Geometry of Architectural Freeform Structures（建筑自由的几何结构）.pdf

Internat. Math. Nachrichten Nr. 209 (2008), 15–28 Geometry of Architectural Freeform Structures 1 1,2 3 Helmut Pottmann , Alexander Schiftner , Johannes Wallner 1 TU Wien 2 Evolute GmbH, Wien 3 TU Graz This article shows to which extent a particular field of mathematics, namely dis- crete differential geometry, has recently become relevant in architectural design. It is very interesting that new mathematics has emerged from this cooperation with a branch of knowledge hitherto not known for its use of mathematical methods. Introduction 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 in- dustry for tasks of 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. Whereas metal forming can generate any reasonable shape of a car body, it is much less clear how to actually construct a complicated geometric shape in an architectural design. One has to segment the shape into simpler parts, so-called panels. According to Lars Spuybroek, “panelization is a hugely important issue” [10]. Since available CAD software does not cover this topic, one may have to resort to simpler shapes, to accept higher costs or to try experimental approaches. Very recent research shows that the use of geometry and computational mathe- matics bears a great potential to advance the field of freeform architecture. It is a major goal of this paper to