Abstract: With the progress of measuring equipment, cloud data that contain more details of the object can be obtained conveniently. On the other hand, large quantity of sampled points bring difficulties to model reconstruction. To simplify the cloud data, we put forward three kinds of criteria, namely, the point number after simplification, the density of data set and the error in normal direction caused by deleting a point. According to these criteria, we present corresponding algorithms to automatically reduce the number of cloud points. The key steps in the algorithms are establishing Riemann graph to represent the neighborhood relationship among sample points, traversing the Riemann graph in optimized way and calculating the least square fitting planes at the sample points. In order to improve the efficiency of algorithms, a spatial partitioning scheme is put forward. Practical examples in the paper show that the proposed algorithms are satisfying.