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Exact and efficient polyhedral envelope containment check

Published: 12 August 2020 Publication History

Abstract

We introduce a new technique to check containment of a triangle within an envelope built around a given triangle mesh. While existing methods conservatively check containment within a Euclidean envelope, our approach makes use of a non-Euclidean envelope where containment can be checked both exactly and efficiently. Exactness is crucial to address major robustness issues in existing geometry processing algorithms, which we demonstrate by integrating our technique in two surface triangle remeshing algorithms and a volumetric tetrahedral meshing algorithm. We provide a quantitative comparison of our method and alternative algorithms, showing that our solution, in addition to being exact, is also more efficient. Indeed, while containment within large envelopes can be checked in a comparable time, we show that our algorithm outperforms alternative methods when the envelope becomes thin.

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    cover image ACM Transactions on Graphics
    ACM Transactions on Graphics  Volume 39, Issue 4
    August 2020
    1732 pages
    ISSN:0730-0301
    EISSN:1557-7368
    DOI:10.1145/3386569
    Issue’s Table of Contents
    Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].

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    Publication History

    Published: 12 August 2020
    Published in TOG Volume 39, Issue 4

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    Author Tags

    1. geometric predicates
    2. robust geometric computation
    3. shape proximity

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    • (2024)Cascading upper bounds for triangle soup Pompeiu‐Hausdorff distanceComputer Graphics Forum10.1111/cgf.1512943:5Online publication date: 31-Jul-2024
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