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THE EXPRESSION OF SPHERICAL ENTITIES AND GENERATING OF VORONOI DIAGRAM BASED ON TRUNCATED ICOSAHEDRON DGG

Based on the analysis of current spherical spatial data structure, the paper discusses the clew of the spherical spatial basal subdivision mode which uses inverse Snyder polyhedron equal area projection on the surfaces of Truncated Icosahedron, and then obtains global multi-resolution overlay by hierarchical subdivision on the initial unfolded projection plane according to the hexagonal grid. The paper also puts forward a essential clew of managing the three leaves nodes and tiles coding based on hexagonal grid, and establish the hexagonal grid expression modes of different spherical entities. Also, on the basis of these clews, we put forward the algorithm of generating the voronoi diagram based on the spherical hexagonal overlay and verified the exactness and efficiency of the algorithm through experiments. By comparing with other similar algorithms, the paper summarized the advantages of the algorithm and gives further research direction at last. About the first author: Tong Xiaochong, postgraduate, Information Engineering University he majors in DGGS, mass data display and image processing. 1. SUMMARIZE Thanks to the fast development of various data acquisition methods, we can obtain all sorts of spatial data,especially the data of global remote sensing and mapping. In order to manage extract and analyse the spatial data much more effectively, it’s important to adopt new supervisor mode of global spatial data. And in order to effectively manage the extensive especially global multi-resolution geographical spatial data, in the 1980 last century many academicians put forward global discrete grid data model based on subdivision of regular polyhedron. The postulate is to split spherical surface into tiles with the approximately equal figure and area, using hierarchical recursive subdivision and corresponding address code of each tile instead of geographical coordinates to do all kinds of operation. Because the address codes not only show the position but also express the scale and precision, it has the potential ability to manage multiscale data. On the other hand, thanks to the especial mathematic characters of voronoi diagram, it becomes the most hopeful methods to solve dynamic GIS (Chen, 2002). And how to effectively combine the both becomes many academicians focus. Voronoi diagram is a widely research issue in computational geometry, for its importance, it is an important geometry that is only inferior to convex hull. It has a lot of egregious funny mathematical characters, and it is a powerful tool to research and solve some issues of geoscience, computer science, mathematics and so on. However, because the earth is an approximate sphere, it has import significant to establish spherical voronoi diagram for the management of the global spatial data and dynamic maintenance of spherical spatial relation. At present, it is less in research of the theoretics of spherical voronoi diagram abroad, but there are several typical algorithms among them, for example, Augenbaum (1985) gave the spherical voronoi diagram algorithm of n points using incremental method, and the time complexity is O(n); Robert(1997) put forward the devider and conquer method to solve the generation of spherical voronoi diagram, and the time complexity is O(nlogn); Zhao(2002) put forward the QTM-based algorithm for the generation of voronoi diagram for spherical objects, etc. Among the three algorithms, the first two methods are both vectorial algorithms aiming at spherical point set, and the last one aims at all kinds of different spherical aggregation based on specifically spherical triangular mesh. Until now, all the vectorial algorithms of spherical voronoi diagram are only effective to point set, and don't have operability for curve set and area set(Chen, 2002; Zhao, 2002). And the paper also adopts the clew of generating of voronoi diagram based on grid, which uses the spherical grid as the basic subdivision cell, adopts the transformation of grid interval, and then goes on with the research of spherical voronoi diagram, but we adopt hexagonal mesh instead of triangular mesh as the basic spherical subdivision cell. Compared with triangles, the hexagons have more advantages, for instance, they have more directions, provides the greatest angular resolution (Golay, 1969), have less interval of sampling, and all directions are the same, etc. So we put forward a spherical hexagonal grid