CGAL users discussion list

[Pierre Alliez <>]

hi Daniel,

about link with area I would advise you to read some work of Ramsay Dyer
(Delaunay mesh construction, etc.) as well as some work of kai Hormann, 
see http://www2.in.tu-clausthal.de/~hormann/pub_chrono.html "optimizing 
3d triangulations using discrete curvature analysis".

Pierre


 a écrit :
> Hello everyone,
>
> My current research leads me to computing a 3D mesh triangulating a (given) 
> set
> of points. It is important that this mesh has a minimal area; I somehow 
> assumed
> this would be taken care of by using Delaunay triangulations, but I am not so
> sure about this now. I'd greatly appreciate any help regarding the connection
> between 3D Delaunay meshes and area.
>
> More technically:
>
> I have read the documentation about 3D surface mesh generation. Not quite 
> what I
> wanted, since my points are given (I have no implicit function), but still
> interesting. The idea centers about the mesh having empty surface Delaunay
> balls. I quote: "A surface Delaunay ball is a ball circumscribing a mesh facet
> and centered on the surface." Since my surfaces are nearly planar I was making
> progress by using 2D Delaunay terrains, hoping that the resulting mesh would
> still have empty balls.
>
> Anyway, I am now doubting there is a strong connection between the Delaunay
> condition of empty balls/circles and minimal area. Perhaps I'll have to write 
> my
> own code for triangulating terrains in such a way that the area is kept 
> minimal?
>
> Best,
>
> Daniel
>
>
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--
Pierre Alliez
INRIA Sophia Antipolis - Mediterranee
Project-team GEOMETRICA
http://www-sop.inria.fr/members/Pierre.Alliez/
Tel: +33 4 92 38 76 77
Fax: +33 4 97 15 53 95