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

CGAL 4.8 - 2D Arrangements

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Arrangement_on_surface_2/circles.cpp
// Constructing an arrangement of circles using the conic-arc traits.
#include <CGAL/Cartesian.h>
#include <CGAL/Exact_rational.h>
#include <CGAL/Arr_circle_segment_traits_2.h>
#include <CGAL/Arrangement_2.h>
typedef CGAL::Cartesian<CGAL::Exact_rational> Kernel;
typedef Kernel::Circle_2 Circle_2;
typedef CGAL::Arr_circle_segment_traits_2<Kernel> Traits_2;
typedef Traits_2::CoordNT CoordNT;
typedef Traits_2::Point_2 Point_2;
typedef Traits_2::Curve_2 Curve_2;
typedef CGAL::Arrangement_2<Traits_2> Arrangement_2;
int main()
{
// Create a circle centered at the origin with radius 5.
Kernel::Point_2 c1 = Kernel::Point_2(0, 0);
CGAL::Exact_rational sqr_r1 = CGAL::Exact_rational(25); // = 5^2
Circle_2 circ1 = Circle_2(c1, sqr_r1, CGAL::CLOCKWISE);
Curve_2 cv1 = Curve_2(circ1);
// Create a circle centered at (7,7) with radius 5.
Kernel::Point_2 c2 = Kernel::Point_2(7, 7);
CGAL::Exact_rational sqr_r2 = CGAL::Exact_rational(25); // = 5^2
Circle_2 circ2 = Circle_2(c2, sqr_r2, CGAL::CLOCKWISE);
Curve_2 cv2 = Curve_2(circ2);
// Create a circle centered at (4,-0.5) with radius 3.5 (= 7/2).
Kernel::Point_2 c3 = Kernel::Point_2(4, CGAL::Exact_rational(-1,2));
CGAL::Exact_rational sqr_r3 = CGAL::Exact_rational(49, 4); // = 3.5^2
Circle_2 circ3 = Circle_2(c3, sqr_r3, CGAL::CLOCKWISE);
Curve_2 cv3 = Curve_2(circ3);
// Construct the arrangement of the three circles.
Arrangement_2 arr;
insert(arr, cv1);
insert(arr, cv2);
insert(arr, cv3);
// Locate the vertex with maximal degree.
Arrangement_2::Vertex_const_iterator vit;
Arrangement_2::Vertex_const_handle v_max;
std::size_t max_degree = 0;
for (vit = arr.vertices_begin(); vit != arr.vertices_end(); ++vit) {
if (vit->degree() > max_degree) {
v_max = vit;
max_degree = vit->degree();
}
}
std::cout << "The vertex with maximal degree in the arrangement is: "
<< "v_max = (" << v_max->point() << ") "
<< "with degree " << max_degree << "." << std::endl;
return 0;
}