Rescue Boat Voronoi Diagrams for Inhomogeneous, Anisotropic, and Time-Varying Distances

Abstract

We introduce a new generalization for the boat-sail distance. Whereas the boat-sail distance was originally defined for static flows of water, we generalize using a time-varying flow. This generalization can be used to model the behavior of a boat on a stormy ocean or in a bay with a tidal ebb and flow. We construct a robust method for computing the boat-sail distance. We then define a new generalized Voronoi diagram, called a ``rescue boat Voronoi diagram'', which identifies the rescue boat that can reach a broken-down ship the fastest. This involves more than a simple generalization for the boat-sail distance, because the broken-down ship hanges its location according to the ocean flow. We examine the properties of this Voronoi diagram and discuss its relationships with existing Voronoi diagrams.