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In this paper, we introduce a flexible framework for the reconstruction of a surface from an unorganized point set, extending the geometric convection approach introduced by Chaine. Given a dense input point cloud, we first extract a triangulated surface that interpolates a subset of the initial data. We compute this surface in an output sensitive manner by decimating the input point set on-the-fly during the reconstruction process. Our simplification procedure relies on a simple criterion that locally detects and reduces oversampling. If needed, we then operate in a dynamic fashion for local refinement or further simplification of the reconstructed surface. Our method allows to locally update the reconstructed surface by inserting or removing sample points without restarting the convection process from scratch. This iterative correction process can be controlled interactively by the user or automatized given some specific local sampling constraints.