Topology Adaptive Interface Tracking Using the Deformable Simplicial Complex

Marek Krzysztof Misztal, Jakob Andreas Bærentzen

    Research output: Contribution to journalJournal articleResearchpeer-review

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    Abstract

    We present a novel, topology-adaptive method for deformable interface tracking, called the Deformable Simplicial Complex (DSC). In the DSC method, the interface is represented explicitly as a piecewise linear curve (in 2D) or surface (in 3D) which is a part of a discretization (triangulation/tetrahedralization) of the space, such that the interface can be retrieved as a set of faces separating triangles/tetrahedra marked as inside from the ones marked as outside (so it is also given implicitly). This representation allows robust topological adaptivity and, thanks to the explicit representation of the interface, it suffers only slightly from numerical diffusion. Furthermore, the use of an unstructured grid yields robust adaptive resolution. Also, topology control is simple in this setting. We present the strengths of the method in several examples: simple geometric flows, fluid simulation, point cloud reconstruction, and cut locus construction.
    Original languageEnglish
    JournalA C M Transactions on Graphics
    Volume31
    Issue number3
    Pages (from-to)No. 24
    Number of pages12
    ISSN0730-0301
    DOIs
    Publication statusPublished - 2012

    Bibliographical note

    © ACM, 2012. This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in A C M Transactions on Graphics, 31, 3, (May 2012) http://doi.acm.org/10.1145/2167076.2167082

    Keywords

    • Algorithms

    Cite this

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    title = "Topology Adaptive Interface Tracking Using the Deformable Simplicial Complex",
    abstract = "We present a novel, topology-adaptive method for deformable interface tracking, called the Deformable Simplicial Complex (DSC). In the DSC method, the interface is represented explicitly as a piecewise linear curve (in 2D) or surface (in 3D) which is a part of a discretization (triangulation/tetrahedralization) of the space, such that the interface can be retrieved as a set of faces separating triangles/tetrahedra marked as inside from the ones marked as outside (so it is also given implicitly). This representation allows robust topological adaptivity and, thanks to the explicit representation of the interface, it suffers only slightly from numerical diffusion. Furthermore, the use of an unstructured grid yields robust adaptive resolution. Also, topology control is simple in this setting. We present the strengths of the method in several examples: simple geometric flows, fluid simulation, point cloud reconstruction, and cut locus construction.",
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    year = "2012",
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    language = "English",
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    Topology Adaptive Interface Tracking Using the Deformable Simplicial Complex. / Misztal, Marek Krzysztof; Bærentzen, Jakob Andreas.

    In: A C M Transactions on Graphics, Vol. 31, No. 3, 2012, p. No. 24.

    Research output: Contribution to journalJournal articleResearchpeer-review

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    T1 - Topology Adaptive Interface Tracking Using the Deformable Simplicial Complex

    AU - Misztal, Marek Krzysztof

    AU - Bærentzen, Jakob Andreas

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    PY - 2012

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    AB - We present a novel, topology-adaptive method for deformable interface tracking, called the Deformable Simplicial Complex (DSC). In the DSC method, the interface is represented explicitly as a piecewise linear curve (in 2D) or surface (in 3D) which is a part of a discretization (triangulation/tetrahedralization) of the space, such that the interface can be retrieved as a set of faces separating triangles/tetrahedra marked as inside from the ones marked as outside (so it is also given implicitly). This representation allows robust topological adaptivity and, thanks to the explicit representation of the interface, it suffers only slightly from numerical diffusion. Furthermore, the use of an unstructured grid yields robust adaptive resolution. Also, topology control is simple in this setting. We present the strengths of the method in several examples: simple geometric flows, fluid simulation, point cloud reconstruction, and cut locus construction.

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