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// Copyright (c) 1997-2000 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/Nef_2/include/CGAL/Nef_2/PM_const_decorator.h $ // $Id: include/CGAL/Nef_2/PM_const_decorator.h b26b07a1242 $ // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial // // // Author(s) : Michael Seel #ifndef CGAL_PM_CONST_DECORATOR_H #define CGAL_PM_CONST_DECORATOR_H #include #include #include #include #include #include #include #include #undef CGAL_NEF_DEBUG #define CGAL_NEF_DEBUG 7 #include #ifndef CGAL_I_DO_WANT_TO_USE_GENINFO #include #endif #include namespace CGAL { template inline CGAL::Circulator_tag query_circulator_or_iterator(const CircFromIt& ) { return CGAL::Circulator_tag(); } template class move_halfedge_around_vertex { public: void forward(HE& e) const { e = (e->prev()->opposite()); } void backward(HE& e) const { e = (e->opposite()->next()); } }; template struct move_halfedge_around_face { void forward(HE& e) const { e = (e->next()); } void backward(HE& e) const { e = (e->prev()); } }; /*{\Moptions print_title=yes}*/ /*{\Moptions constref=yes}*/ /*{\Msubst PM_const_decorator#PMConstDecorator PM_decorator#PMDecorator }*/ /*{\Moptions outfile=PMConstDecorator.man }*/ /*{\Manpage {PMConstDecorator}{}{Topological plane map exploration}{D}}*/ template class PM_decorator; template class PM_const_decorator { typedef PM_const_decorator Self; /*{\Mdefinition An instance |\Mvar| of the data type |\Mname| is a decorator for interfacing the topological structure of a plane map |P| (read-only). A plane map |P| consists of a triple $(V, E, F)$ of vertices, edges, and faces. We collectively call them objects. An edge |e| is a pair of vertices |(v,w)| with incidence operations |v = source(e)|, |w = target(e)|. The list of all edges with source |v| is called the adjacency list |A(v)|. Edges are paired into twins. For each edge |e = (v,w)| there's an edge |twin(e) = (w,v)| and |twin(twin(e)) == e|\cgalFootnote{The existence of the edge pairs makes |P| a bidirected graph, the |twin| links make |P| a map.}. An edge |e = (v,w)| knows two adjacent edges |en = next(e)| and |ep = previous(e)| where |source(en) = w|, |previous(en) = e| and |target(ep) = v| and |next(ep) = e|. By this symmetric |previous-next| relationship all edges are partitioned into face cycles. Two edges $e$ and $e'$ are in the same face cycle if $e = |next|^*(e')$. All edges |e| in the same face cycle have the same incident face $f = |face|(e)$. The cyclic order on the adjacency list of a vertex |v = source(e)| is given by |cyclic_adj_succ(e) = twin(previous(e))| and |cyclic_adj_pred(e) = next(twin(e))|. A vertex |v| is embedded via coordinates |point(v)|. By the embedding of its source and target an edge corresponds to a segment. |P| has the property that the embedding is always \emph{order-preserving}. This means a ray fixed in |point(v)| of a vertex |v| and swept around counterclockwise meets the embeddings of |target(e)| ($e \in A(v)$) in the cyclic order defined by the list order of |A|. The embedded face cycles partition the plane into maximal connected subsets of points. Each such set corresponds to a face. A face is bounded by its incident face cycles. For all the edges in the non-trivial face cycles it holds that the face is left of the edges. There can also be trivial face cycles in form of isolated vertices in the interior of a face. Each such vertex |v| knows its surrounding face |f = face(v)|. We call the embedded map |(V,E)| also the $1$-skeleton of |P|. Plane maps are attributed. To each object $u \in V \cup E \cup F$ we attribute a value |mark(u)| of type |Mark|. |Mark| fits the concepts assignable, default-constructible, and equal-comparable.