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Universal hinge patterns: box pleating, polycubes;
orthogonal maze folding. |
This lecture covers two main topics:
First, continuing our theme from Lecture 4 on efficient origami design, we'll see how subsets of a single hinge pattern are enough to fold any orthogonal shape made up of cubes, whereas other approaches use a completely different set of creases for each origami model you want. In general, we can fold n cubes from an O(n) × O(n) square of paper. In the special case of “orthogonal mazes”, we can waste almost no paper, with the folding only a small constant factor smaller than the original piece of paper. You can try out this yourself. Second, we'll see a few ways in which origami is hard. Specifically, I'll give a brief, practical introduction to NP-hardness, and prove three origami problems NP-hard:
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Handwritten notes, page 1/7 •
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Handwritten notes, page 1/7 • [previous page] • [next page] • [PDF] |
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Slides, page 1/20 •
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http://www.pnas.org/content/107/28/12441 / http://www.pnas.org/content/suppl/2010/06/25/0914069107.DCSupplemental / http://erikdemaine.org/papers/Matter_PNAS/ (covered under the MIT Faculty Open-Access Policy) Slides, page 1/20 • [previous page] • [next page] • [PDF] |
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