Representing Directed Trees as Straight Skeletons

  • Oswin Aichholzer
  • Therese Biedl
  • Thomas Hackl
  • Martin Held
  • Stefan Huber
  • Peter PalfraderEmail author
  • Birgit Vogtenhuber
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9411)


The straight skeleton of a polygon is the geometric graph obtained by tracing the vertices during a mitered offsetting process. It is known that the straight skeleton of a simple polygon is a tree, and one can naturally derive directions on the edges of the tree from the propagation of the shrinking process.

In this paper, we ask the reverse question: Given a tree with directed edges, can it be the straight skeleton of a polygon? And if so, can we find a suitable simple polygon? We answer these questions for all directed trees where the order of edges around each node is fixed.


Voronoi Diagram Simple Polygon Interior Node Geometric Graph Interior Angle 
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.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Oswin Aichholzer
    • 1
  • Therese Biedl
    • 2
  • Thomas Hackl
    • 1
  • Martin Held
    • 3
  • Stefan Huber
    • 4
  • Peter Palfrader
    • 3
    Email author
  • Birgit Vogtenhuber
    • 1
  1. 1.Institut für SoftwaretechnologieTechnische Universität GrazGrazAustria
  2. 2.Cheriton School of Computer ScienceUniversity of WaterlooWaterlooCanada
  3. 3.FB ComputerwissenschaftenUniversität SalzburgSalzburgAustria
  4. 4.Institute of Science and Technology AustriaKlosterneuburgAustria

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