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This paper presents a rule-based procedural generation approach for layout design by design knowledge encoding. Taking linear shopping centres as example, the proposed method encodes the layout design elements of the walkway space, tenant areas, and staircases into generative rules based on geometric operations. The generative rules integrate the shopping centre layout's spatial patterns and geometric features and incorporate user-specified interaction parameters to form a generation tool prototype for early-stage layout design. The results show that the method can deal with the complex spatial elements of linear shopping centres and provide design references for architects, which helps combine generative algorithms with the design process.
KEYWORDS
Computer-aided
architectural design;
Layout design;
Linear shopping
centre;
Procedural
generation;
Rule-based
Abstract This paper presents a rule-based procedural generation approach for layout design by design knowledge encoding. Taking linear shopping centres as example, the proposed method encodes the layout design elements of the walkway space, tenant areas, and staircases into generative rules based on geometric operations. The generative rules integrate the shopping centre layout's spatial patterns and geometric features and incorporate user-specified interaction parameters to form a generation tool prototype for early-stage layout design. The results show that the method can deal with the complex spatial elements of linear shopping centres and provide design references for architects, which helps combine generative algorithms with the design process.
1. Introduction
Layout design is a core problem in early-stage architectural design, involving a combination of spatial elements and geometric relations until the conflict of space resources is resolved and a particular layout effect is achieved. With computer software and hardware development, the layout design process has adapted dynamically with a continuous iteration of new technologies. The role of computers in architectural design has gradually shifted from drawing assistance to design assistance, even to the automatic generation of design schemes (Caetano et al., 2020). In recent years, technologies in computational design have been expanding continually. Applications of evolutionary @lgorithms, mathematical programming, and machine learning have significantly broadened the boundaries of the - automated generation of architectural layouts (Weber et al, 2022). |
The enthusiasm for technological advancements has brought more opportunities and exploration avenues within the architecture industry, prompting architects to reconsider their position in the digitization trend. An obvious perspective lies before us: because design problems are "ill-structured" problems (Simon, 1973), mathematically rational results, although providing necessary references for layout design schemes, are difficult to directly
substitute for design logic. This implies that in computational design systems, architects' roles will not be replaced by a "fully automated" mode but instead require a design thinking transformation, reestablishing parameterized expression mechanisms for the design process (Megahed, 2015). Therefore, an interactive framework that integrates multiple generative design algorithms has been emphasized (Singh and Gu, 2012), which is why we believe that a rule-based and procedural framework need to be reconsidered. In such a framework, an architect's design experience and knowledge serve as the bases for pattern induction and algorithm encoding, potentially forming a series of professional generative rules that can be processed by the computer and implemented by the architect. As a result, problems such as spatial relations and functional configurations are more easily judged by architects in that process to form a cooperative working mode of human and computer.
Such a working mode proves particularly valuable when dealing with complex floor plans for large-scale commercial buildings like shopping centres. With the development of commercial real estate, the layout of shopping centres has gradually iterated, forming efficient and patterned spatial characteristics, thus laying the foundation for the transformation to digital generative systems. Linear spatial combinations (and their deformations) have gradually emerged as predominant patterns in various shopping centre layouts, widely applied for their advantages of spatial efficiency and comprehensibility. However, research on the generation of shopping centre layouts remains relatively scarce despite this. An obvious reason is the high complexity of design conditions and regulatory constraints associated with shopping centres as large public buildings. That leads to challenges in the practical application of optimizationoriented generative algorithms (e.g., evolutionary algorithms), which face the risk of accumulating constraints and decreasing solution efficiency (Fahmy et al., 2014). Therefore, rule-based and procedural generation frameworks become a feasible strategy to circumvent such limitations.
This study focused on the transformation mechanism of layout characteristics into procedural generation rules. Taking linear shopping centres as an example, this study organized the main space elements in layout design into corresponding generation rules and encoded them into procedural generation algorithms through a series of geometric operation methods. The generation algorithms were further integrated into a prototyping tool to assist architects in achieving layouts that align with general design concepts in the early design stages. The method proposed in this paper will provide an example from the perspective of the transformation of design knowledge to generation rules. This will strengthen the close connection between the generative system and the design process.
