A Novel Method for Constructing Hexagonal Global Hierarchical Encoding Structures Using a Semi-Regular Tiling Model

The discrete global grid system (DGGS) is a digital Earth reference framework that supports the fusion, analysis, and processing of heterogeneous data from multiple sources. Hexagonal DGGS is suitable for multi-scale data representation, with commercial and theoretical applications. The establishment of a hierarchical structure and design of encoding operations for hexagonal DGGS are vital for improving application efficiency; however, challenges remain in improving the efficiency of coding operations due to a lack of theoretical support for algorithm design. Therefore, this study describes the spatial cognitive equivalence of the hexagonal hierarchical division as a hybrid partition of triangles and hexagons in a T(6.3.6.3) grid, establishes a “superimposed” partition model of the aperture-3 hexagonal grid, and proposes a coding mathematical model of finite boundary structure, namely hexagonal hierarchy in a finite boundary (HHFB), which is extended to the rhombic triacontahedron and spherical surfaces. The comparative experimental results show that the proposed scheme has a smooth transition at the tile boundary and avoids complex fractal overlay hierarchy. The HHFB scheme achieves 10-fold improvement in encoding addition efficiency compared to PYXIS, with neighbor query speeds reaching sixfold and 12-fold acceleration at odd and even levels, respectively.