In this paper, a 3D surface representation defined around several reference points taken on the surface is introduced. Such representation is obtained from the superposition of a set of indexed levels of geodesic curves and radial lines. A sampling criterion through a generalized version of the Shannon theorem allows the determination of the minimum resolution of both curves that describes faithfully the surface. The choice of several reference points is done to overcome the instability due to landmarks detection errors. Thus, the robustness of the obtained representation under small reference points positions distortion is showed. Then, its accuracy according to pose variation in facial description field is studied. Experimentations are performed on the 3D facial database Bosphorus. Results show also the discrimination power of such representation.