Skeletons and offsetting: A topological point of view
Update: A conference paper on this topic
appeared at EuroCG 2018.
Abstract.
We investigate topological properties of skeleton structures of shapes like
Voronoi diagrams and straight skeletons. We show that these skeleton structures
are homotopy-equivalent to the original shape and discuss the homology of
skeletons in arbitrary dimensions. Motivated by applications in NC-machining,
we investigate offset curves and their evolution and put it into context of
persistent homology. One application is the generalization of maximum inscribed
circles.