@article{Mitchell1987TheDG,
title={The Discrete Geodesic Problem},
author={Joseph S. B. Mitchell and David M. Mount and Christos H. Papadimitriou},
journal={SIAM J. Comput.},
year={1987},
volume={16},
pages={647-668}
}

We present an algorithm for determining the shortest path between a source and a destination on an arbitrary (possibly nonconvex) polyhedral surface. The path is constrained to lie on the surface, and distances are measured according to the Euclidean metric. Our algorithm runs in time O(n log n) and requires O(n2) space, where n is the number of edges of the surface. After we run our algorithm, the distance from the source to any other destination may be determined using standard techniques inâ€¦Â CONTINUE READING