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

For review, we cover some open problems about triangulated hypars, define smoothness (C^k), detail why uncreased polygonal regions of paper must be flat in 3D (normal arguments), and discuss how real paper might differ from mathematical paper.

For new material, we cover algorithms for optimally folding specified M/V patterns by a sequence of simple folds and unfolds. Specifically, we'll see that the patterns MMM... and MVMV... can be folded using O(lg² n) folds, and require Ω(lg² n / lg lg n) folds, while most patterns require Θ(n / lg n) folds.

For real folding, we will make (nonexistent) square hypars and assemble them into a hyparhedron sculpture.