2. Related work
2.1. Design knowledge and analysis of shopping centre layouts
The compilation of rule-based algorithms comes from the digital deconstruction of design knowledge. For shopping centres, direct analyses of their spatial layout patterns and design methods can be found in literature, such as portfolios and datasets (Coleman, 2006). Recent studies have focused on the effect of commercial building design on the integrated urban system, such as a comprehensive design considering transportation systems (Sasmita et al., 2020) or a design analysis oriented to spatial experience enhancement (Yuan et al., 2021). Although those materials are difficult to translate directly into executable algorithms, they still provide effective evaluation criteria and design references by standardizing and systematizing the key stages of the shopping centre design process. Quantitative analysis methods have become mainstream in recent years for evaluating and classifying specific spatial elements of shopping centres (Andi et al., 2021). Through metric measurements and spatial data visualization, case studies can be used to scientifically summarize and deduce patterns in shopping centre spatial layouts.
Specific to the design methods for the major spatial elements of shopping centre layouts, the relevant literature offers more targeted analytical perspectives. The research subjects can generally be divided into three main categories: walkway space, atrium space, and tenant and facility allocation.
In analysing walkways and topological prototypes, spatial syntax is an important quantitative analysis tool. Spatial syntax analysis enables visualizing indicators such as connectivity and depth, enabling comparative analysis of the traffic characteristics of different prototypes (Zhou and Liu, 2021) and evaluation of spatial efficiency and clustering (Derya and Ergener, 2023). Bai and Yao (2018) improved spatial syntax analysis by predicting pedestrian patterns in public spaces, thereby estimating the commercial value of tenants and providing a basis for leasing strategies. Apart from spatial syntax, some studies have used feature extraction using neural networks to analyse pattern types in floor plans. For instance, Yang and Huang (2023) represented vector models of shopping centre plans as graphs and used graph neural networks to classify shopping centre design cases, aiming to uncover complex relations among spatial elements.
Regarding atrium design, due to its significant effect on the spatial layout of shopping centres, some studies have focused on the spatial benefits of different atrium patterns. Kusumowidagdo et al. (2016) clarified the characteristics of atrium spaces as core elements of shopping centres through case studies and discussed the spatial ambiance and crowd attraction of atriums. Yusoff and Jessie (2022) explored the social benefits of atriums by analysing 4 typical atrium patterns and conducting case studies to understand the demand for atriums as social and activity spaces. Furthermore, research combining atrium design with environmental benefits such as lighting and energy consumption is also a common perspective. In such studies, controllable variables of an atrium include different shape prototypes and their parametric deformations (Xue and Liu, 2022) or indicators such as area ratio, quantity, spacing, and distance from exterior walls (Yuan et al., 2022).
Regarding tenant and facility allocation, the types and positions of tenants are crucial considerations in design practice. Placing a certain type of tenant in the most favourable space can achieve better foot traffic and higher turnover benefits. Research methods in this area include using spatial syntax and regression analysis to explore the effect of tenant positions on sales (Aydogan and Salgamcioglu, 2017), as well as combining anchor stores with shopping centre layouts to investigate their spatial combination features (Yuo and Lizieri, 2013). However, discussions on spatial and geometric patterns for tenant allocation are still lacking, which poses obstacles to layout generative design.
2.2. Procedural and rule-based space layout generation
Procedural and rule-based generative design methods are a universal and fundamental strategy that can be applied to various architectural elements such as road networks, parcels, 3D models, floor plans, and facades (Parish and Miiller, 2001). In terms of technical frameworks for layout generation, shape grammars (Veloso et al., 2018), L-systems (Qin et al., 2023), and cellular automata (Çalışır and Cagdas, 2022) are commonly used. However, note that a single technical framework like the above often imposes limitations on the encoding of generation rules, making it difficult to accomplish more flexible or variable generative design tasks. Therefore, much research has focused on small-scale, functionally simple building types such as apartment layouts and villas, so exploring procedural generation for complex layouts has not received sufficient attention.
As mentioned above, complex layouts of large public buildings have been generated by evolutionary algorithms, integer programming, and other experiments (Egor et al., 2020; Lv and Wang, 2020). However, the high complexity reduces solving efficiency and incurs obstacles to practical application. Therefore, combining different algorithm models or writing specific generative rules in accordance With geometric features has become one of the strategies to solve the above difficulties to a certain extent. Becker et al. (2013) combined L-systems with partition grammars to encode different geometric and topological characteristics of corridors and rooms, thereby generating floor layouts for educational buildings. Adáo et al. (2019) established tree-like recursive subdivision rules on a plan, then determined elements such as walls and doorways based on a series of geometric checks. Okhoya et al. (2022) explored spatial planning for complex office layouts using a zzhybrid generation method of shape grammar and space allocation algorithms.
