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  <doc>
    <id>8763</id>
    <completedYear/>
    <publishedYear>2023</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>63</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2023-05-17</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Fast Floating-Point Filters for Robust Predicates</title>
    <abstract language="eng">Geometric predicates are at the core of many algorithms, such as the construction of Delaunay triangulations, mesh processing and spatial relation tests.&#13;
These algorithms have applications in scientific computing, geographic information systems and computer-aided design.&#13;
With floating-point arithmetic, these geometric predicates can incur round-off errors that may lead to incorrect results and inconsistencies, causing computations to fail. &#13;
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.&#13;
The implementation of exact computations and floating-point filters can be a difficult task, and code generation tools have been proposed to address this. &#13;
We present a new C++ meta-programming framework for the generation of fast, robust predicates for arbitrary geometric predicates based on polynomial expressions. &#13;
We combine and extend different approaches to filtering, branch reduction, and overflow avoidance that have previously been proposed.&#13;
We show examples of how this approach produces correct results for data sets that could lead to incorrect predicate results with naive implementations. &#13;
Our benchmark results demonstrate that our implementation surpasses state-of-the-art implementations.</abstract>
    <parentTitle language="eng">BIT Numerical Mathematics</parentTitle>
    <identifier type="arxiv">2208.00497</identifier>
    <identifier type="doi">10.1007/s10543-023-00975-x</identifier>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">2023-04-25</enrichment>
    <author>Tinko Bartels</author>
    <submitter>Martin Weiser</submitter>
    <author>Vissarion Fisikopoulos</author>
    <author>Martin Weiser</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <collection role="projects" number="UJena-Forensic">UJena-Forensic</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
  </doc>
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