Research on Automatic Generation of Park Road Network Based on Skeleton Algorithm

Abstract

This article primarily delves into the automatic generation approach of the park road network. The design of the park road network not only comprehensively takes into account environmental factors like terrain, vegetation, water bodies, and buildings, but also encompasses functional factors such as road coverage and accessibility. It constitutes a relatively complex design task, and traditional design methods rely significantly on the professional proficiency of designers. Based on the park vector terrain, in combination with the graphics skeleton algorithm, this study proposes an automatic generation method of the park road network considering environmental constraints. Through the utilization of the modified Douglas–Peucker algorithm and convex hull operation, the semantic information of environmental constraints is retained, domain knowledge is integrated, the skeleton graph is optimized, and issues such as road smoothness are addressed. This method can not only generate road network schemes rapidly, scientifically, and precisely, but also furnish the requisite digital model for the quantitative evaluation of the road network. Eventually, the study quantitatively assesses the experimental results via the spatial syntax theory to substantiate the efficacy of the method.

1. Introduction

A road network constitutes the framework of a park [1], being accountable for interconnecting various scenic spots within a park. It serves as the “artery”, linking diverse nodes within a park, and determines the degree of connection among them. The “Park Design Code” (GB 51192-2016) [2] puts forward the following stipulations with respect to the design of a park road network: The park road ought to be integrated with other facilities like terrain, water bodies, plants, and buildings to fulfill the requirements of transportation and sightseeing and form a complete scenic composition; the park road should establish a route that presents the landscape space of the park in an orderly manner. The road is required to cover the park to the greatest extent possible and possess strong accessibility.

The configuration of a park road network is correlated with environmental elements such as the topography and vegetation within the park, and it exhibits a certain degree of subjectivity and uncertainty in its evolution. How to promptly generate a rational park road network while integrating it with the environment constitutes the primary issue that designers must confront. Particularly when encountering complex environmental textures, traditional road design demands a comprehensive analysis of numerous objective factors, and it is inevitable that problems like omissions and inadequate considerations will exist. This design process is not only time-consuming but also lacks reasonable and scientific quantitative criteria.

This research put forward a sustainable approach for the automatic generation of park road networks with the aim of assisting designers in achieving their design tasks efficiently and precisely. The research employed skeleton algorithms derived from computer graphics for the automatic generation of road networks, taking into consideration environmental factors. The research utilized an enhanced Douglas–Peucker algorithm and convex hull operations to optimize the skeleton diagram and subsequently validated the efficacy of this method by adopting a park environment encompassing roads, water, and vegetation.

2. Related Research Status

The organization and analysis of traditional park roads frequently employ qualitative research approaches. Along with the advancement of computer science, geography information, and other disciplines, numerous accomplishments have been attained in the research on the automatic generation of road networks. The technologies utilized for road network generation can be approximately categorized as follows.

One type is the road network generation approach based on urban planning and urban evolution. Such approaches focus on how to generate road networks that are in line with reality based on urban planning or urban historical evolution data. Commonly utilized methods encompass simulation techniques such as L-system, the Ant Colony Algorithm, and Cellular Automata. In 1958, Charles Leslie Miller [3] initially proposed the utilization of the Digital Terrain Model (DTM) to accomplish the automatic generation of highway roads; Parish et al. [4] introduced the L-system into road network generation in 2001 and incorporated objective factors such as the environment and personnel distribution; Yang et al. [5] and Claes and Holvoet [6] employed the Ant Colony Algorithm to investigate the road network planning issue; Luca [7] utilized Cellular Automata, which are conceived and developed by the High-Quality Laboratory at Politecnico di Torino, to generate urban models on urban and regional scales. Some researchers apply GIS technology for the path planning of park road systems, yet GIS technology merely plays an auxiliary analysis role in the midst of this, and numerous artificial planning adjustments are still necessary when confronted with complex terrains. These tools offer highly significant support for technicians, but appropriate road generation methods remain limited.

Another type of technology is the road network generation approach based on measured data. This type of approach makes use of measured data, such as urban maps and traffic flows, and extracts the characteristics of the road network through technologies like big data and machine learning to generate artificial road networks that are closer to reality. For instance, Fang, Z. et al. [8] employed deep neural networks and planning-guided methods to automate the generation of street networks; Hartmann et al. [9] and Kempinska and Murcio [10] endeavored to automatically generate road network layouts through deep generative models; Xu et al. [11] proposed approaches for mining regional traffic connection intensity and evaluating urban road networks based on mobile phone data. The application of deep learning methods in road design has become a possibility, yet such methods still have numerous problems. Deep learning and other methods have large sample sizes and typically require a vast amount of data for training, and obtaining sufficient data can be extremely challenging. Training deep learning models usually demand a considerable amount of computing resources and have high requirements for research costs. More significantly, deep learning models are often regarded as “black box” models, and their decision-making processes are difficult to comprehend and explain, and it is challenging to carry out refined control. This aspect is of great significance for the design field, which severely affects the design quality.

