Type of Document	Thesis
Author	Bollig, Evan F.
Author's Email Address	bollig@scs.fsu.edu
URN	etd-02172009-083954
Title	Centroidal Voronoi Tessellation of Manifolds Using the GPU
Degree	Master of Science
Department	Scientific Computing, Department of
Advisory Committee	Advisor Name Title Gordon Erlebacher Committee Chair Max Gunzburger Committee Member Xiaoqiang Wang Committee Member
Keywords	Computational Geometry Manfiolds Centroidal Voronoi Tessellation Jump Flooding CUDA GPGPU
Date of Defense	2008-11-24
Availability	unrestricted
Abstract Within the last decade, commodity Graphics Processing Units (GPUs) specialized for 2D and 3D scene rendering have seen an explosive growth in processing power compared to their general purpose counterpart, the CPU. Currently capable of near teraflop speeds and sporting gigabytes of on-board memory, GPUs have transformed from accessory video game hardware to truly general purpose computational coprocessors. One of the first applications of GPUs for general computing was 2D Voronoi tessellation--partitioning a 2D domain into regions based on a set of seed points, such that regions contain all points closer to one seed than to any other. Although the topic has been revisited many times, related work has failed to consider GPU based production of emph{centroidal} Voronoi tessellations, where seed points are also the regional centers of mass. This thesis presents a first look at centroidal Voronoi tessellation computed entirely on the GPU. An extension to centroidal Voronoi tessellation is also considered for partitioning surfaces (2-manifolds) of the form $f(u,v) ightarrow (u, v, z(u,v))$ using Euclidean based metrics. To complete these tasks, a highly efficient flooding algorithm is used for the Voronoi tessellation, while a regularized sampling approach is employed to compute the centroids of the Voronoi regions. Seeds are updated by a deterministic Lloyd's method.
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