地球剖分格网研究进展综述

doi:10.11947/j.AGCS.2016.F001

摘要/Abstract

摘要： 通过梳理近十多年来地球剖分格网的相关研究文献，从剖分建模（四边形剖分、等积剖分和立体剖分）、编码计算（层次编码运算、填充曲线编码运算和整数坐标编码运算）、质量评价（评价准则、评价因子和层次传播趋势）及典型应用（政府机构应用、商业系统应用和行业领域应用）等4个方面，对该领域研究进展进行了系统的分类分析，较为详细地给出了不同格网模型的结构特点、适用模式及其存在的不足。最后总结出地球剖分格网在理论基础完备性、格网计算高效性及格网质量可靠性等方面研究的前沿问题。

关键词: 地球剖分格网, 格网编码计算, 格网质量评价

Abstract: By analyzing the related literatures on the earth tessellation grid (ETG) in recent 10 years, the research achievements in this field are systematic reviewed in four aspects, i.e. the earth subdivision modeling (include quadrangle subdivision, equal-area subdivision and 3D subdivision), encoding computation (include hierarchical encoding computation, filling curve encoding computation and integer coordinate encoding computation), grid quality assessment (include evaluation criteria, evaluation factors, and propagation trend in diffferent levels) and typical applications (include government agency applications,business software applications and industry applications). The structural characteristics, applicable models and their shortcomings in the different grid models are given in details. Finally, some advanced academic problems in the ETG are given based on the completeness of basic theory, the efficiency of grid computing, and the reliability of grid quality.

Key words: earth tessellation grid, grid encoding computing, grid quality evaluation

中图分类号:

P208

赵学胜, 贲进, 孙文彬, 童晓冲. 地球剖分格网研究进展综述[J]. 测绘学报, 2016, 45(S1): 1-14.

ZHAO Xuesheng, BEN Jin, SUN Wenbin, TONG Xiaochong. Overview of the Research Progress in the Earth Tessellation Grid[J]. Acta Geodaetica et Cartographica Sinica, 2016, 45(S1): 1-14.

参考文献

[1] 周成虎, 欧阳, 马廷. 地理格网模型研究进展[J].地理科学进展, 2009, 28(5):657-662. ZHOU Chenghu, OU Yang, MA Ting. Progresses of Geographical Grid Systems Researches[J]. Progress in Geography, 2009, 28(5):657-662.
[2] DUTTON G H.A Hierarchical Coordinate System for Geoprocessing and Cartography[M].Berlin Heidelberg:Springer-Verlag,1999:230.
[3] KOLAR J. Representation of the Geographic Terrain Surface Using Global Indexing[C]//Proceeding of 12th International Conference on Geoinformatics. Sweden:University of Gävle, 2004:321-328.
[4] 胡鹏, 刘沛兰, 胡海, 等. 地球信息的度量空间和Global GIS[J]. 武汉大学学报(信息科学版), 2005, 30(4):317-321. HU Peng, LIU Peilan, HU Hai, et al. Metric Space of Earth Information and Global GIS[J]. Geomatics and Information Science of Wuhan University, 2005, 30(4):317-321.
[5] VAN OOSTEROM P, STOTER J. 5D Data Modelling:Full Integration of 2D/3D Space, Time and Scale Dimensions[C]//Proceedings of the 6th International Conference, GIScience 2010. Berlin Heidelberg:Springer-Verlag, 2010:310-324.
[6] PRUSS M. The Promise of Discrete Global Grid Systems[J]. GeoConnexion International Magazine, 2014, 7-8:16-17.
[7] 赵学胜, 王磊, 王洪彬, 等. 全球离散格网的建模方法及基本问题[J]. 地理与地理信息科学, 2012, 28(1):29-34. ZHAO Xuesheng, WANG Lei, WANG Hongbin, et al. Modeling Methods and Basic Problems of Discrete Global Grids[J]. Geography and Geo-Information Science, 2012, 28(1):29-34.
[8] CRIDER J E. A Geodesic Map Projection for Quadrilaterals[J]. Cartography and Geographic Information Science, 2009, 36(2):131-147.
