2.2 HyperGami as a Medium for Craft

The previous paragraphs provided a broad outline of HyperGami's purpose and operation. In this section, we focus on those aspects of the application that bring into especially high relief its relationship with craft activities. In every case, these features were not planned in the initial design of the system; rather, they arose from the physical activity and materials themselves -- and from observations of difficulties that we and our students had in creating polyhedral models. Thus, these features may be viewed as conscious attempts to make our computational environment more responsive to the specific needs of the practicing paper modeller.

2.2.1 Linked Nets and Solids

Perhaps the central problem in decorating a polyhedron's folding net -- and a problem that students run into almost immediately in their work -- is the task of imagining what a particular decoration, in its "flat" form, will look like when the folding net is finally assembled into a three-dimensional solid. To take a simple case, we might wish to create an octahedron decorated so that pairs of opposite faces are in the same color. Only one of the folding nets in Figure 4 will in fact achieve this aim; we invite the reader to decide which is the correct net.

Figure 4. Three attempts to decorate an octahedron so that each pair of opposite faces has a characteristic shading.

HyperGami includes two features intended to render this sort of judgment easier for the user. The first allows the user to draw with the mouse on the folding net; as she does so, the system simultaneously presents a line in the appropriate position on the visible 3D solid on the screen. Figure 5 shows this feature in operation: the user is drawing a line on the folding net of the octahedron, and the system is displaying not only that line but also the line that would appear if the folding net were to be assembled into a 3D solid. In HyperGami, this "pen mode" is selected via the Nets/Solids window (visible in Figure 2); and in this mode, if the user drags the mouse over a region off the net (or over a face of the net not visible in the 3D window), the pen simply does not draw at all.

Figure 5. HyperGami's "linked net and solid mode" in operation. As the user draws a line on the folding net in the TwoD window at left, the system simultaneously presents the line that would appear on the folded solid in the ThreeD window at right.

This feature allows the user to get an initial feeling for how the individual faces of the folding net on the screen correspond to their 3D realization in the assembled model. By drawing a line that leaves the boundary of one face and moves onto another (as in Figure 5), the user can for instance observe how two boundary edges of the net will join together in the final solid. A second, more elaborate (and much slower) tool allows the user to decorate an entire net and then "paint" that decoration over the visible solid in HyperGami's 3D window. Figure 6 shows this feature in operation: the user has first decorated the octahedral folding net shown at left and then has directed the system to show her what the eventual solid will look like. (This feature is likewise activated by a selection from the Nets/Solids window.) The 3D rendering of the octahedron now shows how the solid will appear, from this particular angle, when the model is created.

Figure 6. The shading of a decorated net (left) is transferred to the 3D rendering of the solid (at right).