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

CGAL 4.8 - 2D Arrangements

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Arrangement_on_surface_2/conic_multiplicities.cpp
// Handling intersection points with multiplicity between conic arcs.
#include <CGAL/basic.h>
#ifndef CGAL_USE_CORE
#include <iostream>
int main ()
{
std::cout << "Sorry, this example needs CORE ..." << std::endl;
return 0;
}
#else
#include <CGAL/Cartesian.h>
#include <CGAL/CORE_algebraic_number_traits.h>
#include <CGAL/Arr_conic_traits_2.h>
#include <CGAL/Arrangement_2.h>
#include <CGAL/Arr_naive_point_location.h>
#include "arr_print.h"
typedef CGAL::CORE_algebraic_number_traits Nt_traits;
typedef Nt_traits::Rational Rational;
typedef Nt_traits::Algebraic Algebraic;
typedef CGAL::Cartesian<Rational> Rat_kernel;
typedef Rat_kernel::Point_2 Rat_point_2;
typedef Rat_kernel::Segment_2 Rat_segment_2;
typedef Rat_kernel::Circle_2 Rat_circle_2;
typedef CGAL::Cartesian<Algebraic> Alg_kernel;
typedef CGAL::Arr_conic_traits_2<Rat_kernel,
Alg_kernel,
Nt_traits> Traits_2;
typedef Traits_2::Point_2 Point_2;
typedef Traits_2::Curve_2 Conic_arc_2;
typedef CGAL::Arrangement_2<Traits_2> Arrangement_2;
typedef CGAL::Arr_naive_point_location<Arrangement_2> Naive_pl;
int main ()
{
Arrangement_2 arr;
Naive_pl pl (arr);
// Insert a hyperbolic arc, supported by the hyperbola y = x^2/(1-x)
// (or: x^2 + xy - y = 0) with the endpoints (-1, 1/2) and (1/2, 1/2).
// Note that the arc is counterclockwise oriented.
Point_2 ps1 (-1, Rational(1,2));
Point_2 pt1 (Rational(1,2), Rational(1,2));
Conic_arc_2 cv1 (1, 0, 1, 0, -1, 0, CGAL::COUNTERCLOCKWISE, ps1, pt1);
insert (arr, cv1, pl);
// Insert the bottom half of the circle centered at (0, 1/2) whose radius
// is 1/2 (therefore its squared radius is 1/4).
Rat_circle_2 circ2 (Rat_point_2(0, Rational(1,2)), Rational(1,4));
Point_2 ps2 (-Rational(1,2), Rational(1,2));
Point_2 pt2 (Rational(1,2), Rational(1,2));
Conic_arc_2 cv2 (circ2, CGAL::COUNTERCLOCKWISE, ps2, pt2);
insert (arr, cv2, pl);
// Print the resulting arrangement.
print_arrangement (arr);
return 0;
}
#endif