Furthermore, deep learning methods encounter significant challenges in addressing changes in the actual environment, such as diverse terrain variations, lighting conditions, and other scenarios not encompassed in the training data. In contrast to the regular urban layout, the layout within parks is more flexible and subjective. Essentially, the existing research outcomes are scarcely directly transferable to the automatic generation of park road networks.

In recent years, numerous scholars have also employed the skeleton algorithm in domains such as transportation and road design. The practicality and mapping capability of the skeleton algorithm in computer graphics hold significant potential [12]. The skeleton not only possesses the fundamental geometric traits of the shape but also encompasses the topological structure of the shape. It can represent the shape hierarchically, mirroring the local and overall relationship of the shape, and is extensively utilized in fields like image analysis, shape matching, and pattern recognition. For instance, Lee et al. [13] utilized the skeleton algorithm to identify the healthy posture of the human body; Zhang et al. [14] detected pavement cracks via the binocular ranging enhancement algorithm combined with edge detection and the skeleton extraction algorithm; Vitor et al. [15] integrated the skeleton algorithm with a convolutional neural network for the land cover mapping of remote sensing images. This kind of research focuses on using the skeleton algorithm to accomplish the recognition of graphic images instead of the design of graphics.

An increasing number of researchers have also employed the skeleton algorithm in path planning. For example, Han et al. [16] devised a skeleton-based approach for constructing the global path for mobile robots; Dai et al. [17] exploited the skeleton graph to offer a continuous traffic path optimization scheme; Higuchi and Fujimoto [18] proposed a path planning method for the autonomous movement of robots in unknown environments by utilizing skeletonization; Chang et al. [19] put forward a path planning method based on skeleton extraction and the greedy algorithm to guide the flight of unmanned aerial vehicles. Path planning bears certain similarities to road network generation, yet road planning and design entail the consideration of more factors and demonstrate stronger functionality. Nevertheless, in current projects when planning road networks, few can comprehensively take into account these diverse design requirements.

Some scholars have also employed the skeleton algorithm in the research of topological structure extraction and spatial analysis within the realm of architecture and related fields. Rana et al. [20] utilized the skeleton to define the convexity and feasibility of the outdoor public space of buildings; Van et al. [21] exploited the graphical skeleton to analyze the plane layout axis and design techniques of Japanese dry landscape gardens. Nevertheless, this kind of research imposes considerable form restrictions on architectural plans. The cases adopted in their studies are mainly architectural plans, and complex environments have not been verified.

Through the aforementioned analysis, it becomes evident that the issue of road network generation has garnered sustained attention from individuals. However, the majority of the efforts have not completely addressed the aforementioned challenges. Currently, researchers have achieved certain research advancements in both skeleton extraction and pruning. Nevertheless, when applying them to the domains of landscape or road design, some problems persist. Firstly, they are primarily manifested in the hardship of handling complex environmental shapes, particularly the generation of road networks in intricate environments like parks. Secondly, there are diverse elements such as buildings and water bodies in parks. The questions of how to reflect design requirements while extracting the skeleton and how to incorporate domain knowledge into the design scheme constitute important research contents.

This study utilizes the vector terrain of a park as the input data, incorporates the graphic skeleton algorithm into the automatic generation of the park road network, and combines the relevant requirements of the park road network design to optimize the algorithm for diverse environmental textures, thereby attaining the automatic generation of the park road network. This research approach enables designers to comprehensively contemplate environmental constraints in conjunction with domain knowledge, possesses precise operability and high flexibility, and compensates for the shortcomings of deep learning methods. Compared with approaches such as deep learning, the skeleton algorithm has a lower dependence on data and can precisely generate a park road network scheme at a lower time and computing cost, providing an effective auxiliary means for the subsequent park planning and design.

3. Principles of the Method

3.1. Basic Principle of Skeleton

In 1967, Blum [22,23] provided the initial definition of the skeleton using the Grassfire Model. He postulated that the boundary points of the graph were ignited simultaneously, and a fire propagated uniformly in all directions towards the interior until extinguished. The set of extinguished points formed the skeleton of the graph. Blum also presented an equivalent definition of the skeleton as a collection of centers of maximal disks, where a maximal disk is entirely contained within and not enclosed by any other disk within the graph. The skeleton serves as a graphical structure that concurrently encapsulates both shape and topological characteristics, situated internally and depicted as a branching network composed of polylines (Figure 1a). Furthermore, it can effectively handle scenarios involving “holes” within its interior (Figure 1b). Additionally, internal line segments are treated akin to degenerate polygons with processing flow similar to that for “holes” and line segments alike (Figure 1c).

According to the definition of a skeleton, it is composed of individual segments of skeletal branches, which exist in two forms.

The first form is the primary skeleton that is not directly connected to the polygon. It consists of the centers of the maximum inscribed circles within the graph, with each segment preserving local symmetrical information from its corresponding curve. This representation can convey both shape and topological relationships within the graph as a whole. In this study, the primary skeletal branches are abstracted as main pathways within a park.

