Three-dimensional straight skeletons from bisector graphs

F. Aurenhammer and G. Walzl

Abstract:

A straight skeleton of a polygon or of a polytope is a piecewise linear skeletal structure that partitions the underlying object by means of a self-parallel shrinking process. We propose a method for constructing different straight skeletons for a given nonconvex polytope Q in 3-space. The approach is based on so-called bisector graphs on the sphere, and allows for generating straight skeletons with certain optimality properties. The various events that arise during the process of shrinking Q are discussed. We have implemented our method and give some examples of the output.



Reference: F. Aurenhammer and G. Walzl. Three-dimensional straight skeletons from bisector graphs. In Proc. 5th International Conference on Analytic Number Theory and Spatial Tessellations, Voronoi's Impact on Modern Science, volume 5, pages 15-29, Kiev, Ukraine, 2015.