Datum Transformations 

Coordinate transformations are quite common in surveing . They range from simple translations between coordinates and setting-out grids on a construction site , to transformation between global systems.

Whilist the mathematical procedures are well defined for many types of  transformation , problems can arise due to varying scale throughout the network used to established empirically , to be used in different areas of the system 

Basic concept 

it can be seen that the basic  paramenters in a conventional transformation between similar XYZ systems would be : 

(1) Translation of the origin 0 , which would involve shifts in X , Y and Z , i.e X, Y,Z 

(2) Rotation about the three axes x , y and z in order to render the axes of the systems involved parallel x and y would change the polar axes , and z the zero meridian 

(3) One scale parameter (1 + S) would account for the difference of scale between difference coordinate systems

In the addition to the above , the size (a) of the ellipsoid and its shape (F) may also need to be included 

However , not all the parameters are generally used in practice 

The most common transformation is the translation in X , Y and Z only (three parameters ) 

also common is the four-parameter