A Unified Model for Cartesian Coordinate Transformations in
Two- and Three-dimensional Space
1 College of Geomatics Engineering, Nanjing Tech University, 30 South-Puzhu Road, Nanjing 211816, China
2 College of Ocean and Civil Engineering, Dalian Ocean University, 52 Heishijiao Street, Dalian 116023, China
Abstract A unified approach for cartesian coordinate transformations is presented. Firstly, the unified expression of transformation equations in two- and three-dimensional space is given, and then the orthogonal Procrustes analysis is used for estimating the transformation parameters. The orthogonal procrustes analysis provides a non-iterative solution for transformation parameters without any prerequisites on the magnitude of the parameters. Consequently, neither good initial values nor iterations are required during the parameter estimation process. Through numerical examples, it is illustrated that the proposed approach is capable of giving accurate, efficient, stable and reliable parameter estimates and that it is applicable for cartesian coordinate transformations in various situations