}*/ protected: HDS* phds; friend class PM_decorator; public: /*{\Mtypes 6}*/ typedef HDS Plane_map; /*{\Mtypemember The underlying plane map type}*/ typedef typename HDS::Traits Traits; typedef typename Traits::Point Point; /*{\Mtypemember The point type of vertices.}*/ typedef typename Traits::Mark Mark; /*{\Mtypemember All objects (vertices, edges, faces) are attributed by a |Mark| object.}*/ typedef size_t Size_type; #ifdef CGAL_I_DO_WANT_TO_USE_GENINFO /*{\Mtypemember The size type.}*/ typedef void* GenPtr; #else typedef std::any GenPtr; #endif typedef typename HDS::Vertex Vertex; typedef typename HDS::Vertex_base Vertex_base; typedef typename HDS::Vertex_handle Vertex_handle; typedef typename HDS::Vertex_const_handle Vertex_const_handle; typedef typename HDS::Vertex_const_iterator Vertex_const_iterator; typedef typename HDS::Halfedge Halfedge ; typedef typename HDS::Halfedge_base Halfedge_base ; typedef typename HDS::Halfedge_handle Halfedge_handle; typedef typename HDS::Halfedge_const_handle Halfedge_const_handle; typedef typename HDS::Halfedge_const_iterator Halfedge_const_iterator; typedef typename HDS::Face Face; typedef typename HDS::Face_base Face_base; typedef typename HDS::Face_handle Face_handle; typedef typename HDS::Face_const_handle Face_const_handle; typedef typename HDS::Face_const_iterator Face_const_iterator; /*{\Mtext Local types are handles, iterators and circulators of the following kind: |Vertex_const_handle|, |Vertex_const_iterator|, |Halfedge_const_handle|, |Halfedge_const_iterator|, |Face_const_handle|, |Face_\-const_\-ite\-rator|. Additionally the following circulators are defined.}*/ typedef CircFromIt< Halfedge_const_iterator, move_halfedge_around_vertex > Halfedge_around_vertex_const_circulator; /*{\Mtypemember circulating the outgoing halfedges in $A(v)$.}*/ typedef CircFromIt< Halfedge_const_iterator, move_halfedge_around_face > Halfedge_around_face_const_circulator; /*{\Mtypemember circulating the halfedges in the face cycle of a face |f|.}*/ typedef typename Face::Hole_const_iterator Hole_const_iterator; /*{\Mtypemember iterating all holes of a face |f|. The type is convertible to |Halfedge_const_handle|.}*/ typedef typename Face::Isolated_vertex_const_iterator Isolated_vertex_const_iterator; /*{\Mtypemember iterating all isolated vertices of a face |f|. The type generalizes |Vertex_const_handle|.}*/ typedef PntItFromVertIt Point_const_iterator; /*{\Mcreation 3}*/ PM_const_decorator() : phds(0) {} PM_const_decorator(const PM_const_decorator& D) : phds(D.phds) {} PM_const_decorator& operator=( const PM_const_decorator& D) { phds=D.phds; return *this; } PM_const_decorator(const Plane_map& P) /*{\Mcreate constructs a plane map decorator exploring |P|.}*/ : phds(const_cast(&P)) {} /*{\Moperations 4 4}*/ Vertex_const_handle source(Halfedge_const_handle e) const /*{\Mop returns the source of |e|.}*/ { return e->opposite()->vertex(); } Vertex_const_handle target(Halfedge_const_handle e) const /*{\Mop returns the target of |e|.}*/ { return e->vertex(); } Halfedge_const_handle twin(Halfedge_const_handle e) const /*{\Mop returns the twin of |e|.}*/ { return e->opposite(); } bool is_isolated(Vertex_const_handle v) const /*{\Mop returns |true| iff $A(v) = \emptyset$.}*/ { return v->is_isolated(); } Halfedge_const_handle first_out_edge(Vertex_const_handle v) const /*{\Mop returns one halfedge with source |v|. It's the starting point for the circular iteration over the halfedges with source |v|. \precond |!is_isolated(v)|.}*/ { return v->halfedge()->opposite(); } Halfedge_const_handle last_out_edge(Vertex_const_handle v) const /*{\Mop returns the halfedge with source |v| that is the last in the circular iteration before encountering |first_out_edge(v)| again. \precond |!is_isolated(v)|.}*/ { return v->halfedge()->next(); } Halfedge_const_handle cyclic_adj_succ( Halfedge_const_handle e) const /*{\Mop returns the edge after |e| in the cyclic ordered adjacency list of |source(e)|.