Abstract
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.
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The data that support the findings of this study are available in figshare.com with the identifier(s) https://figshare.com/s/62e8675cc3b1277d8537.
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Acknowledgements
We are grateful to the anonymous reviewers for helpful and valuable comments on earlier drafts. Thanks also to the editors of Mathematical Geosciences. We would like to thank Editage (www.editage.cn) for English language editing.
Funding
This work was supported by the special science fund for the Innovation Ecosystem Construction of the National Supercomputing Center in Zhengzhou [NO 0.201400210100] and the National Defense Science and Technology Innovation Fund of the Chinese Academy of Sciences [NO 0.20-163-14-LZ-001-003-01].
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Xinhai Huang: designed and performed the study. Junjie Ding: ran the experiments and created figures. Jin Ben: designed, evaluated and supervised the study; created codes; funding acquisition. Jianbin Zhou: reviewed and edited the manuscript. Qishuang Liang: collected the experimental data; validated the experimental results.
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Huang, X., Ding, J., Ben, J. et al. Unified Multi-structural Element Modeling Methods Using Icosahedral Discrete Global Grid Systems. Math Geosci 56, 361–386 (2024). https://doi.org/10.1007/s11004-023-10082-w
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DOI: https://doi.org/10.1007/s11004-023-10082-w