Reference Ellipsoid and the Geodetic Coordinate System - Geodesy: Introduction to Geodetic Datum and Geodetic Systems - page 212

Fig. 5.30 Reduction of
terrestrial control network
to ellipsoid
Reductions of terrestrial triangulateration elements to the ellipsoid include the
reductions of horizontal directions, observed zenith distances, terrestrial distances,
as well as the reductions of the astronomical azimuths, etc. In addition, computa-
tions of the deflection of the vertical, as an essential element in reduction, are also
one of the concerns in this section.
It should be noted that, although GPS surveying techniques can directly deter-
mine the geodetic coordinates of the position of a point, in applications where
directions, distances, or azimuths on different reference surfaces are needed, we
should still perform the corresponding calculations as shown in Fig. 5.29 .
5.5.2 Reduction of Horizontal Directions to the Ellipsoid
Reducing horizontal directions to the ellipsoid requires correction for deflection of
the vertical, correction for skew normals, and correction from normal section to
geodesic. These three corrections are customarily known as the “three corrections
for horizontal directions”.
Correction for Deflection of the Vertical
The Earth's surface point is projected onto the ellipsoid along the ellipsoidal
normal. The direction of the plumb line at the observation point does not coincide
with the corresponding ellipsoidal normal, which will exert effects on the values of