Length Estimation for Exponential Parameterization and ε-Uniform Samplings

Abstract

Abstract. This paper discusses the problem of estimating the length of the unknown curve γ in Euclidean space, from ε-uniformly (for ε ≥ 0) sampled reduced data Qm = {qi} A recent result [5] proves that for all λ ∈ [0, 1) and ε-uniform samplings, the respective orders amount to βε(λ) = min{4, 4ε}. As such βε(λ) are independent of λ ∈ [0, 1). In addition, the latter renders a discontinuity in asymptotic orders βε(λ) at λ = 1. In this paper we verify experimentally the above mentioned theoretical results established in [5].

Lagrange Piecewise-Quadratic Interpolation Based on Planar Unordered Reduced Data

“…More discussion on applications (including real data examples -see [2] or [14]) and theory of non-reduced data interpolation can be found in [3], [5], [15], [16], [17], [18], [19], [20] or [21]. In particular different parameterizations {t} m i=0 of the unknown interpolation knots {t} m i=0 are discussed e.g.…”