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Volume 3, Issue 2
Advances in Studies and Applications of Centroidal Voronoi Tessellations

Qiang Du, Max Gunzburger & Lili Ju

DOI: 10.4208/nmtma.2010.32s.1

Numer. Math. Theor. Meth. Appl., 3 (2010), pp. 119-142.

Published online: 2010-03

[An open-access article; the PDF is free to any online user.]

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  • 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.

  • Keywords

Voronoi tessellations, centroids, clustering, mesh generation and optimization, image processing, model reduction, point sampling.

  • AMS Subject Headings

5202, 52B55, 62H30, 6502, 65D30, 65U05, 65Y25, 68U05, 68U10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-3-119, author = {Qiang Du, Max Gunzburger and Lili Ju}, title = {Advances in Studies and Applications of Centroidal Voronoi Tessellations}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2010}, volume = {3}, number = {2}, pages = {119--142}, 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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2010.32s.1}, url = {http://global-sci.org/intro/article_detail/nmtma/5992.html} }
TY - JOUR T1 - Advances in Studies and Applications of Centroidal Voronoi Tessellations AU - Qiang Du, Max Gunzburger & Lili Ju JO - Numerical Mathematics: Theory, Methods and Applications VL - 2 SP - 119 EP - 142 PY - 2010 DA - 2010/03 SN - 3 DO - http://doi.org/10.4208/nmtma.2010.32s.1 UR - https://global-sci.org/intro/article_detail/nmtma/5992.html KW - Voronoi tessellations, centroids, clustering, mesh generation and optimization, image processing, model reduction, point sampling. AB -

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.

Qiang Du, Max Gunzburger and Lili Ju. (2010). Advances in Studies and Applications of Centroidal Voronoi Tessellations. Numerical Mathematics: Theory, Methods and Applications. 3 (2). 119-142. doi:10.4208/nmtma.2010.32s.1
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