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SIAM Journal on Scientific Computing
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ICCSA '10 Proceedings of the 2010 International Conference on Computational Science and Its Applications
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Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
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IEEE Transactions on Visualization and Computer Graphics
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ISVD '11 Proceedings of the 2011 Eighth International Symposium on Voronoi Diagrams in Science and Engineering
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IEEE Transactions on Information Theory
Least squares quantization in PCM
IEEE Transactions on Information Theory
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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 (genus1) surfaces. This paper addresses two computational issues related to such a 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.