}*/ { return e->prev()->opposite(); } Halfedge_const_handle cyclic_adj_pred( Halfedge_const_handle e) const /*{\Mop returns the edge before |e| in the cyclic ordered adjacency list of |source(e)|.}*/ { return e->opposite()->next(); } Halfedge_const_handle next(Halfedge_const_handle e) const /*{\Mop returns the next edge in the face cycle containing |e|.}*/ { return e->next(); } Halfedge_const_handle previous(Halfedge_const_handle e) const /*{\Mop returns the previous edge in the face cycle containing |e|.}*/ { return e->prev(); } Face_const_handle face(Halfedge_const_handle e) const /*{\Mop returns the face incident to |e|.}*/ { return e->face(); } Face_const_handle face(Vertex_const_handle v) const /*{\Mop returns the face incident to |v|. \precond |is_isolated(v)|.}*/ { return v->face(); } Halfedge_const_handle halfedge(Face_const_handle f) const /*{\Mop returns a halfedge in the bounding face cycle of |f| (|Halfedge_const_handle()| if there is no bounding face cycle).}*/ { return f->halfedge(); } /*{\Mtext \headerline{Iteration} \setopdims{7.5cm}{0cm}}*/ Vertex_const_iterator vertices_begin() const { return phds->vertices_begin(); } Halfedge_const_iterator halfedges_begin() const { return phds->halfedges_begin(); } Face_const_iterator faces_begin() const { return phds->faces_begin(); } Vertex_const_iterator vertices_end() const { return phds->vertices_end(); } Halfedge_const_iterator halfedges_end() const { return phds->halfedges_end(); } Face_const_iterator faces_end() const { return phds->faces_end(); } Point_const_iterator points_begin() const { return Point_const_iterator(vertices_begin()); } Point_const_iterator points_end() const { return Point_const_iterator(vertices_end()); } Halfedge_around_vertex_const_circulator out_edges(Vertex_const_handle v) const /*{\Mop returns a circulator for the cyclic adjacency list of |v|.}*/ { return Halfedge_around_vertex_const_circulator(first_out_edge(v)); } Halfedge_around_face_const_circulator face_cycle(Face_const_handle f) const /*{\Mop returns a circulator for the outer face cycle of |f|.}*/ { return Halfedge_around_face_const_circulator(f->halfedge()); } Hole_const_iterator holes_begin(Face_const_handle f) const /*{\Mop returns an iterator for all holes in the interior of |f|. A |Hole_iterator| can be assigned to a |Halfedge_around_face_const_circulator|.}*/ { return f->fc_begin(); } Hole_const_iterator holes_end(Face_const_handle f) const /*{\Mop returns the past-the-end iterator of |f|.}*/ { return f->fc_end(); } Isolated_vertex_const_iterator isolated_vertices_begin(Face_const_handle f) const /*{\Mop returns an iterator for all isolated vertices in the interior of |f|.}*/ { return f->iv_begin(); } Isolated_vertex_const_iterator isolated_vertices_end(Face_const_handle f) const /*{\Mop returns the past the end iterator of |f|.}*/ { return f->iv_end(); } /*{\Mtext \headerline{Associated Information}\setopdims{2.5cm}{4cm} The type |Mark| is the general attribute of an object. The type |GenPtr| is equal to type |void*|.}*/ const Point& point(Vertex_const_handle v) const /*{\Mop returns the embedding of |v|.}*/ { return v->point(); } const Mark& mark(Vertex_const_handle v) const /*{\Mop returns the mark of |v|.}*/ { return v->mark(); } const Mark& mark(Halfedge_const_handle e) const /*{\Mop returns the mark of |e|.}*/ { if (&*e < &*(e->opposite())) return e->mark(); else return e->opposite()->mark(); } // we store the mark in the container with smaller memory address ! const Mark& mark(Face_const_handle f) const /*{\Mop returns the mark of |f|.}*/ { return f->mark(); } const GenPtr& info(Vertex_const_handle v) const /*{\Mop returns a generic information slot.