Hermite-interpolatory subdivision schemes

    Research output: Book/ReportReportProfessional

    80 Downloads (Pure)

    Abstract

    Stationary interpolatory subdivision schemes for Hermite data that consist of function values and first derivatives are examined. A general class of Hermite-interpolatory subdivision schemes is proposed, and some of its basic properties are stated. The goal is to characterise and construct certain classes of nonlinear (and linear) Hermite schemes. For linear Hermite subdivision, smoothness conditions known from the literature are discussed. In order to allow a simpler construction of suitable nonlinear Hermite subdivision schemes, these conditions are posed as assumptions. For linear Hermite subdivision, explicit schemes that satisfy sufficient conditions for $C^2$-convergence are constructed. This leads to larger classes of $C^2$ schemes than known from the literature. Finally, convexity preserving Hermite-interpolatory subdivision is examined, and some explicit rational schemes that generate $C^1$ limit functions are presented.
    Original languageUndefined
    Place of PublicationEnschede
    PublisherUniversiteit Twente
    Number of pages17
    Publication statusPublished - 1998

    Publication series

    NameMemorandum Faculteit TW
    PublisherUniversiteit Twente
    No.1461

    Keywords

    • MSC-41A05
    • MSC-65D05
    • stationary linear subdivision
    • Stationary non-linear subdivision
    • MSC-65D17
    • Hermite interpolation
    • Convexity preservation
    • IR-30467
    • METIS-141107
    • MSC-41A29
    • EWI-3281

    Cite this

    Kuijt, F., & van Damme, R. M. J. (1998). Hermite-interpolatory subdivision schemes. (Memorandum Faculteit TW; No. 1461). Enschede: Universiteit Twente.