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/sub p/(p, q) in time O(n). This algorithm is revised, and achieves a ratio of 1.786.
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机译：Hershberger和Suri [1993]于1998年提出了一种非常简单的近似方案，用于计算凸多面体的三维表面上的最短路径的三个维度。给定凸多面体P具有n个顶点和其表面上有两个点p，q，则d， （p，q）表示P表面上p和q之间的最短路径距离。他们的算法ShortestPath在时间O（n）中产生的最大路径为2d / sub p /（p，q）。对该算法进行了修改，并实现了1.786的比率。
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