Yang, PinghaiQian, XiaopingM. Botsch and R. Pajarola and B. Chen and M. Zwicker2014-01-292014-01-292007978-3-905673-51-71811-7813https://doi.org/10.2312/SPBG/SPBG07/029-036Accurate computing of the curvatures of a surface from its discrete form is of fundamental importance for many graphics and engineering applications. The moving least-squares (MLS) surface from Levin [Lev2003] and its variants have been successfully used to define point-set surfaces in a variety of point cloud data based modeling and rendering applications. This paper presents a set of analytical equations for direct computing of surface curvatures from pointset surfaces based on the explicit definition from [AK04a, AK04b]. Besides the Gaussian parameter involved in the MLS definition, these analytical equations allow us to conduct direct and exact differential geometric analysis on the point-set surfaces without specifying any subjective parameters. Our experimental validation on both synthetic and real point cloud data demonstrates that such direct computing from analytical equations provides a viable approach for surface curvature evaluation for unorganized point cloud data.Categories and Subject Descriptors (according to ACM CCS): I.3.5 [Computer Graphics]: Curve, surface, solid, and object representations