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A Voronoi tessellation with $n$ generator points is the partitioning of a bounded region in $\rr^2$ into polygons such that every point in a given polygon is closer to its generator point than to any other generator point. A centroidal Voronoi tessellation (CVT) is a Voronoi tessellation where each polygon’s generator point is also its center of mass. In this project I will demonstrate what kinds of CVTs can exists within specific parameters, such as a square or rectangular region, and a set number generator points. I will also prove that the examples I present are the only CVTs that can possibly exist within their given parameters.
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Shakhnovskiy, Kirill, "Centroidal Voronoi Tessellations with Few Generator Points" (2018). Senior Projects Spring 2018. 189.
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