6.849: Geometric Folding Algorithms: Linkages, Origami, Polyhedra (Fall 2012)

Prof. Erik Demaine TA: Jayson Lynch

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[+] Fold and one cut: software, scissor vs. mathematical cuts, tree folding, density, examples, how many disks, comparison to tree method, continuous flattening.
This class describes several additional details about fold-and-cut: Software: David Benjamin and Anthony Lee's 6.849 Fall 2010 project (skeleton method) JOrigami (disk-packing method) Skeleton method: Odd-degree vertices are possible with mathematical cuts, but not scissor cuts. Two scissor cuts can (usually) simulate mathematical cuts. Correspondence between linear corridors and shadow tree Correspondence between tree folding and origami folding Why dense configurations should happen only with probability 0 Comparison to tree method Examples by past students A magic trick Disk-packing method: Correspondence between disk packing and triangle/quad decomposition How many disks are needed by a disk packing? Comparison to tree method Open problem with curved cuts Continuous flattening: convex polyhedra now solved Comparison to tree method Paper cutting art

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Handwritten notes, page 1/4 • [previous page] • [next page] • [PDF]

Slides, page 1/40 • [previous page] • [next page] • [PDF]

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