6.849: Geometric Folding Algorithms: Linkages, Origami, Polyhedra (Fall 2010)

Prof. Erik Demaine


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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 2 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 3. 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 5). 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.

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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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