Closed space‐filling curves with controlled orientation for 3D printing. (24th May 2022) - Bedel, A.; Coudert‐Osmont, Y.; Martínez, J.; Nishat, R. I.; Whitesides, S.; Lefebvre, S.
Abstract: We explore the optimization of closed space‐filling curves under orientation objectives. By solidifying material along the closed curve, solid layers of 3D prints can be manufactured in a single continuous extrusion motion. The control over orientation enables the deposition to align with specific directions in different areas, or to produce a locally uniform distribution of orientations, patterning the solidified volume in a precisely controlled manner. Our optimization framework proceeds in two steps. First, we cast a combinatorial problem, optimizing Hamiltonian cycles within a specially constructed graph. We rely on a stochastic optimization process based on local operators that modify a cycle while preserving its Hamiltonian property. Second, we use the result to initialize a geometric optimizer that improves the smoothness and uniform coverage of the cycle while further optimizing for alignment and orientation objectives.