Logical Analysis of Huzita-Justin Folds

In this chapter, we see Huzita-Justin folds HO from a logical point of view. We give the logical specification of HO as constraints among geometric objects of origami in the language of the first-order predicate logic. The logical specification is next translated to logical combinations of algebraic expressions, i.e., polynomial equalities, unequalities, and inequalities (if the notion of inequalities is involved). By constraint solving, we obtain solutions that satisfy the logical specification of the origami construction problem. The solutions include fold-lines along which origami has to be folded. The obtained solutions, both in numeric and symbolic forms, make origami computationally tractable for further treatments, such as visualization and automated verification of the correctness of the origami construction.