CGAL users discussion list

[Monique Teillaud <>]

Dear Daniel,

I guess that function periodic_point(face,index) should help you.
http://doc.cgal.org/latest/Periodic_2_triangulation_2/classCGAL_1_1Periodic__2__triangulation__2.html#a16806236a206a836a37e0ce58c961aed

Or periodic_segment(face,index)
http://doc.cgal.org/latest/Periodic_2_triangulation_2/classCGAL_1_1Periodic__2__triangulation__2.html#a50b4f8adcb511d4102b0e3c6f803bb9d

Once you get a periodic point, you know how to translate the point

see also 
http://doc.cgal.org/latest/Periodic_2_triangulation_2/index.html#P2Triangulation2secspace

Then you can just use standard geometric computations from the CGAL kernel.

Hope this helps.
Best,
        Monique

Le 13/11/13 14:15, Daniel Duque a écrit :
> Hello,
>
> I have finally been able to have a look at this exciting new feature of
> CGAL. I would love to say that I understand everything on the manual,
> but sadly this is not the case. At any rate, after building the periodic
> triangulation I get a list of vertices whose Cartesian coordinates are
> all within the original domain. Usually, there is only one covering, so
> there are just as many vertices as the points I used as input.
>
> My question is: imagine I now want to compute geometrical stuff, say
> distances between all neighboring nodes. The triangulation build has the
> proper connectivity, so two vertices that are close to the edge of the
> domain and quite far apart may in fact be periodic neighbors. In order
> to do such a thing, I would do this kind of loop:
>
>   for( Finite_edges_iterator ed=T.finite_edges_begin();
>        ed!=T.finite_edges_end();
>        ed++) {
>
>      FT l2=per_dist2(v0->point(), v1->point());
>
> // ... print out, collect stats, whatever
>
> }
>
> The "finite" I think can be dropped in this case. I have been careful
> not to compute the distance between the points, but a periodic distance,
> following what is called the minimum image convention:
>
> // LL is the size of the periodic domain
>
> FT per_dist(const FT& x1, const FT& x2) {
>    FT dx=x1-x2;
>
>    if(fabs(dx)>LL/2.0)
>      if(dx>0)
>        dx -= LL;
>      else
>        dx += LL;
>    return dx;
> }
>
> FT per_dist2(const Point& P1, const Point& P2) {
>    FT dx=per_dist(P1.x(),P2.x());
>    FT dy=per_dist(P1.y(),P2.y());
>
>    return dx*dx+dy*dy;
> }
>
> I would like to get some reassurance that what I am doing is correct.
> Not very elegant, perhaps, and even redundant (there may be some CGAL
> function that does just this), but in the end correct (all edges are
> taken into account just once, for example).
>
> Thanks very much,
>
> Daniel


--
Monique Teillaud
http://www.inria.fr/sophia/members/Monique.Teillaud/
INRIA Sophia Antipolis - Méditerranée
Institut National de Recherche en Informatique et Automatique