Drawing trees with perfect angular resolution and polynomial area - Christian A. Duncan; David Eppstein; Michael T. Goodrich; Stephen G. Kobourov; Martin Nöllenburg (Discrete and Computational Geometry, 2013)
We study methods for drawing trees with perfect angular resolution, i.e., with angles at each node 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.