Solution of Scott's problem on the number of directions determined by a point set in 3-space

Authors:
Janos Pach;Rom Pinchasi;Micha Sharir
Affiliations:
New York University, New York, NY;Massachusetts Institute of Technology, Cambridge, MA;Tel Aviv University, Tel Aviv, Israel and New York University, New York, NY
Venue:
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Year:
2004

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Abstract

Let P be a set of n points in ℝ3, not all in a common plane. We solve a problem of Scott (1970) by showing that the connecting lines of P assume at least 2n-7 different directions if n is even and at least 2n-5 if n is odd. The bound for odd n is sharp.