一类多参数递归分形插值曲面  

A Class of Recurrent Fractal Interpolation Surfaces with Multi-Parameters

作　　者：牛亚群[1] 魏毅强[1] 

机构地区：[1]太原理工大学数学学院,山西太原030024

出　　处：《中北大学学报（自然科学版）》2012年第1期52-55,共4页Journal of North University of China(Natural Science Edition)

摘　　要：给出了三维空间上的递归迭代函数系,进而由该递归迭代函数系构造了一类多参数递归分形插值曲面.与由传统的迭代函数系所构造的自仿射分形插值曲面相比,这种曲面在模拟自然界不规则物体形状和压缩成像方面具有更灵活的应用.在一定的条件下,证明了这类递归迭代函数系的吸引子是经过给定插值点集的连续的分形插值曲面.Recurrent iterated function systems in the three-dimensional space were introduced,from which,a class of recurrent fractal interpolation surfaces with multi-parameters were constructed.These surfaces,compared with self-affine fractal interpolation surfaces being constructed by the traditional iteration function system,can be more flexibly applied in simulating irregular object shape and image compression.It is proved that,under certain conditions,the class of recurrent iteration function system attractors are continuous curved surfaces passing through the given interpolation points.

关 键 词：递归迭代函数系 吸引子 递归分形插值函数 多参数 

分 类 号：O174[理学—数学]