CGAL 5.6 - 2D Arrangements
Arrangement_on_surface_2/unbounded_rational_functions.cpp
// Constructing an arrangement of unbounded portions of rational functions.
#include <CGAL/config.h>
#ifndef CGAL_USE_CORE
#include <iostream>
int main() {
std::cout << "Sorry, this example needs CORE ..." << std::endl;
return 0;
}
#else
#include "arr_rat_functions.h"
#include "arr_print.h"
int main() {
CGAL::IO::set_pretty_mode(std::cout); // for nice printouts.
// Define a traits class object and a constructor for rational functions.
AK1 ak1;
Traits traits(&ak1);
auto construct = traits.construct_curve_2_object();
// Define a polynomial representing x.
Polynomial x = CGAL::shift(Polynomial(1), 1);
// Define a container storing all arcs.
std::vector<Traits::Curve_2> arcs;
// Create the arcs (C1, C'1) of the rational functions (y = 1 / x, y = -1 / x).
Polynomial P1(1);
Polynomial minusP1(-P1);
Polynomial Q1 = x;
arcs.push_back(construct(P1, Q1));
arcs.push_back(construct(minusP1, Q1));
// Create the bounded segments (C2, C'2) of the parabolas (y = -4*x^2 + 3)
// and (y = 4*x^2 - 3), defined over [-sqrt(3)/2, sqrt(3)/2].
Polynomial P2 = -4*x*x+3;
Polynomial minusP2 = -P2;
std::vector<std::pair<Alg_real, int> > roots;
ak1.solve_1_object()(P2, std::back_inserter(roots));// [-sqrt(3)/2, sqrt(3)/2]
arcs.push_back(construct(P2, roots[0].first, roots[1].first));
arcs.push_back(construct(minusP2, roots[0].first, roots[1].first));
// Create the arcs (C3, C'3) of (i) the rational function (y = 1 / 2*x) for
// x > 0, and (ii) the rational function (y = -1 / 2*x) for x < 0.
Polynomial P3(1);
Polynomial minusP3(-P3);
Polynomial Q3 = 2*x;
arcs.push_back(construct(P3, Q3, Alg_real(0), true));
arcs.push_back(construct(minusP3, Q3, Alg_real(0), false));
// Construct the arrangement of the six arcs and print its size.
Arrangement arr(&traits);
insert(arr, arcs.begin(), arcs.end());
print_unbounded_arrangement_size(arr);
return 0;
}
#endif