“Connected fermat spirals for layered fabrication” by Zhao, Gu, Huang, Garcia, Chen, et al. …

  • ©Haisen Zhao, Fanglin Gu, Qi-xing Huang, Jorge A. Garcia, Yong Chen, Changhe Tu, Bedrich Benes, Hao Zhang, Daniel Cohen-Or, and Baoquan Chen




    Connected fermat spirals for layered fabrication





    We develop a new kind of “space-filling” curves, connected Fermat spirals, and show their compelling properties as a tool path fill pattern for layered fabrication. Unlike classical space-filling curves such as the Peano or Hilbert curves, which constantly wind and bind to preserve locality, connected Fermat spirals are formed mostly by long, low-curvature paths. This geometric property, along with continuity, influences the quality and efficiency of layered fabrication. Given a connected 2D region, we first decompose it into a set of sub-regions, each of which can be filled with a single continuous Fermat spiral. We show that it is always possible to start and end a Fermat spiral fill at approximately the same location on the outer boundary of the filled region. This special property allows the Fermat spiral fills to be joined systematically along a graph traversal of the decomposed sub-regions. The result is a globally continuous curve. We demonstrate that printing 2D layers following tool paths as connected Fermat spirals leads to efficient and quality fabrication, compared to conventional fill patterns.


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