// Copyright (c) 2011 CNRS and LIRIS' Establishments (France).
// 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; either version 3 of the License,
// or (at your option) any later version.
//
// 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.
//
// $URL$
// $Id$
//
// Author(s)     : Guillaume Damiand <guillaume.damiand@liris.cnrs.fr>
//
#ifndef CGAL_LINEAR_CELL_COMPLEX_OPERATIONS_H
#define CGAL_LINEAR_CELL_COMPLEX_OPERATIONS_H 1

#include <CGAL/Cell_iterators.h>
#include <CGAL/Combinatorial_map_operations.h>
#include <vector>

namespace CGAL {

  /** @file Linear_cell_complex_operations.h
   * Basic operators on  a linear cell complex.
   */


  /** Compute the normal of the given facet.
   * @param amap the used linear cell complex.
   * @param adart a dart incident to the facet.
   * @return the normal of the facet.
   */
  template <class LCC>
  typename LCC::Vector compute_normal_of_cell_2
  (const LCC& amap, typename LCC::Dart_const_handle adart)
  {
    // TODO Better approximation by using Newell's method
    // Nx += (Vy - V'y) * (Vz + V'z);
    // Ny += (Vz - V'z) * (Vx + V'x);
    // Nz += (Vx - V'x) * (Vy + V'y);
    // But problem with functor since this is not the sum of normal vectors.
  
    typedef typename LCC::Point Point;
    typedef typename LCC::Vector Vector;
    typename LCC::Dart_const_handle start=adart;
    Vector normal(CGAL::NULL_VECTOR);

    while ( !start->is_free(0) && start->beta(0)!=adart )
      start = start->beta(0);

    if ( start->is_free(1) || start->beta(1)->other_extremity()==NULL )
      return normal;

    unsigned int nb = 0;
    adart = start->beta(1);
  
    const Point* prev = &LCC::point(start);
    const Point* curr = &LCC::point(adart);
    for ( ; adart!=start && adart->other_extremity()!=NULL;
          adart=adart->beta(1) )
    {
      const Point* next = &LCC::point(adart->other_extremity());
      if ( !typename LCC::Traits::Collinear_3()(*prev, *curr, *next) )
      {
        normal = typename LCC::Traits::Construct_sum_of_vectors()
          (normal, typename LCC::Traits::Construct_normal_3()
           (*prev, *curr, *next));
        prev = curr;
        ++nb;
      }
      curr = next;
    }
  
    if ( nb<2 ) return normal;       
    return (typename LCC::Traits::Construct_scaled_vector()(normal, 1.0/nb));  
    //  return normal / std::sqrt(normal * normal);
  }

  /** Compute the normal of the given vertex.
   * @param amap the used linear cell complex.
   * @param adart a dart incident to the vertex.
   * @return the normal of the vertex.
   */
  template <class LCC>
  typename LCC::Vector compute_normal_of_cell_0
  (const LCC& amap, typename LCC::Dart_const_handle adart)
  {
    typedef typename LCC::Point Point;
    typedef typename LCC::Vector Vector;
    Vector normal(CGAL::NULL_VECTOR);
    unsigned int nb = 0;
  
    for ( CMap_one_dart_per_incident_cell_const_iterator<LCC,2,0>
            it(amap, adart); it.cont(); ++it )
    {
      normal = typename LCC::Traits::Construct_sum_of_vectors()
        (normal, CGAL::compute_normal_of_cell_2(amap,it));
      ++nb;
    }
  
    if ( nb<2 ) return normal;       
    return (typename LCC::Traits::Construct_scaled_vector()(normal, 1.0/nb));
  }

  /** Compute the dual of a linear cell complex.
   * @param amap1 the initial map.
   * @param amap2 the map in which we build the dual of amap1.
   * @param adart a dart of the initial map, NULL by default.
   * @return adart of the dual map, the dual of adart if adart!=NULL.
   */
  template<class Map>
  typename Map::Dart_handle dual(Map& amap1, Map& amap2, 
                                 typename Map::Dart_handle adart=NULL)
  {
    CGAL_assertion( amap1.is_without_boundary(Map::dimension) );

    typedef typename Map::Dart_handle Dart_handle;
    typedef typename Map::Dart_range::iterator Dart_iterator;

    std::map< Dart_handle, Dart_handle > dual;
    Dart_handle d, d2, res = NULL;
  
    // We clear the amap2. TODO return a new amap ? (but we need to make
    // a copy contructor and =operator...)
    amap2.clear();
  
    // We create a copy of all the dart of the map.
    for (Dart_iterator it=amap1.darts().begin(); it!=amap1.darts().end(); ++it)
    {
      dual[it] = amap2.create_dart();

      if ( it==adart && res==NULL ) res = dual[it];
    }
  
    // Then we link the darts by using the dual formula :
    // G(B,b1,b2,...,bn-1,bn) => dual(G)=(B, b(n-1)obn, b(n-2)obn,...,b1obn, bn)
    // We suppose darts are run in the same order for both maps.
    Dart_iterator it2=amap2.darts().begin();
    for (Dart_iterator it=amap1.darts().begin(); it!=amap1.darts().end(); 
         ++it, ++it2)
    {
      d = it2; // The supposition on the order allows to avoid d=dual[it];
      CGAL_assertion(it2 == dual[it]);

      // First case outside the loop since we need to use link_beta1
      if ( it->beta(Map::dimension)->beta(Map::dimension-1)!=
           Map::null_dart_handle )
        amap2. template
          link_beta<1>(d, 
                       dual[it->beta(Map::dimension)->beta(Map::dimension-1)]);

      // and during the loop we use link_beta(d1,d2,i)
      for (unsigned int i=Map::dimension-2; i>=1; --i)
      {
        if ( it->beta(Map::dimension)->beta(i)!=Map::null_dart_handle )
          amap2.link_beta(d, dual[it->beta(Map::dimension)->beta(i)],
                          Map::dimension-i);
      }
      CGAL_assertion ( !it->is_free(Map::dimension) );
      amap2.link_beta(d, dual[it->beta(Map::dimension)],Map::dimension);
    }
  
    // Now the map amap is topologically correct, we just need to add
    // its geometry to each vertex (the barycenter of the corresponding
    // volume in the initial map).
    it2 = amap2.darts().begin();
    for (Dart_iterator it(amap1.darts().begin()); it!=amap1.darts().end();
         ++it, ++it2)
    {
      if (Map::vertex_attribute(it2) == NULL)
      {
        amap2.set_vertex_attribute(it2,
                                   amap2.create_vertex_attribute
                                   (amap1.barycenter<Map::dimension>(it)));
      }
    }

    //  CGAL_postcondition(amap2.is_valid());

    if ( res==NULL ) res = amap2.darts().begin();
    return res;
  }

} // namespace CGAL

#endif // CGAL_LINEAR_CELL_COMPLEX_OPERATIONS_H //
// EOF //