# 6.849: Geometric Folding Algorithms: Linkages, Origami, Polyhedra (Fall 2020)

## Prof. Erik Demaine; Martin Demaine; TAs Yevhenii Diomidov & Klara Mundilova

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 [+] Efficient origami design: Tree method, TreeMaker, uniaxial base, active path, rabbit-ear molecule, universal molecule, Margulis Napkin Problem; cube folding, checkerboard folding; Origamizer, watertight, tuck proxy. This lecture is all about efficient origami design. We saw in Lecture 1 how to fold anything impractically. Now we'll see how to fold many shapes practically. First up is the tree method, whose software implementation TreeMaker I demoed at the end of Lecture 2. I'll describe how it lets us fold an optimum stick-figure (tree) origami base, although computing that optimum is actually NP-complete (as we'll see in Lecture 6). This algorithm is used throughout modern complex origami design; I'll show some examples by Robert Lang and our own Jason Ku. Second we'll look at a simple, fully understood case: the smallest square to fold a cube. Third we'll look at a classic problem that we made progress on recently: folding an n × n checkerboard from the smallest bicolor square. Finally we'll look at the latest and most general method, Origamizer, for folding any polyhedron reasonably efficiently. Here we don't have a nice theoretical guarantee on optimality, but the method works well in practice, provably always works, and has other nice features such as watertightness.
 No support for video detected. Install Flash or use an HTML5 browser. Download Video: 360p, 720p Handwritten notes, page 1/7 • [previous page] • [next page] • [PDF] Handwritten notes, page 1/7 • [previous page] • [next page] • [PDF] Slides, page 1/17 • [previous page] • [next page] • [PDF] Images and design by Robert Lang. http://​langorigami.com/​art/​gallery/​gallery.php4?name=snack_time & http://​langorigami.com/​art/​insects/​snack_time_cp.pdf Slides, page 1/17 • [previous page] • [next page] • [PDF]

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