Extended Hermite subdivision schemes

Abstract

Subdivision schemes are efficient tools for building curves and surfaces. For vector subdivision schemes, it is not so straightforward to prove more than the Hölder regularity of the limit function. On the other hand, Hermite subdivision schemes produce function vectors that consist of derivatives of a certain function, so that the notion of convergence automatically includes regularity of the limit. In this paper, we establish an equivalence between a spectral condition and operator factorizations, then we study how such schemes with smooth limit functions can be extended into ones with higher regularity. We conclude by pointing out how this new approach applies to cardinal splines.