一类多参数分形插值曲面迭代函数系

A class of iterated function systems of fractal interpolation surfaces with multiparameters

在三维空间中,构造了一类多参数的迭代函数系,与传统的仅含有一组自由参数的迭代函数系相比,所构造的迭代函数系具有更大的灵活性.在一定的条件下,证明了这类迭代函数系的吸引子是经过给定插值点集的分形插值曲面.讨论了多参数的分形插值曲面关于参数的连续依赖性,给出一个具体例子,通过数值模拟,直观地显示了分形插值曲面在不同参数下的形态.论文的研究为利用多参数分形插值曲面拟合粗糙曲面和非平稳数据提供有价值的理论基础.

In the three-dimensional space, we constructed a class of iterated function systems （IFSs） with muitiparameters. Compared to the traditional IFSs, which have only one family of free parameters, the constructed 1FSs have more flexibility. Under certain conditions, we proved that the attractors of those IFSs were the fractal interpolation surfaces （FISs） passing through the given interpolation data. We investigated the continuous dependency of the FISs with respected to muhiparameters, and gave a specific example for FISs, which intuitively showed the configurations under different parameters. The results of the work provided a theoretical basis for the fitting of rough surfaces and non stable data by using FISs with multiparameters.