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\begin{ccRefClass}{Explorer}\ccCreationVariable{D}

\ccDefinition

... 



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\ccTypes

\ccNestedType{Sphere_point}{embedding vertices.}

\ccNestedType{Sphere_segment}{embedding edges.}

\ccNestedType{Sphere_circle}{embedding loops.}

\ccNestedType{Mark}{attributes of objects (vertices, edges, faces).}

\ccNestedType{Size_type}{size type.}

Local types are handles, iterators and circulators of the following
kind: \ccc{Vertex_handle}, \ccc{Vertex_iterator},
\ccc{Halfedge_handle}, \ccc{Halfedge_iterator}, \ccc{Halfloop_handle},
\ccc{Halfloop_iterator}, \ccc{Face_handle}, \ccc{Face_iterator}.
Additionally the following circulators are defined.



\ccNestedType{Halfedge_around_vertex_const_circulator}{circulating the
  adjacency list of an vertex \ccc{v}.  }

\ccNestedType{Halfedge_around_face_const_circulator}{circulating the
  face cycle of an face \ccc{f}.  }

\ccNestedType{Face_cycle_const_iterator}{iterating all face cycles of
  an face \ccc{f}.  The iterator has method \ccc{bool is_vertex()},
  \ccc{bool is_halfedge()}, \ccc{bool is_halfloop()}, and can be
  converted to the corresponding handles \ccc{Vertex_const_handle},
  \ccc{Halfedge_const_handle}, or \ccc{Halfloop_const_handle}.  }

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\ccCreation

an explorer is copy constructible and available via the corresponding
method of \ccc{Nef_polyhedron_S2}.

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\ccOperations

\ccMethod{Vertex_const_handle source(Halfedge_const_handle e)
  ;}{returns the source of \ccc{e}.  }

\ccMethod{Vertex_const_handle target(Halfedge_const_handle e)
  ;}{returns the target of \ccc{e}.  }

\ccMethod{Halfedge_const_handle twin(Halfedge_const_handle e)
  ;}{returns the twin of \ccc{e}.  }

\ccMethod{Halfloop_const_handle twin(Halfloop_const_handle l)
  ;}{returns the twin of \ccc{l}.  }

\ccMethod{bool is_isolated(Vertex_const_handle v) ;}{returns
  \ccc{true} when \ccc{v} is linked to the interior of a face.  }

\ccMethod{Halfedge_const_handle first_out_edge(Vertex_const_handle v)
  ;}{returns one edge with source \ccc{v}. It's the starting point for
  the circular iteration over the edges with source \ccc{v}.
  \ccPrecond \ccc{!is_isolated(v)}.  }

\ccMethod{Halfedge_const_handle last_out_edge(Vertex_const_handle v)
  ;}{returns one edge with source \ccc{v}. \ccPrecond
  \ccc{!is_isolated(v)}.  }

\ccMethod{Halfedge_const_handle cyclic_adj_succ(Halfedge_const_handle
  e) ;}{returns the edge after \ccc{e} in the cyclic ordered adjacency
  list of \ccc{source(e)}.  }

\ccMethod{Halfedge_const_handle cyclic_adj_pred(Halfedge_const_handle
  e) ;}{returns the edge before \ccc{e} in the cyclic ordered
  adjacency list of \ccc{source(e)}.  }

\ccMethod{Halfedge_const_handle next(Halfedge_const_handle e)
  ;}{returns the next edge in the face cycle containing \ccc{e}.  }

\ccMethod{Halfedge_const_handle previous(Halfedge_const_handle e)
  ;}{returns the previous edge in the face cycle containing \ccc{e}.
  }

\ccMethod{Face_const_handle face(Halfedge_const_handle e) ;}{returns
  the face incident to \ccc{e}.  }

\ccMethod{Face_const_handle face(Halfloop_const_handle l) ;}{returns
  the face incident to \ccc{l}.  }

