Perceptual Quantitative Decision Making and Evaluation of Product Stylable Topology Design

Abstract

Modeling is the primary point to conveying product characteristics. Accurately capturing the image needs of users for modeling is an important way to effectively improve product design efficiency. Quantitative theory type I is a method to solve the internal law between the user’s target image and the product modeling characteristics by building a mathematical model. Aiming at the problems of abundant product modeling design elements, diversified combination methods, and high design cost due to the subjective ambiguity of user images, a topological design method of product modeling based on quantification theory I is proposed. This method uses the semantic difference method and statistical method to obtain the quantitative data of perceptual semantic features of product modeling to represent the explicit and implicit needs of users. Based on the topological transformation, the topological analysis and modeling of the two types of requirements are carried out. The mapping model of product modeling features and style images is constructed using quantitative theory type I, and the topologic value of each modeling design element is calculated. The above method can effectively solve the mapping problem between product modeling features and style images. On this basis, this research provides a decision-making basis for product modeling design. Using a wine jug as a product exemplar for this research, the scheme design and evaluation are carried out to verify the effectiveness and feasibility of the product modeling topological design method.

1. Introduction

Styling is an important part of product design which increases the added value of the product and attracts the attention of users/customers. With the increasing development of internal product technology, styling has become a key element in shaping the image of products because of the diversification of user needs for products. In the pre-design stage, accurately capturing the real needs of users, matching user aesthetics, and quickly matching user needs to deliver effective design solutions have become the focus of exploration in the field of product design [1]. Transforming users’ characteristics of product styling and perceptual needs into rational data quantification models is the direction that product styling designers and related users have been focusing on. This paper combines computer-aided design and topologic content to study and build a product styling design method system to provide a decision basis for later product styling design.

In recent years, with the rapid application of computer-aided design technology, innovative research on product modeling design has focused on modular concept design [2], imagery and modeling design [3], product modeling design system development, and product design solution evaluation, amongst other considerations [4]. At present, the innovative design of product imagery shapes has become a hot topic for research [5]. Many scholars focus on exploring the relationship between product modeling and imagery semantics to meet the perceptual needs of users for product modeling through various methods and means [6]. Bruno et al. [7] applied morphological analysis to extract the styling features of disposable razors and obtain the psychological feelings generated in users by different features. Man Ding et al. [8] summarized the design process of perceptual engineering in imagery acquisition, model establishment, and model optimization. Jian Wang et al. [9] constructed a product styling evolutionary design system and overall process using neural networks from the perspective of the user to improve design efficiency. Methods commonly used in the field of product design include quantitative theory type I, statistical analysis [10], and neural network algorithms [11], which establish a mathematical model between product shape and perceptual imagery and then quantitatively capture the mapping relationship between user needs and product shape. The quantitative theory type I applied to the field of product design has gradually been enriched through various studies, including eyeglass design, pure electric vehicle design, and mobility scooter design [12,13,14].

Topology is the study of various contradictory problems, and the basic theory of topology is used to represent the process of solving contradictory problems by establishing topologically tractable models that can deal with contradictory problems in a formal and quantifiable way, using primitives as logical cells [15]. Topology theory is applied to product concept design, topologic strategy generation systems, and technology prediction [15,16,17]. For example, DOU et al. [18] proposed a problem-oriented topologizable industrial design method and then guided students to complete the design of an outdoor umbrella system through a formal and modular approach. Zaihao Li et al. [19] combined inverse design with topologizability theory to improve the topologizable idea generation method and obtain multiple effective design solutions for a fully automatic binding machine. Zhen Qin et al. [20] proposed a topologizable semantic product design method through semantic extraction, quantitative analysis, graphical parsing, and superiority evaluation to ensure the accuracy of ethnic pattern product design. GU et al. [21] studied and analyzed the color and performance of the human–machine interface in nuclear power plants based on the material element theory in topologizability.

This research represents a significant contribution to the field of product design. Combining topologically related theories to study contradictory problems that arise in the design process can provide a more comprehensive description of certain properties, the number of features, the range and the degree of things, and can then provide solutions to contradictory problems in design through formal transformations and algorithms. At present, there are few studies based on the combination of topologic theory and computer-aided imagery quantification for product modeling design. The following deficiencies still exist at the product modeling level:

(1)

Product modeling design elements are diverse, and their arrangement and combination are particularly rich, which means there is high diversity which can make it difficult to prioritize the problem. The product conveys different psychological feelings to users through external modeling features, and different modeling feature categories will also have certain differential impacts on users, which requires further in-depth research. In addition, specific design parts of the product are not designed for topologically transformable design nor for research based on quantitative analysis.

(2)

Users’ needs for products are perceptual, subjective, and ambiguous. Due to these problems, it takes a lot of time to comprehensively and accurately obtain information about the needs of users and transform these needs into product design requirements during the product design process. Additionally, personal subjectivity usually plays a dominant role in the design process. In product design development, the description of the perceptual needs of users is used to guide the subsequent design, which leads to higher costs and lower efficiency of the product design.

