Origami, the art of paper folding, has a rich mathematical theory. Early investigations go
back to at least the 1930s, but the twenty-first century has seen a remarkable blossoming of …

In this paper, we show that deciding rigid foldability of a given crease pattern using all
creases is weakly NP-hard by a reduction from Partition, and that deciding rigid foldability …

In the study of origami, various parametric methods have been proposed to design crease
patterns under geometric conditions for flat-folding. Each design method contributes to …

Flat origami refers to the folding of flat, zero-curvature paper such that the finished object lies
in a plane. Mathematically, flat origami consists of a continuous, piecewise isometric map $ f …

We prove that testing the flat foldability of an origami crease pattern (either labeled with
mountain and valley folds, or unlabeled) is fixed-parameter tractable when parameterized by …

Folding an m× n square grid pattern along the edges of a grid is called map folding. We
consider a decision problem in terms of whether a partial overlapping order of the squares …

We prove several hardness results on folding origami crease patterns. Flat-folding finite
crease patterns is fixed-parameter tractable in the ply of the folded pattern (how many layers …

In this paper, we investigate the accessible flat-folded states of three common fold models
under the context of two origami problems. The three fold models are the simple fold model …

It has been known since 1996 that deciding whether a collection of creases on a piece of
paper can be fully folded flat without causing self-intersection or adding new creases is an …

The crease patterns of several basic origami shapes fall within the 45-degree grid system,
ie, the square/diagonal grid of a 4× 4 size. This grid system is easily creased on a square …