Questions about opt.distbound and opt.radbound in vol2mesh (CGAL mesh)

[Paul Mignone]

Hi Qian qian, 

Happy New Year! I hope 2013 has started well for you :-)

I've been using iso2mesh for a while now to create volume meshes for Abaqus. I'm using vol2mesh to generate the tetrahedral meshes and controlling the density with the opt.radbound and opt.distbound parameters. I just wanted to clarify the function of the parameters.

1) CGAL mesh uses Delaunay tetralisation, Whereby for a set of P points, no point in P is inside the circumsphere of any tetrahedron. My understanding is that opt.radbound is the maximum radius that these circumspheres can be (thus the maximum element size). This makes sense and the reduction of the opt.radbound value increases the number elements generated.

2) I'm at a loss to explain opt.distbound and the CGAL documentation is not exactly clear on this either (that or I can't find the correct section :-P). According to vol2surf.m, it's defined as the "maximum deviation from the specified isosurfaces". My testing shows that for a given opt.radbound, increasing the opt.distbound value reduces the number of elements generated. Also setting the opt.distbound = 0 reduces the number of elements as well.

I was wondering if you could give brief explanation of the role of opt.distbound? Is it a parameter that 'alters' the mesh geometry reduce mesh density? or a tolerance parameter which allows for more skewed elements, preventing the need for Delaunay refinement? I'm not entirely sure.

Any advice you have on this would be greatly appreciated.

Kind Regards,

Paul

[Qianqian Fang]

On 01/17/2013 11:14 PM, Paul Mignone wrote:

Hi Qian qian, 

Happy New Year! I hope 2013 has started well for you :-)

hi Paul

thanks, happy new year to you too!

I've been using iso2mesh for a while now to create volume meshes for Abaqus. I'm using vol2mesh to generate the tetrahedral meshes and controlling the density with the opt.radbound and opt.distbound parameters. I just wanted to clarify the function of the parameters.

1) CGAL mesh uses Delaunay tetralisation, Whereby for a set of P points, no point in P is inside the circumsphere of any tetrahedron. My understanding is that opt.radbound is the maximum radius that these circumspheres can be (thus the maximum element size). This makes sense and the reduction of the opt.radbound value increases the number elements generated.

there are 4 meshing options, 'cgalmesh', 'cgalpoly', 'cgalsurf' and 'simplify'.
The first two use CGAL 3D mesher to generate the volumetric mesh, while
the latter two call tetgen. In all cases, the resulting meshes are generated
by "constrained Delaunay tetrahedralization", thus, satisfy all the property
you expect from a Delaunay mesh.

radbound is used primarily for the surface extraction step. The definition
of this parameter (radius_bound) is explained in this section:

http://www.cgal.org/Manual/latest/doc_html/cgal_manual/Surface_mesher/Chapter_main.html#Subsection_48.3.1

2) I'm at a loss to explain opt.distbound and the CGAL documentation is not exactly clear on this either (that or I can't find the correct section :-P). According to vol2surf.m, it's defined as the "maximum deviation from the specified isosurfaces". My testing shows that for a given opt.radbound, increasing the opt.distbound value reduces the number of elements generated. Also setting the opt.distbound = 0 reduces the number of elements as well.

In the same section, you can also find the definition for "distance_bound".
The definition in vol2surf is only a simplified version.

I was wondering if you could give brief explanation of the role of opt.distbound? Is it a parameter that 'alters' the mesh geometry reduce mesh density? or a tolerance parameter which allows for more skewed elements, preventing the need for Delaunay refinement? I'm not entirely sure.

overall, radbound and distbound sets the surface mesh density, while
the maxvol sets the tetrahedra volume density. I found that if you use
cgalmesh option, the maxvol parameter sometime are not consistently
followed. I suspect there are some implementation issues. The source
code for the cgalmesher binary is here:

http://iso2mesh.svn.sourceforge.net/viewvc/iso2mesh/trunk/cgalmesh/mesh_3D_image.cpp?revision=245&view=markup

Comments from CGAL developers will be really helpful in this case.

Qianqian

Any advice you have on this would be greatly appreciated.

Kind Regards,

Paul

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