Computational geometry: an introduction
Computational geometry: an introduction
Topologically sweeping an arrangement
Journal of Computer and System Sciences - 18th Annual ACM Symposium on Theory of Computing (STOC), May 28-30, 1986
The complexity and construction of many faces in arrangements of lines and of segments
Discrete & Computational Geometry - Special issue on the complexity of arrangements
On the union of fat wedges and separating a collection of segments by a line
Computational Geometry: Theory and Applications
On a class of O(n2) problems in computational geometry
Computational Geometry: Theory and Applications
Davenport-Schinzel sequences and their geometric applications
Davenport-Schinzel sequences and their geometric applications
Separating and shattering long line segments
Information Processing Letters
Investigations in Geometric Subdivisions: Linear Shattering and Cartographic Map Coloring
Investigations in Geometric Subdivisions: Linear Shattering and Cartographic Map Coloring
Topological sweep of the complete graph
Discrete Applied Mathematics
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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 O(n2log 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.