A pop-up card is a piece of folded paper from which three-dimensional (3D) paper structures pop up when it is opened. The card can be folded flat again afterward. Pop-up cards, also called Origamic Architectures, find their origin in Japan (Chatani, 1985). People enjoy this interesting paper craft through the realization of pop-up books (e.g. Baum, 2000; Sabuda & Carroll, 2003; Sabuda & Reinhart, 2005) and greeting cards. Figure 1 shows an example of pop-up books.
“Alice’s Adventures in Wonderland”, a typical pop-up book (Sabuda & Carroll, 2003)
Constructing a pop-up card is relatively easier than designing one; anyone can simply cut out and fold the pieces and glue them together if a template, which is printed parts, is available. However, it is unfortunately much more difficult for nonprofessionals to design a pop-up card and make its templates from scratch. There are two reasons to this difficulty. The first difficulty is correctly understanding and designing the pop-up mechanisms. The book (Carter & Diaz, 1999) helps to understand mechanisms, but does not tell how to combine them to design a desired look. The second difficulty is determining the positions of pop-up parts so that they do not collide with each other. Professionals usually solve these problems through repetitive trial and error by drawing on their experience during design: cutting component parts out of paper, pasting them on the card, and checking whether they collide. If an error is found, they re-think the design and start over from the beginning. This process requires a lot of time, energy, and paper. Design and simulation in a computer help both nonprofessionals and professionals to design a pop-up card, eliminate the boring repetition, and save time.
Glassner (1998, 2002) proposed methods for designing a pop-up card on a computer. He introduced several simple pop-up mechanisms and described how to use these mechanisms, how to simulate the position of vertices as an intersecting point of three spheres, how to check whether the structure sticks out beyond the cover or if a collision occurs during opening, and how to generate templates. His work is quite useful in designing simple pop-up cards.
In this article, we build on Glassner’s pioneering work and introduce several innovative aspects. We add two new mechanisms based on the V-fold: the box and the cube. We present a detailed description of the interface for design, which Glassner did not describe in any detail. In addition, our system provides real-time error detection feedback during editing operations by examining whether parts protrude from the card when closed or whether they collide with one another during opening and closing. Finally, we report on an informal preliminary user study of our system involving four inexperienced users.
Glassner (1998, 2002) described a stable analytical solution for important vertices in the three main pop-up mechanisms (single-slit, asymmetric single-slit, and V-fold mechanisms) when a pop-up card opens and closes in interactive pop-up card design. In addition, he introduced two simple gimmicks (pull and whirligig gimmicks), but not the underlying calculations. He also implemented his methods in a small program and designed his original pop-up cards. However, he did not describe its interactive behavior in detail, nor did he report any user experience.