菱形三十面体格网系统构建的等积投影方法研究

王蕊, 贲进, 梁晓宇, 梁启爽, 涂祖瑞

王蕊, 贲进, 梁晓宇, 梁启爽, 涂祖瑞. 菱形三十面体格网系统构建的等积投影方法研究[J]. 武汉大学学报 ( 信息科学版). DOI: 10.13203/j.whugis20220231
引用本文: 王蕊, 贲进, 梁晓宇, 梁启爽, 涂祖瑞. 菱形三十面体格网系统构建的等积投影方法研究[J]. 武汉大学学报 ( 信息科学版). DOI: 10.13203/j.whugis20220231
WANG Rui, BEN Jin, LIANG Xiaoyu, LIANG Qishuang, TU Zurui. Research on the Equal-Area Projection for the Construction of the Rhombic Triacontahedron Grid Systems[J]. Geomatics and Information Science of Wuhan University. DOI: 10.13203/j.whugis20220231
Citation: WANG Rui, BEN Jin, LIANG Xiaoyu, LIANG Qishuang, TU Zurui. Research on the Equal-Area Projection for the Construction of the Rhombic Triacontahedron Grid Systems[J]. Geomatics and Information Science of Wuhan University. DOI: 10.13203/j.whugis20220231

菱形三十面体格网系统构建的等积投影方法研究

基金项目: 

河南省重大科技专项国家超级计算郑州中心创新生态系统建设科技专项(201400210100); 国家重点研发计划项目(2018YFB0505301)

详细信息
    作者简介:

    王蕊,博士生,主要从事全球离散格网方面的研究。wr_paper@126.com

    通讯作者:

    贲进,博士,教授。benj@lreis.ac.cn

Research on the Equal-Area Projection for the Construction of the Rhombic Triacontahedron Grid Systems

  • 摘要: 全球离散格网系统(discrete global grid systems,DGGS)是一类新兴的数字地球参考框架,在大尺度多源地理空间数据集的组织、集成与分析方面具有天然优势。现有全球离散格网系统构建方法中,基于多面体投影方法生成的格网系统具有更加优异的几何性质,因而被广泛研究。基础多面体及投影方法是格网系统设计选项中影响格网单元几何性质的主要因素。为构建更加均匀、高效的格网系统,本文选择菱形三十面体作为基础多面体,推导菱形三十面体与地球球体等积投影的正反算解析公式,并将其应用于三种不同单元形状等积全球离散格网的生成。对比实验结果表明,与二十面体 Snyder 等积投影相比,本文提出方法的角度变形减小约 51%,且克服了 Snyder 逆投影迭代求解导致格网生成效率较低的不足,为全球离散格网系统的相关应用提供了优选解决方案。
    Abstract: Objectives: Discrete global grid systems (DGGS) are new reference frameworks for the Digital Earth, and are suitable for organization, integration and analysis of multi-source big geospatial datasets. Among the existing construction methods of DGGS, using polyhedron projection to the sphere can generate DGGS with superior geometric properties and has been widely used at present. Basic polyhedrons and projection methods are main factors of DGGS design choices with respect to grid cell geometrics. Most existing DGGS schemes choose the platonic solids to approximate the Earth, where the icosahedron achieves the smallest distortion due to the most faces but still has difference with spherical surface. To break through the thinking of platonic solids and constructs more uniform and efficient grid systems, this paper chooses a new basic polyhedron, the rhombic triacontahedron, and researches its equal-area projection methods. Methods: The "Slice-and-Dice" approach provides the equal-area mapping between the spherical triangles and the planar triangles for the polyhedral projections, which has different implementations according to the partitioning strategies, and in this paper the vertex-oriented great circle projection is chosen to realize the equal-area mapping between the surface of the rhombic triacontahedron and the sphere because of more uniform angular distortion compared with the Snyder equal-area polyhedral projection. Each diamond face of the rhombic triacontahedron is divided into two triangles along the short diagonal as the basic planar triangles for projection. First, according to the equal surface area of the rhombic triacontahedron and the sphere, we calculate the edge and angle parameters of the rhombic triacontahedron and its corresponding spherical polyhedron. Then, the forward and inverse projection formulas are derived based on the equal-area conditions of the vertex-oriented great circle projection. All procedures are closed form without iterations like the inverse Snyder equal-area polyhedral projection. Results: Three experiments are realized and the results show that: (1) compared with the icosahedron using Snyder equal-area polyhedral projection, the angular distortion caused by the proposed method is reduced by 51%. The mean of angular distortion declines from 0.166 radians to 0.082 radians, and the standard deviation declines from 0.055 to 0.023; (2) the proposed scheme is used to generate three types of global grids with different cell shapes—triangles, quadrilaterals and the hexagons, which verifies the validity of the proposed scheme; (3) the efficiency of grid generation using the proposed inverse projection of the rhombic triacontahedron is about four times that of the icosahedron grids based on the inverse Snyder equal-area projection, which needs iterations. Conclusions: A new DGGS scheme is proposed by introducing the rhombic triacontahedron, which provides a new idea for the development and application of DGGS. The new scheme has more angular distortion, which helps generate more uniform grids and improve the accuracy of subsequent data processing and representation, and can be applied to different cell shapes. The next step is to research data modeling, spatial analysis algorithms and the combination of DGS and high-performance computing based on this scheme, so as to provide better solutions for the organization, processing and analysis of big data on the Earth.
  • [1] Guo Huadong. A Project on Big Earth Data Science Engineering[J]. Bulletin of Chinese Academy of Sciences, 2018, 33(8): 818-823. (郭华东.地球大数据科学工程[J].中国科学院院刊, 2018, 33(8): 818-823.)
    [2]