The second form is secondary skeletons directly linked to polygon vertices. These serve as offshoots from the main skeleton and provide insight into vertex distribution across polygons. In this study, secondary skeletons are conceptualized as secondary pathways in a park, connecting main pathways with environmental boundaries.

Currently, the skeletal algorithms for road generation can approximately be categorized into the following types. The first type is the approach based on topology and geometric analysis, which acquires the skeleton by constructing the Voronoi diagram of the model [24]. The second type is the topology thinning method (topology thinning) [25]. The third type of approach is the one based on the distance field [26], and the fourth type is the generalized potential field method [27].

In 1997, Oswin Aichholzer et al. [28] postulated that the internal structure of simple polygons, namely the straight skeleton, has found extensive applications in numerous fields, such as computing indoor navigation path networks [29], generating roofs [30], and so forth. This approach takes into account both the computing speed and readability, and the processing based on vector graphics is more consistent with the procedure of this study. Hence, in this study, the straight skeleton algorithm is employed to generate the road network scheme.

3.2. 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 Bill Hillier, 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_i/RRA_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:

$${\mathrm{R}\mathrm{A}}_{\mathrm{i}}={\displaystyle \frac{2(\overline{\mathrm{D}}-1)}{\mathrm{n}-2}}$$

$${\mathrm{R}\mathrm{R}\mathrm{A}}_{\mathrm{i}}={\displaystyle \frac{{\mathrm{R}\mathrm{A}}_{\mathrm{i}}}{{\mathrm{D}}_{\mathrm{n}}}}$$

• Connectivity value C_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:

$${\mathrm{C}}_{\mathrm{i}}=\mathrm{k}$$

where k represents the total number of spatial units directly connected to the given spatial unit.

• Control value ctrl_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:

$${\mathrm{c}\mathrm{t}\mathrm{r}\mathrm{l}}_{\mathrm{i}}=\sum _{\mathrm{j}=1}^{\mathrm{k}}{\displaystyle \frac{1}{{\mathrm{C}}_{\mathrm{i}}}}$$

• 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 and the maximum shortest step distance being s, the number of nodes with the shortest step distance is N_d. Then, the depth value can be expressed as follows:

$$\mathrm{D}=\sum _{\mathrm{d}=1}^{\mathrm{s}}\mathrm{d}\times {\mathrm{N}}_{\mathrm{d}}=\left\{\begin{array}{c}\mathrm{if} \mathrm{d}=1 \mathrm{then}=\mathrm{connectivity}\\ \mathrm{if} \mathrm{d}=\mathrm{h} \mathrm{then}=\mathrm{localdepth}\\ \mathrm{if} \mathrm{d}=\mathrm{s} \mathrm{then}=\mathrm{globaldepth}\end{array}\right.$$

• Choice

This refers to the frequency of a certain element in the spatial system as the shortest topological distance between two nodes, examines the superiority of the spatial unit as the shortest travel path, and reflects the possibility of the space being traversed, and the space with higher selectivity is more prone to be traversed by the flow of people. Its expression is [37] as follows:

$$\mathrm{C}\mathrm{h}\mathrm{o}\mathrm{i}\mathrm{c}\mathrm{e}={\sum }_{\mathrm{j}}{\sum }_{\mathrm{k}}{\displaystyle \frac{{\mathrm{d}}_{\mathrm{j}\mathrm{k}}\left(\mathrm{i}\right)}{{\mathrm{d}}_{\mathrm{j}\mathrm{k}}}}\left(\mathrm{j}<\mathrm{k}\right)$$

where ${\mathrm{d}}_{\mathrm{j}\mathrm{k}}$ refers to the shortest path between line j and line k, and ${\mathrm{d}}_{\mathrm{j}\mathrm{k}}\left(\mathrm{i}\right)$ refers to the shortest path containing line i between line j and line k.

3.3. Methodological Process

The graph skeleton demonstrates natural similarities with a road network, allowing it to effectively represent the topological relationships of the graph and connect internal nodes within the park. However, when designing a park road network, complete geometric symmetry is not necessary. Instead, the design should be based on factors such as park boundaries, internal structures, ornaments, water features, and groupings of vegetation that collectively define the environmental texture. Additionally, the characteristics of the skeleton generation algorithm make it highly sensitive to points on polygons; therefore, directly applying this algorithm to road generation may lead to an excessive number of redundant roads. As a result, this study introduces environmental constraints based on the skeleton algorithm and integrates relevant experiential rules and design requirements for park road development in order to explore a method for generating unique park roads.

This study comprises three main steps, as illustrated in Figure 2: (1) importing the vector dataset of park networks necessary for road network generation; (2) creating park road networks while considering environmental constraints, which constitutes the primary focus of this research; (3) assessing the outcomes using spatial syntax theory and methods to validate the efficacy of the approach.

