Voronoi Diagrams from (Possibly Discontinuous) Embeddings

We introduce a new metric framework which is based on an injective embedding of [0,1]
²
into R
^m
, for m ≥ 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.