Unfolding via Mesh Approximation using Surface Flows

Abstract

Manufacturing a 3D object by folding from a 2D material is typically done in four steps: 3D surface approximation, unfolding the surface into a plane, printing and cutting the outline of the unfolded shape, and refolding it to a 3D object. Usually, these steps are treated separately from each other. In this work we jointly address the first two pipeline steps by allowing the 3D representation to smoothly change while unfolding. This way, we increase the chances to overcome possible ununfoldability issues. To join the two pipeline steps, our work proposes and combines different surface flows with a Tabu Unfolder. We empirically investigate the effects that different surface flows have on the performance as well as on the quality of the unfoldings. Additionally, we demonstrate the ability to solve cases by approximation which comparable algorithms either have to segment or can not solve at all.