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Journal Articles Computer Graphics Forum Year : 2022

Closed space-filling curves with controlled orientation for 3D printing

Jonàs Martínez
Rahnuma Islam Nishat
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Sue Whitesides
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Sylvain Lefebvre


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.
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Dates and versions

hal-03185200 , version 1 (30-03-2021)
hal-03185200 , version 2 (19-04-2022)



Adrien Bedel, Yoann Coudert-Osmont, Jonàs Martínez, Rahnuma Islam Nishat, Sue Whitesides, et al.. Closed space-filling curves with controlled orientation for 3D printing. Computer Graphics Forum, In press, ⟨10.1111/cgf.14488⟩. ⟨hal-03185200v2⟩
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