Exploring the Impact of Vertical Access Elements on Visual Richness and Space Quality within Shopping Mall Atriums

Abstract

Shopping malls have become vibrant public spaces, serving as commercial centers and sociocultural hubs. However, the arrangement of stationary elements such as elevators and escalators significantly impacts the visual quality of the atrium and the overall navigation experience within the complex. This research focuses on analyzing the configuration of elevators and escalators in shopping mall atriums and their influence on visual richness and accessibility. Descriptive-analytical and survey methods are employed, utilizing data from 10 successful malls worldwide. The UCL-Depth map software and space syntax variables are used for analysis. Connectivity, clustering-coefficient, and controllability analyses assess visual richness, while integration, mean-depth, entropy, depth, step-depth, and gate-count analyses evaluate accessibility. The research includes a questionnaire to obtain optimal indices for each space syntax variable, enhancing the accuracy of the findings. The results highlight the significant impact of the positioning of vertical access elements within the atrium on its visual richness and the accessibility of shops. The research identifies an optimal configuration: placing the escalator in the middle of the atrium, deviating 30° from the entrance axis, and separately locating the elevators. This configuration provides the highest level of access to shops and the central atrium from any point, minimizing the number of turns required to reach different locations within the mall. Furthermore, the separate placement of elevators improves the flow of individuals between shops and the atrium, resulting in increased integration. In conclusion, selecting an appropriate configuration of elevators and escalators in shopping mall atriums can greatly enhance wayfinding and improve the visual richness and accessibility of the complex. Architects and designers can utilize these findings to optimize the design of public spaces within shopping centers, promoting social interactions and enhancing the overall visitor experience.

1. Introduction

Shopping centers have historically played a pivotal role as communication hubs and social spaces, providing customers with convenient shopping environments and merchants with valuable selling opportunities [1,2,3]. Originating in the 18th century, the concept of shopping malls aimed to create expansive architectural complexes that efficiently organized commercial services [4]. While Western regions experienced a decline in enclosed shopping mall growth during the 2000s, there was a notable surge in Asia, particularly in countries like Malaysia and Thailand [5,6,7].

Atriums within shopping malls serve as versatile spaces with various functions, including showcasing local culture, facilitating commercial activities, and providing areas for social gatherings [8]. The design of atriums plays a vital role in attracting visitors and fostering social interactions [9,10]. However, there has been limited research on the impact of stationary elements such as escalators, elevators, and vegetation on the visual richness and accessibility of atrium spaces. This study aims to investigate the arrangement of these elements in successful atriums worldwide, utilizing space syntax variables to assess their effectiveness in enhancing accessibility within the public spaces of shopping centers.

Shopping centers are considered public places in urban analysis and are part of city architecture [11]. They consist of nodes, edges, routes, neighborhoods, and landmarks, which are the essential elements of a city. They are typically confined to specific districts but include boundaries and landmarks that offer accessibility to urban trails and serve as activity centers [12,13]. Categorized as partial inner-communal spaces managed by private associations, atriums within shopping malls serve physical, spiritual, socio-cultural, and aesthetic purposes on an urban scale, although their accessibility may be comparatively limited to governmental communal complexes [14,15].

Previous studies have primarily focused on the spatial configuration of shopping centers and store placements, examining their impact on user behavior and wayfinding [16,17]. However, there is a research gap regarding the visual quality and accessibility of elements such as escalators, elevators, and plants within shops and atriums. This study aims to address this gap by investigating the arrangement of these elements and their influence on visual richness and accessibility [18].

This study aims to fill a research gap by investigating the visual quality and accessibility of elements like escalators, elevators, and plants within shops and atriums. The objectives include identifying optimal configurations of these elements, analyzing their impact on visual richness and accessibility, and examining their effectiveness in enhancing public space within shopping centers. The research aims to provide valuable insights for architects and designers to optimize the visitor experience, promote social interactions, and improve the design and layout of shopping mall atriums. To address this gap, this literature review aims to present a comprehensive overview of the most significant discussions and findings related to these issues from the period spanning 2012 to 2023.