Moreover, integrating interactive modes into the generative systems framework also helps combine architects' on-site judgements with computer outputs, enabling more flexible solutions to layout generation problems. Khodabakhshi et al. (2022) used the Grasshopper platform to take parameters such as position, area, and aspect ratio constraints as user inputs, thereby establishing topological and geometric operation rules to generate floor plans. Xie and Ding (2023) used requirements for the dimensions of various functional spaces, spatial relations, and orientation preferences as user inputs, combined with spatial representations based on graph theory, to construct a layout generation system for buildings. However, there is still room for improvement in that area of research: some parameter settings are more suitable for computer processing than for architects' habits, and interactive operations' flexibility warrants further improvement.
2.3. Summary of related work
Research on shopping centre layout design has encompassed both qualitative explanations and quantitative analysis, contributing to the synthesis and extraction of design knowledge. Concurrently, within procedural and rule-based frameworks, related work has been attempted across various types of building layouts, with efforts made to enhance tool interactivity.
However, the combination of these two topics remains a research gap. On one hand, the design methods for shopping centre layouts lack effective digital translation. Design guidelines and analysis are the natural conditions for the transformation of knowledge into generative rules, yet existing studies have not explored this avenue. On the other hand, procedural and rule-based research primarily focuses on the construction of overall algorithmic frameworks, with limited attention given to the correspondence between specific design elements and rule algorithms. This study aims to bridge this gap by exploring methods for translating and integrating design knowledge with corresponding rule algorithms, specifically applied to linear shopping centre layouts, which have not yet been extensively validated in this context.
3. Methodology
This paper focuses on translating the main spatial elements of linear shopping centres into rule-based generation algorithms. It mainly follows a procedural generation strategy, that is, according to the architect's design experience, the complete generation process is divided into several stages, and the generation rules are encoded correspondingly. Specifically, the linear shopping centre layout task includes three generation stages: walkway space generation, tenant partitioning, and staircase generation. These three stages can basically reflect the main characteristics of linear shopping centre layouts, which can meet the design reference needs of architects.
Each of the three generation stages contains a detailed process (Table 1). For walkway space generation, the walkway was generated from geometric prototypes to carry out interactive modelling of atrium shapes. The layout of escalators was determined by checking the service radius. For tenant partitioning, a set of grids covering the outline were generated beforehand, and then partition lines were generated on the grids. For staircase generation, the positions of the staircase were first calculated and pre-set, followed by path verification and interactive position adjustments to generate the final layout. All generation rules and algorithms are explained in detail in Section 4.
We implemented the proposed generation methods in Java environment and integrated them into a tool prototype available to architects (Fig. 1). JTS Topology Suite 1.16.1 was used to assist with geometric operations, Processing 3.5.4 and controlP5 2.2.6 were used to implement display and interactive tool interfaces, and ¡Geo 0.9.4.1 was used to import and export graphics files. All of the above libraries are open source materials written in the Java language. Generation tools and experimental cases are shown and discussed in Section 5.
4. Procedures and generation rules
4.1. Walkway space generation
In the case studies of typical linear shopping centre models, a noteworthy aspect is the pivotal role played by walkway space areas in determining floor plan configurations. Walkway spaces are usually linearly centred for maximum circulation and display efficiency and are connected through atriums to form layout patterns on each floor. Therefore, it is essential to systematically translate the main spatial elements of walkway areas into generative rules, laying the foundation for generating other elements.
4.1.1. Straight skeleton
The primary step is to extract the form characteristics of a given shopping centre outline to serve as a reference area for the atrium arrangement. The straight skeleton algorithm is introduced here, which uses a set of topological skeleton lines to represent geometric shapes, and it can represent the medial axis of polygons (Aichholzer, 1995). The straight skeleton extracted from the original algorithm manifests as intersecting segments extended along the bisectors of each vertex. Among them, the line segment not connected with the vertex is the ideal part in this study. By incorporating a depth-first search algorithm in graph theory, the longest chain from the straight skeleton can be extracted, which can represent the planar feature of the linear shopping centre. Finally, the raw walkway space of the shopping centre can be obtained by the curve and buffer operation of the skeleton (Fig. 2).
