A Locked Orthogonal Tree

Details A Locked Orthogonal Tree A Locked Orthogonal Tree

2008-01-29

arxiv.org/abs/0801.4405v1

Computer Science

Computational Geometry

Scientific paper

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.

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