Conformal Geometric Algebra has been introduced into geographic information science as a mathematical theory because of its advantages in terms of uniform multidimensional representation and computation. The traditional intersection computation between two geometric objects of different types is not unified. In this study, we propose algorithms based on Conformal Geometric Algebra to determine the spatial relationships between geographic objects in a unified manner. The unified representation and intersection computation can be realized for geometric objects of different dimensions. Different basic judgment rules are provided for different simple geometries. The algorithms are designed and implemented using MapReduce to improve the efficiency of the algorithms. From the results of several experiments we provide, the correctness and effectiveness of the algorithms can be verified.

Taking cities in Zhejiang Province of China from 2011 to 2020 as the research object, a multi-dimensional urbanization quality evaluation index system was constructed using the comprehensive analysis method, and the urbanization quality of 11 cities in Zhejiang Province was quantitatively measured using the entropy weight method. The system classification and time-space evolution analysis were carried out using ArcGIS software (Environmental Systems Research Institute, Inc., RedLands, CA, USA) to comprehensively study the evolution characteristics and influencing factors of the urbanization quality of cities in Zhejiang Province. This study provides a reference for local governments to formulate feasible urbanization development strategies and policies to promote the high-quality development of urbanization and for the construction of new urbanization in other provinces and cities.

The study of spatial geometric similarity plays a significant role in spatial data retrieval. Many researchers have examined spatial geometric similarity, which is useful for spatial analysis and data retrieval. However, the majority of them focused on objects of the same type. Methods to support the spatial geometric similarity computation for different types of objects are rare, a systematic theory index has not been developed yet, and there has not been a comprehensive computational model of spatial geometric similarity. In this study, we conducted an analysis of the spatial geometric similarity computation based on conformal geometric algebra (CGA), which has certain advantages in the quantitative computation of the measurement information of spatial objects and the qualitative judgment of the topological relations of spatial objects. First, we developed a unified expression model for spatial geometric scenes, integrating shapes of objects and spatial relations between them. Then, we established a model for the spatial geometric similarity computation under various geographical circumstances to provide a novel approach for spatial geometric similarity research. Finally, the computation model was verified through a case study. The study of spatial geometric similarity sheds light on spatial data retrieval, which has scientific significance and practical value.

Theft is an inevitable problem in the context of urbanization and poses a challenge to people’s lives and social stability. The study of theft and criminal behavior using spatiotemporal, big, demographic, and neighborhood data is important for guiding security prevention and control. In this study, we analyzed the theft frequency and location characteristics of the study area through mathematical statistics and hot spot analysis methods to discover the spatiotemporal divergence characteristics of theft in the study area during the pre-COVID-19 and COVID-19 periods. We detected the spatial variation pattern of the regression coefficients of the local areas of thefts in Haining City by modeling the influencing factors using the geographically weighted regression (GWR) analysis method. The results explained the relationship between theft and the influencing factors and showed that the regression coefficients had both positive and negative values in the pre-COVID-19 and COVID-19 periods, indicating that the spatial distribution of theft in urban areas of Haining City was not smooth. Factors related to life and work indicated densely populated areas had increased theft, and theft was negatively correlated with factors related to COVID-19. The other influencing factors were different in terms of their spatial distributions. Therefore, in terms of police prevention and control, video surveillance and police patrols need to be deployed in a focused manner to increase their inhibiting effect on theft according to the different effects of influencing factors during the pre-COVID-19 and COVID-19 periods.