Abstract by Zachary Broyles
Modeling origami in an enclosed space
The main problem that can occur when creating a foldable pattern is that the pattern may mathematically work in its folded state but an in between state could be impossible to achieve. For instance, during the folding process different planes of a pattern might intersect itself. Well known methods of modeling origami can prove self-intersections on one vertex but are limited when it comes to multiple vertices. A fairly new method involves the use of quaternions. Not only can quaternions accurately describe and model an origami pattern of one vertex but it easily extends to modeling origami patterns of multiple vertices. The goal is to use this new method to model origami patterns as they unfold in an enclosed space to determine if the pattern will be able to fold or unfold in the limited space.