4.1.2. Atrium shapes
On the basis of the raw pattern, the layout of the atrium is an important factor affecting the final form of the walkway space. The variable shape of the atrium carries the role of channelling pedestrian flow and regulating visual atmospheres. In this study, several common atrium shapes were parametrically encoded in computer programs for rapid generation and adjustment (Fig. 3(a)). Each shape was described by 3 properties to record geometric information: the centre of the shape, vertices, and vectors from the centre to each vertex (Fig. 3(b)).
Because the shape and scale of the atrium require some subjective control by the architect, the layout of the atrium shape adopts interactively. This involves translation, scaling, and deformation methods for each atrium shape combined with the architect's manual control. The deformation method, which requires a special explanation, updates the atrium's position and shape with interaction under the condition of a fixed atrium area (Fig. 3(c)). This helps the architect adapt the atrium's shape to the limitations of its size without losing the sense of scale. Finally, through the process of chamfering and buffer refinement, some relatively complete walkway space patterns can be obtained (Fig. 4).
4.1.3. Escalator generation
An independent but important element in the walkway space of a shopping centre is the escalator, which serves as the main vertical pedestrian flow guide. Escalators are usually set at atrium intervals and might vary depending on the size of the crowd and design specifications in different regions. Generally, the service radius of an escalator is a significant consideration, so it is valuable to generate and visualize based on its service scope. The placement of escalator positions can be achieved using a greedy strategy.
* First, for all atriums, obtain the estimated number (п) of escalators by dividing the total length (1) of the skeleton path by the escalator service radius (r).
* Subsequently, randomly generate n position points along the skeleton path (Fig. 5(a)). Two iterative rules are set for the position points: (1) points should move toward the midpoint of the skeleton path, and (2) points should be mutually exclusive in accordance with r.
* For the stable state position points in the end, identify the atrium closest to each point as the atrium where the escalator must be placed (Fig. 5(b)).
* Generate the model within the atrium polygon in accordance with the form of the escalator unit. The actual service scopes are visualized for feedback (Fig. 5(c)).
4.2. Tenant partitioning
Tenant partition work is a core but mechanical task in the layout design of shopping centres. Although the partition of tenants often changes in design practice and is closely related to commercial requirements, its spatial layout characteristics are still worthy of attention and exploration. In the context of layout design, tenant layout patterns also have certain commonalities and regularities, and the extraction and digitization of their generation rules will bring specific design references for architects.
4.2.1. Minimum bounding rectangles and grids
At the beginning of the partitioning, it is necessary to generate a simplified grid for the given retail space to simulate the structural modulus. The structural system, including the positioning of columns, requires strict structural verification. However, during the early design phase, a simplified grid system helps control the scale and modulus of tenant partitioning, and facilitates the subsequent layout deepening. Through the observation of the cases, we notice that the structural system of a linear shopping centre can be abstracted as a set of minimum bounding rectangles enclosing the outline, which are further divided into grids. Therefore, geometric rules can be written to search for feasible solutions:
* Traverse and filter out all concave vertices of the outline polygon, because those concave points often correspond to the transformation of the grid system.
* For each concave point (P) and the number of structural systems (m) input by the architect based on design considerations, emit n evenly distributed rays from P toward the interior of the outline (Fig. 6(a)). The quantity of n can be adjusted based on computational considerations.
* Enumerate all combinations of rays for each of the m-1 groups and divide the outline polygon into m subregions (Fig. 6(b)). Calculate the rectangularity of each subregion (the ratio of the polygon area to the bounding rectangle area).
* Find the set of subregions with the highest rectangularity mean and consider their minimum bounding rectangles as the optimal solution (Fig. 6(c)). A simplified grid is generated on each rectangle in accordance with a common modulus. In this study, 8.4 m x 8.4 m was used as the size of a grid cell (Fig. 6(d)).
4.2.2. Partition rule
A fundamental logic of tenant partitioning in shopping centres is to ensure that each tenant has a display interface with a certain width facing the walkway space. At the same time, the end of each tenant's wall should be as perpendicular as possible to the contour of the walkway space. Based on the previously generated walkway space and grids, the partition segments between tenants can be calculated by assessing the intersection angles. The basic rules are as follows:
* First, obtain the intersection points between the walkway space contour and the grid edges, recording the angle 6 at each intersection point.