[9] AMIRI A M, BHOJANI F, SAMAVATI F.One-to-Two Digital Earth[C]//Proceedings of the 9th International Symposium,ISVC 2013.Berlin Heidelberg:Springer-Verlag, 2013:681-692.
[10] BJØRKE J T, NILSEN S. Examination of a Constant-area Quadrilateral Grid in Representation of Global Digital Elevation Models[J]. International Journal of Geographical Information Science, 2004, 18(7):653-664.
[11] SEONG J C. Implementation of An Equal-Area Gridding Method for Global-Scale Image Archiving[J]. Photogrammetric Engineering & Remote Sensing,2005, 71(5):623-627.
[12] SAHR K. Location Coding on Icosahedral Aperture 3 Hexagon Discrete Global Grids[J]. Computers, Environment and Urban Systems,2008, 32(3):174-187.
[13] 赵学胜, 崔马军, 李昂, 等.球面退化四叉树格网单元的邻近搜索算法[J]. 武汉大学学报(信息科学版),2009, 34(4):479-482. ZHAO Xuesheng, CUI Majun, LI Ang, et al. An Adjacent Searching Algorithm of Degenerate Quadtree Grid on Spherical Facet[J]. Geomatics and Information Science of Wuhan University, 2009, 34(4):479-482.
[14] ZHOU Mengyun, CHEN Jing, GONGJianya.A Pole-Oriented Discrete Global Grid System:Quaternary Quadrangle Mesh[J].Computers & Geosciences, 2013, 61:133-143.
[15] SANTINI M, TARAMELLI A, SORICHETTA A. ASPHAA:A GIS-Based Algorithm to Calculate Cell Area on a Latitude-Longitude (Geographic) Regular Grid[J].Transactions in GIS, 2010, 14(3):351-377.
[16] HARRISON E, MAHDAVI-AMIRI A, SAMAVATI F.Analysis of Inverse Snyder Optimizations[M]//GAVRILOVA M L, TAN C J K. Transactions on Computational Science XVI.Berlin Heidelberg:Springer-Verlag,2012:134-148.
[17] TEANBY N A. An Icosahedron-Based Method for Even Binning of Globally Distributed Remote Sensing Data[J].Computers & Geosciences, 2006, 32(9):1442-1450.
[18] ROŞCA D, PLONKA G. Uniform Spherical Grids via Equal Area Projection from the Cube to the Sphere[J]. Journal of Computational and Applied Mathematics,2011, 236(6):1033-1041.
[19] ROŞCA D, PLONKA G. An Area Preserving Projection from the Regular Octahedron to the Sphere[J]. Results in Mathematics,2012,62(3-4):429-444.
[20] HOLHOŞ A, ROŞCA D.An Octahedral Equal Area Partition of the Sphere and Near Optimal Configurations of Points[J]. Computers &Mathematics with Applications, 2014, 67(5):1092-1107.
[21] LEOPARDI P. A Partition of the Unit Sphere into Regions of Equal Area and Small Diameter[J]. Electronic Transactions on Numerical Analysis,2006, 25:309-327.
[22] GÓRSKI K M, HIVON E, BANDAY A J, et al. HEALPix:A Framework for High-Resolution Discretization and Fast Analysis of Data Distributed on the Sphere[J].The Astrophysical Journal, 2005, 622(2):759-771.
[23] VAN LEEUWEN D, STREBE D. A "Slice-and-Dice" Approach to Area Equivalence in Polyhedral Map Projections[J].Cartography and Geographic Information Science, 2006, 33(4):269-286.
[24] MA Ting, ZHOU Chenghu, XIE Yichun, et al. A Discrete Square Global Grid System Based on the Parallels Plane Projection[J]. International Journal of Geographical Information Science, 2009, 23(10):1297-1313.
[25] MASSEY N. Feature Tracking on the Hierarchical Equal Area Triangular Mesh[J].Computers & Geosciences, 2012, 44:42-51.
