中文摘要：

该文给出了矩形域上分形插值数学模型, 分形插值曲面的计算公式, 证明了分形插值曲面迭代函数系唯一性定理, 导出了分形插值曲面的维数定理,并应用实际数据进行了分形插值曲面的实例研究. 为工程中长期寻求的粗糙表面模拟提供了理论基础和实用方法.

英文摘要：

In this paper, the principle of fractal interpolation on rectangular area is introduced, interpolation functions for the fractal interpolation surface are discussed, the theorem of uniqueness of iterated function system of fractal interpolation surface is proved, the theorem of fractal dimension of fractal interpolation surface is derived, and the case that practical data are used to interpolate fractal surface is studied.