English

Representing Directed Trees as Straight Skeletons

Computational Geometry 2015-08-06 v1

Abstract

The straight skeleton of a polygon is the geometric graph obtained by tracing the vertices during a mitered offsetting process. It is known that the straight skeleton of a simple polygon is a tree, and one can naturally derive directions on the edges of the tree from the propagation of the shrinking process. In this paper, we ask the reverse question: Given a tree with directed edges, can it be the straight skeleton of a polygon? And if so, can we find a suitable simple polygon? We answer these questions for all directed trees where the order of edges around each node is fixed.

Keywords

Cite

@article{arxiv.1508.01076,
  title  = {Representing Directed Trees as Straight Skeletons},
  author = {Oswin Aichholzer and Therese Biedl and Thomas Hackl and Martin Held and Stefan Huber and Peter Palfrader and Birgit Vogtenhuber},
  journal= {arXiv preprint arXiv:1508.01076},
  year   = {2015}
}
R2 v1 2026-06-22T10:27:01.277Z