Michael Ostwald
School of Architecture and Built Environment
Faculty of Engineering and Built Environment
University of Newcastle
New South Wales, AUSTRALIA 2308

In recent years the development of computational algorithms for the transformation of shapes has made the process of producing curvilinear forms deceptively simple. Even the most banal CAD program can generate complex three dimensional shapes, and associated building designs, without the designer having to display any detailed knowledge of geometry or indeed the history of similar forms and their relative successes and failures. This paper asks whether such a situation in innately problematic or not?
The production of intricate architectural forms has historically occurred in an environment that is aware of the cultural, political or symbolic importance of the curved form. For example the archetypal Baroque compound curve found in the facade Borromini's S. Carlo alle Quattro Fontane has both regular sinusoidal flowing surfaces along with more dynamic syncopated curves constructed of broken oval segments. Such curves responded to the social, symbolic and phenomenological needs of the era and indeed, because of this, can be seen to have an ethical function (as argued by critics such as Ruskin or more recently Harries). The paper analyses a series of recent examples and experiments which have employed computer generated curvilinear geometric forms to interrogate the extent to which such architectural techniques, which rely on geometric transformation, can be seen as having and ethical foundation. Through this analysis the paper argues for the importance of geometry in architecture as being more than simply a formal tool, but rather a device which has wider significance and more important properties and potentialities.

About the author
Professor This email address is being protected from spambots. You need JavaScript enabled to view it. is Dean of Architecture at the University of Newcastle, a Visiting Professor at RMIT University and a Professional Research Fellow at Victoria University Wellington. His research into design history and philosophy, often with a secondary focus on geometry or computing, has been widely published and he has lectured in Australasia, Europe and North America. His recent books include The Architecture of the New Baroque (2006), Antipodean Structures (2007) and Residue: Architecture as a Condition of Loss (2007). In 2006 he was awarded the Mellon International Prize for humanities scholarship and in 2007 he was awarded a higher doctorate; the Doctor of Science. He is a member of the editorial board of the Nexus Network Journal.

The correct citation for this paper is:
Michael Ostwald, "Geometric Transformations and the Ethics of the Curved Surface in Architecture", pp. 77-92 in Nexus VI: Architecture and Mathematics, eds. Sylvie Duvernoy and Orietta Pedemonte Turin: Kim Williams Books, 2006.