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

CGAL 4.8 - 2D Arrangements

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Arrangement_on_surface_2/face_extension_overlay.cpp
// A face overlay of two arrangements with extended face records.
#include <CGAL/Cartesian.h>
#include <CGAL/Exact_rational.h>
#include <CGAL/Arr_segment_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>
typedef CGAL::Cartesian<CGAL::Exact_rational> Kernel;
typedef CGAL::Arr_segment_traits_2<Kernel> Traits_2;
typedef Traits_2::Point_2 Point_2;
typedef Traits_2::X_monotone_curve_2 Segment_2;
typedef CGAL::Arr_face_extended_dcel<Traits_2, bool> Dcel;
typedef CGAL::Arrangement_2<Traits_2, Dcel> Arrangement_2;
typedef CGAL::Arr_face_overlay_traits<Arrangement_2,
Arrangement_2,
Arrangement_2,
std::logical_and<bool> > Overlay_traits;
int main ()
{
// Construct the first arrangement, containing a square-shaped face.
Arrangement_2 arr1;
Segment_2 s1 (Point_2(2, 2), Point_2(6, 2));
Segment_2 s2 (Point_2(6, 2), Point_2(6, 6));
Segment_2 s3 (Point_2(6, 6), Point_2(2, 6));
Segment_2 s4 (Point_2(2, 6), Point_2(2, 2));
insert_non_intersecting_curve (arr1, s1);
insert_non_intersecting_curve (arr1, s2);
insert_non_intersecting_curve (arr1, s3);
insert_non_intersecting_curve (arr1, s4);
// Mark just the bounded face.
Arrangement_2::Face_iterator fit;
CGAL_assertion (arr1.number_of_faces() == 2);
for (fit = arr1.faces_begin(); fit != arr1.faces_end(); ++fit)
fit->set_data (fit != arr1.unbounded_face());
// Construct the second arrangement, containing a rhombus-shaped face.
Arrangement_2 arr2;
Segment_2 t1 (Point_2(4, 1), Point_2(7, 4));
Segment_2 t2 (Point_2(7, 4), Point_2(4, 7));
Segment_2 t3 (Point_2(4, 7), Point_2(1, 4));
Segment_2 t4 (Point_2(1, 4), Point_2(4, 1));
insert_non_intersecting_curve (arr2, t1);
insert_non_intersecting_curve (arr2, t2);
insert_non_intersecting_curve (arr2, t3);
insert_non_intersecting_curve (arr2, t4);
// Mark just the bounded face.
CGAL_assertion (arr2.number_of_faces() == 2);
for (fit = arr2.faces_begin(); fit != arr2.faces_end(); ++fit)
fit->set_data (fit != arr2.unbounded_face());
// Compute the overlay of the two arrangements, marking only the faces that
// are intersections of two marked faces in arr1 and arr2, respectively.
Arrangement_2 overlay_arr;
Overlay_traits overlay_traits;
overlay (arr1, arr2, overlay_arr, overlay_traits);
// Go over the faces of the overlaid arrangement and print just the marked
// ones.
Arrangement_2::Ccb_halfedge_circulator curr;
std::cout << "The union is: ";
for (fit = overlay_arr.faces_begin(); fit != overlay_arr.faces_end(); ++fit) {
if (! fit->data())
continue;
curr = fit->outer_ccb();
std::cout << curr->source()->point();
do {
std::cout << " --> " << curr->target()->point();
++curr;
} while (curr != fit->outer_ccb());
std::cout << std::endl;
}
return 0;
}