4. Road Network Generation Method

The method for generating park road networks is specifically designed for vector data organized in a layered structure, which includes three primary categories: (1) point-shaped features such as entrances, restrooms, and security kiosks; (2) polygonal entities delineating the natural boundaries of parks, water bodies, and vegetation; and (3) clusters of objects in close proximity that are logically considered as cohesive units, including groupings of buildings and vegetation. Among these categories, point-shaped elements hold particular significance, with substantial implications for road design. It is essential in this study to project semantic points of this nature onto other objects such as park boundaries through coordinate projection to guide algorithmic processes governing road generation. Furthermore, environmental characteristics must be taken into account in park road design to ensure alignment with the requirements for the actual planning of road networks. The method primarily encompasses the following aspects.

4.1. Polygon Simplification Based on Semantic Information

The integration of skeleton algorithms into road design tasks holds significant potential, but also comes with drawbacks. The points generated by the skeleton algorithm prioritize graphic features, potentially leading to an excessive number of points that do not align with actual road requirements. Therefore, it is essential to simplify these points using appropriate methods.

In the context of vector data, polygons are formed by sequentially connected points, and the quantity of these points often dictates the precision of the polygon. However, an excessive number of points may lead to a proliferation of redundant roads after applying the skeleton algorithm (Figure 3a). On the other hand, too few points can result in significant deviation from reality, producing roads that inadequately capture the morphological variations in natural features. Therefore, prior to employing the skeleton algorithm, it is crucial to appropriately simplify the polygons in order to align more closely with actuality in terms of both generated road network morphology and sub-skeleton distribution.

For polygon simplification, this study will utilize the well-established Douglas–Peucker simplification algorithm [38,39]. The Douglas–Peucker algorithm is a widely employed digital curve simplification method that effectively reduces complex curves to approximate forms with minimal points, while preserving the fundamental geometric shape and features of the original curve. It is straightforward to implement [40,41] and adaptable for use in various programming languages and platforms. This algorithm finds extensive application in map digitization, GIS modeling, and computer graphics, and can be seamlessly integrated with graph skeleton algorithms.

The Douglas–Peucker simplification algorithm primarily relies on geometric scale to decide whether a point should be retained or discarded, without considering specific semantic information associated with points on the polygon. However, during road design processes, these specific points often connect essential roads and therefore should consistently be preserved throughout polygon simplification procedures. Consequently, this study has adapted the Douglas–Peucker simplification algorithm to ensure that both geometric scale and semantic information are taken into account during polygon simplification in the following steps:

Step 1: Input the polygon coordinates, semantic point set, and deviation threshold ε.

Step 2: The special points with semantic information are projected onto the polygon based on their coordinates, thereby becoming part of the point set on the polygon and forming a new point set as follows:

$$\mathrm{P}=\left\{{\mathrm{p}}_1\right.\left({\mathrm{x}}^1,{\mathrm{y}}^1\right),{\mathrm{p}}_2\left({\mathrm{x}}^2,{\mathrm{y}}^2\right),\dots ,{\mathrm{p}}_{\mathrm{n}}{(\mathrm{x}}_{\mathrm{n}},{\mathrm{y}}_{\mathrm{n}}\left)\right|\mathrm{n}\in \mathrm{N}\}$$

(1)

Step 3: For each point on the polygon, add a Boolean attribute reservered that is set to true if the point belongs to the new semantic points created in step 2, and false otherwise. The new point set is represented as follows:

$$\mathrm{P}=\left\{\begin{array}{c}{\mathrm{p}}_1\left({\mathrm{x}}_1,{\mathrm{y}}_1,{\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{e}\mathrm{r}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{d}}_1\right),{\mathrm{p}}_2\left({\mathrm{x}}_2,{\mathrm{y}}_2,{\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{e}\mathrm{r}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{d}}_2\right),\\ \dots ,{\mathrm{p}}_{\mathrm{n}}\left({\mathrm{x}}_{\mathrm{n}},{\mathrm{y}}_{\mathrm{n}},{\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{e}\mathrm{r}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{d}}_{\mathrm{n}}\right) | \mathrm{n}\in \mathrm{N}\end{array}\right\}$$

(2)

Step 4: The lengths of the line segments between each pair of points on the polygon are calculated, and the longest segment is selected as separator $\mathrm{l}$. And $\mathrm{l}$ divides the polygon into two segments, denoted as ${\mathrm{L}}_1\left(\mathrm{l}\right)$ and ${\mathrm{L}}_2\left(\mathrm{l}\right)$, with the starting and ending points of separator $\mathrm{l}$ marked as ${\mathrm{p}}_{\mathrm{s}}$ and ${\mathrm{p}}_{\mathrm{e}}$, respectively, i.e., $\mathrm{l}{(\mathrm{p}}_{\mathrm{s}}{,\mathrm{p}}_{\mathrm{e}})$. ${\mathrm{L}}_1\left(\mathrm{l}\right)$ and ${\mathrm{L}}_2\left(\mathrm{l}\right)$ will perform the following steps according to the Douglas–Peucker simplification algorithm.

