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Re: [cgal-discuss] Pachner moves in CGAL Triangulations


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  • From: Adam Getchell <>
  • To:
  • Subject: Re: [cgal-discuss] Pachner moves in CGAL Triangulations
  • Date: Fri, 6 Feb 2015 14:53:23 -0800

Wonderful! I'd be happy to help.

I looked over the contribution process, and talked to Alex Tsui, who is local to me. I will poke around the source -- there looks to be a recent copy at:

https://github.com/openscad/CGAL

A naive search seems to show the relevant function is flip_really( Cell_handle c, int i, Cell_handle n, int in ) 

I also want a function that tells me whether the flip is possible or not, without actually doing it, so it seems I can just copy flip* but remove flip_really.

My idea is to compile a list of (2,2) vertices beforehand which can be flipped, so that the Pachner moves can be done efficiently.

(CDT is in essence doing thousands to millions of Pachner moves to simulate the space of all diffeomorphisms of a manifold, to evaluate the path integral over that space.)

On Tue, Feb 3, 2015 at 8:03 AM, Monique Teillaud <> wrote:
Hi Adam,

Thank you for the precisions. You are right, we don't have the other two.

I guess that we could/should add them...

--
Monique Teillaud
http://www.loria.fr/~teillaud/
INRIA Nancy - Grand Est
Institut National de Recherche en Informatique et Automatique


Le 02/02/15 18:48, Adam Getchell a écrit :
Hi Monica,

Thank you for your reply.

It looks like "flips" implements the (2,3) and its inverse, but not the
(2,6) and (4,4) moves + inverses.

Thank you!

On Mon, Feb 2, 2015 at 1:07 AM, Monique Teillaud
< <mailto:Monique.Teillaud@inria.fr>> wrote:

    Hi,

    Look for "flips" in
    http://doc.cgal.org/latest/__TDS_3/__classTriangulationDataStructur__e__3.html
    <http://doc.cgal.org/latest/TDS_3/classTriangulationDataStructure__3.html>

    If it does not provide everything you need, we could add more in CGAL.

    Best,
    --
    Monique Teillaud
    http://www.loria.fr/~teillaud/
    INRIA Nancy - Grand Est
    Institut National de Recherche en Informatique et Automatique

    Le 02/02/15 02:27, Adam Getchell a écrit :

        Hello all,

        Before I start implementing my own version, are there Pachner moves
        defined in CGAL for triangulations?

        Pachner, Udo. “P.L. Homeomorphic Manifolds Are Equivalent by
        Elementary
        Shellings.” /European Journal of Combinatorics/ 12, no. 2 (March
        1991):
        129–45. doi:10.1016/S0195-6698(13)__80080-7.

        Thanks,
        --
        Adam Getchell
        about.me/adamgetchell <http://about.me/adamgetchell>
        <http://about.me/adamgetchell>
        "Invincibility is in oneself, vulnerability in the opponent." --
        Sun Tzu




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--
Adam Getchell
about.me/adamgetchell <http://about.me/adamgetchell>
"Invincibility is in oneself, vulnerability in the opponent." -- Sun Tzu



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Adam Getchell
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