Generation. Spherical Delaunay Triangulation Index Method

The research of Global GIS has become increasingly important, and the main technologies can be summarized as follows:(1) Representation theory of Spherical vector data; (2) Integration theory of the global multi-scale vector data; (3) The global index method of vector data. The spherical vector data representation theory as the basis for GGIS has caused great concern of scholars home and abroad.Delaunay triangulation has a strict mathematical theory and can form a shape optimization grid. It features dynamic and hierarchy. The data manipulation has flexible structure and the algorithms are mature. So, spherical Delaunay triangulation is considered to be a powerful tool for spherical vector data.There are three types of spherical Delaunay triangulation constructing algorithm as follows. (1) Tetrahedral algorithm, the basic idea is that the 2d simplex subdivision criteria are extended to be 3d simplex. Algorithms not only include the tetrahedral point positioning, external ball detection and LOP tetrahedron division and other more complex numerical calculation steps, but calculation needs to preserve tetrahedral topological connection. (2) Dyadic algorithm of Voronoi diagram, the basic process is that using level dissection result of regular polyhedron (regular triangle, regular hexagon) builds approximate spherical computational domain, and with morphologic expansion and erosion operation simulates the growth of objective. The essence of these operations belongs to grid computing. (3) Projection splicing algorithm, sphere problem is reduced to plane and spherical objective adjacency relationship is indicated as a plane DTIN. Compared with algorithms above, projection splicing algorithm has more efficiency. The main problem lie in splicing process that spherical data is projected to the plane by parallel, based on image point coincidence, relationship between blocks is established and reserved and spherical data is built by splicing the blocks data. Splicing process can lead to significantly decreased of practicality of algorithm.In order to solve the merging problem in constructing sphere Delaunay triangulated network, considering the position feature of sphere datum, an idea of planned sphere with the perspective projection model is proposed in this paper. It places the projected center on sphere and uses the sphere position restriction (i.e. x, y and z coordinates), builds one to one mapping between sphere and plane. The results of simulation experiment show that the time complexity of our algorithm determined by the adopted generation algorithm of plane Delaunay triangulated irregular network. Finally, in order to deal with large amount of data, this paper introduces the concept of the index in the three-dimensional display process. It can extract useful information to improve the three-dimensional display speed. The proposed model and algorithm is expected for the spherical vector data representation theory to provide a new supplement.