TIGHT Intervals for Provably Correct Geometric Computation

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dc.contributor.authorSichetti, Federicoen_US
dc.contributor.authorAttene, Marcoen_US
dc.contributor.authorPuppo, Enricoen_US
dc.contributor.editorComino Trinidad, Marcen_US
dc.contributor.editorMancinelli, Claudioen_US
dc.contributor.editorMaggioli, Filippoen_US
dc.contributor.editorRomanengo, Chiaraen_US
dc.contributor.editorCabiddu, Danielaen_US
dc.contributor.editorGiorgi, Danielaen_US
dc.date.accessioned2025-11-21T07:27:53Z
dc.date.available2025-11-21T07:27:53Z
dc.date.issued2025
dc.description.abstractInterval arithmetic is a practical method for robust computation, bridging the gap between fast, but inexact, floating-point arithmetic and slow, exact arithmetic, such as rational or arbitrary-precision. In this system, numbers are represented as intervals bounded by floating-point numbers, and operations are performed conservatively, guaranteeing that the resulting interval contains the exact mathematical result. We extend a fast C++ library for interval arithmetic by adding support for several transcendental functions. A key feature of our library is that all operations are correctly rounded, ensuring the resulting interval is the smallest floating-point interval that contains the true result. We demonstrate the library's effectiveness by applying it to complex non-polynomial problems, including surface-surface intersection and continuous collision detection for geometric primitives undergoing roto-translational motion.en_US
dc.description.sectionheadersTools in Computer Graphics
dc.description.seriesinformationSmart Tools and Applications in Graphics - Eurographics Italian Chapter Conference
dc.identifier.doi10.2312/stag.20251319
dc.identifier.isbn978-3-03868-296-7
dc.identifier.issn2617-4855
dc.identifier.pages9 pages
dc.identifier.urihttps://doi.org/10.2312/stag.20251319
dc.identifier.urihttps://diglib.eg.org/handle/10.2312/stag20251319
dc.publisherThe Eurographics Associationen_US
dc.rightsAttribution 4.0 International License
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subjectCCS Concepts: Mathematics of computing → Interval arithmetic; Mathematical software performance; Theory of computation → Rounding techniques
dc.subjectMathematics of computing → Interval arithmetic
dc.subjectMathematical software performance
dc.subjectTheory of computation → Rounding techniques
dc.titleTIGHT Intervals for Provably Correct Geometric Computationen_US
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Italian Chapter Conference 2025 - Smart Tools and Apps in Graphics