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

• 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].