CGAL 4.7 - 2D Arrangements: Arrangement_on_surface_2/algebraic_curves.cpp

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

CGAL 4.7 - 2D Arrangements

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Arrangement_on_surface_2/algebraic_curves.cpp
#include <CGAL/basic.h>
#include <iostream>
#if (!CGAL_USE_CORE) && (!CGAL_USE_LEDA) && (!(CGAL_USE_GMP && CGAL_USE_MPFI))
int main ()
{
std::cout << "Sorry, this example needs CORE, LEDA, or GMP+MPFI ..."
<< std::endl;
return 0;
}
#else
#include <CGAL/Arrangement_2.h>
#include <CGAL/Arr_algebraic_segment_traits_2.h>
#if CGAL_USE_GMP && CGAL_USE_MPFI
#include <CGAL/Gmpz.h>
typedef CGAL::Gmpz Integer;
#elif CGAL_USE_CORE
#include <CGAL/CORE_BigInt.h>
typedef CORE::BigInt Integer;
#else
#include <CGAL/leda_integer.h>
typedef LEDA::integer Integer;
#endif
typedef CGAL::Arr_algebraic_segment_traits_2<Integer> Arr_traits_2;
typedef CGAL::Arrangement_2<Arr_traits_2> Arrangement_2;
typedef Arr_traits_2::Curve_2 Curve_2;
typedef Arr_traits_2::Polynomial_2 Polynomial_2;
int main() {
// For nice printouts
CGAL::set_pretty_mode(std::cout);
Arr_traits_2 arr_traits;
// Functor to create a curve from a Polynomial_2
Arr_traits_2::Construct_curve_2 construct_curve
= arr_traits.construct_curve_2_object();
Polynomial_2 x = CGAL::shift(Polynomial_2(1),1,0);
Polynomial_2 y = CGAL::shift(Polynomial_2(1),1,1);
Arrangement_2 arr(&arr_traits);
// Construct an (unbounded line) with equation 3x-5y+2=0
Polynomial_2 f1 = 3*x-5*y+2;
Curve_2 cv1 = construct_curve(f1);
std::cout << "Adding curve " << f1 << " to the arrangement" << std::endl;
CGAL::insert(arr,cv1);
// Construct the ellipse x^2+3*y^2-10=0
Polynomial_2 f2 = CGAL::ipower(x,2)+3*CGAL::ipower(y,2)-10;
Curve_2 cv2 = construct_curve(f2);
std::cout << "Adding curve " << f2 << " to the arrangement" << std::endl;
CGAL::insert(arr,cv2);
// Construct a cubic curve with isoated point, and vertical asymptote
// x^2+y^2+xy^2
Polynomial_2 f3 = CGAL::ipower(x,2)+CGAL::ipower(y,2)+x*CGAL::ipower(y,2);
Curve_2 cv3 = construct_curve(f3);
std::cout << "Adding curve " << f3 << " to the arrangement" << std::endl;
CGAL::insert(arr,cv3);
// Construct a curve of degree 6 with equation x^6+y^6-x^3y^3-12
Polynomial_2 f4 = CGAL::ipower(x,6)+CGAL::ipower(y,6)-
CGAL::ipower(x,3)*CGAL::ipower(y,3)-12;
Curve_2 cv4 = construct_curve(f4);
std::cout << "Adding curve " << f4 << " to the arrangement" << std::endl;
CGAL::insert(arr,cv4);
// 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