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Sliver Elements in 3D Delaunay Triangulation

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Old   July 23, 2003, 03:06
Default Sliver Elements in 3D Delaunay Triangulation
Dinesh Godavarty
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Hello all,

I am working on the unstructured mesh generation in 3D using Delaunay triangulations. As expected, I have got some high Aspect ratio elements. The elements inside the domain can be somewhat corrected using a Laplacian kind of smoothing. But some elements are formed from only the boundary points, hence cannot be "corrected" using smoothing. The element is formed from two well shaped triangles on the surface, and the angle between these triangles is nearly zero. So this element is a sliver formed only from the boundary points. So how do I try to fix these kind of elements? I can't even put a new point at the circumcenter of this element as it well outside the computational domain. Please help me or direct me to literature as I need to finish this problem fast and time is a big issue.

Thanks a lot everyone. And I hope you got the problem.

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Old   July 23, 2003, 10:11
Default Re: Sliver Elements in 3D Delaunay Triangulation
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From my experience (many years ago now) a reasonably robust 3D Delaunayish grid generator is approximately 5% generator and 95% boundary/clustering handling. If you have written the 5% creating the remaining 95% is not going to be fast. It also tends to be something of an iterative process as new geometries bring to light new numerical issues.

I would suggest looking at the code of a well developed grid generator if you can find one. The "grummp" code and supporting papers/documentation may prove useful if you can penetrate the C++ and do not heavily work curved surfaces. I am sure you can find others by following the grid generation links in the resources section.

Without knowing the constraint on your grid/geometry representation one cannot answer your question with any authority. However, if you can change the surface tesselation (assuming you have one - some schemes generate this along with the internal elements) then swapping the shared edge in the surface and retesselating may be sufficient but this is not a general solution.

A more general but more complex solution is to face and edge swap the 3D tesselation to drive it towards a better mesh (a large part of that 95%). This, of course, breaks the Delauyness but Delauyness is nowhere near as useful in 3D as it is in 2D.

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