[catbird]

Then you get a "weighted Voronoi diagram," haha.

If the weights are multiplicative, the edges between adjacent cells become circular arcs. It looks cool, but it's much more difficult to generate and analyze. For instance, the region belonging to a generating point is no longer guaranteed to be convex, and may even have holes or be in multiple disconnected pieces.

Weighted Voronoi diagrams show up sometimes in multi-agent systems where agents have different speeds, e.g. pursuit-evasion problems, or in facility placement (where to build a new store/warehouse, etc).