\ccMethod{Face_const_handle face(Vertex_const_handle v) ;}{returns the
  face incident to \ccc{v}.  \ccPrecond \ccc{is_isolated(v)}.  }

\ccHeading{Iteration} 

\ccMethod{Halfloop_const_handle halfloop() ;}{returns access to the
  loop.  }

\ccMethod{bool has_loop() ;}{returns true iff there is a loop.  }

\ccMethod{Halfedge_around_vertex_const_circulator
  out_edges(Vertex_const_handle v) ;}{returns a circulator for the
  cyclic adjacency list of \ccc{v}.  \ccPrecond the adjacency list is
  not empty.  }

\ccMethod{Face_cycle_const_iterator
  face_cycles_begin(Face_const_handle f) ;}{returns an iterator for
  all bounding face cycles of \ccc{f}.  The iterator is is convertable
  to \ccc{Vertex_const_handle}, \ccc{Halfloop_const_handle}, or
  \ccc{Halfedge_const_handle}.  }

\ccMethod{Face_cycle_const_iterator face_cycles_end(Face_const_handle
  f) ;}{returns the past the end iterator of \ccc{f}.  }

\ccHeading{Statistics and Integrity} 

\ccMethod{Size_type number_of_vertices() ;}{returns the number of
  vertices.  }

\ccMethod{Size_type number_of_halfedges() ;}{returns the number of
  halfedges.  }

\ccMethod{Size_type number_of_edges() ;}{returns the number of edges.
  }

\ccMethod{Size_type number_of_halfloops() ;}{returns the number of
  halfloops.  }

\ccMethod{Size_type number_of_loops() ;}{returns the number of loops.
  }

\ccMethod{Size_type number_of_faces() ;}{returns the number of faces.
  }

\ccMethod{Size_type number_of_face_cycles() ;}{returns the number of
  face cycles.  }

\ccMethod{Size_type number_of_connected_components() ;}{calculates the
  number of connected components of \ccc{P}.  }

\ccMethod{void print_statistics(std::ostream& os = std::cout) ;}{print
  the statistics of \ccc{P}: the number of vertices, edges, and faces.
  }

\ccMethod{void check_integrity_and_topological_planarity(bool
  faces=true) ;}{checks the link structure and the genus of \ccc{P}.
  }

\ccHeading{Associated Information}

\ccMethod{const Sphere_point& point(Vertex_const_handle v) ;}{returns
  the embedding of \ccc{v}.  }

\ccMethod{const Sphere_circle& circle(Halfedge_const_handle e)
  ;}{returns the circle supporting \ccc{e}.  }

\ccMethod{const Sphere_circle& circle(Halfloop_const_handle l)
  ;}{returns the circle supporting \ccc{l}.  }

\ccMethod{Mark mark(Vertex_const_handle v) ;}{returns the mark of
  \ccc{v}.  }

\ccMethod{Mark mark(Halfedge_const_handle e) ;}{returns the mark of
  \ccc{e}.  }

\ccMethod{Mark mark(Halfloop_const_handle l) ;}{returns the mark of
  \ccc{l}.  }

\ccMethod{Mark mark(Face_const_handle f) ;}{returns the mark of
  \ccc{f}.  }

\ccHeading{Iteration} 

The list of all objects can be accessed via iterator ranges.
For comfortable iteration we also provide iterations macros. 
The iterator range access operations are of the following kind:\\
\ccc{Vertex_iterator   vertices_begin()/vertices_end()}\\
\ccc{Halfedge_iterator halfedges_begin()/halfedges_end()}\\
\ccc{Halfloop_iterator halfloops_begin()/halfloops_end()}\\
\ccc{Face_iterator     faces_begin()/faces_end()}

The macros are then \ccc{CGAL_forall_vertices(v,M)},
\ccc{CGAL_forall_halfedges(e,M)}, \ccc{CGAL_forall_faces(f,M)},
\ccc{CGAL_forall_face_cycles_of(fc,F)} where \ccc{M} is a sphere map
and \ccc{F} is a face.

\end{ccRefClass}