Origamic architecture (OA) is a form of papercraft that involves cutting and folding a single sheet of paper to produce a 3D pop-up, and is commonly used to depict architectural structures. Because of the strict geometric and physical constraints, OA design requires considerable skill and effort. In this paper, we present a method to automatically generate an OA design that closely depicts an input 3D model. Our algorithm is guided by a novel set of geometric conditions to guarantee the foldability and stability of the generated pop-ups. The generality of the conditions allows our algorithm to generate valid pop-up structures that are previously not accounted for by other algorithms. Our method takes a novel image-domain approach to convert the input model to an OA design. It performs surface segmentation of the input model in the image domain, and carefully represents each surface with a set of parallel patches. Patches are then modified to make the entire structure foldable and stable. Visual and quantitative comparisons of results have shown our algorithm to be significantly better than the existing methods in the preservation of contours, surfaces, and volume. The designs have also been shown to more closely resemble those created by real artists.

A paper sliceform or lattice-style pop-up is a form of papercraft that uses two sets of parallel paper patches slotted together to make a foldable structure. The structure can be folded flat, as well as fully opened (popped-up) to make the two sets of patches orthogonal to each other. Automatic design of paper sliceforms is still not supported by existing computational models and remains a challenge. We propose novel geometric formulations of valid paper sliceform designs that consider the stability, flat-foldability and physical realizability of the designs. Based on a set of sufficient construction conditions, we also present an automatic algorithm for generating valid sliceform designs that closely depict the given 3D solid models. By approximating the input models using a set of generalized cylinders, our method significantly reduces the search space for stable and flat-foldable sliceforms. To ensure the physical realizability of the designs, the algorithm automatically generates slots or slits on the patches such that no two cycles embedded in two different patches are interlocking each other. This guarantees local pairwise assembility between patches, which is empirically shown to lead to global assembility. Our method has been demonstrated on a number of example models, and the output designs have been successfully made into real paper sliceforms.