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

Authors:
L. Romani
Affiliations:
Department of Mathematics and Applications, University of Milano-Bicocca, Via R. Cozzi 53, 20125 Milano, Italy
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

Citing 12
Cited 13

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Abstract

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 C^2-continuity, simplicity of definition, ease of implementation, user independency, tension control and ability to reproduce salient trigonometric and transcendental curves.