Analysis and design of curved support structures

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 differential-geometric 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.