CGAL users discussion list

[Guillaume Damiand <>]

Hi Peter;


Le 26/08/2018 à 13:41, kloffy a écrit :
> Hi,
>
> I am trying to get my head around combinatorial maps, and I thought I would
> start with the simplest non-trivial example, a 1-simplex (#0-cells=2,
> #1-cells=1).
>
>
> So, first I tried the obvious construction helper:
>
> CGAL::Combinatorial_map<1> cm;
>
> cm.make_edge();
>
> cm.display_characteristics(std::cout);
> std::cout << std::endl;
>
> However, this gives me:
>
> #Darts=2, #0-cells=2, #1-cells=2, #ccs=2
>
> But that's not quite right (#1-cells=2).


A 1D combinatorial map can be seen as a set of 1D curves (possibly opened).

As said in the doc of make_edge (here 
https://doc.cgal.org/latest/Combinatorial_map/classGenericMap.html#a6f455fd64b650495392bddecedbd5afe), 
this method requires that the dimension of the combinatorial map n is >= 2.

Indeed, an edge is made of two darts linked by beta2 and this requires n>=2.

In a 1D cmap, an edge is made of two darts linked by beta1. If you want 
to create such an edge by hand, you must use

cm.dart_link_beta<1>(dh1, dh2);

To have an intuition of what is a combinatorial map, have a look at the 
2 first figures in the user manual (here 
https://doc.cgal.org/latest/Combinatorial_map/index.html).

Hope this help.

Best
Guillaume

> So I tried creating the 1-simplex manually:
>
> CGAL::Combinatorial_map<1> cm;
>
> auto dh1 = cm.create_dart();
> auto dh2 = cm.create_dart();
>
> cm.dart_link_beta<1>(dh1, dh2);
>
> cm.display_characteristics(std::cout);
> std::cout << std::endl;
>
> However, this gives me:
>
> #Darts=2, #0-cells=2, #1-cells=2, #ccs=1
>
> But that's still not quite right (#1-cells=2).
>
>
> I tried a bunch of other things, but I never managed to get the intended
> result (#1-cells=1). My intuition for combinatorial maps is still very poor,
> which was the motivation for this exercise. At this point, I feel like I
> must be missing something. Please forgive me if it is something very
> obvious. Still, I would appreciate any hints...
>
> Cheers,
> Peter
>
>
>
> --
> Sent from: http://cgal-discuss.949826.n4.nabble.com/

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Guillaume DAMIAND

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