Research on the Application of Cement Tile Patterns Based on Shape Grammar

Abstract

The current derivation and application of traditional culture lack a scientific procedural method, and the existing processes are overly cumbersome and complex. The transformation of flat patterns requires manual modeling by professional product designers, resulting in low efficiency, especially when dealing with intricate patterns. To address these issues, this paper takes Xiamen cement encaustic tiles as an example and establishes a standardized process from the extraction of cultural elements to the 3D printing of physical products. Additionally, a one-click transformation plugin from flat patterns to three-dimensional models is developed based on the QT framework and Grasshopper platform. This plugin utilizes an edge recognition algorithm to identify the transformed patterns as editable NURBS curves. The curves are then converted into surfaces using the plugin’s modeling functionality before being encapsulated. With the encapsulated plugin, users only need to input a PNG image of the desired pattern and the basic model of the desired product to obtain a product with the structural features of the specified pattern. This research aids product designers in quickly extracting the most distinctive features, significantly accelerating the development speed of cultural and creative product transformations, improving production efficiency. The simplified operational process enables more people to participate in the design of cultural and creative products, promoting the dissemination and integration of traditional culture with modern technology.

1. Introduction

In recent years, with the growth of the cultural industry and the emergence of the new national trend, there has been a heightened focus on incorporating traditional cultural elements into apparel design, product design, and interior decoration. In 2014, the State Council issued the “Opinions of the State Council on Promoting the Integration and Development of Cultural Creativity and Design Services and Related Industries”, which explicitly stated the following: “Drawing on our rich cultural resources, enriching the depth of creativity and design, expanding the methods of preserving and utilizing tangible and intangible cultural heritage, and fostering the preservation and sustainable development of cultural heritage resources through their integration with industries and markets” [1]. However, the current application of traditional culture tends to be one-dimensional, primarily consisting of simple image stacking, and involving a limited number of individuals, mainly artists with many years of training. The high time cost associated with this process significantly hampers the transformation of exceptional traditional culture. Consequently, the challenge of distilling traditional cultural elements with cultural and artistic value and seamlessly integrating them into product design, streamlining the intricate transformation process, allowing ordinary individuals with basic training to participate in the transformation of cultural products, and thereby amplifying the dissemination of outstanding culture, remains a matter of great concern for both the design industry and the cultural community. Cement encaustic tiles were brought to Xiamen’s Gulangyu by overseas Chinese returning from Nanyang in the late 19th century. In contrast to traditional ceramic craftsmanship, these tiles possess a distinctive texture and a rich decorative language, contributing to a more diverse and artistic spatial design system [2]. Cement flower bricks are handcrafted works that combine decorative art and architectural functionality. Their development journey, from the complete dependence on foreign imports to the ability to self-produce and even export, and from the celebration of foreign exotic styles to the integration of our national artistic characteristics, holds significant value for studying China’s recent history of architectural decorations and artistic evolution [3].

2. Research Status

The shape grammar (SG) is a formal rewriting system designed for generating languages of shapes [4,5]. It encompasses a collection of productions, also known as shape rules, which operate on shapes drawn from a vocabulary of spatial elements and, optionally, non-spatial elements such as labels. Within the framework of a shape grammar, an initial shape serves as the starting point for the generative process. The language defined by a shape grammar comprises the set of shapes generated by the grammar, and these shapes do not contain any non-terminal symbols. It later found application in the domain of product brand identity and innovative design. SG is a design method rooted in shape computation. It allows products to generate new shapes based on specific rules while maintaining brand consistency. Furthermore, it is utilized to create fresh solutions for product styling [6]. Grammar formalisms for design exhibit a diverse array, necessitating distinct representations of the entities undergoing generation and different interpretative mechanisms for this creative process. Similarly, shape grammars manifest in various forms, albeit less extensively. In their early stages, shape grammars predominantly focused on labeled shapes, which involved a combination of line segments and labeled points [7]. Subsequent advancements incorporated plane segments, solids [8], and curves [9]. Stiny [10] proposes an additional dimension by introducing numeric weights as attributes, serving to denote line thicknesses or surface tones. Knight [11,12] delves into various qualitative aspects of design, such as color, considering them as shape attributes. Stiny [13] further proposes an enhancement to shape grammar by incorporating a description function to facilitate the construction of verbal descriptions for designs. In this context, a shape rule combines a specification of recognition and manipulation (search and replace). Expressed in the form a → b, where a specifies the pattern to be recognized, both a and b participate in the manipulation. The manipulation involves replacing the recognized a by b in the shape under investigation. Recognition is not solely based on a one-to-one mapping of spatial (or non-spatial) elements but relies on the existence of a part relationship supporting emergence, allowing the recognition of shapes that may not be anticipated [14]. Recognition necessarily applies under an allowable transformation, such as a similarity transformation, and the resulting manipulation must occur under the same transformation for both a and b. In other words, a rule a → b applies to a shape s under a transformation t if t(a) is a part of s (t(a) ≤ s), yielding the shape s − t(a) + t(b). The definition of an allowable transformation may vary [15]. Shape grammars commonly consider transformations of similarity, permitting translation, rotation, reflection, and uniform scaling.

