Shattering a set of objects in 2D ?
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(n2) and O(n), respectively. It is an improvement over the 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. 218222.). A minor modification of this algorithm applies when objects are simple polygons, keeping the time and space complexities invariant.
shattering duality topological line sweep separator