Digital Geometries: Geometrical Logic In Francesco Borromini’s Churches Of San Carlino And Sant’ivo

In all works of Francesco Borromini (1599 - 1667) technique and knowledge of the past marvellously mingle with the continuous expressive search typical of the 17th century. His works elaborated principles of dynamism, variety and contrast, by means of spectacular visual solutions going well beyond traditional rules and schemes. Both in the monastery of San Carlino alle Quattro Fontane and in the church of Sant’Ivo alla Sapienza (1642-1660), the precise identification of geometrical shapes in the plan, based on simple and consequential ratios, is fundamental for the spatial development and the volumetric structure of the churches. By integrating the historical and archive-based study of Borromini’s drawings with CAD-developed new drawings, reconstructions and models, digital clones can be produced as the basis for geometrical and configuration hypotheses. In San Carlino(1634-1644), the traditional model of sequential architectural elements is generated by rotational movements with respect to the major or minor axis, by a quarter of the oval matrix, thus generating the internal ovoids removed from the structural masonry work or dissected by horizontal or vertical planes depending on the specific requirements, finally modelling the surfaces that give shape to the church. In Sant'Ivo alla Sapienza (1642-1660) the mutual intersection of two identical equilateral triangles, superimposed but overturned with respect to the common centre, produces six points whose straight and curved sides generate an alternating rhythm with straight and curved niches. The mixed-line contour generates convex and concave lines and surfaces and is consistently used in the covering, as the basis for a very peculiar dome unique in its kind. Following CAD modelling of the digital clone of the church, the hypothesis could be made that the ribs are obtained from the transfer of portions of circles with decreasing radius as the section dimension changes. Moreover, in the final part with cherub sculptures, these circumferences suddenly change to connect with the eye. This brief analysis of two well-known examples of Baroque architecture shows that the rational use of the computer has redefined the boundaries of application of the drawing technique, by adapting it to the most different types of language and paving the way for several interpretations and potential developments. The study of the two churches is centred around the idea of a model starting from an accurate geometrical and configuration analysis of the object, and leading to the production of a digital archetype. Unlike surface or wireframe modelling, solid modelling produces 3D models with mathematical and geometrical properties allowing on-the-field interventions of joining or removing elements in order to produce the desired shape out of the shapeless block. Digital instruments thus become fundamental to build a dialogue between mathematical science and creative expression, by revealing the structural and formal development of the analysed object through an adequate graphical representation retrieving the fundamental principles and applications of descriptive and projection geometry in architecture.