Folding and Punching Paper
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 tha...
| Main Authors: | , , , , , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Information Processing Society of Japan
2020
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| Online Access: | https://hdl.handle.net/1721.1/124552 |
| _version_ | 1811075557747589120 |
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| author | Asao, Yasuhiko Demaine, Erik D Demaine, Martin L Hosaka, Hideaki Kawamura, Akitoshi Tachi, Tomohiro Takahashi, Kazune |
| author2 | Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory |
| author_facet | Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory Asao, Yasuhiko Demaine, Erik D Demaine, Martin L Hosaka, Hideaki Kawamura, Akitoshi Tachi, Tomohiro Takahashi, Kazune |
| author_sort | Asao, Yasuhiko |
| collection | MIT |
| description | 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 |
| first_indexed | 2024-09-23T10:08:09Z |
| format | Article |
| id | mit-1721.1/124552 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T10:08:09Z |
| publishDate | 2020 |
| publisher | Information Processing Society of Japan |
| record_format | dspace |
| spelling | mit-1721.1/1245522022-09-26T15:58:53Z Folding and Punching Paper Asao, Yasuhiko Demaine, Erik D Demaine, Martin L Hosaka, Hideaki Kawamura, Akitoshi Tachi, Tomohiro Takahashi, Kazune Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory 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 2020-04-09T12:57:31Z 2020-04-09T12:57:31Z 2017-08 2016-11 2019-06-17T20:57:20Z Article http://purl.org/eprint/type/JournalArticle 1882-6652 https://hdl.handle.net/1721.1/124552 Asao, Yasuhiko et al. "Folding and Punching Paper." Journal of Information Processing 25 (2017): 590-600 © 2017 Information Processing Society of Japan. en http://dx.doi.org/10.2197/ipsjjip.25.590 Journal of Information Processing Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Information Processing Society of Japan MIT web domain |
| spellingShingle | Asao, Yasuhiko Demaine, Erik D Demaine, Martin L Hosaka, Hideaki Kawamura, Akitoshi Tachi, Tomohiro Takahashi, Kazune Folding and Punching Paper |
| title | Folding and Punching Paper |
| title_full | Folding and Punching Paper |
| title_fullStr | Folding and Punching Paper |
| title_full_unstemmed | Folding and Punching Paper |
| title_short | Folding and Punching Paper |
| title_sort | folding and punching paper |
| url | https://hdl.handle.net/1721.1/124552 |
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