GPU-based computation of discrete periodic centroidal Voronoi tessellation in hyperbolic space

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 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.

► We propose a framework for computing discrete periodic CVT in hyperbolic space. ► Two efficient rules are introduced to reduce the site copies of periodic CVT. ► A GPU-based parallel algorithm is proposed to compute the discrete periodic CVT. ► We significantly speed up the computation of periodic CVT for high-genus surfaces. ► The proposed discrete CVT guarantees to converge and produces high-quality results.