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Given: Set of sites

Closest Points
The Voronoi cell of a site is given by the set of all points which are closer to than to any other site :



Halfspace Intersection
Each pair of sites divides the space into a halfspace points which are closer to than to

Then, can be described as the intersection of all halfspaces formed with other sites:



From this definition, it is obvious that all Voronoi cells are convex.