// Copyright (c) 2003  INRIA Sophia-Antipolis (France).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org); you may redistribute it under
// the terms of the Q Public License version 1.0.
// See the file LICENSE.QPL 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/Interpolation/include/CGAL/surface_neighbor_coordinates_3.h,v $
// $Revision: 1.9 $ $Date: 2004/10/03 20:24:31 $
// $Name:  $
//
// Author(s)     : Julia Floetotto

// ATTENTION : the surface is supposed to be a closed surface

#ifndef CGAL_SURFACE_NEIGHBOR_COORDINATES_3_H
#define CGAL_SURFACE_NEIGHBOR_COORDINATES_3_H

#include <utility>
#include <CGAL/Iterator_project.h>
#include <CGAL/Voronoi_intersection_2_traits_3.h>
#include <CGAL/Regular_triangulation_2.h>
#include <CGAL/regular_neighbor_coordinates_2.h>

CGAL_BEGIN_NAMESPACE

template <class OutputIterator, class InputIterator, class Kernel>
inline
Triple< OutputIterator, typename Kernel::FT, bool >
surface_neighbor_coordinates_3(InputIterator
			       first, InputIterator beyond,
			       const typename Kernel::Point_3& p,
			       const typename Kernel::Vector_3& normal,
			       OutputIterator out,
			       const Kernel& K)
{
  typedef Voronoi_intersection_2_traits_3<Kernel> I_gt;
  return surface_neighbor_coordinates_3(first, beyond, p, out, I_gt(p,normal));
}


template <class OutputIterator, class InputIterator, class ITraits>
Triple< OutputIterator, typename ITraits::FT, bool >
surface_neighbor_coordinates_3(InputIterator
			       first, InputIterator beyond,
			       const typename ITraits::Point_2& p,
			       OutputIterator out,
			       const ITraits& traits)
{
  //definition of the Voronoi intersection triangulation:
  typedef Regular_triangulation_2< ITraits>      I_triangulation;

  //build Voronoi intersection triangulation:
  I_triangulation it(traits);
  it.insert(first,beyond);

  return regular_neighbor_coordinates_2(it, p, out);
}


//without Delaunay filtering but with certification:
// a boolean is returned that indicates if a sufficiently large
// neighborhood has been considered so that the
// Voronoi cell of p is not affected by any point outside the smallest
// ball centered on p containing all points in [first,beyond)
template <class OutputIterator, class InputIterator, class Kernel>
Quadruple< OutputIterator, typename Kernel::FT, bool, bool >
surface_neighbor_coordinates_certified_3(InputIterator
			       first, InputIterator beyond,
			       const typename Kernel::Point_3& p,
			       const typename Kernel::Vector_3& normal,
			       OutputIterator out,
			       const Kernel& K)
{
  typedef Voronoi_intersection_2_traits_3<Kernel> I_gt;
  return surface_neighbor_coordinates_certified_3
         (first, beyond, p, out, I_gt(p,normal));
}

//this function takes the radius of the sphere centered on p
// containing the points in [first, beyond] (i.e. the maximal
// distance from p to [first,beyond) as add. parameter:
template <class OutputIterator, class InputIterator, class Kernel>
inline
Quadruple< OutputIterator, typename Kernel::FT, bool, bool >
surface_neighbor_coordinates_certified_3(
                             InputIterator first, InputIterator beyond,
			     const typename Kernel::Point_3& p,
			     const typename Kernel::Vector_3& normal,
			     const typename Kernel::FT& radius,
			     OutputIterator out, const Kernel& K)
{
  typedef Voronoi_intersection_2_traits_3<Kernel> I_gt;
  return surface_neighbor_coordinates_certified_3
         (first, beyond, p, radius, out, I_gt(p,normal));
}

// FIXME : this should probably be replaced by some kernel functor.
//struct necessary to sort the points by distance to p:
//also used in surface_neighbors_3.h
template <class Traits >
struct closer_to_point
  : public std::less<typename Traits::Point_2>
{
  typedef typename Traits::Point_2   Point_2;

  closer_to_point(const Point_2& _p, const Traits& t)
    : p(_p), traits(t) {}

  bool operator()(const Point_2& q, const Point_2& r) const
    {
      return traits.less_distance_to_point_2_object()(p,q,r);
    }

private:
  Point_2 p;
  Traits traits;
};

// Versions with instantiated traits class:
template <class OutputIterator, class InputIterator, class ITraits>
Quadruple< OutputIterator, typename ITraits::FT, bool, bool >
surface_neighbor_coordinates_certified_3(InputIterator
					 first, InputIterator beyond,
					 const typename ITraits::Point_2& p,
					 OutputIterator out,
					 const ITraits& traits)
{
  //find the point in [first,beyond) furthest from p:
  InputIterator furthest = std::max_element(first, beyond,
		                closer_to_point<ITraits>(p, traits));

  return surface_neighbor_coordinates_certified_3
         (first, beyond, p,
          traits.compute_squared_distance_2_object()(p,*furthest),
          out, traits);
}

