| 一类融合逼近和插值的曲线细分 |
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| 引用本文： | 马欢欢,张莉,唐烁,檀结庆.一类融合逼近和插值的曲线细分[J].计算数学,2019,41(4):367-380. |
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| 作者姓名： | 马欢欢 张莉 唐烁 檀结庆 |
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| 作者单位： | 合肥工业大学数学学院,合肥,230009;合肥工业大学数学学院,合肥,230009;合肥工业大学数学学院,合肥,230009;合肥工业大学数学学院,合肥,230009 |
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| 基金项目： | 国家自然科学基金（61472466，6110012）. |
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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Ck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 |
| 收稿时间： | 2017-12-29 |
A CLASS OF COMBINED APPROXIMATING AND INTERPOLATING SUBDIVISION FOR CURVES |
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| Ma Huanhuan,Zhang Li,Tang Shuo,Tan Jieqing.A CLASS OF COMBINED APPROXIMATING AND INTERPOLATING SUBDIVISION FOR CURVES[J].Mathematica Numerica Sinica,2019,41(4):367-380. |
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| Authors: | Ma Huanhuan Zhang Li Tang Shuo Tan Jieqing |
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| Institution: | School of Mathematics, Hefei University of Technology, Hefei 230009, China |
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| 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 Ck 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. |
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| Keywords: | Polynomial generation Continuity Polynomial reproduction Fractals |
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