Abstract
An algorithm was presented in [BDD + 98] for unfolding orthostacks into one piece without overlap by using arbitrary cuts along the surface. It was conjectured that orthostacks could be unfolded using cuts that lie in a plane orthogonal to a coordinate axis and containing a vertex of the orthostack. We prove the existence of a vertex-unfolding using only such cuts.
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References
Biedl, T., Demaine, E., Demaine, M., Lubiw, A., Overmars, M., O’Rourke, J., Robbins, S., Whitesides, S.: Unfolding some classes of orthogonal polyhedra. In: Proceedings of the 10th Canadian Conference on Computational Geometry, Montréal, Canada (August 1998), http://cgm.cs.mcgill.ca/cccg98/proceedings/cccg98-biedl-unfolding.ps.gz
Demaine, E.D., Eppstein, D., Erickson, J., Hart, G.W., O’Rourke, J.: Vertex-unfolding of simplicial manifolds. In: Proceedings of the 18th Annual ACM Symposium on Computational Geometry, Barcelona, Spain, June 2002, pp. 237–243 (2002)
Demaine, E.D., Eppstein, D., Erickson, J., Hart, G.W., O’Rourke, J.: Vertex-unfolding of simplicial manifolds. In: Discrete Geometry: In Honor of W. Kuperberg’s 60th Birthday, pp. 215–228. Marcer Dekker Inc., New York (2003)
Demaine, E.D.: Folding and unfolding linkages, paper, and polyhedra. In: Akiyama, J., Kano, M., Urabe, M. (eds.) JCDCG 2000. LNCS, vol. 2098, pp. 113–124. Springer, Heidelberg (2001)
Demaine, E.D., O’Rourke, J.: A survey of folding and unfolding in computational geometry. In: Goodman, J.E., Pach, J., Welzl, E. (eds.) Discrete and Computational Geometry. Mathematical Sciences Research Institute Publications, Cambridge University Press, Cambridge (2005) (to appear)
O’Rourke, J.: Folding and unfolding in computational geometry. In: Akiyama, J., Kano, M., Urabe, M. (eds.) JCDCG 1998. LNCS, vol. 1763, pp. 258–266. Springer, Heidelberg (2000)
Shephard, G.C.: Convex polytopes with convex nets. Mathematical Proceedings of the Cambridge Philosophical Society 78, 389–403 (1975)
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Demaine, E.D., Iacono, J., Langerman, S. (2005). Grid Vertex-Unfolding Orthostacks. In: Akiyama, J., Kano, M., Tan, X. (eds) Discrete and Computational Geometry. JCDCG 2004. Lecture Notes in Computer Science, vol 3742. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11589440_8
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DOI: https://doi.org/10.1007/11589440_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-30467-8
Online ISBN: 978-3-540-32089-0
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