Step 5: For the input polyline $\mathrm{L}\left(\mathrm{l}\right)$, draw plumb lines of $\mathrm{l}$ for each of the points on $\mathrm{L}$ except ${\mathrm{p}}_{\mathrm{s}}$ and ${\mathrm{p}}_{\mathrm{e}}$, and calculate the heights, comparing them to arrive at the maximum height value ${\mathrm{h}\mathrm{e}\mathrm{i}\mathrm{g}\mathrm{h}\mathrm{t}}_{\mathrm{m}\mathrm{a}\mathrm{x}}$ and the corresponding point ${\mathrm{p}}_{\mathrm{m}}$.

Step 6: If ${\mathrm{h}\mathrm{e}\mathrm{i}\mathrm{g}\mathrm{h}\mathrm{t}}_{\mathrm{m}\mathrm{a}\mathrm{x}}\ge \mathsf{\epsilon }$ or ${\mathrm{h}\mathrm{e}\mathrm{i}\mathrm{g}\mathrm{h}\mathrm{t}}_{\mathrm{m}\mathrm{a}\mathrm{x}}<\mathsf{\epsilon } \mathrm{a}\mathrm{n}\mathrm{d} {\mathrm{p}}_{\mathrm{x}.\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{e}\mathrm{r}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{d}}==\mathrm{t}\mathrm{r}\mathrm{u}\mathrm{e}$, the point is retained. Connect ${\mathrm{p}}_{\mathrm{s}}$, ${\mathrm{p}}_{\mathrm{m}}$ and ${\mathrm{p}}_{\mathrm{m}}$, ${\mathrm{p}}_{\mathrm{e}}$ to form two new lines ${\mathrm{l}}_1{(\mathrm{p}}_{\mathrm{s}}{,\mathrm{p}}_{\mathrm{m}})$ and ${\mathrm{l}}_2{(\mathrm{p}}_{\mathrm{m}}{,\mathrm{p}}_{\mathrm{e}})$ and corresponding polylines $\mathrm{L}\left({\mathrm{l}}_1\right)$ and $\mathrm{L}\left({\mathrm{l}}_2\right)$ and take them to step 5 for simplified calculations; if ${\mathrm{h}\mathrm{e}\mathrm{i}\mathrm{g}\mathrm{h}\mathrm{t}}_{\mathrm{m}\mathrm{a}\mathrm{x}}<\mathsf{\epsilon } \mathrm{a}\mathrm{n}\mathrm{d} {\mathrm{p}}_{\mathrm{x}.\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{e}\mathrm{r}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{d}}==\mathrm{f}\mathrm{a}\mathrm{l}\mathrm{s}\mathrm{e}$, the point between ${\mathrm{p}}_{\mathrm{s}}$ and ${\mathrm{p}}_{\mathrm{e}}$ is simplified.

Step 7: Repeat steps 5 and 6 until there are no more points that can be simplified.

Step 8: Sequentially connect the preserved points to form a simplified polygon with semantic preservation.

Based on the simplified polygon of the appeal method, the skeleton algorithm traverses the points on the polygon to generate the road network and determines the generation of the secondary arterial road based on the semantic attributes of the points. If the point ${\mathrm{p}}_{\mathrm{x}.\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{e}\mathrm{r}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{d}}==\mathrm{t}\mathrm{r}\mathrm{u}\mathrm{e}$, the secondary arterial will be generated, and vice versa, it will not be generated. In the simplification process, the threshold $\mathsf{\epsilon }$ is an important parameter that significantly affects the morphology of the road network (Figure 3).

4.2. Convex Hull Operation Based on Semantic Information

Within the park, certain functional or landscape zones have relatively small areas and encompass multiple distinct sub-regions in close proximity to each other. Each sub-region is typically represented as an individual polygon in vector data, such as a cluster of buildings or vegetation. Introducing the polygon groups representing these sub-regions directly into the skeletonization algorithm results in the formation of impractical pathways within adjacent polygons, significantly disrupting the connectivity of the road network (Figure 4a).

To address the issue of appeal, this study introduces the convex hull operation [42]. The convex hull operation originates from graphics and serves as a practical geometric calculation tool. It fully preserves the geometric shape and boundary features of the original point set and possesses characteristics such as simple output, efficient calculation, and a strong visualization effect. Widely utilized in computer graphics [43] and GIS [44], it plays a crucial role in analyzing various graphics, images, and spatial data.

The classical convex hull algorithms encompass the Gift Wrapping Algorithm [45], Graham’s algorithm [46], the Monotone Chain Algorithm [47], and the Quick Hull Algorithm [48], among others. The Gift Wrapping Algorithm was published by R. A. Jarvis in 1973. Graham’s algorithm is a sequential algorithm used to determine the convex hull of a set of n points in the plane (n ≥ 3). The Quick Hull Algorithm is based on a divide-and-conquer strategy and is very similar to quick sort, which divides the problem into two sub-problems and discards some of the points in the given set as interior points, then concentrating on the remaining points.

