A new three-point approximating C2 subdivision scheme

AbstractA new three-point approximating subdivision scheme is presented which generates C2 curves. Its limit function has a support on [−3,2]. The smoothness of the new scheme is shown using the Laurent polynomial method, and a comparison with the Hassan et al. [M.F. Hassan, N.A. Dodgson, Ternary and three-point univariate subdivision schemes, in: A. Cohen, J.-L. Merrien, L.L. Schumaker (Eds.), Curve and Surface Fitting: Sant-Malo 2002, Nashboro Press, Brentwood, 2003, pp. 199–208] scheme is depicted through two examples. It can be observed that the method developed generates a curve more consistent with the control polygon