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I found a paper about Delaunay triangulation for a set of points that are distributed by the Poisson distribution (https://pdfs.semanticscholar.org/9693/4b7e8e5483893f4874d7ba6afd812bbfe0ba.pdf). The question is "Are there any other cases for specific distribution of the set for Delaunay triangulation or Voronoi plus their applications?"

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