function_objects.h

很多二维 三维几何计算算法 C++ 类库

// Copyright (c) 1999,2002,2005  Utrecht University (The Netherlands),
// ETH Zurich (Switzerland), Freie Universitaet Berlin (Germany),
// INRIA Sophia-Antipolis (France), Martin-Luther-University Halle-Wittenberg
// (Germany), Max-Planck-Institute Saarbruecken (Germany), RISC Linz (Austria),
// and Tel-Aviv University (Israel).  All rights reserved.
//
// This file is part of CGAL (www.cgal.org); you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public License as
// published by the Free Software Foundation; version 2.1 of the License.
// See the file LICENSE.LGPL distributed with CGAL.
//
// Licensees holding a valid commercial license may use this file in
// accordance with the commercial license agreement provided with the software.
//
// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
//
// $URL: svn+ssh://scm.gforge.inria.fr/svn/cgal/branches/CGAL-3.3-branch/Kernel_23/include/CGAL/Kernel/function_objects.h $
// $Id: function_objects.h 37195 2007-03-17 09:51:49Z afabri $
//
//
// Author(s)     : Stefan Schirra, Sylvain Pion

#ifndef CGAL_KERNEL_FUNCTION_OBJECTS_H
#define CGAL_KERNEL_FUNCTION_OBJECTS_H

#include <CGAL/functional_base.h>
#include <CGAL/Origin.h>
#include <CGAL/Bbox_2.h>
#include <CGAL/Bbox_3.h>
#include <CGAL/Kernel/Cartesian_coordinate_iterator_2.h>
#include <CGAL/Kernel/Cartesian_coordinate_iterator_3.h>
#include <CGAL/squared_distance_2.h>
#include <CGAL/squared_distance_3.h>
#include <CGAL/intersection_2.h>
#include <CGAL/intersection_3.h>
#include <CGAL/Kernel/Return_base_tag.h>

CGAL_BEGIN_NAMESPACE

namespace CommonKernelFunctors {

  template <typename K>
  class Are_ordered_along_line_2
  {
    typedef typename K::Point_2     Point_2;
    typedef typename K::Collinear_2 Collinear_2;
    typedef typename K::Collinear_are_ordered_along_line_2
    Collinear_are_ordered_along_line_2;

    Collinear_2 c;
    Collinear_are_ordered_along_line_2 cao;
  public:
    typedef typename K::Bool_type   result_type;
    typedef Arity_tag< 3 >          Arity;

    Are_ordered_along_line_2() {}
    Are_ordered_along_line_2(const Collinear_2& c_,
			     const Collinear_are_ordered_along_line_2& cao_)
      : c(c_), cao(cao_)
    {}

    result_type
    operator()(const Point_2& p, const Point_2& q, const Point_2& r) const
    { return c(p, q, r) && cao(p, q, r); }
  };

  template <typename K>
  class Are_ordered_along_line_3
  {
    typedef typename K::Point_3     Point_3;
    typedef typename K::Collinear_3 Collinear_3;
    typedef typename K::Collinear_are_ordered_along_line_3
    Collinear_are_ordered_along_line_3;

    Collinear_3 c;
    Collinear_are_ordered_along_line_3 cao;
  public:
    typedef typename K::Bool_type   result_type;
    typedef Arity_tag< 3 >          Arity;

    Are_ordered_along_line_3() {}
    Are_ordered_along_line_3(const Collinear_3& c_,
			     const Collinear_are_ordered_along_line_3& cao_)
      : c(c_), cao(cao_)
    {}

    result_type
    operator()(const Point_3& p, const Point_3& q, const Point_3& r) const
    { return c(p, q, r) && cao(p, q, r); }
  };

  template <typename K>
  class Are_strictly_ordered_along_line_2
  {
    typedef typename K::Point_2     Point_2;
    typedef typename K::Collinear_2 Collinear_2;
    typedef typename K::Collinear_are_strictly_ordered_along_line_2
    Collinear_are_strictly_ordered_along_line_2;

