We propose a robust, feature preserving and user-steerable mesh sampling algorithm, based on the one-to-many mapping of a regular sampling of the Gaussian sphere onto a given manifold surface. Most of the operations are local and no global information must be maintained. For this reason, our algorithm is amenable to a parallel or streaming implementation, and is most suitable in situations when it is not possible to hold all the input data in memory at the same time. Using ϵ-nets, we analyze the sampling method and propose solutions to avoid shortcomings inherent to all localized sampling methods. The applicability of Gaussian sampling is demonstrated in a streaming surface simplification and approximation method that handles large meshes with a small memory footprint.