CGAL users discussion list

["Audette, Michel A." <>]

Hi Mariette, 

thanks for your kind support. Your description explains a lot of concepts on which I had questions. 

Warm wishes, 

Michel

Michel Audette, Ph.D.

Assistant Professor,

Department of Modeling, Simulation and Visualization Engineering,

Old Dominion University,

Norfolk, VA.

 

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From: [] on behalf of Mariette Yvinec []
Sent: Tuesday, July 23, 2013 5:08 AM
To:
Subject: Re: [cgal-discuss] would like to understand how the facet and cell size objectives, and node insertion, work in Mesh_3

edge_size bounds the size of edge which are part of 1 dimensional sharp feature approximation
fecet_size bounds the radius of the surface Delaunay sphere of surface facet
( surface facets have by definition an empty  circumsphere centered on the surface)
cell_size bounds the circumradius of any tet in the mesh

The Mesh_3 package of CGAL is based on Delaunay refinement
and therefore can't guarantee to  preserve the discretization of the input surface
even if this surface mesh satisfies the meshing criteria.
Indeed, input surface meshes might not have the Delaunay property.
On one hand, this is a drawback of our meshing algorithm.
On the other hand, since Mesh_3 is able to provide in a single meshing process
multi-component domain mesh, respecting all boundaries and subdividing
surface patches, there is generally no more need to preserve the input surface meshes.
Simply think that the work performed to generate these input surface meshes
is performed at the same time by CGAL meshing packahge

Le 22/07/13 19:52, Audette, Michel A. a écrit :

Dear CGAL users,

I would like to use Mesh_3 to produce a tetrahedral mesh with controlled resolution.

The example in the website where the mesh resolution is controlled is the following...

  Mesh_criteria criteria(edge_size = 0.025,
                         facet_angle = 25, facet_size = 0.05, facet_distance = 0.005,
                         cell_radius_edge_ratio = 3, cell_size = 0.05);
  

Please help me interpret these thresholds. I would think that for a triangle, or facet, whose area is related to edge size, whose objective is s (s=0.025 here) it would be given by s^2*sqrt(3)/4, and that the volume of a tetrahedron of edge size s would be given by sqrt(2)/12 *s^3, and yet, in this example, facet and cell sizes appear to be 2*s. Also, could someone also explain the facet_distance concept to me: is there an intuitive relationship with edge size?

I also found that even when I choose this way of invoking make_mesh_3, i.e.: providing it with a surface mesh input which contrains the volumetric meshing,

  C3t3 c3t3 = CGAL::make_mesh_3<C3t3>(domain, criteria);

for some reason, the volumetric meshing remeshes the surface mesh as well, thereby introducing other points that produce small elements near sharp boundaries. Is it possible for me to tell it to leave alone the boundary meshing and only insert nodes within the boundary?

Thanks for your kind support.

Best wishes,

Michel

Michel Audette, Ph.D.

Assistant Professor,

Department of Modeling, Simulation and Visualization Engineering,

Old Dominion University,

Norfolk, VA.

 

-- 
Mariette Yvinec
Geometrica project team
INRIA  Sophia-Antipolis  

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