* Perform a vertical judgement for 6 that includes the threshold (+20% was used in this study). If it is considered a valid vertical, access and record the grid edge at which the intersection is located.
* Perform a secondary judgement for the threshold of 6 to divide the partition line into two cases. For the case of +10°, extend along the direction of the grid edge toward the building outline, obtaining the straight partition segment for a tenant unit (Fig. 7(a)).
* For the other case, from the grid node closest to the walkway space contour, add a perpendicular segment to the contour, resulting in a partition polyline to ensure a more suitable orientation of the tenant openings relative to the walkway space (Fig. 7(b)).
Figure 7(c) shows the partition results in accordance with the above rules. Two additional points require more clarification. First, the threshold of 6 is an adjustable empirical parameter. Its purpose is to filter out grid edges that are relatively perpendicular to the walkway space contour, excluding cases with small angles that might complicate the setting of tenants. Second, partition polylines are introduced to complement the previous step. By judging the existing 0 threshold again, the shape of partition line is divided into two cases. Such rules are detailed in terms of the relationship between the retail space and the walkway space.
4.2.3. Secondary processing
On the basis of the preliminary partition, there are still special cases where the partition result is difficult to use or cannot meet the specific layout requirements. Therefore, introducing some secondary processing rules can significantly improve the generation effect and meet the requirements of more tenants.
One of them is the union rule (Fig. 8(a)). Using Boolean operations on polygons, the architect can choose and unite the selected tenant shapes. The data relation between the new tenant and other tenant units will be reestablished after the union calculation. The union rule can be used to designate tenants with large areas, and tenants with sufficiently large areas will be automatically marked as anchor stores. It can also be used to artificially eliminate some partition results that have unsatisfactory shapes.
The other aspect is the corner area partition rule (Fig. 8(b)). Referring to the design approaches in the existing cases, some corner tenants usually continue to be partitioned. The starting point O of the secondary divider is the grid node closest to the corner tenant centre. Connect point O and the midpoint of the tenant entrance to obtain the first segment, OP,. Extend the line from О to the outline along the grid edge to obtain the second segment, OP,. Those 2 segments constitute the secondary divider of the corner tenant. The final partition result after the 2 secondary processing rules are applied is shown in Fig. 8(c).
4.3. Staircase generation
In large commercial buildings, staircases are auxiliary spaces important for the layout. In the specifications of different countries and regions, the position and number of staircases differ, but they all must be strictly checked on the in-depth plan. This often leads to a situation where numerous changes are made to the layout to balance regulatory constraints and the design requirements of the floor plan. Therefore, in the early-stage design, it is necessary to be able to generate the approximate positions and scales of the staircases and do simplified verification.
4.3.1. Quantity and pre-set positions
The distribution rules of staircases are generally based on the calculation of numbers and paths. First, the number of staircases and the pre-set positions can be determined in accordance with the basic evacuation requirements. Taking the national standard of China (Ministry of Housing and Urban-Rural Development PRC, 2018) as an example, a general equation to calculate the number N of staircases in a standard floor of a commercial building can be described as
(ProQuest: ... denotes formula omitted.)
where A is the floor area, К is the population density of the commercial building, w is the evacuation width required per 100 people, and Wis the evacuation width of a standard staircase.
Based on the general patterns of auxiliary spaces in shopping centres, staircases are typically located near the outline and connected to the walkway space via evacuation corridors. To ensure that the positions of the staircases are evenly arranged throughout the floor, the outline polygon can be divided into n points (Fig. 9(a)). Each point is used to find the nearest partition line, which acts as the generator for the corridor, and the end of the line acts as the default position for the staircase (Fig. 9(b)).
4.3.2. Path verification and generation
The goal of staircase verification is to cover all the public areas under the condition of a given evacuation distance. Although the distance is difficult to calculate in detail at an early stage, some graph-based calculation methods can be used for preliminary verification. Unlike escalators, the verification of staircases should be cumulative along a feasible path rather than simply covering a circular area.
