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Explicit Ambient Isotopic Approximations of 2-Manifolds

We present an efficient, constructive algorithm for adaptive, piecewise linear, ambient isotopic approximation of a parametric surface. In contrast to previous algorithms, our approach gives an explicit method for computing the sample set and does so within comparable size guarantees. Our algorithm has a further feature of interest: It relies solely on evaluation of the shape operator at chosen points in parameter space and an a priori promise on maximum curvature. The algorithm is thus quite independent of the underlying representation of the surface.