Some Metric Problems on the Global Grid Systems

doi:10.11947/j.AGCS.2016.F007

Abstract

Abstract: The Discrete Global Grid Systems (or the global position location framework) is a kind of scientific and concise spatial reference system, which is the discretization, accurate and systematic representation of the earth information data. In recent years, with the development of GPS and Beidou satellite system and the process of globalization, the global metric and accuracy of spatial analysis should be pay more attention by people. In this paper, first, for the progress and insufficiency over recent years of the earth grid research, the author discusses several quantity issues include:the integrity of meshing, logical consistency, and some related problems. Then regarding the questions of position and metric, the author points out that the Earth is the target object of meshing its characteristics of metric space. The revolutionary demand of "3D structure and centimeter level accuracy" will have a significant impact on global GIS system. Next, the 3D meshing approaches to the ellipsoid of the earth are stressed, and the author also introduces the corresponding experiments and theoretical approach in map algebra on the 3D earth meshing. Finally, this paper reaffirms that the 3 sets of (B, L, H) orthogonal surface should be the most appropriate way on metric for the Earth meshing.

Key words: metric, Discrete Global Grid(DGG), modeling method, ellipsoidal earth surface, map algebra

CLC Number:

P208

HU Hai, YOU Lian, SONG Lili, HU Peng. Some Metric Problems on the Global Grid Systems[J]. Acta Geodaetica et Cartographica Sinica, 2016, 45(S1): 56-65.

