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We describe a two-level method for computing a function whose zero-level setis the surface reconstructed from given points scattered over the surface andassociated with surface normal vectors. The function is defined as a linearcombination of compactly supported radial basis functions (CSRBFs). The methodpreserves the simplicity and efficiency of implicit surface interpolation withCSRBFs and the reconstructed implicit surface owns the attributes, which arepreviously only associated with globally supported or globally regularizedradial basis functions, such as exhibiting less extra zero-level sets, suitablefor inside and outside tests. First, in the coarse scale approximation, wechoose basis function centers on a grid that covers the enlarged bounding boxof the given point set and compute their signed distances to the underlyingsurface using local quadratic approximations of the nearest surface points.Then a fitting to the residual errors on the surface points and additionaloff-surface points is performed with fine scale basis functions. The finalfunction is the sum of the two intermediate functions and is a goodapproximation of the signed distance field to the surface in the bounding box.Examples of surface reconstruction and set operations between shapes areprovided.

A two-level approach to implicit surface modeling with compactly supported radial basis functions