An Epithelium-Inspired Deformation Modeling Framework for 4D Sheets

Abstract:
4D materials are a new type of entity that change their shape and properties in response to external stimuli. With 4D object modeling, the desired object is initially defined in a flat or simple configuration and then local deformations transform the initial shape into the target 3D shape. A significant challenge when producing 4D materials is the determination of the deformations that will lead to the emergence of a specific shape. In order to address the challenge of designing deformations for 4D materials, we turn to developmental biology for inspiration, specifically cell shape change during morphogenesis in an epithelium. We present a generalized modeling framework that can produce complex curved surfaces via a directed deformation process, based on local geometric properties and similar to an epithelium in vivo<\it>. We demonstrate that this approach is capable of defining local deformations that mutate an initially flat grid of cells into a curved target 3D surface.