Origami 4 2009
DOI: 10.1201/b10653-30
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Computational Origami System Eos

Abstract: Origami is the centuries-old art of folding paper, and recently, it is investigated as computer science: Given an origami with creases, the problem to determine if it can be flat after folding all creases is NP-hard. Another hundreds-old art of folding paper is a pop-up book. A model for the pop-up book design problem is given, and its computational complexity is investigated. We show that both of the opening book problem and the closing book problem are NP-hard.

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Cited by 10 publications
(10 citation statements)
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“…They also developed an interactive tool to convert a 3D model to a v-style paper pop-up. Research on the geometric conditions for the validity of paper pop-up is scarce, primarily because determining the foldability of a general pop-up is NP-hard [22].…”
Section: Computational Pop-upsmentioning
confidence: 99%
“…They also developed an interactive tool to convert a 3D model to a v-style paper pop-up. Research on the geometric conditions for the validity of paper pop-up is scarce, primarily because determining the foldability of a general pop-up is NP-hard [22].…”
Section: Computational Pop-upsmentioning
confidence: 99%
“…However, this condition is not automatically guaranteed by their system, and hence needs to be resolved by the user in a trial-and-failure manner. Note that, in general, deciding whether a given pop-up craft can be opened or closed is a NP-hard problem [Uehara and Teramoto 2006]. In our work, we proposed a sufficient condition that the layout can erect in a stable manner as the paper opens, and further provides an automatic algorithm that guarantees the satisfaction of the condition in the output.…”
Section: Related Workmentioning
confidence: 99%
“…However, this technique has its own drawbacks. The folding process occurs in a single step, which restricts possible geometries [16], and requiring substantial design time and skill to achieve the appropriate folding patterns. It also requires extra scaffold material, extra joints for out-ofplane features, and an additional fixing step to lock pop-up joints into place.…”
Section: Introductionmentioning
confidence: 99%