Exponential parameterization to fit reduced data

doi:10.1016/j.amc.2020.125645

Exponential parameterization to fit reduced data

2021-02-01

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Magdalena Wilkołazka *

DOI：10.1016/j.amc.2020.125645

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This paper discusses the topic of interpolating data points Q(m) in arbitrary Euclidean space with Lagrange cubics (gamma) over capL and exponential parameterization which is governed by a single parameter lambda is an element of [0, 1] and replaces a discrete set of unknown knots {t(i)}(i=0)(m) (($) over cap (i) is an element of (I) over cap ) with new values {(t) over cap (i)}(i=0)(m) ((t) over cap (i) is an element of(I) over cap). To compare gamma with (gamma) over cap (L) specific mapping : I -> (I) over cap must also be selected. For certain applications and theoretical considerations phi should be an injective mapping (e.g. in length estimation of gamma which fits Q(m)). We justify two sufficient conditions yielding phi as injective and analyze their asymptotic representatives for Qm getting dense. The algebraic constraints established here are also geometrically visualized with the aid of Mathematica 2 D and 3 D plots. Examples illustrating the latter and numerical investigation for the convergence rate in length estimation of gamma are also supplemented. The reparameterization issue has its applications among all in computer graphics and robot navigation for trajectory planning once e.g. a new curve gamma = gamma omicron phi controlled by the appropriate choice of interpolation knots and phi (and/or possibly Q(m)) needs to be constructed. (c) 2020 Elsevier Inc. All rights reserved.

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Interpolation

Reduced data

Parameterization

Exponential parameterization to fit reduced data

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