CGAL users discussion list

[Mariette Yvinec <>]

Dear Paul

as you noticed, the radious-bound  controls the size of surface Delaunay balls,
hence the size of surface facets.
The distance bound controls the distance between the circumcenter of a mesh facet and the center of a surface Delaunay ball of this facet. This distance is a measure of the accuracy of the approximation of the surface  by the mesh. Increasing
this bounds, means relaxing the required accuracy and therefore decreasing the mesh density.
Decreasing it on the contrary tend to increase the mesh density because a better accuracy is required.
 However, setting the bound  to zero, means that the  mesh has no prescribed
accuracy goal and the distance criteria  is not be taken account.

I hope this helps,
Mariette

Le 21/01/13 08:36, paulm a écrit :

To whom it may concern,

I've been using iso2mesh for a while now to create volume meshes for Abaqus.
I'm using CGAL mesh to generate the tetrahedral meshes and controlling the
density with the opt.radbound (radius_bound) and opt.distbound
(distance_bound) parameters.

I understand that radius_bound is radii of surface Delaunay balls (i.e the
size of each tertrahedral element). According to your documentation,
distance_bound is an upper bound for the distance between the circumcenter
of a mesh facet and the center of a surface Delaunay ball of this facet.

My testing shows that for a fixed radius_bound, increasing the
distance_bound value reduces the number of elements generated to a point.
Also setting the distance_bound = 0 reduces the number of elements as well.
I understand that a tetra element has four faces and the distance_bound is
the limit the circumcentres that these four faces can be from the centre of
the Delaunay ball that surrounds it. Therefore increasing this allowable
distance_bound will increase the size of the element size.

I have three questions. 

1) If increasing this allowable distance_bound will increase the size of the
element size, why doesn't it do it indefinitely. Is it being limited by a
fixed radius_bound?

2) Besides element size, can altering distance_bound change other element
attributes (i.e. variations in element aspect ratio, skewedness etc)?

3) Do you know of any worthwhile papers that discuss distance_bound in
detail?

Thanks for your help and kind regards,

Paul 





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Mariette Yvinec
Geometrica project team
INRIA  Sophia-Antipolis