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Moving an angle around a region

  • Frank Hoffmann
  • Christian Icking
  • Rolf Klein
  • Klaus Kriegel
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1432)

Abstract

Let D be a connected region inside a simple polygon, P. We define the angle hull, \(\mathcal{A}\mathcal{H}\)(D), of D to be the set of all points in P that can see two points of D at a right angle. We show that the perimeter of \(\mathcal{A}\mathcal{H}\)(D) cannot exceed the perimeter of the relative convex hull of D by more than a factor of 2. A special case occurs when P equals the full plane. Here we prove a bound of π/2. Both bounds are tight, and corresponding results are obtained for any other angle.

Key words

Angle hull arrangements of circles computational geometry convex hull curve length envelopes of circles motion planning polygon 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Frank Hoffmann
    • 1
  • Christian Icking
    • 2
  • Rolf Klein
    • 2
  • Klaus Kriegel
    • 1
  1. 1.Institut für InformatikFreie UniversitÄt BerlinBerlin
  2. 2.Praktische Informatik VIFem UniversitÄt HagenHagen

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