Table 1. Literature review.

Authors	Year	Discussion	Technique	Results
[19]	2012	Relation between spatial configuration in a shopping mall with sales and human visual perception	Space syntax	A larger isovist area and a higher integration index result in increased accessibility and gate count within the respective area. As a consequence, the sales rate also rises.
[20]	2013	Optimum rent, area, and positioning the spaces in shopping malls	Bid-rent theory Space syntax	The study of space syntax serves as a practical assessment tool, providing a clear framework for evaluating different alternatives. One of its valuable advantages lies in the allocation of space and the positioning of anchors within a given environment. This makes space syntax a potential tool for determining the optimal placement of shops within a comprehensive arrangement.
[21]	2014	Pedestrian behavior in shopping areas	Case study Survey	At junctions, people generally tend to continue moving straight ahead and avoid re-entering a segment in a particular direction. When visiting multiple outlets, approximately half of the individuals begin with the outlet closest to their entry point. Additionally, nearly half of them choose the shortest route to reach their desired destinations.
[12]	2015	The significant factors of atrium design	Observation Survey	When designing an atrium, two significant features to consider are discernability and the potential to create a social image that encourages social interaction. Visibility plays a crucial role in atrium design as it serves as a space for orientation and wayfinding within the entire complex. Optimal visibility can be achieved by minimizing visual obstacles, such as architectural or decorative elements that obstruct the view of shops from the atrium and visitors within it.
[22]	2016	Role of building’s spatial configuration in shaping movement flows	Space syntax Q-analysis	High spatial integration and intelligibility in shopping malls strongly influence movement patterns in central areas and throughout the entire space. This results in well-connected distribution systems within the mall, effectively guiding the flow of people.
[23]	2017	Understanding the interactions between the socioeconomic variables and spatial design parameters of shopping complexes	Case study Axial space syntax	Syntactic variables, such as escalator integration, positioning, magnet placement, entrance positioning, central area layout, efficient escalator usage, and strategic allocation of tenant types, are crucial for understanding movement distribution in shopping malls. These elements influence movement patterns and enhance the overall user experience, shaping the dynamics of the shopping center.
[24]	2017	Impacts of configuration and tenant types on user movement in shopping malls	Space syntax	Spaces with higher syntactic values, specifically integration and connectivity, significantly impact user flow based on their configuration. Wider passages create a more compact system and enhance visibility for spaces and shops, attracting a larger consumer base.
[25]	2018	Shopping mall interior landscape design	CIM method	Coherency, legibility, spacious communal areas, wide paths, and organized structures are essential in shopping mall design. Clear differentiation between communal spaces and business areas is important. Obstructions to eye-level views should be minimized to alleviate concerns about on-site crimes. Visual connectivity at eye level must be prioritized.
[26]	2018	Integrating traditional observation techniques with Depth-map in atriums	Space syntax	To ensure a comprehensive and reliable assessment, both traditional techniques and Depth-map tools should be used together when evaluating differences in visibility and accessibility in atrium space arrangements.
[27]	2019	How social and physical environments affect human wayfinding and locomotion behaviors in shopping malls	VR	The level of crowdedness did not significantly influence the wayfinding tactics or primary route choices of visitors. However, it did impact movement patterns in the sense that individuals in crowded situations tended to navigate through the boundaries of the environment to avoid the crowds and find less congested areas.
[28]	2020	The article compares two different methodologies for a spatial layout analysis in shopping centers	ERAM Space syntax	Foot traffic positively correlates with sales rate and shop value in commercial buildings, highlighting the importance of visitor numbers for commercial value. The ERAM value, influenced by physical variables like elevator accessibility, distance to escalators, shop variety, and storefront distance, enhances the attractiveness and value of commercial buildings.
[29]	2020	Spatial logic of shopping malls	Bid-rent theory Space syntax	Shops located around convex atriums with a high spatial integration index and excellent accessibility from the center are highly desirable and command the highest rent per unit area. Due to their high accessibility, these shops can attract a large number of consumers, resulting in high footfall or gate counts.
[30]	2020	Influence of visual accessibility and spatial configuration on the navigation of individuals in shopping malls	Case study Space syntax	In shopping malls, individuals show a preference for open spaces that offer greater visual accessibility rather than physical accessibility. Moreover, they tend to walk in straight lines and avoid changing directions whenever possible.
[31]	2021	Integration and continuity analysis in geometrical configuration of the conventional bazaars of Iran	Case study Correlation Space syntax	According to the results, commercial buildings with linear and asymmetric plan patterns provide high-quality spaces for visitors from various points of view and advance individuals’ flow.
[32]	2022	Traditional market structure in Tabriz Grand Bazaar and its effects on mental durability of space and accessibility	Case study Correlation	The results indicate that the absence of nodes or sub-axial intersections along the main path facilitates the flow of individuals. Additionally, having well-defined and distinct entrance and exit points along the main path is crucial. This helps to streamline movement and enhance the overall navigation experience for people within the space.

