Efficient algorithms for Euclidean shortest path and visibility problems with polygonal obstacles

@inproceedings{Kapoor1988EfficientAF,
title={Efficient algorithms for Euclidean shortest path and visibility problems with polygonal obstacles},
author={S. Kapoor and S. Maheshwari},
booktitle={SCG '88},
year={1988}
}

The problem of determining the Euclidean shortest path between two points in the presence of m simple polygonal obstacles is studied. An O( m<supscrpt>2</supscrpt> logn + nlogn ) algorithm is developed, where n is the total number of points in the obstacles. A simple O(E+T) algorithm for determining the visibility graph is also shown, where E is the number of visibility edges and T is the time for triangulating the point set. This is extended to a O(E<subscrpt>s</subscrpt> + nlogn) algorithm… CONTINUE READING