|Abstract:|| The emergence of freeform structures in contemporary architecture raises numerous challenging research problems, most of which are related to the actual fabrication and are of a mathematical nature. The talk will discuss recent progress in this field, with a particular focus on discrete geometric structures. Most of these result from practical requirements on segmenting a freeform shape into planar panels, on the physical realization of supporting beams and nodes and on constraints from statics. Relations to discrete differential geometry provide insight which is important for initializing numerical optimization algorithms for computing such structures. We illustrate this at hand of architectural skins formed by planar quadrilateral or even nearly rectangular panels, their support structures, and the geometry resulting from force equilibrium constraints. Finally, we go beyond discrete analogues of differentiable surface representations by discussing patterns of planar polygonal faces on freeform surfaces.
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