Paper by Erik D. Demaine

Erik D. Demaine and Martin L. Demaine, “Computing Extreme Origami Bases”, Technical Report CS-97-22, Department of Computer Science, University of Waterloo, May 1997.

In this paper, we examine extreme origami bases that fold the boundary of a polygonal sheet of paper to a common plane, generalizing the Husimi and Meguro molecules used in origami design. This also solves the folding-and-cutting problem, where we want to make a specified polygon by one complete straight cut after arbitrary folding of a square sheet of paper. We present an algorithm to construct the crease pattern of an extreme base for paper in the shape of an arbitrary simple polygon. It is based on the straight skeleton, a variant on the medial axis. For convex polygons, we describe exactly how the folding process can be performed. This proves that the folding can even be done with paper that is rigid except at the creases, and allows animation of the folding process. Such descriptions have not been achieved before for an infinite class of origamis.

This work on the fold-and-cut problem has been generalized to arbitrary plane graphs; see my fold-and-cut webpage for links to related papers.

Further updates concerning this technical report:

The paper is 18 pages.

The paper is available in PostScript (471k), gzipped PDF (580k), and ZIPped PDF (580k).
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Related webpages:
The Fold-and-Cut Problem

See also other papers by Erik Demaine.
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Last updated June 22, 2017 by Erik Demaine.