Differentiability of a 4-point ternary subdivision scheme and its application

Hassan et al. proposed a 4-point ternary interpolatory scheme with smaller sizes of the templates for the local averaging rules and With higher order smoothness property compared to most of the existing binary ones. It can be C-2-continuous when the subdivision parameter is chosen in a certain range. In this paper, we further investigate its differentiable properties to extend its application in the generating of smooth curves and surfaces with different continuity. Some important results about-this scheme such as the conditions of C-0, C-1-continuous, Holder exponent and the derivatives of the limit function are obtained and applied. A modified 4-point ternary interpolatory scheme for end points is also proposed to ameliorate the modelling ability of this scheme.