Drawing trees with perfect angular resolution and polynomial area

  • Authors:

  • Christian A. Duncan;David Eppstein;Michael T. Goodrich;Stephen G. Kobourov;Martin Nöllenburg

  • Affiliations:

  • Department of Computer Science, Louisiana Tech. Univ., Ruston, Louisiana;Department of Computer Science, University of California, Irvine, California;Department of Computer Science, University of California, Irvine, California;Department of Computer Science, University of Arizona, Tucson, Arizona;Department of Computer Science, University of California, Irvine, California

  • Venue:
  • GD'10 Proceedings of the 18th international conference on Graph drawing
  • Year:
  • 2010

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Abstract

We study methods for drawing trees with perfect angular resolution, i.e., with angles at each vertex, v, equal to 2π/d(v). We show: 1. Any unordered tree has a crossing-free straight-line drawing with perfect angular resolution and polynomial area. 2. There are ordered trees that require exponential area for any crossing-free straight-line drawing having perfect angular resolution. 3. Any ordered tree has a crossing-free Lombardi-style drawing (where each edge is represented by a circular arc) with perfect angular resolution and polynomial area. Thus, our results explore what is achievable with straight-line drawings and what more is achievable with Lombardi-style drawings, with respect to drawings of trees with perfect angular resolution.