球面菱形网格剖分、编码及数据集成研究

发布时间：2018-12-16 12:28

【摘要】：球面离散网格模型是一种能无限细分，并且不改变形状的球面拟合网格模型，它具有层次性、连续性和近似均匀等特征，有效避免了传统的平面网格在表达全球数据时存在的数据断裂、形变和拓扑不一致等问题，而且能方便地在网格计算环境下实现对空间信息资源的整合、共享与利用。近年来，国际学术界和相关应用部门从不同的侧面对全球离散网格模型进行了研究，在网格构建方面，基于正多面体剖分的球面网格是全球离散网格模型研究的热点。多面体表面的层次剖分图形主要有三角形、菱形、六边形等，在这些网格剖分图形中，菱形网格几何结构简单，具有方向一致性、径向对称性和平移相合性等优点，是一种非常优秀的网格模型。目前对菱形格网的研究大多涉及的是格网的结构特征分析和可视化的应用，并没有对菱形网格的剖分方法进行系统地总结，也没有对球面层次格网的几何形变分布规律及收敛阈值等进行分析，直接影响了格网数据的质量和使用领域。本文以球面菱形网格作为研究对象，主要的研究内容有以下几点： 1、综合分析了球面菱形网格的构建方法，总结了四种基于球面四叉树剖分的菱形网格构建方案，参照不同学者对理想网格评价的标准，以菱形的长短轴之比、最大最小面积比和菱形网格长短轴比均方差和面积均方差作为菱形网格几何变形的度量标准，对这四种网格的形变进行了定量的计算,通过对比分析得出，基于正二十面体大圆弧剖分的菱形网格在角度形变和面积形变上都是最优的，基于正八大圆弧剖分的菱形网格次之，然后是基于正八面体混合剖分的菱形网格，基于正八面体经纬剖分的菱形网格质量最差。 2、参照球面网格编码的标准，研究了球面菱形网格的三元组编码，设计了网格三元组编码和地理坐标之间的转换算法，该算法适用于本文总结的四种球面菱形网格，并且四种网格和地理坐标转换的求解过程是完全一致的，区别在于网格剖分中点的求解结果不同，通过转换方法可知，这四种网格的编码和地理坐标之间的转换精度和复杂度是相同的。在三元组编码的基础上，研究了基于正八面体和正二十面体菱形网格的邻近搜索方法，分别给出了基于这两种多面体剖分的菱形网格邻近关系表，分析得出基于正八面体和正二十面体菱形网格邻近搜索的复杂度是相似的。由于三元组编码作为网格数据存储模型仅适于少量的数据操作，因此本文提出了以Hilbert编码代替三元组网格编码作为网格数据的存储模型，从而解决了二维编码空间到一维存储空间的问题。 3、研究了球面菱形网格对矢量和栅格数据的集成方法，，通过矢量和栅格数据在四种球面菱形网格的集成的可视化，验证了本文对这四种球面菱形网格形变定量分析得出的结论，同样也证明了网格编码方案是可行的、准确的。
[Abstract]:Spherical discrete mesh model is a spherical fitting mesh model with infinite subdivision and no change in shape. It has the characteristics of hierarchy, continuity and approximate uniformity. It can effectively avoid the problems of data rupture, deformation and topology inconsistency in the representation of global data in the traditional planar grid, and it can easily realize the integration, sharing and utilization of spatial information resources in grid computing environment. In recent years, international academic circles and relevant application departments have studied the global discrete grid model from different aspects. In the aspect of grid construction, spherical mesh based on regular polyhedron is a hot topic in the research of global discrete grid model. The hierarchical patterns of polyhedron surface are mainly triangular, rhombic, hexagonal, etc. Among these meshes, the rhombic mesh has the advantages of simple geometric structure, uniform direction, radial symmetry and translation consistency, etc. Is a very good mesh model. At present, most of the researches on rhombic grid are related to the application of structural feature analysis and visualization of grid, and there is no systematic summary of the method of rhombus mesh generation. The distribution of geometric deformation and convergence threshold of spherical hierarchical grid are not analyzed, which directly affects the quality and application of grid data. In this paper, the spherical rhombus mesh is taken as the research object. The main research contents are as follows: 1. The construction method of spherical rhombic mesh is analyzed synthetically, and four kinds of rhombic mesh construction schemes based on spherical quadtree division are summarized. Referring to the criteria for the evaluation of ideal meshes by different scholars, the ratio of long and short rhombic meshes, the maximum to minimum area ratio and the mean square deviation of rhombic grid long-long axis ratio and area mean square are taken as the measurement criteria of geometric deformation of rhombic meshes. The deformation of these four meshes is calculated quantitatively. By comparison and analysis, it is concluded that the rhombus mesh based on the large arc division of the normal icosahedron is optimal in both angular and area deformation. The rhombus mesh based on octahedron arc is the second, then the rhombohedral mesh based on octahedron, and the rhombohedral mesh based on octahedron warp and weft is the worst. 2. Referring to the standard of spherical mesh coding, the ternary coding of spherical rhombic mesh is studied, and the transformation algorithm between grid ternary coding and geographical coordinates is designed. The algorithm is suitable for four spherical rhombic meshes summarized in this paper. And the solution process of the four grid and geographical coordinate transformation is completely consistent, the difference is that the results of the meshes are different. The conversion accuracy and complexity between the four mesh codes and geographical coordinates are the same. On the basis of triple coding, the neighbor search methods based on octahedron and icosahedron rhombic grids are studied, and the adjacent relation tables of rhombic meshes based on these two polyhedrons are given, respectively. The complexity of rhombic search based on octahedron and icosahedron is similar. Because triple coding as a grid data storage model is only suitable for a small number of data operations, this paper proposes a storage model of grid data using Hilbert coding instead of triple trellis coding. Thus, the problem from two-dimensional coding space to one-dimensional storage space is solved. 3. The integration method of spherical rhombus mesh for vector and grid data is studied, and the visualization of integration of vector and grid data in four spherical rhombic meshes is presented. The conclusion of quantitative analysis of the four spherical rhombic mesh deformation is verified, and it is also proved that the scheme is feasible and accurate.
【学位授予单位】：江西理工大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：P208

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