Natural spline interpolation and exponential parameterization for length estimation of curves

R. Kozera, M. Wilkołazka

Research output: Chapter in Book/Conference paperConference paper

3 Citations (Scopus)

Abstract

This paper tackles the problem of estimating a length of a regular parameterized curve γ from an ordered sample of interpolation points in arbitrary Euclidean space by a natural spline. The corresponding tabular parameters are not given and are approximated by the so-called exponential parameterization (depending on λ ∈ [0, 1]). The respective convergence orders α(λ) for estimating length of γ are established for curves sampled more-or-less uniformly. The numerical experiments confirm a slow convergence orders α(λ) = 2 for all λ ∈ [0, 1) and a cubic order α(1) = 3 once natural spline is used.

Original languageEnglish
Title of host publicationInternational Conference of Numerical Analysis and Applied Mathematics, ICNAAM 2016
Place of PublicationUnited States
PublisherAmerican Institute of Physics
Pages400010-1-400010-4
Number of pages4
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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