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GPU-Assisted Computation of Centroidal Voronoi Tessellation

Guodong Rong, Yang Liu, Wenping Wang, Xiaotian Yin, David Gu, Xiaohu Guo
Dept. of Comput. Sci., Univ. of Texas at Dallas, Richardson, TX, USA
IEEE Transactions on Visualization and Computer Graphics (2010) Volume: 17, Issue: X, Pages: 1-13

@article{rong2011gpu,

   title={GPU-assisted computation of centroidal Voronoi tessellation},

   author={Rong, G. and Liu, Y. and Wang, W. and Yin, X. and Gu, D. and Guo, X.},

   journal={Visualization and Computer Graphics, IEEE Transactions on},

   volume={17},

   number={3},

   pages={345–356},

   issn={1077-2626},

   year={2011},

   publisher={IEEE}

}

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Centroidal Voronoi tessellations (CVT) are widely used in computational science and engineering. The most commonly used method is Lloyds method, and recently the L-BFGS method is shown to be faster than Lloyds 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 the surface. In our implementation a new technique is proposed for parallel regional reduction on the GPU for evaluating integrals over Voronoi cells.
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