Interactive surface design with interlocking elements

We present an interactive tool for designing physical surfaces made from flexible interlocking quadrilateral elements of a single size and shape. With the element shape fixed, the design task becomes one of finding a discrete structure---i.e., element connectivity and binary orientations---that leads to a desired geometry. In order to address this challenging problem of combinatorial geometry, we propose a forward modeling tool that allows the user to interactively explore the space of feasible designs. Paralleling principles from conventional modeling software, our approach leverages a library of base shapes that can be instantiated, combined, and extended using two fundamental operations: merging and extrusion. In order to assist the user in building the designs, we furthermore propose a method to automatically generate assembly instructions. We demonstrate the versatility of our method by creating a diverse set of digital and physical examples that can serve as personalized lamps or decorative items.