Voronoi diagrams are not new, and there are many established algorithms (Fortune's, Lloyd's) for generating them (or their duals, the Delaunay triangulation).
There are many recent-ish papers too, containing algorithms which aren't so well known.
Of these approaches available, however, it seems only a few would also be viable to generate higher-dimensional analogues of the Voronoi diagram. I know Lloyd's algorithm can be (relatively) easily adapted for this purpose.
I'm wondering, however, if it's possible to extend other, more exciting algorithms (at least in theory) like Fortune's, or even an arbitrary algorithm, to compute a higher dimensional Voronoi diagram. It seems like—and this is just intuition—Fortune's algorithm and others like it could incorporate elliptic paraboloids to function as well in 3D, but I've seen no mention of this being possible.