[26] BECKERS B, BECKERS P. A General Rule for Disk and Hemisphere Partition into Equal-Area Cells[J]. Computational Geometry, 2012, 45(7):275-283.
[27] 吴立新, 余接情. 地球系统空间格网及其应用模式[J].地理与地理信息科学, 2012, 28(1):7-13. WU Lixin, YU Jieqing.Earth System Spatial Grid and Its Application Modes[J].Geography and Geo-Information Science, 2012, 28(1):7-13.
[28] 曹雪峰. 地球圈层空间网格理论与算法研究[D]. 郑州:解放军信息工程大学,2012. CAO Xuefeng.Research on Earth Sphere Shell Space Grid Theory and Algorithms[D]. Zhengzhou:The PLA Information Engineering University, 2012.
[29] 程承旗, 任伏虎, 濮国梁, 等. 空间信息剖分组织导论[M]. 北京:科学出版社, 2012. CHENG Chengqi, REN Fuhu, PU Guoliang, et al. Introduction to Spatial Information Partition and Organization[M].Beijing:Science Press, 2012.
[30] OHNO N, KAGEYAMA A. Visualization of Spherical Data by Yin-Yang Grid[J]. Computer Physics Communications, 2009, 180(9):1534-1538.
[31] STEMMER K, HARDER H, HANSEN U. A New Method to Simulate Convection with Strongly Temperature-and Pressure-Dependent Viscosity in a Spherical Shell:Applications to the Earth's Mantle[J]. Physics of the Earth and Planetary Interiors, 2006, 157(3-4):223-249.
[32] KOMATITSCH D, RITSEMA J, TROMP J. The Spectral-Element Method, Beowulf Computing, and Global Seismology[J]. Science, 2002, 298(5599):1737-1742.
[33] WU Lixin, YU Jieqing. A New Digital Earth Reference Model:Spheroid-Based 3D Grid for Earth System (3DGES)[C]//Proceedings of the SPIE 7840, 6th International Symposium on Digital Earth:Models, Algorithms, and Virtual Reality. Beijing:SPIE,2009:784003.
[34] 余接情, 吴立新, 訾国杰, 等. 基于SDOG的岩石圈多尺度三维建模与可视化方法[J].中国科学:地球科学, 2012, 42(5):755-763. YU Jieqing, WU Lixin, ZI Guojie, et al. SDOG-based Multi-Scale 3D Modeling and Visualization on Global Lithosphere[J]. Science China Earth Sciences, 2012, 55(6):1012-1020.
[35] KAGEYAMA A, SATO T.The "Yin-Yang Grid":An Overset Grid in Spherical Geometry[J]. Geochemistry, Geophysics, Geosystems, 2004, 5(9):Q09005.
[36] BAUMGARDNER J R. Three-Dimensional Treatment of Convective Flow in the Earth's Mantle[J]. Journal of Statistical Physics, 1985, 39(5):501-511.
[37] BALLARD S, HIPP J R, YOUNG C J. Efficient and Accurate Calculation of Ray Theory Seismic Travel Time Through Variable Resolution 3D Earth Models[J]. Seismological Research Letters, 2009, 80(6):989-999.
[38] BALLARD S, YOUNG C, HIPP J,et al.A global 3D P-velocity Model of the Earth's Crust and Mantle for Improved Event Location[C]//European Geosciences Union General Assembly, 2-7 May, 2010.Vienna, Austria:EGU, 2010.
[39] AMIRI A M, SAMAVATI F, PETERSON P. Categorization and Conversions for Indexing Methods of Discrete Global Grid Systems[J]. ISPRS International Journal of Geo-Information, 2015, 4(1):320-336.
[40] GOODCHILD M F,YANG Shiren. A Hierarchical Spatial Data Structure for Global Geographic Information Systems[J]. CVGIP:Graphical Models and Image Processing,1992, 54(1):31-44.
[41] SAHR K, WHITE D, KIMERLING A J. Geodesic Discrete Global Grid Systems[J]. Cartography and Geographic Information Science, 2003, 30(2):121-134.