provides a summary of the key studies and their contributions, offering valuable insights into the existing knowledge landscape in this field.

2. Methodology

This study’s methodology aimed to investigate the impact of different configurations on visual richness and accessibility in shopping center design. Key aspects included selection criteria for successful malls, additional controls, and longitudinal studies. Malls were selected based on criteria such as sales performance, footfall, tenant satisfaction, and customer reviews to ensure the representation of successful complexes [33,34,35].

Comparisons were made with malls featuring different configurations, particularly in elevator and escalator locations and directions, to evaluate the impact on visual richness and accessibility. Long-term effects were considered through longitudinal studies, providing insights into the sustained impacts of various configurations over time.

The research model (Figure 1) involved literature reviews, space analysis using space syntax, and a questionnaire survey. UCL-Depth map software version 10.08.00r aided in data extraction and examination, including diagrams and graphs. Logical reasoning and the questionnaire survey allowed for comparisons of each index’s effects. The methodology employed in this study involved selection criteria for successful malls, additional controls for comparative analysis, and longitudinal studies. The research model ensured a rigorous analysis of visual richness and accessibility in shopping center design. The nomenclature show in

Table 2. Nomenclature table.

Term	Definition	Term	Definition
Connectivity	Measures the number of spaces immediately connecting a space of origin	Entropy	Measure the distribution of locations of spaces in terms of their depth from space rather than the depth itself
Step depth	Follows the shortest path from the selected root line to all other lines within the system, and the path length is recorded on the line	RAi	Relative asymmetry at the i-th space
Gate count	Used to establish the flows of people at sampled locations	Weighted mean ($\stackrel{-}{\mathrm{X}}$)	Calculated by multiplying the weight associated with quantitative outcome and then summing it all together calculated using Equation (6)
Clustering coefficient (cc)	The number of links between all members of the neighborhood divided by the total number of links that could exist given that number of nodes	Variance (σ)	Standard deviation or a measure of the spread or dispersion within a set of data calculated using Equation (7)
Control	Control value indicates how strongly a room in a configuration relates to other spaces in terms of superiority	Ci	Connectivity index
Impact factor	A factor that is considered during the evaluation of the commercial complex’s parameters and their impact on space quality	K	Number of spaces immediately connected to a specific space
Optimum index	The value that reflects the desired or preferred level of each parameter that contributes to defining high-quality spaces	Ctrl i	Controllability index
Digression index	A comprehensive measure used to assess the deviation or difference between the scores of various indexes and the optimum index within the evaluation of a commercial complex	MDi	Average depth from i-th space

.

