function_objects.h

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// Copyright (c) 1999-2004  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.
//
// $Source: /CVSROOT/CGAL/Packages/Cartesian_kernel/include/CGAL/Cartesian/function_objects.h,v $
// $Revision: 1.41 $ $Date: 2004/06/23 03:33:16 $
// $Name:  $
//
// Author(s)     : Stefan Schirra, Sylvain Pion, Michael Hoffmann

#ifndef CGAL_CARTESIAN_FUNCTION_OBJECTS_H
#define CGAL_CARTESIAN_FUNCTION_OBJECTS_H

#include <CGAL/Kernel/function_objects.h>
#include <CGAL/predicates/kernel_ftC2.h>
#include <CGAL/predicates/kernel_ftC3.h>
#include <CGAL/constructions/kernel_ftC2.h>
#include <CGAL/constructions/kernel_ftC3.h>
#include <CGAL/Cartesian/solve_3.h>

CGAL_BEGIN_NAMESPACE

namespace CartesianKernelFunctors {

  using namespace CommonKernelFunctors;

  template <typename K>
  class Angle_2
  {
    typedef typename K::Point_2 Point_2;
  public:
    typedef Angle            result_type;
    typedef Arity_tag< 3 >   Arity;

    Angle
    operator()(const Point_2& p, const Point_2& q, const Point_2& r) const
    { return angleC2(p.x(), p.y(), q.x(), q.y(), r.x(), r.y()); }
  };

  template <typename K>
  class Angle_3
  {
    typedef typename K::Point_3 Point_3;
  public:
    typedef Angle            result_type;
    typedef Arity_tag< 3 >   Arity;

    Angle
    operator()(const Point_3& p, const Point_3& q, const Point_3& r) const
    { 
      return angleC3(p.x(), p.y(), p.z(),
		     q.x(), q.y(), q.z(),
		     r.x(), r.y(), r.z());
    }
  };

  template <typename K>
  class Are_parallel_2
  {
    typedef typename K::Line_2          Line_2;
    typedef typename K::Segment_2       Segment_2;
    typedef typename K::Ray_2           Ray_2;
  
  public:
    typedef bool             result_type;
    typedef Arity_tag< 2 >   Arity;

    bool
    operator()(const Line_2& l1, const Line_2& l2) const
    { return parallelC2(l1.a(), l1.b(), l2.a(), l2.b()); }

    bool
    operator()(const Segment_2& s1, const Segment_2& s2) const
    { return parallelC2(s1.source().x(), s1.source().y(),
                        s1.target().x(), s1.target().y(),
                        s2.source().x(), s2.source().y(),
                        s2.target().x(), s2.target().y());
    }

    bool
    operator()(const Ray_2& r1, const Ray_2& r2) const
    { return parallelC2(r1.source().x(), r1.source().y(),
                        r1.second_point().x(), r1.second_point().y(),
                        r2.source().x(), r2.source().y(),
                        r2.second_point().x(), r2.second_point().y());
    }
  };

  template <typename K>
  class Are_parallel_3
  {
    typedef typename K::Line_3          Line_3;
    typedef typename K::Segment_3       Segment_3;
    typedef typename K::Ray_3           Ray_3;
    typedef typename K::Plane_3         Plane_3;
  
  public:
    typedef bool             result_type;
    typedef Arity_tag< 2 >   Arity;

    bool
    operator()(const Line_3& l1, const Line_3& l2) const
    { return parallelC3(
                l1.to_vector().x(), l1.to_vector().y(), l1.to_vector().z(),
                l2.to_vector().x(), l2.to_vector().y(), l2.to_vector().z());
    }

    bool
    operator()(const Plane_3& h1, const Plane_3& h2) const
    { return parallelC3(h1.a(), h1.b(), h1.c(),
                        h2.a(), h2.b(), h2.c());
    }

    bool
    operator()(const Segment_3& s1, const Segment_3& s2) const
    { return parallelC3(s1.source().x(), s1.source().y(), s1.source().z(),
                        s1.target().x(), s1.target().y(), s1.target().z(),
                        s2.source().x(), s2.source().y(), s2.source().z(),
                        s2.target().x(), s2.target().y(), s2.target().z());
    }

    bool
    operator()(const Ray_3& r1, const Ray_3& r2) const
    { return parallelC3(r1.source().x(), r1.source().y(), r1.source().z(),
	r1.second_point().x(), r1.second_point().y(), r1.second_point().z(),
                        r2.source().x(), r2.source().y(), r2.source().z(),
	r2.second_point().x(), r2.second_point().y(), r2.second_point().z());
    }
  };

  template <typename K>
  class Bounded_side_3
  {
    typedef typename K::FT              FT;
    typedef typename K::Point_3         Point_3;
    typedef typename K::Sphere_3        Sphere_3;
    typedef typename K::Tetrahedron_3   Tetrahedron_3;
    typedef typename K::Iso_cuboid_3    Iso_cuboid_3;
  public:
    typedef Bounded_side     result_type;
    typedef Arity_tag< 2 >   Arity;

