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Generalizations of Naismith's problem: Minimal transit time between two points in a heterogenous terrian

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  • Naismith obtained a set of empirical rules for the time required to move through a terrain. In this paper we solve the problem of determining the path which minimizes the transit time between two points on a given terrain. We give an interpretation of Naismith’s rule which leads to an elegant geometric construction of the optimal solution. This problem is a paradigm for the navigation of an autonomous vehicle in a heterogenous terrain.
    Mathematics Subject Classification: Primary: 49K05, 49K15; Secondary: 65K10.


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