I. Introduction
In order to meet the needs of applications in dynamic modeling, data organizing, information storage and display, global grid model that uses the subdivided surface of Platonic solids, or regular polyhedron, as the approximations to the surface of the earth has been studied extensively. Among them quaternary triangular meshes (QTM) developed by the partition of either the octahedron or icosahedron is one of the representative methods [1] – [10]. Because it uses triangle as the basic cell to organize spherical data that fall into this area, many spatial analysis methods must be completed based on the triangle. However the geometric structure of the triangle meshes is very complex, it has asymmetry and uncertainty orientation that make it difficult to implement such spatial operation as adjacent analysis, spatial query, data update and so on.