“Curved Support Structures and Meshes with Spherical Vertex Stars” by Kilian, Wang, Schling, Schikore and Pottmann

  • ©Martin Kilian, Hui Wang, Eike Schling, Jonas Schikore, and Helmut Pottmann

  • ©Martin Kilian, Hui Wang, Eike Schling, Jonas Schikore, and Helmut Pottmann

  • ©Martin Kilian, Hui Wang, Eike Schling, Jonas Schikore, and Helmut Pottmann

Conference:


Entry Number: 53

Title:

    Curved Support Structures and Meshes with Spherical Vertex Stars

Presenter(s):



Abstract:


    The computation and construction of curved beams along freeform skins pose many challenges. We show how to use surfaces of constant mean curvature (CMC) to compute beam networks with beneficial properties, both aesthetically and from a fabrication perspective. To explore variations of such networks we introduce a new discretization of CMC surfaces as quadrilateral meshes with spherical vertex stars and right node angles. The computed nonCMC surface variations can be seen as a path in design space – exploring possible solutions in a neighborhood, or represent an actual erection sequence exploiting elastic material behavior.

References:


    • Alexander I. Bobenko and Yuri B. Suris. 2008. Discrete Differential Geometry: Integrable Structure. American Mathematical Society. 
    • Martin Kilian, Davide Pellis, Johannes Wallner, and Helmut Pottmann. 2017. Materialminimizing forms and structures. ACM Trans. Graphics 36, 6 (2017), article 173. 
    • H. Pottmann, A. Schiftner, P. Bo, H. Schmiedhofer, W. Wang, N. Baldassini, and J. Wallner. 2008. Freeform surfaces from single curved panels. ACM Trans. Graphics 27, 3 (2008). 
    • Chengcheng Tang, Martin Kilian, Pengbo Bo, Johannes Wallner, and Helmut Pottmann. 2016. Analysis and design of curved support structures. In Advances in Architectural Geometry 2016, Sigrid Adriaenssens, Fabio Gramazio, Matthias Kohler, Achim Menges, and Mark Pauly (Eds.). VDF Hochschulverlag, ETH Zürich, 8–23. 
    • Chengcheng Tang, Xiang Sun, Alexandra Gomes, Johannes Wallner, and Helmut Pottmann. 2014. Form-finding with Polyhedral Meshes Made Simple. ACM Trans. Graph. 33, 4, Article 70 (July 2014), 9 pages.

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Additional Images:

©Martin Kilian, Hui Wang, Eike Schling, Jonas Schikore, and Helmut Pottmann

Acknowledgements:


    This work was supported by SFB-Transregio program Geometry and Discretization (FWF grant no. I 2978) and by the project Geometry and Computational Design for Architecture and Fabrication at Vienna University of Technology.


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