Therefore, this paper proposes a topology design method based on the combination of topologizable primitive transformation and quantitative theory type I for product modeling. Firstly, by screening representative samples and deconstructing their modeling features, we qualitatively study users’ imagery acquisition and obtain users’ explicit and implicit needs; secondly, we analyze two types of user needs in terms of topologizability through the theory of topologizable primitives. We establish a library of product modeling topologizable design elements and construct a mapping model between them by combining quantitative theory I quantification. We then analyze the topologizable feature values of specific design elements and construct a product modeling design method system based on the target perceptual imagery of the user. Finally, the feasibility and effectiveness of the method are verified through design examples.

2. The Research Method and Process of Product Modeling Topologizable Design

In the field of product design, an accurate and rapid grasp of the real needs of users is an important prerequisite to ensuring the quality and efficiency of product design [22]. The product design process has a large number of modeling elements, and there are complexities and contradictions in the way in which elements are combined [23], connected, and interrelated. User-centered design is the principal method of modern product development [24], emphasizing the real needs and goals of users in the product design stage and designing from the needs and feelings of users. The feelings described by users are often very subjective and vague [25], and there is a possibility of contradiction between the needs of users and the design elements of the product shape, all of which are issues that need to be considered in product design. Based on these characteristics, topology-related theories can be used to provide alternative ideas to overcome the contradiction between users’ explicit and implicit needs in the design system. Therefore, this paper uses a topological model to represent the process of contradiction and adopts a category of quantitative theory to quantitatively analyze the mapping relationship between modeling and imagery. The research content is mainly divided into four parts. The title of each part is shown in the gray background box, and each part contains more detailed content and processes. The dashed line points out the name of the method used between the two steps. The four steps detailed in the methodological part of this paper to build the framework structure are used to conduct the investigation. Based on our findings, subsequent research work can be facilitated, as shown in Figure 1.

3. Research on Product Modeling Design Based on Topology Theory and Quantitative Theory Type I

3.1. Deconstruction of Modeling Features and Acquisition of Target Imagery

The deconstruction of modeling features allows for the analysis of the morphology of the research product, through which the morphological elements and categories of product modeling can be obtained, resulting in a large number of design elements. The user’s target imagery represents his or her psychological and emotional design needs for the product, which will have an important impact on the later product design process. The combination design of modeling features based on a specific user’s target needs can improve the design. The efficiency of the design can also be improved. For product design, first of all, we must research and analyze the user’s needs, target product information, and extract the product modeling features and style imagery to characterize the user’s explicit and implicit needs [26]. After the product is selected for study, a large number of target product samples are collected, and multidimensional scale analysis and cluster analysis are applied to select representative samples. The appearance of the product modeling features is mainly composed of three elements: point, line, and surface, which constitute different modeling units of the product. In the process of decomposition of the product styling design elements, this paper adopts the morphological analysis method proposed by Zwicky [27] to deconstruct the styling of the research samples, to extract the important morphological elements of the product according to the explicit needs of users, to express the product features with morphological feature lines or feature position relationships, and to encode them, allowing for the subsequent evaluation of product design elements.

Implicit demand corresponds to the style characteristics of the product, which is based on the subjective cognition of users regarding the product and usually uses different imagery style feature vocabularies to characterize their psychological feelings. To ensure the accuracy of user needs, this paper uses the semantic difference method to obtain a large number of perceptual vocabulary data and then uses factor analysis to obtain target perceptual imagery through dimensionality reduction analysis. For different research products, more than a dozen groups of perceptual words are usually obtained after research screening, and finally, three to five groups of words are identified and then paired with their opposite semantic adjectives for the target perceptual imagery.

3.2. Product Shape Can Be Topological Design Elements Library

The product modeling expandable design elements library provides a large number of design elements for product design which can be organized and built to facilitate the selection of design elements for later product solutions. The product shape topologizable design elements library consists of a library of shape design elements and a set of style characteristics elements, which provides a method for later design improvement, as shown in Figure 2. By deconstructing the design elements for coding in the previous step, the product modeling elements are decomposed, added, deleted, copied, expanded, and replaced according to the topologically transformable tool. The deconstructed parts are transformed into specific modeling elements, and the topologically transformable mode is represented by T. The specific transformation mode is shown as follows.

(1)

Decompose the transform: ${\rm T}\Pi =\left\{{\Pi }_1,{\Pi }_2,\cdots ,{\Pi }_n\right\}$, where ${\Pi }_1\oplus {\Pi }_2\oplus \cdots \oplus {\Pi }_n=\Pi$.

(2)

Add and delete transformations: add transformation, ${{\rm T}}_1\Pi =\Pi \oplus {\Pi }_1$; delete transformation, ${{\rm T}}_2\Pi =\Pi$ ㊀ ${\Pi }_1$.

(3)

Copy transformation: ${\rm T}{\Pi }^{\prime }=\left\{\Pi ,{\Pi }^{\prime }\right\}$.

(4)

Expansion and contraction transformations: ${\rm T}\Pi =\lambda \Pi$, when $\lambda >1$ is an expansion transformation and when $0<\lambda <1$ is a contraction transformation.

