CGAL users discussion list

[Guillaume Damiand <>]

Hi Peter;

If your goal is to understand the mean of the different beta, I suggest you to start in 2D, and study the examples given in the CGAL user manual.

Indeed, 1D combinatorial map with boundaries (which is what you try to do) is a very special case.

For this reason, it is not possible to build a 1D cmap with #Darts=2, #0-cells=2, #1-cells=1, #ccs=1 because 1 dart represents one 0-cell and one 1-cell. But this is possible in a 2D combinatorial map, as said in my previous email, by creating 2 darts linked by beta2.

In my point of view, this is not a problem because 1D combinatorial map is a very special case, not really interesting. To represend 1D line segment, you can simply use a polygon representation based on vertices and edges.

Best
Guillaume



Le 29/08/2018 à 06:13, Peter Klosowski a écrit :

Hi,

Just following up on this, since I am feeling quite stuck. Is there anybody who could answer the following question?

1) Should it be possible to construct a 1D combinatorial map with the following characteristics?

#Darts=2, #0-cells=2, #1-cells=1, #ccs=1

Bonus questions:

1a) If yes, what is the correct code to construct such a combinatorial map?

1b) If no, what is the best representation of a 1-simplex (1d line segment)?

Any advice would be greatly appreciated. Thank you in advance!

Cheers,

Peter

On Mon, Aug 27, 2018 at 5:58 PM Peter Klosowski <> wrote:

Hi Guillaume,

Many thanks for your suggestions! However, I am still a bit confused. I tried your code:

    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;

But it still gives me:

#Darts=2, #0-cells=2, #1-cells=2, #ccs=1

Am I wrong to expect that an edge would only have a single 1-cell? My expectation comes from the faces of a 1-simplex (https://en.wikipedia.org/wiki/Simplex). Perhaps in combinatorial maps it works differently...

I think the main challenge for me in terms of forming an intuition is to understand the different betas. I can see the value of combinatorial maps to represent cellular structures, and a lot of the concepts and operations make sense. I am just having trouble getting my head around why an edge is made of two darts linked by beta1, as opposed to beta0, for example?

I hope some of that makes sense. Thank you again for the help!

Cheers,

Peter

On Mon, Aug 27, 2018 at 4:43 PM Guillaume Damiand <> wrote:

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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