摘要
科技发展推动人类的空间活动范围遍及陆海空天各个空间层次，空间观测范围扩大到地球系统各个圈层，空间探测能力不断增强。越来越多的科学研究和军事经济活动呈现出全球立体分布、跨空间层次、跨时空尺度、跨专业领域的特点，需要建立在统一的全球空间基础框架和地球各圈层海量、多源空间信息集成的基础上。因此，构建圈层空间网格，建立陆海空天统一空间框架成为一个重要的研究课题。
本文围绕圈层空间网格的理论问题和关键算法展开研究，主要研究成果包括：
1、全面回顾地理空间网格领域的主要成果，总结分析现有空间网格模型中存在的问题，提出圈层空间网格是地理空间网格沿着从平面网格到立体网格，从球面网格到球体网格的轨迹，发展到地球圈层空间的新方向。
2、首次提出圈层空间网格。围绕圈层空间网格的基础理论，提出了圈层空间与圈层空间网格两个新概念，对其概念的内涵与特征进行了分析论述。提出了构建圈层空间网格的基本思路，并与球体退化八叉树网格和地球系统圈层进行了比较，分析了圈层空间网格的理论特征。最后得出圈层空间网格的6点推论。为后续章节研究圈层空间网格的剖分编码模型、实体表达模型与实体空间拓扑关系描述模型、数据集成存储模型奠定理论基础。
3、设计实现了圈层空间网格扩展八叉树（e-Octree）剖分编码模型。提出了e-Octree剖分思路和规则性剖分、退化性剖分、适应性剖分等3种剖分机制。给出剖分曲线、剖分曲面、剖分体元的数学形式，利用微分几何证明了剖分曲线形成的圈层面网格具有等面积特性。提出e-Octree圈体编码模型，对应3种剖分机制设计并实现了圈体编码结构及其与地理坐标换算算法。实验表明，e-Octree剖分编码模型在保持网格统一性的同时提高网格剖分与编码的灵活性，为陆海空天空间实体表达和空间信息组织提供了统一框架。
4、提出并构建了体目标的COG网格表达模型和PNM拓扑关系描述模型。利用数字拓扑理论深入分析体目标网格表达的拓扑连续性问题，提出了拓扑连续八叉树网格（COG）概念，设计了保持体目标拓扑连续性的COG网格生成算法。提出了描述体目标3维拓扑关系的点邻域模型（PNM），定义了点邻域概念及其结构类型的形式化描述，设计实现了3维拓扑关系的编码方法，通过实例证明了PNM区分出的3维拓扑关系种类比9IM更多。COG模型与PNM模型为圈层空间网格的实体表达和空间关系分析提供了理论方法。
5、设计实现了基于空间填充曲线（SFC）的网格数据存取机制。提出了SFC聚簇数模型，从理论上证明连续SFC具有更高的存取效率。以连续SFC Hilbert曲线为基础，设计实现了规则网格Hilbert存储索引。面向多源、多分辨率数据网格存储，提出紧致Hilbert索引，以Gray码为基础建立紧致Hilbert曲线排序算法，给出紧致Hilbert索引的构造算法。实验表明，紧致Hilbert索引在存储效率、查询性能明显优于标准Hilbert索引。
The range of human spatial activities have been promoted to various levels of space such asland, sea, air, sky, while spatial observation scope has been enlarged to every sphere shell ofearth systems, and spatial exploration ability be enhanced. More and more scientific researchand military and economic activities have shown itself such characteristics as globalthree-dimensional distribution, multi-spatial level, multi-temporal and spatial scale, crossspecialties, so that these are depended on the construction of global uniform space frameworkand integration of earth sphere shells information. Therefore, the construction of sphere shellspace grid and the establishment of uniform space framework of land, sea, air, sky becomes animportant problem.
The followings are what we have done in this dissertation:
1. The comprehensive review of current achievements has been taken firstly, and theseproblems in existing space grid models have been pointed out. Then, the sphere shell space gridis the new direction of geographic space grid has been brought forward, which is following thedevelopment of geographic space grid from plan grid to solid grid, from spherical surface tosphere interior.
2. The Sphere Shell Space Grid is putted forward for the first time. The basic conception ofSphere Shell Space and Sphere Shell Space Grid are proposed, and then their connotations andtheoretical characteristics have been discussed in details. The basic idea of subdivision of SphereShell Space Grid is that, the earth spherical surface is set as starting surface; earth has beendivided into several homocentric datum sphere shells along the radial direction, and then the gridsubdivision of each datum sphere shell has been taken place. And Sphere Shell Space Grid iscomared with Sphere Degenerated Octree Grid and Earth System Spheres. At last, there are6ratiocinations concluded from theoretical analysis. This provides a primary guide for theconstruction of Sphere Shell Space Grid.
3. The extended-Octree (e-Octree) subdivision model of Sphere Shell Space Grid isproposed. The design idea and three subdivision mechanisms including regular subdivision,degraded subdivision and adaptive subdivision are presented first. The mathematical form ofpartition curve, partition surface and partition voxel are given out. And then the equal areaproperty of sphere shell surface grid generated by the partition curve has been proved usingdifferential geometry. The e-Octree grid coding model is proposed according to three subdivisionmechanisms, and also the algorithm of conversion between grid code and geographic coordinate.Experiments have shown that e-Octree subdivision and code model has improved the agile ability while holding coherence. This is favorable for spatial entity representation and spatialinformation organization.
4. The COG model and PNM model used for volume object representation and topologicalrelation description is proposed. Firstly, the topological continuity of discrete representation ofvolume object is analyzed based on digital topology, and then the continuous octree grid (COG)concept is given out, and COG generation algorithm is presented up. Secondly, the topologicalrelationship description problem between two volume objects has been addressed on. Theformalization of point neighborhood concept and its configuration types are defined. The3Dtopological relationship is coded based on point neighborhood configuration. Typical examplesanalysis has shown that more kinds of topological relationships have been classified by PNMthan9IM.
5. The storage and access mechanism based on space filling curve (SFC) for Sphere ShellSpace Grid is brought forward. Firstly, the SFC clustering number model is putted forward, andthen the conclusion that continuous SFCs is more efficiency than un-continuous SFCs is provedtheoretically. Secondly, the Hilbert SFC is chosen for spatial data index construction, and theregular octree grid Hilbert index is presented. But it is not sufficient for multi-source,multi-resolution data storage and access, so the compact Hilbert index is presented, which isbased on Gray Code ordering algorithm. The construction of compact Hilbert index is given indetails. Experiments have shown that compact Hilbert index is better than standard Hilbert indexin storage and query evidently.
引文
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