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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.

In this paper we present a non-stationary binary three-point approximating subdivision scheme which can generate a wide variety of C3-continuous limit curves with different initial control parameter α0. The continuity of the scheme is proved by using the conclusion in Dyn and Levin, (1995) 5. The advantage of the scheme is illustrated by a number of examples.