Radix Representation of Triangular Discrete Grid System

[摘要] Discrete Global Grid Systems (DGGSs) are spatial references that use a hierarchical tessellation of cells to partition and address the entire globe. It provides an organizational structure that permits fast integration between multiple sources of large and variable geospatial data. Although many endeavors have been done to describe certain discrete grid systems, there still lack of a uniform mathematical framework for them. This paper simplifies the planar class I aperture 4 triangular discrete grid system into a hierarchical lattice model which is proved to be a radix system in the complex number plane. Mathematical properties of the radix system reveal the discrete grid system is equivalent to the set of complex numbers with special form. The conclusion provides a potential way to build a uniform mathematical framework of DGGS and can be used to design efficient encoding and spatial operation scheme for DGGS.

[发布机构] Department of Remote Sensing, Zhengzhou Institute of Surveying and Mapping, High-Tech Zone, 62 Science Avenue, Zhengzhou, China^1;State Key Laboratory of Resource and Environmental Information System, Chinese Academy of Science, 11A Datun Road, Chaoyang District, Beijing, China^2

[效力级别] 计算机科学 [学科分类] 计算机科学（综合）

[关键词] Discrete global grid systems;Efficient encoding;Hierarchical lattice;Mathematical frameworks;Mathematical properties;Organizational structures;Radix representation;Spatial operations