A geometric study of v-style pop-ups

Li, Xian-Ying, Ju, Tao, Gu, Yan and Hu, Shi-Min ORCID: https://orcid.org/0000-0001-7507-6542 2011. A geometric study of v-style pop-ups. ACM Transactions on Graphics 30 (4) , 98. 10.1145/2010324.1964993

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Abstract

Pop-up books are a fascinating form of paper art with intriguing geometric properties. In this paper, we present a systematic study of a simple but common class of pop-ups consisting of patches falling into four parallel groups, which we call v-style pop-ups. We give sufficient conditions for a v-style paper structure to be pop-uppable. That is, it can be closed flat while maintaining the rigidity of the patches, the closing and opening do not need extra force besides holding two patches and are free of intersections, and the closed paper is contained within the page border. These conditions allow us to identify novel mechanisms for making pop-ups. Based on the theory and mechanisms, we developed an interactive tool for designing v-style pop-ups and an automated construction algorithm from a given geometry, both of which guaranteeing the pop-uppability of the results.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Computer Science & Informatics
Subjects:	Q Science > QA Mathematics > QA76 Computer software T Technology > T Technology (General)
Publisher:	ACM
ISSN:	0730-0301
Date of First Compliant Deposit:	30 March 2016
Last Modified:	06 May 2023 13:05
URI:	https://orca.cardiff.ac.uk/id/eprint/45698

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