TY - JOUR
AB - 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.
AU - Edelsbrunner, Herbert
AU - Maurer, Hermann
AU - Preparata, Franco
AU - Rosenberg, Arnold
AU - Welzl, Emo
AU - Wood, Derick
ID - 4129
IS - 3
JF - BIT Numerical Mathematics
SN - 0006-3835
TI - Stabbing line segments
VL - 22
ER -