Efficient encoding and spatial operation scheme for aperture 4 hexagonal discrete global grid system

Discrete global grid systems (DGGSs) are considered to be promising structures for global geospatial information representation. Square and triangular DGGSs have had the advantage over hexagonal ones in geospatial data processing over the past few decades. Despite a significant body of research supporting hexagonal grids as the superior alternative, the application thereof has been hindered partly owing to the lack of a hierarchy. This study presents an original perspective to combine two types of aperture 4 hexagonal discrete grid systems into a hierarchy. Each cell of the hierarchy is assigned a unique code using a linear quadtree that constructs the hexagonal quaternary balanced structure (HQBS). The mathematical system described by HQBS addressing and the vector operations, including addition, subtraction, multiplication, and division, are defined. Essential spatial operations for HQBS cell retrieval, transformation between HQBS codes and other coordinate systems, and arrangement of HQBS cells on spherical surfaces were studied and implemented. The accuracy and efficiency of algorithms were validated through experiments. The results indicate that the average efficiency of cell retrieval using the HQBS is higher than that using other schemes, thus proving it to be more efficient