岩石断面分形插值生成过程中的稳定性

Stability in Generating Rock Fracture Surface by Fractal Interpolation

在岩石断面数据点的实际测量过程中，必然会产生一些误差，而这些误差又必然会引起分形插值曲线（曲面）的偏离。基于对岩石断面生成过程中通常所用线性分形插值稳定性的研究，表明无论数据点（插值结点）存在横向、纵向还是综合的微小摄动，得到的分形插值曲线也均只有相应的微小摄动。

In measurement of data on rock fracture surface, some errors will certainly occur. These errors will make the fractal interpolation curves (surfaces) have some deviations. Based on study of linear fractal interpolation that is offen used in generating rock fracture surface, it is proved that, when the interpolation data have a small perturbation, the corresponding linear fractal interpolation curves (surfaces) also have a small perturbation.