Optimizing agricultural carbon compensation zoning is crucial for establishing robust mechanisms in agricultural carbon compensation management, with significant implications for achieving national “dual carbon” strategic objectives. This study employs K-means and the three-dimensional magic cube approach to construct a novel evaluation index system for comprehensive carbon compensation zoning. By combining spatial land-use zoning, we delineate carbon compensation zones in Guangshui City, Hubei Province, and analyze the spatiotemporal variations of agricultural carbon balance, proposing optimization strategies. The results show that (1) from 2000 to 2021, agricultural carbon emissions and absorption exhibit a trend of increasing followed by decreasing, with spatial patterns of “higher in the northwest, lower in the southeast” and “higher in the southwest, lower in the northeast”; (2) the Gini coefficient of agricultural carbon emissions averages at 0.24, with economic contribution coefficients and ecological carrying coefficients ranging from 0.04–16.1 and 0.39–1.99, respectively, from 2000 to 2021; and (3) in 2021, Guangshui City comprises seven payment zones, four balance zones, and six compensation zones, ultimately forming eight optimized agricultural carbon compensation zones in alignment with regional agricultural carbon balance objectives. This study provides theoretical references for enhancing county-level agricultural carbon comprehensive compensation management mechanisms.

This study proposes a two-dimensional analytical framework based on urban spatial form and spatial service perspectives, utilizing data on buildings and points of interest (POIs). It integrates fishnet analysis, kernel density analysis, the categorization of POI functionalities, and mixture calculations to enhance our understanding of urban spatial form and function. Taking the main urban area of Zhengzhou as an example, this study identifies image elements that can describe urban spatial characteristics through the results of two-dimensional analysis and enriches the city image in the form of a portrait. The experimental findings demonstrate that the elements of the annular layer, functional landmarks, ring line boundaries, and special districts can fully convey the spatial picture of Zhengzhou City. The performance of the four types of image elements has a high degree of matching with the content of the urban spatial planning of Zhengzhou City, which can effectively identify the urban multi-center structure and development pattern. This paper explores and tests the development status of the city from a new perspective, which can provide an effective reference for the future planning and sustainable development of the city.

Rural settlements serve as the core spatial carriers of rural living space, and their spatial evolution and functional transformation reflect the dynamic restructuring of human–land relationships. In karst mountainous areas, complex topography, fragmented land resources, and uneven distribution of public facilities significantly influence settlement patterns and residents’ living spaces. This study aims to quantify the relationship between settlement clustering characteristics and living-space demand and to construct a spatially explicit framework for rural settlement restructuring from a living-space perspective. Taking the Qixingguan District of Bijie City, Guizhou Province—a representative karst mountainous area in Southwest China—as a case study, we develop an integrated analytical framework encompassing spatial identification, demand measurement, and zoning optimization. Settlement clusters were identified using the Nearest Neighbor Index and Kernel Density Analysis, while accessibility to essential services—including education, healthcare, and shopping—was quantified via a Gaussian-based two-step floating catchment area method. Living-space demand was further assessed by integrating accessibility gradients with residential conditions, and restructuring types were classified based on the Living Space Index and the distance from settlements to town centers. The results indicate that (1) rural settlements in Qixingguan District exhibit significant clustering, with high-density zones concentrated around urban peripheries and along transportation corridors; (2) accessibility to living services follows a distance-decay pattern modulated by transportation networks, forming hotspots in suburban and town-center areas and cold spots in peripheral karst mountainous areas; and (3) based on the comprehensive assessment, settlements are categorized into four types—urbanizing villages, central villages, preserved villages, and relocation villages—with corresponding targeted spatial restructuring strategies proposed. This study advances the geographical understanding of rural settlement restructuring in karst mountainous areas and provides empirical evidence for optimizing human–land relationships and promoting more equitable and sustainable spatial development in mountainous regions.