A Variant Cubic Exponential B-Spline Scheme with Shape Control

Baoxing Zhang and Hongchan Zheng
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Baoxing Zhang: School of Mathematics and Statistics, Hebei University of Economics and Business, Shijiazhuang 050061, China
Hongchan Zheng: School of Mathematics and Statistics, Nothwestern Polytechnical University, Xi’an 710072, China

Mathematics, 2021, vol. 9, issue 23, 1-11

Abstract: This paper presents a variant scheme of the cubic exponential B-spline scheme, which, with two parameters, can generate curves with different shapes. This variant scheme is obtained based on the iteration from the generation of exponentials and a suitably chosen function. For such a scheme, we show its C 2 -convergence and analyze the effect of the parameters on the shape of the generated curves and also discuss its convexity preservation. In addition, a non-uniform version of this variant scheme is derived in order to locally control the shape of the generated curves. Numerical examples are given to illustrate the performance of the new schemes in this paper.

Keywords: non-stationary subdivision; iteration; shape control; convex preservation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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