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Issue No. 03 - March (2011 vol. 17)
ISSN: 1077-2626
pp: 345-356
Guodong Rong , University of Texas at Dallas, Richardson
Yang Liu , LORIA/INRIA Lorraine, Villers les Nancy
Wenping Wang , The University of Hong Kong, Hong Kong
Xiaotian Yin , State University of New York at Stony Brook, Stony Brook
Xianfeng David Gu , State University of New York at Stony Brook, Stony Brook
Xiaohu Guo , University of Texas at Dallas, Richardson
Centroidal Voronoi tessellations (CVT) are widely used in computational science and engineering. The most commonly used method is Lloyd's method, and recently the L-BFGS method is shown to be faster than Lloyd's method for computing the CVT. However, these methods run on the CPU and are still too slow for many practical applications. We present techniques to implement these methods on the GPU for computing the CVT on 2D planes and on surfaces, and demonstrate significant speedup of these GPU-based methods over their CPU counterparts. For CVT computation on a surface, we use a geometry image stored in the GPU to represent the surface for computing the Voronoi diagram on it. In our implementation a new technique is proposed for parallel regional reduction on the GPU for evaluating integrals over Voronoi cells.
Centroidal Voronoi tessellation, graphics hardware, Lloyd's algorithm, L-BFGS algorithm, remeshing.

Y. Liu, W. Wang, G. Rong, X. Yin, X. D. Gu and X. Guo, "GPU-Assisted Computation of Centroidal Voronoi Tessellation," in IEEE Transactions on Visualization & Computer Graphics, vol. 17, no. , pp. 345-356, 2010.
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