According to Stiny’s definition, shape grammar can be expressed as a quadruple formula: SG = (S, L, R, I). In this equation, SG represents the set of shapes derived from S through operations such as scaling and rotation [16]. S represents a finite set of shapes, L represents a finite set of labels, R represents a finite set of inference rules, and I represents the initial shape [17]. There are eight ways in which shape grammars can evolve [18]. Here is a breakdown of these terms:

• Replacement involves replacing the existing product shape with other feature elements. For example, if S = {○, ◇, ☆} and TS = {○, ◇, □}, this represents a replacement.
• Addition and deletion refer to adding or removing part or all of the original shape, respectively. For instance, if S = {○, ◇, ☆}, S₁ = {○, △}, and T₁S = {○, ◇, ☆, △}, it represents an addition and deletion.
• Scaling entails enlarging or shrinking part or all of the initial shape.
• Mirroring involves flipping part or all of the curve of the initial shape along a certain axis.
• Copying refers to duplicating and moving the curve of the initial shape.
• Rotation entails changing the angle of the initial shape.

Formulas and examples of these operations can be found in

Table 1. Formulas and examples of shape grammar reasoning [19].

Title	Formulas	Examples or Additional Explanations
Substitute	$TS=S^{\prime }$	$S$= {○, ◇, ▯}$; TS$={○, ◇, ▷}
Incorporate and Remove	$T_{1}P=P\oplus P_1$ $T_{2}P=P\ominus P_1$	$P$ = {○, ◇, ▷}, $P_1$ = {○, ◇, ◊}, $T_{1}P$ = {○, ◇, ▷, ◊} $P$ = {○, ▷, ▯, ◊, ◇}, $P_1$ = {○, ▷, ▯}, $T_{2}P$ = {◊, ◇}
Resize	$T_{2}S=\lambda S\left[x y 1\right]\left(\begin{array}{ccc}{S}_x& 0& 0\\ 0& S_y& 0\\ 0& 0& 1\end{array}\right)$	When λ > 1, it represents an enlargement transformation. When 0 < λ < 1, it signifies a reduction transformation. When Sx equals Sy, it implies a uniform scaling. When Sx is not equal to Sy, it indicates a non-uniform scaling.
Reflect	$T_{2}S=\lambda S\left[x y 1\right]\left(\begin{array}{ccc}{S}_x& 0& 0\\ 0& S_y& 0\\ 0& 0& 1\end{array}\right)$	When λ < 0, if Sx = −1 and Sy = 1, it corresponds to an S reflection along the y-axis. If Sx = 1 and Sy = −1, it represents an S reflection along the x-axis. Other reflection transformations can be derived from these two fundamental reflection operations.
Replicate	$TS=\left(N+M\right)S=\left[x y 1\right]\left(\begin{array}{ccc}N+1& 0& 0\\ 0& N+1& 0\\ M_x& M_y& 1\end{array}\right)$	N represents the number of copy operations, and M represents the positional changes of the shape after the copy operation. N should be greater than or equal to 0 and belong to the set of integers (N ≥ 0, N∈Z). When N is equal to 0, it indicates that shape S has not been copied, and only the displacement in the x and y directions is represented by Mx and My, respectively.
Rotate	$R=\left(\begin{array}{ccc}co{s}_{\theta }& -si{n}_{\theta }& 0\\ si{n}_{\theta }& co{s}_{\theta }& 0\\ 0& 0& 1\end{array}\right)$	θ represents the angle by which shape S is rotated counterclockwise around the origin of the coordinate axis.
Adjust Cut	$R=\left(\begin{array}{ccc}1& H_x& 0\\ H_y& 1& 0\\ 0& 0& 1\end{array}\right)$	Hx represents the horizontal shear amount along the x-axis, and Hy represents the vertical shear amount along the y-axis.
Bézier Curve	$B\left(t\right)=P_0{\left(1-t\right)}^3+3P_{1}t{\left(1-t\right)}^2+3P_2{t}^2\left(1-t\right) +P_3{t}^3, t\in \left[\mathrm{0,1}\right]$	${P_0,P}_1, { P}_2, P_3$ are the four nodes defining a cubic Bézier curve. This curve begins at P0 and ends at P3. The position of any of these nodes can be adjusted, resulting in a change in the shape of the curve.

