Multi-mode 3D extension methods for equal-area discrete global grid systems for geospatial data representation

doi:10.11947/j.AGCS.2024.20220701

Abstract

Abstract: Discrete global grid systems (DGGS) are new geospatial data models, among which the equal-area DGGS have attracted much attention due to their unique advantages in sampling and spatial analysis. Nevertheless, related researches are limited to the earth surface and lack of theoretical methods for extending to 3D space. Herein, several multi-mode subdivision methods are proposed for extending equal-area 2D DGGS to 3D DGGS and their unified mathematical description and detailed mathematical proof are realized. Then the volume and compactness indicators are introduced to evaluate the properties of 3D grids under different subdivision modes, and we compare these indicators with the spherical degenerated octree grids (SDOG) and the spherical geometric octree grids (SGOG). Finally, the application cases are explored and the principle of selecting subdivision mode under different application requirements is discussed. The experimental results show that the indicators of the degenerated subdivision are better than the regular subdivision and the volume properties of equal volume and degenerate subdivision are better than SDOG, and the compactness properties are better than SGOG. The multi-mode 3D extension method proposed here not only meets the requirements of international standard for equal volume, but also consider the conventional subdivision design options, which provides a basis for different application requirements.

Key words: equal-area, discrete global grid system, 3D extension, subdivision, volume preservation, compactness

CLC Number:

P208

ZHOU Jianbin, DING Junjie, BEN Jin, CHEN Yihang, LIANG Qishuang. Multi-mode 3D extension methods for equal-area discrete global grid systems for geospatial data representation[J]. Acta Geodaetica et Cartographica Sinica, 2024, 53(1): 173-188.

