Distmesh initialization in 3D

[nschloe]

In 2D, distmesh initializes with a triangular space-filling pattern. How do you initialize tets in 3D? Link is fine.

[krober10nd]

In parallel I build a structured grid in blocks each owned by one core and in serial here:

https://github.com/krober10nd/SeismicMesh/blob/c18aa4fa18ee0d7e2525775d2529737fc3de0877/SeismicMesh/generation/mesh_generator.py#L510

[nschloe]

Okay, meshgrid. How so you generate the tets from the points then?

[krober10nd]

I call a Bowyer-Watson Deluanay triangulation algorithm that operates on the local point set (if parallel).

I wrote a Python wrapper to the 2D and 3D Delaunay triangulation class from the cgal package.

https://github.com/krober10nd/SeismicMesh/blob/c18aa4fa18ee0d7e2525775d2529737fc3de0877/SeismicMesh/generation/mesh_generator.py#L311

[krober10nd]

https://github.com/krober10nd/SeismicMesh/blob/api_overhaul/SeismicMesh/generation/cpp/delaunay_class.cpp

[nschloe]

Okay. Do you do any edge/face flip magic or does this then only work for convex domains?

[krober10nd]

Okay. Do you do any edge/face flip magic

No, not doing any of that.

or does this then only work for convex domains?

Per the original DistMesh algorithm paper, I remove points "outside" of the domain each meshing iteration by evaluating the signed distance function with the centroid of each cell. Thus, it can mesh any domain (including convex, non-convex or a disjoint domain).

[krober10nd]

I tried a different way to form the initial point distribution (that works in both 2 and 3d)

https://github.com/krober10nd/SeismicMesh/blob/aa6533bb22ff26f19b881427ef956df989079919/SeismicMesh/generation/utils.py#L28

[nschloe]

There are more tetrahedral space-fillings to play around with, https://demonstrations.wolfram.com/SpaceFillingTetrahedra/, and since those filling are all regular, you can very cheaply create the cells, too. I'm not sure if any of those fillings is better than what you're trying. Eventually, the most natural solution would be the tet-oct honeycomb, but since pre-/post-processing software support for octs is weak, it's not a viable option yet.

[krober10nd]

Very cool. Yea I can put severa in and see when I have more time. I came across a paper that created the honey comb meshes for some numerical analysis.

[nschloe]

I never implemented any of those, too afraid of the index war. That'd perhaps be something for meshzoo one day. Anyway, not a requirement from my side for the paper.

[krober10nd]

I see. Yes, it's just something interesting. The ending mesh quality is reduced if you don't use the staggered grid.

But yea probably a good utility for 'meshzoo'