The NURBS book
Length Estimation for Curves with Different Samplings
Digital and Image Geometry, Advanced Lectures [based on a winter school held at Dagstuhl Castle, Germany in December 2000]
C 1 Interpolation with Cumulative Chord Cubics
Fundamenta Informaticae
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In this paper we verify sharpness of the theoretical results concerning the asymptotic orders of trajectory approximation of the unknown parametric curve γ in arbitrary Euclidean space. The pertinent interpolation schemes (based on piecewise-quadratics and piecewise-cubics) are here considered for the so-called reduced data. The latter forms an ordered collection of points without provision of the associated interpolation knots. To complement such data i.e. to determine the missing knots, cumulative chord parameterization is invoked. Sharpness of cubic and quartic orders of convergence are demonstrated for piecewise-quadratics and piecewise-cubics, respectively. This topic has its ramification in computer vision (e.g. image segmentation), computer graphics (e.g. trajectory modeling) or in engineering (e.g. robotics).