A class of non-stationary ternary 4-point subdivision schemes based on iterations

Abstract

This paper presents a novel class of nonstationary ternary 4-point subdivision schemes, capable of generating C³ continuous limit curves. These schemes are built upon the generalized ternary scheme of order 5 presented in [19] and iterated functions. A distinctive feature is that the shape of the resulting limit curve varies with alterations in the initial parameters. To facilitate localized shaping adjustments, we devise a non-uniform subdivision scheme that extends our non-stationary schemes. This method allows for Tension parameters are to be assigned to each edge of the initial control polygon, offering enhanced flexibility and precision in curve shaping.