We consider geometric shortest path queries between arbitrary pairs of objects on a connected polyhedral surface P of genus g. The query objects are points, vertices, edges, segments, faces, chains, regions and sets of these. The surface P consists of n positively weighted triangular faces. The cost of a path on P is the weighted sum of Euclidean lengths of the sub-paths within each face of P. We present generic algorithms which provide approximate solutions.

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Guo, H. (Hua), Maheshwari, A, Nussbaum, D, & Sack, J.-R. (2007). Shortest path queries between geometric objects on surfaces.