    Collinear_2 c;
    Collinear_are_strictly_ordered_along_line_2 cao;
  public:
    typedef typename K::Bool_type   result_type;
    typedef Arity_tag< 3 >          Arity;

    Are_strictly_ordered_along_line_2() {}
    Are_strictly_ordered_along_line_2(
				      const Collinear_2& c_,
				      const Collinear_are_strictly_ordered_along_line_2& cao_)
      : c(c_), cao(cao_)
    {}

    result_type
    operator()(const Point_2& p, const Point_2& q, const Point_2& r) const
    { return c(p, q, r) && cao(p, q, r); }
  };

  template <typename K>
  class Are_strictly_ordered_along_line_3
  {
    typedef typename K::Point_3     Point_3;
    typedef typename K::Collinear_3 Collinear_3;
    typedef typename K::Collinear_are_strictly_ordered_along_line_3
    Collinear_are_strictly_ordered_along_line_3;

    Collinear_3 c;
    Collinear_are_strictly_ordered_along_line_3 cao;
  public:
    typedef typename K::Bool_type   result_type;
    typedef Arity_tag< 3 >          Arity;

    Are_strictly_ordered_along_line_3() {}
    Are_strictly_ordered_along_line_3(
				      const Collinear_3& c_,
				      const Collinear_are_strictly_ordered_along_line_3& cao_)
      : c(c_), cao(cao_)
    {}

    result_type
    operator()(const Point_3& p, const Point_3& q, const Point_3& r) const
    { return c(p, q, r) && cao(p, q, r); }
  };

  template <typename K>
  class Assign_2
  {
    typedef typename K::Object_2  Object_2;
  public:
    //typedef typename K::Bool_type result_type;
    typedef bool                  result_type;
    typedef Arity_tag< 2 >        Arity;

    template <class T>
    result_type
    operator()(T& t, const Object_2& o) const
    { return assign(t, o); }
  };

  template <typename K>
  class Assign_3
  {
    typedef typename K::Object_3        Object_3;
  public:
    //typedef typename K::Bool_type       result_type;
    typedef bool                        result_type;
    typedef Arity_tag< 2 >              Arity;

    template <class T>
    result_type
    operator()(T& t, const Object_3& o) const
    { return assign(t, o); }
  };

  template <typename K>
  class Compute_area_3
  {
    typedef typename K::FT                FT;
    typedef typename K::Point_3           Point_3;
    typedef typename K::Triangle_3        Triangle_3;
  public:
    typedef FT               result_type;
    typedef Arity_tag< 1 >   Arity;

    FT
    operator()( const Triangle_3& t ) const
    {
	return CGAL_NTS sqrt(K().compute_squared_area_3_object()(t));
    }

    FT
    operator()( const Point_3& p, const Point_3& q, const Point_3& r ) const
    {
	return CGAL_NTS sqrt(K().compute_squared_area_3_object()(p, q, r));
    }
  };

  template <typename K>
  class Compute_squared_distance_2
  {
    typedef typename K::FT   FT;
  public:
    typedef FT               result_type;
    typedef Arity_tag< 2 >   Arity;

    // There are 25 combinaisons, we use a template.
    template <class T1, class T2>
    FT
    operator()( const T1& t1, const T2& t2) const
    { return CGALi::squared_distance(t1, t2, K()); }
  };

  template <typename K>
  class Compute_squared_distance_3
  {
    typedef typename K::FT        FT;
    typedef typename K::Point_3   Point_3;
  public:
    typedef FT               result_type;
    typedef Arity_tag< 2 >   Arity;

    // There are 25 combinaisons, we use a template.
    template <class T1, class T2>
    FT
    operator()( const T1& t1, const T2& t2) const
    { return CGALi::squared_distance(t1, t2, K()); }