The selection of the algorithm is contingent upon factors like the quantity of points, the distribution of the points, as well as the requisite time and space complexity. For instance, the Gift Wrapping and Graham Scan algorithms are straightforward to implement and perform effectively for small- to medium-sized datasets, whereas the Divide and Conquer and Chan’s Algorithm are more efficacious for larger datasets. This study employs the scikit-geometry library for calculating the convex hull of geometric figures. Scikit-geometry (https://scikit-geometry.github.io/scikit-geometry/skeleton.html (accessed on 27 November 2023)) is a library founded on SciPy 1.10.1, offering interfaces for geometric operations, including the computation of convex hulls.

The convex hull operation connects the outermost points of the point set to form a convex polygon. Substituting the original polygon group with the convex polygon in skeleton calculation can effectively prevent the generation of primary skeleton branches within the polygon group and produce secondary skeleton branches that align with practical requirements. However, this operation may also exclude points directly connected to major roads and possessing specific significance; therefore, these semantic points should be represented on the formed convex polygon (Figure 4b), akin to handling semantic points in polygon simplification algorithms. The specific research steps are as follows:

Step 1: Input the polygon group and semantic point set;

Step 2: Convex hull operation is performed on all points of the constructed polygon group to generate a convex hull;

Step 3: Project the semantic point onto the edge of the convex hull to make it a part of the point set on the convex hull;

Step 4: Add a Boolean identifier to all points on the convex hull to distinguish whether they are points after projection;

Step 5: Bring the new convex hull into the skeleton algorithm to recalculate the road network;

Step 6: For the main skeleton generated by the convex hull area, according to the identification in step 4, delete the main skeleton branch whose endpoint is the point on the convex hull and identified as false.

4.3. Optimization of Road Network Coverage

When designing the road network in a park, the road coverage rate is a crucial factor to consider. However, based on the principle of the skeleton algorithm, regardless of the proximity or distance between two internal polygons, only one primary skeleton branch will be generated. This characteristic presents challenges for a single road to meet the requirement of road network coverage rate when adjacent areas are excessively large (Figure 5a).

To enhance the coverage of the road network, it is essential to initially pinpoint areas with inadequate coverage. As per the definition, the graph skeleton itself comprises a collection of maximum inscribed circle centers. Therefore, areas with insufficient coverage can be promptly identified by comparing the radius $\mathrm{r}$ of the maximum inscribed circles with a predetermined value $\mathrm{T}$. Here, value $\mathrm{T}$ denotes the maximum acceptable distance between adjacent spaces in the park interior and can be tailored based on actual site conditions. Upon identifying areas with insufficient coverage, new primary skeleton branches can be generated by inducing additional line segments into the skeleton algorithm (Figure 5b), thereby augmenting road density and enhancing road network coverage (Figure 5c). The specific research steps are outlined as follows:

Step 1: Generate the skeleton based on the input vector data, and make the maximum internal tangent circle centered on the vertices at both ends of each skeleton branch, and obtain the radius $\mathrm{r}$ (Figure 6a).

Step 2: Each segment of the end points of the skeleton branch generated by the two largest tangent circles, respectively, with a radius of $\mathrm{r}$ and $\mathrm{T}$ value comparison, according to the results of the comparison, contains three cases:

(1)

Radius $\mathrm{r}$ is greater than the $\mathrm{T}$ value: such as Figure 6a in the skeleton branch ${\mathrm{O}}_1{\mathrm{O}}_2$, where ${\mathrm{r}}_2>\mathrm{T},{\mathrm{r}}_3>\mathrm{T}$;

(2)

One end is greater than the $\mathrm{T}$ value and one end is less than the $\mathrm{T}$ value: as in Figure 6a for ${\mathrm{O}}_1{\mathrm{O}}_2$ and ${\mathrm{O}}_3{\mathrm{O}}_4$, where ${\mathrm{r}}_1<\mathrm{T}<{\mathrm{r}}_2,{\mathrm{r}}_4<\mathrm{T}<{\mathrm{r}}_3$;

(3)

Radius $\mathrm{r}$ is less than the $\mathrm{T}$ value: as for ${\mathrm{O}}_4{\mathrm{O}}_5$ in Figure 6a, where ${\mathrm{r}}_4<\mathrm{T},{\mathrm{r}}_5<\mathrm{T}$.

Step 3: Determine the area of insufficient coverage and add new line segments based on the comparison results of Step 2:

(1)

Radii $\mathrm{r}$ are greater than $\mathrm{T}$ values: the area corresponding to the skeleton branch is under-covered, and the skeleton branch is added to the input vector data (${\mathrm{O}}_2{\mathrm{O}}_3$ in Figure 6b);

(2)

Only one end is greater than the value of $\mathrm{T}$: the coverage of the area near that end is insufficient; make a circle with that end point as the center and $\mathrm{T}$ as the radius, intersect the skeleton branch at point ${\mathrm{T}}^{\prime }$, and add $\mathrm{O}{\mathrm{T}}^{\prime }$ to the input data (${{\mathrm{T}}^{\prime }}_1{\mathrm{O}}_2$ and ${\mathrm{O}}_3{{\mathrm{T}}^{\prime }}_2$ in Figure 6b);

(3)

Radii $\mathrm{r}$ are less than $\mathrm{T}$ values: the area corresponding to the skeleton branch meets the coverage requirement.

