随机工程曲线的分形插值方法研究

以随机工程曲线的处理为目的，以地形曲线等为例，详细介绍了一种数值插值方法———分形插值法分形插值根据迭代函数系和自仿射理论建立而成，此方法利用（曲线上）有限的插值点，通过选取适当的压缩算子（文中称为垂直尺度因子），可以很精确地构造出原随机曲线，反过来说，也可以把曲线数据压缩到有限的几个点上，是一种有效的数据压缩方法通过计算机编程，具体说明了分形插值的实现过程，其中包括根据分形曲线的自仿射特性而推导出来的计算垂直尺度因子的几何法由于现实中的工程曲线只具有部分自仿射结构或不具有明显的自仿射结构，笔者又在整体线性分形插值的基础上推导出分段线性分形插值，并对两者进行了比较，取得良好的效果最后讨论了分形插值在实际应用中存在的问题及其发展前景

Study on Linear Fractal Interpolation for Random Engineering Curves

In this paper, a method of numeric interpolation for random engineering curves is explored in detail. It is called Linear Fractal Interpolation which regards random curves without formula as its objects. Linear Fractal Interpolation is based on iterated function system (IFS) and self-affine theory. With proper contraction operators it can construct the curve just using some characteristic interpolation points on the curve. In other words, it can largely compress the data of a curve to several points. It is an effective method of compressing data. Through computer programming, the process of fractal interpolation is discussed concretely, including the geometric method of contraction factors calculation which is reasoned out from the self-affine characteristic of fractal models. In fact, engineering curves are only partially self-affine or even not self-affine, so the Piecewise Linear Fractal Interpolation method is derived from Linear Fractal Interpolation. The two methods are compared and good results have been obtained. At last the existing problems in using the method and its prospects are discussed.