AbstractAn iterative solution is presented to provide rapid computation, in a geocentric Cartesian system, of the coordinates of the projection of a fixed point on a topographic surface onto an ellipsoid of revolution.From the cofactor matrix of the geocentric Cartesian coordinates of such a point the cofactor matrix of the total vector of the coordinates of this topographic point and of the coordinates of the projection onto the ellipsoid is also derived in order to compute the ellipsoid height and the relative variance.