Folding and punching paper

Yasuhiko Asao, Erik D. Demaine, Martin L. Demaine, Hideaki Hosaka, Akitoshi Kawamura, Tomohiro Tachi, Kazune Takahashi

Research output: Contribution to journalArticle

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.

Original languageEnglish
Pages (from-to)590-600
Number of pages11
JournalJournal of information processing
Volume25
DOIs
Publication statusPublished - Aug 2017

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All Science Journal Classification (ASJC) codes

  • Computer Science(all)

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Asao, Y., Demaine, E. D., Demaine, M. L., Hosaka, H., Kawamura, A., Tachi, T., & Takahashi, K. (2017). Folding and punching paper. Journal of information processing, 25, 590-600. https://doi.org/10.2197/ipsjjip.25.590

Folding and punching paper. / Asao, Yasuhiko; Demaine, Erik D.; Demaine, Martin L.; Hosaka, Hideaki; Kawamura, Akitoshi; Tachi, Tomohiro; Takahashi, Kazune.

In: Journal of information processing, Vol. 25, 08.2017, p. 590-600.

Research output: Contribution to journalArticle

Asao, Y, Demaine, ED, Demaine, ML, Hosaka, H, Kawamura, A, Tachi, T & Takahashi, K 2017, 'Folding and punching paper', Journal of information processing, vol. 25, pp. 590-600. https://doi.org/10.2197/ipsjjip.25.590
Asao Y, Demaine ED, Demaine ML, Hosaka H, Kawamura A, Tachi T et al. Folding and punching paper. Journal of information processing. 2017 Aug;25:590-600. https://doi.org/10.2197/ipsjjip.25.590
Asao, Yasuhiko ; Demaine, Erik D. ; Demaine, Martin L. ; Hosaka, Hideaki ; Kawamura, Akitoshi ; Tachi, Tomohiro ; Takahashi, Kazune. / Folding and punching paper. In: Journal of information processing. 2017 ; Vol. 25. pp. 590-600.
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