(5)

Permutation transformations: ${\rm T}\Pi ={\Pi }^{\prime }$.

In topologism, the primitive theory uses the ordered triad (object, feature, quantity value) as the basic unit [28], which is combined with qualitative and quantitative approaches to comprehensively describe the change process of objective things, expressed as O = (N, C, V), where N denotes the topologizable object, C denotes the topologizable feature, and V denotes the topologizable quantity value of N about C. Through the use of topological transformation analysis of user demand information to obtain the product styling design elements library and the style features elements set, combined with the quantitative theory type I quantitative analysis of the mapping relationship between the two, it is possible to calculate the specific product styling design elements in different product style features of the topological amount of value in order to establish the product styling topological design elements library. The larger the topologizable value is, the more important the design element is in the design process.

3.3. Analysis of the Correlation between Product Design Elements and Perceptual Imagery

In order to understand the relationship between the elements of product styling features and the perceptual imagery of products of users more clearly, a quantitative class of theories and statistical methods are used to quantitatively analyze the correlation between them, to establish the mapping relationship between product styling design elements and style features, to realize the prediction of the dependent variable, and to finally provide an effective basis for guiding product styling design research.

Using quantitative theory type I to establish a mapping prediction model between styling design elements and perceptual imagery, the correlation between the two can be effectively analyzed. The flow chart of the mapping correlation model is shown in Figure 3, and the main steps of the construction are as follows:

Step 1: Obtain a library of stylistic feature elements and a set of stylistic feature elements of the studied product through design research.

Step 2: Establish a mathematical model using quantitative theory type I and use SPSS software to determine the contribution and degree of influence between each design element and the perceptual imagery of the product.

Step 3: Verify the accuracy of the model, and finally, according to the results, analyze and extract the design elements of styling features that have the greatest influence on certain imagery, predict the new products designed with the extracted features according to the user’s perceptual imagery, and then verify the accuracy of the model prediction through a sample t-test.

Based on a quantitative theory type I [29], the mapping correlation model is as follows: the product design element is the independent variable $X$, the semantic evaluation value of the target imagery is the dependent variable $Y$, there are $r$ design elements, the number of categories of the $j$ design element is represented by $a_j$, $j$ is the item, and $k$ is the category. ${\delta }_i\left(j,k\right)$$\left(j=1,2,\cdots ,r;k=1,2,\cdots a_j\right)$ is the response of the $k$ category in the $j$ design element in the $i$ sample. The mapping relationship between the product design element and the target imagery is then

$${\delta }_i\left(j,k\right)=\{\begin{array}{l}1,\mathrm{When} \mathrm{the} \mathrm{qualitative} \mathrm{data} \mathrm{of} \mathrm{the} j \mathrm{item} \mathrm{in} \mathrm{the} i \mathrm{sample} \mathrm{is} \mathrm{the} k \mathrm{category};\\ 0,\mathrm{Other}\end{array},$$

and ${\delta }_i\left(j,k\right)$ must satisfy

$${\displaystyle \sum _{k=1}^{a_j}{\delta }_i\left(j,k\right)}=1.$$

(1)

Assuming that $X$ is the response matrix and is of order $m\times p$, then

$$X={\left\{{\delta }_i\left(j,k\right)\right\}}_{m\times p}.$$

(2)

Among them, $i=1,2,\cdots ,m;j=1,2,\cdots ,r;k=1,2,\cdots ,a_j$.

Assuming a multivariate linear correlation between the dependent variable $y_i$ and the independent variable $x$, a functional relationship can be established.

$${{\displaystyle y}}_i={\displaystyle \sum _{j=1}^r{\displaystyle \sum _{k=1}^{a_j}{\delta }_i\left(j,k\right)b_{jk}}}+{\epsilon }_i,$$

(3)

$$\left(i=1,2,\cdots ,m\right),$$

where $b_{jk}$ is the coefficient score of the $k$ category of the $j$ item and ${\epsilon }_i$ is the random error of the $i$ sampling.

This paper requires normalization of $b_{jk}$, at which point the prediction equation is constructed as follows.

$$\{\begin{array}{l}{y}_i=\overline{y}+{\displaystyle \sum _{j=1}^r{\displaystyle \sum _{k=1}^{a_j}{\delta }_i\left(j,k\right){\widehat{b}}_{jk}+{\epsilon }_i}}\\ \overline{y}=\frac{1}{m}{\displaystyle \sum _{i=1}^m{y}_i}\end{array},$$

(4)

where $\overline{y}$ is the mean value of the evaluation of the imagery vocabulary for all samples and ${\widehat{b}}_{jk}$ is the relative weight value of each variable. The influence of each stylistic feature class on perceptual imagery can be seen from the relative weight values.

