Analysis and simplification of point cluster based on Delaunay triangulation model

Point cluster object contains much structured information in spatial distribution, which is interesting for the research of spatial analysis and map generalization. This paper divides the spatial distribution information of point cluster into three categories: existing, metrical structure and topological structure, and focuses the discussion on metrical structure. Based on the Delaunay triangulation and Voronoi diagram model, the paper defines four characteristic parameters for describing metrical structure: distribution range, distribution density, distribution centre and distribution axis. Considering Gestalt principles in visual adjacency cognition, the presented method finds the distribution range polygon by progressively stripping the outside triangles. The distribution density is represented by Voronoi cell size and visualized as a grey image. Applying an image processing method, the distribution centre can be extracted from the grey image. A method of point cluster simplification is provided in the paper on the basis of Voronoi diagram establishment in a dynamic way. The relative distribution properties above are preserved in the simplification method.