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Numer. Math. Theor. Meth. Appl., 3 (2010), pp. 119-142. |
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Advances in Studies and Applications of Centroidal Voronoi Tessellations Qiang Du 1*, Max Gunzburger 2, Lili Ju 3 1 Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USA.2 Department of Scientific Computing, Florida State University, Tallahassee, FL 32306, USA. 3 Department of Mathematics, University of South Carolina, Columbia, SC 29208, USA. Received 15 September 2009; Accepted (in revised version) 6 January 2010 Abstract 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. AMS subject classifications: 5202, 52B55, 62H30, 6502, 65D30, 65U05, 65Y25, 68U05, 68U10Key words: Voronoi tessellations, centroids, clustering, mesh generation and optimization, image processing, model reduction, point sampling. *Corresponding author. Email: qdu@math.psu.edu (Q. Du), gunzburg@fsu.edu (M. Gunzburger), ju@math.sc.edu (L. Ju) |