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Erschienen in:
2011 | OriginalPaper | Buchkapitel
Drawing Trees with Perfect Angular Resolution and Polynomial Area
verfasst von : Christian A. Duncan, David Eppstein, Michael T. Goodrich, Stephen G. Kobourov, Martin Nöllenburg
Erschienen in: Graph Drawing
Verlag: Springer Berlin Heidelberg
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We study methods for drawing trees with perfect angular resolution, i.e., with angles at each vertex,
v
, equal to 2
π
/
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.