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 -continuous. Furthermore, the monotonicity preservation and convexity preservation are proved.

中文翻译：

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非平稳三元四点保形细分方案

本文使用连续分数技术构造了一个非平稳的四点三元插值细分方案，与固定的四点三元插值细分方案相比，该方案为用户提供了有效处理尖点的张力参数。然后，将连续的非平稳4点三元方案进行了分析，并且极限曲线是至少-连续的。此外，证明了单调性保持和凸性保持。