[kk58]

I was looking at a similar approach, my question is how do parameterize the manifold and how do you map points on the manifold if it's irregular -think filamentous, so that path trace can be done

And in general this is a question of interest. Are graphs really a good discrete approximation of a manifold?

[A_N_T_O_N_I_O]

I hope you find these two resources useful to address your question. I'm also pretty integrated about the possible answers, but I definitely bet on doing it using graphs. I'm preparing a detailed and concrete explanation on why I guess this conclusion but that one will need to wait for now!

For now as I have already told you, check out these ones.

https://ncatlab.org/nlab/show/manifold

https://www.youtube.com/watch?v=LvmjbXZyoP0