## 2 Materials and Methods
### Methods
#### 2.3.2 Regional Endowment Factors  
In this study, the regional endowment factors were set in three objective aspects: natural characteristics, location characteristics and facility characteristics. Natural characteristics are the earliest factors that determine the function of space and the most basic environmental characteristics in sustainable development [44]. Natural factors included elevation, relief intensity and distance to water. Among them, elevation and relief intensity determine temperature and climate, as well as whether it was suitable for residents to carry out high-intensity construction [36; 45]. The distance to water was taken into  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Primary Land Use Type** & **Secondary Land Use Type** & **Classification of PLES** \\ \hline \multirow{2}{*}{Cultivated land} & Paddy field & Production space \\  & Dry land & Production space \\ \hline \multirow{3}{*}{Woodland} & Forested land & Ecological space \\  & Shrubbery & Ecological space \\  & Other forest land & Ecological space \\ \hline \multirow{3}{*}{Grass land} & High coverage grassland & Ecological space \\  & Moderate coverage grasslands & Ecological space \\  & Low-coverage grassland & Ecological space \\ \hline \multirow{3}{*}{Water} & Rivers and canals & Ecological space \\  & Lake & Ecological space \\  & Reservoir pit & Ecological space \\  & Permanent glacier snow & Ecological space \\  & Beaches & Ecological space \\  & Bench land & Ecological space \\ \hline \multirow{3}{*}{Construction land} & Urban land & Living space \\  & Rural residential area & Living space \\  & Other construction land & Production space \\ \hline \multirow{3}{*}{Unused land} & Sandy soil & Ecological space \\  & Gobi & Ecological space \\  & Salinate field & Ecological space \\  & Marshall & Ecological space \\  & Bare land & Ecological space \\  & Bare rock & Ecological space \\  & Others & Ecological space \\ \hline Ocean & Ocean & Ecological space \\ \hline \hline \end{tabular}
\end{table}
Table 1: Classification of PLES.  
account because of the primary demand for agricultural production in rural areas [46]. Location was an important factor that had to be considered in rural development. Urban area was the provider of rural life resources. Different levels of urban areas had different attractiveness, which reshaped the layout of rural spaces [47]. The distance to the nearest subdistrict, distance to city and distance to capitals were selected in this study. Facilities were important catalysts for the evaluation of development potential of rural spaces [48]. Facilities such as interchanges and roads greatly improve the convenience of rural residents and products in and out [49]. This study chose the distance to the interchanges and roads as the facility indexes.  
The distribution of indexes is shown in Figure 3. High elevation was distributed in the northwest, and low elevation was distributed on the North China Plain in the southeast, as shown in Figure 3a. High relief intensity area was distributed in the transition zone of high elevation and low elevation in the north and west (Figure 3b). Only northwest area and south area were far from the water surface (Figure 3c). As for location characteristics, northeast and west area had higher values of distance to the subdistricts (Figure 3d). North area was far from cities (Figure 3d) and capitals (Figure 3f). In Figure 3g, north area was further from interchanges and roads were more evenly distributed in the study area.  
Figure 3: Distributions of factors. (**a**) Elevation distribution, (**b**) distribution of relief intensity, (**c**) distance to water, (**d**) distance to subdistricts, (**e**) distance to cities, (**f**) distance to capitals, (**g**) distance to interchanges, (**h**) distance to roads.