shows a screenshot of our prototype system

Fig. 2 shows a screenshot of our prototype system. Our system allows the user to design pop-up cards using a mouse and a keyboard. The system consists of a single window for the design and simulation of the pop-up card. Fig. 3 shows the system functions. The user positions parts, adjusts their properties (e.g., length, angle, position and pattern), and generates templates. During interactive editing, the system always examines whether parts protrude from the card or whether they collide with one another. The user can use five mechanisms in our system. The V-fold mechanism, the even-tent mechanism, and the uneven-tent mechanism were introduced by Glassner [4]. The angle fold open box mechanism and the angle fold cube mechanism [17] based on the V-fold are new. The former forms a box, which is an empty rectangular parallelepiped without a top and a bottom as shown in Fig. 4 (a). The latter makes an angle fold open box with a lid as shown in Fig. 4 (b). The lid is folded toward the inside of the box when the card is closed. Fig. 2. Prototype system. OQXG GFKV OCRVGZVWTG UKOWNCVKQP FGNGVG GTTQT EJGEM IGPGTCVG VGORNCVG IGPGTCVGRCTVU Fig. 3. Prototype system functions. &_' &`' Fig. 4. (a) Angle fold open box mechanism. (b) Angle fold cube mechanism. 3.1 Constrained Editing Setting Parts The user first selects a desired mechanism and moves the mouse cursor to a fold line where the black point then appears. If the user clicks the mouse button, the system automatically generates the new part at that position with default lengths and angles that can be adjusted later (see Fig. 5). &_' &`' ENKEM Fig. 5. User interface for setting parts. (a) When the user clicks on a fold line, (b) the system generates a new part there. Editing Shapes The user drags the vertices of a part to edit its shape as shown in Fig. 6. The vertices of a part are highlighted when the user selects that part. The user can then drag the vertices one at a time. When editing lengths, the user can maintain the parallelogram shape by pressing the Shift key while dragging as shown in Fig. 6 (c). The user can also extend a panel of a part as shown in Figs. 6 (d) and (e) or change the angle between two planes or the inclination of the part as shown in Figs. 6 (f)-(i). Deleting Parts The user clicks on a part to delete it. If other parts exist on the part being deleted, they are also deleted. Mapping Textures The user prepares images in advance and can use them as textures. To put a texture on a part, the user selects a panel of a part and an image as shown in Figs. 6 (j) and (k). Generating Templates The system automatically generates 2D templates from the 3D model designed by the user. The system also creates glue tabs and generates guidelines to tell the user where to glue them on.