2.2.3. Depth

Depth is the minimum number of spaces traveled to reach a destination [27] and expresses the accessibility of the axial nodes in the system in a topological sense. The sum of the depths of each other space in the system determines a space's overall depth. The mean depth, which is the average distance from space *i* to all other spaces, reflects how simple it is to access the designed space in the system [27]. This is an essential measure of the accessibility of an area, as shown in the formula:

$$MD\_i = \frac{TD\_i}{n-1} = \frac{\sum\_{j=1}^{n} d\_{ij}}{n-1} \tag{3}$$

where *dij* is the shortest distance between space *i* to space *j*, *TDi* denotes the total depth value of space *i*, and *MDi* is the mean depth value of space *i*.

#### 2.2.4. Integration

Integration shows how space *i* is connected to other spaces and their surroundings, considering the earliest lines and the systematic distances between all points of the system [33] and real relative asymmetry (RRA) is the opposite of integration. RRA eliminates

the effects of the spatial structure itself and the spatial structure based on the mean depth. The formula is as follows:

$$RRA\_i = \frac{2(MD\_i - 1)}{(n - 2) \times D\_n} \tag{4}$$

$$D\_n = \frac{2\left\{n\left[\log\_2\left(\frac{(n+2)}{3}\right) - 1\right] + 1\right\}}{(n-1)\times(n-2)}\tag{5}$$

where *Dn* represents the integration measure's standardized value and *RRAi* denotes the RRA value of space *i*.

#### **3. Results**

Firstly, the basic information about the Sishengci historic district was collected, and the axial lines map of the Sishengci historic district was drawn through the space with the longest and least axial lines according to the relationship between the streets. DepthmapX was used to calculate the axial lines, quantify the relationship between each street space, and analyze them with the field survey. When the axial lines are analyzed, each has different colors and represents different parameter values. Warm colors represent larger parameter values, and cool colors represent smaller parameter values, and the darker the warm color is, the larger the parameter value it represents. The darker the cool color is, the smaller the parameter value it represents.

#### *3.1. Integration Analysis*

Global integration describes how closely a space is connected with all other spaces. The part of axial lines with higher integration in the axial lines system is often the spatial core, whose spatial accessibility and publicness degree is higher and plays an essential role in the district. Analyzing the global integration map (Figure 3) shows that its spatial core position is relatively apparent, and the red axial lines with high integration constitute the spatial core of the Sishengci historic district. In this case, it refers to the axial lines with the highest integration, namely the axial lines formed by Xinglong Street, Huaxingshang Street, Huaxingzheng Street, Huaxing East Street, Fanku Street, Rushian Street, Fuzi Street, and Wangfu Street, which shows a highlighted red color. It passes through the whole Sishengci historic district in the form of a straight line.

**Figure 3.** Global integration map.

This axial line is located on one of the longer horizontal roads in the neighborhood and has high accessibility. These streets are the most accessible and convenient places in the district, where traffic and pedestrian flow are most frequent, and are also critical public spaces. The form of this space still maintains the original traditional form, and this axial line is adjacent to the Jinjiang Theater, Wangfujing Shopping Mall, and other public activity spaces, which is a relatively dense public space.

The Sishengci historic district is crisscrossed with streets and alleys and has many historical relics of cultural protection units. The Sishengci historic district has a high integration of axial lines concentrated throughout, with a prominent center of the district and a very convenient core space for transportation. It continues the spatial structure of the traditional district and is a living place suitable for human-spatial relations, social functions, and spatial relations. The short axial lines located near the Fuhe River and inside the district are less integrated, and the district has more residential buildings. However, some of its spaces are relatively less accessible because they are located relatively deeper in the road. In conclusion, the Sishengci historic district has apparent spatial integration with significant core spaces, while some spaces are less integrated due to the distribution of roads and their locations.

### *3.2. Connectivity Analysis*

The connectivity indicates the number of axial lines directly connected to an axial line. The higher the spatial connectivity, the higher the breadth of visual penetration. The connectivity value map (Figure 4) shows that the connectivity value of the axial lines connecting Xinglong Street, Huaxingshang Street, Huaxingzheng Street, Huaxing East Street, Fanku Street, Rushian Street, Fuzi Street, and Wangfu Street is very high at 12. This axial line is very regular and points to the center of the district, indicating that the road in the center of the district has strong permeability and takes on a crucial traffic function. Among them, Huaxing Street is the most prosperous section of the whole area of commerce and trade. Sichuan Daily Newspaper Press Group, Hampton By Hilton, and Western Culture Industry Center are in this area. The connectivity value of the axial line connecting Yuefu Street and Wucheng Avenue is also high, with a connectivity value of 9, and their directions are consistent with the center of the district. The axial line connectivity value at Hongxing Road is 6, closer to the center of the district and connects the school and transportation stations with the center of the district. In general, the Sishengci historic district extends in two directions, northeast–southwest and northwest–southeast, regardless of the direction of the roads or rivers. The development trend of its historical urban space is basically along this direction. Axial lines with low connectivity values are scattered within the district, which is related to the fact that the roads are irregularly connected, causing obstruction to the sight lines and affecting the connectivity values.

#### *3.3. Control Analysis*

The Sishengci historic district is the earliest cluster of Western-style buildings in Sichuan, China, with a full range of types, including churches, hospitals, schools, and residential houses. The analysis was conducted from the control values and indicates the degree of influence of space on its adjacent spaces; higher values indicate that it is easier to reach. In the control value map (Figure 5), it can be seen that the axial lines formed by Xinglong Street, Huaxingshang Street, Huaxingzheng Street, Huaxing East Street, Fanku Street, Rushian Street, Fuzi Street, and Wangfu Street have the highest control value, which is importantly related to the fact that the roads on the axial lines are connected to many streets in the district. This shows the high control of the central space of the district in the Sishengci historic district. The high intensity of control of the center of the neighborhood over the surrounding spaces adjacent to it indicates that it occupies a certain position in the district and has a strong influence, and the space extending along this direction can become a field for the future spatial development of the historic district. The short axial lines in the district have low control values, indicating that these axial line spaces do not have a high degree of mutual control with each other.

**Figure 4.** Connectivity value map.

**Figure 5.** Control value map.