Step 4: Re-execute the skeleton algorithm with the input data updated in step 3 to obtain a new road network.

5. Practical Site Application

In order to validate the rationality and efficacy of the approach, this study utilized Houxianghe Park in Wuhan as a practical site and leveraged the aforementioned research findings to automatically generate the park’s road network. The rationality of the road network was assessed through spatial syntax analysis.

5.1. Site Overview

Houxianghe Park [49] is located at the southwest corner of Hankou Railway Station in the Hankou District of Wuhan City, covering a total area of 131,000 square meters, including 4.6 hectares of water surface. The key structures within the park consist of the Wuhan Museum located in the northeastern corner and the Wuhan Municipal Design Institute positioned on the western side. The red line demarcation in Figure 7 delineates the scope under investigation for this study.

5.2. Modeling

The study initially obtained vector data of the experimental site from OpenStreetMap and then conducted essential preprocessing using QGIS 3.10 software, which involved removing existing roads and redundant data. However, due to inaccuracies and delays in updating OpenStreetMap data, the downloaded information exhibited disparities with the actual site. Therefore, additional geometric features such as supplementary vegetation clusters were incorporated using editing tools. The final vector data model is depicted in Figure 8.

5.3. Evaluation of Results

Based on the vector data model of Houxianghe Park, the ultimate road network obtained through this research approach is presented in Figure 9a. Spatial syntax was employed to quantitatively assess the rationality of the generated park road network.

Following the generation of a road network model, axial analysis was conducted using Depthmap 10.14.00b software to produce an intuitive color map representing different parameters, where warmer colors indicate higher values. The key parameters examined in this study include integration, connection, control, depth, and choice (Figure 9b–f).

5.3.1. Analysis of the Evaluation Parameters

The integration degree (Figure 9b) indicates the proximity of road links. Warmer roads are more convenient and accessible to local areas within the system. The maximum global integration value is 0.62, while the minimum is 0.35. The road with the highest integration degree is located in the southern area of the park near the water texture, which aligns with the centroid area of the park outline. This centroid area contains water textures and vegetation clusters, forming the core area of the entire park along with a dense road network. In terms of local integration degree (Figure 10), all waterfront spaces in the northwest and southeast directions of the park are depicted in red, indicating strong traffic potential. As we move outward from this core area, there is a gradual decrease in road integration degree. It can be observed that under this road system, space gradually converges from both outside and inside; furthermore, it becomes easier to gather people as space centrality strengthens. The connection values indicate the permeability of roads, with warmer colors signifying higher permeability. The north and west sides of the park, which are connected to the outside world, exhibit greater permeability compared to other boundaries, fostering a stronger sense of accessibility and attracting pedestrians from the Wuhan Museum and Hankou Railway Station to the park’s interior.

The connectivity value (Figure 9c) represents the permeability capacity of the road. The warmer-colored areas around the road indicate higher permeability. A well-connected and safe road network can encourage residents to utilize the park [50]. In terms of connectivity, the values for the north and west borders of the park are 5 and 6, respectively, which exceed the average value of 2.85. Compared to other boundaries, the park is more accessible and open to the outside world, making it more attractive for pedestrians from Wuhan Museum and Hankou Station to visit.

The control value (Figure 9d) indicates the road’s ability to control other roads. A warmer color signifies a stronger control ability over adjacent roads. The figure shows that there are more warm-colored roads than cool-colored ones, suggesting a higher overall road control value in the park. It also indicates strong interaction and directivity between the roads and adjacent roads. Unlike the integration degree, the roads with strong control are mainly situated on the periphery of the park and connect with the main roads outside the park.

The depth value (Figure 9e) indicates the depth of the road. The darker the road, the warmer it is, and the less accessible it becomes. Areas with larger depth values are primarily concentrated on roads near Wuhan Museum and Wuhan Municipal Design Institute in the north of the park. Additionally, areas adjacent to buildings in road planning tend to have larger depth values.

Choice degree (Figure 9f) indicates the frequency of road usage. The warmer colors represent higher usage frequency, with the park road network showing an increase in selection degree from the outer to the inner areas. The annular roads surrounding the water body appear in warmer colors compared to other roads, indicating a higher frequency of use within the entire road network system and a greater likelihood of pedestrian crossing. This suggests that roads along water bodies are more attractive to pedestrians [51].

5.3.2. Conclusion of the Evaluation

By interpreting each parameter in the axis analysis method, it is evident that the park road network generated using the skeleton algorithm can effectively meet the actual usage needs. Morphologically, the road network is strategically interspersed between nodes within the park, satisfying the requirements for the orderly expression of each node. Each road segment seamlessly connects, and the secondary trunk road efficiently links external and internal nodes, creating a relatively open layout. The hydrophilic area at the center serves as the core of the entire park and is also its most integrated area. Pedestrians primarily enter from the north and west borders and can systematically tour through the central ring road to explore all areas of the park.

