We present an efficient approach to generating uniformly distributed resampling points of raw 3D point clouds. A key contribution for making such a resampling method both practical and efficient is the construction of the centroidal Voronoi tessellation on the given point cloud efficiently achieved by applying the proposed Anderson-accelerated Lloyd's method. The calculations involved in the method are mainly carried out over a group of locally approximated quadratic surfaces, instead of directly on the given point cloud, providing us a great advantage in filtering out the affection of distribution of original points on output results. Once the resampling points are initialized, the resampling quality can be improved progressively by optimizing resampling points and updating the local approximated surfaces. In addition, by restricting the movement of resampling points, we can deal with unclosed point clouds without any boundary detection. Our approach outperforms existing resampling methods in generating uniform results, and extensive experiments are conducted to demonstrate its efficacy.