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.