Natural spline interpolation and exponential parameterization for length estimation of curves

R. Kozera; M. Wilkołazka

doi:10.1063/1.4992579

Natural spline interpolation and exponential parameterization for length estimation of curves

R. Kozera, M. Wilkołazka

School of Physics, Mathematics and Computing

Research output: Chapter in Book/Conference paper › Conference paper › peer-review

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 language	English
Title of host publication	International Conference of Numerical Analysis and Applied Mathematics, ICNAAM 2016
Place of Publication	United States
Publisher	American Institute of Physics
Pages	400010-1-400010-4
Number of pages	4
Volume	1863
ISBN (Electronic)	9780735415386
DOIs	https://doi.org/10.1063/1.4992579
Publication status	Published - 21 Jul 2017
Event	International Conference of Numerical Analysis and Applied Mathematics 2016, ICNAAM 2016 - Rhodes, Greece Duration: 19 Sept 2016 → 25 Sept 2016

Conference

Conference	International Conference of Numerical Analysis and Applied Mathematics 2016, ICNAAM 2016
Country/Territory	Greece
City	Rhodes
Period	19/09/16 → 25/09/16

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10.1063/1.4992579

Cite this

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title = "Natural spline interpolation and exponential parameterization for length estimation of curves",

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.",

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Kozera, R & Wilkołazka, M 2017, Natural spline interpolation and exponential parameterization for length estimation of curves. in International Conference of Numerical Analysis and Applied Mathematics, ICNAAM 2016. vol. 1863, 400010, American Institute of Physics, United States, pp. 400010-1-400010-4, International Conference of Numerical Analysis and Applied Mathematics 2016, ICNAAM 2016, Rhodes, Greece, 19/09/16. https://doi.org/10.1063/1.4992579

Natural spline interpolation and exponential parameterization for length estimation of curves. / Kozera, R.; Wilkołazka, M.
International Conference of Numerical Analysis and Applied Mathematics, ICNAAM 2016. Vol. 1863 United States: American Institute of Physics, 2017. p. 400010-1-400010-4 400010.

Research output: Chapter in Book/Conference paper › Conference paper › peer-review

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AU - Wilkołazka, M.

PY - 2017/7/21

Y1 - 2017/7/21

N2 - 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.

AB - 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.

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T2 - International Conference of Numerical Analysis and Applied Mathematics 2016, ICNAAM 2016

Y2 - 19 September 2016 through 25 September 2016

ER -

Natural spline interpolation and exponential parameterization for length estimation of curves

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