Folding and Punching Paper

Folding and Cutting Paper

We present an algorithm to nd a at folding of a piece of paper, so that one complete straight cut on the folding creates any desired plane graph of cuts. The folds are based on the straight skeleton, which lines up the desired edges by folding along various bisectors; and a collection of perpendiculars that make the crease pattern foldable. We prove that the crease pattern is at foldable by dem...

Folding Paper Shopping Bags

One of the most ubiquitous examples of origami is the common paper shopping bag. In a common model of paper folding, there are a finite number of creases, between which the paper must stay rigid and flat, as if made of plastic or metal plates connected by hinges. We show that (maybe surprisingly), the paper shopping bag cannot be flattened under this model using the usual pattern of creases. Th...

Folding and Unfolding Linkages, Paper, and Polyhedra

Folding and unfolding problems have been implicit since Albrecht Dürer in the early 1500’s [Dür77], but have not been studied extensively until recently. Over the past few years, there has been a surge of interest in these problems in discrete and computational geometry. This paper gives a brief survey of some of the recent work in this area, subdivided into three sections based on the type of ...

Semantic Folding Theory - White Paper

Human language is recognized as a very complex domain since decades. No computer system has been able to reach human levels of performance so far. The only known computational system capable of proper language processing is the human brain. While we gather more and more data about the brain, its fundamental computational processes still remain obscure. The lack of a sound computational brain th...

Variations on a Theme in Paper Folding