1. Introduction
According to the product life cycle theory, different design strategies should be adopted in different development periods to achieve sustainable development. Especially in the maturity stage, the number of competitors will increase, the market competition will become more intense, and the competitive version of the product will reach a high peak. At this time, it is not easy to make a breakthrough in technology, but it is easier to make a breakthrough in shape diversity [
1]. At present, the technological diversity of enterprises in manufacturing procedures, product performance, and safety is gradually reduced, but the appearance of products that meet the aesthetic needs of consumers has become a new competitive advantage for enterprises. The appearance, price, and function of a product affect consumers’ purchasing desires and preferences, while ordinary consumers tend to want an attractive appearance [
2,
3]. Ranscombe et al. [
4] pointed out that the appearance of a product will affect its sales and even the market’s lifeblood. Tang et al. [
5] believe that appearance and aesthetics are the key points in product design because the shape of the product will intuitively convey its image and affect the consumer’s first impression of the product. Therefore, companies need to design product shapes that meet consumers’ aesthetic preference. Additionally, Forslund and Söderberg [
6], in the proposed total product design concept, showed that different shape elements in the overall shape of the product would affect consumers’ purchase intentions. Thus, it is necessary to disassemble the overall shape into multiple shape elements for further analysis. In recent years, many scholars have focused on constructing the relationship between product shape and its image vocabulary [
7,
8,
9,
10], and through various techniques [
11] to clarify the image demands of consumers for product shape, and then apply it to the shape design and design evaluation of the product. Although this research can satisfy the image demands of consumers for different product shapes, it cannot produce many product shapes. In this study, a morphological database was constructed based on the original and new morphological charts, from which hundreds of combinations of shapes can be formed theoretically, and then the shapes of consumer preference can be selected from them.
In the research of product shape design, scholars mostly use a 2D curve to define the appearance and features. Since 1988, many studies on 2D curves have been accumulated. Biederman and Ju [
12] studied 2D curves earlier, proposing that 2D curved profiles have the most significant influence on human perception and recognition of product shape. However, when the vertices of the contour line are reduced, or the middle part of the contour line is removed, the product shape is challenging to identify. Hui and Li [
13] proposed a shape blending method based on 2D curves. Subsequently, Hsiao et al. [
14] used four different mathematical calculation methods to blend the 2D curves of shape elements from two different products and then to quickly obtain an innovative product form. In the latest research, Hsiao et al. [
15] applied this method to yacht design by mixing the shape of Taiwan cultural elements with the shape of a yacht, and finally obtained a yacht shape with the image of Taiwan culture. In addition, based on the concept of shape grammar, many scholars use 2D curves to represent the overall shape of the product and maintain the brand characteristics of the shape through various methods. Pugliese and Cagan [
16] described and defined the geometric rules of the shape with the shape grammar of the product to maintain the brand characteristics of the shape. They used the motorcycle as a design case to verify the feasibility of the proposed method. McCormack et al. [
17] take Buick as an example to encode its key shape elements into a reusable method, which can be used to maintain consistency between shapes. Cheutet et al. [
18] proposed a geometric operation method based on shape grammar, that is, analysis and parameterization of 2D curves, so that car designers can decompose and reconstruct new shapes through the obtained geometric parameters. In similar studies, Hsiao et al. [
19] proposed a new method for disassembling and reconstructing 2D curves, which can help designers get a unique shape to maintain the brand characteristics of the automobile. Considering that this paper aims to construct a model for evaluating product shape, 2D curves are still used to define the overall shape and shape elements.
Previous studies have shown that humans tend to perceive the overall shape of objects [
20,
21,
22], so it is necessary to explore the relationship between human perception of product shape and the 2D curve representing the overall shape of the product. However, it is difficult to control the overall shape characteristics of 2D curved profiles using traditional microscopic shape information (e.g., circumference, area, roundness, maximum radius vector, and average radius vector) [
23]. Consequently, it depends on the experience and intuition of designers. Fortunately, Ujiie et al. [
24] have proposed three types of macroscopic shape information that can be used to evaluate a curved profile, namely, angle entropy, curvature entropy, and quadratic curvature entropy. Meanwhile, they proved that the quadratic curvature entropy is more consistent with human cognition of shape. In this paper, quadratic curvature entropy is used as the criterion to evaluate the overall shape of the product.
This study aims to construct a design and evaluation model of product shape based on the 2D curve and to confirm its effectiveness. An outline of this paper is given as follows.
Section 2 describes in detail the research methods and theories involved in this study.
Section 3 describes the framework of the research process and the specific implementation steps.
Section 4 takes a two-wheel balancing vehicle as the design case and evaluates its shape from three sub-evaluation systems, including the fuzzy comprehensive evaluation system (ES-I), the consumer perceptual evaluation system (ES-II), and the macroscopic shape information evaluation system (ES-III).
Section 5 compares the three evaluation results, then examines the effectiveness of the proposed model, and analyzes other factors that may affect the evaluation. Finally, the last section concludes the article.
