Covering folded shapes
Name
Demaine_Covering folded.pdf
Size
413.82 KB
Format
Adobe PDF
Checksum (MD5)
cacc2162cd3b966b97f4866c1f66205d
Author(s)
Aichholzer, Oswin
Aloupis, Greg
Demaine, Erik D.
Demaine, Martin L.
Fekete, Sandor P.
Hoffmann, Michael
Lubiw, Anna
Snoeyink, Jack
Winslow, Andrew
Date Issued
August 2013
Journal
Proceedings of the 25th Canadian Conference on Computational Geometry
Citation
Aichholzer, Oswin, et al. "Covering folded shapes." 25th Canadian Conference on Computational Geometry (August 2013).
Version
Author's final manuscript
Abstract
Can folding a piece of paper at make it larger? We explore whether a shape S must be scaled to cover a flat-folded copy of itself. We consider both single folds and arbitrary folds (continuous piecewise isometries S → R[superscript 2]). The underlying problem is motivated by computational origami, and is related to other covering and fixturing problems, such as Lebesgue's universal cover problem and force closure grasps. In addition to considering special shapes (squares, equilateral triangles, polygons and disks), we give upper and lower bounds on scale factors for single folds of convex objects and arbitrary folds of simply connected objects.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
http://www.cccg.ca/proceedings/2013/
