TY - JOUR
T1 - Edge-unfolding nested polyhedral bands
AU - Aloupis, Greg
AU - Demaine, Erik D.
AU - Langerman, Stefan
AU - Morin, Pat
AU - O'Rourke, Joseph
AU - Streinu, Ileana
AU - Toussaint, Godfried
N1 - Funding Information:
✩ A preliminary version of this paper appeared in Proceedings of the 16th Canadian Conference on Computational Geometry, August 2004, pp. 60–63. * Corresponding author. E-mail addresses: [email protected] (G. Aloupis), [email protected] (E.D. Demaine), [email protected] (S. Langerman), [email protected] (P. Morin), [email protected] (J. O’Rourke), [email protected] (I. Streinu), [email protected] (G. Toussaint). 1 Supported in part by NSERC. 2 Supported in part by NSF CAREER award CCF-0347776 and DOE grant DE-FG02-04ER25647. 3 Chercheur qualifié du FNRS. 4 Supported in part by NSF grant DUE-0123154. 5 Supported in part by NSF grant CCF-0430990. 6 Posed by E. Demaine, M. Demaine, A. Lubiw, and J. O’Rourke, 1998.
PY - 2008/1
Y1 - 2008/1
N2 - A band is the intersection of the surface of a convex polyhedron with the space between two parallel planes, as long as this space does not contain any vertices of the polyhedron. The intersection of the planes and the polyhedron produces two convex polygons. If one of these polygons contains the other in the projection orthogonal to the parallel planes, then the band is nested. We prove that all nested bands can be unfolded, by cutting along exactly one edge and folding continuously to place all faces of the band into a plane, without intersection.
AB - A band is the intersection of the surface of a convex polyhedron with the space between two parallel planes, as long as this space does not contain any vertices of the polyhedron. The intersection of the planes and the polyhedron produces two convex polygons. If one of these polygons contains the other in the projection orthogonal to the parallel planes, then the band is nested. We prove that all nested bands can be unfolded, by cutting along exactly one edge and folding continuously to place all faces of the band into a plane, without intersection.
KW - Folding
KW - Polyhedra
KW - Slice curves
UR - http://www.scopus.com/inward/record.url?scp=84867944320&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84867944320&partnerID=8YFLogxK
U2 - 10.1016/j.comgeo.2007.05.009
DO - 10.1016/j.comgeo.2007.05.009
M3 - Article
AN - SCOPUS:84867944320
SN - 0925-7721
VL - 39
SP - 30
EP - 42
JO - Computational Geometry: Theory and Applications
JF - Computational Geometry: Theory and Applications
IS - 1
ER -