Multi-scale surface representation of point-sampled geometry

With increasing complexity of 3D geometric models and growing demand for advanced modeling functionality, significant effort is being devoted to the design of efficient, reliable, and scalable algorithms for digital geometry processing. We introduce a multi-scale surface representation that enables sophisticated editing functionality at different approximation levels, using the concept of scale-space. The key issue is the interconnection between successive levels in the hierarchy. We use a fairing operator-a geometric low-pass filter to generate successively smoother approximation levels of a given input surface, and use a decomposition operator to encode each level relative to the next smoother level using normal displacements to ensure intuitive detail preservation. As a result, users can 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.