}*/ { return v->info(); } const GenPtr& info(Halfedge_const_handle e) const /*{\Mop returns a generic information slot.}*/ { return e->info(); } const GenPtr& info(Face_const_handle f) const /*{\Mop returns a generic information slot.}*/ { return f->info(); } /*{\Mtext \headerline{Statistics and Integrity}}*/ Size_type number_of_vertices() const /*{\Mop returns the number of vertices.}*/ { return phds->size_of_vertices(); } Size_type number_of_halfedges() const /*{\Mop returns the number of halfedges.}*/ { return phds->size_of_halfedges(); } Size_type number_of_edges() const /*{\Mop returns the number of halfedge pairs.}*/ { return phds->size_of_halfedges()/2; } Size_type number_of_faces() const /*{\Mop returns the number of faces.}*/ { return phds->size_of_faces(); } Size_type number_of_face_cycles() const; /*{\Mop returns the number of face cycles.}*/ Size_type number_of_connected_components() const; /*{\Mop calculates the number of connected components of |P|.}*/ void print_statistics(std::ostream& os = std::cout) const /*{\Mop print the statistics of |P|: the number of vertices, edges, and faces.}*/ { os << "Plane Map - Statistics\n"; os << "|V| = " << number_of_vertices() << std::endl; os << "|E| = " << number_of_edges() << " (" << 2*number_of_edges() << ")" << std::endl; os << "|F| = " << number_of_faces() << std::endl; os << "|Fcs| = " << number_of_face_cycles() << std::endl << std::endl; } void check_integrity_and_topological_planarity(bool faces=true) const; /*{\Mop checks the link structure and the genus of |P|.}*/ }; // PM_const_decorator template std::string PV(VH v) { std::ostringstream os; CGAL::IO::set_pretty_mode(os); if (v != VH()) os << v->point(); else os << "nil"; return os.str(); } template std::string PE(HH e) { std::ostringstream os; if (e==HH()) return "nil"; os << "[" << PV(e->opposite()->vertex()) << "," << PV(e->vertex()) << " " #ifdef CGAL_I_DO_WANT_TO_USE_GENINFO << e->info() #endif << "]"; return os.str(); } template void PM_const_decorator:: check_integrity_and_topological_planarity(bool faces) const { CGAL_NEF_TRACEN("check_integrity_and_topological_planarity:"); using CGAL::Object_index; Object_index VI(vertices_begin(),vertices_end(),'v'); Object_index EI(halfedges_begin(),halfedges_end(),'e'); Object_index FI(faces_begin(),faces_end(),'f'); Vertex_const_handle vit, vend = phds->vertices_end(); int iso_vert_num=0; /* check the source links of out edges and count isolated vertices */ for (vit = vertices_begin() ; vit != vend; ++vit) { if ( is_isolated(vit) ) { if (faces) { CGAL_assertion_msg(vit->face() != Face_const_handle(), VI(vit).c_str()); } ++iso_vert_num; } else { CGAL_assertion_msg( vit->halfedge() != Halfedge_const_handle(), VI(vit).c_str()); CGAL_assertion_msg( vit->halfedge()->vertex() == vit ,VI(vit).c_str()); } } /* check the bidirected links and the face pointer init */ Halfedge_const_iterator eit, eend = phds->halfedges_end(); for (eit = phds->halfedges_begin() ; eit != eend; ++eit) { CGAL_assertion( twin(twin(eit)) == eit ); CGAL_assertion( eit->vertex() != Vertex_const_handle() ); CGAL_assertion( next(eit) != Halfedge_const_handle() ); CGAL_assertion( previous(next(eit)) == eit ); CGAL_assertion( target(eit) == source(next(eit)) ); CGAL_assertion( previous(eit) != Halfedge_const_handle() ); CGAL_assertion( next(previous(eit)) == eit ); CGAL_assertion( target(previous(eit)) == source(eit) ); if ( !faces ) continue; CGAL_assertion( face(eit) != Face_const_handle() ); CGAL_assertion( face(next(eit)) == face(eit) ); CGAL_assertion( face(previous(eit)) == face(eit) ); } bool first=true; int fc_num(0),iv_num(0); Face_const_iterator fit; for (fit = faces_begin(); fit != faces_end(); ++fit) { if (!first && halfedge(fit)!