Advertisement
Published in:
2011 | OriginalPaper | Chapter
Drawing Trees with Perfect Angular Resolution and Polynomial Area
Authors : Christian A. Duncan, David Eppstein, Michael T. Goodrich, Stephen G. Kobourov, Martin Nöllenburg
Published in: Graph Drawing
Publisher: Springer Berlin Heidelberg
Activate our intelligent search to find suitable subject content or patents.
Select sections of text to find matching patents with Artificial Intelligence. powered by
Select sections of text to find additional relevant content using AI-assisted search. powered by
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.