Title: Geometry of Architectural Freeform Structures

Abstract:
Complex freeform structures are one of the most striking trends in contemporary architecture. This direction has been pioneered by architects such as F.~Gehry, who exploit digital technology originally developed for the automotive and airplane industry for architectural design and construction. This is not a simple task at all, since the architectural application differs from the original target industries in many ways, including aesthetics, statics, scale and manufacturing technologies. Manufacturing architectural freeform structures requires the segmentation into panels, which may be either flat, single curved or double curved. The speaker will provide a survey of recent results dealing with the panellization of complex double curved surfaces. The focus will be on a study of quadrilateral meshes with planar faces, in particular of those meshes which discretize the network of principal curvature lines. Conical meshes are one of these meshes; they possess conical offset meshes at a constant face/face distance, which in turn leads to a supporting beam layout with so-called torsion free nodes. Other types of offsets and requirements on the layout of supporting beams exhibit a close relation to differential geometric concepts such as isothermic surfaces in sphere geometries. We will also look at the layout of a planar quad mesh on a general freeform surface while keeping constraints on panel sizes, orientations and structural aspects; here, recent advances are based on subdivision surface fitting and mesh optimization. There are also efforts on segmenting surfaces into planar hexagonal panels. Though being less constrained than planar quad meshes, this problem is still waiting for an elegant solution. Finally, we will look onto results of ongoing research dealing with the segmentation into curved panels.