Analysis for shortest path algorithm on convex polytope in E3

Hershberger and Suri [1993] proposed an extremely simple approximation scheme for computing shortest paths on the surface of a convex polytope in three dimensions in 1998. Given a convex polytope P with n vertices and two points p, q on its surface, let d,(p, q) denote the shortest path distance between p and q on the surface of P. Their algorithm, ShortestPath, produces a path of length at most 2d_p(p, q) in time O(n). This algorithm is revised, and achieves a ratio of 1.786