In this paper, we propose a precise frequency-based representation for oriented point-based surfaces using spherical harmonics. The representation can be useful in many applications, such as filtering, progressive transmission and coding of 3D surfaces. The basic computation in our approach is the spherical harmonics transform of local spherical radial functions induced by a set of points. An important feature of our approach is that the calculations are performed directly on local 2D triangulations of the point-based surface without any prior space voxelization. This property ensures that the complexity of our computation of the spherical harmonics transform is linear in the number of triangles in the local patch. We present some experimental results which demonstrate our technique.