Paper by Martin L. Demaine

Reference:

Erik D. Demaine, Martin L. Demaine, and Anna Lubiw, “Folding and Cutting Paper”, in Revised Papers from the Japan Conference on Discrete and Computational Geometry (JCDCG'98), Lecture Notes in Computer Science, volume 1763, Tokyo, Japan, December 9–12, 1998, pages 104–117.

Abstract:

We present an algorithm to find a flat folding of a piece of paper, so that one complete straight cut on the folding creates any desired plane graph of cuts. The folds are based on the straight skeleton, which lines up the desired edges by folding along various bisectors; and a collection of perpendiculars that make the crease pattern foldable. We prove that the crease pattern is flat foldable by demonstrating a family of folded states with the desired properties.

Comments:

Shorter version in \emph{Abstracts from the Japan Conference on Computational Geometry}, pages 5--9.

Updates:

Ivars Peterson wrote an article describing these results, “Fold-and-Cut Magic”, Science News 162(22), November 30, 2002.

Joseph O'Rourke also wrote an article describing these results, “Computational Geometry Column 36”, International Journal of Computational Geometry and Applications, 9(6):615-618, 1999.

Copyright:

The paper is \copyright Springer-Verlag.

Length:

The paper is 15 pages.

Availability:

The paper is available in PostScript (550k), gzipped PostScript (143k), and PDF (243k).

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Related papers:

SODA99a (Folding and One Straight Cut Suffice)

Related webpages:

The Fold-and-Cut Problem (Erik Demaine)