Shattering a set of objects in 2D

Abstract

In this paper, we propose an algorithm for shattering a set of disjoint line segments of arbitrary length and orientation placed arbitrarily on a 2D plane. The time and space complexities of our algorithm are O( n 2) and O( n), respectively. It is an improvement over the O(n 2 log n) time algorithm proposed in (R. Freimer, J.S.B. Mitchell, C.D. Piatko, On the complexity of shattering using arrangements, Canadian Conference on Computational Geometry, 1990, pp. 218–222.). A minor modification of this algorithm applies when objects are simple polygons, keeping the time and space complexities invariant.