全球离散格网系统是数字化的多分辨率地球参考模型,在结构上支持多源位置相关信息的融合处理.基于正二十面体剖分的六边形全球离散格网系统具有较好的几何属性,相关研究已引起学术界的广泛关注,如何建立封闭球面上的六边形格网系统编码运算方案是当前的研究难点.研究表明,基于正多面体剖分的全球离散格网系统与正多面体格网系统拓扑等价,两者的编码运算结果也完全相同.根据这一原理,结合四孔六边形格网系统在正二十面体表面的分布特点,基于六边形格点四叉树定义顶点瓦片与面瓦片结构,提出了正二十面体四孔六边形格网系统编码运算方案.该方案通过高效编码运算实现了格网单元跨面操作,克服了现有成果需借助低效浮点数运算实现相同操作的缺陷.对比实验表明,该方案的跨面邻近单元搜索效率约是六边形四元平衡结构方案的19.6倍.

The polyhedral discrete global grid system (DGGS) is a multi-resolution discrete earth reference model supporting the fusion and processing of multi-source geospatial information. The orientation of the polyhedron relative to the earth is one of its key design choices, used when constructing the grid system, as the efficiency of indexing will decrease if local areas of interest extend over multiple faces of the spherical polyhedron. To date, most research has focused on global-scale applications while almost no rigorous mathematical models have been established for determining orientation parameters. In this paper, we propose a method for determining the optimal polyhedral orientation of DGGSs for areas of interest on a regional scale. The proposed method avoids splitting local or regional target areas across multiple polyhedral faces. At the same time, it effectively handles geospatial data at a global scale because of the inherent characteristics of DGGSs. Results show that the orientation determined by this method successfully guarantees that target areas are located at the center of a single polyhedral face. The orientation process determined by this novel method reduces distortions and is more adaptable to different geographical areas, scales, and base polyhedrons than those employed by existing procedures.

Hexagonal discrete global grid systems are the preferred data models supporting multisource geospatial information fusion. Related research has aroused widespread concern in the academic community, and hierarchical indexing algorithms are one of the main research focuses. In this paper, we propose an algorithm for indexing the cell of a ringed spatial area based on a hexagonal lattice quad-tree (HLQT) structure and the indexing characteristics. First, we design a single-resolution indexing algorithm in which indexing starts from the initial quad tree and expands ring by ring using coding operations, and a quad-tree structure is applied to accelerate this process. Second, the hierarchical indexing algorithm is implemented based on single-resolution indexing, and a pyramid hierarchical model is established. Finally, we perform comparison experiments with existing algorithms. The results of the experiments indicate that the single-level indexing efficiency of the proposed algorithm is approximately twice that of the traditional method and that the hierarchical indexing efficiency is approximately 67 times that of the traditional method. These findings verify the feasibility and superiority of the algorithm proposed in this paper.

矢量数据是地球空间数据的重要组成部分,数据离散化是其与栅格数据进行同构处理的重要环节,其中离散线的生成是基本问题.针对三角形格网离散线生成算法的不足,提出了借助弱对偶六边形格网,建立等效三角形格网离散线数学模型,并通过降维方式求解的研究方法.首先,根据三角形格网与六边形格网之间的弱对偶关系,基于六边形格网建立等价的三角形格网离散线模型;然后,利用降维思想将二维离散线模型等价变换为一维闭合路径求解;最后,设计并实现了平面三角形格网离散线转化生成算法.将该算法分别与Freeman算法和全路径算法进行了对比实验,实验结果表明,该算法的运算效率可达同类算法的9～10倍,且效果更优,可应用于矢量数据的实时格网化、地形建模、空间分析、模拟仿真等领域,应用前景广阔.

Grid system is a multi-resolution raster data structure, which is widely applied in organization, processing and analysis of multi-scale geospatial data. Research on hexagon grid system with important geometric attributes has attracted extensive attention in academia. Description and calculation of hierarchical relation is one of the research difficulties. According to the complex radix number theory and the affiliation of grid cells in interval hierarchy, the mathematical model of the planar aperture 4 hexagon grid system is established. Based on these, the equivalent encoding scheme is proposed, the encoding operations are defined and the rules of them are generalized. Meanwhile, the coding index and transformation between code and Cartesian coordinates are designed. The results of contrast experiments show that the proposed encoding scheme has structural symmetry compared with similar schemes, which can significantly improve the efficiency of encoding operation and has practical application potential.

