Geometric Folding Algorithms: Linkages, Origami, Polyhedra

This is an advanced class on computational geometry focusing on folding and unfolding of geometric structures including linkages, proteins, paper, and polyhedra. Examples of problems considered in this field include:

• What forms of origami can be designed automatically by algorithms?
• What shapes can result by folding a piece of paper flat and making one complete straight cut?
• What polyhedra can be cut along their surface and unfolded into a flat piece of paper without overlap?
• When can a linkage of rigid bars be untangled or folded into a desired configuration?

Many folding problems have applications in areas including manufacturing, robotics, graphics, and protein folding. This class covers many of the results that have been proved in the past few years, as well as the several exciting open problems that remain open.