Chaikin's perturbation subdivision scheme in non-stationary forms

In this paper two non-stationary forms of Chaikin's perturbation subdivision scheme, mentioned in Dyn et al. (2004), have been proposed with tension parameter ω. Comparison among the proposed subdivision schemes and the existing non-stationary subdivision scheme depicts that the trigonometric form is more efficient in the reproduction of circles and ellipses and the hyperbolic form is more suitable for the construction of many analytical curves.