Discrete global grid system is a new data model which supports the fusion processing of multi-source geospatial information.Research into hexagon grid systems that have excellent geometric attributes has raised academic concern.Description of hierarchical relation and design of encoding scheme are research difficulties.According to the characteristics of the planar aperture 4 hexagon grid system, this paper designs an encoding scheme named Hexagon Lattice Quad Tree (HLQT).Code operations are defined, rules of them are generalized and based on these, transformation between 2-dimensional coordinates and addressing codes is implemented.Compared with similar schemes, HLQT overcomes the disadvantages caught by encoding schemes which divide the odd and even levels or mix the vertices and centers for encoding.In addition, operation rules of HLQT are simpler and easier for complementation.Contrast experiments show that the add operation efficiency of HLQT is about 6 times that of PYXIS and about 5 times that of HQBS, the efficiency of the transform algorithm from 2-dimensional coordinates to codes is about 5 times that of HQBS, and the efficiency of the transform algorithm from codes to 2-dimensional coordinates is about 3 times that of HQBS.

Discrete Global Grid Systems (DGGSs) are spatial references that use a hierarchical tessellation of cells to partition and address the entire globe. They provide an organizational structure that permits fast integration between multiple sources of large and variable geospatial data sufficient for visualization and analysis. Despite a significant body of research supporting hexagonal DGGSs as the superior choice, the application thereof has been hindered owing in part to the lack of a rational hierarchy with an efficient addressing system. This paper presents an algebraic model of encoding scheme for the Aperture 3 Hexagonal (A3H) DGGS. Firstly, the definition of a grid cell, which is composed of vertices, edges, and a center, is introduced to describe fundamental elements of grids. Secondly, by identifying the grid cell with its center, this paper proves that cell centers at different levels can be represented exactly using a mixed positional number system in the complex plane through the recursive geometric relationship between two successive levels, which reveals that grid cells are essentially special complex radix numbers. Thirdly, it is shown that through the recursive geometric relationship of successive odd or even levels, the mixed positional number system can also be applied to uniquely represent cell centers at different levels under specific constraint conditions, according to which the encoding scheme is designed. Finally, it is shown that by extending the scheme to 20 triangular faces of the regular icosahedron, multi-resolution grids on closed surfaces of the icosahedron are addressed perfectly. Contrast experiments show that the proposed encoding scheme has the advantages of theoretical rigor and high programming efficiency and that the efficiency of cross-face adjacent cell searching is 242.9 times that of a similar scheme. Moreover, the proposed complex radix number representation is an ideal formalized description tool for grid systems. The research ideas introduced herein can be used to create a universal theoretical framework for DGGSs.

Vectors are a key type of geospatial data, and their discretization, which involves solving the problem of generating a discrete line, is particularly important. In this study, we propose a method for constructing a discrete line mathematical model for a triangular grid based on a "weak duality" hexagonal grid, to overcome the drawbacks of existing discrete line generation algorithms for a triangular grid. First, a weak duality relationship between triangular and hexagonal grids is explored. Second, an equivalent triangular grid model is established based on the hexagonal grid, using this weak duality relationship. Third, the two-dimensional discrete line model is solved by transforming it into a one-dimensional optimal wandering path model. Finally, we design and implement the dimensionality reduction generation algorithm for a discrete line in a triangular grid. The results of our comparative experiment indicate that the proposed algorithm has a computation speed that is approximately 10 times that of similar existing algorithms; in addition, it has better fitting effectiveness. Our proposed algorithm has broad applications, and it can be used for real-time grid transformation of vector data, discrete global grid system (DGGS), and other similar applications.

Discrete Global Grid System is a new data model which supports the fusion processing of multi-source spatial data.The Fourier Transform connects spatial domain and frequency domain which is significant to the enhancement of remote sensing image based on grid system.According to the subdivision scheme of aperture 3 hexagonal grid,a regular hexagonal structure is designed in this paper.The two-dimensional discrete Fourier on this structure can be transformed into one-dimensional transform which can be accelerated by Cooley-Tukey algorithm.A remote-sensing image is used to verify the proposed method.The experimental result shows the Fast Fourier Transformation investigated in this paper is correct and efficient with a complexity of N log2N,with the increase of data,the efficiency will grow in an exponential manner.

Global discrete grid system will subdivide the earth recursively to form a multi-resolution grid hierarchy with no Overlap and seamless which help build global uniform spatial reference datum and multi-source data processing mode which takes the position as the object and in the aspect of data structure supports the organization, process and analysis of the remote sensing big data. This paper adopts the base transform to realize the mutual transformation of square pixel and hexagonal pixel. This paper designs the corresponding discrete Fourier transform algorithm for any lattice. Finally, the paper show the result of the DFT of the remote sensing image of the hexagonal pixel.