Sorry for my mistake! Please delete or just ignor it.

盖的是数学学院的章，虽然说录取的可能性非常大，但最终解释权应该是浙大研究生院。首先你需要获得吉大的推免资格。 所以，我说若是上报吉大教务处，你就填我的名字没问题。 浙大的面试开学你还需要再过来的话，我还是希望能方面跟你聊一聊的。

>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 <

[hidden email]> 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 <

[hidden email]> 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/>>

>

>--

>===================================================================

>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:

[hidden email]
>Web:

http://liris.cnrs.fr/guillaume.damiand/>===================================================================

>

>

You are currently subscribed to cgal-discuss.