2.1. Space Syntax

Space syntax, grounded in graph theory, serves as a valuable tool for analyzing spatial layouts [36,37]. The Social Logic of Space, introduced by Hillier and Hanson in 1984, presents a syntactic theory that organizes spaces within buildings and complexes. This theory emphasizes how spatial configurations influence social interactions and suggests that buildings, towns, and cities possess distinct properties governed by sociological principles [38,39,40]. It argues that the spatial arrangement of a place provides valuable insights into the economic, social, and ideological relationships of its inhabitants. While often unseen, space plays a fundamental role in sociocultural events, shaped by social, cultural, and economic processes [41,42].

2.2. UCL Depth-Map

UCL Depth-map is used to operate visibility analysis in architecture and urban planning and includes four various syntactic analysis systems:

(1)

In axial line analysis, elements are straight, and the subject of analysis involves individuals movement [43]. A connection graph is produced by considering how each line connects to its adjacent lines. This graph is commonly applied to explore cities, towns, or neighborhood structures [44,45,46].

(2)

Convex space analysis is utilized when dealing with social interactions [43,47]. It is analyzed from two different aspects: (a) spaces with non-linear behavior and (b) spaces among them, like the configuration of dwellings and their interior arrangement [44,48].

(3)

Visibility graph analysis is used when the subject indicates intricate behavior patterns. This system applies single isovists and isovist fields in analysis [43]. The primary concept of this analysis is fields of view that are visible from a specific point. Hence, this model of analysis is centered on the reflection of light and defines the patterns of emotional behavior of individuals in the atmosphere [44,45,49,50,51].

(4)

In agent analysis, simulated “individuals” are distributed into the environment, and by applying their predefined algorithms, they select where to move within such an environment and circumstance.

Axial line analysis is a commonly used analysis system in urban and architectural scales. However, visibility graph analysis is employed to analyze space configuration for our specific investigation of interior spaces. This analysis produces a color-spectrum map, where each index is represented by a color gradient ranging from red (indicating the maximum value) to blue (indicating the minimum value).

2.3. Visual Richness Variables

2.3.1. Connectivity

The connectivity index is the number of spaces immediately connected to an intended space. For example, the connectivity of a particular space that includes three entrance doors from adjacent spaces is three regarding equation [52], Equation (1):

Ci = K

(1)

K is the number of immediately connected spaces to a specific space, and Ci refers to the connection at the i-th space [52]. Consequently, higher connectivity in a space means that the intended space has higher accessibility [53,54].

2.3.2. Controllability

Controllability is an index that determines the space opportunity for being chosen over its adjacent neighbors [53]. Regarding Equation (2) Ctrl I, a higher degree of preference for one space concerning a particular space implies that the former has a higher amount of control over the latter [48], Equation (2):

$$Ctrli:{\sum }_{j=1}^k=1/c_j$$

(2)

K is the number of defined spaces directly linked to space I and C_j indicates the relation at the j-th spaces. Ctrl I signifies the amount of $\frac{1}{c_j}$ control at the i-th space [51].

2.3.3. Clustering Coefficient

The clustering coefficient (cc) gives a measure of the proportion of intervisible space within the visibility neighborhood of a given point. It is defined as the proportion of vertices that are connected within the neighborhood of the current vertex, compared to the number that could be connected [51,54].

2.3.4. Gate Count

Gate count is an index that measures individuals flow at defined locations within space over a specific time [55,56]. The higher gate count illustrates that more individuals tend to cross the defined locations.

2.3.5. Depth

The depth index quantifies the number of steps required for an individual to transition from one particular space to another within a structure. A space is considered deep when there are multiple steps or stages involved in traversing between that space and other areas [57]. If we consider D_i,j as the shortest distance between space i and j in Graph G, then the following equation holds [58], Equation (3):

$$MDi=\frac{{\sum }_j^n=1^{d_{ij}}}{n-1}$$

(3)

MDi is the average depth from i-th space, n is the number of defined spaces, and D_i,j is the quickest route between spaces i and j [58]. The higher the depth, the more private a space, and to approach these spaces, someone must pass through more other spaces.