By building a graph model of the flow lines of all tenants and walkway spaces, the path length can be calculated on the graph to verify an evacuation area that a staircase can cover (Fig. 9(c)). The architect can manually change the initial positions and get real-time feedback on path coverage until a balance is reached between evacuation requirements and layout results (Fig. 9(d)). Finally, the staircase shapes and the corridors are inserted in the final position in accordance with the standard dimensions of the staircase module. Those inserted staircase shapes can be on either side of the tenant's partition line and are therefore randomly generated by default: the architect can then select them and move them to the other side. The polygons of inserted staircases and corridors automatically cut away existing tenant areas (Fig. 10).
5. Results and discussion
5.1. The generation tool prototype
After synthesizing the generation rules and algorithms of the above spatial elements, we organize them into different modules and develop a generation tool prototype for linear shopping centre layout (Fig. 11). The specific functions of each module are as follows:
* Module 1: Site Import. This module provides the function to import a ".3 dm" model file, a common file format in Rhinoceros. Based on the layer naming of the site file, the tool can recognize the outline of the shopping centre to be designed.
* Module 2: Walkway Space Generation. This module includes several algorithms for generating a skeleton, atrium shapes, escalator positions, etc., as mentioned earlier. Through this module, a complete walkway space pattern can be generated.
e Module 3: Tenant Partitioning. This module first automatically generates envelope grids based on the number of grids input by the user and performs the initial tenant partitioning. Users can then select tenants and apply the union or secondary partition rule in accordance with their requirements.
* Module 4: Staircase Generation. By initially estimating the number of staircases based on the building scale and generating points, users can interactively modify the selected position point to generate the modules of the staircases with their connected corridors.
* Module 5: Result Export. Corresponding to Module 1, the generated results are saved again as .3 dm files for further processing and cross-platform use.
5.2. Generation experiments
Three real-world shopping centre projects were used as case studies (Table 2). The outline shapes of these cases are linear, L-shaped and C-shaped, respectively, which are common topological deformation of linear shopping centres. Generation experiments were carried out on these three cases using generation tool and compared with real project drawings (Fig. 12). Analysing the three experimental cases, several insights can be derived from various aspects:
(1) Overall layout. From Fig. 12, it is evident that the generated results replicate the general spatial characteristics of linear shopping centres. Some core characteristics include the configuration of the walkway space, the relationship between tenant and the outer contour, the position of anchor tenants, and the distribution of vertical transportation. Some of these generative processes, such as the shape of the atrium and the union of tenants, involve interactive operations and subjective judgments by the architect. Thus, the architect can flexibly control these elements using the generative tool to achieve results that match actual design needs. This is reflected in the comparison of the count and area of atriums, as well as the count of tenants.
(2) Tenant partition. The generative method introduced in this study is based on grid system and implemented by extending partition lines. This approach captures the typical layout of retail areas. However, some differences and special cases are worth noting. In Case 1, for instance, the actual tenant shapes may be more complex and closely intertwined with auxiliary spaces. Auxiliary spaces which occupy a significant portion along the outline can notably reduce the depth of some tenants, resulting in more irregular shapes for large tenants.
(3) Vertical transportation. Differences in the count of vertical transportation elements, including escalators and staircases, exist between the generated results and the actual projects. For escalators, Cases 1 and 2 show that the actual layout might include more escalators than the generated results, with more flexible positioning, sometimes even having two escalators in one atrium. Only Case 3 closely matches the actual situation in terms of the number and position of escalators. Although the service radius is an important measure, the number and position of escalators may be more closely related to specific commercial needs in actual design tasks.
For staircases, the difference in numbers primarily stems from two reasons. First, the generated results adopt a module where two staircases are placed side by side (e.g., 10 positions corresponding to 20 staircases). While this represents the layout characteristics of most situations, in the designs of Cases 2 and 3, the staircases might be further split and flexibly arranged to meet evacuation requirements more efficiently, leading to redundancy in our generated results. Second, in specific design projects, staircases are more finely classified to meet different evacuation standards, such as staircases dedicated to children or cinemas. This can significantly affect the total number of staircases, resulting in considerable variation.
