/usr/include/CGAL/convex_decomposition_3.h is in libcgal-dev 4.2-5ubuntu1.
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// 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
// 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) : Peter Hachenberger <hachenberger@mpi-sb.mpg.de>
#ifndef CGAL_CONVEX_DECOMPOSITION_3_H
#define CGAL_CONVEX_DECOMPOSITION_3_H
#include <CGAL/Convex_decomposition_3/Single_wall_creator.h>
#include <CGAL/Convex_decomposition_3/Single_wall_creator2.h>
#include <CGAL/Convex_decomposition_3/Reflex_edge_searcher.h>
#include <CGAL/Convex_decomposition_3/Reflex_vertex_searcher.h>
#include <CGAL/Convex_decomposition_3/YVertical_wall_builder.h>
#include <CGAL/Convex_decomposition_3/Ray_hit_generator2.h>
#include <CGAL/Convex_decomposition_3/External_structure_builder.h>
#include <CGAL/Convex_decomposition_3/SFace_separator.h>
#include <CGAL/Convex_decomposition_3/Edge_sorter.h>
#include <CGAL/Convex_decomposition_3/is_reflex_sedge.h>
/*!
\file convex_decomposition_3.h
*/
/// The CGAL namespace.
namespace CGAL {
/*!
\ingroup PkgConvexDecomposition3
The function `convex_decomposition_3()` inserts additional facets
into the given `Nef_polyhedron_3` `N`, such that each bounded
marked volume (the outer volume is unbounded) is subdivided into convex
pieces. The modified polyhedron represents a decomposition into
\f$ O(r^2)\f$ convex pieces, where \f$ r\f$ is the number of edges that have two
adjacent facets that span an angle of more than 180 degrees with
respect to the interior of the polyhedron.
The worst-case running time of our implementation is
\f$ O(n^2r^4\sqrt[3]{nr^2}\log{(nr)})\f$, where \f$ n\f$ is the complexity of
the polyhedron (the complexity of a `Nef_polyhedron_3` is the sum
of its `Vertices`, `Halfedges` and `SHalfedges`) and \f$ r\f$
is the number of reflex edges.
\pre The polyhedron `N` is bounded. Otherwise, the outer volume is ignored.
\post If the polyhedron `N` is non-convex, it is modified to represent the
convex decomposition. If `N` is convex, it is not modified.
\sa `CGAL::Nef_polyhedron_3<Traits>`
*/
template<typename Nef_polyhedron>
void convex_decomposition_3(Nef_polyhedron& N)
{
typedef typename Nef_polyhedron::SNC_structure SNC_structure;
typedef typename SNC_structure::Halfedge_handle Halfedge_handle;
typedef typename Nef_polyhedron::Point_3 Point_3;
typedef typename Nef_polyhedron::Vector_3 Vector_3;
typedef typename Nef_polyhedron::Sphere_point Sphere_point;
typedef typename Nef_polyhedron::FT FT;
typedef typename CGAL::Single_wall_creator<Nef_polyhedron> Single_wall;
typedef typename CGAL::YVertical_wall_builder<Nef_polyhedron> YVertical_wall_builder;
typedef typename CGAL::Reflex_vertex_searcher<Nef_polyhedron> Reflex_vertex_searcher;
typedef typename CGAL::Ray_hit_generator2<Nef_polyhedron> Ray_hit2;
typedef typename CGAL::External_structure_builder<Nef_polyhedron> External_structure_builder;
typedef typename CGAL::SFace_separator<Nef_polyhedron> SFace_separator;
typedef Compare_halfedges_in_reflex_edge_sorter<Halfedge_handle, std::less<Point_3> >
Less_edges;
