Martin Kilian
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 non-CMC 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.
Supplemental Material
- Alexander I. Bobenko and Yuri B. Suris. 2008. Discrete Differential Geometry: Integrable Structure. American Mathematical Society.Google Scholar
- Martin Kilian, Davide Pellis, Johannes Wallner, and Helmut Pottmann. 2017. Material-minimizing forms and structures. ACM Trans. Graphics 36, 6 (2017), article 173. Google ScholarDigital Library
- 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). Google ScholarDigital Library
- 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.Google Scholar
- 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. Google ScholarDigital Library
Index Terms
Curved support structures and meshes with spherical vertex stars
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