An Improved QTM Subdivision Model with Approximate Equal-area

doi:10.11947/j.AGCS.2016.20140598

Abstract

Abstract: To overcome the defect of large area deformation in the traditional QTM subdivision model, an improved subdivision model is proposed which based on the “parallel method” and the thought of the equal area subdivision with changed-longitude-latitude. By adjusting the position of the parallel, this model ensures that the grid area between two adjacent parallels combined with no variation, so as to control area variation and variation accumulation of the QTM grid. The experimental results show that this improved model not only remains some advantages of the traditional QTM model(such as the simple calculation and the clear corresponding relationship with longitude/latitude grid, etc), but also has the following advantages: ①this improved model has a better convergence than the traditional one. The ratio of area_max/min finally converges to 1.38, far less than 1.73 of the “parallel method”; ②the grid units in middle and low latitude regions have small area variations and successive distributions; meanwhile, with the increase of subdivision level, the grid units with large variations gradually concentrate to the poles; ③the area variation of grid unit will not cumulate with the increasing of subdivision level.

Key words: discrete global grid system, QTM, parallel ring method, geometry deformation of grid

CLC Number:

P208

ZHAO Xuesheng, YUAN Zhengyi, ZHAO Longfei, ZHU Sikun. An Improved QTM Subdivision Model with Approximate Equal-area[J]. Acta Geodaetica et Cartographica Sinica, 2016, 45(1): 112-118.

References

[1] LUKATELA H. A Seamless Global Terrain Model in the Hipparchus System[EB/OL]. [2000-12-30]. http://www.geodyssey.com/global/papers.
[2] 赵学胜, 侯妙乐, 白建军. 全球离散格网的空间数字建模[M]. 北京: 测绘出版社, 2007.ZHAO Xuesheng, HOU Miaole, BAI Jianjun. Spatial Digital Modeling of the Global Discrete Grids[M]. Beijing: Surveying and Mapping Press, 2007.
[3] DUTTON G H.Lecture Notes in Earth Sciences:A Hierarchical Coordinate System for Geoprocessing and Cartography[M].Berlin: Springer-Verlag, 1999.
[4] GOODCHILD M F,SHIREN Y.A Hierarchical Spatial Data Structure for Global Geographic Information Systems[J]. CVGIP:Graphical Models andImage Processing, 1992, 54(1): 31-44.
[5] 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.
[6] 关丽, 程承旗, 吕雪锋. 基于球面剖分格网的矢量数据组织模型研究[J]. 地理与地理信息科学, 2009, 25(3): 23-27.GUAN Li, CHENG Chengqi, LV Xuefeng. Study on the Organization Model for Vector Data Based on Global Subdivision Grid[J]. Geography and Geo-Information Science, 2009, 25(3): 23-27.
[7] 赵学胜, 白建军, 王志鹏. 基于QTM的全球地形自适应可视化模型[J]. 测绘学报, 2007, 36(3): 316-320.ZHAO Xuesheng, BAI Jianjun, WANG Zhipeng. An Adaptive Visualized Model of the Global Terrain Based on QTM[J]. Acta Geodaetica et Cartographica Sinica, 2007, 36(3): 316-320.
[8] SATOSHI I, FENG X. A Global Shallow Water Model Using High Order Multi-moment Constrained Finite Volume Method and Icosahedra Grid[J]. Journal of Computational Physics, 2010, 229(5): 1774-1796.
[9] 邢华桥. 基于QTM的全球多分辨率水淹模拟[D]. 北京: 北京建筑工程大学, 2012.XING Huaqiao. Global Multi-resolution Submerging Simulation Based on QTM[D]. Beijing: Beijing University of Civil Engineering and Architecture, 2012.
[10] 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.
[11] LUGO J A, CLARKE K C. Implementation of Triangulated Quadtree Sequencing for a Global Relief Data Structure[C]//Proceedings, AUTO CARTO 12.Charlotte, NC:[s.n.],1995.
[12] 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.
[13] SNYDER J P. An Equal-area Map Projection for Polyhedral Globes[J]. Cartographica: The International Journal for Geographic Information and Geovisualization, 1992, 29(1): 10-21.
[14] BJØRKE J T, GRYTTEN J K, HGER M, et al. A Global Grid Model Based on “Constant Area” Quadrilaterals[C]//ScanGIS.Horten: Norwegian Defence Research Establishment,2003, 3: 238-250.
[15] 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.
[16] LEOPARDI P. A Partition of the Unit Sphere into Regions of Equal Area and Small Diameter[J]. Electronic Transactions on Numerical Analysis, 2006, 25(1): 309-327.
[17] BECKERS B, BECKERS P. A General Rule for Disk and Hemisphere Partition into Equal-area Cells[J]. Computational Geometry, 2012, 45(7): 275-283.
[18] ZHOU Mengyun, CHEN Jing, GONG Jianya. A Pole-oriented Discrete Global Grid System: Quaternary Quadrangle Mesh[J]. Computers & Geosciences, 2013, 61: 133-143.
[19] TALBOT B G, TALBOT L M. Fast-earth: A Global Image Caching Architecture for Fast Access to Remote-sensing Data[C]//Proceedings of 2013 IEEE Aerospace Conference. Big Sky, MT: IEEE,2013: 1-10.
[20] SAHR K, WHITE D, KIMERLING A J. Geodesic Discrete Global Grid Systems[J]. Cartography and Geographic Information Science, 2003, 30(2): 121-134.
[21] SONG Lian,KIMERLINGA J,SAHR K. Developing an Equal Area Global Grid by Small Circle Subdivision[C]//GOODCHILD M, KIMERLING A J.Discrete Global Grids.Santa Barbara, CA:National Center for Geographic Information & Analysis, 2002.
[22] 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.
[23] 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.