一类融合逼近和插值的曲线细分

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摘要采用生成多项式为主的方法对一类融合逼近和插值三重细分格式的支撑区间、多项式生成、连续性、多项式再生及分形性质进行了分析，给出并证明了极限曲线C^k连续的充分条件.通过对融合型细分规则中参数变量的适当选择来实现对极限曲线的形状调整，从而衍生出具有良好性质的新格式，并将这类新格式与现有格式进行比较.数值实例表明这类新格式生成的极限曲线具有较好的保形性.

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关键词：多项式生成性连续性多项式再生性分形

Abstract： Some properties of a combined approximating and interpolating ternary subdivision scheme, such as support, continuity and fractal property, are analyzed by means of the Laurent polynomials. The sufficient conditions of C^k continuity properties are proved. It is pointed out that the parameter can be adjusted to control the shape of the limit curve, which generates brand-new ternary schemes, and some comparisons with other methods are given. Examples show that this new family of schemes have shape preservation property.

Key words： Polynomial generation Continuity Polynomial reproduction Fractals

收稿日期: 2017-12-29; 出版日期: 2019-11-16

基金资助:

国家自然科学基金（61472466，6110012）.

引用本文:

. 一类融合逼近和插值的曲线细分[J]. 计算数学, 2019, 41(4): 367-380.

. A CLASS OF COMBINED APPROXIMATING AND INTERPOLATING SUBDIVISION FOR CURVES[J]. Mathematica Numerica Sinica, 2019, 41(4): 367-380.

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