In geodetic surveying, the curved surface of the Earth is considered by performing
the computations on an ellipsoid (curved surface approximating the size
and shape of the Earth—see Chapter 19). It is now becoming common to do geodetic
computations in a three-dimensional, Earth-centered, Earth-fixed (ECEF)
Cartesian coordinate system. The calculations involve solving equations derived
from solid geometry and calculus. Geodetic methods are employed to determine
relative positions of widely spaced monuments and to compute lengths and directions
of the long lines between them.These monuments serve as the basis for referencing
other subordinate surveys of lesser extents.