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

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1 Author(s)
Kokichi Sugihara ; Grad. Sch. of Adv. Math. Sci., Meiji Univ., Kawasaki, Japan

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.

Published in:

Voronoi Diagrams in Science and Engineering (ISVD), 2011 Eighth International Symposium on

Date of Conference:

28-30 June 2011