, Volume 49, Issue 2, pp 157-182
Date: 27 Nov 2012

Drawing Trees with Perfect Angular Resolution and Polynomial Area

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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. 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.

A preliminary version of this paper appeared at the 18th International Symposium on Graph Drawing (GD’10) [9]