Paper by Martin L. Demaine
- Erik D. Demaine, Martin L. Demaine, David A. Huffman, Duks Koschitz, and Tomohiro Tachi, “Characterization of Curved Creases and Rulings: Design and Analysis of Lens Tessellations”, in Origami6: Proceedings of the 6th International Meeting on Origami in Science, Mathematics and Education (OSME 2014), volume 1, Tokyo, Japan, August 10–13, 2014, pages 209–230, American Mathematical Society.
We describe a general family of curved-crease folding tessellations consisting
of a repeating “lens” motif formed by two convex curved arcs. The
third author invented the first such design in 1992, when he made both a
sketch of the crease pattern and a vinyl model (pictured below). Curve fitting
suggests that this initial design used circular arcs. We show that in fact the
curve can be chosen to be any smooth convex curve without inflection point. We
identify the ruling configuration through qualitative properties that a curved
folding satisfies, and prove that the folded form exists with no additional
creases, through the use of differential geometry.
- The paper is available as arXiv:1502.03191.
- The paper is available in PDF (6290k).
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- Related papers:
- HuffmanLens_OSME2014 (Designing Curved-Crease Tessellations of Lenses: Qualitative Properties of Rulings)
See also other papers by Martin Demaine.
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