  We consider drawings of trees in which all edges incident to leaves can be
extended to infinite rays without crossing, partitioning the plane into
infinite convex polygons. Among all such drawings we seek the one maximizing
the angular resolution of the drawing. We find linear time algorithms for
solving this problem, both for plane trees and for trees without a fixed
embedding. In any such drawing, the edge lengths may be set independently of
the angles, without crossing; we describe multiple strategies for setting these
lengths.
