Computational Complexity of a Pop-up Book∗

The Complexity of a Pop-Up Book

Origami is the centuries-old art of folding paper, and recently, it is investigated as science. In this paper, another hundreds-old art of folding paper, a pop-up book, is studied. A model for the pop-up book design problem is given, and its complexity is investigated. We show that both of the opening book problem and the closing book problem are NP-hard.

Oral Criticism/ Review of the book Form the Whisper of Tradition to the Charm of the Pop: An Investigation in Contemporary Iranian Music by Alireza Miralinaghi and Arvin SedaghatKish

Pop-up book MEMS

We present a design methodology and manufacturing process for the construction of articulated three-dimensional microstructures with features on the micron to centimeter scale. Flexure mechanisms and assembly folds result from the bulk machining and lamination of alternating rigid and compliant layers, similar to rigid-flex printed circuit board construction. Pop-up books and other forms of pap...

Pop - up book MEMS

We present a design methodology and manufacturing process for the construction of articulated three-dimensional microstructures with features on the micron to centimeter scale. Flexure mechanisms and assembly folds result from the bulk machining and lamination of alternating rigid and compliant layers, similar to rigid-flex printed circuit board construction. Pop-up books and other forms of pap...

Algorithms for Designing Pop-Up Cards

We prove that every simple polygon can be made as a (2D) pop-up card/book that opens to any desired angle between 0 and 360◦. More precisely, given a simple polygon attached to the two walls of the open pop-up, our polynomial-time algorithm subdivides the polygon into a single-degree-of-freedom linkage structure, such that closing the pop-up flattens the linkage without collision. This result s...