Step Depth

The step depth index measures the number of turns an individual needs to make from a specific location within a space to reach any other space within the plan. Each point visible from the starting location is considered at depth one, and each subsequent point visible from those locations is assigned a higher depth value. The step depth index focuses on determining the shortest route with the fewest turns required to reach a target point within the plan [59,60].

Mean Depth

The mean depth index is calculated by assigning a depth value to each space based on the number of spaces it is away from the main space or reference point. These depth values are then summed for all spaces and divided by the total number of spaces, which includes the main space. The resulting value represents the average depth or average number of spaces one needs to traverse to reach any other space within the plan, concerning the main space [60,61,62]. Mean depth is calculated for each space, and like the step depth, the shortest path through the visibility graph is considered for each space within the plan [10,59,62].

2.3.6. Entropy

Entropy is an index that illustrates the distribution of spaces in their depth from a defined point rather than the depth itself. If many spaces are near the point, the depth from that point is asymmetric, and the space holds low entropy, and when the depth is more regularly distributed, the entropy is higher [59,61]. This index illustrates culturally substantial topological differences among spatial layouts [62].

2.3.7. Integration

The integration index measures the level of connection or disconnection between a specific space and the overall structure. It indicates the degree to which a space is integrated with other spaces within the structure. The integration index is closely related to the connectivity index, meaning that higher connectivity among spaces results in higher integration within the entire structure [10,54], Equation (4). Integration can be measured by relative asymmetry and fundamental relative asymmetry [63]:

$${RA}_i=\frac{2({MD}_i-1)}{n-2}and {RRA}_i=\frac{RA}{D_n}$$

(4)

where

$$D=2\left\{n\left(\underset{2}{\log }\left(\left(n+2\right)\left(3\right)-1\right)+1\right)\right\}\left[\left(n-a\right)\left(n+1\right)\right]$$

(5)

n is the number of spaces, and MDi is the average depth from the i-th space [53,64], Equation (5). The lower the integration, the more secluded a room is, and the higher the integration index, the more communal a space is [53,65,66].

2.3.8. Survey and Questionnaire

Table 3. Questionnaire results.

	Connectivity		Step Depth		Gate Count		Clustering Coefficient		Controllability		Entropy		Integration		Mean Depth
	IF *	OI **	IF	OI	IF	OI	IF	OI	IF	OI	IF	OI	IF	OI	IF	OI
Average	8	1	9	0	9	1	9	0.5	4	1	7	0	8	1	9	0

* Impact factor; ** optimum index.

presents the questionnaire results obtained from 29 professors and specialized master’s and PhD students in the field. To evaluate the importance of different parameters in enhancing spatial quality in commercial complexes, a survey and questionnaire were conducted. The participants consisted of 29 professors and specialized students in the field, who were selected based on their expertise and knowledge in commercial complex design. The sample size, although relatively small, was determined to be appropriate for obtaining valuable insights within the given resources and time constraints.

The questionnaire aimed to gather participants’ perspectives on the impact of various parameters on spatial quality, using a scale of 0 to 10 for the impact factor rating. A rating of 10 indicated utmost importance, while a rating of 0 represented insignificance. Participants were also asked to provide their optimal index values, ranging from 0 to 1, for defining high-quality spaces within these parameters, denoted as the optimum index (Table 3). While the specific questions and details of the questionnaire are provided in Appendix A, the questions focused on evaluating the significance of parameters related to visual richness variables and their desired level of optimization. These parameters were selected based on previous studies and expert knowledge in the field, which have highlighted their influence on spatial quality in commercial complexes.

