A geometric study of v-style pop-ups
- 25 July 2011
- journal article
- research article
- Published by Association for Computing Machinery (ACM) in ACM Transactions on Graphics
- Vol. 30 (4), 1-10
- https://doi.org/10.1145/2010324.1964993
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.Keywords
Funding Information
- Ministry of Science and Technology of the People's Republic of China (2011CB302203)
- Division of Information and Intelligent Systems (IIS-0846072)
- National Natural Science Foundation of China (U0735001)
This publication has 10 references indexed in Scilit:
- PopupACM Transactions on Graphics, 2010
- An Interface for Assisting the Design and Production of Pop-Up CardLecture Notes in Computer Science, 2009
- Project OrigamiPublished by Taylor & Francis Ltd ,2006
- Robust repair of polygonal modelsACM Transactions on Graphics, 2004
- Computer Aided Design for 180-degree Flat Fold Origamic Architecture with Lattice-type Cross SectionsJournal of Graphic Science of Japan, 2003
- Interactive pop-up card design. 1IEEE Computer Graphics and Applications, 2002
- Interactive pop-up card design. 2IEEE Computer Graphics and Applications, 2002
- Modelling the folding of paper into three dimensions using affine transformationsLinear Algebra and its Applications, 2002
- Mathematical modelling and simulation of pop-up booksComputers & Graphics, 1996
- Curvature and Creases: A Primer on PaperIEEE Transactions on Computers, 1976