Computational laser forming origami of convex surfaces

Laser forming is a fabrication method that uses laser to fold sheets into 3D structures. To overcome the limitations in the traditional practice that relies on tedious manual design, this paper advances laser forming by developing computational methods that procedurally convert a polyhedron P into laser formable 2D patterns and folding instructions or report that P is not laser formable. Due to the limitation of the low-cost laser cutter considered in this paper, we will focus our discussion on laser forming convex surfaces. A 3D surface is called convex if the entire surface lies on the boundary of its convex hull. Our theoretical analysis shows that, even for convex surfaces, the laser formability can be expensive to determine. We then present a framework that efficiently computes patterns and motion instructions for laser forming convex surfaces. An end-to-end laser forming pipeline is presented with several fabrication results to demonstrate the capability and current limitations of the software and hardware framework.