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Existing methods for measuring the spatial information of area maps fail to take into account the diversity of adjacency relations and the heterogeneity of adjacency distances among area objects, resulting in insufficient measurement information. This article proposes a method for measuring area map information that considers the diversity of the node–edge and Gestalt principles. Firstly, this method utilizes the adjacency relations between the Voronoi diagram of area objects to construct an adjacency graph that characterizes the spatial distribution of area objects in area maps. This adjacency graph serves as the information representation of area maps. Secondly, the method selects four characteristic indicators, namely geometric information, node degree, adjacency distance, and adjacency strength, to represent the diversity of nodes and edges in the graph that affect spatial information. Finally, nodes in the adjacency graph are taken as the basic units, and the spatial information of area maps is comprehensively calculated by integrating the four characteristics that represent spatial information. To verify the validity and rationality of the proposed method, a dataset of continuously simplified area maps and a dataset of artificially simulated degrees of randomness were designed to evaluate the performance of the existing method and the method proposed in this paper. The results indicate that the correlation between the measurement results obtained by the method proposed in this paper and the degree of disorder is as high as 0.94, outperforming the existing representative methods. Additionally, the correlation between the measurement results of this method and the degree of simplification reaches 1, indicating that the variation range of the measured values is more consistent with the cognitive assumptions based on artificial simulations compared to the existing methods. The experimental results show that the method proposed in this paper is an effective metric approach for representing spatial information in area maps. [ABSTRACT FROM AUTHOR]

Three-dimensional topological relationships serve as a theoretical foundation for quality control, update processing, and spatial analysis of three-dimensional spatial data in real-world three-dimensional GIS. The existing 3D topological relationship models are all basic relationship models that cannot distinguish the refined topological relationship between the line and the body with multiple intersections. In this study, we develop a 3D refined topological relationship description framework that draws from the two-dimensional refined topological relationship model, defines the unit intersection between the line and the body based on manifold topology, and proposes a method for describing the unit intersections between the line and the body considering Euler numbers and adjacency types. In total, 23 basic types between the line and the body are deduced. An example is provided to illustrate the distinguished refined topological relationship between the line and the body with multiple intersections. Subsequently, an algorithm for determining the basic type of line/body is developed. Finally, a line/body refined topological relationship computation prototype system is developed using the Nef polyhedron model, C++ language, and an open-source geometric algorithm library, and the effectiveness of our method is verified using actual building and pedestrian data. [ABSTRACT FROM AUTHOR]