The problem of computing a shortest cost path between two points on a polyhedral surface is presented. The surface is composed of triangular regions in which each region has an associated positive weight. The computation of Euclidean shortest paths on nonconvex polyhedra used an algorithm to compute the shortest weighted cost path between two points in a planar subdivision. Other schemes that allow the computation of the approximate shortest paths on polyhedral surfaces in both weighted and unweighted scenarios are discussed.

Proceedings of the 1997 13th Annual Symposium on Computational Geometry
School of Computer Science

Lanthier, M, Maheshwari, A, & Sack, J.-R. (1997). Approximating weighted shortest paths on polyhedral surfaces. In Proceedings of the Annual Symposium on Computational Geometry (pp. 485–486).