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Grid Vertex-Unfolding Orthostacks

  • Erik D. Demaine
  • John Iacono
  • Stefan Langerman
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3742)

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.

Keywords

Computational Geometry Middle Phase Polyhedral Complex Planar Slice Polyhedron Vertex 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [BDD+98]
    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
  2. [DEE+02]
    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)Google Scholar
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    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)Google Scholar
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Erik D. Demaine
    • 1
  • John Iacono
    • 2
  • Stefan Langerman
    • 3
  1. 1.MIT Computer Science and Artificial Intelligence LaboratoryCambridgeUSA
  2. 2.Department of Computer and Information SciencePolytechnic University, 5 MetroTech CenterBrooklynUSA
  3. 3.Département d’informatiqueUniversité Libre de Bruxelles, ULBBrusselsBelgium

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