[42] VINCE A, ZHENG X. Arithmetic and Fourier Transform for the PYXIS Multi-resolution Digital Earth Model[J].International Journal of Digital Earth, 2009, 2(1):59-79.
[43] 吕雪锋, 程承旗, 龚健雅, 等. 海量遥感数据存储管理技术综述[J].中国科学:技术科学, 2011, 41(12):1561-1573. LÜ Xuefeng, CHENG Chengqi, GONG Jianya, et al. Review of Data Storage and Management Technologies for Massive Remote Sensing Data[J]. Science China Technological Sciences, 2011, 54(12):3220-3232.
[44] GIBB R G. The rHEALPix Discrete Global Grid System[C]//Proceedings of the 9th Symposium of the International Society for Digital Earth (ISDE). Halifax:IOP, 2016, 34:012012.
[45] OTTOSON P, HAUSKA H. Ellipsoidal Quadtrees for Indexing of Global Geographical Data[J]. International Journal of Geographical Information Science, 2002, 16(3):213-226.
[46] SAHR K M. Discrete Global Grid Systems:A New Class of Geospatial Data Structures[D].Eugene, OR:University of Oregon, 2005.
[47] SAHR K. Central Place Indexing Systems:US,US9311350[P]. 2016-12-04.
[48] TONG Xiaochong, BEN Jin, WANG Ying, et al. Efficient Encoding and Spatial Operation Scheme for Aperture 4 Hexagonal Discrete Global Grid System[J]. International Journal of Geographical Information Science, 2013, 27(5):898-921.
[49] BOSCHETTI L, ROY D P, JUSTICE C O. Using NASA's World Wind Virtual Globe for Interactive Internet Visualization of the Global MODIS Burned Area Product[J]. International Journal of Remote Sensing, 2008, 29(11):3067-3072.
[50] 童晓冲, 贲进. 空间信息剖分组织的全球离散格网理论与方法[M].北京:测绘出版社, 2016. TONG Xiaochong, BEN Jin. The Discrete Global Grid Theory and Method of Spatial Information Partition Organization[M].Beijing:Surveying and Mapping Press, 2016.
[51] MOON B, JAGADISH H V, FALOUTSOS C, et al. Analysis of the Clustering Properties of the Hilbert Space-Filling Curve[J]. IEEE Transactions on Knowledge and Data Engineering, 2001,13(1):124-141.
[52] WHITE D. Global Grids from Recursive Diamond Subdivisions of the Surface of An Octahedron or Icosahedron[J].Environmental Monitoring and Assessment, 2000, 64(1):93-103.
[53] 白建军, 赵学胜, 陈军. 基于线性四叉树的全球离散格网索引[J].武汉大学学报(信息科学版), 2005, 30(9):805-808. BAI Jianjun, ZHAO Xuesheng, CHEN Jun. Indexing of Discrete Global Grids Using Linear Quadtree[J]. Geomatics and Information Science of Wuhan University, 2005, 30(9):805-808.
[54] BARTHOLDI JJ, GOLDSMAN P. Continuous Indexing of Hierarchical Subdivisions of the Globe[J]. International Journal of Geographical Information Science, 2001, 15(6):489-522.
[55] 袁文, 程承旗, 马蔼乃, 等. 球面三角区域四叉树L空间填充曲线[J].中国科学E辑工程科学材料科学, 2004, 34(5):584-600. YUAN Wen, CHENG Chengqi, MA Ainai, et al. LCurve for Spherical Triangle Region Quadtrees[J]. Science in China SeriesE Engineering & Materials Science, 2004, 47(3):265-280.
[56] MAHDAVI-AMIRIA, HARRISONE, SAMAVATIF. Hexagonal Connectivity Maps for Digital Earth[J]. International Journal of Digital Earth, 2015, 8(9):750-769.
[57] VINCE A. Indexing the Aperture 3 Hexagonal Discrete Global Grid[J].Journal of Visual Communication and Image Representation, 2006, 17(6):1227-1236.
[58] BEN Jin, TONG Xiaochong, CHEN Rongguo. A Spatial Indexing Method for the Hexagon Discrete Global Grid System[C]//Proceedings of the 18thInternational Conference onGeoinformatics.Beijing:IEEE,2010:1-5.
