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

Prof. Erik Demaine       TA: Jayson Lynch

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[+] Polyhedron folding: Pita forms, D-forms, seam forms, convex hull and crease properties, rolling belts, Burago-Zalgaller folding into nonconvex polyhedra.

This class focuses on D-forms (introduced by artist Tony Wills) and related constructions called pita forms and seam forms:
  • Pita forms were demonstrated in Lecture 17: take a convex polygon or curved shape and glue up two halves of its perimeter to make a convex surface.
  • D-forms extend this to gluing together two convex polygons or curves.
  • Seam forms further generalize to arbitrarily many, not necessarily convex polygons, but still require Alexandrov's Theorem to apply (actually a smooth version called Alexandrov-Pogorelov).

We'll make physical D-forms and prove two neat properties about them (which originate from a final project in this class from 2007). We'll also briefly review rolling belts, the implementation of Bobenko-Izmestiev's Alexandrov construction, and Burago-Zalgaller's folding of any polygon with any gluing into a nonconvex polyhedron [O'Rourke 2010; Spring 2005].

Download Video: 360p, 720p

Handwritten notes, page 1/3[previous page][next page][PDF]

Handwritten notes, page 1/3[previous page][next page][PDF]

Slides, page 1/11[previous page][next page][PDF]

Figure 25.2 of GFALOP

Slides, page 1/11[previous page][next page][PDF]

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