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Wire cut of double-sided minimal surfaces

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Abstract

We present a systematic method for producing double-sided minimal surfaces by wire-cut machines. A link between minimal surfaces and ruled surfaces is pursued through wire cutting. Weierstrass parameterization is employed to define minimal surfaces (\(\mathbb {R}^3\)) over a complex plane (\(\mathbb {C}\)). Our method consists of three components. First, the orthogonal double-sided cuts match a pair of orthonormal tangent vectors on the surface. Second, A closed-form expression for the principal directions facilitates the global quadrangulation of minimal surfaces. Third, the CNC machine’s toolpath results from the surface’s analytic characterization. Asymptotic cutting and principal cutting are compared in terms of collisions and cutting error. We employed a general-purpose language (Java) to create machine instructions from the Weierstrass representation of minimal surfaces. Thus, the entire workflow from mathematical modeling to production involves no 3D models or CAD/CAM software. Both a 5-axis wire cutter and a customized robotic system were tested.

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Acknowledgements

The digital fabrication was carried out at Prof. Li Biao’s Institute of Algorithms & Applications, Southeast University. We would like to thank Wang Xiao for video recoding and the graduate students from the Institute for their support.

Funding

This research is supported by National Natural Science Foundation of China (51778118, 51478116, 51538006, 51578123) and by Ministry of Housing and Urban-Rural Development of China (UDC2017020212).

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Authors and Affiliations

  1. Key Laboratory of Urban and Architectural Heritage Conservation (Southeast University), Ministry of Education, Nanjing, China

    Hao Hua & Tingli Jia

  2. School of Architecture, Southeast University, 2 Sipailou, Nanjing, 210096, China

    Hao Hua & Tingli Jia

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  1. Hao Hua
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  2. Tingli Jia
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Correspondence to Hao Hua.

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Hua, H., Jia, T. Wire cut of double-sided minimal surfaces. Vis Comput 34, 985–995 (2018). https://doi.org/10.1007/s00371-018-1548-0

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