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Re: [cgal-discuss] 1D Combinatorial Map - 1-Simplex


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  • From: Guillaume Damiand <>
  • To:
  • Subject: Re: [cgal-discuss] 1D Combinatorial Map - 1-Simplex
  • Date: Mon, 27 Aug 2018 08:42:34 +0200
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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



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