Andersson, MattiasGiesen, JoachimPauly, MarkSpeckmann, BettinaMarkus Gross and Hanspeter Pfister and Marc Alexa and Szymon Rusinkiewicz2014-01-292014-01-2920043-905673-09-61811-7813https://doi.org/10.2312/SPBG/SPBG04/167-171Given a locally uniform sample set P of a smooth surface S. We derive upper and lower bounds on the number k of nearest neighbors of a sample point p that have to be chosen from P such that this neighborhood contains all restricted Delaunay neighbors of p. In contrast to the trivial lower bound, the upper bound indicates that a sampling condition that is used in many computational geometry proofs is quite reasonable from a practical point of view.Categories and Subject Descriptors (according to ACM CCS): I.3.5 [Computer Graphics]: Curve, surface, solid, and object representations