Folding and Punching Paper
Name
paper.pdf
Description
Accepted version
Size
6.26 MB
Format
Adobe PDF
Checksum (MD5)
b2cbcf06f6686afceb72bd5ecd574747
Author(s)
Asao, Yasuhiko
Demaine, Erik D
Demaine, Martin L
Hosaka, Hideaki
Kawamura, Akitoshi
Tachi, Tomohiro
Takahashi, Kazune
Date Issued
August 2017
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
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
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.2197/ipsjjip.25.590
