Boat-sail Voronoi diagram on a curved surface

摘要

We propose a new generalized Voronoi diagram, called a "boat-sail Voronoi diagram on a curved surface". This is an extension of the boat-sail Voronoi diagram. The boat-sail Voronoi diagram is the partition of a two-dimensional flow field according to the shortest arrival time of a boat. On the other hand, our new Voronoi diagram subdivides the curbed surface with flow into the regions. In this paper, we derive a partial differential equation to solve the boat-sail Voronoi diagram on a curved surface and show some numerical examples.