Discrete & Computational Geometry

, Volume 49, Issue 2, pp 157–182

Drawing Trees with Perfect Angular Resolution and Polynomial Area

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

DOI: 10.1007/s00454-012-9472-y

Cite this article as:
Duncan, C.A., Eppstein, D., Goodrich, M.T. et al. Discrete Comput Geom (2013) 49: 157. doi:10.1007/s00454-012-9472-y

Abstract

We study methods for drawing trees with perfect angular resolution, i.e., with angles at each node \(v\) equal to \(2\pi /d(v)\). 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.

Keywords

Tree drawings Straight-line drawings Circular-arc drawings  Lombardi drawings Polynomial area Perfect angular resolution 

Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  • Christian A. Duncan
    • 1
  • David Eppstein
    • 2
  • Michael T. Goodrich
    • 2
  • Stephen G. Kobourov
    • 3
  • Martin Nöllenburg
    • 4
  1. 1.Department of Mathematics and Computer ScienceQuinnipiac UniversityHamdenUSA
  2. 2.Department of Computer ScienceUniversity of California, IrvineIrvineUSA
  3. 3.Department of Computer ScienceUniversity of Arizona, TucsonTucsonUSA
  4. 4.Institute of Theoretical InformaticsKarlsruhe Institute of TechnologyKarlsruheGermany