International Symposium on Graph Drawing and Network Visualization

Graph Drawing and Network Visualization pp 335-347

Representing Directed Trees as Straight Skeletons

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

Abstract

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.

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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
  • 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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