Fast Parallel Evaluation of Exact Geometric Predicates on GPUs

Menezes, Marcelo M.; Magalhães, Salles V. G.; Oliveira, Matheus Aguilar de; Franklin, W. Randolph; Chichorro, Rodrigo Eduardo de Oliveira Bauer

doi:10.1016/j.cad.2022.103285

“…Moreover, robust predicates could be extended to provide robust constructions such as points of intersection of linestrings [2]. Recently, GPU implementations of robust predicates have been presented, providing a constant (3 to 4 times) speedup over standard CPU implementations [27,8].…”

Section: Introductionmentioning

confidence: 99%

Fast Floating-Point Filters for Robust Predicates

Bartels

¹

,

Fisikopoulos

²

,

Weiser

³

2022

0

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Geometric predicates are at the core of many algorithms, such as the construction of Delaunay triangulations, mesh processing and spatial relation tests. These algorithms have applications in scientific computing, geographic information systems and computer-aided design. With floating-point arithmetic, these geometric predicates can incur round-off errors that may lead to incorrect results and inconsistencies, causing computations to fail. This issue has been addressed using a combination of exact arithmetic for robustness and floating-point filters to mitigate the computational cost of exact computations. The implementation of exact computations and floating-point filters can be a difficult task, and code generation tools have been proposed to address this. We present a new C++ meta-programming framework for the generation of fast, robust predicates for arbitrary geometric predicates based on polynomial expressions. We combine and extend different approaches to filtering, branch reduction, and overflow avoidance that have previously been proposed. We show examples of how this approach produces correct results for data sets that could lead to incorrect predicate results with naive implementations. Our benchmark results demonstrate that our implementation surpasses state-of-the-art implementations.

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Fast floating-point filters for robust predicates

Bartels

¹

,

Fisikopoulos

²

,

Weiser

³

2023

Bit Numer Math

0

View full text Add to dashboard Cite

Geometric predicates are at the core of many algorithms, such as the construction of Delaunay triangulations, mesh processing and spatial relation tests. These algorithms have applications in scientific computing, geographic information systems and computer-aided design. With floating-point arithmetic, these geometric predicates can incur round-off errors that may lead to incorrect results and inconsistencies, causing computations to fail. This issue has been addressed using a combination of exact arithmetic for robustness and floating-point filters to mitigate the computational cost of exact computations. The implementation of exact computations and floating-point filters can be a difficult task, and code generation tools have been proposed to address this. We present a new C++ meta-programming framework for the generation of fast, robust predicates for arbitrary geometric predicates based on polynomial expressions. We combine and extend different approaches to filtering, branch reduction, and overflow avoidance that have previously been proposed. We show examples of how this approach produces correct results for data sets that could lead to incorrect predicate results with naive implementations. Our benchmark results demonstrate that our implementation surpasses state-of-the-art implementations.

show abstract