Dynamic C-oriented polygonal intersection searching

Abstract

A set of polygons is called c-oriented if the edges of all polygons are oriented in a constant number of previously defined directions. The intersection searching problem is studied for such objects, namely: Given a set of c-oriented polygons P and a c-oriented query polygon q, find all polygons in P that intersect q. It is shown that this problem can be solved in O(log² n + t) time with O(n log n) space and O(n log² n) preprocessing, where n is the cardinality of P and t the number of answers to a query. Furthermore, the solution is extended to the cases in which P is a semidynamic or dynamic set of polygons. Whereas planar intersection searching can be carried out more efficiently for orthogonal objects (e.g., rectangles) it is expensive for arbitrary polygons. This suggests that the c-oriented solution be used in appropriate areas of application, for instance, in VLSI-design.