Grid vertex-unfolding orthostacks

Erik D. Demaine; John Iacono; Stefan Langerman

doi:10.1142/S0218195910003281

Grid vertex-unfolding orthostacks

Erik D. Demaine, John Iacono, Stefan Langerman

Research output: Contribution to journal › Article › peer-review

Abstract

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 containing a vertex of the orthostack. We prove the existence of a vertex unfolding using only such cuts.

Original language	English (US)
Pages (from-to)	245-254
Number of pages	10
Journal	International Journal of Computational Geometry and Applications
Volume	20
Issue number	3
DOIs	https://doi.org/10.1142/S0218195910003281
State	Published - Jun 2010

Keywords

Edge unfolding
cutting
folding
orthogonal polyhedra

ASJC Scopus subject areas

Theoretical Computer Science
Geometry and Topology
Computational Theory and Mathematics
Computational Mathematics
Applied Mathematics

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10.1142/S0218195910003281

Cite this

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title = "Grid vertex-unfolding orthostacks",

abstract = "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 containing a vertex of the orthostack. We prove the existence of a vertex unfolding using only such cuts.",

keywords = "Edge unfolding, cutting, folding, orthogonal polyhedra",

author = "Demaine, {Erik D.} and John Iacono and Stefan Langerman",

note = "Funding Information: pages 76–82. †Research supported in part by NSF grants CCF-0347776, OISE-0334653, and CCF-0430849, and by DOE grant DE-FG02-04ER25647. ‡Research supported in part by NSF grants OISE-0334653 and CCF-0430849. §Ma{\^i}tre de recherches du F.R.S-FNRS.",

year = "2010",

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doi = "10.1142/S0218195910003281",

language = "English (US)",

volume = "20",

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T1 - Grid vertex-unfolding orthostacks

AU - Demaine, Erik D.

AU - Iacono, John

AU - Langerman, Stefan

N1 - Funding Information: pages 76–82. †Research supported in part by NSF grants CCF-0347776, OISE-0334653, and CCF-0430849, and by DOE grant DE-FG02-04ER25647. ‡Research supported in part by NSF grants OISE-0334653 and CCF-0430849. §Maître de recherches du F.R.S-FNRS.

PY - 2010/6

Y1 - 2010/6

N2 - 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 containing a vertex of the orthostack. We prove the existence of a vertex unfolding using only such cuts.

AB - 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 containing a vertex of the orthostack. We prove the existence of a vertex unfolding using only such cuts.

KW - Edge unfolding

KW - cutting

KW - folding

KW - orthogonal polyhedra

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JO - International Journal of Computational Geometry and Applications

JF - International Journal of Computational Geometry and Applications

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ER -

Grid vertex-unfolding orthostacks

Abstract

Keywords

ASJC Scopus subject areas

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