Closed space‐filling curves with controlled orientation for 3D printing
Ahmet Bedel, Yoann Coudert‐Osmont, Jonàs Martínez, Rahnuma Islam Nishat, Sue Whitesides, Sylvain Lefèbvre
Abstract
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.