5. Results and Discussion
From
Section 4.6, it can be seen that the results of the three evaluations are highly consistent, in which the result of the fuzzy comprehensive evaluation is entirely consistent with the result of consumer perceptual evaluation, all of which are shape 3 > shape 1 > shape 4 > shape 2, indicating that the degree of consumer preference for each combination can be accurately evaluated based on those relative weights of shape elements (
Table 6) and those fuzzy memberships of their types (
Table 7). In other words, the order of preferences for hundreds of combinations can be obtained according to
Table 6 and
Table 7. However, the evaluation result of macroscopic shape information is slightly different from the first two, which is reflected in the reverse order of shape 1 and shape 3. Therefore, it is still necessary to analyze the causes of the errors and further explore the potential influencing factors. As can be seen from
Figure 6b, there is a clear difference between the handlebar of shape 1 and the handlebars of the other three shapes, which is embodied in the fact that the handlebar of Shape 1 is relatively simple (i.e., the curvature change is small), and the handlebar of shape 3 is more complicated (i.e., the curvature changes significantly), thus assuming that this is the cause of the error. To verify the correctness of the hypothesis, the handlebars of the two shapes were exchanged (
Figure 7), and then the macroscopic shape information of the two curve contours after the exchange was calculated. The calculation results show that the entropy value of the new shape 3 (i.e., with the handlebar of shape 1) is smaller than the entropy value of the new shape 1 (i.e., with the handlebar of shape 3), indicating that the curvature change of the new shape 3 is more stable and more consistent with the aesthetic preference of consumers. Thus, it can be seen that the difference between the element type and other element types leads to the error of macroscopic shape information evaluation and the other two evaluations. Therefore, if there are apparent differences between the types of shape elements in the evaluation process, it can be verified through the above method to obtain a more accurate evaluation result. Furthermore, the canonical angle of the product (
Figure 6a) contains more shape information than the overall shape profile of the product (
Figure 6b). Although there is no significant effect of this factor in this study, this factor cannot be wholly ignored in the evaluation process of other products.
6. Conclusions
This article proposes a product shape design and evaluation model based on the 2D curve of product shape. This model included three sub-evaluation systems: the fuzzy comprehensive evaluation system (ES-I), the consumer perceptual evaluation system (ES-II), and the macroscopic shape information evaluation system (ES-III). ES-I integrated morphological analysis, fuzzy hierarchical analysis (FAHP), and fuzzy comprehensive evaluation (FCE). ES-II conducted a questionnaire survey of users and potential users who use the target product. ES-III combined information theory, the Markov process, and quadratic curvature entropy. It was found that the evaluation results of ES-I and ES-II were entirely consistent, but there were some differences between ES-III and the first two, which was due to the significant difference between the handlebars of the shape elements of shape 1 and the other three shapes. In ES-I, FAHP could clarify the relative importance of each shape element (
Table 6), and subsequent questionnaires could clarify the fuzzy membership of each type of shape element (
Table 7), while the final fuzzy comprehensive evaluation could help designers quantify and make judgments about perceptual shape preferences. In ES-III, the quadratic curvature entropy closest to human cognition was selected as an index to evaluate the product shape, which could help design engineers without systematic aesthetic training to determine the best product shape quickly. In summary, the three sub-evaluation systems belong to a parallel relationship. If the three evaluation results could be used as a reference in the design process of shape, it could help designers more accurately grasp consumers’ actual shape preferences, thereby helping enterprises reduce design cost and increase product market share.
Humans identify objects based on a preset angle (e.g., the canonical angle of the object) stored in the brain [
31]. Because the front view of the two-wheel balancing vehicle contained more shape information, it was taken as the canonical angle to build the morphological chart in this paper. We built a new morphological chart with the newly designed types of shape elements based on the original morphological chart. Finally, we obtained a merged morphological chart. In terms of the morphological chart, the merged morphological chart dramatically increases the total number of combinations of shapes and improves the possibility of shape innovation. Subsequently, it can be seen from the three evaluation results that the combinations from the new morphological chart are better than those from the original morphological chart, except for shape 3 and shape 1 in ES-III, but the reason has been analyzed.
The present study is subject to some limitations. First, since the current product upgrades are very fast, this might cause the proposed shape evaluation model to fall behind the current products on the market. Therefore, it is necessary to promptly update those types of shape elements in the morphological chart to improve the usability of the evaluation model. Second, considering that consumers’ aesthetic demands are constantly changing over time, it is necessary to regularly investigate the users’ preference for each type of shape element in the morphological chart to conduct an accurate and effective evaluation. Lastly, due to the limitation of research conditions, we only used the 2D curve of the product as the evaluation sample. In the subsequent research, if a three-dimensional morphological chart is used instead of the two-dimensional morphological chart, we could get more intuitive combinations of shapes and make a more accurate evaluation. For instance, the macroscopic shape information could be evaluated from different perspectives of the three-dimensional shape combination. Although the two-wheel balancing vehicle was used as a case study in this paper, the proposed design and evaluation model is also suitable for other products.