=Halfedge_const_handle()) { CGAL_assertion( face(halfedge(fit))==fit ); ++fc_num; } Hole_const_iterator fcit; for( fcit = holes_begin(fit); fcit != holes_end(fit); ++fcit) { CGAL_assertion( face(fcit)==fit ); ++fc_num; } Isolated_vertex_const_iterator ivit; for(ivit = isolated_vertices_begin(fit); ivit != isolated_vertices_end(fit); ++ivit) { CGAL_assertion( face(ivit)==fit ); ++iv_num; } first=false; } CGAL_assertion(iso_vert_num == iv_num); std::size_t v_num = number_of_vertices() - iso_vert_num; std::size_t e_num = number_of_edges(); std::size_t c_num = number_of_connected_components() - iso_vert_num; std::size_t f_num = number_of_face_cycles() - c_num + 1; CGAL_USE(fc_num); CGAL_USE(iv_num); CGAL_USE(v_num); CGAL_USE(e_num); CGAL_USE(f_num); CGAL_NEF_TRACEV(fc_num);CGAL_NEF_TRACEV(iv_num);CGAL_NEF_TRACEV(iso_vert_num); CGAL_NEF_TRACEV(v_num);CGAL_NEF_TRACEV(e_num);CGAL_NEF_TRACEV(c_num);CGAL_NEF_TRACEV(f_num); // CGAL_assertion(fc_num == f_num && iv_num == iso_vert_num); /* this means all face cycles and all isolated vertices are indeed referenced from a face */ /* every isolated vertex increases the component count one face cycle per component is redundant except one finally check the Euler formula: */ CGAL_assertion( v_num - e_num + f_num == 1 + c_num ); } template typename PM_const_decorator::Size_type PM_const_decorator:: number_of_face_cycles() const { Size_type fc_num=0; CGAL::Unique_hash_map visited; // init with bool() == false Halfedge_const_iterator eit = phds->halfedges_begin(); Halfedge_const_iterator eend = phds->halfedges_end(); for ( ; eit != eend; ++eit) { if (visited[eit]) continue; Halfedge_around_face_const_circulator hfc(eit), hend(hfc); CGAL_For_all(hfc,hend) visited[hfc]=true; ++fc_num; } return fc_num; } template size_t PM_const_decorator:: number_of_connected_components() const { typedef Vertex_const_iterator vc_handle; typedef Halfedge_around_vertex_const_circulator hvc_circulator; int comp_num=0; CGAL::Unique_hash_map< vc_handle, bool> handled(false); vc_handle vit = vertices_begin(), vend = vertices_end(); for ( ; vit != vend; ++vit) { if (handled[vit]) continue; std::list L; L.push_back(vit); handled[vit]=true; /* we keep the invariant that all nodes which have been stacked are marked handled */ while (!L.empty()) { vc_handle v=L.front(); L.pop_front(); if ( is_isolated(v) ) continue; hvc_circulator havc(first_out_edge(v)), hend(havc); CGAL_For_all(havc,hend) { if (!handled[target(havc)]) { L.push_back(target(havc)); handled[target(havc)]=true; } } } ++comp_num; } return comp_num; } struct KERNELPNT { template std::string operator() (const PNT& p) const { std::ostringstream os; os << "(" << CGAL::to_double(p.x()) << "," << CGAL::to_double(p.y()) << ")"; return os.str(); } }; template void print_as_leda_graph(std::ostream& os, const PMCDEC& D, const POINTDA& P) { typedef typename PMCDEC::Vertex_const_iterator Vertex_const_iterator; typedef typename PMCDEC::Halfedge_const_iterator Halfedge_const_iterator; int vn(1), en(1); CGAL::Unique_hash_map v_num; CGAL::Unique_hash_map e_num; os << "LEDA.GRAPH\n" << "point\n" << "int\n"; os << D.number_of_vertices() << std::endl; Vertex_const_iterator vit; for (vit = D.vertices_begin(); vit != D.vertices_end(); ++vit) { v_num[vit] = vn++; os << "|{(" << P(D.point(vit)) << ")}|\n"; typename PMCDEC::Halfedge_around_vertex_const_circulator ecirc(D.first_out_edge(vit)),ecend(ecirc); int l=0; CGAL_For_all(ecirc,ecend) e_num[ecirc]=l++; } os << 2* D.number_of_edges() << std::endl; Halfedge_const_iterator eit; for (eit = D.halfedges_begin(); eit != D.halfedges_end(); ++eit) { e_num[eit] = en++; } for (eit = D.halfedges_begin(); eit != D.halfedges_end(); ++eit) { os << v_num[D.source(eit)] << " " << v_num[D.target(eit)] << " " << e_num[D.twin(eit)] << " "; os << "|{" << e_num[eit] << "}|\n"; } os << std::flush; } } //namespace CGAL #endif // CGAL_PM_CONST_DECORATOR_H