References

[1] 李锋, 万刚, 安籽鹏, 等. 基于地球网格剖分的球体3D-Voronoi图生成[J]. 中国体视学与图像分析, 2018, 23(1): 54-59. LI Feng, WAN Gang, AN Zipeng, et al. Generation of spheroid 3D-Voronoi diagram based on global grid division[J]. Chinese Journal of Stereology and Image Analysis, 2018, 23(1): 54-59.
[2] 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.
[3] 孙群, 温伯威, 陈欣. 多源地理空间数据一致性处理研究进展[J]. 测绘学报, 2022, 51(7): 1561-1574. DOI: 10.11947/j.AGCS.2022.20220151. SUN Qun, WEN Bowei, CHEN Xin. Research on consistency processing of multi-source geospatial data[J]. Acta Geodaetica et Cartographica Sinica, 2022, 51(7): 1561-1574. DOI: 10.11947/j.AGCS.2022.20220151.
[4] 赵学胜, 贲进, 孙文彬, 等. 地球剖分格网研究进展综述[J]. 测绘学报, 2016, 45(S1): 1-14. DOI: 10.11947/j.AGCS.2016.F001. ZHAO Xuesheng, BEN Jin, SUN Wenbin, et al. Overview of the research progress in the earth tessellation grid[J]. Acta Geodaetica et Cartographica Sinica, 2016, 45(S1): 1-14. DOI: 10.11947/j.AGCS.2016.F001.
[5] 林冰仙, 许德朋, 盛业华, 等. 正二十面体球面菱形离散格网的编码模型及其映射方法[J]. 测绘学报, 2016, 45(S1): 23-31. DOI: 10.11947/j.AGCS.2016.F001. LIN Bingxian, XU Depeng, SHENG Yehua, et al. Coding model and mapping method of spherical diamond discrete grids based on icosahedron[J]. Acta Geodaetica et Cartographica Sinica, 2016, 45(S1): 23-31. DOI: 10.11947/j.AGCS.2016.F001.
[6] 胡海, 游涟, 宋丽丽, 等. 地球格网化剖分及其度量问题[J]. 测绘学报, 2016, 45(S1): 56-65. DOI: 10.11947/j.AGCS.2016.F007. HU Hai, YOU Lian, SONG Lili, et al. Some metric problems on the global grid systems[J]. Acta Geodaetica et Cartographica Sinica, 2016, 45(S1): 56-65. DOI: 10.11947/j.AGCS.2016.F007.
[7] 周良辰, 盛业华, 林冰仙, 等. 球面菱形离散格网正二十面体剖分法[J]. 测绘学报, 2014, 43(12): 1293-1299. ZHOU Liangchen, SHENG Yehua, LIN Bingxian, et al. Diamond discrete grid subdivision method for spherical surface with icosahedron[J]. Acta Geodaetica et Cartographica Sinica, 2014, 43(12): 1293-1299.
[8] 胡佰林, 王春波, 赵学胜, 等. 基于WGS-84椭球面的退化四叉树经纬线格网剖分[J]. 测绘学报, 2016, 45(S1): 32-39. DOI: 10.11947/j.AGCS.2016.F004. HU Bailin, WANG Chunbo, ZHAO Xuesheng, et al. Degenerate quadtree latitude/longitude grid based on WGS-84 ellipsoidal facet[J]. Acta Geodaetica et Cartographica Sinica, 2016, 45(S1): 32-39. DOI: 10.11947/j.AGCS.2016.F004.
[9] BASSIN C. The current limits of resolution for surface wave tomography in North America[J]. Eos Transactions American Geophysical Union,2000, 81(48):F897.
[10] ZHAO Dapeng. Global tomographic images of mantle plumes and subducting slabs: insight into deep Earth dynamics[J]. Physics of the Earth and Planetary Interiors, 2004, 146(1/2): 3-34.
[11] GFDL.High-resolution atmosphere modeling [EB/OL].[2022-12-10].http://www.gfdl.noaa.gov/high-resolution-atmosphere-modeling.
[12] SUN Zhongqiu, CHENG Chengqi. 3D integrated representation model and visualization based on the global discrete voxel——GeoSOT3D[C]//Proceedings of 2015 International Conference on Geoinformatics.Wuhan:IEEE, 2015:1-5.
[13] MIAO Shuangxi, CHENG Chengqi, ZHAI Weixin, et al. A low-altitude flight conflict detection algorithm based on a multilevel grid spatiotemporal index[J]. ISPRS International Journal of Geo-Information, 2019, 8(6): 289.
[14] ZHAI Weixin, TONG Xiaochong, MIAO Shuangxi, et al. Collision detection for UAVs based on GeoSOT-3D grids[J]. ISPRS International Journal of Geo-Information, 2019, 8(7): 299.
[15] HAN Bing, QU Tengteng, HUANG Zili, et al. Emergency airport site selection using global subdivision grids[J]. Big Earth Data, 2022, 6(3): 276-293.
[16] ULMER B, HALL J, SAMAVATI F. General method for extending discrete global grid systems to three dimensions[J]. ISPRS International Journal of Geo-Information, 2020, 9(4): 233.
[17] KAGEYAMA A, SATO T. “Yin-Yang grid”: an overset grid in spherical geometry[J]. Geochemistry, Geophysics, Geosystems, 2004, 5(9): Q09005.
[18] TACKLEY P J. Modelling compressible mantle convection with large viscosity contrasts in a three-dimensional spherical shell using the Yin-Yang grid[J]. Physics of the Earth and Planetary Interiors, 2008, 171(1/2/3/4): 7-18.
