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- W1521569448 abstract "An edge-unfolding of a polyhedron is produced by cutting along edges and flattening the faces to a net, a connected planar piece with no overlaps. A grid unfolding allows additional cuts along grid edges induced by coordinate planes passing through every vertex. A vertex-unfolding allows faces in the net to be connected at single vertices, not necessarily along edges. We show that any orthogonal polyhedra of genus zero has a grid vertex-unfolding. (There are orthogonal polyhedra that cannot be vertex-unfolded, so some type of “gridding” of the faces is necessary.) For any orthogonal polyhedron P with n vertices, we describe an algorithm that vertex-unfolds P in O(n 2) time. Enroute to explaining this algorithm, we present a simpler vertex-unfolding algorithm that requires a 3×1×1 refinement of the vertex grid." @default.
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- W1521569448 date "2007-11-27" @default.
- W1521569448 modified "2023-10-06" @default.
- W1521569448 title "Grid Vertex-Unfolding Orthogonal Polyhedra" @default.
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- W1521569448 doi "https://doi.org/10.1007/s00454-007-9043-9" @default.
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