The complex correlation coefficient $R$ is a parameter to test the accuracy of the model, which is generally calculated according to Equation (5).

$$R=\frac{{\sigma }_{\widehat{y}y}}{{\sigma }_{\widehat{y}}{\sigma }_y}=\frac{{\sigma }_{\widehat{y}}}{{\sigma }_y}=\sqrt{\frac{{\displaystyle \sum _{i=1}^m{\left(\widehat{y}i-\overline{y}\right)}^2}}{{\displaystyle \sum _{i=1}^m{\left(yi-\overline{y}\right)}^2}}}.$$

(5)

The decision coefficient $R^2$ is the square of the negative correlation coefficient, which can also be used to describe the model’s accuracy. In addition, in practical applications, the magnitude of the predictive contribution of each item to the product target imagery can also be expressed in terms of the score range $r_e$, with the larger the range, the greater the contribution, as expressed by Equation (6).

$$r_e\left(j\right)=\underset{1\le k\le a_j}{max{\widehat{b}}_{jk}}-\underset{1\le k\le a_j}{min{\widehat{b}}_{jk}},$$

(6)

$$\left(j=1,2,\cdots r\right).$$

In this paper, we used SPSS25.0 software for data analysis, inputted the experimental data into SPSS, and then solved the model with the response matrix of design elements as the independent variable and the mean value of the semantic evaluation of sample imagery as the dependent variable. We obtained the constant terms and correlation coefficients of the regression Equations of the target imagery factors after excluding the invalid variables and established the respective linear regression equations.

3.4. Design Solution Evaluation and Validation

Product design is a process of continuous expansion and optimization. Product design based on a combination of topology theory and computer-aided imagery quantification enables the rapid and accurate generation of product design solutions based on user needs.

In order to verify the effectiveness of the proposed method and to verify whether the new product design solution meets the users’ imagery needs, designers and users are invited to conduct an experimental comparison of the semantic difference evaluation between the design solution and the existing products in the market. To ensure the scientific nature of the comparison of the prediction, the imagery vocabulary research is kept consistent with the previous paper, the mean value evaluation value is collated, and the paired-sample t-test method is used to verify whether there is a significant difference [30]. If this prediction model is proved to be valid, this proves that the product modeling topologizable design method proposed, based on this paper, has rationality and validity. According to this method, the explicit expression and the implicit demand of users can be realized by identifying the best modeling design elements for the target demand of users, which provides decision-making support and help for designers to meet the real demand of users more quickly and accurately in product design.

4. Example Applications

4.1. Extraction and Characterization of User Requirements

4.1.1. Selection of Target Products and Deconstruction of Modeling Features

As a representative experimental sample for studying the characteristics of Tang dynasty gold and silverware drinking vessels with beautiful shapes and exquisite workmanship, the frontal view is, for such products, the viewpoint with the most abundant design elements and imagery information [31]. Therefore, this paper selects a wine jug (frontal view) for morphological research. After eliminating images with unclear styling features and high similarity, 30 wine containers were obtained as the initial experimental samples through web data crawling and literature research. In order to avoid the influence of the color and texture of the wine containers on the experimental results, the samples were processed in grayscale to ensure the accuracy of the experimental data.

Firstly, 41 subjects (30 graduate students with design backgrounds, 6 teachers working on antique artifacts, and 5 practitioners related to the wine ware industry) were invited to subjectively classify the 30 initial experimental samples with no restriction on the number of classification groups and the number of groups within groups. The experiment was conducted in the form of a questionnaire, and all test subjects participating in this study provided informed consent prior to the experiment. Secondly, based on the literature [32], the statistical transformation of the classification data was performed using multidimensional scale analysis. ALSCAL analysis was selected in the SPSS.25 software with the number of dimensions selected (two to six) to observe the fit of the indicator Stress coefficient to the RSQ model, and ultimately this model had a Stress value of <0.050 and an RSQ > 0.8 in five dimensions. This indicated that the model fit was reasonable at this point, and the five-dimensional space was obtained. The specific coordinate values of the 30 samples were then obtained. The distance between each sample and the center of this category was calculated by cluster analysis to screen the representative samples used in subsequent experiments. The results are shown in

Table 1. Cluster members and distance values.

Case Number	Clustering	Distance	Case number	Clustering	Distance
T1	6	1.011	T16	6	1.73
T2	1	1.307	T17	1	0.483
T3	3	1.008	T18	5	0.875
T4	3	1.026	T19	4	0.681
T5	5	0.423	T20	1	0.713
T6	6	0.786	T21	2	0.934
T7	6	0.829	T22	4	0.783
T8	1	1.111	T23	6	0.458
T9	1	1.383	T24	6	0.759
T10	1	1.045	T25	6	0.981
T11	2	0.578	T26	3	1.525
T12	6	0.841	T27	5	0.591
T13	2	0.546	T28	6	0.521
T14	6	0.426	T29	5	0.363
T15	4	0.818	T30	6	0.939

. Six samples were finally obtained: T3, T13, T14, T17, T19, and T29.

The shape of the product contains different elements, and the different combinations of these elements can affect the overall shape of the product. Based on the morphological analysis method mentioned in the previous section, after studying the literature relating to the modeling of vessels and discussing this with professional designers, four main design elements of the frontal morphological features of the wine jug product were identified: (a) body, (b) spout, (c) handle, and (d) lid, with a total of 12 modeling feature categories.

