Digitizing of free form surfaces is one of key technologies on the reconstruction of free form surfaces. It is important to know how to sample properly free form surfaces on CMM, which concerns the reconstruction accuracy of free form surfaces and measuring efficiency. The mathematical model of sampling algorithm is proposed based on the concept of the center of gravity. Using the method, the topological information of surfaces can be preserved, and sampling mesh can be self organized. By analyzing and dealing with mesh data received from sampling algorithm, one approach with brevity and higher efficiency is provided on CMM.