Shape preserving C2 interpolatory subdivision schemes

    Research output: Book/ReportReportProfessional

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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.
    Kuijt, F. ; van Damme, Rudolf M.J. / Shape preserving C2 interpolatory subdivision schemes. Enschede : Universiteit Twente, 1998. 18 p. (Memorandum Faculteit TW; 1452).
    @book{f830b5ee946446faa934ebb63356f920,
    title = "Shape preserving C2 interpolatory subdivision schemes",
    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.",
    keywords = "METIS-141121, IR-65649, Convexity, Shape preservation, Rational stationary subdivision, positivity, MSC-65D15, EWI-3272, monotonicity, smoothness, MSC-65D07, MSC-41A15, MSC-41A29",
    author = "F. Kuijt and {van Damme}, {Rudolf M.J.}",
    note = "Imported from MEMORANDA",
    year = "1998",
    language = "Undefined",
    series = "Memorandum Faculteit TW",
    publisher = "Universiteit Twente",
    number = "1452",

    }

    Kuijt, F & van Damme, RMJ 1998, Shape preserving C2 interpolatory subdivision schemes. Memorandum Faculteit TW, no. 1452, Universiteit Twente, Enschede.

    Shape preserving C2 interpolatory subdivision schemes. / Kuijt, F.; van Damme, Rudolf M.J.

    Enschede : Universiteit Twente, 1998. 18 p. (Memorandum Faculteit TW; No. 1452).

    Research output: Book/ReportReportProfessional

    TY - BOOK

    T1 - Shape preserving C2 interpolatory subdivision schemes

    AU - Kuijt, F.

    AU - van Damme, Rudolf M.J.

    N1 - Imported from MEMORANDA

    PY - 1998

    Y1 - 1998

    N2 - 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.

    AB - 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.

    KW - METIS-141121

    KW - IR-65649

    KW - Convexity

    KW - Shape preservation

    KW - Rational stationary subdivision

    KW - positivity

    KW - MSC-65D15

    KW - EWI-3272

    KW - monotonicity

    KW - smoothness

    KW - MSC-65D07

    KW - MSC-41A15

    KW - MSC-41A29

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    T3 - Memorandum Faculteit TW

    BT - Shape preserving C2 interpolatory subdivision schemes

    PB - Universiteit Twente

    CY - Enschede

    ER -

    Kuijt F, van Damme RMJ. Shape preserving C2 interpolatory subdivision schemes. Enschede: Universiteit Twente, 1998. 18 p. (Memorandum Faculteit TW; 1452).