Since the number of classes in the design elements of the wine jug shape was greater than the number of representative samples in order to avoid overfitting and multicollinearity in the quantitative one-class analysis, a total of 6 samples were sampled again from each group of sample clustering centers, for a total of 12 experimental product samples, as shown in Figure 4.

4.1.2. Acquisition of Target Perceptual Imagery

Before constructing a library of product stylistic toposable design elements, it was also necessary to obtain the implicit needs of users. These needs are influenced by multidimensional factors, including social background, ideology, and culture and all of these need to be analyzed comprehensively in conjunction with their cultural and historical background and their level of emotional cognition [33]. To this end, design graduate students, expert designers, and salespeople were invited to form a focus group to extract the vocabulary of stylistic features regarding wine tools from relevant writings and literature. Twelve groups of adjective pairs were identified as preliminary results for the evaluation test of the wine tool product design. The semantic difference method proposed by Osgood was used to evaluate the semantic meaning of the drinkware imagery of 14 target drinkware users [34]. A five-point semantic scale was used, with values ranging from [−2, −1, 0, 1, 2] with −2 and 2 indicating the two ends of the semantic dimension range, −1 and 1 indicating the side closer to the semantic meaning of the two ends, and 0 indicating neutrality. The semantic quantification of “modern” to “traditional” was, for example, “very modern-more modern-moderate-more traditional-very traditional”, as shown in Figure 5.

The testers selected the corresponding scores to rate the samples within the range of values taken, and this evaluation value indicated the degree of this sample in different imagery semantic intervals. Then, the data obtained from the test were collated and calculated. The mean value of each semantic dimension rating value of one sample by all test subjects was taken as the quantified value under that imagery [35]. The final evaluated values of the given perceptual imagery are shown in

Table 2. Semantic evaluation mean values.

Representative Samples	Imagery Vocabulary
	S1	S2	S3	S4	…	S12
T3	1.4286	−0.3571	−0.7143	−0.2857	…	−0.6429
T4	0.5714	−0.1429	−0.4286	0.4286	…	−0.5714
T5	0.2143	−0.0714	0.3571	−0.2857	…	−0.1429
T11	1.5000	0.0000	−1.0714	0.3571	…	−0.2857
T13	1.0000	0.0000	−0.3571	−0.0714	…	−0.2143
T14	0.6429	−0.1429	−0.0714	−0.5000	…	−0.2857
…	…	…	…	…	…	…
T29	0.9286	0.5714	0.6429	−1.0714	…	−0.4286

.

After collating the results, factor analysis was applied using SPSS software for the integration analysis of imagery semantics to determine the target perceptual imagery. By interpreting the total variance (

Table 3. Explaining the total variance.

Ingredients	Extraction of the Sum of Squares of Loads
	Total	Variance/%	Cumulative/%
1	4.748	39.57	39.57
2	3.561	29.673	69.243
3	1.647	13.725	82.968

) and the gravel plot (Figure 6), it can be seen that it was acceptable to extract three principal components and finally filter out three types of common imagery factors. The first type of factor can be defined as the modeling factor, containing the phrases S5 light–bulky, S6 fashionable–classical, S8 heavy–dynamic, and S10 dynamic–stable. The second type of factor can be defined as the temperament factor, including the phrases S3 elegant–vulgar, S9 elegant–mediocre, and S11 rigid–soft. The third type of factor can be defined as the personality factor, including the phrases S4 flamboyant–introverted, S12 flamboyant–soft, and S12 gorgeous–simple. Since there are multiple imagery words within each type of factor, it is necessary to further summarize and refine the factors that can represent all the imagery to finally obtain the implicit demand of users regarding the product style and characteristics and generate the set of elements of the wing jug style characteristics. This was performed as follows: $\mathrm{S}=\mathrm{S}[\mathrm{S}3,\mathrm{S}4,\mathrm{S}10]$ described data quantitatively according to the primitive theoretical model triad O = (N, C, V).

$$\mathsf{O}=\left[\begin{array}{ccc}\mathrm{wine} \mathrm{jug}N& \mathrm{elegant} - \mathrm{vulgar}C& V_1\\ & \mathrm{flamboyant} - \mathrm{introverted}& V_2\\ & \mathrm{dynamic} - \mathrm{stable}& V_3\end{array}\right],$$

(7)

where N is the toppable object, i.e., the wine jug, C is the toppable style feature of the wine jug, and V is the toppable quantity value of the style feature.

4.2. Wine Jug Shape Can Be Topological Design Elements Library

At present, the design features of products are usually extracted by morphological analysis, and two-dimensional morphological feature lines are used to express the design elements. Therefore, in this paper, the two-dimensional line shapes of the wine jug components were extracted after grayscale processing and were transformed into styling design elements after topological transformation. With the help of the above-mentioned topologizable primitive transformation to realize the 2D line expression of specific stylistic design elements of wine jug components, the specific process was as follows, taking wine jug N as an example.

