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基于正二十面体的球面菱形离散格网剖分方法

ivision method of Spherical Rhombus Discrete Grid based on icosahedron

中文摘要英文摘要

基于菱形单元的球面离散格网具有结构简单、方向性一致等优点,能够满足全球多尺度空间数据建模与分析的需求。现有的基于正八面体的球面菱形离散格网由于基础多面体与球体形状相差较大,因此存在较大的几何变形。针对这一问题,本文提出了一种基于正二十面体的球面菱形离散格网剖分方法。该方法根据地球自身地理特征确定了正二十面体与球面的对应关系,针对南北两极处存在的极点奇异性,设计了地理空间坐标与三维直角坐标的转换算法,实现了球面菱形离散格网的层次递归剖分并确定了剖分格网点的地理空间坐标,并通过菱形格网单元面积、长短轴比两方面对剖分结果进行几何形变分析。结果表明,本文所提出的剖分方法可有效的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。

he spherical rhombus discrete grids have the advantages of simple structure and directional uniformity, so they would satisfy the demand of multi-scale spatial data modelling and analysis. Due to the difference between spherical rhombus discrete grids based on octahedron and basic polyhedron, the rhombus discrete grids have large geometrical distortion. As for this question, the paper present a method to generate spherical rhombus discrete grids based on icosahedron. The method builds the relationship between icosahedron and sphere according to the geographical characteristics of Earth Firstly. Except that, the method includes the transformation method of geographic coordinate and Cartesian coordinate and succeeds to divide the grid recursively and confirm the geographic coordinates of grid points. Finally, the paper analyzes the geometrical distortion of cell area and max/min ratio. The result shows that this method can construct spherical rhombus discrete grids effectively, and the whole geometric characteristics are obviously much better than spherical rhombus discrete gird based on octahedron.

周良辰、赵志鹏

测绘学

地理信息系统全球离散格网,菱形,正二十面体,层次递归剖分,几何形变

GISGlobal Discrete Gridsrhombusicosahedronrecursively hierarchical divisiongeometric distortion

周良辰,赵志鹏.基于正二十面体的球面菱形离散格网剖分方法[EB/OL].(2014-02-28)[2025-08-18].http://www.paper.edu.cn/releasepaper/content/201402-665.点此复制

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