Several embodiments of a collapsible screen employing novel folding structures have many possible uses: window shade, room divider, decorative backdrop, wall hanging, and others. A disclosed method allows its user to design many embodiments of the screen. The method incorporates three modifiable sets or databases: a set (220) of patterns, a set (221) of criteria by which a possible embodiment is evaluated for practicability, and a set (222) of transformations which can be applied to the possible embodiment to improve it with respect to the criteria (221). The sets can change to reflect new assumptions, design characteristics, and hardware.