ah yes you're right about the orientability! there's no need to write or look at c++. the idea is to find the (facet, orthant)'s for each connected component, in the way i have described, and encode that information (for each connected component) in an object just like the object you get from `...->...

i had an idea to simplify the above approach: instead of naively constructing a cell-complex representation for a connected component C, i think it should be possible to save the combinatorics of C in an object like the real phase structure R of the patchworked hypersurface H, but restricted to C (i...

hey charles, i've been out of math for a while, so i might be forgetting basic stuff. but afaik there is atm no direct way to do this unfortunately. there is however a pretty straight forward idea for such an algorithm, since we have knowledge of the combinatorics of the surface via the real phase s...