I fondamenti geometrici della progettazione

Descriptive geometry has a historically consolidated relationship with the art and the construction in general, and it could therefore not fail to be affected by the technological evolution we mentioned earlier. The classical corpus of texts on the discipline, based first of all on the representation methods, understood as the theories of the construction of the encoded image, appeared to be completely inadequate compared with the contemporary project procedure and, what is worse, it seemed unrelated to the new representation techniques of the space, while these last, at the same time, did not seem to have a basis theory of general character, but only the algorithms that permit to solve this or that particular problem. In the academic circles, the architects who, due to changing historical events, today are the repository of the discipline of descriptive geometry, have finally seized the wish for renewal that came above all from the youth, faced, on the one hand, with a theory that does not seem to have any more applications and, on the other, with a technique that is incomprehensible, precisely because it is lacking the general concepts of a theory; now, finally, is ongoing a process of revision and renewal of the classic descriptive geometry, which is based on new definitions of the fundamentals and fulfilled through integrations and transformations of the corpus of texts on the discipline. As we will see in a while, the integrations concern, essentially, the representation methods, while the transformations involve above all the construction procedures of the geometric shapes. The representation methods, in general, are distinguishable for two essential reasons: the first, and the most important, is that each of the methods is able to record the characteristics of the shape and the dimension of an object in the space and, at the same time, it is able to transfer the object back into the space once it has been represented. A method, to be considered as such, must be able to perform this path, in both directions, autonomously, that is, without turning to other methods. The second reason that permits to distinguish the methods, the one from the other, concerns the use of each of them within the planning activity: the metric control, as in the case of the representation in plan and elevation, or the formal and perceptual control, as in the case of the perspective. The information systems make use, basically, of two digital representation methods that have been called: mathematical representation and numerical or polygonal representation. The digital representation methods have some other extremely innovative characteristics, which have remarkable impacts on the planning as well as on the theoretical evolution of descriptive geometry and these are: the accuracy and the spatiality. this modality of the geometric expression, which uses the analogy to describe the result of a digital process, may appear to be hybrid, too, and not purely geometric. But, as a matter of fact, we are simply dealing with the fulfilment of one of Monge’s wishes, the synergies between analysis and synthesis, between symbolic languages and graphic languages, which the French mathematician already clearly expressed in the first edition of his most famous work (1798): the analytic geometry and descriptive geometry should be ‘cultivated’ together, since in this way the descriptive geometry would bring its own evidence into the most complex analytical processes and, in turn, the analysis would bring the generality and accuracy of the results to the descriptive geometry. After all, Monge’s idea has not been abandoned: this way of making research, open-minded, deliberately disrespectful of the fences that surround the disciplinary fields of mathematics, has illustrious supporters: from Guido Castelnuovo (1903) to Harold Scott Mc Donald Coxeter (1961). In former times, when electronic computers were still unknown or had far from reached their present-day world-wide distribution, the schools of mathematics have created a rich selection of three-dimensional models, maquettes in plaster, wood and other materials very similar to those which decorate the studio of an architect or a designer. Recently these collections have been subject to studies and additions carried out, precisely, with virtual models. René Thom (1977), while on the one hand he considers the descriptive geometry as an obsolete science, and affirms that he would like to free himself from the manipulation of the Euclidean three-dimensional bodies of the space, on the other hand he recognizes to the qualitative sciences the capability to construct models that are the only ones able to explain our surrounding world, even if they cannot give quantitative results. So, it really looks like as if the synergy hoped for by Monge, and today fully expressed by the union between the concise reasoning of the geometry and the electronic calculation, is able to create a synthesis between quantity and quality, producing results that, while they describe with audacious analogies and with great immediacy the reality of a phenomenon, they also allow a quantitative analysis with controlled accuracy