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A Geometric Study of V-style Pop-ups: Theories and Algorithms

Xian-Ying Li Tsinghua University Tao Ju Washington University in St. Louis

Geometric Modeling and Processing mathscidoc:1608.16041

ACM Transactions on Graphics , 30, (4), 111, 2011.8
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 popuppability of the results.
pop-up, computer art, geometric modeling
[ Download ] [ 2016-08-19 21:55:05 uploaded by xianying ] [ 895 downloads ] [ 0 comments ] [ Cited by 32 ] 
@inproceedings{xian-ying2011a,
  title={A Geometric Study of V-style Pop-ups: Theories and Algorithms},
  author={Xian-Ying Li, and Tao Ju},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160819215505923003310},
  booktitle={ACM Transactions on Graphics },
  volume={30},
  number={4},
  pages={111},
  year={2011},
}
Xian-Ying Li, and Tao Ju. A Geometric Study of V-style Pop-ups: Theories and Algorithms. 2011. Vol. 30. In ACM Transactions on Graphics . pp.111. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160819215505923003310.
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