一类有理插值曲面模型及其可视化约束控制  

A rational interpolation surface model and visualization constraint

作　　者：张云峰[1,2] 包芳勋[3] 张彩明[1,2] 段奇[3] 

机构地区：[1]山东财经大学计算机科学与技术学院,济南250014 [2]山东省数字媒体重点实验室,济南250014 [3]山东大学数学与系统科学学院,济南250100

出　　处：《中国科学：数学》2014年第7期729-740,共12页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:61373080;61202150和61020106001)资助项目

摘　　要：本文构造一类新的基于函数值和偏导数值的双变量加权混合有理插值样条.与已有的有理插值样条相比,这类新的有理插值样条具有以下四方面的特性,其一,插值函数可以由简单的对称基函数来表示;其二,对任何正参数,插值函数满足C1连续,而且,在不限制参数取值的条件之下,插值曲面保持光滑;其三,插值函数不但含有参数,而且带有加权系数,增加了插值函数的自由度;其四,插值曲面的形状随着参数与加权系数的变化而变化.同时,本文讨论此类插值曲面的性质,包括基函数的性质、积分加权系数的性质和插值函数的边界性质.此类插值函数的优势在于,不改变给定插值数据的前提下,通过选择合适的参数和不同的加权系数,对插值区域内的任意点的函数值进行修改.因此可将其应用于曲面设计,根据实际设计需要,自由地修改曲面形状.数值实验表明,此类新的有理样条插值具有良好的约束控制性质.This paper presents a new weighted bivariate blending rational spline interpolation based on function values and partial derivatives. The new spline has some characteristics comparing with the present interpolation. Firstly, the interpolation function can be simply expressed with symmetric basis functions. Secondly, the interpolating function is C1 continuous for any positive parameters. ~rthermore, the interpolation surfaces are smooth under the conditions that parameters is not limited. Thirdly, the interpolation functions has more free- dom with parameters and a weighted coefficient A. Fourthly, the interpolation surfaces could be varied as the parameters and weighted coefficient vary. This paper also deals with the properties of the interpolation surface, including the properties of basis function, the properties of integral weighted coefficients and bounded property of the interpolation. What is more important is that the value of the interpolation function at any point in the interpolating region can be modified under unchanged interpolating data by selecting suitable parameters and different coefficients, so the interpolation surfaces can be modified for the given interpolation data when needed in practical design. Experimental results illustrate the effective constraint of this spline interpolation.

关 键 词：双变量混合插值 加权插值 有理样条 计算机辅助几何设计 

分 类 号：TP391.7[自动化与计算机技术—计算机应用技术]