Paper by Erik D. Demaine

Reference:

Oswin Aichholzer, Greg Aloupis, Erik D. Demaine, Martin L. Demaine, Sándor P. Fekete, Michael Hoffmann, Anna Lubiw, Jack Snoeyink, and Andrew Winslow, “Covering Folded Shapes”, in Proceedings of the 25th Canadian Conference on Computational Geometry (CCCG 2013), Waterloo, Ontario, Canada, August 8–10, 2013, to appear.

Abstract:

Can folding a piece of paper flat 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 → ℝ²). 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.

Comments:

A 6-page version of the paper appeared in the printed proceedings.

Length:

The paper is 9 pages.

Availability:

The paper is available in PDF (449k).

See information on file formats.

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