(1)

Decomposition transformation

First, following the decomposition transformation of jug N, i.e., TO (decomposition transformation, jug, PT), Equation (6) was obtained.

$$T\mathrm{O}=\left[\begin{array}{ccc}\mathrm{decomposition} \mathrm{transformation}& \mathrm{wine} \mathrm{jug}& P_{TA}\\ & & P_{TB}\\ & & P_{TC}\\ & & P_{TD}\end{array}\right],$$

(8)

where P_T is the set of jug parts. $P_T=\left[P_{TA},P_{TB},P_{TC},P_{TD}\right]$ and the design elements that are representative of the pot shape features were selected and expressed as $P_{TA}=\left[P_{TA1},P_{TA2},P_{TA3}\right]$.

(2)

Addition and deletion transformation

The spout PTB part of the wine jug is mostly decorated with patterns, but it has a small impact on the frontal form of the product. Modern wine ware products are mostly without complex animal forms, so this part was deleted and transformed, i.e., T2O (deleted transformation, case leg, PTB), as shown in

Table 4. Part spout deletion transformation.

Parts	Component Elements	Topologically Transformable	Design Elements
Spout		Delete transformation

.

According to the steps described in Table 4, the filtered pot handles were censored and transformed to obtain the design elements of the spout shape features, denoted as $P_{TB}=\left[P_{TB1},P_{TB2},P_{TB3}\right]$.

The handle PTC part of the wine jug is mostly decorated with animal forms, and modern products are mostly simple and atmospheric in style, so the transformation of this part was deleted, i.e., T3O (deleted transformation, case leg, PTC), as shown in

Table 5. Part handle deletion transformation.

Parts	Component Elements	Topologically Transformable	Design Elements
Pot handle		Delete transformation

.

According to the steps described in Table 5, the filtered handles were censored and transformed to obtain the design elements for the handle shape features,$P_{TC}=\left[P_{TC1},P_{TC2}\right]$.

When the part of the lid PTD in the wine jug is a shaped form such as an animal or plant, it can be abstracted, and its godlike form can be retained, so this part was deleted and transformed, i.e., T4O (deleted transformation, lid, PTD), as shown in

Table 6. Part lid deletion transformation.

Parts	Component Elements	Topologically Transformable	Design Elements
Lid		Delete transformation

.

According to the steps described in Table 6, all the parts related to the lid of the filtered pots were added and deleted and transformed to obtain the set of design elements for the lid shape features $P_{TD}=\left[P_{TD1},P_{TD2},P_{TD3},P_{TD4}\right]$.

In summary, the obtained modeling design elements were coded to construct a library of design elements for the wine jug modeling features, as shown in

Table 7. Design element library of wine jug shape features.

Scheme	Modeling Features Category
A pot body	A1 curved shape	A2 curved and straight combined shape	A3 gourd shape
B spout	B1 teapot shape	B2 curved arc	B3 monolithic
C handle	C1 curved shape	C2 curved and straight combined shape
D pot lid	D1 curved shape	D2 curved and straight combined shape	D3 alien	D4 none
				x

.

4.3. Establishment and Solution of the Quantitative Theory Type I Mapping Model

In this paper, the topological design transformation of primitives in topology theory was used to unify the wine jug product modeling features, style features, and their topological quantification values in a single system for consideration. The correlation analysis between the modeling design parameters and imagery semantics was combined with quantification theory to provide design decisions for subsequent product solutions.

4.3.1. Solving the Model

As per Table 7, the qualitative design elements of the design samples were quantified by Equations (1) and (2) and transformed into quantitative data expressed as 1 and 0 to construct a response matrix of design elements that can be identified by quantitative theory type I [36], as shown in

Table 8. Response matrix of design elements for quantitative class I theory.

	A1	A2	A3	B1	B2	B3	C1	C2	D1	D2	D3	D4
T3	1	0	0	1	0	0	1	0	1	0	0	0
T4	0	1	0	0	1	0	1	0	0	0	0	1
T5	0	0	1	1	0	0	1	0	0	1	0	0
T11	1	0	0	0	0	1	1	0	0	1	0	0
T13	1	0	0	0	0	1	1	0	1	0	0	0
T14	1	0	0	1	0	0	0	1	1	0	0	0
T17	1	0	0	1	0	0	1	0	0	1	0	0
T19	0	1	0	0	1	0	0	1	1	0	0	0
T20	0	1	0	1	0	0	0	1	0	0	1	0
T22	0	1	0	0	1	0	1	0	0	1	0	0
T23	1	0	0	1	0	0	0	1	0	1	0	0
T29	0	0	1	1	0	0	1	0	0	1	0	0

. The mathematical model was solved using SPSS software, and multiple linear regression analysis was calculated using Equations (3)–(6). The response matrix of the design elements was the independent variable, and the semantic mean value of the imagery of the drinkware samples was the dependent variable in order to obtain the values of the class score, constant term, complex correlation coefficient R, decisive coefficient R², and score range to be able to obtain the prediction equation of each imagery factor mapping model. The weight of styling elements that influenced product style features and the contribution of specific styling design categories were obtained according to the category scores of each variable: the larger the coefficient, the greater the influence of the stylistic element on the target imagery. The value of the variable coefficient determined the importance of the design element on perceptual imagery. Positive values represent a positive correlation between the feature element and the corresponding vocabulary, while negative values represent a negative correlation.