It is important to note that the sample size of 29 participants may be considered relatively small. However, similar studies in the field have successfully utilized comparable sample sizes to gain valuable insights and draw meaningful conclusions. Moreover, the participants in this study were selected based on their expertise in the field, ensuring a knowledgeable and relevant sample group. While the survey results provide a valuable perspective on the importance of parameters and optimum index values, it is important to interpret them within the context of the study’s limitations and the specific sample group. Further research and replication of the study with a larger and more diverse sample may provide additional insights and strengthen the generalizability of the findings.

2.3.9. Models and Scenarios

In this section, we have developed 10 different shopping center configurations, inspired by renowned shopping centers in Iran, Turkey, Dubai, China, Germany, and Georgia. Each configuration is represented by a modular square measuring 12X12X, where X represents the width of the main entrance. This standardized size facilitates easy comparison between the different patterns. The commercial units in each configuration have a depth of 2X, and the central atrium is designed with a radius of 8X.

To analyze the layouts, we specifically focus on the location and orientation of elevators and escalators within each sample. For instance, in Sample A (Figure 2), the escalator is positioned at the exact center of the X-axis, while the elevators are placed separately on the Y-axis, with a distance of +2X and −2X from the X-axis.

3. Results and Discussions

Figure 3 presents quantitative data and graphs analyzing different space configuration parameters using UCL Depth-map software. The quantitative outputs given in

Table 4. Digression index analysis and syntax quantitative outputs for elevator and escalator configurations (the numbers marked in green indicate the most optimal values).

	Connectivity	Step Depth	Gate Count	Clustering Co-Efficiency	Controllability	Entropy	Integration	Mean Depth
A	0.2507	0.8150	0.2238	0.3276	0.2530	0.6526	0.0774	0.4873
B	0.2544	0.7700	0.2027	0.3448	0.2651	0.6526	0.0793	0.4810
C	0.2525	0.7900	0.2214	0.3448	0.2530	0.6526	0.0777	0.4873
D	0.2544	0.7800	0.2135	0.3448	0.2530	0.6526	0.0783	0.4810
E	0.2581	0.7750	0.2232	0.3276	0.2530	0.6526	0.0785	0.4810
F	0.2535	0.7800	0.2256	0.3276	0.2530	0.6632	0.0777	0.4873
G	0.2590	0.7750	0.2177	0.3620	0.2530	0.6947	0.0748	0.5063
H	0.2627	0.7550	0.2455	0.3448	0.2650	0.6737	0.0797	0.4810
I	0.2627	0.7550	0.2310	0.3621	0.2651	0.6632	0.0811	0.4747
J	0.2572	0.7900	0.2081	0.3448	0.2651	0.6632	0.0783	0.4810

show similar indexes, indicating that the location of escalators and elevators does not significantly affect these variables. However, the graph outputs demonstrate noticeable differences in space quality when the placement of these elements is altered. The Depth-map software calculates average values for each node, representing the index of variables in each sample. For example, the variable index for the time that 50% of the plan in the atrium section is of high quality is equivalent to the time that 50% of the plan in the store’s section is of high quality. As a result, the numerical outputs are relatively close to each other, while the graph outputs exhibit significant variations based on the placement of elevators and escalators. Both sets of results are presented in Figure 3 for further clarification.

In this phase, the graphs obtained for each variable in each sample are analyzed using Image Processing software version 10.08.00r to establish a comparative context. The software determines the percentage contribution of each node to the overall plan. Using these percentages and the minimum and maximum indexes for each variable in each unique sample, the weighted mean, variance, and optimality index are calculated [11,67]. Based on these results and the optimal index obtained from the questionnaire, the weighted mean for each sample is determined as follows [65,67], Equations (6) and (7):

$$\overline{X}=\frac{{\sum }_{i=1}^n{w}_i{x}_i}{{\sum }_i^n{w}_i}$$

(6)

The variance or standard deviation, calculated using the following formula, reflects the level of homogeneity within the spaces. It measures the extent of uneven distribution of the desired index across the plan, including the atrium, entrance, and shops. Hence, a lower percentage indicates a more optimal space in terms of homogeneity [66,68]:

$$\sigma =\sqrt{\frac{1}{N}\sum _{i=1}^N{(x_i-\mu )}^2}$$

(7)

The analysis also includes the calculation of the optimality percentage based on the weighted mean and variance index [69]. A higher optimality index indicates a higher weighted mean and lower variance. This implies that the respective sample is more suitable as an atrium for the shopping mall, considering both accessibility and visual richness aspects (Figure 4).

