Angle and Distance Constraints on Tree Drawings

  • Ulrik Brandes
  • Barbara Schlieper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4372)


We consider planar drawings of trees that must satisfy constraints on the angles between edges incident to a common vertex and on the distances between adjacent vertices. These requirements arise naturally in many applications such as drawing phylogenetic trees or route maps. For straight-line drawings, either class of constraints is always realizable, whereas their combination is not in general. We show that straight-line realizability can be tested in linear time, and give an algorithm that produces drawing satisfying both groups of constraints together in a model where edges are represented as polylines with at most two bends per edge or as continuously differentiable curves.


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Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Ulrik Brandes
    • 1
  • Barbara Schlieper
    • 1
  1. 1.Department of Computer & Information Science, University of Konstanz 

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