, q, bulge);
    }

    Circle_2
    operator()( const Point_2& center,
	        Orientation orientation = COUNTERCLOCKWISE) const
    {
      return this->operator()(Return_base_tag(), center, orientation);
    }
  };

  template <typename K>
  class Construct_iso_cuboid_3
  {
    typedef typename K::RT            RT;
    typedef typename K::Point_3       Point_3;
    typedef typename K::Iso_cuboid_3  Iso_cuboid_3;
    typedef typename Iso_cuboid_3::Rep  Rep;
  public:
    typedef Iso_cuboid_3      result_type;
    typedef Arity_tag< 2 >    Arity;

    Rep // Iso_cuboid_3
    operator()(Return_base_tag, const Point_3& p, const Point_3& q, int) const
    { return Rep(p, q, 0); }

    Rep // Iso_cuboid_3
    operator()(Return_base_tag, const Point_3& p, const Point_3& q) const
    { return Rep(p, q); }

    Rep // Iso_cuboid_3
    operator()(Return_base_tag, const Point_3 &left,   const Point_3 &right,
               const Point_3 &bottom, const Point_3 &top,
               const Point_3 &far_,   const Point_3 &close) const
    { return Rep(left, right, bottom, top, far_, close); }

    Rep // Iso_cuboid_3
    operator()(Return_base_tag, const RT& min_hx, const RT& min_hy, const RT& min_hz,
               const RT& max_hx, const RT& max_hy, const RT& max_hz,
               const RT& hw) const
    { return Rep(min_hx, min_hy, min_hz, max_hx, max_hy, max_hz, hw); }

    Rep // Iso_cuboid_3
    operator()(Return_base_tag, const RT& min_hx, const RT& min_hy, const RT& min_hz,
               const RT& max_hx, const RT& max_hy, const RT& max_hz) const
    { return Rep(min_hx, min_hy, min_hz, max_hx, max_hy, max_hz); }


    Iso_cuboid_3
    operator()(const Point_3& p, const Point_3& q, int) const
    { return this->operator()(Return_base_tag(), p, q, 0); }

    Iso_cuboid_3
    operator()(const Point_3& p, const Point_3& q) const
    { return this->operator()(Return_base_tag(), p, q); }

    Iso_cuboid_3
    operator()(const Point_3 &left,   const Point_3 &right,
               const Point_3 &bottom, const Point_3 &top,
               const Point_3 &far_,   const Point_3 &close) const
    { return this->operator()(Return_base_tag(), left, right, bottom, top, far_, close); }

    Iso_cuboid_3
    operator()(const RT& min_hx, const RT& min_hy, const RT& min_hz,
               const RT& max_hx, const RT& max_hy, const RT& max_hz,
               const RT& hw) const
    { return this->operator()(Return_base_tag(), min_hx, min_hy, min_hz, max_hx, max_hy, max_hz, hw); }

    Iso_cuboid_3
    operator()(const RT& min_hx, const RT& min_hy, const RT& min_hz,
               const RT& max_hx, const RT& max_hy, const RT& max_hz) const
    { return this->operator()(Return_base_tag(), min_hx, min_hy, min_hz, max_hx, max_hy, max_hz); }
  };

  template <typename K>
  class Construct_max_vertex_2 : Has_qrt
  {
    typedef typename K::Point_2          Point_2;
    typedef typename K::Segment_2        Segment_2;
    typedef typename K::Iso_rectangle_2  Iso_rectangle_2;
  public:
    typedef Point_2           result_type;
    typedef Arity_tag< 1 >    Arity;

    const Point_2&
    operator()(const Iso_rectangle_2& r) const
    { return (r.rep().max)(); }

    const Point_2&
    operator()(const Segment_2& s) const
    { return (s.max)(); }
  };


  template <typename K>
  class Construct_min_vertex_2 : Has_qrt
  {
    typedef typename K::Point_2          Point_2;
    typedef typename K::Segment_2        Segment_2;
    typedef typename K::Iso_rectangle_2  Iso_rectangle_2;
  public:
    typedef Point_2           result_type;
    typedef Arity_tag< 1 >    Arity;

    const Point_2&
    operator()(const Iso_rectangle_2& r) const
    { return (r.rep().min)(); }

    const Point_2&
    operator()(const Segment_2& s) const
    { return (s.min)(); }
  };



  template <typename K>
  class Construct_max_vertex_3
  {
    typedef typename K::Point_3          Point_3;
    typedef typename K::Segment_3        Segment_3;
    typedef typename K::Iso_cuboid_3     Iso_cuboid_3;
  public:
    typedef Point_3           result_type;
    typedef Arity_tag< 1 >    Arity;

    Point_3
    operator()(const Iso_cuboid_3& r) const
    { return (r.rep().max)(); }

    const Point_3&
    operator()(const Segment_3& s) const
    { return (s.rep().max)(); }
  };

  template <typename K>
  class Construct_min_vertex_3
  {
    typedef typename K::Point_3          Point_3;
    typedef typename K::Segment_3        Segment_3;
    typedef typename K::Iso_cuboid_3     Iso_cuboid_3;
  public:
    typedef Point_3           result_type;
    typedef Arity_tag< 1 >    Arity;

    Point_3
    operator()(const Iso_cuboid_3& r) const
    { return (r.rep().min)(); }

    const Point_3&
    operator()(const Segment_3& s) const
    { return (s.rep().min)(); }
  };


  template <typename K>
  class Construct_object_2
  {
    typedef typename K::Object_2   Object_2;
  public:
    typedef Object_2         result_type;
    typedef Arity_tag< 1 >   Arity;

    template <class Cls>
    Object_2
    operator()( const Cls& c) const
    { return make_object(c); }
  };

  template <typename K>
  class Construct_object_3
  {
    typedef typename K::Object_3   Object_3;
  public:
    typedef Object_3         result_type;
    typedef Arity_tag< 1 >   Arity;

    template <class Cls>
    Object_3
    operator()( const Cls& c) const
    { return make_object(c); }
  };

  template <typename K>