article

Unfolding Manhattan Towers

Authors:

Mirela Damian,

Robin Flatland,

Joseph O'RourkeAuthors Info & Claims

Computational Geometry: Theory and Applications, Volume 40, Issue 2

Pages 102 - 114

https://doi.org/10.1016/j.comgeo.2007.07.003

Published: 01 July 2008 Publication History

Abstract

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 4x5x1 refinement of the vertex grid.

References

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T. Biedl, E.D. Demaine, M.L. Demaine, A. Lubiw, J. O'Rourke, M. Overmars, S. Robbins, S. Whitesides, Unfolding some classes of orthogonal polyhedra, in: Proc. 10th Canad. Conf. Comput. Geom., 1998, pp. 70--71

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Demaine, E.D., Iacono, J. and Langerman, S., Grid vertex-unfolding of orthostacks. In: LNCS, Springer.

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M. Damian, H. Meijer, Grid edge-unfolding orthostacks with orthogonally convex slabs, in: 14th Annual Fall Workshop Comput. Geom., November 2004, pp. 20--21

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E.D. Demaine, J. O'Rourke, Open problems from CCCG 2004, in: Proc. 16th Canad. Conf. Comput. Geom., 2004

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Demaine, E.D. and O'Rourke, J., A survey of folding and unfolding in computational geometry. In: Goodman, J.E., Pach, J., Welzl, E. (Eds.), Combinatorial and Computational Geometry, Cambridge University Press.

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Demaine, E.D. and O'Rourke, J., Geometric Folding Algorithms: Linkages, Origami, Polyhedra. 2007. Cambridge University Press.

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O'Rourke, J., Art Gallery Theorems and Algorithms. 1987. The International Series of Monographs on Computer Science, 1987.Oxford University Press, New York, NY.

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Ho KChang YYen H(2019)Unfolding some classes of orthogonal polyhedra of arbitrary genusJournal of Combinatorial Optimization10.1007/s10878-018-0299-137:2(482-500)Online publication date: 1-Feb-2019
https://dl.acm.org/doi/10.1007/s10878-018-0299-1
Richaume LAndres ELargeteau-Skapin GZrour R(2019)Unfolding Level 1 Menger Polycubes of Arbitrary Size With Help of Outer FacesDiscrete Geometry for Computer Imagery10.1007/978-3-030-14085-4_36(457-468)Online publication date: 26-Mar-2019
https://dl.acm.org/doi/10.1007/978-3-030-14085-4_36
Akitaya HBallinger BDamian MDemaine EDemaine MFlatland RKostitsyna IKu JLangerman SO’Rourke JUehara R(2018)Toward Unfolding Doubly Covered n-StarsDiscrete and Computational Geometry, Graphs, and Games10.1007/978-3-030-90048-9_10(122-135)Online publication date: 1-Sep-2018
https://dl.acm.org/doi/10.1007/978-3-030-90048-9_10
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Index Terms

Unfolding Manhattan Towers
1. Computing methodologies
  1. Computer graphics
    1. Shape modeling
2. Theory of computation
  1. Randomness, geometry and discrete structures
    1. Computational geometry

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cover image Computational Geometry: Theory and Applications

Computational Geometry: Theory and Applications Volume 40, Issue 2

July, 2008

86 pages

ISSN:0925-7721

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Elsevier Science Publishers B. V.

Netherlands

Publication History

Published: 01 July 2008

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Ho KChang YYen H(2019)Unfolding some classes of orthogonal polyhedra of arbitrary genusJournal of Combinatorial Optimization10.1007/s10878-018-0299-137:2(482-500)Online publication date: 1-Feb-2019
https://dl.acm.org/doi/10.1007/s10878-018-0299-1
Richaume LAndres ELargeteau-Skapin GZrour R(2019)Unfolding Level 1 Menger Polycubes of Arbitrary Size With Help of Outer FacesDiscrete Geometry for Computer Imagery10.1007/978-3-030-14085-4_36(457-468)Online publication date: 26-Mar-2019
https://dl.acm.org/doi/10.1007/978-3-030-14085-4_36
Akitaya HBallinger BDamian MDemaine EDemaine MFlatland RKostitsyna IKu JLangerman SO’Rourke JUehara R(2018)Toward Unfolding Doubly Covered n-StarsDiscrete and Computational Geometry, Graphs, and Games10.1007/978-3-030-90048-9_10(122-135)Online publication date: 1-Sep-2018
https://dl.acm.org/doi/10.1007/978-3-030-90048-9_10
Damian MDemaine EFlatland RO'rourke J(2017)Unfolding Genus-2 Orthogonal Polyhedra with Linear RefinementGraphs and Combinatorics10.1007/s00373-017-1849-533:5(1357-1379)Online publication date: 1-Sep-2017
https://dl.acm.org/doi/10.1007/s00373-017-1849-5

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Index Terms

Recommendations

Epsilon-Unfolding Orthogonal Polyhedra

Star Unfolding from a Geodesic Curve

On the development of the intersection of a plane with a polytope

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