41-Issue 2

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Closed Space-filling Curves with Controlled Orientation for 3D Printing
(The Eurographics Association and John Wiley & Sons Ltd., 2022) Bedel, Adrien; Coudert-Osmont, Yoann; Martínez, Jonàs; Nishat, Rahnuma Islam; Whitesides, Sue; Lefebvre, Sylvain; Chaine, Raphaëlle; Kim, Min H.
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.