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

CGAL 4.8 - 2D Arrangements

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Arrangement_on_surface_2/overlay_unbounded.cpp
// A face overlay of two arrangements with unbounded faces.
#include <string>
#include <boost/lexical_cast.hpp>
#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
#include <CGAL/Arr_linear_traits_2.h>
#include <CGAL/Arrangement_2.h>
#include <CGAL/Arr_extended_dcel.h>
#include <CGAL/Arr_overlay_2.h>
#include <CGAL/Arr_default_overlay_traits.h>
// Define a functor for creating a label from a characer and an integer.
struct Overlay_label
{
std::string operator() (char c, int i) const
{
return boost::lexical_cast<std::string>(c) +
boost::lexical_cast<std::string>(i);
}
};
typedef CGAL::Exact_predicates_exact_constructions_kernel Kernel;
typedef CGAL::Arr_linear_traits_2<Kernel> Traits_2;
typedef Traits_2::Point_2 Point_2;
typedef Traits_2::Segment_2 Segment_2;
typedef Traits_2::Ray_2 Ray_2;
typedef Traits_2::Line_2 Line_2;
typedef Traits_2::X_monotone_curve_2 X_monotone_curves_2;
typedef CGAL::Arr_face_extended_dcel<Traits_2, char> DcelA;
typedef CGAL::Arrangement_2<Traits_2, DcelA> ArrangementA_2;
typedef CGAL::Arr_face_extended_dcel<Traits_2, int> DcelB;
typedef CGAL::Arrangement_2<Traits_2, DcelB> ArrangementB_2;
typedef CGAL::Arr_face_extended_dcel<Traits_2, std::string> DcelRes;
typedef CGAL::Arrangement_2<Traits_2, DcelRes> ArrangementRes_2;
typedef CGAL::Arr_face_overlay_traits<ArrangementA_2,
ArrangementB_2,
ArrangementRes_2,
Overlay_label> Overlay_traits;
int main ()
{
// Construct the first arrangement, induced by two line y = x and y = -x.
ArrangementA_2 arr1;
insert (arr1, Line_2 (Point_2(0, 0), Point_2(1, 1)));
insert (arr1, Line_2 (Point_2(0, 0), Point_2(1, -1)));
// Label the four (unbounded) face of the arrangement as 'A' to 'D'.
// We do so by traversing the incident faces to the halfedges aroung the
// single arrangement vertex (0, 0).
CGAL_assertion (arr1.number_of_vertices() == 1);
ArrangementA_2::Halfedge_around_vertex_circulator first, curr;
char clabel = 'A';
curr = first = arr1.vertices_begin()->incident_halfedges();
do {
curr->face()->set_data (clabel);
++clabel;
++curr;
} while (curr != first);
std::cout << "Done with arr1." << std::endl;
// Construct the second arrangement, containing a single square-shaped face.
ArrangementB_2 arr2;
insert (arr2, Segment_2 (Point_2(-4, -4), Point_2(4, -4)));
insert (arr2, Segment_2 (Point_2(4, -4), Point_2(4, 4)));
insert (arr2, Segment_2 (Point_2(4, 4), Point_2(-4, 4)));
insert (arr2, Segment_2 (Point_2(-4, 4), Point_2(-4, -4)));
// Give the unbounded face the index 1, and the bounded face the index 2.
CGAL_assertion (arr2.number_of_faces() == 2);
ArrangementB_2::Face_iterator fit;
for (fit = arr2.faces_begin(); fit != arr2.faces_end(); ++fit)
fit->set_data ((fit == arr2.unbounded_face()) ? 1 : 2);
std::cout << "Done with arr2." << std::endl;
// Compute the overlay of the two arrangements.
ArrangementRes_2 overlay_arr;
Overlay_traits overlay_traits;
overlay (arr1, arr2, overlay_arr, overlay_traits);
// Go over the faces of the overlaid arrangement and their labels.
ArrangementRes_2::Face_iterator res_fit;
std::cout << "The overlay faces are: ";
for (res_fit = overlay_arr.faces_begin();
res_fit != overlay_arr.faces_end(); ++res_fit)
{
std::cout << res_fit->data() << " ("
<< (res_fit->is_unbounded() ? "unbounded" : "bounded")
<< ")." << std::endl;
}
return 0;
}