C1 interpolation with cumulative chord cubics

    Research output: Contribution to journalArticle

    24 Citations (Scopus)

    Abstract

    Cumulative chord C¹ piecewise-cubics, for unparameterized data from regular curves in Rn, are constructed as follows. In the first step derivatives at given ordered interpolation points are estimated from ordinary (non-C¹) cumulative chord piecewise-cubics. Then Hermite interpolation is used to generate a C¹ piecewise-cubic interpolant. Theoretical estimates of orders of approximation are established, and their sharpness verified through numerical experiments. Good performance of the interpolant is also confirmed experimentally on sparse data.
    Original languageEnglish
    Pages (from-to)285-301
    JournalFundamenta Informaticae
    Volume61
    Issue number3/4
    Publication statusPublished - 2004

    Fingerprint

    Interpolants
    Chord or secant line
    Interpolation
    Interpolate
    Sparse Data
    Hermite Interpolation
    Order of Approximation
    Sharpness
    Numerical Experiment
    Derivatives
    Derivative
    Curve
    Estimate
    Experiments

    Cite this

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    title = "C1 interpolation with cumulative chord cubics",
    abstract = "Cumulative chord C¹ piecewise-cubics, for unparameterized data from regular curves in Rn, are constructed as follows. In the first step derivatives at given ordered interpolation points are estimated from ordinary (non-C¹) cumulative chord piecewise-cubics. Then Hermite interpolation is used to generate a C¹ piecewise-cubic interpolant. Theoretical estimates of orders of approximation are established, and their sharpness verified through numerical experiments. Good performance of the interpolant is also confirmed experimentally on sparse data.",
    author = "Ryszard Kozera and Lyle Noakes",
    year = "2004",
    language = "English",
    volume = "61",
    pages = "285--301",
    journal = "Fundamenta Informaticae",
    issn = "0169-2968",
    publisher = "IOS Press",
    number = "3/4",

    }

    C1 interpolation with cumulative chord cubics. / Kozera, Ryszard; Noakes, Lyle.

    In: Fundamenta Informaticae, Vol. 61, No. 3/4, 2004, p. 285-301.

    Research output: Contribution to journalArticle

    TY - JOUR

    T1 - C1 interpolation with cumulative chord cubics

    AU - Kozera, Ryszard

    AU - Noakes, Lyle

    PY - 2004

    Y1 - 2004

    N2 - Cumulative chord C¹ piecewise-cubics, for unparameterized data from regular curves in Rn, are constructed as follows. In the first step derivatives at given ordered interpolation points are estimated from ordinary (non-C¹) cumulative chord piecewise-cubics. Then Hermite interpolation is used to generate a C¹ piecewise-cubic interpolant. Theoretical estimates of orders of approximation are established, and their sharpness verified through numerical experiments. Good performance of the interpolant is also confirmed experimentally on sparse data.

    AB - Cumulative chord C¹ piecewise-cubics, for unparameterized data from regular curves in Rn, are constructed as follows. In the first step derivatives at given ordered interpolation points are estimated from ordinary (non-C¹) cumulative chord piecewise-cubics. Then Hermite interpolation is used to generate a C¹ piecewise-cubic interpolant. Theoretical estimates of orders of approximation are established, and their sharpness verified through numerical experiments. Good performance of the interpolant is also confirmed experimentally on sparse data.

    M3 - Article

    VL - 61

    SP - 285

    EP - 301

    JO - Fundamenta Informaticae

    JF - Fundamenta Informaticae

    SN - 0169-2968

    IS - 3/4

    ER -