Influence of geometrical distribution of common points on the accuracy of coordinate transformation

Geometrical distribution of common points is of significance for coordinate transformation as the transformation parameters are computed through common points whose coordinates are known. Common points can be divided into a calculating set and a testing set whose geometrical distribution can be described by internal and external distribution parameters. The former contains the number of points, the reference coordinate and the coordinate difference, the latter is defined as the overlapping degree between both sets. Both a rotation matrix and a translation vector are involved in the transformation parameters, and could be evaluated by 3 approaches i.e. the coordinate error method, the RMS error method and the error method of relative Euclidean distance. An invalidation of the third method has been proven that evaluating indexes will remain invariant for a fixed testing set, regardless of variation in the calculating set. According to the classification of geometrical distribution of common points, the influences of internal and external distribution parameters on the accuracy of coordinate transformation are related to the number of points, symmetrical distribution and the overlapping degree, which will be formulated and summarized in detail. Finally, the above conclusions can be verified and proven by computer simulation and practical experiment respectively.