[59] 白建军.基于正八面体的四孔六边形球面格网编码及索引[J]. 遥感学报, 2011, 15(6):1125-1137. BAI Jianjun.Location Coding and Indexing Aperture 4 Hexagonal Discrete Global Grid Based on Octahedron[J]. Journal of Remote Sensing, 2011, 15(6):1125-1137.
[60] KIMERLING J A, SAHR K, WHITE D, et al.Comparing Geometrical Properties of Global Grids[J]. Cartography and Geographic Information Science, 1999, 26(4):271-288.
[61] GOODCHILD M E. Criteria for Evaluation of Global Grid Models for Environmental Monitoring and Analysis[R]. NCGIA Technical Report 94-7, 1994.
[62] CLARKE K C.Criteria and Measures for the Comparison of Global Geocoding Systems[M]//GOODCHILD M F, KIMERLING A J.Discrete Global Grids:A Web Book. Santa Barbara:University of California Press, 2002.
[63] HEIKES R, RANDALL D A. Numerical Integration of the Shallow-Water Equations on A Twisted Icosahedral Grid. Part II. A Detailed Description of the Grid and An Analysis of Numerical Accuracy[J]. Monthly Weather Review, 1995, 123(6):1881-1887.
[64] WHITE D, KIMERLING A J, SAHR K, et al. Comparing Area and Shape Distortion on Polyhedral-Based Recursive Partitions of the Sphere[J]. International Journal of Geographic Information Science, 1998, 12(8):805-827.
[65] GREGORY M J, KIMERLING A J, WHITE D, et al. A Comparison of Intercell Metrics on Discrete Global Grid Systems[J].Computers,Environment and Urban Systems, 2008, 32(3):188-203.
[66] 张斌, 苑争一, 赵学胜, 等. 一种基于模糊相似度的球面格网几何变形评价指标[J]. 地理与地理信息科学, 2015, 31(5):20-24, 29. ZHANG Bin, YUAN Zhengyi, ZHAO Xuesheng, et al. An Geometry Deformation Evaluation Index of the Spherical Discrete Grid Based on the Fuzzy Similarity[J]. Geography and Geo-Information Science, 2015, 31(5):20-24, 29.
[67] 明涛, 庄大方, 袁文, 等. 几种离散格网模型的几何稳定性分析[J]. 地球信息科学, 2007, 9(4):40-43, 99. MING Tao, ZHUANG Dafang, YUAN Wen, et al. Comparison of Geometrical Stability of Several Discrete Grid Systems[J]. Geo-Information Science, 2007, 9(4):40-43, 99.
[68] WHITE D, KIMERLING A, OVERTON W. Cartographic and Geometric Components of a Global Sampling Design for Environmental Monitoring[J]. Cartography and Geographic Information Systems, 1992, 19(1):5-22.
[69] KIMERLING J A, OVERTON S W, WHITE D.Statistical Comparison of Map Projection Distortions within Irregular Areas[J]. Cartography and Geographic Information Science, 1995, 22(3):205-221.
[70] 赵学胜, 孙文彬, 陈军. 基于QTM的全球离散格网变形分布及收敛分析[J]. 中国矿业大学学报, 2005, 34(4):438-442. ZHAO Xuesheng, SUN Wenbin, CHEN Jun. Distortion Distribution and Convergent Analysis of the Global Discrete Grid Based on QTM[J]. Journal of China University of Mining & Technology, 2005, 34(4):438-442.
[71] 赵学胜, 苑争一, 赵龙飞, 等. 一种改进的近似等面积QTM剖分模型[J].测绘学报, 2016, 45(1):112-118. DOI:10.11947/j.AGCS.2016.20140598. ZHAO Xuesheng, YUAN Zhengyi, ZHAO Longfei, et al. An Improved QTM Subdivision Model with Approximate Equal-Area[J]. ActaGeodaetica et CartographicaSinica, 2016, 45(1):112-118. DOI:10.11947/j.AGCS.2016.20140598.
