## 3 Geometry Reconstruction and FEM Implementation  
The main structural elements with complex geometries in the two case studies were reconstructed from the 3D point cloud obtained from laser scanner surveys. In particular, the geometry of the basilica of Santa Maria di Collemaggio was reconstructed in line with the approach reported in [29; 30; 31]. Moreover, for the reconstruction of the geometry of the basilica of Santa Maria Novella, the laser scanner used was a Leica HDS 7000. Due to the complexity of the case studies, several scans were required to fully reconstruct the structures. The scan quality was set to medium (3\(\times\)), with a resolution of 1 pt per 12.27 mm at 10 m. The TLS scans were processed using the Reconstruct software, version 4.4.2, with the Iterative Closest Point (ICP) algorithm [32]. Particular attention was devoted to the definition of the vaults, and the domes' correct geometries were reproduced by means of the contour-level curves (Figure 6a) that define the related surfaces (Figure 6b) [33]. The laser scanner's point clouds allowed for the accurate reconstruction of the main structural elements, taking into account the irregularities typical of historic buildings. These irregularities would not have been detectable using a standard geometric survey. This aspect is particularly important for the accurate definition of the seismic behaviour of such a structure. Moreover, both churches present peculiar facades, not only in terms of their configuration but also due to the presence of multiple openings (Figure 7). To evaluate the seismic performance of the two churches, finite element models (FEMs) were implemented based on the above-mentioned comprehensive geometry reconstructions [34; 35; 36; 37]. In particular, the geometry of both basilicas was schematised by means of the beam elements to represent the main pillars of the transport, the columns, the arches, the R.C. curbs, the structure of the roof, and the plate elements to reproduce the structural behaviour of the facade, the walls, the vaults, and the domes (Figure 8). The mesh size (implemented in Midas GEN 2024 v2.1 software [38]) was adapted to reproduce as accurately as possible the geometric characteristics of the two basilicas, also considering the above-mentioned widespread presence of openings in the walls and in the facade. The FEM of the basilica of Santa Maria di Collemaggio was implemented using 3916 beam elements and 12,652 plate elements. The FEM of the basilica of Santa Maria Novella was schematised by means of 6949 beam elements and 69,330 plate elements. The main mechanical properties of the materials (determined according to as reported in [39; 40]) characterizing the two churches are summarised in Table 1, where E is the Young's modulus, v is the Poisson's ratio, and \(\gamma\) indicates the weight density. When appropriate, the bending and shear stiffness of the main structural elements were reduced using the appropriate scale factors, calculated according to the method reported in [39], in order to consider the possible presence of cracks. Figure 6: Example of vault schematization: (**a**) polylines of sections obtained from the point cloud; and (**b**) surface of the vault. The self-weight of the different elements that characterise the churches and the dead loads, with the related masses, were applied to the FEMs shown in the previous Figure 8. The presence of seismic action was considered by means of seven spectrum-compatible