Provably good sampling and meshing of Lipschitz surfaces

In the last decade, a great deal of work has been devoted to the elaboration of a sampling theory for smooth surfaces. The goal was to ensure a good reconstruction of a given surface S from a finite subset E of S. The sampling conditions proposed so far offer guarantees provided that E is sufficiently dense with respect to the local feature size of S, which can be true only if S is smooth since the local feature size vanishes at singular points. In this paper, we introduce a new measurable quantity, called the Lipschitz radius, which plays a role similar to that of the local feature size in the smooth setting, but which is well-defined and positive on a much larger class of shapes. Specifically, it characterizes the class of Lipschitz surfaces, which includes in particular all piecewise smooth surfaces such that the normal deviation is not too large around singular points. Our main result is that, if S is a Lipschitz surface and E is a sample of S such that any point of S is at di...

• Type: Conference
• Year: 2006
• Where: COMPGEOM
• Authors: Jean-Daniel Boissonnat, Steve Oudot
• Keywords: COMPGEOM 2006, Lipschitz Surfaces, Local Feature Size, Smooth Surfaces