Learn More
We present an on-line strategy that enables a mobile robot with vision to explore an unknown simple polygon. We prove that the resulting tour is less than 26.5 times as long as the shortest watchman tour that could be computed off-line. Our analysis is doubly founded on a novel geometric structure called the angle hull. Let D be a connected region inside a(More)
We present a new class of curves which are self-approaching in the following sense. For any three consecutive points a, b, c on the curve the point b is closer to c than a to c. This is a generalisation of curves with increasing chords which are self-approaching in both directions. We show a tight upper bound of 5.3331. .. for the length of a(More)
The detour and spanning ratio of a graph embedded in measure how well approximates Euclidean space and the complete Euclidean graph, respectively. In this paper we describe " ! $ # & % ') (time algorithms for computing the detour and spanning ratio of a planar polygonal path. By generalizing these algorithms, we obtain " ! $ # & % 1 0 2) (time algorithms(More)