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

CGAL 4.8 - 2D Arrangements

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Arrangement_on_surface_2/algebraic_segments.cpp
#include <CGAL/config.h>
#include <CGAL/use.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;
typedef Arr_traits_2::Algebraic_real_1 Algebraic_real_1;
typedef Arr_traits_2::X_monotone_curve_2 X_monotone_curve_2;
typedef Arr_traits_2::Point_2 Point_2;
int main() {
Arr_traits_2 arr_traits;
Arr_traits_2::Construct_curve_2 construct_curve
= arr_traits.construct_curve_2_object();
Arr_traits_2::Construct_x_monotone_segment_2 construct_x_monotone_segment
= arr_traits.construct_x_monotone_segment_2_object();
Arr_traits_2::Construct_point_2 construct_point
= arr_traits.construct_point_2_object();
Arr_traits_2::Make_x_monotone_2 make_x_monotone
= arr_traits.make_x_monotone_2_object();
Arrangement_2 arr(&arr_traits);
std::vector<X_monotone_curve_2> segs;
Polynomial_2 x = CGAL::shift(Polynomial_2(1),1,0);
Polynomial_2 y = CGAL::shift(Polynomial_2(1),1,1);
// Construct x^4+y^3-1
Curve_2 cv0 = construct_curve(CGAL::ipower(x,4)+CGAL::ipower(y,3)-1);
// Construct all x-monotone segments using the Make_x_mononotone functor
std::vector<CGAL::Object> pre_segs;
make_x_monotone(cv0,std::back_inserter(pre_segs));
// Cast all CGAL::Objects into X_monotone_segment_2
// (the vector might also contain Point_2 objects for isolated points,
// but not for this instance
for(size_t i = 0; i < pre_segs.size(); i++ ) {
X_monotone_curve_2 curr;
bool check = CGAL::assign(curr,pre_segs[i]);
assert(check); CGAL_USE(check);
segs.push_back(curr);
}
// Construct an ellipse with equation 2*x^2+5*y^2-7=0
Curve_2 cv1 = construct_curve(2*CGAL::ipower(x,2)+5*CGAL::ipower(y,2)-7);
// Construct point on the upper arc (counting of arc numbers starts with 0!
Point_2 p11 = construct_point(Algebraic_real_1(0),cv1,1);
construct_x_monotone_segment(cv1,p11,Arr_traits_2::POINT_IN_INTERIOR,
std::back_inserter(segs));
// Construct a vertical cusp x^2-y^3=0
Curve_2 cv2 = construct_curve(CGAL::ipower(x,2)-CGAL::ipower(y,3));
// Construct a segment containing the cusp point.
// This adds to X_monotone_curve_2 objects to the vector,
// because the cusp is a critical point
Point_2 p21 = construct_point(Algebraic_real_1(-2),cv2,0);
Point_2 p22 = construct_point(Algebraic_real_1(2),cv2,0);
construct_x_monotone_segment(cv2,p21,p22,std::back_inserter(segs));
// Construct an unbounded curve, starting at x=3
Point_2 p23 = construct_point(Algebraic_real_1(3),cv2,0);
construct_x_monotone_segment(cv2,p23,Arr_traits_2::MIN_ENDPOINT,
std::back_inserter(segs));
// Construct another conic: y^2-x^2+1
Curve_2 cv3 = construct_curve(CGAL::ipower(y,2)-CGAL::ipower(x,2)+1);
Point_2 p31 = construct_point(Algebraic_real_1(2),cv3,1);
construct_x_monotone_segment(cv3,p31,Arr_traits_2::MAX_ENDPOINT,
std::back_inserter(segs));
// Construct a vertical segment
Point_2 v1 = construct_point(0,0);
Point_2 v2 = construct_point(Algebraic_real_1(0),cv1,1);
construct_x_monotone_segment(v1,v2,std::back_inserter(segs));
CGAL::insert(arr,segs.begin(),segs.end());
// Add some isolated points (must be wrapped into CGAL::Object)
std::vector<CGAL::Object> isolated_points;
isolated_points.push_back
(CGAL::make_object(construct_point(Algebraic_real_1(2),cv3,0)));
isolated_points.push_back
(CGAL::make_object(construct_point(Integer(1),Integer(5))));
isolated_points.push_back
(CGAL::make_object(construct_point(Algebraic_real_1(-1),
Algebraic_real_1(5))));
CGAL::insert(arr,isolated_points.begin(), isolated_points.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