Trees with Convex Faces and Optimal Angles

TL;DR

This paper introduces algorithms for drawing trees with convex faces that maximize angular resolution, allowing independent edge length setting without crossings, applicable to both plane and non-embedded trees.

Contribution

It presents linear time algorithms for constructing convex-face tree drawings with optimal angles, extending to trees without fixed embeddings.

Findings

Linear time algorithms for optimal convex-face tree drawings

Methods for independent edge length setting without crossings

Applicable to both plane and non-embedded trees

Abstract

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.