Drawing Trees with Perfect Angular Resolution and Polynomial Area

  • Christian A. Duncan
  • David Eppstein
  • Michael T. Goodrich
  • Stephen G. Kobourov
  • Martin Nöllenburg
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6502)


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. 1

    Any unordered tree has a crossing-free straight-line drawing with perfect angular resolution and polynomial area.

  2. 2

    There are ordered trees that require exponential area for any crossing-free straight-line drawing having perfect angular resolution.

  3. 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.


Intersection Angle Large Zone Outer Annulus Unordered Tree Heavy Edge 
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-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Christian A. Duncan
    • 1
  • David Eppstein
    • 2
  • Michael T. Goodrich
    • 2
  • Stephen G. Kobourov
    • 3
  • Martin Nöllenburg
    • 2
  1. 1.Department of Computer ScienceLouisiana Tech. Univ.RustonUSA
  2. 2.Department of Computer ScienceUniversity of CaliforniaIrvineUSA
  3. 3.Department of Computer ScienceUniversity of ArizonaTucsonUSA

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