Polygonal chains cannot lock in 4D (1999) [25 citations — 0 self]
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by Roxana Cocan
In Proc. 11th Canad. Conf. Comput. Geom
http://www.cs.ubc.ca/conferences/CCCG/elec_proc/c17.ps.gz
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@INPROCEEDINGS{Cocan99polygonalchains,author = {Roxana Cocan},
title = {Polygonal chains cannot lock in 4D},
booktitle = {In Proc. 11th Canad. Conf. Comput. Geom},
year = {1999},
pages = {5--8}
}
Years of Citing Articles
Abstract:
We prove that, for all dimensions d 4, every simple open polygonal chain may be straightened, and every simple closed polygonal chain may be convexified. Both 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 = 3, where open and closed chains can be "locked."
Citations
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| 40 | Algorithmic motion planning – Sharir - 1997 |
| 37 | Locked and unlocked polygonal chains in 3D – Biedl, Demaine, et al. - 1999 |
| 32 | On the zone theorem for hyperplane arrangements – Edelsbrunner, Seidel, et al. - 1993 |
| 31 | Reconfiguring closed polygonal chains in Euclidean d-space – Lenhart, Whitesides - 1995 |
| 21 | Introduction to knot theory – Crowell, Fox - 1977 |
| 15 | Computational Real Algebraic Geometry – Mishra - 1997 |
| 10 | Stretching chords of space curves – Sallee - 1973 |
| 4 | Projective Geometry – Samuel - 1988 |
| 1 | BDD + 98 – McGraw-Hill, London - 1979 |
| 1 | Polygonal chains cannot lock in 4D. Undergraduate thesis, Smith College – Cocan - 1999 |
| 1 | A new class of stuck unknots – Toussaint - 1999 |
