Multifunctional state assessment was the basis of time sequence design of territory spatial development and overall utilisation. This study aimed to identify the ecological-production-living (PLE) territory spatial function to provide a basis for territory spatial planning. It took Henan Province as the research area. This study developed a methodology to assess differentiation characteristics for PLE function, a method that integrates functional merging and geographic information technology. We used the coordination degree model and spatial autocorrelation analysis to reveal the coordination of spatial functions of the province. The results were as follows: (1) During the study period, the land production function of main grain-producing areas decreased slowly, and production and living function values of the Central Plains urban agglomeration with Zhengzhou as the centre were in an upward trend. The characteristics of urban-rural dualization were prominent, and ecological function value decreased year by year. (2) The laws of territorial spatial functions had different manifestations in different stages (1990–2005 and 2005–2018). By different characteristic laws, the change in production function in the later period was bigger than that in the previous period. The living function maintained a good continuity expansion characteristic before and after. The spatial regularity distribution characteristics of ecological function were weak, and the overall environment became worse than before. (3) The territory space of middle and low coordination function types was the most important type, and the aggregation was relatively weak. Xuchang County and Weihui City showed better states of functional coordination aggregation. Lushi County, Xinxian County, and Shangcheng County, which were in the western and southern mountainous and hilly areas, showed low-low aggregation characteristics. Thus, the government will strengthen targeted control over territorial space. This study provides a reference for the overall deployment of the development and utilisation of territory space in Henan Province.
Three-dimensional (3D) cadastral data models that are based on Euclidean geometry (EG) are incapable of providing a unified representation of geometry and topological relations for 3D spatial units in a cadastral database. This lack of unification causes problems such as complex expression structure and inefficiency in the updating of 3D cadastral objects. The inability of current cadastral data models to express cadastral objects in a unified manner can be attributed to the different expressions of dimensional objects. Because the hierarchical Grassmann structure corresponds to the hierarchical structure of dimensions in conformal geometric algebra (CGA), geometric objects in different dimensions can be constructed by outer products in a unified expression form, which enables the direct extension of two-dimensional (2D) spatial representations to 3D spatial representations. The multivector structure in CGA can be employed to organize and store different dimensional objects in a multidimensional and unified manner. With the advantages of CGA in multidimensional expressions, a new 3D cadastral data model that is based on CGA is proposed in this paper. The geometries and topological relations of 3D spatial units can be represented in a unified form within the multivector structure. Detailed methods for 3D cadastral data model design based on CGA and data organization in CGA are introduced. The new cadastral data model is tested and analyzed with experimental data. The results indicate that the geometry and topological relations of 3D cadastral objects can be represented in a multidimensional manner with an intuitive topological structure and a unified dimensional expression.
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