Drawing Trees with Perfect Angular Resolution and Polynomial Area

We study methods for drawing trees with perfect angular resolution, i.e., with angles at each node v equal to 2π/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. ∗A preliminary version of this paper appeared at the 18th International Symposium on Graph Drawing (GD’10) [10]. †Department of Mathematics and Computer Science, Quinnipiac University, Hamden, CT, USA ‡Department of Computer Science, University of California, Irvine, California, USA §Department of Computer Science, University of Arizona, Tucson, Arizona, USA ¶Institute of Theoretical Informatics, Karlsruhe Institute of Technology, Germany 1 ar X iv :1 00 9. 05 81 v2 [ cs .C G ] 1 0 Se p 20 15