Continuous deformation based panelization for design rationalization

Design rationalization is the process of simplifying a 3D shape to enable cost-efficient manufacturing. A common approach is to approximate the input shape by a collection of simple units, such as flat or spherical panels, that are easy to manufacture and simple to assemble. This panelization process typically involves a segmentation step, with each surface patch intended to be replaced by a single unit, followed by an approximation stage, where the final shapes and locations of the units are determined. While optimal panel parameters for given segments are readily determined, the discrete nature of segmentation - assigning surface elements to segments - prevents a continuous design optimization workflow. In this work, we propose a differentiable reformulation of panelization that enables its use in gradient-based design optimization. Our approach is to treat panelization as a smooth optimization problem, whose objective function encourages the surface to locally deform towards best-matching units. This formulation enables a fully-differentiable rationalization process with implicit segmentation in which panels emerge automatically. We integrate our rationalization process in a simple user interface allowing the designer to guide the optimization towards desired panelizations. We demonstrate the potential of our approach on a diverse set of complex shapes and different panel types.