The Nave Roof

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The nave roof provides further evidence of Gaudí’s use of the virtually present as a point to anchor cohesion to a formal spatial construct. In an account of Gaudí’s intentions published two years after his death, Josep Ràfols i Fontanals (1889–1965), an architect, artist and historian who had collaborated with Gaudí and wrote the first biography of him, observes that the nave roof is an assemblage of hyperbolic paraboloids, all meeting at a point.13 In considering the 1:25 scaled gypsum plaster model, this observation is not readily substantiated by eye. If, however, we reduce the surfaces to their underlying geometry, we can see that with the right combination of parameters the hyperbolic skins relax into the original surfaces.

The role of the computer to find the curves of inflection relies on scripting a set of contiguous associative geometries. The first step was to make a digital model of the surviving and restored original and to use the wire frame outcome as a skeleton onto which a skin could be grafted. The digital model was made in 1996 and measured by a point digitiser, an articulated arm that has a digital probe with a sharpened point. Fourteen years later this already seems an archaic relic, but at the time it was regarded as an invaluable new digital tool. The resulting 3D wire frame model was imported into a parametric geometry design package and was used as reference for building a geometrically precise version. Using the digitised model as a base, a notional flexible model is built around it. This does not need to be accurate in terms of positions and line lengths, for example, but the flexible model needs to be the topological equivalent. Once built it is only a matter of scripting a sequence of likely range of values for the determining parameters, by which the virtual model was built up or relaxed, fattened or made more slim until it finally folded into the original. By building the model from hyperbolic paraboloids that meet at a virtual  point that itself can be varied in height, in minutes the correct (in terms of matching the original) form was found that is also composed entirely of ruled surfaces and planes. Of course, today we would use a genetic algorithm within the script for an automated best-fit solution.

Quite what use Gaudí himself would have made of such versatile virtual design exploration potential is no more than idle speculation, as is the precise manner in which he achieved a complex study such as this, with the virtual apex not physically in evidence. At issue here is the reverse engineering of a stated design solution from Gaudí that requires rebuilding to provide information for the built artefact. The virtual point, so present in the act of making the digital model, is fascinatingly elusive once the form has taken hold.

Text taken from: Chapter 7, ‘Composition and form’, Scripting Cultures: Architectural Design and Programming, John Wiley and Sons Ltd, London, 2012

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