Figure Condition in Datum Transformation

A complete datum transformation between two geodetic coordinate systems requires seven parameters: three translations, three rotations, and one scale factor. When a datum transformation is needed, these parameters, which are generally unknown beforehand, are computed using the common points whose coordinates are available in both systems. Therefore, the accuracies of the computed parameters depend on the accuracies of the coordinates of the common points. Accordingly, the accuracies of the point coordinates transformed by these parameters will depend on the accuracies of the parameters, along with the accuracies of the coordinates before transformation. For this reason, one should investigate whether the figure condition of the computed parameters is satisfied for all the transformation area in which the parameters will be involved. In the cases where the figure condition could not be satisfied for all the transformation area, the design of the network constituted by common points should be revised, either by adding well-distributed new common points to the network, or by dividing the transformation area into parts for which the figure conditions would be satisfied.