Periodic 3D Mesh generation and optimization with non-orthogonal cuboid

[gy114]

Is it possible to have a cuboid that is non-orthogonal, defined by three non-orthogonal "lattice vectors" a1, a2 and a3?

We can still use the orthogonal cuboid setup assuming that the positions of all points are r = xa1+ya2+z*a3. However, when optimizing the mesh, the default algorithms will interpret the geometry assuming orthogonal cuboid, which is simply off by a basis transformation. Is it possible to implement this feature in CGAL, feeding that transformation to the optimizer, such that the algorithms can determine the quality of the mesh based on the actual Cartesian coordinates?

[MaelRL]

Periodic triangulations based on lattices have been studied and there is some code, but it is not yet finished.

Here is the paper: https://inria.hal.science/hal-02923439/document
Here is the stable branch but that has only the skeleton of a normal triangulation: https://github.com/MaelRL/cgal/tree/Generic_Periodic_Triangulations
Here is the WIP branch. It's a lot more evolved than the prototype above, but it's far from finished, and IIRC it has some bugs: https://github.com/MaelRL/cgal/tree/Generic_P2T2

[gy114]

Thanks.