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

CGAL 4.8 - 2D Arrangements

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Arrangement_on_surface_2/rational_functions.cpp
// Constructing an arrangement of arcs 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.
// create a polynomial representing x .-)
Polynomial_1 x = CGAL::shift(Polynomial_1(1),1);
// Traits class object
Traits_2 traits;
Traits_2::Construct_x_monotone_curve_2 construct_arc
= traits.construct_x_monotone_curve_2_object();
// container storing all arcs
std::vector<Traits_2::X_monotone_curve_2> arcs;
// Create an arc supported by the polynomial y = x^4 - 6x^2 + 8,
// defined over the interval [-2.1, 2.1]:
Polynomial_1 P1 = x*x*x*x - 6*x*x + 8;
Alg_real_1 l(Traits_2::Algebraic_kernel_d_1::Bound(-2.1));
Alg_real_1 r(Traits_2::Algebraic_kernel_d_1::Bound(2.1));
arcs.push_back(construct_arc(P1, l, r));
// Create an arc supported by the function y = x / (1 + x^2),
// defined over the interval [-3, 3]:
Polynomial_1 P2 = x;
Polynomial_1 Q2 = 1+x*x;
arcs.push_back(construct_arc(P2, Q2, Alg_real_1(-3), Alg_real_1(3)));
// Create an arc supported by the parbola y = 8 - x^2,
// defined over the interval [-2, 3]:
Polynomial_1 P3 = 8 - x*x;
arcs.push_back(construct_arc(P3, Alg_real_1(-2), Alg_real_1(3)));
// Create an arc supported by the line y = -2x,
// defined over the interval [-3, 0]:
Polynomial_1 P4 = -2*x;
arcs.push_back(construct_arc(P4, Alg_real_1(-3), Alg_real_1(0)));
// Construct the arrangement of the four arcs.
// Print the arcs.
for (unsigned int i(0); i < arcs.size(); ++i)
std::cout << arcs[i]<<std::endl;
Arrangement_2 arr(&traits);
insert(arr, arcs.begin(), arcs.end());
// Print the arrangement size.
std::cout << "The arrangement size:" << std::endl
<< " V = " << arr.number_of_vertices()
<< ", E = " << arr.number_of_edges()
<< ", F = " << arr.number_of_faces() << std::endl;
return 0;
}
#endif