function_objects.h

很多二维 三维几何计算算法 C++ 类库

    result_type
    operator()(const Circle_2& c1, const Circle_2& c2) const
    {
      return c1.center() == c2.center() &&
	c1.squared_radius() == c2.squared_radius() &&
	c1.orientation() == c2.orientation();
    }

    result_type
    operator()(const Triangle_2& t1, const Triangle_2& t2) const
    {
      int i;
      for(i=0; i<3; i++)
	if ( t1.vertex(0) == t2.vertex(i) )
	  break;

      return (i<3) && t1.vertex(1) == t2.vertex(i+1)
                   && t1.vertex(2) == t2.vertex(i+2);
    }

    result_type
    operator()(const Iso_rectangle_2& i1, const Iso_rectangle_2& i2) const
    {
      return ((i1.min)() == (i2.min)()) && ((i1.max)() == (i2.max)());
    }
  };

  template <typename K>
  class Equal_3
  {
    typedef typename K::Point_3       Point_3;
    typedef typename K::Vector_3      Vector_3;
    typedef typename K::Direction_3   Direction_3;
    typedef typename K::Segment_3     Segment_3;
    typedef typename K::Line_3        Line_3;
    typedef typename K::Ray_3         Ray_3;
    typedef typename K::Triangle_3    Triangle_3;
    typedef typename K::Tetrahedron_3 Tetrahedron_3;
    typedef typename K::Sphere_3      Sphere_3;
    typedef typename K::Iso_cuboid_3  Iso_cuboid_3;
    typedef typename K::Plane_3       Plane_3;

  public:
    typedef typename K::Bool_type     result_type;
    typedef Arity_tag< 2 >            Arity;

    // Point_3 is special case since the global operator== would recurse.
    result_type
    operator()(const Point_3 &p, const Point_3 &q) const
    {
      return p.x() == q.x() && p.y() == q.y() && p.z() == q.z();
    }

    result_type
    operator()(const Plane_3 &v1, const Plane_3 &v2) const
    {
      return v1.rep() == v2.rep();
    }

    result_type
    operator()(const Iso_cuboid_3 &v1, const Iso_cuboid_3 &v2) const
    {
      return v1.rep() == v2.rep();
    }

    result_type
    operator()(const Sphere_3 &v1, const Sphere_3 &v2) const
    {
      return v1.rep() == v2.rep();
    }

    result_type
    operator()(const Tetrahedron_3 &v1, const Tetrahedron_3 &v2) const
    {
      return v1.rep() == v2.rep();
    }

    result_type
    operator()(const Triangle_3 &v1, const Triangle_3 &v2) const
    {
      return v1.rep() == v2.rep();
    }

    result_type
    operator()(const Ray_3 &v1, const Ray_3 &v2) const
    {
      return v1.rep() == v2.rep();
    }

    result_type
    operator()(const Line_3 &v1, const Line_3 &v2) const
    {
      return v1.rep() == v2.rep();
    }

    result_type
    operator()(const Direction_3 &v1, const Direction_3 &v2) const
    {
      return v1.rep() == v2.rep();
    }

    result_type
    operator()(const Segment_3 &v1, const Segment_3 &v2) const
    {
      return v1.rep() == v2.rep();
    }

    result_type
    operator()(const Vector_3 &v1, const Vector_3 &v2) const
    {
      return v1.rep() == v2.rep();
    }

    result_type
    operator()(const Vector_3 &v, const Null_vector &n) const
    {
      return v.rep() == n;
    }
  };

  template <typename K>
  class Has_on_boundary_2
  {
    typedef typename K::Point_2          Point_2;
    typedef typename K::Iso_rectangle_2  Iso_rectangle_2;
    typedef typename K::Circle_2         Circle_2;
    typedef typename K::Triangle_2       Triangle_2;
  public:
    typedef typename K::Bool_type        result_type;
    typedef Arity_tag< 2 >               Arity;

    result_type
    operator()( const Circle_2& c, const Point_2& p) const
    { return c.has_on_boundary(p); }

    result_type
    operator()( const Triangle_2& t, const Point_2& p) const
    { return t.has_on_boundary(p); }

    result_type
    operator()( const Iso_rectangle_2& r, const Point_2& p) const
    { return K().bounded_side_2_object()(r,p) == ON_BOUNDARY; }
  };

  template <typename K>
  class Has_on_boundary_3
  {
    typedef typename K::Point_3          Point_3;
    typedef typename K::Iso_cuboid_3     Iso_cuboid_3;
    typedef typename K::Sphere_3         Sphere_3;
    typedef typename K::Tetrahedron_3    Tetrahedron_3;
    typedef typename K::Plane_3          Plane_3;
  public:
    typedef typename K::Bool_type        result_type;
    typedef Arity_tag< 2 >               Arity;

    result_type
    operator()( const Sphere_3& s, const Point_3& p) const
    { return s.rep().has_on_boundary(p); }

    result_type
    operator()( const Tetrahedron_3& t, const Point_3& p) const
    { return t.rep().has_on_boundary(p); }

