Paper by Martin L. Demaine

Reference:

Erik D. Demaine, Martin L. Demaine, Andrea Hawksley, Hiro Ito, Po-Ru Loh, Shelly Manber, and Omari Stephens, “Making Polygons by Simple Folds and One Straight Cut”, in Abstracts from the China-Japan Joint Conference on Computational Geometry, Graphs and Applications (CGGA 2010), Dalian, China, November 3–6, 2010, to appear.

Abstract:

We give an efficient algorithmic characterization of simple polygons whose edges can be aligned onto a common line, with nothing else on that line, by a sequence of all-layers simple folds. In particular, such alignments enable the cutting out of the polygon and its complement with one complete straight cut. We also show that these makable polygons include all convex polygons possessing a line of symmetry.

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Related papers:

SimpleFoldCut_CGGA2010full (Making Polygons by Simple Folds and One Straight Cut)

Related webpages:

Simple Fold & Cut Font