Hierarchical evolution model and coding calculation of three-dimensional Hilbert curve

The coding calculation of grid cells is the core of the discrete global grid system, which supports efficient calculation of indexing and analysis. Hilbert curve has the characteristics of high clustering and strong continuity, and is an important tool for global discrete grid coding. The lattice element coding using Hilbert curve realizes the coordinate equivalent dimensionality reduction expression, but the research on the basic theoretical problems of grid coding still not complete. In this paper, the hierarchical evolution relationship of the three-dimensional Hilbert curve in the octree three-dimensional grid is used as a breakthrough. The state matrix and the evolution matrix are used to construct a hierarchical evolution model, and then the calculation methods of Cartesian coordinates to Hilbert codes and adjacent grid Hilbert codes are designed respectively. Compared with the existing algorithms, the algorithm in this paper is based on a hierarchical evolution model, which avoids cumbersome iteration steps and conversion steps, and the algorithm flow is simple and straightforward. The experimental results show that the calculation efficiency of Cartesian coordinates to Hilbert codes in this paper is "7%~23%" higher than that of the iterative algorithm, and the calculation efficiency of neighbor grid elements Hilbert codes is 4.0~4.5 times higher than that of the conversion algorithm.