Stabbing line segments

An algorithm for the geometric problem of determining a line (called a stabbing line) which intersects each ofn given line segments in the plane is presented. As a matter of fact, the algorithm computes a description of all stabbing lines. A purely geometric fact is proved which infers that this description requiresO(n) space to be specified. Our algorithm computes it inO(n logn) time which is optimal in the worst case.Using the description of the stabbing lines, we are able to decide inO(logn) time whether or not a specified line is a stabbing line. Finally, the problem of maintaining the description of all stabbing lines while inserting and deleting line segments is addressed.

[1]  Kevin Q. Brown Geometric transforms for fast geometric algorithms , 1979 .

[2]  Mark H. Overmars,et al.  Dynamization of Order Decomposable Set Problems , 1981, J. Algorithms.

[3]  Michael L. Fredman,et al.  The inherent complexity of dynamic data structures which accommodate range queries , 1980, 21st Annual Symposium on Foundations of Computer Science (sfcs 1980).

[4]  Michael Ian Shamos,et al.  Geometric intersection problems , 1976, 17th Annual Symposium on Foundations of Computer Science (sfcs 1976).