一类分形曲面的插值稳定性

On stability of a kind of interpolation fractal surface

简要介绍了一类分形插值曲面的原理、数学模型及其插值方法 根据分形插值曲面的生成原理及其具体的迭代函数计算公式,着重讨论了分形曲面的插值稳定性 所导出的结果证实了某种情况下当插值节点有个微小的扰动时,此类曲面上的插值函数值也仅有微小的改变 从而为人工造景。

The principle for construction of a kind of interpolation fractal surface and its iterate function formula are introduced. By applying the method of fractal interpolation, the problem of the stability on the fractal surface is discussed and some results are obtained. The results reveal that if the interpolation knots have small disturbs, so does the corresponding fractal interpolation surface. Thus the reliability of producing or simulating fracture surface by applying the fractal interpolation surface is ensured. The method offers theoretical basis for this kind of problem.