We study methods for drawing trees with perfect angular resolution, i.e., with angles at each vertex, 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.
In a separate paper REF , we study the area requirements for tree drawings with perfect angular resolution.
Drawing Trees with Perfect Angular Resolution and Polynomial Area
Discrete Comput. Geom. 49 (2): 157-182, 2013
Computer Science Mathematics