A dense planar point set from iterated line intersections
Computational Geometry: Theory and Applications
The density of iterated crossing points and a gap result for triangulations of finite point sets
Proceedings of the twenty-second annual symposium on Computational geometry
A result about the density of iterated line intersections in the plane
Computational Geometry: Theory and Applications
Embedding point sets into plane graphs of small dilation
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
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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 @?"j"="1^iS"j, 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 @?"i"="1^~S"i 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.