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α-Visibility

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 7357)

Abstract

We study a new class of visibility problems based on the notion of α-visibility. Given an angle α and a collection of line segments \(\ensuremath{{\cal S}}\) in the plane, a segment t is said to be α-visible from a point p, if there exists an empty triangle with one vertex at p and the side opposite to p on t such that the angle at p is α. In this model of visibility, we study the classical variants of point visibility, weak and complete segment visibility, and the construction of the visibility graph. We also investigate the natural query versions of these problems, when α is either fixed or specified at query time.

Keywords

  • Short Path
  • Query Point
  • Query Time
  • Short Path Problem
  • Simple Polygon

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Research supported by NSERC, HPCVL and SUN Microsystems.

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Ghodsi, M., Maheshwari, A., Nouri, M., Sack, JR., Zarrabi-Zadeh, H. (2012). α-Visibility. In: Fomin, F.V., Kaski, P. (eds) Algorithm Theory – SWAT 2012. SWAT 2012. Lecture Notes in Computer Science, vol 7357. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31155-0_1

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  • DOI: https://doi.org/10.1007/978-3-642-31155-0_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31154-3

  • Online ISBN: 978-3-642-31155-0

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