Paper by Erik D. Demaine
- Reference:
- Erik D. Demaine and Sarah Eisenstat, “Expansive Motions for d-Dimensional Open Chains”, in Proceedings of the 23rd Canadian Conference on Computational Geometry (CCCG 2011), Toronto, Ontario, Canada, August 10–12, 2011, to appear.
- Abstract:
-
We consider the problem of straightening chains in d ≥ 3
dimensions, possibly embedded into higher dimensions, using expansive motions.
For any d ≥ 3, we show that there is an open chain in d dimensions that
is not straight and not self-touching yet has no expansive motion.
Furthermore, for any Δ > 0 and d ≥ 3, we show that there is an
open chain in d dimensions that cannot be straightened using expansive
motions when embedded into ℝd × [−Δ, Δ] (a bounded
extra dimension). On the positive side, we prove that any open chain in
d ≥ 2 dimensions can be straightened using an expansive motion when embedded
into ℝd + 1 (a full extra dimension).
- Length:
- The paper is 6 pages.
- Availability:
- The paper is available in PDF (308k).
- See information on file formats.
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Last updated July 23, 2024 by
Erik Demaine.