Authors: Philip Gibbs
Bellman’s challenge to find the shortest path to escape from a forest of known shape is notoriously difficult. Apart from a few of the simplest cases, there are not even many conjectures for likely solutions let alone proofs. In this work it is shown that when the forest is a convex polygon then at least one shortest escape path is a piecewise curve made from segments taking the form of either straight lines or circular arcs. The circular arcs are formed from the envelope of three sides of the polygon touching the escape path at three points. It is hoped that in future work these results could lead to a practical computational algorithm for finding the shortest escape path for any convex polygon.
Comments: Pages. DOI: 10.13140/RG.2.2.28270.61767
[v1] 2016-06-05 13:16:17
Unique-IP document downloads: 109 times
Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.
Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.