Edge-unfolding nested polyhedral bands
نویسندگان
چکیده
منابع مشابه
Edge-unfolding nested polyhedral bands
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 a...
متن کاملAuthor's Personal Copy Edge-unfolding Nested Polyhedral Bands
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 a...
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A band is defined as 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. An unfolding of a given band is obtained by cutting along exactly one edge and placing all faces of the band into the plane, without causing intersections. We prove that for a specific type of band there ex...
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This note which can be viewed as a complement to [9], presents a self-contained overview of basic properties of nested complexes and their two dual polyhedral realizations: as complete simplicial fans, and as simple polytopes. Most of the results are not new; our aim is to bring into focus a striking similarity between nested complexes and associated fans and polytopes on one side, and cluster ...
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It is shown that a convex medial axis polyhedron has two distinct edge unfoldings: cuttings along edges that unfold the surface to a simple planar polygon. One of these unfoldings is a generalization of the point source unfolding, and is easily established to avoid overlap. The other is a novel unfolding that requires a more complex argument to establish nonoverlap, and might generalize.
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ژورنال
عنوان ژورنال: Computational Geometry
سال: 2008
ISSN: 0925-7721
DOI: 10.1016/j.comgeo.2007.05.009