TIGHT Intervals for Provably Correct Geometric Computation
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Date
2025
Journal Title
Journal ISSN
Volume Title
Publisher
The Eurographics Association
Abstract
Interval 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.
Description
CCS Concepts: Mathematics of computing → Interval arithmetic; Mathematical software performance; Theory of computation → Rounding techniques
@inproceedings{10.2312:stag.20251319,
booktitle = {Smart Tools and Applications in Graphics - Eurographics Italian Chapter Conference},
editor = {Comino Trinidad, Marc and Mancinelli, Claudio and Maggioli, Filippo and Romanengo, Chiara and Cabiddu, Daniela and Giorgi, Daniela},
title = {{TIGHT Intervals for Provably Correct Geometric Computation}},
author = {Sichetti, Federico and Attene, Marco and Puppo, Enrico},
year = {2025},
publisher = {The Eurographics Association},
ISSN = {2617-4855},
ISBN = {978-3-03868-296-7},
DOI = {10.2312/stag.20251319}
}