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["Tardugno, Angelo" <>]

Well, since I'm considering only the acute triangles of the Delaunay 
triangulation I would expect the intersection to exist.

Regards

Angelo 


-----Original Message-----
From: Yajun Wang 
[mailto:]
 
Sent: 22 May 2007 11:40
To: 

Subject: Re: [cgal-discuss] Intersection between Delaunay facet and its dual 
edge

FYI: The Voronoi edge does not necessarily intersect its dual.


regards,
yalding

Tardugno, Angelo 写道:
> Hi CGAL experts,
>  
> I've been trying to compute the intersection between a Delaunay facet
> and ist dual (Voronoi Edge). This operation should result in a point,
> but, surprisingly sometimes (actually very frequently) it returns
> something different.
> Here's part of my code:
>  
> Finite_cells_iterator ci=T.finite_cells_begin();
>   out_stream.open("Vvertex");
>   o_stream.open("s3points");
>   o1stream.open("triangle");
>   o2stream.open("segment");
>  
>   for (;ci !=T.finite_cells_end(); ++ci)
>   {
>    voronoi_vertices = (T.dual(ci));
>    out_stream << 4 << " " << voronoi_vertices << "\n";
>  
>    // Finding the dual of each facet of the delaunay triangulation
> (Voronoi edge)
>    // and compute its intersection with the facet in case the triangle
>    // is acute
>  
>  
>  
>    for (int i=0; i<4; i++)
>    {
>     CGAL::Object o = T.dual(ci,i);
>     K::Triangle_3 t = T.triangle(ci,i);
>     CGAL::Object o2;
>        K::Segment_3 s,s2;
>        K::Ray_3     r;
>     K::Plane_3 plane;
>     K::Point_3 point;
>  
> 
>     K::Construct_supporting_plane_3 construct_plane;
>  
>     
>  
>     if (is_acute(t))
>     {
>         if (CGAL::assign(s,o))
>         {
>       //cout << i << "\n";
>       o1stream << t << "\n";
>       o2stream << s << "\n";
>       plane = construct_plane(t);        // Building the supporting
> plane for the triangle
>       o2 = intersection(s,plane);        // Evaluating intersection
> between voronoi edge and plane
>       if (assign(point,o2))         // Assigning object intersection to
> point
>       {
>        xx = (point.x());
>        yy = (point.y());
>        zz = (point.z());
>        out_stream << 3 << " " << xx << " " << yy  << " " << zz << "\n";
>  
>        n_of_s3_points++;
>       } else
>       {
>       cout << "Something different\n";
>       }
>      }
>         if (CGAL::assign(r,o))
>         {
>       //cout << i << "\n";
>       plane = construct_plane(t);        // Building the supporting
> plane for the triangle
>       o2 = intersection(s,plane);        // Evaluating intersection
> between voronoi edge and plane
>       if (assign(point,o2))         // Assigning object intersection to
> point
>       {
>        xx = (point.x());
>        yy = (point.y());
>        zz = (point.z());
>        o_stream <<  3 << " " << xx << " " << yy  << " " << zz << "\n";
>  
>        n_of_s3_points++;
>       } else
>       {
>             cout << "Something different\n";
>       }
>  
>      }
>     }
>     else cout << "\nObtuse Angle\n";
>  
> 
>    }
>  
>   }
>  
>   o1stream.close();
>   o2stream.close();
>   o_stream.close();
>   out_stream.close();
>  
> After running this program, I checked the files triangle and segment but
> when I check for the first triangle and the first segment it seems like
> the segment isn't the actual dual of the Delaunay facet, since there is
> no intersection between the two. Maybe I've made a mistake when I
> created the dual of the facet or the triangle describing the facet.
> Anyway, I've tried my best to understand what's happening but I have no
> clue.
>  
> Anybody can  help?
>  
> Thanks 
>  
> Angelo Tardugno
>  

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