Fw: Re:Re: 1D Combinatorial Map - 1-Simplex

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Fw: Re:Re: 1D Combinatorial Map - 1-Simplex

xlhu
Hi,
  Sorry for my mistake! Please delete or just ignor it.
Xianliang Hu

-----原始邮件-----
发件人: xlhu <[hidden email]>
发送时间: 2018-08-29 12:36:01 (星期三)
收件人: cgal-discuss <[hidden email]>
抄送:
主题: Re:Re: [cgal-discuss] 1D Combinatorial Map - 1-Simplex

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。


在 2018-08-29 12:13:15,"Peter Klosowski" <[hidden email]> 写道:

>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/
>===================================================================
>
>

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