[72] 白建军, 孙文彬, 赵学胜. 基于QTM的WGS-84椭球面层次剖分及其特点分析[J]. 测绘学报, 2011, 40(2):243-248. BAI Jianjun, SUN Wenbin, ZHAO Xuesheng. Character Analysis and Hierarchical Partition of WGS-84 Ellipsoidal Facet Based on QTM[J].Acta Geodaetica et Cartographica Sinica, 2011, 40(2):243-248.
[73] 贲进, 童晓冲, 张永生, 等. 球面等积六边形离散网格的生成算法及变形分析[J]. 地理与地理信息科学, 2006, 22(1):7-11. BEN Jin, TONG Xiaochong, ZHANG Yongsheng, et al. A Generation Algorithm of Spherical Equal-Area Hexagonal Discrete Gird and Analysis of Its Deformation[J]. Geography and Geo-Information Science, 2006, 22(1):7-11.
[74] PEIXOTO P S,BARROS S R M. Analysis of Grid Imprinting on Geodesic Spherical Icosahedral Grids[J]. Journal of Computational Physics, 2013, 237(1):61-78.
[75] 于文率, 童晓冲, 贲进, 等. 全球六边形离散格网的矢量线数据绘制精度控制[J]. 地球信息科学学报, 2015, 17(7):804-809. YU Wenshuai, TONG Xiaochong, BEN Jin,et al. The Accuracy Control in the Process of Vector Line Data Drawing in the Hexagon Discrete Global Grid System[J]. Journal of Geo-Information Science, 2015, 17(7):804-809.
[76] 陆楠. 导航定位网格编码研究[D].北京:北京大学, 2013. LU Nan.Research on Grid Encoding Navigation and Positioning[D].Beijing:Peking University,2013.
[77] PURSE M, OLIVER S, LEWIS A, et al. Specification of a Global Nested Grid System for Use by Australia and New Zealand[C]//Proceedings of the 7th eResearch Australasia Conference.Brisbane:[s.n.], 2013.
[78] SUESS M, MATOS P, GUTIE? RREZ A, et al. Processing of SMOS Level 1C Data onto a Discrete Global Grid[C]//Proceedings of IEEE International Geoscience and Remote Sensing Symposium.Anchorage, AK:IEEE,2004, 3:1914-1917.
[79] GeoFusion[EB/OL].[2010-03-11].http://www.geofusion.com/.
[80] PETERSON P. Closed-Packed Uniformly Adjacent, Multi-Resolutional Overlapping Spatial Data Ordering:US, US 8400451 B2[P]. 2011-09-13.
[81] PYXIS.The WorldView^TM Difference:A Digital Earth[EB/OL]. http://www.pyxisinnovation.com/Products/Studio.
[82] MAHDAVI-AMIRI A, HARRISON E, SAMAVATI F. Hexagonal Connectivity Maps for Digital Earth[J]. International Journal of Digital Earth, 2014. 8(9):1-20.
[83] MAHDAVI-AMIRI A, HARRISON E, SAMAVATI F. Hierarchical Grid Conversion[J]. Computer-Aided Design, 2016, 79:12-26.
[84] ALDERSON T, MAHDAVI-AMIRI A, SAMAVATI F. Multiresolution on Spherical Curves[J]. Graphical Models, 2016, 86:13-24.
[85] WAGNER W. Implementation Plan for A Soil Moisture Product for NWP[R]. ASCAT Soil Moisture Report Series No.5. Vienna:Institute of Photogrammetry and Remote Sensing, Vienna University of Technology, 2005.
[86] KIESTER A R, SAHR K. Planar and Spherical Hierarchical, Multi-Resolution Cellular Automata[J]. Computers,Environment and Urban Systems, 2008, 32(3):204-213.
[87] VENTRELLA J. Glider Dynamics on the Sphere:Exploring Cellular Automata on Geodesic Grids[J]. Journal of Cellular Automata, 2011, 6(2-3):245-256.
