In this paper, a new parameterized surface, termed SQ-Coons surface, is proposed according to the build mode of Coons patch. The surface is always interpolated to the boundary curves, and its shape details could be controlled by the shape parameters in CE-Bézier basis functions, which makes it suitable for styling design in computer aided design (CAD). In order to exert its geometric advantages in car design, a simplified body CAD template based on characteristic lines is built according to common vehicle features. The template is built entirely from SQ-Coons surfaces, so that the overall style and detail shapes could all be modified by the control points and shape parameters of each surface. By analyzing the curvature of fifty commercial car types generated through the template and various parameters, a set of methods for constraining the range of shape parameters is proposed. On this basis, as an example, the four shape parameters of the hood surface in one model are used as variables to optimize the body shape to achieve the lowest possible aerodynamic drag coefficient in computational fluid dynamics (CFD). The results show that the design method, combining the new surface and the model template, could reflect the modeling characteristics of different cars, and improve the design and scheme adjustment efficiency in the conceptual design stage.

In order to understand the regularity of human motion, characteristic description is widely used in gait analysis. For completely expressing gait information and providing more concise indicators, parametric description is also particularly significant as a means of analysis. Therefore, in this paper, the mathematical models of gait curves based on the generalized extension-Bézier curve were investigated, of which the shape parameters were used as individual gait characteristics to distinguish whether the gait is normal or not and to assist in judging rehabilitation. To evaluate the models, angle data from three joints (hip, knee, and ankle) were recorded with motion capture system when participants (10 healthy males and 6 male patients with ankle fracture) were walking at comfortable velocity along a walkway. Then, the shape parameters of each subject were obtained by applying the mathematical models, and the parameter range of the normal group was further summarized. Through comparison, it could be found that most shape parameters of patients exceed the normal ranges in varying degrees, and are concentrated on specific parameters. The results can not only help to judge the recovery stages of patients but also figure out the corresponding abnormal postures, so as to provide guidance for rehabilitation training.

Aiming at car design, a parametric design method is proposed in this paper. There are two contents in this method, a novel parametric surface, a shape-adjustable automobile styling template, and a design method of integrating the two contents. The surface termed extended SQ-Coons surface constructed in this paper has the advantage of being fine adjusted while always interpolating at the given boundary curves, which is suitable for its application in automobile modeling design. Matching with the surface, a car model template built by multiple quadrilateral surfaces is proposed. The car models built by the template could achieve the parametric adjustability of all modeling features on the premise of maintaining continuity between subsurfaces. Finally, after the integration of the surface and the template, a whole set of parametric automobile surface modeling design method is proposed. In this method, the overall shape of the car body is determined through multi angle hand drawing, and curve control points, segmentation parameters, and shape parameters are used to adjust the detail modeling. The final results show that the novel surface and template proposed could be used to parametrically establish the vehicle models of various shapes and improve the design efficiency in the conceptual design stage.

With the continuous expansion of urban metro systems, balancing passenger experience and operational efficiency has become a central concern in contemporary public transportation design. However, most existing metro service studies continue to focus on perceptual comfort or isolated usability tasks and lack an integrated, behavior-centered perspective that accounts for the full travel chain and diverse user groups. This study develops the Bi-directional Service Behavioral Experience Model (BSBEM), which systematically integrates one-way navigation behaviors and interactive operational behaviors within a unified dual-path framework to identify behavioral patterns and experiential disparities across user groups. Based on the People–Touchpoints–Environments–Messages–Services–Time–Emotion (POEMSTI) behavioral observation framework, this study employs a mixed-method approach combining video-based behavioral coding, usability testing, and subjective evaluation. An empirical study conducted at Beidajie Station on Xi’an Metro Line 2 involved three representative passenger groups: high-frequency commuters, urban leisure travelers, and special-care passengers. Multi-source data were collected to capture temporal, spatial, and interactional dynamics throughout the travel process. Results show that high-frequency commuters demonstrate the highest operational fluency, urban leisure travelers exhibit greater visual dependency and exploratory pauses, and special-care passengers are most affected by accessibility and feedback latency. Further analysis reveals a positive correlation between route complexity and interaction delay, highlighting discontinuous information feedback as a key experiential bottleneck. By jointly modeling one-way and interactive behaviors and linking group-specific patterns to concrete metro touchpoints, this research extends behavioral evaluation in metro systems and offers a novel behavior-based perspective along with empirical evidence for inclusive, adaptive, and human-centered service design.