Surveying requires a reference system, and for the whole earth this reference is formalized through two mathematical surfaces: the geoid, an equipotential surface everywhere perpendicular to gravity (physically approximated by mean sea level) that is not mathematically definable due to non-uniform mass distribution within the earth, and the ellipsoid, a mathematically defined surface fitted to the earth's shape used for planimetric (X, Y) positioning while elevation is still referenced to the geoid. This distinction underlies the division between plane surveying, which treats the earth as flat and ignores curvature (valid for small areas, typically under ~20 km, where the arc-chord difference is negligible), and geodetic surveying, which accounts for the earth's curvature and is required for large-scale or intercontinental positioning. The subject area is geoinformatics/basic surveying, specifically the reference systems (datum, geoid, ellipsoid) that underlie the measurement of geoinformation as a sub-discipline of civil, geodetic, and geographic engineering.
Surveying requires a reference system, and for the whole earth this reference is formalized through two mathematical surfaces: the geoid, an equipotential surface everywhere perpendicular to gravity …