球体坐标与SDOG-ESSG格网码的相互转换算法

基于球体退化八叉树格网的地球系统空间格网(SDOG-ESSG)是地球系统科学与空间信息领域的重要的研究工具和手段。SDOG-ESSG格网码与现有空间参考相互转换的关键问题即球体坐标系与SDOG-ES-SG格网码的正向转换与逆向转换的算法。通过引进6种列-行-层坐标系并导出有关计算公式,借鉴Morton码行列二进制位交错的特性,分别设计了正向转换与逆向转换算法过程,在此基础上,理论分析并实验验证了两算法的时间效率。结果表明,两转换算法非常高效,其时间消耗基本与SDOG-ESSG的主剖次和副剖次呈线性关系,时间复杂度为O(n);在PC环境下,每秒能实现106～107次的转换运算,1次转换相当于101～102次的除法运算。

Transformation Algorithms Between Spheroid Coordinates System and SDOG-ESSG Grid Code

The SDOG-based Earth System Spatial Grid(SDOG-ESSG)is an important tool and methodin the Earth System Science and spatial information domains.This paper focuses on the key problemof transformation between the grid code of SDOG-ESSG and the existing spatial reference,the trans-formation between Spheroid Coordinates System (SCS)and the grid code of SDOG-ESSG.Six col-umn-row-layer number systems were brought in and related formulas were derived.Based on this andthe bit-interleaving method of Morton code,forward and backward transformation algorithms weredeveloped.The time efficiency of both algorithms was analyzed theoretically and experimentally.Theresults show that:a)both algorithms are very high efficient,and the time consumption is linear to theprinciple subdivision level and the further subdivision level of SDOG-ESSG,where the time complexi-ty is O(n);and(b)approximately 106～107times of transformation operations can be done in one sec-ond under current personal computer.Each transformation operation is identical to 101～102 divisionoperation in time.