Edge-unfolding nested polyhedral bands
Edge-unfolding nested polyhedral bands
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边缘展开嵌套多面体带
DOI：
10.1016/j.comgeo.2007.05.009
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发表时间：
2008
期刊：
影响因子：
--
通讯作者：
G. Toussaint
中科院分区：
文献类型：
--
作者：
G. Aloupis;E. Demaine;S. Langerman;Pat Morin;J. O'Rourke;I. Streinu;G. Toussaint
带是一个凸多面体的表面与两个平行平面之间的空间的交点，只要这个空间不包含多面体的任何顶点。平面和多面体的交点产生两个凸多边形。如果其中一个多边形在与平行平面正交的投影中包含另一个多边形，则该带是嵌套的。我们证明了所有嵌套带都可以展开，通过沿着一条边切割并连续折叠，将带的所有面放置在一个平面上，没有交集。
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.