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One often analyzes surfaces through their induced structures such as the convex hull or the homology group. It is important to derive appropriate induced structures. If they are too complicated, it becomes hard to extract the information about the original surface from them. If they are too simple, little or nothing about the surface can be inferred from them. To analyze surfaces computationally, it is important that the induced structures can be computed efficiently. In this work, we address two induced structures for surfaces: curve-skeletons and handle and tunnel loops. We give formal definitions for both structures and propose algorithms to compute them. One can also reverse the direction, namely, given an induced structure, how to recover the original surface. It is hard, sometimes impossible, to recover the surface exactly. We often seek to obtain an approximation with bounded error. The problem of reconstructing surfaces from their sample points is such an example. This problem has been studied for almost three decades though there are still many open gaps. In this work, we focus on how to handle sample points when they are contaminated with noise. We define a smoot