Xin Sun

As a result of China’s rapid urbanization, new urban districts are characterized by a superblock development paradigm that contrasts sharply with core urban areas, where service facilities remain largely congruent with the population distribution. This planning approach has resulted in a pronounced spatial mismatch, with an intensive concentration of public service facilities within commercial cores and a critical lack of facilities proximate to high-density residential clusters. Within the framework of the 15 min community life circle policy, evaluating and optimizing these configurations is imperative for mitigating such structural imbalances. Using Xi’an’s Qujiang New District as a representative empirical case, this study integrates Point of Interest (POI) geospatial data with 330 resident behavioral questionnaires to assess facility distribution and utilization patterns. The findings reveal a distinct spatial pattern of core–periphery polarization, which is significantly influenced by cultural landscapes and commercial land values. Furthermore, the utilization patterns differ markedly across age groups. The reliance of young and middle-aged groups on digital life circles should be viewed not only as a lifestyle preference but also as an adaptation to mitigate physical facility deficits. While digital services compensate for physical facility shortages, they mask the actual lack of community spaces. This further disadvantages older adults, who still rely heavily on walking to access daily services. Addressing the unique characteristics of new urban districts, this study proposes a synergistic physical–digital dual-tier system in which physical infrastructure safeguards the equity baseline, while digital platforms enhance operational efficiency, providing a scientific basis for constructing age-friendly communities.

The parametric method of product design is a pivotal and practical technique in computer-aided design and manufacturing (CAD/CAM) and used in many manufacturing sectors. In this paper, we presented a novel parametric method to design a kitchen product in the residential environment, a kitchen cabinet, by using cubic T-Bézier curves with constraints of geometric continuities. First, we introduced a class of cubic T-Bézier curves with two shape parameters and derived the G¹ and G² continuity conditions of the cubic T-Bézier curves. Then, we constructed shape-controlled complex contour curves of the kitchen cabinet by using closed composite cubic T-Bézier curves. The shapes of the contour curves can be adjusted intuitively and predictably by altering the values of the shape parameters. Finally, we studied shape optimization and representation of ellipses for the contour curves of the kitchen cabinet by finding optimal shape parameters and applicable control points respectively. The provided modeling examples showed that our method in this paper can improve the design and scheme adjustment effectively in the conceptual design stage of kitchen products.