Exact, robust, and efficient regularized Booleans on general 3D meshes

Hichem Barki, Gaël Guennebaud, Sebti Foufou

    Research output: Contribution to journalArticle

    Abstract

    Computing Boolean operations (Booleans) of 3D polyhedra/meshes is a basic and essential task in many domains, such as computational geometry, computer-aided design, and constructive solid geometry. Besides their utility and importance, Booleans are challenging to compute when dealing with meshes, because of topological changes, geometric degeneracies, etc. Most prior art techniques either suffer from robustness issues, deal with a restricted class of input/output meshes, or provide only approximate results. We overcome these limitations and present an exact and robust approach performing on general meshes, required to be only closed and orientable. Our method is based on a few geometric and topological predicates that allow to handle all input/output cases considered as degenerate in existing solutions, such as voids, non-manifold, disconnected, and unbounded meshes, and to robustly deal with special input configurations. Our experimentation showed that our more general approach is also more robust and more efficient than Maya's implementation (×3), CGAL's robust Nef polyhedra (×5), and recent plane-based approaches. Finally, we also present a complete benchmark intended to validate Boolean algorithms under relevant and challenging scenarios, and we successfully ascertain both our algorithm and implementation with it.

    Original languageEnglish (US)
    Pages (from-to)1235-1254
    Number of pages20
    JournalComputers and Mathematics with Applications
    Volume70
    Issue number6
    DOIs
    StatePublished - Jan 1 2015

    Fingerprint

    Mesh
    Computational geometry
    Computer aided design
    Polyhedron
    Constructive Solid Geometry
    Geometry
    Boolean Operation
    Output
    Computational Geometry
    Computer-aided Design
    Voids
    Predicate
    Experimentation
    Benchmark
    Robustness
    Closed
    Scenarios
    Configuration
    Computing

    Keywords

    • 3D meshes
    • Boolean operations
    • Computational geometry
    • Robust geometric computation
    • Solid modeling

    ASJC Scopus subject areas

    • Modeling and Simulation
    • Computational Theory and Mathematics
    • Computational Mathematics

    Cite this

    Exact, robust, and efficient regularized Booleans on general 3D meshes. / Barki, Hichem; Guennebaud, Gaël; Foufou, Sebti.

    In: Computers and Mathematics with Applications, Vol. 70, No. 6, 01.01.2015, p. 1235-1254.

    Research output: Contribution to journalArticle

    Barki, Hichem ; Guennebaud, Gaël ; Foufou, Sebti. / Exact, robust, and efficient regularized Booleans on general 3D meshes. In: Computers and Mathematics with Applications. 2015 ; Vol. 70, No. 6. pp. 1235-1254.
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