Objectives  The spatial distribution of rural settlements has unique regularity and complexity. In order to reduce the difficulty of cartographic generalization, we can cluster rural settlements first. Voronoi diagram has significant advantages in expressing the distribution characteristics of settlements, but now spatial clustering seldom considers direction relation between entities. Direction relation is an important part of spatial relation. In theory, the introduction of direction relation in spatial clustering can help to improve the clustering effect. Therefore, based on Voronoi diagram, this paper proposes a clustering method of rural settlement considering direction relation.

  Methods  First, Voronoi diagrams with distance constraint(DC-Voronoi) are constructed, and Voronoi proximity relations among settlement entities are determined. Second, undirected features are calculated based on the area of entities and the area of DC-Voronoi polygons. Directed features are calculated based on offset direction and offset distance of entities in DC-Voronoi polygons. Aggregation strength values of all entity pairs are calculated by combining undirected features and directed features. Finally, clustering result is obtained by eliminating the proximity of entity pairs whose clustering strength value is less than the threshold. Taken the data of rural settlements in Ningbo as an example, this paper sets silhouette coefficient as result evaluation index.

  Results and Conclusions  Compared with the clustering results of density-based spatial clustering of applications with noise method and clustering by fast search and find of density peaks method, the results show that the proposed method can effectively cluster rural settlements with different distribution patterns, and can accurately identify the boundary of rural settlements. The clustering granularity is moderate, and the clustering results accord with people's cognitive habits.