Paper by Erik D. Demaine
- 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.
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
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.
- This paper is also available from ScienceDirect.
- The paper is 19 pages.
- The paper is available in PostScript (503k), gzipped PostScript (187k), and PDF (250k).
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- Related papers:
- BandUnfolding_CCCG2004 (Unfolding Polyhedral Bands)
See also other papers by Erik Demaine.
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