Un manifesto per il rinnovamento della GD

The renewal of DG is based on the following presuppositions The analysis of the historical evolution of the discipline shows that, from the second half of the twentieth century, the only advancements of the discipline are connected to the experimental field of the drawing. The few original contributions of theoretical nature are unfortunately an exception. The same analysis shows the importance that the drawing has had, as experimental method, not only for the DG but for the geometry in general. The Advent of the digital representation has put at the researchers disposal a tool able to: to generate graphics in the space; synthetically express problems that, in the history, it has only been possible to develop analytically; to generate graphics with an accuracy one hundred times greater; to produce images of superior quality (dynamism, chiaroscuro, interactivity). As Gaspard Monge affirmed, the DG has two privileged fields of application: the first is to represented exactly, on drawings that have only two dimensions, the objects that have three dimensions and that are open to a rigorous definition; the second is to deduce from the exact description of the bodies all that follows consequently from their forms and from their reciprocal positions; in this sense it is a means for the search for the scientific truth and it offers perpetual examples of the passage from the well-known to the unknown… the first aim is today excellently absolved by means of the machines; the second cannot be accomplished by means of the machines, nevertheless the machines represent for the researcher a powerful means of inquiry and of discovery. The renewal of DG can be realized through the following initiatives The introduction of the three-dimensional digital modelling among the methods of the Descriptive Geometry in the shapes of mathematical representation and of the polygonal representation, the first for the metric control, the second for the formal control of the represented objects. The analysis, critical, of the performances of the digital representation: tracing in the space, accuracy, coherent mathematical representation with studied functions (degree of the equations) etc. The study of the algorithms that are at the base of the digital procedures and of their relationship with the historical theories from which they descend. The theoretical re-reading of the classical problems and their experimentation with the digital representation. The proposal of new procedures that takes into account the digital means available. The definition and the adoption of an unified glossary (for instance: digital representation instead of digital modelling and so on). The initiatives that we have described and mainly those which regard the re-reading of the classical authors by means of the digital tools, the optimisation of new solutions of general application, the unification of the glossary, are not such that they can be developed in a narrow ambit, that’s why the authors of this Manifesto invite the colleagues of the other Athenaeums to discuss it and to undersign it in order to concretely participate in the project of the renewal of Descriptive Geometry.