發(fā)布時間：2018-12-16 12:28

【摘要】：球面離散網(wǎng)格模型是一種能無限細分，并且不改變形狀的球面擬合網(wǎng)格模型，它具有層次性、連續(xù)性和近似均勻等特征，有效避免了傳統(tǒng)的平面網(wǎng)格在表達全球數(shù)據(jù)時存在的數(shù)據(jù)斷裂、形變和拓撲不一致等問題，而且能方便地在網(wǎng)格計算環(huán)境下實現(xiàn)對空間信息資源的整合、共享與利用。近年來，國際學術(shù)界和相關(guān)應(yīng)用部門從不同的側(cè)面對全球離散網(wǎng)格模型進行了研究，在網(wǎng)格構(gòu)建方面，基于正多面體剖分的球面網(wǎng)格是全球離散網(wǎng)格模型研究的熱點。 多面體表面的層次剖分圖形主要有三角形、菱形、六邊形等，在這些網(wǎng)格剖分圖形中，菱形網(wǎng)格幾何結(jié)構(gòu)簡單，具有方向一致性、徑向?qū)ΨQ性和平移相合性等優(yōu)點，是一種非常優(yōu)秀的網(wǎng)格模型。目前對菱形格網(wǎng)的研究大多涉及的是格網(wǎng)的結(jié)構(gòu)特征分析和可視化的應(yīng)用，并沒有對菱形網(wǎng)格的剖分方法進行系統(tǒng)地總結(jié)，也沒有對球面層次格網(wǎng)的幾何形變分布規(guī)律及收斂閾值等進行分析，直接影響了格網(wǎng)數(shù)據(jù)的質(zhì)量和使用領(lǐng)域。本文以球面菱形網(wǎng)格作為研究對象，主要的研究內(nèi)容有以下幾點： 1、綜合分析了球面菱形網(wǎng)格的構(gòu)建方法，總結(jié)了四種基于球面四叉樹剖分的菱形網(wǎng)格構(gòu)建方案，參照不同學者對理想網(wǎng)格評價的標準，以菱形的長短軸之比、最大最小面積比和菱形網(wǎng)格長短軸比均方差和面積均方差作為菱形網(wǎng)格幾何變形的度量標準，對這四種網(wǎng)格的形變進行了定量的計算,通過對比分析得出，基于正二十面體大圓弧剖分的菱形網(wǎng)格在角度形變和面積形變上都是最優(yōu)的，基于正八大圓弧剖分的菱形網(wǎng)格次之，然后是基于正八面體混合剖分的菱形網(wǎng)格，基于正八面體經(jīng)緯剖分的菱形網(wǎng)格質(zhì)量最差。 2、參照球面網(wǎng)格編碼的標準，研究了球面菱形網(wǎng)格的三元組編碼，設(shè)計了網(wǎng)格三元組編碼和地理坐標之間的轉(zhuǎn)換算法，該算法適用于本文總結(jié)的四種球面菱形網(wǎng)格，并且四種網(wǎng)格和地理坐標轉(zhuǎn)換的求解過程是完全一致的，區(qū)別在于網(wǎng)格剖分中點的求解結(jié)果不同，通過轉(zhuǎn)換方法可知，這四種網(wǎng)格的編碼和地理坐標之間的轉(zhuǎn)換精度和復雜度是相同的。在三元組編碼的基礎(chǔ)上，研究了基于正八面體和正二十面體菱形網(wǎng)格的鄰近搜索方法，分別給出了基于這兩種多面體剖分的菱形網(wǎng)格鄰近關(guān)系表，分析得出基于正八面體和正二十面體菱形網(wǎng)格鄰近搜索的復雜度是相似的。由于三元組編碼作為網(wǎng)格數(shù)據(jù)存儲模型僅適于少量的數(shù)據(jù)操作，因此本文提出了以Hilbert編碼代替三元組網(wǎng)格編碼作為網(wǎng)格數(shù)據(jù)的存儲模型，從而解決了二維編碼空間到一維存儲空間的問題。 3、研究了球面菱形網(wǎng)格對矢量和柵格數(shù)據(jù)的集成方法，，通過矢量和柵格數(shù)據(jù)在四種球面菱形網(wǎng)格的集成的可視化，驗證了本文對這四種球面菱形網(wǎng)格形變定量分析得出的結(jié)論，同樣也證明了網(wǎng)格編碼方案是可行的、準確的。
[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.
【學位授予單位】：江西理工大學
【學位級別】：碩士
【學位授予年份】：2013
【分類號】：P208

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