## 2 Material and Methods
### GIS-Based Methodology \"Kernel Density Estimation\"  
Geographic information systems (GIS) are a subset of information that collect, integrate, store, edit, analyze, share, and display spatial and geographic information [37]. GIS enhances a spatial and statistical analytical database to digital mapping abilities. While already a popular tool of research and applications in the fields of geography, planning, recent years have seen distinct progress in the use of GIS for the historical analysis of cities [38; 39]. On the other hand, GIS provides a rich set of spatial data analysis and visualization competencies that support urban studies. Furthermore, the principles that emphasize space syntax theory can extend the capabilities of GIS modeling, on the other hand, especially in terms of recent advances and experiments in urban systems analysis. The central essence of GIS first leads to a consideration of the relation between GIS and urban history as a branch of the rapidly developing field of historical GIS. More specifically, this study uses GIS to evaluate the relationship of GIS for examining historically developed urban forms by representing town plan analysis. As [40] interpret, historical GIS demonstrates the well-known ability of GIS software to collect and visualize urban historical spatial data. Kernel density estimation, a spatial analysis technique, has been broadly used in point of interest (POI) data analysis and is frequently used to discover spatial \"hot spots\", such as density of roads, retail areas hotspots, accident hotspots [41; 42; 43]. The methodology is based on the kernel density estimation (KDE) that operates along with denser street networks of Famagusta city throughout different periods. Table 2 shows the formula and illustration for calculating the point and linear density. The point density tool calculates the density of point properties around each output raster cell. The line density tool calculates the density of linear properties in the neighborhood of each output raster cell. Density is calculated in units of length per unit of area. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Description** & **Parameters** & **Description** \\ \hline \multirow{4}{*}{\(D_{i}\)} & \(Di=\sum\limits_{j=1}^{n}d_{ij}\) & \multirow{4}{*}{\(C_{c}\) (P\({}_{i}\))} \\  & \(Di=\) Depth Value & Equation: & \\  & \(n=\) total components & & \\ \hline \multirow{4}{*}{\(MD_{i}\)} & \(MD_{i}=\frac{\sum_{i=1}^{n}d_{ij}}{(n-1)}\) & \multirow{4}{*}{\(d_{ik}\)} & \(d_{ik}\) refers to the length of a geodesic (shortest path) between nodes P\({}_{i}\) and P\({}_{k}\) \\  & \(MD_{i}=\) Mean depth value & & \\ \hline \multirow{4}{*}{\(RA_{i}\)} & \(RA_{i}=\frac{2(MD_{i}-1)}{(n-2)}\), \(RRA_{i}=\frac{RA_{i}}{D}\) & \multirow{4}{*}{\(CB(P_{i})\)} \\  & \(RA=\) relative asymmetry & Equation: & \\ \cline{1-1} \cline{3-4}  & \(RRA=\) real relative asymmetry & & \\ \hline \multirow{4}{*}{Rrt} & \(D=\frac{2(n(\log_{2}\left(\frac{n+2}{2}\right)-1+1}{(n-1)(n-2)}\) & \multirow{4}{*}{\(\mathrm{g}_{ik}(p_{i})\) is the number of geodesics between nodes \(p_{i}\) and \(p_{k}\) that contain node \(p_{i}\), and \(\mathrm{g}_{ik}\) is the number of all geodesics between \(p_{j}\) and \(p_{k}\)[29] \\ \cline{1-1} \cline{3-4}  & & \\ \cline{1-1} \cline{3-4}  & & \\ \cline{1-1} \cline{3-4}  & & \\ \cline{1-1} \cline{3-4}  & & \\ \hline \end{tabular}
\end{table} 
Table 1: Two main morphological variables. \[Density=\frac{1}{(radius)^{2}}\sum_{i=1}^{n}\left[\frac{3}{n}\cdot popi\left(1- \left(\frac{dist_{i}}{radius}\right)^{2}\right)^{2}\right]\]  
For \(dist_{i}<radius\)  
\(i=1\ldots,n\) are the input points. Only include points in the sum if they are within the radius distance of the (x, y) location. \(pop_{i}\) is the population field value of point \(i\), which is an optional parameter. \(dist_{i}\) is the distance between point \(i\) and the (x, y) location. The line density tool calculates the density of linear features in the area of each output raster cell.