Learning to segment and unfold polyhedral mesh from failures

Folding planar sheets to make 3D shapes from is an ancient practice with many new applications, ranging from personal fabrication of customized items to design of surgical instruments for minimally invasive surgery in self-folding machines. Given a polyhedral mesh, unfolding is an operation of cutting and flattening the mesh. The flattened polyhedral nets are then cut out of planar materials and folded back to 3D. Unfolding a polyhedral mesh into planar nets usually require segmentation. Either used as a preprocessing step to simplify the mesh and provide semantics or as the result of unfolding to avoid overlapping, the segmentation and the unfolding operations are decoupled. Consequently, segmented components may not be unfoldable and unfolded nets usually provide no semantic meaning and make folding difficult. In this paper, we propose a strategy that tightly couples unfolding and segmentation. We show that the proposed method produces unfoldable segmentation that resembles carefully designed paper craft. The key idea that enables this capability is an algorithm that learns from failed unfoldings.