2011•Canadian Conference on Computational GeometryRequires access
Expansive Motions for d-Dimensional Open Chains
Sarah Eisenstat, Erik D. Demaine
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Abstract
We consider the problem of straightening chains ind 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 > 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 R d [ ; ] (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 R d+1 (a full extra dimension).