## 2 Materials and Methods
### Parametric Site Selection Methods
The site selection approach consisted of three steps: (A) Simulating the crowd activity path with the Physarealm Algorithm Model (PAM) to identify the cross points of crowd activity paths and park borders. (B) Utilizing the Road Intersection Algorithm Model (RIAM) and Site Slope Algorithm Model (SSAM) to preliminarily screen the range of entrance locations. (C) Determining the location of the park entrance with the Crowd Density Algorithm Model (CDAM) and Crowd Convenience Algorithm Model (CCAM) (Figure 3). (A) Simulating crowd activity using the PAM to determine the cross points of the crowd activity path and the park borders. The key parameters are the POI in the park and the crowd source points surrounding the park. The POI of the park should be selected based on the park's geographical features, such as highlands, water locations, flat sites suitable for crowd activities, woodlands, and other places with outstanding landscape characteristics. The crowd source points should be determined based on the surrounding residential areas, business districts, schools, and other areas where the crowd is concentrated. Areas with dense crowds should be given multiple source points to increase the weight of the crowd. (B) Preliminary screening of the range of entrance locations utilizing the Road Intersection Algorithm Model (RIAM) and the Site Slope Algorithm Model (SSAM). The key parameter of the RIAM is the distance between the entrances and the road intersection, which can be found in the national and local design codes. The SSAM is a model that calculates the slope of the site based on Digital Elevation Model (DEM) data on the R + G platform. (C) Determining the location of the park entrance utilizing the Crowd Density Algorithm Model (CDAM) and the Crowd Convenience Algorithm Model (CCAM) (Figure 3). The CDAM calculates the density of crowd paths and park boundary intersections by comparing the distance between two adjacent intersections. The CCAM calculates the distance between the densely populated points determined by the CDAM and the crowd  
Figure 3: Algorithm model of parametric site selection of park entrance. source points. In different directions of the crowd source, the nearest point is selected as the entrance to the park. Determining the primary and secondary entrances  
To ensure easy access for park visitors and to provide guidance for the entrance construction, it is important to determine the primary and secondary entrances of the park. The location of the primary and secondary entrances can be determined based on the crowd activities [2; 27; 28] which are calculated by running the PAM to find the number of cross points between crowd paths and park borders. The entrance with the highest number of cross points is selected as the primary entrance, while the others are designated as secondary entrances. Rechecking of Park entrance auxiliary sites  
To ensure the convenience of park visitors, it is important to consider the site demand of the entrance square and the parking lot after determining the location of the park entrance. Therefore, it is necessary to recheck whether the area of the entrance square is sufficient for the crowd to gather and evacuate, and whether the parking lot can accommodate the number of vehicles. Calculating the park entrance square area: As the primary passage for park visitors to enter and exit, the functionality of gathering and evacuation must be taken into consideration [27]. Therefore, a specific entrance square area should be planned for people to enter and exit (Formula (1)). \[S=2Q\frac{K}{60}ts \tag{1}\]  
\(S\): Park entrance square area. \(Q\): Number of visitors = park area/per capita park area (more than 10 hectares of 60 m\({}^{2}\)/ person, less than 10 hectares of 30 m\({}^{2}\)/ person [27]). \(K\): Conversion coefficient between the maximum number of visitors in the park and the maximum number of visitors in the park (0.5 for more than 10 hectares, 1 for less than 10 hectares).