Computer Aided Generation of Architectural Typologies

The work we present may be considered as the consolidation of a methodology that was already outlined in the paper presented in the second M&D congress held in San Sebastian (1998). We establish that, in architectural design, the computer is only used in the last step in order to achieve the traditional Euclidean design in a more precise and comfortable way and to improve the quality of the handmade designs. Our proposal consists in modifying the process from the very beginning of the creative act. That is, when the design conception is born. If we want to obtain the maximum benefit of the computer possibilities, we ought to support this conception by means of a language tuned with the mentioned tool. Due to the fact that the internal language used by the computer for producing graphics is mathematical, we must incorporate, in some way, this language in the codification of the creative process. In accordance with this setting, we propose a mathematical grammar for the design based on the construction of modulated standard mathematical functions. This grammar is developed independently from the graphical software and it is specified only when a particular computer program for the effective generation on the graphical objects is selected. To prove and exemplify the possibilities of this methodology, we present: 1. A set of typologies or catalogues of architectural elements mathematically formulated (in the same way as a parabola or an ellipsoid is defined) and provided with several meaningful formal parameters. The structure of this catalogues allows to the users either to call a typology giving concrete values to the parameters or to produce further variations and personalized developments of the catalogue. In particular, for our communication, we have chosen the typology arch (as a generalization of a circumference) and the typology dome (as a generalization of a sphere). Moreover, if we manipulate the arches by extrusion, interpolation, etc., we can produce walls with gaps, naves, cross galleries, halls surrounded by columns, gates with archivolts, etc... We show that, with few parameters, the range of arches and domes and the combination possibilities we can produce is surprisingly ample and versatile. 2. Several complete examples developed by using these catalogues where our formulations are concreted in a specific computer language in order to be implemented in a commercial computer software package.