cgal/Linear_cell_complex/include/CGAL/Linear_cell_complex_operations.h

// Copyright (c) 2010 CNRS, LIRIS, http://liris.cnrs.fr/, 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.
//
// $URL$
// $Id$
//
// Author(s)     : Guillaume Damiand <guillaume.damiand@liris.cnrs.fr>
//
#ifndef CGAL_COMBINATORIAL_MAP_WITH_POINTS_OPERATIONS_H
#define CGAL_COMBINATORIAL_MAP_WITH_POINTS_OPERATIONS_H 1

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

namespace CGAL {

/** @file Combinatorial_map_with_embedding_operations.h
 * Basic operators to modify an embedded combinatorial map.
 * basic operators to modify an embedded combinatorial map: insert a
 * vertex in a facet,  insertion or bursting of a cell.
 */

/** Compute the barycenter of a given cell.
 * @param amap the used combinatorial map.
 * @param adart a dart incident to the cell.
 * @param adim the dimension of the cell.
 * @return the barycenter of the cell.
 */
template<class CMap, unsigned int i>
typename CMap::Point barycenter(const CMap& amap, 
				typename CMap::Dart_const_handle adart)
{
  CGAL_assertion(adart != NULL);

  typename CMap::Vector 
    vec(typename CMap::Construct_vector()(CGAL::ORIGIN, CMap::point(adart)));
  unsigned int nb = 1;
  
  CMap_one_dart_per_incident_cell_const_iterator<CMap,0,i> it(amap, adart); 
  for ( ++it; it.cont(); ++it)
    {
      vec = typename CMap::Construct_sum_of_vectors()
	(vec, typename CMap::Construct_vector()(CGAL::ORIGIN, 
						CMap::point(it) ));
      ++nb;
    }

  return typename CMap::Vector_to_point()
    (typename CMap::Construct_scaled_vector()(vec, 1.0/nb));
}

/** Compute the normal of the given facet.
 * @param amap the used combinatorial map.
 * @param adart a dart incident to the facet.
 * @return the normal of the facet.
 */
template <class CMap>
typename CMap::Vector compute_normal_of_cell_2
(const CMap& amap, typename CMap::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 CMap::Point Point;
  typedef typename CMap::Vector Vector;
  typename CMap::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 = &CMap::point(start);
  const Point* curr = &CMap::point(adart);
  for ( ; adart!=start && adart->other_extremity()!=NULL; adart=adart->beta(1) )
    {
      const Point* next = &CMap::point(adart->other_extremity());
      if ( !typename CMap::Collinear()(*prev, *curr, *next) )
	{
	  normal = typename CMap::Construct_sum_of_vectors()
	    (normal, typename CMap::Construct_normal()(*prev, *curr, *next));
	  prev = curr;
	  ++nb;
	}
      curr = next;
    }
  
  if ( nb<2 ) return normal;       
  return (typename CMap::Construct_scaled_vector()(normal, 1.0/nb));
  
  //  return normal / std::sqrt(normal * normal);
}

/** Compute the normal of the given vertex.
 * @param amap the used combinatorial map.
 * @param adart a dart incident to the vertex.
 * @return the normal of the vertex.
 */
template <class CMap>
typename CMap::Vector compute_normal_of_cell_0
(const CMap& amap, typename CMap::Dart_const_handle adart)
{
  typedef typename CMap::Point Point;
  typedef typename CMap::Vector Vector;
  Vector normal(CGAL::NULL_VECTOR);
  unsigned int nb = 0;
  
  for ( CMap_one_dart_per_incident_cell_const_iterator<CMap,2,0> it(amap, adart); 
	it.cont(); ++it)
    {
      normal = typename CMap::Construct_sum_of_vectors()
	(normal, CGAL::compute_normal_of_cell_2(amap,it));
      ++nb;
    }
  
  if ( nb<2 ) return normal;       
  return (typename CMap::Construct_scaled_vector()(normal, 1.0/nb));
  //  return normal / std::sqrt(normal * normal);
}
  
/** Insert a vertex in the center (barycenter) of the given facet, 
 *  the facet is splitted in triangles, once for each inital edge of the facet.
 * @param amap the used combinatorial map.
 * @param adart a dart of the facet to triangulate.
 * @return A dart incident to the new vertex.
 */
template<class CMap>
typename CMap::Dart_handle insert_center_cell_0_in_cell_2
(CMap& amap, typename CMap::Dart_handle adart)
{
   CGAL_assertion(adart != NULL);

   typename CMap::Vertex_attribute_handle v = 
     amap.create_vertex_attribute(barycenter<CMap,2>(amap, adart));

   typename CMap::Dart_handle first = 
     CGAL::insert_cell_0_in_cell_2(amap, adart);

   if (first != NULL) // If the triangulated facet was not made of one dart
      amap.set_vertex_attribute(first, v);
   else
      amap.erase_vertex_attribute(v);

   //   CGAL_postcondition(amap.is_valid());
   
   return first;
}

/** Insert a vertex in a given edge.
 * @param amap the used combinatorial map.
 * @param adart a dart of the edge (!=NULL).
 * @param apoint the coordinates of the new vertex.
 * @return a dart of the new vertex.
 */
template<class CMap>
typename CMap::Dart_handle insert_cell_0_in_cell_1
(CMap& amap, typename CMap::Dart_handle adart, 
 const typename CMap::Point& apoint)
{ 
  typename CMap::Vertex_attribute_handle v=amap.create_vertex_attribute(apoint);
  typename CMap::Dart_handle res = insert_cell_0_in_cell_1(amap,adart);
  amap.set_vertex_attribute(res, v);
  return res;
}

/** Insert a vertex in the middle of a given edge.
 * @param amap the used combinatorial map.
 * @param adart a dart of the edge (!=NULL).
 * @return a dart of the new vertex.
 */
template<class CMap>
typename CMap::Dart_handle insert_middle_cell_0_in_cell_1
(CMap& amap, typename CMap::Dart_handle adart)
{
  CGAL_assertion(adart!=NULL);

  typename CMap::Dart_handle d2 = adart->other_extremity();

  if ( d2==NULL ) 
    return insert_cell_0_in_cell_1(amap, adart, CMap::point(adart));
  
  return insert_cell_0_in_cell_1(amap, adart, typename CMap::Construct_midpoint()
				 (CMap::point(adart), CMap::point(d2)));
}

/** Insert a dangling edge in a given facet.
 * @param amap the used combinatorial map.
 * @param adart a dart of the facet (!=NULL).
 * @param apoint the coordinates of the new vertex.
 * @return a dart of the new edge, incident to the new vertex.
 */
template<class Map>
typename Map::Dart_handle insert_dangling_cell_1_in_cell_2
(Map& amap, typename Map::Dart_handle adart, const typename Map::Point& apoint)
{
   typename Map::Vertex_attribute_handle 
     v = amap.create_vertex_attribute(apoint);
   typename Map::Dart_handle res = insert_dangling_cell_1_in_cell_2(amap,adart);
   amap.set_vertex_attribute(res, v);
   return res;
}

/** Compute the dual of a combinatorial map.
 * @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
				     (barycenter<Map,Map::dimension>
				      (amap1,it)));
	}
    }

  //  CGAL_postcondition(amap2.is_valid());

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

} // namespace CGAL

#endif // CGAL_COMBINATORIAL_MAP_WITH_EMBEDDING_OPERATIONS_H //
// EOF //