Figure 3 highlights the analysis results, indicating that Sample F outperforms the other samples with the highest index score. This achievement is attributed to its unique configuration, where the escalator is positioned along the entrance axis from +1Y to −3Y, and the paired elevators are located in front of the entrance on the same axis. This arrangement maximizes connectivity in the two-dimensional analysis. However, it should be noted that in a three-dimensional environment, this configuration obstructs the eye-level view of visitors to most stores immediately upon entering the atrium. Nevertheless, the presence of paired elevators after the entrance improves accessibility to other floors and contributes to a relatively cohesive atrium space.

Turning to the digression table (

Table 5. Digression index scores for various parameters in the commercial complex.

Digression Index	Connectivity	Step Depth	Agent	Clustering Coefficient	Controllability	Entropy	Integration	Mean Depth	Score
Impact factor	0.8	0.9	0.9	0.9	0.4	0.7	0.8	0.9
Optimum index	1	0	1	0.5	1	0	1	0
A	0.13	0.26	0.03	0.74	0.28	0.75	0.33	0.22	0.37
B	0.08	0.42	0.00	0.46	0.16	0.94	0.23	0.15	0.34
C	0.04	0.98	0.02	0.17	0.22	0.84	0.32	0.52	0.42
D	0.01	0.03	0.00	0.11	0.14	0.56	0.34	0.29	0.25
E	0.00	0.40	0.07	0.20	0.00	0.79	0.41	0.49	0.35
F	0.00	0.01	0.00	0.06	0.21	0.55	0.27	0.20	0.22
G	0.08	0.33	0.01	0.30	0.00	0.68	0.00	0.05	0.24
H	0.05	0.92	0.05	0.37	0.25	0.90	0.11	0.04	0.37
I	0.01	0.98	0.00	0.84	0.03	0.37	0.19	0.26	0.39
J	0.16	0.07	0.09	0.43	0.27	0.14	0.05	0.98	0.32

), our analysis identifies Sample I and Sample C as the most desirable configurations, achieving a high optimality index of 98% in the step depth analysis. These configurations offer easy accessibility to stores from the shopping mall entrance, with less physical obstruction from the atrium towards the shops. Furthermore, in Figure 4, we observe that variations in the location and orientation of escalators significantly impact the distribution of individuals across different areas of the plan. Sample J emerges as the most desirable configuration in terms of visitor flow, as it leads to an even distribution of individuals throughout the plan.

Among the samples, Sample B stands out with the best clustering coefficient index of 46%. This indicates a moderate variation in space within the plan, enhancing wayfinding quality and reducing the likelihood of confusion for individuals in the atrium. Table 4 results highlight those configurations where the escalator is positioned on the central entrance axis yielding the highest controllability index for shops. This suggests that the location of the escalator influences individuals’ circulation patterns, as they tend to enter the shop areas more frequently than the atrium. Additionally, configurations with the escalator placed on the central entrance axis and separate elevators exhibit high entropy index optimality in the shop’s area. This indicates maximized and nearly asymmetric accessibility to stores from the center of the atrium.

In terms of integration analysis, configurations with separate elevators demonstrate optimal results. Sample E, for instance, where the escalator is located in the exact middle of the −60° Y axis and separate elevators are positioned on the same axis, achieves the highest average integration index. This suggests a lower average depth from the main entrance and the atrium’s center to all shops. Moreover, a higher integration index implies the presence of more communal spaces, making this configuration better suited as a public space within the complex.

