High Quality Content by WIKIPEDIA articles! In geometry, a centroidal Voronoi tessellation (CVT) is a special type of Voronoi tessellation or Voronoi diagrams. A Voronoi tessellation is called centroidal when the generating point of each Voronoi cell is also its mean (center of mass). It can be viewed as an optimal partition corresponding to an optimal distribution of generators. A number of algorithms can be used to generate centroidal Voronoi tessellations, including Lloyd's algorithm and the K-means algorithm. Gersho's conjecture, proven for 1 and 2 dimensions, says that "asymptotically speaking, all cells of the optimal CVT, while forming a tessellation, are congruent to a basic cell which depends on the dimension."

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