## 2 Materials and Methods
### 3D Modelling  
#### 2.4.1 3D Model of Houses  
In this section, we describe the process of generating 3D models for houses in the city using a probabilistic graphical model (PGM). As there are no remaining houses from the study period, we rely on the PGM, which is defined by the variables in Table 3, the graph in Figure 9, and its corresponding conditional probability distributions. To generate a specific house, we condition the variable ZON and sample the others. The process proceeds as follows: the location of a house in the city determines a value for the variable ZON. From there, we probabilistically generate one of the five types of houses using variable TIP, which in turn generates a compatible facade code, _fcode_, for the variable COD. We then use _fcode_ to compute the number of tiles of the house for the variable NTIL. Each zone in the city also defines a slot length for the variable LTIL, which, along with the length of the walls (0.6 m) and the number of slots in NTIL, determines the final length of the house in the variable LENF. This generative model provides a means for defining the essential elements of the house's construction, including the type of house, the arrangement of doors and windows on the facade, the length and number of tiles, and the overall length of the house. The conditional probabilistic distribution (CPD) of NTIL is deterministic from the number of elements in the _fcode_. The CPD of LENF is also deterministic and equal to 0.6 \(\times\) 2 + TIL \(\times\) NTIL, where 0.6 is the length of the house walls. The rest of the CPDs are estimated using the historical documentation in Section 2.2.3. After designing the basic structure of the house, the next step is to determine its spatial position within a city block. The process of modelling the plots begins with vectorizing the blocks (see Figure 6), which have already been transformed into geographic coordinates through georeferencing. In the literature, there are various techniques for block partitioning [41], including those based on the straight skeleton (SS) and recursive subdivisions (RS). In this work, both techniques were used, with SS being used to partition the edges of \begin{table}
\begin{tabular}{l l} \hline \hline
**Variable** & **Description** \\ \hline ZON & Zone of the city: central, intermediate, peripheral. \\ TIP & House type: terrera, granero, sobradada, comercial, armera. \\ COD & House code (_fcode_). \\ NTIL & Number of tiles of the house \\ LTIL & Length of house tiles \\ LENF & Length of house front \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Variables of the probabilistic graphical model in Figure 9.  
the blocks due to its greater control over the length of the plots, while RS was used for the interior of the plots to produce results similar to those of the map. The SS method [41] is based on the partitioning of the block edge and its subsequent subdivision into plots. However, the original algorithm had to be modified to consider several aspects. One of the key observations in [PERSON]'s map is that it is not always necessary to partition each block entirely. This is because the presence of certain elements, such as empty block spaces and walls, can effectively act as natural partitions. Second, the length of the plot fronts generated through a normal distribution in [41] is replaced in this case by the LENF variable in the PGM model described earlier. Finally, the processing of the sides of the blocks is performed by studying the collinearity of their vertices rather than their belonging to logical streets due to the absence of information about the complete street layout of the city in 1588. The importance of each side of the block is calculated using the betweenness centrality (BC), which is a measure widely used in the study of the spatial distribution of cities [42].