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 = 3π(π/2 + 1)/2. Our proof consists of generalizing the proof of Dobkin et al. [2] from the Euclidean Delaunay triangulation to the spherical Delaunay triangulation.

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Conference 26th Canadian Conference on Computational Geometry, CCCG 2014
Citation
Bose, P, Pratt, S. (Simon), & Smid, M. (2014). The convex hull of points on a sphere is a spanner. Presented at the 26th Canadian Conference on Computational Geometry, CCCG 2014.