分形曲面在自然界是大量存在的, 如山脉、地形、岩石、云团、材料断口的粗糙表面等, 都是分形曲面的
实例[1～3]
。近年来, 很多文献介绍了分形曲面的研究方法——随机生成法和分形曲面的插值。在实际工作中,
往往已知分形曲面上的部分信息( 例如, 材料断口的某条迹线、断面上的某些特征) , 需要通过这些部分信息
和特征, 拟合出分形曲面的整体形态, 从而对分形体的整体进行研究[4, 5]
。这就需要用到分形插值曲面的理论
和方法(Fractal surfaces are abundant in nature, such as mountain, terrain, rock, cloud cluster, rough surface of material fracture and so on, all of which are fractal surfaces.
Examples from [1 to 3]
. In recent years, the research methods of fractal surface are introduced in many literature, which are random generation and fractal surface interpolation. In practical work,
It is often known that part of the information on a fractal surface (for example, some traces on a material fracture, some features on a section), needs to pass through these parts of information.
And features, fitting out the whole form of fractal surface, so as to study the whole of the fractal form [4, 5]
. It is necessary to use the theory of fractal interpolation surface
And methods)