References

[1] GOODCHILD M F, GUO Huadong, ANNONI A, et al. Next-Generation Digital Earth[J]. Proceedings of the National Academy of Sciences of the United States of America, 2012, 109(28):11088-11094.
[2] SAHR K, WHITE D, KIMERLING A J. Geodesic Discrete Global Grid Systems[J]. Cartography and Geographic Information Science, 2003, 30(2):121-134.
[3] BAR-ZEEV A. How Google Earth[really] works[EB/OL]. (2007-07-03)[2011-07-16]. http://www.realityprime.com/blog/2007/07/how-google-earth-really-works/.
[4] MAHDAVI-AMIRI A, ALDERSON T, SAMAVATI F. A Survey of Digital Earth[J]. Computers & Graphics, 2015, 53:95-117.
[5] 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.
[6] KOLLER D, LINDSTROM P, RIBARSKY W, et al. Virtual GIS:A Real-Time 3D Geographic Information System[C]//Proceedings of 1995 IEEE Conference on Visualization. Atlanta, GA:IEEE, 1995:94-100, 443.
[7] DUTTON G H. A Hierarchical Coordinate System for Geoprocessing and Cartography[M]. Berlin Heidelberg:Springer, 1999.
[8] HITCHNER L E. A Virtual Planetary Exploration:Very Large Virtual Environment[C]//ACM SIGGRAPH'92 Tutorial on Implementing Immersive Virtual Environments. Moffett Field, CA:NASA Ames Research Center, 1992.
[9] FALBY J S, ZYDA M J, PRATT D R, et al. NPSNET:Hierarchical Data Structures for Real-Time Three-Dimensional Visual Simulation[J]. Computers & Graphics, 1993, 17(1):65-69.
[10] REDDY M, LECLERC Y,IVERSON L,et al.TerraVision II:Visualizing Massive Terrain Databases in VRML[J]. IEEE Computer Graphics and Applications,1999,19(2):30-38.
[11] 李德仁, 肖志峰, 朱欣焰, 等. 空间信息多级网格的划分方法及编码研究[J]. 测绘学报, 2006, 35(1):52-56, 70, doi:10.3321/j.issn:1001-1595.2006.01.011. LI Deren, XIAO Zhifeng, ZHU Xinyan, et al. Research on Grid Division and Encoding of Spatial Information Multi-Grids[J]. Acta Geodaetica et Cartographica Sinica, 2006, 35(1):52-56, 70, doi:10.3321/j.issn:1001-1595.2006.01.011.
[12] 李德仁, 朱欣焰, 龚健雅. 从数字地图到空间信息网格-空间信息多级网格理论思考[J]. 武汉大学学报(信息科学版), 2003, 28(6):642-650. LI Deren, ZHU Xinyan, GONG Jianya. From Digital Map to Spatial Information Multi-grid-A Thought of Spatial Information Multi-grid Theory[J]. Geomatics and Information Science of Wuhan University, 2003, 28(6):642-650.
[13] 李德仁, 邵振峰, 朱欣焰. 论空间信息多级格网及其典型应用[J]. 武汉大学学报(信息科学版), 2004, 29(11):945-950. LI Deren, SHAO Zhenfeng, ZHU Xinyan. Spatial Information Multi-grid and Its Typical Application[J]. Geomatics and Information Science of Wuhan University, 2004, 29(11):945-950.
[14] 邵振峰, 李德仁. 基于网格计算环境下的空间信息多级格网研究[J]. 地理信息世界, 2005, 3(2):31-35. SHAO Zhenfeng, LI Deren. Study on Spatial Information Multi-grid under Grid Computing Environment[J]. Geomatics World, 2005, 3(2):31-35.
[15] NIMA.Digital Terrain Elevation Data[DB/OL].[2005-12-13]. http://www.globalsecurity.org/intell/systems/dted.htm.
[16] BJORKE J T, GRYTTEN J K, GER M, et a1. A global grid model based on "Constant Area" quadrilaterals[C]//VIRANTAUS K, TVEITE H. Proceedings of the 9th Scandinavian Research Conference on Geographical Information Science, ScanGIS'2003. Espoo, Finland:Helsinki University of Technology, 2003, 3:239-250.
[17] 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.
[18] 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.
[19] 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.
[20] 崔马军, 赵学胜. 球面退化四叉树格网的剖分及变形分析[J]. 地理与地理信息科学, 2007, 23(6):23-25. CUI Majun, ZHAO Xuesheng. Tessellation and Distortion Analysis Based on Spherical DQG[J]. Geography and Geo-Information Science, 2007, 23(6):23-25.
[21] 赵学胜, 陈军, 王金庄. 基于O-QTM的球面VORONOI图的生成算法[J]. 测绘学报, 2002, 31(2):157-163, doi:10.3321/j.issn:1001-1595.2002.02.013. ZHAO Xuesheng, CHEN Jun, WANG Jinzhuang. QTM-based Algorithm for the Generating of Voronoi Diagram for Spherical Objects[J]. Acta Geodaetica et Cartographica Sinica, 2002, 31(2):157-163, doi:10.3321/j.issn:1001-1595.2002.02.013.
[22] 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.
[23] 程承旗, 关丽. 基于地图分幅拓展的全球剖分模型及其地址编码研究[J]. 测绘学报, 2010, 39(3):295-302. CHENG Chengqi, GUAN Li. The Global Subdivision Grid Based on Extended Mapping Division and Its Address Coding[J]. Acta Geodaetica et Cartographica Sinica, 2010, 39(3):295-302.
[24] 李世忠, 宋树华, 程承旗, 等. 基于GeoSOT网格的"天绘一号"卫星影像数据组织[J]. 遥感学报, 2012, 16(S1):102-107. LI Shizhong, SONG Shuhua, CHENG Chengqi, et al. Mapping Satellite-1 Remote Sensing Data Organization Based on GeoSOT[J]. Journal of Remote Sensing, 2012, 16(S1):102-107.
[25] 宋树华, 程承旗, 关丽, 等. 全球空间数据剖分模型分析[J]. 地理与地理信息科学, 2008, 24(4):11-15. SONG Shuhua, CHENG Chengqi, GUAN Li, et al. Analysis on Global Geodata Partitioning Models[J]. Geography and Geo-Information Science, 2008, 24(4):11-15.