    result_type
    operator()( const Iso_cuboid_3& c, const Point_3& p) const
    { return c.rep().has_on_boundary(p); }
  };

  template <typename K>
  class Has_on_bounded_side_2
  {
    typedef typename K::Point_2          Point_2;
    typedef typename K::Iso_rectangle_2  Iso_rectangle_2;
    typedef typename K::Circle_2         Circle_2;
    typedef typename K::Triangle_2       Triangle_2;
  public:
    typedef typename K::Bool_type        result_type;
    typedef Arity_tag< 2 >               Arity;

    result_type
    operator()( const Circle_2& c, const Point_2& p) const
    { return c.has_on_bounded_side(p); }

    result_type
    operator()( const Triangle_2& t, const Point_2& p) const
    { return t.has_on_bounded_side(p); }

    result_type
    operator()( const Iso_rectangle_2& r, const Point_2& p) const
    { return K().bounded_side_2_object()(r,p) == ON_BOUNDED_SIDE; }
  };

  template <typename K>
  class Has_on_bounded_side_3
  {
    typedef typename K::Point_3          Point_3;
    typedef typename K::Iso_cuboid_3     Iso_cuboid_3;
    typedef typename K::Sphere_3         Sphere_3;
    typedef typename K::Tetrahedron_3    Tetrahedron_3;
  public:
    typedef typename K::Bool_type        result_type;
    typedef Arity_tag< 2 >               Arity;

    result_type
    operator()( const Sphere_3& s, const Point_3& p) const
    { return s.has_on_bounded_side(p); }

    result_type
    operator()( const Tetrahedron_3& t, const Point_3& p) const
    { return t.rep().has_on_bounded_side(p); }

    result_type
    operator()( const Iso_cuboid_3& c, const Point_3& p) const
    { return c.rep().has_on_bounded_side(p); }
  };

  template <typename K>
  class Has_on_negative_side_2
  {
    typedef typename K::Point_2          Point_2;
    typedef typename K::Line_2           Line_2;
    typedef typename K::Circle_2         Circle_2;
    typedef typename K::Triangle_2       Triangle_2;
  public:
    typedef typename K::Bool_type        result_type;
    typedef Arity_tag< 2 >               Arity;

    result_type
    operator()( const Circle_2& c, const Point_2& p) const
    { return c.has_on_negative_side(p); }

    result_type
    operator()( const Triangle_2& t, const Point_2& p) const
    { return t.has_on_negative_side(p); }

    result_type
    operator()( const Line_2& l, const Point_2& p) const
    { return l.has_on_negative_side(p); }
  };

  template <typename K>
  class Has_on_negative_side_3
  {
    typedef typename K::Point_3          Point_3;
    typedef typename K::Plane_3          Plane_3;
    typedef typename K::Sphere_3         Sphere_3;
    typedef typename K::Tetrahedron_3    Tetrahedron_3;
  public:
    typedef typename K::Bool_type        result_type;
    typedef Arity_tag< 2 >               Arity;

    result_type
    operator()( const Sphere_3& s, const Point_3& p) const
    { return s.has_on_negative_side(p); }

    result_type
    operator()( const Tetrahedron_3& t, const Point_3& p) const
    { return t.rep().has_on_negative_side(p); }

    result_type
    operator()( const Plane_3& pl, const Point_3& p) const
    { return pl.rep().has_on_negative_side(p); }
  };

  template <typename K>
  class Has_on_positive_side_2
  {
    typedef typename K::Point_2          Point_2;
    typedef typename K::Line_2           Line_2;
    typedef typename K::Circle_2         Circle_2;
    typedef typename K::Triangle_2       Triangle_2;
  public:
    typedef typename K::Bool_type        result_type;
    typedef Arity_tag< 2 >               Arity;

    result_type
    operator()( const Circle_2& c, const Point_2& p) const
    { return c.has_on_positive_side(p); }

    result_type
    operator()( const Triangle_2& t, const Point_2& p) const
    { return t.has_on_positive_side(p); }

    result_type
    operator()( const Line_2& l, const Point_2& p) const
    { return l.has_on_positive_side(p); }
  };

  template <typename K>
  class Has_on_positive_side_3
  {
    typedef typename K::Point_3          Point_3;
    typedef typename K::Plane_3          Plane_3;
    typedef typename K::Sphere_3         Sphere_3;
    typedef typename K::Tetrahedron_3    Tetrahedron_3;
  public:
    typedef typename K::Bool_type        result_type;
    typedef Arity_tag< 2 >               Arity;

    result_type
    operator()( const Sphere_3& s, const Point_3& p) const
    { return s.has_on_positive_side(p); }

    result_type
    operator()( const Tetrahedron_3& t, const Point_3& p) const
    { return t.rep().has_on_positive_side(p); }

    result_type
    operator()( const Plane_3& pl, const Point_3& p) const
    { return pl.rep().has_on_positive_side(p); }
  };

