On the Density of Iterated Line Segment Intersections
Loading...
Date
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
Description
Given S_1, a finite set of points in the plane, we define a sequence of point sets S_i as follows: With S_i already determined, let L_i be the set of all the line segments connecting pairs of points of the union of S_1,...,S_i, and let S_i+1 be the set of intersection points of those line segments in L_i, which cross but do not overlap.
We show that with the exception of some starting configurations the set of all crossing points is dense in a particular subset of the plane with nonempty interior. This region is the intersection of all closed half planes which contain all but at most one point from S_1.
20 pages, 17 figures, revised version, still based on Technical Report 004
20 pages, 17 figures, revised version, still based on Technical Report 004