Final Report Summary - ARC (Architectural Freeform Structures from Single-Curved Panels) Complex freeform structures are one of the most striking trends in contemporary architecture. So far, design and manufacturing of such structures are based on digital technologies which have been developed for other industries (automotive, naval, aerospace industry). Architecture differs from these traditional target industries of CAD/CAM technology in many ways including aesthetics, statics, structural aspects, scale and manufacturing technologies. This leads to numerous challenging research problems, some of which have been addressed in the present project. Manufacturing architectural freeform structures requires the segmentation into panels. The simplest panels are flat, which is sometimes undesirable as it leads to a facetted appearance of the structure. Hence, one has to resort to curved panels. In the present project, we have investigated the problem of building architectural freeform structures from single-curved panels. Single-curved surfaces are the first step beyond flat surfaces. A plain piece of paper can be used to demonstrate the many single-curved surfaces that can be created. It can be bent into numerous shapes without needing to be folded. To meet the practical requirements, solid knowledge and large experience in architectural design and engineering is essential. Three partners joined to meet the challenges in this field: (1) TUW, an academic institution with deep fundamental knowledge in applied geometry and geometric computing, (2) Evolute, a high-tech research start-up specializing in geometric computing for architecture and manufacturing and (3) RFR, an established engineering office with world wide experience, specialized in non-conventional lightweight structures and with relevant experience in freeform design.The main results of research within ARC are a solid theoretical basis and new methods to compute surfaces composed of single-curved panels. We also incorporated important practical aspects such as manufacturing technologies for producing the panels. Just to give an example, when one is working with glass, the most general single-curved panels would still be too expensive to produce. Hence, we developed a proper optimization framework to use only panels which are parts of right circular cylinders. Another important direction of research has been to understand the behavior of glass, the limits of cold-bending, and the use of glass as a structural element. We have been able to link shape design with structural analysisFrom the mathematical perspective, our research led to a new type of surface representations, which constitute a link between the classical smooth surfaces and discrete surfaces, a hot topic of active research in mathematics and computational science. The new type of surfaces has been studied with methods from discrete and classical differential geometry and computational mathematics. Our research stimulated further studies from the pure mathematics community. ARC partners Evolute and RFR have had the fantastic opportunity to apply research findings directly to a prestigious project: the The Eiffel Tower Pavilions on the first platform of the Eiffel Tower, designed by the architects Moatti et Rivière. The main challenge was the realization of a double-curved glass facade. ARC's research played a substantial role in providing a cost-effective and elegant solution based on cylindrical glass panels and a remarkable curved supporting structure. The Eiffel Tower Pavilions project is scheduled for completion in summer 2013. Another notable project in which ARC technologies have been successfully used is a curved glass façade for the Arena de Sao Paulo in Brazil, which will host the opening game of the 2014 FIFA World Cup.We are pleased to report that the popularity of the research field ARC is dealing with is rapidly increasing; with the biennial conference Advances in Architectural Geometry showing an increase in the number of participants from 130 in 2008 to 220 in 2010 and most recently 400 in 2012. ARC has sponsored the two most recent conferences.Through the partnership within ARC, a new company – bform Technologies – is being formed. Itsaim will be to fuse design, engineering and mathematical rigor in order to deliver tools that will allow designers and architects to realize concepts that will push the boundaries of form, material and structure. It is by combining expertise and knowledge in such partnerships that it is hoped that the next big problem in the field of architectural geometry can be solved – that of delivering tools that allow for construction-aware geometric design without the need for a redesign phase after the initial geometry definition.