## 2 Materials and Methods
### Spatial Analysis Methodology  
An integrated multi-criteria evaluation (MCE) approach was applied to analyse territorial data. This method consolidates multiple spatial characteristics by assigning positive values to favourable factors and subtracting the influence of elements negatively impacting the evaluated activity. The MCE technique aligns with the weighted linear summation model proposed by [PERSON] and [PERSON] [25], which is mathematically expressed as:  
\[r_{i}=\sum_{j=1}^{n}W_{j}V_{ij}\]  
where:  
\(r_{i}\) represents the suitability score of alternative \(i\),  
\(W_{j}\) denotes the weight assigned to criterion or factor \(j\),  
\(V_{ij}\) corresponds to the evaluated value of alternative \(i\) under criterion \(j\). This approach enables the weighted assessment of spatial elements, offering a structured visualisation that aligns with the research objectives. Various geographic information systems (GISs) have been utilised [25; 32; 33] to process territorial variables from heritage perspectives, ensuring their functional relevance for mobile augmented reality (MAR) and mobile pedestrian navigation (MPN) applications [34; 35; 36]. The selected variables are summarised in Table 3:  
With the identification of key sectors offering the highest potential for pedestrian movement and heritage visualisation, a refined spatial delineation of the study area was established. This process involved the creation of Thiessen polygons using spatial gravity centres derived from the multi-criteria evaluation (MCE) values to define optimal territorial subdivisions. Thiessen polygons provide a geometric approach to partitioning a Euclidean plane, where reference points serve as the basis for defining boundaries through interpolation based on Euclidean distance [37; 38; 39; 40]. After obtaining a Euclidean distance, we have:  
\[\|p-q\|=\sqrt{\left(p_{x}-q_{x}\right)^{2}+\left(p_{y}-q_{y}\right)^{2}}\] \begin{table}
\begin{tabular}{p{142.3 pt} p{142.3 pt} p{142.3 pt}} \hline \hline
**Objective** & **Criterion** & **Description of the Criterion and Function (Fuzzy)** \\ \hline \multirow{8}{*}{Urban environment} & Real estate and heritage sites & Boolean data representation: indicates whether information is present or absent within the dataset. \\  & & Standardisation of data according to type of road: pedestrian, street, passage, highway, etc. Criteria defined based on the ease and difficulty of pedestrian movement. \\  & Properties and plots & Boolean data representation: indicates whether information is present or absent within the dataset. \\  & Elevations (slope) & Symmetrical function: greater suitability between \(0^{\circ}\) and \(25^{\circ}\) of slope for pedestrian movement. \\ \hline \multirow{8}{*}{Heritage background} & Essential characteristics, modifications and architectural alterations. & Standardisation according to reclassification of data from highest to lowest number and type of modifications. \\  & Evolution of its use and functionality & Boolean data representation: indicates whether information is present or absent within the dataset. \\ \cline{1-1}  & Relevant characters linked to the heritage space & Boolean data representation: indicates whether information is present or absent within the dataset. \\ \cline{1-1}  & Relevant photographic documentation & Boolean data representation: indicates whether information is present or absent within the dataset. \\ \cline{1-1}  & Change in functionality & Boolean data representation: indicates whether information is present or absent within the dataset. \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Variables used in the EMC assessment.