Arrangement_on_surface_2/algebraic_segments.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;
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);
        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