| [+] Fold and one cut: history, straight-skeleton method, disk-packing method, simple folds, higher dimensions, flattening polyhedra. | ||||
| This lecture is about my first work in computational origami: folding a piece of paper flat so that one complete straight cut makes a desired pattern of cuts (and resulting polygonal shapes). The problem has a long history (back to the 1700s) and possible applications to airbag folding through a problem called flattening. We'll see two different methods for this problem, each with connections to the tree method of origami design: the first generalizes the universal molecule to nonconvex polygons, but loses the ability to control the shadow tree; the second uses disk packing (but no rivers) and universal molecules for triangles and quadrangles. I'll also talk about a brand new result that started from this class three years ago: what shapes can you make only with simple folds? | ||||
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Handwritten notes, page 1/8 •
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Handwritten notes, page 1/8 • [previous page] • [next page] • [PDF] |
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Slides, page 1/31 •
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“Wakoku Chiyekurabe” by Kan Chu Sen, published in 1721. Out of copyright. Scans by Erik Demaine. See http://erikdemaine.org/foldcut/sen_book.html Slides, page 1/31 • [previous page] • [next page] • [PDF] |
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