Paper by Martin L. 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”, Journal of Computational Geometry, volume 5, number 1, 2014.

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:

This paper is also available from JoCG. and as arXiv:1405.2378.

Length:

The paper is 19 pages.

Availability:

The paper is available in PDF (421k).

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