However, it is also evident that as the topological radius decreases, the local integration degree of the waterfront road on the south side of the park gradually diminishes. Consequently, pedestrians with shorter walking distances are unable to reach the midpoint of the road. This phenomenon can be attributed to the positioning of a large water body in the central area of the park, resulting in an elongated circular road. From an alternative perspective, this park is distinguished by its waterfront features, botanical landscape, and leisure sports activities rather than serving as a historical or cultural viewing park, thus catering to regional tourism while meeting citizens’ needs.

6. Discussion

With the advent of the big data era, the convergence of computer technology and traditional design constitutes an inevitable trend; however, numerous challenges arise in the integration of the two. The generation of traditional road networks demands that designers complete it manually, entailing a considerable number of repetitive tasks. Shortcomings exist in the practical application of machine learning methods, where the generated roads lack inherent logic, fail to incorporate expert prior knowledge, and have insufficient explainability and extensibility.

The objective of this study is to facilitate designers in undertaking road network design more proficiently. For policy makers, it is requisite to review and supervise design schemes to guarantee that they conform to the established policy goals and regulatory demands. The assistive design approach proposed in this study can offer urban planners and policy makers an opportunity to expeditiously explore potential planning schemes. For designers, the design of road networks is an extremely complex task that demands the consideration of numerous factors [52]. This study introduces graphical methods and integrates the merits of interactive design methods to automatically generate road network schemes while retaining the structured information among geographic elements, possessing excellent explanatory and interactive capabilities (

Table 1. Method comparison.

	Work Style	Domain Knowledge	Explainable	Interactivity
Traditional methods	Manual	Yes	Yes	No
Machine learning	automatic	No	No	No
Proposed method	automatic	Yes	Yes	Yes

).

While this study has made strides in automating road network design to some extent, there are still inherent limitations. In the context of park road network design, it is crucial to also account for esthetic considerations [53,54,55], such as incorporating curved and zigzag road profiles to evoke a calming and visually pleasing effect. Thoughtfully integrated undulations and turning points can enhance the enjoyment of pedestrian experiences. However, algorithm-driven intelligent design tends towards standardized and repetitive patterns, facing challenges in fully capturing human esthetic perception and creativity. Further research is needed on how to manifest the personal style and intellectual depth of designers within their design schemes.

Most studies on virtual road networks are typically conducted under flat terrain conditions. However, the undulating topography of the design site introduces variability to the scene and also presents challenges for road network design. Changes in road slope can significantly impact visitors’ visual experience and overall perception of the park. Therefore, a thoughtful approach to designing roads that accommodate changes in elevation is essential for enhancing the landscape’s appeal. In the future, advancements in technology such as digital elevation models and machine learning could be leveraged to accurately reflect topographical variations within road networks. Furthermore, different types of roads can cater to specific functional areas within the park, including tour paths, walking paths, bicycle paths, etc., in order to meet diverse visitor needs. Current research primarily focuses on the macro-level generation of road networks with an emphasis on principles such as accessibility and connectivity. However, there is a need for more comprehensive research that delves into aspects beyond just the slope, width, and functional performance of roads.

7. Conclusions and Future Research

This study focuses on the park road network, integrating the skeleton algorithm from computer graphics into conventional road network design and investigating methods for generating park road networks. It incorporates spatial syntax theory to validate the findings. By inputting semantic information during road network generation, it amalgamates domain knowledge of park road network design to precisely shape the network. The study employs a modified Douglas–Peucker simplification algorithm to streamline polygons while retaining geometric scale and semantic information. For small independent morphological areas in parks that are closely situated, a convex hull operation method is utilized to ensure the smoothness of the road network. Using Houxianghe Park as a case study, this research evaluates design schemes based on connection value, depth value, etc., revealing well-connected roads with high permeability and accessibility; those around water bodies exhibit higher usage frequency. These results indicate that the proposed design aligns with actual usage needs and meets target requirements for road network design. The innovative approach employed in this study can swiftly furnish designers with effective reference solutions, thereby enhancing their work efficiency.

Subsequent work can be further improved in the following three aspects:

• The design of road networks is a creative endeavor that often incorporates esthetics and culture and is inherently subjective. In the future, it will be important to address the challenge of integrating algorithmic principles with design creativity, such as utilizing artificial neural network models, integrated generative adversarial network technology, or equation algorithms to assist designers in achieving esthetic excellence.
• The spatial layout of a road must accurately reflect the complex multi-dimensional elements and consider various two-dimensional, three-dimensional, macro, and micro design needs. These include overall land use planning, cost considerations, terrain changes, road slope, volume, width, function, etc. When generating the geometric algorithm for a road network, it is essential to incorporate more elements related to park planning into the environmental restriction framework to meet future needs.
• Due to space limitations, this study is unable to evaluate and verify the scheme from multiple perspectives. In the future, the skeleton algorithm can be further associated with different evaluation methods to validate its rationality. For example, it can be compared with traditional design methods or deep learning methods in order to enhance its functionality.

Note: All images in the text were drawn by the author.