  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.
