Article Contents
Article Contents

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

• 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.

 Citation:

Open Access Under a Creative Commons license