This paper proposes a new technique for modeling and matching three-dimensional rigid objects by encoding the fluctuation of the surface and the variation of its normal around an oriented point on the surface as the surface expands. The surface of the object is encoded into two two-dimensional curves as the surface signature on each point, and then the collection of the signatures are used to model and match the object. The signatures implicitly encode the curvature and symmetry of the surface around an oriented point. This modeling technique is robust to scale, orientation, noise, patch resolution, occlusion, and cluttering.