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Epsilon-Unfolding Orthogonal Polyhedra.

Bibliographic Details
Main Authors:	Damian, Mirela., Flatland, Robin., O'Rourke, Joesph.
Format:	Villanova Faculty Authorship
Language:	English
Published:	2007
Online Access:	http://ezproxy.villanova.edu/login?url=https://digital.library.villanova.edu/Item/vudl:175671

Main Authors:

Damian, Mirela., Flatland, Robin., O'Rourke, Joesph.

Format:

Villanova Faculty Authorship

Language:

English

Published:

2007

Online Access:

http://ezproxy.villanova.edu/login?url=https://digital.library.villanova.edu/Item/vudl:175671

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spelling	Epsilon-Unfolding Orthogonal Polyhedra. Damian, Mirela. Flatland, Robin. O'Rourke, Joesph. An unfolding of a polyhedron is produced by cutting the surface and flattening to a single, connected, planar piece without overlap (except possibly at boundary points). It is a long unsolved problem to determine whether every polyhedron may be unfolded. Here we prove, via an algorithm, that every orthogonal polyhedron (one whose faces meet at right angles) of genus zero may be unfolded. Our cuts are not necessarily along edges of the polyhedron, but they are always parallel to polyhedron edges. For a polyhedron of n vertices, portions of the unfolding will be rectangular strips which, in the worst case, may need to be as thin as e = 1/2 (n). 2007 Villanova Faculty Authorship vudl:175671 Graphs and Combinatorics 23, June 2007, 179-194. en
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dc.description_txt_mv	An unfolding of a polyhedron is produced by cutting the surface and flattening to a single, connected, planar piece without overlap (except possibly at boundary points). It is a long unsolved problem to determine whether every polyhedron may be unfolded. Here we prove, via an algorithm, that every orthogonal polyhedron (one whose faces meet at right angles) of genus zero may be unfolded. Our cuts are not necessarily along edges of the polyhedron, but they are always parallel to polyhedron edges. For a polyhedron of n vertices, portions of the unfolding will be rectangular strips which, in the worst case, may need to be as thin as e = 1/2 (n).
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Epsilon-Unfolding Orthogonal Polyhedra.
Damian, Mirela.
Flatland, Robin.
O'Rourke, Joesph.
An unfolding of a polyhedron is produced by cutting the surface and flattening to a single, connected, planar piece without overlap (except possibly at boundary points). It is a long unsolved problem to determine whether every polyhedron may be unfolded. Here we prove, via an algorithm, that every orthogonal polyhedron (one whose faces meet at right angles) of genus zero may be unfolded. Our cuts are not necessarily along edges of the polyhedron, but they are always parallel to polyhedron edges. For a polyhedron of n vertices, portions of the unfolding will be rectangular strips which, in the worst case, may need to be as thin as e = 1/2 (n).
2007
Villanova Faculty Authorship
vudl:175671
Graphs and Combinatorics 23, June 2007, 179-194.
en

dc.title_txt_mv

Epsilon-Unfolding Orthogonal Polyhedra.

dc.creator_txt_mv

Damian, Mirela.
Flatland, Robin.
O'Rourke, Joesph.

dc.description_txt_mv

An unfolding of a polyhedron is produced by cutting the surface and flattening to a single, connected, planar piece without overlap (except possibly at boundary points). It is a long unsolved problem to determine whether every polyhedron may be unfolded. Here we prove, via an algorithm, that every orthogonal polyhedron (one whose faces meet at right angles) of genus zero may be unfolded. Our cuts are not necessarily along edges of the polyhedron, but they are always parallel to polyhedron edges. For a polyhedron of n vertices, portions of the unfolding will be rectangular strips which, in the worst case, may need to be as thin as e = 1/2 (n).

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Damian, Mirela.
Flatland, Robin.
O'Rourke, Joesph.

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Flatland, Robin.
O'Rourke, Joesph.
Epsilon-Unfolding Orthogonal Polyhedra.

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Flatland, Robin.
O'Rourke, Joesph.

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