Pointed Binary Encompassing Trees

  • Michael Hoffmann
  • Bettina Speckmann
  • Csaba D. Tóth
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3111)


We show that for any set of disjoint line segments in the plane there exists a pointed binary encompassing treeT, that is, a spanning tree on the segment endpoints that contains all input segments, has maximum degree three, and every vertex vT is pointed, that is, v has an incident angle greater than π. Such a tree can be completed to a minimum pseudo-triangulation. In particular, it follows that every set of disjoint line segments has a minimum pseudo-triangulation of bounded vertex degree.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Michael Hoffmann
    • 1
  • Bettina Speckmann
    • 2
  • Csaba D. Tóth
    • 3
  1. 1.Institute of Theoretical Computer ScienceETH Zürich 
  2. 2.Department of Mathematics and Computer ScienceTU Eindhoven 
  3. 3.Department of Computer ScienceUniversity of California at Santa Barbara 

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