| 四点插值细分格式的改进 |
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| 引用本文： | 江雷,郭德贵.四点插值细分格式的改进[J].烟台大学学报(自然科学与工程版),2002,15(3):171-176. |
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| 作者姓名： | 江雷 郭德贵 |
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| 作者单位： | 1. 华南资讯系统集成有限公司,广东,广州,510665
2. 延边大学,数学系,吉林,延吉,133002 |
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| 基金项目： | 国家基础研究专项基金资助项目 (G19990 32 80 5 ) |
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| 摘 要： | 对四点插值分格式提出了一种新的改进方法，并利用栖西定理和构造Bernstein多项式等方法证明了该方法的收敛性，光滑性，同时还得到曲线端点处的导数，给出曲线光滑拼接的充要条件，为曲线间的光滑拼接提供了理论基础，该方法可以很容易地推广到曲面的情形。
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| 关 键 词： | 四点插值细分格式 柯西定理 Bernstein多项式 CAGD 曲线光滑拼接 细分法 极线曲线 |
| 文章编号： | 1004-8820(2002)03-0171-06 |
An Improvement to the Four-point Interpolation Subdivision Scheme |
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| JIANG Lei ,GUO De gui.An Improvement to the Four-point Interpolation Subdivision Scheme[J].Journal of Yantai University(Natural Science and Engineering edirion),2002,15(3):171-176. |
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| Authors: | JIANG Lei GUO De gui |
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| Institution: | JIANG Lei 1,GUO De gui 2 |
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| Abstract: | A new method to improve the original four point interpolation scheme is presented, the convergence and smoothness are also gained, applying the Cauchy theorem and constructing Bernstein polynomials. Meanwhile, the expression of derivative on the endpoint for the limit curve is obtained. And the sufficient and necessary conditions for the smooth split joint between the curves are obtained. The method can be extended to the split joint problem between surfaces easily. |
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| Keywords: | four point interpolation subdivision Cauchy theorem |
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