A family of non-stationary subdivision schemes reproducing exponential polynomials

Abstract

Exponential B-splines are the most well-known non-stationary subdivision schemes. A crucial limitation of these schemes is that they can reproduce at most two exponential polynomials (Jena etal., 2003) [26]. Although interpolatory schemes can improve the reproducing property of exponential polynomials, they are usually less smooth than the (exponential) B-splines of corresponding orders. In this regard, this paper proposes a new family of non-stationary subdivision schemes which extends the exponential B-splines to allow reproduction of more exponential polynomials. These schemes can represent exactly circular shapes, spirals or parts of conics which are important analytical shapes in geometric modeling. This paper also discusses the Hölder regularities of the proposed schemes. Lastly, some numerical examples are presented to illustrate the performance of the new schemes. © 2013 Elsevier Ltd.