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The problem of dynamic maintenance of the Voronoi diagram for a set of spheres moving independently in d-dimensional space is addressed in this paper. The maintenance of the generalized Voronoi diagram of spheres, moving alone the given trajectories, requires the calculation of topological events, that occur when d + 2 spheres become tangent to a common sphere. The criterion for determination of such a topological event for spheres in the Euclidean metric is presented. This criterion is given in the form of polynomial algebraic equations dependent on the coordinates and trajectories of the moving spheres. These equations are normally solved using numerical methods.

On Dynamic Generalized Voronoi Diagrams in the Euclidean Metric