Based on the analysis results, a multiple linear regression prediction model was constructed to calculate the topizable values of product styling design elements under certain style features by substituting weights and contribution indexes, extracting the feature elements with the maximum topizable values, and then carrying out the program design verification.

The results of the analysis of S3 “elegance-vulgarity”, taking the temperament factor as an example, are shown in

Table 9. Results of the analysis of the temperament factor “elegance-vulgarity”.

Styling Design Elements	Styling Features Category	Score Scope Vx	Category Score Vy
A pot body	A1	0.055	-
	A2		-
	A3		0.055
B spout	B1	0.455	-
	B2		−0.036
	B3		0.419
C handle	C1	1.195	-
	C2		1.195
D pot lid	D1	1.945	−0.370
	D2		-
	D3		−1.925
	D4		0.020
Constants			−0.341
R			0.976
R2			0.954

.

4.3.2. Analysis of Results

The coefficient of the complex correlation of $R$ is 0.976, and the coefficient of determination of $R^2$ is 0.954, which shows that this mapping prediction model has good accuracy and can be used to predict the imagery of wine bottles. In the table, $V_x$ is the range of scores which can be used to evaluate the contribution of each design element to the style characteristics. $V_x$ indicates that the contribution of the element to the style characteristics of the wing jug is greater, and $V_y$ is the category score of the design element under the corresponding style, which can reflect the degree and direction of the influence of each design element category on different imagery styles.

Based on the prediction model established in Equation (4), the perceptual imagery evaluation value of the design scheme can be calculated from the model, and the prediction model of “elegance-vulgarity” is

$$\mathrm{y}=-0.341+0.055A_3-0.036B_2+0.419B_3+1.195C_2-0.370D_1-1.925D_3+0.020D_4.$$

The above table also shows that lid D has the highest score range of 1.945, which has the greatest influence on the elegance of the decanter design, and the D3 feature category is more inclined toward the elegant style. Body A has the lowest score range of 0.055 and has the least influence on the elegance of the design.

For the personality factor representing the imagery S4 “flamboyant-introverted”, the method is the same as above, and the final prediction model is

$$\mathrm{y}=0.43-0.502A_3+0.054B_2+0.563B_3-0.052C_2-1.058D_1-0.021D_3-0.555D_4.$$

For the modeling factor representing the imagery of S10 “dynamic-steady”, the solution method is the same as the above steps, and the final prediction model is

$$\mathrm{y}=0.765-1.158A_3-0.054B_2-0.323B_3-0.11C_2-0.097D_1-0.368D_3-0.568D_4.$$

Based on the above results, design decisions can be made for the subsequent styling of the decanter. To better guide the subsequent styling design of the wine jug as a whole, a topologizable analysis of each styling design element is also required. The topologic value of $V$, i.e., $V=\left(V_x,V_y\right)$, is calculated on the basis of the known scores of the product design elements V and the corresponding scores of each styling feature category by expressing the base elements of the wine jug as Equation (9).

$$O=\left[\begin{array}{ccc}\mathrm{wine} \mathrm{jug}& \mathrm{pot} \mathrm{body} A& V_1\\ & \mathrm{spout} B& V_2\\ & \mathrm{handle} C& V_3\\ & \mathrm{pot} \mathrm{lid} D& V_4\end{array}\right].$$

(9)

According to $V=V_x{V}_y$, the toppable values of each stylistic design element of the wine jug under different imagery can be calculated. Taking the lid element D1 as an example, the toppable values under different imagery style features are shown in

Table 10. Topologizable values of D1 categories under different imagery style features.

V Value	Elegant-Kitsch	Openness-Integrity	Sporty-Steady
Vx	1.945	1.037	0.471
Vy	−0.370	−1.058	−0.097
V	−0.720	−1.097	−0.046

.

i.e.,

$$\mathrm{pot} \mathrm{lid}=\left[\begin{array}{ccc}{D}_1& \mathrm{elegant} - \mathrm{vulgar}& -0.720\\ & \mathrm{flamboyant} - \mathrm{introverted}& -1.097\\ & \mathrm{dynamic} - \mathrm{stable}& -0.046\end{array}\right].$$

(10)

The remaining modeling design elements can be calculated sequentially according to the above method, and the obtained topologizable values are used to assist the later product scheme design, combined with the previously established library of topologizable design elements for the predicted modeling features, which provide a reference for the subsequent product modeling design element combinations.

4.4. Design Solution and Verification

According to the above prediction analysis results, to achieve the product modeling design to meet the user’s explicit and implicit needs, we then selected the combination of features from the established library of modeling design elements for the design and practice of the program and designed the corresponding product modeling design combination program according to the user’s target imagery style characteristics.

