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6.849 Geometric Folding Algorithms: Linkages, Origami, Polyhedra

6.849 Geometric Folding Algorithms: Linkages, Origami, Polyhedra (Fall 2012, MIT OCW). Instructor: Professor Erik Demaine. This course focuses on the algorithms for analyzing and designing geometric foldings. Topics include reconfiguration of foldable structures, linkages made from one-dimensional rods connected by hinges, folding two-dimensional paper (origami), and unfolding and folding three-dimensional polyhedra. Applications to architecture, robotics, manufacturing, and biology are also covered in this course. (from ocw.mit.edu)

This lecture begins with describing polyhedron unfolding for convex and nonconvex polygons. Algorithms for shortest path solutions and unfoldings are presented along with how to determine whether an edge unfolding exists.

This class begins with defining handles and holes, and the Gauss-Bonnet Theorem applied to convex polyhedra. Algorithms for zipper unfolding, edge unfoldable polyhedra, square-packing, band unfolding, and blooming of convex polyhedra are presented.

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