Coordinate manipulations involve the steps above. If you are only interested in geographic coordinates, you do not need to use the forwad and inverse projection equations.
To go back from datum 2 to datum 1, you repeat the same steps and exchange the datum 1/2 on the two sides of datum transformation.
On the fly projections of data sets with different datums or projections must use this process to display points on the screen, or to go from the mouse position to the coordinates.
To plot the UTM grid on a Lambert Conformal Conic projection map, you must first convert to geographic, and then use the equations of the other projection.
last revision 11/28/2018