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3. Application Processes

The first step involves collecting studies, images, and historical information related to cement bricks through literature analysis and field research. It aims to compile data about their developmental history, processing techniques, pattern classifications, and cultural significance. The primary objective is to identify the most representative basic morphological elements, referred to as the initial shape (I). In the second step, the extracted basic morphological elements are entered into a database, and rules for morphological changes are established. The third step entails applying shape grammar to deduce basic patterns. In this study, the author develops a program based on the QT framework, which can rapidly generate numerous SVG patterns according to predefined rules upon importing basic element diagrams. The fourth step involves selecting the output patterns and incorporating them into appropriate carriers. In this study, the author utilizes the Grasshopper platform to develop a tool capable of quickly identifying PNG edges and converting them into vector lines, which are then integrated into basic compositions or structures. The detailed process is as shown in Figure 1.

3.1. Basic Element Extraction

3.1.1. Formation and Development

At the end of the 19th century, overseas Chinese began returning to their homeland, with many returning from the South Seas to Xiamen’s Gulangyu Island. A significant event occurred ten years later when Indonesian overseas Chinese, led by Chen Yansen, founded the Nanzhou Flower Brick Factory. This marked the inception of domestic cement bricks, and their legacy can still be observed today. Notable examples of flower brick applications during that era include Wanshilou in Xiamen, Gulangyu Island’s HaiTianTianCheng, and LuChu. Unfortunately, the outbreak of war brought an abrupt halt to the development of flower bricks [20]. In 1965, as Xiamen underwent the large-scale construction of new overseas Chinese villages, the Nanzhou Brick Factory made a return to Xiamen, fueled by the strong enthusiasm of overseas Chinese. However, this resurgence was short-lived, as the Cultural Revolution categorized the brick as a “bourgeois aesthetic interest”, forcing it to cease production. It was not until the influence of the Cultural Revolution began to wane that flower bricks gradually regained attention [21,22]. However, the intricate manual labor involved could not keep up with the pace of industrial production, and as a result, cement bricks essentially disappeared from people’s view in the 1990s [23].

Following the introduction of flower bricks to the southern Fujian region and their adaptation to the local environment, living conditions, market economy, and people’s preferences, a unique Xiamen flower brick art form emerged. Thanks to its distinctive regional characteristics, remarkable artistic style, and visually striking aesthetics, it became an integral artistic symbol in the architecture of Xiamen [24]. Once introduced to Guangdong, these bricks found wide application in restaurants and cafes, seamlessly integrating with the food culture of “Food in Guangzhou”, as seen in Figure 2.

3.1.2. Manufacturing Technology

Handmade cement tiles, also known as wax painting cement tiles, are characterized by their “no clay, no glaze, no kiln firing” production process. They are created under pressure, following the sequence of “first the surface and then the bottom.” The mold used for cement tiles consists of a shape mold and a pattern mold. The pattern mold is considered the soul of the cement tile, as it plays a pivotal role in determining the tile’s design. Traditionally, pattern molds are crafted by hand. When artisans design and create these pattern molds, they must calculate the intricacies of pattern movements, changes, seams, and the alignment of cement brick patterns with each other. This meticulous craftsmanship is critical to achieving the desired tile patterns and quality [25]. Refer to Figure 3 for a visual representation.