[88] KIDD R A, TROMMLER M, WAGNER W. The Development of a Processing Environment for Time-Series Analysis of SeawindsScatterometer Data[C]//Proceedings of 2003 IEEE International Geoscience and Remote Sensing Symposium.Toulouse:IEEE, 2003, 6:4110-4112.
[89] CHEN Chunguang, XIAO Feng. Shallow Water Model on Cubed-Sphere by Multi-Moment Finite Volume Method[J]. Journal of Computational Physics, 2008, 227(10):5019-5044.
[90] LI S, XIAO Feng. A Global Shallow Water Model Using High Order Multi-Moment Constrained Finite Volume Method and Icosahedral Grid[J]. Journal of Computational Physics, 2010, 229(5):1774-1796.
[91] RINGLER T D, HEIKES R P, RANDALL D A. Modeling the Atmospheric General Circulation Using A Spherical Geodesic Grid:A New Class of Dynamical Cores[J]. Monthly Weather Review, 2000, 128(7):2471-2490.
[92] RANDALL D A, RINGLER T D, HEIKESR P, et al. Climate Modeling with Spherical Geodesic Grids[J]. Computing in Science & Engineering, 2002, 4(5):32-41.
[93] TSATCHA D, SAUXÉ, CLARAMUNT C. A Bidirectional Path-Finding Algorithm and Data Structure for Maritime Routing[J]. International Journal of Geographical Information Science, 2014, 28(7):1355-1377.
[94] BERNARDIN T, COWGILL E, KREYLOS O, et al. Crusta:A New Virtual Globe for Real-Time Visualization of Sub-Meter Digital Topography at Planetary Scales[J]. Computers & Geosciences, 2011, 37(1):75-85.
[95] ADAMS B. Wāhi, A Discrete Global Grid Gazetteer Built Using Linked Open Data[J/OL].International Journal of Digital Earth, 2016, doi:10.1080/17538947.2016.1229819. (in press)
[96] KARSSENBERG D, DE JONG K. Dynamic Environmental Modelling in GIS:1. Modelling in Three Spatial Dimensions[J]. International Journal of Geographical Information Science, 2005, 19(5):559-579.
[97] STADLER G, GURNIS M, BURSTEDDE C, et al. The Dynamics of Plate Tectonics and Mantle Flow:From Local to Global Scales[J]. Science, 2010,329(5995):1033-1038.
[98] SANFORD B, JAMES R, YOUNG C. Efficient and Accurate Calculation of Ray Theory Seismic Travel Time through Variable Resolution 3D Earth Models[J]. Seismological Research Letters, 2009, 80(6):990-1000.
[99] IVAN L, SUSANTO A, DE STERCK H, et al. High-Order Central ENO Finite-Volume Scheme for MHD on Three-Dimensional Cubed-Sphere Grids[C]//Proceedings of the 7th International Conference on Computational Fluid Dynamics (ICCFD7).Big Island, Hawaii:ICCFD, 2012.
[100] YU Jieqing, WU Lixin, LI Zhifeng, et al. An SDOG-based Intrinsic Method for Three-Dimensional Modelling of Large-Scale Spatial Objects[J]. Annals of GIS, 2012, 18(4):267-278.
[101] 张宗佩, 万刚, 曹雪峰, 等. 地月圈层空间立体网格技术及其编码转换方法[J]. 测绘通报, 2015(6):20-23, 27. DOI:10.13474/j.cnki.11-2246.2015.0169. ZHANG Zongpei, WAN Gang, CAO Xuefeng, et al. Earth-Lunar Shell Space Solid Grid Technology and Coding-Conversion[J]. Bulletin of Surveying and Mapping, 2015(6):20-23, 27. DOI:10.13474/j.cnki.11-2246.2015.0169.
[102] 陈磊, 白显宗, 梁彦刚.空间目标轨道数据应用——碰撞预警与态势分析[M]. 北京:国防工业出版社,2015. CHEN Lei,BAI Xianzong, LIANG Yangang. Orbital Data Applicationsfor Space Object:ConjunctionAssessment and Situation analysis[M].Beijing:National Defence Industry Press, 2015.