[19] KAGEYAMA A, YOSHIDA M. Geodynamo and mantle convection simulations on the Earth simulator using the Yin-Yang grid[J]. Journal of Physics: Conference Series, 2005, 16: 325-338.
[20] 李兴良. 球面阴阳网格与新型多离散矩有限体积方法的应用研究[D]. 南京: 南京信息工程大学, 2007. LI Xingliang. On the spherical Yin-Yang grid and application of a novel multi-moment finite volume method[D]. Nanjing: Nanjing University of Information Science & Technology, 2007.
[21] 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.
[22] 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.
[23] ULMER B, SAMAVATI F. Toward volume preserving spheroid degenerated-octree grid[J]. GeoInformatica, 2020, 24(3): 505-529.
[24] OGC. Topic 21: discrete global grid system abstract specification[EB/OL].[2022-12-10]. http://www.opengis.net/doc/AS/dggs/1.0.
[25] OGC. Abstract specification topic 21 v2.0[EB/OL].[2022-12-10]. http://www.opengis.net/doc/AS/dggs/2.0.
[26] 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.
[27] 王金鑫, 郑亚圣, 李耀辉, 等. 利用球体剖分瓦块构建真三维数字地球平台[J]. 测绘学报, 2015, 44(6): 694-701. DOI: 10.11947/j.AGCS.2015.20140128. WANG Jinxin, ZHENG Yasheng, LI Yaohui, et al. Building the platform of digital earth with sphere split bricks[J]. Acta Geodaetica et Cartographica Sinica, 2015, 44(6): 694-701. DOI: 10.11947/j.AGCS.2015.20140128.
[28] 赖广陵, 童晓冲, 丁璐, 等. 三维空间格网的多尺度整数编码与数据索引方法[J]. 测绘学报, 2018, 47(7): 1007-1017. DOI: 10.11947/j.AGCS.2018.20170364. LAI Guangling, TONG Xiaochong, DING Lu, et al. Multiscale integer coding and data index of 3D spatial grid[J]. Acta Geodaetica et Cartographica Sinica, 2018, 47(7): 1007-1017. DOI: 10.11947/j.AGCS.2018.20170364.
[29] 贲进, 童晓冲, 张永生, 等. 对施奈德等积多面体投影的研究[J]. 武汉大学学报(信息科学版), 2006, 31(10): 900-903. BEN Jin, TONG Xiaochong, ZHANG Yongsheng, et al. Snyder equal-area map projection for polyhedral globes[J]. Geomatics and Information Science of Wuhan University, 2006, 31(10): 900-903.
[30] 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.
[31] 王政.全球离散格网质量综合评价指标体系与构建研究[D].北京:中国矿业大学(北京),2021. WANG Zheng. Comprehensive evaluation indicator system of discrete global grid quality and its construction[D]. Beijing: China University of Mining&Technology-Beijing,2021.
[32] 孙文彬, 周长江. 一种近似等积球面菱形格网的构建方法[J]. 武汉大学学报(信息科学版), 2016, 41(8): 1040-1045. SUN Wenbin, ZHOU Changjiang. A method of constructing approximate equal-area diamond gird[J]. Geomatics and Information Science of Wuhan University, 2016, 41(8): 1040-1045.
[33] 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]. Acta Geodaetica et Cartographica Sinica, 2016, 45(1): 112-118. DOI: 10.11947/j.AGCS.2016.20140598.
[34] WADELL H. Volume, shape, and roundness of quartz particles[J]. The Journal of Geology, 1935, 43(3): 250-280.
[35] 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 Geographical Information Science, 1998, 12(8): 805-827.
[36] KMOCH A, VASILYEV I, VIRRO H, et al. Area and shape distortions in open-source discrete global grid systems[J]. Big Earth Data, 2022, 6(3): 256-275.
[37] 张继凯, 聂俊岚, 陈贺敏, 等. 基于菱形块四叉树的全球六边形网格实时绘制方法[J]. 计算机辅助设计与图形学学报, 2017, 29(10): 1824-1834. ZHANG Jikai, NIE Junlan, CHEN Hemin, et al. Real-time rendering method for global hexagon grid based on quad-tree of diamond blocks[J]. Journal of Computer-Aided Design & Computer Graphics, 2017, 29(10): 1824-1834.
[38] 吴翔宇. 城市空间管控的场景网格化建模与应用方法研究[D]. 郑州:信息工程大学, 2020. WU Xiangyu. Research on scene grid modeling and application method for urban space management and control[D]. Zhengzhou: Information Engineering University, 2020.
[39] European Space Agency. Data of Sentinel-1[EB/OL].[2022-12-10].https://s1qc.asf.alaska.edu/aux_poeorb/.
[40] LIN Bingxian, ZHOU Liangchen, XU Depeng, et al. A discrete global grid system for earth system modeling[J]. International Journal of Geographical Information Science, 2018, 32(4): 711-737.
[41] National Centers for Environmental Prediction. Data transfer: NCEP GFS forecasts (0.25 degree grid) g2sub V1.1[EB/OL]. [2022-12-22].https://nomads.ncep.noaa.gov/cgi-bin/filter_gfs_0p25.pl.