In the authors’ recent paper (de Lacy Costello et al., 2010) the authors described the formation of complex tessellations of the plane arising from the various reactions of metal salts with potassium ferricyanide and ferrocyanide loaded gels. In addition to producing colourful tessellations these reactions are naturally computing generalised Voronoi diagrams of the plane. The reactions reported...

A Voronoi diagram of a point set P ⊆ IR is a partition of space into regions, such that the cell of p ∈ P , is V (p, P ) = { x ∣∣∣‖xp‖ ≤‖xp′‖ for all p′ ∈ P }. Vornoi diagrams are a powerful tool and have numerous applications [Aur91]. One problem with Vornoi diagrams is that their descriptive complexity is O(ndd/2e) in IR, in the worst case. See Figure 1 for an exmaple in three dimensions. It ...

This paper studies the Voronoi diagrams on 2-manifold meshes based on geodesic metric (a.k.a. geodesic Voronoi diagrams or GVDs), which have polyline generators. We show that our general setting leads to situations more complicated than conventional 2D Euclidean Voronoi diagrams as well as point-source based GVDs, since a typical bisector contains line segments, hyperbolic segments and paraboli...

The Network Voronoi diagram and its variants have been extensively used in the context of numerous applications in road networks, particularly to efficiently evaluate various spatial proximity queries such as k nearest neighbor (kNN), reverse kNN, and closest pair. Although the existing approaches successfully utilize the network Voronoi diagram as a way to partition the space for their specifi...