Non-Euclidean Origami as a Path Towards Inverse Design

Many of the challenges of aerospace and outer space involve the concentration of electromagnetic radiation. However, the scale and size of these capture device is large, and the devices must be placed in atmospheric orbit to be effective. Origami serves as a compelling solution to this problem as it can be stored for takeoff and deployed in the upper atmosphere. In this work, we introduce a framework for designing parabolic reflectors and show a specific design criterion that allow us to reach a desired concertation efficiency as a function of the number of facets. We extend this criterion and combine it with prior work on inflatable Origami. We introduce a new inflatability constraint based on the maximum volume of the origami structure and show that it can be used in the design of parabolic reflectors. By allowing our Origami to be non-developable (i.e. non-Euclidean), we expand the design space and allow for multiple functional stable state. By combining inflatability and multistability, we show that deployable, functional structure, capable of collecting and transmitting electromagnetic radiation is possible using the techniques of the art of Origami. This foundation provides a path towards general inverse design of inflatable, non-Euclidean origami surfaces.