Summary: We present a method to approximate a simple, regular \(C^{2}\) surface \(W\) in \(\mathbb{R}^3\) by a (tangent continuous) skin surface \(S\). The input of our algorithm is a set of approximate \(W\)-maximal balls, where the boundary of the union of these balls is homeomorphic to \(W\). By generating patches of spheres and hyperboloids over the intersection curves of the balls the algorithm determines a one-parameter family of skin surfaces, where a parameter controls the size of the patches. The skin surface \(S\) is homeomorphic to \(W\), and the approximate \(W\)-maximal balls in the input set are also \(S\)-maximal. The Hausdorff distance between the regions enclosed by the input surface \(W\) and the approximating skin surface \(S\) depends linearly on a parameter related to the sampling density of the approximate \(W\)-maximal balls.