Constructive Geometry
The history of a curve
Some architects herald the adoption of freeform curvilinear design and the utilization of computer-aided manufacturing as cutting edge, or even avant-garde. While it may be so within the confines of architectural design and discourse, there is, in fact, nothing essentially new about these technologies. In comparison to our counterparts in other fields, architects are, in fact, behind the curve. This article seeks to addresses this deficit of knowledge by summarizing the ingenious development of the computational curve, which occurred in other industries. It’s a fascinating story. Any designer who draws curves with only a few clicks of the mouse, may benefit from knowing how this technology – which we now take for granted – was developed.
The need to compute curved 3D surfaces with the assistance of computer numerically controlled (CNC) manufacturing was the very impetus for the first computer aided design (CAD) software over half a century ago, principally developed in the automotive and aerospace industries. Digital animators in the entertainment industry developed methods of intuitively smoothing topologically ambiguous forms. These solutions have migrated into the software tools architects use today. However, the history of curvature obviously long predates the computational era. It extends back to our early ancestors’ most primitive endeavors to bend natural materials to human will.
Curvature has always played an important structural role in buildings, evident in the Roman arches and domes that remain standing to this day. Curved form has run throughout architectural history, extending the our modern era – of which the catenary vaults of Antonin Gaudí, Félix Candela’s thin shell roofs, and Frei Otto’s tensile hyperbolic paraboloids are notable examples. Curvature has also inflected architecture with aesthetic refinement. For example, the use of entasis in Greek antiquity made columns appear to bulge under the strain of their load. After enjoying a relatively brief heyday in the Modernist 1950′s and 60′s, curvilinear architecture had ebbed to an undercurrent by the late 20th century, navigated by only a few eccentric visionaries. Frank Gehry’s iconic Bilbao Guggenheim museum (1997) changed all this. It heralded in a renaissance of curvaceous formalism and broadcasted the arrival of the contemporary digital architectural era to mainstream culture. It is telling that the NURBS (Non-Uniform Rational B-Splines) software – specifically, Dessault’s Catia® – used to conceive and coordinate construction of the museum’s undulating titanium skin was technology originally developed for designing fighter jets. Both Catia’s and NURBS’ roots can be traced back to Paris in the 1960s, where the computational curve was invented nearly simultaneously in two rival car factories. The term ‘spline’ – synonymous today with the computational curve – can be traced back much further into the early history of naval architecture, where it originally referred to a flexible strip of wood used to scribe the smooth cross sections of boat hulls – a technique called lofting, practiced since antiquity. It’s no coincidence that these terms remain in the computer modeling lexicon we use today.
Given the current vogue for freeform surfaces in architecture, as well as the wider prevalence of ergonomic forms in our daily lives – from toothbrushes to bike helmets – it seems surprising so little historical research (architectural or otherwise) has been collected regarding the geometrical underpinnings of 21st century computer-aided design. From the commonplace to the sublime, the spline delineates contemporary aesthetics (curved and straight) because it is the lingua franca of the design, engineering, and manufacturing industries. Yet its history remains under-appreciated and its technical underpinnings are generally not comprehended, even by eager adopters, who tend to take modern 3D software’s point-and-click facileness for granted.
Most accounts of early computer aided geometric design (CAGD) come from (mostly academic) books and papers, written for a highly technical audience within that field. Apart for one or two notable exceptions,i historical developments are presented as an evolution of mathematical equations, without much commentary as to their wider importance for humankind. These texts assume a sophisticated knowledge of advanced mathematics, which, sadly, this author does not possess. Thus, this effort to unravel the story of the spline may be the first nontechnical account written for the intuitive understanding and benefit of the user base – ie. designers. For architects, specifically, it’s worth familiarizing ourselves with the spline’s influence over the wider field of design so that contemporary architectural developments can be placed within a more historically and technically grounded context. Demystifying the curve, I hope, will help to develop a better appreciation – perhaps even a connoisseurship – of what has now become a de facto architectural tool: the spline.
