Idea to get a periodic, non-orthogonal isosurface as a manifold

[gy114]

Hi,

I'm not sure if this is feasible but I think there may be a way to extract the isosurface of a periodic function defined on a lattice using the out-of-box methods available in CGAL. Please advise if this is feasible:

(1) Create a P3DT3 (Periodic 3D Delaunay trangulation) in a cuboid (orthogonal).
(2) Generate a Periodic C3T3 (Periodic 3D mesh).
(3) Create the surface patch as a Polyhedron_3.
(4) Update the coordinates of the points on the surface mesh so that they reflect the actual geometry. (x,y,z) -> (a1x, a2y, a3*z)
(5) Re-mesh the Polyhedron_3 based on the actual geometry.

It may be tricky to "merge" the periodic boundaries of the Polyhedron_3 but I think it may be feasible. I can keep a record of the shortest edge. Also, since the points will be Periodic_points, with the offset() information, I can match the "dangling" points outside the periodic domain back to the canonical point. I'm not sure if that's a good idea for Polyhedron_3.

Please advise.

Thanks.