Hierarchical decompositions and circular ray shooting in simple polygons

Abstract

A hierarchical decomposition of a simple polygon is introduced. The hierarchy has logarithmic depth, linear size, and its regions have at most three neighbors. Using this hierarchy, circular ray shooting queries in a simple polygon on n vertices can be answered in O(log(2) n) query time and O(n log n) space. If the radius of the circle is fixed, the query time can be improved to O(log n) and the space to O(n).