This makes me wonder, what's the difference between the 2D area and the 3D topographic surface area? Is the latter even ever measured?
3D topographic surface area has the "coastline problem" where the more precisely you measure it, the more it grows.2D area is stable under increasing measurement precision.
tracnar · · focus · HN ↗
eigenspace · · focus · HN ↗
2D area is stable under increasing measurement precision.