| Summary: | The study aims at establishing the topological and geometrical relationships that govern the design and construction of pop-up laminar structures. It also proposes a systematic, computer-aided approach for pop-up designs. A pop-up classification model and graph representation schemes are established after a comprehensive study on the available pop-up structures. The folding and development of pop-up structures are analyzed and represented as Mountain-Valley (MV) graphs. The MV graphs illustrate relationships between layers and creases and define the boundary regions of feasible pop-up design. Topological conditions for governing the composition of the structures are also established using vertex-edge graphs. In addition, conditions for flat folding are derived after investigation into the geometry of the structures. While the graphs enable simple representation of pop-up structures without the complexity of geometric designs, the mathematical relationships permit the validation of the structures’ composition and their ability to flat fold. A modular, object-oriented software prototype has been built, and it demonstrates the creation of pop-up designs using the graph structures and the mathematical relationships developed in this research.
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