Unified Multi-structural Element Modeling Methods Using Icosahedral Discrete Global Grid Systems

Discrete global grid systems (DGGS), which provide the reference framework for next-generation Digital Earth, recursively divide the Earth’s surface into discrete multi-resolution hierarchies and support multi-source spatial data fusion and location-related event simulation. Existing DGGS research has primarily focused on cell centers, and therefore lacks rigorous mathematical modeling of multi-structural elements that comprise centers, edges, and vertices, resulting in inefficient data exchange and inaccurate data modeling. To this end, a unified mathematical modeling method was proposed for hexagonal multi-structural elements of grid systems based on triangles. The code operation principles and indexing conversion relationships for multi-structural elements were also deduced. The proposed method provides a unified mathematical model which reveals the mathematical essence of hexagonal multi-structural elements and has theoretical significance for future research on hierarchical data structures. Furthermore, conversion between multi-structural elements of triangles and hexagons, was achieved with low algorithmic complexity. Finally, the use of multi-structural elements can improve the accuracy of data modeling and spatial analysis, which has important applications for the representation of geospatial location data.