Folding a paper strip to minimize thickness

Folding a Paper Strip to Minimize Thickness

In this paper, we study how to fold a specified origami crease pattern in order to minimize the impact of paper thickness. Specifically, origami designs are often expressed by a mountain-valley pattern (plane graph of creases with relative fold orientations), but in general this specification is consistent with exponentially many possible folded states. We analyze the complexity of finding the ...

A Motion Planning Approa h to Folding: From Paper Craft to Protein Folding

From Paper Craft to Protein Folding Guang Song Nan y M. Amato gsong s.tamu.edu amato s.tamu.edu Te hni al Report TR00-017 Department of Computer S ien e Texas A&M University July 21, 2000 Abstra t In this paper, we present a framework for studying folding problems from a motion planning perspe tive. The version of the motion planning problem we onsider is that of determining a sequen e of motio...

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 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...

Variations on a Theme in Paper Folding