Shape preserving C2 interpolatory subdivision schemes

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    Abstract

    Stationary interpolatory subdivision schemes which preserve shape properties such as convexity or monotonicity are constructed. The schemes are rational in the data and generate limit functions that are at least $C^2$. The emphasis is on a class of six-point convexity preserving subdivision schemes that generate $C^2$ limit functions. In addition, a class of six-point monotonicity preserving schemes that also leads to $C^2$ limit functions is introduced. As the algebra is far too complicated for an analytical proof of smoothness, validation has been performed by a simple numerical methodology.
    Original languageUndefined
    Place of PublicationEnschede
    PublisherUniversiteit Twente
    Number of pages18
    Publication statusPublished - 1998

    Publication series

    NameMemorandum Faculteit TW
    PublisherDepartment of Applied Mathematics, University of Twente
    No.1452
    ISSN (Print)0169-2690

    Keywords

    • METIS-141121
    • IR-65649
    • Convexity
    • Shape preservation
    • Rational stationary subdivision
    • positivity
    • MSC-65D15
    • EWI-3272
    • monotonicity
    • smoothness
    • MSC-65D07
    • MSC-41A15
    • MSC-41A29

    Cite this

    Kuijt, F., & van Damme, R. M. J. (1998). Shape preserving C2 interpolatory subdivision schemes. (Memorandum Faculteit TW; No. 1452). Enschede: Universiteit Twente.