On shortest paths in polyhedral spaces
SIAM Journal on Computing
The weighted region problem: finding shortest paths through a weighted planar subdivision
Journal of the ACM (JACM)
Discrete & Computational Geometry - Special issue on ACM symposium on computational geometry, North Conway
Approximate Euclidean shortest path in 3-space
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Strategic directions in computational geometry
ACM Computing Surveys (CSUR) - Special ACM 50th-anniversary issue: strategic directions in computing research
A new algorithm for computing shortest paths in weighted planar subdivisions (extended abstract)
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Approximating weighted shortest paths on polyhedral surfaces
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
An epsilon-Approximation for Weighted Shortest Paths on Polyhedral Surfaces
SWAT '98 Proceedings of the 6th Scandinavian Workshop on Algorithm Theory
Computing an approximation of the 1-center problem on weighted terrain surfaces
Journal of Experimental Algorithmics (JEA)
Shortest Gently Descending Paths
WALCOM '09 Proceedings of the 3rd International Workshop on Algorithms and Computation
SGP '13 Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing
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We discuss the problem of computing shortest anisotropic 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 realism 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 preventing 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 computing 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].