Fast Floating-Point Filters for Robust Predicates
Tinko Bartels, Vissarion Fisikopoulos, Martin Weiser

TL;DR
This paper introduces a C++ meta-programming framework that generates fast, robust geometric predicates using floating-point filters, improving accuracy and performance over existing methods.
Contribution
A novel C++ framework that combines multiple filtering approaches to produce reliable geometric predicates efficiently.
Findings
Outperforms state-of-the-art implementations in benchmarks.
Produces correct results on challenging data sets.
Extends existing filtering techniques with new approaches.
Abstract
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…
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Taxonomy
TopicsModel-Driven Software Engineering Techniques · Scientific Computing and Data Management · Constraint Satisfaction and Optimization
