Let's assume a given (convex) polytope P. There are a number of papers regarding partitions, but I couldn't find a starting point for my problem: I'm looking at a partition of P into polytopes P_i where
- conv(P_i) = P (with conv(.) being the convex hull; instead of looking at the union)
- P_i not necessarily being disjoint
- (optional) the "best partition" in some kind of way (e.g. least amount of edges/sides over all polytopes P_i)
An image to better clarify the idea: stack.imgur Link This shows the polytope P and a "partition" into two polytopes, that form P if you consider the convex hull of both. I'm interested in any tips on how to go about actually finding partitions like that (without just trying out various combinations of initial corner-vertices of P).
