We present a method to reconstruct simplified mesh surfaces from large unstructured point sets, extending recent work on dynamic surface reconstruction. The method consists of two core components: an efficient selective reconstruction algorithm, based on geometric convection, that simplifies the input point set while reconstructing a surface, and a local update algorithm that dynamically refines or coarsens the reconstructed surface according to specific local sampling constraints. We introduce a new data-structure that significantly accelerates the original selective reconstruction algorithm and makes it possible to handle point set models with millions of sample points. Our data-structure mixes a kd-tree with the Delaunay triangulation of the selected points enriched with a sparse subset of landmark sample points. This design efficiently responds to the specific spatial location issues of the geometric convection algorithm. We also develop an out-of-core implementation of the method, that permits to seamlessly reconstruct and interactively update simplified mesh surfaces from point sets that do not fit into main memory.