基于分形插值函数的分形插值曲面的变差与计盒维数  

Variation and Box-counting Dimension of Fractal Interpolation Surface Based on the Fractal Interpolation Function

作　　者：冯志刚[1] 黄艳丽[1] 

机构地区：[1]江苏大学理学院,镇江212013

出　　处：《工程数学学报》2012年第3期393-398,共6页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(51079064)~~

摘　　要：分形插值是拟合数据的一种新方法,它可以反映出曲线和曲面上的粗糙性质.本文介绍了基于仿射分形插值函数的分形插值曲面的构造方法,给出了连续函数中心变差的概念,讨论了中心变差与变差、中心变差与计盒维数之间的关系.研究了这类分形插值曲面所对应的二元连续函数中心变差的性质,并根据二元连续函数中心变差与函数图像计盒维数之间的关系,得到了这类分形插值曲面的计盒维数.Fractal interpolation is a novel method for fitting data, which can reflect the roughness property of curves and surfaces. In this paper, a construction of fractal interpolation surfaces based on affine fractal interpolation functions is introduced. The concept of central variation of the continuous function is proposed. The relationships between variation and central variation, and box-counting dimension of the bivariate continuous function are discussed. Some properties of the central variation of the bivariate continuous function, corresponding to this class of fractal interpolation surfaces, are studied. By using the relation between the box-counting dimension of the graph of the continuous function and its central variation, the box-counting dimension of the fractal interpolation surface is obtained.

关 键 词：仿射分形插值函数 变差 中心变差 分形插值曲面 计盒维数 

分 类 号：O184[理学—数学]