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Given 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.
Volkan Cevher, Kimon Antonakopoulos, Thomas Michaelsen Pethick, Wanyun Xie, Fabian Ricardo Latorre Gomez
Anastasia Ailamaki, Viktor Sanca