基于多项式的递归分形插值曲面的构造  

Construction of recurrent fractal interpolation surfaces with polynomial

作　　者：康云[1] 冯志刚[1] 郭艳芳 

机构地区：[1]江苏大学理学院,江苏镇江212013 [2]山西应用科技学院,山西太原030062

出　　处：《陕西师范大学学报（自然科学版）》2016年第1期14-18,共5页Journal of Shaanxi Normal University：Natural Science Edition

基　　金：国家自然科学基金(51079064)

摘　　要：为了利用多项式构造递归分形插值曲面,根据分形插值方法给定的插值节点,可以构造适当的迭代函数系(IFS),使得迭代函数系的不变集是一个连续插值函数的图像。根据这个多项式,构造含有常数尺度因子的迭代函数系,证明该迭代函数系的不变集就是过插值节点的分形插值曲面。通过改变分形纵向尺度因子的大小可以调节分形插值曲面的粗糙程度。A construction of recurrent fractal interpolation surfaces with polynomial is considered. According to the fractal interpolation method, for the given interpolation points, by constructing a proper iterated function system （IFS）, a continuous interpolation function, whose graph is an invariant set of the IFS can be obtained. In accordance with the polynomial, iterated function sys- tem with constant scaling factors is posed. Then it can be proved that the invariant set of the （IFS） is the interpolation surfaces which passes through interpolation points. By changing the fractal vertical scaling factors, the size roughness of fractal interpolation surface can be regulated.

关 键 词：递归迭代函数系 分形插值曲面 二元连续多项式 不变集 

分 类 号：O174[理学—数学]