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

CGAL 4.8 - 2D Arrangements

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Arrangement_on_surface_2/unbounded_non_intersecting.cpp
// Constructing an arrangement of unbounded linear objects using the insertion
// function for non-intersecting curves.
#include <CGAL/Simple_cartesian.h>
#include <CGAL/Arr_linear_traits_2.h>
#include <CGAL/Arrangement_2.h>
typedef int Number_type;
typedef CGAL::Simple_cartesian<Number_type> 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_curve_2;
typedef CGAL::Arrangement_2<Traits_2> Arrangement_2;
typedef Arrangement_2::Vertex_handle Vertex_handle;
typedef Arrangement_2::Halfedge_handle Halfedge_handle;
int main ()
{
Arrangement_2 arr;
// Insert a line in the (currently single) unbounded face of the arrangement,
// then split it into two at (0,0). Assign v to be the split point.
X_monotone_curve_2 c1 = Line_2 (Point_2 (-1, 0), Point_2 (1, 0));
Halfedge_handle e1 = arr.insert_in_face_interior (c1,
arr.unbounded_face());
X_monotone_curve_2 c1_left = Ray_2 (Point_2 (0, 0), Point_2 (-1, 0));
X_monotone_curve_2 c1_right = Ray_2 (Point_2 (0, 0), Point_2 (1, 0));
e1 = arr.split_edge (e1, c1_left, c1_right);
Vertex_handle v = e1->target();
CGAL_assertion (! v->is_at_open_boundary());
// Add two more rays using the specialized insertion functions.
X_monotone_curve_2 c2 = Ray_2 (Point_2 (0, 0), Point_2 (-1, 1));
X_monotone_curve_2 c3 = Ray_2 (Point_2 (0, 0), Point_2 (1, 1));
arr.insert_from_right_vertex (c2, v);
arr.insert_from_left_vertex (c3, v);
// Insert three more interior-disjoint rays.
X_monotone_curve_2 c4 = Ray_2 (Point_2 (0, -1), Point_2 (-2, -2));
X_monotone_curve_2 c5 = Ray_2 (Point_2 (0, -1), Point_2 (2, -2));
X_monotone_curve_2 c6 = Ray_2 (Point_2 (0, 0), Point_2 (0, 1));
insert_non_intersecting_curve (arr, c4);
insert_non_intersecting_curve (arr, c5);
insert_non_intersecting_curve (arr, c6);
// Print out the size of the resulting arrangement.
std::cout << "The arrangement size:" << std::endl
<< " V = " << arr.number_of_vertices()
<< " (plus " << arr.number_of_vertices_at_infinity()
<< " at infinity)"
<< ", E = " << arr.number_of_edges()
<< ", F = " << arr.number_of_faces()
<< " (" << arr.number_of_unbounded_faces() << " unbounded)"
<< std::endl << std::endl;
// Print the outer CCBs of the unbounded faces.
Arrangement_2::Face_const_iterator fit;
Arrangement_2::Ccb_halfedge_const_circulator first, curr;
Arrangement_2::Halfedge_const_handle he;
int k = 1;
for (fit = arr.faces_begin(); fit != arr.faces_end(); ++fit, k++) {
if (! fit->is_unbounded())
continue;
std::cout << "Face no. " << k << ": ";
curr = first = fit->outer_ccb();
if (! curr->source()->is_at_open_boundary())
std::cout << "(" << curr->source()->point() << ")";
do {
he = curr;
if (! he->is_fictitious())
std::cout << " [" << he->curve() << "] ";
else
std::cout << " [ ... ] ";
if (! he->target()->is_at_open_boundary())
std::cout << "(" << he->target()->point() << ")";
++curr;
} while (curr != first);
std::cout << std::endl;
}
return 0;
}