A C6C6 approximating subdivision scheme

The approximating subdivision scheme, recently developed by Shahid S. Siddiqi and Nadeem Ahmad [An approximating C4C4 stationary subdivision scheme, European Journal of Scientific Research 15 (1) (2006) 97–102], is extended. It is proved that the new scheme generates C6C6 curves. Its limit function has a support on [−6,5][−6,5]. The smoothness of the new scheme is shown using the Laurent polynomial method, and the usefulness of the scheme is illustrated in the examples. The Hölder exponent for the scheme is calculated. It can be observed that the method developed generates curves satisfying the variation diminishing property.