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