孔径为4的全球六边形格网系统索引方法

从集合论的角度描述基于正八面体的、孔径为4的六边形格网系统，通过对偶、中心剖分两项基本操作建立不同层次六边形格网集合与三角形格网集合之间的递推、包含和层次关系。定义三轴整数格网坐标系描述三角面上六边形格网单元的位置，通过若干定理解决了格网索引的核心问题，如单元笛卡尔坐标的计算，邻近、孩子、父亲单元的判定。据此设计了单元索引算法并通过对比实验进行验证。实验结果表明，本文提出索引算法的平均执行效率约是同类算法的600倍，因而更适合计算机处理。

Indexing Schema of the Aperture 4 Hexagonal Discrete Global Grid System

The octahedron-based aperture 4 hexagonal DGGS(OA4HDGGS) is described using the set theory.By defining two basic operations,the dual and the central subdivision,recursive relation,nested relation and hierarchical relation between the set of hexagonal grids and the set of triangular grids are established.Location of the hexagonal cell on triangular face is described in the three-axes integral grid coordinate system,and meanwhile,essential problems of index schema,including the calculation of Cartesian coordinates of the cell,the determination of neighbors,children and parents of the cell,are solved by a few theorems.According to the theorems,indexing algorithms are proposed and validated by contrastive experiments.The experimental results show that our indexing schema is 600 times faster than similar schema,which proves it is more suitable for computer processing.