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// Copyright (c) 2005-2008 Max-Planck-Institute Saarbruecken (Germany). // All rights reserved. // // This file is part of CGAL (www.cgal.org). // // $URL: https://github.com/CGAL/cgal/blob/v6.1/Convex_decomposition_3/include/CGAL/convex_decomposition_3.h $ // $Id: include/CGAL/convex_decomposition_3.h b26b07a1242 $ // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial // // // Author(s) : Peter Hachenberger #ifndef CGAL_CONVEX_DECOMPOSITION_3_H #define CGAL_CONVEX_DECOMPOSITION_3_H #include #include #include #include #include #include #include #include #include #include #include /*! \file convex_decomposition_3.h */ /// The CGAL namespace. namespace CGAL { /*! \ingroup PkgConvexDecomposition3Ref 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 \cgalBigO{r^2} 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 \cgalBigO{n^2r^4\sqrt[3]{nr^2}\log{(nr)}}, 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` */ template 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 Single_wall; typedef typename CGAL::YVertical_wall_builder YVertical_wall_builder; typedef typename CGAL::Reflex_vertex_searcher Reflex_vertex_searcher; typedef typename CGAL::Ray_hit_generator2 Ray_hit2; typedef typename CGAL::External_structure_builder External_structure_builder; typedef typename CGAL::SFace_separator SFace_separator; typedef Compare_halfedges_in_reflex_edge_sorter > Less_edges; typedef Compare_halfedges_in_reflex_edge_sorter > Greater_edges; typedef typename std::multiset Negatively_sorted_set; typedef typename std::multiset 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 Reflex_edge_searcher; typedef typename CGAL::Edge_sorter, Negatively_sorted_set> Edge_sorter; typedef typename CGAL::Edge_sorter, 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(cse))); } } //namespace CGAL #endif // CGAL_CONVEX_DECOMPOSITION_3_H