CGAL users discussion list

["Laurent Rineau (CGAL/GeometryFactory)" <>]

On Tuesday, October 29, 2019 3:48:01 PM CET Gaetan wrote:
> Hi Laurent,
> 
> Thanks for your prompt answer, I see your example works fine.
> Therefore my next question: how can we know the minimum number of initial
> points required per component?
> Is it more related to the initial cells (one initial cell per component) or
> is it something else?

Actually, there is no minimal number of points, in general.

In theory, three points per component is sufficient, if the size of the 
triangle is sufficiently small compared to the they are close enough. See 
that 
article for the details:

  Boissonnat, Jean-Daniel, and Steve Oudot. "Provably good sampling and 
meshing of surfaces." Graphical Models 67.5 (2005): 405-451.

https://geometrica.saclay.inria.fr/team/Steve.Oudot/papers/bo-pgsms-05/bo-pgsms-05.pdf


Imagine you are meshing a torus, and you insert N points on one circle of the 
torus, then the triangulation of those N points will be degenerated, and for 
all triangles of that triangulation, its dual will not intersect the torus at 
all. And that whatever the initial number of points.

Practically, the Surface_mesher package of CGAL tries to find 20 random 
points 
on the surface, and that was enough in all cases. SO I suggest you choose 20 
random points per component.


If you tell me more about you real need, I might find a better solution that 
random points, for the initialization.

-- 
Laurent Rineau, PhD
R&D Engineer at GeometryFactory           http://www.geometryfactory.com/
Release Manager of the CGAL Project       http://www.cgal.org/