3.1.3. Pattern Characteristics and Classification

Flower bricks have their origins in Europe, but with the return of overseas Chinese to southern Fujian, their patterns gradually evolved and enriched. We categorized cement bricks based on their patterns into three main groups, geometric patterns, botanical patterns, and insect patterns, as shown in

Table 2. Tile pattern classification.

Sequences	Geometric Patterns	Floral Patterns	Insect Patterns
1
2
3
4
5

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• Geometric patterns: Geometric patterns are characterized by basic shapes such as triangles, squares, and rhombuses. These shapes are often repeated and rotated to create regular and visually appealing designs. Some patterns incorporate elements of convexity for added visual interest.
• Botanical patterns: Botanical patterns draw inspiration from realistic flowers and plants in their natural forms. These patterns may feature complete flowers as the central motif or use petals and leaves to create borders in combination with geometric elements.
• Insect patterns: Insect patterns are less commonly found in flower bricks. However, when they are used, they are often influenced by pixelated designs, resulting in abstract representations of insects such as butterflies or ladybirds [26].

A prominent feature of decorative cement brick patterns is the extensive use of geometric shapes, which are often arranged with symmetry and order. In more realistic patterns, there is typically a combination of four-sided, independently molded tiles, or a combination of three forms achieved through random splicing. These patterns can be further described as follows:

• Quadripartite continuous: This refers to a unit pattern that is repeated in four directions (top, bottom, left, and right) to create a cyclic arrangement. Adjacent tiles with this pattern can be assembled into a complete and identical pattern, regardless of the angle of rotation. This creates a sense of rigor, symmetry, uniform rhythm, and unity in the decorative pattern. It provides a neat, spacious, and bright effect in the space, reflecting the beauty of order in the decorative arts.
• Random splicing: random splicing involves uniting more than two patterns in a repetitive arrangement, creating an overall staggered and warm appearance with a folkloric charm.
• Independent molding: in the case of independent molding, a single flower tile presents a complete and self-contained pattern, eliminating the need for splicing to form the design [27].

3.1.4. Cultural Connotation

Cement tile patterns encompass a wide spectrum, ranging from abstract geometric designs like triangles, squares, circles, diagonals, and straight lines to intricate representations of plants, flowers, and foliage. These patterns evolve from simple to complex, from rustic to refined, and from realistic to abstract. They collectively form a distinctive pattern art characterized by their meticulous composition, the intrinsic art of the patterns, and their alignment with the cultural context of their time. Even today, they continue to exude their unique charm. Whether these patterns depict flowers, plants, animals, or geometric forms, they are typically presented in a two-dimensional plane space. Few incorporate a sense of volume to create a visual effect reminiscent of three-dimensional space. Instead, they rely on wireframes and color blocks as their primary artistic elements. Their characteristics include repetition, orderly arrangement, symmetry, balance, and rhythmic composition. The use of symbols in their design is rational and humanistic. Designers often reinterpret traditional symbols with new meanings and connect them to Western semiotics, preserving the essence of traditional culture. For instance, patterns featuring magnolia flowers or orchids symbolize “purity”, “justice”, and “high aspirations” in personal cultivation and life pursuits, reflecting a positive and proactive attitude towards new ideas and concepts. Other patterns like clouds, curves, and meter designs, characterized by simple lines and clear structures, imply a smooth and peaceful life. These patterns encapsulate people’s aspirations for a better future, achieving a harmonious fusion of form and conceptual content—a constant pursuit in national design [28].

Geometric patterns, whether composed of simple lines or utilizing color to create a sense of three-dimensionality, consistently convey a more concrete three-dimensional spatial effect. Floral patterns in cement tiles exude a sense of vitality, as if the flowers are in full bloom within the cement. While insect patterns are relatively rare, they possess a unique quality, radiating the beauty of vitality. To showcase these unique cultural elements of cement tiles, we used Photoshop to extract classic geometric and floral patterns in their outline, as illustrated in Figure 4.

3.1.5. Extraction of Color Elements

While there exists a wide variety of flower tile patterns, their color schemes tend to share a fundamental consistency. In the process of collecting numerous flower tile patterns (as seen in Figure 5), we imported these images into Photoshop (PS). By employing the eyedropper tool, we extracted the CMYK values of key locations within the images. The extraction results are presented in Figure 6. This approach provides valuable insights into the color palettes commonly used in flower tile patterns.

