Marcelo de Matos Menezes, Salles Viana Gomes de Magalhães, Matheus Aguilar, W. Randolph Franklin, and Bruno Coelho. Employing GPUs to accelerate exact geometric predicates for 3D geospatial processing. In John Krumm, Andreas Züfle, and Cyrus Shahabi, editors, Spatial Gems, volume 1, chapter 11. ACM, 2022. URL:
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This paper presents a technique to use GPUs to accelerate the computation of 3D geometric predicates. A common predicate is computing the orientation of four 3D points, which is a subproblem in applications such as intersecting two 3D meshes. Since the higher level application may require billions of evaluations, efficiency is important. Accuracy is required since floating roundoff errors can cause topological impossibilities. One solution is to compute with rational numbers, but that is difficult to implement on a GPU because rationals' sizes vary. Our solution is to compute on the GPU with interval arithmetic, but fall back to using rationals on the CPU if the interval computed on the GPU includes the origin; i.e., its sign is unknown. Our experiment with a dataset of hard rock mining drill holes show that this fallback to the CPU is rarely necessary; so that our technique gave a 17 times speedup compared to a sequential implementation.

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