Algorithms for Geometrical Models in Borromini's San Carlino alle Quattro Fontane

Construction of mathematical models of the vault of Borromini’s San Carlino alle Quattro Fontane based on parametric curves and surfaces, including the shape of the vault and rules for its tessellation with crosses and octagonal coffers. Several models of different complexity are optimized and tested measuring their distance from the point cloud of a very accurate 3D survey and the analysis of such measured data is proposed to validate hypothesis of construction procedures by checking symmetries of coffers shape, scale and position in different levels and sectors. Some original algorithms are discussed to produce regular tessellations on a surface with a generic base curve and to construct regular parametric curves section out of simple point cloud data.