Origami is the traditional Japanese art of paper folding

Paper crafting Different types of paper crafting has been studied in the mathematical and computational setting. Here we will briefly review some major forms.

Origami is the traditional Japanese art of paper folding. Typically, origami is folded-flat (meaning the model can be flattened without being damaged) [Hull 1994] using a single piece of paper, and no cutting or gluing is used. Folding algorithms and foldability for origami has been extensively studied in the computational geometry community, and we point readers to a recent book by Demaine and O’Rourke [2007]. More recently, Tachi [2009] proposed an algorithm to automatically generate origami design for arbitrary polyhedral surfaces.

Curved folding has also been considered [Kilian et al. 2008] based on analysis of developable surfaces. By allowing cutting, paper architecture presents a different set of folding and foldability problems than traditional origami, some of which we hope to address in this work. Strip modeling is concerned with representing 3D models as paper strips, or piece-wise developable surfaces. Mitani and Suzuki [2004b] proposed a method for approximately making general surfaces by paper-strips.

Their algorithm is powered by mesh simpli- fication, which is a well-studied but still active topic [Garland and Heckbert 1997; Cohen et al. 1998; Wei and Lou 2010]. Alternative methods also have been proposed in [Shatz et al. 2006] and [Massarwi et al. 2007]. With the use of cutting and splicing, strip modeling can achieve complex and even knotted geometry that is otherwise infeasible in other paper art forms. Paper-cutting is a Chinese folk art that cuts out stylistic patterns and figures from a piece of paper. A simple and efficient algorithm for automatic paper-cutting given input images was proposed in [Xu et al. 2007]. Extensions to 3D paper-cuts and interactive design card of animations with paper-cuts have also been considered [Li et al. 2007].