菱形三十面体格网系统构建的等积投影方法研究  

Equal-Area Projection for Construction of Rhombic Triacontahedron Grid Systems

作　　者：王蕊 贲进[1] 梁晓宇 梁启爽 涂祖瑞 WANG Rui;BEN Jin;LIANG Xiaoyu;LIANG Qishuang;TU Zurui(Institute of Geospatial Information,Information Engineering University,Zhengzhou 450001,China)

机构地区：[1]信息工程大学地理空间信息学院,河南郑州450001

出　　处：《武汉大学学报(信息科学版)》2025年第3期579-586,共8页Geomatics and Information Science of Wuhan University

基　　金：国家重点研发计划(2018YFB0505301);河南省重大科技专项(201400210100)。

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,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3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,所提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。Objectives:Discrete global grid systems(DGGS)are new reference frameworks for digital earth,and are suitable for organization,integration and analysis of multi-source big geospatial datasets.Among the existing construction methods of DGGS,polyhedron projection to sphere can generate DGGS with superior geometric properties and has been widely used.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,but the icosahedron achieves the smallest distortion due to the most faces and still has difference with spherical surface.Methods:This paper chooses rhombic triacontahedron as a new basic polyhedron,and researches its equal-area projection methods.The sliceand-dice approach provides the equal-area mapping between spherical triangles and planar triangles for polyhedral projections,which has different implementations according to the partitioning strategies.The vertex-oriented great circle projection is chosen to realize the equal-area mapping between the surface of rhombic triacontahedron and the sphere because of more uniform angular distortion compared with the Snyder equal-area polyhedral projection.Each diamond face of 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 rhombic triacontahedron and the sphere,we calculate the edge and angle parameters of 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: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 fro

关 键 词：菱形三十面体 格网系统构建 等积投影 

分 类 号：P208[天文地球—地图制图学与地理信息工程]