Graph analysis reveals that changes in the location and orientation of escalators and elevators significantly impact the mean depth index. Sample J, with an optimality index of 98%, represents the most desirable configuration by minimizing turns from the entrance to the stores, elevators, escalators, and other locations within the plan, aligning with the optimal mean depth variable index of 0.

Overall, based on the digression table (Table 5), the most desirable configuration in terms of both accessibility and visual richness for an atrium is Sample C, while the least desirable configuration is Sample F.

The table displays the scores for different indexes used to evaluate the commercial complex. These indexes include connectivity, step depth, agent, clustering coefficient, controllability, entropy, integration, and mean depth. The scores are assessed based on two key factors: the impact factor and the optimum index. The optimum index refers to the ideal index value obtained from the questionnaire. It represents the participants’ consensus on the most suitable index for defining high-quality spaces within the parameters of the commercial complex.

To calculate the digression index, each parameter’s score is compared to the optimum index, incorporating an affection factor. The formula used is as follows: Digression Index: {(ABS ((connectivity Index)-(Optimal Index)) Affection Factor) + (ABS ((Step Depth Index)-(Optimal Index)) Affection Factor) + (ABS ((Gate Count Index)-(Optimal Index)) Affection Factor) + (ABS ((Clustering Coefficient Index)-(Optimal Index)) Affection Factor) + (ABS ((Control Index)-(Optimal Index)) Affection Factor) + (ABS ((Entropy Index)-(Optimal Index)) Affection Factor) + (ABS ((Integration Index)-(Optimal Index)) Affection Factor) + (ABS ((Mean Depth Index)-(Optimal Index)) Affection Factor)}

The digression index allows for a comprehensive assessment of the deviation from the optimum index across all parameters, considering their respective affection factors.

Additionally, the table presents the calculated scores, labeled as “Score”, which are derived from the digression index. The formula for calculating the scores is as follows:

Score = 1 − (Digression Index/8)

This formula normalizes the digression index values to a scale of 0 to 1, representing the overall quality of the spaces within the commercial complex. By utilizing these calculations and considering the impact factor and optimum index, the table provides valuable insights into the evaluation of the commercial complex’s parameters and their impact on space quality.

4. Conclusions

In conclusion, our study provides valuable insights into the impact of elevator and escalator arrangements on the visual quality and accessibility of atriums in shopping centers. However, it is important to acknowledge the limitations of our study. The survey conducted to rate the studied parameters had a relatively small sample size of 29 participants, which may limit the generalizability of the findings.

• Regarding the relationship between the participants and the topic, further information is required to fully understand their expertise or experience in the field of architecture or commercial complex design. This could potentially influence their perception and rating of the parameters.
• Considering these limitations, our study still contributes significantly to the field. Through the analysis of various configurations, we have identified Configuration (C) as the most suitable arrangement. Configuration (C) features a centrally positioned escalator deviating 30° from the entrance axis, accompanied by strategically placed elevators on both sides. This configuration optimizes visibility, allowing all shops around the atrium to be visible upon entering while providing convenient access within the shopping center, thereby reducing the need for directional changes.
• Furthermore, the integration of image processing techniques, specifically UCL Depth-map graphs, enhances the comprehensive analysis of Configuration (C) and validates its effectiveness in improving visual richness and accessibility.
• Architects and designers can leverage the knowledge gained from our study to optimize the design of public spaces within shopping centers, promoting social interactions and enhancing visitor experiences.

In summary, our study addresses a significant research gap by investigating the impact of elevator and escalator arrangements on atriums in shopping centers. The introduction of Configuration (C) as the most suitable arrangement, supported by the image processing results of the UCL Depth-map graph, provides valuable insights that contribute to the field and can guide future designs for vibrant and accessible public spaces within shopping centers.