Curves and surfaces in the churches with ovate plant in Naples. Geometric analogies and differences

During the seventeenth century, several Neapolitan churches were built or renovated according to an oval planimetric layout, including: San Carlo all’Arena; San Sebastiano; Santa Maria Egiziaca a Forcella; Santa Maria di Caravaggio. The study method starts from the churches architectural survey and provides the plant and dome curves and surfaces geometric analysis with 3D modeling. The goal is the churches graphic analysis to define analogies and differences. From a formal point of view, a flat ovate shape is characterized by a curvilinear profile with double orthogonal symmetry. From a geometrical-mathematical point of view, it can be circumscribed either in a polycentric curve (ovate shape is a flat figure generated by the succession of several circumference arcs, whose contact points must satisfy the continuity property) or in an ellipse (geometric place of the points of the plane satisfying specific relations). The restitution and analysis of the three-dimensional geometric model is realized with a commercial application software for the 3D modelling of sculptural surfaces or ‘free form’. The ovate matrix is the configurative origin of the entire spatial layout. The elliptic curve, which approximates the planimetric profile obtained from the survey, has been assumed as a dimensional model and genesis of the three-dimensional modelling of the church. The spatial layout of the church can be traced back to a geometric model composed of a straight cylinder and a dome.