Fast and exact evaluation of geometric predicates using graphics processing units - Menezes, Marcelo de Matos (2021)
Floating point arithmetic’s finite precision presents a major challenge in the field of computational geometry, since even carefully designed algorithms may fail due to round-off errors. While there has been research to develop exact geometric algorithms, the existing techniques so far can still be improved performance-wise. In this work we propose a fast and exact method for efficient geometric predicate evaluation using the graphics process- ing unit, in which, by implementing arithmetic filtering on the GPU, the computation of most predicates can be performed without round-off errors. The (few) results that are unreliable are reevaluated using arbitrary precision rational numbers in parallel on the CPU. We measured the efficiency of our method by implementing geometric algorithms in 3 case studies: 2D segment-segment intersection, 3D segment-triangle intersection, and 3D triangle-triangle intersection. At each step, new techniques were proposed for eliminating the current performance bottleneck. In our last experiments, a comparison of our method against a sequential CPU implementation yielded speedups of up to 1936× for intersection evaluation, and 414× for the entire running time of the algorithm. The achieved efficiency shows that our technique is ideal for accelerating exact geometric computations, and fields such as CAD, GIS, and 3D modeling should benefit from it. Keywords: Computational geometry. Exact computation. Arithmetic filtering. GPGPU.