3.2. Basic Element Extraction

Qt is a versatile cross-platform C++ GUI application development framework that was initially developed by the Qt Company in 1991. It serves a dual purpose by enabling the development of both graphical user interface (GUI) applications and non-GUI programs, including console tools and servers. Qt is an object-oriented framework that leverages unique code generation extensions, such as the Meta Object Compiler (moc), in combination with various macros. This design makes Qt highly extensible and promotes genuine component-based programming [29].

In this paper, the transformation of base shapes is implemented based on the Qt framework. The implementation of shape grammar in this context utilizes GUI components provided by Qt. Two primary classes play a central role: QGraphicsSVGItem and QGraphicsScene.

• QGraphicsSVGItem: this class is responsible for reading, saving, and manipulating graphic elements in the Scalable Vector Graphics (SVG) format.
• QGraphicsScene: QGraphicsScene serves as the scene where the transformation process is visualized.

As an illustrative example, let us consider the logic for the rotation transformation, which is outlined below:

1.

E = initial tuple; Mr = rotation matrix; θ = current rotation angle; φ = angle of each rotation of the tuple.

2.

θ ← 0; Mr ← φ.

3.

$while \mathsf{\theta }<2\mathsf{\pi }$

4.

Update the current rotation angle, θ ← θ + φ.

5.

Add a new element with position Mr × E.

6.

=

This approach demonstrates how the Qt framework is applied to implement shape grammar in this paper.

In this process, the user inputs image elements in SVG format and defines the angle of separation between these elements. The elements are then systematically rotated around the origin, resulting in the creation of a complex image, as depicted in Figure 6. This rotation mechanism enables the generation of intricate and visually compelling compositions by manipulating the arrangement and orientation of the SVG elements.

By importing the base elements and their associated CMYK values, the application of shape grammar facilitates the swift and effortless generation of numerous patterns with variations. Presented below are some of the patterns that have been tested, as shown in Figure 7. These patterns represent the outcomes of applying shape grammar to the base elements, resulting in a diverse array of visually engaging designs.

Under this logic, users can freely choose a base pattern and then proceed to the next step by adjusting the rotation angle, quantity, and colors of the pattern to select their favorite one. These individual patterns are commonly used in household products such as flags, carpets, lampshades, and pillows.

3.3. Grasshopper Platform Plugin Development

Traditional shape grammar derivation is typically limited to two-dimensional plane patterns. Transforming these patterns into three-dimensional models and applying them to real products can be time-consuming. To streamline this process, we developed a plugin capable of quickly identifying image contours and converting them into editable vector curves. When basic shapes are imported, the plugin can efficiently apply these features to the surface of the shape, significantly reducing the product development time.

3.3.1. Introduction to Grasshopper

Grasshopper is a visual 3D design plugin closely associated with Rhino7 software. It is currently one of the most widely used parametric tools, particularly suitable for product modeling and design [30]. Grasshopper offers a rich library of plugins and powerful autonomous editing capabilities, making it popular in architectural skin design and pattern design. It incorporates fundamental graphic design rules such as translation, rotation, scaling, and mirroring and allows users to define their own constraints and parameters. This flexibility is conducive to the construction and processing of texture structure-derived models. Furthermore, Grasshopper can work with NURBS curves and surfaces, enabling the transformation of derived structures into usable product modeling elements.

3.3.2. Introduction to Grasshopper

There are two primary methods for translating traditional picture patterns into 3D modeling:

• Using Photoshop tools: pre-processing involves cropping the effective area from the original image.
• Computer graphics algorithms: This method includes grayscale processing, binarization, and edge detection, resulting in a black and white image suitable for generating 3D models. The processed image possesses characteristics such as clarity, singularity, and balance [31].

3.3.3. Pattern Edge Extraction

The data output from the author’s software is in the form of Image Objects, which are not suitable for operations within the Grasshopper platform. As a first step, they should be converted into bitmap format. Bitmaps store data as pixel points, making it easier to manipulate and perform pixel-level calculations. To enhance the accuracy of edge extraction, pre-processing steps are applied, including image smoothing and greyscaling. The edges of the image are detected using the Sobel algorithm [32]. Subsequently, a contour tracking algorithm is employed to connect the edges into continuous contour lines. Different strategies can be utilized in the contour tracking algorithm to track the contours based on pixel connections in the edge image.

