Grid VertexUnfolding Orthogonal Polyhedra.
An edgeunfolding 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 vertexunfolding permits faces in th...
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2008

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Grid VertexUnfolding Orthogonal Polyhedra. Damian, Mirela. Flatland, Robin. O'Rourke Joseph. An edgeunfolding 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 vertexunfolding permits 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 vertexunfolding. (There are orthogonal polyhedra that cannot be vertexunfolded, so some type of “gridding” of the faces is necessary.) For any orthogonal polyhedron P with n vertices, we describe an algorithm that vertexunfolds P in O(n2) time. Enroute to explaining this algorithm, we present a simpler vertexunfolding algorithm that requires a 3 × 1 refinement of the vertex grid. 2008 Villanova Faculty Authorship vudl:175677 Discrete and Computational Geometry 39(13), March 2008, 213238. en 
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Grid VertexUnfolding Orthogonal Polyhedra. 
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Damian, Mirela. Flatland, Robin. O'Rourke Joseph. 
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An edgeunfolding 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 vertexunfolding
permits 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 vertexunfolding. (There are
orthogonal polyhedra that cannot be vertexunfolded, so some type of “gridding” of the faces
is necessary.) For any orthogonal polyhedron P with n vertices, we describe an algorithm that
vertexunfolds P in O(n2) time. Enroute to explaining this algorithm, we present a simpler
vertexunfolding algorithm that requires a 3 × 1 refinement of the vertex grid. 
dc.date_txt_mv 
2008 
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Villanova Faculty Authorship 
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vudl:175677 
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Discrete and Computational Geometry 39(13), March 2008, 213238. 
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en 
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Damian, Mirela. Flatland, Robin. O'Rourke Joseph. 
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Damian, Mirela. Flatland, Robin. O'Rourke Joseph. Grid VertexUnfolding Orthogonal Polyhedra. 
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Damian, Mirela. Flatland, Robin. O'Rourke Joseph. 
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Discrete and Computational Geometry 39(13), March 2008, 213238. 
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Damian, Mirela. 
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2008 
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Grid VertexUnfolding Orthogonal Polyhedra. 
description 
An edgeunfolding 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 vertexunfolding
permits 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 vertexunfolding. (There are
orthogonal polyhedra that cannot be vertexunfolded, so some type of “gridding” of the faces
is necessary.) For any orthogonal polyhedron P with n vertices, we describe an algorithm that
vertexunfolds P in O(n2) time. Enroute to explaining this algorithm, we present a simpler
vertexunfolding algorithm that requires a 3 × 1 refinement of the vertex grid. 
title 
Grid VertexUnfolding Orthogonal Polyhedra. 
title_full 
Grid VertexUnfolding Orthogonal Polyhedra. 
title_fullStr 
Grid VertexUnfolding Orthogonal Polyhedra. 
title_full_unstemmed 
Grid VertexUnfolding Orthogonal Polyhedra. 
title_short 
Grid VertexUnfolding Orthogonal Polyhedra. 
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grid vertexunfolding orthogonal polyhedra. 
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2008 
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English 
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