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A 3D Convex Hull Algorithm for Graphics Hardware

Mingcen Gao, Thanh-Tung Cao, Tiow-Seng Tan, Zhiyong Huang
National University of Singapore
National University of Singapore, Technical Report, 2011
@article{gao20113d,

   title={A 3D Convex Hull Algorithm for Graphics Hardware},

   author={Gao, M. and Cao, T.T. and Tan, T.S. and Huang, Z.},

   year={2011}

}

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This report presents a novel approach, termed gHull, to compute the convex hull for a given point set in R3 using the graphics processing units (GPUs). While the 2D problem can easily and efficiently be solved in the GPU, there is no known obvious, classical parallel solution that works well in the GPU for the 3D problem. Our novel parallel approach exploits the relationship between the 3D Voronoi diagram and the 3D convex hull so as to maximize the parallelism available in the GPU to compute the answer from the former rather than directly. Our implementation of the approach using the CUDA programming model on nVidia GPUs shows that it is robust and efficient. Our experiment shows that gHull runs up to 10x faster than the fastest CPU convex hull software, QuickHull, on inputs with millions of points.
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