    Bounded_side
    operator()( const Sphere_3& s, const Point_3& p) const
    { return s.bounded_side(p); }

    Bounded_side
    operator()( const Tetrahedron_3& t, const Point_3& p) const
    {
      FT alpha, beta, gamma;

      solve(t.vertex(1)-t.vertex(0),
            t.vertex(2)-t.vertex(0),
            t.vertex(3)-t.vertex(0),
            p - t.vertex(0), alpha, beta, gamma);
      if (   (alpha < 0) || (beta < 0) || (gamma < 0)
          || (alpha + beta + gamma > 1) )
          return ON_UNBOUNDED_SIDE;

      if (   (alpha == 0) || (beta == 0) || (gamma == 0)
          || (alpha+beta+gamma == 1) )
        return ON_BOUNDARY;

      return ON_BOUNDED_SIDE;
    }

    Bounded_side
    operator()( const Iso_cuboid_3& c, const Point_3& p) const
    { return c.bounded_side(p); }
  };

  template <typename K>
  class Collinear_are_ordered_along_line_2
  {
    typedef typename K::Point_2         Point_2;
#ifdef CGAL_kernel_exactness_preconditions 
    typedef typename K::Collinear_2 Collinear_2;
    Collinear_2 c;
#endif // CGAL_kernel_exactness_preconditions 
  public:
    typedef bool             result_type;
    typedef Arity_tag< 3 >   Arity;

#ifdef CGAL_kernel_exactness_preconditions 
    Collinear_are_ordered_along_line_2() {}
    Collinear_are_ordered_along_line_2(const Collinear_2& c_) : c(c_) {}
#endif // CGAL_kernel_exactness_preconditions 

    bool
    operator()(const Point_2& p, const Point_2& q, const Point_2& r) const
    {
      CGAL_kernel_exactness_precondition( c(p, q, r) );
      return collinear_are_ordered_along_lineC2
	(p.x(), p.y(), q.x(), q.y(), r.x(), r.y());
    }
  };

  template <typename K>
  class Collinear_are_ordered_along_line_3
  {
    typedef typename K::Point_3         Point_3;
#ifdef CGAL_kernel_exactness_preconditions 
    typedef typename K::Collinear_3 Collinear_3;
    Collinear_3 c;
#endif // CGAL_kernel_exactness_preconditions 
  public:
    typedef bool             result_type;
    typedef Arity_tag< 3 >   Arity;

#ifdef CGAL_kernel_exactness_preconditions 
    Collinear_are_ordered_along_line_3() {}
    Collinear_are_ordered_along_line_3(const Collinear_3& c_) : c(c_) {}
#endif // CGAL_kernel_exactness_preconditions 

    bool
    operator()(const Point_3& p, const Point_3& q, const Point_3& r) const
    {
      CGAL_kernel_exactness_precondition( c(p, q, r) );
      return collinear_are_ordered_along_lineC3(p.x(), p.y(), p.z(),
						q.x(), q.y(), q.z(),
						r.x(), r.y(), r.z());
    }  
  };

  template <typename K>
  class Collinear_are_strictly_ordered_along_line_2
  {
    typedef typename K::Point_2         Point_2;
#ifdef CGAL_kernel_exactness_preconditions 
    typedef typename K::Collinear_2 Collinear_2;
    Collinear_2 c;
#endif // CGAL_kernel_exactness_preconditions 
  public:
    typedef bool             result_type;
    typedef Arity_tag< 3 >   Arity;

#ifdef CGAL_kernel_exactness_preconditions 
    Collinear_are_strictly_ordered_along_line_2() {}
    Collinear_are_strictly_ordered_along_line_2(const Collinear_2& c_) : c(c_) 
    {}
#endif // CGAL_kernel_exactness_preconditions 

    bool
    operator()(const Point_2& p, const Point_2& q, const Point_2& r) const
    {
      CGAL_kernel_exactness_precondition( c(p, q, r) );
      return collinear_are_strictly_ordered_along_lineC2
	(p.x(), p.y(), q.x(), q.y(), r.x(), r.y());
    }
  };

  template <typename K>
  class Collinear_are_strictly_ordered_along_line_3
  {
    typedef typename K::Point_3         Point_3;
#ifdef CGAL_kernel_exactness_preconditions 
    typedef typename K::Collinear_3 Collinear_3;
    Collinear_3 c;
#endif // CGAL_kernel_exactness_preconditions 
  public:
    typedef bool             result_type;
    typedef Arity_tag< 3 >   Arity;

