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[stzpz <>]

Hello,

I am willing to get the point location of a Bezier curves Arrangement, so I
use Arr_Bezier_curve_traits_2 along with Arr_curve_data_traits_2 to
construct the arrangement with auxiliary data (curve number) attached with
each Bezier curve. And then I perform the point location function to get the
outer connected boundaries of the point. Everything is fine except that the
auxiliary data in the returning boundaries are incorrect. 

I use outer_ccb() to get the outer boundaries of the face, then use
curve().supporting_curve() to get the original bezier curves with auxiliary
data. The data in Bezier curves are correct. However, the auxiliary data
corresponding with them are in correct. Here is the code:

// =================== CODE BEGIN =====================
#include <CGAL/basic.h>
#include <CGAL/Cartesian.h>
#include <CGAL/CORE_algebraic_number_traits.h>
#include <CGAL/Arr_Bezier_curve_traits_2.h>
#include <CGAL/Arrangement_2.h>
#include <CGAL/Arr_curve_data_traits_2.h>
#include <CGAL/Arr_walk_along_line_point_location.h>
#include <CGAL/to_rational.h>
#include <list>
using namespace std;

typedef CGAL::CORE_algebraic_number_traits              Nt_traits;
typedef Nt_traits::Rational                             NT;
typedef Nt_traits::Rational                             Rational;
typedef Nt_traits::Algebraic                            Algebraic;
typedef CGAL::Cartesian<Rational>                       Rat_kernel;
typedef CGAL::Cartesian<Algebraic>                      Alg_kernel;
typedef Rat_kernel::Point_2                             Rat_point_2;
typedef CGAL::Arr_Bezier_curve_traits_2<Rat_kernel, Alg_kernel, Nt_traits>
Traits_org_2;
typedef Traits_org_2::Curve_2 Bezier_curve_2;

typedef unsigned int CurveNumber;
typedef CGAL::Arr_curve_data_traits_2<Traits_org_2, CurveNumber> Traits_2;

typedef Traits_2::Curve_2                               Bezier_curve_num_2;
typedef Traits_2::Point_2                                                     
          Point_2;
typedef CGAL::Arrangement_2<Traits_2>                   Arrangement_2;
typedef CGAL::Arr_walk_along_line_point_location<Arrangement_2>   Naive_pl;

#define TORAT(x) (CGAL::to_rational<Rational>((x)))

void point_loc(Arrangement_2 *arr) {
        Naive_pl pl(*arr);
        
        // this point is inside the face
        Point_2 p(TORAT(50), TORAT(40));

        CGAL::Object obj = pl.locate(p);        
        Arrangement_2::Face_const_handle      f;
    
        if (CGAL::assign(f, obj)) {
        if(!f->is_unbounded()) {
                Arrangement_2::Ccb_halfedge_const_circulator bound_circ = 
f->outer_ccb();

                // first sub curve
                Bezier_curve_num_2 curr_curve_num =
bound_circ->curve().supporting_curve();
                Bezier_curve_2 curr_curve = curr_curve_num;

                // ================ the result is INCORRECT of the next line
===================
                CurveNumber curve_num = curr_curve_num.data();
                cout<<"current curve num: "<<curve_num<<endl;
               //
==================================================================
        }
    }
}

int main (int argc, char *argv[]) {
  const char   *filename = (argc > 1) ? argv[1] : "test5.dat";
  std::ifstream   in_file (filename);

  int               n_curves;
  std::list<Bezier_curve_num_2>  curves;
  Bezier_curve_2             B;
  int               k;
  
  in_file >> n_curves;
  for (k = 0; k < n_curves; k++) {
    in_file >> B;
    Bezier_curve_num_2 bb(B, k);
    curves.push_back (bb);
  }
  
  Arrangement_2                     arr;
  insert (arr, curves.begin(), curves.end());
  
  Arrangement_2::Edge_iterator eit;
  for(eit = arr.edges_begin(); eit != arr.edges_end(); ++eit) {
      // ============= this result is CORRECT ==============
      int num = eit->curve().data();
      std::cout<<"Current curve number:"<<num<<std::endl;
      // =============================================
  }
  
  point_loc(&arr);

  return 0;
}
// =================== CODE END =====================
The data file test5.dat is in below
=================== DATA BEGIN =====================
3
2 0 0 100 100
2 20 80 100 0
2 -10 14 120 40
=================== DATA END ======================

Could anybody help me to find out how to get the correct auxiliary data in
the returning boundaries constructed by point location algorithm?


Besides, it seems that Arr_Bezier_curves_traits_2 cannot handle some special
case of curves like horizontal line segments. For example, using the code
above and another data file below,
=================== DATA BEGIN =====================
3
2 0 0 100 0
2 30 -20 30 80
2 100 -15 -20 75
=================== DATA END ======================
the program will terminate with assertion fails in line 770 of
Bezier_curve_2.h when inserting bezier curves into arrangement. Is it a bug
and how to fix it?


Does anyone know how to solve them? Thanks very much!

Sincerely yours,

Stzpz

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