    FT
    operator()( const Point_3& pt1, const Point_3& pt2) const
    {
      typedef typename K::Vector_3 Vector_3;
      Vector_3 vec = pt2 - pt1;
      return vec*vec;
    }
  };

  template <typename K>
  class Compute_squared_length_2
  {
    typedef typename K::FT          FT;
    typedef typename K::Segment_2   Segment_2;
    typedef typename K::Vector_2    Vector_2;
  public:
    typedef FT               result_type;
    typedef Arity_tag< 1 >   Arity;

    FT
    operator()( const Vector_2& v) const
    { return CGAL_NTS square(K().compute_x_2_object()(v)) +
             CGAL_NTS square(K().compute_y_2_object()(v));}

    FT
    operator()( const Segment_2& s) const
    { return K().compute_squared_distance_2_object()(s.source(), s.target()); }
  };

  template <typename K>
  class Compute_squared_length_3
  {
    typedef typename K::FT          FT;
    typedef typename K::Segment_3   Segment_3;
    typedef typename K::Vector_3    Vector_3;
  public:
    typedef FT               result_type;
    typedef Arity_tag< 1 >   Arity;

    FT
    operator()( const Vector_3& v) const
    { return v.rep().squared_length(); }

    FT
    operator()( const Segment_3& s) const
    { return s.squared_length(); }
  };

  template <typename K>
  class Compute_a_2
  {
    typedef typename K::RT             RT;
    typedef typename K::Line_2         Line_2;

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

    RT
    operator()(const Line_2& l) const
    {
      return l.rep().a();
    }
  };

  template <typename K>
  class Compute_a_3
  {
    typedef typename K::RT             RT;
    typedef typename K::Plane_3        Plane_3;

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

    RT
    operator()(const Plane_3& l) const
    {
      return l.rep().a();
    }
  };


  template <typename K>
  class Compute_b_2
  {
    typedef typename K::RT             RT;
    typedef typename K::Line_2         Line_2;

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

    RT
    operator()(const Line_2& l) const
    {
      return l.rep().b();
    }
  };

  template <typename K>
  class Compute_b_3
  {
    typedef typename K::RT             RT;
    typedef typename K::Plane_3        Plane_3;

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

    RT
    operator()(const Plane_3& l) const
    {
      return l.rep().b();
    }
  };


  template <typename K>
  class Compute_c_2
  {
    typedef typename K::RT             RT;
    typedef typename K::Line_2         Line_2;

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

    RT
    operator()(const Line_2& l) const
    {
      return l.rep().c();
    }
  };

  template <typename K>
  class Compute_c_3
  {
    typedef typename K::RT             RT;
    typedef typename K::Plane_3        Plane_3;

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

    RT
    operator()(const Plane_3& l) const
    {
      return l.rep().c();
    }
  };

  template <typename K>
  class Compute_d_3
  {
    typedef typename K::RT             RT;
    typedef typename K::Plane_3        Plane_3;

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

    RT
    operator()(const Plane_3& l) const
    {
      return l.rep().d();
    }
  };

  template <typename K>
  class Compute_x_at_y_2
  {
    typedef typename K::FT             FT;
    typedef typename K::Point_2        Point_2;
    typedef typename K::Line_2         Line_2;

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

    FT
    operator()(const Line_2& l, const FT& y) const
    {
      CGAL_kernel_precondition( ! l.is_degenerate() );
      return (FT(-l.b())*y - FT(l.c()) )/FT(l.a());
    }
  };

  template <typename K>
  class Compute_y_at_x_2
  {
    typedef typename K::FT             FT;
    typedef typename K::Point_2        Point_2;
    typedef typename K::Line_2         Line_2;

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

    FT
    operator()(const Line_2& l, const FT& x) const
    {
      CGAL_kernel_precondition_msg( ! l.is_vertical(),
		    "Compute_y_at_x(FT x) is undefined for vertical line");
      return (FT(-l.a())*x - FT(l.c()) )/FT(l.b());
    }
  };

  template <typename K>
  class Compute_xmin_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)().x();
    }
  };

  template <typename K>
  class Compute_xmin_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)().x();