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Grid vertexunfolding orthogonal polyhedra
 IN PROC. 23RD SYMPOS. THEORET. ASPECTS COMPUT. SCI., LECTURE NOTES COMPUT. SCI
, 2006
"... 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 t ..."
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Cited by 4 (1 self)
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in the net to be connected at single vertices, not necessarily along edges. We show that any orthogonal polyhedron 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
Grid vertexunfolding orthostacks
 International Journal of Computational Geometry and Applications
"... Communicated by Godfried Toussaint Biedl et al. 1 presented an algorithm for unfolding orthostacks into one piece without overlap by using arbitrary cuts along the surface. They conjectured that orthostacks could be unfolded using cuts that lie in a plane orthogonal to a coordinate axis and containi ..."
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Cited by 7 (1 self)
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Communicated by Godfried Toussaint Biedl et al. 1 presented an algorithm for unfolding orthostacks into one piece without overlap by using arbitrary cuts along the surface. They conjectured that orthostacks could be unfolded using cuts that lie in a plane orthogonal to a coordinate axis
Unfolding Orthogonal Polyhedra
 CONTEMPORARY MATHEMATICS
"... Recent progress is described on the unsolved problem of unfolding the surface of an orthogonal polyhedron to a single nonoverlapping planar piece by cutting edges of the polyhedron. Although this is in general not possible, partitioning the faces into the natural vertexgrid may render it always a ..."
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Cited by 5 (1 self)
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Recent progress is described on the unsolved problem of unfolding the surface of an orthogonal polyhedron to a single nonoverlapping planar piece by cutting edges of the polyhedron. Although this is in general not possible, partitioning the faces into the natural vertexgrid may render it always
Unfolding Orthogonal Polyhedra with Quadratic Refinement: The DeltaUnfolding Algorithm
 GRAPHS AND COMBINATORICS
"... We show that every orthogonal polyhedron homeomorphic to a sphere can be unfolded without overlap while using only polynomially many (orthogonal) cuts. By contrast, the best previous such result used exponentially many cuts. More precisely, given an orthogonal polyhedron with n vertices, the algori ..."
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Cited by 1 (1 self)
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We show that every orthogonal polyhedron homeomorphic to a sphere can be unfolded without overlap while using only polynomially many (orthogonal) cuts. By contrast, the best previous such result used exponentially many cuts. More precisely, given an orthogonal polyhedron with n vertices
Unfolding Orthogonal Terrains
, 2007
"... It is shown that every orthogonal terrain, i.e., an orthogonal (rightangled) polyhedron based on a rectangle that meets every vertical line in a segment, has a grid unfolding: its surface may be unfolded to a single nonoverlapping piece by cutting along grid edges defined by coordinate planes throu ..."
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It is shown that every orthogonal terrain, i.e., an orthogonal (rightangled) polyhedron based on a rectangle that meets every vertical line in a segment, has a grid unfolding: its surface may be unfolded to a single nonoverlapping piece by cutting along grid edges defined by coordinate planes
Unfolding Orthogonal Terrains
, 707
"... It is shown that every orthogonal terrain, i.e., an orthogonal (rightangled) polyhedron based on a rectangle that meets every vertical line in a segment, has a grid unfolding: its surface may be unfolded to a single nonoverlapping piece by cutting along grid edges defined by coordinate planes throu ..."
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It is shown that every orthogonal terrain, i.e., an orthogonal (rightangled) polyhedron based on a rectangle that meets every vertical line in a segment, has a grid unfolding: its surface may be unfolded to a single nonoverlapping piece by cutting along grid edges defined by coordinate planes
Unfolding Orthogonal Terrains
, 707
"... It is shown that every orthogonal terrain, i.e., an orthogonal (rightangled) polyhedron based on a rectangle that meets every vertical line in a segment, has a grid unfolding: its surface may be unfolded to a single nonoverlapping piece by cutting along grid edges defined by coordinate planes throu ..."
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It is shown that every orthogonal terrain, i.e., an orthogonal (rightangled) polyhedron based on a rectangle that meets every vertical line in a segment, has a grid unfolding: its surface may be unfolded to a single nonoverlapping piece by cutting along grid edges defined by coordinate planes
Unfolding Orthogonal Terrains
, 707
"... It is shown that every orthogonal terrain, i.e., an orthogonal (rightangled) polyhedron based on a rectangle that meets every vertical line in a segment, has a grid unfolding: its surface may be unfolded to a single nonoverlapping piece by cutting along grid edges defined by coordinate planes throu ..."
Abstract
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It is shown that every orthogonal terrain, i.e., an orthogonal (rightangled) polyhedron based on a rectangle that meets every vertical line in a segment, has a grid unfolding: its surface may be unfolded to a single nonoverlapping piece by cutting along grid edges defined by coordinate planes
Unfolding Orthogonal Terrains
, 707
"... It is shown that every orthogonal terrain, i.e., an orthogonal (rightangled) polyhedron based on a rectangle that meets every vertical line in a segment, has a grid unfolding: its surface may be unfolded to a single nonoverlapping piece by cutting along grid edges defined by coordinate planes throu ..."
Abstract
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It is shown that every orthogonal terrain, i.e., an orthogonal (rightangled) polyhedron based on a rectangle that meets every vertical line in a segment, has a grid unfolding: its surface may be unfolded to a single nonoverlapping piece by cutting along grid edges defined by coordinate planes
Unfolding Manhattan Towers
, 2007
"... We provide an algorithm for unfolding the surface of any orthogonal polyhedron that falls into a particular shape class we call Manhattan Towers, to a nonoverlapping planar orthogonal polygon. The algorithm cuts along edges of a 4 × 5 × 1 refinement of the vertex grid. ..."
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Cited by 8 (4 self)
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We provide an algorithm for unfolding the surface of any orthogonal polyhedron that falls into a particular shape class we call Manhattan Towers, to a nonoverlapping planar orthogonal polygon. The algorithm cuts along edges of a 4 × 5 × 1 refinement of the vertex grid.
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