[26] 贲进, 童晓冲, 周成虎, 等. 正八面体的六边形离散格网系统生成算法[J]. 地球信息科学学报, 2015, 17(7):789-797. BEN Jin, TONG Xiaochong, ZHOU Chenghu, et al. Construction Algorithm of Octahedron Based Hexagon Grid Systems[J]. Journal of Geo-Information Science, 2015, 17(7):789-797.
[27] 童晓冲, 贲进, 秦志远, 等. 基于全球离散网格框架的局部网格划分[J]. 测绘学报, 2009, 38(6):506-513, doi:10.3321/j.issn:1001-1595.2009.06.007. TONG Xiaochong, BEN Jin, QIN Zhiyuan, et al. The Subdivision of Partial Grid Based on Discrete Global Grid Systems[J]. Acta Geodaetica et Cartographica Sinica, 2009, 38(6):506-513, doi:10.3321/j.issn:1001-1595.2009.06.007.
[28] 袁文, 庄大方, 袁武, 等. 离散三角网格系统距离量测方法[J]. 测绘学报, 2011, 40(1):59-65. YUAN Wen, ZHUANG Dafang, YUAN Wu, et al. Distance Function for the Triangular Grids[J]. Acta Geodaetica et Cartographica Sinica, 2011, 40(1):59-65.
[29] 吴立新, 余接情. 基于球体退化八叉树的全球三维网格与变形特征[J]. 地理与地理信息科学, 2009, 25(1):1-4. WU Lixin, YU Jieqing. Global 3D-Grid Based on Sphere Degenerated Octree and Its Distortion Features[J]. Geography and Geo-Information Science, 2009, 25(1):1-4.
[30] 江锦成, 郭甲腾, 吴立新, 等. 三维地学实体多粒度栅格剖分与布尔运算的并行算法[J]. 科技导报, 2011, 29(35):18-23. JIANG Jincheng, GUO Jiateng, WU Lixin, et al. Multi-Granularity Rasterization and Boolean Operation Parallel Algorithm for 3D Spatial Entities[J]. Science & Technology Review, 2011, 29(35):18-23.
[31] LUKATELA H. Hipparchus Geopositioning Model:An Overview[C]//Proceedings of Eighth International Symposium on Computer-Automated Cartography. Baltimore, Maryland:[s.n.], 1987.
[32] KOLAR J. Representation of the geographic terrain surface using global indexing[C]//Proceeding of 12th International Conference on Geoinformatics. Sweden:[s.n.], 2004.
[33] 陈军. Voronoi动态空间数据模型[M]. 北京:测绘出版社, 2002:8, 1-62, 87-130. CHEN Jun.Voronoi Dynamic Spatial Data Model[M].Beijing:Surveying and Mapping Press, 2002:8, 1-62, 87-130.
[34] 胡毓巨, 龚剑文. 地图投影[M]. 武汉:武汉测绘科技大学出版社, 1997:19-47. HU Liuju, GONG Jianwen. Map Projection[M]. Wuhan:Wuhan Surveying and Mapping Science and Technology University Press, 1997:19-47.
[35] 胡鹏, 吴艳兰, 杨传勇, 等. 大型GIS与数字地球的空间数学基础研究[J]. 武汉大学学报(信息科学版), 2001, 26(4):296-302. HU Peng, WU Yanlan, YANG Chuanyong, et al. Research on System Space Mathematical Base of Large-scale GIS and the Digital Earth[J]. Geomatics and Information Science of Wuhan University, 2001, 26(4):296-302.
[36] 胡鹏, 胡毓钜, 杨传勇, 等. 我国地球空间数据框架的设计思想、技术路线及若干理论问题讨论[J]. 武汉大学学报(信息科学版), 2002, 27(3):283-288. HU Peng, HU Yuju, YANG Chuanyong, et al. Design Thinking, Technical Route and Some Theoretical Issues on the Geospatial Digital Framework[J]. Geomatics and Information Science of Wuhan University, 2002, 27(3):283-288.
[37] 胡鹏, 杨传勇, 胡海, 等. GIS的基本理论问题——地图代数的空间观[J]. 武汉大学学报(信息科学版), 2002, 27(6):616-621. HU Peng, YANG Chuanyong, HU Hai, et al. Basic Theoretical Problem of GIS-Space View of Map Algebr[J]. Geomatics and Information Science of Wuhan University, 2002, 27(6):616-621.
[38] 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.
[39] 胡鹏, 游涟, 杨传勇, 等. 地图代数[M]. 武汉:武汉大学出版社, 2002:1-126. HU Peng, You Lian, YANG Chuanyong, et al. Map Algebra[M]. Wuhan:Wuhan University Press, 2002:1-126.
[40] 孔祥元, 郭际明, 刘宗泉. 大地测量学基础[M]. 2版. 武汉:武汉大学出版社, 2010:4-61, 64-167. KONG Xiangyuan, GUO Jiming, LIU Zongquan. Fundamentals of Geodetic Surveying[M]. 2nd ed. Wuhan:Wuhan University Press, 2008:4-61, 64-167.
[41] 胡鹏, 李圣权, 胡海. 地球信息理论和零初始化问题[M]. 北京:测绘出版社, 2006:1. HU Peng, LI Shengquan, HU Hai. Geographic Information Theory and Zero Initialization Problem[M]. Beijing:Surveying and Mapping Press, 2006:1.
[42] 《数学手册》编写组. 数学手册[M]. 北京:高等教育出版社, 1979:1112-1114, 1121-1123. 《Handbook of Mathematics》Write Groups. Handbook of Mathematics[M]. Beijing:People Education Press, 1979:1112-1114, 1121-1123.
[43] 江泽坚, 吴智泉. 实变函数论[M]. 北京:人民教育出版社, 1961:1-107. JIANG Zejian, WU Zhiquan. Real Function Theory[M]. Beijing:People Education Press, 1961:1-107.
[44] 胡鹏, 游连, 胡海. 地图代数概论[M]. 北京:测绘出版社, 2008:12-30, 217-223. HU Pen,YOU Lian,HU Hai.Introduction to Map Algebra[M]. Beijing:Surveying and Mapping Press, 2008:12-30, 217-223.
[45] 中国测绘学会. 中国测绘学科发展蓝皮书[M]. 北京:测绘出版社, 2003. Chinese Society of Geodesy, Photogrammetry and Cartography. Blue Book of China's Surveying and Mapping Discipline Development[M]. Beijing:Surveying and Mapping Press, 2003.
[46] 胡海, 吴艳兰. 椭球面上混合基线图形的缓冲区和等比例线问题[J]. 测绘工程, 2011, 20(3):1-4, 8, doi:10.3969/j.issn.1006-7949.2011.03.001. HU Hai,WU Yanlan.Problems of Graphics Buffers and the Proportion Line of Ellipsoid Mixed Baseline (or Normal Curve)[J]. Engineering of Surveying and Mapping, 2011, 20(3):1-4,8,doi:10.3969/j.issn.1006-7949.2011.03.001.
[47] HU HAI, LIU XIAOHANG, HU PENG. Voronoi Diagram Generation on the Ellipsoidal Earth[J]. Computers & Geosciences, 2014, 73:81-87.
[48] HU H, YOU L, YANG H, et al. A Global Modeling Method based on Geographical Distance Fields[C]. AAG Annual Meeting, 2016.