merging voronoi

Here we are playing again with the Voronoi diagram (VD). We wanted to see what happen when sites are merged together (MVD, merged VD).

VD partitions the plane in cells where each of these cell represents the closest part of the plane to a particular site. So, if you have sites on a map of various fast food restaurants, the Voronoi diagram tells you which one is physically the closest to your location.

But imagine that we want to consider all restaurant from a particular chain as one entity. We want to know the influence or the domination of a particular chain.

The following images are in pair. The first one is the influence of a chain of restaurant and the second is the actual VD that everyone knows. Cells with the same color represents a chain of restaurant.

In the images, you can see some brighter points (particularly in the first two images), this is the actual location of the site (or restaurant for in our example).

And just like the VD is well known for its role in texture synthesis, we hope to find a way to use the MVD to create some interesting results.

As for the diagram itself, we don't really know what to do with it or how to interpret it. VD has a dual graph called the Delaunay Triangulation. But what would be the dual graph of MVD ? Where do we put the edges ? That's an open question.

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