From approximating subdivision schemes for exponential splines to high-performance interpolating algorithms

• Published in: Journal of computational and applied mathematics Vol. 224; no. 1; pp. 383 - 396
• Main Author: Romani, L.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier B.V 01-02-2009; Elsevier
• Subjects: Analytical shapes reproduction; Approximations and expansions; Binary subdivision; Combinatorics; Combinatorics. Ordered structures; Designs and configurations; Exact sciences and technology; Interpolation; Laurent polynomial formalism; Mathematical analysis; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Numerical approximation; Sciences and techniques of general use; Tension control; Laurent polynomial formalism; Interpolation; Binary subdivision; Analytical shapes reproduction; 65D05; 65D17; Tension control; 65D07; Polynomial; Algorithm; Implementation; Spline approximation; Numerical approximation; Numerical analysis; Algorithm performance; Applied mathematics
• ISSN: 0377-0427; 1879-1778
• DOI: 10.1016/j.cam.2008.05.013

In this work we construct three novel families of approximating subdivision schemes that generate piecewise exponential polynomials and we show how to convert these into interpolating schemes of great interest in curve design for their ability to reproduce important analytical shapes and to provide highly smooth limit curves with a controllable tension.
In particular, throughout this paper we will focus on the derivation of 6-point interpolating schemes that turn out to be unique in combining vital ingredients like
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-continuity, simplicity of definition, ease of implementation, user independency, tension control and ability to reproduce salient trigonometric and transcendental curves.