摘要
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.Whenever possible,we point out some outstanding issues that still need investigating.
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. Whenever possible, we point out some outstanding issues that still need investigating.
基金
supported by the US Department of Energy Office of Science Climate Change Prediction Program through grant numbers DE-FG02-07ER64431 and DE-FG02-07ER64432
the US National Science Foundation under grant numbers DMS-0609575 and DMS-0913491
