As the amount of collected spatial information (2D/3D) increases, the real-time processing of these massive data is among the urgent issues that need to be dealt with. Discretizing the physical earth into a digital gridded earth and assigning an integral computable code to each grid has become an effective way to accelerate real-time processing. Researchers have proposed optimization algorithms for spatial calculations in specific scenarios. However, a complete set of algorithms for real-time processing using grid coding is still lacking. To address this issue, a carefully designed, integral grid-coding algebraic operation framework for GeoSOT-3D (a multilayer latitude and longitude grid model) is proposed. By converting traditional floating-point calculations based on latitude and longitude into binary operations, the complexity of the algorithm is greatly reduced. We then present the detailed algorithms that were designed, including basic operations, vector operations, code conversion operations, spatial operations, metric operations, topological relation operations, and set operations. To verify the feasibility and efficiency of the above algorithms, we developed an experimental platform using C++ language (including major algorithms, and more algorithms may be expanded in the future). Then, we generated random data and conducted experiments. The experimental results show that the computing framework is feasible and can significantly improve the efficiency of spatial processing. The algebraic operation framework is expected to support large geospatial data retrieval and analysis, and experience a revival, on top of parallel and distributed computing, in an era of large geospatial data.
Variations of the Catalan numbers from some nonassociative binary operations
