A Simpler Circular Ray Shooting Algorithm

The circular ray shooting problem is to preprocess a simple polygon P so that, for a query directed circular arc , one can quickly compute the rst intersection point (if any) of on P . We present a solution to this problem with the same preprocessing time, space, and query time complexities as the best known algorithm but our algorithm is simpler. Our algorithm is also more modular and uses tools for which we expect to nd further applications. In the electronic version of this paper we also provide a modi- cation that allows the worst case preprocessing time of both our circular ray shooting algorithm and the best known algorithm to be reduced by an O(log n) factor.