Weak witnesses for Delaunay triangulations of submanifolds
Dominique Attali, Herbert Edelsbrunner, Yuriy Mileyko · 2007
The main result of this paper is an extension of de Silva's Weak Delaunay Theorem to smoothly embedded curves and surfaces in Euclidean space. Assuming a sufficiently fine sampling, we prove that i + 1 points in the sample span an i-simplex in the restricted Delaunay triangulation iff every subset of the i + 1 points has a weak witness.