球面菱形离散格网正二十面体剖分法

doi:10.13485/j.cnki.11-2089.2014.0192

测绘学报 ›› 2014, Vol. 43 ›› Issue (12): 1293-1299.doi: 10.13485/j.cnki.11-2089.2014.0192

球面菱形离散格网正二十面体剖分法

周良辰^1,2, 盛业华^1,2, 林冰仙^1,2, 闾国年^1,2, 赵志鹏^1,2

1. 南京师范大学虚拟地理环境教育部重点实验室, 江苏南京 210023;
2. 江苏省地理信息资源开发与利用协同创新中心, 江苏南京 210023

收稿日期:2014-01-03 修回日期:2014-09-03 出版日期:2014-12-20 发布日期:2014-12-23
通讯作者: 盛业华 E-mail:shengyehua@njnu.edu.cn
作者简介:周良辰(1979-),男,博士,主要研究方向为全球离散格网系统.zhoulch@gmail.com
基金资助:
国家自然科学基金(41301415;41001224;41271383);江苏高校优势学科建设工程资助项目

Diamond Discrete Grid Subdivision Method for Spherical Surface with Icosahedron

ZHOU Liangchen^1,2, SHENG Yehua^1,2, LIN Bingxian^1,2, LÜ Guonian^1,2, ZHAO Zhipeng^1,2

1. Key Laboratory of Virtual Geographic Environment for the Ministry of Education, Nanjing Normal University, Nanjing 210023, China;
2. Jiangsu Center for Collaborative Innovation in Geographical Information Resource Development and Application, Nanjing 210023, China

Received:2014-01-03 Revised:2014-09-03 Online:2014-12-20 Published:2014-12-23

摘要/Abstract

摘要：

基于菱形单元的球面离散格网具有结构简单和方向性一致等优点,使得其适用于全球多尺度空间数据建模与分析.本文提出一种球面菱形离散格网正二十面体剖分法.首先根据地球的主要地理特征确定正二十面体各个顶点在球面上的位置;其次针对南北两极处的极点奇异性,建立了球面经纬度坐标与三维直角坐标之间的转换关系,在此基础上提出球面菱形离散格网层次递归剖分算法,并从菱形格网单元面积、长短轴比两方面对剖分结果进行几何形变分析;最后验证了本文方法的可行性,试验结果表明,该方法可有效地构建基于正二十面体的球面菱形离散格网,其总体几何特性明显优于基于正八面体构建的球面菱形离散格网.

关键词: 全球离散格网, 菱形, 正二十面体, 层次递归剖分, 几何形变

Abstract:

Diamond discrete grids of spherical surface can meet the requirements of multi-scale spatial data modeling and analysis due to the advantages of simple structure and uniform directionality. This paper presents a new diamond discrete grid subdivision method for spherical surface with icosahedron. Firstly, the location of the icosahedron's vertexes on the spherical surface are determined according to the earth's major geographical features. Secondly, to solve the problem of grid convergence in poles, transformation relation between the latitude and longitude coordinates and 3D Cartesian coordinates are created. Then, a recursive subdivision approach of spherical diamond discrete grids is provided, and the geometric deformation of subdivision result is analyzed in terms of cell area and cell axial ratio. Finally, the feasibility of the method proposed is verified. The experiment results show that our subdivision method can construct spherical diamond discrete grids with icosahedron effectively, of which the general geometric characteristics are much better than that of the diamond discrete grids with octahedron.

Key words: discrete global gird, diamond, icosahedron, hierarchy recursively subdivision, geometric distortion

中图分类号:

P208

周良辰, 盛业华, 林冰仙, 闾国年, 赵志鹏. 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, LÜ Guonian, ZHAO Zhipeng. Diamond Discrete Grid Subdivision Method for Spherical Surface with Icosahedron[J]. Acta Geodaetica et Cartographica Sinica, 2014, 43(12): 1293-1299.

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球面菱形离散格网正二十面体剖分法

Diamond Discrete Grid Subdivision Method for Spherical Surface with Icosahedron

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