#ifdef CGAL_kernel_exactness_preconditions 
    Collinear_are_strictly_ordered_along_line_3() {}
    Collinear_are_strictly_ordered_along_line_3(const Collinear_3& c_) : c(c_)
    {}
#endif // CGAL_kernel_exactness_preconditions 

    bool
    operator()(const Point_3& p, const Point_3& q, const Point_3& r) const
    {
      CGAL_kernel_exactness_precondition( c(p, q, r) );
      return collinear_are_strictly_ordered_along_lineC3(p.x(), p.y(), p.z(),
							 q.x(), q.y(), q.z(),
							 r.x(), r.y(), r.z());
    }  
  };

  template <typename K>
  class Collinear_has_on_2
  {
    typedef typename K::Point_2               Point_2;
    typedef typename K::Ray_2                 Ray_2;
    typedef typename K::Segment_2             Segment_2;
    typedef typename K::Construct_point_on_2  Construct_point_on_2;
    typedef typename K::Compare_x_2           Compare_x_2;
    typedef typename K::Compare_y_2           Compare_y_2;
    typedef typename K::Collinear_are_ordered_along_line_2  
    Collinear_are_ordered_along_line_2;
    Construct_point_on_2 cp;
    Compare_x_2 cx;
    Compare_y_2 cy;
    Collinear_are_ordered_along_line_2 co;
  public:
    typedef bool             result_type;
    typedef Arity_tag< 2 >   Arity;

    Collinear_has_on_2() {}
    Collinear_has_on_2(const Construct_point_on_2& cp_,
		       const Compare_x_2& cx_,
		       const Compare_y_2& cy_,
		       const Collinear_are_ordered_along_line_2& co_) 
      : cp(cp_), cx(cx_), cy(cy_), co(co_)
    {}

    bool
    operator()( const Ray_2& r, const Point_2& p) const
    {
      Point_2 source = cp(r,0);      
      Point_2 second = cp(r,1);
      switch(cx(source, second)) {
      case SMALLER:
        return cx(source, p) != LARGER;
      case LARGER:
        return cx(p, source) != LARGER;
      default:
        switch(cy(source, second)){
        case SMALLER:
	  return cy(source, p) != LARGER;
        case LARGER:
	  return cy(p, source) != LARGER;
        default:
	  return true; // p == source
        }
      } // switch
    }
  
    bool
    operator()( const Segment_2& s, const Point_2& p) const
    { 
      return co(cp(s,0), p, cp(s,1));
    }
  };

  template <typename K>
  class Collinear_2
  {
    typedef typename K::Point_2        Point_2;
    typedef typename K::Orientation_2  Orientation_2;
    Orientation_2 o;
  public:
    typedef bool             result_type;
    typedef Arity_tag< 3 >   Arity;

    Collinear_2() {}
    Collinear_2(const Orientation_2 o_) : o(o_) {}

    bool
    operator()(const Point_2& p, const Point_2& q, const Point_2& r) const
    { return o(p, q, r) == COLLINEAR; }
  };

  template <typename K>
  class Collinear_3
  {
    typedef typename K::Point_3    Point_3;
  public:
    typedef bool             result_type;
    typedef Arity_tag< 3 >   Arity;

    bool
    operator()(const Point_3& p, const Point_3& q, const Point_3& r) const
    {
      return collinearC3(p.x(), p.y(), p.z(),
			 q.x(), q.y(), q.z(),
			 r.x(), r.y(), r.z());
    }
  };

  template <typename K>
  class Compare_angle_with_x_axis_2
  {
    typedef typename K::Direction_2  Direction_2;
  public:
    typedef Comparison_result        result_type;
    typedef Arity_tag< 2 >           Arity;

    Comparison_result
    operator()(const Direction_2& d1, const Direction_2& d2) const
    {
      return compare_angle_with_x_axisC2(d1.dx(), d1.dy(), d2.dx(), d2.dy());
    }
  };

  template <typename K>
  class Compare_distance_2
  {
    typedef typename K::Point_2   Point_2;
  public:
    typedef Comparison_result     result_type;
    typedef Arity_tag< 3 >        Arity;

    Comparison_result
    operator()(const Point_2& p, const Point_2& q, const Point_2& r) const
    {
      return cmp_dist_to_pointC2(p.x(), p.y(), q.x(), q.y(), r.x(), r.y());
    }
  };

  template <typename K>
  class Compare_distance_3
  {
    typedef typename K::Point_3   Point_3;
  public:
    typedef Comparison_result     result_type;
    typedef Arity_tag< 3 >        Arity;

    Comparison_result
    operator()(const Point_3& p, const Point_3& q, const Point_3& r) const
    { 
      return cmp_dist_to_pointC3(p.x(), p.y(), p.z(),
				 q.x(), q.y(), q.z(),
				 r.x(), r.y(), r.z());
    }
  };

  template <typename K>
  class Compare_slope_2
  {
    typedef typename K::Line_2     Line_2;
    typedef typename K::Segment_2  Segment_2;
  public:
    typedef Comparison_result      result_type;
    typedef Arity_tag< 2 >         Arity;

    Comparison_result
    operator()(const Line_2& l1, const Line_2& l2) const
    { 
      return compare_slopesC2(l1.a(), l1.b(), l2.a(), l2.b());
    }

    Comparison_result
    operator()(const Segment_2& s1, const Segment_2& s2) const