球面三角格网单元面积的分形计算  

A Fractal Method for Area Calculation of the Spherical Triangular Grid

作　　者：王政 赵学胜[1] 罗富丽 李亚路 孙中昶 WANG Zheng;ZHAO Xuesheng;LUO Fuli;LI Yalu;SUN Zhongchang(College of Geoscience and Surveying Engineering,China University of Mining and Technology,Beijing 100083,China;Institute of Remote Sensing and Digital Earth,Chinese Academy of Sciences,Beijing 100094,China)

机构地区：[1]中国矿业大学(北京)地球科学与测绘工程学院,北京100083 [2]中国科学院遥感与数字地球研究所,北京100094

出　　处：《武汉大学学报（信息科学版）》2020年第10期1541-1546,1554,共7页Geomatics and Information Science of Wuhan University

基　　金：国家自然科学基金(41671394);国家重点研发计划(2018YFB0505301)。

摘　　要：球面三角格网是一种多用途的全球离散格网,是数字地球领域空间信息表达的一种有效方案。针对球面三角格网单元面积计算的一般方法准确度不高的问题,提出一种面积计算的分形方法。在同一剖分层中,把球面三角格网重新编码为0或1,计算相同编码的格网单元的面积,拟合多重分形的面积计算函数,以此作为球面三角格网的面积计算模型。用相对中误差计算该模型的准确度,并用算例进行验证。结果显示,随着多重分形的次数增加,格网单元的面积计算准确度变高,面积计算准确度是可控的。Spherical triangle grid is a versatile discrete global grid, which is an effective scheme for spatial information representation in the digital earth domain. The general methods for calculating the area of a spherical triangular grid are not accurate. So a fractal method for area calculation is proposed. Firstly, in the same level, areas of spherical triangular grid recoded to 0 or 1 are computed respectively. Then multi-fractal area calculation functions are fitted, which is used as an area calculation model. Finally, the accuracy of the model is calculated by relative root mean square error. Experimental result shows that, with the increase of the number of multifractals, the accuracy of area calculation of grid cells increases and is controllable.

关 键 词：全球离散格网 球面三角形 分形编码 单元面积 计算模型 

分 类 号：P228[天文地球—大地测量学与测量工程]