# Research on Automatic Generation of Park Road Network Based on Skeleton Algorithm
## 3 Principles of the Method
### Evaluation Methods  
Road network generation constitutes a complex engineering issue that demands the comprehensive contemplation of multiple factors, such as traffic demand, geographical environment, cost budget, and so on. Evaluation indicators typically encompass connectivity, accessibility, and the like. Spatial grammar is extensively employed to analyze the influence of spatial configuration on architectural and planning applications [31; 32]. Commencing from the overall network structure, it can fully mirror characteristics like the connectivity and accessibility of the road system. Through spatial syntax analysis, planners are capable of more effectively comprehending the performance of the road system and optimizing the design scheme. Spatial syntax [33; 34; 35] refers to a spatial quantitative analysis theory proposed by [PERSON], which effectively models the dynamic relationship between human behavior and the built environment. Its principal parameters encompass integration degree, connectivity value, control value, depth value, and choice, among others. * Integration RA\({}_{\text{i}}\)/RRA\({}_{\text{i}}\)  
Integration value represents the degree of concentration or dispersion of a unit space in relation to other spaces within the system. When a spatial system is aggregated, all unit spaces within the system are relatively proximate to one another, and there are few impediments between them influencing their connections; conversely, unit spaces are more distant and there are more obstacles. Integration value can be expressed by relative asymmetry (RAi) and real relative asymmetry (RRAi) [36]. From the perspective of the scale of node selection, integration value can be classified into two major categories: local integration and global integration. Global integration indicates the closeness between a given spatial unit and any other spatial unit in the urban system, while local integration indicates the interaction relationship between a given spatial unit and the spatial units within a few steps' distance (such as three steps' or ten steps' distance) in the vicinity. It can be expressed as follows:  
\[\text{RA}_{\text{i}}=\frac{2\big{(}\overline{\text{D}}-1\big{)}}{\text{n}-2}\]  
\[\text{RRA}_{\text{i}}=\frac{\text{RA}_{\text{i}}}{\text{D}_{\text{n}}}\]
* Connectivity value C\({}_{\text{i}}\)  
This represents the quantity of any unit spaces within the system that intersect with the given i-unit space. In the actual spatial system, the higher the connection value of a specific space is, the more excellent its spatial permeability becomes. The expression is as follows:  
\[\text{C}_{\text{i}}=\text{k}\]  
where k represents the total number of spatial units directly connected to the given spatial unit. * Control value \(\text{ctrl}_{\text{i}}\)  
The control value pertains to the capacity of a specific spatial unit to govern the spatial units that are connected to it, mirroring the control intensity and influence it exerts on any connected spatial units. This can be expressed as follows:  
\[\text{ctrl}_{\text{i}}=\sum_{\text{j}=1}^{\text{k}}\frac{1}{\text{C}_{\text{ i}}}\]  
* Depth D  
The depth value pertains to the minimal quantity of connections from a given unit space to other spaces within a spatial system. Setting the shortest step distance from a point in the space to any other point is d (where d is an integer), with the minimum being 1 andthe maximum shortest step distance being s, the number of nodes with the shortest step distance is \(\mathrm{N_{d}}\). Then, the depth value can be expressed as follows: \[\mathrm{D}=\sum_{d=1}^{s}d\times\mathrm{N_{d}}= \begin{cases}\text{if }d=1\text{ then }=\text{connectivity}\\ \text{if }d=\text{h then }=\text{localdepth}\\ \text{if }d=\text{s then }=\text{globaldepth}\end{cases}