Drawing Trees with Perfect Angular Resolution and Polynomial Area
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.
Cite
@article{arxiv.1009.0581,
title = {Drawing Trees with Perfect Angular Resolution and Polynomial Area},
author = {Christian A. Duncan and David Eppstein and Michael T. Goodrich and Stephen G. Kobourov and Martin Nöllenburg},
journal= {arXiv preprint arXiv:1009.0581},
year = {2015}
}
Comments
30 pages, 17 figures