The Convex Hull of Points on a Sphere is a Spanner.
Prosenjit K. Bose, Simon Pratt, Michiel Smid · 2014
Let S be a finite set of points on the unit-sphere S2. In 1987, Raghavan suggested that the convex hull of S is a Euclidean t-spanner, for some constant t. We prove that this is the case for t = 3pi(pi/2 + 1)/2. Our proof con-sists of generalizing the proof of Dobkin et al. [2] from the Euclidean Delaunay triangulation to the spherical Delaunay triangulation. 1