Hierarchical Voronoi Diagram And Its Preliminary Application

Spatial information visualization is the procedure that makes the complex scientific phenomenon and natural landscape, as well as some abstract concept to be graphic by using computer graphics and image processing technology, so it is an important technology for information visualization. To be more precise, it uses graphics and image technology to perform the complex spatial data and attribute data in a geographic form. In order to make the timely judgment and right decision for relevance and development tendency in data mining, this paper took Voronoi diagram as the breakthrough point, through the adaptive clustering algorithm of spatial point set and weighted clustering point visualization, a spatial data visualization method is proposed based on hierarchical Voronoi diagrams. In combination of the reference knowledge of probability theory and mathematical statistics, the concrete reference applications have been studied. Lastly, experimental verification is done and the analysis of the experimental results of point group is made. The main research contents and results in this paper are as follows:(1) The analysis of the limitation about spatial data visualization graph. The current graphs mostly applied in spatial data visualization are triangular mesh and network of squares, which have no benefit in geometric morphology expression of spatial data. Owning to the flexibility of graph, it can’t have a full show of dimension information according to the raw data. A better graph is dramatically demand for visualization to improve the effect of the spatial data expression and amass the amount of data information visualized.(2) An adaptive clustering algorithm of spatial point group based on hierarchical tree structure. The general visual tree data structures and clustering tree data structures have been concisely stated. Admittedly, the stable tree structure can achieve the structure division of spatial data, but it lacks of principle in timing and entity integrity. In this paper, an adaptive clustering algorithm could be able to achieve the divisions of spatial data group. Further, which ensures the clustering of spatial data to be integrate and adaptive.(3) LOD (Level of Detail) visualization expression based on hierarchical Voronoi diagrams is proposed. According to the tree structure built by adaptive clustering method, the Voronoi diagram is used to divide and visualize the spatial point group data. In some specially appointed macro background, the micro information within can be observed through the LOD visualization of spatial data.(4) A point set generalization method is proposed based on hierarchical Voronoi diagrams. On the basis of characteristic of hierarchical Voronoi diagrams, the spatial point group is studied. According to the proposed point group similarity algorithm, the geometric mean of the similarity of density, angle, distance and topology is calculated as a rule to decide the similarity among diverse spatial point group based on the hierarchical Voronoi diagrams expression at the same levels of different point group. The synthesized parameters, e.g., the range, orientation and the density of the spatial point group are in accord with the original spatial data.The LOD visualization method based on hierarchical Voronoi diagrams proposed in this paper has conspicuous advantages over synthesizing, similarity calculating and handling the spatial relationship within spatial point group. At last, the empirical results justified that it is feasible and practicable.