//with radius(maximal distance from p to [first,beyond)) as
// add. parameter:
template <class OutputIterator, class InputIterator, class ITraits>
Quadruple< OutputIterator, typename ITraits::FT, bool, bool >
surface_neighbor_coordinates_certified_3(InputIterator
					 first, InputIterator beyond,
					 const typename
					 ITraits::Point_2& p,
					 const typename ITraits::FT&
					 radius,
					 OutputIterator out,
					 const ITraits& traits)
{
  //definition of the Voronoi intersection triangulation:
  typedef Regular_triangulation_2< ITraits>      I_triangulation;

  //build Voronoi intersection triangulation:
  I_triangulation it(traits);
  it.insert(first,beyond);

  //collect the Voronoi vertices of the cell of p in order to
  //determine the furthest distance from p to the boundary of its cell
  std::vector<  typename ITraits::Point_2  > vor_vertices;

  //unfortunately, there is no function call without Face_handle
  // "start" because this would cause type conflicts because
  // of resembling function signatures (-> default constructor)
  Triple< OutputIterator, typename ITraits::FT, bool >
    res = regular_neighbor_coordinates_2
    (it, p, out, std::back_inserter(vor_vertices),
     typename I_triangulation::Face_handle());

  typename ITraits::Point_2 furthest =
    *std::max_element(vor_vertices.begin(),  vor_vertices.end(),
		     closer_to_point<ITraits>(p,traits));
  // if the distance to the furthest sample point is smaller
  // than twice the distance to the furthest vertex, not all neighbors
  // might be found: return false
  if(radius < 4* traits.compute_squared_distance_2_object()
     (p, furthest))
    return make_quadruple(res.first, res.second, res.third, false);

  return make_quadruple(res.first, res.second,res.third, true);
}

// FIXME :
//Sylvain:
//this class should probably be moved to CGAL/function_objects.h
// it is used in the (next two) functions
// it is also used in surface_neighbors_3.h
//
//projection of Vertex_handle (or equiv. Vertices_iterator) to Point
template < class NodeIterator>
struct Project_vertex_iterator_to_point
{
  typedef NodeIterator          argument_type;
  typedef typename std::iterator_traits<NodeIterator>::value_type Node;
  typedef typename Node::Point  Point;
  typedef Point                 result_type;
  typedef Arity_tag<1> Arity;
  Point&       operator()( NodeIterator& x) const { return x->point(); }
  const Point& operator()( const NodeIterator& x) const { return x->point(); }
};

//using Delaunay triangulation for candidate point filtering:
// => no certification is necessary
template <class Dt, class OutputIterator>
inline
Triple< OutputIterator, typename Dt::Geom_traits::FT, bool >
surface_neighbor_coordinates_3(const Dt& dt,
			    const typename Dt::Geom_traits::Point_3& p,
			    const typename Dt::Geom_traits::Vector_3& normal,
			    OutputIterator out,
			    typename Dt::Cell_handle start
			       = typename Dt::Cell_handle())
{
  typedef Voronoi_intersection_2_traits_3<typename Dt::Geom_traits> I_gt;
  return surface_neighbor_coordinates_3(dt, p, out, I_gt(p,normal), start);
}

template <class Dt, class OutputIterator, class ITraits>
Triple< OutputIterator, typename ITraits::FT, bool >
surface_neighbor_coordinates_3(const Dt& dt,
			       const typename ITraits::Point_2& p,
			       OutputIterator out, const ITraits& traits,
			       typename Dt::Cell_handle start
   			       = typename Dt::Cell_handle())
{
  typedef typename ITraits::FT            Coord_type;
  typedef typename ITraits::Point_2       Point_3;

  typedef typename Dt::Cell_handle       Cell_handle;
  typedef typename Dt::Vertex_handle      Vertex_handle;
  typedef typename Dt::Locate_type       Locate_type;

  //the Vertex_handle is, in fact, an iterator over vertex:
  typedef Project_vertex_iterator_to_point< Vertex_handle>   Proj_point;
  typedef Iterator_project<
    typename std::list< Vertex_handle >::iterator,
    Proj_point,
    const Point_3&,
    const Point_3*,
    std::ptrdiff_t,
    std::forward_iterator_tag>  Point_iterator;

  Locate_type lt;
  int li, lj ;
  Cell_handle c = dt.locate(p, lt, li,lj,start);

  //if p is located on a vertex: the only neighbor is found
  if(lt == Dt::VERTEX){
    *out++= std::make_pair(c->vertex(li)->point(),
			   Coord_type(1));
    return make_triple(out, Coord_type(1), true);
  }

  //the candidate points are the points of dt in conflict with p:
  typename std::list< Vertex_handle >  conflict_vertices;
  dt.vertices_in_conflict(p,c,
			 std::back_inserter(conflict_vertices));

  for (typename std::list< Vertex_handle >::iterator it = conflict_vertices.begin();
       it != conflict_vertices.end();){
    if(dt.is_infinite(*it)){
      typename std::list< Vertex_handle >::iterator itp = it;
      it++;
      conflict_vertices.erase(itp);
    } else {
      it++;
    }
  }
  return surface_neighbor_coordinates_3
          (Point_iterator(conflict_vertices.begin()),
           Point_iterator(conflict_vertices.end()),
           p, out, traits);
}

CGAL_END_NAMESPACE

#endif // CGAL_SURFACE_NEIGHBOR_COORDINATES_3_H
