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C. Tang, M. Kilian, P. Bo, J. Wallner, H. Pottmann:
"Analysis and design of curved support structures";
in: "Advances in Architectural Geometry 2016", issued by: S. Adriaenssens, F. Gramazio, M. Kohler, A. Menges, and M. Pauly; VDF Hochschulverlag, ETH Zürich, VDF, Zürich, 2016, (invited), ISBN: 978-3-7281-3778-4, 8 - 23.

Curved beams along freeform skins pose many challenges, not least on the level
of basic geometry. A prototypical instance of this is presented by the glass facades
of the Eiffel tower pavilions, and the interrelation between the differentialgeometric
properties of the glass surface on the one hand, and the layout of beams
on the other hand. This paper discusses how curved beams are represented by
developable surfaces, and studies geometric facts relevant to beam placement
along guiding surfaces. Surprisingly, many of the curves which are interesting
from the viewpoint of pure geometry (geodesics, principal curves, etc.) occur
in this context too. We discuss recent advances in the modelling of developable
surfaces, and show how they permit the interactive design of arrangements of
curved beams, in particular the design of so-called geometric support structures.

developable surfaces, support structures, interactive design, Darboux frame

http://dx.doi.org/10.3218/3778-4_4

http://www.aag2016.ch/information/