AS/NZS ISO 19107:2020 Geographic information — Spatial schema.
5.1.2  Geometry metrics (geodesy)
In defining the geometry metrics, the application schema will be required to specify which underlying surfaces will be supported in calculating geometric measures. In general, the underlying surfaces (called “GeometricReferenceSurface”) are:
— The 2D plane or map geometry uses standard Cartesian geometry and Pythagorean “flat” metrics, and has inherent inaccuracies associated with the curvature of the Earth dependent on the size of the area covered and the characteristics of the chosen projections (coordinate reference systems or CRS).
— A 2D sphere uses classical spherical surfaces (a perfectly round Earth of constant curvature). These systems use great circles as geodesics and do not adjust for the eccentricity of the Earth’s surface. Depending on the CRS, slightly different spheres may be chosen for a “best fit” for a limited locale. While theoretically more accurate than planar, as the area of coverage increases accuracy of measurements do degrade but at a slower rate.
— A 2D ellipsoid uses a surface generated by the rotation of an ellipse about its shorter axis (polar) creating a circular equator and other lines of constant latitude, with orthogonal, elliptical lines of constant longitude. These systems adjust for the eccentricity of the ellipsoid, but do not factor in local gravitational anomalies. Again, varieties of “best fit” ellipsoids are used.
— A continuous 2D surface of an equipotential surface of gravity (such as the geoid or quasi geoid) or a tidal Reference Surface (such as mean sea level or lowest astronomic tide); Potential (or height) differences are referenced to an ellipsoid.
NOTE  Although generally smooth and spatially continuous in two dimensions, such a surface is irregular and there is insufficient information to compute across it. It is usually represented through an analytical approximation using spherical harmonics where the spatial context is referenced to an ellipsoid, such as the Earth Gravity Model 2008 (EGM 2008) referenced to the WGS 84 ellipsoid, or by a digital elevation model referenced to a 2D plane.
Three dimensional geometry models will also be supported. There are essentially two approaches:
— Geocentric Cartesian 3D, using a ‘flat’ 3D Euclidean space: These include geocentric (origin at the centre of the Earth) and projective (origin on the surface of the Earth).
— Using one of the surfaces from the four classes above, and adding a measure of the distance in 3D either above or below the “GeometricReferenceSurface”: The third dimension is measured parallel to a near normal or normal line (orthogonal to the surface, in the general direction of gravitational up).AS/NZS ISO 19107 pdf download.