一种（3,2）1阶有理插值样条曲面及其凸性控制  

A Kind of Rational Spline Surface of Order （3, 2）1 with Convexity Control

作　　者：李莉[1] 唐月红[1] 刘琳[1] 

机构地区：[1]南京航空航天大学理学院,南京211106

出　　处：《工程数学学报》2014年第2期191-206,200-201+205-206,共16页Chinese Journal of Engineering Mathematics

基　　金：南京航空航天大学基本科研业务费(NZ2013201)~~

摘　　要：本文构造了一种基于函数值的带形状参数的(3,2)1阶有理插值样条曲面,并研究该曲面中诸如边界插值、极限、解析和正则等性质.引入双八次九阶矩阵表示的凸性判别函数,推导了判定插值曲面凸性的充要条件.根据该条件给出数值实例,展示如何适当选取参数实现曲面的局部保凸控制.特别发现这种插值曲面的凸性在某些点处即使型值是凸的数据也是相对刚性的.In this paper, a rational interpolating spline surface with parameters of order （3, 2）1 is constructed based on function values. Some properties are studied for the rational spline interpolating surface and its basic functions, for example, boundaries, limits, analysis and canonical. A matrix representation with 9-order coe？cient matrix and 8-degree bibariate polynomial vector function is introduced as identification of the functional convexity. The necessary and su？cient condition for the rational interpolation surface to be local convex is derived. According to the condition, examples are prensented to show how to choose the parameters and to change shapes of the surfaces. Particularly, it is found that the convexity of the interpolation surface is relatively rigid at certain points even if the interpolated data is convex.

关 键 词：有理样条 插值曲面 局部修改 保凸控制 

分 类 号：O241.5[理学—计算数学]