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Folding and Punching Paper

Author(s)
Asao, Yasuhiko; Demaine, Erik D; Demaine, Martin L; Hosaka, Hideaki; Kawamura, Akitoshi; Tachi, Tomohiro; Takahashi, Kazune; ... Show more Show less
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Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/
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Abstract
We show how to fold a piece of paper and punch one hole so as to produce any desired pattern of holes. Given n points on a piece of paper (finite polygon or infinite plane), we give algorithms to fold the paper flat so that those n points and no other points of paper map to a common location, so that punching one hole and unfolding produces exactly the desired pattern of holes. Furthermore, we can forbid creases from passing through the points (allowing noncircular hole punches). Our solutions use relatively few creases (in some cases, polynomially many), and can be expressed as a linear sequence of folding steps of complexity O(1)-a generalization of simple folds which we introduce. Keywords: origami; fold-and-punch problem; fold-and-cut problem; folding complexity; flat folding
Date issued
2017-08
URI
https://hdl.handle.net/1721.1/124552
Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Journal
Journal of Information Processing
Publisher
Information Processing Society of Japan
Citation
Asao, Yasuhiko et al. "Folding and Punching Paper." Journal of Information Processing 25 (2017): 590-600 © 2017 Information Processing Society of Japan.
Version: Author's final manuscript
ISSN
1882-6652

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