typedef Compare_halfedges_in_reflex_edge_sorter<Halfedge_handle, std::greater<Point_3> >
Greater_edges;
typedef typename std::multiset<Halfedge_handle, Less_edges> Negatively_sorted_set;
typedef typename std::multiset<Halfedge_handle, Greater_edges> Positively_sorted_set;
typedef typename Positively_sorted_set::const_iterator Positive_reflex_edge_iterator;
typedef typename Negatively_sorted_set::const_iterator Negative_reflex_edge_iterator;
typedef typename CGAL::Reflex_edge_searcher<Nef_polyhedron, Positively_sorted_set, Negatively_sorted_set>
Reflex_edge_searcher;
typedef typename CGAL::Edge_sorter<Nef_polyhedron, std::less<FT>, Negatively_sorted_set> Edge_sorter;
typedef typename CGAL::Edge_sorter<Nef_polyhedron, std::greater<FT>, Positively_sorted_set> Edge_sorter2;
External_structure_builder esb;
SFace_separator sf_sep;
N.delegate(sf_sep,false, false);
Reflex_edge_searcher res(Sphere_point(1,0,0));
N.delegate(res,false,false);
Edge_sorter es(res.get_negative_redges());
N.delegate(es);
Negative_reflex_edge_iterator nrei;
for(nrei=res.negative_redges_begin(); nrei!=res.negative_redges_end(); ++nrei) {
Halfedge_handle e = (*nrei);
Single_wall W(e,Vector_3(-1,0,0));
if(!W.need_to_create_wall()) continue;
Reflex_vertex_searcher rvs(Sphere_point(1,0,0));
if(rvs.need_to_shoot(e, true)) {
Ray_hit2 rh2a(Vector_3(-1,0,0), e->source());
N.delegate(rh2a);
}
if(rvs.need_to_shoot(e->twin(), true)) {
Ray_hit2 rh2a(Vector_3(-1,0,0), e->twin()->source());
N.delegate(rh2a);
}
}
// int i=0;
for(nrei=res.negative_redges_begin(); nrei!=res.negative_redges_end(); ++nrei) {
Halfedge_handle e = (*nrei);
if(e->point().hx() > 0)
e = e->twin();
Single_wall W(e,Vector_3(-1,0,0));
if(!W.need_to_create_wall()) continue;
N.delegate(W);
}
N.delegate(esb);
N.delegate(res, false, false);
CGAL_assertion(N.is_valid(0,0));
Reflex_edge_searcher& res2 = res;
Edge_sorter2 es2(res2.get_positive_redges());
N.delegate(es2);
Positive_reflex_edge_iterator prei;
for(prei=res2.positive_redges_begin(); prei!=res2.positive_redges_end(); ++prei) {
Halfedge_handle e = (*prei);
CGAL_assertion(e->source()->point() >
e->twin()->source()->point());
Single_wall W(e,Vector_3(1,0,0));
if(!W.need_to_create_wall()) continue;
Reflex_vertex_searcher rvs(Sphere_point(1,0,0));
if(rvs.need_to_shoot(e, false)) {
Ray_hit2 rh2a(Vector_3(1,0,0), e->source());
N.delegate(rh2a);
}
if(rvs.need_to_shoot(e->twin(), false)) {
Ray_hit2 rh2a(Vector_3(1,0,0), e->twin()->source());
N.delegate(rh2a);
}
}
// i=0;
for(prei=res2.positive_redges_begin(); prei!=res2.positive_redges_end(); ++prei) {
Halfedge_handle e = (*prei);
Single_wall W(e,Vector_3(1,0,0));
if(!W.need_to_create_wall()) continue;
N.delegate(W);
}
N.delegate(esb);
CGAL_assertion(N.is_valid(0,0));
YVertical_wall_builder Y;
N.delegate(Y,false,false);
N.delegate(esb);
CGAL_assertion_code(typename Nef_polyhedron::SHalfedge_const_iterator cse);
CGAL_assertion_code(CGAL_forall_shalfedges(cse, N)
if(cse->incident_sface()->mark())
CGAL_assertion(!CGAL::is_reflex_sedge_in_any_direction<Nef_polyhedron>(cse)));
}
} //namespace CGAL
#endif // CGAL_CONVEX_DECOMPOSITION_3_H
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