A Nonstationary Ternary 4-Point Shape-Preserving Subdivision Scheme

Abstract

This paper uses the continued fraction technique to construct a nonstationary 4-point ternary interpolatory subdivision scheme, which provides the user with a tension parameter that effectively handles cusps compared with a stationary 4-point ternary interpolatory subdivision scheme. Then, the continuous nonstationary 4-point ternary scheme is analyzed, and the limit curve is at least C 2 -continuous. Furthermore, the monotonicity preservation and convexity preservation are proved.

A Family of Integer-Point Ternary Parametric Subdivision Schemes

“…In 2021, Tan and Tong [13] presented a nonstationary 4point ternary interpolating subdivision scheme. ey also discussed the shape preserving properties of the proposed subdivision scheme.…”