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.

中文翻译：

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一套基于GeoSOT-3D的积分网格编码代数运算

随着收集到的空间信息（2D/3D）量的增加，这些海量数据的实时处理成为亟待解决的问题之一。将物理地球离散为数字网格地球，并为每个网格分配一个完整的可计算代码，已成为加速实时处理的有效方式。研究人员针对特定场景下的空间计算提出了优化算法。然而，仍然缺乏一套完整的使用网格编码进行实时处理的算法。为了解决这个问题，提出了一个精心设计的、用于 GeoSOT-3D（多层经纬度网格模型）的整体网格编码代数运算框架。通过将传统的基于经纬度的浮点计算转化为二元运算，算法的复杂度大大降低。然后我们介绍了设计的详细算法，包括基本运算、向量运算、代码转换运算、空间运算、度量运算、拓扑关系运算和集合运算。为了验证上述算法的可行性和效率，我们使用C++语言开发了一个实验平台（包括主要算法，未来可能会扩展更多算法）。然后，我们生成随机数据并进行实验。实验结果表明，该计算框架是可行的，能够显着提高空间处理效率。代数运算框架有望支持大型地理空间数据检索和分析，并在并行和分布式计算之上实现复兴，