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GPU-Based Computation of Discrete Periodic Centroidal Voronoi Tessellation in Hyperbolic Space

Liang Shuai, Xiaohu Guo, Miao Jin
University of Texas at Dallas
Computer-Aided Design (SPM 2012 Special Issue), 2012

@article{shuaia2012gpu,

   title={GPU-Based Computation of Discrete Periodic Centroidal Voronoi Tessellation in Hyperbolic Space},

   author={Shuaia, L. and Guoa, X. and Jinb, M.},

   year={2012}

}

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Periodic centroidal Voronoi tessellation (CVT) in hyperbolic space provides a nice theoretical framework for computing the constrained CVT on high-genus (genus > 1) surfaces. This paper addresses two computational issues related to such hyperbolic CVT framework: (1) efficient reduction of unnecessary site copies in neighbor domains on the universal covering space, based on two special rules; (2) GPU-based parallel algorithms to compute a discrete version of the hyperbolic CVT. Our experiments show that with the dramatically reduced number of unnecessary site copies in neighbor domains and the GPU-based parallel algorithms, we significantly speed up the computation of CVT for high-genus surfaces. The proposed discrete hyperbolic CVT guarantees to converge and produces high-quality results.
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