A Locked Orthogonal Tree
Computational Geometry
2008-01-30 v1
Abstract
We give a counterexample to a conjecture of Poon [Poo06] that any orthogonal tree in two dimensions can always be flattened by a continuous motion that preserves edge lengths and avoids self-intersection. We show our example is locked by extending results on strongly locked self-touching linkages due to Connelly, Demaine and Rote [CDR02] to allow zero-length edges as defined in [ADG07], which may be of independent interest. Our results also yield a locked tree with only eleven edges, which is the smallest known example of a locked tree.
Keywords
Cite
@article{arxiv.0801.4405,
title = {A Locked Orthogonal Tree},
author = {David Charlton and Erik D. Demaine and Martin L. Demaine and Gregory Price and Yaa-Lirng Tu},
journal= {arXiv preprint arXiv:0801.4405},
year = {2008}
}