Computational Origami Construction as Constraint Solving and Rewriting

Computational origami is the computer assisted study of origami geometry. An origami is constructed by a finite sequence of fold steps, each consisting in folding along a fold line or unfolding. We base the fold methods on a formal system called Huzita’s axiom system, and show how folding an origami can be formulated by a conditional rewrite system. A rewriting sequence of origami structures is seen as an abstraction of origami construction. We also explain how the basic concepts of constraint and functional and logic programming are related to this computational construction. Our approach is not only useful for computational construction of an origami, but leads to automated theorem proving of the correctness of the origami construction.