Complete spline interpolation and exponential parameterization for length estimation of curves

R. Kozera, L. Noakes, M. Wilkołazka

    Research output: Chapter in Book/Conference paperConference paper

    2 Citations (Scopus)

    Abstract

    We describe the problem of estimating a length of a regular parameterized curve from an ordered sample of interpolation points in arbitrary Euclidean space by modified complete spline. The corresponding tabular parameters are assumed to be unknown and are approximated by the exponential parameterization (controlled by the parameter λ ∈ [0, 1]). In this paper the numerical verification of asymptotic orders α(λ) in length estimation is performed for curves sampled more-or-less uniformly. The numerical experiments confirm a slow linear convergence orders α(λ) = 1 for all λ ∈ [0, 1) and a quartic order α(1) = 4 once modified complete spline is used.

    Original languageEnglish
    Title of host publicationInternational Conference of Numerical Analysis and Applied Mathematics, ICNAAM 2016
    Place of PublicationUSA
    PublisherAmerican Institute of Physics
    Volume1863
    ISBN (Electronic)9780735415386
    DOIs
    Publication statusPublished - 21 Jul 2017
    EventInternational Conference of Numerical Analysis and Applied Mathematics 2016, ICNAAM 2016 - Rhodes, Greece
    Duration: 19 Sep 201625 Sep 2016

    Conference

    ConferenceInternational Conference of Numerical Analysis and Applied Mathematics 2016, ICNAAM 2016
    CountryGreece
    CityRhodes
    Period19/09/1625/09/16

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  • Cite this

    Kozera, R., Noakes, L., & Wilkołazka, M. (2017). Complete spline interpolation and exponential parameterization for length estimation of curves. In International Conference of Numerical Analysis and Applied Mathematics, ICNAAM 2016 (Vol. 1863). [400008] American Institute of Physics. https://doi.org/10.1063/1.4992577