中文摘要：

根据岩石断裂表面粗糙度所具有的统计自仿射分形的特征，提出了改进的自仿射分形插值的概念。运用改进的自仿射分形插值方法，根据实测岩石断裂表面粗糙度数据，对岩石断裂表面粗糙形态进行了分形模拟，给出了二元分形插值数学模型。将以不同数量的观测数据模拟出的插值曲面与实际测量的岩石断裂表面相比较，得出了不同数量信息点的模拟精度，它们之间的关系曲线显示为幂函数关系的规律。这就意味着不仅可以得到模拟结果，还可以得到模拟结果的估计精度。运用少量已知数据值，模拟出未知曲面，给出了由局部模拟整体的方法这对丁根据少量数据研究、模拟和直观显示复杂物体的几何形态，如地形地貌、断层表面和材料裂隙表面，具有重要的应用意义。

英文摘要：

The mathematical model of binary fractal interpolation is introduced. Based on the statistical self-similarity of rock fracture surface, the concept of improved self-affine fractal interpolation is put forward. By using the method of the improved self-affine fractal interpolation, the rock fracture surface is simulated with the measured data from the rock fracture surface. Compared the surfaces simulated with different number of given data to the practical fracture surface, the simulated precision is obtained. The relationship between the number of given data and the simulated precision obtained and shows the power function law. This means that we not only can obtain the simulated result in the interpolation, but also can get the estimation precision of the simulated result. Using a little amount of given data to simulate unknown surface gives the simulating method from the parts to the whole. This is useful for studying, simulating and displaying the shape of complicated objects intuitively with some little information, such as the topographty, the fault surface and the fracture surface of materials.