3.3.4. Vectorization

The contour lines obtained from tracing are converted into vector graphic data, typically represented as a series of vector graphics described by points and curves. Once the contour extraction is complete, the contour lines and offsets are utilized to create a surface. The combination of these two types of data initially forms tree data, which must be converted into list data before surface creation. Subsequently, the surface is stretched to form a unified pattern [33].

3.3.5. Surface Flow

After establishing the basic surface modeling, the surface is subdivided into UV surfaces. Then, a single pattern is applied to the basic surface while controlling the pattern’s sparseness according to the UV surface division [34]. Additionally, controls for pattern sampling density and pattern thickness adjustment are provided to facilitate the selection of various modeling options. The detailed logic is illustrated in Figure 8. This process ensures that the pattern is accurately and efficiently applied to the surface while allowing for customization.

3.3.6. Surface Flow

The developed plug-in comprises seven inputs, including the base surface, the number of UV surfaces, the pattern thickness, the file path for image storage, the curve sampling degree, and rounded corners. The curve sampling degree offers more flexibility when working with complex images. A higher number of samples results in a closer similarity to the original pattern, while a smaller degree of similarity is achieved with fewer samples. This parameter can be adjusted based on the desired effect. Rounded corners involve pre-processing curves to make them more adaptable to product design [35]. Once the plug-in is developed, it can be exported and shared with other designers for installation and use, expediting their product development processes. The completed plug-in is showcased in Figure 9. The packaged plug-in is shown in Figure 10.

The overall software operation logic is shown in Figure 11.

4. Application Cases

Using basic graphic 1 as an example, a variety of combination patterns are generated through the software. Among these, combination pattern 2 is selected. Taking an ordinary plane as a reference, the following steps are performed in the plug-in:

• The path for storing the generated pattern is specified.
• The amount of curve samples is adjusted.
• The angle of the circle is set.
• The UV surface is divided according to the design requirements.

Once these adjustments are made, the design is imported into Keyshot for rendering, resulting in the visual representation shown in Figure 12. This process showcases how the software and plug-in enable the transformation of basic graphics into complex and visually appealing patterns for product design and visualization.

By applying the pattern to the curved shape of a basic lampshade, the texture is elegantly displayed when illuminated, creating a captivating interplay of light and shadow. This approach enhances the aesthetics and visual appeal of the lampshade, adding an artistic dimension to its design. Details can be found in Figure 13.

5. Conclusions

Through research on the origin, development, technology, and pattern classification of cement tiles, this study concludes that beyond its classical decorative style, blending Chinese and Western influences, cement tile patterns also serve as a record of historical changes in social life and the aesthetic values of different social classes. The patterns exhibit characteristics of consistency, continuity, and certainty, with the presence of a “sense of order” enabling their reproduction, combination, and evolution on a large scale. Using this as an example, this paper, based on shape grammar, compiles a software set utilizing tools such as PS, QT, and Grasshopper to accurately and swiftly extract fundamental elements of related cultures and transform them into culturally and creatively relevant products.

With this template, cultural and creative product designers can rapidly and precisely construct an extensive database of elements, offering consumers more choices. The developed plug-ins can be shared on relevant platforms, assisting product designers in avoiding the manual and inefficient modeling of intricate patterns. Instead, they can use the plug-ins to quickly transform 2D to 3D, adjusting sample curves to achieve desired effects. The synergy of this software with additive manufacturing significantly expedites product development. Its user-friendly interface empowers consumers to customize products based on their preferences, resulting in more appealing products and reduced development costs for manufacturers. Applying shape grammar to the Grasshopper platform makes this research more practical. The fusion of traditional culture and modern technology provides a novel approach to cultural heritage, enabling broader consumer participation in the transformation of cultural and creative products, thereby enhancing the breadth and depth of cultural dissemination.

However, this study has notable shortcomings. In the selection of curve samples, precise control over all lines has not been achieved; only passive selection is possible, lacking complete autonomous control. Moreover, this study provides a limited number of basic models, restricting choices [34]. Future research should focus on the C# language application in the Grasshopper platform, using code for a more accurate picture line recognition and further control adjustments [36]. Additionally, establishing a more extensive database of base models will offer consumers more choices. Integrating AI into the software’s recognition process to identify culturally distinctive base elements can simplify the workflow further.