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Advances in studies and applications of centroidal Voronoi tessellations. (English) Zbl 1224.52032
Summary: Centroidal Voronoi tessellations (CVTs) have become a useful tool in many applications ranging from geometric modeling, image and data analysis, and numerical partial differential equations, to problems in physics, astrophysics, chemistry, and biology. In this paper, we briefly review the CVT concept and a few of its generalizations and well-known properties. We then present an overview of recent advances in both mathematical and computational studies and in practical applications of CVTs. We point out some outstanding issues that still need to be investigated.

52C99 Discrete geometry
52C45 Combinatorial complexity of geometric structures
68U05 Computer graphics; computational geometry (digital and algorithmic aspects)
68U10 Computing methodologies for image processing
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