    Sahr K, White D, Kimerling J. Geodesic Discrete Global Grid Systems[J]. Cartography and Geographic Information Science, 2003, 30(2): 121-134.

    [3]

    Yao Xiaochuang, Li Guoqing, Xia Junshi, et al. Enabling the Big Earth Observation Data via Cloud Computing and DGGS: Opportunities and Challenges[J]. Remote Sensing, 2019, 12(1):62.

    [4]

    Bondaruk B, Roberts A, Robertson C. Assessing the State of the Art in Discrete Global Grid Systems: OGC Criteria and Present Functionality[J]. Geomatica, 2020, 74(1):1-22.

    [5]

    Mahdavi-amiri A, Alderson T, Samavati F. A Survey of Digital Earth[J]. Computers & Graphics, 2015, 53.

    [6]

    Mahdavi-amiri A, Bhojani, F, Samavati F. One-To-Two Digital Earth[C] // In Proceedings of the 9th International Symposium on Advances in Visual Computing (ISVC 2013), Rethymnon, Greece, 29-31 July 2013; Springer: Berlin/Heidelberg, Germany, 2013; doi: 10.1007/978-3-642-41939-3_67.

    [7] 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. (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. )
    [8]

    Sahr K. Location Coding on Icosahedral Aperture 3 hHexagon Discrete Global Grids[J]. Computers, Environment and Urban Systems, 2008, 32(3):174-187.

    [9] Wang Rui, Ben Jin, Du Lingyu, Zhou Jianbin, Li Zhuxin. Code Operation Scheme for the Icosahedral Aperture 4 Hexagonal Grid System[J]. Geomatics and Information Science of Wuhan University, 2020, 45(1): 89-96. doi: 10.13203/j.whugis20180191(王蕊, 贲进, 杜灵瑀, 周建彬, 李祝鑫. 正二十面体四孔六边形格网系统编码运算[J]. 武汉大学学报 ● 信息科学版, 2020, 45(1): 89-96.)
    [10]

    White D, Kimerling 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.

    [11] 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(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. )
    [12]

    Wang Rui, Ben Jin, Zhou Jianbin, et al. A Generic Encoding and Operation Scheme for Mixed Aperture Three and Four Hexagonal Discrete Global Grid Systems[J]. International Journal of Geographical Information Science, 2020(10):1-43.

    [13] Zhou Jianbin, Ben Jin, Wang Rui, Zheng Mingyang. Encoding and operation for the aperture 4 hexagonal discrete global grids on uniform tiles[J]. Geomatics and Information Science of Wuhan University. doi: 10.13203/j.whugis20200530(周建彬, 贲进, 王蕊, 郑明阳. 四孔六边形全球离散格网一致瓦片层次结构编码运算[J]. 武汉大学学报 ● 信息科学版.)
    [14]

    Hall J, Wecker L, Ulmer B, et al. Disdyakis Triacontahedron DGGS. ISPRS International Journal of Geo-Information[J], 2020, 9: 315. https://doi.org/10.3390/ijgi9050315

    [15]

    Wang Rui, Ben Jin, Zhou Jianbin, et al. Indexing Mixed Aperture Icosahedral Hexagonal Discrete Global Grid Systems. ISPRS International Journal of Geo-Information[J]. 2020, 9: 171. https://doi.org/10.3390/ijgi9030171

    [16] Ben Jin, Tong Xiaochong, Zhang Yongsheng, Zhang Heng. Snyder Equal-area Map Projection for Polyhedral Globes[J]. Geomatics and Information Science of Wuhan University, 2006, 31(10): 900-903.(贲进, 童晓冲, 张永生, 张衡. 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.)
    [17]

    Leeuwen D V, 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.

    [18]

    Harrison E, Mahdavi-amiri A, Samavati F. Optimization of Inverse Snyder Polyhedral Projection[C] // 2011 International Conference on Cyberworlds, CW 2011,10 Calgary, Alberta, Canada, October 4-6, 2011 IEEE, 2011.

    [19]

    WolframMathWorld. Rhombic Triacontahedron[OL]. https://mathworld.wolfram.com/RhombicTriacontahedron.html

    [20]

    Snyder J . Map Projections--a Working Manual[J]. Geological Survey Professional Paper, U.S. Government Printing Office, 1987.

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出版历程
  • 收稿日期:  2023-03-09
  • 网络出版日期:  2023-04-19

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