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- From: Peter Klosowski <>
- To:
- Subject: Re: [cgal-discuss] 1D Combinatorial Map - 1-Simplex
- Date: Mon, 27 Aug 2018 17:58:38 +1000
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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;
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
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/
>
--
===================================================================
Guillaume DAMIAND
CNRS - LIRIS UMR 5205
Université Claude Bernard
Bâtiment Nautibus (710)
43 Boulevard du 11 Novembre 1918
69622 Villeurbanne Cedex (France)
-------------------------------------------------------------------
Tél: +33 (0)4.72.43.14.34 Fax: +33 (0)4.72.43.15.36
Mail:
Web: http://liris.cnrs.fr/guillaume.damiand/
===================================================================
- [cgal-discuss] 1D Combinatorial Map - 1-Simplex, kloffy, 08/26/2018
- Re: [cgal-discuss] 1D Combinatorial Map - 1-Simplex, Guillaume Damiand, 08/27/2018
- Re: [cgal-discuss] 1D Combinatorial Map - 1-Simplex, Peter Klosowski, 08/27/2018
- Re: [cgal-discuss] 1D Combinatorial Map - 1-Simplex, Peter Klosowski, 08/29/2018
- Re:[cgal-discuss] 1D Combinatorial Map - 1-Simplex, xlhu, 08/29/2018
- Re: [cgal-discuss] 1D Combinatorial Map - 1-Simplex, Guillaume Damiand, 08/29/2018
- Re: [cgal-discuss] 1D Combinatorial Map - 1-Simplex, Peter Klosowski, 08/31/2018
- Re: [cgal-discuss] 1D Combinatorial Map - 1-Simplex, Peter Klosowski, 08/29/2018
- Re: [cgal-discuss] 1D Combinatorial Map - 1-Simplex, Peter Klosowski, 08/27/2018
- Re: [cgal-discuss] 1D Combinatorial Map - 1-Simplex, Guillaume Damiand, 08/27/2018
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