| 保形五次几何Hermite插值的构造算法 |
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| 引用本文： | 方逵,吴泉源.保形五次几何Hermite插值的构造算法[J].数值计算与计算机应用,2005,26(3):224-231. |
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| 作者姓名： | 方逵 吴泉源 |
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| 作者单位： | 1. 长沙大学计算机科学与技术系,长沙,410003;株洲工学院计算机科学与技术系,株洲,412008
2. 国防科技大学计算机学院,长沙,410073 |
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| 基金项目： | 本文得到国家自然科学基金(编号20206033)，湖南省自然科学基金(编号03 JJY3106)，长沙市高新技术项目(K03170-62)资助 |
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| 摘 要： | 讨论了计算机辅助几何设计中的GHI问题,GHI曲线需要型值点处的切线和曲率信息,所以GHI曲线比一般的插值曲线更困难.首先将保概念引入到GHI曲线,再用分段五次Bezier曲线构造了GC2保形GHI算法.该曲线的所有Bezier点由型值点及相应的曲率信息直接计算产生,无需求解矢量方程组,因此该曲线计算简单,局部修改方便.最后,两个数值例子被给出。
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| 关 键 词： | 保形插值 五次Bézier曲线 曲率 |
| 修稿时间： | 2003年12月4日 |
AN ALGORITHM FOR CONSTRUCTING SHAPE PRESERVING QUINTIC GEOMETRIC HERMITE INTERPOLATION |
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| FANG Kui,WU Quanyuan.AN ALGORITHM FOR CONSTRUCTING SHAPE PRESERVING QUINTIC GEOMETRIC HERMITE INTERPOLATION[J].Journal on Numerical Methods and Computer Applications,2005,26(3):224-231. |
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| Authors: | FANG Kui WU Quanyuan |
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| Abstract: | This paper discusses GHI(Geometric Hermite Interpolation) problem in Computer Aided Geometric Design. Because it needs tangent information of data points as well as curvature information, the GHI curve is much more difficult than other general parametric curves. This paper introduces the concept of shape preserving into GHI curve, gives an algorithm for constructing shape preserving GC2 continuous parametric GHI curve by a sequence of quintic Bezier segments and makes all Bezier points originate from the calculation of data points. There is no need to solve the vector system of equations, thus the calculation is simple and local modification is convenient. Finally, two numerical examples illustrate the algorithm in this paper is effective for computer aided geometric Design and computer design and computer graphics. |
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| Keywords: | Shape preserving Interpolation Quintic Bezier curve Curvature |
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