The Zermelo-Voronoi Diagram: a dynamic partition problem

We consider a Dirichlet-Voronoi like partition problem for a small airplane operating in the horizontal plane in the presence of winds that vary uniformly with time. It is shown that the problem can be interpreted as a Dynamic Voronoi Diagram problem, where the generators are not fixed, but rather they are moving targets to be reached in minimum time. The problem is solved by reducing it to a standard Voronoi Diagram by means of a time-varying coordinate transformation.