Algorithms for Designing Pop-Up Cards
Name
Demaine_Algorithms for.pdf
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1.21 MB
Format
Adobe PDF
Checksum (MD5)
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Author(s)
Abel, Zachary Ryan
Demaine, Erik D.
Demaine, Martin L.
Eisenstat, Sarah Charmian
Lubiw, Anna
Schulz, Andre
Souvaine, Diane L.
Viglietta, Giovanni
Winslow, Andrew
Date Issued
February 2013
Journal
Proceedings of the 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)
Publisher
Schloss Dagstuhl Publishing
Citation
Abel, Zachary, Erik D. Demaine, Martin L. Demaine, Sarah Eisenstat, Anna Lubiw, Andre Schulz, Diane L. Souvaine, Giovanni Viglietta, and Andrew Winslow. "Algorithms for Designing Pop-Up Cards." Natacha Portier and Thomas Wilke (Eds.) 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013), February 27-March 2, 2013, Kiel, Germany (Leibniz International Proceedings in Informatics (LIPIcs) ; Volume 20). p.269-280.
Version
Final published version
Abstract
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 solves an open problem of Hara and Sugihara from 2009. We also show how to obtain a more efficient construction for the special case of orthogonal polygons, and how to make 3D orthogonal polyhedra, from pop-ups that open to 90°, 180°, 270°, or 360°.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.4230/LIPIcs.STACS.2013.269
