We discuss the problem of computing shortest an-isotropic paths on terrains. Anisotropic path costs take into account the length of the path traveled, possibly weighted, and the direction of travel along the faces of the terrain. Considering faces to be weighted has added rea- lism to the study of (pure) Euclidean shortest paths. Parameters such as the varied nature of the terrain, friction, or slope of each face, can be captured via face weights. Anisotropic paths add further realism by taking into consideration the direction of travel on each face thereby e.g., eliminating paths that are too steep for vehicles to travel and preven- Ting the vehicles from turning over. Prior to this work an O(nn) time algorithm had been presented for computing anisotropic paths. Here we present the first polynomial time approximation algorithm for comput- ing shortest anisotropic paths. Our algorithm is simple to implement and allows for the computation of shortest anisotropic paths within a desired accuracy. Our result addresses the corresponding problem posed in [12].

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Keywords An- iositropic paths, Approximation, Computational geometry, Shortest path
Lanthier, M, Maheshwari, A, & Sack, J.-R. (1999). Shortest anisotropic paths on terrains.