A GPU Algorithm for Convex Hull

We present a novel algorithm to compute the convex hull of a point set in R using the graphics processing unit (GPU). By exploiting the relationship between the Voronoi diagram and the convex hull, we derive the answer from the former. Our algorithm only requires a few simple atomic operations and does not need explicit locking or any other concurrency control mechanism, thus it can maximize the parallelism available on the modern GPU. Our implementation using the CUDA programming model on Nvidia GPUs is robust, exact, and efficient. The experiments show that it is up to an order of magnitude faster than other sequential convex hull implementations running on the CPU for inputs of millions of points. We further extend our GPU approach to obtain the Delaunay triangulation of points in R by computing their 4D convex hull. Our works demonstrate that the GPU can be used to solve non-trivial computational geometry problems with significant performance benefit, without sacrificing accuracy or robustness. This is an updated version of Technical Report # TRA3/11 with improvement to the algorithm/results. CR Categories: I.3.5 [Computer Graphics]: Computational Geometry and Object Modelling—Geometric algorithms I.3.1 [Computer Graphics]: Hardware Architecture—Graphics processors