Using parameters to increase smoothness of curves and surfaces generated by subdivision (Q923590)

Some subdivision schemes for curves and surfaces are viewed as perturbations of classical schemes for B-splines, and their convergence analysis is presented. The authors develop an idea considered earlier for a particular case by the first and second author and \textit{J. Gregory} [ibid. 4, 257-268 (1987; Zbl 0638.65009)] about the smoothness of curves generated by a certain one parameter family of interpolatory subdivision schemes. It is shown that, under certain mild conditions, a proper perturbation of a convergent subdivision scheme can increase the smoothness of the limit function and thus provide a one-parameter class of schemes with better continuity properties.