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Introduction
Welcome to the Marching Cubes and Periodic Minimal Surfaces tutorial. This video presents some ways to understand minimal surfaces (and triply periodic minimal surfaces - TPMS). It explores their geometry, where these mathematical structures pop up in nature, and what their value can be to architects and designers. This introduction also touches on the basics of the Marching Cubes algorithm and how this computational technique can be used to visualize periodic minimal surfaces.

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Resources
Stephanie Piper is not mentioned in this video, but she is cited in Video_04. We would like to thank her here, though, for finding and citing these videos by Alan Schoen: 'Shapes of Soap Films': Triply-Periodic Minimal Surfaces (Alan H. Schoen) parts 1 through 4:
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Buratti, G. (2018). Algorithmic Modelling of Triply Periodic Minimal Surface. Computational Morphologies, 55–62. https://doi.org/10.1007/978-3-319-60919-5_5

Feng, J., Fu, J., Yao, X., & He, Y. (2022). Triply periodic minimal surface(TPMS) porous structures: From multi-scale design, precise additive manufacturing to multidisciplinary applications. International Journal of Extreme Manufacturing, 4(2). https://doi.org/10.1088/2631-7990/ac5be6

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Knippers, J., Nickel, K. G., & Speck, T. (Eds.). (2016). Biomimetic Research for Architecture and Building Construction: Biological Design and Integrative Structures. https://doi.org/10.1007/978-3-319-46374-2

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Menges, A. (2012). Material Computation: Higher Integration in Morphogenetic Design. Architectural Design, 82(2), 14–21. htps://doi.org/10.1002/AD.1374

Mensch, T. E., Delesky, E. A., Learsch, R. W., Foster, K. E., Yeturu, S. K., Srubar, W. V., & Miyake, G. (2021). Mechanical evaluation of 3D printed biomimetic non-Euclidean saddle geometries mimicking the mantis shrimp. Bioinspiration & biomimetics, 16(5), 056002.

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Rossi, M., Buratti, G. (2018). Computational Morphologies: Design Rules Between Organic Models and Responsive Architecture. Springer International Publishing. Kindle Edition.

Saranathan, V., Narayanan, S., Sandy, A., Dufresne, E. R., & Prum, R. O. (2021). Evolution of single gyroid photonic crystals in bird feathers. Proceedings of the National Academy of Sciences of the United States of America, 118(23),8–10. https://doi.org/10.1073/pnas.2101357118

Saranathan, V., Osuji, C. O., Mochrie, S. G. J., Noh, H., Narayanan, S., Sandy, A., … Prum, R. O. (2010). Structure, function, and self-assembly of single network gyroid (I4 132) photonic crystals in butterfly wing scales. Proceedings of the National Academy of Sciences of the United States of America, 107(26),11676–11681. https://doi.org/10.1073/pnas.0909616107

Tadayon, M., Amini, S., Wang, Z., & Miserez, A. (2018). Biomechanical Design of the Mantis Shrimp Saddle: A Biomineralized Spring Used for Rapid Raptorial Strikes. IScience, 8, 271–282. https://doi.org/10.1016/j.isci.2018.08.022