Paper by Erik D. Demaine

Reference:

Greg Aloupis, Erik D. Demaine, Stefan Langerman, Pat Morin, Joseph O'Rourke, Ileana Streinu, and Godfried Toussaint, “Edge-Unfolding Nested Polyhedral Bands”, Computational Geometry: Theory and Applications, volume 39, number 1, January 2008, pages 30–42. Special issue of selected papers from the 16th Canadian Conference on Computational Geometry, 2004.

BibTeX

@Article{BandUnfolding_CGTA,
  AUTHOR        = {Greg Aloupis and Erik D. Demaine and Stefan Langerman and
                   Pat Morin and Joseph O'Rourke and Ileana Streinu and
                   Godfried Toussaint},
  TITLE         = {Edge-Unfolding Nested Polyhedral Bands},
  JOURNAL       = {Computational Geometry: Theory and Applications},
  journalurl    = {https://www.sciencedirect.com/journal/computational-geometry},
  VOLUME        = 39,
  NUMBER        = 1,
  MONTH         = {January},
  YEAR          = 2008,
  PAGES         = {30--42},
  NOTE          = {Special issue of selected papers from the 16th Canadian
                   Conference on Computational Geometry, 2004.},

  doi           = {https://dx.doi.org/10.1016/J.COMGEO.2007.05.009},
  dblp          = {https://dblp.org/rec/journals/comgeo/AloupisDLMOST08},
  comments      = {This paper is also available from <A HREF="http://dx.doi.org/10.1016/j.comgeo.2007.05.009">ScienceDirect</A>.},
  papers        = {BandUnfolding_CCCG2004},
  length        = {19 pages},
}

Abstract:

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.

Comments:

This paper is also available from ScienceDirect.

Length:

The paper is 19 pages.

Availability:

The paper is available in PostScript (503k), gzipped PostScript (187k), and PDF (250k).

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Related papers:

BandUnfolding_CCCG2004 (Unfolding Polyhedral Bands)