4.4.1. New Wine Decanter Design Scheme

According to the mapping prediction model, the best combination of modeling features for this imagery value is D3 and B2. The C handle contributes to a vulgar design, so we tried to avoid using the C2 style. Based on this, we used a combination of functional, man–machine, aesthetic, and other aspects of the product attribute, as far as possible, to fit the predicted key styling design features. After continuous adjustment and refinement, the final design solution Rhino model effect was agreed upon and is shown in Figure 7a. The rendering effect is shown in Figure 7b.

4.4.2. Design Verification

In order to verify whether the design scheme accurately reflects the expression of the modeling characteristics of elegant imagery according to the temperament factor, the above design scheme was taken as sample 1, and the wine jug with a higher market ranking was selected as the comparison sample 2. The semantic difference method evaluation experiment was conducted for sample 1 and sample 2, respectively, and the imagery vocabulary questionnaire was kept consistent with that of the previous article. Several design professionals were invited to evaluate them, and the data were collated to obtain the imagery of the sample. The evaluated mean values were imported into SPSS, and the data were tested using the paired-samples t-test. The results are shown in

Table 11. Means and p-value test of sample imagery evaluation.

Imagery Vocabulary	Sample
	1	2
S1 Modern–Traditional	0.45	0.64
S2 Coordination–Imbalance	−0.39	−0.71
S3 Elegant–Kitsch	−1.07	−1.18
S5 Flamboyant–Introverted	0.26	0.79
S6 Light–Bulky	−0.53	−0.29
S8 Fashionable–Classical	0.16	0.5
S9 Atmosphere–Compact	0.89	0.43
S10 Thick–Spiritual	−0.23	0.21
S16 Elegance–Mediocrity	−0.69	−0.21
S17 Dynamic–Stable	−0.47	−0.14
S19 Rigid–Soft	0.03	0.5
S20 Gorgeous–Plain	−0.68	−0.29
T-value	Degree of freedom	p-value
2.209	11	0.049

.

From the test results, p = 0.049 < 0.05, which shows that the mean values of the paired samples are significantly different. It can therefore be seen from the data comparison that the perceptual evaluation scores of sample 1 are significantly better than those of sample 2 for the 11 perceptual imagery adjectives, except for the S9 “atmospheric-small” adjective. This proves that the prediction model based on certain imagery is reasonable and effective.

4.4.3. Research on the Application in Different Products

This paper presents a study combining topological transformation and computer-aided design tools to create a new design solution for the contradictory problems in the process of product modeling and design by making certain formal transformations. The process of using this method and the design methods used in it were also analyzed. In this paper, a wine jug product was selected for case study design verification, but since the shape of the jug was relatively simple, only one imagery target was selected for design verification in the discussion, but the results are sufficient to demonstrate the effectiveness of the proposed method.

The focus of the research work in this paper was to try to propose a general product modeling topologizable design method to solve the problems encountered in product design, so the introduction and analysis of the method were extensively elaborated in the previous research part of the paper. For other products, although they were different in terms of styling design features and user requirements, they were similar in the design process of permutation and preference selection, so the proposed method was somewhat general for different cases.

4.5. Research on the Future Work

In the case study of the wine jug, the optimal choice of styling design elements is ideal. This means that this method can play a role in design work and provide designers with design decisions. However, in practice, there are various types of contradictory issues in the design work process, which lead to many design cost increases.

The design method proposed in this paper aims to use computer design to quantitatively assess users’ implicit needs and to assist designers in product design output by mapping the predicted data from the correlation model, helping designers to grasp users’ needs faster and more accurately. This method is also a supplement to the designer’s skills; the designer’s emotion, creativity and innovation is irreplaceable. The research work in this paper is only intended to solve the problem of one part of the product design, the use of computer-aided designers to design and create is a way to improve the efficiency of designers, but the rest of the process, such as brainstorming and sketching and other activities in the early stages of product research, still relies on the designers’ own creativity. The design method proposed in this paper is only used as a means to help designers carry out part of their work.

In the future, we need to pay more attention to the integration of computer assistance in product development and the creation of the designers’ capabilities.

(1)

Product design requires consideration of more complex product features and more implicit user needs to be explored, etc., to facilitate the work of designers.

(2)

For the proposed method, we will conduct a larger-scale case study in the future and then improve the proposed method according to the application.

5. Conclusions

This paper quantified the association between product shape features and user perceptual imagery, explored the product shape topologizable design method through quantitative theory type I, statistics, and other multidisciplinary knowledge, and used the wine jug shape design as an example for design output. The following conclusions were obtained through verification:

(1)

Through the deconstruction of product modeling features and the quantification of target perceptual imagery, the explicit and implicit needs of users were characterized. Combining this with the theory of topologizable primitives, the product modeling features, style imagery, and their topologizable values, and unifying these in the same system, a library of topologizable design elements was established for product modeling.

(2)

Using the quantitative theory type I, a mapping association model between product modeling features and user target imagery was constructed, and the topizable values of the product modeling design elements were calculated. Quantitative model data were obtained to provide a basis for decision making for later product modeling design.

(3)

Study design and validation were conducted using the example of a wine jug product. The results showed that the design output from the data of this prediction model was better than the products already on the market in terms of perceptual imagery evaluation. This further verified the feasibility and effectiveness of the method and system proposed in this paper.