5.3. Discussion on the results
The different results of the three experimental cases show that the generation tool can help architects provide layout design reference in the early stage of design. When dealing with various outline shapes, the series of rules and algorithms proposed in this study ensure a certain degree of flexibility and robustness. Compared to existing research, we further deconstructed the spatial elements of shopping centre layouts and sought suitable rule descriptions and geometric prototypes to standardize and abstract these elements. Some of these descriptions and prototypes are derived from clear and quantifiable design experiences, such as the common atrium shape types, the service radius of escalators, and the evacuation distance of staircases. Others come from observations of the design cases, such as the reflection of the skeleton lines on the walkway space, and the rules of tenant partitioning. The above ideas of knowledge encoding and rule translation help to promote the digital representation of design tasks, and also help to complete the algorithms in computer programs to present design tools. Therefore, our work complements existing research by integrating design guidelines with a rule-based procedural generation framework, which is validated on linear shopping centres.
The experiments based on real-world projects highlight some more specific advantages and challenges for our research. Compared with the real design drawings, the generated results show a certain similarity in the overall layout, especially in the walkway space form, the atriums, and the layout of major tenants. Some detailed design requirements are also reflected in the results, such as the alignment of the tenant partitioning lines with the outline shape, as well as the sufficient and evenly distributed staircases. However, the variability of vertical traffic and the complexity of auxiliary space are not considered by the proposed method in this study. Moreover, the layout of structures will also significantly affect the plan of shopping centres. These aspects are often more rigorous and specific design tasks. Therefore, space allocation based on reasonable auxiliary space design and effective structure arrangement will become a challenging research direction.
Additionally, some further reflections are triggered from the perspective of the collaboration between architects and computers. Ensuring the effectiveness of generative algorithms while maintaining the flexibility and generality of the tools requires more consideration. An evident situation is that obtaining as many design methods as possible from architects' experiences can aid in algorithm development and tool formation. However, overly detailed and specific design rules may lead to a certain degree of design rigidity. Although the generated results may align better with current design practices, the exploration space for design becomes narrower. Therefore, finding the right balance between detail and flexibility is crucial for enhancing the utility of generative algorithms. This balance may require further analysis from the architect's perspective to uncover truly principled and prototypical design knowledge that can address more flexible design needs. On the other hand, the introduction of data-driven methods could help evaluate and select design details, bringing greater changes to rule-based generative design frameworks.
6. Conclusion
In this paper, we introduced a rule-based generative method for linear shopping centres, transforming design knowledge into algorithms and integrating them into a generation tool prototype for case verification. We adopted a procedural strategy, dividing the design process of linear shopping centres into three stages: walkway space generation, tenant partitioning, and staircase generation. In each stage, the generation rules were formulated according to different space elements and design guidelines. In the walkway space generation stage, straight skeleton was used to represent the form of walkway. Several common shapes and deformation rules were specified to achieve atrium placement, and the layout of escalators was generated through service radius calculations. In the tenant partitioning stage, the minimum rectangle combinations were searched using an enumeration method to obtain modular grids. Subsequently, the generation rules for partition lines and secondary processing were encoded. In the staircase generation stage, the number of staircases was calculated according to code requirements. A graph model was constructed to calculate the coverage of evacuation paths, and the final positions were determined interactively to insert the staircase modules. All rules and algorithms were integrated into a generation tool prototype, and three realworld cases were used for generation experiments. The results indicate that the proposed method is applicable to various outline conditions of linear shopping centres. The generated layouts have practical reference value, thereby assisting in the early-stage layout design process.
Our research has achieved a translation mechanism between shopping centre design knowledge and rule-based generative algorithms. This mechanism ensures that architects have a firm grasp of design concepts while maintaining the interpretability of the generation process, effectively integrating the architects' experience into the generative system. Future work can be expanded in two main directions. From a methodological perspective, the data feedback between different generative procedures needs to be further explored. For example, changes in atrium size affecting tenant layouts or the commercial value of tenants influencing the staircase layout. This requires more comprehensive quantitative analysis at each step to establish a bidirectional information transmission mechanism, influencing the execution of generative rules and potentially forming an optimization system. From the perspective of research subjects, we anticipate that this method could be applied to other building types, such as hospitals and hotels. The generative logic in these types is similar to that of shopping centres, and also require the analysis and filtering of rules to balance the practicality and flexibility of the generation algorithm. By mapping the relationship between design knowledge and rule-based algorithms, this approach can provide references and insights for the design of a broader range of building types.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
The study was funded by the National Natural Science Foundation of China (Grant No. 52378008), and the Postgraduate Research & Practice Innovation Program of Jiangsu Province (KYCX24_0418). SHUISHI Architecture and Planning Corp., Ltd is acknowledged to provide information and suggestions for this study.
* Corresponding author.
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