geometrize VS geogram

Interesting question! By virtue of being a tree, the MST produces at most 3 edges coming out of any vertex, so this should be the same in 3D. The MST then adds (sometimes) a 4th edge, so, although you could build both graphs in 3D space, you would still end up with 4 edges coming out of any vertex, I think.

In 3D space the Delaunay triangulation would produce a bunch of irregular tetrahedra, so the edges coming out from every vertex would vary between a minimum of 3, and a maximum of 12, if I get it right (ref: [1] :-).

The 3D Voronoi cells are another story... I found some implementation that you can play with to see how it looks [2] [3], each cell is of a shape called "convex polytope". It feels like these cells are packed like each of the sub-cubes of a rubik, but I'm not 100% sure :-) ... if that's true, you could jump from each vertex to the next in at most 17 directions? (hand-waves :-p)

--

1: https://en.wikipedia.org/wiki/Tetrahedron#/media/File:M_tic....

2: https://github.com/BrunoLevy/geogram/wiki/Delaunay3D

3: https://math.lbl.gov/voro++/examples/

Geogram, it has some pointsets to surface functionality : https://github.com/BrunoLevy/geogram

Thank you very much for this feedback, it is super useful. Do not hesitate to post this type of comment to geogram's github (https://github.com/BrunoLevy/geogram/issues)

Please note that the Logger mechanism can be redirected to a GUI, it is used for instance in the GUI applications made with Geogram (https://github.com/BrunoLevy/geogram/wiki/Applications) and in Graphite (https://github.com/BrunoLevy/GraphiteThree)

About using std::string as path under Windows, I understand that it may cause some problems with users who use general characters in their directories, but it does not prevent the application from running and from loading/writing files. In the future, when std::filesystem is well standardized, I plan to get read of my FileSystem implementation.