Neper contest: Question 1

[rquey]

Through applications that are sometimes unconventional, the goal of the Neper contest is to highlight advanced capabilities that can be truly useful. Anyone can participate, and there is nothing to win! (although they might be some sort or ranking)

Since we are concerned with unusual capabilities or use of Neper, AI tools generally cannot answer the questions (although the Neper documentation can).

Here is question 1: Suppose you have a tessellation that has been regularized. How can you deregularize it?

All questions are marked with the "contest" tag.

[mkasemer]

I have two thoughts, but no strong theoretical basis for them...

1. If regularization deletes small edges, this tends to create more vertices upon edge deletion. Are there certain vertices that will be obviously the result of regularization?
2. Will regularization affect cell face flatness?

[rquey]

1. Regularization reduces the number of vertices. On each edge deletion, 2 vertices collapse into 1. Assuming the original tessellation is not degenerated (which, for Neper, is always the case except for cubes), vertices that were affected by regularization have more than 4 parent edges (without regularization, the "normal" number of 4, except at the vertices of the domain, where it is 3).
2. Always, except on the boundary.

[mkasemer]

With these answers in mind, I think 2 would be the more promising route to follow for identification. If we expect an un-regularized tessellation to have perfectly flat cell faces, then the cells in the regularized tessellation with faces which are not flat would tell us where to begin looking.