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

CGAL 4.8 - 2D Arrangements

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Arrangement_on_surface_2/unbounded_rational_functions.cpp
// Constructing an arrangement of unbounded portions of rational functions.
#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/CORE_BigInt.h> // NT
#include <CGAL/Algebraic_kernel_d_1.h> // Algebraic Kernel
#include <CGAL/Arr_rational_function_traits_2.h> // Traits
#include <CGAL/Arrangement_2.h> // Arrangement
typedef CORE::BigInt Number_type;
typedef CGAL::Algebraic_kernel_d_1<Number_type> AK1;
typedef CGAL::Arr_rational_function_traits_2<AK1> Traits_2;
typedef Traits_2::Polynomial_1 Polynomial_1;
typedef Traits_2::Algebraic_real_1 Alg_real_1;
typedef CGAL::Arrangement_2<Traits_2> Arrangement_2;
int main ()
{
CGAL::set_pretty_mode(std::cout); // for nice printouts.
// Traits class object
AK1 ak1;
Traits_2 traits(&ak1);
// constructor for rational functions
Traits_2::Construct_curve_2 construct = traits.construct_curve_2_object();
// a polynomial representing x .-)
Polynomial_1 x = CGAL::shift(Polynomial_1(1),1);
// container storing all arcs
std::vector<Traits_2::Curve_2> arcs;
// Create the rational functions (y = 1 / x), and (y = -1 / x).
Polynomial_1 P1(1);
Polynomial_1 minusP1(-P1);
Polynomial_1 Q1 = x;
arcs.push_back(construct(P1, Q1));
arcs.push_back(construct(minusP1, Q1));
// Create a bounded segments of the parabolas (y = -4*x^2 + 3) and
// (y = 4*x^2 - 3), defined over [-sqrt(3)/2, sqrt(3)/2].
Polynomial_1 P2 = -4*x*x+3;
Polynomial_1 minusP2 = -P2;
std::vector<std::pair<Alg_real_1,int> > roots;
// [-sqrt(3)/2, sqrt(3)/2]
traits.algebraic_kernel_d_1()->solve_1_object()(P2, std::back_inserter(roots));
arcs.push_back(construct(P2, roots[0].first, roots[1].first));
arcs.push_back(construct(minusP2, roots[0].first, roots[1].first));
// Create the rational function (y = 1 / 2*x) for x > 0, and the
// rational function (y = -1 / 2*x) for x < 0.
Polynomial_1 P3(1);
Polynomial_1 minusP3(-P3);
Polynomial_1 Q3 = 2*x;
arcs.push_back(construct(P3, Q3, Alg_real_1(0), true));
arcs.push_back(construct(minusP3, Q3, Alg_real_1(0), false));
// Construct the arrangement of the six arcs.
//Arrangement_2 arr(&traits);
Arrangement_2 arr;
insert(arr, arcs.begin(), arcs.end());
// Print the arrangement size.
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;
return 0;
}
#endif