Surface interpolation by spatial environment graphs

A new algorithm for the reconstruction of surfaces from three-dimensional point clouds is presented. Its particular features are reconstruction of open surfaces with boundaries from data sets with variable density, and treatment of sharp edges, that is, locations of infinite curvature. While these properties can be demonstrated only empirically, we outline formal arguments which explain why the algorithm works well for compact surfaces of limited curvature without boundary. They are based on a formal definition of ‘reconstruction’, and on demonstration of existence of sampling sets for which the algorithm is successful.

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