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41st Annual Symposium on Foundations of Computer Science
Straightening polygonal arcs and convexifying polygonal cycles
Redondo Beach, California
November 12November 14
ISBN: 0769508502
ASCII Text  x  
R. Connelly, E.D. Demaine, G. Rote, "Straightening polygonal arcs and convexifying polygonal cycles," 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, pp. 432, 41st Annual Symposium on Foundations of Computer Science, 2000.  
BibTex  x  
@article{ 10.1109/SFCS.2000.892131, author = {R. Connelly and E.D. Demaine and G. Rote}, title = {Straightening polygonal arcs and convexifying polygonal cycles}, journal ={2013 IEEE 54th Annual Symposium on Foundations of Computer Science}, volume = {0}, year = {2000}, issn = {02725428}, pages = {432}, doi = {http://doi.ieeecomputersociety.org/10.1109/SFCS.2000.892131}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  CONF JO  2013 IEEE 54th Annual Symposium on Foundations of Computer Science TI  Straightening polygonal arcs and convexifying polygonal cycles SN  02725428 SP EP A1  R. Connelly, A1  E.D. Demaine, A1  G. Rote, PY  2000 KW  computational geometry; graph theory; polygonal arc straightening; polygonal cycle convexifying; planar linkage; polygonal chains; convex cycles; piecewisedifferentiable motion; symmetry; rule conjecture; computational geometry; graph theory VL  0 JA  2013 IEEE 54th Annual Symposium on Foundations of Computer Science ER   
Consider a planar linkage, consisting of disjoint polygonal arcs and cycles of rigid bars joined at incident endpoints (polygonal chains), with the property that no cycle surrounds another arc or cycle. We prove that the linkage can be continuously moved so that the arcs become straight, the cycles become convex, and no bars cross while preserving the bar lengths. Furthermore, our motion is piecewisedifferentiable, does not decrease the distance between any pair of vertices, and preserves any symmetry present in the initial configuration. In particular this result settles the wellstudied carpenter's rule conjecture.
Index Terms:
computational geometry; graph theory; polygonal arc straightening; polygonal cycle convexifying; planar linkage; polygonal chains; convex cycles; piecewisedifferentiable motion; symmetry; rule conjecture; computational geometry; graph theory
Citation:
R. Connelly, E.D. Demaine, G. Rote, "Straightening polygonal arcs and convexifying polygonal cycles," focs, pp.432, 41st Annual Symposium on Foundations of Computer Science, 2000
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