In this article we present a new multiscale surface representation based on point samples. Given an unstructured point cloud as input, our method first computes a series of point-based surface approximations at successively higher levels of smoothness, that is, coarser scales of detail, using geometric low-pass filtering. These point clouds are then encoded relative to each other by expressing each level as a scalar displacement of its predecessor. Low-pass filtering and encoding are combined in an efficient multilevel projection operator using local weighted least squares fitting.
Our representation is motivated by the need for higher-level editing semantics which allow surface modifications at different scales. The user would be able to edit the surface at different approximation levels to perform coarse-scale edits on the whole model as well as very localized modifications on the surface detail. Additionally, the multiscale representation provides a separation in geometric scale which can be understood as a spectral decomposition of the surface geometry. Based on this observation, advanced geometric filtering methods can be implemented that mimic the effects of Fourier filters to achieve effects such as smoothing, enhancement, or band-bass filtering.