Nonstationary interpolatory subdivision schemes reproducing high-order exponential polynomials

Abstract

We present a family of nonstationary interpolatory subdivision schemes which reproduces high-order exponential polynomials. First, by extending the classical $\fbox {D-D}$ interpolatory schemes, we present the explicit expression of the symbols that identify a family of the nonstationary interpolatory subdivision schemes. These schemes can allow reproduction of more exponential polynomials, and represent exactly circular shapes, parts of conics which are important analytical shapes in geometric modeling. Furthermore, a rigorous analysis regarding the smoothness of the new nonstationary interpolatory schemes is provided. Next, based on the recursive formulas of the symbols, a repeated local operation is proposed for rapidly computing new points from the old points. Finally, two examples are presented to illustrate the performance of the new schemes.