  template <typename K>
  class Has_on_unbounded_side_2
  {
    typedef typename K::Point_2          Point_2;
    typedef typename K::Iso_rectangle_2  Iso_rectangle_2;
    typedef typename K::Circle_2         Circle_2;
    typedef typename K::Triangle_2       Triangle_2;
  public:
    typedef typename K::Bool_type        result_type;
    typedef Arity_tag< 2 >               Arity;

    result_type
    operator()( const Circle_2& c, const Point_2& p) const
    { return c.has_on_unbounded_side(p); }

    result_type
    operator()( const Triangle_2& t, const Point_2& p) const
    { return t.has_on_unbounded_side(p); }

    result_type
    operator()( const Iso_rectangle_2& r, const Point_2& p) const
    {
      return K().bounded_side_2_object()(r,p)== ON_UNBOUNDED_SIDE;
    }
  };

  template <typename K>
  class Has_on_unbounded_side_3
  {
    typedef typename K::Point_3          Point_3;
    typedef typename K::Iso_cuboid_3     Iso_cuboid_3;
    typedef typename K::Sphere_3         Sphere_3;
    typedef typename K::Tetrahedron_3    Tetrahedron_3;
  public:
    typedef typename K::Bool_type        result_type;
    typedef Arity_tag< 2 >               Arity;

    result_type
    operator()( const Sphere_3& s, const Point_3& p) const
    { return s.has_on_unbounded_side(p); }

    result_type
    operator()( const Tetrahedron_3& t, const Point_3& p) const
    { return t.rep().has_on_unbounded_side(p); }

    result_type
    operator()( const Iso_cuboid_3& c, const Point_3& p) const
    { return c.rep().has_on_unbounded_side(p); }
  };

  template <typename K>
  class Has_on_2
  {
    typedef typename K::Point_2          Point_2;
    typedef typename K::Line_2           Line_2;
    typedef typename K::Ray_2            Ray_2;
    typedef typename K::Segment_2        Segment_2;
  public:
    typedef typename K::Bool_type        result_type;
    typedef Arity_tag< 2 >               Arity;

    result_type
    operator()( const Line_2& l, const Point_2& p) const
    { return l.has_on(p); }

    result_type
    operator()( const Ray_2& r, const Point_2& p) const
    { return r.has_on(p); }

    result_type
    operator()( const Segment_2& s, const Point_2& p) const
    { return s.has_on(p); }
  };

  template <typename K>
  class Intersect_2
  {
    typedef typename K::Object_2    Object_2;
  public:
    typedef Object_2                result_type;
    typedef Arity_tag< 2 >          Arity;

    // 25 possibilities, so I keep the template.
    template <class T1, class T2>
    Object_2
    operator()(const T1& t1, const T2& t2) const
    { return CGALi::intersection(t1, t2, K()); }
  };

  template <typename K>
  class Intersect_3
  {
    typedef typename K::Object_3    Object_3;
    typedef typename K::Plane_3     Plane_3;
  public:
    typedef Object_3                result_type;
    typedef Arity_tag< 2 >          Arity;

    // n possibilities, so I keep the template.
    template <class T1, class T2>
    Object_3
    operator()(const T1& t1, const T2& t2) const
    { return CGALi::intersection(t1, t2, K() ); }

    Object_3
    operator()(const Plane_3& pl1, const Plane_3& pl2, const Plane_3& pl3)const
    { return CGALi::intersection(pl1, pl2, pl3, K() ); }
  };

  template <typename K>
  class Is_degenerate_2
  {
    typedef typename K::Circle_2          Circle_2;
    typedef typename K::Iso_rectangle_2   Iso_rectangle_2;
    typedef typename K::Line_2            Line_2;
    typedef typename K::Ray_2             Ray_2;
    typedef typename K::Segment_2         Segment_2;
    typedef typename K::Triangle_2        Triangle_2;
  public:
    typedef typename K::Bool_type         result_type;
    typedef Arity_tag< 1 >                Arity;

    result_type
    operator()( const Circle_2& c) const
    { return c.is_degenerate(); }

    result_type
    operator()( const Iso_rectangle_2& r) const
    { return (r.xmin() == r.xmax()) || (r.ymin() == r.ymax()); }

    result_type
    operator()( const Line_2& l) const
    { return CGAL_NTS is_zero(l.a())  && CGAL_NTS is_zero(l.b()); }

    result_type
    operator()( const Ray_2& r) const
    { return r.rep().is_degenerate(); }

    result_type
    operator()( const Segment_2& s) const
    { return s.source() == s.target(); }

    result_type
    operator()( const Triangle_2& t) const
    { return t.is_degenerate(); }
  };

  template <typename K>
  class Is_degenerate_3
  {
    typedef typename K::Iso_cuboid_3      Iso_cuboid_3;
    typedef typename K::Line_3            Line_3;
    typedef typename K::Plane_3           Plane_3;
    typedef typename K::Ray_3             Ray_3;
    typedef typename K::Segment_3         Segment_3;
    typedef typename K::Sphere_3          Sphere_3;
    typedef typename K::Triangle_3        Triang