CGAL users discussion list

["Sebastien Loriot (GeometryFactory)" <>]

stzpz wrote:
> 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?
Actually, there is no bug here.
Basically, Traits_2::X_monotone_curve_2 is a pair
(Traits_org_2::X_monotone_curve_2,CurveNumber)

No information is stored to get back to Traits_2::Curve_2 used
to create the X monotone curve. However, the information hold by
the Curve_2 is always copied to the X_monotone_curve_2.
Thus replacing
  CurveNumber curve_num = curr_curve_num.data();
by
  CurveNumber curve_num = bound_circ->curve().data();
will do what you want.

At this line:
Bezier_curve_num_2 curr_curve_num = bound_circ->curve().supporting_curve();
the constructor of Bezier_curve_num_2 is implicitly called with no data
(we should probably had an explicit keyword to that constructor).

(looking at the doc here:
http://www.cgal.org/Manual/latest/doc_html/cgal_manual/Arrangement_on_surface_2_ref/Class_Arr_curve_data_traits_2.html#Cross_link_anchor_1223
you will see no constructor of X_monotone_curve_2 from Curve_2).

> 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?
There indeed seems to have a bug here.
The fix will be posted here.
In the meantime, translating your data by 1 in the (0,1) direction
makes it work (the problem comes in the case the polynomial for y
coordinates is 0).

S.


> Does anyone know how to solve them? Thanks very much!
>
> Sincerely yours,
>
> Stzpz