Polygonal Chains Cannot Lock in 4D

Details Polygonal Chains Cannot Lock in 4D Polygonal Chains Cannot Lock in 4D

1999-08-11

arxiv.org/abs/cs/9908005v3

Computer Science

Computational Geometry

Major revision of the Aug. 1999 version, including: Proof extended to show trees cannot lock in 4D; new example of the impleme

Scientific paper

We prove that, in all dimensions d>=4, every simple open polygonal chain and every tree may be straightened, and every simple closed polygonal chain may be convexified. These reconfigurations can be achieved by algorithms that use polynomial time in the number of vertices, and result in a polynomial number of ``moves.'' These results contrast to those known for d=2, where trees can ``lock,'' and for d=3, where open and closed chains can lock.

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