It seems that computing a Voronoi diagram with mathematical accuracy for a real-time animation is not really feasible. I found this Processing hack that takes advantage of graphic acceleration to draw an approximate Voronoi diagram. It works by drawing 3D cones at the points of interest of the diagram and rendering a top view — the regions are drawn automatically as the Voronoi edges sit on the intersections between the cones.
Using this hack, it is possible to make a real-time Voronoi diagram animation, albeit with a limited number of points and a restricted applet area. This video was rendered with 364 particles (= sum of powers of 3 from 0 to 5).