## 4 Discussion  
The reconstruction of 3D models was achieved using various methods based on data-driven and model-driven modelling. In the parametric reconstruction of complex structures and roofs, as shown in Table 1, the best results were obtained through the data-driven free-form method proposed (tri- and quad-mesh model). The most significant technical aspects of the proposed method are:  
Regularisation of the roof contour lines by conversion into a mesh plane, in phase 1;  
Production of a \"dummy\" point cloud segmented according to the surveyed facades, in phase 2;  
Quad-mesh simplification as the preferred method for simplifying 3D models, in phase 3. Regularization of contour lines through the conversion into the mesh plane is based on the principle of transforming convex parts of contour lines into plane edges and filling concave parts of contour lines with mesh triangles. Generally, smoothing algorithms are used to regularize the contour lines, but, in the case studied, the contour lines were too damaged for these methods (Figure 8a). However, using the method of conversion into the mesh plane, it was possible to reconstruct and regularise the contour lines of the roof (Figure 8d). One of the most popular methods for reconstructing facades in 3D modelling using ALS data consist in the vertical extrusion of roof contour lines (e.g., using 3D Base-maps by ESRI). This method is very useful but when applied to historic buildings results in the loss of facade data. Instead, through the production of a \"dummy\" point cloud segmented and tailored specifically around the facades surveyed, it is possible to preserve, during the modelling phase, relevant data of the historical and artistically valuable facades. During the research, various methods were tested to simplify the tri-mesh model: transformation into an NURBS model by Rhino 7, decimation of tri-mesh by Autodesk Meshmixer, and polygonisation by Geomagic Design X. All of these methods resulted in a loss of formal coherence of the model with a loss of roof definition. The method that produced the best results in the formal preservation of the 3D model was the transformation into a quad-mesh model with Instant Meshes. In addition, by observing and comparing the results reported in Tables 1 and 2, it can be seen that a simplification of the tri-mesh model by more than 92% did not produce a significant loss of accuracy in the quad-mesh model. For these reasons, we believe that simplification by quad-mesh model transformation is preferable in the simplification of tri-mesh models of complex structures. To investigate the limitations of modelling of complex structures by primitives, some modelling tests were performed using the Polyfit method. This method was able to model the structure as a simple prismatic shape. However, it is not possible to represent structures with a high degree of complexity. The data-driven free-form method proposed, instead, allows modelling of shapes with any degree of complexity. An interesting point is the possibility of replacing, in the pipeline, the Poisson surface reconstruction method with the Delaunay method. To evaluate this possibility, we tried to model the original point cloud and the point cloud processed with the first two phases of \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Model**} & **Vertices** & **Faces** & **Dimension** \\  & **[n.]** & **[n.]** & **[kB]** \\ \hline Triangular mesh & 405,944 & 701,396 & 14,852 \\ Quadrangular mesh & 25,556 & 50,166 & 1012 \\ Simplification rate & 93.70 \% & 92.85 \% & 93.19 \% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Simplification rate in the transformation from triangular mesh to quadrangular mesh. the pipeline with the Delaunay method. In both cases, the result was a mesh model of the structure characterised by excessively irregular facades and a very noisy roof with many aberrations.