关于三次代数曲面光滑拼接问题研究  

Research on Smooth Joining of Cubic Algebraic Surfaces

作　　者：许燕达 贾为兴 崔利宏[1] 

机构地区：[1]辽宁师范大学数学学院,辽宁 大连

出　　处：《应用数学进展》2020年第10期1811-1814,共4页Advances in Applied Mathematics

摘　　要：代数曲面拼接一直是计算机辅助几何设计(CAGD)中的热点话题。本文以现有的代数曲面拼接和Lagrange插值问题的研究成果为理论基础,对三次代数曲面的光滑拼接问题进行了研究。用Lagrange法定义在球面上的二次拼接点组的多项式的分解方法,得出了一组满足沿球面二次代数曲面的三次拼接多项式,并给出了具体的实验算例。Algebraic surface stitching has always been a hot topic in computer aided geometric design (CAGD). Based on the existing research results of algebraic surface stitching and Lagrange interpolation, this paper studies the smooth splicing of cubic algebraic surfaces. In this paper, the decomposition method of the polynomial of the set of quadratic joining points on the sphere is defined by Lagrange method, and a set of cubic splicing polynomials satisfying the quadratic algebraic surface along the spherical surface are obtained, and a concrete experimental example is given.

关 键 词：曲面拼接 LAGRANGE插值 三次代数曲面 拼接点组 

分 类 号：G63[文化科学—教育学]