An extended three point approximating subdivision scheme

In this paper we present a 3-point binary stationary approximating subdivision scheme with a parameter for designing curves. We observe that the schemes generating B-spline curves of order 4 and 5 are particular cases of this scheme. By combining this scheme (for a particular parameter) and the Chaikin scheme we obtain a known 3-point scheme. We highlight some advantages of the scheme over the known 3-point schemes and demonstrate its performance by some examples.