摘要
利用几何与代数相结合的方法,研究一类具有几何约束的三次代数曲线插值和逼近的问题。研究这类三次代数曲线的光滑拼接和保凸性,得到这类三次代数曲线之间的G1、G2光滑拼接定理、保凸性定理及全凸性定理。给出这类代数曲线的插值逼近算法,以及该算法实施的具体步骤和收敛性的证明。通过实例证实了该算法的可行性和有效性,总结了该算法的优点,实例计算结果表明,该算法具有较好的插值和逼近效果。
By using the methods ofgeometry and algebra, the problems ofinterpolation and approximation for a class ofcubic algebraic curves with geometric constraints are investigated. Firstly, the problems of smooth connection and convex-preserving for the class of cubic algebraic curves are investigated. Thus the G1 and G2 smooth connection theorems, convex-preserving theorem and global con- vexity theorem are obtained. Secondly, the algorithm of interpolation and approximation for the class of cubic algebraic curves, detailed operation steps and the proof of convergence are given. Finally, the effectiveness and feasibility of the algorithm are verified with examples, and the advantages of the algorithm are summarized. Numerical examples show the effect of the algorithm is satisfactory.
出处
《计算机工程与设计》
CSCD
北大核心
2011年第5期1691-1697,共7页
Computer Engineering and Design
基金
江西省教育厅科技计划基金项目(GJJ10524)
江西省教改课题基金项目(Jxjg-07-7-9)
关键词
三次代数曲线
光滑拼接
保凸性
全凸性
插值逼近算法
cubic algebraic curves
smooth connection
convex-preserving
global convexity
algorithm of interpolation and approximation
