This piece from Scientific American website explains:Įveryone uses Voronoi tessellations, even without realizing it. Voronoi tesselations are just not interesting mathematical objects, as they arise in everyday situations. Mathematicians have extensively studied Voronoi tessellations, particularly those based on Poisson point processes, forming a core subject in the field of stochastic geometry. The evolution of Voronoi cells, which start off as disks until they collide with each other. That union of sets is the Voronoi tessellation. The union of all the sets covers the underlying space. Each region forms a cell corresponding to the point. Now for each point in the collection, consider the surrounding region that is closer to that point than any other point in the collection. To form a Voronoi tessellation, consider a collection of points scattered on some space, like the plane, where it’s easier to picture things, especially when using a Euclidean metric. At any rate, I will call it a Voronoi tessellation. I’ve read that Descartes studied the object even earlier than Dirichlet, but Voronoi studied it in much more depth. A notable exception is the R library spatstat that does actually call it a Dirichlet tessellation. Historically, Dirichlet beats Voronoi, but it seems wherever I look, the name Voronoi usually wins out, suggesting an example of Stigler’s law of eponymy. The main other name for this object is the Dirichlet tessellation. We can model or approximate all these phenomena and many, many more with a geometric structure called, among other names, a Voronoi tessellation.
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