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

Prof. Erik Demaine


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[+] Origami intro: Piece of paper, crease pattern, mountain-valley assignment.
Simple folds: Folding any shape (silhouette or gift wrapping), 1D flat-foldability characterization, 2D map-folding algorithm.

This lecture kicks off a series of lectures about origami. It focuses on a relatively simple kind of origami, called “simple folds”, which involve folding along one straight line by ±180 degrees. These are some of the most “practical” types of folds from an automated manufacturing standpoint, are well-studied mathematically, and a good warmup before we get to complex origami folds which fold many creases at once.

On the design side, we'll see how simple folds are enough to fold any 2D shape, and with slightly more general folds, we can fold any 3D shape even with a two-color pattern on the surface.

On the foldability side, we'll see how to efficiently determine whether a crease pattern with mountains and valleys indicated can be folded flat in two interesting cases: 1D pieces of paper (in other words, parallel creases in a strip of paper) and 2D rectangular maps.

Download Video: 360p, 720p

Handwritten notes, page 1/9[previous page][next page][PDF]

Handwritten notes, page 1/9[previous page][next page][PDF]

Slides, page 1/4[previous page][next page][PDF]

Figure 16.2 from GFALOP

Slides, page 1/4[previous page][next page][PDF]

The video above should play if your web browser supports either modern Flash or HTML5 video with H.264 or WebM codec. The handwritten notes and slides should advance automatically. If you have any trouble with playback, email Erik.