A directed acyclic graph for pop-up card design

Abstract

Pop-up cards are an interesting form of paper art with intriguing geometrical properties. Normally, there are two types of pop-up cards. Origami architecture is a 90-degree card and a v-fold pop up is a 180-degree card. Recently, some approaches have been proposed to aid in the design of a pop-up card. Most of the works on pop-up crafting have used a software tool to design pop-up cards. However, a design tool for a 90-degree card cannot be adopted for the design of a 180-degree card. For the same reason, a method for producing a 180-degree card also cannot be applied to a 90-degree card. This paper proposes a directed acyclic graph (DAG) for designing both types of pop-up cards. These two types of pop-up cards could be created with DAG data structure. The DAG algorithm ensures that the pop-up card is foldable, stable, and intersection-free when opened and closed. The proposed method is demonstrated with various paper pop-up cards, and experimental examples are presented.