Abstract: We focus on the class of ‘regular’ models defined by Varady et al. for reverse engineering purposes. Given a 3D surface  represented through a dense set of points, we present a novel algorithm that converts  to a hierarchical representation . In , the surface is encoded through patches of various shape and size, which form a hierarchical atlas. If  belongs to the class of regular models, then  captures the most significant features of  at all the levels of detail. In this case, we show that  can be exploited to interactively select regions of interest on  and intuitively re-design the model. Furthermore,  intrinsically encodes a hierarchy of useful ‘segmentations’ of . We present a simple though efficient approach to extract and optimize such segmentations, and we show how they can be used to approximate the input point sets through idealized manifold meshes.