Voronoi diagrams from (possibly disconnected) embeddings

M. Kapl, F. Aurenhammer, and B. Jüttler


We introduce a new metric framework which is based on an injective embedding of $[0,1]^{2}$ into $R^{m}$, for $m \geq 2$, and an additional scaling function for re-scaling the distances. The framework is used to construct a new type of generalized Voronoi diagrams in $[0,1]^{2}$, which is possibly anisotropic. We present different possible applications of these Voronoi diagrams with several examples of generated diagrams.

Reference: M. Kapl, F. Aurenhammer, and B. Jüttler. Voronoi diagrams from (possibly disconnected) embeddings. In Proc. International Symposium on Voronoi Diagrams ISVD 2013, IEEE Computer Society, pages 47-50, St. Petersburg, Russia, 2013.