## 3 Methods
### The Weighted Voronoi Diagram (WVD) Model for Dividing the Service Scope of Emergency Shelters
#### 3.2.2 The Weighted Voronoi Diagram (WVD) Model for Emergency Shelter Services  
The traditional methods of emergency shelter services mainly rely on subjective interpretation, dividing basically the facilities according to the street network and communities, excluding a scientific basis for the division of responsibilities. In this paper, in order to define the service scope of urban emergency shelter, we determine the coverage radius of the emergency shelters, which are used to calculate the weighted distance; next, the service scope of each emergency shelter was determined by WVD. As a special form of the location analysis model, WVD built a space adjacent model that does not depend on the coordinate geometry; its principle is spatial interaction theory, and it can be clearly expressed as a lateral adjacent relation in GIS, a better simulation of the adjacent choice in reality. In the service scope of emergency shelters, through the selection of impact factors and the determination of the weighted values, a weighted Voronoi diagram can be used to make space segmentation, thus the service scope of an emergency shelter can be divided [26]. The specific construction model is presented as:  
\[Voronoi\ (P_{i})\ =\ \{\ p\ |d(p,p_{i})\leq d\Big{(}p,p_{i}\Big{)},j\
eq i \}\ (i=1,2,\ldots,n) \tag{18}\]  
\[P=\ \{p1\,\ p2\,\ \ldots\ldots pn\}(2\ \leq\ n\ <\infty) \tag{19}\]  
\[Voronoi\ (p_{i},w_{i})=\Bigg{\{}p\Bigg{|}\frac{d(p,p_{i})}{w_{i}}\leq\frac{d \Big{(}p,p_{i}\Big{)}}{w_{j}},j\
eq i\Bigg{\}}(i=1,\ 2,\ldots n) \tag{20}\]  
where \(P\) in Equation (19) is the set of the discrete growth points on the Euclidean plane. \(d(p,p_{i})\) and \(d(p,\)\(p_{i})\) are the Euclidean distances between these two growth points, respectively. \(w_{i}\) is weight value of the growth point \(p_{i}\).  
Equation (20) is re-written as Equation (18), defining the weighted distance of each growth point as Euclidean distance, which is divided by the weight value. In this study, the large number of polygons produced by the important growth points has a large scope of influence. The revised model can better reflect the weights of different growth points in the spatial scope, and hence appropriate for the determination of urban emergency shelters.  
By running the Voronoi Map creation function in GIS, the service scope of each emergency shelter during the site selection stage can be obtained. Combining the actual land use situation with the population density, we can calculate the coverage rate of each emergency shelter and verify whether the location of the site is reasonable or not. The specific construction model is presented as:  
\[C=100\ \times\ P(a)/P(c) \tag{21}\]  
\[P(a)=S_{1}\ \times\ 2 \tag{22}\]  
\[P(c)=S_{2}\ \times\ De \tag{23}\]  
where \(C\) is the coverage rate of each emergency shelter. \(P(a)\) is the number of people that can be accommodated by each emergency shelter. \(S_{1}\) is the effective area of each emergency shelter. Equation (22) shows the calculation process of the number of people that can be accommodated by each emergency shelter. In our manuscript, we have adopted the national unified standard (2 m\({}^{2}\) per person of shelter area). \(P(c)\) is the number of people that is within the scope of the service of each emergency shelter. \(S_{2}\) is the service scope of each emergency shelter. \(De\) is the population density of study area.