Computer Science – Computational Geometry
Scientific paper
2010-09-03
Computer Science
Computational Geometry
Expanded version of a paper appearing in the 18th International Symposium on Graph Drawing (GD 2010). 20 pages, 16 figures
Scientific paper
We study methods for drawing trees with perfect angular resolution, i.e., with angles at each vertex, v, equal to 2pi/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.
Duncan Christian A.
Eppstein David
Goodrich Michael T.
Kobourov Stephen G.
Nöllenburg Martin
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