higher dimensional skeletons

from Weighted skeletons and fixed-share decomposition ( Aurenhammer | 2007 | ps | doi )

Higher dimensions

The concept of weighted skeleton (or weighted medial axis) is not limited to two dimensions. Given a convex polytope P in Ęd and an assignment of positive weights to its facets, a unique convex cell complex inside P can be defined, either by the respective shrinking process, or based on weighted distances to the hyperplanes that support P. In fact, the decomposition and optimality results presented in Section 3 and Section 4, respectively, directly generalize to higher dimensions.
Thusly we may draw:


Fun thing here is to compare what happens through the dimensions and see how high you can go before your head explodes. Also what the procedural modeling ramifications of each step are.