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\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.14.2 - CGAL and the Boost Graph Library
// Adapting the dual of an arrangement to a BGL graph.
#include "arr_rational_nt.h"
#include <CGAL/Cartesian.h>
#include <CGAL/Arr_segment_traits_2.h>
#include <CGAL/Arr_extended_dcel.h>
#include <CGAL/Arrangement_2.h>
#include <CGAL/graph_traits_dual_arrangement_2.h>
#include <CGAL/Arr_face_index_map.h>
#include <climits>
#include <boost/graph/breadth_first_search.hpp>
#include <boost/graph/visitors.hpp>
#include "arr_print.h"
// A property map that reads/writes the information to/from the extended
// face.
template <typename Arrangement, class Type> class Extended_face_property_map {
typedef typename Arrangement::Face_handle Face_handle;
// Boost property type definitions.
typedef boost::read_write_property_map_tag category;
typedef Type value_type;
typedef value_type& reference;
typedef Face_handle key_type;
// The get function is required by the property map concept.
friend reference get(const Extended_face_property_map&, key_type key)
{ return key->data(); }
// The put function is required by the property map concept.
friend void put(const Extended_face_property_map&,
key_type key, value_type val)
{ key->set_data(val); }
typedef CGAL::Arrangement_2<Traits_2, Dcel> Ex_arrangement;
typedef CGAL::Dual<Ex_arrangement> Dual_arrangement;
typedef Extended_face_property_map<Ex_arrangement,unsigned int>
typedef Kernel::Point_2 Point_2;
typedef Kernel::Segment_2 Segment_2;
int main()
// Construct an arrangement of seven intersecting line segments.
Point_2 p1(1, 1), p2(1, 4), p3(2, 2), p4(3, 7), p5(4, 4), p6(7, 1), p7(9, 3);
Ex_arrangement arr;
insert(arr, Segment_2(p1, p6));
insert(arr, Segment_2(p1, p4)); insert(arr, Segment_2(p2, p6));
insert(arr, Segment_2(p3, p7)); insert(arr, Segment_2(p3, p5));
insert(arr, Segment_2(p6, p7)); insert(arr, Segment_2(p4, p7));
// Create a mapping of the arrangement faces to indices.
Face_index_map index_map(arr);
// Perform breadth-first search from the unbounded face, using the event
// visitor to associate each arrangement face with its discover time.
unsigned int time = 0;
boost::breadth_first_search(Dual_arrangement(arr), arr.unbounded_face(),
(stamp_times(Face_property_map(), time,
// Print the discover time of each arrangement face.
Ex_arrangement::Face_iterator fit;
for (fit = arr.faces_begin(); fit != arr.faces_end(); ++fit) {
std::cout << "Discover time " << fit->data() << " for ";
if (fit != arr.unbounded_face()) {
std::cout << "face ";
else std::cout << "the unbounded face." << std::endl;
return 0;