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On the Size of a Radial Set

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Discrete and Computational Geometry (JCDCG 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2866))

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Abstract

Let G be a finite set in the plane. A point x ∉ G is called a radial point of G, if every line through x and a point from G includes at least two points of G. In this paper we show that for any line l not passing through the convex hull of G there are at most \((\frac{9}{10}+o(1))|G|\) radial points separated from G by l. As a consequence we prove two nice geometric applications in the plane.

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Author information

Authors and Affiliations

  1. Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA, 02139-4307, USA

    Rom Pinchasi

Authors
  1. Rom Pinchasi
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Editor information

Editors and Affiliations

  1. Research Institute of Education, Tokai University, 2-28-4 Tomigaya, Shibuya-ku Tokio, Japan

    Jin Akiyama

  2. Ibaraki University, Nakanarusawa, Hitachi, 316-8511, Ibaraki, Japan

    Mikio Kano

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© 2003 Springer-Verlag Berlin Heidelberg

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Pinchasi, R. (2003). On the Size of a Radial Set. In: Akiyama, J., Kano, M. (eds) Discrete and Computational Geometry. JCDCG 2002. Lecture Notes in Computer Science, vol 2866. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-44400-8_25

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  • DOI: https://doi.org/10.1007/978-3-540-44400-8_25

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20776-4

  • Online ISBN: 978-3-540-44400-8

  • eBook Packages: Springer Book Archive

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