CGAL 5.4.1 - 2D Arrangements
// Constructing an arrangement of algebraic segments.
#include <iostream>
#include <CGAL/config.h>
int main ()
std::cout << "Sorry, this example needs CORE, LEDA, or GMP+MPFI ..."
<< std::endl;
return 0;
#include <CGAL/basic.h>
#include <CGAL/Arrangement_2.h>
#include <CGAL/Arr_algebraic_segment_traits_2.h>
#include "integer_type.h"
#include "arr_print.h"
typedef CGAL::Arrangement_2<Traits> Arrangement;
typedef Traits::Curve_2 Curve;
typedef Traits::Polynomial_2 Polynomial;
typedef Traits::Algebraic_real_1 Algebraic_real;
typedef Traits::X_monotone_curve_2 X_monotone_curve;
typedef Traits::Point_2 Point;
typedef boost::variant<Point, X_monotone_curve> Make_x_monotone_result;
int main() {
Traits traits;
auto make_xmon = traits.make_x_monotone_2_object();
auto ctr_cv = traits.construct_curve_2_object();
auto ctr_pt = traits.construct_point_2_object();
auto construct_xseg = traits.construct_x_monotone_segment_2_object();
Polynomial x = CGAL::shift(Polynomial(1), 1, 0);
Polynomial y = CGAL::shift(Polynomial(1), 1, 1);
// Construct a curve (C1) with the equation x^4+y^3-1=0.
Curve cv1 = ctr_cv(CGAL::ipower(x, 4) + CGAL::ipower(y, 3) - 1);
// Construct all x-monotone segments using the Make_x_mononotone functor.
std::vector<Make_x_monotone_result> pre_segs;
make_xmon(cv1, std::back_inserter(pre_segs));
// Cast all CGAL::Objects into X_monotone_segment
// (the vector might also contain Point objects for isolated points,
// but not in this case).
std::vector<X_monotone_curve> segs;
for(size_t i = 0; i < pre_segs.size(); ++i) {
auto* curr_p = boost::get<X_monotone_curve>(&pre_segs[i]);
// Construct an ellipse (C2) with the equation 2*x^2+5*y^2-7=0.
Curve cv2 = ctr_cv(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 p11 = ctr_pt(Algebraic_real(0), cv2, 1);
construct_xseg(cv2, p11, Traits::POINT_IN_INTERIOR,
// Construct a vertical cusp (C3) with the equation x^2-y^3=0.
Curve cv3 = ctr_cv(CGAL::ipower(x, 2)-CGAL::ipower(y, 3));
// Construct a segment containing the cusp point.
// This adds two X_monotone_curve objects to the vector,
// because the cusp is a critical point.
Point p21 = ctr_pt(Algebraic_real(-2), cv3, 0);
Point p22 = ctr_pt(Algebraic_real(2), cv3, 0);
construct_xseg(cv3 ,p21, p22, std::back_inserter(segs));
// Construct an unbounded curve, starting at x=3.
Point p23 = ctr_pt(Algebraic_real(3), cv3, 0);
construct_xseg(cv3, p23, Traits::MIN_ENDPOINT, std::back_inserter(segs));
// Construct another conic (C4) with the equation y^2-x^2+1=0.
Curve cv4 = ctr_cv(CGAL::ipower(y,2)-CGAL::ipower(x,2)+1);
Point p31 = ctr_pt(Algebraic_real(2), cv4, 1);
construct_xseg(cv4, p31, Traits::MAX_ENDPOINT, std::back_inserter(segs));
// Construct a vertical segment (C5).
Curve cv5 = ctr_cv(x);
Point v1 = ctr_pt(Algebraic_real(0), cv3, 0);
Point v2 = ctr_pt(Algebraic_real(0), cv2, 1);
construct_xseg(cv5, v1, v2, std::back_inserter(segs));
Arrangement arr(&traits);
CGAL::insert(arr, segs.begin(), segs.end());
// Add some isolated points (must be wrapped into CGAL::Object).
std::vector<CGAL::Object> isolated_pts;
isolated_pts.push_back(CGAL::make_object(ctr_pt(Algebraic_real(2), cv4, 0)));
isolated_pts.push_back(CGAL::make_object(ctr_pt(Integer(1), Integer(2))));
CGAL::insert(arr, isolated_pts.begin(), isolated_pts.end());
print_arrangement_size(arr); // print the arrangement size
return 0;