CGAL users discussion list

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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